LMFDB - Embedded newform 729.2.g.d.28.7

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			28.7
Character	$\chi$	$=$	729.28
Dual form			729.2.g.d.703.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97349 - 1.29799i) q^{2} +(1.41775 - 3.28671i) q^{4} +(1.82524 - 1.93464i) q^{5} +(-4.56284 - 0.533319i) q^{7} +(-0.647845 - 3.67411i) q^{8} +O(q^{10})$	\(q+(1.97349 - 1.29799i) q^{2} +(1.41775 - 3.28671i) q^{4} +(1.82524 - 1.93464i) q^{5} +(-4.56284 - 0.533319i) q^{7} +(-0.647845 - 3.67411i) q^{8} +(1.09096 - 6.18715i) q^{10} +(-0.138834 + 0.463739i) q^{11} +(0.253222 - 4.34765i) q^{13} +(-9.69698 + 4.87000i) q^{14} +(-1.13474 - 1.20275i) q^{16} +(0.936739 - 0.340945i) q^{17} +(0.818296 + 0.297835i) q^{19} +(-3.77088 - 8.74187i) q^{20} +(0.327938 + 1.09539i) q^{22} +(2.03881 - 0.238302i) q^{23} +(-0.120613 - 2.07085i) q^{25} +(-5.14346 - 8.90874i) q^{26} +(-8.22182 + 14.2406i) q^{28} +(0.741930 + 0.372611i) q^{29} +(2.39289 + 3.21420i) q^{31} +(3.45991 + 0.820013i) q^{32} +(1.40611 - 1.88873i) q^{34} +(-9.36007 + 7.85403i) q^{35} +(0.840131 + 0.704953i) q^{37} +(2.00149 - 0.474361i) q^{38} +(-8.29057 - 5.45280i) q^{40} +(-0.244464 - 0.160787i) q^{41} +(10.9207 - 2.58825i) q^{43} +(1.32734 + 1.11377i) q^{44} +(3.71426 - 3.11664i) q^{46} +(-2.41144 + 3.23913i) q^{47} +(13.7238 + 3.25259i) q^{49} +(-2.92597 - 3.93025i) q^{50} +(-13.9305 - 6.99614i) q^{52} +(0.806764 - 1.39736i) q^{53} +(0.643763 + 1.11503i) q^{55} +(0.996538 + 17.1099i) q^{56} +(1.94784 - 0.227670i) q^{58} +(-1.51146 - 5.04861i) q^{59} +(1.59785 + 3.70422i) q^{61} +(8.89434 + 3.23728i) q^{62} +(11.0001 - 4.00372i) q^{64} +(-7.94897 - 8.42541i) q^{65} +(-12.8887 + 6.47296i) q^{67} +(0.207472 - 3.56216i) q^{68} +(-8.27761 + 27.6491i) q^{70} +(-2.20143 + 12.4849i) q^{71} +(1.00775 + 5.71524i) q^{73} +(2.57301 + 0.300742i) q^{74} +(2.13903 - 2.26724i) q^{76} +(0.880799 - 2.04192i) q^{77} +(5.40905 - 3.55759i) q^{79} -4.39806 q^{80} -0.691147 q^{82} +(-10.6112 + 6.97906i) q^{83} +(1.05017 - 2.43456i) q^{85} +(18.1924 - 19.2828i) q^{86} +(1.79377 + 0.209662i) q^{88} +(-2.74643 - 15.5758i) q^{89} +(-3.47410 + 19.7026i) q^{91} +(2.10728 - 7.03882i) q^{92} +(-0.554617 + 9.52241i) q^{94} +(2.06979 - 1.03949i) q^{95} +(-1.39077 - 1.47414i) q^{97} +(31.3056 - 11.3943i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	1.97349	−	1.29799i	1.39547	−	0.917816i	0.395471	−	0.918478i	$-0.370581\pi$
$2$	1.97349	−	1.29799i	1.39547	−	0.917816i	1.00000		0.000662916i	$0.000211013\pi$
$3$		0			0
$3$		0			0
$4$	1.41775	−	3.28671i	0.708873	−	1.64335i
$5$	1.82524	−	1.93464i	0.816273	−	0.865199i	−0.176611	−	0.984281i	$-0.556514\pi$
$5$	1.82524	−	1.93464i	0.816273	−	0.865199i	0.992884	+	0.119082i	$0.0379950\pi$
$6$		0			0
$7$	−4.56284	−	0.533319i	−1.72459	−	0.201576i	−0.804682	−	0.593707i	$-0.797664\pi$
$7$	−4.56284	−	0.533319i	−1.72459	−	0.201576i	−0.919909	+	0.392131i	$0.871738\pi$
$8$	−0.647845	−	3.67411i	−0.229048	−	1.29899i
$9$		0			0
$10$	1.09096	−	6.18715i	0.344992	−	1.95655i
$11$	−0.138834	+	0.463739i	−0.0418601	+	0.139822i	−0.976365	−	0.216127i	$-0.930657\pi$
$11$	−0.138834	+	0.463739i	−0.0418601	+	0.139822i	0.934505	+	0.355950i	$0.115843\pi$
$12$		0			0
$13$	0.253222	−	4.34765i	0.0702311	−	1.20582i	−0.760571	−	0.649254i	$-0.775081\pi$
$13$	0.253222	−	4.34765i	0.0702311	−	1.20582i	0.830803	−	0.556567i	$-0.187882\pi$
$14$	−9.69698	+	4.87000i	−2.59163	+	1.30156i
$15$		0			0
$16$	−1.13474	−	1.20275i	−0.283684	−	0.300688i
$17$	0.936739	−	0.340945i	0.227193	−	0.0826914i	−0.225916	−	0.974147i	$-0.572537\pi$
$17$	0.936739	−	0.340945i	0.227193	−	0.0826914i	0.453108	+	0.891456i	$0.350315\pi$
$18$		0			0
$19$	0.818296	+	0.297835i	0.187730	+	0.0683281i	0.434175	−	0.900829i	$-0.357040\pi$
$19$	0.818296	+	0.297835i	0.187730	+	0.0683281i	−0.246445	+	0.969157i	$0.579262\pi$
$20$	−3.77088	−	8.74187i	−0.843194	−	1.95474i
$21$		0			0
$22$	0.327938	+	1.09539i	0.0699167	+	0.233538i
$23$	2.03881	−	0.238302i	0.425121	−	0.0496895i	0.0991571	−	0.995072i	$-0.468385\pi$
$23$	2.03881	−	0.238302i	0.425121	−	0.0496895i	0.325964	+	0.945382i	$0.394311\pi$
$24$		0			0
$25$	−0.120613	−	2.07085i	−0.0241226	−	0.414170i
$26$	−5.14346	−	8.90874i	−1.00872	−	1.74715i
$27$		0			0
$28$	−8.22182	+	14.2406i	−1.55378	+	2.69122i
$29$	0.741930	+	0.372611i	0.137773	+	0.0691922i	0.516350	−	0.856378i	$-0.327290\pi$
$29$	0.741930	+	0.372611i	0.137773	+	0.0691922i	−0.378577	+	0.925570i	$0.623587\pi$
$30$		0			0
$31$	2.39289	+	3.21420i	0.429775	+	0.577288i	0.963277	−	0.268511i	$-0.0865316\pi$
$31$	2.39289	+	3.21420i	0.429775	+	0.577288i	−0.533502	+	0.845799i	$0.679124\pi$
$32$	3.45991	+	0.820013i	0.611631	+	0.144959i
$33$		0			0
$34$	1.40611	−	1.88873i	0.241145	−	0.323914i
$35$	−9.36007	+	7.85403i	−1.58214	+	1.32757i
$36$		0			0
$37$	0.840131	+	0.704953i	0.138117	+	0.115894i	0.709229	−	0.704979i	$-0.249043\pi$
$37$	0.840131	+	0.704953i	0.138117	+	0.115894i	−0.571112	+	0.820872i	$0.693488\pi$
$38$	2.00149	−	0.474361i	0.324684	−	0.0769516i
$39$		0			0
$40$	−8.29057	−	5.45280i	−1.31085	−	0.862163i
$41$	−0.244464	−	0.160787i	−0.0381789	−	0.0251106i	0.530276	−	0.847825i	$-0.322088\pi$
$41$	−0.244464	−	0.160787i	−0.0381789	−	0.0251106i	−0.568455	+	0.822714i	$0.692459\pi$
$42$		0			0
$43$	10.9207	−	2.58825i	1.66539	−	0.394704i	0.713379	−	0.700779i	$-0.247164\pi$
$43$	10.9207	−	2.58825i	1.66539	−	0.394704i	0.952007	+	0.306075i	$0.0990158\pi$
$44$	1.32734	+	1.11377i	0.200104	+	0.167907i
$45$		0			0
$46$	3.71426	−	3.11664i	0.547638	−	0.459523i
$47$	−2.41144	+	3.23913i	−0.351745	+	0.472475i	−0.942419	−	0.334435i	$-0.891454\pi$
$47$	−2.41144	+	3.23913i	−0.351745	+	0.472475i	0.590674	+	0.806910i	$0.298862\pi$
$48$		0			0
$49$	13.7238	+	3.25259i	1.96054	+	0.464656i
$50$	−2.92597	−	3.93025i	−0.413794	−	0.555822i
$51$		0			0
$52$	−13.9305	−	6.99614i	−1.93181	−	0.970189i
$53$	0.806764	−	1.39736i	0.110818	−	0.191942i	−0.805283	−	0.592891i	$-0.797986\pi$
$53$	0.806764	−	1.39736i	0.110818	−	0.191942i	0.916100	+	0.400950i	$0.131320\pi$
$54$		0			0
$55$	0.643763	+	1.11503i	0.0868050	+	0.150351i
$56$	0.996538	+	17.1099i	0.133168	+	2.28641i
$57$		0			0
$58$	1.94784	−	0.227670i	0.255764	−	0.0298945i
$59$	−1.51146	−	5.04861i	−0.196775	−	0.657273i	−0.998244	−	0.0592374i	$-0.981133\pi$
$59$	−1.51146	−	5.04861i	−0.196775	−	0.657273i	0.801469	−	0.598036i	$-0.204052\pi$
$60$		0			0
$61$	1.59785	+	3.70422i	0.204583	+	0.474277i	0.989358	−	0.145504i	$-0.0464805\pi$
$61$	1.59785	+	3.70422i	0.204583	+	0.474277i	−0.784774	+	0.619781i	$0.787221\pi$
$62$	8.89434	+	3.23728i	1.12958	+	0.411134i
$63$		0			0
$64$	11.0001	−	4.00372i	1.37502	−	0.500465i
$65$	−7.94897	−	8.42541i	−0.985948	−	1.04504i
$66$		0			0
$67$	−12.8887	+	6.47296i	−1.57461	+	0.790798i	−0.999625	−	0.0273685i	$-0.991287\pi$
$67$	−12.8887	+	6.47296i	−1.57461	+	0.790798i	−0.574982	+	0.818166i	$0.694991\pi$
$68$	0.207472	−	3.56216i	0.0251597	−	0.431976i
$69$		0			0
$70$	−8.27761	+	27.6491i	−0.989363	+	3.30470i
$71$	−2.20143	+	12.4849i	−0.261261	+	1.48169i	0.518213	+	0.855252i	$0.326597\pi$
$71$	−2.20143	+	12.4849i	−0.261261	+	1.48169i	−0.779474	+	0.626434i	$0.784514\pi$
$72$		0			0
$73$	1.00775	+	5.71524i	0.117948	+	0.668918i	0.985248	+	0.171132i	$0.0547425\pi$
$73$	1.00775	+	5.71524i	0.117948	+	0.668918i	−0.867300	+	0.497786i	$0.834146\pi$
$74$	2.57301	+	0.300742i	0.299107	+	0.0349606i
$75$		0			0
$76$	2.13903	−	2.26724i	0.245364	−	0.260071i
$77$	0.880799	−	2.04192i	0.100376	−	0.232699i
$78$		0			0
$79$	5.40905	−	3.55759i	0.608566	−	0.400260i	−0.207487	−	0.978238i	$-0.566528\pi$
$79$	5.40905	−	3.55759i	0.608566	−	0.400260i	0.816052	+	0.577978i	$0.196158\pi$
$80$	−4.39806			−0.491718
$81$		0			0
