LMFDB - Embedded newform 432.2.l.b.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	432.323
Dual form			432.2.l.b.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32420 - 0.496490i) q^{2} +(1.50700 + 1.31490i) q^{4} +(-1.75903 - 1.75903i) q^{5} -4.05756 q^{7} +(-1.34273 - 2.48940i) q^{8} +O(q^{10})$	\(q+(-1.32420 - 0.496490i) q^{2} +(1.50700 + 1.31490i) q^{4} +(-1.75903 - 1.75903i) q^{5} -4.05756 q^{7} +(-1.34273 - 2.48940i) q^{8} +(1.45597 + 3.20265i) q^{10} +(1.00080 - 1.00080i) q^{11} +(4.19432 + 4.19432i) q^{13} +(5.37300 + 2.01453i) q^{14} +(0.542074 + 3.96310i) q^{16} +5.82075i q^{17} +(0.687187 - 0.687187i) q^{19} +(-0.337903 - 4.96381i) q^{20} +(-1.82215 + 0.828373i) q^{22} +3.75624i q^{23} +1.18841i q^{25} +(-3.47167 - 7.63654i) q^{26} +(-6.11472 - 5.33528i) q^{28} +(-6.60208 + 6.60208i) q^{29} +0.621706i q^{31} +(1.24982 - 5.51706i) q^{32} +(2.88994 - 7.70782i) q^{34} +(7.13738 + 7.13738i) q^{35} +(-3.34776 + 3.34776i) q^{37} +(-1.25115 + 0.568790i) q^{38} +(-2.01703 + 6.74083i) q^{40} +7.83525 q^{41} +(1.15934 + 1.15934i) q^{43} +(2.82416 - 0.192250i) q^{44} +(1.86493 - 4.97400i) q^{46} -10.8970 q^{47} +9.46376 q^{49} +(0.590031 - 1.57368i) q^{50} +(0.805711 + 11.8359i) q^{52} +(5.59972 + 5.59972i) q^{53} -3.52090 q^{55} +(5.44818 + 10.1009i) q^{56} +(12.0203 - 5.46459i) q^{58} +(-3.51517 + 3.51517i) q^{59} +(1.61583 + 1.61583i) q^{61} +(0.308671 - 0.823262i) q^{62} +(-4.39418 + 6.68515i) q^{64} -14.7559i q^{65} +(-3.84645 + 3.84645i) q^{67} +(-7.65371 + 8.77185i) q^{68} +(-5.90766 - 12.9949i) q^{70} -5.98242i q^{71} -5.11508i q^{73} +(6.09523 - 2.77097i) q^{74} +(1.93917 - 0.132006i) q^{76} +(-4.06082 + 4.06082i) q^{77} -12.8799i q^{79} +(6.01770 - 7.92476i) q^{80} +(-10.3754 - 3.89012i) q^{82} +(7.07602 + 7.07602i) q^{83} +(10.2389 - 10.2389i) q^{85} +(-0.959596 - 2.11080i) q^{86} +(-3.83520 - 1.14759i) q^{88} +2.89496 q^{89} +(-17.0187 - 17.0187i) q^{91} +(-4.93907 + 5.66063i) q^{92} +(14.4298 + 5.41026i) q^{94} -2.41757 q^{95} -8.67960 q^{97} +(-12.5319 - 4.69866i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.32420	−	0.496490i	−0.936349	−	0.351071i
$2$	−1.32420	−	0.496490i	−0.936349	−	0.351071i
$3$		0			0
$3$		0			0
$4$	1.50700	+	1.31490i	0.753498	+	0.657450i
$5$	−1.75903	−	1.75903i	−0.786664	−	0.786664i	0.194282	−	0.980946i	$-0.437762\pi$
$5$	−1.75903	−	1.75903i	−0.786664	−	0.786664i	−0.980946	+	0.194282i	$0.937762\pi$
$6$		0			0
$7$	−4.05756			−1.53361			−0.766806	−	0.641879i	$-0.778155\pi$
$7$	−4.05756			−1.53361			−0.766806	+	0.641879i	$0.778155\pi$
$8$	−1.34273	−	2.48940i	−0.474725	−	0.880134i
$9$		0			0
$10$	1.45597	+	3.20265i	0.460417	+	1.01277i
$11$	1.00080	−	1.00080i	0.301754	−	0.301754i	−0.539946	−	0.841700i	$-0.681555\pi$
$11$	1.00080	−	1.00080i	0.301754	−	0.301754i	0.841700	+	0.539946i	$0.181555\pi$
$12$		0			0
$13$	4.19432	+	4.19432i	1.16330	+	1.16330i	0.983750	+	0.179546i	$0.0574627\pi$
$13$	4.19432	+	4.19432i	1.16330	+	1.16330i	0.179546	+	0.983750i	$0.442537\pi$
$14$	5.37300	+	2.01453i	1.43600	+	0.538407i
$15$		0			0
$16$	0.542074	+	3.96310i	0.135519	+	0.990775i
$17$			5.82075i			1.41174i	0.708341	+	0.705870i	$0.249444\pi$
$17$			5.82075i			1.41174i	−0.708341	+	0.705870i	$0.750556\pi$
$18$		0			0
$19$	0.687187	−	0.687187i	0.157652	−	0.157652i	−0.623874	−	0.781525i	$-0.714442\pi$
$19$	0.687187	−	0.687187i	0.157652	−	0.157652i	0.781525	+	0.623874i	$0.214442\pi$
$20$	−0.337903	−	4.96381i	−0.0755574	−	1.10994i
$21$		0			0
$22$	−1.82215	+	0.828373i	−0.388484	+	0.176610i
$23$			3.75624i			0.783229i	0.920129	+	0.391615i	$0.128083\pi$
$23$			3.75624i			0.783229i	−0.920129	+	0.391615i	$0.871917\pi$
$24$		0			0
$25$			1.18841i			0.237681i
$26$	−3.47167	−	7.63654i	−0.680851	−	1.49765i
$27$		0			0
$28$	−6.11472	−	5.33528i	−1.15557	−	1.00827i
$29$	−6.60208	+	6.60208i	−1.22597	+	1.22597i	−0.260501	+	0.965473i	$0.583888\pi$
$29$	−6.60208	+	6.60208i	−1.22597	+	1.22597i	−0.965473	+	0.260501i	$0.916112\pi$
$30$		0			0
$31$			0.621706i			0.111662i	0.998440	+	0.0558309i	$0.0177808\pi$
$31$			0.621706i			0.111662i	−0.998440	+	0.0558309i	$0.982219\pi$
$32$	1.24982	−	5.51706i	0.220940	−	0.975287i
$33$		0			0
$34$	2.88994	−	7.70782i	0.495621	−	1.32188i
$35$	7.13738	+	7.13738i	1.20644	+	1.20644i
$36$		0			0
$37$	−3.34776	+	3.34776i	−0.550369	+	0.550369i	−0.926547	−	0.376178i	$-0.877238\pi$
$37$	−3.34776	+	3.34776i	−0.550369	+	0.550369i	0.376178	+	0.926547i	$0.377238\pi$
$38$	−1.25115	+	0.568790i	−0.202964	+	0.0922699i
$39$		0			0
$40$	−2.01703	+	6.74083i	−0.318921	+	1.06582i
$41$	7.83525			1.22366			0.611830	−	0.790989i	$-0.290434\pi$
$41$	7.83525			1.22366			0.611830	+	0.790989i	$0.290434\pi$
$42$		0			0
$43$	1.15934	+	1.15934i	0.176798	+	0.176798i	0.789958	−	0.613160i	$-0.210102\pi$
$43$	1.15934	+	1.15934i	0.176798	+	0.176798i	−0.613160	+	0.789958i	$0.710102\pi$
$44$	2.82416	−	0.192250i	0.425759	−	0.0289828i
$45$		0			0
$46$	1.86493	−	4.97400i	0.274969	−	0.733376i
$47$	−10.8970			−1.58949			−0.794747	−	0.606941i	$-0.792397\pi$
$47$	−10.8970			−1.58949			−0.794747	+	0.606941i	$0.792397\pi$
$48$		0			0
$49$	9.46376			1.35197
$50$	0.590031	−	1.57368i	0.0834430	−	0.222552i
$51$		0			0
$52$	0.805711	+	11.8359i	0.111732	+	1.64135i
$53$	5.59972	+	5.59972i	0.769181	+	0.769181i	0.977962	−	0.208781i	$-0.0669496\pi$
$53$	5.59972	+	5.59972i	0.769181	+	0.769181i	−0.208781	+	0.977962i	$0.566950\pi$
$54$		0			0
$55$	−3.52090			−0.474758
$56$	5.44818	+	10.1009i	0.728044	+	1.34978i
$57$		0			0
$58$	12.0203	−	5.46459i	1.57834	−	0.717536i
$59$	−3.51517	+	3.51517i	−0.457636	+	0.457636i	−0.897879	−	0.440242i	$-0.854892\pi$
$59$	−3.51517	+	3.51517i	−0.457636	+	0.457636i	0.440242	+	0.897879i	$0.354892\pi$
$60$		0			0
$61$	1.61583	+	1.61583i	0.206885	+	0.206885i	0.802942	−	0.596057i	$-0.203267\pi$
$61$	1.61583	+	1.61583i	0.206885	+	0.206885i	−0.596057	+	0.802942i	$0.703267\pi$
$62$	0.308671	−	0.823262i	0.0392012	−	0.104554i
$63$		0			0
$64$	−4.39418	+	6.68515i	−0.549272	+	0.835644i
$65$		−	14.7559i		−	1.83025i
$66$		0			0
$67$	−3.84645	+	3.84645i	−0.469919	+	0.469919i	−0.901888	−	0.431969i	$-0.857819\pi$
$67$	−3.84645	+	3.84645i	−0.469919	+	0.469919i	0.431969	+	0.901888i	$0.357819\pi$
$68$	−7.65371	+	8.77185i	−0.928149	+	1.06374i
$69$		0			0
$70$	−5.90766	−	12.9949i	−0.706101	−	1.55319i
$71$		−	5.98242i		−	0.709982i	−0.934870	−	0.354991i	$-0.884484\pi$
$71$		−	5.98242i		−	0.709982i	0.934870	−	0.354991i	$-0.115516\pi$
$72$		0			0
$73$		−	5.11508i		−	0.598674i	−0.954147	−	0.299337i	$-0.903234\pi$
$73$		−	5.11508i		−	0.598674i	0.954147	−	0.299337i	$-0.0967655\pi$
$74$	6.09523	−	2.77097i	0.708556	−	0.322119i
$75$		0			0
$76$	1.93917	−	0.132006i	0.222438	−	0.0151421i
$77$	−4.06082	+	4.06082i	−0.462773	+	0.462773i
$78$		0			0
$79$		−	12.8799i		−	1.44911i	−0.689219	−	0.724553i	$-0.742046\pi$
$79$		−	12.8799i		−	1.44911i	0.689219	−	0.724553i	$-0.257954\pi$
$80$	6.01770	−	7.92476i	0.672799	−	0.886015i
$81$		0			0
$82$	−10.3754	−	3.89012i	−1.14577	−	0.429592i
$83$	7.07602	+	7.07602i	0.776694	+	0.776694i	0.979267	−	0.202573i	$-0.0649304\pi$
