LMFDB - Embedded newform 729.2.g.c.109.4

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			109.4
Character	$\chi$	$=$	729.109
Dual form			729.2.g.c.622.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388502 - 0.411788i) q^{2} +(0.0976541 - 1.67666i) q^{4} +(1.51980 - 0.177639i) q^{5} +(-1.38566 - 0.695905i) q^{7} +(-1.59573 + 1.33897i) q^{8} +O(q^{10})$	\(q+(-0.388502 - 0.411788i) q^{2} +(0.0976541 - 1.67666i) q^{4} +(1.51980 - 0.177639i) q^{5} +(-1.38566 - 0.695905i) q^{7} +(-1.59573 + 1.33897i) q^{8} +(-0.663594 - 0.556821i) q^{10} +(0.219760 + 0.509460i) q^{11} +(-2.50971 - 0.594813i) q^{13} +(0.251767 + 0.840960i) q^{14} +(-2.16496 - 0.253048i) q^{16} +(0.994500 - 5.64009i) q^{17} +(-1.11056 - 6.29830i) q^{19} +(-0.149425 - 2.56552i) q^{20} +(0.124413 - 0.288421i) q^{22} +(4.93448 - 2.47819i) q^{23} +(-2.58700 + 0.613129i) q^{25} +(0.730091 + 1.26456i) q^{26} +(-1.30211 + 2.25532i) q^{28} +(-1.93433 + 6.46110i) q^{29} +(-0.637429 - 0.419244i) q^{31} +(3.22474 + 4.33158i) q^{32} +(-2.70889 + 1.78166i) q^{34} +(-2.22954 - 0.811488i) q^{35} +(-7.41710 + 2.69960i) q^{37} +(-2.16211 + 2.90422i) q^{38} +(-2.18733 + 2.31843i) q^{40} +(-0.471839 + 0.500120i) q^{41} +(4.70771 - 6.32356i) q^{43} +(0.875649 - 0.318710i) q^{44} +(-2.93754 - 1.06918i) q^{46} +(-4.72615 + 3.10844i) q^{47} +(-2.74434 - 3.68628i) q^{49} +(1.25753 + 0.827092i) q^{50} +(-1.24238 + 4.14984i) q^{52} +(5.99254 - 10.3794i) q^{53} +(0.424490 + 0.735238i) q^{55} +(3.14294 - 0.744890i) q^{56} +(3.41210 - 1.71362i) q^{58} +(-0.926748 + 2.14844i) q^{59} +(-0.637878 - 10.9520i) q^{61} +(0.0750029 + 0.425363i) q^{62} +(-0.226129 + 1.28244i) q^{64} +(-3.91991 - 0.458172i) q^{65} +(2.89108 + 9.65687i) q^{67} +(-9.35937 - 2.21821i) q^{68} +(0.532022 + 1.23336i) q^{70} +(-5.17589 - 4.34309i) q^{71} +(5.85966 - 4.91684i) q^{73} +(3.99322 + 2.00547i) q^{74} +(-10.6685 + 1.24697i) q^{76} +(0.0500235 - 0.858871i) q^{77} +(3.31160 + 3.51009i) q^{79} -3.33526 q^{80} +0.389254 q^{82} +(6.22581 + 6.59897i) q^{83} +(0.509539 - 8.74845i) q^{85} +(-4.43292 + 0.518134i) q^{86} +(-1.03283 - 0.518707i) q^{88} +(-10.4080 + 8.73338i) q^{89} +(3.06368 + 2.57073i) q^{91} +(-3.67319 - 8.51542i) q^{92} +(3.11613 + 0.738537i) q^{94} +(-2.80665 - 9.37486i) q^{95} +(6.78651 + 0.793230i) q^{97} +(-0.451787 + 2.56221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−0.388502	−	0.411788i	−0.274712	−	0.291178i	0.575298	−	0.817944i	$-0.304886\pi$
$2$	−0.388502	−	0.411788i	−0.274712	−	0.291178i	−0.850011	+	0.526766i	$0.823405\pi$
$3$		0			0
$3$		0			0
$4$	0.0976541	−	1.67666i	0.0488270	−	0.838328i
$5$	1.51980	−	0.177639i	0.679674	−	0.0794425i	0.230751	−	0.973013i	$-0.425882\pi$
$5$	1.51980	−	0.177639i	0.679674	−	0.0794425i	0.448923	+	0.893570i	$0.351808\pi$
$6$		0			0
$7$	−1.38566	−	0.695905i	−0.523731	−	0.263028i	0.167232	−	0.985918i	$-0.446517\pi$
$7$	−1.38566	−	0.695905i	−0.523731	−	0.263028i	−0.690963	+	0.722890i	$0.742813\pi$
$8$	−1.59573	+	1.33897i	−0.564175	+	0.473399i
$9$		0			0
$10$	−0.663594	−	0.556821i	−0.209847	−	0.176082i
$11$	0.219760	+	0.509460i	0.0662600	+	0.153608i	0.948128	−	0.317888i	$-0.102974\pi$
$11$	0.219760	+	0.509460i	0.0662600	+	0.153608i	−0.881868	+	0.471496i	$0.843714\pi$
$12$		0			0
$13$	−2.50971	−	0.594813i	−0.696069	−	0.164971i	−0.132675	−	0.991160i	$-0.542357\pi$
$13$	−2.50971	−	0.594813i	−0.696069	−	0.164971i	−0.563394	+	0.826188i	$0.690505\pi$
$14$	0.251767	+	0.840960i	0.0672875	+	0.224756i
$15$		0			0
$16$	−2.16496	−	0.253048i	−0.541241	−	0.0632620i
$17$	0.994500	−	5.64009i	0.241202	−	1.36792i	−0.587949	−	0.808898i	$-0.700065\pi$
$17$	0.994500	−	5.64009i	0.241202	−	1.36792i	0.829151	−	0.559025i	$-0.188824\pi$
$18$		0			0
$19$	−1.11056	−	6.29830i	−0.254780	−	1.44493i	−0.796637	−	0.604458i	$-0.793390\pi$
$19$	−1.11056	−	6.29830i	−0.254780	−	1.44493i	0.541857	−	0.840471i	$-0.317721\pi$
$20$	−0.149425	−	2.56552i	−0.0334124	−	0.573668i
$21$		0			0
$22$	0.124413	−	0.288421i	0.0265248	−	0.0614915i
$23$	4.93448	−	2.47819i	1.02891	−	0.516738i	0.147486	−	0.989064i	$-0.452882\pi$
$23$	4.93448	−	2.47819i	1.02891	−	0.516738i	0.881424	+	0.472326i	$0.156586\pi$
$24$		0			0
$25$	−2.58700	+	0.613129i	−0.517399	+	0.122626i
$26$	0.730091	+	1.26456i	0.143183	+	0.248000i
$27$		0			0
$28$	−1.30211	+	2.25532i	−0.246075	+	0.426215i
$29$	−1.93433	+	6.46110i	−0.359196	+	1.19980i	0.567306	+	0.823507i	$0.307986\pi$
$29$	−1.93433	+	6.46110i	−0.359196	+	1.19980i	−0.926502	+	0.376290i	$0.877200\pi$
$30$		0			0
$31$	−0.637429	−	0.419244i	−0.114486	−	0.0752984i	0.490975	−	0.871174i	$-0.336641\pi$
$31$	−0.637429	−	0.419244i	−0.114486	−	0.0752984i	−0.605461	+	0.795875i	$0.707011\pi$
$32$	3.22474	+	4.33158i	0.570059	+	0.765722i
$33$		0			0
$34$	−2.70889	+	1.78166i	−0.464570	+	0.305553i
$35$	−2.22954	−	0.811488i	−0.376862	−	0.137166i
$36$		0			0
$37$	−7.41710	+	2.69960i	−1.21936	+	0.443812i	−0.869942	−	0.493153i	$-0.835844\pi$
$37$	−7.41710	+	2.69960i	−1.21936	+	0.443812i	−0.349422	+	0.936966i	$0.613622\pi$
$38$	−2.16211	+	2.90422i	−0.350740	+	0.471126i
$39$		0			0
$40$	−2.18733	+	2.31843i	−0.345847	+	0.366576i
$41$	−0.471839	+	0.500120i	−0.0736889	+	0.0781056i	−0.763169	−	0.646199i	$-0.776358\pi$
$41$	−0.471839	+	0.500120i	−0.0736889	+	0.0781056i	0.689480	+	0.724305i	$0.257839\pi$
$42$		0			0
$43$	4.70771	−	6.32356i	0.717920	−	0.964333i	−0.282068	−	0.959394i	$-0.591020\pi$
$43$	4.70771	−	6.32356i	0.717920	−	0.964333i	0.999988	−	0.00493908i	$-0.00157216\pi$
$44$	0.875649	−	0.318710i	0.132009	−	0.0480474i
$45$		0			0
$46$	−2.93754	−	1.06918i	−0.433117	−	0.157642i
$47$	−4.72615	+	3.10844i	−0.689379	+	0.453412i	−0.845254	−	0.534365i	$-0.820551\pi$
$47$	−4.72615	+	3.10844i	−0.689379	+	0.453412i	0.155875	+	0.987777i	$0.450180\pi$
$48$		0			0
$49$	−2.74434	−	3.68628i	−0.392048	−	0.526612i
$50$	1.25753	+	0.827092i	0.177842	+	0.116968i
$51$		0			0
$52$	−1.24238	+	4.14984i	−0.172287	+	0.575479i
$53$	5.99254	−	10.3794i	0.823138	−	1.42572i	−0.0801956	−	0.996779i	$-0.525555\pi$
$53$	5.99254	−	10.3794i	0.823138	−	1.42572i	0.903334	−	0.428938i	$-0.141112\pi$
$54$		0			0
$55$	0.424490	+	0.735238i	0.0572382	+	0.0991395i
$56$	3.14294	−	0.744890i	0.419993	−	0.0995401i
