LMFDB - Embedded newform 864.2.y.c.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.1
Character	$\chi$	$=$	864.385
Dual form			864.2.y.c.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69762 + 0.343652i) q^{3} +(-0.494020 - 2.80173i) q^{5} +(1.80000 + 1.51038i) q^{7} +(2.76381 - 1.16678i) q^{9} +O(q^{10})$	\(q+(-1.69762 + 0.343652i) q^{3} +(-0.494020 - 2.80173i) q^{5} +(1.80000 + 1.51038i) q^{7} +(2.76381 - 1.16678i) q^{9} +(0.335277 - 1.90145i) q^{11} +(-1.42662 - 0.519249i) q^{13} +(1.80147 + 4.58649i) q^{15} +(-0.970777 - 1.68144i) q^{17} +(-2.56132 + 4.43634i) q^{19} +(-3.57476 - 1.94548i) q^{21} +(3.09518 - 2.59716i) q^{23} +(-2.90715 + 1.05812i) q^{25} +(-4.29092 + 2.93053i) q^{27} +(4.37469 - 1.59226i) q^{29} +(-0.454752 + 0.381582i) q^{31} +(0.0842647 + 3.34316i) q^{33} +(3.34244 - 5.78928i) q^{35} +(-5.82763 - 10.0938i) q^{37} +(2.60030 + 0.391224i) q^{39} +(-10.2193 - 3.71952i) q^{41} +(1.00136 - 5.67901i) q^{43} +(-4.63437 - 7.16702i) q^{45} +(-0.283878 - 0.238202i) q^{47} +(-0.256778 - 1.45626i) q^{49} +(2.22584 + 2.52082i) q^{51} +1.31215 q^{53} -5.49298 q^{55} +(2.82359 - 8.41141i) q^{57} +(-2.65572 - 15.0613i) q^{59} +(6.99830 + 5.87227i) q^{61} +(6.73715 + 2.07420i) q^{63} +(-0.750012 + 4.25353i) q^{65} +(-11.1398 - 4.05456i) q^{67} +(-4.36191 + 5.47265i) q^{69} +(-0.0203493 - 0.0352460i) q^{71} +(5.90472 - 10.2273i) q^{73} +(4.57161 - 2.79533i) q^{75} +(3.47542 - 2.91622i) q^{77} +(-11.1731 + 4.06668i) q^{79} +(6.27726 - 6.44950i) q^{81} +(-2.50586 + 0.912059i) q^{83} +(-4.23134 + 3.55052i) q^{85} +(-6.87937 + 4.20642i) q^{87} +(-2.72618 + 4.72188i) q^{89} +(-1.78367 - 3.08940i) q^{91} +(0.640863 - 0.804056i) q^{93} +(13.6948 + 4.98448i) q^{95} +(-0.470518 + 2.66844i) q^{97} +(-1.29193 - 5.64644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	−1.69762	+	0.343652i	−0.980120	+	0.198407i
$3$	−1.69762	+	0.343652i	−0.980120	+	0.198407i
$4$		0			0
$5$	−0.494020	−	2.80173i	−0.220932	−	1.25297i	−0.870310	−	0.492504i	$-0.836082\pi$
$5$	−0.494020	−	2.80173i	−0.220932	−	1.25297i	0.649378	−	0.760466i	$-0.275029\pi$
$6$		0			0
$7$	1.80000	+	1.51038i	0.680338	+	0.570871i	0.916105	−	0.400938i	$-0.131316\pi$
$7$	1.80000	+	1.51038i	0.680338	+	0.570871i	−0.235767	+	0.971810i	$0.575760\pi$
$8$		0			0
$9$	2.76381	−	1.16678i	0.921269	−	0.388926i
$10$		0			0
$11$	0.335277	−	1.90145i	0.101090	−	0.573309i	−0.891620	−	0.452784i	$-0.850431\pi$
$11$	0.335277	−	1.90145i	0.101090	−	0.573309i	0.992710	−	0.120526i	$-0.0384580\pi$
$12$		0			0
$13$	−1.42662	−	0.519249i	−0.395674	−	0.144014i	0.136517	−	0.990638i	$-0.456409\pi$
$13$	−1.42662	−	0.519249i	−0.395674	−	0.144014i	−0.532191	+	0.846624i	$0.678631\pi$
$14$		0			0
$15$	1.80147	+	4.58649i	0.465139	+	1.18423i
$16$		0			0
$17$	−0.970777	−	1.68144i	−0.235448	−	0.407808i	0.723955	−	0.689847i	$-0.242322\pi$
$17$	−0.970777	−	1.68144i	−0.235448	−	0.407808i	−0.959403	+	0.282039i	$0.908989\pi$
$18$		0			0
$19$	−2.56132	+	4.43634i	−0.587607	+	1.01777i	0.406937	+	0.913456i	$0.366597\pi$
$19$	−2.56132	+	4.43634i	−0.587607	+	1.01777i	−0.994545	+	0.104310i	$0.966737\pi$
$20$		0			0
$21$	−3.57476	−	1.94548i	−0.780077	−	0.424538i
$22$		0			0
$23$	3.09518	−	2.59716i	0.645390	−	0.541546i	−0.260278	−	0.965534i	$-0.583814\pi$
$23$	3.09518	−	2.59716i	0.645390	−	0.541546i	0.905668	+	0.423987i	$0.139370\pi$
$24$		0			0
$25$	−2.90715	+	1.05812i	−0.581431	+	0.211623i
$26$		0			0
$27$	−4.29092	+	2.93053i	−0.825788	+	0.563981i
$28$		0			0
$29$	4.37469	−	1.59226i	0.812360	−	0.295675i	0.0977619	−	0.995210i	$-0.468832\pi$
$29$	4.37469	−	1.59226i	0.812360	−	0.295675i	0.714599	+	0.699535i	$0.246609\pi$
$30$		0			0
$31$	−0.454752	+	0.381582i	−0.0816758	+	0.0685341i	−0.682711	−	0.730688i	$-0.739199\pi$
$31$	−0.454752	+	0.381582i	−0.0816758	+	0.0685341i	0.601036	+	0.799222i	$0.294755\pi$
$32$		0			0
$33$	0.0842647	+	3.34316i	0.0146686	+	0.581969i
$34$		0			0
$35$	3.34244	−	5.78928i	0.564976	−	0.978567i
$36$		0			0
$37$	−5.82763	−	10.0938i	−0.958057	−	1.65940i	−0.727212	−	0.686413i	$-0.759184\pi$
$37$	−5.82763	−	10.0938i	−0.958057	−	1.65940i	−0.230845	−	0.972991i	$-0.574149\pi$
$38$		0			0
$39$	2.60030	+	0.391224i	0.416382	+	0.0626459i
$40$		0			0
$41$	−10.2193	−	3.71952i	−1.59599	−	0.580892i	−0.617386	−	0.786660i	$-0.711808\pi$
$41$	−10.2193	−	3.71952i	−1.59599	−	0.580892i	−0.978601	+	0.205768i	$0.934031\pi$
$42$		0			0
$43$	1.00136	−	5.67901i	0.152706	−	0.866040i	−0.808147	−	0.588981i	$-0.799529\pi$
$43$	1.00136	−	5.67901i	0.152706	−	0.866040i	0.960853	−	0.277059i	$-0.0893597\pi$
$44$		0			0
$45$	−4.63437	−	7.16702i	−0.690851	−	1.06840i
$46$		0			0
$47$	−0.283878	−	0.238202i	−0.0414079	−	0.0347454i	0.621849	−	0.783137i	$-0.286382\pi$
$47$	−0.283878	−	0.238202i	−0.0414079	−	0.0347454i	−0.663257	+	0.748392i	$0.730826\pi$
$48$		0			0
$49$	−0.256778	−	1.45626i	−0.0366826	−	0.208037i
$50$		0			0
$51$	2.22584	+	2.52082i	0.311679	+	0.352986i
$52$		0			0
$53$	1.31215			0.180238			0.0901188	−	0.995931i	$-0.471275\pi$
$53$	1.31215			0.180238			0.0901188	+	0.995931i	$0.471275\pi$
$54$		0			0
$55$	−5.49298			−0.740674
$56$		0			0
$57$	2.82359	−	8.41141i	0.373993	−	1.11412i
$58$		0			0
$59$	−2.65572	−	15.0613i	−0.345745	−	1.96082i	−0.265858	−	0.964012i	$-0.585655\pi$
$59$	−2.65572	−	15.0613i	−0.345745	−	1.96082i	−0.0798872	−	0.996804i	$-0.525456\pi$
$60$		0			0
$61$	6.99830	+	5.87227i	0.896040	+	0.751867i	0.969412	−	0.245437i	$-0.0789316\pi$
$61$	6.99830	+	5.87227i	0.896040	+	0.751867i	−0.0733720	+	0.997305i	$0.523376\pi$
$62$		0			0
$63$	6.73715	+	2.07420i	0.848801	+	0.261325i
$64$		0			0
$65$	−0.750012	+	4.25353i	−0.0930276	+	0.527586i
$66$		0			0
$67$	−11.1398	−	4.05456i	−1.36095	−	0.495344i	−0.444599	−	0.895730i	$-0.646654\pi$
$67$	−11.1398	−	4.05456i	−1.36095	−	0.495344i	−0.916347	+	0.400386i	$0.868876\pi$
$68$		0			0
$69$	−4.36191	+	5.47265i	−0.525112	+	0.658830i
$70$		0			0
$71$	−0.0203493	−	0.0352460i	−0.00241501	−	0.00418293i	0.864815	−	0.502090i	$-0.167435\pi$
$71$	−0.0203493	−	0.0352460i	−0.00241501	−	0.00418293i	−0.867230	+	0.497907i	$0.834102\pi$
$72$		0			0
$73$	5.90472	−	10.2273i	0.691095	−	1.19701i	−0.280384	−	0.959888i	$-0.590462\pi$
$73$	5.90472	−	10.2273i	0.691095	−	1.19701i	0.971479	−	0.237124i	$-0.0762049\pi$
$74$		0			0
$75$	4.57161	−	2.79533i	0.527884	−	0.322776i
$76$		0			0
$77$	3.47542	−	2.91622i	0.396061	−	0.332335i
$78$		0			0
$79$	−11.1731	+	4.06668i	−1.25707	+	0.457538i	−0.882786	−	0.469775i	$-0.844335\pi$
$79$	−11.1731	+	4.06668i	−1.25707	+	0.457538i	−0.374288	+	0.927312i	$0.622113\pi$
$80$		0			0
$81$	6.27726	−	6.44950i	0.697473	−	0.716611i
$82$		0			0
$83$	−2.50586	+	0.912059i	−0.275054	+	0.100111i	−0.475864	−	0.879519i	$-0.657865\pi$
