LMFDB - Embedded newform 864.2.y.d.193.9

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			193.9
Character	$\chi$	$=$	864.193
Dual form			864.2.y.d.385.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68152 - 0.415309i) q^{3} +(-0.564773 + 3.20298i) q^{5} +(2.06064 - 1.72908i) q^{7} +(2.65504 - 1.39670i) q^{9} +O(q^{10})$	\(q+(1.68152 - 0.415309i) q^{3} +(-0.564773 + 3.20298i) q^{5} +(2.06064 - 1.72908i) q^{7} +(2.65504 - 1.39670i) q^{9} +(-0.560273 - 3.17747i) q^{11} +(5.14100 - 1.87117i) q^{13} +(0.380550 + 5.62045i) q^{15} +(-2.91506 + 5.04904i) q^{17} +(-3.17060 - 5.49163i) q^{19} +(2.74691 - 3.76329i) q^{21} +(4.71915 + 3.95984i) q^{23} +(-5.24168 - 1.90782i) q^{25} +(3.88444 - 3.45125i) q^{27} +(-1.93718 - 0.705076i) q^{29} +(5.75856 + 4.83200i) q^{31} +(-2.26174 - 5.11029i) q^{33} +(4.37443 + 7.57674i) q^{35} +(-1.52449 + 2.64049i) q^{37} +(7.86760 - 5.28152i) q^{39} +(4.33643 - 1.57833i) q^{41} +(1.68001 + 9.52781i) q^{43} +(2.97413 + 9.29286i) q^{45} +(-4.00629 + 3.36167i) q^{47} +(0.0409740 - 0.232375i) q^{49} +(-2.80483 + 9.70072i) q^{51} -8.63550 q^{53} +10.4938 q^{55} +(-7.61215 - 7.91753i) q^{57} +(1.79573 - 10.1841i) q^{59} +(0.675083 - 0.566462i) q^{61} +(3.05606 - 7.46888i) q^{63} +(3.08984 + 17.5233i) q^{65} +(-0.628431 + 0.228730i) q^{67} +(9.57991 + 4.69865i) q^{69} +(2.92691 - 5.06956i) q^{71} +(-5.69150 - 9.85797i) q^{73} +(-9.60634 - 1.03112i) q^{75} +(-6.64862 - 5.57885i) q^{77} +(-6.01891 - 2.19070i) q^{79} +(5.09844 - 7.41660i) q^{81} +(-9.46119 - 3.44359i) q^{83} +(-14.5256 - 12.1885i) q^{85} +(-3.55024 - 0.381073i) q^{87} +(1.40267 + 2.42950i) q^{89} +(7.35835 - 12.7450i) q^{91} +(11.6899 + 5.73354i) q^{93} +(19.3803 - 7.05385i) q^{95} +(-1.47207 - 8.34855i) q^{97} +(-5.92552 - 7.65375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

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

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
$3$	1.68152	−	0.415309i	0.970828	−	0.239779i
$3$	1.68152	−	0.415309i	0.970828	−	0.239779i
$4$		0			0
$5$	−0.564773	+	3.20298i	−0.252574	+	1.43242i	0.549650	+	0.835395i	$0.314761\pi$
$5$	−0.564773	+	3.20298i	−0.252574	+	1.43242i	−0.802224	+	0.597023i	$0.796350\pi$
$6$		0			0
$7$	2.06064	−	1.72908i	0.778849	−	0.653532i	−0.164110	−	0.986442i	$-0.552475\pi$
$7$	2.06064	−	1.72908i	0.778849	−	0.653532i	0.942958	+	0.332911i	$0.108031\pi$
$8$		0			0
$9$	2.65504	−	1.39670i	0.885012	−	0.465568i
$10$		0			0
$11$	−0.560273	−	3.17747i	−0.168929	−	0.958042i	−0.944921	−	0.327299i	$-0.893861\pi$
$11$	−0.560273	−	3.17747i	−0.168929	−	0.958042i	0.775992	−	0.630743i	$-0.217250\pi$
$12$		0			0
$13$	5.14100	−	1.87117i	1.42586	−	0.518970i	0.490117	−	0.871657i	$-0.336954\pi$
$13$	5.14100	−	1.87117i	1.42586	−	0.518970i	0.935741	+	0.352687i	$0.114732\pi$
$14$		0			0
$15$	0.380550	+	5.62045i	0.0982577	+	1.45119i
$16$		0			0
$17$	−2.91506	+	5.04904i	−0.707006	+	1.22457i	0.258956	+	0.965889i	$0.416621\pi$
$17$	−2.91506	+	5.04904i	−0.707006	+	1.22457i	−0.965963	+	0.258682i	$0.916712\pi$
$18$		0			0
$19$	−3.17060	−	5.49163i	−0.727385	−	1.25987i	−0.957985	−	0.286819i	$-0.907402\pi$
$19$	−3.17060	−	5.49163i	−0.727385	−	1.25987i	0.230600	−	0.973049i	$-0.425931\pi$
$20$		0			0
$21$	2.74691	−	3.76329i	0.599425	−	0.821218i
$22$		0			0
$23$	4.71915	+	3.95984i	0.984011	+	0.825683i	0.984690	−	0.174317i	$-0.0557716\pi$
$23$	4.71915	+	3.95984i	0.984011	+	0.825683i	−0.000678723		1.00000i	$0.500216\pi$
$24$		0			0
$25$	−5.24168	−	1.90782i	−1.04834	−	0.381563i
$26$		0			0
$27$	3.88444	−	3.45125i	0.747561	−	0.664193i
$28$		0			0
$29$	−1.93718	−	0.705076i	−0.359725	−	0.130929i	0.155834	−	0.987783i	$-0.450194\pi$
$29$	−1.93718	−	0.705076i	−0.359725	−	0.130929i	−0.515559	+	0.856854i	$0.672416\pi$
$30$		0			0
$31$	5.75856	+	4.83200i	1.03427	+	0.867854i	0.991353	−	0.131225i	$-0.0418911\pi$
$31$	5.75856	+	4.83200i	1.03427	+	0.867854i	0.0429151	+	0.999079i	$0.486336\pi$
$32$		0			0
$33$	−2.26174	−	5.11029i	−0.393719	−	0.889588i
$34$		0			0
$35$	4.37443	+	7.57674i	0.739414	+	1.28070i
$36$		0			0
$37$	−1.52449	+	2.64049i	−0.250624	+	0.434094i	−0.963698	−	0.266995i	$-0.913969\pi$
$37$	−1.52449	+	2.64049i	−0.250624	+	0.434094i	0.713073	+	0.701089i	$0.247303\pi$
$38$		0			0
$39$	7.86760	−	5.28152i	1.25982	−	0.845721i
$40$		0			0
$41$	4.33643	−	1.57833i	0.677237	−	0.246494i	0.0195760	−	0.999808i	$-0.493768\pi$
$41$	4.33643	−	1.57833i	0.677237	−	0.246494i	0.657661	+	0.753314i	$0.271546\pi$
$42$		0			0
$43$	1.68001	+	9.52781i	0.256199	+	1.45298i	0.792976	+	0.609253i	$0.208531\pi$
$43$	1.68001	+	9.52781i	0.256199	+	1.45298i	−0.536777	+	0.843724i	$0.680358\pi$
$44$		0			0
$45$	2.97413	+	9.29286i	0.443357	+	1.38530i
$46$		0			0
$47$	−4.00629	+	3.36167i	−0.584377	+	0.490350i	−0.886381	−	0.462956i	$-0.846789\pi$
$47$	−4.00629	+	3.36167i	−0.584377	+	0.490350i	0.302004	+	0.953307i	$0.402344\pi$
$48$		0			0
$49$	0.0409740	−	0.232375i	0.00585343	−	0.0331964i
$50$		0			0
$51$	−2.80483	+	9.70072i	−0.392755	+	1.35837i
$52$		0			0
$53$	−8.63550			−1.18618			−0.593088	−	0.805137i	$-0.702092\pi$
$53$	−8.63550			−1.18618			−0.593088	+	0.805137i	$0.702092\pi$
$54$		0			0
$55$	10.4938			1.41498
$56$		0			0
$57$	−7.61215	−	7.91753i	−1.00825	−	1.04870i
$58$		0			0
$59$	1.79573	−	10.1841i	0.233784	−	1.32585i	−0.611375	−	0.791341i	$-0.709383\pi$
$59$	1.79573	−	10.1841i	0.233784	−	1.32585i	0.845159	−	0.534514i	$-0.179505\pi$
$60$		0			0
$61$	0.675083	−	0.566462i	0.0864355	−	0.0725280i	−0.598546	−	0.801088i	$-0.704255\pi$
$61$	0.675083	−	0.566462i	0.0864355	−	0.0725280i	0.684982	+	0.728560i	$0.259810\pi$
$62$		0			0
$63$	3.05606	−	7.46888i	0.385027	−	0.940990i
$64$		0			0
$65$	3.08984	+	17.5233i	0.383247	+	2.17350i
$66$		0			0
$67$	−0.628431	+	0.228730i	−0.0767750	+	0.0279438i	−0.380122	−	0.924936i	$-0.624118\pi$
$67$	−0.628431	+	0.228730i	−0.0767750	+	0.0279438i	0.303347	+	0.952880i	$0.401896\pi$
$68$		0			0
$69$	9.57991	+	4.69865i	1.15329	+	0.565651i
$70$		0			0
$71$	2.92691	−	5.06956i	0.347361	−	0.601646i	−0.638419	−	0.769689i	$-0.720411\pi$
$71$	2.92691	−	5.06956i	0.347361	−	0.601646i	0.985780	+	0.168043i	$0.0537447\pi$
$72$		0			0
$73$	−5.69150	−	9.85797i	−0.666140	−	1.15379i	−0.978975	−	0.203981i	$-0.934612\pi$
$73$	−5.69150	−	9.85797i	−0.666140	−	1.15379i	0.312835	−	0.949808i	$-0.398721\pi$
$74$		0			0
$75$	−9.60634	−	1.03112i	−1.10924	−	0.119063i
$76$		0			0
$77$	−6.64862	−	5.57885i	−0.757680	−	0.635769i
$78$		0			0
$79$	−6.01891	−	2.19070i	−0.677180	−	0.246473i	−0.0195439	−	0.999809i	$-0.506221\pi$
$79$	−6.01891	−	2.19070i	−0.677180	−	0.246473i	−0.657636	+	0.753336i	$0.728444\pi$
$80$		0			0
$81$	5.09844	−	7.41660i	0.566494	−	0.824066i
$82$		0			0
