LMFDB - Embedded newform 729.2.g.c.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.1
Character	$\chi$	$=$	729.28
Dual form			729.2.g.c.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.81786 + 1.19562i) q^{2} +(1.08293 - 2.51052i) q^{4} +(-0.443651 + 0.470242i) q^{5} +(1.81697 + 0.212373i) q^{7} +(0.277373 + 1.57306i) q^{8} +(0.244261 - 1.38527i) q^{10} +(0.346986 - 1.15901i) q^{11} +(0.310113 - 5.32444i) q^{13} +(-3.55691 + 1.78635i) q^{14} +(1.36753 + 1.44950i) q^{16} +(-6.43434 + 2.34191i) q^{17} +(-5.97823 - 2.17590i) q^{19} +(0.700110 + 1.62304i) q^{20} +(0.754974 + 2.52179i) q^{22} +(3.09558 - 0.361822i) q^{23} +(0.266422 + 4.57429i) q^{25} +(5.80229 + 10.0499i) q^{26} +(2.50083 - 4.33156i) q^{28} +(-5.26023 - 2.64179i) q^{29} +(-1.65611 - 2.22454i) q^{31} +(-7.32759 - 1.73667i) q^{32} +(8.89668 - 11.9503i) q^{34} +(-0.905967 + 0.760197i) q^{35} +(-1.09453 - 0.918418i) q^{37} +(13.4691 - 3.19224i) q^{38} +(-0.862777 - 0.567457i) q^{40} +(-0.931903 - 0.612922i) q^{41} +(-9.37473 + 2.22185i) q^{43} +(-2.53397 - 2.12625i) q^{44} +(-5.19473 + 4.35890i) q^{46} +(3.64407 - 4.89483i) q^{47} +(-3.55504 - 0.842559i) q^{49} +(-5.95346 - 7.99688i) q^{50} +(-13.0313 - 6.54456i) q^{52} +(4.26135 - 7.38088i) q^{53} +(0.391077 + 0.677365i) q^{55} +(0.169902 + 2.91711i) q^{56} +(12.7209 - 1.48687i) q^{58} +(-0.598878 - 2.00039i) q^{59} +(-1.42194 - 3.29643i) q^{61} +(5.67029 + 2.06382i) q^{62} +(11.6517 - 4.24088i) q^{64} +(2.36619 + 2.50802i) q^{65} +(1.09003 - 0.547434i) q^{67} +(-1.08855 + 18.6897i) q^{68} +(0.738011 - 2.46513i) q^{70} +(1.41528 - 8.02646i) q^{71} +(1.11524 + 6.32482i) q^{73} +(3.08778 + 0.360910i) q^{74} +(-11.9367 + 12.6521i) q^{76} +(0.876607 - 2.03220i) q^{77} +(11.9127 - 7.83511i) q^{79} -1.28832 q^{80} +2.42689 q^{82} +(-5.61402 + 3.69240i) q^{83} +(1.75334 - 4.06469i) q^{85} +(14.3854 - 15.2477i) q^{86} +(1.91944 + 0.224351i) q^{88} +(-2.70557 - 15.3441i) q^{89} +(1.69423 - 9.60848i) q^{91} +(2.44395 - 8.16337i) q^{92} +(-0.772019 + 13.2550i) q^{94} +(3.67544 - 1.84588i) q^{95} +(2.55920 + 2.71259i) q^{97} +(7.46994 - 2.71884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	−1.81786	+	1.19562i	−1.28542	+	0.845434i	−0.993809	−	0.111102i	$-0.964562\pi$
$2$	−1.81786	+	1.19562i	−1.28542	+	0.845434i	−0.291612	+	0.956537i	$0.594192\pi$
$3$		0			0
$3$		0			0
$4$	1.08293	−	2.51052i	0.541467	−	1.25526i
$5$	−0.443651	+	0.470242i	−0.198407	+	0.210299i	−0.818937	−	0.573884i	$-0.805436\pi$
$5$	−0.443651	+	0.470242i	−0.198407	+	0.210299i	0.620530	+	0.784183i	$0.286918\pi$
$6$		0			0
$7$	1.81697	+	0.212373i	0.686750	+	0.0802696i	0.452310	−	0.891861i	$-0.350600\pi$
$7$	1.81697	+	0.212373i	0.686750	+	0.0802696i	0.234440	+	0.972131i	$0.424674\pi$
$8$	0.277373	+	1.57306i	0.0980662	+	0.556161i
$9$		0			0
$10$	0.244261	−	1.38527i	0.0772422	−	0.438062i
$11$	0.346986	−	1.15901i	0.104620	−	0.349456i	−0.889610	−	0.456720i	$-0.849024\pi$
$11$	0.346986	−	1.15901i	0.104620	−	0.349456i	0.994231	+	0.107264i	$0.0342092\pi$
$12$		0			0
$13$	0.310113	−	5.32444i	0.0860099	−	1.47673i	−0.628883	−	0.777500i	$-0.716488\pi$
$13$	0.310113	−	5.32444i	0.0860099	−	1.47673i	0.714893	−	0.699233i	$-0.246475\pi$
$14$	−3.55691	+	1.78635i	−0.950625	+	0.477422i
$15$		0			0
$16$	1.36753	+	1.44950i	0.341884	+	0.362375i
$17$	−6.43434	+	2.34191i	−1.56056	+	0.567996i	−0.970864	−	0.239631i	$-0.922973\pi$
$17$	−6.43434	+	2.34191i	−1.56056	+	0.567996i	−0.589693	+	0.807628i	$0.700751\pi$
$18$		0			0
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.451909	−	0.892064i	$-0.649257\pi$
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.919590	+	0.392879i	$0.871479\pi$
$20$	0.700110	+	1.62304i	0.156549	+	0.362922i
$21$		0			0
$22$	0.754974	+	2.52179i	0.160961	+	0.537648i
$23$	3.09558	−	0.361822i	0.645474	−	0.0754451i	0.212944	−	0.977064i	$-0.431695\pi$
$23$	3.09558	−	0.361822i	0.645474	−	0.0754451i	0.432530	+	0.901619i	$0.357621\pi$
$24$		0			0
$25$	0.266422	+	4.57429i	0.0532845	+	0.914859i
$26$	5.80229	+	10.0499i	1.13792	+	1.97094i
$27$		0			0
$28$	2.50083	−	4.33156i	0.472612	−	0.818588i
$29$	−5.26023	−	2.64179i	−0.976800	−	0.490568i	−0.112559	−	0.993645i	$-0.535905\pi$
$29$	−5.26023	−	2.64179i	−0.976800	−	0.490568i	−0.864241	+	0.503077i	$0.832201\pi$
$30$		0			0
$31$	−1.65611	−	2.22454i	−0.297446	−	0.399540i	0.628125	−	0.778112i	$-0.283822\pi$
$31$	−1.65611	−	2.22454i	−0.297446	−	0.399540i	−0.925572	+	0.378572i	$0.876415\pi$
$32$	−7.32759	−	1.73667i	−1.29535	−	0.307003i
$33$		0			0
$34$	8.89668	−	11.9503i	1.52577	−	2.04946i
$35$	−0.905967	+	0.760197i	−0.153136	+	0.128497i
$36$		0			0
$37$	−1.09453	−	0.918418i	−0.179939	−	0.150987i	0.548369	−	0.836236i	$-0.315249\pi$
$37$	−1.09453	−	0.918418i	−0.179939	−	0.150987i	−0.728309	+	0.685249i	$0.759693\pi$
$38$	13.4691	−	3.19224i	2.18498	−	0.517850i
$39$		0			0
$40$	−0.862777	−	0.567457i	−0.136417	−	0.0897229i
$41$	−0.931903	−	0.612922i	−0.145539	−	0.0957224i	0.474651	−	0.880174i	$-0.342574\pi$
$41$	−0.931903	−	0.612922i	−0.145539	−	0.0957224i	−0.620190	+	0.784452i	$0.712945\pi$
$42$		0			0
$43$	−9.37473	+	2.22185i	−1.42963	+	0.338829i	−0.871285	−	0.490777i	$-0.836713\pi$
$43$	−9.37473	+	2.22185i	−1.42963	+	0.338829i	−0.558348	+	0.829607i	$0.688565\pi$
$44$	−2.53397	−	2.12625i	−0.382010	−	0.320545i
$45$		0			0
$46$	−5.19473	+	4.35890i	−0.765922	+	0.642685i
$47$	3.64407	−	4.89483i	0.531542	−	0.713984i	−0.452532	−	0.891748i	$-0.649479\pi$
$47$	3.64407	−	4.89483i	0.531542	−	0.713984i	0.984073	+	0.177764i	$0.0568864\pi$
$48$		0			0
$49$	−3.55504	−	0.842559i	−0.507862	−	0.120366i
$50$	−5.95346	−	7.99688i	−0.841946	−	1.13093i
$51$		0			0
$52$	−13.0313	−	6.54456i	−1.80711	−	0.907567i
$53$	4.26135	−	7.38088i	0.585342	−	1.01384i	−0.409491	−	0.912314i	$-0.634294\pi$
$53$	4.26135	−	7.38088i	0.585342	−	1.01384i	0.994833	−	0.101528i	$-0.0323731\pi$
$54$		0			0
$55$	0.391077	+	0.677365i	0.0527328	+	0.0913359i
$56$	0.169902	+	2.91711i	0.0227042	+	0.389815i
$57$		0			0
$58$	12.7209	−	1.48687i	1.67034	−	0.195235i
$59$	−0.598878	−	2.00039i	−0.0779672	−	0.260429i	0.910115	−	0.414356i	$-0.135993\pi$
