LMFDB - Embedded newform 729.2.i.a.10.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.17
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.940500 + 0.147092i) q^{2} +(-1.04159 - 0.333973i) q^{4} +(-0.357057 - 0.162302i) q^{5} +(-0.150392 - 1.10107i) q^{7} +(-2.63185 - 1.32176i) q^{8} +O(q^{10})$	\(q+(0.940500 + 0.147092i) q^{2} +(-1.04159 - 0.333973i) q^{4} +(-0.357057 - 0.162302i) q^{5} +(-0.150392 - 1.10107i) q^{7} +(-2.63185 - 1.32176i) q^{8} +(-0.311939 - 0.205165i) q^{10} +(-4.62558 + 0.359528i) q^{11} +(1.29342 + 3.78015i) q^{13} +(0.0205136 - 1.05768i) q^{14} +(-0.501071 - 0.358144i) q^{16} +(-0.303418 + 0.703403i) q^{17} +(-3.78971 + 5.09046i) q^{19} +(0.317702 + 0.288300i) q^{20} +(-4.40324 - 0.342247i) q^{22} +(-3.42277 - 2.65285i) q^{23} +(-3.18646 - 3.65128i) q^{25} +(0.660430 + 3.74549i) q^{26} +(-0.211079 + 1.19709i) q^{28} +(-6.49829 + 3.92174i) q^{29} +(-1.45746 + 0.0565562i) q^{31} +(3.78663 + 3.71390i) q^{32} +(-0.388830 + 0.616920i) q^{34} +(-0.125007 + 0.417552i) q^{35} +(2.67716 - 2.83762i) q^{37} +(-4.31299 + 4.23015i) q^{38} +(0.725194 + 0.899100i) q^{40} +(0.408595 - 1.05829i) q^{41} +(-2.72383 - 10.5745i) q^{43} +(4.93803 + 1.17033i) q^{44} +(-2.82891 - 2.99847i) q^{46} +(-5.25409 - 0.203883i) q^{47} +(5.55387 - 1.54602i) q^{49} +(-2.45979 - 3.90273i) q^{50} +(-0.0847432 - 4.36934i) q^{52} +(11.9489 - 4.34905i) q^{53} +(1.70994 + 0.622369i) q^{55} +(-1.05954 + 3.09663i) q^{56} +(-6.68850 + 2.73255i) q^{58} +(3.80768 + 7.96308i) q^{59} +(-8.01169 + 2.56885i) q^{61} +(-1.37906 - 0.161190i) q^{62} +(3.75063 + 5.03797i) q^{64} +(0.151704 - 1.55965i) q^{65} +(-9.11849 - 5.50304i) q^{67} +(0.550955 - 0.631324i) q^{68} +(-0.178988 + 0.374321i) q^{70} +(-0.0981754 + 1.68561i) q^{71} +(-5.22168 + 3.43435i) q^{73} +(2.93526 - 2.27500i) q^{74} +(5.64740 - 4.03652i) q^{76} +(1.09152 + 5.03900i) q^{77} +(5.04558 - 6.25553i) q^{79} +(0.120783 + 0.209203i) q^{80} +(0.539949 - 0.935219i) q^{82} +(1.55411 + 4.02525i) q^{83} +(0.222501 - 0.201909i) q^{85} +(-1.00633 - 10.3460i) q^{86} +(12.6490 + 5.16770i) q^{88} +(0.222834 + 3.82591i) q^{89} +(3.96768 - 1.99264i) q^{91} +(2.67915 + 3.90629i) q^{92} +(-4.91149 - 0.964585i) q^{94} +(2.17933 - 1.20251i) q^{95} +(2.89765 - 1.31714i) q^{97} +(5.45082 - 0.637109i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.940500	+	0.147092i	0.665034	+	0.104009i	0.478022	−	0.878348i	$-0.341354\pi$
$2$	0.940500	+	0.147092i	0.665034	+	0.104009i	0.187013	+	0.982358i	$0.440119\pi$
$3$		0			0
$3$		0			0
$4$	−1.04159	−	0.333973i	−0.520795	−	0.166986i
$5$	−0.357057	−	0.162302i	−0.159681	−	0.0725837i	0.332376	−	0.943147i	$-0.392150\pi$
$5$	−0.357057	−	0.162302i	−0.159681	−	0.0725837i	−0.492057	+	0.870563i	$0.663755\pi$
$6$		0			0
$7$	−0.150392	−	1.10107i	−0.0568430	−	0.416164i	−0.997125	−	0.0757689i	$-0.975859\pi$
$7$	−0.150392	−	1.10107i	−0.0568430	−	0.416164i	0.940282	−	0.340395i	$-0.110561\pi$
$8$	−2.63185	−	1.32176i	−0.930499	−	0.467314i
$9$		0			0
$10$	−0.311939	−	0.205165i	−0.0986437	−	0.0648790i
$11$	−4.62558	+	0.359528i	−1.39466	+	0.108402i	−0.752715	−	0.658346i	$-0.771256\pi$
$11$	−4.62558	+	0.359528i	−1.39466	+	0.108402i	−0.641948	+	0.766748i	$0.721874\pi$
$12$		0			0
$13$	1.29342	+	3.78015i	0.358729	+	1.04843i	0.967018	+	0.254709i	$0.0819798\pi$
$13$	1.29342	+	3.78015i	0.358729	+	1.04843i	−0.608289	+	0.793716i	$0.708144\pi$
$14$	0.0205136	−	1.05768i	0.00548249	−	0.282676i
$15$		0			0
$16$	−0.501071	−	0.358144i	−0.125268	−	0.0895361i
$17$	−0.303418	+	0.703403i	−0.0735898	+	0.170600i	−0.951040	−	0.309067i	$-0.899983\pi$
$17$	−0.303418	+	0.703403i	−0.0735898	+	0.170600i	0.877451	+	0.479667i	$0.159243\pi$
$18$		0			0
$19$	−3.78971	+	5.09046i	−0.869419	+	1.16783i	0.115239	+	0.993338i	$0.463237\pi$
$19$	−3.78971	+	5.09046i	−0.869419	+	1.16783i	−0.984658	+	0.174495i	$0.944171\pi$
$20$	0.317702	+	0.288300i	0.0710404	+	0.0644657i
$21$		0			0
$22$	−4.40324	−	0.342247i	−0.938774	−	0.0729673i
$23$	−3.42277	−	2.65285i	−0.713697	−	0.553157i	0.189763	−	0.981830i	$-0.439228\pi$
$23$	−3.42277	−	2.65285i	−0.713697	−	0.553157i	−0.903460	+	0.428673i	$0.858981\pi$
$24$		0			0
$25$	−3.18646	−	3.65128i	−0.637292	−	0.730255i
$26$	0.660430	+	3.74549i	0.129521	+	0.734550i
$27$		0			0
$28$	−0.211079	+	1.19709i	−0.0398902	+	0.226228i
$29$	−6.49829	+	3.92174i	−1.20670	+	0.728249i	−0.969946	−	0.243320i	$-0.921763\pi$
$29$	−6.49829	+	3.92174i	−1.20670	+	0.728249i	−0.236757	+	0.971569i	$0.576084\pi$
$30$		0			0
$31$	−1.45746	+	0.0565562i	−0.261768	+	0.0101578i	−0.169325	−	0.985560i	$-0.554159\pi$
$31$	−1.45746	+	0.0565562i	−0.261768	+	0.0101578i	−0.0924428	+	0.995718i	$0.529468\pi$
$32$	3.78663	+	3.71390i	0.669388	+	0.656531i
$33$		0			0
$34$	−0.388830	+	0.616920i	−0.0666838	+	0.105801i
$35$	−0.125007	+	0.417552i	−0.0211300	+	0.0705792i
$36$		0			0
$37$	2.67716	−	2.83762i	0.440122	−	0.466502i	−0.468899	−	0.883252i	$-0.655349\pi$
$37$	2.67716	−	2.83762i	0.440122	−	0.466502i	0.909021	+	0.416750i	$0.136831\pi$
$38$	−4.31299	+	4.23015i	−0.699659	+	0.686221i
$39$		0			0
$40$	0.725194	+	0.899100i	0.114663	+	0.142160i
$41$	0.408595	−	1.05829i	0.0638118	−	0.165277i	−0.897310	−	0.441400i	$-0.854482\pi$
$41$	0.408595	−	1.05829i	0.0638118	−	0.165277i	0.961122	+	0.276123i	$0.0890499\pi$
$42$		0			0
$43$	−2.72383	−	10.5745i	−0.415380	−	1.61260i	−0.744027	−	0.668150i	$-0.767086\pi$
$43$	−2.72383	−	10.5745i	−0.415380	−	1.61260i	0.328647	−	0.944453i	$-0.393407\pi$
$44$	4.93803	+	1.17033i	0.744436	+	0.176435i
$45$		0			0
$46$	−2.82891	−	2.99847i	−0.417099	−	0.442100i
$47$	−5.25409	−	0.203883i	−0.766388	−	0.0297393i	−0.347383	−	0.937723i	$-0.612930\pi$
$47$	−5.25409	−	0.203883i	−0.766388	−	0.0297393i	−0.419005	+	0.907984i	$0.637621\pi$
$48$		0			0
$49$	5.55387	−	1.54602i	0.793409	−	0.220861i
$50$	−2.45979	−	3.90273i	−0.347867	−	0.551929i
$51$		0			0
$52$	−0.0847432	−	4.36934i	−0.0117518	−	0.605918i
$53$	11.9489	−	4.34905i	1.64131	−	0.597389i	0.654044	−	0.756457i	$-0.273071\pi$
$53$	11.9489	−	4.34905i	1.64131	−	0.597389i	0.987268	+	0.159068i	$0.0508489\pi$
$54$		0			0
$55$	1.70994	+	0.622369i	0.230569	+	0.0839202i
$56$	−1.05954	+	3.09663i	−0.141587	+	0.413804i
$57$		0			0
$58$	−6.68850	+	2.73255i	−0.878243	+	0.358802i
$59$	3.80768	+	7.96308i	0.495718	+	1.03671i	0.986247	+	0.165280i	$0.0528529\pi$
$59$	3.80768	+	7.96308i	0.495718	+	1.03671i	−0.490529	+	0.871425i	$0.663196\pi$
$60$		0			0
$61$	−8.01169	+	2.56885i	−1.02579	+	0.328907i	−0.770149	−	0.637864i	$-0.779818\pi$
$61$	−8.01169	+	2.56885i	−1.02579	+	0.328907i	−0.255643	+	0.966771i	$0.582287\pi$
$62$	−1.37906	−	0.161190i	−0.175141	−	0.0204711i
$63$		0			0
$64$	3.75063	+	5.03797i	0.468829	+	0.629746i
$65$	0.151704	−	1.55965i	0.0188166	−	0.193451i
$66$		0			0
$67$	−9.11849	−	5.50304i	−1.11400	−	0.672303i	−0.164597	−	0.986361i	$-0.552632\pi$
$67$	−9.11849	−	5.50304i	−1.11400	−	0.672303i	−0.949404	+	0.314058i	$0.898311\pi$
$68$	0.550955	−	0.631324i	0.0668131	−	0.0765593i
$69$		0			0
$70$	−0.178988	+	0.374321i	−0.0213931	+	0.0447399i
$71$	−0.0981754	+	1.68561i	−0.0116513	+	0.200045i	0.987459	+	0.157875i	$0.0504642\pi$
$71$	−0.0981754	+	1.68561i	−0.0116513	+	0.200045i	−0.999110	+	0.0421701i	$0.986573\pi$
$72$		0			0
$73$	−5.22168	+	3.43435i	−0.611151	+	0.401961i	−0.817012	−	0.576621i	$-0.804371\pi$
$73$	−5.22168	+	3.43435i	−0.611151	+	0.401961i	0.205861	+	0.978581i	$0.434001\pi$
$74$	2.93526	−	2.27500i	0.341217	−	0.264463i
$75$		0			0
$76$	5.64740	−	4.03652i	0.647801	−	0.463021i
$77$	1.09152	+	5.03900i	0.124390	+	0.574247i
$78$		0			0
$79$	5.04558	−	6.25553i	0.567672	−	0.703803i	−0.410439	−	0.911888i	$-0.634624\pi$
$79$	5.04558	−	6.25553i	0.567672	−	0.703803i	0.978111	+	0.208086i	$0.0667232\pi$
