LMFDB - Embedded newform 720.2.u.a.539.14

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			539.14
Character	$\chi$	$=$	720.539
Dual form			720.2.u.a.179.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.956592 - 1.04160i) q^{2} +(-0.169864 + 1.99277i) q^{4} +(1.93984 + 1.11222i) q^{5} -1.78786i q^{7} +(2.23816 - 1.72934i) q^{8} +O(q^{10})$	\(q+(-0.956592 - 1.04160i) q^{2} +(-0.169864 + 1.99277i) q^{4} +(1.93984 + 1.11222i) q^{5} -1.78786i q^{7} +(2.23816 - 1.72934i) q^{8} +(-0.697143 - 3.08448i) q^{10} +(3.34421 + 3.34421i) q^{11} +(-2.90349 - 2.90349i) q^{13} +(-1.86224 + 1.71025i) q^{14} +(-3.94229 - 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 + 0.0693845i) q^{19} +(-2.54591 + 3.67673i) q^{20} +(0.284286 - 6.68237i) q^{22} -1.07695 q^{23} +(2.52593 + 4.31505i) q^{25} +(-0.246821 + 5.80172i) q^{26} +(3.56280 + 0.303692i) q^{28} +(-1.23988 - 1.23988i) q^{29} +8.56612i q^{31} +(3.06600 + 4.75391i) q^{32} +(-4.36907 - 4.75733i) q^{34} +(1.98849 - 3.46816i) q^{35} +(7.62458 - 7.62458i) q^{37} +(0.00589828 - 0.138644i) q^{38} +(6.26508 - 0.865308i) q^{40} +7.91601 q^{41} +(-2.35179 - 2.35179i) q^{43} +(-7.23230 + 6.09619i) q^{44} +(1.03020 + 1.12175i) q^{46} +6.32188i q^{47} +3.80356 q^{49} +(2.07827 - 6.75876i) q^{50} +(6.27919 - 5.29279i) q^{52} +(3.61429 + 3.61429i) q^{53} +(2.76772 + 10.2067i) q^{55} +(-3.09182 - 4.00152i) q^{56} +(-0.105400 + 2.47751i) q^{58} +(2.25080 + 2.25080i) q^{59} +(4.29893 - 4.29893i) q^{61} +(8.92248 - 8.19429i) q^{62} +(2.01876 - 7.74110i) q^{64} +(-2.40297 - 8.86160i) q^{65} +(-5.85271 + 5.85271i) q^{67} +(-0.775822 + 9.10164i) q^{68} +(-5.51461 + 1.24639i) q^{70} -15.1431i q^{71} -6.88118 q^{73} +(-15.2354 - 0.648155i) q^{74} +(-0.150054 + 0.126482i) q^{76} +(5.97897 - 5.97897i) q^{77} -12.9721i q^{79} +(-6.89443 - 5.69797i) q^{80} +(-7.57239 - 8.24532i) q^{82} +(-6.88840 - 6.88840i) q^{83} +(8.85986 + 5.07987i) q^{85} +(-0.199923 + 4.69933i) q^{86} +(13.2682 + 1.70161i) q^{88} +6.31609 q^{89} +(-5.19103 + 5.19103i) q^{91} +(0.182935 - 2.14612i) q^{92} +(6.58487 - 6.04746i) q^{94} +(0.0574238 + 0.211766i) q^{95} -4.56728i q^{97} +(-3.63845 - 3.96179i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.956592	−	1.04160i	−0.676413	−	0.736523i
$2$	−0.956592	−	1.04160i	−0.676413	−	0.736523i
$3$		0			0
$3$		0			0
$4$	−0.169864	+	1.99277i	−0.0849318	+	0.996387i
$5$	1.93984	+	1.11222i	0.867521	+	0.497400i
$5$	1.93984	+	1.11222i	0.867521	+	0.497400i
$6$		0			0
$7$		−	1.78786i		−	0.675747i	−0.941191	−	0.337874i	$-0.890292\pi$
$7$		−	1.78786i		−	0.675747i	0.941191	−	0.337874i	$-0.109708\pi$
$8$	2.23816	−	1.72934i	0.791311	−	0.611414i
$9$		0			0
$10$	−0.697143	−	3.08448i	−0.220456	−	0.975397i
$11$	3.34421	+	3.34421i	1.00832	+	1.00832i	0.999965	+	0.00835103i	$0.00265824\pi$
$11$	3.34421	+	3.34421i	1.00832	+	1.00832i	0.00835103	+	0.999965i	$0.497342\pi$
$12$		0			0
$13$	−2.90349	−	2.90349i	−0.805282	−	0.805282i	0.178634	−	0.983916i	$-0.442832\pi$
$13$	−2.90349	−	2.90349i	−0.805282	−	0.805282i	−0.983916	+	0.178634i	$0.942832\pi$
$14$	−1.86224	+	1.71025i	−0.497703	+	0.457084i
$15$		0			0
$16$	−3.94229	−	0.676999i	−0.985573	−	0.169250i
$17$	4.56733			1.10774			0.553870	−	0.832603i	$-0.313151\pi$
$17$	4.56733			1.10774			0.553870	+	0.832603i	$0.313151\pi$
$18$		0			0
$19$	0.0693845	+	0.0693845i	0.0159179	+	0.0159179i	0.715021	−	0.699103i	$-0.246417\pi$
$19$	0.0693845	+	0.0693845i	0.0159179	+	0.0159179i	−0.699103	+	0.715021i	$0.746417\pi$
$20$	−2.54591	+	3.67673i	−0.569283	+	0.822142i
$21$		0			0
$22$	0.284286	−	6.68237i	0.0606100	−	1.42469i
$23$	−1.07695			−0.224560			−0.112280	−	0.993677i	$-0.535815\pi$
$23$	−1.07695			−0.224560			−0.112280	+	0.993677i	$0.535815\pi$
$24$		0			0
$25$	2.52593	+	4.31505i	0.505186	+	0.863010i
$26$	−0.246821	+	5.80172i	−0.0484056	+	1.13781i
$27$		0			0
$28$	3.56280	+	0.303692i	0.673306	+	0.0573924i
$29$	−1.23988	−	1.23988i	−0.230239	−	0.230239i	0.582553	−	0.812792i	$-0.302054\pi$
$29$	−1.23988	−	1.23988i	−0.230239	−	0.230239i	−0.812792	+	0.582553i	$0.802054\pi$
$30$		0			0
$31$			8.56612i			1.53852i	0.638935	+	0.769261i	$0.279375\pi$
$31$			8.56612i			1.53852i	−0.638935	+	0.769261i	$0.720625\pi$
$32$	3.06600	+	4.75391i	0.541998	+	0.840380i
$33$		0			0
$34$	−4.36907	−	4.75733i	−0.749289	−	0.815875i
$35$	1.98849	−	3.46816i	0.336117	−	0.586225i
$36$		0			0
$37$	7.62458	−	7.62458i	1.25347	−	1.25347i	0.299321	−	0.954153i	$-0.403240\pi$
$37$	7.62458	−	7.62458i	1.25347	−	1.25347i	0.954153	−	0.299321i	$-0.0967600\pi$
$38$	0.00589828	−	0.138644i	0.000956828	−	0.0224910i
$39$		0			0
$40$	6.26508	−	0.865308i	0.990596	−	0.136817i
$41$	7.91601			1.23627			0.618137	−	0.786071i	$-0.287888\pi$
$41$	7.91601			1.23627			0.618137	+	0.786071i	$0.287888\pi$
$42$		0			0
$43$	−2.35179	−	2.35179i	−0.358645	−	0.358645i	0.504668	−	0.863313i	$-0.331615\pi$
$43$	−2.35179	−	2.35179i	−0.358645	−	0.358645i	−0.863313	+	0.504668i	$0.831615\pi$
$44$	−7.23230	+	6.09619i	−1.09031	+	0.919035i
$45$		0			0
$46$	1.03020	+	1.12175i	0.151895	+	0.165394i
$47$			6.32188i			0.922141i	0.887364	+	0.461070i	$0.152534\pi$
$47$			6.32188i			0.922141i	−0.887364	+	0.461070i	$0.847466\pi$
$48$		0			0
$49$	3.80356			0.543365
$50$	2.07827	−	6.75876i	0.293912	−	0.955832i
$51$		0			0
$52$	6.27919	−	5.29279i	0.870766	−	0.733978i
$53$	3.61429	+	3.61429i	0.496461	+	0.496461i	0.910334	−	0.413874i	$-0.135824\pi$
$53$	3.61429	+	3.61429i	0.496461	+	0.496461i	−0.413874	+	0.910334i	$0.635824\pi$
$54$		0			0
$55$	2.76772	+	10.2067i	0.373199	+	1.37627i
$56$	−3.09182	−	4.00152i	−0.413162	−	0.534726i
$57$		0			0
$58$	−0.105400	+	2.47751i	−0.0138397	+	0.325313i
$59$	2.25080	+	2.25080i	0.293030	+	0.293030i	0.838276	−	0.545246i	$-0.183564\pi$
$59$	2.25080	+	2.25080i	0.293030	+	0.293030i	−0.545246	+	0.838276i	$0.683564\pi$
$60$		0			0
$61$	4.29893	−	4.29893i	0.550421	−	0.550421i	−0.376141	−	0.926562i	$-0.622749\pi$
$61$	4.29893	−	4.29893i	0.550421	−	0.550421i	0.926562	+	0.376141i	$0.122749\pi$
$62$	8.92248	−	8.19429i	1.13316	−	1.04068i
$63$		0			0
$64$	2.01876	−	7.74110i	0.252345	−	0.967637i
$65$	−2.40297	−	8.86160i	−0.298052	−	1.09915i
$66$		0			0
$67$	−5.85271	+	5.85271i	−0.715022	+	0.715022i	−0.967581	−	0.252559i	$-0.918728\pi$
