LMFDB - Embedded newform 117.2.q.d.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.1
Root			$-1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.2.q.d.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93649 - 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +2.23607i q^{5} +(-3.00000 + 1.73205i) q^{7} -2.23607i q^{8} +O(q^{10})$	\(q+(-1.93649 - 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +2.23607i q^{5} +(-3.00000 + 1.73205i) q^{7} -2.23607i q^{8} +(2.50000 - 4.33013i) q^{10} +(3.87298 + 2.23607i) q^{11} +(2.50000 + 2.59808i) q^{13} +7.74597 q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.93649 - 3.35410i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(-5.80948 + 3.35410i) q^{20} +(-5.00000 - 8.66025i) q^{22} +(-3.87298 + 6.70820i) q^{23} +(-1.93649 - 7.82624i) q^{26} +(-9.00000 - 5.19615i) q^{28} +(1.93649 - 3.35410i) q^{29} +(-5.80948 + 3.35410i) q^{32} +8.66025i q^{34} +(-3.87298 - 6.70820i) q^{35} +(1.50000 + 0.866025i) q^{37} +7.74597 q^{38} +5.00000 q^{40} +(-1.93649 - 1.11803i) q^{41} +(-1.00000 - 1.73205i) q^{43} +13.4164i q^{44} +(15.0000 - 8.66025i) q^{46} -4.47214i q^{47} +(2.50000 - 4.33013i) q^{49} +(-3.00000 + 10.3923i) q^{52} +11.6190 q^{53} +(-5.00000 + 8.66025i) q^{55} +(3.87298 + 6.70820i) q^{56} +(-7.50000 + 4.33013i) q^{58} +(7.74597 - 4.47214i) q^{59} +(3.50000 + 6.06218i) q^{61} +13.0000 q^{64} +(-5.80948 + 5.59017i) q^{65} +(-3.00000 - 1.73205i) q^{67} +(5.80948 - 10.0623i) q^{68} +17.3205i q^{70} +(-3.87298 + 2.23607i) q^{71} -15.5885i q^{73} +(-1.93649 - 3.35410i) q^{74} +(-9.00000 - 5.19615i) q^{76} -15.4919 q^{77} +8.00000 q^{79} +(1.93649 + 1.11803i) q^{80} +(2.50000 + 4.33013i) q^{82} -4.47214i q^{83} +(7.50000 - 4.33013i) q^{85} +4.47214i q^{86} +(5.00000 - 8.66025i) q^{88} +(3.87298 + 2.23607i) q^{89} +(-12.0000 - 3.46410i) q^{91} -23.2379 q^{92} +(-5.00000 + 8.66025i) q^{94} +(-3.87298 - 6.70820i) q^{95} +(6.00000 - 3.46410i) q^{97} +(-9.68246 + 5.59017i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} - 12 q^{7}+O(q^{10}) $ 4 * q + 6 * q^4 - 12 * q^7	$ 4 q + 6 q^{4} - 12 q^{7} + 10 q^{10} + 10 q^{13} + 2 q^{16} - 12 q^{19} - 20 q^{22} - 36 q^{28} + 6 q^{37} + 20 q^{40} - 4 q^{43} + 60 q^{46} + 10 q^{49} - 12 q^{52} - 20 q^{55} - 30 q^{58} + 14 q^{61} + 52 q^{64} - 12 q^{67} - 36 q^{76} + 32 q^{79} + 10 q^{82} + 30 q^{85} + 20 q^{88} - 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) $ 4 * q + 6 * q^4 - 12 * q^7 + 10 * q^10 + 10 * q^13 + 2 * q^16 - 12 * q^19 - 20 * q^22 - 36 * q^28 + 6 * q^37 + 20 * q^40 - 4 * q^43 + 60 * q^46 + 10 * q^49 - 12 * q^52 - 20 * q^55 - 30 * q^58 + 14 * q^61 + 52 * q^64 - 12 * q^67 - 36 * q^76 + 32 * q^79 + 10 * q^82 + 30 * q^85 + 20 * q^88 - 48 * q^91 - 20 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.93649	−	1.11803i	−1.36931	−	0.790569i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	−1.93649	−	1.11803i	−1.36931	−	0.790569i	−0.990839	+	0.135045i	$0.956882\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	2.59808i	0.750000	+	1.29904i
$5$			2.23607i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$5$			2.23607i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$		−	2.23607i		−	0.790569i
$9$		0			0
$10$	2.50000	−	4.33013i	0.790569	−	1.36931i
$11$	3.87298	+	2.23607i	1.16775	+	0.674200i	0.953149	−	0.302502i	$-0.0978220\pi$
$11$	3.87298	+	2.23607i	1.16775	+	0.674200i	0.214600	+	0.976702i	$0.431155\pi$
$12$		0			0
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$	7.74597			2.07020
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.93649	−	3.35410i	−0.469668	−	0.813489i	0.529730	−	0.848166i	$-0.322293\pi$
$17$	−1.93649	−	3.35410i	−0.469668	−	0.813489i	−0.999399	+	0.0346769i	$0.988960\pi$
$18$		0			0
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$	−5.80948	+	3.35410i	−1.29904	+	0.750000i
$21$		0			0
$22$	−5.00000	−	8.66025i	−1.06600	−	1.84637i
$23$	−3.87298	+	6.70820i	−0.807573	+	1.39876i	0.106967	+	0.994263i	$0.465886\pi$
$23$	−3.87298	+	6.70820i	−0.807573	+	1.39876i	−0.914540	+	0.404495i	$0.867447\pi$
$24$		0			0
$25$		0			0
$26$	−1.93649	−	7.82624i	−0.379777	−	1.53485i
$27$		0			0
$28$	−9.00000	−	5.19615i	−1.70084	−	0.981981i
$29$	1.93649	−	3.35410i	0.359597	−	0.622841i	−0.628296	−	0.777974i	$-0.716247\pi$
$29$	1.93649	−	3.35410i	0.359597	−	0.622841i	0.987894	+	0.155133i	$0.0495807\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−5.80948	+	3.35410i	−1.02698	+	0.592927i
$33$		0			0
$34$			8.66025i			1.48522i
$35$	−3.87298	−	6.70820i	−0.654654	−	1.13389i
$36$		0			0
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	0.618206	−	0.786016i	$-0.287860\pi$
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	−0.371607	+	0.928390i	$0.621193\pi$
$38$	7.74597			1.25656
$39$		0			0
$40$	5.00000			0.790569
$41$	−1.93649	−	1.11803i	−0.302429	−	0.174608i	0.341104	−	0.940025i	$-0.389199\pi$
$41$	−1.93649	−	1.11803i	−0.302429	−	0.174608i	−0.643534	+	0.765418i	$0.722532\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$			13.4164i			2.02260i
$45$		0			0
$46$	15.0000	−	8.66025i	2.21163	−	1.27688i
$47$		−	4.47214i		−	0.652328i	−0.945313	−	0.326164i	$-0.894244\pi$
$47$		−	4.47214i		−	0.652328i	0.945313	−	0.326164i	$-0.105756\pi$
$48$		0			0
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$		0			0
$51$		0			0
$52$	−3.00000	+	10.3923i	−0.416025	+	1.44115i
$53$	11.6190			1.59599			0.797993	−	0.602667i	$-0.205895\pi$
$53$	11.6190			1.59599			0.797993	+	0.602667i	$0.205895\pi$
$54$		0			0
$55$	−5.00000	+	8.66025i	−0.674200	+	1.16775i
$56$	3.87298	+	6.70820i	0.517549	+	0.896421i
$57$		0			0
$58$	−7.50000	+	4.33013i	−0.984798	+	0.568574i
$59$	7.74597	−	4.47214i	1.00844	−	0.582223i	0.0977047	−	0.995215i	$-0.468850\pi$
$59$	7.74597	−	4.47214i	1.00844	−	0.582223i	0.910734	+	0.412993i	$0.135517\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$		0			0
$64$	13.0000			1.62500
$65$	−5.80948	+	5.59017i	−0.720577	+	0.693375i
$66$		0			0
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	5.80948	−	10.0623i	0.704502	−	1.22023i
$69$		0			0
$70$			17.3205i			2.07020i
$71$	−3.87298	+	2.23607i	−0.459639	+	0.265372i	−0.711892	−	0.702289i	$-0.752162\pi$
$71$	−3.87298	+	2.23607i	−0.459639	+	0.265372i	0.252254	+	0.967661i	$0.418828\pi$
$72$		0			0
$73$		−	15.5885i		−	1.82449i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$		−	15.5885i		−	1.82449i	0.409644	−	0.912245i	$-0.365653\pi$
$74$	−1.93649	−	3.35410i	−0.225113	−	0.389906i
$75$		0			0
$76$	−9.00000	−	5.19615i	−1.03237	−	0.596040i
$77$	−15.4919			−1.76547
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	1.93649	+	1.11803i	0.216506	+	0.125000i
