LMFDB - Embedded newform 864.2.v.b.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933793 - 1.06209i) q^{2} +(-0.256062 + 1.98354i) q^{4} +(1.30670 - 0.541253i) q^{5} +(-1.80429 + 1.80429i) q^{7} +(2.34580 - 1.58026i) q^{8} +O(q^{10})$	\(q+(-0.933793 - 1.06209i) q^{2} +(-0.256062 + 1.98354i) q^{4} +(1.30670 - 0.541253i) q^{5} +(-1.80429 + 1.80429i) q^{7} +(2.34580 - 1.58026i) q^{8} +(-1.79505 - 0.882413i) q^{10} +(0.711373 + 1.71741i) q^{11} +(-1.64790 - 0.682581i) q^{13} +(3.60115 + 0.231482i) q^{14} +(-3.86886 - 1.01582i) q^{16} -0.517642i q^{17} +(2.48448 + 1.02911i) q^{19} +(0.739002 + 2.73049i) q^{20} +(1.15976 - 2.35924i) q^{22} +(4.76398 + 4.76398i) q^{23} +(-2.12102 + 2.12102i) q^{25} +(0.813833 + 2.38760i) q^{26} +(-3.11688 - 4.04090i) q^{28} +(-0.367694 + 0.887691i) q^{29} -4.87060 q^{31} +(2.53383 + 5.05764i) q^{32} +(-0.549781 + 0.483371i) q^{34} +(-1.38109 + 3.33425i) q^{35} +(-0.997414 + 0.413142i) q^{37} +(-1.22699 - 3.59971i) q^{38} +(2.20994 - 3.33460i) q^{40} +(-1.37996 - 1.37996i) q^{41} +(4.74827 + 11.4633i) q^{43} +(-3.58870 + 0.971275i) q^{44} +(0.611195 - 9.50833i) q^{46} +10.8254i q^{47} +0.489051i q^{49} +(4.23331 + 0.272117i) q^{50} +(1.77589 - 3.09389i) q^{52} +(-1.87709 - 4.53169i) q^{53} +(1.85910 + 1.85910i) q^{55} +(-1.38127 + 7.08376i) q^{56} +(1.28616 - 0.438396i) q^{58} +(12.7983 - 5.30122i) q^{59} +(-3.76200 + 9.08227i) q^{61} +(4.54813 + 5.17300i) q^{62} +(3.00558 - 7.41394i) q^{64} -2.52276 q^{65} +(-1.27556 + 3.07947i) q^{67} +(1.02676 + 0.132548i) q^{68} +(4.83092 - 1.64666i) q^{70} +(4.55636 - 4.55636i) q^{71} +(5.71852 + 5.71852i) q^{73} +(1.37017 + 0.673552i) q^{74} +(-2.67746 + 4.66456i) q^{76} +(-4.38223 - 1.81518i) q^{77} -5.84936i q^{79} +(-5.60526 + 0.766666i) q^{80} +(-0.177042 + 2.75423i) q^{82} +(-3.04294 - 1.26043i) q^{83} +(-0.280176 - 0.676404i) q^{85} +(7.74117 - 15.7474i) q^{86} +(4.38268 + 2.90455i) q^{88} +(-3.05260 + 3.05260i) q^{89} +(4.20486 - 1.74171i) q^{91} +(-10.6694 + 8.22967i) q^{92} +(11.4975 - 10.1087i) q^{94} +3.80349 q^{95} +7.01433 q^{97} +(0.519415 - 0.456673i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−0.933793	−	1.06209i	−0.660291	−	0.751010i
$2$	−0.933793	−	1.06209i	−0.660291	−	0.751010i
$3$		0			0
$3$		0			0
$4$	−0.256062	+	1.98354i	−0.128031	+	0.991770i
$5$	1.30670	−	0.541253i	0.584375	−	0.242056i	−0.0708538	−	0.997487i	$-0.522572\pi$
$5$	1.30670	−	0.541253i	0.584375	−	0.242056i	0.655228	+	0.755431i	$0.272572\pi$
$6$		0			0
$7$	−1.80429	+	1.80429i	−0.681959	+	0.681959i	−0.960441	−	0.278483i	$-0.910169\pi$
$7$	−1.80429	+	1.80429i	−0.681959	+	0.681959i	0.278483	+	0.960441i	$0.410169\pi$
$8$	2.34580	−	1.58026i	0.829367	−	0.558705i
$9$		0			0
$10$	−1.79505	−	0.882413i	−0.567644	−	0.279044i
$11$	0.711373	+	1.71741i	0.214487	+	0.517818i	0.994103	−	0.108440i	$-0.0345857\pi$
$11$	0.711373	+	1.71741i	0.214487	+	0.517818i	−0.779616	+	0.626258i	$0.784586\pi$
$12$		0			0
$13$	−1.64790	−	0.682581i	−0.457044	−	0.189314i	0.142270	−	0.989828i	$-0.454560\pi$
$13$	−1.64790	−	0.682581i	−0.457044	−	0.189314i	−0.599314	+	0.800514i	$0.704560\pi$
$14$	3.60115	+	0.231482i	0.962449	+	0.0618662i
$15$		0			0
$16$	−3.86886	−	1.01582i	−0.967216	−	0.253954i
$17$		−	0.517642i		−	0.125547i	−0.998028	−	0.0627733i	$-0.980005\pi$
$17$		−	0.517642i		−	0.125547i	0.998028	−	0.0627733i	$-0.0199945\pi$
$18$		0			0
$19$	2.48448	+	1.02911i	0.569980	+	0.236093i	0.649011	−	0.760779i	$-0.275183\pi$
$19$	2.48448	+	1.02911i	0.569980	+	0.236093i	−0.0790315	+	0.996872i	$0.525183\pi$
$20$	0.739002	+	2.73049i	0.165246	+	0.610556i
$21$		0			0
$22$	1.15976	−	2.35924i	0.247262	−	0.502992i
$23$	4.76398	+	4.76398i	0.993358	+	0.993358i	0.999978	−	0.00661976i	$-0.00210715\pi$
$23$	4.76398	+	4.76398i	0.993358	+	0.993358i	−0.00661976	+	0.999978i	$0.502107\pi$
$24$		0			0
$25$	−2.12102	+	2.12102i	−0.424204	+	0.424204i
$26$	0.813833	+	2.38760i	0.159606	+	0.468247i
$27$		0			0
$28$	−3.11688	−	4.04090i	−0.589035	−	0.763658i
$29$	−0.367694	+	0.887691i	−0.0682790	+	0.164840i	−0.954335	−	0.298738i	$-0.903434\pi$
$29$	−0.367694	+	0.887691i	−0.0682790	+	0.164840i	0.886056	+	0.463578i	$0.153434\pi$
$30$		0			0
$31$	−4.87060			−0.874785			−0.437393	−	0.899271i	$-0.644098\pi$
$31$	−4.87060			−0.874785			−0.437393	+	0.899271i	$0.644098\pi$
$32$	2.53383	+	5.05764i	0.447922	+	0.894073i
$33$		0			0
$34$	−0.549781	+	0.483371i	−0.0942867	+	0.0828974i
$35$	−1.38109	+	3.33425i	−0.233447	+	0.563591i
$36$		0			0
$37$	−0.997414	+	0.413142i	−0.163974	+	0.0679202i	−0.463161	−	0.886274i	$-0.653285\pi$
$37$	−0.997414	+	0.413142i	−0.163974	+	0.0679202i	0.299187	+	0.954195i	$0.403285\pi$
$38$	−1.22699	−	3.59971i	−0.199044	−	0.583951i
$39$		0			0
$40$	2.20994	−	3.33460i	0.349423	−	0.527246i
$41$	−1.37996	−	1.37996i	−0.215513	−	0.215513i	0.591092	−	0.806604i	$-0.298697\pi$
$41$	−1.37996	−	1.37996i	−0.215513	−	0.215513i	−0.806604	+	0.591092i	$0.798697\pi$
$42$		0			0
$43$	4.74827	+	11.4633i	0.724104	+	1.74814i	0.661308	+	0.750115i	$0.270002\pi$
$43$	4.74827	+	11.4633i	0.724104	+	1.74814i	0.0627958	+	0.998026i	$0.479998\pi$
$44$	−3.58870	+	0.971275i	−0.541017	+	0.146425i
$45$		0			0
$46$	0.611195	−	9.50833i	0.0901158	−	1.40193i
$47$			10.8254i			1.57905i	0.613719	+	0.789525i	$0.289673\pi$
$47$			10.8254i			1.57905i	−0.613719	+	0.789525i	$0.710327\pi$
$48$		0			0
$49$			0.489051i			0.0698645i
$50$	4.23331	+	0.272117i	0.598680	+	0.0384831i
$51$		0			0
$52$	1.77589	−	3.09389i	0.246272	−	0.429045i
$53$	−1.87709	−	4.53169i	−0.257838	−	0.622475i	0.740957	−	0.671552i	$-0.234372\pi$
$53$	−1.87709	−	4.53169i	−0.257838	−	0.622475i	−0.998795	+	0.0490768i	$0.984372\pi$
$54$		0			0
$55$	1.85910	+	1.85910i	0.250682	+	0.250682i
$56$	−1.38127	+	7.08376i	−0.184580	+	0.946607i
$57$		0			0
$58$	1.28616	−	0.438396i	0.168880	−	0.0575643i
$59$	12.7983	−	5.30122i	1.66619	−	0.690160i	0.667669	−	0.744458i	$-0.267292\pi$
$59$	12.7983	−	5.30122i	1.66619	−	0.690160i	0.998525	+	0.0542984i	$0.0172922\pi$
$60$		0			0
$61$	−3.76200	+	9.08227i	−0.481675	+	1.16287i	0.477139	+	0.878828i	$0.341674\pi$
$61$	−3.76200	+	9.08227i	−0.481675	+	1.16287i	−0.958813	+	0.284037i	$0.908326\pi$
$62$	4.54813	+	5.17300i	0.577613	+	0.656972i
$63$		0			0
$64$	3.00558	−	7.41394i	0.375698	−	0.926742i
$65$	−2.52276			−0.312910
$66$		0			0
$67$	−1.27556	+	3.07947i	−0.155834	+	0.376217i	−0.982444	−	0.186559i	$-0.940266\pi$
$67$	−1.27556	+	3.07947i	−0.155834	+	0.376217i	0.826610	+	0.562776i	$0.190266\pi$
$68$	1.02676	+	0.132548i	0.124513	+	0.0160738i
$69$		0			0
$70$	4.83092	−	1.64666i	0.577406	−	0.196813i
$71$	4.55636	−	4.55636i	0.540740	−	0.540740i	−0.383006	−	0.923746i	$-0.625111\pi$
$71$	4.55636	−	4.55636i	0.540740	−	0.540740i	0.923746	+	0.383006i	$0.125111\pi$
$72$		0			0
$73$	5.71852	+	5.71852i	0.669302	+	0.669302i	0.957555	−	0.288252i	$-0.0930741\pi$
$73$	5.71852	+	5.71852i	0.669302	+	0.669302i	−0.288252	+	0.957555i	$0.593074\pi$
$74$	1.37017	+	0.673552i	0.159279	+	0.0782988i
$75$		0			0
$76$	−2.67746	+	4.66456i	−0.307125	+	0.535062i
$77$	−4.38223	−	1.81518i	−0.499402	−	0.206859i
$78$		0			0
$79$		−	5.84936i		−	0.658104i	−0.944312	−	0.329052i	$-0.893271\pi$
$79$		−	5.84936i		−	0.658104i	0.944312	−	0.329052i	$-0.106729\pi$
$80$	−5.60526	+	0.766666i	−0.626688	+	0.0857158i
$81$		0			0
$82$	−0.177042	+	2.75423i	−0.0195510	+	0.304154i
