LMFDB - Embedded newform 729.2.g.b.109.2

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			109.2
Character	$\chi$	$=$	729.109
Dual form			729.2.g.b.622.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40463 - 1.48883i) q^{2} +(-0.127314 + 2.18589i) q^{4} +(0.0206552 - 0.00241424i) q^{5} +(-1.34442 - 0.675193i) q^{7} +(0.297287 - 0.249453i) q^{8} +O(q^{10})$	\(q+(-1.40463 - 1.48883i) q^{2} +(-0.127314 + 2.18589i) q^{4} +(0.0206552 - 0.00241424i) q^{5} +(-1.34442 - 0.675193i) q^{7} +(0.297287 - 0.249453i) q^{8} +(-0.0326074 - 0.0273608i) q^{10} +(-2.38035 - 5.51826i) q^{11} +(2.13772 + 0.506650i) q^{13} +(0.883173 + 2.95000i) q^{14} +(3.56062 + 0.416176i) q^{16} +(0.699765 - 3.96856i) q^{17} +(0.689869 + 3.91244i) q^{19} +(0.00264759 + 0.0454574i) q^{20} +(-4.87221 + 11.2951i) q^{22} +(-0.900106 + 0.452050i) q^{23} +(-4.86480 + 1.15298i) q^{25} +(-2.24841 - 3.89435i) q^{26} +(1.64706 - 2.85280i) q^{28} +(-1.61295 + 5.38763i) q^{29} +(-2.49542 - 1.64126i) q^{31} +(-4.84524 - 6.50829i) q^{32} +(-6.89141 + 4.53255i) q^{34} +(-0.0293993 - 0.0107005i) q^{35} +(-6.49019 + 2.36224i) q^{37} +(4.85593 - 6.52265i) q^{38} +(0.00553827 - 0.00587022i) q^{40} +(-3.38050 + 3.58312i) q^{41} +(3.93296 - 5.28288i) q^{43} +(12.3654 - 4.50063i) q^{44} +(1.93734 + 0.705135i) q^{46} +(-11.2967 + 7.42995i) q^{47} +(-2.82853 - 3.79938i) q^{49} +(8.54986 + 5.62333i) q^{50} +(-1.37964 + 4.60833i) q^{52} +(-4.73855 + 8.20740i) q^{53} +(-0.0624889 - 0.108234i) q^{55} +(-0.568107 + 0.134644i) q^{56} +(10.2868 - 5.16624i) q^{58} +(0.693406 - 1.60750i) q^{59} +(0.517762 + 8.88963i) q^{61} +(1.06160 + 6.02061i) q^{62} +(-1.63891 + 9.29469i) q^{64} +(0.0453782 + 0.00530396i) q^{65} +(-3.91000 - 13.0603i) q^{67} +(8.58577 + 2.03487i) q^{68} +(0.0253641 + 0.0588007i) q^{70} +(3.48681 + 2.92578i) q^{71} +(-7.30212 + 6.12720i) q^{73} +(12.6333 + 6.34468i) q^{74} +(-8.64002 + 1.00987i) q^{76} +(-0.525707 + 9.02605i) q^{77} +(2.18549 + 2.31648i) q^{79} +0.0745499 q^{80} +10.0830 q^{82} +(1.15185 + 1.22089i) q^{83} +(0.00487269 - 0.0836608i) q^{85} +(-13.3897 + 1.56503i) q^{86} +(-2.08419 - 1.04672i) q^{88} +(7.75680 - 6.50872i) q^{89} +(-2.53191 - 2.12452i) q^{91} +(-0.873538 - 2.02509i) q^{92} +(26.9296 + 6.38244i) q^{94} +(0.0236950 + 0.0791467i) q^{95} +(6.59501 + 0.770846i) q^{97} +(-1.68356 + 9.54793i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−1.40463	−	1.48883i	−0.993226	−	1.05276i	−0.998607	−	0.0527730i	$-0.983194\pi$
$2$	−1.40463	−	1.48883i	−0.993226	−	1.05276i	0.00538008	−	0.999986i	$-0.498287\pi$
$3$		0			0
$3$		0			0
$4$	−0.127314	+	2.18589i	−0.0636569	+	1.09295i
$5$	0.0206552	−	0.00241424i	0.00923728	−	0.00107968i	−0.111473	−	0.993767i	$-0.535557\pi$
$5$	0.0206552	−	0.00241424i	0.00923728	−	0.00107968i	0.120710	+	0.992688i	$0.461483\pi$
$6$		0			0
$7$	−1.34442	−	0.675193i	−0.508143	−	0.255199i	0.176207	−	0.984353i	$-0.443617\pi$
$7$	−1.34442	−	0.675193i	−0.508143	−	0.255199i	−0.684349	+	0.729154i	$0.739914\pi$
$8$	0.297287	−	0.249453i	0.105107	−	0.0881950i
$9$		0			0
$10$	−0.0326074	−	0.0273608i	−0.0103114	−	0.00865225i
$11$	−2.38035	−	5.51826i	−0.717701	−	1.66382i	−0.747500	−	0.664262i	$-0.768746\pi$
$11$	−2.38035	−	5.51826i	−0.717701	−	1.66382i	0.0297984	−	0.999556i	$-0.490513\pi$
$12$		0			0
$13$	2.13772	+	0.506650i	0.592898	+	0.140519i	0.516101	−	0.856527i	$-0.327383\pi$
$13$	2.13772	+	0.506650i	0.592898	+	0.140519i	0.0767963	+	0.997047i	$0.475531\pi$
$14$	0.883173	+	2.95000i	0.236038	+	0.788422i
$15$		0			0
$16$	3.56062	+	0.416176i	0.890154	+	0.104044i
$17$	0.699765	−	3.96856i	0.169718	−	0.962518i	−0.774348	−	0.632760i	$-0.781922\pi$
$17$	0.699765	−	3.96856i	0.169718	−	0.962518i	0.944066	−	0.329758i	$-0.106967\pi$
$18$		0			0
$19$	0.689869	+	3.91244i	0.158267	+	0.897576i	0.955738	+	0.294219i	$0.0950595\pi$
$19$	0.689869	+	3.91244i	0.158267	+	0.897576i	−0.797471	+	0.603357i	$0.793829\pi$
$20$	0.00264759	+	0.0454574i	0.000592020	+	0.0101646i
$21$		0			0
$22$	−4.87221	+	11.2951i	−1.03876	+	2.40811i
$23$	−0.900106	+	0.452050i	−0.187685	+	0.0942590i	−0.540160	−	0.841562i	$-0.681636\pi$
$23$	−0.900106	+	0.452050i	−0.187685	+	0.0942590i	0.352475	+	0.935821i	$0.385340\pi$
$24$		0			0
$25$	−4.86480	+	1.15298i	−0.972961	+	0.230596i
$26$	−2.24841	−	3.89435i	−0.440949	−	0.763746i
$27$		0			0
$28$	1.64706	−	2.85280i	0.311266	−	0.539128i
$29$	−1.61295	+	5.38763i	−0.299517	+	1.00046i	0.667258	+	0.744827i	$0.267468\pi$
$29$	−1.61295	+	5.38763i	−0.299517	+	1.00046i	−0.966775	+	0.255630i	$0.917717\pi$
$30$		0			0
$31$	−2.49542	−	1.64126i	−0.448190	−	0.294779i	0.305278	−	0.952263i	$-0.401250\pi$
$31$	−2.49542	−	1.64126i	−0.448190	−	0.294779i	−0.753469	+	0.657484i	$0.771621\pi$
$32$	−4.84524	−	6.50829i	−0.856525	−	1.15051i
$33$		0			0
$34$	−6.89141	+	4.53255i	−1.18187	+	0.777327i
$35$	−0.0293993	−	0.0107005i	−0.00496939	−	0.00180871i
$36$		0			0
$37$	−6.49019	+	2.36224i	−1.06698	+	0.388349i	−0.815047	−	0.579395i	$-0.803289\pi$
$37$	−6.49019	+	2.36224i	−1.06698	+	0.388349i	−0.251934	+	0.967744i	$0.581067\pi$
$38$	4.85593	−	6.52265i	0.787736	−	1.05811i
$39$		0			0
$40$	0.00553827	−	0.00587022i	0.000875677	−	0.000928164i
$41$	−3.38050	+	3.58312i	−0.527945	+	0.559589i	−0.935380	−	0.353645i	$-0.884942\pi$
$41$	−3.38050	+	3.58312i	−0.527945	+	0.559589i	0.407435	+	0.913234i	$0.366423\pi$
$42$		0			0
$43$	3.93296	−	5.28288i	0.599771	−	0.805632i	−0.393758	−	0.919214i	$-0.628825\pi$
$43$	3.93296	−	5.28288i	0.599771	−	0.805632i	0.993529	+	0.113582i	$0.0362326\pi$
$44$	12.3654	−	4.50063i	1.86415	−	0.678496i
$45$		0			0
$46$	1.93734	+	0.705135i	0.285646	+	0.103967i
$47$	−11.2967	+	7.42995i	−1.64779	+	1.08377i	−0.732677	+	0.680577i	$0.761729\pi$
$47$	−11.2967	+	7.42995i	−1.64779	+	1.08377i	−0.915115	+	0.403193i	$0.867900\pi$
$48$		0			0
$49$	−2.82853	−	3.79938i	−0.404076	−	0.542768i
$50$	8.54986	+	5.62333i	1.20913	+	0.795259i
$51$		0			0
$52$	−1.37964	+	4.60833i	−0.191322	+	0.639061i
$53$	−4.73855	+	8.20740i	−0.650890	+	1.12737i	0.332018	+	0.943273i	$0.392271\pi$
$53$	−4.73855	+	8.20740i	−0.650890	+	1.12737i	−0.982907	+	0.184101i	$0.941063\pi$
$54$		0			0
$55$	−0.0624889	−	0.108234i	−0.00842600	−	0.0145943i
$56$	−0.568107	+	0.134644i	−0.0759165	+	0.0179925i