$81$		0			0
$82$	2.50000	+	4.33013i	0.276079	+	0.478183i
$83$		−	4.47214i		−	0.490881i	−0.969412	−	0.245440i	$-0.921067\pi$
$83$		−	4.47214i		−	0.490881i	0.969412	−	0.245440i	$-0.0789325\pi$
$84$		0			0
$85$	7.50000	−	4.33013i	0.813489	−	0.469668i
$86$			4.47214i			0.482243i
$87$		0			0
$88$	5.00000	−	8.66025i	0.533002	−	0.923186i
$89$	3.87298	+	2.23607i	0.410535	+	0.237023i	0.691020	−	0.722836i	$-0.257162\pi$
$89$	3.87298	+	2.23607i	0.410535	+	0.237023i	−0.280484	+	0.959859i	$0.590495\pi$
$90$		0			0
$91$	−12.0000	−	3.46410i	−1.25794	−	0.363137i
$92$	−23.2379			−2.42272
$93$		0			0
$94$	−5.00000	+	8.66025i	−0.515711	+	0.893237i
$95$	−3.87298	−	6.70820i	−0.397360	−	0.688247i
$96$		0			0
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	−0.163448	−	0.986552i	$-0.552261\pi$
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	0.772655	+	0.634826i	$0.218928\pi$
$98$	−9.68246	+	5.59017i	−0.978076	+	0.564692i
$99$		0			0
$100$		0			0
$101$	1.93649	−	3.35410i	0.192688	−	0.333746i	−0.753452	−	0.657503i	$-0.771613\pi$
$101$	1.93649	−	3.35410i	0.192688	−	0.333746i	0.946140	+	0.323757i	$0.104946\pi$
$102$		0			0
$103$	2.00000			0.197066			0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000			0.197066			0.0985329	+	0.995134i	$0.468585\pi$
$104$	5.80948	−	5.59017i	0.569666	−	0.548161i
$105$		0			0
$106$	−22.5000	−	12.9904i	−2.18539	−	1.26174i
$107$	−3.87298	+	6.70820i	−0.374415	+	0.648507i	−0.990239	−	0.139377i	$-0.955490\pi$
$107$	−3.87298	+	6.70820i	−0.374415	+	0.648507i	0.615824	+	0.787884i	$0.288823\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	19.3649	−	11.1803i	1.84637	−	1.06600i
$111$		0			0
$112$			3.46410i			0.327327i
$113$	9.68246	+	16.7705i	0.910849	+	1.57764i	0.812868	+	0.582449i	$0.197905\pi$
$113$	9.68246	+	16.7705i	0.910849	+	1.57764i	0.0979815	+	0.995188i	$0.468761\pi$
$114$		0			0
$115$	−15.0000	−	8.66025i	−1.39876	−	0.807573i
$116$	11.6190			1.07879
$117$		0			0
$118$	−20.0000			−1.84115
$119$	11.6190	+	6.70820i	1.06511	+	0.614940i
$120$		0			0
$121$	4.50000	+	7.79423i	0.409091	+	0.708566i
$122$		−	15.6525i		−	1.41711i
$123$		0			0
$124$		0			0
$125$			11.1803i			1.00000i
$126$		0			0
$127$	2.00000	−	3.46410i	0.177471	−	0.307389i	−0.763542	−	0.645758i	$-0.776542\pi$
$127$	2.00000	−	3.46410i	0.177471	−	0.307389i	0.941014	+	0.338368i	$0.109875\pi$
$128$	−13.5554	−	7.82624i	−1.19814	−	0.691748i
$129$		0			0
$130$	17.5000	−	4.33013i	1.53485	−	0.379777i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$	3.87298	+	6.70820i	0.334575	+	0.579501i
$135$		0			0
$136$	−7.50000	+	4.33013i	−0.643120	+	0.371305i
$137$	13.5554	−	7.82624i	1.15812	−	0.668641i	0.207267	−	0.978284i	$-0.433543\pi$
$137$	13.5554	−	7.82624i	1.15812	−	0.668641i	0.950853	+	0.309644i	$0.100210\pi$
$138$		0			0
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$	11.6190	−	20.1246i	0.981981	−	1.70084i
$141$		0			0
$142$	10.0000			0.839181
$143$	3.87298	+	15.6525i	0.323875	+	1.30893i
$144$		0			0
$145$	7.50000	+	4.33013i	0.622841	+	0.359597i
$146$	−17.4284	+	30.1869i	−1.44239	+	2.49829i
$147$		0			0
$148$			5.19615i			0.427121i
$149$	−9.68246	+	5.59017i	−0.793218	+	0.457965i	−0.841094	−	0.540889i	$-0.818088\pi$
$149$	−9.68246	+	5.59017i	−0.793218	+	0.457965i	0.0478763	+	0.998853i	$0.484755\pi$
$150$		0			0
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	3.87298	+	6.70820i	0.314140	+	0.544107i
$153$		0			0
$154$	30.0000	+	17.3205i	2.41747	+	1.39573i
$155$		0			0
$156$		0			0
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$	−15.4919	−	8.94427i	−1.23247	−	0.711568i
$159$		0			0
$160$	−7.50000	−	12.9904i	−0.592927	−	1.02698i
$161$		−	26.8328i		−	2.11472i
$162$		0			0
$163$	−12.0000	+	6.92820i	−0.939913	+	0.542659i	−0.889933	−	0.456091i	$-0.849249\pi$
$163$	−12.0000	+	6.92820i	−0.939913	+	0.542659i	−0.0499796	+	0.998750i	$0.515916\pi$
$164$		−	6.70820i		−	0.523823i
$165$		0			0
$166$	−5.00000	+	8.66025i	−0.388075	+	0.672166i
$167$	−7.74597	−	4.47214i	−0.599401	−	0.346064i	0.169405	−	0.985547i	$-0.445815\pi$
$167$	−7.74597	−	4.47214i	−0.599401	−	0.346064i	−0.768806	+	0.639482i	$0.779149\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−19.3649			−1.48522
$171$		0			0
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	−7.74597	−	13.4164i	−0.588915	−	1.02003i	−0.994375	−	0.105918i	$-0.966222\pi$
$173$	−7.74597	−	13.4164i	−0.588915	−	1.02003i	0.405460	−	0.914113i	$-0.367111\pi$
$174$		0			0
$175$		0			0
$176$	3.87298	−	2.23607i	0.291937	−	0.168550i
$177$		0			0
$178$	−5.00000	−	8.66025i	−0.374766	−	0.649113i
$179$	−3.87298	+	6.70820i	−0.289480	+	0.501395i	−0.973686	−	0.227895i	$-0.926816\pi$
$179$	−3.87298	+	6.70820i	−0.289480	+	0.501395i	0.684205	+	0.729289i	$0.260149\pi$
$180$		0			0
$181$	−19.0000			−1.41226			−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000			−1.41226			−0.706129	+	0.708083i	$0.749560\pi$
$182$	19.3649	+	20.1246i	1.43542	+	1.49174i
$183$		0			0
$184$	15.0000	+	8.66025i	1.10581	+	0.638442i
$185$	−1.93649	+	3.35410i	−0.142374	+	0.246598i
$186$		0			0
$187$		−	17.3205i		−	1.26660i
$188$	11.6190	−	6.70820i	0.847399	−	0.489246i
$189$		0			0
$190$			17.3205i			1.25656i
$191$	−7.74597	−	13.4164i	−0.560478	−	0.970777i	−0.997455	−	0.0713041i	$-0.977284\pi$
$191$	−7.74597	−	13.4164i	−0.560478	−	0.970777i	0.436976	−	0.899473i	$-0.356049\pi$
$192$		0			0
$193$	1.50000	+	0.866025i	0.107972	+	0.0623379i	0.553014	−	0.833172i	$-0.313478\pi$
$193$	1.50000	+	0.866025i	0.107972	+	0.0623379i	−0.445041	+	0.895510i	$0.646811\pi$
$194$	−15.4919			−1.11226
$195$		0			0
$196$	15.0000			1.07143
$197$	3.87298	+	2.23607i	0.275939	+	0.159313i	0.631583	−	0.775308i	$-0.282405\pi$
$197$	3.87298	+	2.23607i	0.275939	+	0.159313i	−0.355645	+	0.934621i	$0.615739\pi$
$198$		0			0
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$		0			0
$201$		0			0
$202$	−7.50000	+	4.33013i	−0.527698	+	0.304667i
$203$			13.4164i			0.941647i
$204$		0			0
$205$	2.50000	−	4.33013i	0.174608	−	0.302429i
$206$	−3.87298	−	2.23607i	−0.269844	−	0.155794i
$207$		0			0
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$	−15.4919			−1.07160
$210$		0			0
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	17.4284	+	30.1869i	1.19699	+	2.07325i
$213$		0			0
$214$	15.0000	−	8.66025i	1.02538	−	0.592003i
$215$	3.87298	−	2.23607i	0.264135	−	0.152499i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−30.0000			−2.02260
$221$	3.87298	−	13.4164i	0.260525	−	0.902485i
$222$		0			0
$223$	24.0000	+	13.8564i	1.60716	+	0.927894i	0.990002	+	0.141053i	$0.0450490\pi$
$223$	24.0000	+	13.8564i	1.60716	+	0.927894i	0.617157	+	0.786840i	$0.288284\pi$
$224$	11.6190	−	20.1246i	0.776324	−	1.34463i