$80$	0.120783	+	0.209203i	0.0135040	+	0.0233896i
$81$		0			0
$82$	0.539949	−	0.935219i	0.0596274	−	0.103278i
$83$	1.55411	+	4.02525i	0.170586	+	0.441829i	0.991642	−	0.129018i	$-0.0411826\pi$
$83$	1.55411	+	4.02525i	0.170586	+	0.441829i	−0.821056	+	0.570848i	$0.806615\pi$
$84$		0			0
$85$	0.222501	−	0.201909i	0.0241337	−	0.0219001i
$86$	−1.00633	−	10.3460i	−0.108516	−	1.11564i
$87$		0			0
$88$	12.6490	+	5.16770i	1.34839	+	0.550878i
$89$	0.222834	+	3.82591i	0.0236204	+	0.405546i	0.989308	+	0.145840i	$0.0465885\pi$
$89$	0.222834	+	3.82591i	0.0236204	+	0.405546i	−0.965688	+	0.259706i	$0.916374\pi$
$90$		0			0
$91$	3.96768	−	1.99264i	0.415926	−	0.208886i
$92$	2.67915	+	3.90629i	0.279320	+	0.407259i
$93$		0			0
$94$	−4.91149	−	0.964585i	−0.506581	−	0.0994893i
$95$	2.17933	−	1.20251i	0.223595	−	0.123375i
$96$		0			0
$97$	2.89765	−	1.31714i	0.294212	−	0.133736i	−0.261267	−	0.965267i	$-0.584140\pi$
$97$	2.89765	−	1.31714i	0.294212	−	0.133736i	0.555478	+	0.831531i	$0.312535\pi$
$98$	5.45082	−	0.637109i	0.550616	−	0.0643578i
$99$		0			0
$100$	2.09956	+	4.86733i	0.209956	+	0.486733i
$101$	1.10063	−	5.08107i	0.109517	−	0.505585i	−0.889317	−	0.457292i	$-0.848819\pi$
$101$	1.10063	−	5.08107i	0.109517	−	0.505585i	0.998833	−	0.0482929i	$-0.0153781\pi$
$102$		0			0
$103$	−5.50829	+	8.03128i	−0.542748	+	0.791346i	−0.994929	−	0.100580i	$-0.967930\pi$
$103$	−5.50829	+	8.03128i	−0.542748	+	0.791346i	0.452181	+	0.891926i	$0.350646\pi$
$104$	1.59239	−	11.6584i	0.156147	−	1.14320i
$105$		0			0
$106$	11.8777	−	2.33270i	1.15366	−	0.226572i
$107$	−7.59813	+	6.37559i	−0.734539	+	0.616352i	−0.931365	−	0.364087i	$-0.881381\pi$
$107$	−7.59813	+	6.37559i	−0.734539	+	0.616352i	0.196826	+	0.980438i	$0.436937\pi$
$108$		0			0
$109$	7.60465	+	6.38106i	0.728393	+	0.611195i	0.929693	−	0.368335i	$-0.120072\pi$
$109$	7.60465	+	6.38106i	0.728393	+	0.611195i	−0.201300	+	0.979530i	$0.564517\pi$
$110$	1.51666	+	0.836857i	0.144608	+	0.0797912i
$111$		0			0
$112$	−0.318984	+	0.605575i	−0.0301411	+	0.0572215i
$113$	4.06384	−	15.7768i	0.382294	−	1.48416i	−0.431026	−	0.902340i	$-0.641848\pi$
$113$	4.06384	−	15.7768i	0.382294	−	1.48416i	0.813320	−	0.581817i	$-0.197658\pi$
$114$		0			0
$115$	0.791560	+	1.50274i	0.0738134	+	0.140131i
$116$	8.07831	−	1.91460i	0.750053	−	0.177766i
$117$		0			0
$118$	2.40982	+	8.04936i	0.221842	+	0.741004i
$119$	0.820126	+	0.228298i	0.0751808	+	0.0209280i
$120$		0			0
$121$	10.3988	−	1.62634i	0.945345	−	0.147849i
$122$	−7.91286	+	1.23755i	−0.716397	+	0.112042i
$123$		0			0
$124$	1.53697	+	0.427845i	0.138024	+	0.0384216i
$125$	1.10758	+	3.69956i	0.0990647	+	0.330899i
$126$		0			0
$127$	9.38324	−	2.22387i	0.832628	−	0.197336i	0.207872	−	0.978156i	$-0.433346\pi$
$127$	9.38324	−	2.22387i	0.832628	−	0.197336i	0.624757	+	0.780820i	$0.285198\pi$
$128$	−2.15729	−	4.09552i	−0.190680	−	0.361996i
$129$		0			0
$130$	0.372089	−	1.44454i	0.0326344	−	0.126695i
$131$	−5.12877	+	9.73674i	−0.448103	+	0.850703i	0.551757	+	0.834005i	$0.313957\pi$
$131$	−5.12877	+	9.73674i	−0.448103	+	0.850703i	−0.999861	+	0.0166982i	$0.994685\pi$
$132$		0			0
$133$	6.17489	+	3.40716i	0.535431	+	0.295438i
$134$	−7.76650	−	6.51686i	−0.670923	−	0.562971i
$135$		0			0
$136$	1.72828	−	1.45020i	0.148199	−	0.124354i
$137$	−0.835223	+	0.164033i	−0.0713579	+	0.0140142i	−0.228264	−	0.973599i	$-0.573305\pi$
$137$	−0.835223	+	0.164033i	−0.0713579	+	0.0140142i	0.156906	+	0.987614i	$0.449848\pi$
$138$		0			0
$139$	0.482968	−	3.53595i	0.0409648	−	0.299915i	−0.958904	−	0.283730i	$-0.908428\pi$
$139$	0.482968	−	3.53595i	0.0409648	−	0.299915i	0.999869	−	0.0161853i	$-0.00515216\pi$
$140$	0.269657	−	0.393170i	0.0227902	−	0.0332289i
$141$		0			0
$142$	−0.340272	+	1.57087i	−0.0285550	+	0.131825i
$143$	−7.34187	−	17.0204i	−0.613958	−	1.42331i
$144$		0			0
$145$	2.95677	−	0.345596i	0.245546	−	0.0287002i
$146$	−5.41616	+	2.46195i	−0.448244	+	0.203752i
$147$		0			0
$148$	−3.73619	+	2.06154i	−0.307113	+	0.169458i
$149$	−9.85128	−	1.93473i	−0.807048	−	0.158499i	−0.227861	−	0.973694i	$-0.573173\pi$
$149$	−9.85128	−	1.93473i	−0.807048	−	0.158499i	−0.579187	+	0.815194i	$0.696630\pi$
$150$		0			0
$151$	−9.49804	−	13.8485i	−0.772940	−	1.12697i	−0.988609	−	0.150507i	$-0.951909\pi$
$151$	−9.49804	−	13.8485i	−0.772940	−	1.12697i	0.215669	−	0.976466i	$-0.430807\pi$
$152$	16.7023	−	8.38823i	1.35474	−	0.680375i
$153$		0			0
$154$	0.285377	+	4.89973i	0.0229963	+	0.394832i
$155$	0.529576	+	0.216356i	0.0425366	+	0.0173781i
$156$		0			0
$157$	1.84152	+	18.9325i	0.146969	+	1.51098i	0.721454	+	0.692462i	$0.243474\pi$
$157$	1.84152	+	18.9325i	0.146969	+	1.51098i	−0.574485	+	0.818515i	$0.694797\pi$
$158$	5.66550	−	5.14117i	0.450723	−	0.409010i
$159$		0			0
$160$	−0.749267	−	1.94065i	−0.0592348	−	0.153422i
$161$	−2.40620	+	4.16767i	−0.189635	+	0.328458i
$162$		0			0
$163$	−5.80522	−	10.0549i	−0.454700	−	0.787563i	0.543971	−	0.839104i	$-0.316920\pi$
$163$	−5.80522	−	10.0549i	−0.454700	−	0.787563i	−0.998671	+	0.0515411i	$0.983587\pi$
$164$	−0.779028	+	0.965843i	−0.0608318	+	0.0754196i
$165$		0			0
$166$	0.869563	+	4.01435i	0.0674912	+	0.311574i
$167$	11.7210	−	8.37765i	0.906997	−	0.648282i	−0.0292704	−	0.999572i	$-0.509318\pi$
$167$	11.7210	−	8.37765i	0.906997	−	0.648282i	0.936267	+	0.351289i	$0.114257\pi$
$168$		0			0
$169$	−2.34152	+	1.81481i	−0.180117	+	0.139601i
$170$	0.238962	−	0.157168i	0.0183275	−	0.0120542i
$171$		0			0
$172$	−0.694496	+	11.9240i	−0.0529548	+	0.909199i
$173$	−1.70050	+	3.55628i	−0.129286	+	0.270379i	−0.956624	−	0.291326i	$-0.905904\pi$
$173$	−1.70050	+	3.55628i	−0.129286	+	0.270379i	0.827338	+	0.561705i	$0.189854\pi$
$174$		0			0
$175$	−3.54108	+	4.05763i	−0.267681	+	0.306728i
$176$	2.44651	+	1.47647i	0.184412	+	0.111293i
$177$		0			0
$178$	−0.353184	+	3.63105i	−0.0264723	+	0.272159i
$179$	11.6164	+	15.6036i	0.868252	+	1.16627i	0.984906	+	0.173092i	$0.0553759\pi$
$179$	11.6164	+	15.6036i	0.868252	+	1.16627i	−0.116653	+	0.993173i	$0.537217\pi$
$180$		0			0
$181$	−17.3413	−	2.02691i	−1.28897	−	0.150659i	−0.556151	−	0.831081i	$-0.687722\pi$
$181$	−17.3413	−	2.02691i	−1.28897	−	0.150659i	−0.732820	+	0.680422i	$0.761796\pi$
$182$	4.02471	−	1.29047i	0.298331	−	0.0956560i
$183$		0			0
$184$	5.50178	+	11.5060i	0.405596	+	0.848233i
$185$	−1.41645	+	0.578683i	−0.104139	+	0.0425456i
$186$		0			0
$187$	1.15059	−	3.36273i	0.0841396	−	0.245907i
$188$	5.40452	+	1.96709i	0.394165	+	0.143464i
$189$		0			0
$190$	2.22654	−	0.810396i	0.161530	−	0.0587923i
$191$	0.198851	+	10.2527i	0.0143884	+	0.741861i	0.935652	+	0.352923i	$0.114812\pi$
$191$	0.198851	+	10.2527i	0.0143884	+	0.741861i	−0.921264	+	0.388938i	$0.872842\pi$
$192$		0			0
$193$	−9.34988	−	14.8346i	−0.673019	−	1.06782i	−0.992737	−	0.120305i	$-0.961613\pi$
$193$	−9.34988	−	14.8346i	−0.673019	−	1.06782i	0.319718	−	0.947513i	$-0.396412\pi$
$194$	2.91898	−	0.812554i	0.209571	−	0.0583379i
$195$		0			0
$196$	−6.30118	−	0.244515i	−0.450085	−	0.0174653i
$197$	−3.18875	−	3.37988i	−0.227189	−	0.240806i	0.603745	−	0.797178i	$-0.293675\pi$
$197$	−3.18875	−	3.37988i	−0.227189	−	0.240806i	−0.830934	+	0.556372i	$0.812193\pi$
$198$		0			0
$199$	7.10367	+	1.68360i	0.503566	+	0.119347i	0.474545	−	0.880231i	$-0.342613\pi$
$199$	7.10367	+	1.68360i	0.503566	+	0.119347i	0.0290214	+	0.999579i	$0.490761\pi$
$200$	3.56015	+	13.8214i	0.251741	+	0.977318i
$201$		0			0
$202$	1.78252	−	4.61685i	0.125418	−	0.324841i
$203$	5.29539	+	6.56526i	0.371664	+	0.460791i
$204$		0			0
$205$	−0.317654	+	0.311553i	−0.0221859	+	0.0217598i
$206$	−6.36188	+	6.74320i	−0.443253	+	0.469821i
$207$		0			0
$208$	0.705746	−	2.35735i	0.0489347	−	0.163453i
$209$	15.6994	−	24.9088i	1.08595	−	1.72298i
$210$		0			0