$59$	−0.598878	−	2.00039i	−0.0779672	−	0.260429i	−0.988082	+	0.153927i	$0.950808\pi$
$60$		0			0
$61$	−1.42194	−	3.29643i	−0.182061	−	0.422065i	0.802606	−	0.596510i	$-0.203446\pi$
$61$	−1.42194	−	3.29643i	−0.182061	−	0.422065i	−0.984667	+	0.174445i	$0.944187\pi$
$62$	5.67029	+	2.06382i	0.720128	+	0.262105i
$63$		0			0
$64$	11.6517	−	4.24088i	1.45646	−	0.530110i
$65$	2.36619	+	2.50802i	0.293490	+	0.311082i
$66$		0			0
$67$	1.09003	−	0.547434i	0.133168	−	0.0668796i	−0.380967	−	0.924588i	$-0.624409\pi$
$67$	1.09003	−	0.547434i	0.133168	−	0.0668796i	0.514136	+	0.857709i	$0.328113\pi$
$68$	−1.08855	+	18.6897i	−0.132006	+	2.26646i
$69$		0			0
$70$	0.738011	−	2.46513i	0.0882092	−	0.294639i
$71$	1.41528	−	8.02646i	0.167963	−	0.952565i	−0.777994	−	0.628272i	$-0.783763\pi$
$71$	1.41528	−	8.02646i	0.167963	−	0.952565i	0.945957	−	0.324293i	$-0.105126\pi$
$72$		0			0
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	0.977870	+	0.209215i	$0.0670909\pi$
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	−0.847341	+	0.531049i	$0.821798\pi$
$74$	3.08778	+	0.360910i	0.358947	+	0.0419549i
$75$		0			0
$76$	−11.9367	+	12.6521i	−1.36923	+	1.45130i
$77$	0.876607	−	2.03220i	0.0998986	−	0.231591i
$78$		0			0
$79$	11.9127	−	7.83511i	1.34028	−	0.881518i	0.341978	−	0.939708i	$-0.388903\pi$
$79$	11.9127	−	7.83511i	1.34028	−	0.881518i	0.998306	+	0.0581898i	$0.0185329\pi$
$80$	−1.28832			−0.144039
$81$		0			0
$82$	2.42689			0.268006
$83$	−5.61402	+	3.69240i	−0.616219	+	0.405294i	−0.818888	−	0.573954i	$-0.805409\pi$
$83$	−5.61402	+	3.69240i	−0.616219	+	0.405294i	0.202669	+	0.979247i	$0.435039\pi$
$84$		0			0
$85$	1.75334	−	4.06469i	0.190176	−	0.440878i
$86$	14.3854	−	15.2477i	1.55122	−	1.64420i
$87$		0			0
$88$	1.91944	+	0.224351i	0.204613	+	0.0239159i
$89$	−2.70557	−	15.3441i	−0.286790	−	1.62647i	−0.698820	−	0.715297i	$-0.746291\pi$
$89$	−2.70557	−	15.3441i	−0.286790	−	1.62647i	0.412030	−	0.911170i	$-0.364820\pi$
$90$		0			0
$91$	1.69423	−	9.60848i	0.177604	−	1.00724i
$92$	2.44395	−	8.16337i	0.254800	−	0.851090i
$93$		0			0
$94$	−0.772019	+	13.2550i	−0.0796276	+	1.36715i
$95$	3.67544	−	1.84588i	0.377093	−	0.189383i
$96$		0			0
$97$	2.55920	+	2.71259i	0.259847	+	0.275422i	0.844142	−	0.536120i	$-0.180110\pi$
$97$	2.55920	+	2.71259i	0.259847	+	0.275422i	−0.584295	+	0.811541i	$0.698629\pi$
$98$	7.46994	−	2.71884i	0.754578	−	0.274644i
$99$		0			0
$100$	11.7724	+	4.28480i	1.17724	+	0.428480i
$101$	−1.84200	−	4.27024i	−0.183286	−	0.424904i	0.801657	−	0.597784i	$-0.203952\pi$
$101$	−1.84200	−	4.27024i	−0.183286	−	0.424904i	−0.984943	+	0.172880i	$0.944693\pi$
$102$		0			0
$103$	−1.48234	−	4.95138i	−0.146060	−	0.487874i	0.853382	−	0.521286i	$-0.174548\pi$
$103$	−1.48234	−	4.95138i	−0.146060	−	0.487874i	−0.999442	+	0.0334127i	$0.989362\pi$
$104$	8.46168	−	0.989028i	0.829736	−	0.0969822i
$105$		0			0
$106$	1.07822	+	18.5124i	0.104726	+	1.79808i
$107$	6.49528	+	11.2502i	0.627922	+	1.08759i	0.987968	+	0.154659i	$0.0494278\pi$
$107$	6.49528	+	11.2502i	0.627922	+	1.08759i	−0.360046	+	0.932935i	$0.617239\pi$
$108$		0			0
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	−0.905443	−	0.424469i	$-0.860461\pi$
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	0.820322	+	0.571902i	$0.193794\pi$
$110$	−1.52080	−	0.763773i	−0.145002	−	0.0728229i
$111$		0			0
$112$	2.17693	+	2.92413i	0.205701	+	0.276304i
$113$	13.5138	+	3.20282i	1.27127	+	0.301296i	0.810244	−	0.586092i	$-0.199334\pi$
$113$	13.5138	+	3.20282i	1.27127	+	0.301296i	0.461023	+	0.887388i	$0.347483\pi$
$114$		0			0
$115$	−1.20321	+	1.61620i	−0.112200	+	0.150711i
$116$	−12.3288	+	10.3451i	−1.14470	+	0.960514i
$117$		0			0
$118$	3.48039	+	2.92040i	0.320396	+	0.268844i
$119$	−12.1884	+	2.88869i	−1.11731	+	0.264806i
$120$		0			0
$121$	7.96745	+	5.24027i	0.724314	+	0.476389i
$122$	6.52619	+	4.29234i	0.590853	+	0.388610i
$123$		0			0
$124$	−7.37823	+	1.74867i	−0.662584	+	0.157035i
$125$	−4.74544	−	3.98190i	−0.424445	−	0.356152i
$126$		0			0
$127$	−8.72949	+	7.32491i	−0.774617	+	0.649981i	−0.941887	−	0.335930i	$-0.890949\pi$
$127$	−8.72949	+	7.32491i	−0.774617	+	0.649981i	0.167270	+	0.985911i	$0.446505\pi$
$128$	−7.11678	+	9.55950i	−0.629041	+	0.844948i
$129$		0			0
$130$	−7.30006	−	1.73015i	−0.640258	−	0.151744i
$131$	−8.70702	−	11.6956i	−0.760736	−	1.02185i	−0.998720	−	0.0505763i	$-0.983894\pi$
$131$	−8.70702	−	11.6956i	−0.760736	−	1.02185i	0.237985	−	0.971269i	$-0.423513\pi$
$132$		0			0
$133$	−10.4002	−	5.22315i	−0.901808	−	0.452905i
$134$	−1.32700	+	2.29842i	−0.114635	+	0.198554i
$135$		0			0
$136$	−5.46868	−	9.47202i	−0.468935	−	0.812219i
$137$	0.0215606	+	0.370181i	0.00184204	+	0.0316267i	0.999104	−	0.0423242i	$-0.0134762\pi$
$137$	0.0215606	+	0.370181i	0.00184204	+	0.0316267i	−0.997262	+	0.0739509i	$0.976439\pi$
$138$		0			0
$139$	−14.8762	+	1.73878i	−1.26179	+	0.147482i	−0.720559	−	0.693394i	$-0.756115\pi$
$139$	−14.8762	+	1.73878i	−1.26179	+	0.147482i	−0.541228	+	0.840876i	$0.682040\pi$
$140$	0.927389	+	3.09770i	0.0783787	+	0.261803i
$141$		0			0
$142$	7.02385	+	16.2831i	0.589428	+	1.36645i
$143$	−6.06349	−	2.20693i	−0.507055	−	0.184553i
$144$		0			0
$145$	3.57599	−	1.30155i	0.296970	−	0.108088i
$146$	−9.58945	−	10.1642i	−0.793629	−	0.841197i
$147$		0			0
$148$	−3.49101	+	1.75325i	−0.286960	+	0.144116i
$149$	0.0581597	−	0.998563i	0.00476463	−	0.0818055i	−0.995088	−	0.0989987i	$-0.968436\pi$
$149$	0.0581597	−	0.998563i	0.00476463	−	0.0818055i	0.999852	+	0.0171933i	$0.00547306\pi$
$150$		0			0
$151$	−0.00563064	+	0.0188076i	−0.000458215	+	0.00153054i	−0.958218	−	0.286038i	$-0.907662\pi$
$151$	−0.00563064	+	0.0188076i	−0.000458215	+	0.00153054i	0.957760	+	0.287568i	$0.0928469\pi$
$152$	1.76462	−	10.0076i	0.143129	−	0.811727i
$153$		0			0
$154$	0.836205	+	4.74235i	0.0673833	+	0.382150i
$155$	1.78081	+	0.208147i	0.143038	+	0.0167188i
$156$		0			0
$157$	5.35582	−	5.67684i	0.427441	−	0.453061i	−0.477479	−	0.878643i	$-0.658449\pi$
$157$	5.35582	−	5.67684i	0.427441	−	0.453061i	0.904920	+	0.425582i	$0.139931\pi$
$158$	−12.2878	+	28.4862i	−0.977562	+	2.26624i
$159$		0			0
$160$	4.06755	−	2.67527i	0.321568	−	0.211498i
