LMFDB - Embedded newform 720.2.u.a.179.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.10
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.15480 + 1.91479i) q^{5} -3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +O(q^{10})$	\(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.15480 + 1.91479i) q^{5} -3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +(2.75809 - 1.54692i) q^{10} +(-1.30581 + 1.30581i) q^{11} +(1.56756 - 1.56756i) q^{13} +(-2.11753 + 3.72457i) q^{14} +(-1.90729 + 3.51600i) q^{16} +2.98571 q^{17} +(1.25807 - 1.25807i) q^{19} +(-4.47206 - 0.0259891i) q^{20} +(2.51809 - 0.692674i) q^{22} -7.82148 q^{23} +(-2.33287 - 4.42241i) q^{25} +(-3.02283 + 0.831519i) q^{26} +(5.20664 - 3.09897i) q^{28} +(7.12073 - 7.12073i) q^{29} -0.0502896i q^{31} +(4.80238 - 2.98950i) q^{32} +(-3.67067 - 2.08689i) q^{34} +(5.80096 + 3.49853i) q^{35} +(6.22957 + 6.22957i) q^{37} +(-2.42603 + 0.667350i) q^{38} +(5.47985 + 3.15773i) q^{40} +4.05554 q^{41} +(6.18655 - 6.18655i) q^{43} +(-3.57992 - 0.908456i) q^{44} +(9.61583 + 5.46689i) q^{46} -5.87568i q^{47} -2.17818 q^{49} +(-0.223016 + 7.06755i) q^{50} +(4.29751 + 1.09055i) q^{52} +(4.40639 - 4.40639i) q^{53} +(-0.992408 - 4.00831i) q^{55} +(-8.56716 + 0.170696i) q^{56} +(-13.7314 + 3.77723i) q^{58} +(8.20735 - 8.20735i) q^{59} +(-4.93899 - 4.93899i) q^{61} +(-0.0351503 + 0.0618267i) q^{62} +(-7.99365 + 0.318664i) q^{64} +(1.19133 + 4.81176i) q^{65} +(1.29973 + 1.29973i) q^{67} +(3.05413 + 5.13129i) q^{68} +(-4.68646 - 8.35577i) q^{70} -13.9687i q^{71} -3.85841 q^{73} +(-3.30451 - 12.0129i) q^{74} +(3.44904 + 0.875242i) q^{76} +(3.95602 + 3.95602i) q^{77} +1.07096i q^{79} +(-4.52987 - 7.71234i) q^{80} +(-4.98593 - 2.83465i) q^{82} +(-7.16503 + 7.16503i) q^{83} +(-3.44790 + 5.71702i) q^{85} +(-11.9300 + 3.28169i) q^{86} +(3.76623 + 3.61909i) q^{88} -7.60356 q^{89} +(-4.74899 - 4.74899i) q^{91} +(-8.00071 - 13.4421i) q^{92} +(-4.10686 + 7.22364i) q^{94} +(0.956125 + 3.86176i) q^{95} +9.70129i q^{97} +(2.67788 + 1.52245i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.22941	−	0.698958i	−0.869327	−	0.494238i
$2$	−1.22941	−	0.698958i	−0.869327	−	0.494238i
$3$		0			0
$3$		0			0
$4$	1.02291	+	1.71862i	0.511457	+	0.859309i
$5$	−1.15480	+	1.91479i	−0.516443	+	0.856322i
$5$	−1.15480	+	1.91479i	−0.516443	+	0.856322i
$6$		0			0
$7$		−	3.02955i		−	1.14506i	−0.819883	−	0.572531i	$-0.805962\pi$
$7$		−	3.02955i		−	1.14506i	0.819883	−	0.572531i	$-0.194038\pi$
$8$	−0.0563436	−	2.82787i	−0.0199205	−	0.999802i
$9$		0			0
$10$	2.75809	−	1.54692i	0.872184	−	0.489178i
$11$	−1.30581	+	1.30581i	−0.393717	+	0.393717i	−0.876010	−	0.482293i	$-0.839804\pi$
$11$	−1.30581	+	1.30581i	−0.393717	+	0.393717i	0.482293	+	0.876010i	$0.339804\pi$
$12$		0			0
$13$	1.56756	−	1.56756i	0.434762	−	0.434762i	−0.455483	−	0.890245i	$-0.650533\pi$
$13$	1.56756	−	1.56756i	0.434762	−	0.434762i	0.890245	+	0.455483i	$0.150533\pi$
$14$	−2.11753	+	3.72457i	−0.565933	+	0.995433i
$15$		0			0
$16$	−1.90729	+	3.51600i	−0.476823	+	0.879000i
$17$	2.98571			0.724141			0.362071	−	0.932151i	$-0.382070\pi$
$17$	2.98571			0.724141			0.362071	+	0.932151i	$0.382070\pi$
$18$		0			0
$19$	1.25807	−	1.25807i	0.288621	−	0.288621i	−0.547914	−	0.836535i	$-0.684578\pi$
$19$	1.25807	−	1.25807i	0.288621	−	0.288621i	0.836535	+	0.547914i	$0.184578\pi$
$20$	−4.47206	−	0.0259891i	−0.999983	−	0.00581133i
$21$		0			0
$22$	2.51809	−	0.692674i	0.536858	−	0.147679i
$23$	−7.82148			−1.63089			−0.815446	−	0.578834i	$-0.803508\pi$
$23$	−7.82148			−1.63089			−0.815446	+	0.578834i	$0.803508\pi$
$24$		0			0
$25$	−2.33287	−	4.42241i	−0.466574	−	0.884482i
$26$	−3.02283	+	0.831519i	−0.592826	+	0.163074i
$27$		0			0
$28$	5.20664	−	3.09897i	0.983962	−	0.585651i
$29$	7.12073	−	7.12073i	1.32229	−	1.32229i	0.410365	−	0.911921i	$-0.365401\pi$
$29$	7.12073	−	7.12073i	1.32229	−	1.32229i	0.911921	−	0.410365i	$-0.134599\pi$
$30$		0			0
$31$		−	0.0502896i		−	0.00903227i	−0.999990	−	0.00451614i	$-0.998562\pi$
$31$		−	0.0502896i		−	0.00903227i	0.999990	−	0.00451614i	$-0.00143754\pi$
$32$	4.80238	−	2.98950i	0.848950	−	0.528474i
$33$		0			0
$34$	−3.67067	−	2.08689i	−0.629515	−	0.357898i
$35$	5.80096	+	3.49853i	0.980542	+	0.591359i
$36$		0			0
$37$	6.22957	+	6.22957i	1.02413	+	1.02413i	0.999701	+	0.0244329i	$0.00777799\pi$
$37$	6.22957	+	6.22957i	1.02413	+	1.02413i	0.0244329	+	0.999701i	$0.492222\pi$
$38$	−2.42603	+	0.667350i	−0.393553	+	0.108258i
$39$		0			0
$40$	5.47985	+	3.15773i	0.866440	+	0.499282i
$41$	4.05554			0.633368			0.316684	−	0.948531i	$-0.397430\pi$
$41$	4.05554			0.633368			0.316684	+	0.948531i	$0.397430\pi$
$42$		0			0
$43$	6.18655	−	6.18655i	0.943441	−	0.943441i	−0.0550434	−	0.998484i	$-0.517530\pi$
$43$	6.18655	−	6.18655i	0.943441	−	0.943441i	0.998484	+	0.0550434i	$0.0175297\pi$
$44$	−3.57992	−	0.908456i	−0.539694	−	0.136955i
$45$		0			0
$46$	9.61583	+	5.46689i	1.41778	+	0.806049i
$47$		−	5.87568i		−	0.857057i	−0.903528	−	0.428528i	$-0.859032\pi$
$47$		−	5.87568i		−	0.857057i	0.903528	−	0.428528i	$-0.140968\pi$
$48$		0			0
$49$	−2.17818			−0.311168
$50$	−0.223016	+	7.06755i	−0.0315393	+	0.999503i
$51$		0			0
$52$	4.29751	+	1.09055i	0.595957	+	0.151232i
$53$	4.40639	−	4.40639i	0.605264	−	0.605264i	−0.336440	−	0.941705i	$-0.609223\pi$
$53$	4.40639	−	4.40639i	0.605264	−	0.605264i	0.941705	+	0.336440i	$0.109223\pi$
$54$		0			0
$55$	−0.992408	−	4.00831i	−0.133816	−	0.540481i
$56$	−8.56716	+	0.170696i	−1.14484	+	0.0228102i
$57$		0			0
$58$	−13.7314	+	3.77723i	−1.80302	+	0.495974i
$59$	8.20735	−	8.20735i	1.06851	−	1.06851i	0.0710318	−	0.997474i	$-0.477371\pi$
$59$	8.20735	−	8.20735i	1.06851	−	1.06851i	0.997474	−	0.0710318i	$-0.0226292\pi$
$60$		0			0
$61$	−4.93899	−	4.93899i	−0.632373	−	0.632373i	0.316290	−	0.948663i	$-0.397563\pi$
$61$	−4.93899	−	4.93899i	−0.632373	−	0.632373i	−0.948663	+	0.316290i	$0.897563\pi$
$62$	−0.0351503	+	0.0618267i	−0.00446409	+	0.00785199i
$63$		0			0
$64$	−7.99365	+	0.318664i	−0.999206	+	0.0398330i
$65$	1.19133	+	4.81176i	0.147767	+	0.596826i
$66$		0			0
$67$	1.29973	+	1.29973i	0.158787	+	0.158787i	0.782029	−	0.623242i	$-0.214185\pi$
$67$	1.29973	+	1.29973i	0.158787	+	0.158787i	−0.623242	+	0.782029i	$0.714185\pi$
$68$	3.05413	+	5.13129i	0.370367	+	0.622261i
$69$		0			0
$70$	−4.68646	−	8.35577i	−0.560139	−	0.998705i
$71$		−	13.9687i		−	1.65778i	−0.559414	−	0.828888i	$-0.688974\pi$
$71$		−	13.9687i		−	1.65778i	0.559414	−	0.828888i	$-0.311026\pi$
$72$		0			0
$73$	−3.85841			−0.451593			−0.225796	−	0.974175i	$-0.572498\pi$
$73$	−3.85841			−0.451593			−0.225796	+	0.974175i	$0.572498\pi$
$74$	−3.30451	−	12.0129i	−0.384141	−	1.39647i
$75$		0			0
$76$	3.44904	+	0.875242i	0.395632	+	0.100397i
$77$	3.95602	+	3.95602i	0.450830	+	0.450830i
$78$		0			0
$79$			1.07096i			0.120492i	0.998184	+	0.0602461i	$0.0191885\pi$
$79$			1.07096i			0.120492i	−0.998184	+	0.0602461i	$0.980811\pi$
$80$	−4.52987	−	7.71234i	−0.506455	−	0.862266i
$81$		0			0
$82$	−4.98593	−	2.83465i	−0.550604	−	0.313035i
$83$	−7.16503	+	7.16503i	−0.786464	+	0.786464i	−0.980913	−	0.194448i	$-0.937708\pi$
$83$	−7.16503	+	7.16503i	−0.786464	+	0.786464i	0.194448	+	0.980913i	$0.437708\pi$
$84$		0			0
$85$	−3.44790	+	5.71702i	−0.373977	+	0.620098i