$67$	−5.85271	+	5.85271i	−0.715022	+	0.715022i	0.252559	+	0.967581i	$0.418728\pi$
$68$	−0.775822	+	9.10164i	−0.0940822	+	1.10374i
$69$		0			0
$70$	−5.51461	+	1.24639i	−0.659122	+	0.148973i
$71$		−	15.1431i		−	1.79716i	−0.438812	−	0.898579i	$-0.644601\pi$
$71$		−	15.1431i		−	1.79716i	0.438812	−	0.898579i	$-0.355399\pi$
$72$		0			0
$73$	−6.88118			−0.805381			−0.402691	−	0.915336i	$-0.631925\pi$
$73$	−6.88118			−0.805381			−0.402691	+	0.915336i	$0.631925\pi$
$74$	−15.2354	−	0.648155i	−1.77108	−	0.0753465i
$75$		0			0
$76$	−0.150054	+	0.126482i	−0.0172123	+	0.0145085i
$77$	5.97897	−	5.97897i	0.681367	−	0.681367i
$78$		0			0
$79$		−	12.9721i		−	1.45947i	−0.683730	−	0.729735i	$-0.739643\pi$
$79$		−	12.9721i		−	1.45947i	0.683730	−	0.729735i	$-0.260357\pi$
$80$	−6.89443	−	5.69797i	−0.770821	−	0.637052i
$81$		0			0
$82$	−7.57239	−	8.24532i	−0.836231	−	0.910544i
$83$	−6.88840	−	6.88840i	−0.756100	−	0.756100i	0.219510	−	0.975610i	$-0.429554\pi$
$83$	−6.88840	−	6.88840i	−0.756100	−	0.756100i	−0.975610	+	0.219510i	$0.929554\pi$
$84$		0			0
$85$	8.85986	+	5.07987i	0.960987	+	0.550989i
$86$	−0.199923	+	4.69933i	−0.0215582	+	0.506742i
$87$		0			0
$88$	13.2682	+	1.70161i	1.41439	+	0.181392i
$89$	6.31609			0.669504			0.334752	−	0.942306i	$-0.391347\pi$
$89$	6.31609			0.669504			0.334752	+	0.942306i	$0.391347\pi$
$90$		0			0
$91$	−5.19103	+	5.19103i	−0.544167	+	0.544167i
$92$	0.182935	−	2.14612i	0.0190723	−	0.223749i
$93$		0			0
$94$	6.58487	−	6.04746i	0.679178	−	0.623748i
$95$	0.0574238	+	0.211766i	0.00589155	+	0.0217267i
$96$		0			0
$97$		−	4.56728i		−	0.463737i	−0.972747	−	0.231869i	$-0.925516\pi$
$97$		−	4.56728i		−	0.463737i	0.972747	−	0.231869i	$-0.0744839\pi$
$98$	−3.63845	−	3.96179i	−0.367539	−	0.400201i
$99$		0			0
$100$	−9.02798	+	4.30064i	−0.902798	+	0.430064i
$101$	−6.24690	+	6.24690i	−0.621589	+	0.621589i	−0.945938	−	0.324348i	$-0.894855\pi$
$101$	−6.24690	+	6.24690i	−0.621589	+	0.621589i	0.324348	+	0.945938i	$0.394855\pi$
$102$		0			0
$103$			13.8548i			1.36515i	0.730815	+	0.682576i	$0.239140\pi$
$103$			13.8548i			1.36515i	−0.730815	+	0.682576i	$0.760860\pi$
$104$	−11.5196	−	1.47736i	−1.12959	−	0.144867i
$105$		0			0
$106$	0.307245	−	7.22204i	0.0298423	−	0.701467i
$107$	0.922209	−	0.922209i	0.0891533	−	0.0891533i	−0.661124	−	0.750277i	$-0.729920\pi$
$107$	0.922209	−	0.922209i	0.0891533	−	0.0891533i	0.750277	+	0.661124i	$0.229920\pi$
$108$		0			0
$109$	−2.28662	+	2.28662i	−0.219019	+	0.219019i	−0.808085	−	0.589066i	$-0.799496\pi$
$109$	−2.28662	+	2.28662i	−0.219019	+	0.219019i	0.589066	+	0.808085i	$0.299496\pi$
$110$	7.98373	−	12.6465i	0.761219	−	1.20580i
$111$		0			0
$112$	−1.21038	+	7.04827i	−0.114370	+	0.665999i
$113$	7.53772			0.709089			0.354544	−	0.935039i	$-0.384636\pi$
$113$	7.53772			0.709089			0.354544	+	0.935039i	$0.384636\pi$
$114$		0			0
$115$	−2.08911	−	1.19781i	−0.194811	−	0.111696i
$116$	2.68140	−	2.26018i	0.248962	−	0.209853i
$117$		0			0
$118$	0.191338	−	4.49754i	0.0176141	−	0.414032i
$119$		−	8.16574i		−	0.748552i
$120$		0			0
$121$			11.3674i			1.03340i
$122$	−8.59008	−	0.365446i	−0.777710	−	0.0330859i
$123$		0			0
$124$	−17.0703	−	1.45507i	−1.53296	−	0.130669i
$125$	0.100608	+	11.1799i	0.00899866	+	0.999960i
$126$		0			0
$127$	0.00277854			0.000246555			0.000123278	−	1.00000i	$-0.499961\pi$
$127$	0.00277854			0.000246555			0.000123278		1.00000i	$0.499961\pi$
$128$	−9.99426	+	5.30233i	−0.883376	+	0.468665i
$129$		0			0
$130$	−6.93159	+	10.9799i	−0.607940	+	0.962999i
$131$	8.71989	−	8.71989i	0.761860	−	0.761860i	−0.214798	−	0.976658i	$-0.568909\pi$
$131$	8.71989	−	8.71989i	0.761860	−	0.761860i	0.976658	+	0.214798i	$0.0689095\pi$
$132$		0			0
$133$	0.124050	−	0.124050i	0.0107565	−	0.0107565i
$134$	11.6948	+	0.497531i	1.01028	+	0.0429801i
$135$		0			0
$136$	10.2224	−	7.89846i	0.876566	−	0.677288i
$137$			23.1771i			1.98016i	0.140516	+	0.990078i	$0.455124\pi$
$137$			23.1771i			1.98016i	−0.140516	+	0.990078i	$0.544876\pi$
$138$		0			0
$139$	−7.85331	+	7.85331i	−0.666109	+	0.666109i	−0.956813	−	0.290704i	$-0.906111\pi$
$139$	−7.85331	+	7.85331i	−0.666109	+	0.666109i	0.290704	+	0.956813i	$0.406111\pi$
$140$	6.57348	+	4.55173i	0.555560	+	0.384691i
$141$		0			0
$142$	−15.7731	+	14.4858i	−1.32365	+	1.21562i
$143$		−	19.4197i		−	1.62396i
$144$		0			0
$145$	−1.02614	−	3.78417i	−0.0852164	−	0.314258i
$146$	6.58248	+	7.16744i	0.544770	+	0.593182i
$147$		0			0
$148$	13.8989	+	16.4892i	1.14248	+	1.35540i
$149$	−13.6076	+	13.6076i	−1.11478	+	1.11478i	−0.122285	+	0.992495i	$0.539022\pi$
$149$	−13.6076	+	13.6076i	−1.11478	+	1.11478i	−0.992495	+	0.122285i	$0.960978\pi$
$150$		0			0
$151$	15.2447			1.24059			0.620297	−	0.784367i	$-0.287012\pi$
$151$	15.2447			1.24059			0.620297	+	0.784367i	$0.287012\pi$
$152$	0.275284	+	0.0353044i	0.0223284	+	0.00286357i
$153$		0			0
$154$	−11.9471	−	0.508264i	−0.962728	−	0.0409571i
$155$	−9.52742	+	16.6169i	−0.765261	+	1.33470i
$156$		0			0
$157$	−5.76894	−	5.76894i	−0.460411	−	0.460411i	0.438379	−	0.898790i	$-0.355553\pi$
$157$	−5.76894	−	5.76894i	−0.460411	−	0.460411i	−0.898790	+	0.438379i	$0.855553\pi$
$158$	−13.5117	+	12.4090i	−1.07493	+	0.987204i
$159$		0			0
$160$	0.660154	+	12.6319i	0.0521898	+	0.998637i
$161$			1.92544i			0.151746i
$162$		0			0
$163$	−10.4511	+	10.4511i	−0.818594	+	0.818594i	−0.985904	−	0.167311i	$-0.946492\pi$
$163$	−10.4511	+	10.4511i	−0.818594	+	0.818594i	0.167311	+	0.985904i	$0.446492\pi$
$164$	−1.34464	+	15.7748i	−0.104999	+	1.23181i
$165$		0			0
$166$	−0.585573	+	13.7644i	−0.0454493	+	1.06832i
$167$	−9.41872			−0.728842			−0.364421	−	0.931234i	$-0.618733\pi$
$167$	−9.41872			−0.728842			−0.364421	+	0.931234i	$0.618733\pi$
$168$		0			0
$169$			3.86046i			0.296958i
$170$	−3.18408	−	14.0878i	−0.244208	−	1.08049i
$171$		0			0
$172$	5.08607	−	4.28711i	0.387810	−	0.326889i
$173$	6.21995	−	6.21995i	0.472894	−	0.472894i	−0.429956	−	0.902850i	$-0.641471\pi$
$173$	6.21995	−	6.21995i	0.472894	−	0.472894i	0.902850	+	0.429956i	$0.141471\pi$
$174$		0			0
$175$	7.71471	−	4.51601i	0.583177	−	0.341378i
$176$	−10.9198	−	15.4479i	−0.823112	−	1.16443i
$177$		0			0
$178$	−6.04192	−	6.57884i	−0.452861	−	0.493105i
$179$	−18.4020	+	18.4020i	−1.37543	+	1.37543i	−0.523251	+	0.852179i	$0.675281\pi$
