LMFDB - Embedded newform 864.2.y.a.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.7
Character	$\chi$	$=$	864.97
Dual form			864.2.y.a.481.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11085 - 1.32892i) q^{3} +(-0.229433 - 0.0835067i) q^{5} +(0.342276 - 1.94115i) q^{7} +(-0.532044 - 2.95244i) q^{9} +O(q^{10})$	\(q+(1.11085 - 1.32892i) q^{3} +(-0.229433 - 0.0835067i) q^{5} +(0.342276 - 1.94115i) q^{7} +(-0.532044 - 2.95244i) q^{9} +(-3.98411 + 1.45010i) q^{11} +(3.83365 - 3.21681i) q^{13} +(-0.365838 + 0.212134i) q^{15} +(1.08154 + 1.87328i) q^{17} +(0.276255 - 0.478488i) q^{19} +(-2.19941 - 2.61117i) q^{21} +(-1.16152 - 6.58733i) q^{23} +(-3.78456 - 3.17562i) q^{25} +(-4.51457 - 2.57267i) q^{27} +(2.79626 + 2.34634i) q^{29} +(-0.642226 - 3.64224i) q^{31} +(-2.49867 + 6.90538i) q^{33} +(-0.240628 + 0.416780i) q^{35} +(0.461983 + 0.800178i) q^{37} +(-0.0162873 - 8.66799i) q^{39} +(-6.17451 + 5.18103i) q^{41} +(-2.31707 + 0.843345i) q^{43} +(-0.124481 + 0.721817i) q^{45} +(1.26541 - 7.17649i) q^{47} +(2.92695 + 1.06532i) q^{49} +(3.69085 + 0.643648i) q^{51} +8.04964 q^{53} +1.03518 q^{55} +(-0.328994 - 0.898647i) q^{57} +(9.50973 + 3.46126i) q^{59} +(-0.896160 + 5.08238i) q^{61} +(-5.91323 + 0.0222222i) q^{63} +(-1.14819 + 0.417907i) q^{65} +(-4.53138 + 3.80228i) q^{67} +(-10.0443 - 5.77394i) q^{69} +(0.813668 + 1.40931i) q^{71} +(7.46053 - 12.9220i) q^{73} +(-8.42419 + 1.50174i) q^{75} +(1.45118 + 8.23007i) q^{77} +(-6.71569 - 5.63513i) q^{79} +(-8.43386 + 3.14166i) q^{81} +(-5.08434 - 4.26627i) q^{83} +(-0.0917088 - 0.520106i) q^{85} +(6.22431 - 1.10958i) q^{87} +(-3.82450 + 6.62423i) q^{89} +(-4.93214 - 8.54272i) q^{91} +(-5.55365 - 3.19250i) q^{93} +(-0.103339 + 0.0867117i) q^{95} +(18.2228 - 6.63256i) q^{97} +(6.40105 + 10.9913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.11085	−	1.32892i	0.641347	−	0.767251i
$3$	1.11085	−	1.32892i	0.641347	−	0.767251i
$4$		0			0
$5$	−0.229433	−	0.0835067i	−0.102605	−	0.0373453i	0.290207	−	0.956964i	$-0.406276\pi$
$5$	−0.229433	−	0.0835067i	−0.102605	−	0.0373453i	−0.392813	+	0.919618i	$0.628498\pi$
$6$		0			0
$7$	0.342276	−	1.94115i	0.129368	−	0.733684i	−0.849249	−	0.527993i	$-0.822945\pi$
$7$	0.342276	−	1.94115i	0.129368	−	0.733684i	0.978617	−	0.205691i	$-0.0659442\pi$
$8$		0			0
$9$	−0.532044	−	2.95244i	−0.177348	−	0.984148i
$10$		0			0
$11$	−3.98411	+	1.45010i	−1.20125	+	0.437220i	−0.863662	−	0.504072i	$-0.831835\pi$
$11$	−3.98411	+	1.45010i	−1.20125	+	0.437220i	−0.337592	+	0.941293i	$0.609612\pi$
$12$		0			0
$13$	3.83365	−	3.21681i	1.06326	−	0.892184i	0.0688379	−	0.997628i	$-0.478071\pi$
$13$	3.83365	−	3.21681i	1.06326	−	0.892184i	0.994425	+	0.105444i	$0.0336264\pi$
$14$		0			0
$15$	−0.365838	+	0.212134i	−0.0944589	+	0.0547728i
$16$		0			0
$17$	1.08154	+	1.87328i	0.262311	+	0.454336i	0.966856	−	0.255324i	$-0.0821820\pi$
$17$	1.08154	+	1.87328i	0.262311	+	0.454336i	−0.704545	+	0.709660i	$0.748849\pi$
$18$		0			0
$19$	0.276255	−	0.478488i	0.0633773	−	0.109773i	−0.832596	−	0.553881i	$-0.813146\pi$
$19$	0.276255	−	0.478488i	0.0633773	−	0.109773i	0.895973	+	0.444108i	$0.146480\pi$
$20$		0			0
$21$	−2.19941	−	2.61117i	−0.479950	−	0.569804i
$22$		0			0
$23$	−1.16152	−	6.58733i	−0.242194	−	1.37355i	−0.826919	−	0.562321i	$-0.809909\pi$
$23$	−1.16152	−	6.58733i	−0.242194	−	1.37355i	0.584725	−	0.811232i	$-0.301203\pi$
$24$		0			0
$25$	−3.78456	−	3.17562i	−0.756911	−	0.635124i
$26$		0			0
$27$	−4.51457	−	2.57267i	−0.868830	−	0.495110i
$28$		0			0
$29$	2.79626	+	2.34634i	0.519252	+	0.435705i	0.864371	−	0.502855i	$-0.167717\pi$
$29$	2.79626	+	2.34634i	0.519252	+	0.435705i	−0.345119	+	0.938559i	$0.612161\pi$
$30$		0			0
$31$	−0.642226	−	3.64224i	−0.115347	−	0.654166i	−0.986578	−	0.163292i	$-0.947789\pi$
$31$	−0.642226	−	3.64224i	−0.115347	−	0.654166i	0.871231	−	0.490874i	$-0.163322\pi$
$32$		0			0
$33$	−2.49867	+	6.90538i	−0.434963	+	1.20207i
$34$		0			0
$35$	−0.240628	+	0.416780i	−0.0406736	+	0.0704487i
$36$		0			0
$37$	0.461983	+	0.800178i	0.0759496	+	0.131549i	0.901499	−	0.432782i	$-0.142468\pi$
$37$	0.461983	+	0.800178i	0.0759496	+	0.131549i	−0.825549	+	0.564330i	$0.809135\pi$
$38$		0			0
$39$	−0.0162873	−	8.66799i	−0.00260805	−	1.38799i
$40$		0			0
$41$	−6.17451	+	5.18103i	−0.964297	+	0.809141i	−0.981647	−	0.190708i	$-0.938921\pi$
$41$	−6.17451	+	5.18103i	−0.964297	+	0.809141i	0.0173500	+	0.999849i	$0.494477\pi$
$42$		0			0
$43$	−2.31707	+	0.843345i	−0.353350	+	0.128609i	−0.512596	−	0.858630i	$-0.671316\pi$
$43$	−2.31707	+	0.843345i	−0.353350	+	0.128609i	0.159246	+	0.987239i	$0.449094\pi$
$44$		0			0
$45$	−0.124481	+	0.721817i	−0.0185565	+	0.107602i
$46$		0			0
$47$	1.26541	−	7.17649i	0.184579	−	1.04680i	−0.741916	−	0.670492i	$-0.766083\pi$
$47$	1.26541	−	7.17649i	0.184579	−	1.04680i	0.926495	−	0.376306i	$-0.122806\pi$
$48$		0			0
$49$	2.92695	+	1.06532i	0.418136	+	0.152189i
$50$		0			0
$51$	3.69085	+	0.643648i	0.516822	+	0.0901287i
$52$		0			0
$53$	8.04964			1.10570			0.552852	−	0.833280i	$-0.313540\pi$
$53$	8.04964			1.10570			0.552852	+	0.833280i	$0.313540\pi$
$54$		0			0
$55$	1.03518			0.139583
$56$		0			0
$57$	−0.328994	−	0.898647i	−0.0435764	−	0.119029i
$58$		0			0
$59$	9.50973	+	3.46126i	1.23806	+	0.450618i	0.876351	−	0.481673i	$-0.159971\pi$
$59$	9.50973	+	3.46126i	1.23806	+	0.450618i	0.361710	+	0.932290i	$0.382193\pi$
$60$		0			0
$61$	−0.896160	+	5.08238i	−0.114742	+	0.650732i	0.872136	+	0.489263i	$0.162734\pi$
$61$	−0.896160	+	5.08238i	−0.114742	+	0.650732i	−0.986878	+	0.161469i	$0.948377\pi$
$62$		0			0
$63$	−5.91323	+	0.0222222i	−0.744997	+	0.00279973i
$64$		0			0
$65$	−1.14819	+	0.417907i	−0.142415	+	0.0518350i
$66$		0			0
$67$	−4.53138	+	3.80228i	−0.553596	+	0.464523i	−0.876157	−	0.482026i	$-0.839901\pi$
$67$	−4.53138	+	3.80228i	−0.553596	+	0.464523i	0.322560	+	0.946549i	$0.395457\pi$
$68$		0			0
$69$	−10.0443	−	5.77394i	−1.20919	−	0.695100i
$70$		0			0
$71$	0.813668	+	1.40931i	0.0965646	+	0.167255i	0.910261	−	0.414036i	$-0.135881\pi$
$71$	0.813668	+	1.40931i	0.0965646	+	0.167255i	−0.813696	+	0.581291i	$0.802548\pi$
$72$		0			0
$73$	7.46053	−	12.9220i	0.873189	−	1.51241i	0.0145089	−	0.999895i	$-0.495382\pi$
$73$	7.46053	−	12.9220i	0.873189	−	1.51241i	0.858680	−	0.512512i	$-0.171285\pi$
$74$		0			0
$75$	−8.42419	+	1.50174i	−0.972742	+	0.173406i
$76$		0			0
$77$	1.45118	+	8.23007i	0.165378	+	0.937903i
$78$		0			0
$79$	−6.71569	−	5.63513i	−0.755574	−	0.634002i	0.181397	−	0.983410i	$-0.441938\pi$
$79$	−6.71569	−	5.63513i	−0.755574	−	0.634002i	−0.936971	+	0.349408i	$0.886383\pi$
$80$		0			0
$81$	−8.43386	+	3.14166i	−0.937095	+	0.349073i
$82$		0			0
$83$	−5.08434	−	4.26627i	−0.558079	−	0.468284i	0.319587	−	0.947557i	$-0.396456\pi$
