LMFDB - Embedded newform 720.2.u.a.179.9

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			179.9
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.91479 + 1.15480i) q^{5} +3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +O(q^{10})$	\(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.91479 + 1.15480i) q^{5} +3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +(3.16123 - 0.0813664i) q^{10} +(1.30581 - 1.30581i) q^{11} +(-1.56756 + 1.56756i) q^{13} +(2.11753 - 3.72457i) q^{14} +(-1.90729 + 3.51600i) q^{16} +2.98571 q^{17} +(1.25807 - 1.25807i) q^{19} +(-3.94333 - 2.10954i) q^{20} +(-2.51809 + 0.692674i) q^{22} -7.82148 q^{23} +(2.33287 - 4.42241i) q^{25} +(3.02283 - 0.831519i) q^{26} +(-5.20664 + 3.09897i) q^{28} +(-7.12073 + 7.12073i) q^{29} -0.0502896i q^{31} +(4.80238 - 2.98950i) q^{32} +(-3.67067 - 2.08689i) q^{34} +(-3.49853 - 5.80096i) q^{35} +(-6.22957 - 6.22957i) q^{37} +(-2.42603 + 0.667350i) q^{38} +(3.37351 + 5.34971i) q^{40} -4.05554 q^{41} +(-6.18655 + 6.18655i) q^{43} +(3.57992 + 0.908456i) q^{44} +(9.61583 + 5.46689i) q^{46} -5.87568i q^{47} -2.17818 q^{49} +(-5.95914 + 3.80639i) q^{50} +(-4.29751 - 1.09055i) q^{52} +(4.40639 - 4.40639i) q^{53} +(-0.992408 + 4.00831i) q^{55} +(8.56716 - 0.170696i) q^{56} +(13.7314 - 3.77723i) q^{58} +(-8.20735 + 8.20735i) q^{59} +(-4.93899 - 4.93899i) q^{61} +(-0.0351503 + 0.0618267i) q^{62} +(-7.99365 + 0.318664i) q^{64} +(1.19133 - 4.81176i) q^{65} +(-1.29973 - 1.29973i) q^{67} +(3.05413 + 5.13129i) q^{68} +(0.246504 + 9.57711i) q^{70} +13.9687i q^{71} +3.85841 q^{73} +(3.30451 + 12.0129i) q^{74} +(3.44904 + 0.875242i) q^{76} +(3.95602 + 3.95602i) q^{77} +1.07096i q^{79} +(-0.408208 - 8.93495i) q^{80} +(4.98593 + 2.83465i) q^{82} +(-7.16503 + 7.16503i) q^{83} +(-5.71702 + 3.44790i) q^{85} +(11.9300 - 3.28169i) q^{86} +(-3.76623 - 3.61909i) q^{88} +7.60356 q^{89} +(-4.74899 - 4.74899i) q^{91} +(-8.00071 - 13.4421i) q^{92} +(-4.10686 + 7.22364i) q^{94} +(-0.956125 + 3.86176i) q^{95} -9.70129i q^{97} +(2.67788 + 1.52245i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.91479	+	1.15480i	−0.856322	+	0.516443i
$5$	−1.91479	+	1.15480i	−0.856322	+	0.516443i
$6$		0			0
$7$			3.02955i			1.14506i	0.819883	+	0.572531i	$0.194038\pi$
$7$			3.02955i			1.14506i	−0.819883	+	0.572531i	$0.805962\pi$
$8$	−0.0563436	−	2.82787i	−0.0199205	−	0.999802i
$9$		0			0
$10$	3.16123	−	0.0813664i	0.999669	−	0.0257303i
$11$	1.30581	−	1.30581i	0.393717	−	0.393717i	−0.482293	−	0.876010i	$-0.660196\pi$
$11$	1.30581	−	1.30581i	0.393717	−	0.393717i	0.876010	+	0.482293i	$0.160196\pi$
$12$		0			0
$13$	−1.56756	+	1.56756i	−0.434762	+	0.434762i	−0.890245	−	0.455483i	$-0.849467\pi$
$13$	−1.56756	+	1.56756i	−0.434762	+	0.434762i	0.455483	+	0.890245i	$0.349467\pi$
$14$	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	$0.184578\pi$
$20$	−3.94333	−	2.10954i	−0.881756	−	0.471706i
$21$		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	$0.634599\pi$
$29$	−7.12073	+	7.12073i	−1.32229	+	1.32229i	−0.911921	+	0.410365i	$0.865401\pi$
$30$		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
$35$	−3.49853	−	5.80096i	−0.591359	−	0.980542i
$36$		0			0
$37$	−6.22957	−	6.22957i	−1.02413	−	1.02413i	−0.999701	−	0.0244329i	$-0.992222\pi$
$37$	−6.22957	−	6.22957i	−1.02413	−	1.02413i	−0.0244329	−	0.999701i	$-0.507778\pi$
$38$	−2.42603	+	0.667350i	−0.393553	+	0.108258i
$39$		0			0
$40$	3.37351	+	5.34971i	0.533398	+	0.845864i
$41$	−4.05554			−0.633368			−0.316684	−	0.948531i	$-0.602570\pi$
$41$	−4.05554			−0.633368			−0.316684	+	0.948531i	$0.602570\pi$
$42$		0			0
$43$	−6.18655	+	6.18655i	−0.943441	+	0.943441i	−0.998484	−	0.0550434i	$-0.982470\pi$
$43$	−6.18655	+	6.18655i	−0.943441	+	0.943441i	0.0550434	+	0.998484i	$0.482470\pi$
$44$	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