$83$	7.07602	+	7.07602i	0.776694	+	0.776694i	−0.202573	+	0.979267i	$0.564930\pi$
$84$		0			0
$85$	10.2389	−	10.2389i	1.11057	−	1.11057i
$86$	−0.959596	−	2.11080i	−0.103476	−	0.227613i
$87$		0			0
$88$	−3.83520	−	1.14759i	−0.408834	−	0.122334i
$89$	2.89496			0.306865			0.153433	−	0.988159i	$-0.450967\pi$
$89$	2.89496			0.306865			0.153433	+	0.988159i	$0.450967\pi$
$90$		0			0
$91$	−17.0187	−	17.0187i	−1.78404	−	1.78404i
$92$	−4.93907	+	5.66063i	−0.514934	+	0.590162i
$93$		0			0
$94$	14.4298	+	5.41026i	1.48832	+	0.558026i
$95$	−2.41757			−0.248038
$96$		0			0
$97$	−8.67960			−0.881280			−0.440640	−	0.897684i	$-0.645248\pi$
$97$	−8.67960			−0.881280			−0.440640	+	0.897684i	$0.645248\pi$
$98$	−12.5319	−	4.69866i	−1.26591	−	0.474636i
$99$		0			0
$100$	−1.56263	+	1.79092i	−0.156263	+	0.179092i
$101$	4.24583	+	4.24583i	0.422476	+	0.422476i	0.886055	−	0.463580i	$-0.153435\pi$
$101$	4.24583	+	4.24583i	0.422476	+	0.422476i	−0.463580	+	0.886055i	$0.653435\pi$
$102$		0			0
$103$	−14.8957			−1.46771			−0.733856	−	0.679305i	$-0.762281\pi$
$103$	−14.8957			−1.46771			−0.733856	+	0.679305i	$0.762281\pi$
$104$	4.80950	−	16.0731i	0.471610	−	1.57610i
$105$		0			0
$106$	−4.63493	−	10.1953i	−0.450185	−	0.990259i
$107$	−7.58523	+	7.58523i	−0.733292	+	0.733292i	−0.971270	−	0.237978i	$-0.923515\pi$
$107$	−7.58523	+	7.58523i	−0.733292	+	0.733292i	0.237978	+	0.971270i	$0.423515\pi$
$108$		0			0
$109$	3.71822	+	3.71822i	0.356141	+	0.356141i	0.862388	−	0.506247i	$-0.168968\pi$
$109$	3.71822	+	3.71822i	0.356141	+	0.356141i	−0.506247	+	0.862388i	$0.668968\pi$
$110$	4.66236	+	1.74809i	0.444539	+	0.166674i
$111$		0			0
$112$	−2.19950	−	16.0805i	−0.207833	−	1.51946i
$113$		−	6.59228i		−	0.620150i	−0.950712	−	0.310075i	$-0.899646\pi$
$113$		−	6.59228i		−	0.620150i	0.950712	−	0.310075i	$-0.100354\pi$
$114$		0			0
$115$	6.60735	−	6.60735i	0.616138	−	0.616138i
$116$	−18.6304	+	1.26823i	−1.72979	+	0.117752i
$117$		0			0
$118$	6.40003	−	2.90953i	0.589170	−	0.267844i
$119$		−	23.6180i		−	2.16506i
$120$		0			0
$121$			8.99678i			0.817889i
$122$	−1.33743	−	2.94191i	−0.121085	−	0.266348i
$123$		0			0
$124$	−0.817482	+	0.936909i	−0.0734120	+	0.0841369i
$125$	−6.70473	+	6.70473i	−0.599689	+	0.599689i
$126$		0			0
$127$			5.99979i			0.532395i	0.963918	+	0.266198i	$0.0857674\pi$
$127$			5.99979i			0.532395i	−0.963918	+	0.266198i	$0.914233\pi$
$128$	9.13786	−	6.67079i	0.807681	−	0.589620i
$129$		0			0
$130$	−7.32616	+	19.5397i	−0.642546	+	1.71375i
$131$	−4.96087	−	4.96087i	−0.433433	−	0.433433i	0.456361	−	0.889795i	$-0.349152\pi$
$131$	−4.96087	−	4.96087i	−0.433433	−	0.433433i	−0.889795	+	0.456361i	$0.849152\pi$
$132$		0			0
$133$	−2.78830	+	2.78830i	−0.241776	+	0.241776i
$134$	7.00318	−	3.18374i	0.604983	−	0.275033i
$135$		0			0
$136$	14.4902	−	7.81567i	1.24252	−	0.670188i
$137$	−0.446753			−0.0381687			−0.0190843	−	0.999818i	$-0.506075\pi$
$137$	−0.446753			−0.0381687			−0.0190843	+	0.999818i	$0.506075\pi$
$138$		0			0
$139$	−2.83379	−	2.83379i	−0.240359	−	0.240359i	0.576640	−	0.816998i	$-0.304364\pi$
$139$	−2.83379	−	2.83379i	−0.240359	−	0.240359i	−0.816998	+	0.576640i	$0.804364\pi$
$140$	1.37106	+	20.1409i	0.115876	+	1.70222i
$141$		0			0
$142$	−2.97021	+	7.92190i	−0.249254	+	0.664791i
$143$	8.39538			0.702057
$144$		0			0
$145$	23.2266			1.92886
$146$	−2.53958	+	6.77337i	−0.210177	+	0.560568i
$147$		0			0
$148$	−9.44704	+	0.643091i	−0.776542	+	0.0528618i
$149$	−14.9652	−	14.9652i	−1.22600	−	1.22600i	−0.965465	−	0.260534i	$-0.916101\pi$
$149$	−14.9652	−	14.9652i	−1.22600	−	1.22600i	−0.260534	−	0.965465i	$-0.583899\pi$
$150$		0			0
$151$	20.5591			1.67308			0.836538	−	0.547909i	$-0.184576\pi$
$151$	20.5591			1.67308			0.836538	+	0.547909i	$0.184576\pi$
$152$	−2.63338	−	0.787977i	−0.213596	−	0.0639134i
$153$		0			0
$154$	7.39347	−	3.36117i	0.595783	−	0.270851i
$155$	1.09360	−	1.09360i	0.0878403	−	0.0878403i
$156$		0			0
$157$	0.313683	+	0.313683i	0.0250347	+	0.0250347i	0.719513	−	0.694479i	$-0.244365\pi$
$157$	0.313683	+	0.313683i	0.0250347	+	0.0250347i	−0.694479	+	0.719513i	$0.744365\pi$
$158$	−6.39475	+	17.0556i	−0.508739	+	1.35687i
$159$		0			0
$160$	−11.9032	+	7.50621i	−0.941029	+	0.593418i
$161$		−	15.2411i		−	1.20117i
$162$		0			0
$163$	−15.6404	+	15.6404i	−1.22505	+	1.22505i	−0.259236	+	0.965814i	$0.583471\pi$
$163$	−15.6404	+	15.6404i	−1.22505	+	1.22505i	−0.965814	+	0.259236i	$0.916529\pi$
$164$	11.8077	+	10.3026i	0.922026	+	0.804496i
$165$		0			0
$166$	−5.85687	−	12.8832i	−0.454582	−	0.999931i
$167$		−	10.4958i		−	0.812193i	−0.913830	−	0.406096i	$-0.866890\pi$
$167$		−	10.4958i		−	0.812193i	0.913830	−	0.406096i	$-0.133110\pi$
$168$		0			0
$169$			22.1846i			1.70651i
$170$	−18.6418	+	8.47482i	−1.42976	+	0.649989i
$171$		0			0
$172$	0.222705	+	3.27154i	0.0169811	+	0.249453i
$173$	5.28204	−	5.28204i	0.401586	−	0.401586i	−0.477206	−	0.878792i	$-0.658350\pi$
$173$	5.28204	−	5.28204i	0.401586	−	0.401586i	0.878792	+	0.477206i	$0.158350\pi$
$174$		0			0
$175$		−	4.82202i		−	0.364510i
$176$	4.50879	+	3.42377i	0.339863	+	0.258077i
$177$		0			0
$178$	−3.83350	−	1.43732i	−0.287333	−	0.107732i
$179$	13.6329	+	13.6329i	1.01897	+	1.01897i	0.999817	+	0.0191517i	$0.00609655\pi$
$179$	13.6329	+	13.6329i	1.01897	+	1.01897i	0.0191517	+	0.999817i	$0.493903\pi$
$180$		0			0
$181$	9.09330	−	9.09330i	0.675900	−	0.675900i	−0.283170	−	0.959070i	$-0.591386\pi$
$181$	9.09330	−	9.09330i	0.675900	−	0.675900i	0.959070	+	0.283170i	$0.0913861\pi$
$182$	14.0865	+	30.9857i	1.04416	+	2.29681i
$183$		0			0
$184$	9.35075	−	5.04359i	0.689347	−	0.371819i
$185$	11.7777			0.865911
$186$		0			0
$187$	5.82543	+	5.82543i	0.425998	+	0.425998i
$188$	−16.4218	−	14.3285i	−1.19768	−	1.04501i
$189$		0			0
$190$	3.20134	+	1.20030i	0.232250	+	0.0870789i
$191$	−4.93149			−0.356830			−0.178415	−	0.983955i	$-0.557097\pi$
$191$	−4.93149			−0.356830			−0.178415	+	0.983955i	$0.557097\pi$
$192$		0			0
$193$	−3.99003			−0.287208			−0.143604	−	0.989635i	$-0.545869\pi$
$193$	−3.99003			−0.287208			−0.143604	+	0.989635i	$0.545869\pi$
$194$	11.4935	+	4.30933i	0.825185	+	0.309392i
$195$		0			0
$196$	14.2618	+	12.4439i	1.01870	+	0.888850i
$197$	7.70402	+	7.70402i	0.548889	+	0.548889i	0.926119	−	0.377231i	$-0.123124\pi$
$197$	7.70402	+	7.70402i	0.548889	+	0.548889i	−0.377231	+	0.926119i	$0.623124\pi$
$198$		0			0
$199$	2.05777			0.145871			0.0729356	−	0.997337i	$-0.476763\pi$
$199$	2.05777			0.145871			0.0729356	+	0.997337i	$0.476763\pi$
$200$	2.95841	−	1.59570i	0.209191	−	0.112833i
$201$		0			0
$202$	−3.51430	−	7.73032i	−0.247265	−	0.543903i
$203$	26.7883	−	26.7883i	1.88017	−	1.88017i
$204$		0			0
$205$	−13.7825	−	13.7825i	−0.962610	−	0.962610i
$206$	19.7248	+	7.39554i	1.37429	+	0.515271i
$207$		0			0
$208$	−14.3489	+	18.8961i	−0.994915	+	1.31021i
$209$		−	1.37548i		−	0.0951439i
$210$		0			0
$211$	−4.28179	+	4.28179i	−0.294771	+	0.294771i	−0.838962	−	0.544191i	$-0.816837\pi$
$211$	−4.28179	+	4.28179i	−0.294771	+	0.294771i	0.544191	+	0.838962i	$0.316837\pi$
$212$	1.07568	+	15.8018i	0.0738782	+	1.08527i
