LMFDB - Embedded newform 864.2.v.b.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11341 + 0.871966i) q^{2} +(0.479352 - 1.94171i) q^{4} +(-2.70909 + 1.12214i) q^{5} +(0.103960 - 0.103960i) q^{7} +(1.15939 + 2.57989i) q^{8} +O(q^{10})$	\(q+(-1.11341 + 0.871966i) q^{2} +(0.479352 - 1.94171i) q^{4} +(-2.70909 + 1.12214i) q^{5} +(0.103960 - 0.103960i) q^{7} +(1.15939 + 2.57989i) q^{8} +(2.03785 - 3.61163i) q^{10} +(-2.45541 - 5.92789i) q^{11} +(5.82208 + 2.41158i) q^{13} +(-0.0251002 + 0.206399i) q^{14} +(-3.54044 - 1.86152i) q^{16} +2.21295i q^{17} +(-0.136914 - 0.0567118i) q^{19} +(0.880262 + 5.79815i) q^{20} +(7.90280 + 4.45912i) q^{22} +(4.61190 + 4.61190i) q^{23} +(2.54442 - 2.54442i) q^{25} +(-8.58516 + 2.39158i) q^{26} +(-0.152026 - 0.251692i) q^{28} +(0.234725 - 0.566675i) q^{29} -8.85403 q^{31} +(5.56514 - 1.01452i) q^{32} +(-1.92962 - 2.46392i) q^{34} +(-0.164979 + 0.398293i) q^{35} +(-4.52845 + 1.87575i) q^{37} +(0.201892 - 0.0562413i) q^{38} +(-6.03588 - 5.68815i) q^{40} +(3.66902 + 3.66902i) q^{41} +(1.55993 + 3.76601i) q^{43} +(-12.6872 + 1.92615i) q^{44} +(-9.15633 - 1.11350i) q^{46} +6.58283i q^{47} +6.97838i q^{49} +(-0.614329 + 5.05163i) q^{50} +(7.47341 - 10.1488i) q^{52} +(3.68433 + 8.89477i) q^{53} +(13.3039 + 13.3039i) q^{55} +(0.388734 + 0.147675i) q^{56} +(0.232777 + 0.835612i) q^{58} +(4.19204 - 1.73640i) q^{59} +(2.57150 - 6.20815i) q^{61} +(9.85814 - 7.72041i) q^{62} +(-5.31164 + 5.98218i) q^{64} -18.4787 q^{65} +(-2.81795 + 6.80313i) q^{67} +(4.29691 + 1.06078i) q^{68} +(-0.163610 - 0.587319i) q^{70} +(2.74210 - 2.74210i) q^{71} +(4.87325 + 4.87325i) q^{73} +(3.40642 - 6.03712i) q^{74} +(-0.175748 + 0.238663i) q^{76} +(-0.871527 - 0.360998i) q^{77} +10.4247i q^{79} +(11.6803 + 1.07014i) q^{80} +(-7.28437 - 0.885853i) q^{82} +(-6.12008 - 2.53502i) q^{83} +(-2.48325 - 5.99509i) q^{85} +(-5.02067 - 2.83289i) q^{86} +(12.4465 - 13.2074i) q^{88} +(-7.98297 + 7.98297i) q^{89} +(0.855969 - 0.354554i) q^{91} +(11.1657 - 6.74423i) q^{92} +(-5.74000 - 7.32937i) q^{94} +0.434552 q^{95} -16.1885 q^{97} +(-6.08491 - 7.76978i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.11341	+	0.871966i	−0.787298	+	0.616573i
$2$	−1.11341	+	0.871966i	−0.787298	+	0.616573i
$3$		0			0
$3$		0			0
$4$	0.479352	−	1.94171i	0.239676	−	0.970853i
$5$	−2.70909	+	1.12214i	−1.21154	+	0.501837i	−0.894711	−	0.446646i	$-0.852618\pi$
$5$	−2.70909	+	1.12214i	−1.21154	+	0.501837i	−0.316830	+	0.948482i	$0.602618\pi$
$6$		0			0
$7$	0.103960	−	0.103960i	0.0392931	−	0.0392931i	−0.687187	−	0.726480i	$-0.741155\pi$
$7$	0.103960	−	0.103960i	0.0392931	−	0.0392931i	0.726480	+	0.687187i	$0.241155\pi$
$8$	1.15939	+	2.57989i	0.409905	+	0.912128i
$9$		0			0
$10$	2.03785	−	3.61163i	0.644425	−	1.14210i
$11$	−2.45541	−	5.92789i	−0.740335	−	1.78733i	−0.604514	−	0.796594i	$-0.706633\pi$
$11$	−2.45541	−	5.92789i	−0.740335	−	1.78733i	−0.135821	−	0.990733i	$-0.543367\pi$
$12$		0			0
$13$	5.82208	+	2.41158i	1.61475	+	0.668853i	0.993403	−	0.114680i	$-0.0365842\pi$
$13$	5.82208	+	2.41158i	1.61475	+	0.668853i	0.621351	+	0.783532i	$0.286584\pi$
$14$	−0.0251002	+	0.206399i	−0.00670831	+	0.0551624i
$15$		0			0
$16$	−3.54044	−	1.86152i	−0.885111	−	0.465380i
$17$			2.21295i			0.536720i	0.963319	+	0.268360i	$0.0864817\pi$
$17$			2.21295i			0.536720i	−0.963319	+	0.268360i	$0.913518\pi$
$18$		0			0
$19$	−0.136914	−	0.0567118i	−0.0314103	−	0.0130106i	0.366923	−	0.930251i	$-0.380411\pi$
$19$	−0.136914	−	0.0567118i	−0.0314103	−	0.0130106i	−0.398333	+	0.917241i	$0.630411\pi$
$20$	0.880262	+	5.79815i	0.196833	+	1.29651i
$21$		0			0
$22$	7.90280	+	4.45912i	1.68488	+	0.950688i
$23$	4.61190	+	4.61190i	0.961647	+	0.961647i	0.999291	−	0.0376445i	$-0.0119854\pi$
$23$	4.61190	+	4.61190i	0.961647	+	0.961647i	−0.0376445	+	0.999291i	$0.511985\pi$
$24$		0			0
$25$	2.54442	−	2.54442i	0.508884	−	0.508884i
$26$	−8.58516	+	2.39158i	−1.68369	+	0.469027i
$27$		0			0
$28$	−0.152026	−	0.251692i	−0.0287302	−	0.0475654i
$29$	0.234725	−	0.566675i	0.0435873	−	0.105229i	−0.900586	−	0.434677i	$-0.856863\pi$
$29$	0.234725	−	0.566675i	0.0435873	−	0.105229i	0.944174	+	0.329448i	$0.106863\pi$
$30$		0			0
$31$	−8.85403			−1.59023			−0.795115	−	0.606458i	$-0.792590\pi$
$31$	−8.85403			−1.59023			−0.795115	+	0.606458i	$0.792590\pi$
$32$	5.56514	−	1.01452i	0.983787	−	0.179343i
$33$		0			0
$34$	−1.92962	−	2.46392i	−0.330927	−	0.422559i
$35$	−0.164979	+	0.398293i	−0.0278865	+	0.0673239i
$36$		0			0
$37$	−4.52845	+	1.87575i	−0.744473	+	0.308371i	−0.722484	−	0.691387i	$-0.757000\pi$
$37$	−4.52845	+	1.87575i	−0.744473	+	0.308371i	−0.0219887	+	0.999758i	$0.507000\pi$
$38$	0.201892	−	0.0562413i	0.0327513	−	0.00912355i
$39$		0			0
$40$	−6.03588	−	5.68815i	−0.954356	−	0.899375i
$41$	3.66902	+	3.66902i	0.573004	+	0.573004i	0.932967	−	0.359963i	$-0.117211\pi$
$41$	3.66902	+	3.66902i	0.573004	+	0.573004i	−0.359963	+	0.932967i	$0.617211\pi$
$42$		0			0
$43$	1.55993	+	3.76601i	0.237887	+	0.574311i	0.997064	−	0.0765741i	$-0.0243982\pi$
$43$	1.55993	+	3.76601i	0.237887	+	0.574311i	−0.759177	+	0.650885i	$0.774398\pi$
$44$	−12.6872	+	1.92615i	−1.91267	+	0.290378i
$45$		0			0
$46$	−9.15633	−	1.11350i	−1.35003	−	0.164177i
$47$			6.58283i			0.960204i	0.877213	+	0.480102i	$0.159400\pi$
$47$			6.58283i			0.960204i	−0.877213	+	0.480102i	$0.840600\pi$
$48$		0			0
$49$			6.97838i			0.996912i
$50$	−0.614329	+	5.05163i	−0.0868793	+	0.714408i
$51$		0			0
$52$	7.47341	−	10.1488i	1.03637	−	1.40738i
$53$	3.68433	+	8.89477i	0.506082	+	1.22179i	0.946121	+	0.323812i	$0.104965\pi$
$53$	3.68433	+	8.89477i	0.506082	+	1.22179i	−0.440039	+	0.897979i	$0.645035\pi$
$54$		0			0
$55$	13.3039	+	13.3039i	1.79389	+	1.79389i
$56$	0.388734	+	0.147675i	0.0519468	+	0.0197339i
$57$		0			0
$58$	0.232777	+	0.835612i	0.0305652	+	0.109721i
$59$	4.19204	−	1.73640i	0.545757	−	0.226060i	−0.0927318	−	0.995691i	$-0.529560\pi$
$59$	4.19204	−	1.73640i	0.545757	−	0.226060i	0.638489	+	0.769631i	$0.279560\pi$
$60$		0			0
$61$	2.57150	−	6.20815i	0.329247	−	0.794872i	−0.669402	−	0.742901i	$-0.733449\pi$
$61$	2.57150	−	6.20815i	0.329247	−	0.794872i	0.998649	−	0.0519716i	$-0.0165505\pi$
$62$	9.85814	−	7.72041i	1.25198	−	0.980493i
$63$		0			0
$64$	−5.31164	+	5.98218i	−0.663955	+	0.747772i
$65$	−18.4787			−2.29199
$66$		0			0
$67$	−2.81795	+	6.80313i	−0.344267	+	0.831135i	0.653007	+	0.757352i	$0.273507\pi$
$67$	−2.81795	+	6.80313i	−0.344267	+	0.831135i	−0.997274	+	0.0737829i	$0.976493\pi$
$68$	4.29691	+	1.06078i	0.521076	+	0.128639i
$69$		0			0
$70$	−0.163610	−	0.587319i	−0.0195551	−	0.0701980i
$71$	2.74210	−	2.74210i	0.325427	−	0.325427i	−0.525418	−	0.850844i	$-0.676091\pi$
$71$	2.74210	−	2.74210i	0.325427	−	0.325427i	0.850844	+	0.525418i	$0.176091\pi$
$72$		0			0
$73$	4.87325	+	4.87325i	0.570371	+	0.570371i	0.932232	−	0.361861i	$-0.117859\pi$
$73$	4.87325	+	4.87325i	0.570371	+	0.570371i	−0.361861	+	0.932232i	$0.617859\pi$
$74$	3.40642	−	6.03712i	0.395989	−	0.701801i
$75$		0			0
$76$	−0.175748	+	0.238663i	−0.0201597	+	0.0273765i
$77$	−0.871527	−	0.360998i	−0.0993197	−	0.0411396i
$78$		0			0
$79$			10.4247i			1.17287i	0.809995	+	0.586437i	$0.199470\pi$
$79$			10.4247i			1.17287i	−0.809995	+	0.586437i	$0.800530\pi$
$80$	11.6803	+	1.07014i	1.30589	+	0.119646i
$81$		0			0
$82$	−7.28437	−	0.885853i	−0.804424	−	0.0978261i
$83$	−6.12008	−	2.53502i	−0.671766	−	0.278255i	0.0206141	−	0.999788i	$-0.493438\pi$