$83$	−2.50586	+	0.912059i	−0.275054	+	0.100111i	0.200810	+	0.979630i	$0.435642\pi$
$84$		0			0
$85$	−4.23134	+	3.55052i	−0.458953	+	0.385107i
$86$		0			0
$87$	−6.87937	+	4.20642i	−0.737546	+	0.450975i
$88$		0			0
$89$	−2.72618	+	4.72188i	−0.288975	+	0.500519i	−0.973565	−	0.228409i	$-0.926648\pi$
$89$	−2.72618	+	4.72188i	−0.288975	+	0.500519i	0.684591	+	0.728928i	$0.259981\pi$
$90$		0			0
$91$	−1.78367	−	3.08940i	−0.186979	−	0.323857i
$92$		0			0
$93$	0.640863	−	0.804056i	0.0664544	−	0.0833767i
$94$		0			0
$95$	13.6948	+	4.98448i	1.40505	+	0.511397i
$96$		0			0
$97$	−0.470518	+	2.66844i	−0.0477738	+	0.270939i	−0.999333	−	0.0365280i	$-0.988370\pi$
$97$	−0.470518	+	2.66844i	−0.0477738	+	0.270939i	0.951559	+	0.307467i	$0.0994813\pi$
$98$		0			0
$99$	−1.29193	−	5.64644i	−0.129844	−	0.567489i
$100$		0			0
$101$	14.2919	+	11.9923i	1.42210	+	1.19328i	0.950204	+	0.311628i	$0.100874\pi$
$101$	14.2919	+	11.9923i	1.42210	+	1.19328i	0.471895	+	0.881655i	$0.343570\pi$
$102$		0			0
$103$	−0.548727	−	3.11199i	−0.0540677	−	0.306633i	0.945766	−	0.324848i	$-0.105313\pi$
$103$	−0.548727	−	3.11199i	−0.0540677	−	0.306633i	−0.999834	+	0.0182143i	$0.994202\pi$
$104$		0			0
$105$	−3.68469	+	10.9766i	−0.359589	+	1.07121i
$106$		0			0
$107$	12.4984			1.20827			0.604135	−	0.796882i	$-0.293519\pi$
$107$	12.4984			1.20827			0.604135	+	0.796882i	$0.293519\pi$
$108$		0			0
$109$	11.5015			1.10164			0.550821	−	0.834623i	$-0.314315\pi$
$109$	11.5015			1.10164			0.550821	+	0.834623i	$0.314315\pi$
$110$		0			0
$111$	13.3618	+	15.1327i	1.26825	+	1.43633i
$112$		0			0
$113$	−1.17980	−	6.69097i	−0.110986	−	0.629433i	−0.988660	−	0.150174i	$-0.952017\pi$
$113$	−1.17980	−	6.69097i	−0.110986	−	0.629433i	0.877673	−	0.479259i	$-0.159095\pi$
$114$		0			0
$115$	−8.80563	−	7.38880i	−0.821129	−	0.689009i
$116$		0			0
$117$	−4.54876	+	0.229450i	−0.420533	+	0.0212127i
$118$		0			0
$119$	0.792208	−	4.49284i	0.0726216	−	0.411858i
$120$		0			0
$121$	6.83351	+	2.48719i	0.621228	+	0.226109i
$122$		0			0
$123$	18.6267	+	2.80244i	1.67951	+	0.252688i
$124$		0			0
$125$	−2.71162	−	4.69667i	−0.242535	−	0.420083i
$126$		0			0
$127$	1.23100	−	2.13215i	0.109233	−	0.189198i	−0.806226	−	0.591607i	$-0.798494\pi$
$127$	1.23100	−	2.13215i	0.109233	−	0.189198i	0.915460	+	0.402409i	$0.131827\pi$
$128$		0			0
$129$	0.251671	+	9.98490i	0.0221584	+	0.879121i
$130$		0			0
$131$	−14.8618	+	12.4705i	−1.29848	+	1.08955i	−0.308072	+	0.951363i	$0.599684\pi$
$131$	−14.8618	+	12.4705i	−1.29848	+	1.08955i	−0.990406	+	0.138189i	$0.955872\pi$
$132$		0			0
$133$	−11.3110	+	4.11685i	−0.980785	+	0.356976i
$134$		0			0
$135$	10.3303	+	10.5742i	0.889094	+	0.910086i
$136$		0			0
$137$	−0.773329	+	0.281469i	−0.0660699	+	0.0240475i	−0.374844	−	0.927088i	$-0.622304\pi$
$137$	−0.773329	+	0.281469i	−0.0660699	+	0.0240475i	0.308774	+	0.951136i	$0.400081\pi$
$138$		0			0
$139$	−7.91062	+	6.63780i	−0.670970	+	0.563011i	−0.913352	−	0.407170i	$-0.866516\pi$
$139$	−7.91062	+	6.63780i	−0.670970	+	0.563011i	0.242382	+	0.970181i	$0.422071\pi$
$140$		0			0
$141$	0.563775	+	0.306821i	0.0474784	+	0.0258390i
$142$		0			0
$143$	−1.46564	+	2.53857i	−0.122563	+	0.212286i
$144$		0			0
$145$	−6.62226	−	11.4701i	−0.549949	−	0.952539i
$146$		0			0
$147$	0.936358	+	2.38393i	0.0772295	+	0.196623i
$148$		0			0
$149$	−5.45293	−	1.98470i	−0.446721	−	0.162593i	0.108857	−	0.994057i	$-0.465281\pi$
$149$	−5.45293	−	1.98470i	−0.446721	−	0.162593i	−0.555578	+	0.831464i	$0.687503\pi$
$150$		0			0
$151$	−1.76312	+	9.99914i	−0.143480	+	0.813718i	0.825094	+	0.564995i	$0.191122\pi$
$151$	−1.76312	+	9.99914i	−0.143480	+	0.813718i	−0.968575	+	0.248723i	$0.919989\pi$
$152$		0			0
$153$	−4.64490	−	3.51448i	−0.375518	−	0.284129i
$154$		0			0
$155$	1.29374	+	1.08558i	0.103916	+	0.0871959i
$156$		0			0
$157$	4.12737	+	23.4075i	0.329400	+	1.86812i	0.476753	+	0.879037i	$0.341814\pi$
$157$	4.12737	+	23.4075i	0.329400	+	1.86812i	−0.147353	+	0.989084i	$0.547075\pi$
$158$		0			0
$159$	−2.22753	+	0.450922i	−0.176654	+	0.0357605i
$160$		0			0
$161$	9.49405			0.748236
$162$		0			0
$163$	−11.0691			−0.866999			−0.433499	−	0.901154i	$-0.642721\pi$
$163$	−11.0691			−0.866999			−0.433499	+	0.901154i	$0.642721\pi$
$164$		0			0
$165$	9.32498	−	1.88767i	0.725949	−	0.146955i
$166$		0			0
$167$	−2.50451	−	14.2038i	−0.193805	−	1.09912i	−0.914111	−	0.405464i	$-0.867110\pi$
$167$	−2.50451	−	14.2038i	−0.193805	−	1.09912i	0.720306	−	0.693656i	$-0.244001\pi$
$168$		0			0
$169$	−8.19294	−	6.87469i	−0.630226	−	0.528823i
$170$		0			0
$171$	−1.90278	+	15.2497i	−0.145509	+	1.16617i
$172$		0			0
$173$	−1.61523	+	9.16043i	−0.122804	+	0.696455i	0.859784	+	0.510657i	$0.170598\pi$
$173$	−1.61523	+	9.16043i	−0.122804	+	0.696455i	−0.982588	+	0.185797i	$0.940513\pi$
$174$		0			0
$175$	−6.83105	−	2.48630i	−0.516379	−	0.187947i
$176$		0			0
$177$	9.68423	+	24.6557i	0.727912	+	1.85324i
$178$		0			0
$179$	−2.32944	−	4.03471i	−0.174111	−	0.301568i	0.765743	−	0.643147i	$-0.222372\pi$
$179$	−2.32944	−	4.03471i	−0.174111	−	0.301568i	−0.939853	+	0.341579i	$0.889038\pi$
$180$		0			0
$181$	−6.93368	+	12.0095i	−0.515377	+	0.892658i	0.484464	+	0.874811i	$0.339015\pi$
$181$	−6.93368	+	12.0095i	−0.515377	+	0.892658i	−0.999841	+	0.0178473i	$0.994319\pi$
$182$		0			0
$183$	−13.8984	−	7.56389i	−1.02740	−	0.559139i
$184$		0			0
$185$	−25.4010	+	21.3140i	−1.86752	+	1.56703i
$186$		0			0
$187$	−3.52265	+	1.28214i	−0.257602	+	0.0937593i
$188$		0			0
$189$	−12.1499	−	1.20597i	−0.883775	−	0.0877214i
$190$		0			0
$191$	24.0328	−	8.74723i	1.73895	−	0.632927i	0.739751	−	0.672880i	$-0.234943\pi$
$191$	24.0328	−	8.74723i	1.73895	−	0.632927i	0.999202	+	0.0399533i	$0.0127209\pi$
$192$		0			0
$193$	9.68190	−	8.12408i	0.696918	−	0.584784i	−0.223977	−	0.974594i	$-0.571904\pi$
$193$	9.68190	−	8.12408i	0.696918	−	0.584784i	0.920895	+	0.389811i	$0.127460\pi$
$194$		0			0
$195$	−0.188499	−	7.47861i	−0.0134987	−	0.535554i
$196$		0			0
$197$	11.3194	−	19.6058i	0.806474	−	1.39685i	−0.108817	−	0.994062i	$-0.534706\pi$
$197$	11.3194	−	19.6058i	0.806474	−	1.39685i	0.915291	−	0.402793i	$-0.131960\pi$
$198$		0			0
$199$	−3.77949	−	6.54627i	−0.267921	−	0.464053i	0.700404	−	0.713747i	$-0.253003\pi$
$199$	−3.77949	−	6.54627i	−0.267921	−	0.464053i	−0.968325	+	0.249694i	$0.919670\pi$
$200$		0			0
$201$	20.3045	+	3.05488i	1.43217	+	0.215474i
$202$		0			0
$203$	10.2794	+	3.74139i	0.721472	+	0.262594i
$204$		0			0
$205$	−5.37254	+	30.4692i	−0.375235	+	2.12806i
$206$		0			0
$207$	5.52417	−	10.7895i	0.383956	−	0.749919i
$208$		0			0
$209$	7.57673	+	6.35763i	0.524094	+	0.439767i
$210$		0			0
$211$	1.48481	+	8.42077i	0.102218	+	0.579710i	0.992295	+	0.123899i	$0.0395397\pi$