$213$		0			0
$214$	13.8103	−	6.27835i	0.944055	−	0.429179i
$215$		−	4.07864i		−	0.278161i
$216$		0			0
$217$		−	2.52261i		−	0.171246i
$218$	−3.07760	−	6.76971i	−0.208441	−	0.458503i
$219$		0			0
$220$	−5.30598	−	4.62963i	−0.357729	−	0.312129i
$221$	−24.4141	+	24.4141i	−1.64227	+	1.64227i
$222$		0			0
$223$			13.5753i			0.909068i	0.890729	+	0.454534i	$0.150194\pi$
$223$			13.5753i			0.909068i	−0.890729	+	0.454534i	$0.849806\pi$
$224$	−5.07123	+	22.3858i	−0.338836	+	1.49571i
$225$		0			0
$226$	−3.27300	+	8.72948i	−0.217717	+	0.580677i
$227$	7.04458	+	7.04458i	0.467565	+	0.467565i	0.901125	−	0.433560i	$-0.142743\pi$
$227$	7.04458	+	7.04458i	0.467565	+	0.467565i	−0.433560	+	0.901125i	$0.642743\pi$
$228$		0			0
$229$	−5.38011	+	5.38011i	−0.355528	+	0.355528i	−0.862162	−	0.506634i	$-0.830890\pi$
$229$	−5.38011	+	5.38011i	−0.355528	+	0.355528i	0.506634	+	0.862162i	$0.330890\pi$
$230$	−12.0299	+	5.46895i	−0.793229	+	0.360612i
$231$		0			0
$232$	25.3000	+	7.57040i	1.66102	+	0.497021i
$233$	14.7461			0.966050			0.483025	−	0.875606i	$-0.339538\pi$
$233$	14.7461			0.966050			0.483025	+	0.875606i	$0.339538\pi$
$234$		0			0
$235$	19.1682	+	19.1682i	1.25040	+	1.25040i
$236$	−9.91945	+	0.675250i	−0.645701	+	0.0439550i
$237$		0			0
$238$	−11.7261	+	31.2749i	−0.760091	+	2.02725i
$239$	−22.8811			−1.48006			−0.740029	−	0.672575i	$-0.765188\pi$
$239$	−22.8811			−1.48006			−0.740029	+	0.672575i	$0.765188\pi$
$240$		0			0
$241$	−27.8190			−1.79198			−0.895991	−	0.444073i	$-0.853533\pi$
$241$	−27.8190			−1.79198			−0.895991	+	0.444073i	$0.853533\pi$
$242$	4.46681	−	11.9135i	0.287137	−	0.765830i
$243$		0			0
$244$	0.310393	+	4.55969i	0.0198709	+	0.291904i
$245$	−16.6471	−	16.6471i	−1.06354	−	1.06354i
$246$		0			0
$247$	5.76457			0.366791
$248$	1.54767	−	0.834781i	0.0982773	−	0.0530086i
$249$		0			0
$250$	12.2072	−	5.54955i	0.772052	−	0.350985i
$251$	4.02824	−	4.02824i	0.254260	−	0.254260i	−0.568454	−	0.822715i	$-0.692458\pi$
$251$	4.02824	−	4.02824i	0.254260	−	0.254260i	0.822715	+	0.568454i	$0.192458\pi$
$252$		0			0
$253$	3.75925	+	3.75925i	0.236342	+	0.236342i
$254$	2.97883	−	7.94490i	0.186909	−	0.498508i
$255$		0			0
$256$	−15.4123	+	4.29659i	−0.963269	+	0.268537i
$257$		−	7.38160i		−	0.460452i	−0.973137	−	0.230226i	$-0.926053\pi$
$257$		−	7.38160i		−	0.460452i	0.973137	−	0.230226i	$-0.0739465\pi$
$258$		0			0
$259$	13.5837	−	13.5837i	0.844052	−	0.844052i
$260$	19.4025	−	22.2371i	1.20330	−	1.37909i
$261$		0			0
$262$	4.10615	+	9.03219i	0.253679	+	0.558011i
$263$		−	0.0168854i		−	0.00104120i	−1.00000		0.000520598i	$-0.999834\pi$
$263$		−	0.0168854i		−	0.00104120i	1.00000		0.000520598i	$-0.000165712\pi$
$264$		0			0
$265$		−	19.7002i		−	1.21017i
$266$	5.07662	−	2.30790i	0.311268	−	0.141506i
$267$		0			0
$268$	−10.8543	+	0.738887i	−0.663031	+	0.0451347i
$269$	7.74635	−	7.74635i	0.472303	−	0.472303i	−0.430356	−	0.902659i	$-0.641612\pi$
$269$	7.74635	−	7.74635i	0.472303	−	0.472303i	0.902659	+	0.430356i	$0.141612\pi$
$270$		0			0
$271$			6.40104i			0.388836i	0.980919	+	0.194418i	$0.0622818\pi$
$271$			6.40104i			0.388836i	−0.980919	+	0.194418i	$0.937718\pi$
$272$	−23.0682	+	3.15528i	−1.39872	+	0.191317i
$273$		0			0
$274$	0.591589	+	0.221808i	0.0357392	+	0.0133999i
$275$	1.18936	+	1.18936i	0.0717211	+	0.0717211i
$276$		0			0
$277$	−17.2651	+	17.2651i	−1.03736	+	1.03736i	−0.0380878	+	0.999274i	$0.512127\pi$
$277$	−17.2651	+	17.2651i	−1.03736	+	1.03736i	−0.999274	+	0.0380878i	$0.987873\pi$
$278$	2.34555	+	5.15944i	0.140677	+	0.309443i
$279$		0			0
$280$	8.18422	−	27.3513i	0.489101	−	1.63455i
$281$	−3.85452			−0.229941			−0.114971	−	0.993369i	$-0.536677\pi$
$281$	−3.85452			−0.229941			−0.114971	+	0.993369i	$0.536677\pi$
$282$		0			0
$283$	−3.99744	−	3.99744i	−0.237623	−	0.237623i	0.578242	−	0.815865i	$-0.303739\pi$
$283$	−3.99744	−	3.99744i	−0.237623	−	0.237623i	−0.815865	+	0.578242i	$0.803739\pi$
$284$	7.86628	−	9.01548i	0.466778	−	0.534970i
$285$		0			0
$286$	−11.1171	−	4.16822i	−0.657370	−	0.246472i
$287$	−31.7920			−1.87662
$288$		0			0
$289$	−16.8812			−0.993010
$290$	−30.7565	−	11.5317i	−1.80609	−	0.677167i
$291$		0			0
$292$	6.72582	−	7.70840i	0.393599	−	0.451100i
$293$	2.52168	+	2.52168i	0.147318	+	0.147318i	0.776919	−	0.629601i	$-0.216782\pi$
$293$	2.52168	+	2.52168i	0.147318	+	0.147318i	−0.629601	+	0.776919i	$0.716782\pi$
$294$		0			0
$295$	12.3666			0.720012
$296$	12.8290	+	3.83878i	0.745673	+	0.223125i
$297$		0			0
$298$	12.3868	+	27.2470i	0.717550	+	1.57838i
$299$	−15.7549	+	15.7549i	−0.911127	+	0.911127i
$300$		0			0
$301$	−4.70409	−	4.70409i	−0.271139	−	0.271139i
$302$	−27.2243	−	10.2074i	−1.56658	−	0.587369i
$303$		0			0
$304$	3.09590	+	2.35088i	0.177562	+	0.134832i
$305$		−	5.68459i		−	0.325498i
$306$		0			0
$307$	20.6774	−	20.6774i	1.18012	−	1.18012i	0.200406	−	0.979713i	$-0.435774\pi$
$307$	20.6774	−	20.6774i	1.18012	−	1.18012i	0.979713	−	0.200406i	$-0.0642262\pi$
$308$	−11.4592	+	0.780066i	−0.652949	+	0.0444484i
$309$		0			0
$310$	−1.99111	+	0.905183i	−0.113087	+	0.0514110i
$311$			28.0098i			1.58829i	0.607728	+	0.794145i	$0.292081\pi$
$311$			28.0098i			1.58829i	−0.607728	+	0.794145i	$0.707919\pi$
$312$		0			0
$313$		−	31.7816i		−	1.79640i	−0.439588	−	0.898200i	$-0.644875\pi$
$313$		−	31.7816i		−	1.79640i	0.439588	−	0.898200i	$-0.355125\pi$
$314$	−0.259638	−	0.571119i	−0.0146522	−	0.0322301i
$315$		0			0
$316$	16.9358	−	19.4100i	0.952715	−	1.09190i
$317$	10.2600	−	10.2600i	0.576261	−	0.576261i	−0.357610	−	0.933871i	$-0.616408\pi$
$317$	10.2600	−	10.2600i	0.576261	−	0.576261i	0.933871	+	0.357610i	$0.116408\pi$
$318$		0			0
$319$			13.2148i			0.739885i
$320$	19.4889	−	4.02990i	1.08946	−	0.225278i
$321$		0			0
$322$	−7.56706	+	20.1823i	−0.421696	+	1.12471i
$323$	3.99995	+	3.99995i	0.222563	+	0.222563i
$324$		0			0
$325$	−4.98455	+	4.98455i	−0.276493	+	0.276493i
$326$	28.4763	−	12.9457i	1.57715	−	0.716994i
$327$		0			0
$328$	−10.5206	−	19.5050i	−0.580902	−	1.07699i
$329$	44.2153			2.43767
$330$		0			0
$331$	7.90498	+	7.90498i	0.434497	+	0.434497i	0.890155	−	0.455658i	$-0.150596\pi$
$331$	7.90498	+	7.90498i	0.434497	+	0.434497i	−0.455658	+	0.890155i	$0.650596\pi$
$332$	1.35927	+	19.9678i	0.0745998	+	1.09587i
$333$		0			0
$334$	−5.21108	+	13.8986i	−0.285138	+	0.760496i
$335$	13.5321			0.739337
$336$		0			0
$337$	14.5818			0.794322			0.397161	−	0.917749i	$-0.369995\pi$
$337$	14.5818			0.794322			0.397161	+	0.917749i	$0.369995\pi$
$338$	11.0144	−	29.3768i	0.599107	−	1.59789i
$339$		0			0
$340$	28.8931	−	1.96685i	1.56695	−	0.106667i
$341$	0.622206	+	0.622206i	0.0336943	+	0.0336943i
$342$		0			0
$343$	−9.99683			−0.539778
$344$	1.32938	−	4.44274i	0.0716754	−	0.239536i
$345$		0			0
$346$	−9.61694	+	4.37199i	−0.517010	+	0.235039i
$347$	7.56955	−	7.56955i	0.406354	−	0.406354i	−0.474111	−	0.880465i	$-0.657230\pi$
$347$	7.56955	−	7.56955i	0.406354	−	0.406354i	0.880465	+	0.474111i	$0.157230\pi$
$348$		0			0
$349$	13.7100	+	13.7100i	0.733881	+	0.733881i	0.971386	−	0.237505i	$-0.0763297\pi$
$349$	13.7100	+	13.7100i	0.733881	+	0.733881i	−0.237505	+	0.971386i	$0.576330\pi$
