LMFDB - Embedded newform 820.2.u.b.141.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.8
Character	$\chi$	$=$	820.141
Dual form			820.2.u.b.221.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.85886 q^{3} +(0.809017 - 0.587785i) q^{5} +(0.237547 - 0.731093i) q^{7} +5.17308 q^{9} +(3.90892 + 2.84000i) q^{11} +(-1.47988 - 4.55461i) q^{13} +(2.31287 - 1.68040i) q^{15} +(-2.49705 - 1.81421i) q^{17} +(-2.20281 + 6.77956i) q^{19} +(0.679112 - 2.09009i) q^{21} +(-1.31630 - 4.05115i) q^{23} +(0.309017 - 0.951057i) q^{25} +6.21253 q^{27} +(-7.09820 + 5.15714i) q^{29} +(2.98213 + 2.16664i) q^{31} +(11.1751 + 8.11916i) q^{33} +(-0.237547 - 0.731093i) q^{35} +(2.70239 - 1.96340i) q^{37} +(-4.23077 - 13.0210i) q^{39} +(3.79994 - 5.15368i) q^{41} +(-2.62049 - 8.06504i) q^{43} +(4.18511 - 3.04066i) q^{45} +(1.65715 + 5.10018i) q^{47} +(5.18505 + 3.76716i) q^{49} +(-7.13871 - 5.18658i) q^{51} +(-6.27754 + 4.56090i) q^{53} +4.83169 q^{55} +(-6.29753 + 19.3818i) q^{57} +(3.58782 + 11.0422i) q^{59} +(3.31734 - 10.2097i) q^{61} +(1.22885 - 3.78200i) q^{63} +(-3.87438 - 2.81490i) q^{65} +(-12.7477 + 9.26177i) q^{67} +(-3.76311 - 11.5817i) q^{69} +(-2.67736 - 1.94521i) q^{71} -4.48201 q^{73} +(0.883436 - 2.71894i) q^{75} +(3.00485 - 2.18315i) q^{77} -2.91540 q^{79} +2.24151 q^{81} +9.10452 q^{83} -3.08652 q^{85} +(-20.2927 + 14.7435i) q^{87} +(1.37146 - 4.22092i) q^{89} -3.68138 q^{91} +(8.52549 + 6.19413i) q^{93} +(2.20281 + 6.77956i) q^{95} +(-8.25626 + 5.99852i) q^{97} +(20.2212 + 14.6915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.85886			1.65056			0.825282	−	0.564721i	$-0.191016\pi$
$3$	2.85886			1.65056			0.825282	+	0.564721i	$0.191016\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	0.237547	−	0.731093i	0.0897842	−	0.276327i	−0.896075	−	0.443902i	$-0.853594\pi$
$7$	0.237547	−	0.731093i	0.0897842	−	0.276327i	0.985859	+	0.167575i	$0.0535937\pi$
$8$		0			0
$9$	5.17308			1.72436
$10$		0			0
$11$	3.90892	+	2.84000i	1.17858	+	0.856292i	0.992011	−	0.126150i	$-0.0402619\pi$
$11$	3.90892	+	2.84000i	1.17858	+	0.856292i	0.186573	+	0.982441i	$0.440262\pi$
$12$		0			0
$13$	−1.47988	−	4.55461i	−0.410445	−	1.26322i	−0.916262	−	0.400580i	$-0.868809\pi$
$13$	−1.47988	−	4.55461i	−0.410445	−	1.26322i	0.505816	−	0.862641i	$-0.331191\pi$
$14$		0			0
$15$	2.31287	−	1.68040i	0.597179	−	0.433876i
$16$		0			0
$17$	−2.49705	−	1.81421i	−0.605623	−	0.440011i	0.242247	−	0.970215i	$-0.422115\pi$
$17$	−2.49705	−	1.81421i	−0.605623	−	0.440011i	−0.847870	+	0.530204i	$0.822115\pi$
$18$		0			0
$19$	−2.20281	+	6.77956i	−0.505360	+	1.55534i	0.294805	+	0.955557i	$0.404745\pi$
$19$	−2.20281	+	6.77956i	−0.505360	+	1.55534i	−0.800165	+	0.599780i	$0.795255\pi$
$20$		0			0
$21$	0.679112	−	2.09009i	0.148194	−	0.456096i
$22$		0			0
$23$	−1.31630	−	4.05115i	−0.274467	−	0.844723i	−0.989360	−	0.145489i	$-0.953524\pi$
$23$	−1.31630	−	4.05115i	−0.274467	−	0.844723i	0.714893	−	0.699234i	$-0.246476\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	6.21253			1.19560
$28$		0			0
$29$	−7.09820	+	5.15714i	−1.31810	+	0.957657i	−0.318148	+	0.948041i	$0.603061\pi$
$29$	−7.09820	+	5.15714i	−1.31810	+	0.957657i	−0.999954	+	0.00961602i	$0.996939\pi$
$30$		0			0
$31$	2.98213	+	2.16664i	0.535606	+	0.389141i	0.822451	−	0.568836i	$-0.192606\pi$
$31$	2.98213	+	2.16664i	0.535606	+	0.389141i	−0.286844	+	0.957977i	$0.592606\pi$
$32$		0			0
$33$	11.1751	+	8.11916i	1.94533	+	1.41336i
$34$		0			0
$35$	−0.237547	−	0.731093i	−0.0401527	−	0.123577i
$36$		0			0
$37$	2.70239	−	1.96340i	0.444270	−	0.322781i	−0.343060	−	0.939314i	$-0.611463\pi$
$37$	2.70239	−	1.96340i	0.444270	−	0.322781i	0.787329	+	0.616533i	$0.211463\pi$
$38$		0			0
$39$	−4.23077	−	13.0210i	−0.677466	−	2.08503i
$40$		0			0
$41$	3.79994	−	5.15368i	0.593451	−	0.804870i
$41$	3.79994	−	5.15368i	0.593451	−	0.804870i
$42$		0			0
$43$	−2.62049	−	8.06504i	−0.399621	−	1.22991i	−0.925304	−	0.379226i	$-0.876190\pi$
$43$	−2.62049	−	8.06504i	−0.399621	−	1.22991i	0.525683	−	0.850680i	$-0.323810\pi$
$44$		0			0
$45$	4.18511	−	3.04066i	0.623879	−	0.453275i
$46$		0			0
$47$	1.65715	+	5.10018i	0.241720	+	0.743938i	0.996159	+	0.0875673i	$0.0279093\pi$
$47$	1.65715	+	5.10018i	0.241720	+	0.743938i	−0.754438	+	0.656371i	$0.772091\pi$
$48$		0			0
$49$	5.18505	+	3.76716i	0.740721	+	0.538166i
$50$		0			0
$51$	−7.13871	−	5.18658i	−0.999619	−	0.726266i
$52$		0			0
$53$	−6.27754	+	4.56090i	−0.862287	+	0.626488i	−0.928506	−	0.371317i	$-0.878906\pi$
$53$	−6.27754	+	4.56090i	−0.862287	+	0.626488i	0.0662193	+	0.997805i	$0.478906\pi$
$54$		0			0
$55$	4.83169			0.651505
$56$		0			0
$57$	−6.29753	+	19.3818i	−0.834128	+	2.56718i
$58$		0			0
$59$	3.58782	+	11.0422i	0.467094	+	1.43757i	0.856330	+	0.516430i	$0.172739\pi$
$59$	3.58782	+	11.0422i	0.467094	+	1.43757i	−0.389236	+	0.921138i	$0.627261\pi$
$60$		0			0
$61$	3.31734	−	10.2097i	0.424742	−	1.30722i	−0.478499	−	0.878088i	$-0.658819\pi$
$61$	3.31734	−	10.2097i	0.424742	−	1.30722i	0.903241	−	0.429133i	$-0.141181\pi$
$62$		0			0
$63$	1.22885	−	3.78200i	0.154820	−	0.476488i
$64$		0			0
$65$	−3.87438	−	2.81490i	−0.480558	−	0.349146i
$66$		0			0
$67$	−12.7477	+	9.26177i	−1.55738	+	1.13151i	−0.619271	+	0.785177i	$0.712572\pi$
$67$	−12.7477	+	9.26177i	−1.55738	+	1.13151i	−0.938113	+	0.346328i	$0.887428\pi$
$68$		0			0
$69$	−3.76311	−	11.5817i	−0.453026	−	1.39427i
$70$		0			0
$71$	−2.67736	−	1.94521i	−0.317744	−	0.230855i	0.417468	−	0.908692i	$-0.362918\pi$
$71$	−2.67736	−	1.94521i	−0.317744	−	0.230855i	−0.735212	+	0.677837i	$0.762918\pi$
$72$		0			0
$73$	−4.48201			−0.524580			−0.262290	−	0.964989i	$-0.584478\pi$
$73$	−4.48201			−0.524580			−0.262290	+	0.964989i	$0.584478\pi$
$74$		0			0
$75$	0.883436	−	2.71894i	0.102010	−	0.313956i
$76$		0			0
$77$	3.00485	−	2.18315i	0.342435	−	0.248794i
$78$		0			0
$79$	−2.91540			−0.328008			−0.164004	−	0.986460i	$-0.552441\pi$
$79$	−2.91540			−0.328008			−0.164004	+	0.986460i	$0.552441\pi$
$80$		0			0
$81$	2.24151			0.249057
$82$		0			0
$83$	9.10452			0.999351			0.499675	−	0.866213i	$-0.333453\pi$
$83$	9.10452			0.999351			0.499675	+	0.866213i	$0.333453\pi$
$84$		0			0
$85$	−3.08652			−0.334780
$86$		0			0
$87$	−20.2927	+	14.7435i	−2.17561	+	1.58067i
$88$		0			0
$89$	1.37146	−	4.22092i	0.145375	−	0.447417i	−0.851684	−	0.524055i	$-0.824419\pi$