$83$	−9.46119	−	3.44359i	−1.03850	−	0.377983i	−0.234189	−	0.972191i	$-0.575243\pi$
$83$	−9.46119	−	3.44359i	−1.03850	−	0.377983i	−0.804311	+	0.594208i	$0.797466\pi$
$84$		0			0
$85$	−14.5256	−	12.1885i	−1.57553	−	1.32202i
$86$		0			0
$87$	−3.55024	−	0.381073i	−0.380625	−	0.0408553i
$88$		0			0
$89$	1.40267	+	2.42950i	0.148683	+	0.257526i	0.930741	−	0.365679i	$-0.119163\pi$
$89$	1.40267	+	2.42950i	0.148683	+	0.257526i	−0.782058	+	0.623205i	$0.785830\pi$
$90$		0			0
$91$	7.35835	−	12.7450i	0.771364	−	1.33604i
$92$		0			0
$93$	11.6899	+	5.73354i	1.21219	+	0.594541i
$94$		0			0
$95$	19.3803	−	7.05385i	1.98838	−	0.723709i
$96$		0			0
$97$	−1.47207	−	8.34855i	−0.149466	−	0.847667i	−0.963672	−	0.267089i	$-0.913938\pi$
$97$	−1.47207	−	8.34855i	−0.149466	−	0.847667i	0.814205	−	0.580577i	$-0.197173\pi$
$98$		0			0
$99$	−5.92552	−	7.65375i	−0.595537	−	0.769231i
$100$		0			0
$101$	0.756583	−	0.634848i	0.0752828	−	0.0631698i	−0.604370	−	0.796704i	$-0.706575\pi$
$101$	0.756583	−	0.634848i	0.0752828	−	0.0631698i	0.679653	+	0.733534i	$0.262131\pi$
$102$		0			0
$103$	−1.65038	+	9.35977i	−0.162617	+	0.922246i	0.788871	+	0.614559i	$0.210666\pi$
$103$	−1.65038	+	9.35977i	−0.162617	+	0.922246i	−0.951488	+	0.307687i	$0.900445\pi$
$104$		0			0
$105$	10.5024	+	10.9237i	1.02493	+	1.06605i
$106$		0			0
$107$	−3.54487			−0.342696			−0.171348	−	0.985211i	$-0.554812\pi$
$107$	−3.54487			−0.342696			−0.171348	+	0.985211i	$0.554812\pi$
$108$		0			0
$109$	−14.7774			−1.41542			−0.707709	−	0.706504i	$-0.750271\pi$
$109$	−14.7774			−1.41542			−0.707709	+	0.706504i	$0.750271\pi$
$110$		0			0
$111$	−1.46684	+	5.07318i	−0.139227	+	0.481525i
$112$		0			0
$113$	−2.65157	+	15.0378i	−0.249439	+	1.41464i	0.560515	+	0.828144i	$0.310603\pi$
$113$	−2.65157	+	15.0378i	−0.249439	+	1.41464i	−0.809954	+	0.586494i	$0.800508\pi$
$114$		0			0
$115$	−15.3485	+	12.8790i	−1.43126	+	1.20097i
$116$		0			0
$117$	11.0361	−	12.1485i	1.02029	−	1.12313i
$118$		0			0
$119$	2.72330	+	15.4446i	0.249645	+	1.41581i
$120$		0			0
$121$	0.554237	−	0.201726i	0.0503852	−	0.0183387i
$122$		0			0
$123$	6.63631	−	4.45496i	0.598376	−	0.401690i
$124$		0			0
$125$	0.940071	−	1.62825i	0.0840825	−	0.145635i
$126$		0			0
$127$	−7.55982	−	13.0940i	−0.670826	−	1.16190i	−0.977670	−	0.210145i	$-0.932607\pi$
$127$	−7.55982	−	13.0940i	−0.670826	−	1.16190i	0.306845	−	0.951760i	$-0.400727\pi$
$128$		0			0
$129$	6.78196	+	15.3235i	0.597118	+	1.34916i
$130$		0			0
$131$	3.54087	+	2.97114i	0.309367	+	0.259590i	0.784230	−	0.620470i	$-0.213058\pi$
$131$	3.54087	+	2.97114i	0.309367	+	0.259590i	−0.474863	+	0.880060i	$0.657502\pi$
$132$		0			0
$133$	−16.0289	−	5.83406i	−1.38989	−	0.505877i
$134$		0			0
$135$	8.86047	+	14.3910i	0.762588	+	1.23858i
$136$		0			0
$137$	−0.593168	−	0.215895i	−0.0506778	−	0.0184452i	0.316557	−	0.948574i	$-0.397473\pi$
$137$	−0.593168	−	0.215895i	−0.0506778	−	0.0184452i	−0.367235	+	0.930128i	$0.619695\pi$
$138$		0			0
$139$	−13.7248	−	11.5165i	−1.16412	−	0.976816i	−0.164170	−	0.986432i	$-0.552495\pi$
$139$	−13.7248	−	11.5165i	−1.16412	−	0.976816i	−0.999954	+	0.00961641i	$0.996939\pi$
$140$		0			0
$141$	−5.34053	+	7.31658i	−0.449754	+	0.616167i
$142$		0			0
$143$	−8.82595	−	15.2870i	−0.738063	−	1.27836i
$144$		0			0
$145$	3.35241	−	5.80655i	0.278403	−	0.482208i
$146$		0			0
$147$	−0.0276087	−	0.407761i	−0.00227713	−	0.0336315i
$148$		0			0
$149$	10.9851	−	3.99825i	0.899934	−	0.327549i	0.149708	−	0.988730i	$-0.452167\pi$
$149$	10.9851	−	3.99825i	0.899934	−	0.327549i	0.750226	+	0.661181i	$0.229944\pi$
$150$		0			0
$151$	1.13948	+	6.46232i	0.0927296	+	0.525896i	0.995419	+	0.0956040i	$0.0304782\pi$
$151$	1.13948	+	6.46232i	0.0927296	+	0.525896i	−0.902690	+	0.430292i	$0.858411\pi$
$152$		0			0
$153$	−0.687595	+	17.4769i	−0.0555887	+	1.41292i
$154$		0			0
$155$	−18.7291	+	15.7156i	−1.50436	+	1.26231i
$156$		0			0
$157$	−1.63266	+	9.25927i	−0.130300	+	0.738970i	0.847717	+	0.530448i	$0.177976\pi$
$157$	−1.63266	+	9.25927i	−0.130300	+	0.738970i	−0.978018	+	0.208522i	$0.933135\pi$
$158$		0			0
$159$	−14.5208	+	3.58640i	−1.15157	+	0.284420i
$160$		0			0
$161$	16.5714			1.30601
$162$		0			0
$163$	11.1735			0.875172			0.437586	−	0.899176i	$-0.355833\pi$
$163$	11.1735			0.875172			0.437586	+	0.899176i	$0.355833\pi$
$164$		0			0
$165$	17.6456	−	4.35817i	1.37371	−	0.339283i
$166$		0			0
$167$	−2.17114	+	12.3131i	−0.168008	+	0.952819i	0.777901	+	0.628387i	$0.216284\pi$
$167$	−2.17114	+	12.3131i	−0.168008	+	0.952819i	−0.945909	+	0.324432i	$0.894827\pi$
$168$		0			0
$169$	12.9701	−	10.8832i	0.997697	−	0.837167i
$170$		0			0
$171$	−16.0882	−	10.1521i	−1.23030	−	0.776351i
$172$		0			0
$173$	−1.81394	−	10.2874i	−0.137911	−	0.782133i	−0.972788	−	0.231696i	$-0.925572\pi$
$173$	−1.81394	−	10.2874i	−0.137911	−	0.782133i	0.834877	−	0.550437i	$-0.185539\pi$
$174$		0			0
$175$	−14.1000	+	5.13197i	−1.06586	+	0.387941i
$176$		0			0
$177$	−1.20998	−	17.8706i	−0.0909479	−	1.34323i
$178$		0			0
$179$	5.74874	−	9.95710i	0.429681	−	0.744229i	−0.567164	−	0.823605i	$-0.691959\pi$
$179$	5.74874	−	9.95710i	0.429681	−	0.744229i	0.996845	+	0.0793761i	$0.0252928\pi$
$180$		0			0
$181$	6.41625	+	11.1133i	0.476916	+	0.826043i	0.999650	−	0.0264531i	$-0.00842128\pi$
$181$	6.41625	+	11.1133i	0.476916	+	0.826043i	−0.522734	+	0.852496i	$0.675088\pi$
$182$		0			0
$183$	0.899911	−	1.23289i	0.0665233	−	0.0911376i
$184$		0			0
$185$	−7.59647	−	6.37419i	−0.558503	−	0.468640i
$186$		0			0
$187$	17.6764	+	6.43367i	1.29262	+	0.470477i
$188$		0			0
$189$	2.03694	−	13.8283i	0.148166	−	1.00586i
$190$		0			0
$191$	−17.8711	−	6.50454i	−1.29311	−	0.470652i	−0.398360	−	0.917229i	$-0.630421\pi$
$191$	−17.8711	−	6.50454i	−1.29311	−	0.470652i	−0.894745	+	0.446577i	$0.852643\pi$
$192$		0			0
$193$	−3.90939	−	3.28037i	−0.281404	−	0.236126i	0.491150	−	0.871075i	$-0.336577\pi$
$193$	−3.90939	−	3.28037i	−0.281404	−	0.236126i	−0.772554	+	0.634949i	$0.781021\pi$
$194$		0			0
$195$	12.4732	+	28.1827i	0.893227	+	2.01820i
$196$		0			0
$197$	4.95302	+	8.57889i	0.352888	+	0.611221i	0.986754	−	0.162222i	$-0.0518662\pi$
$197$	4.95302	+	8.57889i	0.352888	+	0.611221i	−0.633866	+	0.773443i	$0.718533\pi$
$198$		0			0
$199$	−4.96471	+	8.59913i	−0.351939	+	0.609576i	−0.986589	−	0.163223i	$-0.947811\pi$
$199$	−4.96471	+	8.59913i	−0.351939	+	0.609576i	0.634650	+	0.772800i	$0.281144\pi$
$200$		0			0
$201$	−0.961727	+	0.645608i	−0.0678350	+	0.0455376i
$202$		0			0
$203$	−5.21096	+	1.89664i	−0.365738	+	0.133118i
$204$		0			0
$205$	2.60627	+	14.7809i	0.182030	+	1.03234i
$206$		0			0
$207$	18.0602	+	3.92226i	1.25527	+	0.272616i
$208$		0			0
$209$	−15.6731	+	13.1513i	−1.08413	+	0.909693i
$210$		0			0
