LMFDB - Embedded newform 864.2.y.a.385.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, 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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.3
Character	$\chi$	$=$	864.385
Dual form			864.2.y.a.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34012 - 1.09730i) q^{3} +(0.181867 + 1.03142i) q^{5} +(-0.246536 - 0.206868i) q^{7} +(0.591863 + 2.94104i) q^{9} +O(q^{10})$	\(q+(-1.34012 - 1.09730i) q^{3} +(0.181867 + 1.03142i) q^{5} +(-0.246536 - 0.206868i) q^{7} +(0.591863 + 2.94104i) q^{9} +(0.447486 - 2.53782i) q^{11} +(-1.61568 - 0.588061i) q^{13} +(0.888052 - 1.58179i) q^{15} +(0.747954 + 1.29549i) q^{17} +(1.58145 - 2.73916i) q^{19} +(0.103392 + 0.547753i) q^{21} +(1.68384 - 1.41291i) q^{23} +(3.66771 - 1.33494i) q^{25} +(2.43403 - 4.59080i) q^{27} +(1.03702 - 0.377445i) q^{29} +(-1.18071 + 0.990730i) q^{31} +(-3.38444 + 2.90997i) q^{33} +(0.168531 - 0.291904i) q^{35} +(-3.26464 - 5.65453i) q^{37} +(1.51994 + 2.56096i) q^{39} +(3.73426 + 1.35916i) q^{41} +(1.52862 - 8.66921i) q^{43} +(-2.92580 + 1.14534i) q^{45} +(-4.47792 - 3.75742i) q^{47} +(-1.19755 - 6.79165i) q^{49} +(0.419196 - 2.55685i) q^{51} +7.88666 q^{53} +2.69894 q^{55} +(-5.12502 + 1.93548i) q^{57} +(-1.63497 - 9.27235i) q^{59} +(-6.77642 - 5.68610i) q^{61} +(0.462492 - 0.847510i) q^{63} +(0.312697 - 1.77339i) q^{65} +(-6.44927 - 2.34734i) q^{67} +(-3.80693 + 0.0457948i) q^{69} +(6.30559 + 10.9216i) q^{71} +(2.92844 - 5.07220i) q^{73} +(-6.38002 - 2.23560i) q^{75} +(-0.635317 + 0.533094i) q^{77} +(4.69022 - 1.70710i) q^{79} +(-8.29940 + 3.48138i) q^{81} +(-0.703168 + 0.255932i) q^{83} +(-1.20017 + 1.00706i) q^{85} +(-1.80391 - 0.632101i) q^{87} +(2.09721 - 3.63248i) q^{89} +(0.276673 + 0.479212i) q^{91} +(2.66942 - 0.0321113i) q^{93} +(3.11283 + 1.13298i) q^{95} +(0.759815 - 4.30912i) q^{97} +(7.72868 - 0.185968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	−1.34012	−	1.09730i	−0.773721	−	0.633527i
$3$	−1.34012	−	1.09730i	−0.773721	−	0.633527i
$4$		0			0
$5$	0.181867	+	1.03142i	0.0813334	+	0.461264i	0.998088	+	0.0618131i	$0.0196883\pi$
$5$	0.181867	+	1.03142i	0.0813334	+	0.461264i	−0.916754	+	0.399451i	$0.869201\pi$
$6$		0			0
$7$	−0.246536	−	0.206868i	−0.0931819	−	0.0781889i	0.595007	−	0.803721i	$-0.297149\pi$
$7$	−0.246536	−	0.206868i	−0.0931819	−	0.0781889i	−0.688189	+	0.725532i	$0.741594\pi$
$8$		0			0
$9$	0.591863	+	2.94104i	0.197288	+	0.980346i
$10$		0			0
$11$	0.447486	−	2.53782i	0.134922	−	0.765182i	−0.839992	−	0.542599i	$-0.817440\pi$
$11$	0.447486	−	2.53782i	0.134922	−	0.765182i	0.974914	−	0.222583i	$-0.0714487\pi$
$12$		0			0
$13$	−1.61568	−	0.588061i	−0.448110	−	0.163099i	0.108101	−	0.994140i	$-0.465523\pi$
$13$	−1.61568	−	0.588061i	−0.448110	−	0.163099i	−0.556211	+	0.831041i	$0.687745\pi$
$14$		0			0
$15$	0.888052	−	1.58179i	0.229294	−	0.408417i
$16$		0			0
$17$	0.747954	+	1.29549i	0.181405	+	0.314203i	0.942359	−	0.334602i	$-0.108602\pi$
$17$	0.747954	+	1.29549i	0.181405	+	0.314203i	−0.760954	+	0.648806i	$0.775269\pi$
$18$		0			0
$19$	1.58145	−	2.73916i	0.362810	−	0.628406i	−0.625612	−	0.780134i	$-0.715151\pi$
$19$	1.58145	−	2.73916i	0.362810	−	0.628406i	0.988422	+	0.151729i	$0.0484840\pi$
$20$		0			0
$21$	0.103392	+	0.547753i	0.0225620	+	0.119530i
$22$		0			0
$23$	1.68384	−	1.41291i	0.351104	−	0.294612i	−0.450129	−	0.892964i	$-0.648622\pi$
$23$	1.68384	−	1.41291i	0.351104	−	0.294612i	0.801233	+	0.598352i	$0.204178\pi$
$24$		0			0
$25$	3.66771	−	1.33494i	0.733543	−	0.266988i
$26$		0			0
$27$	2.43403	−	4.59080i	0.468430	−	0.883501i
$28$		0			0
$29$	1.03702	−	0.377445i	0.192570	−	0.0700898i	−0.243935	−	0.969792i	$-0.578438\pi$
$29$	1.03702	−	0.377445i	0.192570	−	0.0700898i	0.436505	+	0.899702i	$0.356216\pi$
$30$		0			0
$31$	−1.18071	+	0.990730i	−0.212061	+	0.177940i	−0.742631	−	0.669701i	$-0.766422\pi$
$31$	−1.18071	+	0.990730i	−0.212061	+	0.177940i	0.530570	+	0.847641i	$0.321978\pi$
$32$		0			0
$33$	−3.38444	+	2.90997i	−0.589155	+	0.506560i
$34$		0			0
$35$	0.168531	−	0.291904i	0.0284870	−	0.0493409i
$36$		0			0
$37$	−3.26464	−	5.65453i	−0.536704	−	0.929599i	−0.999079	−	0.0429140i	$-0.986336\pi$
$37$	−3.26464	−	5.65453i	−0.536704	−	0.929599i	0.462375	−	0.886685i	$-0.346997\pi$
$38$		0			0
$39$	1.51994	+	2.56096i	0.243385	+	0.410082i
$40$		0			0
$41$	3.73426	+	1.35916i	0.583194	+	0.212265i	0.616733	−	0.787172i	$-0.288456\pi$
$41$	3.73426	+	1.35916i	0.583194	+	0.212265i	−0.0335396	+	0.999437i	$0.510678\pi$
$42$		0			0
$43$	1.52862	−	8.66921i	0.233112	−	1.32204i	−0.613443	−	0.789739i	$-0.710216\pi$
$43$	1.52862	−	8.66921i	0.233112	−	1.32204i	0.846554	−	0.532303i	$-0.178673\pi$
$44$		0			0
$45$	−2.92580	+	1.14534i	−0.436153	+	0.170737i
$46$		0			0
$47$	−4.47792	−	3.75742i	−0.653172	−	0.548076i	0.254860	−	0.966978i	$-0.417971\pi$
$47$	−4.47792	−	3.75742i	−0.653172	−	0.548076i	−0.908031	+	0.418902i	$0.862415\pi$
$48$		0			0
$49$	−1.19755	−	6.79165i	−0.171079	−	0.970236i
$50$		0			0
$51$	0.419196	−	2.55685i	0.0586991	−	0.358031i
$52$		0			0
$53$	7.88666			1.08332			0.541658	−	0.840599i	$-0.317797\pi$
$53$	7.88666			1.08332			0.541658	+	0.840599i	$0.317797\pi$
$54$		0			0
$55$	2.69894			0.363925
$56$		0			0
$57$	−5.12502	+	1.93548i	−0.678825	+	0.256360i
$58$		0			0
$59$	−1.63497	−	9.27235i	−0.212854	−	1.20716i	−0.884591	−	0.466367i	$-0.845563\pi$
$59$	−1.63497	−	9.27235i	−0.212854	−	1.20716i	0.671737	−	0.740790i	$-0.265549\pi$
$60$		0			0
$61$	−6.77642	−	5.68610i	−0.867632	−	0.728030i	0.0959659	−	0.995385i	$-0.469406\pi$
$61$	−6.77642	−	5.68610i	−0.867632	−	0.728030i	−0.963598	+	0.267355i	$0.913850\pi$
$62$		0			0
$63$	0.462492	−	0.847510i	0.0582685	−	0.106776i
$64$		0			0
$65$	0.312697	−	1.77339i	0.0387853	−	0.219963i
$66$		0			0
$67$	−6.44927	−	2.34734i	−0.787904	−	0.286774i	−0.0834396	−	0.996513i	$-0.526591\pi$
$67$	−6.44927	−	2.34734i	−0.787904	−	0.286774i	−0.704465	+	0.709739i	$0.748813\pi$
$68$		0			0
$69$	−3.80693	+	0.0457948i	−0.458301	+	0.00551304i
$70$		0			0
$71$	6.30559	+	10.9216i	0.748336	+	1.29616i	0.948620	+	0.316418i	$0.102480\pi$
$71$	6.30559	+	10.9216i	0.748336	+	1.29616i	−0.200283	+	0.979738i	$0.564186\pi$
$72$		0			0
$73$	2.92844	−	5.07220i	0.342748	−	0.593657i	−0.642194	−	0.766542i	$-0.721976\pi$
$73$	2.92844	−	5.07220i	0.342748	−	0.593657i	0.984942	+	0.172885i	$0.0553091\pi$
$74$		0			0
$75$	−6.38002	−	2.23560i	−0.736701	−	0.258145i
$76$		0			0
$77$	−0.635317	+	0.533094i	−0.0724010	+	0.0607517i
$78$		0			0
$79$	4.69022	−	1.70710i	0.527691	−	0.192064i	−0.0644163	−	0.997923i	$-0.520519\pi$
$79$	4.69022	−	1.70710i	0.527691	−	0.192064i	0.592107	+	0.805859i	$0.298296\pi$
$80$		0			0
$81$	−8.29940	+	3.48138i	−0.922155	+	0.386820i
$82$		0			0
