LMFDB - Embedded newform 729.2.g.d.703.7

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			703.7
Character	$\chi$	$=$	729.703
Dual form			729.2.g.d.28.7

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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	1.00000		0.000662916i	$-0.000211013\pi$
$2$	1.97349	+	1.29799i	1.39547	+	0.917816i	0.395471	+	0.918478i	$0.370581\pi$
$3$		0			0
$3$		0			0
$4$	1.41775	+	3.28671i	0.708873	+	1.64335i
$5$	1.82524	+	1.93464i	0.816273	+	0.865199i	0.992884	−	0.119082i	$-0.0379950\pi$
$5$	1.82524	+	1.93464i	0.816273	+	0.865199i	−0.176611	+	0.984281i	$0.556514\pi$
$6$		0			0
$7$	−4.56284	+	0.533319i	−1.72459	+	0.201576i	−0.919909	−	0.392131i	$-0.871738\pi$
$7$	−4.56284	+	0.533319i	−1.72459	+	0.201576i	−0.804682	+	0.593707i	$0.797664\pi$
$8$	−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	0.934505	−	0.355950i	$-0.115843\pi$
$11$	−0.138834	−	0.463739i	−0.0418601	−	0.139822i	−0.976365	+	0.216127i	$0.930657\pi$
$12$		0			0
$13$	0.253222	+	4.34765i	0.0702311	+	1.20582i	0.830803	+	0.556567i	$0.187882\pi$
$13$	0.253222	+	4.34765i	0.0702311	+	1.20582i	−0.760571	+	0.649254i	$0.775081\pi$
$14$	−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	0.453108	−	0.891456i	$-0.350315\pi$
$17$	0.936739	+	0.340945i	0.227193	+	0.0826914i	−0.225916	+	0.974147i	$0.572537\pi$
$18$		0			0
$19$	0.818296	−	0.297835i	0.187730	−	0.0683281i	−0.246445	−	0.969157i	$-0.579262\pi$
$19$	0.818296	−	0.297835i	0.187730	−	0.0683281i	0.434175	+	0.900829i	$0.357040\pi$
$20$	−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	0.325964	−	0.945382i	$-0.394311\pi$
$23$	2.03881	+	0.238302i	0.425121	+	0.0496895i	0.0991571	+	0.995072i	$0.468385\pi$
$24$		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	−0.378577	−	0.925570i	$-0.623587\pi$
$29$	0.741930	−	0.372611i	0.137773	−	0.0691922i	0.516350	+	0.856378i	$0.327290\pi$
$30$		0			0
$31$	2.39289	−	3.21420i	0.429775	−	0.577288i	−0.533502	−	0.845799i	$-0.679124\pi$
$31$	2.39289	−	3.21420i	0.429775	−	0.577288i	0.963277	+	0.268511i	$0.0865316\pi$
$32$	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	−0.571112	−	0.820872i	$-0.693488\pi$
$37$	0.840131	−	0.704953i	0.138117	−	0.115894i	0.709229	+	0.704979i	$0.249043\pi$
$38$	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	−0.568455	−	0.822714i	$-0.692459\pi$
$41$	−0.244464	+	0.160787i	−0.0381789	+	0.0251106i	0.530276	+	0.847825i	$0.322088\pi$
$42$		0			0
$43$	10.9207	+	2.58825i	1.66539	+	0.394704i	0.952007	−	0.306075i	$-0.0990158\pi$
$43$	10.9207	+	2.58825i	1.66539	+	0.394704i	0.713379	+	0.700779i	$0.247164\pi$
$44$	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	0.590674	−	0.806910i	$-0.298862\pi$
$47$	−2.41144	−	3.23913i	−0.351745	−	0.472475i	−0.942419	+	0.334435i	$0.891454\pi$
$48$		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	0.916100	−	0.400950i	$-0.131320\pi$
$53$	0.806764	+	1.39736i	0.110818	+	0.191942i	−0.805283	+	0.592891i	$0.797986\pi$
$54$		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	0.801469	+	0.598036i	$0.204052\pi$