$89$	1.37146	−	4.22092i	0.145375	−	0.447417i	0.997059	+	0.0766380i	$0.0244186\pi$
$90$		0			0
$91$	−3.68138			−0.385914
$92$		0			0
$93$	8.52549	+	6.19413i	0.884052	+	0.642301i
$94$		0			0
$95$	2.20281	+	6.77956i	0.226004	+	0.695568i
$96$		0			0
$97$	−8.25626	+	5.99852i	−0.838296	+	0.609058i	−0.921894	−	0.387442i	$-0.873359\pi$
$97$	−8.25626	+	5.99852i	−0.838296	+	0.609058i	0.0835982	+	0.996500i	$0.473359\pi$
$98$		0			0
$99$	20.2212	+	14.6915i	2.03230	+	1.47655i
$100$		0			0
$101$	−2.05676	+	6.33007i	−0.204656	+	0.629865i	0.795072	+	0.606515i	$0.207433\pi$
$101$	−2.05676	+	6.33007i	−0.204656	+	0.629865i	−0.999727	+	0.0233499i	$0.992567\pi$
$102$		0			0
$103$	2.04666	−	6.29897i	0.201663	−	0.620656i	−0.798171	−	0.602431i	$-0.794199\pi$
$103$	2.04666	−	6.29897i	0.201663	−	0.620656i	0.999834	−	0.0182242i	$-0.00580127\pi$
$104$		0			0
$105$	−0.679112	−	2.09009i	−0.0662746	−	0.203972i
$106$		0			0
$107$	4.40636	−	13.5614i	0.425979	−	1.31103i	−0.476075	−	0.879404i	$-0.657941\pi$
$107$	4.40636	−	13.5614i	0.425979	−	1.31103i	0.902054	−	0.431623i	$-0.142059\pi$
$108$		0			0
$109$	−8.53169			−0.817188			−0.408594	−	0.912716i	$-0.633981\pi$
$109$	−8.53169			−0.817188			−0.408594	+	0.912716i	$0.633981\pi$
$110$		0			0
$111$	7.72574	−	5.61308i	0.733295	−	0.532770i
$112$		0			0
$113$	9.46434	+	6.87625i	0.890330	+	0.646863i	0.935964	−	0.352095i	$-0.114531\pi$
$113$	9.46434	+	6.87625i	0.890330	+	0.646863i	−0.0456338	+	0.998958i	$0.514531\pi$
$114$		0			0
$115$	−3.44612	−	2.50375i	−0.321352	−	0.233476i
$116$		0			0
$117$	−7.65555	−	23.5613i	−0.707755	−	2.17825i
$118$		0			0
$119$	−1.91952	+	1.39461i	−0.175962	+	0.127844i
$120$		0			0
$121$	3.81489	+	11.7410i	0.346809	+	1.06737i
$122$		0			0
$123$	10.8635	−	14.7337i	0.979529	−	1.32849i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	8.06999	−	5.86319i	0.716096	−	0.520274i	−0.169038	−	0.985609i	$-0.554066\pi$
$127$	8.06999	−	5.86319i	0.716096	−	0.520274i	0.885135	+	0.465335i	$0.154066\pi$
$128$		0			0
$129$	−7.49161	−	23.0568i	−0.659600	−	2.03004i
$130$		0			0
$131$	−10.4631	−	7.60190i	−0.914167	−	0.664181i	0.0278981	−	0.999611i	$-0.491119\pi$
$131$	−10.4631	−	7.60190i	−0.914167	−	0.664181i	−0.942065	+	0.335429i	$0.891119\pi$
$132$		0			0
$133$	4.43322	+	3.22092i	0.384409	+	0.279289i
$134$		0			0
$135$	5.02604	−	3.65163i	0.432573	−	0.314282i
$136$		0			0
$137$	−7.33318			−0.626516			−0.313258	−	0.949668i	$-0.601420\pi$
$137$	−7.33318			−0.626516			−0.313258	+	0.949668i	$0.601420\pi$
$138$		0			0
$139$	−4.05683	+	12.4857i	−0.344096	+	1.05902i	0.617970	+	0.786202i	$0.287955\pi$
$139$	−4.05683	+	12.4857i	−0.344096	+	1.05902i	−0.962066	+	0.272817i	$0.912045\pi$
$140$		0			0
$141$	4.73756	+	14.5807i	0.398974	+	1.22792i
$142$		0			0
$143$	7.15033	−	22.0065i	0.597941	−	1.84027i
$144$		0			0
$145$	−2.71127	+	8.34443i	−0.225159	+	0.692967i
$146$		0			0
$147$	14.8233	+	10.7698i	1.22261	+	0.888276i
$148$		0			0
$149$	11.9389	−	8.67415i	0.978076	−	0.710614i	0.0207983	−	0.999784i	$-0.493379\pi$
$149$	11.9389	−	8.67415i	0.978076	−	0.710614i	0.957278	+	0.289170i	$0.0933792\pi$
$150$		0			0
$151$	0.566861	+	1.74462i	0.0461305	+	0.141975i	0.971469	−	0.237167i	$-0.0762190\pi$
$151$	0.566861	+	1.74462i	0.0461305	+	0.141975i	−0.925338	+	0.379143i	$0.876219\pi$
$152$		0			0
$153$	−12.9174	−	9.38506i	−1.04431	−	0.758737i
$154$		0			0
$155$	3.68611			0.296076
$156$		0			0
$157$	−7.56413	+	23.2800i	−0.603683	+	1.85795i	−0.0980825	+	0.995178i	$0.531271\pi$
$157$	−7.56413	+	23.2800i	−0.603683	+	1.85795i	−0.505601	+	0.862768i	$0.668729\pi$
$158$		0			0
$159$	−17.9466	+	13.0390i	−1.42326	+	1.03406i
$160$		0			0
$161$	−3.27445			−0.258063
$162$		0			0
$163$	−16.5063			−1.29287			−0.646435	−	0.762969i	$-0.723741\pi$
$163$	−16.5063			−1.29287			−0.646435	+	0.762969i	$0.723741\pi$
$164$		0			0
$165$	13.8131			1.07535
$166$		0			0
$167$	−1.24532			−0.0963660			−0.0481830	−	0.998839i	$-0.515343\pi$
$167$	−1.24532			−0.0963660			−0.0481830	+	0.998839i	$0.515343\pi$
$168$		0			0
$169$	−8.03719	+	5.83936i	−0.618245	+	0.449181i
$170$		0			0
$171$	−11.3953	+	35.0712i	−0.871422	+	2.68196i
$172$		0			0
$173$	9.03696			0.687067			0.343534	−	0.939140i	$-0.388376\pi$
$173$	9.03696			0.687067			0.343534	+	0.939140i	$0.388376\pi$
$174$		0			0
$175$	−0.621905	−	0.451840i	−0.0470116	−	0.0341559i
$176$		0			0
$177$	10.2571	+	31.5680i	0.770968	+	2.37280i
$178$		0			0
$179$	9.76620	−	7.09556i	0.729960	−	0.530347i	−0.159591	−	0.987183i	$-0.551017\pi$
$179$	9.76620	−	7.09556i	0.729960	−	0.530347i	0.889551	+	0.456836i	$0.151017\pi$
$180$		0			0
$181$	−14.2111	−	10.3250i	−1.05631	−	0.767451i	−0.0829045	−	0.996557i	$-0.526420\pi$
$181$	−14.2111	−	10.3250i	−1.05631	−	0.767451i	−0.973401	+	0.229106i	$0.926420\pi$
$182$		0			0
$183$	9.48381	−	29.1882i	0.701063	−	2.15765i
$184$		0			0
$185$	1.03222	−	3.17685i	0.0758903	−	0.233566i
$186$		0			0
$187$	−4.60841	−	14.1832i	−0.337000	−	1.03718i
$188$		0			0
$189$	1.47576	−	4.54194i	0.107346	−	0.330377i
$190$		0			0
$191$	8.79622			0.636472			0.318236	−	0.948012i	$-0.396910\pi$
$191$	8.79622			0.636472			0.318236	+	0.948012i	$0.396910\pi$
$192$		0			0
$193$	−8.33429	+	6.05522i	−0.599915	+	0.435864i	−0.845849	−	0.533423i	$-0.820906\pi$
$193$	−8.33429	+	6.05522i	−0.599915	+	0.435864i	0.245933	+	0.969287i	$0.420906\pi$
$194$		0			0
$195$	−11.0763	−	8.04741i	−0.793191	−	0.576287i
$196$		0			0
$197$	−5.65834	−	4.11102i	−0.403140	−	0.292898i	0.367679	−	0.929953i	$-0.380153\pi$
$197$	−5.65834	−	4.11102i	−0.403140	−	0.292898i	−0.770819	+	0.637055i	$0.780153\pi$
$198$		0			0
$199$	0.904123	+	2.78261i	0.0640916	+	0.197254i	0.977975	−	0.208724i	$-0.0669310\pi$
$199$	0.904123	+	2.78261i	0.0640916	+	0.197254i	−0.913883	+	0.405978i	$0.866931\pi$
$200$		0			0
$201$	−36.4440	+	26.4781i	−2.57056	+	1.86762i
$202$		0			0
$203$	2.08420	+	6.41450i	0.146282	+	0.450210i
$204$		0			0
$205$	0.0449576	−	6.40297i	0.00313998	−	0.447203i
$206$		0			0
$207$	−6.80932	−	20.9569i	−0.473280	−	1.45661i
$208$		0			0
$209$	−27.8645	+	20.2448i	−1.92743	+	1.40036i
$210$		0			0
$211$	−0.603257	−	1.85663i	−0.0415299	−	0.127816i	0.928142	−	0.372227i	$-0.121406\pi$
$211$	−0.603257	−	1.85663i	−0.0415299	−	0.127816i	−0.969672	+	0.244411i	$0.921406\pi$
$212$		0			0
$213$	−7.65419	−	5.56110i	−0.524457	−	0.381040i
$214$		0			0
$215$	−6.86053	−	4.98447i	−0.467884	−	0.339938i
