LMFDB - Embedded newform 864.2.bh.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(47,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([9, 9, 7]))

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

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

chi := DirichletCharacter("864.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not 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:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67094 + 0.456011i) q^{3} +(-0.197395 - 1.11948i) q^{5} +(-1.00340 + 1.19580i) q^{7} +(2.58411 - 1.52394i) q^{9} +O(q^{10})$	\(q+(-1.67094 + 0.456011i) q^{3} +(-0.197395 - 1.11948i) q^{5} +(-1.00340 + 1.19580i) q^{7} +(2.58411 - 1.52394i) q^{9} +(0.304741 + 0.0537341i) q^{11} +(0.0478254 - 0.131399i) q^{13} +(0.840330 + 1.78057i) q^{15} +(-2.89584 + 1.67191i) q^{17} +(0.937333 - 1.62351i) q^{19} +(1.13132 - 2.45568i) q^{21} +(-4.72416 + 3.96404i) q^{23} +(3.48419 - 1.26814i) q^{25} +(-3.62297 + 3.72479i) q^{27} +(0.806245 - 0.293449i) q^{29} +(-0.162969 - 0.194219i) q^{31} +(-0.533709 + 0.0491786i) q^{33} +(1.53674 + 0.887239i) q^{35} +(-9.26703 + 5.35032i) q^{37} +(-0.0199941 + 0.241370i) q^{39} +(-3.34464 + 9.18932i) q^{41} +(-0.802030 + 4.54854i) q^{43} +(-2.21611 - 2.59204i) q^{45} +(-9.23039 - 7.74522i) q^{47} +(0.792399 + 4.49392i) q^{49} +(4.07638 - 4.11421i) q^{51} -10.1436 q^{53} -0.351759i q^{55} +(-0.825894 + 3.14023i) q^{57} +(1.10869 - 0.195492i) q^{59} +(-5.61288 + 6.68916i) q^{61} +(-0.770561 + 4.61920i) q^{63} +(-0.156539 - 0.0276021i) q^{65} +(7.44174 + 2.70857i) q^{67} +(6.08617 - 8.77796i) q^{69} +(-5.94039 - 10.2891i) q^{71} +(-4.13874 + 7.16851i) q^{73} +(-5.24360 + 3.70782i) q^{75} +(-0.370032 + 0.310494i) q^{77} +(3.74203 + 10.2812i) q^{79} +(4.35523 - 7.87604i) q^{81} +(-2.59854 - 7.13944i) q^{83} +(2.44330 + 2.91181i) q^{85} +(-1.21337 + 0.857993i) q^{87} +(-2.72824 - 1.57515i) q^{89} +(0.109140 + 0.189035i) q^{91} +(0.360878 + 0.250213i) q^{93} +(-2.00251 - 0.728854i) q^{95} +(2.85712 - 16.2036i) q^{97} +(0.869372 - 0.325552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) $ 192 * q + 12 * q^3 - 12 * q^9	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.67094	+	0.456011i	−0.964720	+	0.263278i
$3$	−1.67094	+	0.456011i	−0.964720	+	0.263278i
$4$		0			0
$5$	−0.197395	−	1.11948i	−0.0882775	−	0.500647i	−0.996601	−	0.0823785i	$-0.973748\pi$
$5$	−0.197395	−	1.11948i	−0.0882775	−	0.500647i	0.908324	−	0.418268i	$-0.137363\pi$
$6$		0			0
$7$	−1.00340	+	1.19580i	−0.379249	+	0.451971i	−0.921577	−	0.388196i	$-0.873099\pi$
$7$	−1.00340	+	1.19580i	−0.379249	+	0.451971i	0.542328	+	0.840167i	$0.317543\pi$
$8$		0			0
$9$	2.58411	−	1.52394i	0.861370	−	0.507979i
$10$		0			0
$11$	0.304741	+	0.0537341i	0.0918830	+	0.0162014i	0.219401	−	0.975635i	$-0.429590\pi$
$11$	0.304741	+	0.0537341i	0.0918830	+	0.0162014i	−0.127518	+	0.991836i	$0.540701\pi$
$12$		0			0
$13$	0.0478254	−	0.131399i	0.0132644	−	0.0364436i	−0.932884	−	0.360178i	$-0.882716\pi$
$13$	0.0478254	−	0.131399i	0.0132644	−	0.0364436i	0.946148	+	0.323734i	$0.104938\pi$
$14$		0			0
$15$	0.840330	+	1.78057i	0.216972	+	0.459742i
$16$		0			0
$17$	−2.89584	+	1.67191i	−0.702344	+	0.405499i	−0.808220	−	0.588881i	$-0.799569\pi$
$17$	−2.89584	+	1.67191i	−0.702344	+	0.405499i	0.105876	+	0.994379i	$0.466235\pi$
$18$		0			0
$19$	0.937333	−	1.62351i	0.215039	−	0.372458i	−0.738246	−	0.674532i	$-0.764345\pi$
$19$	0.937333	−	1.62351i	0.215039	−	0.372458i	0.953285	+	0.302073i	$0.0976788\pi$
$20$		0			0
$21$	1.13132	−	2.45568i	0.246875	−	0.535874i
$22$		0			0
$23$	−4.72416	+	3.96404i	−0.985056	+	0.826560i	−0.984844	−	0.173440i	$-0.944512\pi$
$23$	−4.72416	+	3.96404i	−0.985056	+	0.826560i	−0.000211529		1.00000i	$0.500067\pi$
$24$		0			0
$25$	3.48419	−	1.26814i	0.696838	−	0.253628i
$26$		0			0
$27$	−3.62297	+	3.72479i	−0.697241	+	0.716837i
$28$		0			0
$29$	0.806245	−	0.293449i	0.149716	−	0.0544921i	−0.266075	−	0.963952i	$-0.585727\pi$
$29$	0.806245	−	0.293449i	0.149716	−	0.0544921i	0.415791	+	0.909460i	$0.363505\pi$
$30$		0			0
$31$	−0.162969	−	0.194219i	−0.0292701	−	0.0348827i	0.751211	−	0.660062i	$-0.229470\pi$
$31$	−0.162969	−	0.194219i	−0.0292701	−	0.0348827i	−0.780481	+	0.625180i	$0.785026\pi$
$32$		0			0
$33$	−0.533709	+	0.0491786i	−0.0929068	+	0.00856090i
$34$		0			0
$35$	1.53674	+	0.887239i	0.259757	+	0.149971i
$36$		0			0
$37$	−9.26703	+	5.35032i	−1.52349	+	0.879587i	−0.523876	+	0.851794i	$0.675515\pi$
$37$	−9.26703	+	5.35032i	−1.52349	+	0.879587i	−0.999614	+	0.0277929i	$0.991152\pi$
$38$		0			0
$39$	−0.0199941	+	0.241370i	−0.00320162	+	0.0386501i
$40$		0			0
$41$	−3.34464	+	9.18932i	−0.522345	+	1.43513i	0.345559	+	0.938397i	$0.387689\pi$
$41$	−3.34464	+	9.18932i	−0.522345	+	1.43513i	−0.867903	+	0.496733i	$0.834533\pi$
$42$		0			0
$43$	−0.802030	+	4.54854i	−0.122308	+	0.693645i	0.860562	+	0.509346i	$0.170113\pi$
$43$	−0.802030	+	4.54854i	−0.122308	+	0.693645i	−0.982870	+	0.184299i	$0.940998\pi$
$44$		0			0
$45$	−2.21611	−	2.59204i	−0.330357	−	0.386399i
$46$		0			0
$47$	−9.23039	−	7.74522i	−1.34639	−	1.12976i	−0.979934	−	0.199322i	$-0.936126\pi$
$47$	−9.23039	−	7.74522i	−1.34639	−	1.12976i	−0.366457	−	0.930435i	$-0.619429\pi$
$48$		0			0
$49$	0.792399	+	4.49392i	0.113200	+	0.641989i
$50$		0			0
$51$	4.07638	−	4.11421i	0.570807	−	0.576104i
$52$		0			0
$53$	−10.1436			−1.39333			−0.696666	−	0.717396i	$-0.745334\pi$
$53$	−10.1436			−1.39333			−0.696666	+	0.717396i	$0.745334\pi$
$54$		0			0
$55$		−	0.351759i		−	0.0474311i
$56$		0			0
$57$	−0.825894	+	3.14023i	−0.109392	+	0.415933i
$58$		0			0
$59$	1.10869	−	0.195492i	0.144339	−	0.0254508i	−0.101012	−	0.994885i	$-0.532208\pi$
$59$	1.10869	−	0.195492i	0.144339	−	0.0254508i	0.245351	+	0.969434i	$0.421097\pi$
$60$		0			0
$61$	−5.61288	+	6.68916i	−0.718655	+	0.856460i	−0.994499	−	0.104743i	$-0.966598\pi$
$61$	−5.61288	+	6.68916i	−0.718655	+	0.856460i	0.275844	+	0.961202i	$0.411043\pi$
$62$		0			0
$63$	−0.770561	+	4.61920i	−0.0970816	+	0.581965i
$64$		0			0
$65$	−0.156539	−	0.0276021i	−0.0194163	−	0.00342362i
$66$		0			0
$67$	7.44174	+	2.70857i	0.909153	+	0.330905i	0.753915	−	0.656972i	$-0.228163\pi$
$67$	7.44174	+	2.70857i	0.909153	+	0.330905i	0.155239	+	0.987877i	$0.450385\pi$
$68$		0			0
$69$	6.08617	−	8.77796i	0.732688	−	1.05674i
$70$		0			0
$71$	−5.94039	−	10.2891i	−0.704994	−	1.22109i	−0.966694	−	0.255936i	$-0.917616\pi$
$71$	−5.94039	−	10.2891i	−0.704994	−	1.22109i	0.261699	−	0.965149i	$-0.415717\pi$
$72$		0			0
$73$	−4.13874	+	7.16851i	−0.484403	+	0.839010i	−0.999839	−	0.0179175i	$-0.994296\pi$
$73$	−4.13874	+	7.16851i	−0.484403	+	0.839010i	0.515437	+	0.856928i	$0.327630\pi$
$74$		0			0
$75$	−5.24360	+	3.70782i	−0.605479	+	0.428143i
$76$		0			0
$77$	−0.370032	+	0.310494i	−0.0421691	+	0.0353841i
$78$		0			0
$79$	3.74203	+	10.2812i	0.421012	+	1.15672i	0.951129	+	0.308795i	$0.0999258\pi$
