LMFDB - Embedded newform 864.2.v.a.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.a.325.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01339 - 0.986432i) q^{2} +(0.0539048 + 1.99927i) q^{4} +(-2.55155 + 1.05689i) q^{5} +(1.06497 - 1.06497i) q^{7} +(1.91752 - 2.07921i) q^{8} +O(q^{10})$	\(q+(-1.01339 - 0.986432i) q^{2} +(0.0539048 + 1.99927i) q^{4} +(-2.55155 + 1.05689i) q^{5} +(1.06497 - 1.06497i) q^{7} +(1.91752 - 2.07921i) q^{8} +(3.62825 + 1.44589i) q^{10} +(-0.641664 - 1.54911i) q^{11} +(0.200618 + 0.0830988i) q^{13} +(-2.12975 + 0.0287062i) q^{14} +(-3.99419 + 0.215541i) q^{16} +2.47031i q^{17} +(4.02517 + 1.66728i) q^{19} +(-2.25054 - 5.04427i) q^{20} +(-0.877841 + 2.20281i) q^{22} +(-2.90736 - 2.90736i) q^{23} +(1.85785 - 1.85785i) q^{25} +(-0.121332 - 0.282107i) q^{26} +(2.18658 + 2.07177i) q^{28} +(-1.64618 + 3.97423i) q^{29} -0.400720 q^{31} +(4.26027 + 3.72157i) q^{32} +(2.43680 - 2.50338i) q^{34} +(-1.59177 + 3.84288i) q^{35} +(-4.73288 + 1.96042i) q^{37} +(-2.43439 - 5.66015i) q^{38} +(-2.69516 + 7.33180i) q^{40} +(2.07457 + 2.07457i) q^{41} +(3.45626 + 8.34415i) q^{43} +(3.06251 - 1.36637i) q^{44} +(0.0783673 + 5.81418i) q^{46} +6.94628i q^{47} +4.73166i q^{49} +(-3.71536 + 0.0500780i) q^{50} +(-0.155323 + 0.405570i) q^{52} +(4.57054 + 11.0343i) q^{53} +(3.27447 + 3.27447i) q^{55} +(-0.172195 - 4.25641i) q^{56} +(5.58852 - 2.40358i) q^{58} +(-5.70502 + 2.36310i) q^{59} +(-0.321300 + 0.775687i) q^{61} +(0.406085 + 0.395283i) q^{62} +(-0.646231 - 7.97386i) q^{64} -0.599712 q^{65} +(-5.91697 + 14.2848i) q^{67} +(-4.93883 + 0.133162i) q^{68} +(5.40383 - 2.32415i) q^{70} +(7.28346 - 7.28346i) q^{71} +(-7.84498 - 7.84498i) q^{73} +(6.73006 + 2.68199i) q^{74} +(-3.11637 + 8.13729i) q^{76} +(-2.33312 - 0.966410i) q^{77} -1.11506i q^{79} +(9.96356 - 4.77136i) q^{80} +(-0.0559198 - 4.14877i) q^{82} +(12.4078 + 5.13949i) q^{83} +(-2.61084 - 6.30312i) q^{85} +(4.72841 - 11.8652i) q^{86} +(-4.45134 - 1.63630i) q^{88} +(7.58120 - 7.58120i) q^{89} +(0.302151 - 0.125155i) q^{91} +(5.65588 - 5.96932i) q^{92} +(6.85203 - 7.03927i) q^{94} -12.0325 q^{95} +11.3315 q^{97} +(4.66746 - 4.79500i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.01339	−	0.986432i	−0.716573	−	0.697513i
$2$	−1.01339	−	0.986432i	−0.716573	−	0.697513i
$3$		0			0
$3$		0			0
$4$	0.0539048	+	1.99927i	0.0269524	+	0.999637i
$5$	−2.55155	+	1.05689i	−1.14109	+	0.472653i	−0.871535	−	0.490333i	$-0.836875\pi$
$5$	−2.55155	+	1.05689i	−1.14109	+	0.472653i	−0.269551	+	0.962986i	$0.586875\pi$
$6$		0			0
$7$	1.06497	−	1.06497i	0.402522	−	0.402522i	−0.476599	−	0.879121i	$-0.658131\pi$
$7$	1.06497	−	1.06497i	0.402522	−	0.402522i	0.879121	+	0.476599i	$0.158131\pi$
$8$	1.91752	−	2.07921i	0.677946	−	0.735112i
$9$		0			0
$10$	3.62825	+	1.44589i	1.14735	+	0.457232i
$11$	−0.641664	−	1.54911i	−0.193469	−	0.467075i	0.797141	−	0.603793i	$-0.206345\pi$
$11$	−0.641664	−	1.54911i	−0.193469	−	0.467075i	−0.990610	+	0.136718i	$0.956345\pi$
$12$		0			0
$13$	0.200618	+	0.0830988i	0.0556415	+	0.0230474i	0.410331	−	0.911937i	$-0.365413\pi$
$13$	0.200618	+	0.0830988i	0.0556415	+	0.0230474i	−0.354689	+	0.934984i	$0.615413\pi$
$14$	−2.12975	+	0.0287062i	−0.569201	+	0.00767205i
$15$		0			0
$16$	−3.99419	+	0.215541i	−0.998547	+	0.0538852i
$17$			2.47031i			0.599139i	0.954074	+	0.299569i	$0.0968430\pi$
$17$			2.47031i			0.599139i	−0.954074	+	0.299569i	$0.903157\pi$
$18$		0			0
$19$	4.02517	+	1.66728i	0.923437	+	0.382500i	0.793185	−	0.608981i	$-0.208421\pi$
$19$	4.02517	+	1.66728i	0.923437	+	0.382500i	0.130252	+	0.991481i	$0.458421\pi$
$20$	−2.25054	−	5.04427i	−0.503237	−	1.12793i
$21$		0			0
$22$	−0.877841	+	2.20281i	−0.187156	+	0.469640i
$23$	−2.90736	−	2.90736i	−0.606225	−	0.606225i	0.335732	−	0.941958i	$-0.391016\pi$
$23$	−2.90736	−	2.90736i	−0.606225	−	0.606225i	−0.941958	+	0.335732i	$0.891016\pi$
$24$		0			0
$25$	1.85785	−	1.85785i	0.371570	−	0.371570i
$26$	−0.121332	−	0.282107i	−0.0237953	−	0.0553258i
$27$		0			0
$28$	2.18658	+	2.07177i	0.413225	+	0.391527i
$29$	−1.64618	+	3.97423i	−0.305688	+	0.737995i	0.694147	+	0.719833i	$0.255782\pi$
$29$	−1.64618	+	3.97423i	−0.305688	+	0.737995i	−0.999835	+	0.0181624i	$0.994218\pi$
$30$		0			0
$31$	−0.400720			−0.0719715			−0.0359857	−	0.999352i	$-0.511457\pi$
$31$	−0.400720			−0.0719715			−0.0359857	+	0.999352i	$0.511457\pi$
$32$	4.26027	+	3.72157i	0.753117	+	0.657887i
$33$		0			0
$34$	2.43680	−	2.50338i	0.417907	−	0.429326i
$35$	−1.59177	+	3.84288i	−0.269059	+	0.649566i
$36$		0			0
$37$	−4.73288	+	1.96042i	−0.778080	+	0.322291i	−0.736140	−	0.676829i	$-0.763354\pi$
$37$	−4.73288	+	1.96042i	−0.778080	+	0.322291i	−0.0419397	+	0.999120i	$0.513354\pi$
$38$	−2.43439	−	5.66015i	−0.394911	−	0.918198i
$39$		0			0
$40$	−2.69516	+	7.33180i	−0.426142	+	1.15926i
$41$	2.07457	+	2.07457i	0.323994	+	0.323994i	0.850297	−	0.526303i	$-0.176422\pi$
$41$	2.07457	+	2.07457i	0.323994	+	0.323994i	−0.526303	+	0.850297i	$0.676422\pi$
$42$		0			0
$43$	3.45626	+	8.34415i	0.527075	+	1.27247i	0.933431	+	0.358757i	$0.116799\pi$
$43$	3.45626	+	8.34415i	0.527075	+	1.27247i	−0.406356	+	0.913715i	$0.633201\pi$
$44$	3.06251	−	1.36637i	0.461691	−	0.205987i
$45$		0			0
$46$	0.0783673	+	5.81418i	0.0115546	+	0.857254i
$47$			6.94628i			1.01322i	0.862176	+	0.506610i	$0.169101\pi$
$47$			6.94628i			1.01322i	−0.862176	+	0.506610i	$0.830899\pi$
$48$		0			0
$49$			4.73166i			0.675952i
$50$	−3.71536	+	0.0500780i	−0.525431	+	0.00708210i
$51$		0			0
$52$	−0.155323	+	0.405570i	−0.0215394	+	0.0562424i
$53$	4.57054	+	11.0343i	0.627813	+	1.51567i	0.842335	+	0.538955i	$0.181181\pi$
$53$	4.57054	+	11.0343i	0.627813	+	1.51567i	−0.214522	+	0.976719i	$0.568819\pi$
$54$		0			0
$55$	3.27447	+	3.27447i	0.441529	+	0.441529i
$56$	−0.172195	−	4.25641i	−0.0230106	−	0.568787i
$57$		0			0
$58$	5.58852	−	2.40358i	0.733808	−	0.315606i
$59$	−5.70502	+	2.36310i	−0.742730	+	0.307649i	−0.721771	−	0.692131i	$-0.756672\pi$
$59$	−5.70502	+	2.36310i	−0.742730	+	0.307649i	−0.0209586	+	0.999780i	$0.506672\pi$
$60$		0			0
$61$	−0.321300	+	0.775687i	−0.0411383	+	0.0993166i	−0.943113	−	0.332472i	$-0.892117\pi$
$61$	−0.321300	+	0.775687i	−0.0411383	+	0.0993166i	0.901975	+	0.431789i	$0.142117\pi$
$62$	0.406085	+	0.395283i	0.0515728	+	0.0502010i
$63$		0			0
$64$	−0.646231	−	7.97386i	−0.0807788	−	0.996732i
$65$	−0.599712			−0.0743852
$66$		0			0
$67$	−5.91697	+	14.2848i	−0.722873	+	1.74517i	−0.0578745	+	0.998324i	$0.518432\pi$
$67$	−5.91697	+	14.2848i	−0.722873	+	1.74517i	−0.664998	+	0.746845i	$0.731568\pi$
$68$	−4.93883	+	0.133162i	−0.598921	+	0.0161482i
$69$		0			0
$70$	5.40383	−	2.32415i	0.645881	−	0.277789i
$71$	7.28346	−	7.28346i	0.864387	−	0.864387i	−0.127457	−	0.991844i	$-0.540681\pi$
$71$	7.28346	−	7.28346i	0.864387	−	0.864387i	0.991844	+	0.127457i	$0.0406814\pi$
$72$		0			0
$73$	−7.84498	−	7.84498i	−0.918185	−	0.918185i	0.0787121	−	0.996897i	$-0.474919\pi$
$73$	−7.84498	−	7.84498i	−0.918185	−	0.918185i	−0.996897	+	0.0787121i	$0.974919\pi$
$74$	6.73006	+	2.68199i	0.782353	+	0.311776i
$75$		0			0
$76$	−3.11637	+	8.13729i	−0.357472	+	0.933411i
$77$	−2.33312	−	0.966410i	−0.265884	−	0.110133i
$78$		0			0
$79$		−	1.11506i		−	0.125454i	−0.998031	−	0.0627269i	$-0.980020\pi$
$79$		−	1.11506i		−	0.125454i	0.998031	−	0.0627269i	$-0.0199797\pi$
$80$	9.96356	−	4.77136i	1.11396	−	0.533454i
$81$		0			0