$83$	−6.12008	−	2.53502i	−0.671766	−	0.278255i	−0.692380	+	0.721533i	$0.743438\pi$
$84$		0			0
$85$	−2.48325	−	5.99509i	−0.269346	−	0.650258i
$86$	−5.02067	−	2.83289i	−0.541392	−	0.305479i
$87$		0			0
$88$	12.4465	−	13.2074i	1.32680	−	1.40792i
$89$	−7.98297	+	7.98297i	−0.846193	+	0.846193i	−0.989656	−	0.143463i	$-0.954176\pi$
$89$	−7.98297	+	7.98297i	−0.846193	+	0.846193i	0.143463	+	0.989656i	$0.454176\pi$
$90$		0			0
$91$	0.855969	−	0.354554i	0.0897299	−	0.0371674i
$92$	11.1657	−	6.74423i	1.16410	−	0.703134i
$93$		0			0
$94$	−5.74000	−	7.32937i	−0.592036	−	0.755967i
$95$	0.434552			0.0445841
$96$		0			0
$97$	−16.1885			−1.64369			−0.821845	−	0.569711i	$-0.807055\pi$
$97$	−16.1885			−1.64369			−0.821845	+	0.569711i	$0.807055\pi$
$98$	−6.08491	−	7.76978i	−0.614669	−	0.784867i
$99$		0			0
$100$	−3.72085	−	6.16019i	−0.372085	−	0.616019i
$101$	3.11963	−	1.29219i	0.310414	−	0.128578i	−0.222037	−	0.975038i	$-0.571271\pi$
$101$	3.11963	−	1.29219i	0.310414	−	0.128578i	0.532452	+	0.846460i	$0.321271\pi$
$102$		0			0
$103$	8.49008	−	8.49008i	0.836552	−	0.836552i	−0.151851	−	0.988403i	$-0.548523\pi$
$103$	8.49008	−	8.49008i	0.836552	−	0.836552i	0.988403	+	0.151851i	$0.0485235\pi$
$104$	0.528429	+	17.8163i	0.0518167	+	1.74703i
$105$		0			0
$106$	−11.8581	−	6.69089i	−1.15176	−	0.649877i
$107$	1.34331	+	3.24305i	0.129863	+	0.313517i	0.975415	−	0.220376i	$-0.0707284\pi$
$107$	1.34331	+	3.24305i	0.129863	+	0.313517i	−0.845552	+	0.533893i	$0.820728\pi$
$108$		0			0
$109$	15.7340	+	6.51722i	1.50704	+	0.624236i	0.974945	−	0.222448i	$-0.0714047\pi$
$109$	15.7340	+	6.51722i	1.50704	+	0.624236i	0.532096	+	0.846684i	$0.321405\pi$
$110$	−26.4131	−	3.21211i	−2.51839	−	0.306262i
$111$		0			0
$112$	−0.561587	+	0.174541i	−0.0530650	+	0.0164925i
$113$			15.0322i			1.41411i	0.707159	+	0.707055i	$0.249976\pi$
$113$			15.0322i			1.41411i	−0.707159	+	0.707055i	$0.750024\pi$
$114$		0			0
$115$	−17.6692	−	7.31883i	−1.64766	−	0.682485i
$116$	−0.987801	−	0.727403i	−0.0917151	−	0.0675377i
$117$		0			0
$118$	−3.15337	+	5.58863i	−0.290291	+	0.514475i
$119$	0.230058	+	0.230058i	0.0210894	+	0.0210894i
$120$		0			0
$121$	−21.3327	+	21.3327i	−1.93934	+	1.93934i
$122$	2.55017	+	9.15446i	0.230881	+	0.828806i
$123$		0			0
$124$	−4.24419	+	17.1919i	−0.381140	+	1.54388i
$125$	1.57284	−	3.79718i	0.140679	−	0.339630i
$126$		0			0
$127$	9.20956			0.817216			0.408608	−	0.912710i	$-0.366014\pi$
$127$	9.20956			0.817216			0.408608	+	0.912710i	$0.366014\pi$
$128$	0.697765	−	11.2922i	0.0616743	−	0.998096i
$129$		0			0
$130$	20.5743	−	16.1127i	1.80448	−	1.41318i
$131$	5.53164	−	13.3546i	0.483301	−	1.16679i	−0.474731	−	0.880131i	$-0.657455\pi$
$131$	5.53164	−	13.3546i	0.483301	−	1.16679i	0.958032	−	0.286661i	$-0.0925455\pi$
$132$		0			0
$133$	−0.0201293	+	0.00833784i	−0.00174543	+	0.000722983i
$134$	−2.79457	−	10.0318i	−0.241414	−	0.866616i
$135$		0			0
$136$	−5.70917	+	2.56567i	−0.489558	+	0.220005i
$137$	−4.49306	−	4.49306i	−0.383868	−	0.383868i	0.488626	−	0.872494i	$-0.337498\pi$
$137$	−4.49306	−	4.49306i	−0.383868	−	0.383868i	−0.872494	+	0.488626i	$0.837498\pi$
$138$		0			0
$139$	−6.81127	−	16.4439i	−0.577725	−	1.39475i	−0.894850	−	0.446367i	$-0.852718\pi$
$139$	−6.81127	−	16.4439i	−0.577725	−	1.39475i	0.317125	−	0.948384i	$-0.397282\pi$
$140$	0.694286	+	0.511262i	0.0586779	+	0.0432096i
$141$		0			0
$142$	−0.662056	+	5.44408i	−0.0555585	+	0.456857i
$143$		−	40.4341i		−	3.38127i
$144$		0			0
$145$			1.79857i			0.149363i
$146$	−9.67522	−	1.17660i	−0.800727	−	0.0973765i
$147$		0			0
$148$	1.47143	+	9.69206i	0.120951	+	0.796683i
$149$	3.92523	+	9.47635i	0.321567	+	0.776332i	0.999163	+	0.0408980i	$0.0130219\pi$
$149$	3.92523	+	9.47635i	0.321567	+	0.776332i	−0.677596	+	0.735434i	$0.736978\pi$
$150$		0			0
$151$	8.02344	+	8.02344i	0.652938	+	0.652938i	0.953699	−	0.300761i	$-0.0972408\pi$
$151$	8.02344	+	8.02344i	0.652938	+	0.652938i	−0.300761	+	0.953699i	$0.597241\pi$
$152$	−0.0124268	−	0.418975i	−0.00100794	−	0.0339833i
$153$		0			0
$154$	1.28514	−	0.358003i	0.103560	−	0.0288487i
$155$	23.9863	−	9.93547i	1.92663	−	0.798036i
$156$		0			0
$157$	0.580046	−	1.40036i	0.0462927	−	0.111761i	−0.899042	−	0.437863i	$-0.855735\pi$
$157$	0.580046	−	1.40036i	0.0462927	−	0.111761i	0.945334	+	0.326103i	$0.105735\pi$
$158$	−9.09000	−	11.6070i	−0.723162	−	0.923401i
$159$		0			0
$160$	−13.9380	+	8.99328i	−1.10190	+	0.710981i
$161$	0.958903			0.0755721
$162$		0			0
$163$	0.468891	−	1.13200i	0.0367264	−	0.0886654i	−0.904452	−	0.426575i	$-0.859720\pi$
$163$	0.468891	−	1.13200i	0.0367264	−	0.0886654i	0.941178	+	0.337910i	$0.109720\pi$
$164$	8.88290	−	5.36540i	0.693638	−	0.418967i
$165$		0			0
$166$	9.02459	−	2.51399i	0.700444	−	0.195123i
$167$	0.0351278	−	0.0351278i	0.00271827	−	0.00271827i	−0.705746	−	0.708465i	$-0.749388\pi$
$167$	0.0351278	−	0.0351278i	0.00271827	−	0.00271827i	0.708465	+	0.705746i	$0.249388\pi$
$168$		0			0
$169$	18.8884	+	18.8884i	1.45296	+	1.45296i
$170$	7.99237	+	4.50967i	0.612987	+	0.345876i
$171$		0			0
$172$	8.06023	−	1.22369i	0.614587	−	0.0933052i
$173$	−12.1569	−	5.03557i	−0.924275	−	0.382847i	−0.130771	−	0.991413i	$-0.541745\pi$
$173$	−12.1569	−	5.03557i	−0.924275	−	0.382847i	−0.793504	+	0.608565i	$0.791745\pi$
$174$		0			0
$175$		−	0.529035i		−	0.0399913i
$176$	−2.34164	+	25.5582i	−0.176507	+	1.92652i
$177$		0			0
$178$	1.92742	−	15.8492i	0.144466	−	1.18795i
$179$	−0.169903	−	0.0703763i	−0.0126992	−	0.00526017i	0.376325	−	0.926488i	$-0.377188\pi$
$179$	−0.169903	−	0.0703763i	−0.0126992	−	0.00526017i	−0.389024	+	0.921228i	$0.627188\pi$
$180$		0			0
$181$	1.78537	+	4.31025i	0.132705	+	0.320379i	0.976239	−	0.216698i	$-0.0695287\pi$
$181$	1.78537	+	4.31025i	0.132705	+	0.320379i	−0.843534	+	0.537076i	$0.819529\pi$
$182$	−0.643883	+	1.14114i	−0.0477278	+	0.0845868i
$183$		0			0
$184$	−6.55120	+	17.2451i	−0.482961	+	1.27133i
$185$	10.1631	−	10.1631i	0.747208	−	0.747208i
$186$		0			0
$187$	13.1182	−	5.43372i	0.959295	−	0.397353i
$188$	12.7819	+	3.15549i	0.932217	+	0.230138i
$189$		0			0
$190$	−0.483833	+	0.378914i	−0.0351009	+	0.0274893i
$191$	20.4471			1.47950			0.739751	−	0.672881i	$-0.234943\pi$
$191$	20.4471			1.47950			0.739751	+	0.672881i	$0.234943\pi$
$192$		0			0
$193$	−5.47189			−0.393876			−0.196938	−	0.980416i	$-0.563100\pi$
$193$	−5.47189			−0.393876			−0.196938	+	0.980416i	$0.563100\pi$
$194$	18.0244	−	14.1158i	1.29407	−	1.01346i
$195$		0			0
$196$	13.5500	+	3.34510i	0.967855	+	0.238936i
$197$	3.99952	−	1.65666i	0.284954	−	0.118032i	−0.235628	−	0.971843i	$-0.575715\pi$
$197$	3.99952	−	1.65666i	0.284954	−	0.118032i	0.520583	+	0.853811i	$0.325715\pi$
$198$		0			0
$199$	−6.23859	+	6.23859i	−0.442242	+	0.442242i	−0.892765	−	0.450523i	$-0.851237\pi$
$199$	−6.23859	+	6.23859i	−0.442242	+	0.442242i	0.450523	+	0.892765i	$0.351237\pi$
$200$	9.51429	+	3.61435i	0.672762	+	0.255573i
$201$		0			0
$202$	−2.34667	+	4.15894i	−0.165111	+	0.292622i
$203$	−0.0345095	−	0.0833133i	−0.00242209	−	0.00584745i
$204$		0			0
$205$	−14.0568	−	5.82253i	−0.981772	−	0.406663i
$206$	−2.04986	+	16.8560i	−0.142820	+	1.17441i
$207$		0			0
$208$	−16.1235	−	19.3760i	−1.11797	−	1.34348i
$209$			0.950865i			0.0657727i
$210$		0			0
$211$	6.05933	+	2.50986i	0.417142	+	0.172786i	0.581375	−	0.813636i	$-0.302515\pi$
$211$	6.05933	+	2.50986i	0.417142	+	0.172786i	−0.164233	+	0.986422i	$0.552515\pi$