$79$	3.74203	+	10.2812i	0.421012	+	1.15672i	−0.530117	+	0.847925i	$0.677852\pi$
$80$		0			0
$81$	4.35523	−	7.87604i	0.483915	−	0.875115i
$82$		0			0
$83$	−2.59854	−	7.13944i	−0.285227	−	0.783656i	−0.996717	−	0.0809595i	$-0.974202\pi$
$83$	−2.59854	−	7.13944i	−0.285227	−	0.783656i	0.711490	−	0.702696i	$-0.248021\pi$
$84$		0			0
$85$	2.44330	+	2.91181i	0.265013	+	0.315830i
$86$		0			0
$87$	−1.21337	+	0.857993i	−0.130087	+	0.0919865i
$88$		0			0
$89$	−2.72824	−	1.57515i	−0.289193	−	0.166966i	0.348385	−	0.937352i	$-0.386730\pi$
$89$	−2.72824	−	1.57515i	−0.289193	−	0.166966i	−0.637578	+	0.770386i	$0.720064\pi$
$90$		0			0
$91$	0.109140	+	0.189035i	0.0114409	+	0.0198163i
$92$		0			0
$93$	0.360878	+	0.250213i	0.0374213	+	0.0259459i
$94$		0			0
$95$	−2.00251	−	0.728854i	−0.205453	−	0.0747788i
$96$		0			0
$97$	2.85712	−	16.2036i	0.290097	−	1.64522i	−0.396392	−	0.918081i	$-0.629738\pi$
$97$	2.85712	−	16.2036i	0.290097	−	1.64522i	0.686489	−	0.727140i	$-0.259151\pi$
$98$		0			0
$99$	0.869372	−	0.325552i	0.0873752	−	0.0327192i
$100$		0			0
$101$	7.25512	+	6.08777i	0.721912	+	0.605756i	0.927913	−	0.372796i	$-0.121601\pi$
$101$	7.25512	+	6.08777i	0.721912	+	0.605756i	−0.206002	+	0.978552i	$0.566045\pi$
$102$		0			0
$103$	0.169891	−	0.0299564i	0.0167399	−	0.00295169i	−0.165272	−	0.986248i	$-0.552850\pi$
$103$	0.169891	−	0.0299564i	0.0167399	−	0.00295169i	0.182012	+	0.983296i	$0.441739\pi$
$104$		0			0
$105$	−2.97240	−	0.781756i	−0.290077	−	0.0762915i
$106$		0			0
$107$			17.1176i			1.65482i	0.561600	+	0.827409i	$0.310186\pi$
$107$			17.1176i			1.65482i	−0.561600	+	0.827409i	$0.689814\pi$
$108$		0			0
$109$			10.2745i			0.984122i	0.870561	+	0.492061i	$0.163756\pi$
$109$			10.2745i			0.984122i	−0.870561	+	0.492061i	$0.836244\pi$
$110$		0			0
$111$	13.0449	−	13.1660i	1.23817	−	1.24966i
$112$		0			0
$113$	5.74068	−	1.01224i	0.540038	−	0.0952232i	0.103025	−	0.994679i	$-0.467148\pi$
$113$	5.74068	−	1.01224i	0.540038	−	0.0952232i	0.437012	+	0.899456i	$0.356037\pi$
$114$		0			0
$115$	5.37019	+	4.50612i	0.500773	+	0.420198i
$116$		0			0
$117$	−0.0766580	−	0.412433i	−0.00708704	−	0.0381294i
$118$		0			0
$119$	0.906400	−	5.14045i	0.0830895	−	0.471224i
$120$		0			0
$121$	−10.2466	−	3.72947i	−0.931513	−	0.339043i
$122$		0			0
$123$	1.39828	−	16.8800i	0.126078	−	1.52202i
$124$		0			0
$125$	−4.94929	−	8.57243i	−0.442678	−	0.766741i
$126$		0			0
$127$	−5.69723	−	3.28930i	−0.505548	−	0.291878i	0.225454	−	0.974254i	$-0.427613\pi$
$127$	−5.69723	−	3.28930i	−0.505548	−	0.291878i	−0.731002	+	0.682376i	$0.760947\pi$
$128$		0			0
$129$	−0.734034	−	7.96608i	−0.0646281	−	0.701374i
$130$		0			0
$131$	−5.20185	−	6.19932i	−0.454487	−	0.541637i	0.489332	−	0.872097i	$-0.337240\pi$
$131$	−5.20185	−	6.19932i	−0.454487	−	0.541637i	−0.943820	+	0.330460i	$0.892796\pi$
$132$		0			0
$133$	1.00088	+	2.74989i	0.0867872	+	0.238446i
$134$		0			0
$135$	4.88499	+	3.32059i	0.420433	+	0.285791i
$136$		0			0
$137$	0.597670	+	1.64209i	0.0510624	+	0.140293i	0.962602	−	0.270919i	$-0.0873277\pi$
$137$	0.597670	+	1.64209i	0.0510624	+	0.140293i	−0.911540	+	0.411212i	$0.865105\pi$
$138$		0			0
$139$	−3.96803	+	3.32957i	−0.336564	+	0.282411i	−0.795368	−	0.606127i	$-0.792722\pi$
$139$	−3.96803	+	3.32957i	−0.336564	+	0.282411i	0.458804	+	0.888537i	$0.348278\pi$
$140$		0			0
$141$	18.9554	+	8.73267i	1.59633	+	0.735424i
$142$		0			0
$143$	0.0216350	−	0.0374729i	0.00180921	−	0.00313364i
$144$		0			0
$145$	−0.487659	−	0.844649i	−0.0404978	−	0.0701443i
$146$		0			0
$147$	−3.37333	−	7.14775i	−0.278228	−	0.589536i
$148$		0			0
$149$	−3.11540	−	1.13391i	−0.255223	−	0.0928937i	0.211240	−	0.977434i	$-0.432250\pi$
$149$	−3.11540	−	1.13391i	−0.255223	−	0.0928937i	−0.466463	+	0.884541i	$0.654472\pi$
$150$		0			0
$151$	20.7577	+	3.66015i	1.68924	+	0.297858i	0.933916	−	0.357494i	$-0.116369\pi$
$151$	20.7577	+	3.66015i	1.68924	+	0.297858i	0.755323	+	0.655352i	$0.227480\pi$
$152$		0			0
$153$	−4.93527	+	8.73348i	−0.398993	+	0.706060i
$154$		0			0
$155$	−0.185255	+	0.220778i	−0.0148800	+	0.0177333i
$156$		0			0
$157$	14.3727	−	2.53429i	1.14706	−	0.202258i	0.432371	−	0.901696i	$-0.357677\pi$
$157$	14.3727	−	2.53429i	1.14706	−	0.202258i	0.714694	+	0.699437i	$0.246566\pi$
$158$		0			0
$159$	16.9494	−	4.62559i	1.34417	−	0.366833i
$160$		0			0
$161$		−	9.62668i		−	0.758689i
$162$		0			0
$163$	14.0341			1.09924			0.549618	−	0.835416i	$-0.314773\pi$
$163$	14.0341			1.09924			0.549618	+	0.835416i	$0.314773\pi$
$164$		0			0
$165$	0.160406	+	0.587769i	0.0124876	+	0.0457578i
$166$		0			0
$167$	1.95599	+	11.0930i	0.151359	+	0.858402i	0.962039	+	0.272912i	$0.0879867\pi$
$167$	1.95599	+	11.0930i	0.151359	+	0.858402i	−0.810680	+	0.585490i	$0.800902\pi$
$168$		0			0
$169$	9.94360	+	8.34367i	0.764892	+	0.641821i
$170$		0			0
$171$	−0.0519539	−	5.62376i	−0.00397301	−	0.430060i
$172$		0			0
$173$	1.82380	−	10.3433i	0.138661	−	0.786385i	−0.833579	−	0.552400i	$-0.813712\pi$
$173$	1.82380	−	10.3433i	0.138661	−	0.786385i	0.972240	−	0.233985i	$-0.0751767\pi$
$174$		0			0
$175$	−1.97958	+	5.43886i	−0.149642	+	0.411139i
$176$		0			0
$177$	−1.76341	+	0.832229i	−0.132546	+	0.0625541i
$178$		0			0
$179$	−5.54626	+	3.20213i	−0.414547	+	0.239339i	−0.692741	−	0.721186i	$-0.743597\pi$
$179$	−5.54626	+	3.20213i	−0.414547	+	0.239339i	0.278195	+	0.960525i	$0.410264\pi$
$180$		0			0
$181$	0.729525	+	0.421192i	0.0542252	+	0.0313069i	0.526868	−	0.849947i	$-0.323366\pi$
$181$	0.729525	+	0.421192i	0.0542252	+	0.0313069i	−0.472642	+	0.881254i	$0.656700\pi$
$182$		0			0
$183$	6.32847	−	13.7368i	0.467814	−	1.01545i
$184$		0			0
$185$	7.81884	+	9.31813i	0.574852	+	0.685082i
$186$		0			0
$187$	−0.972321	+	0.353896i	−0.0711031	+	0.0258794i
$188$		0			0
$189$	−0.818841	−	8.06981i	−0.0595619	−	0.586992i
$190$		0			0
$191$	18.2133	−	6.62910i	1.31787	−	0.479665i	0.415094	−	0.909779i	$-0.363749\pi$
$191$	18.2133	−	6.62910i	1.31787	−	0.479665i	0.902775	+	0.430114i	$0.141527\pi$
$192$		0			0
$193$	8.27835	−	6.94636i	0.595888	−	0.500010i	−0.294233	−	0.955734i	$-0.595064\pi$
$193$	8.27835	−	6.94636i	0.595888	−	0.500010i	0.890121	+	0.455724i	$0.150620\pi$
$194$		0			0
$195$	0.274155	−	0.0252620i	0.0196327	−	0.00180905i
$196$		0			0
$197$	6.42195	−	11.1231i	0.457545	−	0.792492i	−0.541285	−	0.840839i	$-0.682062\pi$
$197$	6.42195	−	11.1231i	0.457545	−	0.792492i	0.998831	+	0.0483474i	$0.0153955\pi$
$198$		0			0
$199$	−12.3619	+	7.13715i	−0.876313	+	0.505939i	−0.869441	−	0.494037i	$-0.835521\pi$
$199$	−12.3619	+	7.13715i	−0.876313	+	0.505939i	−0.00687175	+	0.999976i	$0.502187\pi$
$200$		0			0
$201$	−13.6699	−	1.13236i	−0.964198	−	0.0798705i
$202$		0			0
$203$	−0.458077	+	1.25856i	−0.0321507	+	0.0883333i
$204$		0			0
$205$	10.9475	+	1.93033i	0.764604	+	0.134820i
$206$		0			0
$207$	−6.16680	+	17.4428i	−0.428622	+	1.21236i
$208$		0			0
$209$	0.372882	−	0.444384i	0.0257928	−	0.0307387i