$83$	−5.08434	−	4.26627i	−0.558079	−	0.468284i	−0.877666	+	0.479273i	$0.840900\pi$
$84$		0			0
$85$	−0.0917088	−	0.520106i	−0.00994721	−	0.0564134i
$86$		0			0
$87$	6.22431	−	1.10958i	0.667316	−	0.118959i
$88$		0			0
$89$	−3.82450	+	6.62423i	−0.405396	+	0.702167i	−0.994368	−	0.105987i	$-0.966200\pi$
$89$	−3.82450	+	6.62423i	−0.405396	+	0.702167i	0.588971	+	0.808154i	$0.299533\pi$
$90$		0			0
$91$	−4.93214	−	8.54272i	−0.517029	−	0.895520i
$92$		0			0
$93$	−5.55365	−	3.19250i	−0.575887	−	0.331047i
$94$		0			0
$95$	−0.103339	+	0.0867117i	−0.0106024	+	0.00889643i
$96$		0			0
$97$	18.2228	−	6.63256i	1.85025	−	0.673434i	0.865128	−	0.501551i	$-0.167237\pi$
$97$	18.2228	−	6.63256i	1.85025	−	0.673434i	0.985117	−	0.171884i	$-0.0549853\pi$
$98$		0			0
$99$	6.40105	+	10.9913i	0.643330	+	1.10467i
$100$		0			0
$101$	−2.76068	+	15.6566i	−0.274698	+	1.55789i	0.465222	+	0.885194i	$0.345974\pi$
$101$	−2.76068	+	15.6566i	−0.274698	+	1.55789i	−0.739920	+	0.672695i	$0.765137\pi$
$102$		0			0
$103$	14.5586	+	5.29891i	1.43450	+	0.522117i	0.938219	−	0.346042i	$-0.112475\pi$
$103$	14.5586	+	5.29891i	1.43450	+	0.522117i	0.496286	+	0.868159i	$0.334697\pi$
$104$		0			0
$105$	0.286566	+	0.782753i	0.0279659	+	0.0763889i
$106$		0			0
$107$	−6.23188			−0.602459			−0.301230	−	0.953552i	$-0.597397\pi$
$107$	−6.23188			−0.602459			−0.301230	+	0.953552i	$0.597397\pi$
$108$		0			0
$109$	−1.17366			−0.112416			−0.0562079	−	0.998419i	$-0.517901\pi$
$109$	−1.17366			−0.112416			−0.0562079	+	0.998419i	$0.517901\pi$
$110$		0			0
$111$	1.57656	+	0.274937i	0.149641	+	0.0260959i
$112$		0			0
$113$	4.12382	+	1.50095i	0.387936	+	0.141197i	0.528623	−	0.848857i	$-0.322709\pi$
$113$	4.12382	+	1.50095i	0.387936	+	0.141197i	−0.140686	+	0.990054i	$0.544931\pi$
$114$		0			0
$115$	−0.283594	+	1.60834i	−0.0264453	+	0.149979i
$116$		0			0
$117$	−11.5371	−	9.60715i	−1.06661	−	0.888182i
$118$		0			0
$119$	4.00649	−	1.45824i	0.367274	−	0.133677i
$120$		0			0
$121$	5.34384	−	4.48401i	0.485804	−	0.407638i
$122$		0			0
$123$	0.0262325	+	13.9607i	0.00236530	+	1.25880i
$124$		0			0
$125$	1.21351	+	2.10186i	0.108540	+	0.187996i
$126$		0			0
$127$	9.40316	−	16.2868i	0.834396	−	1.44522i	−0.0601253	−	0.998191i	$-0.519150\pi$
$127$	9.40316	−	16.2868i	0.834396	−	1.44522i	0.894521	−	0.447025i	$-0.147517\pi$
$128$		0			0
$129$	−1.45317	+	4.01602i	−0.127945	+	0.353591i
$130$		0			0
$131$	0.508090	+	2.88152i	0.0443920	+	0.251760i	0.998926	−	0.0463440i	$-0.0147570\pi$
$131$	0.508090	+	2.88152i	0.0443920	+	0.251760i	−0.954534	+	0.298104i	$0.903646\pi$
$132$		0			0
$133$	−0.834260	−	0.700027i	−0.0723395	−	0.0607000i
$134$		0			0
$135$	0.820956	+	0.967251i	0.0706566	+	0.0832477i
$136$		0			0
$137$	3.52441	+	2.95733i	0.301111	+	0.252662i	0.780806	−	0.624773i	$-0.214808\pi$
$137$	3.52441	+	2.95733i	0.301111	+	0.252662i	−0.479696	+	0.877435i	$0.659253\pi$
$138$		0			0
$139$	3.78380	+	21.4590i	0.320938	+	1.82013i	0.536803	+	0.843707i	$0.319632\pi$
$139$	3.78380	+	21.4590i	0.320938	+	1.82013i	−0.215865	+	0.976423i	$0.569257\pi$
$140$		0			0
$141$	−8.13129	−	9.65360i	−0.684778	−	0.812980i
$142$		0			0
$143$	−10.6090	+	18.3753i	−0.887168	+	1.53662i
$144$		0			0
$145$	−0.445618	−	0.771834i	−0.0370066	−	0.0640973i
$146$		0			0
$147$	4.66712	−	2.70627i	0.384938	−	0.223209i
$148$		0			0
$149$	12.3245	−	10.3415i	1.00967	−	0.847210i	0.0213712	−	0.999772i	$-0.493197\pi$
$149$	12.3245	−	10.3415i	1.00967	−	0.847210i	0.988294	+	0.152562i	$0.0487524\pi$
$150$		0			0
$151$	−16.3827	+	5.96280i	−1.33320	+	0.485246i	−0.907665	−	0.419696i	$-0.862137\pi$
$151$	−16.3827	+	5.96280i	−1.33320	+	0.485246i	−0.425536	+	0.904941i	$0.639915\pi$
$152$		0			0
$153$	4.95532	−	4.18984i	0.400614	−	0.338729i
$154$		0			0
$155$	−0.156804	+	0.889280i	−0.0125948	+	0.0714287i
$156$		0			0
$157$	3.15664	+	1.14892i	0.251927	+	0.0916939i	0.464897	−	0.885365i	$-0.346091\pi$
$157$	3.15664	+	1.14892i	0.251927	+	0.0916939i	−0.212970	+	0.977059i	$0.568314\pi$
$158$		0			0
$159$	8.94191	−	10.6973i	0.709139	−	0.848352i
$160$		0			0
$161$	−13.1845			−1.03909
$162$		0			0
$163$	13.5164			1.05869			0.529343	−	0.848408i	$-0.322438\pi$
$163$	13.5164			1.05869			0.529343	+	0.848408i	$0.322438\pi$
$164$		0			0
$165$	1.14992	−	1.37567i	0.0895213	−	0.107095i
$166$		0			0
$167$	15.5367	+	5.65491i	1.20227	+	0.437590i	0.864015	−	0.503465i	$-0.167942\pi$
$167$	15.5367	+	5.65491i	1.20227	+	0.437590i	0.338253	+	0.941055i	$0.390164\pi$
$168$		0			0
$169$	2.09155	−	11.8618i	0.160889	−	0.912444i
$170$		0			0
$171$	−1.55969	−	0.561052i	−0.119272	−	0.0429047i
$172$		0			0
$173$	9.43105	−	3.43262i	0.717029	−	0.260977i	0.0423652	−	0.999102i	$-0.486511\pi$
$173$	9.43105	−	3.43262i	0.717029	−	0.260977i	0.674664	+	0.738125i	$0.264288\pi$
$174$		0			0
$175$	−7.45971	+	6.25944i	−0.563901	+	0.473169i
$176$		0			0
$177$	15.1636	−	8.79272i	1.13976	−	0.660902i
$178$		0			0
$179$	7.19994	+	12.4707i	0.538148	+	0.932100i	0.999004	+	0.0446252i	$0.0142094\pi$
$179$	7.19994	+	12.4707i	0.538148	+	0.932100i	−0.460855	+	0.887475i	$0.652457\pi$
$180$		0			0
$181$	3.86902	−	6.70135i	0.287582	−	0.498107i	−0.685650	−	0.727932i	$-0.740482\pi$
$181$	3.86902	−	6.70135i	0.287582	−	0.498107i	0.973232	+	0.229824i	$0.0738152\pi$
$182$		0			0
$183$	5.75857	+	6.83666i	0.425685	+	0.505381i
$184$		0			0
$185$	−0.0391738	−	0.222166i	−0.00288012	−	0.0163340i
$186$		0			0
$187$	−7.02539	−	5.89500i	−0.513747	−	0.431085i
$188$		0			0
$189$	−6.53916	+	7.88288i	−0.475654	+	0.573396i
$190$		0			0
$191$	−8.17187	−	6.85701i	−0.591296	−	0.496156i	0.297339	−	0.954772i	$-0.403901\pi$
$191$	−8.17187	−	6.85701i	−0.591296	−	0.496156i	−0.888635	+	0.458616i	$0.848345\pi$
$192$		0			0
$193$	−2.17976	−	12.3620i	−0.156903	−	0.889840i	−0.957026	−	0.290004i	$-0.906344\pi$
$193$	−2.17976	−	12.3620i	−0.156903	−	0.889840i	0.800123	−	0.599836i	$-0.204768\pi$
$194$		0			0
$195$	−0.720098	+	1.99008i	−0.0515673	+	0.142513i
$196$		0			0
$197$	−1.54791	+	2.68106i	−0.110284	+	0.191018i	−0.915885	−	0.401441i	$-0.868509\pi$
$197$	−1.54791	+	2.68106i	−0.110284	+	0.191018i	0.805601	+	0.592459i	$0.201843\pi$
$198$		0			0
$199$	7.17374	+	12.4253i	0.508533	+	0.880805i	0.999951	+	0.00988120i	$0.00314533\pi$
$199$	7.17374	+	12.4253i	0.508533	+	0.880805i	−0.491418	+	0.870924i	$0.663521\pi$
$200$		0			0
$201$	0.0192516	+	10.2456i	0.00135790	+	0.722668i
$202$		0			0
$203$	5.51168	−	4.62485i	0.386844	−	0.324601i
$204$		0			0
$205$	1.84929	−	0.673085i	0.129160	−	0.0470103i
$206$		0			0
$207$	−18.8307	+	6.93408i	−1.30883	+	0.481952i
$208$		0			0
$209$	−0.406776	+	2.30694i	−0.0281373	+	0.159575i
$210$		0			0
$211$	22.6786	+	8.25435i	1.56126	+	0.568253i	0.971025	−	0.238977i	$-0.0768120\pi$