$83$	−3.04294	−	1.26043i	−0.334006	−	0.138350i	0.209376	−	0.977835i	$-0.432857\pi$
$83$	−3.04294	−	1.26043i	−0.334006	−	0.138350i	−0.543383	+	0.839485i	$0.682857\pi$
$84$		0			0
$85$	−0.280176	−	0.676404i	−0.0303893	−	0.0733663i
$86$	7.74117	−	15.7474i	0.834751	−	1.69809i
$87$		0			0
$88$	4.38268	+	2.90455i	0.467195	+	0.309626i
$89$	−3.05260	+	3.05260i	−0.323575	+	0.323575i	−0.850137	−	0.526562i	$-0.823481\pi$
$89$	−3.05260	+	3.05260i	−0.323575	+	0.323575i	0.526562	+	0.850137i	$0.323481\pi$
$90$		0			0
$91$	4.20486	−	1.74171i	0.440790	−	0.182581i
$92$	−10.6694	+	8.22967i	−1.11236	+	0.858003i
$93$		0			0
$94$	11.4975	−	10.1087i	1.18588	−	1.04263i
$95$	3.80349			0.390229
$96$		0			0
$97$	7.01433			0.712197			0.356099	−	0.934448i	$-0.384107\pi$
$97$	7.01433			0.712197			0.356099	+	0.934448i	$0.384107\pi$
$98$	0.519415	−	0.456673i	0.0524689	−	0.0461309i
$99$		0			0
$100$	−3.66402	−	4.75024i	−0.366402	−	0.475024i
$101$	10.5605	−	4.37432i	1.05081	−	0.435261i	0.210631	−	0.977566i	$-0.432448\pi$
$101$	10.5605	−	4.37432i	1.05081	−	0.435261i	0.840182	+	0.542304i	$0.182448\pi$
$102$		0			0
$103$	−5.89474	+	5.89474i	−0.580826	+	0.580826i	−0.935130	−	0.354304i	$-0.884718\pi$
$103$	−5.89474	+	5.89474i	−0.580826	+	0.580826i	0.354304	+	0.935130i	$0.384718\pi$
$104$	−4.94429	+	1.00290i	−0.484828	+	0.0983421i
$105$		0			0
$106$	−3.06024	+	6.22529i	−0.297237	+	0.604654i
$107$	0.0550999	+	0.133023i	0.00532671	+	0.0128598i	0.926521	−	0.376244i	$-0.122785\pi$
$107$	0.0550999	+	0.133023i	0.00532671	+	0.0128598i	−0.921194	+	0.389104i	$0.872785\pi$
$108$		0			0
$109$	7.76546	+	3.21656i	0.743796	+	0.308090i	0.722207	−	0.691677i	$-0.243128\pi$
$109$	7.76546	+	3.21656i	0.743796	+	0.308090i	0.0215885	+	0.999767i	$0.493128\pi$
$110$	0.238514	−	3.71055i	0.0227414	−	0.353787i
$111$		0			0
$112$	8.81340	−	5.14773i	0.832788	−	0.486415i
$113$		−	7.19446i		−	0.676798i	−0.941003	−	0.338399i	$-0.890115\pi$
$113$		−	7.19446i		−	0.676798i	0.941003	−	0.338399i	$-0.109885\pi$
$114$		0			0
$115$	8.80362	+	3.64658i	0.820942	+	0.340045i
$116$	−1.66662	−	0.956639i	−0.154742	−	0.0888217i
$117$		0			0
$118$	−17.5813	−	8.64265i	−1.61849	−	0.795621i
$119$	0.933978	+	0.933978i	0.0856176	+	0.0856176i
$120$		0			0
$121$	5.33474	−	5.33474i	0.484976	−	0.484976i
$122$	13.1591	−	4.48538i	1.19137	−	0.406088i
$123$		0			0
$124$	1.24717	−	9.66103i	0.112000	−	0.867586i
$125$	−4.32980	+	10.4531i	−0.387269	+	0.934950i
$126$		0			0
$127$	10.2361			0.908305			0.454152	−	0.890924i	$-0.349942\pi$
$127$	10.2361			0.908305			0.454152	+	0.890924i	$0.349942\pi$
$128$	−10.6808	+	3.73089i	−0.944062	+	0.329767i
$129$		0			0
$130$	2.35573	+	2.67939i	0.206611	+	0.234998i
$131$	−2.91260	+	7.03163i	−0.254475	+	0.614356i	−0.998555	−	0.0537337i	$-0.982888\pi$
$131$	−2.91260	+	7.03163i	−0.254475	+	0.614356i	0.744081	+	0.668090i	$0.232888\pi$
$132$		0			0
$133$	−6.33955	+	2.62593i	−0.549709	+	0.227697i
$134$	4.46177	−	1.52083i	0.385438	−	0.131380i
$135$		0			0
$136$	−0.818007	−	1.21429i	−0.0701435	−	0.104124i
$137$	−7.77803	−	7.77803i	−0.664522	−	0.664522i	0.291921	−	0.956443i	$-0.405706\pi$
$137$	−7.77803	−	7.77803i	−0.664522	−	0.664522i	−0.956443	+	0.291921i	$0.905706\pi$
$138$		0			0
$139$	−0.563579	−	1.36060i	−0.0478022	−	0.115405i	0.898175	−	0.439639i	$-0.144893\pi$
$139$	−0.563579	−	1.36060i	−0.0478022	−	0.115405i	−0.945977	+	0.324234i	$0.894893\pi$
$140$	−6.25998	−	3.59323i	−0.529065	−	0.303683i
$141$		0			0
$142$	−9.09394	−	0.584558i	−0.763147	−	0.0490550i
$143$		−	3.31568i		−	0.277271i
$144$		0			0
$145$			1.35896i			0.112856i
$146$	0.733658	−	11.4135i	0.0607180	−	0.944587i
$147$		0			0
$148$	−0.564085	−	2.08420i	−0.0463675	−	0.171320i
$149$	−5.60194	−	13.5243i	−0.458929	−	1.10795i	−0.968832	−	0.247720i	$-0.920319\pi$
$149$	−5.60194	−	13.5243i	−0.458929	−	1.10795i	0.509903	−	0.860232i	$-0.329681\pi$
$150$		0			0
$151$	−11.4726	−	11.4726i	−0.933629	−	0.933629i	0.0643019	−	0.997930i	$-0.479518\pi$
$151$	−11.4726	−	11.4726i	−0.933629	−	0.933629i	−0.997930	+	0.0643019i	$0.979518\pi$
$152$	7.45436	−	1.51204i	0.604629	−	0.122642i
$153$		0			0
$154$	2.16422	+	6.34932i	0.174397	+	0.511642i
$155$	−6.36442	+	2.63623i	−0.511202	+	0.211747i
$156$		0			0
$157$	−6.23813	+	15.0602i	−0.497857	+	1.20193i	0.452778	+	0.891623i	$0.350433\pi$
$157$	−6.23813	+	15.0602i	−0.497857	+	1.20193i	−0.950635	+	0.310311i	$0.899567\pi$
$158$	−6.21253	+	5.46209i	−0.494242	+	0.434540i
$159$		0			0
$160$	6.04842	+	5.23738i	0.478170	+	0.414051i
$161$	−17.1912			−1.35486
$162$		0			0
$163$	−4.41941	+	10.6694i	−0.346155	+	0.835693i	0.650911	+	0.759154i	$0.274387\pi$
$163$	−4.41941	+	10.6694i	−0.346155	+	0.835693i	−0.997067	+	0.0765389i	$0.975613\pi$
$164$	3.09055	−	2.38384i	0.241332	−	0.186147i
$165$		0			0
$166$	1.50279	+	4.40885i	0.116639	+	0.342193i
$167$	4.17288	−	4.17288i	0.322907	−	0.322907i	−0.526974	−	0.849881i	$-0.676673\pi$
$167$	4.17288	−	4.17288i	0.322907	−	0.322907i	0.849881	+	0.526974i	$0.176673\pi$
$168$		0			0
$169$	−6.94274	−	6.94274i	−0.534057	−	0.534057i
$170$	−0.456774	+	0.929192i	−0.0350330	+	0.0712658i
$171$		0			0
$172$	−23.9538	+	6.48306i	−1.82646	+	0.494328i
$173$	−19.1300	−	7.92390i	−1.45443	−	0.602443i	−0.491178	−	0.871059i	$-0.663434\pi$
$173$	−19.1300	−	7.92390i	−1.45443	−	0.602443i	−0.963247	+	0.268617i	$0.913434\pi$
$174$		0			0
$175$		−	7.65389i		−	0.578580i
$176$	−1.00763	−	7.36704i	−0.0759533	−	0.555311i
$177$		0			0
$178$	6.09262	+	0.391633i	0.456661	+	0.0293541i
$179$	21.8229	+	9.03935i	1.63112	+	0.675633i	0.995357	−	0.0962505i	$-0.0306850\pi$
$179$	21.8229	+	9.03935i	1.63112	+	0.675633i	0.635764	+	0.771883i	$0.280685\pi$
$180$		0			0
$181$	0.588576	+	1.42095i	0.0437485	+	0.105618i	0.944243	−	0.329249i	$-0.106795\pi$
$181$	0.588576	+	1.42095i	0.0437485	+	0.105618i	−0.900495	+	0.434867i	$0.856795\pi$
$182$	−5.77632	−	2.83954i	−0.428170	−	0.210481i
$183$		0			0
$184$	18.7037	+	3.64705i	1.37885	+	0.268864i
$185$	−1.07971	+	1.07971i	−0.0793816	+	0.0793816i
$186$		0			0
$187$	0.889002	−	0.368237i	0.0650103	−	0.0269281i
$188$	−21.4727	−	2.77198i	−1.56605	−	0.202167i
$189$		0			0
$190$	−3.55167	−	4.03964i	−0.257665	−	0.293066i
$191$	−20.6967			−1.49756			−0.748781	−	0.662817i	$-0.769361\pi$
$191$	−20.6967			−1.49756			−0.748781	+	0.662817i	$0.769361\pi$
$192$		0			0
$193$	12.8348			0.923872			0.461936	−	0.886913i	$-0.347155\pi$
$193$	12.8348			0.923872			0.461936	+	0.886913i	$0.347155\pi$
$194$	−6.54993	−	7.44984i	−0.470258	−	0.534867i
$195$		0			0
$196$	−0.970053	−	0.125227i	−0.0692895	−	0.00894481i
$197$	8.18203	−	3.38911i	0.582946	−	0.241464i	−0.0716667	−	0.997429i	$-0.522832\pi$
$197$	8.18203	−	3.38911i	0.582946	−	0.241464i	0.654613	+	0.755965i	$0.272832\pi$
$198$		0			0
$199$	1.95304	−	1.95304i	0.138447	−	0.138447i	−0.634486	−	0.772934i	$-0.718788\pi$
$199$	1.95304	−	1.95304i	0.138447	−	0.138447i	0.772934	+	0.634486i	$0.218788\pi$
$200$	−1.62374	+	8.32725i	−0.114816	+	0.588826i
$201$		0			0
$202$	−14.5073	−	7.13152i	−1.02073	−	0.501772i
$203$	−0.938227	−	2.26508i	−0.0658507	−	0.158978i
$204$		0			0
$205$	−2.55010	−	1.05628i	−0.178106	−	0.0737741i
$206$	11.7652	+	0.756267i	0.819721	+	0.0526916i
$207$		0			0
$208$	5.68211	+	4.31478i	0.393983	+	0.299176i
$209$			4.99895i			0.345785i
$210$		0			0
$211$	−16.2712	−	6.73973i	−1.12015	−	0.463982i	−0.255730	−	0.966748i	$-0.582316\pi$
$211$	−16.2712	−	6.73973i	−1.12015	−	0.463982i	−0.864423	+	0.502766i	$0.832316\pi$