$57$		0			0
$58$	3.41210	−	1.71362i	0.448030	−	0.225009i
$59$	−0.926748	+	2.14844i	−0.120652	+	0.279703i	−0.967829	−	0.251607i	$-0.919041\pi$
$59$	−0.926748	+	2.14844i	−0.120652	+	0.279703i	0.847177	+	0.531310i	$0.178300\pi$
$60$		0			0
$61$	−0.637878	−	10.9520i	−0.0816720	−	1.40225i	−0.751498	−	0.659735i	$-0.770668\pi$
$61$	−0.637878	−	10.9520i	−0.0816720	−	1.40225i	0.669826	−	0.742518i	$-0.266369\pi$
$62$	0.0750029	+	0.425363i	0.00952538	+	0.0540211i
$63$		0			0
$64$	−0.226129	+	1.28244i	−0.0282661	+	0.160305i
$65$	−3.91991	−	0.458172i	−0.486206	−	0.0568293i
$66$		0			0
$67$	2.89108	+	9.65687i	0.353201	+	1.17977i	0.931436	+	0.363904i	$0.118556\pi$
$67$	2.89108	+	9.65687i	0.353201	+	1.17977i	−0.578235	+	0.815870i	$0.696258\pi$
$68$	−9.35937	−	2.21821i	−1.13499	−	0.268998i
$69$		0			0
$70$	0.532022	+	1.23336i	0.0635887	+	0.147415i
$71$	−5.17589	−	4.34309i	−0.614265	−	0.515430i	0.281730	−	0.959494i	$-0.409092\pi$
$71$	−5.17589	−	4.34309i	−0.614265	−	0.515430i	−0.895995	+	0.444064i	$0.853536\pi$
$72$		0			0
$73$	5.85966	−	4.91684i	0.685821	−	0.575472i	−0.231880	−	0.972744i	$-0.574488\pi$
$73$	5.85966	−	4.91684i	0.685821	−	0.575472i	0.917701	+	0.397272i	$0.130043\pi$
$74$	3.99322	+	2.00547i	0.464203	+	0.233131i
$75$		0			0
$76$	−10.6685	+	1.24697i	−1.22376	+	0.143037i
$77$	0.0500235	−	0.858871i	0.00570071	−	0.0978774i
$78$		0			0
$79$	3.31160	+	3.51009i	0.372584	+	0.394916i	0.886351	−	0.463014i	$-0.153232\pi$
$79$	3.31160	+	3.51009i	0.372584	+	0.394916i	−0.513767	+	0.857930i	$0.671750\pi$
$80$	−3.33526			−0.372893
$81$		0			0
$82$	0.389254			0.0429859
$83$	6.22581	+	6.59897i	0.683371	+	0.724331i	0.972486	−	0.232963i	$-0.0748422\pi$
$83$	6.22581	+	6.59897i	0.683371	+	0.724331i	−0.289114	+	0.957295i	$0.593361\pi$
$84$		0			0
$85$	0.509539	−	8.74845i	0.0552673	−	0.948903i
$86$	−4.43292	+	0.518134i	−0.478014	+	0.0558719i
$87$		0			0
$88$	−1.03283	−	0.518707i	−0.110100	−	0.0552943i
$89$	−10.4080	+	8.73338i	−1.10325	+	0.925736i	−0.997639	−	0.0686717i	$-0.978124\pi$
$89$	−10.4080	+	8.73338i	−1.10325	+	0.925736i	−0.105610	+	0.994408i	$0.533679\pi$
$90$		0			0
$91$	3.06368	+	2.57073i	0.321161	+	0.269486i
$92$	−3.67319	−	8.51542i	−0.382957	−	0.887794i
$93$		0			0
$94$	3.11613	+	0.738537i	0.321405	+	0.0761743i
$95$	−2.80665	−	9.37486i	−0.287956	−	0.961840i
$96$		0			0
$97$	6.78651	+	0.793230i	0.689066	+	0.0805403i	0.453418	−	0.891298i	$-0.350205\pi$
$97$	6.78651	+	0.793230i	0.689066	+	0.0805403i	0.235648	+	0.971838i	$0.424279\pi$
$98$	−0.451787	+	2.56221i	−0.0456374	+	0.258823i
$99$		0			0
$100$	0.775376	+	4.39737i	0.0775376	+	0.439737i
$101$	−1.02027	−	17.5174i	−0.101521	−	1.74305i	−0.537653	−	0.843166i	$-0.680689\pi$
$101$	−1.02027	−	17.5174i	−0.101521	−	1.74305i	0.436132	−	0.899883i	$-0.356348\pi$
$102$		0			0
$103$	0.794793	−	1.84254i	0.0783133	−	0.181551i	−0.874561	−	0.484915i	$-0.838851\pi$
$103$	0.794793	−	1.84254i	0.0783133	−	0.181551i	0.952875	+	0.303364i	$0.0981099\pi$
$104$	4.80125	−	2.41128i	0.470802	−	0.236445i
$105$		0			0
$106$	−6.60222	+	1.56475i	−0.641264	+	0.151982i
$107$	10.0295	+	17.3715i	0.969584	+	1.67937i	0.696760	+	0.717304i	$0.254624\pi$
$107$	10.0295	+	17.3715i	0.969584	+	1.67937i	0.272823	+	0.962064i	$0.412043\pi$
$108$		0			0
$109$	3.01856	−	5.22830i	0.289126	−	0.500780i	−0.684476	−	0.729036i	$-0.739969\pi$
$109$	3.01856	−	5.22830i	0.289126	−	0.500780i	0.973601	+	0.228256i	$0.0733022\pi$
$110$	0.137847	−	0.460441i	0.0131432	−	0.0439014i
$111$		0			0
$112$	2.82381	+	1.85725i	0.266825	+	0.175494i
$113$	−0.116771	−	0.156851i	−0.0109849	−	0.0147553i	0.796597	−	0.604511i	$-0.206631\pi$
$113$	−0.116771	−	0.156851i	−0.0109849	−	0.0147553i	−0.807582	+	0.589756i	$0.799224\pi$
$114$		0			0
$115$	7.05918	−	4.64290i	0.658272	−	0.432952i
$116$	10.6441	+	3.87415i	0.988284	+	0.359706i
$117$		0			0
$118$	1.24475	−	0.453051i	0.114588	−	0.0417067i
$119$	−5.30301	+	7.12318i	−0.486126	+	0.652980i
$120$		0			0
$121$	7.33740	−	7.77719i	0.667037	−	0.707018i
$122$	−4.26207	+	4.51753i	−0.385869	+	0.408998i
$123$		0			0
$124$	−0.765175	+	1.02781i	−0.0687147	+	0.0922999i
$125$	−11.0121	+	4.00808i	−0.984954	+	0.358494i
$126$		0			0
$127$	2.47378	+	0.900382i	0.219512	+	0.0798959i	0.449435	−	0.893313i	$-0.351625\pi$
$127$	2.47378	+	0.900382i	0.219512	+	0.0798959i	−0.229923	+	0.973209i	$0.573847\pi$
$128$	9.63945	−	6.33997i	0.852015	−	0.560379i
$129$		0			0
$130$	1.33422	+	1.79218i	0.117019	+	0.157184i
$131$	7.65077	+	5.03199i	0.668451	+	0.439647i	0.837850	−	0.545900i	$-0.183812\pi$
$131$	7.65077	+	5.03199i	0.668451	+	0.439647i	−0.169399	+	0.985548i	$0.554183\pi$
$132$		0			0
$133$	−2.84416	+	9.50015i	−0.246620	+	0.823768i
$134$	2.85339	−	4.94222i	0.246496	−	0.426943i
$135$		0			0
$136$	5.96498	+	10.3317i	0.511493	+	0.885932i
$137$	10.3872	−	2.46181i	0.887438	−	0.210327i	0.238477	−	0.971148i	$-0.423352\pi$
$137$	10.3872	−	2.46181i	0.887438	−	0.210327i	0.648961	+	0.760822i	$0.275204\pi$
$138$		0			0
$139$	2.20466	−	1.10722i	0.186997	−	0.0939134i	−0.352837	−	0.935685i	$-0.614783\pi$
$139$	2.20466	−	1.10722i	0.186997	−	0.0939134i	0.539834	+	0.841771i	$0.318487\pi$
$140$	−1.57831	+	3.65893i	−0.133391	+	0.309236i
$141$		0			0
$142$	0.222412	+	3.81867i	0.0186644	+	0.320456i
$143$	−0.248500	−	1.40931i	−0.0207806	−	0.117853i
$144$		0			0
$145$	−1.79204	+	10.1632i	−0.148821	+	0.844006i
$146$	−4.30118	−	0.502736i	−0.355969	−	0.0416068i
$147$		0			0
$148$	3.80200	+	12.6995i	0.312522	+	1.04390i
$149$	1.15987	+	0.274895i	0.0950204	+	0.0225203i	0.277851	−	0.960624i	$-0.410378\pi$
$149$	1.15987	+	0.274895i	0.0950204	+	0.0225203i	−0.182831	+	0.983144i	$0.558526\pi$
$150$		0			0
$151$	5.97206	+	13.8448i	0.485999	+	1.12667i	0.968102	+	0.250558i	$0.0806140\pi$
$151$	5.97206	+	13.8448i	0.485999	+	1.12667i	−0.482102	+	0.876115i	$0.660127\pi$
$152$	10.2054	+	8.56335i	0.827768	+	0.694580i
$153$		0			0
$154$	−0.373107	+	0.313074i	−0.0300658	+	0.0252282i
$155$	−1.04324	−	0.523933i	−0.0837948	−	0.0420833i
$156$		0			0
$157$	0.220147	−	0.0257314i	0.0175696	−	0.00205359i	−0.107304	−	0.994226i	$-0.534222\pi$
$157$	0.220147	−	0.0257314i	0.0175696	−	0.00205359i	0.124873	+	0.992173i	$0.460148\pi$
