LMFDB - Embedded newform 729.2.g.b.136.1

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			136.1
Character	$\chi$	$=$	729.136
Dual form			729.2.g.b.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46032 - 0.583106i) q^{2} +(3.92589 + 1.97166i) q^{4} +(1.69595 - 2.27806i) q^{5} +(-0.459677 - 0.302334i) q^{7} +(-4.63542 - 3.88958i) q^{8} +O(q^{10})$	\(q+(-2.46032 - 0.583106i) q^{2} +(3.92589 + 1.97166i) q^{4} +(1.69595 - 2.27806i) q^{5} +(-0.459677 - 0.302334i) q^{7} +(-4.63542 - 3.88958i) q^{8} +(-5.50094 + 4.61584i) q^{10} +(-3.04678 + 0.356118i) q^{11} +(-1.33201 + 4.44921i) q^{13} +(0.954659 + 1.01188i) q^{14} +(3.88972 + 5.22480i) q^{16} +(0.523880 + 2.97107i) q^{17} +(-0.875112 + 4.96301i) q^{19} +(11.1497 - 5.59959i) q^{20} +(7.70371 + 0.900434i) q^{22} +(-6.95489 + 4.57430i) q^{23} +(-0.879290 - 2.93703i) q^{25} +(5.87152 - 10.1698i) q^{26} +(-1.20854 - 2.09326i) q^{28} +(-1.09088 + 1.15626i) q^{29} +(-0.286769 - 4.92363i) q^{31} +(-1.72989 - 4.01033i) q^{32} +(0.443539 - 7.61526i) q^{34} +(-1.46833 + 0.534427i) q^{35} +(-3.36770 - 1.22574i) q^{37} +(5.04702 - 11.7003i) q^{38} +(-16.7222 + 3.96323i) q^{40} +(1.11236 - 0.263633i) q^{41} +(-0.142801 + 0.331049i) q^{43} +(-12.6635 - 4.60913i) q^{44} +(19.7786 - 7.19880i) q^{46} +(-0.472617 + 8.11452i) q^{47} +(-2.65266 - 6.14956i) q^{49} +(0.450731 + 7.73876i) q^{50} +(-14.0016 + 14.8409i) q^{52} +(0.345591 + 0.598582i) q^{53} +(-4.35594 + 7.54471i) q^{55} +(0.954842 + 3.18939i) q^{56} +(3.35813 - 2.20868i) q^{58} +(-0.587776 - 0.0687011i) q^{59} +(3.11195 - 1.56288i) q^{61} +(-2.16546 + 12.2809i) q^{62} +(-0.344558 - 1.95409i) q^{64} +(7.87655 + 10.5800i) q^{65} +(6.89831 + 7.31178i) q^{67} +(-3.80124 + 12.6970i) q^{68} +(3.92418 - 0.458671i) q^{70} +(-1.87423 + 1.57266i) q^{71} +(3.96729 + 3.32895i) q^{73} +(7.57088 + 4.97944i) q^{74} +(-13.2210 + 17.7588i) q^{76} +(1.50820 + 0.757447i) q^{77} +(-2.18924 - 0.518860i) q^{79} +18.4992 q^{80} -2.89048 q^{82} +(-2.96386 - 0.702448i) q^{83} +(7.65676 + 3.84537i) q^{85} +(0.544373 - 0.731219i) q^{86} +(15.5082 + 10.1999i) q^{88} +(8.84763 + 7.42404i) q^{89} +(1.95744 - 1.64249i) q^{91} +(-36.3231 + 4.24556i) q^{92} +(5.89442 - 19.6887i) q^{94} +(9.82189 + 10.4106i) q^{95} +(-2.51009 - 3.37164i) q^{97} +(2.94055 + 16.6767i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.46032	−	0.583106i	−1.73971	−	0.412319i	−0.766500	−	0.642244i	$-0.778004\pi$
$2$	−2.46032	−	0.583106i	−1.73971	−	0.412319i	−0.973208	+	0.229925i	$0.926152\pi$
$3$		0			0
$3$		0			0
$4$	3.92589	+	1.97166i	1.96295	+	0.985829i
$5$	1.69595	−	2.27806i	0.758454	−	1.01878i	−0.240388	−	0.970677i	$-0.577275\pi$
$5$	1.69595	−	2.27806i	0.758454	−	1.01878i	0.998842	−	0.0481037i	$-0.0153178\pi$
$6$		0			0
$7$	−0.459677	−	0.302334i	−0.173742	−	0.114272i	0.459660	−	0.888095i	$-0.347971\pi$
$7$	−0.459677	−	0.302334i	−0.173742	−	0.114272i	−0.633401	+	0.773823i	$0.718342\pi$
$8$	−4.63542	−	3.88958i	−1.63887	−	1.37517i
$9$		0			0
$10$	−5.50094	+	4.61584i	−1.73955	+	1.45966i
$11$	−3.04678	+	0.356118i	−0.918639	+	0.107373i	−0.562253	−	0.826965i	$-0.690065\pi$
$11$	−3.04678	+	0.356118i	−0.918639	+	0.107373i	−0.356386	+	0.934339i	$0.615991\pi$
$12$		0			0
$13$	−1.33201	+	4.44921i	−0.369432	+	1.23399i	0.548129	+	0.836394i	$0.315340\pi$
$13$	−1.33201	+	4.44921i	−0.369432	+	1.23399i	−0.917561	+	0.397595i	$0.869845\pi$
$14$	0.954659	+	1.01188i	0.255143	+	0.270436i
$15$		0			0
$16$	3.88972	+	5.22480i	0.972429	+	1.30620i
$17$	0.523880	+	2.97107i	0.127060	+	0.720591i	0.980063	+	0.198686i	$0.0636673\pi$
$17$	0.523880	+	2.97107i	0.127060	+	0.720591i	−0.853004	+	0.521905i	$0.825222\pi$
$18$		0			0
$19$	−0.875112	+	4.96301i	−0.200765	+	1.13859i	0.703202	+	0.710990i	$0.251753\pi$
$19$	−0.875112	+	4.96301i	−0.200765	+	1.13859i	−0.903967	+	0.427602i	$0.859358\pi$
$20$	11.1497	−	5.59959i	2.49315	−	1.25211i
$21$		0			0
$22$	7.70371	+	0.900434i	1.64244	+	0.191973i
$23$	−6.95489	+	4.57430i	−1.45019	+	0.953808i	−0.452109	+	0.891963i	$0.649328\pi$
$23$	−6.95489	+	4.57430i	−1.45019	+	0.953808i	−0.998086	+	0.0618450i	$0.980302\pi$
$24$		0			0
$25$	−0.879290	−	2.93703i	−0.175858	−	0.587407i
$26$	5.87152	−	10.1698i	1.15150	−	1.99446i
$27$		0			0
$28$	−1.20854	−	2.09326i	−0.228393	−	0.395589i
$29$	−1.09088	+	1.15626i	−0.202571	+	0.214712i	−0.820693	−	0.571370i	$-0.806412\pi$
$29$	−1.09088	+	1.15626i	−0.202571	+	0.214712i	0.618122	+	0.786082i	$0.287894\pi$
$30$		0			0
$31$	−0.286769	−	4.92363i	−0.0515052	−	0.884311i	−0.920804	−	0.390024i	$-0.872467\pi$
$31$	−0.286769	−	4.92363i	−0.0515052	−	0.884311i	0.869299	−	0.494286i	$-0.164570\pi$
$32$	−1.72989	−	4.01033i	−0.305804	−	0.708934i
$33$		0			0
$34$	0.443539	−	7.61526i	0.0760662	−	1.30601i
$35$	−1.46833	+	0.534427i	−0.248193	+	0.0903347i
$36$		0			0
$37$	−3.36770	−	1.22574i	−0.553646	−	0.201511i	0.0500195	−	0.998748i	$-0.484072\pi$
$37$	−3.36770	−	1.22574i	−0.553646	−	0.201511i	−0.603666	+	0.797237i	$0.706294\pi$
$38$	5.04702	−	11.7003i	0.818734	−	1.89804i
$39$		0			0
$40$	−16.7222	+	3.96323i	−2.64401	+	0.626641i
$41$	1.11236	−	0.263633i	0.173721	−	0.0411726i	−0.142835	−	0.989747i	$-0.545622\pi$
$41$	1.11236	−	0.263633i	0.173721	−	0.0411726i	0.316556	+	0.948574i	$0.397474\pi$
$42$		0			0
$43$	−0.142801	+	0.331049i	−0.0217769	+	0.0504846i	−0.928758	−	0.370688i	$-0.879122\pi$
$43$	−0.142801	+	0.331049i	−0.0217769	+	0.0504846i	0.906981	+	0.421172i	$0.138381\pi$
$44$	−12.6635	−	4.60913i	−1.90909	−	0.694852i
$45$		0			0
$46$	19.7786	−	7.19880i	2.91619	−	1.06141i
$47$	−0.472617	+	8.11452i	−0.0689383	+	1.18362i	0.769507	+	0.638638i	$0.220502\pi$
$47$	−0.472617	+	8.11452i	−0.0689383	+	1.18362i	−0.838445	+	0.544986i	$0.816535\pi$
$48$		0			0
$49$	−2.65266	−	6.14956i	−0.378952	−	0.878509i
$50$	0.450731	+	7.73876i	0.0637431	+	1.09443i
$51$		0			0
$52$	−14.0016	+	14.8409i	−1.94168	+	2.05806i
$53$	0.345591	+	0.598582i	0.0474706	+	0.0822215i	0.888784	−	0.458326i	$-0.151551\pi$
$53$	0.345591	+	0.598582i	0.0474706	+	0.0822215i	−0.841314	+	0.540547i	$0.818217\pi$
$54$		0			0
$55$	−4.35594	+	7.54471i	−0.587355	+	1.01733i
$56$	0.954842	+	3.18939i	0.127596	+	0.426201i
$57$		0			0
$58$	3.35813	−	2.20868i	0.440944	−	0.290013i
$59$	−0.587776	−	0.0687011i	−0.0765219	−	0.00894412i	0.0777458	−	0.996973i	$-0.475228\pi$
$59$	−0.587776	−	0.0687011i	−0.0765219	−	0.00894412i	−0.154268	+	0.988029i	$0.549302\pi$
$60$		0			0
$61$	3.11195	−	1.56288i	0.398444	−	0.200106i	−0.238282	−	0.971196i	$-0.576584\pi$
$61$	3.11195	−	1.56288i	0.398444	−	0.200106i	0.636727	+	0.771090i	$0.280288\pi$
$62$	−2.16546	+	12.2809i	−0.275014	+	1.55968i
$63$		0			0
$64$	−0.344558	−	1.95409i	−0.0430698	−	0.244261i
$65$	7.87655	+	10.5800i	0.976966	+	1.31229i
$66$		0			0
$67$	6.89831	+	7.31178i	0.842763	+	0.893276i	0.995478	−	0.0949940i	$-0.0302832\pi$
$67$	6.89831	+	7.31178i	0.842763	+	0.893276i	−0.152715	+	0.988270i	$0.548802\pi$
$68$	−3.80124	+	12.6970i	−0.460968	+	1.53974i
$69$		0			0
$70$	3.92418	−	0.458671i	0.469030	−	0.0548217i
$71$	−1.87423	+	1.57266i	−0.222430	+	0.186641i	−0.747192	−	0.664608i	$-0.768599\pi$
$71$	−1.87423	+	1.57266i	−0.222430	+	0.186641i	0.524762	+	0.851249i	$0.324154\pi$
$72$		0			0
$73$	3.96729	+	3.32895i	0.464336	+	0.389624i	0.844724	−	0.535203i	$-0.179765\pi$
$73$	3.96729	+	3.32895i	0.464336	+	0.389624i	−0.380387	+	0.924827i	$0.624209\pi$
$74$	7.57088	+	4.97944i	0.880097	+	0.578849i
$75$		0			0
$76$	−13.2210	+	17.7588i	−1.51655	+	2.03708i
$77$	1.50820	+	0.757447i	0.171875	+	0.0863191i
$78$		0			0
$79$	−2.18924	−	0.518860i	−0.246309	−	0.0583763i	0.105607	−	0.994408i	$-0.466322\pi$
$79$	−2.18924	−	0.518860i	−0.246309	−	0.0583763i	−0.351916	+	0.936032i	$0.614470\pi$