$212$	19.0371	−	2.89017i	1.30747	−	0.198498i
$213$		0			0
$214$	−4.32348	−	2.43951i	−0.295547	−	0.166761i
$215$	−8.45198	−	8.45198i	−0.576420	−	0.576420i
$216$		0			0
$217$	−0.920462	+	0.920462i	−0.0624851	+	0.0624851i
$218$	−23.2011	+	6.46315i	−1.57138	+	0.437740i
$219$		0			0
$220$	32.2094	−	19.4550i	2.17156	−	1.31165i
$221$	−5.33672	+	12.8840i	−0.358987	+	0.866671i
$222$		0			0
$223$	17.2782			1.15703			0.578517	−	0.815670i	$-0.303632\pi$
$223$	17.2782			1.15703			0.578517	+	0.815670i	$0.303632\pi$
$224$	0.473081	−	0.684019i	0.0316091	−	0.0457029i
$225$		0			0
$226$	−13.1076	−	16.7369i	−0.871901	−	1.11333i
$227$	−1.80066	+	4.34717i	−0.119514	+	0.288532i	−0.972303	−	0.233723i	$-0.924909\pi$
$227$	−1.80066	+	4.34717i	−0.119514	+	0.288532i	0.852789	+	0.522255i	$0.174909\pi$
$228$		0			0
$229$	8.11150	−	3.35989i	0.536023	−	0.222028i	−0.0982160	−	0.995165i	$-0.531314\pi$
$229$	8.11150	−	3.35989i	0.536023	−	0.222028i	0.634239	+	0.773137i	$0.281314\pi$
$230$	26.0548	−	7.25812i	1.71800	−	0.478586i
$231$		0			0
$232$	1.73410	−	0.0514332i	0.113849	−	0.00337675i
$233$	−2.65249	−	2.65249i	−0.173771	−	0.173771i	0.614863	−	0.788634i	$-0.289211\pi$
$233$	−2.65249	−	2.65249i	−0.173771	−	0.173771i	−0.788634	+	0.614863i	$0.789211\pi$
$234$		0			0
$235$	−7.38686	−	17.8335i	−0.481866	−	1.16333i
$236$	−1.36212	−	8.97205i	−0.0886662	−	0.584031i
$237$		0			0
$238$	−0.456751	−	0.0555456i	−0.0296068	−	0.00360049i
$239$		−	6.07668i		−	0.393068i	−0.980497	−	0.196534i	$-0.937031\pi$
$239$		−	6.07668i		−	0.393068i	0.980497	−	0.196534i	$-0.0629685\pi$
$240$		0			0
$241$		−	22.9953i		−	1.48126i	−0.671913	−	0.740630i	$-0.734527\pi$
$241$		−	22.9953i		−	1.48126i	0.671913	−	0.740630i	$-0.265473\pi$
$242$	5.15060	−	42.3534i	0.331093	−	2.72258i
$243$		0			0
$244$	−10.8217	−	7.96898i	−0.692792	−	0.510162i
$245$	−7.83073	−	18.9051i	−0.500287	−	1.20780i
$246$		0			0
$247$	−0.660361	−	0.660361i	−0.0420178	−	0.0420178i
$248$	−10.2652	−	22.8424i	−0.651844	−	1.45049i
$249$		0			0
$250$	1.55979	+	5.59927i	0.0986500	+	0.354129i
$251$	−3.05607	+	1.26587i	−0.192898	+	0.0799008i	−0.477041	−	0.878881i	$-0.658291\pi$
$251$	−3.05607	+	1.26587i	−0.192898	+	0.0799008i	0.284144	+	0.958782i	$0.408291\pi$
$252$		0			0
$253$	16.0147	−	38.6629i	1.00684	−	2.43072i
$254$	−10.2540	+	8.03042i	−0.643393	+	0.503873i
$255$		0			0
$256$	9.06949	+	13.1812i	0.566843	+	0.823826i
$257$	4.05144			0.252722			0.126361	−	0.991984i	$-0.459670\pi$
$257$	4.05144			0.252722			0.126361	+	0.991984i	$0.459670\pi$
$258$		0			0
$259$	−0.275775	+	0.665779i	−0.0171358	+	0.0413695i
$260$	−8.85777	+	35.8801i	−0.549336	+	2.22519i
$261$		0			0
$262$	5.48575	+	19.6925i	0.338911	+	1.21660i
$263$	−7.96691	+	7.96691i	−0.491261	+	0.491261i	−0.908703	−	0.417442i	$-0.862927\pi$
$263$	−7.96691	+	7.96691i	−0.491261	+	0.491261i	0.417442	+	0.908703i	$0.362927\pi$
$264$		0			0
$265$	−19.9624	−	19.9624i	−1.22628	−	1.22628i
$266$	0.0151418	−	0.0268355i	0.000928405	−	0.00164539i
$267$		0			0
$268$	11.8589	+	8.73272i	0.724397	+	0.533436i
$269$	−13.3531	−	5.53105i	−0.814155	−	0.337234i	−0.0635444	−	0.997979i	$-0.520240\pi$
$269$	−13.3531	−	5.53105i	−0.814155	−	0.337234i	−0.750610	+	0.660745i	$0.770240\pi$
$270$		0			0
$271$		−	16.2842i		−	0.989195i	−0.869122	−	0.494598i	$-0.835315\pi$
$271$		−	16.2842i		−	0.989195i	0.869122	−	0.494598i	$-0.164685\pi$
$272$	4.11946	−	7.83484i	0.249779	−	0.475057i
$273$		0			0
$274$	8.92040	+	1.08481i	0.538901	+	0.0655359i
$275$	−21.3307	−	8.83546i	−1.28629	−	0.532798i
$276$		0			0
$277$	2.21965	+	5.35871i	0.133366	+	0.321974i	0.976428	−	0.215842i	$-0.0692496\pi$
$277$	2.21965	+	5.35871i	0.133366	+	0.321974i	−0.843062	+	0.537816i	$0.819250\pi$
$278$	21.9222	+	12.3695i	1.31481	+	0.741875i
$279$		0			0
$280$	−1.21883	+	0.0361503i	−0.0728388	+	0.00216039i
$281$	18.2054	−	18.2054i	1.08605	−	1.08605i	0.0901138	−	0.995931i	$-0.471277\pi$
$281$	18.2054	−	18.2054i	1.08605	−	1.08605i	0.995931	−	0.0901138i	$-0.0287231\pi$
$282$		0			0
$283$	−17.9055	+	7.41670i	−1.06437	+	0.440877i	−0.845001	−	0.534765i	$-0.820400\pi$
$283$	−17.9055	+	7.41670i	−1.06437	+	0.440877i	−0.219370	+	0.975642i	$0.570400\pi$
$284$	−4.00992	−	6.63877i	−0.237945	−	0.393939i
$285$		0			0
$286$	35.2571	+	45.0196i	2.08480	+	2.66207i
$287$	0.762860			0.0450302
$288$		0			0
$289$	12.1028			0.711931
$290$	−1.56829	−	2.00254i	−0.0920931	−	0.117593i
$291$		0			0
$292$	11.7984	−	7.12642i	0.690450	−	0.417042i
$293$	−11.8974	+	4.92807i	−0.695054	+	0.287901i	−0.702104	−	0.712074i	$-0.747756\pi$
$293$	−11.8974	+	4.92807i	−0.695054	+	0.287901i	0.00705007	+	0.999975i	$0.497756\pi$
$294$		0			0
$295$	−9.40811	+	9.40811i	−0.547762	+	0.547762i
$296$	−10.0894	−	9.50818i	−0.586437	−	0.552652i
$297$		0			0
$298$	−12.6334	−	7.12837i	−0.731835	−	0.412935i
$299$	15.7288	+	37.9728i	0.909622	+	2.19602i
$300$		0			0
$301$	0.553683	+	0.229343i	0.0319138	+	0.0132191i
$302$	−15.9295	−	1.93719i	−0.916641	−	0.111473i
$303$		0			0
$304$	0.379168	+	0.455654i	0.0217468	+	0.0261335i
$305$			19.7040i			1.12825i
$306$		0			0
$307$	15.3702	+	6.36654i	0.877223	+	0.363358i	0.775419	−	0.631447i	$-0.217539\pi$
$307$	15.3702	+	6.36654i	0.877223	+	0.363358i	0.101804	+	0.994804i	$0.467539\pi$
$308$	−1.11872	+	1.51920i	−0.0637450	+	0.0865646i
$309$		0			0
$310$	−18.0432	+	31.9775i	−1.02478	+	1.81620i
$311$	7.70248	+	7.70248i	0.436767	+	0.436767i	0.890923	−	0.454155i	$-0.150059\pi$
$311$	7.70248	+	7.70248i	0.436767	+	0.436767i	−0.454155	+	0.890923i	$0.650059\pi$
$312$		0			0
$313$	−10.5231	+	10.5231i	−0.594802	+	0.594802i	−0.938925	−	0.344123i	$-0.888176\pi$
$313$	−10.5231	+	10.5231i	−0.594802	+	0.594802i	0.344123	+	0.938925i	$0.388176\pi$
$314$	0.575234	+	2.06495i	0.0324624	+	0.116532i
$315$		0			0
$316$	20.2418	+	4.99711i	1.13869	+	0.281109i
$317$	−6.57566	+	15.8750i	−0.369326	+	0.891631i	0.624535	+	0.780997i	$0.285288\pi$
$317$	−6.57566	+	15.8750i	−0.369326	+	0.891631i	−0.993861	+	0.110635i	$0.964712\pi$
$318$		0			0
$319$	−3.93554			−0.220348
$320$	7.67685	−	22.1667i	0.429149	−	1.23915i
$321$		0			0
$322$	−1.06765	+	0.836130i	−0.0594978	+	0.0465957i
$323$	0.125501	−	0.302985i	0.00698304	−	0.0168586i
$324$		0			0
$325$	20.9499	−	8.67773i	1.16209	−	0.481354i
$326$	0.465002	+	1.66924i	0.0257541	+	0.0924506i
$327$		0			0
$328$	−5.21184	+	13.7195i	−0.287776	+	0.757531i
$329$	0.684349	+	0.684349i	0.0377294	+	0.0377294i
$330$		0			0
$331$	−10.3554	−	25.0003i	−0.569187	−	1.37414i	−0.902242	−	0.431231i	$-0.858079\pi$
$331$	−10.3554	−	25.0003i	−0.569187	−	1.37414i	0.333055	−	0.942907i	$-0.391921\pi$
$332$	−7.85593	+	10.6682i	−0.431150	+	0.585495i
$333$		0			0
$334$	−0.00848130	+	0.0697417i	−0.000464076	+	0.00381610i
$335$		−	21.5924i		−	1.17972i
$336$		0			0
$337$		−	2.65115i		−	0.144417i	−0.997390	−	0.0722087i	$-0.976995\pi$
$337$		−	2.65115i		−	0.144417i	0.997390	−	0.0722087i	$-0.0230048\pi$
$338$	−37.5006	−	4.56046i	−2.03976	−	0.248056i
$339$		0			0
$340$	−12.8310	+	1.94798i	−0.695861	+	0.105644i
$341$	21.7403	+	52.4857i	1.17730	+	2.84226i
$342$		0			0
$343$	1.45319	+	1.45319i	0.0784648	+	0.0784648i
$344$	−7.90731	+	8.39071i	−0.426334	+	0.452397i
$345$		0			0
$346$	17.9265	−	4.99379i	0.963733	−	0.268468i
$347$	22.3756	−	9.26828i	1.20119	−	0.497547i	0.309804	−	0.950801i	$-0.399737\pi$
$347$	22.3756	−	9.26828i	1.20119	−	0.497547i	0.891382	+	0.453253i	$0.149737\pi$
$348$		0			0