$161$	5.70142			0.449335
$162$		0			0
$163$	−15.3947			−1.20581			−0.602905	−	0.797813i	$-0.705990\pi$
$163$	−15.3947			−1.20581			−0.602905	+	0.797813i	$0.705990\pi$
$164$	−2.54795	+	1.67581i	−0.198961	+	0.130859i
$165$		0			0
$166$	5.79078	−	13.4245i	0.449452	−	1.04195i
$167$	−2.50809	+	2.65842i	−0.194082	+	0.205714i	−0.817105	−	0.576489i	$-0.804423\pi$
$167$	−2.50809	+	2.65842i	−0.194082	+	0.205714i	0.623024	+	0.782203i	$0.285904\pi$
$168$		0			0
$169$	−15.3414	−	1.79315i	−1.18010	−	0.137934i
$170$	1.67253	+	9.48537i	0.128277	+	0.727494i
$171$		0			0
$172$	−4.57421	+	25.9416i	−0.348780	+	1.97803i
$173$	−3.80949	+	12.7246i	−0.289630	+	0.967432i	0.682085	+	0.731273i	$0.261074\pi$
$173$	−3.80949	+	12.7246i	−0.289630	+	0.967432i	−0.971715	+	0.236158i	$0.924112\pi$
$174$		0			0
$175$	−0.487377	+	8.36794i	−0.0368422	+	0.632556i
$176$	2.15451	−	1.08203i	0.162402	−	0.0815614i
$177$		0			0
$178$	23.2641	+	24.6585i	1.74372	+	1.84823i
$179$	−0.392738	+	0.142945i	−0.0293546	+	0.0106842i	−0.356656	−	0.934236i	$-0.616083\pi$
$179$	−0.392738	+	0.142945i	−0.0293546	+	0.0106842i	0.327301	+	0.944920i	$0.393861\pi$
$180$		0			0
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.511717	−	0.859154i	$-0.670990\pi$
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.944252	+	0.329225i	$0.893213\pi$
$182$	8.40826	+	19.4925i	0.623262	+	1.44488i
$183$		0			0
$184$	1.42780	+	4.76918i	0.105259	+	0.351589i
$185$	0.917468	−	0.107237i	0.0674536	−	0.00788419i
$186$		0			0
$187$	0.481679	+	8.27010i	0.0352238	+	0.604770i
$188$	−8.34230	−	14.4493i	−0.608425	−	1.05382i
$189$		0			0
$190$	−4.47446	+	7.75000i	−0.324612	+	0.562244i
$191$	6.15645	+	3.09189i	0.445465	+	0.223721i	0.657368	−	0.753570i	$-0.271670\pi$
$191$	6.15645	+	3.09189i	0.445465	+	0.223721i	−0.211903	+	0.977291i	$0.567966\pi$
$192$		0			0
$193$	−5.22298	−	7.01568i	−0.375958	−	0.505000i	0.573365	−	0.819300i	$-0.305638\pi$
$193$	−5.22298	−	7.01568i	−0.375958	−	0.505000i	−0.949324	+	0.314300i	$0.898230\pi$
$194$	−7.89550	−	1.87127i	−0.566864	−	0.134349i
$195$		0			0
$196$	−5.96514	+	8.01257i	−0.426081	+	0.572326i
$197$	−6.47094	+	5.42976i	−0.461035	+	0.386855i	−0.843512	−	0.537111i	$-0.819516\pi$
$197$	−6.47094	+	5.42976i	−0.461035	+	0.386855i	0.382476	+	0.923965i	$0.375071\pi$
$198$		0			0
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	0.917561	−	0.397595i	$-0.130155\pi$
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	−0.232222	+	0.972663i	$0.574599\pi$
$200$	−7.12174	+	1.68788i	−0.503583	+	0.119351i
$201$		0			0
$202$	8.45410	+	5.56035i	0.594828	+	0.391225i
$203$	−8.99664	−	5.91718i	−0.631440	−	0.415305i
$204$		0			0
$205$	0.701662	−	0.166297i	0.0490062	−	0.0116147i
$206$	8.61468	+	7.22858i	0.600213	+	0.503639i
$207$		0			0
$208$	8.14187	−	6.83184i	0.564537	−	0.473703i
$209$	−4.59626	+	6.17384i	−0.317930	+	0.427054i
$210$		0			0
$211$	−5.52292	−	1.30896i	−0.380213	−	0.0901122i	0.0360651	−	0.999349i	$-0.488518\pi$
$211$	−5.52292	−	1.30896i	−0.380213	−	0.0901122i	−0.416278	+	0.909237i	$0.636666\pi$
$212$	−13.9151	−	18.6912i	−0.955694	−	1.28372i
$213$		0			0
$214$	−25.2585	−	12.6853i	−1.72663	−	0.867148i
$215$	3.11430	−	5.39413i	0.212393	−	0.367876i
$216$		0			0
$217$	−2.53667	−	4.39364i	−0.172200	−	0.298260i
$218$	−0.224859	−	3.86067i	−0.0152294	−	0.261478i
$219$		0			0
$220$	2.12405	−	0.248266i	0.143204	−	0.0167381i
$221$	10.4740	+	34.9855i	0.704555	+	2.35338i
$222$		0			0
$223$	2.98361	+	6.91679i	0.199797	+	0.463183i	0.988429	−	0.151683i	$-0.0484694\pi$
$223$	2.98361	+	6.91679i	0.199797	+	0.463183i	−0.788632	+	0.614866i	$0.789210\pi$
$224$	−12.9452	−	4.71166i	−0.864936	−	0.314811i
$225$		0			0
$226$	−28.3955	+	10.3351i	−1.88884	+	0.687481i
$227$	9.36249	+	9.92366i	0.621410	+	0.658656i	0.959254	−	0.282546i	$-0.0911789\pi$
$227$	9.36249	+	9.92366i	0.621410	+	0.658656i	−0.337843	+	0.941202i	$0.609697\pi$
$228$		0			0
$229$	14.2932	−	7.17833i	0.944523	−	0.474357i	0.0912534	−	0.995828i	$-0.470913\pi$
$229$	14.2932	−	7.17833i	0.944523	−	0.474357i	0.853269	+	0.521471i	$0.174616\pi$
$230$	0.254909	−	4.37661i	0.0168082	−	0.288585i
$231$		0			0
$232$	2.69665	−	9.00742i	0.177043	−	0.591366i
$233$	−0.930605	+	5.27772i	−0.0609660	+	0.345755i	0.939032	+	0.343829i	$0.111724\pi$
$233$	−0.930605	+	5.27772i	−0.0609660	+	0.345755i	−0.999998	+	0.00192589i	$0.999387\pi$
$234$		0			0
$235$	0.685064	+	3.88519i	0.0446886	+	0.253442i
$236$	−5.67057	−	0.662795i	−0.369123	−	0.0431443i
$237$		0			0
$238$	18.7029	−	19.8239i	1.21233	−	1.28500i
$239$	−6.39415	+	14.8233i	−0.413603	+	0.958840i	0.576319	+	0.817225i	$0.304489\pi$
$239$	−6.39415	+	14.8233i	−0.413603	+	0.958840i	−0.989922	+	0.141615i	$0.954771\pi$
$240$		0			0
$241$	19.5404	−	12.8519i	1.25871	−	0.827864i	0.267938	−	0.963436i	$-0.413658\pi$
$241$	19.5404	−	12.8519i	1.25871	−	0.827864i	0.990767	+	0.135572i	$0.0432873\pi$
$242$	−20.7491			−1.33380
$243$		0			0
$244$	−9.81564			−0.628382
$245$	1.97340	−	1.29793i	0.126076	−	0.0829215i
$246$		0			0
$247$	−13.4394	+	31.1559i	−0.855125	+	1.98240i
$248$	3.03998	−	3.22219i	0.193039	−	0.204609i
$249$		0			0
$250$	13.3874	+	1.56476i	0.846693	+	0.0989643i
$251$	4.21745	+	23.9183i	0.266203	+	1.50971i	0.765588	+	0.643331i	$0.222448\pi$
$251$	4.21745	+	23.9183i	0.266203	+	1.50971i	−0.499385	+	0.866380i	$0.666441\pi$
$252$		0			0
$253$	0.654768	−	3.71337i	0.0411649	−	0.233458i
$254$	7.11114	−	23.7529i	0.446193	−	1.49039i
$255$		0			0
$256$	0.0658029	−	1.12979i	0.00411268	−	0.0706120i
$257$	8.60919	−	4.32370i	0.537027	−	0.269705i	−0.159547	−	0.987190i	$-0.551003\pi$
$257$	8.60919	−	4.32370i	0.537027	−	0.269705i	0.696573	+	0.717485i	$0.254707\pi$
$258$		0			0
$259$	−1.79368	−	1.90119i	−0.111454	−	0.118134i
$260$	8.85887	−	3.22437i	0.549404	−	0.199967i
$261$		0			0
$262$	29.8116	+	10.8505i	1.84177	+	0.670349i
$263$	2.63068	+	6.09861i	0.162215	+	0.376056i	0.979866	−	0.199658i	$-0.0639832\pi$
$263$	2.63068	+	6.09861i	0.162215	+	0.376056i	−0.817651	+	0.575715i	$0.804724\pi$
$264$		0			0
$265$	1.58025	+	5.27841i	0.0970740	+	0.324250i
$266$	25.1510	−	2.93972i	1.54210	−	0.180246i
