LMFDB - Embedded newform 432.2.l.b.107.2

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			107.2
Character	$\chi$	$=$	432.107
Dual form			432.2.l.b.323.2

$q$-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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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	−0.980946	−	0.194282i	$-0.937762\pi$
$5$	−1.75903	+	1.75903i	−0.786664	+	0.786664i	0.194282	+	0.980946i	$0.437762\pi$
$6$		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	0.841700	−	0.539946i	$-0.181555\pi$
$11$	1.00080	+	1.00080i	0.301754	+	0.301754i	−0.539946	+	0.841700i	$0.681555\pi$
$12$		0			0
$13$	4.19432	−	4.19432i	1.16330	−	1.16330i	0.179546	−	0.983750i	$-0.442537\pi$
$13$	4.19432	−	4.19432i	1.16330	−	1.16330i	0.983750	−	0.179546i	$-0.0574627\pi$
$14$	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	$-0.750556\pi$
$17$		−	5.82075i		−	1.41174i	0.708341	−	0.705870i	$-0.249444\pi$
$18$		0			0
$19$	0.687187	+	0.687187i	0.157652	+	0.157652i	0.781525	−	0.623874i	$-0.214442\pi$
$19$	0.687187	+	0.687187i	0.157652	+	0.157652i	−0.623874	+	0.781525i	$0.714442\pi$
$20$	−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	$-0.871917\pi$
$23$		−	3.75624i		−	0.783229i	0.920129	−	0.391615i	$-0.128083\pi$
$24$		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	−0.965473	−	0.260501i	$-0.916112\pi$
$29$	−6.60208	−	6.60208i	−1.22597	−	1.22597i	−0.260501	−	0.965473i	$-0.583888\pi$
$30$		0			0
$31$		−	0.621706i		−	0.111662i	−0.998440	−	0.0558309i	$-0.982219\pi$
$31$		−	0.621706i		−	0.111662i	0.998440	−	0.0558309i	$-0.0177808\pi$
$32$	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	0.376178	−	0.926547i	$-0.377238\pi$
$37$	−3.34776	−	3.34776i	−0.550369	−	0.550369i	−0.926547	+	0.376178i	$0.877238\pi$
$38$	−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	−0.613160	−	0.789958i	$-0.710102\pi$
$43$	1.15934	−	1.15934i	0.176798	−	0.176798i	0.789958	+	0.613160i	$0.210102\pi$
$44$	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	−0.208781	−	0.977962i	$-0.566950\pi$
$53$	5.59972	−	5.59972i	0.769181	−	0.769181i	0.977962	+	0.208781i	$0.0669496\pi$
$54$		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	0.440242	−	0.897879i	$-0.354892\pi$
$59$	−3.51517	−	3.51517i	−0.457636	−	0.457636i	−0.897879	+	0.440242i	$0.854892\pi$
$60$		0			0
$61$	1.61583	−	1.61583i	0.206885	−	0.206885i	−0.596057	−	0.802942i	$-0.703267\pi$
$61$	1.61583	−	1.61583i	0.206885	−	0.206885i	0.802942	+	0.596057i	$0.203267\pi$
$62$	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	0.431969	−	0.901888i	$-0.357819\pi$
$67$	−3.84645	−	3.84645i	−0.469919	−	0.469919i	−0.901888	+	0.431969i	$0.857819\pi$
$68$	−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	$0.115516\pi$
$71$			5.98242i			0.709982i	−0.934870	+	0.354991i	$0.884484\pi$
$72$		0			0
$73$			5.11508i			0.598674i	0.954147	+	0.299337i	$0.0967655\pi$
$73$			5.11508i			0.598674i	−0.954147	+	0.299337i	$0.903234\pi$
$74$	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	$0.257954\pi$
$79$			12.8799i			1.44911i	−0.689219	+	0.724553i	$0.742046\pi$
$80$	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	−0.202573	−	0.979267i	$-0.564930\pi$