$211$	22.6786	+	8.25435i	1.56126	+	0.568253i	0.590237	+	0.807230i	$0.299034\pi$
$212$		0			0
$213$	2.77672	+	0.484233i	0.190258	+	0.0331791i
$214$		0			0
$215$	0.602037			0.0410586
$216$		0			0
$217$	−7.28994			−0.494874
$218$		0			0
$219$	−8.88479	−	24.2688i	−0.600379	−	1.63993i
$220$		0			0
$221$	10.1722	+	3.70238i	0.684257	+	0.249049i
$222$		0			0
$223$	−3.30725	+	18.7563i	−0.221470	+	1.25602i	0.647851	+	0.761767i	$0.275668\pi$
$223$	−3.30725	+	18.7563i	−0.221470	+	1.25602i	−0.869320	+	0.494249i	$0.835443\pi$
$224$		0			0
$225$	−7.36229	+	12.8633i	−0.490819	+	0.857551i
$226$		0			0
$227$	−9.03860	+	3.28978i	−0.599913	+	0.218350i	−0.624084	−	0.781357i	$-0.714528\pi$
$227$	−9.03860	+	3.28978i	−0.599913	+	0.218350i	0.0241709	+	0.999708i	$0.492305\pi$
$228$		0			0
$229$	−13.4260	+	11.2657i	−0.887215	+	0.744462i	−0.967650	−	0.252298i	$-0.918814\pi$
$229$	−13.4260	+	11.2657i	−0.887215	+	0.744462i	0.0804347	+	0.996760i	$0.474369\pi$
$230$		0			0
$231$	12.5491	+	7.21383i	0.825672	+	0.474635i
$232$		0			0
$233$	3.95030	+	6.84213i	0.258793	+	0.448243i	0.965919	−	0.258845i	$-0.0833419\pi$
$233$	3.95030	+	6.84213i	0.258793	+	0.448243i	−0.707126	+	0.707088i	$0.750009\pi$
$234$		0			0
$235$	−0.889611	+	1.54085i	−0.0580318	+	0.100514i
$236$		0			0
$237$	−14.9487	+	2.66483i	−0.971023	+	0.173100i
$238$		0			0
$239$	−0.382321	−	2.16825i	−0.0247303	−	0.140252i	0.969943	−	0.243334i	$-0.0782409\pi$
$239$	−0.382321	−	2.16825i	−0.0247303	−	0.140252i	−0.994673	+	0.103081i	$0.967130\pi$
$240$		0			0
$241$	8.00819	+	6.71967i	0.515853	+	0.432852i	0.863183	−	0.504891i	$-0.168467\pi$
$241$	8.00819	+	6.71967i	0.515853	+	0.432852i	−0.347330	+	0.937743i	$0.612912\pi$
$242$		0			0
$243$	−5.19371	+	14.6978i	−0.333177	+	0.942864i
$244$		0			0
$245$	−0.582577	−	0.488840i	−0.0372195	−	0.0312309i
$246$		0			0
$247$	−0.480141	−	2.72302i	−0.0305507	−	0.173261i
$248$		0			0
$249$	−11.3174	+	2.01750i	−0.717213	+	0.127854i
$250$		0			0
$251$	−0.597898	+	1.03559i	−0.0377390	+	0.0653658i	−0.884278	−	0.466961i	$-0.845349\pi$
$251$	−0.597898	+	1.03559i	−0.0377390	+	0.0653658i	0.846539	+	0.532327i	$0.178682\pi$
$252$		0			0
$253$	14.1799	+	24.5603i	0.891482	+	1.54409i
$254$		0			0
$255$	−0.793053	−	0.455884i	−0.0496629	−	0.0285486i
$256$		0			0
$257$	−9.69587	+	8.13580i	−0.604812	+	0.507498i	−0.892988	−	0.450080i	$-0.851396\pi$
$257$	−9.69587	+	8.13580i	−0.604812	+	0.507498i	0.288176	+	0.957577i	$0.406951\pi$
$258$		0			0
$259$	1.71139	−	0.622895i	0.106341	−	0.0387048i
$260$		0			0
$261$	5.43971	−	9.50416i	0.336709	−	0.588293i
$262$		0			0
$263$	−0.504119	+	2.85900i	−0.0310853	+	0.176293i	−0.996398	−	0.0848045i	$-0.972973\pi$
$263$	−0.504119	+	2.85900i	−0.0310853	+	0.176293i	0.965312	+	0.261098i	$0.0840845\pi$
$264$		0			0
$265$	−1.84685	−	0.672199i	−0.113451	−	0.0412928i
$266$		0			0
$267$	4.55462	+	12.4409i	0.278738	+	0.761373i
$268$		0			0
$269$	−3.76701			−0.229679			−0.114839	−	0.993384i	$-0.536635\pi$
$269$	−3.76701			−0.229679			−0.114839	+	0.993384i	$0.536635\pi$
$270$		0			0
$271$	10.6952			0.649687			0.324843	−	0.945768i	$-0.394688\pi$
$271$	10.6952			0.649687			0.324843	+	0.945768i	$0.394688\pi$
$272$		0			0
$273$	−16.8314	−	2.93523i	−1.01868	−	0.177648i
$274$		0			0
$275$	19.6830	+	7.16404i	1.18693	+	0.432008i
$276$		0			0
$277$	1.37491	−	7.79748i	0.0826101	−	0.468505i	−0.915237	−	0.402917i	$-0.867996\pi$
$277$	1.37491	−	7.79748i	0.0826101	−	0.468505i	0.997847	−	0.0655885i	$-0.0208925\pi$
$278$		0			0
$279$	−10.4118	+	3.83397i	−0.623340	+	0.229534i
$280$		0			0
$281$	−25.3944	+	9.24280i	−1.51490	+	0.551379i	−0.959869	−	0.280449i	$-0.909517\pi$
$281$	−25.3944	+	9.24280i	−1.51490	+	0.551379i	−0.555033	+	0.831828i	$0.687294\pi$
$282$		0			0
$283$	−9.43004	+	7.91275i	−0.560558	+	0.470364i	−0.878497	−	0.477747i	$-0.841454\pi$
$283$	−9.43004	+	7.91275i	−0.560558	+	0.470364i	0.317940	+	0.948111i	$0.397009\pi$
$284$		0			0
$285$	0.000439036		0.233652i	2.60063e−5		0.0138404i
$286$		0			0
$287$	7.94375	+	13.7590i	0.468905	+	0.812167i
$288$		0			0
$289$	6.16056	−	10.6704i	0.362386	−	0.627671i
$290$		0			0
$291$	11.4286	−	31.5844i	0.669956	−	1.85151i
$292$		0			0
$293$	2.62555	+	14.8903i	0.153386	+	0.869898i	0.960246	+	0.279155i	$0.0900542\pi$
$293$	2.62555	+	14.8903i	0.153386	+	0.869898i	−0.806860	+	0.590743i	$0.798835\pi$
$294$		0			0
$295$	−1.89281	−	1.58825i	−0.110203	−	0.0924716i
$296$		0			0
$297$	21.7172	+	3.70322i	1.26016	+	0.214883i
$298$		0			0
$299$	−25.6431	−	21.5171i	−1.48298	−	1.24437i
$300$		0			0
$301$	0.843977	+	4.78643i	0.0486460	+	0.275885i
$302$		0			0
$303$	17.7396	+	21.0608i	1.01911	+	1.20991i
$304$		0			0
$305$	0.630021	−	1.09123i	0.0360749	−	0.0624836i
$306$		0			0
$307$	−10.1810	−	17.6340i	−0.581062	−	1.00643i	−0.995354	−	0.0962844i	$-0.969304\pi$
$307$	−10.1810	−	17.6340i	−0.581062	−	1.00643i	0.414292	−	0.910144i	$-0.364029\pi$
$308$		0			0
$309$	23.2142	−	13.4610i	1.32061	−	0.765767i
$310$		0			0
$311$	20.7107	−	17.3784i	1.17440	−	0.985437i	0.174399	−	0.984675i	$-0.444202\pi$
$311$	20.7107	−	17.3784i	1.17440	−	0.985437i	1.00000		0.000762067i	$-0.000242573\pi$
$312$		0			0
$313$	−16.7979	+	6.11394i	−0.949474	+	0.345580i	−0.769900	−	0.638164i	$-0.779694\pi$
$313$	−16.7979	+	6.11394i	−0.949474	+	0.345580i	−0.179574	+	0.983744i	$0.557472\pi$
$314$		0			0
$315$	1.35854	+	0.488696i	0.0765453	+	0.0275349i
$316$		0			0
$317$	5.14474	−	29.1773i	0.288957	−	1.63876i	−0.401839	−	0.915710i	$-0.631629\pi$
$317$	5.14474	−	29.1773i	0.288957	−	1.63876i	0.690797	−	0.723049i	$-0.257260\pi$
$318$		0			0
$319$	−14.5430	−	5.29323i	−0.814253	−	0.296364i
$320$		0			0
$321$	−6.92266	+	8.28166i	−0.386385	+	0.462237i
$322$		0			0
$323$	1.19512			0.0664983
$324$		0			0
$325$	−24.7240			−1.37144
$326$		0			0
$327$	−1.30375	+	1.55969i	−0.0720976	+	0.0862512i
$328$		0			0
$329$	−13.4975	−	4.91269i	−0.744141	−	0.270845i
$330$		0			0
$331$	5.13150	−	29.1022i	0.282053	−	1.59960i	−0.433574	−	0.901118i	$-0.642748\pi$
$331$	5.13150	−	29.1022i	0.282053	−	1.59960i	0.715627	−	0.698483i	$-0.246141\pi$
$332$		0			0
$333$	2.11669	−	1.78971i	0.115994	−	0.0980755i
$334$		0			0
$335$	1.35716	−	0.493967i	0.0741498	−	0.0269883i
$336$		0			0
$337$	10.3714	−	8.70266i	0.564967	−	0.474064i	−0.315004	−	0.949090i	$-0.602006\pi$
$337$	10.3714	−	8.70266i	0.564967	−	0.474064i	0.879972	+	0.475026i	$0.157561\pi$
$338$		0			0
$339$	6.57556	−	3.81289i	0.357135	−	0.207088i
$340$		0			0
$341$	7.84030	+	13.5798i	0.424576	+	0.735387i
$342$		0			0
$343$	9.96860	−	17.2661i	0.538254	−	0.932283i
$344$		0			0
$345$	1.82233	+	2.16349i	0.0981107	+	0.116479i
$346$		0			0
$347$	0.164047	+	0.930354i	0.00880648	+	0.0499440i	0.988894	−	0.148620i	$-0.0474832\pi$