$82$	−0.691147			−0.0763245
$83$	−10.6112	+	6.97906i	−1.16473	+	0.766052i	−0.976382	−	0.216052i	$-0.930682\pi$
$83$	−10.6112	+	6.97906i	−1.16473	+	0.766052i	−0.188343	+	0.982103i	$0.560312\pi$
$84$		0			0
$85$	1.05017	−	2.43456i	0.113907	−	0.264066i
$86$	18.1924	−	19.2828i	1.96173	−	2.07931i
$87$		0			0
$88$	1.79377	+	0.209662i	0.191217	+	0.0223500i
$89$	−2.74643	−	15.5758i	−0.291121	−	1.65103i	−0.682563	−	0.730827i	$-0.739135\pi$
$89$	−2.74643	−	15.5758i	−0.291121	−	1.65103i	0.391442	−	0.920203i	$-0.371976\pi$
$90$		0			0
$91$	−3.47410	+	19.7026i	−0.364184	+	2.06539i
$92$	2.10728	−	7.03882i	0.219699	−	0.733847i
$93$		0			0
$94$	−0.554617	+	9.52241i	−0.0572044	+	0.982162i
$95$	2.06979	−	1.03949i	0.212356	−	0.106649i
$96$		0			0
$97$	−1.39077	−	1.47414i	−0.141212	−	0.149676i	0.652908	−	0.757438i	$-0.273549\pi$
$97$	−1.39077	−	1.47414i	−0.141212	−	0.149676i	−0.794119	+	0.607762i	$0.792068\pi$
$98$	31.3056	−	11.3943i	3.16234	−	1.15100i
$99$		0			0
$100$	−6.97727	−	2.53952i	−0.697727	−	0.253952i
$101$	−2.85953	−	6.62915i	−0.284534	−	0.659625i	0.714672	−	0.699460i	$-0.246576\pi$
$101$	−2.85953	−	6.62915i	−0.284534	−	0.659625i	−0.999206	+	0.0398351i	$0.987317\pi$
$102$		0			0
$103$	−1.25810	−	4.20236i	−0.123965	−	0.414071i	0.873368	−	0.487061i	$-0.161931\pi$
$103$	−1.25810	−	4.20236i	−0.123965	−	0.414071i	−0.997333	+	0.0729900i	$0.976746\pi$
$104$	−16.1378	+	1.88624i	−1.58244	+	0.184961i
$105$		0			0
$106$	−0.221607	−	3.80484i	−0.0215244	−	0.369559i
$107$	3.17835	+	5.50506i	0.307263	+	0.532194i	0.977763	−	0.209715i	$-0.0672537\pi$
$107$	3.17835	+	5.50506i	0.307263	+	0.532194i	−0.670500	+	0.741910i	$0.733920\pi$
$108$		0			0
$109$	4.40215	−	7.62475i	0.421649	−	0.730318i	−0.574452	−	0.818539i	$-0.694785\pi$
$109$	4.40215	−	7.62475i	0.421649	−	0.730318i	0.996101	+	0.0882203i	$0.0281179\pi$
$110$	2.71776	+	1.36491i	0.259128	+	0.130139i
$111$		0			0
$112$	4.53617	+	6.09313i	0.428628	+	0.575747i
$113$	−17.2381	−	4.08550i	−1.62162	−	0.384332i	−0.683312	−	0.730126i	$-0.739461\pi$
$113$	−17.2381	−	4.08550i	−1.62162	−	0.384332i	−0.938310	+	0.345795i	$0.887609\pi$
$114$		0			0
$115$	3.26029	−	4.37933i	0.304024	−	0.408374i
$116$	2.27653	−	1.91024i	0.211371	−	0.177361i
$117$		0			0
$118$	−9.53588	−	8.00156i	−0.877849	−	0.736603i
$119$	−4.45602	+	1.05610i	−0.408483	+	0.0968122i
$120$		0			0
$121$	8.99459	+	5.91583i	0.817690	+	0.537803i
$122$	7.96137	+	5.23628i	0.720789	+	0.474070i
$123$		0			0
$124$	13.9567	−	3.30779i	1.25334	−	0.297048i
$125$	5.96099	+	5.00187i	0.533167	+	0.447381i
$126$		0			0
$127$	4.25250	−	3.56827i	0.377349	−	0.316633i	−0.434312	−	0.900763i	$-0.643008\pi$
$127$	4.25250	−	3.56827i	0.377349	−	0.316633i	0.811660	+	0.584130i	$0.198564\pi$
$128$	12.2652	−	16.4750i	1.08410	−	1.45620i
$129$		0			0
$130$	−26.6233	−	6.30984i	−2.33502	−	0.553410i
$131$	10.9874	+	14.7587i	0.959975	+	1.28947i	0.957186	+	0.289474i	$0.0934804\pi$
$131$	10.9874	+	14.7587i	0.959975	+	1.28947i	0.00278912	+	0.999996i	$0.499112\pi$
$132$		0			0
$133$	−3.57491	−	1.79539i	−0.309984	−	0.155680i
$134$	−17.0340	+	29.5037i	−1.47151	+	2.54873i
$135$		0			0
$136$	−1.85953	−	3.22081i	−0.159454	−	0.276182i
$137$	−0.332173	−	5.70318i	−0.0283794	−	0.487256i	−0.982314	−	0.187241i	$-0.940045\pi$
$137$	−0.332173	−	5.70318i	−0.0283794	−	0.487256i	0.953935	−	0.300015i	$-0.0969916\pi$
$138$		0			0
$139$	9.52866	−	1.11374i	0.808210	−	0.0944662i	0.298055	−	0.954549i	$-0.403662\pi$
$139$	9.52866	−	1.11374i	0.808210	−	0.0944662i	0.510155	+	0.860082i	$0.329588\pi$
$140$	12.5437	+	41.8988i	1.06014	+	3.54110i
$141$		0			0
$142$	11.8607	+	27.4963i	0.995332	+	2.30744i
$143$	1.98102	+	0.721031i	0.165661	+	0.0602957i
$144$		0			0
$145$	2.07507	−	0.755265i	0.172325	−	0.0627213i
$146$	9.40710	+	9.97094i	0.778537	+	0.825201i
$147$		0			0
$148$	3.50807	−	1.76182i	0.288361	−	0.144821i
$149$	−0.957819	+	16.4451i	−0.0784676	+	1.34724i	0.697555	+	0.716531i	$0.254271\pi$
$149$	−0.957819	+	16.4451i	−0.0784676	+	1.34724i	−0.776022	+	0.630705i	$0.782766\pi$
$150$		0			0
$151$	−3.37514	+	11.2737i	−0.274665	+	0.917444i	0.703690	+	0.710507i	$0.251535\pi$
$151$	−3.37514	+	11.2737i	−0.274665	+	0.917444i	−0.978354	+	0.206936i	$0.933651\pi$
$152$	0.564151	−	3.19946i	0.0457587	−	0.259511i
$153$		0			0
$154$	−0.912137	−	5.17298i	−0.0735021	−	0.416851i
$155$	10.5859	+	1.23732i	0.850283	+	0.0993838i
$156$		0			0
$157$	9.29415	−	9.85123i	0.741754	−	0.786213i	−0.241119	−	0.970495i	$-0.577514\pi$
$157$	9.29415	−	9.85123i	0.741754	−	0.786213i	0.982873	+	0.184282i	$0.0589960\pi$
$158$	6.05702	−	14.0418i	0.481871	−	1.11710i
$159$		0			0
$160$	7.90160	−	5.19696i	0.624676	−	0.410856i
$161$	−9.42984			−0.743176
$162$		0			0
$163$	−13.5555			−1.06175			−0.530874	−	0.847451i	$-0.678136\pi$
$163$	−13.5555			−1.06175			−0.530874	+	0.847451i	$0.678136\pi$
$164$	−0.875047	+	0.575527i	−0.0683297	+	0.0449411i
$165$		0			0
$166$	−11.8823	+	27.5463i	−0.922246	+	2.13801i
$167$	−7.59882	+	8.05428i	−0.588014	+	0.623259i	−0.951243	−	0.308441i	$-0.900193\pi$
$167$	−7.59882	+	8.05428i	−0.588014	+	0.623259i	0.363229	+	0.931700i	$0.381674\pi$
$168$		0			0
$169$	−5.92585	−	0.692633i	−0.455835	−	0.0532794i
$170$	−1.08753	−	6.16770i	−0.0834099	−	0.473041i
$171$		0			0
$172$	6.97594	−	39.5625i	0.531910	−	3.01661i
$173$	−3.71850	+	12.4207i	−0.282713	+	0.944326i	0.692194	+	0.721711i	$0.256644\pi$
$173$	−3.71850	+	12.4207i	−0.282713	+	0.944326i	−0.974907	+	0.222614i	$0.928541\pi$
$174$		0			0
$175$	−0.554085	+	9.51328i	−0.0418849	+	0.719136i
$176$	0.715302	−	0.359238i	0.0539179	−	0.0270786i
$177$		0			0
$178$	−25.6372	−	27.1739i	−1.92159	−	2.03677i
$179$	−23.7701	+	8.65162i	−1.77666	+	0.646652i	−0.776806	+	0.629740i	$0.783161\pi$
$179$	−23.7701	+	8.65162i	−1.77666	+	0.646652i	−0.999857	+	0.0169124i	$0.994616\pi$
$180$		0			0
$181$	10.2266	+	3.72217i	0.760135	+	0.276667i	0.692864	−	0.721068i	$-0.256348\pi$
$181$	10.2266	+	3.72217i	0.760135	+	0.276667i	0.0672712	+	0.997735i	$0.478571\pi$
$182$	18.7176	+	43.3923i	1.38744	+	3.21645i
$183$		0			0
$184$	−2.19638	−	7.33643i	−0.161919	−	0.540849i
$185$	2.89728	−	0.338643i	0.213012	−	0.0248975i
$186$		0			0
$187$	0.0280580	+	0.481737i	0.00205180	+	0.0352281i
$188$	7.22725	+	12.5180i	0.527101	+	0.912966i
$189$		0			0
$190$	2.73548	−	4.73799i	0.198453	−	0.343730i
$191$	10.5589	+	5.30288i	0.764015	+	0.383703i	0.787734	−	0.616016i	$-0.211254\pi$
$191$	10.5589	+	5.30288i	0.764015	+	0.383703i	−0.0237184	+	0.999719i	$0.507551\pi$
$192$		0			0
$193$	−5.14242	−	6.90746i	−0.370159	−	0.497210i	0.577546	−	0.816358i	$-0.304011\pi$
$193$	−5.14242	−	6.90746i	−0.370159	−	0.497210i	−0.947705	+	0.319148i	$0.896603\pi$
$194$	−4.65809	−	1.10399i	−0.334432	−	0.0792617i
$195$		0			0
$196$	30.1471	−	40.4946i	2.15337	−	2.89247i
$197$	11.2572	−	9.44590i	0.802041	−	0.672992i	−0.146653	−	0.989188i	$-0.546850\pi$
$197$	11.2572	−	9.44590i	0.802041	−	0.672992i	0.948694	+	0.316196i	$0.102406\pi$
$198$		0			0
$199$	−10.9420	−	9.18142i	−0.775657	−	0.650853i	0.166494	−	0.986042i	$-0.446755\pi$
$199$	−10.9420	−	9.18142i	−0.775657	−	0.650853i	−0.942151	+	0.335189i	$0.891200\pi$
$200$	−7.53040	+	1.78474i	−0.532479	+	0.126200i
$201$		0			0
$202$	−14.2478	−	9.37094i	−1.00247	−	0.659337i
$203$	−3.18659	−	2.09585i	−0.223655	−	0.147100i
$204$		0			0
$205$	−0.757271	+	0.179477i	−0.0528901	+	0.0125352i
$206$	−7.93747	−	6.66033i	−0.553030	−	0.464047i
$207$		0			0
$208$	−5.51648	+	4.62888i	−0.382499	+	0.320955i
$209$	−0.251725	+	0.338125i	−0.0174122	+	0.0233886i
$210$		0			0
$211$	2.70553	+	0.641223i	0.186257	+	0.0441436i	0.322685	−	0.946506i	$-0.395414\pi$
$211$	2.70553	+	0.641223i	0.186257	+	0.0441436i	−0.136429	+	0.990650i	$0.543563\pi$