$212$	9.46944	−	2.56289i	0.650364	−	0.176020i
$213$		0			0
$214$	0.0898301	−	0.182737i	0.00614066	−	0.0124916i
$215$	12.4091	+	12.4091i	0.846296	+	0.846296i
$216$		0			0
$217$	8.78799	−	8.78799i	0.596567	−	0.596567i
$218$	−3.83506	−	11.2512i	−0.259743	−	0.762027i
$219$		0			0
$220$	−4.16365	+	3.21156i	−0.280713	+	0.216523i
$221$	−0.353333	+	0.853021i	−0.0237677	+	0.0573804i
$222$		0			0
$223$	−19.6614			−1.31662			−0.658312	−	0.752746i	$-0.728729\pi$
$223$	−19.6614			−1.31662			−0.658312	+	0.752746i	$0.728729\pi$
$224$	−13.6972	−	4.55369i	−0.915185	−	0.304256i
$225$		0			0
$226$	−7.64115	+	6.71813i	−0.508281	+	0.446884i
$227$	−8.16512	+	19.7123i	−0.541938	+	1.30835i	0.381416	+	0.924404i	$0.375437\pi$
$227$	−8.16512	+	19.7123i	−0.541938	+	1.30835i	−0.923354	+	0.383950i	$0.874563\pi$
$228$		0			0
$229$	−24.9883	+	10.3505i	−1.65127	+	0.683979i	−0.997362	−	0.0725935i	$-0.976872\pi$
$229$	−24.9883	+	10.3505i	−1.65127	+	0.683979i	−0.653910	+	0.756573i	$0.726872\pi$
$230$	−4.34777	−	12.7554i	−0.286683	−	0.841064i
$231$		0			0
$232$	0.540242	+	2.66340i	0.0354686	+	0.174861i
$233$	−17.5856	−	17.5856i	−1.15207	−	1.15207i	−0.986137	−	0.165932i	$-0.946937\pi$
$233$	−17.5856	−	17.5856i	−1.15207	−	1.15207i	−0.165932	−	0.986137i	$-0.553063\pi$
$234$		0			0
$235$	5.85930	+	14.1456i	0.382218	+	0.922757i
$236$	7.23803	+	26.7433i	0.471156	+	1.74084i
$237$		0			0
$238$	0.119825	−	1.86411i	0.00776709	−	0.120832i
$239$			1.36566i			0.0883373i	0.999024	+	0.0441686i	$0.0140639\pi$
$239$			1.36566i			0.0883373i	−0.999024	+	0.0441686i	$0.985936\pi$
$240$		0			0
$241$		−	25.6431i		−	1.65181i	−0.563806	−	0.825907i	$-0.690664\pi$
$241$		−	25.6431i		−	1.65181i	0.563806	−	0.825907i	$-0.309336\pi$
$242$	−10.6475	−	0.684421i	−0.684448	−	0.0439963i
$243$		0			0
$244$	−17.0517	−	9.78770i	−1.09163	−	0.626593i
$245$	0.264701	+	0.639044i	0.0169111	+	0.0408270i
$246$		0			0
$247$	−3.39172	−	3.39172i	−0.215810	−	0.215810i
$248$	−11.4255	+	7.69679i	−0.725518	+	0.488747i
$249$		0			0
$250$	15.1452	−	5.16236i	0.957867	−	0.326497i
$251$	4.30544	−	1.78337i	0.271757	−	0.112565i	−0.242644	−	0.970115i	$-0.578015\pi$
$251$	4.30544	−	1.78337i	0.271757	−	0.112565i	0.514400	+	0.857550i	$0.328015\pi$
$252$		0			0
$253$	−4.79272	+	11.5707i	−0.301316	+	0.727441i
$254$	−9.55837	−	10.8716i	−0.599746	−	0.682146i
$255$		0			0
$256$	13.9362	+	7.86012i	0.871014	+	0.491258i
$257$	26.0388			1.62425			0.812126	−	0.583482i	$-0.198310\pi$
$257$	26.0388			1.62425			0.812126	+	0.583482i	$0.198310\pi$
$258$		0			0
$259$	1.05420	−	2.54506i	0.0655046	−	0.158142i
$260$	0.645982	−	5.00399i	0.0400621	−	0.310334i
$261$		0			0
$262$	10.1880	−	3.47265i	0.629415	−	0.214541i
$263$	0.569946	−	0.569946i	0.0351444	−	0.0351444i	−0.689316	−	0.724461i	$-0.742089\pi$
$263$	0.569946	−	0.569946i	0.0351444	−	0.0351444i	0.724461	+	0.689316i	$0.242089\pi$
$264$		0			0
$265$	−4.90558	−	4.90558i	−0.301348	−	0.301348i
$266$	8.70879	+	4.28109i	0.533970	+	0.262490i
$267$		0			0
$268$	−5.78162	−	3.31865i	−0.353169	−	0.202719i
$269$	−22.2223	−	9.20478i	−1.35492	−	0.561225i	−0.417261	−	0.908787i	$-0.637010\pi$
$269$	−22.2223	−	9.20478i	−1.35492	−	0.561225i	−0.937657	+	0.347562i	$0.887010\pi$
$270$		0			0
$271$		−	4.90508i		−	0.297963i	−0.988840	−	0.148981i	$-0.952401\pi$
$271$		−	4.90508i		−	0.297963i	0.988840	−	0.148981i	$-0.0475994\pi$
$272$	−0.525830	+	2.00269i	−0.0318831	+	0.121431i
$273$		0			0
$274$	−0.997883	+	15.5240i	−0.0602843	+	0.937840i
$275$	−5.15149	−	2.13382i	−0.310647	−	0.128674i
$276$		0			0
$277$	6.29325	+	15.1932i	0.378125	+	0.912874i	0.992317	+	0.123718i	$0.0394817\pi$
$277$	6.29325	+	15.1932i	0.378125	+	0.912874i	−0.614193	+	0.789156i	$0.710518\pi$
$278$	−0.918811	+	1.86909i	−0.0551066	+	0.112101i
$279$		0			0
$280$	2.02920	+	10.0040i	0.121268	+	0.597852i
$281$	19.4082	−	19.4082i	1.15779	−	1.15779i	0.172845	−	0.984949i	$-0.444704\pi$
$281$	19.4082	−	19.4082i	1.15779	−	1.15779i	0.984949	−	0.172845i	$-0.0552959\pi$
$282$		0			0
$283$	3.10722	−	1.28705i	0.184705	−	0.0765075i	−0.288414	−	0.957506i	$-0.593128\pi$
$283$	3.10722	−	1.28705i	0.184705	−	0.0765075i	0.473119	+	0.880998i	$0.343128\pi$
$284$	7.87101	+	10.2044i	0.467058	+	0.605521i
$285$		0			0
$286$	−3.52154	+	3.09616i	−0.208233	+	0.183080i
$287$	4.97969			0.293942
$288$		0			0
$289$	16.7320			0.984238
$290$	1.44334	−	1.26899i	0.0847557	−	0.0745176i
$291$		0			0
$292$	−12.8072	+	9.87862i	−0.749486	+	0.578103i
$293$	−15.6158	+	6.46826i	−0.912282	+	0.377880i	−0.788930	−	0.614483i	$-0.789365\pi$
$293$	−15.6158	+	6.46826i	−0.912282	+	0.377880i	−0.123352	+	0.992363i	$0.539365\pi$
$294$		0			0
$295$	13.8542	−	13.8542i	0.806624	−	0.806624i
$296$	−1.68687	+	2.54532i	−0.0980471	+	0.147944i
$297$		0			0
$298$	−9.13293	+	18.5786i	−0.529056	+	1.07623i
$299$	−4.59874	−	11.1023i	−0.265952	−	0.642065i
$300$		0			0
$301$	−29.2505	−	12.1159i	−1.68597	−	0.698351i
$302$	−1.47188	+	22.8980i	−0.0846972	+	1.31763i
$303$		0			0
$304$	−8.56675	−	6.50526i	−0.491337	−	0.373102i
$305$			13.9040i			0.796141i
$306$		0			0
$307$	21.6639	+	8.97347i	1.23642	+	0.512143i	0.902595	−	0.430491i	$-0.141660\pi$
$307$	21.6639	+	8.97347i	1.23642	+	0.512143i	0.333828	+	0.942634i	$0.391660\pi$
$308$	4.72260	−	8.22753i	0.269095	−	0.468807i
$309$		0			0
$310$	8.74295	+	4.29788i	0.496566	+	0.244103i
$311$	10.6004	+	10.6004i	0.601092	+	0.601092i	0.940602	−	0.339510i	$-0.110261\pi$
$311$	10.6004	+	10.6004i	0.601092	+	0.601092i	−0.339510	+	0.940602i	$0.610261\pi$
$312$		0			0
$313$	0.267221	−	0.267221i	0.0151042	−	0.0151042i	−0.699514	−	0.714619i	$-0.746600\pi$
$313$	0.267221	−	0.267221i	0.0151042	−	0.0151042i	0.714619	+	0.699514i	$0.246600\pi$
$314$	21.8204	−	7.43765i	1.23139	−	0.419731i
$315$		0			0
$316$	11.6024	+	1.49780i	0.652688	+	0.0842576i
$317$	1.33209	−	3.21594i	0.0748175	−	0.180625i	−0.882046	−	0.471163i	$-0.843834\pi$
$317$	1.33209	−	3.21594i	0.0748175	−	0.180625i	0.956863	+	0.290538i	$0.0938342\pi$
$318$		0			0
$319$	−1.78609			−0.100002
$320$	−0.0854185	−	11.3146i	−0.00477504	−	0.632504i
$321$		0			0
$322$	16.0530	+	18.2586i	0.894601	+	1.01751i
$323$	0.532709	−	1.28607i	0.0296407	−	0.0715591i
$324$		0			0
$325$	4.94299	−	2.04745i	0.274188	−	0.113572i
$326$	15.4587	−	5.26921i	0.856177	−	0.291835i
$327$		0			0
$328$	−5.41779	−	1.05642i	−0.299147	−	0.0583311i
$329$	−19.5322	−	19.5322i	−1.07685	−	1.07685i
$330$		0			0
$331$	7.72025	+	18.6383i	0.424343	+	1.02446i	0.981051	+	0.193747i	$0.0620642\pi$
$331$	7.72025	+	18.6383i	0.424343	+	1.02446i	−0.556708	+	0.830708i	$0.687936\pi$
$332$	3.27929	−	5.71305i	0.179974	−	0.313544i
$333$		0			0
$334$	−8.32858	−	0.535361i	−0.455720	−	0.0292936i
$335$			4.71434i			0.257572i
$336$		0			0
$337$		−	21.0685i		−	1.14767i	−0.818970	−	0.573837i	$-0.805454\pi$
$337$		−	21.0685i		−	1.14767i	0.818970	−	0.573837i	$-0.194546\pi$
$338$	−0.890720	+	13.8569i	−0.0484488	+	0.753715i
$339$		0			0
$340$	1.41342	−	0.382538i	0.0766532	−	0.0207461i
$341$	−3.46481	−	8.36480i	−0.187630	−	0.452979i
$342$		0			0
$343$	−13.5124	−	13.5124i	−0.729603	−	0.729603i
$344$	29.2535	+	19.3872i	1.57724	+	1.04529i
$345$		0			0
$346$	9.44756	+	27.7170i	0.507904	+	1.49007i
$347$	20.5149	−	8.49755i	1.10130	−	0.456173i	0.243365	−	0.969935i	$-0.421749\pi$
$347$	20.5149	−	8.49755i	1.10130	−	0.456173i	0.857933	+	0.513762i	$0.171749\pi$
$348$		0			0