$267$		0			0
$268$	−0.193914	−	3.32938i	−0.0118452	−	0.203374i
$269$	−14.6832	−	25.4321i	−0.895251	−	1.55062i	−0.833494	−	0.552529i	$-0.813663\pi$
$269$	−14.6832	−	25.4321i	−0.895251	−	1.55062i	−0.0617568	−	0.998091i	$-0.519670\pi$
$270$		0			0
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	−0.422799	−	0.906223i	$-0.638952\pi$
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	0.996212	−	0.0869568i	$-0.0277142\pi$
$272$	−12.1938	−	6.12395i	−0.739356	−	0.371319i
$273$		0			0
$274$	−0.481791	−	0.647158i	−0.0291061	−	0.0390963i
$275$	5.39412	+	1.27843i	0.325277	+	0.0770922i
$276$		0			0
$277$	8.38334	−	11.2608i	0.503706	−	0.676594i	−0.475441	−	0.879748i	$-0.657712\pi$
$277$	8.38334	−	11.2608i	0.503706	−	0.676594i	0.979147	+	0.203153i	$0.0651189\pi$
$278$	24.9640	−	20.9473i	1.49724	−	1.25633i
$279$		0			0
$280$	−1.44713	−	1.21428i	−0.0864824	−	0.0725673i
$281$	−21.4853	+	5.09210i	−1.28170	+	0.303769i	−0.814388	−	0.580321i	$-0.802927\pi$
$281$	−21.4853	+	5.09210i	−1.28170	+	0.303769i	−0.467316	+	0.884091i	$0.654779\pi$
$282$		0			0
$283$	−3.30559	−	2.17412i	−0.196497	−	0.129238i	0.447448	−	0.894310i	$-0.352333\pi$
$283$	−3.30559	−	2.17412i	−0.196497	−	0.129238i	−0.643945	+	0.765072i	$0.722703\pi$
$284$	−18.6180	−	12.2452i	−1.10477	−	0.726620i
$285$		0			0
$286$	13.6612	−	3.23777i	0.807806	−	0.191454i
$287$	−1.56307	−	1.31157i	−0.0922652	−	0.0774197i
$288$		0			0
$289$	22.8934	−	19.2099i	1.34667	−	1.12999i
$290$	−4.94447	+	6.64158i	−0.290349	+	0.390007i
$291$		0			0
$292$	17.0863	+	4.04954i	0.999902	+	0.236981i
$293$	4.76369	+	6.39875i	0.278298	+	0.373819i	0.919192	−	0.393811i	$-0.128843\pi$
$293$	4.76369	+	6.39875i	0.278298	+	0.373819i	−0.640894	+	0.767630i	$0.721436\pi$
$294$		0			0
$295$	1.20636	+	0.605857i	0.0702371	+	0.0352744i
$296$	1.14114	−	1.97650i	0.0663271	−	0.114882i
$297$		0			0
$298$	1.08818	+	1.88478i	0.0630366	+	0.109183i
$299$	−0.966516	−	16.5944i	−0.0558951	−	0.959682i
$300$		0			0
$301$	−17.5055	+	2.04610i	−1.00900	+	0.117935i
$302$	−0.0122512	−	0.0409218i	−0.000704976	−	0.00235478i
$303$		0			0
$304$	−5.02146	−	11.6411i	−0.288001	−	0.667661i
$305$	2.18097	+	0.793808i	0.124882	+	0.0454533i
$306$		0			0
$307$	1.95823	−	0.712736i	0.111762	−	0.0406780i	−0.285534	−	0.958369i	$-0.592171\pi$
$307$	1.95823	−	0.712736i	0.111762	−	0.0406780i	0.397296	+	0.917691i	$0.369949\pi$
$308$	−4.15259	−	4.40149i	−0.236616	−	0.250798i
$309$		0			0
$310$	−3.48613	+	1.75080i	−0.197999	+	0.0994387i
$311$	0.873011	−	14.9890i	0.0495039	−	0.849949i	−0.878584	−	0.477588i	$-0.841511\pi$
$311$	0.873011	−	14.9890i	0.0495039	−	0.849949i	0.928088	−	0.372361i	$-0.121452\pi$
$312$		0			0
$313$	−1.46009	+	4.87703i	−0.0825290	+	0.275666i	−0.989287	−	0.145986i	$-0.953364\pi$
$313$	−1.46009	+	4.87703i	−0.0825290	+	0.275666i	0.906758	+	0.421652i	$0.138550\pi$
$314$	−2.94876	+	16.7232i	−0.166408	+	0.943747i
$315$		0			0
$316$	−6.76955	−	38.3920i	−0.380817	−	2.15972i
$317$	27.5207	+	3.21671i	1.54572	+	0.180669i	0.845779	−	0.533533i	$-0.179136\pi$
$317$	27.5207	+	3.21671i	1.54572	+	0.180669i	0.699940	+	0.714202i	$0.253210\pi$
$318$		0			0
$319$	−4.88710	+	5.18002i	−0.273625	+	0.290025i
$320$	−3.17505	+	7.36060i	−0.177491	+	0.411470i
$321$		0			0
$322$	−10.3644	+	6.81676i	−0.577585	+	0.379883i
$323$	43.5617			2.42384
$324$		0			0
$325$	24.4382			1.35559
$326$	27.9855	−	18.4063i	1.54997	−	1.01943i
$327$		0			0
$328$	0.705679	−	1.63595i	0.0389646	−	0.0903301i
$329$	7.66069	−	8.11986i	0.422347	−	0.447662i
$330$		0			0
$331$	−27.0847	−	3.16575i	−1.48871	−	0.174005i	−0.667492	−	0.744617i	$-0.732632\pi$
$331$	−27.0847	−	3.16575i	−1.48871	−	0.174005i	−0.821220	+	0.570612i	$0.806706\pi$
$332$	3.19024	+	18.0928i	0.175087	+	0.992969i
$333$		0			0
$334$	1.38088	−	7.83136i	0.0755584	−	0.428513i
$335$	−0.226166	+	0.755448i	−0.0123568	+	0.0412745i
$336$		0			0
$337$	0.739519	−	12.6970i	0.0402842	−	0.691652i	−0.916353	−	0.400371i	$-0.868881\pi$
$337$	0.739519	−	12.6970i	0.0402842	−	0.691652i	0.956637	−	0.291281i	$-0.0940816\pi$
$338$	30.0324	−	15.0828i	1.63355	−	0.820397i
$339$		0			0
$340$	−8.30575	−	8.80358i	−0.450443	−	0.477441i
$341$	−3.15292	+	1.14757i	−0.170740	+	0.0621444i
$342$		0			0
$343$	−18.3136	−	6.66560i	−0.988840	−	0.359908i
$344$	−6.09541	−	14.1307i	−0.328642	−	0.761879i
$345$		0			0
$346$	−8.28871	−	27.6862i	−0.445604	−	1.48842i
$347$	−8.35624	+	0.976704i	−0.448586	+	0.0524322i	−0.337387	−	0.941366i	$-0.609543\pi$
$347$	−8.35624	+	0.976704i	−0.448586	+	0.0524322i	−0.111199	+	0.993798i	$0.535469\pi$
$348$		0			0
$349$	−1.75267	−	30.0922i	−0.0938184	−	1.61080i	−0.636783	−	0.771043i	$-0.719735\pi$
$349$	−1.75267	−	30.0922i	−0.0938184	−	1.61080i	0.542964	−	0.839756i	$-0.317302\pi$
$350$	−9.11893	−	15.7944i	−0.487427	−	0.844249i
$351$		0			0
$352$	−4.55540	+	7.89018i	−0.242803	+	0.420548i
$353$	20.7603	+	10.4262i	1.10496	+	0.554932i	0.905231	−	0.424919i	$-0.139698\pi$
$353$	20.7603	+	10.4262i	1.10496	+	0.554932i	0.199729	+	0.979851i	$0.435994\pi$
$354$		0			0
$355$	3.14649	+	4.22647i	0.166998	+	0.224318i
$356$	−41.4516	−	9.82421i	−2.19693	−	0.520682i
$357$		0			0
$358$	0.543034	−	0.729421i	0.0287002	−	0.0385511i
$359$	3.19290	−	2.67916i	0.168515	−	0.141401i	−0.554630	−	0.832097i	$-0.687140\pi$
$359$	3.19290	−	2.67916i	0.168515	−	0.141401i	0.723145	+	0.690696i	$0.242696\pi$
$360$		0			0
$361$	16.4498	+	13.8030i	0.865780	+	0.726476i
$362$	44.1325	−	10.4596i	2.31955	−	0.549744i
$363$		0			0
$364$	−22.2876	−	14.6588i	−1.16819	−	0.768328i
$365$	−3.46897	−	2.28158i	−0.181574	−	0.119423i
$366$		0			0
$367$	−11.4051	+	2.70306i	−0.595341	+	0.141098i	−0.517230	−	0.855846i	$-0.673037\pi$
$367$	−11.4051	+	2.70306i	−0.595341	+	0.141098i	−0.0781107	+	0.996945i	$0.524889\pi$
$368$	4.75778	+	3.99225i	0.248016	+	0.208110i
$369$		0			0
$370$	−1.53961	+	1.29189i	−0.0800407	+	0.0671621i
$371$	9.31026	−	12.5058i	0.483364	−	0.649271i
$372$		0			0
$373$	35.3913	+	8.38790i	1.83249	+	0.434309i	0.993885	−	0.110423i	$-0.0352207\pi$
$373$	35.3913	+	8.38790i	1.83249	+	0.434309i	0.838610	+	0.544733i	$0.183369\pi$
$374$	−10.7636	−	14.4580i	−0.556571	−	0.747604i