$158$	0.158850	−	2.72735i	0.0126375	−	0.216977i
$159$		0			0
$160$	5.67041	+	6.01028i	0.448285	+	0.475155i
$161$	−8.56210			−0.674788
$162$		0			0
$163$	17.3001			1.35505			0.677524	−	0.735501i	$-0.263053\pi$
$163$	17.3001			1.35505			0.677524	+	0.735501i	$0.263053\pi$
$164$	0.792452	+	0.839950i	0.0618801	+	0.0655891i
$165$		0			0
$166$	0.298639	−	5.12743i	0.0231789	−	0.397966i
$167$	−0.0920849	+	0.0107632i	−0.00712574	+	0.000832880i	−0.119655	−	0.992816i	$-0.538179\pi$
$167$	−0.0920849	+	0.0107632i	−0.00712574	+	0.000832880i	0.112529	+	0.993648i	$0.464105\pi$
$168$		0			0
$169$	−5.67237	−	2.84877i	−0.436336	−	0.219136i
$170$	−3.80047	+	3.18897i	−0.291482	+	0.244583i
$171$		0			0
$172$	−10.1427	−	8.51073i	−0.773374	−	0.648937i
$173$	3.19933	+	7.41688i	0.243241	+	0.563895i	0.995477	−	0.0949977i	$-0.0302844\pi$
$173$	3.19933	+	7.41688i	0.243241	+	0.563895i	−0.752237	+	0.658893i	$0.771025\pi$
$174$		0			0
$175$	4.01138	+	0.950715i	0.303232	+	0.0718673i
$176$	−0.346854	−	1.15857i	−0.0261451	−	0.0873307i
$177$		0			0
$178$	7.63984	+	0.892969i	0.572630	+	0.0669309i
$179$	3.38574	−	19.2015i	0.253062	−	1.43519i	−0.547936	−	0.836520i	$-0.684586\pi$
$179$	3.38574	−	19.2015i	0.253062	−	1.43519i	0.800998	−	0.598667i	$-0.204303\pi$
$180$		0			0
$181$	−1.07822	−	6.11490i	−0.0801436	−	0.454517i	−0.998299	−	0.0582970i	$-0.981433\pi$
$181$	−1.07822	−	6.11490i	−0.0801436	−	0.454517i	0.918156	−	0.396220i	$-0.129678\pi$
$182$	−0.131649	−	2.26032i	−0.00975845	−	0.167546i
$183$		0			0
$184$	−4.55585	+	10.5616i	−0.335862	+	0.778615i
$185$	−10.7929	+	5.42042i	−0.793512	+	0.398517i
$186$		0			0
$187$	3.09195	−	0.732806i	0.226106	−	0.0535881i
$188$	4.75025	+	8.22767i	0.346447	+	0.600064i
$189$		0			0
$190$	−2.77007	+	4.79790i	−0.200962	+	0.348076i
$191$	2.51720	−	8.40803i	0.182138	−	0.608384i	−0.817342	−	0.576152i	$-0.804553\pi$
$191$	2.51720	−	8.40803i	0.182138	−	0.608384i	0.999480	−	0.0322315i	$-0.0102614\pi$
$192$		0			0
$193$	11.5993	+	7.62896i	0.834934	+	0.549145i	0.893461	−	0.449141i	$-0.148270\pi$
$193$	11.5993	+	7.62896i	0.834934	+	0.549145i	−0.0585270	+	0.998286i	$0.518640\pi$
$194$	−2.30993	−	3.10278i	−0.165843	−	0.222766i
$195$		0			0
$196$	−6.44862	+	4.24133i	−0.460616	+	0.302952i
$197$	11.0092	+	4.00701i	0.784371	+	0.285488i	0.702994	−	0.711196i	$-0.251846\pi$
$197$	11.0092	+	4.00701i	0.784371	+	0.285488i	0.0813770	+	0.996683i	$0.474068\pi$
$198$		0			0
$199$	6.43206	−	2.34108i	0.455957	−	0.165955i	−0.103824	−	0.994596i	$-0.533108\pi$
$199$	6.43206	−	2.34108i	0.455957	−	0.165955i	0.559780	+	0.828641i	$0.310886\pi$
$200$	3.30718	−	4.44231i	0.233853	−	0.314119i
$201$		0			0
$202$	−6.81709	+	7.22569i	−0.479649	+	0.508398i
$203$	7.17664	−	7.60679i	0.503701	−	0.533892i
$204$		0			0
$205$	−0.628259	+	0.843898i	−0.0438795	+	0.0589404i
$206$	−1.06751	+	0.388543i	−0.0743772	+	0.0270711i
$207$		0			0
$208$	5.28292	+	1.92283i	0.366305	+	0.133324i
$209$	2.96467	−	1.94990i	0.205071	−	0.134877i
$210$		0			0
$211$	4.27769	+	5.74593i	0.294488	+	0.395566i	0.924601	−	0.380938i	$-0.124399\pi$
$211$	4.27769	+	5.74593i	0.294488	+	0.395566i	−0.630113	+	0.776504i	$0.716991\pi$
$212$	−16.8174	−	11.0610i	−1.15503	−	0.759673i
$213$		0			0
$214$	3.25692	−	10.8789i	0.222639	−	0.743665i
$215$	6.03146	−	10.4468i	0.411342	−	0.712466i
$216$		0			0
$217$	0.591507	+	1.02452i	0.0401541	+	0.0695490i
$218$	−3.32567	+	0.788198i	−0.225243	+	0.0533835i
$219$		0			0
$220$	1.27419	−	0.639924i	0.0859061	−	0.0431437i
$221$	−5.85070	+	13.5635i	−0.393561	+	0.912377i
$222$		0			0
$223$	0.198760	+	3.41258i	0.0133099	+	0.228523i	0.998403	+	0.0564987i	$0.0179937\pi$
$223$	0.198760	+	3.41258i	0.0133099	+	0.228523i	−0.985093	+	0.172024i	$0.944969\pi$
$224$	−1.45403	−	8.24622i	−0.0971515	−	0.550974i
$225$		0			0
$226$	−0.0192235	+	0.109022i	−0.00127873	+	0.00725202i
$227$	5.60340	+	0.654943i	0.371911	+	0.0434701i	0.299995	−	0.953941i	$-0.403015\pi$
$227$	5.60340	+	0.654943i	0.371911	+	0.0434701i	0.0719151	+	0.997411i	$0.477089\pi$
$228$		0			0
$229$	−2.35125	−	7.85374i	−0.155375	−	0.518989i	0.844487	−	0.535576i	$-0.179905\pi$
$229$	−2.35125	−	7.85374i	−0.155375	−	0.518989i	−0.999862	+	0.0165863i	$0.994720\pi$
$230$	−4.65440	−	1.10311i	−0.306902	−	0.0727371i
$231$		0			0
$232$	−5.56459	−	12.9002i	−0.365333	−	0.846938i
$233$	−0.223451	−	0.187498i	−0.0146388	−	0.0122834i	0.635439	−	0.772151i	$-0.280819\pi$
$233$	−0.223451	−	0.187498i	−0.0146388	−	0.0122834i	−0.650078	+	0.759868i	$0.725264\pi$
$234$		0			0
$235$	−6.63061	+	5.56374i	−0.432533	+	0.362938i
$236$	3.51170	+	1.76364i	0.228592	+	0.114803i
$237$		0			0
$238$	4.99347	−	0.583653i	0.323678	−	0.0378326i
$239$	0.971145	−	16.6739i	0.0628181	−	1.07855i	−0.808712	−	0.588204i	$-0.799835\pi$
$239$	0.971145	−	16.6739i	0.0628181	−	1.07855i	0.871530	−	0.490341i	$-0.163128\pi$
$240$		0			0
$241$	−14.7816	−	15.6675i	−0.952163	−	1.00923i	−0.999946	−	0.0103764i	$-0.996697\pi$
$241$	−14.7816	−	15.6675i	−0.952163	−	1.00923i	0.0477828	−	0.998858i	$-0.484784\pi$
$242$	−6.05315			−0.389111
$243$		0			0
$244$	−18.4249			−1.17954
$245$	−4.82566	−	5.11490i	−0.308300	−	0.326779i
$246$		0			0
$247$	−0.959122	+	16.4675i	−0.0610275	+	1.04780i
$248$	1.57852	−	0.184502i	0.100236	−	0.0117159i
$249$		0			0
$250$	5.92871	+	2.97751i	0.374965	+	0.188314i
$251$	−10.4865	+	8.79918i	−0.661899	+	0.555399i	−0.910655	−	0.413167i	$-0.864423\pi$
$251$	−10.4865	+	8.79918i	−0.661899	+	0.555399i	0.248756	+	0.968566i	$0.419978\pi$
$252$		0			0
$253$	2.34694	+	1.96931i	0.147551	+	0.123810i
$254$	−0.590301	−	1.36847i	−0.0370388	−	0.0858656i
$255$		0			0
$256$	−3.82143	−	0.905695i	−0.238839	−	0.0566059i
$257$	2.14362	+	7.16020i	0.133716	+	0.446641i	0.998454	−	0.0555810i	$-0.0177011\pi$
$257$	2.14362	+	7.16020i	0.133716	+	0.446641i	−0.864739	+	0.502222i	$0.832516\pi$
$258$		0			0
$259$	12.1563	+	1.42086i	0.755353	+	0.0882881i
$260$	−1.15099	+	6.52760i	−0.0713815	+	0.404825i
$261$		0			0
$262$	−0.900226	−	5.10544i	−0.0556162	−	0.315415i
$263$	1.61650	+	27.7542i	0.0996775	+	1.71140i	0.564036	+	0.825750i	$0.309248\pi$
$263$	1.61650	+	27.7542i	0.0996775	+	1.71140i	−0.464359	+	0.885647i	$0.653715\pi$
$264$		0			0
$265$	7.26366	−	16.8391i	0.446203	−	1.03442i