$83$	−0.703168	+	0.255932i	−0.0771827	+	0.0280922i	−0.380323	−	0.924854i	$-0.624187\pi$
$83$	−0.703168	+	0.255932i	−0.0771827	+	0.0280922i	0.303140	+	0.952946i	$0.401965\pi$
$84$		0			0
$85$	−1.20017	+	1.00706i	−0.130177	+	0.109231i
$86$		0			0
$87$	−1.80391	−	0.632101i	−0.193399	−	0.0677684i
$88$		0			0
$89$	2.09721	−	3.63248i	0.222304	−	0.385042i	−0.733203	−	0.680010i	$-0.761976\pi$
$89$	2.09721	−	3.63248i	0.222304	−	0.385042i	0.955507	+	0.294968i	$0.0953088\pi$
$90$		0			0
$91$	0.276673	+	0.479212i	0.0290032	+	0.0502351i
$92$		0			0
$93$	2.66942	−	0.0321113i	0.276806	−	0.00332979i
$94$		0			0
$95$	3.11283	+	1.13298i	0.319370	+	0.116241i
$96$		0			0
$97$	0.759815	−	4.30912i	0.0771475	−	0.437525i	−0.921629	−	0.388072i	$-0.873141\pi$
$97$	0.759815	−	4.30912i	0.0771475	−	0.437525i	0.998776	−	0.0494530i	$-0.0157478\pi$
$98$		0			0
$99$	7.72868	−	0.185968i	0.776761	−	0.0186905i
$100$		0			0
$101$	12.6503	+	10.6149i	1.25875	+	1.05622i	0.995814	+	0.0914041i	$0.0291355\pi$
$101$	12.6503	+	10.6149i	1.25875	+	1.05622i	0.262937	+	0.964813i	$0.415309\pi$
$102$		0			0
$103$	0.718649	+	4.07566i	0.0708106	+	0.401587i	0.999526	+	0.0307930i	$0.00980325\pi$
$103$	0.718649	+	4.07566i	0.0708106	+	0.401587i	−0.928715	+	0.370794i	$0.879086\pi$
$104$		0			0
$105$	−0.546160	+	0.206259i	−0.0532997	+	0.0201288i
$106$		0			0
$107$	−5.72525			−0.553481			−0.276741	−	0.960945i	$-0.589254\pi$
$107$	−5.72525			−0.553481			−0.276741	+	0.960945i	$0.589254\pi$
$108$		0			0
$109$	−4.47428			−0.428558			−0.214279	−	0.976772i	$-0.568740\pi$
$109$	−4.47428			−0.428558			−0.214279	+	0.976772i	$0.568740\pi$
$110$		0			0
$111$	−1.82969	+	11.1601i	−0.173667	+	1.05927i
$112$		0			0
$113$	−0.618951	−	3.51024i	−0.0582260	−	0.330216i	0.941756	−	0.336298i	$-0.109175\pi$
$113$	−0.618951	−	3.51024i	−0.0582260	−	0.330216i	−0.999982	+	0.00608229i	$0.998064\pi$
$114$		0			0
$115$	1.76353	+	1.47978i	0.164450	+	0.137990i
$116$		0			0
$117$	0.773245	−	5.09983i	0.0714865	−	0.471480i
$118$		0			0
$119$	0.0835991	−	0.474114i	0.00766352	−	0.0434620i
$120$		0			0
$121$	4.09632	+	1.49094i	0.372393	+	0.135540i
$122$		0			0
$123$	−3.51296	−	5.91905i	−0.316753	−	0.533703i
$124$		0			0
$125$	4.66224	+	8.07524i	0.417004	+	0.722271i
$126$		0			0
$127$	−6.63179	+	11.4866i	−0.588476	+	1.01927i	0.405956	+	0.913892i	$0.366938\pi$
$127$	−6.63179	+	11.4866i	−0.588476	+	1.01927i	−0.994432	+	0.105378i	$0.966395\pi$
$128$		0			0
$129$	−11.5613	+	9.94046i	−1.01791	+	0.875209i
$130$		0			0
$131$	5.76796	−	4.83989i	0.503949	−	0.422863i	−0.355045	−	0.934849i	$-0.615534\pi$
$131$	5.76796	−	4.83989i	0.503949	−	0.422863i	0.858994	+	0.511986i	$0.171090\pi$
$132$		0			0
$133$	−0.956530	+	0.348148i	−0.0829417	+	0.0301883i
$134$		0			0
$135$	5.17771	+	1.67559i	0.445627	+	0.144212i
$136$		0			0
$137$	7.23016	−	2.63156i	0.617714	−	0.224830i	−0.0141608	−	0.999900i	$-0.504508\pi$
$137$	7.23016	−	2.63156i	0.617714	−	0.224830i	0.631875	+	0.775070i	$0.282285\pi$
$138$		0			0
$139$	−15.6236	+	13.1097i	−1.32517	+	1.11195i	−0.339993	+	0.940428i	$0.610425\pi$
$139$	−15.6236	+	13.1097i	−1.32517	+	1.11195i	−0.985180	+	0.171525i	$0.945131\pi$
$140$		0			0
$141$	1.87795	+	9.94903i	0.158152	+	0.837860i
$142$		0			0
$143$	−2.21539	+	3.83717i	−0.185260	+	0.320880i
$144$		0			0
$145$	0.577904	+	1.00096i	0.0479923	+	0.0831251i
$146$		0			0
$147$	−5.84762	+	10.4157i	−0.482303	+	0.859075i
$148$		0			0
$149$	22.1097	+	8.04726i	1.81129	+	0.659257i	0.996876	+	0.0789785i	$0.0251658\pi$
$149$	22.1097	+	8.04726i	1.81129	+	0.659257i	0.814418	+	0.580279i	$0.197056\pi$
$150$		0			0
$151$	1.12514	−	6.38101i	0.0915629	−	0.519279i	−0.904184	−	0.427144i	$-0.859520\pi$
$151$	1.12514	−	6.38101i	0.0915629	−	0.519279i	0.995747	−	0.0921350i	$-0.0293691\pi$
$152$		0			0
$153$	−3.36741	+	2.96651i	−0.272239	+	0.239829i
$154$		0			0
$155$	−1.23659	−	1.03762i	−0.0993252	−	0.0833437i
$156$		0			0
$157$	−1.84520	−	10.4646i	−0.147263	−	0.835168i	−0.965523	−	0.260320i	$-0.916172\pi$
$157$	−1.84520	−	10.4646i	−0.147263	−	0.835168i	0.818260	−	0.574849i	$-0.194939\pi$
$158$		0			0
$159$	−10.5691	−	8.65404i	−0.838184	−	0.686310i
$160$		0			0
$161$	−0.707413			−0.0557519
$162$		0			0
$163$	16.5560			1.29677			0.648384	−	0.761313i	$-0.275445\pi$
$163$	16.5560			1.29677			0.648384	+	0.761313i	$0.275445\pi$
$164$		0			0
$165$	−3.61691	−	2.96155i	−0.281576	−	0.230556i
$166$		0			0
$167$	1.53218	+	8.68944i	0.118564	+	0.672409i	0.984924	+	0.172989i	$0.0553425\pi$
$167$	1.53218	+	8.68944i	0.118564	+	0.672409i	−0.866360	+	0.499420i	$0.833546\pi$
$168$		0			0
$169$	−7.69396	−	6.45600i	−0.591843	−	0.496615i
$170$		0			0
$171$	8.99196	+	3.02991i	0.687633	+	0.231703i
$172$		0			0
$173$	−1.45437	+	8.24814i	−0.110574	+	0.627095i	0.878273	+	0.478159i	$0.158696\pi$
$173$	−1.45437	+	8.24814i	−0.110574	+	0.627095i	−0.988847	+	0.148936i	$0.952415\pi$
$174$		0			0
$175$	−1.18038	−	0.429623i	−0.0892284	−	0.0324765i
$176$		0			0
$177$	−7.98350	+	14.2201i	−0.600077	+	1.06885i
$178$		0			0
$179$	9.42617	+	16.3266i	0.704545	+	1.22031i	0.966855	+	0.255324i	$0.0821823\pi$
$179$	9.42617	+	16.3266i	0.704545	+	1.22031i	−0.262310	+	0.964984i	$0.584484\pi$
$180$		0			0
$181$	−0.865464	+	1.49903i	−0.0643295	+	0.111422i	−0.896396	−	0.443253i	$-0.853824\pi$
$181$	−0.865464	+	1.49903i	−0.0643295	+	0.111422i	0.832067	+	0.554675i	$0.187158\pi$
$182$		0			0
$183$	2.84189	+	15.0558i	0.210079	+	1.11296i
$184$		0			0
$185$	5.23845	−	4.39559i	0.385139	−	0.323170i
$186$		0			0
$187$	3.62243	−	1.31846i	0.264898	−	0.0964152i
$188$		0			0
$189$	−1.54977	+	0.628275i	−0.112729	+	0.0457003i
$190$		0			0
$191$	−22.5701	+	8.21484i	−1.63312	+	0.594405i	−0.985816	−	0.167831i	$-0.946324\pi$
$191$	−22.5701	+	8.21484i	−1.63312	+	0.594405i	−0.647299	+	0.762236i	$0.724102\pi$
$192$		0			0
$193$	9.35612	−	7.85071i	0.673468	−	0.565107i	−0.240622	−	0.970619i	$-0.577351\pi$
$193$	9.35612	−	7.85071i	0.673468	−	0.565107i	0.914090	+	0.405512i	$0.132907\pi$
$194$		0			0
$195$	−2.36500	+	2.03345i	−0.169361	+	0.145618i
$196$		0			0
$197$	−3.91303	+	6.77757i	−0.278792	+	0.482882i	−0.971085	−	0.238735i	$-0.923267\pi$
$197$	−3.91303	+	6.77757i	−0.278792	+	0.482882i	0.692293	+	0.721617i	$0.256601\pi$
$198$		0			0
$199$	11.8573	+	20.5374i	0.840540	+	1.45586i	0.889439	+	0.457054i	$0.151095\pi$
$199$	11.8573	+	20.5374i	0.840540	+	1.45586i	−0.0488990	+	0.998804i	$0.515571\pi$
$200$		0			0
$201$	6.06708	+	10.2225i	0.427939	+	0.721041i
$202$		0			0
$203$	−0.333745	−	0.121473i	−0.0234243	−	0.00852574i
$204$		0			0
$205$	−0.722724	+	4.09877i	−0.0504773	+	0.286271i
$206$		0			0
$207$	5.15201	+	4.11598i	0.358090	+	0.286080i
$208$		0			0
$209$	−6.24381	−	5.23918i	−0.431893	−	0.362402i
$210$		0			0
