LMFDB - Embedded newform 864.2.bi.a.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.5
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59297 - 0.680026i) q^{3} +(-0.802661 + 0.956575i) q^{5} +(-1.53564 + 4.21915i) q^{7} +(2.07513 + 2.16653i) q^{9} +O(q^{10})$	\(q+(-1.59297 - 0.680026i) q^{3} +(-0.802661 + 0.956575i) q^{5} +(-1.53564 + 4.21915i) q^{7} +(2.07513 + 2.16653i) q^{9} +(-2.65692 + 2.22942i) q^{11} +(1.13739 - 6.45047i) q^{13} +(1.92911 - 0.977968i) q^{15} +(-4.79072 - 2.76592i) q^{17} +(0.384700 - 0.222107i) q^{19} +(5.31537 - 5.67671i) q^{21} +(5.25020 - 1.91092i) q^{23} +(0.597471 + 3.38843i) q^{25} +(-1.83233 - 4.86236i) q^{27} +(0.291217 - 0.0513494i) q^{29} +(-1.11024 - 3.05035i) q^{31} +(5.74847 - 1.74464i) q^{33} +(-2.80333 - 4.85551i) q^{35} +(4.64969 - 8.05350i) q^{37} +(-6.19832 + 9.50198i) q^{39} +(-0.506402 - 0.0892924i) q^{41} +(-2.67021 - 3.18223i) q^{43} +(-3.73807 + 0.246030i) q^{45} +(-12.6155 - 4.59165i) q^{47} +(-10.0807 - 8.45871i) q^{49} +(5.75059 + 7.66386i) q^{51} +5.35987i q^{53} -4.33101i q^{55} +(-0.763855 + 0.0922041i) q^{57} +(-6.85558 - 5.75251i) q^{59} +(-4.56402 - 1.66117i) q^{61} +(-12.3276 + 5.42827i) q^{63} +(5.25742 + 6.26555i) q^{65} +(-1.71380 - 0.302189i) q^{67} +(-9.66291 - 0.526231i) q^{69} +(2.64712 - 4.58494i) q^{71} +(5.95564 + 10.3155i) q^{73} +(1.35246 - 5.80397i) q^{75} +(-5.32617 - 14.6335i) q^{77} +(10.1272 - 1.78569i) q^{79} +(-0.387669 + 8.99165i) q^{81} +(-0.824241 - 4.67450i) q^{83} +(6.49114 - 2.36258i) q^{85} +(-0.498820 - 0.116237i) q^{87} +(-11.8169 + 6.82247i) q^{89} +(25.4689 + 14.7045i) q^{91} +(-0.305739 + 5.61412i) q^{93} +(-0.0963222 + 0.546271i) q^{95} +(9.23564 - 7.74962i) q^{97} +(-10.3436 - 1.12995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.59297	−	0.680026i	−0.919704	−	0.392613i
$3$	−1.59297	−	0.680026i	−0.919704	−	0.392613i
$4$		0			0
$5$	−0.802661	+	0.956575i	−0.358961	+	0.427793i	−0.915057	−	0.403325i	$-0.867854\pi$
$5$	−0.802661	+	0.956575i	−0.358961	+	0.427793i	0.556096	+	0.831118i	$0.312299\pi$
$6$		0			0
$7$	−1.53564	+	4.21915i	−0.580419	+	1.59469i	0.207048	+	0.978331i	$0.433615\pi$
$7$	−1.53564	+	4.21915i	−0.580419	+	1.59469i	−0.787467	+	0.616357i	$0.788608\pi$
$8$		0			0
$9$	2.07513	+	2.16653i	0.691710	+	0.722175i
$10$		0			0
$11$	−2.65692	+	2.22942i	−0.801092	+	0.672196i	−0.948464	−	0.316885i	$-0.897363\pi$
$11$	−2.65692	+	2.22942i	−0.801092	+	0.672196i	0.147372	+	0.989081i	$0.452919\pi$
$12$		0			0
$13$	1.13739	−	6.45047i	0.315456	−	1.78904i	−0.254195	−	0.967153i	$-0.581811\pi$
$13$	1.13739	−	6.45047i	0.315456	−	1.78904i	0.569651	−	0.821887i	$-0.307078\pi$
$14$		0			0
$15$	1.92911	−	0.977968i	0.498095	−	0.252510i
$16$		0			0
$17$	−4.79072	−	2.76592i	−1.16192	−	0.670835i	−0.210157	−	0.977668i	$-0.567397\pi$
$17$	−4.79072	−	2.76592i	−1.16192	−	0.670835i	−0.951763	+	0.306833i	$0.900731\pi$
$18$		0			0
$19$	0.384700	−	0.222107i	0.0882562	−	0.0509547i	−0.455222	−	0.890378i	$-0.650440\pi$
$19$	0.384700	−	0.222107i	0.0882562	−	0.0509547i	0.543479	+	0.839423i	$0.317107\pi$
$20$		0			0
$21$	5.31537	−	5.67671i	1.15991	−	1.23876i
$22$		0			0
$23$	5.25020	−	1.91092i	1.09474	−	0.398454i	0.269367	−	0.963038i	$-0.413185\pi$
$23$	5.25020	−	1.91092i	1.09474	−	0.398454i	0.825376	+	0.564584i	$0.190963\pi$
$24$		0			0
$25$	0.597471	+	3.38843i	0.119494	+	0.677686i
$26$		0			0
$27$	−1.83233	−	4.86236i	−0.352633	−	0.935762i
$28$		0			0
$29$	0.291217	−	0.0513494i	0.0540776	−	0.00953535i	−0.146544	−	0.989204i	$-0.546815\pi$
$29$	0.291217	−	0.0513494i	0.0540776	−	0.00953535i	0.200622	+	0.979669i	$0.435704\pi$
$30$		0			0
$31$	−1.11024	−	3.05035i	−0.199404	−	0.547859i	0.799177	−	0.601095i	$-0.205269\pi$
$31$	−1.11024	−	3.05035i	−0.199404	−	0.547859i	−0.998582	+	0.0532358i	$0.983047\pi$
$32$		0			0
$33$	5.74847	−	1.74464i	1.00068	−	0.303702i
$34$		0			0
$35$	−2.80333	−	4.85551i	−0.473849	−	0.820730i
$36$		0			0
$37$	4.64969	−	8.05350i	0.764405	−	1.32399i	−0.176156	−	0.984362i	$-0.556366\pi$
$37$	4.64969	−	8.05350i	0.764405	−	1.32399i	0.940561	−	0.339626i	$-0.110300\pi$
$38$		0			0
$39$	−6.19832	+	9.50198i	−0.992526	+	1.52153i
$40$		0			0
$41$	−0.506402	−	0.0892924i	−0.0790868	−	0.0139451i	0.133965	−	0.990986i	$-0.457229\pi$
$41$	−0.506402	−	0.0892924i	−0.0790868	−	0.0139451i	−0.213052	+	0.977041i	$0.568340\pi$
$42$		0			0
$43$	−2.67021	−	3.18223i	−0.407203	−	0.485286i	0.522999	−	0.852333i	$-0.324813\pi$
$43$	−2.67021	−	3.18223i	−0.407203	−	0.485286i	−0.930202	+	0.367047i	$0.880369\pi$
$44$		0			0
$45$	−3.73807	+	0.246030i	−0.557239	+	0.0366760i
$46$		0			0
$47$	−12.6155	−	4.59165i	−1.84015	−	0.669761i	−0.989595	−	0.143882i	$-0.954041\pi$
$47$	−12.6155	−	4.59165i	−1.84015	−	0.669761i	−0.850559	−	0.525879i	$-0.823736\pi$
$48$		0			0
$49$	−10.0807	−	8.45871i	−1.44010	−	1.20839i
$50$		0			0
$51$	5.75059	+	7.66386i	0.805244	+	1.07315i
$52$		0			0
$53$			5.35987i			0.736235i	0.929779	+	0.368117i	$0.119998\pi$
$53$			5.35987i			0.736235i	−0.929779	+	0.368117i	$0.880002\pi$
$54$		0			0
$55$		−	4.33101i		−	0.583994i
$56$		0			0
$57$	−0.763855	+	0.0922041i	−0.101175	+	0.0122127i
$58$		0			0
$59$	−6.85558	−	5.75251i	−0.892520	−	0.748913i	0.0761941	−	0.997093i	$-0.475723\pi$
$59$	−6.85558	−	5.75251i	−0.892520	−	0.748913i	−0.968714	+	0.248180i	$0.920168\pi$
$60$		0			0
$61$	−4.56402	−	1.66117i	−0.584363	−	0.212691i	0.0328851	−	0.999459i	$-0.489530\pi$
$61$	−4.56402	−	1.66117i	−0.584363	−	0.212691i	−0.617248	+	0.786768i	$0.711753\pi$
$62$		0			0
$63$	−12.3276	+	5.42827i	−1.55313	+	0.683898i
$64$		0			0
$65$	5.25742	+	6.26555i	0.652102	+	0.777145i
$66$		0			0
$67$	−1.71380	−	0.302189i	−0.209374	−	0.0369182i	0.0679775	−	0.997687i	$-0.478345\pi$
$67$	−1.71380	−	0.302189i	−0.209374	−	0.0369182i	−0.277351	+	0.960769i	$0.589457\pi$
$68$		0			0
$69$	−9.66291	−	0.526231i	−1.16328	−	0.0633508i
$70$		0			0
$71$	2.64712	−	4.58494i	0.314155	−	0.544132i	−0.665103	−	0.746752i	$-0.731612\pi$
$71$	2.64712	−	4.58494i	0.314155	−	0.544132i	0.979257	+	0.202620i	$0.0649456\pi$
$72$		0			0
$73$	5.95564	+	10.3155i	0.697055	+	1.20734i	0.969483	+	0.245159i	$0.0788402\pi$
$73$	5.95564	+	10.3155i	0.697055	+	1.20734i	−0.272427	+	0.962176i	$0.587826\pi$
$74$		0			0
$75$	1.35246	−	5.80397i	0.156169	−	0.670185i
$76$		0			0
$77$	−5.32617	−	14.6335i	−0.606974	−	1.66765i
$78$		0			0
$79$	10.1272	−	1.78569i	1.13939	−	0.200906i	0.428054	−	0.903753i	$-0.359199\pi$
$79$	10.1272	−	1.78569i	1.13939	−	0.200906i	0.711341	+	0.702847i	$0.248088\pi$
$80$		0			0
$81$	−0.387669	+	8.99165i	−0.0430744	+	0.999072i
$82$		0			0
$83$	−0.824241	−	4.67450i	−0.0904722	−	0.513093i	−0.996041	−	0.0888942i	$-0.971667\pi$