$179$	−18.4020	+	18.4020i	−1.37543	+	1.37543i	−0.852179	+	0.523251i	$0.824719\pi$
$180$		0			0
$181$	−18.5731	−	18.5731i	−1.38053	−	1.38053i	−0.843677	−	0.536851i	$-0.819614\pi$
$181$	−18.5731	−	18.5731i	−1.38053	−	1.38053i	−0.536851	−	0.843677i	$-0.680386\pi$
$182$	10.3727	+	0.441282i	0.768873	+	0.0327100i
$183$		0			0
$184$	−2.41040	+	1.86242i	−0.177697	+	0.137299i
$185$	23.2707	−	6.31023i	1.71089	−	0.463937i
$186$		0			0
$187$	15.2741	+	15.2741i	1.11695	+	1.11695i
$188$	−12.5981	−	1.07386i	−0.918809	−	0.0783190i
$189$		0			0
$190$	0.165644	−	0.262386i	0.0120171	−	0.0190355i
$191$	4.73383			0.342528			0.171264	−	0.985225i	$-0.445215\pi$
$191$	4.73383			0.342528			0.171264	+	0.985225i	$0.445215\pi$
$192$		0			0
$193$		−	16.7218i		−	1.20366i	−0.798625	−	0.601829i	$-0.794439\pi$
$193$		−	16.7218i		−	1.20366i	0.798625	−	0.601829i	$-0.205561\pi$
$194$	−4.75728	+	4.36902i	−0.341553	+	0.313678i
$195$		0			0
$196$	−0.646086	+	7.57963i	−0.0461490	+	0.541402i
$197$	−7.93066	−	7.93066i	−0.565036	−	0.565036i	0.365698	−	0.930734i	$-0.380830\pi$
$197$	−7.93066	−	7.93066i	−0.565036	−	0.565036i	−0.930734	+	0.365698i	$0.880830\pi$
$198$		0			0
$199$	−2.34717			−0.166386			−0.0831932	−	0.996533i	$-0.526512\pi$
$199$	−2.34717			−0.166386			−0.0831932	+	0.996533i	$0.526512\pi$
$200$	13.1156	+	5.28959i	0.927416	+	0.374031i
$201$		0			0
$202$	12.4825	+	0.531040i	0.878266	+	0.0373638i
$203$	−2.21672	+	2.21672i	−0.155583	+	0.155583i
$204$		0			0
$205$	15.3558	+	8.80435i	1.07249	+	0.614922i
$206$	14.4311	−	13.2534i	1.00547	−	0.923406i
$207$		0			0
$208$	9.48073	+	13.4120i	0.657371	+	0.929958i
$209$			0.464072i			0.0321006i
$210$		0			0
$211$	−3.00077	−	3.00077i	−0.206581	−	0.206581i	0.596231	−	0.802813i	$-0.296664\pi$
$211$	−3.00077	−	3.00077i	−0.206581	−	0.206581i	−0.802813	+	0.596231i	$0.796664\pi$
$212$	−7.81639	+	6.58852i	−0.536832	+	0.452502i
$213$		0			0
$214$	−1.84275	−	0.0783956i	−0.125968	−	0.00535902i
$215$	−1.94638	−	7.17781i	−0.132742	−	0.489522i
$216$		0			0
$217$	15.3150			1.03965
$218$	4.56911	+	0.194382i	0.309459	+	0.0131652i
$219$		0			0
$220$	−20.8098	+	3.78169i	−1.40300	+	0.254962i
$221$	−13.2612	−	13.2612i	−0.892042	−	0.892042i
$222$		0			0
$223$	−24.6842			−1.65298			−0.826489	−	0.562952i	$-0.809665\pi$
$223$	−24.6842			−1.65298			−0.826489	+	0.562952i	$0.809665\pi$
$224$	8.49932	−	5.48158i	0.567885	−	0.366254i
$225$		0			0
$226$	−7.21052	−	7.85129i	−0.479637	−	0.522260i
$227$	−5.05360	−	5.05360i	−0.335419	−	0.335419i	0.519221	−	0.854640i	$-0.326222\pi$
$227$	−5.05360	−	5.05360i	−0.335419	−	0.335419i	−0.854640	+	0.519221i	$0.826222\pi$
$228$		0			0
$229$	−13.4816	−	13.4816i	−0.890886	−	0.890886i	0.103720	−	0.994606i	$-0.466925\pi$
$229$	−13.4816	−	13.4816i	−0.890886	−	0.890886i	−0.994606	+	0.103720i	$0.966925\pi$
$230$	0.750789	+	3.32183i	0.0495056	+	0.219035i
$231$		0			0
$232$	−4.91921	−	0.630877i	−0.322962	−	0.0414191i
$233$		−	11.8466i		−	0.776096i	−0.921639	−	0.388048i	$-0.873149\pi$
$233$		−	11.8466i		−	0.776096i	0.921639	−	0.388048i	$-0.126851\pi$
$234$		0			0
$235$	−7.03132	+	12.2634i	−0.458673	+	0.799977i
$236$	−4.86767	+	4.10301i	−0.316858	+	0.267083i
$237$		0			0
$238$	−8.50544	+	7.81128i	−0.551326	+	0.506330i
$239$	−24.8620			−1.60819			−0.804093	−	0.594503i	$-0.797349\pi$
$239$	−24.8620			−1.60819			−0.804093	+	0.594503i	$0.797349\pi$
$240$		0			0
$241$	18.8396			1.21356			0.606782	−	0.794868i	$-0.292460\pi$
$241$	18.8396			1.21356			0.606782	+	0.794868i	$0.292460\pi$
$242$	11.8403	−	10.8740i	0.761125	−	0.699007i
$243$		0			0
$244$	7.83656	+	9.29702i	0.501684	+	0.595181i
$245$	7.37828	+	4.23039i	0.471381	+	0.270270i
$246$		0			0
$247$		−	0.402914i		−	0.0256368i
$248$	14.8138	+	19.1724i	0.940674	+	1.21745i
$249$		0			0
$250$	11.5487	−	10.7994i	0.730406	−	0.683013i
$251$	21.6723	+	21.6723i	1.36795	+	1.36795i	0.863364	+	0.504582i	$0.168353\pi$
$251$	21.6723	+	21.6723i	1.36795	+	1.36795i	0.504582	+	0.863364i	$0.331647\pi$
$252$		0			0
$253$	−3.60155	−	3.60155i	−0.226428	−	0.226428i
$254$	−0.00265793	−	0.00289413i	−0.000166773	−	0.000181594i
$255$		0			0
$256$	15.0833	+	5.33786i	0.942709	+	0.333616i
$257$	0.914423			0.0570402			0.0285201	−	0.999593i	$-0.490921\pi$
$257$	0.914423			0.0570402			0.0285201	+	0.999593i	$0.490921\pi$
$258$		0			0
$259$	−13.6317	−	13.6317i	−0.847031	−	0.847031i
$260$	18.0673	−	3.28332i	1.12049	−	0.203623i
$261$		0			0
$262$	−17.4240	−	0.741265i	−1.07646	−	0.0457955i
$263$	1.19643			0.0737752			0.0368876	−	0.999319i	$-0.488256\pi$
$263$	1.19643			0.0737752			0.0368876	+	0.999319i	$0.488256\pi$
$264$		0			0
$265$	2.99124	+	11.0310i	0.183751	+	0.677630i
$266$	−0.247875	−	0.0105453i	−0.0151982	−	0.000646574i
$267$		0			0
$268$	−10.6690	−	12.6573i	−0.651711	−	0.773167i
$269$	−7.54542	−	7.54542i	−0.460053	−	0.460053i	0.438620	−	0.898673i	$-0.355467\pi$
$269$	−7.54542	−	7.54542i	−0.460053	−	0.460053i	−0.898673	+	0.438620i	$0.855467\pi$
$270$		0			0
$271$		−	4.45852i		−	0.270836i	−0.990789	−	0.135418i	$-0.956762\pi$
$271$		−	4.45852i		−	0.270836i	0.990789	−	0.135418i	$-0.0432377\pi$
$272$	−18.0057	−	3.09207i	−1.09176	−	0.187485i
$273$		0			0
$274$	24.1413	−	22.1711i	1.45843	−	1.33940i
$275$	−5.98318	+	22.8777i	−0.360800	+	1.37957i
$276$		0			0
$277$	−5.28152	+	5.28152i	−0.317336	+	0.317336i	−0.847743	−	0.530407i	$-0.822039\pi$
$277$	−5.28152	+	5.28152i	−0.317336	+	0.317336i	0.530407	+	0.847743i	$0.322039\pi$
$278$	15.6924	+	0.667599i	0.941169	+	0.0400399i
$279$		0			0
$280$	−1.54705	−	11.2011i	−0.0924539	−	0.669393i
$281$	−26.3280			−1.57060			−0.785298	−	0.619118i	$-0.787490\pi$
$281$	−26.3280			−1.57060			−0.785298	+	0.619118i	$0.787490\pi$
$282$		0			0
$283$	−13.6186	−	13.6186i	−0.809540	−	0.809540i	0.175024	−	0.984564i	$-0.444000\pi$
$283$	−13.6186	−	13.6186i	−0.809540	−	0.809540i	−0.984564	+	0.175024i	$0.944000\pi$
$284$	30.1768	+	2.57226i	1.79066	+	0.152636i
$285$		0			0
$286$	−20.2276	+	18.5767i	−1.19608	+	1.09847i
$287$		−	14.1527i		−	0.835409i
$288$		0			0
$289$	3.86046			0.227086
$290$	−2.96000	+	4.68874i	−0.173817	+	0.275332i
$291$		0			0
$292$	1.16886	−	13.7126i	0.0684024	−	0.802471i
$293$	−9.23746	−	9.23746i	−0.539658	−	0.539658i	0.383770	−	0.923429i	$-0.374625\pi$