$57$		0			0
$58$	10.2868	−	5.16624i	1.35073	−	0.678361i
$59$	0.693406	−	1.60750i	0.0902737	−	0.209278i	−0.867097	−	0.498139i	$-0.834017\pi$
$59$	0.693406	−	1.60750i	0.0902737	−	0.209278i	0.957371	+	0.288860i	$0.0932764\pi$
$60$		0			0
$61$	0.517762	+	8.88963i	0.0662926	+	1.13820i	0.853356	+	0.521328i	$0.174563\pi$
$61$	0.517762	+	8.88963i	0.0662926	+	1.13820i	−0.787063	+	0.616872i	$0.788400\pi$
$62$	1.06160	+	6.02061i	0.134823	+	0.764619i
$63$		0			0
$64$	−1.63891	+	9.29469i	−0.204863	+	1.16184i
$65$	0.0453782	+	0.00530396i	0.00562848	+	0.000657875i
$66$		0			0
$67$	−3.91000	−	13.0603i	−0.477683	−	1.59557i	−0.769201	−	0.639007i	$-0.779345\pi$
$67$	−3.91000	−	13.0603i	−0.477683	−	1.59557i	0.291518	−	0.956565i	$-0.405840\pi$
$68$	8.58577	+	2.03487i	1.04118	+	0.246764i
$69$		0			0
$70$	0.0253641	+	0.0588007i	0.00303159	+	0.00702803i
$71$	3.48681	+	2.92578i	0.413808	+	0.347226i	0.825802	−	0.563960i	$-0.190723\pi$
$71$	3.48681	+	2.92578i	0.413808	+	0.347226i	−0.411994	+	0.911187i	$0.635167\pi$
$72$		0			0
$73$	−7.30212	+	6.12720i	−0.854648	+	0.717135i	−0.960808	−	0.277214i	$-0.910589\pi$
$73$	−7.30212	+	6.12720i	−0.854648	+	0.717135i	0.106160	+	0.994349i	$0.466144\pi$
$74$	12.6333	+	6.34468i	1.46859	+	0.737554i
$75$		0			0
$76$	−8.64002	+	1.00987i	−0.991078	+	0.115840i
$77$	−0.525707	+	9.02605i	−0.0599099	+	1.02861i
$78$		0			0
$79$	2.18549	+	2.31648i	0.245886	+	0.260624i	0.838549	−	0.544827i	$-0.183405\pi$
$79$	2.18549	+	2.31648i	0.245886	+	0.260624i	−0.592662	+	0.805451i	$0.701923\pi$
$80$	0.0745499			0.00833493
$81$		0			0
$82$	10.0830			1.11348
$83$	1.15185	+	1.22089i	0.126432	+	0.134010i	0.787497	−	0.616319i	$-0.211377\pi$
$83$	1.15185	+	1.22089i	0.126432	+	0.134010i	−0.661065	+	0.750329i	$0.729895\pi$
$84$		0			0
$85$	0.00487269	−	0.0836608i	0.000528517	−	0.00907429i
$86$	−13.3897	+	1.56503i	−1.44384	+	0.168761i
$87$		0			0
$88$	−2.08419	−	1.04672i	−0.222176	−	0.111581i
$89$	7.75680	−	6.50872i	0.822219	−	0.689923i	−0.131272	−	0.991346i	$-0.541906\pi$
$89$	7.75680	−	6.50872i	0.822219	−	0.689923i	0.953491	+	0.301423i	$0.0974616\pi$
$90$		0			0
$91$	−2.53191	−	2.12452i	−0.265416	−	0.222711i
$92$	−0.873538	−	2.02509i	−0.0910726	−	0.211130i
$93$		0			0
$94$	26.9296	+	6.38244i	2.77758	+	0.658298i
$95$	0.0236950	+	0.0791467i	0.00243105	+	0.00812028i
$96$		0			0
$97$	6.59501	+	0.770846i	0.669621	+	0.0782675i	0.444109	−	0.895973i	$-0.353520\pi$
$97$	6.59501	+	0.770846i	0.669621	+	0.0782675i	0.225512	+	0.974240i	$0.427594\pi$
$98$	−1.68356	+	9.54793i	−0.170065	+	0.964486i
$99$		0			0
$100$	−1.90093	−	10.7807i	−0.190093	−	1.07807i
$101$	−0.162759	−	2.79446i	−0.0161951	−	0.278059i	−0.996677	−	0.0814513i	$-0.974044\pi$
$101$	−0.162759	−	2.79446i	−0.0161951	−	0.278059i	0.980482	−	0.196608i	$-0.0629926\pi$
$102$		0			0
$103$	1.79204	−	4.15443i	0.176575	−	0.409348i	−0.806827	−	0.590788i	$-0.798817\pi$
$103$	1.79204	−	4.15443i	0.176575	−	0.409348i	0.983402	+	0.181441i	$0.0580761\pi$
$104$	0.761902	−	0.382642i	0.0747106	−	0.0375211i
$105$		0			0
$106$	18.8753	−	4.47353i	1.83333	−	0.434508i
$107$	−2.05630	−	3.56161i	−0.198790	−	0.344314i	0.749347	−	0.662178i	$-0.230368\pi$
$107$	−2.05630	−	3.56161i	−0.198790	−	0.344314i	−0.948136	+	0.317864i	$0.897034\pi$
$108$		0			0
$109$	4.81003	−	8.33121i	0.460717	−	0.797985i	−0.538280	−	0.842766i	$-0.680926\pi$
$109$	4.81003	−	8.33121i	0.460717	−	0.797985i	0.998997	+	0.0447810i	$0.0142590\pi$
$110$	−0.0733674	+	0.245064i	−0.00699531	+	0.0233660i
$111$		0			0
$112$	−4.50596	−	2.96362i	−0.425773	−	0.280035i
$113$	1.10519	+	1.48453i	0.103968	+	0.139653i	0.851062	−	0.525065i	$-0.175959\pi$
$113$	1.10519	+	1.48453i	0.103968	+	0.139653i	−0.747094	+	0.664718i	$0.768552\pi$
$114$		0			0
$115$	−0.0175005	+	0.0115103i	−0.00163193	+	0.00107334i
$116$	−11.5714	−	4.21166i	−1.07438	−	0.391042i
$117$		0			0
$118$	−3.36726	+	1.22558i	−0.309982	+	0.112824i
$119$	−3.62032	+	4.86294i	−0.331874	+	0.445785i
$120$		0			0
$121$	−17.2365	+	18.2696i	−1.56695	+	1.66087i
$122$	12.5078	−	13.2575i	1.13241	−	1.20028i
$123$		0			0
$124$	3.90533	−	5.24576i	0.350709	−	0.471083i
$125$	−0.195408	+	0.0711227i	−0.0174778	+	0.00636141i
$126$		0			0
$127$	−17.8824	−	6.50866i	−1.58681	−	0.577550i	−0.610136	−	0.792296i	$-0.708885\pi$
$127$	−17.8824	−	6.50866i	−1.58681	−	0.577550i	−0.976670	+	0.214746i	$0.931108\pi$
$128$	2.58223	−	1.69836i	0.228239	−	0.150115i
$129$		0			0
$130$	−0.0558432	−	0.0750104i	−0.00489777	−	0.00657885i
$131$	−0.664609	−	0.437120i	−0.0580672	−	0.0381914i	0.520143	−	0.854079i	$-0.325878\pi$
$131$	−0.664609	−	0.437120i	−0.0580672	−	0.0381914i	−0.578211	+	0.815888i	$0.696249\pi$
$132$		0			0
$133$	1.71418	−	5.72576i	0.148638	−	0.496486i
$134$	−13.9524	+	24.1663i	−1.20531	+	2.08765i
$135$		0			0
$136$	−0.781940	−	1.35436i	−0.0670508	−	0.116135i
$137$	4.11394	−	0.975023i	0.351478	−	0.0833018i	−0.0510845	−	0.998694i	$-0.516268\pi$
$137$	4.11394	−	0.975023i	0.351478	−	0.0833018i	0.402562	+	0.915393i	$0.368120\pi$
$138$		0			0
$139$	4.89213	−	2.45692i	0.414945	−	0.208393i	−0.229064	−	0.973411i	$-0.573566\pi$
$139$	4.89213	−	2.45692i	0.414945	−	0.208393i	0.644008	+	0.765018i	$0.277270\pi$
$140$	0.0271330	−	0.0629014i	0.00229316	−	0.00531614i
$141$		0			0
$142$	−0.541716	−	9.30091i	−0.0454598	−	0.780515i
$143$	−2.29269	−	13.0025i	−0.191725	−	1.08733i
$144$		0			0
$145$	−0.0203087	+	0.115176i	−0.00168655	+	0.00956488i
$146$	19.3791	+	2.26510i	1.60383	+	0.187461i
$147$		0			0
$148$	−4.33731	−	14.4876i	−0.356525	−	1.19087i
$149$	−7.56671	−	1.79334i	−0.619889	−	0.146916i	−0.0913410	−	0.995820i	$-0.529115\pi$
$149$	−7.56671	−	1.79334i	−0.619889	−	0.146916i	−0.528548	+	0.848903i	$0.677263\pi$
$150$		0			0
$151$	−5.24505	−	12.1594i	−0.426836	−	0.989516i	−0.986939	−	0.161094i	$-0.948498\pi$
$151$	−5.24505	−	12.1594i	−0.426836	−	0.989516i	0.560103	−	0.828423i	$-0.310761\pi$
$152$	1.18106	+	0.991027i	0.0957966	+	0.0803829i
$153$		0			0
$154$	14.1766	−	11.8956i	1.14239	−	0.958575i
$155$	−0.0555057	−	0.0278760i	−0.00445833	−	0.00223906i
$156$		0			0
$157$	6.90749	−	0.807370i	0.551278	−	0.0644352i	0.164106	−	0.986443i	$-0.447526\pi$
$157$	6.90749	−	0.807370i	0.551278	−	0.0644352i	0.387172	+	0.922008i	$0.373452\pi$
