LMFDB - Embedded newform 864.2.y.a.193.6

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			193.6
Character	$\chi$	$=$	864.193
Dual form			864.2.y.a.385.6

$q$-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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

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

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	−0.916754	−	0.399451i	$-0.869201\pi$
$5$	0.181867	−	1.03142i	0.0813334	−	0.461264i	0.998088	−	0.0618131i	$-0.0196883\pi$
$6$		0			0
$7$	0.246536	−	0.206868i	0.0931819	−	0.0781889i	−0.595007	−	0.803721i	$-0.702851\pi$
$7$	0.246536	−	0.206868i	0.0931819	−	0.0781889i	0.688189	+	0.725532i	$0.258406\pi$
$8$		0			0
$9$	0.591863	−	2.94104i	0.197288	−	0.980346i
$10$		0			0
$11$	−0.447486	−	2.53782i	−0.134922	−	0.765182i	−0.974914	−	0.222583i	$-0.928551\pi$
$11$	−0.447486	−	2.53782i	−0.134922	−	0.765182i	0.839992	−	0.542599i	$-0.182560\pi$
$12$		0			0
$13$	−1.61568	+	0.588061i	−0.448110	+	0.163099i	−0.556211	−	0.831041i	$-0.687745\pi$
$13$	−1.61568	+	0.588061i	−0.448110	+	0.163099i	0.108101	+	0.994140i	$0.465523\pi$
$14$		0			0
$15$	−0.888052	−	1.58179i	−0.229294	−	0.408417i
$16$		0			0
$17$	0.747954	−	1.29549i	0.181405	−	0.314203i	−0.760954	−	0.648806i	$-0.775269\pi$
$17$	0.747954	−	1.29549i	0.181405	−	0.314203i	0.942359	+	0.334602i	$0.108602\pi$
$18$		0			0
$19$	−1.58145	−	2.73916i	−0.362810	−	0.628406i	0.625612	−	0.780134i	$-0.284849\pi$
$19$	−1.58145	−	2.73916i	−0.362810	−	0.628406i	−0.988422	+	0.151729i	$0.951516\pi$
$20$		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	$-0.351378\pi$
$23$	−1.68384	−	1.41291i	−0.351104	−	0.294612i	−0.801233	+	0.598352i	$0.795822\pi$
$24$		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	0.436505	−	0.899702i	$-0.356216\pi$
$29$	1.03702	+	0.377445i	0.192570	+	0.0700898i	−0.243935	+	0.969792i	$0.578438\pi$
$30$		0			0
$31$	1.18071	+	0.990730i	0.212061	+	0.177940i	0.742631	−	0.669701i	$-0.233578\pi$
$31$	1.18071	+	0.990730i	0.212061	+	0.177940i	−0.530570	+	0.847641i	$0.678022\pi$
$32$		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	0.462375	+	0.886685i	$0.346997\pi$
$37$	−3.26464	+	5.65453i	−0.536704	+	0.929599i	−0.999079	+	0.0429140i	$0.986336\pi$
$38$		0			0
$39$	−1.51994	+	2.56096i	−0.243385	+	0.410082i
$40$		0			0
$41$	3.73426	−	1.35916i	0.583194	−	0.212265i	−0.0335396	−	0.999437i	$-0.510678\pi$
$41$	3.73426	−	1.35916i	0.583194	−	0.212265i	0.616733	+	0.787172i	$0.288456\pi$
$42$		0			0
$43$	−1.52862	−	8.66921i	−0.233112	−	1.32204i	−0.846554	−	0.532303i	$-0.821327\pi$
$43$	−1.52862	−	8.66921i	−0.233112	−	1.32204i	0.613443	−	0.789739i	$-0.289784\pi$
$44$		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	$-0.582029\pi$
$47$	4.47792	−	3.75742i	0.653172	−	0.548076i	0.908031	+	0.418902i	$0.137585\pi$
$48$		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	−0.671737	−	0.740790i	$-0.734451\pi$
$59$	1.63497	−	9.27235i	0.212854	−	1.20716i	0.884591	−	0.466367i	$-0.154437\pi$
$60$		0			0
$61$	−6.77642	+	5.68610i	−0.867632	+	0.728030i	−0.963598	−	0.267355i	$-0.913850\pi$
$61$	−6.77642	+	5.68610i	−0.867632	+	0.728030i	0.0959659	+	0.995385i	$0.469406\pi$
$62$		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	$-0.473409\pi$
$67$	6.44927	−	2.34734i	0.787904	−	0.286774i	0.704465	+	0.709739i	$0.251187\pi$
$68$		0			0
$69$	−3.80693	−	0.0457948i	−0.458301	−	0.00551304i
$70$		0			0
$71$	−6.30559	+	10.9216i	−0.748336	+	1.29616i	0.200283	+	0.979738i	$0.435814\pi$
$71$	−6.30559	+	10.9216i	−0.748336	+	1.29616i	−0.948620	+	0.316418i	$0.897520\pi$
$72$		0			0
$73$	2.92844	+	5.07220i	0.342748	+	0.593657i	0.984942	−	0.172885i	$-0.0553091\pi$
$73$	2.92844	+	5.07220i	0.342748	+	0.593657i	−0.642194	+	0.766542i	$0.721976\pi$