$86$	−11.9300	+	3.28169i	−1.28644	+	0.353874i
$87$		0			0
$88$	3.76623	+	3.61909i	0.401482	+	0.385796i
$89$	−7.60356			−0.805975			−0.402988	−	0.915205i	$-0.632028\pi$
$89$	−7.60356			−0.805975			−0.402988	+	0.915205i	$0.632028\pi$
$90$		0			0
$91$	−4.74899	−	4.74899i	−0.497830	−	0.497830i
$92$	−8.00071	−	13.4421i	−0.834131	−	1.40144i
$93$		0			0
$94$	−4.10686	+	7.22364i	−0.423590	+	0.745062i
$95$	0.956125	+	3.86176i	0.0980963	+	0.396209i
$96$		0			0
$97$			9.70129i			0.985017i	0.870308	+	0.492508i	$0.163920\pi$
$97$			9.70129i			0.985017i	−0.870308	+	0.492508i	$0.836080\pi$
$98$	2.67788	+	1.52245i	0.270507	+	0.153791i
$99$		0			0
$100$	5.21410	−	8.53306i	0.521410	−	0.853306i
$101$	6.49754	+	6.49754i	0.646530	+	0.646530i	0.952153	−	0.305623i	$-0.0988647\pi$
$101$	6.49754	+	6.49754i	0.646530	+	0.646530i	−0.305623	+	0.952153i	$0.598865\pi$
$102$		0			0
$103$		−	13.3352i		−	1.31396i	−0.753908	−	0.656980i	$-0.771833\pi$
$103$		−	13.3352i		−	1.31396i	0.753908	−	0.656980i	$-0.228167\pi$
$104$	−4.52116	−	4.34452i	−0.443336	−	0.426015i
$105$		0			0
$106$	−8.49716	+	2.33739i	−0.825317	+	0.227028i
$107$	2.06506	+	2.06506i	0.199637	+	0.199637i	0.799844	−	0.600208i	$-0.204915\pi$
$107$	2.06506	+	2.06506i	0.199637	+	0.199637i	−0.600208	+	0.799844i	$0.704915\pi$
$108$		0			0
$109$	−9.84623	−	9.84623i	−0.943098	−	0.943098i	0.0553682	−	0.998466i	$-0.482367\pi$
$109$	−9.84623	−	9.84623i	−0.943098	−	0.943098i	−0.998466	+	0.0553682i	$0.982367\pi$
$110$	−1.58156	+	5.62152i	−0.150796	+	0.535991i
$111$		0			0
$112$	10.6519	+	5.77823i	1.00651	+	0.545992i
$113$	2.82213			0.265484			0.132742	−	0.991151i	$-0.457622\pi$
$113$	2.82213			0.265484			0.132742	+	0.991151i	$0.457622\pi$
$114$		0			0
$115$	9.03225	−	14.9765i	0.842262	−	1.39657i
$116$	19.5217	+	4.95391i	1.81255	+	0.459959i
$117$		0			0
$118$	−15.8268	+	4.35363i	−1.45698	+	0.400784i
$119$		−	9.04536i		−	0.829187i
$120$		0			0
$121$			7.58971i			0.689974i
$122$	2.61991	+	9.52420i	0.237196	+	0.862281i
$123$		0			0
$124$	0.0864285	−	0.0514419i	0.00776151	−	0.00461962i
$125$	11.1620	+	0.640034i	0.998360	+	0.0572464i
$126$		0			0
$127$	4.95854			0.439999			0.219999	−	0.975500i	$-0.429394\pi$
$127$	4.95854			0.439999			0.219999	+	0.975500i	$0.429394\pi$
$128$	10.0502	+	5.19546i	0.888324	+	0.459218i
$129$		0			0
$130$	1.89858	−	6.74834i	0.166517	−	0.591868i
$131$	9.28233	+	9.28233i	0.811001	+	0.811001i	0.984784	−	0.173783i	$-0.0555991\pi$
$131$	9.28233	+	9.28233i	0.811001	+	0.811001i	−0.173783	+	0.984784i	$0.555599\pi$
$132$		0			0
$133$	−3.81139	−	3.81139i	−0.330489	−	0.330489i
$134$	−0.689448	−	2.50636i	−0.0595592	−	0.216517i
$135$		0			0
$136$	−0.168226	−	8.44319i	−0.0144252	−	0.723997i
$137$			6.60046i			0.563916i	0.959427	+	0.281958i	$0.0909838\pi$
$137$			6.60046i			0.563916i	−0.959427	+	0.281958i	$0.909016\pi$
$138$		0			0
$139$	−0.376168	−	0.376168i	−0.0319062	−	0.0319062i	0.690974	−	0.722880i	$-0.257182\pi$
$139$	−0.376168	−	0.376168i	−0.0319062	−	0.0319062i	−0.722880	+	0.690974i	$0.757182\pi$
$140$	−0.0787351	+	13.5483i	−0.00665433	+	1.14504i
$141$		0			0
$142$	−9.76352	+	17.1733i	−0.819336	+	1.44115i
$143$			4.09387i			0.342346i
$144$		0			0
$145$	5.41171	+	21.8578i	0.449418	+	1.81519i
$146$	4.74358	+	2.69687i	0.392582	+	0.223194i
$147$		0			0
$148$	−4.33392	+	17.0786i	−0.356246	+	1.40385i
$149$	−8.71533	−	8.71533i	−0.713988	−	0.713988i	0.253379	−	0.967367i	$-0.418458\pi$
$149$	−8.71533	−	8.71533i	−0.713988	−	0.713988i	−0.967367	+	0.253379i	$0.918458\pi$
$150$		0			0
$151$	7.25811			0.590657			0.295328	−	0.955396i	$-0.404571\pi$
$151$	7.25811			0.590657			0.295328	+	0.955396i	$0.404571\pi$
$152$	−3.62854	−	3.48677i	−0.294313	−	0.282814i
$153$		0			0
$154$	−2.09849	−	7.62868i	−0.169101	−	0.614736i
$155$	0.0962941	+	0.0580744i	0.00773453	+	0.00466465i
$156$		0			0
$157$	−16.0087	+	16.0087i	−1.27764	+	1.27764i	−0.335647	+	0.941988i	$0.608955\pi$
$157$	−16.0087	+	16.0087i	−1.27764	+	1.27764i	−0.941988	+	0.335647i	$0.891045\pi$
$158$	0.748555	−	1.31665i	0.0595518	−	0.104747i
$159$		0			0
$160$	0.178479	+	12.6479i	0.0141100	+	0.999900i
$161$			23.6956i			1.86747i
$162$		0			0
$163$	−3.07484	−	3.07484i	−0.240840	−	0.240840i	0.576357	−	0.817198i	$-0.304474\pi$
$163$	−3.07484	−	3.07484i	−0.240840	−	0.240840i	−0.817198	+	0.576357i	$0.804474\pi$
$164$	4.14847	+	6.96991i	0.323941	+	0.544259i
$165$		0			0
$166$	13.8168	−	3.80073i	1.07240	−	0.294994i
$167$	6.32858			0.489720			0.244860	−	0.969558i	$-0.421258\pi$
$167$	6.32858			0.489720			0.244860	+	0.969558i	$0.421258\pi$
$168$		0			0
$169$			8.08553i			0.621964i
$170$	8.23485	−	4.61864i	0.631584	−	0.354234i
$171$		0			0
$172$	16.9606	+	4.30400i	1.29324	+	0.328177i
$173$	3.51897	+	3.51897i	0.267542	+	0.267542i	0.828109	−	0.560567i	$-0.189417\pi$
$173$	3.51897	+	3.51897i	0.267542	+	0.267542i	−0.560567	+	0.828109i	$0.689417\pi$
$174$		0			0
$175$	−13.3979	+	7.06755i	−1.01279	+	0.534257i
$176$	−2.10067	−	7.08179i	−0.158344	−	0.533810i
$177$		0			0
$178$	9.34791	+	5.31457i	0.700656	+	0.398344i
$179$	6.22219	+	6.22219i	0.465068	+	0.465068i	0.900312	−	0.435244i	$-0.143338\pi$
$179$	6.22219	+	6.22219i	0.465068	+	0.465068i	−0.435244	+	0.900312i	$0.643338\pi$
$180$		0			0
$181$	14.9790	−	14.9790i	1.11338	−	1.11338i	0.120689	−	0.992690i	$-0.461490\pi$
$181$	14.9790	−	14.9790i	1.11338	−	1.11338i	0.992690	−	0.120689i	$-0.0385103\pi$
$182$	2.51913	+	9.15782i	0.186730	+	0.678823i
$183$		0			0
$184$	0.440690	+	22.1181i	0.0324881	+	1.63057i
$185$	−19.1222	+	4.73443i	−1.40590	+	0.348082i
$186$		0			0
$187$	−3.89877	+	3.89877i	−0.285107	+	0.285107i
$188$	10.0981	−	6.01032i	0.736476	−	0.438348i
$189$		0			0
$190$	1.52374	−	5.41600i	0.110544	−	0.392918i
$191$	−20.4321			−1.47842			−0.739208	−	0.673477i	$-0.764800\pi$
$191$	−20.4321			−1.47842			−0.739208	+	0.673477i	$0.764800\pi$
$192$		0			0
$193$			0.107996i			0.00777370i	0.999992	+	0.00388685i	$0.00123723\pi$
$193$			0.107996i			0.00777370i	−0.999992	+	0.00388685i	$0.998763\pi$
$194$	6.78080	−	11.9269i	0.486833	−	0.856301i
$195$		0			0
$196$	−2.22809	−	3.74345i	−0.159149	−	0.267389i
$197$	13.3111	−	13.3111i	0.948378	−	0.948378i	−0.0503537	−	0.998731i	$-0.516035\pi$
$197$	13.3111	−	13.3111i	0.948378	−	0.948378i	0.998731	+	0.0503537i	$0.0160349\pi$
$198$		0			0
$199$	−27.0544			−1.91784			−0.958918	−	0.283684i	$-0.908443\pi$
$199$	−27.0544			−1.91784			−0.958918	+	0.283684i	$0.908443\pi$
$200$	−12.3745	+	6.84622i	−0.875012	+	0.484101i
$201$		0			0
$202$	−3.44666	−	12.5297i	−0.242506	−	0.881585i
$203$	−21.5726	−	21.5726i	−1.51410	−	1.51410i
$204$		0			0
$205$	−4.68334	+	7.76552i	−0.327098	+	0.542367i
$206$	−9.32078	+	16.3945i	−0.649409	+	1.14226i
$207$		0			0
$208$	2.52174	+	8.50131i	0.174851	+	0.589460i
$209$			3.28560i			0.227270i
$210$		0			0
$211$	−5.20964	+	5.20964i	−0.358646	+	0.358646i	−0.863314	−	0.504667i	$-0.831615\pi$
$211$	−5.20964	+	5.20964i	−0.358646	+	0.358646i	0.504667	+	0.863314i	$0.331615\pi$
$212$	12.0803	+	3.06554i	0.829676	+	0.210542i
$213$		0			0
$214$	−1.09542	−	3.98220i	−0.0748814	−	0.272217i
$215$	4.70174	+	18.9902i	0.320656	+	1.29512i
$216$		0			0
$217$	−0.152355			−0.0103425
$218$	5.22298	+	18.9872i	0.353745	+	1.28597i
$219$		0			0
