LMFDB - Embedded newform 729.2.g.b.55.6

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			55.6
Character	$\chi$	$=$	729.55
Dual form			729.2.g.b.676.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.588281 - 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(0.0932044 + 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(2.50387 - 0.911335i) q^{8} +O(q^{10})$	\(q+(0.588281 - 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(0.0932044 + 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(2.50387 - 0.911335i) q^{8} +(2.23724 + 0.814290i) q^{10} +(3.38752 + 2.22800i) q^{11} +(1.67851 + 0.196189i) q^{13} +(-1.68684 + 2.26582i) q^{14} +(0.254067 - 4.36216i) q^{16} +(-4.14727 + 3.47997i) q^{17} +(3.70167 + 3.10607i) q^{19} +(0.226595 - 0.240177i) q^{20} +(5.03133 - 3.30916i) q^{22} +(-0.651612 + 0.154435i) q^{23} +(2.41405 - 0.282162i) q^{25} +(1.25499 - 2.17371i) q^{26} +(0.195884 + 0.339282i) q^{28} +(2.85835 + 3.83943i) q^{29} +(1.39576 - 4.66216i) q^{31} +(-1.03731 - 0.520955i) q^{32} +(2.30618 + 7.70319i) q^{34} +(0.529392 - 3.00233i) q^{35} +(-2.07926 - 11.7921i) q^{37} +(6.41363 - 3.22105i) q^{38} +(1.69174 + 3.92190i) q^{40} +(4.00621 + 9.28743i) q^{41} +(7.64192 - 3.83792i) q^{43} +(-0.145031 - 0.822509i) q^{44} +(-0.172714 + 0.979511i) q^{46} +(-0.0578400 - 0.193199i) q^{47} +(-3.02305 - 1.51823i) q^{49} +(1.03533 - 3.45825i) q^{50} +(-0.207877 - 0.279228i) q^{52} +(-2.48138 - 4.29788i) q^{53} +(-3.24965 + 5.62856i) q^{55} +(-5.03340 + 0.588321i) q^{56} +(6.91768 - 1.63952i) q^{58} +(-1.58520 + 1.04260i) q^{59} +(0.124028 - 0.131462i) q^{61} +(-5.53710 - 4.64618i) q^{62} +(5.37384 - 4.50919i) q^{64} +(-0.157509 + 2.70433i) q^{65} +(-7.95826 + 10.6898i) q^{67} +(1.10767 + 0.129468i) q^{68} +(-3.78311 - 2.48819i) q^{70} +(-9.41216 - 3.42575i) q^{71} +(-10.9327 + 3.97917i) q^{73} +(-17.3051 - 4.10138i) q^{74} +(-0.0578765 - 0.993701i) q^{76} +(-5.29176 - 5.60894i) q^{77} +(-1.45390 + 3.37053i) q^{79} +7.00426 q^{80} +15.0229 q^{82} +(2.17367 - 5.03914i) q^{83} +(-5.95539 - 6.31235i) q^{85} +(-0.738510 - 12.6797i) q^{86} +(10.5124 + 2.49148i) q^{88} +(6.65218 - 2.42120i) q^{89} +(-3.02021 - 1.09927i) q^{91} +(0.115251 + 0.0758017i) q^{92} +(-0.297508 - 0.0347738i) q^{94} +(-4.62550 + 6.21312i) q^{95} +(0.0778051 - 1.33586i) q^{97} +(-3.84894 + 3.22965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	0.588281	−	1.36379i	0.415977	−	0.964344i	−0.573440	−	0.819247i	$-0.694392\pi$
$2$	0.588281	−	1.36379i	0.415977	−	0.964344i	0.989418	−	0.145096i	$-0.0463492\pi$
$3$		0			0
$3$		0			0
$4$	−0.141360	−	0.149832i	−0.0706798	−	0.0749162i
$5$	0.0932044	+	1.60026i	0.0416823	+	0.715657i	0.952816	+	0.303547i	$0.0981710\pi$
$5$	0.0932044	+	1.60026i	0.0416823	+	0.715657i	−0.911134	+	0.412110i	$0.864792\pi$
$6$		0			0
$7$	−1.85061	−	0.438602i	−0.699465	−	0.165776i	−0.134527	−	0.990910i	$-0.542952\pi$
$7$	−1.85061	−	0.438602i	−0.699465	−	0.165776i	−0.564937	+	0.825134i	$0.691100\pi$
$8$	2.50387	−	0.911335i	0.885253	−	0.322206i
$9$		0			0
$10$	2.23724	+	0.814290i	0.707478	+	0.257501i
$11$	3.38752	+	2.22800i	1.02137	+	0.671769i	0.945592	−	0.325356i	$-0.105484\pi$
$11$	3.38752	+	2.22800i	1.02137	+	0.671769i	0.0757828	+	0.997124i	$0.475854\pi$
$12$		0			0
$13$	1.67851	+	0.196189i	0.465534	+	0.0544131i	0.345627	−	0.938372i	$-0.387666\pi$
$13$	1.67851	+	0.196189i	0.465534	+	0.0544131i	0.119907	+	0.992785i	$0.461740\pi$
$14$	−1.68684	+	2.26582i	−0.450826	+	0.605565i
$15$		0			0
$16$	0.254067	−	4.36216i	0.0635167	−	1.09054i
$17$	−4.14727	+	3.47997i	−1.00586	+	0.844017i	−0.987785	−	0.155820i	$-0.950198\pi$
$17$	−4.14727	+	3.47997i	−1.00586	+	0.844017i	−0.0180743	+	0.999837i	$0.505754\pi$
$18$		0			0
$19$	3.70167	+	3.10607i	0.849220	+	0.712581i	0.959618	−	0.281307i	$-0.0907679\pi$
$19$	3.70167	+	3.10607i	0.849220	+	0.712581i	−0.110397	+	0.993888i	$0.535212\pi$
$20$	0.226595	−	0.240177i	0.0506682	−	0.0537052i
$21$		0			0
$22$	5.03133	−	3.30916i	1.07268	−	0.705515i
$23$	−0.651612	+	0.154435i	−0.135870	+	0.0322019i	−0.297988	−	0.954570i	$-0.596316\pi$
$23$	−0.651612	+	0.154435i	−0.135870	+	0.0322019i	0.162118	+	0.986771i	$0.448168\pi$
$24$		0			0
$25$	2.41405	−	0.282162i	0.482811	−	0.0564325i
$26$	1.25499	−	2.17371i	0.246124	−	0.426300i
$27$		0			0
$28$	0.195884	+	0.339282i	0.0370187	+	0.0641182i
$29$	2.85835	+	3.83943i	0.530782	+	0.712965i	0.983947	−	0.178462i	$-0.0571123\pi$
$29$	2.85835	+	3.83943i	0.530782	+	0.712965i	−0.453164	+	0.891427i	$0.649705\pi$
$30$		0			0
$31$	1.39576	−	4.66216i	0.250686	−	0.837349i	−0.736316	−	0.676638i	$-0.763436\pi$
$31$	1.39576	−	4.66216i	0.250686	−	0.837349i	0.987002	−	0.160711i	$-0.0513786\pi$
$32$	−1.03731	−	0.520955i	−0.183372	−	0.0920927i
$33$		0			0
$34$	2.30618	+	7.70319i	0.395507	+	1.32109i
$35$	0.529392	−	3.00233i	0.0894836	−	0.507487i
$36$		0			0
$37$	−2.07926	−	11.7921i	−0.341829	−	1.93861i	−0.344973	−	0.938613i	$-0.612112\pi$
$37$	−2.07926	−	11.7921i	−0.341829	−	1.93861i	0.00314382	−	0.999995i	$-0.498999\pi$
$38$	6.41363	−	3.22105i	1.04043	−	0.522523i
$39$		0			0
$40$	1.69174	+	3.92190i	0.267488	+	0.620107i
$41$	4.00621	+	9.28743i	0.625664	+	1.45045i	0.876009	+	0.482296i	$0.160197\pi$
$41$	4.00621	+	9.28743i	0.625664	+	1.45045i	−0.250344	+	0.968157i	$0.580544\pi$
$42$		0			0
$43$	7.64192	−	3.83792i	1.16538	−	0.585277i	0.242421	−	0.970171i	$-0.422059\pi$
$43$	7.64192	−	3.83792i	1.16538	−	0.585277i	0.922961	+	0.384895i	$0.125762\pi$
$44$	−0.145031	−	0.822509i	−0.0218642	−	0.123998i
$45$		0			0
$46$	−0.172714	+	0.979511i	−0.0254653	+	0.144421i
$47$	−0.0578400	−	0.193199i	−0.00843683	−	0.0281810i	0.953667	−	0.300863i	$-0.0972746\pi$
$47$	−0.0578400	−	0.193199i	−0.00843683	−	0.0281810i	−0.962104	+	0.272682i	$0.912089\pi$
$48$		0			0
$49$	−3.02305	−	1.51823i	−0.431864	−	0.216890i
$50$	1.03533	−	3.45825i	0.146418	−	0.489070i
$51$		0			0
$52$	−0.207877	−	0.279228i	−0.0288274	−	0.0387219i
$53$	−2.48138	−	4.29788i	−0.340844	−	0.590359i	0.643746	−	0.765240i	$-0.277379\pi$
$53$	−2.48138	−	4.29788i	−0.340844	−	0.590359i	−0.984590	+	0.174880i	$0.944046\pi$
$54$		0			0
$55$	−3.24965	+	5.62856i	−0.438183	+	0.758955i
$56$	−5.03340	+	0.588321i	−0.672617	+	0.0786177i
