LMFDB - Embedded newform 820.2.x.a.273.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			273.17
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70683 + 0.706990i) q^{3} +(-1.61561 - 1.54590i) q^{5} +(0.839794 - 2.02744i) q^{7} +(0.292099 + 0.292099i) q^{9} +(0.586281 + 1.41541i) q^{11} +(-1.97247 - 0.817025i) q^{13} +(-1.66462 - 3.78080i) q^{15} +(5.04679 - 2.09045i) q^{17} +(1.32157 - 3.19056i) q^{19} +(2.86676 - 2.86676i) q^{21} +(3.85618 - 3.85618i) q^{23} +(0.220378 + 4.99514i) q^{25} +(-1.82892 - 4.41541i) q^{27} +(0.308258 + 0.744201i) q^{29} -3.52846i q^{31} +2.83035i q^{33} +(-4.49100 + 1.97731i) q^{35} +(0.0174564 - 0.0174564i) q^{37} +(-2.78904 - 2.78904i) q^{39} +(-4.42642 - 4.62675i) q^{41} -2.82587i q^{43} +(-0.0203612 - 0.923472i) q^{45} +(1.59565 - 0.660939i) q^{47} +(1.54448 + 1.54448i) q^{49} +10.0919 q^{51} +(0.328043 - 0.791967i) q^{53} +(1.24088 - 3.19308i) q^{55} +(4.51140 - 4.51140i) q^{57} +13.1291i q^{59} +(-1.70431 - 1.70431i) q^{61} +(0.837515 - 0.346910i) q^{63} +(1.92370 + 4.36924i) q^{65} +(-11.0250 + 4.56671i) q^{67} +(9.30812 - 3.85555i) q^{69} +(15.3613 - 6.36284i) q^{71} +13.5325i q^{73} +(-3.15537 + 8.68164i) q^{75} +3.36201 q^{77} +(-9.73933 + 4.03416i) q^{79} -10.0686i q^{81} +(5.60246 + 5.60246i) q^{83} +(-11.3853 - 4.42449i) q^{85} +1.48816i q^{87} +(3.26033 + 7.87112i) q^{89} +(-3.31294 + 3.31294i) q^{91} +(2.49459 - 6.02247i) q^{93} +(-7.06744 + 3.11168i) q^{95} +(6.06726 + 14.6477i) q^{97} +(-0.242187 + 0.584691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70683	+	0.706990i	0.985436	+	0.408181i	0.816437	−	0.577435i	$-0.195946\pi$
$3$	1.70683	+	0.706990i	0.985436	+	0.408181i	0.169000	+	0.985616i	$0.445946\pi$
$4$		0			0
$5$	−1.61561	−	1.54590i	−0.722522	−	0.691348i
$5$	−1.61561	−	1.54590i	−0.722522	−	0.691348i
$6$		0			0
$7$	0.839794	−	2.02744i	0.317412	−	0.766301i	−0.681978	−	0.731373i	$-0.738880\pi$
$7$	0.839794	−	2.02744i	0.317412	−	0.766301i	0.999390	−	0.0349277i	$-0.0111201\pi$
$8$		0			0
$9$	0.292099	+	0.292099i	0.0973662	+	0.0973662i
$10$		0			0
$11$	0.586281	+	1.41541i	0.176770	+	0.426762i	0.987286	−	0.158956i	$-0.0508128\pi$
$11$	0.586281	+	1.41541i	0.176770	+	0.426762i	−0.810515	+	0.585718i	$0.800813\pi$
$12$		0			0
$13$	−1.97247	−	0.817025i	−0.547066	−	0.226602i	0.0919935	−	0.995760i	$-0.470676\pi$
$13$	−1.97247	−	0.817025i	−0.547066	−	0.226602i	−0.639059	+	0.769158i	$0.720676\pi$
$14$		0			0
$15$	−1.66462	−	3.78080i	−0.429804	−	0.976199i
$16$		0			0
$17$	5.04679	−	2.09045i	1.22403	−	0.507008i	0.325338	−	0.945598i	$-0.394522\pi$
$17$	5.04679	−	2.09045i	1.22403	−	0.507008i	0.898687	+	0.438590i	$0.144522\pi$
$18$		0			0
$19$	1.32157	−	3.19056i	0.303190	−	0.731966i	−0.696703	−	0.717359i	$-0.745351\pi$
$19$	1.32157	−	3.19056i	0.303190	−	0.731966i	0.999893	−	0.0146062i	$-0.00464945\pi$
$20$		0			0
$21$	2.86676	−	2.86676i	0.625579	−	0.625579i
$22$		0			0
$23$	3.85618	−	3.85618i	0.804070	−	0.804070i	−0.179659	−	0.983729i	$-0.557499\pi$
$23$	3.85618	−	3.85618i	0.804070	−	0.804070i	0.983729	+	0.179659i	$0.0574995\pi$
$24$		0			0
$25$	0.220378	+	4.99514i	0.0440756	+	0.999028i
$26$		0			0
$27$	−1.82892	−	4.41541i	−0.351976	−	0.849745i
$28$		0			0
$29$	0.308258	+	0.744201i	0.0572421	+	0.138195i	0.949913	−	0.312514i	$-0.101171\pi$
$29$	0.308258	+	0.744201i	0.0572421	+	0.138195i	−0.892671	+	0.450709i	$0.851171\pi$
$30$		0			0
$31$		−	3.52846i		−	0.633731i	−0.948471	−	0.316865i	$-0.897370\pi$
$31$		−	3.52846i		−	0.633731i	0.948471	−	0.316865i	$-0.102630\pi$
$32$		0			0
$33$			2.83035i			0.492701i
$34$		0			0
$35$	−4.49100	+	1.97731i	−0.759118	+	0.334227i
$36$		0			0
$37$	0.0174564	−	0.0174564i	0.00286981	−	0.00286981i	−0.705670	−	0.708540i	$-0.749354\pi$
$37$	0.0174564	−	0.0174564i	0.00286981	−	0.00286981i	0.708540	+	0.705670i	$0.249354\pi$
$38$		0			0
$39$	−2.78904	−	2.78904i	−0.446604	−	0.446604i
$40$		0			0
$41$	−4.42642	−	4.62675i	−0.691291	−	0.722577i
$41$	−4.42642	−	4.62675i	−0.691291	−	0.722577i
$42$		0			0
$43$		−	2.82587i		−	0.430942i	−0.976510	−	0.215471i	$-0.930871\pi$
$43$		−	2.82587i		−	0.430942i	0.976510	−	0.215471i	$-0.0691286\pi$
$44$		0			0
$45$	−0.0203612	−	0.923472i	−0.00303527	−	0.137663i
$46$		0			0
$47$	1.59565	−	0.660939i	0.232749	−	0.0964079i	−0.263261	−	0.964725i	$-0.584798\pi$
$47$	1.59565	−	0.660939i	0.232749	−	0.0964079i	0.496010	+	0.868317i	$0.334798\pi$
$48$		0			0
$49$	1.54448	+	1.54448i	0.220641	+	0.220641i
$50$		0			0
$51$	10.0919			1.41315
$52$		0			0
$53$	0.328043	−	0.791967i	0.0450602	−	0.108785i	−0.899747	−	0.436412i	$-0.856249\pi$
$53$	0.328043	−	0.791967i	0.0450602	−	0.108785i	0.944807	+	0.327627i	$0.106249\pi$
$54$		0			0
$55$	1.24088	−	3.19308i	0.167320	−	0.430555i
$56$		0			0
$57$	4.51140	−	4.51140i	0.597549	−	0.597549i
$58$		0			0
$59$			13.1291i			1.70926i	0.519238	+	0.854630i	$0.326216\pi$
$59$			13.1291i			1.70926i	−0.519238	+	0.854630i	$0.673784\pi$
$60$		0			0
$61$	−1.70431	−	1.70431i	−0.218215	−	0.218215i	0.589531	−	0.807746i	$-0.299313\pi$
$61$	−1.70431	−	1.70431i	−0.218215	−	0.218215i	−0.807746	+	0.589531i	$0.799313\pi$
$62$		0			0
$63$	0.837515	−	0.346910i	0.105517	−	0.0437066i
$64$		0			0
$65$	1.92370	+	4.36924i	0.238606	+	0.541938i
$66$		0			0
$67$	−11.0250	+	4.56671i	−1.34692	+	0.557912i	−0.935433	−	0.353504i	$-0.884990\pi$
$67$	−11.0250	+	4.56671i	−1.34692	+	0.557912i	−0.411486	+	0.911416i	$0.634990\pi$
$68$		0			0
$69$	9.30812	−	3.85555i	1.12057	−	0.464153i
$70$		0			0
$71$	15.3613	−	6.36284i	1.82305	−	0.755130i	0.849144	−	0.528161i	$-0.177118\pi$
$71$	15.3613	−	6.36284i	1.82305	−	0.755130i	0.973902	−	0.226969i	$-0.0728817\pi$
$72$		0			0
$73$			13.5325i			1.58386i	0.610613	+	0.791929i	$0.290923\pi$
$73$			13.5325i			1.58386i	−0.610613	+	0.791929i	$0.709077\pi$
$74$		0			0
$75$	−3.15537	+	8.68164i	−0.364351	+	1.00247i
$76$		0			0
$77$	3.36201			0.383137
$78$		0			0
$79$	−9.73933	+	4.03416i	−1.09576	+	0.453879i	−0.856012	−	0.516957i	$-0.827065\pi$
$79$	−9.73933	+	4.03416i	−1.09576	+	0.453879i	−0.239748	+	0.970835i	$0.577065\pi$
$80$		0			0
$81$		−	10.0686i		−	1.11874i
$82$		0			0
$83$	5.60246	+	5.60246i	0.614950	+	0.614950i	0.944232	−	0.329282i	$-0.106807\pi$
$83$	5.60246	+	5.60246i	0.614950	+	0.614950i	−0.329282	+	0.944232i	$0.606807\pi$
$84$		0			0
$85$	−11.3853	−	4.42449i	−1.23490	−	0.479903i
$86$		0			0
$87$			1.48816i			0.159547i
$88$		0			0
$89$	3.26033	+	7.87112i	0.345594	+	0.834338i	0.997129	+	0.0757192i	$0.0241253\pi$