$210$		0			0
$211$	−4.92283	−	27.9187i	−0.338901	−	1.92200i	−0.384674	−	0.923053i	$-0.625686\pi$
$211$	−4.92283	−	27.9187i	−0.338901	−	1.92200i	0.0457722	−	0.998952i	$-0.485425\pi$
$212$		0			0
$213$	14.6180	+	14.4836i	1.00161	+	0.992397i
$214$		0			0
$215$	5.25031			0.358068
$216$		0			0
$217$	0.395770			0.0268666
$218$		0			0
$219$	3.64669	−	13.8655i	0.246420	−	0.936942i
$220$		0			0
$221$	0.0811934	+	0.460471i	0.00546166	+	0.0309746i
$222$		0			0
$223$	−11.8309	+	14.0995i	−0.792255	+	0.944173i	−0.999417	−	0.0341339i	$-0.989133\pi$
$223$	−11.8309	+	14.0995i	−0.792255	+	0.944173i	0.207162	+	0.978307i	$0.433577\pi$
$224$		0			0
$225$	7.07096	−	8.58671i	0.471398	−	0.572447i
$226$		0			0
$227$	−6.81639	−	1.20191i	−0.452420	−	0.0797738i	−0.0572047	−	0.998362i	$-0.518219\pi$
$227$	−6.81639	−	1.20191i	−0.452420	−	0.0797738i	−0.395215	+	0.918589i	$0.629330\pi$
$228$		0			0
$229$	9.67163	−	26.5726i	0.639119	−	1.75597i	−0.0153550	−	0.999882i	$-0.504888\pi$
$229$	9.67163	−	26.5726i	0.639119	−	1.75597i	0.654474	−	0.756084i	$-0.272890\pi$
$230$		0			0
$231$	0.476715	−	0.687557i	0.0313655	−	0.0452379i
$232$		0			0
$233$	−10.2324	+	5.90766i	−0.670344	+	0.387024i	−0.796207	−	0.605024i	$-0.793163\pi$
$233$	−10.2324	+	5.90766i	−0.670344	+	0.387024i	0.125863	+	0.992048i	$0.459830\pi$
$234$		0			0
$235$	−6.84859	+	11.8621i	−0.446753	+	0.773798i
$236$		0			0
$237$	−10.9410	−	15.4728i	−0.710697	−	1.00507i
$238$		0			0
$239$	−13.3950	+	11.2397i	−0.866451	+	0.727039i	−0.963348	−	0.268256i	$-0.913553\pi$
$239$	−13.3950	+	11.2397i	−0.866451	+	0.727039i	0.0968965	+	0.995294i	$0.469108\pi$
$240$		0			0
$241$	10.2723	−	3.73881i	0.661697	−	0.240838i	0.0107281	−	0.999942i	$-0.496585\pi$
$241$	10.2723	−	3.73881i	0.661697	−	0.240838i	0.650969	+	0.759104i	$0.274363\pi$
$242$		0			0
$243$	−3.68580	+	15.1464i	−0.236444	+	0.971645i
$244$		0			0
$245$	4.87444	−	1.77415i	0.311416	−	0.113346i
$246$		0			0
$247$	−0.168499	−	0.200810i	−0.0107214	−	0.0127772i
$248$		0			0
$249$	7.59769	+	10.7446i	0.481484	+	0.680914i
$250$		0			0
$251$	−3.98996	−	2.30361i	−0.251844	−	0.145402i	0.368764	−	0.929523i	$-0.379781\pi$
$251$	−3.98996	−	2.30361i	−0.251844	−	0.145402i	−0.620608	+	0.784121i	$0.713114\pi$
$252$		0			0
$253$	−1.65265	+	0.954159i	−0.103901	+	0.0599875i
$254$		0			0
$255$	−5.41043	−	3.75130i	−0.338814	−	0.234915i
$256$		0			0
$257$	5.58655	−	15.3489i	0.348480	−	0.957440i	−0.634370	−	0.773030i	$-0.718740\pi$
$257$	5.58655	−	15.3489i	0.348480	−	0.957440i	0.982849	−	0.184410i	$-0.0590374\pi$
$258$		0			0
$259$	2.90059	−	16.4500i	0.180234	−	1.02216i
$260$		0			0
$261$	1.63623	−	1.98697i	0.101280	−	0.122990i
$262$		0			0
$263$	10.4528	+	8.77094i	0.644547	+	0.540839i	0.905411	−	0.424536i	$-0.139563\pi$
$263$	10.4528	+	8.77094i	0.644547	+	0.540839i	−0.260864	+	0.965376i	$0.584007\pi$
$264$		0			0
$265$	2.00229	+	11.3556i	0.123000	+	0.697567i
$266$		0			0
$267$	5.27702	+	1.38788i	0.322949	+	0.0849370i
$268$		0			0
$269$	−31.1716			−1.90057			−0.950284	−	0.311386i	$-0.899207\pi$
$269$	−31.1716			−1.90057			−0.950284	+	0.311386i	$0.899207\pi$
$270$		0			0
$271$		−	9.88906i		−	0.600718i	−0.953826	−	0.300359i	$-0.902894\pi$
$271$		−	9.88906i		−	0.600718i	0.953826	−	0.300359i	$-0.0971064\pi$
$272$		0			0
$273$	−0.268568	−	0.266099i	−0.0162545	−	0.0161050i
$274$		0			0
$275$	1.12992	−	0.199235i	0.0681367	−	0.0120143i
$276$		0			0
$277$	−12.0526	+	14.3638i	−0.724172	+	0.863034i	−0.995029	−	0.0995853i	$-0.968248\pi$
$277$	−12.0526	+	14.3638i	−0.724172	+	0.863034i	0.270857	+	0.962619i	$0.412693\pi$
$278$		0			0
$279$	−0.717107	−	0.253528i	−0.0429321	−	0.0151783i
$280$		0			0
$281$	−21.7819	−	3.84074i	−1.29940	−	0.229120i	−0.519203	−	0.854651i	$-0.673771\pi$
$281$	−21.7819	−	3.84074i	−1.29940	−	0.229120i	−0.780199	+	0.625531i	$0.784882\pi$
$282$		0			0
$283$	−15.4272	−	5.61504i	−0.917051	−	0.333779i	−0.159987	−	0.987119i	$-0.551145\pi$
$283$	−15.4272	−	5.61504i	−0.917051	−	0.333779i	−0.757065	+	0.653340i	$0.773367\pi$
$284$		0			0
$285$	3.67845	+	0.304708i	0.217892	+	0.0180494i
$286$		0			0
$287$	−7.63261	−	13.2201i	−0.450539	−	0.780356i
$288$		0			0
$289$	−2.90941	+	5.03925i	−0.171142	+	0.296426i
$290$		0			0
$291$	2.61490	+	28.3781i	0.153288	+	1.66355i
$292$		0			0
$293$	−10.6985	+	8.97707i	−0.625011	+	0.524446i	−0.899374	−	0.437180i	$-0.855977\pi$
$293$	−10.6985	+	8.97707i	−0.625011	+	0.524446i	0.274363	+	0.961626i	$0.411533\pi$
$294$		0			0
$295$	−0.437698	−	1.20256i	−0.0254837	−	0.0700160i
$296$		0			0
$297$	−1.30422	+	0.940422i	−0.0756784	+	0.0545688i
$298$		0			0
$299$	0.294937	+	0.810333i	0.0170566	+	0.0468628i
$300$		0			0
$301$	−4.63440	−	5.52306i	−0.267122	−	0.318344i
$302$		0			0
$303$	−14.8990	−	6.86391i	−0.855925	−	0.394321i
$304$		0			0
$305$	8.59634	+	4.96310i	0.492225	+	0.284186i
$306$		0			0
$307$	4.91201	+	8.50786i	0.280343	+	0.485569i	0.971469	−	0.237165i	$-0.0762183\pi$
$307$	4.91201	+	8.50786i	0.280343	+	0.485569i	−0.691126	+	0.722734i	$0.742885\pi$
$308$		0			0
$309$	−0.270218	+	0.127528i	−0.0153722	+	0.00725479i
$310$		0			0
$311$	7.55182	+	2.74864i	0.428225	+	0.155861i	0.547136	−	0.837044i	$-0.315718\pi$
$311$	7.55182	+	2.74864i	0.428225	+	0.155861i	−0.118911	+	0.992905i	$0.537940\pi$
$312$		0			0
$313$	−1.47213	+	8.34885i	−0.0832096	+	0.471905i	0.914519	+	0.404543i	$0.132569\pi$
$313$	−1.47213	+	8.34885i	−0.0832096	+	0.471905i	−0.997729	+	0.0673622i	$0.978542\pi$
$314$		0			0
$315$	5.32321	−	0.0491773i	0.299929	−	0.00277083i
$316$		0			0
$317$	9.45211	+	7.93126i	0.530883	+	0.445464i	0.868406	−	0.495853i	$-0.165145\pi$
$317$	9.45211	+	7.93126i	0.530883	+	0.445464i	−0.337523	+	0.941317i	$0.609589\pi$
$318$		0			0
$319$	0.261464	−	0.0461032i	0.0146392	−	0.00258128i
$320$		0			0
$321$	−7.80580	−	28.6025i	−0.435677	−	1.59644i
$322$		0			0
$323$			6.26856i			0.348792i
$324$		0			0
$325$		−	0.518469i		−	0.0287595i
$326$		0			0
$327$	−4.68530	−	17.1682i	−0.259098	−	0.949402i
$328$		0			0
$329$	18.5235	−	3.26620i	1.02123	−	0.180071i
$330$		0			0
$331$	−1.19816	−	1.00538i	−0.0658568	−	0.0552604i	0.609265	−	0.792967i	$-0.291465\pi$
$331$	−1.19816	−	1.00538i	−0.0658568	−	0.0552604i	−0.675122	+	0.737706i	$0.735909\pi$
$332$		0			0
$333$	−15.7935	+	27.9482i	−0.865476	+	1.53155i
$334$		0			0
$335$	1.56323	−	8.86554i	0.0854086	−	0.484376i
$336$		0			0
$337$	−3.50370	−	1.27524i	−0.190859	−	0.0694669i	0.244823	−	0.969568i	$-0.421270\pi$
$337$	−3.50370	−	1.27524i	−0.190859	−	0.0694669i	−0.435681	+	0.900101i	$0.643493\pi$
$338$		0			0
$339$	−9.13076	+	4.30920i	−0.495915	+	0.234044i
$340$		0			0
$341$	−0.0392272	−	0.0679435i	−0.00212427	−	0.00367935i
$342$		0			0
$343$	−15.6321	−	9.02517i	−0.844052	−	0.487314i
$344$		0			0
$345$	−11.0281	−	5.08062i	−0.593734	−	0.273531i
$346$		0			0
$347$	10.5821	+	12.6113i	0.568079	+	0.677010i	0.971235	−	0.238121i	$-0.0765315\pi$