$349$	11.3311	−	27.3557i	0.606539	−	1.46432i	−0.260200	−	0.965555i	$-0.583789\pi$
$349$	11.3311	−	27.3557i	0.606539	−	1.46432i	0.866740	−	0.498761i	$-0.166211\pi$
$350$	−8.12910	+	7.14715i	−0.434519	+	0.382031i
$351$		0			0
$352$	−6.88352	+	7.94948i	−0.366893	+	0.423709i
$353$	32.2163			1.71470			0.857349	−	0.514735i	$-0.172110\pi$
$353$	32.2163			1.71470			0.857349	+	0.514735i	$0.172110\pi$
$354$		0			0
$355$	3.48765	−	8.41994i	0.185105	−	0.446884i
$356$	−5.27329	−	6.83660i	−0.279484	−	0.362339i
$357$		0			0
$358$	−10.7775	−	31.6187i	−0.569609	−	1.67110i
$359$	9.51100	−	9.51100i	0.501971	−	0.501971i	−0.410079	−	0.912050i	$-0.634499\pi$
$359$	9.51100	−	9.51100i	0.501971	−	0.501971i	0.912050	+	0.410079i	$0.134499\pi$
$360$		0			0
$361$	−8.32143	−	8.32143i	−0.437970	−	0.437970i
$362$	0.959564	−	1.95199i	0.0504336	−	0.102594i
$363$		0			0
$364$	2.37805	+	8.78651i	0.124644	+	0.460538i
$365$	10.5676	+	4.37723i	0.553132	+	0.229115i
$366$		0			0
$367$		−	30.7748i		−	1.60643i	−0.595687	−	0.803217i	$-0.703120\pi$
$367$		−	30.7748i		−	1.60643i	0.595687	−	0.803217i	$-0.296880\pi$
$368$	−13.5919	−	23.2705i	−0.708525	−	1.21306i
$369$		0			0
$370$	2.15497	+	0.138521i	0.112031	+	0.00720137i
$371$	11.5633	+	4.78968i	0.600337	+	0.248668i
$372$		0			0
$373$	−4.45555	−	10.7566i	−0.230699	−	0.556958i	0.765561	−	0.643364i	$-0.222462\pi$
$373$	−4.45555	−	10.7566i	−0.230699	−	0.556958i	−0.996260	+	0.0864062i	$0.972462\pi$
$374$	−1.22124	−	0.600341i	−0.0631490	−	0.0310429i
$375$		0			0
$376$	17.1069	+	25.3943i	0.882223	+	1.30961i
$377$	1.21184	−	1.21184i	0.0624130	−	0.0624130i
$378$		0			0
$379$	14.7550	−	6.11172i	0.757913	−	0.313938i	0.0299476	−	0.999551i	$-0.490466\pi$
$379$	14.7550	−	6.11172i	0.757913	−	0.313938i	0.727966	+	0.685613i	$0.240466\pi$
$380$	−0.973928	+	7.54437i	−0.0499614	+	0.387018i
$381$		0			0
$382$	19.3265	+	21.9817i	0.988827	+	1.12468i
$383$	−25.7139			−1.31392			−0.656960	−	0.753925i	$-0.728158\pi$
$383$	−25.7139			−1.31392			−0.656960	+	0.753925i	$0.728158\pi$
$384$		0			0
$385$	−6.70874			−0.341909
$386$	−11.9851	−	13.6317i	−0.610024	−	0.693837i
$387$		0			0
$388$	−1.79610	+	13.9132i	−0.0911833	+	0.706336i
$389$	23.2940	−	9.64868i	1.18105	−	0.489207i	0.296220	−	0.955120i	$-0.404274\pi$
$389$	23.2940	−	9.64868i	1.18105	−	0.489207i	0.884831	+	0.465912i	$0.154274\pi$
$390$		0			0
$391$	2.46604	−	2.46604i	0.124713	−	0.124713i
$392$	0.772826	+	1.14722i	0.0390336	+	0.0579433i
$393$		0			0
$394$	−11.2399	−	5.52531i	−0.566256	−	0.278361i
$395$	−3.16598	−	7.64336i	−0.159298	−	0.384579i
$396$		0			0
$397$	8.22244	+	3.40585i	0.412672	+	0.170935i	0.579354	−	0.815076i	$-0.303305\pi$
$397$	8.22244	+	3.40585i	0.412672	+	0.170935i	−0.166681	+	0.986011i	$0.553305\pi$
$398$	−3.89804	−	0.250566i	−0.195391	−	0.0125597i
$399$		0			0
$400$	10.3605	−	6.05137i	0.518026	−	0.302569i
$401$			35.1422i			1.75492i	0.479651	+	0.877460i	$0.340763\pi$
$401$			35.1422i			1.75492i	−0.479651	+	0.877460i	$0.659237\pi$
$402$		0			0
$403$	8.02624	+	3.32458i	0.399816	+	0.165609i
$404$	5.97249	+	22.0674i	0.297142	+	1.09789i
$405$		0			0
$406$	−1.52961	+	3.11160i	−0.0759131	+	0.154426i
$407$	−1.41907	−	1.41907i	−0.0703405	−	0.0703405i
$408$		0			0
$409$	26.4049	−	26.4049i	1.30564	−	1.30564i	0.381109	−	0.924530i	$-0.375542\pi$
$409$	26.4049	−	26.4049i	1.30564	−	1.30564i	0.924530	−	0.381109i	$-0.124458\pi$
$410$	1.25939	+	3.69478i	0.0621971	+	0.182472i
$411$		0			0
$412$	−10.1830	−	13.2019i	−0.501683	−	0.650410i
$413$	−13.5269	+	32.6568i	−0.665615	+	1.60694i
$414$		0			0
$415$	−4.65843			−0.228673
$416$	−0.723242	−	10.0640i	−0.0354599	−	0.493429i
$417$		0			0
$418$	5.30932	−	4.66798i	0.259687	−	0.228318i
$419$	−10.4161	+	25.1467i	−0.508859	+	1.22849i	0.435682	+	0.900101i	$0.356507\pi$
$419$	−10.4161	+	25.1467i	−0.508859	+	1.22849i	−0.944541	+	0.328394i	$0.893493\pi$
$420$		0			0
$421$	8.38160	−	3.47177i	0.408494	−	0.169204i	−0.168967	−	0.985622i	$-0.554043\pi$
$421$	8.38160	−	3.47177i	0.408494	−	0.169204i	0.577462	+	0.816418i	$0.304043\pi$
$422$	8.03570	+	23.5749i	0.391172	+	1.14761i
$423$		0			0
$424$	−11.5645	−	7.66417i	−0.561622	−	0.372205i
$425$	1.09793	+	1.09793i	0.0532574	+	0.0532574i
$426$		0			0
$427$	−9.59933	−	23.1748i	−0.464544	−	1.12151i
$428$	−0.277965	+	0.0752308i	−0.0134360	+	0.00363642i
$429$		0			0
$430$	1.59203	−	24.7671i	0.0767745	−	1.19438i
$431$		−	38.3713i		−	1.84828i	−0.382053	−	0.924140i	$-0.624783\pi$
$431$		−	38.3713i		−	1.84828i	0.382053	−	0.924140i	$-0.375217\pi$
$432$		0			0
$433$			5.36929i			0.258032i	0.991643	+	0.129016i	$0.0411818\pi$
$433$			5.36929i			0.258032i	−0.991643	+	0.129016i	$0.958818\pi$
$434$	−17.5398	−	1.12746i	−0.841936	−	0.0541196i
$435$		0			0
$436$	−8.36861	+	14.5795i	−0.400784	+	0.698229i
$437$	6.93339	+	16.7387i	0.331669	+	0.800720i
$438$		0			0
$439$	−7.99663	−	7.99663i	−0.381658	−	0.381658i	0.490041	−	0.871699i	$-0.336982\pi$
$439$	−7.99663	−	7.99663i	−0.381658	−	0.381658i	−0.871699	+	0.490041i	$0.836982\pi$
$440$	7.29895	+	1.42323i	0.347964	+	0.0678499i
$441$		0			0
$442$	1.23592	−	0.421274i	0.0587868	−	0.0200380i
$443$	−14.7373	+	6.10437i	−0.700188	+	0.290027i	−0.704238	−	0.709964i	$-0.748711\pi$
$443$	−14.7373	+	6.10437i	−0.700188	+	0.290027i	0.00404935	+	0.999992i	$0.498711\pi$
$444$		0			0
$445$	−2.33660	+	5.64106i	−0.110766	+	0.267412i
$446$	18.3597	+	20.8821i	0.869355	+	0.988797i
$447$		0			0
$448$	7.95396	+	18.7999i	0.375789	+	0.888210i
$449$	−7.52272			−0.355019			−0.177510	−	0.984119i	$-0.556804\pi$
$449$	−7.52272			−0.355019			−0.177510	+	0.984119i	$0.556804\pi$
$450$		0			0
$451$	1.38828	−	3.35161i	0.0653716	−	0.157821i
$452$	14.2705	+	1.84223i	0.671228	+	0.0866510i
$453$		0			0
$454$	28.5608	−	9.73517i	1.34042	−	0.456894i
$455$	4.55179	−	4.55179i	0.213391	−	0.213391i
$456$		0			0
$457$	9.36999	+	9.36999i	0.438310	+	0.438310i	0.891443	−	0.453133i	$-0.149694\pi$
$457$	9.36999	+	9.36999i	0.438310	+	0.438310i	−0.453133	+	0.891443i	$0.649694\pi$
$458$	34.3270	+	16.8745i	1.60399	+	0.788495i
$459$		0			0
$460$	−9.48740	+	16.5286i	−0.442352	+	0.770649i
$461$	30.8800	+	12.7909i	1.43822	+	0.595732i	0.959367	−	0.282161i	$-0.0910512\pi$
$461$	30.8800	+	12.7909i	1.43822	+	0.595732i	0.478857	+	0.877893i	$0.341051\pi$
$462$		0			0
$463$			25.0609i			1.16468i	0.812947	+	0.582338i	$0.197862\pi$
$463$			25.0609i			1.16468i	−0.812947	+	0.582338i	$0.802138\pi$
$464$	2.32429	−	3.06085i	0.107902	−	0.142096i
$465$		0			0
$466$	−2.25614	+	35.0987i	−0.104514	+	1.62592i
$467$	22.8306	+	9.45674i	1.05647	+	0.437606i	0.842199	−	0.539167i	$-0.181261\pi$
$467$	22.8306	+	9.45674i	1.05647	+	0.437606i	0.214275	+	0.976773i	$0.431261\pi$
$468$		0			0
$469$	−3.25478	−	7.85774i	−0.150292	−	0.362837i
$470$	9.55249	−	19.4321i	0.440624	−	0.896338i
$471$		0			0
$472$	21.6450	−	32.6602i	0.996290	−	1.50331i
$473$	−16.3094	+	16.3094i	−0.749907	+	0.749907i
$474$		0			0
$475$	−7.45240	+	3.08689i	−0.341940	+	0.141636i
$476$	−2.09174	+	1.61343i	−0.0958747	+	0.0739513i
$477$		0			0
$478$	1.45045	−	1.27524i	0.0663421	−	0.0583283i
$479$	−10.5351			−0.481359			−0.240679	−	0.970605i	$-0.577370\pi$
$479$	−10.5351			−0.481359			−0.240679	+	0.970605i	$0.577370\pi$
$480$		0			0
$481$	1.92564			0.0878015
$482$	−27.2352	+	23.9453i	−1.24053	+	1.09068i
$483$		0			0
$484$	9.21565	+	11.9477i	0.418893	+	0.543077i
$485$	9.16563	−	3.79653i	0.416190	−	0.172392i
$486$		0			0