$216$		0			0
$217$	2.29241	−	1.66554i	0.155619	−	0.113064i
$218$		0			0
$219$	−12.8134			−0.865852
$220$		0			0
$221$	−4.56769	+	14.0579i	−0.307256	+	0.945636i
$222$		0			0
$223$	3.92302	+	12.0738i	0.262705	+	0.808523i	0.992213	+	0.124551i	$0.0397490\pi$
$223$	3.92302	+	12.0738i	0.262705	+	0.808523i	−0.729508	+	0.683972i	$0.760251\pi$
$224$		0			0
$225$	1.59857	−	4.91989i	0.106571	−	0.327993i
$226$		0			0
$227$	6.57983	−	20.2506i	0.436718	−	1.34408i	−0.454597	−	0.890697i	$-0.650217\pi$
$227$	6.57983	−	20.2506i	0.436718	−	1.34408i	0.891315	−	0.453384i	$-0.149783\pi$
$228$		0			0
$229$	−7.55201	−	5.48686i	−0.499051	−	0.362582i	0.309604	−	0.950866i	$-0.399804\pi$
$229$	−7.55201	−	5.48686i	−0.499051	−	0.362582i	−0.808654	+	0.588284i	$0.799804\pi$
$230$		0			0
$231$	8.59046	−	6.24133i	0.565211	−	0.410649i
$232$		0			0
$233$	2.31290	+	7.11839i	0.151523	+	0.466341i	0.997792	−	0.0664153i	$-0.0211562\pi$
$233$	2.31290	+	7.11839i	0.151523	+	0.466341i	−0.846269	+	0.532756i	$0.821156\pi$
$234$		0			0
$235$	4.33847	+	3.15209i	0.283011	+	0.205619i
$236$		0			0
$237$	−8.33471			−0.541397
$238$		0			0
$239$	6.47632	−	19.9321i	0.418919	−	1.28930i	−0.489780	−	0.871846i	$-0.662923\pi$
$239$	6.47632	−	19.9321i	0.418919	−	1.28930i	0.908699	−	0.417453i	$-0.137077\pi$
$240$		0			0
$241$	−23.1567	+	16.8243i	−1.49165	+	1.08375i	−0.518091	+	0.855325i	$0.673357\pi$
$241$	−23.1567	+	16.8243i	−1.49165	+	1.08375i	−0.973562	+	0.228424i	$0.926643\pi$
$242$		0			0
$243$	−12.2294			−0.784518
$244$		0			0
$245$	6.40907			0.409461
$246$		0			0
$247$	34.1381			2.17216
$248$		0			0
$249$	26.0285			1.64949
$250$		0			0
$251$	10.0298	−	7.28711i	0.633078	−	0.459958i	−0.224387	−	0.974500i	$-0.572038\pi$
$251$	10.0298	−	7.28711i	0.633078	−	0.459958i	0.857465	+	0.514542i	$0.172038\pi$
$252$		0			0
$253$	6.35995	−	19.5739i	0.399847	−	1.23060i
$254$		0			0
$255$	−8.82393			−0.552576
$256$		0			0
$257$	−4.31119	−	3.13226i	−0.268925	−	0.195385i	0.445148	−	0.895457i	$-0.353151\pi$
$257$	−4.31119	−	3.13226i	−0.268925	−	0.195385i	−0.714072	+	0.700072i	$0.753151\pi$
$258$		0			0
$259$	−0.793485	−	2.44210i	−0.0493047	−	0.151744i
$260$		0			0
$261$	−36.7195	+	26.6783i	−2.27288	+	1.65135i
$262$		0			0
$263$	4.25477	+	3.09127i	0.262360	+	0.190616i	0.711187	−	0.703003i	$-0.248158\pi$
$263$	4.25477	+	3.09127i	0.262360	+	0.190616i	−0.448827	+	0.893619i	$0.648158\pi$
$264$		0			0
$265$	−2.39781	+	7.37969i	−0.147296	+	0.453331i
$266$		0			0
$267$	3.92082	−	12.0670i	0.239950	−	0.738490i
$268$		0			0
$269$	2.78002	+	8.55604i	0.169501	+	0.521671i	0.999340	−	0.0363327i	$-0.0115676\pi$
$269$	2.78002	+	8.55604i	0.169501	+	0.521671i	−0.829839	+	0.558003i	$0.811568\pi$
$270$		0			0
$271$	−0.825446	+	2.54046i	−0.0501423	+	0.154322i	−0.972992	−	0.230837i	$-0.925854\pi$
$271$	−0.825446	+	2.54046i	−0.0501423	+	0.154322i	0.922850	+	0.385159i	$0.125854\pi$
$272$		0			0
$273$	−10.5246			−0.636975
$274$		0			0
$275$	3.90892	−	2.84000i	0.235717	−	0.171258i
$276$		0			0
$277$	−15.7299	−	11.4284i	−0.945118	−	0.686668i	0.00452929	−	0.999990i	$-0.498558\pi$
$277$	−15.7299	−	11.4284i	−0.945118	−	0.686668i	−0.949647	+	0.313321i	$0.898558\pi$
$278$		0			0
$279$	15.4268	+	11.2082i	0.923578	+	0.671019i
$280$		0			0
$281$	7.65208	+	23.5507i	0.456485	+	1.40492i	0.869383	+	0.494139i	$0.164517\pi$
$281$	7.65208	+	23.5507i	0.456485	+	1.40492i	−0.412898	+	0.910777i	$0.635483\pi$
$282$		0			0
$283$	2.01111	−	1.46115i	0.119548	−	0.0868566i	−0.526405	−	0.850234i	$-0.676460\pi$
$283$	2.01111	−	1.46115i	0.119548	−	0.0868566i	0.645953	+	0.763377i	$0.276460\pi$
$284$		0			0
$285$	6.29753	+	19.3818i	0.373034	+	1.14808i
$286$		0			0
$287$	−2.86516	−	4.00235i	−0.169125	−	0.236251i
$288$		0			0
$289$	−2.30940	−	7.10762i	−0.135847	−	0.418095i
$290$		0			0
$291$	−23.6035	+	17.1489i	−1.38366	+	1.00529i
$292$		0			0
$293$	1.40531	+	4.32510i	0.0820992	+	0.252675i	0.983677	−	0.179941i	$-0.0575906\pi$
$293$	1.40531	+	4.32510i	0.0820992	+	0.252675i	−0.901578	+	0.432616i	$0.857591\pi$
$294$		0			0
$295$	9.39303	+	6.82444i	0.546883	+	0.397334i
$296$		0			0
$297$	24.2843	+	17.6436i	1.40912	+	1.02378i
$298$		0			0
$299$	−16.5034	+	11.9905i	−0.954419	+	0.693426i
$300$		0			0
$301$	−6.51878			−0.375736
$302$		0			0
$303$	−5.88000	+	18.0968i	−0.337797	+	1.03963i
$304$		0			0
$305$	−3.31734	−	10.2097i	−0.189950	−	0.584607i
$306$		0			0
$307$	9.56143	−	29.4270i	0.545699	−	1.67949i	−0.173622	−	0.984812i	$-0.555547\pi$
$307$	9.56143	−	29.4270i	0.545699	−	1.67949i	0.719321	−	0.694678i	$-0.244453\pi$
$308$		0			0
$309$	5.85111	−	18.0079i	0.332858	−	1.02443i
$310$		0			0
$311$	−19.1592	−	13.9200i	−1.08642	−	0.789329i	−0.107627	−	0.994191i	$-0.534325\pi$
$311$	−19.1592	−	13.9200i	−1.08642	−	0.789329i	−0.978791	+	0.204863i	$0.934325\pi$
$312$		0			0
$313$	5.81689	−	4.22621i	0.328790	−	0.238880i	−0.411127	−	0.911578i	$-0.634865\pi$
$313$	5.81689	−	4.22621i	0.328790	−	0.238880i	0.739917	+	0.672698i	$0.234865\pi$
$314$		0			0
$315$	−1.22885	−	3.78200i	−0.0692377	−	0.213092i
$316$		0			0
$317$	9.88866	+	7.18453i	0.555403	+	0.403524i	0.829773	−	0.558100i	$-0.188470\pi$
$317$	9.88866	+	7.18453i	0.555403	+	0.403524i	−0.274371	+	0.961624i	$0.588470\pi$
$318$		0			0
$319$	−42.3926			−2.37353
$320$		0			0
$321$	12.5972	−	38.7701i	0.703105	−	2.16393i
$322$		0			0
$323$	17.8001	−	12.9325i	0.990423	−	0.719584i
$324$		0			0
$325$	−4.78900			−0.265646
$326$		0			0
$327$	−24.3909			−1.34882
$328$		0			0
$329$	4.12236			0.227273
$330$		0			0
$331$	17.6997			0.972863			0.486431	−	0.873719i	$-0.338298\pi$
$331$	17.6997			0.972863			0.486431	+	0.873719i	$0.338298\pi$
$332$		0			0
$333$	13.9797	−	10.1568i	0.766081	−	0.556590i
$334$		0			0
$335$	−4.86920	+	14.9859i	−0.266033	+	0.818765i
$336$		0			0
$337$	11.2866			0.614823			0.307411	−	0.951577i	$-0.400537\pi$
$337$	11.2866			0.614823			0.307411	+	0.951577i	$0.400537\pi$
$338$		0			0
$339$	27.0572	+	19.6582i	1.46955	+	1.06769i
$340$		0			0
$341$	5.50365	+	16.9385i	0.298039	+	0.917270i
$342$		0			0
$343$	8.33917	−	6.05876i	0.450273	−	0.327142i
$344$		0			0
$345$	−9.85196	−	7.15787i	−0.530412	−	0.385367i
$346$		0			0
$347$	−5.90342	+	18.1688i	−0.316912	+	0.975355i	0.658048	+	0.752976i	$0.271382\pi$
$347$	−5.90342	+	18.1688i	−0.316912	+	0.975355i	−0.974960	+	0.222379i	$0.928618\pi$
$348$		0			0