$266$	5.01701	−	2.51964i	0.307613	−	0.154489i
$267$		0			0
$268$	16.4736	−	3.90431i	1.00628	−	0.238493i
$269$	12.3392	+	21.3722i	0.752337	+	1.30309i	0.946688	+	0.322153i	$0.104407\pi$
$269$	12.3392	+	21.3722i	0.752337	+	1.30309i	−0.194351	+	0.980932i	$0.562260\pi$
$270$		0			0
$271$	2.61782	−	4.53419i	0.159021	−	0.275432i	−0.775495	−	0.631354i	$-0.782500\pi$
$271$	2.61782	−	4.53419i	0.159021	−	0.275432i	0.934516	+	0.355921i	$0.115833\pi$
$272$	−3.58027	+	11.9589i	−0.217086	+	0.725117i
$273$		0			0
$274$	−5.04919	−	3.32090i	−0.305033	−	0.200623i
$275$	−0.880882	−	1.18323i	−0.0531192	−	0.0713514i
$276$		0			0
$277$	−0.378193	+	0.248742i	−0.0227234	+	0.0149454i	−0.560820	−	0.827938i	$-0.689514\pi$
$277$	−0.378193	+	0.248742i	−0.0227234	+	0.0149454i	0.538096	+	0.842883i	$0.319144\pi$
$278$	−1.31246	−	0.477695i	−0.0787159	−	0.0286502i
$279$		0			0
$280$	4.64431	−	1.69039i	0.277550	−	0.101020i
$281$	8.30803	−	11.1596i	0.495616	−	0.665727i	−0.481989	−	0.876177i	$-0.660085\pi$
$281$	8.30803	−	11.1596i	0.495616	−	0.665727i	0.977605	+	0.210450i	$0.0674929\pi$
$282$		0			0
$283$	10.6410	−	11.2788i	0.632540	−	0.670453i	−0.329249	−	0.944243i	$-0.606796\pi$
$283$	10.6410	−	11.2788i	0.632540	−	0.670453i	0.961790	+	0.273790i	$0.0882772\pi$
$284$	−7.78731	+	8.25407i	−0.462092	+	0.489789i
$285$		0			0
$286$	−0.483796	+	0.649850i	−0.0286074	+	0.0384265i
$287$	1.00185	−	0.364642i	0.0591371	−	0.0215241i
$288$		0			0
$289$	−14.8468	−	5.40379i	−0.873341	−	0.317870i
$290$	4.88129	−	3.21047i	0.286639	−	0.188526i
$291$		0			0
$292$	−7.67162	−	10.3048i	−0.448948	−	0.603041i
$293$	10.6137	+	6.98073i	0.620058	+	0.407819i	0.820305	−	0.571927i	$-0.193804\pi$
$293$	10.6137	+	6.98073i	0.620058	+	0.407819i	−0.200246	+	0.979746i	$0.564174\pi$
$294$		0			0
$295$	−1.02682	+	3.42982i	−0.0597839	+	0.199692i
$296$	8.22097	−	14.2391i	0.477834	−	0.827633i
$297$		0			0
$298$	−0.337414	−	0.584419i	−0.0195459	−	0.0338545i
$299$	−13.8582	+	3.28445i	−0.801439	+	0.189944i
$300$		0			0
$301$	−10.9239	+	5.48619i	−0.629643	+	0.316219i
$302$	3.38096	−	7.83795i	0.194552	−	0.451023i
$303$		0			0
$304$	0.810551	+	13.9166i	0.0464883	+	0.798173i
$305$	−2.91494	−	16.5314i	−0.166909	−	0.946587i
$306$		0			0
$307$	2.09466	−	11.8794i	0.119548	−	0.677993i	−0.864849	−	0.502032i	$-0.832586\pi$
$307$	2.09466	−	11.8794i	0.119548	−	0.677993i	0.984397	−	0.175960i	$-0.0563031\pi$
$308$	−1.43515	−	0.167744i	−0.0817750	−	0.00955813i
$309$		0			0
$310$	0.189550	+	0.633142i	0.0107657	+	0.0359600i
$311$	18.9624	+	4.49416i	1.07526	+	0.254840i	0.729846	−	0.683611i	$-0.239592\pi$
$311$	18.9624	+	4.49416i	1.07526	+	0.254840i	0.345410	+	0.938452i	$0.387740\pi$
$312$		0			0
$313$	−7.31968	−	16.9689i	−0.413733	−	0.959141i	−0.989895	−	0.141805i	$-0.954709\pi$
$313$	−7.31968	−	16.9689i	−0.413733	−	0.959141i	0.576162	−	0.817336i	$-0.304550\pi$
$314$	−0.0961233	−	0.0806570i	−0.00542455	−	0.00455174i
$315$		0			0
$316$	6.20860	−	5.20964i	0.349261	−	0.293065i
$317$	−15.8725	−	7.97145i	−0.891486	−	0.447721i	−0.0567610	−	0.998388i	$-0.518077\pi$
$317$	−15.8725	−	7.97145i	−0.891486	−	0.447721i	−0.834725	+	0.550667i	$0.814374\pi$
$318$		0			0
$319$	−3.71676	+	0.434427i	−0.208099	+	0.0243232i
$320$	−0.115859	+	1.98922i	−0.00647669	+	0.111201i
$321$		0			0
$322$	3.32639	+	3.52577i	0.185373	+	0.196483i
$323$	−36.6274			−2.03800
$324$		0			0
$325$	6.85731			0.380375
$326$	−6.72112	−	7.12397i	−0.372249	−	0.394560i
$327$		0			0
$328$	0.0832784	−	1.42984i	0.00459828	−	0.0789495i
$329$	8.71202	−	1.01829i	0.480309	−	0.0561401i
$330$		0			0
$331$	−9.22416	−	4.63255i	−0.507005	−	0.254628i	0.176860	−	0.984236i	$-0.443406\pi$
$331$	−9.22416	−	4.63255i	−0.507005	−	0.254628i	−0.683865	+	0.729608i	$0.739702\pi$
$332$	11.6722	−	9.79412i	0.640594	−	0.537522i
$333$		0			0
$334$	0.0402073	+	0.0337380i	0.00220005	+	0.00184606i
$335$	6.10928	+	14.1629i	0.333786	+	0.773803i
$336$		0			0
$337$	−26.9086	−	6.37746i	−1.46581	−	0.347402i	−0.581207	−	0.813756i	$-0.697419\pi$
$337$	−26.9086	−	6.37746i	−1.46581	−	0.347402i	−0.884598	+	0.466353i	$0.845567\pi$
$338$	1.03064	+	3.44257i	0.0560593	+	0.187251i
$339$		0			0
$340$	−14.6184	−	1.70864i	−0.792793	−	0.0926642i
$341$	0.0735067	−	0.416877i	0.00398061	−	0.0225752i
$342$		0			0
$343$	3.12222	+	17.7070i	0.168584	+	0.956088i
$344$	0.954852	+	16.3942i	0.0514822	+	0.883915i
$345$		0			0
$346$	1.81124	−	4.19892i	0.0973727	−	0.225735i
$347$	−16.4381	+	8.25552i	−0.882443	+	0.443180i	−0.831502	−	0.555522i	$-0.812519\pi$
$347$	−16.4381	+	8.25552i	−0.882443	+	0.443180i	−0.0509416	+	0.998702i	$0.516222\pi$
$348$		0			0
$349$	−1.06469	+	0.252335i	−0.0569913	+	0.0135072i	−0.259013	−	0.965874i	$-0.583397\pi$
$349$	−1.06469	+	0.252335i	−0.0569913	+	0.0135072i	0.202021	+	0.979381i	$0.435249\pi$
$350$	−1.16694	−	2.02119i	−0.0623754	−	0.108037i
$351$		0			0
$352$	−1.49810	+	2.59478i	−0.0798489	+	0.138302i
$353$	6.48166	−	21.6503i	0.344984	−	1.15233i	−0.592870	−	0.805298i	$-0.702005\pi$
$353$	6.48166	−	21.6503i	0.344984	−	1.15233i	0.937854	−	0.347029i	$-0.112809\pi$
$354$		0			0
$355$	−8.63781	−	5.68118i	−0.458447	−	0.301525i
$356$	13.6265	+	18.3035i	0.722202	+	0.970085i
$357$		0			0
$358$	−9.22231	+	6.06561i	−0.487414	+	0.320577i
$359$	1.21503	+	0.442236i	0.0641270	+	0.0233403i	0.373884	−	0.927475i	$-0.378026\pi$
$359$	1.21503	+	0.442236i	0.0641270	+	0.0233403i	−0.309758	+	0.950816i	$0.600248\pi$
$360$		0			0
$361$	−20.5811	+	7.49089i	−1.08321	+	0.394257i
$362$	−2.09915	+	2.81965i	−0.110329	+	0.148197i
$363$		0			0
$364$	4.60941	−	4.88569i	0.241599	−	0.256080i
$365$	8.03207	−	8.51350i	0.420418	−	0.445617i
$366$		0			0
$367$	−16.2845	+	21.8739i	−0.850046	+	1.14181i	0.138421	+	0.990373i	$0.455797\pi$
$367$	−16.2845	+	21.8739i	−0.850046	+	1.14181i	−0.988467	+	0.151436i	$0.951610\pi$
$368$	−11.3101	+	4.11653i	−0.589578	+	0.214589i
$369$		0			0
$370$	6.42514	+	2.33856i	0.334027	+	0.121576i
$371$	−15.5267	+	10.2121i	−0.806106	+	0.530184i
$372$		0			0
$373$	3.58766	+	4.81906i	0.185762	+	0.249521i	0.885242	−	0.465130i	$-0.153993\pi$
$373$	3.58766	+	4.81906i	0.185762	+	0.249521i	−0.699480	+	0.714652i	$0.746585\pi$
$374$	−1.50299	−	0.988532i	−0.0777177	−	0.0511158i
$375$		0			0