$158$	0.379025	−	6.50761i	0.0301536	−	0.517718i
$159$		0			0
$160$	−0.115792	−	0.122732i	−0.00915415	−	0.00970284i
$161$	1.51534			0.119426
$162$		0			0
$163$	5.19903			0.407219			0.203610	−	0.979052i	$-0.434733\pi$
$163$	5.19903			0.407219			0.203610	+	0.979052i	$0.434733\pi$
$164$	−7.40193	−	7.84559i	−0.577994	−	0.612638i
$165$		0			0
$166$	0.199763	−	3.42981i	0.0155046	−	0.266204i
$167$	9.38508	−	1.09696i	0.726239	−	0.0848852i	0.255063	−	0.966924i	$-0.417904\pi$
$167$	9.38508	−	1.09696i	0.726239	−	0.0848852i	0.471176	+	0.882039i	$0.343830\pi$
$168$		0			0
$169$	−7.30406	−	3.66824i	−0.561851	−	0.282172i
$170$	−0.131401	+	0.110258i	−0.0100780	+	0.00845642i
$171$		0			0
$172$	11.0471	+	9.26962i	0.842333	+	0.706802i
$173$	−3.56610	−	8.26714i	−0.271125	−	0.628539i	0.727198	−	0.686428i	$-0.240822\pi$
$173$	−3.56610	−	8.26714i	−0.271125	−	0.628539i	−0.998323	+	0.0578889i	$0.981563\pi$
$174$		0			0
$175$	7.31882	+	1.73459i	0.553251	+	0.131123i
$176$	−6.17893	−	20.6390i	−0.465754	−	1.55573i
$177$		0			0
$178$	−20.5858	−	2.40614i	−1.54297	−	0.180348i
$179$	−1.67669	+	9.50897i	−0.125321	+	0.710733i	0.855795	+	0.517315i	$0.173069\pi$
$179$	−1.67669	+	9.50897i	−0.125321	+	0.710733i	−0.981116	+	0.193418i	$0.938043\pi$
$180$		0			0
$181$	−1.70395	−	9.66360i	−0.126654	−	0.718290i	−0.980312	−	0.197456i	$-0.936732\pi$
$181$	−1.70395	−	9.66360i	−0.126654	−	0.718290i	0.853658	−	0.520834i	$-0.174379\pi$
$182$	0.393361	+	6.75375i	0.0291579	+	0.500621i
$183$		0			0
$184$	−0.154824	+	0.358923i	−0.0114138	+	0.0264601i
$185$	−0.128353	+	0.0644613i	−0.00943671	+	0.00473929i
$186$		0			0
$187$	−23.5653	+	5.58507i	−1.72326	+	0.408421i
$188$	−14.8029	−	25.6393i	−1.07961	−	1.86994i
$189$		0			0
$190$	0.0845529	−	0.146450i	0.00613411	−	0.0106246i
$191$	−1.01268	+	3.38259i	−0.0732750	+	0.244755i	−0.986778	−	0.162076i	$-0.948181\pi$
$191$	−1.01268	+	3.38259i	−0.0732750	+	0.244755i	0.913503	+	0.406831i	$0.133366\pi$
$192$		0			0
$193$	−18.0456	−	11.8688i	−1.29895	−	0.854334i	−0.303806	−	0.952734i	$-0.598257\pi$
$193$	−18.0456	−	11.8688i	−1.29895	−	0.854334i	−0.995147	+	0.0983996i	$0.968628\pi$
$194$	−8.11592	−	10.9016i	−0.582689	−	0.782687i
$195$		0			0
$196$	8.66515	−	5.69916i	0.618939	−	0.407083i
$197$	−15.5802	−	5.67071i	−1.11004	−	0.404022i	−0.279032	−	0.960282i	$-0.590014\pi$
$197$	−15.5802	−	5.67071i	−1.11004	−	0.404022i	−0.831008	+	0.556260i	$0.812236\pi$
$198$		0			0
$199$	19.4015	−	7.06158i	1.37534	−	0.500582i	0.454576	−	0.890708i	$-0.349791\pi$
$199$	19.4015	−	7.06158i	1.37534	−	0.500582i	0.920761	+	0.390126i	$0.127569\pi$
$200$	−1.15863	+	1.55631i	−0.0819273	+	0.110047i
$201$		0			0
$202$	−3.93185	+	4.16751i	−0.276644	+	0.293225i
$203$	5.80616	−	6.15417i	0.407513	−	0.431938i
$204$		0			0
$205$	−0.0611743	+	0.0821713i	−0.00427260	+	0.00573909i
$206$	−8.70238	+	3.16741i	−0.606324	+	0.220684i
$207$		0			0
$208$	7.40076	+	2.69365i	0.513150	+	0.186771i
$209$	19.9478	−	13.1198i	1.37981	−	0.907518i
$210$		0			0
$211$	1.29830	+	1.74392i	0.0893789	+	0.120057i	0.844563	−	0.535456i	$-0.179860\pi$
$211$	1.29830	+	1.74392i	0.0893789	+	0.120057i	−0.755184	+	0.655512i	$0.772453\pi$
$212$	−17.3372	−	11.4029i	−1.19073	−	0.783153i
$213$		0			0
$214$	−2.41427	+	8.06422i	−0.165036	+	0.551259i
$215$	0.0684818	−	0.118614i	0.00467042	−	0.00808941i
$216$		0			0
$217$	2.24672	+	3.89143i	0.152517	+	0.264168i
$218$	−19.1600	+	4.54101i	−1.29768	+	0.307556i
$219$		0			0
$220$	0.244544	−	0.122814i	0.0164871	−	0.00828015i
$221$	3.50658	−	8.12916i	0.235878	−	0.546826i
$222$		0			0
$223$	−1.31271	−	22.5383i	−0.0879053	−	1.50928i	−0.697513	−	0.716572i	$-0.745710\pi$
$223$	−1.31271	−	22.5383i	−0.0879053	−	1.50928i	0.609608	−	0.792703i	$-0.291327\pi$
$224$	2.11969	+	12.0213i	0.141627	+	0.803209i
$225$		0			0
$226$	0.657816	−	3.73066i	0.0437573	−	0.248160i
$227$	−18.3292	−	2.14238i	−1.21655	−	0.142194i	−0.516500	−	0.856287i	$-0.672765\pi$
$227$	−18.3292	−	2.14238i	−1.21655	−	0.142194i	−0.700051	+	0.714093i	$0.746840\pi$
$228$		0			0
$229$	3.23973	+	10.8215i	0.214087	+	0.715102i	0.995808	+	0.0914724i	$0.0291573\pi$
$229$	3.23973	+	10.8215i	0.214087	+	0.715102i	−0.781720	+	0.623629i	$0.785657\pi$
$230$	0.0417186	+	0.00988748i	0.00275084	+	0.000651961i
$231$		0			0
$232$	0.864452	+	2.00402i	0.0567540	+	0.131571i
$233$	−12.6194	−	10.5889i	−0.826724	−	0.693703i	0.127813	−	0.991798i	$-0.459204\pi$
$233$	−12.6194	−	10.5889i	−0.826724	−	0.693703i	−0.954536	+	0.298095i	$0.903649\pi$
$234$		0			0
$235$	−0.215398	+	0.180740i	−0.0140510	+	0.0117902i
$236$	3.42553	+	1.72037i	0.222983	+	0.111986i
$237$		0			0
$238$	12.3253	−	1.44062i	0.798930	−	0.0933815i
$239$	−0.637064	+	10.9380i	−0.0412082	+	0.707518i	0.912923	+	0.408131i	$0.133819\pi$
$239$	−0.637064	+	10.9380i	−0.0412082	+	0.707518i	−0.954132	+	0.299387i	$0.903218\pi$
$240$		0			0
$241$	13.6890	+	14.5095i	0.881785	+	0.934637i	0.998284	−	0.0585536i	$-0.0186489\pi$
$241$	13.6890	+	14.5095i	0.881785	+	0.934637i	−0.116500	+	0.993191i	$0.537167\pi$
$242$	51.4113			3.30484
$243$		0			0
$244$	−19.4977			−1.24821
$245$	−0.0675965	−	0.0716481i	−0.00431858	−	0.00457743i
$246$		0			0
$247$	−0.507489	+	8.71324i	−0.0322907	+	0.554410i
$248$	−1.15127	+	0.134564i	−0.0731059	+	0.00854485i
$249$		0			0
$250$	0.380366	+	0.191027i	0.0240565	+	0.0120816i
$251$	15.8375	−	13.2893i	0.999656	−	0.838811i	0.0127196	−	0.999919i	$-0.495951\pi$
$251$	15.8375	−	13.2893i	0.999656	−	0.838811i	0.986937	+	0.161108i	$0.0515067\pi$
$252$		0			0
$253$	4.63709	+	3.89098i	0.291532	+	0.244624i
$254$	15.4280	+	35.7661i	0.968037	+	2.24416i
$255$		0			0
$256$	12.2117	+	2.89422i	0.763230	+	0.180889i
$257$	3.38202	+	11.2967i	0.210964	+	0.704670i	0.996327	+	0.0856337i	$0.0272915\pi$
$257$	3.38202	+	11.2967i	0.210964	+	0.704670i	−0.785362	+	0.619036i	$0.787523\pi$
$258$		0			0
$259$	10.3205	+	1.20629i	0.641285	+	0.0749554i
$260$	−0.0173712	+	0.0985168i	−0.00107731	+	0.00610975i
$261$		0			0
$262$	0.282737	+	1.60348i	0.0174676	+	0.0990634i
$263$	0.113826	+	1.95432i	0.00701881	+	0.120508i	0.999998	+	0.00221532i	$0.000705158\pi$
$263$	0.113826	+	1.95432i	0.00701881	+	0.120508i	−0.992979	+	0.118293i	$0.962258\pi$
$264$		0			0
$265$	−0.0780609	+	0.180965i	−0.00479524	+	0.0111166i