$212$	−3.44891	−	4.63269i	−0.236872	−	0.318175i
$213$		0			0
$214$	13.4180	+	6.73875i	0.917232	+	0.460651i
$215$	14.9255	−	25.8518i	1.01791	−	1.76308i
$216$		0			0
$217$	−9.20416	−	15.9421i	−0.624819	−	1.08222i
$218$	−1.20921	−	20.7613i	−0.0818980	−	1.40613i
$219$		0			0
$220$	4.57747	−	0.535030i	0.308613	−	0.0360717i
$221$	−1.24511	−	4.15895i	−0.0837550	−	0.279761i
$222$		0			0
$223$	−9.44242	−	21.8900i	−0.632311	−	1.46586i	−0.869268	−	0.494341i	$-0.835409\pi$
$223$	−9.44242	−	21.8900i	−0.632311	−	1.46586i	0.236957	−	0.971520i	$-0.423850\pi$
$224$	−15.3497	−	5.58682i	−1.02559	−	0.373285i
$225$		0			0
$226$	−39.3222	+	14.3121i	−2.61567	+	0.952027i
$227$	−2.30985	−	2.44830i	−0.153310	−	0.162499i	0.646166	−	0.763197i	$-0.276371\pi$
$227$	−2.30985	−	2.44830i	−0.153310	−	0.162499i	−0.799477	+	0.600697i	$0.794890\pi$
$228$		0			0
$229$	8.24425	−	4.14042i	0.544795	−	0.273607i	−0.155043	−	0.987908i	$-0.549552\pi$
$229$	8.24425	−	4.14042i	0.544795	−	0.273607i	0.699838	+	0.714301i	$0.253255\pi$
$230$	0.749848	−	12.8744i	0.0494435	−	0.848912i
$231$		0			0
$232$	0.888360	−	2.96733i	0.0583237	−	0.194815i
$233$	−0.733258	+	4.15851i	−0.0480373	+	0.272433i	−0.999360	−	0.0357624i	$-0.988614\pi$
$233$	−0.733258	+	4.15851i	−0.0480373	+	0.272433i	0.951323	+	0.308196i	$0.0997252\pi$
$234$		0			0
$235$	1.86509	+	10.5775i	0.121665	+	0.689998i
$236$	−18.7362	−	2.18994i	−1.21962	−	0.142553i
$237$		0			0
$238$	−7.42313	+	7.86806i	−0.481170	+	0.510011i
$239$	−1.78727	+	4.14335i	−0.115609	+	0.268011i	−0.966189	−	0.257833i	$-0.916991\pi$
$239$	−1.78727	+	4.14335i	−0.115609	+	0.268011i	0.850581	+	0.525845i	$0.176251\pi$
$240$		0			0
$241$	−7.03651	+	4.62799i	−0.453261	+	0.298115i	−0.755537	−	0.655106i	$-0.772624\pi$
$241$	−7.03651	+	4.62799i	−0.453261	+	0.298115i	0.302276	+	0.953221i	$0.402254\pi$
$242$	25.4294			1.63467
$243$		0			0
$244$	14.4400			0.924428
$245$	31.3418	−	20.6138i	2.00235	−	1.31697i
$246$		0			0
$247$	1.50209	−	3.48225i	0.0955760	−	0.221570i
$248$	10.2591	−	10.8740i	0.651455	−	0.690502i
$249$		0			0
$250$	18.2563	+	2.13386i	1.15463	+	0.134957i
$251$	1.59517	+	9.04665i	0.100686	+	0.571020i	0.992856	+	0.119319i	$0.0380713\pi$
$251$	1.59517	+	9.04665i	0.100686	+	0.571020i	−0.892170	+	0.451700i	$0.850818\pi$
$252$		0			0
$253$	−0.172546	+	0.978558i	−0.0108479	+	0.0615214i
$254$	3.76071	−	12.5617i	0.235968	−	0.788188i
$255$		0			0
$256$	1.45963	−	25.0609i	0.0912270	−	1.56631i
$257$	−7.35681	+	3.69473i	−0.458905	+	0.230471i	−0.663206	−	0.748437i	$-0.730804\pi$
$257$	−7.35681	+	3.69473i	−0.458905	+	0.230471i	0.204300	+	0.978908i	$0.434508\pi$
$258$		0			0
$259$	−3.45742	−	3.66465i	−0.214833	−	0.227710i
$260$	−38.9615	+	14.1808i	−2.41629	+	0.879457i
$261$		0			0
$262$	40.8401	+	14.8646i	2.52311	+	0.918338i
$263$	0.170742	+	0.395824i	0.0105284	+	0.0244076i	0.923399	−	0.383841i	$-0.125399\pi$
$263$	0.170742	+	0.395824i	0.0105284	+	0.0244076i	−0.912871	+	0.408249i	$0.866140\pi$
$264$		0			0
$265$	−1.23085	−	4.11131i	−0.0756103	−	0.252556i
$266$	−9.38545	+	1.09700i	−0.575459	+	0.0672615i
$267$		0			0
$268$	3.00177	+	51.5384i	0.183362	+	3.14821i
$269$	−5.33884	−	9.24714i	−0.325515	−	0.563808i	0.656102	−	0.754673i	$-0.272204\pi$
$269$	−5.33884	−	9.24714i	−0.325515	−	0.563808i	−0.981616	+	0.190864i	$0.938871\pi$
$270$		0			0
$271$	7.65288	−	13.2552i	0.464880	−	0.805195i	−0.534316	−	0.845285i	$-0.679431\pi$
$271$	7.65288	−	13.2552i	0.464880	−	0.805195i	0.999196	+	0.0400894i	$0.0127643\pi$
$272$	−1.47302	−	0.739781i	−0.0893152	−	0.0448558i
$273$		0			0
$274$	−8.05820	−	10.8240i	−0.486814	−	0.653904i
$275$	0.977078	+	0.231572i	0.0589200	+	0.0139643i
$276$		0			0
$277$	−7.41708	+	9.96287i	−0.445649	+	0.598611i	−0.967014	−	0.254723i	$-0.918016\pi$
$277$	−7.41708	+	9.96287i	−0.445649	+	0.598611i	0.521365	+	0.853334i	$0.325423\pi$
$278$	17.3591	−	14.5660i	1.04113	−	0.873613i
$279$		0			0
$280$	34.9205	+	29.3018i	2.08690	+	1.75112i
$281$	−30.5667	+	7.24444i	−1.82346	+	0.432167i	−0.992298	−	0.123870i	$-0.960470\pi$
$281$	−30.5667	+	7.24444i	−1.82346	+	0.432167i	−0.831158	+	0.556037i	$0.812321\pi$
$282$		0			0
$283$	0.490426	+	0.322558i	0.0291528	+	0.0191741i	0.564002	−	0.825774i	$-0.309261\pi$
$283$	0.490426	+	0.322558i	0.0291528	+	0.0191741i	−0.534849	+	0.844948i	$0.679631\pi$
$284$	37.9132	+	24.9359i	2.24973	+	1.47967i
$285$		0			0
$286$	4.84542	−	1.14838i	0.286515	−	0.0679054i
$287$	1.02970	+	0.864021i	0.0607813	+	0.0510015i
$288$		0			0
$289$	−12.2615	+	10.2886i	−0.721266	+	0.605214i
$290$	3.11482	−	4.18393i	0.182908	−	0.245689i
$291$		0			0
$292$	20.2131	+	4.79058i	1.18288	+	0.280348i
$293$	−17.8876	−	24.0272i	−1.04500	−	1.40368i	−0.910858	−	0.412720i	$-0.864579\pi$
$293$	−17.8876	−	24.0272i	−1.04500	−	1.40368i	−0.134144	−	0.990962i	$-0.542829\pi$
$294$		0			0
$295$	−12.5260	−	6.29082i	−0.729294	−	0.366265i
$296$	2.04580	−	3.54343i	0.118910	−	0.205958i
$297$		0			0
$298$	19.4553	+	33.6976i	1.12702	+	1.95205i
$299$	−0.519785	−	8.92437i	−0.0300600	−	0.516110i
$300$		0			0
$301$	−51.2096	+	5.98555i	−2.95167	+	0.345001i
$302$	7.97236	+	26.6295i	0.458758	+	1.53236i
$303$		0			0
$304$	−0.570328	−	1.32217i	−0.0327106	−	0.0758316i
$305$	10.0828	+	3.66984i	0.577340	+	0.210135i
$306$		0			0
$307$	2.24152	−	0.815848i	0.127930	−	0.0465629i	−0.277262	−	0.960794i	$-0.589427\pi$
$307$	2.24152	−	0.815848i	0.127930	−	0.0465629i	0.405192	+	0.914232i	$0.367205\pi$
$308$	−5.46245	−	5.78986i	−0.311252	−	0.329908i
$309$		0			0
$310$	22.4973	−	11.2986i	1.27776	−	0.641716i
$311$	1.55349	−	26.6724i	0.0880903	−	1.51245i	−0.607676	−	0.794185i	$-0.707898\pi$
$311$	1.55349	−	26.6724i	0.0880903	−	1.51245i	0.695767	−	0.718268i	$-0.255065\pi$
$312$		0			0
$313$	−2.01014	+	6.71433i	−0.113620	+	0.379516i	−0.995818	−	0.0913623i	$-0.970878\pi$
$313$	−2.01014	+	6.71433i	−0.113620	+	0.379516i	0.882198	+	0.470879i	$0.156063\pi$
$314$	5.55519	−	31.5050i	0.313497	−	1.77793i
$315$		0			0
$316$	−4.02409	−	22.8217i	−0.226373	−	1.28382i
$317$	13.9881	+	1.63498i	0.785651	+	0.0918294i	0.499453	−	0.866341i	$-0.333534\pi$
$317$	13.9881	+	1.63498i	0.785651	+	0.0918294i	0.286198	+	0.958171i	$0.407609\pi$
$318$		0			0
$319$	−0.275799	+	0.292330i	−0.0154418	+	0.0163674i
$320$	12.3321	−	28.5891i	0.689387	−	1.59818i
$321$		0			0
$322$	−18.6097	+	12.2398i	−1.03708	+	0.682098i
$323$	0.868075			0.0483010
$324$		0			0
$325$	−9.03387			−0.501109
$326$	−26.7517	+	17.5948i	−1.48164	+	0.974489i
$327$		0			0
$328$	−0.432373	+	1.00235i	−0.0238738	+	0.0553457i
$329$	12.7305	−	13.4935i	0.701855	−	0.743923i
$330$		0			0
$331$	−28.9840	−	3.38774i	−1.59310	−	0.186207i	−0.727203	−	0.686422i	$-0.759180\pi$
$331$	−28.9840	−	3.38774i	−1.59310	−	0.186207i	−0.865901	+	0.500215i	$0.833254\pi$
$332$	7.89421	+	44.7703i	0.433251	+	2.45709i
$333$		0			0
$334$	−4.54187	+	25.7582i	−0.248520	+	1.40943i
$335$	−11.0022	+	36.7498i	−0.601113	+	2.00786i
$336$		0			0
$337$	−0.0414447	+	0.711578i	−0.00225764	+	0.0387621i	−0.999249	−	0.0387528i	$-0.987662\pi$
$337$	−0.0414447	+	0.711578i	−0.00225764	+	0.0387621i	0.996991	+	0.0775149i	$0.0246985\pi$
$338$	−12.5937	+	6.32477i	−0.685005	+	0.344022i
$339$		0			0
$340$	−6.51283	−	6.90319i	−0.353208	−	0.374378i
$341$	−1.82276	+	0.663432i	−0.0987082	+	0.0359269i
$342$		0			0
$343$	−30.6666	−	11.1617i	−1.65584	−	0.602678i
$344$	−16.5844	−	38.4470i	−0.894171	−	2.07292i
$345$		0			0
$346$	8.78342	+	29.3387i	0.472200	+	1.57726i
$347$	−13.7105	+	1.60252i	−0.736016	+	0.0860279i	−0.475838	−	0.879533i	$-0.657855\pi$
$347$	−13.7105	+	1.60252i	−0.736016	+	0.0860279i	−0.260178	+	0.965561i	$0.583781\pi$
$348$		0			0
$349$	1.00932	+	17.3293i	0.0540276	+	0.927618i	0.911039	+	0.412320i	$0.135282\pi$
