LMFDB - Embedded newform 162.2.e.b.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			127.1
Root			$0.500000 - 0.168222i$ of defining polynomial
Character	$\chi$	$=$	162.127
Dual form			162.2.e.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.696050 - 0.253341i) q^{5} +(0.717657 - 4.07003i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.370360 + 0.641483i) q^{10} +(4.27215 - 1.55493i) q^{11} +(0.662744 - 0.556108i) q^{13} +(-3.16592 + 2.65653i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-2.17975 - 3.77544i) q^{17} +(-0.777964 + 1.34747i) q^{19} +(0.128625 - 0.729467i) q^{20} +(-4.27215 - 1.55493i) q^{22} +(0.608539 + 3.45119i) q^{23} +(-3.40992 - 2.86126i) q^{25} -0.865150 q^{26} +4.13282 q^{28} +(2.50318 + 2.10042i) q^{29} +(1.85778 + 10.5360i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.757019 + 4.29327i) q^{34} +(-1.53063 + 2.65113i) q^{35} +(0.880842 + 1.52566i) q^{37} +(1.46209 - 0.532159i) q^{38} +(-0.567425 + 0.476126i) q^{40} +(1.97401 - 1.65639i) q^{41} +(2.58757 - 0.941797i) q^{43} +(2.27316 + 3.93723i) q^{44} +(1.75222 - 3.03493i) q^{46} +(-1.68378 + 9.54918i) q^{47} +(-9.47229 - 3.44763i) q^{49} +(0.772966 + 4.38371i) q^{50} +(0.662744 + 0.556108i) q^{52} -4.00839 q^{53} -3.36756 q^{55} +(-3.16592 - 2.65653i) q^{56} +(-0.567425 - 3.21803i) q^{58} +(1.34517 + 0.489601i) q^{59} +(-0.751711 + 4.26317i) q^{61} +(5.34926 - 9.26519i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.602188 + 0.219178i) q^{65} +(10.0444 - 8.42825i) q^{67} +(3.33957 - 2.80223i) q^{68} +(2.87665 - 1.04701i) q^{70} +(-2.54213 - 4.40310i) q^{71} +(0.286636 - 0.496469i) q^{73} +(0.305913 - 1.73492i) q^{74} +(-1.46209 - 0.532159i) q^{76} +(-3.26270 - 18.5037i) q^{77} +(5.17820 + 4.34502i) q^{79} +0.740720 q^{80} -2.57689 q^{82} +(-7.06556 - 5.92871i) q^{83} +(0.560740 + 3.18011i) q^{85} +(-2.58757 - 0.941797i) q^{86} +(0.789461 - 4.47725i) q^{88} +(-6.19947 + 10.7378i) q^{89} +(-1.78776 - 3.09648i) q^{91} +(-3.29309 + 1.19859i) q^{92} +(7.42794 - 6.23278i) q^{94} +(0.882872 - 0.740818i) q^{95} +(-5.40770 + 1.96824i) q^{97} +(5.04010 + 8.72971i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.696050	−	0.253341i	−0.311283	−	0.113298i	0.181655	−	0.983362i	$-0.441855\pi$
$5$	−0.696050	−	0.253341i	−0.311283	−	0.113298i	−0.492938	+	0.870065i	$0.664077\pi$
$6$		0			0
$7$	0.717657	−	4.07003i	0.271249	−	1.53833i	−0.479382	−	0.877606i	$-0.659139\pi$
$7$	0.717657	−	4.07003i	0.271249	−	1.53833i	0.750631	−	0.660722i	$-0.229750\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	0.370360	+	0.641483i	0.117118	+	0.202855i
$11$	4.27215	−	1.55493i	1.28810	−	0.468830i	0.394998	−	0.918682i	$-0.370745\pi$
$11$	4.27215	−	1.55493i	1.28810	−	0.468830i	0.893103	+	0.449852i	$0.148523\pi$
$12$		0			0
$13$	0.662744	−	0.556108i	0.183812	−	0.154237i	−0.546239	−	0.837630i	$-0.683941\pi$
$13$	0.662744	−	0.556108i	0.183812	−	0.154237i	0.730051	+	0.683393i	$0.239496\pi$
$14$	−3.16592	+	2.65653i	−0.846129	+	0.709986i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.17975	−	3.77544i	−0.528667	−	0.915678i	−0.999441	−	0.0334246i	$-0.989359\pi$
$17$	−2.17975	−	3.77544i	−0.528667	−	0.915678i	0.470774	−	0.882254i	$-0.343975\pi$
$18$		0			0
$19$	−0.777964	+	1.34747i	−0.178477	+	0.309132i	−0.941359	−	0.337406i	$-0.890450\pi$
$19$	−0.777964	+	1.34747i	−0.178477	+	0.309132i	0.762882	+	0.646538i	$0.223784\pi$
$20$	0.128625	−	0.729467i	0.0287614	−	0.163114i
$21$		0			0
$22$	−4.27215	−	1.55493i	−0.910825	−	0.331513i
$23$	0.608539	+	3.45119i	0.126889	+	0.719624i	0.980168	+	0.198169i	$0.0634994\pi$
$23$	0.608539	+	3.45119i	0.126889	+	0.719624i	−0.853279	+	0.521455i	$0.825389\pi$
$24$		0			0
$25$	−3.40992	−	2.86126i	−0.681984	−	0.572252i
$26$	−0.865150			−0.169670
$27$		0			0
$28$	4.13282			0.781029
$29$	2.50318	+	2.10042i	0.464829	+	0.390038i	0.844904	−	0.534918i	$-0.179657\pi$
$29$	2.50318	+	2.10042i	0.464829	+	0.390038i	−0.380075	+	0.924956i	$0.624102\pi$
$30$		0			0
$31$	1.85778	+	10.5360i	0.333667	+	1.89232i	0.440016	+	0.897990i	$0.354973\pi$
$31$	1.85778	+	10.5360i	0.333667	+	1.89232i	−0.106350	+	0.994329i	$0.533916\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$		0			0
$34$	−0.757019	+	4.29327i	−0.129828	+	0.736290i
$35$	−1.53063	+	2.65113i	−0.258724	+	0.448123i
$36$		0			0
$37$	0.880842	+	1.52566i	0.144810	+	0.250817i	0.929302	−	0.369321i	$-0.120410\pi$
$37$	0.880842	+	1.52566i	0.144810	+	0.250817i	−0.784492	+	0.620139i	$0.787076\pi$
$38$	1.46209	−	0.532159i	0.237183	−	0.0863275i
$39$		0			0
$40$	−0.567425	+	0.476126i	−0.0897177	+	0.0752821i
$41$	1.97401	−	1.65639i	0.308289	−	0.258685i	−0.475495	−	0.879718i	$-0.657731\pi$
$41$	1.97401	−	1.65639i	0.308289	−	0.258685i	0.783784	+	0.621033i	$0.213287\pi$
$42$		0			0
$43$	2.58757	−	0.941797i	0.394600	−	0.143623i	−0.137096	−	0.990558i	$-0.543777\pi$
$43$	2.58757	−	0.941797i	0.394600	−	0.143623i	0.531696	+	0.846935i	$0.321555\pi$
$44$	2.27316	+	3.93723i	0.342692	+	0.593560i
$45$		0			0
$46$	1.75222	−	3.03493i	0.258350	−	0.447476i
$47$	−1.68378	+	9.54918i	−0.245604	+	1.39289i	0.573481	+	0.819219i	$0.305593\pi$
$47$	−1.68378	+	9.54918i	−0.245604	+	1.39289i	−0.819085	+	0.573672i	$0.805519\pi$
$48$		0			0
$49$	−9.47229	−	3.44763i	−1.35318	−	0.492519i
$50$	0.772966	+	4.38371i	0.109314	+	0.619950i
$51$		0			0
$52$	0.662744	+	0.556108i	0.0919060	+	0.0771183i
$53$	−4.00839			−0.550595			−0.275297	−	0.961359i	$-0.588776\pi$
$53$	−4.00839			−0.550595			−0.275297	+	0.961359i	$0.588776\pi$
$54$		0			0
$55$	−3.36756			−0.454081
$56$	−3.16592	−	2.65653i	−0.423064	−	0.354993i
$57$		0			0
$58$	−0.567425	−	3.21803i	−0.0745065	−	0.422548i
$59$	1.34517	+	0.489601i	0.175126	+	0.0637406i	0.428095	−	0.903734i	$-0.359185\pi$
$59$	1.34517	+	0.489601i	0.175126	+	0.0637406i	−0.252969	+	0.967474i	$0.581407\pi$
$60$		0			0
$61$	−0.751711	+	4.26317i	−0.0962468	+	0.545843i	0.898111	+	0.439768i	$0.144939\pi$
