LMFDB - Embedded newform 896.2.bh.a.81.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, degree $8$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.9
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32101 + 1.01365i) q^{3} +(2.54115 - 3.31169i) q^{5} +(1.39322 + 2.24921i) q^{7} +(-0.0588677 + 0.219697i) q^{9} +O(q^{10})$	\(q+(-1.32101 + 1.01365i) q^{3} +(2.54115 - 3.31169i) q^{5} +(1.39322 + 2.24921i) q^{7} +(-0.0588677 + 0.219697i) q^{9} +(0.165561 - 1.25756i) q^{11} +(-1.61250 + 3.89292i) q^{13} +6.95061i q^{15} +(2.00901 + 1.15990i) q^{17} +(3.76690 - 0.495921i) q^{19} +(-4.12037 - 1.55899i) q^{21} +(-0.648431 + 2.41998i) q^{23} +(-3.21575 - 12.0014i) q^{25} +(-2.05655 - 4.96494i) q^{27} +(5.85081 + 2.42349i) q^{29} +(0.789008 - 1.36660i) q^{31} +(1.05601 + 1.82907i) q^{33} +(10.9891 + 1.10164i) q^{35} +(4.22120 - 5.50118i) q^{37} +(-1.81592 - 6.77709i) q^{39} +(6.81824 + 6.81824i) q^{41} +(-1.49817 + 0.620564i) q^{43} +(0.577978 + 0.753235i) q^{45} +(-6.27272 + 3.62156i) q^{47} +(-3.11785 + 6.26730i) q^{49} +(-3.82966 + 0.504184i) q^{51} +(0.0609370 - 0.462862i) q^{53} +(-3.74393 - 3.74393i) q^{55} +(-4.47342 + 4.47342i) q^{57} +(14.1005 + 1.85637i) q^{59} +(0.302505 + 2.29776i) q^{61} +(-0.576161 + 0.173682i) q^{63} +(8.79453 + 15.2326i) q^{65} +(4.10470 - 3.14964i) q^{67} +(-1.59642 - 3.85410i) q^{69} +(-5.18029 + 5.18029i) q^{71} +(-0.384811 + 0.103110i) q^{73} +(16.4132 + 12.5943i) q^{75} +(3.05917 - 1.37968i) q^{77} +(13.6466 - 7.87887i) q^{79} +(7.15850 + 4.13296i) q^{81} +(-0.548270 + 1.32364i) q^{83} +(8.94643 - 3.70573i) q^{85} +(-10.1856 + 2.72921i) q^{87} +(1.33006 + 0.356387i) q^{89} +(-11.0025 + 1.79686i) q^{91} +(0.342964 + 2.60507i) q^{93} +(7.92991 - 13.7350i) q^{95} -16.0816 q^{97} +(0.266536 + 0.110403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

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
$3$	−1.32101	+	1.01365i	−0.762686	+	0.585230i	−0.915166	−	0.403077i	$-0.867941\pi$
$3$	−1.32101	+	1.01365i	−0.762686	+	0.585230i	0.152480	+	0.988307i	$0.451274\pi$
$4$		0			0
$5$	2.54115	−	3.31169i	1.13644	−	1.48103i	0.283534	−	0.958962i	$-0.408493\pi$
$5$	2.54115	−	3.31169i	1.13644	−	1.48103i	0.852903	−	0.522070i	$-0.174840\pi$
$6$		0			0
$7$	1.39322	+	2.24921i	0.526589	+	0.850120i
$7$	1.39322	+	2.24921i	0.526589	+	0.850120i
$8$		0			0
$9$	−0.0588677	+	0.219697i	−0.0196226	+	0.0732325i
$10$		0			0
$11$	0.165561	−	1.25756i	0.0499184	−	0.379168i	−0.948191	−	0.317702i	$-0.897089\pi$
$11$	0.165561	−	1.25756i	0.0499184	−	0.379168i	0.998109	−	0.0614663i	$-0.0195777\pi$
$12$		0			0
$13$	−1.61250	+	3.89292i	−0.447227	+	1.07970i	0.526130	+	0.850404i	$0.323643\pi$
$13$	−1.61250	+	3.89292i	−0.447227	+	1.07970i	−0.973357	+	0.229297i	$0.926357\pi$
$14$		0			0
$15$			6.95061i			1.79464i
$16$		0			0
$17$	2.00901	+	1.15990i	0.487256	+	0.281318i	0.723436	−	0.690392i	$-0.242562\pi$
$17$	2.00901	+	1.15990i	0.487256	+	0.281318i	−0.236179	+	0.971710i	$0.575895\pi$
$18$		0			0
$19$	3.76690	−	0.495921i	0.864185	−	0.113772i	0.314615	−	0.949219i	$-0.398125\pi$
$19$	3.76690	−	0.495921i	0.864185	−	0.113772i	0.549571	+	0.835447i	$0.314791\pi$
$20$		0			0
$21$	−4.12037	−	1.55899i	−0.899138	−	0.340199i
$22$		0			0
$23$	−0.648431	+	2.41998i	−0.135207	+	0.504600i	0.864790	+	0.502134i	$0.167452\pi$
$23$	−0.648431	+	2.41998i	−0.135207	+	0.504600i	−0.999997	+	0.00246609i	$0.999215\pi$
$24$		0			0
$25$	−3.21575	−	12.0014i	−0.643151	−	2.40027i
$26$		0			0
$27$	−2.05655	−	4.96494i	−0.395783	−	0.955504i
$28$		0			0
$29$	5.85081	+	2.42349i	1.08647	+	0.450030i	0.852774	−	0.522280i	$-0.174918\pi$
$29$	5.85081	+	2.42349i	1.08647	+	0.450030i	0.233695	+	0.972310i	$0.424918\pi$
$30$		0			0
$31$	0.789008	−	1.36660i	0.141710	−	0.245449i	−0.786431	−	0.617679i	$-0.788073\pi$
$31$	0.789008	−	1.36660i	0.141710	−	0.245449i	0.928141	+	0.372230i	$0.121407\pi$
$32$		0			0
$33$	1.05601	+	1.82907i	0.183828	+	0.318400i
$34$		0			0
$35$	10.9891	+	1.10164i	1.85749	+	0.186211i
$36$		0			0
$37$	4.22120	−	5.50118i	0.693961	−	0.904388i	−0.304886	−	0.952389i	$-0.598618\pi$
$37$	4.22120	−	5.50118i	0.693961	−	0.904388i	0.998847	+	0.0480011i	$0.0152851\pi$
$38$		0			0
$39$	−1.81592	−	6.77709i	−0.290779	−	1.08520i
$40$		0			0
$41$	6.81824	+	6.81824i	1.06483	+	1.06483i	0.997747	+	0.0670826i	$0.0213691\pi$
$41$	6.81824	+	6.81824i	1.06483	+	1.06483i	0.0670826	+	0.997747i	$0.478631\pi$
$42$		0			0
$43$	−1.49817	+	0.620564i	−0.228470	+	0.0946352i	−0.493982	−	0.869472i	$-0.664459\pi$
$43$	−1.49817	+	0.620564i	−0.228470	+	0.0946352i	0.265512	+	0.964108i	$0.414459\pi$
$44$		0			0
$45$	0.577978	+	0.753235i	0.0861598	+	0.112286i
$46$		0			0
$47$	−6.27272	+	3.62156i	−0.914970	+	0.528258i	−0.882027	−	0.471199i	$-0.843821\pi$
$47$	−6.27272	+	3.62156i	−0.914970	+	0.528258i	−0.0329432	+	0.999457i	$0.510488\pi$
$48$		0			0
$49$	−3.11785	+	6.26730i	−0.445408	+	0.895328i
$50$		0			0
$51$	−3.82966	+	0.504184i	−0.536259	+	0.0705999i
$52$		0			0
$53$	0.0609370	−	0.462862i	0.00837034	−	0.0635791i	−0.986750	−	0.162249i	$-0.948125\pi$
$53$	0.0609370	−	0.462862i	0.00837034	−	0.0635791i	0.995120	+	0.0986696i	$0.0314587\pi$
$54$		0			0
$55$	−3.74393	−	3.74393i	−0.504831	−	0.504831i
$56$		0			0
$57$	−4.47342	+	4.47342i	−0.592519	+	0.592519i
$58$		0			0
$59$	14.1005	+	1.85637i	1.83573	+	0.241678i	0.967210	−	0.253979i	$-0.0817394\pi$
$59$	14.1005	+	1.85637i	1.83573	+	0.241678i	0.868518	+	0.495657i	$0.165073\pi$
$60$		0			0
$61$	0.302505	+	2.29776i	0.0387318	+	0.294197i	0.999838	+	0.0180171i	$0.00573535\pi$
$61$	0.302505	+	2.29776i	0.0387318	+	0.294197i	−0.961106	+	0.276180i	$0.910931\pi$
$62$		0			0
$63$	−0.576161	+	0.173682i	−0.0725894	+	0.0218819i
$64$		0			0
$65$	8.79453	+	15.2326i	1.09083	+	1.88937i
$66$		0			0
$67$	4.10470	−	3.14964i	0.501468	−	0.384790i	−0.326825	−	0.945085i	$-0.605979\pi$
$67$	4.10470	−	3.14964i	0.501468	−	0.384790i	0.828293	+	0.560295i	$0.189312\pi$
$68$		0			0
$69$	−1.59642	−	3.85410i	−0.192186	−	0.463979i
$70$		0			0
$71$	−5.18029	+	5.18029i	−0.614788	+	0.614788i	−0.944190	−	0.329402i	$-0.893153\pi$
$71$	−5.18029	+	5.18029i	−0.614788	+	0.614788i	0.329402	+	0.944190i	$0.393153\pi$
$72$		0			0
$73$	−0.384811	+	0.103110i	−0.0450387	+	0.0120681i	−0.281268	−	0.959629i	$-0.590755\pi$
$73$	−0.384811	+	0.103110i	−0.0450387	+	0.0120681i	0.236229	+	0.971697i	$0.424088\pi$
$74$		0			0
$75$	16.4132	+	12.5943i	1.89523	+	1.45426i
$76$		0			0
$77$	3.05917	−	1.37968i	0.348625	−	0.157229i
$78$		0			0
$79$	13.6466	−	7.87887i	1.53536	−	0.886442i	0.536262	−	0.844052i	$-0.319836\pi$
$79$	13.6466	−	7.87887i	1.53536	−	0.886442i	0.999101	−	0.0423907i	$-0.0134974\pi$
$80$		0			0
$81$	7.15850	+	4.13296i	0.795389	+	0.459218i
$82$		0			0
$83$	−0.548270	+	1.32364i	−0.0601804	+	0.145288i	−0.951109	−	0.308854i	$-0.900054\pi$