$220$	5.87360	−	5.80573i	0.395998	−	0.391422i
$221$	4.68027	−	4.68027i	0.314829	−	0.314829i
$222$		0			0
$223$	8.50474			0.569519			0.284760	−	0.958599i	$-0.408086\pi$
$223$	8.50474			0.569519			0.284760	+	0.958599i	$0.408086\pi$
$224$	−9.05684	−	14.5491i	−0.605135	−	0.972100i
$225$		0			0
$226$	−3.46956	−	1.97255i	−0.230792	−	0.131212i
$227$	−14.4132	+	14.4132i	−0.956639	+	0.956639i	−0.999098	−	0.0424594i	$-0.986481\pi$
$227$	−14.4132	+	14.4132i	−0.956639	+	0.956639i	0.0424594	+	0.999098i	$0.486481\pi$
$228$		0			0
$229$	−15.5816	+	15.5816i	−1.02966	+	1.02966i	−0.0301163	+	0.999546i	$0.509588\pi$
$229$	−15.5816	+	15.5816i	−1.02966	+	1.02966i	−0.999546	+	0.0301163i	$0.990412\pi$
$230$	−21.5723	+	12.0992i	−1.42244	+	0.797796i
$231$		0			0
$232$	−20.5377	−	19.7353i	−1.34836	−	1.29568i
$233$		−	17.5226i		−	1.14794i	−0.818875	−	0.573972i	$-0.805402\pi$
$233$		−	17.5226i		−	1.14794i	0.818875	−	0.573972i	$-0.194598\pi$
$234$		0			0
$235$	11.2507	+	6.78524i	0.733916	+	0.442620i
$236$	22.5007	+	5.70987i	1.46467	+	0.371681i
$237$		0			0
$238$	−6.32233	+	11.1205i	−0.409816	+	0.720834i
$239$	−23.9921			−1.55192			−0.775960	−	0.630782i	$-0.782734\pi$
$239$	−23.9921			−1.55192			−0.775960	+	0.630782i	$0.782734\pi$
$240$		0			0
$241$	28.5345			1.83807			0.919033	−	0.394181i	$-0.128972\pi$
$241$	28.5345			1.83807			0.919033	+	0.394181i	$0.128972\pi$
$242$	5.30489	−	9.33090i	0.341011	−	0.599813i
$243$		0			0
$244$	3.43607	−	13.5404i	0.219972	−	0.866835i
$245$	2.51536	−	4.17076i	0.160700	−	0.266460i
$246$		0			0
$247$		−	3.94419i		−	0.250963i
$248$	−0.142212	+	0.00283350i	−0.00903048	+	0.000179927i
$249$		0			0
$250$	−13.2754	−	8.58864i	−0.839608	−	0.543193i
$251$	0.638332	−	0.638332i	0.0402912	−	0.0402912i	−0.686674	−	0.726965i	$-0.740930\pi$
$251$	0.638332	−	0.638332i	0.0402912	−	0.0402912i	0.726965	+	0.686674i	$0.240930\pi$
$252$		0			0
$253$	10.2134	−	10.2134i	0.642110	−	0.642110i
$254$	−6.09609	−	3.46581i	−0.382503	−	0.217464i
$255$		0			0
$256$	−8.72449	−	13.4121i	−0.545280	−	0.838254i
$257$	−6.32219			−0.394367			−0.197184	−	0.980367i	$-0.563180\pi$
$257$	−6.32219			−0.394367			−0.197184	+	0.980367i	$0.563180\pi$
$258$		0			0
$259$	18.8728	−	18.8728i	1.17270	−	1.17270i
$260$	−7.05095	+	6.96947i	−0.437281	+	0.432228i
$261$		0			0
$262$	−4.92386	−	17.8998i	−0.304197	−	1.10585i
$263$	0.335400			0.0206817			0.0103408	−	0.999947i	$-0.496708\pi$
$263$	0.335400			0.0206817			0.0103408	+	0.999947i	$0.496708\pi$
$264$		0			0
$265$	3.34883	+	13.5258i	0.205717	+	0.830885i
$266$	2.02177	+	7.34977i	0.123963	+	0.450643i
$267$		0			0
$268$	−0.904224	+	3.56325i	−0.0552343	+	0.217660i
$269$	8.03777	−	8.03777i	0.490071	−	0.490071i	−0.418257	−	0.908329i	$-0.637359\pi$
$269$	8.03777	−	8.03777i	0.490071	−	0.490071i	0.908329	+	0.418257i	$0.137359\pi$
$270$		0			0
$271$			28.1406i			1.70942i	0.519105	+	0.854711i	$0.326265\pi$
$271$			28.1406i			1.70942i	−0.519105	+	0.854711i	$0.673735\pi$
$272$	−5.69462	+	10.4978i	−0.345287	+	0.636520i
$273$		0			0
$274$	4.61345	−	8.11470i	0.278709	−	0.490227i
$275$	8.82112	+	2.72854i	0.531934	+	0.164537i
$276$		0			0
$277$	4.06316	+	4.06316i	0.244132	+	0.244132i	0.818557	−	0.574425i	$-0.194774\pi$
$277$	4.06316	+	4.06316i	0.244132	+	0.244132i	−0.574425	+	0.818557i	$0.694774\pi$
$278$	0.199541	+	0.725393i	0.0119676	+	0.0435062i
$279$		0			0
$280$	9.56652	−	16.6015i	0.571709	−	0.992128i
$281$	0.511034			0.0304858			0.0152429	−	0.999884i	$-0.495148\pi$
$281$	0.511034			0.0304858			0.0152429	+	0.999884i	$0.495148\pi$
$282$		0			0
$283$	13.0685	−	13.0685i	0.776839	−	0.776839i	−0.202453	−	0.979292i	$-0.564891\pi$
$283$	13.0685	−	13.0685i	0.776839	−	0.776839i	0.979292	+	0.202453i	$0.0648914\pi$
$284$	24.0068	−	14.2888i	1.42454	−	0.847882i
$285$		0			0
$286$	2.86144	−	5.03305i	0.169201	−	0.297611i
$287$		−	12.2865i		−	0.725246i
$288$		0			0
$289$	−8.08553			−0.475620
$290$	8.62443	−	30.6548i	0.506444	−	1.80011i
$291$		0			0
$292$	−3.94683	−	6.63113i	−0.230970	−	0.388058i
$293$	−19.3164	+	19.3164i	−1.12848	+	1.12848i	−0.138054	+	0.990425i	$0.544085\pi$
$293$	−19.3164	+	19.3164i	−1.12848	+	1.12848i	−0.990425	+	0.138054i	$0.955915\pi$
$294$		0			0
$295$	6.23753	+	25.1932i	0.363163	+	1.46681i
$296$	17.2654	−	17.9674i	1.00353	−	1.04433i
$297$		0			0
$298$	4.62309	+	16.8064i	0.267809	+	0.973569i
$299$	−12.2606	+	12.2606i	−0.709050	+	0.709050i
$300$		0			0
$301$	−18.7425	−	18.7425i	−1.08030	−	1.08030i
$302$	−8.92322	−	5.07312i	−0.513474	−	0.291925i
$303$		0			0
$304$	2.02387	+	6.82288i	0.116077	+	0.391319i
$305$	15.1607	−	3.75360i	0.868098	−	0.214930i
$306$		0			0
$307$	−17.1442	−	17.1442i	−0.978471	−	0.978471i	0.0213024	−	0.999773i	$-0.493219\pi$
$307$	−17.1442	−	17.1442i	−0.978471	−	0.978471i	−0.999773	+	0.0213024i	$0.993219\pi$
$308$	−2.75221	+	10.8456i	−0.156822	+	0.617983i
$309$		0			0
$310$	−0.0777937	−	0.138703i	−0.00441839	−	0.00787780i
$311$		−	21.2420i		−	1.20452i	−0.798299	−	0.602261i	$-0.794267\pi$
$311$		−	21.2420i		−	1.20452i	0.798299	−	0.602261i	$-0.205733\pi$
$312$		0			0
$313$	19.9351			1.12680			0.563400	−	0.826184i	$-0.309493\pi$
$313$	19.9351			1.12680			0.563400	+	0.826184i	$0.309493\pi$
$314$	30.8708	−	8.49191i	1.74214	−	0.479226i
$315$		0			0
$316$	−1.84057	+	1.09550i	−0.103540	+	0.0616266i
$317$	14.9282	+	14.9282i	0.838450	+	0.838450i	0.988655	−	0.150205i	$-0.0479934\pi$
$317$	14.9282	+	14.9282i	0.838450	+	0.838450i	−0.150205	+	0.988655i	$0.547993\pi$
$318$		0			0
$319$			18.5967i			1.04121i
$320$	8.62090	−	15.6742i	0.481923	−	0.876214i
$321$		0			0
$322$	16.5622	−	29.1317i	0.922976	−	1.62344i
$323$	3.75623	−	3.75623i	0.209002	−	0.209002i
$324$		0			0
$325$	−10.5893	−	3.27547i	−0.587388	−	0.181690i
$326$	1.63107	+	5.92944i	0.0903365	+	0.328401i
$327$		0			0
$328$	−0.228504	−	11.4685i	−0.0126170	−	0.633243i
$329$	−17.8007			−0.981383
$330$		0			0
$331$	5.72462	+	5.72462i	0.314653	+	0.314653i	0.846709	−	0.532056i	$-0.178580\pi$
$331$	5.72462	+	5.72462i	0.314653	+	0.314653i	−0.532056	+	0.846709i	$0.678580\pi$
$332$	−19.6432	−	4.98473i	−1.07806	−	0.273573i
$333$		0			0
$334$	−7.78044	−	4.42341i	−0.425727	−	0.242038i
$335$	−3.98964	+	0.987785i	−0.217977	+	0.0539685i
$336$		0			0
$337$		−	28.0570i		−	1.52836i	−0.645003	−	0.764180i	$-0.723144\pi$
$337$		−	28.0570i		−	1.52836i	0.645003	−	0.764180i	$-0.276856\pi$
$338$	5.65145	−	9.94046i	0.307398	−	0.540690i
$339$		0			0
$340$	−13.3523	−	0.0775958i	−0.724129	−	0.00420822i
$341$	0.0656687	+	0.0656687i	0.00355616	+	0.00355616i
$342$		0			0
$343$		−	14.6080i		−	0.788756i
$344$	−17.8433	−	17.1462i	−0.962047	−	0.924460i
$345$		0			0
$346$	−1.86666	−	6.78588i	−0.100352	−	0.364811i
$347$	8.55200	+	8.55200i	0.459095	+	0.459095i	0.898358	−	0.439263i	$-0.144760\pi$
$347$	8.55200	+	8.55200i	0.459095	+	0.459095i	−0.439263	+	0.898358i	$0.644760\pi$
$348$		0			0
$349$	5.51139	+	5.51139i	0.295018	+	0.295018i	0.839059	−	0.544041i	$-0.183106\pi$
$349$	5.51139	+	5.51139i	0.295018	+	0.295018i	−0.544041	+	0.839059i	$0.683106\pi$
$350$	21.4115	+	0.675640i	1.14449	+	0.0361145i
$351$		0			0
$352$	−2.36729	+	10.1747i	−0.126177	+	0.542315i
$353$	−22.2023			−1.18171			−0.590853	−	0.806779i	$-0.701209\pi$
$353$	−22.2023			−1.18171			−0.590853	+	0.806779i	$0.701209\pi$
