LMFDB - Embedded newform 864.2.bh.b.47.4

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			47.4
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.4

$q$-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	$0.0262516\pi$
$5$	0.197395	+	1.11948i	0.0882775	+	0.500647i	−0.908324	+	0.418268i	$0.862637\pi$
$6$		0			0
$7$	1.00340	−	1.19580i	0.379249	−	0.451971i	−0.542328	−	0.840167i	$-0.682457\pi$
$7$	1.00340	−	1.19580i	0.379249	−	0.451971i	0.921577	+	0.388196i	$0.126901\pi$
$8$		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	−0.946148	−	0.323734i	$-0.895062\pi$
$13$	−0.0478254	+	0.131399i	−0.0132644	+	0.0364436i	0.932884	+	0.360178i	$0.117284\pi$
$14$		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	0.000211529	−	1.00000i	$-0.499933\pi$
$23$	4.72416	−	3.96404i	0.985056	−	0.826560i	0.984844	+	0.173440i	$0.0554882\pi$
$24$		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	−0.415791	−	0.909460i	$-0.636495\pi$
$29$	−0.806245	+	0.293449i	−0.149716	+	0.0544921i	0.266075	+	0.963952i	$0.414273\pi$
$30$		0			0
$31$	0.162969	+	0.194219i	0.0292701	+	0.0348827i	0.780481	−	0.625180i	$-0.214974\pi$
$31$	0.162969	+	0.194219i	0.0292701	+	0.0348827i	−0.751211	+	0.660062i	$0.770530\pi$
$32$		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	$-0.324485\pi$
$37$	9.26703	−	5.35032i	1.52349	−	0.879587i	0.999614	−	0.0277929i	$-0.00884788\pi$
$38$		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	$0.0638739\pi$
$47$	9.23039	+	7.74522i	1.34639	+	1.12976i	0.366457	+	0.930435i	$0.380571\pi$
$48$		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	$-0.254666\pi$
$53$	10.1436			1.39333			0.696666	+	0.717396i	$0.254666\pi$
$54$		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	−0.275844	−	0.961202i	$-0.588957\pi$
$61$	5.61288	−	6.68916i	0.718655	−	0.856460i	0.994499	+	0.104743i	$0.0334019\pi$
$62$		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	$0.0823838\pi$
$71$	5.94039	+	10.2891i	0.704994	+	1.22109i	−0.261699	+	0.965149i	$0.584283\pi$
$72$		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	$-0.900074\pi$
$79$	−3.74203	−	10.2812i	−0.421012	−	1.15672i	0.530117	−	0.847925i	$-0.322148\pi$
$80$		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	0.206002	−	0.978552i	$-0.433955\pi$
$101$	−7.25512	−	6.08777i	−0.721912	−	0.605756i	−0.927913	+	0.372796i	$0.878399\pi$
$102$		0			0
$103$	−0.169891	+	0.0299564i	−0.0167399	+	0.00295169i	−0.182012	−	0.983296i	$-0.558261\pi$
$103$	−0.169891	+	0.0299564i	−0.0167399	+	0.00295169i	0.165272	+	0.986248i	$0.447150\pi$
$104$		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	$-0.836244\pi$
$109$		−	10.2745i		−	0.984122i	0.870561	−	0.492061i	$-0.163756\pi$
$110$		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	0.731002	−	0.682376i	$-0.239053\pi$
$127$	5.69723	+	3.28930i	0.505548	+	0.291878i	−0.225454	+	0.974254i	$0.572387\pi$
$128$		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	0.466463	−	0.884541i	$-0.345528\pi$
$149$	3.11540	+	1.13391i	0.255223	+	0.0928937i	−0.211240	+	0.977434i	$0.567750\pi$
$150$		0			0
$151$	−20.7577	−	3.66015i	−1.68924	−	0.297858i	−0.755323	−	0.655352i	$-0.772520\pi$
$151$	−20.7577	−	3.66015i	−1.68924	−	0.297858i	−0.933916	+	0.357494i	$0.883631\pi$
$152$		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	−0.714694	−	0.699437i	$-0.753434\pi$
$157$	−14.3727	+	2.53429i	−1.14706	+	0.202258i	−0.432371	+	0.901696i	$0.642323\pi$
$158$		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	$-0.912013\pi$
$167$	−1.95599	−	11.0930i	−0.151359	−	0.858402i	0.810680	−	0.585490i	$-0.199098\pi$
$168$		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	$0.186288\pi$
$173$	−1.82380	+	10.3433i	−0.138661	+	0.786385i	−0.972240	+	0.233985i	$0.924823\pi$
$174$		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	0.472642	−	0.881254i	$-0.343300\pi$
$181$	−0.729525	−	0.421192i	−0.0542252	−	0.0313069i	−0.526868	+	0.849947i	$0.676634\pi$