$61$	−0.751711	+	4.26317i	−0.0962468	+	0.545843i	−0.994358	+	0.106075i	$0.966172\pi$
$62$	5.34926	−	9.26519i	0.679357	−	1.17668i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.602188	+	0.219178i	−0.0746922	+	0.0271857i
$66$		0			0
$67$	10.0444	−	8.42825i	1.22712	−	1.02967i	0.228697	−	0.973498i	$-0.426554\pi$
$67$	10.0444	−	8.42825i	1.22712	−	1.02967i	0.998421	−	0.0561764i	$-0.0178909\pi$
$68$	3.33957	−	2.80223i	0.404983	−	0.339821i
$69$		0			0
$70$	2.87665	−	1.04701i	0.343825	−	0.125142i
$71$	−2.54213	−	4.40310i	−0.301695	−	0.522551i	0.674825	−	0.737978i	$-0.264219\pi$
$71$	−2.54213	−	4.40310i	−0.301695	−	0.522551i	−0.976520	+	0.215427i	$0.930886\pi$
$72$		0			0
$73$	0.286636	−	0.496469i	0.0335483	−	0.0581073i	−0.848764	−	0.528772i	$-0.822653\pi$
$73$	0.286636	−	0.496469i	0.0335483	−	0.0581073i	0.882312	+	0.470665i	$0.155986\pi$
$74$	0.305913	−	1.73492i	0.0355617	−	0.201680i
$75$		0			0
$76$	−1.46209	−	0.532159i	−0.167714	−	0.0610428i
$77$	−3.26270	−	18.5037i	−0.371819	−	2.10869i
$78$		0			0
$79$	5.17820	+	4.34502i	0.582593	+	0.488853i	0.885797	−	0.464072i	$-0.153612\pi$
$79$	5.17820	+	4.34502i	0.582593	+	0.488853i	−0.303205	+	0.952925i	$0.598057\pi$
$80$	0.740720			0.0828151
$81$		0			0
$82$	−2.57689			−0.284570
$83$	−7.06556	−	5.92871i	−0.775546	−	0.650761i	0.166577	−	0.986029i	$-0.446729\pi$
$83$	−7.06556	−	5.92871i	−0.775546	−	0.650761i	−0.942123	+	0.335268i	$0.891173\pi$
$84$		0			0
$85$	0.560740	+	3.18011i	0.0608208	+	0.344932i
$86$	−2.58757	−	0.941797i	−0.279024	−	0.101557i
$87$		0			0
$88$	0.789461	−	4.47725i	0.0841568	−	0.477277i
$89$	−6.19947	+	10.7378i	−0.657142	+	1.13820i	0.324210	+	0.945985i	$0.394902\pi$
$89$	−6.19947	+	10.7378i	−0.657142	+	1.13820i	−0.981352	+	0.192219i	$0.938432\pi$
$90$		0			0
$91$	−1.78776	−	3.09648i	−0.187408	−	0.324600i
$92$	−3.29309	+	1.19859i	−0.343329	+	0.124961i
$93$		0			0
$94$	7.42794	−	6.23278i	0.766134	−	0.642862i
$95$	0.882872	−	0.740818i	0.0905808	−	0.0760063i
$96$		0			0
$97$	−5.40770	+	1.96824i	−0.549069	+	0.199845i	−0.601633	−	0.798773i	$-0.705483\pi$
$97$	−5.40770	+	1.96824i	−0.549069	+	0.199845i	0.0525637	+	0.998618i	$0.483261\pi$
$98$	5.04010	+	8.72971i	0.509127	+	0.881834i
$99$		0			0
$100$	2.22567	−	3.85497i	0.222567	−	0.385497i
$101$	1.91700	−	10.8718i	0.190748	−	1.08179i	−0.727596	−	0.686006i	$-0.759363\pi$
$101$	1.91700	−	10.8718i	0.190748	−	1.08179i	0.918345	−	0.395782i	$-0.129526\pi$
$102$		0			0
$103$	6.03419	+	2.19627i	0.594567	+	0.216405i	0.621737	−	0.783226i	$-0.286427\pi$
$103$	6.03419	+	2.19627i	0.594567	+	0.216405i	−0.0271702	+	0.999631i	$0.508650\pi$
$104$	−0.150232	−	0.852007i	−0.0147314	−	0.0835461i
$105$		0			0
$106$	3.07060	+	2.57654i	0.298243	+	0.250256i
$107$	17.2923			1.67171			0.835854	−	0.548952i	$-0.184973\pi$
$107$	17.2923			1.67171			0.835854	+	0.548952i	$0.184973\pi$
$108$		0			0
$109$	−9.94570			−0.952626			−0.476313	−	0.879276i	$-0.658027\pi$
$109$	−9.94570			−0.952626			−0.476313	+	0.879276i	$0.658027\pi$
$110$	2.57970	+	2.16462i	0.245964	+	0.206389i
$111$		0			0
$112$	0.717657	+	4.07003i	0.0678122	+	0.384582i
$113$	2.30350	+	0.838405i	0.216695	+	0.0788705i	0.448087	−	0.893990i	$-0.352106\pi$
$113$	2.30350	+	0.838405i	0.216695	+	0.0788705i	−0.231392	+	0.972861i	$0.574328\pi$
$114$		0			0
$115$	0.450757	−	2.55637i	0.0420333	−	0.238383i
$116$	−1.63383	+	2.82988i	−0.151698	+	0.262748i
$117$		0			0
$118$	−0.715749	−	1.23971i	−0.0658900	−	0.114125i
$119$	−16.9305	+	6.16219i	−1.55201	+	0.564887i
$120$		0			0
$121$	7.40693	−	6.21515i	0.673357	−	0.565014i
$122$	3.31616	−	2.78258i	0.300231	−	0.251923i
$123$		0			0
$124$	−10.0533	+	3.65911i	−0.902815	+	0.328598i
$125$	3.50040	+	6.06287i	0.313085	+	0.542279i
$126$		0			0
$127$	−4.05136	+	7.01715i	−0.359500	+	0.622672i	−0.987877	−	0.155237i	$-0.950386\pi$
$127$	−4.05136	+	7.01715i	−0.359500	+	0.622672i	0.628378	+	0.777908i	$0.283719\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$		0			0
$130$	0.602188	+	0.219178i	0.0528153	+	0.0192232i
$131$	2.76007	+	15.6532i	0.241149	+	1.36762i	0.829269	+	0.558849i	$0.188757\pi$
$131$	2.76007	+	15.6532i	0.241149	+	1.36762i	−0.588120	+	0.808773i	$0.700132\pi$
$132$		0			0
$133$	4.92595	+	4.13336i	0.427134	+	0.358408i
$134$	−13.1120			−1.13271
$135$		0			0
$136$	−4.35950			−0.373824
$137$	9.46551	+	7.94250i	0.808693	+	0.678574i	0.950295	−	0.311350i	$-0.100781\pi$
$137$	9.46551	+	7.94250i	0.808693	+	0.678574i	−0.141603	+	0.989924i	$0.545225\pi$
$138$		0			0
$139$	−0.761169	−	4.31680i	−0.0645615	−	0.366146i	−0.999922	−	0.0124519i	$-0.996036\pi$
$139$	−0.761169	−	4.31680i	−0.0645615	−	0.366146i	0.935361	−	0.353695i	$-0.115075\pi$
$140$	−2.87665	−	1.04701i	−0.243121	−	0.0884888i
$141$		0			0
$142$	−0.882872	+	5.00702i	−0.0740890	+	0.420179i
$143$	1.96663	−	3.40630i	0.164458	−	0.284849i
$144$		0			0
$145$	−1.21021	−	2.09615i	−0.100503	−	0.174076i
$146$	−0.538700	+	0.196071i	−0.0445832	+	0.0162269i
$147$		0			0
$148$	−1.34953	+	1.13239i	−0.110931	+	0.0930818i
$149$	−5.23476	+	4.39248i	−0.428848	+	0.359846i	−0.831517	−	0.555499i	$-0.812527\pi$
$149$	−5.23476	+	4.39248i	−0.428848	+	0.359846i	0.402669	+	0.915346i	$0.368083\pi$
$150$		0			0
$151$	4.89254	−	1.78074i	0.398149	−	0.144915i	−0.135182	−	0.990821i	$-0.543162\pi$
$151$	4.89254	−	1.78074i	0.398149	−	0.144915i	0.533332	+	0.845906i	$0.320940\pi$
$152$	0.777964	+	1.34747i	0.0631012	+	0.109295i
$153$		0			0
$154$	−9.39457	+	16.2719i	−0.757036	+	1.31122i
$155$	1.37609	−	7.80422i	0.110531	−	0.626850i
$156$		0			0
$157$	−3.73260	−	1.35856i	−0.297894	−	0.108424i	0.188749	−	0.982025i	$-0.439557\pi$
$157$	−3.73260	−	1.35856i	−0.297894	−	0.108424i	−0.486643	+	0.873601i	$0.661779\pi$
$158$	−1.17380	−	6.65696i	−0.0933826	−	0.529599i
$159$		0			0
$160$	−0.567425	−	0.476126i	−0.0448589	−	0.0376411i
$161$	14.4832			1.14144
$162$		0			0
$163$	2.34707			0.183837			0.0919184	−	0.995767i	$-0.470700\pi$
