LMFDB - Embedded newform 729.2.g.b.28.8

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			28.8
Character	$\chi$	$=$	729.28
Dual form			729.2.g.b.703.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	0.291612	−	0.956537i	$-0.405808\pi$
$2$	1.81786	−	1.19562i	1.28542	−	0.845434i	0.993809	+	0.111102i	$0.0354381\pi$
$3$		0			0
$3$		0			0
$4$	1.08293	−	2.51052i	0.541467	−	1.25526i
$5$	0.443651	−	0.470242i	0.198407	−	0.210299i	−0.620530	−	0.784183i	$-0.713082\pi$
$5$	0.443651	−	0.470242i	0.198407	−	0.210299i	0.818937	+	0.573884i	$0.194564\pi$
$6$		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	−0.994231	−	0.107264i	$-0.965791\pi$
$11$	−0.346986	+	1.15901i	−0.104620	+	0.349456i	0.889610	+	0.456720i	$0.150976\pi$
$12$		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	0.589693	−	0.807628i	$-0.299249\pi$
$17$	6.43434	−	2.34191i	1.56056	−	0.567996i	0.970864	+	0.239631i	$0.0770266\pi$
$18$		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	−0.432530	−	0.901619i	$-0.642379\pi$
$23$	−3.09558	+	0.361822i	−0.645474	+	0.0754451i	−0.212944	+	0.977064i	$0.568305\pi$
$24$		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	0.864241	−	0.503077i	$-0.167799\pi$
$29$	5.26023	+	2.64179i	0.976800	+	0.490568i	0.112559	+	0.993645i	$0.464095\pi$
$30$		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	0.620190	−	0.784452i	$-0.287055\pi$
$41$	0.931903	+	0.612922i	0.145539	+	0.0957224i	−0.474651	+	0.880174i	$0.657426\pi$
$42$		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	−0.984073	−	0.177764i	$-0.943114\pi$
$47$	−3.64407	+	4.89483i	−0.531542	+	0.713984i	0.452532	+	0.891748i	$0.350521\pi$
$48$		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	$0.365706\pi$
$53$	−4.26135	+	7.38088i	−0.585342	+	1.01384i	−0.994833	+	0.101528i	$0.967627\pi$
$54$		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	0.988082	−	0.153927i	$-0.0491921\pi$
$59$	0.598878	+	2.00039i	0.0779672	+	0.260429i	−0.910115	+	0.414356i	$0.864007\pi$
$60$		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	$0.216237\pi$
$71$	−1.41528	+	8.02646i	−0.167963	+	0.952565i	−0.945957	+	0.324293i	$0.894874\pi$
$72$		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	−0.202669	−	0.979247i	$-0.564961\pi$
$83$	5.61402	−	3.69240i	0.616219	−	0.405294i	0.818888	+	0.573954i	$0.194591\pi$
$84$		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	$0.253709\pi$
$89$	2.70557	+	15.3441i	0.286790	+	1.62647i	−0.412030	+	0.911170i	$0.635180\pi$
$90$		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	0.984943	−	0.172880i	$-0.0553072\pi$
$101$	1.84200	+	4.27024i	0.183286	+	0.424904i	−0.801657	+	0.597784i	$0.796048\pi$
$102$		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	$-0.950572\pi$
$107$	−6.49528	−	11.2502i	−0.627922	−	1.08759i	0.360046	−	0.932935i	$-0.382761\pi$
$108$		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	−0.461023	−	0.887388i	$-0.652517\pi$
$113$	−13.5138	−	3.20282i	−1.27127	−	0.301296i	−0.810244	+	0.586092i	$0.800666\pi$
$114$		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	$0.0161058\pi$
$131$	8.70702	+	11.6956i	0.760736	+	1.02185i	−0.237985	+	0.971269i	$0.576487\pi$
$132$		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	0.997262	−	0.0739509i	$-0.0235608\pi$
$137$	−0.0215606	−	0.370181i	−0.00184204	−	0.0316267i	−0.999104	+	0.0423242i	$0.986524\pi$
$138$		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	−0.999852	−	0.0171933i	$-0.994527\pi$
$149$	−0.0581597	+	0.998563i	−0.00476463	+	0.0818055i	0.995088	+	0.0989987i	$0.0315640\pi$
$150$		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	−0.623024	−	0.782203i	$-0.714096\pi$
$167$	2.50809	−	2.65842i	0.194082	−	0.205714i	0.817105	+	0.576489i	$0.195577\pi$
$168$		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	$-0.738926\pi$
$173$	3.80949	−	12.7246i	0.289630	−	0.967432i	0.971715	−	0.236158i	$-0.0758884\pi$
$174$		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	−0.327301	−	0.944920i	$-0.606139\pi$
$179$	0.392738	−	0.142945i	0.0293546	−	0.0106842i	0.356656	+	0.934236i	$0.383917\pi$
$180$		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	0.211903	−	0.977291i	$-0.432034\pi$
$191$	−6.15645	−	3.09189i	−0.445465	−	0.223721i	−0.657368	+	0.753570i	$0.728330\pi$