$347$	0.164047	+	0.930354i	0.00880648	+	0.0499440i	−0.980088	+	0.198564i	$0.936372\pi$
$348$		0			0
$349$	8.45767	+	7.09683i	0.452729	+	0.379884i	0.840447	−	0.541893i	$-0.182292\pi$
$349$	8.45767	+	7.09683i	0.452729	+	0.379884i	−0.387719	+	0.921778i	$0.626737\pi$
$350$		0			0
$351$	−25.5831	+	4.65984i	−1.36552	+	0.248724i
$352$		0			0
$353$	−9.51919	−	7.98755i	−0.506655	−	0.425134i	0.353295	−	0.935512i	$-0.385061\pi$
$353$	−9.51919	−	7.98755i	−0.506655	−	0.425134i	−0.859950	+	0.510378i	$0.829506\pi$
$354$		0			0
$355$	−0.0689949	−	0.391289i	−0.00366187	−	0.0207675i
$356$		0			0
$357$	2.51271	−	6.94417i	0.132986	−	0.367525i
$358$		0			0
$359$	−16.8576	+	29.1982i	−0.889711	+	1.54102i	−0.0494931	+	0.998774i	$0.515761\pi$
$359$	−16.8576	+	29.1982i	−0.889711	+	1.54102i	−0.840218	+	0.542250i	$0.817573\pi$
$360$		0			0
$361$	9.34737	+	16.1901i	0.491967	+	0.852111i
$362$		0			0
$363$	−0.0227033	−	12.0826i	−0.00119162	−	0.634170i
$364$		0			0
$365$	−2.79076	+	2.34173i	−0.146075	+	0.122572i
$366$		0			0
$367$	−23.6315	+	8.60117i	−1.23356	+	0.448977i	−0.874814	−	0.484459i	$-0.839016\pi$
$367$	−23.6315	+	8.60117i	−1.23356	+	0.448977i	−0.358742	+	0.933437i	$0.616794\pi$
$368$		0			0
$369$	18.5818	+	15.4734i	0.967331	+	0.805511i
$370$		0			0
$371$	2.75520	−	15.6255i	0.143043	−	0.811237i
$372$		0			0
$373$	−11.1973	−	4.07550i	−0.579777	−	0.211021i	0.0354504	−	0.999371i	$-0.488713\pi$
$373$	−11.1973	−	4.07550i	−0.579777	−	0.211021i	−0.615227	+	0.788350i	$0.710936\pi$
$374$		0			0
$375$	4.14122	+	0.722188i	0.213852	+	0.0372936i
$376$		0			0
$377$	18.2676			0.940830
$378$		0			0
$379$	−16.4615			−0.845568			−0.422784	−	0.906230i	$-0.638947\pi$
$379$	−16.4615			−0.845568			−0.422784	+	0.906230i	$0.638947\pi$
$380$		0			0
$381$	−11.1983	−	30.5881i	−0.573706	−	1.56708i
$382$		0			0
$383$	−35.0860	−	12.7703i	−1.79281	−	0.652530i	−0.999016	−	0.0443439i	$-0.985880\pi$
$383$	−35.0860	−	12.7703i	−1.79281	−	0.652530i	−0.793795	−	0.608186i	$-0.791898\pi$
$384$		0			0
$385$	0.354317	−	2.00943i	0.0180577	−	0.102410i
$386$		0			0
$387$	3.72271	+	6.39233i	0.189236	+	0.324940i
$388$		0			0
$389$	27.9496	−	10.1728i	1.41710	−	0.515783i	0.483896	−	0.875125i	$-0.339221\pi$
$389$	27.9496	−	10.1728i	1.41710	−	0.515783i	0.933206	+	0.359342i	$0.116999\pi$
$390$		0			0
$391$	11.0837	−	9.30029i	0.560524	−	0.470336i
$392$		0			0
$393$	4.39371	+	2.52572i	0.221633	+	0.127405i
$394$		0			0
$395$	1.07023	+	1.85369i	0.0538490	+	0.0932692i
$396$		0			0
$397$	−0.475634	+	0.823822i	−0.0238714	+	0.0413465i	−0.877714	−	0.479184i	$-0.840933\pi$
$397$	−0.475634	+	0.823822i	−0.0238714	+	0.0413465i	0.853843	+	0.520531i	$0.174266\pi$
$398$		0			0
$399$	−1.85701	+	0.331040i	−0.0929669	+	0.0165727i
$400$		0			0
$401$	−4.23881	−	24.0395i	−0.211676	−	1.20047i	−0.886582	−	0.462571i	$-0.846927\pi$
$401$	−4.23881	−	24.0395i	−0.211676	−	1.20047i	0.674906	−	0.737903i	$-0.264184\pi$
$402$		0			0
$403$	−14.1785	−	11.8972i	−0.706281	−	0.592640i
$404$		0			0
$405$	2.19735	−	0.0165157i	0.109187	−	0.000820674i
$406$		0			0
$407$	−3.00093	−	2.51808i	−0.148750	−	0.124816i
$408$		0			0
$409$	−0.728922	−	4.13392i	−0.0360429	−	0.204409i	0.961468	−	0.274915i	$-0.0886498\pi$
$409$	−0.728922	−	4.13392i	−0.0360429	−	0.204409i	−0.997511	+	0.0705058i	$0.977539\pi$
$410$		0			0
$411$	7.84513	−	1.39851i	0.386972	−	0.0689835i
$412$		0			0
$413$	9.97377	−	17.2751i	0.490777	−	0.850051i
$414$		0			0
$415$	0.810252	+	1.40340i	0.0397737	+	0.0688901i
$416$		0			0
$417$	32.7205	+	18.8093i	1.60233	+	0.921095i
$418$		0			0
$419$	28.0144	−	23.5069i	1.36859	−	1.14839i	0.395371	−	0.918522i	$-0.370616\pi$
$419$	28.0144	−	23.5069i	1.36859	−	1.14839i	0.973223	−	0.229865i	$-0.0738284\pi$
$420$		0			0
$421$	−30.7775	+	11.2021i	−1.50000	+	0.545957i	−0.956062	−	0.293165i	$-0.905291\pi$
$421$	−30.7775	+	11.2021i	−1.50000	+	0.545957i	−0.543943	+	0.839122i	$0.683069\pi$
$422$		0			0
$423$	−21.8614	+	0.0821563i	−1.06294	+	0.00399458i
$424$		0			0
$425$	1.85568	−	10.5241i	0.0900135	−	0.510492i
$426$		0			0
$427$	9.55891	+	3.47916i	0.462588	+	0.168368i
$428$		0			0
$429$	12.6343	+	34.5106i	0.609990	+	1.66619i
$430$		0			0
$431$	−7.58906			−0.365552			−0.182776	−	0.983155i	$-0.558508\pi$
$431$	−7.58906			−0.365552			−0.182776	+	0.983155i	$0.558508\pi$
$432$		0			0
$433$	−15.3377			−0.737081			−0.368540	−	0.929612i	$-0.620142\pi$
$433$	−15.3377			−0.737081			−0.368540	+	0.929612i	$0.620142\pi$
$434$		0			0
$435$	−1.52072	−	0.265198i	−0.0729128	−	0.0127153i
$436$		0			0
$437$	−3.47283	−	1.26401i	−0.166128	−	0.0604657i
$438$		0			0
$439$	−0.405198	+	2.29799i	−0.0193391	+	0.109677i	−0.992949	−	0.118540i	$-0.962179\pi$
$439$	−0.405198	+	2.29799i	−0.0193391	+	0.109677i	0.973610	+	0.228217i	$0.0732897\pi$
$440$		0			0
$441$	1.58804	−	9.20846i	0.0756211	−	0.438498i
$442$		0			0
$443$	−16.8362	+	6.12787i	−0.799911	+	0.291144i	−0.709449	−	0.704756i	$-0.751056\pi$
$443$	−16.8362	+	6.12787i	−0.799911	+	0.291144i	−0.0904612	+	0.995900i	$0.528834\pi$
$444$		0			0
$445$	1.43063	−	1.20044i	0.0678185	−	0.0569065i
$446$		0			0
$447$	−0.0523609	−	27.8661i	−0.00247658	−	1.31802i
$448$		0			0
$449$	−19.5088	−	33.7903i	−0.920679	−	1.59466i	−0.798366	−	0.602172i	$-0.794302\pi$
$449$	−19.5088	−	33.7903i	−0.920679	−	1.59466i	−0.122313	−	0.992492i	$-0.539031\pi$
$450$		0			0
$451$	17.0869	−	29.5954i	0.804592	−	1.39359i
$452$		0			0
$453$	−10.2745	+	28.3949i	−0.482740	+	1.33411i
$454$		0			0
$455$	0.418220	+	2.37184i	0.0196065	+	0.111194i
$456$		0			0
$457$	−7.39917	−	6.20864i	−0.346118	−	0.290428i	0.453111	−	0.891454i	$-0.350314\pi$
$457$	−7.39917	−	6.20864i	−0.346118	−	0.290428i	−0.799229	+	0.601026i	$0.794759\pi$
$458$		0			0
$459$	−0.0633581	−	11.2395i	−0.00295730	−	0.524614i
$460$		0			0
$461$	−19.9395	−	16.7312i	−0.928676	−	0.779251i	0.0469035	−	0.998899i	$-0.485065\pi$
$461$	−19.9395	−	16.7312i	−0.928676	−	0.779251i	−0.975579	+	0.219648i	$0.929509\pi$
$462$		0			0
$463$	6.27677	+	35.5974i	0.291706	+	1.65435i	0.680295	+	0.732938i	$0.261852\pi$
$463$	6.27677	+	35.5974i	0.291706	+	1.65435i	−0.388589	+	0.921411i	$0.627037\pi$
$464$		0			0
$465$	1.00759	+	1.19623i	0.0467261	+	0.0554739i
$466$		0			0
$467$	12.0603	−	20.8890i	0.558084	−	0.966629i	−0.439573	−	0.898207i	$-0.644870\pi$
$467$	12.0603	−	20.8890i	0.558084	−	0.966629i	0.997656	−	0.0684224i	$-0.0217966\pi$
$468$		0			0
$469$	5.82980	+	10.0975i	0.269195	+	0.466260i
$470$		0			0
$471$	5.03336	−	2.91863i	0.231925	−	0.134484i
$472$		0			0
$473$	8.00853	−	6.71995i	0.368233	−	0.308984i
$474$		0			0
$475$	−2.56500	+	0.933583i	−0.117690	+	0.0428357i
$476$		0			0
$477$	−4.28276	−	23.7661i	−0.196094	−	1.08818i
$478$		0			0
$479$	6.18401	−	35.0713i	0.282555	−	1.60245i	−0.431337	−	0.902191i	$-0.641958\pi$