$80$	18.4992			2.06827
$81$		0			0
$82$	−2.89048			−0.319200
$83$	−2.96386	−	0.702448i	−0.325326	−	0.0771037i	0.0647077	−	0.997904i	$-0.479389\pi$
$83$	−2.96386	−	0.702448i	−0.325326	−	0.0771037i	−0.390034	+	0.920801i	$0.627537\pi$
$84$		0			0
$85$	7.65676	+	3.84537i	0.830493	+	0.417089i
$86$	0.544373	−	0.731219i	0.0587012	−	0.0788494i
$87$		0			0
$88$	15.5082	+	10.1999i	1.65318	+	1.08732i
$89$	8.84763	+	7.42404i	0.937846	+	0.786947i	0.977209	−	0.212278i	$-0.0680884\pi$
$89$	8.84763	+	7.42404i	0.937846	+	0.786947i	−0.0393628	+	0.999225i	$0.512533\pi$
$90$		0			0
$91$	1.95744	−	1.64249i	0.205195	−	0.172179i
$92$	−36.3231	+	4.24556i	−3.78695	+	0.442631i
$93$		0			0
$94$	5.89442	−	19.6887i	0.607963	−	2.03074i
$95$	9.82189	+	10.4106i	1.00770	+	1.06810i
$96$		0			0
$97$	−2.51009	−	3.37164i	−0.254861	−	0.342338i	0.656216	−	0.754573i	$-0.272156\pi$
$97$	−2.51009	−	3.37164i	−0.254861	−	0.342338i	−0.911078	+	0.412234i	$0.864748\pi$
$98$	2.94055	+	16.6767i	0.297040	+	1.68460i
$99$		0			0
$100$	2.33883	−	13.2641i	0.233883	−	1.32641i
$101$	−3.44101	+	1.72814i	−0.342394	+	0.171957i	−0.611683	−	0.791103i	$-0.709507\pi$
$101$	−3.44101	+	1.72814i	−0.342394	+	0.171957i	0.269290	+	0.963059i	$0.413211\pi$
$102$		0			0
$103$	1.79574	+	0.209892i	0.176940	+	0.0206813i	0.204101	−	0.978950i	$-0.434573\pi$
$103$	1.79574	+	0.209892i	0.176940	+	0.0206813i	−0.0271617	+	0.999631i	$0.508647\pi$
$104$	23.4799	−	15.4430i	2.30240	−	1.51431i
$105$		0			0
$106$	−0.501228	−	1.67422i	−0.0486836	−	0.162615i
$107$	−6.20251	+	10.7431i	−0.599619	+	1.03857i	0.393258	+	0.919428i	$0.371348\pi$
$107$	−6.20251	+	10.7431i	−0.599619	+	1.03857i	−0.992877	+	0.119143i	$0.961985\pi$
$108$		0			0
$109$	4.85004	+	8.40052i	0.464550	+	0.804624i	0.999181	−	0.0404618i	$-0.0128829\pi$
$109$	4.85004	+	8.40052i	0.464550	+	0.804624i	−0.534631	+	0.845085i	$0.679550\pi$
$110$	15.1164	−	16.0224i	1.44129	−	1.52768i
$111$		0			0
$112$	−0.208378	−	3.57771i	−0.0196899	−	0.338062i
$113$	−5.83166	−	13.5193i	−0.548596	−	1.27179i	−0.936687	−	0.350168i	$-0.886125\pi$
$113$	−5.83166	−	13.5193i	−0.548596	−	1.27179i	0.388091	−	0.921621i	$-0.373135\pi$
$114$		0			0
$115$	−1.37463	+	23.6015i	−0.128185	+	2.20085i
$116$	−6.56242	+	2.38852i	−0.609305	+	0.221769i
$117$		0			0
$118$	1.40606	+	0.511762i	0.129438	+	0.0471115i
$119$	0.657441	−	1.52412i	0.0602675	−	0.139716i
$120$		0			0
$121$	−1.54744	+	0.366751i	−0.140677	+	0.0333410i
$122$	−8.56772	+	2.03059i	−0.775685	+	0.183841i
$123$		0			0
$124$	8.58190	−	19.8951i	0.770677	−	1.78663i
$125$	5.16184	+	1.87876i	0.461689	+	0.168041i
$126$		0			0
$127$	−15.1515	+	5.51470i	−1.34448	+	0.489350i	−0.911220	−	0.411919i	$-0.864859\pi$
$127$	−15.1515	+	5.51470i	−1.34448	+	0.489350i	−0.433259	+	0.901270i	$0.642636\pi$
$128$	−0.799616	+	13.7289i	−0.0706767	+	1.21347i
$129$		0			0
$130$	−13.2095	−	30.6232i	−1.15855	−	2.68583i
$131$	−1.05577	−	18.1269i	−0.0922430	−	1.58375i	−0.654029	−	0.756469i	$-0.726923\pi$
$131$	−1.05577	−	18.1269i	−0.0922430	−	1.58375i	0.561786	−	0.827282i	$-0.310114\pi$
$132$		0			0
$133$	1.90276	−	2.01680i	0.164990	−	0.174879i
$134$	−12.7085	−	22.0118i	−1.09785	−	1.90153i
$135$		0			0
$136$	9.12781	−	15.8098i	0.782703	−	1.35568i
$137$	1.41150	+	4.71474i	0.120593	+	0.402808i	0.996875	−	0.0789896i	$-0.0251694\pi$
$137$	1.41150	+	4.71474i	0.120593	+	0.402808i	−0.876283	+	0.481797i	$0.839984\pi$
$138$		0			0
$139$	7.09813	−	4.66851i	0.602055	−	0.395978i	−0.211574	−	0.977362i	$-0.567859\pi$
$139$	7.09813	−	4.66851i	0.602055	−	0.395978i	0.813629	+	0.581384i	$0.197489\pi$
$140$	−6.81821	−	0.796934i	−0.576244	−	0.0673532i
$141$		0			0
$142$	5.52823	−	2.77638i	0.463918	−	0.232989i
$143$	2.47389	−	14.0301i	0.206877	−	1.17326i
$144$		0			0
$145$	0.783959	+	4.44605i	0.0651042	+	0.369224i
$146$	−7.81967	−	10.5036i	−0.647161	−	0.869288i
$147$		0			0
$148$	−10.8045	−	11.4521i	−0.888123	−	0.941356i
$149$	−3.03838	+	10.1489i	−0.248914	+	0.831430i	0.738633	+	0.674107i	$0.235471\pi$
$149$	−3.03838	+	10.1489i	−0.248914	+	0.831430i	−0.987547	+	0.157323i	$0.949714\pi$
$150$		0			0
$151$	−12.9525	+	1.51393i	−1.05406	+	0.123202i	−0.625431	−	0.780279i	$-0.715077\pi$
$151$	−12.9525	+	1.51393i	−1.05406	+	0.123202i	−0.428628	+	0.903481i	$0.641003\pi$
$152$	23.3605	−	19.6018i	1.89479	−	1.58992i
$153$		0			0
$154$	−3.26898	−	2.74300i	−0.263422	−	0.221038i
$155$	−11.7027	−	7.69698i	−0.939983	−	0.618236i
$156$		0			0
$157$	−13.2259	+	17.7654i	−1.05554	+	1.41783i	−0.152484	+	0.988306i	$0.548727\pi$
$157$	−13.2259	+	17.7654i	−1.05554	+	1.41783i	−0.903054	+	0.429528i	$0.858680\pi$
$158$	5.08369	+	2.55312i	0.404436	+	0.203116i
$159$		0			0
$160$	−12.0696	−	2.86055i	−0.954186	−	0.226146i
$161$	4.57997			0.360952
$162$		0			0
$163$	−17.2006			−1.34725			−0.673626	−	0.739072i	$-0.735264\pi$
$163$	−17.2006			−1.34725			−0.673626	+	0.739072i	$0.735264\pi$
$164$	4.88679	+	1.15819i	0.381594	+	0.0904395i
$165$		0			0
$166$	6.88244	+	3.45649i	0.534181	+	0.268276i
$167$	7.03085	−	9.44407i	0.544064	−	0.730804i	−0.442029	−	0.897001i	$-0.645741\pi$
$167$	7.03085	−	9.44407i	0.544064	−	0.730804i	0.986093	+	0.166196i	$0.0531486\pi$
$168$		0			0
$169$	−7.15987	−	4.70912i	−0.550759	−	0.362240i
$170$	−16.5958	−	13.9255i	−1.27284	−	1.06804i
$171$		0			0
$172$	−1.21334	+	1.01811i	−0.0925161	+	0.0776302i
$173$	11.8803	−	1.38861i	0.903242	−	0.105574i	0.348223	−	0.937412i	$-0.386785\pi$
$173$	11.8803	−	1.38861i	0.903242	−	0.105574i	0.555019	+	0.831838i	$0.312711\pi$
$174$		0			0
$175$	−0.483776	+	1.61593i	−0.0365701	+	0.122153i
$176$	−13.7118	−	14.5336i	−1.03356	−	1.09551i
$177$		0			0
$178$	−17.4390	−	23.4246i	−1.30711	−	1.75575i
$179$	−0.609280	−	3.45540i	−0.0455397	−	0.258268i	0.953535	−	0.301283i	$-0.0974149\pi$
$179$	−0.609280	−	3.45540i	−0.0455397	−	0.258268i	−0.999074	+	0.0430146i	$0.986304\pi$
$180$		0			0
$181$	3.84769	−	21.8214i	0.285997	−	1.62197i	−0.415706	−	0.909499i	$-0.636466\pi$
$181$	3.84769	−	21.8214i	0.285997	−	1.62197i	0.701703	−	0.712470i	$-0.252423\pi$
$182$	−5.77367	+	2.89965i	−0.427973	+	0.214936i
$183$		0			0
$184$	50.0309	+	5.84778i	3.68833	+	0.431104i
$185$	−8.50378	+	5.59303i	−0.625210	+	0.411207i
$186$		0			0
$187$	−2.65420	−	8.86564i	−0.194094	−	0.648320i
$188$	−17.8545	+	30.9249i	−1.30217	+	2.25543i
$189$		0			0
$190$	−18.0945	−	31.3406i	−1.31271	−	2.27369i
$191$	−1.79565	+	1.90328i	−0.129929	+	0.137717i	−0.789071	−	0.614301i	$-0.789438\pi$
$191$	−1.79565	+	1.90328i	−0.129929	+	0.137717i	0.659143	+	0.752018i	$0.270919\pi$
$192$		0			0
$193$	−0.716560	−	12.3029i	−0.0515791	−	0.885579i	−0.920528	−	0.390677i	$-0.872241\pi$
$193$	−0.716560	−	12.3029i	−0.0515791	−	0.885579i	0.868949	−	0.494902i	$-0.164796\pi$
$194$	4.20961	+	9.75897i	0.302232	+	0.700653i
$195$		0			0
$196$	1.71076	−	29.3727i	0.122197	−	2.09805i
$197$	25.6304	−	9.32871i	1.82609	−	0.664643i	0.832174	−	0.554514i	$-0.187096\pi$
$197$	25.6304	−	9.32871i	1.82609	−	0.664643i	0.993917	−	0.110129i	$-0.0351264\pi$
$198$		0			0
$199$	−0.718928	−	0.261668i	−0.0509634	−	0.0185492i	0.316413	−	0.948622i	$-0.397522\pi$
$199$	−0.718928	−	0.261668i	−0.0509634	−	0.0185492i	−0.367376	+	0.930072i	$0.619744\pi$
$200$	−7.34794	+	17.0344i	−0.519578	+	1.20452i
$201$		0			0
$202$	9.47368	−	2.24530i	0.666566	−	0.157979i
$203$	0.851028	−	0.201697i	0.0597305	−	0.0141564i
$204$		0			0
$205$	1.28593	−	2.98113i	0.0898135	−	0.208211i
$206$	−4.29571	−	1.56351i	−0.299296	−	0.108935i
$207$		0			0
$208$	−28.4273	+	10.3467i	−1.97108	+	0.717415i
$209$	0.898861	−	15.4328i	0.0621755	−	1.06751i
$210$		0			0
$211$	7.42324	+	17.2090i	0.511037	+	1.18472i	0.957111	+	0.289721i	$0.0935625\pi$
$211$	7.42324	+	17.2090i	0.511037	+	1.18472i	−0.446074	+	0.894996i	$0.647178\pi$