$349$	−7.56347	+	18.2598i	−0.404863	+	0.977426i	0.581605	+	0.813472i	$0.302425\pi$
$349$	−7.56347	+	18.2598i	−0.404863	+	0.977426i	−0.986468	+	0.163955i	$0.947575\pi$
$350$	0.461300	+	0.589031i	0.0246575	+	0.0314850i
$351$		0			0
$352$	−19.6787	−	30.4985i	−1.04888	−	1.62558i
$353$	13.5186			0.719521			0.359761	−	0.933045i	$-0.382858\pi$
$353$	13.5186			0.719521			0.359761	+	0.933045i	$0.382858\pi$
$354$		0			0
$355$	−4.35156	+	10.5056i	−0.230957	+	0.557579i
$356$	11.6739	+	19.3272i	0.618717	+	1.02434i
$357$		0			0
$358$	0.250537	−	0.0697925i	0.0132413	−	0.00368865i
$359$	−14.2729	+	14.2729i	−0.753297	+	0.753297i	−0.975093	−	0.221796i	$-0.928808\pi$
$359$	−14.2729	+	14.2729i	−0.753297	+	0.753297i	0.221796	+	0.975093i	$0.428808\pi$
$360$		0			0
$361$	−13.4195	−	13.4195i	−0.706289	−	0.706289i
$362$	−5.74623	−	3.24229i	−0.302015	−	0.170411i
$363$		0			0
$364$	−0.278129	−	1.83200i	−0.0145779	−	0.0960227i
$365$	−18.6705	−	7.73359i	−0.977260	−	0.404794i
$366$		0			0
$367$			19.2022i			1.00234i	0.865348	+	0.501172i	$0.167098\pi$
$367$			19.2022i			1.00234i	−0.865348	+	0.501172i	$0.832902\pi$
$368$	−7.74302	−	24.9133i	−0.403633	−	1.29870i
$369$		0			0
$370$	−2.45380	+	20.1776i	−0.127567	+	1.04898i
$371$	1.30772	+	0.541676i	0.0678935	+	0.0281224i
$372$		0			0
$373$	−8.73051	−	21.0773i	−0.452048	−	1.09134i	−0.971542	−	0.236867i	$-0.923879\pi$
$373$	−8.73051	−	21.0773i	−0.452048	−	1.09134i	0.519494	−	0.854474i	$-0.326121\pi$
$374$	−9.86784	+	17.4885i	−0.510254	+	0.904310i
$375$		0			0
$376$	−16.9830	+	7.63205i	−0.875829	+	0.393593i
$377$	2.73317	−	2.73317i	0.140765	−	0.140765i
$378$		0			0
$379$	−17.7998	+	7.37290i	−0.914312	+	0.378721i	−0.789706	−	0.613486i	$-0.789767\pi$
$379$	−17.7998	+	7.37290i	−0.914312	+	0.378721i	−0.124606	+	0.992206i	$0.539767\pi$
$380$	0.208303	−	0.843772i	0.0106857	−	0.0432846i
$381$		0			0
$382$	−22.7660	+	17.8292i	−1.16481	+	0.912221i
$383$	−9.29759			−0.475084			−0.237542	−	0.971377i	$-0.576342\pi$
$383$	−9.29759			−0.475084			−0.237542	+	0.971377i	$0.576342\pi$
$384$		0			0
$385$	2.76613			0.140975
$386$	6.09245	−	4.77130i	0.310097	−	0.242853i
$387$		0			0
$388$	−7.75997	+	31.4333i	−0.393953	+	1.59578i
$389$	−20.7514	+	8.59553i	−1.05214	+	0.435811i	−0.840655	−	0.541571i	$-0.817830\pi$
$389$	−20.7514	+	8.59553i	−1.05214	+	0.435811i	−0.211485	+	0.977381i	$0.567830\pi$
$390$		0			0
$391$	−10.2059	+	10.2059i	−0.516135	+	0.516135i
$392$	−18.0034	+	8.09065i	−0.909312	+	0.408640i
$393$		0			0
$394$	−3.00855	+	5.33198i	−0.151569	+	0.268621i
$395$	−11.6980	−	28.2415i	−0.588591	−	1.42098i
$396$		0			0
$397$	−14.4613	−	5.99007i	−0.725792	−	0.300633i	−0.0109706	−	0.999940i	$-0.503492\pi$
$397$	−14.4613	−	5.99007i	−0.725792	−	0.300633i	−0.714822	+	0.699307i	$0.753492\pi$
$398$	1.50625	−	12.3859i	0.0755017	−	0.620850i
$399$		0			0
$400$	−13.7449	+	4.27189i	−0.687244	+	0.213595i
$401$			0.299530i			0.0149578i	0.999972	+	0.00747890i	$0.00238063\pi$
$401$			0.299530i			0.0149578i	−0.999972	+	0.00747890i	$0.997619\pi$
$402$		0			0
$403$	−51.5488	−	21.3522i	−2.56783	−	1.06363i
$404$	−1.01366	−	6.67681i	−0.0504314	−	0.332184i
$405$		0			0
$406$	0.111070	+	0.0626706i	0.00551229	+	0.00311029i
$407$	22.2385	+	22.2385i	1.10232	+	1.10232i
$408$		0			0
$409$	3.25402	−	3.25402i	0.160901	−	0.160901i	−0.622065	−	0.782966i	$-0.713706\pi$
$409$	3.25402	−	3.25402i	0.160901	−	0.160901i	0.782966	+	0.622065i	$0.213706\pi$
$410$	20.7280	−	5.77423i	1.02368	−	0.285169i
$411$		0			0
$412$	−12.4155	−	20.5550i	−0.611668	−	1.01267i
$413$	0.255288	−	0.616319i	0.0125619	−	0.0303271i
$414$		0			0
$415$	19.4245			0.953510
$416$	34.8472	+	7.51420i	1.70853	+	0.368414i
$417$		0			0
$418$	−0.829122	−	1.05870i	−0.0405537	−	0.0517827i
$419$	−3.29846	+	7.96319i	−0.161140	+	0.389027i	−0.983741	−	0.179592i	$-0.942522\pi$
$419$	−3.29846	+	7.96319i	−0.161140	+	0.389027i	0.822601	+	0.568619i	$0.192522\pi$
$420$		0			0
$421$	18.5634	−	7.68923i	0.904727	−	0.374750i	0.118691	−	0.992931i	$-0.462130\pi$
$421$	18.5634	−	7.68923i	0.904727	−	0.374750i	0.786036	+	0.618181i	$0.212130\pi$
$422$	−8.93501	+	2.48904i	−0.434950	+	0.121164i
$423$		0			0
$424$	−18.6759	+	19.8177i	−0.906984	+	0.962430i
$425$	5.63069	+	5.63069i	0.273129	+	0.273129i
$426$		0			0
$427$	−0.378065	−	0.912730i	−0.0182959	−	0.0441701i
$428$	6.94097	−	1.05376i	0.335504	−	0.0509355i
$429$		0			0
$430$	16.7803	+	2.04066i	0.809219	+	0.0984093i
$431$			15.9187i			0.766778i	0.923587	+	0.383389i	$0.125243\pi$
$431$			15.9187i			0.766778i	−0.923587	+	0.383389i	$0.874757\pi$
$432$		0			0
$433$			41.1903i			1.97948i	0.142877	+	0.989740i	$0.454365\pi$
$433$			41.1903i			1.97948i	−0.142877	+	0.989740i	$0.545635\pi$
$434$	0.222238	−	1.82746i	0.0106678	−	0.0877209i
$435$		0			0
$436$	20.1966	−	27.4267i	0.967243	−	1.31350i
$437$	−0.369886	−	0.892984i	−0.0176941	−	0.0427172i
$438$		0			0
$439$	−5.58206	−	5.58206i	−0.266417	−	0.266417i	0.561238	−	0.827655i	$-0.310325\pi$
$439$	−5.58206	−	5.58206i	−0.266417	−	0.266417i	−0.827655	+	0.561238i	$0.810325\pi$
$440$	−18.8981	+	49.7468i	−0.900934	+	2.37159i
$441$		0			0
$442$	−5.29245	−	18.9986i	−0.251736	−	0.903670i
$443$	−12.9536	+	5.36555i	−0.615443	+	0.254925i	−0.668554	−	0.743664i	$-0.733086\pi$
$443$	−12.9536	+	5.36555i	−0.615443	+	0.254925i	0.0531107	+	0.998589i	$0.483086\pi$
$444$		0			0
$445$	12.6685	−	30.5846i	0.600547	−	1.44985i
$446$	−19.2377	+	15.0660i	−0.910930	+	0.713396i
$447$		0			0
$448$	0.0697089	+	1.17410i	0.00329344	+	0.0554711i
$449$	−27.5435			−1.29986			−0.649929	−	0.759995i	$-0.725201\pi$
$449$	−27.5435			−1.29986			−0.649929	+	0.759995i	$0.725201\pi$
$450$		0			0
$451$	12.7406	−	30.7585i	0.599931	−	1.44836i
$452$	29.1881	+	7.20570i	1.37289	+	0.338928i
$453$		0			0
$454$	−1.78572	−	6.41028i	−0.0838079	−	0.300849i
$455$	−1.92104	+	1.92104i	−0.0900595	+	0.0900595i
$456$		0			0
$457$	5.65142	+	5.65142i	0.264362	+	0.264362i	0.826824	−	0.562461i	$-0.190145\pi$
$457$	5.65142	+	5.65142i	0.264362	+	0.264362i	−0.562461	+	0.826824i	$0.690145\pi$
$458$	−6.10169	+	10.8139i	−0.285113	+	0.505299i
$459$		0			0
$460$	−22.6808	+	30.8001i	−1.05750	+	1.43606i
$461$	−30.4680	−	12.6202i	−1.41903	−	0.587783i	−0.464416	−	0.885617i	$-0.653736\pi$
$461$	−30.4680	−	12.6202i	−1.41903	−	0.587783i	−0.954618	+	0.297834i	$0.903736\pi$
$462$		0			0
$463$		−	2.21705i		−	0.103035i	−0.998672	−	0.0515176i	$-0.983594\pi$
$463$		−	2.21705i		−	0.103035i	0.998672	−	0.0515176i	$-0.0164058\pi$
$464$	−1.88591	+	1.56934i	−0.0875510	+	0.0728547i
$465$		0			0
$466$	5.26619	+	0.640422i	0.243952	+	0.0296670i
$467$	−18.1070	−	7.50016i	−0.837892	−	0.347066i	−0.0778697	−	0.996964i	$-0.524812\pi$
$467$	−18.1070	−	7.50016i	−0.837892	−	0.347066i	−0.760022	+	0.649897i	$0.774812\pi$
$468$		0			0
$469$	0.414298	+	1.00020i	0.0191305	+	0.0461852i
$470$	23.7748	+	13.4148i	1.09665	+	0.618779i
$471$		0			0
$472$	9.33991	+	8.80183i	0.429904	+	0.405137i
$473$	18.4942	−	18.4942i	0.850365	−	0.850365i
$474$		0			0
$475$	−0.492667	+	0.204069i	−0.0226051	+	0.00936334i
$476$	0.556984	−	0.336426i	0.0255293	−	0.0154201i
$477$		0			0
$478$	5.29865	+	6.76582i	0.242355	+	0.309461i
$479$	−32.8286			−1.49997			−0.749987	−	0.661452i	$-0.769941\pi$
$479$	−32.8286			−1.49997			−0.749987	+	0.661452i	$0.769941\pi$
$480$		0			0
$481$	−30.8885			−1.40839
$482$	20.0512	+	25.6032i	0.913305	+	1.16619i
$483$		0			0
$484$	31.1960	+	51.6477i	1.41800	+	2.34762i