$349$	0.322827	−	0.993558i	0.0172805	−	0.0531839i	−0.942044	−	0.335488i	$-0.891099\pi$
$349$	0.322827	−	0.993558i	0.0172805	−	0.0531839i	0.959325	+	0.282304i	$0.0910988\pi$
$350$		0			0
$351$	−9.19381	−	28.2956i	−0.490729	−	1.51031i
$352$		0			0
$353$	4.56574	−	14.0519i	0.243010	−	0.747907i	−0.752948	−	0.658081i	$-0.771369\pi$
$353$	4.56574	−	14.0519i	0.243010	−	0.747907i	0.995957	−	0.0898269i	$-0.0286314\pi$
$354$		0			0
$355$	−3.30940			−0.175645
$356$		0			0
$357$	−5.48765	+	3.98701i	−0.290437	+	0.211015i
$358$		0			0
$359$	25.6545	+	18.6391i	1.35399	+	0.983732i	0.998802	+	0.0489381i	$0.0155837\pi$
$359$	25.6545	+	18.6391i	1.35399	+	0.983732i	0.355190	+	0.934794i	$0.384416\pi$
$360$		0			0
$361$	−25.7387	−	18.7003i	−1.35467	−	0.984224i
$362$		0			0
$363$	10.9062	+	33.5660i	0.572429	+	1.76176i
$364$		0			0
$365$	−3.62602	+	2.63446i	−0.189795	+	0.137894i
$366$		0			0
$367$	1.53396	+	4.72106i	0.0800723	+	0.246437i	0.983077	−	0.183194i	$-0.0586436\pi$
$367$	1.53396	+	4.72106i	0.0800723	+	0.246437i	−0.903004	+	0.429631i	$0.858644\pi$
$368$		0			0
$369$	19.6574	−	26.6604i	1.02332	−	1.38789i
$370$		0			0
$371$	1.84324	+	5.67290i	0.0956960	+	0.294522i
$372$		0			0
$373$	−6.92187	+	5.02903i	−0.358401	+	0.260393i	−0.752385	−	0.658724i	$-0.771097\pi$
$373$	−6.92187	+	5.02903i	−0.358401	+	0.260393i	0.393984	+	0.919117i	$0.371097\pi$
$374$		0			0
$375$	−0.883436	−	2.71894i	−0.0456205	−	0.140405i
$376$		0			0
$377$	33.9932	+	24.6975i	1.75074	+	1.27199i
$378$		0			0
$379$	8.38669	+	6.09329i	0.430796	+	0.312991i	0.781967	−	0.623320i	$-0.214217\pi$
$379$	8.38669	+	6.09329i	0.430796	+	0.312991i	−0.351171	+	0.936311i	$0.614217\pi$
$380$		0			0
$381$	23.0710	−	16.7620i	1.18196	−	0.858746i
$382$		0			0
$383$	30.6127			1.56424			0.782118	−	0.623130i	$-0.214139\pi$
$383$	30.6127			1.56424			0.782118	+	0.623130i	$0.214139\pi$
$384$		0			0
$385$	1.14775	−	3.53242i	0.0584949	−	0.180029i
$386$		0			0
$387$	−13.5560	−	41.7211i	−0.689090	−	2.12080i
$388$		0			0
$389$	4.00929	−	12.3393i	0.203279	−	0.625628i	−0.796501	−	0.604637i	$-0.793318\pi$
$389$	4.00929	−	12.3393i	0.203279	−	0.625628i	0.999780	−	0.0209905i	$-0.00668197\pi$
$390$		0			0
$391$	−4.06278	+	12.5040i	−0.205464	+	0.632353i
$392$		0			0
$393$	−29.9126	−	21.7328i	−1.50889	−	1.09627i
$394$		0			0
$395$	−2.35860	+	1.71363i	−0.118674	+	0.0862219i
$396$		0			0
$397$	−6.13128	−	18.8701i	−0.307720	−	0.947065i	−0.978648	−	0.205543i	$-0.934104\pi$
$397$	−6.13128	−	18.8701i	−0.307720	−	0.947065i	0.670928	−	0.741523i	$-0.265896\pi$
$398$		0			0
$399$	12.6739	+	9.20816i	0.634491	+	0.460985i
$400$		0			0
$401$	30.2977			1.51299			0.756497	−	0.653997i	$-0.226909\pi$
$401$	30.2977			1.51299			0.756497	+	0.653997i	$0.226909\pi$
$402$		0			0
$403$	5.45501	−	16.7888i	0.271734	−	0.836310i
$404$		0			0
$405$	1.81342	−	1.31753i	0.0901095	−	0.0654684i
$406$		0			0
$407$	16.1395			0.800004
$408$		0			0
$409$	32.6573			1.61480			0.807400	−	0.590005i	$-0.200874\pi$
$409$	32.6573			1.61480			0.807400	+	0.590005i	$0.200874\pi$
$410$		0			0
$411$	−20.9645			−1.03410
$412$		0			0
$413$	8.92513			0.439177
$414$		0			0
$415$	7.36571	−	5.35150i	0.361569	−	0.262695i
$416$		0			0
$417$	−11.5979	+	35.6947i	−0.567953	+	1.74798i
$418$		0			0
$419$	25.1426			1.22830			0.614149	−	0.789190i	$-0.289499\pi$
$419$	25.1426			1.22830			0.614149	+	0.789190i	$0.289499\pi$
$420$		0			0
$421$	24.8867	+	18.0813i	1.21290	+	0.881227i	0.995491	−	0.0948528i	$-0.0302380\pi$
$421$	24.8867	+	18.0813i	1.21290	+	0.881227i	0.217413	+	0.976080i	$0.430238\pi$
$422$		0			0
$423$	8.57257	+	26.3836i	0.416812	+	1.28282i
$424$		0			0
$425$	−2.49705	+	1.81421i	−0.121125	+	0.0880022i
$426$		0			0
$427$	−6.67624	−	4.85057i	−0.323086	−	0.234736i
$428$		0			0
$429$	20.4418	−	62.9134i	0.986940	−	3.03749i
$430$		0			0
$431$	8.42087	−	25.9168i	0.405619	−	1.24837i	−0.514759	−	0.857335i	$-0.672118\pi$
$431$	8.42087	−	25.9168i	0.405619	−	1.24837i	0.920377	−	0.391031i	$-0.127882\pi$
$432$		0			0
$433$	−0.117735	−	0.362351i	−0.00565798	−	0.0174135i	0.948188	−	0.317711i	$-0.102914\pi$
$433$	−0.117735	−	0.362351i	−0.00565798	−	0.0174135i	−0.953846	+	0.300297i	$0.902914\pi$
$434$		0			0
$435$	−7.75114	+	23.8556i	−0.371639	+	1.14379i
$436$		0			0
$437$	30.3646			1.45253
$438$		0			0
$439$	−8.78334	+	6.38147i	−0.419206	+	0.304571i	−0.777318	−	0.629108i	$-0.783420\pi$
$439$	−8.78334	+	6.38147i	−0.419206	+	0.304571i	0.358112	+	0.933678i	$0.383420\pi$
$440$		0			0
$441$	26.8227	+	19.4878i	1.27727	+	0.927991i
$442$		0			0
$443$	−4.27995	−	3.10957i	−0.203347	−	0.147740i	0.481452	−	0.876473i	$-0.340110\pi$
$443$	−4.27995	−	3.10957i	−0.203347	−	0.147740i	−0.684798	+	0.728733i	$0.740110\pi$
$444$		0			0
$445$	−1.37146	−	4.22092i	−0.0650135	−	0.200091i
$446$		0			0
$447$	34.1318	−	24.7982i	1.61438	−	1.17291i
$448$		0			0
$449$	−0.762554	−	2.34690i	−0.0359872	−	0.110757i	0.931449	−	0.363871i	$-0.118545\pi$
$449$	−0.762554	−	2.34690i	−0.0359872	−	0.110757i	−0.967436	+	0.253114i	$0.918545\pi$
$450$		0			0
$451$	29.4901	−	9.35352i	1.38864	−	0.440440i
$452$		0			0
$453$	1.62058	+	4.98762i	0.0761414	+	0.234339i
$454$		0			0
$455$	−2.97830	+	2.16386i	−0.139625	+	0.101443i
$456$		0			0
$457$	−5.92546	−	18.2367i	−0.277181	−	0.853076i	−0.988634	−	0.150342i	$-0.951962\pi$
$457$	−5.92546	−	18.2367i	−0.277181	−	0.853076i	0.711453	−	0.702734i	$-0.248038\pi$
$458$		0			0
$459$	−15.5130	−	11.2708i	−0.724084	−	0.526078i
$460$		0			0
$461$	9.70209	+	7.04898i	0.451871	+	0.328304i	0.790334	−	0.612676i	$-0.209907\pi$
$461$	9.70209	+	7.04898i	0.451871	+	0.328304i	−0.338463	+	0.940980i	$0.609907\pi$
$462$		0			0
$463$	6.80707	−	4.94563i	0.316351	−	0.229843i	−0.418266	−	0.908325i	$-0.637362\pi$
$463$	6.80707	−	4.94563i	0.316351	−	0.229843i	0.734617	+	0.678482i	$0.237362\pi$
$464$		0			0
$465$	10.5381			0.488692
$466$		0			0
$467$	−4.52619	+	13.9302i	−0.209447	+	0.644611i	0.790054	+	0.613037i	$0.210052\pi$
$467$	−4.52619	+	13.9302i	−0.209447	+	0.644611i	−0.999501	+	0.0315748i	$0.989948\pi$
$468$		0			0
$469$	3.74304	+	11.5199i	0.172837	+	0.531939i
$470$		0			0
$471$	−21.6248	+	66.5542i	−0.996417	+	3.06666i
$472$		0			0
$473$	12.6614	−	38.9678i	0.582172	−	1.79174i
$474$		0			0
$475$	5.76704	+	4.19000i	0.264610	+	0.192250i
$476$		0			0
$477$	−32.4742	+	23.5939i	−1.48689	+	1.08029i
$478$		0			0
$479$	−10.4977	−	32.3087i	−0.479654	−	1.47622i	−0.839576	−	0.543242i	$-0.817197\pi$
