LMFDB - Embedded newform 864.2.v.a.109.2

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			109.2
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39716 + 0.218946i) q^{2} +(1.90413 - 0.611807i) q^{4} +(-2.13352 + 0.883735i) q^{5} +(0.426205 - 0.426205i) q^{7} +(-2.52642 + 1.27169i) q^{8} +O(q^{10})$	\(q+(-1.39716 + 0.218946i) q^{2} +(1.90413 - 0.611807i) q^{4} +(-2.13352 + 0.883735i) q^{5} +(0.426205 - 0.426205i) q^{7} +(-2.52642 + 1.27169i) q^{8} +(2.78739 - 1.70185i) q^{10} +(-0.144287 - 0.348341i) q^{11} +(0.0788424 + 0.0326576i) q^{13} +(-0.502162 + 0.688794i) q^{14} +(3.25138 - 2.32991i) q^{16} -2.60658i q^{17} +(-2.91702 - 1.20827i) q^{19} +(-3.52182 + 2.98805i) q^{20} +(0.277861 + 0.455097i) q^{22} +(3.52617 + 3.52617i) q^{23} +(0.235404 - 0.235404i) q^{25} +(-0.117306 - 0.0283657i) q^{26} +(0.550793 - 1.07230i) q^{28} +(3.48138 - 8.40479i) q^{29} +3.54897 q^{31} +(-4.03259 + 3.96715i) q^{32} +(0.570702 + 3.64182i) q^{34} +(-0.532667 + 1.28597i) q^{35} +(6.59514 - 2.73180i) q^{37} +(4.34010 + 1.04948i) q^{38} +(4.26634 - 4.94587i) q^{40} +(3.51963 + 3.51963i) q^{41} +(-2.74958 - 6.63808i) q^{43} +(-0.487858 - 0.575008i) q^{44} +(-5.69867 - 4.15459i) q^{46} -3.40368i q^{47} +6.63670i q^{49} +(-0.277357 + 0.380439i) q^{50} +(0.170106 + 0.0139478i) q^{52} +(-1.68239 - 4.06164i) q^{53} +(0.615681 + 0.615681i) q^{55} +(-0.534770 + 1.61878i) q^{56} +(-3.02385 + 12.5051i) q^{58} +(2.70405 - 1.12005i) q^{59} +(2.88389 - 6.96232i) q^{61} +(-4.95849 + 0.777033i) q^{62} +(4.76559 - 6.42567i) q^{64} -0.197073 q^{65} +(-1.00349 + 2.42263i) q^{67} +(-1.59473 - 4.96326i) q^{68} +(0.462664 - 1.91334i) q^{70} +(9.57606 - 9.57606i) q^{71} +(7.59378 + 7.59378i) q^{73} +(-8.61637 + 5.26075i) q^{74} +(-6.29361 - 0.516044i) q^{76} +(-0.209961 - 0.0869686i) q^{77} -13.3063i q^{79} +(-4.87788 + 7.84429i) q^{80} +(-5.68810 - 4.14688i) q^{82} +(2.41425 + 1.00002i) q^{83} +(2.30353 + 5.56121i) q^{85} +(5.29500 + 8.67247i) q^{86} +(0.807513 + 0.696565i) q^{88} +(5.44699 - 5.44699i) q^{89} +(0.0475219 - 0.0196842i) q^{91} +(8.87160 + 4.55693i) q^{92} +(0.745224 + 4.75550i) q^{94} +7.29133 q^{95} +5.79690 q^{97} +(-1.45308 - 9.27254i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * 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 $

$2$	−1.39716	+	0.218946i	−0.987943	+	0.154818i
$2$	−1.39716	+	0.218946i	−0.987943	+	0.154818i
$3$		0			0
$3$		0			0
$4$	1.90413	−	0.611807i	0.952063	−	0.305903i
$5$	−2.13352	+	0.883735i	−0.954141	+	0.395218i	−0.804786	−	0.593565i	$-0.797720\pi$
$5$	−2.13352	+	0.883735i	−0.954141	+	0.395218i	−0.149355	+	0.988784i	$0.547720\pi$
$6$		0			0
$7$	0.426205	−	0.426205i	0.161091	−	0.161091i	−0.621959	−	0.783050i	$-0.713663\pi$
$7$	0.426205	−	0.426205i	0.161091	−	0.161091i	0.783050	+	0.621959i	$0.213663\pi$
$8$	−2.52642	+	1.27169i	−0.893224	+	0.449612i
$9$		0			0
$10$	2.78739	−	1.70185i	0.881450	−	0.538172i
$11$	−0.144287	−	0.348341i	−0.0435043	−	0.105029i	0.900634	−	0.434579i	$-0.143103\pi$
$11$	−0.144287	−	0.348341i	−0.0435043	−	0.105029i	−0.944138	+	0.329550i	$0.893103\pi$
$12$		0			0
$13$	0.0788424	+	0.0326576i	0.0218669	+	0.00905758i	0.393590	−	0.919286i	$-0.371233\pi$
$13$	0.0788424	+	0.0326576i	0.0218669	+	0.00905758i	−0.371723	+	0.928344i	$0.621233\pi$
$14$	−0.502162	+	0.688794i	−0.134208	+	0.184088i
$15$		0			0
$16$	3.25138	−	2.32991i	0.812846	−	0.582478i
$17$		−	2.60658i		−	0.632189i	−0.948728	−	0.316095i	$-0.897628\pi$
$17$		−	2.60658i		−	0.632189i	0.948728	−	0.316095i	$-0.102372\pi$
$18$		0			0
$19$	−2.91702	−	1.20827i	−0.669211	−	0.277196i	0.0220975	−	0.999756i	$-0.492966\pi$
$19$	−2.91702	−	1.20827i	−0.669211	−	0.277196i	−0.691309	+	0.722559i	$0.742966\pi$
$20$	−3.52182	+	2.98805i	−0.787503	+	0.668147i
$21$		0			0
$22$	0.277861	+	0.455097i	0.0592401	+	0.0970270i
$23$	3.52617	+	3.52617i	0.735257	+	0.735257i	0.971656	−	0.236399i	$-0.0759672\pi$
$23$	3.52617	+	3.52617i	0.735257	+	0.735257i	−0.236399	+	0.971656i	$0.575967\pi$
$24$		0			0
$25$	0.235404	−	0.235404i	0.0470809	−	0.0470809i
$26$	−0.117306	−	0.0283657i	−0.0230056	−	0.00556297i
$27$		0			0
$28$	0.550793	−	1.07230i	0.104090	−	0.202646i
$29$	3.48138	−	8.40479i	0.646475	−	1.56073i	−0.171317	−	0.985216i	$-0.554802\pi$
$29$	3.48138	−	8.40479i	0.646475	−	1.56073i	0.817792	−	0.575513i	$-0.195198\pi$
$30$		0			0
$31$	3.54897			0.637414			0.318707	−	0.947853i	$-0.396751\pi$
$31$	3.54897			0.637414			0.318707	+	0.947853i	$0.396751\pi$
$32$	−4.03259	+	3.96715i	−0.712867	+	0.701299i
$33$		0			0
$34$	0.570702	+	3.64182i	0.0978745	+	0.624567i
$35$	−0.532667	+	1.28597i	−0.0900372	+	0.217369i
$36$		0			0
$37$	6.59514	−	2.73180i	1.08423	−	0.449105i	0.232242	−	0.972658i	$-0.425394\pi$
$37$	6.59514	−	2.73180i	1.08423	−	0.449105i	0.851993	+	0.523553i	$0.175394\pi$
$38$	4.34010	+	1.04948i	0.704058	+	0.170248i
$39$		0			0
$40$	4.26634	−	4.94587i	0.674567	−	0.782011i
$41$	3.51963	+	3.51963i	0.549674	+	0.549674i	0.926346	−	0.376673i	$-0.122932\pi$
$41$	3.51963	+	3.51963i	0.549674	+	0.549674i	−0.376673	+	0.926346i	$0.622932\pi$
$42$		0			0
$43$	−2.74958	−	6.63808i	−0.419307	−	1.01230i	−0.982549	−	0.186005i	$-0.940446\pi$
$43$	−2.74958	−	6.63808i	−0.419307	−	1.01230i	0.563241	−	0.826292i	$-0.309554\pi$
$44$	−0.487858	−	0.575008i	−0.0735474	−	0.0866857i
$45$		0			0
$46$	−5.69867	−	4.15459i	−0.840223	−	0.612561i
$47$		−	3.40368i		−	0.496478i	−0.968699	−	0.248239i	$-0.920148\pi$
$47$		−	3.40368i		−	0.496478i	0.968699	−	0.248239i	$-0.0798519\pi$
$48$		0			0
$49$			6.63670i			0.948100i
$50$	−0.277357	+	0.380439i	−0.0392243	+	0.0538022i
$51$		0			0
$52$	0.170106	+	0.0139478i	0.0235894	+	0.00193421i
$53$	−1.68239	−	4.06164i	−0.231094	−	0.557910i	0.765213	−	0.643777i	$-0.222634\pi$
$53$	−1.68239	−	4.06164i	−0.231094	−	0.557910i	−0.996307	+	0.0858677i	$0.972634\pi$
$54$		0			0
$55$	0.615681	+	0.615681i	0.0830184	+	0.0830184i
$56$	−0.534770	+	1.61878i	−0.0714617	+	0.216318i
$57$		0			0
$58$	−3.02385	+	12.5051i	−0.397051	+	1.64200i
$59$	2.70405	−	1.12005i	0.352037	−	0.145819i	−0.199655	−	0.979866i	$-0.563982\pi$
$59$	2.70405	−	1.12005i	0.352037	−	0.145819i	0.551693	+	0.834048i	$0.313982\pi$
$60$		0			0
$61$	2.88389	−	6.96232i	0.369244	−	0.891434i	−0.624631	−	0.780920i	$-0.714750\pi$
$61$	2.88389	−	6.96232i	0.369244	−	0.891434i	0.993875	−	0.110513i	$-0.0352495\pi$
$62$	−4.95849	+	0.777033i	−0.629728	+	0.0986833i
$63$		0			0
$64$	4.76559	−	6.42567i	0.595698	−	0.803208i
$65$	−0.197073			−0.0244439
$66$		0			0
$67$	−1.00349	+	2.42263i	−0.122595	+	0.295971i	−0.973248	−	0.229757i	$-0.926207\pi$
$67$	−1.00349	+	2.42263i	−0.122595	+	0.295971i	0.850653	+	0.525728i	$0.176207\pi$
$68$	−1.59473	−	4.96326i	−0.193389	−	0.601884i
$69$		0			0
$70$	0.462664	−	1.91334i	0.0552989	−	0.228688i
$71$	9.57606	−	9.57606i	1.13647	−	1.13647i	0.147391	−	0.989078i	$-0.452912\pi$
$71$	9.57606	−	9.57606i	1.13647	−	1.13647i	0.989078	−	0.147391i	$-0.0470877\pi$
$72$		0			0
$73$	7.59378	+	7.59378i	0.888784	+	0.888784i	0.994406	−	0.105622i	$-0.0336833\pi$
$73$	7.59378	+	7.59378i	0.888784	+	0.888784i	−0.105622	+	0.994406i	$0.533683\pi$
$74$	−8.61637	+	5.26075i	−1.00163	+	0.611549i
$75$		0			0
$76$	−6.29361	−	0.516044i	−0.721926	−	0.0591943i
$77$	−0.209961	−	0.0869686i	−0.0239272	−	0.00991099i
$78$		0			0
$79$		−	13.3063i		−	1.49708i	−0.663090	−	0.748540i	$-0.730755\pi$
$79$		−	13.3063i		−	1.49708i	0.663090	−	0.748540i	$-0.269245\pi$
$80$	−4.87788	+	7.84429i	−0.545364	+	0.877018i