$485$	43.8560	−	18.1658i	1.99140	−	0.824864i
$486$		0			0
$487$	8.00548	−	8.00548i	0.362763	−	0.362763i	−0.502066	−	0.864829i	$-0.667427\pi$
$487$	8.00548	−	8.00548i	0.362763	−	0.362763i	0.864829	+	0.502066i	$0.167427\pi$
$488$	18.9977	−	0.563470i	0.859985	−	0.0255071i
$489$		0			0
$490$	25.2034	+	14.2209i	1.13857	+	0.642435i
$491$	9.65556	+	23.3106i	0.435749	+	1.05199i	0.977402	+	0.211390i	$0.0677989\pi$
$491$	9.65556	+	23.3106i	0.435749	+	1.05199i	−0.541652	+	0.840603i	$0.682201\pi$
$492$		0			0
$493$	1.25403	+	0.519435i	0.0564785	+	0.0233942i
$494$	1.31106	+	0.159439i	0.0589875	+	0.00717348i
$495$		0			0
$496$	31.3472	+	16.4819i	1.40753	+	0.740061i
$497$		−	0.570135i		−	0.0255741i
$498$		0			0
$499$	−10.0010	−	4.14254i	−0.447705	−	0.185446i	0.147428	−	0.989073i	$-0.452901\pi$
$499$	−10.0010	−	4.14254i	−0.447705	−	0.185446i	−0.595133	+	0.803627i	$0.702901\pi$
$500$	−6.61906	−	4.87418i	−0.296013	−	0.217980i
$501$		0			0
$502$	2.29886	−	4.07422i	0.102603	−	0.181841i
$503$	−0.259100	−	0.259100i	−0.0115527	−	0.0115527i	0.701307	−	0.712860i	$-0.252600\pi$
$503$	−0.259100	−	0.259100i	−0.0115527	−	0.0115527i	−0.712860	+	0.701307i	$0.752600\pi$
$504$		0			0
$505$	−7.00132	+	7.00132i	−0.311555	+	0.311555i
$506$	15.8819	+	57.0119i	0.706035	+	2.53449i
$507$		0			0
$508$	4.41462	−	17.8823i	0.195867	−	0.793397i
$509$	17.2463	−	41.6364i	0.764431	−	1.84550i	0.336538	−	0.941670i	$-0.390744\pi$
$509$	17.2463	−	41.6364i	0.764431	−	1.84550i	0.427893	−	0.903829i	$-0.359256\pi$
$510$		0			0
$511$	1.01324			0.0448232
$512$	−21.5916	−	6.76778i	−0.954223	−	0.299096i
$513$		0			0
$514$	−4.51090	+	3.53272i	−0.198967	+	0.155821i
$515$	−13.4733	+	32.5274i	−0.593704	+	1.43333i
$516$		0			0
$517$	39.0223	−	16.1636i	1.71620	−	0.710873i
$518$	−0.273487	−	0.981749i	−0.0120163	−	0.0431356i
$519$		0			0
$520$	−21.4239	−	47.6728i	−0.939501	−	2.09059i
$521$	29.6467	+	29.6467i	1.29885	+	1.29885i	0.929154	+	0.369693i	$0.120537\pi$
$521$	29.6467	+	29.6467i	1.29885	+	1.29885i	0.369693	+	0.929154i	$0.379463\pi$
$522$		0			0
$523$	2.55510	+	6.16856i	0.111727	+	0.269732i	0.969846	−	0.243718i	$-0.0783671\pi$
$523$	2.55510	+	6.16856i	0.111727	+	0.269732i	−0.858119	+	0.513450i	$0.828367\pi$
$524$	−23.2790	−	17.1423i	−1.01695	−	0.748866i
$525$		0			0
$526$	1.92354	−	15.8173i	0.0838705	−	0.689667i
$527$		−	19.5936i		−	0.853509i
$528$		0			0
$529$			19.5392i			0.849529i
$530$	39.6328	+	4.81975i	1.72154	+	0.209356i
$531$		0			0
$532$	0.00654061	+	0.0430820i	0.000283571	+	0.00186784i
$533$	12.5132	+	30.2094i	0.542005	+	1.30852i
$534$		0			0
$535$	−7.27831	−	7.27831i	−0.314669	−	0.314669i
$536$	−20.8184	+	0.617472i	−0.899218	+	0.0266707i
$537$		0			0
$538$	19.6904	−	5.48516i	0.848912	−	0.236482i
$539$	41.3671	−	17.1348i	1.78181	−	0.738049i
$540$		0			0
$541$	−6.21660	+	15.0082i	−0.267272	+	0.645252i	−0.999353	−	0.0359654i	$-0.988549\pi$
$541$	−6.21660	+	15.0082i	−0.267272	+	0.645252i	0.732081	+	0.681218i	$0.238549\pi$
$542$	14.1993	+	18.1310i	0.609911	+	0.778791i
$543$		0			0
$544$	2.24508	+	12.3154i	0.0962569	+	0.528018i
$545$	−49.9379			−2.13911
$546$		0			0
$547$	14.4297	−	34.8365i	0.616971	−	1.48950i	−0.238233	−	0.971208i	$-0.576568\pi$
$547$	14.4297	−	34.8365i	0.616971	−	1.48950i	0.855204	−	0.518291i	$-0.173432\pi$
$548$	−10.8780	+	6.57045i	−0.464683	+	0.280676i
$549$		0			0
$550$	31.4539	−	8.76216i	1.34120	−	0.373620i
$551$	−0.0642744	+	0.0642744i	−0.00273818	+	0.00273818i
$552$		0			0
$553$	1.08375	+	1.08375i	0.0460858	+	0.0460858i
$554$	−7.14399	−	4.03097i	−0.303519	−	0.171260i
$555$		0			0
$556$	−35.1941	+	5.34309i	−1.49256	+	0.226598i
$557$	9.72338	+	4.02756i	0.411993	+	0.170653i	0.579046	−	0.815295i	$-0.303425\pi$
$557$	9.72338	+	4.02756i	0.411993	+	0.170653i	−0.167053	+	0.985948i	$0.553425\pi$
$558$		0			0
$559$			25.6879i			1.08648i
$560$	1.32553	−	1.10302i	0.0560138	−	0.0466113i
$561$		0			0
$562$	−4.39555	+	36.1446i	−0.185415	+	1.52467i
$563$	−24.6470	−	10.2091i	−1.03875	−	0.430263i	−0.202884	−	0.979203i	$-0.565032\pi$
$563$	−24.6470	−	10.2091i	−1.03875	−	0.430263i	−0.835862	+	0.548940i	$0.815032\pi$
$564$		0			0
$565$	−16.8682	−	40.7235i	−0.709652	−	1.71325i
$566$	13.4690	−	23.8708i	0.566144	−	1.00336i
$567$		0			0
$568$	10.2534	+	3.89515i	0.430225	+	0.163437i
$569$	11.6321	−	11.6321i	0.487641	−	0.487641i	−0.419920	−	0.907561i	$-0.637942\pi$
$569$	11.6321	−	11.6321i	0.487641	−	0.487641i	0.907561	+	0.419920i	$0.137942\pi$
$570$		0			0
$571$	−12.6477	+	5.23886i	−0.529291	+	0.219239i	−0.631293	−	0.775545i	$-0.717475\pi$
$571$	−12.6477	+	5.23886i	−0.529291	+	0.219239i	0.102002	+	0.994784i	$0.467475\pi$
$572$	−78.5111	−	19.3821i	−3.28271	−	0.810408i
$573$		0			0
$574$	−0.849374	+	0.665188i	−0.0354522	+	0.0277644i
$575$	23.4692			0.978734
$576$		0			0
$577$	−6.58449			−0.274116			−0.137058	−	0.990563i	$-0.543765\pi$
$577$	−6.58449			−0.274116			−0.137058	+	0.990563i	$0.543765\pi$
$578$	−13.4754	+	10.5533i	−0.560502	+	0.438958i
$579$		0			0
$580$	3.49229	+	0.862146i	0.145009	+	0.0357987i
$581$	−0.899782	+	0.372702i	−0.0373292	+	0.0154623i
$582$		0			0
$583$	43.6807	−	43.6807i	1.80907	−	1.80907i
$584$	−6.92245	+	18.2224i	−0.286453	+	0.754049i
$585$		0			0
$586$	8.94955	−	15.8611i	0.369703	−	0.655215i
$587$	8.31848	+	20.0826i	0.343341	+	0.828897i	0.997373	+	0.0724312i	$0.0230758\pi$
$587$	8.31848	+	20.0826i	0.343341	+	0.828897i	−0.654033	+	0.756466i	$0.726924\pi$
$588$		0			0
$589$	1.21224	+	0.502128i	0.0499496	+	0.0206898i
$590$	2.27151	−	18.6786i	0.0935166	−	0.768986i
$591$		0			0
$592$	19.5245	+	1.78883i	0.802451	+	0.0735204i
$593$		−	27.2466i		−	1.11888i	−0.828870	−	0.559441i	$-0.811016\pi$
$593$		−	27.2466i		−	1.11888i	0.828870	−	0.559441i	$-0.188984\pi$
$594$		0			0
$595$	−0.881405	−	0.365090i	−0.0361341	−	0.0149672i
$596$	20.2818	−	3.07914i	0.830777	−	0.126127i
$597$		0			0
$598$	−50.6236	−	28.5642i	−2.07015	−	1.16808i
$599$	−0.762457	−	0.762457i	−0.0311532	−	0.0311532i	0.691359	−	0.722512i	$-0.257012\pi$
$599$	−0.762457	−	0.762457i	−0.0311532	−	0.0311532i	−0.722512	+	0.691359i	$0.757012\pi$
$600$		0			0
$601$	23.5435	−	23.5435i	0.960358	−	0.960358i	−0.0388853	−	0.999244i	$-0.512381\pi$
$601$	23.5435	−	23.5435i	0.960358	−	0.960358i	0.999244	+	0.0388853i	$0.0123807\pi$
$602$	−0.816454	+	0.227440i	−0.0332762	+	0.00926978i
$603$		0			0
$604$	19.4252	−	11.7331i	0.790400	−	0.477413i
$605$	33.8539	−	81.7305i	1.37636	−	3.32282i
$606$		0			0
$607$	19.4844			0.790847			0.395423	−	0.918499i	$-0.370598\pi$
$607$	19.4844			0.790847			0.395423	+	0.918499i	$0.370598\pi$
$608$	−0.819483	−	0.176707i	−0.0332344	−	0.00716642i
$609$		0			0
$610$	−17.1812	−	21.9386i	−0.695647	−	0.888267i
$611$	−15.8750	+	38.3257i	−0.642235	+	1.55049i
$612$		0			0
$613$	−31.3025	+	12.9659i	−1.26430	+	0.523688i	−0.911225	−	0.411909i	$-0.864862\pi$
$613$	−31.3025	+	12.9659i	−1.26430	+	0.523688i	−0.353070	+	0.935597i	$0.614862\pi$
$614$	−22.6647	+	6.31373i	−0.914672	+	0.254801i
$615$		0			0
$616$	−0.0791024	−	2.66698i	−0.00318712	−	0.107456i
$617$	−10.4435	−	10.4435i	−0.420440	−	0.420440i	0.464915	−	0.885355i	$-0.346085\pi$
$617$	−10.4435	−	10.4435i	−0.420440	−	0.420440i	−0.885355	+	0.464915i	$0.846085\pi$
$618$		0			0
$619$	0.884297	+	2.13488i	0.0355429	+	0.0858082i	0.940654	−	0.339366i	$-0.110213\pi$
$619$	0.884297	+	2.13488i	0.0355429	+	0.0858082i	−0.905111	+	0.425175i	$0.860213\pi$
$620$	−7.79386	−	51.3370i	−0.313009	−	2.06174i