$212$	0.176556	+	3.03136i	0.0121259	+	0.208194i
$213$		0			0
$214$	21.5245	−	22.8146i	1.47138	−	1.55958i
$215$	0.511968	+	0.886754i	0.0349159	+	0.0604761i
$216$		0			0
$217$	−1.35676	+	2.34998i	−0.0921030	+	0.159527i
$218$	−7.03425	−	23.4960i	−0.476420	−	1.59135i
$219$		0			0
$220$	−31.9766	+	21.0313i	−2.15586	+	1.41793i
$221$	−13.9167	−	1.62663i	−0.936140	−	0.109419i
$222$		0			0
$223$	−2.46984	+	1.24040i	−0.165393	+	0.0830634i	−0.529570	−	0.848266i	$-0.677647\pi$
$223$	−2.46984	+	1.24040i	−0.165393	+	0.0830634i	0.364177	+	0.931330i	$0.381350\pi$
$224$	−0.417271	+	2.36646i	−0.0278801	+	0.158116i
$225$		0			0
$226$	6.46455	+	36.6623i	0.430015	+	2.43874i
$227$	3.99691	+	5.36878i	0.265284	+	0.356339i	0.914727	−	0.404072i	$-0.132405\pi$
$227$	3.99691	+	5.36878i	0.265284	+	0.356339i	−0.649443	+	0.760410i	$0.724998\pi$
$228$		0			0
$229$	9.01098	+	9.55108i	0.595462	+	0.631153i	0.953081	−	0.302715i	$-0.0978929\pi$
$229$	9.01098	+	9.55108i	0.595462	+	0.631153i	−0.357619	+	0.933868i	$0.616411\pi$
$230$	17.1442	−	57.2656i	1.13046	−	3.77598i
$231$		0			0
$232$	9.55404	−	1.11671i	0.627253	−	0.0733154i
$233$	−10.3133	+	8.65393i	−0.675650	+	0.566938i	−0.914732	−	0.404062i	$-0.867598\pi$
$233$	−10.3133	+	8.65393i	−0.675650	+	0.566938i	0.239082	+	0.970999i	$0.423154\pi$
$234$		0			0
$235$	17.6838	+	14.8385i	1.15357	+	0.967957i
$236$	−2.17209	−	1.42861i	−0.141391	−	0.0929943i
$237$		0			0
$238$	−2.50624	+	3.36646i	−0.162455	+	0.218215i
$239$	13.3538	+	6.70652i	0.863784	+	0.433808i	0.824795	−	0.565431i	$-0.191290\pi$
$239$	13.3538	+	6.70652i	0.863784	+	0.433808i	0.0389881	+	0.999240i	$0.487587\pi$
$240$		0			0
$241$	18.7257	+	4.43806i	1.20623	+	0.285881i	0.784087	−	0.620650i	$-0.213131\pi$
$241$	18.7257	+	4.43806i	1.20623	+	0.285881i	0.422139	+	0.906531i	$0.361279\pi$
$242$	4.02106			0.258484
$243$		0			0
$244$	15.2987			0.979396
$245$	−18.5079	−	4.38645i	−1.18242	−	0.280240i
$246$		0			0
$247$	−20.9158	−	10.5043i	−1.33084	−	0.668373i
$248$	−17.8216	+	23.9385i	−1.13167	+	1.52010i
$249$		0			0
$250$	−11.6043	−	7.63225i	−0.733919	−	0.482706i
$251$	−12.4058	−	10.4097i	−0.783047	−	0.657054i	0.160967	−	0.986960i	$-0.448539\pi$
$251$	−12.4058	−	10.4097i	−0.783047	−	0.657054i	−0.944014	+	0.329905i	$0.892983\pi$
$252$		0			0
$253$	19.5610	−	16.4136i	1.22979	−	1.03192i
$254$	40.4932	−	4.73298i	2.54077	−	0.296973i
$255$		0			0
$256$	8.83453	−	29.5094i	0.552158	−	1.84434i
$257$	−15.1675	−	16.0766i	−0.946123	−	1.00283i	−0.999991	−	0.00428415i	$-0.998636\pi$
$257$	−15.1675	−	16.0766i	−0.946123	−	1.00283i	0.0538674	−	0.998548i	$-0.482845\pi$
$258$		0			0
$259$	1.17747	+	1.58162i	0.0731644	+	0.0982768i
$260$	10.0623	+	57.0660i	0.624036	+	3.53908i
$261$		0			0
$262$	−7.97236	+	45.2135i	−0.492534	+	2.79330i
$263$	−14.2109	+	7.13699i	−0.876283	+	0.440086i	−0.829296	−	0.558810i	$-0.811258\pi$
$263$	−14.2109	+	7.13699i	−0.876283	+	0.440086i	−0.0469868	+	0.998896i	$0.514962\pi$
$264$		0			0
$265$	1.94971	+	0.227889i	0.119770	+	0.0139991i
$266$	−5.85740	+	3.85247i	−0.359140	+	0.236210i
$267$		0			0
$268$	12.6657	+	42.3064i	0.773681	+	2.58427i
$269$	9.83880	−	17.0413i	0.599882	−	1.03903i	−0.392956	−	0.919557i	$-0.628547\pi$
$269$	9.83880	−	17.0413i	0.599882	−	1.03903i	0.992838	−	0.119469i	$-0.0381192\pi$
$270$		0			0
$271$	4.61312	+	7.99016i	0.280227	+	0.485367i	0.971441	−	0.237283i	$-0.0762569\pi$
$271$	4.61312	+	7.99016i	0.280227	+	0.485367i	−0.691214	+	0.722651i	$0.742924\pi$
$272$	−13.4855	+	14.2938i	−0.817678	+	0.866688i
$273$		0			0
$274$	−0.723547	−	12.4228i	−0.0437111	−	0.750490i
$275$	3.72493	+	8.63536i	0.224622	+	0.520732i
$276$		0			0
$277$	−1.74780	+	30.0086i	−0.105015	+	1.80304i	0.376303	+	0.926497i	$0.377195\pi$
$277$	−1.74780	+	30.0086i	−0.105015	+	1.80304i	−0.481318	+	0.876546i	$0.659842\pi$
$278$	−20.1859	+	7.34707i	−1.21067	+	0.440648i
$279$		0			0
$280$	8.88501	+	3.23388i	0.530981	+	0.193261i
$281$	−3.40673	+	7.89769i	−0.203228	+	0.471137i	−0.989099	−	0.147255i	$-0.952956\pi$
$281$	−3.40673	+	7.89769i	−0.203228	+	0.471137i	0.785870	+	0.618392i	$0.212215\pi$
$282$		0			0
$283$	−28.0407	+	6.64576i	−1.66685	+	0.395050i	−0.952451	−	0.304693i	$-0.901446\pi$
$283$	−28.0407	+	6.64576i	−1.66685	+	0.395050i	−0.714395	+	0.699743i	$0.753298\pi$
$284$	−10.4588	+	2.47877i	−0.620614	+	0.147088i
$285$		0			0
$286$	−14.2676	+	33.0760i	−0.843661	+	1.95583i
$287$	−0.591030	−	0.215117i	−0.0348874	−	0.0126980i
$288$		0			0
$289$	7.42196	−	2.70137i	0.436586	−	0.158904i
$290$	0.663732	−	11.3958i	0.0389757	−	0.669187i
$291$		0			0
$292$	9.01161	+	20.8913i	0.527365	+	1.22257i
$293$	0.531061	+	9.11796i	0.0310249	+	0.532677i	0.977637	+	0.210301i	$0.0674444\pi$
$293$	0.531061	+	9.11796i	0.0310249	+	0.532677i	−0.946612	+	0.322376i	$0.895519\pi$
$294$		0			0
$295$	−1.15335	+	1.22248i	−0.0671504	+	0.0711753i
$296$	10.8431	+	18.7808i	0.630241	+	1.09161i
$297$		0			0
$298$	13.3933	−	23.1978i	0.775852	−	1.34381i
$299$	−11.0881	−	37.0367i	−0.641240	−	2.14189i
$300$		0			0
$301$	0.165730	−	0.109002i	0.00955251	−	0.00628278i
$302$	32.7501	+	3.82793i	1.88455	+	0.220273i
$303$		0			0
$304$	−29.3346	+	14.7324i	−1.68246	+	0.844962i
$305$	1.71739	−	9.73979i	0.0983373	−	0.557699i
$306$		0			0
$307$	−5.83738	−	33.1054i	−0.333157	−	1.88943i	−0.444721	−	0.895669i	$-0.646697\pi$
$307$	−5.83738	−	33.1054i	−0.333157	−	1.88943i	0.111564	−	0.993757i	$-0.464414\pi$
$308$	4.42761	+	5.94731i	0.252287	+	0.338880i
$309$		0			0
$310$	24.3042	+	25.7609i	1.38039	+	1.46312i
$311$	−5.91511	+	19.7578i	−0.335415	+	1.12036i	0.609428	+	0.792841i	$0.291399\pi$
$311$	−5.91511	+	19.7578i	−0.335415	+	1.12036i	−0.944843	+	0.327523i	$0.893786\pi$
$312$		0			0
$313$	33.5867	−	3.92572i	1.89843	−	0.221895i	0.915035	−	0.403374i	$-0.132163\pi$
$313$	33.5867	−	3.92572i	1.89843	−	0.221895i	0.983395	+	0.181479i	$0.0580885\pi$
$314$	42.8989	−	35.9965i	2.42093	−	2.03140i
$315$		0			0
$316$	−7.57172	−	6.35343i	−0.425943	−	0.357408i
$317$	7.02772	+	4.62221i	0.394716	+	0.259609i	0.731316	−	0.682039i	$-0.238907\pi$
$317$	7.02772	+	4.62221i	0.394716	+	0.259609i	−0.336600	+	0.941648i	$0.609277\pi$
$318$		0			0
$319$	2.91190	−	3.91135i	0.163035	−	0.218994i
$320$	−5.03589	−	2.52912i	−0.281515	−	0.141382i
$321$		0			0
$322$	−11.2682	−	2.67061i	−0.627952	−	0.148827i
$323$	−15.2039			−0.845968
$324$		0			0
$325$	14.2387			0.789820
$326$	42.3189	+	10.0298i	2.34383	+	0.555497i
$327$		0			0
$328$	−6.18166	−	3.10455i	−0.341325	−	0.171420i
$329$	2.67055	−	3.58717i	0.147232	−	0.197767i
$330$		0			0
$331$	−5.43598	−	3.57530i	−0.298788	−	0.196516i	0.391259	−	0.920281i	$-0.372040\pi$
$331$	−5.43598	−	3.57530i	−0.298788	−	0.196516i	−0.690047	+	0.723765i	$0.742410\pi$
$332$	−10.2508	−	8.60146i	−0.562587	−	0.472066i
$333$		0			0
$334$	−22.8050	+	19.1357i	−1.24784	+	1.04706i
$335$	28.3559	−	3.31433i	1.54925	−	0.181081i
$336$		0			0
$337$	−0.981997	+	3.28010i	−0.0534928	+	0.178678i	−0.980561	−	0.196214i	$-0.937135\pi$
$337$	−0.981997	+	3.28010i	−0.0534928	+	0.178678i	0.927068	+	0.374893i	$0.122320\pi$
$338$	14.8697	+	15.7609i	0.808803	+	0.857281i
$339$		0			0
$340$	22.4779	+	30.1930i	1.21903	+	1.63745i
$341$	2.62711	+	14.8991i	0.142266	+	0.806832i
$342$		0			0
$343$	−1.30863	+	7.42162i	−0.0706595	+	0.400730i
$344$	1.94958	−	0.979118i	0.105115	−	0.0527905i
$345$		0			0
$346$	−30.0390	−	3.51106i	−1.61491	−	0.188756i
$347$	21.1741	−	13.9264i	1.13669	−	0.747611i	0.165566	−	0.986199i	$-0.447055\pi$
$347$	21.1741	−	13.9264i	1.13669	−	0.747611i	0.971121	+	0.238588i	$0.0766845\pi$
$348$		0			0
$349$	−3.00800	−	10.0474i	−0.161015	−	0.537826i	0.838965	−	0.544185i	$-0.183161\pi$
$349$	−3.00800	−	10.0474i	−0.161015	−	0.537826i	−0.999980	+	0.00635893i	$0.997976\pi$