$479$	6.18401	−	35.0713i	0.282555	−	1.60245i	0.713892	−	0.700256i	$-0.246931\pi$
$480$		0			0
$481$	4.34511	+	1.58149i	0.198120	+	0.0721097i
$482$		0			0
$483$	−14.6460	+	17.5212i	−0.666415	+	0.797240i
$484$		0			0
$485$	−4.73477			−0.214995
$486$		0			0
$487$	35.9255			1.62794			0.813969	−	0.580908i	$-0.197302\pi$
$487$	35.9255			1.62794			0.813969	+	0.580908i	$0.197302\pi$
$488$		0			0
$489$	15.0146	−	17.9622i	0.678986	−	0.812279i
$490$		0			0
$491$	4.02110	+	1.46356i	0.181470	+	0.0660495i	0.431157	−	0.902277i	$-0.358106\pi$
$491$	4.02110	+	1.46356i	0.181470	+	0.0660495i	−0.249687	+	0.968327i	$0.580328\pi$
$492$		0			0
$493$	−1.37109	+	7.77582i	−0.0617506	+	0.350205i
$494$		0			0
$495$	−0.550759	−	3.05630i	−0.0247548	−	0.137371i
$496$		0			0
$497$	3.01418	−	1.09707i	0.135205	−	0.0492105i
$498$		0			0
$499$	−11.5668	+	9.70571i	−0.517802	+	0.434487i	−0.863865	−	0.503724i	$-0.831963\pi$
$499$	−11.5668	+	9.70571i	−0.517802	+	0.434487i	0.346063	+	0.938211i	$0.387518\pi$
$500$		0			0
$501$	24.7738	−	14.3653i	1.10681	−	0.641794i
$502$		0			0
$503$	4.92925	+	8.53771i	0.219784	+	0.380678i	0.954742	−	0.297435i	$-0.0961313\pi$
$503$	4.92925	+	8.53771i	0.219784	+	0.380678i	−0.734958	+	0.678113i	$0.762798\pi$
$504$		0			0
$505$	1.94082	−	3.36160i	0.0863653	−	0.149589i
$506$		0			0
$507$	−13.4399	−	15.9561i	−0.596888	−	0.708636i
$508$		0			0
$509$	−7.33088	−	41.5755i	−0.324935	−	1.84280i	−0.510128	−	0.860098i	$-0.670402\pi$
$509$	−7.33088	−	41.5755i	−0.324935	−	1.84280i	0.185193	−	0.982702i	$-0.440709\pi$
$510$		0			0
$511$	−22.5300	−	18.9049i	−0.996667	−	0.836303i
$512$		0			0
$513$	−2.47817	+	1.44946i	−0.109414	+	0.0639951i
$514$		0			0
$515$	−2.89773	−	2.43149i	−0.127689	−	0.107144i
$516$		0			0
$517$	5.36508	+	30.4269i	0.235956	+	1.33817i
$518$		0			0
$519$	5.91477	−	16.3462i	0.259630	−	0.717518i
$520$		0			0
$521$	2.96921	−	5.14283i	0.130084	−	0.225311i	−0.793625	−	0.608407i	$-0.791809\pi$
$521$	2.96921	−	5.14283i	0.130084	−	0.225311i	0.923709	+	0.383096i	$0.125142\pi$
$522$		0			0
$523$	−17.5906	−	30.4677i	−0.769182	−	1.33226i	−0.938007	−	0.346616i	$-0.887331\pi$
$523$	−17.5906	−	30.4677i	−0.769182	−	1.33226i	0.168826	−	0.985646i	$-0.446003\pi$
$524$		0			0
$525$	0.0316926	+	16.8666i	0.00138318	+	0.736119i
$526$		0			0
$527$	6.12833	−	5.14228i	0.266954	−	0.224001i
$528$		0			0
$529$	−20.4308	+	7.43621i	−0.888296	+	0.323313i
$530$		0			0
$531$	5.15958	−	29.9185i	0.223907	−	1.29835i
$532$		0			0
$533$	−7.00450	+	39.7245i	−0.303399	+	1.72066i
$534$		0			0
$535$	1.42980	+	0.520404i	0.0618156	+	0.0224990i
$536$		0			0
$537$	24.5705	+	4.28485i	1.06029	+	0.184905i
$538$		0			0
$539$	−13.2061			−0.568828
$540$		0			0
$541$	−27.2214			−1.17034			−0.585169	−	0.810912i	$-0.698972\pi$
$541$	−27.2214			−1.17034			−0.585169	+	0.810912i	$0.698972\pi$
$542$		0			0
$543$	−4.60765	−	12.5858i	−0.197733	−	0.540107i
$544$		0			0
$545$	0.269275	+	0.0980081i	0.0115345	+	0.00419821i
$546$		0			0
$547$	−2.38321	+	13.5159i	−0.101899	+	0.577897i	0.890515	+	0.454954i	$0.150344\pi$
$547$	−2.38321	+	13.5159i	−0.101899	+	0.577897i	−0.992414	+	0.122943i	$0.960767\pi$
$548$		0			0
$549$	15.4822	−	0.0581830i	0.660766	−	0.00248319i
$550$		0			0
$551$	1.89518	−	0.689788i	0.0807373	−	0.0293860i
$552$		0			0
$553$	−13.2372	+	11.1074i	−0.562904	+	0.472333i
$554$		0			0
$555$	−0.338756	−	0.194733i	−0.0143794	−	0.00826596i
$556$		0			0
$557$	−8.54925	−	14.8077i	−0.362244	−	0.627424i	0.626086	−	0.779754i	$-0.284656\pi$
$557$	−8.54925	−	14.8077i	−0.362244	−	0.627424i	−0.988330	+	0.152330i	$0.951322\pi$
$558$		0			0
$559$	−6.16996	+	10.6867i	−0.260961	+	0.451998i
$560$		0			0
$561$	−15.6381	+	2.78772i	−0.660241	+	0.117698i
$562$		0			0
$563$	7.74516	+	43.9250i	0.326420	+	1.85122i	0.499505	+	0.866311i	$0.333515\pi$
$563$	7.74516	+	43.9250i	0.326420	+	1.85122i	−0.173085	+	0.984907i	$0.555374\pi$
$564$		0			0
$565$	−0.820800	−	0.688733i	−0.0345313	−	0.0289752i
$566$		0			0
$567$	3.21171	+	17.4467i	0.134879	+	0.732691i
$568$		0			0
$569$	26.1405	+	21.9345i	1.09587	+	0.919541i	0.997140	−	0.0755737i	$-0.0240788\pi$
$569$	26.1405	+	21.9345i	1.09587	+	0.919541i	0.0987261	+	0.995115i	$0.468523\pi$
$570$		0			0
$571$	6.71944	+	38.1078i	0.281200	+	1.59476i	0.718552	+	0.695473i	$0.244805\pi$
$571$	6.71944	+	38.1078i	0.281200	+	1.59476i	−0.437353	+	0.899290i	$0.644084\pi$
$572$		0			0
$573$	−18.1901	+	3.24266i	−0.759902	+	0.135464i
$574$		0			0
$575$	−16.5230	+	28.6187i	−0.689057	+	1.19348i
$576$		0			0
$577$	12.7635	+	22.1069i	0.531349	+	0.920324i	0.999331	+	0.0365858i	$0.0116482\pi$
$577$	12.7635	+	22.1069i	0.531349	+	0.920324i	−0.467981	+	0.883739i	$0.655018\pi$
$578$		0			0
$579$	−18.8495	−	10.8356i	−0.783359	−	0.450312i
$580$		0			0
$581$	−10.0217	+	8.40920i	−0.415770	+	0.348873i
$582$		0			0
$583$	−32.0706	+	11.6728i	−1.32823	+	0.483436i
$584$		0			0
$585$	1.84473	+	3.16762i	0.0762704	+	0.130965i
$586$		0			0
$587$	2.42286	−	13.7407i	0.100002	−	0.567139i	−0.893097	−	0.449863i	$-0.851473\pi$
$587$	2.42286	−	13.7407i	0.100002	−	0.567139i	0.993099	−	0.117276i	$-0.0374162\pi$
$588$		0			0
$589$	−1.92019	−	0.698891i	−0.0791199	−	0.0287973i
$590$		0			0
$591$	1.84342	+	5.03529i	0.0758281	+	0.207124i
$592$		0			0
$593$	−21.7128			−0.891636			−0.445818	−	0.895124i	$-0.647087\pi$
$593$	−21.7128			−0.891636			−0.445818	+	0.895124i	$0.647087\pi$
$594$		0			0
$595$	−1.04099			−0.0426765
$596$		0			0
$597$	24.4811	+	4.26926i	1.00194	+	0.174729i
$598$		0			0
$599$	7.49342	+	2.72738i	0.306173	+	0.111438i	0.490537	−	0.871420i	$-0.336800\pi$
$599$	7.49342	+	2.72738i	0.306173	+	0.111438i	−0.184365	+	0.982858i	$0.559023\pi$
$600$		0			0
$601$	−2.72942	+	15.4793i	−0.111335	+	0.631415i	0.877164	+	0.480191i	$0.159433\pi$
$601$	−2.72942	+	15.4793i	−0.111335	+	0.631415i	−0.988500	+	0.151224i	$0.951679\pi$
$602$		0			0
$603$	13.6369	+	11.3557i	0.555338	+	0.462439i
$604$		0			0
$605$	−1.60050	+	0.582533i	−0.0650695	+	0.0236833i
$606$		0			0
$607$	24.5410	−	20.5923i	0.996088	−	0.835817i	0.00965028	−	0.999953i	$-0.496928\pi$
$607$	24.5410	−	20.5923i	0.996088	−	0.835817i	0.986438	+	0.164136i	$0.0524837\pi$
$608$		0			0
$609$	−0.0234164	−	12.4621i	−0.000948882	−	0.504989i
$610$		0			0
$611$	−18.2343	−	31.5827i	−0.737681	−	1.27770i
$612$		0			0
$613$	18.0341	−	31.2360i	0.728391	−	1.26161i	−0.229172	−	0.973386i	$-0.573602\pi$
$613$	18.0341	−	31.2360i	0.728391	−	1.26161i	0.957563	−	0.288224i	$-0.0930647\pi$
$614$		0			0
$615$	1.15980	−	3.20524i	0.0467675	−	0.129248i
$616$		0			0
$617$	5.20376	+	29.5120i	0.209496	+	1.18811i	0.890207	+	0.455557i	$0.150560\pi$
$617$	5.20376	+	29.5120i	0.209496	+	1.18811i	−0.680711	+	0.732552i	$0.738329\pi$
$618$		0			0