$163$	2.34707			0.183837			0.0919184	+	0.995767i	$0.470700\pi$
$164$	1.97401	+	1.65639i	0.154145	+	0.129343i
$165$		0			0
$166$	1.60163	+	9.08331i	0.124311	+	0.705002i
$167$	−0.989141	−	0.360018i	−0.0765420	−	0.0278590i	0.303465	−	0.952842i	$-0.401856\pi$
$167$	−0.989141	−	0.360018i	−0.0765420	−	0.0278590i	−0.380007	+	0.924983i	$0.624079\pi$
$168$		0			0
$169$	−2.12745	+	12.0654i	−0.163650	+	0.928107i
$170$	1.61459	−	2.79654i	0.123833	−	0.214485i
$171$		0			0
$172$	1.37682	+	2.38471i	0.104981	+	0.181833i
$173$	6.42081	−	2.33699i	0.488166	−	0.177678i	−0.0861981	−	0.996278i	$-0.527472\pi$
$173$	6.42081	−	2.33699i	0.488166	−	0.177678i	0.574364	+	0.818600i	$0.305250\pi$
$174$		0			0
$175$	−14.0926	+	11.8251i	−1.06530	+	0.893892i
$176$	−3.48269	+	2.92232i	−0.262517	+	0.220278i
$177$		0			0
$178$	11.6512	−	4.24069i	0.873294	−	0.317853i
$179$	−1.09877	−	1.90312i	−0.0821258	−	0.142246i	0.822037	−	0.569434i	$-0.192838\pi$
$179$	−1.09877	−	1.90312i	−0.0821258	−	0.142246i	−0.904163	+	0.427188i	$0.859504\pi$
$180$		0			0
$181$	7.86998	−	13.6312i	0.584971	−	1.01320i	−0.409908	−	0.912127i	$-0.634439\pi$
$181$	7.86998	−	13.6312i	0.584971	−	1.01320i	0.994879	−	0.101073i	$-0.0322275\pi$
$182$	−0.620881	+	3.52119i	−0.0460228	+	0.261008i
$183$		0			0
$184$	3.29309	+	1.19859i	0.242770	+	0.0883610i
$185$	−0.226596	−	1.28509i	−0.0166597	−	0.0944818i
$186$		0			0
$187$	−15.1828	−	12.7399i	−1.11027	−	0.931631i
$188$	−9.69649			−0.707189
$189$		0			0
$190$	−1.15251			−0.0836117
$191$	−6.00686	−	5.04036i	−0.434641	−	0.364707i	0.399058	−	0.916926i	$-0.369337\pi$
$191$	−6.00686	−	5.04036i	−0.434641	−	0.364707i	−0.833700	+	0.552218i	$0.813782\pi$
$192$		0			0
$193$	−2.87224	−	16.2893i	−0.206748	−	1.17253i	−0.894665	−	0.446738i	$-0.852586\pi$
$193$	−2.87224	−	16.2893i	−0.206748	−	1.17253i	0.687916	−	0.725790i	$-0.258526\pi$
$194$	5.40770	+	1.96824i	0.388251	+	0.141312i
$195$		0			0
$196$	1.75041	−	9.92706i	0.125029	−	0.709075i
$197$	−5.68810	+	9.85208i	−0.405260	+	0.701931i	−0.994352	−	0.106135i	$-0.966152\pi$
$197$	−5.68810	+	9.85208i	−0.405260	+	0.701931i	0.589091	+	0.808066i	$0.299486\pi$
$198$		0			0
$199$	−0.936258	−	1.62165i	−0.0663696	−	0.114955i	0.830931	−	0.556375i	$-0.187808\pi$
$199$	−0.936258	−	1.62165i	−0.0663696	−	0.114955i	−0.897301	+	0.441420i	$0.854475\pi$
$200$	−4.18288	+	1.52245i	−0.295775	+	0.107653i
$201$		0			0
$202$	−8.45678	+	7.09608i	−0.595017	+	0.499279i
$203$	10.3452	−	8.68065i	0.726090	−	0.609262i
$204$		0			0
$205$	−1.79364	+	0.652833i	−0.125274	+	0.0455958i
$206$	−3.21073	−	5.56114i	−0.223702	−	0.387463i
$207$		0			0
$208$	−0.432575	+	0.749242i	−0.0299937	+	0.0519506i
$209$	−1.22834	+	6.96629i	−0.0849663	+	0.481868i
$210$		0			0
$211$	−5.14025	−	1.87090i	−0.353870	−	0.128798i	0.158968	−	0.987284i	$-0.449183\pi$
$211$	−5.14025	−	1.87090i	−0.353870	−	0.128798i	−0.512837	+	0.858486i	$0.671406\pi$
$212$	−0.696050	−	3.94749i	−0.0478049	−	0.271115i
$213$		0			0
$214$	−13.2467	−	11.1153i	−0.905522	−	0.759824i
$215$	−2.03967			−0.139104
$216$		0			0
$217$	44.2150			3.00151
$218$	7.61885	+	6.39297i	0.516014	+	0.432987i
$219$		0			0
$220$	−0.584770	−	3.31639i	−0.0394252	−	0.223591i
$221$	−3.54417	−	1.28997i	−0.238407	−	0.0867729i
$222$		0			0
$223$	−0.219638	+	1.24563i	−0.0147080	+	0.0834134i	−0.991278	−	0.131786i	$-0.957929\pi$
$223$	−0.219638	+	1.24563i	−0.0147080	+	0.0834134i	0.976570	+	0.215199i	$0.0690400\pi$
$224$	2.06641	−	3.57913i	0.138068	−	0.239140i
$225$		0			0
$226$	−1.22567	−	2.12292i	−0.0815301	−	0.141214i
$227$	9.34189	−	3.40017i	0.620043	−	0.225677i	−0.0128486	−	0.999917i	$-0.504090\pi$
$227$	9.34189	−	3.40017i	0.620043	−	0.225677i	0.632892	+	0.774240i	$0.281868\pi$
$228$		0			0
$229$	−7.64692	+	6.41653i	−0.505323	+	0.424016i	−0.859480	−	0.511170i	$-0.829212\pi$
$229$	−7.64692	+	6.41653i	−0.505323	+	0.424016i	0.354157	+	0.935186i	$0.384768\pi$
$230$	−1.98850	+	1.66855i	−0.131118	+	0.110021i
$231$		0			0
$232$	3.07060	−	1.11761i	0.201595	−	0.0733746i
$233$	−13.5765	−	23.5152i	−0.889428	−	1.54053i	−0.840553	−	0.541729i	$-0.817770\pi$
$233$	−13.5765	−	23.5152i	−0.889428	−	1.54053i	−0.0488748	−	0.998805i	$-0.515564\pi$
$234$		0			0
$235$	3.59119	−	6.22013i	0.234264	−	0.405757i
$236$	−0.248577	+	1.40975i	−0.0161810	+	0.0917669i
$237$		0			0
$238$	16.9305	+	6.16219i	1.09744	+	0.399435i
$239$	3.39241	+	19.2393i	0.219437	+	1.24449i	0.873039	+	0.487651i	$0.162146\pi$
$239$	3.39241	+	19.2393i	0.219437	+	1.24449i	−0.653602	+	0.756839i	$0.726743\pi$
$240$		0			0
$241$	12.4216	+	10.4229i	0.800144	+	0.671400i	0.948234	−	0.317573i	$-0.102868\pi$
$241$	12.4216	+	10.4229i	0.800144	+	0.671400i	−0.148090	+	0.988974i	$0.547312\pi$
$242$	−9.66906			−0.621551
$243$		0			0
$244$	−4.32893			−0.277132
$245$	5.71975	+	4.79944i	0.365422	+	0.306625i
$246$		0			0
$247$	0.233750	+	1.32566i	0.0148731	+	0.0843498i
$248$	10.0533	+	3.65911i	0.638386	+	0.232354i
$249$		0			0
$250$	1.21568	−	6.89444i	0.0768861	−	0.436043i
$251$	11.7303	−	20.3174i	0.740408	−	1.28242i	−0.211902	−	0.977291i	$-0.567966\pi$
$251$	11.7303	−	20.3174i	0.740408	−	1.28242i	0.952310	−	0.305133i	$-0.0987010\pi$
$252$		0			0
$253$	7.96615	+	13.7978i	0.500827	+	0.867458i
$254$	7.61406	−	2.77129i	0.477749	−	0.173886i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−16.8456	+	14.1352i	−1.05080	+	0.881728i	−0.993178	−	0.116611i	$-0.962797\pi$
$257$	−16.8456	+	14.1352i	−1.05080	+	0.881728i	−0.0576244	+	0.998338i	$0.518353\pi$
$258$		0			0
$259$	6.84164	−	2.49015i	0.425119	−	0.154731i
$260$	−0.320417	−	0.554979i	−0.0198714	−	0.0344183i
$261$		0			0
$262$	7.94732	−	13.7652i	0.490987	−	0.850414i
$263$	4.07773	−	23.1260i	0.251444	−	1.42601i	−0.553595	−	0.832786i	$-0.686745\pi$
$263$	4.07773	−	23.1260i	0.251444	−	1.42601i	0.805039	−	0.593222i	$-0.202144\pi$
$264$		0			0
$265$	2.79004	+	1.01549i	0.171391	+	0.0623811i
$266$	−1.11662	−	6.33268i	−0.0684645	−	0.388281i
$267$		0			0
$268$	10.0444	+	8.42825i	0.613559	+	0.514837i