$57$		0			0
$58$	6.91768	−	1.63952i	0.908336	−	0.215280i
$59$	−1.58520	+	1.04260i	−0.206375	+	0.135735i	−0.648489	−	0.761224i	$-0.724599\pi$
$59$	−1.58520	+	1.04260i	−0.206375	+	0.135735i	0.442114	+	0.896959i	$0.354229\pi$
$60$		0			0
$61$	0.124028	−	0.131462i	0.0158802	−	0.0168320i	−0.719385	−	0.694612i	$-0.755576\pi$
$61$	0.124028	−	0.131462i	0.0158802	−	0.0168320i	0.735265	+	0.677780i	$0.237058\pi$
$62$	−5.53710	−	4.64618i	−0.703212	−	0.590065i
$63$		0			0
$64$	5.37384	−	4.50919i	0.671730	−	0.563648i
$65$	−0.157509	+	2.70433i	−0.0195366	+	0.335431i
$66$		0			0
$67$	−7.95826	+	10.6898i	−0.972256	+	1.30597i	−0.0202796	+	0.999794i	$0.506456\pi$
$67$	−7.95826	+	10.6898i	−0.972256	+	1.30597i	−0.951976	+	0.306172i	$0.900952\pi$
$68$	1.10767	+	0.129468i	0.134324	+	0.0157003i
$69$		0			0
$70$	−3.78311	−	2.48819i	−0.452168	−	0.297396i
$71$	−9.41216	−	3.42575i	−1.11702	−	0.406561i	−0.283455	−	0.958985i	$-0.591481\pi$
$71$	−9.41216	−	3.42575i	−1.11702	−	0.406561i	−0.833563	+	0.552424i	$0.813703\pi$
$72$		0			0
$73$	−10.9327	+	3.97917i	−1.27957	+	0.465726i	−0.890291	−	0.455392i	$-0.849499\pi$
$73$	−10.9327	+	3.97917i	−1.27957	+	0.465726i	−0.389282	+	0.921119i	$0.627277\pi$
$74$	−17.3051	−	4.10138i	−2.01168	−	0.476776i
$75$		0			0
$76$	−0.0578765	−	0.993701i	−0.00663889	−	0.113985i
$77$	−5.29176	−	5.60894i	−0.603052	−	0.639198i
$78$		0			0
$79$	−1.45390	+	3.37053i	−0.163577	+	0.379214i	−0.980215	−	0.197936i	$-0.936576\pi$
$79$	−1.45390	+	3.37053i	−0.163577	+	0.379214i	0.816638	+	0.577150i	$0.195835\pi$
$80$	7.00426			0.783100
$81$		0			0
$82$	15.0229			1.65900
$83$	2.17367	−	5.03914i	0.238592	−	0.553117i	−0.756282	−	0.654246i	$-0.772986\pi$
$83$	2.17367	−	5.03914i	0.238592	−	0.553117i	0.994873	+	0.101129i	$0.0322454\pi$
$84$		0			0
$85$	−5.95539	−	6.31235i	−0.645953	−	0.684670i
$86$	−0.738510	−	12.6797i	−0.0796356	−	1.36729i
$87$		0			0
$88$	10.5124	+	2.49148i	1.12062	+	0.265592i
$89$	6.65218	−	2.42120i	0.705130	−	0.256646i	0.0355305	−	0.999369i	$-0.488688\pi$
$89$	6.65218	−	2.42120i	0.705130	−	0.256646i	0.669600	+	0.742722i	$0.266466\pi$
$90$		0			0
$91$	−3.02021	−	1.09927i	−0.316604	−	0.115234i
$92$	0.115251	+	0.0758017i	0.0120157	+	0.00790287i
$93$		0			0
$94$	−0.297508	−	0.0347738i	−0.0306857	−	0.00358664i
$95$	−4.62550	+	6.21312i	−0.474566	+	0.637453i
$96$		0			0
$97$	0.0778051	−	1.33586i	0.00789992	−	0.135636i	−0.992052	−	0.125829i	$-0.959841\pi$
$97$	0.0778051	−	1.33586i	0.00789992	−	0.135636i	0.999952	−	0.00980765i	$-0.00312192\pi$
$98$	−3.84894	+	3.22965i	−0.388802	+	0.326244i
$99$		0			0
$100$	−0.383526	−	0.321817i	−0.0383526	−	0.0321817i
$101$	3.40131	−	3.60518i	0.338443	−	0.358729i	−0.535690	−	0.844415i	$-0.679949\pi$
$101$	3.40131	−	3.60518i	0.338443	−	0.358729i	0.874134	+	0.485686i	$0.161430\pi$
$102$		0			0
$103$	1.90445	−	1.25258i	0.187652	−	0.123420i	−0.452207	−	0.891913i	$-0.649363\pi$
$103$	1.90445	−	1.25258i	0.187652	−	0.123420i	0.639859	+	0.768493i	$0.278993\pi$
$104$	4.38156	−	1.03845i	0.429648	−	0.101828i
$105$		0			0
$106$	−7.32115	+	0.855719i	−0.711092	+	0.0831148i
$107$	−2.21467	+	3.83593i	−0.214101	+	0.370833i	−0.952994	−	0.302989i	$-0.902015\pi$
$107$	−2.21467	+	3.83593i	−0.214101	+	0.370833i	0.738893	+	0.673822i	$0.235349\pi$
$108$		0			0
$109$	−9.21824	−	15.9665i	−0.882947	−	1.52931i	−0.848049	−	0.529918i	$-0.822223\pi$
$109$	−9.21824	−	15.9665i	−0.882947	−	1.52931i	−0.0348978	−	0.999391i	$-0.511111\pi$
$110$	5.76445	+	7.74301i	0.549619	+	0.738267i
$111$		0			0
$112$	−2.38343	+	7.96121i	−0.225213	+	0.752264i
$113$	−8.05934	−	4.04755i	−0.758159	−	0.380762i	0.0273390	−	0.999626i	$-0.491297\pi$
$113$	−8.05934	−	4.04755i	−0.758159	−	0.380762i	−0.785498	+	0.618865i	$0.787593\pi$
$114$		0			0
$115$	−0.307869	−	1.02835i	−0.0287089	−	0.0958944i
$116$	0.171216	−	0.971014i	0.0158970	−	0.0901563i
$117$		0			0
$118$	0.489346	+	2.77522i	0.0450479	+	0.255479i
$119$	9.20129	−	4.62106i	0.843481	−	0.423612i
$120$		0			0
$121$	2.15438	+	4.99442i	0.195853	+	0.454038i
$122$	−0.106323	−	0.246485i	−0.00962604	−	0.0223157i
$123$		0			0
$124$	−0.895846	+	0.449911i	−0.0804493	+	0.0404032i
$125$	2.06830	+	11.7299i	0.184994	+	1.04915i
$126$		0			0
$127$	−0.304561	+	1.72725i	−0.0270254	+	0.153269i	−0.995334	−	0.0964872i	$-0.969239\pi$
$127$	−0.304561	+	1.72725i	−0.0270254	+	0.153269i	0.968309	+	0.249756i	$0.0803504\pi$
$128$	−3.65408	−	12.2055i	−0.322978	−	1.07882i
$129$		0			0
$130$	3.59547	+	1.80571i	0.315344	+	0.158372i
$131$	2.05452	−	6.86256i	0.179504	−	0.599585i	−0.820121	−	0.572191i	$-0.806094\pi$
$131$	2.05452	−	6.86256i	0.179504	−	0.599585i	0.999625	−	0.0273945i	$-0.00872103\pi$
$132$		0			0
$133$	−5.48801	−	7.37168i	−0.475871	−	0.639205i
$134$	9.89692	+	17.1420i	0.854964	+	1.48084i
$135$		0			0
$136$	−7.21281	+	12.4930i	−0.618493	+	1.07126i
$137$	−17.3549	+	2.02850i	−1.48273	+	0.173307i	−0.818624	−	0.574329i	$-0.805263\pi$
$137$	−17.3549	+	2.02850i	−1.48273	+	0.173307i	−0.664109	+	0.747636i	$0.731189\pi$
$138$		0			0
$139$	−18.4877	+	4.38167i	−1.56811	+	0.371649i	−0.920630	−	0.390435i	$-0.872325\pi$
$139$	−18.4877	+	4.38167i	−1.56811	+	0.371649i	−0.647478	+	0.762084i	$0.724176\pi$
$140$	−0.524681	+	0.345088i	−0.0443436	+	0.0291653i
$141$		0			0
$142$	−10.2090	+	10.8209i	−0.856719	+	0.908069i
$143$	5.24886	+	4.40431i	0.438931	+	0.368307i
$144$		0			0
$145$	−5.87767	+	4.93195i	−0.488114	+	0.409576i
$146$	−1.00474	+	17.2507i	−0.0831528	+	1.42768i
$147$		0			0
$148$	−1.47291	+	1.97847i	−0.121073	+	0.162629i
$149$	7.32320	+	0.855959i	0.599940	+	0.0701229i	0.410642	−	0.911797i	$-0.365305\pi$
$149$	7.32320	+	0.855959i	0.599940	+	0.0701229i	0.189298	+	0.981920i	$0.439379\pi$
$150$		0			0
$151$	2.23139	+	1.46761i	0.181588	+	0.119432i	0.637048	−	0.770824i	$-0.280155\pi$
$151$	2.23139	+	1.46761i	0.181588	+	0.119432i	−0.455461	+	0.890256i	$0.650525\pi$
$152$	12.0992	+	4.40374i	0.981372	+	0.357190i
$153$		0			0
$154$	−10.7624	+	3.91721i	−0.867262	+	0.315658i
$155$	7.59075	+	1.79904i	0.609704	+	0.144502i
$156$		0			0
$157$	0.332250	+	5.70452i	0.0265165	+	0.455270i	0.985267	+	0.171022i	$0.0547069\pi$
$157$	0.332250	+	5.70452i	0.0265165	+	0.455270i	−0.958751	+	0.284248i	$0.908256\pi$