$621$		0			0
$622$	−15.2923	−	1.85970i	−0.613165	−	0.0745671i
$623$			1.65981i			0.0664991i
$624$		0			0
$625$			30.0436i			1.20174i
$626$	2.54072	−	20.8923i	0.101548	−	0.835025i
$627$		0			0
$628$	−2.44103	−	1.79754i	−0.0974078	−	0.0717297i
$629$	−4.15094	−	10.0213i	−0.165509	−	0.399574i
$630$		0			0
$631$	5.30466	+	5.30466i	0.211175	+	0.211175i	0.804767	−	0.593591i	$-0.202290\pi$
$631$	5.30466	+	5.30466i	0.211175	+	0.211175i	−0.593591	+	0.804767i	$0.702290\pi$
$632$	−26.8946	+	12.0863i	−1.06981	+	0.480767i
$633$		0			0
$634$	−6.52111	−	23.4091i	−0.258986	−	0.929696i
$635$	−24.9495	+	10.3344i	−0.990091	+	0.410109i
$636$		0			0
$637$	−16.8290	+	40.6287i	−0.666787	+	1.60977i
$638$	4.38186	−	3.43165i	0.173479	−	0.135861i
$639$		0			0
$640$	10.7811	+	31.3745i	0.426160	+	1.24018i
$641$	−44.4168			−1.75436			−0.877179	−	0.480163i	$-0.840578\pi$
$641$	−44.4168			−1.75436			−0.877179	+	0.480163i	$0.840578\pi$
$642$		0			0
$643$	7.60023	−	18.3486i	0.299724	−	0.723598i	−0.700229	−	0.713918i	$-0.746919\pi$
$643$	7.60023	−	18.3486i	0.299724	−	0.723598i	0.999953	−	0.00967946i	$-0.00308112\pi$
$644$	0.459652	−	1.86191i	0.0181128	−	0.0733694i
$645$		0			0
$646$	0.124460	+	0.446778i	0.00489679	+	0.0175783i
$647$	−34.4364	+	34.4364i	−1.35384	+	1.35384i	−0.472511	+	0.881325i	$0.656652\pi$
$647$	−34.4364	+	34.4364i	−1.35384	+	1.35384i	−0.881325	+	0.472511i	$0.843348\pi$
$648$		0			0
$649$	−20.5864	−	20.5864i	−0.808086	−	0.808086i
$650$	−15.7591	+	27.9294i	−0.618122	+	1.09548i
$651$		0			0
$652$	−1.97326	−	1.45308i	−0.0772786	−	0.0569069i
$653$	39.6908	+	16.4405i	1.55322	+	0.643365i	0.983895	−	0.178747i	$-0.0572043\pi$
$653$	39.6908	+	16.4405i	1.55322	+	0.643365i	0.569326	+	0.822112i	$0.307204\pi$
$654$		0			0
$655$			42.3859i			1.65616i
$656$	−6.16000	−	19.8199i	−0.240508	−	0.773837i
$657$		0			0
$658$	−1.35869	−	0.165230i	−0.0529672	−	0.00644135i
$659$	22.7805	+	9.43601i	0.887404	+	0.367575i	0.779364	−	0.626572i	$-0.215543\pi$
$659$	22.7805	+	9.43601i	0.887404	+	0.367575i	0.108040	+	0.994147i	$0.465543\pi$
$660$		0			0
$661$	10.0305	+	24.2157i	0.390140	+	0.941881i	0.989909	+	0.141707i	$0.0452592\pi$
$661$	10.0305	+	24.2157i	0.390140	+	0.941881i	−0.599769	+	0.800173i	$0.704741\pi$
$662$	33.3292	+	18.8059i	1.29538	+	0.730911i
$663$		0			0
$664$	−0.555477	−	18.7282i	−0.0215567	−	0.726795i
$665$	0.0451759	−	0.0451759i	0.00175185	−	0.00175185i
$666$		0			0
$667$	3.69597	−	1.53092i	0.143109	−	0.0592776i
$668$	−0.0513692	−	0.0850463i	−0.00198754	−	0.00329054i
$669$		0			0
$670$	18.8278	+	24.0412i	0.727383	+	0.928791i
$671$	−43.1154			−1.66445
$672$		0			0
$673$	24.0093			0.925491			0.462745	−	0.886491i	$-0.346864\pi$
$673$	24.0093			0.925491			0.462745	+	0.886491i	$0.346864\pi$
$674$	2.31171	+	2.95181i	0.0890439	+	0.113700i
$675$		0			0
$676$	45.7300	−	27.6216i	1.75885	−	1.06237i
$677$	26.8088	−	11.1046i	1.03034	−	0.426783i	0.197508	−	0.980301i	$-0.436715\pi$
$677$	26.8088	−	11.1046i	1.03034	−	0.426783i	0.832837	+	0.553518i	$0.186715\pi$
$678$		0			0
$679$	−1.68295	+	1.68295i	−0.0645857	+	0.0645857i
$680$	12.5876	−	13.3571i	0.482713	−	0.512222i
$681$		0			0
$682$	−69.9716	−	39.4812i	−2.67935	−	1.51181i
$683$	−11.2367	−	27.1277i	−0.429959	−	1.03801i	−0.979300	−	0.202415i	$-0.935121\pi$
$683$	−11.2367	−	27.1277i	−0.429959	−	1.03801i	0.549341	−	0.835598i	$-0.314879\pi$
$684$		0			0
$685$	17.2139	+	7.13025i	0.657711	+	0.272433i
$686$	−2.88512	−	0.350860i	−0.110154	−	0.0133959i
$687$		0			0
$688$	1.48765	−	16.2372i	0.0567160	−	0.619037i
$689$			60.6711i			2.31139i
$690$		0			0
$691$	11.4155	+	4.72846i	0.434266	+	0.179879i	0.589098	−	0.808062i	$-0.299483\pi$
$691$	11.4155	+	4.72846i	0.434266	+	0.179879i	−0.154831	+	0.987941i	$0.549483\pi$
$692$	−15.6050	+	21.1914i	−0.593215	+	0.805576i
$693$		0			0
$694$	−16.8315	+	29.8301i	−0.638916	+	1.13234i
$695$	36.9047	+	36.9047i	1.39987	+	1.39987i
$696$		0			0
$697$	−8.11936	+	8.11936i	−0.307543	+	0.307543i
$698$	−7.50072	−	26.9257i	−0.283907	−	1.01915i
$699$		0			0
$700$	−1.02723	−	0.253594i	−0.0388256	−	0.00958494i
$701$	−1.29537	+	3.12731i	−0.0489255	+	0.118117i	−0.946453	−	0.322842i	$-0.895362\pi$
$701$	−1.29537	+	3.12731i	−0.0489255	+	0.118117i	0.897527	+	0.440959i	$0.145362\pi$
$702$		0			0
$703$	0.726387			0.0273962
$704$	48.5040	+	16.7981i	1.82806	+	0.633103i
$705$		0			0
$706$	−15.0517	+	11.7877i	−0.566478	+	0.443637i
$707$	0.189980	−	0.458651i	0.00714492	−	0.0172494i
$708$		0			0
$709$	−8.62991	+	3.57463i	−0.324103	+	0.134248i	−0.538802	−	0.842432i	$-0.681123\pi$
$709$	−8.62991	+	3.57463i	−0.324103	+	0.134248i	0.214699	+	0.976680i	$0.431123\pi$
$710$	−4.31546	−	15.4914i	−0.161956	−	0.581382i
$711$		0			0
$712$	−29.8505	−	11.3398i	−1.11870	−	0.424977i
$713$	−40.8339	−	40.8339i	−1.52924	−	1.52924i
$714$		0			0
$715$	45.3727	+	109.539i	1.69684	+	4.09654i
$716$	−0.218094	+	0.296167i	−0.00815054	+	0.0110683i
$717$		0			0
$718$	3.44608	−	28.3371i	0.128607	−	1.05753i
$719$		−	27.2259i		−	1.01535i	−0.861547	−	0.507677i	$-0.830504\pi$
$719$		−	27.2259i		−	1.01535i	0.861547	−	0.507677i	$-0.169496\pi$
$720$		0			0
$721$		−	1.76525i		−	0.0657414i
$722$	26.6427	+	3.24003i	0.991539	+	0.120581i
$723$		0			0
$724$	9.22506	−	1.40053i	0.342847	−	0.0520502i
$725$	−0.844623	−	2.03910i	−0.0313685	−	0.0757303i
$726$		0			0
$727$	14.7795	+	14.7795i	0.548142	+	0.548142i	0.925903	−	0.377761i	$-0.123306\pi$
$727$	14.7795	+	14.7795i	0.548142	+	0.548142i	−0.377761	+	0.925903i	$0.623306\pi$
$728$	1.90711	+	1.79724i	0.0706822	+	0.0666101i
$729$		0			0
$730$	27.5313	−	7.66943i	1.01898	−	0.283858i
$731$	−8.33400	+	3.45206i	−0.308244	+	0.127679i
$732$		0			0
$733$	9.31269	−	22.4828i	0.343972	−	0.830422i	−0.653334	−	0.757070i	$-0.726630\pi$
$733$	9.31269	−	22.4828i	0.343972	−	0.830422i	0.997306	−	0.0733521i	$-0.0233697\pi$
$734$	−16.7436	−	21.3798i	−0.618018	−	0.789143i
$735$		0			0
$736$	30.3447	+	20.9870i	1.11852	+	0.773591i
$737$	47.2475			1.74038
$738$		0			0
$739$	−0.759150	+	1.83275i	−0.0279258	+	0.0674188i	−0.937227	−	0.348719i	$-0.886617\pi$
$739$	−0.759150	+	1.83275i	−0.0279258	+	0.0674188i	0.909301	+	0.416138i	$0.136617\pi$
$740$	−14.8621	−	24.6055i	−0.546341	−	0.904516i
$741$		0			0
$742$	−1.92835	+	0.537182i	−0.0707919	+	0.0197206i
$743$	−3.29885	+	3.29885i	−0.121023	+	0.121023i	−0.765024	−	0.644001i	$-0.777273\pi$
$743$	−3.29885	+	3.29885i	−0.121023	+	0.121023i	0.644001	+	0.765024i	$0.277273\pi$
$744$		0			0
$745$	−21.2676	−	21.2676i	−0.779184	−	0.779184i
$746$	28.0993	+	15.8549i	1.02879	+	0.580490i
$747$		0			0
$748$	−4.26248	−	28.0763i	−0.155852	−	1.02657i
$749$	0.476797	+	0.197496i	0.0174218	+	0.00721634i
$750$		0			0
$751$		−	53.4430i		−	1.95016i	−0.221850	−	0.975081i	$-0.571209\pi$
$751$		−	53.4430i		−	1.95016i	0.221850	−	0.975081i	$-0.428791\pi$
$752$	12.2541	−	23.3061i	0.446860	−	0.849887i
$753$		0			0
$754$	−0.659901	+	5.42636i	−0.0240322	+	0.197616i
$755$	−30.7396	−	12.7328i	−1.11873	−	0.463393i
$756$		0			0
$757$	−0.204624	−	0.494007i	−0.00743720	−	0.0179550i	0.920117	−	0.391643i	$-0.128093\pi$
$757$	−0.204624	−	0.494007i	−0.00743720	−	0.0179550i	−0.927555	+	0.373688i	$0.878093\pi$
$758$	13.3895	−	23.7298i	0.486327	−	0.861906i
$759$		0			0
$760$	0.503814	+	1.12109i	0.0182753	+	0.0406664i
$761$	27.0608	−	27.0608i	0.980952	−	0.980952i	−0.0188700	−	0.999822i	$-0.506007\pi$