$59$	−1.51146	+	5.04861i	−0.196775	+	0.657273i	−0.998244	+	0.0592374i	$0.981133\pi$
$60$		0			0
$61$	1.59785	−	3.70422i	0.204583	−	0.474277i	−0.784774	−	0.619781i	$-0.787221\pi$
$61$	1.59785	−	3.70422i	0.204583	−	0.474277i	0.989358	+	0.145504i	$0.0464805\pi$
$62$	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	−0.574982	−	0.818166i	$-0.694991\pi$
$67$	−12.8887	−	6.47296i	−1.57461	−	0.790798i	−0.999625	+	0.0273685i	$0.991287\pi$
$68$	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	−0.779474	−	0.626434i	$-0.784514\pi$
$71$	−2.20143	−	12.4849i	−0.261261	−	1.48169i	0.518213	−	0.855252i	$-0.326597\pi$
$72$		0			0
$73$	1.00775	−	5.71524i	0.117948	−	0.668918i	−0.867300	−	0.497786i	$-0.834146\pi$
$73$	1.00775	−	5.71524i	0.117948	−	0.668918i	0.985248	−	0.171132i	$-0.0547425\pi$
$74$	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	0.816052	−	0.577978i	$-0.196158\pi$
$79$	5.40905	+	3.55759i	0.608566	+	0.400260i	−0.207487	+	0.978238i	$0.566528\pi$
$80$	−4.39806			−0.491718
$81$		0			0
$82$	−0.691147			−0.0763245
$83$	−10.6112	−	6.97906i	−1.16473	−	0.766052i	−0.188343	−	0.982103i	$-0.560312\pi$
$83$	−10.6112	−	6.97906i	−1.16473	−	0.766052i	−0.976382	+	0.216052i	$0.930682\pi$
$84$		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	0.391442	+	0.920203i	$0.371976\pi$
$89$	−2.74643	+	15.5758i	−0.291121	+	1.65103i	−0.682563	+	0.730827i	$0.739135\pi$
$90$		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	−0.794119	−	0.607762i	$-0.792068\pi$
$97$	−1.39077	+	1.47414i	−0.141212	+	0.149676i	0.652908	+	0.757438i	$0.273549\pi$
$98$	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	−0.999206	−	0.0398351i	$-0.987317\pi$
$101$	−2.85953	+	6.62915i	−0.284534	+	0.659625i	0.714672	+	0.699460i	$0.246576\pi$
$102$		0			0
$103$	−1.25810	+	4.20236i	−0.123965	+	0.414071i	−0.997333	−	0.0729900i	$-0.976746\pi$
$103$	−1.25810	+	4.20236i	−0.123965	+	0.414071i	0.873368	+	0.487061i	$0.161931\pi$
$104$	−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	−0.670500	−	0.741910i	$-0.733920\pi$
$107$	3.17835	−	5.50506i	0.307263	−	0.532194i	0.977763	+	0.209715i	$0.0672537\pi$
$108$		0			0
$109$	4.40215	+	7.62475i	0.421649	+	0.730318i	0.996101	−	0.0882203i	$-0.0281179\pi$
$109$	4.40215	+	7.62475i	0.421649	+	0.730318i	−0.574452	+	0.818539i	$0.694785\pi$
$110$	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	−0.938310	−	0.345795i	$-0.887609\pi$
$113$	−17.2381	+	4.08550i	−1.62162	+	0.384332i	−0.683312	+	0.730126i	$0.739461\pi$
$114$		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	0.811660	−	0.584130i	$-0.198564\pi$
$127$	4.25250	+	3.56827i	0.377349	+	0.316633i	−0.434312	+	0.900763i	$0.643008\pi$
$128$	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	0.00278912	−	0.999996i	$-0.499112\pi$
$131$	10.9874	−	14.7587i	0.959975	−	1.28947i	0.957186	−	0.289474i	$-0.0934804\pi$
$132$		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	0.953935	+	0.300015i	$0.0969916\pi$
$137$	−0.332173	+	5.70318i	−0.0283794	+	0.487256i	−0.982314	+	0.187241i	$0.940045\pi$
$138$		0			0
$139$	9.52866	+	1.11374i	0.808210	+	0.0944662i	0.510155	−	0.860082i	$-0.329588\pi$