$83$	−0.824241	−	4.67450i	−0.0904722	−	0.513093i	0.905569	−	0.424199i	$-0.139444\pi$
$84$		0			0
$85$	6.49114	−	2.36258i	0.704063	−	0.256258i
$86$		0			0
$87$	−0.498820	−	0.116237i	−0.0534791	−	0.0124619i
$88$		0			0
$89$	−11.8169	+	6.82247i	−1.25258	+	0.723180i	−0.971622	−	0.236539i	$-0.923987\pi$
$89$	−11.8169	+	6.82247i	−1.25258	+	0.723180i	−0.280963	+	0.959719i	$0.590654\pi$
$90$		0			0
$91$	25.4689	+	14.7045i	2.66986	+	1.54145i
$92$		0			0
$93$	−0.305739	+	5.61412i	−0.0317036	+	0.582157i
$94$		0			0
$95$	−0.0963222	+	0.546271i	−0.00988245	+	0.0560462i
$96$		0			0
$97$	9.23564	−	7.74962i	0.937737	−	0.786855i	−0.0394529	−	0.999221i	$-0.512562\pi$
$97$	9.23564	−	7.74962i	0.937737	−	0.786855i	0.977190	+	0.212367i	$0.0681171\pi$
$98$		0			0
$99$	−10.3436	−	1.12995i	−1.03957	−	0.113564i
$100$		0			0
$101$	1.78121	−	4.89384i	0.177237	−	0.486956i	−0.818983	−	0.573818i	$-0.805462\pi$
$101$	1.78121	−	4.89384i	0.177237	−	0.486956i	0.996220	+	0.0868621i	$0.0276840\pi$
$102$		0			0
$103$	6.96942	−	8.30583i	0.686717	−	0.818397i	−0.304237	−	0.952596i	$-0.598402\pi$
$103$	6.96942	−	8.30583i	0.686717	−	0.818397i	0.990954	+	0.134199i	$0.0428461\pi$
$104$		0			0
$105$	1.16376	+	9.64103i	0.113571	+	0.940868i
$106$		0			0
$107$	−0.104795			−0.0101309			−0.00506546	−	0.999987i	$-0.501612\pi$
$107$	−0.104795			−0.0101309			−0.00506546	+	0.999987i	$0.501612\pi$
$108$		0			0
$109$	−7.66261			−0.733945			−0.366973	−	0.930232i	$-0.619606\pi$
$109$	−7.66261			−0.733945			−0.366973	+	0.930232i	$0.619606\pi$
$110$		0			0
$111$	−12.8834	+	9.66711i	−1.22284	+	0.917561i
$112$		0			0
$113$	4.82750	−	5.75319i	0.454133	−	0.541215i	−0.489590	−	0.871953i	$-0.662853\pi$
$113$	4.82750	−	5.75319i	0.454133	−	0.541215i	0.943722	+	0.330739i	$0.107298\pi$
$114$		0			0
$115$	−2.38620	+	6.55603i	−0.222514	+	0.611353i
$116$		0			0
$117$	16.3354	−	10.9214i	1.51020	−	1.00968i
$118$		0			0
$119$	19.0267	−	15.9653i	1.74417	−	1.46354i
$120$		0			0
$121$	0.178779	−	1.01391i	0.0162526	−	0.0921733i
$122$		0			0
$123$	0.745964	+	0.486607i	0.0672613	+	0.0438759i
$124$		0			0
$125$	−9.12796	−	5.27003i	−0.816430	−	0.471366i
$126$		0			0
$127$	5.42591	−	3.13265i	0.481472	−	0.277978i	−0.239558	−	0.970882i	$-0.577003\pi$
$127$	5.42591	−	3.13265i	0.481472	−	0.277978i	0.721030	+	0.692904i	$0.243669\pi$
$128$		0			0
$129$	2.08957	+	6.88502i	0.183977	+	0.606193i
$130$		0			0
$131$	−18.7682	+	6.83105i	−1.63978	+	0.596832i	−0.987001	−	0.160715i	$-0.948620\pi$
$131$	−18.7682	+	6.83105i	−1.63978	+	0.596832i	−0.652781	+	0.757547i	$0.726398\pi$
$132$		0			0
$133$	0.346338	+	1.96418i	0.0300313	+	0.170316i
$134$		0			0
$135$	6.12195	+	2.15006i	0.526894	+	0.185048i
$136$		0			0
$137$	−7.91580	+	1.39577i	−0.676292	+	0.119249i	−0.501237	−	0.865310i	$-0.667122\pi$
$137$	−7.91580	+	1.39577i	−0.676292	+	0.119249i	−0.175055	+	0.984559i	$0.556010\pi$
$138$		0			0
$139$	4.61004	+	12.6660i	0.391019	+	1.07431i	0.966537	+	0.256526i	$0.0825780\pi$
$139$	4.61004	+	12.6660i	0.391019	+	1.07431i	−0.575519	+	0.817789i	$0.695200\pi$
$140$		0			0
$141$	16.9737	+	15.8932i	1.42944	+	1.33845i
$142$		0			0
$143$	11.3589	+	19.6741i	0.949876	+	1.64523i
$144$		0			0
$145$	−0.184629	+	0.319787i	−0.0153326	+	0.0265569i
$146$		0			0
$147$	10.3061	+	20.3296i	0.850037	+	1.67676i
$148$		0			0
$149$	−2.55194	−	0.449976i	−0.209063	−	0.0368635i	0.0681356	−	0.997676i	$-0.478295\pi$
$149$	−2.55194	−	0.449976i	−0.209063	−	0.0368635i	−0.277199	+	0.960813i	$0.589406\pi$
$150$		0			0
$151$	−2.20436	−	2.62705i	−0.179388	−	0.213787i	0.668856	−	0.743392i	$-0.266784\pi$
$151$	−2.20436	−	2.62705i	−0.179388	−	0.213787i	−0.848244	+	0.529606i	$0.822340\pi$
$152$		0			0
$153$	−3.94892	−	16.1189i	−0.319251	−	1.30313i
$154$		0			0
$155$	3.80903	+	1.38637i	0.305949	+	0.111356i
$156$		0			0
$157$	1.37068	+	1.15014i	0.109392	+	0.0917910i	0.695843	−	0.718194i	$-0.255031\pi$
$157$	1.37068	+	1.15014i	0.109392	+	0.0917910i	−0.586451	+	0.809985i	$0.699475\pi$
$158$		0			0
$159$	3.64485	−	8.53813i	0.289055	−	0.677118i
$160$		0			0
$161$			25.0859i			1.97704i
$162$		0			0
$163$		−	6.53813i		−	0.512106i	−0.966663	−	0.256053i	$-0.917578\pi$
$163$		−	6.53813i		−	0.512106i	0.966663	−	0.256053i	$-0.0824221\pi$
$164$		0			0
$165$	−2.94520	+	6.89919i	−0.229284	+	0.537101i
$166$		0			0
$167$	−0.418954	−	0.351544i	−0.0324196	−	0.0272033i	0.626434	−	0.779475i	$-0.284514\pi$
$167$	−0.418954	−	0.351544i	−0.0324196	−	0.0272033i	−0.658853	+	0.752271i	$0.728958\pi$
$168$		0			0
$169$	−28.0989	−	10.2272i	−2.16146	−	0.786706i
$170$		0			0
$171$	1.27950	+	0.372562i	0.0978460	+	0.0284905i
$172$		0			0
$173$	7.84501	+	9.34932i	0.596445	+	0.710815i	0.976831	−	0.214012i	$-0.0686533\pi$
$173$	7.84501	+	9.34932i	0.596445	+	0.710815i	−0.380386	+	0.924828i	$0.624209\pi$
$174$		0			0
$175$	−15.2138	−	2.68260i	−1.15005	−	0.202786i
$176$		0			0
$177$	7.00890	+	13.8256i	0.526821	+	1.03919i
$178$		0			0
$179$	0.986094	−	1.70796i	0.0737041	−	0.127659i	−0.826818	−	0.562470i	$-0.809851\pi$
$179$	0.986094	−	1.70796i	0.0737041	−	0.127659i	0.900522	+	0.434810i	$0.143185\pi$
$180$		0			0
$181$	−3.50842	−	6.07677i	−0.260779	−	0.451683i	0.705670	−	0.708541i	$-0.250646\pi$
$181$	−3.50842	−	6.07677i	−0.260779	−	0.451683i	−0.966449	+	0.256858i	$0.917313\pi$
$182$		0			0
$183$	6.14073	+	5.74985i	0.453936	+	0.425041i
$184$		0			0
$185$	3.97165	+	10.9120i	0.292001	+	0.802267i
$186$		0			0
$187$	18.8950	−	3.33169i	1.38174	−	0.243638i
$188$		0			0
$189$	23.3288	−	0.264034i	1.69692	−	0.0192057i
$190$		0			0
$191$	−2.00511	−	11.3715i	−0.145085	−	0.822816i	−0.967299	−	0.253638i	$-0.918373\pi$
$191$	−2.00511	−	11.3715i	−0.145085	−	0.822816i	0.822214	−	0.569178i	$-0.192738\pi$
$192$		0			0
$193$	20.9176	−	7.61338i	1.50568	−	0.548023i	0.548157	−	0.836376i	$-0.315330\pi$
$193$	20.9176	−	7.61338i	1.50568	−	0.548023i	0.957524	+	0.288353i	$0.0931076\pi$
$194$		0			0
$195$	−4.11420	−	13.5560i	−0.294624	−	0.970767i
$196$		0			0
$197$	−8.68443	+	5.01396i	−0.618740	+	0.357230i	−0.776378	−	0.630267i	$-0.782945\pi$
$197$	−8.68443	+	5.01396i	−0.618740	+	0.357230i	0.157638	+	0.987497i	$0.449612\pi$
$198$		0			0
$199$	−11.9455	−	6.89675i	−0.846795	−	0.488898i	0.0127729	−	0.999918i	$-0.495934\pi$
$199$	−11.9455	−	6.89675i	−0.846795	−	0.488898i	−0.859568	+	0.511021i	$0.829267\pi$
$200$		0			0
$201$	2.52454	+	1.64680i	0.178067	+	0.116157i
$202$		0			0
$203$	−0.230555	+	1.30754i	−0.0161818	+	0.0917715i
$204$		0			0
$205$	0.491884	−	0.412740i	0.0343547	−	0.0288270i
$206$		0			0
$207$	15.0349	+	7.40930i	1.04500	+	0.514982i
$208$		0			0
$209$	−0.526948	+	1.44778i	−0.0364498	+	0.100145i
$210$		0			0
$211$	−4.23912	+	5.05199i	−0.291833	+	0.347793i	−0.891962	−	0.452110i	$-0.850672\pi$