$83$	−0.548270	+	1.32364i	−0.0601804	+	0.145288i	0.890929	+	0.454143i	$0.150054\pi$
$84$		0			0
$85$	8.94643	−	3.70573i	0.970377	−	0.401943i
$86$		0			0
$87$	−10.1856	+	2.72921i	−1.09201	+	0.292602i
$88$		0			0
$89$	1.33006	+	0.356387i	0.140986	+	0.0377770i	0.328622	−	0.944462i	$-0.393416\pi$
$89$	1.33006	+	0.356387i	0.140986	+	0.0377770i	−0.187636	+	0.982239i	$0.560083\pi$
$90$		0			0
$91$	−11.0025	+	1.79686i	−1.15338	+	0.188363i
$92$		0			0
$93$	0.342964	+	2.60507i	0.0355638	+	0.270134i
$94$		0			0
$95$	7.92991	−	13.7350i	0.813591	−	1.40918i
$96$		0			0
$97$	−16.0816			−1.63284			−0.816419	−	0.577460i	$-0.804044\pi$
$97$	−16.0816			−1.63284			−0.816419	+	0.577460i	$0.804044\pi$
$98$		0			0
$99$	0.266536	+	0.110403i	0.0267879	+	0.0110959i
$100$		0			0
$101$	3.12542	+	0.411469i	0.310991	+	0.0409427i	0.284406	−	0.958704i	$-0.408204\pi$
$101$	3.12542	+	0.411469i	0.310991	+	0.0409427i	0.0265844	+	0.999647i	$0.491537\pi$
$102$		0			0
$103$	−7.73406	−	2.07233i	−0.762059	−	0.204193i	−0.143199	−	0.989694i	$-0.545739\pi$
$103$	−7.73406	−	2.07233i	−0.762059	−	0.204193i	−0.618861	+	0.785501i	$0.712405\pi$
$104$		0			0
$105$	−15.6333	+	9.68376i	−1.52566	+	0.945038i
$106$		0			0
$107$	2.20490	+	1.69188i	0.213155	+	0.163560i	0.709821	−	0.704382i	$-0.248776\pi$
$107$	2.20490	+	1.69188i	0.213155	+	0.163560i	−0.496666	+	0.867942i	$0.665442\pi$
$108$		0			0
$109$	−4.11168	−	5.35845i	−0.393828	−	0.513247i	0.553788	−	0.832657i	$-0.313182\pi$
$109$	−4.11168	−	5.35845i	−0.393828	−	0.513247i	−0.947616	+	0.319411i	$0.896515\pi$
$110$		0			0
$111$			11.5459i			1.09589i
$112$		0			0
$113$			2.67948i			0.252065i	0.992026	+	0.126032i	$0.0402243\pi$
$113$			2.67948i			0.252065i	−0.992026	+	0.126032i	$0.959776\pi$
$114$		0			0
$115$	6.36645	+	8.29693i	0.593675	+	0.773692i
$116$		0			0
$117$	−0.760340	−	0.583429i	−0.0702934	−	0.0539380i
$118$		0			0
$119$	0.190142	+	6.13468i	0.0174303	+	0.562365i
$120$		0			0
$121$	9.07114	+	2.43061i	0.824649	+	0.220964i
$122$		0			0
$123$	−15.9183	−	2.09568i	−1.43530	−	0.188961i
$124$		0			0
$125$	−28.6338	−	11.8605i	−2.56108	−	1.06083i
$126$		0			0
$127$	−4.47242			−0.396863			−0.198431	−	0.980115i	$-0.563585\pi$
$127$	−4.47242			−0.396863			−0.198431	+	0.980115i	$0.563585\pi$
$128$		0			0
$129$	1.35007	−	2.33839i	0.118867	−	0.205884i
$130$		0			0
$131$	−0.934913	−	7.10137i	−0.0816837	−	0.620450i	−0.982502	−	0.186253i	$-0.940366\pi$
$131$	−0.934913	−	7.10137i	−0.0816837	−	0.620450i	0.900818	−	0.434197i	$-0.142968\pi$
$132$		0			0
$133$	6.36356	+	7.78160i	0.551791	+	0.674750i
$134$		0			0
$135$	−21.6683	−	5.80602i	−1.86491	−	0.499702i
$136$		0			0
$137$	8.50713	−	2.27948i	0.726813	−	0.194749i	0.123603	−	0.992332i	$-0.460555\pi$
$137$	8.50713	−	2.27948i	0.726813	−	0.194749i	0.603210	+	0.797583i	$0.293888\pi$
$138$		0			0
$139$	−0.926075	+	0.383593i	−0.0785487	+	0.0325359i	−0.421612	−	0.906776i	$-0.638536\pi$
$139$	−0.926075	+	0.383593i	−0.0785487	+	0.0325359i	0.343063	+	0.939312i	$0.388536\pi$
$140$		0			0
$141$	4.61535	−	11.1424i	0.388683	−	0.938363i
$142$		0			0
$143$	4.62860	+	2.67232i	0.387063	+	0.223471i
$144$		0			0
$145$	22.8936	−	13.2176i	1.90121	−	1.09766i
$146$		0			0
$147$	−2.23411	−	11.4396i	−0.184266	−	0.943520i
$148$		0			0
$149$	−16.7488	−	12.8518i	−1.37211	−	1.05286i	−0.991773	−	0.128012i	$-0.959140\pi$
$149$	−16.7488	−	12.8518i	−1.37211	−	1.05286i	−0.380340	−	0.924847i	$-0.624193\pi$
$150$		0			0
$151$	4.96439	−	1.33020i	0.403996	−	0.108251i	−0.0510981	−	0.998694i	$-0.516272\pi$
$151$	4.96439	−	1.33020i	0.403996	−	0.108251i	0.455095	+	0.890443i	$0.349605\pi$
$152$		0			0
$153$	−0.373093	+	0.373093i	−0.0301628	+	0.0301628i
$154$		0			0
$155$	−2.52078	−	6.08569i	−0.202474	−	0.488814i
$156$		0			0
$157$	−13.6213	+	10.4520i	−1.08710	+	0.834160i	−0.986984	−	0.160816i	$-0.948588\pi$
$157$	−13.6213	+	10.4520i	−1.08710	+	0.834160i	−0.100114	+	0.994976i	$0.531921\pi$
$158$		0			0
$159$	0.388681	+	0.673215i	0.0308244	+	0.0533894i
$160$		0			0
$161$	−6.34644	+	1.91312i	−0.500169	+	0.150775i
$162$		0			0
$163$	−1.59533	−	12.1177i	−0.124956	−	0.949134i	−0.932966	−	0.359965i	$-0.882789\pi$
$163$	−1.59533	−	12.1177i	−0.124956	−	0.949134i	0.808010	−	0.589169i	$-0.200545\pi$
$164$		0			0
$165$	8.74079	+	1.15075i	0.680470	+	0.0895855i
$166$		0			0
$167$	5.88876	−	5.88876i	0.455686	−	0.455686i	−0.441551	−	0.897236i	$-0.645571\pi$
$167$	5.88876	−	5.88876i	0.455686	−	0.455686i	0.897236	+	0.441551i	$0.145571\pi$
$168$		0			0
$169$	−3.36227	−	3.36227i	−0.258636	−	0.258636i
$170$		0			0
$171$	−0.112796	+	0.856771i	−0.00862573	+	0.0655189i
$172$		0			0
$173$	−21.9445	+	2.88905i	−1.66841	+	0.219651i	−0.904743	−	0.425958i	$-0.859937\pi$
$173$	−21.9445	+	2.88905i	−1.66841	+	0.219651i	−0.763668	+	0.645609i	$0.776604\pi$
$174$		0			0
$175$	22.5133	−	23.9535i	1.70184	−	1.81071i
$176$		0			0
$177$	−20.5086	+	11.8407i	−1.54152	+	0.889998i
$178$		0			0
$179$	−10.7657	−	14.0302i	−0.804670	−	1.04867i	−0.997721	−	0.0674774i	$-0.978505\pi$
$179$	−10.7657	−	14.0302i	−0.804670	−	1.04867i	0.193051	−	0.981189i	$-0.438162\pi$
$180$		0			0
$181$	−5.71614	+	2.36770i	−0.424877	+	0.175990i	−0.584868	−	0.811129i	$-0.698854\pi$
$181$	−5.71614	+	2.36770i	−0.424877	+	0.175990i	0.159991	+	0.987119i	$0.448854\pi$
$182$		0			0
$183$	−2.72873	−	2.72873i	−0.201713	−	0.201713i
$184$		0			0
$185$	−7.49149	−	27.9586i	−0.550785	−	2.05556i
$186$		0			0
$187$	1.79126	−	2.33441i	0.130990	−	0.170709i
$188$		0			0
$189$	8.30195	−	11.5429i	0.603878	−	0.839621i
$190$		0			0
$191$	2.68802	+	4.65580i	0.194499	+	0.336882i	0.946736	−	0.322011i	$-0.104359\pi$
$191$	2.68802	+	4.65580i	0.194499	+	0.336882i	−0.752237	+	0.658892i	$0.771025\pi$
$192$		0			0
$193$	4.91411	−	8.51148i	0.353725	−	0.612670i	−0.633174	−	0.774010i	$-0.718248\pi$
$193$	4.91411	−	8.51148i	0.353725	−	0.612670i	0.986899	+	0.161340i	$0.0515815\pi$
$194$		0			0
$195$	−27.0581	−	11.2079i	−1.93767	−	0.802611i
$196$		0			0
$197$	−3.54380	−	8.55548i	−0.252485	−	0.609553i	0.745918	−	0.666037i	$-0.232011\pi$
$197$	−3.54380	−	8.55548i	−0.252485	−	0.609553i	−0.998403	+	0.0564844i	$0.982011\pi$
$198$		0			0
$199$	−1.46919	−	5.48310i	−0.104148	−	0.388686i	0.894099	−	0.447869i	$-0.147817\pi$
$199$	−1.46919	−	5.48310i	−0.104148	−	0.388686i	−0.998247	+	0.0591831i	$0.981150\pi$
$200$		0			0
$201$	−2.22972	+	8.32143i	−0.157272	+	0.586948i
$202$		0			0
$203$	2.70058	+	16.5361i	0.189543	+	1.16061i
$204$		0			0
$205$	39.9060	−	5.25373i	2.78716	−	0.366936i
$206$		0			0
$207$	−0.493491	−	0.284917i	−0.0343000	−	0.0198031i
$208$		0			0
$209$		−	4.81919i		−	0.333351i
$210$		0			0
$211$	4.24055	−	10.2376i	0.291932	−	0.704785i	−0.708068	−	0.706145i	$-0.750433\pi$
$211$	4.24055	−	10.2376i	0.291932	−	0.704785i	0.999999	+	0.00135960i	$0.000432775\pi$