$158$	3.74138	+	3.96563i	0.297648	+	0.315489i
$159$		0			0
$160$	0.736981	−	1.70851i	0.0582635	−	0.135070i
$161$	1.27361			0.100375
$162$		0			0
$163$	16.0381			1.25620			0.628100	−	0.778132i	$-0.283833\pi$
$163$	16.0381			1.25620			0.628100	+	0.778132i	$0.283833\pi$
$164$	0.825242	−	1.91313i	0.0644406	−	0.149390i
$165$		0			0
$166$	−5.59359	−	5.92886i	−0.434147	−	0.460168i
$167$	1.11336	+	19.1157i	0.0861545	+	1.47922i	0.713599	+	0.700554i	$0.247064\pi$
$167$	1.11336	+	19.1157i	0.0861545	+	1.47922i	−0.627445	+	0.778661i	$0.715899\pi$
$168$		0			0
$169$	−9.87069	−	2.33940i	−0.759284	−	0.179954i
$170$	−12.1121	+	4.40846i	−0.928959	+	0.338113i
$171$		0			0
$172$	−1.65530	−	0.602480i	−0.126216	−	0.0459387i
$173$	−19.7483	−	12.9886i	−1.50143	−	0.987509i	−0.991895	−	0.127061i	$-0.959446\pi$
$173$	−19.7483	−	12.9886i	−1.50143	−	0.987509i	−0.509539	−	0.860448i	$-0.670184\pi$
$174$		0			0
$175$	−4.59123	−	0.536637i	−0.347064	−	0.0405660i
$176$	10.5796	−	14.2108i	0.797464	−	1.07118i
$177$		0			0
$178$	0.611352	−	10.4965i	0.0458228	−	0.786747i
$179$	3.43489	−	2.88222i	0.256736	−	0.215427i	−0.505331	−	0.862926i	$-0.668629\pi$
$179$	3.43489	−	2.88222i	0.256736	−	0.215427i	0.762066	+	0.647499i	$0.224185\pi$
$180$		0			0
$181$	2.92076	+	2.45081i	0.217098	+	0.182167i	0.744851	−	0.667231i	$-0.232521\pi$
$181$	2.92076	+	2.45081i	0.217098	+	0.182167i	−0.527752	+	0.849398i	$0.676965\pi$
$182$	−3.27590	+	3.47225i	−0.242826	+	0.257380i
$183$		0			0
$184$	−1.49081	+	0.980522i	−0.109904	+	0.0722850i
$185$	18.6766	−	4.42643i	1.37313	−	0.325438i
$186$		0			0
$187$	−21.8023	+	2.54833i	−1.59434	+	0.186352i
$188$	−0.0207712	+	0.0359768i	−0.00151490	+	0.00262388i
$189$		0			0
$190$	5.75229	+	9.96325i	0.417315	+	0.722810i
$191$	10.9862	+	14.7571i	0.794936	+	1.06778i	0.996100	+	0.0882265i	$0.0281199\pi$
$191$	10.9862	+	14.7571i	0.794936	+	1.06778i	−0.201165	+	0.979557i	$0.564473\pi$
$192$		0			0
$193$	4.71004	−	15.7326i	0.339036	−	1.13246i	−0.603223	−	0.797573i	$-0.706117\pi$
$193$	4.71004	−	15.7326i	0.339036	−	1.13246i	0.942259	−	0.334886i	$-0.108698\pi$
$194$	−1.77606	−	0.891972i	−0.127514	−	0.0640398i
$195$		0			0
$196$	0.199856	+	0.667566i	0.0142754	+	0.0476833i
$197$	3.25113	−	18.4381i	0.231633	−	1.31366i	−0.617956	−	0.786213i	$-0.712039\pi$
$197$	3.25113	−	18.4381i	0.231633	−	1.31366i	0.849589	−	0.527445i	$-0.176850\pi$
$198$		0			0
$199$	0.155470	+	0.881713i	0.0110210	+	0.0625029i	0.989822	−	0.142309i	$-0.0454527\pi$
$199$	0.155470	+	0.881713i	0.0110210	+	0.0625029i	−0.978801	+	0.204812i	$0.934342\pi$
$200$	5.78734	−	2.90651i	0.409227	−	0.205521i
$201$		0			0
$202$	−2.91577	−	6.75953i	−0.205153	−	0.475599i
$203$	−3.60571	−	8.35897i	−0.253071	−	0.586685i
$204$		0			0
$205$	−14.4889	+	7.27659i	−1.01195	+	0.508219i
$206$	−0.587899	−	3.33414i	−0.0409609	−	0.232301i
$207$		0			0
$208$	1.28226	−	7.27206i	0.0889088	−	0.504227i
$209$	5.61912	+	18.7692i	0.388683	+	1.29829i
$210$		0			0
$211$	13.3695	+	6.71439i	0.920391	+	0.462238i	0.844909	−	0.534909i	$-0.179654\pi$
$211$	13.3695	+	6.71439i	0.920391	+	0.462238i	0.0754817	+	0.997147i	$0.475951\pi$
$212$	−0.293194	+	0.979338i	−0.0201367	+	0.0672612i
$213$		0			0
$214$	3.92854	+	5.27695i	0.268550	+	0.360725i
$215$	6.85392	+	11.8713i	0.467433	+	0.809618i
$216$		0			0
$217$	−4.62784	+	8.01565i	−0.314158	+	0.544138i
$218$	−27.1978	+	3.17896i	−1.84206	+	0.215306i
$219$		0			0
$220$	1.30271	−	0.308748i	0.0878286	−	0.0208158i
$221$	−7.64395	+	5.02750i	−0.514188	+	0.338186i
$222$		0			0
$223$	4.25530	−	4.51035i	0.284956	−	0.302036i	−0.569046	−	0.822306i	$-0.692687\pi$
$223$	4.25530	−	4.51035i	0.284956	−	0.302036i	0.854002	+	0.520270i	$0.174169\pi$
$224$	1.69116	+	1.41905i	0.112995	+	0.0948142i
$225$		0			0
$226$	−10.2612	+	8.61013i	−0.682562	+	0.572737i
$227$	0.830506	−	14.2592i	0.0551226	−	0.946419i	−0.851468	−	0.524407i	$-0.824287\pi$
$227$	0.830506	−	14.2592i	0.0551226	−	0.946419i	0.906590	−	0.422012i	$-0.138676\pi$
$228$		0			0
$229$	11.6644	−	15.6680i	0.770804	−	1.03537i	−0.227300	−	0.973825i	$-0.572990\pi$
$229$	11.6644	−	15.6680i	0.770804	−	1.03537i	0.998104	−	0.0615447i	$-0.0196027\pi$
$230$	−1.58357	−	0.185093i	−0.104417	−	0.0122046i
$231$		0			0
$232$	10.6560	+	7.00853i	0.699598	+	0.460133i
$233$	−8.91628	−	3.24526i	−0.584125	−	0.212604i	0.0330187	−	0.999455i	$-0.489488\pi$
$233$	−8.91628	−	3.24526i	−0.584125	−	0.212604i	−0.617143	+	0.786851i	$0.711710\pi$
$234$		0			0
$235$	0.303777	−	0.110566i	0.0198162	−	0.00721252i
$236$	0.380298	+	0.0901324i	0.0247553	+	0.00586712i
$237$		0			0
$238$	−0.889207	−	15.2671i	−0.0576387	−	0.989619i
$239$	7.55122	+	8.00383i	0.488448	+	0.517725i	0.923976	−	0.382451i	$-0.124920\pi$
$239$	7.55122	+	8.00383i	0.488448	+	0.517725i	−0.435528	+	0.900175i	$0.643438\pi$
$240$		0			0
$241$	−0.867612	+	2.01135i	−0.0558878	+	0.129562i	−0.943872	−	0.330312i	$-0.892846\pi$
$241$	−0.867612	+	2.01135i	−0.0558878	+	0.129562i	0.887984	+	0.459874i	$0.152105\pi$
$242$	8.07871			0.519319
$243$		0			0
$244$	−0.0372298			−0.00238340
$245$	2.14780	−	4.97916i	0.137218	−	0.318107i
$246$		0			0
$247$	5.60389	+	5.93978i	0.356567	+	0.377939i
$248$	−0.753987	−	12.9455i	−0.0478782	−	0.822038i
$249$		0			0
$250$	17.2138	+	4.07975i	1.08870	+	0.258026i
$251$	−6.59388	+	2.39998i	−0.416202	+	0.151485i	−0.541629	−	0.840618i	$-0.682192\pi$
$251$	−6.59388	+	2.39998i	−0.416202	+	0.151485i	0.125427	+	0.992103i	$0.459970\pi$
$252$		0			0
$253$	−2.55143	−	0.928643i	−0.160407	−	0.0583833i
$254$	2.17644	+	1.43147i	0.136562	+	0.0898181i
$255$		0			0
$256$	−4.86005	−	0.568059i	−0.303753	−	0.0355037i
$257$	0.279271	−	0.375126i	0.0174205	−	0.0233997i	−0.793328	−	0.608795i	$-0.791653\pi$
$257$	0.279271	−	0.375126i	0.0174205	−	0.0233997i	0.810748	+	0.585395i	$0.199061\pi$
$258$		0			0
$259$	−1.32414	+	22.7345i	−0.0822778	+	1.41265i
$260$	0.427461	−	0.358683i	0.0265100	−	0.0222446i
$261$		0			0
$262$	−8.15045	−	6.83904i	−0.503536	−	0.422517i
$263$	13.0974	−	13.8824i	0.807621	−	0.856028i	−0.184302	−	0.982870i	$-0.559003\pi$
$263$	13.0974	−	13.8824i	0.807621	−	0.856028i	0.991923	+	0.126842i	$0.0404841\pi$
$264$		0			0
$265$	6.64644	−	4.37143i	0.408288	−	0.268535i