$487$	−5.75385	+	5.75385i	−0.260732	+	0.260732i	−0.825351	−	0.564619i	$-0.809023\pi$
$487$	−5.75385	+	5.75385i	−0.260732	+	0.260732i	0.564619	+	0.825351i	$0.309023\pi$
$488$	5.52740	+	27.2501i	0.250214	+	1.23356i
$489$		0			0
$490$	0.431545	−	0.877870i	0.0194952	−	0.0396581i
$491$	−9.51626	−	22.9743i	−0.429463	−	1.03682i	−0.979458	−	0.201648i	$-0.935370\pi$
$491$	−9.51626	−	22.9743i	−0.429463	−	1.03682i	0.549995	−	0.835168i	$-0.314630\pi$
$492$		0			0
$493$	0.459506	+	0.190334i	0.0206951	+	0.00857220i
$494$	−0.435142	+	6.76948i	−0.0195779	+	0.304573i
$495$		0			0
$496$	18.8437	+	4.94764i	0.846106	+	0.222156i
$497$			16.4420i			0.737525i
$498$		0			0
$499$	21.6439	+	8.96518i	0.968912	+	0.401337i	0.810307	−	0.586006i	$-0.199300\pi$
$499$	21.6439	+	8.96518i	0.968912	+	0.401337i	0.158605	+	0.987342i	$0.449300\pi$
$500$	−19.6254	−	11.2650i	−0.877673	−	0.503784i
$501$		0			0
$502$	−5.91448	−	2.90745i	−0.263976	−	0.129766i
$503$	27.4853	+	27.4853i	1.22551	+	1.22551i	0.965645	+	0.259863i	$0.0836775\pi$
$503$	27.4853	+	27.4853i	1.22551	+	1.22551i	0.259863	+	0.965645i	$0.416323\pi$
$504$		0			0
$505$	11.4319	−	11.4319i	0.508711	−	0.508711i
$506$	16.7645	−	5.71430i	0.745271	−	0.254032i
$507$		0			0
$508$	−2.62107	+	20.3037i	−0.116291	+	0.900829i
$509$	−4.55791	+	11.0038i	−0.202026	+	0.487733i	−0.992126	−	0.125245i	$-0.960028\pi$
$509$	−4.55791	+	11.0038i	−0.202026	+	0.487733i	0.790100	+	0.612978i	$0.210028\pi$
$510$		0			0
$511$	−20.6358			−0.912873
$512$	−4.66541	−	22.1412i	−0.206184	−	0.978513i
$513$		0			0
$514$	−24.3148	−	27.6554i	−1.07248	−	1.21983i
$515$	−4.51212	+	10.8932i	−0.198828	+	0.480013i
$516$		0			0
$517$	−18.5916	+	7.70091i	−0.817660	+	0.338686i
$518$	−3.68748	+	1.25691i	−0.162018	+	0.0552253i
$519$		0			0
$520$	−5.91789	+	3.98660i	−0.259517	+	0.174824i
$521$	14.4058	+	14.4058i	0.631131	+	0.631131i	0.948352	−	0.317221i	$-0.102750\pi$
$521$	14.4058	+	14.4058i	0.631131	+	0.631131i	−0.317221	+	0.948352i	$0.602750\pi$
$522$		0			0
$523$	0.846551	+	2.04376i	0.0370171	+	0.0893672i	0.941307	−	0.337552i	$-0.109599\pi$
$523$	0.846551	+	2.04376i	0.0370171	+	0.0893672i	−0.904290	+	0.426919i	$0.859599\pi$
$524$	−13.2017	−	7.57778i	−0.576719	−	0.331037i
$525$		0			0
$526$	−1.13754	−	0.0731212i	−0.0495993	−	0.00318824i
$527$			2.52123i			0.109826i
$528$		0			0
$529$			22.3910i			0.973522i
$530$	−0.629362	+	9.79096i	−0.0273378	+	0.425292i
$531$		0			0
$532$	−3.58532	−	13.2472i	−0.155443	−	0.574337i
$533$	1.33209	+	3.21596i	0.0576993	+	0.139299i
$534$		0			0
$535$	0.143998	+	0.143998i	0.00622558	+	0.00622558i
$536$	1.87414	+	9.23953i	0.0809505	+	0.399087i
$537$		0			0
$538$	10.9747	+	32.1974i	0.473155	+	1.38813i
$539$	−0.839900	+	0.347898i	−0.0361770	+	0.0149850i
$540$		0			0
$541$	−0.213663	+	0.515827i	−0.00918608	+	0.0221772i	−0.928406	−	0.371567i	$-0.878821\pi$
$541$	−0.213663	+	0.515827i	−0.00918608	+	0.0221772i	0.919220	+	0.393744i	$0.128821\pi$
$542$	−5.20963	+	4.58033i	−0.223773	+	0.196742i
$543$		0			0
$544$	2.61805	−	1.31162i	0.112248	−	0.0562351i
$545$	11.8881			0.509230
$546$		0			0
$547$	−11.7460	+	28.3574i	−0.502223	+	1.21247i	0.446048	+	0.895009i	$0.352831\pi$
$547$	−11.7460	+	28.3574i	−0.502223	+	1.21247i	−0.948270	+	0.317464i	$0.897169\pi$
$548$	17.4197	−	13.4364i	0.744132	−	0.573974i
$549$		0			0
$550$	2.54412	+	7.46388i	0.108482	+	0.318261i
$551$	−1.82706	+	1.82706i	−0.0778353	+	0.0778353i
$552$		0			0
$553$	10.5540	+	10.5540i	0.448800	+	0.448800i
$554$	10.2600	−	20.8713i	0.435905	−	0.886738i
$555$		0			0
$556$	2.84312	−	0.769484i	0.120575	−	0.0326334i
$557$	−1.04776	−	0.433995i	−0.0443949	−	0.0183890i	0.360376	−	0.932807i	$-0.382649\pi$
$557$	−1.04776	−	0.433995i	−0.0443949	−	0.0183890i	−0.404770	+	0.914418i	$0.632649\pi$
$558$		0			0
$559$		−	22.1315i		−	0.936061i
$560$	8.73025	−	11.4968i	0.368920	−	0.485830i
$561$		0			0
$562$	−38.7364	−	2.48997i	−1.63400	−	0.105033i
$563$	−17.2452	−	7.14320i	−0.726799	−	0.301050i	−0.0115632	−	0.999933i	$-0.503681\pi$
$563$	−17.2452	−	7.14320i	−0.726799	−	0.301050i	−0.715236	+	0.698883i	$0.753681\pi$
$564$		0			0
$565$	−3.89402	−	9.40101i	−0.163823	−	0.395503i
$566$	−4.26847	−	2.09830i	−0.179417	−	0.0881983i
$567$		0			0
$568$	3.48811	−	17.8885i	0.146358	−	0.750586i
$569$	6.34223	−	6.34223i	0.265880	−	0.265880i	−0.561558	−	0.827438i	$-0.689798\pi$
$569$	6.34223	−	6.34223i	0.265880	−	0.265880i	0.827438	+	0.561558i	$0.189798\pi$
$570$		0			0
$571$	6.50744	−	2.69547i	0.272328	−	0.112802i	−0.242340	−	0.970191i	$-0.577915\pi$
$571$	6.50744	−	2.69547i	0.272328	−	0.112802i	0.514668	+	0.857389i	$0.327915\pi$
$572$	6.57678	+	0.849018i	0.274989	+	0.0354992i
$573$		0			0
$574$	−4.65000	−	5.28887i	−0.194087	−	0.220753i
$575$	−20.2090			−0.842774
$576$		0			0
$577$	−17.6367			−0.734225			−0.367112	−	0.930177i	$-0.619654\pi$
$577$	−17.6367			−0.734225			−0.367112	+	0.930177i	$0.619654\pi$
$578$	−15.6243	−	17.7709i	−0.649884	−	0.739172i
$579$		0			0
$580$	−2.69556	−	0.347978i	−0.111927	−	0.0144490i
$581$	7.76454	−	3.21618i	0.322127	−	0.133430i
$582$		0			0
$583$	6.44744	−	6.44744i	0.267026	−	0.267026i
$584$	22.4513	+	4.37780i	0.929040	+	0.181155i
$585$		0			0
$586$	21.4517	+	10.5453i	0.886163	+	0.435622i
$587$	−8.02425	−	19.3722i	−0.331196	−	0.799578i	−0.998498	−	0.0547907i	$-0.982551\pi$
$587$	−8.02425	−	19.3722i	−0.331196	−	0.799578i	0.667302	−	0.744787i	$-0.267449\pi$
$588$		0			0
$589$	−12.1009	−	5.01237i	−0.498610	−	0.206531i
$590$	−27.6514	−	1.77743i	−1.13839	−	0.0731756i
$591$		0			0
$592$	4.27854	−	0.585201i	0.175847	−	0.0240516i
$593$			13.0297i			0.535066i	0.963549	+	0.267533i	$0.0862084\pi$
$593$			13.0297i			0.535066i	−0.963549	+	0.267533i	$0.913792\pi$
$594$		0			0
$595$	1.72595	+	0.714912i	0.0707570	+	0.0293085i
$596$	28.2604	−	7.64863i	1.15759	−	0.313300i
$597$		0			0
$598$	−7.49740	+	15.2516i	−0.306591	+	0.623683i
$599$	−8.65583	−	8.65583i	−0.353668	−	0.353668i	0.507805	−	0.861472i	$-0.330457\pi$
$599$	−8.65583	−	8.65583i	−0.353668	−	0.353668i	−0.861472	+	0.507805i	$0.830457\pi$
$600$		0			0
$601$	−18.2194	+	18.2194i	−0.743187	+	0.743187i	−0.973190	−	0.230003i	$-0.926126\pi$
$601$	−18.2194	+	18.2194i	−0.743187	+	0.743187i	0.230003	+	0.973190i	$0.426126\pi$
$602$	14.4457	+	42.3803i	0.588762	+	1.72729i
$603$		0			0
$604$	25.6941	−	19.8187i	1.04548	−	0.806412i
$605$	4.08347	−	9.85836i	0.166017	−	0.400799i
$606$		0			0
$607$	−0.0787106			−0.00319477			−0.00159738	−	0.999999i	$-0.500508\pi$
$607$	−0.0787106			−0.00319477			−0.00159738	+	0.999999i	$0.500508\pi$
$608$	1.09041	+	15.1732i	0.0442220	+	0.615355i
$609$		0			0
$610$	14.7673	−	12.9835i	0.597910	−	0.525685i
$611$	7.38923	−	17.8392i	0.298936	−	0.721696i
$612$		0			0
$613$	−15.3530	+	6.35941i	−0.620100	+	0.256854i	−0.670540	−	0.741873i	$-0.733938\pi$
$613$	−15.3530	+	6.35941i	−0.620100	+	0.256854i	0.0504400	+	0.998727i	$0.483938\pi$
$614$	−10.6990	−	31.3883i	−0.431775	−	1.26673i
$615$		0			0
$616$	−13.1483	+	2.66699i	−0.529760	+	0.107456i
$617$	−26.1711	−	26.1711i	−1.05361	−	1.05361i	−0.998479	−	0.0551288i	$-0.982443\pi$
$617$	−26.1711	−	26.1711i	−1.05361	−	1.05361i	−0.0551288	−	0.998479i	$-0.517557\pi$
$618$		0			0
$619$	−1.49785	−	3.61614i	−0.0602038	−	0.145345i	0.890915	−	0.454170i	$-0.150064\pi$
$619$	−1.49785	−	3.61614i	−0.0602038	−	0.145345i	−0.951119	+	0.308825i	$0.900064\pi$
$620$	−3.59938	−	13.2991i	−0.144555	−	0.534105i