$211$	1.37015	−	7.77053i	0.0943253	−	0.534945i	−0.900627	−	0.434594i	$-0.856892\pi$
$211$	1.37015	−	7.77053i	0.0943253	−	0.534945i	0.994952	−	0.100352i	$-0.0319969\pi$
$212$		0			0
$213$	2.81624	−	9.74015i	0.192965	−	0.667384i
$214$		0			0
$215$	−31.4663			−2.14598
$216$		0			0
$217$	20.2212			1.37271
$218$		0			0
$219$	−13.6645	−	14.2127i	−0.923361	−	0.960404i
$220$		0			0
$221$	−5.53873	+	31.4117i	−0.372575	+	2.11298i
$222$		0			0
$223$	14.9853	−	12.5742i	1.00349	−	0.842028i	0.0160262	−	0.999872i	$-0.494898\pi$
$223$	14.9853	−	12.5742i	1.00349	−	0.842028i	0.987464	+	0.157843i	$0.0504540\pi$
$224$		0			0
$225$	−16.5815	+	2.25575i	−1.10543	+	0.150383i
$226$		0			0
$227$	0.0320519	+	0.181775i	0.00212736	+	0.0120649i	0.985853	−	0.167612i	$-0.0536057\pi$
$227$	0.0320519	+	0.181775i	0.00212736	+	0.0120649i	−0.983726	+	0.179677i	$0.942495\pi$
$228$		0			0
$229$	−19.8906	+	7.23957i	−1.31441	+	0.478405i	−0.901662	−	0.432442i	$-0.857652\pi$
$229$	−19.8906	+	7.23957i	−1.31441	+	0.478405i	−0.412744	+	0.910847i	$0.635430\pi$
$230$		0			0
$231$	−13.4968	−	6.61974i	−0.888021	−	0.435547i
$232$		0			0
$233$	−6.85266	+	11.8692i	−0.448933	+	0.777574i	−0.998317	−	0.0579958i	$-0.981529\pi$
$233$	−6.85266	+	11.8692i	−0.448933	+	0.777574i	0.549384	+	0.835570i	$0.314862\pi$
$234$		0			0
$235$	−8.50475	−	14.7307i	−0.554788	−	0.960922i
$236$		0			0
$237$	−11.0308	−	1.18401i	−0.716524	−	0.0769098i
$238$		0			0
$239$	10.2875	+	8.63226i	0.665445	+	0.558374i	0.911713	−	0.410827i	$-0.134760\pi$
$239$	10.2875	+	8.63226i	0.665445	+	0.558374i	−0.246269	+	0.969202i	$0.579205\pi$
$240$		0			0
$241$	−1.38596	−	0.504447i	−0.0892773	−	0.0324943i	0.296995	−	0.954879i	$-0.404015\pi$
$241$	−1.38596	−	0.504447i	−0.0892773	−	0.0324943i	−0.386273	+	0.922385i	$0.626238\pi$
$242$		0			0
$243$	5.49297	−	14.5886i	0.352374	−	0.935859i
$244$		0			0
$245$	0.721153	+	0.262478i	0.0460728	+	0.0167691i
$246$		0			0
$247$	−26.5758	−	22.2998i	−1.69098	−	1.41890i
$248$		0			0
$249$	−17.3394	−	1.86116i	−1.09884	−	0.117946i
$250$		0			0
$251$	−9.08471	−	15.7352i	−0.573422	−	0.993195i	−0.996211	−	0.0869675i	$-0.972282\pi$
$251$	−9.08471	−	15.7352i	−0.573422	−	0.993195i	0.422790	−	0.906228i	$-0.361051\pi$
$252$		0			0
$253$	9.93824	−	17.2135i	0.624812	−	1.08221i
$254$		0			0
$255$	−29.4872	−	14.4625i	−1.84656	−	0.905679i
$256$		0			0
$257$	−12.6315	+	4.59750i	−0.787933	+	0.286784i	−0.704477	−	0.709727i	$-0.748818\pi$
$257$	−12.6315	+	4.59750i	−0.787933	+	0.286784i	−0.0834565	+	0.996511i	$0.526596\pi$
$258$		0			0
$259$	1.42421	+	8.07707i	0.0884958	+	0.501885i
$260$		0			0
$261$	−6.12807	+	0.833662i	−0.379318	+	0.0516024i
$262$		0			0
$263$	10.5468	−	8.84986i	0.650347	−	0.545706i	−0.256829	−	0.966457i	$-0.582678\pi$
$263$	10.5468	−	8.84986i	0.650347	−	0.545706i	0.907176	+	0.420751i	$0.138233\pi$
$264$		0			0
$265$	4.87709	−	27.6594i	0.299597	−	1.69910i
$266$		0			0
$267$	3.36761	+	3.50271i	0.206095	+	0.214362i
$268$		0			0
$269$	−9.01937			−0.549921			−0.274960	−	0.961456i	$-0.588665\pi$
$269$	−9.01937			−0.549921			−0.274960	+	0.961456i	$0.588665\pi$
$270$		0			0
$271$	−1.45681			−0.0884949			−0.0442474	−	0.999021i	$-0.514089\pi$
$271$	−1.45681			−0.0884949			−0.0442474	+	0.999021i	$0.514089\pi$
$272$		0			0
$273$	7.08010	−	24.4870i	0.428507	−	1.48202i
$274$		0			0
$275$	−3.12525	+	17.7242i	−0.188459	+	1.06881i
$276$		0			0
$277$	3.07457	−	2.57987i	0.184733	−	0.155010i	−0.545731	−	0.837960i	$-0.683748\pi$
$277$	3.07457	−	2.57987i	0.184733	−	0.155010i	0.730464	+	0.682951i	$0.239304\pi$
$278$		0			0
$279$	22.0381	+	4.78615i	1.31938	+	0.286540i
$280$		0			0
$281$	−3.65931	−	20.7530i	−0.218296	−	1.23802i	−0.875094	−	0.483953i	$-0.839201\pi$
$281$	−3.65931	−	20.7530i	−0.218296	−	1.23802i	0.656798	−	0.754067i	$-0.271910\pi$
$282$		0			0
$283$	−20.6804	+	7.52704i	−1.22932	+	0.447436i	−0.873365	−	0.487066i	$-0.838067\pi$
$283$	−20.6804	+	7.52704i	−1.22932	+	0.447436i	−0.355956	+	0.934503i	$0.615845\pi$
$284$		0			0
$285$	29.6589	−	19.9100i	1.75684	−	1.17937i
$286$		0			0
$287$	6.20675	−	10.7504i	0.366373	−	0.634577i
$288$		0			0
$289$	−8.49517	−	14.7141i	−0.499716	−	0.865533i
$290$		0			0
$291$	−5.94255	−	13.4269i	−0.348359	−	0.787099i
$292$		0			0
$293$	−20.6932	−	17.3636i	−1.20891	−	1.01439i	−0.999330	−	0.0366028i	$-0.988346\pi$
$293$	−20.6932	−	17.3636i	−1.20891	−	1.01439i	−0.209579	−	0.977792i	$-0.567209\pi$
$294$		0			0
$295$	31.6053	+	11.5034i	1.84013	+	0.669753i
$296$		0			0
$297$	−13.1426	−	10.4090i	−0.762609	−	0.603994i
$298$		0			0
$299$	31.6707	+	11.5272i	1.83156	+	0.666635i
$300$		0			0
$301$	19.9363	+	16.7285i	1.14911	+	0.964215i
$302$		0			0
$303$	1.00855	−	1.38173i	0.0579398	−	0.0793782i
$304$		0			0
$305$	1.43310	+	2.48220i	0.0820591	+	0.142131i
$306$		0			0
$307$	−4.81461	+	8.33915i	−0.274784	+	0.475941i	−0.970081	−	0.242783i	$-0.921940\pi$
$307$	−4.81461	+	8.33915i	−0.274784	+	0.475941i	0.695296	+	0.718723i	$0.255273\pi$
$308$		0			0
$309$	1.11205	+	16.4241i	0.0632620	+	0.934334i
$310$		0			0
$311$	0.214371	−	0.0780247i	0.0121559	−	0.00442438i	−0.335935	−	0.941885i	$-0.609052\pi$
$311$	0.214371	−	0.0780247i	0.0121559	−	0.00442438i	0.348091	+	0.937461i	$0.386830\pi$
$312$		0			0
$313$	5.17797	+	29.3657i	0.292676	+	1.65985i	0.676501	+	0.736442i	$0.263496\pi$
$313$	5.17797	+	29.3657i	0.292676	+	1.65985i	−0.383825	+	0.923406i	$0.625393\pi$
$314$		0			0
$315$	22.1967	+	14.0067i	1.25064	+	0.789190i
$316$		0			0
$317$	−5.98396	+	5.02114i	−0.336093	+	0.282015i	−0.795177	−	0.606378i	$-0.792622\pi$
$317$	−5.98396	+	5.02114i	−0.336093	+	0.282015i	0.459084	+	0.888393i	$0.348178\pi$
$318$		0			0
$319$	−1.15500	+	6.55036i	−0.0646679	+	0.366750i
$320$		0			0
$321$	−5.96078	+	1.47222i	−0.332698	+	0.0821711i
$322$		0			0
$323$	36.9699			2.05706
$324$		0			0
$325$	−30.5173			−1.69280
$326$		0			0
$327$	−24.8485	+	6.13719i	−1.37413	+	0.339387i
$328$		0			0
$329$	−2.44290	+	13.8544i	−0.134682	+	0.763817i
$330$		0			0
$331$	−4.66458	+	3.91404i	−0.256388	+	0.215135i	−0.761917	−	0.647674i	$-0.775742\pi$
$331$	−4.66458	+	3.91404i	−0.256388	+	0.215135i	0.505529	+	0.862810i	$0.331297\pi$
$332$		0			0
$333$	−0.359591	+	9.13986i	−0.0197055	+	0.500861i
$334$		0			0
$335$	−0.377698	−	2.14203i	−0.0206359	−	0.117032i
$336$		0			0
$337$	9.23843	−	3.36251i	0.503249	−	0.183168i	−0.0779056	−	0.996961i	$-0.524823\pi$
$337$	9.23843	−	3.36251i	0.503249	−	0.183168i	0.581155	+	0.813793i	$0.302601\pi$
$338$		0			0
$339$	1.78666	+	26.3876i	0.0970380	+	1.43318i
$340$		0			0
$341$	12.1272	−	21.0049i	0.656723	−	1.13748i
$342$		0			0
$343$	9.09755	+	15.7574i	0.491221	+	0.850820i
$344$		0			0
$345$	−20.4602	+	28.0307i	−1.10154	+	1.50912i
$346$		0			0