$212$		0			0
$213$	1.59223	−	12.0942i	0.109098	−	0.828682i
$214$		0			0
$215$	−1.75197	+	6.53844i	−0.119483	+	0.445918i
$216$		0			0
$217$	4.17304	−	0.129342i	0.283284	−	0.00878029i
$218$		0			0
$219$	0.403822	−	0.526271i	0.0272878	−	0.0355621i
$220$		0			0
$221$	−7.75493	+	5.95057i	−0.521653	+	0.400279i
$222$		0			0
$223$	−22.9225			−1.53501			−0.767504	−	0.641045i	$-0.778501\pi$
$223$	−22.9225			−1.53501			−0.767504	+	0.641045i	$0.778501\pi$
$224$		0			0
$225$	2.82597			0.188398
$226$		0			0
$227$	−8.70075	+	6.67632i	−0.577489	+	0.443123i	−0.855755	−	0.517381i	$-0.826907\pi$
$227$	−8.70075	+	6.67632i	−0.577489	+	0.443123i	0.278266	+	0.960504i	$0.410240\pi$
$228$		0			0
$229$	−10.2952	+	13.4169i	−0.680325	+	0.886617i	−0.998104	−	0.0615479i	$-0.980396\pi$
$229$	−10.2952	+	13.4169i	−0.680325	+	0.886617i	0.317779	+	0.948165i	$0.397063\pi$
$230$		0			0
$231$	−2.64269	+	4.92349i	−0.173876	+	0.323942i
$232$		0			0
$233$	6.14774	−	22.9437i	0.402752	−	1.50309i	−0.405413	−	0.914133i	$-0.632872\pi$
$233$	6.14774	−	22.9437i	0.402752	−	1.50309i	0.808165	−	0.588956i	$-0.200461\pi$
$234$		0			0
$235$	−3.94644	+	29.9762i	−0.257438	+	1.95543i
$236$		0			0
$237$	−10.0409	+	24.2409i	−0.652228	+	1.57462i
$238$		0			0
$239$			6.64906i			0.430092i	0.976604	+	0.215046i	$0.0689902\pi$
$239$			6.64906i			0.430092i	−0.976604	+	0.215046i	$0.931010\pi$
$240$		0			0
$241$	−5.30906	−	3.06519i	−0.341986	−	0.197446i	0.319164	−	0.947700i	$-0.396598\pi$
$241$	−5.30906	−	3.06519i	−0.341986	−	0.197446i	−0.661150	+	0.750254i	$0.729931\pi$
$242$		0			0
$243$	2.33830	−	0.307843i	0.150002	−	0.0197481i
$244$		0			0
$245$	12.8324	+	26.2515i	0.819833	+	1.67715i
$246$		0			0
$247$	−4.14354	+	15.4639i	−0.263647	+	0.983944i
$248$		0			0
$249$	−0.617434	−	2.30430i	−0.0391283	−	0.146029i
$250$		0			0
$251$	10.0895	+	24.3583i	0.636846	+	1.53748i	0.830859	+	0.556483i	$0.187850\pi$
$251$	10.0895	+	24.3583i	0.636846	+	1.53748i	−0.194013	+	0.980999i	$0.562150\pi$
$252$		0			0
$253$	2.93591	+	1.21609i	0.184579	+	0.0764551i
$254$		0			0
$255$	−8.06203	+	13.9638i	−0.504864	+	0.874450i
$256$		0			0
$257$	7.23584	+	12.5328i	0.451359	+	0.781777i	0.998471	−	0.0552825i	$-0.0176059\pi$
$257$	7.23584	+	12.5328i	0.451359	+	0.781777i	−0.547111	+	0.837060i	$0.684273\pi$
$258$		0			0
$259$	18.2544	+	1.82998i	1.13427	+	0.113709i
$260$		0			0
$261$	−0.876858	+	1.14274i	−0.0542761	+	0.0707340i
$262$		0			0
$263$	5.12788	+	19.1375i	0.316199	+	1.18007i	0.922868	+	0.385116i	$0.125839\pi$
$263$	5.12788	+	19.1375i	0.316199	+	1.18007i	−0.606669	+	0.794954i	$0.707495\pi$
$264$		0			0
$265$	−1.37801	−	1.37801i	−0.0846503	−	0.0846503i
$266$		0			0
$267$	−2.11827	+	0.877416i	−0.129636	+	0.0536970i
$268$		0			0
$269$	−17.2044	−	22.4213i	−1.04897	−	1.36705i	−0.927233	−	0.374486i	$-0.877819\pi$
$269$	−17.2044	−	22.4213i	−1.04897	−	1.36705i	−0.121740	−	0.992562i	$-0.538847\pi$
$270$		0			0
$271$	−9.19867	+	5.31086i	−0.558780	+	0.322612i	−0.752656	−	0.658415i	$-0.771227\pi$
$271$	−9.19867	+	5.31086i	−0.558780	+	0.322612i	0.193876	+	0.981026i	$0.437894\pi$
$272$		0			0
$273$	12.7131	−	13.5264i	0.769432	−	0.818654i
$274$		0			0
$275$	−15.6248	+	2.05704i	−0.942211	+	0.124044i
$276$		0			0
$277$	−0.516139	+	3.92046i	−0.0310118	+	0.235558i	−0.999930	−	0.0118230i	$-0.996237\pi$
$277$	−0.516139	+	3.92046i	−0.0310118	+	0.235558i	0.968918	+	0.247381i	$0.0795699\pi$
$278$		0			0
$279$	0.253792	+	0.253792i	0.0151941	+	0.0151941i
$280$		0			0
$281$	−14.9195	+	14.9195i	−0.890020	+	0.890020i	−0.994524	−	0.104504i	$-0.966674\pi$
$281$	−14.9195	+	14.9195i	−0.890020	+	0.890020i	0.104504	+	0.994524i	$0.466674\pi$
$282$		0			0
$283$	−1.78250	−	0.234671i	−0.105959	−	0.0139497i	0.0773603	−	0.997003i	$-0.475351\pi$
$283$	−1.78250	−	0.234671i	−0.105959	−	0.0139497i	−0.183319	+	0.983053i	$0.558684\pi$
$284$		0			0
$285$	3.44696	+	26.1822i	0.204180	+	1.55090i
$286$		0			0
$287$	−5.83629	+	24.8350i	−0.344505	+	1.46596i
$288$		0			0
$289$	−5.80925	−	10.0619i	−0.341721	−	0.591878i
$290$		0			0
$291$	21.2440	−	16.3011i	1.24534	−	0.955585i
$292$		0			0
$293$	−1.02254	−	2.46863i	−0.0597374	−	0.144219i	0.891192	−	0.453625i	$-0.149870\pi$
$293$	−1.02254	−	2.46863i	−0.0597374	−	0.144219i	−0.950930	+	0.309407i	$0.899870\pi$
$294$		0			0
$295$	41.9792	−	41.9792i	2.44412	−	2.44412i
$296$		0			0
$297$	−6.58419	+	1.76423i	−0.382053	+	0.102371i
$298$		0			0
$299$	−8.37518	−	6.42650i	−0.484349	−	0.371654i
$300$		0			0
$301$	−3.48307	−	2.50512i	−0.200761	−	0.144393i
$302$		0			0
$303$	−4.54580	+	2.62452i	−0.261149	+	0.150775i
$304$		0			0
$305$	8.37816	+	4.83713i	0.479732	+	0.276973i
$306$		0			0
$307$	0.593605	−	1.43309i	0.0338789	−	0.0817908i	−0.906035	−	0.423204i	$-0.860905\pi$
$307$	0.593605	−	1.43309i	0.0338789	−	0.0817908i	0.939913	+	0.341413i	$0.110905\pi$
$308$		0			0
$309$	12.3174	−	5.10203i	0.700712	−	0.290245i
$310$		0			0
$311$	−20.7463	+	5.55897i	−1.17642	+	0.315220i	−0.793504	−	0.608565i	$-0.791746\pi$
$311$	−20.7463	+	5.55897i	−1.17642	+	0.315220i	−0.382913	+	0.923785i	$0.625079\pi$
$312$		0			0
$313$	0.446320	+	0.119591i	0.0252275	+	0.00675969i	0.271411	−	0.962464i	$-0.412510\pi$
$313$	0.446320	+	0.119591i	0.0252275	+	0.00675969i	−0.246183	+	0.969223i	$0.579176\pi$
$314$		0			0
$315$	−0.888929	+	2.34942i	−0.0500854	+	0.132375i
$316$		0			0
$317$	1.11551	+	8.47316i	0.0626534	+	0.475900i	0.993794	+	0.111239i	$0.0354819\pi$
$317$	1.11551	+	8.47316i	0.0626534	+	0.475900i	−0.931140	+	0.364661i	$0.881185\pi$
$318$		0			0
$319$	4.01634	−	6.95650i	0.224872	−	0.389489i
$320$		0			0
$321$	−4.62766			−0.258291
$322$		0			0
$323$	8.14295	+	3.37292i	0.453086	+	0.187674i
$324$		0			0
$325$	51.9057	+	6.83352i	2.87921	+	0.379055i
$326$		0			0
$327$	10.8632	+	2.91078i	0.600734	+	0.160966i
$328$		0			0
$329$	−16.8849	−	9.06300i	−0.930896	−	0.499659i
$330$		0			0
$331$	−27.4540	−	21.0662i	−1.50901	−	1.15790i	−0.942668	−	0.333732i	$-0.891692\pi$
$331$	−27.4540	−	21.0662i	−1.50901	−	1.15790i	−0.566341	−	0.824171i	$-0.691641\pi$
$332$		0			0
$333$	0.960101	+	1.25123i	0.0526132	+	0.0685669i
$334$		0			0
$335$		−	21.5972i		−	1.17998i
$336$		0			0
$337$			2.28509i			0.124477i	0.998061	+	0.0622384i	$0.0198239\pi$
$337$			2.28509i			0.124477i	−0.998061	+	0.0622384i	$0.980176\pi$
$338$		0			0
$339$	−2.71605	−	3.53963i	−0.147516	−	0.192246i
$340$		0			0
$341$	−1.58795	−	1.21848i	−0.0859924	−	0.0659843i
$342$		0			0
$343$	−18.4403	+	1.71906i	−0.995683	+	0.0928203i
$344$		0			0
$345$	−16.8203	−	4.50699i	−0.905575	−	0.242648i
$346$		0			0
$347$	20.5755	+	2.70882i	1.10455	+	0.145417i	0.660676	−	0.750671i	$-0.270270\pi$
$347$	20.5755	+	2.70882i	1.10455	+	0.145417i	0.443876	+	0.896088i	$0.353603\pi$
$348$		0			0
$349$	9.73058	+	4.03054i	0.520866	+	0.215750i	0.627597	−	0.778538i	$-0.284039\pi$
