LMFDB - Embedded newform 864.2.y.d.97.8

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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	864.97
Dual form			864.2.y.d.481.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01321 + 1.40478i) q^{3} +(-1.03120 - 0.375327i) q^{5} +(0.257635 - 1.46112i) q^{7} +(-0.946819 + 2.84667i) q^{9} +O(q^{10})$	\(q+(1.01321 + 1.40478i) q^{3} +(-1.03120 - 0.375327i) q^{5} +(0.257635 - 1.46112i) q^{7} +(-0.946819 + 2.84667i) q^{9} +(-3.59661 + 1.30906i) q^{11} +(0.587485 - 0.492959i) q^{13} +(-0.517571 - 1.82890i) q^{15} +(3.99661 + 6.92233i) q^{17} +(-2.12655 + 3.68329i) q^{19} +(2.31359 - 1.11850i) q^{21} +(1.45270 + 8.23865i) q^{23} +(-2.90771 - 2.43986i) q^{25} +(-4.95827 + 1.55420i) q^{27} +(3.82432 + 3.20898i) q^{29} +(1.04049 + 5.90094i) q^{31} +(-5.48306 - 3.72610i) q^{33} +(-0.814071 + 1.41001i) q^{35} +(-2.67115 - 4.62657i) q^{37} +(1.28774 + 0.325818i) q^{39} +(2.24532 - 1.88405i) q^{41} +(-1.43450 + 0.522115i) q^{43} +(2.04480 - 2.58013i) q^{45} +(1.08751 - 6.16757i) q^{47} +(4.50936 + 1.64127i) q^{49} +(-5.67496 + 12.6281i) q^{51} -3.23082 q^{53} +4.20017 q^{55} +(-7.32885 + 0.744605i) q^{57} +(-0.643906 - 0.234363i) q^{59} +(2.22831 - 12.6374i) q^{61} +(3.91539 + 2.11681i) q^{63} +(-0.790837 + 0.287841i) q^{65} +(-5.83956 + 4.89997i) q^{67} +(-10.1016 + 10.3882i) q^{69} +(-1.69534 - 2.93642i) q^{71} +(1.02957 - 1.78327i) q^{73} +(0.481351 - 6.55679i) q^{75} +(0.986080 + 5.59234i) q^{77} +(0.799634 + 0.670973i) q^{79} +(-7.20707 - 5.39056i) q^{81} +(4.60378 + 3.86303i) q^{83} +(-1.52318 - 8.63836i) q^{85} +(-0.633089 + 8.62370i) q^{87} +(4.89625 - 8.48056i) q^{89} +(-0.568914 - 0.985388i) q^{91} +(-7.23529 + 7.44055i) q^{93} +(3.57534 - 3.00007i) q^{95} +(5.38189 - 1.95885i) q^{97} +(-0.321123 - 11.4778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	1.01321	+	1.40478i	0.584976	+	0.811051i
$3$	1.01321	+	1.40478i	0.584976	+	0.811051i
$4$		0			0
$5$	−1.03120	−	0.375327i	−0.461168	−	0.167851i	0.100979	−	0.994889i	$-0.467802\pi$
$5$	−1.03120	−	0.375327i	−0.461168	−	0.167851i	−0.562147	+	0.827037i	$0.690025\pi$
$6$		0			0
$7$	0.257635	−	1.46112i	0.0973767	−	0.552251i	−0.896616	−	0.442808i	$-0.853982\pi$
$7$	0.257635	−	1.46112i	0.0973767	−	0.552251i	0.993993	−	0.109443i	$-0.0349066\pi$
$8$		0			0
$9$	−0.946819	+	2.84667i	−0.315606	+	0.948890i
$10$		0			0
$11$	−3.59661	+	1.30906i	−1.08442	+	0.394697i	−0.821551	−	0.570135i	$-0.806891\pi$
$11$	−3.59661	+	1.30906i	−1.08442	+	0.394697i	−0.262869	+	0.964832i	$0.584669\pi$
$12$		0			0
$13$	0.587485	−	0.492959i	0.162939	−	0.136722i	−0.557673	−	0.830061i	$-0.688306\pi$
$13$	0.587485	−	0.492959i	0.162939	−	0.136722i	0.720612	+	0.693339i	$0.243861\pi$
$14$		0			0
$15$	−0.517571	−	1.82890i	−0.133636	−	0.472220i
$16$		0			0
$17$	3.99661	+	6.92233i	0.969320	+	1.67891i	0.697531	+	0.716554i	$0.254282\pi$
$17$	3.99661	+	6.92233i	0.969320	+	1.67891i	0.271788	+	0.962357i	$0.412385\pi$
$18$		0			0
$19$	−2.12655	+	3.68329i	−0.487864	+	0.845005i	−0.999903	−	0.0139575i	$-0.995557\pi$
$19$	−2.12655	+	3.68329i	−0.487864	+	0.845005i	0.512039	+	0.858962i	$0.328890\pi$
$20$		0			0
$21$	2.31359	−	1.11850i	0.504866	−	0.244076i
$22$		0			0
$23$	1.45270	+	8.23865i	0.302908	+	1.71788i	0.633190	+	0.773996i	$0.281745\pi$
$23$	1.45270	+	8.23865i	0.302908	+	1.71788i	−0.330282	+	0.943882i	$0.607144\pi$
$24$		0			0
$25$	−2.90771	−	2.43986i	−0.581543	−	0.487972i
$26$		0			0
$27$	−4.95827	+	1.55420i	−0.954220	+	0.299105i
$28$		0			0
$29$	3.82432	+	3.20898i	0.710158	+	0.595893i	0.924643	−	0.380834i	$-0.124363\pi$
$29$	3.82432	+	3.20898i	0.710158	+	0.595893i	−0.214486	+	0.976727i	$0.568807\pi$
$30$		0			0
$31$	1.04049	+	5.90094i	0.186878	+	1.05984i	0.923518	+	0.383555i	$0.125300\pi$
$31$	1.04049	+	5.90094i	0.186878	+	1.05984i	−0.736640	+	0.676285i	$0.763589\pi$
$32$		0			0
$33$	−5.48306	−	3.72610i	−0.954479	−	0.648632i
$34$		0			0
$35$	−0.814071	+	1.41001i	−0.137603	+	0.238336i
$36$		0			0
$37$	−2.67115	−	4.62657i	−0.439135	−	0.760603i	0.558488	−	0.829512i	$-0.311382\pi$
$37$	−2.67115	−	4.62657i	−0.439135	−	0.760603i	−0.997623	+	0.0689089i	$0.978048\pi$
$38$		0			0
$39$	1.28774	+	0.325818i	0.206204	+	0.0521727i
$40$		0			0
$41$	2.24532	−	1.88405i	0.350660	−	0.294239i	−0.450395	−	0.892829i	$-0.648717\pi$
$41$	2.24532	−	1.88405i	0.350660	−	0.294239i	0.801055	+	0.598591i	$0.204272\pi$
$42$		0			0
$43$	−1.43450	+	0.522115i	−0.218759	+	0.0796218i	−0.449075	−	0.893494i	$-0.648246\pi$
$43$	−1.43450	+	0.522115i	−0.218759	+	0.0796218i	0.230316	+	0.973116i	$0.426024\pi$
$44$		0			0
$45$	2.04480	−	2.58013i	0.304820	−	0.384623i
$46$		0			0
$47$	1.08751	−	6.16757i	0.158629	−	0.899632i	−0.796763	−	0.604292i	$-0.793456\pi$
$47$	1.08751	−	6.16757i	0.158629	−	0.899632i	0.955392	−	0.295340i	$-0.0954330\pi$
$48$		0			0
$49$	4.50936	+	1.64127i	0.644194	+	0.234467i
$50$		0			0
$51$	−5.67496	+	12.6281i	−0.794653	+	1.76829i
$52$		0			0
$53$	−3.23082			−0.443788			−0.221894	−	0.975071i	$-0.571224\pi$
$53$	−3.23082			−0.443788			−0.221894	+	0.975071i	$0.571224\pi$
$54$		0			0
$55$	4.20017			0.566350
$56$		0			0
$57$	−7.32885	+	0.744605i	−0.970730	+	0.0986253i
$58$		0			0
$59$	−0.643906	−	0.234363i	−0.0838294	−	0.0305114i	0.299765	−	0.954013i	$-0.403092\pi$
$59$	−0.643906	−	0.234363i	−0.0838294	−	0.0305114i	−0.383594	+	0.923502i	$0.625314\pi$
$60$		0			0
$61$	2.22831	−	12.6374i	0.285306	−	1.61805i	−0.418885	−	0.908039i	$-0.637579\pi$
$61$	2.22831	−	12.6374i	0.285306	−	1.61805i	0.704191	−	0.710011i	$-0.251310\pi$
$62$		0			0
$63$	3.91539	+	2.11681i	0.493293	+	0.266694i
$64$		0			0
$65$	−0.790837	+	0.287841i	−0.0980913	+	0.0357023i
$66$		0			0
$67$	−5.83956	+	4.89997i	−0.713416	+	0.598627i	−0.925555	−	0.378612i	$-0.876401\pi$
$67$	−5.83956	+	4.89997i	−0.713416	+	0.598627i	0.212139	+	0.977239i	$0.431957\pi$
$68$		0			0
$69$	−10.1016	+	10.3882i	−1.21609	+	1.25059i
$70$		0			0
$71$	−1.69534	−	2.93642i	−0.201200	−	0.348489i	0.747715	−	0.664020i	$-0.231151\pi$
$71$	−1.69534	−	2.93642i	−0.201200	−	0.348489i	−0.948915	+	0.315530i	$0.897818\pi$
$72$		0			0
$73$	1.02957	−	1.78327i	0.120502	−	0.208716i	−0.799464	−	0.600715i	$-0.794883\pi$
$73$	1.02957	−	1.78327i	0.120502	−	0.208716i	0.919966	+	0.391998i	$0.128216\pi$
$74$		0			0
$75$	0.481351	−	6.55679i	0.0555817	−	0.757113i
$76$		0			0
$77$	0.986080	+	5.59234i	0.112374	+	0.637306i
$78$		0			0
$79$	0.799634	+	0.670973i	0.0899658	+	0.0754903i	0.686661	−	0.726977i	$-0.259076\pi$
$79$	0.799634	+	0.670973i	0.0899658	+	0.0754903i	−0.596696	+	0.802468i	$0.703520\pi$
$80$		0			0
$81$	−7.20707	−	5.39056i	−0.800785	−	0.598951i
$82$		0			0
$83$	4.60378	+	3.86303i	0.505330	+	0.424022i	0.859482	−	0.511166i	$-0.170786\pi$