$211$	0.857576	+	4.86356i	0.0590380	+	0.334821i	0.999993	−	0.00371025i	$-0.00118101\pi$
$211$	0.857576	+	4.86356i	0.0590380	+	0.334821i	−0.940955	+	0.338531i	$0.890070\pi$
$212$		0			0
$213$	3.53401	−	21.5554i	0.242147	−	1.47695i
$214$		0			0
$215$	9.21959			0.628771
$216$		0			0
$217$	0.496037			0.0336732
$218$		0			0
$219$	−9.49020	+	3.58400i	−0.641288	+	0.242184i
$220$		0			0
$221$	−0.446627	−	2.53295i	−0.0300434	−	0.170385i
$222$		0			0
$223$	−18.6212	−	15.6250i	−1.24697	−	1.04633i	−0.996946	−	0.0780890i	$-0.975118\pi$
$223$	−18.6212	−	15.6250i	−1.24697	−	1.04633i	−0.250021	−	0.968241i	$-0.580437\pi$
$224$		0			0
$225$	6.09689	+	9.99678i	0.406459	+	0.666452i
$226$		0			0
$227$	−1.40056	+	7.94297i	−0.0929584	+	0.527193i	0.902395	+	0.430909i	$0.141807\pi$
$227$	−1.40056	+	7.94297i	−0.0929584	+	0.527193i	−0.995354	+	0.0962844i	$0.969304\pi$
$228$		0			0
$229$	−14.0543	−	5.11535i	−0.928735	−	0.338032i	−0.167027	−	0.985952i	$-0.553417\pi$
$229$	−14.0543	−	5.11535i	−0.928735	−	0.338032i	−0.761708	+	0.647921i	$0.775639\pi$
$230$		0			0
$231$	1.43637	−	0.0172785i	0.0945060	−	0.00113684i
$232$		0			0
$233$	−3.58172	−	6.20373i	−0.234647	−	0.406420i	0.724523	−	0.689250i	$-0.242060\pi$
$233$	−3.58172	−	6.20373i	−0.234647	−	0.406420i	−0.959170	+	0.282830i	$0.908727\pi$
$234$		0			0
$235$	3.06109	−	5.30196i	0.199683	−	0.345862i
$236$		0			0
$237$	−8.15867	−	2.85885i	−0.529963	−	0.185702i
$238$		0			0
$239$	14.1037	−	11.8344i	0.912293	−	0.765505i	−0.0602605	−	0.998183i	$-0.519193\pi$
$239$	14.1037	−	11.8344i	0.912293	−	0.765505i	0.972554	+	0.232678i	$0.0747487\pi$
$240$		0			0
$241$	21.3061	−	7.75477i	1.37244	−	0.499529i	0.452565	−	0.891731i	$-0.350509\pi$
$241$	21.3061	−	7.75477i	1.37244	−	0.499529i	0.919879	+	0.392202i	$0.128287\pi$
$242$		0			0
$243$	14.9423	+	4.44145i	0.958552	+	0.284919i
$244$		0			0
$245$	6.78724	−	2.47035i	0.433621	−	0.157825i
$246$		0			0
$247$	−4.16592	+	3.49562i	−0.265071	+	0.222421i
$248$		0			0
$249$	1.22317	+	0.428606i	0.0775150	+	0.0271618i
$250$		0			0
$251$	−14.4055	+	24.9510i	−0.909266	+	1.57489i	−0.0941787	+	0.995555i	$0.530022\pi$
$251$	−14.4055	+	24.9510i	−0.909266	+	1.57489i	−0.815087	+	0.579339i	$0.803311\pi$
$252$		0			0
$253$	−2.83221	−	4.90554i	−0.178060	−	0.308408i
$254$		0			0
$255$	2.71342	−	0.0326406i	0.169921	−	0.00204403i
$256$		0			0
$257$	−15.0346	−	5.47216i	−0.937836	−	0.341344i	−0.172525	−	0.985005i	$-0.555193\pi$
$257$	−15.0346	−	5.47216i	−0.937836	−	0.341344i	−0.765311	+	0.643661i	$0.777415\pi$
$258$		0			0
$259$	−0.364890	+	2.06940i	−0.0226732	+	0.128586i
$260$		0			0
$261$	1.72385	+	2.82652i	0.106704	+	0.174957i
$262$		0			0
$263$	−22.6058	−	18.9685i	−1.39393	−	1.16965i	−0.963718	−	0.266922i	$-0.913993\pi$
$263$	−22.6058	−	18.9685i	−1.39393	−	1.16965i	−0.430214	−	0.902727i	$-0.641562\pi$
$264$		0			0
$265$	1.43432	+	8.13445i	0.0881098	+	0.499695i
$266$		0			0
$267$	−6.79645	+	2.56670i	−0.415936	+	0.157079i
$268$		0			0
$269$	−1.34127			−0.0817789			−0.0408895	−	0.999164i	$-0.513019\pi$
$269$	−1.34127			−0.0817789			−0.0408895	+	0.999164i	$0.513019\pi$
$270$		0			0
$271$	1.44491			0.0877718			0.0438859	−	0.999037i	$-0.486026\pi$
$271$	1.44491			0.0877718			0.0438859	+	0.999037i	$0.486026\pi$
$272$		0			0
$273$	0.155063	−	0.945797i	0.00938486	−	0.0572422i
$274$		0			0
$275$	−1.74658	−	9.90537i	−0.105323	−	0.597316i
$276$		0			0
$277$	−16.5578	−	13.8937i	−0.994864	−	0.834790i	−0.00859964	−	0.999963i	$-0.502737\pi$
$277$	−16.5578	−	13.8937i	−0.994864	−	0.834790i	−0.986265	+	0.165173i	$0.947182\pi$
$278$		0			0
$279$	−3.61259	−	2.88612i	−0.216280	−	0.172788i
$280$		0			0
$281$	1.01318	−	5.74604i	0.0604414	−	0.342780i	−0.939559	−	0.342388i	$-0.888764\pi$
$281$	1.01318	−	5.74604i	0.0604414	−	0.342780i	1.00000		0.000391885i	$-0.000124741\pi$
$282$		0			0
$283$	−22.7260	−	8.27158i	−1.35092	−	0.491694i	−0.437684	−	0.899129i	$-0.644201\pi$
$283$	−22.7260	−	8.27158i	−1.35092	−	0.491694i	−0.913234	+	0.407434i	$0.866423\pi$
$284$		0			0
$285$	−2.92836	−	4.93404i	−0.173461	−	0.292267i
$286$		0			0
$287$	−0.639463	−	1.10758i	−0.0377463	−	0.0653785i
$288$		0			0
$289$	7.38113	−	12.7845i	0.434184	−	0.752029i
$290$		0			0
$291$	−5.74665	+	4.94101i	−0.336875	+	0.289647i
$292$		0			0
$293$	−14.9393	+	12.5355i	−0.872761	+	0.732333i	−0.964678	−	0.263434i	$-0.915145\pi$
$293$	−14.9393	+	12.5355i	−0.872761	+	0.732333i	0.0919169	+	0.995767i	$0.470701\pi$
$294$		0			0
$295$	9.26633	−	3.37267i	0.539507	−	0.196364i
$296$		0			0
$297$	−10.5614	−	8.23146i	−0.612837	−	0.477638i
$298$		0			0
$299$	−3.55142	+	1.29261i	−0.205384	+	0.0747537i
$300$		0			0
$301$	−2.17024	+	1.82105i	−0.125091	+	0.104964i
$302$		0			0
$303$	−5.30527	−	28.1064i	−0.304780	−	1.61467i
$304$		0			0
$305$	4.63234	−	8.02344i	0.265247	−	0.459421i
$306$		0			0
$307$	12.0075	+	20.7977i	0.685306	+	1.18698i	0.973341	+	0.229365i	$0.0736648\pi$
$307$	12.0075	+	20.7977i	0.685306	+	1.18698i	−0.288035	+	0.957620i	$0.593002\pi$
$308$		0			0
$309$	3.50915	−	6.25046i	0.199628	−	0.355576i
$310$		0			0
$311$	22.9629	+	8.35782i	1.30211	+	0.473928i	0.897682	−	0.440643i	$-0.145249\pi$
$311$	22.9629	+	8.35782i	1.30211	+	0.473928i	0.404425	+	0.914571i	$0.367472\pi$
$312$		0			0
$313$	−4.93265	+	27.9744i	−0.278810	+	1.58121i	0.447784	+	0.894142i	$0.352213\pi$
$313$	−4.93265	+	27.9744i	−0.278810	+	1.58121i	−0.726594	+	0.687067i	$0.758898\pi$
$314$		0			0
$315$	0.958249	+	0.322889i	0.0539912	+	0.0181927i
$316$		0			0
$317$	−11.9821	−	10.0542i	−0.672984	−	0.564700i	0.240963	−	0.970534i	$-0.422537\pi$
$317$	−11.9821	−	10.0542i	−0.672984	−	0.564700i	−0.913947	+	0.405834i	$0.866981\pi$
$318$		0			0
$319$	−0.493835	−	2.80068i	−0.0276495	−	0.156808i
$320$		0			0
$321$	7.67255	+	6.28233i	0.428240	+	0.350645i
$322$		0			0
$323$	4.73141			0.263263
$324$		0			0
$325$	−6.71089			−0.372253
$326$		0			0
$327$	5.99609	+	4.90963i	0.331584	+	0.271503i
$328$		0			0
$329$	0.326677	+	1.85268i	0.0180103	+	0.102142i
$330$		0			0
$331$	0.468765	+	0.393341i	0.0257657	+	0.0216200i	0.655580	−	0.755126i	$-0.272424\pi$
$331$	0.468765	+	0.393341i	0.0257657	+	0.0216200i	−0.629814	+	0.776746i	$0.716869\pi$
$332$		0			0
$333$	14.6980	−	12.9481i	0.805443	−	0.709554i
$334$		0			0
$335$	1.24818	−	7.07881i	0.0681956	−	0.386756i
$336$		0			0
$337$	8.02356	+	2.92034i	0.437071	+	0.159081i	0.551178	−	0.834388i	$-0.314178\pi$
$337$	8.02356	+	2.92034i	0.437071	+	0.159081i	−0.114107	+	0.993468i	$0.536401\pi$
$338$		0			0
$339$	−3.02232	+	5.38334i	−0.164150	+	0.292383i
$340$		0			0
$341$	1.98595	+	3.43976i	0.107545	+	0.186273i
$342$		0			0
$343$	−2.23614	+	3.87311i	−0.120740	+	0.209129i
$344$		0			0
$345$	−0.739589	−	3.91821i	−0.0398181	−	0.210950i
$346$		0			0
$347$	19.7786	−	16.5962i	1.06177	−	0.890933i	0.0674905	−	0.997720i	$-0.478501\pi$