$621$		0			0
$622$	1.35998	−	21.1571i	0.0545301	−	0.848321i
$623$		−	11.0156i		−	0.441329i
$624$		0			0
$625$			1.00465i			0.0401862i
$626$	−0.533341	−	0.0342831i	−0.0213166	−	0.00137023i
$627$		0			0
$628$	−28.2751	−	16.2299i	−1.12830	−	0.647645i
$629$	0.213860	+	0.516303i	0.00852715	+	0.0205864i
$630$		0			0
$631$	−25.0685	−	25.0685i	−0.997961	−	0.997961i	0.00203659	−	0.999998i	$-0.499352\pi$
$631$	−25.0685	−	25.0685i	−0.997961	−	0.997961i	−0.999998	+	0.00203659i	$0.999352\pi$
$632$	−9.24348	−	13.7214i	−0.367686	−	0.545809i
$633$		0			0
$634$	−4.65951	+	1.58823i	−0.185053	+	0.0630767i
$635$	13.3755	−	5.54031i	0.530790	−	0.219860i
$636$		0			0
$637$	0.333817	−	0.805906i	0.0132263	−	0.0319312i
$638$	1.66784	+	1.89699i	0.0660305	+	0.0751025i
$639$		0			0
$640$	−11.9373	+	10.6562i	−0.471864	+	0.421223i
$641$	46.6586			1.84291			0.921453	−	0.388490i	$-0.127003\pi$
$641$	46.6586			1.84291			0.921453	+	0.388490i	$0.127003\pi$
$642$		0			0
$643$	9.45947	−	22.8372i	0.373045	−	0.900611i	−0.620186	−	0.784455i	$-0.712943\pi$
$643$	9.45947	−	22.8372i	0.373045	−	0.900611i	0.993231	−	0.116156i	$-0.0370572\pi$
$644$	4.40202	−	34.0995i	0.173464	−	1.34371i
$645$		0			0
$646$	−1.86336	+	0.635142i	−0.0733131	+	0.0249893i
$647$	−3.00368	+	3.00368i	−0.118087	+	0.118087i	−0.763681	−	0.645594i	$-0.776610\pi$
$647$	−3.00368	+	3.00368i	−0.118087	+	0.118087i	0.645594	+	0.763681i	$0.276610\pi$
$648$		0			0
$649$	18.2087	+	18.2087i	0.714754	+	0.714754i
$650$	−6.79031	−	3.33799i	−0.266338	−	0.130927i
$651$		0			0
$652$	−20.0316	−	11.4981i	−0.784497	−	0.450301i
$653$	−12.2943	−	5.09247i	−0.481114	−	0.199284i	0.128927	−	0.991654i	$-0.458847\pi$
$653$	−12.2943	−	5.09247i	−0.481114	−	0.199284i	−0.610041	+	0.792370i	$0.708847\pi$
$654$		0			0
$655$			10.7647i			0.420611i
$656$	3.93708	+	6.74065i	0.153717	+	0.263178i
$657$		0			0
$658$	−2.50589	+	38.9840i	−0.0976898	+	1.51975i
$659$	−9.62745	−	3.98782i	−0.375032	−	0.155343i	0.187202	−	0.982321i	$-0.440058\pi$
$659$	−9.62745	−	3.98782i	−0.375032	−	0.155343i	−0.562234	+	0.826978i	$0.690058\pi$
$660$		0			0
$661$	9.19635	+	22.2020i	0.357697	+	0.863556i	0.995623	+	0.0934588i	$0.0297923\pi$
$661$	9.19635	+	22.2020i	0.357697	+	0.863556i	−0.637927	+	0.770097i	$0.720208\pi$
$662$	12.5864	−	25.6039i	0.489186	−	0.995125i
$663$		0			0
$664$	−9.12994	+	1.85191i	−0.354310	+	0.0718681i
$665$	−6.86261	+	6.86261i	−0.266120	+	0.266120i
$666$		0			0
$667$	−5.98062	+	2.47726i	−0.231571	+	0.0959197i
$668$	7.20857	+	9.34560i	0.278908	+	0.361592i
$669$		0			0
$670$	5.00705	−	4.40222i	0.193439	−	0.170073i
$671$	−18.2741			−0.705465
$672$		0			0
$673$	−24.6607			−0.950601			−0.475300	−	0.879824i	$-0.657661\pi$
$673$	−24.6607			−0.950601			−0.475300	+	0.879824i	$0.657661\pi$
$674$	−22.3766	+	19.6736i	−0.861914	+	0.757799i
$675$		0			0
$676$	15.5490	−	11.9934i	0.598038	−	0.461286i
$677$	27.0377	−	11.1994i	1.03914	−	0.430427i	0.203138	−	0.979150i	$-0.434886\pi$
$677$	27.0377	−	11.1994i	1.03914	−	0.430427i	0.836004	+	0.548724i	$0.184886\pi$
$678$		0			0
$679$	−12.6559	+	12.6559i	−0.485689	+	0.485689i
$680$	−1.72613	−	1.14396i	−0.0661940	−	0.0438689i
$681$		0			0
$682$	−5.64873	+	11.4909i	−0.216301	+	0.440010i
$683$	−18.0235	−	43.5126i	−0.689651	−	1.66497i	−0.745483	−	0.666525i	$-0.767781\pi$
$683$	−18.0235	−	43.5126i	−0.689651	−	1.66497i	0.0558316	−	0.998440i	$-0.482219\pi$
$684$		0			0
$685$	−14.3734	−	5.95367i	−0.549181	−	0.227478i
$686$	−1.73358	+	26.9692i	−0.0661884	+	1.02969i
$687$		0			0
$688$	−6.72575	−	49.1734i	−0.256417	−	1.87472i
$689$			8.74902i			0.333311i
$690$		0			0
$691$	10.9245	+	4.52508i	0.415588	+	0.172142i	0.580672	−	0.814137i	$-0.302790\pi$
$691$	10.9245	+	4.52508i	0.415588	+	0.172142i	−0.165085	+	0.986279i	$0.552790\pi$
$692$	20.6158	−	35.9161i	0.783696	−	1.36532i
$693$		0			0
$694$	−28.1818	−	13.8537i	−1.06977	−	0.525879i
$695$	−1.47286	−	1.47286i	−0.0558687	−	0.0558687i
$696$		0			0
$697$	−0.714323	+	0.714323i	−0.0270569	+	0.0270569i
$698$	−39.6350	+	13.5099i	−1.50021	+	0.511358i
$699$		0			0
$700$	15.1818	+	1.95987i	0.573818	+	0.0740761i
$701$	−9.38301	+	22.6526i	−0.354391	+	0.855576i	0.641676	+	0.766976i	$0.278239\pi$
$701$	−9.38301	+	22.6526i	−0.354391	+	0.855576i	−0.996067	+	0.0886005i	$0.971761\pi$
$702$		0			0
$703$	−2.90323			−0.109497
$704$	14.8708	−	0.112266i	0.560466	−	0.00423119i
$705$		0			0
$706$	−30.0833	−	34.2165i	−1.13220	−	1.28775i
$707$	−11.1618	+	26.9469i	−0.419781	+	1.01344i
$708$		0			0
$709$	41.7647	−	17.2995i	1.56851	−	0.649696i	0.581966	−	0.813213i	$-0.302284\pi$
$709$	41.7647	−	17.2995i	1.56851	−	0.649696i	0.986541	+	0.163517i	$0.0522838\pi$
$710$	−12.1995	+	4.15828i	−0.457838	+	0.156058i
$711$		0			0
$712$	−2.33691	+	11.9847i	−0.0875793	+	0.449145i
$713$	−23.2034	−	23.2034i	−0.868975	−	0.868975i
$714$		0			0
$715$	−1.79462	−	4.33260i	−0.0671150	−	0.162030i
$716$	−23.5179	+	40.9720i	−0.878906	+	1.53120i
$717$		0			0
$718$	−18.9828	−	1.22022i	−0.708433	−	0.0455380i
$719$		−	13.6669i		−	0.509689i	−0.966982	−	0.254844i	$-0.917976\pi$
$719$		−	13.6669i		−	0.509689i	0.966982	−	0.254844i	$-0.0820242\pi$
$720$		0			0
$721$		−	21.2717i		−	0.792199i
$722$	−1.06760	+	16.6086i	−0.0397319	+	0.618107i
$723$		0			0
$724$	−2.96922	+	0.803614i	−0.110350	+	0.0298661i
$725$	−1.10293	−	2.66270i	−0.0409616	−	0.0988901i
$726$		0			0
$727$	8.78411	+	8.78411i	0.325785	+	0.325785i	0.850981	−	0.525196i	$-0.176008\pi$
$727$	8.78411	+	8.78411i	0.325785	+	0.325785i	−0.525196	+	0.850981i	$0.676008\pi$
$728$	7.11143	−	10.7305i	0.263567	−	0.397698i
$729$		0			0
$730$	−5.21892	−	15.3111i	−0.193161	−	0.566690i
$731$	5.93390	−	2.45790i	0.219473	−	0.0909088i
$732$		0			0
$733$	−12.4695	+	30.1041i	−0.460573	+	1.11192i	0.507590	+	0.861599i	$0.330537\pi$
$733$	−12.4695	+	30.1041i	−0.460573	+	1.11192i	−0.968163	+	0.250322i	$0.919463\pi$
$734$	−32.6856	+	28.7373i	−1.20645	+	1.06071i
$735$		0			0
$736$	−12.0234	+	36.1656i	−0.443187	+	1.33308i
$737$	−6.19609			−0.228236
$738$		0			0
$739$	−5.81870	+	14.0476i	−0.214045	+	0.516749i	−0.994037	−	0.109039i	$-0.965223\pi$
$739$	−5.81870	+	14.0476i	−0.214045	+	0.516749i	0.779993	+	0.625788i	$0.215223\pi$
$740$	−1.86517	−	2.41811i	−0.0685650	−	0.0888916i
$741$		0			0
$742$	−5.71068	−	16.7538i	−0.209646	−	0.615052i
$743$	13.4938	−	13.4938i	0.495040	−	0.495040i	−0.414850	−	0.909890i	$-0.636166\pi$
$743$	13.4938	−	13.4938i	0.495040	−	0.495040i	0.909890	+	0.414850i	$0.136166\pi$
$744$		0			0
$745$	−14.6401	−	14.6401i	−0.536373	−	0.536373i
$746$	−7.26394	+	14.7767i	−0.265952	+	0.541012i
$747$		0			0
$748$	0.502773	+	1.85766i	0.0183832	+	0.0679229i
$749$	−0.339429	−	0.140596i	−0.0124025	−	0.00513726i
$750$		0			0
$751$			12.3426i			0.450387i	0.974314	+	0.225194i	$0.0723015\pi$
$751$			12.3426i			0.450387i	−0.974314	+	0.225194i	$0.927699\pi$
$752$	10.9967	−	41.8821i	0.401007	−	1.52728i
$753$		0			0
$754$	−2.41869	−	0.155473i	−0.0880836	−	0.00566201i
$755$	−21.2009	−	8.78169i	−0.771579	−	0.319599i
$756$		0			0
$757$	6.58267	+	15.8920i	0.239251	+	0.577603i	0.997206	−	0.0747040i	$-0.0238012\pi$
$757$	6.58267	+	15.8920i	0.239251	+	0.577603i	−0.757955	+	0.652307i	$0.773801\pi$
$758$	−20.2693	−	9.96403i	−0.736214	−	0.361910i
$759$		0			0
$760$	8.92223	−	6.01048i	0.323643	−	0.218023i
$761$	−7.00449	+	7.00449i	−0.253913	+	0.253913i	−0.822573	−	0.568660i	$-0.807462\pi$