$211$	−4.23912	+	5.05199i	−0.291833	+	0.347793i	0.600129	+	0.799903i	$0.295116\pi$
$212$		0			0
$213$	−7.33466	+	5.50358i	−0.502563	+	0.377099i
$214$		0			0
$215$	5.18732			0.353772
$216$		0			0
$217$	14.5748			0.989403
$218$		0			0
$219$	−2.47239	−	20.4823i	−0.167069	−	1.38406i
$220$		0			0
$221$	−23.2904	+	27.7565i	−1.56668	+	1.86710i
$222$		0			0
$223$	−6.14794	+	16.8913i	−0.411696	+	1.13113i	0.544592	+	0.838701i	$0.316684\pi$
$223$	−6.14794	+	16.8913i	−0.411696	+	1.13113i	−0.956288	+	0.292425i	$0.905538\pi$
$224$		0			0
$225$	−6.10129	+	8.32587i	−0.406752	+	0.555058i
$226$		0			0
$227$	4.25935	−	3.57402i	0.282703	−	0.237216i	−0.490398	−	0.871498i	$-0.663149\pi$
$227$	4.25935	−	3.57402i	0.282703	−	0.237216i	0.773102	+	0.634282i	$0.218704\pi$
$228$		0			0
$229$	−0.559691	+	3.17416i	−0.0369854	+	0.209755i	−0.997700	−	0.0677833i	$-0.978407\pi$
$229$	−0.559691	+	3.17416i	−0.0369854	+	0.209755i	0.960715	+	0.277538i	$0.0895185\pi$
$230$		0			0
$231$	−1.46673	+	26.9328i	−0.0965037	+	1.77205i
$232$		0			0
$233$	8.18937	+	4.72813i	0.536503	+	0.309750i	0.743661	−	0.668557i	$-0.233088\pi$
$233$	8.18937	+	4.72813i	0.536503	+	0.309750i	−0.207157	+	0.978308i	$0.566421\pi$
$234$		0			0
$235$	14.5182	−	8.38209i	0.947063	−	0.546787i
$236$		0			0
$237$	−17.3466	−	4.04217i	−1.12678	−	0.262567i
$238$		0			0
$239$	−5.74005	+	2.08921i	−0.371293	+	0.135140i	−0.520926	−	0.853602i	$-0.674413\pi$
$239$	−5.74005	+	2.08921i	−0.371293	+	0.135140i	0.149633	+	0.988742i	$0.452191\pi$
$240$		0			0
$241$	−0.412734	−	2.34073i	−0.0265865	−	0.150780i	0.968625	−	0.248528i	$-0.0799470\pi$
$241$	−0.412734	−	2.34073i	−0.0265865	−	0.150780i	−0.995211	+	0.0977487i	$0.968836\pi$
$242$		0			0
$243$	6.73210	−	14.0598i	0.431864	−	0.901939i
$244$		0			0
$245$	16.1828	−	2.85346i	1.03388	−	0.182301i
$246$		0			0
$247$	−0.995138	−	2.73412i	−0.0633191	−	0.173968i
$248$		0			0
$249$	−1.86579	+	8.00687i	−0.118240	+	0.507415i
$250$		0			0
$251$	7.06754	+	12.2413i	0.446099	+	0.772666i	0.998128	−	0.0611586i	$-0.0194795\pi$
$251$	7.06754	+	12.2413i	0.446099	+	0.772666i	−0.552029	+	0.833825i	$0.686146\pi$
$252$		0			0
$253$	−9.68913	+	16.7821i	−0.609151	+	1.05508i
$254$		0			0
$255$	−11.9468	−	0.650611i	−0.748139	−	0.0407428i
$256$		0			0
$257$	−23.9112	−	4.21618i	−1.49154	−	0.262998i	−0.632359	−	0.774675i	$-0.717913\pi$
$257$	−23.9112	−	4.21618i	−1.49154	−	0.262998i	−0.859178	+	0.511677i	$0.829024\pi$
$258$		0			0
$259$	26.8387	+	31.9851i	1.66767	+	1.98746i
$260$		0			0
$261$	0.715563	+	0.524372i	0.0442922	+	0.0324578i
$262$		0			0
$263$	16.2439	+	5.91228i	1.00164	+	0.364567i	0.790217	−	0.612828i	$-0.209968\pi$
$263$	16.2439	+	5.91228i	1.00164	+	0.364567i	0.211423	+	0.977395i	$0.432190\pi$
$264$		0			0
$265$	−5.12712	−	4.30216i	−0.314956	−	0.264280i
$266$		0			0
$267$	23.4634	−	2.83224i	1.43594	−	0.173330i
$268$		0			0
$269$		−	11.5835i		−	0.706260i	−0.935574	−	0.353130i	$-0.885117\pi$
$269$		−	11.5835i		−	0.706260i	0.935574	−	0.353130i	$-0.114883\pi$
$270$		0			0
$271$		−	11.2650i		−	0.684300i	−0.939645	−	0.342150i	$-0.888845\pi$
$271$		−	11.2650i		−	0.684300i	0.939645	−	0.342150i	$-0.111155\pi$
$272$		0			0
$273$	−30.5718	−	40.7433i	−1.85029	−	2.46590i
$274$		0			0
$275$	−9.14167	−	7.67077i	−0.551263	−	0.462565i
$276$		0			0
$277$	−19.7369	−	7.18366i	−1.18588	−	0.431624i	−0.327603	−	0.944815i	$-0.606241\pi$
$277$	−19.7369	−	7.18366i	−1.18588	−	0.431624i	−0.858274	+	0.513191i	$0.828463\pi$
$278$		0			0
$279$	4.30478	−	8.73523i	0.257720	−	0.522965i
$280$		0			0
$281$	−21.0657	−	25.1051i	−1.25667	−	1.49765i	−0.789857	−	0.613291i	$-0.789845\pi$
$281$	−21.0657	−	25.1051i	−1.25667	−	1.49765i	−0.466817	−	0.884354i	$-0.654599\pi$
$282$		0			0
$283$	−16.0444	−	2.82907i	−0.953743	−	0.168171i	−0.324940	−	0.945735i	$-0.605344\pi$
$283$	−16.0444	−	2.82907i	−0.953743	−	0.168171i	−0.628804	+	0.777564i	$0.716455\pi$
$284$		0			0
$285$	0.524917	−	0.804693i	0.0310934	−	0.0476659i
$286$		0			0
$287$	1.15439	−	1.99947i	0.0681416	−	0.118025i
$288$		0			0
$289$	6.80067	+	11.7791i	0.400039	+	0.692888i
$290$		0			0
$291$	−19.9821	+	6.06447i	−1.17137	+	0.355506i
$292$		0			0
$293$	−1.58017	−	4.34149i	−0.0923147	−	0.253633i	0.884939	−	0.465708i	$-0.154200\pi$
$293$	−1.58017	−	4.34149i	−0.0923147	−	0.253633i	−0.977253	+	0.212075i	$0.931978\pi$
$294$		0			0
$295$	11.0054	−	1.94055i	0.640760	−	0.112983i
$296$		0			0
$297$	15.7086	+	8.83386i	0.911506	+	0.512593i
$298$		0			0
$299$	−6.35478	−	36.0398i	−0.367507	−	2.08423i
$300$		0			0
$301$	17.5268	−	6.37924i	1.01023	−	0.367693i
$302$		0			0
$303$	−6.16537	+	6.58449i	−0.354191	+	0.378269i
$304$		0			0
$305$	5.25240	−	3.03247i	0.300751	−	0.173639i
$306$		0			0
$307$	−27.2828	−	15.7517i	−1.55711	−	0.898999i	−0.997531	−	0.0702235i	$-0.977629\pi$
$307$	−27.2828	−	15.7517i	−1.55711	−	0.898999i	−0.559581	−	0.828776i	$-0.689038\pi$
$308$		0			0
$309$	−16.7503	+	8.49158i	−0.952890	+	0.483069i
$310$		0			0
$311$	1.20932	−	6.85837i	0.0685741	−	0.388903i	−0.931133	−	0.364681i	$-0.881178\pi$
$311$	1.20932	−	6.85837i	0.0685741	−	0.388903i	0.999707	−	0.0242219i	$-0.00771081\pi$
$312$		0			0
$313$	−11.5479	+	9.68987i	−0.652728	+	0.547704i	−0.907897	−	0.419193i	$-0.862313\pi$
$313$	−11.5479	+	9.68987i	−0.652728	+	0.547704i	0.255169	+	0.966896i	$0.417869\pi$
$314$		0			0
$315$	4.70231	−	16.1493i	0.264945	−	0.909909i
$316$		0			0
$317$	−5.00855	+	13.7609i	−0.281308	+	0.772888i	0.715899	+	0.698204i	$0.246017\pi$
$317$	−5.00855	+	13.7609i	−0.281308	+	0.772888i	−0.997207	+	0.0746842i	$0.976205\pi$
$318$		0			0
$319$	−0.659261	+	0.785677i	−0.0369115	+	0.0439895i
$320$		0			0
$321$	0.166936	+	0.0712633i	0.00931744	+	0.00397753i
$322$		0			0
$323$	−2.45732			−0.136729
$324$		0			0
$325$	22.5365			1.25010
$326$		0			0
$327$	12.2063	+	5.21077i	0.675012	+	0.288156i
$328$		0			0
$329$	38.7457	−	46.1754i	2.13612	−	2.54573i
$330$		0			0
$331$	−6.30943	+	17.3350i	−0.346798	+	0.952818i	0.636574	+	0.771215i	$0.280351\pi$
$331$	−6.30943	+	17.3350i	−0.346798	+	0.952818i	−0.983372	+	0.181603i	$0.941871\pi$
$332$		0			0
$333$	27.0968	−	6.63839i	1.48490	−	0.363782i
$334$		0			0
$335$	1.66466	−	1.39682i	0.0909503	−	0.0763164i
$336$		0			0
$337$	0.228141	−	1.29385i	0.0124276	−	0.0704807i	−0.977963	−	0.208777i	$-0.933052\pi$
$337$	0.228141	−	1.29385i	0.0124276	−	0.0704807i	0.990391	+	0.138297i	$0.0441627\pi$
$338$		0			0
$339$	−11.6024	+	5.88186i	−0.630156	+	0.319459i
$340$		0			0
$341$	9.75033	+	5.62936i	0.528010	+	0.304847i
$342$		0			0
$343$	23.9502	−	13.8277i	1.29319	−	0.746623i
$344$		0			0
$345$	8.25942	−	8.82091i	0.444672	−	0.474902i
$346$		0			0
$347$	−16.0691	+	5.84866i	−0.862632	+	0.313972i	−0.735180	−	0.677872i	$-0.762902\pi$