$74$		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	$-0.479481\pi$
$79$	−4.69022	−	1.70710i	−0.527691	−	0.192064i	−0.592107	+	0.805859i	$0.701704\pi$
$80$		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	$-0.375813\pi$
$83$	0.703168	+	0.255932i	0.0771827	+	0.0280922i	−0.303140	+	0.952946i	$0.598035\pi$
$84$		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	0.955507	−	0.294968i	$-0.0953088\pi$
$89$	2.09721	+	3.63248i	0.222304	+	0.385042i	−0.733203	+	0.680010i	$0.761976\pi$
$90$		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	0.998776	+	0.0494530i	$0.0157478\pi$
$97$	0.759815	+	4.30912i	0.0771475	+	0.437525i	−0.921629	+	0.388072i	$0.873141\pi$
$98$		0			0
$99$	−7.72868	−	0.185968i	−0.776761	−	0.0186905i
$100$		0			0
$101$	12.6503	−	10.6149i	1.25875	−	1.05622i	0.262937	−	0.964813i	$-0.415309\pi$
$101$	12.6503	−	10.6149i	1.25875	−	1.05622i	0.995814	−	0.0914041i	$-0.0291355\pi$
$102$		0			0
$103$	−0.718649	+	4.07566i	−0.0708106	+	0.401587i	0.928715	+	0.370794i	$0.120914\pi$
$103$	−0.718649	+	4.07566i	−0.0708106	+	0.401587i	−0.999526	+	0.0307930i	$0.990197\pi$
$104$		0			0
$105$	−0.546160	−	0.206259i	−0.0532997	−	0.0201288i
$106$		0			0
$107$	5.72525			0.553481			0.276741	−	0.960945i	$-0.410746\pi$
$107$	5.72525			0.553481			0.276741	+	0.960945i	$0.410746\pi$
$108$		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	−0.999982	−	0.00608229i	$-0.998064\pi$
$113$	−0.618951	+	3.51024i	−0.0582260	+	0.330216i	0.941756	+	0.336298i	$0.109175\pi$
$114$		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	0.994432	+	0.105378i	$0.0336051\pi$
$127$	6.63179	+	11.4866i	0.588476	+	1.01927i	−0.405956	+	0.913892i	$0.633062\pi$
$128$		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	$-0.384466\pi$
$131$	−5.76796	−	4.83989i	−0.503949	−	0.422863i	−0.858994	+	0.511986i	$0.828910\pi$
$132$		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	0.631875	−	0.775070i	$-0.282285\pi$
$137$	7.23016	+	2.63156i	0.617714	+	0.224830i	−0.0141608	+	0.999900i	$0.504508\pi$
$138$		0			0
$139$	15.6236	+	13.1097i	1.32517	+	1.11195i	0.985180	+	0.171525i	$0.0548693\pi$
$139$	15.6236	+	13.1097i	1.32517	+	1.11195i	0.339993	+	0.940428i	$0.389575\pi$
$140$		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	0.814418	−	0.580279i	$-0.197056\pi$
$149$	22.1097	−	8.04726i	1.81129	−	0.659257i	0.996876	−	0.0789785i	$-0.0251658\pi$
$150$		0			0
$151$	−1.12514	−	6.38101i	−0.0915629	−	0.519279i	−0.995747	−	0.0921350i	$-0.970631\pi$
$151$	−1.12514	−	6.38101i	−0.0915629	−	0.519279i	0.904184	−	0.427144i	$-0.140480\pi$
$152$		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	0.818260	+	0.574849i	$0.194939\pi$
$157$	−1.84520	+	10.4646i	−0.147263	+	0.835168i	−0.965523	+	0.260320i	$0.916172\pi$
$158$		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	$-0.724555\pi$
$163$	−16.5560			−1.29677			−0.648384	+	0.761313i	$0.724555\pi$
$164$		0			0
$165$	−3.61691	+	2.96155i	−0.281576	+	0.230556i
$166$		0			0
$167$	−1.53218	+	8.68944i	−0.118564	+	0.672409i	0.866360	+	0.499420i	$0.166454\pi$
$167$	−1.53218	+	8.68944i	−0.118564	+	0.672409i	−0.984924	+	0.172989i	$0.944657\pi$
$168$		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	−0.988847	−	0.148936i	$-0.952415\pi$
$173$	−1.45437	−	8.24814i	−0.110574	−	0.627095i	0.878273	−	0.478159i	$-0.158696\pi$
$174$		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	0.262310	+	0.964984i	$0.415516\pi$
$179$	−9.42617	+	16.3266i	−0.704545	+	1.22031i	−0.966855	+	0.255324i	$0.917818\pi$
$180$		0			0
$181$	−0.865464	−	1.49903i	−0.0643295	−	0.111422i	0.832067	−	0.554675i	$-0.187158\pi$
$181$	−0.865464	−	1.49903i	−0.0643295	−	0.111422i	−0.896396	+	0.443253i	$0.853824\pi$
$182$		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	$-0.0536762\pi$