$266$	−13.2819	+	3.14787i	−0.814365	+	0.193008i
$267$		0			0
$268$	2.72665	−	0.318700i	0.166557	−	0.0194677i
$269$	2.12061	−	3.67300i	0.129296	−	0.223947i	−0.794108	−	0.607776i	$-0.792062\pi$
$269$	2.12061	−	3.67300i	0.129296	−	0.223947i	0.923404	+	0.383830i	$0.125395\pi$
$270$		0			0
$271$	−3.83162	−	6.63656i	−0.232754	−	0.403142i	0.725863	−	0.687839i	$-0.241440\pi$
$271$	−3.83162	−	6.63656i	−0.232754	−	0.403142i	−0.958618	+	0.284697i	$0.908107\pi$
$272$	14.1265	+	18.9752i	0.856544	+	1.15054i
$273$		0			0
$274$	−7.44313	+	24.8618i	−0.449656	+	1.50196i
$275$	8.80630	+	4.42269i	0.531040	+	0.266698i
$276$		0			0
$277$	−4.25476	−	14.2119i	−0.255644	−	0.853909i	−0.985408	−	0.170210i	$-0.945555\pi$
$277$	−4.25476	−	14.2119i	−0.255644	−	0.853909i	0.729764	−	0.683699i	$-0.239630\pi$
$278$	−4.90030	+	27.7910i	−0.293901	+	1.66679i
$279$		0			0
$280$	−1.41060	−	7.99991i	−0.0842995	−	0.478086i
$281$	−0.994631	+	0.499522i	−0.0593347	+	0.0297990i	−0.478219	−	0.878241i	$-0.658718\pi$
$281$	−0.994631	+	0.499522i	−0.0593347	+	0.0297990i	0.418884	+	0.908040i	$0.362421\pi$
$282$		0			0
$283$	−2.61783	−	6.06882i	−0.155614	−	0.360754i	0.822518	−	0.568739i	$-0.192569\pi$
$283$	−2.61783	−	6.06882i	−0.155614	−	0.360754i	−0.978132	+	0.207985i	$0.933309\pi$
$284$	0.817211	+	1.89451i	0.0484926	+	0.112418i
$285$		0			0
$286$	9.09435	−	4.56735i	0.537760	−	0.270073i
$287$	−3.34043	−	18.9445i	−0.197179	−	1.11826i
$288$		0			0
$289$	2.13761	−	12.1230i	0.125742	−	0.713117i
$290$	3.26841	+	10.9173i	0.191928	+	0.641084i
$291$		0			0
$292$	2.14165	+	1.07557i	0.125330	+	0.0629432i
$293$	0.892759	−	2.98202i	0.0521555	−	0.174212i	−0.927943	−	0.372721i	$-0.878425\pi$
$293$	0.892759	−	2.98202i	0.0521555	−	0.174212i	0.980099	+	0.198509i	$0.0636100\pi$
$294$		0			0
$295$	−1.81618	−	2.43955i	−0.105742	−	0.142036i
$296$	−15.9528	−	27.6310i	−0.927235	−	1.60602i
$297$		0			0
$298$	5.47544	−	9.48374i	0.317184	−	0.549379i
$299$	−1.12403	+	0.131381i	−0.0650045	+	0.00759794i
$300$		0			0
$301$	−15.8255	+	3.75072i	−0.912168	+	0.216188i
$302$	3.31418	−	2.17977i	0.190710	−	0.125432i
$303$		0			0
$304$	14.4896	−	15.3581i	0.831037	−	0.880848i
$305$	0.221933	+	0.186224i	0.0127079	+	0.0106632i
$306$		0			0
$307$	−5.76257	+	4.83537i	−0.328887	+	0.275969i	−0.792246	−	0.610202i	$-0.791088\pi$
$307$	−5.76257	+	4.83537i	−0.328887	+	0.275969i	0.463359	+	0.886171i	$0.346644\pi$
$308$	−0.0923596	+	1.58575i	−0.00526268	+	0.0903567i
$309$		0			0
$310$	6.91900	−	9.29383i	0.392973	−	0.527854i
$311$	−15.2831	−	1.78634i	−0.866628	−	0.101294i	−0.328851	−	0.944382i	$-0.606662\pi$
$311$	−15.2831	−	1.78634i	−0.866628	−	0.101294i	−0.537777	+	0.843087i	$0.680736\pi$
$312$		0			0
$313$	3.31693	+	2.18158i	0.187484	+	0.123310i	0.639781	−	0.768557i	$-0.279025\pi$
$313$	3.31693	+	2.18158i	0.187484	+	0.123310i	−0.452297	+	0.891867i	$0.649395\pi$
$314$	7.97521	+	2.90274i	0.450067	+	0.163811i
$315$		0			0
$316$	0.710537	−	0.258614i	0.0399708	−	0.0145482i
$317$	−8.34397	−	1.97756i	−0.468644	−	0.111071i	−0.0104930	−	0.999945i	$-0.503340\pi$
$317$	−8.34397	−	1.97756i	−0.468644	−	0.111071i	−0.458151	+	0.888874i	$0.651488\pi$
$318$		0			0
$319$	1.12844	+	19.3746i	0.0631805	+	1.08477i
$320$	7.71673	+	8.17925i	0.431378	+	0.457234i
$321$		0			0
$322$	0.749242	−	1.73694i	0.0417536	−	0.0967958i
$323$	−26.1608			−1.45563
$324$		0			0
$325$	4.10736			0.227835
$326$	9.43490	−	21.8726i	0.522551	−	1.21141i
$327$		0			0
$328$	18.4950	+	19.6035i	1.02121	+	1.08242i
$329$	0.0223016	+	0.382905i	0.00122953	+	0.0211102i
$330$		0			0
$331$	−9.07927	−	2.15183i	−0.499042	−	0.118275i	−0.0266164	−	0.999646i	$-0.508473\pi$
$331$	−9.07927	−	2.15183i	−0.499042	−	0.118275i	−0.472425	+	0.881371i	$0.656621\pi$
$332$	−1.06230	+	0.386644i	−0.0583010	+	0.0212198i
$333$		0			0
$334$	26.7247	+	9.72699i	1.46231	+	0.532237i
$335$	−17.8482	−	11.7389i	−0.975150	−	0.641366i
$336$		0			0
$337$	−4.37776	−	0.511687i	−0.238472	−	0.0278734i	−0.00398267	−	0.999992i	$-0.501268\pi$
$337$	−4.37776	−	0.511687i	−0.238472	−	0.0278734i	−0.234489	+	0.972119i	$0.575342\pi$
$338$	−8.99717	+	12.0853i	−0.489382	+	0.657354i
$339$		0			0
$340$	−0.103942	+	1.78462i	−0.00563706	+	0.0967847i
$341$	15.1155	−	12.6834i	0.818548	−	0.686844i
$342$		0			0
$343$	15.1270	+	12.6931i	0.816782	+	0.685362i
$344$	15.6368	−	16.5740i	0.843078	−	0.893610i
$345$		0			0
$346$	−29.3313	+	19.2915i	−1.57686	+	1.03712i
$347$	−19.4982	+	4.62117i	−1.04672	+	0.248077i	−0.717777	−	0.696273i	$-0.754840\pi$
$347$	−19.4982	+	4.62117i	−1.04672	+	0.248077i	−0.328943	+	0.944350i	$0.606692\pi$
$348$		0			0
$349$	33.4202	−	3.90626i	1.78894	−	0.209097i	0.844001	−	0.536342i	$-0.180194\pi$
$349$	33.4202	−	3.90626i	1.78894	−	0.209097i	0.944939	+	0.327245i	$0.106120\pi$
$350$	−3.43279	+	5.94576i	−0.183490	+	0.317814i
$351$		0			0
$352$	−2.35320	−	4.07587i	−0.125426	−	0.217244i
$353$	−4.81620	−	6.46927i	−0.256340	−	0.344325i	0.655259	−	0.755404i	$-0.272559\pi$
$353$	−4.81620	−	6.46927i	−0.256340	−	0.344325i	−0.911600	+	0.411079i	$0.865152\pi$
$354$		0			0
$355$	4.60483	−	15.3812i	0.244399	−	0.816349i
$356$	−1.30312	−	0.654453i	−0.0690654	−	0.0346859i
$357$		0			0
$358$	−1.91005	−	6.38002i	−0.100949	−	0.337194i
$359$	2.83469	−	16.0764i	0.149609	−	0.848477i	−0.813940	−	0.580948i	$-0.802682\pi$
$359$	2.83469	−	16.0764i	0.149609	−	0.848477i	0.963550	−	0.267529i	$-0.0862071\pi$
$360$		0			0
$361$	0.755367	+	4.28390i	0.0397562	+	0.225468i
$362$	5.06061	−	2.54153i	0.265980	−	0.133580i
$363$		0			0
$364$	0.262230	+	0.607917i	0.0137446	+	0.0318635i
$365$	−7.38667	−	17.1242i	−0.386636	−	0.896323i
$366$		0			0
$367$	11.7615	−	5.90686i	0.613947	−	0.308336i	−0.114516	−	0.993421i	$-0.536532\pi$
$367$	11.7615	−	5.90686i	0.613947	−	0.308336i	0.728462	+	0.685086i	$0.240235\pi$
$368$	0.508116	+	2.88167i	0.0264874	+	0.150217i
$369$		0			0
$370$	4.95036	−	28.0749i	0.257357	−	1.45954i
$371$	2.70701	+	9.04204i	0.140541	+	0.469439i
$372$		0			0
$373$	0.194504	+	0.0976835i	0.0100710	+	0.00505786i	0.453828	−	0.891090i	$-0.350058\pi$
$373$	0.194504	+	0.0976835i	0.0100710	+	0.00505786i	−0.443757	+	0.896147i	$0.646354\pi$
$374$	−9.35050	+	31.2329i	−0.483503	+	1.61501i
$375$		0			0
$376$	−0.320893	−	0.431034i	−0.0165488	−	0.0222289i