$347$	19.7786	−	16.5962i	1.06177	−	0.890933i	0.994282	+	0.106787i	$0.0340563\pi$
$348$		0			0
$349$	18.6979	−	6.80548i	1.00088	−	0.364289i	0.210953	−	0.977496i	$-0.432343\pi$
$349$	18.6979	−	6.80548i	1.00088	−	0.364289i	0.789922	+	0.613207i	$0.210121\pi$
$350$		0			0
$351$	−6.63230	+	5.98593i	−0.354006	+	0.319505i
$352$		0			0
$353$	−16.6357	+	6.05490i	−0.885429	+	0.322270i	−0.744399	−	0.667735i	$-0.767264\pi$
$353$	−16.6357	+	6.05490i	−0.885429	+	0.322270i	−0.141031	+	0.990005i	$0.545042\pi$
$354$		0			0
$355$	−10.1180	+	8.48999i	−0.537006	+	0.450602i
$356$		0			0
$357$	−0.632279	+	0.543638i	−0.0334637	+	0.0287724i
$358$		0			0
$359$	4.15770	−	7.20134i	0.219435	−	0.380072i	−0.735200	−	0.677850i	$-0.762912\pi$
$359$	4.15770	−	7.20134i	0.219435	−	0.380072i	0.954635	+	0.297777i	$0.0962453\pi$
$360$		0			0
$361$	4.49802	+	7.79079i	0.236738	+	0.410042i
$362$		0			0
$363$	−3.85357	−	6.49294i	−0.202260	−	0.340791i
$364$		0			0
$365$	5.76415	+	2.09798i	0.301710	+	0.109813i
$366$		0			0
$367$	6.19321	−	35.1234i	0.323283	−	1.83343i	−0.198194	−	0.980163i	$-0.563508\pi$
$367$	6.19321	−	35.1234i	0.323283	−	1.83343i	0.521477	−	0.853265i	$-0.325381\pi$
$368$		0			0
$369$	−1.78717	+	11.7870i	−0.0930363	+	0.613609i
$370$		0			0
$371$	−1.94435	−	1.63150i	−0.100945	−	0.0847033i
$372$		0			0
$373$	3.04549	+	17.2718i	0.157689	+	0.894301i	0.956286	+	0.292434i	$0.0944652\pi$
$373$	3.04549	+	17.2718i	0.157689	+	0.894301i	−0.798596	+	0.601867i	$0.794424\pi$
$374$		0			0
$375$	2.61298	−	15.9377i	0.134934	−	0.823019i
$376$		0			0
$377$	−1.89746			−0.0977241
$378$		0			0
$379$	21.8978			1.12481			0.562406	−	0.826861i	$-0.309876\pi$
$379$	21.8978			1.12481			0.562406	+	0.826861i	$0.309876\pi$
$380$		0			0
$381$	21.4917	−	8.11639i	1.10105	−	0.415815i
$382$		0			0
$383$	−2.59662	−	14.7261i	−0.132681	−	0.752470i	−0.976447	−	0.215759i	$-0.930777\pi$
$383$	−2.59662	−	14.7261i	−0.132681	−	0.752470i	0.843766	−	0.536712i	$-0.180334\pi$
$384$		0			0
$385$	−0.665386	−	0.558325i	−0.0339112	−	0.0284549i
$386$		0			0
$387$	26.4012	−	0.635268i	1.34205	−	0.0322925i
$388$		0			0
$389$	0.209841	−	1.19007i	0.0106394	−	0.0603389i	−0.979026	−	0.203736i	$-0.934692\pi$
$389$	0.209841	−	1.19007i	0.0106394	−	0.0603389i	0.989665	+	0.143397i	$0.0458027\pi$
$390$		0			0
$391$	3.08985	+	1.12461i	0.156260	+	0.0568741i
$392$		0			0
$393$	−13.0406	+	0.156869i	−0.657811	+	0.00791301i
$394$		0			0
$395$	2.61373	+	4.52711i	0.131511	+	0.227784i
$396$		0			0
$397$	−7.51495	+	13.0163i	−0.377164	+	0.653268i	−0.990648	−	0.136439i	$-0.956434\pi$
$397$	−7.51495	+	13.0163i	−0.377164	+	0.653268i	0.613484	+	0.789707i	$0.289767\pi$
$398$		0			0
$399$	1.66389	+	0.583039i	0.0832988	+	0.0291885i
$400$		0			0
$401$	0.929698	−	0.780109i	0.0464269	−	0.0389568i	−0.619279	−	0.785171i	$-0.712575\pi$
$401$	0.929698	−	0.780109i	0.0464269	−	0.0389568i	0.665706	+	0.746214i	$0.268131\pi$
$402$		0			0
$403$	2.49026	−	0.906379i	0.124048	−	0.0451500i
$404$		0			0
$405$	−5.10015	−	7.92701i	−0.253428	−	0.393896i
$406$		0			0
$407$	−15.8111	+	5.75476i	−0.783725	+	0.285253i
$408$		0			0
$409$	−6.52951	+	5.47891i	−0.322863	+	0.270915i	−0.789784	−	0.613384i	$-0.789808\pi$
$409$	−6.52951	+	5.47891i	−0.322863	+	0.270915i	0.466921	+	0.884299i	$0.345363\pi$
$410$		0			0
$411$	−12.5769	−	4.40704i	−0.620374	−	0.217383i
$412$		0			0
$413$	−1.51508	+	2.62419i	−0.0745521	+	0.129128i
$414$		0			0
$415$	−0.391856	−	0.678715i	−0.0192355	−	0.0333168i
$416$		0			0
$417$	35.3228	−	0.424909i	1.72977	−	0.0208079i
$418$		0			0
$419$	6.17983	+	2.24928i	0.301905	+	0.109884i	0.488531	−	0.872547i	$-0.337533\pi$
$419$	6.17983	+	2.24928i	0.301905	+	0.109884i	−0.186626	+	0.982431i	$0.559755\pi$
$420$		0			0
$421$	−6.61938	+	37.5403i	−0.322609	+	1.82960i	0.203364	+	0.979103i	$0.434813\pi$
$421$	−6.61938	+	37.5403i	−0.322609	+	1.82960i	−0.525973	+	0.850501i	$0.676299\pi$
$422$		0			0
$423$	8.40040	−	15.3936i	0.408441	−	0.748463i
$424$		0			0
$425$	4.47269	+	3.75303i	0.216957	+	0.182049i
$426$		0			0
$427$	0.494360	+	2.80366i	0.0239238	+	0.135678i
$428$		0			0
$429$	7.17942	−	2.71133i	0.346626	−	0.130904i
$430$		0			0
$431$	16.5436			0.796879			0.398439	−	0.917195i	$-0.369552\pi$
$431$	16.5436			0.796879			0.398439	+	0.917195i	$0.369552\pi$
$432$		0			0
$433$	11.9325			0.573437			0.286719	−	0.958015i	$-0.407436\pi$
$433$	11.9325			0.573437			0.286719	+	0.958015i	$0.407436\pi$
$434$		0			0
$435$	0.323890	−	1.97554i	0.0155293	−	0.0947200i
$436$		0			0
$437$	−1.20726	−	6.84674i	−0.0577513	−	0.327524i
$438$		0			0
$439$	−27.3437	−	22.9441i	−1.30504	−	1.09506i	−0.989250	−	0.146231i	$-0.953286\pi$
$439$	−27.3437	−	22.9441i	−1.30504	−	1.09506i	−0.315791	−	0.948829i	$-0.602270\pi$
$440$		0			0
$441$	19.2657	−	7.54177i	0.917415	−	0.359132i
$442$		0			0
$443$	1.63428	−	9.26847i	0.0776470	−	0.440358i	−0.921055	−	0.389432i	$-0.872671\pi$
$443$	1.63428	−	9.26847i	0.0776470	−	0.440358i	0.998702	−	0.0509265i	$-0.0162174\pi$
$444$		0			0
$445$	4.12802	+	1.50248i	0.195687	+	0.0712243i
$446$		0			0
$447$	−20.7994	−	35.0453i	−0.983779	−	1.65758i
$448$		0			0
$449$	−4.87748	−	8.44805i	−0.230183	−	0.398688i	0.727679	−	0.685918i	$-0.240599\pi$
$449$	−4.87748	−	8.44805i	−0.230183	−	0.398688i	−0.957862	+	0.287230i	$0.907266\pi$
$450$		0			0
$451$	5.12034	−	8.86868i	0.241107	−	0.417610i
$452$		0			0
$453$	−8.50971	+	7.31672i	−0.399821	+	0.343769i
$454$		0			0
$455$	−0.443950	+	0.372519i	−0.0208127	+	0.0174639i
$456$		0			0
$457$	8.39950	−	3.05717i	0.392912	−	0.143008i	−0.138006	−	0.990431i	$-0.544069\pi$
$457$	8.39950	−	3.05717i	0.392912	−	0.143008i	0.530918	+	0.847423i	$0.321847\pi$
$458$		0			0
$459$	7.76790	−	0.280436i	0.362575	−	0.0130896i
$460$		0			0
$461$	−4.14623	+	1.50910i	−0.193109	+	0.0702859i	−0.436764	−	0.899576i	$-0.643876\pi$
$461$	−4.14623	+	1.50910i	−0.193109	+	0.0702859i	0.243655	+	0.969862i	$0.421653\pi$
$462$		0			0
$463$	8.29681	−	6.96185i	0.385585	−	0.323545i	−0.429305	−	0.903160i	$-0.641241\pi$
$463$	8.29681	−	6.96185i	0.385585	−	0.323545i	0.814890	+	0.579615i	$0.196797\pi$
$464$		0			0
$465$	0.518600	+	2.74745i	0.0240495	+	0.127410i
$466$		0			0
$467$	−10.1549	+	17.5889i	−0.469914	+	0.813915i	−0.999408	−	0.0343986i	$-0.989048\pi$
$467$	−10.1549	+	17.5889i	−0.469914	+	0.813915i	0.529494	+	0.848314i	$0.322382\pi$
$468$		0			0
$469$	1.10439	+	1.91286i	0.0509959	+	0.0883275i
$470$		0			0
$471$	−9.01005	+	16.0486i	−0.415161	+	0.739482i
$472$		0			0
$473$	−21.3169	−	7.75871i	−0.980151	−	0.356746i
$474$		0			0
$475$	2.14371	−	12.1576i	0.0983602	−	0.557828i
$476$		0			0
$477$	4.66782	+	23.1950i	0.213725	+	1.06202i
$478$		0			0
$479$	−19.4296	−	16.3034i	−0.887762	−	0.744921i	0.0799982	−	0.996795i	$-0.474509\pi$