$139$	9.52866	+	1.11374i	0.808210	+	0.0944662i	0.298055	+	0.954549i	$0.403662\pi$
$140$	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	−0.776022	−	0.630705i	$-0.782766\pi$
$149$	−0.957819	−	16.4451i	−0.0784676	−	1.34724i	0.697555	−	0.716531i	$-0.254271\pi$
$150$		0			0
$151$	−3.37514	−	11.2737i	−0.274665	−	0.917444i	−0.978354	−	0.206936i	$-0.933651\pi$
$151$	−3.37514	−	11.2737i	−0.274665	−	0.917444i	0.703690	−	0.710507i	$-0.251535\pi$
$152$	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	0.982873	−	0.184282i	$-0.0589960\pi$
$157$	9.29415	+	9.85123i	0.741754	+	0.786213i	−0.241119	+	0.970495i	$0.577514\pi$
$158$	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	0.363229	−	0.931700i	$-0.381674\pi$
$167$	−7.59882	−	8.05428i	−0.588014	−	0.623259i	−0.951243	+	0.308441i	$0.900193\pi$
$168$		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	−0.974907	−	0.222614i	$-0.928541\pi$
$173$	−3.71850	−	12.4207i	−0.282713	−	0.944326i	0.692194	−	0.721711i	$-0.256644\pi$
$174$		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	−0.999857	−	0.0169124i	$-0.994616\pi$
$179$	−23.7701	−	8.65162i	−1.77666	−	0.646652i	−0.776806	−	0.629740i	$-0.783161\pi$
$180$		0			0
$181$	10.2266	−	3.72217i	0.760135	−	0.276667i	0.0672712	−	0.997735i	$-0.478571\pi$
$181$	10.2266	−	3.72217i	0.760135	−	0.276667i	0.692864	+	0.721068i	$0.256348\pi$
$182$	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	−0.0237184	−	0.999719i	$-0.507551\pi$
$191$	10.5589	−	5.30288i	0.764015	−	0.383703i	0.787734	+	0.616016i	$0.211254\pi$
$192$		0			0
$193$	−5.14242	+	6.90746i	−0.370159	+	0.497210i	−0.947705	−	0.319148i	$-0.896603\pi$
$193$	−5.14242	+	6.90746i	−0.370159	+	0.497210i	0.577546	+	0.816358i	$0.304011\pi$
$194$	−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	0.948694	−	0.316196i	$-0.102406\pi$
$197$	11.2572	+	9.44590i	0.802041	+	0.672992i	−0.146653	+	0.989188i	$0.546850\pi$
$198$		0			0
$199$	−10.9420	+	9.18142i	−0.775657	+	0.650853i	−0.942151	−	0.335189i	$-0.891200\pi$
$199$	−10.9420	+	9.18142i	−0.775657	+	0.650853i	0.166494	+	0.986042i	$0.446755\pi$
$200$	−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	−0.136429	−	0.990650i	$-0.543563\pi$
$211$	2.70553	−	0.641223i	0.186257	−	0.0441436i	0.322685	+	0.946506i	$0.395414\pi$
$212$	−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	0.236957	+	0.971520i	$0.423850\pi$
$223$	−9.44242	+	21.8900i	−0.632311	+	1.46586i	−0.869268	+	0.494341i	$0.835409\pi$
$224$	−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	−0.799477	−	0.600697i	$-0.794890\pi$
$227$	−2.30985	+	2.44830i	−0.153310	+	0.162499i	0.646166	+	0.763197i	$0.276371\pi$
$228$		0			0
$229$	8.24425	+	4.14042i	0.544795	+	0.273607i	0.699838	−	0.714301i	$-0.253255\pi$
$229$	8.24425	+	4.14042i	0.544795	+	0.273607i	−0.155043	+	0.987908i	$0.549552\pi$
$230$	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	0.951323	−	0.308196i	$-0.0997252\pi$
$233$	−0.733258	−	4.15851i	−0.0480373	−	0.272433i	−0.999360	+	0.0357624i	$0.988614\pi$
$234$		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	0.850581	−	0.525845i	$-0.176251\pi$