$376$	3.37953	−	11.2884i	0.174286	−	0.582155i
$377$	8.69775	−	15.0649i	0.447957	−	0.775884i
$378$		0			0
$379$	−12.1466	−	21.0386i	−0.623931	−	1.08068i	−0.988747	−	0.149601i	$-0.952201\pi$
$379$	−12.1466	−	21.0386i	−0.623931	−	1.08068i	0.364815	−	0.931080i	$-0.381132\pi$
$380$	−15.9925	+	3.79029i	−0.820397	+	0.194438i
$381$		0			0
$382$	−4.44027	+	2.22999i	−0.227184	+	0.114096i
$383$	9.87965	−	22.9036i	0.504827	−	1.17032i	−0.455195	−	0.890392i	$-0.650430\pi$
$383$	9.87965	−	22.9036i	0.504827	−	1.17032i	0.960021	−	0.279928i	$-0.0903105\pi$
$384$		0			0
$385$	−0.0765432	−	1.31420i	−0.00390100	−	0.0669776i
$386$	−1.36483	−	7.74031i	−0.0694678	−	0.393971i
$387$		0			0
$388$	1.99270	−	11.3012i	0.101164	−	0.573731i
$389$	−7.03720	−	0.822530i	−0.356800	−	0.0417039i	−0.0641951	−	0.997937i	$-0.520448\pi$
$389$	−7.03720	−	0.822530i	−0.356800	−	0.0417039i	−0.292605	+	0.956233i	$0.594522\pi$
$390$		0			0
$391$	−9.06986	−	30.2954i	−0.458682	−	1.53211i
$392$	9.31505	+	2.20771i	0.470481	+	0.111506i
$393$		0			0
$394$	−2.62705	−	6.09018i	−0.132349	−	0.306819i
$395$	5.65649	+	4.74636i	0.284609	+	0.238815i
$396$		0			0
$397$	−8.11749	+	6.81138i	−0.407405	+	0.341854i	−0.823348	−	0.567537i	$-0.807896\pi$
$397$	−8.11749	+	6.81138i	−0.407405	+	0.341854i	0.415942	+	0.909391i	$0.363452\pi$
$398$	−3.46290	−	1.73913i	−0.173579	−	0.0871748i
$399$		0			0
$400$	5.75591	−	0.672769i	0.287795	−	0.0336384i
$401$	−2.16882	+	37.2372i	−0.108306	+	1.85954i	0.309370	+	0.950942i	$0.399882\pi$
$401$	−2.16882	+	37.2372i	−0.108306	+	1.85954i	−0.417675	+	0.908596i	$0.637155\pi$
$402$		0			0
$403$	1.35039	+	1.43133i	0.0672678	+	0.0712997i
$404$	−29.4703			−1.46620
$405$		0			0
$406$	−5.92053			−0.293831
$407$	−3.00532	−	3.18545i	−0.148968	−	0.157897i
$408$		0			0
$409$	−0.145832	+	2.50384i	−0.00721094	+	0.123807i	0.992782	+	0.119937i	$0.0382691\pi$
$409$	−0.145832	+	2.50384i	−0.00721094	+	0.123807i	−0.999993	+	0.00387063i	$0.998768\pi$
$410$	0.591587	−	0.0691466i	0.0292164	−	0.00341491i
$411$		0			0
$412$	−3.01169	−	1.51253i	−0.148375	−	0.0745168i
$413$	2.77927	−	2.33209i	0.136759	−	0.114754i
$414$		0			0
$415$	10.6342	+	8.92316i	0.522013	+	0.438021i
$416$	−5.51669	−	12.7891i	−0.270478	−	0.627039i
$417$		0			0
$418$	−1.95473	−	0.463279i	−0.0956088	−	0.0226597i
$419$	1.70938	+	5.70974i	0.0835088	+	0.278939i	0.989537	−	0.144278i	$-0.0460860\pi$
$419$	1.70938	+	5.70974i	0.0835088	+	0.278939i	−0.906028	+	0.423217i	$0.860901\pi$
$420$		0			0
$421$	−37.4970	−	4.38277i	−1.82749	−	0.213603i	−0.868239	−	0.496147i	$-0.834748\pi$
$421$	−37.4970	−	4.38277i	−1.82749	−	0.213603i	−0.959255	+	0.282543i	$0.908822\pi$
$422$	0.704216	−	3.99380i	0.0342807	−	0.194415i
$423$		0			0
$424$	4.33526	+	24.5865i	0.210539	+	1.19403i
$425$	0.885337	+	15.2006i	0.0429451	+	0.737339i
$426$		0			0
$427$	−6.73764	+	15.6196i	−0.326057	+	0.755885i
$428$	30.1055	−	15.1195i	1.45520	−	0.730830i
$429$		0			0
$430$	−6.64510	+	1.57492i	−0.320455	+	0.0759493i
$431$	3.59352	+	6.22416i	0.173094	+	0.299807i	0.939500	−	0.342549i	$-0.111290\pi$
$431$	3.59352	+	6.22416i	0.173094	+	0.299807i	−0.766406	+	0.642356i	$0.777957\pi$
$432$		0			0
$433$	0.408870	−	0.708184i	0.0196490	−	0.0340331i	−0.856034	−	0.516920i	$-0.827078\pi$
$433$	0.408870	−	0.708184i	0.0196490	−	0.0340331i	0.875683	+	0.482887i	$0.160412\pi$
$434$	0.192084	−	0.641604i	0.00922031	−	0.0307980i
$435$		0			0
$436$	−8.47128	−	5.57165i	−0.405701	−	0.266834i
$437$	−21.0884	−	28.3266i	−1.00879	−	1.35505i
$438$		0			0
$439$	26.6153	−	17.5051i	1.27028	−	0.835475i	0.278130	−	0.960544i	$-0.410285\pi$
$439$	26.6153	−	17.5051i	1.27028	−	0.835475i	0.992148	+	0.125069i	$0.0399151\pi$
$440$	−1.66183	−	0.604858i	−0.0792249	−	0.0288355i
$441$		0			0
$442$	7.85828	−	2.86018i	0.373780	−	0.136045i
$443$	−4.15638	+	5.58298i	−0.197475	+	0.265255i	−0.889820	−	0.456311i	$-0.849170\pi$
$443$	−4.15638	+	5.58298i	−0.197475	+	0.265255i	0.692345	+	0.721567i	$0.256578\pi$
$444$		0			0
$445$	−14.2667	+	15.1218i	−0.676307	+	0.716844i
$446$	1.32804	−	1.40764i	0.0628845	−	0.0666537i
$447$		0			0
$448$	1.20579	−	1.61966i	0.0569684	−	0.0765218i
$449$	0.124194	−	0.0452028i	0.00586106	−	0.00213325i	−0.339088	−	0.940755i	$-0.610118\pi$
$449$	0.124194	−	0.0452028i	0.00586106	−	0.00213325i	0.344949	+	0.938621i	$0.387896\pi$
$450$		0			0
$451$	−0.358482	−	0.130477i	−0.0168803	−	0.00614392i
$452$	−0.274388	+	0.180468i	−0.0129061	+	0.00848849i
$453$		0			0
$454$	−1.90723	−	2.56186i	−0.0895109	−	0.120234i
$455$	5.11283	+	3.36276i	0.239693	+	0.157649i
$456$		0			0
$457$	3.25090	−	10.8588i	0.152071	−	0.507951i	−0.847675	−	0.530516i	$-0.821998\pi$
$457$	3.25090	−	10.8588i	0.152071	−	0.507951i	0.999745	+	0.0225649i	$0.00718325\pi$
$458$	−2.32061	+	4.01941i	−0.108435	+	0.187815i
$459$		0			0
$460$	−7.09518	−	12.2892i	−0.330814	−	0.572987i
$461$	−2.65502	+	0.629252i	−0.123657	+	0.0293072i	−0.291978	−	0.956425i	$-0.594313\pi$
$461$	−2.65502	+	0.629252i	−0.123657	+	0.0293072i	0.168322	+	0.985732i	$0.446165\pi$
$462$		0			0
$463$	−26.1753	+	13.1457i	−1.21647	+	0.610933i	−0.937036	−	0.349232i	$-0.886443\pi$
$463$	−26.1753	+	13.1457i	−1.21647	+	0.610933i	−0.279432	+	0.960165i	$0.590146\pi$
$464$	5.82272	−	13.4986i	0.270313	−	0.626656i
$465$		0			0
$466$	0.00960187	+	0.164858i	0.000444798	+	0.00763689i
$467$	−4.38748	−	24.8826i	−0.203028	−	1.15143i	−0.900512	−	0.434831i	$-0.856808\pi$
$467$	−4.38748	−	24.8826i	−0.203028	−	1.15143i	0.697484	−	0.716600i	$-0.254303\pi$
$468$		0			0
$469$	2.71421	−	15.3931i	0.125331	−	0.710786i
$470$	4.86709	+	0.568881i	0.224502	+	0.0262405i
$471$		0			0
$472$	−1.39787	−	4.66922i	−0.0643423	−	0.214918i
$473$	4.25616	+	1.00873i	0.195699	+	0.0463814i
$474$		0			0
$475$	6.73468	+	15.6128i	0.309009	+	0.716362i
$476$	11.4253	+	9.58692i	0.523675	+	0.439416i
$477$		0			0
$478$	−7.24341	+	6.07794i	−0.331306	+	0.277999i
$479$	−2.17396	−	1.09180i	−0.0993307	−	0.0498858i	0.398440	−	0.917194i	$-0.369552\pi$
$479$	−2.17396	−	1.09180i	−0.0993307	−	0.0498858i	−0.497771	+	0.867309i	$0.665848\pi$
$480$		0			0
$481$	20.2205	−	2.36344i	0.921977	−	0.107764i
$482$	−0.709039	+	12.1737i	−0.0322959	+	0.554498i
$483$		0			0
$484$	−12.3231	−	13.0618i	−0.560143	−	0.593717i