$50$	−5.95914	+	3.80639i	−0.842750	+	0.538305i
$51$		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	$0.522629\pi$
$59$	−8.20735	+	8.20735i	−1.06851	+	1.06851i	−0.997474	+	0.0710318i	$0.977371\pi$
$60$		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	0.623242	−	0.782029i	$-0.285815\pi$
$67$	−1.29973	−	1.29973i	−0.158787	−	0.158787i	−0.782029	+	0.623242i	$0.785815\pi$
$68$	3.05413	+	5.13129i	0.370367	+	0.622261i
$69$		0			0
$70$	0.246504	+	9.57711i	0.0294628	+	1.14468i
$71$			13.9687i			1.65778i	0.559414	+	0.828888i	$0.311026\pi$
$71$			13.9687i			1.65778i	−0.559414	+	0.828888i	$0.688974\pi$
$72$		0			0
$73$	3.85841			0.451593			0.225796	−	0.974175i	$-0.427502\pi$
$73$	3.85841			0.451593			0.225796	+	0.974175i	$0.427502\pi$
$74$	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	$0.980811\pi$
$80$	−0.408208	−	8.93495i	−0.0456391	−	0.998958i
$81$		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
$85$	−5.71702	+	3.44790i	−0.620098	+	0.373977i
$86$	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	$-0.367972\pi$
$89$	7.60356			0.805975			0.402988	+	0.915205i	$0.367972\pi$
$90$		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	$-0.836080\pi$
$97$		−	9.70129i		−	0.985017i	0.870308	−	0.492508i	$-0.163920\pi$
$98$	2.67788	+	1.52245i	0.270507	+	0.153791i
$99$		0			0
$100$	9.98676	−	0.514436i	0.998676	−	0.0514436i
$101$	−6.49754	−	6.49754i	−0.646530	−	0.646530i	0.305623	−	0.952153i	$-0.401135\pi$
$101$	−6.49754	−	6.49754i	−0.646530	−	0.646530i	−0.952153	+	0.305623i	$0.901135\pi$
$102$		0			0
$103$			13.3352i			1.31396i	0.753908	+	0.656980i	$0.228167\pi$
$103$			13.3352i			1.31396i	−0.753908	+	0.656980i	$0.771833\pi$
$104$	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	$0.982367\pi$
$110$	4.02172	−	4.23422i	0.383456	−	0.403717i
$111$		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
$115$	14.9765	−	9.03225i	1.39657	−	0.842262i
$116$	−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
$125$	0.640034	+	11.1620i	0.0572464	+	0.998360i
$126$		0			0
$127$	−4.95854			−0.439999			−0.219999	−	0.975500i	$-0.570606\pi$
$127$	−4.95854			−0.439999			−0.219999	+	0.975500i	$0.570606\pi$
$128$	10.0502	+	5.19546i	0.888324	+	0.459218i
$129$		0			0
$130$	−4.82786	+	5.08295i	−0.423431	+	0.445805i
$131$	−9.28233	−	9.28233i	−0.811001	−	0.811001i	0.173783	−	0.984784i	$-0.444401\pi$
$131$	−9.28233	−	9.28233i	−0.811001	−	0.811001i	−0.984784	+	0.173783i	$0.944401\pi$
$132$		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	$0.757182\pi$
$140$	6.39094	−	11.9465i	0.540133	−	1.00967i
$141$		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	0.967367	−	0.253379i	$-0.0815420\pi$
$149$	8.71533	+	8.71533i	0.713988	+	0.713988i	−0.253379	+	0.967367i	$0.581542\pi$
$150$		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
$155$	0.0580744	+	0.0962941i	0.00466465	+	0.00773453i
$156$		0			0
$157$	16.0087	−	16.0087i	1.27764	−	1.27764i	0.335647	−	0.941988i	$-0.391045\pi$
$157$	16.0087	−	16.0087i	1.27764	−	1.27764i	0.941988	−	0.335647i	$-0.108955\pi$
$158$	0.748555	−	1.31665i	0.0595518	−	0.104747i
$159$		0			0
$160$	−5.74330	+	11.2701i	−0.454048	+	0.890977i
$161$		−	23.6956i		−	1.86747i
$162$		0			0
$163$	3.07484	+	3.07484i	0.240840	+	0.240840i	0.817198	−	0.576357i	$-0.195526\pi$
$163$	3.07484	+	3.07484i	0.240840	+	0.240840i	−0.576357	+	0.817198i	$0.695526\pi$
$164$	−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
$170$	9.43852	−	0.242937i	0.723901	−	0.0186324i
$171$		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	0.435244	−	0.900312i	$-0.356662\pi$
$179$	−6.22219	−	6.22219i	−0.465068	−	0.465068i	−0.900312	+	0.435244i	$0.856662\pi$
$180$		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
$190$	3.87468	−	4.07941i	0.281099	−	0.295952i
$191$	20.4321			1.47842			0.739208	−	0.673477i	$-0.235200\pi$