$347$	10.5821	+	12.6113i	0.568079	+	0.677010i	−0.403157	+	0.915131i	$0.632087\pi$
$348$		0			0
$349$	−4.27016	−	11.7322i	−0.228576	−	0.628009i	0.771389	−	0.636364i	$-0.219562\pi$
$349$	−4.27016	−	11.7322i	−0.228576	−	0.628009i	−0.999965	+	0.00835575i	$0.997340\pi$
$350$		0			0
$351$	0.316165	+	0.654195i	0.0168756	+	0.0349183i
$352$		0			0
$353$	−4.28550	−	11.7743i	−0.228094	−	0.626683i	0.771865	−	0.635787i	$-0.219324\pi$
$353$	−4.28550	−	11.7743i	−0.228094	−	0.626683i	−0.999959	+	0.00910380i	$0.997102\pi$
$354$		0			0
$355$	−10.3458	+	8.68115i	−0.549097	+	0.460747i
$356$		0			0
$357$	0.829556	+	9.00273i	0.0439048	+	0.476475i
$358$		0			0
$359$	−4.23246	+	7.33084i	−0.223381	+	0.386907i	−0.955832	−	0.293912i	$-0.905043\pi$
$359$	−4.23246	+	7.33084i	−0.223381	+	0.386907i	0.732452	+	0.680819i	$0.238376\pi$
$360$		0			0
$361$	7.74281	+	13.4109i	0.407516	+	0.705839i
$362$		0			0
$363$	18.8222	+	1.55916i	0.987911	+	0.0818348i
$364$		0			0
$365$	8.84196	+	3.21821i	0.462809	+	0.168449i
$366$		0			0
$367$	24.6277	+	4.34252i	1.28555	+	0.226678i	0.774337	−	0.632774i	$-0.218084\pi$
$367$	24.6277	+	4.34252i	1.28555	+	0.226678i	0.511217	+	0.859452i	$0.329195\pi$
$368$		0			0
$369$	5.36103	+	28.8432i	0.279084	+	1.50152i
$370$		0			0
$371$	10.1781	−	12.1298i	0.528419	−	0.629746i
$372$		0			0
$373$	3.36619	−	0.593550i	0.174295	−	0.0307329i	−0.0858196	−	0.996311i	$-0.527351\pi$
$373$	3.36619	−	0.593550i	0.174295	−	0.0307329i	0.260114	+	0.965578i	$0.416240\pi$
$374$		0			0
$375$	12.1791	+	12.0671i	0.628927	+	0.623143i
$376$		0			0
$377$		−	0.119974i		−	0.00617898i
$378$		0			0
$379$	−7.34327			−0.377199			−0.188599	−	0.982054i	$-0.560395\pi$
$379$	−7.34327			−0.377199			−0.188599	+	0.982054i	$0.560395\pi$
$380$		0			0
$381$	11.0197	+	2.89824i	0.564557	+	0.148481i
$382$		0			0
$383$	3.05463	+	17.3237i	0.156084	+	0.885197i	0.957788	+	0.287476i	$0.0928161\pi$
$383$	3.05463	+	17.3237i	0.156084	+	0.885197i	−0.801704	+	0.597722i	$0.796073\pi$
$384$		0			0
$385$	0.420634	+	0.352954i	0.0214375	+	0.0179882i
$386$		0			0
$387$	4.85915	+	12.9762i	0.247004	+	0.659615i
$388$		0			0
$389$	−0.224873	+	1.27532i	−0.0114015	+	0.0646611i	−0.989978	−	0.141224i	$-0.954896\pi$
$389$	−0.224873	+	1.27532i	−0.0114015	+	0.0646611i	0.978576	+	0.205885i	$0.0660073\pi$
$390$		0			0
$391$	7.05288	−	19.3776i	0.356679	−	0.979969i
$392$		0			0
$393$	11.5190	+	7.98662i	0.581054	+	0.402872i
$394$		0			0
$395$	10.7709	−	6.21857i	0.541942	−	0.312890i
$396$		0			0
$397$	−17.5858	−	10.1532i	−0.882605	−	0.509572i	−0.0110887	−	0.999939i	$-0.503530\pi$
$397$	−17.5858	−	10.1532i	−0.882605	−	0.509572i	−0.871517	+	0.490366i	$0.836863\pi$
$398$		0			0
$399$	−2.92639	−	4.13850i	−0.146503	−	0.207184i
$400$		0			0
$401$	−9.86298	−	11.7542i	−0.492534	−	0.586979i	0.461326	−	0.887230i	$-0.347374\pi$
$401$	−9.86298	−	11.7542i	−0.492534	−	0.586979i	−0.953860	+	0.300252i	$0.902929\pi$
$402$		0			0
$403$	−0.0333142	+	0.0121254i	−0.00165950	+	0.000604009i
$404$		0			0
$405$	−9.67676	−	3.32091i	−0.480842	−	0.165017i
$406$		0			0
$407$	−3.11154	+	1.13251i	−0.154233	+	0.0561364i
$408$		0			0
$409$	1.68842	−	1.41676i	0.0834872	−	0.0700541i	−0.600089	−	0.799933i	$-0.704868\pi$
$409$	1.68842	−	1.41676i	0.0834872	−	0.0700541i	0.683576	+	0.729879i	$0.260424\pi$
$410$		0			0
$411$	−1.74748	−	2.47129i	−0.0861969	−	0.121900i
$412$		0			0
$413$	−0.878686	+	1.52193i	−0.0432373	+	0.0748892i
$414$		0			0
$415$	−7.47952	+	4.31831i	−0.367155	+	0.211977i
$416$		0			0
$417$	5.11204	−	7.37300i	0.250338	−	0.361057i
$418$		0			0
$419$	−4.16445	+	11.4417i	−0.203447	+	0.558966i	−0.998892	−	0.0470599i	$-0.985015\pi$
$419$	−4.16445	+	11.4417i	−0.203447	+	0.558966i	0.795445	+	0.606025i	$0.207237\pi$
$420$		0			0
$421$	32.6371	+	5.75480i	1.59063	+	0.280472i	0.897726	−	0.440555i	$-0.145218\pi$
$421$	32.6371	+	5.75480i	1.59063	+	0.280472i	0.692908	+	0.721026i	$0.256329\pi$
$422$		0			0
$423$	−35.6556	−	5.94795i	−1.73363	−	0.289199i
$424$		0			0
$425$	−7.96944	+	9.49761i	−0.386574	+	0.460702i
$426$		0			0
$427$	−2.36698	−	13.4238i	−0.114546	−	0.649623i
$428$		0			0
$429$	−0.0190628	+	0.0724809i	−0.000920361	+	0.00349941i
$430$		0			0
$431$	15.3243			0.738144			0.369072	−	0.929401i	$-0.379676\pi$
$431$	15.3243			0.738144			0.369072	+	0.929401i	$0.379676\pi$
$432$		0			0
$433$	−11.0812			−0.532527			−0.266263	−	0.963900i	$-0.585789\pi$
$433$	−11.0812			−0.532527			−0.266263	+	0.963900i	$0.585789\pi$
$434$		0			0
$435$	1.20002	+	1.18898i	0.0575365	+	0.0570074i
$436$		0			0
$437$	2.00754	+	11.3853i	0.0960339	+	0.544635i
$438$		0			0
$439$	−12.5546	+	14.9619i	−0.599197	+	0.714095i	−0.977345	−	0.211650i	$-0.932116\pi$
$439$	−12.5546	+	14.9619i	−0.599197	+	0.714095i	0.378149	+	0.925745i	$0.376561\pi$
$440$		0			0
$441$	8.89610	+	10.4052i	0.423624	+	0.495486i
$442$		0			0
$443$	26.8265	+	4.73024i	1.27457	+	0.224740i	0.769671	−	0.638440i	$-0.220420\pi$
$443$	26.8265	+	4.73024i	1.27457	+	0.224740i	0.504895	+	0.863181i	$0.331531\pi$
$444$		0			0
$445$	−1.22481	+	3.36514i	−0.0580615	+	0.159523i
$446$		0			0
$447$	5.72273	+	0.474049i	0.270676	+	0.0224217i
$448$		0			0
$449$	−11.0074	+	6.35515i	−0.519473	+	0.299918i	−0.736719	−	0.676199i	$-0.763626\pi$
$449$	−11.0074	+	6.35515i	−0.519473	+	0.299918i	0.217246	+	0.976117i	$0.430293\pi$
$450$		0			0
$451$	−1.51303	+	2.62064i	−0.0712458	+	0.123401i
$452$		0			0
$453$	−36.3541	+	3.34984i	−1.70806	+	0.157389i
$454$		0			0
$455$	0.190078	−	0.159494i	0.00891098	−	0.00747720i
$456$		0			0
$457$	−30.1853	+	10.9866i	−1.41201	+	0.513929i	−0.931719	−	0.363180i	$-0.881691\pi$
$457$	−30.1853	+	10.9866i	−1.41201	+	0.513929i	−0.480290	+	0.877110i	$0.659469\pi$
$458$		0			0
$459$	4.26400	−	16.8437i	0.199027	−	0.786196i
$460$		0			0
$461$	26.5921	−	9.67873i	1.23852	−	0.450783i	0.362011	−	0.932174i	$-0.382090\pi$
$461$	26.5921	−	9.67873i	1.23852	−	0.450783i	0.876506	+	0.481391i	$0.159868\pi$
$462$		0			0
$463$	−21.1708	−	25.2304i	−0.983891	−	1.17256i	−0.985000	−	0.172556i	$-0.944797\pi$
$463$	−21.1708	−	25.2304i	−0.983891	−	1.17256i	0.00110903	−	0.999999i	$-0.499647\pi$
$464$		0			0
$465$	0.208873	−	0.453386i	0.00968627	−	0.0210253i
$466$		0			0
$467$	−34.6222	−	19.9891i	−1.60212	−	0.924986i	−0.991062	−	0.133402i	$-0.957410\pi$
$467$	−34.6222	−	19.9891i	−1.60212	−	0.924986i	−0.611061	−	0.791584i	$-0.709257\pi$
$468$		0			0
$469$	−10.7060	+	6.18108i	−0.494355	+	0.285416i
$470$		0			0
$471$	−22.8603	+	10.7888i	−1.05335	+	0.497120i
$472$		0			0
$473$	−0.488823	+	1.34303i	−0.0224761	+	0.0617526i
$474$		0			0
$475$	1.20701	−	6.84529i	0.0553814	−	0.314083i
$476$		0			0
$477$	−26.2122	+	15.4582i	−1.20017	+	0.707783i
$478$		0			0
$479$	16.5419	+	13.8803i	0.755818	+	0.634207i	0.937035	−	0.349236i	$-0.113559\pi$
$479$	16.5419	+	13.8803i	0.755818	+	0.634207i	−0.181216	+	0.983443i	$0.558003\pi$
$480$		0			0