$354$		0			0
$355$	26.7471	+	16.1310i	1.41959	+	0.856146i
$356$	−7.77779	−	13.0676i	−0.412222	−	0.692582i
$357$		0			0
$358$	−3.30059	−	11.9987i	−0.174442	−	0.634150i
$359$		−	6.73781i		−	0.355608i	−0.984066	−	0.177804i	$-0.943101\pi$
$359$		−	6.73781i		−	0.355608i	0.984066	−	0.177804i	$-0.0568993\pi$
$360$		0			0
$361$			15.8345i			0.833396i
$362$	−28.8851	+	7.94568i	−1.51816	+	0.417616i
$363$		0			0
$364$	3.30388	−	13.0195i	0.173171	−	0.682408i
$365$	4.45569	−	7.38806i	0.233222	−	0.386709i
$366$		0			0
$367$	7.64267			0.398944			0.199472	−	0.979904i	$-0.436077\pi$
$367$	7.64267			0.398944			0.199472	+	0.979904i	$0.436077\pi$
$368$	14.9178	−	27.5003i	0.777646	−	1.43355i
$369$		0			0
$370$	26.8183	+	7.54508i	1.39422	+	0.392250i
$371$	−13.3494	−	13.3494i	−0.693065	−	0.693065i
$372$		0			0
$373$	−5.20096	−	5.20096i	−0.269296	−	0.269296i	0.559521	−	0.828816i	$-0.310985\pi$
$373$	−5.20096	−	5.20096i	−0.269296	−	0.269296i	−0.828816	+	0.559521i	$0.810985\pi$
$374$	7.51829	−	2.06813i	0.388761	−	0.106940i
$375$		0			0
$376$	−16.6156	+	0.331057i	−0.856886	+	0.0170730i
$377$		−	22.3243i		−	1.14976i
$378$		0			0
$379$	7.64201	+	7.64201i	0.392544	+	0.392544i	0.875593	−	0.483049i	$-0.160471\pi$
$379$	7.64201	+	7.64201i	0.392544	+	0.392544i	−0.483049	+	0.875593i	$0.660471\pi$
$380$	−5.65886	+	5.59347i	−0.290293	+	0.286939i
$381$		0			0
$382$	25.1195	+	14.2812i	1.28523	+	0.730690i
$383$		−	28.1288i		−	1.43732i	−0.695363	−	0.718658i	$-0.744757\pi$
$383$		−	28.1288i		−	1.43732i	0.695363	−	0.718658i	$-0.255243\pi$
$384$		0			0
$385$	−12.1434	+	3.00655i	−0.618884	+	0.153228i
$386$	0.0754844	−	0.132771i	0.00384206	−	0.00675788i
$387$		0			0
$388$	−16.6728	+	9.92359i	−0.846433	+	0.503794i
$389$	−8.26812	−	8.26812i	−0.419210	−	0.419210i	0.465721	−	0.884931i	$-0.345795\pi$
$389$	−8.26812	−	8.26812i	−0.419210	−	0.419210i	−0.884931	+	0.465721i	$0.845795\pi$
$390$		0			0
$391$	−23.3527			−1.18100
$392$	0.122726	+	6.15959i	0.00619861	+	0.311106i
$393$		0			0
$394$	−25.6688	+	7.06095i	−1.29317	+	0.355726i
$395$	−2.05066	−	1.23674i	−0.103180	−	0.0622273i
$396$		0			0
$397$	6.70437	−	6.70437i	0.336482	−	0.336482i	−0.518559	−	0.855042i	$-0.673531\pi$
$397$	6.70437	−	6.70437i	0.336482	−	0.336482i	0.855042	+	0.518559i	$0.173531\pi$
$398$	33.2610	+	18.9099i	1.66723	+	0.947868i
$399$		0			0
$400$	19.9986	+	0.232449i	0.999932	+	0.0116225i
$401$			33.5732i			1.67657i	0.545235	+	0.838283i	$0.316440\pi$
$401$			33.5732i			1.67657i	−0.545235	+	0.838283i	$0.683560\pi$
$402$		0			0
$403$	−0.0788317	−	0.0788317i	−0.00392689	−	0.00392689i
$404$	−4.52036	+	17.8132i	−0.224896	+	0.886241i
$405$		0			0
$406$	11.4433	+	41.6000i	0.567922	+	2.06457i
$407$	−16.2693			−0.806438
$408$		0			0
$409$		−	3.99913i		−	0.197744i	−0.995100	−	0.0988720i	$-0.968477\pi$
$409$		−	3.99913i		−	0.197744i	0.995100	−	0.0988720i	$-0.0315234\pi$
$410$	11.1855	−	6.27357i	0.552414	−	0.309830i
$411$		0			0
$412$	22.9182	−	13.6408i	1.12910	−	0.672035i
$413$	−24.8646	−	24.8646i	−1.22351	−	1.22351i
$414$		0			0
$415$	−5.44538	−	21.9937i	−0.267303	−	1.07963i
$416$	2.84180	−	12.2142i	0.139331	−	0.598851i
$417$		0			0
$418$	2.29650	−	4.03937i	0.112325	−	0.197572i
$419$	18.7540	+	18.7540i	0.916195	+	0.916195i	0.996750	−	0.0805555i	$-0.0256694\pi$
$419$	18.7540	+	18.7540i	0.916195	+	0.916195i	−0.0805555	+	0.996750i	$0.525669\pi$
$420$		0			0
$421$	1.12082	−	1.12082i	0.0546255	−	0.0546255i	−0.679266	−	0.733892i	$-0.737702\pi$
$421$	1.12082	−	1.12082i	0.0546255	−	0.0546255i	0.733892	+	0.679266i	$0.237702\pi$
$422$	10.0461	−	2.76348i	0.489038	−	0.134524i
$423$		0			0
$424$	−12.7090	−	12.2124i	−0.617201	−	0.593087i
$425$	−6.96528	−	13.2040i	−0.337866	−	0.640490i
$426$		0			0
$427$	−14.9629	+	14.9629i	−0.724106	+	0.724106i
$428$	−1.43667	+	5.66142i	−0.0694438	+	0.273655i
$429$		0			0
$430$	7.49298	−	26.6331i	0.361344	−	1.28436i
$431$	−37.3679			−1.79995			−0.899975	−	0.435941i	$-0.856416\pi$
$431$	−37.3679			−1.79995			−0.899975	+	0.435941i	$0.856416\pi$
$432$		0			0
$433$		−	4.89665i		−	0.235318i	−0.993054	−	0.117659i	$-0.962461\pi$
$433$		−	4.89665i		−	0.235318i	0.993054	−	0.117659i	$-0.0375389\pi$
$434$	0.187307	+	0.106490i	0.00899102	+	0.00511166i
$435$		0			0
$436$	6.85005	−	26.9938i	0.328058	−	1.29277i
$437$	−9.83997	+	9.83997i	−0.470710	+	0.470710i
$438$		0			0
$439$	30.8742			1.47354			0.736772	−	0.676141i	$-0.236349\pi$
$439$	30.8742			1.47354			0.736772	+	0.676141i	$0.236349\pi$
$440$	−11.2791	+	3.03224i	−0.537708	+	0.144556i
$441$		0			0
$442$	−9.02530	+	2.48267i	−0.429290	+	0.118089i
$443$	21.6532	+	21.6532i	1.02878	+	1.02878i	0.999574	+	0.0292029i	$0.00929690\pi$
$443$	21.6532	+	21.6532i	1.02878	+	1.02878i	0.0292029	+	0.999574i	$0.490703\pi$
$444$		0			0
$445$	8.78059	−	14.5592i	0.416240	−	0.690174i
$446$	−10.4558	−	5.94446i	−0.495098	−	0.281478i
$447$		0			0
$448$	0.965410	+	24.2172i	0.0456113	+	1.14415i
$449$		−	0.573598i		−	0.0270698i	−0.999908	−	0.0135349i	$-0.995692\pi$
$449$		−	0.573598i		−	0.0270698i	0.999908	−	0.0135349i	$-0.00430842\pi$
$450$		0			0
$451$	−5.29577	+	5.29577i	−0.249368	+	0.249368i
$452$	2.88680	+	4.85016i	0.135784	+	0.228132i
$453$		0			0
$454$	27.7940	−	7.64557i	1.30444	−	0.358824i
$455$	14.5775	−	3.60920i	0.683403	−	0.169202i
$456$		0			0
$457$	−30.6962			−1.43591			−0.717953	−	0.696092i	$-0.754921\pi$
$457$	−30.6962			−1.43591			−0.717953	+	0.696092i	$0.754921\pi$
$458$	30.0472	−	8.26535i	1.40401	−	0.386215i
$459$		0			0
$460$	34.9781	+	0.203273i	1.63086	+	0.00947765i
$461$	−3.93792	+	3.93792i	−0.183407	+	0.183407i	−0.792839	−	0.609431i	$-0.791398\pi$
$461$	−3.93792	+	3.93792i	−0.183407	+	0.183407i	0.609431	+	0.792839i	$0.291398\pi$
$462$		0			0
$463$	−34.4600			−1.60149			−0.800746	−	0.599004i	$-0.795563\pi$
$463$	−34.4600			−1.60149			−0.800746	+	0.599004i	$0.795563\pi$
$464$	11.4552	+	38.6178i	0.531793	+	1.79279i
$465$		0			0
$466$	−12.2476	+	21.5425i	−0.567358	+	0.997938i
$467$	−1.24171	+	1.24171i	−0.0574594	+	0.0574594i	−0.735253	−	0.677793i	$-0.762936\pi$
$467$	−1.24171	+	1.24171i	−0.0574594	+	0.0574594i	0.677793	+	0.735253i	$0.262936\pi$
$468$		0			0
$469$	3.93759	−	3.93759i	0.181821	−	0.181821i
$470$	−9.08919	−	16.2057i	−0.419253	−	0.747511i
$471$		0			0
$472$	−23.6717	−	22.7469i	−1.08958	−	1.04701i
$473$			16.1569i			0.742897i
$474$		0			0
$475$	−8.49862	−	2.62879i	−0.389943	−	0.120617i
$476$	15.5455	−	9.25263i	0.712527	−	0.424094i
$477$		0			0
$478$	29.4962	+	16.7695i	1.34913	+	0.767018i
$479$	29.6130			1.35305			0.676527	−	0.736418i	$-0.263484\pi$
$479$	29.6130			1.35305			0.676527	+	0.736418i	$0.263484\pi$
$480$		0			0
$481$	19.5304			0.890509
$482$	−35.0806	−	19.9444i	−1.59788	−	0.908442i
$483$		0			0
$484$	−13.0438	+	7.76363i	−0.592901	+	0.352892i
$485$	−18.5760	−	11.2031i	−0.843491	−	0.508705i
$486$		0			0
$487$			20.4343i			0.925966i	0.886367	+	0.462983i	$0.153221\pi$
$487$			20.4343i			0.925966i	−0.886367	+	0.462983i	$0.846779\pi$
$488$	−13.6885	+	14.2451i	−0.619650	+	0.644844i
$489$		0			0
$490$	−6.00760	+	3.36945i	−0.271396	+	0.152216i
$491$	1.49438	−	1.49438i	0.0674405	−	0.0674405i	−0.672582	−	0.740023i	$-0.734815\pi$
$491$	1.49438	−	1.49438i	0.0674405	−	0.0674405i	0.740023	+	0.672582i	$0.234815\pi$