$191$	20.4321			1.47842			0.739208	+	0.673477i	$0.235200\pi$
$192$		0			0
$193$		−	0.107996i		−	0.00777370i	−0.999992	−	0.00388685i	$-0.998763\pi$
$193$		−	0.107996i		−	0.00777370i	0.999992	−	0.00388685i	$-0.00123723\pi$
$194$	−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	$0.908443\pi$
$200$	−12.6374	−	6.34787i	−0.893601	−	0.448862i
$201$		0			0
$202$	3.44666	+	12.5297i	0.242506	+	0.881585i
$203$	−21.5726	−	21.5726i	−1.51410	−	1.51410i
$204$		0			0
$205$	7.76552	−	4.68334i	0.542367	−	0.327098i
$206$	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
$220$	−7.90390	+	2.39459i	−0.532881	+	0.161443i
$221$	−4.68027	+	4.68027i	−0.314829	+	0.314829i
$222$		0			0
$223$	−8.50474			−0.569519			−0.284760	−	0.958599i	$-0.591914\pi$
$223$	−8.50474			−0.569519			−0.284760	+	0.958599i	$0.591914\pi$
$224$	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	$0.990412\pi$
$230$	−24.7255	+	0.636406i	−1.63035	+	0.0419634i
$231$		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
$235$	6.78524	+	11.2507i	0.442620	+	0.733916i
$236$	−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	$-0.217266\pi$
$239$	23.9921			1.55192			0.775960	+	0.630782i	$0.217266\pi$
$240$		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
$245$	4.17076	−	2.51536i	0.266460	−	0.160700i
$246$		0			0
$247$			3.94419i			0.250963i
$248$	−0.142212	+	0.00283350i	−0.00903048	+	0.000179927i
$249$		0			0
$250$	7.01491	−	14.1701i	0.443662	−	0.896194i
$251$	−0.638332	+	0.638332i	−0.0402912	+	0.0402912i	−0.726965	−	0.686674i	$-0.759070\pi$
$251$	−0.638332	+	0.638332i	−0.0402912	+	0.0402912i	0.686674	+	0.726965i	$0.259070\pi$
$252$		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
$260$	9.48821	−	2.87458i	0.588434	−	0.178274i
$261$		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	−0.908329	−	0.418257i	$-0.862641\pi$
$269$	−8.03777	+	8.03777i	−0.490071	+	0.490071i	0.418257	+	0.908329i	$0.362641\pi$
$270$		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
$275$	−2.72854	−	8.82112i	−0.164537	−	0.531934i
$276$		0			0
$277$	−4.06316	−	4.06316i	−0.244132	−	0.244132i	0.574425	−	0.818557i	$-0.305226\pi$
$277$	−4.06316	−	4.06316i	−0.244132	−	0.244132i	−0.818557	+	0.574425i	$0.805226\pi$
$278$	0.199541	+	0.725393i	0.0119676	+	0.0435062i
$279$		0			0
$280$	−16.2072	+	10.2202i	−0.968567	+	0.610774i
$281$	−0.511034			−0.0304858			−0.0152429	−	0.999884i	$-0.504852\pi$
$281$	−0.511034			−0.0304858			−0.0152429	+	0.999884i	$0.504852\pi$
$282$		0			0
$283$	−13.0685	+	13.0685i	−0.776839	+	0.776839i	−0.979292	−	0.202453i	$-0.935109\pi$
$283$	−13.0685	+	13.0685i	−0.776839	+	0.776839i	0.202453	+	0.979292i	$0.435109\pi$
$284$	−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
$290$	−21.9309	+	23.0897i	−1.28783	+	1.35587i
$291$		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	0.999773	−	0.0213024i	$-0.00678126\pi$
$307$	17.1442	+	17.1442i	0.978471	+	0.978471i	−0.0213024	+	0.999773i	$0.506781\pi$
$308$	−2.75221	+	10.8456i	−0.156822	+	0.617983i
$309$		0			0
$310$	−0.00409188	−	0.158977i	−0.000232403	−	0.00902928i
$311$			21.2420i			1.20452i	0.798299	+	0.602261i	$0.205733\pi$
$311$			21.2420i			1.20452i	−0.798299	+	0.602261i	$0.794267\pi$
$312$		0			0
$313$	−19.9351			−1.12680			−0.563400	−	0.826184i	$-0.690507\pi$
$313$	−19.9351			−1.12680			−0.563400	+	0.826184i	$0.690507\pi$
$314$	−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
$320$	14.9382	−	9.84125i	0.835071	−	0.550143i
$321$		0			0
$322$	−16.5622	+	29.1317i	−0.922976	+	1.62344i
$323$	3.75623	−	3.75623i	0.209002	−	0.209002i
$324$		0			0
$325$	3.27547	+	10.5893i	0.181690	+	0.587388i
$326$	−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	$0.276856\pi$
$337$			28.0570i			1.52836i	−0.645003	+	0.764180i	$0.723144\pi$
$338$	5.65145	−	9.94046i	0.307398	−	0.540690i