$481$	0.259829	+	1.47356i	0.0118472	+	0.0671886i
$482$		0			0
$483$	4.38987	+	16.0857i	0.199746	+	0.731922i
$484$		0			0
$485$	−18.7035			−0.849284
$486$		0			0
$487$		−	8.08507i		−	0.366370i	−0.983079	−	0.183185i	$-0.941359\pi$
$487$		−	8.08507i		−	0.366370i	0.983079	−	0.183185i	$-0.0586407\pi$
$488$		0			0
$489$	−23.4502	+	6.39970i	−1.06045	+	0.289404i
$490$		0			0
$491$	28.3285	−	4.99508i	1.27845	−	0.225425i	0.507127	−	0.861871i	$-0.330707\pi$
$491$	28.3285	−	4.99508i	1.27845	−	0.225425i	0.771321	+	0.636446i	$0.219596\pi$
$492$		0			0
$493$	−1.84413	+	2.19775i	−0.0830556	+	0.0989818i
$494$		0			0
$495$	−0.536058	−	0.908983i	−0.0240940	−	0.0408557i
$496$		0			0
$497$	18.2643	+	3.22048i	0.819264	+	0.144458i
$498$		0			0
$499$	3.07692	+	1.11991i	0.137742	+	0.0501340i	0.409971	−	0.912098i	$-0.365539\pi$
$499$	3.07692	+	1.11991i	0.137742	+	0.0501340i	−0.272229	+	0.962232i	$0.587761\pi$
$500$		0			0
$501$	−8.32688	−	17.6438i	−0.372018	−	0.788268i
$502$		0			0
$503$	−9.84071	−	17.0446i	−0.438776	−	0.759982i	0.558820	−	0.829289i	$-0.311254\pi$
$503$	−9.84071	−	17.0446i	−0.438776	−	0.759982i	−0.997595	+	0.0693075i	$0.977921\pi$
$504$		0			0
$505$	5.38301	−	9.32365i	0.239541	−	0.414897i
$506$		0			0
$507$	−20.4200	−	9.40742i	−0.906884	−	0.417798i
$508$		0			0
$509$	−5.51037	+	4.62375i	−0.244243	+	0.204944i	−0.756688	−	0.653776i	$-0.773184\pi$
$509$	−5.51037	+	4.62375i	−0.244243	+	0.204944i	0.512446	+	0.858720i	$0.328740\pi$
$510$		0			0
$511$	−4.41932	−	12.1420i	−0.195499	−	0.537130i
$512$		0			0
$513$	2.65131	+	9.37330i	0.117058	+	0.413841i
$514$		0			0
$515$	−0.0670711	−	0.184276i	−0.00295551	−	0.00812019i
$516$		0			0
$517$	−2.39670	−	2.85628i	−0.105407	−	0.125619i
$518$		0			0
$519$	1.66918	+	18.1147i	0.0732689	+	0.795148i
$520$		0			0
$521$	18.5587	+	10.7149i	0.813071	+	0.469427i	0.848021	−	0.529962i	$-0.177794\pi$
$521$	18.5587	+	10.7149i	0.813071	+	0.469427i	−0.0349500	+	0.999389i	$0.511127\pi$
$522$		0			0
$523$	5.19655	+	9.00069i	0.227229	+	0.393573i	0.956986	−	0.290134i	$-0.0937000\pi$
$523$	5.19655	+	9.00069i	0.227229	+	0.393573i	−0.729757	+	0.683707i	$0.760367\pi$
$524$		0			0
$525$	0.827595	−	9.99074i	0.0361192	−	0.436032i
$526$		0			0
$527$	0.796649	+	0.289957i	0.0347026	+	0.0126307i
$528$		0			0
$529$	2.61017	−	14.8030i	0.113485	−	0.643608i
$530$		0			0
$531$	2.56705	−	2.19474i	0.111401	−	0.0952436i
$532$		0			0
$533$	1.04751	+	0.878965i	0.0453727	+	0.0380722i
$534$		0			0
$535$	19.1628	−	3.37891i	0.828479	−	0.146083i
$536$		0			0
$537$	7.80728	−	7.87974i	0.336909	−	0.340036i
$538$		0			0
$539$			1.41206i			0.0608218i
$540$		0			0
$541$		−	27.7453i		−	1.19287i	−0.802663	−	0.596433i	$-0.796584\pi$
$541$		−	27.7453i		−	1.19287i	0.802663	−	0.596433i	$-0.203416\pi$
$542$		0			0
$543$	−1.41106	−	0.371116i	−0.0605545	−	0.0159261i
$544$		0			0
$545$	11.5021	−	2.02814i	0.492697	−	0.0868759i
$546$		0			0
$547$	27.6681	+	23.2163i	1.18300	+	0.992658i	0.999954	+	0.00955436i	$0.00304129\pi$
$547$	27.6681	+	23.2163i	1.18300	+	0.992658i	0.183049	+	0.983104i	$0.441403\pi$
$548$		0			0
$549$	−4.31042	+	25.8392i	−0.183964	+	1.10279i
$550$		0			0
$551$	0.279303	−	1.58400i	0.0118987	−	0.0674809i
$552$		0			0
$553$	−16.0490	−	5.84135i	−0.682472	−	0.248400i
$554$		0			0
$555$	−17.3140	−	12.0046i	−0.734939	−	0.509567i
$556$		0			0
$557$	13.0134	+	22.5399i	0.551395	+	0.955045i	0.998174	+	0.0604003i	$0.0192377\pi$
$557$	13.0134	+	22.5399i	0.551395	+	0.955045i	−0.446779	+	0.894644i	$0.647429\pi$
$558$		0			0
$559$	0.559316	+	0.322921i	0.0236566	+	0.0136581i
$560$		0			0
$561$	1.46331	−	1.03473i	0.0617811	−	0.0436863i
$562$		0			0
$563$	−5.61995	−	6.69760i	−0.236853	−	0.282270i	0.634505	−	0.772919i	$-0.281204\pi$
$563$	−5.61995	−	6.69760i	−0.236853	−	0.282270i	−0.871357	+	0.490649i	$0.836760\pi$
$564$		0			0
$565$	−2.26636	−	6.22676i	−0.0953463	−	0.261962i
$566$		0			0
$567$	5.04816	+	13.1108i	0.212003	+	0.550602i
$568$		0			0
$569$	−2.09174	−	5.74701i	−0.0876904	−	0.240927i	0.888094	−	0.459662i	$-0.152029\pi$
$569$	−2.09174	−	5.74701i	−0.0876904	−	0.240927i	−0.975784	+	0.218734i	$0.929807\pi$
$570$		0			0
$571$	−21.0799	+	17.6881i	−0.882165	+	0.740225i	−0.966623	−	0.256202i	$-0.917529\pi$
$571$	−21.0799	+	17.6881i	−0.882165	+	0.740225i	0.0844577	+	0.996427i	$0.473084\pi$
$572$		0			0
$573$	−27.4105	+	19.3823i	−1.14509	+	0.809708i
$574$		0			0
$575$	−11.4329	+	19.8024i	−0.476786	+	0.825817i
$576$		0			0
$577$	−8.41032	−	14.5671i	−0.350126	−	0.606437i	0.636145	−	0.771570i	$-0.280528\pi$
$577$	−8.41032	−	14.5671i	−0.350126	−	0.606437i	−0.986271	+	0.165133i	$0.947195\pi$
$578$		0			0
$579$	−10.6650	+	15.3820i	−0.443224	+	0.639254i
$580$		0			0
$581$	11.1447	+	4.05636i	0.462362	+	0.168286i
$582$		0			0
$583$	−3.09118	−	0.545058i	−0.128023	−	0.0225740i
$584$		0			0
$585$	−0.446578	+	0.167229i	−0.0184637	+	0.00691407i
$586$		0			0
$587$	4.54734	−	5.41931i	0.187689	−	0.223679i	−0.663992	−	0.747740i	$-0.731139\pi$
$587$	4.54734	−	5.41931i	0.187689	−	0.223679i	0.851681	+	0.524061i	$0.175584\pi$
$588$		0			0
$589$	−0.468072	+	0.0825338i	−0.0192866	+	0.00340074i
$590$		0			0
$591$	−5.65845	+	21.5146i	−0.232758	+	0.884994i
$592$		0			0
$593$			14.0252i			0.575948i	0.957638	+	0.287974i	$0.0929817\pi$
$593$			14.0252i			0.575948i	−0.957638	+	0.287974i	$0.907018\pi$
$594$		0			0
$595$	−5.93355			−0.243252
$596$		0			0
$597$	17.4014	−	17.5629i	0.712194	−	0.718804i
$598$		0			0
$599$	1.01621	+	5.76321i	0.0415212	+	0.235478i	0.998505	−	0.0546635i	$-0.0174086\pi$
$599$	1.01621	+	5.76321i	0.0415212	+	0.235478i	−0.956984	+	0.290142i	$0.906298\pi$
$600$		0			0
$601$	−2.21998	−	1.86278i	−0.0905548	−	0.0759845i	0.596386	−	0.802697i	$-0.296603\pi$
$601$	−2.21998	−	1.86278i	−0.0905548	−	0.0759845i	−0.686941	+	0.726713i	$0.741047\pi$
$602$		0			0
$603$	23.3580	−	4.34150i	0.951210	−	0.176799i
$604$		0			0
$605$	−2.15244	+	12.2071i	−0.0875091	+	0.496289i
$606$		0			0
$607$	13.6186	−	37.4167i	0.552761	−	1.51870i	−0.277164	−	0.960822i	$-0.589395\pi$
$607$	13.6186	−	37.4167i	0.552761	−	1.51870i	0.829925	−	0.557875i	$-0.188383\pi$
$608$		0			0
$609$	0.191506	−	2.31187i	0.00776021	−	0.0936815i
$610$		0			0
$611$	−1.45916	+	0.842448i	−0.0590314	+	0.0340818i
$612$		0			0
$613$	−29.2218	−	16.8712i	−1.18026	−	0.681423i	−0.224185	−	0.974547i	$-0.571972\pi$
$613$	−29.2218	−	16.8712i	−1.18026	−	0.681423i	−0.956075	+	0.293124i	$0.905305\pi$
$614$		0			0
$615$	−19.1729	+	1.76668i	−0.773124	+	0.0712395i
$616$		0			0
$617$	11.3474	+	13.5233i	0.456829	+	0.544428i	0.944462	−	0.328621i	$-0.106584\pi$
$617$	11.3474	+	13.5233i	0.456829	+	0.544428i	−0.487633	+	0.873049i	$0.662140\pi$
$618$		0			0
$619$	−15.9656	+	5.81099i	−0.641711	+	0.233564i	−0.642320	−	0.766436i	$-0.722028\pi$
$619$	−15.9656	+	5.81099i	−0.641711	+	0.233564i	0.000609711		1.00000i	$0.499806\pi$
$620$		0			0
$621$	2.35025	−	31.9581i	0.0943124	−	1.28244i