$479$	−19.4296	−	16.3034i	−0.887762	−	0.744921i	−0.967760	+	0.251874i	$0.918953\pi$
$480$		0			0
$481$	1.94942	+	11.0557i	0.0888861	+	0.504098i
$482$		0			0
$483$	0.948020	+	0.776244i	0.0431364	+	0.0353203i
$484$		0			0
$485$	4.58270			0.208090
$486$		0			0
$487$	15.4975			0.702258			0.351129	−	0.936327i	$-0.385798\pi$
$487$	15.4975			0.702258			0.351129	+	0.936327i	$0.385798\pi$
$488$		0			0
$489$	−22.1871	−	18.1669i	−1.00334	−	0.821537i
$490$		0			0
$491$	−4.45652	−	25.2742i	−0.201120	−	1.14061i	−0.903429	−	0.428737i	$-0.858959\pi$
$491$	−4.45652	−	25.2742i	−0.201120	−	1.14061i	0.702309	−	0.711872i	$-0.252152\pi$
$492$		0			0
$493$	1.26462	+	1.06114i	0.0569557	+	0.0477915i
$494$		0			0
$495$	1.59740	+	7.93768i	0.0717979	+	0.356772i
$496$		0			0
$497$	0.704779	−	3.99700i	0.0316136	−	0.179290i
$498$		0			0
$499$	−17.1662	−	6.24799i	−0.768465	−	0.279698i	−0.0721106	−	0.997397i	$-0.522973\pi$
$499$	−17.1662	−	6.24799i	−0.768465	−	0.279698i	−0.696354	+	0.717698i	$0.745196\pi$
$500$		0			0
$501$	7.48162	−	13.3262i	0.334254	−	0.595370i
$502$		0			0
$503$	−4.09566	−	7.09389i	−0.182616	−	0.316301i	0.760154	−	0.649743i	$-0.225123\pi$
$503$	−4.09566	−	7.09389i	−0.182616	−	0.316301i	−0.942771	+	0.333442i	$0.891790\pi$
$504$		0			0
$505$	−8.64769	+	14.9782i	−0.384817	+	0.666523i
$506$		0			0
$507$	3.22669	+	17.0944i	0.143302	+	0.759190i
$508$		0			0
$509$	−11.9723	+	10.0460i	−0.530665	+	0.445280i	−0.868331	−	0.495985i	$-0.834807\pi$
$509$	−11.9723	+	10.0460i	−0.530665	+	0.445280i	0.337666	+	0.941266i	$0.390362\pi$
$510$		0			0
$511$	−1.77124	+	0.644680i	−0.0783552	+	0.0285190i
$512$		0			0
$513$	−8.72562	−	13.9273i	−0.385246	−	0.614907i
$514$		0			0
$515$	−4.07301	+	1.48246i	−0.179478	+	0.0653248i
$516$		0			0
$517$	−11.5395	+	9.68277i	−0.507505	+	0.425848i
$518$		0			0
$519$	10.9997	−	9.45765i	0.482835	−	0.415145i
$520$		0			0
$521$	−5.49345	+	9.51493i	−0.240672	+	0.416857i	−0.960906	−	0.276875i	$-0.910701\pi$
$521$	−5.49345	+	9.51493i	−0.240672	+	0.416857i	0.720234	+	0.693732i	$0.244035\pi$
$522$		0			0
$523$	−9.83499	−	17.0347i	−0.430054	−	0.744876i	0.566823	−	0.823839i	$-0.308172\pi$
$523$	−9.83499	−	17.0347i	−0.430054	−	0.744876i	−0.996877	+	0.0789637i	$0.974839\pi$
$524$		0			0
$525$	1.11043	+	1.87098i	0.0484631	+	0.0816563i
$526$		0			0
$527$	−2.16660	−	0.788577i	−0.0943785	−	0.0343510i
$528$		0			0
$529$	−3.15491	+	17.8924i	−0.137170	+	0.777929i
$530$		0			0
$531$	26.3027	−	10.2965i	1.14144	−	0.446828i
$532$		0			0
$533$	−5.23411	−	4.39194i	−0.226715	−	0.190236i
$534$		0			0
$535$	−1.04123	−	5.90513i	−0.0450165	−	0.255301i
$536$		0			0
$537$	5.28296	−	32.2230i	0.227977	−	1.39053i
$538$		0			0
$539$	−17.7719			−0.765490
$540$		0			0
$541$	25.2629			1.08614			0.543068	−	0.839689i	$-0.317262\pi$
$541$	25.2629			1.08614			0.543068	+	0.839689i	$0.317262\pi$
$542$		0			0
$543$	2.80471	−	1.05921i	0.120362	−	0.0454550i
$544$		0			0
$545$	−0.813724	−	4.61486i	−0.0348561	−	0.197679i
$546$		0			0
$547$	22.4512	+	18.8388i	0.959944	+	0.805489i	0.980944	−	0.194291i	$-0.0622406\pi$
$547$	22.4512	+	18.8388i	0.959944	+	0.805489i	−0.0210000	+	0.999779i	$0.506685\pi$
$548$		0			0
$549$	12.7123	−	23.2951i	0.542548	−	0.994211i
$550$		0			0
$551$	0.606120	−	3.43748i	0.0258216	−	0.146441i
$552$		0			0
$553$	−1.50945	−	0.549396i	−0.0641884	−	0.0233627i
$554$		0			0
$555$	−11.8435	+	0.142469i	−0.502727	+	0.00604745i
$556$		0			0
$557$	−10.2679	−	17.7846i	−0.435067	−	0.753557i	0.562234	−	0.826978i	$-0.309942\pi$
$557$	−10.2679	−	17.7846i	−0.435067	−	0.753557i	−0.997301	+	0.0734204i	$0.976609\pi$
$558$		0			0
$559$	−7.56778	+	13.1078i	−0.320083	+	0.554400i
$560$		0			0
$561$	−6.30125	−	2.20800i	−0.266039	−	0.0932219i
$562$		0			0
$563$	16.4415	−	13.7961i	0.692928	−	0.581436i	−0.226824	−	0.973936i	$-0.572834\pi$
$563$	16.4415	−	13.7961i	0.692928	−	0.581436i	0.919752	+	0.392500i	$0.128390\pi$
$564$		0			0
$565$	3.50797	−	1.27680i	0.147581	−	0.0537152i
$566$		0			0
$567$	2.76629	+	0.858596i	0.116173	+	0.0360577i
$568$		0			0
$569$	−5.69444	+	2.07261i	−0.238723	+	0.0868881i	−0.458611	−	0.888637i	$-0.651653\pi$
$569$	−5.69444	+	2.07261i	−0.238723	+	0.0868881i	0.219888	+	0.975525i	$0.429431\pi$
$570$		0			0
$571$	−22.2095	+	18.6360i	−0.929438	+	0.779891i	−0.975717	−	0.219037i	$-0.929708\pi$
$571$	−22.2095	+	18.6360i	−0.929438	+	0.779891i	0.0462781	+	0.998929i	$0.485264\pi$
$572$		0			0
$573$	39.2609	+	13.7573i	1.64015	+	0.574718i
$574$		0			0
$575$	4.28969	−	7.42996i	0.178892	−	0.309851i
$576$		0			0
$577$	8.63865	+	14.9626i	0.359632	+	0.622900i	0.987899	−	0.155097i	$-0.0495690\pi$
$577$	8.63865	+	14.9626i	0.359632	+	0.622900i	−0.628267	+	0.777997i	$0.716236\pi$
$578$		0			0
$579$	−21.1529	+	0.254455i	−0.879086	+	0.0105748i
$580$		0			0
$581$	0.226300	+	0.0823666i	0.00938852	+	0.00341714i
$582$		0			0
$583$	3.52917	−	20.0149i	0.146163	−	0.828934i
$584$		0			0
$585$	5.40069	−	0.129952i	0.223291	−	0.00537285i
$586$		0			0
$587$	17.0536	+	14.3097i	0.703878	+	0.590624i	0.922874	−	0.385102i	$-0.125834\pi$
$587$	17.0536	+	14.3097i	0.703878	+	0.590624i	−0.218996	+	0.975726i	$0.570278\pi$
$588$		0			0
$589$	0.846534	+	4.80093i	0.0348808	+	0.197819i
$590$		0			0
$591$	12.6810	−	4.78901i	0.521626	−	0.196994i
$592$		0			0
$593$	−35.3680			−1.45239			−0.726195	−	0.687489i	$-0.758713\pi$
$593$	−35.3680			−1.45239			−0.726195	+	0.687489i	$0.758713\pi$
$594$		0			0
$595$	0.504214			0.0206708
$596$		0			0
$597$	6.64549	−	40.5337i	0.271982	−	1.65893i
$598$		0			0
$599$	3.25619	+	18.4667i	0.133044	+	0.754531i	0.976202	+	0.216864i	$0.0695829\pi$
$599$	3.25619	+	18.4667i	0.133044	+	0.754531i	−0.843158	+	0.537666i	$0.819306\pi$
$600$		0			0
$601$	−15.9833	−	13.4116i	−0.651972	−	0.547069i	0.255697	−	0.966757i	$-0.417695\pi$
$601$	−15.9833	−	13.4116i	−0.651972	−	0.547069i	−0.907668	+	0.419688i	$0.862140\pi$
$602$		0			0
$603$	3.08654	−	20.3569i	0.125694	−	0.828995i
$604$		0			0
$605$	−0.792797	+	4.49618i	−0.0322318	+	0.182796i
$606$		0			0
$607$	−0.305399	−	0.111156i	−0.0123958	−	0.00451169i	0.335815	−	0.941928i	$-0.390988\pi$
$607$	−0.305399	−	0.111156i	−0.0123958	−	0.00451169i	−0.348211	+	0.937416i	$0.613211\pi$
$608$		0			0
$609$	0.313967	+	0.529007i	0.0127226	+	0.0214365i
$610$		0			0
$611$	5.02531	+	8.70409i	0.203302	+	0.352130i
$612$		0			0
$613$	−16.4316	+	28.4603i	−0.663665	+	1.14950i	0.315981	+	0.948766i	$0.397667\pi$
$613$	−16.4316	+	28.4603i	−0.663665	+	1.14950i	−0.979645	+	0.200735i	$0.935667\pi$
$614$		0			0
$615$	5.46613	−	4.69982i	0.220415	−	0.189515i
$616$		0			0
$617$	11.3969	−	9.56314i	0.458822	−	0.384998i	−0.383875	−	0.923385i	$-0.625411\pi$
$617$	11.3969	−	9.56314i	0.458822	−	0.384998i	0.842697	+	0.538387i	$0.180966\pi$