$377$	4.04451	+	7.00529i	0.208303	+	0.360791i
$378$		0			0
$379$	12.0931	−	20.9458i	0.621180	−	1.07592i	−0.368086	−	0.929792i	$-0.619987\pi$
$379$	12.0931	−	20.9458i	0.621180	−	1.07592i	0.989266	−	0.146124i	$-0.0466797\pi$
$380$	1.58478	−	0.185235i	0.0812977	−	0.00950234i
$381$		0			0
$382$	26.5885	−	6.30159i	1.36039	−	0.322417i
$383$	−7.06738	+	4.64829i	−0.361126	+	0.237516i	−0.717086	−	0.696985i	$-0.754524\pi$
$383$	−7.06738	+	4.64829i	−0.361126	+	0.237516i	0.355960	+	0.934501i	$0.384154\pi$
$384$		0			0
$385$	8.48253	−	8.99096i	0.432310	−	0.458222i
$386$	−18.6851	−	15.6787i	−0.951048	−	0.798024i
$387$		0			0
$388$	−0.211154	+	0.177179i	−0.0107197	+	0.00899491i
$389$	−1.46030	+	25.0723i	−0.0740400	+	1.27122i	0.732799	+	0.680446i	$0.238214\pi$
$389$	−1.46030	+	25.0723i	−0.0740400	+	1.27122i	−0.806839	+	0.590772i	$0.798823\pi$
$390$		0			0
$391$	2.16498	−	2.90807i	0.109488	−	0.147067i
$392$	−8.95294	−	1.04645i	−0.452192	−	0.0528536i
$393$		0			0
$394$	−23.2330	−	15.2806i	−1.17046	−	0.769826i
$395$	−5.52922	−	2.01247i	−0.278205	−	0.101258i
$396$		0			0
$397$	23.8173	−	8.66880i	1.19536	−	0.435074i	0.333756	−	0.942660i	$-0.391684\pi$
$397$	23.8173	−	8.66880i	1.19536	−	0.435074i	0.861602	+	0.507585i	$0.169462\pi$
$398$	1.29393	+	0.306667i	0.0648588	+	0.0153718i
$399$		0			0
$400$	−0.617506	−	10.6022i	−0.0308753	−	0.530108i
$401$	−16.2900	−	17.2664i	−0.813483	−	0.862242i	0.179097	−	0.983831i	$-0.442682\pi$
$401$	−16.2900	−	17.2664i	−0.813483	−	0.862242i	−0.992580	+	0.121589i	$0.961201\pi$
$402$		0			0
$403$	3.25746	−	7.55163i	0.162265	−	0.376174i
$404$	−1.02098			−0.0507957
$405$		0			0
$406$	−13.5210			−0.671037
$407$	19.2293	−	44.5785i	0.953160	−	2.20967i
$408$		0			0
$409$	−6.44213	−	6.82826i	−0.318543	−	0.337636i	0.548240	−	0.836321i	$-0.315298\pi$
$409$	−6.44213	−	6.82826i	−0.318543	−	0.337636i	−0.866783	+	0.498685i	$0.833816\pi$
$410$	1.40020	+	24.0404i	0.0691508	+	1.18727i
$411$		0			0
$412$	−0.456890	−	0.108285i	−0.0225093	−	0.00533481i
$413$	3.39087	−	1.23418i	0.166854	−	0.0607298i
$414$		0			0
$415$	8.26652	+	3.00877i	0.405787	+	0.147695i
$416$	−1.63892	−	1.07794i	−0.0803547	−	0.0528501i
$417$		0			0
$418$	28.9028	+	3.37825i	1.41368	+	0.165236i
$419$	7.01065	−	9.41694i	0.342493	−	0.460048i	−0.597187	−	0.802102i	$-0.703715\pi$
$419$	7.01065	−	9.41694i	0.342493	−	0.460048i	0.939680	+	0.342054i	$0.111123\pi$
$420$		0			0
$421$	−0.393410	+	6.75459i	−0.0191736	+	0.329199i	0.975058	+	0.221948i	$0.0712416\pi$
$421$	−0.393410	+	6.75459i	−0.0191736	+	0.329199i	−0.994232	+	0.107250i	$0.965795\pi$
$422$	17.0220	−	14.2831i	0.828618	−	0.695293i
$423$		0			0
$424$	−10.1299	−	8.49998i	−0.491950	−	0.412795i
$425$	−9.02980	+	9.57103i	−0.438010	+	0.464263i
$426$		0			0
$427$	−0.287187	+	0.188886i	−0.0138980	+	0.00914083i
$428$	0.887812	−	0.210415i	0.0429140	−	0.0101708i
$429$		0			0
$430$	20.2220	−	2.36361i	0.975191	−	0.113984i
$431$	−3.90563	+	6.76475i	−0.188128	+	0.325846i	−0.944626	−	0.328149i	$-0.893575\pi$
$431$	−3.90563	+	6.76475i	−0.188128	+	0.325846i	0.756498	+	0.653996i	$0.226908\pi$
$432$		0			0
$433$	−2.20878	−	3.82573i	−0.106147	−	0.183853i	0.808059	−	0.589102i	$-0.200518\pi$
$433$	−2.20878	−	3.82573i	−0.106147	−	0.183853i	−0.914206	+	0.405249i	$0.867185\pi$
$434$	8.20918	+	11.0268i	0.394053	+	0.529305i
$435$		0			0
$436$	−1.08921	+	3.63820i	−0.0521635	+	0.174238i
$437$	−2.89173	−	1.45228i	−0.138330	−	0.0694721i
$438$		0			0
$439$	4.31161	+	14.4018i	0.205782	+	0.687360i	0.997110	+	0.0759684i	$0.0242048\pi$
$439$	4.31161	+	14.4018i	0.205782	+	0.687360i	−0.791328	+	0.611392i	$0.790610\pi$
$440$	−3.00721	+	17.0547i	−0.143363	+	0.813052i
$441$		0			0
$442$	2.35966	+	13.3823i	0.112238	+	0.636531i
$443$	−10.1485	+	5.09675i	−0.482168	+	0.242154i	−0.673243	−	0.739422i	$-0.735099\pi$
$443$	−10.1485	+	5.09675i	−0.482168	+	0.242154i	0.191075	+	0.981576i	$0.438803\pi$
$444$		0			0
$445$	4.49455	+	10.4195i	0.213062	+	0.493934i
$446$	−3.64786	−	8.45668i	−0.172731	−	0.400435i
$447$		0			0
$448$	−11.9226	+	5.98776i	−0.563291	+	0.282895i
$449$	1.16004	+	6.57891i	0.0547457	+	0.310478i	0.999868	−	0.0162381i	$-0.00516898\pi$
$449$	1.16004	+	6.57891i	0.0547457	+	0.310478i	−0.945122	+	0.326716i	$0.894058\pi$
$450$		0			0
$451$	−7.12134	+	40.3871i	−0.335331	+	1.90176i
$452$	0.532810	+	1.77971i	0.0250613	+	0.0837105i
$453$		0			0
$454$	−18.9580	−	9.52106i	−0.889743	−	0.446846i
$455$	1.47761	−	4.93557i	0.0692716	−	0.231383i
$456$		0			0
$457$	7.17351	+	9.63570i	0.335563	+	0.450739i	0.937593	−	0.347734i	$-0.113049\pi$
$457$	7.17351	+	9.63570i	0.335563	+	0.450739i	−0.602030	+	0.798473i	$0.705641\pi$
$458$	−14.5059	−	25.1249i	−0.677815	−	1.17401i
$459$		0			0
$460$	−0.110560	+	0.191496i	−0.00515490	+	0.00892855i
$461$	6.95142	−	0.812504i	0.323760	−	0.0378421i	0.0473393	−	0.998879i	$-0.484926\pi$
$461$	6.95142	−	0.812504i	0.323760	−	0.0378421i	0.276421	+	0.961037i	$0.410852\pi$
$462$		0			0
$463$	27.2778	−	6.46495i	1.26771	−	0.300452i	0.458879	−	0.888499i	$-0.348251\pi$
$463$	27.2778	−	6.46495i	1.26771	−	0.300452i	0.808827	+	0.588047i	$0.200103\pi$
$464$	17.4744	−	11.4931i	0.811229	−	0.533554i
$465$		0			0
$466$	−9.67112	+	10.2508i	−0.448006	+	0.474858i
$467$	10.9662	+	9.20178i	0.507458	+	0.425807i	0.860233	−	0.509900i	$-0.170318\pi$
$467$	10.9662	+	9.20178i	0.507458	+	0.425807i	−0.352776	+	0.935708i	$0.614762\pi$
$468$		0			0
$469$	19.4162	−	16.2921i	0.896557	−	0.752300i
$470$	0.0279179	−	0.479331i	0.00128776	−	0.0221099i
$471$		0			0
$472$	−3.01898	+	4.05519i	−0.138960	+	0.186655i
$473$	34.4380	+	4.02523i	1.58346	+	0.185080i
$474$		0			0
$475$	9.81243	+	6.45374i	0.450225	+	0.296118i
$476$	−1.99307	−	0.725420i	−0.0913524	−	0.0332496i
$477$		0			0
$478$	15.3578	−	5.58977i	0.702448	−	0.255670i
$479$	21.8904	+	5.18813i	1.00020	+	0.237052i	0.697926	−	0.716170i	$-0.254106\pi$
$479$	21.8904	+	5.18813i	1.00020	+	0.237052i	0.302273	+	0.953221i	$0.402255\pi$
$480$		0			0
$481$	−1.17658	−	20.2010i	−0.0536473	−	0.921088i
$482$	2.23266	+	2.36648i	0.101695	+	0.107790i
$483$		0			0
$484$	0.443783	−	1.02881i	0.0201720	−	0.0467639i
$485$	2.14498			0.0973984
$486$		0			0