$239$	−1.78727	−	4.14335i	−0.115609	−	0.268011i	−0.966189	+	0.257833i	$0.916991\pi$
$240$		0			0
$241$	−7.03651	−	4.62799i	−0.453261	−	0.298115i	0.302276	−	0.953221i	$-0.402254\pi$
$241$	−7.03651	−	4.62799i	−0.453261	−	0.298115i	−0.755537	+	0.655106i	$0.772624\pi$
$242$	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	−0.892170	−	0.451700i	$-0.850818\pi$
$251$	1.59517	−	9.04665i	0.100686	−	0.571020i	0.992856	−	0.119319i	$-0.0380713\pi$
$252$		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	0.204300	−	0.978908i	$-0.434508\pi$
$257$	−7.35681	−	3.69473i	−0.458905	−	0.230471i	−0.663206	+	0.748437i	$0.730804\pi$
$258$		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	−0.912871	−	0.408249i	$-0.866140\pi$
$263$	0.170742	−	0.395824i	0.0105284	−	0.0244076i	0.923399	+	0.383841i	$0.125399\pi$
$264$		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	−0.981616	−	0.190864i	$-0.938871\pi$
$269$	−5.33884	+	9.24714i	−0.325515	+	0.563808i	0.656102	+	0.754673i	$0.272204\pi$
$270$		0			0
$271$	7.65288	+	13.2552i	0.464880	+	0.805195i	0.999196	−	0.0400894i	$-0.0127643\pi$
$271$	7.65288	+	13.2552i	0.464880	+	0.805195i	−0.534316	+	0.845285i	$0.679431\pi$
$272$	−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	0.521365	−	0.853334i	$-0.325423\pi$
$277$	−7.41708	−	9.96287i	−0.445649	−	0.598611i	−0.967014	+	0.254723i	$0.918016\pi$
$278$	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	−0.831158	−	0.556037i	$-0.812321\pi$
$281$	−30.5667	−	7.24444i	−1.82346	−	0.432167i	−0.992298	+	0.123870i	$0.960470\pi$
$282$		0			0
$283$	0.490426	−	0.322558i	0.0291528	−	0.0191741i	−0.534849	−	0.844948i	$-0.679631\pi$
$283$	0.490426	−	0.322558i	0.0291528	−	0.0191741i	0.564002	+	0.825774i	$0.309261\pi$
$284$	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	−0.134144	+	0.990962i	$0.542829\pi$
$293$	−17.8876	+	24.0272i	−1.04500	+	1.40368i	−0.910858	+	0.412720i	$0.864579\pi$
$294$		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	0.405192	−	0.914232i	$-0.367205\pi$
$307$	2.24152	+	0.815848i	0.127930	+	0.0465629i	−0.277262	+	0.960794i	$0.589427\pi$
$308$	−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	0.695767	+	0.718268i	$0.255065\pi$
$311$	1.55349	+	26.6724i	0.0880903	+	1.51245i	−0.607676	+	0.794185i	$0.707898\pi$
$312$		0			0
$313$	−2.01014	−	6.71433i	−0.113620	−	0.379516i	0.882198	−	0.470879i	$-0.156063\pi$
$313$	−2.01014	−	6.71433i	−0.113620	−	0.379516i	−0.995818	+	0.0913623i	$0.970878\pi$
$314$	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	0.286198	−	0.958171i	$-0.407609\pi$
$317$	13.9881	−	1.63498i	0.785651	−	0.0918294i	0.499453	+	0.866341i	$0.333534\pi$
$318$		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	−0.865901	−	0.500215i	$-0.833254\pi$
$331$	−28.9840	+	3.38774i	−1.59310	+	0.186207i	−0.727203	+	0.686422i	$0.759180\pi$
$332$	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	0.996991	−	0.0775149i	$-0.0246985\pi$
$337$	−0.0414447	−	0.711578i	−0.00225764	−	0.0387621i	−0.999249	+	0.0387528i	$0.987662\pi$