$83$	4.60378	+	3.86303i	0.505330	+	0.424022i	−0.354152	+	0.935188i	$0.615231\pi$
$84$		0			0
$85$	−1.52318	−	8.63836i	−0.165212	−	0.936962i
$86$		0			0
$87$	−0.633089	+	8.62370i	−0.0678743	+	0.924557i
$88$		0			0
$89$	4.89625	−	8.48056i	0.519002	−	0.898937i	−0.480755	−	0.876855i	$-0.659637\pi$
$89$	4.89625	−	8.48056i	0.519002	−	0.898937i	0.999756	−	0.0220819i	$-0.00702946\pi$
$90$		0			0
$91$	−0.568914	−	0.985388i	−0.0596384	−	0.103297i
$92$		0			0
$93$	−7.23529	+	7.44055i	−0.750265	+	0.771549i
$94$		0			0
$95$	3.57534	−	3.00007i	0.366822	−	0.307801i
$96$		0			0
$97$	5.38189	−	1.95885i	0.546448	−	0.198891i	−0.0540194	−	0.998540i	$-0.517203\pi$
$97$	5.38189	−	1.95885i	0.546448	−	0.198891i	0.600468	+	0.799649i	$0.294981\pi$
$98$		0			0
$99$	−0.321123	−	11.4778i	−0.0322741	−	1.15356i
$100$		0			0
$101$	−1.04173	+	5.90795i	−0.103656	+	0.587863i	0.888092	+	0.459665i	$0.152030\pi$
$101$	−1.04173	+	5.90795i	−0.103656	+	0.587863i	−0.991749	+	0.128198i	$0.959081\pi$
$102$		0			0
$103$	−15.2056	−	5.53439i	−1.49825	−	0.545320i	−0.542646	−	0.839961i	$-0.682578\pi$
$103$	−15.2056	−	5.53439i	−1.49825	−	0.545320i	−0.955608	+	0.294641i	$0.904800\pi$
$104$		0			0
$105$	−2.80558	+	0.285045i	−0.273797	+	0.0278175i
$106$		0			0
$107$	−14.5822			−1.40971			−0.704857	−	0.709349i	$-0.748989\pi$
$107$	−14.5822			−1.40971			−0.704857	+	0.709349i	$0.748989\pi$
$108$		0			0
$109$	11.9208			1.14181			0.570904	−	0.821016i	$-0.306593\pi$
$109$	11.9208			1.14181			0.570904	+	0.821016i	$0.306593\pi$
$110$		0			0
$111$	3.79288	−	8.44006i	0.360005	−	0.801095i
$112$		0			0
$113$	12.6603	+	4.60799i	1.19099	+	0.433483i	0.860069	−	0.510177i	$-0.170420\pi$
$113$	12.6603	+	4.60799i	1.19099	+	0.433483i	0.330916	+	0.943660i	$0.392642\pi$
$114$		0			0
$115$	1.59417	−	9.04096i	0.148657	−	0.843074i
$116$		0			0
$117$	0.847049	+	2.13912i	0.0783097	+	0.197762i
$118$		0			0
$119$	11.1440	−	4.05609i	1.02157	−	0.371821i
$120$		0			0
$121$	2.79551	−	2.34571i	0.254137	−	0.213246i
$122$		0			0
$123$	4.92165	+	1.24525i	0.443770	+	0.112280i
$124$		0			0
$125$	4.82615	+	8.35914i	0.431664	+	0.747665i
$126$		0			0
$127$	6.29488	−	10.9031i	0.558581	−	0.967490i	−0.439035	−	0.898470i	$-0.644679\pi$
$127$	6.29488	−	10.9031i	0.558581	−	0.967490i	0.997615	−	0.0690198i	$-0.0219872\pi$
$128$		0			0
$129$	−2.18690	−	1.48615i	−0.192546	−	0.130848i
$130$		0			0
$131$	1.92349	+	10.9087i	0.168056	+	0.953095i	0.945857	+	0.324584i	$0.105224\pi$
$131$	1.92349	+	10.9087i	0.168056	+	0.953095i	−0.777800	+	0.628511i	$0.783665\pi$
$132$		0			0
$133$	4.83385	+	4.05608i	0.419148	+	0.351707i
$134$		0			0
$135$	5.69632	+	0.258282i	0.490261	+	0.0222293i
$136$		0			0
$137$	10.1007	+	8.47545i	0.862957	+	0.724107i	0.962603	−	0.270916i	$-0.0873266\pi$
$137$	10.1007	+	8.47545i	0.862957	+	0.724107i	−0.0996460	+	0.995023i	$0.531771\pi$
$138$		0			0
$139$	1.43599	+	8.14389i	0.121799	+	0.690756i	0.983158	+	0.182759i	$0.0585027\pi$
$139$	1.43599	+	8.14389i	0.121799	+	0.690756i	−0.861359	+	0.507997i	$0.830386\pi$
$140$		0			0
$141$	9.76596	−	4.72132i	0.822442	−	0.397607i
$142$		0			0
$143$	−1.46764	+	2.54204i	−0.122731	+	0.212576i
$144$		0			0
$145$	−2.73923	−	4.74448i	−0.227481	−	0.394008i
$146$		0			0
$147$	2.26329	+	7.99761i	0.186673	+	0.659632i
$148$		0			0
$149$	−5.68201	+	4.76777i	−0.465488	+	0.390591i	−0.845146	−	0.534536i	$-0.820486\pi$
$149$	−5.68201	+	4.76777i	−0.465488	+	0.390591i	0.379657	+	0.925127i	$0.376042\pi$
$150$		0			0
$151$	17.0505	−	6.20588i	1.38755	−	0.505027i	0.463092	−	0.886310i	$-0.346740\pi$
$151$	17.0505	−	6.20588i	1.38755	−	0.505027i	0.924458	+	0.381283i	$0.124518\pi$
$152$		0			0
$153$	−23.4897	+	4.82284i	−1.89903	+	0.389903i
$154$		0			0
$155$	1.14182	−	6.47559i	0.0917133	−	0.520132i
$156$		0			0
$157$	−14.8156	−	5.39246i	−1.18242	−	0.430365i	−0.325362	−	0.945589i	$-0.605486\pi$
$157$	−14.8156	−	5.39246i	−1.18242	−	0.430365i	−0.857055	+	0.515225i	$0.827708\pi$
$158$		0			0
$159$	−3.27350	−	4.53860i	−0.259605	−	0.359934i
$160$		0			0
$161$	12.4119			0.978196
$162$		0			0
$163$	18.2090			1.42624			0.713119	−	0.701043i	$-0.247282\pi$
$163$	18.2090			1.42624			0.713119	+	0.701043i	$0.247282\pi$
$164$		0			0
$165$	4.25564	+	5.90031i	0.331301	+	0.459339i
$166$		0			0
$167$	6.45633	+	2.34991i	0.499606	+	0.181842i	0.579517	−	0.814960i	$-0.303241\pi$
$167$	6.45633	+	2.34991i	0.499606	+	0.181842i	−0.0799108	+	0.996802i	$0.525464\pi$
$168$		0			0
$169$	−2.15530	+	12.2233i	−0.165792	+	0.940253i
$170$		0			0
$171$	−8.47166	−	9.54099i	−0.647844	−	0.729618i
$172$		0			0
$173$	−4.98041	+	1.81272i	−0.378654	+	0.137819i	−0.524333	−	0.851513i	$-0.675685\pi$
$173$	−4.98041	+	1.81272i	−0.378654	+	0.137819i	0.145680	+	0.989332i	$0.453463\pi$
$174$		0			0
$175$	−4.31405	+	3.61992i	−0.326112	+	0.273640i
$176$		0			0
$177$	−0.323183	−	1.14200i	−0.0242919	−	0.0858383i
$178$		0			0
$179$	−5.79903	−	10.0442i	−0.433440	−	0.750740i	0.563727	−	0.825961i	$-0.309367\pi$
$179$	−5.79903	−	10.0442i	−0.433440	−	0.750740i	−0.997167	+	0.0752212i	$0.976034\pi$
$180$		0			0
$181$	5.90043	−	10.2198i	0.438575	−	0.759635i	−0.559004	−	0.829165i	$-0.688817\pi$
$181$	5.90043	−	10.2198i	0.438575	−	0.759635i	0.997580	+	0.0695297i	$0.0221499\pi$
$182$		0			0
$183$	20.0105	−	9.67400i	1.47922	−	0.715123i
$184$		0			0
$185$	1.01802	+	5.77349i	0.0748465	+	0.424475i
$186$		0			0
$187$	−23.4360	−	19.6651i	−1.71381	−	1.43806i
$188$		0			0
$189$	0.993444	+	7.64504i	0.0722624	+	0.556095i
$190$		0			0
$191$	−20.6098	−	17.2937i	−1.49127	−	1.25133i	−0.893017	−	0.450023i	$-0.851416\pi$
$191$	−20.6098	−	17.2937i	−1.49127	−	1.25133i	−0.598257	−	0.801304i	$-0.704140\pi$
$192$		0			0
$193$	−0.0998988	−	0.566554i	−0.00719087	−	0.0407815i	0.981001	−	0.194002i	$-0.0621467\pi$
$193$	−0.0998988	−	0.566554i	−0.00719087	−	0.0407815i	−0.988192	+	0.153220i	$0.951036\pi$
$194$		0			0
$195$	−1.20564	−	0.819310i	−0.0863374	−	0.0586720i
$196$		0			0
$197$	−8.52358	+	14.7633i	−0.607280	+	1.05184i	0.384407	+	0.923164i	$0.374406\pi$
$197$	−8.52358	+	14.7633i	−0.607280	+	1.05184i	−0.991687	+	0.128676i	$0.958927\pi$
$198$		0			0
$199$	10.9506	+	18.9671i	0.776270	+	1.34454i	0.934078	+	0.357069i	$0.116224\pi$
$199$	10.9506	+	18.9671i	0.776270	+	1.34454i	−0.157808	+	0.987470i	$0.550443\pi$
$200$		0			0
$201$	−12.8001	−	3.23861i	−0.902848	−	0.228434i
$202$		0			0
$203$	5.67398	−	4.76103i	0.398235	−	0.334159i
$204$		0			0
$205$	−3.02251	+	1.10010i	−0.211101	+	0.0768346i
$206$		0			0
$207$	−24.8282	−	3.66516i	−1.72568	−	0.254746i
$208$		0			0
$209$	2.82673	−	16.0312i	0.195529	−	1.10890i
$210$		0			0
$211$	4.84275	+	1.76262i	0.333389	+	0.121344i	0.503290	−	0.864117i	$-0.332123\pi$