$182$		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	−0.902775	−	0.430114i	$-0.858473\pi$
$191$	−18.2133	+	6.62910i	−1.31787	+	0.479665i	−0.415094	+	0.909779i	$0.636251\pi$
$192$		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	−0.998831	−	0.0483474i	$-0.984605\pi$
$197$	−6.42195	+	11.1231i	−0.457545	+	0.792492i	0.541285	+	0.840839i	$0.317938\pi$
$198$		0			0
$199$	12.3619	−	7.13715i	0.876313	−	0.505939i	0.00687175	−	0.999976i	$-0.497813\pi$
$199$	12.3619	−	7.13715i	0.876313	−	0.505939i	0.869441	+	0.494037i	$0.164479\pi$
$200$		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	−0.207162	−	0.978307i	$-0.566423\pi$
$223$	11.8309	−	14.0995i	0.792255	−	0.944173i	0.999417	+	0.0341339i	$0.0108673\pi$
$224$		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	$0.495112\pi$
$229$	−9.67163	+	26.5726i	−0.639119	+	1.75597i	−0.654474	+	0.756084i	$0.727110\pi$
$230$		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	−0.0968965	−	0.995294i	$-0.530892\pi$
$239$	13.3950	−	11.2397i	0.866451	−	0.727039i	0.963348	+	0.268256i	$0.0864472\pi$
$240$		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	0.260864	−	0.965376i	$-0.415993\pi$
$263$	−10.4528	−	8.77094i	−0.644547	−	0.540839i	−0.905411	+	0.424536i	$0.860437\pi$
$264$		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	$-0.100793\pi$
$269$	31.1716			1.90057			0.950284	+	0.311386i	$0.100793\pi$
$270$		0			0
$271$			9.88906i			0.600718i	0.953826	+	0.300359i	$0.0971064\pi$
$271$			9.88906i			0.600718i	−0.953826	+	0.300359i	$0.902894\pi$
$272$		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	−0.270857	−	0.962619i	$-0.587307\pi$
$277$	12.0526	−	14.3638i	0.724172	−	0.863034i	0.995029	+	0.0995853i	$0.0317516\pi$
$278$		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	−0.274363	−	0.961626i	$-0.588467\pi$
$293$	10.6985	−	8.97707i	0.625011	−	0.524446i	0.899374	+	0.437180i	$0.144023\pi$
$294$		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	0.118911	−	0.992905i	$-0.462060\pi$
$311$	−7.55182	−	2.74864i	−0.428225	−	0.155861i	−0.547136	+	0.837044i	$0.684282\pi$
$312$		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	0.337523	−	0.941317i	$-0.390411\pi$
$317$	−9.45211	−	7.93126i	−0.530883	−	0.445464i	−0.868406	+	0.495853i	$0.834855\pi$
$318$		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	0.999965	−	0.00835575i	$-0.00265975\pi$
$349$	4.27016	+	11.7322i	0.228576	+	0.628009i	−0.771389	+	0.636364i	$0.780438\pi$
$350$		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	−0.732452	−	0.680819i	$-0.761624\pi$
$359$	4.23246	−	7.33084i	0.223381	−	0.386907i	0.955832	+	0.293912i	$0.0949573\pi$
$360$		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	−0.511217	−	0.859452i	$-0.670805\pi$
$367$	−24.6277	−	4.34252i	−1.28555	−	0.226678i	−0.774337	+	0.632774i	$0.781916\pi$
$368$		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	−0.260114	−	0.965578i	$-0.583760\pi$
$373$	−3.36619	+	0.593550i	−0.174295	+	0.0307329i	0.0858196	+	0.996311i	$0.472649\pi$
$374$		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	$-0.907184\pi$
$383$	−3.05463	−	17.3237i	−0.156084	−	0.885197i	0.801704	−	0.597722i	$-0.203927\pi$
$384$		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	−0.978576	−	0.205885i	$-0.933993\pi$
$389$	0.224873	−	1.27532i	0.0114015	−	0.0646611i	0.989978	+	0.141224i	$0.0451038\pi$
$390$		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	0.871517	−	0.490366i	$-0.163137\pi$
$397$	17.5858	+	10.1532i	0.882605	+	0.509572i	0.0110887	+	0.999939i	$0.496470\pi$
$398$		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	−0.692908	−	0.721026i	$-0.743671\pi$
$421$	−32.6371	−	5.75480i	−1.59063	−	0.280472i	−0.897726	+	0.440555i	$0.854782\pi$
$422$		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	$-0.620324\pi$
$431$	−15.3243			−0.738144			−0.369072	+	0.929401i	$0.620324\pi$