$225$		0			0
$226$		−	43.3013i		−	2.88036i
$227$	19.3649	−	11.1803i	1.28529	−	0.742065i	0.307483	−	0.951553i	$-0.400513\pi$
$227$	19.3649	−	11.1803i	1.28529	−	0.742065i	0.977811	+	0.209488i	$0.0671798\pi$
$228$		0			0
$229$		−	20.7846i		−	1.37349i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$		−	20.7846i		−	1.37349i	0.726900	−	0.686743i	$-0.240960\pi$
$230$	19.3649	+	33.5410i	1.27688	+	2.21163i
$231$		0			0
$232$	−7.50000	−	4.33013i	−0.492399	−	0.284287i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	10.0000			0.652328
$236$	23.2379	+	13.4164i	1.51266	+	0.873334i
$237$		0			0
$238$	−15.0000	−	25.9808i	−0.972306	−	1.68408i
$239$		−	4.47214i		−	0.289278i	−0.989484	−	0.144639i	$-0.953798\pi$
$239$		−	4.47214i		−	0.289278i	0.989484	−	0.144639i	$-0.0462022\pi$
$240$		0			0
$241$	−16.5000	+	9.52628i	−1.06286	+	0.613642i	−0.926222	−	0.376980i	$-0.876963\pi$
$241$	−16.5000	+	9.52628i	−1.06286	+	0.613642i	−0.136637	+	0.990621i	$0.543629\pi$
$242$		−	20.1246i		−	1.29366i
$243$		0			0
$244$	−10.5000	+	18.1865i	−0.672194	+	1.16427i
$245$	9.68246	+	5.59017i	0.618590	+	0.357143i
$246$		0			0
$247$	−12.0000	−	3.46410i	−0.763542	−	0.220416i
$248$		0			0
$249$		0			0
$250$	12.5000	−	21.6506i	0.790569	−	1.36931i
$251$	−7.74597	−	13.4164i	−0.488921	−	0.846836i	0.510998	−	0.859582i	$-0.329276\pi$
$251$	−7.74597	−	13.4164i	−0.488921	−	0.846836i	−0.999919	+	0.0127459i	$0.995943\pi$
$252$		0			0
$253$	−30.0000	+	17.3205i	−1.88608	+	1.08893i
$254$	−7.74597	+	4.47214i	−0.486025	+	0.280607i
$255$		0			0
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	1.93649	−	3.35410i	0.120795	−	0.209223i	−0.799286	−	0.600950i	$-0.794789\pi$
$257$	1.93649	−	3.35410i	0.120795	−	0.209223i	0.920081	+	0.391727i	$0.128122\pi$
$258$		0			0
$259$	−6.00000			−0.372822
$260$	−23.2379	−	6.70820i	−1.44115	−	0.416025i
$261$		0			0
$262$		0			0
$263$	−3.87298	+	6.70820i	−0.238818	+	0.413646i	−0.960376	−	0.278709i	$-0.910093\pi$
$263$	−3.87298	+	6.70820i	−0.238818	+	0.413646i	0.721557	+	0.692355i	$0.243427\pi$
$264$		0			0
$265$			25.9808i			1.59599i
$266$	−23.2379	+	13.4164i	−1.42481	+	0.822613i
$267$		0			0
$268$		−	10.3923i		−	0.634811i
$269$	−7.74597	−	13.4164i	−0.472280	−	0.818013i	0.527217	−	0.849731i	$-0.323236\pi$
$269$	−7.74597	−	13.4164i	−0.472280	−	0.818013i	−0.999497	+	0.0317179i	$0.989902\pi$
$270$		0			0
$271$	6.00000	+	3.46410i	0.364474	+	0.210429i	0.671042	−	0.741420i	$-0.265847\pi$
$271$	6.00000	+	3.46410i	0.364474	+	0.210429i	−0.306568	+	0.951849i	$0.599181\pi$
$272$	−3.87298			−0.234834
$273$		0			0
$274$	−35.0000			−2.11443
$275$		0			0
$276$		0			0
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$			17.8885i			1.07288i
$279$		0			0
$280$	−15.0000	+	8.66025i	−0.896421	+	0.517549i
$281$			15.6525i			0.933748i	0.884324	+	0.466874i	$0.154620\pi$
$281$			15.6525i			0.933748i	−0.884324	+	0.466874i	$0.845380\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$	−11.6190	−	6.70820i	−0.689458	−	0.398059i
$285$		0			0
$286$	10.0000	−	34.6410i	0.591312	−	2.04837i
$287$	7.74597			0.457230
$288$		0			0
$289$	1.00000	−	1.73205i	0.0588235	−	0.101885i
$290$	−9.68246	−	16.7705i	−0.568574	−	0.984798i
$291$		0			0
$292$	40.5000	−	23.3827i	2.37008	−	1.36837i
$293$	1.93649	−	1.11803i	0.113131	−	0.0653162i	−0.442367	−	0.896834i	$-0.645861\pi$
$293$	1.93649	−	1.11803i	0.113131	−	0.0653162i	0.555498	+	0.831518i	$0.312528\pi$
$294$		0			0
$295$	10.0000	+	17.3205i	0.582223	+	1.00844i
$296$	1.93649	−	3.35410i	0.112556	−	0.194953i
$297$		0			0
$298$	25.0000			1.44821
$299$	−27.1109	+	6.70820i	−1.56786	+	0.387945i
$300$		0			0
$301$	6.00000	+	3.46410i	0.345834	+	0.199667i
$302$	11.6190	−	20.1246i	0.668595	−	1.15804i
$303$		0			0
$304$			3.46410i			0.198680i
$305$	−13.5554	+	7.82624i	−0.776182	+	0.448129i
$306$		0			0
$307$		−	10.3923i		−	0.593120i	−0.955014	−	0.296560i	$-0.904160\pi$
$307$		−	10.3923i		−	0.593120i	0.955014	−	0.296560i	$-0.0958395\pi$
$308$	−23.2379	−	40.2492i	−1.32410	−	2.29341i
$309$		0			0
$310$		0			0
$311$	23.2379			1.31770			0.658850	−	0.752274i	$-0.271043\pi$
$311$	23.2379			1.31770			0.658850	+	0.752274i	$0.271043\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−21.3014	−	12.2984i	−1.20211	−	0.694037i
$315$		0			0
$316$	12.0000	+	20.7846i	0.675053	+	1.16923i
$317$			29.0689i			1.63267i	0.577578	+	0.816336i	$0.303998\pi$
$317$			29.0689i			1.63267i	−0.577578	+	0.816336i	$0.696002\pi$
$318$		0			0
$319$	15.0000	−	8.66025i	0.839839	−	0.484881i
$320$			29.0689i			1.62500i
$321$		0			0
$322$	−30.0000	+	51.9615i	−1.67183	+	2.89570i
$323$	11.6190	+	6.70820i	0.646496	+	0.373254i
$324$		0			0
$325$		0			0
$326$	30.9839			1.71604
$327$		0			0
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	7.74597	+	13.4164i	0.427049	+	0.739671i
$330$		0			0
$331$	24.0000	−	13.8564i	1.31916	−	0.761617i	0.335566	−	0.942017i	$-0.391072\pi$
$331$	24.0000	−	13.8564i	1.31916	−	0.761617i	0.983593	+	0.180400i	$0.0577391\pi$
$332$	11.6190	−	6.70820i	0.637673	−	0.368161i
$333$		0			0
$334$	10.0000	+	17.3205i	0.547176	+	0.947736i
$335$	3.87298	−	6.70820i	0.211604	−	0.366508i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	15.4919	−	24.5967i	0.842650	−	1.33789i
$339$		0			0
$340$	22.5000	+	12.9904i	1.22023	+	0.704502i
$341$		0			0
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$	−3.87298	+	2.23607i	−0.208817	+	0.120561i
$345$		0			0
$346$			34.6410i			1.86231i
$347$	3.87298	+	6.70820i	0.207913	+	0.360115i	0.951057	−	0.309016i	$-0.0999997\pi$
$347$	3.87298	+	6.70820i	0.207913	+	0.360115i	−0.743144	+	0.669131i	$0.766666\pi$
$348$		0			0
$349$	−12.0000	−	6.92820i	−0.642345	−	0.370858i	0.143172	−	0.989698i	$-0.454270\pi$
$349$	−12.0000	−	6.92820i	−0.642345	−	0.370858i	−0.785517	+	0.618840i	$0.787603\pi$
$350$		0			0
$351$		0			0
$352$	−30.0000			−1.59901
$353$	−1.93649	−	1.11803i	−0.103069	−	0.0595069i	0.447579	−	0.894244i	$-0.352286\pi$
$353$	−1.93649	−	1.11803i	−0.103069	−	0.0595069i	−0.550648	+	0.834737i	$0.685620\pi$
$354$		0			0
$355$	−5.00000	−	8.66025i	−0.265372	−	0.459639i
$356$			13.4164i			0.711068i
$357$		0			0
$358$	15.0000	−	8.66025i	0.792775	−	0.457709i
$359$		−	31.3050i		−	1.65221i	−0.563515	−	0.826106i	$-0.690551\pi$
$359$		−	31.3050i		−	1.65221i	0.563515	−	0.826106i	$-0.309449\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	36.7933	+	21.2426i	1.93382	+	1.11649i
$363$		0			0
$364$	−9.00000	−	36.3731i	−0.471728	−	1.90647i
$365$	34.8569			1.82449
$366$		0			0
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	−0.988840	−	0.148983i	$-0.952400\pi$
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	0.623443	+	0.781869i	$0.285733\pi$