$211$	4.84275	+	1.76262i	0.333389	+	0.121344i	−0.169901	+	0.985461i	$0.554345\pi$
$212$		0			0
$213$	2.40729	−	5.35680i	0.164945	−	0.367042i
$214$		0			0
$215$	1.67522			0.114249
$216$		0			0
$217$	8.89004			0.603495
$218$		0			0
$219$	3.54828	−	0.360502i	0.239770	−	0.0243605i
$220$		0			0
$221$	5.76037	+	2.09660i	0.387484	+	0.141033i
$222$		0			0
$223$	2.87829	−	16.3236i	0.192745	−	1.09311i	−0.722849	−	0.691006i	$-0.757168\pi$
$223$	2.87829	−	16.3236i	0.192745	−	1.09311i	0.915594	−	0.402104i	$-0.131721\pi$
$224$		0			0
$225$	9.69856	−	5.96720i	0.646571	−	0.397813i
$226$		0			0
$227$	25.5957	−	9.31608i	1.69885	−	0.618330i	0.703155	−	0.711037i	$-0.251774\pi$
$227$	25.5957	−	9.31608i	1.69885	−	0.618330i	0.995693	+	0.0927066i	$0.0295518\pi$
$228$		0			0
$229$	18.4697	−	15.4980i	1.22052	−	1.02413i	0.221718	−	0.975111i	$-0.428834\pi$
$229$	18.4697	−	15.4980i	1.22052	−	1.02413i	0.998798	−	0.0490230i	$-0.0156108\pi$
$230$		0			0
$231$	−6.85691	+	7.05143i	−0.451151	+	0.463950i
$232$		0			0
$233$	−8.11918	−	14.0628i	−0.531905	−	0.921287i	−0.999306	−	0.0372415i	$-0.988143\pi$
$233$	−8.11918	−	14.0628i	−0.531905	−	0.921287i	0.467401	−	0.884045i	$-0.345190\pi$
$234$		0			0
$235$	−3.43630	+	5.95184i	−0.224159	+	0.388255i
$236$		0			0
$237$	−0.132374	+	1.80315i	−0.00859860	+	0.117127i
$238$		0			0
$239$	3.27646	+	18.5817i	0.211937	+	1.20195i	0.886144	+	0.463410i	$0.153374\pi$
$239$	3.27646	+	18.5817i	0.211937	+	1.20195i	−0.674207	+	0.738542i	$0.735515\pi$
$240$		0			0
$241$	−1.23897	−	1.03962i	−0.0798093	−	0.0669680i	0.602010	−	0.798488i	$-0.294367\pi$
$241$	−1.23897	−	1.03962i	−0.0798093	−	0.0669680i	−0.681820	+	0.731520i	$0.738811\pi$
$242$		0			0
$243$	0.270297	−	15.5861i	0.0173395	−	0.999850i
$244$		0			0
$245$	−4.03405	−	3.38497i	−0.257726	−	0.216258i
$246$		0			0
$247$	0.566394	+	3.21218i	0.0360388	+	0.204386i
$248$		0			0
$249$	−0.762123	+	10.3813i	−0.0482976	+	0.657891i
$250$		0			0
$251$	1.85089	−	3.20584i	0.116827	−	0.202351i	−0.801682	−	0.597751i	$-0.796061\pi$
$251$	1.85089	−	3.20584i	0.116827	−	0.202351i	0.918509	+	0.395401i	$0.129394\pi$
$252$		0			0
$253$	−16.0097	−	27.7296i	−1.00652	−	1.74334i
$254$		0			0
$255$	10.5917	−	10.8922i	0.663279	−	0.682095i
$256$		0			0
$257$	2.84772	−	2.38952i	0.177636	−	0.149054i	−0.549635	−	0.835405i	$-0.685233\pi$
$257$	2.84772	−	2.38952i	0.177636	−	0.149054i	0.727271	+	0.686351i	$0.240789\pi$
$258$		0			0
$259$	−7.44815	+	2.71090i	−0.462805	+	0.168447i
$260$		0			0
$261$	−12.7559	+	7.84825i	−0.789568	+	0.485794i
$262$		0			0
$263$	3.04703	−	17.2805i	0.187888	−	1.06556i	−0.734301	−	0.678824i	$-0.762490\pi$
$263$	3.04703	−	17.2805i	0.187888	−	1.06556i	0.922189	−	0.386740i	$-0.126399\pi$
$264$		0			0
$265$	3.33163	+	1.21262i	0.204661	+	0.0744904i
$266$		0			0
$267$	16.8742	−	1.71441i	1.03269	−	0.104920i
$268$		0			0
$269$	2.48647			0.151603			0.0758015	−	0.997123i	$-0.475848\pi$
$269$	2.48647			0.151603			0.0758015	+	0.997123i	$0.475848\pi$
$270$		0			0
$271$	−3.75905			−0.228346			−0.114173	−	0.993461i	$-0.536422\pi$
$271$	−3.75905			−0.228346			−0.114173	+	0.993461i	$0.536422\pi$
$272$		0			0
$273$	0.807826	−	1.79760i	0.0488919	−	0.108796i
$274$		0			0
$275$	13.6518	+	4.96887i	0.823237	+	0.299634i
$276$		0			0
$277$	1.64314	−	9.31869i	0.0987265	−	0.559906i	−0.894815	−	0.446437i	$-0.852693\pi$
$277$	1.64314	−	9.31869i	0.0987265	−	0.559906i	0.993542	−	0.113469i	$-0.0361962\pi$
$278$		0			0
$279$	−17.7832	−	2.62517i	−1.06465	−	0.157165i
$280$		0			0
$281$	−0.263993	+	0.0960856i	−0.0157485	+	0.00573199i	−0.349882	−	0.936794i	$-0.613778\pi$
$281$	−0.263993	+	0.0960856i	−0.0157485	+	0.00573199i	0.334134	+	0.942526i	$0.391556\pi$
$282$		0			0
$283$	12.3803	−	10.3883i	0.735934	−	0.617522i	−0.195808	−	0.980642i	$-0.562733\pi$
$283$	12.3803	−	10.3883i	0.735934	−	0.617522i	0.931742	+	0.363120i	$0.118289\pi$
$284$		0			0
$285$	7.83700	+	1.98288i	0.464224	+	0.117456i
$286$		0			0
$287$	−2.17434	−	3.76607i	−0.128347	−	0.222304i
$288$		0			0
$289$	−23.4458	+	40.6092i	−1.37916	+	2.38878i
$290$		0			0
$291$	8.20473	+	5.57566i	0.480970	+	0.326851i
$292$		0			0
$293$	0.0947490	+	0.537348i	0.00553529	+	0.0313922i	0.987450	−	0.157930i	$-0.0504820\pi$
$293$	0.0947490	+	0.537348i	0.00553529	+	0.0313922i	−0.981915	+	0.189322i	$0.939371\pi$
$294$		0			0
$295$	0.576035	+	0.483351i	0.0335380	+	0.0281418i
$296$		0			0
$297$	15.7985	−	12.0805i	0.916719	−	0.700983i
$298$		0			0
$299$	4.91475	+	4.12397i	0.284228	+	0.238495i
$300$		0			0
$301$	0.393295	+	2.23049i	0.0226692	+	0.128563i
$302$		0			0
$303$	−9.35486	+	4.52258i	−0.537423	+	0.259815i
$304$		0			0
$305$	−7.04099	+	12.1954i	−0.403166	+	0.698304i
$306$		0			0
$307$	12.1462	+	21.0378i	0.693220	+	1.20069i	0.970777	+	0.239983i	$0.0771419\pi$
$307$	12.1462	+	21.0378i	0.693220	+	1.20069i	−0.277557	+	0.960709i	$0.589525\pi$
$308$		0			0
$309$	−7.63185	−	26.9681i	−0.434161	−	1.53416i
$310$		0			0
$311$	−24.2583	+	20.3551i	−1.37556	+	1.15423i	−0.404737	+	0.914433i	$0.632637\pi$
$311$	−24.2583	+	20.3551i	−1.37556	+	1.15423i	−0.970823	+	0.239798i	$0.922919\pi$
$312$		0			0
$313$	6.70456	−	2.44026i	0.378964	−	0.137932i	−0.145513	−	0.989356i	$-0.546483\pi$
$313$	6.70456	−	2.44026i	0.378964	−	0.137932i	0.524477	+	0.851425i	$0.324261\pi$
$314$		0			0
$315$	−3.24306	−	3.65242i	−0.182726	−	0.205790i
$316$		0			0
$317$	−1.97463	+	11.1987i	−0.110906	+	0.628981i	0.877789	+	0.479047i	$0.159018\pi$
$317$	−1.97463	+	11.1987i	−0.110906	+	0.628981i	−0.988696	+	0.149935i	$0.952094\pi$
$318$		0			0
$319$	−17.9553	−	6.53521i	−1.00531	−	0.365902i
$320$		0			0
$321$	−14.7748	−	20.4848i	−0.824649	−	1.14335i
$322$		0			0
$323$	−33.9959			−1.89158
$324$		0			0
$325$	−2.91099			−0.161473
$326$		0			0
$327$	12.0783	+	16.7462i	0.667931	+	0.926065i
$328$		0			0
$329$	−8.73137	−	3.17796i	−0.481376	−	0.175206i
$330$		0			0
$331$	4.04388	−	22.9340i	0.222272	−	1.26056i	−0.645561	−	0.763708i	$-0.723377\pi$
$331$	4.04388	−	22.9340i	0.222272	−	1.26056i	0.867833	−	0.496856i	$-0.165512\pi$
$332$		0			0
$333$	15.6994	−	3.22337i	0.860323	−	0.176639i
$334$		0			0
$335$	7.86087	−	2.86112i	0.429485	−	0.156320i
$336$		0			0
$337$	−23.1717	+	19.4433i	−1.26224	+	1.05915i	−0.266802	+	0.963751i	$0.585967\pi$
$337$	−23.1717	+	19.4433i	−1.26224	+	1.05915i	−0.995439	+	0.0953952i	$0.969589\pi$
$338$		0			0
$339$	6.35435	+	22.4539i	0.345121	+	1.21953i
$340$		0			0
$341$	−11.4669	−	19.8613i	−0.620970	−	1.07555i
$342$		0			0
$343$	8.75266	−	15.1601i	0.472599	−	0.818566i
$344$		0			0
$345$	14.3158	−	6.92092i	0.770736	−	0.372610i
$346$		0			0
$347$	−1.75279	−	9.94056i	−0.0940946	−	0.533637i	−0.995021	−	0.0996652i	$-0.968223\pi$
$347$	−1.75279	−	9.94056i	−0.0940946	−	0.533637i	0.900926	−	0.433972i	$-0.142888\pi$