$192$		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	−0.382476	−	0.923965i	$-0.624929\pi$
$197$	6.47094	−	5.42976i	0.461035	−	0.386855i	0.843512	+	0.537111i	$0.180484\pi$
$198$		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	0.337843	−	0.941202i	$-0.390303\pi$
$227$	−9.36249	−	9.92366i	−0.621410	−	0.658656i	−0.959254	+	0.282546i	$0.908821\pi$
$228$		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	$-0.888276\pi$
$233$	0.930605	−	5.27772i	0.0609660	−	0.345755i	0.999998	−	0.00192589i	$-0.000613031\pi$
$234$		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	$-0.695511\pi$
$239$	6.39415	−	14.8233i	0.413603	−	0.958840i	0.989922	−	0.141615i	$-0.0452294\pi$
$240$		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	$-0.777552\pi$
$251$	−4.21745	−	23.9183i	−0.266203	−	1.50971i	0.499385	−	0.866380i	$-0.333559\pi$
$252$		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	−0.696573	−	0.717485i	$-0.745293\pi$
$257$	−8.60919	+	4.32370i	−0.537027	+	0.269705i	0.159547	+	0.987190i	$0.448997\pi$
$258$		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	0.817651	−	0.575715i	$-0.195276\pi$
$263$	−2.63068	−	6.09861i	−0.162215	−	0.376056i	−0.979866	+	0.199658i	$0.936017\pi$
$264$		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	$0.186337\pi$
$269$	14.6832	+	25.4321i	0.895251	+	1.55062i	0.0617568	+	0.998091i	$0.480330\pi$
$270$		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	0.467316	−	0.884091i	$-0.345221\pi$
$281$	21.4853	−	5.09210i	1.28170	−	0.303769i	0.814388	+	0.580321i	$0.197073\pi$
$282$		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	0.640894	−	0.767630i	$-0.278564\pi$
$293$	−4.76369	−	6.39875i	−0.278298	−	0.373819i	−0.919192	+	0.393811i	$0.871157\pi$
$294$		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	$0.158489\pi$
$311$	−0.873011	+	14.9890i	−0.0495039	+	0.849949i	−0.928088	+	0.372361i	$0.878548\pi$
$312$		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	−0.699940	−	0.714202i	$-0.746790\pi$
$317$	−27.5207	−	3.21671i	−1.54572	−	0.180669i	−0.845779	+	0.533533i	$0.820864\pi$
$318$		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	0.111199	−	0.993798i	$-0.464531\pi$
$347$	8.35624	−	0.976704i	0.448586	−	0.0524322i	0.337387	+	0.941366i	$0.390457\pi$
$348$		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	−0.199729	−	0.979851i	$-0.564006\pi$
$353$	−20.7603	−	10.4262i	−1.10496	−	0.554932i	−0.905231	+	0.424919i	$0.860302\pi$
$354$		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	−0.723145	−	0.690696i	$-0.757304\pi$
$359$	−3.19290	+	2.67916i	−0.168515	+	0.141401i	0.554630	+	0.832097i	$0.312860\pi$
$360$		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	0.955744	−	0.294201i	$-0.0950536\pi$
$383$	−0.0867894	−	0.289897i	−0.00443473	−	0.0148130i	−0.960178	+	0.279388i	$0.909868\pi$
$384$		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	0.844852	−	0.535000i	$-0.179688\pi$
$389$	5.16022	+	5.46952i	0.261634	+	0.277315i	−0.583218	+	0.812315i	$0.698207\pi$
$390$		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	−0.998117	−	0.0613379i	$-0.980463\pi$
$401$	−5.37775	+	12.4670i	−0.268552	+	0.622574i	0.729565	+	0.683911i	$0.239723\pi$
$402$		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	0.0417867	−	0.999127i	$-0.486695\pi$
$419$	17.7708	−	8.92485i	0.868163	−	0.436008i	0.826376	+	0.563119i	$0.190399\pi$
$420$		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	$-0.992494\pi$
$431$	−10.8013	−	18.7084i	−0.520281	−	0.901153i	0.479441	−	0.877574i	$-0.340839\pi$
$432$		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	−0.267484	−	0.963562i	$-0.586192\pi$
$443$	−1.55899	+	0.369487i	−0.0740699	+	0.0175549i	0.193414	+	0.981117i	$0.438044\pi$
$444$		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	0.432841	−	0.901470i	$-0.357511\pi$
$449$	−8.04720	−	6.75241i	−0.379771	−	0.318666i	−0.812613	+	0.582804i	$0.801955\pi$
$450$		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	$-0.724024\pi$
$461$	−1.99431	−	34.2409i	−0.0928841	−	1.59476i	0.554229	−	0.832364i	$-0.313013\pi$
$462$		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	0.557897	−	0.829910i	$-0.311608\pi$