$618$		0			0
$619$	22.8422	−	8.31388i	0.918106	−	0.334163i	0.160621	−	0.987016i	$-0.448650\pi$
$619$	22.8422	−	8.31388i	0.918106	−	0.334163i	0.757485	+	0.652853i	$0.226428\pi$
$620$		0			0
$621$	−2.38787	−	11.1692i	−0.0958218	−	0.448206i
$622$		0			0
$623$	−1.26848	+	0.461691i	−0.0508208	+	0.0184972i
$624$		0			0
$625$	7.46869	−	6.26698i	0.298748	−	0.250679i
$626$		0			0
$627$	2.61852	+	13.8725i	0.104574	+	0.554014i
$628$		0			0
$629$	4.88360	−	8.45865i	0.194722	−	0.337269i
$630$		0			0
$631$	21.9407	+	38.0024i	0.873445	+	1.51285i	0.858410	+	0.512964i	$0.171453\pi$
$631$	21.9407	+	38.0024i	0.873445	+	1.51285i	0.0150352	+	0.999887i	$0.495214\pi$
$632$		0			0
$633$	4.18753	−	7.45879i	0.166439	−	0.296460i
$634$		0			0
$635$	−13.0536	−	4.75112i	−0.518016	−	0.188542i
$636$		0			0
$637$	−2.05904	+	11.6774i	−0.0815821	+	0.462675i
$638$		0			0
$639$	−28.3888	+	25.0091i	−1.12304	+	0.989344i
$640$		0			0
$641$	−19.8521	−	16.6579i	−0.784110	−	0.657947i	0.160170	−	0.987089i	$-0.448796\pi$
$641$	−19.8521	−	16.6579i	−0.784110	−	0.657947i	−0.944280	+	0.329143i	$0.893240\pi$
$642$		0			0
$643$	−3.55745	−	20.1753i	−0.140292	−	0.795635i	−0.971027	−	0.238968i	$-0.923191\pi$
$643$	−3.55745	−	20.1753i	−0.140292	−	0.795635i	0.830735	−	0.556667i	$-0.187920\pi$
$644$		0			0
$645$	−12.3554	−	10.1167i	−0.486493	−	0.398343i
$646$		0			0
$647$	33.4434			1.31480			0.657399	−	0.753543i	$-0.271657\pi$
$647$	33.4434			1.31480			0.657399	+	0.753543i	$0.271657\pi$
$648$		0			0
$649$	−24.2632			−0.952414
$650$		0			0
$651$	−0.664751	−	0.544302i	−0.0260537	−	0.0213329i
$652$		0			0
$653$	−6.05292	−	34.3278i	−0.236869	−	1.34335i	−0.838642	−	0.544683i	$-0.816650\pi$
$653$	−6.05292	−	34.3278i	−0.236869	−	1.34335i	0.601773	−	0.798667i	$-0.294461\pi$
$654$		0			0
$655$	6.04095	+	5.06896i	0.236040	+	0.198061i
$656$		0			0
$657$	16.6508	+	5.61060i	0.649608	+	0.218890i
$658$		0			0
$659$	−0.719007	+	4.07769i	−0.0280085	+	0.158844i	−0.995604	−	0.0936604i	$-0.970143\pi$
$659$	−0.719007	+	4.07769i	−0.0280085	+	0.158844i	0.967596	+	0.252505i	$0.0812543\pi$
$660$		0			0
$661$	13.0352	+	4.74442i	0.507010	+	0.184537i	0.582844	−	0.812584i	$-0.301940\pi$
$661$	13.0352	+	4.74442i	0.507010	+	0.184537i	−0.0758343	+	0.997120i	$0.524162\pi$
$662$		0			0
$663$	−2.18087	+	3.88455i	−0.0846980	+	0.150863i
$664$		0			0
$665$	−0.533048	−	0.923266i	−0.0206707	−	0.0358027i
$666$		0			0
$667$	1.21288	−	2.10077i	0.0469629	−	0.0813422i
$668$		0			0
$669$	7.80934	+	41.3725i	0.301926	+	1.59955i
$670$		0			0
$671$	−17.4627	+	14.6529i	−0.674138	+	0.565669i
$672$		0			0
$673$	30.0985	−	10.9550i	1.16021	−	0.422283i	0.311039	−	0.950397i	$-0.399323\pi$
$673$	30.0985	−	10.9550i	1.16021	−	0.422283i	0.849173	+	0.528115i	$0.177101\pi$
$674$		0			0
$675$	2.79889	−	20.0870i	0.107729	−	0.773151i
$676$		0			0
$677$	−15.2483	+	5.54992i	−0.586039	+	0.213301i	−0.617986	−	0.786189i	$-0.712051\pi$
$677$	−15.2483	+	5.54992i	−0.586039	+	0.213301i	0.0319474	+	0.999490i	$0.489829\pi$
$678$		0			0
$679$	−1.07874	+	0.905173i	−0.0413984	+	0.0347373i
$680$		0			0
$681$	10.5927	−	9.10772i	0.405915	−	0.349009i
$682$		0			0
$683$	−15.7562	+	27.2905i	−0.602894	+	1.04424i	0.389486	+	0.921032i	$0.372653\pi$
$683$	−15.7562	+	27.2905i	−0.602894	+	1.04424i	−0.992380	+	0.123211i	$0.960681\pi$
$684$		0			0
$685$	4.02917	+	6.97873i	0.153947	+	0.266644i
$686$		0			0
$687$	13.2214	+	22.2770i	0.504429	+	0.849920i
$688$		0			0
$689$	−12.7423	−	4.63784i	−0.485445	−	0.176687i
$690$		0			0
$691$	−3.59534	+	20.3902i	−0.136773	+	0.775679i	0.836835	+	0.547454i	$0.184403\pi$
$691$	−3.59534	+	20.3902i	−0.136773	+	0.775679i	−0.973609	+	0.228224i	$0.926708\pi$
$692$		0			0
$693$	−1.94387	−	1.55297i	−0.0738415	−	0.0589925i
$694$		0			0
$695$	−16.3630	−	13.7302i	−0.620685	−	0.520817i
$696$		0			0
$697$	1.03227	+	5.85430i	0.0391001	+	0.221747i
$698$		0			0
$699$	−2.00740	+	12.2440i	−0.0759269	+	0.463110i
$700$		0			0
$701$	−35.0656			−1.32441			−0.662206	−	0.749322i	$-0.730379\pi$
$701$	−35.0656			−1.32441			−0.662206	+	0.749322i	$0.730379\pi$
$702$		0			0
$703$	−20.6515			−0.778887
$704$		0			0
$705$	−9.92008	+	3.74635i	−0.373612	+	0.141096i
$706$		0			0
$707$	−0.922876	−	5.23389i	−0.0347083	−	0.196841i
$708$		0			0
$709$	−17.8442	−	14.9731i	−0.670153	−	0.562325i	0.242958	−	0.970037i	$-0.421882\pi$
$709$	−17.8442	−	14.9731i	−0.670153	−	0.562325i	−0.913111	+	0.407712i	$0.866327\pi$
$710$		0			0
$711$	7.79661	+	12.7837i	0.292396	+	0.479427i
$712$		0			0
$713$	−0.588307	+	3.33646i	−0.0220323	+	0.124951i
$714$		0			0
$715$	−4.36063	−	1.58714i	−0.163078	−	0.0593557i
$716$		0			0
$717$	−31.8866	+	0.383574i	−1.19083	+	0.0143248i
$718$		0			0
$719$	8.79180	+	15.2278i	0.327879	+	0.567903i	0.982091	−	0.188409i	$-0.0603329\pi$
$719$	8.79180	+	15.2278i	0.327879	+	0.567903i	−0.654212	+	0.756311i	$0.727000\pi$
$720$		0			0
$721$	0.665952	−	1.15346i	0.0248014	−	0.0429572i
$722$		0			0
$723$	−37.0621	−	12.9868i	−1.37835	−	0.482984i
$724$		0			0
$725$	3.29963	−	2.76872i	0.122545	−	0.102828i
$726$		0			0
$727$	−25.2990	+	9.20808i	−0.938288	+	0.341509i	−0.765490	−	0.643448i	$-0.777503\pi$
$727$	−25.2990	+	9.20808i	−0.938288	+	0.341509i	−0.172799	+	0.984957i	$0.555281\pi$
$728$		0			0
$729$	−15.1510	−	22.3483i	−0.561147	−	0.827716i
$730$		0			0
$731$	12.3742	−	4.50386i	0.457678	−	0.166581i
$732$		0			0
$733$	15.5623	−	13.0583i	0.574806	−	0.482319i	−0.308431	−	0.951247i	$-0.599804\pi$
$733$	15.5623	−	13.0583i	0.574806	−	0.482319i	0.883237	+	0.468927i	$0.155359\pi$
$734$		0			0
$735$	−11.8065	−	4.13707i	−0.435488	−	0.152598i
$736$		0			0
$737$	−8.84310	+	15.3167i	−0.325740	+	0.564198i
$738$		0			0
$739$	−1.69937	−	2.94339i	−0.0625123	−	0.108274i	0.833075	−	0.553159i	$-0.186578\pi$
$739$	−1.69937	−	2.94339i	−0.0625123	−	0.108274i	−0.895588	+	0.444885i	$0.853245\pi$
$740$		0			0
$741$	9.41859	−	0.113299i	0.346000	−	0.00416215i
$742$		0			0
$743$	16.7495	+	6.09631i	0.614479	+	0.223652i	0.630462	−	0.776220i	$-0.282866\pi$
$743$	16.7495	+	6.09631i	0.614479	+	0.223652i	−0.0159831	+	0.999872i	$0.505088\pi$
$744$		0			0
$745$	−4.27908	+	24.2679i	−0.156773	+	0.889105i
$746$		0			0
$747$	−1.16888	−	1.91657i	−0.0427672	−	0.0701234i
$748$		0			0
$749$	1.41148	+	1.18437i	0.0515744	+	0.0432761i
$750$		0			0
$751$	7.69043	+	43.6146i	0.280628	+	1.59152i	0.720497	+	0.693458i	$0.243914\pi$
$751$	7.69043	+	43.6146i	0.280628	+	1.59152i	−0.439869	+	0.898062i	$0.644975\pi$
$752$		0			0
$753$	46.6839	−	17.6303i	1.70126	−	0.642484i
$754$		0			0
$755$	6.78612			0.246972
$756$		0			0
$757$	−0.210674			−0.00765708			−0.00382854	−	0.999993i	$-0.501219\pi$
$757$	−0.210674			−0.00765708			−0.00382854	+	0.999993i	$0.501219\pi$
$758$		0			0
$759$	−1.58733	+	9.68181i	−0.0576165	+	0.351428i