$82$	−0.0559198	−	4.14877i	−0.00617531	−	0.458155i
$83$	12.4078	+	5.13949i	1.36193	+	0.564132i	0.939590	−	0.342303i	$-0.111207\pi$
$83$	12.4078	+	5.13949i	1.36193	+	0.564132i	0.422345	+	0.906435i	$0.361207\pi$
$84$		0			0
$85$	−2.61084	−	6.30312i	−0.283185	−	0.683669i
$86$	4.72841	−	11.8652i	0.509877	−	1.27946i
$87$		0			0
$88$	−4.45134	−	1.63630i	−0.474514	−	0.174430i
$89$	7.58120	−	7.58120i	0.803606	−	0.803606i	−0.180052	−	0.983657i	$-0.557626\pi$
$89$	7.58120	−	7.58120i	0.803606	−	0.803606i	0.983657	+	0.180052i	$0.0576265\pi$
$90$		0			0
$91$	0.302151	−	0.125155i	0.0316740	−	0.0131198i
$92$	5.65588	−	5.96932i	0.589666	−	0.622344i
$93$		0			0
$94$	6.85203	−	7.03927i	0.706733	−	0.726045i
$95$	−12.0325			−1.23451
$96$		0			0
$97$	11.3315			1.15054			0.575268	−	0.817965i	$-0.304898\pi$
$97$	11.3315			1.15054			0.575268	+	0.817965i	$0.304898\pi$
$98$	4.66746	−	4.79500i	0.471485	−	0.484368i
$99$		0			0
$100$	3.81449	+	3.61420i	0.381449	+	0.361420i
$101$	−13.3604	+	5.53404i	−1.32940	+	0.550657i	−0.930485	−	0.366329i	$-0.880615\pi$
$101$	−13.3604	+	5.53404i	−1.32940	+	0.550657i	−0.398919	+	0.916986i	$0.630615\pi$
$102$		0			0
$103$	−1.19791	+	1.19791i	−0.118033	+	0.118033i	−0.763656	−	0.645623i	$-0.776598\pi$
$103$	−1.19791	+	1.19791i	−0.118033	+	0.118033i	0.645623	+	0.763656i	$0.276598\pi$
$104$	0.557469	−	0.257784i	0.0546644	−	0.0252778i
$105$		0			0
$106$	6.25283	−	15.6905i	0.607328	−	1.52400i
$107$	3.88920	+	9.38936i	0.375983	+	0.907704i	0.992710	+	0.120527i	$0.0384584\pi$
$107$	3.88920	+	9.38936i	0.375983	+	0.907704i	−0.616727	+	0.787177i	$0.711542\pi$
$108$		0			0
$109$	−17.7432	−	7.34947i	−1.69949	−	0.703952i	−0.699546	−	0.714587i	$-0.746615\pi$
$109$	−17.7432	−	7.34947i	−1.69949	−	0.703952i	−0.999943	+	0.0106353i	$0.996615\pi$
$110$	−0.0882628	−	6.54835i	−0.00841553	−	0.624360i
$111$		0			0
$112$	−4.02416	+	4.48325i	−0.380247	+	0.423627i
$113$		−	2.09557i		−	0.197135i	−0.995130	−	0.0985675i	$-0.968574\pi$
$113$		−	2.09557i		−	0.197135i	0.995130	−	0.0985675i	$-0.0314260\pi$
$114$		0			0
$115$	10.4910	+	4.34551i	0.978290	+	0.405221i
$116$	−8.03430	−	3.07693i	−0.745966	−	0.285686i
$117$		0			0
$118$	8.11242	+	3.23288i	0.746809	+	0.297611i
$119$	2.63082	+	2.63082i	0.241167	+	0.241167i
$120$		0			0
$121$	5.79015	−	5.79015i	0.526378	−	0.526378i
$122$	1.09076	−	0.469130i	0.0987531	−	0.0424731i
$123$		0			0
$124$	−0.0216007	−	0.801149i	−0.00193980	−	0.0719453i
$125$	2.50757	−	6.05381i	0.224284	−	0.541469i
$126$		0			0
$127$	−0.315628			−0.0280075			−0.0140037	−	0.999902i	$-0.504458\pi$
$127$	−0.315628			−0.0280075			−0.0140037	+	0.999902i	$0.504458\pi$
$128$	−7.21078	+	8.71806i	−0.637349	+	0.770575i
$129$		0			0
$130$	0.607740	+	0.591575i	0.0533024	+	0.0518846i
$131$	−7.05023	+	17.0208i	−0.615981	+	1.48711i	0.240351	+	0.970686i	$0.422737\pi$
$131$	−7.05023	+	17.0208i	−0.615981	+	1.48711i	−0.856333	+	0.516425i	$0.827263\pi$
$132$		0			0
$133$	6.06231	−	2.51109i	0.525669	−	0.217739i
$134$	20.0872	−	8.63936i	1.73527	−	0.746327i
$135$		0			0
$136$	5.13630	+	4.73688i	0.440434	+	0.406184i
$137$	8.11269	+	8.11269i	0.693114	+	0.693114i	0.962916	−	0.269802i	$-0.0869583\pi$
$137$	8.11269	+	8.11269i	0.693114	+	0.693114i	−0.269802	+	0.962916i	$0.586958\pi$
$138$		0			0
$139$	−4.29165	−	10.3610i	−0.364013	−	0.878805i	−0.994705	−	0.102772i	$-0.967229\pi$
$139$	−4.29165	−	10.3610i	−0.364013	−	0.878805i	0.630692	−	0.776033i	$-0.282771\pi$
$140$	−7.76878	−	2.97524i	−0.656582	−	0.251454i
$141$		0			0
$142$	−14.5656	+	0.196324i	−1.22232	+	0.0164752i
$143$		−	0.364102i		−	0.0304477i
$144$		0			0
$145$		−	11.8802i		−	0.986601i
$146$	0.211460	+	15.6885i	0.0175006	+	1.29839i
$147$		0			0
$148$	−4.17454	−	9.35664i	−0.343145	−	0.769111i
$149$	3.40608	+	8.22301i	0.279037	+	0.673655i	0.999810	−	0.0195168i	$-0.00621279\pi$
$149$	3.40608	+	8.22301i	0.279037	+	0.673655i	−0.720773	+	0.693172i	$0.756213\pi$
$150$		0			0
$151$	16.0158	+	16.0158i	1.30334	+	1.30334i	0.926123	+	0.377222i	$0.123121\pi$
$151$	16.0158	+	16.0158i	1.30334	+	1.30334i	0.377222	+	0.926123i	$0.376879\pi$
$152$	11.1850	−	5.17213i	0.907221	−	0.419515i
$153$		0			0
$154$	1.41106	+	3.28081i	0.113706	+	0.264375i
$155$	1.02246	−	0.423515i	0.0821257	−	0.0340176i
$156$		0			0
$157$	0.331918	−	0.801320i	0.0264899	−	0.0639523i	−0.910081	−	0.414430i	$-0.863981\pi$
$157$	0.331918	−	0.801320i	0.0264899	−	0.0639523i	0.936571	+	0.350478i	$0.113981\pi$
$158$	−1.09993	+	1.12999i	−0.0875056	+	0.0898968i
$159$		0			0
$160$	−14.8036	−	4.99313i	−1.17032	−	0.394742i
$161$	−6.19251			−0.488038
$162$		0			0
$163$	0.362108	−	0.874207i	0.0283625	−	0.0684732i	−0.909064	−	0.416657i	$-0.863202\pi$
$163$	0.362108	−	0.874207i	0.0283625	−	0.0684732i	0.937426	+	0.348184i	$0.113202\pi$
$164$	−4.03581	+	4.25947i	−0.315144	+	0.332609i
$165$		0			0
$166$	−7.50416	−	17.4478i	−0.582436	−	1.35421i
$167$	−4.08322	+	4.08322i	−0.315969	+	0.315969i	−0.847217	−	0.531247i	$-0.821723\pi$
$167$	−4.08322	+	4.08322i	−0.315969	+	0.315969i	0.531247	+	0.847217i	$0.321723\pi$
$168$		0			0
$169$	−9.15905	−	9.15905i	−0.704542	−	0.704542i
$170$	−3.57181	+	8.96291i	−0.273945	+	0.687424i
$171$		0			0
$172$	−16.4959	+	7.35980i	−1.25780	+	0.561180i
$173$	−22.6412	−	9.37829i	−1.72138	−	0.713018i	−0.999786	−	0.0206997i	$-0.993411\pi$
$173$	−22.6412	−	9.37829i	−1.72138	−	0.713018i	−0.721592	−	0.692318i	$-0.756589\pi$
$174$		0			0
$175$		−	3.95712i		−	0.299130i
$176$	2.89682	+	6.04915i	0.218356	+	0.455972i
$177$		0			0
$178$	−15.1610	+	0.204350i	−1.13637	+	0.0153167i
$179$	17.3563	+	7.18923i	1.29727	+	0.537348i	0.921145	−	0.389219i	$-0.127255\pi$
$179$	17.3563	+	7.18923i	1.29727	+	0.537348i	0.376129	+	0.926567i	$0.377255\pi$
$180$		0			0
$181$	−7.64604	−	18.4592i	−0.568326	−	1.37206i	−0.902965	−	0.429713i	$-0.858615\pi$
$181$	−7.64604	−	18.4592i	−0.568326	−	1.37206i	0.334640	−	0.942346i	$-0.391385\pi$
$182$	−0.429653	−	0.171221i	−0.0318480	−	0.0126917i
$183$		0			0
$184$	−11.6199	+	0.470090i	−0.856632	+	0.0346555i
$185$	10.0042	−	10.0042i	0.735524	−	0.735524i
$186$		0			0
$187$	3.82680	−	1.58511i	0.279843	−	0.115915i
$188$	−13.8875	+	0.374438i	−1.01285	+	0.0273087i
$189$		0			0
$190$	12.1936	+	11.8693i	0.884617	+	0.861087i
$191$	−9.33264			−0.675286			−0.337643	−	0.941274i	$-0.609630\pi$
$191$	−9.33264			−0.675286			−0.337643	+	0.941274i	$0.609630\pi$
$192$		0			0
$193$	−21.7032			−1.56223			−0.781116	−	0.624386i	$-0.785349\pi$
$193$	−21.7032			−1.56223			−0.781116	+	0.624386i	$0.785349\pi$
$194$	−11.4832	−	11.1777i	−0.824442	−	0.802513i
$195$		0			0
$196$	−9.45989	+	0.255059i	−0.675706	+	0.0182185i
$197$	−2.29950	+	0.952484i	−0.163833	+	0.0678617i	−0.463093	−	0.886310i	$-0.653260\pi$
$197$	−2.29950	+	0.952484i	−0.163833	+	0.0678617i	0.299260	+	0.954172i	$0.403260\pi$
$198$		0			0
$199$	−1.79300	+	1.79300i	−0.127102	+	0.127102i	−0.767796	−	0.640694i	$-0.778647\pi$
$199$	−1.79300	+	1.79300i	−0.127102	+	0.127102i	0.640694	+	0.767796i	$0.278647\pi$
$200$	−0.300395	−	7.42532i	−0.0212411	−	0.525049i
$201$		0			0
$202$	18.9982	+	7.57095i	1.33671	+	0.532690i
$203$	2.47931	+	5.98558i	0.174013	+	0.420106i
$204$		0			0
$205$	−7.48596	−	3.10079i	−0.522842	−	0.216568i
$206$	2.39560	−	0.0322894i	0.166909	−	0.00224971i
$207$		0			0
$208$	−0.819218	−	0.288671i	−0.0568025	−	0.0200157i
$209$		−	7.30528i		−	0.505317i
$210$		0			0