$485$	10.4550			0.474739
$486$		0			0
$487$	−36.5650			−1.65692			−0.828458	−	0.560051i	$-0.810782\pi$
$487$	−36.5650			−1.65692			−0.828458	+	0.560051i	$0.810782\pi$
$488$	15.6823	+	16.6222i	0.709902	+	0.752453i
$489$		0			0
$490$	−0.231477	+	3.97430i	−0.0104570	+	0.179541i
$491$	−6.53557	+	0.763899i	−0.294946	+	0.0344743i	−0.262279	−	0.964992i	$-0.584474\pi$
$491$	−6.53557	+	0.763899i	−0.294946	+	0.0344743i	−0.0326670	+	0.999466i	$0.510400\pi$
$492$		0			0
$493$	34.5175	+	17.3353i	1.55459	+	0.780745i
$494$	7.15374	−	6.00270i	0.321862	−	0.270074i
$495$		0			0
$496$	1.27392	+	1.06895i	0.0572008	+	0.0479972i
$497$	4.14966	+	9.61998i	0.186137	+	0.431515i
$498$		0			0
$499$	31.8682	+	7.55291i	1.42662	+	0.338115i	0.870164	−	0.492763i	$-0.164013\pi$
$499$	31.8682	+	7.55291i	1.42662	+	0.338115i	0.556455	+	0.830878i	$0.312161\pi$
$500$	5.64480	+	18.8549i	0.252443	+	0.843218i
$501$		0			0
$502$	7.69741	+	0.899698i	0.343552	+	0.0401555i
$503$	−0.367724	+	2.08547i	−0.0163960	+	0.0929864i	−0.991908	−	0.126961i	$-0.959478\pi$
$503$	−0.367724	+	2.08547i	−0.0163960	+	0.0929864i	0.975512	+	0.219948i	$0.0705887\pi$
$504$		0			0
$505$	−4.66238	−	26.4417i	−0.207473	−	1.17664i
$506$	−0.100850	−	1.73152i	−0.00448331	−	0.0769755i
$507$		0			0
$508$	1.75120	−	4.05975i	0.0776971	−	0.180122i
$509$	−40.0232	+	20.1004i	−1.77400	+	0.890934i	−0.832412	+	0.554158i	$0.813040\pi$
$509$	−40.0232	+	20.1004i	−1.77400	+	0.890934i	−0.941585	+	0.336777i	$0.890663\pi$
$510$		0			0
$511$	−11.5412	+	2.73530i	−0.510551	+	0.121003i
$512$	−10.4258	−	18.0581i	−0.460761	−	0.798062i
$513$		0			0
$514$	2.11568	−	3.66447i	0.0933188	−	0.161633i
$515$	0.880618	−	2.94147i	0.0388047	−	0.129617i
$516$		0			0
$517$	−2.62224	−	1.72467i	−0.115326	−	0.0758511i
$518$	−4.13764	−	5.55781i	−0.181797	−	0.244196i
$519$		0			0
$520$	6.86860	−	4.51755i	0.301208	−	0.198108i
$521$	33.1780	+	12.0758i	1.45356	+	0.529051i	0.943582	−	0.331139i	$-0.107433\pi$
$521$	33.1780	+	12.0758i	1.45356	+	0.529051i	0.509973	+	0.860190i	$0.329655\pi$
$522$		0			0
$523$	19.7616	−	7.19262i	0.864113	−	0.314511i	0.128332	−	0.991731i	$-0.459038\pi$
$523$	19.7616	−	7.19262i	0.864113	−	0.314511i	0.735781	+	0.677220i	$0.236815\pi$
$524$	9.18405	−	12.3363i	0.401207	−	0.538915i
$525$		0			0
$526$	10.8008	−	11.4482i	0.470939	−	0.499166i
$527$	−2.99849	+	3.17822i	−0.130616	+	0.138445i
$528$		0			0
$529$	4.47299	−	6.00827i	0.194478	−	0.261229i
$530$	−9.75607	+	3.55092i	−0.423777	+	0.154242i
$531$		0			0
$532$	15.6507	+	5.69640i	0.678546	+	0.246970i
$533$	1.48166	−	0.974502i	0.0641777	−	0.0422103i
$534$		0			0
$535$	18.3286	+	24.6196i	0.792414	+	1.06440i
$536$	−17.5437	−	11.5386i	−0.757771	−	0.498394i
$537$		0			0
$538$	4.00699	−	13.3843i	0.172754	−	0.577038i
$539$	1.27492	−	2.20823i	0.0549147	−	0.0951150i
$540$		0			0
$541$	−7.11418	−	12.3221i	−0.305863	−	0.529770i	0.671590	−	0.740923i	$-0.265611\pi$
$541$	−7.11418	−	12.3221i	−0.305863	−	0.529770i	−0.977453	+	0.211153i	$0.932278\pi$
$542$	−2.88415	+	0.683557i	−0.123885	+	0.0293613i
$543$		0			0
$544$	27.6375	−	13.8801i	1.18495	−	0.595103i
$545$	3.65885	−	8.48217i	0.156728	−	0.363336i
$546$		0			0
$547$	−0.134083	−	2.30212i	−0.00573299	−	0.0984316i	0.994228	−	0.107290i	$-0.0342173\pi$
$547$	−0.134083	−	2.30212i	−0.00573299	−	0.0984316i	−0.999961	+	0.00885834i	$0.997180\pi$
$548$	−3.11325	−	17.6561i	−0.132992	−	0.754233i
$549$		0			0
$550$	−0.145016	+	0.822424i	−0.00618348	+	0.0350683i
$551$	42.8421	+	5.00753i	1.82514	+	0.213328i
$552$		0			0
$553$	−2.14607	−	7.16836i	−0.0912600	−	0.304830i
$554$	0.249358	+	0.0590989i	0.0105942	+	0.00251087i
$555$		0			0
$556$	−1.64114	−	3.80458i	−0.0695997	−	0.161350i
$557$	31.5724	+	26.4924i	1.33777	+	1.12252i	0.982194	+	0.187871i	$0.0601586\pi$
$557$	31.5724	+	26.4924i	1.33777	+	1.12252i	0.355573	+	0.934649i	$0.384286\pi$
$558$		0			0
$559$	−15.5763	+	13.0701i	−0.658809	+	0.552806i
$560$	4.62154	+	2.32102i	0.195296	+	0.0980812i
$561$		0			0
$562$	−7.82309	+	0.914388i	−0.329997	+	0.0385711i
$563$	0.722839	−	12.4107i	0.0304640	−	0.523047i	−0.948212	−	0.317638i	$-0.897110\pi$
$563$	0.722839	−	12.4107i	0.0304640	−	0.523047i	0.978676	−	0.205409i	$-0.0658526\pi$
$564$		0			0
$565$	−0.205331	−	0.217638i	−0.00863835	−	0.00915612i
$566$	−8.77850			−0.368988
$567$		0			0
$568$	14.0746			0.590557
$569$	−5.21404	−	5.52656i	−0.218584	−	0.231685i	0.608798	−	0.793325i	$-0.291652\pi$
$569$	−5.21404	−	5.52656i	−0.218584	−	0.231685i	−0.827382	+	0.561640i	$0.810171\pi$
$570$		0			0
$571$	−0.970116	+	16.6562i	−0.0405981	+	0.697042i	0.915197	+	0.403008i	$0.132035\pi$
$571$	−0.970116	+	16.6562i	−0.0405981	+	0.697042i	−0.955795	+	0.294035i	$0.905002\pi$
$572$	−2.38720	+	0.279024i	−0.0998138	+	0.0116666i
$573$		0			0
$574$	−0.539374	−	0.270884i	−0.0225130	−	0.0113065i
$575$	−11.2460	+	9.43653i	−0.468991	+	0.393531i
$576$		0			0
$577$	7.89417	+	6.62400i	0.328639	+	0.275761i	0.792145	−	0.610333i	$-0.208964\pi$
$577$	7.89417	+	6.62400i	0.328639	+	0.275761i	−0.463506	+	0.886094i	$0.653409\pi$
$578$	3.54279	+	8.21312i	0.147361	+	0.341621i
$579$		0			0
$580$	16.8652	+	3.99711i	0.700287	+	0.165971i
$581$	−4.03461	−	13.4765i	−0.167384	−	0.559100i
$582$		0			0
$583$	6.60479	+	0.771990i	0.273543	+	0.0319726i
$584$	−2.76690	+	15.6919i	−0.114495	+	0.649334i
$585$		0			0
$586$	−1.24886	−	7.08262i	−0.0515898	−	0.292580i
$587$	−0.721063	−	12.3802i	−0.0297614	−	0.510984i	−0.979942	−	0.199284i	$-0.936138\pi$
$587$	−0.721063	−	12.3802i	−0.0297614	−	0.510984i	0.950180	−	0.311700i	$-0.100899\pi$
$588$		0			0
$589$	−1.93262	+	4.48031i	−0.0796322	+	0.184608i
$590$	1.81128	−	0.909660i	0.0745693	−	0.0374501i
$591$		0			0
$592$	16.7409	−	3.96766i	0.688046	−	0.163070i
$593$	−6.28620	−	10.8880i	−0.258143	−	0.447117i	0.707601	−	0.706612i	$-0.249777\pi$
$593$	−6.28620	−	10.8880i	−0.258143	−	0.447117i	−0.965745	+	0.259495i	$0.916444\pi$
$594$		0			0
$595$	−6.79414	+	11.7678i	−0.278533	+	0.482433i
$596$	0.574170	−	1.91786i	0.0235189	−	0.0785587i
$597$		0			0
$598$	6.73642	+	4.43061i	0.275473	+	0.181181i
$599$	−6.33816	−	8.51362i	−0.258970	−	0.347857i	0.653554	−	0.756880i	$-0.273277\pi$
$599$	−6.33816	−	8.51362i	−0.258970	−	0.347857i	−0.912524	+	0.409023i	$0.865870\pi$