$83$	7.07602	−	7.07602i	0.776694	−	0.776694i	0.979267	+	0.202573i	$0.0649304\pi$
$84$		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	−0.463580	−	0.886055i	$-0.653435\pi$
$101$	4.24583	−	4.24583i	0.422476	−	0.422476i	0.886055	+	0.463580i	$0.153435\pi$
$102$		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	0.237978	−	0.971270i	$-0.423515\pi$
$107$	−7.58523	−	7.58523i	−0.733292	−	0.733292i	−0.971270	+	0.237978i	$0.923515\pi$
$108$		0			0
$109$	3.71822	−	3.71822i	0.356141	−	0.356141i	−0.506247	−	0.862388i	$-0.668968\pi$
$109$	3.71822	−	3.71822i	0.356141	−	0.356141i	0.862388	+	0.506247i	$0.168968\pi$
$110$	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	$0.100354\pi$
$113$			6.59228i			0.620150i	−0.950712	+	0.310075i	$0.899646\pi$
$114$		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	$-0.914233\pi$
$127$		−	5.99979i		−	0.532395i	0.963918	−	0.266198i	$-0.0857674\pi$
$128$	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	−0.889795	−	0.456361i	$-0.849152\pi$
$131$	−4.96087	+	4.96087i	−0.433433	+	0.433433i	0.456361	+	0.889795i	$0.349152\pi$
$132$		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	−0.816998	−	0.576640i	$-0.804364\pi$
$139$	−2.83379	+	2.83379i	−0.240359	+	0.240359i	0.576640	+	0.816998i	$0.304364\pi$
$140$	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	−0.260534	+	0.965465i	$0.583899\pi$
$149$	−14.9652	+	14.9652i	−1.22600	+	1.22600i	−0.965465	+	0.260534i	$0.916101\pi$
$150$		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	−0.694479	−	0.719513i	$-0.744365\pi$
$157$	0.313683	−	0.313683i	0.0250347	−	0.0250347i	0.719513	+	0.694479i	$0.244365\pi$
$158$	−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	−0.965814	−	0.259236i	$-0.916529\pi$
$163$	−15.6404	−	15.6404i	−1.22505	−	1.22505i	−0.259236	−	0.965814i	$-0.583471\pi$
$164$	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	$0.133110\pi$
$167$			10.4958i			0.812193i	−0.913830	+	0.406096i	$0.866890\pi$
$168$		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	0.878792	−	0.477206i	$-0.158350\pi$
$173$	5.28204	+	5.28204i	0.401586	+	0.401586i	−0.477206	+	0.878792i	$0.658350\pi$
$174$		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	0.0191517	−	0.999817i	$-0.493903\pi$
$179$	13.6329	−	13.6329i	1.01897	−	1.01897i	0.999817	−	0.0191517i	$-0.00609655\pi$
$180$		0			0
$181$	9.09330	+	9.09330i	0.675900	+	0.675900i	0.959070	−	0.283170i	$-0.0913861\pi$
$181$	9.09330	+	9.09330i	0.675900	+	0.675900i	−0.283170	+	0.959070i	$0.591386\pi$
$182$	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	−0.377231	−	0.926119i	$-0.623124\pi$
$197$	7.70402	−	7.70402i	0.548889	−	0.548889i	0.926119	+	0.377231i	$0.123124\pi$
$198$		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	0.544191	−	0.838962i	$-0.316837\pi$
$211$	−4.28179	−	4.28179i	−0.294771	−	0.294771i	−0.838962	+	0.544191i	$0.816837\pi$
$212$	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	$-0.849806\pi$
$223$		−	13.5753i		−	0.909068i	0.890729	−	0.454534i	$-0.150194\pi$
$224$	−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	−0.433560	−	0.901125i	$-0.642743\pi$
$227$	7.04458	−	7.04458i	0.467565	−	0.467565i	0.901125	+	0.433560i	$0.142743\pi$
$228$		0			0