$211$	6.80050	+	2.81686i	0.468165	+	0.193920i	0.604279	−	0.796773i	$-0.293461\pi$
$211$	6.80050	+	2.81686i	0.468165	+	0.193920i	−0.136114	+	0.990693i	$0.543461\pi$
$212$	−21.8142	+	9.73257i	−1.49820	+	0.668436i
$213$		0			0
$214$	5.32070	−	13.3515i	0.363716	−	0.912689i
$215$	−17.6376	−	17.6376i	−1.20288	−	1.20288i
$216$		0			0
$217$	−0.426757	+	0.426757i	−0.0289701	+	0.0289701i
$218$	10.7310	+	24.9503i	0.726793	+	1.68985i
$219$		0			0
$220$	−6.37005	+	6.72307i	−0.429469	+	0.453269i
$221$	−0.205280	+	0.495590i	−0.0138086	+	0.0333370i
$222$		0			0
$223$	−18.0231			−1.20691			−0.603457	−	0.797396i	$-0.706210\pi$
$223$	−18.0231			−1.20691			−0.603457	+	0.797396i	$0.706210\pi$
$224$	8.50045	−	0.573707i	0.567960	−	0.0383324i
$225$		0			0
$226$	−2.06714	+	2.12363i	−0.137504	+	0.141261i
$227$	6.04429	−	14.5922i	0.401174	−	0.968519i	−0.586208	−	0.810161i	$-0.699380\pi$
$227$	6.04429	−	14.5922i	0.401174	−	0.968519i	0.987382	−	0.158359i	$-0.0506202\pi$
$228$		0			0
$229$	23.7048	−	9.81887i	1.56646	−	0.648849i	0.580264	−	0.814429i	$-0.302950\pi$
$229$	23.7048	−	9.81887i	1.56646	−	0.648849i	0.986196	+	0.165580i	$0.0529496\pi$
$230$	−6.34488	−	14.7523i	−0.418369	−	0.972740i
$231$		0			0
$232$	5.10667	+	11.0434i	0.335269	+	0.725035i
$233$	−5.25503	−	5.25503i	−0.344268	−	0.344268i	0.513701	−	0.857969i	$-0.328274\pi$
$233$	−5.25503	−	5.25503i	−0.344268	−	0.344268i	−0.857969	+	0.513701i	$0.828274\pi$
$234$		0			0
$235$	−7.34142	−	17.7238i	−0.478901	−	1.15617i
$236$	−5.03200	−	11.2785i	−0.327555	−	0.734168i
$237$		0			0
$238$	−0.0709133	−	5.26116i	−0.00459662	−	0.341030i
$239$		−	11.3541i		−	0.734435i	−0.930135	−	0.367218i	$-0.880310\pi$
$239$		−	11.3541i		−	0.734435i	0.930135	−	0.367218i	$-0.119690\pi$
$240$		0			0
$241$			8.73589i			0.562728i	0.959601	+	0.281364i	$0.0907869\pi$
$241$			8.73589i			0.562728i	−0.959601	+	0.281364i	$0.909213\pi$
$242$	−11.5793	+	0.156073i	−0.744343	+	0.0100327i
$243$		0			0
$244$	−1.56813	−	0.600554i	−0.100389	−	0.0384465i
$245$	−5.00082	−	12.0731i	−0.319491	−	0.771319i
$246$		0			0
$247$	0.668973	+	0.668973i	0.0425657	+	0.0425657i
$248$	−0.768389	+	0.833182i	−0.0487928	+	0.0529071i
$249$		0			0
$250$	−8.51281	+	3.66130i	−0.538397	+	0.231561i
$251$	3.10762	−	1.28722i	0.196151	−	0.0812484i	−0.282446	−	0.959283i	$-0.591146\pi$
$251$	3.10762	−	1.28722i	0.196151	−	0.0812484i	0.478597	+	0.878035i	$0.341146\pi$
$252$		0			0
$253$	−2.63828	+	6.36937i	−0.165867	+	0.400439i
$254$	0.319853	+	0.311346i	0.0200694	+	0.0195356i
$255$		0			0
$256$	15.9071	−	1.72182i	0.994193	−	0.107614i
$257$	17.4895			1.09096			0.545481	−	0.838123i	$-0.316347\pi$
$257$	17.4895			1.09096			0.545481	+	0.838123i	$0.316347\pi$
$258$		0			0
$259$	−2.95259	+	7.12819i	−0.183465	+	0.442924i
$260$	−0.0323274	−	1.19899i	−0.00200486	−	0.0743581i
$261$		0			0
$262$	23.9344	−	10.2940i	1.47867	−	0.635968i
$263$	3.49965	−	3.49965i	0.215798	−	0.215798i	−0.590927	−	0.806725i	$-0.701238\pi$
$263$	3.49965	−	3.49965i	0.215798	−	0.215798i	0.806725	+	0.590927i	$0.201238\pi$
$264$		0			0
$265$	−23.3239	−	23.3239i	−1.43278	−	1.43278i
$266$	−8.62048	−	3.43535i	−0.528556	−	0.210635i
$267$		0			0
$268$	−28.8782	−	11.0596i	−1.76402	−	0.675574i
$269$	−4.75769	−	1.97070i	−0.290081	−	0.120156i	0.232898	−	0.972501i	$-0.425179\pi$
$269$	−4.75769	−	1.97070i	−0.290081	−	0.120156i	−0.522979	+	0.852346i	$0.675179\pi$
$270$		0			0
$271$			17.7865i			1.08046i	0.841519	+	0.540228i	$0.181662\pi$
$271$			17.7865i			1.08046i	−0.841519	+	0.540228i	$0.818338\pi$
$272$	−0.532453	−	9.86690i	−0.0322847	−	0.598268i
$273$		0			0
$274$	−0.218676	−	16.2239i	−0.0132107	−	0.980122i
$275$	−4.07013	−	1.68590i	−0.245438	−	0.101664i
$276$		0			0
$277$	8.43247	+	20.3578i	0.506658	+	1.22318i	0.945796	+	0.324761i	$0.105284\pi$
$277$	8.43247	+	20.3578i	0.506658	+	1.22318i	−0.439138	+	0.898419i	$0.644716\pi$
$278$	−5.87128	+	14.7331i	−0.352136	+	0.883631i
$279$		0			0
$280$	4.93790	+	10.6784i	0.295096	+	0.638159i
$281$	11.8872	−	11.8872i	0.709128	−	0.709128i	−0.257224	−	0.966352i	$-0.582808\pi$
$281$	11.8872	−	11.8872i	0.709128	−	0.709128i	0.966352	+	0.257224i	$0.0828077\pi$
$282$		0			0
$283$	19.5034	−	8.07857i	1.15936	−	0.480221i	0.281696	−	0.959504i	$-0.409103\pi$
$283$	19.5034	−	8.07857i	1.15936	−	0.480221i	0.877661	+	0.479283i	$0.159103\pi$
$284$	14.9542	+	14.1690i	0.887371	+	0.840776i
$285$		0			0
$286$	−0.359162	+	0.368976i	−0.0212377	+	0.0218180i
$287$	4.41873			0.260830
$288$		0			0
$289$	10.8976			0.641033
$290$	−11.7190	+	12.0393i	−0.688166	+	0.706971i
$291$		0			0
$292$	15.2614	−	16.1071i	0.893104	−	0.942599i
$293$	−0.0912242	+	0.0377863i	−0.00532938	+	0.00220750i	−0.385347	−	0.922772i	$-0.625918\pi$
$293$	−0.0912242	+	0.0377863i	−0.00532938	+	0.00220750i	0.380017	+	0.924979i	$0.375918\pi$
$294$		0			0
$295$	12.0591	−	12.0591i	0.702108	−	0.702108i
$296$	−4.99926	+	13.5998i	−0.290576	+	0.790472i
$297$		0			0
$298$	4.65976	−	11.6929i	0.269933	−	0.677354i
$299$	−0.341671	−	0.824866i	−0.0197593	−	0.0477032i
$300$		0			0
$301$	12.5671	+	5.20548i	0.724357	+	0.300039i
$302$	−0.431702	−	32.0286i	−0.0248417	−	1.84304i
$303$		0			0
$304$	−16.4367	−	5.79184i	−0.942707	−	0.332185i
$305$		−	2.31878i		−	0.132773i
$306$		0			0
$307$	−20.9576	−	8.68093i	−1.19611	−	0.495447i	−0.306373	−	0.951912i	$-0.599115\pi$
$307$	−20.9576	−	8.68093i	−1.19611	−	0.495447i	−0.889741	+	0.456465i	$0.849115\pi$
$308$	1.80635	−	4.71664i	0.102926	−	0.268755i
$309$		0			0
$310$	−1.45391	−	0.579399i	−0.0825767	−	0.0329076i
$311$	−13.1533	−	13.1533i	−0.745857	−	0.745857i	0.227842	−	0.973698i	$-0.426833\pi$
$311$	−13.1533	−	13.1533i	−0.745857	−	0.745857i	−0.973698	+	0.227842i	$0.926833\pi$
$312$		0			0
$313$	−13.9390	+	13.9390i	−0.787876	+	0.787876i	−0.981146	−	0.193270i	$-0.938091\pi$
$313$	−13.9390	+	13.9390i	−0.787876	+	0.787876i	0.193270	+	0.981146i	$0.438091\pi$
$314$	−1.12681	+	0.484633i	−0.0635895	+	0.0273494i
$315$		0			0
$316$	2.22931	−	0.0601069i	0.125408	−	0.00338128i
$317$	−10.6180	+	25.6342i	−0.596368	+	1.43976i	0.280889	+	0.959740i	$0.409371\pi$
$317$	−10.6180	+	25.6342i	−0.596368	+	1.43976i	−0.877257	+	0.480020i	$0.840629\pi$
$318$		0			0
$319$	7.21282			0.403840
$320$	10.0763	+	19.6627i	0.563284	+	1.09918i
$321$		0			0
$322$	6.27541	+	6.10849i	0.349715	+	0.340413i
$323$	−4.11870	+	9.94343i	−0.229171	+	0.553267i
$324$		0			0
$325$	0.527103	−	0.218333i	0.0292384	−	0.0121109i
$326$	−1.22930	+	0.528715i	−0.0680847	+	0.0292828i
$327$		0			0
$328$	8.29151	−	0.335437i	0.457822	−	0.0185214i
$329$	7.39760	+	7.39760i	0.407843	+	0.407843i
$330$		0			0
$331$	2.74170	+	6.61905i	0.150697	+	0.363816i	0.981143	−	0.193284i	$-0.0619139\pi$
$331$	2.74170	+	6.61905i	0.150697	+	0.363816i	−0.830445	+	0.557100i	$0.811914\pi$
$332$	−9.60640	+	25.0837i	−0.527220	+	1.37664i
$333$		0			0
$334$	8.16571	−	0.110063i	0.446808	−	0.00602236i
$335$		−	42.7019i		−	2.33306i
$336$		0			0
$337$			19.6368i			1.06968i	0.844952	+	0.534842i	$0.179629\pi$
$337$			19.6368i			1.06968i	−0.844952	+	0.534842i	$0.820371\pi$
$338$	0.246881	+	18.3164i	0.0134285	+	0.996282i
$339$		0			0
$340$	12.4609	−	5.55955i	0.675788	−	0.301509i
$341$	0.257128	+	0.620761i	0.0139242	+	0.0336161i
$342$		0			0
$343$	12.4939	+	12.4939i	0.674608	+	0.674608i
$344$	23.9767	+	8.81379i	1.29274	+	0.475208i
$345$		0			0
$346$	13.6932	+	31.8378i	0.736153	+	1.71161i