$81$		0			0
$82$	−5.68810	−	4.14688i	−0.628146	−	0.457947i
$83$	2.41425	+	1.00002i	0.264998	+	0.109766i	0.511227	−	0.859446i	$-0.329191\pi$
$83$	2.41425	+	1.00002i	0.264998	+	0.109766i	−0.246228	+	0.969212i	$0.579191\pi$
$84$		0			0
$85$	2.30353	+	5.56121i	0.249853	+	0.603198i
$86$	5.29500	+	8.67247i	0.570974	+	0.935176i
$87$		0			0
$88$	0.807513	+	0.696565i	0.0860812	+	0.0742541i
$89$	5.44699	−	5.44699i	0.577380	−	0.577380i	−0.356801	−	0.934181i	$-0.616132\pi$
$89$	5.44699	−	5.44699i	0.577380	−	0.577380i	0.934181	+	0.356801i	$0.116132\pi$
$90$		0			0
$91$	0.0475219	−	0.0196842i	0.00498165	−	0.00206347i
$92$	8.87160	+	4.55693i	0.924929	+	0.475093i
$93$		0			0
$94$	0.745224	+	4.75550i	0.0768639	+	0.490492i
$95$	7.29133			0.748075
$96$		0			0
$97$	5.79690			0.588586			0.294293	−	0.955715i	$-0.404916\pi$
$97$	5.79690			0.588586			0.294293	+	0.955715i	$0.404916\pi$
$98$	−1.45308	−	9.27254i	−0.146783	−	0.936668i
$99$		0			0
$100$	0.304218	−	0.592262i	0.0304218	−	0.0592262i
$101$	6.92874	−	2.86998i	0.689436	−	0.285574i	−0.0103294	−	0.999947i	$-0.503288\pi$
$101$	6.92874	−	2.86998i	0.689436	−	0.285574i	0.699765	+	0.714373i	$0.253288\pi$
$102$		0			0
$103$	0.0213971	−	0.0213971i	0.00210832	−	0.00210832i	−0.706052	−	0.708160i	$-0.749525\pi$
$103$	0.0213971	−	0.0213971i	0.00210832	−	0.00210832i	0.708160	+	0.706052i	$0.249525\pi$
$104$	−0.240719	+	0.0177567i	−0.0236045	+	0.00174118i
$105$		0			0
$106$	3.23985	+	5.30642i	0.314682	+	0.515405i
$107$	−4.92590	−	11.8922i	−0.476205	−	1.14966i	−0.961375	−	0.275241i	$-0.911242\pi$
$107$	−4.92590	−	11.8922i	−0.476205	−	1.14966i	0.485170	−	0.874420i	$-0.338758\pi$
$108$		0			0
$109$	4.57285	+	1.89414i	0.438000	+	0.181426i	0.590777	−	0.806835i	$-0.298821\pi$
$109$	4.57285	+	1.89414i	0.438000	+	0.181426i	−0.152777	+	0.988261i	$0.548821\pi$
$110$	−0.995008	−	0.725406i	−0.0948703	−	0.0691647i
$111$		0			0
$112$	0.392736	−	2.37878i	0.0371101	−	0.224774i
$113$			6.65377i			0.625934i	0.949764	+	0.312967i	$0.101323\pi$
$113$			6.65377i			0.625934i	−0.949764	+	0.312967i	$0.898677\pi$
$114$		0			0
$115$	−10.6394	−	4.40697i	−0.992126	−	0.410952i
$116$	1.48687	−	18.1337i	0.138052	−	1.68367i
$117$		0			0
$118$	−3.53277	+	2.15694i	−0.325217	+	0.198562i
$119$	−1.11094	−	1.11094i	−0.101840	−	0.101840i
$120$		0			0
$121$	7.67765	−	7.67765i	0.697968	−	0.697968i
$122$	−2.50488	+	10.3589i	−0.226782	+	0.937851i
$123$		0			0
$124$	6.75768	−	2.17128i	0.606858	−	0.194987i
$125$	4.12447	−	9.95734i	0.368904	−	0.890612i
$126$		0			0
$127$	−15.2223			−1.35076			−0.675382	−	0.737468i	$-0.736021\pi$
$127$	−15.2223			−1.35076			−0.675382	+	0.737468i	$0.736021\pi$
$128$	−5.25142	+	10.0211i	−0.464165	+	0.885749i
$129$		0			0
$130$	0.275343	−	0.0431483i	0.0241491	−	0.00378436i
$131$	−1.78255	+	4.30346i	−0.155742	+	0.375995i	−0.982421	−	0.186679i	$-0.940228\pi$
$131$	−1.78255	+	4.30346i	−0.155742	+	0.375995i	0.826679	+	0.562674i	$0.190228\pi$
$132$		0			0
$133$	−1.75822	+	0.728280i	−0.152457	+	0.0631499i
$134$	0.871608	−	3.60452i	0.0752954	−	0.311383i
$135$		0			0
$136$	3.31478	+	6.58532i	0.284240	+	0.564687i
$137$	14.9433	+	14.9433i	1.27669	+	1.27669i	0.942507	+	0.334185i	$0.108461\pi$
$137$	14.9433	+	14.9433i	1.27669	+	1.27669i	0.334185	+	0.942507i	$0.391539\pi$
$138$		0			0
$139$	−2.22562	−	5.37312i	−0.188774	−	0.455742i	0.800950	−	0.598732i	$-0.204328\pi$
$139$	−2.22562	−	5.37312i	−0.188774	−	0.455742i	−0.989724	+	0.142990i	$0.954328\pi$
$140$	−0.227498	+	2.77454i	−0.0192271	+	0.234492i
$141$		0			0
$142$	−11.2827	+	15.4760i	−0.946821	+	1.29871i
$143$		−	0.0321761i		−	0.00269070i
$144$		0			0
$145$			21.0084i			1.74465i
$146$	−12.2724	−	8.94711i	−1.01567	−	0.740468i
$147$		0			0
$148$	10.8866	−	9.23664i	0.894877	−	0.759247i
$149$	−1.09317	−	2.63915i	−0.0895560	−	0.216207i	0.872755	−	0.488158i	$-0.162331\pi$
$149$	−1.09317	−	2.63915i	−0.0895560	−	0.216207i	−0.962311	+	0.271951i	$0.912331\pi$
$150$		0			0
$151$	0.234956	+	0.234956i	0.0191204	+	0.0191204i	0.716602	−	0.697482i	$-0.245696\pi$
$151$	0.234956	+	0.234956i	0.0191204	+	0.0191204i	−0.697482	+	0.716602i	$0.745696\pi$
$152$	8.90618	−	0.656965i	0.722386	−	0.0532869i
$153$		0			0
$154$	0.312391	+	0.0755391i	0.0251732	+	0.00608711i
$155$	−7.57181	+	3.13635i	−0.608183	+	0.251917i
$156$		0			0
$157$	−7.67210	+	18.5221i	−0.612300	+	1.47822i	0.248166	+	0.968717i	$0.420172\pi$
$157$	−7.67210	+	18.5221i	−0.612300	+	1.47822i	−0.860467	+	0.509507i	$0.829828\pi$
$158$	2.91337	+	18.5911i	0.231775	+	1.47903i
$159$		0			0
$160$	5.09772	−	12.0277i	0.403010	−	0.950876i
$161$	3.00575			0.236886
$162$		0			0
$163$	−2.77553	+	6.70071i	−0.217396	+	0.524840i	−0.994525	−	0.104501i	$-0.966675\pi$
$163$	−2.77553	+	6.70071i	−0.217396	+	0.524840i	0.777129	+	0.629342i	$0.216675\pi$
$164$	8.85514	+	4.54848i	0.691471	+	0.355177i
$165$		0			0
$166$	−3.59205	−	0.868593i	−0.278797	−	0.0674159i
$167$	15.3418	−	15.3418i	1.18718	−	1.18718i	0.209342	−	0.977843i	$-0.432868\pi$
$167$	15.3418	−	15.3418i	1.18718	−	1.18718i	0.977843	−	0.209342i	$-0.0671320\pi$
$168$		0			0
$169$	−9.18724	−	9.18724i	−0.706711	−	0.706711i
$170$	−4.43601	−	7.26556i	−0.340226	−	0.557243i
$171$		0			0
$172$	−9.29677	−	10.9575i	−0.708872	−	0.835503i
$173$	−1.45461	−	0.602520i	−0.110592	−	0.0458087i	0.326701	−	0.945128i	$-0.394063\pi$
$173$	−1.45461	−	0.602520i	−0.110592	−	0.0458087i	−0.437293	+	0.899319i	$0.644063\pi$
$174$		0			0
$175$		−	0.200661i		−	0.0151686i
$176$	−1.28074	−	0.796412i	−0.0965392	−	0.0600318i
$177$		0			0
$178$	−6.41773	+	8.80293i	−0.481029	+	0.659807i
$179$	−15.8279	−	6.55615i	−1.18304	−	0.490029i	−0.297555	−	0.954705i	$-0.596171\pi$
$179$	−15.8279	−	6.55615i	−1.18304	−	0.490029i	−0.885481	+	0.464675i	$0.846171\pi$
$180$		0			0
$181$	3.91205	+	9.44453i	0.290781	+	0.702007i	0.999996	−	0.00298575i	$-0.000950396\pi$
$181$	3.91205	+	9.44453i	0.290781	+	0.702007i	−0.709215	+	0.704992i	$0.750950\pi$
$182$	−0.0620860	+	0.0379068i	−0.00460212	+	0.00280984i
$183$		0			0
$184$	−13.3928	−	4.42437i	−0.987330	−	0.326169i
$185$	−11.6567	+	11.6567i	−0.857019	+	0.857019i
$186$		0			0
$187$	−0.907979	+	0.376097i	−0.0663980	+	0.0275029i
$188$	−2.08240	−	6.48104i	−0.151874	−	0.472678i
$189$		0			0
$190$	−10.1872	+	1.59641i	−0.739055	+	0.115816i
$191$	−4.94060			−0.357489			−0.178744	−	0.983896i	$-0.557204\pi$
$191$	−4.94060			−0.357489			−0.178744	+	0.983896i	$0.557204\pi$
$192$		0			0
$193$	−13.3414			−0.960334			−0.480167	−	0.877177i	$-0.659424\pi$
$193$	−13.3414			−0.960334			−0.480167	+	0.877177i	$0.659424\pi$
$194$	−8.09921	+	1.26921i	−0.581490	+	0.0911239i
$195$		0			0
$196$	4.06038	+	12.6371i	0.290027	+	0.902650i
$197$	−9.85498	+	4.08207i	−0.702138	+	0.290835i	−0.705047	−	0.709161i	$-0.749074\pi$
$197$	−9.85498	+	4.08207i	−0.702138	+	0.290835i	0.00290884	+	0.999996i	$0.499074\pi$
$198$		0			0
$199$	−11.8004	+	11.8004i	−0.836508	+	0.836508i	−0.988397	−	0.151889i	$-0.951464\pi$
$199$	−11.8004	+	11.8004i	−0.836508	+	0.836508i	0.151889	+	0.988397i	$0.451464\pi$
$200$	−0.295368	+	0.894093i	−0.0208857	+	0.0632219i
$201$		0			0
$202$	−9.05221	+	5.52685i	−0.636911	+	0.388868i
$203$	−2.09838	−	5.06595i	−0.147278	−	0.355560i
$204$		0			0
$205$	−10.6196	−	4.39879i	−0.741707	−	0.307225i
$206$	−0.0252104	+	0.0345800i	−0.00175649	+	0.00240930i
$207$		0			0
$208$	0.332436	−	0.0775135i	0.0230503	−	0.00537460i
$209$			1.19046i			0.0823456i
$210$		0			0