$350$	2.13250	−	3.69360i	0.113987	−	0.197431i
$351$		0			0
$352$	6.69874	+	11.6026i	0.357044	+	0.618419i
$353$	−7.81817	+	8.28678i	−0.416119	+	0.441061i	−0.901197	−	0.433411i	$-0.857310\pi$
$353$	−7.81817	+	8.28678i	−0.416119	+	0.441061i	0.485077	+	0.874471i	$0.338791\pi$
$354$		0			0
$355$	0.404021	+	6.93677i	0.0214432	+	0.368165i
$356$	20.0972	+	46.5905i	1.06515	+	2.46929i
$357$		0			0
$358$	−0.515841	+	8.85665i	−0.0272631	+	0.468089i
$359$	15.7087	−	5.71751i	0.829075	−	0.301759i	0.107596	−	0.994195i	$-0.465685\pi$
$359$	15.7087	−	5.71751i	0.829075	−	0.301759i	0.721479	+	0.692436i	$0.243463\pi$
$360$		0			0
$361$	−6.01147	−	2.18800i	−0.316393	−	0.115158i
$362$	−22.1907	+	51.4439i	−1.16632	+	2.70383i
$363$		0			0
$364$	10.9231	−	2.58883i	0.572527	−	0.135691i
$365$	14.3119	−	3.39198i	0.749120	−	0.177545i
$366$		0			0
$367$	−8.72297	+	20.2221i	−0.455335	+	1.05559i	0.523701	+	0.851902i	$0.324551\pi$
$367$	−8.72297	+	20.2221i	−0.455335	+	1.05559i	−0.979037	+	0.203684i	$0.934708\pi$
$368$	−50.9523	−	18.5451i	−2.65607	−	0.966732i
$369$		0			0
$370$	24.1833	−	8.80202i	1.25723	−	0.457595i
$371$	0.0221114	−	0.379638i	0.00114797	−	0.0197098i
$372$		0			0
$373$	−12.0459	−	27.9255i	−0.623713	−	1.44593i	−0.877933	−	0.478783i	$-0.841078\pi$
$373$	−12.0459	−	27.9255i	−0.623713	−	1.44593i	0.254220	−	0.967146i	$-0.418181\pi$
$374$	1.36056	+	23.3600i	0.0703531	+	1.20792i
$375$		0			0
$376$	33.7528	−	35.7759i	1.74067	−	1.84500i
$377$	−3.69139	−	6.39368i	−0.190116	−	0.329291i
$378$		0			0
$379$	6.15029	−	10.6526i	0.315919	−	0.547189i	−0.663713	−	0.747987i	$-0.731020\pi$
$379$	6.15029	−	10.6526i	0.315919	−	0.547189i	0.979633	+	0.200799i	$0.0643537\pi$
$380$	18.0336	+	60.2363i	0.925103	+	3.09006i
$381$		0			0
$382$	5.52770	−	3.63562i	0.282822	−	0.186015i
$383$	7.21709	+	0.843557i	0.368776	+	0.0431038i	0.298463	−	0.954421i	$-0.403526\pi$
$383$	7.21709	+	0.843557i	0.368776	+	0.0431038i	0.0703132	+	0.997525i	$0.477600\pi$
$384$		0			0
$385$	4.28335	−	2.15118i	0.218300	−	0.109634i
$386$	−5.41091	+	30.6868i	−0.275408	+	1.56192i
$387$		0			0
$388$	−3.20664	−	18.1858i	−0.162792	−	0.923242i
$389$	−11.4593	−	15.3925i	−0.581008	−	0.780429i	0.410306	−	0.911948i	$-0.365422\pi$
$389$	−11.4593	−	15.3925i	−0.581008	−	0.780429i	−0.991314	+	0.131519i	$0.958015\pi$
$390$		0			0
$391$	−17.2341	−	18.2671i	−0.871566	−	0.923806i
$392$	−11.6230	+	38.8235i	−0.587050	+	1.96088i
$393$		0			0
$394$	−68.4986	+	8.00634i	−3.45091	+	0.403354i
$395$	−4.89485	+	4.10727i	−0.246287	+	0.206659i
$396$		0			0
$397$	−20.5339	−	17.2300i	−1.03057	−	0.864749i	−0.0396493	−	0.999214i	$-0.512624\pi$
$397$	−20.5339	−	17.2300i	−1.03057	−	0.864749i	−0.990918	+	0.134465i	$0.957069\pi$
$398$	1.61621	+	1.06300i	0.0810133	+	0.0532833i
$399$		0			0
$400$	11.9252	−	16.0183i	0.596261	−	0.800917i
$401$	−18.5786	−	9.33051i	−0.927769	−	0.465943i	−0.0802899	−	0.996772i	$-0.525585\pi$
$401$	−18.5786	−	9.33051i	−0.927769	−	0.465943i	−0.847479	+	0.530828i	$0.821881\pi$
$402$		0			0
$403$	22.2882	+	5.28241i	1.11026	+	0.263136i
$404$	−16.9164			−0.841620
$405$		0			0
$406$	−2.21141			−0.109751
$407$	10.6971	+	2.53527i	0.530238	+	0.125669i
$408$		0			0
$409$	−1.50498	−	0.755829i	−0.0744164	−	0.0373733i	0.411202	−	0.911544i	$-0.365109\pi$
$409$	−1.50498	−	0.755829i	−0.0744164	−	0.0373733i	−0.485618	+	0.874171i	$0.661405\pi$
$410$	−4.90212	+	6.58469i	−0.242099	+	0.325195i
$411$		0			0
$412$	6.63605	+	4.36460i	0.326935	+	0.215028i
$413$	0.249416	+	0.209285i	0.0122730	+	0.0102982i
$414$		0			0
$415$	−6.62680	+	5.56054i	−0.325297	+	0.272956i
$416$	20.1470	−	2.35485i	0.987789	−	0.115456i
$417$		0			0
$418$	−11.2105	+	37.4456i	−0.548322	+	1.83152i
$419$	−5.23343	−	5.54711i	−0.255670	−	0.270994i	0.586807	−	0.809727i	$-0.300385\pi$
$419$	−5.23343	−	5.54711i	−0.255670	−	0.270994i	−0.842477	+	0.538733i	$0.818903\pi$
$420$		0			0
$421$	−19.3997	−	26.0583i	−0.945482	−	1.27000i	−0.962817	−	0.270154i	$-0.912926\pi$
$421$	−19.3997	−	26.0583i	−0.945482	−	1.27000i	0.0173347	−	0.999850i	$-0.494482\pi$
$422$	−8.22886	−	46.6682i	−0.400575	−	2.27177i
$423$		0			0
$424$	0.726270	−	4.11888i	0.0352708	−	0.200031i
$425$	8.26549	−	4.15109i	0.400935	−	0.201357i
$426$		0			0
$427$	−1.90300	−	0.222429i	−0.0920928	−	0.0107641i
$428$	−45.5320	+	29.9469i	−2.20087	+	1.44754i
$429$		0			0
$430$	−0.742532	−	2.48023i	−0.0358081	−	0.119607i
$431$	−4.62511	+	8.01093i	−0.222784	+	0.385873i	−0.955652	−	0.294497i	$-0.904848\pi$
$431$	−4.62511	+	8.01093i	−0.222784	+	0.385873i	0.732868	+	0.680370i	$0.238181\pi$
$432$		0			0
$433$	3.78051	+	6.54803i	0.181680	+	0.314678i	0.942453	−	0.334340i	$-0.108513\pi$
$433$	3.78051	+	6.54803i	0.181680	+	0.314678i	−0.760773	+	0.649018i	$0.775180\pi$
$434$	4.70836	−	4.99057i	0.226008	−	0.239555i
$435$		0			0
$436$	2.47780	+	42.5422i	0.118665	+	2.03740i
$437$	−16.6160	−	38.5202i	−0.794851	−	1.84267i
$438$		0			0
$439$	−1.25460	+	21.5407i	−0.0598790	+	1.02808i	0.825853	+	0.563885i	$0.190694\pi$
$439$	−1.25460	+	21.5407i	−0.0598790	+	1.02808i	−0.885732	+	0.464197i	$0.846343\pi$
$440$	49.5374	−	18.0301i	2.36160	−	0.859553i
$441$		0			0
$442$	33.2911	+	12.1170i	1.58350	+	0.576345i
$443$	5.26928	−	12.2156i	0.250351	−	0.580379i	−0.745979	−	0.665969i	$-0.768018\pi$
$443$	5.26928	−	12.2156i	0.250351	−	0.580379i	0.996330	+	0.0855900i	$0.0272775\pi$
$444$		0			0
$445$	31.9176	−	7.56461i	1.51304	−	0.358597i
$446$	6.79988	−	1.61160i	0.321984	−	0.0763116i
$447$		0			0
$448$	−0.432402	+	1.00242i	−0.0204291	+	0.0473599i
$449$	−17.4340	−	6.34547i	−0.822763	−	0.299461i	−0.103878	−	0.994590i	$-0.533125\pi$
$449$	−17.4340	−	6.34547i	−0.822763	−	0.299461i	−0.718885	+	0.695129i	$0.755347\pi$
$450$		0			0
$451$	−3.29522	+	1.19936i	−0.155166	+	0.0564758i
$452$	3.76097	−	64.5734i	0.176901	−	3.03728i
$453$		0			0
$454$	−6.70310	−	15.5395i	−0.314592	−	0.729307i
$455$	−0.421959	−	7.24475i	−0.0197817	−	0.339639i
$456$		0			0
$457$	−22.9040	+	24.2768i	−1.07140	+	1.13562i	−0.0810997	+	0.996706i	$0.525843\pi$
$457$	−22.9040	+	24.2768i	−1.07140	+	1.13562i	−0.990304	+	0.138916i	$0.955638\pi$
$458$	−16.6006	−	28.7531i	−0.775694	−	1.34354i
$459$		0			0
$460$	−51.9307	+	89.9466i	−2.42128	+	4.19378i
$461$	7.16885	+	23.9456i	0.333887	+	1.11526i	0.945913	+	0.324421i	$0.105170\pi$
$461$	7.16885	+	23.9456i	0.333887	+	1.11526i	−0.612026	+	0.790838i	$0.709645\pi$
$462$		0			0
$463$	−9.27264	+	6.09871i	−0.430936	+	0.283431i	−0.746389	−	0.665510i	$-0.768214\pi$
$463$	−9.27264	+	6.09871i	−0.430936	+	0.283431i	0.315453	+	0.948941i	$0.397844\pi$
$464$	−10.2844	−	1.20208i	−0.477443	−	0.0558050i
$465$		0			0
$466$	30.4203	−	15.2776i	1.40919	−	0.707723i
$467$	−2.57679	+	14.6137i	−0.119240	+	0.676242i	0.865324	+	0.501213i	$0.167113\pi$
$467$	−2.57679	+	14.6137i	−0.119240	+	0.676242i	−0.984563	+	0.175028i	$0.943998\pi$
$468$		0			0
$469$	−0.960392	−	5.44665i	−0.0443468	−	0.251503i
$470$	−34.8555	−	46.8190i	−1.60776	−	2.15960i
$471$		0			0
$472$	2.45737	+	2.60466i	0.113110	+	0.119889i
$473$	0.317190	−	1.05949i	0.0145844	−	0.0487153i
$474$		0			0
$475$	15.3460	−	1.79369i	0.704123	−	0.0823001i
$476$	5.58609	−	4.68728i	0.256038	−	0.214841i
$477$		0			0
$478$	−28.9439	−	24.2868i	−1.32386	−	1.11085i
$479$	22.5193	+	14.8112i	1.02893	+	0.676739i	0.947439	−	0.319935i	$-0.103661\pi$
$479$	22.5193	+	14.8112i	1.02893	+	0.676739i	0.0814921	+	0.996674i	$0.474031\pi$
$480$		0			0
$481$	9.93937	−	13.3509i	0.453196	−	0.608749i
$482$	−43.4833	−	21.8381i	−1.98061	−	0.994699i
$483$		0			0
$484$	−6.79821	−	1.61120i	−0.309009	−	0.0732366i
$485$	−11.9378			−0.542068
$486$		0			0
$487$	−0.903717			−0.0409513			−0.0204757	−	0.999790i	$-0.506518\pi$