$347$	−9.02545	−	7.57325i	−0.484512	−	0.406554i	0.367543	−	0.930007i	$-0.380199\pi$
$347$	−9.02545	−	7.57325i	−0.484512	−	0.406554i	−0.852055	+	0.523453i	$0.824644\pi$
$348$		0			0
$349$	8.41404	+	3.06246i	0.450393	+	0.163930i	0.557250	−	0.830345i	$-0.311856\pi$
$349$	8.41404	+	3.06246i	0.450393	+	0.163930i	−0.106857	+	0.994274i	$0.534079\pi$
$350$		0			0
$351$	13.5120	−	25.0113i	0.721220	−	1.33501i
$352$		0			0
$353$	13.8109	+	5.02674i	0.735077	+	0.267546i	0.682312	−	0.731061i	$-0.260974\pi$
$353$	13.8109	+	5.02674i	0.735077	+	0.267546i	0.0527649	+	0.998607i	$0.483197\pi$
$354$		0			0
$355$	14.5847	+	12.2380i	0.774075	+	0.649526i
$356$		0			0
$357$	10.9936	+	24.8395i	0.581842	+	1.31464i
$358$		0			0
$359$	−14.6259	−	25.3327i	−0.771924	−	1.33701i	−0.936507	−	0.350648i	$-0.885961\pi$
$359$	−14.6259	−	25.3327i	−0.771924	−	1.33701i	0.164584	−	0.986363i	$-0.447372\pi$
$360$		0			0
$361$	−10.6054	+	18.3690i	−0.558177	+	0.966791i
$362$		0			0
$363$	0.848183	−	0.569386i	0.0445181	−	0.0298850i
$364$		0			0
$365$	34.7893	−	12.6623i	1.82096	−	0.662774i
$366$		0			0
$367$	−2.55671	−	14.4998i	−0.133459	−	0.756883i	−0.975920	−	0.218127i	$-0.930005\pi$
$367$	−2.55671	−	14.4998i	−0.133459	−	0.756883i	0.842462	−	0.538756i	$-0.181106\pi$
$368$		0			0
$369$	9.30892	−	10.2472i	0.484603	−	0.533450i
$370$		0			0
$371$	−17.7947	+	14.9315i	−0.923852	+	0.775204i
$372$		0			0
$373$	−1.73515	+	9.84055i	−0.0898429	+	0.509524i	0.906363	+	0.422499i	$0.138847\pi$
$373$	−1.73515	+	9.84055i	−0.0898429	+	0.509524i	−0.996206	+	0.0870249i	$0.972264\pi$
$374$		0			0
$375$	0.904523	−	3.12836i	0.0467094	−	0.161548i
$376$		0			0
$377$	−11.2784			−0.580866
$378$		0			0
$379$	8.45579			0.434345			0.217172	−	0.976133i	$-0.430317\pi$
$379$	8.45579			0.434345			0.217172	+	0.976133i	$0.430317\pi$
$380$		0			0
$381$	−18.1501	−	18.8782i	−0.929856	−	0.967159i
$382$		0			0
$383$	−3.06233	+	17.3673i	−0.156478	+	0.887430i	0.800944	+	0.598739i	$0.204331\pi$
$383$	−3.06233	+	17.3673i	−0.156478	+	0.887430i	−0.957422	+	0.288691i	$0.906780\pi$
$384$		0			0
$385$	21.6239	−	18.1446i	1.10206	−	0.924737i
$386$		0			0
$387$	17.7680	+	22.9502i	0.903199	+	1.16662i
$388$		0			0
$389$	0.675681	+	3.83198i	0.0342584	+	0.194289i	0.997134	−	0.0756568i	$-0.0241053\pi$
$389$	0.675681	+	3.83198i	0.0342584	+	0.194289i	−0.962876	+	0.269946i	$0.912994\pi$
$390$		0			0
$391$	−33.7500	+	12.2840i	−1.70681	+	0.621228i
$392$		0			0
$393$	7.18799	+	3.52549i	0.362586	+	0.177837i
$394$		0			0
$395$	10.4161	−	18.0412i	0.524091	−	0.907753i
$396$		0			0
$397$	3.31869	+	5.74814i	0.166560	+	0.288491i	0.937208	−	0.348770i	$-0.113401\pi$
$397$	3.31869	+	5.74814i	0.166560	+	0.288491i	−0.770648	+	0.637261i	$0.780067\pi$
$398$		0			0
$399$	−29.3760	−	3.15314i	−1.47064	−	0.157854i
$400$		0			0
$401$	25.0587	+	21.0267i	1.25137	+	1.05003i	0.996546	+	0.0830386i	$0.0264625\pi$
$401$	25.0587	+	21.0267i	1.25137	+	1.05003i	0.254825	+	0.966987i	$0.417982\pi$
$402$		0			0
$403$	38.6463	+	14.0661i	1.92511	+	0.700682i
$404$		0			0
$405$	20.8758	+	20.5189i	1.03733	+	1.01959i
$406$		0			0
$407$	9.24420	+	3.36461i	0.458218	+	0.166778i
$408$		0			0
$409$	19.2858	+	16.1827i	0.953624	+	0.800185i	0.979904	−	0.199469i	$-0.0639218\pi$
$409$	19.2858	+	16.1827i	0.953624	+	0.800185i	−0.0262803	+	0.999655i	$0.508366\pi$
$410$		0			0
$411$	−1.08709	−	0.116685i	−0.0536221	−	0.00575566i
$412$		0			0
$413$	−13.9088	−	24.0907i	−0.684406	−	1.18543i
$414$		0			0
$415$	16.3732	−	28.3592i	0.803728	−	1.39210i
$416$		0			0
$417$	−27.8615	−	13.6652i	−1.36438	−	0.669187i
$418$		0			0
$419$	29.4147	−	10.7061i	1.43700	−	0.523025i	0.498071	−	0.867136i	$-0.334042\pi$
$419$	29.4147	−	10.7061i	1.43700	−	0.523025i	0.938929	+	0.344111i	$0.111820\pi$
$420$		0			0
$421$	4.89732	+	27.7741i	0.238681	+	1.35363i	0.834722	+	0.550672i	$0.185628\pi$
$421$	4.89732	+	27.7741i	0.238681	+	1.35363i	−0.596041	+	0.802954i	$0.703260\pi$
$422$		0			0
$423$	−5.94158	+	14.5210i	−0.288889	+	0.706033i
$424$		0			0
$425$	24.9124	−	20.9040i	1.20843	−	1.01399i
$426$		0			0
$427$	0.411644	−	2.33455i	0.0199208	−	0.112977i
$428$		0			0
$429$	−21.1899	−	22.0399i	−1.02306	−	1.06410i
$430$		0			0
$431$	12.8779			0.620307			0.310153	−	0.950686i	$-0.399620\pi$
$431$	12.8779			0.620307			0.310153	+	0.950686i	$0.399620\pi$
$432$		0			0
$433$	28.0867			1.34976			0.674881	−	0.737927i	$-0.264195\pi$
$433$	28.0867			1.34976			0.674881	+	0.737927i	$0.264195\pi$
$434$		0			0
$435$	3.22565	−	11.1561i	0.154658	−	0.534896i
$436$		0			0
$437$	6.78346	−	38.4709i	0.324497	−	1.84031i
$438$		0			0
$439$	2.13021	−	1.78746i	0.101669	−	0.0853107i	−0.590536	−	0.807011i	$-0.701084\pi$
$439$	2.13021	−	1.78746i	0.101669	−	0.0853107i	0.692205	+	0.721701i	$0.256639\pi$
$440$		0			0
$441$	−0.215771	−	0.674193i	−0.0102748	−	0.0321044i
$442$		0			0
$443$	5.14550	+	29.1816i	0.244470	+	1.38646i	0.821720	+	0.569892i	$0.193015\pi$
$443$	5.14550	+	29.1816i	0.244470	+	1.38646i	−0.577250	+	0.816568i	$0.695874\pi$
$444$		0			0
$445$	−8.57383	+	3.12062i	−0.406438	+	0.147931i
$446$		0			0
$447$	16.8112	−	11.2854i	0.795142	−	0.533779i
$448$		0			0
$449$	0.579456	−	1.00365i	0.0273462	−	0.0473650i	−0.852028	−	0.523496i	$-0.824628\pi$
$449$	0.579456	−	1.00365i	0.0273462	−	0.0473650i	0.879375	+	0.476130i	$0.157961\pi$
$450$		0			0
$451$	−7.44468	−	12.8946i	−0.350556	−	0.607181i
$452$		0			0
$453$	4.59992	+	10.3933i	0.216123	+	0.488320i
$454$		0			0
$455$	36.6663	+	30.7667i	1.71894	+	1.44237i
$456$		0			0
$457$	−37.4916	−	13.6458i	−1.75378	−	0.638325i	−0.753957	−	0.656924i	$-0.771857\pi$
$457$	−37.4916	−	13.6458i	−1.75378	−	0.638325i	−0.999827	+	0.0185983i	$0.994080\pi$
$458$		0			0
$459$	6.10209	+	29.6733i	0.284821	+	1.38503i
$460$		0			0
$461$	−8.12859	−	2.95857i	−0.378586	−	0.137794i	0.145716	−	0.989326i	$-0.453451\pi$
$461$	−8.12859	−	2.95857i	−0.378586	−	0.137794i	−0.524302	+	0.851532i	$0.675674\pi$
$462$		0			0
$463$	−9.72810	−	8.16285i	−0.452103	−	0.379360i	0.388112	−	0.921612i	$-0.373127\pi$
$463$	−9.72810	−	8.16285i	−0.452103	−	0.379360i	−0.840216	+	0.542252i	$0.817572\pi$
$464$		0			0
$465$	−24.9666	+	34.2045i	−1.15780	+	1.58620i
$466$		0			0
$467$	−11.5154	−	19.9453i	−0.532869	−	0.922956i	−0.999263	−	0.0383793i	$-0.987780\pi$
$467$	−11.5154	−	19.9453i	−0.532869	−	0.922956i	0.466394	−	0.884577i	$-0.345553\pi$
$468$		0			0
$469$	−0.899476	+	1.55794i	−0.0415339	+	0.0719389i
$470$		0			0
$471$	1.10010	+	16.2477i	0.0506902	+	0.748656i
$472$		0			0
$473$	29.3330	−	10.6763i	1.34873	−	0.490899i
$474$		0			0
$475$	6.14223	+	34.8343i	0.281825	+	1.59831i
$476$		0			0
$477$	−22.9276	+	12.0612i	−1.04978	+	0.552246i
$478$		0			0