$266$	−10.9324	+	5.49048i	−0.670311	+	0.336643i
$267$		0			0
$268$	29.0463	−	6.88410i	1.77428	−	0.420513i
$269$	10.6534	+	18.4522i	0.649547	+	1.12505i	0.983231	+	0.182364i	$0.0583749\pi$
$269$	10.6534	+	18.4522i	0.649547	+	1.12505i	−0.333684	+	0.942685i	$0.608292\pi$
$270$		0			0
$271$	−6.85691	+	11.8765i	−0.416528	+	0.721447i	−0.995587	−	0.0938378i	$-0.970086\pi$
$271$	−6.85691	+	11.8765i	−0.416528	+	0.721447i	0.579060	+	0.815285i	$0.303420\pi$
$272$	4.14322	−	13.8393i	0.251219	−	0.839131i
$273$		0			0
$274$	−7.23023	−	4.75539i	−0.436794	−	0.287284i
$275$	17.9424	+	24.1008i	1.08196	+	1.45333i
$276$		0			0
$277$	−4.00219	+	2.63228i	−0.240468	+	0.158158i	−0.664023	−	0.747712i	$-0.731152\pi$
$277$	−4.00219	+	2.63228i	−0.240468	+	0.158158i	0.423555	+	0.905870i	$0.360782\pi$
$278$	−10.5296	−	3.83245i	−0.631522	−	0.229855i
$279$		0			0
$280$	−0.0114093	+	0.00415264i	−0.000681835	+	0.000248168i
$281$	8.31713	−	11.1718i	0.496158	−	0.666456i	−0.481551	−	0.876418i	$-0.659927\pi$
$281$	8.31713	−	11.1718i	0.496158	−	0.666456i	0.977710	+	0.209962i	$0.0673339\pi$
$282$		0			0
$283$	−2.05833	+	2.18170i	−0.122355	+	0.129689i	−0.785655	−	0.618665i	$-0.787674\pi$
$283$	−2.05833	+	2.18170i	−0.122355	+	0.129689i	0.663300	+	0.748354i	$0.269155\pi$
$284$	−6.83937	+	7.24931i	−0.405842	+	0.430167i
$285$		0			0
$286$	−16.1381	+	21.6772i	−0.954265	+	1.28180i
$287$	6.96410	−	2.53472i	0.411078	−	0.149620i
$288$		0			0
$289$	0.714943	+	0.260218i	0.0420555	+	0.0153069i
$290$	0.200004	−	0.131545i	0.0117446	−	0.00772457i
$291$		0			0
$292$	−12.4638	−	16.7417i	−0.729386	−	0.979736i
$293$	−20.1656	−	13.2631i	−1.17809	−	0.774840i	−0.199344	−	0.979930i	$-0.563881\pi$
$293$	−20.1656	−	13.2631i	−1.17809	−	0.774840i	−0.978743	+	0.205090i	$0.934251\pi$
$294$		0			0
$295$	0.0104415	−	0.0348772i	0.000607930	−	0.00203063i
$296$	−1.34018	+	2.32126i	−0.0778964	+	0.134920i
$297$		0			0
$298$	7.95849	+	13.7845i	0.461023	+	0.798515i
$299$	−2.15321	+	0.510320i	−0.124523	+	0.0295126i
$300$		0			0
$301$	−8.85451	+	4.44690i	−0.510365	+	0.256315i
$302$	−10.7358	+	24.8884i	−0.617777	+	1.43217i
$303$		0			0
$304$	0.828093	+	14.2178i	0.0474944	+	0.815447i
$305$	0.0321562	+	0.182367i	0.00184126	+	0.0104423i
$306$		0			0
$307$	3.34825	−	18.9889i	0.191095	−	1.08375i	−0.726776	−	0.686874i	$-0.758982\pi$
$307$	3.34825	−	18.9889i	0.191095	−	1.08375i	0.917871	−	0.396879i	$-0.129907\pi$
$308$	−19.6631	−	2.29828i	−1.12041	−	0.130957i
$309$		0			0
$310$	0.0364627	+	0.121794i	0.00207094	+	0.00691743i
$311$	11.1317	+	2.63826i	0.631221	+	0.149602i	0.533758	−	0.845637i	$-0.320779\pi$
$311$	11.1317	+	2.63826i	0.631221	+	0.149602i	0.0974626	+	0.995239i	$0.468927\pi$
$312$		0			0
$313$	2.23047	+	5.17081i	0.126074	+	0.292272i	0.969549	−	0.244896i	$-0.0787537\pi$
$313$	2.23047	+	5.17081i	0.126074	+	0.292272i	−0.843476	+	0.537167i	$0.819494\pi$
$314$	−10.9045	−	9.14999i	−0.615378	−	0.516364i
$315$		0			0
$316$	−5.34182	+	4.48232i	−0.300501	+	0.252150i
$317$	−5.41268	−	2.71835i	−0.304006	−	0.152678i	0.290256	−	0.956949i	$-0.406260\pi$
$317$	−5.41268	−	2.71835i	−0.304006	−	0.152678i	−0.594262	+	0.804271i	$0.702556\pi$
$318$		0			0
$319$	33.5697	−	3.92373i	1.87954	−	0.219687i
$320$	−0.0114122	+	0.195940i	−0.000637963	+	0.0109534i
$321$		0			0
$322$	−2.12850	−	2.25608i	−0.118617	−	0.125726i
$323$	16.0095			0.890794
$324$		0			0
$325$	−10.9838			−0.609269
$326$	−7.30274	−	7.74045i	−0.404461	−	0.428704i
$327$		0			0
$328$	−0.111157	+	1.90849i	−0.00613761	+	0.105379i
$329$	20.2041	−	2.36152i	1.11389	−	0.130195i
$330$		0			0
$331$	9.12957	+	4.58504i	0.501807	+	0.252017i	0.681650	−	0.731679i	$-0.261263\pi$
$331$	9.12957	+	4.58504i	0.501807	+	0.252017i	−0.179843	+	0.983695i	$0.557559\pi$
$332$	−2.81538	+	2.36238i	−0.154514	+	0.129653i
$333$		0			0
$334$	−14.8158	−	12.4319i	−0.810684	−	0.680244i
$335$	−0.112293	−	0.260324i	−0.00613520	−	0.0142230i
$336$		0			0
$337$	−8.86331	−	2.10064i	−0.482815	−	0.114429i	−0.0180019	−	0.999838i	$-0.505731\pi$
$337$	−8.86331	−	2.10064i	−0.482815	−	0.114429i	−0.464814	+	0.885409i	$0.653879\pi$
$338$	4.79817	+	16.0270i	0.260986	+	0.871754i
$339$		0			0
$340$	0.182253	+	0.0213024i	0.00988408	+	0.00115528i
$341$	−3.11696	+	17.6771i	−0.168793	+	0.957271i
$342$		0			0
$343$	3.06613	+	17.3889i	0.165555	+	0.938911i
$344$	−0.148615	−	2.55162i	−0.00801278	−	0.137574i
$345$		0			0
$346$	−7.29927	+	16.9216i	−0.392411	+	0.909711i
$347$	−2.57936	+	1.29540i	−0.138467	+	0.0695408i	−0.516684	−	0.856176i	$-0.672834\pi$
$347$	−2.57936	+	1.29540i	−0.138467	+	0.0695408i	0.378217	+	0.925717i	$0.376537\pi$
$348$		0			0
$349$	−26.6592	+	6.31836i	−1.42704	+	0.338214i	−0.870319	−	0.492488i	$-0.836088\pi$
$349$	−26.6592	+	6.31836i	−1.42704	+	0.338214i	−0.556718	+	0.830702i	$0.687939\pi$
$350$	−7.69776	−	13.3329i	−0.411463	−	0.712674i
$351$		0			0
$352$	−24.3811	+	42.2293i	−1.29952	+	2.25083i
$353$	0.796715	−	2.66121i	0.0424049	−	0.141642i	−0.934166	−	0.356839i	$-0.883854\pi$
$353$	0.796715	−	2.66121i	0.0424049	−	0.141642i	0.976571	+	0.215197i	$0.0690395\pi$
$354$		0			0
$355$	0.0790843	+	0.0520146i	0.00419736	+	0.00276065i
$356$	13.2398	+	17.7842i	0.701710	+	0.942560i
$357$		0			0
$358$	16.5123	−	10.8603i	0.872703	−	0.573986i
$359$	17.4937	+	6.36718i	0.923281	+	0.336047i	0.759543	−	0.650457i	$-0.225423\pi$
$359$	17.4937	+	6.36718i	0.923281	+	0.336047i	0.163738	+	0.986504i	$0.447645\pi$
$360$		0			0
$361$	3.02287	−	1.10024i	0.159099	−	0.0579071i
$362$	−11.9940	+	16.1107i	−0.630390	+	0.846761i
$363$		0			0
$364$	4.96633	−	5.26401i	0.260307	−	0.275909i
$365$	−0.136034	+	0.144188i	−0.00712035	+	0.00754713i
$366$		0			0
$367$	−2.47011	+	3.31794i	−0.128939	+	0.173195i	−0.861904	−	0.507071i	$-0.830728\pi$
$367$	−2.47011	+	3.31794i	−0.128939	+	0.173195i	0.732965	+	0.680266i	$0.238136\pi$
$368$	−3.39306	+	1.23497i	−0.176876	+	0.0643775i
$369$		0			0
$370$	0.276261	+	0.100551i	0.0143621	+	0.00522738i
$371$	11.9122	−	7.83476i	0.618449	−	0.406760i
$372$		0			0
$373$	−2.32880	−	3.12813i	−0.120581	−	0.161968i	0.737734	−	0.675091i	$-0.235896\pi$
$373$	−2.32880	−	3.12813i	−0.120581	−	0.161968i	−0.858315	+	0.513123i	$0.828488\pi$
$374$	41.4158	+	27.2396i	2.14156	+	1.40852i
$375$		0			0