$89$	3.26033	+	7.87112i	0.345594	+	0.834338i	−0.651535	+	0.758618i	$0.725875\pi$
$90$		0			0
$91$	−3.31294	+	3.31294i	−0.347291	+	0.347291i
$92$		0			0
$93$	2.49459	−	6.02247i	0.258677	−	0.624501i
$94$		0			0
$95$	−7.06744	+	3.11168i	−0.725105	+	0.319251i
$96$		0			0
$97$	6.06726	+	14.6477i	0.616037	+	1.48724i	0.856270	+	0.516529i	$0.172776\pi$
$97$	6.06726	+	14.6477i	0.616037	+	1.48724i	−0.240233	+	0.970715i	$0.577224\pi$
$98$		0			0
$99$	−0.242187	+	0.584691i	−0.0243407	+	0.0587636i
$100$		0			0
$101$	−1.78406	−	0.738981i	−0.177520	−	0.0735314i	0.292153	−	0.956372i	$-0.405628\pi$
$101$	−1.78406	−	0.738981i	−0.177520	−	0.0735314i	−0.469673	+	0.882840i	$0.655628\pi$
$102$		0			0
$103$	−11.7635			−1.15909			−0.579545	−	0.814940i	$-0.696770\pi$
$103$	−11.7635			−1.15909			−0.579545	+	0.814940i	$0.696770\pi$
$104$		0			0
$105$	−9.06330	+	0.199832i	−0.884487	+	0.0195016i
$106$		0			0
$107$	1.74549	+	1.74549i	0.168743	+	0.168743i	0.786427	−	0.617684i	$-0.211929\pi$
$107$	1.74549	+	1.74549i	0.168743	+	0.168743i	−0.617684	+	0.786427i	$0.711929\pi$
$108$		0			0
$109$	−6.84842	−	2.83671i	−0.655960	−	0.271708i	0.0297774	−	0.999557i	$-0.490520\pi$
$109$	−6.84842	−	2.83671i	−0.655960	−	0.271708i	−0.685737	+	0.727849i	$0.740520\pi$
$110$		0			0
$111$	0.0421365	−	0.0174535i	0.00399942	−	0.00165661i
$112$		0			0
$113$	11.4758	−	11.4758i	1.07956	−	1.07956i	0.0830063	−	0.996549i	$-0.473548\pi$
$113$	11.4758	−	11.4758i	1.07956	−	1.07956i	0.996549	−	0.0830063i	$-0.0264521\pi$
$114$		0			0
$115$	−12.1914	+	0.268802i	−1.13685	+	0.0250659i
$116$		0			0
$117$	−0.337505	−	0.814808i	−0.0312023	−	0.0753291i
$118$		0			0
$119$		−	11.9876i		−	1.09890i
$120$		0			0
$121$	6.11852	−	6.11852i	0.556229	−	0.556229i
$122$		0			0
$123$	−4.28406	−	11.0265i	−0.386281	−	0.994225i
$124$		0			0
$125$	7.36595	−	8.41087i	0.658831	−	0.752291i
$126$		0			0
$127$	8.98635	+	8.98635i	0.797409	+	0.797409i	0.982686	−	0.185277i	$-0.0593182\pi$
$127$	8.98635	+	8.98635i	0.797409	+	0.797409i	−0.185277	+	0.982686i	$0.559318\pi$
$128$		0			0
$129$	1.99786	−	4.82327i	0.175902	−	0.424665i
$130$		0			0
$131$	−6.50969	+	6.50969i	−0.568754	+	0.568754i	−0.931779	−	0.363025i	$-0.881744\pi$
$131$	−6.50969	+	6.50969i	−0.568754	+	0.568754i	0.363025	+	0.931779i	$0.381744\pi$
$132$		0			0
$133$	−5.35883	−	5.35883i	−0.464670	−	0.464670i
$134$		0			0
$135$	−3.87096	+	9.96089i	−0.333159	+	0.857297i
$136$		0			0
$137$	−7.68508	+	3.18326i	−0.656580	+	0.271965i	−0.685999	−	0.727603i	$-0.740634\pi$
$137$	−7.68508	+	3.18326i	−0.656580	+	0.271965i	0.0294183	+	0.999567i	$0.490634\pi$
$138$		0			0
$139$			3.46194i			0.293638i	0.989163	+	0.146819i	$0.0469035\pi$
$139$			3.46194i			0.293638i	−0.989163	+	0.146819i	$0.953097\pi$
$140$		0			0
$141$	3.19077			0.268711
$142$		0			0
$143$		−	3.27086i		−	0.273523i
$144$		0			0
$145$	0.652437	−	1.67887i	0.0541819	−	0.139423i
$146$		0			0
$147$	1.54423	+	3.72810i	0.127366	+	0.307488i
$148$		0			0
$149$	4.79620	−	11.5790i	0.392920	−	0.948592i	−0.596381	−	0.802702i	$-0.703395\pi$
$149$	4.79620	−	11.5790i	0.392920	−	0.948592i	0.989301	−	0.145891i	$-0.0466048\pi$
$150$		0			0
$151$	0.694150	+	1.67583i	0.0564891	+	0.136377i	0.949604	−	0.313451i	$-0.101485\pi$
$151$	0.694150	+	1.67583i	0.0564891	+	0.136377i	−0.893115	+	0.449828i	$0.851485\pi$
$152$		0			0
$153$	2.08478	+	0.863542i	0.168544	+	0.0698132i
$154$		0			0
$155$	−5.45466	+	5.70061i	−0.438128	+	0.457884i
$156$		0			0
$157$	8.67386	+	3.59283i	0.692249	+	0.286739i	0.700937	−	0.713223i	$-0.252765\pi$
$157$	8.67386	+	3.59283i	0.692249	+	0.286739i	−0.00868785	+	0.999962i	$0.502765\pi$
$158$		0			0
$159$	1.11983	−	1.11983i	0.0888080	−	0.0888080i
$160$		0			0
$161$	−4.57979	−	11.0566i	−0.360938	−	0.871381i
$162$		0			0
$163$	−6.76379	+	6.76379i	−0.529781	+	0.529781i	−0.920507	−	0.390726i	$-0.872224\pi$
$163$	−6.76379	+	6.76379i	−0.529781	+	0.529781i	0.390726	+	0.920507i	$0.372224\pi$
$164$		0			0
$165$	4.37544	−	4.57274i	0.340628	−	0.355987i
$166$		0			0
$167$	−3.68428	+	8.89463i	−0.285098	+	0.688287i	−0.999940	−	0.0109991i	$-0.996499\pi$
$167$	−3.68428	+	8.89463i	−0.285098	+	0.688287i	0.714842	+	0.699286i	$0.246499\pi$
$168$		0			0
$169$	−5.96927	−	5.96927i	−0.459174	−	0.459174i
$170$		0			0
$171$	1.31799	−	0.545929i	0.100789	−	0.0417482i
$172$		0			0
$173$	−0.639686			−0.0486344			−0.0243172	−	0.999704i	$-0.507741\pi$
$173$	−0.639686			−0.0486344			−0.0243172	+	0.999704i	$0.507741\pi$
$174$		0			0
$175$	10.3124	+	3.74808i	0.779546	+	0.283328i
$176$		0			0
$177$	−9.28213	+	22.4090i	−0.697688	+	1.68437i
$178$		0			0
$179$	−1.17928	−	0.488474i	−0.0881436	−	0.0365103i	0.338176	−	0.941083i	$-0.390190\pi$
$179$	−1.17928	−	0.488474i	−0.0881436	−	0.0365103i	−0.426320	+	0.904573i	$0.640190\pi$
$180$		0			0
$181$	−8.11484	−	3.36128i	−0.603172	−	0.249842i	0.0601342	−	0.998190i	$-0.480847\pi$
$181$	−8.11484	−	3.36128i	−0.603172	−	0.249842i	−0.663306	+	0.748348i	$0.730847\pi$
$182$		0			0
$183$	−1.70403	−	4.11390i	−0.125966	−	0.304108i
$184$		0			0
$185$	−0.0551885	+	0.00121683i	−0.00405754	+	8.94628e-5i
$186$		0			0
$187$	5.91767	+	5.91767i	0.432743	+	0.432743i
$188$		0			0
$189$	−10.4879			−0.762882
$190$		0			0
$191$	−1.66354	+	4.01614i	−0.120370	+	0.290598i	−0.972567	−	0.232622i	$-0.925269\pi$
$191$	−1.66354	+	4.01614i	−0.120370	+	0.290598i	0.852198	+	0.523220i	$0.175269\pi$
$192$		0			0
$193$	6.85045	+	2.83755i	0.493106	+	0.204251i	0.615358	−	0.788248i	$-0.289012\pi$
$193$	6.85045	+	2.83755i	0.493106	+	0.204251i	−0.122252	+	0.992499i	$0.539012\pi$
$194$		0			0
$195$	0.194415	+	8.81757i	0.0139223	+	0.631440i
$196$		0			0
$197$	10.6263			0.757090			0.378545	−	0.925583i	$-0.376425\pi$
$197$	10.6263			0.757090			0.378545	+	0.925583i	$0.376425\pi$
$198$		0			0
$199$	−3.23900	−	1.34164i	−0.229607	−	0.0951062i	0.264914	−	0.964272i	$-0.414656\pi$
$199$	−3.23900	−	1.34164i	−0.229607	−	0.0951062i	−0.494521	+	0.869166i	$0.664656\pi$
$200$		0			0
$201$	−22.0464			−1.55503
$202$		0			0
$203$	1.76770			0.124068
$204$		0			0
$205$	−0.00113573	+	14.3178i	−7.93230e−5	+	1.00000i
$206$		0			0
$207$	2.25277			0.156578
$208$		0			0
$209$	5.29077			0.365970
$210$		0			0
$211$	3.43096	+	1.42115i	0.236197	+	0.0978361i	0.497643	−	0.867382i	$-0.334199\pi$
$211$	3.43096	+	1.42115i	0.236197	+	0.0978361i	−0.261445	+	0.965218i	$0.584199\pi$
$212$		0			0
$213$	30.7175			2.10473
$214$		0			0
$215$	−4.36852	+	4.56550i	−0.297931	+	0.311365i
$216$		0			0
