LMFDB - Embedded newform 729.2.g.d.352.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			352.8
Character	$\chi$	$=$	729.352
Dual form			729.2.g.d.379.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.715589 - 2.39023i) q^{2} +(-3.53018 - 2.32184i) q^{4} +(-0.557507 + 1.29245i) q^{5} +(0.185491 + 3.18476i) q^{7} +(-4.25325 + 3.56890i) q^{8} +O(q^{10})$	\(q+(0.715589 - 2.39023i) q^{2} +(-3.53018 - 2.32184i) q^{4} +(-0.557507 + 1.29245i) q^{5} +(0.185491 + 3.18476i) q^{7} +(-4.25325 + 3.56890i) q^{8} +(2.69030 + 2.25743i) q^{10} +(-2.82875 + 3.79967i) q^{11} +(-1.46355 + 1.55128i) q^{13} +(7.74507 + 1.83561i) q^{14} +(2.13982 + 4.96066i) q^{16} +(0.520249 - 2.95048i) q^{17} +(1.23380 + 6.99724i) q^{19} +(4.96894 - 3.26813i) q^{20} +(7.05788 + 9.48038i) q^{22} +(0.175833 - 3.01894i) q^{23} +(2.07161 + 2.19577i) q^{25} +(2.66061 + 4.60832i) q^{26} +(6.73968 - 11.6735i) q^{28} +(2.14282 - 0.507857i) q^{29} +(-3.36550 + 1.69022i) q^{31} +(2.35903 - 0.275731i) q^{32} +(-6.68005 - 3.35485i) q^{34} +(-4.21955 - 1.53579i) q^{35} +(-6.31317 + 2.29781i) q^{37} +(17.6079 + 2.05807i) q^{38} +(-2.24139 - 7.48677i) q^{40} +(1.21463 + 4.05715i) q^{41} +(-0.788553 - 0.0921686i) q^{43} +(18.8082 - 6.84563i) q^{44} +(-7.09015 - 2.58060i) q^{46} +(-5.17009 - 2.59652i) q^{47} +(-3.15564 + 0.368841i) q^{49} +(6.73083 - 3.38035i) q^{50} +(8.76842 - 2.07815i) q^{52} +(4.83254 - 8.37020i) q^{53} +(-3.33382 - 5.77435i) q^{55} +(-12.1550 - 12.8836i) q^{56} +(0.319479 - 5.48525i) q^{58} +(-0.958961 - 1.28811i) q^{59} +(0.969734 - 0.637804i) q^{61} +(1.63170 + 9.25383i) q^{62} +(-0.847235 + 4.80491i) q^{64} +(-1.18900 - 2.75641i) q^{65} +(-5.82050 - 1.37948i) q^{67} +(-8.68709 + 9.20778i) q^{68} +(-6.69036 + 8.98671i) q^{70} +(2.74773 + 2.30562i) q^{71} +(8.55952 - 7.18229i) q^{73} +(0.974659 + 16.7342i) q^{74} +(11.8909 - 27.5662i) q^{76} +(-12.6258 - 8.30409i) q^{77} +(-1.34462 + 4.49133i) q^{79} -7.60435 q^{80} +10.5667 q^{82} +(-4.29047 + 14.3312i) q^{83} +(3.52329 + 2.31730i) q^{85} +(-0.784584 + 1.81887i) q^{86} +(-1.52926 - 26.2565i) q^{88} +(3.17449 - 2.66371i) q^{89} +(-5.21193 - 4.37333i) q^{91} +(-7.63020 + 10.2491i) q^{92} +(-9.90595 + 10.4997i) q^{94} +(-9.73140 - 2.30638i) q^{95} +(4.98577 + 11.5583i) q^{97} +(-1.37652 + 7.80666i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 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 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{16}{27}\right)$

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 $

$2$	0.715589	−	2.39023i	0.505998	−	1.69015i	−0.198212	−	0.980159i	$-0.563513\pi$
$2$	0.715589	−	2.39023i	0.505998	−	1.69015i	0.704210	−	0.709992i	$-0.251301\pi$
$3$		0			0
$3$		0			0
$4$	−3.53018	−	2.32184i	−1.76509	−	1.16092i
$5$	−0.557507	+	1.29245i	−0.249325	+	0.577999i	−0.996213	−	0.0869504i	$-0.972288\pi$
$5$	−0.557507	+	1.29245i	−0.249325	+	0.577999i	0.746888	+	0.664950i	$0.231547\pi$
$6$		0			0
$7$	0.185491	+	3.18476i	0.0701091	+	1.20373i	0.831534	+	0.555474i	$0.187463\pi$
$7$	0.185491	+	3.18476i	0.0701091	+	1.20373i	−0.761425	+	0.648253i	$0.775500\pi$
$8$	−4.25325	+	3.56890i	−1.50375	+	1.26180i
$9$		0			0
$10$	2.69030	+	2.25743i	0.850749	+	0.713863i
$11$	−2.82875	+	3.79967i	−0.852900	+	1.14564i	0.135045	+	0.990839i	$0.456882\pi$
$11$	−2.82875	+	3.79967i	−0.852900	+	1.14564i	−0.987945	+	0.154804i	$0.950525\pi$
$12$		0			0
$13$	−1.46355	+	1.55128i	−0.405917	+	0.430247i	−0.897793	−	0.440419i	$-0.854830\pi$
$13$	−1.46355	+	1.55128i	−0.405917	+	0.430247i	0.491875	+	0.870666i	$0.336312\pi$
$14$	7.74507	+	1.83561i	2.06996	+	0.490589i
$15$		0			0
$16$	2.13982	+	4.96066i	0.534955	+	1.24017i
$17$	0.520249	−	2.95048i	0.126179	−	0.715596i	−0.854422	−	0.519580i	$-0.826088\pi$
$17$	0.520249	−	2.95048i	0.126179	−	0.715596i	0.980601	−	0.196016i	$-0.0628004\pi$
$18$		0			0
$19$	1.23380	+	6.99724i	0.283053	+	1.60528i	0.712157	+	0.702020i	$0.247718\pi$
$19$	1.23380	+	6.99724i	0.283053	+	1.60528i	−0.429103	+	0.903255i	$0.641170\pi$
$20$	4.96894	−	3.26813i	1.11109	−	0.730775i
$21$		0			0
$22$	7.05788	+	9.48038i	1.50475	+	2.02122i
$23$	0.175833	−	3.01894i	0.0366637	−	0.629492i	−0.929061	−	0.369925i	$-0.879383\pi$
$23$	0.175833	−	3.01894i	0.0366637	−	0.629492i	0.965725	−	0.259567i	$-0.0835797\pi$
$24$		0			0
$25$	2.07161	+	2.19577i	0.414321	+	0.439155i
$26$	2.66061	+	4.60832i	0.521789	+	0.903765i
$27$		0			0
$28$	6.73968	−	11.6735i	1.27368	−	2.20608i
$29$	2.14282	−	0.507857i	0.397911	−	0.0943066i	−0.0267883	−	0.999641i	$-0.508528\pi$
$29$	2.14282	−	0.507857i	0.397911	−	0.0943066i	0.424699	+	0.905335i	$0.360380\pi$
$30$		0			0
$31$	−3.36550	+	1.69022i	−0.604461	+	0.303572i	−0.724583	−	0.689187i	$-0.757968\pi$
$31$	−3.36550	+	1.69022i	−0.604461	+	0.303572i	0.120122	+	0.992759i	$0.461671\pi$
$32$	2.35903	−	0.275731i	0.417021	−	0.0487428i
$33$		0			0
$34$	−6.68005	−	3.35485i	−1.14562	−	0.575351i
$35$	−4.21955	−	1.53579i	−0.713233	−	0.259596i
$36$		0			0
$37$	−6.31317	+	2.29781i	−1.03788	+	0.377757i	−0.804076	−	0.594527i	$-0.797339\pi$
$37$	−6.31317	+	2.29781i	−1.03788	+	0.377757i	−0.233803	+	0.972284i	$0.575117\pi$
$38$	17.6079	+	2.05807i	2.85638	+	0.333863i
$39$		0			0
$40$	−2.24139	−	7.48677i	−0.354395	−	1.18376i
$41$	1.21463	+	4.05715i	0.189693	+	0.633620i	0.998935	+	0.0461439i	$0.0146933\pi$
$41$	1.21463	+	4.05715i	0.189693	+	0.633620i	−0.809241	+	0.587476i	$0.800122\pi$
$42$		0			0
$43$	−0.788553	−	0.0921686i	−0.120253	−	0.0140556i	0.0557534	−	0.998445i	$-0.482244\pi$
$43$	−0.788553	−	0.0921686i	−0.120253	−	0.0140556i	−0.176007	+	0.984389i	$0.556318\pi$
$44$	18.8082	−	6.84563i	2.83544	−	1.03202i
$45$		0			0
$46$	−7.09015	−	2.58060i	−1.04538	−	0.380489i
$47$	−5.17009	−	2.59652i	−0.754135	−	0.378741i	0.0298224	−	0.999555i	$-0.490506\pi$
$47$	−5.17009	−	2.59652i	−0.754135	−	0.378741i	−0.783958	+	0.620814i	$0.786802\pi$
$48$		0			0
$49$	−3.15564	+	0.368841i	−0.450805	+	0.0526916i
$50$	6.73083	−	3.38035i	0.951884	−	0.478054i
$51$		0			0
$52$	8.76842	−	2.07815i	1.21596	−	0.288188i
$53$	4.83254	−	8.37020i	0.663800	−	1.14973i	−0.315809	−	0.948823i	$-0.602276\pi$
$53$	4.83254	−	8.37020i	0.663800	−	1.14973i	0.979609	−	0.200912i	$-0.0643906\pi$
$54$		0			0
$55$	−3.33382	−	5.77435i	−0.449532	−	0.778613i
$56$	−12.1550	−	12.8836i	−1.62428	−	1.72164i
$57$		0			0
$58$	0.319479	−	5.48525i	0.0419497	−	0.720248i
$59$	−0.958961	−	1.28811i	−0.124846	−	0.167697i	0.735306	−	0.677736i	$-0.237039\pi$
$59$	−0.958961	−	1.28811i	−0.124846	−	0.167697i	−0.860152	+	0.510038i	$0.829631\pi$
$60$		0			0
$61$	0.969734	−	0.637804i	0.124162	−	0.0816624i	−0.485909	−	0.874009i	$-0.661511\pi$
$61$	0.969734	−	0.637804i	0.124162	−	0.0816624i	0.610071	+	0.792347i	$0.291141\pi$
$62$	1.63170	+	9.25383i	0.207226	+	1.17524i
$63$		0			0
$64$	−0.847235	+	4.80491i	−0.105904	+	0.600613i
$65$	−1.18900	−	2.75641i	−0.147477	−	0.341891i
$66$		0			0
$67$	−5.82050	−	1.37948i	−0.711088	−	0.168531i	−0.140874	−	0.990027i	$-0.544991\pi$
$67$	−5.82050	−	1.37948i	−0.711088	−	0.168531i	−0.570213	+	0.821497i	$0.693139\pi$
$68$	−8.68709	+	9.20778i	−1.05346	+	1.11661i
$69$		0			0
$70$	−6.69036	+	8.98671i	−0.799651	+	1.07412i
$71$	2.74773	+	2.30562i	0.326095	+	0.273626i	0.791107	−	0.611678i	$-0.209505\pi$
$71$	2.74773	+	2.30562i	0.326095	+	0.273626i	−0.465011	+	0.885305i	$0.653950\pi$
$72$		0			0
$73$	8.55952	−	7.18229i	1.00182	−	0.840623i	0.0145810	−	0.999894i	$-0.495359\pi$
$73$	8.55952	−	7.18229i	1.00182	−	0.840623i	0.987235	+	0.159270i	$0.0509141\pi$
$74$	0.974659	+	16.7342i	0.113302	+	1.94532i
$75$		0			0
$76$	11.8909	−	27.5662i	1.36398	−	3.16206i
$77$	−12.6258	−	8.30409i	−1.43884	−	0.946339i
$78$		0			0
$79$	−1.34462	+	4.49133i	−0.151281	+	0.505314i	−0.999712	−	0.0239917i	$-0.992362\pi$