$600$		0			0
$601$	−27.2363	+	17.9136i	−1.11099	+	0.730711i	−0.965954	−	0.258714i	$-0.916701\pi$
$601$	−27.2363	+	17.9136i	−1.11099	+	0.730711i	−0.145039	+	0.989426i	$0.546331\pi$
$602$	6.50310	+	2.36694i	0.265047	+	0.0964691i
$603$		0			0
$604$	23.7961	−	8.66108i	0.968251	−	0.352414i
$605$	9.76983	−	13.1232i	0.397200	−	0.533533i
$606$		0			0
$607$	−6.61094	+	7.00718i	−0.268330	+	0.284413i	−0.847502	−	0.530792i	$-0.821894\pi$
$607$	−6.61094	+	7.00718i	−0.268330	+	0.284413i	0.579172	+	0.815205i	$0.303376\pi$
$608$	23.7003	−	25.1209i	0.961175	−	1.01879i
$609$		0			0
$610$	−5.67499	+	7.62283i	−0.229774	+	0.308639i
$611$	13.7102	−	4.99010i	0.554655	−	0.201878i
$612$		0			0
$613$	1.91768	+	0.697977i	0.0774542	+	0.0281910i	0.380457	−	0.924799i	$-0.375767\pi$
$613$	1.91768	+	0.697977i	0.0774542	+	0.0281910i	−0.303002	+	0.952990i	$0.597989\pi$
$614$	−5.70557	+	3.75261i	−0.230258	+	0.151443i
$615$		0			0
$616$	1.07018	+	1.43750i	0.0431189	+	0.0579187i
$617$	−1.76446	−	1.16050i	−0.0710345	−	0.0467201i	0.513495	−	0.858093i	$-0.328351\pi$
$617$	−1.76446	−	1.16050i	−0.0710345	−	0.0467201i	−0.584529	+	0.811372i	$0.698721\pi$
$618$		0			0
$619$	−6.56125	+	21.9161i	−0.263719	+	0.880882i	0.718879	+	0.695135i	$0.244656\pi$
$619$	−6.56125	+	21.9161i	−0.263719	+	0.880882i	−0.982598	+	0.185747i	$0.940530\pi$
$620$	−0.980332	+	1.69798i	−0.0393711	+	0.0681927i
$621$		0			0
$622$	−5.51627	−	9.55446i	−0.221182	−	0.383099i
$623$	20.4996	−	4.85850i	0.821300	−	0.194652i
$624$		0			0
$625$	−4.14487	+	2.08163i	−0.165795	+	0.0832652i
$626$	−4.14389	+	9.60662i	−0.165623	+	0.383958i
$627$		0			0
$628$	−0.0216446	−	0.371623i	−0.000863712	−	0.0148294i
$629$	7.84970	+	44.5179i	0.312988	+	1.77504i
$630$		0			0
$631$	−5.86931	+	33.2865i	−0.233654	+	1.32512i	0.611777	+	0.791030i	$0.290455\pi$
$631$	−5.86931	+	33.2865i	−0.233654	+	1.32512i	−0.845431	+	0.534085i	$0.820656\pi$
$632$	−9.98433	−	1.16700i	−0.397155	−	0.0464208i
$633$		0			0
$634$	2.88394	+	9.63302i	0.114536	+	0.382576i
$635$	3.91958	+	0.928959i	0.155544	+	0.0368646i
$636$		0			0
$637$	4.69485	+	10.8839i	0.186017	+	0.431235i
$638$	1.62286	+	1.36174i	0.0642497	+	0.0539119i
$639$		0			0
$640$	13.5238	−	11.3478i	0.534575	−	0.448561i
$641$	1.48538	+	0.745985i	0.0586689	+	0.0294646i	0.477892	−	0.878419i	$-0.341401\pi$
$641$	1.48538	+	0.745985i	0.0586689	+	0.0294646i	−0.419223	+	0.907883i	$0.637697\pi$
$642$		0			0
$643$	40.1211	−	4.68949i	1.58222	−	0.184935i	0.720917	−	0.693022i	$-0.243721\pi$
$643$	40.1211	−	4.68949i	1.58222	−	0.184935i	0.861306	+	0.508087i	$0.169647\pi$
$644$	−0.836123	+	14.3557i	−0.0329479	+	0.565693i
$645$		0			0
$646$	14.2298	+	15.0827i	0.559865	+	0.593422i
$647$	−18.1307			−0.712790			−0.356395	−	0.934335i	$-0.615994\pi$
$647$	−18.1307			−0.712790			−0.356395	+	0.934335i	$0.615994\pi$
$648$		0			0
$649$	−1.29821			−0.0509591
$650$	−2.66408	−	2.82376i	−0.104494	−	0.110757i
$651$		0			0
$652$	1.68942	−	29.0063i	0.0661630	−	1.13597i
$653$	−21.7635	+	2.54379i	−0.851672	+	0.0995462i	−0.530718	−	0.847549i	$-0.678078\pi$
$653$	−21.7635	+	2.54379i	−0.851672	+	0.0995462i	−0.320954	+	0.947095i	$0.604004\pi$
$654$		0			0
$655$	12.5215	+	6.28854i	0.489256	+	0.245713i
$656$	1.14807	−	0.963344i	0.0448246	−	0.0376123i
$657$		0			0
$658$	−3.80395	−	3.19190i	−0.148294	−	0.124433i
$659$	−11.8101	−	27.3790i	−0.460058	−	1.06653i	−0.977523	−	0.210830i	$-0.932383\pi$
$659$	−11.8101	−	27.3790i	−0.460058	−	1.06653i	0.517465	−	0.855704i	$-0.326876\pi$
$660$		0			0
$661$	−40.0583	−	9.49398i	−1.55809	−	0.369273i	−0.640865	−	0.767653i	$-0.721424\pi$
$661$	−40.0583	−	9.49398i	−1.55809	−	0.369273i	−0.917220	+	0.398380i	$0.869572\pi$
$662$	1.67598	+	5.59815i	0.0651387	+	0.217578i
$663$		0			0
$664$	−18.7705	−	2.19396i	−0.728439	−	0.0851423i
$665$	−2.63495	+	14.9435i	−0.102179	+	0.579486i
$666$		0			0
$667$	6.46693	+	36.6758i	0.250401	+	1.42009i
$668$	0.00905368	+	0.155446i	0.000350297	+	0.00601438i
$669$		0			0
$670$	3.45865	−	8.01805i	0.133619	−	0.309764i
$671$	5.43940	−	2.73177i	0.209986	−	0.105459i
$672$		0			0
$673$	15.6718	−	3.71429i	0.604104	−	0.143175i	0.0828284	−	0.996564i	$-0.473605\pi$
$673$	15.6718	−	3.71429i	0.604104	−	0.143175i	0.521275	+	0.853389i	$0.325457\pi$
$674$	7.82789	+	13.5583i	0.301519	+	0.522246i
$675$		0			0
$676$	−5.33034	+	9.23242i	−0.205013	+	0.355093i
$677$	−2.21576	+	7.40115i	−0.0851585	+	0.284449i	−0.989953	−	0.141400i	$-0.954840\pi$
$677$	−2.21576	+	7.40115i	−0.0851585	+	0.284449i	0.904794	+	0.425850i	$0.140025\pi$
$678$		0			0
$679$	−8.85180	−	5.82192i	−0.339701	−	0.223425i
$680$	10.9009	+	14.6424i	0.418029	+	0.561511i
$681$		0			0
$682$	−0.200223	+	0.131689i	−0.00766692	+	0.00504261i
$683$	−12.5132	−	4.55444i	−0.478805	−	0.174271i	0.0913320	−	0.995820i	$-0.470888\pi$
$683$	−12.5132	−	4.55444i	−0.478805	−	0.174271i	−0.570137	+	0.821550i	$0.693110\pi$
$684$		0			0
$685$	15.3491	−	5.58662i	0.586459	−	0.213454i
$686$	6.07854	−	8.16490i	0.232080	−	0.311737i
$687$		0			0
$688$	−11.7922	+	12.4990i	−0.449573	+	0.476520i
$689$	−21.2133	+	22.4848i	−0.808163	+	0.856603i
$690$		0			0
$691$	9.99890	−	13.4308i	0.380376	−	0.510934i	−0.570166	−	0.821529i	$-0.693121\pi$
$691$	9.99890	−	13.4308i	0.380376	−	0.510934i	0.950542	+	0.310596i	$0.100529\pi$
$692$	12.7480	−	4.63988i	0.484605	−	0.176382i
$693$		0			0
$694$	9.78576	+	3.56173i	0.371462	+	0.135201i
$695$	3.15395	−	2.07439i	0.119636	−	0.0786860i
$696$		0			0
$697$	2.35148	+	3.15858i	0.0890686	+	0.119640i
$698$	0.517541	+	0.340392i	0.0195892	+	0.0128840i
$699$		0			0
$700$	1.98575	−	6.63286i	0.0750542	−	0.250699i
$701$	1.93133	−	3.34516i	0.0729452	−	0.126345i	−0.827246	−	0.561840i	$-0.810094\pi$
$701$	1.93133	−	3.34516i	0.0729452	−	0.126345i	0.900191	+	0.435496i	$0.143427\pi$
$702$		0			0
$703$	25.2400	+	43.7170i	0.951946	+	1.64882i
$704$	−0.703045	+	0.166625i	−0.0264970	+	0.00627991i
$705$		0			0
$706$	−11.4335	+	5.74210i	−0.430304	+	0.216107i
$707$	−10.7767	+	24.9832i	−0.405300	+	0.939591i
$708$		0			0
$709$	1.51553	+	26.0207i	0.0569170	+	0.977227i	0.899019	+	0.437909i	$0.144281\pi$
$709$	1.51553	+	26.0207i	0.0569170	+	0.977227i	−0.842102	+	0.539318i	$0.818682\pi$