$217$	−7.15375	−	2.96318i	−0.485628	−	0.201154i
$218$		0			0
$219$	−9.56734	+	23.0976i	−0.646501	+	1.56079i
$220$		0			0
$221$	−11.6626			−0.784511
$222$		0			0
$223$	1.15589	+	1.15589i	0.0774043	+	0.0774043i	0.744749	−	0.667345i	$-0.232569\pi$
$223$	1.15589	+	1.15589i	0.0774043	+	0.0774043i	−0.667345	+	0.744749i	$0.732569\pi$
$224$		0			0
$225$	−1.39470	+	1.52345i	−0.0929801	+	0.101563i
$226$		0			0
$227$	7.40634	+	17.8805i	0.491576	+	1.18677i	0.953918	+	0.300068i	$0.0970094\pi$
$227$	7.40634	+	17.8805i	0.491576	+	1.18677i	−0.462341	+	0.886702i	$0.652991\pi$
$228$		0			0
$229$	−16.4735	−	6.82354i	−1.08860	−	0.450912i	−0.235081	−	0.971976i	$-0.575536\pi$
$229$	−16.4735	−	6.82354i	−1.08860	−	0.450912i	−0.853518	+	0.521063i	$0.825536\pi$
$230$		0			0
$231$	5.73837	+	2.37691i	0.377557	+	0.156389i
$232$		0			0
$233$	4.34190	−	10.4823i	0.284447	−	0.686716i	−0.715482	−	0.698631i	$-0.753793\pi$
$233$	4.34190	−	10.4823i	0.284447	−	0.686716i	0.999929	+	0.0119150i	$0.00379276\pi$
$234$		0			0
$235$	−3.59969	−	1.39890i	−0.234818	−	0.0912539i
$236$		0			0
$237$	−19.4754			−1.26507
$238$		0			0
$239$	−22.4413	+	9.29549i	−1.45161	+	0.601276i	−0.962581	−	0.270993i	$-0.912648\pi$
$239$	−22.4413	+	9.29549i	−1.45161	+	0.601276i	−0.489026	+	0.872269i	$0.662648\pi$
$240$		0			0
$241$	−9.33424	−	9.33424i	−0.601271	−	0.601271i	0.339379	−	0.940650i	$-0.389783\pi$
$241$	−9.33424	−	9.33424i	−0.601271	−	0.601271i	−0.940650	+	0.339379i	$0.889783\pi$
$242$		0			0
$243$	1.63166	−	3.93917i	0.104671	−	0.252698i
$244$		0			0
$245$	−0.107661	−	4.88290i	−0.00687819	−	0.311957i
$246$		0			0
$247$	−5.21354	+	5.21354i	−0.331730	+	0.331730i
$248$		0			0
$249$	5.60154	+	13.5233i	0.354983	+	0.857004i
$250$		0			0
$251$	6.18482	−	6.18482i	0.390382	−	0.390382i	−0.484442	−	0.874824i	$-0.660977\pi$
$251$	6.18482	−	6.18482i	0.390382	−	0.390382i	0.874824	+	0.484442i	$0.160977\pi$
$252$		0			0
$253$	7.71888	+	3.19727i	0.485282	+	0.201010i
$254$		0			0
$255$	−16.3046	−	15.6011i	−1.02103	−	0.976979i
$256$		0			0
$257$	16.5885	+	6.87120i	1.03476	+	0.428614i	0.834430	−	0.551114i	$-0.185797\pi$
$257$	16.5885	+	6.87120i	1.03476	+	0.428614i	0.200335	+	0.979728i	$0.435797\pi$
$258$		0			0
$259$	−0.0207320	−	0.0500515i	−0.00128823	−	0.00311005i
$260$		0			0
$261$	−0.127338	+	0.307422i	−0.00788204	+	0.0190289i
$262$		0			0
$263$	5.63992	+	13.6160i	0.347772	+	0.839597i	0.996882	+	0.0789021i	$0.0251414\pi$
$263$	5.63992	+	13.6160i	0.347772	+	0.839597i	−0.649110	+	0.760694i	$0.724859\pi$
$264$		0			0
$265$	−1.75429	+	0.772385i	−0.107765	+	0.0474472i
$266$		0			0
$267$			15.7397i			0.963251i
$268$		0			0
$269$	17.7792			1.08402			0.542008	−	0.840373i	$-0.317664\pi$
$269$	17.7792			1.08402			0.542008	+	0.840373i	$0.317664\pi$
$270$		0			0
$271$			18.0311i			1.09531i	0.836704	+	0.547655i	$0.184479\pi$
$271$			18.0311i			1.09531i	−0.836704	+	0.547655i	$0.815521\pi$
$272$		0			0
$273$	−7.99683	+	3.31240i	−0.483990	+	0.200475i
$274$		0			0
$275$	−6.94096	+	3.24048i	−0.418556	+	0.195408i
$276$		0			0
$277$	17.6786	+	17.6786i	1.06220	+	1.06220i	0.997933	+	0.0642693i	$0.0204717\pi$
$277$	17.6786	+	17.6786i	1.06220	+	1.06220i	0.0642693	+	0.997933i	$0.479528\pi$
$278$		0			0
$279$	1.03066	−	1.03066i	0.0617039	−	0.0617039i
$280$		0			0
$281$	8.05724	−	19.4519i	0.480655	−	1.16040i	−0.478644	−	0.878009i	$-0.658871\pi$
$281$	8.05724	−	19.4519i	0.480655	−	1.16040i	0.959298	−	0.282394i	$-0.0911286\pi$
$282$		0			0
$283$	−5.24406	−	5.24406i	−0.311727	−	0.311727i	0.533851	−	0.845578i	$-0.320744\pi$
$283$	−5.24406	−	5.24406i	−0.311727	−	0.311727i	−0.845578	+	0.533851i	$0.820744\pi$
$284$		0			0
$285$	−14.2628	+	0.314474i	−0.844857	+	0.0186278i
$286$		0			0
$287$	−13.0977	+	5.08879i	−0.773135	+	0.300382i
$288$		0			0
$289$	9.07926	−	9.07926i	0.534074	−	0.534074i
$290$		0			0
$291$			29.2905i			1.71704i
$292$		0			0
$293$	6.89817	+	16.6536i	0.402995	+	0.972917i	0.986935	+	0.161119i	$0.0515105\pi$
$293$	6.89817	+	16.6536i	0.402995	+	0.972917i	−0.583940	+	0.811797i	$0.698490\pi$
$294$		0			0
$295$	20.2963	−	21.2114i	1.18169	−	1.23498i
$296$		0			0
$297$	5.17734	−	5.17734i	0.300420	−	0.300420i
$298$		0			0
$299$	−10.7568	+	4.45562i	−0.622083	+	0.257675i
$300$		0			0
$301$	−5.72929	−	2.37315i	−0.330231	−	0.136786i
$302$		0			0
$303$	−2.52262	−	2.52262i	−0.144921	−	0.144921i
$304$		0			0
$305$	0.118802	+	5.38820i	0.00680257	+	0.308527i
$306$		0			0
$307$	3.56609			0.203528			0.101764	−	0.994809i	$-0.467551\pi$
$307$	3.56609			0.203528			0.101764	+	0.994809i	$0.467551\pi$
$308$		0			0
$309$	−20.0782	−	8.31666i	−1.14221	−	0.473118i
$310$		0			0
$311$	7.24586	−	17.4931i	0.410875	−	0.991940i	−0.574028	−	0.818836i	$-0.694620\pi$
$311$	7.24586	−	17.4931i	0.410875	−	0.991940i	0.984903	−	0.173105i	$-0.0553800\pi$
$312$		0			0
$313$	3.01215	+	7.27197i	0.170257	+	0.411036i	0.985859	−	0.167577i	$-0.0535942\pi$
$313$	3.01215	+	7.27197i	0.170257	+	0.411036i	−0.815602	+	0.578613i	$0.803594\pi$
$314$		0			0
$315$	−1.88938	−	0.734245i	−0.106455	−	0.0413700i
$316$		0			0
$317$	−1.30252	+	3.14456i	−0.0731569	+	0.176616i	−0.956228	−	0.292623i	$-0.905472\pi$
$317$	−1.30252	+	3.14456i	−0.0731569	+	0.176616i	0.883071	+	0.469239i	$0.155472\pi$
$318$		0			0
$319$	−0.872622	+	0.872622i	−0.0488574	+	0.0488574i
$320$		0			0
$321$	1.74520	+	4.21329i	0.0974076	+	0.235163i
$322$		0			0
$323$		−	18.8648i		−	1.04966i
$324$		0			0
$325$	3.64647	−	10.0328i	0.202270	−	0.556522i
$326$		0			0
$327$	−9.68354	−	9.68354i	−0.535501	−	0.535501i
$328$		0			0
$329$		−	3.79014i		−	0.208957i
$330$		0			0
$331$	0.786048	−	0.325592i	0.0432051	−	0.0178961i	−0.360976	−	0.932575i	$-0.617556\pi$
$331$	0.786048	−	0.325592i	0.0432051	−	0.0178961i	0.404181	+	0.914679i	$0.367556\pi$
$332$		0			0
$333$	0.0101980			0.000558845
$334$		0			0
$335$	24.8718	+	9.66557i	1.35889	+	0.528086i
$336$		0			0
$337$		−	10.7961i		−	0.588099i	−0.955790	−	0.294049i	$-0.904997\pi$
$337$		−	10.7961i		−	0.588099i	0.955790	−	0.294049i	$-0.0950030\pi$
$338$		0			0
$339$	27.7005	−	11.4739i	1.50449	−	0.623179i
$340$		0			0
$341$	4.99422	−	2.06867i	0.270452	−	0.112025i
$342$		0			0
$343$	18.6205	−	7.71286i	1.00541	−	0.416455i
$344$		0			0
$345$	−20.9986	−	8.16038i	−1.13052	−	0.439340i
$346$		0			0
$347$	−11.2734	+	4.66959i	−0.605187	+	0.250677i	−0.664169	−	0.747582i	$-0.731215\pi$
$347$	−11.2734	+	4.66959i	−0.605187	+	0.250677i	0.0589820	+	0.998259i	$0.481215\pi$
$348$		0			0