$432$		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	−0.378149	−	0.925745i	$-0.623439\pi$
$439$	12.5546	−	14.9619i	0.599197	−	0.714095i	0.977345	+	0.211650i	$0.0678837\pi$
$440$		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	−0.876506	−	0.481391i	$-0.840132\pi$
$461$	−26.5921	+	9.67873i	−1.23852	+	0.450783i	−0.362011	+	0.932174i	$0.617910\pi$
$462$		0			0
$463$	21.1708	+	25.2304i	0.983891	+	1.17256i	0.985000	+	0.172556i	$0.0552025\pi$
$463$	21.1708	+	25.2304i	0.983891	+	1.17256i	−0.00110903	+	0.999999i	$0.500353\pi$
$464$		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	0.181216	−	0.983443i	$-0.441997\pi$
$479$	−16.5419	−	13.8803i	−0.755818	−	0.634207i	−0.937035	+	0.349236i	$0.886441\pi$
$480$		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	$0.0586407\pi$
$487$			8.08507i			0.366370i	−0.983079	+	0.183185i	$0.941359\pi$
$488$		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	0.997595	−	0.0693075i	$-0.0220790\pi$
$503$	9.84071	+	17.0446i	0.438776	+	0.759982i	−0.558820	+	0.829289i	$0.688746\pi$
$504$		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	−0.512446	−	0.858720i	$-0.671260\pi$
$509$	5.51037	−	4.62375i	0.244243	−	0.204944i	0.756688	+	0.653776i	$0.226816\pi$
$510$		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	$0.203416\pi$
$541$			27.7453i			1.19287i	−0.802663	+	0.596433i	$0.796584\pi$
$542$		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	$-0.980762\pi$
$557$	−13.0134	−	22.5399i	−0.551395	−	0.955045i	0.446779	−	0.894644i	$-0.352571\pi$
$558$		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	0.956984	−	0.290142i	$-0.0937025\pi$
$599$	−1.01621	−	5.76321i	−0.0415212	−	0.235478i	−0.998505	+	0.0546635i	$0.982591\pi$
$600$		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	$0.410605\pi$
$607$	−13.6186	+	37.4167i	−0.552761	+	1.51870i	−0.829925	+	0.557875i	$0.811617\pi$
$608$		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	0.956075	−	0.293124i	$-0.0946948\pi$
$613$	29.2218	+	16.8712i	1.18026	+	0.681423i	0.224185	+	0.974547i	$0.428028\pi$
$614$		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	−0.649357	−	0.760484i	$-0.724962\pi$
$631$	−7.92367	+	4.57473i	−0.315436	+	0.182117i	0.333920	+	0.942601i	$0.391628\pi$
$632$		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	$-0.443348\pi$
$647$	9.00640			0.354078			0.177039	+	0.984204i	$0.443348\pi$
$648$		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	$-0.793374\pi$
$653$	−6.51091	−	36.9252i	−0.254791	−	1.44499i	0.541816	−	0.840497i	$-0.317737\pi$
$654$		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	−0.998641	−	0.0521240i	$-0.983401\pi$
$661$	−5.14540	+	14.1369i	−0.200133	+	0.549861i	0.798508	+	0.601985i	$0.205623\pi$
$662$		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	−0.783984	−	0.620781i	$-0.786815\pi$
$677$	−25.6424	+	9.33309i	−0.985519	+	0.358700i	−0.201536	+	0.979481i	$0.564593\pi$
$678$		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	$-0.709787\pi$
$701$	−32.4272			−1.22476			−0.612379	+	0.790565i	$0.709787\pi$
$702$		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	−0.632455	−	0.774597i	$-0.717953\pi$
$709$	6.39578	−	7.62219i	0.240199	−	0.286258i	0.872654	+	0.488339i	$0.162397\pi$
$710$		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	0.983071	−	0.183225i	$-0.0586538\pi$
$719$	8.92530	+	15.4591i	0.332858	+	0.576526i	−0.650213	+	0.759752i	$0.725321\pi$
$720$		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	$0.184651\pi$
$727$	14.7757	+	40.5958i	0.547999	+	1.50561i	−0.288409	+	0.957507i	$0.593126\pi$
$728$		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	0.893561	−	0.448942i	$-0.148199\pi$
$733$	8.02132	+	9.55943i	0.296274	+	0.353086i	−0.597287	+	0.802028i	$0.703755\pi$
$734$		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	0.100081	−	0.994979i	$-0.468090\pi$