$211$	1.48481	+	8.42077i	0.102218	+	0.579710i	−0.890076	+	0.455811i	$0.849349\pi$
$212$		0			0
$213$	0.0466576	+	0.0528411i	0.00319693	+	0.00362061i
$214$		0			0
$215$	−16.4057			−1.11886
$216$		0			0
$217$	−1.39489			−0.0946913
$218$		0			0
$219$	−6.50934	+	19.3912i	−0.439860	+	1.31033i
$220$		0			0
$221$	0.511851	+	2.90285i	0.0344308	+	0.195267i
$222$		0			0
$223$	15.8321	+	13.2847i	1.06019	+	0.889608i	0.994128	−	0.108207i	$-0.0345110\pi$
$223$	15.8321	+	13.2847i	1.06019	+	0.889608i	0.0660654	+	0.997815i	$0.478955\pi$
$224$		0			0
$225$	−6.80022	+	6.31643i	−0.453348	+	0.421096i
$226$		0			0
$227$	3.96678	−	22.4967i	0.263284	−	1.49316i	−0.510592	−	0.859823i	$-0.670574\pi$
$227$	3.96678	−	22.4967i	0.263284	−	1.49316i	0.773876	−	0.633337i	$-0.218315\pi$
$228$		0			0
$229$	23.1067	+	8.41016i	1.52694	+	0.555759i	0.962869	−	0.269970i	$-0.0870139\pi$
$229$	23.1067	+	8.41016i	1.52694	+	0.555759i	0.564067	+	0.825729i	$0.309236\pi$
$230$		0			0
$231$	−4.89777	+	6.14497i	−0.322250	+	0.404309i
$232$		0			0
$233$	−0.795951	−	1.37863i	−0.0521445	−	0.0903169i	0.838775	−	0.544478i	$-0.183272\pi$
$233$	−0.795951	−	1.37863i	−0.0521445	−	0.0903169i	−0.890919	+	0.454161i	$0.849939\pi$
$234$		0			0
$235$	−0.527136	+	0.913026i	−0.0343866	+	0.0595593i
$236$		0			0
$237$	17.5702	−	10.7433i	1.14130	−	0.697855i
$238$		0			0
$239$	2.01565	−	1.69133i	0.130382	−	0.109403i	−0.575265	−	0.817967i	$-0.695101\pi$
$239$	2.01565	−	1.69133i	0.130382	−	0.109403i	0.705647	+	0.708564i	$0.250657\pi$
$240$		0			0
$241$	−5.46081	+	1.98757i	−0.351761	+	0.128031i	−0.511857	−	0.859071i	$-0.671042\pi$
$241$	−5.46081	+	1.98757i	−0.351761	+	0.128031i	0.160095	+	0.987102i	$0.448820\pi$
$242$		0			0
$243$	−8.44000	+	13.1060i	−0.541426	+	0.840748i
$244$		0			0
$245$	−3.95319	+	1.43885i	−0.252560	+	0.0919244i
$246$		0			0
$247$	5.95761	−	4.99903i	0.379074	−	0.318080i
$248$		0			0
$249$	3.94056	−	2.40947i	0.249723	−	0.152694i
$250$		0			0
$251$	5.72525	−	9.91643i	0.361375	−	0.625919i	−0.626813	−	0.779170i	$-0.715641\pi$
$251$	5.72525	−	9.91643i	0.361375	−	0.625919i	0.988187	+	0.153251i	$0.0489742\pi$
$252$		0			0
$253$	−3.90064	−	6.75611i	−0.245231	−	0.424753i
$254$		0			0
$255$	5.96305	−	7.48152i	0.373421	−	0.468511i
$256$		0			0
$257$	5.86226	+	2.13369i	0.365678	+	0.133096i	0.518322	−	0.855185i	$-0.326557\pi$
$257$	5.86226	+	2.13369i	0.365678	+	0.133096i	−0.152645	+	0.988281i	$0.548779\pi$
$258$		0			0
$259$	4.75567	−	26.9708i	0.295503	−	1.67588i
$260$		0			0
$261$	10.2330	−	9.50499i	0.633407	−	0.588344i
$262$		0			0
$263$	−7.37014	−	6.18428i	−0.454462	−	0.381339i	0.386626	−	0.922236i	$-0.373640\pi$
$263$	−7.37014	−	6.18428i	−0.454462	−	0.381339i	−0.841089	+	0.540897i	$0.818085\pi$
$264$		0			0
$265$	−0.648228	−	3.67629i	−0.0398203	−	0.225832i
$266$		0			0
$267$	3.00533	−	8.95281i	0.183923	−	0.547903i
$268$		0			0
$269$	25.0108			1.52494			0.762469	−	0.647025i	$-0.223987\pi$
$269$	25.0108			1.52494			0.762469	+	0.647025i	$0.223987\pi$
$270$		0			0
$271$	13.7589			0.835795			0.417898	−	0.908494i	$-0.362767\pi$
$271$	13.7589			0.835795			0.417898	+	0.908494i	$0.362767\pi$
$272$		0			0
$273$	4.08966	+	4.63166i	0.247517	+	0.280321i
$274$		0			0
$275$	1.03726	+	5.88258i	0.0625489	+	0.354733i
$276$		0			0
$277$	−17.8834	−	15.0060i	−1.07451	−	0.901621i	−0.0790565	−	0.996870i	$-0.525191\pi$
$277$	−17.8834	−	15.0060i	−1.07451	−	0.901621i	−0.995453	+	0.0952492i	$0.969635\pi$
$278$		0			0
$279$	−0.811624	+	1.58521i	−0.0485907	+	0.0949042i
$280$		0			0
$281$	−3.94531	+	22.3750i	−0.235357	+	1.33478i	0.606502	+	0.795082i	$0.292572\pi$
$281$	−3.94531	+	22.3750i	−0.235357	+	1.33478i	−0.841860	+	0.539697i	$0.818539\pi$
$282$		0			0
$283$	30.0985	+	10.9550i	1.78917	+	0.651205i	0.999279	+	0.0379596i	$0.0120858\pi$
$283$	30.0985	+	10.9550i	1.78917	+	0.651205i	0.789892	+	0.613246i	$0.210136\pi$
$284$		0			0
$285$	−24.9614	−	3.75552i	−1.47858	−	0.222458i
$286$		0			0
$287$	−12.7769	−	22.1302i	−0.754196	−	1.30631i
$288$		0			0
$289$	6.61518	−	11.4578i	0.389128	−	0.673990i
$290$		0			0
$291$	−0.118254	−	4.69168i	−0.00693220	−	0.275031i
$292$		0			0
$293$	1.56649	−	1.31444i	0.0915153	−	0.0767905i	−0.595882	−	0.803072i	$-0.703197\pi$
$293$	1.56649	−	1.31444i	0.0915153	−	0.0767905i	0.687398	+	0.726281i	$0.258753\pi$
$294$		0			0
$295$	−40.8857	+	14.8812i	−2.38046	+	0.866416i
$296$		0			0
$297$	4.13361	+	9.14152i	0.239856	+	0.530445i
$298$		0			0
$299$	−5.76423	+	2.09801i	−0.333354	+	0.121331i
$300$		0			0
$301$	10.3799	−	8.70980i	0.598289	−	0.502024i
$302$		0			0
$303$	−28.3834	−	15.4470i	−1.63058	−	0.887405i
$304$		0			0
$305$	12.9952	−	22.5083i	0.744103	−	1.28882i
$306$		0			0
$307$	6.69570	+	11.5973i	0.382144	+	0.661892i	0.991368	−	0.131106i	$-0.0418527\pi$
$307$	6.69570	+	11.5973i	0.382144	+	0.661892i	−0.609225	+	0.792997i	$0.708519\pi$
$308$		0			0
$309$	2.00097	+	5.09439i	0.113831	+	0.289810i
$310$		0			0
$311$	7.58501	+	2.76072i	0.430106	+	0.156546i	0.547996	−	0.836481i	$-0.315391\pi$
$311$	7.58501	+	2.76072i	0.430106	+	0.156546i	−0.117890	+	0.993027i	$0.537613\pi$
$312$		0			0
$313$	0.939271	−	5.32687i	0.0530907	−	0.301093i	−0.946687	−	0.322153i	$-0.895593\pi$
$313$	0.939271	−	5.32687i	0.0530907	−	0.301093i	0.999778	+	0.0210609i	$0.00670440\pi$
$314$		0			0
$315$	2.48306	−	19.9003i	0.139905	−	1.12126i
$316$		0			0
$317$	−8.49456	−	7.12778i	−0.477102	−	0.400336i	0.372275	−	0.928122i	$-0.378578\pi$
$317$	−8.49456	−	7.12778i	−0.477102	−	0.400336i	−0.849377	+	0.527786i	$0.823022\pi$
$318$		0			0
$319$	−1.56087	−	8.85212i	−0.0873918	−	0.495624i
$320$		0			0
$321$	−21.2176	+	4.29511i	−1.18425	+	0.239730i
$322$		0			0
$323$	9.94589			0.553404
$324$		0			0
$325$	4.69684			0.260534
$326$		0			0
$327$	−19.5251	+	3.95250i	−1.07974	+	0.218574i
$328$		0			0
$329$	−0.151206	−	0.857530i	−0.00833624	−	0.0472772i
$330$		0			0
$331$	21.6578	+	18.1731i	1.19042	+	0.998882i	0.999852	+	0.0172086i	$0.00547794\pi$
$331$	21.6578	+	18.1731i	1.19042	+	0.998882i	0.190570	+	0.981674i	$0.438967\pi$
$332$		0			0
$333$	−27.8836	−	21.0976i	−1.52801	−	1.15614i
$334$		0			0
$335$	−5.85648	+	33.2138i	−0.319974	+	1.81466i
$336$		0			0
$337$	26.4752	+	9.63618i	1.44219	+	0.524916i	0.940400	−	0.340071i	$-0.110451\pi$
$337$	26.4752	+	9.63618i	1.44219	+	0.524916i	0.501795	+	0.864987i	$0.332673\pi$
$338$		0			0
$339$	4.30221	+	10.9533i	0.233664	+	0.594899i
$340$		0			0
$341$	0.573092	+	0.992624i	0.0310347	+	0.0537536i
$342$		0			0
$343$	9.96140	−	17.2536i	0.537865	−	0.931609i
$344$		0			0
$345$	17.4878	+	9.51728i	0.941509	+	0.512393i
$346$		0			0
$347$	−7.70464	+	6.46496i	−0.413607	+	0.347057i	−0.825725	−	0.564073i	$-0.809234\pi$