$211$	1.76050	+	1.72668i	0.121198	+	0.118870i	0.758289	−	0.651918i	$-0.226036\pi$
$211$	1.76050	+	1.72668i	0.121198	+	0.118870i	−0.637092	+	0.770788i	$0.719863\pi$
$212$	−13.8984	+	0.539320i	−0.954543	+	0.0370406i
$213$		0			0
$214$	−8.08384	+	4.87862i	−0.552600	+	0.333496i
$215$	−0.743711	+	4.21779i	−0.0507207	+	0.287651i
$216$		0			0
$217$	0.281464	+	1.59626i	0.0191070	+	0.108361i
$218$	6.21358	+	7.11997i	0.420837	+	0.482225i
$219$		0			0
$220$	−1.57321	−	1.21933i	−0.106066	−	0.0822071i
$221$	−3.05142	−	0.237175i	−0.205260	−	0.0159541i
$222$		0			0
$223$	16.5656	+	15.0325i	1.10931	+	1.00665i	0.999920	+	0.0126506i	$0.00402692\pi$
$223$	16.5656	+	15.0325i	1.10931	+	1.00665i	0.109394	+	0.993998i	$0.465109\pi$
$224$	3.51977	−	4.72788i	0.235175	−	0.315895i
$225$		0			0
$226$	6.14268	−	14.2403i	0.408605	−	0.947253i
$227$	−20.5081	−	14.6583i	−1.36117	−	0.972908i	−0.999170	−	0.0407311i	$-0.987031\pi$
$227$	−20.5081	−	14.6583i	−1.36117	−	0.972908i	−0.362003	−	0.932177i	$-0.617907\pi$
$228$		0			0
$229$	0.0946606	−	4.88068i	0.00625535	−	0.322524i	−0.983593	−	0.180399i	$-0.942261\pi$
$229$	0.0946606	−	4.88068i	0.00625535	−	0.322524i	0.989849	−	0.142125i	$-0.0453934\pi$
$230$	0.523422	+	1.52976i	0.0345135	+	0.100869i
$231$		0			0
$232$	22.2861	−	1.73222i	1.46316	−	0.113726i
$233$	−11.6084	−	7.63498i	−0.760493	−	0.500184i	0.109053	−	0.994036i	$-0.465218\pi$
$233$	−11.6084	−	7.63498i	−0.760493	−	0.500184i	−0.869546	+	0.493852i	$0.835589\pi$
$234$		0			0
$235$	1.84292	+	0.925548i	0.120219	+	0.0603761i
$236$	−1.30659	−	9.56593i	−0.0850518	−	0.622689i
$237$		0			0
$238$	0.737748	+	0.335348i	0.0478211	+	0.0217374i
$239$	−14.8029	−	4.74634i	−0.957517	−	0.307015i	−0.214828	−	0.976652i	$-0.568919\pi$
$239$	−14.8029	−	4.74634i	−0.957517	−	0.307015i	−0.742689	+	0.669636i	$0.766450\pi$
$240$		0			0
$241$	−21.0712	−	3.29547i	−1.35731	−	0.212280i	−0.566361	−	0.824157i	$-0.691649\pi$
$241$	−21.0712	−	3.29547i	−1.35731	−	0.212280i	−0.790953	+	0.611877i	$0.790415\pi$
$242$	10.0193			0.644065
$243$		0			0
$244$	9.20283			0.589151
$245$	−2.23397	−	0.349386i	−0.142723	−	0.0223215i
$246$		0			0
$247$	−24.1444	−	7.74159i	−1.53627	−	0.492586i
$248$	3.91058	+	1.77758i	0.248322	+	0.112876i
$249$		0			0
$250$	0.497502	+	3.64236i	0.0314648	+	0.230363i
$251$	2.20899	+	1.10940i	0.139430	+	0.0700246i	0.517147	−	0.855897i	$-0.326994\pi$
$251$	2.20899	+	1.10940i	0.139430	+	0.0700246i	−0.377716	+	0.925921i	$0.623290\pi$
$252$		0			0
$253$	16.7861	+	11.0404i	1.05533	+	0.694102i
$254$	9.15206	−	0.711354i	0.574251	−	0.0446343i
$255$		0			0
$256$	−5.49313	−	16.0543i	−0.343321	−	1.00339i
$257$	0.0492650	−	2.54009i	0.00307307	−	0.158447i	−0.995132	−	0.0985537i	$-0.968578\pi$
$257$	0.0492650	−	2.54009i	0.00307307	−	0.158447i	0.998205	−	0.0598929i	$-0.0190759\pi$
$258$		0			0
$259$	−3.52704	−	2.52097i	−0.219159	−	0.156646i
$260$	−0.678895	+	1.57385i	−0.0421033	+	0.0976063i
$261$		0			0
$262$	−6.25581	+	8.40301i	−0.386485	+	0.519140i
$263$	0.600598	+	0.545013i	0.0370344	+	0.0336070i	0.690315	−	0.723509i	$-0.257472\pi$
$263$	0.600598	+	0.545013i	0.0370344	+	0.0336070i	−0.653281	+	0.757116i	$0.726608\pi$
$264$		0			0
$265$	−4.97231	−	0.386478i	−0.305446	−	0.0237412i
$266$	5.30632	+	4.11271i	0.325351	+	0.252166i
$267$		0			0
$268$	7.65987	+	8.77724i	0.467901	+	0.536155i
$269$	4.96702	+	28.1694i	0.302845	+	1.71752i	0.633481	+	0.773759i	$0.281626\pi$
$269$	4.96702	+	28.1694i	0.302845	+	1.71752i	−0.330636	+	0.943758i	$0.607263\pi$
$270$		0			0
$271$	3.22640	−	18.2978i	0.195990	−	1.11151i	−0.715012	−	0.699112i	$-0.753579\pi$
$271$	3.22640	−	18.2978i	0.195990	−	1.11151i	0.911002	−	0.412401i	$-0.135310\pi$
$272$	0.403954	−	0.243787i	0.0244933	−	0.0147818i
$273$		0			0
$274$	−0.809656	+	0.0314183i	−0.0489131	+	0.00189805i
$275$	16.0519	+	15.7436i	0.967969	+	0.949377i
$276$		0			0
$277$	−9.54791	+	15.1488i	−0.573678	+	0.910203i	0.426306	+	0.904579i	$0.359815\pi$
$277$	−9.54791	+	15.1488i	−0.573678	+	0.910203i	−0.999984	+	0.00562358i	$0.998210\pi$
$278$	0.974339	−	3.25452i	0.0584370	−	0.195193i
$279$		0			0
$280$	0.880905	−	0.933705i	0.0526442	−	0.0557996i
$281$	−5.50448	+	5.39875i	−0.328370	+	0.322063i	−0.845634	−	0.533763i	$-0.820777\pi$
$281$	−5.50448	+	5.39875i	−0.328370	+	0.322063i	0.517265	+	0.855826i	$0.326950\pi$
$282$		0			0
$283$	4.11812	+	5.10566i	0.244797	+	0.303500i	0.885827	−	0.464015i	$-0.153592\pi$
$283$	4.11812	+	5.10566i	0.244797	+	0.303500i	−0.641031	+	0.767515i	$0.721493\pi$
$284$	0.665205	−	1.72292i	0.0394726	−	0.102237i
$285$		0			0
$286$	−4.40148	−	17.0876i	−0.260265	−	1.01041i
$287$	−1.22669	−	0.290732i	−0.0724095	−	0.0171614i
$288$		0			0
$289$	11.2634	+	11.9385i	0.662553	+	0.702265i
$290$	2.83167	+	0.109882i	0.166282	+	0.00645248i
$291$		0			0
$292$	6.58583	−	1.83329i	0.385407	−	0.107285i
$293$	−4.63624	−	7.35590i	−0.270852	−	0.429736i	0.682819	−	0.730588i	$-0.260754\pi$
$293$	−4.63624	−	7.35590i	−0.270852	−	0.429736i	−0.953671	+	0.300852i	$0.902729\pi$
$294$		0			0
$295$	−0.0671312	−	3.46127i	−0.00390853	−	0.201523i
$296$	−10.7965	+	3.92962i	−0.627536	+	0.228405i
$297$		0			0
$298$	−8.98055	−	3.26865i	−0.520229	−	0.189348i
$299$	5.60110	−	16.3698i	0.323920	−	0.946692i
$300$		0			0
$301$	−11.2336	+	4.58945i	−0.647496	+	0.264531i
$302$	−6.89592	−	14.4216i	−0.396815	−	0.829869i
$303$		0			0
$304$	3.72204	−	1.19342i	0.213473	−	0.0684475i
$305$	3.27756	+	0.383092i	0.187672	+	0.0219358i
$306$		0			0
$307$	−16.1248	−	21.6594i	−0.920293	−	1.23617i	−0.971394	−	0.237475i	$-0.923680\pi$
$307$	−16.1248	−	21.6594i	−0.920293	−	1.23617i	0.0511002	−	0.998694i	$-0.483727\pi$
$308$	0.545975	−	5.61311i	0.0311098	−	0.319837i
$309$		0			0
$310$	0.466243	+	0.281379i	0.0264808	+	0.0159813i
$311$	−6.95454	+	7.96902i	−0.394356	+	0.451882i	−0.915938	−	0.401319i	$-0.868552\pi$
$311$	−6.95454	+	7.96902i	−0.394356	+	0.451882i	0.521582	+	0.853201i	$0.325342\pi$
$312$		0			0
$313$	−14.3560	+	30.0230i	−0.811449	+	1.69700i	−0.0992062	+	0.995067i	$0.531630\pi$
$313$	−14.3560	+	30.0230i	−0.811449	+	1.69700i	−0.712242	+	0.701934i	$0.752320\pi$
$314$	−1.05286	+	18.0769i	−0.0594163	+	1.02014i
$315$		0			0
$316$	−7.34460	+	4.83062i	−0.413166	+	0.271744i
$317$	7.07476	−	5.48336i	0.397358	−	0.307976i	−0.394252	−	0.919002i	$-0.628996\pi$
$317$	7.07476	−	5.48336i	0.397358	−	0.307976i	0.791610	+	0.611027i	$0.209243\pi$
$318$		0			0
$319$	28.6484	−	20.4766i	1.60400	−	1.14647i
$320$	−0.521514	−	2.40758i	−0.0291535	−	0.134588i
$321$		0			0
$322$	−2.87607	+	3.56576i	−0.160277	+	0.198712i
$323$	−2.43078	−	4.21023i	−0.135252	−	0.234264i
$324$		0			0
$325$	9.68096	−	16.7679i	0.537003	−	0.930117i
$326$	−3.98081	−	10.3106i	−0.220477	−	0.571049i
$327$		0			0
$328$	−2.47417	+	2.24519i	−0.136613	+	0.123970i
$329$	0.565687	+	5.81577i	0.0311873	+	0.320634i
$330$		0			0
$331$	−14.8658	−	6.07336i	−0.817100	−	0.333822i	−0.0691742	−	0.997605i	$-0.522036\pi$
$331$	−14.8658	−	6.07336i	−0.817100	−	0.333822i	−0.747926	+	0.663783i	$0.768950\pi$
$332$	−0.274425	−	4.71170i	−0.0150610	−	0.258588i
$333$		0			0
$334$	12.2559	−	6.15513i	0.670611	−	0.336794i
$335$	2.36266	+	3.44485i	0.129086	+	0.188212i
$336$		0			0
$337$	27.4879	+	5.39844i	1.49736	+	0.294072i	0.873253	−	0.487267i	$-0.162006\pi$
$337$	27.4879	+	5.39844i	1.49736	+	0.294072i	0.624107	+	0.781339i	$0.285463\pi$
$338$	−2.46914	+	1.36241i	−0.134304	+	0.0741056i
$339$		0			0
$340$	−0.299187	+	0.135997i	−0.0162257	+	0.00737549i
$341$	6.72128	−	0.785604i	0.363977	−	0.0425429i
$342$		0			0
$343$	−5.61865	−	13.0255i	−0.303379	−	0.703311i
$344$	−6.80835	+	31.4309i	−0.367082	+	1.69464i
$345$		0			0
$346$	−2.12242	+	3.09456i	−0.114102	+	0.166364i
$347$	0.329112	−	2.40953i	0.0176677	−	0.129350i	−0.979853	−	0.199718i	$-0.935997\pi$