$487$	−0.903717			−0.0409513			−0.0204757	+	0.999790i	$0.506518\pi$
$488$	−20.5041	−	4.85957i	−0.928179	−	0.219982i
$489$		0			0
$490$	42.9775	+	21.5841i	1.94153	+	0.975071i
$491$	−6.96650	+	9.35763i	−0.314394	+	0.422304i	−0.931029	−	0.364945i	$-0.881088\pi$
$491$	−6.96650	+	9.35763i	−0.314394	+	0.422304i	0.616636	+	0.787249i	$0.288495\pi$
$492$		0			0
$493$	−4.00682	−	2.63533i	−0.180458	−	0.118689i
$494$	45.3344	+	38.0401i	2.03969	+	1.71151i
$495$		0			0
$496$	24.6095	−	20.6498i	1.10500	−	0.927205i
$497$	1.33701	−	0.156274i	0.0599730	−	0.00700984i
$498$		0			0
$499$	−7.81408	+	26.1008i	−0.349806	+	1.16843i	0.584330	+	0.811517i	$0.301358\pi$
$499$	−7.81408	+	26.1008i	−0.349806	+	1.16843i	−0.934136	+	0.356918i	$0.883828\pi$
$500$	16.5606	+	17.5532i	0.740612	+	0.785003i
$501$		0			0
$502$	24.4523	+	32.8451i	1.09136	+	1.46595i
$503$	−2.64245	−	14.9861i	−0.117821	−	0.668197i	−0.985315	−	0.170749i	$-0.945381\pi$
$503$	−2.64245	−	14.9861i	−0.117821	−	0.668197i	0.867493	−	0.497449i	$-0.165730\pi$
$504$		0			0
$505$	−1.89899	+	10.7697i	−0.0845039	+	0.479245i
$506$	−57.6973	+	28.9767i	−2.56496	+	1.28817i
$507$		0			0
$508$	−70.3563	−	8.22347i	−3.12156	−	0.364858i
$509$	4.45422	−	2.92958i	0.197430	−	0.129851i	−0.446945	−	0.894561i	$-0.647488\pi$
$509$	4.45422	−	2.92958i	0.197430	−	0.129851i	0.644375	+	0.764710i	$0.277118\pi$
$510$		0			0
$511$	−0.817216	−	2.72969i	−0.0361515	−	0.120754i
$512$	−25.1908	+	43.6317i	−1.11328	+	1.92827i
$513$		0			0
$514$	27.9425	+	48.3979i	1.23249	+	2.13474i
$515$	3.52364	−	3.73484i	0.155270	−	0.164577i
$516$		0			0
$517$	−1.44976	−	24.8915i	−0.0637605	−	1.09473i
$518$	−1.97470	−	4.57787i	−0.0867634	−	0.201140i
$519$		0			0
$520$	4.64080	−	79.6794i	0.203512	−	3.49417i
$521$	−28.8252	+	10.4915i	−1.26286	+	0.459642i	−0.884727	−	0.466110i	$-0.845655\pi$
$521$	−28.8252	+	10.4915i	−1.26286	+	0.459642i	−0.378130	+	0.925752i	$0.623433\pi$
$522$		0			0
$523$	−10.5116	−	3.82592i	−0.459641	−	0.167296i	0.101813	−	0.994804i	$-0.467536\pi$
$523$	−10.5116	−	3.82592i	−0.459641	−	0.167296i	−0.561454	+	0.827508i	$0.689758\pi$
$524$	31.5951	−	73.2458i	1.38024	−	3.19976i
$525$		0			0
$526$	39.1250	−	9.27280i	1.70593	−	0.404313i
$527$	14.4782	−	3.43140i	0.630682	−	0.149474i
$528$		0			0
$529$	18.3364	−	42.5085i	0.797235	−	1.84820i
$530$	−4.66404	−	1.69757i	−0.202593	−	0.0737377i
$531$		0			0
$532$	11.4465	−	4.16617i	0.496267	−	0.180627i
$533$	−0.308706	+	5.30027i	−0.0133715	+	0.229580i
$534$		0			0
$535$	13.9542	+	32.3494i	0.603292	+	1.39859i
$536$	−3.53681	−	60.7247i	−0.152767	−	2.62291i
$537$		0			0
$538$	−34.1435	+	36.1900i	−1.47203	+	1.56026i
$539$	10.2720	+	17.7917i	0.442448	+	0.766343i
$540$		0			0
$541$	−15.8581	+	27.4670i	−0.681792	+	1.18090i	0.292642	+	0.956222i	$0.405466\pi$
$541$	−15.8581	+	27.4670i	−0.681792	+	1.18090i	−0.974434	+	0.224676i	$0.927868\pi$
$542$	−6.69063	−	22.3483i	−0.287387	−	0.959941i
$543$		0			0
$544$	11.0087	−	7.24056i	0.471996	−	0.310436i
$545$	27.3623	+	3.19820i	1.17207	+	0.136996i
$546$		0			0
$547$	36.5560	−	18.3591i	1.56302	−	0.784979i	0.563858	−	0.825871i	$-0.309316\pi$
$547$	36.5560	−	18.3591i	1.56302	−	0.784979i	0.999164	+	0.0408923i	$0.0130201\pi$
$548$	−3.75446	+	21.2926i	−0.160382	+	0.909574i
$549$		0			0
$550$	−4.12919	−	23.4178i	−0.176069	−	0.998538i
$551$	−4.78390	−	6.42589i	−0.203801	−	0.273752i
$552$		0			0
$553$	0.849475	+	0.900391i	0.0361234	+	0.0382885i
$554$	21.7984	−	72.8116i	0.926124	−	3.09347i
$555$		0			0
$556$	37.0712	−	4.33300i	1.57217	−	0.183760i
$557$	10.6022	−	8.89628i	0.449229	−	0.376948i	−0.389921	−	0.920848i	$-0.627498\pi$
$557$	10.6022	−	8.89628i	0.449229	−	0.376948i	0.839150	+	0.543901i	$0.183053\pi$
$558$		0			0
$559$	−1.28270	−	1.07631i	−0.0542523	−	0.0455231i
$560$	−8.50365	−	5.59294i	−0.359345	−	0.236345i
$561$		0			0
$562$	12.9868	−	17.4444i	0.547817	−	0.735846i
$563$	23.5042	+	11.8042i	0.990583	+	0.497490i	0.868851	−	0.495073i	$-0.164859\pi$
$563$	23.5042	+	11.8042i	0.990583	+	0.497490i	0.121732	+	0.992563i	$0.461155\pi$
$564$		0			0
$565$	−40.6880	−	9.64324i	−1.71176	−	0.405694i
$566$	72.8642			3.06271
$567$		0			0
$568$	14.8048			0.621196
$569$	5.56831	+	1.31971i	0.233436	+	0.0553253i	0.345669	−	0.938357i	$-0.387652\pi$
$569$	5.56831	+	1.31971i	0.233436	+	0.0553253i	−0.112233	+	0.993682i	$0.535800\pi$
$570$		0			0
$571$	2.83704	+	1.42481i	0.118726	+	0.0596266i	0.507171	−	0.861845i	$-0.330691\pi$
$571$	2.83704	+	1.42481i	0.118726	+	0.0596266i	−0.388445	+	0.921472i	$0.626988\pi$
$572$	37.3748	−	50.2031i	1.56272	−	2.09910i
$573$		0			0
$574$	1.32869	+	0.873891i	0.0554583	+	0.0364755i
$575$	19.5502	+	16.4046i	0.815301	+	0.684119i
$576$		0			0
$577$	15.3813	−	12.9064i	0.640332	−	0.537302i	−0.263788	−	0.964581i	$-0.584972\pi$
$577$	15.3813	−	12.9064i	0.640332	−	0.537302i	0.904120	+	0.427278i	$0.140528\pi$
$578$	−19.8356	+	2.31845i	−0.825051	+	0.0964347i
$579$		0			0
$580$	−5.68835	+	19.0004i	−0.236196	+	0.788950i
$581$	1.15004	+	1.21898i	0.0477119	+	0.0505716i
$582$		0			0
$583$	−1.26611	−	1.70068i	−0.0524368	−	0.0704348i
$584$	−5.44184	−	30.8622i	−0.225185	−	1.27709i
$585$		0			0
$586$	4.01016	−	22.7428i	0.165658	−	0.939495i
$587$	28.8186	−	14.4733i	1.18947	−	0.597375i	0.259764	−	0.965672i	$-0.416355\pi$
$587$	28.8186	−	14.4733i	1.18947	−	0.597375i	0.929708	+	0.368297i	$0.120059\pi$
$588$		0			0
$589$	24.6870	+	2.88550i	1.01721	+	0.118895i
$590$	3.55043	−	2.33516i	0.146169	−	0.0961369i
$591$		0			0
$592$	−6.69514	−	22.3633i	−0.275169	−	0.919127i
$593$	7.37965	−	12.7819i	0.303046	−	0.524891i	−0.673779	−	0.738933i	$-0.735330\pi$
$593$	7.37965	−	12.7819i	0.303046	−	0.524891i	0.976824	+	0.214043i	$0.0686632\pi$
$594$		0			0
$595$	−2.35705	−	4.08253i	−0.0966296	−	0.167367i
$596$	−31.9385	+	33.8528i	−1.30825	+	1.38667i
$597$		0			0
$598$	5.68384	+	97.5877i	0.232429	+	3.99066i
$599$	−0.125919	−	0.291913i	−0.00514491	−	0.0119272i	0.915624	−	0.402035i	$-0.131697\pi$
$599$	−0.125919	−	0.291913i	−0.00514491	−	0.0119272i	−0.920769	+	0.390108i	$0.872438\pi$
$600$		0			0
$601$	0.562808	−	9.66304i	0.0229574	−	0.394163i	−0.967183	−	0.254082i	$-0.918227\pi$
$601$	0.562808	−	9.66304i	0.0229574	−	0.394163i	0.990140	−	0.140081i	$-0.0447364\pi$
$602$	−0.471308	+	0.171542i	−0.0192091	+	0.00699154i
$603$		0			0
$604$	−53.8351	−	19.5944i	−2.19052	−	0.797283i
$605$	−1.78891	+	4.14717i	−0.0727297	+	0.168606i
$606$		0			0
$607$	6.22786	−	1.47603i	0.252781	−	0.0599102i	−0.102272	−	0.994757i	$-0.532611\pi$
$607$	6.22786	−	1.47603i	0.252781	−	0.0599102i	0.355053	+	0.934846i	$0.384463\pi$
$608$	21.4172	−	5.07596i	0.868581	−	0.205857i
$609$		0			0
$610$	−9.90466	+	22.9616i	−0.401028	+	0.929687i
$611$	−35.4737	−	12.9114i	−1.43511	−	0.522338i
$612$		0			0
$613$	4.35986	−	1.58686i	0.176093	−	0.0640927i	−0.252469	−	0.967605i	$-0.581243\pi$
$613$	4.35986	−	1.58686i	0.176093	−	0.0640927i	0.428562	+	0.903512i	$0.359020\pi$
$614$	−4.94217	+	84.8537i	−0.199450	+	3.42442i
$615$		0			0
$616$	−4.04499	−	9.37735i	−0.162977	−	0.377824i
$617$	1.14923	+	19.7316i	0.0462664	+	0.794363i	0.939029	+	0.343837i	$0.111727\pi$
$617$	1.14923	+	19.7316i	0.0462664	+	0.794363i	−0.892763	+	0.450527i	$0.851236\pi$
$618$		0			0
$619$	−0.277120	+	0.293730i	−0.0111384	+	0.0118060i	−0.732919	−	0.680316i	$-0.761843\pi$
$619$	−0.277120	+	0.293730i	−0.0111384	+	0.0118060i	0.721780	+	0.692122i	$0.243324\pi$
$620$	−30.7677	−	53.2912i	−1.23566	−	2.14023i
$621$		0			0
$622$	26.0740	−	45.1615i	1.04547	−	1.81081i
$623$	−1.82251	−	6.08760i	−0.0730172	−	0.243895i
$624$		0			0
$625$	25.8415	−	16.9962i	1.03366	−	0.679849i
$626$	−84.9230	−	9.92608i	−3.39421	−	0.396726i
$627$		0			0
$628$	−86.9506	+	43.6682i	−3.46971	+	1.74255i