$760$		0			0
$761$	9.36171	+	53.0929i	0.339362	+	1.92462i	0.378987	+	0.925402i	$0.376272\pi$
$761$	9.36171	+	53.0929i	0.339362	+	1.92462i	−0.0396253	+	0.999215i	$0.512616\pi$
$762$		0			0
$763$	1.10307	+	0.925587i	0.0399339	+	0.0335085i
$764$		0			0
$765$	−3.67214	−	2.93370i	−0.132766	−	0.106068i
$766$		0			0
$767$	−2.81112	+	15.9426i	−0.101504	+	0.575655i
$768$		0			0
$769$	−9.42665	−	3.43102i	−0.339934	−	0.123726i	0.166412	−	0.986056i	$-0.446782\pi$
$769$	−9.42665	−	3.43102i	−0.339934	−	0.123726i	−0.506346	+	0.862331i	$0.669004\pi$
$770$		0			0
$771$	14.1437	+	23.8309i	0.509372	+	0.858249i
$772$		0			0
$773$	3.86291	+	6.69076i	0.138939	+	0.240650i	0.927095	−	0.374826i	$-0.122297\pi$
$773$	3.86291	+	6.69076i	0.138939	+	0.240650i	−0.788156	+	0.615475i	$0.788964\pi$
$774$		0			0
$775$	−3.00793	+	5.20988i	−0.108048	+	0.187145i
$776$		0			0
$777$	2.75975	−	2.37285i	0.0990054	−	0.0851256i
$778$		0			0
$779$	9.62851	−	8.07928i	0.344977	−	0.289470i
$780$		0			0
$781$	30.5388	−	11.1152i	1.09276	−	0.397733i
$782$		0			0
$783$	0.791368	−	5.67948i	0.0282812	−	0.202968i
$784$		0			0
$785$	10.4578	−	3.80634i	0.373256	−	0.135854i
$786$		0			0
$787$	−3.08895	+	2.59194i	−0.110109	+	0.0923927i	−0.696180	−	0.717867i	$-0.745118\pi$
$787$	−3.08895	+	2.59194i	−0.110109	+	0.0923927i	0.586071	+	0.810260i	$0.300674\pi$
$788$		0			0
$789$	9.48040	+	50.2255i	0.337511	+	1.78807i
$790$		0			0
$791$	−0.573565	+	0.993443i	−0.0203936	+	0.0353228i
$792$		0			0
$793$	7.60479	+	13.1719i	0.270054	+	0.467747i
$794$		0			0
$795$	7.00377	−	12.4751i	0.248398	−	0.442445i
$796$		0			0
$797$	−31.0110	−	11.2871i	−1.09846	−	0.399808i	−0.271715	−	0.962378i	$-0.587591\pi$
$797$	−31.0110	−	11.2871i	−1.09846	−	0.399808i	−0.826750	+	0.562569i	$0.809813\pi$
$798$		0			0
$799$	1.51844	−	8.61149i	0.0537185	−	0.304653i
$800$		0			0
$801$	11.9245	+	4.01805i	0.421332	+	0.141971i
$802$		0			0
$803$	−11.5619	−	9.70160i	−0.408011	−	0.342362i
$804$		0			0
$805$	−0.128655	−	0.729639i	−0.00453449	−	0.0257164i
$806$		0			0
$807$	1.79747	+	1.47178i	0.0632740	+	0.0518091i
$808$		0			0
$809$	43.4750			1.52850			0.764250	−	0.644920i	$-0.223109\pi$
$809$	43.4750			1.52850			0.764250	+	0.644920i	$0.223109\pi$
$810$		0			0
$811$	−6.47515			−0.227373			−0.113687	−	0.993517i	$-0.536266\pi$
$811$	−6.47515			−0.227373			−0.113687	+	0.993517i	$0.536266\pi$
$812$		0			0
$813$	−1.93635	−	1.58550i	−0.0679109	−	0.0556058i
$814$		0			0
$815$	3.01099	+	17.0762i	0.105471	+	0.598153i
$816$		0			0
$817$	−21.3289	−	17.8971i	−0.746203	−	0.626139i
$818$		0			0
$819$	−1.24563	+	1.09733i	−0.0435257	+	0.0383439i
$820$		0			0
$821$	3.13623	−	17.7864i	0.109455	−	0.620750i	−0.879892	−	0.475174i	$-0.842385\pi$
$821$	3.13623	−	17.7864i	0.109455	−	0.620750i	0.989347	−	0.145577i	$-0.0465037\pi$
$822$		0			0
$823$	18.0049	+	6.55327i	0.627613	+	0.228432i	0.636192	−	0.771531i	$-0.280509\pi$
$823$	18.0049	+	6.55327i	0.627613	+	0.228432i	−0.00857899	+	0.999963i	$0.502731\pi$
$824$		0			0
$825$	−8.52853	+	15.1910i	−0.296925	+	0.528881i
$826$		0			0
$827$	5.81649	+	10.0745i	0.202259	+	0.350323i	0.949256	−	0.314504i	$-0.101838\pi$
$827$	5.81649	+	10.0745i	0.202259	+	0.350323i	−0.746997	+	0.664828i	$0.768505\pi$
$828$		0			0
$829$	27.9982	−	48.4944i	0.972419	−	1.68428i	0.284216	−	0.958760i	$-0.408267\pi$
$829$	27.9982	−	48.4944i	0.972419	−	1.68428i	0.688203	−	0.725518i	$-0.258400\pi$
$830$		0			0
$831$	6.94401	+	36.7882i	0.240885	+	1.27617i
$832$		0			0
$833$	7.90283	−	6.63126i	0.273817	−	0.229760i
$834$		0			0
$835$	−8.68380	+	3.16064i	−0.300515	+	0.109379i
$836$		0			0
$837$	1.67437	+	7.83186i	0.0578747	+	0.270709i
$838$		0			0
$839$	−12.4816	+	4.54293i	−0.430913	+	0.156840i	−0.548365	−	0.836239i	$-0.684750\pi$
$839$	−12.4816	+	4.54293i	−0.430913	+	0.156840i	0.117452	+	0.993079i	$0.462527\pi$
$840$		0			0
$841$	−21.2823	+	17.8580i	−0.733874	+	0.615793i
$842$		0			0
$843$	−7.66293	+	6.58864i	−0.263925	+	0.226925i
$844$		0			0
$845$	5.25956	−	9.10983i	0.180934	−	0.313388i
$846$		0			0
$847$	−0.701463	−	1.21497i	−0.0241026	−	0.0417469i
$848$		0			0
$849$	21.3792	+	36.0222i	0.733732	+	1.23628i
$850$		0			0
$851$	−13.4865	−	4.90867i	−0.462310	−	0.168267i
$852$		0			0
$853$	−7.48365	+	42.4419i	−0.256235	+	1.45318i	0.536647	+	0.843807i	$0.319691\pi$
$853$	−7.48365	+	42.4419i	−0.256235	+	1.45318i	−0.792882	+	0.609375i	$0.791420\pi$
$854$		0			0
$855$	−1.48976	+	9.82552i	−0.0509487	+	0.336026i
$856$		0			0
$857$	21.7758	+	18.2720i	0.743846	+	0.624161i	0.933868	−	0.357619i	$-0.116411\pi$
$857$	21.7758	+	18.2720i	0.743846	+	0.624161i	−0.190021	+	0.981780i	$0.560856\pi$
$858$		0			0
$859$	4.61762	+	26.1878i	0.157551	+	0.893517i	0.956416	+	0.292007i	$0.0943230\pi$
$859$	4.61762	+	26.1878i	0.157551	+	0.893517i	−0.798865	+	0.601510i	$0.794566\pi$
$860$		0			0
$861$	−0.358391	+	2.18598i	−0.0122139	+	0.0744980i
$862$		0			0
$863$	−26.4469			−0.900263			−0.450131	−	0.892962i	$-0.648623\pi$
$863$	−26.4469			−0.900263			−0.450131	+	0.892962i	$0.648623\pi$
$864$		0			0
$865$	−8.77179			−0.298250
$866$		0			0
$867$	−23.9201	+	9.03348i	−0.812368	+	0.306793i
$868$		0			0
$869$	−2.23351	−	12.6668i	−0.0757665	−	0.429693i
$870$		0			0
$871$	9.03960	+	7.58513i	0.306295	+	0.257012i
$872$		0			0
$873$	13.1230	−	0.315767i	0.444146	−	0.0106871i
$874$		0			0
$875$	0.521101	−	2.95531i	0.0176164	−	0.0999077i
$876$		0			0
$877$	33.2885	+	12.1160i	1.12407	+	0.409130i	0.836138	−	0.548520i	$-0.184808\pi$
$877$	33.2885	+	12.1160i	1.12407	+	0.409130i	0.287937	+	0.957649i	$0.407031\pi$
$878$		0			0
$879$	33.7757	−	0.406298i	1.13923	−	0.0137041i
$880$		0			0
$881$	−0.850030	−	1.47229i	−0.0286382	−	0.0496029i	0.851351	−	0.524596i	$-0.175784\pi$
$881$	−0.850030	−	1.47229i	−0.0286382	−	0.0496029i	−0.879989	+	0.474993i	$0.842450\pi$
$882$		0			0
$883$	21.8979	−	37.9283i	0.736923	−	1.27639i	−0.216952	−	0.976182i	$-0.569612\pi$
$883$	21.8979	−	37.9283i	0.736923	−	1.27639i	0.953875	−	0.300205i	$-0.0970551\pi$
$884$		0			0
$885$	−16.1189	−	5.64816i	−0.541830	−	0.189861i
$886$		0			0
$887$	−24.4845	+	20.5449i	−0.822108	+	0.689830i	−0.953465	−	0.301505i	$-0.902511\pi$
$887$	−24.4845	+	20.5449i	−0.822108	+	0.689830i	0.131357	+	0.991335i	$0.458067\pi$
$888$		0			0
$889$	4.01119	−	1.45995i	0.134531	−	0.0489652i
$890$		0			0
$891$	5.12126	+	22.6203i	0.171569	+	0.757807i
$892$		0			0
$893$	−17.3738	+	6.32354i	−0.581391	+	0.211609i
$894$		0			0
$895$	−15.1253	+	12.6916i	−0.505582	+	0.424233i
$896$		0			0
$897$	6.17773	+	2.16472i	0.206268	+	0.0722778i
$898$		0			0
$899$	−0.850472	+	1.47306i	−0.0283648	+	0.0491293i
$900$		0			0
$901$	5.89886	+	10.2171i	0.196520	+	0.340382i
$902$		0			0
$903$	4.90664	−	0.0590234i	0.163283	−	0.00196418i