$479$	−10.4977	−	32.3087i	−0.479654	−	1.47622i	0.359922	−	0.932982i	$-0.382803\pi$
$480$		0			0
$481$	−12.9417	−	9.40271i	−0.590092	−	0.428727i
$482$		0			0
$483$	−9.36120			−0.425949
$484$		0			0
$485$	−3.15361	+	9.70581i	−0.143198	+	0.440718i
$486$		0			0
$487$	3.66282	−	2.66119i	0.165978	−	0.120590i	−0.501695	−	0.865044i	$-0.667290\pi$
$487$	3.66282	−	2.66119i	0.165978	−	0.120590i	0.667674	+	0.744454i	$0.267290\pi$
$488$		0			0
$489$	−47.1891			−2.13396
$490$		0			0
$491$	14.4510			0.652163			0.326081	−	0.945342i	$-0.394272\pi$
$491$	14.4510			0.652163			0.326081	+	0.945342i	$0.394272\pi$
$492$		0			0
$493$	27.0807			1.21965
$494$		0			0
$495$	24.9947			1.12343
$496$		0			0
$497$	−2.05813	+	1.49532i	−0.0923198	+	0.0670742i
$498$		0			0
$499$	−4.77435	+	14.6939i	−0.213729	+	0.657791i	0.785512	+	0.618846i	$0.212400\pi$
$499$	−4.77435	+	14.6939i	−0.213729	+	0.657791i	−0.999241	+	0.0389449i	$0.987600\pi$
$500$		0			0
$501$	−3.56021			−0.159058
$502$		0			0
$503$	−6.13857	−	4.45993i	−0.273705	−	0.198859i	0.442462	−	0.896787i	$-0.354105\pi$
$503$	−6.13857	−	4.45993i	−0.273705	−	0.198859i	−0.716167	+	0.697929i	$0.754105\pi$
$504$		0			0
$505$	2.05676	+	6.33007i	0.0915248	+	0.281684i
$506$		0			0
$507$	−22.9772	+	16.6939i	−1.02045	+	0.741402i
$508$		0			0
$509$	−26.6896	−	19.3912i	−1.18300	−	0.859498i	−0.190491	−	0.981689i	$-0.561008\pi$
$509$	−26.6896	−	19.3912i	−1.18300	−	0.859498i	−0.992507	+	0.122191i	$0.961008\pi$
$510$		0			0
$511$	−1.06469	+	3.27677i	−0.0470990	+	0.144956i
$512$		0			0
$513$	−13.6850	+	42.1182i	−0.604209	+	1.85956i
$514$		0			0
$515$	−2.04666	−	6.29897i	−0.0901865	−	0.277566i
$516$		0			0
$517$	−8.00684	+	24.6425i	−0.352140	+	1.08378i
$518$		0			0
$519$	25.8354			1.13405
$520$		0			0
$521$	15.6809	−	11.3929i	0.686994	−	0.499130i	−0.188677	−	0.982039i	$-0.560420\pi$
$521$	15.6809	−	11.3929i	0.686994	−	0.499130i	0.875670	+	0.482909i	$0.160420\pi$
$522$		0			0
$523$	26.8776	+	19.5277i	1.17528	+	0.853888i	0.991631	−	0.129104i	$-0.0412102\pi$
$523$	26.8776	+	19.5277i	1.17528	+	0.853888i	0.183645	+	0.982993i	$0.441210\pi$
$524$		0			0
$525$	−1.77794	−	1.29175i	−0.0775956	−	0.0563765i
$526$		0			0
$527$	−3.51577	−	10.8204i	−0.153149	−	0.471345i
$528$		0			0
$529$	3.92821	−	2.85401i	0.170792	−	0.124087i
$530$		0			0
$531$	18.5601	+	57.1220i	0.805438	+	2.47888i
$532$		0			0
$533$	−29.0965	−	9.68040i	−1.26031	−	0.419305i
$534$		0			0
$535$	−4.40636	−	13.5614i	−0.190503	−	0.586309i
$536$		0			0
$537$	27.9202	−	20.2852i	1.20485	−	0.875371i
$538$		0			0
$539$	9.56923	+	29.4511i	0.412176	+	1.26855i
$540$		0			0
$541$	7.95819	+	5.78197i	0.342149	+	0.248586i	0.745568	−	0.666429i	$-0.232178\pi$
$541$	7.95819	+	5.78197i	0.342149	+	0.248586i	−0.403419	+	0.915015i	$0.632178\pi$
$542$		0			0
$543$	−40.6277	−	29.5177i	−1.74350	−	1.26673i
$544$		0			0
$545$	−6.90228	+	5.01480i	−0.295661	+	0.214811i
$546$		0			0
$547$	−8.06669			−0.344907			−0.172453	−	0.985018i	$-0.555169\pi$
$547$	−8.06669			−0.344907			−0.172453	+	0.985018i	$0.555169\pi$
$548$		0			0
$549$	17.1609	−	52.8157i	0.732408	−	2.25412i
$550$		0			0
$551$	−19.3271	−	59.4828i	−0.823364	−	2.53405i
$552$		0			0
$553$	−0.692542	+	2.13143i	−0.0294499	+	0.0906374i
$554$		0			0
$555$	2.95097	−	9.08216i	0.125262	−	0.385516i
$556$		0			0
$557$	−10.2008	−	7.41131i	−0.432221	−	0.314027i	0.350315	−	0.936632i	$-0.386074\pi$
$557$	−10.2008	−	7.41131i	−0.432221	−	0.314027i	−0.782536	+	0.622605i	$0.786074\pi$
$558$		0			0
$559$	−32.8551	+	23.8706i	−1.38962	+	1.00962i
$560$		0			0
$561$	−13.1748	−	40.5478i	−0.556240	−	1.71193i
$562$		0			0
$563$	6.21103	+	4.51258i	0.261764	+	0.190182i	0.710924	−	0.703269i	$-0.248277\pi$
$563$	6.21103	+	4.51258i	0.261764	+	0.190182i	−0.449161	+	0.893451i	$0.648277\pi$
$564$		0			0
$565$	11.6986			0.492163
$566$		0			0
$567$	0.532463	−	1.63875i	0.0223613	−	0.0688211i
$568$		0			0
$569$	14.6695	−	10.6580i	0.614978	−	0.446807i	−0.236186	−	0.971708i	$-0.575897\pi$
$569$	14.6695	−	10.6580i	0.614978	−	0.446807i	0.851164	+	0.524900i	$0.175897\pi$
$570$		0			0
$571$	2.95700			0.123747			0.0618734	−	0.998084i	$-0.480293\pi$
$571$	2.95700			0.123747			0.0618734	+	0.998084i	$0.480293\pi$
$572$		0			0
$573$	25.1471			1.05054
$574$		0			0
$575$	−4.25963			−0.177639
$576$		0			0
$577$	43.7372			1.82080			0.910401	−	0.413726i	$-0.135773\pi$
$577$	43.7372			1.82080			0.910401	+	0.413726i	$0.135773\pi$
$578$		0			0
$579$	−23.8266	+	17.3110i	−0.990198	+	0.719421i
$580$		0			0
$581$	2.16275	−	6.65625i	0.0897259	−	0.276148i
$582$		0			0
$583$	−37.4914			−1.55273
$584$		0			0
$585$	−20.0425	−	14.5617i	−0.828655	−	0.602053i
$586$		0			0
$587$	5.28254	+	16.2580i	0.218034	+	0.671039i	0.998924	+	0.0463708i	$0.0147656\pi$
$587$	5.28254	+	16.2580i	0.218034	+	0.671039i	−0.780891	+	0.624668i	$0.785234\pi$
$588$		0			0
$589$	−21.2580	+	15.4448i	−0.875919	+	0.636392i
$590$		0			0
$591$	−16.1764	−	11.7528i	−0.665408	−	0.483447i
$592$		0			0
$593$	4.95975	−	15.2645i	0.203672	−	0.626839i	−0.796093	−	0.605175i	$-0.793103\pi$
$593$	4.95975	−	15.2645i	0.203672	−	0.626839i	0.999765	−	0.0216648i	$-0.00689667\pi$
$594$		0			0
$595$	−0.733192	+	2.25653i	−0.0300580	+	0.0925089i
$596$		0			0
$597$	2.58476	+	7.95508i	0.105787	+	0.325580i
$598$		0			0
$599$	−11.0064	+	33.8743i	−0.449710	+	1.38407i	0.427524	+	0.904004i	$0.359386\pi$
$599$	−11.0064	+	33.8743i	−0.449710	+	1.38407i	−0.877235	+	0.480062i	$0.840614\pi$
$600$		0			0
$601$	−1.16368			−0.0474675			−0.0237337	−	0.999718i	$-0.507555\pi$
$601$	−1.16368			−0.0474675			−0.0237337	+	0.999718i	$0.507555\pi$
$602$		0			0
$603$	−65.9451	+	47.9119i	−2.68549	+	1.95112i
$604$		0			0
$605$	9.98752	+	7.25636i	0.406050	+	0.295013i
$606$		0			0
$607$	−34.0081	−	24.7083i	−1.38035	−	1.00288i	−0.996848	−	0.0793386i	$-0.974719\pi$
$607$	−34.0081	−	24.7083i	−1.38035	−	1.00288i	−0.383498	−	0.923542i	$-0.625281\pi$
$608$		0			0
$609$	5.95843	+	18.3382i	0.241448	+	0.743100i
$610$		0			0
$611$	20.7769	−	15.0953i	0.840545	−	0.610692i
$612$		0			0
$613$	12.1793	+	37.4840i	0.491917	+	1.51397i	0.821706	+	0.569911i	$0.193022\pi$
$613$	12.1793	+	37.4840i	0.491917	+	1.51397i	−0.329789	+	0.944055i	$0.606978\pi$
$614$		0			0
$615$	0.128527	−	18.3052i	0.00518273	−	0.738136i
$616$		0			0
$617$	4.09822	+	12.6130i	0.164988	+	0.507782i	0.999035	−	0.0439115i	$-0.0139820\pi$