$349$	9.73058	+	4.03054i	0.520866	+	0.215750i	−0.106731	+	0.994288i	$0.534039\pi$
$350$		0			0
$351$	22.6443			1.20866
$352$		0			0
$353$	−5.41395	+	9.37723i	−0.288155	+	0.499100i	−0.973369	−	0.229242i	$-0.926375\pi$
$353$	−5.41395	+	9.37723i	−0.288155	+	0.499100i	0.685214	+	0.728342i	$0.259709\pi$
$354$		0			0
$355$	3.99163	+	30.3194i	0.211854	+	1.60919i
$356$		0			0
$357$	−6.46958	−	7.91125i	−0.342407	−	0.418708i
$358$		0			0
$359$	11.6651	+	3.12565i	0.615659	+	0.164965i	0.553153	−	0.833079i	$-0.313424\pi$
$359$	11.6651	+	3.12565i	0.615659	+	0.164965i	0.0625052	+	0.998045i	$0.480091\pi$
$360$		0			0
$361$	−4.40902	+	1.18139i	−0.232054	+	0.0621786i
$362$		0			0
$363$	−14.4469	+	5.98409i	−0.758264	+	0.314083i
$364$		0			0
$365$	−0.636394	+	1.53639i	−0.0333104	+	0.0804183i
$366$		0			0
$367$	22.8596	+	13.1980i	1.19326	+	0.688931i	0.959045	−	0.283253i	$-0.0914137\pi$
$367$	22.8596	+	13.1980i	1.19326	+	0.688931i	0.234218	+	0.972184i	$0.424747\pi$
$368$		0			0
$369$	−1.89932	+	1.09657i	−0.0988748	+	0.0570854i
$370$		0			0
$371$	1.12597	−	0.507811i	0.0584575	−	0.0263643i
$372$		0			0
$373$	−21.2880	−	16.3348i	−1.10225	−	0.845786i	−0.113230	−	0.993569i	$-0.536120\pi$
$373$	−21.2880	−	16.3348i	−1.10225	−	0.845786i	−0.989020	+	0.147783i	$0.952786\pi$
$374$		0			0
$375$	49.8479	−	13.3567i	2.57413	−	0.689737i
$376$		0			0
$377$	−18.8689	+	18.8689i	−0.971796	+	0.971796i
$378$		0			0
$379$	3.24022	+	7.82259i	0.166439	+	0.401820i	0.984989	−	0.172615i	$-0.0552218\pi$
$379$	3.24022	+	7.82259i	0.166439	+	0.401820i	−0.818550	+	0.574435i	$0.805222\pi$
$380$		0			0
$381$	5.90811	−	4.53346i	0.302682	−	0.232256i
$382$		0			0
$383$	−17.3541	−	30.0581i	−0.886751	−	1.53590i	−0.843693	−	0.536826i	$-0.819623\pi$
$383$	−17.3541	−	30.0581i	−0.886751	−	1.53590i	−0.0430579	−	0.999073i	$-0.513710\pi$
$384$		0			0
$385$	3.20473	−	13.6370i	0.163328	−	0.695005i
$386$		0			0
$387$	−0.0481422	−	0.365676i	−0.00244721	−	0.0185884i
$388$		0			0
$389$	5.50299	+	0.724483i	0.279013	+	0.0367327i	0.268734	−	0.963214i	$-0.413395\pi$
$389$	5.50299	+	0.724483i	0.279013	+	0.0367327i	0.0102789	+	0.999947i	$0.496728\pi$
$390$		0			0
$391$	−4.10964	+	4.10964i	−0.207834	+	0.207834i
$392$		0			0
$393$	8.43332	+	8.43332i	0.425405	+	0.425405i
$394$		0			0
$395$	8.58568	−	65.2147i	0.431992	−	3.28131i
$396$		0			0
$397$	−0.944366	+	0.124328i	−0.0473964	+	0.00623985i	−0.154187	−	0.988042i	$-0.549276\pi$
$397$	−0.944366	+	0.124328i	−0.0473964	+	0.00623985i	0.106791	+	0.994282i	$0.465943\pi$
$398$		0			0
$399$	−16.2941	−	3.82917i	−0.815727	−	0.191698i
$400$		0			0
$401$	11.3137	−	6.53197i	0.564979	−	0.326191i	−0.190162	−	0.981753i	$-0.560901\pi$
$401$	11.3137	−	6.53197i	0.564979	−	0.326191i	0.755142	+	0.655562i	$0.227568\pi$
$402$		0			0
$403$	4.04780	+	5.27519i	0.201635	+	0.262776i
$404$		0			0
$405$	31.8779	−	13.2043i	1.58403	−	0.656125i
$406$		0			0
$407$	−6.21918	−	6.21918i	−0.308273	−	0.308273i
$408$		0			0
$409$	0.592873	+	2.21263i	0.0293157	+	0.109408i	0.979033	−	0.203700i	$-0.0652967\pi$
$409$	0.592873	+	2.21263i	0.0293157	+	0.109408i	−0.949718	+	0.313107i	$0.898630\pi$
$410$		0			0
$411$	−8.92743	+	11.6344i	−0.440357	+	0.573885i
$412$		0			0
$413$	15.4698	+	34.3012i	0.761219	+	1.68785i
$414$		0			0
$415$	2.99025	+	5.17927i	0.146786	+	0.254240i
$416$		0			0
$417$	0.834528	−	1.44544i	0.0408670	−	0.0707837i
$418$		0			0
$419$	−0.0988360	−	0.0409392i	−0.00482845	−	0.00200001i	0.380268	−	0.924876i	$-0.375832\pi$
$419$	−0.0988360	−	0.0409392i	−0.00482845	−	0.00200001i	−0.385096	+	0.922876i	$0.625832\pi$
$420$		0			0
$421$	−9.88575	−	23.8663i	−0.481802	−	1.16317i	−0.958752	−	0.284243i	$-0.908258\pi$
$421$	−9.88575	−	23.8663i	−0.481802	−	1.16317i	0.476950	−	0.878930i	$-0.341742\pi$
$422$		0			0
$423$	−0.426386	−	1.59129i	−0.0207316	−	0.0773713i
$424$		0			0
$425$	7.45992	−	27.8408i	0.361859	−	1.35048i
$426$		0			0
$427$	−4.74667	+	3.88168i	−0.229707	+	0.187848i
$428$		0			0
$429$	−8.82323	+	1.16160i	−0.425990	+	0.0560826i
$430$		0			0
$431$	−13.1352	−	7.58359i	−0.632699	−	0.365289i	0.149098	−	0.988822i	$-0.452363\pi$
$431$	−13.1352	−	7.58359i	−0.632699	−	0.365289i	−0.781796	+	0.623534i	$0.785696\pi$
$432$		0			0
$433$		−	18.3358i		−	0.881161i	−0.897713	−	0.440581i	$-0.854773\pi$
$433$		−	18.3358i		−	0.881161i	0.897713	−	0.440581i	$-0.145227\pi$
$434$		0			0
$435$	−16.8447	+	40.6667i	−0.807642	+	1.94982i
$436$		0			0
$437$	−1.24245	+	9.43738i	−0.0594347	+	0.451451i
$438$		0			0
$439$	6.25293	−	23.3362i	0.298436	−	1.11378i	−0.640014	−	0.768363i	$-0.721071\pi$
$439$	6.25293	−	23.3362i	0.298436	−	1.11378i	0.938450	−	0.345415i	$-0.112262\pi$
$440$		0			0
$441$	−1.19337	−	1.05393i	−0.0568270	−	0.0501869i
$442$		0			0
$443$	8.56427	−	11.1612i	0.406901	−	0.530283i	−0.544286	−	0.838900i	$-0.683199\pi$
$443$	8.56427	−	11.1612i	0.406901	−	0.530283i	0.951187	+	0.308616i	$0.0998660\pi$
$444$		0			0
$445$	4.56011	−	3.49910i	0.216170	−	0.165873i
$446$		0			0
$447$	35.1525			1.66266
$448$		0			0
$449$	24.2879			1.14622			0.573110	−	0.819479i	$-0.305737\pi$
$449$	24.2879			1.14622			0.573110	+	0.819479i	$0.305737\pi$
$450$		0			0
$451$	9.70316	−	7.44550i	0.456904	−	0.350595i
$452$		0			0
$453$	−5.20966	+	6.78936i	−0.244771	+	0.318992i
$454$		0			0
$455$	−22.0084	+	41.0031i	−1.03177	+	1.92226i
$456$		0			0
$457$	3.21754	−	12.0080i	0.150510	−	0.561712i	−0.848938	−	0.528493i	$-0.822757\pi$
$457$	3.21754	−	12.0080i	0.150510	−	0.561712i	0.999448	−	0.0332192i	$-0.0105759\pi$
$458$		0			0
$459$	1.62723	−	12.3600i	0.0759525	−	0.576916i
$460$		0			0
$461$	0.0475722	−	0.114850i	0.00221566	−	0.00534908i	−0.922768	−	0.385356i	$-0.874079\pi$
$461$	0.0475722	−	0.114850i	0.00221566	−	0.00534908i	0.924983	+	0.380007i	$0.124079\pi$
$462$		0			0
$463$			29.8463i			1.38707i	0.720421	+	0.693537i	$0.243948\pi$
$463$			29.8463i			1.38707i	−0.720421	+	0.693537i	$0.756052\pi$
$464$		0			0
$465$	9.49872	+	5.48409i	0.440493	+	0.254318i
$466$		0			0
$467$	−3.07009	+	0.404186i	−0.142067	+	0.0187035i	−0.201224	−	0.979545i	$-0.564492\pi$
$467$	−3.07009	+	0.404186i	−0.142067	+	0.0187035i	0.0591572	+	0.998249i	$0.481159\pi$
$468$		0			0
$469$	12.8030	+	4.84414i	0.591186	+	0.223682i
$470$		0			0
$471$	7.39926	−	27.6144i	0.340940	−	1.27241i
$472$		0			0
$473$	0.532357	+	1.98678i	0.0244778	+	0.0913523i
$474$		0			0
$475$	−18.0651	−	43.6131i	−0.828886	−	2.00111i
$476$		0			0
$477$	0.0981025	+	0.0406354i	0.00449180	+	0.00186057i
$478$		0			0
$479$	−1.01212	+	1.75304i	−0.0462449	+	0.0800985i	−0.888221	−	0.459416i	$-0.848059\pi$
$479$	−1.01212	+	1.75304i	−0.0462449	+	0.0800985i	0.841976	+	0.539514i	$0.181392\pi$
$480$		0			0
$481$	14.6089	+	25.3034i	0.666110	+	1.15374i
$482$		0			0
$483$	6.44449	−	8.96030i	0.293234	−	0.407708i
$484$		0			0