$347$	−7.70464	+	6.46496i	−0.413607	+	0.347057i	0.412118	+	0.911131i	$0.364789\pi$
$348$		0			0
$349$	−13.8904	+	5.05569i	−0.743536	+	0.270625i	−0.685883	−	0.727712i	$-0.740584\pi$
$349$	−13.8904	+	5.05569i	−0.743536	+	0.270625i	−0.0576528	+	0.998337i	$0.518362\pi$
$350$		0			0
$351$	7.64321	−	1.95271i	0.407964	−	0.104228i
$352$		0			0
$353$	−18.1803	+	6.61707i	−0.967638	+	0.352191i	−0.777022	−	0.629474i	$-0.783271\pi$
$353$	−18.1803	+	6.61707i	−0.967638	+	0.352191i	−0.190616	+	0.981665i	$0.561048\pi$
$354$		0			0
$355$	−0.0886966	+	0.0744253i	−0.00470753	+	0.00395009i
$356$		0			0
$357$	0.199104	+	7.89936i	0.0105377	+	0.418078i
$358$		0			0
$359$	−3.39021	+	5.87202i	−0.178928	+	0.309913i	−0.941514	−	0.336974i	$-0.890596\pi$
$359$	−3.39021	+	5.87202i	−0.178928	+	0.309913i	0.762585	+	0.646888i	$0.223930\pi$
$360$		0			0
$361$	−3.62074	−	6.27130i	−0.190565	−	0.330069i
$362$		0			0
$363$	−12.4554	−	1.87396i	−0.653740	−	0.0983572i
$364$		0			0
$365$	−31.5711	−	11.4909i	−1.65251	−	0.601463i
$366$		0			0
$367$	4.85813	−	27.5518i	0.253592	−	1.43819i	−0.546068	−	0.837741i	$-0.683876\pi$
$367$	4.85813	−	27.5518i	0.253592	−	1.43819i	0.799661	−	0.600452i	$-0.205013\pi$
$368$		0			0
$369$	−32.5840	+	1.64361i	−1.69626	+	0.0855631i
$370$		0			0
$371$	2.36188	+	1.98185i	0.122622	+	0.102892i
$372$		0			0
$373$	−0.215272	−	1.22087i	−0.0111464	−	0.0632142i	0.978727	−	0.205166i	$-0.0657734\pi$
$373$	−0.215272	−	1.22087i	−0.0111464	−	0.0632142i	−0.989874	+	0.141952i	$0.954662\pi$
$374$		0			0
$375$	6.21731	+	7.04129i	0.321061	+	0.363611i
$376$		0			0
$377$	−7.06782			−0.364011
$378$		0			0
$379$	−1.91414			−0.0983229			−0.0491615	−	0.998791i	$-0.515655\pi$
$379$	−1.91414			−0.0983229			−0.0491615	+	0.998791i	$0.515655\pi$
$380$		0			0
$381$	−1.35705	+	4.04261i	−0.0695236	+	0.207109i
$382$		0			0
$383$	−2.26886	−	12.8673i	−0.115933	−	0.657489i	−0.986284	−	0.165057i	$-0.947219\pi$
$383$	−2.26886	−	12.8673i	−0.115933	−	0.657489i	0.870351	−	0.492432i	$-0.163892\pi$
$384$		0			0
$385$	−9.88739	−	8.29651i	−0.503908	−	0.422829i
$386$		0			0
$387$	−3.85857	−	16.8640i	−0.196142	−	0.857248i
$388$		0			0
$389$	−2.21102	+	12.5393i	−0.112103	+	0.635769i	0.876040	+	0.482238i	$0.160176\pi$
$389$	−2.21102	+	12.5393i	−0.112103	+	0.635769i	−0.988144	+	0.153532i	$0.950935\pi$
$390$		0			0
$391$	−7.37170	−	2.68308i	−0.372803	−	0.135689i
$392$		0			0
$393$	20.9441	−	26.2774i	1.05649	−	1.32552i
$394$		0			0
$395$	16.9135	+	29.2950i	0.851010	+	1.47399i
$396$		0			0
$397$	−4.01156	+	6.94823i	−0.201335	+	0.348722i	−0.948959	−	0.315400i	$-0.897861\pi$
$397$	−4.01156	+	6.94823i	−0.201335	+	0.348722i	0.747624	+	0.664122i	$0.231194\pi$
$398$		0			0
$399$	17.7869	−	10.8759i	0.890460	−	0.544475i
$400$		0			0
$401$	−7.63777	+	6.40885i	−0.381412	+	0.320043i	−0.813256	−	0.581905i	$-0.802307\pi$
$401$	−7.63777	+	6.40885i	−0.381412	+	0.320043i	0.431844	+	0.901948i	$0.357863\pi$
$402$		0			0
$403$	0.846896	−	0.308245i	0.0421869	−	0.0153548i
$404$		0			0
$405$	−21.1708	−	14.4010i	−1.05199	−	0.715591i
$406$		0			0
$407$	−21.1467	+	7.69676i	−1.04820	+	0.381514i
$408$		0			0
$409$	16.0434	−	13.4620i	0.793293	−	0.665652i	−0.153265	−	0.988185i	$-0.548979\pi$
$409$	16.0434	−	13.4620i	0.793293	−	0.665652i	0.946558	+	0.322533i	$0.104534\pi$
$410$		0			0
$411$	1.21609	−	0.743581i	0.0599852	−	0.0366782i
$412$		0			0
$413$	17.9681	−	31.1216i	0.884150	−	1.53139i
$414$		0			0
$415$	3.79329	+	6.57016i	0.186205	+	0.322517i
$416$		0			0
$417$	11.1481	−	13.9869i	0.545926	−	0.684944i
$418$		0			0
$419$	−4.93124	−	1.79482i	−0.240907	−	0.0876828i	0.218745	−	0.975782i	$-0.429804\pi$
$419$	−4.93124	−	1.79482i	−0.240907	−	0.0876828i	−0.459652	+	0.888099i	$0.652026\pi$
$420$		0			0
$421$	1.94271	−	11.0177i	0.0946820	−	0.536968i	−0.900162	−	0.435555i	$-0.856552\pi$
$421$	1.94271	−	11.0177i	0.0946820	−	0.536968i	0.994844	−	0.101414i	$-0.0323366\pi$
$422$		0			0
$423$	−1.06251	−	0.327122i	−0.0516612	−	0.0159052i
$424$		0			0
$425$	4.60135	+	3.86099i	0.223198	+	0.187286i
$426$		0			0
$427$	3.72759	+	21.1402i	0.180391	+	1.02305i
$428$		0			0
$429$	1.61572	−	4.81318i	0.0780075	−	0.232383i
$430$		0			0
$431$	−19.1117			−0.920577			−0.460289	−	0.887769i	$-0.652254\pi$
$431$	−19.1117			−0.920577			−0.460289	+	0.887769i	$0.652254\pi$
$432$		0			0
$433$	−28.8254			−1.38526			−0.692629	−	0.721294i	$-0.743548\pi$
$433$	−28.8254			−1.38526			−0.692629	+	0.721294i	$0.743548\pi$
$434$		0			0
$435$	15.1838	+	17.1961i	0.728006	+	0.824489i
$436$		0			0
$437$	3.59415	+	20.3834i	0.171932	+	0.975072i
$438$		0			0
$439$	5.54367	+	4.65169i	0.264585	+	0.222013i	0.765422	−	0.643528i	$-0.222530\pi$
$439$	5.54367	+	4.65169i	0.264585	+	0.222013i	−0.500837	+	0.865541i	$0.666975\pi$
$440$		0			0
$441$	−2.40882	−	3.72522i	−0.114706	−	0.177392i
$442$		0			0
$443$	−2.48430	+	14.0892i	−0.118033	+	0.669396i	0.867171	+	0.498010i	$0.165936\pi$
$443$	−2.48430	+	14.0892i	−0.118033	+	0.669396i	−0.985204	+	0.171386i	$0.945175\pi$
$444$		0			0
$445$	14.5762	+	5.30531i	0.690979	+	0.251496i
$446$		0			0
$447$	9.93903	+	1.49536i	0.470100	+	0.0707281i
$448$		0			0
$449$	−17.4025	−	30.1421i	−0.821276	−	1.42249i	−0.904732	−	0.425981i	$-0.859929\pi$
$449$	−17.4025	−	30.1421i	−0.821276	−	1.42249i	0.0834562	−	0.996511i	$-0.473404\pi$
$450$		0			0
$451$	−10.4988	+	18.1844i	−0.494369	+	0.856272i
$452$		0			0
$453$	−0.443121	−	17.5806i	−0.0208197	−	0.826009i
$454$		0			0
$455$	−7.77449	+	6.52357i	−0.364474	+	0.305830i
$456$		0			0
$457$	−21.1768	+	7.70774i	−0.990610	+	0.360553i	−0.785957	−	0.618282i	$-0.787829\pi$
$457$	−21.1768	+	7.70774i	−0.990610	+	0.360553i	−0.204654	+	0.978834i	$0.565607\pi$
$458$		0			0
$459$	9.09302	+	4.37002i	0.424426	+	0.203975i
$460$		0			0
$461$	24.3814	−	8.87410i	1.13555	−	0.413308i	0.295248	−	0.955421i	$-0.404598\pi$
$461$	24.3814	−	8.87410i	1.13555	−	0.413308i	0.840306	+	0.542113i	$0.182375\pi$
$462$		0			0
$463$	−6.39853	+	5.36901i	−0.297365	+	0.249519i	−0.779247	−	0.626717i	$-0.784398\pi$
$463$	−6.39853	+	5.36901i	−0.297365	+	0.249519i	0.481881	+	0.876236i	$0.339954\pi$
$464$		0			0
$465$	−2.56934	−	1.39830i	−0.119151	−	0.0648447i
$466$		0			0
$467$	−9.07494	+	15.7183i	−0.419938	+	0.727355i	−0.995933	−	0.0900991i	$-0.971282\pi$
$467$	−9.07494	+	15.7183i	−0.419938	+	0.727355i	0.575994	+	0.817454i	$0.304615\pi$
$468$		0			0
$469$	−13.9278	−	24.1236i	−0.643125	−	1.11393i
$470$		0			0
$471$	−15.0507	−	38.3186i	−0.693501	−	1.76563i
$472$		0			0
$473$	−10.4626	−	3.80808i	−0.481072	−	0.175096i
$474$		0			0
$475$	2.75199	−	15.6073i	0.126270	−	0.716112i
$476$		0			0
$477$	3.62653	−	1.53099i	0.166047	−	0.0700991i
$478$		0			0
$479$	16.4864	+	13.8338i	0.753285	+	0.632081i	0.936369	−	0.351016i	$-0.114164\pi$