$619$	19.7922	+	16.6077i	0.795518	+	0.667519i	0.947104	−	0.320925i	$-0.103994\pi$
$619$	19.7922	+	16.6077i	0.795518	+	0.667519i	−0.151587	+	0.988444i	$0.548438\pi$
$620$		0			0
$621$	−11.7032	+	32.7272i	−0.469634	+	1.31330i
$622$		0			0
$623$	11.5496	+	9.69123i	0.462723	+	0.388271i
$624$		0			0
$625$	4.18655	+	23.7431i	0.167462	+	0.949723i
$626$		0			0
$627$	2.61387	+	3.10323i	0.104388	+	0.123931i
$628$		0			0
$629$	−0.999303	+	1.73084i	−0.0398448	+	0.0690133i
$630$		0			0
$631$	3.90871	+	6.77008i	0.155603	+	0.269513i	0.933278	−	0.359154i	$-0.116935\pi$
$631$	3.90871	+	6.77008i	0.155603	+	0.269513i	−0.777675	+	0.628666i	$0.783601\pi$
$632$		0			0
$633$	36.1618	−	20.9687i	1.43730	−	0.833433i
$634$		0			0
$635$	−3.51745	+	2.95149i	−0.139586	+	0.117126i
$636$		0			0
$637$	14.6479	−	5.33138i	0.580369	−	0.211237i
$638$		0			0
$639$	3.72801	−	3.15213i	0.147478	−	0.124696i
$640$		0			0
$641$	5.70485	−	32.3538i	0.225328	−	1.27790i	−0.636729	−	0.771087i	$-0.719713\pi$
$641$	5.70485	−	32.3538i	0.225328	−	1.27790i	0.862057	−	0.506811i	$-0.169176\pi$
$642$		0			0
$643$	5.44503	+	1.98183i	0.214731	+	0.0781558i	0.447146	−	0.894461i	$-0.352440\pi$
$643$	5.44503	+	1.98183i	0.214731	+	0.0781558i	−0.232415	+	0.972617i	$0.574663\pi$
$644$		0			0
$645$	0.668770	−	0.800058i	0.0263328	−	0.0315022i
$646$		0			0
$647$	−7.72943			−0.303875			−0.151938	−	0.988390i	$-0.548551\pi$
$647$	−7.72943			−0.303875			−0.151938	+	0.988390i	$0.548551\pi$
$648$		0			0
$649$	−42.9069			−1.68424
$650$		0			0
$651$	−8.09800	+	9.68773i	−0.317386	+	0.379692i
$652$		0			0
$653$	−29.1979	−	10.6272i	−1.14260	−	0.415873i	−0.299749	−	0.954018i	$-0.596903\pi$
$653$	−29.1979	−	10.6272i	−1.14260	−	0.415873i	−0.842852	+	0.538145i	$0.819125\pi$
$654$		0			0
$655$	0.124054	−	0.703544i	0.00484718	−	0.0274897i
$656$		0			0
$657$	−42.1209	−	15.1517i	−1.64329	−	0.591125i
$658$		0			0
$659$	−36.3296	+	13.2229i	−1.41520	+	0.515091i	−0.932651	−	0.360779i	$-0.882511\pi$
$659$	−36.3296	+	13.2229i	−1.41520	+	0.515091i	−0.482548	+	0.875869i	$0.660289\pi$
$660$		0			0
$661$	−10.0786	+	8.45699i	−0.392014	+	0.328939i	−0.817397	−	0.576075i	$-0.804584\pi$
$661$	−10.0786	+	8.45699i	−0.392014	+	0.328939i	0.425383	+	0.905013i	$0.360139\pi$
$662$		0			0
$663$	16.2199	−	9.40525i	0.629929	−	0.365270i
$664$		0			0
$665$	0.132950	+	0.230275i	0.00515556	+	0.00892969i
$666$		0			0
$667$	12.2082	−	21.1452i	0.472703	−	0.818746i
$668$		0			0
$669$	21.2518	+	25.2304i	0.821641	+	0.975465i
$670$		0			0
$671$	−3.79954	−	21.5483i	−0.146680	−	0.831861i
$672$		0			0
$673$	14.8306	+	12.4443i	0.571676	+	0.479693i	0.882202	−	0.470872i	$-0.156061\pi$
$673$	14.8306	+	12.4443i	0.571676	+	0.479693i	−0.310526	+	0.950565i	$0.600505\pi$
$674$		0			0
$675$	8.91584	+	24.0730i	0.343171	+	0.926569i
$676$		0			0
$677$	−13.4716	−	11.3041i	−0.517758	−	0.434450i	0.346092	−	0.938201i	$-0.387509\pi$
$677$	−13.4716	−	11.3041i	−0.517758	−	0.434450i	−0.863849	+	0.503751i	$0.831953\pi$
$678$		0			0
$679$	−6.63753	−	37.6433i	−0.254725	−	1.44462i
$680$		0			0
$681$	−5.66864	+	15.6660i	−0.217223	+	0.600322i
$682$		0			0
$683$	−2.23314	+	3.86791i	−0.0854486	+	0.148001i	−0.905582	−	0.424171i	$-0.860566\pi$
$683$	−2.23314	+	3.86791i	−0.0854486	+	0.148001i	0.820134	+	0.572172i	$0.193899\pi$
$684$		0			0
$685$	−0.561658	−	0.972821i	−0.0214599	−	0.0371696i
$686$		0			0
$687$	0.0570405	+	30.3565i	0.00217623	+	1.15817i
$688$		0			0
$689$	30.8595	−	25.8942i	1.17565	−	0.986490i
$690$		0			0
$691$	17.4241	−	6.34186i	0.662844	−	0.241256i	0.0113805	−	0.999935i	$-0.496377\pi$
$691$	17.4241	−	6.34186i	0.662844	−	0.241256i	0.651464	+	0.758680i	$0.274155\pi$
$692$		0			0
$693$	23.5267	−	8.66329i	0.893707	−	0.329091i
$694$		0			0
$695$	0.923843	−	5.23938i	0.0350434	−	0.198741i
$696$		0			0
$697$	−16.3835	−	5.96309i	−0.620568	−	0.225868i
$698$		0			0
$699$	13.4808	+	2.35092i	0.509891	+	0.0889199i
$700$		0			0
$701$	16.3357			0.616992			0.308496	−	0.951226i	$-0.400174\pi$
$701$	16.3357			0.616992			0.308496	+	0.951226i	$0.400174\pi$
$702$		0			0
$703$	0.510501			0.0192539
$704$		0			0
$705$	1.05944	+	2.89387i	0.0399010	+	0.108989i
$706$		0			0
$707$	29.4468	+	10.7178i	1.10746	+	0.403083i
$708$		0			0
$709$	−4.43515	+	25.1530i	−0.166566	+	0.944641i	0.780870	+	0.624694i	$0.214776\pi$
$709$	−4.43515	+	25.1530i	−0.166566	+	0.944641i	−0.947435	+	0.319947i	$0.896335\pi$
$710$		0			0
$711$	−13.0644	+	22.8258i	−0.489952	+	0.856035i
$712$		0			0
$713$	−23.2467	+	8.46110i	−0.870595	+	0.316871i
$714$		0			0
$715$	3.96851	−	3.32997i	0.148414	−	0.124534i
$716$		0			0
$717$	−3.30612	−	1.90052i	−0.123469	−	0.0709761i
$718$		0			0
$719$	14.1749	+	24.5516i	0.528634	+	0.915621i	0.999443	+	0.0333859i	$0.0106290\pi$
$719$	14.1749	+	24.5516i	0.528634	+	0.915621i	−0.470808	+	0.882236i	$0.656038\pi$
$720$		0			0
$721$	15.2690	−	26.4468i	0.568649	−	0.984928i
$722$		0			0
$723$	17.8257	−	3.17771i	0.662947	−	0.118180i
$724$		0			0
$725$	−3.13152	−	17.7597i	−0.116302	−	0.659579i
$726$		0			0
$727$	−18.1996	−	15.2713i	−0.674985	−	0.566380i	0.239551	−	0.970884i	$-0.423000\pi$
$727$	−18.1996	−	15.2713i	−0.674985	−	0.566380i	−0.914536	+	0.404504i	$0.867444\pi$
$728$		0			0
$729$	13.7628	+	23.2290i	0.509732	+	0.860333i
$730$		0			0
$731$	−4.08581	−	3.42841i	−0.151119	−	0.126804i
$732$		0			0
$733$	−0.387242	−	2.19616i	−0.0143031	−	0.0811170i	0.976821	−	0.214059i	$-0.0686686\pi$
$733$	−0.387242	−	2.19616i	−0.0143031	−	0.0811170i	−0.991124	+	0.132942i	$0.957557\pi$
$734$		0			0
$735$	−1.29678	+	0.231171i	−0.0478325	+	0.00852686i
$736$		0			0
$737$	12.5398	−	21.7196i	0.461911	−	0.800053i
$738$		0			0
$739$	19.9254	+	34.5118i	0.732968	+	1.26954i	0.955609	+	0.294637i	$0.0951989\pi$
$739$	19.9254	+	34.5118i	0.732968	+	1.26954i	−0.222641	+	0.974900i	$0.571468\pi$
$740$		0			0
$741$	−4.15203	−	2.38678i	−0.152529	−	0.0876807i
$742$		0			0
$743$	−12.6128	+	10.5834i	−0.462717	+	0.388266i	−0.844130	−	0.536139i	$-0.819882\pi$
$743$	−12.6128	+	10.5834i	−0.462717	+	0.388266i	0.381413	+	0.924405i	$0.375438\pi$
$744$		0			0
$745$	−3.69124	+	1.34350i	−0.135236	+	0.0492220i
$746$		0			0
$747$	−9.89083	+	17.2811i	−0.361886	+	0.632281i
$748$		0			0
$749$	−2.13303	+	12.0970i	−0.0779391	+	0.442015i
$750$		0			0
$751$	−3.64682	−	1.32733i	−0.133074	−	0.0484350i	0.274625	−	0.961552i	$-0.411446\pi$
$751$	−3.64682	−	1.32733i	−0.133074	−	0.0484350i	−0.407699	+	0.913116i	$0.633669\pi$
$752$		0			0
$753$	0.712040	+	1.94494i	0.0259482	+	0.0708774i
$754$		0			0
$755$	4.25665			0.154915
$756$		0			0
$757$	−47.9586			−1.74309			−0.871543	−	0.490318i	$-0.836880\pi$
$757$	−47.9586			−1.74309			−0.871543	+	0.490318i	$0.836880\pi$
$758$		0			0
$759$	48.3903	+	8.43879i	1.75646	+	0.306309i
$760$		0			0