$79$	−1.34462	+	4.49133i	−0.151281	+	0.505314i	0.848431	+	0.529306i	$0.177548\pi$
$80$	−7.60435			−0.850192
$81$		0			0
$82$	10.5667			1.16690
$83$	−4.29047	+	14.3312i	−0.470940	+	1.57305i	0.311451	+	0.950262i	$0.399185\pi$
$83$	−4.29047	+	14.3312i	−0.470940	+	1.57305i	−0.782391	+	0.622787i	$0.786000\pi$
$84$		0			0
$85$	3.52329	+	2.31730i	0.382154	+	0.251347i
$86$	−0.784584	+	1.81887i	−0.0846039	+	0.196134i
$87$		0			0
$88$	−1.52926	−	26.2565i	−0.163020	−	2.79895i
$89$	3.17449	−	2.66371i	0.336495	−	0.282353i	−0.458845	−	0.888516i	$-0.651737\pi$
$89$	3.17449	−	2.66371i	0.336495	−	0.282353i	0.795340	+	0.606164i	$0.207292\pi$
$90$		0			0
$91$	−5.21193	−	4.37333i	−0.546358	−	0.458449i
$92$	−7.63020	+	10.2491i	−0.795503	+	1.06855i
$93$		0			0
$94$	−9.90595	+	10.4997i	−1.02172	+	1.08296i
$95$	−9.73140	−	2.30638i	−0.998421	−	0.236630i
$96$		0			0
$97$	4.98577	+	11.5583i	0.506229	+	1.17357i	0.959375	+	0.282134i	$0.0910423\pi$
$97$	4.98577	+	11.5583i	0.506229	+	1.17357i	−0.453146	+	0.891436i	$0.649698\pi$
$98$	−1.37652	+	7.80666i	−0.139050	+	0.788591i
$99$		0			0
$100$	−2.21491	−	12.5614i	−0.221491	−	1.25614i
$101$	3.76387	−	2.47554i	0.374519	−	0.246325i	−0.348269	−	0.937395i	$-0.613231\pi$
$101$	3.76387	−	2.47554i	0.374519	−	0.246325i	0.722788	+	0.691070i	$0.242860\pi$
$102$		0			0
$103$	8.33642	+	11.1978i	0.821412	+	1.10335i	0.992993	+	0.118177i	$0.0377051\pi$
$103$	8.33642	+	11.1978i	0.821412	+	1.10335i	−0.171581	+	0.985170i	$0.554888\pi$
$104$	0.688509	−	11.8212i	0.0675139	−	1.15917i
$105$		0			0
$106$	−16.5486	−	17.5405i	−1.60734	−	1.70369i
$107$	−2.27719	−	3.94420i	−0.220144	−	0.381301i	0.734708	−	0.678384i	$-0.237319\pi$
$107$	−2.27719	−	3.94420i	−0.220144	−	0.381301i	−0.954852	+	0.297083i	$0.903986\pi$
$108$		0			0
$109$	−3.56879	+	6.18132i	−0.341828	+	0.592063i	−0.984772	−	0.173850i	$-0.944379\pi$
$109$	−3.56879	+	6.18132i	−0.341828	+	0.592063i	0.642944	+	0.765913i	$0.277713\pi$
$110$	−16.1877	+	3.83655i	−1.54344	+	0.365801i
$111$		0			0
$112$	−15.4016	+	7.73498i	−1.45532	+	0.730887i
$113$	−7.77675	+	0.908972i	−0.731575	+	0.0855089i	−0.473721	−	0.880675i	$-0.657089\pi$
$113$	−7.77675	+	0.908972i	−0.731575	+	0.0855089i	−0.257854	+	0.966184i	$0.583015\pi$
$114$		0			0
$115$	3.80379	+	1.91033i	0.354705	+	0.178139i
$116$	−8.74368	−	3.18244i	−0.811830	−	0.295482i
$117$		0			0
$118$	−3.76510	+	1.37039i	−0.346606	+	0.126154i
$119$	9.49307	+	1.10958i	0.870228	+	0.101715i
$120$		0			0
$121$	−3.28084	−	10.9588i	−0.298258	−	0.996251i
$122$	−0.830570	−	2.77430i	−0.0751963	−	0.251173i
$123$		0			0
$124$	15.8052	+	1.84736i	1.41935	+	0.165898i
$125$	−10.6062	+	3.86035i	−0.948650	+	0.345280i
$126$		0			0
$127$	9.61531	+	3.49969i	0.853220	+	0.310547i	0.731353	−	0.681999i	$-0.238889\pi$
$127$	9.61531	+	3.49969i	0.853220	+	0.310547i	0.121868	+	0.992546i	$0.461112\pi$
$128$	15.1235	+	7.59530i	1.33674	+	0.671336i
$129$		0			0
$130$	−7.43931	+	0.869531i	−0.652471	+	0.0762629i
$131$	7.69068	−	3.86240i	0.671938	−	0.337460i	−0.0799048	−	0.996802i	$-0.525462\pi$
$131$	7.69068	−	3.86240i	0.671938	−	0.337460i	0.751843	+	0.659343i	$0.229165\pi$
$132$		0			0
$133$	−22.0557	+	5.22729i	−1.91247	+	0.453264i
$134$	−7.46238	+	12.9252i	−0.644652	+	1.11657i
$135$		0			0
$136$	8.31720	+	14.4058i	0.713194	+	1.23529i
$137$	−0.733364	−	0.777320i	−0.0626555	−	0.0664110i	0.695288	−	0.718732i	$-0.255277\pi$
$137$	−0.733364	−	0.777320i	−0.0626555	−	0.0664110i	−0.757943	+	0.652321i	$0.773796\pi$
$138$		0			0
$139$	0.433062	−	7.43539i	0.0367318	−	0.630661i	−0.928833	−	0.370499i	$-0.879187\pi$
$139$	0.433062	−	7.43539i	0.0367318	−	0.630661i	0.965565	−	0.260163i	$-0.0837762\pi$
$140$	11.3299	+	15.2187i	0.957552	+	1.28621i
$141$		0			0
$142$	7.47721	−	4.91784i	0.627474	−	0.412696i
$143$	−1.75431	−	9.94920i	−0.146703	−	0.831994i
$144$		0			0
$145$	−0.538257	+	3.05261i	−0.0446998	+	0.253505i
$146$	−11.0423	−	25.5988i	−0.913864	−	2.11857i
$147$		0			0
$148$	27.6218	+	6.54648i	2.27049	+	0.538117i
$149$	1.67541	−	1.77583i	0.137255	−	0.145482i	−0.655100	−	0.755542i	$-0.727373\pi$
$149$	1.67541	−	1.77583i	0.137255	−	0.145482i	0.792355	+	0.610061i	$0.208855\pi$
$150$		0			0
$151$	12.7659	−	17.1476i	1.03888	−	1.39545i	0.123739	−	0.992315i	$-0.460512\pi$
$151$	12.7659	−	17.1476i	1.03888	−	1.39545i	0.915139	−	0.403139i	$-0.132081\pi$
$152$	−30.2201	−	25.3577i	−2.45117	−	2.05678i
$153$		0			0
$154$	−28.8836	+	24.2362i	−2.32751	+	1.95301i
$155$	−0.308226	−	5.29203i	−0.0247573	−	0.425066i
$156$		0			0
$157$	−2.55930	+	5.93312i	−0.204254	+	0.473515i	−0.989295	−	0.145930i	$-0.953383\pi$
$157$	−2.55930	+	5.93312i	−0.204254	+	0.473515i	0.785041	+	0.619444i	$0.212642\pi$
$158$	9.77315	+	6.42790i	0.777510	+	0.511376i
$159$		0			0
$160$	−0.958807	+	3.20264i	−0.0758003	+	0.253191i
$161$	9.64722			0.760307
$162$		0			0
$163$	−6.49040			−0.508367			−0.254184	−	0.967156i	$-0.581807\pi$
$163$	−6.49040			−0.508367			−0.254184	+	0.967156i	$0.581807\pi$
$164$	5.13217	−	17.1426i	0.400755	−	1.33861i
$165$		0			0
$166$	31.1846	+	20.5105i	2.42040	+	1.59192i
$167$	−1.54614	+	3.58435i	−0.119644	+	0.277366i	−0.967505	−	0.252853i	$-0.918631\pi$
$167$	−1.54614	+	3.58435i	−0.119644	+	0.277366i	0.847861	+	0.530219i	$0.177890\pi$
$168$		0			0
$169$	0.491414	+	8.43725i	0.0378011	+	0.649019i
$170$	8.06013	−	6.76325i	0.618184	−	0.518718i
$171$		0			0
$172$	2.56973	+	2.15626i	0.195940	+	0.164413i
$173$	9.75204	−	13.0993i	0.741434	−	0.995918i	−0.258122	−	0.966112i	$-0.583104\pi$
$173$	9.75204	−	13.0993i	0.741434	−	0.995918i	0.999556	−	0.0298060i	$-0.00948894\pi$
$174$		0			0
$175$	−6.60875	+	7.00487i	−0.499575	+	0.529518i
$176$	−24.9019	−	5.90186i	−1.87705	−	0.444869i
$177$		0			0
$178$	−4.09526	−	9.49389i	−0.306953	−	0.711597i
$179$	−3.76729	+	21.3654i	−0.281581	+	1.59692i	0.435670	+	0.900107i	$0.356512\pi$
$179$	−3.76729	+	21.3654i	−0.281581	+	1.59692i	−0.717250	+	0.696816i	$0.754599\pi$
$180$		0			0
$181$	−1.10326	−	6.25687i	−0.0820043	−	0.465070i	−0.997963	−	0.0637968i	$-0.979679\pi$
$181$	−1.10326	−	6.25687i	−0.0820043	−	0.465070i	0.915959	−	0.401273i	$-0.131432\pi$
$182$	−14.1829	+	9.32822i	−1.05130	+	0.691454i
$183$		0			0
$184$	10.0264	+	13.4678i	0.739157	+	0.992861i
$185$	0.549845	−	9.44047i	0.0404254	−	0.694078i
$186$		0			0
$187$	9.73919	+	10.3229i	0.712200	+	0.754888i
$188$	12.2227	+	21.1703i	0.891429	+	1.54400i
$189$		0			0
$190$	−12.4765	+	21.6099i	−0.905139	+	1.56775i
$191$	13.4289	−	3.18271i	0.971680	−	0.230292i	0.286028	−	0.958221i	$-0.407665\pi$
$191$	13.4289	−	3.18271i	0.971680	−	0.230292i	0.685653	+	0.727929i	$0.259517\pi$
$192$		0			0
$193$	3.37500	−	1.69499i	0.242938	−	0.122008i	−0.323165	−	0.946343i	$-0.604747\pi$
$193$	3.37500	−	1.69499i	0.242938	−	0.122008i	0.566103	+	0.824335i	$0.308450\pi$
$194$	31.1949	−	3.64616i	2.23966	−	0.261779i
$195$		0			0
$196$	11.9964	+	6.02480i	0.856883	+	0.430343i
$197$	−5.18414	−	1.88687i	−0.369355	−	0.134434i	0.150673	−	0.988584i	$-0.451856\pi$
$197$	−5.18414	−	1.88687i	−0.369355	−	0.134434i	−0.520027	+	0.854150i	$0.674078\pi$
$198$		0			0
$199$	15.9504	−	5.80546i	1.13069	−	0.411538i	0.292148	−	0.956373i	$-0.405630\pi$
$199$	15.9504	−	5.80546i	1.13069	−	0.411538i	0.838543	+	0.544835i	$0.183408\pi$
$200$	−16.6475	−	1.94582i	−1.17716	−	0.137590i
$201$		0			0
$202$	−3.22373	−	10.7680i	−0.226821	−	0.757634i
$203$	2.01488	+	6.73016i	0.141417	+	0.472364i
$204$		0			0
$205$	−5.92081	−	0.692043i	−0.413527	−	0.0483344i
$206$	32.7307	−	11.9130i	2.28046	−	0.830018i
$207$		0			0
$208$	−10.8271	−	3.94075i	−0.750725	−	0.273242i
$209$	−30.0773	−	15.1054i	−2.08049	−	1.04486i
$210$		0			0
$211$	−19.1764	+	2.24141i	−1.32016	+	0.154305i	−0.746828	−	0.665017i	$-0.768424\pi$