$347$	1.95833	−	0.811165i	0.105128	−	0.0435456i	−0.329499	−	0.944156i	$-0.606880\pi$
$347$	1.95833	−	0.811165i	0.105128	−	0.0435456i	0.434628	+	0.900610i	$0.356880\pi$
$348$		0			0
$349$	−1.58408	+	3.82430i	−0.0847937	+	0.204710i	−0.960589	−	0.277973i	$-0.910338\pi$
$349$	−1.58408	+	3.82430i	−0.0847937	+	0.204710i	0.875795	+	0.482683i	$0.160338\pi$
$350$	−3.90343	+	4.01009i	−0.208647	+	0.214348i
$351$		0			0
$352$	3.03147	−	8.98764i	0.161578	−	0.479043i
$353$	−1.02289			−0.0544427			−0.0272213	−	0.999629i	$-0.508666\pi$
$353$	−1.02289			−0.0544427			−0.0272213	+	0.999629i	$0.508666\pi$
$354$		0			0
$355$	−10.8863	+	26.2819i	−0.577785	+	1.39490i
$356$	15.5656	+	14.7482i	0.824973	+	0.781655i
$357$		0			0
$358$	−10.4970	−	24.4063i	−0.554783	−	1.28991i
$359$	14.0008	−	14.0008i	0.738935	−	0.738935i	−0.233437	−	0.972372i	$-0.574997\pi$
$359$	14.0008	−	14.0008i	0.738935	−	0.738935i	0.972372	+	0.233437i	$0.0749972\pi$
$360$		0			0
$361$	−0.0128620	−	0.0128620i	−0.000676949	−	0.000676949i
$362$	−10.4603	+	26.2486i	−0.549782	+	1.37959i
$363$		0			0
$364$	0.266507	+	0.597336i	0.0139687	+	0.0313089i
$365$	28.3081	+	11.7256i	1.48171	+	0.613745i
$366$		0			0
$367$			14.6975i			0.767205i	0.923498	+	0.383602i	$0.125317\pi$
$367$			14.6975i			0.767205i	−0.923498	+	0.383602i	$0.874683\pi$
$368$	12.2392	+	10.9859i	0.638011	+	0.572678i
$369$		0			0
$370$	−20.0066	+	0.269662i	−1.04009	+	0.0140191i
$371$	16.6187	+	6.88370i	0.862801	+	0.357384i
$372$		0			0
$373$	−11.4499	−	27.6425i	−0.592854	−	1.43128i	−0.880735	−	0.473609i	$-0.842951\pi$
$373$	−11.4499	−	27.6425i	−0.592854	−	1.43128i	0.287881	−	0.957666i	$-0.407049\pi$
$374$	−5.44163	−	2.16854i	−0.281380	−	0.112133i
$375$		0			0
$376$	14.4428	+	13.3196i	0.744829	+	0.686908i
$377$	−0.660507	+	0.660507i	−0.0340178	+	0.0340178i
$378$		0			0
$379$	3.82982	−	1.58636i	0.196725	−	0.0814860i	−0.282146	−	0.959371i	$-0.591046\pi$
$379$	3.82982	−	1.58636i	0.196725	−	0.0814860i	0.478871	+	0.877885i	$0.341046\pi$
$380$	−0.648611	−	24.0563i	−0.0332730	−	1.23406i
$381$		0			0
$382$	9.45757	+	9.20601i	0.483892	+	0.471021i
$383$	−14.5735			−0.744669			−0.372335	−	0.928099i	$-0.621443\pi$
$383$	−14.5735			−0.744669			−0.372335	+	0.928099i	$0.621443\pi$
$384$		0			0
$385$	6.97445			0.355451
$386$	21.9938	+	21.4087i	1.11945	+	1.08968i
$387$		0			0
$388$	0.610820	+	22.6547i	0.0310097	+	1.15012i
$389$	−3.10307	+	1.28533i	−0.157332	+	0.0651689i	−0.459960	−	0.887940i	$-0.652136\pi$
$389$	−3.10307	+	1.28533i	−0.157332	+	0.0651689i	0.302628	+	0.953109i	$0.402136\pi$
$390$		0			0
$391$	7.18208	−	7.18208i	0.363213	−	0.363213i
$392$	9.83812	+	9.07306i	0.496900	+	0.458259i
$393$		0			0
$394$	3.26984	+	1.30307i	0.164732	+	0.0656475i
$395$	1.17849	+	2.84512i	0.0592962	+	0.143154i
$396$		0			0
$397$	−7.10206	−	2.94177i	−0.356442	−	0.147643i	0.197274	−	0.980348i	$-0.436791\pi$
$397$	−7.10206	−	2.94177i	−0.356442	−	0.147643i	−0.553717	+	0.832705i	$0.686791\pi$
$398$	3.58567	−	0.0483299i	0.179733	−	0.00242256i
$399$		0			0
$400$	−7.02016	+	7.82104i	−0.351008	+	0.391052i
$401$		−	21.1661i		−	1.05698i	−0.848938	−	0.528492i	$-0.822757\pi$
$401$		−	21.1661i		−	1.05698i	0.848938	−	0.528492i	$-0.177243\pi$
$402$		0			0
$403$	−0.0803918	−	0.0332994i	−0.00400460	−	0.00165876i
$404$	−11.7842	−	26.4127i	−0.586288	−	1.31408i
$405$		0			0
$406$	3.39187	−	8.51138i	0.168336	−	0.422413i
$407$	6.07383	+	6.07383i	0.301069	+	0.301069i
$408$		0			0
$409$	0.215933	−	0.215933i	0.0106772	−	0.0106772i	−0.701748	−	0.712425i	$-0.747597\pi$
$409$	0.215933	−	0.215933i	0.0106772	−	0.0106772i	0.712425	+	0.701748i	$0.247597\pi$
$410$	4.52746	+	10.5267i	0.223595	+	0.519876i
$411$		0			0
$412$	−2.45952	−	2.33037i	−0.121172	−	0.114809i
$413$	−3.55906	+	8.59233i	−0.175130	+	0.422801i
$414$		0			0
$415$	−37.0910			−1.82072
$416$	0.545430	+	1.10064i	0.0267419	+	0.0539632i
$417$		0			0
$418$	−7.20616	+	7.40307i	−0.352465	+	0.362096i
$419$	3.86557	−	9.33231i	0.188845	−	0.455913i	−0.800892	−	0.598808i	$-0.795641\pi$
$419$	3.86557	−	9.33231i	0.188845	−	0.455913i	0.989738	+	0.142895i	$0.0456411\pi$
$420$		0			0
$421$	37.6604	−	15.5995i	1.83546	−	0.760271i	0.873643	−	0.486567i	$-0.161751\pi$
$421$	37.6604	−	15.5995i	1.83546	−	0.760271i	0.961814	−	0.273704i	$-0.0882488\pi$
$422$	−4.11289	−	9.56279i	−0.200213	−	0.465509i
$423$		0			0
$424$	31.7067	+	11.6553i	1.53981	+	0.566032i
$425$	4.58947	+	4.58947i	0.222622	+	0.222622i
$426$		0			0
$427$	0.483910	+	1.16826i	0.0234181	+	0.0565362i
$428$	−18.5623	+	8.28171i	−0.897241	+	0.400312i
$429$		0			0
$430$	0.475419	+	35.2720i	0.0229267	+	1.70097i
$431$		−	4.40885i		−	0.212367i	−0.994347	−	0.106183i	$-0.966137\pi$
$431$		−	4.40885i		−	0.212367i	0.994347	−	0.106183i	$-0.0338631\pi$
$432$		0			0
$433$			28.0896i			1.34990i	0.737864	+	0.674950i	$0.235835\pi$
$433$			28.0896i			1.34990i	−0.737864	+	0.674950i	$0.764165\pi$
$434$	0.853436	−	0.0115031i	0.0409662	−	0.000552169i
$435$		0			0
$436$	13.7372	−	35.8697i	0.657891	−	1.71785i
$437$	−6.85522	−	16.5500i	−0.327930	−	0.791693i
$438$		0			0
$439$	22.5409	+	22.5409i	1.07582	+	1.07582i	0.996879	+	0.0789394i	$0.0251534\pi$
$439$	22.5409	+	22.5409i	1.07582	+	1.07582i	0.0789394	+	0.996879i	$0.474847\pi$
$440$	13.0872	−	0.529448i	0.623907	−	0.0252405i
$441$		0			0
$442$	0.696893	−	0.299729i	0.0331478	−	0.0142567i
$443$	14.5643	−	6.03274i	0.691972	−	0.286624i	−0.00884947	−	0.999961i	$-0.502817\pi$
$443$	14.5643	−	6.03274i	0.691972	−	0.286624i	0.700822	+	0.713337i	$0.252817\pi$
$444$		0			0
$445$	−11.3313	+	27.3562i	−0.537156	+	1.29681i
$446$	18.2643	+	17.7785i	0.864841	+	0.841838i
$447$		0			0
$448$	−9.18017	−	7.80373i	−0.433722	−	0.368692i
$449$	29.0474			1.37083			0.685415	−	0.728152i	$-0.259621\pi$
$449$	29.0474			1.37083			0.685415	+	0.728152i	$0.259621\pi$
$450$		0			0
$451$	1.88257	−	4.54493i	0.0886468	−	0.214012i
$452$	4.18962	−	0.112961i	0.197063	−	0.00531325i
$453$		0			0
$454$	−20.5194	+	8.82527i	−0.963025	+	0.414191i
$455$	−0.638678	+	0.638678i	−0.0299417	+	0.0299417i
$456$		0			0
$457$	3.80735	+	3.80735i	0.178100	+	0.178100i	0.790527	−	0.612427i	$-0.209807\pi$
$457$	3.80735	+	3.80735i	0.178100	+	0.178100i	−0.612427	+	0.790527i	$0.709807\pi$
$458$	−33.7078	−	13.4329i	−1.57506	−	0.627678i
$459$		0			0
$460$	−8.12235	+	21.2086i	−0.378707	+	0.988856i
$461$	−7.41893	−	3.07302i	−0.345534	−	0.143125i	0.203166	−	0.979144i	$-0.434877\pi$
$461$	−7.41893	−	3.07302i	−0.345534	−	0.143125i	−0.548700	+	0.836020i	$0.684877\pi$
$462$		0			0
$463$		−	13.3665i		−	0.621195i	−0.950541	−	0.310598i	$-0.899471\pi$
$463$		−	13.3665i		−	0.621195i	0.950541	−	0.310598i	$-0.100529\pi$
$464$	5.71854	−	16.2286i	0.265477	−	0.753395i
$465$		0			0
$466$	0.141648	+	10.5091i	0.00656173	+	0.486825i
$467$	−10.7946	−	4.47125i	−0.499513	−	0.206905i	0.118678	−	0.992933i	$-0.462134\pi$
$467$	−10.7946	−	4.47125i	−0.499513	−	0.206905i	−0.618191	+	0.786028i	$0.712134\pi$
$468$		0			0
$469$	8.91155	+	21.5144i	0.411497	+	0.993441i
$470$	−10.0436	+	25.2028i	−0.463276	+	1.16252i
$471$		0			0
$472$	−6.02612	+	16.3932i	−0.277374	+	0.754559i
$473$	10.7083	−	10.7083i	0.492367	−	0.492367i
$474$		0			0
$475$	10.5757	−	4.38060i	0.485247	−	0.200996i
$476$	−5.11791	+	5.40154i	−0.234579	+	0.247579i
$477$		0			0
$478$	−11.2000	+	11.5061i	−0.512278	+	0.526276i
$479$	31.9090			1.45796			0.728980	−	0.684535i	$-0.239995\pi$