$487$	−41.7203			−1.89053			−0.945264	−	0.326307i	$-0.894196\pi$
$487$	−41.7203			−1.89053			−0.945264	+	0.326307i	$0.894196\pi$
$488$	0.190745	−	0.442196i	0.00863460	−	0.0200173i
$489$		0			0
$490$	−5.52701	−	5.85829i	−0.249685	−	0.264650i
$491$	−0.643607	−	11.0503i	−0.0290456	−	0.498694i	−0.981190	−	0.193045i	$-0.938164\pi$
$491$	−0.643607	−	11.0503i	−0.0290456	−	0.498694i	0.952144	−	0.305649i	$-0.0988733\pi$
$492$		0			0
$493$	−25.2154	−	5.97617i	−1.13565	−	0.269153i
$494$	11.3973	−	4.14826i	0.512787	−	0.186639i
$495$		0			0
$496$	−19.9825	−	7.27302i	−0.897239	−	0.326568i
$497$	15.9157	+	10.4679i	0.713917	+	0.469550i
$498$		0			0
$499$	−7.76171	−	0.907214i	−0.347462	−	0.0406125i	−0.0594278	−	0.998233i	$-0.518928\pi$
$499$	−7.76171	−	0.907214i	−0.347462	−	0.0406125i	−0.288034	+	0.957620i	$0.593002\pi$
$500$	1.46514	−	1.96803i	0.0655232	−	0.0880130i
$501$		0			0
$502$	−0.605994	+	10.4045i	−0.0270468	+	0.464376i
$503$	−18.1547	+	15.2336i	−0.809478	+	0.679233i	−0.950483	−	0.310776i	$-0.899411\pi$
$503$	−18.1547	+	15.2336i	−0.809478	+	0.679233i	0.141005	+	0.990009i	$0.454967\pi$
$504$		0			0
$505$	6.08624	+	5.10696i	0.270834	+	0.227257i
$506$	−2.76743	+	2.93330i	−0.123027	+	0.130401i
$507$		0			0
$508$	0.301851	−	0.198530i	0.0133925	−	0.00880836i
$509$	−12.1281	+	2.87442i	−0.537570	+	0.127406i	−0.490428	−	0.871482i	$-0.663159\pi$
$509$	−12.1281	+	2.87442i	−0.537570	+	0.127406i	−0.0471419	+	0.998888i	$0.515011\pi$
$510$		0			0
$511$	21.9774	−	2.56879i	0.972222	−	0.113636i
$512$	9.10692	−	15.7736i	0.402473	−	0.697103i
$513$		0			0
$514$	−0.347303	−	0.601546i	−0.0153189	−	0.0265331i
$515$	2.18195	+	2.93087i	0.0961484	+	0.129150i
$516$		0			0
$517$	0.234514	−	0.783332i	0.0103139	−	0.0344509i
$518$	30.2261	+	15.1801i	1.32806	+	0.666976i
$519$		0			0
$520$	2.07017	+	6.91484i	0.0907829	+	0.303236i
$521$	−3.66734	+	20.7985i	−0.160669	+	0.911200i	0.792749	+	0.609548i	$0.208649\pi$
$521$	−3.66734	+	20.7985i	−0.160669	+	0.911200i	−0.953418	+	0.301652i	$0.902462\pi$
$522$		0			0
$523$	7.23247	+	41.0174i	0.316254	+	1.79356i	0.565102	+	0.825021i	$0.308837\pi$
$523$	7.23247	+	41.0174i	0.316254	+	1.79356i	−0.248848	+	0.968543i	$0.580052\pi$
$524$	−1.31866	+	0.662256i	−0.0576059	+	0.0289308i
$525$		0			0
$526$	−11.2277	−	26.0288i	−0.489553	−	1.13491i
$527$	10.4356	+	24.1924i	0.454581	+	1.05384i
$528$		0			0
$529$	−20.1528	+	10.1211i	−0.876209	+	0.440049i
$530$	−2.05173	−	11.6360i	−0.0891217	−	0.505434i
$531$		0			0
$532$	−0.328733	+	1.86434i	−0.0142524	+	0.0808293i
$533$	4.90235	+	16.3750i	0.212344	+	0.709279i
$534$		0			0
$535$	−6.34489	−	3.18653i	−0.274314	−	0.137766i
$536$	−10.1845	+	34.0185i	−0.439902	+	1.46938i
$537$		0			0
$538$	−3.76168	−	5.05281i	−0.162177	−	0.217842i
$539$	−6.85799	−	11.8784i	−0.295395	−	0.511638i
$540$		0			0
$541$	−4.87647	+	8.44629i	−0.209656	+	0.363134i	−0.951606	−	0.307320i	$-0.900568\pi$
$541$	−4.87647	+	8.44629i	−0.209656	+	0.363134i	0.741950	+	0.670455i	$0.233901\pi$
$542$	−11.3049	+	1.32136i	−0.485588	+	0.0567571i
$543$		0			0
$544$	6.11490	−	1.44926i	0.262174	−	0.0621364i
$545$	24.6913	−	16.2397i	1.05766	−	0.695632i
$546$		0			0
$547$	−0.475687	+	0.504198i	−0.0203389	+	0.0215580i	−0.737463	−	0.675387i	$-0.763976\pi$
$547$	−0.475687	+	0.504198i	−0.0203389	+	0.0215580i	0.717124	+	0.696945i	$0.245458\pi$
$548$	2.75722	+	2.31358i	0.117783	+	0.0988314i
$549$		0			0
$550$	11.2122	−	9.40814i	0.478089	−	0.401164i
$551$	−1.34487	+	23.0905i	−0.0572934	+	0.983689i
$552$		0			0
$553$	4.16893	−	5.59984i	0.177281	−	0.238130i
$554$	−21.8850	−	2.55799i	−0.929804	−	0.108678i
$555$		0			0
$556$	3.26993	+	2.15067i	0.138676	+	0.0912087i
$557$	28.7125	+	10.4505i	1.21659	+	0.442801i	0.868984	−	0.494841i	$-0.164774\pi$
$557$	28.7125	+	10.4505i	1.21659	+	0.442801i	0.347602	+	0.937642i	$0.386996\pi$
$558$		0			0
$559$	13.5800	−	4.94270i	0.574371	−	0.209054i
$560$	−12.9621	−	3.07208i	−0.547751	−	0.129819i
$561$		0			0
$562$	0.0961204	+	1.65032i	0.00405460	+	0.0696147i
$563$	−6.68923	−	7.09017i	−0.281918	−	0.298815i	0.570905	−	0.821016i	$-0.306593\pi$
$563$	−6.68923	−	7.09017i	−0.281918	−	0.298815i	−0.852822	+	0.522201i	$0.825111\pi$
$564$		0			0
$565$	5.72596	−	13.2743i	0.240893	−	0.558453i
$566$	−9.81660			−0.412622
$567$		0			0
$568$	−26.6889			−1.11984
$569$	7.79560	−	18.0722i	0.326808	−	0.757627i	−0.673029	−	0.739616i	$-0.735007\pi$
$569$	7.79560	−	18.0722i	0.326808	−	0.757627i	0.999838	−	0.0180113i	$-0.00573349\pi$
$570$		0			0
$571$	22.6458	+	24.0031i	0.947697	+	1.00450i	0.999983	+	0.00586776i	$0.00186778\pi$
$571$	22.6458	+	24.0031i	0.947697	+	1.00450i	−0.0522860	+	0.998632i	$0.516651\pi$
$572$	−0.0820673	−	1.40904i	−0.00343140	−	0.0589149i
$573$		0			0
$574$	−27.8014	−	6.58906i	−1.16041	−	0.275022i
$575$	−1.52945	+	0.556674i	−0.0637824	+	0.0232149i
$576$		0			0
$577$	−19.1279	−	6.96197i	−0.796303	−	0.289831i	−0.0883494	−	0.996090i	$-0.528159\pi$
$577$	−19.1279	−	6.96197i	−0.796303	−	0.289831i	−0.707954	+	0.706259i	$0.750381\pi$
$578$	−15.2757	−	10.0470i	−0.635384	−	0.417899i
$579$		0			0
$580$	1.56983	+	0.183487i	0.0651837	+	0.00761888i
$581$	−6.23280	+	8.37210i	−0.258580	+	0.347333i
$582$		0			0
$583$	1.16997	−	20.0877i	0.0484553	−	0.831946i
$584$	−23.7477	+	19.9267i	−0.982686	+	0.824571i
$585$		0			0
$586$	−3.54165	−	2.97180i	−0.146304	−	0.122764i
$587$	−24.1185	+	25.5641i	−0.995477	+	1.05514i	0.00300161	+	0.999995i	$0.499045\pi$
$587$	−24.1185	+	25.5641i	−0.995477	+	1.05514i	−0.998478	+	0.0551480i	$0.982437\pi$
$588$		0			0
$589$	19.6476	−	12.9224i	0.809566	−	0.532460i
$590$	−4.39545	+	1.04174i	−0.180958	+	0.0428878i
$591$		0			0
$592$	−51.9672	+	6.07410i	−2.13584	+	0.249644i
$593$	4.46816	−	7.73909i	0.183485	−	0.317806i	−0.759580	−	0.650414i	$-0.774595\pi$
$593$	4.46816	−	7.73909i	0.183485	−	0.317806i	0.943065	+	0.332608i	$0.107929\pi$
$594$		0			0
$595$	8.25249	+	14.2937i	0.338319	+	0.585986i
$596$	−0.906953	−	1.21825i	−0.0371503	−	0.0499015i
$597$		0			0
$598$	−0.482071	+	1.61023i	−0.0197134	+	0.0658472i
$599$	35.4506	+	17.8040i	1.44847	+	0.727451i	0.987152	−	0.159782i	$-0.0510791\pi$
$599$	35.4506	+	17.8040i	1.44847	+	0.727451i	0.461322	+	0.887233i	$0.347375\pi$
$600$		0			0