$761$	2.45259	+	0.892671i	0.0889064	+	0.0323593i	0.386090	−	0.922461i	$-0.373825\pi$
$761$	2.45259	+	0.892671i	0.0889064	+	0.0323593i	−0.297184	+	0.954820i	$0.596047\pi$
$762$		0			0
$763$	−0.401715	+	2.27824i	−0.0145431	+	0.0824777i
$764$		0			0
$765$	−1.48679	+	0.547484i	−0.0537551	+	0.0197943i
$766$		0			0
$767$	47.5912	−	17.3218i	1.71842	−	0.625453i
$768$		0			0
$769$	−31.9317	+	26.7938i	−1.15148	+	0.966211i	−0.999753	−	0.0222112i	$-0.992929\pi$
$769$	−31.9317	+	26.7938i	−1.15148	+	0.966211i	−0.151732	+	0.988422i	$0.548485\pi$
$770$		0			0
$771$	0.0411930	+	21.9226i	0.00148353	+	0.789525i
$772$		0			0
$773$	−13.9807	−	24.2153i	−0.502852	−	0.870965i	−0.999995	−	0.00329613i	$-0.998951\pi$
$773$	−13.9807	−	24.2153i	−0.502852	−	0.870965i	0.497143	−	0.867669i	$-0.334383\pi$
$774$		0			0
$775$	−9.13584	+	15.8237i	−0.328169	+	0.568405i
$776$		0			0
$777$	1.07331	−	2.96624i	0.0385049	−	0.106413i
$778$		0			0
$779$	0.773320	+	4.38572i	0.0277071	+	0.157135i
$780$		0			0
$781$	−5.28538	−	4.43496i	−0.189126	−	0.158695i
$782$		0			0
$783$	−6.58757	−	17.7866i	−0.235420	−	0.635640i
$784$		0			0
$785$	−0.628293	−	0.527200i	−0.0224247	−	0.0188166i
$786$		0			0
$787$	6.64060	+	37.6607i	0.236712	+	1.34246i	0.838978	+	0.544165i	$0.183153\pi$
$787$	6.64060	+	37.6607i	0.236712	+	1.34246i	−0.602266	+	0.798295i	$0.705736\pi$
$788$		0			0
$789$	3.23938	+	3.84584i	0.115325	+	0.136916i
$790$		0			0
$791$	4.32504	−	7.49120i	0.153781	−	0.266356i
$792$		0			0
$793$	12.9135	+	22.3668i	0.458572	+	0.794270i
$794$		0			0
$795$	−2.94486	+	1.70760i	−0.104444	+	0.0605624i
$796$		0			0
$797$	−0.467636	+	0.392393i	−0.0165645	+	0.0138993i	−0.651032	−	0.759050i	$-0.725664\pi$
$797$	−0.467636	+	0.392393i	−0.0165645	+	0.0138993i	0.634468	+	0.772949i	$0.281219\pi$
$798$		0			0
$799$	14.8121	−	5.39117i	0.524016	−	0.190726i
$800$		0			0
$801$	21.5925	+	7.76725i	0.762932	+	0.274442i
$802$		0			0
$803$	−10.9854	+	62.3012i	−0.387666	+	2.19856i
$804$		0			0
$805$	3.02496	+	1.10100i	0.106616	+	0.0388050i
$806$		0			0
$807$	−4.18457	+	5.00605i	−0.147304	+	0.176221i
$808$		0			0
$809$	−5.91527			−0.207970			−0.103985	−	0.994579i	$-0.533159\pi$
$809$	−5.91527			−0.207970			−0.103985	+	0.994579i	$0.533159\pi$
$810$		0			0
$811$	−29.7972			−1.04632			−0.523160	−	0.852234i	$-0.675247\pi$
$811$	−29.7972			−1.04632			−0.523160	+	0.852234i	$0.675247\pi$
$812$		0			0
$813$	11.8807	−	14.2130i	0.416675	−	0.498473i
$814$		0			0
$815$	−3.10111	−	1.12871i	−0.108627	−	0.0395370i
$816$		0			0
$817$	−0.236573	+	1.34167i	−0.00827663	+	0.0469391i
$818$		0			0
$819$	−22.5978	+	19.1070i	−0.789630	+	0.667651i
$820$		0			0
$821$	5.11604	−	1.86209i	0.178551	−	0.0649873i	−0.251198	−	0.967936i	$-0.580824\pi$
$821$	5.11604	−	1.86209i	0.178551	−	0.0649873i	0.429749	+	0.902949i	$0.358602\pi$
$822$		0			0
$823$	−8.42781	+	7.07177i	−0.293775	+	0.246507i	−0.777748	−	0.628577i	$-0.783638\pi$
$823$	−8.42781	+	7.07177i	−0.293775	+	0.246507i	0.483973	+	0.875083i	$0.339193\pi$
$824$		0			0
$825$	31.3852	−	18.1990i	1.09269	−	0.633607i
$826$		0			0
$827$	14.9870	+	25.9582i	0.521148	+	0.902654i	0.999698	+	0.0245939i	$0.00782928\pi$
$827$	14.9870	+	25.9582i	0.521148	+	0.902654i	−0.478550	+	0.878060i	$0.658837\pi$
$828$		0			0
$829$	9.45799	−	16.3817i	0.328489	−	0.568960i	−0.653723	−	0.756734i	$-0.726794\pi$
$829$	9.45799	−	16.3817i	0.328489	−	0.568960i	0.982212	+	0.187774i	$0.0601271\pi$
$830$		0			0
$831$	−8.83490	−	10.4889i	−0.306479	−	0.363857i
$832$		0			0
$833$	1.16996	+	6.63517i	0.0405367	+	0.229895i
$834$		0			0
$835$	−3.09241	−	2.59484i	−0.107017	−	0.0897982i
$836$		0			0
$837$	−6.47091	+	18.0954i	−0.223667	+	0.625469i
$838$		0			0
$839$	3.39946	+	2.85248i	0.117362	+	0.0984786i	0.699580	−	0.714554i	$-0.253370\pi$
$839$	3.39946	+	2.85248i	0.117362	+	0.0984786i	−0.582218	+	0.813033i	$0.697815\pi$
$840$		0			0
$841$	−2.72204	−	15.4375i	−0.0938635	−	0.532327i
$842$		0			0
$843$	−15.9263	+	44.0144i	−0.548532	+	1.51594i
$844$		0			0
$845$	−1.47041	+	2.54682i	−0.0505836	+	0.0876133i
$846$		0			0
$847$	−6.87506	−	11.9079i	−0.236230	−	0.409162i
$848$		0			0
$849$	0.0400636	+	21.3216i	0.00137498	+	0.731755i
$850$		0			0
$851$	4.73443	−	3.97266i	0.162294	−	0.136181i
$852$		0			0
$853$	40.1208	−	14.6028i	1.37371	−	0.499990i	0.453445	−	0.891284i	$-0.350195\pi$
$853$	40.1208	−	14.6028i	1.37371	−	0.499990i	0.920265	+	0.391295i	$0.127973\pi$
$854$		0			0
$855$	0.310992	+	0.258968i	0.0106357	+	0.00885652i
$856$		0			0
$857$	6.21214	−	35.2308i	0.212203	−	1.20346i	−0.673492	−	0.739194i	$-0.735207\pi$
$857$	6.21214	−	35.2308i	0.212203	−	1.20346i	0.885695	−	0.464267i	$-0.153682\pi$
$858$		0			0
$859$	−30.4608	−	11.0868i	−1.03931	−	0.378277i	−0.234690	−	0.972070i	$-0.575407\pi$
$859$	−30.4608	−	11.0868i	−1.03931	−	0.378277i	−0.804618	+	0.593793i	$0.797630\pi$
$860$		0			0
$861$	27.1088	+	4.72751i	0.923866	+	0.161113i
$862$		0			0
$863$	14.4214			0.490910			0.245455	−	0.969408i	$-0.421063\pi$
$863$	14.4214			0.490910			0.245455	+	0.969408i	$0.421063\pi$
$864$		0			0
$865$	−2.45044			−0.0833174
$866$		0			0
$867$	−7.33665	−	20.0400i	−0.249166	−	0.680596i
$868$		0			0
$869$	34.9275	+	12.7126i	1.18483	+	0.431244i
$870$		0			0
$871$	−5.14050	+	29.1532i	−0.174179	+	0.987820i
$872$		0			0
$873$	−29.2776	−	50.2730i	−0.990896	−	1.70148i
$874$		0			0
$875$	4.49537	−	1.63618i	0.151971	−	0.0553130i
$876$		0			0
$877$	20.7086	−	17.3766i	0.699279	−	0.586765i	−0.222289	−	0.974981i	$-0.571353\pi$
$877$	20.7086	−	17.3766i	0.699279	−	0.586765i	0.921568	+	0.388216i	$0.126908\pi$
$878$		0			0
$879$	22.7045	+	13.0516i	0.765804	+	0.440221i
$880$		0			0
$881$	7.82153	+	13.5473i	0.263514	+	0.456419i	0.967173	−	0.254118i	$-0.0817852\pi$
$881$	7.82153	+	13.5473i	0.263514	+	0.456419i	−0.703659	+	0.710538i	$0.748452\pi$
$882$		0			0
$883$	−28.2946	+	49.0077i	−0.952189	+	1.64924i	−0.211516	+	0.977375i	$0.567840\pi$
$883$	−28.2946	+	49.0077i	−0.952189	+	1.64924i	−0.740673	+	0.671865i	$0.765493\pi$
$884$		0			0
$885$	−4.21327	+	0.751079i	−0.141628	+	0.0252472i
$886$		0			0
$887$	−7.50425	−	42.5587i	−0.251968	−	1.42898i	−0.803737	−	0.594985i	$-0.797158\pi$
$887$	−7.50425	−	42.5587i	−0.251968	−	1.42898i	0.551769	−	0.833997i	$-0.313953\pi$
$888$		0			0
$889$	−28.3965	−	23.8275i	−0.952388	−	0.799149i
$890$		0			0
$891$	29.0457	−	24.7466i	0.973067	−	0.829043i
$892$		0			0
$893$	−3.08429	−	2.58803i	−0.103212	−	0.0866050i
$894$		0			0
$895$	−0.610518	−	3.46242i	−0.0204074	−	0.115736i
$896$		0			0
$897$	−57.0800	+	10.1754i	−1.90584	+	0.339745i
$898$		0			0
$899$	6.75011	−	11.6915i	0.225129	−	0.389935i
$900$		0			0
$901$	8.70598	+	15.0792i	0.290038	+	0.502361i
$902$		0			0
$903$	7.29830	+	4.19541i	0.242872	+	0.139615i
$904$		0			0