$347$	−16.0691	+	5.84866i	−0.862632	+	0.313972i	−0.127452	+	0.991845i	$0.540680\pi$
$348$		0			0
$349$	4.43111	+	25.1301i	0.237192	+	1.34518i	0.837949	+	0.545749i	$0.183755\pi$
$349$	4.43111	+	25.1301i	0.237192	+	1.34518i	−0.600757	+	0.799432i	$0.705134\pi$
$350$		0			0
$351$	−33.4486	+	6.28901i	−1.78535	+	0.335683i
$352$		0			0
$353$	8.75020	−	1.54290i	0.465726	−	0.0821201i	0.0641392	−	0.997941i	$-0.479570\pi$
$353$	8.75020	−	1.54290i	0.465726	−	0.0821201i	0.401587	+	0.915821i	$0.368459\pi$
$354$		0			0
$355$	2.26110	+	6.21232i	0.120007	+	0.329715i
$356$		0			0
$357$	−41.1658	+	12.4936i	−2.17873	+	0.661234i
$358$		0			0
$359$	2.90793	+	5.03668i	0.153474	+	0.265826i	0.932503	−	0.361164i	$-0.117620\pi$
$359$	2.90793	+	5.03668i	0.153474	+	0.265826i	−0.779028	+	0.626989i	$0.784287\pi$
$360$		0			0
$361$	−9.40134	+	16.2836i	−0.494807	+	0.857031i
$362$		0			0
$363$	−0.974273	+	1.49355i	−0.0511361	+	0.0783911i
$364$		0			0
$365$	−14.6479	−	2.58282i	−0.766706	−	0.135191i
$366$		0			0
$367$	−8.25207	−	9.83443i	−0.430754	−	0.513353i	0.506385	−	0.862307i	$-0.330981\pi$
$367$	−8.25207	−	9.83443i	−0.430754	−	0.513353i	−0.937140	+	0.348954i	$0.886537\pi$
$368$		0			0
$369$	−0.857396	−	1.28243i	−0.0446343	−	0.0667605i
$370$		0			0
$371$	−22.6141	−	8.23086i	−1.17407	−	0.427325i
$372$		0			0
$373$	1.87221	+	1.57097i	0.0969392	+	0.0813416i	0.689969	−	0.723839i	$-0.257624\pi$
$373$	1.87221	+	1.57097i	0.0969392	+	0.0813416i	−0.593030	+	0.805180i	$0.702068\pi$
$374$		0			0
$375$	10.9568	+	14.6023i	0.565809	+	0.754058i
$376$		0			0
$377$		−	1.93689i		−	0.0997550i
$378$		0			0
$379$			0.898166i			0.0461357i	0.999734	+	0.0230678i	$0.00734338\pi$
$379$			0.898166i			0.0461357i	−0.999734	+	0.0230678i	$0.992657\pi$
$380$		0			0
$381$	−10.7736	+	1.30047i	−0.551949	+	0.0666252i
$382$		0			0
$383$	1.64350	+	1.37906i	0.0839787	+	0.0704665i	0.683811	−	0.729660i	$-0.260321\pi$
$383$	1.64350	+	1.37906i	0.0839787	+	0.0704665i	−0.599832	+	0.800126i	$0.704766\pi$
$384$		0			0
$385$	18.2732	+	6.65090i	0.931288	+	0.338961i
$386$		0			0
$387$	1.35336	−	12.3886i	0.0687949	−	0.629749i
$388$		0			0
$389$	22.8072	+	27.1805i	1.15637	+	1.37811i	0.912893	+	0.408200i	$0.133843\pi$
$389$	22.8072	+	27.1805i	1.15637	+	1.37811i	0.243476	+	0.969907i	$0.421712\pi$
$390$		0			0
$391$	−30.4377	−	5.36699i	−1.53930	−	0.271420i
$392$		0			0
$393$	34.5425	+	1.88115i	1.74244	+	0.0948912i
$394$		0			0
$395$	−6.42053	+	11.1207i	−0.323052	+	0.559542i
$396$		0			0
$397$	5.11297	+	8.85593i	0.256613	+	0.444466i	0.965332	−	0.261024i	$-0.0840602\pi$
$397$	5.11297	+	8.85593i	0.256613	+	0.444466i	−0.708720	+	0.705490i	$0.750727\pi$
$398$		0			0
$399$	0.783987	−	3.36441i	0.0392484	−	0.168431i
$400$		0			0
$401$	−3.48754	−	9.58194i	−0.174160	−	0.478499i	0.821646	−	0.569999i	$-0.193056\pi$
$401$	−3.48754	−	9.58194i	−0.174160	−	0.478499i	−0.995805	+	0.0914993i	$0.970834\pi$
$402$		0			0
$403$	−20.9390	+	3.69211i	−1.04305	+	0.183917i
$404$		0			0
$405$	−8.29001	−	7.58808i	−0.411934	−	0.377055i
$406$		0			0
$407$	5.60079	+	31.7636i	0.277621	+	1.57447i
$408$		0			0
$409$	−8.42415	+	3.06614i	−0.416548	+	0.151611i	−0.541787	−	0.840516i	$-0.682252\pi$
$409$	−8.42415	+	3.06614i	−0.416548	+	0.151611i	0.125240	+	0.992126i	$0.460030\pi$
$410$		0			0
$411$	13.5588	+	3.15952i	0.668807	+	0.155848i
$412$		0			0
$413$	34.7984	−	20.0909i	1.71232	−	0.988608i
$414$		0			0
$415$	5.13310	+	2.96360i	0.251974	+	0.145477i
$416$		0			0
$417$	1.26952	−	23.3115i	0.0621687	−	1.14157i
$418$		0			0
$419$	−3.72339	+	21.1164i	−0.181899	+	1.03160i	0.747975	+	0.663727i	$0.231026\pi$
$419$	−3.72339	+	21.1164i	−0.181899	+	1.03160i	−0.929875	+	0.367877i	$0.880085\pi$
$420$		0			0
$421$	−22.2053	+	18.6324i	−1.08222	+	0.908089i	−0.996103	−	0.0881963i	$-0.971890\pi$
$421$	−22.2053	+	18.6324i	−1.08222	+	0.908089i	−0.0861151	+	0.996285i	$0.527445\pi$
$422$		0			0
$423$	−16.2308	−	36.8600i	−0.789168	−	1.79219i
$424$		0			0
$425$	6.50982	−	17.8856i	0.315772	−	0.867578i
$426$		0			0
$427$	14.0174	−	16.7053i	0.678351	−	0.808428i
$428$		0			0
$429$	−4.71546	−	39.0647i	−0.227664	−	1.88606i
$430$		0			0
$431$	3.63905			0.175287			0.0876433	−	0.996152i	$-0.472066\pi$
$431$	3.63905			0.175287			0.0876433	+	0.996152i	$0.472066\pi$
$432$		0			0
$433$	8.29088			0.398434			0.199217	−	0.979955i	$-0.436160\pi$
$433$	8.29088			0.398434			0.199217	+	0.979955i	$0.436160\pi$
$434$		0			0
$435$	0.511573	−	0.383860i	0.0245280	−	0.0184047i
$436$		0			0
$437$	1.59533	−	1.90123i	0.0763148	−	0.0909484i
$438$		0			0
$439$	−0.223040	+	0.612796i	−0.0106451	+	0.0292472i	−0.944901	−	0.327355i	$-0.893843\pi$
$439$	−0.223040	+	0.612796i	−0.0106451	+	0.0292472i	0.934256	+	0.356602i	$0.116065\pi$
$440$		0			0
$441$	−2.59275	−	39.3930i	−0.123464	−	1.87586i
$442$		0			0
$443$	−15.5781	+	13.0715i	−0.740136	+	0.621048i	−0.932874	−	0.360202i	$-0.882708\pi$
$443$	−15.5781	+	13.0715i	−0.740136	+	0.621048i	0.192738	+	0.981250i	$0.438263\pi$
$444$		0			0
$445$	2.95874	−	16.7798i	0.140258	−	0.795441i
$446$		0			0
$447$	3.75918	+	2.45218i	0.177803	+	0.115984i
$448$		0			0
$449$	−7.13315	−	4.11833i	−0.336634	−	0.194356i	0.322149	−	0.946689i	$-0.395595\pi$
$449$	−7.13315	−	4.11833i	−0.336634	−	0.194356i	−0.658783	+	0.752333i	$0.728928\pi$
$450$		0			0
$451$	1.54454	−	0.891741i	0.0727296	−	0.0419905i
$452$		0			0
$453$	1.72502	+	5.68385i	0.0810486	+	0.267050i
$454$		0			0
$455$	−34.5088	+	12.5602i	−1.61780	+	0.588830i
$456$		0			0
$457$	−6.37017	−	36.1270i	−0.297984	−	1.68995i	−0.654821	−	0.755784i	$-0.727256\pi$
$457$	−6.37017	−	36.1270i	−0.297984	−	1.68995i	0.356838	−	0.934166i	$-0.383855\pi$
$458$		0			0
$459$	−4.67072	+	28.3623i	−0.218010	+	1.32384i
$460$		0			0
$461$	34.0483	−	6.00363i	1.58579	−	0.279617i	0.689902	−	0.723903i	$-0.257654\pi$
$461$	34.0483	−	6.00363i	1.58579	−	0.279617i	0.895885	+	0.444285i	$0.146542\pi$
$462$		0			0
$463$	−2.35339	−	6.46588i	−0.109371	−	0.300495i	0.872918	−	0.487868i	$-0.162225\pi$
$463$	−2.35339	−	6.46588i	−0.109371	−	0.300495i	−0.982289	+	0.187372i	$0.940003\pi$
$464$		0			0
$465$	−5.12492	−	4.79870i	−0.237662	−	0.222534i
$466$		0			0
$467$	2.00277	+	3.46890i	0.0926771	+	0.160521i	0.908637	−	0.417587i	$-0.137124\pi$
$467$	2.00277	+	3.46890i	0.0926771	+	0.160521i	−0.815960	+	0.578109i	$0.803791\pi$
$468$		0			0
$469$	3.90676	−	6.76671i	0.180397	−	0.312458i
$470$		0			0
$471$	−1.40134	−	2.76424i	−0.0645701	−	0.127369i
$472$		0			0
$473$	14.1891	+	2.50192i	0.652414	+	0.115038i
$474$		0			0
$475$	0.982439	+	1.17083i	0.0450774	+	0.0537212i
$476$		0			0
$477$	−11.6123	+	11.1224i	−0.531691	+	0.509261i
$478$		0			0
$479$	21.7698	+	7.92356i	0.994687	+	0.362037i	0.787534	−	0.616272i	$-0.211358\pi$