$349$	−18.0059	−	18.0059i	−0.963833	−	0.963833i	0.0355354	−	0.999368i	$-0.488686\pi$
$349$	−18.0059	−	18.0059i	−0.963833	−	0.963833i	−0.999368	+	0.0355354i	$0.988686\pi$
$350$		0			0
$351$			10.2035i			0.544625i
$352$		0			0
$353$	0.280814	−	0.280814i	0.0149462	−	0.0149462i	−0.699594	−	0.714540i	$-0.746636\pi$
$353$	0.280814	−	0.280814i	0.0149462	−	0.0149462i	0.714540	+	0.699594i	$0.246636\pi$
$354$		0			0
$355$	−34.6541	−	13.4671i	−1.83925	−	0.714761i
$356$		0			0
$357$	8.47512	−	20.4608i	0.448551	−	1.08290i
$358$		0			0
$359$	16.5490			0.873421			0.436711	−	0.899602i	$-0.356143\pi$
$359$	16.5490			0.873421			0.436711	+	0.899602i	$0.356143\pi$
$360$		0			0
$361$	5.00189	+	5.00189i	0.263257	+	0.263257i
$362$		0			0
$363$	14.7690	−	6.11751i	0.775171	−	0.321086i
$364$		0			0
$365$	20.9199	−	21.8632i	1.09500	−	1.14437i
$366$		0			0
$367$		−	31.1563i		−	1.62634i	−0.582024	−	0.813172i	$-0.697739\pi$
$367$		−	31.1563i		−	1.62634i	0.582024	−	0.813172i	$-0.302261\pi$
$368$		0			0
$369$	0.0585154	−	2.64442i	0.00304619	−	0.137663i
$370$		0			0
$371$	−1.33018	−	1.33018i	−0.0690594	−	0.0690594i
$372$		0			0
$373$	8.37971	−	8.37971i	0.433885	−	0.433885i	−0.456063	−	0.889948i	$-0.650741\pi$
$373$	8.37971	−	8.37971i	0.433885	−	0.433885i	0.889948	+	0.456063i	$0.150741\pi$
$374$		0			0
$375$	18.5188	−	9.14824i	0.956307	−	0.472413i
$376$		0			0
$377$		−	1.71977i		−	0.0885727i
$378$		0			0
$379$		−	11.9437i		−	0.613505i	−0.951789	−	0.306752i	$-0.900758\pi$
$379$		−	11.9437i		−	0.613505i	0.951789	−	0.306752i	$-0.0992423\pi$
$380$		0			0
$381$	8.98487	+	21.6914i	0.460309	+	1.11128i
$382$		0			0
$383$	−6.96687	−	16.8195i	−0.355990	−	0.859436i	−0.995856	−	0.0909493i	$-0.971010\pi$
$383$	−6.96687	−	16.8195i	−0.355990	−	0.859436i	0.639865	−	0.768487i	$-0.278990\pi$
$384$		0			0
$385$	−5.43169	−	5.19734i	−0.276825	−	0.264881i
$386$		0			0
$387$	0.825433	−	0.825433i	0.0419591	−	0.0419591i
$388$		0			0
$389$	19.2200	−	19.2200i	0.974491	−	0.974491i	−0.0251915	−	0.999683i	$-0.508020\pi$
$389$	19.2200	−	19.2200i	0.974491	−	0.974491i	0.999683	+	0.0251915i	$0.00801956\pi$
$390$		0			0
$391$	11.4002	−	27.5225i	0.576532	−	1.39187i
$392$		0			0
$393$	−15.7132	+	6.50861i	−0.792625	+	0.328316i
$394$		0			0
$395$	21.9713	+	8.53841i	1.10550	+	0.429614i
$396$		0			0
$397$	27.4971	+	11.3897i	1.38004	+	0.571631i	0.944492	−	0.328535i	$-0.106555\pi$
$397$	27.4971	+	11.3897i	1.38004	+	0.571631i	0.435547	+	0.900166i	$0.356555\pi$
$398$		0			0
$399$	−5.35795	−	12.9352i	−0.268233	−	0.647572i
$400$		0			0
$401$	8.65346	+	8.65346i	0.432133	+	0.432133i	0.889353	−	0.457220i	$-0.151155\pi$
$401$	8.65346	+	8.65346i	0.432133	+	0.432133i	−0.457220	+	0.889353i	$0.651155\pi$
$402$		0			0
$403$	−2.88284	+	6.95980i	−0.143605	+	0.346692i
$404$		0			0
$405$	−15.5651	+	16.2670i	−0.773436	+	0.808311i
$406$		0			0
$407$	0.0349423	+	0.0144736i	0.00173202	+	0.000717427i
$408$		0			0
$409$	−23.3667			−1.15541			−0.577704	−	0.816247i	$-0.696051\pi$
$409$	−23.3667			−1.15541			−0.577704	+	0.816247i	$0.696051\pi$
$410$		0			0
$411$	−15.3676			−0.758029
$412$		0			0
$413$	26.6184	+	11.0257i	1.30981	+	0.542540i
$414$		0			0
$415$	−0.390528	−	17.7122i	−0.0191703	−	0.869459i
$416$		0			0
$417$	−2.44756	+	5.90893i	−0.119857	+	0.289362i
$418$		0			0
$419$	−20.5411	−	20.5411i	−1.00350	−	1.00350i	−0.999994	−	0.00350533i	$-0.998884\pi$
$419$	−20.5411	−	20.5411i	−1.00350	−	1.00350i	−0.00350533	−	0.999994i	$-0.501116\pi$
$420$		0			0
$421$	−3.57901	−	8.64048i	−0.174430	−	0.421111i	0.812351	−	0.583168i	$-0.198187\pi$
$421$	−3.57901	−	8.64048i	−0.174430	−	0.421111i	−0.986781	+	0.162057i	$0.948187\pi$
$422$		0			0
$423$	0.659146	+	0.273027i	0.0320488	+	0.0132750i
$424$		0			0
$425$	11.5543	+	24.7487i	0.560465	+	1.20049i
$426$		0			0
$427$	−4.88666	+	2.02412i	−0.236482	+	0.0979541i
$428$		0			0
$429$	2.31247	−	5.58279i	0.111647	−	0.269540i
$430$		0			0
$431$	5.47732	−	5.47732i	0.263833	−	0.263833i	−0.562776	−	0.826609i	$-0.690267\pi$
$431$	5.47732	−	5.47732i	0.263833	−	0.263833i	0.826609	+	0.562776i	$0.190267\pi$
$432$		0			0
$433$	−25.8241	+	25.8241i	−1.24103	+	1.24103i	−0.281454	+	0.959575i	$0.590817\pi$
$433$	−25.8241	+	25.8241i	−1.24103	+	1.24103i	−0.959575	+	0.281454i	$0.909183\pi$
$434$		0			0
$435$	2.30054	−	2.40428i	0.110303	−	0.115276i
$436$		0			0
$437$	−7.20716	−	17.3996i	−0.344765	−	0.832337i
$438$		0			0
$439$	−2.97081	−	7.17216i	−0.141789	−	0.342309i	0.836993	−	0.547214i	$-0.184311\pi$
$439$	−2.97081	−	7.17216i	−0.141789	−	0.342309i	−0.978782	+	0.204905i	$0.934311\pi$
$440$		0			0
$441$			0.902283i			0.0429658i
$442$		0			0
$443$		−	25.2161i		−	1.19805i	−0.800729	−	0.599026i	$-0.795554\pi$
$443$		−	25.2161i		−	1.19805i	0.800729	−	0.599026i	$-0.204446\pi$
$444$		0			0
$445$	6.90057	−	17.7568i	0.327119	−	0.841753i
$446$		0			0
$447$	16.3725	−	16.3725i	0.774395	−	0.774395i
$448$		0			0
$449$	16.7231	+	16.7231i	0.789210	+	0.789210i	0.981365	−	0.192154i	$-0.0615474\pi$
$449$	16.7231	+	16.7231i	0.789210	+	0.789210i	−0.192154	+	0.981365i	$0.561547\pi$
$450$		0			0
$451$	3.95361	−	8.97777i	0.186168	−	0.422747i
$452$		0			0
$453$			3.35110i			0.157448i
$454$		0			0
$455$	10.4739	−	0.230934i	0.491024	−	0.0108264i
$456$		0			0
$457$	25.2997	−	10.4795i	1.18347	−	0.490209i	0.297846	−	0.954614i	$-0.403732\pi$
$457$	25.2997	−	10.4795i	1.18347	−	0.490209i	0.885623	+	0.464405i	$0.153732\pi$
$458$		0			0
$459$	−18.4603	−	18.4603i	−0.861655	−	0.861655i
$460$		0			0
$461$	−17.6572			−0.822377			−0.411188	−	0.911550i	$-0.634886\pi$
$461$	−17.6572			−0.822377			−0.411188	+	0.911550i	$0.634886\pi$
$462$		0			0
$463$	−9.23966	+	22.3065i	−0.429404	+	1.03667i	0.550073	+	0.835116i	$0.314600\pi$
$463$	−9.23966	+	22.3065i	−0.429404	+	1.03667i	−0.979477	+	0.201556i	$0.935400\pi$
$464$		0			0
$465$	−13.3404	+	5.87356i	−0.618647	+	0.272380i
$466$		0			0
$467$	−25.8871	+	25.8871i	−1.19791	+	1.19791i	−0.223124	+	0.974790i	$0.571626\pi$
$467$	−25.8871	+	25.8871i	−1.19791	+	1.19791i	−0.974790	+	0.223124i	$0.928374\pi$
$468$		0			0
$469$			26.1876i			1.20923i
$470$		0			0
$471$	12.2647	+	12.2647i	0.565126	+	0.565126i
$472$		0			0
$473$	3.99976	−	1.65676i	0.183909	−	0.0761777i
$474$		0			0
$475$	16.2286	+	5.89832i	0.744618	+	0.270634i
$476$		0			0
$477$	0.327153	−	0.135511i	0.0149793	−	0.00620464i
$478$		0			0
$479$	−2.72007	+	1.12669i	−0.124283	+	0.0514798i	−0.443958	−	0.896047i	$-0.646426\pi$
$479$	−2.72007	+	1.12669i	−0.124283	+	0.0514798i	0.319675	+	0.947527i	$0.396426\pi$