$347$	0.329112	−	2.40953i	0.0176677	−	0.129350i	0.997521	+	0.0703676i	$0.0224172\pi$
$348$		0			0
$349$	20.8986	−	4.10434i	1.11867	−	0.219700i	0.400999	−	0.916079i	$-0.368663\pi$
$349$	20.8986	−	4.10434i	1.11867	−	0.219700i	0.717675	+	0.696378i	$0.245206\pi$
$350$	−3.92723	+	3.29534i	−0.209919	+	0.176143i
$351$		0			0
$352$	−18.8506	−	15.8175i	−1.00474	−	0.843077i
$353$	27.5285	+	15.1896i	1.46520	+	0.808461i	0.997165	−	0.0752510i	$-0.0239758\pi$
$353$	27.5285	+	15.1896i	1.46520	+	0.808461i	0.468031	+	0.883712i	$0.344963\pi$
$354$		0			0
$355$	0.308632	−	0.585923i	0.0163805	−	0.0310976i
$356$	1.04565	−	4.05945i	0.0554192	−	0.215151i
$357$		0			0
$358$	8.63010	+	16.3838i	0.456115	+	0.865913i
$359$	−31.2258	+	7.40065i	−1.64804	+	0.390592i	−0.946669	−	0.322209i	$-0.895575\pi$
$359$	−31.2258	+	7.40065i	−1.64804	+	0.390592i	−0.701367	+	0.712800i	$0.747427\pi$
$360$		0			0
$361$	−6.10166	−	20.3810i	−0.321140	−	1.07268i
$362$	−16.0114	−	4.45707i	−0.841540	−	0.234259i
$363$		0			0
$364$	−4.79819	+	0.750423i	−0.251493	+	0.0393328i
$365$	2.42184	−	0.378769i	0.126765	−	0.0198257i
$366$		0			0
$367$	−33.0532	−	9.20099i	−1.72536	−	0.480288i	−0.743319	−	0.668937i	$-0.766750\pi$
$367$	−33.0532	−	9.20099i	−1.72536	−	0.480288i	−0.982045	+	0.188649i	$0.939589\pi$
$368$	0.764950	+	2.55511i	0.0398758	+	0.133194i
$369$		0			0
$370$	−1.41729	+	0.335904i	−0.0736814	+	0.0174628i
$371$	−6.58563	−	12.5025i	−0.341909	−	0.649098i
$372$		0			0
$373$	−5.61132	+	21.7845i	−0.290543	+	1.12796i	0.641943	+	0.766752i	$0.278129\pi$
$373$	−5.61132	+	21.7845i	−0.290543	+	1.12796i	−0.932486	+	0.361206i	$0.882365\pi$
$374$	1.57676	−	2.99341i	0.0815324	−	0.154785i
$375$		0			0
$376$	13.5585	+	7.48126i	0.699226	+	0.385817i
$377$	−23.2298	−	19.4921i	−1.19639	−	1.00389i
$378$		0			0
$379$	−23.0011	+	19.3002i	−1.18148	+	0.991384i	−0.181517	+	0.983388i	$0.558101\pi$
$379$	−23.0011	+	19.3002i	−1.18148	+	0.991384i	−0.999968	+	0.00799581i	$0.997455\pi$
$380$	−2.67158	+	0.524681i	−0.137049	+	0.0269156i
$381$		0			0
$382$	−1.32107	+	9.67194i	−0.0675918	+	0.494860i
$383$	−13.5359	+	19.7359i	−0.691653	+	1.00846i	0.306740	+	0.951793i	$0.400762\pi$
$383$	−13.5359	+	19.7359i	−0.691653	+	1.00846i	−0.998393	+	0.0566619i	$0.981954\pi$
$384$		0			0
$385$	0.428107	−	1.97636i	0.0218184	−	0.100725i
$386$	−6.61152	−	15.3272i	−0.336518	−	0.780136i
$387$		0			0
$388$	−3.45805	+	0.404188i	−0.175556	+	0.0205196i
$389$	17.5107	−	7.95959i	0.887828	−	0.403567i	0.0826350	−	0.996580i	$-0.473666\pi$
$389$	17.5107	−	7.95959i	0.887828	−	0.403567i	0.805193	+	0.593012i	$0.202062\pi$
$390$		0			0
$391$	2.90455	−	1.60266i	0.146890	−	0.0810502i
$392$	−16.6604	−	3.27200i	−0.841478	−	0.165261i
$393$		0			0
$394$	−2.50187	−	3.64781i	−0.126042	−	0.183774i
$395$	−2.81684	+	1.41467i	−0.141731	+	0.0711799i
$396$		0			0
$397$	1.10975	+	19.0537i	0.0556968	+	0.956277i	0.904206	+	0.427097i	$0.140464\pi$
$397$	1.10975	+	19.0537i	0.0556968	+	0.956277i	−0.848509	+	0.529181i	$0.822499\pi$
$398$	6.43337	+	2.62832i	0.322475	+	0.131746i
$399$		0			0
$400$	0.288959	+	2.97076i	0.0144480	+	0.148538i
$401$	−28.6191	+	25.9705i	−1.42917	+	1.29690i	−0.538221	+	0.842804i	$0.680903\pi$
$401$	−28.6191	+	25.9705i	−1.42917	+	1.29690i	−0.890951	+	0.454100i	$0.849961\pi$
$402$		0			0
$403$	−2.09890	−	5.43628i	−0.104554	−	0.270801i
$404$	−2.84334	+	4.92481i	−0.141461	+	0.245018i
$405$		0			0
$406$	4.01462	+	6.95353i	0.199242	+	0.345098i
$407$	−11.3632	+	14.0881i	−0.563252	+	0.698323i
$408$		0			0
$409$	−0.408156	−	1.88426i	−0.0201820	−	0.0931705i	0.966132	−	0.258048i	$-0.0830794\pi$
$409$	−0.408156	−	1.88426i	−0.0201820	−	0.0931705i	−0.986314	+	0.164878i	$0.947277\pi$
$410$	−0.344580	+	0.246291i	−0.0170176	+	0.0121635i
$411$		0			0
$412$	8.41961	−	6.52569i	0.414804	−	0.321498i
$413$	8.19524	−	5.39010i	0.403262	−	0.265229i
$414$		0			0
$415$	0.0984010	−	1.68948i	0.00483032	−	0.0829333i
$416$	−9.14142	+	19.1177i	−0.448195	+	0.937320i
$417$		0			0
$418$	18.4292	−	21.1175i	0.901402	−	1.03289i
$419$	29.1371	+	17.5844i	1.42344	+	0.859052i	0.998924	−	0.0463675i	$-0.0147645\pi$
$419$	29.1371	+	17.5844i	1.42344	+	0.859052i	0.424518	+	0.905419i	$0.360444\pi$
$420$		0			0
$421$	−0.769645	+	7.91264i	−0.0375102	+	0.385639i	0.957692	+	0.287796i	$0.0929225\pi$
$421$	−0.769645	+	7.91264i	−0.0375102	+	0.385639i	−0.995202	+	0.0978425i	$0.968806\pi$
$422$	1.40177	+	1.88290i	0.0682370	+	0.0916581i
$423$		0			0
$424$	−37.1962	−	4.34761i	−1.80641	−	0.211139i
$425$	3.53515	−	1.13350i	0.171480	−	0.0549828i
$426$		0			0
$427$	4.03337	+	8.43508i	0.195188	+	0.408202i
$428$	10.0434	−	4.10319i	0.485467	−	0.198335i
$429$		0			0
$430$	−1.31986	+	3.85744i	−0.0636494	+	0.186022i
$431$	−21.7964	−	7.93323i	−1.04989	−	0.382130i	−0.241271	−	0.970458i	$-0.577564\pi$
$431$	−21.7964	−	7.93323i	−1.04989	−	0.382130i	−0.808623	+	0.588328i	$0.799787\pi$
$432$		0			0
$433$	6.59338	−	2.39979i	0.316857	−	0.115327i	−0.178695	−	0.983904i	$-0.557188\pi$
$433$	6.59338	−	2.39979i	0.316857	−	0.115327i	0.495553	+	0.868578i	$0.334965\pi$
$434$	0.0299203	+	1.54268i	0.00143622	+	0.0740512i
$435$		0			0
$436$	−5.78983	−	9.18620i	−0.277283	−	0.439939i
$437$	26.4755	−	7.36997i	1.26650	−	0.352553i
$438$		0			0
$439$	−31.8377	−	1.23545i	−1.51953	−	0.0589648i	−0.734580	−	0.678522i	$-0.762621\pi$
$439$	−31.8377	−	1.23545i	−1.51953	−	0.0589648i	−0.784952	+	0.619557i	$0.787312\pi$
$440$	−3.67769	−	3.89813i	−0.175327	−	0.185836i
$441$		0			0
$442$	−2.83497	−	0.671901i	−0.134846	−	0.0319591i
$443$	−2.79697	−	10.8585i	−0.132888	−	0.515903i	−0.999846	−	0.0175228i	$-0.994422\pi$
$443$	−2.79697	−	10.8585i	−0.132888	−	0.515903i	0.866958	−	0.498381i	$-0.166072\pi$
$444$		0			0
$445$	0.541389	−	1.40223i	0.0256643	−	0.0664723i
$446$	13.3688	+	16.5747i	0.633031	+	0.784835i
$447$		0			0
$448$	4.98308	−	4.88737i	0.235428	−	0.230906i
$449$	13.4033	−	14.2067i	0.632541	−	0.670454i	−0.329249	−	0.944243i	$-0.606796\pi$
$449$	13.4033	−	14.2067i	0.632541	−	0.670454i	0.961790	+	0.273789i	$0.0882771\pi$
$450$		0			0
$451$	−1.50950	+	5.04209i	−0.0710797	+	0.237423i
$452$	−9.50188	+	15.0758i	−0.446931	+	0.709104i
$453$		0			0
$454$	−17.1318	−	16.8027i	−0.804035	−	0.788592i
$455$	−1.74010	+	0.0675237i	−0.0815770	+	0.00316556i
$456$		0			0
$457$	21.8682	−	13.1975i	1.02295	−	0.617354i	0.0971125	−	0.995273i	$-0.469039\pi$
$457$	21.8682	−	13.1975i	1.02295	−	0.617354i	0.925839	+	0.377919i	$0.123360\pi$
$458$	0.806935	−	4.57635i	0.0377056	−	0.213839i
$459$		0			0
$460$	−0.322608	−	1.82960i	−0.0150417	−	0.0853055i
$461$	−13.7940	−	15.8062i	−0.642453	−	0.736169i	0.336177	−	0.941799i	$-0.390866\pi$
$461$	−13.7940	−	15.8062i	−0.642453	−	0.736169i	−0.978630	+	0.205630i	$0.934076\pi$
$462$		0			0
$463$	17.0498	+	13.2146i	0.792371	+	0.614133i	0.926270	−	0.376861i	$-0.122997\pi$
$463$	17.0498	+	13.2146i	0.792371	+	0.614133i	−0.133899	+	0.990995i	$0.542750\pi$
$464$	4.66066	+	0.362255i	0.216366	+	0.0168173i
$465$		0			0
$466$	−9.79469	−	8.88821i	−0.453730	−	0.411738i
$467$	8.72873	−	11.7247i	0.403918	−	0.542556i	−0.552899	−	0.833248i	$-0.686478\pi$
$467$	8.72873	−	11.7247i	0.403918	−	0.542556i	0.956816	+	0.290693i	$0.0938858\pi$
$468$		0			0
$469$	−4.68786	+	10.8677i	−0.216465	+	0.501823i
$470$	1.59713	+	1.14156i	0.0736699	+	0.0526561i
$471$		0			0
$472$	0.504085	−	25.9905i	0.0232024	−	1.19631i
$473$	16.4011	+	47.9341i	0.754124	+	2.20401i
$474$		0			0
$475$	30.6625	−	2.38327i	1.40689	−	0.109352i
$476$	−0.777990	−	0.511692i	−0.0356591	−	0.0234534i
$477$		0			0
$478$	−13.2239	−	6.64131i	−0.604849	−	0.303767i
$479$	−3.36659	−	24.6478i	−0.153824	−	1.12619i	−0.892148	−	0.451743i	$-0.850802\pi$
$479$	−3.36659	−	24.6478i	−0.153824	−	1.12619i	0.738325	−	0.674446i	$-0.235617\pi$