$467$	9.76380	+	3.55373i	0.451815	+	0.164447i	−0.106082	+	0.994357i	$0.533831\pi$
$468$		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	0.563408	−	0.826179i	$-0.309490\pi$
$479$	20.1592	+	2.35628i	0.921100	+	0.107661i	0.357691	+	0.933840i	$0.383564\pi$
$480$		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	−0.549566	−	0.835450i	$-0.685207\pi$
$491$	7.01152	−	7.43178i	0.316426	−	0.335391i	0.865991	+	0.500059i	$0.166688\pi$
$492$		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	−0.0530509	−	0.998592i	$-0.516895\pi$
$503$	12.2947	−	4.47489i	0.548192	−	0.199526i	0.601243	+	0.799066i	$0.294672\pi$
$504$		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	−0.755377	−	0.655291i	$-0.772546\pi$
$509$	−30.2154	+	3.53167i	−1.33927	+	0.156538i	−0.583895	+	0.811829i	$0.698472\pi$
$510$		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	−0.805525	−	0.592561i	$-0.798117\pi$
$521$	−8.25925	+	6.93034i	−0.361845	+	0.303624i	0.443681	+	0.896185i	$0.353672\pi$
$522$		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	$0.145382\pi$
$557$	−2.28246	+	12.9445i	−0.0967109	+	0.548475i	−0.994210	+	0.107458i	$0.965729\pi$
$558$		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	−0.961447	−	0.274991i	$-0.911325\pi$
$563$	−2.41169	+	5.59094i	−0.101641	+	0.235630i	0.859806	+	0.510621i	$0.170584\pi$
$564$		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	−0.224945	−	0.974371i	$-0.572220\pi$
$569$	13.8505	−	9.10960i	0.580642	−	0.381894i	0.805587	+	0.592477i	$0.201850\pi$
$570$		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	$0.241591\pi$
$587$	17.6431	+	40.9013i	0.728209	+	1.68818i	0.00267106	+	0.999996i	$0.499150\pi$
$588$		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	0.587756	−	0.809038i	$-0.300011\pi$
$593$	−9.90549	−	17.1568i	−0.406770	−	0.704546i	−0.994526	+	0.104493i	$0.966678\pi$
$594$		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	0.744575	−	0.667539i	$-0.232652\pi$
$599$	27.1755	+	6.44071i	1.11036	+	0.263160i	0.365785	+	0.930699i	$0.380800\pi$
$600$		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	0.993770	−	0.111450i	$-0.0355494\pi$
$617$	14.9530	+	20.0854i	0.601986	+	0.808608i	−0.391784	+	0.920057i	$0.628142\pi$
$618$		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	−0.0608823	−	0.998145i	$-0.519391\pi$
$641$	−8.86918	−	1.03666i	−0.350312	−	0.0409456i	−0.289429	+	0.957199i	$0.593466\pi$
$642$		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	$-0.0928736\pi$
$647$	48.7223			1.91547			0.957736	+	0.287649i	$0.0928736\pi$
$648$		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	−0.659634	−	0.751587i	$-0.729289\pi$
$653$	3.29734	−	3.49498i	0.129035	−	0.136769i	0.788669	+	0.614818i	$0.210770\pi$
$654$		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	$0.256559\pi$
$659$	−7.25407	+	24.2303i	−0.282579	+	0.943878i	−0.974966	+	0.222352i	$0.928626\pi$
$660$		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	0.683872	−	0.729602i	$-0.260295\pi$
$677$	13.1923	+	6.62542i	0.507021	+	0.254636i	−0.176851	+	0.984238i	$0.556591\pi$
$678$		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	−0.281263	−	0.959631i	$-0.590753\pi$
$683$	16.0712	−	13.4854i	0.614948	−	0.516003i	0.896211	+	0.443628i	$0.146309\pi$
$684$		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	$0.474691\pi$
$701$	−21.8053	+	37.7679i	−0.823576	+	1.42647i	−0.903003	+	0.429634i	$0.858643\pi$
$702$		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	$-0.834607\pi$
$719$	3.15002	−	17.8647i	0.117476	−	0.666240i	0.985494	−	0.169708i	$-0.0542824\pi$
$720$		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	−0.0912051	−	0.995832i	$-0.529072\pi$
$743$	17.8025	−	8.94076i	0.653111	−	0.328005i	0.744316	+	0.667827i	$0.232776\pi$
$744$		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	−0.523397	−	0.852089i	$-0.675335\pi$
$761$	−37.8907	−	8.98027i	−1.37354	−	0.325534i	−0.850141	+	0.526555i	$0.823484\pi$
$762$		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	0.683546	−	0.729907i	$-0.260437\pi$
$773$	2.31945	+	1.94625i	0.0834247	+	0.0700016i	−0.600122	+	0.799909i	$0.704881\pi$
$774$		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)

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