$368$	3.87298	+	6.70820i	0.201893	+	0.349689i
$369$		0			0
$370$	7.50000	−	4.33013i	0.389906	−	0.225113i
$371$	−34.8569	+	20.1246i	−1.80968	+	1.04482i
$372$		0			0
$373$	18.5000	+	32.0429i	0.957894	+	1.65912i	0.727603	+	0.685999i	$0.240634\pi$
$373$	18.5000	+	32.0429i	0.957894	+	1.65912i	0.230291	+	0.973122i	$0.426032\pi$
$374$	−19.3649	+	33.5410i	−1.00134	+	1.73436i
$375$		0			0
$376$	−10.0000			−0.515711
$377$	13.5554	−	3.35410i	0.698141	−	0.172745i
$378$		0			0
$379$	−12.0000	−	6.92820i	−0.616399	−	0.355878i	0.159067	−	0.987268i	$-0.449151\pi$
$379$	−12.0000	−	6.92820i	−0.616399	−	0.355878i	−0.775466	+	0.631390i	$0.782485\pi$
$380$	11.6190	−	20.1246i	0.596040	−	1.03237i
$381$		0			0
$382$			34.6410i			1.77239i
$383$	−15.4919	+	8.94427i	−0.791601	+	0.457031i	−0.840526	−	0.541772i	$-0.817754\pi$
$383$	−15.4919	+	8.94427i	−0.791601	+	0.457031i	0.0489250	+	0.998802i	$0.484420\pi$
$384$		0			0
$385$		−	34.6410i		−	1.76547i
$386$	−1.93649	−	3.35410i	−0.0985648	−	0.170719i
$387$		0			0
$388$	18.0000	+	10.3923i	0.913812	+	0.527589i
$389$	11.6190			0.589104			0.294552	−	0.955635i	$-0.404830\pi$
$389$	11.6190			0.589104			0.294552	+	0.955635i	$0.404830\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	−9.68246	−	5.59017i	−0.489038	−	0.282346i
$393$		0			0
$394$	−5.00000	−	8.66025i	−0.251896	−	0.436297i
$395$			17.8885i			0.900070i
$396$		0			0
$397$	−12.0000	+	6.92820i	−0.602263	+	0.347717i	−0.769931	−	0.638127i	$-0.779710\pi$
$397$	−12.0000	+	6.92820i	−0.602263	+	0.347717i	0.167668	+	0.985843i	$0.446376\pi$
$398$		−	49.1935i		−	2.46585i
$399$		0			0
$400$		0			0
$401$	−25.1744	−	14.5344i	−1.25715	−	0.725815i	−0.284630	−	0.958638i	$-0.591871\pi$
$401$	−25.1744	−	14.5344i	−1.25715	−	0.725815i	−0.972519	+	0.232822i	$0.925204\pi$
$402$		0			0
$403$		0			0
$404$	11.6190			0.578064
$405$		0			0
$406$	15.0000	−	25.9808i	0.744438	−	1.28940i
$407$	3.87298	+	6.70820i	0.191977	+	0.332513i
$408$		0			0
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	−0.673830	−	0.738886i	$-0.735352\pi$
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	0.302979	+	0.952997i	$0.402019\pi$
$410$	−9.68246	+	5.59017i	−0.478183	+	0.276079i
$411$		0			0
$412$	3.00000	+	5.19615i	0.147799	+	0.255996i
$413$	−15.4919	+	26.8328i	−0.762308	+	1.32036i
$414$		0			0
$415$	10.0000			0.490881
$416$	−23.2379	−	6.70820i	−1.13933	−	0.328897i
$417$		0			0
$418$	30.0000	+	17.3205i	1.46735	+	0.847174i
$419$	7.74597	−	13.4164i	0.378415	−	0.655434i	−0.612417	−	0.790535i	$-0.709802\pi$
$419$	7.74597	−	13.4164i	0.378415	−	0.655434i	0.990832	+	0.135101i	$0.0431358\pi$
$420$		0			0
$421$		−	15.5885i		−	0.759735i	−0.925041	−	0.379867i	$-0.875970\pi$
$421$		−	15.5885i		−	0.759735i	0.925041	−	0.379867i	$-0.124030\pi$
$422$	15.4919	−	8.94427i	0.754136	−	0.435400i
$423$		0			0
$424$		−	25.9808i		−	1.26174i
$425$		0			0
$426$		0			0
$427$	−21.0000	−	12.1244i	−1.01626	−	0.586739i
$428$	−23.2379			−1.12325
$429$		0			0
$430$	−10.0000			−0.482243
$431$	3.87298	+	2.23607i	0.186555	+	0.107708i	0.590369	−	0.807134i	$-0.298982\pi$
$431$	3.87298	+	2.23607i	0.186555	+	0.107708i	−0.403814	+	0.914841i	$0.632316\pi$
$432$		0			0
$433$	−17.5000	−	30.3109i	−0.840996	−	1.45665i	−0.889053	−	0.457804i	$-0.848636\pi$
$433$	−17.5000	−	30.3109i	−0.840996	−	1.45665i	0.0480569	−	0.998845i	$-0.484697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	26.8328i		−	1.28359i
$438$		0			0
$439$	−1.00000	+	1.73205i	−0.0477274	+	0.0826663i	−0.888902	−	0.458097i	$-0.848531\pi$
$439$	−1.00000	+	1.73205i	−0.0477274	+	0.0826663i	0.841175	+	0.540763i	$0.181865\pi$
$440$	19.3649	+	11.1803i	0.923186	+	0.533002i
$441$		0			0
$442$	−22.5000	+	21.6506i	−1.07022	+	1.02982i
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	−30.9839	−	53.6656i	−1.46713	−	2.54114i
$447$		0			0
$448$	−39.0000	+	22.5167i	−1.84258	+	1.06381i
$449$	−3.87298	+	2.23607i	−0.182777	+	0.105527i	−0.588597	−	0.808427i	$-0.700319\pi$
$449$	−3.87298	+	2.23607i	−0.182777	+	0.105527i	0.405820	+	0.913953i	$0.366986\pi$
$450$		0			0
$451$	−5.00000	−	8.66025i	−0.235441	−	0.407795i
$452$	−29.0474	+	50.3115i	−1.36627	+	2.36646i
$453$		0			0
$454$	−50.0000			−2.34662
$455$	7.74597	−	26.8328i	0.363137	−	1.25794i
$456$		0			0
$457$	10.5000	+	6.06218i	0.491169	+	0.283577i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	10.5000	+	6.06218i	0.491169	+	0.283577i	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−23.2379	+	40.2492i	−1.08584	+	1.88072i
$459$		0			0
$460$		−	51.9615i		−	2.42272i
$461$	1.93649	−	1.11803i	0.0901914	−	0.0520720i	−0.454226	−	0.890887i	$-0.650084\pi$
$461$	1.93649	−	1.11803i	0.0901914	−	0.0520720i	0.544417	+	0.838814i	$0.316751\pi$
$462$		0			0
$463$		−	10.3923i		−	0.482971i	−0.970404	−	0.241486i	$-0.922365\pi$
$463$		−	10.3923i		−	0.482971i	0.970404	−	0.241486i	$-0.0776347\pi$
$464$	−1.93649	−	3.35410i	−0.0898994	−	0.155710i
$465$		0			0
$466$		0			0
$467$	−23.2379			−1.07532			−0.537661	−	0.843161i	$-0.680692\pi$
$467$	−23.2379			−1.07532			−0.537661	+	0.843161i	$0.680692\pi$
$468$		0			0
$469$	12.0000			0.554109
$470$	−19.3649	−	11.1803i	−0.893237	−	0.515711i
$471$		0			0
$472$	−10.0000	−	17.3205i	−0.460287	−	0.797241i
$473$		−	8.94427i		−	0.411258i
$474$		0			0
$475$		0			0
$476$			40.2492i			1.84482i
$477$		0			0
$478$	−5.00000	+	8.66025i	−0.228695	+	0.396111i
$479$	15.4919	+	8.94427i	0.707845	+	0.408674i	0.810262	−	0.586067i	$-0.199325\pi$
$479$	15.4919	+	8.94427i	0.707845	+	0.408674i	−0.102418	+	0.994741i	$0.532658\pi$
$480$		0			0
$481$	1.50000	+	6.06218i	0.0683941	+	0.276412i
$482$	42.6028			1.94051
$483$		0			0
$484$	−13.5000	+	23.3827i	−0.613636	+	1.06285i
$485$	7.74597	+	13.4164i	0.351726	+	0.609208i
$486$		0			0
$487$	33.0000	−	19.0526i	1.49537	−	0.863354i	0.495387	−	0.868672i	$-0.335026\pi$
$487$	33.0000	−	19.0526i	1.49537	−	0.863354i	0.999986	+	0.00531860i	$0.00169297\pi$
$488$	13.5554	−	7.82624i	0.613626	−	0.354277i
$489$		0			0
$490$	−12.5000	−	21.6506i	−0.564692	−	0.978076i
$491$	19.3649	−	33.5410i	0.873926	−	1.51369i	0.0160245	−	0.999872i	$-0.494899\pi$
$491$	19.3649	−	33.5410i	0.873926	−	1.51369i	0.857902	−	0.513813i	$-0.171768\pi$
$492$		0			0
$493$	−15.0000			−0.675566
$494$	19.3649	+	20.1246i	0.871269	+	0.905449i
$495$		0			0
$496$		0			0
$497$	7.74597	−	13.4164i	0.347454	−	0.601808i
$498$		0			0
$499$		−	20.7846i		−	0.930447i	−0.885193	−	0.465223i	$-0.845974\pi$
$499$		−	20.7846i		−	0.930447i	0.885193	−	0.465223i	$-0.154026\pi$
$500$	−29.0474	+	16.7705i	−1.29904	+	0.750000i
$501$		0			0
$502$			34.6410i			1.54610i
$503$	3.87298	+	6.70820i	0.172688	+	0.299104i	0.939359	−	0.342936i	$-0.111422\pi$