$375$		0			0
$376$	8.71063	+	4.37464i	0.449216	+	0.225605i
$377$	−15.6973	+	27.1885i	−0.808452	+	1.40028i
$378$		0			0
$379$	5.02516	+	8.70383i	0.258125	+	0.447086i	0.965740	−	0.259513i	$-0.0835620\pi$
$379$	5.02516	+	8.70383i	0.258125	+	0.447086i	−0.707615	+	0.706599i	$0.750229\pi$
$380$	−0.653855	−	11.2263i	−0.0335420	−	0.575895i
$381$		0			0
$382$	−14.8883	+	1.74019i	−0.761751	+	0.0890360i
$383$	0.0867894	+	0.289897i	0.00443473	+	0.0148130i	0.960178	−	0.279388i	$-0.0901316\pi$
$383$	0.0867894	+	0.289897i	0.00443473	+	0.0148130i	−0.955744	+	0.294201i	$0.904946\pi$
$384$		0			0
$385$	0.566721	+	1.31381i	0.0288828	+	0.0669578i
$386$	17.8828	+	6.50880i	0.910209	+	0.331289i
$387$		0			0
$388$	9.58146	−	3.48737i	0.486425	−	0.177044i
$389$	−5.16022	−	5.46952i	−0.261634	−	0.277315i	0.583218	−	0.812315i	$-0.301793\pi$
$389$	−5.16022	−	5.46952i	−0.261634	−	0.277315i	−0.844852	+	0.535000i	$0.820312\pi$
$390$		0			0
$391$	−19.0707	+	9.57766i	−0.964446	+	0.484363i
$392$	0.339325	−	5.82599i	0.0171385	−	0.294257i
$393$		0			0
$394$	5.27130	−	17.6074i	0.265564	−	0.887046i
$395$	−1.60068	+	9.07791i	−0.0805390	+	0.456759i
$396$		0			0
$397$	2.95983	+	16.7860i	0.148549	+	0.842466i	0.964448	+	0.264271i	$0.0851314\pi$
$397$	2.95983	+	16.7860i	0.148549	+	0.842466i	−0.815899	+	0.578195i	$0.803757\pi$
$398$	−27.2742	−	3.18790i	−1.36713	−	0.159795i
$399$		0			0
$400$	−6.26610	+	6.64168i	−0.313305	+	0.332084i
$401$	5.37775	−	12.4670i	0.268552	−	0.622574i	−0.729565	−	0.683911i	$-0.760277\pi$
$401$	5.37775	−	12.4670i	0.268552	−	0.622574i	0.998117	+	0.0613379i	$0.0195367\pi$
$402$		0			0
$403$	−12.3580	+	8.12800i	−0.615597	+	0.404884i
$404$	−12.7153			−0.632609
$405$		0			0
$406$	23.4293			1.16278
$407$	−1.44425	+	0.949896i	−0.0715886	+	0.0470846i
$408$		0			0
$409$	−0.266304	+	0.617363i	−0.0131679	+	0.0305266i	−0.924673	−	0.380762i	$-0.875662\pi$
$409$	−0.266304	+	0.617363i	−0.0131679	+	0.0305266i	0.911505	+	0.411288i	$0.134921\pi$
$410$	−1.07669	+	1.14123i	−0.0531741	+	0.0563613i
$411$		0			0
$412$	−14.0358	−	1.64055i	−0.691496	−	0.0808242i
$413$	−0.663313	−	3.76184i	−0.0326395	−	0.185108i
$414$		0			0
$415$	0.754343	−	4.27809i	0.0370292	−	0.210003i
$416$	−11.5192	+	38.4767i	−0.564774	+	1.88648i
$417$		0			0
$418$	0.973746	−	16.7186i	0.0476275	−	0.817733i
$419$	−17.7708	+	8.92485i	−0.868163	+	0.436008i	−0.826376	−	0.563119i	$-0.809601\pi$
$419$	−17.7708	+	8.92485i	−0.868163	+	0.436008i	−0.0417867	+	0.999127i	$0.513305\pi$
$420$		0			0
$421$	−8.61615	−	9.13258i	−0.419925	−	0.445095i	0.482529	−	0.875880i	$-0.339718\pi$
$421$	−8.61615	−	9.13258i	−0.419925	−	0.445095i	−0.902455	+	0.430785i	$0.858237\pi$
$422$	11.6049	−	4.22384i	0.564918	−	0.205613i
$423$		0			0
$424$	12.7926	+	4.65611i	0.621262	+	0.226121i
$425$	−12.4268	−	28.8086i	−0.602790	−	1.39742i
$426$		0			0
$427$	−1.88355	−	6.29150i	−0.0911515	−	0.304467i
$428$	35.2777	−	4.12338i	1.70521	−	0.199311i
$429$		0			0
$430$	0.787992	+	13.5293i	0.0380003	+	0.652441i
$431$	10.8013	+	18.7084i	0.520281	+	0.901153i	0.999722	+	0.0235787i	$0.00750603\pi$
$431$	10.8013	+	18.7084i	0.520281	+	0.901153i	−0.479441	+	0.877574i	$0.659161\pi$
$432$		0			0
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	−0.910067	−	0.414461i	$-0.863970\pi$
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	0.813968	+	0.580910i	$0.197303\pi$
$434$	9.86445	+	4.95412i	0.473509	+	0.237805i
$435$		0			0
$436$	2.90193	+	3.89797i	0.138977	+	0.186679i
$437$	−19.2934	−	4.57262i	−0.922928	−	0.218738i
$438$		0			0
$439$	−18.6380	+	25.0352i	−0.889544	+	1.19486i	0.0904630	+	0.995900i	$0.471165\pi$
$439$	−18.6380	+	25.0352i	−0.889544	+	1.19486i	−0.980007	+	0.198965i	$0.936242\pi$
$440$	−0.957063	+	0.803071i	−0.0456262	+	0.0382849i
$441$		0			0
$442$	−60.8697	−	51.0758i	−2.89528	−	2.42943i
$443$	1.55899	−	0.369487i	0.0740699	−	0.0175549i	−0.193414	−	0.981117i	$-0.561956\pi$
$443$	1.55899	−	0.369487i	0.0740699	−	0.0175549i	0.267484	+	0.963562i	$0.413808\pi$
$444$		0			0
$445$	8.41576	+	5.53513i	0.398945	+	0.262390i
$446$	−13.6937	−	9.00647i	−0.648414	−	0.426469i
$447$		0			0
$448$	22.0715	−	5.23103i	1.04278	−	0.247143i
$449$	8.04720	+	6.75241i	0.379771	+	0.318666i	0.812613	−	0.582804i	$-0.198045\pi$
$449$	8.04720	+	6.75241i	0.379771	+	0.318666i	−0.432841	+	0.901470i	$0.642489\pi$
$450$		0			0
$451$	−1.03374	+	0.867414i	−0.0486771	+	0.0408449i
$452$	22.6753	−	30.4582i	1.06655	−	1.43263i
$453$		0			0
$454$	−28.8847	−	6.84579i	−1.35562	−	0.321289i
$455$	3.76667	+	5.05951i	0.176584	+	0.237194i
$456$		0			0
$457$	36.7648	+	18.4640i	1.71979	+	0.863709i	0.982050	+	0.188620i	$0.0604014\pi$
$457$	36.7648	+	18.4640i	1.71979	+	0.863709i	0.737736	+	0.675089i	$0.235895\pi$
$458$	−17.4005	+	30.1385i	−0.813071	+	1.40828i
$459$		0			0
$460$	2.75450	+	4.77093i	0.128429	+	0.222446i
$461$	1.99431	+	34.2409i	0.0928841	+	1.59476i	0.647113	+	0.762394i	$0.275976\pi$
$461$	1.99431	+	34.2409i	0.0928841	+	1.59476i	−0.554229	+	0.832364i	$0.686987\pi$
$462$		0			0
$463$	33.1075	−	3.86972i	1.53864	−	0.179841i	0.695890	−	0.718149i	$-0.255010\pi$
$463$	33.1075	−	3.86972i	1.53864	−	0.179841i	0.842748	+	0.538308i	$0.180936\pi$
$464$	−3.36427	−	11.2374i	−0.156182	−	0.521685i
$465$		0			0
$466$	−4.61847	−	10.7068i	−0.213946	−	0.495984i
$467$	−9.76380	−	3.55373i	−0.451815	−	0.164447i	0.106082	−	0.994357i	$-0.466169\pi$
$467$	−9.76380	−	3.55373i	−0.451815	−	0.164447i	−0.557897	+	0.829910i	$0.688392\pi$
$468$		0			0
$469$	2.09681	−	0.763177i	0.0968218	−	0.0352402i
$470$	−5.89058	−	6.24365i	−0.271712	−	0.287998i
$471$		0			0
$472$	2.98062	−	1.49693i	0.137194	−	0.0689016i
$473$	−0.677743	+	11.6364i	−0.0311627	+	0.535042i
$474$		0			0
$475$	8.36046	−	27.9259i	0.383604	−	1.28133i
$476$	−5.94706	+	33.7274i	−0.272583	+	1.54589i
$477$		0			0
$478$	−6.09945	−	34.5917i	−0.278982	−	1.58219i
$479$	−20.1592	−	2.35628i	−0.921100	−	0.107661i	−0.357691	−	0.933840i	$-0.616436\pi$
$479$	−20.1592	−	2.35628i	−0.921100	−	0.107661i	−0.563408	+	0.826179i	$0.690510\pi$
$480$		0			0
$481$	−5.22949	+	5.54293i	−0.238444	+	0.252736i
$482$	−20.1556	+	46.7259i	−0.918062	+	2.12831i