$338$	−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	−0.260178	−	0.965561i	$-0.583781\pi$
$347$	−13.7105	−	1.60252i	−0.736016	−	0.0860279i	−0.475838	+	0.879533i	$0.657855\pi$
$348$		0			0
$349$	1.00932	−	17.3293i	0.0540276	−	0.927618i	−0.857011	−	0.515298i	$-0.827681\pi$
$349$	1.00932	−	17.3293i	0.0540276	−	0.927618i	0.911039	−	0.412320i	$-0.135282\pi$
$350$	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	−0.680746	−	0.732520i	$-0.738344\pi$
$353$	−9.38828	+	4.71497i	−0.499688	+	0.250953i	0.181058	+	0.983472i	$0.442048\pi$
$354$		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	0.589092	−	0.808066i	$-0.299485\pi$
$359$	−1.97814	−	1.65986i	−0.104402	−	0.0876039i	−0.693495	+	0.720462i	$0.743930\pi$
$360$		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	0.749746	−	0.661726i	$-0.230176\pi$
$367$	21.5090	+	5.09773i	1.12276	+	0.266099i	0.373015	+	0.927825i	$0.378324\pi$
$368$	−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	−0.483407	−	0.875396i	$-0.660601\pi$
$373$	−10.0915	+	2.39173i	−0.522519	+	0.123839i	−0.0391118	+	0.999235i	$0.512453\pi$
$374$	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	−0.746046	−	0.665894i	$-0.768050\pi$
$379$	3.96481	−	6.86725i	0.203658	−	0.352747i	0.949704	+	0.313148i	$0.101383\pi$
$380$	−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	−0.984102	−	0.177604i	$-0.943165\pi$
$383$	−1.25841	+	4.20338i	−0.0643018	+	0.214783i	0.919800	+	0.392387i	$0.128351\pi$
$384$		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	−0.671083	−	0.741382i	$-0.734171\pi$
$389$	2.13138	−	2.25913i	0.108065	−	0.114543i	0.779148	+	0.626840i	$0.215652\pi$
$390$		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	−0.678832	−	0.734294i	$-0.737514\pi$
$397$	4.18830	−	23.7530i	0.210205	−	1.19213i	0.889037	−	0.457836i	$-0.151375\pi$
$398$	−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	−0.901887	−	0.431972i	$-0.857818\pi$
$401$	−11.9585	−	27.7230i	−0.597180	−	1.38442i	0.304707	−	0.952446i	$-0.401441\pi$
$402$		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	0.959804	−	0.280671i	$-0.0905569\pi$
$409$	1.96158	+	4.54746i	0.0969940	+	0.224857i	−0.862810	+	0.505528i	$0.831298\pi$
$410$	−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	−0.191821	−	0.981430i	$-0.561439\pi$
$419$	−22.3854	−	11.2423i	−1.09360	−	0.549225i	−0.901775	+	0.432205i	$0.857736\pi$
$420$		0			0
$421$	21.4522	−	22.7380i	1.04552	−	1.10818i	0.0515303	−	0.998671i	$-0.483590\pi$
$421$	21.4522	−	22.7380i	1.04552	−	1.10818i	0.993986	−	0.109511i	$-0.0349284\pi$
$422$	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	−0.880744	−	0.473593i	$-0.842957\pi$
$431$	−0.627551	+	1.08695i	−0.0302281	+	0.0523566i	0.850516	+	0.525950i	$0.176290\pi$
$432$		0			0
$433$	16.4409	+	28.4764i	0.790097	+	1.36849i	0.925906	+	0.377753i	$0.123303\pi$
$433$	16.4409	+	28.4764i	0.790097	+	1.36849i	−0.135809	+	0.990735i	$0.543363\pi$
$434$	−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	0.999819	+	0.0190010i	$0.00604858\pi$
$439$	15.3218	+	20.5808i	0.731271	+	0.982267i	−0.268549	+	0.963266i	$0.586544\pi$