$743$	−12.6154	−	4.59162i	−0.462813	−	0.168450i	−0.562894	+	0.826529i	$0.690312\pi$
$744$		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	−0.778195	−	0.628022i	$-0.783865\pi$
$751$	−35.4795	+	6.25599i	−1.29466	+	0.228284i	−0.516468	+	0.856306i	$0.672754\pi$
$752$		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	$-0.984688\pi$
$757$		−	2.64599i		−	0.0961700i	0.998843	−	0.0480850i	$-0.0153118\pi$
$758$		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	$-0.908682\pi$
$773$	−20.1465	−	34.8948i	−0.724620	−	1.25508i	0.234510	−	0.972114i	$-0.424651\pi$
$774$		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	0.0138504	−	0.999904i	$-0.495591\pi$
$797$	−17.4544	−	6.35287i	−0.618265	−	0.225030i	−0.632116	+	0.774874i	$0.717813\pi$
$798$		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	−0.944520	−	0.328455i	$-0.893472\pi$
$821$	1.58671	−	8.99871i	0.0553767	−	0.314057i	0.999896	+	0.0143980i	$0.00458318\pi$
$822$		0			0
$823$	−1.75350	+	4.81770i	−0.0611231	+	0.167934i	−0.966495	−	0.256685i	$-0.917370\pi$
$823$	−1.75350	+	4.81770i	−0.0611231	+	0.167934i	0.905372	+	0.424619i	$0.139592\pi$
$824$		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	−0.200401	−	0.979714i	$-0.564225\pi$
$829$	−33.0841	−	19.1011i	−1.14906	−	0.663409i	−0.948658	+	0.316304i	$0.897558\pi$
$830$		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	−0.583352	−	0.812220i	$-0.698259\pi$
$839$	−14.7185	+	5.35711i	−0.508140	+	0.184948i	0.0752114	+	0.997168i	$0.476037\pi$
$840$		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	−0.593348	−	0.804946i	$-0.702194\pi$
$853$	−41.6544	−	7.34480i	−1.42622	−	0.251481i	−0.832873	+	0.553465i	$0.813305\pi$
$854$		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	$-0.523439\pi$
$863$	−4.32239			−0.147136			−0.0735680	+	0.997290i	$0.523439\pi$
$864$		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	−0.842285	−	0.539032i	$-0.818790\pi$
$877$	4.42513	−	12.1579i	0.149426	−	0.410544i	0.991711	+	0.128488i	$0.0410123\pi$
$878$		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	−0.970893	−	0.239512i	$-0.923013\pi$
$887$	−26.9119	+	22.5818i	−0.903614	+	0.758222i	0.0672794	+	0.997734i	$0.478568\pi$
$888$		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	0.134708	−	0.990885i	$-0.456990\pi$
$911$	−24.6814	−	20.7102i	−0.817732	−	0.686159i	−0.952440	+	0.304727i	$0.901435\pi$
$912$		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	$-0.868352\pi$
$919$		−	24.3669i		−	0.803790i	0.915686	−	0.401895i	$-0.131648\pi$
$920$		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	−0.544704	−	0.838629i	$-0.683358\pi$
$941$	5.72402	−	4.80302i	0.186598	−	0.156574i	0.731301	+	0.682055i	$0.238913\pi$
$942$		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	0.161290	−	0.986907i	$-0.448435\pi$
$967$	20.2251	−	3.56623i	0.650394	−	0.114682i	0.489105	+	0.872225i	$0.337324\pi$
$968$		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	$-0.830108\pi$
$983$	3.82764	−	21.7076i	0.122083	−	0.692366i	0.982998	−	0.183617i	$-0.0587806\pi$
$984$		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	0.604778	−	0.796394i	$-0.293262\pi$
$991$	6.84594	+	3.95251i	0.217469	+	0.125556i	−0.387309	+	0.921950i	$0.626595\pi$
$992$		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	$0.0111346\pi$
$997$	8.09252	+	22.2340i	0.256293	+	0.704159i	−0.743095	+	0.669185i	$0.766643\pi$
$998$		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.47.4		192
4.3	odd	2		216.2.v.b.155.23	yes	192
8.3	odd	2	inner	864.2.bh.b.47.3		192
8.5	even	2		216.2.v.b.155.2	yes	192
12.11	even	2		648.2.v.b.467.10		192
24.5	odd	2		648.2.v.b.467.31		192
27.23	odd	18	inner	864.2.bh.b.239.3		192
108.23	even	18		216.2.v.b.131.2	✓	192
108.31	odd	18		648.2.v.b.179.31		192
216.77	odd	18		216.2.v.b.131.23	yes	192
216.85	even	18		648.2.v.b.179.10		192
216.131	even	18	inner	864.2.bh.b.239.4		192

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