$211$	−19.1764	+	2.24141i	−1.32016	+	0.154305i	−0.573333	+	0.819322i	$0.694350\pi$
$212$	−36.4939	+	18.3279i	−2.50641	+	1.25877i
$213$		0			0
$214$	−11.0571	+	2.62058i	−0.755848	+	0.179139i
$215$	0.558746	−	0.967777i	0.0381062	−	0.0660018i
$216$		0			0
$217$	−6.00721	−	10.4048i	−0.407796	−	0.706323i
$218$	12.2210	+	12.9535i	0.827712	+	0.877323i
$219$		0			0
$220$	−1.63810	+	28.1251i	−0.110441	+	1.89619i
$221$	3.81560	+	5.12524i	0.256665	+	0.344761i
$222$		0			0
$223$	12.6459	−	8.31736i	0.846834	−	0.556972i	−0.0502979	−	0.998734i	$-0.516017\pi$
$223$	12.6459	−	8.31736i	0.846834	−	0.556972i	0.897132	+	0.441763i	$0.145647\pi$
$224$	1.31572	+	7.46180i	0.0879100	+	0.498562i
$225$		0			0
$226$	−3.39230	+	19.2387i	−0.225653	+	1.27974i
$227$	2.49594	+	5.78625i	0.165662	+	0.384047i	0.980744	−	0.195298i	$-0.0625676\pi$
$227$	2.49594	+	5.78625i	0.165662	+	0.384047i	−0.815082	+	0.579345i	$0.803308\pi$
$228$		0			0
$229$	9.06545	+	2.14855i	0.599062	+	0.141980i	0.518949	−	0.854805i	$-0.326324\pi$
$229$	9.06545	+	2.14855i	0.599062	+	0.141980i	0.0801134	+	0.996786i	$0.474472\pi$
$230$	7.28809	−	7.72493i	0.480563	−	0.509367i
$231$		0			0
$232$	−7.30143	+	9.80753i	−0.479363	+	0.643896i
$233$	−16.1221	−	13.5280i	−1.05619	−	0.886251i	−0.0624612	−	0.998047i	$-0.519895\pi$
$233$	−16.1221	−	13.5280i	−1.05619	−	0.886251i	−0.993731	+	0.111797i	$0.964339\pi$
$234$		0			0
$235$	6.23822	−	5.23449i	0.406937	−	0.341460i
$236$	0.394529	+	6.77380i	0.0256816	+	0.440937i
$237$		0			0
$238$	9.44530	−	21.8967i	0.612248	−	1.41935i
$239$	13.7021	+	9.01199i	0.886313	+	0.582937i	0.908996	−	0.416806i	$-0.136850\pi$
$239$	13.7021	+	9.01199i	0.886313	+	0.582937i	−0.0226828	+	0.999743i	$0.507221\pi$
$240$		0			0
$241$	−0.473874	+	1.58285i	−0.0305249	+	0.101960i	−0.971895	−	0.235417i	$-0.924355\pi$
$241$	−0.473874	+	1.58285i	−0.0305249	+	0.101960i	0.941370	+	0.337377i	$0.109540\pi$
$242$	−28.5417			−1.83473
$243$		0			0
$244$	−4.90421			−0.313960
$245$	1.28258	−	4.28412i	0.0819412	−	0.273703i
$246$		0			0
$247$	−12.6604	−	8.32687i	−0.805561	−	0.529826i
$248$	8.28208	−	19.2000i	0.525913	−	1.21920i
$249$		0			0
$250$	1.63744	+	28.1138i	0.103561	+	1.77807i
$251$	−16.6349	+	13.9583i	−1.04998	+	0.881040i	−0.993092	−	0.117340i	$-0.962563\pi$
$251$	−16.6349	+	13.9583i	−1.04998	+	0.881040i	−0.0568910	+	0.998380i	$0.518119\pi$
$252$		0			0
$253$	10.9736	+	9.20793i	0.689903	+	0.578898i
$254$	15.2457	−	20.4785i	0.956599	−	1.28494i
$255$		0			0
$256$	22.2804	−	23.6158i	1.39252	−	1.47599i
$257$	5.98895	+	1.41941i	0.373580	+	0.0885402i	0.413117	−	0.910678i	$-0.364440\pi$
$257$	5.98895	+	1.41941i	0.373580	+	0.0885402i	−0.0395367	+	0.999218i	$0.512588\pi$
$258$		0			0
$259$	−8.48901	−	19.6797i	−0.527481	−	1.22284i
$260$	−2.20255	+	12.4913i	−0.136596	+	0.774677i
$261$		0			0
$262$	−3.72869	−	21.1464i	−0.230359	−	1.30643i
$263$	−21.3300	+	14.0290i	−1.31527	+	0.865065i	−0.996567	−	0.0827912i	$-0.973617\pi$
$263$	−21.3300	+	14.0290i	−1.31527	+	0.865065i	−0.318700	+	0.947856i	$0.603246\pi$
$264$		0			0
$265$	8.12385	+	10.9122i	0.499044	+	0.670333i
$266$	−3.28835	+	56.4588i	−0.201622	+	3.46171i
$267$		0			0
$268$	17.3445	+	18.3841i	1.05948	+	1.12299i
$269$	8.19176	+	14.1885i	0.499460	+	0.865091i	1.00000		0.000622889i	$-0.000198272\pi$
$269$	8.19176	+	14.1885i	0.499460	+	0.865091i	−0.500539	+	0.865714i	$0.666865\pi$
$270$		0			0
$271$	13.6365	−	23.6192i	0.828361	−	1.43476i	−0.0709627	−	0.997479i	$-0.522607\pi$
$271$	13.6365	−	23.6192i	0.828361	−	1.43476i	0.899323	−	0.437284i	$-0.144060\pi$
$272$	15.7496	−	3.73271i	0.954957	−	0.226329i
$273$		0			0
$274$	−2.38277	+	1.19667i	−0.143948	+	0.0722935i
$275$	−14.2033	+	1.66012i	−0.856490	+	0.100109i
$276$		0			0
$277$	−20.4671	−	10.2790i	−1.22975	−	0.617603i	−0.289202	−	0.957268i	$-0.593390\pi$
$277$	−20.4671	−	10.2790i	−1.22975	−	0.617603i	−0.940547	+	0.339665i	$0.889686\pi$
$278$	−17.4624	−	6.35580i	−1.04733	−	0.381196i
$279$		0			0
$280$	23.4278	−	8.52704i	1.40008	−	0.509588i
$281$	−29.7846	−	3.48132i	−1.77680	−	0.207678i	−0.836486	−	0.547989i	$-0.815394\pi$
$281$	−29.7846	−	3.48132i	−1.77680	−	0.207678i	−0.940313	+	0.340311i	$0.889468\pi$
$282$		0			0
$283$	−4.45027	−	14.8649i	−0.264541	−	0.883630i	−0.982296	−	0.187334i	$-0.940015\pi$
$283$	−4.45027	−	14.8649i	−0.264541	−	0.883630i	0.717755	−	0.696296i	$-0.245170\pi$
$284$	−4.34671	−	14.5190i	−0.257930	−	0.861545i
$285$		0			0
$286$	−25.0363	−	2.92632i	−1.48043	−	0.173037i
$287$	−12.6958	+	4.62088i	−0.749407	+	0.272762i
$288$		0			0
$289$	7.54012	+	2.74438i	0.443536	+	0.161434i
$290$	6.91128	+	3.47097i	0.405844	+	0.203823i
$291$		0			0
$292$	−46.8927	+	5.48097i	−2.74419	+	0.320750i
$293$	−6.88017	+	3.45535i	−0.401944	+	0.201864i	−0.638274	−	0.769809i	$-0.720351\pi$
$293$	−6.88017	+	3.45535i	−0.401944	+	0.201864i	0.236331	+	0.971673i	$0.424055\pi$
$294$		0			0
$295$	2.19944	−	0.521276i	0.128056	−	0.0303499i
$296$	18.6508	−	32.3042i	1.08406	−	1.87764i
$297$		0			0
$298$	−3.04574	−	5.27538i	−0.176435	−	0.305595i
$299$	4.42587	+	4.69115i	0.255955	+	0.271296i
$300$		0			0
$301$	0.147265	−	2.52845i	0.00848824	−	0.145737i
$302$	−31.8517	−	42.7842i	−1.83286	−	2.46196i
$303$		0			0
$304$	−32.0708	+	21.0933i	−1.83939	+	1.20978i
$305$	0.283694	+	1.60891i	0.0162443	+	0.0921258i
$306$		0			0
$307$	2.28454	−	12.9563i	0.130386	−	0.739454i	−0.847577	−	0.530673i	$-0.821939\pi$
$307$	2.28454	−	12.9563i	0.130386	−	0.739454i	0.977962	−	0.208781i	$-0.0669496\pi$
$308$	25.2905	+	58.6299i	1.44106	+	3.34075i
$309$		0			0
$310$	−12.8698	−	3.05019i	−0.730953	−	0.173239i
$311$	3.76092	−	3.98634i	0.213262	−	0.226045i	−0.611908	−	0.790929i	$-0.709598\pi$
$311$	3.76092	−	3.98634i	0.213262	−	0.226045i	0.825170	+	0.564884i	$0.191079\pi$
$312$		0			0
$313$	14.4395	−	19.3956i	0.816167	−	1.09630i	−0.177520	−	0.984117i	$-0.556808\pi$
$313$	14.4395	−	19.3956i	0.816167	−	1.09630i	0.993687	−	0.112185i	$-0.0357850\pi$
$314$	12.3501	+	10.3630i	0.696959	+	0.584818i
$315$		0			0
$316$	15.1749	−	12.7332i	0.853653	−	0.716300i
$317$	−0.601533	−	10.3279i	−0.0337855	−	0.580074i	−0.972140	−	0.234400i	$-0.924687\pi$
$317$	−0.601533	−	10.3279i	−0.0337855	−	0.580074i	0.938355	−	0.345674i	$-0.112350\pi$
$318$		0			0
$319$	−4.13180	+	9.57859i	−0.231337	+	0.536298i
$320$	−5.73774	−	3.77377i	−0.320750	−	0.210960i
$321$		0			0
$322$	6.90344	−	23.0591i	0.384714	−	1.28503i
$323$	21.2871			1.18444
$324$		0			0
$325$	−6.43816			−0.357125
$326$	−4.64446	+	15.5136i	−0.257233	+	0.859217i
$327$		0			0
$328$	−19.6457	−	12.9212i	−1.08475	−	0.713452i
$329$	7.31028	−	16.9471i	0.403029	−	0.934326i
$330$		0			0
$331$	1.78877	+	30.7120i	0.0983196	+	1.68808i	0.582277	+	0.812991i	$0.302162\pi$
$331$	1.78877	+	30.7120i	0.0983196	+	1.68808i	−0.483957	+	0.875092i	$0.660801\pi$
$332$	48.4207	−	40.6298i	2.65743	−	2.22985i
$333$		0			0
$334$	7.46105	+	6.26056i	0.408250	+	0.342563i
$335$	5.02788	−	6.75361i	0.274702	−	0.368989i
$336$		0			0
$337$	22.6048	−	23.9597i	1.23136	−	1.30517i	0.294427	−	0.955674i	$-0.404871\pi$
$337$	22.6048	−	23.9597i	1.23136	−	1.30517i	0.936938	−	0.349496i	$-0.113647\pi$
$338$	20.5187	+	4.86301i	1.11607	+	0.264513i
$339$		0			0
$340$	−7.05745	−	16.3610i	−0.382744	−	0.887300i
$341$	3.09789	−	17.5690i	0.167760	−	0.951414i
$342$		0			0
$343$	2.11774	+	12.0103i	0.114347	+	0.648496i
$344$	3.68285	−	2.42225i	0.198566	−	0.130599i
$345$		0			0
$346$	−24.3319	−	32.6834i	−1.30809	−	1.75707i
$347$	1.50790	−	25.8897i	0.0809485	−	1.38983i	−0.676262	−	0.736661i	$-0.736401\pi$
$347$	1.50790	−	25.8897i	0.0809485	−	1.38983i	0.757211	−	0.653171i	$-0.226562\pi$
$348$		0			0
$349$	−10.1417	−	10.7495i	−0.542871	−	0.575410i	0.396620	−	0.917983i	$-0.370183\pi$