$479$	−6.88888	+	5.78045i	−0.314761	+	0.264116i	−0.786456	−	0.617646i	$-0.788087\pi$
$479$	−6.88888	+	5.78045i	−0.314761	+	0.264116i	0.471696	+	0.881761i	$0.343642\pi$
$480$		0			0
$481$	−2.89659	+	16.4274i	−0.132073	+	0.749023i
$482$		0			0
$483$	27.8651	−	6.88223i	1.26791	−	0.313152i
$484$		0			0
$485$	27.5717			1.25196
$486$		0			0
$487$	25.9250			1.17477			0.587387	−	0.809306i	$-0.300157\pi$
$487$	25.9250			1.17477			0.587387	+	0.809306i	$0.300157\pi$
$488$		0			0
$489$	18.7884	−	4.64044i	0.849641	−	0.209848i
$490$		0			0
$491$	6.07279	−	34.4405i	0.274061	−	1.55428i	−0.467868	−	0.883798i	$-0.654978\pi$
$491$	6.07279	−	34.4405i	0.274061	−	1.55428i	0.741929	−	0.670479i	$-0.233911\pi$
$492$		0			0
$493$	9.20695	−	7.72555i	0.414660	−	0.347941i
$494$		0			0
$495$	27.8614	−	14.6567i	1.25228	−	0.658771i
$496$		0			0
$497$	−2.73437	−	15.5074i	−0.122653	−	0.695602i
$498$		0			0
$499$	21.2567	−	7.73682i	0.951582	−	0.346347i	0.180853	−	0.983510i	$-0.442114\pi$
$499$	21.2567	−	7.73682i	0.951582	−	0.346347i	0.770729	+	0.637163i	$0.219892\pi$
$500$		0			0
$501$	1.46294	+	21.6065i	0.0653592	+	0.965308i
$502$		0			0
$503$	−0.826127	+	1.43089i	−0.0368352	+	0.0638004i	−0.883855	−	0.467760i	$-0.845061\pi$
$503$	−0.826127	+	1.43089i	−0.0368352	+	0.0638004i	0.847020	+	0.531561i	$0.178394\pi$
$504$		0			0
$505$	1.60611	+	2.78187i	0.0714711	+	0.123791i
$506$		0			0
$507$	17.2896	−	23.6869i	0.767857	−	1.05197i
$508$		0			0
$509$	−23.4960	−	19.7155i	−1.04144	−	0.873875i	−0.0492757	−	0.998785i	$-0.515691\pi$
$509$	−23.4960	−	19.7155i	−1.04144	−	0.873875i	−0.992168	+	0.124910i	$0.960136\pi$
$510$		0			0
$511$	−28.7734	−	10.4727i	−1.27286	−	0.463283i
$512$		0			0
$513$	−31.2690	−	10.3894i	−1.38056	−	0.458704i
$514$		0			0
$515$	−29.0471	−	10.5723i	−1.27997	−	0.465871i
$516$		0			0
$517$	12.9262	+	10.8464i	0.568494	+	0.477023i
$518$		0			0
$519$	−7.32261	−	16.5451i	−0.321427	−	0.726248i
$520$		0			0
$521$	−1.00330	−	1.73777i	−0.0439555	−	0.0761332i	0.843211	−	0.537583i	$-0.180663\pi$
$521$	−1.00330	−	1.73777i	−0.0439555	−	0.0761332i	−0.887166	+	0.461450i	$0.847329\pi$
$522$		0			0
$523$	18.7387	−	32.4563i	0.819385	−	1.41922i	−0.0867517	−	0.996230i	$-0.527649\pi$
$523$	18.7387	−	32.4563i	0.819385	−	1.41922i	0.906136	−	0.422986i	$-0.139018\pi$
$524$		0			0
$525$	−21.5781	+	14.4854i	−0.941745	+	0.632194i
$526$		0			0
$527$	−41.1835	+	14.9896i	−1.79398	+	0.652956i
$528$		0			0
$529$	2.59616	+	14.7236i	0.112877	+	0.640155i
$530$		0			0
$531$	−9.45641	−	29.5472i	−0.410373	−	1.28224i
$532$		0			0
$533$	19.3403	−	16.2284i	0.837720	−	0.702931i
$534$		0			0
$535$	2.00205	−	11.3542i	0.0865560	−	0.490884i
$536$		0			0
$537$	5.53136	−	19.1306i	0.238696	−	0.825546i
$538$		0			0
$539$	−0.761320			−0.0327924
$540$		0			0
$541$	35.6056			1.53080			0.765402	−	0.643553i	$-0.222540\pi$
$541$	35.6056			1.53080			0.765402	+	0.643553i	$0.222540\pi$
$542$		0			0
$543$	15.4045	+	16.0225i	0.661071	+	0.687591i
$544$		0			0
$545$	8.34587	−	47.3318i	0.357498	−	2.02747i
$546$		0			0
$547$	22.1618	−	18.5959i	0.947569	−	0.795105i	−0.0313173	−	0.999509i	$-0.509970\pi$
$547$	22.1618	−	18.5959i	0.947569	−	0.795105i	0.978887	+	0.204405i	$0.0655258\pi$
$548$		0			0
$549$	1.00119	−	2.44687i	0.0427298	−	0.104430i
$550$		0			0
$551$	2.27000	+	12.8738i	0.0967051	+	0.548442i
$552$		0			0
$553$	−16.1907	+	5.89294i	−0.688499	+	0.250593i
$554$		0			0
$555$	−15.4209	−	7.56347i	−0.654580	−	0.321051i
$556$		0			0
$557$	−10.2160	+	17.6947i	−0.432867	+	0.749747i	−0.997119	−	0.0758553i	$-0.975831\pi$
$557$	−10.2160	+	17.6947i	−0.432867	+	0.749747i	0.564252	+	0.825603i	$0.309165\pi$
$558$		0			0
$559$	26.4651	+	45.8389i	1.11936	+	1.93878i
$560$		0			0
$561$	32.3952	+	3.47721i	1.36773	+	0.146808i
$562$		0			0
$563$	22.4358	+	18.8259i	0.945557	+	0.793417i	0.978544	−	0.206039i	$-0.0660574\pi$
$563$	22.4358	+	18.8259i	0.945557	+	0.793417i	−0.0329866	+	0.999456i	$0.510502\pi$
$564$		0			0
$565$	−46.6683	−	16.9859i	−1.96335	−	0.714601i
$566$		0			0
$567$	−2.31785	−	24.0986i	−0.0973405	−	1.01204i
$568$		0			0
$569$	10.3423	+	3.76427i	0.433570	+	0.157807i	0.549579	−	0.835442i	$-0.314788\pi$
$569$	10.3423	+	3.76427i	0.433570	+	0.157807i	−0.116009	+	0.993248i	$0.537010\pi$
$570$		0			0
$571$	−11.8720	−	9.96180i	−0.496828	−	0.416888i	0.359638	−	0.933092i	$-0.382900\pi$
$571$	−11.8720	−	9.96180i	−0.496828	−	0.416888i	−0.856466	+	0.516204i	$0.827345\pi$
$572$		0			0
$573$	−32.7520	−	3.51551i	−1.36824	−	0.146863i
$574$		0			0
$575$	−17.1816	−	29.7595i	−0.716524	−	1.24106i
$576$		0			0
$577$	−20.1394	+	34.8824i	−0.838413	+	1.45217i	0.0528078	+	0.998605i	$0.483183\pi$
$577$	−20.1394	+	34.8824i	−0.838413	+	1.45217i	−0.891221	+	0.453569i	$0.850150\pi$
$578$		0			0
$579$	−7.93610	−	3.89241i	−0.329813	−	0.161763i
$580$		0			0
$581$	−25.4504	+	9.26317i	−1.05586	+	0.384301i
$582$		0			0
$583$	4.83824	+	27.4390i	0.200379	+	1.13641i
$584$		0			0
$585$	32.6785	+	42.2095i	1.35109	+	1.74515i
$586$		0			0
$587$	−26.7300	+	22.4292i	−1.10327	+	0.925751i	−0.997640	−	0.0686550i	$-0.978129\pi$
$587$	−26.7300	+	22.4292i	−1.10327	+	0.925751i	−0.105626	+	0.994406i	$0.533685\pi$
$588$		0			0
$589$	8.27754	−	46.9442i	0.341070	−	1.93430i
$590$		0			0
$591$	11.8915	+	12.3686i	0.489151	+	0.508775i
$592$		0			0
$593$	−10.0296			−0.411865			−0.205932	−	0.978566i	$-0.566023\pi$
$593$	−10.0296			−0.411865			−0.205932	+	0.978566i	$0.566023\pi$
$594$		0			0
$595$	−51.0069			−2.09108
$596$		0			0
$597$	−4.77698	+	16.5215i	−0.195509	+	0.676181i
$598$		0			0
$599$	3.22169	−	18.2711i	0.131635	−	0.746538i	−0.845509	−	0.533960i	$-0.820703\pi$
$599$	3.22169	−	18.2711i	0.131635	−	0.746538i	0.977144	−	0.212577i	$-0.0681858\pi$
$600$		0			0
$601$	−7.81619	+	6.55856i	−0.318829	+	0.267529i	−0.788130	−	0.615509i	$-0.788950\pi$
$601$	−7.81619	+	6.55856i	−0.318829	+	0.267529i	0.469301	+	0.883038i	$0.344506\pi$
$602$		0			0
$603$	−1.34904	+	1.48502i	−0.0549371	+	0.0604746i
$604$		0			0
$605$	0.333107	+	1.88914i	0.0135427	+	0.0768045i
$606$		0			0
$607$	−21.8117	+	7.93882i	−0.885311	+	0.322227i	−0.744351	−	0.667789i	$-0.767241\pi$
$607$	−21.8117	+	7.93882i	−0.885311	+	0.322227i	−0.140960	+	0.990015i	$0.545019\pi$
$608$		0			0
$609$	−7.97466	+	5.35340i	−0.323150	+	0.216931i
$610$		0			0
$611$	−14.3061	+	24.7788i	−0.578761	+	1.00244i
$612$		0			0
$613$	18.0851	+	31.3243i	0.730450	+	1.26518i	0.956691	+	0.291105i	$0.0940231\pi$
$613$	18.0851	+	31.3243i	0.730450	+	1.26518i	−0.226241	+	0.974071i	$0.572644\pi$
$614$		0			0
$615$	10.5212	+	23.7720i	0.424254	+	0.958581i
$616$		0			0
$617$	10.7773	+	9.04324i	0.433879	+	0.364067i	0.833413	−	0.552651i	$-0.186384\pi$
$617$	10.7773	+	9.04324i	0.433879	+	0.364067i	−0.399534	+	0.916718i	$0.630828\pi$