$601$	−6.78673	−	22.6693i	−0.276837	−	0.924699i	−0.977452	−	0.211159i	$-0.932276\pi$
$601$	−6.78673	−	22.6693i	−0.276837	−	0.924699i	0.700615	−	0.713539i	$-0.252909\pi$
$602$	−4.19466	+	23.7891i	−0.170962	+	0.969572i
$603$		0			0
$604$	−0.0955328	−	0.541794i	−0.00388718	−	0.0220453i
$605$	−7.79156	+	3.91307i	−0.316772	+	0.159089i
$606$		0			0
$607$	7.03429	+	16.3073i	0.285513	+	0.661893i	0.999258	−	0.0385121i	$-0.0122618\pi$
$607$	7.03429	+	16.3073i	0.285513	+	0.661893i	−0.713745	+	0.700405i	$0.753003\pi$
$608$	−2.22164	−	5.15035i	−0.0900995	−	0.208874i
$609$		0			0
$610$	0.384529	−	0.193118i	0.0155691	−	0.00781911i
$611$	−0.0591812	−	0.335633i	−0.00239422	−	0.0135783i
$612$		0			0
$613$	−0.410662	+	2.32898i	−0.0165865	+	0.0940666i	−0.991977	−	0.126417i	$-0.959652\pi$
$613$	−0.410662	+	2.32898i	−0.0165865	+	0.0940666i	0.975391	+	0.220483i	$0.0707635\pi$
$614$	3.20441	+	10.7035i	0.129319	+	0.431957i
$615$		0			0
$616$	−18.3615	−	9.22150i	−0.739807	−	0.371545i
$617$	9.69418	−	32.3808i	0.390273	−	1.30360i	−0.506931	−	0.861986i	$-0.669220\pi$
$617$	9.69418	−	32.3808i	0.390273	−	1.30360i	0.897204	−	0.441616i	$-0.145595\pi$
$618$		0			0
$619$	28.3599	+	38.0940i	1.13988	+	1.53113i	0.809345	+	0.587334i	$0.199823\pi$
$619$	28.3599	+	38.0940i	1.13988	+	1.53113i	0.330537	+	0.943793i	$0.392770\pi$
$620$	−0.803470	−	1.39165i	−0.0322681	−	0.0558901i
$621$		0			0
$622$	−11.4270	+	19.7921i	−0.458180	+	0.793591i
$623$	−13.3725	+	1.56303i	−0.535759	+	0.0626213i
$624$		0			0
$625$	−6.75322	+	1.60054i	−0.270129	+	0.0640217i
$626$	4.92649	−	3.24021i	0.196902	−	0.129505i
$627$		0			0
$628$	0.807755	−	0.856170i	0.0322329	−	0.0341649i
$629$	49.6594	+	41.6692i	1.98005	+	1.66146i
$630$		0			0
$631$	−14.6874	+	12.3242i	−0.584695	+	0.490617i	−0.886485	−	0.462757i	$-0.846860\pi$
$631$	−14.6874	+	12.3242i	−0.584695	+	0.490617i	0.301790	+	0.953374i	$0.402416\pi$
$632$	−0.568709	+	9.76436i	−0.0226220	+	0.388406i
$633$		0			0
$634$	−7.60557	+	10.2161i	−0.302056	+	0.405731i
$635$	−2.79244	−	0.326389i	−0.110814	−	0.0129523i
$636$		0			0
$637$	−4.77634	−	3.14145i	−0.189246	−	0.124469i
$638$	27.0866	+	9.85872i	1.07237	+	0.390311i
$639$		0			0
$640$	19.1913	−	6.98507i	0.758603	−	0.276109i
$641$	−2.04822	−	0.485436i	−0.0808997	−	0.0191736i	0.189967	−	0.981791i	$-0.439162\pi$
$641$	−2.04822	−	0.485436i	−0.0808997	−	0.0191736i	−0.270866	+	0.962617i	$0.587310\pi$
$642$		0			0
$643$	2.54772	+	43.7427i	0.100472	+	1.72504i	0.552905	+	0.833244i	$0.313519\pi$
$643$	2.54772	+	43.7427i	0.100472	+	1.72504i	−0.452433	+	0.891798i	$0.649444\pi$
$644$	−0.180037	−	0.190829i	−0.00709447	−	0.00751970i
$645$		0			0
$646$	−15.3899	+	35.6778i	−0.605507	+	1.40372i
$647$	−2.17952			−0.0856859			−0.0428430	−	0.999082i	$-0.513642\pi$
$647$	−2.17952			−0.0856859			−0.0428430	+	0.999082i	$0.513642\pi$
$648$		0			0
$649$	−7.69281			−0.301969
$650$	2.41628	−	5.60157i	0.0947743	−	0.219712i
$651$		0			0
$652$	−2.26714	−	2.40303i	−0.0887880	−	0.0941098i
$653$	−1.08815	−	18.6828i	−0.0425826	−	0.731115i	−0.950262	−	0.311451i	$-0.899185\pi$
$653$	−1.08815	−	18.6828i	−0.0425826	−	0.731115i	0.907680	−	0.419664i	$-0.137852\pi$
$654$		0			0
$655$	11.1734	+	2.64814i	0.436579	+	0.103471i
$656$	41.5311	−	15.1161i	1.62152	−	0.590183i
$657$		0			0
$658$	0.535320	+	0.194841i	0.0208689	+	0.00759568i
$659$	−11.9512	−	7.86043i	−0.465553	−	0.306199i	0.294974	−	0.955505i	$-0.404689\pi$
$659$	−11.9512	−	7.86043i	−0.465553	−	0.306199i	−0.760527	+	0.649306i	$0.775059\pi$
$660$		0			0
$661$	−24.8243	−	2.90155i	−0.965555	−	0.112857i	−0.381321	−	0.924443i	$-0.624531\pi$
$661$	−24.8243	−	2.90155i	−0.965555	−	0.112857i	−0.584234	+	0.811586i	$0.698605\pi$
$662$	−8.27579	+	11.1163i	−0.321648	+	0.432048i
$663$		0			0
$664$	0.850255	−	14.5983i	0.0329963	−	0.566524i
$665$	11.2851	−	9.46931i	0.437617	−	0.367204i
$666$		0			0
$667$	−2.45548	−	2.06039i	−0.0950764	−	0.0797786i
$668$	2.70676	−	2.86900i	0.104728	−	0.111005i
$669$		0			0
$670$	−26.5091	+	17.4353i	−1.02414	+	0.673586i
$671$	0.713045	−	0.168995i	0.0275268	−	0.00652397i
$672$		0			0
$673$	29.4895	−	3.44683i	1.13674	−	0.132866i	0.473163	−	0.880975i	$-0.343112\pi$
$673$	29.4895	−	3.44683i	1.13674	−	0.132866i	0.663576	+	0.748109i	$0.269038\pi$
$674$	−3.27319	+	5.66933i	−0.126078	+	0.218374i
$675$		0			0
$676$	1.04480	+	1.80964i	0.0401846	+	0.0696017i
$677$	−23.1605	−	31.1099i	−0.890129	−	1.19565i	−0.979860	−	0.199685i	$-0.936008\pi$
$677$	−23.1605	−	31.1099i	−0.890129	−	1.19565i	0.0897310	−	0.995966i	$-0.471399\pi$
$678$		0			0
$679$	−0.729900	+	2.43803i	−0.0280110	+	0.0935632i
$680$	−20.6642	−	10.3780i	−0.792436	−	0.397977i
$681$		0			0
$682$	−8.40530	−	28.0757i	−0.321856	−	1.07507i
$683$	2.81006	−	15.9367i	0.107524	−	0.609799i	−0.882658	−	0.470016i	$-0.844248\pi$
$683$	2.81006	−	15.9367i	0.107524	−	0.609799i	0.990182	−	0.139784i	$-0.0446407\pi$
$684$		0			0
$685$	−4.86369	−	27.5833i	−0.185832	−	1.05391i
$686$	26.2096	−	13.1630i	1.00069	−	0.502564i
$687$		0			0
$688$	−14.8000	−	34.3103i	−0.564246	−	1.30807i
$689$	−3.32182	−	7.70084i	−0.126551	−	0.293379i
$690$		0			0
$691$	−15.7344	+	7.90210i	−0.598564	+	0.300610i	−0.722164	−	0.691722i	$-0.756852\pi$
$691$	−15.7344	+	7.90210i	−0.598564	+	0.300610i	0.123600	+	0.992332i	$0.460556\pi$
$692$	0.845488	+	4.79500i	0.0321406	+	0.182279i
$693$		0			0
$694$	−5.16814	+	29.3100i	−0.196180	+	1.11259i
$695$	−8.73495	−	29.1768i	−0.331335	−	1.10674i
$696$		0			0
$697$	−48.9348	−	24.5760i	−1.85354	−	0.930881i
$698$	14.3331	−	47.8760i	0.542517	−	1.81213i
$699$		0			0
$700$	0.568608	+	0.763773i	0.0214914	+	0.0288679i
$701$	9.33660	+	16.1715i	0.352639	+	0.610788i	0.986711	−	0.162486i	$-0.0519512\pi$
$701$	9.33660	+	16.1715i	0.352639	+	0.610788i	−0.634072	+	0.773274i	$0.718618\pi$
$702$		0			0
$703$	28.9303	−	50.1087i	1.09113	−	1.88989i
$704$	28.2504	−	3.30200i	1.06473	−	0.124449i
$705$		0			0
$706$	−11.6560	+	2.76252i	−0.438679	+	0.103969i
$707$	−7.87574	+	5.17996i	−0.296198	+	0.194812i
$708$		0			0
$709$	−22.6076	+	23.9627i	−0.849047	+	0.899938i	−0.996013	−	0.0892040i	$-0.971568\pi$
$709$	−22.6076	+	23.9627i	−0.849047	+	0.899938i	0.146966	+	0.989142i	$0.453049\pi$
$710$	−18.2677	−	15.3285i	−0.685576	−	0.575267i
$711$		0			0