$480$		0			0
$481$	−0.0486945	+	0.0201699i	−0.00222028	+	0.000919670i
$482$		0			0
$483$		−	22.1095i		−	1.00602i
$484$		0			0
$485$	12.8415	−	33.0443i	0.583104	−	1.50046i
$486$		0			0
$487$	10.8202			0.490308			0.245154	−	0.969484i	$-0.421161\pi$
$487$	10.8202			0.490308			0.245154	+	0.969484i	$0.421161\pi$
$488$		0			0
$489$	−16.3265	+	6.76267i	−0.738312	+	0.305819i
$490$		0			0
$491$		−	25.9547i		−	1.17132i	−0.810557	−	0.585660i	$-0.800835\pi$
$491$		−	25.9547i		−	1.17132i	0.810557	−	0.585660i	$-0.199165\pi$
$492$		0			0
$493$	3.11142	+	3.11142i	0.140131	+	0.140131i
$494$		0			0
$495$	1.29515	−	0.570234i	0.0582128	−	0.0256301i
$496$		0			0
$497$		−	36.4875i		−	1.63669i
$498$		0			0
$499$	10.2955	+	24.8555i	0.460890	+	1.11269i	0.968033	+	0.250824i	$0.0807017\pi$
$499$	10.2955	+	24.8555i	0.460890	+	1.11269i	−0.507143	+	0.861862i	$0.669298\pi$
$500$		0			0
$501$	−12.5768	+	12.5768i	−0.561892	+	0.561892i
$502$		0			0
$503$	3.88904	−	9.38898i	0.173404	−	0.418634i	−0.813154	−	0.582049i	$-0.802251\pi$
$503$	3.88904	−	9.38898i	0.173404	−	0.418634i	0.986557	+	0.163415i	$0.0522511\pi$
$504$		0			0
$505$	1.73995	+	3.95188i	0.0774266	+	0.175856i
$506$		0			0
$507$	−5.96828	−	14.4087i	−0.265061	−	0.639913i
$508$		0			0
$509$	−10.6238	+	25.6480i	−0.470890	+	1.13683i	0.492881	+	0.870097i	$0.335944\pi$
$509$	−10.6238	+	25.6480i	−0.470890	+	1.13683i	−0.963771	+	0.266731i	$0.914056\pi$
$510$		0			0
$511$	27.4363	+	11.3645i	1.21371	+	0.502736i
$512$		0			0
$513$	−16.5047			−0.728700
$514$		0			0
$515$	19.0052	+	18.1852i	0.837468	+	0.801334i
$516$		0			0
$517$	1.87100	+	1.87100i	0.0822864	+	0.0822864i
$518$		0			0
$519$	−1.09183	−	0.452252i	−0.0479261	−	0.0198517i
$520$		0			0
$521$	34.8534	−	14.4368i	1.52696	−	0.632486i	0.547986	−	0.836488i	$-0.315395\pi$
$521$	34.8534	−	14.4368i	1.52696	−	0.632486i	0.978970	+	0.204002i	$0.0653949\pi$
$522$		0			0
$523$	−6.30411	+	6.30411i	−0.275659	+	0.275659i	−0.831373	−	0.555714i	$-0.812445\pi$
$523$	−6.30411	+	6.30411i	−0.275659	+	0.275659i	0.555714	+	0.831373i	$0.312445\pi$
$524$		0			0
$525$	14.9517	+	13.6881i	0.652544	+	0.597398i
$526$		0			0
$527$	−7.37606	−	17.8074i	−0.321306	−	0.775702i
$528$		0			0
$529$		−	6.74030i		−	0.293056i
$530$		0			0
$531$	−3.83498	+	3.83498i	−0.166424	+	0.166424i
$532$		0			0
$533$	4.95083	+	12.7426i	0.214444	+	0.551945i
$534$		0			0
$535$	−0.121672	−	5.51838i	−0.00526034	−	0.238580i
$536$		0			0
$537$	−1.66748	−	1.66748i	−0.0719571	−	0.0719571i
$538$		0			0
$539$	−1.28057	+	3.09158i	−0.0551582	+	0.133164i
$540$		0			0
$541$	−7.11334	+	7.11334i	−0.305826	+	0.305826i	−0.843288	−	0.537462i	$-0.819383\pi$
$541$	−7.11334	+	7.11334i	−0.305826	+	0.305826i	0.537462	+	0.843288i	$0.319383\pi$
$542$		0			0
$543$	−11.4742	−	11.4742i	−0.492407	−	0.492407i
$544$		0			0
$545$	6.67909	+	15.1700i	0.286101	+	0.649811i
$546$		0			0
$547$	−6.24325	+	2.58604i	−0.266942	+	0.110571i	−0.512140	−	0.858902i	$-0.671147\pi$
$547$	−6.24325	+	2.58604i	−0.266942	+	0.110571i	0.245198	+	0.969473i	$0.421147\pi$
$548$		0			0
$549$		−	0.995654i		−	0.0424935i
$550$		0			0
$551$	2.78181			0.118509
$552$		0			0
$553$			23.1338i			0.983748i
$554$		0			0
$555$	−0.0950574	−	0.0369408i	−0.00403496	−	0.00156805i
$556$		0			0
$557$	9.49237	+	22.9166i	0.402205	+	0.971008i	0.987130	+	0.159921i	$0.0511238\pi$
$557$	9.49237	+	22.9166i	0.402205	+	0.971008i	−0.584925	+	0.811087i	$0.698876\pi$
$558$		0			0
$559$	−2.30881	+	5.57396i	−0.0976522	+	0.235753i
$560$		0			0
$561$	5.91670	+	14.2842i	0.249803	+	0.603078i
$562$		0			0
$563$	−2.00314	−	0.829727i	−0.0844222	−	0.0349688i	0.340073	−	0.940399i	$-0.389548\pi$
$563$	−2.00314	−	0.829727i	−0.0844222	−	0.0349688i	−0.424495	+	0.905430i	$0.639548\pi$
$564$		0			0
$565$	−36.2809	+	0.799942i	−1.52635	+	0.0336538i
$566$		0			0
$567$	−20.4135	−	8.45557i	−0.857288	−	0.355100i
$568$		0			0
$569$	2.95151	−	2.95151i	0.123734	−	0.123734i	−0.642528	−	0.766262i	$-0.722114\pi$
$569$	2.95151	−	2.95151i	0.123734	−	0.123734i	0.766262	+	0.642528i	$0.222114\pi$
$570$		0			0
$571$	−12.5534	−	30.3066i	−0.525344	−	1.26829i	−0.934544	−	0.355848i	$-0.884192\pi$
$571$	−12.5534	−	30.3066i	−0.525344	−	1.26829i	0.409200	−	0.912445i	$-0.365808\pi$
$572$		0			0
$573$	−5.67875	+	5.67875i	−0.237233	+	0.237233i
$574$		0			0
$575$	20.1120	+	18.4124i	0.838728	+	0.767848i
$576$		0			0
$577$	−0.781835	+	1.88752i	−0.0325482	+	0.0785783i	−0.939318	−	0.343048i	$-0.888541\pi$
$577$	−0.781835	+	1.88752i	−0.0325482	+	0.0785783i	0.906770	+	0.421626i	$0.138541\pi$
$578$		0			0
$579$	9.68640	+	9.68640i	0.402553	+	0.402553i
$580$		0			0
$581$	16.0636	−	6.65374i	0.666429	−	0.276044i
$582$		0			0
$583$	1.31328			0.0543906
$584$		0			0
$585$	−0.714338	+	1.83816i	−0.0295342	+	0.0759986i
$586$		0			0
$587$	−16.8394	+	40.6539i	−0.695035	+	1.67796i	0.0393446	+	0.999226i	$0.487473\pi$
$587$	−16.8394	+	40.6539i	−0.695035	+	1.67796i	−0.734380	+	0.678738i	$0.762527\pi$
$588$		0			0
$589$	−11.2578	−	4.66313i	−0.463869	−	0.192141i
$590$		0			0
$591$	18.1372	+	7.51266i	0.746064	+	0.309030i
$592$		0			0
$593$	−0.545871	−	1.31785i	−0.0224162	−	0.0541176i	0.912275	−	0.409578i	$-0.134324\pi$
$593$	−0.545871	−	1.31785i	−0.0224162	−	0.0541176i	−0.934691	+	0.355460i	$0.884324\pi$
$594$		0			0
$595$	−18.5317	+	19.3673i	−0.759724	+	0.793981i
$596$		0			0
$597$	−4.57988	−	4.57988i	−0.187442	−	0.187442i
$598$		0			0
$599$	31.1989			1.27475			0.637376	−	0.770553i	$-0.280020\pi$
$599$	31.1989			1.27475			0.637376	+	0.770553i	$0.280020\pi$
$600$		0			0
$601$	15.4848	−	37.3836i	0.631638	−	1.52491i	−0.205925	−	0.978568i	$-0.566020\pi$
$601$	15.4848	−	37.3836i	0.631638	−	1.52491i	0.837563	−	0.546341i	$-0.183980\pi$
$602$		0			0
$603$	−4.55432	−	1.88646i	−0.185466	−	0.0768226i
$604$		0			0
$605$	−19.3438	+	0.426501i	−0.786436	+	0.0173397i
$606$		0			0
$607$	13.1173			0.532416			0.266208	−	0.963916i	$-0.414229\pi$
$607$	13.1173			0.532416			0.266208	+	0.963916i	$0.414229\pi$
$608$		0			0
$609$	3.01715	+	1.24974i	0.122261	+	0.0506422i
$610$		0			0
$611$	−3.68738			−0.149175
$612$		0			0
$613$	−41.4090			−1.67249			−0.836246	−	0.548354i	$-0.815255\pi$
$613$	−41.4090			−1.67249			−0.836246	+	0.548354i	$0.815255\pi$
$614$		0			0
$615$	−10.1245	+	24.4372i	−0.408259	+	0.985404i
$616$		0			0
$617$	35.6217			1.43407			0.717037	−	0.697035i	$-0.245498\pi$
$617$	35.6217			1.43407			0.717037	+	0.697035i	$0.245498\pi$
$618$		0			0