$629$	1.87750	−	10.6478i	0.0748607	−	0.424556i
$630$		0			0
$631$	5.92526	+	33.6038i	0.235881	+	1.33775i	0.840750	+	0.541423i	$0.182114\pi$
$631$	5.92526	+	33.6038i	0.235881	+	1.33775i	−0.604869	+	0.796325i	$0.706775\pi$
$632$	8.12991	+	10.9204i	0.323390	+	0.434389i
$633$		0			0
$634$	−14.5952	−	15.4700i	−0.579650	−	0.614393i
$635$	−13.1334	+	43.8688i	−0.521185	+	1.74088i
$636$		0			0
$637$	30.8940	−	3.61099i	1.22407	−	0.143073i
$638$	−9.44493	+	7.92524i	−0.373928	+	0.313763i
$639$		0			0
$640$	29.9191	+	25.1051i	1.18266	+	0.992367i
$641$	−23.5687	−	15.5014i	−0.930908	−	0.612268i	−0.00911872	−	0.999958i	$-0.502903\pi$
$641$	−23.5687	−	15.5014i	−0.930908	−	0.612268i	−0.921790	+	0.387690i	$0.873273\pi$
$642$		0			0
$643$	19.3475	−	25.9882i	0.762991	−	1.02487i	−0.235602	−	0.971850i	$-0.575706\pi$
$643$	19.3475	−	25.9882i	0.762991	−	1.02487i	0.998593	−	0.0530250i	$-0.0168863\pi$
$644$	17.9805	+	9.03013i	0.708530	+	0.355837i
$645$		0			0
$646$	37.4065	+	8.86550i	1.47174	+	0.348808i
$647$	3.64502			0.143300			0.0716502	−	0.997430i	$-0.477173\pi$
$647$	3.64502			0.143300			0.0716502	+	0.997430i	$0.477173\pi$
$648$		0			0
$649$	1.81529			0.0712563
$650$	−35.0317	−	8.30267i	−1.37406	−	0.325658i
$651$		0			0
$652$	−67.5276	−	33.9136i	−2.64459	−	1.32816i
$653$	−23.6422	+	31.7570i	−0.925192	+	1.24275i	0.0446469	+	0.999003i	$0.485784\pi$
$653$	−23.6422	+	31.7570i	−0.925192	+	1.24275i	−0.969839	+	0.243746i	$0.921624\pi$
$654$		0			0
$655$	−43.0847	−	28.3372i	−1.68346	−	1.10723i
$656$	5.70418	+	4.78638i	0.222711	+	0.186877i
$657$		0			0
$658$	−8.66210	+	7.26837i	−0.337684	+	0.283350i
$659$	−20.8347	+	2.43523i	−0.811605	+	0.0948630i	−0.511764	−	0.859126i	$-0.671008\pi$
$659$	−20.8347	+	2.43523i	−0.811605	+	0.0948630i	−0.299841	+	0.953989i	$0.596934\pi$
$660$		0			0
$661$	9.28632	−	31.0185i	0.361196	−	1.20648i	−0.563610	−	0.826041i	$-0.690588\pi$
$661$	9.28632	−	31.0185i	0.361196	−	1.20648i	0.924806	−	0.380438i	$-0.124227\pi$
$662$	11.2895	+	11.9661i	0.438777	+	0.465077i
$663$		0			0
$664$	11.0065	+	14.7843i	0.427136	+	0.573743i
$665$	−1.36742	−	7.75501i	−0.0530261	−	0.300726i
$666$		0			0
$667$	2.29783	−	13.0317i	0.0889725	−	0.504588i
$668$	46.2229	−	23.2140i	1.78842	−	0.898176i
$669$		0			0
$670$	−71.6972	−	8.38020i	−2.76991	−	0.323755i
$671$	−8.92486	+	5.86997i	−0.344540	+	0.226608i
$672$		0			0
$673$	−12.0711	−	40.3204i	−0.465308	−	1.55424i	−0.792860	−	0.609403i	$-0.791409\pi$
$673$	−12.0711	−	40.3204i	−0.465308	−	1.55424i	0.327553	−	0.944833i	$-0.393776\pi$
$674$	4.32867	−	7.49748i	0.166734	−	0.288792i
$675$		0			0
$676$	−18.8241	−	32.6043i	−0.724005	−	1.25401i
$677$	−4.44446	+	4.71086i	−0.170815	+	0.181053i	−0.807126	−	0.590380i	$-0.798978\pi$
$677$	−4.44446	+	4.71086i	−0.170815	+	0.181053i	0.636311	+	0.771433i	$0.280459\pi$
$678$		0			0
$679$	0.134470	+	2.30875i	0.00516047	+	0.0886018i
$680$	−20.5354	−	47.6065i	−0.787498	−	1.82563i
$681$		0			0
$682$	2.22422	−	38.1884i	0.0851699	−	1.46231i
$683$	−7.47167	+	2.71946i	−0.285895	+	0.104057i	−0.480987	−	0.876728i	$-0.659722\pi$
$683$	−7.47167	+	2.71946i	−0.285895	+	0.104057i	0.195092	+	0.980785i	$0.437499\pi$
$684$		0			0
$685$	13.1343	+	4.78050i	0.501836	+	0.182654i
$686$	7.54725	−	17.4965i	0.288155	−	0.668019i
$687$		0			0
$688$	−2.28512	+	0.541583i	−0.0871194	+	0.0206477i
$689$	−3.12354	+	0.740294i	−0.118998	+	0.0282029i
$690$		0			0
$691$	−9.30311	+	21.5670i	−0.353907	+	0.820448i	0.644531	+	0.764578i	$0.277053\pi$
$691$	−9.30311	+	21.5670i	−0.353907	+	0.820448i	−0.998438	+	0.0558703i	$0.982207\pi$
$692$	49.3786	+	17.9724i	1.87709	+	0.683206i
$693$		0			0
$694$	−60.2157	+	21.9167i	−2.28576	+	0.831948i
$695$	1.40294	−	24.0876i	0.0532166	−	0.913693i
$696$		0			0
$697$	1.36602	+	3.16678i	0.0517415	+	0.119950i
$698$	1.54193	+	26.4739i	0.0583628	+	1.00205i
$699$		0			0
$700$	−5.08531	+	5.39011i	−0.192207	+	0.203727i
$701$	1.42901	+	2.47512i	0.0539731	+	0.0934841i	0.891750	−	0.452529i	$-0.149478\pi$
$701$	1.42901	+	2.47512i	0.0539731	+	0.0934841i	−0.837777	+	0.546013i	$0.816145\pi$
$702$		0			0
$703$	9.03048	−	15.6413i	0.340591	−	0.589921i
$704$	1.74568	+	5.83097i	0.0657927	+	0.219763i
$705$		0			0
$706$	24.0673	−	15.8293i	0.905784	−	0.595743i
$707$	2.10423	+	0.245949i	0.0791378	+	0.00924988i
$708$		0			0
$709$	39.8196	−	19.9981i	1.49546	−	0.751046i	0.501957	−	0.864893i	$-0.332614\pi$
$709$	39.8196	−	19.9981i	1.49546	−	0.751046i	0.993498	+	0.113847i	$0.0363172\pi$
$710$	3.05085	−	17.3023i	0.114497	−	0.649342i
$711$		0			0
$712$	−12.1361	−	68.8271i	−0.454818	−	2.57940i
$713$	24.5166	+	32.9316i	0.918155	+	1.23330i
$714$		0			0
$715$	−27.7659	−	29.4301i	−1.03838	−	1.10062i
$716$	4.42089	−	14.7668i	0.165217	−	0.551862i
$717$		0			0
$718$	−41.9824	+	4.90704i	−1.56677	+	0.183129i
$719$	−13.1209	+	11.0097i	−0.489327	+	0.410594i	−0.853785	−	0.520626i	$-0.825699\pi$
$719$	−13.1209	+	11.0097i	−0.489327	+	0.410594i	0.364458	+	0.931220i	$0.381254\pi$
$720$		0			0
$721$	−0.762003	−	0.639396i	−0.0283785	−	0.0238124i
$722$	13.5143	+	8.88850i	0.502951	+	0.330796i
$723$		0			0
$724$	58.1299	−	78.0820i	2.16038	−	2.90189i
$725$	4.35517	+	2.18725i	0.161747	+	0.0812325i
$726$		0			0
$727$	7.66719	+	1.81716i	0.284360	+	0.0673947i	0.370321	−	0.928904i	$-0.379248\pi$
$727$	7.66719	+	1.81716i	0.284360	+	0.0673947i	−0.0859605	+	0.996299i	$0.527396\pi$
$728$	−15.4621			−0.573065
$729$		0			0
$730$	−37.1898			−1.37645
$731$	−1.05838	−	0.250841i	−0.0391457	−	0.00927769i
$732$		0			0
$733$	12.4489	+	6.25207i	0.459810	+	0.230925i	0.663598	−	0.748090i	$-0.269029\pi$
$733$	12.4489	+	6.25207i	0.459810	+	0.230925i	−0.203787	+	0.979015i	$0.565325\pi$
$734$	33.2530	−	44.6665i	1.22739	−	1.64867i
$735$		0			0
$736$	30.3757	+	19.9784i	1.11966	+	0.736413i
$737$	−23.6215	−	19.8208i	−0.870109	−	0.730108i
$738$		0			0
$739$	−14.0426	+	11.7832i	−0.516566	+	0.433450i	−0.863433	−	0.504464i	$-0.831690\pi$
$739$	−14.0426	+	11.7832i	−0.516566	+	0.433450i	0.346867	+	0.937914i	$0.387246\pi$
$740$	−44.4125	+	5.19107i	−1.63264	+	0.190828i
$741$		0			0
$742$	−0.275771	+	0.921138i	−0.0101239	+	0.0338161i
$743$	−2.97495	−	3.15327i	−0.109140	−	0.115682i	0.670500	−	0.741910i	$-0.266080\pi$
$743$	−2.97495	−	3.15327i	−0.109140	−	0.115682i	−0.779640	+	0.626227i	$0.784598\pi$
$744$		0			0
$745$	17.9669	+	24.1337i	0.658255	+	0.884190i
$746$	13.3532	+	75.7298i	0.488896	+	2.77266i
$747$		0			0
$748$	7.05991	−	40.0387i	0.258136	−	1.46396i
$749$	6.09915	−	3.06311i	0.222858	−	0.111923i
$750$		0			0
$751$	−18.1620	−	2.12283i	−0.662740	−	0.0774632i	−0.221928	−	0.975063i	$-0.571235\pi$
$751$	−18.1620	−	2.12283i	−0.662740	−	0.0774632i	−0.440811	+	0.897600i	$0.645309\pi$
$752$	−44.2351	+	29.0939i	−1.61309	+	1.06094i
$753$		0			0
$754$	5.35381	+	17.8830i	0.194974	+	0.651260i
$755$	−18.5180	+	32.0742i	−0.673940	+	1.16730i
$756$		0			0
$757$	3.24094	+	5.61347i	0.117794	+	0.204025i	0.918893	−	0.394507i	$-0.129084\pi$
$757$	3.24094	+	5.61347i	0.117794	+	0.204025i	−0.801099	+	0.598532i	$0.795751\pi$
$758$	−21.3433	+	22.6226i	−0.775224	+	0.821689i
$759$		0			0
$760$	−5.03575	−	86.4605i	−0.182666	−	3.13625i
$761$	12.0226	+	27.8715i	0.435818	+	1.01034i	0.984671	+	0.174421i	$0.0558053\pi$
$761$	12.0226	+	27.8715i	0.435818	+	1.01034i	−0.548853	+	0.835919i	$0.684935\pi$
$762$		0			0
$763$	0.310312	−	5.32786i	0.0112341	−	0.192881i
$764$	−10.8022	+	3.93167i	−0.390809	+	0.142243i
$765$		0			0
$766$	−17.2645	−	6.28375i	−0.623791	−	0.227041i
$767$	1.08859	−	2.52363i	0.0393066	−	0.0911228i
$768$		0			0
$769$	−47.7208	+	11.3100i	−1.72086	+	0.407851i	−0.968123	−	0.250474i	$-0.919414\pi$
$769$	−47.7208	+	11.3100i	−1.72086	+	0.407851i	−0.752734	+	0.658325i	$0.771265\pi$