$479$	31.9090			1.45796			0.728980	+	0.684535i	$0.239995\pi$
$480$		0			0
$481$	−1.11241			−0.0507215
$482$	8.61736	−	8.85284i	0.392510	−	0.403236i
$483$		0			0
$484$	11.8882	+	11.2640i	0.540374	+	0.511999i
$485$	−28.9127	+	11.9761i	−1.31286	+	0.543805i
$486$		0			0
$487$	3.23254	−	3.23254i	0.146480	−	0.146480i	−0.630063	−	0.776544i	$-0.716971\pi$
$487$	3.23254	−	3.23254i	0.146480	−	0.146480i	0.776544	+	0.630063i	$0.216971\pi$
$488$	0.996717	+	2.15545i	0.0451193	+	0.0975725i
$489$		0			0
$490$	−6.84148	+	17.1676i	−0.309066	+	0.775555i
$491$	1.47303	+	3.55621i	0.0664770	+	0.160490i	0.953627	−	0.300992i	$-0.0973179\pi$
$491$	1.47303	+	3.55621i	0.0664770	+	0.160490i	−0.887150	+	0.461482i	$0.847318\pi$
$492$		0			0
$493$	−9.81758	−	4.06658i	−0.442162	−	0.183149i
$494$	−0.0180321	−	1.33782i	−0.000811301	−	0.0601916i
$495$		0			0
$496$	1.60055	−	0.0863715i	0.0718669	−	0.00387820i
$497$		−	15.5134i		−	0.695870i
$498$		0			0
$499$	13.3249	+	5.51934i	0.596502	+	0.247079i	0.660445	−	0.750874i	$-0.270368\pi$
$499$	13.3249	+	5.51934i	0.596502	+	0.247079i	−0.0639429	+	0.997954i	$0.520368\pi$
$500$	12.2384	+	4.68699i	0.547318	+	0.209609i
$501$		0			0
$502$	−4.41897	−	1.76100i	−0.197228	−	0.0785974i
$503$	−8.68166	−	8.68166i	−0.387096	−	0.387096i	0.486554	−	0.873650i	$-0.338254\pi$
$503$	−8.68166	−	8.68166i	−0.387096	−	0.387096i	−0.873650	+	0.486554i	$0.838254\pi$
$504$		0			0
$505$	28.2407	−	28.2407i	1.25670	−	1.25670i
$506$	8.95654	−	3.85215i	0.398167	−	0.171249i
$507$		0			0
$508$	−0.0170139	−	0.631027i	−0.000754868	−	0.0279973i
$509$	3.62215	−	8.74464i	0.160549	−	0.387600i	−0.823050	−	0.567969i	$-0.807729\pi$
$509$	3.62215	−	8.74464i	0.160549	−	0.387600i	0.983599	+	0.180369i	$0.0577293\pi$
$510$		0			0
$511$	−16.7094			−0.739180
$512$	−17.8185	−	13.9464i	−0.787473	−	0.616349i
$513$		0			0
$514$	−17.7236	−	17.2522i	−0.781754	−	0.760960i
$515$	1.79047	−	4.32257i	0.0788973	−	0.190475i
$516$		0			0
$517$	10.7606	−	4.45718i	0.473250	−	0.196026i
$518$	10.0236	−	4.31108i	0.440411	−	0.189418i
$519$		0			0
$520$	−1.14996	+	1.24693i	−0.0504291	+	0.0546814i
$521$	−21.7902	−	21.7902i	−0.954646	−	0.954646i	0.0443696	−	0.999015i	$-0.485872\pi$
$521$	−21.7902	−	21.7902i	−0.954646	−	0.954646i	−0.999015	+	0.0443696i	$0.985872\pi$
$522$		0			0
$523$	−16.5532	−	39.9629i	−0.723820	−	1.74746i	−0.662164	−	0.749359i	$-0.730362\pi$
$523$	−16.5532	−	39.9629i	−0.723820	−	1.74746i	−0.0616566	−	0.998097i	$-0.519638\pi$
$524$	−34.4092	−	13.1778i	−1.50317	−	0.575676i
$525$		0			0
$526$	−6.99867	+	0.0943325i	−0.305156	+	0.00411309i
$527$		−	0.989905i		−	0.0431209i
$528$		0			0
$529$		−	6.09457i		−	0.264981i
$530$	0.628692	+	46.6436i	0.0273086	+	2.02607i
$531$		0			0
$532$	5.34714	+	11.9849i	0.231828	+	0.519609i
$533$	0.243803	+	0.588592i	0.0105603	+	0.0254947i
$534$		0			0
$535$	−19.8470	−	19.8470i	−0.858059	−	0.858059i
$536$	18.3552	+	39.6941i	0.792826	+	1.71452i
$537$		0			0
$538$	2.87742	+	6.69021i	0.124054	+	0.288436i
$539$	7.32988	−	3.03614i	0.315720	−	0.130776i
$540$		0			0
$541$	−13.2688	+	32.0337i	−0.570469	+	1.37724i	0.330687	+	0.943741i	$0.392720\pi$
$541$	−13.2688	+	32.0337i	−0.570469	+	1.37724i	−0.901156	+	0.433495i	$0.857280\pi$
$542$	17.5452	−	18.0246i	0.753631	−	0.774224i
$543$		0			0
$544$	−9.19344	+	10.5242i	−0.394165	+	0.451222i
$545$	53.0401			2.27199
$546$		0			0
$547$	−4.79017	+	11.5645i	−0.204813	+	0.494462i	−0.992592	−	0.121496i	$-0.961231\pi$
$547$	−4.79017	+	11.5645i	−0.204813	+	0.494462i	0.787779	+	0.615958i	$0.211231\pi$
$548$	−15.7822	+	16.6568i	−0.674181	+	0.711543i
$549$		0			0
$550$	2.46159	+	5.72338i	0.104962	+	0.244046i
$551$	−13.2523	+	13.2523i	−0.564567	+	0.564567i
$552$		0			0
$553$	−1.18751	−	1.18751i	−0.0504980	−	0.0504980i
$554$	11.5362	−	28.9483i	0.490126	−	1.22990i
$555$		0			0
$556$	20.4830	−	9.13868i	0.868675	−	0.387567i
$557$	−19.6641	−	8.14513i	−0.833194	−	0.345120i	−0.0750278	−	0.997181i	$-0.523905\pi$
$557$	−19.6641	−	8.14513i	−0.833194	−	0.345120i	−0.758166	+	0.652061i	$0.773905\pi$
$558$		0			0
$559$			1.96120i			0.0829499i
$560$	5.52955	−	15.6923i	0.233666	−	0.663121i
$561$		0			0
$562$	−23.7721	+	0.320416i	−1.00277	+	0.0135159i
$563$	−28.0864	−	11.6338i	−1.18370	−	0.490305i	−0.298002	−	0.954565i	$-0.596320\pi$
$563$	−28.0864	−	11.6338i	−1.18370	−	0.490305i	−0.885699	+	0.464261i	$0.846320\pi$
$564$		0			0
$565$	2.21478	+	5.34695i	0.0931765	+	0.224948i
$566$	−27.7334	−	11.0521i	−1.16572	−	0.464552i
$567$		0			0
$568$	−1.17766	−	29.1100i	−0.0494135	−	1.22143i
$569$	−14.0389	+	14.0389i	−0.588541	+	0.588541i	−0.937236	−	0.348696i	$-0.886625\pi$
$569$	−14.0389	+	14.0389i	−0.588541	+	0.588541i	0.348696	+	0.937236i	$0.386625\pi$
$570$		0			0
$571$	10.3624	−	4.29225i	0.433653	−	0.179625i	−0.155169	−	0.987888i	$-0.549592\pi$
$571$	10.3624	−	4.29225i	0.433653	−	0.179625i	0.588822	+	0.808263i	$0.299592\pi$
$572$	0.727939	−	0.0196268i	0.0304367	−	0.000820639i
$573$		0			0
$574$	−4.47789	−	4.35878i	−0.186903	−	0.181932i
$575$	−10.8029			−0.450510
$576$		0			0
$577$	38.9659			1.62217			0.811086	−	0.584927i	$-0.198877\pi$
$577$	38.9659			1.62217			0.811086	+	0.584927i	$0.198877\pi$
$578$	−11.0434	−	10.7497i	−0.459346	−	0.447128i
$579$		0			0
$580$	23.7519	−	0.640402i	0.986242	−	0.0265912i
$581$	18.6874	−	7.74058i	0.775285	−	0.321133i
$582$		0			0
$583$	14.1606	−	14.1606i	0.586472	−	0.586472i
$584$	−31.3543	+	1.26845i	−1.29745	+	0.0524890i
$585$		0			0
$586$	0.129719	+	0.0516943i	0.00535864	+	0.00213547i
$587$	15.1693	+	36.6219i	0.626104	+	1.51155i	0.844426	+	0.535672i	$0.179941\pi$
$587$	15.1693	+	36.6219i	0.626104	+	1.51155i	−0.218323	+	0.975877i	$0.570059\pi$
$588$		0			0
$589$	−1.61297	−	0.668113i	−0.0664612	−	0.0275291i
$590$	−24.1160	+	0.325051i	−0.992840	+	0.0133821i
$591$		0			0
$592$	18.4815	−	8.85042i	0.759583	−	0.363750i
$593$		−	0.283795i		−	0.0116541i	−0.999983	−	0.00582703i	$-0.998145\pi$
$593$		−	0.283795i		−	0.0116541i	0.999983	−	0.00582703i	$-0.00185481\pi$
$594$		0			0
$595$	−9.49313	−	3.93218i	−0.389180	−	0.161204i
$596$	−16.2564	+	7.25294i	−0.665889	+	0.297092i
$597$		0			0
$598$	−0.467429	+	1.17294i	−0.0191146	+	0.0479652i
$599$	−3.46739	−	3.46739i	−0.141674	−	0.141674i	0.632713	−	0.774387i	$-0.281941\pi$
$599$	−3.46739	−	3.46739i	−0.141674	−	0.141674i	−0.774387	+	0.632713i	$0.781941\pi$
$600$		0			0
$601$	−5.43849	+	5.43849i	−0.221841	+	0.221841i	−0.809273	−	0.587432i	$-0.800139\pi$
$601$	−5.43849	+	5.43849i	−0.221841	+	0.221841i	0.587432	+	0.809273i	$0.300139\pi$
$602$	−7.60051	−	17.6718i	−0.309774	−	0.720248i
$603$		0			0
$604$	−31.1566	+	32.8832i	−1.26774	+	1.33800i
$605$	−8.65432	+	20.8934i	−0.351848	+	0.849436i
$606$		0			0
$607$	−8.67444			−0.352085			−0.176042	−	0.984383i	$-0.556330\pi$
$607$	−8.67444			−0.352085			−0.176042	+	0.984383i	$0.556330\pi$
$608$	10.9434	+	22.0830i	0.443815	+	0.895584i
$609$		0			0
$610$	−2.28732	+	2.34982i	−0.0926108	+	0.0951414i
$611$	−0.577227	+	1.39355i	−0.0233521	+	0.0563770i
$612$		0			0
$613$	13.8988	−	5.75707i	0.561367	−	0.232526i	−0.0839113	−	0.996473i	$-0.526741\pi$
$613$	13.8988	−	5.75707i	0.561367	−	0.232526i	0.645279	+	0.763947i	$0.276741\pi$
$614$	12.6750	+	29.4704i	0.511522	+	1.18933i
$615$		0			0
$616$	−6.48318	+	2.99794i	−0.261215	+	0.120790i
$617$	−16.6151	−	16.6151i	−0.668897	−	0.668897i	0.288564	−	0.957461i	$-0.406822\pi$