$350$	−2.39408	+	6.38530i	−0.127969	+	0.341309i
$351$		0			0
$352$	−4.27066	−	6.77232i	−0.227627	−	0.360966i
$353$			20.8149i			1.10786i	0.832562	+	0.553932i	$0.186873\pi$
$353$			20.8149i			1.10786i	−0.832562	+	0.553932i	$0.813127\pi$
$354$		0			0
$355$	−10.5233	+	10.5233i	−0.558518	+	0.558518i
$356$	4.36269	+	3.80659i	0.231222	+	0.201749i
$357$		0			0
$358$	−11.2840	−	24.8212i	−0.596379	−	1.31184i
$359$		−	32.1091i		−	1.69465i	−0.531073	−	0.847326i	$-0.678211\pi$
$359$		−	32.1091i		−	1.69465i	0.531073	−	0.847326i	$-0.321789\pi$
$360$		0			0
$361$			18.0555i			0.950292i
$362$	−16.5561	+	7.52659i	−0.870167	+	0.395589i
$363$		0			0
$364$	−3.26922	−	48.0250i	−0.171354	−	2.51719i
$365$	−8.99760	+	8.99760i	−0.470956	+	0.470956i
$366$		0			0
$367$		−	12.7686i		−	0.666516i	−0.942836	−	0.333258i	$-0.891852\pi$
$367$		−	12.7686i		−	0.666516i	0.942836	−	0.333258i	$-0.108148\pi$
$368$	−14.8863	+	2.03616i	−0.776004	+	0.106142i
$369$		0			0
$370$	−15.5959	−	5.84749i	−0.810795	−	0.303996i
$371$	−22.7212	−	22.7212i	−1.17963	−	1.17963i
$372$		0			0
$373$	5.28996	−	5.28996i	0.273903	−	0.273903i	−0.556766	−	0.830669i	$-0.687958\pi$
$373$	5.28996	−	5.28996i	0.273903	−	0.273903i	0.830669	+	0.556766i	$0.187958\pi$
$374$	−4.82175	−	10.6063i	−0.249327	−	0.548438i
$375$		0			0
$376$	14.6317	+	27.1270i	0.754573	+	1.39897i
$377$	−55.3824			−2.85234
$378$		0			0
$379$	16.9070	+	16.9070i	0.868453	+	0.868453i	0.992301	−	0.123848i	$-0.0395237\pi$
$379$	16.9070	+	16.9070i	0.868453	+	0.868453i	−0.123848	+	0.992301i	$0.539524\pi$
$380$	−3.64327	−	3.17887i	−0.186896	−	0.163072i
$381$		0			0
$382$	6.53027	+	2.44843i	0.334118	+	0.125273i
$383$	21.2707			1.08688			0.543441	−	0.839447i	$-0.317121\pi$
$383$	21.2707			1.08688			0.543441	+	0.839447i	$0.317121\pi$
$384$		0			0
$385$	14.2862			0.728094
$386$	5.28358	+	1.98101i	0.268927	+	0.100831i
$387$		0			0
$388$	−13.0801	−	11.4128i	−0.664042	−	0.579397i
$389$	12.7435	+	12.7435i	0.646119	+	0.646119i	0.952053	−	0.305934i	$-0.0989687\pi$
$389$	12.7435	+	12.7435i	0.646119	+	0.646119i	−0.305934	+	0.952053i	$0.598969\pi$
$390$		0			0
$391$	−21.8641			−1.10572
$392$	−12.7072	−	23.5590i	−0.641812	−	1.18991i
$393$		0			0
$394$	−6.37668	−	14.0266i	−0.321252	−	0.706650i
$395$	−22.6563	+	22.6563i	−1.13996	+	1.13996i
$396$		0			0
$397$	−15.8930	−	15.8930i	−0.797646	−	0.797646i	0.185078	−	0.982724i	$-0.440746\pi$
$397$	−15.8930	−	15.8930i	−0.797646	−	0.797646i	−0.982724	+	0.185078i	$0.940746\pi$
$398$	−2.72489	−	1.02166i	−0.136586	−	0.0512112i
$399$		0			0
$400$	−4.70977	+	0.644204i	−0.235488	+	0.0322102i
$401$			7.88676i			0.393846i	0.980419	+	0.196923i	$0.0630949\pi$
$401$			7.88676i			0.393846i	−0.980419	+	0.196923i	$0.936905\pi$
$402$		0			0
$403$	−2.60764	+	2.60764i	−0.129896	+	0.129896i
$404$	0.815605	+	11.9813i	0.0405779	+	0.596091i
$405$		0			0
$406$	−48.7731	+	22.1729i	−2.42057	+	1.10042i
$407$			6.70091i			0.332152i
$408$		0			0
$409$		−	37.6316i		−	1.86077i	−0.366590	−	0.930383i	$-0.619475\pi$
$409$		−	37.6316i		−	1.86077i	0.366590	−	0.930383i	$-0.380525\pi$
$410$	11.4079	+	25.0936i	0.563394	+	1.23928i
$411$		0			0
$412$	−22.4477	−	19.5863i	−1.10592	−	0.964948i
$413$	14.2630	−	14.2630i	0.701837	−	0.701837i
$414$		0			0
$415$		−	24.8939i		−	1.22199i
$416$	28.3825	−	17.8981i	1.39157	−	0.877529i
$417$		0			0
$418$	−0.682911	+	1.82141i	−0.0334023	+	0.0890879i
$419$	−3.53206	−	3.53206i	−0.172552	−	0.172552i	0.615547	−	0.788100i	$-0.288935\pi$
$419$	−3.53206	−	3.53206i	−0.172552	−	0.172552i	−0.788100	+	0.615547i	$0.788935\pi$
$420$		0			0
$421$	−4.65377	+	4.65377i	−0.226811	+	0.226811i	−0.811359	−	0.584548i	$-0.801272\pi$
$421$	−4.65377	+	4.65377i	−0.226811	+	0.226811i	0.584548	+	0.811359i	$0.301272\pi$
$422$	7.79580	−	3.54407i	0.379494	−	0.172523i
$423$		0			0
$424$	6.42103	−	21.4588i	0.311833	−	1.04213i
$425$	−6.91741			−0.335544
$426$		0			0
$427$	−6.55630	−	6.55630i	−0.317282	−	0.317282i
$428$	−21.4047	+	1.45709i	−1.03464	+	0.0704312i
$429$		0			0
$430$	−2.02500	+	5.40093i	−0.0976544	+	0.260456i
$431$	16.7496			0.806801			0.403400	−	0.915024i	$-0.367828\pi$
$431$	16.7496			0.806801			0.403400	+	0.915024i	$0.367828\pi$
$432$		0			0
$433$	−29.0456			−1.39584			−0.697921	−	0.716174i	$-0.745892\pi$
$433$	−29.0456			−1.39584			−0.697921	+	0.716174i	$0.745892\pi$
$434$	−1.25245	+	3.34043i	−0.0601195	+	0.160346i
$435$		0			0
$436$	0.714254	+	10.4924i	0.0342066	+	0.502496i
$437$	2.58124	+	2.58124i	0.123477	+	0.123477i
$438$		0			0
$439$	10.1281			0.483386			0.241693	−	0.970353i	$-0.422297\pi$
$439$	10.1281			0.483386			0.241693	+	0.970353i	$0.422297\pi$
$440$	4.72760	+	8.76490i	0.225379	+	0.417850i
$441$		0			0
$442$	44.4504	−	20.2077i	2.11429	−	0.961184i
$443$	−19.2674	+	19.2674i	−0.915421	+	0.915421i	−0.996692	−	0.0812713i	$-0.974102\pi$
$443$	−19.2674	+	19.2674i	−0.915421	+	0.915421i	0.0812713	+	0.996692i	$0.474102\pi$
$444$		0			0
$445$	−5.09234	−	5.09234i	−0.241400	−	0.241400i
$446$	6.73999	−	17.9763i	0.319148	−	0.851205i
$447$		0			0
$448$	17.8296	−	27.1254i	0.842370	−	1.28155i
$449$			13.6600i			0.644655i	0.946628	+	0.322328i	$0.104465\pi$
$449$			13.6600i			0.644655i	−0.946628	+	0.322328i	$0.895535\pi$
$450$		0			0
$451$	7.84155	−	7.84155i	0.369244	−	0.369244i
$452$	8.66819	−	9.93454i	0.407718	−	0.467282i
$453$		0			0
$454$	−5.83085	−	12.8260i	−0.273655	−	0.601953i
$455$			59.8729i			2.80689i
$456$		0			0
$457$			12.9308i			0.604877i	0.953169	+	0.302439i	$0.0978007\pi$
$457$			12.9308i			0.604877i	−0.953169	+	0.302439i	$0.902199\pi$
$458$	9.79550	−	4.45316i	0.457714	−	0.208083i
$459$		0			0
$460$	18.6453	−	1.26924i	0.869339	−	0.0591788i
$461$	−12.9378	+	12.9378i	−0.602573	+	0.602573i	−0.940995	−	0.338421i	$-0.890107\pi$
$461$	−12.9378	+	12.9378i	−0.602573	+	0.602573i	0.338421	+	0.940995i	$0.390107\pi$
$462$		0			0
$463$			11.3129i			0.525755i	0.964829	+	0.262878i	$0.0846715\pi$
$463$			11.3129i			0.525755i	−0.964829	+	0.262878i	$0.915328\pi$
$464$	−29.7435	−	22.5859i	−1.38081	−	1.04852i
$465$		0			0
$466$	−19.5268	−	7.32130i	−0.904560	−	0.339152i
$467$	16.4934	+	16.4934i	0.763225	+	0.763225i	0.976904	−	0.213679i	$-0.0685445\pi$
$467$	16.4934	+	16.4934i	0.763225	+	0.763225i	−0.213679	+	0.976904i	$0.568545\pi$
$468$		0			0
$469$	15.6072	−	15.6072i	0.720673	−	0.720673i
$470$	−15.8657	−	34.8994i	−0.731830	−	1.60979i
$471$		0			0
$472$	13.4706	+	4.03074i	0.620033	+	0.185530i
$473$	2.32055			0.106699
$474$		0			0
$475$	0.816657	+	0.816657i	0.0374708	+	0.0374708i
$476$	31.0554	−	35.5923i	1.42342	−	1.63137i
$477$		0			0
$478$	30.2991	+	11.3603i	1.38585	+	0.519606i
$479$	38.1456			1.74292			0.871458	−	0.490471i	$-0.163175\pi$
$479$	38.1456			1.74292			0.871458	+	0.490471i	$0.163175\pi$
$480$		0			0
$481$	−28.0832			−1.28048
$482$	36.8379	+	13.8119i	1.67792	+	0.629113i
$483$		0			0
$484$	−11.8299	+	13.5581i	−0.537722	+	0.616278i
$485$	15.2677	+	15.2677i	0.693271	+	0.693271i
$486$		0			0
$487$	23.2262			1.05248			0.526239	−	0.850336i	$-0.323602\pi$