$479$	16.4864	+	13.8338i	0.753285	+	0.632081i	−0.183084	+	0.983097i	$0.558608\pi$
$480$		0			0
$481$	3.07267	+	17.4260i	0.140102	+	0.794557i
$482$		0			0
$483$	−16.1173	+	3.26265i	−0.733361	+	0.148456i
$484$		0			0
$485$	7.70868			0.350033
$486$		0			0
$487$	21.9247			0.993501			0.496750	−	0.867893i	$-0.334526\pi$
$487$	21.9247			0.993501			0.496750	+	0.867893i	$0.334526\pi$
$488$		0			0
$489$	18.7911	−	3.80391i	0.849762	−	0.172019i
$490$		0			0
$491$	5.40958	+	30.6793i	0.244131	+	1.38454i	0.822502	+	0.568762i	$0.192577\pi$
$491$	5.40958	+	30.6793i	0.244131	+	1.38454i	−0.578371	+	0.815774i	$0.696311\pi$
$492$		0			0
$493$	−6.92413	−	5.81004i	−0.311847	−	0.261671i
$494$		0			0
$495$	−15.1815	+	6.40909i	−0.682360	+	0.288067i
$496$		0			0
$497$	0.0166061	−	0.0941781i	0.000744887	−	0.00422447i
$498$		0			0
$499$	20.9044	+	7.60859i	0.935811	+	0.340607i	0.764510	−	0.644612i	$-0.222981\pi$
$499$	20.9044	+	7.60859i	0.935811	+	0.340607i	0.171300	+	0.985219i	$0.445203\pi$
$500$		0			0
$501$	9.13284	+	23.2519i	0.408025	+	1.03882i
$502$		0			0
$503$	15.0234	+	26.0213i	0.669860	+	1.16023i	0.977943	+	0.208873i	$0.0669794\pi$
$503$	15.0234	+	26.0213i	0.669860	+	1.16023i	−0.308082	+	0.951360i	$0.599687\pi$
$504$		0			0
$505$	26.5388	−	45.9665i	1.18096	−	2.04548i
$506$		0			0
$507$	16.2710	+	8.85508i	0.722619	+	0.393268i
$508$		0			0
$509$	3.65568	−	3.06748i	0.162035	−	0.135964i	−0.558165	−	0.829730i	$-0.688494\pi$
$509$	3.65568	−	3.06748i	0.162035	−	0.135964i	0.720200	+	0.693766i	$0.244050\pi$
$510$		0			0
$511$	26.0756	−	9.49075i	1.15352	−	0.419846i
$512$		0			0
$513$	−2.01039	−	26.5420i	−0.0887609	−	1.17186i
$514$		0			0
$515$	−8.44786	+	3.07477i	−0.372257	+	0.135490i
$516$		0			0
$517$	−0.548108	+	0.459917i	−0.0241058	+	0.0202271i
$518$		0			0
$519$	−0.405953	−	16.1060i	−0.0178194	−	0.706974i
$520$		0			0
$521$	9.58324	−	16.5987i	0.419849	−	0.727200i	−0.576075	−	0.817397i	$-0.695416\pi$
$521$	9.58324	−	16.5987i	0.419849	−	0.727200i	0.995924	+	0.0901968i	$0.0287496\pi$
$522$		0			0
$523$	−15.2972	−	26.4956i	−0.668901	−	1.15857i	−0.978212	−	0.207609i	$-0.933432\pi$
$523$	−15.2972	−	26.4956i	−0.668901	−	1.15857i	0.309311	−	0.950961i	$-0.399902\pi$
$524$		0			0
$525$	12.4509	+	1.87328i	0.543403	+	0.0817567i
$526$		0			0
$527$	1.08307	+	0.394205i	0.0471792	+	0.0171718i
$528$		0			0
$529$	−1.15903	+	6.57319i	−0.0503927	+	0.285791i
$530$		0			0
$531$	−24.9131	−	38.5279i	−1.08114	−	1.67197i
$532$		0			0
$533$	12.6478	+	10.6127i	0.547835	+	0.459688i
$534$		0			0
$535$	−6.17448	−	35.0172i	−0.266946	−	1.51393i
$536$		0			0
$537$	5.34103	+	6.04887i	0.230483	+	0.261028i
$538$		0			0
$539$	−2.85510			−0.122978
$540$		0			0
$541$	8.78402			0.377654			0.188827	−	0.982010i	$-0.439531\pi$
$541$	8.78402			0.377654			0.188827	+	0.982010i	$0.439531\pi$
$542$		0			0
$543$	7.64366	−	22.7703i	0.328021	−	0.977167i
$544$		0			0
$545$	−5.68196	−	32.2240i	−0.243388	−	1.38032i
$546$		0			0
$547$	18.0559	+	15.1507i	0.772016	+	0.647798i	0.941224	−	0.337782i	$-0.109677\pi$
$547$	18.0559	+	15.1507i	0.772016	+	0.647798i	−0.169208	+	0.985580i	$0.554121\pi$
$548$		0			0
$549$	26.1936	+	8.06436i	1.11791	+	0.344179i
$550$		0			0
$551$	−4.14120	+	23.4859i	−0.176421	+	1.00053i
$552$		0			0
$553$	−26.2539	−	9.55565i	−1.11643	−	0.406347i
$554$		0			0
$555$	35.7966	−	44.9120i	1.51948	−	1.90641i
$556$		0			0
$557$	5.92188	+	10.2570i	0.250918	+	0.434603i	0.963779	−	0.266703i	$-0.0859341\pi$
$557$	5.92188	+	10.2570i	0.250918	+	0.434603i	−0.712861	+	0.701306i	$0.752601\pi$
$558$		0			0
$559$	−4.37738	+	7.58185i	−0.185144	+	0.320678i
$560$		0			0
$561$	5.53950	−	3.38715i	0.233878	−	0.143005i
$562$		0			0
$563$	−25.5532	+	21.4417i	−1.07694	+	0.903660i	−0.995663	−	0.0930314i	$-0.970344\pi$
$563$	−25.5532	+	21.4417i	−1.07694	+	0.903660i	−0.0812770	+	0.996692i	$0.525900\pi$
$564$		0			0
$565$	−18.1634	+	6.61094i	−0.764141	+	0.278124i
$566$		0			0
$567$	21.0403	−	2.12806i	0.883610	−	0.0893700i
$568$		0			0
$569$	−13.3376	+	4.85450i	−0.559143	+	0.203511i	−0.606104	−	0.795385i	$-0.707269\pi$
$569$	−13.3376	+	4.85450i	−0.559143	+	0.203511i	0.0469612	+	0.998897i	$0.485046\pi$
$570$		0			0
$571$	25.6956	−	21.5611i	1.07533	−	0.902306i	0.0798017	−	0.996811i	$-0.474571\pi$
$571$	25.6956	−	21.5611i	1.07533	−	0.902306i	0.995524	+	0.0945050i	$0.0301268\pi$
$572$		0			0
$573$	−37.7925	+	23.1084i	−1.57880	+	0.965365i
$574$		0			0
$575$	−6.25006	+	10.8254i	−0.260645	+	0.451451i
$576$		0			0
$577$	18.9361	+	32.7984i	0.788322	+	1.36541i	0.926994	+	0.375075i	$0.122383\pi$
$577$	18.9361	+	32.7984i	0.788322	+	1.36541i	−0.138672	+	0.990338i	$0.544284\pi$
$578$		0			0
$579$	−13.6443	+	17.1188i	−0.567038	+	0.711432i
$580$		0			0
$581$	−5.88812	−	2.14310i	−0.244280	−	0.0889108i
$582$		0			0
$583$	0.439934	−	2.49499i	0.0182202	−	0.103332i
$584$		0			0
$585$	2.89004	+	12.6310i	0.119488	+	0.522229i
$586$		0			0
$587$	−23.1980	−	19.4654i	−0.957484	−	0.803424i	0.0230583	−	0.999734i	$-0.492660\pi$
$587$	−23.1980	−	19.4654i	−0.957484	−	0.803424i	−0.980542	+	0.196310i	$0.937104\pi$
$588$		0			0
$589$	−0.528062	−	2.99479i	−0.0217584	−	0.123398i
$590$		0			0
$591$	−12.4785	+	37.1731i	−0.513295	+	1.52910i
$592$		0			0
$593$	−13.4316			−0.551570			−0.275785	−	0.961219i	$-0.588938\pi$
$593$	−13.4316			−0.551570			−0.275785	+	0.961219i	$0.588938\pi$
$594$		0			0
$595$	−12.9791			−0.532090
$596$		0			0
$597$	8.66577	+	9.81423i	0.354666	+	0.401670i
$598$		0			0
$599$	−4.86621	−	27.5977i	−0.198828	−	1.12761i	−0.906861	−	0.421430i	$-0.861528\pi$
$599$	−4.86621	−	27.5977i	−0.198828	−	1.12761i	0.708033	−	0.706179i	$-0.249583\pi$
$600$		0			0
$601$	17.2775	+	14.4976i	0.704766	+	0.591369i	0.923125	−	0.384500i	$-0.125626\pi$
$601$	17.2775	+	14.4976i	0.704766	+	0.591369i	−0.218359	+	0.975868i	$0.570070\pi$
$602$		0			0
$603$	−35.5191	+	1.79166i	−1.44645	+	0.0729622i
$604$		0			0
$605$	3.59255	−	20.3743i	0.146058	−	0.828335i
$606$		0			0
$607$	−29.6613	−	10.7958i	−1.20391	−	0.438189i	−0.339325	−	0.940669i	$-0.610199\pi$
$607$	−29.6613	−	10.7958i	−1.20391	−	0.438189i	−0.864589	+	0.502480i	$0.832421\pi$
$608$		0			0
$609$	−18.7362	−	2.81892i	−0.759229	−	0.114228i
$610$		0			0
$611$	0.281302	+	0.487229i	0.0113802	+	0.0197112i
$612$		0			0
$613$	7.93681	−	13.7470i	0.320565	−	0.555235i	−0.660040	−	0.751231i	$-0.729461\pi$
$613$	7.93681	−	13.7470i	0.320565	−	0.555235i	0.980605	+	0.195996i	$0.0627940\pi$
$614$		0			0
$615$	−1.35027	−	53.5713i	−0.0544483	−	2.16020i
$616$		0			0
$617$	−0.142349	+	0.119445i	−0.00573077	+	0.00480868i	−0.645648	−	0.763635i	$-0.723413\pi$
$617$	−0.142349	+	0.119445i	−0.00573077	+	0.00480868i	0.639918	+	0.768443i	$0.278968\pi$