$479$	21.7698	+	7.92356i	0.994687	+	0.362037i	0.207154	+	0.978308i	$0.433580\pi$
$480$		0			0
$481$	−46.6604	−	39.1527i	−2.12753	−	1.78521i
$482$		0			0
$483$	17.0590	−	39.9611i	0.776213	−	1.81830i
$484$		0			0
$485$			15.0549i			0.683608i
$486$		0			0
$487$			1.39420i			0.0631771i	0.999501	+	0.0315886i	$0.0100566\pi$
$487$			1.39420i			0.0631771i	−0.999501	+	0.0315886i	$0.989943\pi$
$488$		0			0
$489$	−4.44609	+	10.4151i	−0.201059	+	0.470985i
$490$		0			0
$491$	11.3201	+	9.49865i	0.510867	+	0.428668i	0.861434	−	0.507869i	$-0.169567\pi$
$491$	11.3201	+	9.49865i	0.510867	+	0.428668i	−0.350567	+	0.936538i	$0.614011\pi$
$492$		0			0
$493$	−1.53717	−	0.559483i	−0.0692306	−	0.0251979i
$494$		0			0
$495$	9.38325	−	8.98742i	0.421746	−	0.403954i
$496$		0			0
$497$	15.2795	+	18.2094i	0.685380	+	0.816804i
$498$		0			0
$499$	−20.9484	−	3.69377i	−0.937779	−	0.165356i	−0.316187	−	0.948697i	$-0.602403\pi$
$499$	−20.9484	−	3.69377i	−0.937779	−	0.165356i	−0.621592	+	0.783341i	$0.713514\pi$
$500$		0			0
$501$	0.428323	+	0.844899i	0.0191361	+	0.0377473i
$502$		0			0
$503$	18.7862	−	32.5387i	0.837637	−	1.45083i	−0.0542287	−	0.998529i	$-0.517270\pi$
$503$	18.7862	−	32.5387i	0.837637	−	1.45083i	0.891865	−	0.452301i	$-0.149397\pi$
$504$		0			0
$505$	3.25162	+	5.63196i	0.144695	+	0.250619i
$506$		0			0
$507$	37.8061	+	35.3996i	1.67903	+	1.57215i
$508$		0			0
$509$	−12.8522	−	35.3112i	−0.569665	−	1.56514i	−0.805029	−	0.593235i	$-0.797850\pi$
$509$	−12.8522	−	35.3112i	−0.569665	−	1.56514i	0.235364	−	0.971907i	$-0.424372\pi$
$510$		0			0
$511$	−52.6683	+	9.28684i	−2.32991	+	0.410826i
$512$		0			0
$513$	−1.78486	−	1.46358i	−0.0788036	−	0.0646185i
$514$		0			0
$515$	2.35106	+	13.3335i	0.103600	+	0.587546i
$516$		0			0
$517$	43.7550	−	15.9255i	1.92434	−	0.700404i
$518$		0			0
$519$	−6.13912	−	20.2280i	−0.269477	−	0.887912i
$520$		0			0
$521$	−28.6464	+	16.5390i	−1.25502	+	0.724586i	−0.972102	−	0.234558i	$-0.924636\pi$
$521$	−28.6464	+	16.5390i	−1.25502	+	0.724586i	−0.282918	+	0.959144i	$0.591302\pi$
$522$		0			0
$523$	−16.6429	−	9.60881i	−0.727745	−	0.420164i	0.0898515	−	0.995955i	$-0.471361\pi$
$523$	−16.6429	−	9.60881i	−0.727745	−	0.420164i	−0.817597	+	0.575791i	$0.804694\pi$
$524$		0			0
$525$	22.4109	+	14.6191i	0.978093	+	0.638029i
$526$		0			0
$527$	−3.11820	+	17.6842i	−0.135831	+	0.770336i
$528$		0			0
$529$	6.29401	−	5.28130i	0.273653	−	0.229622i
$530$		0			0
$531$	−1.76325	−	26.7900i	−0.0765184	−	1.16259i
$532$		0			0
$533$	−1.15196	+	3.16497i	−0.0498968	+	0.137090i
$534$		0			0
$535$	0.0841149	−	0.100244i	0.00363660	−	0.00433394i
$536$		0			0
$537$	−2.73228	+	2.05017i	−0.117907	+	0.0884715i
$538$		0			0
$539$	45.6416			1.96592
$540$		0			0
$541$	−12.1883			−0.524015			−0.262008	−	0.965066i	$-0.584385\pi$
$541$	−12.1883			−0.524015			−0.262008	+	0.965066i	$0.584385\pi$
$542$		0			0
$543$	1.45647	+	12.0660i	0.0625030	+	0.517800i
$544$		0			0
$545$	6.15048	−	7.32986i	0.263458	−	0.313977i
$546$		0			0
$547$	−0.299500	+	0.822870i	−0.0128057	+	0.0351834i	−0.945931	−	0.324369i	$-0.894848\pi$
$547$	−0.299500	+	0.822870i	−0.0128057	+	0.0351834i	0.933125	+	0.359552i	$0.117070\pi$
$548$		0			0
$549$	−5.87198	−	13.3352i	−0.250610	−	0.569133i
$550$		0			0
$551$	0.100626	−	0.0844353i	0.00428682	−	0.00359707i
$552$		0			0
$553$	−8.01762	+	45.4702i	−0.340944	+	1.93359i
$554$		0			0
$555$	1.09372	−	20.0834i	0.0464258	−	0.852492i
$556$		0			0
$557$	−29.9665	−	17.3012i	−1.26972	−	0.733074i	−0.294786	−	0.955563i	$-0.595248\pi$
$557$	−29.9665	−	17.3012i	−1.26972	−	0.733074i	−0.974935	+	0.222489i	$0.928582\pi$
$558$		0			0
$559$	−23.5640	+	13.6047i	−0.996650	+	0.575416i
$560$		0			0
$561$	−32.3648	−	7.54177i	−1.36644	−	0.318414i
$562$		0			0
$563$	32.7876	−	11.9337i	1.38183	−	0.502947i	0.459100	−	0.888384i	$-0.348172\pi$
$563$	32.7876	−	11.9337i	1.38183	−	0.502947i	0.922734	+	0.385438i	$0.125950\pi$
$564$		0			0
$565$	1.62851	+	9.23572i	0.0685118	+	0.388550i
$566$		0			0
$567$	−37.3418	−	15.4436i	−1.56821	−	0.648571i
$568$		0			0
$569$	31.1300	−	5.48907i	1.30504	−	0.230114i	0.522460	−	0.852664i	$-0.325015\pi$
$569$	31.1300	−	5.48907i	1.30504	−	0.230114i	0.782580	+	0.622550i	$0.213903\pi$
$570$		0			0
$571$	−6.40729	−	17.6039i	−0.268137	−	0.736699i	−0.998557	−	0.0537015i	$-0.982898\pi$
$571$	−6.40729	−	17.6039i	−0.268137	−	0.736699i	0.730420	−	0.682998i	$-0.239324\pi$
$572$		0			0
$573$	−4.53885	+	19.4781i	−0.189613	+	0.813709i
$574$		0			0
$575$	9.61185	+	16.6482i	0.400842	+	0.694279i
$576$		0			0
$577$	−3.35388	+	5.80909i	−0.139624	+	0.241836i	−0.927354	−	0.374185i	$-0.877923\pi$
$577$	−3.35388	+	5.80909i	−0.139624	+	0.241836i	0.787730	+	0.616020i	$0.211256\pi$
$578$		0			0
$579$	−38.4985	−	2.09658i	−1.59994	−	0.0871310i
$580$		0			0
$581$	20.9882	+	3.70078i	0.870736	+	0.153534i
$582$		0			0
$583$	−11.9494	−	14.2408i	−0.494894	−	0.589792i
$584$		0			0
$585$	−2.66464	+	24.3922i	−0.110169	+	1.00849i
$586$		0			0
$587$	23.3512	+	8.49915i	0.963808	+	0.350797i	0.775525	−	0.631317i	$-0.217485\pi$
$587$	23.3512	+	8.49915i	0.963808	+	0.350797i	0.188283	+	0.982115i	$0.439708\pi$
$588$		0			0
$589$	−1.10461	−	0.926879i	−0.0455147	−	0.0381914i
$590$		0			0
$591$	17.2437	−	2.08147i	0.709310	−	0.0856201i
$592$		0			0
$593$			28.3375i			1.16368i	0.813303	+	0.581840i	$0.197667\pi$
$593$			28.3375i			1.16368i	−0.813303	+	0.581840i	$0.802333\pi$
$594$		0			0
$595$			31.0152i			1.27150i
$596$		0			0
$597$	14.3389	+	19.1096i	0.586853	+	0.782104i
$598$		0			0
$599$	−6.02742	−	5.05761i	−0.246274	−	0.206648i	0.511292	−	0.859407i	$-0.329167\pi$
$599$	−6.02742	−	5.05761i	−0.246274	−	0.206648i	−0.757566	+	0.652759i	$0.773612\pi$
$600$		0			0
$601$	30.1656	+	10.9794i	1.23048	+	0.447859i	0.873763	−	0.486353i	$-0.161673\pi$
$601$	30.1656	+	10.9794i	1.23048	+	0.447859i	0.356719	+	0.934212i	$0.383895\pi$
$602$		0			0
$603$	−2.90165	−	4.34007i	−0.118164	−	0.176741i
$604$		0			0
$605$	0.826378	+	0.984839i	0.0335970	+	0.0400394i
$606$		0			0
$607$	−34.1052	−	6.01367i	−1.38429	−	0.244087i	−0.568616	−	0.822603i	$-0.692521\pi$
$607$	−34.1052	−	6.01367i	−1.38429	−	0.244087i	−0.815671	+	0.578516i	$0.803632\pi$
$608$		0			0
$609$	1.25643	−	1.92610i	0.0509131	−	0.0780494i
$610$		0			0
$611$	−43.9671	+	76.1532i	−1.77872	+	3.08083i
$612$		0			0
$613$	−15.5087	−	26.8619i	−0.626391	−	1.08494i	−0.988270	−	0.152716i	$-0.951198\pi$
$613$	−15.5087	−	26.8619i	−0.626391	−	1.08494i	0.361879	−	0.932225i	$-0.382135\pi$
$614$		0			0
$615$	−1.06423	+	0.322990i	−0.0429140	+	0.0130242i
$616$		0			0
$617$	−11.5278	−	31.6724i	−0.464092	−	1.27508i	−0.922382	−	0.386280i	$-0.873760\pi$
$617$	−11.5278	−	31.6724i	−0.464092	−	1.27508i	0.458290	−	0.888803i	$-0.348462\pi$