$503$	3.87298	+	6.70820i	0.172688	+	0.299104i	−0.766671	+	0.642040i	$0.778088\pi$
$504$		0			0
$505$	7.50000	+	4.33013i	0.333746	+	0.192688i
$506$	77.4597			3.44350
$507$		0			0
$508$	12.0000			0.532414
$509$	−25.1744	−	14.5344i	−1.11584	−	0.644228i	−0.175501	−	0.984479i	$-0.556154\pi$
$509$	−25.1744	−	14.5344i	−1.11584	−	0.644228i	−0.940334	+	0.340251i	$0.889488\pi$
$510$		0			0
$511$	27.0000	+	46.7654i	1.19441	+	2.06878i
$512$			11.1803i			0.494106i
$513$		0			0
$514$	−7.50000	+	4.33013i	−0.330811	+	0.190994i
$515$			4.47214i			0.197066i
$516$		0			0
$517$	10.0000	−	17.3205i	0.439799	−	0.761755i
$518$	11.6190	+	6.70820i	0.510507	+	0.294742i
$519$		0			0
$520$	12.5000	+	12.9904i	0.548161	+	0.569666i
$521$	−11.6190			−0.509035			−0.254518	−	0.967068i	$-0.581917\pi$
$521$	−11.6190			−0.509035			−0.254518	+	0.967068i	$0.581917\pi$
$522$		0			0
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	−0.518766	−	0.854916i	$-0.673608\pi$
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	0.999762	+	0.0218062i	$0.00694167\pi$
$524$		0			0
$525$		0			0
$526$	15.0000	−	8.66025i	0.654031	−	0.377605i
$527$		0			0
$528$		0			0
$529$	−18.5000	−	32.0429i	−0.804348	−	1.39317i
$530$	29.0474	−	50.3115i	1.26174	−	2.18539i
$531$		0			0
$532$	36.0000			1.56080
$533$	−1.93649	−	7.82624i	−0.0838788	−	0.338992i
$534$		0			0
$535$	−15.0000	−	8.66025i	−0.648507	−	0.374415i
$536$	−3.87298	+	6.70820i	−0.167287	+	0.289750i
$537$		0			0
$538$			34.6410i			1.49348i
$539$	19.3649	−	11.1803i	0.834106	−	0.481571i
$540$		0			0
$541$			25.9808i			1.11700i	0.829504	+	0.558500i	$0.188623\pi$
$541$			25.9808i			1.11700i	−0.829504	+	0.558500i	$0.811377\pi$
$542$	−7.74597	−	13.4164i	−0.332718	−	0.576284i
$543$		0			0
$544$	22.5000	+	12.9904i	0.964680	+	0.556958i
$545$		0			0
$546$		0			0
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$	40.6663	+	23.4787i	1.73718	+	1.00296i
$549$		0			0
$550$		0			0
$551$			13.4164i			0.571558i
$552$		0			0
$553$	−24.0000	+	13.8564i	−1.02058	+	0.589234i
$554$			24.5967i			1.04502i
$555$		0			0
$556$	12.0000	−	20.7846i	0.508913	−	0.881464i
$557$	−25.1744	−	14.5344i	−1.06667	−	0.615844i	−0.139403	−	0.990236i	$-0.544518\pi$
$557$	−25.1744	−	14.5344i	−1.06667	−	0.615844i	−0.927271	+	0.374392i	$0.877852\pi$
$558$		0			0
$559$	2.00000	−	6.92820i	0.0845910	−	0.293032i
$560$	−7.74597			−0.327327
$561$		0			0
$562$	17.5000	−	30.3109i	0.738193	−	1.27859i
$563$	15.4919	+	26.8328i	0.652907	+	1.13087i	0.982414	+	0.186715i	$0.0597842\pi$
$563$	15.4919	+	26.8328i	0.652907	+	1.13087i	−0.329507	+	0.944153i	$0.606883\pi$
$564$		0			0
$565$	−37.5000	+	21.6506i	−1.57764	+	0.910849i
$566$	−19.3649	+	11.1803i	−0.813968	+	0.469945i
$567$		0			0
$568$	5.00000	+	8.66025i	0.209795	+	0.363376i
$569$	7.74597	−	13.4164i	0.324728	−	0.562445i	−0.656729	−	0.754126i	$-0.728061\pi$
$569$	7.74597	−	13.4164i	0.324728	−	0.562445i	0.981457	+	0.191681i	$0.0613940\pi$
$570$		0			0
$571$	−34.0000			−1.42286			−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000			−1.42286			−0.711428	+	0.702759i	$0.751951\pi$
$572$	−34.8569	+	33.5410i	−1.45744	+	1.40242i
$573$		0			0
$574$	−15.0000	−	8.66025i	−0.626088	−	0.361472i
$575$		0			0
$576$		0			0
$577$		−	5.19615i		−	0.216319i	−0.994134	−	0.108159i	$-0.965504\pi$
$577$		−	5.19615i		−	0.216319i	0.994134	−	0.108159i	$-0.0344957\pi$
$578$	−3.87298	+	2.23607i	−0.161095	+	0.0930082i
$579$		0			0
$580$			25.9808i			1.07879i
$581$	7.74597	+	13.4164i	0.321357	+	0.556606i
$582$		0			0
$583$	45.0000	+	25.9808i	1.86371	+	1.07601i
$584$	−34.8569			−1.44239
$585$		0			0
$586$	−5.00000			−0.206548
$587$	−30.9839	−	17.8885i	−1.27884	−	0.738339i	−0.302206	−	0.953243i	$-0.597723\pi$
$587$	−30.9839	−	17.8885i	−1.27884	−	0.738339i	−0.976635	+	0.214903i	$0.931056\pi$
$588$		0			0
$589$		0			0
$590$		−	44.7214i		−	1.84115i
$591$		0			0
$592$	1.50000	−	0.866025i	0.0616496	−	0.0355934i
$593$			2.23607i			0.0918243i	0.998945	+	0.0459122i	$0.0146194\pi$
$593$			2.23607i			0.0918243i	−0.998945	+	0.0459122i	$0.985381\pi$
$594$		0			0
$595$	−15.0000	+	25.9808i	−0.614940	+	1.06511i
$596$	−29.0474	−	16.7705i	−1.18983	−	0.686947i
$597$		0			0
$598$	60.0000	+	17.3205i	2.45358	+	0.708288i
$599$	−46.4758			−1.89895			−0.949475	−	0.313843i	$-0.898383\pi$
$599$	−46.4758			−1.89895			−0.949475	+	0.313843i	$0.898383\pi$
$600$		0			0
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	0.402568	+	0.915390i	$0.368118\pi$
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	−0.994035	+	0.109061i	$0.965216\pi$
$602$	−7.74597	−	13.4164i	−0.315702	−	0.546812i
$603$		0			0
$604$	−27.0000	+	15.5885i	−1.09861	+	0.634285i
$605$	−17.4284	+	10.0623i	−0.708566	+	0.409091i
$606$		0			0
$607$	−10.0000	−	17.3205i	−0.405887	−	0.703018i	0.588537	−	0.808470i	$-0.299704\pi$
$607$	−10.0000	−	17.3205i	−0.405887	−	0.703018i	−0.994424	+	0.105453i	$0.966371\pi$
$608$	11.6190	−	20.1246i	0.471211	−	0.816161i
$609$		0			0
$610$	35.0000			1.41711
$611$	11.6190	−	11.1803i	0.470052	−	0.452308i
$612$		0			0
$613$	1.50000	+	0.866025i	0.0605844	+	0.0349784i	0.529986	−	0.848006i	$-0.322197\pi$
$613$	1.50000	+	0.866025i	0.0605844	+	0.0349784i	−0.469402	+	0.882985i	$0.655530\pi$
$614$	−11.6190	+	20.1246i	−0.468903	+	0.812163i
$615$		0			0
$616$			34.6410i			1.39573i
$617$	25.1744	−	14.5344i	1.01348	−	0.585135i	0.101273	−	0.994859i	$-0.467708\pi$
$617$	25.1744	−	14.5344i	1.01348	−	0.585135i	0.912210	+	0.409724i	$0.134375\pi$
$618$		0			0
$619$			20.7846i			0.835404i	0.908584	+	0.417702i	$0.137164\pi$
$619$			20.7846i			0.835404i	−0.908584	+	0.417702i	$0.862836\pi$
$620$		0			0
$621$		0			0
$622$	−45.0000	−	25.9808i	−1.80434	−	1.04173i
$623$	−15.4919			−0.620671
$624$		0			0
$625$	−25.0000			−1.00000
$626$	42.6028	+	24.5967i	1.70275	+	0.983084i
$627$		0			0
$628$	16.5000	+	28.5788i	0.658422	+	1.14042i
$629$		−	6.70820i		−	0.267474i
$630$		0			0
$631$	6.00000	−	3.46410i	0.238856	−	0.137904i	−0.375795	−	0.926703i	$-0.622630\pi$
$631$	6.00000	−	3.46410i	0.238856	−	0.137904i	0.614651	+	0.788799i	$0.289297\pi$
$632$		−	17.8885i		−	0.711568i
$633$		0			0
$634$	32.5000	−	56.2917i	1.29074	−	2.23563i
$635$	7.74597	+	4.47214i	0.307389	+	0.177471i
$636$		0			0
$637$	17.5000	−	4.33013i	0.693375	−	0.171566i
$638$	−38.7298			−1.53333
$639$		0			0
$640$	17.5000	−	30.3109i	0.691748	−	1.19814i
$641$	9.68246	+	16.7705i	0.382434	+	0.662395i	0.991410	−	0.130794i	$-0.0417526\pi$
$641$	9.68246	+	16.7705i	0.382434	+	0.662395i	−0.608975	+	0.793189i	$0.708419\pi$
$642$		0			0
$643$	24.0000	−	13.8564i	0.946468	−	0.546443i	0.0544858	−	0.998515i	$-0.482648\pi$
$643$	24.0000	−	13.8564i	0.946468	−	0.546443i	0.891982	+	0.452071i	$0.149315\pi$