$349$	−10.1417	−	10.7495i	−0.542871	−	0.575410i	−0.939491	+	0.342573i	$0.888702\pi$
$350$	12.0141	+	20.8091i	0.642182	+	1.11229i
$351$		0			0
$352$	−5.62541	+	9.74350i	−0.299836	+	0.519330i
$353$	6.74749	−	1.59918i	0.359133	−	0.0851160i	−0.0470887	−	0.998891i	$-0.514994\pi$
$353$	6.74749	−	1.59918i	0.359133	−	0.0851160i	0.406221	+	0.913775i	$0.366846\pi$
$354$		0			0
$355$	−4.51176	+	2.26589i	−0.239459	+	0.120261i
$356$	−17.3912	+	2.03274i	−0.921731	+	0.107735i
$357$		0			0
$358$	48.3724	+	24.2935i	2.55656	+	1.28395i
$359$	28.2850	+	10.2949i	1.49283	+	0.543344i	0.954192	−	0.299195i	$-0.0967182\pi$
$359$	28.2850	+	10.2949i	1.49283	+	0.543344i	0.538634	+	0.842540i	$0.318940\pi$
$360$		0			0
$361$	−29.5849	+	10.7680i	−1.55710	+	0.566738i
$362$	−15.7449	−	1.84031i	−0.827532	−	0.0967246i
$363$		0			0
$364$	8.24489	+	27.5399i	0.432150	+	1.44348i
$365$	4.51073	+	15.0669i	0.236102	+	0.788637i
$366$		0			0
$367$	22.8542	+	2.67127i	1.19298	+	0.139439i	0.689315	−	0.724461i	$-0.257911\pi$
$367$	22.8542	+	2.67127i	1.19298	+	0.139439i	0.503663	+	0.863900i	$0.331985\pi$
$368$	15.3522	−	5.58774i	0.800288	−	0.291281i
$369$		0			0
$370$	−22.1715	−	8.06976i	−1.15264	−	0.419527i
$371$	27.5535	+	13.8379i	1.43051	+	0.718427i
$372$		0			0
$373$	31.2968	−	3.65807i	1.62049	−	0.189408i	0.743097	−	0.669184i	$-0.233356\pi$
$373$	31.2968	−	3.65807i	1.62049	−	0.189408i	0.877391	+	0.479776i	$0.159282\pi$
$374$	31.6435	−	15.8920i	1.63625	−	0.821754i
$375$		0			0
$376$	31.2564	−	7.40790i	1.61192	−	0.382033i
$377$	−2.34830	+	4.06738i	−0.120944	+	0.209481i
$378$		0			0
$379$	9.45804	+	16.3818i	0.485827	+	0.841477i	0.999867	−	0.0162889i	$-0.00518516\pi$
$379$	9.45804	+	16.3818i	0.485827	+	0.841477i	−0.514040	+	0.857766i	$0.671852\pi$
$380$	28.9985	+	30.7367i	1.48759	+	1.57676i
$381$		0			0
$382$	2.00216	−	34.3757i	0.102439	−	1.75881i
$383$	17.8025	+	23.9129i	0.909666	+	1.22189i	0.974588	+	0.224003i	$0.0719127\pi$
$383$	17.8025	+	23.9129i	0.909666	+	1.22189i	−0.0649222	+	0.997890i	$0.520680\pi$
$384$		0			0
$385$	17.7715	−	11.6885i	0.905721	−	0.595702i
$386$	−1.63631	−	9.27997i	−0.0832859	−	0.472338i
$387$		0			0
$388$	9.23585	−	52.3791i	0.468879	−	2.65915i
$389$	2.30996	+	5.35509i	0.117120	+	0.271514i	0.966685	−	0.255970i	$-0.0823948\pi$
$389$	2.30996	+	5.35509i	0.117120	+	0.271514i	−0.849565	+	0.527484i	$0.823136\pi$
$390$		0			0
$391$	−8.81583	−	2.08939i	−0.445836	−	0.105665i
$392$	12.1054	−	12.8309i	0.611413	−	0.648059i
$393$		0			0
$394$	−8.21978	+	11.0411i	−0.414107	+	0.556242i
$395$	−5.05517	−	4.24179i	−0.254353	−	0.213428i
$396$		0			0
$397$	4.50462	−	3.77983i	0.226081	−	0.189704i	−0.522710	−	0.852510i	$-0.675079\pi$
$397$	4.50462	−	3.77983i	0.226081	−	0.189704i	0.748791	+	0.662806i	$0.230635\pi$
$398$	−2.46250	−	42.2794i	−0.123434	−	2.11928i
$399$		0			0
$400$	−6.45963	+	14.9751i	−0.322981	+	0.748755i
$401$	−8.96488	−	5.89630i	−0.447685	−	0.294447i	0.305577	−	0.952167i	$-0.401151\pi$
$401$	−8.96488	−	5.89630i	−0.447685	−	0.294447i	−0.753262	+	0.657720i	$0.771521\pi$
$402$		0			0
$403$	2.30360	−	7.69455i	0.114750	−	0.383293i
$404$	−19.0349			−0.947023
$405$		0			0
$406$	17.5285			0.869924
$407$	9.12748	−	30.4879i	0.452432	−	1.51123i
$408$		0			0
$409$	−2.78148	−	1.82941i	−0.137535	−	0.0904584i	0.478877	−	0.877882i	$-0.341044\pi$
$409$	−2.78148	−	1.82941i	−0.137535	−	0.0904584i	−0.616412	+	0.787424i	$0.711414\pi$
$410$	−5.89101	+	13.6569i	−0.290936	+	0.674467i
$411$		0			0
$412$	−3.42971	−	58.8858i	−0.168970	−	2.90110i
$413$	3.92444	−	3.29300i	0.193109	−	0.162038i
$414$		0			0
$415$	−16.1303	−	13.5349i	−0.791805	−	0.664403i
$416$	−3.02483	+	4.06305i	−0.148305	+	0.199208i
$417$		0			0
$418$	−57.6284	+	61.0826i	−2.81870	+	2.98765i
$419$	2.78252	+	0.659469i	0.135935	+	0.0322172i	0.298020	−	0.954560i	$-0.403674\pi$
$419$	2.78252	+	0.659469i	0.135935	+	0.0322172i	−0.162085	+	0.986777i	$0.551822\pi$
$420$		0			0
$421$	−2.48989	−	5.77221i	−0.121350	−	0.281321i	0.846703	−	0.532065i	$-0.178584\pi$
$421$	−2.48989	−	5.77221i	−0.121350	−	0.281321i	−0.968053	+	0.250745i	$0.919325\pi$
$422$	−8.36498	+	47.4401i	−0.407201	+	2.30935i
$423$		0			0
$424$	9.31841	+	52.8473i	0.452542	+	2.56649i
$425$	7.55633	−	4.96988i	0.366536	−	0.241074i
$426$		0			0
$427$	2.21113	+	2.97006i	0.107004	+	0.143731i
$428$	−1.11891	+	19.2110i	−0.0540847	+	0.928599i
$429$		0			0
$430$	−1.91338	−	2.02807i	−0.0922715	−	0.0978020i
$431$	−8.66111	−	15.0015i	−0.417191	−	0.722596i	0.578465	−	0.815707i	$-0.303652\pi$
$431$	−8.66111	−	15.0015i	−0.417191	−	0.722596i	−0.995656	+	0.0931115i	$0.970319\pi$
$432$		0			0
$433$	−6.83316	+	11.8354i	−0.328381	+	0.568772i	−0.982191	−	0.187887i	$-0.939836\pi$
$433$	−6.83316	+	11.8354i	−0.328381	+	0.568772i	0.653810	+	0.756659i	$0.273170\pi$
$434$	−29.1686	+	6.91308i	−1.40014	+	0.331839i
$435$		0			0
$436$	26.9505	−	13.5350i	1.29069	−	0.648210i
$437$	21.3412	−	2.49442i	1.02089	−	0.119324i
$438$		0			0
$439$	−33.3216	−	16.7347i	−1.59035	−	0.798705i	−0.590389	−	0.807119i	$-0.701025\pi$
$439$	−33.3216	−	16.7347i	−1.59035	−	0.798705i	−0.999965	+	0.00841378i	$0.997322\pi$
$440$	34.7876	+	12.6617i	1.65843	+	0.603621i
$441$		0			0
$442$	14.9809	−	5.45261i	0.712570	−	0.259354i
$443$	4.43485	+	0.518360i	0.210706	+	0.0246280i	0.220791	−	0.975321i	$-0.429136\pi$
$443$	4.43485	+	0.518360i	0.210706	+	0.0246280i	−0.0100849	+	0.999949i	$0.503210\pi$
$444$		0			0
$445$	1.67290	+	5.58789i	0.0793032	+	0.264891i
$446$	−10.8311	−	36.1786i	−0.512870	−	1.71310i
$447$		0			0
$448$	−15.4596	−	1.80697i	−0.730400	−	0.0853715i
$449$	−3.44438	+	1.25365i	−0.162550	+	0.0591635i	−0.422014	−	0.906589i	$-0.638677\pi$
$449$	−3.44438	+	1.25365i	−0.162550	+	0.0591635i	0.259463	+	0.965753i	$0.416454\pi$
$450$		0			0
$451$	−18.8517	−	6.86146i	−0.887693	−	0.323094i
$452$	29.5638	+	14.8475i	1.39056	+	0.698368i
$453$		0			0
$454$	15.6166	−	1.82531i	0.732922	−	0.0856662i
$455$	8.55797	−	4.29798i	0.401204	−	0.201492i
$456$		0			0
$457$	−17.8758	+	4.23665i	−0.836197	+	0.198182i	−0.626340	−	0.779550i	$-0.715448\pi$
$457$	−17.8758	+	4.23665i	−0.836197	+	0.198182i	−0.209856	+	0.977732i	$0.567300\pi$
$458$	11.6227	−	20.1311i	0.543092	−	0.940664i
$459$		0			0
$460$	−8.99256	−	15.5756i	−0.419280	−	0.726215i
$461$	8.27825	+	8.77444i	0.385557	+	0.408666i	0.890862	−	0.454275i	$-0.150101\pi$
$461$	8.27825	+	8.77444i	0.385557	+	0.408666i	−0.505305	+	0.862941i	$0.668620\pi$
$462$		0			0
$463$	−0.160092	+	2.74867i	−0.00744010	+	0.127742i	0.992543	+	0.121897i	$0.0388976\pi$
$463$	−0.160092	+	2.74867i	−0.00744010	+	0.127742i	−0.999983	+	0.00584512i	$0.998139\pi$
$464$	7.10455	+	9.54306i	0.329820	+	0.443025i
$465$		0			0
$466$	−43.8719	+	28.8550i	−2.03233	+	1.33668i
$467$	5.46587	+	30.9985i	0.252930	+	1.43444i	0.801330	+	0.598223i	$0.204126\pi$
$467$	5.46587	+	30.9985i	0.252930	+	1.43444i	−0.548399	+	0.836216i	$0.684763\pi$
$468$		0			0
$469$	3.31368	−	18.7928i	0.153011	−	0.867771i
$470$	−8.04765	−	18.6566i	−0.371210	−	0.860563i
$471$		0			0
$472$	8.67582	+	2.05621i	0.399337	+	0.0946446i
$473$	2.58083	−	2.73552i	0.118667	−	0.125779i
$474$		0			0
$475$	−12.8084	+	17.2047i	−0.587689	+	0.789404i
$476$	−30.9360	−	25.9584i	−1.41795	−	1.18980i
$477$		0			0
$478$	31.3458	−	26.3023i	1.43372	−	1.20304i
$479$	−0.162090	−	2.78298i	−0.00740607	−	0.127157i	−0.999985	−	0.00555190i	$-0.998233\pi$
$479$	−0.162090	−	2.78298i	−0.00740607	−	0.127157i	0.992579	−	0.121605i	$-0.0388043\pi$
$480$		0			0
$481$	5.67514	−	13.1564i	0.258764	−	0.599882i
$482$	3.44428	+	2.26534i	0.156883	+	0.103183i
$483$		0			0
$484$	−13.8625	+	46.3039i	−0.630113	+	2.10472i
$485$	−17.7181			−0.804538
$486$		0			0
$487$	−31.6987			−1.43640			−0.718202	−	0.695835i	$-0.755035\pi$