$229$	−5.38011	−	5.38011i	−0.355528	−	0.355528i	0.506634	−	0.862162i	$-0.330890\pi$
$229$	−5.38011	−	5.38011i	−0.355528	−	0.355528i	−0.862162	+	0.506634i	$0.830890\pi$
$230$	−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	0.822715	−	0.568454i	$-0.192458\pi$
$251$	4.02824	+	4.02824i	0.254260	+	0.254260i	−0.568454	+	0.822715i	$0.692458\pi$
$252$		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	$0.0739465\pi$
$257$			7.38160i			0.460452i	−0.973137	+	0.230226i	$0.926053\pi$
$258$		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	$0.000165712\pi$
$263$			0.0168854i			0.00104120i	−1.00000		0.000520598i	$0.999834\pi$
$264$		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	0.902659	−	0.430356i	$-0.141612\pi$
$269$	7.74635	+	7.74635i	0.472303	+	0.472303i	−0.430356	+	0.902659i	$0.641612\pi$
$270$		0			0
$271$		−	6.40104i		−	0.388836i	−0.980919	−	0.194418i	$-0.937718\pi$
$271$		−	6.40104i		−	0.388836i	0.980919	−	0.194418i	$-0.0622818\pi$
$272$	−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	−0.999274	−	0.0380878i	$-0.987873\pi$
$277$	−17.2651	−	17.2651i	−1.03736	−	1.03736i	−0.0380878	−	0.999274i	$-0.512127\pi$
$278$	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	−0.815865	−	0.578242i	$-0.803739\pi$
$283$	−3.99744	+	3.99744i	−0.237623	+	0.237623i	0.578242	+	0.815865i	$0.303739\pi$
$284$	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	−0.629601	−	0.776919i	$-0.716782\pi$
$293$	2.52168	−	2.52168i	0.147318	−	0.147318i	0.776919	+	0.629601i	$0.216782\pi$
$294$		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	0.979713	+	0.200406i	$0.0642262\pi$
$307$	20.6774	+	20.6774i	1.18012	+	1.18012i	0.200406	+	0.979713i	$0.435774\pi$
$308$	−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	$-0.707919\pi$
$311$		−	28.0098i		−	1.58829i	0.607728	−	0.794145i	$-0.292081\pi$
$312$		0			0
$313$			31.7816i			1.79640i	0.439588	+	0.898200i	$0.355125\pi$
$313$			31.7816i			1.79640i	−0.439588	+	0.898200i	$0.644875\pi$
$314$	−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	0.933871	−	0.357610i	$-0.116408\pi$
$317$	10.2600	+	10.2600i	0.576261	+	0.576261i	−0.357610	+	0.933871i	$0.616408\pi$
$318$		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	−0.455658	−	0.890155i	$-0.650596\pi$
$331$	7.90498	−	7.90498i	0.434497	−	0.434497i	0.890155	+	0.455658i	$0.150596\pi$
$332$	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	0.880465	−	0.474111i	$-0.157230\pi$
$347$	7.56955	+	7.56955i	0.406354	+	0.406354i	−0.474111	+	0.880465i	$0.657230\pi$
$348$		0			0
$349$	13.7100	−	13.7100i	0.733881	−	0.733881i	−0.237505	−	0.971386i	$-0.576330\pi$
$349$	13.7100	−	13.7100i	0.733881	−	0.733881i	0.971386	+	0.237505i	$0.0763297\pi$
$350$	−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	$-0.813127\pi$
$353$		−	20.8149i		−	1.10786i	0.832562	−	0.553932i	$-0.186873\pi$
$354$		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	$0.321789\pi$
$359$			32.1091i			1.69465i	−0.531073	+	0.847326i	$0.678211\pi$
$360$		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	$0.108148\pi$
$367$			12.7686i			0.666516i	−0.942836	+	0.333258i	$0.891852\pi$
$368$	−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	0.830669	−	0.556766i	$-0.187958\pi$