$349$	1.00932	+	17.3293i	0.0540276	+	0.927618i	−0.857011	+	0.515298i	$0.827681\pi$
$350$	11.2546	+	19.4936i	0.601585	+	1.04198i
$351$		0			0
$352$	−0.860625	+	1.49065i	−0.0458714	+	0.0794517i
$353$	−9.38828	−	4.71497i	−0.499688	−	0.250953i	0.181058	−	0.983472i	$-0.442048\pi$
$353$	−9.38828	−	4.71497i	−0.499688	−	0.250953i	−0.680746	+	0.732520i	$0.738344\pi$
$354$		0			0
$355$	20.1357	+	27.0470i	1.06869	+	1.43550i
$356$	−55.0868	−	13.0558i	−2.91959	−	0.691956i
$357$		0			0
$358$	−35.6805	+	47.9272i	−1.88577	+	2.53303i
$359$	−1.97814	+	1.65986i	−0.104402	+	0.0876039i	−0.693495	−	0.720462i	$-0.743930\pi$
$359$	−1.97814	+	1.65986i	−0.104402	+	0.0876039i	0.589092	+	0.808066i	$0.299485\pi$
$360$		0			0
$361$	−13.9739	−	11.7255i	−0.735471	−	0.617133i
$362$	25.0134	−	5.92829i	1.31468	−	0.311584i
$363$		0			0
$364$	59.8312	+	39.3516i	3.13601	+	2.06259i
$365$	12.8963	+	8.48206i	0.675026	+	0.443971i
$366$		0			0
$367$	21.5090	−	5.09773i	1.12276	−	0.266099i	0.373015	−	0.927825i	$-0.378324\pi$
$367$	21.5090	−	5.09773i	1.12276	−	0.266099i	0.749746	+	0.661726i	$0.230176\pi$
$368$	−2.60013	−	2.18177i	−0.135541	−	0.113732i
$369$		0			0
$370$	5.27820	−	4.42894i	0.274401	−	0.230249i
$371$	−4.42637	+	5.94565i	−0.229806	+	0.308683i
$372$		0			0
$373$	−10.0915	−	2.39173i	−0.522519	−	0.123839i	−0.0391118	−	0.999235i	$-0.512453\pi$
$373$	−10.0915	−	2.39173i	−0.522519	−	0.123839i	−0.483407	+	0.875396i	$0.660601\pi$
$374$	0.680661	+	0.914286i	0.0351961	+	0.0472766i
$375$		0			0
$376$	13.4632	+	6.76145i	0.694309	+	0.348695i
$377$	1.80786	−	3.13130i	0.0931094	−	0.161270i
$378$		0			0
$379$	3.96481	+	6.86725i	0.203658	+	0.352747i	0.949704	−	0.313148i	$-0.101383\pi$
$379$	3.96481	+	6.86725i	0.203658	+	0.352747i	−0.746046	+	0.665894i	$0.768050\pi$
$380$	−0.482053	−	8.27654i	−0.0247288	−	0.424577i
$381$		0			0
$382$	27.7210	−	3.24012i	1.41833	−	0.165779i
$383$	−1.25841	−	4.20338i	−0.0643018	−	0.214783i	0.919800	−	0.392387i	$-0.128351\pi$
$383$	−1.25841	−	4.20338i	−0.0643018	−	0.214783i	−0.984102	+	0.177604i	$0.943165\pi$
$384$		0			0
$385$	−2.34272	−	5.43103i	−0.119396	−	0.276791i
$386$	−19.1143	−	6.95704i	−0.972893	−	0.354104i
$387$		0			0
$388$	−6.81682	+	2.48112i	−0.346071	+	0.125960i
$389$	2.13138	+	2.25913i	0.108065	+	0.114543i	0.779148	−	0.626840i	$-0.215652\pi$
$389$	2.13138	+	2.25913i	0.108065	+	0.114543i	−0.671083	+	0.741382i	$0.734171\pi$
$390$		0			0
$391$	1.82858	−	0.918349i	0.0924754	−	0.0464429i
$392$	3.05951	−	52.5298i	0.154529	−	2.65316i
$393$		0			0
$394$	9.95532	−	33.2531i	0.501542	−	1.67527i
$395$	2.99016	−	16.9581i	0.150451	−	0.853252i
$396$		0			0
$397$	4.18830	+	23.7530i	0.210205	+	1.19213i	0.889037	+	0.457836i	$0.151375\pi$
$397$	4.18830	+	23.7530i	0.210205	+	1.19213i	−0.678832	+	0.734294i	$0.737514\pi$
$398$	−33.5113	−	3.91691i	−1.67977	−	0.196337i
$399$		0			0
$400$	−2.35385	+	2.49494i	−0.117693	+	0.124747i
$401$	−11.9585	+	27.7230i	−0.597180	+	1.38442i	0.304707	+	0.952446i	$0.401441\pi$
$401$	−11.9585	+	27.7230i	−0.597180	+	1.38442i	−0.901887	+	0.431972i	$0.857818\pi$
$402$		0			0
$403$	14.5802	−	9.58953i	0.726290	−	0.477688i
$404$	−25.8422			−1.28570
$405$		0			0
$406$	−9.00910			−0.447114
$407$	−0.443553	+	0.291729i	−0.0219861	+	0.0144605i
$408$		0			0
$409$	1.96158	−	4.54746i	0.0969940	−	0.224857i	−0.862810	−	0.505528i	$-0.831298\pi$
$409$	1.96158	−	4.54746i	0.0969940	−	0.224857i	0.959804	+	0.280671i	$0.0905569\pi$
$410$	−1.26151	+	1.33712i	−0.0623016	+	0.0660359i
$411$		0			0
$412$	−15.5956	−	1.82286i	−0.768340	−	0.0898061i
$413$	4.20401	+	23.8421i	0.206866	+	1.17319i
$414$		0			0
$415$	−5.86592	+	33.2673i	−0.287947	+	1.63303i
$416$	4.44125	−	14.8348i	0.217750	−	0.727337i
$417$		0			0
$418$	−0.0578953	+	0.994025i	−0.00283175	+	0.0486193i
$419$	−22.3854	+	11.2423i	−1.09360	+	0.549225i	−0.901775	−	0.432205i	$-0.857736\pi$
$419$	−22.3854	+	11.2423i	−1.09360	+	0.549225i	−0.191821	+	0.981430i	$0.561439\pi$
$420$		0			0
$421$	21.4522	+	22.7380i	1.04552	+	1.10818i	0.993986	+	0.109511i	$0.0349284\pi$
$421$	21.4522	+	22.7380i	1.04552	+	1.10818i	0.0515303	+	0.998671i	$0.483590\pi$
$422$	6.17165	−	2.24630i	0.300431	−	0.109348i
$423$		0			0
$424$	−5.65670	−	2.05887i	−0.274714	−	0.0999876i
$425$	−0.819029	−	1.89872i	−0.0397288	−	0.0921016i
$426$		0			0
$427$	−5.31518	−	17.7539i	−0.257219	−	0.859173i
$428$	22.5996	−	2.64152i	1.09239	−	0.127683i
$429$		0			0
$430$	−4.09984	−	70.3915i	−0.197712	−	3.39458i
$431$	−0.627551	−	1.08695i	−0.0302281	−	0.0523566i	0.850516	−	0.525950i	$-0.176290\pi$
$431$	−0.627551	−	1.08695i	−0.0302281	−	0.0523566i	−0.880744	+	0.473593i	$0.842957\pi$
$432$		0			0
$433$	16.4409	−	28.4764i	0.790097	−	1.36849i	−0.135809	−	0.990735i	$-0.543363\pi$
$433$	16.4409	−	28.4764i	0.790097	−	1.36849i	0.925906	−	0.377753i	$-0.123303\pi$
$434$	−38.8569	−	19.5147i	−1.86519	−	0.936735i
$435$		0			0
$436$	−18.8192	−	25.2785i	−0.901275	−	1.21062i
$437$	1.73932	+	0.412227i	0.0832031	+	0.0197195i
$438$		0			0
$439$	15.3218	−	20.5808i	0.731271	−	0.982267i	−0.268549	−	0.963266i	$-0.586544\pi$
$439$	15.3218	−	20.5808i	0.731271	−	0.982267i	0.999819	−	0.0190010i	$-0.00604858\pi$
$440$	3.67969	−	3.08762i	0.175422	−	0.147197i
$441$		0			0
$442$	−7.85548	−	6.59153i	−0.373647	−	0.313527i
$443$	18.9389	−	4.48861i	0.899816	−	0.213260i	0.245424	−	0.969416i	$-0.421073\pi$
$443$	18.9389	−	4.48861i	0.899816	−	0.213260i	0.654392	+	0.756156i	$0.272925\pi$
$444$		0			0
$445$	−35.1465	−	23.1162i	−1.66610	−	1.09581i
$446$	−47.0475	−	30.9436i	−2.22776	−	1.46522i
$447$		0			0
$448$	−52.3271	+	12.4017i	−2.47222	+	0.585927i
$449$	−1.02554	−	0.860532i	−0.0483983	−	0.0406110i	0.618268	−	0.785968i	$-0.287835\pi$
$449$	−1.02554	−	0.860532i	−0.0483983	−	0.0406110i	−0.666666	+	0.745357i	$0.732279\pi$
$450$		0			0
$451$	0.108503	−	0.0910448i	0.00510920	−	0.00428713i
$452$	−37.8671	+	50.8643i	−1.78112	+	2.39246i
$453$		0			0
$454$	−7.73634	−	1.83355i	−0.363085	−	0.0860526i
$455$	31.7764	+	42.6831i	1.48970	+	2.00102i
$456$		0			0
$457$	17.7196	+	8.89911i	0.828887	+	0.416283i	0.812059	−	0.583575i	$-0.198347\pi$
$457$	17.7196	+	8.89911i	0.828887	+	0.416283i	0.0168285	+	0.999858i	$0.494643\pi$
$458$	10.8958	−	18.8720i	0.509126	−	0.881832i
$459$		0			0
$460$	−9.77130	−	16.9244i	−0.455589	−	0.789104i
$461$	1.80652	+	31.0168i	0.0841382	+	1.44460i	0.731202	+	0.682161i	$0.238960\pi$
$461$	1.80652	+	31.0168i	0.0841382	+	1.44460i	−0.647064	+	0.762436i	$0.724003\pi$
$462$		0			0
$463$	−4.19118	+	0.489879i	−0.194781	+	0.0227666i	−0.212924	−	0.977069i	$-0.568299\pi$
$463$	−4.19118	+	0.489879i	−0.194781	+	0.0227666i	0.0181432	+	0.999835i	$0.494225\pi$
$464$	−0.393737	−	1.31517i	−0.0182788	−	0.0610553i
$465$		0			0
$466$	3.95062	+	9.15856i	0.183009	+	0.424262i
$467$	−27.5275	−	10.0192i	−1.27382	−	0.463633i	−0.385438	−	0.922734i	$-0.625950\pi$
$467$	−27.5275	−	10.0192i	−1.27382	−	0.463633i	−0.888384	+	0.459100i	$0.848172\pi$
$468$		0			0
$469$	62.2613	−	22.6613i	2.87496	−	1.04640i
$470$	17.4102	+	18.4537i	0.803071	+	0.851206i
$471$		0			0
$472$	−17.5700	+	8.82398i	−0.808724	+	0.406156i
$473$	−0.315893	+	5.42367i	−0.0145248	+	0.249381i
$474$		0			0
$475$	0.518075	−	1.73049i	0.0237709	−	0.0794003i
$476$	−2.84643	+	16.1429i	−0.130466	+	0.739910i
$477$		0			0
$478$	1.85086	+	10.4967i	0.0846562	+	0.480109i
$479$	25.3863	+	2.96724i	1.15993	+	0.135577i	0.674212	−	0.738538i	$-0.264483\pi$
$479$	25.3863	+	2.96724i	1.15993	+	0.135577i	0.485720	+	0.874115i	$0.338558\pi$
$480$		0			0
$481$	3.27763	−	3.47409i	0.149447	−	0.158405i
$482$	−7.87944	+	18.2666i	−0.358899	+	0.832021i
$483$		0			0
$484$	32.1957	−	21.1754i	1.46344	−	0.962519i
$485$	−5.39043			−0.244767
$486$		0			0
$487$	−3.18751			−0.144440			−0.0722199	−	0.997389i	$-0.523008\pi$