$269$	−18.3001			−1.11578			−0.557888	−	0.829916i	$-0.688388\pi$
$269$	−18.3001			−1.11578			−0.557888	+	0.829916i	$0.688388\pi$
$270$		0			0
$271$	−16.4825			−1.00124			−0.500620	−	0.865667i	$-0.666895\pi$
$271$	−16.4825			−1.00124			−0.500620	+	0.865667i	$0.666895\pi$
$272$	3.33957	+	2.80223i	0.202491	+	0.169910i
$273$		0			0
$274$	−2.14566	−	12.1686i	−0.129624	−	0.735133i
$275$	−19.0167	−	6.92153i	−1.14675	−	0.417384i
$276$		0			0
$277$	1.95736	−	11.1008i	0.117606	−	0.666980i	−0.867820	−	0.496878i	$-0.834479\pi$
$277$	1.95736	−	11.1008i	0.117606	−	0.666980i	0.985427	−	0.170101i	$-0.0544094\pi$
$278$	−2.19170	+	3.79613i	−0.131449	+	0.227677i
$279$		0			0
$280$	1.53063	+	2.65113i	0.0914728	+	0.158435i
$281$	−0.681601	+	0.248083i	−0.0406609	+	0.0147994i	−0.362271	−	0.932073i	$-0.617998\pi$
$281$	−0.681601	+	0.248083i	−0.0406609	+	0.0147994i	0.321610	+	0.946872i	$0.395776\pi$
$282$		0			0
$283$	−16.9589	+	14.2302i	−1.00810	+	0.845897i	−0.988086	−	0.153903i	$-0.950816\pi$
$283$	−16.9589	+	14.2302i	−1.00810	+	0.845897i	−0.0200144	+	0.999800i	$0.506371\pi$
$284$	3.89477	−	3.26810i	0.231112	−	0.193926i
$285$		0			0
$286$	−3.69605	+	1.34525i	−0.218552	+	0.0795464i
$287$	−5.32491	−	9.22302i	−0.314320	−	0.544418i
$288$		0			0
$289$	−1.00263	+	1.73660i	−0.0589780	+	0.102153i
$290$	−0.420303	+	2.38366i	−0.0246811	+	0.139973i
$291$		0			0
$292$	0.538700	+	0.196071i	0.0315251	+	0.0114742i
$293$	1.13889	+	6.45895i	0.0665344	+	0.377336i	0.999834	+	0.0182360i	$0.00580504\pi$
$293$	1.13889	+	6.45895i	0.0665344	+	0.377336i	−0.933299	+	0.359100i	$0.883084\pi$
$294$		0			0
$295$	−0.812267	−	0.681573i	−0.0472920	−	0.0396827i
$296$	1.76168			0.102396
$297$		0			0
$298$	6.83349			0.395854
$299$	2.32254	+	1.94884i	0.134316	+	0.112705i
$300$		0			0
$301$	−1.97616	−	11.2074i	−0.113904	−	0.645982i
$302$	−4.89254	−	1.78074i	−0.281534	−	0.102470i
$303$		0			0
$304$	0.270184	−	1.53229i	0.0154961	−	0.0878829i
$305$	1.60326	−	2.77694i	0.0918027	−	0.159007i
$306$		0			0
$307$	−3.98740	−	6.90639i	−0.227573	−	0.394168i	0.729515	−	0.683965i	$-0.239746\pi$
$307$	−3.98740	−	6.90639i	−0.227573	−	0.394168i	−0.957088	+	0.289796i	$0.906412\pi$
$308$	17.6560	−	6.42626i	1.00604	−	0.366170i
$309$		0			0
$310$	−6.07060	+	5.09384i	−0.344787	+	0.289311i
$311$	−10.8380	+	9.09419i	−0.614569	+	0.515684i	−0.896091	−	0.443870i	$-0.853605\pi$
$311$	−10.8380	+	9.09419i	−0.614569	+	0.515684i	0.281522	+	0.959555i	$0.409161\pi$
$312$		0			0
$313$	−22.5917	+	8.22270i	−1.27696	+	0.464774i	−0.889425	−	0.457082i	$-0.848895\pi$
$313$	−22.5917	+	8.22270i	−1.27696	+	0.464774i	−0.387532	+	0.921856i	$0.626672\pi$
$314$	1.98607	+	3.43998i	0.112081	+	0.194129i
$315$		0			0
$316$	−3.37983	+	5.85403i	−0.190130	+	0.329315i
$317$	−3.15913	+	17.9163i	−0.177435	+	1.00628i	0.757862	+	0.652415i	$0.226244\pi$
$317$	−3.15913	+	17.9163i	−0.177435	+	1.00628i	−0.935296	+	0.353866i	$0.884867\pi$
$318$		0			0
$319$	13.9600	+	5.08101i	0.781608	+	0.284482i
$320$	0.128625	+	0.729467i	0.00719034	+	0.0407785i
$321$		0			0
$322$	−11.0948	−	9.30962i	−0.618287	−	0.518805i
$323$	6.78307			0.377420
$324$		0			0
$325$	−3.85107			−0.213619
$326$	−1.79796	−	1.50867i	−0.0995798	−	0.0835574i
$327$		0			0
$328$	−0.447473	−	2.53774i	−0.0247075	−	0.140123i
$329$	37.6571	+	13.7061i	2.07610	+	0.755640i
$330$		0			0
$331$	3.11884	−	17.6878i	0.171427	−	0.972212i	−0.770760	−	0.637125i	$-0.780123\pi$
$331$	3.11884	−	17.6878i	0.171427	−	0.972212i	0.942187	−	0.335086i	$-0.108766\pi$
$332$	4.61172	−	7.98773i	0.253101	−	0.438384i
$333$		0			0
$334$	0.526311	+	0.911597i	0.0287985	+	0.0498804i
$335$	−9.12662	+	3.32182i	−0.498640	+	0.181490i
$336$		0			0
$337$	−17.9989	+	15.1029i	−0.980462	+	0.822705i	−0.984159	−	0.177288i	$-0.943268\pi$
$337$	−17.9989	+	15.1029i	−0.980462	+	0.822705i	0.00369714	+	0.999993i	$0.498823\pi$
$338$	9.38520	−	7.87512i	0.510488	−	0.428350i
$339$		0			0
$340$	−3.03443	+	1.10444i	−0.164565	+	0.0598968i
$341$	24.3195	+	42.1225i	1.31697	+	2.28106i
$342$		0			0
$343$	−6.36495	+	11.0244i	−0.343675	+	0.595263i
$344$	0.478163	−	2.71180i	0.0257808	−	0.146210i
$345$		0			0
$346$	−6.42081	−	2.33699i	−0.345185	−	0.125637i
$347$	−1.44691	−	8.20582i	−0.0776741	−	0.440512i	−0.998698	−	0.0510063i	$-0.983757\pi$
$347$	−1.44691	−	8.20582i	−0.0776741	−	0.440512i	0.921024	−	0.389505i	$-0.127354\pi$
$348$		0			0
$349$	−4.05619	−	3.40354i	−0.217123	−	0.182188i	0.527739	−	0.849407i	$-0.323040\pi$
$349$	−4.05619	−	3.40354i	−0.217123	−	0.182188i	−0.744861	+	0.667219i	$0.767484\pi$
$350$	18.3966			0.983337
$351$		0			0
$352$	4.54632			0.242320
$353$	−26.4759	−	22.2159i	−1.40917	−	1.18243i	−0.956852	−	0.290577i	$-0.906153\pi$
$353$	−26.4759	−	22.2159i	−1.40917	−	1.18243i	−0.452318	−	0.891857i	$-0.649403\pi$
$354$		0			0
$355$	0.653961	+	3.70880i	0.0347087	+	0.196843i
$356$	−11.6512	−	4.24069i	−0.617512	−	0.224756i
$357$		0			0
$358$	−0.381598	+	2.16415i	−0.0201681	+	0.114379i
$359$	−12.8489	+	22.2549i	−0.678138	+	1.17457i	0.297403	+	0.954752i	$0.403880\pi$
$359$	−12.8489	+	22.2549i	−0.678138	+	1.17457i	−0.975541	+	0.219818i	$0.929454\pi$
$360$		0			0
$361$	8.28954	+	14.3579i	0.436292	+	0.755680i
$362$	−14.7907	+	5.38339i	−0.777384	+	0.282944i
$363$		0			0
$364$	2.73900	−	2.29829i	0.143563	−	0.120463i
$365$	−0.325289	+	0.272950i	−0.0170264	+	0.0142869i
$366$		0			0
$367$	−10.6739	+	3.88499i	−0.557174	+	0.202795i	−0.605231	−	0.796050i	$-0.706919\pi$
$367$	−10.6739	+	3.88499i	−0.557174	+	0.202795i	0.0480573	+	0.998845i	$0.484697\pi$
$368$	−1.75222	−	3.03493i	−0.0913406	−	0.158207i
$369$		0			0
$370$	−0.652458	+	1.13009i	−0.0339197	+	0.0587506i
$371$	−2.87665	+	16.3143i	−0.149348	+	0.846995i
$372$		0			0
$373$	26.9731	+	9.81739i	1.39661	+	0.508325i	0.927171	−	0.374639i	$-0.122233\pi$
$373$	26.9731	+	9.81739i	1.39661	+	0.508325i	0.469441	+	0.882964i	$0.344455\pi$
$374$	3.44166	+	19.5186i	0.177964	+	1.00928i
$375$		0			0