$373$	5.28996	+	5.28996i	0.273903	+	0.273903i	−0.556766	+	0.830669i	$0.687958\pi$
$374$	−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	−0.123848	−	0.992301i	$-0.539524\pi$
$379$	16.9070	−	16.9070i	0.868453	−	0.868453i	0.992301	+	0.123848i	$0.0395237\pi$
$380$	−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	−0.305934	−	0.952053i	$-0.598969\pi$
$389$	12.7435	−	12.7435i	0.646119	−	0.646119i	0.952053	+	0.305934i	$0.0989687\pi$
$390$		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	−0.982724	−	0.185078i	$-0.940746\pi$
$397$	−15.8930	+	15.8930i	−0.797646	+	0.797646i	0.185078	+	0.982724i	$0.440746\pi$
$398$	−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	$-0.936905\pi$
$401$		−	7.88676i		−	0.393846i	0.980419	−	0.196923i	$-0.0630949\pi$
$402$		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	$0.380525\pi$
$409$			37.6316i			1.86077i	−0.366590	+	0.930383i	$0.619475\pi$
$410$	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	−0.788100	−	0.615547i	$-0.788935\pi$
$419$	−3.53206	+	3.53206i	−0.172552	+	0.172552i	0.615547	+	0.788100i	$0.288935\pi$
$420$		0			0
$421$	−4.65377	−	4.65377i	−0.226811	−	0.226811i	0.584548	−	0.811359i	$-0.301272\pi$
$421$	−4.65377	−	4.65377i	−0.226811	−	0.226811i	−0.811359	+	0.584548i	$0.801272\pi$
$422$	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	0.0812713	−	0.996692i	$-0.474102\pi$
$443$	−19.2674	−	19.2674i	−0.915421	−	0.915421i	−0.996692	+	0.0812713i	$0.974102\pi$
$444$		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	$-0.895535\pi$
$449$		−	13.6600i		−	0.644655i	0.946628	−	0.322328i	$-0.104465\pi$
$450$		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	$-0.902199\pi$
$457$		−	12.9308i		−	0.604877i	0.953169	−	0.302439i	$-0.0978007\pi$
$458$	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	0.338421	−	0.940995i	$-0.390107\pi$
$461$	−12.9378	−	12.9378i	−0.602573	−	0.602573i	−0.940995	+	0.338421i	$0.890107\pi$
$462$		0			0
$463$		−	11.3129i		−	0.525755i	−0.964829	−	0.262878i	$-0.915328\pi$
$463$		−	11.3129i		−	0.525755i	0.964829	−	0.262878i	$-0.0846715\pi$
$464$	−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	−0.213679	−	0.976904i	$-0.568545\pi$
$467$	16.4934	−	16.4934i	0.763225	−	0.763225i	0.976904	+	0.213679i	$0.0685445\pi$
$468$		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	0.428062	−	0.903749i	$-0.359196\pi$
$491$	−10.5405	−	10.5405i	−0.475687	−	0.475687i	−0.903749	+	0.428062i	$0.859196\pi$
$492$		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	0.942575	−	0.333994i	$-0.108396\pi$
$499$	13.5947	+	13.5947i	0.608582	+	0.608582i	−0.333994	+	0.942575i	$0.608396\pi$
$500$	−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	$0.162580\pi$
$503$			21.9271i			0.977680i	−0.872373	+	0.488840i	$0.837420\pi$
$504$		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	0.598286	−	0.801283i	$-0.295849\pi$
$509$	−4.57982	−	4.57982i	−0.202997	−	0.202997i	−0.801283	+	0.598286i	$0.795849\pi$
$510$		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	−0.623615	−	0.781731i	$-0.714337\pi$
$523$	3.61599	−	3.61599i	0.158116	−	0.158116i	0.781731	+	0.623615i	$0.214337\pi$
$524$	−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	−0.524671	−	0.851305i	$-0.675812\pi$