$622$		0			0
$623$	4.62108	−	1.68194i	0.185140	−	0.0673854i
$624$		0			0
$625$	5.58200	−	4.68385i	0.223280	−	0.187354i
$626$		0			0
$627$	−0.420421	+	0.912578i	−0.0167900	+	0.0364449i
$628$		0			0
$629$	17.8905	−	30.9873i	0.713343	−	1.23555i
$630$		0			0
$631$	7.92367	−	4.57473i	0.315436	−	0.182117i	−0.333920	−	0.942601i	$-0.608372\pi$
$631$	7.92367	−	4.57473i	0.315436	−	0.182117i	0.649357	+	0.760484i	$0.275038\pi$
$632$		0			0
$633$	20.9570	+	44.4058i	0.832966	+	1.76497i
$634$		0			0
$635$	−2.55770	+	7.02723i	−0.101499	+	0.278867i
$636$		0			0
$637$	0.628394	+	0.110803i	0.0248979	+	0.00439017i
$638$		0			0
$639$	−31.0305	−	17.5353i	−1.22755	−	0.693684i
$640$		0			0
$641$	23.0639	−	27.4865i	0.910971	−	1.08565i	−0.0850364	−	0.996378i	$-0.527101\pi$
$641$	23.0639	−	27.4865i	0.910971	−	1.08565i	0.996007	−	0.0892746i	$-0.0284549\pi$
$642$		0			0
$643$	5.81770	+	32.9938i	0.229428	+	1.30115i	0.854037	+	0.520212i	$0.174147\pi$
$643$	5.81770	+	32.9938i	0.229428	+	1.30115i	−0.624609	+	0.780937i	$0.714742\pi$
$644$		0			0
$645$	−8.77297	+	2.39420i	−0.345436	+	0.0942714i
$646$		0			0
$647$	−9.00640			−0.354078			−0.177039	−	0.984204i	$-0.556652\pi$
$647$	−9.00640			−0.354078			−0.177039	+	0.984204i	$0.556652\pi$
$648$		0			0
$649$	0.348368			0.0136746
$650$		0			0
$651$	−0.661310	+	0.180475i	−0.0259188	+	0.00707339i
$652$		0			0
$653$	6.51091	+	36.9252i	0.254791	+	1.44499i	0.796607	+	0.604497i	$0.206626\pi$
$653$	6.51091	+	36.9252i	0.254791	+	1.44499i	−0.541816	+	0.840497i	$0.682263\pi$
$654$		0			0
$655$	−5.91320	+	7.04707i	−0.231048	+	0.275352i
$656$		0			0
$657$	0.229399	+	24.8314i	0.00894972	+	0.968764i
$658$		0			0
$659$	−43.3312	−	7.64046i	−1.68794	−	0.297630i	−0.754486	−	0.656316i	$-0.772114\pi$
$659$	−43.3312	−	7.64046i	−1.68794	−	0.297630i	−0.933458	+	0.358686i	$0.883225\pi$
$660$		0			0
$661$	5.14540	−	14.1369i	0.200133	−	0.549861i	−0.798508	−	0.601985i	$-0.794377\pi$
$661$	5.14540	−	14.1369i	0.200133	−	0.549861i	0.998641	+	0.0521240i	$0.0165991\pi$
$662$		0			0
$663$	−0.345649	−	0.732396i	−0.0134239	−	0.0284439i
$664$		0			0
$665$	2.88088	−	1.66328i	0.111716	−	0.0644991i
$666$		0			0
$667$	−2.64559	+	4.58229i	−0.102437	+	0.177427i
$668$		0			0
$669$	13.3392	−	28.9545i	0.515724	−	1.11945i
$670$		0			0
$671$	−2.06991	+	1.73686i	−0.0799081	+	0.0670508i
$672$		0			0
$673$	−9.04230	+	3.29113i	−0.348555	+	0.126864i	−0.510364	−	0.859958i	$-0.670489\pi$
$673$	−9.04230	+	3.29113i	−0.348555	+	0.126864i	0.161809	+	0.986822i	$0.448267\pi$
$674$		0			0
$675$	−7.89955	+	17.5723i	−0.304054	+	0.676360i
$676$		0			0
$677$	25.6424	−	9.33309i	0.985519	−	0.358700i	0.201536	−	0.979481i	$-0.435407\pi$
$677$	25.6424	−	9.33309i	0.985519	−	0.358700i	0.783984	+	0.620781i	$0.213185\pi$
$678$		0			0
$679$	16.5094	+	19.6752i	0.633574	+	0.755064i
$680$		0			0
$681$	11.9379	−	1.10002i	0.457461	−	0.0421527i
$682$		0			0
$683$	10.6515	+	6.14967i	0.407570	+	0.235311i	0.689745	−	0.724052i	$-0.257723\pi$
$683$	10.6515	+	6.14967i	0.407570	+	0.235311i	−0.282175	+	0.959363i	$0.591056\pi$
$684$		0			0
$685$	1.72030	−	0.993218i	0.0657295	−	0.0379489i
$686$		0			0
$687$	−4.04337	+	48.8117i	−0.154264	+	1.86228i
$688$		0			0
$689$	−0.485122	+	1.33286i	−0.0184817	+	0.0507780i
$690$		0			0
$691$	7.30917	−	41.4523i	0.278054	−	1.57692i	−0.451038	−	0.892505i	$-0.648946\pi$
$691$	7.30917	−	41.4523i	0.278054	−	1.57692i	0.729091	−	0.684416i	$-0.239943\pi$
$692$		0			0
$693$	−0.483031	+	1.36626i	−0.0183488	+	0.0518998i
$694$		0			0
$695$	4.51066	+	3.78489i	0.171099	+	0.143569i
$696$		0			0
$697$	−5.67821	−	32.2027i	−0.215078	−	1.21977i
$698$		0			0
$699$	14.4038	−	14.5374i	0.544800	−	0.549856i
$700$		0			0
$701$	32.4272			1.22476			0.612379	−	0.790565i	$-0.290213\pi$
$701$	32.4272			1.22476			0.612379	+	0.790565i	$0.290213\pi$
$702$		0			0
$703$			20.0601i			0.756582i
$704$		0			0
$705$	6.03436	−	22.9439i	0.227267	−	0.864119i
$706$		0			0
$707$	−14.5596	+	2.56724i	−0.547568	+	0.0965511i
$708$		0			0
$709$	−6.39578	+	7.62219i	−0.240199	+	0.286258i	−0.872654	−	0.488339i	$-0.837603\pi$
$709$	−6.39578	+	7.62219i	−0.240199	+	0.286258i	0.632455	+	0.774597i	$0.282047\pi$
$710$		0			0
$711$	25.3376	+	20.8650i	0.950236	+	0.782498i
$712$		0			0
$713$	1.53978	+	0.271505i	0.0576653	+	0.0101680i
$714$		0			0
$715$	−0.0462208	−	0.0168230i	−0.00172856	−	0.000629144i
$716$		0			0
$717$	17.2569	−	24.8893i	0.644470	−	0.929506i
$718$		0			0
$719$	−8.92530	−	15.4591i	−0.332858	−	0.576526i	0.650213	−	0.759752i	$-0.274679\pi$
$719$	−8.92530	−	15.4591i	−0.332858	−	0.576526i	−0.983071	+	0.183225i	$0.941346\pi$
$720$		0			0
$721$	−0.134646	+	0.233215i	−0.00501450	+	0.00868536i
$722$		0			0
$723$	−15.4595	+	10.9316i	−0.574945	+	0.406551i
$724$		0			0
$725$	2.43698	−	2.04487i	0.0905070	−	0.0759444i
$726$		0			0
$727$	−14.7757	−	40.5958i	−0.547999	−	1.50561i	−0.836408	−	0.548107i	$-0.815349\pi$
$727$	−14.7757	−	40.5958i	−0.547999	−	1.50561i	0.288409	−	0.957507i	$-0.406874\pi$
$728$		0			0
$729$	−0.748184	−	26.9896i	−0.0277105	−	0.999616i
$730$		0			0
$731$	−5.28221	−	14.5128i	−0.195370	−	0.536773i
$732$		0			0
$733$	−8.02132	−	9.55943i	−0.296274	−	0.353086i	0.597287	−	0.802028i	$-0.296245\pi$
$733$	−8.02132	−	9.55943i	−0.296274	−	0.353086i	−0.893561	+	0.448942i	$0.851801\pi$
$734$		0			0
$735$	−7.33588	+	5.18730i	−0.270588	+	0.191337i
$736$		0			0
$737$	2.12226	+	1.22529i	0.0781746	+	0.0451341i
$738$		0			0
$739$	2.39698	+	4.15168i	0.0881742	+	0.152722i	0.906739	−	0.421691i	$-0.138563\pi$
$739$	2.39698	+	4.15168i	0.0881742	+	0.152722i	−0.818565	+	0.574414i	$0.805230\pi$
$740$		0			0
$741$	0.373124	+	0.258704i	0.0137071	+	0.00950374i
$742$		0			0
$743$	12.6154	+	4.59162i	0.462813	+	0.168450i	0.562894	−	0.826529i	$-0.309688\pi$
$743$	12.6154	+	4.59162i	0.462813	+	0.168450i	−0.100081	+	0.994979i	$0.531910\pi$
$744$		0			0
$745$	−0.654429	+	3.71145i	−0.0239764	+	0.135977i
$746$		0			0
$747$	−17.5950	−	14.4891i	−0.643767	−	0.530128i
$748$		0			0
$749$	−20.4693	−	17.1757i	−0.747930	−	0.627588i
$750$		0			0
$751$	35.4795	−	6.25599i	1.29466	−	0.228284i	0.516468	−	0.856306i	$-0.327246\pi$
$751$	35.4795	−	6.25599i	1.29466	−	0.228284i	0.778195	+	0.628022i	$0.216135\pi$
$752$		0			0
$753$	7.71748	+	2.02973i	0.281241	+	0.0739676i
$754$		0			0
$755$		−	23.9603i		−	0.872006i
$756$		0			0
$757$			2.64599i			0.0961700i	0.998843	+	0.0480850i	$0.0153118\pi$
$757$			2.64599i			0.0961700i	−0.998843	+	0.0480850i	$0.984688\pi$
$758$		0			0
$759$	2.32638	−	2.34797i	0.0844423	−	0.0852260i
$760$		0			0
$761$	−37.1178	+	6.54488i	−1.34552	+	0.237252i	−0.799574	−	0.600568i	$-0.794941\pi$
$761$	−37.1178	+	6.54488i	−1.34552	+	0.237252i	−0.545947	+	0.837820i	$0.683830\pi$
$762$		0			0
$763$	−12.2863	−	10.3095i	−0.444795	−	0.373227i
$764$		0			0
$765$	10.7512	+	3.80100i	0.388709	+	0.137425i
$766$		0			0
$767$	0.0273360	−	0.155030i	0.000987045	−	0.00559781i