$761$	−7.00449	+	7.00449i	−0.253913	+	0.253913i	0.568660	+	0.822573i	$0.307462\pi$
$762$		0			0
$763$	−19.8148	+	8.20755i	−0.717343	+	0.297133i
$764$	5.29964	−	41.0528i	0.191734	−	1.48524i
$765$		0			0
$766$	24.0115	+	27.3105i	0.867570	+	0.986767i
$767$	−24.7087			−0.892181
$768$		0			0
$769$	36.2549			1.30738			0.653692	−	0.756760i	$-0.273219\pi$
$769$	36.2549			1.30738			0.653692	+	0.756760i	$0.273219\pi$
$770$	6.26457	+	7.12527i	0.225759	+	0.256777i
$771$		0			0
$772$	−3.28651	+	25.4584i	−0.118284	+	0.916269i
$773$	43.2541	−	17.9164i	1.55574	−	0.644409i	0.571398	−	0.820673i	$-0.306401\pi$
$773$	43.2541	−	17.9164i	1.55574	−	0.644409i	0.984343	+	0.176264i	$0.0564014\pi$
$774$		0			0
$775$	10.3306	−	10.3306i	0.371088	−	0.371088i
$776$	16.4542	−	11.0844i	0.590673	−	0.397908i
$777$		0			0
$778$	−31.9995	−	15.7304i	−1.14724	−	0.563961i
$779$	−2.00836	−	4.84860i	−0.0719569	−	0.173719i
$780$		0			0
$781$	11.0664	+	4.58385i	0.395986	+	0.164023i
$782$	−4.92191	−	0.316380i	−0.176007	−	0.0113137i
$783$		0			0
$784$	0.496787	−	1.89207i	0.0177424	−	0.0675740i
$785$			23.0556i			0.822889i
$786$		0			0
$787$	−9.41043	−	3.89793i	−0.335446	−	0.138946i	0.208602	−	0.978001i	$-0.433109\pi$
$787$	−9.41043	−	3.89793i	−0.335446	−	0.138946i	−0.544047	+	0.839055i	$0.683109\pi$
$788$	4.62733	+	17.0972i	0.164842	+	0.609063i
$789$		0			0
$790$	−5.16155	+	10.4999i	−0.183640	+	0.373569i
$791$	12.9809	+	12.9809i	0.461548	+	0.461548i
$792$		0			0
$793$	12.3988	−	12.3988i	0.440293	−	0.440293i
$794$	−4.06075	−	11.9133i	−0.144111	−	0.422788i
$795$		0			0
$796$	3.37384	+	4.37404i	0.119583	+	0.155034i
$797$	2.80422	−	6.76999i	0.0993306	−	0.239805i	−0.866401	−	0.499350i	$-0.833572\pi$
$797$	2.80422	−	6.76999i	0.0993306	−	0.239805i	0.965731	+	0.259544i	$0.0835724\pi$
$798$		0			0
$799$	5.60369			0.198244
$800$	−16.1017	−	5.35305i	−0.569280	−	0.189259i
$801$		0			0
$802$	37.3241	−	32.8156i	1.31796	−	1.15876i
$803$	−5.75302	+	13.8890i	−0.203020	+	0.490133i
$804$		0			0
$805$	−22.4638	+	9.30481i	−0.791745	+	0.327952i
$806$	−3.96385	−	11.6290i	−0.139621	−	0.409616i
$807$		0			0
$808$	17.8604	−	26.9497i	0.628327	−	0.948085i
$809$	19.8036	+	19.8036i	0.696257	+	0.696257i	0.963601	−	0.267344i	$-0.0861461\pi$
$809$	19.8036	+	19.8036i	0.696257	+	0.696257i	−0.267344	+	0.963601i	$0.586146\pi$
$810$		0			0
$811$	−1.67737	−	4.04953i	−0.0589004	−	0.142198i	0.891689	−	0.452648i	$-0.149520\pi$
$811$	−1.67737	−	4.04953i	−0.0589004	−	0.142198i	−0.950590	+	0.310449i	$0.899520\pi$
$812$	4.73312	−	1.28101i	0.166100	−	0.0449547i
$813$		0			0
$814$	−0.182059	+	2.83229i	−0.00638118	+	0.0992716i
$815$			16.3338i			0.572146i
$816$		0			0
$817$			33.3669i			1.16736i
$818$	−52.7011	−	3.38762i	−1.84265	−	0.118445i
$819$		0			0
$820$	2.74817	−	4.78774i	0.0959701	−	0.167195i
$821$	2.36006	+	5.69769i	0.0823666	+	0.198851i	0.959697	−	0.281036i	$-0.0906779\pi$
$821$	2.36006	+	5.69769i	0.0823666	+	0.198851i	−0.877331	+	0.479886i	$0.840678\pi$
$822$		0			0
$823$	34.1014	+	34.1014i	1.18870	+	1.18870i	0.977427	+	0.211272i	$0.0677604\pi$
$823$	34.1014	+	34.1014i	1.18870	+	1.18870i	0.211272	+	0.977427i	$0.432240\pi$
$824$	−4.51271	+	23.1431i	−0.157208	+	0.806228i
$825$		0			0
$826$	47.3157	−	16.1279i	1.64632	−	0.561163i
$827$	−2.27839	+	0.943740i	−0.0792274	+	0.0328171i	−0.421945	−	0.906621i	$-0.638653\pi$
$827$	−2.27839	+	0.943740i	−0.0792274	+	0.0328171i	0.342718	+	0.939438i	$0.388653\pi$
$828$		0			0
$829$	0.578335	−	1.39622i	0.0200864	−	0.0484929i	−0.913518	−	0.406798i	$-0.866645\pi$
$829$	0.578335	−	1.39622i	0.0200864	−	0.0484929i	0.933605	+	0.358305i	$0.116645\pi$
$830$	4.35001	+	4.94766i	0.150991	+	0.171736i
$831$		0			0
$832$	−10.0135	+	10.1658i	−0.347156	+	0.352437i
$833$	0.253154			0.00877125
$834$		0			0
$835$	3.19412	−	7.71130i	0.110537	−	0.266861i
$836$	−9.91562	−	1.28004i	−0.342939	−	0.0442711i
$837$		0			0
$838$	36.4344	−	12.4190i	1.25861	−	0.429006i
$839$	5.47884	−	5.47884i	0.189151	−	0.189151i	−0.606178	−	0.795329i	$-0.707298\pi$
$839$	5.47884	−	5.47884i	0.189151	−	0.189151i	0.795329	+	0.606178i	$0.207298\pi$
$840$		0			0
$841$	19.8533	+	19.8533i	0.684597	+	0.684597i
$842$	−11.5140	−	5.66008i	−0.396799	−	0.195059i
$843$		0			0
$844$	17.5349	−	30.5487i	0.603578	−	1.05153i
$845$	−12.8299	−	5.31431i	−0.441361	−	0.182818i
$846$		0			0
$847$			19.2509i			0.661468i
$848$	2.65883	+	19.4393i	0.0913045	+	0.667547i
$849$		0			0
$850$	0.140859	−	2.19134i	0.00483143	−	0.0751622i
$851$	−6.71986	−	2.78346i	−0.230354	−	0.0954157i
$852$		0			0
$853$	12.8758	+	31.0849i	0.440858	+	1.06433i	0.975648	+	0.219340i	$0.0703905\pi$
$853$	12.8758	+	31.0849i	0.440858	+	1.06433i	−0.534791	+	0.844985i	$0.679609\pi$
$854$	−15.6499	+	31.8358i	−0.535529	+	1.08940i
$855$		0			0
$856$	0.339464	+	0.224974i	0.0116026	+	0.00768944i
$857$	9.65031	−	9.65031i	0.329648	−	0.329648i	−0.522804	−	0.852453i	$-0.675114\pi$
$857$	9.65031	−	9.65031i	0.329648	−	0.329648i	0.852453	+	0.522804i	$0.175114\pi$
$858$		0			0
$859$	−16.8654	+	6.98586i	−0.575438	+	0.238354i	−0.651372	−	0.758758i	$-0.725806\pi$
$859$	−16.8654	+	6.98586i	−0.575438	+	0.238354i	0.0759337	+	0.997113i	$0.475806\pi$
$860$	−27.7915	+	21.4365i	−0.947683	+	0.730979i
$861$		0			0
$862$	−40.7537	+	35.8308i	−1.38808	+	1.22040i
$863$	−55.2469			−1.88062			−0.940312	−	0.340312i	$-0.889467\pi$
$863$	−55.2469			−1.88062			−0.940312	+	0.340312i	$0.889467\pi$
$864$		0			0
$865$	−29.2860			−0.995754
$866$	5.70266	−	5.01381i	0.193784	−	0.170376i
$867$		0			0
$868$	15.1811	+	19.6816i	0.515279	+	0.668037i
$869$	10.0457	−	4.16107i	0.340778	−	0.141155i
$870$		0			0
$871$	4.20397	−	4.20397i	0.142446	−	0.142446i
$872$	23.2992	−	4.72600i	0.789011	−	0.160042i
$873$		0			0
$874$	11.3036	−	22.9943i	0.382350	−	0.777795i
$875$	−11.0482	−	26.6726i	−0.373496	−	0.901699i
$876$		0			0
$877$	38.0391	+	15.7563i	1.28449	+	0.532053i	0.917338	−	0.398109i	$-0.130333\pi$
$877$	38.0391	+	15.7563i	1.28449	+	0.532053i	0.367150	+	0.930162i	$0.380333\pi$
$878$	−1.02593	+	15.9603i	−0.0346234	+	0.538635i
$879$		0			0
$880$	−5.30411	−	9.08113i	−0.178802	−	0.306125i
$881$		−	24.5016i		−	0.825481i	−0.910849	−	0.412740i	$-0.864572\pi$
$881$		−	24.5016i		−	0.825481i	0.910849	−	0.412740i	$-0.135428\pi$
$882$		0			0
$883$	3.21810	+	1.33298i	0.108298	+	0.0448584i	0.436174	−	0.899862i	$-0.356333\pi$
$883$	3.21810	+	1.33298i	0.108298	+	0.0448584i	−0.327877	+	0.944721i	$0.606333\pi$
$884$	−1.60153	−	0.919276i	−0.0538651	−	0.0309186i
$885$		0			0
$886$	20.2449	+	9.95205i	0.680142	+	0.334346i
$887$	−27.1931	−	27.1931i	−0.913054	−	0.913054i	0.0834576	−	0.996511i	$-0.473404\pi$
$887$	−27.1931	−	27.1931i	−0.913054	−	0.913054i	−0.996511	+	0.0834576i	$0.973404\pi$
$888$		0			0
$889$	−18.4689	+	18.4689i	−0.619426	+	0.619426i
$890$	8.17320	−	2.78590i	0.273966	−	0.0933837i
$891$		0			0
$892$	5.03453	−	38.9991i	0.168568	−	1.30579i
$893$	−11.1405	+	26.8956i	−0.372803	+	0.900027i
$894$		0			0
$895$	33.4086			1.11673
$896$	12.5398	−	26.0030i	0.418924	−	0.868699i
$897$		0			0
$898$	7.02466	+	7.98979i	0.234416	+	0.266623i
$899$	1.79089	−	4.32359i	0.0597294	−	0.144200i
$900$		0			0
$901$	−2.34579	+	0.971659i	−0.0781497	+	0.0323707i
$902$	−4.85607	+	1.65523i	−0.161689	+	0.0551132i
$903$		0			0
$904$	−11.3691	−	16.8768i	−0.378130	−	0.561313i
$905$	1.53819	+	1.53819i	0.0511310	+	0.0511310i
$906$		0			0
$907$	17.3229	+	41.8211i	0.575196	+	1.38865i	0.897080	+	0.441868i	$0.145684\pi$