$487$	23.2262			1.05248			0.526239	+	0.850336i	$0.323602\pi$
$488$	1.85282	−	6.19204i	0.0838731	−	0.280300i
$489$		0			0
$490$	13.7789	+	30.3091i	0.622468	+	1.36923i
$491$	−10.5405	+	10.5405i	−0.475687	+	0.475687i	−0.903749	−	0.428062i	$-0.859196\pi$
$491$	−10.5405	+	10.5405i	−0.475687	+	0.475687i	0.428062	+	0.903749i	$0.359196\pi$
$492$		0			0
$493$	−38.4291	−	38.4291i	−1.73076	−	1.73076i
$494$	−7.63342	−	2.86205i	−0.343444	−	0.128770i
$495$		0			0
$496$	−2.46388	+	0.337011i	−0.110632	+	0.0151322i
$497$			24.2740i			1.08884i
$498$		0			0
$499$	13.5947	−	13.5947i	0.608582	−	0.608582i	−0.333994	−	0.942575i	$-0.608396\pi$
$499$	13.5947	−	13.5947i	0.608582	−	0.608582i	0.942575	+	0.333994i	$0.108396\pi$
$500$	−18.9200	+	1.28795i	−0.846130	+	0.0575989i
$501$		0			0
$502$	−7.33417	+	3.33421i	−0.327340	+	0.148813i
$503$		−	21.9271i		−	0.977680i	−0.872373	−	0.488840i	$-0.837420\pi$
$503$		−	21.9271i		−	0.977680i	0.872373	−	0.488840i	$-0.162580\pi$
$504$		0			0
$505$		−	14.9371i		−	0.664693i
$506$	−3.11156	−	6.84442i	−0.138326	−	0.304272i
$507$		0			0
$508$	−7.88912	+	9.04166i	−0.350023	+	0.401159i
$509$	−4.57982	+	4.57982i	−0.202997	+	0.202997i	−0.801283	−	0.598286i	$-0.795849\pi$
$509$	−4.57982	+	4.57982i	−0.202997	+	0.202997i	0.598286	+	0.801283i	$0.295849\pi$
$510$		0			0
$511$			20.7547i			0.918134i
$512$	22.5421	+	1.96252i	0.996232	+	0.0867320i
$513$		0			0
$514$	−3.66489	+	9.77470i	−0.161651	+	0.431143i
$515$	26.2020	+	26.2020i	1.15460	+	1.15460i
$516$		0			0
$517$	−10.9058	+	10.9058i	−0.479636	+	0.479636i
$518$	−24.7317	+	11.2434i	−1.08665	+	0.494005i
$519$		0			0
$520$	−36.7333	+	19.8131i	−1.61086	+	0.868863i
$521$	−38.1860			−1.67296			−0.836479	−	0.547999i	$-0.815390\pi$
$521$	−38.1860			−1.67296			−0.836479	+	0.547999i	$0.815390\pi$
$522$		0			0
$523$	3.61599	+	3.61599i	0.158116	+	0.158116i	0.781731	−	0.623615i	$-0.214337\pi$
$523$	3.61599	+	3.61599i	0.158116	+	0.158116i	−0.623615	+	0.781731i	$0.714337\pi$
$524$	−0.952962	−	13.9991i	−0.0416304	−	0.611552i
$525$		0			0
$526$	−0.00838341	+	0.0223596i	−0.000365534	+	0.000974923i
$527$	−3.61880			−0.157637
$528$		0			0
$529$	8.89070			0.386552
$530$	−9.78095	+	26.0870i	−0.424857	+	1.13315i
$531$		0			0
$532$	−7.86830	+	0.535621i	−0.341134	+	0.0232221i
$533$	32.8635	+	32.8635i	1.42348	+	1.42348i
$534$		0			0
$535$	26.6854			1.15371
$536$	14.7401	+	4.41061i	0.636674	+	0.190509i
$537$		0			0
$538$	−14.1037	+	6.41171i	−0.608053	+	0.276429i
$539$	9.47136	−	9.47136i	0.407960	−	0.407960i
$540$		0			0
$541$	7.59731	+	7.59731i	0.326634	+	0.326634i	0.851305	−	0.524671i	$-0.175812\pi$
$541$	7.59731	+	7.59731i	0.326634	+	0.326634i	−0.524671	+	0.851305i	$0.675812\pi$
$542$	3.17805	−	8.47624i	0.136509	−	0.364086i
$543$		0			0
$544$	32.1134	+	7.27492i	1.37685	+	0.311910i
$545$		−	13.0810i		−	0.560327i
$546$		0			0
$547$	12.5715	−	12.5715i	0.537521	−	0.537521i	−0.385279	−	0.922800i	$-0.625895\pi$
$547$	12.5715	−	12.5715i	0.537521	−	0.537521i	0.922800	+	0.385279i	$0.125895\pi$
$548$	−0.673255	−	0.587435i	−0.0287600	−	0.0250940i
$549$		0			0
$550$	−0.984442	−	2.16545i	−0.0419768	−	0.0923352i
$551$			9.07373i			0.386554i
$552$		0			0
$553$			52.2611i			2.22237i
$554$	31.4344	−	14.2905i	1.33552	−	0.607145i
$555$		0			0
$556$	−0.544358	−	7.99665i	−0.0230859	−	0.339134i
$557$	1.70457	−	1.70457i	0.0722248	−	0.0722248i	−0.670072	−	0.742296i	$-0.733737\pi$
$557$	1.70457	−	1.70457i	0.0722248	−	0.0722248i	0.742296	+	0.670072i	$0.233737\pi$
$558$		0			0
$559$			9.72530i			0.411336i
$560$	−24.4172	+	32.1551i	−1.03181	+	1.35880i
$561$		0			0
$562$	5.10414	+	1.91373i	0.215305	+	0.0807258i
$563$	−29.2641	−	29.2641i	−1.23333	−	1.23333i	−0.962675	−	0.270660i	$-0.912758\pi$
$563$	−29.2641	−	29.2641i	−1.23333	−	1.23333i	−0.270660	−	0.962675i	$-0.587242\pi$
$564$		0			0
$565$	−11.5961	+	11.5961i	−0.487850	+	0.487850i
$566$	3.30871	+	7.27808i	0.139075	+	0.305921i
$567$		0			0
$568$	−14.8926	+	8.03274i	−0.624879	+	0.337046i
$569$	−11.3200			−0.474560			−0.237280	−	0.971441i	$-0.576256\pi$
$569$	−11.3200			−0.474560			−0.237280	+	0.971441i	$0.576256\pi$
$570$		0			0
$571$	21.9138	+	21.9138i	0.917064	+	0.917064i	0.996815	−	0.0797504i	$-0.0254123\pi$
$571$	21.9138	+	21.9138i	0.917064	+	0.917064i	−0.0797504	+	0.996815i	$0.525412\pi$
$572$	12.6518	+	11.0391i	0.528999	+	0.461568i
$573$		0			0
$574$	42.0988	+	15.7844i	1.75717	+	0.658827i
$575$	−4.46393			−0.186159
$576$		0			0
$577$	−13.3981			−0.557769			−0.278885	−	0.960325i	$-0.589965\pi$
$577$	−13.3981			−0.557769			−0.278885	+	0.960325i	$0.589965\pi$
$578$	22.3540	+	8.38132i	0.929803	+	0.348617i
$579$		0			0
$580$	35.0023	+	30.5406i	1.45339	+	1.26813i
$581$	−28.7113	−	28.7113i	−1.19115	−	1.19115i
$582$		0			0
$583$	11.2084			0.464206
$584$	−12.7334	+	6.86814i	−0.526914	+	0.284206i
$585$		0			0
$586$	−2.08721	−	4.59118i	−0.0862219	−	0.189660i
$587$	30.9886	−	30.9886i	1.27904	−	1.27904i	0.337829	−	0.941208i	$-0.390307\pi$
$587$	30.9886	−	30.9886i	1.27904	−	1.27904i	0.941208	−	0.337829i	$-0.109693\pi$
$588$		0			0
$589$	0.427229	+	0.427229i	0.0176037	+	0.0176037i
$590$	−16.3758	−	6.13990i	−0.674183	−	0.252776i
$591$		0			0
$592$	−15.0823	−	11.4528i	−0.619877	−	0.470706i
$593$		−	1.39217i		−	0.0571696i	−0.999591	−	0.0285848i	$-0.990900\pi$
$593$		−	1.39217i		−	0.0571696i	0.999591	−	0.0285848i	$-0.00910006\pi$
$594$		0			0
$595$	−41.5449	+	41.5449i	−1.70318	+	1.70318i
$596$	−2.87476	−	42.2303i	−0.117755	−	1.72982i
$597$		0			0
$598$	28.6847	−	13.0404i	1.17300	−	0.533262i
$599$			2.53068i			0.103401i	0.998663	+	0.0517004i	$0.0164641\pi$
$599$			2.53068i			0.103401i	−0.998663	+	0.0517004i	$0.983536\pi$
$600$		0			0
$601$		−	31.6102i		−	1.28941i	−0.764432	−	0.644704i	$-0.776981\pi$
$601$		−	31.6102i		−	1.28941i	0.764432	−	0.644704i	$-0.223019\pi$
$602$	3.89361	+	8.56468i	0.158692	+	0.349070i
$603$		0			0
$604$	30.9825	+	27.0332i	1.26066	+	1.09996i
$605$	15.8257	−	15.8257i	0.643404	−	0.643404i
$606$		0			0
$607$		−	17.0447i		−	0.691823i	−0.938267	−	0.345912i	$-0.887570\pi$
$607$		−	17.0447i		−	0.691823i	0.938267	−	0.345912i	$-0.112430\pi$
$608$	−2.93239	−	4.65012i	−0.118924	−	0.188587i
$609$		0			0
$610$	−2.82234	+	7.52751i	−0.114273	+	0.304780i
$611$	−45.7056	−	45.7056i	−1.84905	−	1.84905i
$612$		0			0
$613$	1.57535	−	1.57535i	0.0636279	−	0.0636279i	−0.674577	−	0.738205i	$-0.735674\pi$
$613$	1.57535	−	1.57535i	0.0636279	−	0.0636279i	0.738205	+	0.674577i	$0.235674\pi$
$614$	−37.6470	+	17.1148i	−1.51931	+	0.690697i
$615$		0			0
$616$	15.5615	+	4.65641i	0.626992	+	0.187612i
$617$	−12.7382			−0.512819			−0.256410	−	0.966568i	$-0.582540\pi$
$617$	−12.7382			−0.512819			−0.256410	+	0.966568i	$0.582540\pi$
$618$		0			0
$619$	−14.5538	−	14.5538i	−0.584967	−	0.584967i	0.351297	−	0.936264i	$-0.385741\pi$
$619$	−14.5538	−	14.5538i	−0.584967	−	0.584967i	−0.936264	+	0.351297i	$0.885741\pi$
$620$	3.08603	−	0.210077i	0.123938	−	0.00843688i
$621$		0			0
$622$	13.9066	−	37.0905i	0.557603	−	1.48719i
$623$	−11.7465			−0.470612
$624$		0			0
$625$	29.5297			1.18119
$626$	−15.7792	+	42.0850i	−0.630664	+	1.68206i