$339$		0			0
$340$	−11.7736	−	6.29846i	−0.638516	−	0.341582i
$341$	−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	$0.683106\pi$
$350$	−11.5317	−	18.0535i	−0.616393	−	0.965001i
$351$		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
$355$	−16.1310	−	26.7471i	−0.856146	−	1.41959i
$356$	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	$0.0568993\pi$
$359$			6.73781i			0.355608i	−0.984066	+	0.177804i	$0.943101\pi$
$360$		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
$365$	−7.38806	+	4.45569i	−0.386709	+	0.233222i
$366$		0			0
$367$	−7.64267			−0.398944			−0.199472	−	0.979904i	$-0.563923\pi$
$367$	−7.64267			−0.398944			−0.199472	+	0.979904i	$0.563923\pi$
$368$	14.9178	−	27.5003i	0.777646	−	1.43355i
$369$		0			0
$370$	−20.2000	−	19.1862i	−1.05015	−	0.997444i
$371$	13.3494	+	13.3494i	0.693065	+	0.693065i
$372$		0			0
$373$	5.20096	+	5.20096i	0.269296	+	0.269296i	0.828816	−	0.559521i	$-0.189015\pi$
$373$	5.20096	+	5.20096i	0.269296	+	0.269296i	−0.559521	+	0.828816i	$0.689015\pi$
$374$	−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	$0.660471\pi$
$380$	−7.61493	+	2.30704i	−0.390638	+	0.118349i
$381$		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	0.884931	−	0.465721i	$-0.154205\pi$
$389$	8.26812	+	8.26812i	0.419210	+	0.419210i	−0.465721	+	0.884931i	$0.654205\pi$
$390$		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
$395$	−1.23674	−	2.05066i	−0.0622273	−	0.103180i
$396$		0			0
$397$	−6.70437	+	6.70437i	−0.336482	+	0.336482i	−0.855042	−	0.518559i	$-0.826469\pi$
$397$	−6.70437	+	6.70437i	−0.336482	+	0.336482i	0.518559	+	0.855042i	$0.326469\pi$
$398$	33.2610	+	18.9099i	1.66723	+	0.947868i
$399$		0			0
$400$	11.0997	+	16.6372i	0.554986	+	0.831860i
$401$		−	33.5732i		−	1.67657i	−0.545235	−	0.838283i	$-0.683560\pi$
$401$		−	33.5732i		−	1.67657i	0.545235	−	0.838283i	$-0.316440\pi$
$402$		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	$-0.0315234\pi$
$410$	−12.8205	+	0.329984i	−0.633159	+	0.0162968i
$411$		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	0.0805555	−	0.996750i	$-0.474331\pi$
$419$	−18.7540	−	18.7540i	−0.916195	−	0.916195i	−0.996750	+	0.0805555i	$0.974331\pi$
$420$		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
$430$	−19.0537	+	20.0605i	−0.918853	+	0.967403i
$431$	37.3679			1.79995			0.899975	−	0.435941i	$-0.143584\pi$
$431$	37.3679			1.79995			0.899975	+	0.435941i	$0.143584\pi$
$432$		0			0
$433$			4.89665i			0.235318i	0.993054	+	0.117659i	$0.0375389\pi$
$433$			4.89665i			0.235318i	−0.993054	+	0.117659i	$0.962461\pi$
$434$	−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	$0.236349\pi$
$440$	11.3909	+	2.58055i	0.543039	+	0.123023i
$441$		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
$445$	−14.5592	+	8.78059i	−0.690174	+	0.416240i
$446$	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	$0.00430842\pi$
$449$			0.573598i			0.0270698i	−0.999908	+	0.0135349i	$0.995692\pi$
$450$		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	$-0.245079\pi$
$457$	30.6962			1.43591			0.717953	+	0.696092i	$0.245079\pi$
$458$	30.0472	−	8.26535i	1.40401	−	0.386215i
$459$		0			0
$460$	30.8427	+	16.4997i	1.43805	+	0.769302i
$461$	3.93792	−	3.93792i	0.183407	−	0.183407i	−0.609431	−	0.792839i	$-0.708602\pi$
$461$	3.93792	−	3.93792i	0.183407	−	0.183407i	0.792839	+	0.609431i	$0.208602\pi$
$462$		0			0
$463$	34.4600			1.60149			0.800746	−	0.599004i	$-0.204437\pi$
$463$	34.4600			1.60149			0.800746	+	0.599004i	$0.204437\pi$
$464$	−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
$470$	−0.478083	−	18.5744i	−0.0220523	−	0.856773i
$471$		0			0
$472$	23.6717	+	22.7469i	1.08958	+	1.04701i
$473$			16.1569i			0.742897i
$474$		0			0
$475$	−2.62879	−	8.49862i	−0.120617	−	0.389943i
$476$	−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	$-0.736516\pi$