$487$	−3.18751			−0.144440			−0.0722199	+	0.997389i	$0.523008\pi$
$488$	12.5746	−	8.27042i	0.569224	−	0.374385i
$489$		0			0
$490$	35.0964	−	81.3625i	1.58549	−	3.67558i
$491$	−11.4689	+	12.1563i	−0.517583	+	0.548606i	−0.932461	−	0.361271i	$-0.882343\pi$
$491$	−11.4689	+	12.1563i	−0.517583	+	0.548606i	0.414878	+	0.909877i	$0.363824\pi$
$492$		0			0
$493$	0.822035	+	0.0960821i	0.0370226	+	0.00432732i
$494$	−1.55554	−	8.82189i	−0.0699869	−	0.396916i
$495$		0			0
$496$	1.15059	−	6.52532i	0.0516630	−	0.292995i
$497$	16.7032	−	55.7926i	0.749241	−	2.50264i
$498$		0			0
$499$	−1.06686	+	18.3172i	−0.0477590	+	0.819991i	0.886353	+	0.463010i	$0.153231\pi$
$499$	−1.06686	+	18.3172i	−0.0477590	+	0.819991i	−0.934112	+	0.356980i	$0.883806\pi$
$500$	24.8908	−	12.5007i	1.11315	−	0.559046i
$501$		0			0
$502$	14.8905	+	15.7830i	0.664595	+	0.704430i
$503$	21.3376	−	7.76624i	0.951395	−	0.346280i	0.180739	−	0.983531i	$-0.442151\pi$
$503$	21.3376	−	7.76624i	0.951395	−	0.346280i	0.770656	+	0.637251i	$0.219929\pi$
$504$		0			0
$505$	−18.0444	−	6.56762i	−0.802965	−	0.292255i
$506$	0.929637	+	2.15514i	0.0413274	+	0.0958077i
$507$		0			0
$508$	−5.69890	−	19.0356i	−0.252848	−	0.844570i
$509$	26.2920	−	3.07310i	1.16537	−	0.136213i	0.488670	−	0.872469i	$-0.337482\pi$
$509$	26.2920	−	3.07310i	1.16537	−	0.136213i	0.676703	+	0.736256i	$0.263408\pi$
$510$		0			0
$511$	−1.55016	−	26.6152i	−0.0685749	−	1.17739i
$512$	−9.10887	−	15.7770i	−0.402559	−	0.697253i
$513$		0			0
$514$	−9.72291	+	16.8406i	−0.428859	+	0.742806i
$515$	−10.4264	−	5.23635i	−0.459443	−	0.230741i
$516$		0			0
$517$	−1.16732	−	1.56798i	−0.0513386	−	0.0689596i
$518$	−11.5799	−	2.74448i	−0.508789	−	0.120585i
$519$		0			0
$520$	−25.8062	+	34.6638i	−1.13168	+	1.52011i
$521$	26.2017	−	21.9858i	1.14792	−	0.963216i	0.148247	−	0.988950i	$-0.452637\pi$
$521$	26.2017	−	21.9858i	1.14792	−	0.963216i	0.999669	+	0.0257345i	$0.00819245\pi$
$522$		0			0
$523$	17.6317	+	14.7948i	0.770982	+	0.646931i	0.940960	−	0.338517i	$-0.109925\pi$
$523$	17.6317	+	14.7948i	0.770982	+	0.646931i	−0.169978	+	0.985448i	$0.554370\pi$
$524$	64.0848	−	15.1884i	2.79956	−	0.663507i
$525$		0			0
$526$	0.850733	+	0.559536i	0.0370937	+	0.0243969i
$527$	3.33738	+	2.19503i	0.145378	+	0.0956169i
$528$		0			0
$529$	−18.2801	+	4.33246i	−0.794786	+	0.188368i
$530$	−7.76550	−	6.51603i	−0.337312	−	0.283038i
$531$		0			0
$532$	−10.9692	+	9.20428i	−0.475576	+	0.399056i
$533$	−0.760948	+	1.02213i	−0.0329603	+	0.0442734i
$534$		0			0
$535$	16.4516	+	3.89910i	0.711264	+	0.168573i
$536$	32.1323	+	43.1611i	1.38790	+	1.86428i
$537$		0			0
$538$	−22.5388	−	11.3194i	−0.971719	−	0.488015i
$539$	−3.41368	+	5.91266i	−0.147038	+	0.254676i
$540$		0			0
$541$	14.1264	+	24.4676i	0.607340	+	1.05194i	0.991677	+	0.128751i	$0.0410970\pi$
$541$	14.1264	+	24.4676i	0.607340	+	1.05194i	−0.384336	+	0.923193i	$0.625570\pi$
$542$	−2.10214	−	36.0924i	−0.0902947	−	1.55030i
$543$		0			0
$544$	3.52061	−	0.411500i	0.150945	−	0.0176429i
$545$	−6.71618	−	22.4336i	−0.287690	−	0.960950i
$546$		0			0
$547$	7.19544	+	16.6809i	0.307655	+	0.713224i	0.999965	−	0.00837626i	$-0.00266628\pi$
$547$	7.19544	+	16.6809i	0.307655	+	0.713224i	−0.692310	+	0.721600i	$0.743407\pi$
$548$	−19.2156	−	6.99392i	−0.820851	−	0.298765i
$549$		0			0
$550$	2.22883	−	0.811229i	0.0950378	−	0.0345909i
$551$	0.496141	+	0.525879i	0.0211363	+	0.0224032i
$552$		0			0
$553$	−26.5780	+	13.3480i	−1.13021	+	0.567613i
$554$	−1.70589	+	29.2889i	−0.0724762	+	1.24437i
$555$		0			0
$556$	9.84869	−	32.8969i	0.417677	−	1.39514i
$557$	1.02531	−	5.81482i	0.0434438	−	0.246382i	−0.955350	−	0.295475i	$-0.904522\pi$
$557$	1.02531	−	5.81482i	0.0434438	−	0.246382i	0.998794	+	0.0490932i	$0.0156331\pi$
$558$		0			0
$559$	−8.48744	−	48.1347i	−0.358980	−	2.03588i
$560$	20.0677	+	2.34557i	0.848013	+	0.0991185i
$561$		0			0
$562$	−50.9200	+	53.9720i	−2.14793	+	2.27667i
$563$	9.14633	−	21.2036i	0.385472	−	0.893624i	−0.609436	−	0.792835i	$-0.708604\pi$
$563$	9.14633	−	21.2036i	0.385472	−	0.893624i	0.994908	−	0.100789i	$-0.0321367\pi$
$564$		0			0
$565$	−39.3677	+	25.8925i	−1.65621	+	1.08931i
$566$	1.38653			0.0582802
$567$		0			0
$568$	47.2971			1.98454
$569$	7.64736	−	5.02975i	0.320594	−	0.210858i	−0.379003	−	0.925395i	$-0.623733\pi$
$569$	7.64736	−	5.02975i	0.320594	−	0.210858i	0.699597	+	0.714537i	$0.253363\pi$
$570$		0			0
$571$	4.50616	−	10.4465i	0.188577	−	0.437171i	−0.797531	−	0.603279i	$-0.793861\pi$
$571$	4.50616	−	10.4465i	0.188577	−	0.437171i	0.986108	+	0.166108i	$0.0531200\pi$
$572$	5.17840	−	5.48878i	0.216520	−	0.229498i
$573$		0			0
$574$	3.15359	+	0.368602i	0.131628	+	0.0153852i
$575$	−0.739396	−	4.19332i	−0.0308349	−	0.174874i
$576$		0			0
$577$	−3.91622	+	22.2100i	−0.163034	+	0.924613i	0.788034	+	0.615632i	$0.211099\pi$
$577$	−3.91622	+	22.2100i	−0.163034	+	0.924613i	−0.951068	+	0.308981i	$0.900012\pi$
$578$	−10.8435	+	36.2199i	−0.451031	+	1.50655i
$579$		0			0
$580$	0.459594	−	7.89093i	0.0190836	−	0.327653i
$581$	52.1390	−	26.1852i	2.16309	−	1.08635i
$582$		0			0
$583$	0.536001	+	0.568128i	0.0221989	+	0.0235295i
$584$	20.3456	−	7.40518i	0.841906	−	0.306429i
$585$		0			0
$586$	−66.4879	−	24.1996i	−2.74659	−	0.999677i
$587$	−10.0049	−	23.1939i	−0.412945	−	0.957314i	−0.990059	−	0.140651i	$-0.955081\pi$
$587$	−10.0049	−	23.1939i	−0.412945	−	0.957314i	0.577114	−	0.816663i	$-0.304179\pi$
$588$		0			0
$589$	1.00079	+	3.34286i	0.0412366	+	0.137740i
$590$	−32.8855	+	3.84376i	−1.35387	+	0.158245i
$591$		0			0
$592$	−0.105444	−	1.81040i	−0.00433372	−	0.0744071i
$593$	−13.0866	−	22.6667i	−0.537404	−	0.930811i	−0.999043	−	0.0437427i	$-0.986072\pi$
$593$	−13.0866	−	22.6667i	−0.537404	−	0.930811i	0.461639	−	0.887068i	$-0.347262\pi$
$594$		0			0
$595$	−6.09015	+	10.5485i	−0.249672	+	0.432444i
$596$	52.6923	+	26.4631i	2.15836	+	1.08397i
$597$		0			0
$598$	−12.6095	−	16.9375i	−0.515641	−	0.692626i
$599$	−13.6393	−	3.23257i	−0.557285	−	0.132079i	−0.0576847	−	0.998335i	$-0.518372\pi$
$599$	−13.6393	−	3.23257i	−0.557285	−	0.132079i	−0.499601	+	0.866256i	$0.666520\pi$
$600$		0			0
$601$	−8.14178	+	10.9363i	−0.332110	+	0.446102i	−0.936542	−	0.350555i	$-0.885993\pi$
$601$	−8.14178	+	10.9363i	−0.332110	+	0.446102i	0.604432	+	0.796657i	$0.293400\pi$
$602$	−93.2927	+	78.2819i	−3.80233	+	3.19053i
$603$		0			0
$604$	32.2684	+	27.0764i	1.31298	+	1.10172i
$605$	27.8623	−	6.60350i	1.13277	−	0.268470i
$606$		0			0
$607$	−17.8052	−	11.7107i	−0.722691	−	0.475321i	0.134112	−	0.990966i	$-0.457182\pi$
$607$	−17.8052	−	11.7107i	−0.722691	−	0.475321i	−0.856802	+	0.515645i	$0.827552\pi$
$608$	2.58700	+	1.70149i	0.104917	+	0.0690047i
$609$		0			0
$610$	24.6618	−	5.84494i	0.998526	−	0.236655i
$611$	13.4720	+	11.3043i	0.545017	+	0.457324i
$612$		0			0
$613$	19.6311	−	16.4725i	0.792894	−	0.665317i	−0.153566	−	0.988138i	$-0.549076\pi$
$613$	19.6311	−	16.4725i	0.792894	−	0.665317i	0.946460	+	0.322821i	$0.104631\pi$
$614$	3.36467	−	4.51954i	0.135787	−	0.182394i
$615$		0			0
$616$	−8.07287	−	1.91331i	−0.325265	−	0.0770893i
$617$	−7.05717	−	9.47942i	−0.284111	−	0.381627i	0.637041	−	0.770830i	$-0.280158\pi$
$617$	−7.05717	−	9.47942i	−0.284111	−	0.381627i	−0.921152	+	0.389203i	$0.872751\pi$
$618$		0			0
$619$	27.0251	+	13.5725i	1.08623	+	0.545526i	0.899516	−	0.436888i	$-0.143919\pi$
$619$	27.0251	+	13.5725i	1.08623	+	0.545526i	0.186716	+	0.982414i	$0.440216\pi$
$620$	19.0749	−	33.0387i	0.766066	−	1.32687i
$621$		0			0
$622$	−31.5546	−	54.6542i	−1.26523	−	2.19143i
$623$	4.22465	+	72.5345i	0.169257	+	2.90603i
$624$		0			0
$625$	30.8588	−	3.60687i	1.23435	−	0.144275i
$626$	4.74812	+	15.8598i	0.189773	+	0.633886i
$627$		0			0
$628$	−19.2013	−	44.5137i	−0.766217	−	1.77629i