$618$		0			0
$619$	−4.04428	+	1.47200i	−0.162553	+	0.0591645i	−0.422015	−	0.906589i	$-0.638677\pi$
$619$	−4.04428	+	1.47200i	−0.162553	+	0.0591645i	0.259462	+	0.965753i	$0.416455\pi$
$620$		0			0
$621$	−5.67011	+	20.2147i	−0.227534	+	0.811190i
$622$		0			0
$623$	−12.0390	+	4.38183i	−0.482332	+	0.175555i
$624$		0			0
$625$	−23.6688	+	19.8605i	−0.946754	+	0.794421i
$626$		0			0
$627$	−15.0472	−	8.18907i	−0.600927	−	0.327040i
$628$		0			0
$629$	−11.3147	+	19.5976i	−0.451145	+	0.781407i
$630$		0			0
$631$	13.1399	+	22.7590i	0.523091	+	0.906020i	0.999639	+	0.0268714i	$0.00855447\pi$
$631$	13.1399	+	22.7590i	0.523091	+	0.906020i	−0.476548	+	0.879148i	$0.658112\pi$
$632$		0			0
$633$	−5.41445	−	13.7850i	−0.215205	−	0.547904i
$634$		0			0
$635$	−6.58185	−	2.39560i	−0.261193	−	0.0950663i
$636$		0			0
$637$	−0.389836	+	2.21087i	−0.0154459	+	0.0875979i
$638$		0			0
$639$	−0.0973657	−	0.0736700i	−0.00385173	−	0.00291434i
$640$		0			0
$641$	2.94661	+	2.47250i	0.116384	+	0.0976578i	0.699122	−	0.715002i	$-0.253574\pi$
$641$	2.94661	+	2.47250i	0.116384	+	0.0976578i	−0.582738	+	0.812660i	$0.698019\pi$
$642$		0			0
$643$	−2.85395	−	16.1856i	−0.112549	−	0.638296i	−0.987935	−	0.154871i	$-0.950504\pi$
$643$	−2.85395	−	16.1856i	−0.112549	−	0.638296i	0.875386	−	0.483425i	$-0.160607\pi$
$644$		0			0
$645$	27.8506	−	5.63785i	1.09662	−	0.221990i
$646$		0			0
$647$	7.05868			0.277505			0.138753	−	0.990327i	$-0.455691\pi$
$647$	7.05868			0.277505			0.138753	+	0.990327i	$0.455691\pi$
$648$		0			0
$649$	−29.5288			−1.15911
$650$		0			0
$651$	2.36799	−	0.479356i	0.0928088	−	0.0187875i
$652$		0			0
$653$	−0.950595	−	5.39109i	−0.0371997	−	0.210970i	0.960542	−	0.278134i	$-0.0897160\pi$
$653$	−0.950595	−	5.39109i	−0.0371997	−	0.210970i	−0.997742	+	0.0671643i	$0.978605\pi$
$654$		0			0
$655$	42.2809	+	35.4779i	1.65205	+	1.38624i
$656$		0			0
$657$	4.38655	−	35.1557i	0.171136	−	1.37156i
$658$		0			0
$659$	7.27612	−	41.2649i	0.283437	−	1.60745i	−0.427377	−	0.904073i	$-0.640562\pi$
$659$	7.27612	−	41.2649i	0.283437	−	1.60745i	0.710815	−	0.703379i	$-0.248327\pi$
$660$		0			0
$661$	−0.891513	−	0.324484i	−0.0346759	−	0.0126210i	0.324624	−	0.945843i	$-0.394762\pi$
$661$	−0.891513	−	0.324484i	−0.0346759	−	0.0126210i	−0.359300	+	0.933222i	$0.616984\pi$
$662$		0			0
$663$	−1.86650	−	4.75203i	−0.0724887	−	0.184554i
$664$		0			0
$665$	17.1221	+	29.6564i	0.663968	+	1.15003i
$666$		0			0
$667$	9.40511	−	16.2901i	0.364167	−	0.630756i
$668$		0			0
$669$	−31.4421	−	17.1116i	−1.21562	−	0.661572i
$670$		0			0
$671$	13.5122	−	11.3381i	0.521633	−	0.437702i
$672$		0			0
$673$	7.54529	−	2.74626i	0.290850	−	0.105861i	−0.192475	−	0.981302i	$-0.561651\pi$
$673$	7.54529	−	2.74626i	0.290850	−	0.105861i	0.483324	+	0.875441i	$0.339429\pi$
$674$		0			0
$675$	9.37352	−	13.0598i	0.360787	−	0.502672i
$676$		0			0
$677$	−21.5823	+	7.85532i	−0.829476	+	0.301905i	−0.721644	−	0.692265i	$-0.756613\pi$
$677$	−21.5823	+	7.85532i	−0.829476	+	0.301905i	−0.107832	+	0.994169i	$0.534391\pi$
$678$		0			0
$679$	−4.87730	+	4.09254i	−0.187173	+	0.157057i
$680$		0			0
$681$	0.996964	+	39.5540i	0.0382038	+	1.51571i
$682$		0			0
$683$	−8.96599	+	15.5296i	−0.343074	+	0.594222i	−0.985002	−	0.172543i	$-0.944802\pi$
$683$	−8.96599	+	15.5296i	−0.343074	+	0.594222i	0.641928	+	0.766765i	$0.278135\pi$
$684$		0			0
$685$	1.17064	+	2.02760i	0.0447278	+	0.0774708i
$686$		0			0
$687$	−42.1165	−	6.33657i	−1.60685	−	0.241755i
$688$		0			0
$689$	−1.87195	−	0.681332i	−0.0713154	−	0.0259567i
$690$		0			0
$691$	6.37607	−	36.1605i	0.242557	−	1.37561i	−0.583541	−	0.812083i	$-0.698333\pi$
$691$	6.37607	−	36.1605i	0.242557	−	1.37561i	0.826098	−	0.563526i	$-0.190556\pi$
$692$		0			0
$693$	6.20281	−	12.1149i	0.235625	−	0.460208i
$694$		0			0
$695$	22.5053	+	18.8842i	0.853675	+	0.716319i
$696$		0			0
$697$	3.66653	+	20.7939i	0.138880	+	0.787626i
$698$		0			0
$699$	1.82499	+	2.06685i	0.0690274	+	0.0781755i
$700$		0			0
$701$	−2.35049			−0.0887768			−0.0443884	−	0.999014i	$-0.514134\pi$
$701$	−2.35049			−0.0887768			−0.0443884	+	0.999014i	$0.514134\pi$
$702$		0			0
$703$	59.7058			2.25185
$704$		0			0
$705$	0.581112	−	1.73112i	0.0218859	−	0.0651977i
$706$		0			0
$707$	7.61248	+	43.1725i	0.286297	+	1.62367i
$708$		0			0
$709$	17.9355	+	15.0497i	0.673582	+	0.565202i	0.914123	−	0.405436i	$-0.132880\pi$
$709$	17.9355	+	15.0497i	0.673582	+	0.565202i	−0.240541	+	0.970639i	$0.577325\pi$
$710$		0			0
$711$	−26.1354	+	24.2761i	−0.980156	+	0.910424i
$712$		0			0
$713$	−0.416507	+	2.36213i	−0.0155983	+	0.0884625i
$714$		0			0
$715$	7.83642	+	2.85222i	0.293066	+	0.106667i
$716$		0			0
$717$	−2.84057	+	3.56392i	−0.106083	+	0.133097i
$718$		0			0
$719$	−19.0258	−	32.9536i	−0.709541	−	1.22896i	−0.965027	−	0.262149i	$-0.915569\pi$
$719$	−19.0258	−	32.9536i	−0.709541	−	1.22896i	0.255486	−	0.966813i	$-0.417764\pi$
$720$		0			0
$721$	3.71258	−	6.43038i	0.138264	−	0.239480i
$722$		0			0
$723$	8.58733	−	5.25075i	0.319366	−	0.195277i
$724$		0			0
$725$	−11.0331	+	9.25788i	−0.409759	+	0.343829i
$726$		0			0
$727$	−24.6081	+	8.95661i	−0.912663	+	0.332182i	−0.755316	−	0.655361i	$-0.772517\pi$
$727$	−24.6081	+	8.95661i	−0.912663	+	0.332182i	−0.157348	+	0.987543i	$0.550294\pi$
$728$		0			0
$729$	9.82400	−	25.1493i	0.363852	−	0.931457i
$730$		0			0
$731$	−10.5210	+	3.82932i	−0.389133	+	0.141633i
$732$		0			0
$733$	5.68641	−	4.77146i	0.210032	−	0.176238i	−0.531703	−	0.846931i	$-0.678448\pi$
$733$	5.68641	−	4.77146i	0.210032	−	0.176238i	0.741735	+	0.670693i	$0.234003\pi$
$734$		0			0
$735$	6.21655	−	3.80113i	0.229301	−	0.140207i
$736$		0			0
$737$	−11.4445	+	19.8224i	−0.421563	+	0.730169i
$738$		0			0
$739$	18.6118	+	32.2366i	0.684647	+	1.18584i	0.973548	+	0.228484i	$0.0733769\pi$
$739$	18.6118	+	32.2366i	0.684647	+	1.18584i	−0.288901	+	0.957359i	$0.593290\pi$
$740$		0			0
$741$	−8.39581	+	10.5338i	−0.308428	+	0.386968i
$742$		0			0
$743$	−32.4095	−	11.7961i	−1.18899	−	0.432757i	−0.329621	−	0.944113i	$-0.606921\pi$
$743$	−32.4095	−	11.7961i	−1.18899	−	0.432757i	−0.859369	+	0.511356i	$0.829143\pi$
$744$		0			0
$745$	−2.86674	+	16.2581i	−0.105029	+	0.595651i
$746$		0			0
$747$	−5.86155	+	5.44454i	−0.214463	+	0.199205i
$748$		0			0
$749$	22.4973	+	18.8774i	0.822032	+	0.689767i
$750$		0			0
$751$	3.93601	+	22.3222i	0.143627	+	0.814548i	0.968459	+	0.249171i	$0.0801582\pi$
$751$	3.93601	+	22.3222i	0.143627	+	0.814548i	−0.824833	+	0.565377i	$0.808731\pi$
$752$		0			0
$753$	−6.31149	+	18.8018i	−0.230003	+	0.685175i
$754$		0			0
$755$	28.8859			1.05126
$756$		0			0
$757$	13.0664			0.474905			0.237452	−	0.971399i	$-0.423688\pi$
$757$	13.0664			0.474905			0.237452	+	0.971399i	$0.423688\pi$
$758$		0			0