$768$		0			0
$769$	4.28819	+	1.56077i	0.154636	+	0.0562830i	0.418179	−	0.908365i	$-0.362669\pi$
$769$	4.28819	+	1.56077i	0.154636	+	0.0562830i	−0.263542	+	0.964648i	$0.584891\pi$
$770$		0			0
$771$	−2.33554	+	28.1947i	−0.0841125	+	1.01541i
$772$		0			0
$773$	20.1465	+	34.8948i	0.724620	+	1.25508i	0.959130	+	0.282965i	$0.0913180\pi$
$773$	20.1465	+	34.8948i	0.724620	+	1.25508i	−0.234510	+	0.972114i	$0.575349\pi$
$774$		0			0
$775$	−0.814112	−	0.470028i	−0.0292438	−	0.0168839i
$776$		0			0
$777$	2.65468	+	28.8098i	0.0952360	+	1.03355i
$778$		0			0
$779$	11.7839	+	14.0435i	0.422202	+	0.503161i
$780$		0			0
$781$	−1.25741	−	3.45470i	−0.0449936	−	0.123619i
$782$		0			0
$783$	−1.82796	+	4.06625i	−0.0653260	+	0.145316i
$784$		0			0
$785$	−5.67418	−	15.5897i	−0.202520	−	0.556419i
$786$		0			0
$787$	35.2016	−	29.5377i	1.25480	−	1.05290i	0.258586	−	0.965988i	$-0.416743\pi$
$787$	35.2016	−	29.5377i	1.25480	−	1.05290i	0.996216	−	0.0869155i	$-0.0277010\pi$
$788$		0			0
$789$	−21.4657	−	9.88917i	−0.764199	−	0.352064i
$790$		0			0
$791$	−4.54975	+	7.88040i	−0.161770	+	0.280195i
$792$		0			0
$793$	0.610513	+	1.05744i	0.0216799	+	0.0375508i
$794$		0			0
$795$	−8.52397	−	18.0614i	−0.302314	−	0.640573i
$796$		0			0
$797$	17.4544	+	6.35287i	0.618265	+	0.225030i	0.632116	−	0.774874i	$-0.282187\pi$
$797$	17.4544	+	6.35287i	0.618265	+	0.225030i	−0.0138504	+	0.999904i	$0.504409\pi$
$798$		0			0
$799$	39.6791	+	6.99649i	1.40374	+	0.247518i
$800$		0			0
$801$	−9.45050	+	0.0873064i	−0.333917	+	0.00308482i
$802$		0			0
$803$	−1.64644	+	1.96215i	−0.0581015	+	0.0692427i
$804$		0			0
$805$	−10.7769	+	1.90025i	−0.379835	+	0.0669752i
$806$		0			0
$807$	52.0860	−	14.2146i	1.83352	−	0.500377i
$808$		0			0
$809$		−	38.3771i		−	1.34927i	−0.738152	−	0.674634i	$-0.764302\pi$
$809$		−	38.3771i		−	1.34927i	0.738152	−	0.674634i	$-0.235698\pi$
$810$		0			0
$811$	−42.0052			−1.47500			−0.737500	−	0.675347i	$-0.763994\pi$
$811$	−42.0052			−1.47500			−0.737500	+	0.675347i	$0.763994\pi$
$812$		0			0
$813$	4.50952	+	16.5241i	0.158156	+	0.579524i
$814$		0			0
$815$	−2.77025	−	15.7109i	−0.0970378	−	0.550329i
$816$		0			0
$817$	6.63282	+	5.56560i	0.232053	+	0.194716i
$818$		0			0
$819$	0.570107	+	0.322166i	0.0199211	+	0.0112574i
$820$		0			0
$821$	−1.58671	+	8.99871i	−0.0553767	+	0.314057i	−0.999896	−	0.0143980i	$-0.995417\pi$
$821$	−1.58671	+	8.99871i	−0.0553767	+	0.314057i	0.944520	+	0.328455i	$0.106528\pi$
$822$		0			0
$823$	1.75350	−	4.81770i	0.0611231	−	0.167934i	−0.905372	−	0.424619i	$-0.860408\pi$
$823$	1.75350	−	4.81770i	0.0611231	−	0.167934i	0.966495	+	0.256685i	$0.0826302\pi$
$824$		0			0
$825$	−1.79718	+	0.848167i	−0.0625698	+	0.0295294i
$826$		0			0
$827$	33.0077	−	19.0570i	1.14779	−	0.662677i	0.199443	−	0.979909i	$-0.436087\pi$
$827$	33.0077	−	19.0570i	1.14779	−	0.662677i	0.948348	+	0.317232i	$0.102753\pi$
$828$		0			0
$829$	33.0841	+	19.1011i	1.14906	+	0.663409i	0.948658	−	0.316304i	$-0.102442\pi$
$829$	33.0841	+	19.1011i	1.14906	+	0.663409i	0.200401	+	0.979714i	$0.435775\pi$
$830$		0			0
$831$	13.5892	−	29.4971i	0.471405	−	1.02324i
$832$		0			0
$833$	−9.80811	−	11.6888i	−0.339831	−	0.404995i
$834$		0			0
$835$	12.0323	−	4.37939i	0.416394	−	0.151555i
$836$		0			0
$837$	1.31386	+	0.0966231i	0.0454135	+	0.00333978i
$838$		0			0
$839$	14.7185	−	5.35711i	0.508140	−	0.184948i	−0.0752114	−	0.997168i	$-0.523963\pi$
$839$	14.7185	−	5.35711i	0.508140	−	0.184948i	0.583352	+	0.812220i	$0.301741\pi$
$840$		0			0
$841$	−21.6514	+	18.1677i	−0.746599	+	0.626471i
$842$		0			0
$843$	38.1478	−	3.51513i	1.31388	−	0.121067i
$844$		0			0
$845$	7.37776	−	12.7787i	0.253803	−	0.439599i
$846$		0			0
$847$	14.7412	−	8.51082i	0.506513	−	0.292435i
$848$		0			0
$849$	28.3385	+	2.34745i	0.972575	+	0.0805643i
$850$		0			0
$851$	22.5700	−	62.0107i	0.773691	−	2.12570i
$852$		0			0
$853$	41.6544	+	7.34480i	1.42622	+	0.251481i	0.832873	−	0.553465i	$-0.186695\pi$
$853$	41.6544	+	7.34480i	1.42622	+	0.251481i	0.593348	+	0.804946i	$0.297806\pi$
$854$		0			0
$855$	−6.28543	+	1.16826i	−0.214957	+	0.0399537i
$856$		0			0
$857$	−4.31862	+	5.14673i	−0.147521	+	0.175809i	−0.834745	−	0.550637i	$-0.814385\pi$
$857$	−4.31862	+	5.14673i	−0.147521	+	0.175809i	0.687224	+	0.726446i	$0.258829\pi$
$858$		0			0
$859$	2.84404	+	16.1294i	0.0970374	+	0.550327i	0.994104	+	0.108431i	$0.0345827\pi$
$859$	2.84404	+	16.1294i	0.0970374	+	0.550327i	−0.897067	+	0.441896i	$0.854306\pi$
$860$		0			0
$861$	18.7822	+	18.6095i	0.640095	+	0.634208i
$862$		0			0
$863$	4.32239			0.147136			0.0735680	−	0.997290i	$-0.476561\pi$
$863$	4.32239			0.147136			0.0735680	+	0.997290i	$0.476561\pi$
$864$		0			0
$865$	−11.9391			−0.405942
$866$		0			0
$867$	2.56351	−	9.74702i	0.0870614	−	0.331026i
$868$		0			0
$869$	0.587904	+	3.33417i	0.0199433	+	0.113104i
$870$		0			0
$871$	0.711808	−	0.848300i	0.0241187	−	0.0287436i
$872$		0			0
$873$	−17.3101	−	46.2258i	−0.585857	−	1.56451i
$874$		0			0
$875$	15.2171	+	2.68318i	0.514430	+	0.0907079i
$876$		0			0
$877$	−4.42513	+	12.1579i	−0.149426	+	0.410544i	−0.991711	−	0.128488i	$-0.958988\pi$
$877$	−4.42513	+	12.1579i	−0.149426	+	0.410544i	0.842285	+	0.539032i	$0.181210\pi$
$878$		0			0
$879$	13.7829	−	19.8788i	0.464885	−	0.670495i
$880$		0			0
$881$	−39.0715	+	22.5580i	−1.31635	+	0.759997i	−0.983140	−	0.182854i	$-0.941466\pi$
$881$	−39.0715	+	22.5580i	−1.31635	+	0.759997i	−0.333214	+	0.942851i	$0.608133\pi$
$882$		0			0
$883$	17.6542	−	30.5779i	0.594110	−	1.02903i	−0.399562	−	0.916706i	$-0.630838\pi$
$883$	17.6542	−	30.5779i	0.594110	−	1.02903i	0.993672	−	0.112323i	$-0.0358290\pi$
$884$		0			0
$885$	1.27975	+	1.80982i	0.0430183	+	0.0608365i
$886$		0			0
$887$	26.9119	−	22.5818i	0.903614	−	0.758222i	−0.0672794	−	0.997734i	$-0.521432\pi$
$887$	26.9119	−	22.5818i	0.903614	−	0.758222i	0.970893	+	0.239512i	$0.0769874\pi$
$888$		0			0
$889$	9.64995	−	3.51229i	0.323649	−	0.117799i
$890$		0			0
$891$	1.75043	−	2.16613i	0.0586417	−	0.0725681i
$892$		0			0
$893$	−21.2264	+	7.72577i	−0.710314	+	0.258533i
$894$		0			0
$895$	4.67952	+	5.57684i	0.156419	+	0.186413i
$896$		0			0
$897$	−0.862344	−	1.21953i	−0.0287928	−	0.0407188i
$898$		0			0
$899$	−0.188386	−	0.108765i	−0.00628303	−	0.00362751i
$900$		0			0
$901$	29.3742	−	16.9592i	0.978598	−	0.564994i
$902$		0			0
$903$	10.2624	+	7.11539i	0.341511	+	0.236785i
$904$		0			0
$905$	0.327511	−	0.899830i	0.0108868	−	0.0299114i
$906$		0			0
$907$	−2.41766	+	13.7112i	−0.0802771	+	0.455274i	0.917999	+	0.396583i	$0.129804\pi$
$907$	−2.41766	+	13.7112i	−0.0802771	+	0.455274i	−0.998276	+	0.0586915i	$0.981307\pi$
$908$		0			0
$909$	28.0254	+	4.67511i	0.929544	+	0.155064i
$910$		0			0
$911$	24.6814	+	20.7102i	0.817732	+	0.686159i	0.952440	−	0.304727i	$-0.0985651\pi$
$911$	24.6814	+	20.7102i	0.817732	+	0.686159i	−0.134708	+	0.990885i	$0.543010\pi$
$912$		0			0