$492$		0			0
$493$	21.2604	−	21.2604i	0.957522	−	0.957522i
$494$	−2.75683	+	4.84904i	−0.124035	+	0.218169i
$495$		0			0
$496$	0.176818	+	0.0959168i	0.00793936	+	0.00430679i
$497$	−42.3188			−1.89826
$498$		0			0
$499$	−7.82960	+	7.82960i	−0.350501	+	0.350501i	−0.860296	−	0.509795i	$-0.829721\pi$
$499$	−7.82960	+	7.82960i	−0.350501	+	0.350501i	0.509795	+	0.860296i	$0.329721\pi$
$500$	10.3178	+	19.8379i	0.461426	+	0.887179i
$501$		0			0
$502$	−1.23094	+	0.338606i	−0.0549396	+	0.0151127i
$503$	−6.45561			−0.287841			−0.143921	−	0.989589i	$-0.545971\pi$
$503$	−6.45561			−0.287841			−0.143921	+	0.989589i	$0.545971\pi$
$504$		0			0
$505$	−19.9448	+	4.93809i	−0.887533	+	0.219742i
$506$	−19.6952	+	5.41774i	−0.875558	+	0.240848i
$507$		0			0
$508$	5.07216	+	8.52182i	0.225041	+	0.378095i
$509$	3.08846	−	3.08846i	0.136894	−	0.136894i	−0.635339	−	0.772233i	$-0.719140\pi$
$509$	3.08846	−	3.08846i	0.136894	−	0.136894i	0.772233	+	0.635339i	$0.219140\pi$
$510$		0			0
$511$			11.6892i			0.517102i
$512$	1.35153	+	22.5870i	0.0597298	+	0.998215i
$513$		0			0
$514$	7.77258	+	4.41894i	0.342834	+	0.194911i
$515$	25.5342	+	15.3995i	1.12517	+	0.678585i
$516$		0			0
$517$	7.67253	+	7.67253i	0.337438	+	0.337438i
$518$	−36.3937	+	10.0112i	−1.59905	+	0.439865i
$519$		0			0
$520$	13.5399	−	3.64004i	0.593764	−	0.159626i
$521$	6.66855			0.292155			0.146077	−	0.989273i	$-0.453335\pi$
$521$	6.66855			0.292155			0.146077	+	0.989273i	$0.453335\pi$
$522$		0			0
$523$	13.2266	−	13.2266i	0.578361	−	0.578361i	−0.356091	−	0.934451i	$-0.615891\pi$
$523$	13.2266	−	13.2266i	0.578361	−	0.578361i	0.934451	+	0.356091i	$0.115891\pi$
$524$	−6.45774	+	25.4478i	−0.282108	+	1.11169i
$525$		0			0
$526$	−0.412346	−	0.234431i	−0.0179791	−	0.0102217i
$527$		−	0.150150i		−	0.00654064i
$528$		0			0
$529$	38.1756			1.65981
$530$	5.33690	−	18.9695i	0.231820	−	0.823984i
$531$		0			0
$532$	2.65159	−	10.4490i	0.114961	−	0.453023i
$533$	6.35728	−	6.35728i	0.275364	−	0.275364i
$534$		0			0
$535$	−6.33889	+	1.56943i	−0.274054	+	0.0678524i
$536$	3.60223	−	3.74869i	0.155593	−	0.161919i
$537$		0			0
$538$	−15.4998	+	4.26368i	−0.668244	+	0.183820i
$539$	2.84429	−	2.84429i	0.122512	−	0.122512i
$540$		0			0
$541$	21.3672	+	21.3672i	0.918646	+	0.918646i	0.996931	−	0.0782848i	$-0.0249444\pi$
$541$	21.3672	+	21.3672i	0.918646	+	0.918646i	−0.0782848	+	0.996931i	$0.524944\pi$
$542$	19.6691	−	34.5965i	0.844861	−	1.48605i
$543$		0			0
$544$	14.3385	−	8.92578i	0.614759	−	0.382690i
$545$	30.2239	−	7.48307i	1.29465	−	0.320539i
$546$		0			0
$547$	14.3033	+	14.3033i	0.611566	+	0.611566i	0.943354	−	0.331788i	$-0.107652\pi$
$547$	14.3033	+	14.3033i	0.611566	+	0.611566i	−0.331788	+	0.943354i	$0.607652\pi$
$548$	−11.3437	+	6.75171i	−0.484578	+	0.288419i
$549$		0			0
$550$	−8.93767	−	9.52010i	−0.381104	−	0.405939i
$551$		−	17.9168i		−	0.763279i
$552$		0			0
$553$	3.24452			0.137971
$554$	−2.15533	−	7.83529i	−0.0915711	−	0.332890i
$555$		0			0
$556$	0.261701	−	1.03128i	0.0110986	−	0.0437359i
$557$	−5.11093	−	5.11093i	−0.216557	−	0.216557i	0.590489	−	0.807046i	$-0.298935\pi$
$557$	−5.11093	−	5.11093i	−0.216557	−	0.216557i	−0.807046	+	0.590489i	$0.798935\pi$
$558$		0			0
$559$		−	19.3955i		−	0.820344i
$560$	−23.3649	+	13.7235i	−0.987349	+	0.579923i
$561$		0			0
$562$	−0.628273	−	0.357192i	−0.0265021	−	0.0150672i
$563$	14.2208	−	14.2208i	0.599336	−	0.599336i	−0.340800	−	0.940136i	$-0.610698\pi$
$563$	14.2208	−	14.2208i	0.599336	−	0.599336i	0.940136	+	0.340800i	$0.110698\pi$
$564$		0			0
$565$	−3.25900	+	5.40379i	−0.137107	+	0.227339i
$566$	−25.2008	+	6.93223i	−1.05927	+	0.291383i
$567$		0			0
$568$	−39.5015	+	0.787045i	−1.65745	+	0.0330237i
$569$	−9.55464			−0.400551			−0.200276	−	0.979740i	$-0.564184\pi$
$569$	−9.55464			−0.400551			−0.200276	+	0.979740i	$0.564184\pi$
$570$		0			0
$571$	−23.2036	−	23.2036i	−0.971041	−	0.971041i	0.0285510	−	0.999592i	$-0.490911\pi$
$571$	−23.2036	−	23.2036i	−0.971041	−	0.971041i	−0.999592	+	0.0285510i	$0.990911\pi$
$572$	−7.03579	+	4.18768i	−0.294181	+	0.175096i
$573$		0			0
$574$	−8.58772	+	15.1051i	−0.358444	+	0.630476i
$575$	18.2465	+	34.5898i	0.760932	+	1.44249i
$576$		0			0
$577$		−	40.8559i		−	1.70085i	−0.526095	−	0.850426i	$-0.676344\pi$
$577$		−	40.8559i		−	1.70085i	0.526095	−	0.850426i	$-0.323656\pi$
$578$	9.94046	+	5.65145i	0.413469	+	0.235069i
$579$		0			0
$580$	−32.0294	+	31.6593i	−1.32995	+	1.31458i
$581$	21.7068	+	21.7068i	0.900551	+	0.900551i
$582$		0			0
$583$			11.5078i			0.476606i
$584$	0.217397	+	10.9111i	0.00899594	+	0.451503i
$585$		0			0
$586$	37.2493	−	10.2465i	1.53875	−	0.423279i
$587$	20.0208	+	20.0208i	0.826345	+	0.826345i	0.987009	−	0.160664i	$-0.0513635\pi$
$587$	20.0208	+	20.0208i	0.826345	+	0.826345i	−0.160664	+	0.987009i	$0.551364\pi$
$588$		0			0
$589$	−0.0632678	−	0.0632678i	−0.00260690	−	0.00260690i
$590$	9.94051	−	35.3327i	0.409244	−	1.45462i
$591$		0			0
$592$	−33.7847	+	10.0216i	−1.38854	+	0.411883i
$593$	0.595901			0.0244707			0.0122354	−	0.999925i	$-0.496105\pi$
$593$	0.595901			0.0244707			0.0122354	+	0.999925i	$0.496105\pi$
$594$		0			0
$595$	17.3200	+	10.4456i	0.710051	+	0.428227i
$596$	6.06328	−	23.8934i	0.248362	−	0.978710i
$597$		0			0
$598$	23.6430	−	6.50371i	0.966835	−	0.265956i
$599$			26.0628i			1.06490i	0.846462	+	0.532449i	$0.178728\pi$
$599$			26.0628i			1.06490i	−0.846462	+	0.532449i	$0.821272\pi$
$600$		0			0
$601$		−	38.7272i		−	1.57971i	−0.613291	−	0.789857i	$-0.710155\pi$
$601$		−	38.7272i		−	1.57971i	0.613291	−	0.789857i	$-0.289845\pi$
$602$	9.94204	+	36.1425i	0.405207	+	1.47306i
$603$		0			0
$604$	7.42443	+	12.4739i	0.302096	+	0.507556i
$605$	−14.5327	−	8.76461i	−0.590840	−	0.356332i
$606$		0			0
$607$	40.5499			1.64587			0.822934	−	0.568136i	$-0.192335\pi$
$607$	40.5499			1.64587			0.822934	+	0.568136i	$0.192335\pi$
$608$	2.28074	−	9.80273i	0.0924961	−	0.397553i
$609$		0			0
$610$	−21.2624	−	5.98196i	−0.860888	−	0.242203i
$611$	−9.21047	−	9.21047i	−0.372616	−	0.372616i
$612$		0			0
$613$	−5.91500	−	5.91500i	−0.238905	−	0.238905i	0.577492	−	0.816396i	$-0.304032\pi$
$613$	−5.91500	−	5.91500i	−0.238905	−	0.238905i	−0.816396	+	0.577492i	$0.804032\pi$
$614$	9.09423	+	33.0604i	0.367013	+	1.33421i
$615$		0			0
$616$	10.9642	−	11.4100i	0.441760	−	0.459722i
$617$			37.5004i			1.50971i	0.655893	+	0.754854i	$0.272292\pi$
$617$			37.5004i			1.50971i	−0.655893	+	0.754854i	$0.727708\pi$
$618$		0			0
$619$	−19.2329	−	19.2329i	−0.773034	−	0.773034i	0.205602	−	0.978636i	$-0.434085\pi$
$619$	−19.2329	−	19.2329i	−0.773034	−	0.773034i	−0.978636	+	0.205602i	$0.934085\pi$
$620$	−0.00130698	+	0.224898i	−5.24895e−5	+	0.00903212i
$621$		0			0
$622$	−14.8473	+	26.1152i	−0.595321	+	1.04712i
$623$			23.0354i			0.922892i
$624$		0			0
$625$	−14.1154	+	20.6338i	−0.564617	+	0.825353i
$626$	−24.5085	−	13.9338i	−0.979557	−	0.556907i
$627$		0			0
$628$	−43.8884	−	11.1373i	−1.75134	−	0.444427i
$629$	18.5997	+	18.5997i	0.741618	+	0.741618i
$630$		0			0
$631$	−46.9373			−1.86855			−0.934273	−	0.356559i	$-0.883950\pi$
$631$	−46.9373			−1.86855			−0.934273	+	0.356559i	$0.883950\pi$
$632$	3.02852	−	0.0603416i	0.120468	−	0.00240026i
$633$		0			0
$634$	−7.91873	−	28.7871i	−0.314493	−	1.14328i
$635$	−5.72612	+	9.49457i	−0.227234	+	0.376781i