$629$	1.02733	+	0.373919i	0.0409625	+	0.0149091i
$630$		0			0
$631$	−0.842816	+	0.306760i	−0.0335520	+	0.0122119i	−0.358742	−	0.933437i	$-0.616794\pi$
$631$	−0.842816	+	0.306760i	−0.0335520	+	0.0122119i	0.325190	+	0.945649i	$0.394572\pi$
$632$	−16.5752	−	17.5687i	−0.659326	−	0.698845i
$633$		0			0
$634$	29.7276	−	14.9298i	1.18064	−	0.592937i
$635$	0.858510	−	14.7400i	0.0340689	−	0.584941i
$636$		0			0
$637$	17.6163	−	58.8425i	0.697983	−	2.33142i
$638$	−0.164847	+	0.934896i	−0.00652637	+	0.0370129i
$639$		0			0
$640$	−9.48635	−	53.7998i	−0.374981	−	2.12662i
$641$	−6.35661	−	0.742982i	−0.251071	−	0.0293460i	−0.0103737	−	0.999946i	$-0.503302\pi$
$641$	−6.35661	−	0.742982i	−0.251071	−	0.0293460i	−0.240697	+	0.970600i	$0.577376\pi$
$642$		0			0
$643$	10.2749	−	10.8908i	0.405203	−	0.429491i	−0.492349	−	0.870398i	$-0.663862\pi$
$643$	10.2749	−	10.8908i	0.405203	−	0.429491i	0.897553	+	0.440907i	$0.145343\pi$
$644$	−13.3691	+	30.9931i	−0.526818	+	1.22130i
$645$		0			0
$646$	1.71314	−	1.12675i	0.0674026	−	0.0443314i
$647$	6.78181			0.266620			0.133310	−	0.991074i	$-0.457439\pi$
$647$	6.78181			0.266620			0.133310	+	0.991074i	$0.457439\pi$
$648$		0			0
$649$	2.55108			0.100139
$650$	−17.8283	+	11.7259i	−0.699283	+	0.459926i
$651$		0			0
$652$	−19.2183	+	44.5529i	−0.752645	+	1.74483i
$653$	24.5260	−	25.9960i	0.959776	−	1.01730i	−0.0400604	−	0.999197i	$-0.512755\pi$
$653$	24.5260	−	25.9960i	0.959776	−	1.01730i	0.999836	−	0.0181055i	$-0.00576347\pi$
$654$		0			0
$655$	48.6075	+	5.68140i	1.89925	+	0.221991i
$656$	0.0840162	+	0.476480i	0.00328028	+	0.0186034i
$657$		0			0
$658$	7.60912	−	43.1535i	0.296634	−	1.68230i
$659$	3.84564	−	12.8453i	0.149805	−	0.500383i	−0.849840	−	0.527041i	$-0.823301\pi$
$659$	3.84564	−	12.8453i	0.149805	−	0.500383i	0.999645	+	0.0266581i	$0.00848655\pi$
$660$		0			0
$661$	0.462308	−	7.93752i	0.0179817	−	0.308734i	−0.977310	−	0.211812i	$-0.932063\pi$
$661$	0.462308	−	7.93752i	0.0179817	−	0.308734i	0.995292	−	0.0969213i	$-0.0308995\pi$
$662$	−61.5970	+	30.9352i	−2.39403	+	1.20233i
$663$		0			0
$664$	32.5162	+	34.4652i	1.26187	+	1.33751i
$665$	−9.99851	+	3.63916i	−0.387726	+	0.141121i
$666$		0			0
$667$	1.60145	+	0.582879i	0.0620083	+	0.0225692i
$668$	15.6989	+	36.3940i	0.607407	+	1.40813i
$669$		0			0
$670$	25.9881	+	86.8062i	1.00401	+	3.35361i
$671$	−1.93963	+	0.226710i	−0.0748784	+	0.00875203i
$672$		0			0
$673$	1.71928	+	29.5189i	0.0662735	+	1.13787i	0.853461	+	0.521158i	$0.174500\pi$
$673$	1.71928	+	29.5189i	0.0662735	+	1.13787i	−0.787187	+	0.616714i	$0.788463\pi$
$674$	0.841829	+	1.45809i	0.0324260	+	0.0561635i
$675$		0			0
$676$	−10.6778	+	18.4946i	−0.410686	+	0.711329i
$677$	−23.1884	−	11.6456i	−0.891201	−	0.447578i	−0.0565769	−	0.998398i	$-0.518019\pi$
$677$	−23.1884	−	11.6456i	−0.891201	−	0.447578i	−0.834624	+	0.550820i	$0.814315\pi$
$678$		0			0
$679$	5.55970	+	7.46797i	0.213362	+	0.286594i
$680$	−9.62521	−	2.28122i	−0.369110	−	0.0874807i
$681$		0			0
$682$	−2.73609	+	3.67520i	−0.104770	+	0.140731i
$683$	−11.3957	+	9.56212i	−0.436044	+	0.365885i	−0.834227	−	0.551422i	$-0.814086\pi$
$683$	−11.3957	+	9.56212i	−0.436044	+	0.365885i	0.398182	+	0.917306i	$0.369641\pi$
$684$		0			0
$685$	−11.6399	−	9.76706i	−0.444739	−	0.373180i
$686$	−75.0082	+	17.7773i	−2.86383	+	0.678740i
$687$		0			0
$688$	−15.5051	−	10.1979i	−0.591126	−	0.388790i
$689$	−5.87093	−	3.86137i	−0.223664	−	0.147106i
$690$		0			0
$691$	−20.7330	+	4.91380i	−0.788719	+	0.186930i	−0.605187	−	0.796084i	$-0.706901\pi$
$691$	−20.7330	+	4.91380i	−0.788719	+	0.186930i	−0.183533	+	0.983014i	$0.558753\pi$
$692$	35.5512	+	29.8310i	1.35145	+	1.13400i
$693$		0			0
$694$	−24.9774	+	20.9586i	−0.948130	+	0.795576i
$695$	15.2374	−	20.4674i	0.577988	−	0.776373i
$696$		0			0
$697$	−0.283819	−	0.0672662i	−0.0107504	−	0.00254789i
$698$	24.4851	+	32.8893i	0.926776	+	1.24488i
$699$		0			0
$700$	30.4818	+	15.3085i	1.15210	+	0.578608i
$701$	−11.9432	+	20.6862i	−0.451088	+	0.781308i	−0.998454	−	0.0555858i	$-0.982297\pi$
$701$	−11.9432	+	20.6862i	−0.451088	+	0.781308i	0.547366	+	0.836894i	$0.315631\pi$
$702$		0			0
$703$	0.477515	+	0.827081i	0.0180098	+	0.0311939i
$704$	0.329485	+	5.65704i	0.0124179	+	0.213208i
$705$		0			0
$706$	−24.6477	+	2.88090i	−0.927628	+	0.108424i
$707$	9.51214	+	31.7728i	0.357741	+	1.19494i
$708$		0			0
$709$	−12.0674	−	27.9754i	−0.453201	−	1.05064i	−0.979701	−	0.200463i	$-0.935756\pi$
$709$	−12.0674	−	27.9754i	−0.453201	−	1.05064i	0.526501	−	0.850175i	$-0.323504\pi$
$710$	74.8443	+	27.2411i	2.80886	+	1.02234i
$711$		0			0
$712$	−55.4479	+	20.1814i	−2.07800	+	0.756329i
$713$	5.64459	+	5.98291i	0.211391	+	0.224062i
$714$		0			0
$715$	5.01078	−	2.51651i	0.187392	−	0.0941120i
$716$	−5.26469	+	90.3913i	−0.196751	+	3.37808i
$717$		0			0
$718$	−1.74938	+	5.84332i	−0.0652861	+	0.218071i
$719$	−7.27531	+	41.2603i	−0.271323	+	1.53875i	0.479081	+	0.877771i	$0.340970\pi$
$719$	−7.27531	+	41.2603i	−0.271323	+	1.53875i	−0.750404	+	0.660979i	$0.770141\pi$
$720$		0			0
$721$	3.49933	+	19.8457i	0.130322	+	0.739091i
$722$	−42.7971	−	5.00226i	−1.59274	−	0.186165i
$723$		0			0
$724$	26.7324	−	28.3347i	0.993501	−	1.05305i
$725$	0.682135	−	1.58137i	0.0253339	−	0.0587305i
$726$		0			0
$727$	17.2998	−	11.3783i	0.641614	−	0.421996i	−0.186578	−	0.982440i	$-0.559740\pi$
$727$	17.2998	−	11.3783i	0.641614	−	0.421996i	0.828193	+	0.560444i	$0.189369\pi$
$728$	74.6402			2.76635
$729$		0			0
$730$	36.4605			1.34946
$731$	9.34737	−	6.14786i	0.345725	−	0.227387i
$732$		0			0
$733$	−15.8953	+	36.8495i	−0.587107	+	1.36107i	0.322884	+	0.946439i	$0.395348\pi$
$733$	−15.8953	+	36.8495i	−0.587107	+	1.36107i	−0.909991	+	0.414629i	$0.863911\pi$
$734$	35.8311	−	37.9788i	1.32255	−	1.40182i
$735$		0			0
$736$	7.24949	+	0.847344i	0.267220	+	0.0312335i
$737$	−1.21236	−	6.87566i	−0.0446580	−	0.253268i
$738$		0			0
$739$	5.98018	−	33.9153i	0.219985	−	1.24759i	−0.652060	−	0.758168i	$-0.726095\pi$
$739$	5.98018	−	33.9153i	0.219985	−	1.24759i	0.872044	−	0.489427i	$-0.162794\pi$
$740$	2.99458	−	10.0026i	0.110083	−	0.367703i
$741$		0			0
$742$	−1.01804	+	17.4791i	−0.0373734	+	0.641677i
$743$	10.9077	−	5.47805i	0.400164	−	0.200970i	−0.237323	−	0.971431i	$-0.576270\pi$
$743$	10.9077	−	5.47805i	0.400164	−	0.200970i	0.637488	+	0.770461i	$0.279974\pi$
$744$		0			0
$745$	30.0672	+	31.8694i	1.10158	+	1.16760i
$746$	−23.0200	+	8.37859i	−0.842822	+	0.306762i
$747$		0			0
$748$	1.62311	+	0.590763i	0.0593467	+	0.0216004i
$749$	−11.5663	−	26.8138i	−0.422625	−	0.979754i
$750$		0			0
$751$	11.3725	+	37.9869i	0.414989	+	1.38616i	0.868845	+	0.495085i	$0.164863\pi$
$751$	11.3725	+	37.9869i	0.414989	+	1.38616i	−0.453855	+	0.891075i	$0.649952\pi$
$752$	6.63221	−	0.775194i	0.241852	−	0.0282684i
$753$		0			0
$754$	−0.496593	−	8.52618i	−0.0180849	−	0.310505i
$755$	15.6502	+	27.1070i	0.569570	+	0.986525i
$756$		0			0
$757$	−9.73596	+	16.8632i	−0.353859	+	0.612902i	−0.986922	−	0.161198i	$-0.948464\pi$
$757$	−9.73596	+	16.8632i	−0.353859	+	0.612902i	0.633063	+	0.774101i	$0.281798\pi$
$758$	16.7381	+	8.40620i	0.607956	+	0.305327i
$759$		0			0
$760$	−5.16011	−	6.93123i	−0.187177	−	0.251422i
$761$	5.54788	+	1.31487i	0.201110	+	0.0476640i	0.329936	−	0.944003i	$-0.392973\pi$
$761$	5.54788	+	1.31487i	0.201110	+	0.0476640i	−0.128826	+	0.991667i	$0.541121\pi$
$762$		0			0
$763$	−24.1527	+	32.4427i	−0.874387	+	1.17451i
$764$	32.3989	−	27.1859i	1.17215	−	0.983551i
$765$		0			0
$766$	−7.93940	−	6.66195i	−0.286862	−	0.240706i
$767$	−22.3323	+	5.29286i	−0.806374	+	0.191114i
$768$		0			0
$769$	21.3465	+	14.0398i	0.769775	+	0.506289i	0.872615	−	0.488409i	$-0.162423\pi$
$769$	21.3465	+	14.0398i	0.769775	+	0.506289i	−0.102840	+	0.994698i	$0.532793\pi$