$619$	43.1362			1.73379			0.866896	−	0.498490i	$-0.166112\pi$
$619$	43.1362			1.73379			0.866896	+	0.498490i	$0.166112\pi$
$620$		0			0
$621$	−24.0793	−	9.97396i	−0.966268	−	0.400241i
$622$		0			0
$623$	18.6962			0.749049
$624$		0			0
$625$	−24.9029	+	2.20164i	−0.996115	+	0.0880656i
$626$		0			0
$627$	9.03042	+	3.74052i	0.360640	+	0.149382i
$628$		0			0
$629$	0.0516070	−	0.124590i	0.00205770	−	0.00496774i
$630$		0			0
$631$	−21.0721			−0.838869			−0.419434	−	0.907786i	$-0.637772\pi$
$631$	−21.0721			−0.838869			−0.419434	+	0.907786i	$0.637772\pi$
$632$		0			0
$633$	4.85131	+	4.85131i	0.192822	+	0.192822i
$634$		0			0
$635$	−0.626408	−	28.4104i	−0.0248582	−	1.12743i
$636$		0			0
$637$	−1.78457	−	4.30834i	−0.0707073	−	0.170702i
$638$		0			0
$639$	6.34558	+	2.62842i	0.251027	+	0.103979i
$640$		0			0
$641$	−13.7244	−	5.68483i	−0.542081	−	0.224537i	0.0948041	−	0.995496i	$-0.469778\pi$
$641$	−13.7244	−	5.68483i	−0.542081	−	0.224537i	−0.636885	+	0.770959i	$0.719778\pi$
$642$		0			0
$643$	3.08761	−	7.45415i	0.121763	−	0.293963i	−0.851231	−	0.524791i	$-0.824143\pi$
$643$	3.08761	−	7.45415i	0.121763	−	0.293963i	0.972995	+	0.230828i	$0.0741435\pi$
$644$		0			0
$645$	−10.6841	+	4.70402i	−0.420685	+	0.185220i
$646$		0			0
$647$	−30.7649			−1.20949			−0.604747	−	0.796418i	$-0.706726\pi$
$647$	−30.7649			−1.20949			−0.604747	+	0.796418i	$0.706726\pi$
$648$		0			0
$649$	−18.5830	+	7.69733i	−0.729447	+	0.302147i
$650$		0			0
$651$	−10.1153	−	10.1153i	−0.396448	−	0.396448i
$652$		0			0
$653$	−17.3828	+	41.9657i	−0.680240	+	1.64225i	0.0833314	+	0.996522i	$0.473444\pi$
$653$	−17.3828	+	41.9657i	−0.680240	+	1.64225i	−0.763572	+	0.645723i	$0.776556\pi$
$654$		0			0
$655$	20.5804	−	0.453768i	0.804144	−	0.0177302i
$656$		0			0
$657$	−3.95282	+	3.95282i	−0.154214	+	0.154214i
$658$		0			0
$659$	13.8053	+	33.3290i	0.537779	+	1.29831i	0.926270	+	0.376861i	$0.122997\pi$
$659$	13.8053	+	33.3290i	0.537779	+	1.29831i	−0.388491	+	0.921453i	$0.627003\pi$
$660$		0			0
$661$	−1.38851	+	1.38851i	−0.0540066	+	0.0540066i	−0.733594	−	0.679588i	$-0.762159\pi$
$661$	−1.38851	+	1.38851i	−0.0540066	+	0.0540066i	0.679588	+	0.733594i	$0.262159\pi$
$662$		0			0
$663$	−19.9060	−	8.24535i	−0.773086	−	0.320223i
$664$		0			0
$665$	0.373546	+	16.9420i	0.0144855	+	0.656982i
$666$		0			0
$667$	4.05847	+	1.68107i	0.157145	+	0.0650915i
$668$		0			0
$669$	1.15570	+	2.79011i	0.0446820	+	0.107872i
$670$		0			0
$671$	1.41309	−	3.41150i	0.0545518	−	0.131700i
$672$		0			0
$673$	−8.80234	−	21.2507i	−0.339305	−	0.819155i	−0.997783	−	0.0665550i	$-0.978799\pi$
$673$	−8.80234	−	21.2507i	−0.339305	−	0.819155i	0.658477	−	0.752600i	$-0.271201\pi$
$674$		0			0
$675$	21.6525	−	10.1088i	0.833406	−	0.389087i
$676$		0			0
$677$		−	40.5460i		−	1.55831i	−0.626831	−	0.779155i	$-0.715648\pi$
$677$		−	40.5460i		−	1.55831i	0.626831	−	0.779155i	$-0.284352\pi$
$678$		0			0
$679$	34.7925			1.33521
$680$		0			0
$681$			35.7551i			1.37014i
$682$		0			0
$683$	6.61730	−	2.74098i	0.253204	−	0.104881i	−0.252471	−	0.967604i	$-0.581243\pi$
$683$	6.61730	−	2.74098i	0.253204	−	0.104881i	0.505675	+	0.862724i	$0.331243\pi$
$684$		0			0
$685$	17.3371	+	6.73747i	0.662416	+	0.257425i
$686$		0			0
$687$	−23.2932	−	23.2932i	−0.888691	−	0.888691i
$688$		0			0
$689$	−1.29411	+	1.29411i	−0.0493018	+	0.0493018i
$690$		0			0
$691$	−16.9315	+	40.8763i	−0.644105	+	1.55501i	0.176987	+	0.984213i	$0.443365\pi$
$691$	−16.9315	+	40.8763i	−0.644105	+	1.55501i	−0.821093	+	0.570795i	$0.806635\pi$
$692$		0			0
$693$	0.982039	+	0.982039i	0.0373046	+	0.0373046i
$694$		0			0
$695$	5.35182	−	5.59314i	0.203006	−	0.212160i
$696$		0			0
$697$	−32.0112	−	14.0970i	−1.21251	−	0.533962i
$698$		0			0
$699$	14.8217	−	14.8217i	0.560609	−	0.560609i
$700$		0			0
$701$			45.5000i			1.71851i	0.511547	+	0.859255i	$0.329072\pi$
$701$			45.5000i			1.71851i	−0.511547	+	0.859255i	$0.670928\pi$
$702$		0			0
$703$	−0.0326258	−	0.0787656i	−0.00123050	−	0.00297070i
$704$		0			0
$705$	−5.15504	−	4.93262i	−0.194150	−	0.185773i
$706$		0			0
$707$	−2.99648	+	2.99648i	−0.112694	+	0.112694i
$708$		0			0
$709$	33.8133	−	14.0059i	1.26989	−	0.526004i	0.356956	−	0.934121i	$-0.383815\pi$
$709$	33.8133	−	14.0059i	1.26989	−	0.526004i	0.912929	+	0.408117i	$0.133815\pi$
$710$		0			0
$711$	−4.02321	−	1.66647i	−0.150882	−	0.0624975i
$712$		0			0
$713$	−13.6064	−	13.6064i	−0.509564	−	0.509564i
$714$		0			0
$715$	−5.05643	+	5.28443i	−0.189100	+	0.197626i
$716$		0			0
$717$	−44.8752			−1.67590
$718$		0			0
$719$	6.34398	+	2.62776i	0.236591	+	0.0979991i	0.497829	−	0.867275i	$-0.334131\pi$
$719$	6.34398	+	2.62776i	0.236591	+	0.0979991i	−0.261238	+	0.965274i	$0.584131\pi$
$720$		0			0
$721$	−9.87889	+	23.8497i	−0.367909	+	0.888211i
$722$		0			0
$723$	−9.33270	−	22.5311i	−0.347087	−	0.837942i
$724$		0			0
$725$	−3.64945	+	1.70380i	−0.135537	+	0.0632775i
$726$		0			0
$727$	12.6052	−	30.4317i	0.467502	−	1.12865i	−0.497748	−	0.867322i	$-0.665840\pi$
$727$	12.6052	−	30.4317i	0.467502	−	1.12865i	0.965250	−	0.261328i	$-0.0841604\pi$
$728$		0			0
$729$	−15.7889	+	15.7889i	−0.584773	+	0.584773i
$730$		0			0
$731$	−5.90734	−	14.2616i	−0.218491	−	0.527483i
$732$		0			0
$733$			18.6732i			0.689711i	0.938656	+	0.344855i	$0.112072\pi$
$733$			18.6732i			0.689711i	−0.938656	+	0.344855i	$0.887928\pi$
$734$		0			0
$735$	3.26840	−	8.41037i	0.120557	−	0.310221i
$736$		0			0
$737$	−12.9275	−	12.9275i	−0.476191	−	0.476191i
$738$		0			0
$739$			19.1830i			0.705659i	0.935688	+	0.352829i	$0.114780\pi$
$739$			19.1830i			0.705659i	−0.935688	+	0.352829i	$0.885220\pi$
$740$		0			0
$741$	−12.5845	+	5.21268i	−0.462304	+	0.191493i
$742$		0			0
$743$	−33.0297			−1.21174			−0.605871	−	0.795563i	$-0.707175\pi$
$743$	−33.0297			−1.21174			−0.605871	+	0.795563i	$0.707175\pi$
$744$		0			0
$745$	−25.6488	+	11.2928i	−0.939701	+	0.413734i
$746$		0			0
$747$			3.27294i			0.119751i
$748$		0			0
$749$	5.00472	−	2.07302i	0.182869	−	0.0757467i
$750$		0			0
$751$	−33.5347	+	13.8905i	−1.22370	+	0.506872i	−0.898583	−	0.438803i	$-0.855403\pi$
$751$	−33.5347	+	13.8905i	−1.22370	+	0.506872i	−0.325114	+	0.945675i	$0.605403\pi$
$752$		0			0
$753$	14.9290	−	6.18380i	0.544043	−	0.225350i
$754$		0			0
$755$	1.46919	−	3.78057i	0.0534692	−	0.137589i
$756$		0			0
$757$	−10.3527	+	4.28824i	−0.376276	+	0.155859i	−0.562803	−	0.826591i	$-0.690277\pi$
$757$	−10.3527	+	4.28824i	−0.376276	+	0.155859i	0.186527	+	0.982450i	$0.440277\pi$
$758$		0			0
$759$	10.9143	+	10.9143i	0.396166	+	0.396166i