$440$	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	0.654392	−	0.756156i	$-0.272925\pi$
$443$	18.9389	+	4.48861i	0.899816	+	0.213260i	0.245424	+	0.969416i	$0.421073\pi$
$444$		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	−0.666666	−	0.745357i	$-0.732279\pi$
$449$	−1.02554	+	0.860532i	−0.0483983	+	0.0406110i	0.618268	+	0.785968i	$0.287835\pi$
$450$		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	0.0168285	−	0.999858i	$-0.494643\pi$
$457$	17.7196	−	8.89911i	0.828887	−	0.416283i	0.812059	+	0.583575i	$0.198347\pi$
$458$	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	−0.647064	−	0.762436i	$-0.724003\pi$
$461$	1.80652	−	31.0168i	0.0841382	−	1.44460i	0.731202	−	0.682161i	$-0.238960\pi$
$462$		0			0
$463$	−4.19118	−	0.489879i	−0.194781	−	0.0227666i	0.0181432	−	0.999835i	$-0.494225\pi$
$463$	−4.19118	−	0.489879i	−0.194781	−	0.0227666i	−0.212924	+	0.977069i	$0.568299\pi$
$464$	−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	−0.888384	−	0.459100i	$-0.848172\pi$
$467$	−27.5275	+	10.0192i	−1.27382	+	0.463633i	−0.385438	+	0.922734i	$0.625950\pi$
$468$		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	0.485720	−	0.874115i	$-0.338558\pi$
$479$	25.3863	−	2.96724i	1.15993	−	0.135577i	0.674212	+	0.738538i	$0.264483\pi$
$480$		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	0.414878	−	0.909877i	$-0.363824\pi$
$491$	−11.4689	−	12.1563i	−0.517583	−	0.548606i	−0.932461	+	0.361271i	$0.882343\pi$
$492$		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	−0.934112	−	0.356980i	$-0.883806\pi$
$499$	−1.06686	−	18.3172i	−0.0477590	−	0.819991i	0.886353	−	0.463010i	$-0.153231\pi$
$500$	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	0.770656	−	0.637251i	$-0.219929\pi$
$503$	21.3376	+	7.76624i	0.951395	+	0.346280i	0.180739	+	0.983531i	$0.442151\pi$
$504$		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	0.676703	−	0.736256i	$-0.263408\pi$
$509$	26.2920	+	3.07310i	1.16537	+	0.136213i	0.488670	+	0.872469i	$0.337482\pi$
$510$		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	0.999669	−	0.0257345i	$-0.00819245\pi$
$521$	26.2017	+	21.9858i	1.14792	+	0.963216i	0.148247	+	0.988950i	$0.452637\pi$
$522$		0			0
$523$	17.6317	−	14.7948i	0.770982	−	0.646931i	−0.169978	−	0.985448i	$-0.554370\pi$
$523$	17.6317	−	14.7948i	0.770982	−	0.646931i	0.940960	+	0.338517i	$0.109925\pi$
$524$	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	−0.384336	−	0.923193i	$-0.625570\pi$
$541$	14.1264	−	24.4676i	0.607340	−	1.05194i	0.991677	−	0.128751i	$-0.0410970\pi$
$542$	−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	−0.692310	−	0.721600i	$-0.743407\pi$
$547$	7.19544	−	16.6809i	0.307655	−	0.713224i	0.999965	+	0.00837626i	$0.00266628\pi$
$548$	−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	0.998794	−	0.0490932i	$-0.0156331\pi$
$557$	1.02531	+	5.81482i	0.0434438	+	0.246382i	−0.955350	+	0.295475i	$0.904522\pi$
$558$		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	0.994908	+	0.100789i	$0.0321367\pi$
$563$	9.14633	+	21.2036i	0.385472	+	0.893624i	−0.609436	+	0.792835i	$0.708604\pi$