$376$	−1.50493	+	5.02682i	−0.0776109	+	0.259238i
$377$	−6.17768	+	10.7001i	−0.318167	+	0.551081i
$378$		0			0
$379$	−15.6974	−	27.1887i	−0.806321	−	1.39659i	−0.915395	−	0.402556i	$-0.868122\pi$
$379$	−15.6974	−	27.1887i	−0.806321	−	1.39659i	0.109074	−	0.994034i	$-0.465211\pi$
$380$	−0.176023	+	0.0417182i	−0.00902979	+	0.00214010i
$381$		0			0
$382$	6.45853	−	3.24359i	0.330447	−	0.165957i
$383$	8.98318	−	20.8253i	0.459019	−	1.06413i	−0.518842	−	0.854870i	$-0.673637\pi$
$383$	8.98318	−	20.8253i	0.459019	−	1.06413i	0.977861	−	0.209255i	$-0.0671039\pi$
$384$		0			0
$385$	0.0109325	+	0.187704i	0.000557172	+	0.00956627i
$386$	7.67694	+	43.5381i	0.390746	+	2.21603i
$387$		0			0
$388$	−2.52462	+	14.3178i	−0.128168	+	0.726879i
$389$	15.8771	+	1.85576i	0.804999	+	0.0940909i	0.508633	−	0.860983i	$-0.330151\pi$
$389$	15.8771	+	1.85576i	0.804999	+	0.0940909i	0.296366	+	0.955074i	$0.404225\pi$
$390$		0			0
$391$	1.16413	+	3.88846i	0.0588725	+	0.196648i
$392$	−1.78865	−	0.423918i	−0.0903406	−	0.0214111i
$393$		0			0
$394$	13.4417	+	31.1614i	0.677184	+	1.56989i
$395$	0.0507341	+	0.0425710i	0.00255271	+	0.00214198i
$396$		0			0
$397$	−19.5239	+	16.3825i	−0.979876	+	0.822214i	−0.984071	−	0.177778i	$-0.943109\pi$
$397$	−19.5239	+	16.3825i	−0.979876	+	0.822214i	0.00419466	+	0.999991i	$0.498665\pi$
$398$	−37.7655	−	18.9665i	−1.89301	−	0.950707i
$399$		0			0
$400$	−17.8015	+	2.08070i	−0.890077	+	0.104035i
$401$	0.571828	−	9.81791i	0.0285557	−	0.490283i	−0.953464	−	0.301506i	$-0.902511\pi$
$401$	0.571828	−	9.81791i	0.0285557	−	0.490283i	0.982020	−	0.188777i	$-0.0604523\pi$
$402$		0			0
$403$	−4.50297	−	4.77287i	−0.224309	−	0.237753i
$404$	6.12911			0.304935
$405$		0			0
$406$	−17.3180			−0.859479
$407$	28.4843	+	30.1916i	1.41192	+	1.49654i
$408$		0			0
$409$	−1.42157	+	24.4075i	−0.0702923	+	1.20687i	0.760143	+	0.649756i	$0.225129\pi$
$409$	−1.42157	+	24.4075i	−0.0702923	+	1.20687i	−0.830435	+	0.557115i	$0.811908\pi$
$410$	0.208266	−	0.0243428i	0.0102855	−	0.00120221i
$411$		0			0
$412$	8.85298	+	4.44613i	0.436155	+	0.219045i
$413$	−2.01760	+	1.69296i	−0.0992795	+	0.0833054i
$414$		0			0
$415$	0.0267392	+	0.0224368i	0.00131257	+	0.00110138i
$416$	−7.06036	−	16.3678i	−0.346163	−	0.802495i
$417$		0			0
$418$	−47.5525	−	11.2701i	−2.32587	−	0.551240i
$419$	−1.24944	−	4.17342i	−0.0610392	−	0.203885i	0.922030	−	0.387117i	$-0.126529\pi$
$419$	−1.24944	−	4.17342i	−0.0610392	−	0.203885i	−0.983070	+	0.183232i	$0.941344\pi$
$420$		0			0
$421$	−1.25840	−	0.147086i	−0.0613308	−	0.00716854i	0.0853722	−	0.996349i	$-0.472792\pi$
$421$	−1.25840	−	0.147086i	−0.0613308	−	0.00716854i	−0.146703	+	0.989181i	$0.546866\pi$
$422$	0.772757	−	4.38252i	0.0376172	−	0.213338i
$423$		0			0
$424$	0.638656	+	3.62200i	0.0310159	+	0.175900i
$425$	1.17145	+	20.1131i	0.0568239	+	0.975629i
$426$		0			0
$427$	5.30612	−	12.3010i	0.256781	−	0.595286i
$428$	8.04709	−	4.04140i	0.388971	−	0.195349i
$429$		0			0
$430$	−0.272787	+	0.0646518i	−0.0131550	+	0.00311779i
$431$	−17.8588	−	30.9323i	−0.860227	−	1.48996i	−0.871709	−	0.490023i	$-0.836988\pi$
$431$	−17.8588	−	30.9323i	−0.860227	−	1.48996i	0.0114820	−	0.999934i	$-0.496345\pi$
$432$		0			0
$433$	16.1789	−	28.0227i	0.777509	−	1.34668i	−0.155865	−	0.987778i	$-0.549816\pi$
$433$	16.1789	−	28.0227i	0.777509	−	1.34668i	0.933374	−	0.358906i	$-0.116850\pi$
$434$	2.63784	−	8.81101i	0.126621	−	0.422942i
$435$		0			0
$436$	17.5988	+	11.5749i	0.842828	+	0.554337i
$437$	−2.38958	−	3.20976i	−0.114309	−	0.153544i
$438$		0			0
$439$	−7.42177	+	4.88138i	−0.354222	+	0.232975i	−0.714131	−	0.700012i	$-0.753178\pi$
$439$	−7.42177	+	4.88138i	−0.354222	+	0.232975i	0.359909	+	0.932987i	$0.382808\pi$
$440$	−0.0455764	−	0.0165885i	−0.00217277	−	0.000790824i
$441$		0			0
$442$	−17.0284	+	6.19781i	−0.809956	+	0.294800i
$443$	−8.03162	+	10.7883i	−0.381594	+	0.512570i	−0.950876	−	0.309573i	$-0.899814\pi$
$443$	−8.03162	+	10.7883i	−0.381594	+	0.512570i	0.569282	+	0.822142i	$0.307221\pi$
$444$		0			0
$445$	0.144504	−	0.153166i	0.00685016	−	0.00726075i
$446$	−31.7117	+	33.6124i	−1.50159	+	1.59159i
$447$		0			0
$448$	8.47908	−	11.3894i	0.400599	−	0.538098i
$449$	16.7390	−	6.09251i	0.789964	−	0.287524i	0.0846431	−	0.996411i	$-0.473025\pi$
$449$	16.7390	−	6.09251i	0.789964	−	0.287524i	0.705321	+	0.708888i	$0.250803\pi$
$450$		0			0
$451$	27.8193	+	10.1254i	1.30996	+	0.476787i
$452$	−3.38573	+	2.22683i	−0.159251	+	0.104741i
$453$		0			0
$454$	22.5562	+	30.2982i	1.05861	+	1.42197i
$455$	−0.0574262	−	0.0377698i	−0.00269218	−	0.00177068i
$456$		0			0
$457$	−0.357881	+	1.19541i	−0.0167410	+	0.0559188i	−0.965952	−	0.258722i	$-0.916699\pi$
$457$	−0.357881	+	1.19541i	−0.0167410	+	0.0559188i	0.949211	+	0.314640i	$0.101884\pi$
$458$	11.5606	−	20.0236i	0.540192	−	0.935640i
$459$		0			0
$460$	−0.0229321	−	0.0397196i	−0.00106922	−	0.00185194i
$461$	18.3577	−	4.35086i	0.855004	−	0.202640i	0.220335	−	0.975424i	$-0.429285\pi$
$461$	18.3577	−	4.35086i	0.855004	−	0.202640i	0.634668	+	0.772785i	$0.281137\pi$
$462$		0			0
$463$	−10.6291	+	5.33813i	−0.493976	+	0.248084i	−0.678305	−	0.734781i	$-0.737285\pi$
$463$	−10.6291	+	5.33813i	−0.493976	+	0.248084i	0.184329	+	0.982865i	$0.440989\pi$
$464$	−7.98529	+	18.5120i	−0.370708	+	0.859398i
$465$		0			0
$466$	1.96057	+	33.6616i	0.0908215	+	1.55934i
$467$	−1.20388	−	6.82753i	−0.0557088	−	0.315940i	0.944201	−	0.329370i	$-0.106836\pi$
$467$	−1.20388	−	6.82753i	−0.0557088	−	0.315940i	−0.999910	+	0.0134295i	$0.995725\pi$
$468$		0			0
$469$	−3.56155	+	20.1986i	−0.164457	+	0.932683i
$470$	0.571645	+	0.0668157i	0.0263680	+	0.00308198i
$471$		0			0
$472$	−0.194854	−	0.650859i	−0.00896890	−	0.0299582i
$473$	−38.5141	−	9.12801i	−1.77088	−	0.419706i
$474$		0			0
$475$	−7.86704	−	18.2379i	−0.360965	−	0.836810i
$476$	−10.1689	−	8.53276i	−0.466093	−	0.391098i
$477$		0			0
$478$	17.1796	−	14.4154i	0.785775	−	0.659343i
$479$	−32.5667	−	16.3556i	−1.48801	−	0.747307i	−0.495402	−	0.868664i	$-0.664979\pi$
$479$	−32.5667	−	16.3556i	−1.48801	−	0.747307i	−0.992609	+	0.121357i	$0.961276\pi$
$480$		0			0
$481$	−15.0711	+	1.76155i	−0.687181	+	0.0803200i
$482$	2.37406	−	40.7610i	0.108135	−	1.85661i
$483$		0			0
$484$	−37.7410	−	40.0031i	−1.71550	−	1.81832i