$348$		0			0
$349$	−14.6267	−	12.2733i	−0.782950	−	0.656973i	0.161040	−	0.986948i	$-0.448515\pi$
$349$	−14.6267	−	12.2733i	−0.782950	−	0.656973i	−0.943990	+	0.329975i	$0.892960\pi$
$350$		0			0
$351$	−2.14676	+	3.35729i	−0.114585	+	0.179199i
$352$		0			0
$353$	17.6175	+	14.7828i	0.937685	+	0.786811i	0.977181	−	0.212408i	$-0.0681307\pi$
$353$	17.6175	+	14.7828i	0.937685	+	0.786811i	−0.0394958	+	0.999220i	$0.512575\pi$
$354$		0			0
$355$	0.646125	+	3.66436i	0.0342928	+	0.194484i
$356$		0			0
$357$	16.9891	+	11.5452i	0.899159	+	0.611038i
$358$		0			0
$359$	−13.4960	+	23.3757i	−0.712289	+	1.23372i	0.251707	+	0.967804i	$0.419008\pi$
$359$	−13.4960	+	23.3757i	−0.712289	+	1.23372i	−0.963996	+	0.265917i	$0.914325\pi$
$360$		0			0
$361$	0.455580	+	0.789088i	0.0239779	+	0.0415309i
$362$		0			0
$363$	6.12764	+	1.55038i	0.321618	+	0.0813740i
$364$		0			0
$365$	−1.73101	+	1.45249i	−0.0906052	+	0.0760268i
$366$		0			0
$367$	−21.2054	+	7.71813i	−1.10691	+	0.402883i	−0.829860	−	0.557971i	$-0.811580\pi$
$367$	−21.2054	+	7.71813i	−1.10691	+	0.402883i	−0.277053	+	0.960855i	$0.589358\pi$
$368$		0			0
$369$	3.23735	+	8.17553i	0.168530	+	0.425601i
$370$		0			0
$371$	−0.832372	+	4.72062i	−0.0432146	+	0.245082i
$372$		0			0
$373$	22.5045	+	8.19096i	1.16524	+	0.424112i	0.850966	−	0.525221i	$-0.176017\pi$
$373$	22.5045	+	8.19096i	1.16524	+	0.424112i	0.314272	+	0.949333i	$0.398240\pi$
$374$		0			0
$375$	−6.85287	+	15.2492i	−0.353881	+	0.787467i
$376$		0			0
$377$	3.82863			0.197184
$378$		0			0
$379$	16.3981			0.842312			0.421156	−	0.906988i	$-0.361624\pi$
$379$	16.3981			0.842312			0.421156	+	0.906988i	$0.361624\pi$
$380$		0			0
$381$	21.6944	−	2.20414i	1.11144	−	0.112921i
$382$		0			0
$383$	13.1401	+	4.78261i	0.671429	+	0.244380i	0.655163	−	0.755488i	$-0.272600\pi$
$383$	13.1401	+	4.78261i	0.671429	+	0.244380i	0.0162658	+	0.999868i	$0.494822\pi$
$384$		0			0
$385$	1.08211	−	6.13694i	0.0551493	−	0.312767i
$386$		0			0
$387$	−0.128079	−	4.57789i	−0.00651062	−	0.232707i
$388$		0			0
$389$	3.20129	−	1.16518i	0.162312	−	0.0590768i	−0.259586	−	0.965720i	$-0.583586\pi$
$389$	3.20129	−	1.16518i	0.162312	−	0.0590768i	0.421898	+	0.906643i	$0.361364\pi$
$390$		0			0
$391$	−51.2248	+	42.9827i	−2.59055	+	2.17373i
$392$		0			0
$393$	−13.3754	+	13.7548i	−0.674700	+	0.693840i
$394$		0			0
$395$	−0.572751	−	0.992033i	−0.0288182	−	0.0499146i
$396$		0			0
$397$	−19.0210	+	32.9453i	−0.954636	+	1.65348i	−0.219437	+	0.975627i	$0.570422\pi$
$397$	−19.0210	+	32.9453i	−0.954636	+	1.65348i	−0.735199	+	0.677851i	$0.762911\pi$
$398$		0			0
$399$	−0.800210	+	10.9002i	−0.0400606	+	0.545690i
$400$		0			0
$401$	−2.56934	−	14.5715i	−0.128307	−	0.727665i	−0.979289	−	0.202469i	$-0.935103\pi$
$401$	−2.56934	−	14.5715i	−0.128307	−	0.727665i	0.850982	−	0.525195i	$-0.176008\pi$
$402$		0			0
$403$	3.52019	+	2.95379i	0.175353	+	0.147139i
$404$		0			0
$405$	5.40873	+	8.26377i	0.268762	+	0.410630i
$406$		0			0
$407$	15.6636	+	13.1433i	0.776414	+	0.651489i
$408$		0			0
$409$	0.333588	+	1.89187i	0.0164949	+	0.0935470i	0.991944	−	0.126679i	$-0.0404317\pi$
$409$	0.333588	+	1.89187i	0.0164949	+	0.0935470i	−0.975449	+	0.220226i	$0.929321\pi$
$410$		0			0
$411$	−1.67209	+	22.7766i	−0.0824782	+	1.12349i
$412$		0			0
$413$	−0.508324	+	0.880442i	−0.0250130	+	0.0433237i
$414$		0			0
$415$	−3.29753	−	5.71149i	−0.161869	−	0.280366i
$416$		0			0
$417$	−9.98543	+	10.2687i	−0.488988	+	0.502860i
$418$		0			0
$419$	12.7415	−	10.6914i	0.622465	−	0.522310i	−0.276112	−	0.961125i	$-0.589046\pi$
$419$	12.7415	−	10.6914i	0.622465	−	0.522310i	0.898577	+	0.438815i	$0.144602\pi$
$420$		0			0
$421$	7.88581	−	2.87020i	0.384331	−	0.139885i	−0.142627	−	0.989777i	$-0.545555\pi$
$421$	7.88581	−	2.87020i	0.384331	−	0.139885i	0.526958	+	0.849892i	$0.323333\pi$
$422$		0			0
$423$	16.5274	+	8.93535i	0.803588	+	0.434452i
$424$		0			0
$425$	5.26853	−	29.8793i	0.255561	−	1.44936i
$426$		0			0
$427$	−17.8906	−	6.51165i	−0.865787	−	0.315121i
$428$		0			0
$429$	−5.05803	+	0.513892i	−0.244204	+	0.0248109i
$430$		0			0
$431$	−12.9057			−0.621647			−0.310823	−	0.950468i	$-0.600605\pi$
$431$	−12.9057			−0.621647			−0.310823	+	0.950468i	$0.600605\pi$
$432$		0			0
$433$	33.8125			1.62493			0.812464	−	0.583012i	$-0.198126\pi$
$433$	33.8125			1.62493			0.812464	+	0.583012i	$0.198126\pi$
$434$		0			0
$435$	3.88955	−	8.65517i	0.186490	−	0.414983i
$436$		0			0
$437$	−33.4346	−	12.1692i	−1.59939	−	0.582132i
$438$		0			0
$439$	−3.53808	+	20.0654i	−0.168863	+	0.957672i	0.776128	+	0.630576i	$0.217181\pi$
$439$	−3.53808	+	20.0654i	−0.168863	+	0.957672i	−0.944991	+	0.327096i	$0.893930\pi$
$440$		0			0
$441$	−8.94170	+	11.2827i	−0.425795	+	0.537270i
$442$		0			0
$443$	3.89661	−	1.41825i	0.185133	−	0.0673830i	−0.247790	−	0.968814i	$-0.579704\pi$
$443$	3.89661	−	1.41825i	0.185133	−	0.0673830i	0.432923	+	0.901431i	$0.357482\pi$
$444$		0			0
$445$	−8.23201	+	6.90748i	−0.390235	+	0.327446i
$446$		0			0
$447$	−12.4547	−	3.15123i	−0.589088	−	0.149048i
$448$		0			0
$449$	−0.0516246	−	0.0894164i	−0.00243632	−	0.00421982i	0.864805	−	0.502108i	$-0.167442\pi$
$449$	−0.0516246	−	0.0894164i	−0.00243632	−	0.00421982i	−0.867241	+	0.497889i	$0.834109\pi$
$450$		0			0
$451$	−5.60921	+	9.71544i	−0.264128	+	0.457482i
$452$		0			0
$453$	25.9936	+	17.6644i	1.22129	+	0.829945i
$454$		0			0
$455$	0.216823	+	1.22966i	0.0101648	+	0.0576476i
$456$		0			0
$457$	26.0331	+	21.8444i	1.21778	+	1.02184i	0.998938	+	0.0460745i	$0.0146712\pi$
$457$	26.0331	+	21.8444i	1.21778	+	1.02184i	0.218838	+	0.975761i	$0.429773\pi$
$458$		0			0
$459$	−30.5749	−	28.1113i	−1.42712	−	1.31212i
$460$		0			0
$461$	−24.2305	−	20.3318i	−1.12853	−	0.946945i	−0.129522	−	0.991577i	$-0.541344\pi$
$461$	−24.2305	−	20.3318i	−1.12853	−	0.946945i	−0.999004	+	0.0446312i	$0.985789\pi$
$462$		0			0
$463$	1.01022	+	5.72926i	0.0469490	+	0.266261i	0.999242	−	0.0389236i	$-0.0123929\pi$
$463$	1.01022	+	5.72926i	0.0469490	+	0.266261i	−0.952293	+	0.305185i	$0.901282\pi$
$464$		0			0
$465$	10.2537	−	4.95711i	0.475504	−	0.229881i
$466$		0			0
$467$	−19.9588	+	34.5697i	−0.923584	+	1.59969i	−0.129762	+	0.991545i	$0.541421\pi$
$467$	−19.9588	+	34.5697i	−0.923584	+	1.59969i	−0.793822	+	0.608150i	$0.791912\pi$
$468$		0			0
$469$	5.65497	+	9.79469i	0.261122	+	0.452277i
$470$		0			0
$471$	−7.43612	−	26.2764i	−0.342638	−	1.21075i
$472$		0			0
$473$	4.47586	−	3.75569i	0.205800	−	0.172687i
$474$		0			0
$475$	15.1701	−	5.52147i	0.696052	−	0.253342i
$476$		0			0
$477$	3.05900	−	9.19709i	0.140062	−	0.421106i
$478$		0			0
$479$	6.44872	−	36.5725i	0.294649	−	1.67104i	−0.373974	−	0.927439i	$-0.622005\pi$
$479$	6.44872	−	36.5725i	0.294649	−	1.67104i	0.668623	−	0.743601i	$-0.266884\pi$