$617$	4.09822	+	12.6130i	0.164988	+	0.507782i	−0.834047	+	0.551693i	$0.813982\pi$
$618$		0			0
$619$	−35.8815	+	26.0694i	−1.44220	+	1.04782i	−0.454620	+	0.890686i	$0.650225\pi$
$619$	−35.8815	+	26.0694i	−1.44220	+	1.04782i	−0.987578	+	0.157132i	$0.949775\pi$
$620$		0			0
$621$	−8.17754	−	25.1679i	−0.328153	−	1.00995i
$622$		0			0
$623$	−2.76010	−	2.00533i	−0.110581	−	0.0803419i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−79.6608	+	57.8770i	−3.18135	+	2.31138i
$628$		0			0
$629$	−10.3100			−0.411087
$630$		0			0
$631$	6.58660	−	20.2715i	0.262208	−	0.806995i	−0.730115	−	0.683324i	$-0.760534\pi$
$631$	6.58660	−	20.2715i	0.262208	−	0.806995i	0.992323	−	0.123670i	$-0.0394665\pi$
$632$		0			0
$633$	−1.72463	−	5.30786i	−0.0685478	−	0.210968i
$634$		0			0
$635$	3.08246	−	9.48685i	0.122324	−	0.376474i
$636$		0			0
$637$	9.48467	−	29.1908i	0.375796	−	1.15658i
$638$		0			0
$639$	−13.8502	−	10.0627i	−0.547905	−	0.398076i
$640$		0			0
$641$	2.96977	−	2.15767i	0.117299	−	0.0852227i	−0.527589	−	0.849500i	$-0.676904\pi$
$641$	2.96977	−	2.15767i	0.117299	−	0.0852227i	0.644888	+	0.764277i	$0.276904\pi$
$642$		0			0
$643$	−14.7333	−	45.3444i	−0.581024	−	1.78821i	−0.614684	−	0.788774i	$-0.710716\pi$
$643$	−14.7333	−	45.3444i	−0.581024	−	1.78821i	0.0336601	−	0.999433i	$-0.489284\pi$
$644$		0			0
$645$	−19.6133	−	14.2499i	−0.772273	−	0.561089i
$646$		0			0
$647$	−0.401346			−0.0157785			−0.00788926	−	0.999969i	$-0.502511\pi$
$647$	−0.401346			−0.0157785			−0.00788926	+	0.999969i	$0.502511\pi$
$648$		0			0
$649$	−17.3352	+	53.3524i	−0.680467	+	2.09426i
$650$		0			0
$651$	6.55369	−	4.76153i	0.256859	−	0.186619i
$652$		0			0
$653$	−25.6655			−1.00437			−0.502185	−	0.864760i	$-0.667470\pi$
$653$	−25.6655			−1.00437			−0.502185	+	0.864760i	$0.667470\pi$
$654$		0			0
$655$	−12.9331			−0.505339
$656$		0			0
$657$	−23.1858			−0.904564
$658$		0			0
$659$	11.0251			0.429477			0.214739	−	0.976672i	$-0.431110\pi$
$659$	11.0251			0.429477			0.214739	+	0.976672i	$0.431110\pi$
$660$		0			0
$661$	−9.70799	+	7.05327i	−0.377597	+	0.274340i	−0.760354	−	0.649509i	$-0.774975\pi$
$661$	−9.70799	+	7.05327i	−0.377597	+	0.274340i	0.382757	+	0.923849i	$0.374975\pi$
$662$		0			0
$663$	−13.0584	+	40.1895i	−0.507145	+	1.56083i
$664$		0			0
$665$	5.47976			0.212496
$666$		0			0
$667$	30.2357	+	21.9675i	1.17073	+	0.850586i
$668$		0			0
$669$	11.2154	+	34.5174i	0.433611	+	1.33452i
$670$		0			0
$671$	41.9628	−	30.4878i	1.61996	−	1.17697i
$672$		0			0
$673$	39.9527	+	29.0273i	1.54006	+	1.11892i	0.950297	+	0.311345i	$0.100780\pi$
$673$	39.9527	+	29.0273i	1.54006	+	1.11892i	0.589765	+	0.807575i	$0.299220\pi$
$674$		0			0
$675$	1.91978	−	5.90846i	0.0738922	−	0.227417i
$676$		0			0
$677$	−8.93493	+	27.4989i	−0.343397	+	1.05687i	0.619039	+	0.785360i	$0.287522\pi$
$677$	−8.93493	+	27.4989i	−0.343397	+	1.05687i	−0.962436	+	0.271508i	$0.912478\pi$
$678$		0			0
$679$	2.42423	+	7.46102i	0.0930335	+	0.286328i
$680$		0			0
$681$	18.8108	−	57.8937i	0.720831	−	2.21849i
$682$		0			0
$683$	23.6128			0.903518			0.451759	−	0.892140i	$-0.350797\pi$
$683$	23.6128			0.903518			0.451759	+	0.892140i	$0.350797\pi$
$684$		0			0
$685$	−5.93267	+	4.31033i	−0.226676	+	0.164689i
$686$		0			0
$687$	−21.5901	−	15.6862i	−0.823715	−	0.598464i
$688$		0			0
$689$	30.0631	+	21.8422i	1.14531	+	0.832120i
$690$		0			0
$691$	1.56863	+	4.82775i	0.0596735	+	0.183656i	0.976450	−	0.215745i	$-0.0692180\pi$
$691$	1.56863	+	4.82775i	0.0596735	+	0.183656i	−0.916776	+	0.399401i	$0.869218\pi$
$692$		0			0
$693$	15.5443	−	11.2936i	0.590481	−	0.429010i
$694$		0			0
$695$	4.05683	+	12.4857i	0.153884	+	0.473608i
$696$		0			0
$697$	−18.8385	+	5.97510i	−0.713559	+	0.226323i
$698$		0			0
$699$	6.61227	+	20.3505i	0.250099	+	0.769725i
$700$		0			0
$701$	−26.6110	+	19.3340i	−1.00508	+	0.730235i	−0.963172	−	0.268886i	$-0.913344\pi$
$701$	−26.6110	+	19.3340i	−1.00508	+	0.730235i	−0.0419103	+	0.999121i	$0.513344\pi$
$702$		0			0
$703$	7.35813	+	22.6460i	0.277517	+	0.854110i
$704$		0			0
$705$	12.4031	+	9.01137i	0.467127	+	0.339388i
$706$		0			0
$707$	4.13929	+	3.00737i	0.155674	+	0.113104i
$708$		0			0
$709$	36.0213	−	26.1710i	1.35281	−	0.982873i	0.353942	−	0.935267i	$-0.384841\pi$
$709$	36.0213	−	26.1710i	1.35281	−	0.982873i	0.998866	−	0.0476055i	$-0.0151590\pi$
$710$		0			0
$711$	−15.0816			−0.565603
$712$		0			0
$713$	4.85203	−	14.9330i	0.181710	−	0.559246i
$714$		0			0
$715$	−7.15033	−	22.0065i	−0.267407	−	0.822995i
$716$		0			0
$717$	18.5149	−	56.9830i	0.691452	−	2.12807i
$718$		0			0
$719$	12.6548	−	38.9475i	0.471945	−	1.45250i	−0.378090	−	0.925769i	$-0.623419\pi$
$719$	12.6548	−	38.9475i	0.471945	−	1.45250i	0.850034	−	0.526727i	$-0.176581\pi$
$720$		0			0
$721$	−4.11895	−	2.99260i	−0.153398	−	0.111450i
$722$		0			0
$723$	−66.2017	+	48.0983i	−2.46207	+	1.78880i
$724$		0			0
$725$	2.71127	+	8.34443i	0.100694	+	0.309904i
$726$		0			0
$727$	2.66747	+	1.93803i	0.0989310	+	0.0718776i	0.636151	−	0.771565i	$-0.280526\pi$
$727$	2.66747	+	1.93803i	0.0989310	+	0.0718776i	−0.537220	+	0.843442i	$0.680526\pi$
$728$		0			0
$729$	−41.6867			−1.54395
$730$		0			0
$731$	−8.08819	+	24.8929i	−0.299153	+	0.920697i
$732$		0			0
$733$	−23.2465	+	16.8896i	−0.858630	+	0.623831i	−0.927512	−	0.373794i	$-0.878057\pi$
$733$	−23.2465	+	16.8896i	−0.858630	+	0.623831i	0.0688822	+	0.997625i	$0.478057\pi$
$734$		0			0
$735$	18.3226			0.675841
$736$		0			0
$737$	−76.1333			−2.80441
$738$		0			0
$739$	−47.8558			−1.76040			−0.880202	−	0.474599i	$-0.842593\pi$
$739$	−47.8558			−1.76040			−0.880202	+	0.474599i	$0.842593\pi$
$740$		0			0
$741$	97.5961			3.58528
$742$		0			0
$743$	−11.8645	+	8.62004i	−0.435265	+	0.316239i	−0.783751	−	0.621075i	$-0.786696\pi$
$743$	−11.8645	+	8.62004i	−0.435265	+	0.316239i	0.348486	+	0.937314i	$0.386696\pi$
$744$		0			0
$745$	4.56027	−	14.0351i	0.167075	−	0.514205i
$746$		0			0
$747$	47.0984			1.72324
$748$		0			0
$749$	−8.86791	−	6.44292i	−0.324026	−	0.235419i
$750$		0			0
$751$	−7.39232	−	22.7512i	−0.269750	−	0.830204i	−0.990561	−	0.137073i	$-0.956231\pi$
$751$	−7.39232	−	22.7512i	−0.269750	−	0.830204i	0.720811	−	0.693131i	$-0.243769\pi$
$752$		0			0
$753$	28.6739	−	20.8328i	1.04494	−	0.759190i
$754$		0			0
$755$	1.48406	+	1.07823i	0.0540106	+	0.0392410i
$756$		0			0