$191$	22.5701	+	8.21484i	1.63312	+	0.594405i	0.647299	+	0.762236i	$0.275898\pi$
$192$		0			0
$193$	9.35612	+	7.85071i	0.673468	+	0.565107i	0.914090	−	0.405512i	$-0.132907\pi$
$193$	9.35612	+	7.85071i	0.673468	+	0.565107i	−0.240622	+	0.970619i	$0.577351\pi$
$194$		0			0
$195$	2.36500	+	2.03345i	0.169361	+	0.145618i
$196$		0			0
$197$	−3.91303	−	6.77757i	−0.278792	−	0.482882i	0.692293	−	0.721617i	$-0.256601\pi$
$197$	−3.91303	−	6.77757i	−0.278792	−	0.482882i	−0.971085	+	0.238735i	$0.923267\pi$
$198$		0			0
$199$	−11.8573	+	20.5374i	−0.840540	+	1.45586i	0.0488990	+	0.998804i	$0.484429\pi$
$199$	−11.8573	+	20.5374i	−0.840540	+	1.45586i	−0.889439	+	0.457054i	$0.848905\pi$
$200$		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	$-0.998819\pi$
$211$	−0.857576	+	4.86356i	−0.0590380	+	0.334821i	0.940955	+	0.338531i	$0.109930\pi$
$212$		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	0.250021	−	0.968241i	$-0.419563\pi$
$223$	18.6212	−	15.6250i	1.24697	−	1.04633i	0.996946	−	0.0780890i	$-0.0248818\pi$
$224$		0			0
$225$	6.09689	−	9.99678i	0.406459	−	0.666452i
$226$		0			0
$227$	1.40056	+	7.94297i	0.0929584	+	0.527193i	0.995354	+	0.0962844i	$0.0306958\pi$
$227$	1.40056	+	7.94297i	0.0929584	+	0.527193i	−0.902395	+	0.430909i	$0.858193\pi$
$228$		0			0
$229$	−14.0543	+	5.11535i	−0.928735	+	0.338032i	−0.761708	−	0.647921i	$-0.775639\pi$
$229$	−14.0543	+	5.11535i	−0.928735	+	0.338032i	−0.167027	+	0.985952i	$0.553417\pi$
$230$		0			0
$231$	−1.43637	−	0.0172785i	−0.0945060	−	0.00113684i
$232$		0			0
$233$	−3.58172	+	6.20373i	−0.234647	+	0.406420i	−0.959170	−	0.282830i	$-0.908727\pi$
$233$	−3.58172	+	6.20373i	−0.234647	+	0.406420i	0.724523	+	0.689250i	$0.242060\pi$
$234$		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	$-0.480807\pi$
$239$	−14.1037	−	11.8344i	−0.912293	−	0.765505i	−0.972554	+	0.232678i	$0.925251\pi$
$240$		0			0
$241$	21.3061	+	7.75477i	1.37244	+	0.499529i	0.919879	−	0.392202i	$-0.128287\pi$
$241$	21.3061	+	7.75477i	1.37244	+	0.499529i	0.452565	+	0.891731i	$0.350509\pi$
$242$		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	0.815087	+	0.579339i	$0.196689\pi$
$251$	14.4055	+	24.9510i	0.909266	+	1.57489i	0.0941787	+	0.995555i	$0.469978\pi$
$252$		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	−0.765311	−	0.643661i	$-0.777415\pi$
$257$	−15.0346	+	5.47216i	−0.937836	+	0.341344i	−0.172525	+	0.985005i	$0.555193\pi$
$258$		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	0.430214	−	0.902727i	$-0.358438\pi$
$263$	22.6058	−	18.9685i	1.39393	−	1.16965i	0.963718	−	0.266922i	$-0.0860065\pi$
$264$		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	$-0.513974\pi$
$271$	−1.44491			−0.0877718			−0.0438859	+	0.999037i	$0.513974\pi$
$272$		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	−0.986265	−	0.165173i	$-0.947182\pi$
$277$	−16.5578	+	13.8937i	−0.994864	+	0.834790i	−0.00859964	+	0.999963i	$0.502737\pi$
$278$		0			0
$279$	3.61259	−	2.88612i	0.216280	−	0.172788i
$280$		0			0
$281$	1.01318	+	5.74604i	0.0604414	+	0.342780i	1.00000		0.000391885i	$0.000124741\pi$
$281$	1.01318	+	5.74604i	0.0604414	+	0.342780i	−0.939559	+	0.342388i	$0.888764\pi$
$282$		0			0
$283$	22.7260	−	8.27158i	1.35092	−	0.491694i	0.437684	−	0.899129i	$-0.355799\pi$
$283$	22.7260	−	8.27158i	1.35092	−	0.491694i	0.913234	+	0.407434i	$0.133577\pi$
$284$		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	0.0919169	−	0.995767i	$-0.470701\pi$
$293$	−14.9393	−	12.5355i	−0.872761	−	0.732333i	−0.964678	+	0.263434i	$0.915145\pi$
$294$		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	0.288035	+	0.957620i	$0.406998\pi$
$307$	−12.0075	+	20.7977i	−0.685306	+	1.18698i	−0.973341	+	0.229365i	$0.926335\pi$