$760$		0			0
$761$			19.6909i			0.713796i	0.934143	+	0.356898i	$0.116166\pi$
$761$			19.6909i			0.713796i	−0.934143	+	0.356898i	$0.883834\pi$
$762$		0			0
$763$	−11.5025	+	11.5025i	−0.416419	+	0.416419i
$764$		0			0
$765$	−2.03323	−	4.61800i	−0.0735115	−	0.166964i
$766$		0			0
$767$	10.7268	−	25.8967i	0.387322	−	0.935077i
$768$		0			0
$769$	38.1078			1.37420			0.687102	−	0.726561i	$-0.258883\pi$
$769$	38.1078			1.37420			0.687102	+	0.726561i	$0.258883\pi$
$770$		0			0
$771$	23.4559	+	23.4559i	0.844743	+	0.844743i
$772$		0			0
$773$	15.8079	−	6.54786i	0.568572	−	0.235510i	−0.0798298	−	0.996809i	$-0.525438\pi$
$773$	15.8079	−	6.54786i	0.568572	−	0.235510i	0.648402	+	0.761298i	$0.275438\pi$
$774$		0			0
$775$	17.6252	−	0.777596i	0.633115	−	0.0279321i
$776$		0			0
$777$		−	0.100087i		−	0.00359059i
$778$		0			0
$779$	−20.6118	+	8.00818i	−0.738494	+	0.286923i
$780$		0			0
$781$	18.0120	+	18.0120i	0.644521	+	0.644521i
$782$		0			0
$783$	2.72217	−	2.72217i	0.0972823	−	0.0972823i
$784$		0			0
$785$	−8.45939	−	19.2135i	−0.301929	−	0.685760i
$786$		0			0
$787$			29.1395i			1.03871i	0.854559	+	0.519355i	$0.173828\pi$
$787$			29.1395i			1.03871i	−0.854559	+	0.519355i	$0.826172\pi$
$788$		0			0
$789$			27.2275i			0.969323i
$790$		0			0
$791$	−13.6292	−	32.9039i	−0.484600	−	1.16993i
$792$		0			0
$793$	1.96924	+	4.75418i	0.0699299	+	0.168826i
$794$		0			0
$795$	−3.54034	+	0.0780593i	−0.125563	+	0.00276848i
$796$		0			0
$797$	8.40058	−	8.40058i	0.297564	−	0.297564i	−0.542495	−	0.840059i	$-0.682520\pi$
$797$	8.40058	−	8.40058i	0.297564	−	0.297564i	0.840059	+	0.542495i	$0.182520\pi$
$798$		0			0
$799$	6.67124	−	6.67124i	0.236011	−	0.236011i
$800$		0			0
$801$	−1.34681	+	3.25148i	−0.0475871	+	0.114885i
$802$		0			0
$803$	−19.1540	+	7.93385i	−0.675930	+	0.279979i
$804$		0			0
$805$	−9.69325	+	24.9430i	−0.341642	+	0.879125i
$806$		0			0
$807$	30.3460	+	12.5697i	1.06823	+	0.442475i
$808$		0			0
$809$	3.26868	+	7.89129i	0.114921	+	0.277443i	0.970866	−	0.239623i	$-0.0770240\pi$
$809$	3.26868	+	7.89129i	0.114921	+	0.277443i	−0.855945	+	0.517066i	$0.827024\pi$
$810$		0			0
$811$	−27.3262	−	27.3262i	−0.959553	−	0.959553i	0.0396598	−	0.999213i	$-0.487373\pi$
$811$	−27.3262	−	27.3262i	−0.959553	−	0.959553i	−0.999213	+	0.0396598i	$0.987373\pi$
$812$		0			0
$813$	−12.7478	+	30.7759i	−0.447085	+	1.07936i
$814$		0			0
$815$	21.3838	−	0.471481i	0.749041	−	0.0165153i
$816$		0			0
$817$	−9.01613	−	3.73460i	−0.315434	−	0.130657i
$818$		0			0
$819$	−1.93541			−0.0676287
$820$		0			0
$821$	−16.0691			−0.560816			−0.280408	−	0.959881i	$-0.590470\pi$
$821$	−16.0691			−0.560816			−0.280408	+	0.959881i	$0.590470\pi$
$822$		0			0
$823$	−23.1536	−	9.59055i	−0.807085	−	0.334306i	−0.0592949	−	0.998241i	$-0.518885\pi$
$823$	−23.1536	−	9.59055i	−0.807085	−	0.334306i	−0.747790	+	0.663935i	$0.768885\pi$
$824$		0			0
$825$	−14.1380	+	0.623747i	−0.492222	+	0.0217161i
$826$		0			0
$827$	17.4959	−	42.2388i	0.608391	−	1.46879i	−0.256358	−	0.966582i	$-0.582523\pi$
$827$	17.4959	−	42.2388i	0.608391	−	1.46879i	0.864749	−	0.502204i	$-0.167477\pi$
$828$		0			0
$829$	20.0332	+	20.0332i	0.695782	+	0.695782i	0.963498	−	0.267716i	$-0.0862688\pi$
$829$	20.0332	+	20.0332i	0.695782	+	0.695782i	−0.267716	+	0.963498i	$0.586269\pi$
$830$		0			0
$831$	17.6757	+	42.6728i	0.613162	+	1.48030i
$832$		0			0
$833$	11.0233	+	4.56602i	0.381936	+	0.158203i
$834$		0			0
$835$	19.7026	−	8.67471i	0.681836	−	0.300201i
$836$		0			0
$837$	−15.5796	+	6.45328i	−0.538510	+	0.223058i
$838$		0			0
$839$	−8.16794	+	19.7191i	−0.281989	+	0.680781i	−0.999882	−	0.0153726i	$-0.995107\pi$
$839$	−8.16794	+	19.7191i	−0.281989	+	0.680781i	0.717893	+	0.696153i	$0.245107\pi$
$840$		0			0
$841$	20.0473	−	20.0473i	0.691286	−	0.691286i
$842$		0			0
$843$	27.5046	−	27.5046i	0.947310	−	0.947310i
$844$		0			0
$845$	0.416098	+	18.8719i	0.0143142	+	0.649213i
$846$		0			0
$847$	−7.26664	−	17.5432i	−0.249685	−	0.602793i
$848$		0			0
$849$	−5.24320	−	12.6582i	−0.179946	−	0.434428i
$850$		0			0
$851$		−	0.134630i		−	0.00461506i
$852$		0			0
$853$			41.9999i			1.43805i	0.694985	+	0.719024i	$0.255411\pi$
$853$			41.9999i			1.43805i	−0.694985	+	0.719024i	$0.744589\pi$
$854$		0			0
$855$	−2.97331	−	1.15547i	−0.101685	−	0.0395164i
$856$		0			0
$857$	29.6838	−	29.6838i	1.01398	−	1.01398i	0.0140787	−	0.999901i	$-0.495518\pi$
$857$	29.6838	−	29.6838i	1.01398	−	1.01398i	0.999901	−	0.0140787i	$-0.00448153\pi$
$858$		0			0
$859$	−16.7773	−	16.7773i	−0.572435	−	0.572435i	0.360373	−	0.932808i	$-0.382649\pi$
$859$	−16.7773	−	16.7773i	−0.572435	−	0.572435i	−0.932808	+	0.360373i	$0.882649\pi$
$860$		0			0
$861$	−25.9533	−	0.574292i	−0.884486	−	0.0195718i
$862$		0			0
$863$		−	6.88230i		−	0.234276i	−0.993116	−	0.117138i	$-0.962628\pi$
$863$		−	6.88230i		−	0.234276i	0.993116	−	0.117138i	$-0.0373720\pi$
$864$		0			0
$865$	1.03348	+	0.988891i	0.0351394	+	0.0336233i
$866$		0			0
$867$	21.9157	−	9.07777i	0.744295	−	0.308297i
$868$		0			0
$869$	−11.4200	−	11.4200i	−0.387396	−	0.387396i
$870$		0			0
$871$	25.4777			0.863277
$872$		0			0
$873$	−2.50632	+	6.05080i	−0.0848262	+	0.204788i
$874$		0			0
$875$	−10.8667	−	21.9974i	−0.367360	−	0.743649i
$876$		0			0
$877$	−9.35790	+	9.35790i	−0.315994	+	0.315994i	−0.847226	−	0.531232i	$-0.821729\pi$
$877$	−9.35790	+	9.35790i	−0.315994	+	0.315994i	0.531232	+	0.847226i	$0.321729\pi$
$878$		0			0
$879$			33.3018i			1.12324i
$880$		0			0
$881$	−1.08279	−	1.08279i	−0.0364803	−	0.0364803i	0.688631	−	0.725112i	$-0.258212\pi$
$881$	−1.08279	−	1.08279i	−0.0364803	−	0.0364803i	−0.725112	+	0.688631i	$0.758212\pi$
$882$		0			0
$883$	0.562341	−	0.232929i	0.0189243	−	0.00783869i	−0.373201	−	0.927750i	$-0.621740\pi$
$883$	0.562341	−	0.232929i	0.0189243	−	0.00783869i	0.392125	+	0.919912i	$0.371740\pi$
$884$		0			0
$885$	49.6384	−	21.8550i	1.66858	−	0.734647i
$886$		0			0
$887$	−42.7964	+	17.7269i	−1.43696	+	0.595210i	−0.959060	−	0.283202i	$-0.908603\pi$
$887$	−42.7964	+	17.7269i	−1.43696	+	0.595210i	−0.477904	+	0.878412i	$0.658603\pi$
$888$		0			0
$889$	25.7660	−	10.6726i	0.864163	−	0.357948i
$890$		0			0
$891$	14.2512	−	5.90305i	0.477434	−	0.197760i
$892$		0			0
$893$		−	5.96450i		−	0.199594i
$894$		0			0
$895$	1.15012	+	2.61224i	0.0384444	+	0.0873174i
$896$		0			0
$897$	−21.5101			−0.718201
$898$		0			0
$899$	2.62588	−	1.08768i	0.0875781	−	0.0362760i
$900$		0			0
$901$		−	4.68264i		−	0.156001i
$902$		0			0
$903$	−8.10111	−	8.10111i	−0.269588	−	0.269588i