$376$	7.42794	+	6.23278i	0.383067	+	0.321431i
$377$	2.82703			0.145599
$378$		0			0
$379$	−23.0493			−1.18396			−0.591981	−	0.805952i	$-0.701654\pi$
$379$	−23.0493			−1.18396			−0.591981	+	0.805952i	$0.701654\pi$
$380$	0.882872	+	0.740818i	0.0452904	+	0.0380031i
$381$		0			0
$382$	1.36165	+	7.72227i	0.0696678	+	0.395106i
$383$	−23.1212	−	8.41541i	−1.18144	−	0.430007i	−0.324727	−	0.945808i	$-0.605272\pi$
$383$	−23.1212	−	8.41541i	−1.18144	−	0.430007i	−0.856709	+	0.515800i	$0.827495\pi$
$384$		0			0
$385$	−2.41675	+	13.7061i	−0.123169	+	0.698525i
$386$	−8.27028	+	14.3246i	−0.420946	+	0.729101i
$387$		0			0
$388$	−2.87738	−	4.98377i	−0.146077	−	0.253012i
$389$	34.8878	−	12.6981i	1.76888	−	0.643820i	0.768891	−	0.639380i	$-0.220809\pi$
$389$	34.8878	−	12.6981i	1.76888	−	0.643820i	0.999990	−	0.00444021i	$-0.00141337\pi$
$390$		0			0
$391$	11.7033	−	9.82024i	0.591862	−	0.496631i
$392$	−7.72188	+	6.47943i	−0.390014	+	0.327260i
$393$		0			0
$394$	10.6901	−	3.89089i	0.538561	−	0.196020i
$395$	−2.50351	−	4.33620i	−0.125965	−	0.218178i
$396$		0			0
$397$	−3.19629	+	5.53614i	−0.160417	+	0.277851i	−0.935018	−	0.354599i	$-0.884617\pi$
$397$	−3.19629	+	5.53614i	−0.160417	+	0.277851i	0.774601	+	0.632450i	$0.217951\pi$
$398$	−0.325159	+	1.84407i	−0.0162987	+	0.0924348i
$399$		0			0
$400$	4.18288	+	1.52245i	0.209144	+	0.0761223i
$401$	−5.67599	−	32.1901i	−0.283445	−	1.60750i	−0.710787	−	0.703407i	$-0.751661\pi$
$401$	−5.67599	−	32.1901i	−0.283445	−	1.60750i	0.427342	−	0.904090i	$-0.359450\pi$
$402$		0			0
$403$	7.09038	+	5.94953i	0.353197	+	0.296367i
$404$	11.0395			0.549238
$405$		0			0
$406$	−13.5047			−0.670226
$407$	6.13539	+	5.14821i	0.304120	+	0.255187i
$408$		0			0
$409$	−3.79522	−	21.5238i	−0.187662	−	1.06428i	−0.922488	−	0.386027i	$-0.873847\pi$
$409$	−3.79522	−	21.5238i	−0.187662	−	1.06428i	0.734826	−	0.678256i	$-0.237264\pi$
$410$	1.79364	+	0.652833i	0.0885818	+	0.0322411i
$411$		0			0
$412$	−1.11507	+	6.32390i	−0.0549357	+	0.311556i
$413$	2.95806	−	5.12351i	0.145557	−	0.252112i
$414$		0			0
$415$	3.41599	+	5.91668i	0.167685	+	0.290438i
$416$	0.812975	−	0.295899i	0.0398594	−	0.0145076i
$417$		0			0
$418$	5.41881	−	4.54692i	0.265043	−	0.222397i
$419$	20.0021	−	16.7838i	0.977168	−	0.819941i	−0.00649160	−	0.999979i	$-0.502066\pi$
$419$	20.0021	−	16.7838i	0.977168	−	0.819941i	0.983660	+	0.180037i	$0.0576219\pi$
$420$		0			0
$421$	35.2362	−	12.8249i	1.71731	−	0.625049i	0.719707	−	0.694278i	$-0.244276\pi$
$421$	35.2362	−	12.8249i	1.71731	−	0.625049i	0.997601	+	0.0692288i	$0.0220539\pi$
$422$	2.73507	+	4.73728i	0.133141	+	0.230607i
$423$		0			0
$424$	−2.00419	+	3.47137i	−0.0973323	+	0.168584i
$425$	−3.36975	+	19.1108i	−0.163457	+	0.927009i
$426$		0			0
$427$	16.8118	+	6.11898i	0.813578	+	0.296118i
$428$	3.00277	+	17.0296i	0.145144	+	0.823155i
$429$		0			0
$430$	1.56248	+	1.31107i	0.0753494	+	0.0632256i
$431$	−6.13162			−0.295350			−0.147675	−	0.989036i	$-0.547179\pi$
$431$	−6.13162			−0.295350			−0.147675	+	0.989036i	$0.547179\pi$
$432$		0			0
$433$	−20.9401			−1.00632			−0.503158	−	0.864195i	$-0.667829\pi$
$433$	−20.9401			−1.00632			−0.503158	+	0.864195i	$0.667829\pi$
$434$	−33.8707	−	28.4209i	−1.62585	−	1.36425i
$435$		0			0
$436$	−1.72705	−	9.79461i	−0.0827109	−	0.469077i
$437$	−5.12381	−	1.86492i	−0.245105	−	0.0892110i
$438$		0			0
$439$	−4.98629	+	28.2787i	−0.237983	+	1.34967i	0.598258	+	0.801304i	$0.295860\pi$
$439$	−4.98629	+	28.2787i	−0.237983	+	1.34967i	−0.836240	+	0.548363i	$0.815251\pi$
$440$	−1.68378	+	2.91639i	−0.0802709	+	0.139033i
$441$		0			0
$442$	1.88581	+	3.26632i	0.0896989	+	0.155363i
$443$	−14.2882	+	5.20050i	−0.678855	+	0.247083i	−0.658356	−	0.752707i	$-0.728748\pi$
$443$	−14.2882	+	5.20050i	−0.678855	+	0.247083i	−0.0204992	+	0.999790i	$0.506526\pi$
$444$		0			0
$445$	7.03547	−	5.90346i	0.333513	−	0.279851i
$446$	0.968926	−	0.813026i	0.0458800	−	0.0384979i
$447$		0			0
$448$	−3.88358	+	1.41351i	−0.183482	+	0.0667820i
$449$	−6.21048	−	10.7569i	−0.293091	−	0.507648i	0.681448	−	0.731866i	$-0.261351\pi$
$449$	−6.21048	−	10.7569i	−0.293091	−	0.507648i	−0.974539	+	0.224218i	$0.928017\pi$
$450$		0			0
$451$	5.85769	−	10.1458i	0.275828	−	0.477748i
$452$	−0.425670	+	2.41409i	−0.0200218	+	0.113549i
$453$		0			0
$454$	−9.34189	−	3.40017i	−0.438437	−	0.159578i
$455$	0.459899	+	2.60822i	0.0215604	+	0.122275i
$456$		0			0
$457$	−8.30728	−	6.97064i	−0.388598	−	0.326073i	0.427468	−	0.904030i	$-0.359405\pi$
$457$	−8.30728	−	6.97064i	−0.388598	−	0.326073i	−0.816067	+	0.577957i	$0.803850\pi$
$458$	9.98234			0.466444
$459$		0			0
$460$	2.59581			0.121030
$461$	6.28283	+	5.27192i	0.292621	+	0.245538i	0.777265	−	0.629173i	$-0.216606\pi$
$461$	6.28283	+	5.27192i	0.292621	+	0.245538i	−0.484644	+	0.874711i	$0.661051\pi$
$462$		0			0
$463$	−5.84350	−	33.1401i	−0.271571	−	1.54015i	−0.749649	−	0.661836i	$-0.769778\pi$
$463$	−5.84350	−	33.1401i	−0.271571	−	1.54015i	0.478078	−	0.878317i	$-0.341333\pi$
$464$	−3.07060	−	1.11761i	−0.142549	−	0.0518837i
$465$		0			0
$466$	−4.71508	+	26.7405i	−0.218422	+	1.23873i
$467$	5.43426	−	9.41241i	0.251467	−	0.435554i	−0.712463	−	0.701710i	$-0.752420\pi$
$467$	5.43426	−	9.41241i	0.251467	−	0.435554i	0.963930	+	0.266156i	$0.0857535\pi$
$468$		0			0
$469$	−27.0948	−	46.9296i	−1.25112	−	2.16701i
$470$	−6.74924	+	2.45652i	−0.311319	+	0.113311i
$471$		0			0
$472$	1.09659	−	0.920149i	0.0504747	−	0.0423533i
$473$	9.59003	−	8.04699i	0.440950	−	0.370001i
$474$		0			0
$475$	6.50827	−	2.36882i	0.298620	−	0.108689i
$476$	−9.00852	−	15.6032i	−0.412905	−	0.715172i
$477$		0			0
$478$	9.76807	−	16.9188i	0.446781	−	0.773847i
$479$	3.26943	−	18.5418i	0.149384	−	0.847198i	−0.814358	−	0.580363i	$-0.802911\pi$
$479$	3.26943	−	18.5418i	0.149384	−	0.847198i	0.963742	−	0.266836i	$-0.0859781\pi$
$480$		0			0
$481$	1.43221	+	0.521280i	0.0653030	+	0.0237683i
$482$	−2.81574	−	15.9689i	−0.128254	−	0.727362i
$483$		0			0