$618$		0			0
$619$	−43.9503	+	7.74963i	−1.76651	+	0.311484i	−0.960056	−	0.279809i	$-0.909729\pi$
$619$	−43.9503	+	7.74963i	−1.76651	+	0.311484i	−0.806457	+	0.591292i	$0.798618\pi$
$620$		0			0
$621$	−18.9117	−	22.0269i	−0.758900	−	0.883911i
$622$		0			0
$623$	−10.6385	−	60.3340i	−0.426223	−	2.41723i
$624$		0			0
$625$	−3.79816	+	1.38242i	−0.151926	+	0.0552967i
$626$		0			0
$627$	1.82394	−	1.94793i	0.0728412	−	0.0777930i
$628$		0			0
$629$	−44.5508	+	25.7214i	−1.77636	+	1.02558i
$630$		0			0
$631$	28.2689	+	16.3211i	1.12537	+	0.649731i	0.942766	−	0.333455i	$-0.108215\pi$
$631$	28.2689	+	16.3211i	1.12537	+	0.649731i	0.182602	+	0.983187i	$0.441548\pi$
$632$		0			0
$633$	10.1883	−	5.16498i	0.404949	−	0.205289i
$634$		0			0
$635$	−1.35855	+	7.70474i	−0.0539126	+	0.305753i
$636$		0			0
$637$	−66.0284	+	55.4044i	−2.61614	+	2.19520i
$638$		0			0
$639$	15.4265	−	3.77930i	0.610263	−	0.149507i
$640$		0			0
$641$	−2.72085	+	7.47548i	−0.107467	+	0.295264i	−0.981757	−	0.190141i	$-0.939106\pi$
$641$	−2.72085	+	7.47548i	−0.107467	+	0.295264i	0.874290	+	0.485405i	$0.161328\pi$
$642$		0			0
$643$	30.1295	−	35.9070i	1.18819	−	1.41603i	0.301630	−	0.953425i	$-0.402469\pi$
$643$	30.1295	−	35.9070i	1.18819	−	1.41603i	0.886563	−	0.462608i	$-0.153086\pi$
$644$		0			0
$645$	−8.26326	−	3.52751i	−0.325366	−	0.138896i
$646$		0			0
$647$	−7.29605			−0.286837			−0.143419	−	0.989662i	$-0.545810\pi$
$647$	−7.29605			−0.286837			−0.143419	+	0.989662i	$0.545810\pi$
$648$		0			0
$649$	31.0395			1.21841
$650$		0			0
$651$	−23.2173	−	9.91125i	−0.909958	−	0.388452i
$652$		0			0
$653$	17.1866	−	20.4822i	0.672565	−	0.801531i	−0.316566	−	0.948570i	$-0.602530\pi$
$653$	17.1866	−	20.4822i	0.672565	−	0.801531i	0.989131	+	0.147039i	$0.0469744\pi$
$654$		0			0
$655$	8.53007	−	23.4362i	0.333297	−	0.915727i
$656$		0			0
$657$	−9.99002	+	34.3090i	−0.389748	+	1.33852i
$658$		0			0
$659$	19.3659	−	16.2499i	0.754387	−	0.633006i	−0.182272	−	0.983248i	$-0.558345\pi$
$659$	19.3659	−	16.2499i	0.754387	−	0.633006i	0.936659	+	0.350242i	$0.113901\pi$
$660$		0			0
$661$	−8.11698	+	46.0337i	−0.315714	+	1.79050i	0.252473	+	0.967604i	$0.418756\pi$
$661$	−8.11698	+	46.0337i	−0.315714	+	1.79050i	−0.568187	+	0.822899i	$0.692355\pi$
$662$		0			0
$663$	55.9762	−	28.3772i	2.17393	−	1.10208i
$664$		0			0
$665$	−2.15688	−	1.24528i	−0.0836402	−	0.0482897i
$666$		0			0
$667$	1.43082	−	0.826087i	0.0554017	−	0.0319862i
$668$		0			0
$669$	21.2800	−	22.7267i	0.822733	−	0.878664i
$670$		0			0
$671$	15.8297	−	5.76154i	0.611099	−	0.222422i
$672$		0			0
$673$	−2.41144	−	13.6760i	−0.0929543	−	0.527170i	−0.995355	−	0.0962722i	$-0.969308\pi$
$673$	−2.41144	−	13.6760i	−0.0929543	−	0.527170i	0.902401	−	0.430898i	$-0.141803\pi$
$674$		0			0
$675$	15.3810	−	9.11385i	0.592015	−	0.350792i
$676$		0			0
$677$	4.42664	−	0.780535i	0.170129	−	0.0299984i	−0.0879344	−	0.996126i	$-0.528027\pi$
$677$	4.42664	−	0.780535i	0.170129	−	0.0299984i	0.258064	+	0.966128i	$0.416915\pi$
$678$		0			0
$679$	18.5141	+	50.8672i	0.710508	+	1.95210i
$680$		0			0
$681$	−9.21547	+	2.79685i	−0.353137	+	0.107176i
$682$		0			0
$683$	−18.8047	−	32.5706i	−0.719541	−	1.24628i	−0.961182	−	0.275915i	$-0.911019\pi$
$683$	−18.8047	−	32.5706i	−0.719541	−	1.24628i	0.241641	−	0.970366i	$-0.422314\pi$
$684$		0			0
$685$	5.01855	−	8.69238i	0.191749	−	0.332119i
$686$		0			0
$687$	3.05009	−	4.67576i	0.116368	−	0.178391i
$688$		0			0
$689$	34.5737	+	6.09628i	1.31715	+	0.232250i
$690$		0			0
$691$	3.81582	+	4.54751i	0.145160	+	0.172996i	0.833726	−	0.552179i	$-0.186204\pi$
$691$	3.81582	+	4.54751i	0.145160	+	0.172996i	−0.688565	+	0.725175i	$0.741759\pi$
$692$		0			0
$693$	20.6514	−	41.9058i	0.784483	−	1.59187i
$694$		0			0
$695$	−15.8163	−	5.75665i	−0.599945	−	0.218362i
$696$		0			0
$697$	2.17906	+	1.82845i	0.0825376	+	0.0692573i
$698$		0			0
$699$	−9.83020	−	13.1008i	−0.371812	−	0.495517i
$700$		0			0
$701$		−	26.4610i		−	0.999418i	−0.866193	−	0.499709i	$-0.833440\pi$
$701$		−	26.4610i		−	0.999418i	0.866193	−	0.499709i	$-0.166560\pi$
$702$		0			0
$703$		−	4.13091i		−	0.155800i
$704$		0			0
$705$	−28.8271	+	3.47969i	−1.08569	+	0.131053i
$706$		0			0
$707$	17.9125	+	15.0304i	0.673671	+	0.565277i
$708$		0			0
$709$	3.27703	+	1.19274i	0.123071	+	0.0447943i	0.402822	−	0.915278i	$-0.368029\pi$
$709$	3.27703	+	1.19274i	0.123071	+	0.0447943i	−0.279750	+	0.960073i	$0.590252\pi$
$710$		0			0
$711$	24.8839	+	18.2352i	0.933220	+	0.683874i
$712$		0			0
$713$	−11.6579	−	13.8934i	−0.436593	−	0.520312i
$714$		0			0
$715$	−27.9371	−	4.92606i	−1.04479	−	0.184224i
$716$		0			0
$717$	10.5645	+	0.575329i	0.394537	+	0.0214861i
$718$		0			0
$719$	6.60217	−	11.4353i	0.246219	−	0.426464i	−0.716254	−	0.697839i	$-0.754145\pi$
$719$	6.60217	−	11.4353i	0.246219	−	0.426464i	0.962474	+	0.271375i	$0.0874783\pi$
$720$		0			0
$721$	24.3410	+	42.1598i	0.906505	+	1.57011i
$722$		0			0
$723$	−0.934283	+	4.00939i	−0.0347464	+	0.149111i
$724$		0			0
$725$	0.347988	+	0.956088i	0.0129239	+	0.0355082i
$726$		0			0
$727$	36.1290	−	6.37052i	1.33995	−	0.236269i	0.542704	−	0.839924i	$-0.317400\pi$
$727$	36.1290	−	6.37052i	1.33995	−	0.236269i	0.797246	+	0.603654i	$0.206289\pi$
$728$		0			0
$729$	−20.2851	+	17.8189i	−0.751300	+	0.659961i
$730$		0			0
$731$	3.99042	+	22.6308i	0.147591	+	0.837030i
$732$		0			0
$733$	10.9142	−	3.97245i	0.403125	−	0.146726i	−0.132497	−	0.991183i	$-0.542299\pi$
$733$	10.9142	−	3.97245i	0.403125	−	0.146726i	0.535622	+	0.844458i	$0.320077\pi$
$734$		0			0
$735$	−27.7192	−	6.45922i	−1.02244	−	0.238252i
$736$		0			0
$737$	5.22713	−	3.01788i	0.192544	−	0.111165i
$738$		0			0
$739$	15.6119	+	9.01353i	0.574293	+	0.331568i	0.758862	−	0.651251i	$-0.225756\pi$
$739$	15.6119	+	9.01353i	0.574293	+	0.331568i	−0.184569	+	0.982820i	$0.559089\pi$
$740$		0			0
$741$	−0.274043	+	5.03210i	−0.0100672	+	0.184859i
$742$		0			0
$743$	−7.50951	+	42.5886i	−0.275497	+	1.56242i	0.461880	+	0.886942i	$0.347175\pi$
$743$	−7.50951	+	42.5886i	−0.275497	+	1.56242i	−0.737378	+	0.675481i	$0.763936\pi$
$744$		0			0
$745$	2.47878	−	2.07994i	0.0908155	−	0.0762032i
$746$		0			0
$747$	8.41703	−	11.4859i	0.307963	−	0.420249i
$748$		0			0
$749$	0.160928	−	0.442146i	0.00588018	−	0.0161557i
$750$		0			0
$751$	19.1574	−	22.8309i	0.699064	−	0.833112i	−0.293356	−	0.956003i	$-0.594772\pi$
$751$	19.1574	−	22.8309i	0.699064	−	0.833112i	0.992420	+	0.122891i	$0.0392166\pi$
$752$		0			0
$753$	−2.93398	−	24.3062i	−0.106920	−	0.885769i
$754$		0			0
$755$	4.28233			0.155850
$756$		0			0
$757$	2.49737			0.0907686			0.0453843	−	0.998970i	$-0.485549\pi$
$757$	2.49737			0.0907686			0.0453843	+	0.998970i	$0.485549\pi$
$758$		0			0
$759$	26.8468	−	20.1445i	0.974476	−	0.731201i