$644$	69.7137	−	40.2492i	2.74710	−	1.58604i
$645$		0			0
$646$	−15.0000	−	25.9808i	−0.590167	−	1.02220i
$647$	−15.4919	+	26.8328i	−0.609051	+	1.05491i	0.382346	+	0.924019i	$0.375116\pi$
$647$	−15.4919	+	26.8328i	−0.609051	+	1.05491i	−0.991397	+	0.130888i	$0.958217\pi$
$648$		0			0
$649$	40.0000			1.57014
$650$		0			0
$651$		0			0
$652$	−36.0000	−	20.7846i	−1.40987	−	0.813988i
$653$	7.74597	−	13.4164i	0.303123	−	0.525025i	−0.673719	−	0.738988i	$-0.735304\pi$
$653$	7.74597	−	13.4164i	0.303123	−	0.525025i	0.976842	+	0.213963i	$0.0686373\pi$
$654$		0			0
$655$		0			0
$656$	−1.93649	+	1.11803i	−0.0756073	+	0.0436519i
$657$		0			0
$658$		−	34.6410i		−	1.35045i
$659$	15.4919	+	26.8328i	0.603480	+	1.04526i	0.992290	+	0.123940i	$0.0395530\pi$
$659$	15.4919	+	26.8328i	0.603480	+	1.04526i	−0.388810	+	0.921318i	$0.627114\pi$
$660$		0			0
$661$	−16.5000	−	9.52628i	−0.641776	−	0.370529i	0.143523	−	0.989647i	$-0.454157\pi$
$661$	−16.5000	−	9.52628i	−0.641776	−	0.370529i	−0.785298	+	0.619118i	$0.787490\pi$
$662$	−61.9677			−2.40844
$663$		0			0
$664$	−10.0000			−0.388075
$665$	23.2379	+	13.4164i	0.901127	+	0.520266i
$666$		0			0
$667$	15.0000	+	25.9808i	0.580802	+	1.00598i
$668$		−	26.8328i		−	1.03819i
$669$		0			0
$670$	−15.0000	+	8.66025i	−0.579501	+	0.334575i
$671$			31.3050i			1.20851i
$672$		0			0
$673$	21.5000	−	37.2391i	0.828764	−	1.43546i	−0.0702442	−	0.997530i	$-0.522378\pi$
$673$	21.5000	−	37.2391i	0.828764	−	1.43546i	0.899008	−	0.437932i	$-0.144289\pi$
$674$	−21.3014	−	12.2984i	−0.820500	−	0.473716i
$675$		0			0
$676$	−34.5000	+	18.1865i	−1.32692	+	0.699482i
$677$	−46.4758			−1.78621			−0.893105	−	0.449848i	$-0.851478\pi$
$677$	−46.4758			−1.78621			−0.893105	+	0.449848i	$0.851478\pi$
$678$		0			0
$679$	−12.0000	+	20.7846i	−0.460518	+	0.797640i
$680$	−9.68246	−	16.7705i	−0.371305	−	0.643120i
$681$		0			0
$682$		0			0
$683$	30.9839	−	17.8885i	1.18556	−	0.684486i	0.228269	−	0.973598i	$-0.426693\pi$
$683$	30.9839	−	17.8885i	1.18556	−	0.684486i	0.957295	+	0.289112i	$0.0933600\pi$
$684$		0			0
$685$	17.5000	+	30.3109i	0.668641	+	1.15812i
$686$	−7.74597	+	13.4164i	−0.295742	+	0.512241i
$687$		0			0
$688$	−2.00000			−0.0762493
$689$	29.0474	+	30.1869i	1.10662	+	1.15003i
$690$		0			0
$691$	−21.0000	−	12.1244i	−0.798878	−	0.461232i	0.0442009	−	0.999023i	$-0.485926\pi$
$691$	−21.0000	−	12.1244i	−0.798878	−	0.461232i	−0.843079	+	0.537790i	$0.819259\pi$
$692$	23.2379	−	40.2492i	0.883372	−	1.53005i
$693$		0			0
$694$		−	17.3205i		−	0.657477i
$695$	15.4919	−	8.94427i	0.587643	−	0.339276i
$696$		0			0
$697$			8.66025i			0.328031i
$698$	15.4919	+	26.8328i	0.586378	+	1.01564i
$699$		0			0
$700$		0			0
$701$	46.4758			1.75537			0.877683	−	0.479241i	$-0.159088\pi$
$701$	46.4758			1.75537			0.877683	+	0.479241i	$0.159088\pi$
$702$		0			0
$703$	−6.00000			−0.226294
$704$	50.3488	+	29.0689i	1.89759	+	1.09557i
$705$		0			0
$706$	2.50000	+	4.33013i	0.0940887	+	0.162966i
$707$			13.4164i			0.504576i
$708$		0			0
$709$	10.5000	−	6.06218i	0.394336	−	0.227670i	−0.289701	−	0.957117i	$-0.593556\pi$
$709$	10.5000	−	6.06218i	0.394336	−	0.227670i	0.684037	+	0.729447i	$0.260223\pi$
$710$			22.3607i			0.839181i
$711$		0			0
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$		0			0
$714$		0			0
$715$	−35.0000	+	8.66025i	−1.30893	+	0.323875i
$716$	−23.2379			−0.868441
$717$		0			0
$718$	−35.0000	+	60.6218i	−1.30619	+	2.26238i
$719$	15.4919	+	26.8328i	0.577752	+	1.00070i	0.995737	+	0.0922413i	$0.0294031\pi$
$719$	15.4919	+	26.8328i	0.577752	+	1.00070i	−0.417985	+	0.908454i	$0.637264\pi$
$720$		0			0
$721$	−6.00000	+	3.46410i	−0.223452	+	0.129010i
$722$	13.5554	−	7.82624i	0.504481	−	0.291262i
$723$		0			0
$724$	−28.5000	−	49.3634i	−1.05919	−	1.83458i
$725$		0			0
$726$		0			0
$727$	−46.0000			−1.70605			−0.853023	−	0.521874i	$-0.825233\pi$
$727$	−46.0000			−1.70605			−0.853023	+	0.521874i	$0.825233\pi$
$728$	−7.74597	+	26.8328i	−0.287085	+	0.994490i
$729$		0			0
$730$	−67.5000	−	38.9711i	−2.49829	−	1.44239i
$731$	−3.87298	+	6.70820i	−0.143247	+	0.248112i
$732$		0			0
$733$			36.3731i			1.34347i	0.740792	+	0.671735i	$0.234451\pi$
$733$			36.3731i			1.34347i	−0.740792	+	0.671735i	$0.765549\pi$
$734$	27.1109	−	15.6525i	1.00068	−	0.577743i
$735$		0			0
$736$		−	51.9615i		−	1.91533i
$737$	−7.74597	−	13.4164i	−0.285326	−	0.494200i
$738$		0			0
$739$	−30.0000	−	17.3205i	−1.10357	−	0.637145i	−0.166412	−	0.986056i	$-0.553218\pi$
$739$	−30.0000	−	17.3205i	−1.10357	−	0.637145i	−0.937156	+	0.348911i	$0.886552\pi$
$740$	−11.6190			−0.427121
$741$		0			0
$742$	90.0000			3.30400
$743$	−7.74597	−	4.47214i	−0.284172	−	0.164067i	0.351139	−	0.936323i	$-0.385795\pi$
$743$	−7.74597	−	4.47214i	−0.284172	−	0.164067i	−0.635311	+	0.772257i	$0.719128\pi$
$744$		0			0
$745$	−12.5000	−	21.6506i	−0.457965	−	0.793218i
$746$		−	82.7345i		−	3.02913i
$747$		0			0
$748$	45.0000	−	25.9808i	1.64536	−	0.949951i
$749$		−	26.8328i		−	0.980450i
$750$		0			0
$751$	−19.0000	+	32.9090i	−0.693320	+	1.20087i	0.277424	+	0.960748i	$0.410519\pi$
$751$	−19.0000	+	32.9090i	−0.693320	+	1.20087i	−0.970744	+	0.240118i	$0.922814\pi$
$752$	−3.87298	−	2.23607i	−0.141233	−	0.0815410i
$753$		0			0
$754$	−30.0000	−	8.66025i	−1.09254	−	0.315388i
$755$	−23.2379			−0.845714
$756$		0			0
$757$	23.0000	−	39.8372i	0.835949	−	1.44791i	−0.0573060	−	0.998357i	$-0.518251\pi$
$757$	23.0000	−	39.8372i	0.835949	−	1.44791i	0.893255	−	0.449550i	$-0.148416\pi$
$758$	15.4919	+	26.8328i	0.562692	+	0.974612i
$759$		0			0
$760$	−15.0000	+	8.66025i	−0.544107	+	0.314140i
$761$	−27.1109	+	15.6525i	−0.982769	+	0.567402i	−0.903105	−	0.429420i	$-0.858718\pi$
$761$	−27.1109	+	15.6525i	−0.982769	+	0.567402i	−0.0796638	+	0.996822i	$0.525385\pi$
$762$		0			0
$763$		0			0
$764$	23.2379	−	40.2492i	0.840718	−	1.45617i
$765$		0			0
$766$	40.0000			1.44526
$767$	30.9839	+	8.94427i	1.11876	+	0.322959i
$768$		0			0
$769$	42.0000	+	24.2487i	1.51456	+	0.874431i	0.999854	+	0.0170631i	$0.00543163\pi$
$769$	42.0000	+	24.2487i	1.51456	+	0.874431i	0.514704	+	0.857368i	$0.327902\pi$
$770$	−38.7298	+	67.0820i	−1.39573	+	2.41747i
$771$		0			0
$772$			5.19615i			0.187014i
$773$	−3.87298	+	2.23607i	−0.139302	+	0.0804258i	−0.568031	−	0.823007i	$-0.692295\pi$
$773$	−3.87298	+	2.23607i	−0.139302	+	0.0804258i	0.428730	+	0.903433i	$0.358961\pi$
$774$		0			0
$775$		0			0
$776$	−7.74597	−	13.4164i	−0.278064	−	0.481621i
$777$		0			0
$778$	−22.5000	−	12.9904i	−0.806664	−	0.465728i
$779$	7.74597			0.277528
$780$		0			0
$781$	−20.0000			−0.715656
$782$	−58.0948	−	33.5410i	−2.07746	−	1.19942i
$783$		0			0
$784$	−2.50000	−	4.33013i	−0.0892857	−	0.154647i
$785$			24.5967i			0.877896i
$786$		0			0