$479$	−29.6130			−1.35305			−0.676527	+	0.736418i	$0.736516\pi$
$480$		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
$485$	11.2031	+	18.5760i	0.508705	+	0.843491i
$486$		0			0
$487$		−	20.4343i		−	0.925966i	−0.886367	−	0.462983i	$-0.846779\pi$
$487$		−	20.4343i		−	0.925966i	0.886367	−	0.462983i	$-0.153221\pi$
$488$	−13.6885	+	14.2451i	−0.619650	+	0.644844i
$489$		0			0
$490$	−6.88571	+	0.177230i	−0.311065	+	0.00800645i
$491$	−1.49438	+	1.49438i	−0.0674405	+	0.0674405i	−0.740023	−	0.672582i	$-0.765185\pi$
$491$	−1.49438	+	1.49438i	−0.0674405	+	0.0674405i	0.672582	+	0.740023i	$0.265185\pi$
$492$		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	$0.329721\pi$
$500$	−18.5285	+	12.5178i	−0.828620	+	0.559811i
$501$		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	−0.772233	−	0.635339i	$-0.780860\pi$
$509$	−3.08846	+	3.08846i	−0.136894	+	0.136894i	0.635339	+	0.772233i	$0.280860\pi$
$510$		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
$515$	−15.3995	−	25.5342i	−0.678585	−	1.12517i
$516$		0			0
$517$	−7.67253	−	7.67253i	−0.337438	−	0.337438i
$518$	−36.3937	+	10.0112i	−1.59905	+	0.439865i
$519$		0			0
$520$	−13.6741	−	3.09782i	−0.599651	−	0.135848i
$521$	−6.66855			−0.292155			−0.146077	−	0.989273i	$-0.546665\pi$
$521$	−6.66855			−0.292155			−0.146077	+	0.989273i	$0.546665\pi$
$522$		0			0
$523$	−13.2266	+	13.2266i	−0.578361	+	0.578361i	−0.934451	−	0.356091i	$-0.884109\pi$
$523$	−13.2266	+	13.2266i	−0.578361	+	0.578361i	0.356091	+	0.934451i	$0.384109\pi$
$524$	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
$530$	13.5711	−	14.2881i	0.589490	−	0.620637i
$531$		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	0.331788	−	0.943354i	$-0.392348\pi$
$547$	−14.3033	−	14.3033i	−0.611566	−	0.611566i	−0.943354	+	0.331788i	$0.892348\pi$
$548$	−11.3437	+	6.75171i	−0.484578	+	0.288419i
$549$		0			0
$550$	−2.81109	+	12.7519i	−0.119865	+	0.543745i
$551$			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
$560$	27.0689	−	1.23669i	1.14387	−	0.0522596i
$561$		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
$565$	−5.40379	+	3.25900i	−0.227339	+	0.137107i
$566$	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	$-0.435816\pi$
$569$	9.55464			0.400551			0.200276	+	0.979740i	$0.435816\pi$
$570$		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	$0.323656\pi$
$577$			40.8559i			1.70085i	−0.526095	+	0.850426i	$0.676344\pi$
$578$	9.94046	+	5.65145i	0.413469	+	0.235069i
$579$		0			0
$580$	43.1008	−	13.0580i	1.78966	−	0.542203i
$581$	−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
$590$	−25.2775	+	26.6131i	−1.04066	+	1.09565i
$591$		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
$595$	−10.4456	−	17.3200i	−0.428227	−	0.710051i
$596$	−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	$-0.821272\pi$
$599$		−	26.0628i		−	1.06490i	0.846462	−	0.532449i	$-0.178728\pi$
$600$		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
$605$	−8.76461	−	14.5327i	−0.356332	−	0.590840i
$606$		0			0
$607$	−40.5499			−1.64587			−0.822934	−	0.568136i	$-0.807665\pi$
$607$	−40.5499			−1.64587			−0.822934	+	0.568136i	$0.807665\pi$
$608$	2.28074	−	9.80273i	0.0924961	−	0.397553i
$609$		0			0
$610$	−16.0151	−	15.2114i	−0.648434	−	0.615892i
$611$	9.21047	+	9.21047i	0.372616	+	0.372616i
$612$		0			0
$613$	5.91500	+	5.91500i	0.238905	+	0.238905i	0.816396	−	0.577492i	$-0.195968\pi$
$613$	5.91500	+	5.91500i	0.238905	+	0.238905i	−0.577492	+	0.816396i	$0.695968\pi$
$614$	−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	$0.934085\pi$
$620$	−0.106088	+	0.198308i	−0.00426058	+	0.00796426i
$621$		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
$635$	9.49457	−	5.72612i	0.376781	−	0.227234i
$636$		0			0
$637$	3.41441	−	3.41441i	0.135284	−	0.135284i
$638$	12.9983	−	22.8630i	0.514607	−	0.905154i