$487$	−31.6987			−1.43640			−0.718202	+	0.695835i	$0.755035\pi$
$488$	−1.84826	+	6.17362i	−0.0836668	+	0.279466i
$489$		0			0
$490$	−9.32226	−	6.13135i	−0.421137	−	0.276986i
$491$	−13.9396	+	32.3157i	−0.629086	+	1.45838i	0.243489	+	0.969904i	$0.421708\pi$
$491$	−13.9396	+	32.3157i	−0.629086	+	1.45838i	−0.872574	+	0.488481i	$0.837551\pi$
$492$		0			0
$493$	−0.383622	−	6.58654i	−0.0172775	−	0.296643i
$494$	−28.9628	+	24.3027i	−1.30310	+	1.09343i
$495$		0			0
$496$	−15.5862	−	13.0783i	−0.699839	−	0.587235i
$497$	−6.83316	+	9.17853i	−0.306509	+	0.411713i
$498$		0			0
$499$	5.48286	−	5.81149i	0.245446	−	0.260158i	−0.592925	−	0.805258i	$-0.702027\pi$
$499$	5.48286	−	5.81149i	0.245446	−	0.260158i	0.838371	+	0.545100i	$0.183508\pi$
$500$	46.4050	+	10.9982i	2.07529	+	0.491854i
$501$		0			0
$502$	21.4599	+	49.7496i	0.957802	+	2.22043i
$503$	−2.70376	+	15.3338i	−0.120555	+	0.683700i	0.863294	+	0.504701i	$0.168397\pi$
$503$	−2.70376	+	15.3338i	−0.120555	+	0.683700i	−0.983849	+	0.178999i	$0.942714\pi$
$504$		0			0
$505$	1.10111	+	6.24473i	0.0489989	+	0.277887i
$506$	29.8617	−	19.6403i	1.32751	−	0.873120i
$507$		0			0
$508$	−25.8181	−	34.6797i	−1.14549	−	1.53866i
$509$	1.00472	−	17.2503i	0.0445332	−	0.764606i	−0.899939	−	0.436015i	$-0.856389\pi$
$509$	1.00472	−	17.2503i	0.0445332	−	0.764606i	0.944472	−	0.328591i	$-0.106574\pi$
$510$		0			0
$511$	24.4616	+	25.9278i	1.08212	+	1.14698i
$512$	−23.5802	−	40.8420i	−1.04211	−	1.80498i
$513$		0			0
$514$	7.67834	−	13.2993i	0.338677	−	0.586606i
$515$	−19.1201	+	4.53155i	−0.842532	+	0.199684i
$516$		0			0
$517$	24.4908	−	12.2997i	1.07710	−	0.540942i
$518$	−53.1138	+	6.20812i	−2.33369	+	0.272769i
$519$		0			0
$520$	14.8945	+	7.48028i	0.653166	+	0.328032i
$521$	−33.0219	−	12.0190i	−1.44672	−	0.526562i	−0.505045	−	0.863093i	$-0.668524\pi$
$521$	−33.0219	−	12.0190i	−1.44672	−	0.526562i	−0.941672	+	0.336531i	$0.890746\pi$
$522$		0			0
$523$	2.55225	−	0.928943i	0.111602	−	0.0406198i	−0.285616	−	0.958344i	$-0.592198\pi$
$523$	2.55225	−	0.928943i	0.111602	−	0.0406198i	0.397218	+	0.917724i	$0.369976\pi$
$524$	−36.1173	−	4.22151i	−1.57779	−	0.184418i
$525$		0			0
$526$	18.2690	+	61.0228i	0.796567	+	2.66072i
$527$	3.23605	+	10.8092i	0.140965	+	0.470854i
$528$		0			0
$529$	13.7614	+	1.60848i	0.598322	+	0.0699339i
$530$	31.8961	−	11.6092i	1.38548	−	0.504273i
$531$		0			0
$532$	89.9974	+	32.7564i	3.90188	+	1.42017i
$533$	−8.07144	−	4.05363i	−0.349613	−	0.175582i
$534$		0			0
$535$	6.36722	−	0.744221i	0.275279	−	0.0321755i
$536$	29.6793	−	14.9055i	1.28195	−	0.643819i
$537$		0			0
$538$	39.7759	−	9.42706i	1.71486	−	0.406429i
$539$	7.52504	−	13.0337i	0.324126	−	0.561403i
$540$		0			0
$541$	19.9581	+	34.5684i	0.858065	+	1.48621i	0.873772	+	0.486336i	$0.161667\pi$
$541$	19.9581	+	34.5684i	0.858065	+	1.48621i	−0.0157071	+	0.999877i	$0.505000\pi$
$542$	−46.6972	−	49.4962i	−2.00582	−	2.12604i
$543$		0			0
$544$	0.413744	−	7.10371i	0.0177391	−	0.304569i
$545$	−5.99940	−	8.05859i	−0.256986	−	0.345192i
$546$		0			0
$547$	7.76427	−	5.10664i	0.331976	−	0.218344i	−0.372567	−	0.928005i	$-0.621522\pi$
$547$	7.76427	−	5.10664i	0.331976	−	0.218344i	0.704543	+	0.709661i	$0.251152\pi$
$548$	0.784096	+	4.44683i	0.0334949	+	0.189959i
$549$		0			0
$550$	−6.19562	+	35.1371i	−0.264182	+	1.49825i
$551$	6.19740	+	14.3672i	0.264018	+	0.612063i
$552$		0			0
$553$	−14.5532	−	3.44918i	−0.618867	−	0.146674i
$554$	−39.2152	+	41.5657i	−1.66609	+	1.76596i
$555$		0			0
$556$	−18.7925	+	25.2428i	−0.796981	+	1.07053i
$557$	28.8895	+	24.2411i	1.22409	+	1.02713i	0.998601	+	0.0528835i	$0.0168412\pi$
$557$	28.8895	+	24.2411i	1.22409	+	1.02713i	0.225485	+	0.974247i	$0.427603\pi$
$558$		0			0
$559$	1.29707	−	1.08837i	0.0548602	−	0.0460332i
$560$	−1.41054	−	24.2181i	−0.0596062	−	1.02340i
$561$		0			0
$562$	−29.6347	+	68.7009i	−1.25006	+	2.89797i
$563$	33.3297	+	21.9213i	1.40468	+	0.923873i	0.999955	+	0.00943546i	$0.00300344\pi$
$563$	33.3297	+	21.9213i	1.40468	+	0.923873i	0.404726	+	0.914438i	$0.367367\pi$
$564$		0			0
$565$	3.16079	−	10.5578i	0.132976	−	0.444169i
$566$	−38.7153			−1.62732
$567$		0			0
$568$	−19.9153			−0.835626
$569$	−8.95072	+	29.8975i	−0.375234	+	1.25337i	0.536960	+	0.843608i	$0.319573\pi$
$569$	−8.95072	+	29.8975i	−0.375234	+	1.25337i	−0.912194	+	0.409760i	$0.865613\pi$
$570$		0			0
$571$	17.9710	+	11.8197i	0.752064	+	0.494640i	0.866738	−	0.498763i	$-0.166212\pi$
$571$	17.9710	+	11.8197i	0.752064	+	0.494640i	−0.114675	+	0.993403i	$0.536583\pi$
$572$	−16.9074	+	39.1957i	−0.706933	+	1.63885i
$573$		0			0
$574$	1.96003	+	33.6525i	0.0818102	+	1.40463i
$575$	6.99316	−	5.86796i	0.291635	−	0.244711i
$576$		0			0
$577$	1.05985	+	0.889324i	0.0441223	+	0.0370230i	0.664582	−	0.747215i	$-0.268610\pi$
$577$	1.05985	+	0.889324i	0.0441223	+	0.0370230i	−0.620460	+	0.784238i	$0.713054\pi$
$578$	11.9553	−	16.0588i	0.497276	−	0.667958i
$579$		0			0
$580$	8.98779	−	9.52650i	0.373198	−	0.395567i
$581$	−46.4372	−	11.0058i	−1.92654	−	0.456598i
$582$		0			0
$583$	18.1340	+	42.0392i	0.751032	+	1.74109i
$584$	−10.7729	+	61.0961i	−0.445785	+	2.52817i
$585$		0			0
$586$	3.33572	+	18.9178i	0.137797	+	0.781488i
$587$	6.69705	−	4.40472i	0.276417	−	0.181802i	−0.403730	−	0.914878i	$-0.632286\pi$
$587$	6.69705	−	4.40472i	0.276417	−	0.181802i	0.680147	+	0.733076i	$0.261916\pi$
$588$		0			0
$589$	−15.9792	−	21.4638i	−0.658412	−	0.884400i
$590$	0.327921	−	5.63019i	0.0135003	−	0.231791i
$591$		0			0
$592$	−24.9077	−	26.4006i	−1.02370	−	1.08506i
$593$	−10.7066	−	18.5444i	−0.439668	−	0.761527i	0.557996	−	0.829844i	$-0.311571\pi$
$593$	−10.7066	−	18.5444i	−0.439668	−	0.761527i	−0.997664	+	0.0683166i	$0.978237\pi$
$594$		0			0
$595$	−6.72652	+	11.6507i	−0.275761	+	0.477631i
$596$	−10.0377	+	2.37897i	−0.411159	+	0.0974465i
$597$		0			0
$598$	14.3800	−	7.22193i	0.588044	−	0.295327i
$599$	23.1091	−	2.70107i	0.944213	−	0.110363i	0.369967	−	0.929045i	$-0.379369\pi$
$599$	23.1091	−	2.70107i	0.944213	−	0.110363i	0.574247	+	0.818682i	$0.305295\pi$
$600$		0			0
$601$	−28.2127	−	14.1690i	−1.15082	−	0.577964i	−0.232030	−	0.972709i	$-0.574537\pi$
$601$	−28.2127	−	14.1690i	−1.15082	−	0.577964i	−0.918791	+	0.394744i	$0.870833\pi$
$602$	−5.93821	−	2.16133i	−0.242023	−	0.0880893i
$603$		0			0
$604$	−84.8800	+	30.8938i	−3.45372	+	1.25705i
$605$	15.9927	+	1.86928i	0.650195	+	0.0759969i
$606$		0			0
$607$	1.35006	+	4.50953i	0.0547974	+	0.183036i	0.981007	−	0.193973i	$-0.0621376\pi$
$607$	1.35006	+	4.50953i	0.0547974	+	0.183036i	−0.926209	+	0.377010i	$0.876952\pi$
$608$	4.83992	+	16.1665i	0.196285	+	0.655637i
$609$		0			0
$610$	4.04868	+	0.473222i	0.163926	+	0.0191602i
$611$	11.5946	−	4.22010i	0.469069	−	0.170727i
$612$		0			0
$613$	41.2145	+	15.0009i	1.66464	+	0.605879i	0.991082	−	0.133255i	$-0.0425429\pi$
$613$	41.2145	+	15.0009i	1.66464	+	0.605879i	0.673558	+	0.739134i	$0.264765\pi$
$614$	−29.3338	−	14.7320i	−1.18381	−	0.594534i
$615$		0			0
$616$	83.3369	−	9.74069i	3.35774	−	0.392464i
$617$	−15.9174	+	7.99400i	−0.640809	+	0.321826i	−0.739365	−	0.673305i	$-0.764874\pi$
$617$	−15.9174	+	7.99400i	−0.640809	+	0.321826i	0.0985557	+	0.995132i	$0.468578\pi$
$618$		0			0
$619$	5.45381	−	1.29258i	0.219207	−	0.0519531i	−0.119545	−	0.992829i	$-0.538143\pi$
$619$	5.45381	−	1.29258i	0.219207	−	0.0519531i	0.338752	+	0.940876i	$0.389995\pi$
$620$	−11.1991	+	19.3975i	−0.449768	+	0.779021i
$621$		0			0
$622$	−6.83702	−	11.8421i	−0.274139	−	0.474823i
$623$	9.07212	+	9.61589i	0.363467	+	0.385252i
$624$		0			0
$625$	0.0461192	−	0.791837i	0.00184477	−	0.0316735i
$626$	−36.0272	−	48.3930i	−1.43994	−	1.93417i
$627$		0			0
$628$	22.8105	−	15.0027i	0.910238	−	0.598673i
$629$	3.49521	+	19.8223i	0.139363	+	0.790367i