$485$	−40.8657	+	53.2572i	−1.85562	+	2.41829i
$486$		0			0
$487$	−3.08575	−	11.5162i	−0.139829	−	0.521847i	−0.999931	−	0.0117264i	$-0.996267\pi$
$487$	−3.08575	−	11.5162i	−0.139829	−	0.521847i	0.860103	−	0.510121i	$-0.170399\pi$
$488$		0			0
$489$	14.3906	+	14.3906i	0.650764	+	0.650764i
$490$		0			0
$491$	−31.5965	+	13.0877i	−1.42593	+	0.590639i	−0.956343	−	0.292248i	$-0.905597\pi$
$491$	−31.5965	+	13.0877i	−1.42593	+	0.590639i	−0.469586	+	0.882887i	$0.655597\pi$
$492$		0			0
$493$	8.94333	+	11.6552i	0.402787	+	0.524923i
$494$		0			0
$495$	1.04293	−	0.602134i	0.0468761	−	0.0270639i
$496$		0			0
$497$	−18.8689	−	4.43424i	−0.846384	−	0.198903i
$498$		0			0
$499$	−1.44990	+	0.190883i	−0.0649064	+	0.00854509i	−0.162909	−	0.986641i	$-0.552088\pi$
$499$	−1.44990	+	0.190883i	−0.0649064	+	0.00854509i	0.0980030	+	0.995186i	$0.468755\pi$
$500$		0			0
$501$	−1.80999	+	13.7482i	−0.0808644	+	0.614226i
$502$		0			0
$503$	21.3971	+	21.3971i	0.954048	+	0.954048i	0.998990	−	0.0449420i	$-0.0143103\pi$
$503$	21.3971	+	21.3971i	0.954048	+	0.954048i	−0.0449420	+	0.998990i	$0.514310\pi$
$504$		0			0
$505$	9.30480	−	9.30480i	0.414058	−	0.414058i
$506$		0			0
$507$	7.84975	+	1.03344i	0.348619	+	0.0458966i
$508$		0			0
$509$	−0.0313504	−	0.238130i	−0.00138958	−	0.0105549i	0.990736	−	0.135802i	$-0.0433610\pi$
$509$	−0.0313504	−	0.238130i	−0.00138958	−	0.0105549i	−0.992126	+	0.125247i	$0.960028\pi$
$510$		0			0
$511$	−0.768042	−	0.721863i	−0.0339762	−	0.0319333i
$512$		0			0
$513$	−10.2090	−	17.6825i	−0.450739	−	0.780704i
$514$		0			0
$515$	−26.5163	+	20.3467i	−1.16845	+	0.896582i
$516$		0			0
$517$	3.51580	+	8.48789i	0.154625	+	0.373297i
$518$		0			0
$519$	26.0605	−	26.0605i	1.14393	−	1.14393i
$520$		0			0
$521$	−3.42793	+	0.918510i	−0.150180	+	0.0402406i	−0.333126	−	0.942882i	$-0.608103\pi$
$521$	−3.42793	+	0.918510i	−0.150180	+	0.0402406i	0.182946	+	0.983123i	$0.441437\pi$
$522$		0			0
$523$	25.2915	+	19.4068i	1.10592	+	0.848601i	0.989490	−	0.144598i	$-0.0461890\pi$
$523$	25.2915	+	19.4068i	1.10592	+	0.848601i	0.116428	+	0.993199i	$0.462856\pi$
$524$		0			0
$525$	−5.45988	+	54.4633i	−0.238289	+	2.37697i
$526$		0			0
$527$	3.17025	−	1.83035i	0.138098	−	0.0797311i
$528$		0			0
$529$	14.4828	+	8.36162i	0.629685	+	0.363549i
$530$		0			0
$531$	−1.23790	+	2.98856i	−0.0537204	+	0.129693i
$532$		0			0
$533$	−37.5372	+	15.5484i	−1.62592	+	0.673478i
$534$		0			0
$535$	11.2059	−	3.00262i	0.484475	−	0.129815i
$536$		0			0
$537$	28.4434	+	7.62137i	1.22742	+	0.328887i
$538$		0			0
$539$	7.36529	+	4.95850i	0.317246	+	0.213578i
$540$		0			0
$541$	−3.80171	−	28.8768i	−0.163448	−	1.24151i	−0.854786	−	0.518980i	$-0.826312\pi$
$541$	−3.80171	−	28.8768i	−0.163448	−	1.24151i	0.691338	−	0.722531i	$-0.257022\pi$
$542$		0			0
$543$	5.15107	−	8.92191i	0.221054	−	0.382876i
$544$		0			0
$545$	−28.1939			−1.20770
$546$		0			0
$547$	−15.8038	−	6.54617i	−0.675724	−	0.279894i	0.0183143	−	0.999832i	$-0.494170\pi$
$547$	−15.8038	−	6.54617i	−0.675724	−	0.279894i	−0.694038	+	0.719938i	$0.744170\pi$
$548$		0			0
$549$	−0.522619	−	0.0688040i	−0.0223048	−	0.00293648i
$550$		0			0
$551$	23.2413	+	6.22748i	0.990111	+	0.265299i
$552$		0			0
$553$	36.7340	+	19.7170i	1.56209	+	0.838452i
$554$		0			0
$555$	38.2365	+	29.3399i	1.62305	+	1.24541i
$556$		0			0
$557$	−12.7103	−	16.5644i	−0.538554	−	0.701857i	0.442242	−	0.896896i	$-0.354183\pi$
$557$	−12.7103	−	16.5644i	−0.538554	−	0.701857i	−0.980795	+	0.195039i	$0.937517\pi$
$558$		0			0
$559$		−	6.83293i		−	0.289002i
$560$		0			0
$561$			4.89949i			0.206857i
$562$		0			0
$563$	−10.3108	−	13.4373i	−0.434548	−	0.566315i	0.523827	−	0.851824i	$-0.324504\pi$
$563$	−10.3108	−	13.4373i	−0.434548	−	0.566315i	−0.958376	+	0.285510i	$0.907837\pi$
$564$		0			0
$565$	8.87362	+	6.80897i	0.373316	+	0.286455i
$566$		0			0
$567$	0.677514	+	21.8591i	0.0284529	+	0.917995i
$568$		0			0
$569$	7.72602	+	2.07018i	0.323891	+	0.0867864i	0.417101	−	0.908860i	$-0.363046\pi$
$569$	7.72602	+	2.07018i	0.323891	+	0.0867864i	−0.0932098	+	0.995646i	$0.529713\pi$
$570$		0			0
$571$	−25.4025	−	3.34430i	−1.06306	−	0.139955i	−0.421347	−	0.906899i	$-0.638443\pi$
$571$	−25.4025	−	3.34430i	−1.06306	−	0.139955i	−0.641713	+	0.766945i	$0.721776\pi$
$572$		0			0
$573$	−8.27025	−	3.42565i	−0.345495	−	0.143109i
$574$		0			0
$575$	31.1282			1.29814
$576$		0			0
$577$	0.467156	−	0.809139i	0.0194480	−	0.0336849i	−0.856138	−	0.516748i	$-0.827142\pi$
$577$	0.467156	−	0.809139i	0.0194480	−	0.0336849i	0.875586	+	0.483063i	$0.160476\pi$
$578$		0			0
$579$	2.13605	+	16.2249i	0.0887714	+	0.674286i
$580$		0			0
$581$	−3.74100	+	0.610956i	−0.155203	+	0.0253467i
$582$		0			0
$583$	−0.571987	−	0.153264i	−0.0236893	−	0.00634753i
$584$		0			0
$585$	−3.86427	+	1.03543i	−0.159768	+	0.0428097i
$586$		0			0
$587$	1.27162	−	0.526722i	0.0524853	−	0.0217401i	−0.356286	−	0.934377i	$-0.615957\pi$
$587$	1.27162	−	0.526722i	0.0524853	−	0.0217401i	0.408772	+	0.912637i	$0.365957\pi$
$588$		0			0
$589$	2.29439	−	5.53914i	0.0945385	−	0.228236i
$590$		0			0
$591$	13.3536	+	7.70973i	0.549296	+	0.317136i
$592$		0			0
$593$	12.1161	−	6.99521i	0.497547	−	0.287259i	−0.230153	−	0.973154i	$-0.573923\pi$
$593$	12.1161	−	6.99521i	0.497547	−	0.287259i	0.727700	+	0.685895i	$0.240589\pi$
$594$		0			0
$595$	20.7993	+	14.9594i	0.852690	+	0.613277i
$596$		0			0
$597$	7.49874	+	5.75399i	0.306903	+	0.235495i
$598$		0			0
$599$	−28.0243	+	7.50909i	−1.14504	+	0.306813i	−0.780977	−	0.624560i	$-0.785278\pi$
$599$	−28.0243	+	7.50909i	−1.14504	+	0.306813i	−0.364065	+	0.931373i	$0.618612\pi$
$600$		0			0
$601$	26.1999	−	26.1999i	1.06871	−	1.06871i	0.0712567	−	0.997458i	$-0.477299\pi$
$601$	26.1999	−	26.1999i	1.06871	−	1.06871i	0.997458	−	0.0712567i	$-0.0227009\pi$
$602$		0			0
$603$	0.450334	+	1.08720i	0.0183390	+	0.0442743i
$604$		0			0
$605$	31.1005	−	23.8643i	1.26442	−	0.970221i
$606$		0			0
$607$	13.3344	+	23.0959i	0.541227	+	0.937432i	0.998834	+	0.0482775i	$0.0153732\pi$
$607$	13.3344	+	23.0959i	0.541227	+	0.937432i	−0.457607	+	0.889154i	$0.651293\pi$
$608$		0			0
$609$	−20.3293	−	19.1070i	−0.823785	−	0.774255i
$610$		0			0
$611$	−3.98366	−	30.2589i	−0.161162	−	1.22415i
$612$		0			0
$613$	−47.5085	−	6.25461i	−1.91885	−	0.252621i	−0.926521	−	0.376243i	$-0.877216\pi$
$613$	−47.5085	−	6.25461i	−1.91885	−	0.252621i	−0.992329	+	0.123622i	$0.960549\pi$
$614$		0			0
$615$	−47.3909	+	47.3909i	−1.91099	+	1.91099i
$616$		0			0
$617$	9.12258	+	9.12258i	0.367261	+	0.367261i	0.866478	−	0.499216i	$-0.166379\pi$
$617$	9.12258	+	9.12258i	0.367261	+	0.367261i	−0.499216	+	0.866478i	$0.666379\pi$
$618$		0			0
$619$	4.84273	−	36.7842i	0.194646	−	1.47848i	−0.563349	−	0.826219i	$-0.690487\pi$
$619$	4.84273	−	36.7842i	0.194646	−	1.47848i	0.757994	−	0.652261i	$-0.226179\pi$
$620$		0			0