$480$		0			0
$481$	−3.84997	−	1.40127i	−0.175543	−	0.0638926i
$482$		0			0
$483$	12.5759	+	17.4360i	0.572221	+	0.793366i
$484$		0			0
$485$	−6.28503			−0.285389
$486$		0			0
$487$	34.9626			1.58431			0.792154	−	0.610322i	$-0.208960\pi$
$487$	34.9626			1.58431			0.792154	+	0.610322i	$0.208960\pi$
$488$		0			0
$489$	18.4495	+	25.5797i	0.834315	+	1.15675i
$490$		0			0
$491$	25.6249	+	9.32669i	1.15643	+	0.420908i	0.847822	−	0.530280i	$-0.177913\pi$
$491$	25.6249	+	9.32669i	1.15643	+	0.420908i	0.308612	+	0.951188i	$0.400136\pi$
$492$		0			0
$493$	−6.92934	+	39.2982i	−0.312082	+	1.76990i
$494$		0			0
$495$	−3.97679	+	11.9565i	−0.178744	+	0.537404i
$496$		0			0
$497$	−4.72724	+	1.72057i	−0.212046	+	0.0771783i
$498$		0			0
$499$	−1.55751	+	1.30691i	−0.0697237	+	0.0585052i	−0.676984	−	0.735998i	$-0.736713\pi$
$499$	−1.55751	+	1.30691i	−0.0697237	+	0.0585052i	0.607260	+	0.794503i	$0.292269\pi$
$500$		0			0
$501$	3.24050	+	11.4507i	0.144775	+	0.511579i
$502$		0			0
$503$	−1.65507	−	2.86667i	−0.0737959	−	0.127818i	0.826766	−	0.562546i	$-0.190178\pi$
$503$	−1.65507	−	2.86667i	−0.0737959	−	0.127818i	−0.900562	+	0.434728i	$0.856845\pi$
$504$		0			0
$505$	3.29165	−	5.70130i	0.146476	−	0.253705i
$506$		0			0
$507$	−19.3548	+	9.35702i	−0.859577	+	0.415560i
$508$		0			0
$509$	−0.704978	−	3.99813i	−0.0312476	−	0.177214i	0.965190	−	0.261551i	$-0.0842339\pi$
$509$	−0.704978	−	3.99813i	−0.0312476	−	0.177214i	−0.996437	+	0.0843370i	$0.973123\pi$
$510$		0			0
$511$	−2.34032	−	1.96376i	−0.103530	−	0.0868717i
$512$		0			0
$513$	4.81945	−	21.5678i	0.212784	−	0.952243i
$514$		0			0
$515$	13.6029	+	11.4142i	0.599414	+	0.502968i
$516$		0			0
$517$	4.16237	+	23.6060i	0.183061	+	1.03819i
$518$		0			0
$519$	−7.59267	−	5.15972i	−0.333281	−	0.226487i
$520$		0			0
$521$	4.25397	−	7.36809i	0.186370	−	0.322802i	−0.757668	−	0.652641i	$-0.773661\pi$
$521$	4.25397	−	7.36809i	0.186370	−	0.322802i	0.944037	+	0.329839i	$0.106994\pi$
$522$		0			0
$523$	20.6700	+	35.8016i	0.903838	+	1.56549i	0.822470	+	0.568809i	$0.192596\pi$
$523$	20.6700	+	35.8016i	0.903838	+	1.56549i	0.0813679	+	0.996684i	$0.474071\pi$
$524$		0			0
$525$	−9.45623	−	2.39257i	−0.412704	−	0.104420i
$526$		0			0
$527$	−36.6898	+	30.7864i	−1.59823	+	1.34108i
$528$		0			0
$529$	−44.1522	+	16.0701i	−1.91966	+	0.698699i
$530$		0			0
$531$	1.27681	−	1.61109i	0.0554090	−	0.0699153i
$532$		0			0
$533$	0.390335	−	2.21370i	0.0169073	−	0.0958859i
$534$		0			0
$535$	15.0372	+	5.47310i	0.650115	+	0.236623i
$536$		0			0
$537$	8.23430	−	18.3233i	0.355336	−	0.790707i
$538$		0			0
$539$	−18.3669			−0.791120
$540$		0			0
$541$	22.3224			0.959715			0.479857	−	0.877347i	$-0.340688\pi$
$541$	22.3224			0.959715			0.479857	+	0.877347i	$0.340688\pi$
$542$		0			0
$543$	20.3350	−	2.06602i	0.872659	−	0.0886613i
$544$		0			0
$545$	−12.2928	−	4.47421i	−0.526566	−	0.191654i
$546$		0			0
$547$	3.09613	−	17.5590i	0.132381	−	0.750770i	−0.844267	−	0.535923i	$-0.819964\pi$
$547$	3.09613	−	17.5590i	0.132381	−	0.750770i	0.976648	−	0.214847i	$-0.0689252\pi$
$548$		0			0
$549$	33.8646	+	18.3086i	1.44531	+	0.781391i
$550$		0			0
$551$	−19.9522	+	7.26201i	−0.849993	+	0.309372i
$552$		0			0
$553$	1.18638	−	0.995494i	0.0504502	−	0.0423327i
$554$		0			0
$555$	−7.07902	+	7.27984i	−0.300488	+	0.309012i
$556$		0			0
$557$	8.03044	+	13.9091i	0.340260	+	0.589348i	0.984481	−	0.175491i	$-0.0561514\pi$
$557$	8.03044	+	13.9091i	0.340260	+	0.589348i	−0.644221	+	0.764840i	$0.722818\pi$
$558$		0			0
$559$	−0.585366	+	1.01388i	−0.0247583	+	0.0428827i
$560$		0			0
$561$	3.87967	−	52.8473i	0.163800	−	2.23122i
$562$		0			0
$563$	−1.98341	−	11.2485i	−0.0835910	−	0.474068i	−0.997652	−	0.0684907i	$-0.978182\pi$
$563$	−1.98341	−	11.2485i	−0.0835910	−	0.474068i	0.914061	−	0.405577i	$-0.132929\pi$
$564$		0			0
$565$	−11.3259	−	9.50354i	−0.476483	−	0.399817i
$566$		0			0
$567$	−9.73304	+	9.14158i	−0.408749	+	0.383910i
$568$		0			0
$569$	−19.7472	−	16.5698i	−0.827844	−	0.694644i	0.126951	−	0.991909i	$-0.459481\pi$
$569$	−19.7472	−	16.5698i	−0.827844	−	0.694644i	−0.954795	+	0.297265i	$0.903925\pi$
$570$		0			0
$571$	0.922111	+	5.22955i	0.0385891	+	0.218850i	0.998004	−	0.0631480i	$-0.0201140\pi$
$571$	0.922111	+	5.22955i	0.0385891	+	0.218850i	−0.959415	+	0.281998i	$0.909003\pi$
$572$		0			0
$573$	3.41181	−	46.4744i	0.142530	−	1.94150i
$574$		0			0
$575$	15.8771	−	27.5000i	0.662123	−	1.14683i
$576$		0			0
$577$	−19.4548	−	33.6967i	−0.809914	−	1.40281i	−0.912923	−	0.408132i	$-0.866180\pi$
$577$	−19.4548	−	33.6967i	−0.809914	−	1.40281i	0.103009	−	0.994680i	$-0.467153\pi$
$578$		0			0
$579$	0.694666	−	0.714373i	0.0288693	−	0.0296883i
$580$		0			0
$581$	6.83043	−	5.73141i	0.283374	−	0.237779i
$582$		0			0
$583$	11.6200	−	4.22934i	0.481252	−	0.175162i
$584$		0			0
$585$	−0.0706098	−	2.52379i	−0.00291936	−	0.104346i
$586$		0			0
$587$	0.569330	−	3.22883i	0.0234988	−	0.133268i	−0.970801	−	0.239884i	$-0.922890\pi$
$587$	0.569330	−	3.22883i	0.0234988	−	0.133268i	0.994300	+	0.106616i	$0.0340016\pi$
$588$		0			0
$589$	−23.9475	−	8.71619i	−0.986741	−	0.359144i
$590$		0			0
$591$	−29.3753	+	2.98451i	−1.20834	+	0.122766i
$592$		0			0
$593$	−20.7992			−0.854123			−0.427061	−	0.904223i	$-0.640451\pi$
$593$	−20.7992			−0.854123			−0.427061	+	0.904223i	$0.640451\pi$
$594$		0			0
$595$	−13.0141			−0.533526
$596$		0			0
$597$	−15.5493	+	34.6008i	−0.636390	+	1.41612i
$598$		0			0
$599$	2.57496	+	0.937210i	0.105210	+	0.0382934i	0.394089	−	0.919072i	$-0.371060\pi$
$599$	2.57496	+	0.937210i	0.105210	+	0.0382934i	−0.288879	+	0.957366i	$0.593282\pi$
$600$		0			0
$601$	−1.57384	+	8.92568i	−0.0641982	+	0.364086i	0.935737	+	0.352699i	$0.114736\pi$
$601$	−1.57384	+	8.92568i	−0.0641982	+	0.364086i	−0.999935	+	0.0113874i	$0.996375\pi$
$602$		0			0
$603$	−8.41961	−	21.2627i	−0.342873	−	0.865884i
$604$		0			0
$605$	−3.76314	+	1.36967i	−0.152994	+	0.0556851i
$606$		0			0
$607$	−2.63764	+	2.21324i	−0.107058	+	0.0898327i	−0.694746	−	0.719256i	$-0.744483\pi$
$607$	−2.63764	+	2.21324i	−0.107058	+	0.0898327i	0.587687	+	0.809088i	$0.300039\pi$
$608$		0			0
$609$	12.4371	+	3.14678i	0.503978	+	0.127514i
$610$		0			0
$611$	−2.40146	−	4.15945i	−0.0971527	−	0.168273i
$612$		0			0
$613$	−11.7554	+	20.3609i	−0.474795	+	0.822370i	−0.999583	−	0.0288633i	$-0.990811\pi$
$613$	−11.7554	+	20.3609i	−0.474795	+	0.822370i	0.524788	+	0.851233i	$0.324145\pi$
$614$		0			0
$615$	−4.60784	−	3.13133i	−0.185806	−	0.126268i
$616$		0			0
$617$	−4.17400	−	23.6720i	−0.168039	−	0.952997i	−0.945875	−	0.324530i	$-0.894794\pi$
$617$	−4.17400	−	23.6720i	−0.168039	−	0.952997i	0.777836	−	0.628467i	$-0.216317\pi$
$618$		0			0