$211$	−25.1075	−	10.3999i	−1.72847	−	0.715957i	−0.999507	−	0.0314079i	$-0.990001\pi$
$211$	−25.1075	−	10.3999i	−1.72847	−	0.715957i	−0.728967	−	0.684549i	$-0.759999\pi$
$212$	−5.68842	−	6.70458i	−0.390682	−	0.460473i
$213$		0			0
$214$	9.48603	+	15.5368i	0.648452	+	1.06207i
$215$	11.7326	+	11.7326i	0.800157	+	0.800157i
$216$		0			0
$217$	1.51259	−	1.51259i	0.102681	−	0.102681i
$218$	−6.80373	−	1.64521i	−0.460807	−	0.111428i
$219$		0			0
$220$	1.54901	+	0.795656i	0.104434	+	0.0536431i
$221$	0.0851247	−	0.205509i	0.00572611	−	0.0138240i
$222$		0			0
$223$	−16.9364			−1.13414			−0.567072	−	0.823668i	$-0.691924\pi$
$223$	−16.9364			−1.13414			−0.567072	+	0.823668i	$0.691924\pi$
$224$	−0.0278913	+	3.40953i	−0.00186357	+	0.227809i
$225$		0			0
$226$	−1.45682	−	9.29639i	−0.0969060	−	0.618387i
$227$	−10.5187	+	25.3944i	−0.698151	+	1.68549i	0.0295252	+	0.999564i	$0.490600\pi$
$227$	−10.5187	+	25.3944i	−0.698151	+	1.68549i	−0.727676	+	0.685921i	$0.759400\pi$
$228$		0			0
$229$	18.0463	−	7.47503i	1.19253	−	0.493964i	0.303955	−	0.952686i	$-0.401693\pi$
$229$	18.0463	−	7.47503i	1.19253	−	0.493964i	0.888579	+	0.458723i	$0.151693\pi$
$230$	15.8298	+	3.82780i	1.04379	+	0.252398i
$231$		0			0
$232$	1.89290	+	25.6613i	0.124275	+	1.68474i
$233$	3.04248	+	3.04248i	0.199320	+	0.199320i	0.799708	−	0.600389i	$-0.204987\pi$
$233$	3.04248	+	3.04248i	0.199320	+	0.199320i	−0.600389	+	0.799708i	$0.704987\pi$
$234$		0			0
$235$	3.00795	+	7.26184i	0.196217	+	0.473710i
$236$	4.46359	−	3.78708i	0.290555	−	0.246518i
$237$		0			0
$238$	1.79540	+	1.30893i	0.116378	+	0.0848452i
$239$		−	6.50603i		−	0.420840i	−0.977611	−	0.210420i	$-0.932517\pi$
$239$		−	6.50603i		−	0.420840i	0.977611	−	0.210420i	$-0.0674831\pi$
$240$		0			0
$241$			9.33084i			0.601053i	0.953774	+	0.300526i	$0.0971623\pi$
$241$			9.33084i			0.601053i	−0.953774	+	0.300526i	$0.902838\pi$
$242$	−9.04593	+	12.4079i	−0.581495	+	0.797611i
$243$		0			0
$244$	1.23169	−	15.0215i	0.0788507	−	0.961654i
$245$	−5.86508	−	14.1596i	−0.374706	−	0.904621i
$246$		0			0
$247$	−0.190526	−	0.190526i	−0.0121229	−	0.0121229i
$248$	−8.96618	+	4.51320i	−0.569353	+	0.286589i
$249$		0			0
$250$	−3.58243	+	14.8151i	−0.226573	+	0.936987i
$251$	−17.0668	+	7.06931i	−1.07725	+	0.446211i	−0.849543	−	0.527519i	$-0.823122\pi$
$251$	−17.0668	+	7.06931i	−1.07725	+	0.446211i	−0.227705	+	0.973730i	$0.573122\pi$
$252$		0			0
$253$	0.719526	−	1.73709i	0.0452362	−	0.109210i
$254$	21.2681	−	3.33287i	1.33448	−	0.209123i
$255$		0			0
$256$	5.14301	−	15.1509i	0.321438	−	0.946931i
$257$	−9.05297			−0.564709			−0.282354	−	0.959310i	$-0.591115\pi$
$257$	−9.05297			−0.564709			−0.282354	+	0.959310i	$0.591115\pi$
$258$		0			0
$259$	1.64658	−	3.97519i	0.102313	−	0.247006i
$260$	−0.375251	+	0.120570i	−0.0232721	+	0.00747746i
$261$		0			0
$262$	1.54829	−	6.40292i	0.0956536	−	0.395574i
$263$	−9.55339	+	9.55339i	−0.589087	+	0.589087i	−0.937384	−	0.348297i	$-0.886760\pi$
$263$	−9.55339	+	9.55339i	−0.589087	+	0.589087i	0.348297	+	0.937384i	$0.386760\pi$
$264$		0			0
$265$	7.17883	+	7.17883i	0.440992	+	0.440992i
$266$	2.29707	−	1.40248i	0.140842	−	0.0859917i
$267$		0			0
$268$	−0.428582	+	5.22693i	−0.0261798	+	0.319286i
$269$	−3.32220	−	1.37610i	−0.202558	−	0.0839024i	0.279098	−	0.960263i	$-0.409965\pi$
$269$	−3.32220	−	1.37610i	−0.202558	−	0.0839024i	−0.481656	+	0.876360i	$0.659965\pi$
$270$		0			0
$271$		−	17.1114i		−	1.03945i	−0.854335	−	0.519723i	$-0.826035\pi$
$271$		−	17.1114i		−	1.03945i	0.854335	−	0.519723i	$-0.173965\pi$
$272$	−6.07311	−	8.47501i	−0.368237	−	0.513873i
$273$		0			0
$274$	−24.1500	−	17.6064i	−1.45895	−	1.06364i
$275$	−0.115967	−	0.0480350i	−0.00699306	−	0.00289662i
$276$		0			0
$277$	9.34128	+	22.5518i	0.561263	+	1.35501i	0.908757	+	0.417326i	$0.137033\pi$
$277$	9.34128	+	22.5518i	0.561263	+	1.35501i	−0.347494	+	0.937682i	$0.612967\pi$
$278$	4.28597	+	7.01983i	0.257056	+	0.421021i
$279$		0			0
$280$	−0.289623	−	3.92629i	−0.0173083	−	0.234641i
$281$	−11.2554	+	11.2554i	−0.671444	+	0.671444i	−0.958049	−	0.286605i	$-0.907473\pi$
$281$	−11.2554	+	11.2554i	−0.671444	+	0.671444i	0.286605	+	0.958049i	$0.407473\pi$
$282$		0			0
$283$	23.1436	−	9.58640i	1.37575	−	0.569852i	0.432405	−	0.901679i	$-0.357665\pi$
$283$	23.1436	−	9.58640i	1.37575	−	0.569852i	0.943340	+	0.331827i	$0.107665\pi$
$284$	12.3753	−	24.0927i	0.734340	−	1.42964i
$285$		0			0
$286$	0.00704483	+	0.0449552i	0.000416569	+	0.00265826i
$287$	3.00017			0.177094
$288$		0			0
$289$	10.2057			0.600337
$290$	−4.59972	−	29.3522i	−0.270105	−	1.72362i
$291$		0			0
$292$	19.1054	+	9.81358i	1.11806	+	0.574296i
$293$	−19.2802	+	7.98612i	−1.12636	+	0.466554i	−0.866543	−	0.499103i	$-0.833663\pi$
$293$	−19.2802	+	7.98612i	−1.12636	+	0.466554i	−0.259819	+	0.965657i	$0.583663\pi$
$294$		0			0
$295$	−4.77933	+	4.77933i	−0.278263	+	0.278263i
$296$	−13.1881	+	15.2887i	−0.766542	+	0.888636i
$297$		0			0
$298$	2.10517	+	3.44797i	0.121949	+	0.199736i
$299$	0.162855	+	0.393168i	0.00941817	+	0.0227375i
$300$		0			0
$301$	−4.00107	−	1.65730i	−0.230618	−	0.0955251i
$302$	−0.379714	−	0.276829i	−0.0218501	−	0.0159297i
$303$		0			0
$304$	−12.2995	+	2.86786i	−0.705427	+	0.164483i
$305$			17.4029i			0.996485i
$306$		0			0
$307$	22.1744	+	9.18495i	1.26556	+	0.524213i	0.911612	−	0.411051i	$-0.134838\pi$
$307$	22.1744	+	9.18495i	1.26556	+	0.524213i	0.353950	+	0.935264i	$0.384838\pi$
$308$	−0.452999	−	0.0371436i	−0.0258120	−	0.00211646i
$309$		0			0
$310$	9.89236	−	6.03981i	0.561848	−	0.343038i
$311$	7.33587	+	7.33587i	0.415979	+	0.415979i	0.883815	−	0.467836i	$-0.154966\pi$
$311$	7.33587	+	7.33587i	0.415979	+	0.415979i	−0.467836	+	0.883815i	$0.654966\pi$
$312$		0			0
$313$	13.8107	−	13.8107i	0.780628	−	0.780628i	−0.199309	−	0.979937i	$-0.563870\pi$
$313$	13.8107	−	13.8107i	0.780628	−	0.780628i	0.979937	+	0.199309i	$0.0638697\pi$
$314$	6.66383	−	27.5582i	0.376062	−	1.55520i
$315$		0			0
$316$	−8.14091	−	25.3369i	−0.457962	−	1.42531i
$317$	5.63141	−	13.5954i	0.316291	−	0.763595i	−0.683153	−	0.730275i	$-0.739392\pi$
$317$	5.63141	−	13.5954i	0.316291	−	0.763595i	0.999445	−	0.0333201i	$-0.0106081\pi$
$318$		0			0
$319$	−3.43005			−0.192046
$320$	−4.48891	+	17.9208i	−0.250938	+	1.00180i
$321$		0			0
$322$	−4.19951	+	0.658097i	−0.234030	+	0.0366743i
$323$	−3.14946	+	7.60347i	−0.175241	+	0.423068i
$324$		0			0
$325$	0.0262476	−	0.0108721i	0.00145595	−	0.000603076i
$326$	2.41076	−	9.96967i	0.133520	−	0.552169i
$327$		0			0
$328$	−13.3679	−	4.41616i	−0.738121	−	0.243842i
$329$	−1.45067	−	1.45067i	−0.0799779	−	0.0799779i
$330$		0			0
$331$	−2.92360	−	7.05819i	−0.160695	−	0.387953i	0.822939	−	0.568130i	$-0.192333\pi$
$331$	−2.92360	−	7.05819i	−0.160695	−	0.387953i	−0.983634	+	0.180177i	$0.942333\pi$
$332$	5.20885	+	0.427099i	0.285873	+	0.0234401i
$333$		0			0
$334$	−18.0760	+	24.7940i	−0.989072	+	1.35667i
$335$		−	6.05556i		−	0.330850i
$336$		0			0
$337$		−	27.7524i		−	1.51177i	−0.654703	−	0.755886i	$-0.727206\pi$
$337$		−	27.7524i		−	1.51177i	0.654703	−	0.755886i	$-0.272794\pi$
$338$	14.8476	+	10.8246i	0.807602	+	0.588778i
$339$		0			0
$340$	7.78859	+	9.17992i	0.422396	+	0.497851i
$341$	−0.512071	−	1.23625i	−0.0277302	−	0.0669467i
$342$		0			0
$343$	5.81203	+	5.81203i	0.313820	+	0.313820i
$344$	15.3882	+	13.2739i	0.829677	+	0.715683i
$345$		0			0
$346$	2.16425	+	0.523336i	0.116351	+	0.0281347i
$347$	−7.46847	+	3.09354i	−0.400929	+	0.166070i	−0.574031	−	0.818834i	$-0.694621\pi$