$630$		0			0
$631$	−2.84022	+	16.1077i	−0.113067	+	0.641237i	0.874622	+	0.484806i	$0.161110\pi$
$631$	−2.84022	+	16.1077i	−0.113067	+	0.641237i	−0.987689	+	0.156431i	$0.950001\pi$
$632$	−10.3101	−	23.9015i	−0.410115	−	0.950752i
$633$		0			0
$634$	−25.1166	−	5.95275i	−0.997509	−	0.236414i
$635$	−9.88375	+	10.4762i	−0.392225	+	0.415734i
$636$		0			0
$637$	4.04627	−	5.43509i	0.160319	−	0.215346i
$638$	19.9384	+	16.7303i	0.789369	+	0.662360i
$639$		0			0
$640$	−18.2480	+	15.3119i	−0.721314	+	0.605255i
$641$	−1.35646	−	23.2895i	−0.0535770	−	0.919881i	−0.912832	−	0.408334i	$-0.866110\pi$
$641$	−1.35646	−	23.2895i	−0.0535770	−	0.919881i	0.859255	−	0.511547i	$-0.170927\pi$
$642$		0			0
$643$	−5.78038	+	13.4004i	−0.227956	+	0.528461i	−0.993354	−	0.115096i	$-0.963283\pi$
$643$	−5.78038	+	13.4004i	−0.227956	+	0.528461i	0.765399	+	0.643556i	$0.222542\pi$
$644$	−34.0564	−	22.3992i	−1.34201	−	0.882654i
$645$		0			0
$646$	15.2328	−	50.8811i	0.599326	−	2.00189i
$647$	1.33592			0.0525205			0.0262602	−	0.999655i	$-0.491640\pi$
$647$	1.33592			0.0525205			0.0262602	+	0.999655i	$0.491640\pi$
$648$		0			0
$649$	7.60705			0.298603
$650$	−4.60708	+	15.3887i	−0.180705	+	0.603595i
$651$		0			0
$652$	22.9123	+	15.0696i	0.897314	+	0.590172i
$653$	6.52701	−	15.1313i	0.255422	−	0.592134i	−0.741464	−	0.670993i	$-0.765868\pi$
$653$	6.52701	−	15.1313i	0.255422	−	0.592134i	0.996886	+	0.0788584i	$0.0251275\pi$
$654$		0			0
$655$	0.704343	+	12.0931i	0.0275210	+	0.472517i
$656$	−17.5271	+	14.7069i	−0.684316	+	0.574210i
$657$		0			0
$658$	−35.2765	−	29.6005i	−1.37522	−	1.15395i
$659$	−26.8793	+	36.1051i	−1.04707	+	1.40646i	−0.137695	+	0.990475i	$0.543969\pi$
$659$	−26.8793	+	36.1051i	−1.04707	+	1.40646i	−0.909373	+	0.415981i	$0.863438\pi$
$660$		0			0
$661$	−17.0678	+	18.0908i	−0.663860	+	0.703651i	−0.968555	−	0.248799i	$-0.919964\pi$
$661$	−17.0678	+	18.0908i	−0.663860	+	0.703651i	0.304695	+	0.952450i	$0.401446\pi$
$662$	74.6888	+	17.7016i	2.90286	+	0.687991i
$663$		0			0
$664$	−32.8980	−	76.2662i	−1.27669	−	2.95970i
$665$	5.54020	−	31.4200i	0.214840	−	1.21842i
$666$		0			0
$667$	−1.15641	−	6.55832i	−0.0447764	−	0.253939i
$668$	13.7804	−	9.06353i	0.533181	−	0.350679i
$669$		0			0
$670$	−12.5448	−	16.8506i	−0.484649	−	0.650996i
$671$	−0.319689	+	5.48886i	−0.0123415	+	0.211895i
$672$		0			0
$673$	−1.35906	−	1.44052i	−0.0523880	−	0.0555280i	0.700650	−	0.713506i	$-0.252894\pi$
$673$	−1.35906	−	1.44052i	−0.0523880	−	0.0555280i	−0.753038	+	0.657978i	$0.771412\pi$
$674$	−41.0936	−	71.1762i	−1.58287	−	2.74161i
$675$		0			0
$676$	17.8551	−	30.9260i	0.686735	−	1.18946i
$677$	27.7238	−	6.57067i	1.06551	−	0.252531i	0.339778	−	0.940506i	$-0.389648\pi$
$677$	27.7238	−	6.57067i	1.06551	−	0.252531i	0.725735	+	0.687974i	$0.241500\pi$
$678$		0			0
$679$	−35.8857	+	18.0225i	−1.37717	+	0.691639i
$680$	−23.2556	+	2.71819i	−0.891813	+	0.104238i
$681$		0			0
$682$	−39.7772	−	19.9769i	−1.52315	−	0.764953i
$683$	27.6811	+	10.0751i	1.05919	+	0.385512i	0.812123	−	0.583487i	$-0.198312\pi$
$683$	27.6811	+	10.0751i	1.05919	+	0.385512i	0.247064	+	0.968999i	$0.420534\pi$
$684$		0			0
$685$	1.41350	−	0.514472i	0.0540071	−	0.0196570i
$686$	30.2229	+	3.53255i	1.15392	+	0.134873i
$687$		0			0
$688$	−1.23014	−	4.10897i	−0.0468988	−	0.156653i
$689$	5.91182	+	19.7468i	0.225222	+	0.752295i
$690$		0			0
$691$	−48.2758	−	5.64264i	−1.83650	−	0.214656i	−0.873997	−	0.485931i	$-0.838481\pi$
$691$	−48.2758	−	5.64264i	−1.83650	−	0.214656i	−0.962502	+	0.271275i	$0.912555\pi$
$692$	−64.8408	+	23.6001i	−2.46488	+	0.897141i
$693$		0			0
$694$	−60.8034	−	22.1306i	−2.30807	−	0.840067i
$695$	9.36840	+	4.70499i	0.355364	+	0.178470i
$696$		0			0
$697$	12.6024	−	1.47301i	0.477351	−	0.0557944i
$698$	−32.9512	+	16.5487i	−1.24722	+	0.626378i
$699$		0			0
$700$	39.5942	−	9.38401i	1.49652	−	0.354682i
$701$	3.03784	−	5.26170i	0.114738	−	0.198732i	−0.802937	−	0.596064i	$-0.796731\pi$
$701$	3.03784	−	5.26170i	0.114738	−	0.198732i	0.917675	+	0.397332i	$0.130064\pi$
$702$		0			0
$703$	−23.8675	−	41.3397i	−0.900179	−	1.55916i
$704$	−15.8605	−	16.8111i	−0.597763	−	0.633592i
$705$		0			0
$706$	1.00601	−	17.2724i	0.0378615	−	0.650057i
$707$	8.58216	+	11.5278i	0.322765	+	0.433549i
$708$		0			0
$709$	18.1324	−	11.9259i	0.680978	−	0.447886i	−0.161317	−	0.986903i	$-0.551574\pi$
$709$	18.1324	−	11.9259i	0.680978	−	0.447886i	0.842295	+	0.539016i	$0.181204\pi$
$710$	2.18745	+	12.4056i	0.0820934	+	0.465575i
$711$		0			0
$712$	−3.99536	+	22.6588i	−0.149733	+	0.849175i
$713$	4.51089	+	10.4574i	0.168934	+	0.391634i
$714$		0			0
$715$	13.8368	+	3.27939i	0.517469	+	0.122642i
$716$	62.9061	−	66.6765i	2.35091	−	2.49182i
$717$		0			0
$718$	44.8477	−	60.2409i	1.67370	−	2.24817i
$719$	−11.8323	−	9.92847i	−0.441270	−	0.370269i	0.394915	−	0.918718i	$-0.370774\pi$
$719$	−11.8323	−	9.92847i	−0.441270	−	0.370269i	−0.836184	+	0.548449i	$0.815219\pi$
$720$		0			0
$721$	−34.1158	+	28.6266i	−1.27054	+	1.06611i
$722$	4.56746	+	78.4203i	0.169983	+	2.91850i
$723$		0			0
$724$	−10.6327	+	24.6495i	−0.395162	+	0.916090i
$725$	5.55421	+	3.65306i	0.206278	+	0.135671i
$726$		0			0
$727$	7.38711	−	24.6747i	0.273973	−	0.915132i	−0.704665	−	0.709540i	$-0.748903\pi$
$727$	7.38711	−	24.6747i	0.273973	−	0.915132i	0.978638	−	0.205592i	$-0.0659121\pi$
$728$	37.7756			1.40006
$729$		0			0
$730$	39.2412			1.45238
$731$	−0.682185	+	2.27866i	−0.0252315	+	0.0842791i
$732$		0			0
$733$	−24.3865	−	16.0392i	−0.900735	−	0.592423i	0.0124701	−	0.999922i	$-0.496031\pi$
$733$	−24.3865	−	16.0392i	−0.900735	−	0.592423i	−0.913206	+	0.407499i	$0.866401\pi$
$734$	22.7392	−	52.7153i	0.839318	−	1.94576i
$735$		0			0
$736$	−0.417619	−	7.17024i	−0.0153936	−	0.264299i
$737$	21.7063	−	18.2138i	0.799563	−	0.670913i
$738$		0			0
$739$	15.6599	+	13.1402i	0.576058	+	0.483370i	0.883650	−	0.468148i	$-0.155079\pi$
$739$	15.6599	+	13.1402i	0.576058	+	0.483370i	−0.307592	+	0.951518i	$0.599523\pi$
$740$	−23.8603	+	32.0499i	−0.877121	+	1.17818i
$741$		0			0
$742$	52.7928	−	55.9571i	1.93808	−	2.05425i
$743$	−22.8643	−	5.41895i	−0.838811	−	0.198802i	−0.211311	−	0.977419i	$-0.567773\pi$
$743$	−22.8643	−	5.41895i	−0.838811	−	0.198802i	−0.627500	+	0.778617i	$0.715922\pi$
$744$		0			0
$745$	1.36111	+	3.15541i	0.0498673	+	0.115605i
$746$	13.6520	−	77.4244i	0.499836	−	2.83471i
$747$		0			0
$748$	−10.4129	−	59.0546i	−0.380734	−	2.15925i
$749$	12.1390	−	7.98392i	0.443548	−	0.291726i
$750$		0			0
$751$	20.9583	+	28.1519i	0.764781	+	1.02728i	0.998488	+	0.0549718i	$0.0175069\pi$
$751$	20.9583	+	28.1519i	0.764781	+	1.02728i	−0.233707	+	0.972307i	$0.575086\pi$
$752$	1.81738	−	31.2032i	0.0662729	−	1.13786i
$753$		0			0
$754$	8.04157	+	8.52356i	0.292857	+	0.310410i
$755$	15.0453	+	26.0592i	0.547554	+	0.948391i
$756$		0			0
$757$	−23.1445	+	40.0875i	−0.841202	+	1.45701i	0.0476764	+	0.998863i	$0.484818\pi$
$757$	−23.1445	+	40.0875i	−0.841202	+	1.45701i	−0.888879	+	0.458142i	$0.848515\pi$
$758$	45.9244	−	10.8843i	1.66805	−	0.395335i
$759$		0			0
$760$	49.6213	−	24.9207i	1.79995	−	0.903971i
$761$	−7.03624	+	0.822418i	−0.255063	+	0.0298126i	−0.242664	−	0.970110i	$-0.578021\pi$
$761$	−7.03624	+	0.822418i	−0.255063	+	0.0298126i	−0.0123997	+	0.999923i	$0.503947\pi$
$762$		0			0
$763$	−20.3480	−	10.2192i	−0.736648	−	0.369958i
$764$	−54.7961	−	19.9441i	−1.98245	−	0.721554i
$765$		0			0
$766$	69.8968	−	25.4404i	2.52547	−	0.919198i
$767$	3.40170	+	0.397602i	0.122828	+	0.0143566i
$768$		0			0
$769$	12.4254	+	41.5036i	0.448070	+	1.49666i	0.822155	+	0.569264i	$0.192772\pi$
$769$	12.4254	+	41.5036i	0.448070	+	1.49666i	−0.374085	+	0.927395i	$0.622043\pi$
$770$	−15.2212	−	50.8423i	−0.548534	−	1.83223i
$771$		0			0