$770$	−11.6728	−	7.67729i	−0.420657	−	0.276670i
$771$		0			0
$772$	−29.9935	+	7.10858i	−1.07949	+	0.255843i
$773$	−32.7547	−	27.4845i	−1.17811	−	0.988548i	−0.999990	−	0.00453893i	$-0.998555\pi$
$773$	−32.7547	−	27.4845i	−1.17811	−	0.988548i	−0.178116	−	0.984009i	$-0.557000\pi$
$774$		0			0
$775$	6.36752	−	5.34298i	0.228728	−	0.191926i
$776$	−4.51513	+	6.06487i	−0.162084	+	0.217716i
$777$		0			0
$778$	7.13859	+	1.69188i	0.255931	+	0.0606567i
$779$	−0.152156	−	0.204381i	−0.00545156	−	0.00732271i
$780$		0			0
$781$	−5.48410	−	2.75422i	−0.196236	−	0.0985537i
$782$	2.41669	−	4.18583i	0.0864207	−	0.149685i
$783$		0			0
$784$	−11.6608	−	20.1971i	−0.416457	−	0.721325i
$785$	−2.09453	−	35.9618i	−0.0747571	−	1.28353i
$786$		0			0
$787$	43.3294	−	5.06448i	1.54452	−	0.180529i	0.699256	−	0.714871i	$-0.253515\pi$
$787$	43.3294	−	5.06448i	1.54452	−	0.180529i	0.845268	+	0.534342i	$0.179441\pi$
$788$	−15.0861	−	50.3910i	−0.537419	−	1.79510i
$789$		0			0
$790$	−16.1103	−	37.3478i	−0.573178	−	1.32878i
$791$	76.4757	+	27.8349i	2.71916	+	0.989695i
$792$		0			0
$793$	16.5093	−	6.00888i	0.586261	−	0.213382i
$794$	39.0967	+	41.4401i	1.38749	+	1.47065i
$795$		0			0
$796$	−45.6896	+	22.9462i	−1.61942	+	0.813306i
$797$	1.86657	−	32.0477i	0.0661172	−	1.13519i	−0.788194	−	0.615426i	$-0.788984\pi$
$797$	1.86657	−	32.0477i	0.0661172	−	1.13519i	0.854312	−	0.519761i	$-0.173979\pi$
$798$		0			0
$799$	−1.15453	+	3.85639i	−0.0408442	+	0.136429i
$800$	1.28081	−	7.26385i	0.0452836	−	0.256816i
$801$		0			0
$802$	12.3840	+	70.2331i	0.437294	+	2.48002i
$803$	−2.79029	−	0.326138i	−0.0984671	−	0.0115092i
$804$		0			0
$805$	−17.2118	+	18.2434i	−0.606635	+	0.642995i
$806$	16.3268	−	37.8497i	0.575087	−	1.33320i
$807$		0			0
$808$	−22.5037	+	14.8009i	−0.791677	+	0.520694i
$809$	40.7617			1.43310			0.716552	−	0.697533i	$-0.245719\pi$
$809$	40.7617			1.43310			0.716552	+	0.697533i	$0.245719\pi$
$810$		0			0
$811$	22.4762			0.789245			0.394623	−	0.918843i	$-0.370875\pi$
$811$	22.4762			0.789245			0.394623	+	0.918843i	$0.370875\pi$
$812$	−11.4062	+	7.50199i	−0.400280	+	0.263268i
$813$		0			0
$814$	−0.496688	+	1.15145i	−0.0174089	+	0.0403584i
$815$	−24.7421	+	26.2250i	−0.866676	+	0.918623i
$816$		0			0
$817$	9.70721	+	1.13461i	0.339612	+	0.0396950i
$818$	−2.03137	−	11.5205i	−0.0710253	−	0.402804i
$819$		0			0
$820$	−0.483732	+	2.74338i	−0.0168927	+	0.0958030i
$821$	−14.6326	+	48.8763i	−0.510681	+	1.70579i	0.180905	+	0.983501i	$0.442097\pi$
$821$	−14.6326	+	48.8763i	−0.510681	+	1.70579i	−0.691586	+	0.722294i	$0.743088\pi$
$822$		0			0
$823$	2.30488	−	39.5732i	0.0803429	−	1.37943i	−0.681569	−	0.731754i	$-0.738702\pi$
$823$	2.30488	−	39.5732i	0.0803429	−	1.37943i	0.761912	−	0.647681i	$-0.224261\pi$
$824$	−14.6249	+	7.34490i	−0.509482	+	0.255872i
$825$		0			0
$826$	39.2433	+	41.5955i	1.36545	+	1.44729i
$827$	23.9691	−	8.72402i	0.833486	−	0.303364i	0.110197	−	0.993910i	$-0.464852\pi$
$827$	23.9691	−	8.72402i	0.833486	−	0.303364i	0.723289	+	0.690546i	$0.242630\pi$
$828$		0			0
$829$	26.7012	+	9.71844i	0.927371	+	0.337536i	0.761167	−	0.648556i	$-0.224627\pi$
$829$	26.7012	+	9.71844i	0.927371	+	0.337536i	0.166204	+	0.986091i	$0.446849\pi$
$830$	31.6042	+	73.2667i	1.09700	+	2.54312i
$831$		0			0
$832$	−14.6213	−	48.8386i	−0.506902	−	1.69317i
$833$	13.9645	−	1.63222i	0.483843	−	0.0565531i
$834$		0			0
$835$	1.71247	+	29.4020i	0.0592626	+	1.01750i
$836$	0.754437	+	1.30672i	0.0260927	+	0.0451940i
$837$		0			0
$838$	−29.5849	+	51.2426i	−1.02199	+	1.77015i
$839$	25.5873	+	12.8504i	0.883373	+	0.443647i	0.831834	−	0.555024i	$-0.187291\pi$
$839$	25.5873	+	12.8504i	0.883373	+	0.443647i	0.0515390	+	0.998671i	$0.483587\pi$
$840$		0			0
$841$	−16.9060	−	22.7087i	−0.582965	−	0.783058i
$842$	71.8494	+	17.0286i	2.47609	+	0.586845i
$843$		0			0
$844$	5.94327	−	7.98320i	0.204576	−	0.274793i
$845$	−12.1561	+	10.2002i	−0.418183	+	0.350897i
$846$		0			0
$847$	−37.8858	−	31.7900i	−1.30177	−	1.09232i
$848$	−2.59613	+	0.615295i	−0.0891516	+	0.0211293i
$849$		0			0
$850$	−4.08087	−	2.68403i	−0.139973	−	0.0920614i
$851$	1.88086	+	1.23706i	0.0644750	+	0.0424058i
$852$		0			0
$853$	11.3511	−	2.69026i	0.388655	−	0.0921129i	−0.0316427	−	0.999499i	$-0.510074\pi$
$853$	11.3511	−	2.69026i	0.388655	−	0.0921129i	0.420298	+	0.907386i	$0.361926\pi$
$854$	−33.5338	−	28.1382i	−1.14750	−	0.962871i
$855$		0			0
$856$	18.1671	−	15.2440i	0.620940	−	0.521030i
$857$	−20.3208	+	27.2955i	−0.694144	+	0.932397i	−0.999805	−	0.0197430i	$-0.993715\pi$
$857$	−20.3208	+	27.2955i	−0.694144	+	0.932397i	0.305661	+	0.952140i	$0.401123\pi$
$858$		0			0
$859$	−32.6432	−	7.73657i	−1.11377	−	0.263968i	−0.367772	−	0.929916i	$-0.619879\pi$
$859$	−32.6432	−	7.73657i	−1.11377	−	0.263968i	−0.745998	+	0.665948i	$0.768027\pi$
$860$	−63.8066	−	85.7071i	−2.17579	−	2.92259i
$861$		0			0
$862$	−2.64932	−	1.33054i	−0.0902361	−	0.0453183i
$863$	−28.6243	+	49.5787i	−0.974383	+	1.68768i	−0.292425	+	0.956288i	$0.594462\pi$
$863$	−28.6243	+	49.5787i	−0.974383	+	1.68768i	−0.681958	+	0.731392i	$0.738871\pi$
$864$		0			0
$865$	17.2424	+	29.8647i	0.586259	+	1.01543i
$866$	−4.51608	−	77.5380i	−0.153462	−	2.63485i
$867$		0			0
$868$	−65.4461	+	7.64955i	−2.22138	+	0.259643i
$869$	0.898830	+	3.00230i	0.0304907	+	0.101846i
$870$		0			0
$871$	24.8785	+	57.6747i	0.842974	+	1.95423i
$872$	−30.8661	−	11.2343i	−1.04526	−	0.380443i
$873$		0			0
$874$	3.96761	−	1.44409i	0.134206	−	0.0488471i
$875$	−24.5315	−	26.0018i	−0.829315	−	0.879022i
$876$		0			0
$877$	34.7636	−	17.4589i	1.17388	−	0.589546i	0.248519	−	0.968627i	$-0.420056\pi$
$877$	34.7636	−	17.4589i	1.17388	−	0.589546i	0.925363	+	0.379081i	$0.123760\pi$
$878$	3.52393	−	60.5036i	0.118927	−	2.04190i
$879$		0			0
$880$	0.610602	−	2.03955i	0.0205834	−	0.0687533i
$881$	−5.31981	+	30.1701i	−0.179229	+	1.01646i	0.753920	+	0.656966i	$0.228161\pi$
$881$	−5.31981	+	30.1701i	−0.179229	+	1.01646i	−0.933149	+	0.359491i	$0.882950\pi$
$882$		0			0
$883$	3.08095	+	17.4729i	0.103682	+	0.588011i	0.991738	+	0.128276i	$0.0409444\pi$
$883$	3.08095	+	17.4729i	0.103682	+	0.588011i	−0.888056	+	0.459735i	$0.847944\pi$
$884$	−15.4345	−	1.80403i	−0.519118	−	0.0606762i
$885$		0			0
$886$	31.5497	−	33.4407i	1.05993	−	1.12346i
$887$	−3.14340	+	7.28723i	−0.105545	+	0.244681i	−0.962802	−	0.270208i	$-0.912908\pi$
$887$	−3.14340	+	7.28723i	−0.105545	+	0.244681i	0.857257	+	0.514889i	$0.172167\pi$
$888$		0			0
$889$	−21.3065	+	14.0135i	−0.714597	+	0.469998i
$890$	−99.3659			−3.33075
$891$		0			0
$892$	−85.3329			−2.85716
$893$	−2.93800	+	1.93235i	−0.0983163	+	0.0646637i
$894$		0			0
$895$	−26.6484	+	61.7781i	−0.890759	+	2.06501i
$896$	−64.7507	+	68.6317i	−2.16317	+	2.29282i
$897$		0			0
$898$	−3.14086	−	0.367114i	−0.104812	−	0.0122508i
$899$	0.577706	+	3.27633i	0.0192676	+	0.109272i
$900$		0			0
$901$	0.279306	−	1.58402i	0.00930502	−	0.0527714i
$902$	0.0959549	−	0.320512i	0.00319495	−	0.0106719i
$903$		0			0
$904$	−3.84298	+	65.9814i	−0.127816	+	2.19451i
$905$	25.8671	−	12.9909i	0.859850	−	0.431833i
$906$		0			0
$907$	−33.1870	−	35.1762i	−1.10196	−	1.16801i	−0.984583	−	0.174917i	$-0.944034\pi$
$907$	−33.1870	−	35.1762i	−1.10196	−	1.16801i	−0.117373	−	0.993088i	$-0.537447\pi$
$908$	−11.3216	+	4.12074i	−0.375722	+	0.136752i
$909$		0			0
$910$	118.113	+	42.9895i	3.91540	+	1.42509i
$911$	−20.9442	−	48.5541i	−0.693913	−	1.60867i	−0.789862	−	0.613284i	$-0.789848\pi$
$911$	−20.9442	−	48.5541i	−0.693913	−	1.60867i	0.0959499	−	0.995386i	$-0.469411\pi$
$912$		0			0
$913$	−1.76327	−	5.88973i	−0.0583557	−	0.194922i
$914$	46.5204	−	5.43746i	1.53876	−	0.179855i
$915$		0			0
$916$	−1.92008	−	32.9665i	−0.0634412	−	1.08924i
$917$	−42.2627	−	73.2012i	−1.39564	−	2.41732i