$483$		0			0
$484$	21.7841	−	14.3276i	0.990184	−	0.651255i
$485$	−2.41096			−0.109476
$486$		0			0
$487$	−27.5716			−1.24939			−0.624694	−	0.780870i	$-0.714776\pi$
$487$	−27.5716			−1.24939			−0.624694	+	0.780870i	$0.714776\pi$
$488$	4.79108	−	3.15114i	0.216882	−	0.142646i
$489$		0			0
$490$	−2.03553	+	4.71890i	−0.0919561	+	0.213178i
$491$	−7.01152	+	7.43178i	−0.316426	+	0.335391i	−0.865991	−	0.500059i	$-0.833312\pi$
$491$	−7.01152	+	7.43178i	−0.316426	+	0.335391i	0.549566	+	0.835450i	$0.314793\pi$
$492$		0			0
$493$	40.0329	+	4.67918i	1.80299	+	0.210740i
$494$	−12.8199	−	72.7055i	−0.576796	−	3.27117i
$495$		0			0
$496$	0.959690	−	5.44267i	0.0430914	−	0.244383i
$497$	4.27613	−	14.2833i	0.191811	−	0.640692i
$498$		0			0
$499$	0.508397	−	8.72884i	0.0227590	−	0.390756i	−0.967623	−	0.252399i	$-0.918781\pi$
$499$	0.508397	−	8.72884i	0.0227590	−	0.390756i	0.990382	−	0.138358i	$-0.0441824\pi$
$500$	−15.1356	+	7.60141i	−0.676887	+	0.339945i
$501$		0			0
$502$	−36.2641	−	38.4377i	−1.61854	−	1.71556i
$503$	−12.2947	+	4.47489i	−0.548192	+	0.199526i	−0.601243	−	0.799066i	$-0.705328\pi$
$503$	−12.2947	+	4.47489i	−0.548192	+	0.199526i	0.0530509	+	0.998592i	$0.483105\pi$
$504$		0			0
$505$	2.82525	+	1.02831i	0.125722	+	0.0457591i
$506$	3.24953	+	7.53325i	0.144459	+	0.334894i
$507$		0			0
$508$	8.93590	+	29.8480i	0.396467	+	1.32429i
$509$	30.2154	−	3.53167i	1.33927	−	0.156538i	0.583895	−	0.811829i	$-0.301528\pi$
$509$	30.2154	−	3.53167i	1.33927	−	0.156538i	0.755377	+	0.655291i	$0.227454\pi$
$510$		0			0
$511$	0.683128	+	11.7289i	0.0302198	+	0.518854i
$512$	−10.6866	−	18.5097i	−0.472284	−	0.818019i
$513$		0			0
$514$	−10.4808	+	18.1532i	−0.462287	+	0.800705i
$515$	2.98599	+	1.49962i	0.131578	+	0.0660812i
$516$		0			0
$517$	−4.40874	−	5.92196i	−0.193896	−	0.260448i
$518$	5.53376	+	1.31153i	0.243139	+	0.0576251i
$519$		0			0
$520$	−3.28895	+	4.41782i	−0.144230	+	0.193734i
$521$	8.25925	−	6.93034i	0.361845	−	0.303624i	−0.443681	−	0.896185i	$-0.646328\pi$
$521$	8.25925	−	6.93034i	0.361845	−	0.303624i	0.805525	+	0.592561i	$0.201883\pi$
$522$		0			0
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	0.825517	−	0.564377i	$-0.190884\pi$
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	−0.412453	+	0.910979i	$0.635328\pi$
$524$	−38.7911	+	9.19366i	−1.69460	+	0.401627i
$525$		0			0
$526$	−12.0739	−	7.94111i	−0.526446	−	0.346249i
$527$	15.8657	+	10.4350i	0.691119	+	0.454556i
$528$		0			0
$529$	−12.9283	+	3.06406i	−0.562100	+	0.133220i
$530$	−9.18367	−	7.70601i	−0.398913	−	0.334728i
$531$		0			0
$532$	−24.3755	+	20.4535i	−1.05681	+	0.886772i
$533$	−3.55246	+	4.77178i	−0.153874	+	0.206689i
$534$		0			0
$535$	−8.17194	−	1.93678i	−0.353304	−	0.0837345i
$536$	1.16349	+	1.56284i	0.0502552	+	0.0675044i
$537$		0			0
$538$	57.0992	+	28.6763i	2.46172	+	1.23632i
$539$	−2.21009	+	3.82798i	−0.0951952	+	0.164883i
$540$		0			0
$541$	7.99279	+	13.8439i	0.343637	+	0.595196i	0.985105	−	0.171953i	$-0.0550078\pi$
$541$	7.99279	+	13.8439i	0.343637	+	0.595196i	−0.641468	+	0.767149i	$0.721674\pi$
$542$	2.38843	+	41.0078i	0.102592	+	1.76144i
$543$		0			0
$544$	51.2153	−	5.98621i	2.19584	−	0.256657i
$545$	−0.329554	−	1.10079i	−0.0141165	−	0.0471525i
$546$		0			0
$547$	0.489796	+	1.13547i	0.0209422	+	0.0485494i	0.928366	−	0.371667i	$-0.121214\pi$
$547$	0.489796	+	1.13547i	0.0209422	+	0.0485494i	−0.907424	+	0.420216i	$0.861954\pi$
$548$	0.952696	+	0.346753i	0.0406972	+	0.0148126i
$549$		0			0
$550$	−11.3343	+	4.12534i	−0.483295	+	0.175905i
$551$	25.6986	+	27.2389i	1.09480	+	1.16042i
$552$		0			0
$553$	23.3090	−	11.7062i	0.991199	−	0.497799i
$554$	−1.77606	+	30.4938i	−0.0754577	+	1.29556i
$555$		0			0
$556$	−11.7447	+	39.2302i	−0.498088	+	1.66373i
$557$	2.28246	−	12.9445i	0.0967109	−	0.548475i	−0.897499	−	0.441017i	$-0.854618\pi$
$557$	2.28246	−	12.9445i	0.0967109	−	0.548475i	0.994210	−	0.107458i	$-0.0342710\pi$
$558$		0			0
$559$	8.92289	+	50.6042i	0.377398	+	2.14033i
$560$	−2.34085	−	0.273606i	−0.0989189	−	0.0115620i
$561$		0			0
$562$	32.9689	−	34.9450i	1.39071	−	1.47407i
$563$	2.41169	−	5.59094i	0.101641	−	0.235630i	−0.859806	−	0.510621i	$-0.829416\pi$
$563$	2.41169	−	5.59094i	0.101641	−	0.235630i	0.961447	+	0.274991i	$0.0886749\pi$
$564$		0			0
$565$	−7.50149	+	4.93381i	−0.315590	+	0.207567i
$566$	8.60852			0.361843
$567$		0			0
$568$	13.0187			0.546251
$569$	−13.8505	+	9.10960i	−0.580642	+	0.381894i	−0.805587	−	0.592477i	$-0.798150\pi$
$569$	−13.8505	+	9.10960i	−0.580642	+	0.381894i	0.224945	+	0.974371i	$0.427780\pi$
$570$		0			0
$571$	13.8023	−	31.9973i	0.577608	−	1.33905i	−0.339574	−	0.940579i	$-0.610283\pi$
$571$	13.8023	−	31.9973i	0.577608	−	1.33905i	0.917182	−	0.398468i	$-0.130458\pi$
$572$	−12.1069	+	12.8326i	−0.506216	+	0.536557i
$573$		0			0
$574$	4.40959	+	0.515408i	0.184053	+	0.0215127i
$575$	2.47981	+	14.0637i	0.103415	+	0.586497i
$576$		0			0
$577$	5.38675	−	30.5498i	0.224254	−	1.27180i	−0.639854	−	0.768497i	$-0.721005\pi$
$577$	5.38675	−	30.5498i	0.224254	−	1.27180i	0.864107	−	0.503308i	$-0.167884\pi$
$578$	−18.6492	+	62.2928i	−0.775706	+	2.59104i
$579$		0			0
$580$	0.604979	−	10.3871i	0.0251204	−	0.431301i
$581$	−10.9847	+	5.51671i	−0.455721	+	0.228872i
$582$		0			0
$583$	−7.07592	−	7.50004i	−0.293055	−	0.310620i
$584$	−9.63999	+	3.50867i	−0.398906	+	0.145190i
$585$		0			0
$586$	−16.3102	−	5.93644i	−0.673769	−	0.245232i
$587$	−17.6431	−	40.9013i	−0.728209	−	1.68818i	−0.725538	−	0.688182i	$-0.758409\pi$
$587$	−17.6431	−	40.9013i	−0.728209	−	1.68818i	−0.00267106	−	0.999996i	$-0.500850\pi$
$588$		0			0
$589$	5.06023	+	16.9023i	0.208503	+	0.696449i
$590$	−2.91737	+	0.340992i	−0.120106	+	0.0140384i
$591$		0			0
$592$	−0.165556	−	2.84249i	−0.00680432	−	0.116826i
$593$	9.90549	+	17.1568i	0.406770	+	0.704546i	0.994526	−	0.104493i	$-0.0333219\pi$
$593$	9.90549	+	17.1568i	0.406770	+	0.704546i	−0.587756	+	0.809038i	$0.699989\pi$
$594$		0			0
$595$	4.04899	−	7.01306i	0.165992	−	0.287507i
$596$	−2.44393	−	1.22739i	−0.100107	−	0.0502758i
$597$		0			0
$598$	21.5977	+	29.0108i	0.883197	+	1.18634i
$599$	−27.1755	−	6.44071i	−1.11036	−	0.263160i	−0.365785	−	0.930699i	$-0.619200\pi$