$347$	−7.46847	+	3.09354i	−0.400929	+	0.166070i	0.173102	+	0.984904i	$0.444621\pi$
$348$		0			0
$349$	1.75419	−	4.23499i	0.0938996	−	0.226694i	−0.869950	−	0.493139i	$-0.835849\pi$
$349$	1.75419	−	4.23499i	0.0938996	−	0.226694i	0.963850	+	0.266446i	$0.0858493\pi$
$350$	0.0439340	+	0.280356i	0.00234837	+	0.0149857i
$351$		0			0
$352$	1.96377	+	0.832304i	0.104669	+	0.0443620i
$353$	8.53930			0.454501			0.227251	−	0.973836i	$-0.427026\pi$
$353$	8.53930			0.454501			0.227251	+	0.973836i	$0.427026\pi$
$354$		0			0
$355$	−11.9681	+	28.8935i	−0.635199	+	1.53351i
$356$	7.03925	−	13.7043i	0.373079	−	0.726324i
$357$		0			0
$358$	23.5496	+	5.69453i	1.24464	+	0.300965i
$359$	2.09979	−	2.09979i	0.110823	−	0.110823i	−0.649521	−	0.760344i	$-0.725031\pi$
$359$	2.09979	−	2.09979i	0.110823	−	0.110823i	0.760344	+	0.649521i	$0.225031\pi$
$360$		0			0
$361$	−6.38592	−	6.38592i	−0.336101	−	0.336101i
$362$	−7.53362	−	12.3390i	−0.395958	−	0.648524i
$363$		0			0
$364$	0.0784447	−	0.0665554i	0.00411162	−	0.00348845i
$365$	−22.9124	−	9.49062i	−1.19929	−	0.496762i
$366$		0			0
$367$		−	27.5428i		−	1.43772i	−0.695154	−	0.718861i	$-0.744664\pi$
$367$		−	27.5428i		−	1.43772i	0.695154	−	0.718861i	$-0.255336\pi$
$368$	19.6806	+	3.24926i	1.02592	+	0.169380i
$369$		0			0
$370$	13.7341	−	18.8385i	0.714003	−	0.979368i
$371$	−2.44814	−	1.01405i	−0.127101	−	0.0526470i
$372$		0			0
$373$	5.56276	+	13.4297i	0.288029	+	0.695363i	0.999976	−	0.00686942i	$-0.00218662\pi$
$373$	5.56276	+	13.4297i	0.288029	+	0.695363i	−0.711948	+	0.702233i	$0.752187\pi$
$374$	1.18625	−	0.724267i	0.0613395	−	0.0374510i
$375$		0			0
$376$	4.32845	+	8.59913i	0.223223	+	0.443466i
$377$	0.548960	−	0.548960i	0.0282729	−	0.0282729i
$378$		0			0
$379$	33.5936	−	13.9149i	1.72559	−	0.714761i	0.725951	−	0.687746i	$-0.241400\pi$
$379$	33.5936	−	13.9149i	1.72559	−	0.714761i	0.999635	−	0.0270152i	$-0.00860026\pi$
$380$	13.8836	−	4.46089i	0.712214	−	0.228839i
$381$		0			0
$382$	6.90281	−	1.08172i	0.353179	−	0.0553458i
$383$	27.8606			1.42361			0.711804	−	0.702378i	$-0.247878\pi$
$383$	27.8606			1.42361			0.711804	+	0.702378i	$0.247878\pi$
$384$		0			0
$385$	0.524813			0.0267470
$386$	18.6401	−	2.92105i	0.948755	−	0.148677i
$387$		0			0
$388$	11.0380	−	3.54658i	0.560371	−	0.180051i
$389$	35.3315	−	14.6348i	1.79138	−	0.742014i	0.801879	−	0.597486i	$-0.203834\pi$
$389$	35.3315	−	14.6348i	1.79138	−	0.742014i	0.989501	−	0.144527i	$-0.0461662\pi$
$390$		0			0
$391$	9.19126	−	9.19126i	0.464822	−	0.464822i
$392$	−8.43985	−	16.7671i	−0.426277	−	0.846865i
$393$		0			0
$394$	12.8753	−	7.86102i	0.648646	−	0.396032i
$395$	11.7593	+	28.3894i	0.591673	+	1.42843i
$396$		0			0
$397$	−23.3605	−	9.67622i	−1.17243	−	0.485636i	−0.290433	−	0.956895i	$-0.593799\pi$
$397$	−23.3605	−	9.67622i	−1.17243	−	0.485636i	−0.881995	+	0.471260i	$0.843799\pi$
$398$	13.9034	−	19.0707i	0.696915	−	0.955929i
$399$		0			0
$400$	0.216918	−	1.31386i	0.0108459	−	0.0656931i
$401$			26.3181i			1.31426i	0.753776	+	0.657131i	$0.228230\pi$
$401$			26.3181i			1.31426i	−0.753776	+	0.657131i	$0.771770\pi$
$402$		0			0
$403$	0.279809	+	0.115901i	0.0139383	+	0.00577343i
$404$	11.4373	−	9.70385i	0.569028	−	0.482785i
$405$		0			0
$406$	4.04095	+	6.61852i	0.200549	+	0.328471i
$407$	−1.90319	−	1.90319i	−0.0943377	−	0.0943377i
$408$		0			0
$409$	24.4523	−	24.4523i	1.20909	−	1.20909i	0.237764	−	0.971323i	$-0.423586\pi$
$409$	24.4523	−	24.4523i	1.20909	−	1.20909i	0.971323	−	0.237764i	$-0.0764144\pi$
$410$	15.8004	+	3.82070i	0.780328	+	0.188691i
$411$		0			0
$412$	0.0276518	−	0.0538336i	0.00136231	−	0.00265219i
$413$	0.675108	−	1.62985i	0.0332199	−	0.0801999i
$414$		0			0
$415$	−6.03461			−0.296227
$416$	−0.447496	+	0.181085i	−0.0219403	+	0.00887840i
$417$		0			0
$418$	−0.260646	−	1.66326i	−0.0127486	−	0.0813527i
$419$	8.40061	−	20.2809i	0.410397	−	0.990786i	−0.574635	−	0.818410i	$-0.694856\pi$
$419$	8.40061	−	20.2809i	0.410397	−	0.990786i	0.985031	−	0.172375i	$-0.0551442\pi$
$420$		0			0
$421$	16.7888	−	6.95414i	0.818236	−	0.338924i	0.0660009	−	0.997820i	$-0.478976\pi$
$421$	16.7888	−	6.95414i	0.818236	−	0.338924i	0.752235	+	0.658895i	$0.228976\pi$
$422$	37.3563	+	9.03312i	1.81848	+	0.439725i
$423$		0			0
$424$	9.41559	+	8.12193i	0.457261	+	0.394436i
$425$	−0.613601	−	0.613601i	−0.0297640	−	0.0297640i
$426$		0			0
$427$	−1.73825	−	4.19651i	−0.0841198	−	0.203083i
$428$	−16.6553	−	19.6305i	−0.805062	−	0.948876i
$429$		0			0
$430$	−18.9612	−	13.8235i	−0.914388	−	0.666630i
$431$			27.1791i			1.30917i	0.755987	+	0.654586i	$0.227157\pi$
$431$			27.1791i			1.30917i	−0.755987	+	0.654586i	$0.772843\pi$
$432$		0			0
$433$			39.7349i			1.90954i	0.297347	+	0.954770i	$0.403898\pi$
$433$			39.7349i			1.90954i	−0.297347	+	0.954770i	$0.596102\pi$
$434$	−1.78216	+	2.44451i	−0.0855463	+	0.117340i
$435$		0			0
$436$	9.86613	+	0.808973i	0.472502	+	0.0387428i
$437$	−6.02535	−	14.5465i	−0.288232	−	0.695853i
$438$		0			0
$439$	18.9434	+	18.9434i	0.904118	+	0.904118i	0.995789	−	0.0916713i	$-0.0292209\pi$
$439$	18.9434	+	18.9434i	0.904118	+	0.904118i	−0.0916713	+	0.995789i	$0.529221\pi$
$440$	−2.33843	−	0.772510i	−0.111480	−	0.0368280i
$441$		0			0
$442$	−0.0739376	+	0.305767i	−0.00351685	+	0.0145439i
$443$	−35.6628	+	14.7720i	−1.69439	+	0.701840i	−0.999845	−	0.0176064i	$-0.994395\pi$
$443$	−35.6628	+	14.7720i	−1.69439	+	0.701840i	−0.694548	+	0.719447i	$0.744395\pi$
$444$		0			0
$445$	−6.80759	+	16.4350i	−0.322711	+	0.779093i
$446$	23.6629	−	3.70816i	1.12047	−	0.175586i
$447$		0			0
$448$	−0.707535	−	4.76977i	−0.0334279	−	0.225351i
$449$	3.94369			0.186114			0.0930571	−	0.995661i	$-0.470336\pi$
$449$	3.94369			0.186114			0.0930571	+	0.995661i	$0.470336\pi$
$450$		0			0
$451$	0.718191	−	1.73387i	0.0338183	−	0.0816446i
$452$	4.07082	+	12.6696i	0.191475	+	0.595928i
$453$		0			0
$454$	9.13633	−	37.7831i	0.428789	−	1.77325i
$455$	−0.0839935	+	0.0839935i	−0.00393767	+	0.00393767i
$456$		0			0
$457$	−19.8204	−	19.8204i	−0.927160	−	0.927160i	0.0703611	−	0.997522i	$-0.477585\pi$
$457$	−19.8204	−	19.8204i	−0.927160	−	0.927160i	−0.997522	+	0.0703611i	$0.977585\pi$
$458$	−23.5770	+	14.3950i	−1.10168	+	0.672634i
$459$		0			0
$460$	−22.9549	−	1.88219i	−1.07028	−	0.0877573i
$461$	−21.9774	−	9.10334i	−1.02359	−	0.423985i	−0.193195	−	0.981160i	$-0.561885\pi$
$461$	−21.9774	−	9.10334i	−1.02359	−	0.423985i	−0.830395	+	0.557175i	$0.811885\pi$
$462$		0			0
$463$			2.29173i			0.106506i	0.998581	+	0.0532528i	$0.0169589\pi$
$463$			2.29173i			0.106506i	−0.998581	+	0.0532528i	$0.983041\pi$
$464$	−8.26313	−	35.4385i	−0.383606	−	1.64519i
$465$		0			0
$466$	−4.91698	−	3.58470i	−0.227775	−	0.166058i
$467$	−17.4766	−	7.23903i	−0.808719	−	0.334982i	−0.0602760	−	0.998182i	$-0.519198\pi$
$467$	−17.4766	−	7.23903i	−0.808719	−	0.334982i	−0.748443	+	0.663200i	$0.769198\pi$
$468$		0			0
$469$	0.604847	+	1.46023i	0.0279292	+	0.0674271i
$470$	−5.79255	−	9.48739i	−0.267190	−	0.437621i
$471$		0			0
$472$	−5.40720	+	6.26845i	−0.248886	+	0.288529i
$473$	−1.91558	+	1.91558i	−0.0880786	+	0.0880786i
$474$		0			0
$475$	−0.971113	+	0.402248i	−0.0445577	+	0.0184564i
$476$	−2.79505	−	1.43569i	−0.128111	−	0.0658047i
$477$		0			0
$478$	1.42447	+	9.08998i	0.0651538	+	0.415766i
$479$	22.5095			1.02848			0.514242	−	0.857645i	$-0.328073\pi$
$479$	22.5095			1.02848			0.514242	+	0.857645i	$0.328073\pi$
$480$		0			0
$481$	0.609191			0.0277767
$482$	−2.04295	−	13.0367i	−0.0930540	−	0.593806i
$483$		0			0