$757$	7.48111	−	23.0245i	0.271906	−	0.836839i	−0.718116	−	0.695923i	$-0.754995\pi$
$757$	7.48111	−	23.0245i	0.271906	−	0.836839i	0.990022	−	0.140916i	$-0.0450047\pi$
$758$		0			0
$759$	18.1822	−	55.9591i	0.659972	−	2.03119i
$760$		0			0
$761$	−15.2468	−	46.9248i	−0.552696	−	1.70102i	−0.701951	−	0.712225i	$-0.747687\pi$
$761$	−15.2468	−	46.9248i	−0.552696	−	1.70102i	0.149255	−	0.988799i	$-0.452313\pi$
$762$		0			0
$763$	−2.02667	+	6.23746i	−0.0733705	+	0.225811i
$764$		0			0
$765$	−15.9668			−0.577281
$766$		0			0
$767$	44.9832	−	32.6822i	1.62425	−	1.18009i
$768$		0			0
$769$	−13.3559	−	9.70366i	−0.481627	−	0.349923i	0.320328	−	0.947307i	$-0.396207\pi$
$769$	−13.3559	−	9.70366i	−0.481627	−	0.349923i	−0.801955	+	0.597384i	$0.796207\pi$
$770$		0			0
$771$	−12.3251	−	8.95470i	−0.443877	−	0.322496i
$772$		0			0
$773$	−3.91253	−	12.0415i	−0.140724	−	0.433104i	0.855712	−	0.517452i	$-0.173119\pi$
$773$	−3.91253	−	12.0415i	−0.140724	−	0.433104i	−0.996436	+	0.0843478i	$0.973119\pi$
$774$		0			0
$775$	2.98213	−	2.16664i	0.107121	−	0.0778281i
$776$		0			0
$777$	−2.26846	−	6.98161i	−0.0813806	−	0.250464i
$778$		0			0
$779$	26.5691	+	37.1145i	0.951938	+	1.32977i
$780$		0			0
$781$	−4.94118	−	15.2074i	−0.176809	−	0.544163i
$782$		0			0
$783$	−44.0977	+	32.0389i	−1.57592	+	1.14498i
$784$		0			0
$785$	7.56413	+	23.2800i	0.269975	+	0.830899i
$786$		0			0
$787$	3.21073	+	2.33273i	0.114450	+	0.0831530i	0.643538	−	0.765414i	$-0.277466\pi$
$787$	3.21073	+	2.33273i	0.114450	+	0.0831530i	−0.529088	+	0.848567i	$0.677466\pi$
$788$		0			0
$789$	12.1638	+	8.83751i	0.433042	+	0.314624i
$790$		0			0
$791$	7.27540	−	5.28589i	0.258683	−	0.187945i
$792$		0			0
$793$	−51.4106			−1.82564
$794$		0			0
$795$	−6.85500	+	21.0975i	−0.243122	+	0.748252i
$796$		0			0
$797$	12.3019	+	37.8613i	0.435755	+	1.34111i	0.892311	+	0.451421i	$0.149083\pi$
$797$	12.3019	+	37.8613i	0.435755	+	1.34111i	−0.456557	+	0.889694i	$0.650917\pi$
$798$		0			0
$799$	5.11483	−	15.7418i	0.180950	−	0.556906i
$800$		0			0
$801$	7.09468	−	21.8352i	0.250678	−	0.771508i
$802$		0			0
$803$	−17.5198	−	12.7289i	−0.618262	−	0.449193i
$804$		0			0
$805$	−2.64909	+	1.92467i	−0.0933680	+	0.0678359i
$806$		0			0
$807$	7.94770	+	24.4605i	0.279772	+	0.861051i
$808$		0			0
$809$	2.60692	+	1.89404i	0.0916545	+	0.0665909i	0.632669	−	0.774423i	$-0.281959\pi$
$809$	2.60692	+	1.89404i	0.0916545	+	0.0665909i	−0.541014	+	0.841013i	$0.681959\pi$
$810$		0			0
$811$	11.5120			0.404240			0.202120	−	0.979361i	$-0.435217\pi$
$811$	11.5120			0.404240			0.202120	+	0.979361i	$0.435217\pi$
$812$		0			0
$813$	−2.35984	+	7.26283i	−0.0827630	+	0.254718i
$814$		0			0
$815$	−13.3538	+	9.70213i	−0.467765	+	0.339851i
$816$		0			0
$817$	60.4498			2.11487
$818$		0			0
$819$	−19.0441			−0.665454
$820$		0			0
$821$	39.4540			1.37695			0.688477	−	0.725258i	$-0.258280\pi$
$821$	39.4540			1.37695			0.688477	+	0.725258i	$0.258280\pi$
$822$		0			0
$823$	20.5703			0.717035			0.358518	−	0.933523i	$-0.383282\pi$
$823$	20.5703			0.717035			0.358518	+	0.933523i	$0.383282\pi$
$824$		0			0
$825$	11.1751	−	8.11916i	0.389066	−	0.282673i
$826$		0			0
$827$	−12.9536	+	39.8672i	−0.450442	+	1.38632i	0.425961	+	0.904741i	$0.359936\pi$
$827$	−12.9536	+	39.8672i	−0.450442	+	1.38632i	−0.876403	+	0.481578i	$0.840064\pi$
$828$		0			0
$829$	−45.6016			−1.58381			−0.791904	−	0.610645i	$-0.790910\pi$
$829$	−45.6016			−1.58381			−0.791904	+	0.610645i	$0.790910\pi$
$830$		0			0
$831$	−44.9696	−	32.6723i	−1.55998	−	1.13339i
$832$		0			0
$833$	−6.11289	−	18.8136i	−0.211799	−	0.651851i
$834$		0			0
$835$	−1.00749	+	0.731983i	−0.0348656	+	0.0253313i
$836$		0			0
$837$	18.5266	+	13.4603i	0.640372	+	0.465257i
$838$		0			0
$839$	3.08417	−	9.49209i	0.106477	−	0.327703i	−0.883597	−	0.468248i	$-0.844885\pi$
$839$	3.08417	−	9.49209i	0.106477	−	0.327703i	0.990074	+	0.140545i	$0.0448854\pi$
$840$		0			0
$841$	14.8268	−	45.6322i	0.511268	−	1.57352i
$842$		0			0
$843$	21.8762	+	67.3281i	0.753457	+	2.31890i
$844$		0			0
$845$	−3.06993	+	9.44828i	−0.105609	+	0.325031i
$846$		0			0
$847$	9.49001			0.326080
$848$		0			0
$849$	5.74947	−	4.17723i	0.197321	−	0.143362i
$850$		0			0
$851$	−11.5112	−	8.36336i	−0.394598	−	0.286692i
$852$		0			0
$853$	13.5655	+	9.85591i	0.464474	+	0.337460i	0.795284	−	0.606238i	$-0.207322\pi$
$853$	13.5655	+	9.85591i	0.464474	+	0.337460i	−0.330810	+	0.943697i	$0.607322\pi$
$854$		0			0
$855$	11.3953	+	35.0712i	0.389712	+	1.19941i
$856$		0			0
$857$	−15.6121	+	11.3429i	−0.533300	+	0.387465i	−0.821591	−	0.570078i	$-0.806913\pi$
$857$	−15.6121	+	11.3429i	−0.533300	+	0.387465i	0.288291	+	0.957543i	$0.406913\pi$
$858$		0			0
$859$	−1.36305	−	4.19505i	−0.0465068	−	0.143133i	0.925107	−	0.379707i	$-0.123975\pi$
$859$	−1.36305	−	4.19505i	−0.0465068	−	0.143133i	−0.971613	+	0.236574i	$0.923975\pi$
$860$		0			0
$861$	−8.19109	−	11.4422i	−0.279152	−	0.389948i
$862$		0			0
$863$	5.69115	+	17.5156i	0.193729	+	0.596237i	0.999989	+	0.00467541i	$0.00148824\pi$
$863$	5.69115	+	17.5156i	0.193729	+	0.596237i	−0.806260	+	0.591561i	$0.798512\pi$
$864$		0			0
$865$	7.31105	−	5.31179i	0.248583	−	0.180606i
$866$		0			0
$867$	−6.60226	−	20.3197i	−0.224225	−	0.690093i
$868$		0			0
$869$	−11.3961	−	8.27972i	−0.386585	−	0.280870i
$870$		0			0
$871$	61.0489	+	44.3546i	2.06856	+	1.50290i
$872$		0			0
$873$	−42.7103	+	31.0308i	−1.44552	+	1.05023i
$874$		0			0
$875$	−0.768717			−0.0259874
$876$		0			0
$877$	15.4605	−	47.5825i	0.522064	−	1.60675i	−0.247986	−	0.968764i	$-0.579769\pi$
$877$	15.4605	−	47.5825i	0.522064	−	1.60675i	0.770050	−	0.637984i	$-0.220231\pi$
$878$		0			0
$879$	4.01759	+	12.3649i	0.135510	+	0.417057i
$880$		0			0
$881$	−12.0327	+	37.0328i	−0.405392	+	1.24767i	0.515176	+	0.857084i	$0.327727\pi$
$881$	−12.0327	+	37.0328i	−0.405392	+	1.24767i	−0.920568	+	0.390583i	$0.872273\pi$
$882$		0			0
$883$	−4.70968	+	14.4949i	−0.158493	+	0.487792i	−0.998498	−	0.0547868i	$-0.982552\pi$
$883$	−4.70968	+	14.4949i	−0.158493	+	0.487792i	0.840005	+	0.542579i	$0.182552\pi$
$884$		0			0
$885$	26.8534	+	19.5101i	0.902666	+	0.655825i
$886$		0			0
$887$	−41.4598	+	30.1223i	−1.39208	+	1.01141i	−0.396451	+	0.918056i	$0.629758\pi$
$887$	−41.4598	+	30.1223i	−1.39208	+	1.01141i	−0.995633	+	0.0933529i	$0.970242\pi$
$888$		0			0
$889$	−2.36954	−	7.29270i	−0.0794719	−	0.244589i
$890$		0			0
$891$	8.76188	+	6.36588i	0.293534	+	0.213265i