$599$	−27.1755	−	6.44071i	−1.11036	−	0.263160i	−0.744575	+	0.667539i	$0.767348\pi$
$600$		0			0
$601$	−6.05803	+	8.13735i	−0.247112	+	0.331929i	−0.908322	−	0.418272i	$-0.862636\pi$
$601$	−6.05803	+	8.13735i	−0.247112	+	0.331929i	0.661210	+	0.750201i	$0.270043\pi$
$602$	29.3761	−	24.6495i	1.19728	−	1.00464i
$603$		0			0
$604$	0.0411194	+	0.0345033i	0.00167313	+	0.00140392i
$605$	−5.99897	+	1.42178i	−0.243893	+	0.0578036i
$606$		0			0
$607$	−9.03698	−	5.94371i	−0.366800	−	0.241248i	0.352706	−	0.935734i	$-0.385261\pi$
$607$	−9.03698	−	5.94371i	−0.366800	−	0.241248i	−0.719506	+	0.694486i	$0.755632\pi$
$608$	40.0272	+	26.3263i	1.62332	+	1.06767i
$609$		0			0
$610$	−4.91379	+	1.16459i	−0.198954	+	0.0471529i
$611$	−24.9321	−	20.9205i	−1.00865	−	0.846355i
$612$		0			0
$613$	4.13859	−	3.47269i	0.167156	−	0.140261i	−0.555372	−	0.831602i	$-0.687424\pi$
$613$	4.13859	−	3.47269i	0.167156	−	0.140261i	0.722528	+	0.691341i	$0.242980\pi$
$614$	−2.70762	+	3.63696i	−0.109270	+	0.146776i
$615$		0			0
$616$	3.43993	+	0.815278i	0.138599	+	0.0328485i
$617$	−14.9530	−	20.0854i	−0.601986	−	0.808608i	0.391784	−	0.920057i	$-0.371858\pi$
$617$	−14.9530	−	20.0854i	−0.601986	−	0.808608i	−0.993770	+	0.111450i	$0.964451\pi$
$618$		0			0
$619$	22.7743	+	11.4377i	0.915376	+	0.459719i	0.843156	−	0.537669i	$-0.180695\pi$
$619$	22.7743	+	11.4377i	0.915376	+	0.459719i	0.0722206	+	0.997389i	$0.476991\pi$
$620$	2.45106	−	4.24535i	0.0984368	−	0.170498i
$621$		0			0
$622$	16.3342	+	28.2917i	0.654943	+	1.13439i
$623$	−1.65727	−	28.4543i	−0.0663973	−	1.14000i
$624$		0			0
$625$	−18.7775	+	2.19478i	−0.751102	+	0.0877912i
$626$	−3.17687	−	10.6115i	−0.126973	−	0.424120i
$627$		0			0
$628$	−8.45183	−	19.5936i	−0.337265	−	0.781868i
$629$	9.19342	+	3.34613i	0.366566	+	0.133419i
$630$		0			0
$631$	−18.7709	+	6.83203i	−0.747256	+	0.271979i	−0.687451	−	0.726231i	$-0.741270\pi$
$631$	−18.7709	+	6.83203i	−0.747256	+	0.271979i	−0.0598054	+	0.998210i	$0.519048\pi$
$632$	15.6294	+	16.5662i	0.621702	+	0.658966i
$633$		0			0
$634$	−53.8748	+	27.0570i	−2.13964	+	1.07457i
$635$	0.428361	−	7.35468i	0.0169990	−	0.291862i
$636$		0			0
$637$	−5.58862	+	18.6673i	−0.221429	+	0.739625i
$638$	2.69069	−	15.2597i	0.106526	−	0.604137i
$639$		0			0
$640$	−1.33792	−	7.58769i	−0.0528857	−	0.299930i
$641$	8.86918	+	1.03666i	0.350312	+	0.0409456i	0.289429	−	0.957199i	$-0.406534\pi$
$641$	8.86918	+	1.03666i	0.350312	+	0.0409456i	0.0608823	+	0.998145i	$0.480609\pi$
$642$		0			0
$643$	−9.19558	+	9.74674i	−0.362638	+	0.384374i	−0.882844	−	0.469667i	$-0.844374\pi$
$643$	−9.19558	+	9.74674i	−0.362638	+	0.384374i	0.520205	+	0.854041i	$0.325855\pi$
$644$	6.17427	−	14.3136i	0.243300	−	0.564033i
$645$		0			0
$646$	−79.1890	+	52.0834i	−3.11565	+	2.04920i
$647$	−48.7223			−1.91547			−0.957736	−	0.287649i	$-0.907126\pi$
$647$	−48.7223			−1.91547			−0.957736	+	0.287649i	$0.907126\pi$
$648$		0			0
$649$	−2.52628			−0.0991653
$650$	−44.4251	+	29.2189i	−1.74250	+	1.14606i
$651$		0			0
$652$	−16.6715	+	38.6489i	−0.652906	+	1.51361i
$653$	−3.29734	+	3.49498i	−0.129035	+	0.136769i	−0.788669	−	0.614818i	$-0.789230\pi$
$653$	−3.29734	+	3.49498i	−0.129035	+	0.136769i	0.659634	+	0.751587i	$0.270711\pi$
$654$		0			0
$655$	9.36262	+	1.09433i	0.365828	+	0.0427592i
$656$	−0.385978	−	2.18899i	−0.0150699	−	0.0854656i
$657$		0			0
$658$	−4.21775	+	23.9201i	−0.164425	+	0.932501i
$659$	7.25407	−	24.2303i	0.282579	−	0.943878i	−0.692388	−	0.721526i	$-0.743441\pi$
$659$	7.25407	−	24.2303i	0.282579	−	0.943878i	0.974966	−	0.222352i	$-0.0713736\pi$
$660$		0			0
$661$	0.821956	−	14.1124i	0.0319704	−	0.548910i	−0.943855	−	0.330359i	$-0.892830\pi$
$661$	0.821956	−	14.1124i	0.0319704	−	0.548910i	0.975826	−	0.218551i	$-0.0701329\pi$
$662$	53.0213	−	26.6283i	2.06073	−	1.03494i
$663$		0			0
$664$	−7.36555	−	7.80703i	−0.285839	−	0.302971i
$665$	7.07019	−	2.57334i	0.274170	−	0.0997898i
$666$		0			0
$667$	−17.2393	−	6.27461i	−0.667510	−	0.242954i
$668$	3.95792	+	9.17550i	0.153137	+	0.355011i
$669$		0			0
$670$	−0.492094	−	1.64371i	−0.0190112	−	0.0635020i
$671$	−4.31401	+	0.504235i	−0.166540	+	0.0194658i
$672$		0			0
$673$	−0.155093	−	2.66284i	−0.00597839	−	0.102645i	0.993999	−	0.109390i	$-0.0348899\pi$
$673$	−0.155093	−	2.66284i	−0.00597839	−	0.102645i	−0.999977	+	0.00674548i	$0.997853\pi$
$674$	13.8366	+	23.9656i	0.532965	+	0.923122i
$675$		0			0
$676$	−21.1154	+	36.5730i	−0.812131	+	1.40665i
$677$	−13.1923	−	6.62542i	−0.507021	−	0.254636i	0.176851	−	0.984238i	$-0.443409\pi$
$677$	−13.1923	−	6.62542i	−0.507021	−	0.254636i	−0.683872	+	0.729602i	$0.739705\pi$
$678$		0			0
$679$	4.07390	+	5.47220i	0.156342	+	0.210004i
$680$	6.88033	+	1.63067i	0.263849	+	0.0625333i
$681$		0			0
$682$	4.35951	−	5.85584i	0.166934	−	0.224232i
$683$	−16.0712	+	13.4854i	−0.614948	+	0.516003i	−0.896211	−	0.443628i	$-0.853691\pi$
$683$	−16.0712	+	13.4854i	−0.614948	+	0.516003i	0.281263	+	0.959631i	$0.409247\pi$
$684$		0			0
$685$	−0.183640	−	0.154092i	−0.00701653	−	0.00588756i
$686$	41.2611	−	9.77905i	1.57535	−	0.373366i
$687$		0			0
$688$	−16.0408	−	10.5502i	−0.611552	−	0.402224i
$689$	−37.9775	−	24.9782i	−1.44683	−	0.951594i
$690$		0			0
$691$	33.8949	−	8.03323i	1.28942	−	0.305598i	0.471979	−	0.881610i	$-0.343540\pi$
$691$	33.8949	−	8.03323i	1.28942	−	0.305598i	0.817442	+	0.576011i	$0.195392\pi$
$692$	27.8199	+	23.3437i	1.05755	+	0.887394i
$693$		0			0
$694$	14.0227	−	11.7664i	0.532294	−	0.446648i
$695$	5.78221	−	7.76686i	0.219332	−	0.294614i
$696$		0			0
$697$	7.43159	+	1.76132i	0.281492	+	0.0667147i
$698$	39.1651	+	52.6079i	1.48242	+	1.99124i
$699$		0			0
$700$	20.4801	+	10.2855i	0.774075	+	0.388755i
$701$	21.8053	−	37.7679i	0.823576	−	1.42647i	−0.0794276	−	0.996841i	$-0.525309\pi$
$701$	21.8053	−	37.7679i	0.823576	−	1.42647i	0.903003	−	0.429634i	$-0.141357\pi$
$702$		0			0
$703$	4.54496	+	7.87209i	0.171416	+	0.296902i
$704$	−0.872254	−	14.9760i	−0.0328743	−	0.564430i
$705$		0			0
$706$	−50.2052	+	5.86815i	−1.88950	+	0.220851i
$707$	−2.43997	−	8.15008i	−0.0917647	−	0.306515i
$708$		0			0