$619$	−33.1638	−	27.8277i	−1.33296	−	1.11849i	−0.983375	−	0.181587i	$-0.941877\pi$
$619$	−33.1638	−	27.8277i	−1.33296	−	1.11849i	−0.349590	−	0.936903i	$-0.613679\pi$
$620$		0			0
$621$	−20.0074	−	38.5917i	−0.802868	−	1.54863i
$622$		0			0
$623$	−11.1297	−	9.33889i	−0.445900	−	0.374155i
$624$		0			0
$625$	1.45629	+	8.25906i	0.0582518	+	0.330362i
$626$		0			0
$627$	25.3843	−	12.2720i	1.01375	−	0.490095i
$628$		0			0
$629$	21.3511	−	36.9812i	0.851324	−	1.47454i
$630$		0			0
$631$	−19.4721	−	33.7266i	−0.775171	−	1.34264i	−0.934698	−	0.355443i	$-0.884330\pi$
$631$	−19.4721	−	33.7266i	−0.775171	−	1.34264i	0.159527	−	0.987194i	$-0.449003\pi$
$632$		0			0
$633$	2.43062	+	8.58891i	0.0966087	+	0.341378i
$634$		0			0
$635$	−10.5835	+	8.88062i	−0.419994	+	0.352417i
$636$		0			0
$637$	3.45826	−	1.25870i	0.137021	−	0.0498717i
$638$		0			0
$639$	9.96421	−	2.04583i	0.394178	−	0.0809317i
$640$		0			0
$641$	−4.39068	+	24.9008i	−0.173421	+	0.983521i	0.766529	+	0.642210i	$0.221982\pi$
$641$	−4.39068	+	24.9008i	−0.173421	+	0.983521i	−0.939950	+	0.341311i	$0.889129\pi$
$642$		0			0
$643$	25.3485	+	9.22609i	0.999647	+	0.363842i	0.789448	−	0.613817i	$-0.210367\pi$
$643$	25.3485	+	9.22609i	0.999647	+	0.363842i	0.210198	+	0.977659i	$0.432589\pi$
$644$		0			0
$645$	1.69735	+	2.35332i	0.0668331	+	0.0926620i
$646$		0			0
$647$	28.3235			1.11351			0.556756	−	0.830676i	$-0.312046\pi$
$647$	28.3235			1.11351			0.556756	+	0.830676i	$0.312046\pi$
$648$		0			0
$649$	2.62268			0.102949
$650$		0			0
$651$	9.00746	+	12.4886i	0.353030	+	0.489465i
$652$		0			0
$653$	31.5410	+	11.4800i	1.23429	+	0.449246i	0.875066	−	0.484004i	$-0.160818\pi$
$653$	31.5410	+	11.4800i	1.23429	+	0.449246i	0.359228	+	0.933250i	$0.383040\pi$
$654$		0			0
$655$	2.11081	−	11.9710i	0.0824762	−	0.467746i
$656$		0			0
$657$	4.10157	+	4.61929i	0.160018	+	0.180216i
$658$		0			0
$659$	1.88527	−	0.686184i	0.0734399	−	0.0267299i	−0.305039	−	0.952340i	$-0.598669\pi$
$659$	1.88527	−	0.686184i	0.0734399	−	0.0267299i	0.378479	+	0.925610i	$0.376447\pi$
$660$		0			0
$661$	−22.5767	+	18.9441i	−0.878133	+	0.736841i	−0.965794	−	0.259310i	$-0.916505\pi$
$661$	−22.5767	+	18.9441i	−0.878133	+	0.736841i	0.0876617	+	0.996150i	$0.472061\pi$
$662$		0			0
$663$	2.89119	+	10.2164i	0.112284	+	0.396770i
$664$		0			0
$665$	−3.46232	−	5.99692i	−0.134263	−	0.232551i
$666$		0			0
$667$	−20.8821	+	36.1689i	−0.808559	+	1.40047i
$668$		0			0
$669$	25.8474	−	12.4958i	0.999318	−	0.483117i
$670$		0			0
$671$	8.52872	+	48.3688i	0.329247	+	1.86726i
$672$		0			0
$673$	−2.05732	−	1.72630i	−0.0793038	−	0.0665438i	0.602274	−	0.798289i	$-0.294261\pi$
$673$	−2.05732	−	1.72630i	−0.0793038	−	0.0665438i	−0.681578	+	0.731746i	$0.738706\pi$
$674$		0			0
$675$	18.2093	+	7.57834i	0.700875	+	0.291690i
$676$		0			0
$677$	−24.6451	−	20.6797i	−0.947188	−	0.794785i	0.0316334	−	0.999500i	$-0.489929\pi$
$677$	−24.6451	−	20.6797i	−0.947188	−	0.794785i	−0.978822	+	0.204714i	$0.934374\pi$
$678$		0			0
$679$	−1.47555	−	8.36825i	−0.0566263	−	0.321144i
$680$		0			0
$681$	39.0209	+	26.5173i	1.49528	+	1.01614i
$682$		0			0
$683$	14.0155	−	24.2756i	0.536290	−	0.928881i	−0.462810	−	0.886457i	$-0.653159\pi$
$683$	14.0155	−	24.2756i	0.536290	−	0.928881i	0.999100	−	0.0424234i	$-0.0135078\pi$
$684$		0			0
$685$	−7.23475	−	12.5310i	−0.276426	−	0.478783i
$686$		0			0
$687$	40.4849	+	10.2433i	1.54460	+	0.390806i
$688$		0			0
$689$	−1.89806	+	1.59266i	−0.0723104	+	0.0606756i
$690$		0			0
$691$	−14.5580	+	5.29868i	−0.553813	+	0.201571i	−0.603740	−	0.797182i	$-0.706323\pi$
$691$	−14.5580	+	5.29868i	−0.553813	+	0.201571i	0.0499270	+	0.998753i	$0.484101\pi$
$692$		0			0
$693$	−16.8532	−	2.48788i	−0.640200	−	0.0945069i
$694$		0			0
$695$	1.57583	−	8.93697i	0.0597746	−	0.338998i
$696$		0			0
$697$	22.0156	+	8.01304i	0.833902	+	0.303515i
$698$		0			0
$699$	11.5288	−	25.6542i	0.436058	−	0.970333i
$700$		0			0
$701$	−26.6475			−1.00646			−0.503232	−	0.864151i	$-0.667856\pi$
$701$	−26.6475			−1.00646			−0.503232	+	0.864151i	$0.667856\pi$
$702$		0			0
$703$	22.7213			0.856951
$704$		0			0
$705$	−11.8427	+	1.20321i	−0.446023	+	0.0453155i
$706$		0			0
$707$	8.36383	+	3.04418i	0.314554	+	0.114488i
$708$		0			0
$709$	0.381291	−	2.16241i	0.0143197	−	0.0812110i	−0.976810	−	0.214106i	$-0.931316\pi$
$709$	0.381291	−	2.16241i	0.0143197	−	0.0812110i	0.991130	+	0.132895i	$0.0424273\pi$
$710$		0			0
$711$	−2.66715	+	1.64101i	−0.100026	+	0.0615425i
$712$		0			0
$713$	−47.1043	+	17.1446i	−1.76407	+	0.642069i
$714$		0			0
$715$	2.46753	−	2.07051i	0.0922806	−	0.0774326i
$716$		0			0
$717$	−22.7835	+	23.4299i	−0.850866	+	0.875004i
$718$		0			0
$719$	1.54874	+	2.68250i	0.0577583	+	0.100040i	0.893459	−	0.449145i	$-0.148271\pi$
$719$	1.54874	+	2.68250i	0.0577583	+	0.100040i	−0.835700	+	0.549185i	$0.814938\pi$
$720$		0			0
$721$	−12.0039	+	20.7914i	−0.447048	+	0.774311i
$722$		0			0
$723$	0.205103	−	2.79384i	0.00762788	−	0.103904i
$724$		0			0
$725$	−3.29054	−	18.6616i	−0.122208	−	0.693075i
$726$		0			0
$727$	13.8814	+	11.6479i	0.514834	+	0.431997i	0.862826	−	0.505501i	$-0.168692\pi$
$727$	13.8814	+	11.6479i	0.514834	+	0.431997i	−0.347993	+	0.937497i	$0.613137\pi$
$728$		0			0
$729$	22.1689	−	15.4123i	0.821072	−	0.570825i
$730$		0			0
$731$	−9.34738	−	7.84338i	−0.345725	−	0.290098i
$732$		0			0
$733$	0.191572	+	1.08646i	0.00707589	+	0.0401293i	0.988141	−	0.153547i	$-0.0490698\pi$
$733$	0.191572	+	1.08646i	0.00707589	+	0.0401293i	−0.981065	+	0.193677i	$0.937959\pi$
$734$		0			0
$735$	0.667808	−	9.09663i	0.0246325	−	0.335534i
$736$		0			0
$737$	14.5883	−	25.2677i	0.537366	−	0.930746i
$738$		0			0
$739$	−12.4569	−	21.5760i	−0.458236	−	0.793687i	0.540632	−	0.841259i	$-0.318185\pi$
$739$	−12.4569	−	21.5760i	−0.458236	−	0.793687i	−0.998868	+	0.0475717i	$0.984852\pi$
$740$		0			0
$741$	−3.93853	+	4.05027i	−0.144686	+	0.148790i
$742$		0			0
$743$	26.7907	−	22.4801i	0.982856	−	0.824714i	−0.00166183	−	0.999999i	$-0.500529\pi$
$743$	26.7907	−	22.4801i	0.982856	−	0.824714i	0.984518	+	0.175285i	$0.0560845\pi$
$744$		0			0
$745$	7.64878	−	2.78393i	0.280229	−	0.101995i
$746$		0			0
$747$	−15.3557	+	9.44785i	−0.561836	+	0.345679i
$748$		0			0
$749$	−3.75688	+	21.3063i	−0.137273	+	0.778516i
$750$		0			0
$751$	−12.4613	−	4.53553i	−0.454718	−	0.165504i	0.104499	−	0.994525i	$-0.466676\pi$
$751$	−12.4613	−	4.53553i	−0.454718	−	0.165504i	−0.559217	+	0.829021i	$0.688898\pi$
$752$		0			0
$753$	6.37883	−	0.648084i	0.232458	−	0.0236175i
$754$		0			0
$755$	−19.9118			−0.724663
$756$		0			0
$757$	44.6742			1.62371			0.811856	−	0.583858i	$-0.198458\pi$
$757$	44.6742			1.62371			0.811856	+	0.583858i	$0.198458\pi$
$758$		0			0
$759$	22.7329	−	50.5860i	0.825150	−	1.83615i
$760$		0			0