$293$	−9.23746	−	9.23746i	−0.539658	−	0.539658i	−0.923429	+	0.383770i	$0.874625\pi$
$294$		0			0
$295$	1.86280	+	6.86958i	0.108457	+	0.399962i
$296$	3.87956	−	30.2506i	0.225495	−	1.75828i
$297$		0			0
$298$	27.1907	+	1.15676i	1.57511	+	0.0670096i
$299$	3.12692	+	3.12692i	0.180834	+	0.180834i
$300$		0			0
$301$	−4.20468	+	4.20468i	−0.242353	+	0.242353i
$302$	−14.5829	−	15.8789i	−0.839153	−	0.913725i
$303$		0			0
$304$	−0.226561	−	0.320507i	−0.0129942	−	0.0183824i
$305$	13.1206	−	3.55786i	0.751282	−	0.203723i
$306$		0			0
$307$	−2.37148	+	2.37148i	−0.135348	+	0.135348i	−0.771535	−	0.636187i	$-0.780511\pi$
$307$	−2.37148	+	2.37148i	−0.135348	+	0.135348i	0.636187	+	0.771535i	$0.280511\pi$
$308$	10.8991	+	12.9303i	0.621035	+	0.736775i
$309$		0			0
$310$	26.4220	−	5.97181i	1.50067	−	0.339176i
$311$		−	14.5352i		−	0.824214i	−0.911135	−	0.412107i	$-0.864793\pi$
$311$		−	14.5352i		−	0.824214i	0.911135	−	0.412107i	$-0.135207\pi$
$312$		0			0
$313$	−21.2104			−1.19888			−0.599442	−	0.800418i	$-0.704611\pi$
$313$	−21.2104			−1.19888			−0.599442	+	0.800418i	$0.704611\pi$
$314$	−0.490409	+	11.5274i	−0.0276754	+	0.650531i
$315$		0			0
$316$	25.8504	+	2.20348i	1.45420	+	0.123955i
$317$	0.575423	−	0.575423i	0.0323190	−	0.0323190i	−0.690763	−	0.723082i	$-0.742725\pi$
$317$	0.575423	−	0.575423i	0.0323190	−	0.0323190i	0.723082	+	0.690763i	$0.242725\pi$
$318$		0			0
$319$		−	8.29280i		−	0.464308i
$320$	12.5259	−	12.7712i	0.700217	−	0.713930i
$321$		0			0
$322$	2.00554	−	1.84186i	0.111764	−	0.102643i
$323$	0.316902	+	0.316902i	0.0176329	+	0.0176329i
$324$		0			0
$325$	5.19468	−	19.8627i	0.288149	−	1.10178i
$326$	20.8833	+	0.888433i	1.15662	+	0.0492058i
$327$		0			0
$328$	17.7173	−	13.6895i	0.978276	−	0.755875i
$329$	11.3026			0.623134
$330$		0			0
$331$	5.54595	−	5.54595i	0.304833	−	0.304833i	−0.538068	−	0.842901i	$-0.680846\pi$
$331$	5.54595	−	5.54595i	0.304833	−	0.304833i	0.842901	+	0.538068i	$0.180846\pi$
$332$	14.8971	−	12.5569i	0.817585	−	0.689151i
$333$		0			0
$334$	9.00987	+	9.81054i	0.492998	+	0.536809i
$335$	−17.8628	+	4.84380i	−0.975949	+	0.264645i
$336$		0			0
$337$			16.3650i			0.891460i	0.895167	+	0.445730i	$0.147056\pi$
$337$			16.3650i			0.891460i	−0.895167	+	0.445730i	$0.852944\pi$
$338$	4.02106	−	3.69289i	0.218717	−	0.200866i
$339$		0			0
$340$	−11.6280	+	16.7928i	−0.630617	+	0.910718i
$341$	−28.6469	+	28.6469i	−1.55132	+	1.55132i
$342$		0			0
$343$		−	19.3152i		−	1.04293i
$344$	−9.33075	−	1.19665i	−0.503080	−	0.0645188i
$345$		0			0
$346$	−12.4287	−	0.528749i	−0.668168	−	0.0284257i
$347$	−18.6768	+	18.6768i	−1.00262	+	1.00262i	−0.00262421	+	0.999997i	$0.500835\pi$
$347$	−18.6768	+	18.6768i	−1.00262	+	1.00262i	−0.999997	+	0.00262421i	$0.999165\pi$
$348$		0			0
$349$	15.2350	−	15.2350i	0.815511	−	0.815511i	−0.169943	−	0.985454i	$-0.554358\pi$
$349$	15.2350	−	15.2350i	0.815511	−	0.815511i	0.985454	+	0.169943i	$0.0543583\pi$
$350$	−12.0837	−	3.71566i	−0.645901	−	0.198610i
$351$		0			0
$352$	−5.64470	+	26.1514i	−0.300863	+	1.39387i
$353$	8.23255			0.438175			0.219087	−	0.975705i	$-0.429692\pi$
$353$	8.23255			0.438175			0.219087	+	0.975705i	$0.429692\pi$
$354$		0			0
$355$	16.8425	−	29.3752i	0.893906	−	1.55907i
$356$	−1.07287	+	12.5865i	−0.0568621	+	0.667085i
$357$		0			0
$358$	36.7707	+	1.56433i	1.94339	+	0.0826773i
$359$			4.96843i			0.262224i	0.991368	+	0.131112i	$0.0418547\pi$
$359$			4.96843i			0.262224i	−0.991368	+	0.131112i	$0.958145\pi$
$360$		0			0
$361$		−	18.9904i		−	0.999493i
$362$	−1.57887	+	37.1126i	−0.0829837	+	1.95060i
$363$		0			0
$364$	−9.46277	−	11.2263i	−0.495984	−	0.588418i
$365$	−13.3484	−	7.65339i	−0.698685	−	0.400597i
$366$		0			0
$367$	25.3790			1.32477			0.662385	−	0.749163i	$-0.269544\pi$
$367$	25.3790			1.32477			0.662385	+	0.749163i	$0.269544\pi$
$368$	4.24566	+	0.729096i	0.221320	+	0.0380067i
$369$		0			0
$370$	−28.8333	−	18.2024i	−1.49897	−	0.946298i
$371$	6.46184	−	6.46184i	0.335482	−	0.335482i
$372$		0			0
$373$	2.85715	−	2.85715i	0.147938	−	0.147938i	−0.629259	−	0.777196i	$-0.716641\pi$
$373$	2.85715	−	2.85715i	0.147938	−	0.147938i	0.777196	+	0.629259i	$0.216641\pi$
$374$	1.29843	−	30.5205i	0.0671401	−	1.57818i
$375$		0			0
$376$	10.9327	+	14.1494i	0.563810	+	0.729700i
$377$			7.19992i			0.370815i
$378$		0			0
$379$	−8.96148	+	8.96148i	−0.460320	+	0.460320i	−0.898760	−	0.438440i	$-0.855531\pi$
$379$	−8.96148	+	8.96148i	−0.460320	+	0.460320i	0.438440	+	0.898760i	$0.355531\pi$
$380$	−0.431755	+	0.0784613i	−0.0221486	+	0.00402498i
$381$		0			0
$382$	−4.52834	−	4.93076i	−0.231690	−	0.252280i
$383$			9.83688i			0.502641i	0.967904	+	0.251321i	$0.0808648\pi$
$383$			9.83688i			0.502641i	−0.967904	+	0.251321i	$0.919135\pi$
$384$		0			0
$385$	18.2482	−	4.94829i	0.930012	−	0.252188i
$386$	−17.4174	+	15.9959i	−0.886522	+	0.814170i
$387$		0			0
$388$	9.10156	+	0.775814i	0.462062	+	0.0393860i
$389$	−8.69886	+	8.69886i	−0.441050	+	0.441050i	−0.892365	−	0.451315i	$-0.850955\pi$
$389$	−8.69886	+	8.69886i	−0.441050	+	0.441050i	0.451315	+	0.892365i	$0.350955\pi$
$390$		0			0
$391$	−4.91879			−0.248754
$392$	8.51299	−	6.57765i	0.429971	−	0.332221i
$393$		0			0
$394$	−0.674174	+	15.8470i	−0.0339644	+	0.798359i
$395$	14.4278	−	25.1637i	0.725941	−	1.26612i
$396$		0			0
$397$	−2.52696	−	2.52696i	−0.126824	−	0.126824i	0.640845	−	0.767670i	$-0.278584\pi$
$397$	−2.52696	−	2.52696i	−0.126824	−	0.126824i	−0.767670	+	0.640845i	$0.778584\pi$
$398$	2.24528	+	2.44481i	0.112546	+	0.122547i
$399$		0			0
$400$	−7.03668	−	18.7212i	−0.351834	−	0.936062i
$401$			11.5176i			0.575161i	0.957757	+	0.287580i	$0.0928508\pi$
$401$			11.5176i			0.575161i	−0.957757	+	0.287580i	$0.907149\pi$
$402$		0			0
$403$	24.8716	−	24.8716i	1.23894	−	1.23894i
$404$	−11.3875	−	13.5098i	−0.566551	−	0.672136i
$405$		0			0
$406$	4.42944	+	0.188441i	0.219829	+	0.00935215i
$407$	50.9963			2.52779
$408$		0			0
$409$			17.5055i			0.865591i	0.901492	+	0.432795i	$0.142473\pi$
$409$			17.5055i			0.865591i	−0.901492	+	0.432795i	$0.857527\pi$
$410$	−5.51859	−	24.4167i	−0.272544	−	1.20586i
$411$		0			0
$412$	−27.6094	−	2.35342i	−1.36022	−	0.115945i
$413$	4.02412	−	4.02412i	0.198014	−	0.198014i
$414$		0			0
$415$	−5.70095	−	21.0238i	−0.279849	−	1.03202i
$416$	4.90080	−	22.7050i	0.240282	−	1.11320i