$484$	7.40693	+	6.21515i	0.336679	+	0.282507i
$485$	4.26267			0.193558
$486$		0			0
$487$	32.9521			1.49320			0.746601	−	0.665272i	$-0.231685\pi$
$487$	32.9521			1.49320			0.746601	+	0.665272i	$0.231685\pi$
$488$	3.31616	+	2.78258i	0.150115	+	0.125962i
$489$		0			0
$490$	−1.29656	−	7.35317i	−0.0585727	−	0.332183i
$491$	32.5492	+	11.8469i	1.46892	+	0.534645i	0.947808	−	0.318841i	$-0.103294\pi$
$491$	32.5492	+	11.8469i	1.46892	+	0.534645i	0.521116	+	0.853486i	$0.325516\pi$
$492$		0			0
$493$	2.47369	−	14.0290i	0.111409	−	0.631834i
$494$	0.673056	−	1.16577i	0.0302822	−	0.0524503i
$495$		0			0
$496$	−5.34926	−	9.26519i	−0.240189	−	0.416019i
$497$	−19.7451	+	7.18664i	−0.885690	+	0.322365i
$498$		0			0
$499$	18.1706	−	15.2470i	0.813428	−	0.682547i	−0.137995	−	0.990433i	$-0.544066\pi$
$499$	18.1706	−	15.2470i	0.813428	−	0.682547i	0.951423	+	0.307886i	$0.0996214\pi$
$500$	−5.36292	+	4.50002i	−0.239837	+	0.201247i
$501$		0			0
$502$	−22.0457	+	8.02398i	−0.983948	+	0.358128i
$503$	16.0067	+	27.7243i	0.713701	+	1.23617i	0.963458	+	0.267858i	$0.0863160\pi$
$503$	16.0067	+	27.7243i	0.713701	+	1.23617i	−0.249757	+	0.968309i	$0.580351\pi$
$504$		0			0
$505$	−4.08861	+	7.08168i	−0.181941	+	0.315131i
$506$	2.76661	−	15.6902i	0.122991	−	0.697517i
$507$		0			0
$508$	−7.61406	−	2.77129i	−0.337819	−	0.122956i
$509$	−6.91488	−	39.2162i	−0.306497	−	1.73823i	−0.616376	−	0.787452i	$-0.711400\pi$
$509$	−6.91488	−	39.2162i	−0.306497	−	1.73823i	0.309879	−	0.950776i	$-0.399711\pi$
$510$		0			0
$511$	−1.81494	−	1.52291i	−0.0802881	−	0.0673697i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	21.9904			0.969956
$515$	−3.64369	−	3.05742i	−0.160560	−	0.134726i
$516$		0			0
$517$	7.65500	+	43.4136i	0.336666	+	1.90933i
$518$	−6.84164	−	2.49015i	−0.300604	−	0.109411i
$519$		0			0
$520$	−0.111280	+	0.631099i	−0.00487994	+	0.0276755i
$521$	1.81609	−	3.14555i	0.0795642	−	0.137809i	−0.823498	−	0.567319i	$-0.807980\pi$
$521$	1.81609	−	3.14555i	0.0795642	−	0.137809i	0.903062	+	0.429510i	$0.141314\pi$
$522$		0			0
$523$	−6.50104	−	11.2601i	−0.284270	−	0.492371i	0.688162	−	0.725558i	$-0.258418\pi$
$523$	−6.50104	−	11.2601i	−0.284270	−	0.492371i	−0.972432	+	0.233187i	$0.925085\pi$
$524$	−14.9361	+	5.43628i	−0.652485	+	0.237485i
$525$		0			0
$526$	−17.9888	+	15.0944i	−0.784349	+	0.658147i
$527$	35.7285	−	29.9797i	1.55636	−	1.30594i
$528$		0			0
$529$	10.0725	−	3.66609i	0.437935	−	0.159395i
$530$	−1.48455	−	2.57131i	−0.0644847	−	0.111691i
$531$		0			0
$532$	−3.21518	+	5.56886i	−0.139396	+	0.241441i
$533$	0.387131	−	2.19553i	0.0167685	−	0.0950989i
$534$		0			0
$535$	−12.0363	−	4.38085i	−0.520374	−	0.189401i
$536$	−2.27688	−	12.9128i	−0.0983462	−	0.557749i
$537$		0			0
$538$	14.0187	+	11.7631i	0.604388	+	0.507142i
$539$	−45.8278			−1.97394
$540$		0			0
$541$	−31.1320			−1.33847			−0.669235	−	0.743051i	$-0.733378\pi$
$541$	−31.1320			−1.33847			−0.669235	+	0.743051i	$0.733378\pi$
$542$	12.6263	+	10.5947i	0.542347	+	0.455083i
$543$		0			0
$544$	−0.757019	−	4.29327i	−0.0324569	−	0.184072i
$545$	6.92270	+	2.51966i	0.296536	+	0.107930i
$546$		0			0
$547$	3.35773	−	19.0426i	0.143566	−	0.814204i	−0.824941	−	0.565219i	$-0.808792\pi$
$547$	3.35773	−	19.0426i	0.143566	−	0.814204i	0.968507	−	0.248985i	$-0.0800970\pi$
$548$	−6.17817	+	10.7009i	−0.263918	+	0.457120i
$549$		0			0
$550$	10.1186	+	17.5259i	0.431459	+	0.747308i
$551$	−4.77764	+	1.73892i	−0.203534	+	0.0740804i
$552$		0			0
$553$	21.4005	−	17.9572i	0.910044	−	0.763617i
$554$	−8.63485	+	7.24550i	−0.366860	+	0.307832i
$555$		0			0
$556$	4.11905	−	1.49921i	0.174686	−	0.0635807i
$557$	−0.618509	−	1.07129i	−0.0262070	−	0.0453919i	0.852624	−	0.522524i	$-0.175010\pi$
$557$	−0.618509	−	1.07129i	−0.0262070	−	0.0453919i	−0.878831	+	0.477132i	$0.841676\pi$
$558$		0			0
$559$	1.19115	−	2.06314i	0.0503804	−	0.0872614i
$560$	0.531583	−	3.01476i	0.0224635	−	0.127397i
$561$		0			0
$562$	0.681601	+	0.248083i	0.0287516	+	0.0104647i
$563$	3.63180	+	20.5969i	0.153062	+	0.868057i	0.960536	+	0.278155i	$0.0897228\pi$
$563$	3.63180	+	20.5969i	0.153062	+	0.868057i	−0.807474	+	0.589903i	$0.799166\pi$
$564$		0			0
$565$	−1.39095	−	1.16714i	−0.0585176	−	0.0491021i
$566$	22.1382			0.930539
$567$		0			0
$568$	−5.08426			−0.213331
$569$	4.70347	+	3.94668i	0.197180	+	0.165453i	0.736032	−	0.676947i	$-0.236697\pi$
$569$	4.70347	+	3.94668i	0.197180	+	0.165453i	−0.538852	+	0.842400i	$0.681142\pi$
$570$		0			0
$571$	2.98710	+	16.9407i	0.125006	+	0.708946i	0.981304	+	0.192464i	$0.0616478\pi$
$571$	2.98710	+	16.9407i	0.125006	+	0.708946i	−0.856298	+	0.516483i	$0.827241\pi$
$572$	3.69605	+	1.34525i	0.154540	+	0.0562478i
$573$		0			0
$574$	−1.84932	+	10.4880i	−0.0771893	+	0.437762i
$575$	7.79970	−	13.5095i	0.325270	−	0.563384i
$576$		0			0
$577$	7.08481	+	12.2713i	0.294945	+	0.510859i	0.974972	−	0.222328i	$-0.0713655\pi$
$577$	7.08481	+	12.2713i	0.294945	+	0.510859i	−0.680027	+	0.733187i	$0.738032\pi$
$578$	1.88432	−	0.685836i	0.0783773	−	0.0285270i
$579$		0			0
$580$	1.85416	−	1.55582i	0.0769897	−	0.0646020i
$581$	−29.2007	+	24.5023i	−1.21145	+	1.01653i
$582$		0			0
$583$	−17.1244	+	6.23278i	−0.709221	+	0.258135i
$584$	−0.286636	−	0.496469i	−0.0118611	−	0.0205440i
$585$		0			0
$586$	3.27929	−	5.67990i	0.135466	−	0.234635i
$587$	−5.83795	+	33.1087i	−0.240958	+	1.36654i	0.588737	+	0.808324i	$0.299625\pi$
$587$	−5.83795	+	33.1087i	−0.240958	+	1.36654i	−0.829695	+	0.558217i	$0.811486\pi$
$588$		0			0
$589$	−15.6422	−	5.69331i	−0.644527	−	0.234589i
$590$	0.184126	+	1.04423i	0.00758035	+	0.0429903i
$591$		0			0
$592$	−1.34953	−	1.13239i	−0.0554653	−	0.0465409i
$593$	−6.82673			−0.280340			−0.140170	−	0.990127i	$-0.544765\pi$
$593$	−6.82673			−0.280340			−0.140170	+	0.990127i	$0.544765\pi$
$594$		0			0
$595$	13.3456			0.547116
$596$	−5.23476	−	4.39248i	−0.214424	−	0.179923i
$597$		0			0
$598$	−0.526477	−	2.98580i	−0.0215293	−	0.122099i