$627$		0			0
$628$	0.0602573	+	0.885182i	0.00240453	+	0.0353226i
$629$	−19.4865	−	19.4865i	−0.776978	−	0.776978i
$630$		0			0
$631$	−40.2449			−1.60213			−0.801063	−	0.598580i	$-0.795732\pi$
$631$	−40.2449			−1.60213			−0.801063	+	0.598580i	$0.795732\pi$
$632$	−32.0633	+	17.2942i	−1.27541	+	0.687927i
$633$		0			0
$634$	−18.6803	+	8.49230i	−0.741889	+	0.337272i
$635$	10.5538	−	10.5538i	0.418816	−	0.418816i
$636$		0			0
$637$	39.6940	+	39.6940i	1.57273	+	1.57273i
$638$	6.56099	−	17.4990i	0.259752	−	0.692790i
$639$		0			0
$640$	−27.8080	−	4.33966i	−1.09921	−	0.171540i
$641$		−	14.9945i		−	0.592246i	−0.955150	−	0.296123i	$-0.904306\pi$
$641$		−	14.9945i		−	0.592246i	0.955150	−	0.296123i	$-0.0956938\pi$
$642$		0			0
$643$	1.20351	−	1.20351i	0.0474620	−	0.0474620i	−0.682977	−	0.730439i	$-0.739315\pi$
$643$	1.20351	−	1.20351i	0.0474620	−	0.0474620i	0.730439	+	0.682977i	$0.239315\pi$
$644$	20.0406	−	22.9683i	0.789709	−	0.905079i
$645$		0			0
$646$	−3.31079	−	7.28265i	−0.130261	−	0.286532i
$647$		−	1.36253i		−	0.0535666i	−0.999641	−	0.0267833i	$-0.991474\pi$
$647$		−	1.36253i		−	0.0535666i	0.999641	−	0.0267833i	$-0.00852640\pi$
$648$		0			0
$649$			7.03600i			0.276187i
$650$	9.07531	−	4.12575i	0.355963	−	0.161825i
$651$		0			0
$652$	−44.1356	+	3.00445i	−1.72848	+	0.117663i
$653$	24.5411	−	24.5411i	0.960369	−	0.960369i	−0.0388753	−	0.999244i	$-0.512377\pi$
$653$	24.5411	−	24.5411i	0.960369	−	0.960369i	0.999244	+	0.0388753i	$0.0123775\pi$
$654$		0			0
$655$			17.4527i			0.681933i
$656$	4.24729	+	31.0519i	0.165829	+	1.21237i
$657$		0			0
$658$	−58.5497	−	21.9524i	−2.28251	−	0.855795i
$659$	11.6974	+	11.6974i	0.455667	+	0.455667i	0.897230	−	0.441563i	$-0.145576\pi$
$659$	11.6974	+	11.6974i	0.455667	+	0.455667i	−0.441563	+	0.897230i	$0.645576\pi$
$660$		0			0
$661$	18.9436	−	18.9436i	0.736822	−	0.736822i	−0.235140	−	0.971962i	$-0.575555\pi$
$661$	18.9436	−	18.9436i	0.736822	−	0.736822i	0.971962	+	0.235140i	$0.0755547\pi$
$662$	−6.54301	−	14.3925i	−0.254301	−	0.559380i
$663$		0			0
$664$	8.11386	−	27.1162i	0.314879	−	1.05231i
$665$	9.80943			0.380394
$666$		0			0
$667$	−24.7990	−	24.7990i	−0.960219	−	0.960219i
$668$	13.8010	−	15.8172i	0.533976	−	0.611986i
$669$		0			0
$670$	−17.9191	−	6.71854i	−0.692277	−	0.259560i
$671$	3.23425			0.124857
$672$		0			0
$673$	−5.97189			−0.230199			−0.115100	−	0.993354i	$-0.536719\pi$
$673$	−5.97189			−0.230199			−0.115100	+	0.993354i	$0.536719\pi$
$674$	−19.3092	−	7.23972i	−0.743763	−	0.278864i
$675$		0			0
$676$	−29.1706	+	33.4322i	−1.12195	+	1.28585i
$677$	0.215189	+	0.215189i	0.00827040	+	0.00827040i	0.711230	−	0.702959i	$-0.248138\pi$
$677$	0.215189	+	0.215189i	0.00827040	+	0.00827040i	−0.702959	+	0.711230i	$0.748138\pi$
$678$		0			0
$679$	35.2179			1.35154
$680$	−39.2367	−	11.7406i	−1.50466	−	0.450233i
$681$		0			0
$682$	−0.515005	−	1.13284i	−0.0197205	−	0.0433788i
$683$	−0.979632	+	0.979632i	−0.0374846	+	0.0374846i	−0.725601	−	0.688116i	$-0.758438\pi$
$683$	−0.979632	+	0.979632i	−0.0374846	+	0.0374846i	0.688116	+	0.725601i	$0.258438\pi$
$684$		0			0
$685$	0.785854	+	0.785854i	0.0300259	+	0.0300259i
$686$	13.2378	+	4.96332i	0.505420	+	0.189500i
$687$		0			0
$688$	−3.96614	+	5.22303i	−0.151207	+	0.199126i
$689$			46.9741i			1.78957i
$690$		0			0
$691$	−28.0692	+	28.0692i	−1.06780	+	1.06780i	−0.0702745	+	0.997528i	$0.522388\pi$
$691$	−28.0692	+	28.0692i	−1.06780	+	1.06780i	−0.997528	+	0.0702745i	$0.977612\pi$
$692$	14.9054	−	1.01466i	0.566617	−	0.0385715i
$693$		0			0
$694$	−13.7818	+	6.26537i	−0.523149	+	0.237830i
$695$			9.96946i			0.378163i
$696$		0			0
$697$			45.6070i			1.72749i
$698$	−11.3479	−	24.9617i	−0.429524	−	0.944813i
$699$		0			0
$700$	6.34047	−	7.26676i	0.239647	−	0.274658i
$701$	12.9101	−	12.9101i	0.487609	−	0.487609i	−0.419942	−	0.907551i	$-0.637950\pi$
$701$	12.9101	−	12.9101i	0.487609	−	0.487609i	0.907551	+	0.419942i	$0.137950\pi$
$702$		0			0
$703$			4.60108i			0.173533i
$704$	2.29281	+	11.0882i	0.0864137	+	0.417903i
$705$		0			0
$706$	10.3344	−	27.5630i	0.388939	−	1.03735i
$707$	−17.2277	−	17.2277i	−0.647913	−	0.647913i
$708$		0			0
$709$	19.0440	−	19.0440i	0.715211	−	0.715211i	−0.252410	−	0.967620i	$-0.581223\pi$
$709$	19.0440	−	19.0440i	0.715211	−	0.715211i	0.967620	+	0.252410i	$0.0812231\pi$
$710$	19.1596	−	8.71019i	0.719047	−	0.326888i
$711$		0			0
$712$	−3.88714	−	7.20670i	−0.145677	−	0.270083i
$713$	−2.33528			−0.0874568
$714$		0			0
$715$	−14.7678	−	14.7678i	−0.552283	−	0.552283i
$716$	2.61882	+	38.4705i	0.0978698	+	1.43771i
$717$		0			0
$718$	−15.9418	+	42.5187i	−0.594943	+	1.58678i
$719$	14.6710			0.547138			0.273569	−	0.961852i	$-0.411796\pi$
$719$	14.6710			0.547138			0.273569	+	0.961852i	$0.411796\pi$
$720$		0			0
$721$	60.4399			2.25090
$722$	8.96439	−	23.9091i	0.333620	−	0.889805i
$723$		0			0
$724$	25.6604	−	1.74678i	0.953659	−	0.0649187i
$725$	−7.84594	−	7.84594i	−0.291391	−	0.291391i
$726$		0			0
$727$	−26.1517			−0.969911			−0.484956	−	0.874539i	$-0.661164\pi$
$727$	−26.1517			−0.969911			−0.484956	+	0.874539i	$0.661164\pi$
$728$	−19.5148	+	65.2177i	−0.723267	+	2.41713i
$729$		0			0
$730$	16.3818	−	7.44738i	0.606318	−	0.275640i
$731$	−6.74824	+	6.74824i	−0.249593	+	0.249593i
$732$		0			0
$733$	19.3081	+	19.3081i	0.713162	+	0.713162i	0.967196	−	0.254033i	$-0.0817572\pi$
$733$	19.3081	+	19.3081i	0.713162	+	0.713162i	−0.254033	+	0.967196i	$0.581757\pi$
$734$	−6.33948	+	16.9082i	−0.233995	+	0.624091i
$735$		0			0
$736$	20.7234	+	4.69463i	0.763874	+	0.173047i
$737$			7.69909i			0.283599i
$738$		0			0
$739$	10.6350	−	10.6350i	0.391215	−	0.391215i	−0.483906	−	0.875120i	$-0.660782\pi$
$739$	10.6350	−	10.6350i	0.391215	−	0.391215i	0.875120	+	0.483906i	$0.160782\pi$
$740$	17.7489	+	15.4865i	0.652462	+	0.569293i
$741$		0			0
$742$	18.8065	+	41.3682i	0.690408	+	1.51867i
$743$			46.6974i			1.71316i	0.516014	+	0.856580i	$0.327415\pi$
$743$			46.6974i			1.71316i	−0.516014	+	0.856580i	$0.672585\pi$
$744$		0			0
$745$			52.6487i			1.92890i
$746$	−9.63135	+	4.37854i	−0.352629	+	0.160310i
$747$		0			0
$748$	1.11904	+	16.4388i	0.0409162	+	0.601061i
$749$	30.7775	−	30.7775i	1.12459	−	1.12459i
$750$		0			0
$751$			27.5084i			1.00380i	0.864927	+	0.501898i	$0.167365\pi$
$751$			27.5084i			1.00380i	−0.864927	+	0.501898i	$0.832635\pi$
$752$	−5.90700	−	43.1860i	−0.215406	−	1.57483i
$753$		0			0
$754$	73.3373	+	27.4968i	2.67079	+	1.00137i
$755$	−36.1642	−	36.1642i	−1.31615	−	1.31615i
$756$		0			0
$757$	7.32819	−	7.32819i	0.266347	−	0.266347i	−0.561279	−	0.827627i	$-0.689691\pi$
$757$	7.32819	−	7.32819i	0.266347	−	0.266347i	0.827627	+	0.561279i	$0.189691\pi$
$758$	−13.9940	−	30.7823i	−0.508286	−	1.11806i
$759$		0			0
$760$	3.24614	+	6.01829i	0.117750	+	0.218306i
$761$	50.2955			1.82321			0.911604	−	0.411069i	$-0.134844\pi$
$761$	50.2955			1.82321			0.911604	+	0.411069i	$0.134844\pi$
$762$		0			0
$763$	−15.0869	−	15.0869i	−0.546182	−	0.546182i
$764$	−7.43174	−	6.48442i	−0.268871	−	0.234598i
$765$		0			0
$766$	−28.1666	−	10.5607i	−1.01770	−	0.381573i
$767$	−29.4875			−1.06473