$541$	7.59731	−	7.59731i	0.326634	−	0.326634i	0.851305	+	0.524671i	$0.175812\pi$
$542$	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	0.922800	−	0.385279i	$-0.125895\pi$
$547$	12.5715	+	12.5715i	0.537521	+	0.537521i	−0.385279	+	0.922800i	$0.625895\pi$
$548$	−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	0.742296	−	0.670072i	$-0.233737\pi$
$557$	1.70457	+	1.70457i	0.0722248	+	0.0722248i	−0.670072	+	0.742296i	$0.733737\pi$
$558$		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	−0.270660	+	0.962675i	$0.587242\pi$
$563$	−29.2641	+	29.2641i	−1.23333	+	1.23333i	−0.962675	+	0.270660i	$0.912758\pi$
$564$		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	−0.0797504	−	0.996815i	$-0.525412\pi$
$571$	21.9138	−	21.9138i	0.917064	−	0.917064i	0.996815	+	0.0797504i	$0.0254123\pi$
$572$	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	0.941208	+	0.337829i	$0.109693\pi$
$587$	30.9886	+	30.9886i	1.27904	+	1.27904i	0.337829	+	0.941208i	$0.390307\pi$
$588$		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	$0.00910006\pi$
$593$			1.39217i			0.0571696i	−0.999591	+	0.0285848i	$0.990900\pi$
$594$		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	$-0.983536\pi$
$599$		−	2.53068i		−	0.103401i	0.998663	−	0.0517004i	$-0.0164641\pi$
$600$		0			0
$601$			31.6102i			1.28941i	0.764432	+	0.644704i	$0.223019\pi$
$601$			31.6102i			1.28941i	−0.764432	+	0.644704i	$0.776981\pi$
$602$	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	$0.112430\pi$
$607$			17.0447i			0.691823i	−0.938267	+	0.345912i	$0.887570\pi$
$608$	−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	0.738205	−	0.674577i	$-0.235674\pi$
$613$	1.57535	+	1.57535i	0.0636279	+	0.0636279i	−0.674577	+	0.738205i	$0.735674\pi$
$614$	−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	−0.936264	−	0.351297i	$-0.885741\pi$
$619$	−14.5538	+	14.5538i	−0.584967	+	0.584967i	0.351297	+	0.936264i	$0.385741\pi$
$620$	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	$0.0956938\pi$
$641$			14.9945i			0.592246i	−0.955150	+	0.296123i	$0.904306\pi$
$642$		0			0
$643$	1.20351	+	1.20351i	0.0474620	+	0.0474620i	0.730439	−	0.682977i	$-0.239315\pi$
$643$	1.20351	+	1.20351i	0.0474620	+	0.0474620i	−0.682977	+	0.730439i	$0.739315\pi$
$644$	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	$0.00852640\pi$
$647$			1.36253i			0.0535666i	−0.999641	+	0.0267833i	$0.991474\pi$
$648$		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	0.999244	−	0.0388753i	$-0.0123775\pi$
$653$	24.5411	+	24.5411i	0.960369	+	0.960369i	−0.0388753	+	0.999244i	$0.512377\pi$
$654$		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	−0.441563	−	0.897230i	$-0.645576\pi$
$659$	11.6974	−	11.6974i	0.455667	−	0.455667i	0.897230	+	0.441563i	$0.145576\pi$
$660$		0			0
$661$	18.9436	+	18.9436i	0.736822	+	0.736822i	0.971962	−	0.235140i	$-0.0755547\pi$
$661$	18.9436	+	18.9436i	0.736822	+	0.736822i	−0.235140	+	0.971962i	$0.575555\pi$
$662$	−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	−0.702959	−	0.711230i	$-0.748138\pi$
$677$	0.215189	−	0.215189i	0.00827040	−	0.00827040i	0.711230	+	0.702959i	$0.248138\pi$
$678$		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	0.688116	−	0.725601i	$-0.258438\pi$