$618$		0			0
$619$	−30.4395	−	11.0791i	−1.22347	−	0.445306i	−0.352112	−	0.935958i	$-0.614536\pi$
$619$	−30.4395	−	11.0791i	−1.22347	−	0.445306i	−0.871355	+	0.490652i	$0.836759\pi$
$620$		0			0
$621$	31.9976	−	0.905203i	1.28402	−	0.0363245i
$622$		0			0
$623$	7.09119	+	2.58098i	0.284103	+	0.103405i
$624$		0			0
$625$	−16.6809	−	13.9970i	−0.667238	−	0.559879i
$626$		0			0
$627$	−20.8928	+	28.6233i	−0.834378	+	1.14311i
$628$		0			0
$629$	−8.88796	−	15.3944i	−0.354386	−	0.613815i
$630$		0			0
$631$	21.0060	−	36.3834i	0.836234	−	1.44840i	−0.0567872	−	0.998386i	$-0.518086\pi$
$631$	21.0060	−	36.3834i	0.836234	−	1.44840i	0.893022	−	0.450014i	$-0.148581\pi$
$632$		0			0
$633$	−0.923226	−	13.6354i	−0.0366949	−	0.541957i
$634$		0			0
$635$	46.2094	−	16.8189i	1.83377	−	0.667436i
$636$		0			0
$637$	−0.224166	−	1.27131i	−0.00888179	−	0.0503712i
$638$		0			0
$639$	0.690390	−	17.5479i	0.0273114	−	0.694184i
$640$		0			0
$641$	−2.50140	+	2.09893i	−0.0987995	+	0.0829026i	−0.690849	−	0.722999i	$-0.742763\pi$
$641$	−2.50140	+	2.09893i	−0.0987995	+	0.0829026i	0.592050	+	0.805901i	$0.298319\pi$
$642$		0			0
$643$	0.713743	−	4.04783i	0.0281473	−	0.159631i	−0.967494	−	0.252892i	$-0.918618\pi$
$643$	0.713743	−	4.04783i	0.0281473	−	0.159631i	0.995642	+	0.0932614i	$0.0297292\pi$
$644$		0			0
$645$	−52.9112	+	13.0682i	−2.08338	+	0.514561i
$646$		0			0
$647$	−28.8322			−1.13351			−0.566755	−	0.823886i	$-0.691801\pi$
$647$	−28.8322			−1.13351			−0.566755	+	0.823886i	$0.691801\pi$
$648$		0			0
$649$	−33.3657			−1.30972
$650$		0			0
$651$	34.0025	−	8.39806i	1.33266	−	0.329146i
$652$		0			0
$653$	−1.59346	+	9.03696i	−0.0623569	+	0.353644i	0.937625	+	0.347648i	$0.113020\pi$
$653$	−1.59346	+	9.03696i	−0.0623569	+	0.353644i	−0.999982	+	0.00599555i	$0.998092\pi$
$654$		0			0
$655$	−11.5163	+	9.66333i	−0.449979	+	0.377578i
$656$		0			0
$657$	−28.8798	−	18.2239i	−1.12671	−	0.710984i
$658$		0			0
$659$	2.65656	+	15.0661i	0.103485	+	0.586892i	0.991815	+	0.127686i	$0.0407549\pi$
$659$	2.65656	+	15.0661i	0.103485	+	0.586892i	−0.888330	+	0.459206i	$0.848134\pi$
$660$		0			0
$661$	32.5671	−	11.8535i	1.26671	−	0.461046i	0.380698	−	0.924700i	$-0.375684\pi$
$661$	32.5671	−	11.8535i	1.26671	−	0.461046i	0.886017	+	0.463653i	$0.153462\pi$
$662$		0			0
$663$	3.73206	+	55.1198i	0.144941	+	2.14067i
$664$		0			0
$665$	27.7391	−	48.0455i	1.07568	−	1.86313i
$666$		0			0
$667$	−6.34986	−	10.9983i	−0.245867	−	0.425855i
$668$		0			0
$669$	19.9760	−	27.3673i	0.772316	−	1.05808i
$670$		0			0
$671$	−2.17814	−	1.82768i	−0.0840863	−	0.0705568i
$672$		0			0
$673$	40.9521	+	14.9053i	1.57859	+	0.574558i	0.974896	−	0.222661i	$-0.0714743\pi$
$673$	40.9521	+	14.9053i	1.57859	+	0.574558i	0.603690	+	0.797219i	$0.293697\pi$
$674$		0			0
$675$	−26.9453	+	10.6795i	−1.03713	+	0.411056i
$676$		0			0
$677$	−11.6974	−	4.25750i	−0.449567	−	0.163629i	0.107307	−	0.994226i	$-0.465777\pi$
$677$	−11.6974	−	4.25750i	−0.449567	−	0.163629i	−0.556874	+	0.830597i	$0.687999\pi$
$678$		0			0
$679$	−17.4687	−	14.6580i	−0.670389	−	0.562523i
$680$		0			0
$681$	0.129389	+	0.292348i	0.00495819	+	0.0112028i
$682$		0			0
$683$	21.3778	+	37.0274i	0.817998	+	1.41681i	0.907155	+	0.420797i	$0.138250\pi$
$683$	21.3778	+	37.0274i	0.817998	+	1.41681i	−0.0891562	+	0.996018i	$0.528417\pi$
$684$		0			0
$685$	1.02651	−	1.77798i	0.0392211	−	0.0679330i
$686$		0			0
$687$	−30.4398	+	20.4342i	−1.16135	+	0.779615i
$688$		0			0
$689$	−44.3951	+	16.1585i	−1.69132	+	0.615590i
$690$		0			0
$691$	6.36903	+	36.1205i	0.242289	+	1.37409i	0.826705	+	0.562636i	$0.190213\pi$
$691$	6.36903	+	36.1205i	0.242289	+	1.37409i	−0.584416	+	0.811455i	$0.698676\pi$
$692$		0			0
$693$	−25.4443	−	5.52592i	−0.966550	−	0.209912i
$694$		0			0
$695$	44.6385	−	37.4562i	1.69324	−	1.42079i
$696$		0			0
$697$	−4.67191	+	26.4957i	−0.176961	+	1.00360i
$698$		0			0
$699$	−6.59354	+	22.8042i	−0.249390	+	0.862535i
$700$		0			0
$701$	3.40794			0.128716			0.0643580	−	0.997927i	$-0.479500\pi$
$701$	3.40794			0.128716			0.0643580	+	0.997927i	$0.479500\pi$
$702$		0			0
$703$	19.3342			0.729201
$704$		0			0
$705$	−20.4187	−	21.2378i	−0.769013	−	0.799863i
$706$		0			0
$707$	0.461340	−	2.61639i	0.0173505	−	0.0983994i
$708$		0			0
$709$	34.9712	−	29.3443i	1.31337	−	1.10205i	0.325706	−	0.945471i	$-0.394398\pi$
$709$	34.9712	−	29.3443i	1.31337	−	1.10205i	0.987665	−	0.156579i	$-0.0500466\pi$
$710$		0			0
$711$	−19.0402	+	2.59023i	−0.714063	+	0.0971412i
$712$		0			0
$713$	8.04155	+	45.6059i	0.301159	+	1.70795i
$714$		0			0
$715$	53.9487	−	19.6357i	2.01757	−	0.734334i
$716$		0			0
$717$	20.8838	+	10.2428i	0.779918	+	0.382526i
$718$		0			0
$719$	−4.12256	+	7.14048i	−0.153745	+	0.266295i	−0.932602	−	0.360908i	$-0.882467\pi$
$719$	−4.12256	+	7.14048i	−0.153745	+	0.266295i	0.778856	+	0.627203i	$0.215800\pi$
$720$		0			0
$721$	12.7830	+	22.1408i	0.476063	+	0.824565i
$722$		0			0
$723$	−2.54002	−	0.272639i	−0.0944643	−	0.0101395i
$724$		0			0
$725$	8.80892	+	7.39156i	0.327155	+	0.274516i
$726$		0			0
$727$	5.89865	+	2.14693i	0.218769	+	0.0796253i	0.449079	−	0.893492i	$-0.351752\pi$
$727$	5.89865	+	2.14693i	0.218769	+	0.0796253i	−0.230311	+	0.973117i	$0.573974\pi$
$728$		0			0
$729$	3.17777	−	26.8123i	0.117695	−	0.993050i
$730$		0			0
$731$	−53.0036	−	19.2917i	−1.96041	−	0.713530i
$732$		0			0
$733$	24.4337	+	20.5023i	0.902481	+	0.757271i	0.970674	−	0.240401i	$-0.0772789\pi$
$733$	24.4337	+	20.5023i	0.902481	+	0.757271i	−0.0681930	+	0.997672i	$0.521723\pi$
$734$		0			0
$735$	1.32164	+	0.141862i	0.0487496	+	0.00523265i
$736$		0			0
$737$	1.07887	+	1.86867i	0.0397409	+	0.0688332i
$738$		0			0
$739$	−17.0345	+	29.5046i	−0.626624	+	1.08534i	0.361600	+	0.932333i	$0.382230\pi$
$739$	−17.0345	+	29.5046i	−0.626624	+	1.08534i	−0.988224	+	0.153011i	$0.951103\pi$
$740$		0			0
$741$	−53.9492	−	26.4604i	−1.98187	−	0.972047i
$742$		0			0
$743$	25.8288	−	9.40090i	0.947565	−	0.344886i	0.178416	−	0.983955i	$-0.442903\pi$
$743$	25.8288	−	9.40090i	0.947565	−	0.344886i	0.769149	+	0.639070i	$0.220680\pi$
$744$		0			0
$745$	6.60225	+	37.4432i	0.241888	+	1.37181i
$746$		0			0
$747$	−29.9295	+	4.07161i	−1.09506	+	0.148972i
$748$		0			0
$749$	−7.30470	+	6.12937i	−0.266908	+	0.223962i
$750$		0			0
$751$	−5.81665	+	32.9879i	−0.212253	+	1.20375i	0.673358	+	0.739317i	$0.264851\pi$
$751$	−5.81665	+	32.9879i	−0.212253	+	1.20375i	−0.885611	+	0.464428i	$0.846260\pi$
$752$		0			0
$753$	−21.8111	−	22.6861i	−0.794841	−	0.826727i
$754$		0			0
$755$	−21.3422			−0.776724
$756$		0			0
$757$	7.54003			0.274047			0.137023	−	0.990568i	$-0.456246\pi$
$757$	7.54003			0.274047			0.137023	+	0.990568i	$0.456246\pi$
$758$		0			0
$759$	9.56244	−	33.0724i	0.347094	−	1.20045i