$617$	−16.6151	−	16.6151i	−0.668897	−	0.668897i	−0.957461	+	0.288564i	$0.906822\pi$
$618$		0			0
$619$	−8.48574	−	20.4864i	−0.341071	−	0.823417i	−0.997608	−	0.0691240i	$-0.977980\pi$
$619$	−8.48574	−	20.4864i	−0.341071	−	0.823417i	0.656537	−	0.754293i	$-0.272020\pi$
$620$	0.901838	+	2.02134i	0.0362187	+	0.0811790i
$621$		0			0
$622$	0.354546	+	26.3043i	0.0142160	+	1.05470i
$623$		−	16.1476i		−	0.646938i
$624$		0			0
$625$			31.2338i			1.24935i
$626$	27.8754	−	0.375722i	1.11412	−	0.0150169i
$627$		0			0
$628$	1.61995	+	0.620399i	0.0646431	+	0.0247566i
$629$	−4.84286	−	11.6917i	−0.193097	−	0.466178i
$630$		0			0
$631$	15.4553	+	15.4553i	0.615265	+	0.615265i	0.944313	−	0.329048i	$-0.106728\pi$
$631$	15.4553	+	15.4553i	0.615265	+	0.615265i	−0.329048	+	0.944313i	$0.606728\pi$
$632$	−2.31844	−	2.13815i	−0.0922226	−	0.0850509i
$633$		0			0
$634$	36.0466	−	15.5034i	1.43159	−	0.615718i
$635$	0.805340	−	0.333583i	0.0319589	−	0.0132378i
$636$		0			0
$637$	−0.393195	+	0.949257i	−0.0155790	+	0.0376109i
$638$	−7.30938	−	7.11496i	−0.289381	−	0.281684i
$639$		0			0
$640$	9.18466	−	29.8655i	0.363056	−	1.18054i
$641$	−36.9354			−1.45886			−0.729431	−	0.684054i	$-0.760215\pi$
$641$	−36.9354			−1.45886			−0.729431	+	0.684054i	$0.760215\pi$
$642$		0			0
$643$	−17.3696	+	41.9338i	−0.684989	+	1.65371i	0.0696525	+	0.997571i	$0.477811\pi$
$643$	−17.3696	+	41.9338i	−0.684989	+	1.65371i	−0.754641	+	0.656138i	$0.772189\pi$
$644$	−0.333806	−	12.3805i	−0.0131538	−	0.487861i
$645$		0			0
$646$	13.9824	−	6.01372i	0.550128	−	0.236607i
$647$	−15.1450	+	15.1450i	−0.595413	+	0.595413i	−0.939089	−	0.343675i	$-0.888328\pi$
$647$	−15.1450	+	15.1450i	−0.595413	+	0.595413i	0.343675	+	0.939089i	$0.388328\pi$
$648$		0			0
$649$	7.32141	+	7.32141i	0.287390	+	0.287390i
$650$	−0.749530	−	0.298695i	−0.0293990	−	0.0117158i
$651$		0			0
$652$	1.76730	+	0.676830i	0.0692128	+	0.0265067i
$653$	−1.47400	−	0.610551i	−0.0576821	−	0.0238927i	0.353656	−	0.935376i	$-0.384938\pi$
$653$	−1.47400	−	0.610551i	−0.0576821	−	0.0238927i	−0.411338	+	0.911483i	$0.634938\pi$
$654$		0			0
$655$		−	50.8805i		−	1.98807i
$656$	−8.73340	−	7.83909i	−0.340982	−	0.306065i
$657$		0			0
$658$	−0.199401	−	14.7939i	−0.00777347	−	0.576725i
$659$	13.5105	+	5.59624i	0.526295	+	0.217999i	0.629980	−	0.776612i	$-0.283063\pi$
$659$	13.5105	+	5.59624i	0.526295	+	0.217999i	−0.103685	+	0.994610i	$0.533063\pi$
$660$		0			0
$661$	10.5090	+	25.3710i	0.408753	+	0.986818i	0.985466	+	0.169871i	$0.0543350\pi$
$661$	10.5090	+	25.3710i	0.408753	+	0.986818i	−0.576713	+	0.816947i	$0.695665\pi$
$662$	3.75084	−	9.41216i	0.145781	−	0.365814i
$663$		0			0
$664$	34.4783	−	15.9434i	1.33802	−	0.618724i
$665$	−12.8143	+	12.8143i	−0.496918	+	0.496918i
$666$		0			0
$667$	16.3405	−	6.76846i	0.632707	−	0.262076i
$668$	−8.38359	−	7.94338i	−0.324371	−	0.307339i
$669$		0			0
$670$	−42.1226	+	43.2736i	−1.62734	+	1.67180i
$671$	1.40779			0.0543473
$672$		0			0
$673$	32.0626			1.23592			0.617960	−	0.786209i	$-0.287959\pi$
$673$	32.0626			1.23592			0.617960	+	0.786209i	$0.287959\pi$
$674$	19.3704	−	19.8997i	0.746118	−	0.766507i
$675$		0			0
$676$	17.8177	−	18.8052i	0.685297	−	0.723275i
$677$	11.1934	−	4.63644i	0.430196	−	0.178193i	−0.157069	−	0.987588i	$-0.550205\pi$
$677$	11.1934	−	4.63644i	0.430196	−	0.178193i	0.587265	+	0.809395i	$0.300205\pi$
$678$		0			0
$679$	12.0677	−	12.0677i	0.463116	−	0.463116i
$680$	−18.1118	−	6.65788i	−0.694557	−	0.255318i
$681$		0			0
$682$	0.351769	−	0.882710i	0.0134699	−	0.0338007i
$683$	7.34378	+	17.7294i	0.281002	+	0.678398i	0.999860	−	0.0167589i	$-0.00533478\pi$
$683$	7.34378	+	17.7294i	0.281002	+	0.678398i	−0.718858	+	0.695157i	$0.755335\pi$
$684$		0			0
$685$	−29.2741	−	12.1257i	−1.11851	−	0.463300i
$686$	−0.336771	−	24.9856i	−0.0128580	−	0.953953i
$687$		0			0
$688$	−15.6035	−	32.5832i	−0.594877	−	1.24222i
$689$			2.59348i			0.0988038i
$690$		0			0
$691$	−4.70873	−	1.95042i	−0.179128	−	0.0741974i	0.291317	−	0.956627i	$-0.405907\pi$
$691$	−4.70873	−	1.95042i	−0.179128	−	0.0741974i	−0.470445	+	0.882429i	$0.655907\pi$
$692$	17.5293	−	45.7715i	0.666364	−	1.73997i
$693$		0			0
$694$	−2.78470	−	1.10973i	−0.105706	−	0.0421248i
$695$	21.9007	+	21.9007i	0.830740	+	0.830740i
$696$		0			0
$697$	−5.12485	+	5.12485i	−0.194117	+	0.194117i
$698$	5.37769	−	2.31291i	0.203549	−	0.0875450i
$699$		0			0
$700$	7.91136	−	0.213308i	0.299021	−	0.00806227i
$701$	1.15816	−	2.79604i	0.0437430	−	0.105605i	−0.900498	−	0.434860i	$-0.856798\pi$
$701$	1.15816	−	2.79604i	0.0437430	−	0.105605i	0.944241	+	0.329255i	$0.106798\pi$
$702$		0			0
$703$	−22.3192			−0.841785
$704$	−11.9377	+	6.11762i	−0.449921	+	0.230566i
$705$		0			0
$706$	1.03658	+	1.00901i	0.0390121	+	0.0379745i
$707$	−8.33482	+	20.1220i	−0.313463	+	0.756767i
$708$		0			0
$709$	−14.8900	+	6.16763i	−0.559205	+	0.231630i	−0.644340	−	0.764739i	$-0.722868\pi$
$709$	−14.8900	+	6.16763i	−0.559205	+	0.231630i	0.0851351	+	0.996369i	$0.472868\pi$
$710$	36.9573	−	15.8951i	1.38698	−	0.596532i
$711$		0			0
$712$	−1.22580	−	30.3000i	−0.0459389	−	1.13554i
$713$	1.16504	+	1.16504i	0.0436310	+	0.0436310i
$714$		0			0
$715$	0.384814	+	0.929023i	0.0143912	+	0.0347435i
$716$	−13.4377	+	35.0876i	−0.502189	+	1.31129i
$717$		0			0
$718$	−27.9991	+	0.377390i	−1.04492	+	0.0140841i
$719$			37.4998i			1.39851i	0.714874	+	0.699253i	$0.246484\pi$
$719$			37.4998i			1.39851i	−0.714874	+	0.699253i	$0.753516\pi$
$720$		0			0
$721$			2.55148i			0.0950220i
$722$	0.000346694		0.0257217i	1.29026e−5		0.000957264i
$723$		0			0
$724$	36.4928	−	16.2816i	1.35624	−	0.605099i
$725$	4.32516	+	10.4419i	0.160632	+	0.387801i
$726$		0			0
$727$	−27.4159	−	27.4159i	−1.01680	−	1.01680i	−0.999856	−	0.0169443i	$-0.994606\pi$
$727$	−27.4159	−	27.4159i	−1.01680	−	1.01680i	−0.0169443	−	0.999856i	$-0.505394\pi$
$728$	0.319157	−	0.868223i	0.0118287	−	0.0321785i
$729$		0			0
$730$	−17.1205	−	39.8065i	−0.633659	−	1.47331i
$731$	−20.6127	+	8.53805i	−0.762387	+	0.315791i
$732$		0			0
$733$	−10.1543	+	24.5147i	−0.375059	+	0.905472i	0.617818	+	0.786321i	$0.288017\pi$
$733$	−10.1543	+	24.5147i	−0.375059	+	0.905472i	−0.992876	+	0.119150i	$0.961983\pi$
$734$	14.4981	−	14.8943i	0.535135	−	0.549758i
$735$		0			0
$736$	−1.56621	−	23.2060i	−0.0577311	−	0.855386i
$737$	25.9255			0.954979
$738$		0			0
$739$	3.16518	−	7.64142i	0.116433	−	0.281094i	−0.854910	−	0.518776i	$-0.826388\pi$
$739$	3.16518	−	7.64142i	0.116433	−	0.281094i	0.971343	+	0.237682i	$0.0763877\pi$
$740$	20.5404	+	19.4619i	0.755081	+	0.715433i
$741$		0			0
$742$	−10.0509	−	23.3691i	−0.368980	−	0.857906i
$743$	−18.7647	+	18.7647i	−0.688410	+	0.688410i	−0.961880	−	0.273470i	$-0.911828\pi$
$743$	−18.7647	+	18.7647i	−0.688410	+	0.688410i	0.273470	+	0.961880i	$0.411828\pi$
$744$		0			0
$745$	−17.3815	−	17.3815i	−0.636810	−	0.636810i
$746$	−15.6643	+	39.3071i	−0.573510	+	1.43914i
$747$		0			0
$748$	3.37535	+	7.56537i	0.123415	+	0.276617i
$749$	14.1413	+	5.85753i	0.516713	+	0.214029i
$750$		0			0
$751$		−	34.8687i		−	1.27238i	−0.771534	−	0.636188i	$-0.780510\pi$
$751$		−	34.8687i		−	1.27238i	0.771534	−	0.636188i	$-0.219490\pi$
$752$	−1.49721	−	27.7448i	−0.0545975	−	1.01175i
$753$		0			0
$754$	1.32089	−	0.0178038i	0.0481041	−	0.000648378i
$755$	−57.7918	−	23.9381i	−2.10326	−	0.871198i
$756$		0			0
$757$	−6.42379	−	15.5084i	−0.233477	−	0.563662i	0.763105	−	0.646274i	$-0.223674\pi$