$417$		0			0
$418$	0.483378	−	0.443928i	0.0236428	−	0.0217132i
$419$	−3.30068	+	3.30068i	−0.161249	+	0.161249i	−0.783120	−	0.621871i	$-0.786373\pi$
$419$	−3.30068	+	3.30068i	−0.161249	+	0.161249i	0.621871	+	0.783120i	$0.286373\pi$
$420$		0			0
$421$	−6.14311	−	6.14311i	−0.299397	−	0.299397i	0.541381	−	0.840778i	$-0.317902\pi$
$421$	−6.14311	−	6.14311i	−0.299397	−	0.299397i	−0.840778	+	0.541381i	$0.817902\pi$
$422$	−0.255091	+	5.99611i	−0.0124176	+	0.291886i
$423$		0			0
$424$	14.3397	+	1.83903i	0.696398	+	0.0893113i
$425$	11.5368	+	19.7082i	0.559615	+	0.955990i
$426$		0			0
$427$	−7.68588	−	7.68588i	−0.371946	−	0.371946i
$428$	1.68110	+	1.99440i	0.0812592	+	0.0964031i
$429$		0			0
$430$	−5.61451	+	8.89358i	−0.270756	+	0.428887i
$431$	8.73359			0.420682			0.210341	−	0.977628i	$-0.432543\pi$
$431$	8.73359			0.420682			0.210341	+	0.977628i	$0.432543\pi$
$432$		0			0
$433$			2.28479i			0.109800i	0.998492	+	0.0548999i	$0.0174840\pi$
$433$			2.28479i			0.109800i	−0.998492	+	0.0548999i	$0.982516\pi$
$434$	−14.6502	−	15.9521i	−0.703234	−	0.765727i
$435$		0			0
$436$	−4.16831	−	4.94513i	−0.199626	−	0.236829i
$437$	−0.0747238	−	0.0747238i	−0.00357452	−	0.00357452i
$438$		0			0
$439$	27.7235			1.32317			0.661585	−	0.749870i	$-0.269884\pi$
$439$	27.7235			1.32317			0.661585	+	0.749870i	$0.269884\pi$
$440$	23.8455	+	18.0580i	1.13679	+	0.860879i
$441$		0			0
$442$	−1.12731	+	26.4984i	−0.0536208	+	1.26040i
$443$	15.8575	−	15.8575i	0.753410	−	0.753410i	−0.221704	−	0.975114i	$-0.571162\pi$
$443$	15.8575	−	15.8575i	0.753410	−	0.753410i	0.975114	+	0.221704i	$0.0711618\pi$
$444$		0			0
$445$	12.2522	+	7.02488i	0.580809	+	0.333011i
$446$	23.6127	+	25.7111i	1.11810	+	1.21746i
$447$		0			0
$448$	−13.8400	−	3.60926i	−0.653878	−	0.170521i
$449$		−	22.7098i		−	1.07174i	−0.844301	−	0.535870i	$-0.819984\pi$
$449$		−	22.7098i		−	1.07174i	0.844301	−	0.535870i	$-0.180016\pi$
$450$		0			0
$451$	26.4728	+	26.4728i	1.24655	+	1.24655i
$452$	−1.28038	+	15.0210i	−0.0602242	+	0.706527i
$453$		0			0
$454$	−0.429599	+	10.0981i	−0.0201621	+	0.473925i
$455$	−15.8433	+	4.29618i	−0.742746	+	0.201408i
$456$		0			0
$457$	23.3185			1.09079			0.545397	−	0.838178i	$-0.316379\pi$
$457$	23.3185			1.09079			0.545397	+	0.838178i	$0.316379\pi$
$458$	−1.14605	+	26.9387i	−0.0535513	+	1.25876i
$459$		0			0
$460$	2.74182	−	3.95966i	0.127838	−	0.184620i
$461$	6.98422	+	6.98422i	0.325288	+	0.325288i	0.850791	−	0.525504i	$-0.176123\pi$
$461$	6.98422	+	6.98422i	0.325288	+	0.325288i	−0.525504	+	0.850791i	$0.676123\pi$
$462$		0			0
$463$	0.177929			0.00826905			0.00413453	−	0.999991i	$-0.498684\pi$
$463$	0.177929			0.00826905			0.00413453	+	0.999991i	$0.498684\pi$
$464$	4.04856	+	5.72735i	0.187950	+	0.265885i
$465$		0			0
$466$	−12.3394	+	11.3324i	−0.571613	+	0.524961i
$467$	−25.8586	−	25.8586i	−1.19659	−	1.19659i	−0.975180	−	0.221414i	$-0.928933\pi$
$467$	−25.8586	−	25.8586i	−1.19659	−	1.19659i	−0.221414	−	0.975180i	$-0.571067\pi$
$468$		0			0
$469$	10.4638	+	10.4638i	0.483175	+	0.483175i
$470$	19.4997	−	4.40725i	0.899453	−	0.203291i
$471$		0			0
$472$	8.93008	+	1.14526i	0.411040	+	0.0527149i
$473$		−	15.7298i		−	0.723255i
$474$		0			0
$475$	−0.124137	+	0.474658i	−0.00569581	+	0.0217788i
$476$	16.2725	+	1.38706i	0.745847	+	0.0635758i
$477$		0			0
$478$	23.7828	+	25.8962i	1.08780	+	1.18447i
$479$	−6.74528			−0.308200			−0.154100	−	0.988055i	$-0.549248\pi$
$479$	−6.74528			−0.308200			−0.154100	+	0.988055i	$0.549248\pi$
$480$		0			0
$481$	−44.2757			−2.01880
$482$	−18.0218	−	19.6233i	−0.820870	−	0.893818i
$483$		0			0
$484$	−22.6527	−	1.93091i	−1.02967	−	0.0877687i
$485$	5.07982	−	8.85978i	0.230663	−	0.402302i
$486$		0			0
$487$		−	27.5084i		−	1.24652i	−0.782014	−	0.623261i	$-0.785807\pi$
$487$		−	27.5084i		−	1.24652i	0.782014	−	0.623261i	$-0.214193\pi$
$488$	2.18739	−	17.0560i	0.0990186	−	0.772090i
$489$		0			0
$490$	−2.65162	−	11.7320i	−0.119788	−	0.529997i
$491$	−1.96277	−	1.96277i	−0.0885786	−	0.0885786i	0.661429	−	0.750008i	$-0.269950\pi$
$491$	−1.96277	−	1.96277i	−0.0885786	−	0.0885786i	−0.750008	+	0.661429i	$0.769950\pi$
$492$		0			0
$493$	−5.66291	−	5.66291i	−0.255045	−	0.255045i
$494$	−0.419675	+	0.385424i	−0.0188821	+	0.0173411i
$495$		0			0
$496$	5.79926	−	33.7702i	0.260394	−	1.51633i
$497$	−27.0738			−1.21442
$498$		0			0
$499$	−10.0400	−	10.0400i	−0.449452	−	0.449452i	0.445720	−	0.895172i	$-0.352948\pi$
$499$	−10.0400	−	10.0400i	−0.449452	−	0.449452i	−0.895172	+	0.445720i	$0.852948\pi$
$500$	−22.2961	−	1.69857i	−0.997111	−	0.0759622i
$501$		0			0
$502$	1.84233	−	43.3055i	0.0822274	−	1.93282i
$503$	15.8104			0.704952			0.352476	−	0.935821i	$-0.385340\pi$
$503$	15.8104			0.704952			0.352476	+	0.935821i	$0.385340\pi$
$504$		0			0
$505$	−19.0659	+	5.17003i	−0.848421	+	0.230063i
$506$	−0.306163	+	7.19659i	−0.0136106	+	0.319927i
$507$		0			0
$508$	−0.000471972		0.00553700i	−2.09404e−5		0.000245664i
$509$	16.6015	+	16.6015i	0.735849	+	0.735849i	0.971772	−	0.235922i	$-0.0758111\pi$
$509$	16.6015	+	16.6015i	0.735849	+	0.735849i	−0.235922	+	0.971772i	$0.575811\pi$
$510$		0			0
$511$			12.3026i			0.544234i
$512$	−8.86869	−	20.8170i	−0.391945	−	0.919989i
$513$		0			0
$514$	−0.874730	−	0.952464i	−0.0385827	−	0.0420114i
$515$	−15.4096	+	26.8760i	−0.679027	+	1.18430i
$516$		0			0
$517$	−21.1417	+	21.1417i	−0.929809	+	0.929809i
$518$	−1.15881	+	27.2387i	−0.0509152	+	1.19680i
$519$		0			0
$520$	−20.7030	−	15.6782i	−0.907886	−	0.687533i
$521$	7.96468			0.348939			0.174469	−	0.984663i	$-0.444179\pi$
$521$	7.96468			0.348939			0.174469	+	0.984663i	$0.444179\pi$
$522$		0			0
$523$	−15.2514	−	15.2514i	−0.666897	−	0.666897i	0.290099	−	0.956997i	$-0.406312\pi$
$523$	−15.2514	−	15.2514i	−0.666897	−	0.666897i	−0.956997	+	0.290099i	$0.906312\pi$
$524$	15.8956	+	18.8579i	0.694401	+	0.823813i
$525$		0			0
$526$	−1.14450	−	1.24621i	−0.0499025	−	0.0543372i
$527$			39.1243i			1.70428i
$528$		0			0
$529$	−21.8402			−0.949573
$530$	8.62851	−	13.6679i	0.374798	−	0.593694i
$531$		0			0
$532$	0.226132	+	0.268275i	0.00980405	+	0.0116312i
$533$	−22.9840	−	22.9840i	−0.995549	−	0.995549i
$534$		0			0
$535$	2.81463	−	0.763235i	0.121687	−	0.0329975i
$536$	−2.97799	+	23.2207i	−0.128630	+	1.00298i
$537$		0			0