$905$	−1.44729	+	1.21442i	−0.0481095	+	0.0403686i
$906$		0			0
$907$	30.4072	−	11.0673i	1.00965	−	0.367484i	0.216353	−	0.976315i	$-0.430584\pi$
$907$	30.4072	−	11.0673i	1.00965	−	0.367484i	0.793300	+	0.608831i	$0.208361\pi$
$908$		0			0
$909$	47.6940	−	0.179236i	1.58191	−	0.00594489i
$910$		0			0
$911$	−5.78870	+	32.8294i	−0.191788	+	1.08769i	0.725131	+	0.688611i	$0.241779\pi$
$911$	−5.78870	+	32.8294i	−0.191788	+	1.08769i	−0.916919	+	0.399074i	$0.869332\pi$
$912$		0			0
$913$	26.4430	+	9.62448i	0.875137	+	0.318524i
$914$		0			0
$915$	−0.750297	−	2.04943i	−0.0248040	−	0.0677522i
$916$		0			0
$917$	5.76736			0.190455
$918$		0			0
$919$	41.9853			1.38497			0.692484	−	0.721434i	$-0.256517\pi$
$919$	41.9853			1.38497			0.692484	+	0.721434i	$0.256517\pi$
$920$		0			0
$921$	−34.7437	−	6.05897i	−1.14485	−	0.199650i
$922$		0			0
$923$	7.65282	+	2.78540i	0.251896	+	0.0916825i
$924$		0			0
$925$	0.792661	−	4.49540i	0.0260625	−	0.147808i
$926$		0			0
$927$	7.89891	−	45.8028i	0.259434	−	1.50436i
$928$		0			0
$929$	6.87308	−	2.50160i	0.225499	−	0.0820748i	−0.226800	−	0.973941i	$-0.572826\pi$
$929$	6.87308	−	2.50160i	0.225499	−	0.0820748i	0.452299	+	0.891867i	$0.350604\pi$
$930$		0			0
$931$	1.31833	−	1.10621i	0.0432065	−	0.0362546i
$932$		0			0
$933$	−0.0879898	−	46.8276i	−0.00288066	−	1.53307i
$934$		0			0
$935$	1.11958	+	1.93917i	0.0366142	+	0.0634177i
$936$		0			0
$937$	0.445689	−	0.771957i	0.0145600	−	0.0252187i	−0.858654	−	0.512556i	$-0.828699\pi$
$937$	0.445689	−	0.771957i	0.0145600	−	0.0252187i	0.873214	+	0.487338i	$0.162032\pi$
$938$		0			0
$939$	−10.5350	+	29.1147i	−0.343796	+	0.950122i
$940$		0			0
$941$	−0.127316	−	0.722042i	−0.00415037	−	0.0235379i	0.982662	−	0.185405i	$-0.0593596\pi$
$941$	−0.127316	−	0.722042i	−0.00415037	−	0.0235379i	−0.986813	+	0.161867i	$0.948248\pi$
$942$		0			0
$943$	41.3010	+	34.6556i	1.34495	+	1.12854i
$944$		0			0
$945$	2.15857	−	1.26253i	0.0702183	−	0.0410700i
$946$		0			0
$947$	−14.1216	−	11.8494i	−0.458890	−	0.385054i	0.383833	−	0.923403i	$-0.374604\pi$
$947$	−14.1216	−	11.8494i	−0.458890	−	0.385054i	−0.842722	+	0.538348i	$0.819048\pi$
$948$		0			0
$949$	−12.9667	−	73.5376i	−0.420916	−	2.38713i
$950$		0			0
$951$	−33.0592	−	39.2484i	−1.07202	−	1.27272i
$952$		0			0
$953$	−20.7956	+	36.0191i	−0.673636	+	1.16677i	0.303230	+	0.952918i	$0.401935\pi$
$953$	−20.7956	+	36.0191i	−0.673636	+	1.16677i	−0.976866	+	0.213854i	$0.931398\pi$
$954$		0			0
$955$	1.30229	+	2.25563i	0.0421410	+	0.0729904i
$956$		0			0
$957$	−23.1893	+	13.4465i	−0.749604	+	0.434664i
$958$		0			0
$959$	6.94694	−	5.82917i	0.224328	−	0.188234i
$960$		0			0
$961$	16.2770	−	5.92434i	0.525064	−	0.191108i
$962$		0			0
$963$	3.31563	+	18.3993i	0.106845	+	0.592909i
$964$		0			0
$965$	−0.532205	+	3.01828i	−0.0171323	+	0.0971620i
$966$		0			0
$967$	−9.89319	−	3.60083i	−0.318143	−	0.115795i	0.178012	−	0.984028i	$-0.443033\pi$
$967$	−9.89319	−	3.60083i	−0.318143	−	0.115795i	−0.496156	+	0.868234i	$0.665256\pi$
$968$		0			0
$969$	1.32759	−	1.58822i	0.0426485	−	0.0510208i
$970$		0			0
$971$	59.7428			1.91724			0.958619	−	0.284694i	$-0.0918919\pi$
$971$	59.7428			1.91724			0.958619	+	0.284694i	$0.0918919\pi$
$972$		0			0
$973$	42.9502			1.37692
$974$		0			0
$975$	−27.4646	+	32.8562i	−0.879571	+	1.05224i
$976$		0			0
$977$	−26.8889	−	9.78675i	−0.860252	−	0.313106i	−0.126039	−	0.992025i	$-0.540226\pi$
$977$	−26.8889	−	9.78675i	−0.860252	−	0.313106i	−0.734213	+	0.678919i	$0.762449\pi$
$978$		0			0
$979$	5.63145	−	31.9375i	0.179982	−	1.02073i
$980$		0			0
$981$	0.624436	+	3.46515i	0.0199367	+	0.110634i
$982$		0			0
$983$	−5.30199	+	1.92977i	−0.169107	+	0.0615500i	−0.425186	−	0.905106i	$-0.639791\pi$
$983$	−5.30199	+	1.92977i	−0.169107	+	0.0615500i	0.256079	+	0.966656i	$0.417569\pi$
$984$		0			0
$985$	0.579028	−	0.485862i	0.0184494	−	0.0154809i
$986$		0			0
$987$	−21.5222	+	12.4798i	−0.685059	+	0.397237i
$988$		0			0
$989$	8.24672	+	14.2837i	0.262231	+	0.454197i
$990$		0			0
$991$	3.95024	−	6.84201i	0.125483	−	0.217344i	−0.796438	−	0.604720i	$-0.793285\pi$
$991$	3.95024	−	6.84201i	0.125483	−	0.217344i	0.921922	+	0.387376i	$0.126618\pi$
$992$		0			0
$993$	−32.9741	−	39.1474i	−1.04640	−	1.24230i
$994$		0			0
$995$	−0.608297	−	3.44982i	−0.0192843	−	0.109367i
$996$		0			0
$997$	−29.5309	−	24.7794i	−0.935254	−	0.784771i	0.0414991	−	0.999139i	$-0.486787\pi$
$997$	−29.5309	−	24.7794i	−0.935254	−	0.784771i	−0.976753	+	0.214367i	$0.931231\pi$
$998$		0			0
$999$	−0.0270637	−	4.80099i	−0.000856257	−	0.151897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.97.7	yes	48
4.3	odd	2	inner	864.2.y.a.97.2	✓	48
27.22	even	9	inner	864.2.y.a.481.7	yes	48
108.103	odd	18	inner	864.2.y.a.481.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.97.2	✓	48	4.3	odd	2	inner
864.2.y.a.97.7	yes	48	1.1	even	1	trivial
864.2.y.a.481.2	yes	48	108.103	odd	18	inner
864.2.y.a.481.7	yes	48	27.22	even	9	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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11085 - 1.32892i) q^{3} +(-0.229433 - 0.0835067i) q^{5} +(0.342276 - 1.94115i) q^{7} +(-0.532044 - 2.95244i) q^{9} +O(q^{10})\)	\(q+(1.11085 - 1.32892i) q^{3} +(-0.229433 - 0.0835067i) q^{5} +(0.342276 - 1.94115i) q^{7} +(-0.532044 - 2.95244i) q^{9} +(-3.98411 + 1.45010i) q^{11} +(3.83365 - 3.21681i) q^{13} +(-0.365838 + 0.212134i) q^{15} +(1.08154 + 1.87328i) q^{17} +(0.276255 - 0.478488i) q^{19} +(-2.19941 - 2.61117i) q^{21} +(-1.16152 - 6.58733i) q^{23} +(-3.78456 - 3.17562i) q^{25} +(-4.51457 - 2.57267i) q^{27} +(2.79626 + 2.34634i) q^{29} +(-0.642226 - 3.64224i) q^{31} +(-2.49867 + 6.90538i) q^{33} +(-0.240628 + 0.416780i) q^{35} +(0.461983 + 0.800178i) q^{37} +(-0.0162873 - 8.66799i) q^{39} +(-6.17451 + 5.18103i) q^{41} +(-2.31707 + 0.843345i) q^{43} +(-0.124481 + 0.721817i) q^{45} +(1.26541 - 7.17649i) q^{47} +(2.92695 + 1.06532i) q^{49} +(3.69085 + 0.643648i) q^{51} +8.04964 q^{53} +1.03518 q^{55} +(-0.328994 - 0.898647i) q^{57} +(9.50973 + 3.46126i) q^{59} +(-0.896160 + 5.08238i) q^{61} +(-5.91323 + 0.0222222i) q^{63} +(-1.14819 + 0.417907i) q^{65} +(-4.53138 + 3.80228i) q^{67} +(-10.0443 - 5.77394i) q^{69} +(0.813668 + 1.40931i) q^{71} +(7.46053 - 12.9220i) q^{73} +(-8.42419 + 1.50174i) q^{75} +(1.45118 + 8.23007i) q^{77} +(-6.71569 - 5.63513i) q^{79} +(-8.43386 + 3.14166i) q^{81} +(-5.08434 - 4.26627i) q^{83} +(-0.0917088 - 0.520106i) q^{85} +(6.22431 - 1.10958i) q^{87} +(-3.82450 + 6.62423i) q^{89} +(-4.93214 - 8.54272i) q^{91} +(-5.55365 - 3.19250i) q^{93} +(-0.103339 + 0.0867117i) q^{95} +(18.2228 - 6.63256i) q^{97} +(6.40105 + 10.9913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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