$484$	9.92197	−	19.3165i	0.450999	−	0.878020i
$485$	−12.3678	+	5.12292i	−0.561594	+	0.232620i
$486$		0			0
$487$	−7.20407	+	7.20407i	−0.326448	+	0.326448i	−0.851234	−	0.524786i	$-0.824145\pi$
$487$	−7.20407	+	7.20407i	−0.326448	+	0.326448i	0.524786	+	0.851234i	$0.324145\pi$
$488$	1.56804	+	21.2572i	0.0709816	+	0.962266i
$489$		0			0
$490$	11.2946	+	18.4991i	0.510240	+	0.835702i
$491$	7.53320	+	18.1868i	0.339969	+	0.820757i	0.997718	+	0.0675201i	$0.0215087\pi$
$491$	7.53320	+	18.1868i	0.339969	+	0.820757i	−0.657749	+	0.753237i	$0.728491\pi$
$492$		0			0
$493$	−21.9078	−	9.07450i	−0.986677	−	0.408695i
$494$	0.307911	+	0.224481i	0.0138535	+	0.0100999i
$495$		0			0
$496$	11.5391	−	8.26879i	0.518119	−	0.371280i
$497$		−	8.16274i		−	0.366149i
$498$		0			0
$499$	−34.4834	−	14.2835i	−1.54369	−	0.639417i	−0.561527	−	0.827458i	$-0.689786\pi$
$499$	−34.4834	−	14.2835i	−1.54369	−	0.639417i	−0.982161	+	0.188042i	$0.939786\pi$
$500$	1.76153	−	21.4834i	0.0787780	−	0.960767i
$501$		0			0
$502$	22.2973	−	13.6137i	0.995179	−	0.607609i
$503$	−15.6296	−	15.6296i	−0.696889	−	0.696889i	0.266849	−	0.963738i	$-0.414017\pi$
$503$	−15.6296	−	15.6296i	−0.696889	−	0.696889i	−0.963738	+	0.266849i	$0.914017\pi$
$504$		0			0
$505$	−12.2463	+	12.2463i	−0.544955	+	0.544955i
$506$	−0.624966	+	2.58453i	−0.0277831	+	0.114897i
$507$		0			0
$508$	−28.9852	+	9.31312i	−1.28601	+	0.413203i
$509$	−8.52634	+	20.5844i	−0.377923	+	0.912387i	0.614432	+	0.788970i	$0.289385\pi$
$509$	−8.52634	+	20.5844i	−0.377923	+	0.912387i	−0.992355	+	0.123417i	$0.960615\pi$
$510$		0			0
$511$	6.47302			0.286349
$512$	−3.86839	+	22.2943i	−0.170960	+	0.985278i
$513$		0			0
$514$	12.6485	−	1.98211i	0.557900	−	0.0874273i
$515$	−0.0267418	+	0.0645605i	−0.00117839	+	0.00284488i
$516$		0			0
$517$	−1.18564	+	0.491109i	−0.0521444	+	0.0215989i
$518$	−1.43018	+	5.91450i	−0.0628387	+	0.259868i
$519$		0			0
$520$	0.497888	−	0.250616i	0.0218338	−	0.0109903i
$521$	4.68739	+	4.68739i	0.205358	+	0.205358i	0.802291	−	0.596933i	$-0.203614\pi$
$521$	4.68739	+	4.68739i	0.205358	+	0.205358i	−0.596933	+	0.802291i	$0.703614\pi$
$522$		0			0
$523$	6.71504	+	16.2115i	0.293628	+	0.708881i	0.999999	+	0.00103957i	$0.000330905\pi$
$523$	6.71504	+	16.2115i	0.293628	+	0.708881i	−0.706371	+	0.707841i	$0.749669\pi$
$524$	−0.761315	+	9.28491i	−0.0332582	+	0.405613i
$525$		0			0
$526$	11.2560	−	15.4393i	0.490783	−	0.673186i
$527$		−	9.25068i		−	0.402966i
$528$		0			0
$529$			1.86775i			0.0812063i
$530$	−11.6018	−	8.45822i	−0.503949	−	0.367401i
$531$		0			0
$532$	−2.90231	+	2.46243i	−0.125831	+	0.106760i
$533$	0.162553	+	0.392438i	0.00704096	+	0.0169984i
$534$		0			0
$535$	21.0191	+	21.0191i	0.908733	+	0.908733i
$536$	−0.545619	−	7.39671i	−0.0235671	−	0.319489i
$537$		0			0
$538$	4.94295	+	1.19525i	0.213106	+	0.0515310i
$539$	2.31183	−	0.957592i	0.0995776	−	0.0412464i
$540$		0			0
$541$	14.0016	−	33.8028i	0.601975	−	1.45330i	−0.269571	−	0.962981i	$-0.586882\pi$
$541$	14.0016	−	33.8028i	0.601975	−	1.45330i	0.871545	−	0.490315i	$-0.163118\pi$
$542$	3.74649	+	23.9075i	0.160925	+	1.02691i
$543$		0			0
$544$	10.3407	+	10.5113i	0.443354	+	0.450667i
$545$	−11.4302			−0.489616
$546$		0			0
$547$	4.43851	−	10.7155i	0.189777	−	0.458163i	−0.800139	−	0.599814i	$-0.795241\pi$
$547$	4.43851	−	10.7155i	0.189777	−	0.458163i	0.989917	+	0.141651i	$0.0452412\pi$
$548$	37.5963	+	19.3115i	1.60604	+	0.824947i
$549$		0			0
$550$	0.172542	+	0.0417222i	0.00735720	+	0.00177904i
$551$	−20.3105	+	20.3105i	−0.865257	+	0.865257i
$552$		0			0
$553$	−5.67123	−	5.67123i	−0.241165	−	0.241165i
$554$	−17.9889	−	29.4633i	−0.764276	−	1.25178i
$555$		0			0
$556$	−7.52517	−	8.86944i	−0.319138	−	0.376148i
$557$	19.8667	+	8.22907i	0.841781	+	0.348677i	0.761555	−	0.648100i	$-0.224436\pi$
$557$	19.8667	+	8.22907i	0.841781	+	0.348677i	0.0802253	+	0.996777i	$0.474436\pi$
$558$		0			0
$559$		−	0.613157i		−	0.0259338i
$560$	1.26430	+	5.42226i	0.0534263	+	0.229132i
$561$		0			0
$562$	13.2614	−	18.1900i	0.559396	−	0.767300i
$563$	−21.9128	−	9.07659i	−0.923515	−	0.382533i	−0.130301	−	0.991475i	$-0.541594\pi$
$563$	−21.9128	−	9.07659i	−0.923515	−	0.382533i	−0.793215	+	0.608942i	$0.791594\pi$
$564$		0			0
$565$	−5.88016	−	14.1960i	−0.247380	−	0.597229i
$566$	−30.2365	+	18.4610i	−1.27093	+	0.775972i
$567$		0			0
$568$	−12.0153	+	36.3710i	−0.504152	+	1.52609i
$569$	0.463796	−	0.463796i	0.0194434	−	0.0194434i	−0.697318	−	0.716762i	$-0.745624\pi$
$569$	0.463796	−	0.463796i	0.0194434	−	0.0194434i	0.716762	+	0.697318i	$0.245624\pi$
$570$		0			0
$571$	4.63800	−	1.92112i	0.194094	−	0.0803965i	−0.283519	−	0.958967i	$-0.591502\pi$
$571$	4.63800	−	1.92112i	0.194094	−	0.0803965i	0.477613	+	0.878570i	$0.341502\pi$
$572$	−0.0196855	−	0.0612673i	−0.000823094	−	0.00256171i
$573$		0			0
$574$	−4.19172	+	0.656876i	−0.174959	+	0.0274175i
$575$	1.66015			0.0692331
$576$		0			0
$577$	−39.5904			−1.64817			−0.824084	−	0.566467i	$-0.808310\pi$
$577$	−39.5904			−1.64817			−0.824084	+	0.566467i	$0.808310\pi$
$578$	−14.2590	+	2.23450i	−0.593098	+	0.0929431i
$579$		0			0
$580$	12.8531	+	40.0027i	0.533696	+	1.66102i
$581$	1.45518	−	0.602755i	0.0603710	−	0.0250065i
$582$		0			0
$583$	−1.17209	+	1.17209i	−0.0485429	+	0.0485429i
$584$	−28.8420	−	9.52810i	−1.19349	−	0.394276i
$585$		0			0
$586$	25.1890	−	15.3792i	1.04055	−	0.635310i
$587$	−15.1156	−	36.4923i	−0.623888	−	1.50620i	−0.847103	−	0.531429i	$-0.821655\pi$
$587$	−15.1156	−	36.4923i	−0.623888	−	1.50620i	0.223215	−	0.974769i	$-0.428345\pi$
$588$		0			0
$589$	−10.3524	−	4.28812i	−0.426564	−	0.176689i
$590$	5.63108	−	7.72391i	0.231828	−	0.317988i
$591$		0			0
$592$	15.0785	−	24.2482i	0.619722	−	0.996596i
$593$			38.6527i			1.58728i	0.608389	+	0.793639i	$0.291816\pi$
$593$			38.6527i			1.58728i	−0.608389	+	0.793639i	$0.708184\pi$
$594$		0			0
$595$	3.35199	+	1.38844i	0.137418	+	0.0569205i
$596$	−3.69618	−	4.35645i	−0.151401	−	0.178447i
$597$		0			0
$598$	−0.313618	−	0.513663i	−0.0128248	−	0.0210052i
$599$	−12.3395	−	12.3395i	−0.504178	−	0.504178i	0.408556	−	0.912733i	$-0.366033\pi$
$599$	−12.3395	−	12.3395i	−0.504178	−	0.504178i	−0.912733	+	0.408556i	$0.866033\pi$
$600$		0			0
$601$	10.1201	−	10.1201i	0.412806	−	0.412806i	−0.469909	−	0.882715i	$-0.655713\pi$
$601$	10.1201	−	10.1201i	0.412806	−	0.412806i	0.882715	+	0.469909i	$0.155713\pi$
$602$	5.95301	+	1.43950i	0.242627	+	0.0586695i
$603$		0			0
$604$	0.591133	+	0.303638i	0.0240529	+	0.0123548i
$605$	−9.59545	+	23.1655i	−0.390110	+	0.941810i
$606$		0			0
$607$	28.0431			1.13824			0.569118	−	0.822256i	$-0.307285\pi$
$607$	28.0431			1.13824			0.569118	+	0.822256i	$0.307285\pi$
$608$	16.5565	−	6.69980i	0.671456	−	0.271713i
$609$		0			0
$610$	−3.81029	−	24.3146i	−0.154274	−	0.984471i
$611$	0.111156	−	0.268354i	0.00449689	−	0.0108565i
$612$		0			0
$613$	38.0929	−	15.7786i	1.53856	−	0.637291i	0.557355	−	0.830274i	$-0.311816\pi$
$613$	38.0929	−	15.7786i	1.53856	−	0.637291i	0.981202	+	0.192983i	$0.0618162\pi$
$614$	−32.9923	−	7.97786i	−1.33146	−	0.321960i
$615$		0			0
$616$	0.641046	−	0.0472868i	0.0258285	−	0.00190524i
$617$	−7.23007	−	7.23007i	−0.291071	−	0.291071i	0.546432	−	0.837503i	$-0.315986\pi$
$617$	−7.23007	−	7.23007i	−0.291071	−	0.291071i	−0.837503	+	0.546432i	$0.815986\pi$
$618$		0			0
$619$	7.02220	+	16.9531i	0.282246	+	0.681402i	0.999887	−	0.0150108i	$-0.00477826\pi$
$619$	7.02220	+	16.9531i	0.282246	+	0.681402i	−0.717641	+	0.696413i	$0.754778\pi$