$485$	0.138082			0.00626998
$486$		0			0
$487$	35.1072			1.59086			0.795429	−	0.606046i	$-0.207245\pi$
$487$	35.1072			1.59086			0.795429	+	0.606046i	$0.207245\pi$
$488$	2.37147	+	2.51361i	0.107351	+	0.113786i
$489$		0			0
$490$	−0.0117232	+	0.201279i	−0.000529598	+	0.00909285i
$491$	−24.8882	+	2.90901i	−1.12319	+	0.131282i	−0.657348	−	0.753588i	$-0.728322\pi$
$491$	−24.8882	+	2.90901i	−1.12319	+	0.131282i	−0.465839	+	0.884869i	$0.654248\pi$
$492$		0			0
$493$	20.2525	+	10.1712i	0.912125	+	0.458086i
$494$	13.6853	−	11.4834i	0.615732	−	0.516661i
$495$		0			0
$496$	−8.20217	−	6.88244i	−0.368288	−	0.309031i
$497$	−2.71227	−	6.28775i	−0.121662	−	0.282044i
$498$		0			0
$499$	−20.6324	−	4.88996i	−0.923632	−	0.218905i	−0.258829	−	0.965923i	$-0.583336\pi$
$499$	−20.6324	−	4.88996i	−0.923632	−	0.218905i	−0.664803	+	0.747019i	$0.731485\pi$
$500$	−0.130589	−	0.436196i	−0.00584010	−	0.0195073i
$501$		0			0
$502$	−42.0313	−	4.91276i	−1.87595	−	0.219267i
$503$	4.86905	−	27.6138i	0.217100	−	1.23124i	−0.660124	−	0.751156i	$-0.729496\pi$
$503$	4.86905	−	27.6138i	0.217100	−	1.23124i	0.877225	−	0.480080i	$-0.159392\pi$
$504$		0			0
$505$	−0.0101083	−	0.0573271i	−0.000449814	−	0.00255102i
$506$	−0.720426	−	12.3692i	−0.0320268	−	0.549880i
$507$		0			0
$508$	16.5039	−	38.2604i	0.732243	−	1.69753i
$509$	19.4334	−	9.75981i	0.861369	−	0.432596i	0.0374468	−	0.999299i	$-0.488078\pi$
$509$	19.4334	−	9.75981i	0.861369	−	0.432596i	0.823922	+	0.566703i	$0.191781\pi$
$510$		0			0
$511$	13.9542	−	3.30719i	0.617295	−	0.146302i
$512$	−15.9347	−	27.5996i	−0.704219	−	1.21974i
$513$		0			0
$514$	12.0683	−	20.9030i	0.532312	−	0.921992i
$515$	0.0269852	−	0.0901368i	0.00118911	−	0.00397190i
$516$		0			0
$517$	67.8904	+	44.6522i	2.98582	+	1.96380i
$518$	−12.7006	−	17.0598i	−0.558031	−	0.749566i
$519$		0			0
$520$	0.0148134	−	0.00974295i	0.000649612	−	0.000427257i
$521$	1.12952	+	0.411112i	0.0494852	+	0.0180112i	0.366644	−	0.930361i	$-0.380507\pi$
$521$	1.12952	+	0.411112i	0.0494852	+	0.0180112i	−0.317159	+	0.948372i	$0.602729\pi$
$522$		0			0
$523$	−11.8149	+	4.30029i	−0.516631	+	0.188038i	−0.587159	−	0.809471i	$-0.699754\pi$
$523$	−11.8149	+	4.30029i	−0.516631	+	0.188038i	0.0705281	+	0.997510i	$0.477532\pi$
$524$	1.04011	−	1.39711i	0.0454375	−	0.0610332i
$525$		0			0
$526$	2.74975	−	2.91457i	0.119895	−	0.127081i
$527$	−8.25966	+	8.75473i	−0.359796	+	0.381362i
$528$		0			0
$529$	−13.1288	+	17.6350i	−0.570818	+	0.766741i
$530$	0.379073	−	0.137971i	0.0164659	−	0.00599309i
$531$		0			0
$532$	12.2977	+	4.47598i	0.533171	+	0.194058i
$533$	−9.04195	+	5.94699i	−0.391650	+	0.257593i
$534$		0			0
$535$	−0.0510718	−	0.0686013i	−0.00220802	−	0.00296589i
$536$	−4.42033	−	2.90730i	−0.190929	−	0.125576i
$537$		0			0
$538$	12.5080	−	41.7796i	0.539257	−	1.80124i
$539$	−14.2331	+	24.6524i	−0.613062	+	1.06185i
$540$		0			0
$541$	18.1901	+	31.5062i	0.782053	+	1.35456i	0.930744	+	0.365672i	$0.119161\pi$
$541$	18.1901	+	31.5062i	0.782053	+	1.35456i	−0.148691	+	0.988884i	$0.547506\pi$
$542$	27.3135	−	6.47342i	1.17322	−	0.278057i
$543$		0			0
$544$	−29.2191	+	14.6744i	−1.25276	+	0.629159i
$545$	0.0792384	−	0.183695i	0.00339420	−	0.00786864i
$546$		0			0
$547$	−0.668405	−	11.4761i	−0.0285789	−	0.490681i	−0.981981	−	0.188979i	$-0.939482\pi$
$547$	−0.668405	−	11.4761i	−0.0285789	−	0.490681i	0.953402	−	0.301702i	$-0.0975548\pi$
$548$	1.60753	+	9.11678i	0.0686705	+	0.389450i
$549$		0			0
$550$	10.6794	−	60.5658i	0.455370	−	2.58253i
$551$	−22.1915	−	2.59381i	−0.945390	−	0.110500i
$552$		0			0
$553$	−1.37414	−	4.58994i	−0.0584343	−	0.195184i
$554$	9.54061	+	2.26117i	0.405342	+	0.0960677i
$555$		0			0
$556$	4.74773	+	11.0065i	0.201348	+	0.466778i
$557$	24.9391	+	20.9264i	1.05670	+	0.886679i	0.993782	−	0.111340i	$-0.0355142\pi$
$557$	24.9391	+	20.9264i	1.05670	+	0.886679i	0.0629202	+	0.998019i	$0.479959\pi$
$558$		0			0
$559$	11.0841	−	9.30071i	0.468810	−	0.393378i
$560$	−0.100226	−	0.0503356i	−0.00423534	−	0.00212707i
$561$		0			0
$562$	−28.3154	+	3.30960i	−1.19442	+	0.139607i
$563$	−0.469030	+	8.05293i	−0.0197672	+	0.339390i	0.973896	+	0.226994i	$0.0728897\pi$
$563$	−0.469030	+	8.05293i	−0.0197672	+	0.339390i	−0.993663	+	0.112397i	$0.964147\pi$
$564$		0			0
$565$	0.0264120	+	0.0279950i	0.00111116	+	0.00117776i
$566$	6.13938			0.258057
$567$		0			0
$568$	1.76643			0.0741177
$569$	7.17849	+	7.60875i	0.300938	+	0.318975i	0.860142	−	0.510054i	$-0.170375\pi$
$569$	7.17849	+	7.60875i	0.300938	+	0.318975i	−0.559204	+	0.829030i	$0.688893\pi$
$570$		0			0
$571$	1.42915	−	24.5376i	0.0598082	−	1.02687i	−0.826253	−	0.563299i	$-0.809532\pi$
$571$	1.42915	−	24.5376i	0.0598082	−	1.02687i	0.886061	−	0.463568i	$-0.153431\pi$
$572$	28.7140	−	3.35619i	1.20059	−	0.140329i
$573$		0			0
$574$	−13.5558	−	6.80797i	−0.565807	−	0.284159i
$575$	3.85763	−	3.23694i	0.160874	−	0.134990i
$576$		0			0
$577$	16.7824	+	14.0821i	0.698659	+	0.586244i	0.921392	−	0.388635i	$-0.127053\pi$
$577$	16.7824	+	14.0821i	0.698659	+	0.586244i	−0.222733	+	0.974880i	$0.571498\pi$
$578$	−0.616815	−	1.42994i	−0.0256561	−	0.0594775i
$579$		0			0
$580$	−0.249178	−	0.0590563i	−0.0103466	−	0.00245218i
$581$	−0.724233	−	2.41911i	−0.0300462	−	0.100361i
$582$		0			0
$583$	56.5700	+	6.61208i	2.34289	+	0.273844i
$584$	−0.642372	+	3.64307i	−0.0265815	+	0.150751i
$585$		0			0
$586$	8.57882	+	48.6529i	0.354388	+	2.00983i
$587$	−2.58921	−	44.4549i	−0.106868	−	1.83485i	−0.447069	−	0.894499i	$-0.647532\pi$
$587$	−2.58921	−	44.4549i	−0.106868	−	1.83485i	0.340201	−	0.940353i	$-0.389505\pi$
$588$		0			0
$589$	4.69983	−	10.8954i	0.193653	−	0.448939i
$590$	−0.0665925	+	0.0334440i	−0.00274157	+	0.00137687i
$591$		0			0
$592$	−24.0922	+	5.70995i	−0.990183	+	0.234678i
$593$	0.181983	+	0.315204i	0.00747314	+	0.0129439i	0.869738	−	0.493514i	$-0.164288\pi$
$593$	0.181983	+	0.315204i	0.00747314	+	0.0129439i	−0.862265	+	0.506458i	$0.830955\pi$
$594$		0			0
$595$	−0.0630381	+	0.109185i	−0.00258431	+	0.00447616i
$596$	4.88341	−	16.3117i	0.200032	−	0.668154i
$597$		0			0
$598$	3.78425	+	2.48894i	0.154749	+	0.101780i
$599$	−16.6827	−	22.4087i	−0.681635	−	0.915594i	0.317835	−	0.948146i	$-0.397044\pi$
$599$	−16.6827	−	22.4087i	−0.681635	−	0.915594i	−0.999470	+	0.0325516i	$0.989637\pi$