$709$	7.23533	+	16.7734i	0.271728	+	0.629937i	0.998370	−	0.0570799i	$-0.0181790\pi$
$709$	7.23533	+	16.7734i	0.271728	+	0.629937i	−0.726641	+	0.687017i	$0.758920\pi$
$710$	−10.7731	−	3.92111i	−0.404309	−	0.147156i
$711$		0			0
$712$	23.3867	−	8.51206i	0.876453	−	0.319003i
$713$	−5.93152	−	6.28704i	−0.222137	−	0.235452i
$714$		0			0
$715$	3.72787	−	1.87221i	0.139414	−	0.0700165i
$716$	−0.0664428	+	1.14078i	−0.00248308	+	0.0426329i
$717$		0			0
$718$	−2.60097	+	8.68786i	−0.0970675	+	0.324228i
$719$	−3.15002	+	17.8647i	−0.117476	+	0.666240i	0.868018	+	0.496532i	$0.165393\pi$
$719$	−3.15002	+	17.8647i	−0.117476	+	0.666240i	−0.985494	+	0.169708i	$0.945718\pi$
$720$		0			0
$721$	−1.64184	−	9.31131i	−0.0611451	−	0.346771i
$722$	−46.4067	−	5.42417i	−1.72708	−	0.201867i
$723$		0			0
$724$	−39.1113	+	41.4555i	−1.45356	+	1.54068i
$725$	10.6829	−	24.7657i	0.396752	−	0.919774i
$726$		0			0
$727$	−16.9219	+	11.1297i	−0.627599	+	0.412778i	−0.823077	−	0.567930i	$-0.807744\pi$
$727$	−16.9219	+	11.1297i	−0.627599	+	0.412778i	0.195478	+	0.980708i	$0.437374\pi$
$728$	15.5847			0.577606
$729$		0			0
$730$	9.03402			0.334364
$731$	55.1169	−	36.2509i	2.03857	−	1.34079i
$732$		0			0
$733$	−0.700264	+	1.62339i	−0.0258648	+	0.0599615i	−0.930659	−	0.365888i	$-0.880765\pi$
$733$	−0.700264	+	1.62339i	−0.0258648	+	0.0599615i	0.904794	+	0.425849i	$0.140025\pi$
$734$	17.5010	−	18.5500i	0.645974	−	0.684693i
$735$		0			0
$736$	−23.3115	−	2.72473i	−0.859274	−	0.100435i
$737$	−0.256258	−	1.45331i	−0.00943939	−	0.0535334i
$738$		0			0
$739$	−1.58340	+	8.97988i	−0.0582461	+	0.330330i	−0.999982	−	0.00602346i	$-0.998083\pi$
$739$	−1.58340	+	8.97988i	−0.0582461	+	0.330330i	0.941736	+	0.336354i	$0.109194\pi$
$740$	0.724337	−	2.41946i	0.0266272	−	0.0889409i
$741$		0			0
$742$	−1.97244	+	33.8654i	−0.0724104	+	1.24324i
$743$	−17.8025	+	8.94076i	−0.653111	+	0.328005i	−0.744316	−	0.667827i	$-0.767224\pi$
$743$	−17.8025	+	8.94076i	−0.653111	+	0.328005i	0.0912051	+	0.995832i	$0.470928\pi$
$744$		0			0
$745$	0.443764	+	0.470363i	0.0162583	+	0.0172327i
$746$	−74.3653	+	27.0667i	−2.72271	+	0.990984i
$747$		0			0
$748$	21.2839	+	7.74671i	0.778217	+	0.283248i
$749$	9.41249	+	21.8206i	0.343925	+	0.797308i
$750$		0			0
$751$	11.0579	+	36.9360i	0.403509	+	1.34781i	0.882631	+	0.470066i	$0.155770\pi$
$751$	11.0579	+	36.9360i	0.403509	+	1.34781i	−0.479122	+	0.877748i	$0.659045\pi$
$752$	12.0784	−	1.41177i	0.440456	−	0.0514819i
$753$		0			0
$754$	−3.97179	−	68.1930i	−0.144644	−	2.48344i
$755$	−0.00634611	−	0.0109918i	−0.000230959	−	0.000400032i
$756$		0			0
$757$	25.4729	−	44.1204i	0.925829	−	1.60358i	0.135606	−	0.990763i	$-0.456702\pi$
$757$	25.4729	−	44.1204i	0.925829	−	1.60358i	0.790223	−	0.612820i	$-0.209965\pi$
$758$	−19.5415	−	9.81413i	−0.709781	−	0.356465i
$759$		0			0
$760$	3.92315	+	5.26970i	0.142307	+	0.191152i
$761$	37.8907	+	8.98027i	1.37354	+	0.325534i	0.850141	−	0.526555i	$-0.176516\pi$
$761$	37.8907	+	8.98027i	1.37354	+	0.325534i	0.523397	+	0.852089i	$0.324665\pi$
$762$		0			0
$763$	−1.94161	+	2.60804i	−0.0702911	+	0.0944173i
$764$	14.4293	−	12.1076i	0.522033	−	0.438038i
$765$		0			0
$766$	−0.504379	−	0.423224i	−0.0182239	−	0.0152917i
$767$	−10.8367	+	2.56834i	−0.391290	+	0.0927373i
$768$		0			0
$769$	−28.5331	−	18.7665i	−1.02893	−	0.676739i	−0.0814918	−	0.996674i	$-0.525968\pi$
$769$	−28.5331	−	18.7665i	−1.02893	−	0.676739i	−0.947439	+	0.319935i	$0.896339\pi$
$770$	−2.60104	−	1.71073i	−0.0937349	−	0.0616504i
$771$		0			0
$772$	−23.2692	+	5.51490i	−0.837476	+	0.198485i
$773$	−2.31945	−	1.94625i	−0.0834247	−	0.0700016i	0.600122	−	0.799909i	$-0.295119\pi$
$773$	−2.31945	−	1.94625i	−0.0834247	−	0.0700016i	−0.683546	+	0.729907i	$0.739563\pi$
$774$		0			0
$775$	9.73449	−	8.16820i	0.349673	−	0.293411i
$776$	−3.55722	+	4.77817i	−0.127697	+	0.171526i
$777$		0			0
$778$	15.9200	+	3.77312i	0.570761	+	0.135273i
$779$	4.23747	+	5.69191i	0.151823	+	0.203934i
$780$		0			0
$781$	−8.81169	−	4.42540i	−0.315307	−	0.158353i
$782$	23.2165	−	40.2122i	0.830222	−	1.43799i
$783$		0			0

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81786 + 1.19562i) q^{2} +(1.08293 - 2.51052i) q^{4} +(-0.443651 + 0.470242i) q^{5} +(1.81697 + 0.212373i) q^{7} +(0.277373 + 1.57306i) q^{8} +(0.244261 - 1.38527i) q^{10} +(0.346986 - 1.15901i) q^{11} +(0.310113 - 5.32444i) q^{13} +(-3.55691 + 1.78635i) q^{14} +(1.36753 + 1.44950i) q^{16} +(-6.43434 + 2.34191i) q^{17} +(-5.97823 - 2.17590i) q^{19} +(0.700110 + 1.62304i) q^{20} +(0.754974 + 2.52179i) q^{22} +(3.09558 - 0.361822i) q^{23} +(0.266422 + 4.57429i) q^{25} +(5.80229 + 10.0499i) q^{26} +(2.50083 - 4.33156i) q^{28} +(-5.26023 - 2.64179i) q^{29} +(-1.65611 - 2.22454i) q^{31} +(-7.32759 - 1.73667i) q^{32} +(8.89668 - 11.9503i) q^{34} +(-0.905967 + 0.760197i) q^{35} +(-1.09453 - 0.918418i) q^{37} +(13.4691 - 3.19224i) q^{38} +(-0.862777 - 0.567457i) q^{40} +(-0.931903 - 0.612922i) q^{41} +(-9.37473 + 2.22185i) q^{43} +(-2.53397 - 2.12625i) q^{44} +(-5.19473 + 4.35890i) q^{46} +(3.64407 - 4.89483i) q^{47} +(-3.55504 - 0.842559i) q^{49} +(-5.95346 - 7.99688i) q^{50} +(-13.0313 - 6.54456i) q^{52} +(4.26135 - 7.38088i) q^{53} +(0.391077 + 0.677365i) q^{55} +(0.169902 + 2.91711i) q^{56} +(12.7209 - 1.48687i) q^{58} +(-0.598878 - 2.00039i) q^{59} +(-1.42194 - 3.29643i) q^{61} +(5.67029 + 2.06382i) q^{62} +(11.6517 - 4.24088i) q^{64} +(2.36619 + 2.50802i) q^{65} +(1.09003 - 0.547434i) q^{67} +(-1.08855 + 18.6897i) q^{68} +(0.738011 - 2.46513i) q^{70} +(1.41528 - 8.02646i) q^{71} +(1.11524 + 6.32482i) q^{73} +(3.08778 + 0.360910i) q^{74} +(-11.9367 + 12.6521i) q^{76} +(0.876607 - 2.03220i) q^{77} +(11.9127 - 7.83511i) q^{79} -1.28832 q^{80} +2.42689 q^{82} +(-5.61402 + 3.69240i) q^{83} +(1.75334 - 4.06469i) q^{85} +(14.3854 - 15.2477i) q^{86} +(1.91944 + 0.224351i) q^{88} +(-2.70557 - 15.3441i) q^{89} +(1.69423 - 9.60848i) q^{91} +(2.44395 - 8.16337i) q^{92} +(-0.772019 + 13.2550i) q^{94} +(3.67544 - 1.84588i) q^{95} +(2.55920 + 2.71259i) q^{97} +(7.46994 - 2.71884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

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