$538$	−0.641426	+	15.0772i	−0.0276538	+	0.650025i
$539$	12.7199	+	12.7199i	0.547884	+	0.547884i
$540$		0			0
$541$	−6.80924	+	6.80924i	−0.292752	+	0.292752i	−0.838167	−	0.545414i	$-0.816372\pi$
$541$	−6.80924	+	6.80924i	−0.292752	+	0.292752i	0.545414	+	0.838167i	$0.316372\pi$
$542$	−4.64399	+	4.26498i	−0.199477	+	0.183197i
$543$		0			0
$544$	14.0034	+	21.7126i	0.600392	+	0.930922i
$545$	−6.97890	+	1.89245i	−0.298943	+	0.0810635i
$546$		0			0
$547$	−24.8809	+	24.8809i	−1.06383	+	1.06383i	−0.0660132	+	0.997819i	$0.521028\pi$
$547$	−24.8809	+	24.8809i	−1.06383	+	1.06383i	−0.997819	+	0.0660132i	$0.978972\pi$
$548$	−46.1868	−	3.93695i	−1.97300	−	0.168178i
$549$		0			0
$550$	29.5528	−	15.6525i	1.26014	−	0.667425i
$551$		−	0.172056i		−	0.00732985i
$552$		0			0
$553$	−23.1922			−0.986233
$554$	10.5535	+	0.448974i	0.448375	+	0.0190751i
$555$		0			0
$556$	−14.3159	−	16.9839i	−0.607129	−	0.720276i
$557$	−3.05959	+	3.05959i	−0.129639	+	0.129639i	−0.768949	−	0.639310i	$-0.779220\pi$
$557$	−3.05959	+	3.05959i	−0.129639	+	0.129639i	0.639310	+	0.768949i	$0.279220\pi$
$558$		0			0
$559$			13.6568i			0.577621i
$560$	−10.1872	+	12.3263i	−0.430486	+	0.520880i
$561$		0			0
$562$	25.1851	+	27.4232i	1.06237	+	1.15678i
$563$	32.0945	+	32.0945i	1.35262	+	1.35262i	0.882716	+	0.469906i	$0.155712\pi$
$563$	32.0945	+	32.0945i	1.35262	+	1.35262i	0.469906	+	0.882716i	$0.344288\pi$
$564$		0			0
$565$	14.6219	+	8.38360i	0.615150	+	0.352701i
$566$	−1.15769	+	27.2125i	−0.0486615	+	1.14383i
$567$		0			0
$568$	−26.1876	−	33.8928i	−1.09881	−	1.42211i
$569$	28.4585			1.19304			0.596521	−	0.802597i	$-0.296549\pi$
$569$	28.4585			1.19304			0.596521	+	0.802597i	$0.296549\pi$
$570$		0			0
$571$	−26.7837	+	26.7837i	−1.12086	+	1.12086i	−0.129250	+	0.991612i	$0.541257\pi$
$571$	−26.7837	+	26.7837i	−1.12086	+	1.12086i	−0.991612	+	0.129250i	$0.958743\pi$
$572$	38.6991	+	3.29870i	1.61809	+	0.137926i
$573$		0			0
$574$	−14.7415	+	13.5384i	−0.615297	+	0.565081i
$575$	−2.72031	−	4.64710i	−0.113445	−	0.193798i
$576$		0			0
$577$			33.4904i			1.39423i	0.716962	+	0.697113i	$0.245532\pi$
$577$			33.4904i			1.39423i	−0.716962	+	0.697113i	$0.754468\pi$
$578$	−3.69289	−	4.02106i	−0.153604	−	0.167254i
$579$		0			0
$580$	7.71530	−	1.40207i	0.320360	−	0.0582180i
$581$	−12.3155	+	12.3155i	−0.510933	+	0.510933i
$582$		0			0
$583$			24.1738i			1.00118i
$584$	−15.4012	+	11.8999i	−0.637306	+	0.492422i
$585$		0			0
$586$	−0.785264	+	18.4582i	−0.0324389	+	0.762502i
$587$	−12.3666	+	12.3666i	−0.510425	+	0.510425i	−0.914657	−	0.404232i	$-0.867539\pi$
$587$	−12.3666	+	12.3666i	−0.510425	+	0.510425i	0.404232	+	0.914657i	$0.367539\pi$
$588$		0			0
$589$	−0.594357	+	0.594357i	−0.0244900	+	0.0244900i
$590$	5.37342	−	8.51168i	0.221220	−	0.350420i
$591$		0			0
$592$	−35.2202	+	24.8965i	−1.44754	+	1.02324i
$593$	−24.1105			−0.990099			−0.495050	−	0.868865i	$-0.664850\pi$
$593$	−24.1105			−0.990099			−0.495050	+	0.868865i	$0.664850\pi$
$594$		0			0
$595$	9.08210	−	15.8402i	0.372330	−	0.649385i
$596$	−24.8055	−	29.4284i	−1.01607	−	1.20543i
$597$		0			0
$598$	0.265815	−	6.24818i	0.0108700	−	0.255507i
$599$		−	18.0184i		−	0.736213i	−0.929784	−	0.368107i	$-0.880006\pi$
$599$		−	18.0184i		−	0.736213i	0.929784	−	0.368107i	$-0.119994\pi$
$600$		0			0
$601$		−	18.8361i		−	0.768342i	−0.923262	−	0.384171i	$-0.874487\pi$
$601$		−	18.8361i		−	0.768342i	0.923262	−	0.384171i	$-0.125513\pi$
$602$	8.40175	+	0.357433i	0.342430	+	0.0145679i
$603$		0			0
$604$	−2.58951	+	30.3792i	−0.105366	+	1.23611i
$605$	−12.6431	+	22.0510i	−0.514015	+	0.896499i
$606$		0			0
$607$	10.4336			0.423486			0.211743	−	0.977325i	$-0.432086\pi$
$607$	10.4336			0.423486			0.211743	+	0.977325i	$0.432086\pi$
$608$	−0.117114	+	0.542581i	−0.00474962	+	0.0220046i
$609$		0			0
$610$	−16.2569	−	10.2630i	−0.658223	−	0.415536i
$611$	18.3555	−	18.3555i	0.742583	−	0.742583i
$612$		0			0
$613$	−9.35631	+	9.35631i	−0.377898	+	0.377898i	−0.870343	−	0.492445i	$-0.836103\pi$
$613$	−9.35631	+	9.35631i	−0.377898	+	0.377898i	0.492445	+	0.870343i	$0.336103\pi$
$614$	4.73868	+	0.201596i	0.191237	+	0.00813577i
$615$		0			0
$616$	3.04224	−	23.7216i	0.122575	−	0.955771i
$617$		−	22.8927i		−	0.921626i	−0.887497	−	0.460813i	$-0.847558\pi$
$617$		−	22.8927i		−	0.921626i	0.887497	−	0.460813i	$-0.152442\pi$
$618$		0			0
$619$	32.9542	−	32.9542i	1.32454	−	1.32454i	0.414484	−	0.910057i	$-0.363962\pi$
$619$	32.9542	−	32.9542i	1.32454	−	1.32454i	0.910057	−	0.414484i	$-0.136038\pi$
$620$	−31.4953	−	21.8086i	−1.26488	−	0.875854i
$621$		0			0
$622$	−15.1398	+	13.9042i	−0.607052	+	0.557509i
$623$		−	11.2923i		−	0.452415i
$624$		0			0
$625$	−12.2393	+	21.7991i	−0.489573	+	0.871962i
$626$	20.2897	+	22.0928i	0.810941	+	0.883006i
$627$		0			0
$628$	12.4761	−	10.5163i	0.497851	−	0.419644i
$629$	34.8239	−	34.8239i	1.38852	−	1.38852i
$630$		0			0
$631$	14.9668			0.595817			0.297908	−	0.954594i	$-0.403711\pi$
$631$	14.9668			0.595817			0.297908	+	0.954594i	$0.403711\pi$
$632$	−22.4331	−	29.0336i	−0.892341	−	1.15489i
$633$		0			0
$634$	−1.14981	−	0.0489159i	−0.0456646	−	0.00194270i
$635$	0.00538991	+	0.00309035i	0.000213892	+	0.000122637i
$636$		0			0
$637$	−11.0436	−	11.0436i	−0.437562	−	0.437562i
$638$	−8.63778	+	7.93283i	−0.341973	+	0.314064i
$639$		0			0
$640$	−25.2846	−	0.830157i	−0.999461	−	0.0328148i
$641$		−	3.08889i		−	0.122004i	−0.998138	−	0.0610019i	$-0.980570\pi$
$641$		−	3.08889i		−	0.122004i	0.998138	−	0.0610019i	$-0.0194296\pi$
$642$		0			0
$643$	−18.1306	+	18.1306i	−0.715001	+	0.715001i	−0.967577	−	0.252576i	$-0.918722\pi$
$643$	−18.1306	+	18.1306i	−0.715001	+	0.715001i	0.252576	+	0.967577i	$0.418722\pi$
$644$	−3.83696	−	0.327062i	−0.151198	−	0.0128880i
$645$		0			0
$646$	0.0269394	−	0.633231i	0.00105992	−	0.0249141i
$647$	6.79255			0.267043			0.133521	−	0.991046i	$-0.457372\pi$
$647$	6.79255			0.267043			0.133521	+	0.991046i	$0.457372\pi$
$648$		0			0
$649$			15.0543i			0.590933i
$650$	−25.6582	+	13.5897i	−1.00640	+	0.533032i
$651$		0			0
$652$	−19.0514	−	22.6019i	−0.746111	−	0.885160i
$653$	−12.2088	+	12.2088i	−0.477769	+	0.477769i	−0.904417	−	0.426649i	$-0.859694\pi$
$653$	−12.2088	+	12.2088i	−0.477769	+	0.477769i	0.426649	+	0.904417i	$0.359694\pi$
$654$		0			0
$655$	26.6136	−	7.21672i	1.03988	−	0.281981i