$600$		0			0
$601$	−17.6392	+	11.6015i	−0.719519	+	0.473235i	−0.855715	−	0.517447i	$-0.826882\pi$
$601$	−17.6392	+	11.6015i	−0.719519	+	0.473235i	0.136197	+	0.990682i	$0.456512\pi$
$602$	19.0580	+	6.93655i	0.776746	+	0.282713i
$603$		0			0
$604$	27.2469	−	9.91706i	1.10866	−	0.403519i
$605$	−0.311916	+	0.418976i	−0.0126812	+	0.0170338i
$606$		0			0
$607$	28.5674	−	30.2797i	1.15952	−	1.22902i	0.190588	−	0.981670i	$-0.438960\pi$
$607$	28.5674	−	30.2797i	1.15952	−	1.22902i	0.968927	−	0.247345i	$-0.0795581\pi$
$608$	22.1207	−	23.4466i	0.897113	−	0.950885i
$609$		0			0
$610$	0.226345	−	0.304034i	0.00916443	−	0.0123100i
$611$	−27.9136	+	10.1597i	−1.12926	+	0.411018i
$612$		0			0
$613$	−14.2653	−	5.19214i	−0.576170	−	0.209709i	0.0374659	−	0.999298i	$-0.488071\pi$
$613$	−14.2653	−	5.19214i	−0.576170	−	0.209709i	−0.613636	+	0.789589i	$0.710294\pi$
$614$	−32.9742	+	21.6875i	−1.33073	+	0.875236i
$615$		0			0
$616$	2.09529	+	2.81446i	0.0844216	+	0.113398i
$617$	−30.5643	−	20.1025i	−1.23047	−	0.809295i	−0.243457	−	0.969912i	$-0.578281\pi$
$617$	−30.5643	−	20.1025i	−1.23047	−	0.809295i	−0.987017	+	0.160616i	$0.948652\pi$
$618$		0			0
$619$	5.79913	−	19.3704i	0.233087	−	0.778563i	−0.758787	−	0.651338i	$-0.774208\pi$
$619$	5.79913	−	19.3704i	0.233087	−	0.778563i	0.991874	−	0.127225i	$-0.0406070\pi$
$620$	0.0680007	−	0.117781i	0.00273097	−	0.00473018i
$621$		0			0
$622$	−11.7081	−	20.2790i	−0.469450	−	0.813112i
$623$	−14.8230	+	3.51312i	−0.593872	+	0.140750i
$624$		0			0
$625$	22.3350	−	11.2171i	0.893401	−	0.448683i
$626$	4.56544	−	10.5839i	0.182472	−	0.423017i
$627$		0			0
$628$	0.885406	+	15.2018i	0.0353316	+	0.606619i
$629$	4.83308	+	27.4098i	0.192707	+	1.09290i
$630$		0			0
$631$	−1.06905	+	6.06286i	−0.0425580	+	0.241358i	−0.998665	−	0.0516602i	$-0.983549\pi$
$631$	−1.06905	+	6.06286i	−0.0425580	+	0.241358i	0.956107	+	0.293019i	$0.0946598\pi$
$632$	1.22757	+	0.143482i	0.0488301	+	0.00570741i
$633$		0			0
$634$	3.55569	+	11.8768i	0.141214	+	0.471689i
$635$	−0.385078	−	0.0912651i	−0.0152813	−	0.00362174i
$636$		0			0
$637$	−4.12167	−	9.55510i	−0.163306	−	0.378587i
$638$	−52.9949	−	44.4680i	−2.09809	−	1.76051i
$639$		0			0
$640$	0.0492363	−	0.0413141i	0.00194623	−	0.00163308i
$641$	36.6056	+	18.3840i	1.44583	+	0.726125i	0.986747	−	0.162267i	$-0.0518804\pi$
$641$	36.6056	+	18.3840i	1.44583	+	0.726125i	0.459087	+	0.888391i	$0.348177\pi$
$642$		0			0
$643$	−24.3862	+	2.85034i	−0.961700	+	0.112407i	−0.582431	−	0.812880i	$-0.697898\pi$
$643$	−24.3862	+	2.85034i	−0.961700	+	0.112407i	−0.379269	+	0.925287i	$0.623824\pi$
$644$	−0.192924	+	3.31237i	−0.00760226	+	0.130526i
$645$		0			0
$646$	−22.4875	−	23.8354i	−0.884760	−	0.937791i
$647$	−44.0995			−1.73373			−0.866866	−	0.498542i	$-0.833869\pi$
$647$	−44.0995			−1.73373			−0.866866	+	0.498542i	$0.833869\pi$
$648$		0			0
$649$	−10.5211			−0.412990
$650$	15.4282	+	16.3529i	0.605143	+	0.641414i
$651$		0			0
$652$	−0.661908	+	11.3645i	−0.0259223	+	0.445069i
$653$	−9.78245	+	1.14340i	−0.382817	+	0.0447449i	−0.305325	−	0.952248i	$-0.598765\pi$
$653$	−9.78245	+	1.14340i	−0.382817	+	0.0447449i	−0.0774916	+	0.996993i	$0.524691\pi$
$654$		0			0
$655$	−0.0147829	−	0.00742427i	−0.000577617	−	0.000290090i
$656$	−13.5279	+	11.3512i	−0.528174	+	0.443191i
$657$		0			0
$658$	−31.8953	−	26.7634i	−1.24341	−	1.04334i
$659$	15.1344	+	35.0856i	0.589554	+	1.36674i	0.908068	+	0.418823i	$0.137557\pi$
$659$	15.1344	+	35.0856i	0.589554	+	1.36674i	−0.318514	+	0.947918i	$0.603184\pi$
$660$		0			0
$661$	−30.7975	−	7.29915i	−1.19788	−	0.283904i	−0.417192	−	0.908819i	$-0.636986\pi$
$661$	−30.7975	−	7.29915i	−1.19788	−	0.283904i	−0.780693	+	0.624915i	$0.785134\pi$
$662$	−5.99738	−	20.0326i	−0.233095	−	0.778591i
$663$		0			0
$664$	0.646984	+	0.0756216i	0.0251078	+	0.00293469i
$665$	0.0215833	−	0.122405i	0.000836965	−	0.00474666i
$666$		0			0
$667$	−0.983652	−	5.57857i	−0.0380872	−	0.216003i
$668$	1.20298	+	20.6545i	0.0465449	+	0.799145i
$669$		0			0
$670$	−0.229846	+	0.532844i	−0.00887974	+	0.0205855i
$671$	47.8228	−	24.0175i	1.84618	−	0.927187i
$672$		0			0
$673$	−8.90549	+	2.11064i	−0.343281	+	0.0813592i	−0.398640	−	0.917107i	$-0.630518\pi$
$673$	−8.90549	+	2.11064i	−0.343281	+	0.0813592i	0.0553590	+	0.998467i	$0.482370\pi$
$674$	9.32222	+	16.1466i	0.359079	+	0.621942i
$675$		0			0
$676$	8.94828	−	15.4989i	0.344165	−	0.596111i
$677$	−0.383509	+	1.28101i	−0.0147394	+	0.0492332i	−0.965043	−	0.262092i	$-0.915588\pi$
$677$	−0.383509	+	1.28101i	−0.0147394	+	0.0492332i	0.950303	+	0.311325i	$0.100773\pi$
$678$		0			0
$679$	−8.34598	−	5.48924i	−0.320289	−	0.210658i
$680$	−0.0194209	−	0.0260868i	−0.000744756	−	0.00100038i
$681$		0			0
$682$	30.6964	−	20.1893i	1.17542	−	0.773089i
$683$	−13.8418	−	5.03800i	−0.529642	−	0.192774i	0.0633367	−	0.997992i	$-0.479826\pi$
$683$	−13.8418	−	5.03800i	−0.529642	−	0.192774i	−0.592978	+	0.805218i	$0.702048\pi$
$684$		0			0
$685$	0.0826203	−	0.0300713i	0.00315676	−	0.00114897i
$686$	21.5822	−	28.9899i	0.824012	−	1.10684i
$687$		0			0
$688$	16.2024	−	17.1735i	0.617709	−	0.654734i
$689$	−14.2880	+	15.1444i	−0.544329	+	0.576955i
$690$		0			0
$691$	9.57469	−	12.8610i	0.364238	−	0.489257i	−0.581791	−	0.813339i	$-0.697648\pi$
$691$	9.57469	−	12.8610i	0.364238	−	0.489257i	0.946029	+	0.324081i	$0.105055\pi$
$692$	18.5251	−	6.74259i	0.704219	−	0.256315i
$693$		0			0
$694$	5.55168	+	2.02065i	0.210739	+	0.0767027i
$695$	0.0951161	−	0.0625589i	0.00360796	−	0.00237299i
$696$		0			0
$697$	11.8543	+	15.9231i	0.449013	+	0.603129i
$698$	46.8534	+	30.8160i	1.77343	+	1.16640i
$699$		0			0
$700$	−4.72342	+	15.7773i	−0.178529	+	0.596327i
$701$	1.43354	−	2.48297i	0.0541441	−	0.0937804i	−0.837683	−	0.546157i	$-0.816090\pi$
$701$	1.43354	−	2.48297i	0.0541441	−	0.0937804i	0.891827	+	0.452376i	$0.149424\pi$
$702$		0			0
$703$	−13.7195	−	23.7629i	−0.517441	−	0.896234i
$704$	55.1917	−	13.0807i	2.08012	−	0.492996i
$705$		0			0
$706$	−5.08117	+	2.55186i	−0.191233	+	0.0960406i
$707$	−1.66798	+	3.86682i	−0.0627309	+	0.145427i
$708$		0			0
$709$	−1.26949	−	21.7963i	−0.0476766	−	0.818576i	−0.934389	−	0.356254i	$-0.884054\pi$
$709$	−1.26949	−	21.7963i	−0.0476766	−	0.818576i	0.886712	−	0.462321i	$-0.152983\pi$