$761$	27.0608	−	27.0608i	0.980952	−	0.980952i	0.999822	+	0.0188700i	$0.00600687\pi$
$762$		0			0
$763$	2.31323	−	0.958170i	0.0837444	−	0.0346881i
$764$	9.80136	−	39.7023i	0.354601	−	1.43638i
$765$		0			0
$766$	10.3520	−	8.10718i	0.374033	−	0.292924i
$767$	28.5938			1.03246
$768$		0			0
$769$	−42.1236			−1.51901			−0.759507	−	0.650499i	$-0.774560\pi$
$769$	−42.1236			−1.51901			−0.759507	+	0.650499i	$0.774560\pi$
$770$	−3.07983	+	2.41197i	−0.110989	+	0.0869215i
$771$		0			0
$772$	−2.62296	+	10.6248i	−0.0944024	+	0.382395i
$773$	−2.05352	+	0.850597i	−0.0738601	+	0.0305939i	−0.419308	−	0.907844i	$-0.637727\pi$
$773$	−2.05352	+	0.850597i	−0.0738601	+	0.0305939i	0.345448	+	0.938438i	$0.387727\pi$
$774$		0			0
$775$	−22.5284	+	22.5284i	−0.809243	+	0.809243i
$776$	−18.7687	−	41.7645i	−0.673758	−	1.49926i
$777$		0			0
$778$	15.6098	−	27.6649i	0.559639	−	0.991834i
$779$	−0.294265	−	0.710418i	−0.0105431	−	0.0254534i
$780$		0			0
$781$	−22.9878	−	9.52187i	−0.822569	−	0.340719i
$782$	2.46413	−	20.2625i	0.0881172	−	0.724587i
$783$		0			0
$784$	12.9904	−	24.7066i	0.463943	−	0.882378i
$785$			4.44458i			0.158634i
$786$		0			0
$787$	32.6127	+	13.5086i	1.16252	+	0.481530i	0.878712	−	0.477352i	$-0.158403\pi$
$787$	32.6127	+	13.5086i	1.16252	+	0.481530i	0.283804	+	0.958882i	$0.408403\pi$
$788$	−1.29956	−	8.56002i	−0.0462950	−	0.304938i
$789$		0			0
$790$	37.6503	+	21.2440i	1.33954	+	0.755828i
$791$	1.56274	+	1.56274i	0.0555647	+	0.0555647i
$792$		0			0
$793$	29.9429	−	29.9429i	1.06330	−	1.06330i
$794$	21.3245	−	5.94038i	0.756777	−	0.210816i
$795$		0			0
$796$	9.12302	+	15.1040i	0.323357	+	0.535346i
$797$	−5.04281	+	12.1744i	−0.178626	+	0.431240i	−0.987679	−	0.156495i	$-0.949980\pi$
$797$	−5.04281	+	12.1744i	−0.178626	+	0.431240i	0.809053	+	0.587735i	$0.199980\pi$
$798$		0			0
$799$	−14.5675			−0.515361
$800$	11.5787	−	16.7414i	0.409369	−	0.591898i
$801$		0			0
$802$	−0.261180	−	0.333498i	−0.00922257	−	0.0117762i
$803$	16.9223	−	40.8539i	0.597174	−	1.44170i
$804$		0			0
$805$	−2.59775	+	1.07602i	−0.0915587	+	0.0379249i
$806$	76.0132	−	21.1751i	2.67745	−	0.745861i
$807$		0			0
$808$	6.95056	+	6.55013i	0.244520	+	0.230433i
$809$	21.0801	+	21.0801i	0.741138	+	0.741138i	0.972797	−	0.231659i	$-0.0744153\pi$
$809$	21.0801	+	21.0801i	0.741138	+	0.741138i	−0.231659	+	0.972797i	$0.574415\pi$
$810$		0			0
$811$	−5.46994	−	13.2056i	−0.192075	−	0.463711i	0.798276	−	0.602292i	$-0.205746\pi$
$811$	−5.46994	−	13.2056i	−0.192075	−	0.463711i	−0.990351	+	0.138581i	$0.955746\pi$
$812$	−0.178312	+	0.0270709i	−0.00625753	+	0.000950004i
$813$		0			0
$814$	−44.1516	−	5.36929i	−1.54751	−	0.188193i
$815$			3.59286i			0.125852i
$816$		0			0
$817$		−	0.604087i		−	0.0211343i
$818$	−0.785656	+	6.46045i	−0.0274698	+	0.225884i
$819$		0			0
$820$	−18.0438	+	24.5032i	−0.630117	+	0.855689i
$821$	7.22280	+	17.4374i	0.252077	+	0.608568i	0.998371	−	0.0570479i	$-0.0181688\pi$
$821$	7.22280	+	17.4374i	0.252077	+	0.608568i	−0.746294	+	0.665616i	$0.768169\pi$
$822$		0			0
$823$	−26.0676	−	26.0676i	−0.908661	−	0.908661i	0.0875032	−	0.996164i	$-0.472111\pi$
$823$	−26.0676	−	26.0676i	−0.908661	−	0.908661i	−0.996164	+	0.0875032i	$0.972111\pi$
$824$	31.7467	+	12.0602i	1.10595	+	0.420135i
$825$		0			0
$826$	0.253170	+	0.908816i	0.00880890	+	0.0316217i
$827$	14.5783	−	6.03854i	0.506938	−	0.209981i	−0.114531	−	0.993420i	$-0.536536\pi$
$827$	14.5783	−	6.03854i	0.506938	−	0.209981i	0.621468	+	0.783439i	$0.286536\pi$
$828$		0			0
$829$	−16.0177	+	38.6700i	−0.556316	+	1.34307i	0.356347	+	0.934354i	$0.384022\pi$
$829$	−16.0177	+	38.6700i	−0.556316	+	1.34307i	−0.912663	+	0.408712i	$0.865978\pi$
$830$	−21.6274	+	16.9375i	−0.750697	+	0.587909i
$831$		0			0
$832$	−45.3513	+	22.0192i	−1.57227	+	0.763380i
$833$	−15.4428			−0.535063
$834$		0			0
$835$	−0.0557459	+	0.134582i	−0.00192917	+	0.00465742i
$836$	1.84630	+	0.455799i	0.0638557	+	0.0157641i
$837$		0			0
$838$	−3.27110	−	11.7424i	−0.112998	−	0.405635i
$839$	−16.7883	+	16.7883i	−0.579598	+	0.579598i	−0.934792	−	0.355194i	$-0.884415\pi$
$839$	−16.7883	+	16.7883i	−0.579598	+	0.579598i	0.355194	+	0.934792i	$0.384415\pi$
$840$		0			0
$841$	20.2401	+	20.2401i	0.697933	+	0.697933i
$842$	−13.9639	+	24.7479i	−0.481229	+	0.852870i
$843$		0			0
$844$	7.77796	−	10.5623i	0.267728	−	0.363571i
$845$	−72.3660	−	29.9750i	−2.48946	−	1.03117i
$846$		0			0
$847$			4.43548i			0.152405i
$848$	3.51361	−	38.3499i	0.120658	−	1.31694i
$849$		0			0
$850$	−11.1790	−	1.35948i	−0.383437	−	0.0466299i
$851$	−29.5355	−	12.2340i	−1.01246	−	0.419376i
$852$		0			0
$853$	9.97946	+	24.0926i	0.341690	+	0.824913i	0.997545	+	0.0700264i	$0.0223083\pi$
$853$	9.97946	+	24.0926i	0.341690	+	0.824913i	−0.655855	+	0.754887i	$0.727692\pi$
$854$	1.21681	+	0.686580i	0.0416384	+	0.0234943i
$855$		0			0
$856$	−6.80928	+	7.22555i	−0.232736	+	0.246964i
$857$	6.68740	−	6.68740i	0.228437	−	0.228437i	−0.583602	−	0.812040i	$-0.698357\pi$
$857$	6.68740	−	6.68740i	0.228437	−	0.228437i	0.812040	+	0.583602i	$0.198357\pi$
$858$		0			0
$859$	37.9207	−	15.7073i	1.29384	−	0.535925i	0.373711	−	0.927545i	$-0.378085\pi$
$859$	37.9207	−	15.7073i	1.29384	−	0.535925i	0.920127	+	0.391620i	$0.128085\pi$
$860$	−20.4627	+	12.3598i	−0.697773	+	0.421465i
$861$		0			0
$862$	−13.8806	−	17.7240i	−0.472774	−	0.603683i
$863$	29.4927			1.00394			0.501972	−	0.864884i	$-0.332608\pi$
$863$	29.4927			1.00394			0.501972	+	0.864884i	$0.332608\pi$
$864$		0			0
$865$	38.5848			1.31192
$866$	−35.9166	−	45.8616i	−1.22049	−	1.55844i
$867$		0			0
$868$	1.34604	+	2.22849i	0.0456876	+	0.0756400i
$869$	61.7967	−	25.5970i	2.09631	−	0.868319i
$870$		0			0
$871$	−32.8126	+	32.8126i	−1.11181	+	1.11181i
$872$	1.42806	+	48.1478i	0.0483603	+	1.63049i
$873$		0			0
$874$	1.19049	+	0.671727i	0.0402688	+	0.0227215i
$875$	−0.231241	−	0.558266i	−0.00781738	−	0.0188728i
$876$		0			0
$877$	37.8880	+	15.6937i	1.27939	+	0.529939i	0.915805	−	0.401624i	$-0.131554\pi$
$877$	37.8880	+	15.6937i	1.27939	+	0.529939i	0.363581	+	0.931563i	$0.381554\pi$
$878$	11.0825	+	1.34774i	0.374015	+	0.0454840i
$879$		0			0
$880$	−22.3362	−	71.8670i	−0.752953	−	2.42264i
$881$		−	11.2691i		−	0.379666i	−0.981816	−	0.189833i	$-0.939205\pi$
$881$		−	11.2691i		−	0.379666i	0.981816	−	0.189833i	$-0.0607946\pi$
$882$		0			0
$883$	−36.8069	−	15.2459i	−1.23865	−	0.513066i	−0.335359	−	0.942090i	$-0.608858\pi$
$883$	−36.8069	−	15.2459i	−1.23865	−	0.513066i	−0.903293	+	0.429024i	$0.858858\pi$
$884$	22.4587	+	16.5383i	0.755369	+	0.556243i
$885$		0			0
$886$	9.74404	−	17.2691i	0.327357	−	0.580167i
$887$	7.26689	+	7.26689i	0.243998	+	0.243998i	0.818502	−	0.574504i	$-0.194805\pi$
$887$	7.26689	+	7.26689i	0.243998	+	0.243998i	−0.574504	+	0.818502i	$0.694805\pi$
$888$		0			0
$889$	0.957423	−	0.957423i	0.0321109	−	0.0321109i
$890$	12.5634	+	45.0996i	0.421128	+	1.51174i
$891$		0			0
$892$	8.28233	−	33.5492i	0.277313	−	1.12331i
$893$	0.373324	−	0.901284i	0.0124928	−	0.0301603i
$894$		0			0
$895$	0.539255			0.0180253
$896$	−1.10139	−	1.24647i	−0.0367949	−	0.0416417i
$897$		0			0
$898$	30.6671	−	24.0170i	1.02338	−	0.801457i
$899$	−2.07826	+	5.01736i	−0.0693138	+	0.167338i
$900$		0			0
$901$	−19.6837	+	8.15326i	−0.655760	+	0.271625i
$902$	12.6349	+	45.3561i	0.420696	+	1.51019i
$903$		0			0
$904$	−38.7814	+	17.4281i	−1.28985	+	0.579651i
$905$	−9.67342	−	9.67342i	−0.321555	−	0.321555i
$906$		0			0
$907$	−17.4961	−	42.2392i	−0.580947	−	1.40253i	−0.891955	−	0.452124i	$-0.850667\pi$