$904$		0			0
$905$	7.91420	+	17.9753i	0.263077	+	0.597518i
$906$		0			0
$907$			41.5613i			1.38002i	0.723800	+	0.690009i	$0.242394\pi$
$907$			41.5613i			1.38002i	−0.723800	+	0.690009i	$0.757606\pi$
$908$		0			0
$909$	−0.305266	−	0.736976i	−0.0101250	−	0.0244440i
$910$		0			0
$911$	−24.1303	+	24.1303i	−0.799472	+	0.799472i	−0.983012	−	0.183540i	$-0.941244\pi$
$911$	−24.1303	+	24.1303i	−0.799472	+	0.799472i	0.183540	+	0.983012i	$0.441244\pi$
$912$		0			0
$913$	−4.64515	+	11.2144i	−0.153732	+	0.371142i
$914$		0			0
$915$	−3.60663	+	9.28071i	−0.119232	+	0.306811i
$916$		0			0
$917$	7.73121	+	18.6648i	0.255307	+	0.616366i
$918$		0			0
$919$	−3.34841	+	8.08377i	−0.110454	+	0.266659i	−0.969435	−	0.245348i	$-0.921098\pi$
$919$	−3.34841	+	8.08377i	−0.110454	+	0.266659i	0.858981	+	0.512007i	$0.171098\pi$
$920$		0			0
$921$	6.08670	+	2.52119i	0.200564	+	0.0830762i
$922$		0			0
$923$	−35.4983			−1.16844
$924$		0			0
$925$	0.0910441	+	0.0833501i	0.00299351	+	0.00274053i
$926$		0			0
$927$	−3.43609	−	3.43609i	−0.112856	−	0.112856i
$928$		0			0
$929$	−20.2055	−	8.36941i	−0.662922	−	0.274591i	0.0257455	−	0.999669i	$-0.491804\pi$
$929$	−20.2055	−	8.36941i	−0.662922	−	0.274591i	−0.688668	+	0.725077i	$0.741804\pi$
$930$		0			0
$931$	6.96893	−	2.88662i	0.228397	−	0.0946053i
$932$		0			0
$933$	24.7349	−	24.7349i	0.809783	−	0.809783i
$934$		0			0
$935$	−0.412501	−	18.7088i	−0.0134902	−	0.611842i
$936$		0			0
$937$	−20.3564	−	49.1446i	−0.665013	−	1.60548i	−0.789845	−	0.613306i	$-0.789839\pi$
$937$	−20.3564	−	49.1446i	−0.665013	−	1.60548i	0.124832	−	0.992178i	$-0.460161\pi$
$938$		0			0
$939$			14.5416i			0.474546i
$940$		0			0
$941$	−32.0022	+	32.0022i	−1.04324	+	1.04324i	−0.0442201	+	0.999022i	$0.514080\pi$
$941$	−32.0022	+	32.0022i	−1.04324	+	1.04324i	−0.999022	+	0.0442201i	$0.985920\pi$
$942$		0			0
$943$	−34.9107	−	0.772500i	−1.13685	−	0.0251561i
$944$		0			0
$945$	16.9443	+	16.2132i	0.551199	+	0.527417i
$946$		0			0
$947$	−9.41121	−	9.41121i	−0.305823	−	0.305823i	0.537464	−	0.843287i	$-0.319383\pi$
$947$	−9.41121	−	9.41121i	−0.305823	−	0.305823i	−0.843287	+	0.537464i	$0.819383\pi$
$948$		0			0
$949$	11.0564	−	26.6925i	0.358906	−	0.866475i
$950$		0			0
$951$	−4.44635	+	4.44635i	−0.144183	+	0.144183i
$952$		0			0
$953$	2.23847	+	2.23847i	0.0725111	+	0.0725111i	0.742432	−	0.669921i	$-0.233672\pi$
$953$	2.23847	+	2.23847i	0.0725111	+	0.0725111i	−0.669921	+	0.742432i	$0.733672\pi$
$954$		0			0
$955$	8.89619	−	3.91684i	0.287874	−	0.126746i
$956$		0			0
$957$	−2.10635	+	0.872478i	−0.0680886	+	0.0282032i
$958$		0			0
$959$			18.2543i			0.589463i
$960$		0			0
$961$	18.5500			0.598386
$962$		0			0
$963$			1.01971i			0.0328597i
$964$		0			0
$965$	−6.68107	−	15.1745i	−0.215071	−	0.488484i
$966$		0			0
$967$	−20.6775	−	49.9199i	−0.664944	−	1.60532i	−0.789958	−	0.613161i	$-0.789898\pi$
$967$	−20.6775	−	49.9199i	−0.664944	−	1.60532i	0.125014	−	0.992155i	$-0.460102\pi$
$968$		0			0
$969$	13.3372	−	32.1989i	0.428453	−	1.03438i
$970$		0			0
$971$	19.7535	+	47.6892i	0.633921	+	1.53042i	0.834654	+	0.550774i	$0.185667\pi$
$971$	19.7535	+	47.6892i	0.633921	+	1.53042i	−0.200734	+	0.979646i	$0.564333\pi$
$972$		0			0
$973$	7.01888	+	2.90732i	0.225015	+	0.0932043i
$974$		0			0
$975$	13.3170	−	14.5463i	0.426485	−	0.465854i
$976$		0			0
$977$	41.8857	+	17.3496i	1.34004	+	0.555063i	0.933503	−	0.358570i	$-0.116736\pi$
$977$	41.8857	+	17.3496i	1.34004	+	0.555063i	0.406538	+	0.913634i	$0.366736\pi$
$978$		0			0
$979$	−9.22939	+	9.22939i	−0.294972	+	0.294972i
$980$		0			0
$981$	−1.17182	−	2.82901i	−0.0374132	−	0.0903234i
$982$		0			0
$983$	36.1887	−	36.1887i	1.15424	−	1.15424i	0.168548	−	0.985693i	$-0.446092\pi$
$983$	36.1887	−	36.1887i	1.15424	−	1.15424i	0.985693	−	0.168548i	$-0.0539079\pi$
$984$		0			0
$985$	−17.1679	−	16.4272i	−0.547014	−	0.523413i
$986$		0			0
$987$	2.67959	−	6.46910i	0.0852923	−	0.205914i
$988$		0			0
$989$	−10.8971	−	10.8971i	−0.346507	−	0.346507i
$990$		0			0
$991$	−13.6566	+	5.65675i	−0.433816	+	0.179692i	−0.588895	−	0.808210i	$-0.700437\pi$
$991$	−13.6566	+	5.65675i	−0.433816	+	0.179692i	0.155079	+	0.987902i	$0.450437\pi$
$992$		0			0
$993$	1.57184			0.0498808
$994$		0			0
$995$	3.15892	+	7.17474i	0.100144	+	0.227454i
$996$		0			0
$997$	−23.7745	+	57.3967i	−0.752945	+	1.81777i	−0.210699	+	0.977551i	$0.567574\pi$
$997$	−23.7745	+	57.3967i	−0.752945	+	1.81777i	−0.542246	+	0.840220i	$0.682426\pi$
$998$		0			0
$999$	−0.109003	−	0.0451507i	−0.00344871	−	0.00142850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.17	✓	84
5.2	odd	4		820.2.y.a.437.17	yes	84
41.38	odd	8		820.2.y.a.653.17	yes	84
205.202	even	8	inner	820.2.x.a.817.17	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.17	✓	84	1.1	even	1	trivial
820.2.x.a.817.17	yes	84	205.202	even	8	inner
820.2.y.a.437.17	yes	84	5.2	odd	4
820.2.y.a.653.17	yes	84	41.38	odd	8

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.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70683 + 0.706990i) q^{3} +(-1.61561 - 1.54590i) q^{5} +(0.839794 - 2.02744i) q^{7} +(0.292099 + 0.292099i) q^{9} +(0.586281 + 1.41541i) q^{11} +(-1.97247 - 0.817025i) q^{13} +(-1.66462 - 3.78080i) q^{15} +(5.04679 - 2.09045i) q^{17} +(1.32157 - 3.19056i) q^{19} +(2.86676 - 2.86676i) q^{21} +(3.85618 - 3.85618i) q^{23} +(0.220378 + 4.99514i) q^{25} +(-1.82892 - 4.41541i) q^{27} +(0.308258 + 0.744201i) q^{29} -3.52846i q^{31} +2.83035i q^{33} +(-4.49100 + 1.97731i) q^{35} +(0.0174564 - 0.0174564i) q^{37} +(-2.78904 - 2.78904i) q^{39} +(-4.42642 - 4.62675i) q^{41} -2.82587i q^{43} +(-0.0203612 - 0.923472i) q^{45} +(1.59565 - 0.660939i) q^{47} +(1.54448 + 1.54448i) q^{49} +10.0919 q^{51} +(0.328043 - 0.791967i) q^{53} +(1.24088 - 3.19308i) q^{55} +(4.51140 - 4.51140i) q^{57} +13.1291i q^{59} +(-1.70431 - 1.70431i) q^{61} +(0.837515 - 0.346910i) q^{63} +(1.92370 + 4.36924i) q^{65} +(-11.0250 + 4.56671i) q^{67} +(9.30812 - 3.85555i) q^{69} +(15.3613 - 6.36284i) q^{71} +13.5325i q^{73} +(-3.15537 + 8.68164i) q^{75} +3.36201 q^{77} +(-9.73933 + 4.03416i) q^{79} -10.0686i q^{81} +(5.60246 + 5.60246i) q^{83} +(-11.3853 - 4.42449i) q^{85} +1.48816i q^{87} +(3.26033 + 7.87112i) q^{89} +(-3.31294 + 3.31294i) q^{91} +(2.49459 - 6.02247i) q^{93} +(-7.06744 + 3.11168i) q^{95} +(6.06726 + 14.6477i) q^{97} +(-0.242187 + 0.584691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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