$636$		0			0
$637$	−3.41441	+	3.41441i	−0.135284	+	0.135284i
$638$	12.9983	−	22.8630i	0.514607	−	0.905154i
$639$		0			0
$640$	−21.5542	+	13.2444i	−0.852006	+	0.523531i
$641$		−	8.84689i		−	0.349431i	−0.984619	−	0.174716i	$-0.944099\pi$
$641$		−	8.84689i		−	0.349431i	0.984619	−	0.174716i	$-0.0559006\pi$
$642$		0			0
$643$	18.7263	+	18.7263i	0.738491	+	0.738491i	0.972286	−	0.233795i	$-0.0751143\pi$
$643$	18.7263	+	18.7263i	0.738491	+	0.738491i	−0.233795	+	0.972286i	$0.575114\pi$
$644$	−40.7236	+	24.2385i	−1.60474	+	0.955133i
$645$		0			0
$646$	−7.24341	+	1.99251i	−0.284988	+	0.0783944i
$647$	32.7789			1.28867			0.644335	−	0.764744i	$-0.277134\pi$
$647$	32.7789			1.28867			0.644335	+	0.764744i	$0.277134\pi$
$648$		0			0
$649$			21.4345i			0.841378i
$650$	10.7292	+	11.4284i	0.420834	+	0.448258i
$651$		0			0
$652$	2.13918	−	8.42979i	0.0837766	−	0.330136i
$653$	−1.54050	−	1.54050i	−0.0602843	−	0.0602843i	0.676322	−	0.736606i	$-0.263573\pi$
$653$	−1.54050	−	1.54050i	−0.0602843	−	0.0602843i	−0.736606	+	0.676322i	$0.763573\pi$
$654$		0			0
$655$	−28.4930	+	7.05451i	−1.11331	+	0.275643i
$656$	−7.73509	+	14.2593i	−0.302004	+	0.556731i
$657$		0			0
$658$	21.8844	+	12.4419i	0.853143	+	0.485037i
$659$	6.00170	+	6.00170i	0.233793	+	0.233793i	0.814274	−	0.580481i	$-0.197135\pi$
$659$	6.00170	+	6.00170i	0.233793	+	0.233793i	−0.580481	+	0.814274i	$0.697135\pi$
$660$		0			0
$661$	5.39733	−	5.39733i	0.209932	−	0.209932i	−0.594307	−	0.804239i	$-0.702573\pi$
$661$	5.39733	−	5.39733i	0.209932	−	0.209932i	0.804239	+	0.594307i	$0.202573\pi$
$662$	−3.03665	−	11.0392i	−0.118023	−	0.429050i
$663$		0			0
$664$	20.6655	+	19.8580i	0.801975	+	0.770642i
$665$	11.6994	−	2.89663i	0.453684	−	0.112326i
$666$		0			0
$667$	−55.6947	+	55.6947i	−2.15651	+	2.15651i
$668$	6.47360	+	10.8764i	0.250471	+	0.420821i
$669$		0			0
$670$	5.59534	+	1.57420i	0.216167	+	0.0608165i
$671$	12.8988			0.497952
$672$		0			0
$673$			0.683677i			0.0263538i	0.999913	+	0.0131769i	$0.00419446\pi$
$673$			0.683677i			0.0263538i	−0.999913	+	0.0131769i	$0.995806\pi$
$674$	−19.6106	+	34.4936i	−0.755374	+	1.32864i
$675$		0			0
$676$	−13.8959	+	8.27081i	−0.534459	+	0.318108i
$677$	20.9613	−	20.9613i	0.805610	−	0.805610i	−0.178356	−	0.983966i	$-0.557078\pi$
$677$	20.9613	−	20.9613i	0.805610	−	0.805610i	0.983966	+	0.178356i	$0.0570779\pi$
$678$		0			0
$679$	29.3905			1.12791
$680$	16.3612	+	9.42808i	0.627425	+	0.361550i
$681$		0			0
$682$	−0.0348343	−	0.126634i	−0.00133387	−	0.00484905i
$683$	−9.01650	−	9.01650i	−0.345007	−	0.345007i	0.513239	−	0.858246i	$-0.328445\pi$
$683$	−9.01650	−	9.01650i	−0.345007	−	0.345007i	−0.858246	+	0.513239i	$0.828445\pi$
$684$		0			0
$685$	−12.6385	−	7.62222i	−0.482893	−	0.291230i
$686$	−10.2104	+	17.9592i	−0.389833	+	0.685686i
$687$		0			0
$688$	9.95236	+	33.5515i	0.379430	+	1.27914i
$689$		−	13.8145i		−	0.526292i
$690$		0			0
$691$	−11.0043	+	11.0043i	−0.418623	+	0.418623i	−0.884729	−	0.466106i	$-0.845657\pi$
$691$	−11.0043	+	11.0043i	−0.418623	+	0.418623i	0.466106	+	0.884729i	$0.345657\pi$
$692$	−2.44815	+	9.64737i	−0.0930649	+	0.366738i
$693$		0			0
$694$	−4.53645	−	16.4914i	−0.172201	−	0.626006i
$695$	1.15468	−	0.285886i	0.0437997	−	0.0108443i
$696$		0			0
$697$	12.1087			0.458648
$698$	−2.92355	−	10.6280i	−0.110658	−	0.402276i
$699$		0			0
$700$	−25.8513	−	15.7964i	−0.977089	−	0.597047i
$701$	24.8888	−	24.8888i	0.940038	−	0.940038i	−0.0582634	−	0.998301i	$-0.518556\pi$
$701$	24.8888	−	24.8888i	0.940038	−	0.940038i	0.998301	+	0.0582634i	$0.0185563\pi$
$702$		0			0
$703$	15.6745			0.591173
$704$	10.0221	−	10.8543i	0.377722	−	0.409087i
$705$		0			0
$706$	27.2957	+	15.5184i	1.02729	+	0.584044i
$707$	19.6846	−	19.6846i	0.740317	−	0.740317i
$708$		0			0
$709$	12.7063	−	12.7063i	0.477196	−	0.477196i	−0.427038	−	0.904234i	$-0.640443\pi$
$709$	12.7063	−	12.7063i	0.477196	−	0.477196i	0.904234	+	0.427038i	$0.140443\pi$
$710$	−21.6084	−	38.5268i	−0.810947	−	1.44589i
$711$		0			0
$712$	0.428412	+	21.5018i	0.0160554	+	0.805815i
$713$			0.393339i			0.0147307i
$714$		0			0
$715$	−7.83891	−	4.72760i	−0.293159	−	0.176802i
$716$	−4.32879	+	17.0583i	−0.161774	+	0.637499i
$717$		0			0
$718$	−4.70945	+	8.28355i	−0.175755	+	0.309139i
$719$	1.74421			0.0650482			0.0325241	−	0.999471i	$-0.489645\pi$
$719$	1.74421			0.0650482			0.0325241	+	0.999471i	$0.489645\pi$
$720$		0			0
$721$	−40.3998			−1.50457
$722$	11.0677	−	19.4672i	0.411896	−	0.724493i
$723$		0			0
$724$	41.0654	+	10.4209i	1.52618	+	0.387290i
$725$	−48.1025	−	14.8790i	−1.78648	−	0.552594i
$726$		0			0
$727$		−	2.82244i		−	0.104679i	−0.998629	−	0.0523393i	$-0.983332\pi$
$727$		−	2.82244i		−	0.104679i	0.998629	−	0.0523393i	$-0.0166677\pi$
$728$	−13.1619	+	13.6971i	−0.487814	+	0.507648i
$729$		0			0
$730$	−10.6418	+	5.96864i	−0.393872	+	0.220909i
$731$	18.4713	−	18.4713i	0.683184	−	0.683184i
$732$		0			0
$733$	7.06892	−	7.06892i	0.261097	−	0.261097i	−0.564403	−	0.825500i	$-0.690894\pi$
$733$	7.06892	−	7.06892i	0.261097	−	0.261097i	0.825500	+	0.564403i	$0.190894\pi$
$734$	−9.39600	−	5.34190i	−0.346813	−	0.197173i
$735$		0			0
$736$	−37.5618	+	23.3823i	−1.38454	+	0.861883i
$737$	−3.39440			−0.125034
$738$		0			0
$739$	0.328385	−	0.328385i	0.0120798	−	0.0120798i	−0.701041	−	0.713121i	$-0.747281\pi$
$739$	0.328385	−	0.328385i	0.0120798	−	0.0120798i	0.713121	+	0.701041i	$0.247281\pi$
$740$	−27.6971	−	28.0209i	−1.01817	−	1.03007i
$741$		0			0
$742$	7.08125	+	25.7426i	0.259961	+	0.945039i
$743$	35.2559			1.29341			0.646707	−	0.762739i	$-0.276146\pi$
$743$	35.2559			1.29341			0.646707	+	0.762739i	$0.276146\pi$
$744$		0			0
$745$	26.7525	−	6.62359i	0.980137	−	0.242670i
$746$	2.75888	+	10.0294i	0.101010	+	0.367202i
$747$		0			0
$748$	−10.6886	−	2.71239i	−0.390814	−	0.0991747i
$749$	6.25619	−	6.25619i	0.228596	−	0.228596i
$750$		0			0
$751$		−	36.1388i		−	1.31872i	−0.751826	−	0.659362i	$-0.770827\pi$
$751$		−	36.1388i		−	1.31872i	0.751826	−	0.659362i	$-0.229173\pi$
$752$	20.6589	+	11.2066i	0.753352	+	0.408664i
$753$		0			0
$754$	−15.6037	+	27.4458i	−0.568255	+	0.999517i
$755$	−8.38167	+	13.8978i	−0.305040	+	0.505792i
$756$		0			0
$757$	15.0827	+	15.0827i	0.548188	+	0.548188i	0.925917	−	0.377728i	$-0.123295\pi$
$757$	15.0827	+	15.0827i	0.548188	+	0.548188i	−0.377728	+	0.925917i	$0.623295\pi$
$758$	−4.05374	−	14.7366i	−0.147239	−	0.535259i
$759$		0			0
$760$	10.8667	−	2.92138i	0.394176	−	0.105970i
$761$	27.3466			0.991312			0.495656	−	0.868519i	$-0.334928\pi$
$761$	27.3466			0.991312			0.495656	+	0.868519i	$0.334928\pi$
$762$		0			0
$763$	−29.8296	+	29.8296i	−1.07991	+	1.07991i
$764$	−20.9003	−	35.1150i	−0.756147	−	1.27042i
$765$		0			0
$766$	−19.6609	+	34.5820i	−0.710377	+	1.24950i
$767$		−	25.7310i		−	0.929091i
$768$		0			0
$769$	−15.0021			−0.540989			−0.270494	−	0.962722i	$-0.587187\pi$
$769$	−15.0021			−0.540989			−0.270494	+	0.962722i	$0.587187\pi$
$770$	17.0307	+	4.79142i	0.613743	+	0.172671i
$771$		0			0
$772$	−0.185603	+	0.110470i	−0.00668000	+	0.00397591i
$773$	−13.7968	+	13.7968i	−0.496236	+	0.496236i	−0.910264	−	0.414028i	$-0.864121\pi$
$773$	−13.7968	+	13.7968i	−0.496236	+	0.496236i	0.414028	+	0.910264i	$0.364121\pi$
$774$		0			0
$775$	−0.222401	+	0.117319i	−0.00798888	+	0.00421423i