$308$		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	$-0.854751\pi$
$311$	−22.9629	+	8.35782i	−1.30211	+	0.473928i	−0.404425	+	0.914571i	$0.632528\pi$
$312$		0			0
$313$	−4.93265	−	27.9744i	−0.278810	−	1.58121i	−0.726594	−	0.687067i	$-0.758898\pi$
$313$	−4.93265	−	27.9744i	−0.278810	−	1.58121i	0.447784	−	0.894142i	$-0.352213\pi$
$314$		0			0
$315$	−0.958249	+	0.322889i	−0.0539912	+	0.0181927i
$316$		0			0
$317$	−11.9821	+	10.0542i	−0.672984	+	0.564700i	−0.913947	−	0.405834i	$-0.866981\pi$
$317$	−11.9821	+	10.0542i	−0.672984	+	0.564700i	0.240963	+	0.970534i	$0.422537\pi$
$318$		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	$-0.727576\pi$
$331$	−0.468765	+	0.393341i	−0.0257657	+	0.0216200i	0.629814	+	0.776746i	$0.283131\pi$
$332$		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	−0.114107	−	0.993468i	$-0.536401\pi$
$337$	8.02356	−	2.92034i	0.437071	−	0.159081i	0.551178	+	0.834388i	$0.314178\pi$
$338$		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	$-0.521499\pi$
$347$	−19.7786	−	16.5962i	−1.06177	−	0.890933i	−0.994282	+	0.106787i	$0.965944\pi$
$348$		0			0
$349$	18.6979	+	6.80548i	1.00088	+	0.364289i	0.789922	−	0.613207i	$-0.210121\pi$
$349$	18.6979	+	6.80548i	1.00088	+	0.364289i	0.210953	+	0.977496i	$0.432343\pi$
$350$		0			0
$351$	6.63230	+	5.98593i	0.354006	+	0.319505i
$352$		0			0
$353$	−16.6357	−	6.05490i	−0.885429	−	0.322270i	−0.141031	−	0.990005i	$-0.545042\pi$
$353$	−16.6357	−	6.05490i	−0.885429	−	0.322270i	−0.744399	+	0.667735i	$0.767264\pi$
$354$		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	$-0.237088\pi$
$359$	−4.15770	−	7.20134i	−0.219435	−	0.380072i	−0.954635	+	0.297777i	$0.903755\pi$
$360$		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	−0.521477	−	0.853265i	$-0.674619\pi$
$367$	−6.19321	−	35.1234i	−0.323283	−	1.83343i	0.198194	−	0.980163i	$-0.436492\pi$
$368$		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	−0.798596	−	0.601867i	$-0.794424\pi$
$373$	3.04549	−	17.2718i	0.157689	−	0.894301i	0.956286	−	0.292434i	$-0.0944652\pi$
$374$		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	$-0.690124\pi$
$379$	−21.8978			−1.12481			−0.562406	+	0.826861i	$0.690124\pi$
$380$		0			0
$381$	21.4917	+	8.11639i	1.10105	+	0.415815i
$382$		0			0
$383$	2.59662	−	14.7261i	0.132681	−	0.752470i	−0.843766	−	0.536712i	$-0.819666\pi$
$383$	2.59662	−	14.7261i	0.132681	−	0.752470i	0.976447	−	0.215759i	$-0.0692225\pi$
$384$		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	0.989665	−	0.143397i	$-0.0458027\pi$
$389$	0.209841	+	1.19007i	0.0106394	+	0.0603389i	−0.979026	+	0.203736i	$0.934692\pi$
$390$		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	0.613484	−	0.789707i	$-0.289767\pi$
$397$	−7.51495	−	13.0163i	−0.377164	−	0.653268i	−0.990648	+	0.136439i	$0.956434\pi$
$398$		0			0
$399$	−1.66389	+	0.583039i	−0.0832988	+	0.0291885i
$400$		0			0
$401$	0.929698	+	0.780109i	0.0464269	+	0.0389568i	0.665706	−	0.746214i	$-0.268131\pi$
$401$	0.929698	+	0.780109i	0.0464269	+	0.0389568i	−0.619279	+	0.785171i	$0.712575\pi$
$402$		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	0.466921	−	0.884299i	$-0.345363\pi$
$409$	−6.52951	−	5.47891i	−0.322863	−	0.270915i	−0.789784	+	0.613384i	$0.789808\pi$
$410$		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	$-0.662467\pi$
$419$	−6.17983	+	2.24928i	−0.301905	+	0.109884i	0.186626	+	0.982431i	$0.440245\pi$
$420$		0			0
$421$	−6.61938	−	37.5403i	−0.322609	−	1.82960i	−0.525973	−	0.850501i	$-0.676299\pi$
$421$	−6.61938	−	37.5403i	−0.322609	−	1.82960i	0.203364	−	0.979103i	$-0.434813\pi$
$422$		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	$-0.630448\pi$
$431$	−16.5436			−0.796879			−0.398439	+	0.917195i	$0.630448\pi$
$432$		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	0.315791	−	0.948829i	$-0.397730\pi$