$768$		0			0
$769$	3.40476			0.122779			0.0613893	−	0.998114i	$-0.480447\pi$
$769$	3.40476			0.122779			0.0613893	+	0.998114i	$0.480447\pi$
$770$	−18.9178	−	7.09297i	−0.681750	−	0.255613i
$771$		0			0
$772$	−6.01295	−	5.24649i	−0.216411	−	0.188825i
$773$	−19.8286	−	19.8286i	−0.713186	−	0.713186i	0.254014	−	0.967201i	$-0.418249\pi$
$773$	−19.8286	−	19.8286i	−0.713186	−	0.713186i	−0.967201	+	0.254014i	$0.918249\pi$
$774$		0			0
$775$	−0.738839			−0.0265399
$776$	11.6543	+	21.6069i	0.418366	+	0.775644i
$777$		0			0
$778$	−10.5478	−	23.2018i	−0.378159	−	0.831826i
$779$	5.38428	−	5.38428i	0.192912	−	0.192912i
$780$		0			0
$781$	−5.98722	−	5.98722i	−0.214240	−	0.214240i
$782$	28.9524	+	10.8553i	1.03534	+	0.388185i
$783$		0			0
$784$	5.13006	+	37.5058i	0.183216	+	1.33949i
$785$		−	1.10356i		−	0.0393877i
$786$		0			0
$787$	6.05353	−	6.05353i	0.215785	−	0.215785i	−0.590934	−	0.806720i	$-0.701241\pi$
$787$	6.05353	−	6.05353i	0.215785	−	0.215785i	0.806720	+	0.590934i	$0.201241\pi$
$788$	1.47991	+	21.7399i	0.0527196	+	0.774454i
$789$		0			0
$790$	41.2499	−	18.7528i	1.46761	−	0.667193i
$791$			26.7486i			0.951069i
$792$		0			0
$793$			13.5546i			0.481337i
$794$	13.1547	+	28.9362i	0.466844	+	1.02691i
$795$		0			0
$796$	3.10105	+	2.70576i	0.109914	+	0.0959030i
$797$	25.7512	−	25.7512i	0.912155	−	0.912155i	−0.0842867	−	0.996442i	$-0.526861\pi$
$797$	25.7512	−	25.7512i	0.912155	−	0.912155i	0.996442	+	0.0842867i	$0.0268612\pi$
$798$		0			0
$799$		−	63.4289i		−	2.24395i
$800$	6.55650	+	1.48530i	0.231807	+	0.0525132i
$801$		0			0
$802$	3.91569	−	10.4436i	0.138268	−	0.368777i
$803$	−5.11919	−	5.11919i	−0.180652	−	0.180652i
$804$		0			0
$805$	−26.8097	+	26.8097i	−0.944917	+	0.944917i
$806$	4.74769	−	2.15836i	0.167230	−	0.0760250i
$807$		0			0
$808$	4.86856	−	16.2705i	0.171275	−	0.572395i
$809$	−27.7490			−0.975602			−0.487801	−	0.872955i	$-0.662201\pi$
$809$	−27.7490			−0.975602			−0.487801	+	0.872955i	$0.662201\pi$
$810$		0			0
$811$	−18.2938	−	18.2938i	−0.642382	−	0.642382i	0.308758	−	0.951141i	$-0.400087\pi$
$811$	−18.2938	−	18.2938i	−0.642382	−	0.642382i	−0.951141	+	0.308758i	$0.900087\pi$
$812$	75.5938	−	5.14592i	2.65282	−	0.180586i
$813$		0			0
$814$	3.32693	−	8.87332i	0.116609	−	0.311010i
$815$	55.0240			1.92741
$816$		0			0
$817$	1.59337			0.0557449
$818$	−18.6837	+	49.8317i	−0.653261	+	1.74233i
$819$		0			0
$820$	−2.64756	−	38.8927i	−0.0924566	−	1.35819i
$821$	−7.56118	−	7.56118i	−0.263887	−	0.263887i	0.562744	−	0.826631i	$-0.309746\pi$
$821$	−7.56118	−	7.56118i	−0.263887	−	0.263887i	−0.826631	+	0.562744i	$0.809746\pi$
$822$		0			0
$823$	−14.4336			−0.503125			−0.251563	−	0.967841i	$-0.580944\pi$
$823$	−14.4336			−0.503125			−0.251563	+	0.967841i	$0.580944\pi$
$824$	20.0008	+	37.0812i	0.696760	+	1.29178i
$825$		0			0
$826$	−25.9685	+	11.8056i	−0.903559	+	0.410769i
$827$	−12.2504	+	12.2504i	−0.425987	+	0.425987i	−0.887259	−	0.461272i	$-0.847393\pi$
$827$	−12.2504	+	12.2504i	−0.425987	+	0.425987i	0.461272	+	0.887259i	$0.347393\pi$
$828$		0			0
$829$	−7.58610	−	7.58610i	−0.263476	−	0.263476i	0.562988	−	0.826465i	$-0.309652\pi$
$829$	−7.58610	−	7.58610i	−0.263476	−	0.263476i	−0.826465	+	0.562988i	$0.809652\pi$
$830$	−12.3596	+	32.9645i	−0.429007	+	1.14421i
$831$		0			0
$832$	−46.4702	+	9.60907i	−1.61107	+	0.333135i
$833$			55.0862i			1.90862i
$834$		0			0
$835$	−18.4626	+	18.4626i	−0.638923	+	0.638923i
$836$	1.80862	−	2.07284i	0.0625524	−	0.0716907i
$837$		0			0
$838$	2.92351	+	6.43077i	0.100991	+	0.222147i
$839$		−	10.7285i		−	0.370389i	−0.982702	−	0.185195i	$-0.940708\pi$
$839$		−	10.7285i		−	0.370389i	0.982702	−	0.185195i	$-0.0592916\pi$
$840$		0			0
$841$		−	58.1748i		−	2.00603i
$842$	8.47305	−	3.85196i	0.292001	−	0.132747i
$843$		0			0
$844$	−12.0828	+	0.822514i	−0.415906	+	0.0283121i
$845$	39.0236	−	39.0236i	1.34245	−	1.34245i
$846$		0			0
$847$		−	36.5049i		−	1.25432i
$848$	−19.1568	+	25.2277i	−0.657847	+	0.866324i
$849$		0			0
$850$	9.16002	+	3.43442i	0.314186	+	0.117800i
$851$	−12.5750	−	12.5750i	−0.431065	−	0.431065i
$852$		0			0
$853$	27.3234	−	27.3234i	0.935535	−	0.935535i	−0.0625097	−	0.998044i	$-0.519910\pi$
$853$	27.3234	−	27.3234i	0.935535	−	0.935535i	0.998044	+	0.0625097i	$0.0199104\pi$
$854$	5.42670	+	11.9370i	0.185698	+	0.408475i
$855$		0			0
$856$	29.0675	+	8.69776i	0.993508	+	0.297283i
$857$	−19.6552			−0.671410			−0.335705	−	0.941967i	$-0.608974\pi$
$857$	−19.6552			−0.671410			−0.335705	+	0.941967i	$0.608974\pi$
$858$		0			0
$859$	21.6586	+	21.6586i	0.738982	+	0.738982i	0.972381	−	0.233399i	$-0.0749847\pi$
$859$	21.6586	+	21.6586i	0.738982	+	0.738982i	−0.233399	+	0.972381i	$0.574985\pi$
$860$	5.36301	−	6.14650i	0.182877	−	0.209594i
$861$		0			0
$862$	−22.1798	−	8.31601i	−0.755447	−	0.283245i
$863$	28.2608			0.962008			0.481004	−	0.876718i	$-0.340272\pi$
$863$	28.2608			0.962008			0.481004	+	0.876718i	$0.340272\pi$
$864$		0			0
$865$	−18.5826			−0.631827
$866$	38.4621	+	14.4208i	1.30700	+	0.490040i
$867$		0			0
$868$	3.31698	−	3.80156i	0.112586	−	0.129033i
$869$	−12.8903	−	12.8903i	−0.437273	−	0.437273i
$870$		0			0
$871$	−32.2665			−1.09331
$872$	4.26357	−	14.2487i	0.144383	−	0.482521i
$873$		0			0
$874$	−2.13651	−	4.69962i	−0.0722685	−	0.158967i
$875$	27.2048	−	27.2048i	0.919690	−	0.919690i
$876$		0			0
$877$	0.760817	+	0.760817i	0.0256910	+	0.0256910i	0.719836	−	0.694145i	$-0.244217\pi$
$877$	0.760817	+	0.760817i	0.0256910	+	0.0256910i	−0.694145	+	0.719836i	$0.744217\pi$
$878$	−13.4116	−	5.02848i	−0.452618	−	0.169703i
$879$		0			0
$880$	−1.90859	−	13.9537i	−0.0643385	−	0.470378i
$881$		−	22.2041i		−	0.748076i	−0.927413	−	0.374038i	$-0.877973\pi$
$881$		−	22.2041i		−	0.748076i	0.927413	−	0.374038i	$-0.122027\pi$
$882$		0			0
$883$	8.67095	−	8.67095i	0.291801	−	0.291801i	−0.545991	−	0.837791i	$-0.683847\pi$
$883$	8.67095	−	8.67095i	0.291801	−	0.291801i	0.837791	+	0.545991i	$0.183847\pi$
$884$	−68.8941	+	4.68985i	−2.31716	+	0.157737i
$885$		0			0
$886$	35.0799	−	15.9478i	1.17853	−	0.535775i
$887$		−	15.5195i		−	0.521093i	−0.965461	−	0.260546i	$-0.916097\pi$
$887$		−	15.5195i		−	0.521093i	0.965461	−	0.260546i	$-0.0839027\pi$
$888$		0			0
$889$		−	24.3445i		−	0.816488i
$890$	4.21497	+	9.27155i	0.141286	+	0.310783i
$891$		0			0
$892$	−17.8501	+	20.4579i	−0.597667	+	0.684981i
$893$	−7.48830	+	7.48830i	−0.250586	+	0.250586i
$894$		0			0
$895$		−	47.9614i		−	1.60317i
$896$	−37.0774	+	27.0671i	−1.23867	+	0.904249i
$897$		0			0
$898$	6.78205	−	18.0885i	0.226320	−	0.603622i
$899$	−4.10455	−	4.10455i	−0.136895	−	0.136895i
$900$		0			0
$901$	−32.5946	+	32.5946i	−1.08588	+	1.08588i
$902$	−14.2770	+	6.49051i	−0.475372	+	0.216110i
$903$		0			0
$904$	−16.4108	+	8.85163i	−0.545815	+	0.294401i
$905$	−31.9909			−1.06341
$906$		0			0
$907$	−20.4064	−	20.4064i	−0.677585	−	0.677585i	0.281868	−	0.959453i	$-0.409046\pi$
$907$	−20.4064	−	20.4064i	−0.677585	−	0.677585i	−0.959453	+	0.281868i	$0.909046\pi$
$908$	1.35323	+	19.8791i	0.0449087	+	0.659710i
$909$		0			0
$910$	29.7263	−	79.2835i	0.985417	−	2.62822i