$656$	−31.2072	−	5.35913i	−1.21844	−	0.209239i
$657$		0			0
$658$	−10.8120	−	11.7728i	−0.421496	−	0.458953i
$659$	24.8761	−	24.8761i	0.969034	−	0.969034i	−0.0305007	−	0.999535i	$-0.509710\pi$
$659$	24.8761	−	24.8761i	0.969034	−	0.969034i	0.999535	+	0.0305007i	$0.00971017\pi$
$660$		0			0
$661$	−21.1349	−	21.1349i	−0.822052	−	0.822052i	0.164350	−	0.986402i	$-0.447447\pi$
$661$	−21.1349	−	21.1349i	−0.822052	−	0.822052i	−0.986402	+	0.164350i	$0.947447\pi$
$662$	−11.0819	−	0.471454i	−0.430710	−	0.0183236i
$663$		0			0
$664$	−27.3298	−	3.50498i	−1.06060	−	0.136019i
$665$	0.378607	−	0.102666i	0.0146818	−	0.00398120i
$666$		0			0
$667$	1.33529	+	1.33529i	0.0517025	+	0.0517025i
$668$	1.59990	−	18.7694i	0.0619019	−	0.726209i
$669$		0			0
$670$	22.1327	+	13.9724i	0.855062	+	0.539800i
$671$	28.7530			1.11000
$672$		0			0
$673$			48.6471i			1.87521i	0.347705	+	0.937604i	$0.386961\pi$
$673$			48.6471i			1.87521i	−0.347705	+	0.937604i	$0.613039\pi$
$674$	17.0458	−	15.6547i	0.656581	−	0.602995i
$675$		0			0
$676$	−7.69302	−	0.655751i	−0.295886	−	0.0252212i
$677$	8.69556	+	8.69556i	0.334197	+	0.334197i	0.854178	−	0.519981i	$-0.174061\pi$
$677$	8.69556	+	8.69556i	0.334197	+	0.334197i	−0.519981	+	0.854178i	$0.674061\pi$
$678$		0			0
$679$	−8.16566			−0.313369
$680$	28.6147	−	3.95214i	1.09732	−	0.151558i
$681$		0			0
$682$	57.2420	+	2.43523i	2.19191	+	0.0932498i
$683$	26.4514	−	26.4514i	1.01213	−	1.01213i	0.0122093	−	0.999925i	$-0.496114\pi$
$683$	26.4514	−	26.4514i	1.01213	−	1.01213i	0.999925	−	0.0122093i	$-0.00388645\pi$
$684$		0			0
$685$	−25.7781	+	44.9599i	−0.984930	+	1.71783i
$686$	−20.1188	+	18.4768i	−0.768138	+	0.705448i
$687$		0			0
$688$	7.67929	+	10.8636i	0.292770	+	0.414172i
$689$		−	20.9881i		−	0.799582i
$690$		0			0
$691$	8.89820	+	8.89820i	0.338503	+	0.338503i	0.855804	−	0.517301i	$-0.173063\pi$
$691$	8.89820	+	8.89820i	0.338503	+	0.338503i	−0.517301	+	0.855804i	$0.673063\pi$
$692$	11.3384	+	13.4515i	0.431021	+	0.511349i
$693$		0			0
$694$	37.3198	+	1.58768i	1.41664	+	0.0602677i
$695$	−23.9688	+	6.49953i	−0.909187	+	0.246541i
$696$		0			0
$697$	36.1550			1.36947
$698$	−30.4425	−	1.29511i	−1.15226	−	0.0490205i
$699$		0			0
$700$	7.68894	+	16.1408i	0.290615	+	0.610064i
$701$	−15.7989	−	15.7989i	−0.596716	−	0.596716i	0.342721	−	0.939437i	$-0.388651\pi$
$701$	−15.7989	−	15.7989i	−0.596716	−	0.596716i	−0.939437	+	0.342721i	$0.888651\pi$
$702$		0			0
$703$	1.05806			0.0399053
$704$	32.6390	−	19.1367i	1.23013	−	0.721241i
$705$		0			0
$706$	−7.87519	−	8.57503i	−0.296387	−	0.322726i
$707$	11.1686	+	11.1686i	0.420037	+	0.420037i
$708$		0			0
$709$	18.9259	+	18.9259i	0.710776	+	0.710776i	0.966697	−	0.255922i	$-0.0823790\pi$
$709$	18.9259	+	18.9259i	0.710776	+	0.710776i	−0.255922	+	0.966697i	$0.582379\pi$
$710$	−46.7086	+	10.5569i	−1.75294	+	0.396194i
$711$		0			0
$712$	14.1364	−	10.9227i	0.529785	−	0.409344i
$713$		−	9.22531i		−	0.345490i
$714$		0			0
$715$	21.5990	−	37.6711i	0.807757	−	1.40882i
$716$	−33.5452	−	39.7968i	−1.25364	−	1.48728i
$717$		0			0
$718$	5.17512	−	4.75276i	0.193134	−	0.177372i
$719$	10.6789			0.398256			0.199128	−	0.979973i	$-0.436189\pi$
$719$	10.6789			0.398256			0.199128	+	0.979973i	$0.436189\pi$
$720$		0			0
$721$	24.7704			0.922498
$722$	−19.7804	+	18.1660i	−0.736150	+	0.676070i
$723$		0			0
$724$	40.1669	−	33.8571i	1.49279	−	1.25829i
$725$	2.21828	−	8.48197i	0.0823850	−	0.315012i
$726$		0			0
$727$		−	32.2573i		−	1.19636i	−0.801363	−	0.598179i	$-0.795891\pi$
$727$		−	32.2573i		−	1.19636i	0.801363	−	0.598179i	$-0.204109\pi$
$728$	−2.64131	+	20.5954i	−0.0978935	+	0.763317i
$729$		0			0
$730$	4.79716	+	21.2248i	0.177551	+	0.785566i
$731$	−10.7414	−	10.7414i	−0.397285	−	0.397285i
$732$		0			0
$733$	29.6986	+	29.6986i	1.09694	+	1.09694i	0.994766	+	0.102175i	$0.0325801\pi$
$733$	29.6986	+	29.6986i	1.09694	+	1.09694i	0.102175	+	0.994766i	$0.467420\pi$
$734$	−24.2773	−	26.4347i	−0.896092	−	0.975724i
$735$		0			0
$736$	−3.30194	−	5.11973i	−0.121711	−	0.188716i
$737$	−39.1453			−1.44194
$738$		0			0
$739$	19.7806	+	19.7806i	0.727640	+	0.727640i	0.970149	−	0.242509i	$-0.0779704\pi$
$739$	19.7806	+	19.7806i	0.727640	+	0.727640i	−0.242509	+	0.970149i	$0.577970\pi$
$740$	8.62202	+	47.4450i	0.316952	+	1.74411i
$741$		0			0
$742$	−12.9120	−	0.549312i	−0.474014	−	0.0201659i
$743$	−34.3449			−1.25999			−0.629996	−	0.776598i	$-0.716944\pi$
$743$	−34.3449			−1.25999			−0.629996	+	0.776598i	$0.716944\pi$
$744$		0			0
$745$	−41.5312	+	11.2619i	−1.52159	+	0.412604i
$746$	−5.70913	−	0.242882i	−0.209026	−	0.00889255i
$747$		0			0
$748$	−33.0323	+	27.8433i	−1.20778	+	1.01805i
$749$	−1.64878	−	1.64878i	−0.0602451	−	0.0602451i
$750$		0			0
$751$			48.4556i			1.76817i	0.467326	+	0.884085i	$0.345217\pi$
$751$			48.4556i			1.76817i	−0.467326	+	0.884085i	$0.654783\pi$
$752$	4.27991	−	24.9227i	0.156072	−	0.908837i
$753$		0			0
$754$	7.49944	−	6.88739i	0.273114	−	0.250824i
$755$	29.5722	+	16.9554i	1.07624	+	0.617071i
$756$		0			0
$757$	−24.8358	+	24.8358i	−0.902672	+	0.902672i	−0.995667	−	0.0929947i	$-0.970356\pi$
$757$	−24.8358	+	24.8358i	−0.902672	+	0.902672i	0.0929947	+	0.995667i	$0.470356\pi$
$758$	17.9068	+	0.761803i	0.650403	+	0.0276699i
$759$		0			0
$760$	0.494739	+	0.374661i	0.0179461	+	0.0135904i
$761$	−26.2421			−0.951274			−0.475637	−	0.879642i	$-0.657782\pi$
$761$	−26.2421			−0.951274			−0.475637	+	0.879642i	$0.657782\pi$
$762$		0			0
$763$	4.08816	+	4.08816i	0.148001	+	0.148001i
$764$	−0.804105	+	9.43345i	−0.0290915	+	0.341290i
$765$		0			0
$766$	10.2461	−	9.40988i	0.370207	−	0.339993i
$767$		−	13.0704i		−	0.471943i
$768$		0			0
$769$	25.4168			0.916552			0.458276	−	0.888810i	$-0.348467\pi$
$769$	25.4168			0.916552			0.458276	+	0.888810i	$0.348467\pi$
$770$	−22.6102	−	14.2738i	−0.814815	−	0.514392i
$771$		0			0
$772$	33.3227	+	2.84042i	1.19931	+	0.102229i
$773$	30.1984	+	30.1984i	1.08616	+	1.08616i	0.995920	+	0.0902412i	$0.0287638\pi$
$773$	30.1984	+	30.1984i	1.08616	+	1.08616i	0.0902412	+	0.995920i	$0.471236\pi$
$774$		0			0
$775$	−36.9633	+	21.6374i	−1.32776	+	0.777240i
$776$	−7.89839	−	10.2223i	−0.283536	−	0.366960i
$777$		0			0
$778$	17.3820	+	0.739478i	0.623175	+	0.0265116i
$779$	0.549249	+	0.549249i	0.0196789	+	0.0196789i