$480$		0			0
$481$	14.1893	+	6.44984i	0.646977	+	0.294087i
$482$	−19.3327	−	6.19878i	−0.880581	−	0.282347i
$483$		0			0
$484$	−11.3744	−	1.77893i	−0.517020	−	0.0808605i
$485$	−1.24840			−0.0566869
$486$		0			0
$487$	−10.7019			−0.484950			−0.242475	−	0.970158i	$-0.577959\pi$
$487$	−10.7019			−0.484950			−0.242475	+	0.970158i	$0.577959\pi$
$488$	24.4810	+	3.82876i	1.10820	+	0.173320i
$489$		0			0
$490$	−2.04966	−	0.657196i	−0.0925940	−	0.0296891i
$491$	−6.92439	−	3.14752i	−0.312493	−	0.142046i	0.251424	−	0.967877i	$-0.419101\pi$
$491$	−6.92439	−	3.14752i	−0.312493	−	0.142046i	−0.563917	+	0.825832i	$0.690706\pi$
$492$		0			0
$493$	−0.786861	−	5.76085i	−0.0354385	−	0.259455i
$494$	−21.5691	−	10.8324i	−0.970440	−	0.487373i
$495$		0			0
$496$	0.750549	+	0.493644i	0.0337006	+	0.0221653i
$497$	1.87073	−	0.145405i	0.0839137	−	0.00652229i
$498$		0			0
$499$	6.31030	+	18.4426i	0.282488	+	0.825602i	0.992591	+	0.121504i	$0.0387718\pi$
$499$	6.31030	+	18.4426i	0.282488	+	0.825602i	−0.710103	+	0.704098i	$0.751352\pi$
$500$	0.0819114	−	4.22333i	0.00366319	−	0.188873i
$501$		0			0
$502$	1.91438	+	1.36831i	0.0854428	+	0.0610708i
$503$	−9.06053	+	21.0047i	−0.403989	+	0.936552i	0.587840	+	0.808977i	$0.299979\pi$
$503$	−9.06053	+	21.0047i	−0.403989	+	0.936552i	−0.991829	+	0.127575i	$0.959281\pi$
$504$		0			0
$505$	−1.21765	+	1.63559i	−0.0541849	+	0.0727830i
$506$	14.1634	+	12.8526i	0.629638	+	0.571366i
$507$		0			0
$508$	−10.5162	−	0.817384i	−0.466581	−	0.0362656i
$509$	−6.63287	−	5.14086i	−0.293997	−	0.227865i	0.454914	−	0.890535i	$-0.349670\pi$
$509$	−6.63287	−	5.14086i	−0.293997	−	0.227865i	−0.748911	+	0.662671i	$0.769423\pi$
$510$		0			0
$511$	4.56675	+	5.23292i	0.202021	+	0.231491i
$512$	−1.19722	−	6.78980i	−0.0529103	−	0.300069i
$513$		0			0
$514$	0.419960	−	2.38171i	0.0185236	−	0.105053i
$515$	3.27027	−	1.97362i	0.144105	−	0.0869679i
$516$		0			0
$517$	24.3765	−	0.945919i	1.07208	−	0.0416015i
$518$	−2.94636	−	2.88977i	−0.129456	−	0.126969i
$519$		0			0
$520$	−2.46076	+	3.90425i	−0.107911	+	0.171213i
$521$	3.44428	−	11.5047i	0.150897	−	0.504031i	−0.848798	−	0.528717i	$-0.822673\pi$
$521$	3.44428	−	11.5047i	0.150897	−	0.504031i	0.999695	+	0.0246860i	$0.00785860\pi$
$522$		0			0
$523$	−7.17926	+	7.60957i	−0.313927	+	0.332743i	−0.865055	−	0.501678i	$-0.832716\pi$
$523$	−7.17926	+	7.60957i	−0.313927	+	0.332743i	0.551128	+	0.834421i	$0.314198\pi$
$524$	8.59389	−	8.42882i	0.375426	−	0.368215i
$525$		0			0
$526$	0.484695	+	0.600928i	0.0211337	+	0.0262017i
$527$	0.402440	−	1.04234i	0.0175305	−	0.0454052i
$528$		0			0
$529$	−1.05939	−	4.11279i	−0.0460602	−	0.178817i
$530$	−4.61961	−	1.09487i	−0.200663	−	0.0475580i
$531$		0			0
$532$	−5.29381	−	5.61111i	−0.229516	−	0.243272i
$533$	4.52897	+	0.175745i	0.196171	+	0.00761235i
$534$		0			0
$535$	3.74774	−	1.04325i	0.162029	−	0.0451038i
$536$	16.7248	+	26.5357i	0.722400	+	1.14617i
$537$		0			0
$538$	0.528007	+	27.2239i	0.0227640	+	1.17371i
$539$	−25.1340	+	9.14802i	−1.08260	+	0.394033i
$540$		0			0
$541$	−14.9118	−	5.42745i	−0.641109	−	0.233344i	0.000950499	−	1.00000i	$-0.499697\pi$
$541$	−14.9118	−	5.42745i	−0.641109	−	0.233344i	−0.642059	+	0.766655i	$0.721920\pi$
$542$	5.72588	−	16.7345i	0.245948	−	0.718810i
$543$		0			0
$544$	−3.76130	+	1.53666i	−0.161264	+	0.0658838i
$545$	−1.67963	−	3.51265i	−0.0719475	−	0.150465i
$546$		0			0
$547$	−22.4648	+	7.20303i	−0.960524	+	0.307979i	−0.743911	−	0.668278i	$-0.767032\pi$
$547$	−22.4648	+	7.20303i	−0.960524	+	0.307979i	−0.216612	+	0.976258i	$0.569501\pi$
$548$	0.924743	+	0.108087i	0.0395031	+	0.00461725i
$549$		0			0
$550$	12.7811	+	17.1680i	0.544988	+	0.732046i
$551$	4.66317	−	47.9416i	0.198658	−	2.04238i
$552$		0			0
$553$	−7.64658	−	4.61473i	−0.325166	−	0.196238i
$554$	−11.2081	+	12.8430i	−0.476185	+	0.545648i
$555$		0			0
$556$	−1.68396	+	3.52171i	−0.0714160	+	0.149354i
$557$	1.97633	−	33.9323i	0.0837399	−	1.43776i	−0.650829	−	0.759224i	$-0.725579\pi$
$557$	1.97633	−	33.9323i	0.0837399	−	1.43776i	0.734569	−	0.678534i	$-0.237384\pi$
$558$		0			0
$559$	36.4503	−	23.9738i	1.54169	−	1.01398i
$560$	0.212181	−	0.164453i	0.00896630	−	0.00694941i
$561$		0			0
$562$	−5.97107	+	4.26787i	−0.251875	+	0.180029i
$563$	−3.96849	−	18.3206i	−0.167252	−	0.772121i	−0.981478	−	0.191574i	$-0.938641\pi$
$563$	−3.96849	−	18.3206i	−0.167252	−	0.772121i	0.814226	−	0.580548i	$-0.197162\pi$
$564$		0			0
$565$	−4.01163	+	4.97364i	−0.168771	+	0.209243i
$566$	3.12209	+	5.40762i	0.131231	+	0.227299i
$567$		0			0
$568$	2.48636	−	4.30650i	0.104325	−	0.180697i
$569$	11.9415	+	30.9294i	0.500615	+	1.29663i	0.921100	+	0.389326i	$0.127292\pi$
$569$	11.9415	+	30.9294i	0.500615	+	1.29663i	−0.420485	+	0.907300i	$0.638140\pi$
$570$		0			0
$571$	7.18835	−	6.52308i	0.300823	−	0.272982i	−0.507589	−	0.861599i	$-0.669463\pi$
$571$	7.18835	−	6.52308i	0.300823	−	0.272982i	0.808412	+	0.588617i	$0.200327\pi$
$572$	1.96289	+	20.1802i	0.0820724	+	0.843778i
$573$		0			0
$574$	−1.11094	−	0.453870i	−0.0463699	−	0.0189442i
$575$	1.22024	+	20.9507i	0.0508874	+	0.873704i
$576$		0			0
$577$	−11.0269	+	5.53794i	−0.459057	+	0.230547i	−0.663271	−	0.748379i	$-0.730832\pi$
$577$	−11.0269	+	5.53794i	−0.459057	+	0.230547i	0.204214	+	0.978926i	$0.434536\pi$
$578$	8.83718	+	12.8849i	0.367578	+	0.535942i
$579$		0			0
$580$	−3.19516	−	0.627509i	−0.132672	−	0.0260559i
$581$	4.19835	−	2.31655i	0.174177	−	0.0961067i
$582$		0			0
$583$	−53.7071	+	24.4129i	−2.22432	+	1.01108i
$584$	18.2821	−	2.13687i	0.756518	−	0.0884242i
$585$		0			0
$586$	−3.27840	−	7.60017i	−0.135429	−	0.313960i
$587$	−1.79851	+	8.30283i	−0.0742323	+	0.342694i	−0.999312	−	0.0370777i	$-0.988195\pi$
$587$	−1.79851	+	8.30283i	−0.0742323	+	0.342694i	0.925080	+	0.379772i	$0.123998\pi$
$588$		0			0
$589$	5.23547	−	7.63350i	0.215724	−	0.314533i
$590$	0.445986	−	3.26520i	0.0183610	−	0.134426i
$591$		0			0
$592$	−2.35772	+	0.463042i	−0.0969019	+	0.0190309i
$593$	1.12023	−	0.939984i	0.0460023	−	0.0386005i	−0.619497	−	0.784999i	$-0.712663\pi$
$593$	1.12023	−	0.939984i	0.0460023	−	0.0386005i	0.665499	+	0.746399i	$0.268219\pi$
$594$		0			0
$595$	−0.255778	−	0.214623i	−0.0104859	−	0.00879870i
$596$	9.61486	+	5.30525i	0.393840	+	0.217312i
$597$		0			0
$598$	7.67570	−	14.5720i	0.313883	−	0.595892i
$599$	3.44672	−	13.3810i	0.140829	−	0.546733i	−0.858590	−	0.512663i	$-0.828659\pi$
$599$	3.44672	−	13.3810i	0.140829	−	0.546733i	0.999419	−	0.0340702i	$-0.0108470\pi$
$600$		0			0
$601$	18.3187	+	34.7772i	0.747236	+	1.41859i	0.902487	+	0.430718i	$0.141739\pi$
$601$	18.3187	+	34.7772i	0.747236	+	1.41859i	−0.155251	+	0.987875i	$0.549619\pi$
$602$	−11.2403	+	2.66400i	−0.458121	+	0.108577i
$603$		0			0
$604$	5.26806	+	17.5965i	0.214354	+	0.715993i
$605$	−3.97692	−	1.10705i	−0.161685	−	0.0450080i
$606$		0			0
$607$	3.76661	−	0.589087i	0.152882	−	0.0239103i	−0.0776146	−	0.996983i	$-0.524730\pi$
$607$	3.76661	−	0.589087i	0.152882	−	0.0239103i	0.230497	+	0.973073i	$0.425965\pi$
$608$	−33.2557	+	5.20110i	−1.34870	+	0.210932i
$609$		0			0
$610$	3.02620	+	0.842399i	0.122527	+	0.0341077i
$611$	−6.02502	−	20.1250i	−0.243746	−	0.814169i
$612$		0			0
$613$	0.316498	−	0.0750113i	0.0127832	−	0.00302968i	−0.224219	−	0.974539i	$-0.571983\pi$
$613$	0.316498	−	0.0750113i	0.0127832	−	0.00302968i	0.237003	+	0.971509i	$0.423835\pi$
$614$	−11.9795	−	22.7425i	−0.483453	−	0.917814i
$615$		0			0
$616$	3.78766	−	14.7046i	0.152609	−	0.592466i
$617$	−1.38931	+	2.63755i	−0.0559317	+	0.106184i	−0.911133	−	0.412112i	$-0.864791\pi$
$617$	−1.38931	+	2.63755i	−0.0559317	+	0.106184i	0.855202	+	0.518296i	$0.173433\pi$
$618$		0			0
$619$	31.9363	+	17.6217i	1.28363	+	0.708277i	0.970424	−	0.241408i	$-0.0776093\pi$