$564$		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	0.699597	−	0.714537i	$-0.253363\pi$
$569$	7.64736	+	5.02975i	0.320594	+	0.210858i	−0.379003	+	0.925395i	$0.623733\pi$
$570$		0			0
$571$	4.50616	+	10.4465i	0.188577	+	0.437171i	0.986108	−	0.166108i	$-0.0531200\pi$
$571$	4.50616	+	10.4465i	0.188577	+	0.437171i	−0.797531	+	0.603279i	$0.793861\pi$
$572$	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	−0.951068	−	0.308981i	$-0.900012\pi$
$577$	−3.91622	−	22.2100i	−0.163034	−	0.924613i	0.788034	−	0.615632i	$-0.211099\pi$
$578$	−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	0.577114	+	0.816663i	$0.304179\pi$
$587$	−10.0049	+	23.1939i	−0.412945	+	0.957314i	−0.990059	+	0.140651i	$0.955081\pi$
$588$		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	0.461639	+	0.887068i	$0.347262\pi$
$593$	−13.0866	+	22.6667i	−0.537404	+	0.930811i	−0.999043	+	0.0437427i	$0.986072\pi$
$594$		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	−0.499601	−	0.866256i	$-0.666520\pi$
$599$	−13.6393	+	3.23257i	−0.557285	+	0.132079i	−0.0576847	+	0.998335i	$0.518372\pi$
$600$		0			0
$601$	−8.14178	−	10.9363i	−0.332110	−	0.446102i	0.604432	−	0.796657i	$-0.293400\pi$
$601$	−8.14178	−	10.9363i	−0.332110	−	0.446102i	−0.936542	+	0.350555i	$0.885993\pi$
$602$	−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	−0.856802	−	0.515645i	$-0.827552\pi$
$607$	−17.8052	+	11.7107i	−0.722691	+	0.475321i	0.134112	+	0.990966i	$0.457182\pi$
$608$	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	0.946460	−	0.322821i	$-0.104631\pi$
$613$	19.6311	+	16.4725i	0.792894	+	0.665317i	−0.153566	+	0.988138i	$0.549076\pi$
$614$	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	−0.921152	−	0.389203i	$-0.872751\pi$
$617$	−7.05717	+	9.47942i	−0.284111	+	0.381627i	0.637041	+	0.770830i	$0.280158\pi$
$618$		0			0
$619$	27.0251	−	13.5725i	1.08623	−	0.545526i	0.186716	−	0.982414i	$-0.440216\pi$
$619$	27.0251	−	13.5725i	1.08623	−	0.545526i	0.899516	+	0.436888i	$0.143919\pi$
$620$	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	0.325190	−	0.945649i	$-0.394572\pi$
$631$	−0.842816	−	0.306760i	−0.0335520	−	0.0122119i	−0.358742	+	0.933437i	$0.616794\pi$
$632$	−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	−0.240697	−	0.970600i	$-0.577376\pi$
$641$	−6.35661	+	0.742982i	−0.251071	+	0.0293460i	−0.0103737	+	0.999946i	$0.503302\pi$
$642$		0			0
$643$	10.2749	+	10.8908i	0.405203	+	0.429491i	0.897553	−	0.440907i	$-0.145343\pi$
$643$	10.2749	+	10.8908i	0.405203	+	0.429491i	−0.492349	+	0.870398i	$0.663862\pi$
$644$	−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	0.999836	+	0.0181055i	$0.00576347\pi$
$653$	24.5260	+	25.9960i	0.959776	+	1.01730i	−0.0400604	+	0.999197i	$0.512755\pi$
$654$		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	0.999645	−	0.0266581i	$-0.00848655\pi$
$659$	3.84564	+	12.8453i	0.149805	+	0.500383i	−0.849840	+	0.527041i	$0.823301\pi$
$660$		0			0
$661$	0.462308	+	7.93752i	0.0179817	+	0.308734i	0.995292	+	0.0969213i	$0.0308995\pi$
$661$	0.462308	+	7.93752i	0.0179817	+	0.308734i	−0.977310	+	0.211812i	$0.932063\pi$