$760$		0			0
$761$	−22.2267	+	26.4888i	−0.805717	+	0.960216i	−0.999784	−	0.0207718i	$-0.993388\pi$
$761$	−22.2267	+	26.4888i	−0.805717	+	0.960216i	0.194067	+	0.980988i	$0.437832\pi$
$762$		0			0
$763$	11.7670	−	32.3297i	0.425996	−	1.17041i
$764$		0			0
$765$	18.5885	+	9.16056i	0.672070	+	0.331201i
$766$		0			0
$767$	−44.9039	+	37.6788i	−1.62139	+	1.36050i
$768$		0			0
$769$	1.08819	−	6.17146i	0.0392413	−	0.222548i	−0.958880	−	0.283810i	$-0.908401\pi$
$769$	1.08819	−	6.17146i	0.0392413	−	0.222548i	0.998122	+	0.0612619i	$0.0195125\pi$
$770$		0			0
$771$	35.2227	+	22.9765i	1.26852	+	0.827477i
$772$		0			0
$773$	27.9281	+	16.1243i	1.00450	+	0.579951i	0.909578	−	0.415534i	$-0.136405\pi$
$773$	27.9281	+	16.1243i	1.00450	+	0.579951i	0.0949263	+	0.995484i	$0.469738\pi$
$774$		0			0
$775$	9.67256	−	5.58446i	0.347449	−	0.200600i
$776$		0			0
$777$	−21.0026	−	69.2023i	−0.753464	−	2.48262i
$778$		0			0
$779$	−0.214645	+	0.0781245i	−0.00769047	+	0.00279910i
$780$		0			0
$781$	3.18858	+	18.0834i	0.114096	+	0.647073i
$782$		0			0
$783$	−0.783286	−	1.32191i	−0.0279924	−	0.0472413i
$784$		0			0
$785$	−2.20038	+	0.387987i	−0.0785351	+	0.0138479i
$786$		0			0
$787$	3.35226	+	9.21026i	0.119495	+	0.328310i	0.984991	−	0.172606i	$-0.0552187\pi$
$787$	3.35226	+	9.21026i	0.119495	+	0.328310i	−0.865496	+	0.500916i	$0.832996\pi$
$788$		0			0
$789$	−21.8556	−	20.4644i	−0.778078	−	0.728551i
$790$		0			0
$791$	16.8602	+	29.2028i	0.599481	+	1.03833i
$792$		0			0
$793$	−15.9064	+	27.5507i	−0.564853	+	0.978355i
$794$		0			0
$795$	5.24178	+	10.3398i	0.185907	+	0.366715i
$796$		0			0
$797$	−2.06130	−	0.363462i	−0.0730149	−	0.0128745i	0.137021	−	0.990568i	$-0.456247\pi$
$797$	−2.06130	−	0.363462i	−0.0730149	−	0.0128745i	−0.210036	+	0.977694i	$0.567358\pi$
$798$		0			0
$799$	47.7370	+	56.8907i	1.68881	+	2.01265i
$800$		0			0
$801$	−39.3026	−	11.4440i	−1.38869	−	0.404355i
$802$		0			0
$803$	−38.8212	−	14.1298i	−1.36997	−	0.498629i
$804$		0			0
$805$	−23.9965	−	20.1355i	−0.845766	−	0.709682i
$806$		0			0
$807$	−7.87710	+	18.4523i	−0.277287	+	0.649550i
$808$		0			0
$809$			31.1682i			1.09582i	0.836538	+	0.547908i	$0.184576\pi$
$809$			31.1682i			1.09582i	−0.836538	+	0.547908i	$0.815424\pi$
$810$		0			0
$811$		−	20.0460i		−	0.703911i	−0.936017	−	0.351956i	$-0.885517\pi$
$811$		−	20.0460i		−	0.703911i	0.936017	−	0.351956i	$-0.114483\pi$
$812$		0			0
$813$	−7.66049	+	17.9448i	−0.268665	+	0.629353i
$814$		0			0
$815$	6.25420	+	5.24790i	0.219075	+	0.183826i
$816$		0			0
$817$	−1.73402	−	0.631133i	−0.0606658	−	0.0220806i
$818$		0			0
$819$	20.9936	+	85.6926i	0.733577	+	2.99434i
$820$		0			0
$821$	0.468140	+	0.557907i	0.0163382	+	0.0194711i	0.774152	−	0.633000i	$-0.218177\pi$
$821$	0.468140	+	0.557907i	0.0163382	+	0.0194711i	−0.757813	+	0.652471i	$0.773732\pi$
$822$		0			0
$823$	−10.5574	−	1.86155i	−0.368007	−	0.0648895i	−0.0134132	−	0.999910i	$-0.504270\pi$
$823$	−10.5574	−	1.86155i	−0.368007	−	0.0648895i	−0.354594	+	0.935021i	$0.615381\pi$
$824$		0			0
$825$	9.34612	+	18.4359i	0.325390	+	0.641856i
$826$		0			0
$827$	25.2893	−	43.8023i	0.879395	−	1.52316i	0.0273886	−	0.999625i	$-0.491281\pi$
$827$	25.2893	−	43.8023i	0.879395	−	1.52316i	0.852006	−	0.523532i	$-0.175386\pi$
$828$		0			0
$829$	11.2821	+	19.5412i	0.391844	+	0.678693i	0.992693	−	0.120669i	$-0.0385040\pi$
$829$	11.2821	+	19.5412i	0.391844	+	0.678693i	−0.600849	+	0.799363i	$0.705171\pi$
$830$		0			0
$831$	26.5554	+	24.8650i	0.921195	+	0.862557i
$832$		0			0
$833$	24.8977	+	68.4058i	0.862653	+	2.37012i
$834$		0			0
$835$	0.672556	−	0.118590i	0.0232748	−	0.00410397i
$836$		0			0
$837$	−12.7976	+	10.9876i	−0.442349	+	0.379788i
$838$		0			0
$839$	1.99376	+	11.3072i	0.0688322	+	0.390367i	0.999688	+	0.0249799i	$0.00795218\pi$
$839$	1.99376	+	11.3072i	0.0688322	+	0.390367i	−0.930856	+	0.365387i	$0.880937\pi$
$840$		0			0
$841$	−27.1689	+	9.88868i	−0.936859	+	0.340989i
$842$		0			0
$843$	16.4850	+	54.3170i	0.567772	+	1.87078i
$844$		0			0
$845$	32.3370	−	18.6698i	1.11243	−	0.642260i
$846$		0			0
$847$	4.00328	+	2.31130i	0.137554	+	0.0794170i
$848$		0			0
$849$	23.6345	+	15.4173i	0.811135	+	0.529119i
$850$		0			0
$851$	9.02225	−	51.1677i	0.309279	−	1.75401i
$852$		0			0
$853$	10.5544	−	8.85621i	0.361377	−	0.303231i	−0.443963	−	0.896045i	$-0.646428\pi$
$853$	10.5544	−	8.85621i	0.361377	−	0.303231i	0.805339	+	0.592814i	$0.201983\pi$
$854$		0			0
$855$	−1.38339	+	0.924898i	−0.0473110	+	0.0316308i
$856$		0			0
$857$	13.1678	−	36.1782i	0.449803	−	1.23582i	−0.483058	−	0.875588i	$-0.660474\pi$
$857$	13.1678	−	36.1782i	0.449803	−	1.23582i	0.932861	−	0.360236i	$-0.117304\pi$
$858$		0			0
$859$	−22.0396	+	26.2657i	−0.751980	+	0.896175i	−0.997313	−	0.0732640i	$-0.976658\pi$
$859$	−22.0396	+	26.2657i	−0.751980	+	0.896175i	0.245332	+	0.969439i	$0.421103\pi$
$860$		0			0
$861$	−3.19860	+	2.40008i	−0.109008	+	0.0817945i
$862$		0			0
$863$	−37.1288			−1.26388			−0.631940	−	0.775017i	$-0.717741\pi$
$863$	−37.1288			−1.26388			−0.631940	+	0.775017i	$0.717741\pi$
$864$		0			0
$865$	−15.2402			−0.518182
$866$		0			0
$867$	−2.82319	−	23.3884i	−0.0958806	−	0.794313i
$868$		0			0
$869$	−22.9260	+	27.3221i	−0.777711	+	0.926840i
$870$		0			0
$871$	−3.89852	+	10.7111i	−0.132096	+	0.362932i
$872$		0			0
$873$	35.9549	+	3.92778i	1.21689	+	0.132935i
$874$		0			0
$875$	36.2524	−	30.4193i	1.22555	−	1.02836i
$876$		0			0
$877$	−5.17235	+	29.3338i	−0.174658	+	0.990533i	0.763880	+	0.645358i	$0.223292\pi$
$877$	−5.17235	+	29.3338i	−0.174658	+	0.990533i	−0.938538	+	0.345175i	$0.887819\pi$
$878$		0			0
$879$	−0.435151	+	7.99044i	−0.0146773	+	0.269511i
$880$		0			0
$881$	47.9766	+	27.6993i	1.61637	+	0.933213i	0.987848	+	0.155423i	$0.0496739\pi$
$881$	47.9766	+	27.6993i	1.61637	+	0.933213i	0.628524	+	0.777790i	$0.283659\pi$
$882$		0			0
$883$	−6.80457	+	3.92862i	−0.228992	+	0.132209i	−0.610107	−	0.792319i	$-0.708874\pi$
$883$	−6.80457	+	3.92862i	−0.228992	+	0.132209i	0.381115	+	0.924528i	$0.375540\pi$
$884$		0			0
$885$	−18.8510	−	4.39272i	−0.633668	−	0.147660i
$886$		0			0
$887$	23.4489	−	8.53471i	0.787338	−	0.286568i	0.0831090	−	0.996540i	$-0.473515\pi$
$887$	23.4489	−	8.53471i	0.787338	−	0.286568i	0.704229	+	0.709973i	$0.251293\pi$
$888$		0			0
$889$	4.88485	+	27.7034i	0.163833	+	0.929141i
$890$		0			0
$891$	−19.0162	−	24.7544i	−0.637065	−	0.829303i
$892$		0			0
$893$	−5.87300	+	1.03557i	−0.196533	+	0.0346540i
$894$		0			0
$895$	0.842296	+	2.31419i	0.0281548	+	0.0773548i
$896$		0			0
$897$	−14.3850	+	61.7318i	−0.480300	+	2.06117i
$898$		0			0
$899$	−0.479954	−	0.831304i	−0.0160074	−	0.0277255i
$900$		0			0
$901$	14.8250	−	25.6776i	0.493892	−	0.855446i
$902$		0			0