$683$	−0.979632	−	0.979632i	−0.0374846	−	0.0374846i	−0.725601	+	0.688116i	$0.758438\pi$
$684$		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	−0.997528	−	0.0702745i	$-0.977612\pi$
$691$	−28.0692	−	28.0692i	−1.06780	−	1.06780i	−0.0702745	−	0.997528i	$-0.522388\pi$
$692$	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	0.907551	−	0.419942i	$-0.137950\pi$
$701$	12.9101	+	12.9101i	0.487609	+	0.487609i	−0.419942	+	0.907551i	$0.637950\pi$
$702$		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	0.967620	−	0.252410i	$-0.0812231\pi$
$709$	19.0440	+	19.0440i	0.715211	+	0.715211i	−0.252410	+	0.967620i	$0.581223\pi$
$710$	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	−0.254033	−	0.967196i	$-0.581757\pi$
$733$	19.3081	−	19.3081i	0.713162	−	0.713162i	0.967196	+	0.254033i	$0.0817572\pi$
$734$	−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	0.875120	−	0.483906i	$-0.160782\pi$
$739$	10.6350	+	10.6350i	0.391215	+	0.391215i	−0.483906	+	0.875120i	$0.660782\pi$
$740$	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	$-0.672585\pi$
$743$		−	46.6974i		−	1.71316i	0.516014	−	0.856580i	$-0.327415\pi$
$744$		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	$-0.832635\pi$
$751$		−	27.5084i		−	1.00380i	0.864927	−	0.501898i	$-0.167365\pi$
$752$	−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	0.827627	−	0.561279i	$-0.189691\pi$
$757$	7.32819	+	7.32819i	0.266347	+	0.266347i	−0.561279	+	0.827627i	$0.689691\pi$
$758$	−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	−0.967201	−	0.254014i	$-0.918249\pi$
$773$	−19.8286	+	19.8286i	−0.713186	+	0.713186i	0.254014	+	0.967201i	$0.418249\pi$
$774$		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	0.806720	−	0.590934i	$-0.201241\pi$
$787$	6.05353	+	6.05353i	0.215785	+	0.215785i	−0.590934	+	0.806720i	$0.701241\pi$
$788$	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	0.996442	−	0.0842867i	$-0.0268612\pi$
$797$	25.7512	+	25.7512i	0.912155	+	0.912155i	−0.0842867	+	0.996442i	$0.526861\pi$
$798$		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	−0.951141	−	0.308758i	$-0.900087\pi$
$811$	−18.2938	+	18.2938i	−0.642382	+	0.642382i	0.308758	+	0.951141i	$0.400087\pi$
$812$	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	−0.826631	−	0.562744i	$-0.809746\pi$
$821$	−7.56118	+	7.56118i	−0.263887	+	0.263887i	0.562744	+	0.826631i	$0.309746\pi$
$822$		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	0.461272	−	0.887259i	$-0.347393\pi$
$827$	−12.2504	−	12.2504i	−0.425987	−	0.425987i	−0.887259	+	0.461272i	$0.847393\pi$
$828$		0			0
$829$	−7.58610	+	7.58610i	−0.263476	+	0.263476i	−0.826465	−	0.562988i	$-0.809652\pi$
$829$	−7.58610	+	7.58610i	−0.263476	+	0.263476i	0.562988	+	0.826465i	$0.309652\pi$
$830$	−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	$0.0592916\pi$
$839$			10.7285i			0.370389i	−0.982702	+	0.185195i	$0.940708\pi$
$840$		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	0.998044	−	0.0625097i	$-0.0199104\pi$
$853$	27.3234	+	27.3234i	0.935535	+	0.935535i	−0.0625097	+	0.998044i	$0.519910\pi$
$854$	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	−0.233399	−	0.972381i	$-0.574985\pi$