$772$	−15.8499	−	1.85258i	−0.570449	−	0.0666759i
$773$	33.8164	−	12.3082i	1.21629	−	0.442694i	0.347409	−	0.937714i	$-0.387062\pi$
$773$	33.8164	−	12.3082i	1.21629	−	0.442694i	0.868881	+	0.495020i	$0.164839\pi$
$774$		0			0
$775$	−10.6833	−	3.88841i	−0.383756	−	0.139676i
$776$	−62.4562	−	31.3667i	−2.24205	−	1.12600i
$777$		0			0
$778$	14.4529	−	1.68930i	0.518162	−	0.0605644i
$779$	−26.8902	+	13.5048i	−0.963442	+	0.483859i
$780$		0			0
$781$	−16.5332	+	3.91845i	−0.591605	+	0.140213i
$782$	−11.3026	+	19.5768i	−0.404182	+	0.700063i
$783$		0			0
$784$	−8.58220	−	14.8648i	−0.306507	−	0.530886i
$785$	−6.24141	−	6.61551i	−0.222765	−	0.236118i
$786$		0			0
$787$	−1.22106	+	20.9648i	−0.0435262	+	0.747315i	0.903979	+	0.427576i	$0.140632\pi$
$787$	−1.22106	+	20.9648i	−0.0435262	+	0.747315i	−0.947506	+	0.319739i	$0.896405\pi$
$788$	13.9199	+	18.6977i	0.495877	+	0.666078i
$789$		0			0
$790$	−13.7563	+	9.04767i	−0.489427	+	0.321901i
$791$	−4.33738	−	24.5985i	−0.154219	−	0.874622i
$792$		0			0
$793$	−0.429848	+	2.43779i	−0.0152643	+	0.0865683i
$794$	−5.81122	−	13.4719i	−0.206232	−	0.478100i
$795$		0			0
$796$	−69.7870	−	16.5398i	−2.47353	−	0.586238i
$797$	28.9625	−	30.6985i	1.02591	−	1.08740i	0.0297709	−	0.999557i	$-0.490522\pi$
$797$	28.9625	−	30.6985i	1.02591	−	1.08740i	0.996135	−	0.0878396i	$-0.0279963\pi$
$798$		0			0
$799$	−10.3507	+	13.9034i	−0.366181	+	0.491867i
$800$	5.49242	+	4.60868i	0.194186	+	0.162942i
$801$		0			0
$802$	−20.5087	+	17.2089i	−0.724188	+	0.607666i
$803$	3.07760	+	52.8403i	0.108606	+	1.86469i
$804$		0			0
$805$	−5.37839	+	12.4685i	−0.189563	+	0.439457i
$806$	−16.7433	−	11.0123i	−0.589759	−	0.387891i
$807$		0			0
$808$	−7.17373	+	23.9619i	−0.252371	+	0.842978i
$809$	15.1427			0.532390			0.266195	−	0.963919i	$-0.414233\pi$
$809$	15.1427			0.532390			0.266195	+	0.963919i	$0.414233\pi$
$810$		0			0
$811$	30.4862			1.07051			0.535257	−	0.844689i	$-0.320215\pi$
$811$	30.4862			1.07051			0.535257	+	0.844689i	$0.320215\pi$
$812$	8.51344	−	28.4369i	0.298763	−	0.997938i
$813$		0			0
$814$	−66.3417	−	43.6336i	−2.32528	−	1.52936i
$815$	3.61844	−	8.38849i	0.126748	−	0.293836i
$816$		0			0
$817$	−0.327992	−	5.63141i	−0.0114750	−	0.197018i
$818$	−6.36311	+	5.33928i	−0.222481	+	0.186684i
$819$		0			0
$820$	19.2947	+	16.1902i	0.673800	+	0.565386i
$821$	−26.5397	+	35.6490i	−0.926242	+	1.24416i	0.0432575	+	0.999064i	$0.486226\pi$
$821$	−26.5397	+	35.6490i	−0.926242	+	1.24416i	−0.969499	+	0.245095i	$0.921181\pi$
$822$		0			0
$823$	16.2645	−	17.2393i	0.566943	−	0.600925i	−0.378944	−	0.925419i	$-0.623713\pi$
$823$	16.2645	−	17.2393i	0.566943	−	0.600925i	0.945887	+	0.324495i	$0.105194\pi$
$824$	−75.4205	−	17.8750i	−2.62740	−	0.622704i
$825$		0			0
$826$	−5.06275	−	11.7368i	−0.176155	−	0.408374i
$827$	0.904516	−	5.12977i	0.0314531	−	0.178379i	−0.965034	−	0.262124i	$-0.915577\pi$
$827$	0.904516	−	5.12977i	0.0314531	−	0.178379i	0.996487	+	0.0837448i	$0.0266881\pi$
$828$		0			0
$829$	1.35636	+	7.69231i	0.0471084	+	0.267165i	0.999260	−	0.0384608i	$-0.0122455\pi$
$829$	1.35636	+	7.69231i	0.0471084	+	0.267165i	−0.952152	+	0.305626i	$0.901134\pi$
$830$	−43.8943	+	28.8697i	−1.52359	+	1.00208i
$831$		0			0
$832$	−6.21377	−	8.34654i	−0.215424	−	0.289364i
$833$	−0.553459	+	9.50253i	−0.0191762	+	0.329243i
$834$		0			0
$835$	−3.77060	−	3.99660i	−0.130487	−	0.138308i
$836$	71.1060	+	123.159i	2.45925	+	4.25955i
$837$		0			0
$838$	3.56743	−	6.17897i	0.123235	−	0.213449i
$839$	−29.2828	+	6.94015i	−1.01095	+	0.239601i	−0.702534	−	0.711650i	$-0.747948\pi$
$839$	−29.2828	+	6.94015i	−1.01095	+	0.239601i	−0.308420	+	0.951250i	$0.599800\pi$
$840$		0			0
$841$	−21.5816	+	10.8387i	−0.744193	+	0.373748i
$842$	−15.5787	+	1.82089i	−0.536877	+	0.0627519i
$843$		0			0
$844$	72.9005	+	36.6120i	2.50934	+	1.26024i
$845$	−11.1787	−	4.06870i	−0.384557	−	0.139967i
$846$		0			0
$847$	34.2925	−	12.4814i	1.17830	−	0.428867i
$848$	51.8625	+	6.06185i	1.78096	+	0.208165i
$849$		0			0
$850$	−6.47194	−	21.6178i	−0.221986	−	0.741484i
$851$	5.82687	+	19.4631i	0.199743	+	0.667187i
$852$		0			0
$853$	−5.53554	−	0.647012i	−0.189533	−	0.0221533i	0.0207966	−	0.999784i	$-0.493380\pi$
$853$	−5.53554	−	0.647012i	−0.189533	−	0.0221533i	−0.210330	+	0.977630i	$0.567454\pi$
$854$	8.68141	−	3.15978i	0.297072	−	0.108125i
$855$		0			0
$856$	23.7619	+	8.64862i	0.812165	+	0.295604i
$857$	15.6491	+	7.85928i	0.534564	+	0.268468i	0.695536	−	0.718491i	$-0.255167\pi$
$857$	15.6491	+	7.85928i	0.534564	+	0.268468i	−0.160973	+	0.986959i	$0.551463\pi$
$858$		0			0
$859$	33.3514	−	3.89822i	1.13794	−	0.133006i	0.473810	−	0.880627i	$-0.342878\pi$
$859$	33.3514	−	3.89822i	1.13794	−	0.133006i	0.664125	+	0.747621i	$0.268804\pi$
$860$	−4.21949	+	2.11911i	−0.143884	+	0.0722610i
$861$		0			0
$862$	−42.0549	+	9.96718i	−1.43239	+	0.339484i
$863$	−5.63576	+	9.76143i	−0.191844	+	0.332283i	−0.945861	−	0.324571i	$-0.894780\pi$
$863$	−5.63576	+	9.76143i	−0.191844	+	0.332283i	0.754018	+	0.656854i	$0.228113\pi$
$864$		0			0
$865$	11.4933	+	19.9069i	0.390782	+	0.676855i
$866$	23.3996	+	24.8021i	0.795151	+	0.842811i
$867$		0			0
$868$	−2.95169	+	50.6785i	−0.100187	+	1.72014i
$869$	−13.2620	−	17.8140i	−0.449883	−	0.604297i
$870$		0			0
$871$	10.6586	−	7.01026i	0.361153	−	0.237534i
$872$	−6.88157	−	39.0273i	−0.233039	−	1.32163i
$873$		0			0
$874$	9.30925	−	52.7954i	0.314890	−	1.78583i
$875$	−14.2617	−	33.0623i	−0.482132	−	1.11771i
$876$		0			0
$877$	35.8093	+	8.48696i	1.20919	+	0.286584i	0.785293	−	0.619124i	$-0.212512\pi$
$877$	35.8093	+	8.48696i	1.20919	+	0.286584i	0.423901	+	0.905708i	$0.360660\pi$
$878$	−63.8445	+	67.6712i	−2.15465	+	2.28379i
$879$		0			0
$880$	21.5108	−	28.8940i	0.725129	−	0.974018i
$881$	−10.8033	−	9.06508i	−0.363974	−	0.305410i	0.442398	−	0.896819i	$-0.354128\pi$
$881$	−10.8033	−	9.06508i	−0.363974	−	0.305410i	−0.806372	+	0.591408i	$0.798572\pi$
$882$		0			0
$883$	−26.7963	+	22.4847i	−0.901767	+	0.756672i	−0.970535	−	0.240961i	$-0.922538\pi$
$883$	−26.7963	+	22.4847i	−0.901767	+	0.756672i	0.0687683	+	0.997633i	$0.478093\pi$
$884$	−1.56979	−	26.9522i	−0.0527976	−	0.906500i
$885$		0			0
$886$	4.41253	−	10.2294i	0.148242	−	0.343664i
$887$	−36.5713	−	24.0533i	−1.22794	−	0.807631i	−0.241288	−	0.970454i	$-0.577570\pi$
$887$	−36.5713	−	24.0533i	−1.22794	−	0.807631i	−0.986655	+	0.162823i	$0.947940\pi$
$888$		0			0
$889$	−9.36211	+	31.2716i	−0.313995	+	1.04882i
$890$	14.5535			0.487833
$891$		0			0
$892$	−63.9539			−2.14134
$893$	11.7896	−	39.3799i	0.394523	−	1.31780i
$894$		0			0
$895$	−25.5133	−	16.7804i	−0.852815	−	0.560905i
$896$	−21.3840	+	49.5736i	−0.714388	+	1.65614i
$897$		0			0
$898$	0.531760	+	9.12997i	0.0177451	+	0.304671i
$899$	−6.35325	+	5.33101i	−0.211893	+	0.177799i
$900$		0			0
$901$	−22.1820	−	18.6129i	−0.738988	−	0.620085i
$902$	−29.8906	+	40.1500i	−0.995248	+	1.33685i
$903$		0			0
$904$	29.8324	−	31.6205i	0.992211	−	1.05168i
$905$	8.70174	+	2.06235i	0.289256	+	0.0685548i
$906$		0			0
$907$	−6.62314	−	15.3542i	−0.219918	−	0.509827i	0.772163	−	0.635424i	$-0.219175\pi$
$907$	−6.62314	−	15.3542i	−0.219918	−	0.509827i	−0.992081	+	0.125597i	$0.959915\pi$
$908$	4.62359	−	26.2217i	0.153439	−	0.870196i
$909$		0			0
$910$	−4.14918	−	23.5311i	−0.137544	−	0.780050i
$911$	15.9499	−	10.4904i	0.528445	−	0.347564i	−0.257083	−	0.966389i	$-0.582762\pi$
$911$	15.9499	−	10.4904i	0.528445	−	0.347564i	0.785529	+	0.618825i	$0.212391\pi$
$912$		0			0
$913$	−42.3170	−	56.8416i	−1.40049	−	1.88118i
$914$	−2.66517	+	45.7592i	−0.0881559	+	1.51358i
$915$		0			0
$916$	−27.0141	−	28.6333i	−0.892570	−	0.946069i
$917$	13.7274	+	23.7765i	0.453319	+	0.785171i
$918$		0			0
$919$	−2.23912	+	3.87828i	−0.0738619	+	0.127933i	−0.900591	−	0.434668i	$-0.856866\pi$