$761$	1.00517	+	0.365853i	0.0364375	+	0.0132622i	0.360175	−	0.932885i	$-0.382717\pi$
$761$	1.00517	+	0.365853i	0.0364375	+	0.0132622i	−0.323737	+	0.946147i	$0.604939\pi$
$762$		0			0
$763$	3.07122	−	17.4177i	0.111186	−	0.630565i
$764$		0			0
$765$	26.0327	+	3.84298i	0.941216	+	0.138943i
$766$		0			0
$767$	−0.493816	+	0.179734i	−0.0178307	+	0.00648983i
$768$		0			0
$769$	0.192611	−	0.161619i	0.00694572	−	0.00582815i	−0.639308	−	0.768951i	$-0.720779\pi$
$769$	0.192611	−	0.161619i	0.00694572	−	0.00582815i	0.646254	+	0.763122i	$0.276335\pi$
$770$		0			0
$771$	6.24209	+	1.57934i	0.224803	+	0.0568786i
$772$		0			0
$773$	−2.28396	−	3.95593i	−0.0821483	−	0.142285i	0.822024	−	0.569453i	$-0.192845\pi$
$773$	−2.28396	−	3.95593i	−0.0821483	−	0.142285i	−0.904172	+	0.427168i	$0.859511\pi$
$774$		0			0
$775$	11.3720	−	19.6969i	0.408495	−	0.707534i
$776$		0			0
$777$	−11.3547	−	7.71630i	−0.407349	−	0.276821i
$778$		0			0
$779$	2.16471	+	12.2767i	0.0775587	+	0.439858i
$780$		0			0
$781$	9.94146	+	8.34187i	0.355733	+	0.298496i
$782$		0			0
$783$	−23.9494	−	9.96727i	−0.855882	−	0.356201i
$784$		0			0
$785$	13.2540	+	11.1214i	0.473056	+	0.396941i
$786$		0			0
$787$	−4.12116	−	23.3722i	−0.146903	−	0.833130i	−0.965819	−	0.259217i	$-0.916536\pi$
$787$	−4.12116	−	23.3722i	−0.146903	−	0.833130i	0.818916	−	0.573914i	$-0.194575\pi$
$788$		0			0
$789$	27.3626	−	13.2284i	0.974136	−	0.470943i
$790$		0			0
$791$	9.99456	−	17.3111i	0.355366	−	0.615511i
$792$		0			0
$793$	−4.92060	−	8.52274i	−0.174736	−	0.302651i
$794$		0			0
$795$	1.67218	+	5.90885i	0.0593061	+	0.209565i
$796$		0			0
$797$	−11.3817	+	9.55037i	−0.403160	+	0.338292i	−0.821714	−	0.569901i	$-0.806982\pi$
$797$	−11.3817	+	9.55037i	−0.403160	+	0.338292i	0.418553	+	0.908192i	$0.362537\pi$
$798$		0			0
$799$	47.0403	−	17.1213i	1.66417	−	0.605707i
$800$		0			0
$801$	19.5055	+	21.9676i	0.689193	+	0.776186i
$802$		0			0
$803$	−1.36857	+	7.76152i	−0.0482956	+	0.273898i
$804$		0			0
$805$	−12.7992	−	4.65853i	−0.451113	−	0.164192i
$806$		0			0
$807$	2.51931	+	3.49295i	0.0886841	+	0.122958i
$808$		0			0
$809$	−17.4444			−0.613313			−0.306657	−	0.951820i	$-0.599210\pi$
$809$	−17.4444			−0.613313			−0.306657	+	0.951820i	$0.599210\pi$
$810$		0			0
$811$	−27.6602			−0.971282			−0.485641	−	0.874158i	$-0.661414\pi$
$811$	−27.6602			−0.971282			−0.485641	+	0.874158i	$0.661414\pi$
$812$		0			0
$813$	−3.80870	−	5.28064i	−0.133577	−	0.185200i
$814$		0			0
$815$	−18.7772	−	6.83433i	−0.657736	−	0.239396i
$816$		0			0
$817$	1.12743	−	6.39398i	0.0394438	−	0.223697i
$818$		0			0
$819$	3.34373	−	0.686528i	0.116840	−	0.0239892i
$820$		0			0
$821$	45.6460	−	16.6138i	1.59306	−	0.579825i	0.615067	−	0.788475i	$-0.289129\pi$
$821$	45.6460	−	16.6138i	1.59306	−	0.579825i	0.977990	+	0.208650i	$0.0669068\pi$
$822$		0			0
$823$	−0.831691	+	0.697871i	−0.0289909	+	0.0243263i	−0.657168	−	0.753744i	$-0.728246\pi$
$823$	−0.831691	+	0.697871i	−0.0289909	+	0.0243263i	0.628177	+	0.778070i	$0.283801\pi$
$824$		0			0
$825$	6.85200	+	24.2124i	0.238556	+	0.842966i
$826$		0			0
$827$	−20.9224	−	36.2387i	−0.727544	−	1.26014i	−0.957918	−	0.287042i	$-0.907328\pi$
$827$	−20.9224	−	36.2387i	−0.727544	−	1.26014i	0.230374	−	0.973102i	$-0.426005\pi$
$828$		0			0
$829$	−25.8381	+	44.7529i	−0.897394	+	1.55433i	−0.0665806	+	0.997781i	$0.521209\pi$
$829$	−25.8381	+	44.7529i	−0.897394	+	1.55433i	−0.830813	+	0.556551i	$0.812124\pi$
$830$		0			0
$831$	14.7556	−	7.13352i	0.511865	−	0.247459i
$832$		0			0
$833$	6.66071	+	37.7748i	0.230780	+	1.30882i
$834$		0			0
$835$	−5.77580	−	4.84647i	−0.199880	−	0.167719i
$836$		0			0
$837$	−14.3303	−	27.6413i	−0.495327	−	0.955424i
$838$		0			0
$839$	−32.9100	−	27.6148i	−1.13618	−	0.953368i	−0.136873	−	0.990589i	$-0.543705\pi$
$839$	−32.9100	−	27.6148i	−1.13618	−	0.953368i	−0.999307	+	0.0372207i	$0.988150\pi$
$840$		0			0
$841$	−0.707967	−	4.01508i	−0.0244127	−	0.138451i
$842$		0			0
$843$	−0.402459	−	0.273498i	−0.0138614	−	0.00941976i
$844$		0			0
$845$	6.81028	−	11.7958i	0.234281	−	0.405786i
$846$		0			0
$847$	−2.70714	−	4.68890i	−0.0930184	−	0.161113i
$848$		0			0
$849$	27.1372	+	6.86611i	0.931345	+	0.235644i
$850$		0			0
$851$	34.2363	−	28.7277i	1.17361	−	0.984773i
$852$		0			0
$853$	11.5161	−	4.19151i	0.394303	−	0.143515i	−0.137256	−	0.990536i	$-0.543828\pi$
$853$	11.5161	−	4.19151i	0.394303	−	0.143515i	0.531559	+	0.847021i	$0.321606\pi$
$854$		0			0
$855$	5.15501	+	13.0183i	0.176298	+	0.445218i
$856$		0			0
$857$	3.62979	−	20.5855i	0.123991	−	0.703189i	−0.857911	−	0.513799i	$-0.828238\pi$
$857$	3.62979	−	20.5855i	0.123991	−	0.703189i	0.981902	−	0.189390i	$-0.0606510\pi$
$858$		0			0
$859$	23.9772	+	8.72700i	0.818093	+	0.297762i	0.716963	−	0.697112i	$-0.245532\pi$
$859$	23.9772	+	8.72700i	0.818093	+	0.297762i	0.101131	+	0.994873i	$0.467754\pi$
$860$		0			0
$861$	3.08744	−	6.87029i	0.105220	−	0.234139i
$862$		0			0
$863$	43.7009			1.48760			0.743798	−	0.668404i	$-0.233022\pi$
$863$	43.7009			1.48760			0.743798	+	0.668404i	$0.233022\pi$
$864$		0			0
$865$	5.81618			0.197756
$866$		0			0
$867$	−80.8025	+	8.20946i	−2.74420	+	0.278808i
$868$		0			0
$869$	−3.75432	−	1.36646i	−0.127357	−	0.0463540i
$870$		0			0
$871$	−1.01517	+	5.75732i	−0.0343978	+	0.195079i
$872$		0			0
$873$	0.480522	+	17.1752i	0.0162632	+	0.581291i
$874$		0			0
$875$	13.4571	−	4.89798i	0.454932	−	0.165582i
$876$		0			0
$877$	6.91263	−	5.80038i	0.233423	−	0.195865i	−0.518572	−	0.855034i	$-0.673536\pi$
$877$	6.91263	−	5.80038i	0.233423	−	0.195865i	0.751995	+	0.659169i	$0.229092\pi$
$878$		0			0
$879$	−0.658856	+	0.677547i	−0.0222227	+	0.0228531i
$880$		0			0
$881$	21.0277	+	36.4211i	0.708441	+	1.22706i	0.965435	+	0.260644i	$0.0839347\pi$
$881$	21.0277	+	36.4211i	0.708441	+	1.22706i	−0.256994	+	0.966413i	$0.582732\pi$
$882$		0			0
$883$	24.8315	−	43.0095i	0.835648	−	1.44738i	−0.0578536	−	0.998325i	$-0.518426\pi$
$883$	24.8315	−	43.0095i	0.835648	−	1.44738i	0.893502	−	0.449060i	$-0.148241\pi$
$884$		0			0
$885$	−0.0953585	+	1.29894i	−0.00320544	+	0.0436633i
$886$		0			0
$887$	−6.83332	−	38.7537i	−0.229441	−	1.30122i	−0.854011	−	0.520254i	$-0.825837\pi$
$887$	−6.83332	−	38.7537i	−0.229441	−	1.30122i	0.624571	−	0.780968i	$-0.285274\pi$
$888$		0			0
$889$	−14.3089	−	12.0066i	−0.479904	−	0.402688i
$890$		0			0
$891$	32.9776	+	9.95328i	1.10479	+	0.333447i
$892$		0			0
$893$	20.4043	+	17.1212i	0.682804	+	0.572941i
$894$		0			0
$895$	2.21011	+	12.5342i	0.0738759	+	0.418971i
$896$		0			0
$897$	−0.813603	+	11.0826i	−0.0271654	+	0.370037i
$898$		0			0
$899$	−14.9568	+	25.9060i	−0.498838	+	0.864013i
$900$		0			0
$901$	−12.9123	−	22.3648i	−0.430172	−	0.745080i
$902$		0			0
$903$	−2.73486	+	2.81244i	−0.0910103	+	0.0935922i