$759$	8.94354	+	10.1288i	0.324630	+	0.367653i
$760$		0			0
$761$	−0.530019	−	3.00589i	−0.0192132	−	0.108963i	0.973693	−	0.227864i	$-0.0731741\pi$
$761$	−0.530019	−	3.00589i	−0.0192132	−	0.108963i	−0.992906	+	0.118901i	$0.962063\pi$
$762$		0			0
$763$	20.7027	+	17.3716i	0.749489	+	0.628896i
$764$		0			0
$765$	−7.55194	+	14.7500i	−0.273041	+	0.533286i
$766$		0			0
$767$	−4.03186	+	22.8658i	−0.145582	+	0.825637i
$768$		0			0
$769$	37.4729	+	13.6390i	1.35131	+	0.491835i	0.913355	−	0.407164i	$-0.133482\pi$
$769$	37.4729	+	13.6390i	1.35131	+	0.491835i	0.437951	+	0.898999i	$0.355704\pi$
$770$		0			0
$771$	−10.6851	−	1.60761i	−0.384815	−	0.0578966i
$772$		0			0
$773$	−8.57837	−	14.8582i	−0.308543	−	0.534411i	0.669501	−	0.742811i	$-0.266508\pi$
$773$	−8.57837	−	14.8582i	−0.308543	−	0.534411i	−0.978044	+	0.208400i	$0.933175\pi$
$774$		0			0
$775$	0.918274	−	1.59050i	0.0329854	−	0.0571324i
$776$		0			0
$777$	1.19524	+	47.4203i	0.0428788	+	1.70119i
$778$		0			0
$779$	42.6760	−	35.8094i	1.52903	−	1.28301i
$780$		0			0
$781$	−0.0738412	+	0.0268760i	−0.00264225	+	0.000961699i
$782$		0			0
$783$	−14.1053	+	19.6524i	−0.504083	+	0.702320i
$784$		0			0
$785$	63.5424	−	23.1275i	2.26793	−	0.825457i
$786$		0			0
$787$	14.4255	−	12.1045i	0.514215	−	0.431477i	−0.348395	−	0.937348i	$-0.613273\pi$
$787$	14.4255	−	12.1045i	0.514215	−	0.431477i	0.862609	+	0.505871i	$0.168829\pi$
$788$		0			0
$789$	14.6369	+	7.96578i	0.521088	+	0.283589i
$790$		0			0
$791$	7.98228	−	13.8257i	0.283817	−	0.491586i
$792$		0			0
$793$	−6.93478	−	12.0114i	−0.246261	−	0.426537i
$794$		0			0
$795$	2.36380	+	6.01816i	0.0838355	+	0.213442i
$796$		0			0
$797$	−19.7070	−	7.17276i	−0.698058	−	0.254072i	−0.0314763	−	0.999504i	$-0.510021\pi$
$797$	−19.7070	−	7.17276i	−0.698058	−	0.254072i	−0.666581	+	0.745432i	$0.732243\pi$
$798$		0			0
$799$	−0.124939	+	0.708564i	−0.00442002	+	0.0250672i
$800$		0			0
$801$	−2.02525	+	16.2312i	−0.0715587	+	0.573502i
$802$		0			0
$803$	−17.4670	−	14.6565i	−0.616396	−	0.517217i
$804$		0			0
$805$	−4.69025	−	26.5997i	−0.165310	−	0.937518i
$806$		0			0
$807$	−42.4588	+	8.59501i	−1.49462	+	0.302559i
$808$		0			0
$809$	21.3465			0.750504			0.375252	−	0.926923i	$-0.377556\pi$
$809$	21.3465			0.750504			0.375252	+	0.926923i	$0.377556\pi$
$810$		0			0
$811$	−44.8933			−1.57642			−0.788208	−	0.615409i	$-0.788991\pi$
$811$	−44.8933			−1.57642			−0.788208	+	0.615409i	$0.788991\pi$
$812$		0			0
$813$	−23.3574	+	4.72828i	−0.819179	+	0.165828i
$814$		0			0
$815$	5.46836	+	31.0126i	0.191548	+	1.08632i
$816$		0			0
$817$	22.6292	+	18.9881i	0.791695	+	0.664311i
$818$		0			0
$819$	−8.53435	−	6.45736i	−0.298214	−	0.225639i
$820$		0			0
$821$	−6.07227	+	34.4375i	−0.211924	+	1.20188i	0.674242	+	0.738510i	$0.264470\pi$
$821$	−6.07227	+	34.4375i	−0.211924	+	1.20188i	−0.886166	+	0.463368i	$0.846641\pi$
$822$		0			0
$823$	34.8744	+	12.6932i	1.21564	+	0.442458i	0.868658	−	0.495412i	$-0.164983\pi$
$823$	34.8744	+	12.6932i	1.21564	+	0.442458i	0.346986	+	0.937870i	$0.387205\pi$
$824$		0			0
$825$	−3.78242	−	9.62991i	−0.131687	−	0.335270i
$826$		0			0
$827$	5.12288	+	8.87309i	0.178140	+	0.308548i	0.941243	−	0.337729i	$-0.109659\pi$
$827$	5.12288	+	8.87309i	0.178140	+	0.308548i	−0.763103	+	0.646276i	$0.776325\pi$
$828$		0			0
$829$	5.58981	−	9.68184i	0.194142	−	0.336264i	−0.752477	−	0.658619i	$-0.771141\pi$
$829$	5.58981	−	9.68184i	0.194142	−	0.336264i	0.946619	+	0.322355i	$0.104474\pi$
$830$		0			0
$831$	35.5160	+	19.3287i	1.23204	+	0.670506i
$832$		0			0
$833$	−2.19934	+	1.84546i	−0.0762025	+	0.0639415i
$834$		0			0
$835$	−38.5578	+	14.0339i	−1.33435	+	0.485663i
$836$		0			0
$837$	0.833066	−	2.97000i	0.0287950	−	0.102658i
$838$		0			0
$839$	−0.930523	+	0.338683i	−0.0321252	+	0.0116926i	−0.358033	−	0.933709i	$-0.616552\pi$
$839$	−0.930523	+	0.338683i	−0.0321252	+	0.0116926i	0.325908	+	0.945402i	$0.394330\pi$
$840$		0			0
$841$	−5.61262	+	4.70955i	−0.193539	+	0.162398i
$842$		0			0
$843$	−0.991568	−	39.3399i	−0.0341514	−	1.35494i
$844$		0			0
$845$	−15.2135	+	26.3506i	−0.523361	+	0.906489i
$846$		0			0
$847$	8.54373	+	14.7982i	0.293566	+	0.508471i
$848$		0			0
$849$	−54.8605	−	8.25393i	−1.88281	−	0.283274i
$850$		0			0
$851$	−44.2527	−	16.1067i	−1.51696	−	0.552130i
$852$		0			0
$853$	0.607451	−	3.44502i	0.0207987	−	0.117955i	−0.972641	−	0.232314i	$-0.925370\pi$
$853$	0.607451	−	3.44502i	0.0207987	−	0.117955i	0.993440	+	0.114359i	$0.0364814\pi$
$854$		0			0
$855$	43.6654	−	2.20259i	1.49333	−	0.0753268i
$856$		0			0
$857$	34.2918	+	28.7742i	1.17138	+	0.982908i	0.999997	−	0.00229535i	$-0.000730634\pi$
$857$	34.2918	+	28.7742i	1.17138	+	0.982908i	0.171387	+	0.985204i	$0.445175\pi$
$858$		0			0
$859$	7.82298	+	44.3663i	0.266917	+	1.51376i	0.763521	+	0.645783i	$0.223469\pi$
$859$	7.82298	+	44.3663i	0.266917	+	1.51376i	−0.496605	+	0.867977i	$0.665420\pi$
$860$		0			0
$861$	29.2953	+	33.1778i	0.998383	+	1.13070i
$862$		0			0
$863$	−5.15005			−0.175310			−0.0876549	−	0.996151i	$-0.527937\pi$
$863$	−5.15005			−0.175310			−0.0876549	+	0.996151i	$0.527937\pi$
$864$		0			0
$865$	26.4630			0.899769
$866$		0			0
$867$	−7.29254	+	21.7243i	−0.247668	+	0.737797i
$868$		0			0
$869$	3.98651	+	22.6086i	0.135233	+	0.766945i
$870$		0			0
$871$	13.7870	+	11.5687i	0.467155	+	0.391990i
$872$		0			0
$873$	1.81305	+	7.92404i	0.0613626	+	0.268188i
$874$		0			0
$875$	2.21283	−	12.5496i	0.0748075	−	0.424254i
$876$		0			0
$877$	−25.9786	−	9.45544i	−0.877235	−	0.319288i	−0.136142	−	0.990689i	$-0.543470\pi$
$877$	−25.9786	−	9.45544i	−0.877235	−	0.319288i	−0.741093	+	0.671402i	$0.765692\pi$
$878$		0			0
$879$	−2.20759	+	2.76974i	−0.0744602	+	0.0934211i
$880$		0			0
$881$	18.3197	+	31.7306i	0.617206	+	1.06903i	0.989993	+	0.141116i	$0.0450689\pi$
$881$	18.3197	+	31.7306i	0.617206	+	1.06903i	−0.372787	+	0.927917i	$0.621598\pi$
$882$		0			0
$883$	4.39624	−	7.61451i	0.147945	−	0.256249i	−0.782523	−	0.622622i	$-0.786067\pi$
$883$	4.39624	−	7.61451i	0.147945	−	0.256249i	0.930468	+	0.366373i	$0.119401\pi$
$884$		0			0
$885$	64.2943	−	39.3130i	2.16123	−	1.32149i
$886$		0			0
$887$	25.7702	−	21.6237i	0.865277	−	0.726054i	−0.0978210	−	0.995204i	$-0.531187\pi$
$887$	25.7702	−	21.6237i	0.865277	−	0.726054i	0.963098	+	0.269150i	$0.0867428\pi$
$888$		0			0
$889$	5.43617	−	1.97860i	0.182323	−	0.0663603i
$890$		0			0
$891$	−10.1588	−	14.0983i	−0.340332	−	0.472310i
$892$		0			0
$893$	1.78385	−	0.649268i	0.0596942	−	0.0217269i
$894$		0			0
$895$	−10.1534	+	8.51968i	−0.339389	+	0.284782i
$896$		0			0
$897$	9.06448	−	5.54251i	0.302654	−	0.185059i
$898$		0			0
$899$	−1.38182	+	2.39339i	−0.0460864	+	0.0798239i
$900$		0			0
$901$	−1.27381	−	2.20630i	−0.0424366	−	0.0735024i