$907$	−17.4961	−	42.2392i	−0.580947	−	1.40253i	0.311008	−	0.950407i	$-0.399333\pi$
$908$	7.57778	+	5.58017i	0.251477	+	0.185184i
$909$		0			0
$910$	0.463818	−	3.81397i	0.0153754	−	0.126432i
$911$			55.1750i			1.82803i	0.405683	+	0.914014i	$0.367034\pi$
$911$			55.1750i			1.82803i	−0.405683	+	0.914014i	$0.632966\pi$
$912$		0			0
$913$			42.5037i			1.40667i
$914$	−11.2202	−	1.36449i	−0.371131	−	0.0451333i
$915$		0			0
$916$	−2.63566	−	17.3607i	−0.0870848	−	0.573614i
$917$	−0.813268	−	1.96340i	−0.0268565	−	0.0648373i
$918$		0			0
$919$	−0.307633	−	0.307633i	−0.0101479	−	0.0101479i	0.702015	−	0.712163i	$-0.252284\pi$
$919$	−0.307633	−	0.307633i	−0.0101479	−	0.0101479i	−0.712163	+	0.702015i	$0.752284\pi$
$920$	−1.60371	−	54.0700i	−0.0528728	−	1.78263i
$921$		0			0
$922$	44.9277	−	12.5155i	1.47961	−	0.412178i
$923$	22.5775	−	9.35190i	0.743147	−	0.307821i
$924$		0			0
$925$	−6.74960	+	16.2950i	−0.221926	+	0.535776i
$926$	1.93319	+	2.46848i	0.0635287	+	0.0811193i
$927$		0			0
$928$	0.731374	−	3.39176i	0.0240085	−	0.111340i
$929$	45.1678			1.48191			0.740954	−	0.671556i	$-0.234374\pi$
$929$	45.1678			1.48191			0.740954	+	0.671556i	$0.234374\pi$
$930$		0			0
$931$	0.395757	−	0.955442i	0.0129704	−	0.0313133i
$932$	−6.42184	+	3.87889i	−0.210354	+	0.127057i
$933$		0			0
$934$	26.7003	−	7.43794i	0.873662	−	0.243377i
$935$	−29.4408	+	29.4408i	−0.962819	+	0.962819i
$936$		0			0
$937$	16.2272	+	16.2272i	0.530118	+	0.530118i	0.920607	−	0.390489i	$-0.127694\pi$
$937$	16.2272	+	16.2272i	0.530118	+	0.530118i	−0.390489	+	0.920607i	$0.627694\pi$
$938$	−1.33343	−	0.752381i	−0.0435379	−	0.0245661i
$939$		0			0
$940$	−38.1682	+	5.79461i	−1.24491	+	0.189000i
$941$	1.99341	+	0.825700i	0.0649835	+	0.0269170i	0.414938	−	0.909849i	$-0.363803\pi$
$941$	1.99341	+	0.825700i	0.0649835	+	0.0269170i	−0.349955	+	0.936767i	$0.613803\pi$
$942$		0			0
$943$			33.8422i			1.10205i
$944$	−18.0740	−	1.65594i	−0.588259	−	0.0538962i
$945$		0			0
$946$	−4.46527	+	36.7179i	−0.145179	+	1.19380i
$947$	−51.1001	−	21.1663i	−1.66053	−	0.687814i	−0.662412	−	0.749140i	$-0.730467\pi$
$947$	−51.1001	−	21.1663i	−1.66053	−	0.687814i	−0.998118	+	0.0613258i	$0.980467\pi$
$948$		0			0
$949$	16.6202	+	40.1247i	0.539514	+	1.30250i
$950$	0.370597	−	0.656801i	0.0120238	−	0.0213094i
$951$		0			0
$952$	−0.326798	+	0.860251i	−0.0105916	+	0.0278809i
$953$	27.7706	−	27.7706i	0.899578	−	0.899578i	−0.0958204	−	0.995399i	$-0.530547\pi$
$953$	27.7706	−	27.7706i	0.899578	−	0.899578i	0.995399	+	0.0958204i	$0.0305474\pi$
$954$		0			0
$955$	−55.3931	+	22.9446i	−1.79248	+	0.742468i
$956$	−11.7991	−	2.91287i	−0.381611	−	0.0942088i
$957$		0			0
$958$	36.5516	−	28.6254i	1.18093	−	0.924844i
$959$	−0.934195			−0.0301667
$960$		0			0
$961$	47.3938			1.52883
$962$	34.3915	−	26.9337i	1.10883	−	0.868378i
$963$		0			0
$964$	−44.6502	−	11.0229i	−1.43809	−	0.355022i
$965$	14.8238	−	6.14024i	0.477196	−	0.197661i
$966$		0			0
$967$	−2.12831	+	2.12831i	−0.0684419	+	0.0684419i	−0.740499	−	0.672057i	$-0.765411\pi$
$967$	−2.12831	+	2.12831i	−0.0684419	+	0.0684419i	0.672057	+	0.740499i	$0.265411\pi$
$968$	−79.7689	−	30.3031i	−2.56387	−	0.973979i
$969$		0			0
$970$	−32.9897	+	58.4668i	−1.05923	+	1.87726i
$971$	−5.57382	−	13.4564i	−0.178872	−	0.431836i	0.808858	−	0.588004i	$-0.200086\pi$
$971$	−5.57382	−	13.4564i	−0.178872	−	0.431836i	−0.987731	+	0.156168i	$0.950086\pi$
$972$		0			0
$973$	−2.41760	−	1.00140i	−0.0775046	−	0.0321035i
$974$	−1.93286	+	15.8939i	−0.0619327	+	0.509272i
$975$		0			0
$976$	−20.6608	+	17.1927i	−0.661338	+	0.550325i
$977$		−	59.1447i		−	1.89221i	−0.323863	−	0.946104i	$-0.604982\pi$
$977$		−	59.1447i		−	1.89221i	0.323863	−	0.946104i	$-0.395018\pi$
$978$		0			0
$979$	66.9237	+	27.7207i	2.13889	+	0.885957i
$980$	−40.4617	+	6.14281i	−1.29250	+	0.196225i
$981$		0			0
$982$	−31.0766	−	17.5349i	−0.991695	−	0.559560i
$983$	9.92459	+	9.92459i	0.316545	+	0.316545i	0.847439	−	0.530893i	$-0.178144\pi$
$983$	9.92459	+	9.92459i	0.316545	+	0.316545i	−0.530893	+	0.847439i	$0.678144\pi$
$984$		0			0
$985$	−8.97606	+	8.97606i	−0.286001	+	0.286001i
$986$	−1.84917	+	0.515126i	−0.0588896	+	0.0164049i
$987$		0			0
$988$	−1.59877	+	0.965682i	−0.0508637	+	0.0307224i
$989$	−10.1742	+	24.5627i	−0.323520	+	0.781047i
$990$		0			0
$991$	−42.3825			−1.34632			−0.673162	−	0.739495i	$-0.735065\pi$
$991$	−42.3825			−1.34632			−0.673162	+	0.739495i	$0.735065\pi$
$992$	−49.2739	+	8.98256i	−1.56445	+	0.285196i
$993$		0			0
$994$	0.497138	+	0.634792i	0.0157683	+	0.0201344i
$995$	9.90030	−	23.9014i	0.313861	−	0.757727i
$996$		0			0
$997$	−14.0138	+	5.80470i	−0.443821	+	0.183837i	−0.593391	−	0.804915i	$-0.702211\pi$
$997$	−14.0138	+	5.80470i	−0.443821	+	0.183837i	0.149570	+	0.988751i	$0.452211\pi$
$998$	14.7473	−	4.10818i	0.466818	−	0.130042i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.8	✓	128
3.2	odd	2	inner	864.2.v.b.109.25	yes	128
32.5	even	8	inner	864.2.v.b.325.8	yes	128
96.5	odd	8	inner	864.2.v.b.325.25	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.8	✓	128	1.1	even	1	trivial
864.2.v.b.109.25	yes	128	3.2	odd	2	inner
864.2.v.b.325.8	yes	128	32.5	even	8	inner
864.2.v.b.325.25	yes	128	96.5	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11341 + 0.871966i) q^{2} +(0.479352 - 1.94171i) q^{4} +(-2.70909 + 1.12214i) q^{5} +(0.103960 - 0.103960i) q^{7} +(1.15939 + 2.57989i) q^{8} +O(q^{10})\)	\(q+(-1.11341 + 0.871966i) q^{2} +(0.479352 - 1.94171i) q^{4} +(-2.70909 + 1.12214i) q^{5} +(0.103960 - 0.103960i) q^{7} +(1.15939 + 2.57989i) q^{8} +(2.03785 - 3.61163i) q^{10} +(-2.45541 - 5.92789i) q^{11} +(5.82208 + 2.41158i) q^{13} +(-0.0251002 + 0.206399i) q^{14} +(-3.54044 - 1.86152i) q^{16} +2.21295i q^{17} +(-0.136914 - 0.0567118i) q^{19} +(0.880262 + 5.79815i) q^{20} +(7.90280 + 4.45912i) q^{22} +(4.61190 + 4.61190i) q^{23} +(2.54442 - 2.54442i) q^{25} +(-8.58516 + 2.39158i) q^{26} +(-0.152026 - 0.251692i) q^{28} +(0.234725 - 0.566675i) q^{29} -8.85403 q^{31} +(5.56514 - 1.01452i) q^{32} +(-1.92962 - 2.46392i) q^{34} +(-0.164979 + 0.398293i) q^{35} +(-4.52845 + 1.87575i) q^{37} +(0.201892 - 0.0562413i) q^{38} +(-6.03588 - 5.68815i) q^{40} +(3.66902 + 3.66902i) q^{41} +(1.55993 + 3.76601i) q^{43} +(-12.6872 + 1.92615i) q^{44} +(-9.15633 - 1.11350i) q^{46} +6.58283i q^{47} +6.97838i q^{49} +(-0.614329 + 5.05163i) q^{50} +(7.47341 - 10.1488i) q^{52} +(3.68433 + 8.89477i) q^{53} +(13.3039 + 13.3039i) q^{55} +(0.388734 + 0.147675i) q^{56} +(0.232777 + 0.835612i) q^{58} +(4.19204 - 1.73640i) q^{59} +(2.57150 - 6.20815i) q^{61} +(9.85814 - 7.72041i) q^{62} +(-5.31164 + 5.98218i) q^{64} -18.4787 q^{65} +(-2.81795 + 6.80313i) q^{67} +(4.29691 + 1.06078i) q^{68} +(-0.163610 - 0.587319i) q^{70} +(2.74210 - 2.74210i) q^{71} +(4.87325 + 4.87325i) q^{73} +(3.40642 - 6.03712i) q^{74} +(-0.175748 + 0.238663i) q^{76} +(-0.871527 - 0.360998i) q^{77} +10.4247i q^{79} +(11.6803 + 1.07014i) q^{80} +(-7.28437 - 0.885853i) q^{82} +(-6.12008 - 2.53502i) q^{83} +(-2.48325 - 5.99509i) q^{85} +(-5.02067 - 2.83289i) q^{86} +(12.4465 - 13.2074i) q^{88} +(-7.98297 + 7.98297i) q^{89} +(0.855969 - 0.354554i) q^{91} +(11.1657 - 6.74423i) q^{92} +(-5.74000 - 7.32937i) q^{94} +0.434552 q^{95} -16.1885 q^{97} +(-6.08491 - 7.76978i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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