$621$	13.3486	−	1.75737i	0.535660	−	0.0705210i
$622$		0			0
$623$	1.05148	+	3.48810i	0.0421266	+	0.139748i
$624$		0			0
$625$	−58.2403	+	33.6251i	−2.32961	+	1.34500i
$626$		0			0
$627$	4.88496	+	6.36621i	0.195087	+	0.254242i
$628$		0			0
$629$	14.8613	−	6.15574i	0.592557	−	0.245445i
$630$		0			0
$631$	1.05556	+	1.05556i	0.0420211	+	0.0420211i	0.727805	−	0.685784i	$-0.240541\pi$
$631$	1.05556	+	1.05556i	0.0420211	+	0.0420211i	−0.685784	+	0.727805i	$0.740541\pi$
$632$		0			0
$633$	4.77550	+	17.8224i	0.189809	+	0.708377i
$634$		0			0
$635$	−11.3651	+	14.8113i	−0.451009	+	0.587767i
$636$		0			0
$637$	−19.3705	−	22.2436i	−0.767488	−	0.881322i
$638$		0			0
$639$	−0.833145	−	1.44305i	−0.0329587	−	0.0570861i
$640$		0			0
$641$	13.0811	−	22.6571i	0.516672	−	0.894902i	−0.483140	−	0.875543i	$-0.660504\pi$
$641$	13.0811	−	22.6571i	0.516672	−	0.894902i	0.999813	−	0.0193595i	$-0.00616271\pi$
$642$		0			0
$643$	23.2625	+	9.63565i	0.917384	+	0.379993i	0.790879	−	0.611973i	$-0.209624\pi$
$643$	23.2625	+	9.63565i	0.917384	+	0.379993i	0.126505	+	0.991966i	$0.459624\pi$
$644$		0			0
$645$	−4.31330	−	10.4132i	−0.169836	−	0.410020i
$646$		0			0
$647$	3.92711	+	14.6562i	0.154391	+	0.576194i	0.999157	+	0.0410580i	$0.0130728\pi$
$647$	3.92711	+	14.6562i	0.154391	+	0.576194i	−0.844766	+	0.535136i	$0.820260\pi$
$648$		0			0
$649$	4.66897	−	17.4248i	0.183273	−	0.683985i
$650$		0			0
$651$	−5.38152	+	4.40085i	−0.210918	+	0.172483i
$652$		0			0
$653$	12.9792	−	1.70875i	0.507916	−	0.0668684i	0.127786	−	0.991802i	$-0.459213\pi$
$653$	12.9792	−	1.70875i	0.507916	−	0.0668684i	0.380129	+	0.924933i	$0.375879\pi$
$654$		0			0
$655$	−25.8933	−	14.9495i	−1.01173	−	0.584125i
$656$		0			0
$657$		−	0.0906117i		−	0.00353510i
$658$		0			0
$659$	−9.26965	+	22.3789i	−0.361094	+	0.871759i	0.634046	+	0.773295i	$0.281393\pi$
$659$	−9.26965	+	22.3789i	−0.361094	+	0.871759i	−0.995141	+	0.0984636i	$0.968607\pi$
$660$		0			0
$661$	−3.85289	+	29.2656i	−0.149860	+	1.13830i	0.736877	+	0.676027i	$0.236300\pi$
$661$	−3.85289	+	29.2656i	−0.149860	+	1.13830i	−0.886737	+	0.462274i	$0.847034\pi$
$662$		0			0
$663$	4.21257	−	15.7215i	0.163603	−	0.610574i
$664$		0			0
$665$	41.9410	−	1.29995i	1.62640	−	0.0504097i
$666$		0			0
$667$	−9.65863	+	12.5874i	−0.373984	+	0.487385i
$668$		0			0
$669$	30.2809	−	23.2354i	1.17073	−	0.898332i
$670$		0			0
$671$	2.93964			0.113484
$672$		0			0
$673$	21.9438			0.845872			0.422936	−	0.906160i	$-0.360999\pi$
$673$	21.9438			0.845872			0.422936	+	0.906160i	$0.360999\pi$
$674$		0			0
$675$	−52.9727	+	40.6474i	−2.03892	+	1.56452i
$676$		0			0
$677$	−9.61314	+	12.5281i	−0.369463	+	0.481493i	−0.940675	−	0.339309i	$-0.889807\pi$
$677$	−9.61314	+	12.5281i	−0.369463	+	0.481493i	0.571212	+	0.820803i	$0.306473\pi$
$678$		0			0
$679$	−22.4053	−	36.1708i	−0.859835	−	1.38811i
$680$		0			0
$681$	4.72635	−	17.6390i	0.181114	−	0.675928i
$682$		0			0
$683$	3.89910	−	29.6166i	0.149195	−	1.13325i	−0.738975	−	0.673733i	$-0.764690\pi$
$683$	3.89910	−	29.6166i	0.149195	−	1.13325i	0.888170	−	0.459515i	$-0.151977\pi$
$684$		0			0
$685$	14.0690	−	33.9655i	0.537547	−	1.29775i
$686$		0			0
$687$		−	28.1596i		−	1.07436i
$688$		0			0
$689$	1.70362	+	0.983588i	0.0649029	+	0.0374717i
$690$		0			0
$691$	29.1987	−	3.84408i	1.11077	−	0.146236i	0.447261	−	0.894404i	$-0.352400\pi$
$691$	29.1987	−	3.84408i	1.11077	−	0.146236i	0.663509	+	0.748168i	$0.269066\pi$
$692$		0			0
$693$	0.123026	+	0.753310i	0.00467336	+	0.0286159i
$694$		0			0
$695$	−1.08295	+	4.04164i	−0.0410788	+	0.153308i
$696$		0			0
$697$	5.78942	+	21.6064i	0.219290	+	0.818401i
$698$		0			0
$699$	15.1356	+	36.5405i	0.572480	+	1.38209i
$700$		0			0
$701$	16.1923	+	6.70707i	0.611575	+	0.253323i	0.666902	−	0.745146i	$-0.267620\pi$
$701$	16.1923	+	6.70707i	0.611575	+	0.253323i	−0.0553270	+	0.998468i	$0.517620\pi$
$702$		0			0
$703$	13.1727	−	22.8157i	0.496817	−	0.860512i
$704$		0			0
$705$	−25.1720	−	43.5992i	−0.948033	−	1.64204i
$706$		0			0
$707$	3.42893	+	7.60297i	0.128958	+	0.285939i
$708$		0			0
$709$	19.3751	−	25.2501i	0.727648	−	0.948289i	−0.272255	−	0.962225i	$-0.587769\pi$
$709$	19.3751	−	25.2501i	0.727648	−	0.948289i	0.999903	+	0.0139360i	$0.00443611\pi$
$710$		0			0
$711$	0.927623	+	3.46193i	0.0347886	+	0.129833i
$712$		0			0
$713$	2.79553	+	2.79553i	0.104693	+	0.104693i
$714$		0			0
$715$	20.6119	−	8.53772i	0.770840	−	0.319292i
$716$		0			0
$717$	−6.73981	−	8.78349i	−0.251703	−	0.328025i
$718$		0			0
$719$	12.9677	−	7.48692i	0.483615	−	0.279215i	−0.238307	−	0.971190i	$-0.576592\pi$
$719$	12.9677	−	7.48692i	0.483615	−	0.279215i	0.721922	+	0.691975i	$0.243259\pi$
$720$		0			0
$721$	−6.11417	−	20.2827i	−0.227704	−	0.755368i
$722$		0			0
$723$	10.1203	−	1.33237i	0.376380	−	0.0495513i
$724$		0			0
$725$	10.2703	−	78.0110i	0.381431	−	2.89726i
$726$		0			0
$727$	−2.54725	−	2.54725i	−0.0944723	−	0.0944723i	0.658291	−	0.752763i	$-0.271280\pi$
$727$	−2.54725	−	2.54725i	−0.0944723	−	0.0944723i	−0.752763	+	0.658291i	$0.771280\pi$
$728$		0			0
$729$	−20.3115	+	20.3115i	−0.752280	+	0.752280i
$730$		0			0
$731$	−3.72964	−	0.491017i	−0.137946	−	0.0181609i
$732$		0			0
$733$	−2.16025	−	16.4087i	−0.0797908	−	0.606071i	−0.983893	−	0.178756i	$-0.942793\pi$
$733$	−2.16025	−	16.4087i	−0.0797908	−	0.606071i	0.904103	−	0.427315i	$-0.140541\pi$
$734$		0			0
$735$	−43.5615	−	21.6710i	−1.60679	−	0.799346i
$736$		0			0
$737$	−3.28128	−	5.68335i	−0.120868	−	0.209349i
$738$		0			0
$739$	−4.80934	+	3.69034i	−0.176915	+	0.135751i	−0.693423	−	0.720531i	$-0.743898\pi$
$739$	−4.80934	+	3.69034i	−0.176915	+	0.135751i	0.516508	+	0.856282i	$0.327232\pi$
$740$		0			0
$741$	−10.2013	−	24.6281i	−0.374753	−	0.904735i
$742$		0			0
$743$	−32.7737	+	32.7737i	−1.20235	+	1.20235i	−0.228898	+	0.973450i	$0.573512\pi$
$743$	−32.7737	+	32.7737i	−1.20235	+	1.20235i	−0.973450	+	0.228898i	$0.926488\pi$
$744$		0			0
$745$	−85.1222	+	22.8084i	−3.11864	+	0.835636i
$746$		0			0
$747$	−0.258525	−	0.198373i	−0.00945893	−	0.00725809i
$748$		0			0
$749$	−0.733463	+	7.31643i	−0.0268002	+	0.267337i
$750$		0			0
$751$	−33.0454	+	19.0788i	−1.20584	+	0.696194i	−0.961849	−	0.273582i	$-0.911792\pi$
$751$	−33.0454	+	19.0788i	−1.20584	+	0.696194i	−0.243995	+	0.969776i	$0.578458\pi$
$752$		0			0
$753$	−38.0191	−	21.9503i	−1.38549	−	0.799915i
$754$		0			0
$755$	8.21003	−	19.8208i	0.298794	−	0.721352i
$756$		0			0
$757$	−17.8387	+	7.38905i	−0.648360	+	0.268559i	−0.682531	−	0.730857i	$-0.739121\pi$
$757$	−17.8387	+	7.38905i	−0.648360	+	0.268559i	0.0341712	+	0.999416i	$0.489121\pi$
$758$		0			0
$759$	−5.11105	+	1.36950i	−0.185520	+	0.0497098i
$760$		0			0
$761$	9.60552	+	2.57379i	0.348200	+	0.0932999i	0.428680	−	0.903456i	$-0.358979\pi$
$761$	9.60552	+	2.57379i	0.348200	+	0.0932999i	−0.0804803	+	0.996756i	$0.525645\pi$