$599$	−27.5399	−	10.0237i	−1.12525	−	0.409557i	−0.288684	−	0.957424i	$-0.593218\pi$
$599$	−27.5399	−	10.0237i	−1.12525	−	0.409557i	−0.836565	+	0.547867i	$0.815440\pi$
$600$		0			0
$601$	−0.803257	+	4.55550i	−0.0327655	+	0.185823i	−0.996798	−	0.0799624i	$-0.974520\pi$
$601$	−0.803257	+	4.55550i	−0.0327655	+	0.185823i	0.964032	+	0.265785i	$0.0856311\pi$
$602$	−5.69013	+	9.85559i	−0.231912	+	0.401684i
$603$		0			0
$604$	2.60327	+	4.50899i	0.105925	+	0.183468i
$605$	−6.73014	+	2.44957i	−0.273619	+	0.0995893i
$606$		0			0
$607$	−10.3745	+	8.70526i	−0.421089	+	0.353335i	−0.828577	−	0.559875i	$-0.810849\pi$
$607$	−10.3745	+	8.70526i	−0.421089	+	0.353335i	0.407488	+	0.913210i	$0.366405\pi$
$608$	−1.19191	+	1.00013i	−0.0483383	+	0.0405607i
$609$		0			0
$610$	−3.01315	+	1.09670i	−0.121999	+	0.0444040i
$611$	4.19446	+	7.26502i	0.169690	+	0.293911i
$612$		0			0
$613$	−14.9136	+	25.8311i	−0.602354	+	1.04331i	0.390110	+	0.920768i	$0.372437\pi$
$613$	−14.9136	+	25.8311i	−0.602354	+	1.04331i	−0.992464	+	0.122539i	$0.960896\pi$
$614$	−1.38481	+	7.85365i	−0.0558864	+	0.316948i
$615$		0			0
$616$	−17.6560	−	6.42626i	−0.711381	−	0.258922i
$617$	5.84851	+	33.1685i	0.235452	+	1.33531i	0.841660	+	0.540008i	$0.181579\pi$
$617$	5.84851	+	33.1685i	0.235452	+	1.33531i	−0.606208	+	0.795306i	$0.707310\pi$
$618$		0			0
$619$	27.2839	+	22.8939i	1.09663	+	0.920182i	0.997194	−	0.0748615i	$-0.0238515\pi$
$619$	27.2839	+	22.8939i	1.09663	+	0.920182i	0.0994367	+	0.995044i	$0.468296\pi$
$620$	7.92461			0.318260
$621$		0			0
$622$	14.1480			0.567285
$623$	39.2541	+	32.9381i	1.57268	+	1.31964i
$624$		0			0
$625$	2.96435	+	16.8117i	0.118574	+	0.672467i
$626$	22.5917	+	8.22270i	0.902945	+	0.328645i
$627$		0			0
$628$	0.689756	−	3.91180i	0.0275243	−	0.156098i
$629$	3.84003	−	6.65113i	0.153112	−	0.265198i
$630$		0			0
$631$	19.6546	+	34.0427i	0.782436	+	1.35522i	0.930519	+	0.366243i	$0.119356\pi$
$631$	19.6546	+	34.0427i	0.782436	+	1.35522i	−0.148083	+	0.988975i	$0.547310\pi$
$632$	6.35200	−	2.31194i	0.252669	−	0.0919640i
$633$		0			0
$634$	13.9364	−	11.6941i	0.553486	−	0.464430i
$635$	4.59768	−	3.85791i	0.182453	−	0.153097i
$636$		0			0
$637$	−8.19495	+	2.98272i	−0.324696	+	0.118180i
$638$	−7.42794	−	12.8656i	−0.294075	−	0.509353i
$639$		0			0
$640$	0.370360	−	0.641483i	0.0146398	−	0.0253568i
$641$	4.79194	−	27.1764i	0.189270	−	1.07340i	−0.731075	−	0.682297i	$-0.760981\pi$
$641$	4.79194	−	27.1764i	0.189270	−	1.07340i	0.920345	−	0.391107i	$-0.127908\pi$
$642$		0			0
$643$	−30.6010	−	11.1378i	−1.20678	−	0.439234i	−0.341197	−	0.939992i	$-0.610832\pi$
$643$	−30.6010	−	11.1378i	−1.20678	−	0.439234i	−0.865587	+	0.500758i	$0.833055\pi$
$644$	2.51498	+	14.2632i	0.0991041	+	0.562047i
$645$		0			0
$646$	−5.19613	−	4.36007i	−0.204439	−	0.171545i
$647$	11.8337			0.465232			0.232616	−	0.972569i	$-0.425272\pi$
$647$	11.8337			0.465232			0.232616	+	0.972569i	$0.425272\pi$
$648$		0			0
$649$	6.50805			0.255463
$650$	2.95009	+	2.47542i	0.115712	+	0.0970940i
$651$		0			0
$652$	0.407565	+	2.31141i	0.0159615	+	0.0905219i
$653$	−1.90882	−	0.694752i	−0.0746978	−	0.0271878i	0.304401	−	0.952544i	$-0.401544\pi$
$653$	−1.90882	−	0.694752i	−0.0746978	−	0.0271878i	−0.379099	+	0.925356i	$0.623766\pi$
$654$		0			0
$655$	2.04444	−	11.5946i	0.0798830	−	0.453039i
$656$	−1.28845	+	2.23165i	−0.0503054	+	0.0871314i
$657$		0			0
$658$	−20.0369	−	34.7050i	−0.781120	−	1.35294i
$659$	45.4410	−	16.5392i	1.77013	−	0.644275i	0.770151	−	0.637861i	$-0.220181\pi$
$659$	45.4410	−	16.5392i	1.77013	−	0.644275i	0.999979	−	0.00641394i	$-0.00204163\pi$
$660$		0			0
$661$	−13.0788	+	10.9744i	−0.508706	+	0.426855i	−0.860673	−	0.509157i	$-0.829957\pi$
$661$	−13.0788	+	10.9744i	−0.508706	+	0.426855i	0.351968	+	0.936012i	$0.385513\pi$
$662$	−13.7587	+	11.5449i	−0.534747	+	0.448706i
$663$		0			0
$664$	−8.66720	+	3.15460i	−0.336352	+	0.122422i
$665$	−2.38155	−	4.12497i	−0.0923527	−	0.159960i
$666$		0			0
$667$	−5.72567	+	9.91715i	−0.221699	+	0.383993i
$668$	0.182786	−	1.03663i	0.00707220	−	0.0401084i
$669$		0			0
$670$	9.12662	+	3.32182i	0.352592	+	0.128333i
$671$	3.41752	+	19.3817i	0.131932	+	0.748224i
$672$		0			0
$673$	−22.8356	−	19.1613i	−0.880247	−	0.738615i	0.0859825	−	0.996297i	$-0.472597\pi$
$673$	−22.8356	−	19.1613i	−0.880247	−	0.738615i	−0.966230	+	0.257681i	$0.917042\pi$
$674$	23.4959			0.905027
$675$		0			0
$676$	−12.2515			−0.471212
$677$	−6.10334	−	5.12131i	−0.234570	−	0.196828i	0.517924	−	0.855427i	$-0.326705\pi$
$677$	−6.10334	−	5.12131i	−0.234570	−	0.196828i	−0.752494	+	0.658599i	$0.771149\pi$
$678$		0			0
$679$	4.12994	+	23.4221i	0.158493	+	0.898856i
$680$	3.03443	+	1.10444i	0.116365	+	0.0423534i
$681$		0			0
$682$	8.44606	−	47.9000i	0.323416	−	1.83419i
$683$	−15.1593	+	26.2566i	−0.580054	+	1.00468i	0.415419	+	0.909630i	$0.363635\pi$
$683$	−15.1593	+	26.2566i	−0.580054	+	1.00468i	−0.995472	+	0.0950521i	$0.969698\pi$
$684$		0			0
$685$	−4.57630	−	7.92638i	−0.174851	−	0.302851i
$686$	11.9622	−	4.35388i	0.456719	−	0.166232i
$687$		0			0
$688$	−2.10940	+	1.77000i	−0.0804202	+	0.0674806i
$689$	−2.65653	+	2.22910i	−0.101206	+	0.0849218i
$690$		0			0
$691$	−24.9197	+	9.07005i	−0.947992	+	0.345041i	−0.769317	−	0.638867i	$-0.779403\pi$
$691$	−24.9197	+	9.07005i	−0.947992	+	0.345041i	−0.178675	+	0.983908i	$0.557181\pi$
$692$	3.41644	+	5.91745i	0.129874	+	0.224948i
$693$		0			0
$694$	−4.16620	+	7.21608i	−0.158147	+	0.273919i
$695$	−0.563813	+	3.19754i	−0.0213867	+	0.121290i
$696$		0			0
$697$	−10.5565	−	3.84224i	−0.399855	−	0.145535i
$698$	0.919463	+	5.21453i	0.0348022	+	0.197373i
$699$		0			0
$700$	−14.0926	−	11.8251i	−0.532649	−	0.446946i
$701$	−46.2262			−1.74594			−0.872971	−	0.487773i	$-0.837809\pi$
$701$	−46.2262			−1.74594			−0.872971	+	0.487773i	$0.837809\pi$
$702$		0			0
$703$	−2.74105			−0.103381
$704$	−3.48269	−	2.92232i	−0.131259	−	0.110139i
$705$		0			0
$706$	6.00160	+	34.0368i	0.225873	+	1.28099i
$707$	−42.8730	−	15.6045i	−1.61240	−	0.586867i