$620$	−12.4988	+	10.6045i	−0.501965	+	0.425886i
$621$		0			0
$622$	−11.8556	−	8.64324i	−0.475365	−	0.346562i
$623$		−	4.64307i		−	0.186021i
$624$		0			0
$625$			26.5537i			1.06215i
$626$	−16.2720	+	22.3196i	−0.650360	+	0.892071i
$627$		0			0
$628$	−3.27670	+	39.9622i	−0.130755	+	1.59467i
$629$	−7.12066	−	17.1908i	−0.283919	−	0.685442i
$630$		0			0
$631$	8.25675	+	8.25675i	0.328696	+	0.328696i	0.852091	−	0.523394i	$-0.175335\pi$
$631$	8.25675	+	8.25675i	0.328696	+	0.328696i	−0.523394	+	0.852091i	$0.675335\pi$
$632$	16.9216	+	33.6174i	0.673105	+	1.33723i
$633$		0			0
$634$	−4.89133	+	20.2280i	−0.194259	+	0.803356i
$635$	32.4772	−	13.4525i	1.28882	−	0.533846i
$636$		0			0
$637$	−0.216738	+	0.523253i	−0.00858749	+	0.0207320i
$638$	4.79233	−	0.750996i	0.189730	−	0.0297322i
$639$		0			0
$640$	2.34804	−	26.0211i	0.0928144	−	1.02858i
$641$	36.1110			1.42630			0.713148	−	0.701013i	$-0.247269\pi$
$641$	36.1110			1.42630			0.713148	+	0.701013i	$0.247269\pi$
$642$		0			0
$643$	−13.2161	+	31.9065i	−0.521192	+	1.25827i	0.415972	+	0.909377i	$0.363441\pi$
$643$	−13.2161	+	31.9065i	−0.521192	+	1.25827i	−0.937164	+	0.348890i	$0.886559\pi$
$644$	5.72332	−	1.83894i	0.225530	−	0.0724642i
$645$		0			0
$646$	2.73556	−	11.3128i	0.107629	−	0.445098i
$647$	10.4590	−	10.4590i	0.411185	−	0.411185i	−0.470966	−	0.882151i	$-0.656095\pi$
$647$	10.4590	−	10.4590i	0.411185	−	0.411185i	0.882151	+	0.470966i	$0.156095\pi$
$648$		0			0
$649$	−0.780321	−	0.780321i	−0.0306303	−	0.0306303i
$650$	−0.0342917	+	0.0209369i	−0.00134503	+	0.000821213i
$651$		0			0
$652$	−1.18541	+	14.4571i	−0.0464241	+	0.566183i
$653$	2.41115	+	0.998731i	0.0943556	+	0.0390834i	0.429362	−	0.903132i	$-0.358738\pi$
$653$	2.41115	+	0.998731i	0.0943556	+	0.0390834i	−0.335006	+	0.942216i	$0.608738\pi$
$654$		0			0
$655$		−	10.7568i		−	0.420305i
$656$	19.6441	+	3.24324i	0.766973	+	0.126627i
$657$		0			0
$658$	2.34444	+	1.70920i	0.0913957	+	0.0666316i
$659$	−2.81457	−	1.16583i	−0.109640	−	0.0454144i	0.327189	−	0.944959i	$-0.393899\pi$
$659$	−2.81457	−	1.16583i	−0.109640	−	0.0454144i	−0.436829	+	0.899544i	$0.643899\pi$
$660$		0			0
$661$	2.83586	+	6.84638i	0.110302	+	0.266293i	0.969386	−	0.245542i	$-0.0789659\pi$
$661$	2.83586	+	6.84638i	0.110302	+	0.266293i	−0.859084	+	0.511835i	$0.828966\pi$
$662$	5.63010	+	9.22133i	0.218820	+	0.358397i
$663$		0			0
$664$	−7.37112	+	0.543731i	−0.286055	+	0.0211009i
$665$	3.10761	−	3.10761i	0.120508	−	0.120508i
$666$		0			0
$667$	41.9126	−	17.3608i	1.62286	−	0.672212i
$668$	19.8265	−	38.5989i	0.767110	−	1.49344i
$669$		0			0
$670$	1.32584	+	8.46060i	0.0512217	+	0.326861i
$671$	−2.84137			−0.109690
$672$		0			0
$673$	−11.8536			−0.456922			−0.228461	−	0.973553i	$-0.573369\pi$
$673$	−11.8536			−0.456922			−0.228461	+	0.973553i	$0.573369\pi$
$674$	6.07629	+	38.7747i	0.234050	+	1.49354i
$675$		0			0
$676$	−23.1145	−	11.8728i	−0.889018	−	0.456648i
$677$	12.6222	−	5.22830i	0.485112	−	0.200940i	−0.126703	−	0.991941i	$-0.540440\pi$
$677$	12.6222	−	5.22830i	0.485112	−	0.200940i	0.611815	+	0.791001i	$0.290440\pi$
$678$		0			0
$679$	2.47067	−	2.47067i	0.0948157	−	0.0948157i
$680$	−12.8918	−	11.1206i	−0.494379	−	0.426454i
$681$		0			0
$682$	0.986119	+	1.61513i	0.0377605	+	0.0618464i
$683$	10.1426	+	24.4864i	0.388096	+	0.936947i	0.990343	+	0.138637i	$0.0442722\pi$
$683$	10.1426	+	24.4864i	0.388096	+	0.936947i	−0.602247	+	0.798310i	$0.705728\pi$
$684$		0			0
$685$	−45.0878	−	18.6760i	−1.72272	−	0.713573i
$686$	−9.39288	−	6.84783i	−0.358622	−	0.261451i
$687$		0			0
$688$	−24.4061	−	15.1767i	−0.930474	−	0.578605i
$689$		−	0.375172i		−	0.0142929i
$690$		0			0
$691$	−1.41964	−	0.588035i	−0.0540058	−	0.0223699i	0.355517	−	0.934670i	$-0.384305\pi$
$691$	−1.41964	−	0.588035i	−0.0540058	−	0.0223699i	−0.409523	+	0.912300i	$0.634305\pi$
$692$	−3.13839	−	0.257332i	−0.119304	−	0.00978229i
$693$		0			0
$694$	9.75735	−	5.95737i	0.370384	−	0.226139i
$695$	9.49682	+	9.49682i	0.360235	+	0.360235i
$696$		0			0
$697$	9.17420	−	9.17420i	0.347498	−	0.347498i
$698$	−1.52365	+	6.30104i	−0.0576711	+	0.238498i
$699$		0			0
$700$	−0.122766	−	0.382084i	−0.00464012	−	0.0144414i
$701$	0.888440	−	2.14488i	0.0335559	−	0.0810111i	−0.906213	−	0.422821i	$-0.861040\pi$
$701$	0.888440	−	2.14488i	0.0335559	−	0.0810111i	0.939769	+	0.341810i	$0.111040\pi$
$702$		0			0
$703$	−22.5389			−0.850072
$704$	−2.92593	−	0.732905i	−0.110275	−	0.0276224i
$705$		0			0
$706$	−11.9308	+	1.86965i	−0.449021	+	0.0703651i
$707$	1.72987	−	4.17627i	0.0650583	−	0.157065i
$708$		0			0
$709$	−12.8278	+	5.31345i	−0.481758	+	0.199551i	−0.610327	−	0.792150i	$-0.708962\pi$
$709$	−12.8278	+	5.31345i	−0.481758	+	0.199551i	0.128569	+	0.991701i	$0.458962\pi$
$710$	10.3952	−	42.9892i	0.390125	−	1.61336i
$711$		0			0
$712$	−6.83447	+	20.6883i	−0.256133	+	0.775327i
$713$	12.5143	+	12.5143i	0.468663	+	0.468663i
$714$		0			0
$715$	0.0284351	+	0.0686484i	0.00106341	+	0.00256731i
$716$	−34.1495	−	2.80008i	−1.27623	−	0.104644i
$717$		0			0
$718$	−2.47401	+	3.39349i	−0.0923291	+	0.126644i
$719$		−	6.47893i		−	0.241623i	−0.992675	−	0.120812i	$-0.961450\pi$
$719$		−	6.47893i		−	0.241623i	0.992675	−	0.120812i	$-0.0385497\pi$
$720$		0			0
$721$		−	0.0182391i		−	0.000679259i
$722$	10.3203	+	7.52399i	0.384083	+	0.280014i
$723$		0			0
$724$	13.2273	+	15.5902i	0.491588	+	0.579403i
$725$	−1.15899	−	2.79806i	−0.0430439	−	0.103917i
$726$		0			0
$727$	35.6807	+	35.6807i	1.32333	+	1.32333i	0.911067	+	0.412259i	$0.135260\pi$
$727$	35.6807	+	35.6807i	1.32333	+	1.32333i	0.412259	+	0.911067i	$0.364740\pi$
$728$	−0.0950279	+	0.110164i	−0.00352197	+	0.00408294i
$729$		0			0
$730$	34.0903	+	8.24336i	1.26174	+	0.305100i
$731$	−17.3027	+	7.16702i	−0.639964	+	0.265082i
$732$		0			0
$733$	−3.42508	+	8.26889i	−0.126508	+	0.305418i	−0.974426	−	0.224710i	$-0.927856\pi$
$733$	−3.42508	+	8.26889i	−0.126508	+	0.305418i	0.847917	+	0.530129i	$0.177856\pi$
$734$	6.03039	+	38.4817i	0.222586	+	1.42039i
$735$		0			0
$736$	−28.2084	−	0.230756i	−1.03978	−	0.00850578i
$737$	0.988691			0.0364189
$738$		0			0
$739$	−5.93367	+	14.3251i	−0.218274	+	0.526959i	−0.994649	−	0.103312i	$-0.967056\pi$
$739$	−5.93367	+	14.3251i	−0.218274	+	0.526959i	0.776375	+	0.630271i	$0.217056\pi$
$740$	−15.0642	+	29.3275i	−0.553770	+	1.07810i
$741$		0			0
$742$	3.64247	+	0.880785i	0.133719	+	0.0323346i
$743$	22.3336	−	22.3336i	0.819340	−	0.819340i	−0.166673	−	0.986012i	$-0.553302\pi$
$743$	22.3336	−	22.3336i	0.819340	−	0.819340i	0.986012	+	0.166673i	$0.0533023\pi$
$744$		0			0
$745$	4.66461	+	4.66461i	0.170898	+	0.170898i
$746$	−10.7125	−	17.5455i	−0.392211	−	0.642387i
$747$		0			0
$748$	−1.49881	+	1.27164i	−0.0548018	+	0.0464959i
$749$	−7.16796	−	2.96907i	−0.261912	−	0.108487i
$750$		0			0
$751$		−	5.55037i		−	0.202536i	−0.994859	−	0.101268i	$-0.967710\pi$
$751$		−	5.55037i		−	0.202536i	0.994859	−	0.101268i	$-0.0322900\pi$
$752$	−7.93029	−	11.0667i	−0.289188	−	0.403560i
$753$		0			0
$754$	−0.646793	+	0.887179i	−0.0235548	+	0.0323091i
$755$	−0.708923	−	0.293645i	−0.0258003	−	0.0106869i
$756$		0			0
$757$	−18.1068	−	43.7136i	−0.658102	−	1.58880i	−0.800733	−	0.599022i	$-0.795556\pi$
$757$	−18.1068	−	43.7136i	−0.658102	−	1.58880i	0.142631	−	0.989776i	$-0.454444\pi$
$758$	−43.8891	+	26.7966i	−1.59412	+	0.973296i
$759$		0			0
$760$	−18.4210	+	9.27235i	−0.668199	+	0.336343i
$761$	−21.5039	+	21.5039i	−0.779515	+	0.779515i	−0.979748	−	0.200233i	$-0.935830\pi$