$902$		0			0
$903$	−14.6280	+	18.3530i	−0.486790	+	0.610749i
$904$		0			0
$905$	37.0727	+	13.4934i	1.23234	+	0.448534i
$906$		0			0
$907$	8.31614	−	47.1632i	0.276133	−	1.56603i	−0.459207	−	0.888329i	$-0.651866\pi$
$907$	8.31614	−	47.1632i	0.276133	−	1.56603i	0.735340	−	0.677699i	$-0.237023\pi$
$908$		0			0
$909$	53.4925	+	16.4690i	1.77423	+	0.546243i
$910$		0			0
$911$	24.1748	+	20.2850i	0.800946	+	0.672074i	0.948429	−	0.316991i	$-0.102673\pi$
$911$	24.1748	+	20.2850i	0.800946	+	0.672074i	−0.147482	+	0.989065i	$0.547117\pi$
$912$		0			0
$913$	0.894078	+	5.07057i	0.0295897	+	0.167811i
$914$		0			0
$915$	−14.3258	+	42.6764i	−0.473598	+	1.41084i
$916$		0			0
$917$	−45.5865			−1.50540
$918$		0			0
$919$	−5.57506			−0.183904			−0.0919522	−	0.995763i	$-0.529311\pi$
$919$	−5.57506			−0.183904			−0.0919522	+	0.995763i	$0.529311\pi$
$920$		0			0
$921$	−15.3522	−	17.3868i	−0.505871	−	0.572913i
$922$		0			0
$923$	0.0107293	+	0.0608491i	0.000353161	+	0.00200287i
$924$		0			0
$925$	27.6222	+	23.1778i	0.908212	+	0.762081i
$926$		0			0
$927$	−5.14757	−	7.96069i	−0.169069	−	0.261463i
$928$		0			0
$929$	−3.28612	+	18.6365i	−0.107814	+	0.611445i	0.882245	+	0.470791i	$0.156032\pi$
$929$	−3.28612	+	18.6365i	−0.107814	+	0.611445i	−0.990059	+	0.140654i	$0.955080\pi$
$930$		0			0
$931$	7.11816	+	2.59080i	0.233288	+	0.0849100i
$932$		0			0
$933$	−13.8252	−	2.08004i	−0.452616	−	0.0680975i
$934$		0			0
$935$	5.33246	+	9.23610i	0.174390	+	0.302053i
$936$		0			0
$937$	−5.63145	+	9.75396i	−0.183972	+	0.318648i	−0.943229	−	0.332142i	$-0.892229\pi$
$937$	−5.63145	+	9.75396i	−0.183972	+	0.318648i	0.759258	+	0.650790i	$0.225562\pi$
$938$		0			0
$939$	0.236065	+	9.36577i	0.00770371	+	0.305640i
$940$		0			0
$941$	35.5407	−	29.8222i	1.15859	−	0.972176i	0.158709	−	0.987325i	$-0.449267\pi$
$941$	35.5407	−	29.8222i	1.15859	−	0.972176i	0.999885	+	0.0151498i	$0.00482251\pi$
$942$		0			0
$943$	−41.2908	+	15.0286i	−1.34461	+	0.489399i
$944$		0			0
$945$	2.62350	+	34.6365i	0.0853423	+	1.12672i
$946$		0			0
$947$	21.8028	−	7.93556i	0.708495	−	0.257871i	0.0374612	−	0.999298i	$-0.488073\pi$
$947$	21.8028	−	7.93556i	0.708495	−	0.257871i	0.671033	+	0.741427i	$0.265851\pi$
$948$		0			0
$949$	−13.7343	+	11.5245i	−0.445835	+	0.374100i
$950$		0			0
$951$	16.8700	+	9.18108i	0.547047	+	0.297717i
$952$		0			0
$953$	−2.98408	+	5.16857i	−0.0966637	+	0.167426i	−0.910302	−	0.413945i	$-0.864150\pi$
$953$	−2.98408	+	5.16857i	−0.0966637	+	0.167426i	0.813638	+	0.581372i	$0.197484\pi$
$954$		0			0
$955$	−36.3800	−	63.0120i	−1.17723	−	2.03902i
$956$		0			0
$957$	5.69180	+	14.4911i	0.183990	+	0.468431i
$958$		0			0
$959$	−1.81712	−	0.661378i	−0.0586779	−	0.0213570i
$960$		0			0
$961$	−5.32190	+	30.1820i	−0.171674	+	0.973613i
$962$		0			0
$963$	34.5433	−	14.5829i	1.11314	−	0.469928i
$964$		0			0
$965$	−27.5445	−	23.1126i	−0.886689	−	0.744020i
$966$		0			0
$967$	−1.55531	−	8.82060i	−0.0500154	−	0.283651i	0.949534	−	0.313664i	$-0.101556\pi$
$967$	−1.55531	−	8.82060i	−0.0500154	−	0.283651i	−0.999550	+	0.0300124i	$0.990445\pi$
$968$		0			0
$969$	−16.8843	+	3.41792i	−0.542402	+	0.109799i
$970$		0			0
$971$	−42.0756			−1.35027			−0.675135	−	0.737694i	$-0.735915\pi$
$971$	−42.0756			−1.35027			−0.675135	+	0.737694i	$0.735915\pi$
$972$		0			0
$973$	−24.2648			−0.777893
$974$		0			0
$975$	−7.97344	+	1.61408i	−0.255354	+	0.0516919i
$976$		0			0
$977$	−7.01863	−	39.8047i	−0.224546	−	1.27346i	−0.863551	−	0.504261i	$-0.831765\pi$
$977$	−7.01863	−	39.8047i	−0.224546	−	1.27346i	0.639005	−	0.769202i	$-0.279346\pi$
$978$		0			0
$979$	8.06441	+	6.76684i	0.257740	+	0.216269i
$980$		0			0
$981$	31.7879	−	13.4197i	1.01491	−	0.428457i
$982$		0			0
$983$	−1.87234	+	10.6185i	−0.0597182	+	0.338679i	−0.999999	−	0.00172231i	$-0.999452\pi$
$983$	−1.87234	+	10.6185i	−0.0597182	+	0.338679i	0.940280	+	0.340401i	$0.110563\pi$
$984$		0			0
$985$	−60.5221	−	22.0282i	−1.92839	−	0.701878i
$986$		0			0
$987$	0.551381	+	1.40380i	0.0175506	+	0.0446833i
$988$		0			0
$989$	−11.6499	−	20.1783i	−0.370446	−	0.641631i
$990$		0			0
$991$	21.8636	−	37.8689i	0.694520	−	1.20294i	−0.275822	−	0.961209i	$-0.588950\pi$
$991$	21.8636	−	37.8689i	0.694520	−	1.20294i	0.970342	−	0.241735i	$-0.0777166\pi$
$992$		0			0
$993$	−43.0119	−	23.4082i	−1.36494	−	0.742836i
$994$		0			0
$995$	−16.4737	+	13.8231i	−0.522252	+	0.438222i
$996$		0			0
$997$	39.2948	−	14.3021i	1.24448	−	0.452953i	0.365945	−	0.930636i	$-0.380746\pi$
$997$	39.2948	−	14.3021i	1.24448	−	0.452953i	0.878532	+	0.477684i	$0.158523\pi$
$998$		0			0
$999$	54.5860	+	26.2335i	1.72702	+	0.829990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.385.1	yes	54
4.3	odd	2		864.2.y.b.385.9	yes	54
27.4	even	9	inner	864.2.y.c.193.1	yes	54
108.31	odd	18		864.2.y.b.193.9	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.9	✓	54	108.31	odd	18
864.2.y.b.385.9	yes	54	4.3	odd	2
864.2.y.c.193.1	yes	54	27.4	even	9	inner
864.2.y.c.385.1	yes	54	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69762 + 0.343652i) q^{3} +(-0.494020 - 2.80173i) q^{5} +(1.80000 + 1.51038i) q^{7} +(2.76381 - 1.16678i) q^{9} +O(q^{10})\)	\(q+(-1.69762 + 0.343652i) q^{3} +(-0.494020 - 2.80173i) q^{5} +(1.80000 + 1.51038i) q^{7} +(2.76381 - 1.16678i) q^{9} +(0.335277 - 1.90145i) q^{11} +(-1.42662 - 0.519249i) q^{13} +(1.80147 + 4.58649i) q^{15} +(-0.970777 - 1.68144i) q^{17} +(-2.56132 + 4.43634i) q^{19} +(-3.57476 - 1.94548i) q^{21} +(3.09518 - 2.59716i) q^{23} +(-2.90715 + 1.05812i) q^{25} +(-4.29092 + 2.93053i) q^{27} +(4.37469 - 1.59226i) q^{29} +(-0.454752 + 0.381582i) q^{31} +(0.0842647 + 3.34316i) q^{33} +(3.34244 - 5.78928i) q^{35} +(-5.82763 - 10.0938i) q^{37} +(2.60030 + 0.391224i) q^{39} +(-10.2193 - 3.71952i) q^{41} +(1.00136 - 5.67901i) q^{43} +(-4.63437 - 7.16702i) q^{45} +(-0.283878 - 0.238202i) q^{47} +(-0.256778 - 1.45626i) q^{49} +(2.22584 + 2.52082i) q^{51} +1.31215 q^{53} -5.49298 q^{55} +(2.82359 - 8.41141i) q^{57} +(-2.65572 - 15.0613i) q^{59} +(6.99830 + 5.87227i) q^{61} +(6.73715 + 2.07420i) q^{63} +(-0.750012 + 4.25353i) q^{65} +(-11.1398 - 4.05456i) q^{67} +(-4.36191 + 5.47265i) q^{69} +(-0.0203493 - 0.0352460i) q^{71} +(5.90472 - 10.2273i) q^{73} +(4.57161 - 2.79533i) q^{75} +(3.47542 - 2.91622i) q^{77} +(-11.1731 + 4.06668i) q^{79} +(6.27726 - 6.44950i) q^{81} +(-2.50586 + 0.912059i) q^{83} +(-4.23134 + 3.55052i) q^{85} +(-6.87937 + 4.20642i) q^{87} +(-2.72618 + 4.72188i) q^{89} +(-1.78367 - 3.08940i) q^{91} +(0.640863 - 0.804056i) q^{93} +(13.6948 + 4.98448i) q^{95} +(-0.470518 + 2.66844i) q^{97} +(-1.29193 - 5.64644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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