$776$	27.4339	−	0.546606i	0.984821	−	0.0196220i
$777$		0			0
$778$	4.38587	+	15.9440i	0.157241	+	0.571620i
$779$	5.10215	−	5.10215i	0.182803	−	0.182803i
$780$		0			0
$781$	18.2404	+	18.2404i	0.652695	+	0.652695i
$782$	28.7101	+	16.3225i	1.02667	+	0.583693i
$783$		0			0
$784$	4.15441	−	7.65846i	0.148372	−	0.273516i
$785$	−12.1665	−	49.1403i	−0.434242	−	1.75389i
$786$		0			0
$787$	−29.8134	−	29.8134i	−1.06273	−	1.06273i	−0.997896	−	0.0648379i	$-0.979347\pi$
$787$	−29.8134	−	29.8134i	−1.06273	−	1.06273i	−0.0648379	−	0.997896i	$-0.520653\pi$
$788$	36.4929	+	9.26058i	1.30000	+	0.329894i
$789$		0			0
$790$	1.65668	+	2.95380i	0.0589421	+	0.105091i
$791$		−	8.54978i		−	0.303995i
$792$		0			0
$793$	−15.4843			−0.549863
$794$	−12.9285	+	3.55637i	−0.458816	+	0.126211i
$795$		0			0
$796$	−27.6744	−	46.4962i	−0.980891	−	1.64801i
$797$	24.9525	+	24.9525i	0.883864	+	0.883864i	0.993925	−	0.110061i	$-0.0351047\pi$
$797$	24.9525	+	24.9525i	0.883864	+	0.883864i	−0.110061	+	0.993925i	$0.535105\pi$
$798$		0			0
$799$		−	17.5431i		−	0.620630i
$800$	−24.4241	−	14.2640i	−0.863524	−	0.504308i
$801$		0			0
$802$	23.4663	−	41.2754i	0.828623	−	1.45748i
$803$	5.03836	−	5.03836i	0.177800	−	0.177800i
$804$		0			0
$805$	−45.3721	−	27.3637i	−1.59916	−	0.964442i
$806$	0.0418167	+	0.152017i	0.00147293	+	0.00535457i
$807$		0			0
$808$	18.0081	−	18.7403i	0.633522	−	0.659281i
$809$	22.1769			0.779697			0.389848	−	0.920879i	$-0.372527\pi$
$809$	22.1769			0.779697			0.389848	+	0.920879i	$0.372527\pi$
$810$		0			0
$811$	27.8631	+	27.8631i	0.978404	+	0.978404i	0.999772	−	0.0213673i	$-0.00680193\pi$
$811$	27.8631	+	27.8631i	0.978404	+	0.978404i	−0.0213673	+	0.999772i	$0.506802\pi$
$812$	15.0081	−	59.1420i	0.526682	−	2.07548i
$813$		0			0
$814$	20.0017	+	11.3715i	0.701058	+	0.398572i
$815$	9.43853	−	2.33686i	0.330617	−	0.0818567i
$816$		0			0
$817$		−	15.5662i		−	0.544594i
$818$	−2.79522	+	4.91658i	−0.0977326	+	0.171904i
$819$		0			0
$820$	−18.1366	−	0.105400i	−0.633358	−	0.00368071i
$821$	30.2046	+	30.2046i	1.05415	+	1.05415i	0.998447	+	0.0557017i	$0.0177396\pi$
$821$	30.2046	+	30.2046i	1.05415	+	1.05415i	0.0557017	+	0.998447i	$0.482260\pi$
$822$		0			0
$823$			12.8080i			0.446457i	0.974766	+	0.223229i	$0.0716596\pi$
$823$			12.8080i			0.446457i	−0.974766	+	0.223229i	$0.928340\pi$
$824$	−37.7103	+	0.751356i	−1.31370	+	0.0261747i
$825$		0			0
$826$	13.1895	+	47.9481i	0.458923	+	1.66833i
$827$	21.4283	+	21.4283i	0.745135	+	0.745135i	0.973561	−	0.228426i	$-0.0733579\pi$
$827$	21.4283	+	21.4283i	0.745135	+	0.745135i	−0.228426	+	0.973561i	$0.573358\pi$
$828$		0			0
$829$	−17.4113	−	17.4113i	−0.604718	−	0.604718i	0.336843	−	0.941561i	$-0.390641\pi$
$829$	−17.4113	−	17.4113i	−0.604718	−	0.604718i	−0.941561	+	0.336843i	$0.890641\pi$
$830$	−8.67809	+	30.8455i	−0.301221	+	1.07066i
$831$		0			0
$832$	−12.0310	+	13.0300i	−0.417099	+	0.451735i
$833$	−6.50340			−0.225329
$834$		0			0
$835$	−7.30824	+	12.1179i	−0.252912	+	0.419358i
$836$	−5.64670	+	3.36089i	−0.195295	+	0.116239i
$837$		0			0
$838$	−9.94818	−	36.1648i	−0.343654	−	1.24929i
$839$			36.5655i			1.26238i	0.775628	+	0.631190i	$0.217433\pi$
$839$			36.5655i			1.26238i	−0.775628	+	0.631190i	$0.782567\pi$
$840$		0			0
$841$		−	72.4096i		−	2.49688i
$842$	−2.16136	+	0.594546i	−0.0744854	+	0.0204894i
$843$		0			0
$844$	−14.2824	−	3.62436i	−0.491620	−	0.124756i
$845$	−15.4821	−	9.33718i	−0.532601	−	0.321209i
$846$		0			0
$847$	22.9934			0.790063
$848$	7.08859	+	23.8971i	0.243423	+	0.820631i
$849$		0			0
$850$	−0.665862	+	21.1017i	−0.0228389	+	0.723781i
$851$	−48.7244	−	48.7244i	−1.67025	−	1.67025i
$852$		0			0
$853$	−26.8053	−	26.8053i	−0.917795	−	0.917795i	0.0790740	−	0.996869i	$-0.474804\pi$
$853$	−26.8053	−	26.8053i	−0.917795	−	0.917795i	−0.996869	+	0.0790740i	$0.974804\pi$
$854$	28.8541	−	7.93715i	0.987365	−	0.271604i
$855$		0			0
$856$	5.72335	−	5.95606i	0.195620	−	0.203574i
$857$		−	9.52133i		−	0.325243i	−0.986689	−	0.162621i	$-0.948005\pi$
$857$		−	9.52133i		−	0.325243i	0.986689	−	0.162621i	$-0.0519949\pi$
$858$		0			0
$859$	−6.51000	−	6.51000i	−0.222118	−	0.222118i	0.587272	−	0.809390i	$-0.300202\pi$
$859$	−6.51000	−	6.51000i	−0.222118	−	0.222118i	−0.809390	+	0.587272i	$0.800202\pi$
$860$	−27.8274	+	27.5059i	−0.948907	+	0.937942i
$861$		0			0
$862$	45.9406	+	26.1186i	1.56474	+	0.889604i
$863$			42.9889i			1.46336i	0.681648	+	0.731680i	$0.261263\pi$
$863$			42.9889i			1.46336i	−0.681648	+	0.731680i	$0.738737\pi$
$864$		0			0
$865$	−10.8018	+	2.67439i	−0.367272	+	0.0909321i
$866$	−3.42255	+	6.02000i	−0.116303	+	0.204568i
$867$		0			0
$868$	−0.155846	−	0.261840i	−0.00528976	−	0.00888741i
$869$	−1.39847	−	1.39847i	−0.0474398	−	0.0474398i
$870$		0			0
$871$	4.07480			0.138069
$872$	−27.2890	+	28.3986i	−0.924124	+	0.961698i
$873$		0			0
$874$	18.9751	−	5.21966i	0.641843	−	0.176558i
$875$	1.93901	−	33.8159i	0.0655507	−	1.14318i
$876$		0			0
$877$	−18.5212	+	18.5212i	−0.625417	+	0.625417i	−0.946911	−	0.321494i	$-0.895815\pi$
$877$	−18.5212	+	18.5212i	−0.625417	+	0.625417i	0.321494	+	0.946911i	$0.395815\pi$
$878$	−37.9571	−	21.5798i	−1.28099	−	0.728282i
$879$		0			0
$880$	15.9860	+	4.15571i	0.538889	+	0.140089i
$881$		−	12.3100i		−	0.414735i	−0.978263	−	0.207368i	$-0.933510\pi$
$881$		−	12.3100i		−	0.414735i	0.978263	−	0.207368i	$-0.0664896\pi$
$882$		0			0
$883$	6.84210	+	6.84210i	0.230255	+	0.230255i	0.812799	−	0.582544i	$-0.197943\pi$
$883$	6.84210	+	6.84210i	0.230255	+	0.230255i	−0.582544	+	0.812799i	$0.697943\pi$
$884$	12.8311	+	3.25608i	0.431557	+	0.109514i
$885$		0			0
$886$	−11.4861	−	41.7555i	−0.385882	−	1.40280i
$887$	−26.1330			−0.877461			−0.438730	−	0.898619i	$-0.644572\pi$
$887$	−26.1330			−0.877461			−0.438730	+	0.898619i	$0.644572\pi$
$888$		0			0
$889$		−	15.0221i		−	0.503826i
$890$	−20.9713	+	11.7621i	−0.702959	+	0.394265i
$891$		0			0
$892$	8.69962	+	14.6164i	0.291285	+	0.489393i
$893$	−7.39202	−	7.39202i	−0.247365	−	0.247365i
$894$		0			0
$895$	−19.0996	+	4.72882i	−0.638429	+	0.158067i
$896$	15.7399	−	30.4477i	0.525833	−	1.01719i
$897$		0			0
$898$	−0.400921	+	0.705189i	−0.0133789	+	0.0235325i
$899$	−0.358098	−	0.358098i	−0.0119433	−	0.0119433i
$900$		0			0
$901$	13.1562	−	13.1562i	0.438297	−	0.438297i
$902$	10.2122	−	2.80917i	0.340029	−	0.0935350i
$903$		0			0
$904$	−0.159009	−	7.98060i	−0.00528856	−	0.265431i
$905$	11.3839	+	45.9794i	0.378415	+	1.52841i
$906$		0			0
$907$	19.0593	−	19.0593i	0.632853	−	0.632853i	−0.315930	−	0.948783i	$-0.602316\pi$
$907$	19.0593	−	19.0593i	0.632853	−	0.632853i	0.948783	+	0.315930i	$0.102316\pi$
$908$	−39.5143	−	10.0273i	−1.31133	−	0.332768i
$909$		0			0
$910$	−20.4444	−	5.75185i	−0.677726	−	0.190672i
$911$	33.6231			1.11398			0.556992	−	0.830518i	$-0.311955\pi$
$911$	33.6231			1.11398			0.556992	+	0.830518i	$0.311955\pi$
$912$		0			0
$913$		−	18.7124i		−	0.619289i
$914$	37.7383	+	21.4553i	1.24827	+	0.709679i
$915$		0			0
$916$	−42.7175	−	10.8402i	−1.41143	−	0.358169i
$917$	28.1213	−	28.1213i	0.928647	−	0.928647i
$918$		0			0
$919$	−0.574098			−0.0189377			−0.00946887	−	0.999955i	$-0.503014\pi$
$919$	−0.574098			−0.0189377			−0.00946887	+	0.999955i	$0.503014\pi$
$920$	−42.8605	−	24.6982i	−1.41307	−	0.814274i