$918$		0			0
$919$	24.1233	−	41.7828i	0.795754	−	1.37829i	−0.126605	−	0.991953i	$-0.540408\pi$
$919$	24.1233	−	41.7828i	0.795754	−	1.37829i	0.922359	−	0.386333i	$-0.126258\pi$
$920$	−18.2023	−	9.14154i	−0.600112	−	0.301388i
$921$		0			0
$922$	43.8246	+	58.8666i	1.44329	+	1.93867i
$923$	53.7226	+	12.7325i	1.76830	+	0.419095i
$924$		0			0
$925$	1.35852	−	1.82481i	0.0446679	−	0.0599994i
$926$	−7.63541	+	6.40687i	−0.250915	+	0.210543i
$927$		0			0
$928$	2.26146	+	1.89759i	0.0742361	+	0.0622915i
$929$	34.3701	−	8.14586i	1.12765	−	0.267257i	0.375868	−	0.926673i	$-0.377345\pi$
$929$	34.3701	−	8.14586i	1.12765	−	0.267257i	0.751778	+	0.659416i	$0.229197\pi$
$930$		0			0
$931$	10.2614	+	6.74900i	0.336302	+	0.221190i
$932$	12.6282	+	8.30573i	0.413652	+	0.272063i
$933$		0			0
$934$	−67.3302	+	15.9576i	−2.20311	+	0.522147i
$935$	0.983202	+	0.825005i	0.0321542	+	0.0269805i
$936$		0			0
$937$	19.9472	−	16.7377i	0.651647	−	0.546797i	−0.255923	−	0.966697i	$-0.582379\pi$
$937$	19.9472	−	16.7377i	0.651647	−	0.546797i	0.907570	+	0.419900i	$0.137935\pi$
$938$	93.4583	−	125.536i	3.05152	−	4.09890i
$939$		0			0
$940$	37.4093	+	8.86616i	1.22016	+	0.289182i
$941$	−27.9851	−	37.5905i	−0.912287	−	1.22541i	−0.973823	−	0.227309i	$-0.927007\pi$
$941$	−27.9851	−	37.5905i	−0.912287	−	1.22541i	0.0615357	−	0.998105i	$-0.480400\pi$
$942$		0			0
$943$	−0.536731	−	0.269557i	−0.0174784	−	0.00877797i
$944$	−4.35712	+	7.54675i	−0.141812	+	0.245626i
$945$		0			0
$946$	6.41644	+	11.1136i	0.208617	+	0.361334i
$947$	1.35580	+	23.2782i	0.0440575	+	0.756438i	0.945917	+	0.324409i	$0.105165\pi$
$947$	1.35580	+	23.2782i	0.0440575	+	0.756438i	−0.901859	+	0.432030i	$0.857798\pi$
$948$		0			0
$949$	25.1031	−	2.93413i	0.814880	−	0.0952458i
$950$	−1.22374	−	4.08757i	−0.0397033	−	0.132618i
$951$		0			0
$952$	6.76703	+	15.6877i	0.219321	+	0.508443i
$953$	24.3435	+	8.86030i	0.788563	+	0.287013i	0.704738	−	0.709467i	$-0.251064\pi$
$953$	24.3435	+	8.86030i	0.788563	+	0.287013i	0.0838242	+	0.996481i	$0.473287\pi$
$954$		0			0
$955$	29.5317	−	10.7487i	0.955625	−	0.347819i
$956$	11.0841	+	11.7485i	0.358485	+	0.379972i
$957$		0			0
$958$	53.9512	−	27.0953i	1.74309	−	0.875410i
$959$	−1.52597	+	26.1999i	−0.0492761	+	0.846038i
$960$		0			0
$961$	4.28570	−	14.3152i	0.138248	−	0.461781i
$962$	1.95906	−	11.1104i	0.0631628	−	0.358214i
$963$		0			0
$964$	5.23484	+	29.6883i	0.168603	+	0.956194i
$965$	−22.7496	−	2.65905i	−0.732337	−	0.0855979i
$966$		0			0
$967$	−10.3477	+	10.9679i	−0.332759	+	0.352704i	−0.872051	−	0.489415i	$-0.837210\pi$
$967$	−10.3477	+	10.9679i	−0.332759	+	0.352704i	0.539292	+	0.842119i	$0.318692\pi$
$968$	15.9083	−	36.8797i	0.511313	−	1.18536i
$969$		0			0
$970$	−10.6380	+	6.99671i	−0.341565	+	0.224651i
$971$	−8.71600			−0.279710			−0.139855	−	0.990172i	$-0.544664\pi$
$971$	−8.71600			−0.279710			−0.139855	+	0.990172i	$0.544664\pi$
$972$		0			0
$973$	−44.0717			−1.41287
$974$	−6.29053	+	4.13735i	−0.201562	+	0.132569i
$975$		0			0
$976$	2.64212	−	6.12512i	0.0845722	−	0.196060i
$977$	−9.01539	+	9.55575i	−0.288428	+	0.305716i	−0.855345	−	0.518059i	$-0.826655\pi$
$977$	−9.01539	+	9.55575i	−0.288428	+	0.305716i	0.566917	+	0.823775i	$0.308136\pi$
$978$		0			0
$979$	7.60439	+	0.888825i	0.243037	+	0.0284070i
$980$	−23.3169	−	132.236i	−0.744830	−	4.22414i
$981$		0			0
$982$	−6.85503	+	38.8768i	−0.218753	+	1.24061i
$983$	2.55043	−	8.51902i	0.0813460	−	0.271714i	−0.907634	−	0.419762i	$-0.862114\pi$
$983$	2.55043	−	8.51902i	0.0813460	−	0.271714i	0.988980	+	0.148047i	$0.0472988\pi$
$984$		0			0
$985$	2.27264	−	39.0197i	0.0724123	−	1.24327i
$986$	1.74699	−	0.877374i	0.0556356	−	0.0279413i
$987$		0			0
$988$	−9.31553	−	9.87389i	−0.296367	−	0.314130i
$989$	21.6484	−	7.87936i	0.688378	−	0.250549i
$990$		0			0
$991$	−51.9890	−	18.9225i	−1.65149	−	0.601092i	−0.662495	−	0.749066i	$-0.730502\pi$
$991$	−51.9890	−	18.9225i	−1.65149	−	0.601092i	−0.988991	+	0.147975i	$0.952725\pi$
$992$	5.64347	+	13.0830i	0.179180	+	0.415387i
$993$		0			0
$994$	−39.4544	−	131.787i	−1.25142	−	4.18002i
$995$	−37.7346	+	4.41054i	−1.19627	+	0.139823i
$996$		0			0
$997$	−1.53794	−	26.4053i	−0.0487069	−	0.836266i	−0.930877	−	0.365334i	$-0.880955\pi$
$997$	−1.53794	−	26.4053i	−0.0487069	−	0.836266i	0.882170	−	0.470932i	$-0.156082\pi$
$998$	21.6701	+	37.5337i	0.685954	+	1.18811i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.28.7		144
3.2	odd	2		729.2.g.a.28.2		144
9.2	odd	6		729.2.g.b.271.7		144
9.4	even	3		81.2.g.a.40.7	✓	144
9.5	odd	6		243.2.g.a.91.2		144
9.7	even	3		729.2.g.c.271.2		144
81.2	odd	54		729.2.g.b.460.7		144
81.25	even	27		81.2.g.a.79.7	yes	144
81.29	odd	54		729.2.g.a.703.2		144
81.32	odd	54		6561.2.a.d.1.63		72
81.49	even	27		6561.2.a.c.1.10		72
81.52	even	27	inner	729.2.g.d.703.7		144
81.56	odd	54		243.2.g.a.235.2		144
81.79	even	27		729.2.g.c.460.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.7	✓	144	9.4	even	3
81.2.g.a.79.7	yes	144	81.25	even	27
243.2.g.a.91.2		144	9.5	odd	6
243.2.g.a.235.2		144	81.56	odd	54
729.2.g.a.28.2		144	3.2	odd	2
729.2.g.a.703.2		144	81.29	odd	54
729.2.g.b.271.7		144	9.2	odd	6
729.2.g.b.460.7		144	81.2	odd	54
729.2.g.c.271.2		144	9.7	even	3
729.2.g.c.460.2		144	81.79	even	27
729.2.g.d.28.7		144	1.1	even	1	trivial
729.2.g.d.703.7		144	81.52	even	27	inner
6561.2.a.c.1.10		72	81.49	even	27
6561.2.a.d.1.63		72	81.32	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)

\(f(q)\)	\(=\)	\(q+(1.97349 - 1.29799i) q^{2} +(1.41775 - 3.28671i) q^{4} +(1.82524 - 1.93464i) q^{5} +(-4.56284 - 0.533319i) q^{7} +(-0.647845 - 3.67411i) q^{8} +O(q^{10})\)	\(q+(1.97349 - 1.29799i) q^{2} +(1.41775 - 3.28671i) q^{4} +(1.82524 - 1.93464i) q^{5} +(-4.56284 - 0.533319i) q^{7} +(-0.647845 - 3.67411i) q^{8} +(1.09096 - 6.18715i) q^{10} +(-0.138834 + 0.463739i) q^{11} +(0.253222 - 4.34765i) q^{13} +(-9.69698 + 4.87000i) q^{14} +(-1.13474 - 1.20275i) q^{16} +(0.936739 - 0.340945i) q^{17} +(0.818296 + 0.297835i) q^{19} +(-3.77088 - 8.74187i) q^{20} +(0.327938 + 1.09539i) q^{22} +(2.03881 - 0.238302i) q^{23} +(-0.120613 - 2.07085i) q^{25} +(-5.14346 - 8.90874i) q^{26} +(-8.22182 + 14.2406i) q^{28} +(0.741930 + 0.372611i) q^{29} +(2.39289 + 3.21420i) q^{31} +(3.45991 + 0.820013i) q^{32} +(1.40611 - 1.88873i) q^{34} +(-9.36007 + 7.85403i) q^{35} +(0.840131 + 0.704953i) q^{37} +(2.00149 - 0.474361i) q^{38} +(-8.29057 - 5.45280i) q^{40} +(-0.244464 - 0.160787i) q^{41} +(10.9207 - 2.58825i) q^{43} +(1.32734 + 1.11377i) q^{44} +(3.71426 - 3.11664i) q^{46} +(-2.41144 + 3.23913i) q^{47} +(13.7238 + 3.25259i) q^{49} +(-2.92597 - 3.93025i) q^{50} +(-13.9305 - 6.99614i) q^{52} +(0.806764 - 1.39736i) q^{53} +(0.643763 + 1.11503i) q^{55} +(0.996538 + 17.1099i) q^{56} +(1.94784 - 0.227670i) q^{58} +(-1.51146 - 5.04861i) q^{59} +(1.59785 + 3.70422i) q^{61} +(8.89434 + 3.23728i) q^{62} +(11.0001 - 4.00372i) q^{64} +(-7.94897 - 8.42541i) q^{65} +(-12.8887 + 6.47296i) q^{67} +(0.207472 - 3.56216i) q^{68} +(-8.27761 + 27.6491i) q^{70} +(-2.20143 + 12.4849i) q^{71} +(1.00775 + 5.71524i) q^{73} +(2.57301 + 0.300742i) q^{74} +(2.13903 - 2.26724i) q^{76} +(0.880799 - 2.04192i) q^{77} +(5.40905 - 3.55759i) q^{79} -4.39806 q^{80} -0.691147 q^{82} +(-10.6112 + 6.97906i) q^{83} +(1.05017 - 2.43456i) q^{85} +(18.1924 - 19.2828i) q^{86} +(1.79377 + 0.209662i) q^{88} +(-2.74643 - 15.5758i) q^{89} +(-3.47410 + 19.7026i) q^{91} +(2.10728 - 7.03882i) q^{92} +(-0.554617 + 9.52241i) q^{94} +(2.06979 - 1.03949i) q^{95} +(-1.39077 - 1.47414i) q^{97} +(31.3056 - 11.3943i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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

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