$439$	27.3437	−	22.9441i	1.30504	−	1.09506i	0.989250	−	0.146231i	$-0.0467143\pi$
$440$		0			0
$441$	19.2657	+	7.54177i	0.917415	+	0.359132i
$442$		0			0
$443$	−1.63428	−	9.26847i	−0.0776470	−	0.440358i	−0.998702	−	0.0509265i	$-0.983783\pi$
$443$	−1.63428	−	9.26847i	−0.0776470	−	0.440358i	0.921055	−	0.389432i	$-0.127329\pi$
$444$		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	−0.957862	−	0.287230i	$-0.907266\pi$
$449$	−4.87748	+	8.44805i	−0.230183	+	0.398688i	0.727679	+	0.685918i	$0.240599\pi$
$450$		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	0.530918	−	0.847423i	$-0.321847\pi$
$457$	8.39950	+	3.05717i	0.392912	+	0.143008i	−0.138006	+	0.990431i	$0.544069\pi$
$458$		0			0
$459$	−7.76790	−	0.280436i	−0.362575	−	0.0130896i
$460$		0			0
$461$	−4.14623	−	1.50910i	−0.193109	−	0.0702859i	0.243655	−	0.969862i	$-0.421653\pi$
$461$	−4.14623	−	1.50910i	−0.193109	−	0.0702859i	−0.436764	+	0.899576i	$0.643876\pi$
$462$		0			0
$463$	−8.29681	−	6.96185i	−0.385585	−	0.323545i	0.429305	−	0.903160i	$-0.358759\pi$
$463$	−8.29681	−	6.96185i	−0.385585	−	0.323545i	−0.814890	+	0.579615i	$0.803203\pi$
$464$		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	$-0.0109516\pi$
$467$	10.1549	+	17.5889i	0.469914	+	0.813915i	−0.529494	+	0.848314i	$0.677618\pi$
$468$		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	$-0.525491\pi$
$479$	19.4296	−	16.3034i	0.887762	−	0.744921i	0.967760	+	0.251874i	$0.0810470\pi$
$480$		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	$-0.614202\pi$
$487$	−15.4975			−0.702258			−0.351129	+	0.936327i	$0.614202\pi$
$488$		0			0
$489$	−22.1871	+	18.1669i	−1.00334	+	0.821537i
$490$		0			0
$491$	4.45652	−	25.2742i	0.201120	−	1.14061i	−0.702309	−	0.711872i	$-0.747848\pi$
$491$	4.45652	−	25.2742i	0.201120	−	1.14061i	0.903429	−	0.428737i	$-0.141041\pi$
$492$		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	$-0.477027\pi$
$499$	17.1662	−	6.24799i	0.768465	−	0.279698i	0.696354	+	0.717698i	$0.254804\pi$
$500$		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	$-0.774877\pi$
$503$	4.09566	−	7.09389i	0.182616	−	0.316301i	0.942771	+	0.333442i	$0.108210\pi$
$504$		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	0.337666	−	0.941266i	$-0.390362\pi$
$509$	−11.9723	−	10.0460i	−0.530665	−	0.445280i	−0.868331	+	0.495985i	$0.834807\pi$
$510$		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	0.720234	−	0.693732i	$-0.244035\pi$
$521$	−5.49345	−	9.51493i	−0.240672	−	0.416857i	−0.960906	+	0.276875i	$0.910701\pi$
$522$		0			0
$523$	9.83499	−	17.0347i	0.430054	−	0.744876i	−0.566823	−	0.823839i	$-0.691828\pi$
$523$	9.83499	−	17.0347i	0.430054	−	0.744876i	0.996877	+	0.0789637i	$0.0251611\pi$
$524$		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	$-0.937759\pi$
$547$	−22.4512	+	18.8388i	−0.959944	+	0.805489i	0.0210000	+	0.999779i	$0.493315\pi$
$548$		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	−0.997301	−	0.0734204i	$-0.976609\pi$
$557$	−10.2679	+	17.7846i	−0.435067	+	0.753557i	0.562234	+	0.826978i	$0.309942\pi$
$558$		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	$-0.427166\pi$
$563$	−16.4415	−	13.7961i	−0.692928	−	0.581436i	−0.919752	+	0.392500i	$0.871610\pi$
$564$		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	0.219888	−	0.975525i	$-0.429431\pi$
$569$	−5.69444	−	2.07261i	−0.238723	−	0.0868881i	−0.458611	+	0.888637i	$0.651653\pi$
$570$		0			0
$571$	22.2095	+	18.6360i	0.929438	+	0.779891i	0.975717	−	0.219037i	$-0.0702916\pi$
$571$	22.2095	+	18.6360i	0.929438	+	0.779891i	−0.0462781	+	0.998929i	$0.514736\pi$
$572$		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	−0.628267	−	0.777997i	$-0.716236\pi$