$708$		0			0
$709$	5.30328	−	30.0764i	0.199169	−	1.12954i	−0.707186	−	0.707027i	$-0.750036\pi$
$709$	5.30328	−	30.0764i	0.199169	−	1.12954i	0.906355	−	0.422516i	$-0.138853\pi$
$710$	1.88301	−	3.26146i	0.0706680	−	0.122401i
$711$		0			0
$712$	6.19947	+	10.7378i	0.232335	+	0.402416i
$713$	−35.2312	+	12.8231i	−1.31942	+	0.480229i
$714$		0			0
$715$	−2.23183	+	1.87272i	−0.0834656	+	0.0700359i
$716$	1.68341	−	1.41255i	0.0629120	−	0.0527894i
$717$		0			0
$718$	24.1480	−	8.78915i	0.901195	−	0.328008i
$719$	3.46256	+	5.99733i	0.129132	+	0.223663i	0.923340	−	0.383982i	$-0.125448\pi$
$719$	3.46256	+	5.99733i	0.129132	+	0.223663i	−0.794209	+	0.607645i	$0.792114\pi$
$720$		0			0
$721$	13.2694	−	22.9832i	0.494177	−	0.855939i
$722$	2.87893	−	16.3272i	0.107143	−	0.607636i
$723$		0			0
$724$	14.7907	+	5.38339i	0.549693	+	0.200072i
$725$	−2.52580	−	14.3245i	−0.0938057	−	0.531999i
$726$		0			0
$727$	−16.6231	−	13.9485i	−0.616517	−	0.517319i	0.280189	−	0.959945i	$-0.409603\pi$
$727$	−16.6231	−	13.9485i	−0.616517	−	0.517319i	−0.896707	+	0.442625i	$0.854047\pi$
$728$	−3.57551			−0.132517
$729$		0			0
$730$	0.424635			0.0157164
$731$	−9.19595	−	7.71631i	−0.340124	−	0.285398i
$732$		0			0
$733$	6.80782	+	38.6090i	0.251452	+	1.42606i	0.805017	+	0.593251i	$0.202156\pi$
$733$	6.80782	+	38.6090i	0.251452	+	1.42606i	−0.553565	+	0.832806i	$0.686733\pi$
$734$	10.6739	+	3.88499i	0.393981	+	0.143397i
$735$		0			0
$736$	−0.608539	+	3.45119i	−0.0224310	+	0.127213i
$737$	29.8057	−	51.6251i	1.09791	−	1.90163i
$738$		0			0
$739$	15.4039	+	26.6804i	0.566643	+	0.981454i	0.996895	+	0.0787451i	$0.0250913\pi$
$739$	15.4039	+	26.6804i	0.566643	+	0.981454i	−0.430252	+	0.902709i	$0.641575\pi$
$740$	1.22622	−	0.446307i	0.0450767	−	0.0164066i
$741$		0			0
$742$	12.6903	−	10.6484i	0.465874	−	0.390915i
$743$	−24.4602	+	20.5245i	−0.897357	+	0.752972i	−0.969672	−	0.244410i	$-0.921406\pi$
$743$	−24.4602	+	20.5245i	−0.897357	+	0.752972i	0.0723153	+	0.997382i	$0.476961\pi$
$744$		0			0
$745$	4.75645	−	1.73121i	0.174263	−	0.0634265i
$746$	−14.3521	−	24.8585i	−0.525466	−	0.910134i
$747$		0			0
$748$	9.90985	−	17.1644i	0.362340	−	0.627591i
$749$	12.4099	−	70.3801i	0.453448	−	2.57163i
$750$		0			0
$751$	−2.85191	−	1.03801i	−0.104068	−	0.0378776i	0.289462	−	0.957190i	$-0.406524\pi$
$751$	−2.85191	−	1.03801i	−0.104068	−	0.0378776i	−0.393529	+	0.919312i	$0.628746\pi$
$752$	−1.68378	−	9.54918i	−0.0614010	−	0.348223i
$753$		0			0
$754$	−2.16563	−	1.81718i	−0.0788675	−	0.0661777i
$755$	−3.85659			−0.140356
$756$		0			0
$757$	10.7254			0.389823			0.194912	−	0.980821i	$-0.437558\pi$
$757$	10.7254			0.389823			0.194912	+	0.980821i	$0.437558\pi$
$758$	17.6568	+	14.8158i	0.641323	+	0.538134i
$759$		0			0
$760$	−0.200131	−	1.13500i	−0.00725951	−	0.0411707i
$761$	25.4656	+	9.26871i	0.923126	+	0.335990i	0.759481	−	0.650529i	$-0.225453\pi$
$761$	25.4656	+	9.26871i	0.923126	+	0.335990i	0.163645	+	0.986519i	$0.447675\pi$
$762$		0			0
$763$	−7.13760	+	40.4793i	−0.258398	+	1.46545i
$764$	3.92070	−	6.79085i	0.141846	−	0.245684i
$765$		0			0
$766$	12.3025	+	21.3086i	0.444508	+	0.769910i
$767$	1.16377	−	0.423579i	0.0420214	−	0.0152945i
$768$		0			0
$769$	20.6292	−	17.3100i	0.743910	−	0.624214i	−0.189975	−	0.981789i	$-0.560841\pi$
$769$	20.6292	−	17.3100i	0.743910	−	0.624214i	0.933885	+	0.357575i	$0.116396\pi$
$770$	10.6614	−	8.94599i	0.384211	−	0.322391i
$771$		0			0
$772$	15.5431	−	5.65721i	0.559407	−	0.203607i
$773$	−7.19832	−	12.4679i	−0.258906	−	0.448438i	0.707043	−	0.707170i	$-0.250029\pi$
$773$	−7.19832	−	12.4679i	−0.258906	−	0.448438i	−0.965949	+	0.258733i	$0.916695\pi$
$774$		0			0
$775$	23.8113	−	41.2424i	0.855328	−	1.48147i
$776$	−0.999303	+	5.66733i	−0.0358729	+	0.203445i
$777$		0			0
$778$	−34.8878	−	12.6981i	−1.25079	−	0.455250i
$779$	0.696235	+	3.94855i	0.0249452	+	0.141471i
$780$		0			0
$781$	−17.7069

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.696050 - 0.253341i) q^{5} +(0.717657 - 4.07003i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.370360 + 0.641483i) q^{10} +(4.27215 - 1.55493i) q^{11} +(0.662744 - 0.556108i) q^{13} +(-3.16592 + 2.65653i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-2.17975 - 3.77544i) q^{17} +(-0.777964 + 1.34747i) q^{19} +(0.128625 - 0.729467i) q^{20} +(-4.27215 - 1.55493i) q^{22} +(0.608539 + 3.45119i) q^{23} +(-3.40992 - 2.86126i) q^{25} -0.865150 q^{26} +4.13282 q^{28} +(2.50318 + 2.10042i) q^{29} +(1.85778 + 10.5360i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.757019 + 4.29327i) q^{34} +(-1.53063 + 2.65113i) q^{35} +(0.880842 + 1.52566i) q^{37} +(1.46209 - 0.532159i) q^{38} +(-0.567425 + 0.476126i) q^{40} +(1.97401 - 1.65639i) q^{41} +(2.58757 - 0.941797i) q^{43} +(2.27316 + 3.93723i) q^{44} +(1.75222 - 3.03493i) q^{46} +(-1.68378 + 9.54918i) q^{47} +(-9.47229 - 3.44763i) q^{49} +(0.772966 + 4.38371i) q^{50} +(0.662744 + 0.556108i) q^{52} -4.00839 q^{53} -3.36756 q^{55} +(-3.16592 - 2.65653i) q^{56} +(-0.567425 - 3.21803i) q^{58} +(1.34517 + 0.489601i) q^{59} +(-0.751711 + 4.26317i) q^{61} +(5.34926 - 9.26519i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.602188 + 0.219178i) q^{65} +(10.0444 - 8.42825i) q^{67} +(3.33957 - 2.80223i) q^{68} +(2.87665 - 1.04701i) q^{70} +(-2.54213 - 4.40310i) q^{71} +(0.286636 - 0.496469i) q^{73} +(0.305913 - 1.73492i) q^{74} +(-1.46209 - 0.532159i) q^{76} +(-3.26270 - 18.5037i) q^{77} +(5.17820 + 4.34502i) q^{79} +0.740720 q^{80} -2.57689 q^{82} +(-7.06556 - 5.92871i) q^{83} +(0.560740 + 3.18011i) q^{85} +(-2.58757 - 0.941797i) q^{86} +(0.789461 - 4.47725i) q^{88} +(-6.19947 + 10.7378i) q^{89} +(-1.78776 - 3.09648i) q^{91} +(-3.29309 + 1.19859i) q^{92} +(7.42794 - 6.23278i) q^{94} +(0.882872 - 0.740818i) q^{95} +(-5.40770 + 1.96824i) q^{97} +(5.04010 + 8.72971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

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