$907$	17.3229	+	41.8211i	0.575196	+	1.38865i	−0.321884	+	0.946779i	$0.604316\pi$
$908$	−37.0094	−	21.2434i	−1.22820	−	0.704988i
$909$		0			0
$910$	−9.08484	−	0.583973i	−0.301159	−	0.0193585i
$911$			0.841826i			0.0278909i	0.999903	+	0.0139455i	$0.00443912\pi$
$911$			0.841826i			0.0278909i	−0.999903	+	0.0139455i	$0.995561\pi$
$912$		0			0
$913$		−	6.12260i		−	0.202629i
$914$	1.20212	−	18.7014i	0.0397627	−	0.618587i
$915$		0			0
$916$	−14.1321	−	52.2156i	−0.466936	−	1.72525i
$917$	−7.43194	−	17.9423i	−0.245424	−	0.592507i
$918$		0			0
$919$	34.6859	+	34.6859i	1.14418	+	1.14418i	0.987677	+	0.156506i	$0.0500230\pi$
$919$	34.6859	+	34.6859i	1.14418	+	1.14418i	0.156506	+	0.987677i	$0.449977\pi$
$920$	26.4141	−	5.35781i	0.870846	−	0.176642i
$921$		0			0
$922$	−15.2504	−	44.7413i	−0.502246	−	1.47348i
$923$	−10.6185	+	4.39832i	−0.349512	+	0.144772i
$924$		0			0
$925$	1.23925	−	2.99182i	0.0407464	−	0.0983704i
$926$	26.6168	−	23.4016i	0.874683	−	0.769026i
$927$		0			0
$928$	−5.42129	+	0.389597i	−0.177963	+	0.0127891i
$929$	−43.0957			−1.41392			−0.706962	−	0.707252i	$-0.749935\pi$
$929$	−43.0957			−1.41392			−0.706962	+	0.707252i	$0.749935\pi$
$930$		0			0
$931$	−0.503286	+	1.21504i	−0.0164945	+	0.0398213i
$932$	39.3847	−	30.3787i	1.29009	−	0.995087i
$933$		0			0
$934$	−11.2752	−	33.0787i	−0.368934	−	1.08237i
$935$	0.962350	−	0.962350i	0.0314722	−	0.0314722i
$936$		0			0
$937$	−31.6863	−	31.6863i	−1.03515	−	1.03515i	−0.999359	−	0.0357872i	$-0.988606\pi$
$937$	−31.6863	−	31.6863i	−1.03515	−	1.03515i	−0.0357872	−	0.999359i	$-0.511394\pi$
$938$	−5.30632	+	10.7944i	−0.173257	+	0.352449i
$939$		0			0
$940$	−29.5587	+	8.00000i	−0.964098	+	0.260931i
$941$	−7.88532	−	3.26621i	−0.257054	−	0.106475i	0.250435	−	0.968133i	$-0.419426\pi$
$941$	−7.88532	−	3.26621i	−0.257054	−	0.106475i	−0.507489	+	0.861658i	$0.669426\pi$
$942$		0			0
$943$		−	13.1482i		−	0.428163i
$944$	−54.8999	+	7.50899i	−1.78684	+	0.244397i
$945$		0			0
$946$	32.5516	+	2.09242i	1.05834	+	0.0680303i
$947$	−49.1893	−	20.3749i	−1.59844	−	0.662094i	−0.607244	−	0.794516i	$-0.707725\pi$
$947$	−49.1893	−	20.3749i	−1.59844	−	0.662094i	−0.991194	+	0.132421i	$0.957725\pi$
$948$		0			0
$949$	−5.52018	−	13.3269i	−0.179193	−	0.432609i
$950$	10.2375	+	5.03259i	0.332150	+	0.163279i
$951$		0			0
$952$	3.66685	+	0.715005i	0.118843	+	0.0231734i
$953$	15.2407	−	15.2407i	0.493696	−	0.493696i	−0.415772	−	0.909469i	$-0.636489\pi$
$953$	15.2407	−	15.2407i	0.493696	−	0.493696i	0.909469	+	0.415772i	$0.136489\pi$
$954$		0			0
$955$	−27.0444	+	11.2022i	−0.875137	+	0.362494i
$956$	−2.70884	−	0.349694i	−0.0876103	−	0.0113099i
$957$		0			0
$958$	9.83756	+	11.1892i	0.317837	+	0.361505i
$959$	28.0677			0.906353
$960$		0			0
$961$	−7.27727			−0.234751
$962$	−1.79815	−	2.04520i	−0.0579746	−	0.0659398i
$963$		0			0
$964$	50.8640	+	6.56621i	1.63822	+	0.211483i
$965$	16.7713	−	6.94690i	0.539887	−	0.223629i
$966$		0			0
$967$	1.37586	−	1.37586i	0.0442448	−	0.0442448i	−0.684638	−	0.728883i	$-0.740040\pi$
$967$	1.37586	−	1.37586i	0.0442448	−	0.0442448i	0.728883	+	0.684638i	$0.240040\pi$
$968$	4.08400	−	20.9445i	0.131265	−	0.673182i
$969$		0			0
$970$	−12.5911	−	6.18954i	−0.404274	−	0.198734i
$971$	−7.72652	−	18.6535i	−0.247956	−	0.598618i	0.750074	−	0.661353i	$-0.230018\pi$
$971$	−7.72652	−	18.6535i	−0.247956	−	0.598618i	−0.998030	+	0.0627352i	$0.980018\pi$
$972$		0			0
$973$	3.47178	+	1.43806i	0.111300	+	0.0461021i
$974$	11.4840	+	0.738191i	0.367971	+	0.0236532i
$975$		0			0
$976$	23.7806	−	31.3166i	0.761198	−	1.00242i
$977$			33.6324i			1.07600i	0.842946	+	0.537998i	$0.180819\pi$
$977$			33.6324i			1.07600i	−0.842946	+	0.537998i	$0.819181\pi$
$978$		0			0
$979$	−7.41408	−	3.07101i	−0.236955	−	0.0981500i
$980$	−1.33535	+	0.361410i	−0.0426562	+	0.0115448i
$981$		0			0
$982$	−15.5145	+	31.5603i	−0.495088	+	1.00713i
$983$	1.05431	+	1.05431i	0.0336274	+	0.0336274i	0.723721	−	0.690093i	$-0.242430\pi$
$983$	1.05431	+	1.05431i	0.0336274	+	0.0336274i	−0.690093	+	0.723721i	$0.742430\pi$
$984$		0			0
$985$	8.85711	−	8.85711i	0.282211	−	0.282211i
$986$	−0.226932	−	0.665768i	−0.00722700	−	0.0212024i
$987$		0			0
$988$	7.59611	−	5.85913i	0.241665	−	0.186404i
$989$	−31.9904	+	77.2317i	−1.01724	+	2.45582i
$990$		0			0
$991$	−47.7674			−1.51738			−0.758691	−	0.651451i	$-0.774161\pi$
$991$	−47.7674			−1.51738			−0.758691	+	0.651451i	$0.774161\pi$
$992$	−12.3413	−	24.6337i	−0.391836	−	0.782121i
$993$		0			0
$994$	17.4629	−	15.3534i	0.553888	−	0.486981i
$995$	1.49495	−	3.60913i	0.0473932	−	0.114417i
$996$		0			0
$997$	7.46469	−	3.09197i	0.236409	−	0.0979238i	−0.261334	−	0.965248i	$-0.584162\pi$
$997$	7.46469	−	3.09197i	0.236409	−	0.0979238i	0.497743	+	0.867325i	$0.334162\pi$
$998$	−10.6891	−	31.3593i	−0.338357	−	0.992661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.9	✓	128
3.2	odd	2	inner	864.2.v.b.109.24	yes	128
32.5	even	8	inner	864.2.v.b.325.9	yes	128
96.5	odd	8	inner	864.2.v.b.325.24	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.9	✓	128	1.1	even	1	trivial
864.2.v.b.109.24	yes	128	3.2	odd	2	inner
864.2.v.b.325.9	yes	128	32.5	even	8	inner
864.2.v.b.325.24	yes	128	96.5	odd	8	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933793 - 1.06209i) q^{2} +(-0.256062 + 1.98354i) q^{4} +(1.30670 - 0.541253i) q^{5} +(-1.80429 + 1.80429i) q^{7} +(2.34580 - 1.58026i) q^{8} +O(q^{10})\)	\(q+(-0.933793 - 1.06209i) q^{2} +(-0.256062 + 1.98354i) q^{4} +(1.30670 - 0.541253i) q^{5} +(-1.80429 + 1.80429i) q^{7} +(2.34580 - 1.58026i) q^{8} +(-1.79505 - 0.882413i) q^{10} +(0.711373 + 1.71741i) q^{11} +(-1.64790 - 0.682581i) q^{13} +(3.60115 + 0.231482i) q^{14} +(-3.86886 - 1.01582i) q^{16} -0.517642i q^{17} +(2.48448 + 1.02911i) q^{19} +(0.739002 + 2.73049i) q^{20} +(1.15976 - 2.35924i) q^{22} +(4.76398 + 4.76398i) q^{23} +(-2.12102 + 2.12102i) q^{25} +(0.813833 + 2.38760i) q^{26} +(-3.11688 - 4.04090i) q^{28} +(-0.367694 + 0.887691i) q^{29} -4.87060 q^{31} +(2.53383 + 5.05764i) q^{32} +(-0.549781 + 0.483371i) q^{34} +(-1.38109 + 3.33425i) q^{35} +(-0.997414 + 0.413142i) q^{37} +(-1.22699 - 3.59971i) q^{38} +(2.20994 - 3.33460i) q^{40} +(-1.37996 - 1.37996i) q^{41} +(4.74827 + 11.4633i) q^{43} +(-3.58870 + 0.971275i) q^{44} +(0.611195 - 9.50833i) q^{46} +10.8254i q^{47} +0.489051i q^{49} +(4.23331 + 0.272117i) q^{50} +(1.77589 - 3.09389i) q^{52} +(-1.87709 - 4.53169i) q^{53} +(1.85910 + 1.85910i) q^{55} +(-1.38127 + 7.08376i) q^{56} +(1.28616 - 0.438396i) q^{58} +(12.7983 - 5.30122i) q^{59} +(-3.76200 + 9.08227i) q^{61} +(4.54813 + 5.17300i) q^{62} +(3.00558 - 7.41394i) q^{64} -2.52276 q^{65} +(-1.27556 + 3.07947i) q^{67} +(1.02676 + 0.132548i) q^{68} +(4.83092 - 1.64666i) q^{70} +(4.55636 - 4.55636i) q^{71} +(5.71852 + 5.71852i) q^{73} +(1.37017 + 0.673552i) q^{74} +(-2.67746 + 4.66456i) q^{76} +(-4.38223 - 1.81518i) q^{77} -5.84936i q^{79} +(-5.60526 + 0.766666i) q^{80} +(-0.177042 + 2.75423i) q^{82} +(-3.04294 - 1.26043i) q^{83} +(-0.280176 - 0.676404i) q^{85} +(7.74117 - 15.7474i) q^{86} +(4.38268 + 2.90455i) q^{88} +(-3.05260 + 3.05260i) q^{89} +(4.20486 - 1.74171i) q^{91} +(-10.6694 + 8.22967i) q^{92} +(11.4975 - 10.1087i) q^{94} +3.80349 q^{95} +7.01433 q^{97} +(0.519415 - 0.456673i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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