$577$	8.63865	−	14.9626i	0.359632	−	0.622900i	0.987899	+	0.155097i	$0.0495690\pi$
$578$		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	$-0.874166\pi$
$587$	−17.0536	+	14.3097i	−0.703878	+	0.590624i	0.218996	+	0.975726i	$0.429722\pi$
$588$		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	0.843158	+	0.537666i	$0.180694\pi$
$599$	−3.25619	+	18.4667i	−0.133044	+	0.754531i	−0.976202	+	0.216864i	$0.930417\pi$
$600$		0			0
$601$	−15.9833	+	13.4116i	−0.651972	+	0.547069i	−0.907668	−	0.419688i	$-0.862140\pi$
$601$	−15.9833	+	13.4116i	−0.651972	+	0.547069i	0.255697	+	0.966757i	$0.417695\pi$
$602$		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	$-0.609012\pi$
$607$	0.305399	−	0.111156i	0.0123958	−	0.00451169i	0.348211	+	0.937416i	$0.386789\pi$
$608$		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	−0.979645	−	0.200735i	$-0.935667\pi$
$613$	−16.4316	−	28.4603i	−0.663665	−	1.14950i	0.315981	−	0.948766i	$-0.397667\pi$
$614$		0			0
$615$	−5.46613	−	4.69982i	−0.220415	−	0.189515i
$616$		0			0
$617$	11.3969	+	9.56314i	0.458822	+	0.384998i	0.842697	−	0.538387i	$-0.180966\pi$
$617$	11.3969	+	9.56314i	0.458822	+	0.384998i	−0.383875	+	0.923385i	$0.625411\pi$
$618$		0			0
$619$	−22.8422	−	8.31388i	−0.918106	−	0.334163i	−0.160621	−	0.987016i	$-0.551350\pi$
$619$	−22.8422	−	8.31388i	−0.918106	−	0.334163i	−0.757485	+	0.652853i	$0.773572\pi$
$620$		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	−0.0150352	+	0.999887i	$0.504786\pi$
$631$	−21.9407	+	38.0024i	−0.873445	+	1.51285i	−0.858410	+	0.512964i	$0.828547\pi$
$632$		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	−0.944280	−	0.329143i	$-0.893240\pi$
$641$	−19.8521	+	16.6579i	−0.784110	+	0.657947i	0.160170	+	0.987089i	$0.448796\pi$
$642$		0			0
$643$	3.55745	−	20.1753i	0.140292	−	0.795635i	−0.830735	−	0.556667i	$-0.812080\pi$
$643$	3.55745	−	20.1753i	0.140292	−	0.795635i	0.971027	−	0.238968i	$-0.0768091\pi$
$644$		0			0
$645$	−12.3554	+	10.1167i	−0.486493	+	0.398343i
$646$		0			0
$647$	−33.4434			−1.31480			−0.657399	−	0.753543i	$-0.728343\pi$
$647$	−33.4434			−1.31480			−0.657399	+	0.753543i	$0.728343\pi$
$648$		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	0.601773	+	0.798667i	$0.294461\pi$
$653$	−6.05292	+	34.3278i	−0.236869	+	1.34335i	−0.838642	+	0.544683i	$0.816650\pi$
$654$		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	$-0.0298568\pi$
$659$	0.719007	+	4.07769i	0.0280085	+	0.158844i	−0.967596	+	0.252505i	$0.918746\pi$
$660$		0			0
$661$	13.0352	−	4.74442i	0.507010	−	0.184537i	−0.0758343	−	0.997120i	$-0.524162\pi$
$661$	13.0352	−	4.74442i	0.507010	−	0.184537i	0.582844	+	0.812584i	$0.301940\pi$
$662$		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	0.849173	−	0.528115i	$-0.177101\pi$
$673$	30.0985	+	10.9550i	1.16021	+	0.422283i	0.311039	+	0.950397i	$0.399323\pi$
$674$		0			0
$675$	−2.79889	−	20.0870i	−0.107729	−	0.773151i
$676$		0			0
$677$	−15.2483	−	5.54992i	−0.586039	−	0.213301i	0.0319474	−	0.999490i	$-0.489829\pi$
$677$	−15.2483	−	5.54992i	−0.586039	−	0.213301i	−0.617986	+	0.786189i	$0.712051\pi$
$678$		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	0.992380	+	0.123211i	$0.0393193\pi$
$683$	15.7562	+	27.2905i	0.602894	+	1.04424i	−0.389486	+	0.921032i	$0.627347\pi$
$684$		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	0.973609	+	0.228224i	$0.0732920\pi$
$691$	3.59534	+	20.3902i	0.136773	+	0.775679i	−0.836835	+	0.547454i	$0.815597\pi$
$692$		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	−0.913111	−	0.407712i	$-0.866327\pi$
$709$	−17.8442	+	14.9731i	−0.670153	+	0.562325i	0.242958	+	0.970037i	$0.421882\pi$
$710$		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	$-0.939667\pi$
$719$	−8.79180	+	15.2278i	−0.327879	+	0.567903i	0.654212	+	0.756311i	$0.273000\pi$