$770$	−11.7928	+	2.79494i	−0.424982	+	0.100723i
$771$		0			0
$772$	21.4439	−	49.7125i	0.771782	−	1.78919i
$773$	37.0514	+	13.4856i	1.33265	+	0.485044i	0.907489	−	0.420075i	$-0.137996\pi$
$773$	37.0514	+	13.4856i	1.33265	+	0.485044i	0.425158	+	0.905119i	$0.360219\pi$
$774$		0			0
$775$	−14.2087	+	5.17155i	−0.510392	+	0.185768i
$776$	−1.47893	+	25.3922i	−0.0530904	+	0.911526i
$777$		0			0
$778$	19.2180	+	44.5523i	0.688999	+	1.59728i
$779$	0.334978	+	5.75135i	0.0120018	+	0.206063i
$780$		0			0
$781$	5.15030	−	5.45900i	0.184292	−	0.195338i
$782$	31.7498	+	54.9922i	1.13537	+	1.96652i
$783$		0			0
$784$	21.8121	−	37.7797i	0.779003	−	1.34927i
$785$	18.0403	+	60.2586i	0.643884	+	2.15072i
$786$		0			0
$787$	1.03387	−	0.679987i	0.0368535	−	0.0242389i	−0.530949	−	0.847404i	$-0.678164\pi$
$787$	1.03387	−	0.679987i	0.0368535	−	0.0242389i	0.567802	+	0.823165i	$0.307794\pi$
$788$	119.015	+	13.9109i	4.23975	+	0.495555i
$789$		0			0
$790$	14.4379	−	7.25097i	0.513677	−	0.257978i
$791$	−1.40667	+	7.97762i	−0.0500154	+	0.283652i
$792$		0			0
$793$	2.80844	+	15.9275i	0.0997308	+	0.565601i
$794$	40.4731	+	54.3648i	1.43634	+	1.92933i
$795$		0			0
$796$	−2.30651	−	2.44476i	−0.0817522	−	0.0866523i
$797$	−7.58178	+	25.3249i	−0.268560	+	0.897054i	0.712223	+	0.701953i	$0.247688\pi$
$797$	−7.58178	+	25.3249i	−0.268560	+	0.897054i	−0.980783	+	0.195101i	$0.937497\pi$
$798$		0			0
$799$	−24.3564	+	2.84686i	−0.861668	+	0.100715i
$800$	−10.2574	+	8.60699i	−0.362654	+	0.304303i
$801$		0			0
$802$	40.2685	+	33.7893i	1.42193	+	1.19314i
$803$	−13.2730	−	8.72977i	−0.468393	−	0.308067i
$804$		0			0
$805$	7.76742	−	10.4335i	0.273766	−	0.367731i
$806$	−51.7560	−	25.9928i	−1.82303	−	0.915559i
$807$		0			0
$808$	22.6723	+	5.37343i	0.797608	+	0.189037i
$809$	51.6224			1.81495			0.907473	−	0.420110i	$-0.138008\pi$
$809$	51.6224			1.81495			0.907473	+	0.420110i	$0.138008\pi$
$810$		0			0
$811$	29.2739			1.02795			0.513973	−	0.857806i	$-0.328173\pi$
$811$	29.2739			1.02795			0.513973	+	0.857806i	$0.328173\pi$
$812$	3.73872	+	0.886094i	0.131203	+	0.0310958i
$813$		0			0
$814$	−24.8401	−	12.4752i	−0.870644	−	0.437254i
$815$	−29.1714	+	39.1840i	−1.02183	+	1.37255i
$816$		0			0
$817$	−1.51803	−	0.998427i	−0.0531093	−	0.0349305i
$818$	3.26200	+	2.73714i	0.114053	+	0.0957019i
$819$		0			0
$820$	10.9262	−	9.16818i	0.381560	−	0.320167i
$821$	−14.4247	+	1.68601i	−0.503426	+	0.0588421i	−0.364016	−	0.931393i	$-0.618595\pi$
$821$	−14.4247	+	1.68601i	−0.503426	+	0.0588421i	−0.139410	+	0.990235i	$0.544521\pi$
$822$		0			0
$823$	−9.48427	+	31.6797i	−0.330601	+	1.10428i	0.617568	+	0.786517i	$0.288118\pi$
$823$	−9.48427	+	31.6797i	−0.330601	+	1.10428i	−0.948169	+	0.317766i	$0.897067\pi$
$824$	−7.50762	−	7.95761i	−0.261540	−	0.277217i
$825$		0			0
$826$	−0.491608	−	0.660344i	−0.0171052	−	0.0229763i
$827$	−1.95177	−	11.0690i	−0.0678697	−	0.384908i	−0.999755	−	0.0221541i	$-0.992948\pi$
$827$	−1.95177	−	11.0690i	−0.0678697	−	0.384908i	0.931885	−	0.362754i	$-0.118164\pi$
$828$		0			0
$829$	4.25374	−	24.1242i	0.147739	−	0.837867i	−0.817389	−	0.576086i	$-0.804579\pi$
$829$	4.25374	−	24.1242i	0.147739	−	0.837867i	0.965127	−	0.261781i	$-0.0843097\pi$
$830$	19.5464	−	9.81658i	0.678466	−	0.340739i
$831$		0			0
$832$	9.15309	+	1.06984i	0.317326	+	0.0370901i
$833$	16.8811	−	11.1029i	0.584896	−	0.384692i
$834$		0			0
$835$	−9.59018	−	32.0334i	−0.331882	−	1.10856i
$836$	33.9571	−	58.8154i	1.17443	−	2.03417i
$837$		0			0
$838$	9.64135	+	16.6993i	0.333055	+	0.576868i
$839$	−0.246108	+	0.260860i	−0.00849661	+	0.00900588i	−0.731608	−	0.681726i	$-0.761230\pi$
$839$	−0.246108	+	0.260860i	−0.00849661	+	0.00900588i	0.723111	+	0.690731i	$0.242711\pi$
$840$		0			0
$841$	1.53927	+	26.4283i	0.0530783	+	0.911319i
$842$	32.5347	+	75.4238i	1.12122	+	2.59928i
$843$		0			0
$844$	−4.78742	+	82.1968i	−0.164790	+	2.82933i
$845$	−22.8705	+	8.32418i	−0.786769	+	0.286360i
$846$		0			0
$847$	0.822205	+	0.299258i	0.0282513	+	0.0102826i
$848$	−1.78322	+	4.13396i	−0.0612359	+	0.141961i
$849$		0			0
$850$	−22.7563	+	5.39334i	−0.780534	+	0.184990i
$851$	29.0289	−	6.87997i	0.995097	−	0.235842i
$852$		0			0
$853$	−20.5035	+	47.5324i	−0.702026	+	1.62748i	0.0743682	+	0.997231i	$0.476306\pi$
$853$	−20.5035	+	47.5324i	−0.702026	+	1.62748i	−0.776394	+	0.630248i	$0.782953\pi$
$854$	4.55230	+	1.65690i	0.155776	+	0.0566980i
$855$		0			0
$856$	70.5372	−	25.6734i	2.41091	−	0.877500i
$857$	0.810865	−	13.9220i	0.0276986	−	0.475567i	−0.955727	−	0.294255i	$-0.904929\pi$
$857$	0.810865	−	13.9220i	0.0276986	−	0.475567i	0.983426	−	0.181312i	$-0.0580344\pi$
$858$		0			0
$859$	10.7959	+	25.0277i	0.368351	+	0.853933i	0.997084	+	0.0763121i	$0.0243145\pi$
$859$	10.7959	+	25.0277i	0.368351	+	0.853933i	−0.628733	+	0.777621i	$0.716426\pi$
$860$	0.261555	+	4.49073i	0.00891895	+	0.153133i
$861$		0			0
$862$	16.0505	−	17.0125i	0.546682	−	0.579449i
$863$	22.6402	+	39.2140i	0.770682	+	1.33486i	0.937190	+	0.348820i	$0.113417\pi$
$863$	22.6402	+	39.2140i	0.770682	+	1.33486i	−0.166508	+	0.986040i	$0.553249\pi$
$864$		0			0
$865$	16.9851	−	29.4191i	0.577511	−	1.00028i
$866$	−5.48306	−	18.3147i	−0.186322	−	0.622359i
$867$		0			0
$868$	−9.95986	+	6.55070i	−0.338060	+	0.222345i
$869$	6.85492	+	0.801225i	0.232537	+	0.0271797i
$870$		0			0
$871$	−41.7202	+	20.9527i	−1.41364	+	0.709955i
$872$	10.1925	−	57.8045i	0.345161	−	1.95751i
$873$		0			0
$874$	18.4193	+	104.461i	0.623041	+	3.53344i
$875$	−1.80477	−	2.42422i	−0.0610123	−	0.0819537i
$876$		0			0
$877$	19.6790	+	20.8585i	0.664511	+	0.704341i	0.968690	−	0.248274i	$-0.0798635\pi$
$877$	19.6790	+	20.8585i	0.664511	+	0.704341i	−0.304179	+	0.952615i	$0.598382\pi$
$878$	15.6473	−	52.2655i	0.528069	−	1.76387i
$879$		0			0
$880$	−56.3630	+	6.58789i	−1.90000	+	0.222078i
$881$	0.153779	−	0.129036i	0.00518096	−	0.00434734i	−0.640193	−	0.768214i	$-0.721146\pi$
$881$	0.153779	−	0.129036i	0.00518096	−	0.00434734i	0.645374	+	0.763866i	$0.276701\pi$
$882$		0			0
$883$	−20.9026	−	17.5394i	−0.703428	−	0.590247i	0.219318	−	0.975653i	$-0.429617\pi$
$883$	−20.9026	−	17.5394i	−0.703428	−	0.590247i	−0.922747	+	0.385407i	$0.874061\pi$
$884$	−51.4284	−	33.8250i	−1.72973	−	1.13766i
$885$		0			0
$886$	−20.0871	+	26.9816i	−0.674839	+	0.906466i
$887$	14.2246	+	7.14384i	0.477614	+	0.239867i	0.671284	−	0.741200i	$-0.265743\pi$
$887$	14.2246	+	7.14384i	0.477614	+	0.239867i	−0.193671	+	0.981067i	$0.562039\pi$
$888$		0			0
$889$	8.63208	+	2.04584i	0.289511	+	0.0686153i
$890$	−82.9385			−2.78010
$891$		0			0
$892$	−12.1420			−0.406543
$893$	−39.8588	−	9.44672i	−1.33383	−	0.316122i
$894$		0			0
$895$	−8.90492	−	4.47222i	−0.297659	−	0.149490i
$896$	4.51827	−	6.06909i	0.150945	−	0.202754i
$897$		0			0
$898$	39.1932	+	25.7778i	1.30789	+	0.860215i
$899$	6.00584	+	5.03950i	0.200306	+	0.168077i
$900$		0			0
$901$	−1.59738	+	1.34036i	−0.0532165	+	0.0446539i
$902$	8.80666	−	1.02935i	0.293230	−	0.0342736i
$903$		0			0
$904$	−25.5522	+	85.3503i	−0.849854	+	2.83871i
$905$	−43.1849	−	45.7733i	−1.43551	−	1.52156i
$906$		0			0
$907$	−3.55386	−	4.77366i	−0.118004	−	0.158507i	0.739196	−	0.673490i	$-0.235206\pi$
$907$	−3.55386	−	4.77366i	−0.118004	−	0.158507i	−0.857200	+	0.514983i	$0.827798\pi$
$908$	5.10604	+	28.9578i	0.169450	+	0.960999i
$909$		0			0
$910$	−3.18631	+	18.0705i	−0.105625	+	0.599030i
$911$	14.1527	−	7.10775i	0.468900	−	0.235490i	−0.198629	−	0.980075i	$-0.563649\pi$
$911$	14.1527	−	7.10775i	0.468900	−	0.235490i	0.667528	+	0.744585i	$0.267352\pi$
$912$		0			0
$913$	9.28039	+	1.08472i	0.307136	+	0.0358991i
$914$	70.5071	−	46.3733i	2.33217	−	1.53389i
$915$		0			0
$916$	16.5447	+	55.2631i	0.546652	+	1.82594i
$917$	−4.99506	+	8.65170i	−0.164951	+	0.285704i