$761$	−21.5039	+	21.5039i	−0.779515	+	0.779515i	0.200233	+	0.979748i	$0.435830\pi$
$762$		0			0
$763$	2.75627	−	1.14168i	0.0997836	−	0.0413317i
$764$	−9.40751	+	3.02269i	−0.340352	+	0.109357i
$765$		0			0
$766$	−38.9257	+	6.09997i	−1.40644	+	0.220401i
$767$	0.249772			0.00901874
$768$		0			0
$769$	−23.5969			−0.850926			−0.425463	−	0.904976i	$-0.639889\pi$
$769$	−23.5969			−0.850926			−0.425463	+	0.904976i	$0.639889\pi$
$770$	−0.733249	+	0.114906i	−0.0264245	+	0.00414092i
$771$		0			0
$772$	−25.4037	+	8.16235i	−0.914298	+	0.293769i
$773$	26.4134	−	10.9408i	0.950024	−	0.393513i	0.146784	−	0.989169i	$-0.453108\pi$
$773$	26.4134	−	10.9408i	0.950024	−	0.393513i	0.803240	+	0.595656i	$0.203108\pi$
$774$		0			0
$775$	0.835443	−	0.835443i	0.0300100	−	0.0300100i
$776$	−14.6454	+	7.37189i	−0.525739	+	0.264635i
$777$		0			0
$778$	−46.1597	+	28.1829i	−1.65490	+	1.01041i
$779$	−6.01418	−	14.5195i	−0.215480	−	0.520215i
$780$		0			0
$781$	−4.71744	−	1.95403i	−0.168803	−	0.0699206i
$782$	−10.8293	+	14.8541i	−0.387254	+	0.531180i
$783$		0			0
$784$	15.4629	+	21.5785i	0.552248	+	0.770659i
$785$		−	46.2974i		−	1.65243i
$786$		0			0
$787$	7.40697	+	3.06807i	0.264030	+	0.109365i	0.510771	−	0.859717i	$-0.329360\pi$
$787$	7.40697	+	3.06807i	0.264030	+	0.109365i	−0.246741	+	0.969081i	$0.579360\pi$
$788$	−16.2677	+	13.8021i	−0.579512	+	0.491680i
$789$		0			0
$790$	−22.6454	−	37.0899i	−0.805686	−	1.31960i
$791$	2.83587	+	2.83587i	0.100832	+	0.100832i
$792$		0			0
$793$	0.454745	−	0.454745i	0.0161485	−	0.0161485i
$794$	34.7569	+	8.40456i	1.23348	+	0.298267i
$795$		0			0
$796$	−15.2499	+	29.6890i	−0.540517	+	1.05230i
$797$	7.94480	−	19.1804i	0.281419	−	0.679406i	−0.718450	−	0.695579i	$-0.755148\pi$
$797$	7.94480	−	19.1804i	0.281419	−	0.679406i	0.999869	+	0.0161725i	$0.00514810\pi$
$798$		0			0
$799$	−8.87199			−0.313868
$800$	−0.0154051	+	1.88317i	−0.000544652	+	0.0665802i
$801$		0			0
$802$	−5.76225	−	36.7706i	−0.203472	−	1.29842i
$803$	1.54953	−	3.74091i	0.0546819	−	0.132014i
$804$		0			0
$805$	−6.41283	+	2.65628i	−0.226023	+	0.0936216i
$806$	−0.416315	−	0.100669i	−0.0146641	−	0.00354591i
$807$		0			0
$808$	−13.8552	+	16.0620i	−0.487423	+	0.565060i
$809$	−30.9672	−	30.9672i	−1.08875	−	1.08875i	−0.995657	−	0.0930927i	$-0.970325\pi$
$809$	−30.9672	−	30.9672i	−1.08875	−	1.08875i	−0.0930927	−	0.995657i	$-0.529675\pi$
$810$		0			0
$811$	0.215110	+	0.519321i	0.00755353	+	0.0182358i	0.927611	−	0.373547i	$-0.121858\pi$
$811$	0.215110	+	0.519321i	0.00755353	+	0.0182358i	−0.920058	+	0.391783i	$0.871858\pi$
$812$	−7.09497	−	8.36239i	−0.248984	−	0.293462i
$813$		0			0
$814$	3.07576	+	2.24237i	0.107805	+	0.0785951i
$815$		−	16.7490i		−	0.586691i
$816$		0			0
$817$			22.6857i			0.793672i
$818$	−28.8101	+	39.5175i	−1.00732	+	1.38170i
$819$		0			0
$820$	−22.9123	−	1.87869i	−0.800133	−	0.0656068i
$821$	7.36228	+	17.7741i	0.256945	+	0.620321i	0.998733	−	0.0503134i	$-0.0160220\pi$
$821$	7.36228	+	17.7741i	0.256945	+	0.620321i	−0.741788	+	0.670634i	$0.766022\pi$
$822$		0			0
$823$	30.8972	+	30.8972i	1.07701	+	1.07701i	0.996776	+	0.0802314i	$0.0255659\pi$
$823$	30.8972	+	30.8972i	1.07701	+	1.07701i	0.0802314	+	0.996776i	$0.474434\pi$
$824$	−0.0268474	+	0.0812685i	−0.000935275	+	0.00283112i
$825$		0			0
$826$	−0.586385	+	2.42498i	−0.0204029	+	0.0843759i
$827$	20.8744	−	8.64647i	0.725875	−	0.300667i	0.0110192	−	0.999939i	$-0.496492\pi$
$827$	20.8744	−	8.64647i	0.725875	−	0.300667i	0.714856	+	0.699272i	$0.246492\pi$
$828$		0			0
$829$	4.37840	−	10.5704i	0.152068	−	0.367125i	−0.829426	−	0.558616i	$-0.811332\pi$
$829$	4.37840	−	10.5704i	0.152068	−	0.367125i	0.981494	+	0.191492i	$0.0613325\pi$
$830$	8.43133	−	1.32126i	0.292656	−	0.0458614i
$831$		0			0
$832$	0.585577	−	0.350982i	0.0203012	−	0.0121681i
$833$	17.2991			0.599379
$834$		0			0
$835$	−19.1740	+	46.2902i	−0.663544	+	1.60194i
$836$	0.728329	+	2.26678i	0.0251898	+	0.0783981i
$837$		0			0
$838$	−7.29660	+	30.1750i	−0.252057	+	1.04238i
$839$	−12.5396	+	12.5396i	−0.432914	+	0.432914i	−0.889618	−	0.456705i	$-0.849030\pi$
$839$	−12.5396	+	12.5396i	−0.432914	+	0.432914i	0.456705	+	0.889618i	$0.349030\pi$
$840$		0			0
$841$	−38.0143	−	38.0143i	−1.31084	−	1.31084i
$842$	−21.9341	+	13.3919i	−0.755898	+	0.461516i
$843$		0			0
$844$	−54.1706	−	4.44171i	−1.86463	−	0.152890i
$845$	27.7203	+	11.4821i	0.953606	+	0.394997i
$846$		0			0
$847$		−	6.54451i		−	0.224872i
$848$	−14.9334	−	9.28615i	−0.512814	−	0.318888i
$849$		0			0
$850$	0.991647	+	0.722955i	0.0340132	+	0.0247972i
$851$	32.8884	+	13.6228i	1.12740	+	0.466984i
$852$		0			0
$853$	14.4092	+	34.7869i	0.493362	+	1.19108i	0.952999	+	0.302974i	$0.0979796\pi$
$853$	14.4092	+	34.7869i	0.493362	+	1.19108i	−0.459637	+	0.888107i	$0.652020\pi$
$854$	3.34743	+	5.48262i	0.114547	+	0.187611i
$855$		0			0
$856$	27.5681	+	23.7804i	0.942259	+	0.812797i
$857$	29.3107	−	29.3107i	1.00123	−	1.00123i	0.00123369	−	0.999999i	$-0.499607\pi$
$857$	29.3107	−	29.3107i	1.00123	−	1.00123i	0.999999	−	0.00123369i	$-0.000392697\pi$
$858$		0			0
$859$	−35.4358	+	14.6780i	−1.20905	+	0.500807i	−0.893914	−	0.448238i	$-0.852052\pi$
$859$	−35.4358	+	14.6780i	−1.20905	+	0.500807i	−0.315140	+	0.949045i	$0.602052\pi$
$860$	29.5184	+	15.1623i	1.00657	+	0.517029i
$861$		0			0
$862$	−5.95077	−	37.9737i	−0.202684	−	1.29339i
$863$	−24.0443			−0.818476			−0.409238	−	0.912428i	$-0.634205\pi$
$863$	−24.0443			−0.818476			−0.409238	+	0.912428i	$0.634205\pi$
$864$		0			0
$865$	3.63592			0.123625
$866$	−8.69981	−	55.5162i	−0.295632	−	1.88652i
$867$		0			0
$868$	1.95475	−	3.80557i	0.0663485	−	0.129170i
$869$	−4.63514	+	1.91994i	−0.157236	+	0.0651294i
$870$		0			0
$871$	−0.158234	+	0.158234i	−0.00536157	+	0.00536157i
$872$	−13.9617	+	1.02989i	−0.472803	+	0.0348763i
$873$		0			0
$874$	11.6033	+	19.0046i	0.392487	+	0.642840i
$875$	−2.48600	−	6.00174i	−0.0840423	−	0.202896i
$876$		0			0
$877$	−31.8799	−	13.2051i	−1.07651	−	0.445905i	−0.227226	−	0.973842i	$-0.572966\pi$
$877$	−31.8799	−	13.2051i	−1.07651	−	0.445905i	−0.849283	+	0.527937i	$0.822966\pi$
$878$	−30.6146	−	22.3194i	−1.03319	−	0.753243i
$879$		0			0
$880$	3.43630	+	0.567333i	0.115838	+	0.0191248i
$881$			19.0541i			0.641951i	0.947088	+	0.320975i	$0.104011\pi$
$881$			19.0541i			0.641951i	−0.947088	+	0.320975i	$0.895989\pi$
$882$		0			0
$883$	−22.0595	−	9.13733i	−0.742360	−	0.307496i	−0.0207400	−	0.999785i	$-0.506602\pi$
$883$	−22.0595	−	9.13733i	−0.742360	−	0.307496i	−0.721620	+	0.692289i	$0.756602\pi$
$884$	0.0363561	−	0.443395i	0.00122279	−	0.0149130i
$885$		0			0
$886$	46.5925	−	28.4472i	1.56531	−	0.955701i
$887$	4.29581	+	4.29581i	0.144239	+	0.144239i	0.775539	−	0.631300i	$-0.217478\pi$
$887$	4.29581	+	4.29581i	0.144239	+	0.144239i	−0.631300	+	0.775539i	$0.717478\pi$
$888$		0			0
$889$	−6.48784	+	6.48784i	−0.217595	+	0.217595i
$890$	5.91293	−	24.4528i	0.198202	−	0.819661i
$891$		0			0
$892$	−32.2490	+	10.3618i	−1.07978	+	0.346939i
$893$	−4.11257	+	9.92863i	−0.137622	+	0.332249i
$894$		0			0
$895$	39.5632			1.32245
$896$	2.03286	+	6.50923i	0.0679132	+	0.217458i
$897$		0			0
$898$	−5.50997	+	0.863455i	−0.183870	+	0.0288139i
$899$	12.3553	−	29.8283i	0.412072	−	0.994830i
$900$		0			0
$901$	−10.5870	+	4.38529i	−0.352705	+	0.146095i
$902$	−0.623806	+	2.57974i	−0.0207705	+	0.0858959i
$903$		0			0
$904$	−8.46156	−	16.8102i	−0.281427	−	0.559099i
$905$	−16.6929	−	16.6929i	−0.554892	−	0.554892i
$906$		0			0