$762$		0			0
$763$	6.32376	−	16.7135i	0.228936	−	0.605071i
$764$		0			0
$765$	0.287484	+	2.18366i	0.0103940	+	0.0789502i
$766$		0			0
$767$	−29.9637	+	51.8987i	−1.08193	+	1.87395i
$768$		0			0
$769$	−17.8563			−0.643913			−0.321957	−	0.946754i	$-0.604341\pi$
$769$	−17.8563			−0.643913			−0.321957	+	0.946754i	$0.604341\pi$
$770$		0			0
$771$	−22.2625	−	9.22144i	−0.801765	−	0.332102i
$772$		0			0
$773$	−4.84788	−	0.638235i	−0.174366	−	0.0229557i	0.0428375	−	0.999082i	$-0.486360\pi$
$773$	−4.84788	−	0.638235i	−0.174366	−	0.0229557i	−0.217204	+	0.976126i	$0.569694\pi$
$774$		0			0
$775$	−18.9383	−	5.07451i	−0.680285	−	0.182282i
$776$		0			0
$777$	−25.9692	+	16.0861i	−0.931638	+	0.577084i
$778$		0			0
$779$	29.0649	+	22.3023i	1.04136	+	0.799063i
$780$		0			0
$781$	5.65686	+	7.37217i	0.202419	+	0.263797i
$782$		0			0
$783$		−	34.0330i		−	1.21624i
$784$		0			0
$785$			71.6696i			2.55800i
$786$		0			0
$787$	9.50913	+	12.3925i	0.338964	+	0.441747i	0.931469	−	0.363820i	$-0.118528\pi$
$787$	9.50913	+	12.3925i	0.338964	+	0.441747i	−0.592505	+	0.805567i	$0.701861\pi$
$788$		0			0
$789$	−26.1727	−	20.0830i	−0.931773	−	0.714974i
$790$		0			0
$791$	−6.02671	+	3.73312i	−0.214285	+	0.132735i
$792$		0			0
$793$	−9.43276	−	2.52750i	−0.334967	−	0.0897542i
$794$		0			0
$795$	3.21718	+	0.423549i	0.114101	+	0.0150217i
$796$		0			0
$797$	16.1610	+	6.69409i	0.572450	+	0.237117i	0.650080	−	0.759866i	$-0.274735\pi$
$797$	16.1610	+	6.69409i	0.572450	+	0.237117i	−0.0776299	+	0.996982i	$0.524735\pi$
$798$		0			0
$799$	−16.8026			−0.594434
$800$		0			0
$801$	−0.156595	+	0.271230i	−0.00553300	+	0.00958344i
$802$		0			0
$803$	0.0659569	+	0.500992i	0.00232757	+	0.0176796i
$804$		0			0
$805$	−9.79159	+	25.8789i	−0.345108	+	0.912113i
$806$		0			0
$807$	45.4545	+	12.1795i	1.60007	+	0.428739i
$808$		0			0
$809$	43.8659	−	11.7538i	1.54224	−	0.413242i	0.615252	−	0.788330i	$-0.289054\pi$
$809$	43.8659	−	11.7538i	1.54224	−	0.413242i	0.926989	+	0.375088i	$0.122387\pi$
$810$		0			0
$811$	−31.4530	+	13.0282i	−1.10446	+	0.457483i	−0.859027	−	0.511930i	$-0.828931\pi$
$811$	−31.4530	+	13.0282i	−1.10446	+	0.457483i	−0.245435	+	0.969413i	$0.578931\pi$
$812$		0			0
$813$	6.76821	−	16.3399i	0.237372	−	0.573066i
$814$		0			0
$815$	−44.1841	−	25.5097i	−1.54770	−	0.893567i
$816$		0			0
$817$	−5.33572	+	3.08058i	−0.186673	+	0.107776i
$818$		0			0
$819$	0.252929	−	2.52301i	0.00883804	−	0.0881610i
$820$		0			0
$821$	31.6522	+	24.2876i	1.10467	+	0.847643i	0.989331	−	0.145683i	$-0.0465381\pi$
$821$	31.6522	+	24.2876i	1.10467	+	0.847643i	0.115338	+	0.993326i	$0.463205\pi$
$822$		0			0
$823$	−1.84743	+	0.495017i	−0.0643973	+	0.0172552i	−0.290874	−	0.956761i	$-0.593946\pi$
$823$	−1.84743	+	0.495017i	−0.0643973	+	0.0172552i	0.226477	+	0.974017i	$0.427279\pi$
$824$		0			0
$825$	18.5554	−	18.5554i	0.646017	−	0.646017i
$826$		0			0
$827$	−7.25041	−	17.5040i	−0.252121	−	0.608675i	0.746254	−	0.665662i	$-0.231851\pi$
$827$	−7.25041	−	17.5040i	−0.252121	−	0.608675i	−0.998375	+	0.0569871i	$0.981851\pi$
$828$		0			0
$829$	25.7567	−	19.7638i	0.894566	−	0.686425i	−0.0555050	−	0.998458i	$-0.517677\pi$
$829$	25.7567	−	19.7638i	0.894566	−	0.686425i	0.950071	+	0.312034i	$0.101010\pi$
$830$		0			0
$831$	−3.29214	−	5.70216i	−0.114203	−	0.197806i
$832$		0			0
$833$	−13.5332	+	8.97466i	−0.468899	+	0.310953i
$834$		0			0
$835$	−4.53753	−	34.4659i	−0.157028	−	1.19274i
$836$		0			0
$837$	−8.40774	−	1.10690i	−0.290614	−	0.0382601i
$838$		0			0
$839$	28.1317	−	28.1317i	0.971216	−	0.971216i	−0.0283813	−	0.999597i	$-0.509035\pi$
$839$	28.1317	−	28.1317i	0.971216	−	0.971216i	0.999597	+	0.0283813i	$0.00903527\pi$
$840$		0			0
$841$	7.85263	+	7.85263i	0.270780	+	0.270780i
$842$		0			0
$843$	4.58570	−	34.8318i	0.157940	−	1.19967i
$844$		0			0
$845$	−19.6788	+	2.59076i	−0.676971	+	0.0891250i
$846$		0			0
$847$	7.17121	+	23.7892i	0.246406	+	0.817408i
$848$		0			0
$849$	2.59258	−	1.49683i	0.0889771	−	0.0513709i
$850$		0			0
$851$	10.5756	+	13.7823i	0.362526	+	0.472453i
$852$		0			0
$853$	−24.5977	+	10.1887i	−0.842208	+	0.348854i	−0.761724	−	0.647902i	$-0.775647\pi$
$853$	−24.5977	+	10.1887i	−0.842208	+	0.348854i	−0.0804840	+	0.996756i	$0.525647\pi$
$854$		0			0
$855$	2.55073	+	2.55073i	0.0872331	+	0.0872331i
$856$		0			0
$857$	7.31269	+	27.2913i	0.249797	+	0.932254i	0.970912	+	0.239438i	$0.0769633\pi$
$857$	7.31269	+	27.2913i	0.249797	+	0.932254i	−0.721115	+	0.692815i	$0.756370\pi$
$858$		0			0
$859$	18.6610	−	24.3195i	0.636706	−	0.829772i	−0.357871	−	0.933771i	$-0.616497\pi$
$859$	18.6610	−	24.3195i	0.636706	−	0.829772i	0.994577	+	0.103999i	$0.0331640\pi$
$860$		0			0
$861$	−17.4641	−	38.7232i	−0.595175	−	1.31968i
$862$		0			0
$863$	7.75978	+	13.4403i	0.264146	+	0.457514i	0.967340	−	0.253484i	$-0.0815766\pi$
$863$	7.75978	+	13.4403i	0.264146	+	0.457514i	−0.703193	+	0.710999i	$0.748243\pi$
$864$		0			0
$865$	−46.1967	+	80.0150i	−1.57073	+	2.72059i
$866$		0			0
$867$	17.8733	+	7.40338i	0.607010	+	0.251432i
$868$		0			0
$869$	−7.64879	−	18.4658i	−0.259468	−	0.626410i
$870$		0			0
$871$	5.64248	+	21.0580i	0.191188	+	0.713524i
$872$		0			0
$873$	0.946686	−	3.53308i	0.0320405	−	0.119577i
$874$		0			0
$875$	−13.2166	−	80.9276i	−0.446801	−	2.73585i
$876$		0			0
$877$	33.2146	−	4.37279i	1.12158	−	0.147659i	0.453150	−	0.891434i	$-0.350300\pi$
$877$	33.2146	−	4.37279i	1.12158	−	0.147659i	0.668429	+	0.743776i	$0.266967\pi$
$878$		0			0
$879$	3.85310	+	2.22459i	0.129962	+	0.0750336i
$880$		0			0
$881$			7.07606i			0.238399i	0.992870	+	0.119199i	$0.0380327\pi$
$881$			7.07606i			0.238399i	−0.992870	+	0.119199i	$0.961967\pi$
$882$		0			0
$883$	11.2844	−	27.2429i	0.379750	−	0.916796i	−0.612263	−	0.790654i	$-0.709740\pi$
$883$	11.2844	−	27.2429i	0.379750	−	0.916796i	0.992012	−	0.126142i	$-0.0402595\pi$
$884$		0			0
$885$	−12.9029	+	98.0070i	−0.433725	+	3.29447i
$886$		0			0
$887$	9.85694	−	36.7866i	0.330964	−	1.23517i	−0.577215	−	0.816592i	$-0.695861\pi$
$887$	9.85694	−	36.7866i	0.330964	−	1.23517i	0.908179	−	0.418582i	$-0.137473\pi$
$888$		0			0
$889$	−6.23108	−	10.0594i	−0.208984	−	0.337381i
$890$		0			0
$891$	6.38260	−	8.31797i	0.213825	−	0.278663i
$892$		0			0
$893$	−21.8327	+	16.7528i	−0.730603	+	0.560611i
$894$		0			0
$895$	−73.8210			−2.46756
$896$		0			0
$897$	17.5779			0.586910
$898$		0			0
$899$	7.92828	−	6.08358i	0.264423	−	0.202899i
$900$		0			0
$901$	0.659298	−	0.859214i	0.0219644	−	0.0286246i
$902$		0			0
$903$	7.14048	−	0.221317i	0.237620	−	0.00736496i
$904$		0			0
$905$	−6.68446	+	24.9468i	−0.222199	+	0.829258i
$906$		0			0
$907$	−7.14968	+	54.3072i	−0.237401	+	1.80324i	0.293663	+	0.955909i	$0.405126\pi$
$907$	−7.14968	+	54.3072i	−0.237401	+	1.80324i	−0.531064	+	0.847332i	$0.678208\pi$
$908$		0			0
$909$	−0.274385	+	0.662424i	−0.00910077	+	0.0219712i