$757$	−6.42379	−	15.5084i	−0.233477	−	0.563662i	−0.996582	+	0.0826120i	$0.973674\pi$
$758$	−5.44593	−	2.17026i	−0.197805	−	0.0788273i
$759$		0			0
$760$	−23.0726	+	25.0182i	−0.836932	+	0.907504i
$761$	−6.68334	+	6.68334i	−0.242271	+	0.242271i	−0.817789	−	0.575518i	$-0.804800\pi$
$761$	−6.68334	+	6.68334i	−0.242271	+	0.242271i	0.575518	+	0.817789i	$0.304800\pi$
$762$		0			0
$763$	−26.7230	+	11.0690i	−0.967439	+	0.400726i
$764$	−0.503074	−	18.6585i	−0.0182006	−	0.675041i
$765$		0			0
$766$	14.7686	+	14.3757i	0.533609	+	0.519416i
$767$	−1.34090			−0.0484171
$768$		0			0
$769$	−26.5261			−0.956556			−0.478278	−	0.878209i	$-0.658739\pi$
$769$	−26.5261			−0.956556			−0.478278	+	0.878209i	$0.658739\pi$
$770$	−7.06781	−	6.87982i	−0.254706	−	0.247931i
$771$		0			0
$772$	−1.16991	−	43.3907i	−0.0421059	−	1.56166i
$773$	−24.9537	+	10.3362i	−0.897523	+	0.371766i	−0.783267	−	0.621685i	$-0.786448\pi$
$773$	−24.9537	+	10.3362i	−0.897523	+	0.371766i	−0.114256	+	0.993451i	$0.536448\pi$
$774$		0			0
$775$	−0.744478	+	0.744478i	−0.0267424	+	0.0267424i
$776$	21.7283	−	23.5605i	0.780001	−	0.845772i
$777$		0			0
$778$	4.41250	+	1.75843i	0.158196	+	0.0630426i
$779$	4.89162	+	11.8094i	0.175260	+	0.423116i
$780$		0			0
$781$	−15.9564	−	6.60937i	−0.570966	−	0.236502i
$782$	−14.3629	+	0.193592i	−0.513614	+	0.00692282i
$783$		0			0
$784$	−1.01987	−	18.8992i	−0.0364238	−	0.674970i
$785$			2.39540i			0.0854957i
$786$		0			0
$787$	7.66436	+	3.17468i	0.273205	+	0.113165i	0.515080	−	0.857142i	$-0.327762\pi$
$787$	7.66436	+	3.17468i	0.273205	+	0.113165i	−0.241875	+	0.970307i	$0.577762\pi$
$788$	−2.02823	−	4.54599i	−0.0722527	−	0.161944i
$789$		0			0
$790$	1.61226	−	4.04571i	0.0573615	−	0.143940i
$791$	−2.23173	−	2.23173i	−0.0793512	−	0.0793512i
$792$		0			0
$793$	−0.128917	+	0.128917i	−0.00457799	+	0.00457799i
$794$	4.29528	+	9.98685i	0.152434	+	0.354420i
$795$		0			0
$796$	−3.68134	−	3.48804i	−0.130482	−	0.123630i
$797$	−0.898165	+	2.16836i	−0.0318146	+	0.0768073i	−0.938988	−	0.343949i	$-0.888235\pi$
$797$	−0.898165	+	2.16836i	−0.0318146	+	0.0768073i	0.907174	+	0.420756i	$0.138235\pi$
$798$		0			0
$799$	−17.1595			−0.607059
$800$	14.8291	−	1.00083i	0.524286	−	0.0353848i
$801$		0			0
$802$	−20.8789	+	21.4494i	−0.737260	+	0.757406i
$803$	−7.11892	+	17.1866i	−0.251221	+	0.606502i
$804$		0			0
$805$	15.8005	−	6.54478i	0.556894	−	0.230673i
$806$	0.0486204	+	0.113046i	0.00171258	+	0.00398188i
$807$		0			0
$808$	−14.1123	+	38.3906i	−0.496470	+	1.35058i
$809$	−10.3243	−	10.3243i	−0.362984	−	0.362984i	0.501926	−	0.864910i	$-0.332625\pi$
$809$	−10.3243	−	10.3243i	−0.362984	−	0.362984i	−0.864910	+	0.501926i	$0.832625\pi$
$810$		0			0
$811$	−6.28975	−	15.1848i	−0.220863	−	0.533211i	0.774145	−	0.633009i	$-0.218180\pi$
$811$	−6.28975	−	15.1848i	−0.220863	−	0.533211i	−0.995008	+	0.0997982i	$0.968180\pi$
$812$	−11.8332	+	5.27947i	−0.415263	+	0.185273i
$813$		0			0
$814$	−0.163719	−	12.1466i	−0.00573835	−	0.425737i
$815$			2.61329i			0.0915395i
$816$		0			0
$817$			39.3492i			1.37665i
$818$	−0.431827	+	0.00582044i	−0.0150985	+	0.000203507i
$819$		0			0
$820$	5.79579	−	15.1336i	0.202398	−	0.528489i
$821$	−14.6985	−	35.4853i	−0.512982	−	1.23845i	−0.942141	−	0.335218i	$-0.891190\pi$
$821$	−14.6985	−	35.4853i	−0.512982	−	1.23845i	0.429159	−	0.903229i	$-0.358810\pi$
$822$		0			0
$823$	−21.1995	−	21.1995i	−0.738968	−	0.738968i	0.233410	−	0.972378i	$-0.425012\pi$
$823$	−21.1995	−	21.1995i	−0.738968	−	0.738968i	−0.972378	+	0.233410i	$0.925012\pi$
$824$	0.193689	+	4.78771i	0.00674749	+	0.166788i
$825$		0			0
$826$	12.0824	−	5.19658i	0.420402	−	0.180812i
$827$	36.7381	−	15.2174i	1.27751	−	0.529162i	0.362271	−	0.932073i	$-0.382002\pi$
$827$	36.7381	−	15.2174i	1.27751	−	0.529162i	0.915239	+	0.402911i	$0.132002\pi$
$828$		0			0
$829$	−12.5928	+	30.4018i	−0.437367	+	1.05590i	0.539488	+	0.841993i	$0.318618\pi$
$829$	−12.5928	+	30.4018i	−0.437367	+	1.05590i	−0.976855	+	0.213904i	$0.931382\pi$
$830$	37.5875	+	36.5877i	1.30468	+	1.26998i
$831$		0			0
$832$	0.532972	−	1.65340i	0.0184775	−	0.0573214i
$833$	−11.6887			−0.404989
$834$		0			0
$835$	6.10304	−	14.7340i	0.211204	−	0.509892i
$836$	14.6052	−	0.393789i	0.505133	−	0.0136195i
$837$		0			0
$838$	−13.1230	+	5.64412i	−0.453327	+	0.194973i
$839$	3.59337	−	3.59337i	0.124057	−	0.124057i	−0.642353	−	0.766409i	$-0.722041\pi$
$839$	3.59337	−	3.59337i	0.124057	−	0.124057i	0.766409	+	0.642353i	$0.222041\pi$
$840$		0			0
$841$	7.42153	+	7.42153i	0.255915	+	0.255915i
$842$	−53.5524	−	21.3412i	−1.84554	−	0.735465i
$843$		0			0
$844$	−5.26509	+	13.7479i	−0.181232	+	0.473222i
$845$	33.0498	+	13.6897i	1.13695	+	0.470939i
$846$		0			0
$847$		−	12.3327i		−	0.423757i
$848$	−20.6340	−	43.0878i	−0.708573	−	1.47964i
$849$		0			0
$850$	−0.123708	−	9.17810i	−0.00424316	−	0.314806i
$851$	19.4598	+	8.06051i	0.667073	+	0.276311i
$852$		0			0
$853$	−7.16945	−	17.3086i	−0.245477	−	0.592635i	0.752332	−	0.658784i	$-0.228929\pi$
$853$	−7.16945	−	17.3086i	−0.245477	−	0.592635i	−0.997810	+	0.0661489i	$0.978929\pi$
$854$	0.662023	−	1.66125i	0.0226540	−	0.0568467i
$855$		0			0
$856$	26.9801	+	9.91783i	0.922160	+	0.338984i
$857$	0.162401	−	0.162401i	0.00554752	−	0.00554752i	−0.704328	−	0.709875i	$-0.748751\pi$
$857$	0.162401	−	0.162401i	0.00554752	−	0.00554752i	0.709875	+	0.704328i	$0.248751\pi$
$858$		0			0
$859$	−21.5375	+	8.92113i	−0.734850	+	0.304385i	−0.718543	−	0.695482i	$-0.755191\pi$
$859$	−21.5375	+	8.92113i	−0.734850	+	0.304385i	−0.0163069	+	0.999867i	$0.505191\pi$
$860$	34.3117	−	36.2132i	1.17002	−	1.23486i
$861$		0			0
$862$	−4.34903	+	4.46787i	−0.148128	+	0.152176i
$863$	19.2090			0.653881			0.326941	−	0.945045i	$-0.393982\pi$
$863$	19.2090			0.653881			0.326941	+	0.945045i	$0.393982\pi$
$864$		0			0
$865$	67.6818			2.30125
$866$	27.7085	−	28.4656i	0.941572	−	0.967301i
$867$		0			0
$868$	−0.876207	−	0.830199i	−0.0297404	−	0.0281788i
$869$	−1.72735	+	0.715493i	−0.0585964	+	0.0242714i
$870$		0			0
$871$	−2.37410	+	2.37410i	−0.0804434	+	0.0804434i
$872$	−49.3040	+	22.7991i	−1.66965	+	0.772074i
$873$		0			0
$874$	−9.37843	+	23.5337i	−0.317230	+	0.796040i
$875$	−3.77665	−	9.11765i	−0.127674	−	0.308233i
$876$		0			0
$877$	41.4921	+	17.1866i	1.40109	+	0.580351i	0.950034	−	0.312145i	$-0.101048\pi$
$877$	41.4921	+	17.1866i	1.40109	+	0.580351i	0.451056	+	0.892496i	$0.351048\pi$
$878$	−0.607586	−	45.0777i	−0.0205050	−	1.52130i
$879$		0			0
$880$	−13.7846	−	12.3731i	−0.464680	−	0.417096i
$881$			44.2399i			1.49048i	0.666797	+	0.745239i	$0.267665\pi$
$881$			44.2399i			1.49048i	−0.666797	+	0.745239i	$0.732335\pi$
$882$		0			0
$883$	−3.83168	−	1.58713i	−0.128946	−	0.0534112i	0.317277	−	0.948333i	$-0.397231\pi$
$883$	−3.83168	−	1.58713i	−0.128946	−	0.0534112i	−0.446224	+	0.894922i	$0.647231\pi$
$884$	−1.00188	−	0.383696i	−0.0336970	−	0.0129051i
$885$		0			0
$886$	−20.7102	−	8.25322i	−0.695772	−	0.277272i
$887$	−0.311191	−	0.311191i	−0.0104488	−	0.0104488i	0.701863	−	0.712312i	$-0.252352\pi$
$887$	−0.311191	−	0.311191i	−0.0104488	−	0.0104488i	−0.712312	+	0.701863i	$0.752352\pi$
$888$		0			0
$889$	−0.336136	+	0.336136i	−0.0112736	+	0.0112736i
$890$	38.4681	−	16.5449i	1.28945	−	0.554585i
$891$		0			0
$892$	−0.971529	−	36.0330i	−0.0325292	−	1.20648i
$893$	−11.5814	+	27.9600i	−0.387556	+	0.935644i
$894$		0			0
$895$	−51.8837			−1.73428