$760$		0			0
$761$	7.68694	−	43.5948i	0.278651	−	1.58031i	−0.448468	−	0.893799i	$-0.648030\pi$
$761$	7.68694	−	43.5948i	0.278651	−	1.58031i	0.727119	−	0.686511i	$-0.240859\pi$
$762$		0			0
$763$	−30.4509	+	25.5513i	−1.10240	+	0.925021i
$764$		0			0
$765$	−55.5897	−	12.0728i	−2.00985	−	0.436493i
$766$		0			0
$767$	−9.82433	−	55.7165i	−0.354736	−	2.01181i
$768$		0			0
$769$	49.0666	−	17.8588i	1.76939	−	0.644004i	0.769401	−	0.638767i	$-0.220555\pi$
$769$	49.0666	−	17.8588i	1.76939	−	0.644004i	0.999986	−	0.00523747i	$-0.00166714\pi$
$770$		0			0
$771$	−19.3308	+	12.9768i	−0.696182	+	0.467348i
$772$		0			0
$773$	4.32470	−	7.49061i	0.155549	−	0.269418i	−0.777710	−	0.628623i	$-0.783619\pi$
$773$	4.32470	−	7.49061i	0.155549	−	0.269418i	0.933259	+	0.359205i	$0.116952\pi$
$774$		0			0
$775$	−20.9659	−	36.3141i	−0.753119	−	1.30444i
$776$		0			0
$777$	5.74931	+	12.9903i	0.206255	+	0.466024i
$778$		0			0
$779$	−22.4167	−	18.8098i	−0.803161	−	0.673932i
$780$		0			0
$781$	−17.7482	−	6.45983i	−0.635081	−	0.231151i
$782$		0			0
$783$	−9.95825	+	3.94686i	−0.355879	+	0.141049i
$784$		0			0
$785$	−28.7352	−	10.4588i	−1.02560	−	0.373289i
$786$		0			0
$787$	19.4595	+	16.3285i	0.693657	+	0.582047i	0.919961	−	0.392010i	$-0.128220\pi$
$787$	19.4595	+	16.3285i	0.693657	+	0.582047i	−0.226304	+	0.974057i	$0.572664\pi$
$788$		0			0
$789$	14.0593	−	19.2614i	0.500526	−	0.685725i
$790$		0			0
$791$	20.5377	+	35.5723i	0.730235	+	1.26480i
$792$		0			0
$793$	2.41066	−	4.17538i	0.0856049	−	0.148272i
$794$		0			0
$795$	−3.28624	−	48.5354i	−0.116551	−	1.72137i
$796$		0			0
$797$	15.9926	−	5.82083i	0.566487	−	0.206184i	−0.0428697	−	0.999081i	$-0.513650\pi$
$797$	15.9926	−	5.82083i	0.566487	−	0.206184i	0.609357	+	0.792896i	$0.291428\pi$
$798$		0			0
$799$	−5.29463	−	30.0274i	−0.187311	−	1.06229i
$800$		0			0
$801$	7.11742	+	4.49129i	0.251482	+	0.158692i
$802$		0			0
$803$	−28.1346	+	23.6077i	−0.992848	+	0.833098i
$804$		0			0
$805$	−9.35905	+	53.0778i	−0.329863	+	1.87075i
$806$		0			0
$807$	−15.1663	+	3.74583i	−0.533878	+	0.131859i
$808$		0			0
$809$	−17.0805			−0.600518			−0.300259	−	0.953858i	$-0.597073\pi$
$809$	−17.0805			−0.600518			−0.300259	+	0.953858i	$0.597073\pi$
$810$		0			0
$811$	−42.6593			−1.49797			−0.748986	−	0.662586i	$-0.769459\pi$
$811$	−42.6593			−1.49797			−0.748986	+	0.662586i	$0.769459\pi$
$812$		0			0
$813$	−2.44966	+	0.605026i	−0.0859133	+	0.0212192i
$814$		0			0
$815$	−6.31046	+	35.7884i	−0.221046	+	1.25361i
$816$		0			0
$817$	46.9966	−	39.4348i	1.64420	−	1.37965i
$818$		0			0
$819$	1.73566	−	44.1159i	0.0606489	−	1.54154i
$820$		0			0
$821$	0.591469	+	3.35439i	0.0206424	+	0.117069i	0.993388	−	0.114807i	$-0.0366249\pi$
$821$	0.591469	+	3.35439i	0.0206424	+	0.117069i	−0.972745	+	0.231876i	$0.925514\pi$
$822$		0			0
$823$	−31.4685	+	11.4536i	−1.09692	+	0.399247i	−0.826181	−	0.563405i	$-0.809491\pi$
$823$	−31.4685	+	11.4536i	−1.09692	+	0.399247i	−0.270741	+	0.962652i	$0.587269\pi$
$824$		0			0
$825$	2.10583	+	31.1015i	0.0733155	+	1.08282i
$826$		0			0
$827$	16.4421	−	28.4785i	0.571747	−	0.990294i	−0.424640	−	0.905362i	$-0.639599\pi$
$827$	16.4421	−	28.4785i	0.571747	−	0.990294i	0.996387	−	0.0849320i	$-0.0270673\pi$
$828$		0			0
$829$	12.8827	+	22.3135i	0.447434	+	0.774978i	0.998218	−	0.0596693i	$-0.0190046\pi$
$829$	12.8827	+	22.3135i	0.447434	+	0.774978i	−0.550784	+	0.834648i	$0.685671\pi$
$830$		0			0
$831$	4.09852	−	5.61501i	0.142176	−	0.194783i
$832$		0			0
$833$	1.05383	+	0.884267i	0.0365130	+	0.0306380i
$834$		0			0
$835$	−38.2126	−	13.9082i	−1.32240	−	0.481315i
$836$		0			0
$837$	39.0452	−	1.10458i	1.34960	−	0.0381798i
$838$		0			0
$839$	−9.03050	−	3.28683i	−0.311767	−	0.113474i	0.181398	−	0.983410i	$-0.441938\pi$
$839$	−9.03050	−	3.28683i	−0.311767	−	0.113474i	−0.493165	+	0.869936i	$0.664160\pi$
$840$		0			0
$841$	−18.9598	−	15.9091i	−0.653785	−	0.548590i
$842$		0			0
$843$	−14.7721	−	33.3769i	−0.508779	−	1.14956i
$844$		0			0
$845$	27.5335	+	47.6894i	0.947181	+	1.64057i
$846$		0			0
$847$	0.793282	−	1.37400i	0.0272575	−	0.0472114i
$848$		0			0
$849$	−31.6485	+	21.2456i	−1.08617	+	0.729149i
$850$		0			0
$851$	−17.6502	+	6.42415i	−0.605041	+	0.220217i
$852$		0			0
$853$	9.01467	+	51.1248i	0.308657	+	1.75048i	0.605773	+	0.795637i	$0.292864\pi$
$853$	9.01467	+	51.1248i	0.308657	+	1.75048i	−0.297117	+	0.954841i	$0.596025\pi$
$854$		0			0
$855$	41.6032	−	45.7967i	1.42280	−	1.56621i
$856$		0			0
$857$	7.34872	−	6.16631i	0.251028	−	0.210637i	−0.508587	−	0.861011i	$-0.669832\pi$
$857$	7.34872	−	6.16631i	0.251028	−	0.210637i	0.759615	+	0.650373i	$0.225388\pi$
$858$		0			0
$859$	−5.78620	+	32.8151i	−0.197422	+	1.11964i	0.711504	+	0.702682i	$0.248014\pi$
$859$	−5.78620	+	32.8151i	−0.197422	+	1.11964i	−0.908927	+	0.416956i	$0.863097\pi$
$860$		0			0
$861$	5.97206	−	20.6548i	0.203527	−	0.703913i
$862$		0			0
$863$	44.0499			1.49948			0.749738	−	0.661735i	$-0.230180\pi$
$863$	44.0499			1.49948			0.749738	+	0.661735i	$0.230180\pi$
$864$		0			0
$865$	33.9747			1.15517
$866$		0			0
$867$	−20.3957	−	21.2139i	−0.692675	−	0.720462i
$868$		0			0
$869$	−3.58865	+	20.3523i	−0.121737	+	0.690404i
$870$		0			0
$871$	−2.80277	+	2.35180i	−0.0949683	+	0.0796878i
$872$		0			0
$873$	−15.5689	−	20.1097i	−0.526926	−	0.680609i
$874$		0			0
$875$	−0.878231	−	4.98070i	−0.0296896	−	0.168378i
$876$		0			0
$877$	−18.1318	+	6.59944i	−0.612267	+	0.222847i	−0.629495	−	0.777004i	$-0.716738\pi$
$877$	−18.1318	+	6.59944i	−0.612267	+	0.222847i	0.0172276	+	0.999852i	$0.494516\pi$
$878$		0			0
$879$	−42.0073	−	20.6033i	−1.41687	−	0.694932i
$880$		0			0
$881$	−7.27852	+	12.6068i	−0.245219	+	0.424733i	−0.962193	−	0.272368i	$-0.912193\pi$
$881$	−7.27852	+	12.6068i	−0.245219	+	0.424733i	0.716974	+	0.697100i	$0.245527\pi$
$882$		0			0
$883$	−11.4464	−	19.8257i	−0.385202	−	0.667189i	0.606595	−	0.795011i	$-0.292535\pi$
$883$	−11.4464	−	19.8257i	−0.385202	−	0.667189i	−0.991797	+	0.127822i	$0.959202\pi$
$884$		0			0
$885$	57.9225	+	6.21724i	1.94704	+	0.208990i
$886$		0			0
$887$	−24.1934	−	20.3007i	−0.812334	−	0.681629i	0.138829	−	0.990316i	$-0.455666\pi$
$887$	−24.1934	−	20.3007i	−0.812334	−	0.681629i	−0.951164	+	0.308687i	$0.900110\pi$
$888$		0			0
$889$	−38.2187	−	13.9105i	−1.28181	−	0.466542i
$890$		0			0
$891$	−26.4225	−	12.0448i	−0.885187	−	0.403516i
$892$		0			0
$893$	31.1634	+	11.3425i	1.04284	+	0.379564i
$894$		0			0
$895$	28.6457	+	24.0366i	0.957521	+	0.803455i
$896$		0			0
$897$	58.0424	+	6.23011i	1.93798	+	0.208017i
$898$		0			0
$899$	−7.74843	−	13.4207i	−0.258425	−	0.447605i
$900$		0			0
$901$	25.1730	−	43.6009i	0.838635	−	1.45256i
$902$		0			0
$903$	40.4708	+	19.8497i	1.34678	+	0.660555i