$911$	−9.07361			−0.300622			−0.150311	−	0.988639i	$-0.548028\pi$
$911$	−9.07361			−0.300622			−0.150311	+	0.988639i	$0.548028\pi$
$912$		0			0
$913$	14.1634			0.468741
$914$	6.42001	−	17.1229i	0.212355	−	0.566376i
$915$		0			0
$916$	−15.1821	+	1.03350i	−0.501632	+	0.0341477i
$917$	20.1290	+	20.1290i	0.664718	+	0.664718i
$918$		0			0
$919$	6.22281			0.205271			0.102636	−	0.994719i	$-0.467272\pi$
$919$	6.22281			0.205271			0.102636	+	0.994719i	$0.467272\pi$
$920$	−25.3202	−	7.57644i	−0.834781	−	0.249788i
$921$		0			0
$922$	23.5557	−	10.7087i	0.775765	−	0.352673i
$923$	25.0922	−	25.0922i	0.825919	−	0.825919i
$924$		0			0
$925$	−3.97850	−	3.97850i	−0.130812	−	0.130812i
$926$	5.61674	−	14.9805i	0.184577	−	0.492290i
$927$		0			0
$928$	28.1726	+	44.6755i	0.924811	+	1.46654i
$929$		−	0.548796i		−	0.0180054i	−0.999959	−	0.00900270i	$-0.997134\pi$
$929$		−	0.548796i		−	0.0180054i	0.999959	−	0.00900270i	$-0.00286569\pi$
$930$		0			0
$931$	6.50337	−	6.50337i	0.213139	−	0.213139i
$932$	22.2223	+	19.3897i	0.727917	+	0.635130i
$933$		0			0
$934$	−13.6517	−	30.0294i	−0.446699	−	0.982592i
$935$		−	20.4943i		−	0.670234i
$936$		0			0
$937$		−	2.66669i		−	0.0871171i	−0.999051	−	0.0435586i	$-0.986130\pi$
$937$		−	2.66669i		−	0.0871171i	0.999051	−	0.0435586i	$-0.0138695\pi$
$938$	−28.4158	+	12.9182i	−0.927809	+	0.421794i
$939$		0			0
$940$	3.68214	+	54.0908i	0.120098	+	1.76425i
$941$	−22.0091	+	22.0091i	−0.717477	+	0.717477i	−0.968088	−	0.250611i	$-0.919369\pi$
$941$	−22.0091	+	22.0091i	−0.717477	+	0.717477i	0.250611	+	0.968088i	$0.419369\pi$
$942$		0			0
$943$			29.4310i			0.958406i
$944$	−15.8365	−	12.0255i	−0.515433	−	0.391396i
$945$		0			0
$946$	−3.07286	−	1.15213i	−0.0999073	−	0.0374589i
$947$	−20.9185	−	20.9185i	−0.679760	−	0.679760i	0.280185	−	0.959946i	$-0.409604\pi$
$947$	−20.9185	−	20.9185i	−0.679760	−	0.679760i	−0.959946	+	0.280185i	$0.909604\pi$
$948$		0			0
$949$	21.4543	−	21.4543i	0.696435	−	0.696435i
$950$	−0.675953	−	1.48688i	−0.0219308	−	0.0482406i
$951$		0			0
$952$	−58.7946	+	31.7125i	−1.90554	+	1.02781i
$953$	29.3435			0.950531			0.475265	−	0.879843i	$-0.342352\pi$
$953$	29.3435			0.950531			0.475265	+	0.879843i	$0.342352\pi$
$954$		0			0
$955$	8.67467	+	8.67467i	0.280706	+	0.280706i
$956$	−34.4818	−	30.0864i	−1.11522	−	0.973064i
$957$		0			0
$958$	−50.5122	−	18.9389i	−1.63198	−	0.611887i
$959$	1.81272			0.0585359
$960$		0			0
$961$	30.6135			0.987532
$962$	37.1877	+	13.9430i	1.19898	+	0.449541i
$963$		0			0
$964$	−41.9232	−	36.5792i	−1.35025	−	1.17814i
$965$	7.01859	+	7.01859i	0.225936	+	0.225936i
$966$		0			0
$967$	−29.0587			−0.934466			−0.467233	−	0.884134i	$-0.654749\pi$
$967$	−29.0587			−0.934466			−0.467233	+	0.884134i	$0.654749\pi$
$968$	22.3966	−	12.0802i	0.719852	−	0.388273i
$969$		0			0
$970$	−12.6372	−	27.7977i	−0.405756	−	0.892531i
$971$	−8.91899	+	8.91899i	−0.286224	+	0.286224i	−0.835585	−	0.549361i	$-0.814871\pi$
$971$	−8.91899	+	8.91899i	−0.286224	+	0.286224i	0.549361	+	0.835585i	$0.314871\pi$
$972$		0			0
$973$	11.4982	+	11.4982i	0.368617	+	0.368617i
$974$	−30.7560	−	11.5316i	−0.985487	−	0.369495i
$975$		0			0
$976$	−5.52778	+	7.27958i	−0.176940	+	0.233014i
$977$		−	53.0530i		−	1.69732i	−0.528942	−	0.848658i	$-0.677411\pi$
$977$		−	53.0530i		−	1.69732i	0.528942	−	0.848658i	$-0.322589\pi$
$978$		0			0
$979$	2.89729	−	2.89729i	0.0925977	−	0.0925977i
$980$	−3.19783	−	46.9763i	−0.102151	−	1.50060i
$981$		0			0
$982$	19.1910	−	8.72447i	0.612409	−	0.278409i
$983$		−	19.9905i		−	0.637599i	−0.947822	−	0.318800i	$-0.896720\pi$
$983$		−	19.9905i		−	0.637599i	0.947822	−	0.318800i	$-0.103280\pi$
$984$		0			0
$985$		−	27.1033i		−	0.863582i
$986$	31.8080	+	69.9673i	1.01297	+	2.22821i
$987$		0			0
$988$	8.68718	+	7.57983i	0.276376	+	0.241147i
$989$	−4.35476	+	4.35476i	−0.138473	+	0.138473i
$990$		0			0
$991$			43.6264i			1.38584i	0.721015	+	0.692919i	$0.243676\pi$
$991$			43.6264i			1.38584i	−0.721015	+	0.692919i	$0.756324\pi$
$992$	3.42999	+	0.777024i	0.108902	+	0.0246705i
$993$		0			0
$994$	12.0518	−	32.1435i	0.382259	−	1.01953i
$995$	−3.61968	−	3.61968i	−0.114752	−	0.114752i
$996$		0			0
$997$	8.42356	−	8.42356i	0.266777	−	0.266777i	−0.561023	−	0.827800i	$-0.689592\pi$
$997$	8.42356	−	8.42356i	0.266777	−	0.266777i	0.827800	+	0.561023i	$0.189592\pi$
$998$	−24.7517	+	11.2524i	−0.783500	+	0.356189i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.323.2	yes	32
3.2	odd	2	inner	432.2.l.b.323.15	yes	32
4.3	odd	2		1728.2.l.b.431.4		32
12.11	even	2		1728.2.l.b.431.13		32
16.5	even	4		1728.2.l.b.1295.13		32
16.11	odd	4	inner	432.2.l.b.107.15	yes	32
48.5	odd	4		1728.2.l.b.1295.4		32
48.11	even	4	inner	432.2.l.b.107.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.2	✓	32	48.11	even	4	inner
432.2.l.b.107.15	yes	32	16.11	odd	4	inner
432.2.l.b.323.2	yes	32	1.1	even	1	trivial
432.2.l.b.323.15	yes	32	3.2	odd	2	inner
1728.2.l.b.431.4		32	4.3	odd	2
1728.2.l.b.431.13		32	12.11	even	2
1728.2.l.b.1295.4		32	48.5	odd	4
1728.2.l.b.1295.13		32	16.5	even	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32420 - 0.496490i) q^{2} +(1.50700 + 1.31490i) q^{4} +(-1.75903 - 1.75903i) q^{5} -4.05756 q^{7} +(-1.34273 - 2.48940i) q^{8} +O(q^{10})\)	\(q+(-1.32420 - 0.496490i) q^{2} +(1.50700 + 1.31490i) q^{4} +(-1.75903 - 1.75903i) q^{5} -4.05756 q^{7} +(-1.34273 - 2.48940i) q^{8} +(1.45597 + 3.20265i) q^{10} +(1.00080 - 1.00080i) q^{11} +(4.19432 + 4.19432i) q^{13} +(5.37300 + 2.01453i) q^{14} +(0.542074 + 3.96310i) q^{16} +5.82075i q^{17} +(0.687187 - 0.687187i) q^{19} +(-0.337903 - 4.96381i) q^{20} +(-1.82215 + 0.828373i) q^{22} +3.75624i q^{23} +1.18841i q^{25} +(-3.47167 - 7.63654i) q^{26} +(-6.11472 - 5.33528i) q^{28} +(-6.60208 + 6.60208i) q^{29} +0.621706i q^{31} +(1.24982 - 5.51706i) q^{32} +(2.88994 - 7.70782i) q^{34} +(7.13738 + 7.13738i) q^{35} +(-3.34776 + 3.34776i) q^{37} +(-1.25115 + 0.568790i) q^{38} +(-2.01703 + 6.74083i) q^{40} +7.83525 q^{41} +(1.15934 + 1.15934i) q^{43} +(2.82416 - 0.192250i) q^{44} +(1.86493 - 4.97400i) q^{46} -10.8970 q^{47} +9.46376 q^{49} +(0.590031 - 1.57368i) q^{50} +(0.805711 + 11.8359i) q^{52} +(5.59972 + 5.59972i) q^{53} -3.52090 q^{55} +(5.44818 + 10.1009i) q^{56} +(12.0203 - 5.46459i) q^{58} +(-3.51517 + 3.51517i) q^{59} +(1.61583 + 1.61583i) q^{61} +(0.308671 - 0.823262i) q^{62} +(-4.39418 + 6.68515i) q^{64} -14.7559i q^{65} +(-3.84645 + 3.84645i) q^{67} +(-7.65371 + 8.77185i) q^{68} +(-5.90766 - 12.9949i) q^{70} -5.98242i q^{71} -5.11508i q^{73} +(6.09523 - 2.77097i) q^{74} +(1.93917 - 0.132006i) q^{76} +(-4.06082 + 4.06082i) q^{77} -12.8799i q^{79} +(6.01770 - 7.92476i) q^{80} +(-10.3754 - 3.89012i) q^{82} +(7.07602 + 7.07602i) q^{83} +(10.2389 - 10.2389i) q^{85} +(-0.959596 - 2.11080i) q^{86} +(-3.83520 - 1.14759i) q^{88} +2.89496 q^{89} +(-17.0187 - 17.0187i) q^{91} +(-4.93907 + 5.66063i) q^{92} +(14.4298 + 5.41026i) q^{94} -2.41757 q^{95} -8.67960 q^{97} +(-12.5319 - 4.69866i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Introduction

L-functions

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