$619$	31.9363	+	17.6217i	1.28363	+	0.708277i	0.313206	+	0.949685i	$0.398597\pi$
$620$	−0.479345	−	0.402218i	−0.0192510	−	0.0161535i
$621$		0			0
$622$	−7.71292	+	6.47191i	−0.309260	+	0.259500i
$623$	4.17907	−	0.820743i	0.167431	−	0.0328824i
$624$		0			0
$625$	−3.07421	+	22.5072i	−0.122968	+	0.900288i
$626$	−17.9179	+	26.1250i	−0.716145	+	1.04417i
$627$		0			0
$628$	4.40482	−	20.3349i	0.175772	−	0.811452i
$629$	1.18369	+	2.74411i	0.0471969	+	0.109415i
$630$		0			0
$631$	−9.29712	+	1.08668i	−0.370112	+	0.0432599i	−0.299116	−	0.954217i	$-0.596692\pi$
$631$	−9.29712	+	1.08668i	−0.370112	+	0.0432599i	−0.0709961	+	0.997477i	$0.522618\pi$
$632$	−21.5475	+	9.79456i	−0.857115	+	0.389607i
$633$		0			0
$634$	7.46037	−	4.11646i	0.296289	−	0.163486i
$635$	−3.71129	−	0.728873i	−0.147278	−	0.0289245i
$636$		0			0
$637$	13.0277	+	18.9948i	0.516175	+	0.752601i
$638$	29.9557	−	15.0443i	1.18596	−	0.595611i
$639$		0			0
$640$	0.105564	+	1.81247i	0.00417279	+	0.0716440i
$641$	3.21730	+	1.31441i	0.127076	+	0.0519162i	0.440846	−	0.897583i	$-0.354679\pi$
$641$	3.21730	+	1.31441i	0.127076	+	0.0519162i	−0.313770	+	0.949499i	$0.601592\pi$
$642$		0			0
$643$	1.19955	+	12.3325i	0.0473057	+	0.486345i	0.988793	+	0.149296i	$0.0477006\pi$
$643$	1.19955	+	12.3325i	0.0473057	+	0.486345i	−0.941487	+	0.337050i	$0.890571\pi$
$644$	3.89817	−	3.53740i	0.153609	−	0.139393i
$645$		0			0
$646$	−1.66686	−	4.31727i	−0.0655817	−	0.169861i
$647$	4.01369	−	6.95191i	0.157794	−	0.273308i	−0.776279	−	0.630390i	$-0.782895\pi$
$647$	4.01369	−	6.95191i	0.157794	−	0.273308i	0.934073	+	0.357082i	$0.116228\pi$
$648$		0			0
$649$	−20.4757	−	35.4649i	−0.803740	−	1.39212i
$650$	11.5714	−	14.3462i	0.453867	−	0.562706i
$651$		0			0
$652$	2.68859	+	12.4119i	0.105293	+	0.486088i
$653$	31.6299	−	22.6077i	1.23777	−	0.884708i	0.241453	−	0.970412i	$-0.422376\pi$
$653$	31.6299	−	22.6077i	1.23777	−	0.884708i	0.996321	+	0.0857048i	$0.0273142\pi$
$654$		0			0
$655$	3.41156	−	2.64416i	0.133301	−	0.103316i
$656$	−0.583755	+	0.383941i	−0.0227918	+	0.0149904i
$657$		0			0
$658$	−0.323422	+	5.55294i	−0.0126083	+	0.216476i
$659$	5.42348	−	11.3422i	0.211269	−	0.441831i	−0.769067	−	0.639168i	$-0.779279\pi$
$659$	5.42348	−	11.3422i	0.211269	−	0.441831i	0.980336	+	0.197337i	$0.0632294\pi$
$660$		0			0
$661$	26.8019	−	30.7116i	1.04247	−	1.19454i	0.0619620	−	0.998079i	$-0.480264\pi$
$661$	26.8019	−	30.7116i	1.04247	−	1.19454i	0.980511	−	0.196463i	$-0.0629456\pi$
$662$	−13.0880	−	7.89863i	−0.508679	−	0.306989i
$663$		0			0
$664$	1.23025	−	12.6480i	0.0477428	−	0.490839i
$665$	−1.65180	−	2.21875i	−0.0640539	−	0.0860393i
$666$		0			0
$667$	32.6459	+	3.81576i	1.26406	+	0.147747i
$668$	−15.0064	+	4.81160i	−0.580614	+	0.186166i
$669$		0			0
$670$	1.71538	+	3.58741i	0.0662708	+	0.138594i
$671$	36.1351	−	14.7628i	1.39498	−	0.569912i
$672$		0			0
$673$	4.14611	−	12.1175i	0.159821	−	0.467093i	−0.836961	−	0.547263i	$-0.815670\pi$
$673$	4.14611	−	12.1175i	0.159821	−	0.467093i	0.996781	+	0.0801697i	$0.0255462\pi$
$674$	25.0583	+	9.12047i	0.965209	+	0.351307i
$675$		0			0
$676$	3.04500	−	1.10829i	0.117115	−	0.0426265i
$677$	0.345142	+	17.7954i	0.0132649	+	0.683933i	0.946144	+	0.323745i	$0.104942\pi$
$677$	0.345142	+	17.7954i	0.0132649	+	0.683933i	−0.932880	+	0.360188i	$0.882712\pi$
$678$		0			0
$679$	−1.88605	−	2.99242i	−0.0723798	−	0.114838i
$680$	−0.852467	+	0.237300i	−0.0326906	+	0.00910005i
$681$		0			0
$682$	6.43692	+	0.249782i	0.246482	+	0.00956464i
$683$	27.8472	+	29.5163i	1.06554	+	1.12941i	0.991227	+	0.132174i	$0.0421958\pi$
$683$	27.8472	+	29.5163i	1.06554	+	1.12941i	0.0743157	+	0.997235i	$0.476323\pi$
$684$		0			0
$685$	0.324845	+	0.0769897i	0.0124117	+	0.00294162i
$686$	−3.36840	−	13.0769i	−0.128606	−	0.499280i
$687$		0			0
$688$	−2.42238	+	6.27412i	−0.0923524	+	0.239199i
$689$	31.8950	+	39.5436i	1.21510	+	1.50649i
$690$		0			0
$691$	20.7433	−	20.3449i	0.789112	−	0.773956i	−0.189012	−	0.981975i	$-0.560529\pi$
$691$	20.7433	−	20.3449i	0.789112	−	0.773956i	0.978125	+	0.208019i	$0.0667015\pi$
$692$	2.95892	−	3.13627i	0.112481	−	0.119223i
$693$		0			0
$694$	0.663951	−	2.21775i	0.0252032	−	0.0841847i
$695$	−0.746339	+	1.18415i	−0.0283102	+	0.0449173i
$696$		0			0
$697$	0.620427	+	0.608511i	0.0235004	+	0.0230490i
$698$	20.2588	−	0.786134i	0.766807	−	0.0297556i
$699$		0			0
$700$	5.04349	−	3.04376i	0.190626	−	0.115043i
$701$	5.01081	−	28.4177i	0.189256	−	1.07332i	−0.731109	−	0.682261i	$-0.760997\pi$
$701$	5.01081	−	28.4177i	0.189256	−	1.07332i	0.920365	−	0.391061i	$-0.127892\pi$
$702$		0			0
$703$	4.29916	+	24.3817i	0.162146	+	0.919575i
$704$	−19.1601	−	21.9551i	−0.722124	−	0.827462i
$705$		0			0
$706$	23.6563	+	18.3350i	0.890318	+	0.690048i
$707$	−5.76012	−	0.447712i	−0.216632	−	0.0168379i
$708$		0			0
$709$	8.75818	+	7.94763i	0.328920	+	0.298479i	0.819687	−	0.572812i	$-0.194147\pi$
$709$	8.75818	+	7.94763i	0.328920	+	0.298479i	−0.490767	+	0.871291i	$0.663283\pi$
$710$	0.376453	−	0.505664i	0.0141280	−	0.0189772i
$711$		0			0
$712$	4.47049	−	10.3638i	0.167539	−	0.388398i
$713$	5.13860	+	3.67285i	0.192442	+	0.137549i
$714$		0			0
$715$	−0.140979	+	7.26883i	−0.00527231	+	0.271839i
$716$	−6.88839	−	20.1321i	−0.257431	−	0.752372i
$717$		0			0
$718$	−30.4565	+	2.36726i	−1.13663	+	0.0883455i
$719$	−31.8384	−	20.9405i	−1.18737	−	0.780948i	−0.207047	−	0.978331i	$-0.566385\pi$
$719$	−31.8384	−	20.9405i	−1.18737	−	0.780948i	−0.980326	+	0.197383i	$0.936756\pi$
$720$		0			0
$721$	9.67139	+	4.85715i	0.360181	+	0.180890i
$722$	−2.74075	−	20.0658i	−0.102000	−	0.746772i
$723$		0			0
$724$	17.3856	+	7.90274i	0.646132	+	0.293703i
$725$	35.0259	+	11.2306i	1.30083	+	0.417094i
$726$		0			0
$727$	−2.32391	−	0.363453i	−0.0861892	−	0.0134797i	0.111277	−	0.993789i	$-0.464506\pi$
$727$	−2.32391	−	0.363453i	−0.0861892	−	0.0134797i	−0.197466	+	0.980310i	$0.563271\pi$
$728$	−13.0761			−0.484634
$729$		0			0
$730$	2.33345			0.0863650
$731$	8.26462	+	1.29256i	0.305678	+	0.0478072i
$732$		0			0
$733$	24.3818	+	7.81773i	0.900564	+	0.288754i	0.719316	−	0.694683i	$-0.244455\pi$
$733$	24.3818	+	7.81773i	0.900564	+	0.288754i	0.181248	+	0.983437i	$0.441986\pi$
$734$	−29.7332	−	13.5154i	−1.09747	−	0.498862i
$735$		0			0
$736$	−3.10835	−	22.7572i	−0.114575	−	0.838841i
$737$	44.1568	+	22.1764i	1.62654	+	0.816877i
$738$		0			0
$739$	41.9094	+	27.5642i	1.54166	+	1.01397i	0.982793	+	0.184710i	$0.0591345\pi$
$739$	41.9094	+	27.5642i	1.54166	+	1.01397i	0.558868	+	0.829257i	$0.311236\pi$
$740$	1.66862	−	0.129696i	0.0613399	−	0.00476771i
$741$		0			0
$742$	−4.35477	−	12.7273i	−0.159869	−	0.467234i
$743$	0.898413	−	46.3220i	0.0329596	−	1.69939i	−0.510440	−	0.859913i	$-0.670517\pi$
$743$	0.898413	−	46.3220i	0.0329596	−	1.69939i	0.543400	−	0.839474i	$-0.317137\pi$
$744$		0			0
$745$	3.20346	+	2.28969i	0.117366	+	0.0838878i
$746$	−8.48177	+	19.6629i	−0.310540	+	0.719912i
$747$		0			0
$748$	−2.32151	+	3.11832i	−0.0848826	+	0.114017i
$749$	8.16265	+	7.40721i	0.298257	+	0.270654i
$750$		0			0
$751$	−30.5145	−	2.37178i	−1.11349	−	0.0865474i	−0.492462	−	0.870334i	$-0.663903\pi$
$751$	−30.5145	−	2.37178i	−1.11349	−	0.0865474i	−0.621030	+	0.783787i	$0.713286\pi$
$752$	2.55966	+	1.98388i	0.0933410	+	0.0723448i
$753$		0			0
$754$	−18.9805	−	21.7492i	−0.691228	−	0.792060i
$755$	1.14370	+	6.48625i	0.0416235	+	0.236059i
$756$		0			0
$757$	1.58189	−	8.97132i	0.0574946	−	0.326068i	−0.942472	−	0.334286i	$-0.891505\pi$
$757$	1.58189	−	8.97132i	0.0574946	−	0.326068i	0.999966	+	0.00821807i	$0.00261592\pi$
$758$	−24.4714	+	14.7686i	−0.888841	+	0.536418i
$759$		0			0
$760$	−7.32511	+	0.284248i	−0.265710	+	0.0103107i
$761$	−7.41919	−	7.27669i	−0.268946	−	0.263780i	0.553211	−	0.833041i	$-0.313402\pi$