$787$	24.0000	−	13.8564i	0.855508	−	0.493928i	−0.00699773	−	0.999976i	$-0.502227\pi$
$787$	24.0000	−	13.8564i	0.855508	−	0.493928i	0.862505	+	0.506048i	$0.168894\pi$
$788$			13.4164i			0.477940i
$789$		0			0
$790$	20.0000	−	34.6410i	0.711568	−	1.23247i
$791$	−58.0948	−	33.5410i	−2.06561	−	1.19258i
$792$		0			0
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$	30.9839			1.09958
$795$		0			0
$796$	−33.0000	+	57.1577i	−1.16965	+	2.02590i
$797$	15.4919	+	26.8328i	0.548752	+	0.950467i	0.998360	+	0.0572411i	$0.0182304\pi$
$797$	15.4919	+	26.8328i	0.548752	+	0.950467i	−0.449608	+	0.893226i	$0.648436\pi$
$798$		0			0
$799$	−15.0000	+	8.66025i	−0.530662	+	0.306378i
$800$		0			0
$801$		0			0
$802$	32.5000	+	56.2917i	1.14761	+	1.98773i
$803$	34.8569	−	60.3738i	1.23007	−	2.13055i
$804$		0			0
$805$	60.0000			2.11472
$806$		0			0
$807$		0			0
$808$	−7.50000	−	4.33013i	−0.263849	−	0.152333i
$809$	−21.3014	+	36.8951i	−0.748918	+	1.29716i	0.199424	+	0.979913i	$0.436093\pi$
$809$	−21.3014	+	36.8951i	−0.748918	+	1.29716i	−0.948342	+	0.317250i	$0.897241\pi$
$810$		0			0
$811$			41.5692i			1.45969i	0.683611	+	0.729846i	$0.260408\pi$
$811$			41.5692i			1.45969i	−0.683611	+	0.729846i	$0.739592\pi$
$812$	−34.8569	+	20.1246i	−1.22324	+	0.706235i
$813$		0			0
$814$		−	17.3205i		−	0.607083i
$815$	−15.4919	−	26.8328i	−0.542659	−	0.939913i
$816$		0			0
$817$	6.00000	+	3.46410i	0.209913	+	0.121194i
$818$	19.3649			0.677078
$819$		0			0
$820$	15.0000			0.523823
$821$	3.87298	+	2.23607i	0.135168	+	0.0780393i	0.566059	−	0.824365i	$-0.308467\pi$
$821$	3.87298	+	2.23607i	0.135168	+	0.0780393i	−0.430891	+	0.902404i	$0.641801\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		−	4.47214i		−	0.155794i
$825$		0			0
$826$	60.0000	−	34.6410i	2.08767	−	1.20532i
$827$		−	17.8885i		−	0.622046i	−0.950402	−	0.311023i	$-0.899328\pi$
$827$		−	17.8885i		−	0.622046i	0.950402	−	0.311023i	$-0.100672\pi$
$828$		0			0
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	−0.730791	−	0.682601i	$-0.760849\pi$
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	0.956545	+	0.291583i	$0.0941820\pi$
$830$	−19.3649	−	11.1803i	−0.672166	−	0.388075i
$831$		0			0
$832$	32.5000	+	33.7750i	1.12673	+	1.17094i
$833$	−19.3649			−0.670955
$834$		0			0
$835$	10.0000	−	17.3205i	0.346064	−	0.599401i
$836$	−23.2379	−	40.2492i	−0.803700	−	1.39205i
$837$		0			0
$838$	−30.0000	+	17.3205i	−1.03633	+	0.598327i
$839$	−15.4919	+	8.94427i	−0.534841	+	0.308791i	−0.742985	−	0.669308i	$-0.766591\pi$
$839$	−15.4919	+	8.94427i	−0.534841	+	0.308791i	0.208145	+	0.978098i	$0.433258\pi$
$840$		0			0
$841$	7.00000	+	12.1244i	0.241379	+	0.418081i
$842$	−17.4284	+	30.1869i	−0.600623	+	1.04031i
$843$		0			0
$844$	−24.0000			−0.826114
$845$	−29.0474	−	1.11803i	−0.999260	−	0.0384615i
$846$		0			0
$847$	−27.0000	−	15.5885i	−0.927731	−	0.535626i
$848$	5.80948	−	10.0623i	0.199498	−	0.345541i
$849$		0			0
$850$		0			0
$851$	−11.6190	+	6.70820i	−0.398292	+	0.229954i
$852$		0			0
$853$			5.19615i			0.177913i	0.996036	+	0.0889564i	$0.0283532\pi$
$853$			5.19615i			0.177913i	−0.996036	+	0.0889564i	$0.971647\pi$
$854$	27.1109	+	46.9574i	0.927715	+	1.60685i
$855$		0			0
$856$	15.0000	+	8.66025i	0.512689	+	0.296001i
$857$	−34.8569			−1.19069			−0.595344	−	0.803471i	$-0.702984\pi$
$857$	−34.8569			−1.19069			−0.595344	+	0.803471i	$0.702984\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	11.6190	+	6.70820i	0.396203	+	0.228748i
$861$		0			0
$862$	−5.00000	−	8.66025i	−0.170301	−	0.294969i
$863$		−	31.3050i		−	1.06563i	−0.846231	−	0.532816i	$-0.821134\pi$
$863$		−	31.3050i		−	1.06563i	0.846231	−	0.532816i	$-0.178866\pi$
$864$		0			0
$865$	30.0000	−	17.3205i	1.02003	−	0.588915i
$866$			78.2624i			2.65946i
$867$		0			0
$868$		0			0
$869$	30.9839	+	17.8885i	1.05106	+	0.606827i
$870$		0			0
$871$	−3.00000	−	12.1244i	−0.101651	−	0.410818i
$872$		0			0
$873$		0			0
$874$	−30.0000	+	51.9615i	−1.01477	+	1.75762i
$875$	−19.3649	−	33.5410i	−0.654654	−	1.13389i
$876$		0			0
$877$	−25.5000	+	14.7224i	−0.861074	+	0.497141i	−0.864372	−	0.502853i	$-0.832284\pi$
$877$	−25.5000	+	14.7224i	−0.861074	+	0.497141i	0.00329792	+	0.999995i	$0.498950\pi$
$878$	3.87298	−	2.23607i	0.130707	−	0.0754636i
$879$		0			0
$880$	5.00000	+	8.66025i	0.168550	+	0.291937i
$881$	13.5554	−	23.4787i	0.456694	−	0.791018i	−0.542089	−	0.840321i	$-0.682367\pi$
$881$	13.5554	−	23.4787i	0.456694	−	0.791018i	0.998784	+	0.0493028i	$0.0156999\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	40.6663	−	10.0623i	1.36776	−	0.338432i
$885$		0			0
$886$		0			0
$887$	7.74597	−	13.4164i	0.260084	−	0.450479i	−0.706180	−	0.708032i	$-0.749583\pi$
$887$	7.74597	−	13.4164i	0.260084	−	0.450479i	0.966264	+	0.257554i	$0.0829164\pi$
$888$		0			0
$889$			13.8564i			0.464729i
$890$	19.3649	−	11.1803i	0.649113	−	0.374766i
$891$		0			0
$892$			83.1384i			2.78368i
$893$	7.74597	+	13.4164i	0.259209	+	0.448963i
$894$		0			0
$895$	−15.0000	−	8.66025i	−0.501395	−	0.289480i
$896$	54.2218			1.81142
$897$		0			0
$898$	10.0000			0.333704
$899$		0			0
$900$		0			0
$901$	−22.5000	−	38.9711i	−0.749584	−	1.29832i
$902$			22.3607i			0.744529i
$903$		0			0
$904$	37.5000	−	21.6506i	1.24723	−	0.720089i
$905$		−	42.4853i		−	1.41226i
$906$		0			0
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$	58.0948	+	33.5410i	1.92794	+	1.11310i
$909$		0			0
$910$	−45.0000	+	43.3013i	−1.49174	+	1.43542i
$911$	46.4758			1.53981			0.769906	−	0.638157i	$-0.220303\pi$
$911$	46.4758			1.53981			0.769906	+	0.638157i	$0.220303\pi$
$912$		0			0
$913$	10.0000	−	17.3205i	0.330952	−	0.573225i
$914$	−13.5554	−	23.4787i	−0.448374	−	0.776607i
$915$		0			0
$916$	54.0000	−	31.1769i	1.78421	−	1.03011i
$917$		0			0
$918$		0			0
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$	−19.3649	+	33.5410i	−0.638442	+	1.10581i
$921$		0			0
$922$	−5.00000			−0.164666
$923$	−15.4919	−	4.47214i	−0.509923	−	0.147202i
$924$		0			0
$925$		0			0
$926$	−11.6190	+	20.1246i	−0.381822	+	0.661336i
$927$		0			0
$928$			25.9808i			0.852860i
$929$	48.4123	−	27.9508i	1.58836	−	0.917038i	0.594778	−	0.803890i	$-0.297240\pi$
$929$	48.4123	−	27.9508i	1.58836	−	0.917038i	0.993578	−	0.113147i	$-0.0360932\pi$
$930$		0			0
$931$			17.3205i			0.567657i
$932$		0			0
$933$		0			0
$934$	45.0000	+	25.9808i	1.47244	+	0.850117i
$935$	38.7298			1.26660
$936$		0			0
$937$	−1.00000			−0.0326686			−0.0163343	−	0.999867i	$-0.505200\pi$
$937$	−1.00000			−0.0326686			−0.0163343	+	0.999867i	$0.505200\pi$
$938$	−23.2379	−	13.4164i	−0.758744	−	0.438061i
$939$		0			0
$940$	15.0000	+	25.9808i	0.489246	+	0.847399i
$941$		−	4.47214i		−	0.145787i	−0.997340	−	0.0728937i	$-0.976777\pi$