$907$	−0.992723	−	2.39665i	−0.0329628	−	0.0795793i	0.906541	−	0.422118i	$-0.138713\pi$
$907$	−0.992723	−	2.39665i	−0.0329628	−	0.0795793i	−0.939504	+	0.342539i	$0.888713\pi$
$908$	−4.49246	+	54.7895i	−0.149088	+	1.81825i
$909$		0			0
$910$	0.0989624	−	0.135743i	0.00328057	−	0.00449982i
$911$		−	20.6522i		−	0.684239i	−0.939656	−	0.342119i	$-0.888855\pi$
$911$		−	20.6522i		−	0.684239i	0.939656	−	0.342119i	$-0.111145\pi$
$912$		0			0
$913$		−	0.985271i		−	0.0326077i
$914$	32.0320	+	23.3527i	1.05952	+	0.772440i
$915$		0			0
$916$	29.7892	−	25.2743i	0.984262	−	0.835085i
$917$	1.07443	+	2.59389i	0.0354807	+	0.0856579i
$918$		0			0
$919$	−16.6238	−	16.6238i	−0.548369	−	0.548369i	0.377600	−	0.925969i	$-0.376750\pi$
$919$	−16.6238	−	16.6238i	−0.548369	−	0.548369i	−0.925969	+	0.377600i	$0.876750\pi$
$920$	32.4838	−	2.39617i	1.07096	−	0.0789994i
$921$		0			0
$922$	32.6992	+	7.90698i	1.07689	+	0.260402i
$923$	1.06773	−	0.442268i	0.0351448	−	0.0145574i
$924$		0			0
$925$	0.909449	−	2.19560i	0.0299025	−	0.0721910i
$926$	−0.501765	−	3.20191i	−0.0164890	−	0.105221i
$927$		0			0
$928$	19.3041	+	47.7042i	0.633687	+	1.56597i
$929$	−1.04471			−0.0342759			−0.0171379	−	0.999853i	$-0.505455\pi$
$929$	−1.04471			−0.0342759			−0.0171379	+	0.999853i	$0.505455\pi$
$930$		0			0
$931$	8.01893	−	19.3594i	0.262810	−	0.634479i
$932$	7.65468	+	3.93186i	0.250737	+	0.128792i
$933$		0			0
$934$	26.0025	+	6.28767i	0.850829	+	0.205739i
$935$	1.60482	−	1.60482i	0.0524834	−	0.0524834i
$936$		0			0
$937$	7.27552	+	7.27552i	0.237681	+	0.237681i	0.815889	−	0.578208i	$-0.196248\pi$
$937$	7.27552	+	7.27552i	0.237681	+	0.237681i	−0.578208	+	0.815889i	$0.696248\pi$
$938$	−1.16478	−	1.90775i	−0.0380315	−	0.0622902i
$939$		0			0
$940$	10.1704	+	11.9872i	0.331721	+	0.390978i
$941$	10.9545	+	4.53751i	0.357107	+	0.147919i	0.554022	−	0.832502i	$-0.313092\pi$
$941$	10.9545	+	4.53751i	0.357107	+	0.147919i	−0.196915	+	0.980421i	$0.563092\pi$
$942$		0			0
$943$			24.8216i			0.808303i
$944$	6.18228	−	9.94193i	0.201216	−	0.323582i
$945$		0			0
$946$	2.25697	−	3.09579i	0.0733804	−	0.100653i
$947$	40.3968	+	16.7329i	1.31272	+	0.543746i	0.925677	−	0.378315i	$-0.123496\pi$
$947$	40.3968	+	16.7329i	1.31272	+	0.543746i	0.387043	+	0.922062i	$0.373496\pi$
$948$		0			0
$949$	0.350717	+	0.846706i	0.0113848	+	0.0274852i
$950$	1.26873	−	0.774628i	0.0411631	−	0.0251322i
$951$		0			0
$952$	4.21948	+	1.39392i	0.136754	+	0.0451773i
$953$	9.40298	−	9.40298i	0.304592	−	0.304592i	−0.538215	−	0.842808i	$-0.680901\pi$
$953$	9.40298	−	9.40298i	0.304592	−	0.304592i	0.842808	+	0.538215i	$0.180901\pi$
$954$		0			0
$955$	10.5409	−	4.36618i	0.341095	−	0.141286i
$956$	−3.98043	−	12.3883i	−0.128736	−	0.400666i
$957$		0			0
$958$	−31.4494	+	4.92836i	−1.01608	+	0.159228i
$959$	12.7378			0.411326
$960$		0			0
$961$	−18.4048			−0.593704
$962$	−0.851138	+	0.133380i	−0.0274418	+	0.00430034i
$963$		0			0
$964$	5.70867	+	17.7671i	0.183864	+	0.572240i
$965$	28.4642	−	11.7902i	0.916294	−	0.379541i
$966$		0			0
$967$	−6.32392	+	6.32392i	−0.203363	+	0.203363i	−0.801439	−	0.598076i	$-0.795932\pi$
$967$	−6.32392	+	6.32392i	−0.203363	+	0.203363i	0.598076	+	0.801439i	$0.295932\pi$
$968$	−9.63334	+	29.1606i	−0.309627	+	0.937257i
$969$		0			0
$970$	16.1582	−	9.86544i	0.518809	−	0.316760i
$971$	13.7581	+	33.2150i	0.441519	+	1.06592i	0.975416	+	0.220372i	$0.0707270\pi$
$971$	13.7581	+	33.2150i	0.441519	+	1.06592i	−0.533897	+	0.845550i	$0.679273\pi$
$972$		0			0
$973$	−3.23862	−	1.34148i	−0.103825	−	0.0430059i
$974$	8.48795	−	11.6426i	0.271971	−	0.373052i
$975$		0			0
$976$	−6.84497	−	29.3564i	−0.219102	−	0.939675i
$977$		−	13.5218i		−	0.432602i	−0.976327	−	0.216301i	$-0.930601\pi$
$977$		−	13.5218i		−	0.432602i	0.976327	−	0.216301i	$-0.0693993\pi$
$978$		0			0
$979$	−2.68334	−	1.11148i	−0.0857599	−	0.0355229i
$980$	−19.8308	−	23.3733i	−0.633470	−	0.746632i
$981$		0			0
$982$	−14.5070	−	23.7605i	−0.462938	−	0.758228i
$983$	−11.0690	−	11.0690i	−0.353047	−	0.353047i	0.508195	−	0.861242i	$-0.330313\pi$
$983$	−11.0690	−	11.0690i	−0.353047	−	0.353047i	−0.861242	+	0.508195i	$0.830313\pi$
$984$		0			0
$985$	17.4184	−	17.4184i	0.554995	−	0.554995i
$986$	32.5955	+	7.88192i	1.03805	+	0.251012i
$987$		0			0
$988$	−0.479350	−	0.246220i	−0.0152502	−	0.00783330i
$989$	13.7115	−	33.1025i	0.436000	−	1.05260i
$990$		0			0
$991$	−37.0259			−1.17617			−0.588083	−	0.808801i	$-0.700117\pi$
$991$	−37.0259			−1.17617			−0.588083	+	0.808801i	$0.700117\pi$
$992$	−14.3115	+	14.0793i	−0.454391	+	0.447017i
$993$		0			0
$994$	1.78720	+	11.4047i	0.0566866	+	0.361734i
$995$	14.7480	−	35.6049i	0.467543	−	1.12875i
$996$		0			0
$997$	−3.26525	+	1.35251i	−0.103411	+	0.0428344i	−0.433789	−	0.901014i	$-0.642824\pi$
$997$	−3.26525	+	1.35251i	−0.103411	+	0.0428344i	0.330378	+	0.943849i	$0.392824\pi$
$998$	51.3062	+	12.4063i	1.62407	+	0.392716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.2	✓	128
3.2	odd	2	inner	864.2.v.a.109.31	yes	128
32.5	even	8	inner	864.2.v.a.325.2	yes	128
96.5	odd	8	inner	864.2.v.a.325.31	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.2	✓	128	1.1	even	1	trivial
864.2.v.a.109.31	yes	128	3.2	odd	2	inner
864.2.v.a.325.2	yes	128	32.5	even	8	inner
864.2.v.a.325.31	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)

\(f(q)\)	\(=\)	\(q+(-1.39716 + 0.218946i) q^{2} +(1.90413 - 0.611807i) q^{4} +(-2.13352 + 0.883735i) q^{5} +(0.426205 - 0.426205i) q^{7} +(-2.52642 + 1.27169i) q^{8} +O(q^{10})\)	\(q+(-1.39716 + 0.218946i) q^{2} +(1.90413 - 0.611807i) q^{4} +(-2.13352 + 0.883735i) q^{5} +(0.426205 - 0.426205i) q^{7} +(-2.52642 + 1.27169i) q^{8} +(2.78739 - 1.70185i) q^{10} +(-0.144287 - 0.348341i) q^{11} +(0.0788424 + 0.0326576i) q^{13} +(-0.502162 + 0.688794i) q^{14} +(3.25138 - 2.32991i) q^{16} -2.60658i q^{17} +(-2.91702 - 1.20827i) q^{19} +(-3.52182 + 2.98805i) q^{20} +(0.277861 + 0.455097i) q^{22} +(3.52617 + 3.52617i) q^{23} +(0.235404 - 0.235404i) q^{25} +(-0.117306 - 0.0283657i) q^{26} +(0.550793 - 1.07230i) q^{28} +(3.48138 - 8.40479i) q^{29} +3.54897 q^{31} +(-4.03259 + 3.96715i) q^{32} +(0.570702 + 3.64182i) q^{34} +(-0.532667 + 1.28597i) q^{35} +(6.59514 - 2.73180i) q^{37} +(4.34010 + 1.04948i) q^{38} +(4.26634 - 4.94587i) q^{40} +(3.51963 + 3.51963i) q^{41} +(-2.74958 - 6.63808i) q^{43} +(-0.487858 - 0.575008i) q^{44} +(-5.69867 - 4.15459i) q^{46} -3.40368i q^{47} +6.63670i q^{49} +(-0.277357 + 0.380439i) q^{50} +(0.170106 + 0.0139478i) q^{52} +(-1.68239 - 4.06164i) q^{53} +(0.615681 + 0.615681i) q^{55} +(-0.534770 + 1.61878i) q^{56} +(-3.02385 + 12.5051i) q^{58} +(2.70405 - 1.12005i) q^{59} +(2.88389 - 6.96232i) q^{61} +(-4.95849 + 0.777033i) q^{62} +(4.76559 - 6.42567i) q^{64} -0.197073 q^{65} +(-1.00349 + 2.42263i) q^{67} +(-1.59473 - 4.96326i) q^{68} +(0.462664 - 1.91334i) q^{70} +(9.57606 - 9.57606i) q^{71} +(7.59378 + 7.59378i) q^{73} +(-8.61637 + 5.26075i) q^{74} +(-6.29361 - 0.516044i) q^{76} +(-0.209961 - 0.0869686i) q^{77} -13.3063i q^{79} +(-4.87788 + 7.84429i) q^{80} +(-5.68810 - 4.14688i) q^{82} +(2.41425 + 1.00002i) q^{83} +(2.30353 + 5.56121i) q^{85} +(5.29500 + 8.67247i) q^{86} +(0.807513 + 0.696565i) q^{88} +(5.44699 - 5.44699i) q^{89} +(0.0475219 - 0.0196842i) q^{91} +(8.87160 + 4.55693i) q^{92} +(0.745224 + 4.75550i) q^{94} +7.29133 q^{95} +5.79690 q^{97} +(-1.45308 - 9.27254i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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