$639$		0			0
$640$	−25.2438	+	1.65779i	−0.997851	+	0.0655298i
$641$			8.84689i			0.349431i	0.984619	+	0.174716i	$0.0559006\pi$
$641$			8.84689i			0.349431i	−0.984619	+	0.174716i	$0.944099\pi$
$642$		0			0
$643$	−18.7263	−	18.7263i	−0.738491	−	0.738491i	0.233795	−	0.972286i	$-0.424886\pi$
$643$	−18.7263	−	18.7263i	−0.738491	−	0.738491i	−0.972286	+	0.233795i	$0.924886\pi$
$644$	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
$650$	3.37456	−	15.3080i	0.132361	−	0.600430i
$651$		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	0.580481	−	0.814274i	$-0.302865\pi$
$659$	−6.00170	−	6.00170i	−0.233793	−	0.233793i	−0.814274	+	0.580481i	$0.802865\pi$
$660$		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
$670$	−4.21450	−	4.00299i	−0.162820	−	0.154649i
$671$	−12.8988			−0.497952
$672$		0			0
$673$		−	0.683677i		−	0.0263538i	−0.999913	−	0.0131769i	$-0.995806\pi$
$673$		−	0.683677i		−	0.0263538i	0.999913	−	0.0131769i	$-0.00419446\pi$
$674$	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
$680$	10.0723	+	15.9727i	0.386256	+	0.612525i
$681$		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
$685$	−7.62222	−	12.6385i	−0.291230	−	0.482893i
$686$	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
$700$	1.55851	+	30.2554i	0.0589061	+	1.14355i
$701$	−24.8888	+	24.8888i	−0.940038	+	0.940038i	−0.998301	−	0.0582634i	$-0.981444\pi$
$701$	−24.8888	+	24.8888i	−0.940038	+	0.940038i	0.0582634	+	0.998301i	$0.481444\pi$
$702$		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	$0.140443\pi$
$710$	1.13658	+	44.1582i	0.0426551	+	1.65723i
$711$		0			0
$712$	−0.428412	−	21.5018i	−0.0160554	−	0.805815i
$713$			0.393339i			0.0147307i
$714$		0			0
$715$	−4.72760	−	7.83891i	−0.176802	−	0.293159i
$716$	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	$-0.510355\pi$
$719$	−1.74421			−0.0650482			−0.0325241	+	0.999471i	$0.510355\pi$
$720$		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
$725$	14.8790	+	48.1025i	0.552594	+	1.78648i
$726$		0			0
$727$			2.82244i			0.104679i	0.998629	+	0.0523393i	$0.0166677\pi$
$727$			2.82244i			0.104679i	−0.998629	+	0.0523393i	$0.983332\pi$
$728$	−13.1619	+	13.6971i	−0.487814	+	0.507648i
$729$		0			0
$730$	12.1973	−	0.313945i	0.451443	−	0.0116196i
$731$	−18.4713	+	18.4713i	−0.683184	+	0.683184i
$732$		0			0
$733$	−7.06892	+	7.06892i	−0.261097	+	0.261097i	−0.825500	−	0.564403i	$-0.809106\pi$
$733$	−7.06892	+	7.06892i	−0.261097	+	0.261097i	0.564403	+	0.825500i	$0.309106\pi$
$734$	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	$0.247281\pi$
$740$	11.4238	+	37.7067i	0.419946	+	1.38613i
$741$		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
$755$	−13.8978	+	8.38167i	−0.505792	+	0.305040i
$756$		0			0
$757$	−15.0827	−	15.0827i	−0.548188	−	0.548188i	0.377728	−	0.925917i	$-0.376705\pi$
$757$	−15.0827	−	15.0827i	−0.548188	−	0.548188i	−0.925917	+	0.377728i	$0.876705\pi$
$758$	−4.05374	−	14.7366i	−0.147239	−	0.535259i
$759$		0			0
$760$	10.9744	+	2.48621i	0.398084	+	0.0901842i
$761$	−27.3466			−0.991312			−0.495656	−	0.868519i	$-0.665072\pi$
$761$	−27.3466			−0.991312			−0.495656	+	0.868519i	$0.665072\pi$
$762$		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	$0.587187\pi$
$770$	12.8278	+	12.1840i	0.462281	+	0.439081i
$771$		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	$0.0206530\pi$
$787$	29.8134	+	29.8134i	1.06273	+	1.06273i	0.0648379	+	0.997896i	$0.479347\pi$
$788$	36.4929	+	9.26058i	1.30000	+	0.329894i
$789$		0			0
$790$	0.0871400	+	3.38554i	0.00310030	+	0.120452i
$791$			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
$800$	−2.01745	−	28.2122i	−0.0713275	−	0.997453i
$801$		0			0
$802$	−23.4663	+	41.2754i	−0.828623	+	1.45748i
$803$	5.03836	−	5.03836i	0.177800	−	0.177800i
$804$		0			0
$805$	27.3637	+	45.3721i	0.964442	+	1.59916i