$761$	−7.41919	−	7.27669i	−0.268946	−	0.263780i	−0.822157	+	0.569261i	$0.807229\pi$
$762$		0			0
$763$	5.88229	−	9.33289i	0.212953	−	0.337873i
$764$	3.21701	−	10.7456i	0.116387	−	0.388760i
$765$		0			0
$766$	−15.6335	+	16.5706i	−0.564862	+	0.598719i
$767$	−25.1768	+	24.6932i	−0.909080	+	0.891619i
$768$		0			0
$769$	21.8945	+	27.1450i	0.789537	+	0.978873i	0.999999	+	0.00127076i	$0.000404497\pi$
$769$	21.8945	+	27.1450i	0.789537	+	0.978873i	−0.210462	+	0.977602i	$0.567497\pi$
$770$	0.693342	−	1.79580i	0.0249863	−	0.0647161i
$771$		0			0
$772$	4.78440	+	18.5742i	0.172194	+	0.668499i
$773$	−32.9406	−	7.80706i	−1.18479	−	0.280800i	−0.409443	−	0.912336i	$-0.634277\pi$
$773$	−32.9406	−	7.80706i	−1.18479	−	0.280800i	−0.775347	+	0.631535i	$0.782425\pi$
$774$		0			0
$775$	4.85065	+	5.14139i	0.174241	+	0.184684i
$776$	−9.36712	−	0.363487i	−0.336260	−	0.0130484i
$777$		0			0
$778$	17.6396	−	4.91032i	0.632411	−	0.176044i
$779$	3.83872	+	6.09054i	0.137536	+	0.218216i
$780$		0			0
$781$	−0.151905	−	7.83220i	−0.00543560	−	0.280258i
$782$	2.96747	−	1.08007i	0.106117	−	0.0386233i
$783$		0			0
$784$	−3.33658	−	1.21442i	−0.119164	−	0.0433720i
$785$	2.41526	−	7.05886i	0.0862043	−	0.251941i
$786$		0			0
$787$	−4.66150	+	1.90443i	−0.166165	+	0.0678857i	−0.459756	−	0.888045i	$-0.652063\pi$
$787$	−4.66150	+	1.90443i	−0.166165	+	0.0678857i	0.293591	+	0.955931i	$0.405150\pi$
$788$	2.19258	+	4.58540i	0.0781076	+	0.163348i
$789$		0			0
$790$	−2.85733	+	0.916166i	−0.101659	+	0.0325957i
$791$	−17.9825	−	2.10185i	−0.639384	−	0.0747332i
$792$		0			0
$793$	−20.0731	−	26.9628i	−0.712816	−	0.957478i
$794$	−1.75892	+	18.0832i	−0.0624216	+	0.641750i
$795$		0			0
$796$	−6.83684	−	4.12606i	−0.242325	−	0.146244i
$797$	14.5754	−	16.7016i	0.516289	−	0.591601i	−0.434797	−	0.900529i	$-0.643180\pi$
$797$	14.5754	−	16.7016i	0.516289	−	0.591601i	0.951086	+	0.308927i	$0.0999699\pi$
$798$		0			0
$799$	1.73760	−	3.63388i	0.0614719	−	0.128557i
$800$	1.49454	−	25.6602i	0.0528399	−	0.907226i
$801$		0			0
$802$	−30.7364	+	20.2156i	−1.08534	+	0.713838i
$803$	22.9185	−	17.7632i	0.808777	−	0.626850i
$804$		0			0
$805$	1.53557	−	1.09756i	0.0541218	−	0.0386840i
$806$	−1.17438	−	5.42156i	−0.0413659	−	0.190966i
$807$		0			0
$808$	−9.61266	+	11.9178i	−0.338172	+	0.419268i
$809$	2.90798	+	5.03677i	0.102239	+	0.177084i	0.912607	−	0.408838i	$-0.134066\pi$
$809$	2.90798	+	5.03677i	0.102239	+	0.177084i	−0.810368	+	0.585922i	$0.800733\pi$
$810$		0			0
$811$	6.21676	−	10.7677i	0.218300	−	0.378107i	−0.735988	−	0.676994i	$-0.763282\pi$
$811$	6.21676	−	10.7677i	0.218300	−	0.378107i	0.954288	+	0.298887i	$0.0966155\pi$
$812$	−3.32301	−	8.60682i	−0.116615	−	0.302040i
$813$		0			0
$814$	−12.7593	+	11.5785i	−0.447214	+	0.405825i
$815$	0.440854	+	4.53238i	0.0154425	+	0.158762i
$816$		0			0
$817$	64.1519	+	26.2089i	2.24439	+	0.916934i
$818$	−0.106712	−	1.83218i	−0.00373111	−	0.0640607i
$819$		0			0
$820$	0.434915	−	0.218423i	0.0151879	−	0.00762765i
$821$	4.06720	+	5.93012i	0.141946	+	0.206963i	0.889130	−	0.457655i	$-0.151311\pi$
$821$	4.06720	+	5.93012i	0.141946	+	0.206963i	−0.747184	+	0.664618i	$0.768594\pi$
$822$		0			0
$823$	13.1088	+	2.57449i	0.456945	+	0.0897410i	0.415888	−	0.909416i	$-0.363471\pi$
$823$	13.1088	+	2.57449i	0.456945	+	0.0897410i	0.0410566	+	0.999157i	$0.486928\pi$
$824$	25.1125	−	13.8565i	0.874834	−	0.482713i
$825$		0			0
$826$	8.50047	−	3.86394i	0.295769	−	0.134444i
$827$	−8.03170	+	0.938772i	−0.279290	+	0.0326443i	−0.254585	−	0.967050i	$-0.581939\pi$
$827$	−8.03170	+	0.938772i	−0.279290	+	0.0326443i	−0.0247051	+	0.999695i	$0.507865\pi$
$828$		0			0
$829$	−3.77387	−	8.74882i	−0.131072	−	0.303859i	0.840024	−	0.542550i	$-0.182541\pi$
$829$	−3.77387	−	8.74882i	−0.131072	−	0.303859i	−0.971096	+	0.238691i	$0.923282\pi$
$830$	0.341054	−	1.57448i	0.0118382	−	0.0546511i
$831$		0			0
$832$	−14.1932	+	20.6941i	−0.492060	+	0.717440i
$833$	−0.597667	+	4.37570i	−0.0207079	+	0.151609i
$834$		0			0
$835$	−5.54476	+	1.08896i	−0.191885	+	0.0376849i
$836$	−24.6712	+	20.7016i	−0.853273	+	0.715981i
$837$		0			0
$838$	24.8170	+	20.8239i	0.857289	+	0.719350i
$839$	−12.6316	−	6.96981i	−0.436091	−	0.240625i	0.249846	−	0.968285i	$-0.419620\pi$
$839$	−12.6316	−	6.96981i	−0.436091	−	0.240625i	−0.685937	+	0.727661i	$0.740608\pi$
$840$		0			0
$841$	13.3325	−	25.3111i	0.459741	−	0.872797i
$842$	−1.88773	+	7.32864i	−0.0650556	+	0.252561i
$843$		0			0
$844$	−1.25705	−	2.38645i	−0.0432695	−	0.0821451i
$845$	1.13060	−	0.267958i	0.0388939	−	0.00921802i
$846$		0			0
$847$	−3.35461	−	11.2052i	−0.115266	−	0.385015i
$848$	−7.54485	−	2.10025i	−0.259091	−	0.0721230i
$849$		0			0
$850$	3.49154	−	0.546067i	0.119759	−	0.0187299i
$851$	−16.6911	+	2.61044i	−0.572163	+	0.0894846i
$852$		0			0
$853$	−6.82093	−	1.89874i	−0.233544	−	0.0650115i	0.149423	−	0.988773i	$-0.452258\pi$
$853$	−6.82093	−	1.89874i	−0.233544	−	0.0650115i	−0.382967	+	0.923762i	$0.625098\pi$
$854$	2.55266	+	8.52647i	0.0873501	+	0.291770i
$855$		0			0
$856$	28.4242	−	6.73665i	0.971518	−	0.230254i
$857$	26.7977	+	50.8741i	0.915391	+	1.73783i	0.624405	+	0.781101i	$0.285341\pi$
$857$	26.7977	+	50.8741i	0.915391	+	1.73783i	0.290986	+	0.956727i	$0.406017\pi$
$858$		0			0
$859$	0.527589	−	2.04822i	0.0180011	−	0.0698845i	−0.958759	−	0.284221i	$-0.908265\pi$
$859$	0.527589	−	2.04822i	0.0180011	−	0.0698845i	0.976760	+	0.214336i	$0.0687589\pi$
$860$	2.18327	−	4.14484i	0.0744489	−	0.141338i
$861$		0			0
$862$	−19.3326	−	10.6673i	−0.658470	−	0.363329i
$863$	33.9211	+	28.4632i	1.15469	+	0.968899i	0.999819	−	0.0190357i	$-0.00605961\pi$
$863$	33.9211	+	28.4632i	1.15469	+	0.968899i	0.154870	+	0.987935i	$0.450504\pi$
$864$		0			0
$865$	1.18437	−	0.993801i	0.0402696	−	0.0337902i
$866$	6.55406	−	1.28718i	0.222716	−	0.0437400i
$867$		0			0
$868$	0.239937	−	1.75665i	0.00814400	−	0.0596246i
$869$	−21.0897	+	30.7495i	−0.715418	+	1.04310i
$870$		0			0
$871$	9.00831	−	41.5870i	0.305235	−	1.40912i
$872$	−11.5800	−	26.8455i	−0.392150	−	0.909105i
$873$		0			0
$874$	25.9843	−	3.03713i	0.878933	−	0.102732i
$875$	3.90690	−	1.77590i	0.132077	−	0.0600365i
$876$		0			0
$877$	−44.8381	+	24.7406i	−1.51407	+	0.835431i	−0.999754	−	0.0221677i	$-0.992943\pi$
$877$	−44.8381	+	24.7406i	−1.51407	+	0.835431i	−0.514320	+	0.857598i	$0.671956\pi$
$878$	−29.7617	−	5.84500i	−1.00441	−	0.197259i
$879$		0			0
$880$	−0.633906	−	0.924258i	−0.0213690	−	0.0311567i
$881$	17.1749	−	8.62558i	0.578638	−	0.290603i	−0.135308	−	0.990804i	$-0.543202\pi$
$881$	17.1749	−	8.62558i	0.578638	−	0.290603i	0.713946	+	0.700201i	$0.246906\pi$
$882$		0			0
$883$	0.494568	+	8.49141i	0.0166435	+	0.285759i	0.996352	+	0.0853331i	$0.0271954\pi$
$883$	0.494568	+	8.49141i	0.0166435	+	0.285759i	−0.979709	+	0.200426i	$0.935768\pi$
$884$	3.09912	+	1.26613i	0.104235	+	0.0425845i
$885$		0			0
$886$	−1.03336	−	10.6238i	−0.0347163	−	0.356915i
$887$	22.3767	−	20.3057i	0.751334	−	0.681800i	−0.203454	−	0.979084i	$-0.565217\pi$
$887$	22.3767	−	20.3057i	0.751334	−	0.681800i	0.954789	+	0.297285i	$0.0960811\pi$
$888$		0			0
$889$	−3.85980	−	9.99713i	−0.129453	−	0.335293i
$890$	0.715434	−	1.23917i	0.0239814	−	0.0415370i
$891$		0			0
$892$	−12.2341	−	21.1901i	−0.409629	−	0.709498i
$893$	20.9493	−	25.9731i	0.701043	−	0.869157i
$894$		0			0
$895$	−1.61523	−	7.45673i	−0.0539912	−	0.249251i
$896$	−4.18500	+	2.99126i	−0.139811	+	0.0999310i
$897$		0			0
$898$	14.6955	−	11.3899i	0.490395	−	0.380085i
$899$	9.24923	−	6.08331i	0.308479	−	0.202890i
$900$		0			0
$901$	−0.566387	+	9.72449i	−0.0188691	+	0.323970i
$902$	−2.16134	+	4.52005i	−0.0719646	+	0.150501i
$903$		0			0
$904$	−31.5486	+	36.1507i	−1.04929	+	1.20236i
$905$	5.86287	+	3.53826i	0.194888	+	0.117616i
$906$		0			0