$892$		0			0
$893$	−38.2274			−1.27923
$894$		0			0
$895$	3.73036	−	11.4809i	0.124692	−	0.383763i
$896$		0			0
$897$	−47.1810	+	34.2790i	−1.57533	+	1.14454i
$898$		0			0
$899$	−32.3414			−1.07865
$900$		0			0
$901$	23.9498			0.797882
$902$		0			0
$903$	−18.6363			−0.620177
$904$		0			0
$905$	−17.5659			−0.583912
$906$		0			0
$907$	38.6457	−	28.0777i	1.28321	−	0.932306i	0.283565	−	0.958953i	$-0.408483\pi$
$907$	38.6457	−	28.0777i	1.28321	−	0.932306i	0.999645	+	0.0266469i	$0.00848299\pi$
$908$		0			0
$909$	−10.6398	+	32.7459i	−0.352900	+	1.08611i
$910$		0			0
$911$	35.3139			1.17000			0.585001	−	0.811033i	$-0.301094\pi$
$911$	35.3139			1.17000			0.585001	+	0.811033i	$0.301094\pi$
$912$		0			0
$913$	35.5889	+	25.8568i	1.17782	+	0.855736i
$914$		0			0
$915$	−9.48381	−	29.1882i	−0.313525	−	0.964931i
$916$		0			0
$917$	−8.04318	+	5.84371i	−0.265609	+	0.192976i
$918$		0			0
$919$	19.3568	+	14.0635i	0.638521	+	0.463913i	0.859342	−	0.511402i	$-0.170874\pi$
$919$	19.3568	+	14.0635i	0.638521	+	0.463913i	−0.220821	+	0.975314i	$0.570874\pi$
$920$		0			0
$921$	27.3348	−	84.1278i	0.900711	−	2.77210i
$922$		0			0
$923$	−4.89752	+	15.0730i	−0.161204	+	0.496134i
$924$		0			0
$925$	−1.03222	−	3.17685i	−0.0339392	−	0.104454i
$926$		0			0
$927$	10.5875	−	32.5850i	0.347740	−	1.07023i
$928$		0			0
$929$	29.2048			0.958178			0.479089	−	0.877766i	$-0.340967\pi$
$929$	29.2048			0.958178			0.479089	+	0.877766i	$0.340967\pi$
$930$		0			0
$931$	−36.9614	+	26.8540i	−1.21136	+	0.880104i
$932$		0			0
$933$	−54.7734	−	39.7952i	−1.79320	−	1.30284i
$934$		0			0
$935$	−12.0650	−	8.76571i	−0.394567	−	0.286669i
$936$		0			0
$937$	−8.80009	−	27.0839i	−0.287487	−	0.884793i	−0.985642	−	0.168847i	$-0.945996\pi$
$937$	−8.80009	−	27.0839i	−0.287487	−	0.884793i	0.698156	−	0.715946i	$-0.254004\pi$
$938$		0			0
$939$	16.6297	−	12.0822i	0.542688	−	0.394286i
$940$		0			0
$941$	17.0072	+	52.3428i	0.554419	+	1.70633i	0.697472	+	0.716612i	$0.254308\pi$
$941$	17.0072	+	52.3428i	0.554419	+	1.70633i	−0.143053	+	0.989715i	$0.545692\pi$
$942$		0			0
$943$	−25.8802	−	8.61035i	−0.842776	−	0.280391i
$944$		0			0
$945$	−1.47576	−	4.54194i	−0.0480066	−	0.147749i
$946$		0			0
$947$	−2.68564	+	1.95123i	−0.0872714	+	0.0634064i	−0.630565	−	0.776136i	$-0.717177\pi$
$947$	−2.68564	+	1.95123i	−0.0872714	+	0.0634064i	0.543294	+	0.839543i	$0.317177\pi$
$948$		0			0
$949$	6.63285	+	20.4138i	0.215311	+	0.662660i
$950$		0			0
$951$	28.2703	+	20.5396i	0.916727	+	0.666041i
$952$		0			0
$953$	27.3380	+	19.8622i	0.885566	+	0.643401i	0.934718	−	0.355390i	$-0.115652\pi$
$953$	27.3380	+	19.8622i	0.885566	+	0.643401i	−0.0491524	+	0.998791i	$0.515652\pi$
$954$		0			0
$955$	7.11629	−	5.17029i	0.230278	−	0.167307i
$956$		0			0
$957$	−121.194			−3.91766
$958$		0			0
$959$	−1.74197	+	5.36124i	−0.0562512	+	0.173123i
$960$		0			0
$961$	−5.38078	−	16.5603i	−0.173573	−	0.534204i
$962$		0			0
$963$	22.7944	−	70.1541i	0.734540	−	2.26068i
$964$		0			0
$965$	−3.18342	+	9.79755i	−0.102478	+	0.315394i
$966$		0			0
$967$	−20.1668	−	14.6521i	−0.648522	−	0.471179i	0.214245	−	0.976780i	$-0.431271\pi$
$967$	−20.1668	−	14.6521i	−0.648522	−	0.471179i	−0.862767	+	0.505601i	$0.831271\pi$
$968$		0			0
$969$	50.8879	−	36.9722i	1.63476	−	1.18772i
$970$		0			0
$971$	−6.75308	−	20.7838i	−0.216717	−	0.666985i	−0.999027	−	0.0440968i	$-0.985959\pi$
$971$	−6.75308	−	20.7838i	−0.216717	−	0.666985i	0.782311	−	0.622889i	$-0.214041\pi$
$972$		0			0
$973$	8.16449	+	5.93185i	0.261741	+	0.190166i
$974$		0			0
$975$	−13.6911			−0.438465
$976$		0			0
$977$	6.78881	−	20.8938i	0.217193	−	0.668452i	−0.781797	−	0.623533i	$-0.785697\pi$
$977$	6.78881	−	20.8938i	0.217193	−	0.668452i	0.998991	−	0.0449196i	$-0.0143032\pi$
$978$		0			0
$979$	17.3484	−	12.6043i	0.554456	−	0.402836i
$980$		0			0
$981$	−44.1351			−1.40913
$982$		0			0
$983$	60.9624			1.94440			0.972200	−	0.234153i	$-0.0752315\pi$
$983$	60.9624			1.94440			0.972200	+	0.234153i	$0.0752315\pi$
$984$		0			0
$985$	−6.99409			−0.222850
$986$		0			0
$987$	11.7852			0.375129
$988$		0			0
$989$	−29.2233	+	21.2320i	−0.929248	+	0.675138i
$990$		0			0
$991$	−2.86246	+	8.80976i	−0.0909292	+	0.279851i	−0.986171	−	0.165729i	$-0.947002\pi$
$991$	−2.86246	+	8.80976i	−0.0909292	+	0.279851i	0.895242	+	0.445580i	$0.147002\pi$
$992$		0			0
$993$	50.6009			1.60577
$994$		0			0
$995$	2.36703	+	1.71974i	0.0750398	+	0.0545196i
$996$		0			0
$997$	12.3868	+	38.1225i	0.392292	+	1.20735i	0.931050	+	0.364891i	$0.118894\pi$
$997$	12.3868	+	38.1225i	0.392292	+	1.20735i	−0.538758	+	0.842461i	$0.681106\pi$
$998$		0			0
$999$	16.7887	−	12.1977i	0.531169	−	0.385917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.141.8	✓	32
41.16	even	5	inner	820.2.u.b.221.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.141.8	✓	32	1.1	even	1	trivial
820.2.u.b.221.8	yes	32	41.16	even	5	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.85886 q^{3} +(0.809017 - 0.587785i) q^{5} +(0.237547 - 0.731093i) q^{7} +5.17308 q^{9} +(3.90892 + 2.84000i) q^{11} +(-1.47988 - 4.55461i) q^{13} +(2.31287 - 1.68040i) q^{15} +(-2.49705 - 1.81421i) q^{17} +(-2.20281 + 6.77956i) q^{19} +(0.679112 - 2.09009i) q^{21} +(-1.31630 - 4.05115i) q^{23} +(0.309017 - 0.951057i) q^{25} +6.21253 q^{27} +(-7.09820 + 5.15714i) q^{29} +(2.98213 + 2.16664i) q^{31} +(11.1751 + 8.11916i) q^{33} +(-0.237547 - 0.731093i) q^{35} +(2.70239 - 1.96340i) q^{37} +(-4.23077 - 13.0210i) q^{39} +(3.79994 - 5.15368i) q^{41} +(-2.62049 - 8.06504i) q^{43} +(4.18511 - 3.04066i) q^{45} +(1.65715 + 5.10018i) q^{47} +(5.18505 + 3.76716i) q^{49} +(-7.13871 - 5.18658i) q^{51} +(-6.27754 + 4.56090i) q^{53} +4.83169 q^{55} +(-6.29753 + 19.3818i) q^{57} +(3.58782 + 11.0422i) q^{59} +(3.31734 - 10.2097i) q^{61} +(1.22885 - 3.78200i) q^{63} +(-3.87438 - 2.81490i) q^{65} +(-12.7477 + 9.26177i) q^{67} +(-3.76311 - 11.5817i) q^{69} +(-2.67736 - 1.94521i) q^{71} -4.48201 q^{73} +(0.883436 - 2.71894i) q^{75} +(3.00485 - 2.18315i) q^{77} -2.91540 q^{79} +2.24151 q^{81} +9.10452 q^{83} -3.08652 q^{85} +(-20.2927 + 14.7435i) q^{87} +(1.37146 - 4.22092i) q^{89} -3.68138 q^{91} +(8.52549 + 6.19413i) q^{93} +(2.20281 + 6.77956i) q^{95} +(-8.25626 + 5.99852i) q^{97} +(20.2212 + 14.6915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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