$710$	1.01637	+	5.76409i	0.0381435	+	0.216323i
$711$		0			0
$712$	4.91462	−	27.8722i	0.184183	−	1.04455i
$713$	−4.18434	−	0.489080i	−0.156705	−	0.0183162i
$714$		0			0
$715$	−0.628018	−	2.09773i	−0.0234866	−	0.0784506i
$716$	−31.8637	−	7.55182i	−1.19080	−	0.282225i
$717$		0			0
$718$	−0.289935	−	0.672145i	−0.0108203	−	0.0250842i
$719$	−23.6830	−	19.8724i	−0.883225	−	0.741114i	0.0836145	−	0.996498i	$-0.473354\pi$
$719$	−23.6830	−	19.8724i	−0.883225	−	0.741114i	−0.966840	+	0.255384i	$0.917798\pi$
$720$		0			0
$721$	−2.38355	+	2.00003i	−0.0887679	+	0.0744851i
$722$	11.0804	+	5.56481i	0.412371	+	0.207101i
$723$		0			0
$724$	−10.3579	+	1.21066i	−0.384947	+	0.0449939i
$725$	1.04261	−	17.9008i	0.0387214	−	0.664821i
$726$		0			0
$727$	−5.52707	−	5.85835i	−0.204988	−	0.217274i	0.616721	−	0.787182i	$-0.288461\pi$
$727$	−5.52707	−	5.85835i	−0.204988	−	0.217274i	−0.821709	+	0.569907i	$0.806979\pi$
$728$	−8.33093			−0.308765
$729$		0			0
$730$	−6.62623			−0.245248
$731$	−30.9836	−	32.8407i	−1.14597	−	1.21466i
$732$		0			0
$733$	−2.55023	+	43.7857i	−0.0941947	+	1.61726i	0.538339	+	0.842728i	$0.319052\pi$
$733$	−2.55023	+	43.7857i	−0.0941947	+	1.61726i	−0.632534	+	0.774533i	$0.717985\pi$
$734$	15.3340	−	1.79229i	0.565988	−	0.0661545i
$735$		0			0
$736$	26.6469	+	13.3826i	0.982217	+	0.493288i
$737$	−4.28445	+	3.59508i	−0.157820	+	0.132426i
$738$		0			0
$739$	14.3344	+	12.0280i	0.527300	+	0.442457i	0.867168	−	0.498016i	$-0.165938\pi$
$739$	14.3344	+	12.0280i	0.527300	+	0.442457i	−0.339868	+	0.940473i	$0.610382\pi$
$740$	8.03420	+	18.6254i	0.295343	+	0.684682i
$741$		0			0
$742$	10.2374	+	2.42630i	0.375825	+	0.0890722i
$743$	−3.17887	−	10.6182i	−0.116622	−	0.389543i	0.879670	−	0.475584i	$-0.157763\pi$
$743$	−3.17887	−	10.6182i	−0.116622	−	0.389543i	−0.996292	+	0.0860415i	$0.972578\pi$
$744$		0			0
$745$	1.81160	+	0.211746i	0.0663720	+	0.00775777i
$746$	0.590619	−	3.34957i	0.0216241	−	0.122636i
$747$		0			0
$748$	−0.926721	−	5.25570i	−0.0338843	−	0.192167i
$749$	−1.80849	−	31.0506i	−0.0660808	−	1.13456i
$750$		0			0
$751$	−3.26992	+	7.58052i	−0.119321	+	0.276617i	−0.967400	−	0.253252i	$-0.918500\pi$
$751$	−3.26992	+	7.58052i	−0.119321	+	0.276617i	0.848079	+	0.529869i	$0.177759\pi$
$752$	11.0185	−	5.53371i	0.401804	−	0.201794i
$753$		0			0
$754$	−9.58266	+	2.27113i	−0.348980	+	0.0827097i
$755$	11.5357	+	19.9804i	0.419827	+	0.727161i
$756$		0			0
$757$	11.2400	−	19.4682i	0.408524	−	0.707583i	−0.586201	−	0.810166i	$-0.699377\pi$
$757$	11.2400	−	19.4682i	0.408524	−	0.707583i	0.994725	+	0.102582i	$0.0327105\pi$
$758$	−3.94445	+	13.1754i	−0.143269	+	0.478551i
$759$		0			0
$760$	17.0313	+	11.2017i	0.617791	+	0.406328i
$761$	−18.1438	−	24.3714i	−0.657713	−	0.883462i	0.340677	−	0.940180i	$-0.389344\pi$
$761$	−18.1438	−	24.3714i	−0.657713	−	0.883462i	−0.998390	+	0.0567187i	$0.981936\pi$
$762$		0			0
$763$	−7.82110	+	5.14402i	−0.283143	+	0.186226i
$764$	−13.8516	−	5.04156i	−0.501132	−	0.182397i
$765$		0			0
$766$	−13.2697	+	4.82977i	−0.479454	+	0.174507i
$767$	3.60379	−	4.84073i	0.130125	−	0.174789i
$768$		0			0
$769$	−3.76312	+	3.98867i	−0.135702	+	0.143835i	−0.791660	−	0.610961i	$-0.790783\pi$
$769$	−3.76312	+	3.98867i	−0.135702	+	0.143835i	0.655959	+	0.754797i	$0.272265\pi$
$770$	−0.511433	+	0.542087i	−0.0184308	+	0.0195355i
$771$		0			0
$772$	13.9239	−	18.7030i	0.501130	−	0.673135i
$773$	−5.96931	+	2.17265i	−0.214701	+	0.0781448i	−0.447132	−	0.894468i	$-0.647554\pi$
$773$	−5.96931	+	2.17265i	−0.214701	+	0.0781448i	0.232430	+	0.972613i	$0.425332\pi$
$774$		0			0
$775$	1.90608	+	0.693755i	0.0684683	+	0.0249204i
$776$	−11.8915	+	7.82119i	−0.426881	+	0.280764i
$777$		0			0
$778$	2.39526	+	3.21739i	0.0858741	+	0.115349i
$779$	3.67391	+	2.41637i	0.131632	+	0.0865754i
$780$		0			0
$781$	1.07518	−	3.59134i	0.0384729	−	0.128508i

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)

\(f(q)\)	\(=\)	\(q+(-0.388502 - 0.411788i) q^{2} +(0.0976541 - 1.67666i) q^{4} +(1.51980 - 0.177639i) q^{5} +(-1.38566 - 0.695905i) q^{7} +(-1.59573 + 1.33897i) q^{8} +O(q^{10})\)	\(q+(-0.388502 - 0.411788i) q^{2} +(0.0976541 - 1.67666i) q^{4} +(1.51980 - 0.177639i) q^{5} +(-1.38566 - 0.695905i) q^{7} +(-1.59573 + 1.33897i) q^{8} +(-0.663594 - 0.556821i) q^{10} +(0.219760 + 0.509460i) q^{11} +(-2.50971 - 0.594813i) q^{13} +(0.251767 + 0.840960i) q^{14} +(-2.16496 - 0.253048i) q^{16} +(0.994500 - 5.64009i) q^{17} +(-1.11056 - 6.29830i) q^{19} +(-0.149425 - 2.56552i) q^{20} +(0.124413 - 0.288421i) q^{22} +(4.93448 - 2.47819i) q^{23} +(-2.58700 + 0.613129i) q^{25} +(0.730091 + 1.26456i) q^{26} +(-1.30211 + 2.25532i) q^{28} +(-1.93433 + 6.46110i) q^{29} +(-0.637429 - 0.419244i) q^{31} +(3.22474 + 4.33158i) q^{32} +(-2.70889 + 1.78166i) q^{34} +(-2.22954 - 0.811488i) q^{35} +(-7.41710 + 2.69960i) q^{37} +(-2.16211 + 2.90422i) q^{38} +(-2.18733 + 2.31843i) q^{40} +(-0.471839 + 0.500120i) q^{41} +(4.70771 - 6.32356i) q^{43} +(0.875649 - 0.318710i) q^{44} +(-2.93754 - 1.06918i) q^{46} +(-4.72615 + 3.10844i) q^{47} +(-2.74434 - 3.68628i) q^{49} +(1.25753 + 0.827092i) q^{50} +(-1.24238 + 4.14984i) q^{52} +(5.99254 - 10.3794i) q^{53} +(0.424490 + 0.735238i) q^{55} +(3.14294 - 0.744890i) q^{56} +(3.41210 - 1.71362i) q^{58} +(-0.926748 + 2.14844i) q^{59} +(-0.637878 - 10.9520i) q^{61} +(0.0750029 + 0.425363i) q^{62} +(-0.226129 + 1.28244i) q^{64} +(-3.91991 - 0.458172i) q^{65} +(2.89108 + 9.65687i) q^{67} +(-9.35937 - 2.21821i) q^{68} +(0.532022 + 1.23336i) q^{70} +(-5.17589 - 4.34309i) q^{71} +(5.85966 - 4.91684i) q^{73} +(3.99322 + 2.00547i) q^{74} +(-10.6685 + 1.24697i) q^{76} +(0.0500235 - 0.858871i) q^{77} +(3.31160 + 3.51009i) q^{79} -3.33526 q^{80} +0.389254 q^{82} +(6.22581 + 6.59897i) q^{83} +(0.509539 - 8.74845i) q^{85} +(-4.43292 + 0.518134i) q^{86} +(-1.03283 - 0.518707i) q^{88} +(-10.4080 + 8.73338i) q^{89} +(3.06368 + 2.57073i) q^{91} +(-3.67319 - 8.51542i) q^{92} +(3.11613 + 0.738537i) q^{94} +(-2.80665 - 9.37486i) q^{95} +(6.78651 + 0.793230i) q^{97} +(-0.451787 + 2.56221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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

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