$913$	−0.408252	−	2.31531i	−0.0135112	−	0.0766257i
$914$		0			0
$915$	−16.6272	−	4.37304i	−0.549679	−	0.144568i
$916$		0			0
$917$	12.6327			0.417168
$918$		0			0
$919$			24.3669i			0.803790i	0.915686	+	0.401895i	$0.131648\pi$
$919$			24.3669i			0.803790i	−0.915686	+	0.401895i	$0.868352\pi$
$920$		0			0
$921$	−12.0874	−	11.9762i	−0.398293	−	0.394630i
$922$		0			0
$923$	−1.63607	+	0.288484i	−0.0538520	+	0.00949557i
$924$		0			0
$925$	−25.5031	+	30.3935i	−0.838538	+	0.999331i
$926$		0			0
$927$	0.393365	−	0.336314i	0.0129198	−	0.0110460i
$928$		0			0
$929$	37.4234	+	6.59875i	1.22782	+	0.216498i	0.749689	−	0.661790i	$-0.230203\pi$
$929$	37.4234	+	6.59875i	1.22782	+	0.216498i	0.478132	+	0.878288i	$0.341314\pi$
$930$		0			0
$931$	8.03866	+	2.92583i	0.263457	+	0.0958903i
$932$		0			0
$933$	−13.8721	−	1.14911i	−0.454152	−	0.0376202i
$934$		0			0
$935$	0.588110	+	1.01864i	0.0192333	+	0.0333130i
$936$		0			0
$937$	9.10276	−	15.7664i	0.297374	−	0.515067i	−0.678160	−	0.734914i	$-0.737222\pi$
$937$	9.10276	−	15.7664i	0.297374	−	0.515067i	0.975534	+	0.219847i	$0.0705558\pi$
$938$		0			0
$939$	−1.34732	−	14.6218i	−0.0439682	−	0.477164i
$940$		0			0
$941$	−5.72402	+	4.80302i	−0.186598	+	0.156574i	−0.731301	−	0.682055i	$-0.761087\pi$
$941$	−5.72402	+	4.80302i	−0.186598	+	0.156574i	0.544704	+	0.838629i	$0.316642\pi$
$942$		0			0
$943$	−20.6262	−	56.6701i	−0.671683	−	1.84543i
$944$		0			0
$945$	−8.87236	+	2.50961i	−0.288618	+	0.0816377i
$946$		0			0
$947$	−0.976619	−	2.68324i	−0.0317359	−	0.0871936i	0.922813	−	0.385249i	$-0.125884\pi$
$947$	−0.976619	−	2.68324i	−0.0317359	−	0.0871936i	−0.954549	+	0.298055i	$0.903662\pi$
$948$		0			0
$949$	0.743999	+	0.886663i	0.0241512	+	0.0287823i
$950$		0			0
$951$	−19.4107	−	8.94243i	−0.629435	−	0.289978i
$952$		0			0
$953$	2.01026	+	1.16062i	0.0651186	+	0.0375963i	0.532206	−	0.846615i	$-0.321363\pi$
$953$	2.01026	+	1.16062i	0.0651186	+	0.0375963i	−0.467087	+	0.884211i	$0.654697\pi$
$954$		0			0
$955$	−11.0163	−	19.0809i	−0.356481	−	0.617443i
$956$		0			0
$957$	−0.415869	+	0.196266i	−0.0134431	+	0.00634439i
$958$		0			0
$959$	−2.56331	−	0.932970i	−0.0827737	−	0.0301272i
$960$		0			0
$961$	5.37193	−	30.4657i	0.173288	−	0.982766i
$962$		0			0
$963$	26.0861	+	44.2337i	0.840613	+	1.42541i
$964$		0			0
$965$	−9.41041	−	7.89627i	−0.302932	−	0.254190i
$966$		0			0
$967$	−20.2251	+	3.56623i	−0.650394	+	0.114682i	−0.489105	−	0.872225i	$-0.662676\pi$
$967$	−20.2251	+	3.56623i	−0.650394	+	0.114682i	−0.161290	+	0.986907i	$0.551565\pi$
$968$		0			0
$969$	−2.85853	−	10.4744i	−0.0918292	−	0.336487i
$970$		0			0
$971$			48.5665i			1.55857i	0.626667	+	0.779287i	$0.284419\pi$
$971$			48.5665i			1.55857i	−0.626667	+	0.779287i	$0.715581\pi$
$972$		0			0
$973$		−	8.08587i		−	0.259221i
$974$		0			0
$975$	0.236428	+	0.866333i	0.00757174	+	0.0277449i
$976$		0			0
$977$	−43.8828	+	7.73772i	−1.40393	+	0.247552i	−0.823759	−	0.566940i	$-0.808127\pi$
$977$	−43.8828	+	7.73772i	−1.40393	+	0.247552i	−0.580175	+	0.814492i	$0.697016\pi$
$978$		0			0
$979$	−0.746768	−	0.626613i	−0.0238668	−	0.0200266i
$980$		0			0
$981$	15.6577	+	26.5505i	0.499913	+	0.847693i
$982$		0			0
$983$	−3.82764	+	21.7076i	−0.122083	+	0.692366i	0.860915	+	0.508749i	$0.169892\pi$
$983$	−3.82764	+	21.7076i	−0.122083	+	0.692366i	−0.982998	+	0.183617i	$0.941219\pi$
$984$		0			0
$985$	−13.7198	−	4.99360i	−0.437149	−	0.159109i
$986$		0			0
$987$	−29.4624	+	13.9046i	−0.937797	+	0.442587i
$988$		0			0
$989$	−14.2417	−	24.6673i	−0.452859	−	0.784375i
$990$		0			0
$991$	−6.84594	−	3.95251i	−0.217469	−	0.125556i	0.387309	−	0.921950i	$-0.373405\pi$
$991$	−6.84594	−	3.95251i	−0.217469	−	0.125556i	−0.604778	+	0.796394i	$0.706738\pi$
$992$		0			0
$993$	2.46052	+	1.13355i	0.0780822	+	0.0359722i
$994$		0			0
$995$	10.4301	+	12.4301i	0.330655	+	0.394060i
$996$		0			0
$997$	−8.09252	−	22.2340i	−0.256293	−	0.704159i	−0.999388	−	0.0349732i	$-0.988865\pi$
$997$	−8.09252	−	22.2340i	−0.256293	−	0.704159i	0.743095	−	0.669185i	$-0.233357\pi$
$998$		0			0
$999$	13.6453	−	53.9018i	0.431719	−	1.70538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.47.3		192
4.3	odd	2		216.2.v.b.155.2	yes	192
8.3	odd	2	inner	864.2.bh.b.47.4		192
8.5	even	2		216.2.v.b.155.23	yes	192
12.11	even	2		648.2.v.b.467.31		192
24.5	odd	2		648.2.v.b.467.10		192
27.23	odd	18	inner	864.2.bh.b.239.4		192
108.23	even	18		216.2.v.b.131.23	yes	192
108.31	odd	18		648.2.v.b.179.10		192
216.77	odd	18		216.2.v.b.131.2	✓	192
216.85	even	18		648.2.v.b.179.31		192
216.131	even	18	inner	864.2.bh.b.239.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.2	✓	192	216.77	odd	18
216.2.v.b.131.23	yes	192	108.23	even	18
216.2.v.b.155.2	yes	192	4.3	odd	2
216.2.v.b.155.23	yes	192	8.5	even	2
648.2.v.b.179.10		192	108.31	odd	18
648.2.v.b.179.31		192	216.85	even	18
648.2.v.b.467.10		192	24.5	odd	2
648.2.v.b.467.31		192	12.11	even	2
864.2.bh.b.47.3		192	1.1	even	1	trivial
864.2.bh.b.47.4		192	8.3	odd	2	inner
864.2.bh.b.239.3		192	216.131	even	18	inner
864.2.bh.b.239.4		192	27.23	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67094 + 0.456011i) q^{3} +(-0.197395 - 1.11948i) q^{5} +(-1.00340 + 1.19580i) q^{7} +(2.58411 - 1.52394i) q^{9} +O(q^{10})\)	\(q+(-1.67094 + 0.456011i) q^{3} +(-0.197395 - 1.11948i) q^{5} +(-1.00340 + 1.19580i) q^{7} +(2.58411 - 1.52394i) q^{9} +(0.304741 + 0.0537341i) q^{11} +(0.0478254 - 0.131399i) q^{13} +(0.840330 + 1.78057i) q^{15} +(-2.89584 + 1.67191i) q^{17} +(0.937333 - 1.62351i) q^{19} +(1.13132 - 2.45568i) q^{21} +(-4.72416 + 3.96404i) q^{23} +(3.48419 - 1.26814i) q^{25} +(-3.62297 + 3.72479i) q^{27} +(0.806245 - 0.293449i) q^{29} +(-0.162969 - 0.194219i) q^{31} +(-0.533709 + 0.0491786i) q^{33} +(1.53674 + 0.887239i) q^{35} +(-9.26703 + 5.35032i) q^{37} +(-0.0199941 + 0.241370i) q^{39} +(-3.34464 + 9.18932i) q^{41} +(-0.802030 + 4.54854i) q^{43} +(-2.21611 - 2.59204i) q^{45} +(-9.23039 - 7.74522i) q^{47} +(0.792399 + 4.49392i) q^{49} +(4.07638 - 4.11421i) q^{51} -10.1436 q^{53} -0.351759i q^{55} +(-0.825894 + 3.14023i) q^{57} +(1.10869 - 0.195492i) q^{59} +(-5.61288 + 6.68916i) q^{61} +(-0.770561 + 4.61920i) q^{63} +(-0.156539 - 0.0276021i) q^{65} +(7.44174 + 2.70857i) q^{67} +(6.08617 - 8.77796i) q^{69} +(-5.94039 - 10.2891i) q^{71} +(-4.13874 + 7.16851i) q^{73} +(-5.24360 + 3.70782i) q^{75} +(-0.370032 + 0.310494i) q^{77} +(3.74203 + 10.2812i) q^{79} +(4.35523 - 7.87604i) q^{81} +(-2.59854 - 7.13944i) q^{83} +(2.44330 + 2.91181i) q^{85} +(-1.21337 + 0.857993i) q^{87} +(-2.72824 - 1.57515i) q^{89} +(0.109140 + 0.189035i) q^{91} +(0.360878 + 0.250213i) q^{93} +(-2.00251 - 0.728854i) q^{95} +(2.85712 - 16.2036i) q^{97} +(0.869372 - 0.325552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 192 * q + 12 * q^3 - 12 * q^9	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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