$859$	21.6586	−	21.6586i	0.738982	−	0.738982i	0.972381	+	0.233399i	$0.0749847\pi$
$860$	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	−0.694145	−	0.719836i	$-0.744217\pi$
$877$	0.760817	−	0.760817i	0.0256910	−	0.0256910i	0.719836	+	0.694145i	$0.244217\pi$
$878$	−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	$0.122027\pi$
$881$			22.2041i			0.748076i	−0.927413	+	0.374038i	$0.877973\pi$
$882$		0			0
$883$	8.67095	+	8.67095i	0.291801	+	0.291801i	0.837791	−	0.545991i	$-0.183847\pi$
$883$	8.67095	+	8.67095i	0.291801	+	0.291801i	−0.545991	+	0.837791i	$0.683847\pi$
$884$	−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	$0.0839027\pi$
$887$			15.5195i			0.521093i	−0.965461	+	0.260546i	$0.916097\pi$
$888$		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	−0.959453	−	0.281868i	$-0.909046\pi$
$907$	−20.4064	+	20.4064i	−0.677585	+	0.677585i	0.281868	+	0.959453i	$0.409046\pi$
$908$	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	$0.00286569\pi$
$929$			0.548796i			0.0180054i	−0.999959	+	0.00900270i	$0.997134\pi$
$930$		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	$0.0138695\pi$
$937$			2.66669i			0.0871171i	−0.999051	+	0.0435586i	$0.986130\pi$
$938$	−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	0.250611	−	0.968088i	$-0.419369\pi$
$941$	−22.0091	−	22.0091i	−0.717477	−	0.717477i	−0.968088	+	0.250611i	$0.919369\pi$
$942$		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	−0.959946	−	0.280185i	$-0.909604\pi$
$947$	−20.9185	+	20.9185i	−0.679760	+	0.679760i	0.280185	+	0.959946i	$0.409604\pi$
$948$		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	0.549361	−	0.835585i	$-0.314871\pi$
$971$	−8.91899	−	8.91899i	−0.286224	−	0.286224i	−0.835585	+	0.549361i	$0.814871\pi$
$972$		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	$0.322589\pi$
$977$			53.0530i			1.69732i	−0.528942	+	0.848658i	$0.677411\pi$
$978$		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	$0.103280\pi$
$983$			19.9905i			0.637599i	−0.947822	+	0.318800i	$0.896720\pi$
$984$		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	$-0.756324\pi$
$991$		−	43.6264i		−	1.38584i	0.721015	−	0.692919i	$-0.243676\pi$
$992$	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	0.827800	−	0.561023i	$-0.189592\pi$
$997$	8.42356	+	8.42356i	0.266777	+	0.266777i	−0.561023	+	0.827800i	$0.689592\pi$
$998$	−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.107.2	✓	32
3.2	odd	2	inner	432.2.l.b.107.15	yes	32
4.3	odd	2		1728.2.l.b.1295.4		32
12.11	even	2		1728.2.l.b.1295.13		32
16.3	odd	4	inner	432.2.l.b.323.15	yes	32
16.13	even	4		1728.2.l.b.431.13		32
48.29	odd	4		1728.2.l.b.431.4		32
48.35	even	4	inner	432.2.l.b.323.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.2	✓	32	1.1	even	1	trivial
432.2.l.b.107.15	yes	32	3.2	odd	2	inner
432.2.l.b.323.2	yes	32	48.35	even	4	inner
432.2.l.b.323.15	yes	32	16.3	odd	4	inner
1728.2.l.b.431.4		32	48.29	odd	4
1728.2.l.b.431.13		32	16.13	even	4
1728.2.l.b.1295.4		32	4.3	odd	2
1728.2.l.b.1295.13		32	12.11	even	2

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

Modular forms

Varieties

Fields

Representations

Groups

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