$662$	−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	−0.787187	−	0.616714i	$-0.788463\pi$
$673$	1.71928	−	29.5189i	0.0662735	−	1.13787i	0.853461	−	0.521158i	$-0.174500\pi$
$674$	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	−0.834624	−	0.550820i	$-0.814315\pi$
$677$	−23.1884	+	11.6456i	−0.891201	+	0.447578i	−0.0565769	+	0.998398i	$0.518019\pi$
$678$		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	0.398182	−	0.917306i	$-0.369641\pi$
$683$	−11.3957	−	9.56212i	−0.436044	−	0.365885i	−0.834227	+	0.551422i	$0.814086\pi$
$684$		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	−0.183533	−	0.983014i	$-0.558753\pi$
$691$	−20.7330	−	4.91380i	−0.788719	−	0.186930i	−0.605187	+	0.796084i	$0.706901\pi$
$692$	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	0.547366	−	0.836894i	$-0.315631\pi$
$701$	−11.9432	−	20.6862i	−0.451088	−	0.781308i	−0.998454	+	0.0555858i	$0.982297\pi$
$702$		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	0.526501	+	0.850175i	$0.323504\pi$
$709$	−12.0674	+	27.9754i	−0.453201	+	1.05064i	−0.979701	+	0.200463i	$0.935756\pi$
$710$	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	−0.750404	−	0.660979i	$-0.770141\pi$
$719$	−7.27531	−	41.2603i	−0.271323	−	1.53875i	0.479081	−	0.877771i	$-0.340970\pi$
$720$		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	0.828193	−	0.560444i	$-0.189369\pi$
$727$	17.2998	+	11.3783i	0.641614	+	0.421996i	−0.186578	+	0.982440i	$0.559740\pi$
$728$	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	−0.909991	−	0.414629i	$-0.863911\pi$
$733$	−15.8953	−	36.8495i	−0.587107	−	1.36107i	0.322884	−	0.946439i	$-0.395348\pi$
$734$	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	0.872044	+	0.489427i	$0.162794\pi$
$739$	5.98018	+	33.9153i	0.219985	+	1.24759i	−0.652060	+	0.758168i	$0.726095\pi$
$740$	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	0.637488	−	0.770461i	$-0.279974\pi$
$743$	10.9077	+	5.47805i	0.400164	+	0.200970i	−0.237323	+	0.971431i	$0.576270\pi$
$744$		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	−0.453855	−	0.891075i	$-0.649952\pi$
$751$	11.3725	−	37.9869i	0.414989	−	1.38616i	0.868845	−	0.495085i	$-0.164863\pi$
$752$	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	0.633063	−	0.774101i	$-0.281798\pi$
$757$	−9.73596	−	16.8632i	−0.353859	−	0.612902i	−0.986922	+	0.161198i	$0.948464\pi$
$758$	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	−0.128826	−	0.991667i	$-0.541121\pi$
$761$	5.54788	−	1.31487i	0.201110	−	0.0476640i	0.329936	+	0.944003i	$0.392973\pi$
$762$		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	−0.102840	−	0.994698i	$-0.532793\pi$
$769$	21.3465	−	14.0398i	0.769775	−	0.506289i	0.872615	+	0.488409i	$0.162423\pi$
$770$	−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	−0.178116	+	0.984009i	$0.557000\pi$
$773$	−32.7547	+	27.4845i	−1.17811	+	0.988548i	−0.999990	+	0.00453893i	$0.998555\pi$
$774$		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

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

L-functions

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