$904$		0			0
$905$	−39.2193	+	14.2747i	−1.30370	+	0.474506i
$906$		0			0
$907$	−5.80643	−	32.9299i	−0.192799	−	1.09342i	−0.915518	−	0.402277i	$-0.868219\pi$
$907$	−5.80643	−	32.9299i	−0.192799	−	1.09342i	0.722718	−	0.691143i	$-0.242892\pi$
$908$		0			0
$909$	1.12206	−	2.74227i	0.0372164	−	0.0909553i
$910$		0			0
$911$	−8.58327	+	7.20222i	−0.284376	+	0.238620i	−0.773806	−	0.633423i	$-0.781649\pi$
$911$	−8.58327	+	7.20222i	−0.284376	+	0.238620i	0.489430	+	0.872043i	$0.337205\pi$
$912$		0			0
$913$	−5.64104	+	31.9920i	−0.186691	+	1.05878i
$914$		0			0
$915$	3.44067	+	3.57870i	0.113745	+	0.118308i
$916$		0			0
$917$	12.4338			0.410600
$918$		0			0
$919$	8.04947			0.265527			0.132764	−	0.991148i	$-0.457615\pi$
$919$	8.04947			0.265527			0.132764	+	0.991148i	$0.457615\pi$
$920$		0			0
$921$	−4.63255	+	16.0220i	−0.152648	+	0.527944i
$922$		0			0
$923$	5.56125	−	31.5394i	0.183051	−	1.03813i
$924$		0			0
$925$	13.0285	−	10.9322i	0.428373	−	0.359448i
$926$		0			0
$927$	8.69100	+	27.1556i	0.285450	+	0.891908i
$928$		0			0
$929$	−2.72177	−	15.4359i	−0.0892985	−	0.506437i	−0.996346	−	0.0854086i	$-0.972780\pi$
$929$	−2.72177	−	15.4359i	−0.0892985	−	0.506437i	0.907048	−	0.421028i	$-0.138331\pi$
$930$		0			0
$931$	−1.40603	+	0.511753i	−0.0460808	+	0.0167720i
$932$		0			0
$933$	0.328066	−	0.220231i	0.0107404	−	0.00721003i
$934$		0			0
$935$	−30.5901	+	52.9836i	−1.00040	+	1.73275i
$936$		0			0
$937$	−28.6918	−	49.6956i	−0.937320	−	1.62349i	−0.770444	−	0.637508i	$-0.779965\pi$
$937$	−28.6918	−	49.6956i	−0.937320	−	1.62349i	−0.166876	−	0.985978i	$-0.553368\pi$
$938$		0			0
$939$	20.9027	+	47.2287i	0.682134	+	1.54125i
$940$		0			0
$941$	42.8893	+	35.9884i	1.39815	+	1.17319i	0.961913	+	0.273355i	$0.0881333\pi$
$941$	42.8893	+	35.9884i	1.39815	+	1.17319i	0.436236	+	0.899832i	$0.356311\pi$
$942$		0			0
$943$	26.7142	+	9.72317i	0.869934	+	0.316630i
$944$		0			0
$945$	43.1414	+	14.3341i	1.40339	+	0.466290i
$946$		0			0
$947$	4.45385	+	1.62107i	0.144731	+	0.0526776i	0.413370	−	0.910563i	$-0.364352\pi$
$947$	4.45385	+	1.62107i	0.144731	+	0.0526776i	−0.268639	+	0.963241i	$0.586574\pi$
$948$		0			0
$949$	−47.7060	−	40.0301i	−1.54860	−	1.29943i
$950$		0			0
$951$	−7.97684	+	10.9283i	−0.258667	+	0.354376i
$952$		0			0
$953$	−11.0214	−	19.0896i	−0.357018	−	0.618373i	0.630443	−	0.776235i	$-0.282873\pi$
$953$	−11.0214	−	19.0896i	−0.357018	−	0.618373i	−0.987461	+	0.157862i	$0.949540\pi$
$954$		0			0
$955$	30.9270	−	53.5672i	1.00078	−	1.73339i
$956$		0			0
$957$	0.778256	+	11.4943i	0.0251574	+	0.371557i
$958$		0			0
$959$	−1.59561	+	0.580753i	−0.0515248	+	0.0187535i
$960$		0			0
$961$	4.42964	+	25.1217i	0.142892	+	0.810378i
$962$		0			0
$963$	−9.41177	+	4.95113i	−0.303290	+	0.159548i
$964$		0			0
$965$	12.7149	−	10.6691i	0.409307	−	0.343449i
$966$		0			0
$967$	−3.57065	+	20.2502i	−0.114824	+	0.651202i	0.872012	+	0.489484i	$0.162815\pi$
$967$	−3.57065	+	20.2502i	−0.114824	+	0.651202i	−0.986837	+	0.161718i	$0.948296\pi$
$968$		0			0
$969$	62.1658	−	15.3539i	1.99705	−	0.493240i
$970$		0			0
$971$	14.6328			0.469590			0.234795	−	0.972045i	$-0.424558\pi$
$971$	14.6328			0.469590			0.234795	+	0.972045i	$0.424558\pi$
$972$		0			0
$973$	−48.1948			−1.54506
$974$		0			0
$975$	−51.3156	+	12.6741i	−1.64341	+	0.405897i
$976$		0			0
$977$	7.78445	−	44.1478i	0.249047	−	1.41241i	−0.561857	−	0.827234i	$-0.689913\pi$
$977$	7.78445	−	44.1478i	0.249047	−	1.41241i	0.810904	−	0.585180i	$-0.198976\pi$
$978$		0			0
$979$	6.93376	−	5.81812i	0.221604	−	0.185948i
$980$		0			0
$981$	−39.2346	+	20.6396i	−1.25266	+	0.658973i
$982$		0			0
$983$	−4.65731	−	26.4129i	−0.148545	−	0.842442i	−0.964452	−	0.264258i	$-0.914873\pi$
$983$	−4.65731	−	26.4129i	−0.148545	−	0.842442i	0.815907	−	0.578184i	$-0.196238\pi$
$984$		0			0
$985$	−30.2754	+	11.0193i	−0.964654	+	0.351105i
$986$		0			0
$987$	1.64606	+	24.3110i	0.0523946	+	0.773829i
$988$		0			0
$989$	−29.8004	+	51.6157i	−0.947596	+	1.64129i
$990$		0			0
$991$	12.9156	+	22.3704i	0.410277	+	0.710620i	0.994920	−	0.100671i	$-0.0320988\pi$
$991$	12.9156	+	22.3704i	0.410277	+	0.710620i	−0.584643	+	0.811291i	$0.698765\pi$
$992$		0			0
$993$	−6.21805	+	8.51879i	−0.197324	+	0.270336i
$994$		0			0
$995$	−24.7389	−	20.7584i	−0.784277	−	0.658087i
$996$		0			0
$997$	6.37253	+	2.31941i	0.201820	+	0.0734565i	0.440952	−	0.897530i	$-0.354641\pi$
$997$	6.37253	+	2.31941i	0.201820	+	0.0734565i	−0.239132	+	0.970987i	$0.576863\pi$
$998$		0			0
$999$	3.19121	+	15.5182i	0.100965	+	0.490975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.193.9	yes	60
4.3	odd	2	inner	864.2.y.d.193.2	✓	60
27.7	even	9	inner	864.2.y.d.385.9	yes	60
108.7	odd	18	inner	864.2.y.d.385.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.193.2	✓	60	4.3	odd	2	inner
864.2.y.d.193.9	yes	60	1.1	even	1	trivial
864.2.y.d.385.2	yes	60	108.7	odd	18	inner
864.2.y.d.385.9	yes	60	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)

\(f(q)\)	\(=\)	\(q+(1.68152 - 0.415309i) q^{3} +(-0.564773 + 3.20298i) q^{5} +(2.06064 - 1.72908i) q^{7} +(2.65504 - 1.39670i) q^{9} +O(q^{10})\)	\(q+(1.68152 - 0.415309i) q^{3} +(-0.564773 + 3.20298i) q^{5} +(2.06064 - 1.72908i) q^{7} +(2.65504 - 1.39670i) q^{9} +(-0.560273 - 3.17747i) q^{11} +(5.14100 - 1.87117i) q^{13} +(0.380550 + 5.62045i) q^{15} +(-2.91506 + 5.04904i) q^{17} +(-3.17060 - 5.49163i) q^{19} +(2.74691 - 3.76329i) q^{21} +(4.71915 + 3.95984i) q^{23} +(-5.24168 - 1.90782i) q^{25} +(3.88444 - 3.45125i) q^{27} +(-1.93718 - 0.705076i) q^{29} +(5.75856 + 4.83200i) q^{31} +(-2.26174 - 5.11029i) q^{33} +(4.37443 + 7.57674i) q^{35} +(-1.52449 + 2.64049i) q^{37} +(7.86760 - 5.28152i) q^{39} +(4.33643 - 1.57833i) q^{41} +(1.68001 + 9.52781i) q^{43} +(2.97413 + 9.29286i) q^{45} +(-4.00629 + 3.36167i) q^{47} +(0.0409740 - 0.232375i) q^{49} +(-2.80483 + 9.70072i) q^{51} -8.63550 q^{53} +10.4938 q^{55} +(-7.61215 - 7.91753i) q^{57} +(1.79573 - 10.1841i) q^{59} +(0.675083 - 0.566462i) q^{61} +(3.05606 - 7.46888i) q^{63} +(3.08984 + 17.5233i) q^{65} +(-0.628431 + 0.228730i) q^{67} +(9.57991 + 4.69865i) q^{69} +(2.92691 - 5.06956i) q^{71} +(-5.69150 - 9.85797i) q^{73} +(-9.60634 - 1.03112i) q^{75} +(-6.64862 - 5.57885i) q^{77} +(-6.01891 - 2.19070i) q^{79} +(5.09844 - 7.41660i) q^{81} +(-9.46119 - 3.44359i) q^{83} +(-14.5256 - 12.1885i) q^{85} +(-3.55024 - 0.381073i) q^{87} +(1.40267 + 2.42950i) q^{89} +(7.35835 - 12.7450i) q^{91} +(11.6899 + 5.73354i) q^{93} +(19.3803 - 7.05385i) q^{95} +(-1.47207 - 8.34855i) q^{97} +(-5.92552 - 7.65375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 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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