$806$	−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	$-0.627473\pi$
$809$	−22.1769			−0.779697			−0.389848	+	0.920879i	$0.627473\pi$
$810$		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
$820$	15.9923	+	8.55530i	0.558476	+	0.298764i
$821$	−30.2046	−	30.2046i	−1.05415	−	1.05415i	−0.998447	−	0.0557017i	$-0.982260\pi$
$821$	−30.2046	−	30.2046i	−1.05415	−	1.05415i	−0.0557017	−	0.998447i	$-0.517740\pi$
$822$		0			0
$823$		−	12.8080i		−	0.446457i	−0.974766	−	0.223229i	$-0.928340\pi$
$823$		−	12.8080i		−	0.446457i	0.974766	−	0.223229i	$-0.0716596\pi$
$824$	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	$0.890641\pi$
$830$	−22.0673	+	23.2333i	−0.765968	+	0.806440i
$831$		0			0
$832$	12.0310	−	13.0300i	0.417099	−	0.451735i
$833$	−6.50340			−0.225329
$834$		0			0
$835$	−12.1179	+	7.30824i	−0.419358	+	0.252912i
$836$	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	$-0.782567\pi$
$839$		−	36.5655i		−	1.26238i	0.775628	−	0.631190i	$-0.217433\pi$
$840$		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
$845$	−9.33718	−	15.4821i	−0.321209	−	0.532601i
$846$		0			0
$847$	−22.9934			−0.790063
$848$	7.08859	+	23.8971i	0.243423	+	0.820631i
$849$		0			0
$850$	−17.7923	+	11.3648i	−0.610270	+	0.389809i
$851$	48.7244	+	48.7244i	1.67025	+	1.67025i
$852$		0			0
$853$	26.8053	+	26.8053i	0.917795	+	0.917795i	0.996869	−	0.0790740i	$-0.0251963\pi$
$853$	26.8053	+	26.8053i	0.917795	+	0.917795i	−0.0790740	+	0.996869i	$0.525196\pi$
$854$	−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	$0.800202\pi$
$860$	37.4464	−	11.3449i	1.27691	−	0.386857i
$861$		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
$875$	−33.8159	+	1.93901i	−1.14318	+	0.0655507i
$876$		0			0
$877$	18.5212	−	18.5212i	0.625417	−	0.625417i	−0.321494	−	0.946911i	$-0.604185\pi$
$877$	18.5212	−	18.5212i	0.625417	−	0.625417i	0.946911	+	0.321494i	$0.104185\pi$
$878$	−37.9571	−	21.5798i	−1.28099	−	0.728282i
$879$		0			0
$880$	−12.2004	−	11.1343i	−0.411276	−	0.375338i
$881$			12.3100i			0.414735i	0.978263	+	0.207368i	$0.0664896\pi$
$881$			12.3100i			0.414735i	−0.978263	+	0.207368i	$0.933510\pi$
$882$		0			0
$883$	−6.84210	−	6.84210i	−0.230255	−	0.230255i	0.582544	−	0.812799i	$-0.302057\pi$
$883$	−6.84210	−	6.84210i	−0.230255	−	0.230255i	−0.812799	+	0.582544i	$0.802057\pi$
$884$	−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
$890$	24.0366	−	0.618674i	0.805708	−	0.0207380i
$891$		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	−0.948783	−	0.315930i	$-0.897684\pi$
$907$	−19.0593	+	19.0593i	−0.632853	+	0.632853i	0.315930	+	0.948783i	$0.397684\pi$
$908$	−39.5143	−	10.0273i	−1.31133	−	0.332768i
$909$		0			0
$910$	−15.3991	−	14.6262i	−0.510474	−	0.484855i
$911$	−33.6231			−1.11398			−0.556992	−	0.830518i	$-0.688045\pi$
$911$	−33.6231			−1.11398			−0.556992	+	0.830518i	$0.688045\pi$
$912$		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	$0.503014\pi$
$920$	−26.3858	−	41.8427i	−0.869915	−	1.37951i
$921$		0			0
$922$	−7.59378	+	2.08889i	−0.250088	+	0.0687940i
$923$	−21.8967	−	21.8967i	−0.720738	−	0.720738i
$924$		0			0
$925$	−42.0825	+	13.0169i	−1.38366	+	0.427994i
$926$	−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	$-0.918829\pi$
$929$		−	15.3771i		−	0.504506i	0.967661	−	0.252253i	$-0.0811714\pi$
$930$		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	$-0.697222\pi$
$937$	−35.5511			−1.16140			−0.580702	+	0.814117i	$0.697222\pi$
$938$	−7.59314	+	2.08872i	−0.247925	+	0.0681990i
$939$		0			0
$940$	−12.3950	+	23.1698i	−0.404279	+	0.755714i
$941$	11.8428	−	11.8428i	0.386065	−	0.386065i	−0.487216	−	0.873281i	$-0.661988\pi$
$941$	11.8428	−	11.8428i	0.386065	−	0.386065i	0.873281	+	0.487216i	$0.161988\pi$
$942$		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
$950$	−2.70831	+	12.2857i	−0.0878693	+	0.398602i