$710$	−0.0336439	−	0.190804i	−0.00126263	−	0.00716075i
$711$		0			0
$712$	0.682370	−	3.86991i	0.0255729	−	0.145031i
$713$	2.98807	+	0.349256i	0.111904	+	0.0130797i
$714$		0			0
$715$	−0.0787473	−	0.263034i	−0.00294498	−	0.00983692i
$716$	−20.5721	−	4.87568i	−0.768816	−	0.182213i
$717$		0			0
$718$	−15.0926	−	34.9886i	−0.563251	−	1.30576i
$719$	11.5460	+	9.68821i	0.430591	+	0.361309i	0.832175	−	0.554513i	$-0.187096\pi$
$719$	11.5460	+	9.68821i	0.430591	+	0.361309i	−0.401583	+	0.915822i	$0.631540\pi$
$720$		0			0
$721$	−5.21430	+	4.37531i	−0.194191	+	0.162945i
$722$	−5.88409	−	2.95510i	−0.218983	−	0.109977i
$723$		0			0
$724$	21.3406	−	2.49435i	0.793115	−	0.0927019i
$725$	1.63486	−	28.0694i	0.0607171	−	1.04247i
$726$		0			0
$727$	36.8022	+	39.0081i	1.36492	+	1.44673i	0.758717	+	0.651421i	$0.225827\pi$
$727$	36.8022	+	39.0081i	1.36492	+	1.44673i	0.606203	+	0.795310i	$0.292692\pi$
$728$	−1.28267			−0.0475390
$729$		0			0
$730$	0.405748			0.0150174
$731$	−18.2133	−	19.3050i	−0.673643	−	0.714020i
$732$		0			0
$733$	0.560345	−	9.62076i	0.0206968	−	0.355351i	−0.972021	−	0.234892i	$-0.924526\pi$
$733$	0.560345	−	9.62076i	0.0206968	−	0.355351i	0.992718	−	0.120459i	$-0.0384366\pi$
$734$	8.40944	−	0.982922i	0.310398	−	0.0362803i
$735$		0			0
$736$	7.30330	+	3.66786i	0.269203	+	0.135199i
$737$	−62.7631	+	52.6645i	−2.31191	+	1.93992i
$738$		0			0
$739$	−15.1436	−	12.7070i	−0.557067	−	0.467435i	0.320259	−	0.947330i	$-0.396230\pi$
$739$	−15.1436	−	12.7070i	−0.557067	−	0.467435i	−0.877326	+	0.479895i	$0.840675\pi$
$740$	−0.124565	−	0.288773i	−0.00457908	−	0.0106155i
$741$		0			0
$742$	−28.3968	−	6.73017i	−1.04248	−	0.247072i
$743$	14.6008	+	48.7700i	0.535651	+	1.78920i	0.610516	+	0.792004i	$0.290962\pi$
$743$	14.6008	+	48.7700i	0.535651	+	1.78920i	−0.0748649	+	0.997194i	$0.523853\pi$
$744$		0			0
$745$	−0.160621	−	0.0187740i	−0.00588471	−	0.000687825i
$746$	−1.38612	+	7.86105i	−0.0507493	+	0.287814i
$747$		0			0
$748$	−9.20818	−	52.2222i	−0.336685	−	1.90943i
$749$	0.359751	+	6.17669i	0.0131450	+	0.225691i
$750$		0			0
$751$	0.985759	−	2.28525i	0.0359709	−	0.0833898i	−0.899284	−	0.437366i	$-0.855911\pi$
$751$	0.985759	−	2.28525i	0.0359709	−	0.0833898i	0.935254	+	0.353976i	$0.115171\pi$
$752$	−43.3153	+	21.7538i	−1.57955	+	0.793279i
$753$		0			0
$754$	24.6079	−	5.83218i	0.896166	−	0.212395i
$755$	−0.137693	−	0.238491i	−0.00501116	−	0.00867959i
$756$		0			0
$757$	−12.1617	+	21.0647i	−0.442025	+	0.765610i	−0.997840	−	0.0656966i	$-0.979073\pi$
$757$	−12.1617	+	21.0647i	−0.442025	+	0.765610i	0.555815	+	0.831306i	$0.312406\pi$
$758$	−18.4301	+	61.5609i	−0.669412	+	2.23599i
$759$		0			0
$760$	0.0267876	+	0.0176185i	0.000971688	+	0.000639089i
$761$	12.3365	+	16.5709i	0.447199	+	0.600693i	0.967370	−	0.253370i	$-0.0815389\pi$
$761$	12.3365	+	16.5709i	0.447199	+	0.600693i	−0.520170	+	0.854063i	$0.674131\pi$
$762$		0			0
$763$	−12.0919	+	7.95294i	−0.437755	+	0.287916i
$764$	−7.26505	−	2.64426i	−0.262840	−	0.0956660i
$765$		0			0
$766$	−43.6234	+	15.8776i	−1.57618	+	0.573681i
$767$	2.29675	−	3.08507i	0.0829307	−	0.111395i
$768$		0			0
$769$	20.9653	−	22.2219i	0.756029	−	0.801344i	−0.229056	−	0.973413i	$-0.573564\pi$
$769$	20.9653	−	22.2219i	0.756029	−	0.801344i	0.985085	+	0.172069i	$0.0550453\pi$
$770$	0.264102	−	0.279932i	0.00951758	−	0.0100880i
$771$		0			0
$772$	28.2414	−	37.9348i	1.01643	−	1.36530i
$773$	10.0042	−	3.64122i	0.359825	−	0.130966i	−0.155780	−	0.987792i	$-0.549789\pi$
$773$	10.0042	−	3.64122i	0.359825	−	0.130966i	0.515606	+	0.856826i	$0.327567\pi$
$774$		0			0
$775$	14.0321	+	5.10725i	0.504046	+	0.183458i
$776$	2.15290	−	1.41598i	0.0772845	−	0.0508308i
$777$		0			0
$778$	−19.5386	−	26.2449i	−0.700492	−	0.940924i
$779$	−16.3508	−	10.7541i	−0.585830	−	0.385306i
$780$		0			0
$781$	7.84541	−	26.2055i	0.280731	−	0.937707i
$782$	4.15406	−	7.19504i	0.148549	−	0.257294i

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)

\(f(q)\)	\(=\)	\(q+(-1.40463 - 1.48883i) q^{2} +(-0.127314 + 2.18589i) q^{4} +(0.0206552 - 0.00241424i) q^{5} +(-1.34442 - 0.675193i) q^{7} +(0.297287 - 0.249453i) q^{8} +O(q^{10})\)	\(q+(-1.40463 - 1.48883i) q^{2} +(-0.127314 + 2.18589i) q^{4} +(0.0206552 - 0.00241424i) q^{5} +(-1.34442 - 0.675193i) q^{7} +(0.297287 - 0.249453i) q^{8} +(-0.0326074 - 0.0273608i) q^{10} +(-2.38035 - 5.51826i) q^{11} +(2.13772 + 0.506650i) q^{13} +(0.883173 + 2.95000i) q^{14} +(3.56062 + 0.416176i) q^{16} +(0.699765 - 3.96856i) q^{17} +(0.689869 + 3.91244i) q^{19} +(0.00264759 + 0.0454574i) q^{20} +(-4.87221 + 11.2951i) q^{22} +(-0.900106 + 0.452050i) q^{23} +(-4.86480 + 1.15298i) q^{25} +(-2.24841 - 3.89435i) q^{26} +(1.64706 - 2.85280i) q^{28} +(-1.61295 + 5.38763i) q^{29} +(-2.49542 - 1.64126i) q^{31} +(-4.84524 - 6.50829i) q^{32} +(-6.89141 + 4.53255i) q^{34} +(-0.0293993 - 0.0107005i) q^{35} +(-6.49019 + 2.36224i) q^{37} +(4.85593 - 6.52265i) q^{38} +(0.00553827 - 0.00587022i) q^{40} +(-3.38050 + 3.58312i) q^{41} +(3.93296 - 5.28288i) q^{43} +(12.3654 - 4.50063i) q^{44} +(1.93734 + 0.705135i) q^{46} +(-11.2967 + 7.42995i) q^{47} +(-2.82853 - 3.79938i) q^{49} +(8.54986 + 5.62333i) q^{50} +(-1.37964 + 4.60833i) q^{52} +(-4.73855 + 8.20740i) q^{53} +(-0.0624889 - 0.108234i) q^{55} +(-0.568107 + 0.134644i) q^{56} +(10.2868 - 5.16624i) q^{58} +(0.693406 - 1.60750i) q^{59} +(0.517762 + 8.88963i) q^{61} +(1.06160 + 6.02061i) q^{62} +(-1.63891 + 9.29469i) q^{64} +(0.0453782 + 0.00530396i) q^{65} +(-3.91000 - 13.0603i) q^{67} +(8.58577 + 2.03487i) q^{68} +(0.0253641 + 0.0588007i) q^{70} +(3.48681 + 2.92578i) q^{71} +(-7.30212 + 6.12720i) q^{73} +(12.6333 + 6.34468i) q^{74} +(-8.64002 + 1.00987i) q^{76} +(-0.525707 + 9.02605i) q^{77} +(2.18549 + 2.31648i) q^{79} +0.0745499 q^{80} +10.0830 q^{82} +(1.15185 + 1.22089i) q^{83} +(0.00487269 - 0.0836608i) q^{85} +(-13.3897 + 1.56503i) q^{86} +(-2.08419 - 1.04672i) q^{88} +(7.75680 - 6.50872i) q^{89} +(-2.53191 - 2.12452i) q^{91} +(-0.873538 - 2.02509i) q^{92} +(26.9296 + 6.38244i) q^{94} +(0.0236950 + 0.0791467i) q^{95} +(6.59501 + 0.770846i) q^{97} +(-1.68356 + 9.54793i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

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