$896$	1.60521	+	16.9638i	0.0536263	+	0.566721i
$897$		0			0
$898$	−29.4362	−	28.6533i	−0.982299	−	0.956171i
$899$	0.659657	−	1.59255i	0.0220008	−	0.0531146i
$900$		0			0
$901$	−27.2581	+	11.2907i	−0.908099	+	0.376147i
$902$	−6.39104	+	2.74874i	−0.212798	+	0.0915231i
$903$		0			0
$904$	−4.35714	−	4.01830i	−0.144916	−	0.133647i
$905$	39.0185	+	39.0185i	1.29702	+	1.29702i
$906$		0			0
$907$	−16.4695	−	39.7608i	−0.546859	−	1.32024i	−0.919803	−	0.392381i	$-0.871651\pi$
$907$	−16.4695	−	39.7608i	−0.546859	−	1.32024i	0.372943	−	0.927854i	$-0.378349\pi$
$908$	29.4996	+	11.2976i	0.978980	+	0.374924i
$909$		0			0
$910$	1.27724	−	0.0172155i	0.0423401	−	0.000570687i
$911$		−	52.9909i		−	1.75567i	−0.478967	−	0.877833i	$-0.658989\pi$
$911$		−	52.9909i		−	1.75567i	0.478967	−	0.877833i	$-0.341011\pi$
$912$		0			0
$913$		−	22.5189i		−	0.745268i
$914$	−0.102626	−	7.61401i	−0.00339458	−	0.251849i
$915$		0			0
$916$	20.9084	+	46.8632i	0.690833	+	1.54840i
$917$	10.6184	+	25.6350i	0.350649	+	0.846541i
$918$		0			0
$919$	39.2031	+	39.2031i	1.29319	+	1.29319i	0.932803	+	0.360386i	$0.117355\pi$
$919$	39.2031	+	39.2031i	1.29319	+	1.29319i	0.360386	+	0.932803i	$0.382645\pi$
$920$	29.1519	−	13.4804i	0.961110	−	0.444435i
$921$		0			0
$922$	4.48692	+	10.4324i	0.147769	+	0.343574i
$923$	2.06644	−	0.855947i	0.0680177	−	0.0281739i
$924$		0			0
$925$	−5.15080	+	12.4351i	−0.169357	+	0.408865i
$926$	−13.1852	+	13.5455i	−0.433292	+	0.445132i
$927$		0			0
$928$	−21.8035	+	10.8049i	−0.715736	+	0.354689i
$929$	−51.0527			−1.67498			−0.837492	−	0.546449i	$-0.815979\pi$
$929$	−51.0527			−1.67498			−0.837492	+	0.546449i	$0.815979\pi$
$930$		0			0
$931$	−7.88900	+	19.0457i	−0.258552	+	0.624199i
$932$	10.2230	−	10.7895i	0.334864	−	0.353422i
$933$		0			0
$934$	6.52848	+	15.1792i	0.213618	+	0.496679i
$935$	−8.08897	+	8.08897i	−0.264537	+	0.264537i
$936$		0			0
$937$	−2.64379	−	2.64379i	−0.0863688	−	0.0863688i	0.662602	−	0.748971i	$-0.269452\pi$
$937$	−2.64379	−	2.64379i	−0.0863688	−	0.0863688i	−0.748971	+	0.662602i	$0.769452\pi$
$938$	12.1916	−	30.5930i	0.398071	−	0.998897i
$939$		0			0
$940$	35.0389	−	15.6329i	1.14284	−	0.509889i
$941$	−1.31796	−	0.545918i	−0.0429643	−	0.0177964i	0.361098	−	0.932528i	$-0.382402\pi$
$941$	−1.31796	−	0.545918i	−0.0429643	−	0.0177964i	−0.404062	+	0.914732i	$0.632402\pi$
$942$		0			0
$943$		−	12.0630i		−	0.392827i
$944$	22.2776	−	10.6683i	0.725073	−	0.347224i
$945$		0			0
$946$	−21.4146	+	0.288640i	−0.696249	+	0.00938449i
$947$	36.7409	+	15.2186i	1.19392	+	0.494538i	0.889029	−	0.457850i	$-0.151380\pi$
$947$	36.7409	+	15.2186i	1.19392	+	0.494538i	0.304890	+	0.952388i	$0.401380\pi$
$948$		0			0
$949$	−0.921937	−	2.22575i	−0.0299273	−	0.0722510i
$950$	−15.0384	−	5.99297i	−0.487912	−	0.194438i
$951$		0			0
$952$	10.5147	−	0.425376i	0.340782	−	0.0137865i
$953$	−12.8933	+	12.8933i	−0.417655	+	0.417655i	−0.884395	−	0.466740i	$-0.845428\pi$
$953$	−12.8933	+	12.8933i	−0.417655	+	0.417655i	0.466740	+	0.884395i	$0.345428\pi$
$954$		0			0
$955$	23.8127	−	9.86353i	0.770560	−	0.319176i
$956$	22.6999	−	0.612039i	0.734168	−	0.0197948i
$957$		0			0
$958$	−32.3362	−	31.4761i	−1.04473	−	1.01695i
$959$	17.2796			0.557987
$960$		0			0
$961$	−30.8394			−0.994820
$962$	1.12730	+	1.09732i	0.0363456	+	0.0353789i
$963$		0			0
$964$	−17.4654	+	0.470906i	−0.562524	+	0.0151669i
$965$	55.3768	−	22.9378i	1.78264	−	0.738394i
$966$		0			0
$967$	22.3041	−	22.3041i	0.717251	−	0.717251i	−0.250791	−	0.968041i	$-0.580691\pi$
$967$	22.3041	−	22.3041i	0.717251	−	0.717251i	0.968041	+	0.250791i	$0.0806906\pi$
$968$	−0.936209	−	23.1417i	−0.0300909	−	0.743802i
$969$		0			0
$970$	41.1134	+	16.3841i	1.32007	+	0.526061i
$971$	−11.6863	−	28.2133i	−0.375032	−	0.905408i	−0.992881	−	0.119111i	$-0.961996\pi$
$971$	−11.6863	−	28.2133i	−0.375032	−	0.905408i	0.617849	−	0.786297i	$-0.288004\pi$
$972$		0			0
$973$	−15.6046	−	6.46365i	−0.500262	−	0.207215i
$974$	−6.46450	+	0.0871326i	−0.207136	+	0.00279191i
$975$		0			0
$976$	1.11614	−	3.16749i	0.0357268	−	0.101389i
$977$			54.9206i			1.75706i	0.477683	+	0.878532i	$0.341477\pi$
$977$			54.9206i			1.75706i	−0.477683	+	0.878532i	$0.658523\pi$
$978$		0			0
$979$	−16.6087	−	6.87956i	−0.530817	−	0.219872i
$980$	23.8678	−	10.6488i	0.762428	−	0.340164i
$981$		0			0
$982$	2.01521	−	5.05687i	0.0643080	−	0.161371i
$983$	12.6090	+	12.6090i	0.402164	+	0.402164i	0.878995	−	0.476831i	$-0.158215\pi$
$983$	12.6090	+	12.6090i	0.402164	+	0.402164i	−0.476831	+	0.878995i	$0.658215\pi$
$984$		0			0
$985$	4.86061	−	4.86061i	0.154872	−	0.154872i
$986$	5.93761	+	13.8054i	0.189092	+	0.439653i
$987$		0			0
$988$	−1.30140	+	1.37352i	−0.0414030	+	0.0436975i
$989$	14.2108	−	34.3080i	0.451878	−	1.09093i
$990$		0			0
$991$	48.7460			1.54847			0.774234	−	0.632899i	$-0.218135\pi$
$991$	48.7460			1.54847			0.774234	+	0.632899i	$0.218135\pi$
$992$	−1.70718	−	1.49131i	−0.0542030	−	0.0473491i
$993$		0			0
$994$	−15.3029	+	15.7211i	−0.485378	+	0.498641i
$995$	2.67992	−	6.46990i	0.0849592	−	0.205110i
$996$		0			0
$997$	41.2051	−	17.0677i	1.30498	−	0.540540i	0.381563	−	0.924343i	$-0.375386\pi$
$997$	41.2051	−	17.0677i	1.30498	−	0.540540i	0.923415	+	0.383803i	$0.125386\pi$
$998$	−8.05878	−	18.7373i	−0.255096	−	0.593118i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.01339 - 0.986432i) q^{2} +(0.0539048 + 1.99927i) q^{4} +(-2.55155 + 1.05689i) q^{5} +(1.06497 - 1.06497i) q^{7} +(1.91752 - 2.07921i) q^{8} +O(q^{10})\)	\(q+(-1.01339 - 0.986432i) q^{2} +(0.0539048 + 1.99927i) q^{4} +(-2.55155 + 1.05689i) q^{5} +(1.06497 - 1.06497i) q^{7} +(1.91752 - 2.07921i) q^{8} +(3.62825 + 1.44589i) q^{10} +(-0.641664 - 1.54911i) q^{11} +(0.200618 + 0.0830988i) q^{13} +(-2.12975 + 0.0287062i) q^{14} +(-3.99419 + 0.215541i) q^{16} +2.47031i q^{17} +(4.02517 + 1.66728i) q^{19} +(-2.25054 - 5.04427i) q^{20} +(-0.877841 + 2.20281i) q^{22} +(-2.90736 - 2.90736i) q^{23} +(1.85785 - 1.85785i) q^{25} +(-0.121332 - 0.282107i) q^{26} +(2.18658 + 2.07177i) q^{28} +(-1.64618 + 3.97423i) q^{29} -0.400720 q^{31} +(4.26027 + 3.72157i) q^{32} +(2.43680 - 2.50338i) q^{34} +(-1.59177 + 3.84288i) q^{35} +(-4.73288 + 1.96042i) q^{37} +(-2.43439 - 5.66015i) q^{38} +(-2.69516 + 7.33180i) q^{40} +(2.07457 + 2.07457i) q^{41} +(3.45626 + 8.34415i) q^{43} +(3.06251 - 1.36637i) q^{44} +(0.0783673 + 5.81418i) q^{46} +6.94628i q^{47} +4.73166i q^{49} +(-3.71536 + 0.0500780i) q^{50} +(-0.155323 + 0.405570i) q^{52} +(4.57054 + 11.0343i) q^{53} +(3.27447 + 3.27447i) q^{55} +(-0.172195 - 4.25641i) q^{56} +(5.58852 - 2.40358i) q^{58} +(-5.70502 + 2.36310i) q^{59} +(-0.321300 + 0.775687i) q^{61} +(0.406085 + 0.395283i) q^{62} +(-0.646231 - 7.97386i) q^{64} -0.599712 q^{65} +(-5.91697 + 14.2848i) q^{67} +(-4.93883 + 0.133162i) q^{68} +(5.40383 - 2.32415i) q^{70} +(7.28346 - 7.28346i) q^{71} +(-7.84498 - 7.84498i) q^{73} +(6.73006 + 2.68199i) q^{74} +(-3.11637 + 8.13729i) q^{76} +(-2.33312 - 0.966410i) q^{77} -1.11506i q^{79} +(9.96356 - 4.77136i) q^{80} +(-0.0559198 - 4.14877i) q^{82} +(12.4078 + 5.13949i) q^{83} +(-2.61084 - 6.30312i) q^{85} +(4.72841 - 11.8652i) q^{86} +(-4.45134 - 1.63630i) q^{88} +(7.58120 - 7.58120i) q^{89} +(0.302151 - 0.125155i) q^{91} +(5.65588 - 5.96932i) q^{92} +(6.85203 - 7.03927i) q^{94} -12.0325 q^{95} +11.3315 q^{97} +(4.66746 - 4.79500i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more