$951$		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
$955$	−39.1233	+	23.5950i	−1.26600	+	0.763517i
$956$	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
$965$	0.124713	+	0.206789i	0.00401467	+	0.00665679i
$966$		0			0
$967$		−	16.3210i		−	0.524847i	−0.964953	−	0.262424i	$-0.915478\pi$
$967$		−	16.3210i		−	0.524847i	0.964953	−	0.262424i	$-0.0845218\pi$
$968$	21.4627	−	0.427632i	0.689837	−	0.0137446i
$969$		0			0
$970$	−0.789359	−	30.6680i	−0.0253448	−	0.984691i
$971$	5.74815	−	5.74815i	0.184467	−	0.184467i	−0.608832	−	0.793299i	$-0.708362\pi$
$971$	5.74815	−	5.74815i	0.184467	−	0.184467i	0.793299	+	0.608832i	$0.208362\pi$
$972$		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
$980$	8.58927	+	4.59494i	0.274374	+	0.146780i
$981$		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
$995$	51.8036	−	31.2424i	1.64228	−	0.990452i
$996$		0			0
$997$	−29.7206	−	29.7206i	−0.941260	−	0.941260i	0.0571081	−	0.998368i	$-0.481812\pi$
$997$	−29.7206	−	29.7206i	−0.941260	−	0.941260i	−0.998368	+	0.0571081i	$0.981812\pi$
$998$	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.179.9	✓	96
3.2	odd	2	inner	720.2.u.a.179.40	yes	96
4.3	odd	2		2880.2.u.a.2159.8		96
5.4	even	2	inner	720.2.u.a.179.39	yes	96
12.11	even	2		2880.2.u.a.2159.41		96
15.14	odd	2	inner	720.2.u.a.179.10	yes	96
16.5	even	4		2880.2.u.a.719.17		96
16.11	odd	4	inner	720.2.u.a.539.10	yes	96
20.19	odd	2		2880.2.u.a.2159.32		96
48.5	odd	4		2880.2.u.a.719.32		96
48.11	even	4	inner	720.2.u.a.539.39	yes	96
60.59	even	2		2880.2.u.a.2159.17		96
80.59	odd	4	inner	720.2.u.a.539.40	yes	96
80.69	even	4		2880.2.u.a.719.41		96
240.59	even	4	inner	720.2.u.a.539.9	yes	96
240.149	odd	4		2880.2.u.a.719.8		96

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

\(f(q)\)	\(=\)	\(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.91479 + 1.15480i) q^{5} +3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +O(q^{10})\)	\(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.91479 + 1.15480i) q^{5} +3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +(3.16123 - 0.0813664i) q^{10} +(1.30581 - 1.30581i) q^{11} +(-1.56756 + 1.56756i) q^{13} +(2.11753 - 3.72457i) q^{14} +(-1.90729 + 3.51600i) q^{16} +2.98571 q^{17} +(1.25807 - 1.25807i) q^{19} +(-3.94333 - 2.10954i) q^{20} +(-2.51809 + 0.692674i) q^{22} -7.82148 q^{23} +(2.33287 - 4.42241i) q^{25} +(3.02283 - 0.831519i) q^{26} +(-5.20664 + 3.09897i) q^{28} +(-7.12073 + 7.12073i) q^{29} -0.0502896i q^{31} +(4.80238 - 2.98950i) q^{32} +(-3.67067 - 2.08689i) q^{34} +(-3.49853 - 5.80096i) q^{35} +(-6.22957 - 6.22957i) q^{37} +(-2.42603 + 0.667350i) q^{38} +(3.37351 + 5.34971i) q^{40} -4.05554 q^{41} +(-6.18655 + 6.18655i) q^{43} +(3.57992 + 0.908456i) q^{44} +(9.61583 + 5.46689i) q^{46} -5.87568i q^{47} -2.17818 q^{49} +(-5.95914 + 3.80639i) q^{50} +(-4.29751 - 1.09055i) q^{52} +(4.40639 - 4.40639i) q^{53} +(-0.992408 + 4.00831i) q^{55} +(8.56716 - 0.170696i) q^{56} +(13.7314 - 3.77723i) q^{58} +(-8.20735 + 8.20735i) q^{59} +(-4.93899 - 4.93899i) q^{61} +(-0.0351503 + 0.0618267i) q^{62} +(-7.99365 + 0.318664i) q^{64} +(1.19133 - 4.81176i) q^{65} +(-1.29973 - 1.29973i) q^{67} +(3.05413 + 5.13129i) q^{68} +(0.246504 + 9.57711i) q^{70} +13.9687i q^{71} +3.85841 q^{73} +(3.30451 + 12.0129i) q^{74} +(3.44904 + 0.875242i) q^{76} +(3.95602 + 3.95602i) q^{77} +1.07096i q^{79} +(-0.408208 - 8.93495i) q^{80} +(4.98593 + 2.83465i) q^{82} +(-7.16503 + 7.16503i) q^{83} +(-5.71702 + 3.44790i) q^{85} +(11.9300 - 3.28169i) q^{86} +(-3.76623 - 3.61909i) q^{88} +7.60356 q^{89} +(-4.74899 - 4.74899i) q^{91} +(-8.00071 - 13.4421i) q^{92} +(-4.10686 + 7.22364i) q^{94} +(-0.956125 + 3.86176i) q^{95} -9.70129i q^{97} +(2.67788 + 1.52245i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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