$921$		0			0
$922$	7.59378	−	2.08889i	0.250088	−	0.0687940i
$923$	−21.8967	−	21.8967i	−0.720738	−	0.720738i
$924$		0			0
$925$	13.0169	−	42.0825i	0.427994	−	1.38366i
$926$	42.3656	+	24.0861i	1.39222	+	0.791518i
$927$		0			0
$928$	12.9091	−	55.4839i	0.423761	−	1.82135i
$929$			15.3771i			0.504506i	0.967661	+	0.252253i	$0.0811714\pi$
$929$			15.3771i			0.504506i	−0.967661	+	0.252253i	$0.918829\pi$
$930$		0			0
$931$	−2.74030	+	2.74030i	−0.0898096	+	0.0898096i
$932$	30.1147	−	17.9241i	0.986438	−	0.587124i
$933$		0			0
$934$	2.39448	−	0.658671i	0.0783497	−	0.0215524i
$935$	−2.96304	−	11.9677i	−0.0969019	−	0.391384i
$936$		0			0
$937$	35.5511			1.16140			0.580702	−	0.814117i	$-0.302778\pi$
$937$	35.5511			1.16140			0.580702	+	0.814117i	$0.302778\pi$
$938$	−7.59314	+	2.08872i	−0.247925	+	0.0681990i
$939$		0			0
$940$	−0.152703	+	26.2764i	−0.00498064	+	0.857042i
$941$	−11.8428	+	11.8428i	−0.386065	+	0.386065i	−0.873281	−	0.487216i	$-0.838012\pi$
$941$	−11.8428	+	11.8428i	−0.386065	+	0.386065i	0.487216	+	0.873281i	$0.338012\pi$
$942$		0			0
$943$	−31.7203			−1.03296
$944$	13.2032	+	44.5108i	0.429728	+	1.44870i
$945$		0			0
$946$	11.2930	−	19.8636i	0.367168	−	0.645820i
$947$	−28.9882	+	28.9882i	−0.941991	+	0.941991i	−0.998407	−	0.0564161i	$-0.982033\pi$
$947$	−28.9882	+	28.9882i	−0.941991	+	0.941991i	0.0564161	+	0.998407i	$0.482033\pi$
$948$		0			0
$949$	−6.04828	+	6.04828i	−0.196335	+	0.196335i
$950$	8.61090	+	9.17204i	0.279375	+	0.297580i
$951$		0			0
$952$	−25.5791	+	0.509648i	−0.829022	+	0.0165178i
$953$			8.85819i			0.286945i	0.989654	+	0.143472i	$0.0458268\pi$
$953$			8.85819i			0.286945i	−0.989654	+	0.143472i	$0.954173\pi$
$954$		0			0
$955$	23.5950	−	39.1233i	0.763517	−	1.26600i
$956$	−24.5419	−	41.2332i	−0.793741	−	1.33358i
$957$		0			0
$958$	−36.4067	−	20.6983i	−1.17625	−	0.668731i
$959$	19.9964			0.645719
$960$		0			0
$961$	30.9975			0.999918
$962$	−24.0109	−	13.6509i	−0.774143	−	0.440124i
$963$		0			0
$964$	29.1883	+	49.0398i	0.940092	+	1.57947i
$965$	−0.206789	−	0.124713i	−0.00665679	−	0.00401467i
$966$		0			0
$967$			16.3210i			0.524847i	0.964953	+	0.262424i	$0.0845218\pi$
$967$			16.3210i			0.524847i	−0.964953	+	0.262424i	$0.915478\pi$
$968$	21.4627	−	0.427632i	0.689837	−	0.0137446i
$969$		0			0
$970$	15.0071	+	26.7570i	0.481848	+	0.859116i
$971$	−5.74815	+	5.74815i	−0.184467	+	0.184467i	−0.793299	−	0.608832i	$-0.791638\pi$
$971$	−5.74815	+	5.74815i	−0.184467	+	0.184467i	0.608832	+	0.793299i	$0.291638\pi$
$972$		0			0
$973$	−1.13962	+	1.13962i	−0.0365346	+	0.0365346i
$974$	14.2827	−	25.1222i	0.457647	−	0.804967i
$975$		0			0
$976$	26.7856	−	7.94539i	0.857385	−	0.254326i
$977$	−39.0104			−1.24805			−0.624027	−	0.781403i	$-0.714504\pi$
$977$	−39.0104			−1.24805			−0.624027	+	0.781403i	$0.714504\pi$
$978$		0			0
$979$	9.92881	−	9.92881i	0.317326	−	0.317326i
$980$	9.74093	+	0.0566087i	0.311163	+	0.00180830i
$981$		0			0
$982$	−2.88172	+	0.792703i	−0.0919595	+	0.0252962i
$983$	−0.0416029			−0.00132693			−0.000663463	−	1.00000i	$-0.500211\pi$
$983$	−0.0416029			−0.00132693			−0.000663463		1.00000i	$0.500211\pi$
$984$		0			0
$985$	10.1164	+	40.8597i	0.322334	+	1.30190i
$986$	−40.9980	+	11.2777i	−1.30564	+	0.359156i
$987$		0			0
$988$	6.77856	−	4.03457i	0.215655	−	0.128357i
$989$	−48.3880	+	48.3880i	−1.53865	+	1.53865i
$990$		0			0
$991$			8.76665i			0.278482i	0.990259	+	0.139241i	$0.0444663\pi$
$991$			8.76665i			0.278482i	−0.990259	+	0.139241i	$0.955534\pi$
$992$	−0.150341	−	0.241510i	−0.00477332	−	0.00766794i
$993$		0			0
$994$	52.0273	+	29.5791i	1.65021	+	0.938191i
$995$	31.2424	−	51.8036i	0.990452	−	1.64228i
$996$		0			0
$997$	29.7206	+	29.7206i	0.941260	+	0.941260i	0.998368	−	0.0571081i	$-0.0181880\pi$
$997$	29.7206	+	29.7206i	0.941260	+	0.941260i	−0.0571081	+	0.998368i	$0.518188\pi$
$998$	15.0984	−	4.15325i	0.477931	−	0.131469i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.10	yes	96
3.2	odd	2	inner	720.2.u.a.179.39	yes	96
4.3	odd	2		2880.2.u.a.2159.17		96
5.4	even	2	inner	720.2.u.a.179.40	yes	96
12.11	even	2		2880.2.u.a.2159.32		96
15.14	odd	2	inner	720.2.u.a.179.9	✓	96
16.5	even	4		2880.2.u.a.719.8		96
16.11	odd	4	inner	720.2.u.a.539.9	yes	96
20.19	odd	2		2880.2.u.a.2159.41		96
48.5	odd	4		2880.2.u.a.719.41		96
48.11	even	4	inner	720.2.u.a.539.40	yes	96
60.59	even	2		2880.2.u.a.2159.8		96
80.59	odd	4	inner	720.2.u.a.539.39	yes	96
80.69	even	4		2880.2.u.a.719.32		96
240.59	even	4	inner	720.2.u.a.539.10	yes	96
240.149	odd	4		2880.2.u.a.719.17		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.9	✓	96	15.14	odd	2	inner
720.2.u.a.179.10	yes	96	1.1	even	1	trivial
720.2.u.a.179.39	yes	96	3.2	odd	2	inner
720.2.u.a.179.40	yes	96	5.4	even	2	inner
720.2.u.a.539.9	yes	96	16.11	odd	4	inner
720.2.u.a.539.10	yes	96	240.59	even	4	inner
720.2.u.a.539.39	yes	96	80.59	odd	4	inner
720.2.u.a.539.40	yes	96	48.11	even	4	inner
2880.2.u.a.719.8		96	16.5	even	4
2880.2.u.a.719.17		96	240.149	odd	4
2880.2.u.a.719.32		96	80.69	even	4
2880.2.u.a.719.41		96	48.5	odd	4
2880.2.u.a.2159.8		96	60.59	even	2
2880.2.u.a.2159.17		96	4.3	odd	2
2880.2.u.a.2159.32		96	12.11	even	2
2880.2.u.a.2159.41		96	20.19	odd	2

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.15480 + 1.91479i) q^{5} -3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +O(q^{10})\)	\(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.15480 + 1.91479i) q^{5} -3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +(2.75809 - 1.54692i) q^{10} +(-1.30581 + 1.30581i) q^{11} +(1.56756 - 1.56756i) q^{13} +(-2.11753 + 3.72457i) q^{14} +(-1.90729 + 3.51600i) q^{16} +2.98571 q^{17} +(1.25807 - 1.25807i) q^{19} +(-4.47206 - 0.0259891i) q^{20} +(2.51809 - 0.692674i) q^{22} -7.82148 q^{23} +(-2.33287 - 4.42241i) q^{25} +(-3.02283 + 0.831519i) q^{26} +(5.20664 - 3.09897i) q^{28} +(7.12073 - 7.12073i) q^{29} -0.0502896i q^{31} +(4.80238 - 2.98950i) q^{32} +(-3.67067 - 2.08689i) q^{34} +(5.80096 + 3.49853i) q^{35} +(6.22957 + 6.22957i) q^{37} +(-2.42603 + 0.667350i) q^{38} +(5.47985 + 3.15773i) q^{40} +4.05554 q^{41} +(6.18655 - 6.18655i) q^{43} +(-3.57992 - 0.908456i) q^{44} +(9.61583 + 5.46689i) q^{46} -5.87568i q^{47} -2.17818 q^{49} +(-0.223016 + 7.06755i) q^{50} +(4.29751 + 1.09055i) q^{52} +(4.40639 - 4.40639i) q^{53} +(-0.992408 - 4.00831i) q^{55} +(-8.56716 + 0.170696i) q^{56} +(-13.7314 + 3.77723i) q^{58} +(8.20735 - 8.20735i) q^{59} +(-4.93899 - 4.93899i) q^{61} +(-0.0351503 + 0.0618267i) q^{62} +(-7.99365 + 0.318664i) q^{64} +(1.19133 + 4.81176i) q^{65} +(1.29973 + 1.29973i) q^{67} +(3.05413 + 5.13129i) q^{68} +(-4.68646 - 8.35577i) q^{70} -13.9687i q^{71} -3.85841 q^{73} +(-3.30451 - 12.0129i) q^{74} +(3.44904 + 0.875242i) q^{76} +(3.95602 + 3.95602i) q^{77} +1.07096i q^{79} +(-4.52987 - 7.71234i) q^{80} +(-4.98593 - 2.83465i) q^{82} +(-7.16503 + 7.16503i) q^{83} +(-3.44790 + 5.71702i) q^{85} +(-11.9300 + 3.28169i) q^{86} +(3.76623 + 3.61909i) q^{88} -7.60356 q^{89} +(-4.74899 - 4.74899i) q^{91} +(-8.00071 - 13.4421i) q^{92} +(-4.10686 + 7.22364i) q^{94} +(0.956125 + 3.86176i) q^{95} +9.70129i q^{97} +(2.67788 + 1.52245i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

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