$910$		0			0
$911$		−	7.05636i		−	0.233787i	−0.993144	−	0.116894i	$-0.962706\pi$
$911$		−	7.05636i		−	0.233787i	0.993144	−	0.116894i	$-0.0372937\pi$
$912$		0			0
$913$	1.57378	+	0.908623i	0.0520846	+	0.0300710i
$914$		0			0
$915$	−15.9708	+	2.10260i	−0.527978	+	0.0695097i
$916$		0			0
$917$	14.6699	−	11.9966i	0.484443	−	0.396163i
$918$		0			0
$919$	11.6689	−	43.5489i	0.384922	−	1.43655i	−0.453369	−	0.891323i	$-0.649778\pi$
$919$	11.6689	−	43.5489i	0.384922	−	1.43655i	0.838290	−	0.545224i	$-0.183555\pi$
$920$		0			0
$921$	0.668489	+	2.49484i	0.0220275	+	0.0822076i
$922$		0			0
$923$	−11.8132	−	28.5197i	−0.388837	−	0.938737i
$924$		0			0
$925$	−79.5959	−	32.9697i	−2.61710	−	1.08404i
$926$		0			0
$927$	0.910573	−	1.57716i	0.0299071	−	0.0518007i
$928$		0			0
$929$	9.17286	+	15.8879i	0.300952	+	0.521264i	0.976352	−	0.216188i	$-0.0693623\pi$
$929$	9.17286	+	15.8879i	0.300952	+	0.521264i	−0.675400	+	0.737452i	$0.736029\pi$
$930$		0			0
$931$	−8.63654	+	25.1545i	−0.283051	+	0.824404i
$932$		0			0
$933$	21.7713	−	28.3729i	0.712761	−	0.928888i
$934$		0			0
$935$	−3.17900	−	11.8642i	−0.103964	−	0.388000i
$936$		0			0
$937$	2.34099	+	2.34099i	0.0764767	+	0.0764767i	0.744310	−	0.667834i	$-0.232778\pi$
$937$	2.34099	+	2.34099i	0.0764767	+	0.0764767i	−0.667834	+	0.744310i	$0.732778\pi$
$938$		0			0
$939$	−0.710817	+	0.294430i	−0.0231966	+	0.00960836i
$940$		0			0
$941$	26.5622	+	34.6166i	0.865904	+	1.12847i	0.990670	+	0.136282i	$0.0435152\pi$
$941$	26.5622	+	34.6166i	0.865904	+	1.12847i	−0.124766	+	0.992186i	$0.539818\pi$
$942$		0			0
$943$	−20.9211	+	12.0788i	−0.681286	+	0.393341i
$944$		0			0
$945$	−17.1299	−	56.8257i	−0.557237	−	1.84854i
$946$		0			0
$947$	26.9862	−	3.55280i	0.876933	−	0.115450i	0.321399	−	0.946944i	$-0.395847\pi$
$947$	26.9862	−	3.55280i	0.876933	−	0.115450i	0.555534	+	0.831494i	$0.312514\pi$
$948$		0			0
$949$	0.219109	−	1.66430i	0.00711259	−	0.0540255i
$950$		0			0
$951$	−10.0624	−	10.0624i	−0.326296	−	0.326296i
$952$		0			0
$953$	−10.9528	+	10.9528i	−0.354796	+	0.354796i	−0.861891	−	0.507094i	$-0.830720\pi$
$953$	−10.9528	+	10.9528i	−0.354796	+	0.354796i	0.507094	+	0.861891i	$0.330720\pi$
$954$		0			0
$955$	22.2492	+	2.92917i	0.719968	+	0.0947856i
$956$		0			0
$957$	1.74581	+	13.2608i	0.0564341	+	0.428660i
$958$		0			0
$959$	16.9794	+	15.9585i	0.548292	+	0.515325i
$960$		0			0
$961$	14.2549	+	24.6903i	0.459837	+	0.796460i
$962$		0			0
$963$	−0.501498	+	0.384813i	−0.0161606	+	0.0124004i
$964$		0			0
$965$	−15.6999	−	37.9029i	−0.505398	−	1.22014i
$966$		0			0
$967$	−10.0966	+	10.0966i	−0.324686	+	0.324686i	−0.850562	−	0.525875i	$-0.823738\pi$
$967$	−10.0966	+	10.0966i	−0.324686	+	0.324686i	0.525875	+	0.850562i	$0.323738\pi$
$968$		0			0
$969$	−14.1759	+	3.79842i	−0.455395	+	0.122023i
$970$		0			0
$971$	−16.9836	−	13.0320i	−0.545031	−	0.418217i	0.299205	−	0.954189i	$-0.403279\pi$
$971$	−16.9836	−	13.0320i	−0.545031	−	0.418217i	−0.844236	+	0.535972i	$0.819945\pi$
$972$		0			0
$973$	−2.15301	−	1.54850i	−0.0690223	−	0.0496427i
$974$		0			0
$975$	−75.4948	+	43.5869i	−2.41777	+	1.39590i
$976$		0			0
$977$	−35.3343	−	20.4002i	−1.13044	−	0.652662i	−0.186397	−	0.982475i	$-0.559681\pi$
$977$	−35.3343	−	20.4002i	−1.13044	−	0.652662i	−0.944046	+	0.329813i	$0.893014\pi$
$978$		0			0
$979$	0.668382	−	1.61362i	0.0213616	−	0.0515714i
$980$		0			0
$981$	1.41928	−	0.587886i	0.0453142	−	0.0187698i
$982$		0			0
$983$	−5.29721	+	1.41938i	−0.168955	+	0.0452713i	−0.342305	−	0.939589i	$-0.611208\pi$
$983$	−5.29721	+	1.41938i	−0.168955	+	0.0452713i	0.173350	+	0.984860i	$0.444541\pi$
$984$		0			0
$985$	−37.3384	−	10.0048i	−1.18970	−	0.318779i
$986$		0			0
$987$	31.4919	−	5.14305i	1.00240	−	0.163705i
$988$		0			0
$989$	−0.530289	−	4.02794i	−0.0168622	−	0.128081i
$990$		0			0
$991$	21.6395	−	37.4807i	0.687402	−	1.19062i	−0.285274	−	0.958446i	$-0.592084\pi$
$991$	21.6395	−	37.4807i	0.687402	−	1.19062i	0.972675	−	0.232169i	$-0.0745822\pi$
$992$		0			0
$993$	57.6208			1.82854
$994$		0			0
$995$	−21.8917	−	9.06786i	−0.694015	−	0.287470i
$996$		0			0
$997$	7.14636	+	0.940836i	0.226327	+	0.0297966i	0.242837	−	0.970067i	$-0.421922\pi$
$997$	7.14636	+	0.940836i	0.226327	+	0.0297966i	−0.0165094	+	0.999864i	$0.505255\pi$
$998$		0			0
$999$	−35.9941	−	9.64460i	−1.13880	−	0.305142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.9		240
4.3	odd	2		224.2.bd.a.221.2	yes	240
7.2	even	3	inner	896.2.bh.a.849.9		240
28.23	odd	6		224.2.bd.a.93.18	yes	240
32.11	odd	8		224.2.bd.a.53.18	✓	240
32.21	even	8	inner	896.2.bh.a.305.9		240
224.107	odd	24		224.2.bd.a.149.2	yes	240
224.149	even	24	inner	896.2.bh.a.177.9		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.18	✓	240	32.11	odd	8
224.2.bd.a.93.18	yes	240	28.23	odd	6
224.2.bd.a.149.2	yes	240	224.107	odd	24
224.2.bd.a.221.2	yes	240	4.3	odd	2
896.2.bh.a.81.9		240	1.1	even	1	trivial
896.2.bh.a.177.9		240	224.149	even	24	inner
896.2.bh.a.305.9		240	32.21	even	8	inner
896.2.bh.a.849.9		240	7.2	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32101 + 1.01365i) q^{3} +(2.54115 - 3.31169i) q^{5} +(1.39322 + 2.24921i) q^{7} +(-0.0588677 + 0.219697i) q^{9} +O(q^{10})\)	\(q+(-1.32101 + 1.01365i) q^{3} +(2.54115 - 3.31169i) q^{5} +(1.39322 + 2.24921i) q^{7} +(-0.0588677 + 0.219697i) q^{9} +(0.165561 - 1.25756i) q^{11} +(-1.61250 + 3.89292i) q^{13} +6.95061i q^{15} +(2.00901 + 1.15990i) q^{17} +(3.76690 - 0.495921i) q^{19} +(-4.12037 - 1.55899i) q^{21} +(-0.648431 + 2.41998i) q^{23} +(-3.21575 - 12.0014i) q^{25} +(-2.05655 - 4.96494i) q^{27} +(5.85081 + 2.42349i) q^{29} +(0.789008 - 1.36660i) q^{31} +(1.05601 + 1.82907i) q^{33} +(10.9891 + 1.10164i) q^{35} +(4.22120 - 5.50118i) q^{37} +(-1.81592 - 6.77709i) q^{39} +(6.81824 + 6.81824i) q^{41} +(-1.49817 + 0.620564i) q^{43} +(0.577978 + 0.753235i) q^{45} +(-6.27272 + 3.62156i) q^{47} +(-3.11785 + 6.26730i) q^{49} +(-3.82966 + 0.504184i) q^{51} +(0.0609370 - 0.462862i) q^{53} +(-3.74393 - 3.74393i) q^{55} +(-4.47342 + 4.47342i) q^{57} +(14.1005 + 1.85637i) q^{59} +(0.302505 + 2.29776i) q^{61} +(-0.576161 + 0.173682i) q^{63} +(8.79453 + 15.2326i) q^{65} +(4.10470 - 3.14964i) q^{67} +(-1.59642 - 3.85410i) q^{69} +(-5.18029 + 5.18029i) q^{71} +(-0.384811 + 0.103110i) q^{73} +(16.4132 + 12.5943i) q^{75} +(3.05917 - 1.37968i) q^{77} +(13.6466 - 7.87887i) q^{79} +(7.15850 + 4.13296i) q^{81} +(-0.548270 + 1.32364i) q^{83} +(8.94643 - 3.70573i) q^{85} +(-10.1856 + 2.72921i) q^{87} +(1.33006 + 0.356387i) q^{89} +(-11.0025 + 1.79686i) q^{91} +(0.342964 + 2.60507i) q^{93} +(7.92991 - 13.7350i) q^{95} -16.0816 q^{97} +(0.266536 + 0.110403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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Database

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