$712$	14.4497	−	12.1247i	0.541526	−	0.454394i
$713$	−0.189493	+	3.25347i	−0.00709657	+	0.121843i
$714$		0			0
$715$	−6.55882	+	8.81003i	−0.245286	+	0.329476i
$716$	−0.917404	−	0.107229i	−0.0342850	−	0.00400734i
$717$		0			0
$718$	−20.2571	−	13.3233i	−0.755990	−	0.497222i
$719$	−43.1137	−	15.6921i	−1.60787	−	0.585216i	−0.626852	−	0.779139i	$-0.715657\pi$
$719$	−43.1137	−	15.6921i	−1.60787	−	0.585216i	−0.981017	+	0.193922i	$0.937879\pi$
$720$		0			0
$721$	−4.07379	+	1.48274i	−0.151716	+	0.0552200i
$722$	6.28670	+	1.48997i	0.233967	+	0.0554511i
$723$		0			0
$724$	−0.0456669	−	0.784070i	−0.00169720	−	0.0291397i
$725$	7.98355	+	8.46207i	0.296502	+	0.314273i
$726$		0			0
$727$	6.39466	−	14.8245i	0.237165	−	0.549810i	−0.757516	−	0.652817i	$-0.773587\pi$
$727$	6.39466	−	14.8245i	0.237165	−	0.549810i	0.994681	+	0.103007i	$0.0328464\pi$
$728$	−8.56403			−0.317404
$729$		0			0
$730$	−27.6992			−1.02519
$731$	−18.3372	+	42.5105i	−0.678227	+	1.57231i
$732$		0			0
$733$	17.6698	+	18.7289i	0.652648	+	0.691767i	0.966197	−	0.257805i	$-0.0829993\pi$
$733$	17.6698	+	18.7289i	0.652648	+	0.691767i	−0.313549	+	0.949572i	$0.601518\pi$
$734$	−1.13663	−	19.5151i	−0.0419536	−	0.720316i
$735$		0			0
$736$	0.756375	+	0.179264i	0.0278803	+	0.00660776i
$737$	−50.7756	+	18.4808i	−1.87034	+	0.680750i
$738$		0			0
$739$	−16.9934	−	6.18508i	−0.625111	−	0.227522i	0.00999089	−	0.999950i	$-0.496820\pi$
$739$	−16.9934	−	6.18508i	−0.625111	−	0.227522i	−0.635102	+	0.772428i	$0.719042\pi$
$740$	−3.30334	−	2.17264i	−0.121433	−	0.0798678i
$741$		0			0
$742$	13.9239	+	1.62747i	0.511162	+	0.0597463i
$743$	26.4761	−	35.5636i	0.971314	−	1.30470i	0.0189230	−	0.999821i	$-0.493976\pi$
$743$	26.4761	−	35.5636i	0.971314	−	1.30470i	0.952391	−	0.304880i	$-0.0986163\pi$
$744$		0			0
$745$	−0.687201	+	11.7988i	−0.0251771	+	0.432274i
$746$	0.247642	−	0.207797i	0.00906683	−	0.00760798i
$747$		0			0
$748$	3.46379	+	2.90646i	0.126649	+	0.106271i
$749$	5.78095	−	6.12744i	0.211231	−	0.223892i
$750$		0			0
$751$	−2.09320	+	1.37672i	−0.0763819	+	0.0502372i	−0.587126	−	0.809496i	$-0.699741\pi$
$751$	−2.09320	+	1.37672i	−0.0763819	+	0.0502372i	0.510744	+	0.859733i	$0.329370\pi$
$752$	−0.857459	+	0.203222i	−0.0312683	+	0.00741073i
$753$		0			0
$754$	11.9330	−	1.39477i	0.434575	−	0.0507946i
$755$	−2.14057	+	3.70758i	−0.0779034	+	0.134933i
$756$		0			0
$757$	21.8769	+	37.8919i	0.795129	+	1.37720i	0.922757	+	0.385381i	$0.125930\pi$
$757$	21.8769	+	37.8919i	0.795129	+	1.37720i	−0.127629	+	0.991822i	$0.540737\pi$
$758$	−21.4515	−	28.8144i	−0.779155	−	1.04659i
$759$		0			0
$760$	−5.91942	+	19.7722i	−0.214720	+	0.717215i
$761$	−41.2979	−	20.7406i	−1.49705	−	0.751846i	−0.503366	−	0.864073i	$-0.667905\pi$
$761$	−41.2979	−	20.7406i	−1.49705	−	0.751846i	−0.993683	+	0.112227i	$0.964202\pi$
$762$		0			0
$763$	10.0564	+	33.5908i	0.364067	+	1.21607i
$764$	0.658078	−	3.73214i	0.0238084	−	0.135024i
$765$		0			0
$766$	2.18168	+	12.3729i	0.0788272	+	0.447051i
$767$	−2.86531	+	1.43901i	−0.103460	+	0.0519598i
$768$		0			0
$769$	11.5490	+	26.7737i	0.416469	+	0.965483i	0.989311	+	0.145818i	$0.0465814\pi$
$769$	11.5490	+	26.7737i	0.416469	+	0.965483i	−0.572843	+	0.819665i	$0.694159\pi$
$770$	−7.27165	−	16.8576i	−0.262052	−	0.607505i
$771$		0			0
$772$	−3.02306	+	1.51824i	−0.108802	+	0.0546427i
$773$	6.90323	+	39.1502i	0.248292	+	1.40813i	0.812721	+	0.582653i	$0.197985\pi$
$773$	6.90323	+	39.1502i	0.248292	+	1.40813i	−0.564429	+	0.825481i	$0.690904\pi$
$774$		0			0
$775$	2.05395	−	11.6485i	0.0737801	−	0.418427i
$776$	−1.02260	−	3.41574i	−0.0367094	−	0.122618i
$777$		0			0
$778$	33.3343	+	16.7411i	1.19509	+	0.600198i
$779$	−14.0177	+	46.8225i	−0.502238	+	1.67759i
$780$		0			0
$781$	−24.2513	−	32.5751i	−0.867779	−	1.16563i
$782$	−2.69238	−	4.66333i	−0.0962792	−	0.166760i

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)

\(f(q)\)	\(=\)	\(q+(0.588281 - 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(0.0932044 + 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(2.50387 - 0.911335i) q^{8} +O(q^{10})\)	\(q+(0.588281 - 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(0.0932044 + 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(2.50387 - 0.911335i) q^{8} +(2.23724 + 0.814290i) q^{10} +(3.38752 + 2.22800i) q^{11} +(1.67851 + 0.196189i) q^{13} +(-1.68684 + 2.26582i) q^{14} +(0.254067 - 4.36216i) q^{16} +(-4.14727 + 3.47997i) q^{17} +(3.70167 + 3.10607i) q^{19} +(0.226595 - 0.240177i) q^{20} +(5.03133 - 3.30916i) q^{22} +(-0.651612 + 0.154435i) q^{23} +(2.41405 - 0.282162i) q^{25} +(1.25499 - 2.17371i) q^{26} +(0.195884 + 0.339282i) q^{28} +(2.85835 + 3.83943i) q^{29} +(1.39576 - 4.66216i) q^{31} +(-1.03731 - 0.520955i) q^{32} +(2.30618 + 7.70319i) q^{34} +(0.529392 - 3.00233i) q^{35} +(-2.07926 - 11.7921i) q^{37} +(6.41363 - 3.22105i) q^{38} +(1.69174 + 3.92190i) q^{40} +(4.00621 + 9.28743i) q^{41} +(7.64192 - 3.83792i) q^{43} +(-0.145031 - 0.822509i) q^{44} +(-0.172714 + 0.979511i) q^{46} +(-0.0578400 - 0.193199i) q^{47} +(-3.02305 - 1.51823i) q^{49} +(1.03533 - 3.45825i) q^{50} +(-0.207877 - 0.279228i) q^{52} +(-2.48138 - 4.29788i) q^{53} +(-3.24965 + 5.62856i) q^{55} +(-5.03340 + 0.588321i) q^{56} +(6.91768 - 1.63952i) q^{58} +(-1.58520 + 1.04260i) q^{59} +(0.124028 - 0.131462i) q^{61} +(-5.53710 - 4.64618i) q^{62} +(5.37384 - 4.50919i) q^{64} +(-0.157509 + 2.70433i) q^{65} +(-7.95826 + 10.6898i) q^{67} +(1.10767 + 0.129468i) q^{68} +(-3.78311 - 2.48819i) q^{70} +(-9.41216 - 3.42575i) q^{71} +(-10.9327 + 3.97917i) q^{73} +(-17.3051 - 4.10138i) q^{74} +(-0.0578765 - 0.993701i) q^{76} +(-5.29176 - 5.60894i) q^{77} +(-1.45390 + 3.37053i) q^{79} +7.00426 q^{80} +15.0229 q^{82} +(2.17367 - 5.03914i) q^{83} +(-5.95539 - 6.31235i) q^{85} +(-0.738510 - 12.6797i) q^{86} +(10.5124 + 2.49148i) q^{88} +(6.65218 - 2.42120i) q^{89} +(-3.02021 - 1.09927i) q^{91} +(0.115251 + 0.0758017i) q^{92} +(-0.297508 - 0.0347738i) q^{94} +(-4.62550 + 6.21312i) q^{95} +(0.0778051 - 1.33586i) q^{97} +(-3.84894 + 3.22965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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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