$903$	−32.2578	−	1.75672i	−1.07347	−	0.0584601i
$904$		0			0
$905$	8.62896	+	1.52152i	0.286836	+	0.0505770i
$906$		0			0
$907$	1.49400	+	1.78048i	0.0496073	+	0.0591197i	0.790278	−	0.612749i	$-0.209936\pi$
$907$	1.49400	+	1.78048i	0.0496073	+	0.0591197i	−0.740670	+	0.671869i	$0.765492\pi$
$908$		0			0
$909$	14.2989	−	6.29632i	0.474264	−	0.208836i
$910$		0			0
$911$	37.2453	+	13.5562i	1.23399	+	0.449137i	0.874963	−	0.484190i	$-0.160885\pi$
$911$	37.2453	+	13.5562i	1.23399	+	0.449137i	0.359030	+	0.933326i	$0.383108\pi$
$912$		0			0
$913$	12.6114	+	10.5822i	0.417376	+	0.350220i
$914$		0			0
$915$	−10.4291	+	1.25888i	−0.344775	+	0.0416174i
$916$		0			0
$917$		−	89.6757i		−	2.96135i
$918$		0			0
$919$		−	23.7423i		−	0.783188i	−0.920138	−	0.391594i	$-0.871924\pi$
$919$		−	23.7423i		−	0.783188i	0.920138	−	0.391594i	$-0.128076\pi$
$920$		0			0
$921$	32.7492	+	43.6451i	1.07912	+	1.43816i
$922$		0			0
$923$	−26.5642	−	22.2900i	−0.874372	−	0.733685i
$924$		0			0
$925$	30.0668	+	10.9434i	0.988590	+	0.359817i
$926$		0			0
$927$	32.4572	−	2.13625i	1.06604	−	0.0701637i
$928$		0			0
$929$	−21.0775	−	25.1192i	−0.691530	−	0.824133i	0.300010	−	0.953936i	$-0.403010\pi$
$929$	−21.0775	−	25.1192i	−0.691530	−	0.824133i	−0.991540	+	0.129803i	$0.958566\pi$
$930$		0			0
$931$	−5.75678	−	1.01508i	−0.188671	−	0.0332678i
$932$		0			0
$933$	−6.59028	+	10.1028i	−0.215756	+	0.330752i
$934$		0			0
$935$	−11.9793	+	20.7487i	−0.391763	+	0.678554i
$936$		0			0
$937$	13.5311	+	23.4365i	0.442040	+	0.765636i	0.997841	−	0.0656795i	$-0.0209215\pi$
$937$	13.5311	+	23.4365i	0.442040	+	0.765636i	−0.555801	+	0.831316i	$0.687588\pi$
$938$		0			0
$939$	24.9849	−	7.58281i	0.815352	−	0.247456i
$940$		0			0
$941$	6.17955	+	16.9782i	0.201448	+	0.553473i	0.998743	−	0.0501161i	$-0.0159591\pi$
$941$	6.17955	+	16.9782i	0.201448	+	0.553473i	−0.797296	+	0.603589i	$0.793737\pi$
$942$		0			0
$943$	−2.82935	+	0.498890i	−0.0921362	+	0.0162461i
$944$		0			0
$945$	−18.4726	+	22.5277i	−0.600913	+	0.732826i
$946$		0			0
$947$	8.28270	+	46.9735i	0.269152	+	1.52643i	0.756947	+	0.653477i	$0.226690\pi$
$947$	8.28270	+	46.9735i	0.269152	+	1.52643i	−0.487795	+	0.872958i	$0.662199\pi$
$948$		0			0
$949$	73.3136	−	26.6840i	2.37986	−	0.866199i
$950$		0			0
$951$	17.3362	−	18.5148i	0.562166	−	0.600383i
$952$		0			0
$953$	−26.1006	+	15.0692i	−0.845480	+	0.488138i	−0.859123	−	0.511769i	$-0.828990\pi$
$953$	−26.1006	+	15.0692i	−0.845480	+	0.488138i	0.0136432	+	0.999907i	$0.495657\pi$
$954$		0			0
$955$	12.4872	+	7.20946i	0.404075	+	0.233293i
$956$		0			0
$957$	1.58447	−	0.803248i	0.0512185	−	0.0259653i
$958$		0			0
$959$	6.26690	−	35.5413i	0.202369	−	1.14769i
$960$		0			0
$961$	15.6754	−	13.1532i	0.505657	−	0.424296i
$962$		0			0
$963$	−0.217463	−	0.227041i	−0.00700766	−	0.00731630i
$964$		0			0
$965$	−9.50697	+	26.1202i	−0.306040	+	0.840839i
$966$		0			0
$967$	−35.1247	+	41.8600i	−1.12953	+	1.34613i	−0.198966	+	0.980006i	$0.563758\pi$
$967$	−35.1247	+	41.8600i	−1.12953	+	1.34613i	−0.930568	+	0.366119i	$0.880686\pi$
$968$		0			0
$969$	3.91445	+	1.67104i	0.125750	+	0.0536816i
$970$		0			0
$971$	42.9541			1.37846			0.689232	−	0.724541i	$-0.257948\pi$
$971$	42.9541			1.37846			0.689232	+	0.724541i	$0.257948\pi$
$972$		0			0
$973$	−60.5191			−1.94015
$974$		0			0
$975$	−35.9001	−	15.3254i	−1.14972	−	0.490806i
$976$		0			0
$977$	3.89771	−	4.64511i	0.124699	−	0.148610i	−0.700083	−	0.714062i	$-0.746854\pi$
$977$	3.89771	−	4.64511i	0.124699	−	0.148610i	0.824782	+	0.565451i	$0.191298\pi$
$978$		0			0
$979$	16.1863	−	44.4715i	0.517317	−	1.42132i
$980$		0			0
$981$	−15.9009	−	16.6012i	−0.507677	−	0.530037i
$982$		0			0
$983$	−6.76137	+	5.67347i	−0.215654	+	0.180955i	−0.744215	−	0.667940i	$-0.767176\pi$
$983$	−6.76137	+	5.67347i	−0.215654	+	0.180955i	0.528561	+	0.848895i	$0.322732\pi$
$984$		0			0
$985$	2.17443	−	12.3318i	0.0692831	−	0.392924i
$986$		0			0
$987$	−93.1213	+	47.2080i	−2.96409	+	1.50265i
$988$		0			0
$989$	−20.1001	−	11.6048i	−0.639147	−	0.369012i
$990$		0			0
$991$	−21.4204	+	12.3671i	−0.680440	+	0.392852i	−0.800021	−	0.599972i	$-0.795178\pi$
$991$	−21.4204	+	12.3671i	−0.680440	+	0.392852i	0.119581	+	0.992824i	$0.461845\pi$
$992$		0			0
$993$	21.8390	−	23.3236i	0.693040	−	0.740153i
$994$		0			0
$995$	16.1855	−	5.89103i	0.513114	−	0.186758i
$996$		0			0
$997$	−9.48267	−	53.7789i	−0.300319	−	1.70319i	−0.644759	−	0.764386i	$-0.723042\pi$
$997$	−9.48267	−	53.7789i	−0.300319	−	1.70319i	0.344440	−	0.938808i	$-0.388069\pi$
$998$		0			0
$999$	−47.6788	−	7.85177i	−1.50849	−	0.248419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.5	✓	216
4.3	odd	2	inner	864.2.bi.a.95.32	yes	216
27.2	odd	18	inner	864.2.bi.a.191.32	yes	216
108.83	even	18	inner	864.2.bi.a.191.5	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.5	✓	216	1.1	even	1	trivial
864.2.bi.a.95.32	yes	216	4.3	odd	2	inner
864.2.bi.a.191.5	yes	216	108.83	even	18	inner
864.2.bi.a.191.32	yes	216	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59297 - 0.680026i) q^{3} +(-0.802661 + 0.956575i) q^{5} +(-1.53564 + 4.21915i) q^{7} +(2.07513 + 2.16653i) q^{9} +O(q^{10})\)	\(q+(-1.59297 - 0.680026i) q^{3} +(-0.802661 + 0.956575i) q^{5} +(-1.53564 + 4.21915i) q^{7} +(2.07513 + 2.16653i) q^{9} +(-2.65692 + 2.22942i) q^{11} +(1.13739 - 6.45047i) q^{13} +(1.92911 - 0.977968i) q^{15} +(-4.79072 - 2.76592i) q^{17} +(0.384700 - 0.222107i) q^{19} +(5.31537 - 5.67671i) q^{21} +(5.25020 - 1.91092i) q^{23} +(0.597471 + 3.38843i) q^{25} +(-1.83233 - 4.86236i) q^{27} +(0.291217 - 0.0513494i) q^{29} +(-1.11024 - 3.05035i) q^{31} +(5.74847 - 1.74464i) q^{33} +(-2.80333 - 4.85551i) q^{35} +(4.64969 - 8.05350i) q^{37} +(-6.19832 + 9.50198i) q^{39} +(-0.506402 - 0.0892924i) q^{41} +(-2.67021 - 3.18223i) q^{43} +(-3.73807 + 0.246030i) q^{45} +(-12.6155 - 4.59165i) q^{47} +(-10.0807 - 8.45871i) q^{49} +(5.75059 + 7.66386i) q^{51} +5.35987i q^{53} -4.33101i q^{55} +(-0.763855 + 0.0922041i) q^{57} +(-6.85558 - 5.75251i) q^{59} +(-4.56402 - 1.66117i) q^{61} +(-12.3276 + 5.42827i) q^{63} +(5.25742 + 6.26555i) q^{65} +(-1.71380 - 0.302189i) q^{67} +(-9.66291 - 0.526231i) q^{69} +(2.64712 - 4.58494i) q^{71} +(5.95564 + 10.3155i) q^{73} +(1.35246 - 5.80397i) q^{75} +(-5.32617 - 14.6335i) q^{77} +(10.1272 - 1.78569i) q^{79} +(-0.387669 + 8.99165i) q^{81} +(-0.824241 - 4.67450i) q^{83} +(6.49114 - 2.36258i) q^{85} +(-0.498820 - 0.116237i) q^{87} +(-11.8169 + 6.82247i) q^{89} +(25.4689 + 14.7045i) q^{91} +(-0.305739 + 5.61412i) q^{93} +(-0.0963222 + 0.546271i) q^{95} +(9.23564 - 7.74962i) q^{97} +(-10.3436 - 1.12995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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