$919$	−2.23912	+	3.87828i	−0.0738619	+	0.127933i	0.826729	+	0.562600i	$0.190199\pi$
$920$	−22.9962	+	5.45020i	−0.758163	+	0.179688i
$921$		0			0
$922$	26.8968	−	13.5081i	0.885799	−	0.444865i
$923$	−7.59810	+	0.888091i	−0.250095	+	0.0292319i
$924$		0			0
$925$	−18.1239	−	9.10215i	−0.595909	−	0.299277i
$926$	6.45541	+	2.34958i	0.212138	+	0.0772119i
$927$		0			0
$928$	4.91493	−	1.78889i	0.161340	−	0.0587231i
$929$	40.4819	+	4.73166i	1.32817	+	0.155241i	0.750413	−	0.660969i	$-0.229855\pi$
$929$	40.4819	+	4.73166i	1.32817	+	0.155241i	0.577755	+	0.816210i	$0.303929\pi$
$930$		0			0
$931$	−6.47430	−	21.6257i	−0.212187	−	0.708753i
$932$	25.5040	+	85.1892i	0.835410	+	2.79046i
$933$		0			0
$934$	78.0050	+	9.11748i	2.55240	+	0.298333i
$935$	−18.7715	+	6.83227i	−0.613894	+	0.223439i
$936$		0			0
$937$	−25.7954	−	9.38877i	−0.842700	−	0.306718i	−0.115640	−	0.993291i	$-0.536892\pi$
$937$	−25.7954	−	9.38877i	−0.842700	−	0.306718i	−0.727060	+	0.686574i	$0.759114\pi$
$938$	−42.5480	−	21.3684i	−1.38924	−	0.697703i
$939$		0			0
$940$	−34.1756	+	3.99456i	−1.11469	+	0.130288i
$941$	−2.25860	+	1.13431i	−0.0736281	+	0.0369774i	−0.485232	−	0.874385i	$-0.661265\pi$
$941$	−2.25860	+	1.13431i	−0.0736281	+	0.0369774i	0.411604	+	0.911363i	$0.364969\pi$
$942$		0			0
$943$	12.4619	−	2.95351i	0.405814	−	0.0961796i
$944$	4.33786	−	7.51340i	0.141185	−	0.244540i
$945$		0			0
$946$	−4.69172	−	8.12630i	−0.152541	−	0.264209i
$947$	8.76188	+	9.28705i	0.284723	+	0.301789i	0.853911	−	0.520418i	$-0.174224\pi$
$947$	8.76188	+	9.28705i	0.284723	+	0.301789i	−0.569188	+	0.822207i	$0.692743\pi$
$948$		0			0
$949$	−1.38560	+	23.7899i	−0.0449785	+	0.772252i
$950$	31.9576	+	42.9265i	1.03684	+	1.39272i
$951$		0			0
$952$	−44.3364	+	29.1605i	−1.43695	+	0.945096i
$953$	1.62376	+	9.20879i	0.0525987	+	0.298302i	0.999747	−	0.0224940i	$-0.00716067\pi$
$953$	1.62376	+	9.20879i	0.0525987	+	0.298302i	−0.947148	+	0.320796i	$0.896050\pi$
$954$		0			0
$955$	−3.37322	+	19.1305i	−0.109155	+	0.619048i
$956$	−27.4464	−	63.6279i	−0.887679	−	2.05787i
$957$		0			0
$958$	−6.76795	−	1.60403i	−0.218663	−	0.0518240i
$959$	2.33955	−	2.47978i	0.0755480	−	0.0800762i
$960$		0			0
$961$	−10.0422	+	13.4890i	−0.323941	+	0.435128i
$962$	−27.3859	−	22.9795i	−0.882958	−	0.740890i
$963$		0			0
$964$	5.34797	−	4.48748i	0.172247	−	0.144532i
$965$	0.309096	+	5.30698i	0.00995016	+	0.170838i
$966$		0			0
$967$	−0.850061	+	1.97066i	−0.0273361	+	0.0633722i	−0.931337	−	0.364158i	$-0.881357\pi$
$967$	−0.850061	+	1.97066i	−0.0273361	+	0.0633722i	0.904001	+	0.427530i	$0.140616\pi$
$968$	53.0649	+	34.9013i	1.70557	+	1.12177i
$969$		0			0
$970$	−12.6789	+	42.3505i	−0.407095	+	1.35979i
$971$	−18.8603			−0.605255			−0.302627	−	0.953109i	$-0.597864\pi$
$971$	−18.8603			−0.605255			−0.302627	+	0.953109i	$0.597864\pi$
$972$		0			0
$973$	23.7603			0.761719
$974$	−22.6832	+	75.7673i	−0.726818	+	2.42774i
$975$		0			0
$976$	5.23898	+	3.44573i	0.167696	+	0.110295i
$977$	23.8103	−	55.1986i	0.761760	−	1.76596i	0.128950	−	0.991651i	$-0.458839\pi$
$977$	23.8103	−	55.1986i	0.761760	−	1.76596i	0.632810	−	0.774307i	$-0.281901\pi$
$978$		0			0
$979$	1.14139	+	19.5970i	0.0364791	+	0.626322i
$980$	−14.4748	+	12.1458i	−0.462380	+	0.387983i
$981$		0			0
$982$	67.2670	+	56.4437i	2.14657	+	1.80119i
$983$	19.1834	−	25.7678i	0.611857	−	0.821866i	−0.382937	−	0.923774i	$-0.625087\pi$
$983$	19.1834	−	25.7678i	0.611857	−	0.821866i	0.994794	+	0.101908i	$0.0324948\pi$
$984$		0			0
$985$	5.32887	−	5.64827i	0.169792	−	0.179969i
$986$	−16.0179	−	3.79631i	−0.510114	−	0.120899i
$987$		0			0
$988$	25.3598	+	58.7907i	0.806803	+	1.87038i
$989$	−0.416905	+	2.36439i	−0.0132568	+	0.0751831i
$990$		0			0
$991$	−2.05455	−	11.6519i	−0.0652648	−	0.370135i	−0.999895	−	0.0145131i	$-0.995380\pi$
$991$	−2.05455	−	11.6519i	−0.0652648	−	0.370135i	0.934630	−	0.355622i	$-0.115731\pi$
$992$	−7.47326	+	4.91524i	−0.237276	+	0.156059i
$993$		0			0
$994$	17.0491	+	22.9009i	0.540765	+	0.726373i
$995$	−1.38920	+	23.8516i	−0.0440405	+	0.756146i
$996$		0			0
$997$	29.1522	+	30.8995i	0.923259	+	0.978597i	0.999829	−	0.0184671i	$-0.00587859\pi$
$997$	29.1522	+	30.8995i	0.923259	+	0.978597i	−0.0765708	+	0.997064i	$0.524397\pi$
$998$	−9.96735	−	17.2640i	−0.315511	−	0.546481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.352.8		144
3.2	odd	2		729.2.g.a.352.1		144
9.2	odd	6		729.2.g.b.595.8		144
9.4	even	3		81.2.g.a.22.8	✓	144
9.5	odd	6		243.2.g.a.199.1		144
9.7	even	3		729.2.g.c.595.1		144
81.11	odd	54		729.2.g.b.136.8		144
81.16	even	27		81.2.g.a.70.8	yes	144
81.23	odd	54		6561.2.a.d.1.67		72
81.38	odd	54		729.2.g.a.379.1		144
81.43	even	27	inner	729.2.g.d.379.8		144
81.58	even	27		6561.2.a.c.1.6		72
81.65	odd	54		243.2.g.a.127.1		144
81.70	even	27		729.2.g.c.136.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.8	✓	144	9.4	even	3
81.2.g.a.70.8	yes	144	81.16	even	27
243.2.g.a.127.1		144	81.65	odd	54
243.2.g.a.199.1		144	9.5	odd	6
729.2.g.a.352.1		144	3.2	odd	2
729.2.g.a.379.1		144	81.38	odd	54
729.2.g.b.136.8		144	81.11	odd	54
729.2.g.b.595.8		144	9.2	odd	6
729.2.g.c.136.1		144	81.70	even	27
729.2.g.c.595.1		144	9.7	even	3
729.2.g.d.352.8		144	1.1	even	1	trivial
729.2.g.d.379.8		144	81.43	even	27	inner
6561.2.a.c.1.6		72	81.58	even	27
6561.2.a.d.1.67		72	81.23	odd	54

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)

\(f(q)\)	\(=\)	\(q+(0.715589 - 2.39023i) q^{2} +(-3.53018 - 2.32184i) q^{4} +(-0.557507 + 1.29245i) q^{5} +(0.185491 + 3.18476i) q^{7} +(-4.25325 + 3.56890i) q^{8} +O(q^{10})\)	\(q+(0.715589 - 2.39023i) q^{2} +(-3.53018 - 2.32184i) q^{4} +(-0.557507 + 1.29245i) q^{5} +(0.185491 + 3.18476i) q^{7} +(-4.25325 + 3.56890i) q^{8} +(2.69030 + 2.25743i) q^{10} +(-2.82875 + 3.79967i) q^{11} +(-1.46355 + 1.55128i) q^{13} +(7.74507 + 1.83561i) q^{14} +(2.13982 + 4.96066i) q^{16} +(0.520249 - 2.95048i) q^{17} +(1.23380 + 6.99724i) q^{19} +(4.96894 - 3.26813i) q^{20} +(7.05788 + 9.48038i) q^{22} +(0.175833 - 3.01894i) q^{23} +(2.07161 + 2.19577i) q^{25} +(2.66061 + 4.60832i) q^{26} +(6.73968 - 11.6735i) q^{28} +(2.14282 - 0.507857i) q^{29} +(-3.36550 + 1.69022i) q^{31} +(2.35903 - 0.275731i) q^{32} +(-6.68005 - 3.35485i) q^{34} +(-4.21955 - 1.53579i) q^{35} +(-6.31317 + 2.29781i) q^{37} +(17.6079 + 2.05807i) q^{38} +(-2.24139 - 7.48677i) q^{40} +(1.21463 + 4.05715i) q^{41} +(-0.788553 - 0.0921686i) q^{43} +(18.8082 - 6.84563i) q^{44} +(-7.09015 - 2.58060i) q^{46} +(-5.17009 - 2.59652i) q^{47} +(-3.15564 + 0.368841i) q^{49} +(6.73083 - 3.38035i) q^{50} +(8.76842 - 2.07815i) q^{52} +(4.83254 - 8.37020i) q^{53} +(-3.33382 - 5.77435i) q^{55} +(-12.1550 - 12.8836i) q^{56} +(0.319479 - 5.48525i) q^{58} +(-0.958961 - 1.28811i) q^{59} +(0.969734 - 0.637804i) q^{61} +(1.63170 + 9.25383i) q^{62} +(-0.847235 + 4.80491i) q^{64} +(-1.18900 - 2.75641i) q^{65} +(-5.82050 - 1.37948i) q^{67} +(-8.68709 + 9.20778i) q^{68} +(-6.69036 + 8.98671i) q^{70} +(2.74773 + 2.30562i) q^{71} +(8.55952 - 7.18229i) q^{73} +(0.974659 + 16.7342i) q^{74} +(11.8909 - 27.5662i) q^{76} +(-12.6258 - 8.30409i) q^{77} +(-1.34462 + 4.49133i) q^{79} -7.60435 q^{80} +10.5667 q^{82} +(-4.29047 + 14.3312i) q^{83} +(3.52329 + 2.31730i) q^{85} +(-0.784584 + 1.81887i) q^{86} +(-1.52926 - 26.2565i) q^{88} +(3.17449 - 2.66371i) q^{89} +(-5.21193 - 4.37333i) q^{91} +(-7.63020 + 10.2491i) q^{92} +(-9.90595 + 10.4997i) q^{94} +(-9.73140 - 2.30638i) q^{95} +(4.98577 + 11.5583i) q^{97} +(-1.37652 + 7.80666i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 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 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

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