$904$		0			0
$905$	−9.92033	+	8.32414i	−0.329763	+	0.276704i
$906$		0			0
$907$	−7.67993	+	2.79527i	−0.255008	+	0.0928153i	−0.466361	−	0.884594i	$-0.654435\pi$
$907$	−7.67993	+	2.79527i	−0.255008	+	0.0928153i	0.211353	+	0.977410i	$0.432213\pi$
$908$		0			0
$909$	−15.8317	−	8.55922i	−0.525103	−	0.283891i
$910$		0			0
$911$	−0.564876	+	3.20357i	−0.0187152	+	0.106139i	−0.992734	−	0.120326i	$-0.961606\pi$
$911$	−0.564876	+	3.20357i	−0.0187152	+	0.106139i	0.974019	+	0.226465i	$0.0727170\pi$
$912$		0			0
$913$	−21.6149	−	7.86720i	−0.715350	−	0.260366i
$914$		0			0
$915$	−24.2658	+	2.46538i	−0.802202	+	0.0815030i
$916$		0			0
$917$	16.4344			0.542712
$918$		0			0
$919$	−8.48587			−0.279923			−0.139961	−	0.990157i	$-0.544698\pi$
$919$	−8.48587			−0.279923			−0.139961	+	0.990157i	$0.544698\pi$
$920$		0			0
$921$	−17.2469	+	38.3784i	−0.568305	+	1.26461i
$922$		0			0
$923$	−2.44352	−	0.889370i	−0.0804296	−	0.0292740i
$924$		0			0
$925$	−3.52125	+	19.9700i	−0.115778	+	0.656609i
$926$		0			0
$927$	30.1516	−	38.0453i	0.990307	−	1.24957i
$928$		0			0
$929$	−2.41070	+	0.877422i	−0.0790924	+	0.0287873i	−0.381263	−	0.924466i	$-0.624511\pi$
$929$	−2.41070	+	0.877422i	−0.0790924	+	0.0287873i	0.302171	+	0.953254i	$0.402289\pi$
$930$		0			0
$931$	−15.6347	+	13.1190i	−0.512405	+	0.429959i
$932$		0			0
$933$	−53.1731	−	13.4536i	−1.74081	−	0.440451i
$934$		0			0
$935$	16.7864	+	29.0749i	0.548974	+	0.950852i
$936$		0			0
$937$	−9.59378	+	16.6169i	−0.313415	+	0.542851i	−0.979099	−	0.203383i	$-0.934806\pi$
$937$	−9.59378	+	16.6169i	−0.313415	+	0.542851i	0.665684	+	0.746234i	$0.268140\pi$
$938$		0			0
$939$	10.2211	+	6.94594i	0.333554	+	0.226672i
$940$		0			0
$941$	1.50073	+	8.51108i	0.0489225	+	0.277453i	0.999449	−	0.0331901i	$-0.0105667\pi$
$941$	1.50073	+	8.51108i	0.0489225	+	0.277453i	−0.950527	+	0.310643i	$0.899456\pi$
$942$		0			0
$943$	18.7838	+	15.7615i	0.611684	+	0.513264i
$944$		0			0
$945$	1.84495	−	8.25645i	0.0600162	−	0.268582i
$946$		0			0
$947$	13.9033	+	11.6662i	0.451796	+	0.379102i	0.840102	−	0.542429i	$-0.182495\pi$
$947$	13.9033	+	11.6662i	0.451796	+	0.379102i	−0.388306	+	0.921531i	$0.626940\pi$
$948$		0			0
$949$	−0.274221	−	1.55518i	−0.00890158	−	0.0504834i
$950$		0			0
$951$	−17.7324	+	8.57268i	−0.575013	+	0.277988i
$952$		0			0
$953$	−27.2074	+	47.1247i	−0.881335	+	1.52652i	−0.0314785	+	0.999504i	$0.510022\pi$
$953$	−27.2074	+	47.1247i	−0.881335	+	1.52652i	−0.849857	+	0.527013i	$0.823312\pi$
$954$		0			0
$955$	14.7621	+	25.5687i	0.477691	+	0.827385i
$956$		0			0
$957$	−9.01196	−	31.8449i	−0.291315	−	1.02940i
$958$		0			0
$959$	14.9859	−	12.5747i	0.483920	−	0.406057i
$960$		0			0
$961$	−4.60800	+	1.67717i	−0.148645	+	0.0541024i
$962$		0			0
$963$	13.8067	−	41.5107i	0.444915	−	1.33766i
$964$		0			0
$965$	−0.109627	+	0.621727i	−0.00352903	+	0.0200141i
$966$		0			0
$967$	−26.7200	−	9.72530i	−0.859259	−	0.312745i	−0.125449	−	0.992100i	$-0.540037\pi$
$967$	−26.7200	−	9.72530i	−0.859259	−	0.312745i	−0.733809	+	0.679355i	$0.762259\pi$
$968$		0			0
$969$	−34.4450	−	47.7568i	−1.10653	−	1.53417i
$970$		0			0
$971$	−10.1445			−0.325552			−0.162776	−	0.986663i	$-0.552045\pi$
$971$	−10.1445			−0.325552			−0.162776	+	0.986663i	$0.552045\pi$
$972$		0			0
$973$	12.2691			0.393331
$974$		0			0
$975$	−2.94944	−	4.08930i	−0.0944576	−	0.130962i
$976$		0			0
$977$	1.64008	+	0.596939i	0.0524707	+	0.0190978i	0.368122	−	0.929777i	$-0.380001\pi$
$977$	1.64008	+	0.596939i	0.0524707	+	0.0190978i	−0.315651	+	0.948875i	$0.602223\pi$
$978$		0			0
$979$	−6.50837	+	36.9108i	−0.208008	+	1.17967i
$980$		0			0
$981$	−11.2869	+	33.9347i	−0.360362	+	1.08345i
$982$		0			0
$983$	41.9097	−	15.2539i	1.33671	−	0.486523i	0.427935	−	0.903809i	$-0.359241\pi$
$983$	41.9097	−	15.2539i	1.33671	−	0.486523i	0.908775	+	0.417287i	$0.137019\pi$
$984$		0			0
$985$	14.3306	−	12.0248i	0.456611	−	0.383142i
$986$		0			0
$987$	−4.38236	−	15.4856i	−0.139492	−	0.492912i
$988$		0			0
$989$	−6.38542	−	11.0599i	−0.203044	−	0.351683i
$990$		0			0
$991$	−1.66057	+	2.87619i	−0.0527498	+	0.0913653i	−0.891195	−	0.453621i	$-0.850132\pi$
$991$	−1.66057	+	2.87619i	−0.0527498	+	0.0913653i	0.838445	+	0.544987i	$0.183465\pi$
$992$		0			0
$993$	36.3145	−	17.5561i	1.15241	−	0.557127i
$994$		0			0
$995$	−4.17347	−	23.6689i	−0.132308	−	0.750356i
$996$		0			0
$997$	33.1027	+	27.7765i	1.04837	+	0.879689i	0.992922	−	0.118772i	$-0.0378958\pi$
$997$	33.1027	+	27.7765i	1.04837	+	0.879689i	0.0554513	+	0.998461i	$0.482340\pi$
$998$		0			0
$999$	20.4349	+	18.7883i	0.646532	+	0.594436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.97.8	yes	60
4.3	odd	2	inner	864.2.y.d.97.3	✓	60
27.22	even	9	inner	864.2.y.d.481.8	yes	60
108.103	odd	18	inner	864.2.y.d.481.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.97.3	✓	60	4.3	odd	2	inner
864.2.y.d.97.8	yes	60	1.1	even	1	trivial
864.2.y.d.481.3	yes	60	108.103	odd	18	inner
864.2.y.d.481.8	yes	60	27.22	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)

\(f(q)\)	\(=\)	\(q+(1.01321 + 1.40478i) q^{3} +(-1.03120 - 0.375327i) q^{5} +(0.257635 - 1.46112i) q^{7} +(-0.946819 + 2.84667i) q^{9} +O(q^{10})\)	\(q+(1.01321 + 1.40478i) q^{3} +(-1.03120 - 0.375327i) q^{5} +(0.257635 - 1.46112i) q^{7} +(-0.946819 + 2.84667i) q^{9} +(-3.59661 + 1.30906i) q^{11} +(0.587485 - 0.492959i) q^{13} +(-0.517571 - 1.82890i) q^{15} +(3.99661 + 6.92233i) q^{17} +(-2.12655 + 3.68329i) q^{19} +(2.31359 - 1.11850i) q^{21} +(1.45270 + 8.23865i) q^{23} +(-2.90771 - 2.43986i) q^{25} +(-4.95827 + 1.55420i) q^{27} +(3.82432 + 3.20898i) q^{29} +(1.04049 + 5.90094i) q^{31} +(-5.48306 - 3.72610i) q^{33} +(-0.814071 + 1.41001i) q^{35} +(-2.67115 - 4.62657i) q^{37} +(1.28774 + 0.325818i) q^{39} +(2.24532 - 1.88405i) q^{41} +(-1.43450 + 0.522115i) q^{43} +(2.04480 - 2.58013i) q^{45} +(1.08751 - 6.16757i) q^{47} +(4.50936 + 1.64127i) q^{49} +(-5.67496 + 12.6281i) q^{51} -3.23082 q^{53} +4.20017 q^{55} +(-7.32885 + 0.744605i) q^{57} +(-0.643906 - 0.234363i) q^{59} +(2.22831 - 12.6374i) q^{61} +(3.91539 + 2.11681i) q^{63} +(-0.790837 + 0.287841i) q^{65} +(-5.83956 + 4.89997i) q^{67} +(-10.1016 + 10.3882i) q^{69} +(-1.69534 - 2.93642i) q^{71} +(1.02957 - 1.78327i) q^{73} +(0.481351 - 6.55679i) q^{75} +(0.986080 + 5.59234i) q^{77} +(0.799634 + 0.670973i) q^{79} +(-7.20707 - 5.39056i) q^{81} +(4.60378 + 3.86303i) q^{83} +(-1.52318 - 8.63836i) q^{85} +(-0.633089 + 8.62370i) q^{87} +(4.89625 - 8.48056i) q^{89} +(-0.568914 - 0.985388i) q^{91} +(-7.23529 + 7.44055i) q^{93} +(3.57534 - 3.00007i) q^{95} +(5.38189 - 1.95885i) q^{97} +(-0.321123 - 11.4778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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