$720$		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	$-0.222497\pi$
$727$	25.2990	+	9.20808i	0.938288	+	0.341509i	0.172799	+	0.984957i	$0.444719\pi$
$728$		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	0.883237	−	0.468927i	$-0.155359\pi$
$733$	15.5623	+	13.0583i	0.574806	+	0.482319i	−0.308431	+	0.951247i	$0.599804\pi$
$734$		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	$-0.813422\pi$
$739$	1.69937	−	2.94339i	0.0625123	−	0.108274i	0.895588	+	0.444885i	$0.146755\pi$
$740$		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	$-0.717134\pi$
$743$	−16.7495	+	6.09631i	−0.614479	+	0.223652i	0.0159831	+	0.999872i	$0.494912\pi$
$744$		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	0.439869	+	0.898062i	$0.355025\pi$
$751$	−7.69043	+	43.6146i	−0.280628	+	1.59152i	−0.720497	+	0.693458i	$0.756086\pi$
$752$		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	−0.0396253	−	0.999215i	$-0.512616\pi$
$761$	9.36171	−	53.0929i	0.339362	−	1.92462i	0.378987	−	0.925402i	$-0.376272\pi$
$762$		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	−0.506346	−	0.862331i	$-0.669004\pi$
$769$	−9.42665	+	3.43102i	−0.339934	+	0.123726i	0.166412	+	0.986056i	$0.446782\pi$
$770$		0			0
$771$	−14.1437	+	23.8309i	−0.509372	+	0.858249i
$772$		0			0
$773$	3.86291	−	6.69076i	0.138939	−	0.240650i	−0.788156	−	0.615475i	$-0.788964\pi$
$773$	3.86291	−	6.69076i	0.138939	−	0.240650i	0.927095	+	0.374826i	$0.122297\pi$
$774$		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	$-0.254882\pi$
$787$	3.08895	+	2.59194i	0.110109	+	0.0923927i	−0.586071	+	0.810260i	$0.699326\pi$
$788$		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	−0.826750	−	0.562569i	$-0.809813\pi$
$797$	−31.0110	+	11.2871i	−1.09846	+	0.399808i	−0.271715	+	0.962378i	$0.587591\pi$
$798$		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	$-0.463734\pi$
$811$	6.47515			0.227373			0.113687	+	0.993517i	$0.463734\pi$
$812$		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	0.989347	+	0.145577i	$0.0465037\pi$
$821$	3.13623	+	17.7864i	0.109455	+	0.620750i	−0.879892	+	0.475174i	$0.842385\pi$
$822$		0			0
$823$	−18.0049	+	6.55327i	−0.627613	+	0.228432i	−0.636192	−	0.771531i	$-0.719491\pi$
$823$	−18.0049	+	6.55327i	−0.627613	+	0.228432i	0.00857899	+	0.999963i	$0.497269\pi$
$824$		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	$-0.898162\pi$
$827$	−5.81649	+	10.0745i	−0.202259	+	0.350323i	0.746997	+	0.664828i	$0.231495\pi$
$828$		0			0
$829$	27.9982	+	48.4944i	0.972419	+	1.68428i	0.688203	+	0.725518i	$0.258400\pi$
$829$	27.9982	+	48.4944i	0.972419	+	1.68428i	0.284216	+	0.958760i	$0.408267\pi$
$830$		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	$-0.315250\pi$
$839$	12.4816	+	4.54293i	0.430913	+	0.156840i	−0.117452	+	0.993079i	$0.537473\pi$
$840$		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	−0.792882	−	0.609375i	$-0.791420\pi$
$853$	−7.48365	−	42.4419i	−0.256235	−	1.45318i	0.536647	−	0.843807i	$-0.319691\pi$
$854$		0			0
$855$	1.48976	+	9.82552i	0.0509487	+	0.336026i
$856$		0			0
$857$	21.7758	−	18.2720i	0.743846	−	0.624161i	−0.190021	−	0.981780i	$-0.560856\pi$
$857$	21.7758	−	18.2720i	0.743846	−	0.624161i	0.933868	+	0.357619i	$0.116411\pi$
$858$		0			0
$859$	−4.61762	+	26.1878i	−0.157551	+	0.893517i	0.798865	+	0.601510i	$0.205434\pi$
$859$	−4.61762	+	26.1878i	−0.157551	+	0.893517i	−0.956416	+	0.292007i	$0.905677\pi$
$860$		0			0
$861$	−0.358391	−	2.18598i	−0.0122139	−	0.0744980i
$862$		0			0
$863$	26.4469			0.900263			0.450131	−	0.892962i	$-0.351377\pi$
$863$	26.4469			0.900263			0.450131	+	0.892962i	$0.351377\pi$
$864$		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	0.287937	−	0.957649i	$-0.407031\pi$