$904$		0			0
$905$	−1.70353	−	0.620033i	−0.0566271	−	0.0206106i
$906$		0			0
$907$	−4.47611	+	25.3853i	−0.148627	+	0.842904i	0.815757	+	0.578395i	$0.196321\pi$
$907$	−4.47611	+	25.3853i	−0.148627	+	0.842904i	−0.964383	+	0.264509i	$0.914790\pi$
$908$		0			0
$909$	−23.7314	+	43.4875i	−0.787122	+	1.44239i
$910$		0			0
$911$	37.1435	+	31.1671i	1.23062	+	1.03261i	0.998199	+	0.0599970i	$0.0191091\pi$
$911$	37.1435	+	31.1671i	1.23062	+	1.03261i	0.232421	+	0.972615i	$0.425335\pi$
$912$		0			0
$913$	0.334852	+	1.89904i	0.0110820	+	0.0628491i
$914$		0			0
$915$	−15.0120	+	5.66934i	−0.496283	+	0.187423i
$916$		0			0
$917$	−2.42323			−0.0800221
$918$		0			0
$919$	−5.24729			−0.173092			−0.0865460	−	0.996248i	$-0.527583\pi$
$919$	−5.24729			−0.173092			−0.0865460	+	0.996248i	$0.527583\pi$
$920$		0			0
$921$	6.72970	−	41.0473i	0.221751	−	1.35255i
$922$		0			0
$923$	−3.76527	−	21.3539i	−0.123935	−	0.702873i
$924$		0			0
$925$	−19.5222	−	16.3811i	−0.641887	−	0.538607i
$926$		0			0
$927$	−11.5613	+	4.52581i	−0.379724	+	0.148647i
$928$		0			0
$929$	−3.50255	+	19.8640i	−0.114915	+	0.651715i	0.871877	+	0.489724i	$0.162903\pi$
$929$	−3.50255	+	19.8640i	−0.114915	+	0.651715i	−0.986792	+	0.161991i	$0.948208\pi$
$930$		0			0
$931$	−20.4973	−	7.46040i	−0.671771	−	0.244505i
$932$		0			0
$933$	−21.6021	−	36.3977i	−0.707221	−	1.19161i
$934$		0			0
$935$	2.01868	+	3.49646i	0.0660180	+	0.114346i
$936$		0			0
$937$	−6.81168	+	11.7982i	−0.222528	+	0.385430i	−0.955575	−	0.294748i	$-0.904764\pi$
$937$	−6.81168	+	11.7982i	−0.222528	+	0.385430i	0.733047	+	0.680178i	$0.238097\pi$
$938$		0			0
$939$	37.3067	−	32.0766i	1.21746	−	1.04678i
$940$		0			0
$941$	−19.6330	+	16.4741i	−0.640019	+	0.537040i	−0.904024	−	0.427482i	$-0.859401\pi$
$941$	−19.6330	+	16.4741i	−0.640019	+	0.537040i	0.264005	+	0.964521i	$0.414956\pi$
$942$		0			0
$943$	8.20825	−	2.98756i	0.267298	−	0.0972884i
$944$		0			0
$945$	−0.929866	−	1.48420i	−0.0302486	−	0.0482810i
$946$		0			0
$947$	18.6120	−	6.77420i	0.604807	−	0.220132i	−0.0214223	−	0.999771i	$-0.506819\pi$
$947$	18.6120	−	6.77420i	0.604807	−	0.220132i	0.626230	+	0.779639i	$0.284597\pi$
$948$		0			0
$949$	−7.71419	+	6.47297i	−0.250413	+	0.210122i
$950$		0			0
$951$	5.02506	+	26.6219i	0.162949	+	0.863273i
$952$		0			0
$953$	−1.79210	+	3.10401i	−0.0580518	+	0.100549i	−0.893591	−	0.448882i	$-0.851822\pi$
$953$	−1.79210	+	3.10401i	−0.0580518	+	0.100549i	0.835539	+	0.549431i	$0.185156\pi$
$954$		0			0
$955$	−12.5777	−	21.7852i	−0.407005	−	0.704953i
$956$		0			0
$957$	−2.41139	+	4.29514i	−0.0779490	+	0.138842i
$958$		0			0
$959$	−2.32688	−	0.846916i	−0.0751390	−	0.0273484i
$960$		0			0
$961$	−4.97057	+	28.1895i	−0.160341	+	0.909339i
$962$		0			0
$963$	−3.38857	−	16.8382i	−0.109195	−	0.542603i
$964$		0			0
$965$	9.79894	+	8.22229i	0.315439	+	0.264685i
$966$		0			0
$967$	−2.52398	−	14.3142i	−0.0811657	−	0.460314i	−0.998118	−	0.0613174i	$-0.980470\pi$
$967$	−2.52398	−	14.3142i	−0.0811657	−	0.460314i	0.916953	−	0.398996i	$-0.130641\pi$
$968$		0			0
$969$	−6.34068	−	5.19178i	−0.203692	−	0.166784i
$970$		0			0
$971$	−44.4111			−1.42522			−0.712610	−	0.701561i	$-0.752487\pi$
$971$	−44.4111			−1.42522			−0.712610	+	0.701561i	$0.752487\pi$
$972$		0			0
$973$	6.56376			0.210424
$974$		0			0
$975$	8.99342	+	7.36386i	0.288020	+	0.235832i
$976$		0			0
$977$	4.35103	+	24.6759i	0.139202	+	0.789453i	0.971841	+	0.235637i	$0.0757176\pi$
$977$	4.35103	+	24.6759i	0.139202	+	0.789453i	−0.832639	+	0.553816i	$0.813171\pi$
$978$		0			0
$979$	−8.28011	−	6.94784i	−0.264634	−	0.222054i
$980$		0			0
$981$	−2.64816	−	13.1590i	−0.0845492	−	0.420135i
$982$		0			0
$983$	2.44921	−	13.8901i	0.0781176	−	0.443027i	−0.920513	−	0.390712i	$-0.872229\pi$
$983$	2.44921	−	13.8901i	0.0781176	−	0.443027i	0.998631	−	0.0523149i	$-0.0166600\pi$
$984$		0			0
$985$	−7.70216	−	2.80336i	−0.245411	−	0.0893224i
$986$		0			0
$987$	1.59516	−	2.84128i	0.0507744	−	0.0904390i
$988$		0			0
$989$	−9.67485	−	16.7573i	−0.307642	−	0.532852i
$990$		0			0
$991$	−12.9749	+	22.4733i	−0.412163	+	0.713887i	−0.995126	−	0.0986118i	$-0.968560\pi$
$991$	−12.9749	+	22.4733i	−0.412163	+	0.713887i	0.582963	+	0.812499i	$0.301893\pi$
$992$		0			0
$993$	−0.196590	−	1.04150i	−0.00623861	−	0.0330511i
$994$		0			0
$995$	−19.0262	+	15.9649i	−0.603172	+	0.506121i
$996$		0			0
$997$	46.8359	−	17.0469i	1.48331	−	0.539879i	0.531629	−	0.846977i	$-0.321580\pi$
$997$	46.8359	−	17.0469i	1.48331	−	0.539879i	0.951678	+	0.307098i	$0.0993579\pi$
$998$		0			0
$999$	−33.9051	+	1.22404i	−1.07271	+	0.0387268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.385.3	yes	48
4.3	odd	2	inner	864.2.y.a.385.6	yes	48
27.4	even	9	inner	864.2.y.a.193.3	✓	48
108.31	odd	18	inner	864.2.y.a.193.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.193.3	✓	48	27.4	even	9	inner
864.2.y.a.193.6	yes	48	108.31	odd	18	inner
864.2.y.a.385.3	yes	48	1.1	even	1	trivial
864.2.y.a.385.6	yes	48	4.3	odd	2	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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34012 - 1.09730i) q^{3} +(0.181867 + 1.03142i) q^{5} +(-0.246536 - 0.206868i) q^{7} +(0.591863 + 2.94104i) q^{9} +O(q^{10})\)	\(q+(-1.34012 - 1.09730i) q^{3} +(0.181867 + 1.03142i) q^{5} +(-0.246536 - 0.206868i) q^{7} +(0.591863 + 2.94104i) q^{9} +(0.447486 - 2.53782i) q^{11} +(-1.61568 - 0.588061i) q^{13} +(0.888052 - 1.58179i) q^{15} +(0.747954 + 1.29549i) q^{17} +(1.58145 - 2.73916i) q^{19} +(0.103392 + 0.547753i) q^{21} +(1.68384 - 1.41291i) q^{23} +(3.66771 - 1.33494i) q^{25} +(2.43403 - 4.59080i) q^{27} +(1.03702 - 0.377445i) q^{29} +(-1.18071 + 0.990730i) q^{31} +(-3.38444 + 2.90997i) q^{33} +(0.168531 - 0.291904i) q^{35} +(-3.26464 - 5.65453i) q^{37} +(1.51994 + 2.56096i) q^{39} +(3.73426 + 1.35916i) q^{41} +(1.52862 - 8.66921i) q^{43} +(-2.92580 + 1.14534i) q^{45} +(-4.47792 - 3.75742i) q^{47} +(-1.19755 - 6.79165i) q^{49} +(0.419196 - 2.55685i) q^{51} +7.88666 q^{53} +2.69894 q^{55} +(-5.12502 + 1.93548i) q^{57} +(-1.63497 - 9.27235i) q^{59} +(-6.77642 - 5.68610i) q^{61} +(0.462492 - 0.847510i) q^{63} +(0.312697 - 1.77339i) q^{65} +(-6.44927 - 2.34734i) q^{67} +(-3.80693 + 0.0457948i) q^{69} +(6.30559 + 10.9216i) q^{71} +(2.92844 - 5.07220i) q^{73} +(-6.38002 - 2.23560i) q^{75} +(-0.635317 + 0.533094i) q^{77} +(4.69022 - 1.70710i) q^{79} +(-8.29940 + 3.48138i) q^{81} +(-0.703168 + 0.255932i) q^{83} +(-1.20017 + 1.00706i) q^{85} +(-1.80391 - 0.632101i) q^{87} +(2.09721 - 3.63248i) q^{89} +(0.276673 + 0.479212i) q^{91} +(2.66942 - 0.0321113i) q^{93} +(3.11283 + 1.13298i) q^{95} +(0.759815 - 4.30912i) q^{97} +(7.72868 - 0.185968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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