$918$		0			0
$919$	−8.54952	−	14.8082i	−0.282023	−	0.488477i	0.689860	−	0.723943i	$-0.257672\pi$
$919$	−8.54952	−	14.8082i	−0.282023	−	0.488477i	−0.971883	+	0.235465i	$0.924339\pi$
$920$	98.1718	−	104.056i	3.23663	−	3.43062i
$921$		0			0
$922$	−3.67481	−	63.0941i	−0.121024	−	2.07789i
$923$	−4.50062	−	10.4336i	−0.148140	−	0.343427i
$924$		0			0
$925$	−0.638861	+	10.9688i	−0.0210056	+	0.360653i
$926$	26.3699	−	9.59784i	0.866567	−	0.315405i
$927$		0			0
$928$	6.52409	+	2.37457i	0.214164	+	0.0779492i
$929$	−11.2496	+	26.0796i	−0.369089	+	0.855644i	0.627914	+	0.778282i	$0.283909\pi$
$929$	−11.2496	+	26.0796i	−0.369089	+	0.855644i	−0.997003	+	0.0773615i	$0.975350\pi$
$930$		0			0
$931$	32.8417	−	7.78363i	1.07634	−	0.255098i
$932$	−57.5517	+	13.6400i	−1.88517	+	0.446793i
$933$		0			0
$934$	14.8611	−	34.4518i	0.486269	−	1.12730i
$935$	−24.6979	−	8.98929i	−0.807707	−	0.293981i
$936$		0			0
$937$	−28.6531	+	10.4289i	−0.936056	+	0.340696i	−0.764607	−	0.644497i	$-0.777067\pi$
$937$	−28.6531	+	10.4289i	−0.936056	+	0.340696i	−0.171448	+	0.985193i	$0.554845\pi$
$938$	−0.813107	+	13.9605i	−0.0265489	+	0.455827i
$939$		0			0
$940$	40.1684	+	93.1209i	1.31015	+	3.03727i
$941$	0.720775	+	12.3752i	0.0234966	+	0.403421i	0.989466	+	0.144765i	$0.0462426\pi$
$941$	0.720775	+	12.3752i	0.0234966	+	0.403421i	−0.965970	+	0.258656i	$0.916720\pi$
$942$		0			0
$943$	−6.53038	+	6.92180i	−0.212658	+	0.225405i
$944$	−1.92733	−	3.33824i	−0.0627293	−	0.108650i
$945$		0			0
$946$	−1.39818	+	2.42173i	−0.0454589	+	0.0787371i
$947$	1.46419	+	4.89074i	0.0475798	+	0.158928i	0.978478	−	0.206351i	$-0.0661589\pi$
$947$	1.46419	+	4.89074i	0.0475798	+	0.158928i	−0.930898	+	0.365279i	$0.880974\pi$
$948$		0			0
$949$	−20.0957	+	13.2171i	−0.652333	+	0.429046i
$950$	−38.8020	−	4.53530i	−1.25890	−	0.147145i
$951$		0			0
$952$	−8.97570	+	4.50776i	−0.290904	+	0.146097i
$953$	−1.39463	+	7.90935i	−0.0451766	+	0.256209i	−0.999029	−	0.0440683i	$-0.985968\pi$
$953$	−1.39463	+	7.90935i	−0.0451766	+	0.256209i	0.953852	+	0.300277i	$0.0970792\pi$
$954$		0			0
$955$	1.29045	+	7.31849i	0.0417579	+	0.236821i
$956$	39.2025	+	52.6581i	1.26790	+	1.70309i
$957$		0			0
$958$	−46.7681	−	49.5713i	−1.51101	−	1.60158i
$959$	0.776593	−	2.59400i	0.0250775	−	0.0837647i
$960$		0			0
$961$	6.63046	−	0.774990i	0.213886	−	0.0249997i
$962$	−32.2390	+	27.0518i	−1.03943	+	0.872184i
$963$		0			0
$964$	64.7646	+	54.3440i	2.08593	+	1.75030i
$965$	−29.2419	−	19.2327i	−0.941331	−	0.619123i
$966$		0			0
$967$	0.943379	−	1.26718i	0.0303370	−	0.0407497i	−0.786696	−	0.617341i	$-0.788210\pi$
$967$	0.943379	−	1.26718i	0.0303370	−	0.0407497i	0.817033	+	0.576591i	$0.195617\pi$
$968$	8.59956	+	4.31886i	0.276400	+	0.138813i
$969$		0			0
$970$	29.3708	+	6.96102i	0.943041	+	0.223505i
$971$	−2.19584			−0.0704678			−0.0352339	−	0.999379i	$-0.511218\pi$
$971$	−2.19584			−0.0704678			−0.0352339	+	0.999379i	$0.511218\pi$
$972$		0			0
$973$	−4.67430			−0.149851
$974$	2.22343	+	0.526963i	0.0712434	+	0.0168850i
$975$		0			0
$976$	20.2703	+	10.1801i	0.648838	+	0.325858i
$977$	26.1116	−	35.0740i	0.835384	−	1.12212i	−0.155558	−	0.987827i	$-0.549718\pi$
$977$	26.1116	−	35.0740i	0.835384	−	1.12212i	0.990942	−	0.134289i	$-0.0428750\pi$
$978$		0			0
$979$	−29.6006	−	19.4686i	−0.946039	−	0.622220i
$980$	−64.0114	−	53.7119i	−2.04477	−	1.71576i
$981$		0			0
$982$	22.5963	−	18.9606i	0.721077	−	0.605055i
$983$	−50.2996	+	5.87918i	−1.60431	+	0.187517i	−0.870615	−	0.491964i	$-0.836279\pi$
$983$	−50.2996	+	5.87918i	−1.60431	+	0.187517i	−0.733693	+	0.679481i	$0.762205\pi$
$984$		0			0
$985$	22.2166	−	74.2088i	0.707881	−	2.36449i
$986$	8.32139	+	8.82016i	0.265007	+	0.280891i
$987$		0			0
$988$	−61.4023	−	82.4776i	−1.95347	−	2.62396i
$989$	−0.521157	−	2.95563i	−0.0165718	−	0.0939834i
$990$		0			0
$991$	−9.22768	+	52.3328i	−0.293127	+	1.66241i	0.381592	+	0.924331i	$0.375376\pi$
$991$	−9.22768	+	52.3328i	−0.293127	+	1.66241i	−0.674719	+	0.738075i	$0.735735\pi$
$992$	−19.2493	+	9.66738i	−0.611167	+	0.306940i
$993$		0			0
$994$	−3.38059	−	0.395135i	−0.107226	−	0.0125329i
$995$	−1.81537	+	1.19398i	−0.0575509	+	0.0378519i
$996$		0			0
$997$	7.25184	+	24.2228i	0.229668	+	0.767145i	0.992681	+	0.120762i	$0.0385338\pi$
$997$	7.25184	+	24.2228i	0.229668	+	0.767145i	−0.763013	+	0.646383i	$0.776281\pi$
$998$	34.4447	−	59.6600i	1.09033	−	1.88850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.136.1		144
3.2	odd	2		729.2.g.c.136.8		144
9.2	odd	6		729.2.g.d.379.1		144
9.4	even	3		243.2.g.a.127.8		144
9.5	odd	6		81.2.g.a.70.1	yes	144
9.7	even	3		729.2.g.a.379.8		144
81.5	odd	54		729.2.g.c.595.8		144
81.20	odd	54		6561.2.a.c.1.69		72
81.22	even	27		729.2.g.a.352.8		144
81.32	odd	54		81.2.g.a.22.1	✓	144
81.49	even	27		243.2.g.a.199.8		144
81.59	odd	54		729.2.g.d.352.1		144
81.61	even	27		6561.2.a.d.1.4		72
81.76	even	27	inner	729.2.g.b.595.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.1	✓	144	81.32	odd	54
81.2.g.a.70.1	yes	144	9.5	odd	6
243.2.g.a.127.8		144	9.4	even	3
243.2.g.a.199.8		144	81.49	even	27
729.2.g.a.352.8		144	81.22	even	27
729.2.g.a.379.8		144	9.7	even	3
729.2.g.b.136.1		144	1.1	even	1	trivial
729.2.g.b.595.1		144	81.76	even	27	inner
729.2.g.c.136.8		144	3.2	odd	2
729.2.g.c.595.8		144	81.5	odd	54
729.2.g.d.352.1		144	81.59	odd	54
729.2.g.d.379.1		144	9.2	odd	6
6561.2.a.c.1.69		72	81.20	odd	54
6561.2.a.d.1.4		72	81.61	even	27

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)

\(f(q)\)	\(=\)	\(q+(-2.46032 - 0.583106i) q^{2} +(3.92589 + 1.97166i) q^{4} +(1.69595 - 2.27806i) q^{5} +(-0.459677 - 0.302334i) q^{7} +(-4.63542 - 3.88958i) q^{8} +O(q^{10})\)	\(q+(-2.46032 - 0.583106i) q^{2} +(3.92589 + 1.97166i) q^{4} +(1.69595 - 2.27806i) q^{5} +(-0.459677 - 0.302334i) q^{7} +(-4.63542 - 3.88958i) q^{8} +(-5.50094 + 4.61584i) q^{10} +(-3.04678 + 0.356118i) q^{11} +(-1.33201 + 4.44921i) q^{13} +(0.954659 + 1.01188i) q^{14} +(3.88972 + 5.22480i) q^{16} +(0.523880 + 2.97107i) q^{17} +(-0.875112 + 4.96301i) q^{19} +(11.1497 - 5.59959i) q^{20} +(7.70371 + 0.900434i) q^{22} +(-6.95489 + 4.57430i) q^{23} +(-0.879290 - 2.93703i) q^{25} +(5.87152 - 10.1698i) q^{26} +(-1.20854 - 2.09326i) q^{28} +(-1.09088 + 1.15626i) q^{29} +(-0.286769 - 4.92363i) q^{31} +(-1.72989 - 4.01033i) q^{32} +(0.443539 - 7.61526i) q^{34} +(-1.46833 + 0.534427i) q^{35} +(-3.36770 - 1.22574i) q^{37} +(5.04702 - 11.7003i) q^{38} +(-16.7222 + 3.96323i) q^{40} +(1.11236 - 0.263633i) q^{41} +(-0.142801 + 0.331049i) q^{43} +(-12.6635 - 4.60913i) q^{44} +(19.7786 - 7.19880i) q^{46} +(-0.472617 + 8.11452i) q^{47} +(-2.65266 - 6.14956i) q^{49} +(0.450731 + 7.73876i) q^{50} +(-14.0016 + 14.8409i) q^{52} +(0.345591 + 0.598582i) q^{53} +(-4.35594 + 7.54471i) q^{55} +(0.954842 + 3.18939i) q^{56} +(3.35813 - 2.20868i) q^{58} +(-0.587776 - 0.0687011i) q^{59} +(3.11195 - 1.56288i) q^{61} +(-2.16546 + 12.2809i) q^{62} +(-0.344558 - 1.95409i) q^{64} +(7.87655 + 10.5800i) q^{65} +(6.89831 + 7.31178i) q^{67} +(-3.80124 + 12.6970i) q^{68} +(3.92418 - 0.458671i) q^{70} +(-1.87423 + 1.57266i) q^{71} +(3.96729 + 3.32895i) q^{73} +(7.57088 + 4.97944i) q^{74} +(-13.2210 + 17.7588i) q^{76} +(1.50820 + 0.757447i) q^{77} +(-2.18924 - 0.518860i) q^{79} +18.4992 q^{80} -2.89048 q^{82} +(-2.96386 - 0.702448i) q^{83} +(7.65676 + 3.84537i) q^{85} +(0.544373 - 0.731219i) q^{86} +(15.5082 + 10.1999i) q^{88} +(8.84763 + 7.42404i) q^{89} +(1.95744 - 1.64249i) q^{91} +(-36.3231 + 4.24556i) q^{92} +(5.89442 - 19.6887i) q^{94} +(9.82189 + 10.4106i) q^{95} +(-2.51009 - 3.37164i) q^{97} +(2.94055 + 16.6767i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

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