$941$		−	4.47214i		−	0.145787i	0.997340	−	0.0728937i	$-0.0232234\pi$
$942$		0			0
$943$	15.0000	−	8.66025i	0.488467	−	0.282017i
$944$		−	8.94427i		−	0.291111i
$945$		0			0
$946$	−10.0000	+	17.3205i	−0.325128	+	0.563138i
$947$	15.4919	+	8.94427i	0.503420	+	0.290650i	0.730125	−	0.683314i	$-0.239462\pi$
$947$	15.4919	+	8.94427i	0.503420	+	0.290650i	−0.226705	+	0.973964i	$0.572795\pi$
$948$		0			0
$949$	40.5000	−	38.9711i	1.31469	−	1.26506i
$950$		0			0
$951$		0			0
$952$	15.0000	−	25.9808i	0.486153	−	0.842041i
$953$	−7.74597	−	13.4164i	−0.250916	−	0.434600i	0.712862	−	0.701304i	$-0.247399\pi$
$953$	−7.74597	−	13.4164i	−0.250916	−	0.434600i	−0.963778	+	0.266704i	$0.914065\pi$
$954$		0			0
$955$	30.0000	−	17.3205i	0.970777	−	0.560478i
$956$	11.6190	−	6.70820i	0.375784	−	0.216959i
$957$		0			0
$958$	−20.0000	−	34.6410i	−0.646171	−	1.11920i
$959$	−27.1109	+	46.9574i	−0.875456	+	1.51633i
$960$		0			0
$961$	31.0000			1.00000
$962$	3.87298	−	13.4164i	0.124870	−	0.432562i
$963$		0			0
$964$	−49.5000	−	28.5788i	−1.59429	−	0.920462i
$965$	−1.93649	+	3.35410i	−0.0623379	+	0.107972i
$966$		0			0
$967$		−	10.3923i		−	0.334194i	−0.985940	−	0.167097i	$-0.946561\pi$
$967$		−	10.3923i		−	0.334194i	0.985940	−	0.167097i	$-0.0534393\pi$
$968$	17.4284	−	10.0623i	0.560171	−	0.323415i
$969$		0			0
$970$		−	34.6410i		−	1.11226i
$971$	15.4919	+	26.8328i	0.497160	+	0.861106i	0.999995	−	0.00327648i	$-0.00104294\pi$
$971$	15.4919	+	26.8328i	0.497160	+	0.861106i	−0.502835	+	0.864383i	$0.667710\pi$
$972$		0			0
$973$	24.0000	+	13.8564i	0.769405	+	0.444216i
$974$	−85.2056			−2.73016
$975$		0			0
$976$	7.00000			0.224065
$977$	9.68246	+	5.59017i	0.309769	+	0.178845i	0.646823	−	0.762640i	$-0.276097\pi$
$977$	9.68246	+	5.59017i	0.309769	+	0.178845i	−0.337054	+	0.941485i	$0.609430\pi$
$978$		0			0
$979$	10.0000	+	17.3205i	0.319601	+	0.553566i
$980$			33.5410i			1.07143i
$981$		0			0
$982$	−75.0000	+	43.3013i	−2.39335	+	1.38180i
$983$			8.94427i			0.285278i	0.989775	+	0.142639i	$0.0455588\pi$
$983$			8.94427i			0.285278i	−0.989775	+	0.142639i	$0.954441\pi$
$984$		0			0
$985$	−5.00000	+	8.66025i	−0.159313	+	0.275939i
$986$	29.0474	+	16.7705i	0.925057	+	0.534082i
$987$		0			0
$988$	−9.00000	−	36.3731i	−0.286328	−	1.15718i
$989$	15.4919			0.492615
$990$		0			0
$991$	−7.00000	+	12.1244i	−0.222362	+	0.385143i	−0.955525	−	0.294911i	$-0.904710\pi$
$991$	−7.00000	+	12.1244i	−0.222362	+	0.385143i	0.733163	+	0.680053i	$0.238043\pi$
$992$		0			0
$993$		0			0
$994$	−30.0000	+	17.3205i	−0.951542	+	0.549373i
$995$	−42.6028	+	24.5967i	−1.35060	+	0.779769i
$996$		0			0
$997$	−14.5000	−	25.1147i	−0.459220	−	0.795392i	0.539700	−	0.841857i	$-0.318538\pi$
$997$	−14.5000	−	25.1147i	−0.459220	−	0.795392i	−0.998920	+	0.0464655i	$0.985204\pi$
$998$	−23.2379	+	40.2492i	−0.735583	+	1.27407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.q.d.82.1	yes	4
3.2	odd	2	inner	117.2.q.d.82.2	yes	4
4.3	odd	2		1872.2.by.l.433.2		4
12.11	even	2		1872.2.by.l.433.1		4
13.4	even	6		1521.2.b.g.1351.2		4
13.6	odd	12		1521.2.a.u.1.4		4
13.7	odd	12		1521.2.a.u.1.1		4
13.9	even	3		1521.2.b.g.1351.3		4
13.10	even	6	inner	117.2.q.d.10.1	✓	4
39.17	odd	6		1521.2.b.g.1351.4		4
39.20	even	12		1521.2.a.u.1.3		4
39.23	odd	6	inner	117.2.q.d.10.2	yes	4
39.32	even	12		1521.2.a.u.1.2		4
39.35	odd	6		1521.2.b.g.1351.1		4
52.23	odd	6		1872.2.by.l.1297.1		4
156.23	even	6		1872.2.by.l.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.q.d.10.1	✓	4	13.10	even	6	inner
117.2.q.d.10.2	yes	4	39.23	odd	6	inner
117.2.q.d.82.1	yes	4	1.1	even	1	trivial
117.2.q.d.82.2	yes	4	3.2	odd	2	inner
1521.2.a.u.1.1		4	13.7	odd	12
1521.2.a.u.1.2		4	39.32	even	12
1521.2.a.u.1.3		4	39.20	even	12
1521.2.a.u.1.4		4	13.6	odd	12
1521.2.b.g.1351.1		4	39.35	odd	6
1521.2.b.g.1351.2		4	13.4	even	6
1521.2.b.g.1351.3		4	13.9	even	3
1521.2.b.g.1351.4		4	39.17	odd	6
1872.2.by.l.433.1		4	12.11	even	2
1872.2.by.l.433.2		4	4.3	odd	2
1872.2.by.l.1297.1		4	52.23	odd	6
1872.2.by.l.1297.2		4	156.23	even	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93649 - 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +2.23607i q^{5} +(-3.00000 + 1.73205i) q^{7} -2.23607i q^{8} +O(q^{10})\)	\(q+(-1.93649 - 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +2.23607i q^{5} +(-3.00000 + 1.73205i) q^{7} -2.23607i q^{8} +(2.50000 - 4.33013i) q^{10} +(3.87298 + 2.23607i) q^{11} +(2.50000 + 2.59808i) q^{13} +7.74597 q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.93649 - 3.35410i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(-5.80948 + 3.35410i) q^{20} +(-5.00000 - 8.66025i) q^{22} +(-3.87298 + 6.70820i) q^{23} +(-1.93649 - 7.82624i) q^{26} +(-9.00000 - 5.19615i) q^{28} +(1.93649 - 3.35410i) q^{29} +(-5.80948 + 3.35410i) q^{32} +8.66025i q^{34} +(-3.87298 - 6.70820i) q^{35} +(1.50000 + 0.866025i) q^{37} +7.74597 q^{38} +5.00000 q^{40} +(-1.93649 - 1.11803i) q^{41} +(-1.00000 - 1.73205i) q^{43} +13.4164i q^{44} +(15.0000 - 8.66025i) q^{46} -4.47214i q^{47} +(2.50000 - 4.33013i) q^{49} +(-3.00000 + 10.3923i) q^{52} +11.6190 q^{53} +(-5.00000 + 8.66025i) q^{55} +(3.87298 + 6.70820i) q^{56} +(-7.50000 + 4.33013i) q^{58} +(7.74597 - 4.47214i) q^{59} +(3.50000 + 6.06218i) q^{61} +13.0000 q^{64} +(-5.80948 + 5.59017i) q^{65} +(-3.00000 - 1.73205i) q^{67} +(5.80948 - 10.0623i) q^{68} +17.3205i q^{70} +(-3.87298 + 2.23607i) q^{71} -15.5885i q^{73} +(-1.93649 - 3.35410i) q^{74} +(-9.00000 - 5.19615i) q^{76} -15.4919 q^{77} +8.00000 q^{79} +(1.93649 + 1.11803i) q^{80} +(2.50000 + 4.33013i) q^{82} -4.47214i q^{83} +(7.50000 - 4.33013i) q^{85} +4.47214i q^{86} +(5.00000 - 8.66025i) q^{88} +(3.87298 + 2.23607i) q^{89} +(-12.0000 - 3.46410i) q^{91} -23.2379 q^{92} +(-5.00000 + 8.66025i) q^{94} +(-3.87298 - 6.70820i) q^{95} +(6.00000 - 3.46410i) q^{97} +(-9.68246 + 5.59017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} - 12 q^{7}+O(q^{10}) \) 4 * q + 6 * q^4 - 12 * q^7	\( 4 q + 6 q^{4} - 12 q^{7} + 10 q^{10} + 10 q^{13} + 2 q^{16} - 12 q^{19} - 20 q^{22} - 36 q^{28} + 6 q^{37} + 20 q^{40} - 4 q^{43} + 60 q^{46} + 10 q^{49} - 12 q^{52} - 20 q^{55} - 30 q^{58} + 14 q^{61} + 52 q^{64} - 12 q^{67} - 36 q^{76} + 32 q^{79} + 10 q^{82} + 30 q^{85} + 20 q^{88} - 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) \) 4 * q + 6 * q^4 - 12 * q^7 + 10 * q^10 + 10 * q^13 + 2 * q^16 - 12 * q^19 - 20 * q^22 - 36 * q^28 + 6 * q^37 + 20 * q^40 - 4 * q^43 + 60 * q^46 + 10 * q^49 - 12 * q^52 - 20 * q^55 - 30 * q^58 + 14 * q^61 + 52 * q^64 - 12 * q^67 - 36 * q^76 + 32 * q^79 + 10 * q^82 + 30 * q^85 + 20 * q^88 - 48 * q^91 - 20 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more