$907$	2.31511	−	23.8014i	0.0768718	−	0.790312i	−0.875063	−	0.484010i	$-0.839180\pi$
$907$	2.31511	−	23.8014i	0.0768718	−	0.790312i	0.951934	−	0.306302i	$-0.0990917\pi$
$908$	16.4656	+	22.1171i	0.546430	+	0.733983i
$909$		0			0
$910$	−1.64649	−	0.192448i	−0.0545808	−	0.00637958i
$911$	22.4595	−	7.20136i	0.744118	−	0.238592i	0.0910031	−	0.995851i	$-0.470993\pi$
$911$	22.4595	−	7.20136i	0.744118	−	0.238592i	0.653115	+	0.757259i	$0.273462\pi$
$912$		0			0
$913$	−8.63586	−	18.0604i	−0.285805	−	0.597711i
$914$	22.5083	−	9.19565i	0.744508	−	0.304165i
$915$		0			0
$916$	−1.72861	+	5.05205i	−0.0571149	+	0.166924i
$917$	11.4921	+	4.18279i	0.379504	+	0.138128i
$918$		0			0
$919$	21.5278	−	7.83548i	0.710137	−	0.258469i	0.0384042	−	0.999262i	$-0.487773\pi$
$919$	21.5278	−	7.83548i	0.710137	−	0.258469i	0.671733	+	0.740794i	$0.265550\pi$
$920$	−0.0969990	−	5.00124i	−0.00319796	−	0.164886i
$921$		0			0
$922$	−10.6483	−	16.8947i	−0.350685	−	0.556399i
$923$	−6.49883	+	1.80907i	−0.213912	+	0.0595463i
$924$		0			0
$925$	−18.8916	−	0.733080i	−0.621152	−	0.0241035i
$926$	14.0916	+	14.9362i	0.463078	+	0.490834i
$927$		0			0
$928$	−39.1716	−	9.28383i	−1.28587	−	0.304757i
$929$	2.05767	+	7.98837i	0.0675100	+	0.262090i	0.993237	−	0.116102i	$-0.0370399\pi$
$929$	2.05767	+	7.98837i	0.0675100	+	0.262090i	−0.925727	+	0.378192i	$0.876546\pi$
$930$		0			0
$931$	−13.1776	+	34.1307i	−0.431877	+	1.11859i
$932$	9.54135	+	11.8294i	0.312537	+	0.387486i
$933$		0			0
$934$	9.93399	−	9.74319i	0.325050	−	0.318807i
$935$	−0.956605	+	1.01394i	−0.0312843	+	0.0331594i
$936$		0			0
$937$	14.1188	−	47.1602i	0.461242	−	1.54066i	−0.338886	−	0.940827i	$-0.610050\pi$
$937$	14.1188	−	47.1602i	0.461242	−	1.54066i	0.800128	−	0.599829i	$-0.204765\pi$
$938$	−6.00748	+	9.53152i	−0.196151	+	0.311215i
$939$		0			0
$940$	−1.61046	−	1.57953i	−0.0525274	−	0.0515185i
$941$	−51.8955	+	2.01378i	−1.69175	+	0.0656475i	−0.866516	−	0.499149i	$-0.833646\pi$
$941$	−51.8955	+	2.01378i	−1.69175	+	0.0656475i	−0.825230	+	0.564797i	$0.808955\pi$
$942$		0			0
$943$	−4.20600	+	2.53834i	−0.136966	+	0.0826596i
$944$	0.944014	−	5.35377i	0.0307250	−	0.174250i
$945$		0			0
$946$	8.37456	+	47.4945i	0.272280	+	1.54418i
$947$	15.1964	+	17.4131i	0.493816	+	0.565851i	0.945205	−	0.326476i	$-0.105861\pi$
$947$	15.1964	+	17.4131i	0.493816	+	0.565851i	−0.451389	+	0.892327i	$0.649071\pi$
$948$		0			0
$949$	−19.7362	−	15.2967i	−0.640663	−	0.496552i
$950$	29.1886	+	2.26872i	0.947004	+	0.0736069i
$951$		0			0
$952$	−1.85669	−	1.68486i	−0.0601757	−	0.0546065i
$953$	12.6522	−	16.9949i	0.409846	−	0.550519i	−0.548492	−	0.836156i	$-0.684798\pi$
$953$	12.6522	−	16.9949i	0.409846	−	0.550519i	0.958338	+	0.285637i	$0.0922052\pi$
$954$		0			0
$955$	1.59304	−	3.69308i	0.0515495	−	0.119505i
$956$	13.8334	+	9.88749i	0.447403	+	0.319784i
$957$		0			0
$958$	0.459205	−	23.6765i	0.0148362	−	0.764953i
$959$	0.306222	+	0.894968i	0.00988843	+	0.0289000i
$960$		0			0
$961$	−28.7858	+	2.23741i	−0.928574	+	0.0721744i
$962$	12.3963	+	8.15320i	0.399674	+	0.262870i
$963$		0			0
$964$	20.8469	+	10.4697i	0.671435	+	0.337207i
$965$	0.930750	+	6.81430i	0.0299619	+	0.219360i
$966$		0			0
$967$	−33.0181	−	15.0086i	−1.06179	−	0.482643i	−0.194736	−	0.980856i	$-0.562385\pi$
$967$	−33.0181	−	15.0086i	−1.06179	−	0.482643i	−0.867055	+	0.498212i	$0.833990\pi$
$968$	−29.5177	−	9.46447i	−0.948735	−	0.304200i
$969$		0			0
$970$	−1.17412	−	0.183629i	−0.0376987	−	0.00589597i
$971$	23.0707			0.740375			0.370188	−	0.928957i	$-0.379293\pi$
$971$	23.0707			0.740375			0.370188	+	0.928957i	$0.379293\pi$
$972$		0			0
$973$	−3.96595			−0.127143
$974$	−10.0652	−	1.57416i	−0.322508	−	0.0504394i
$975$		0			0
$976$	4.93445	+	1.58217i	0.157948	+	0.0506439i
$977$	−28.6479	−	13.0221i	−0.916528	−	0.416613i	−0.100706	−	0.994916i	$-0.532110\pi$
$977$	−28.6479	−	13.0221i	−0.916528	−	0.416613i	−0.815822	+	0.578303i	$0.803715\pi$
$978$		0			0
$979$	−2.40626	−	17.6169i	−0.0769043	−	0.563039i
$980$	2.21019	+	1.11000i	0.0706021	+	0.0354577i
$981$		0			0
$982$	−6.04941	−	3.97876i	−0.193045	−	0.126967i
$983$	−6.97813	+	0.542383i	−0.222568	+	0.0172993i	−0.188292	−	0.982113i	$-0.560295\pi$
$983$	−6.97813	+	0.542383i	−0.222568	+	0.0172993i	−0.0342757	+	0.999412i	$0.510912\pi$
$984$		0			0
$985$	0.590003	+	1.72435i	0.0187991	+	0.0549423i
$986$	0.107328	−	5.53382i	0.00341803	−	0.176233i
$987$		0			0
$988$	22.5631	+	16.1271i	0.717828	+	0.513073i
$989$	−18.7296	+	43.4201i	−0.595567	+	1.38068i
$990$		0			0
$991$	9.37403	−	12.5915i	0.297776	−	0.399982i	−0.627904	−	0.778291i	$-0.716087\pi$
$991$	9.37403	−	12.5915i	0.297776	−	0.399982i	0.925679	+	0.378309i	$0.123494\pi$
$992$	−5.72892	−	5.19872i	−0.181893	−	0.165059i
$993$		0			0
$994$	1.78081	+	0.138416i	0.0564839	+	0.00439027i
$995$	−2.26316	−	1.75408i	−0.0717471	−	0.0556082i
$996$		0			0
$997$	15.9004	+	18.2198i	0.503570	+	0.577027i	0.947792	−	0.318890i	$-0.103310\pi$
$997$	15.9004	+	18.2198i	0.503570	+	0.577027i	−0.444222	+	0.895917i	$0.646520\pi$
$998$	3.22210	+	18.2734i	0.101994	+	0.578435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.17		1404
3.2	odd	2		243.2.i.a.13.10	✓	1404
243.56	odd	162		243.2.i.a.187.10	yes	1404
243.187	even	81	inner	729.2.i.a.73.17		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.10	✓	1404	3.2	odd	2
243.2.i.a.187.10	yes	1404	243.56	odd	162
729.2.i.a.10.17		1404	1.1	even	1	trivial
729.2.i.a.73.17		1404	243.187	even	81	inner

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.940500 + 0.147092i) q^{2} +(-1.04159 - 0.333973i) q^{4} +(-0.357057 - 0.162302i) q^{5} +(-0.150392 - 1.10107i) q^{7} +(-2.63185 - 1.32176i) q^{8} +O(q^{10})\)	\(q+(0.940500 + 0.147092i) q^{2} +(-1.04159 - 0.333973i) q^{4} +(-0.357057 - 0.162302i) q^{5} +(-0.150392 - 1.10107i) q^{7} +(-2.63185 - 1.32176i) q^{8} +(-0.311939 - 0.205165i) q^{10} +(-4.62558 + 0.359528i) q^{11} +(1.29342 + 3.78015i) q^{13} +(0.0205136 - 1.05768i) q^{14} +(-0.501071 - 0.358144i) q^{16} +(-0.303418 + 0.703403i) q^{17} +(-3.78971 + 5.09046i) q^{19} +(0.317702 + 0.288300i) q^{20} +(-4.40324 - 0.342247i) q^{22} +(-3.42277 - 2.65285i) q^{23} +(-3.18646 - 3.65128i) q^{25} +(0.660430 + 3.74549i) q^{26} +(-0.211079 + 1.19709i) q^{28} +(-6.49829 + 3.92174i) q^{29} +(-1.45746 + 0.0565562i) q^{31} +(3.78663 + 3.71390i) q^{32} +(-0.388830 + 0.616920i) q^{34} +(-0.125007 + 0.417552i) q^{35} +(2.67716 - 2.83762i) q^{37} +(-4.31299 + 4.23015i) q^{38} +(0.725194 + 0.899100i) q^{40} +(0.408595 - 1.05829i) q^{41} +(-2.72383 - 10.5745i) q^{43} +(4.93803 + 1.17033i) q^{44} +(-2.82891 - 2.99847i) q^{46} +(-5.25409 - 0.203883i) q^{47} +(5.55387 - 1.54602i) q^{49} +(-2.45979 - 3.90273i) q^{50} +(-0.0847432 - 4.36934i) q^{52} +(11.9489 - 4.34905i) q^{53} +(1.70994 + 0.622369i) q^{55} +(-1.05954 + 3.09663i) q^{56} +(-6.68850 + 2.73255i) q^{58} +(3.80768 + 7.96308i) q^{59} +(-8.01169 + 2.56885i) q^{61} +(-1.37906 - 0.161190i) q^{62} +(3.75063 + 5.03797i) q^{64} +(0.151704 - 1.55965i) q^{65} +(-9.11849 - 5.50304i) q^{67} +(0.550955 - 0.631324i) q^{68} +(-0.178988 + 0.374321i) q^{70} +(-0.0981754 + 1.68561i) q^{71} +(-5.22168 + 3.43435i) q^{73} +(2.93526 - 2.27500i) q^{74} +(5.64740 - 4.03652i) q^{76} +(1.09152 + 5.03900i) q^{77} +(5.04558 - 6.25553i) q^{79} +(0.120783 + 0.209203i) q^{80} +(0.539949 - 0.935219i) q^{82} +(1.55411 + 4.02525i) q^{83} +(0.222501 - 0.201909i) q^{85} +(-1.00633 - 10.3460i) q^{86} +(12.6490 + 5.16770i) q^{88} +(0.222834 + 3.82591i) q^{89} +(3.96768 - 1.99264i) q^{91} +(2.67915 + 3.90629i) q^{92} +(-4.91149 - 0.964585i) q^{94} +(2.17933 - 1.20251i) q^{95} +(2.89765 - 1.31714i) q^{97} +(5.45082 - 0.637109i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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