$877$	33.2885	−	12.1160i	1.12407	−	0.409130i	0.836138	+	0.548520i	$0.184808\pi$
$878$		0			0
$879$	−33.7757	−	0.406298i	−1.13923	−	0.0137041i
$880$		0			0
$881$	−0.850030	+	1.47229i	−0.0286382	+	0.0496029i	−0.879989	−	0.474993i	$-0.842450\pi$
$881$	−0.850030	+	1.47229i	−0.0286382	+	0.0496029i	0.851351	+	0.524596i	$0.175784\pi$
$882$		0			0
$883$	−21.8979	−	37.9283i	−0.736923	−	1.27639i	−0.953875	−	0.300205i	$-0.902945\pi$
$883$	−21.8979	−	37.9283i	−0.736923	−	1.27639i	0.216952	−	0.976182i	$-0.430388\pi$
$884$		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	$-0.0974889\pi$
$887$	24.4845	+	20.5449i	0.822108	+	0.689830i	−0.131357	+	0.991335i	$0.541933\pi$
$888$		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	0.964383	+	0.264509i	$0.0852098\pi$
$907$	4.47611	+	25.3853i	0.148627	+	0.842904i	−0.815757	+	0.578395i	$0.803679\pi$
$908$		0			0
$909$	−23.7314	−	43.4875i	−0.787122	−	1.44239i
$910$		0			0
$911$	−37.1435	+	31.1671i	−1.23062	+	1.03261i	−0.232421	+	0.972615i	$0.574665\pi$
$911$	−37.1435	+	31.1671i	−1.23062	+	1.03261i	−0.998199	+	0.0599970i	$0.980891\pi$
$912$		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	$-0.472417\pi$
$919$	5.24729			0.173092			0.0865460	+	0.996248i	$0.472417\pi$
$920$		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	−0.986792	−	0.161991i	$-0.948208\pi$
$929$	−3.50255	−	19.8640i	−0.114915	−	0.651715i	0.871877	−	0.489724i	$-0.162903\pi$
$930$		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	0.733047	−	0.680178i	$-0.238097\pi$
$937$	−6.81168	−	11.7982i	−0.222528	−	0.385430i	−0.955575	+	0.294748i	$0.904764\pi$
$938$		0			0
$939$	−37.3067	−	32.0766i	−1.21746	−	1.04678i
$940$		0			0
$941$	−19.6330	−	16.4741i	−0.640019	−	0.537040i	0.264005	−	0.964521i	$-0.414956\pi$
$941$	−19.6330	−	16.4741i	−0.640019	−	0.537040i	−0.904024	+	0.427482i	$0.859401\pi$
$942$		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	$-0.493181\pi$
$947$	−18.6120	−	6.77420i	−0.604807	−	0.220132i	−0.626230	+	0.779639i	$0.715403\pi$
$948$		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	0.835539	−	0.549431i	$-0.185156\pi$
$953$	−1.79210	−	3.10401i	−0.0580518	−	0.100549i	−0.893591	+	0.448882i	$0.851822\pi$
$954$		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	−0.916953	−	0.398996i	$-0.869359\pi$
$967$	2.52398	−	14.3142i	0.0811657	−	0.460314i	0.998118	−	0.0613174i	$-0.0195302\pi$
$968$		0			0
$969$	−6.34068	+	5.19178i	−0.203692	+	0.166784i
$970$		0			0
$971$	44.4111			1.42522			0.712610	−	0.701561i	$-0.247513\pi$
$971$	44.4111			1.42522			0.712610	+	0.701561i	$0.247513\pi$
$972$		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	−0.832639	−	0.553816i	$-0.813171\pi$
$977$	4.35103	−	24.6759i	0.139202	−	0.789453i	0.971841	−	0.235637i	$-0.0757176\pi$
$978$		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	−0.998631	−	0.0523149i	$-0.983340\pi$
$983$	−2.44921	−	13.8901i	−0.0781176	−	0.443027i	0.920513	−	0.390712i	$-0.127771\pi$
$984$		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	$-0.0314402\pi$
$991$	12.9749	+	22.4733i	0.412163	+	0.713887i	−0.582963	+	0.812499i	$0.698107\pi$
$992$		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	0.951678	−	0.307098i	$-0.0993579\pi$
$997$	46.8359	+	17.0469i	1.48331	+	0.539879i	0.531629	+	0.846977i	$0.321580\pi$
$998$		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.193.6	yes	48
4.3	odd	2	inner	864.2.y.a.193.3	✓	48
27.7	even	9	inner	864.2.y.a.385.6	yes	48
108.7	odd	18	inner	864.2.y.a.385.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.193.3	✓	48	4.3	odd	2	inner
864.2.y.a.193.6	yes	48	1.1	even	1	trivial
864.2.y.a.385.3	yes	48	108.7	odd	18	inner
864.2.y.a.385.6	yes	48	27.7	even	9	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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