$780$		0			0
$781$	50.6417	−	50.6417i	1.81210	−	1.81210i
$782$	4.70528	+	5.12341i	0.168260	+	0.183213i
$783$		0			0
$784$	−14.9947	−	2.57501i	−0.535526	−	0.0919645i
$785$	−4.77447	−	17.6071i	−0.170408	−	0.628425i
$786$		0			0
$787$	19.3428	−	19.3428i	0.689496	−	0.689496i	−0.272625	−	0.962120i	$-0.587892\pi$
$787$	19.3428	−	19.3428i	0.689496	−	0.689496i	0.962120	+	0.272625i	$0.0878917\pi$
$788$	17.1511	−	14.4569i	0.610984	−	0.515005i
$789$		0			0
$790$	−40.0120	+	9.04338i	−1.42356	+	0.321749i
$791$		−	13.4764i		−	0.479165i
$792$		0			0
$793$	−24.9637			−0.886489
$794$	−0.214813	+	5.04935i	−0.00762343	+	0.179195i
$795$		0			0
$796$	0.398698	−	4.67737i	0.0141315	−	0.165785i
$797$	32.3328	−	32.3328i	1.14529	−	1.14529i	0.157820	−	0.987468i	$-0.449553\pi$
$797$	32.3328	−	32.3328i	1.14529	−	1.14529i	0.987468	−	0.157820i	$-0.0504466\pi$
$798$		0			0
$799$			28.8741i			1.02149i
$800$	−12.7688	+	25.2380i	−0.451446	+	0.892298i
$801$		0			0
$802$	11.9967	−	11.0176i	0.423619	−	0.389046i
$803$	−23.0121	−	23.0121i	−0.812079	−	0.812079i
$804$		0			0
$805$	−2.14151	+	3.73504i	−0.0754784	+	0.131643i
$806$	−49.6983	−	2.11430i	−1.75055	−	0.0744731i
$807$		0			0
$808$	−3.17856	+	24.7846i	−0.111821	+	0.871919i
$809$	−4.09587			−0.144003			−0.0720015	−	0.997405i	$-0.522939\pi$
$809$	−4.09587			−0.144003			−0.0720015	+	0.997405i	$0.522939\pi$
$810$		0			0
$811$	1.34586	−	1.34586i	0.0472594	−	0.0472594i	−0.683082	−	0.730342i	$-0.739361\pi$
$811$	1.34586	−	1.34586i	0.0472594	−	0.0472594i	0.730342	+	0.683082i	$0.239361\pi$
$812$	−4.04089	−	4.79397i	−0.141807	−	0.168235i
$813$		0			0
$814$	−48.7827	−	53.1178i	−1.70983	−	1.86178i
$815$	−31.8974	+	8.64950i	−1.11732	+	0.302979i
$816$		0			0
$817$		−	0.326356i		−	0.0114178i
$818$	18.2337	−	16.7456i	0.637528	−	0.585497i
$819$		0			0
$820$	−20.1535	+	29.1050i	−0.703789	+	1.01639i
$821$	16.3658	−	16.3658i	0.571171	−	0.571171i	−0.361285	−	0.932456i	$-0.617662\pi$
$821$	16.3658	−	16.3658i	0.571171	−	0.571171i	0.932456	+	0.361285i	$0.117662\pi$
$822$		0			0
$823$		−	33.6816i		−	1.17407i	−0.809562	−	0.587034i	$-0.800295\pi$
$823$		−	33.6816i		−	1.17407i	0.809562	−	0.587034i	$-0.199705\pi$
$824$	23.9596	+	31.0093i	0.834674	+	1.08026i
$825$		0			0
$826$	−8.04097	−	0.342085i	−0.279781	−	0.0119027i
$827$	1.94113	−	1.94113i	0.0674997	−	0.0674997i	−0.672551	−	0.740051i	$-0.734801\pi$
$827$	1.94113	−	1.94113i	0.0674997	−	0.0674997i	0.740051	+	0.672551i	$0.234801\pi$
$828$		0			0
$829$	−31.5836	+	31.5836i	−1.09695	+	1.09695i	−0.102179	+	0.994766i	$0.532581\pi$
$829$	−31.5836	+	31.5836i	−1.09695	+	1.09695i	−0.994766	+	0.102179i	$0.967419\pi$
$830$	−16.4449	+	26.0493i	−0.570811	+	0.904185i
$831$		0			0
$832$	−28.3376	+	16.6147i	−0.982430	+	0.576012i
$833$	17.3721			0.601907
$834$		0			0
$835$	−18.2708	−	10.4757i	−0.632286	−	0.362526i
$836$	−0.924791	−	0.0788290i	−0.0319846	−	0.00272636i
$837$		0			0
$838$	6.59540	+	0.280586i	0.227834	+	0.00969270i
$839$			25.0492i			0.864795i	0.901683	+	0.432398i	$0.142332\pi$
$839$			25.0492i			0.864795i	−0.901683	+	0.432398i	$0.857668\pi$
$840$		0			0
$841$		−	25.9254i		−	0.893980i
$842$	−0.522217	+	12.2751i	−0.0179968	+	0.423029i
$843$		0			0
$844$	6.48957	−	5.47013i	0.223380	−	0.188290i
$845$	−4.29368	+	7.48866i	−0.147707	+	0.257618i
$846$		0			0
$847$	20.3234			0.698319
$848$	−11.8017	−	16.6954i	−0.405272	−	0.573324i
$849$		0			0
$850$	9.49215	−	30.8694i	0.325578	−	1.05881i
$851$	−8.21131	+	8.21131i	−0.281480	+	0.281480i
$852$		0			0
$853$	5.21199	−	5.21199i	0.178455	−	0.178455i	−0.612227	−	0.790682i	$-0.709726\pi$
$853$	5.21199	−	5.21199i	0.178455	−	0.178455i	0.790682	+	0.612227i	$0.209726\pi$
$854$	−0.653366	+	15.3579i	−0.0223577	+	0.525535i
$855$		0			0
$856$	0.469241	−	3.65887i	0.0160383	−	0.125058i
$857$			42.7298i			1.45962i	0.683649	+	0.729811i	$0.260392\pi$
$857$			42.7298i			1.45962i	−0.683649	+	0.729811i	$0.739608\pi$
$858$		0			0
$859$	−12.0244	+	12.0244i	−0.410268	+	0.410268i	−0.881832	−	0.471564i	$-0.843690\pi$
$859$	−12.0244	+	12.0244i	−0.410268	+	0.410268i	0.471564	+	0.881832i	$0.343690\pi$
$860$	14.6344	−	2.65945i	0.499028	−	0.0906865i
$861$		0			0
$862$	−8.35449	−	9.09692i	−0.284555	−	0.309842i
$863$			2.21809i			0.0755047i	0.999287	+	0.0377523i	$0.0120198\pi$
$863$			2.21809i			0.0755047i	−0.999287	+	0.0377523i	$0.987980\pi$
$864$		0			0
$865$	18.9836	−	5.14773i	0.645463	−	0.175028i
$866$	2.37984	−	2.18561i	0.0808701	−	0.0742700i
$867$		0			0
$868$	−2.60146	+	30.5194i	−0.0882995	+	1.03590i
$869$	43.3812	−	43.3812i	1.47161	−	1.47161i
$870$		0			0
$871$	33.9865			1.15159
$872$	−1.16349	+	9.07218i	−0.0394006	+	0.307223i
$873$		0			0
$874$	−0.00635217	+	0.149313i	−0.000214865	+	0.00505057i
$875$	19.9881	−	0.179873i	0.675720	−	0.00608082i
$876$		0			0
$877$	−37.6890	−	37.6890i	−1.27267	−	1.27267i	−0.944683	−	0.327984i	$-0.893631\pi$
$877$	−37.6890	−	37.6890i	−1.27267	−	1.27267i	−0.327984	−	0.944683i	$-0.606369\pi$
$878$	−26.5201	−	28.8768i	−0.895009	−	0.974545i
$879$		0			0
$880$	−4.00123	−	42.1116i	−0.134881	−	1.41958i
$881$			16.4850i			0.555395i	0.960669	+	0.277698i	$0.0895713\pi$
$881$			16.4850i			0.555395i	−0.960669	+	0.277698i	$0.910429\pi$
$882$		0			0
$883$	25.2952	−	25.2952i	0.851251	−	0.851251i	−0.139036	−	0.990287i	$-0.544400\pi$
$883$	25.2952	−	25.2952i	0.851251	−	0.851251i	0.990287	+	0.139036i	$0.0444004\pi$
$884$	28.6791	−	24.1739i	0.964582	−	0.813057i
$885$		0			0
$886$	−31.6862	−	1.34802i	−1.06452	−	0.0452876i
$887$	51.1894			1.71877			0.859386	−	0.511327i	$-0.170846\pi$
$887$	51.1894			1.71877			0.859386	+	0.511327i	$0.170846\pi$
$888$		0			0
$889$		−	0.00496763i		−	0.000166609i
$890$	−4.40321	−	19.4818i	−0.147596	−	0.653032i
$891$		0			0
$892$	4.19295	−	49.1901i	0.140390	−	1.64701i
$893$	−0.438641	+	0.438641i	−0.0146785	+	0.0146785i
$894$		0			0
$895$	−56.1639	+	15.2298i	−1.87735	+	0.509076i
$896$	9.47983	+	17.8683i	0.316699	+	0.596939i
$897$		0			0
$898$	−23.6545	+	21.7240i	−0.789361	+	0.724938i
$899$	10.6209	−	10.6209i	0.354228	−	0.354228i
$900$		0			0
$901$	16.5076	+	16.5076i	0.549949	+	0.549949i
$902$	2.25041	−	52.8977i	0.0749306	−	1.76130i
$903$		0			0
$904$	16.8706	−	13.0353i	0.561109	−	0.433547i
$905$	−15.3714	−	56.6862i	−0.510963	−	1.88431i
$906$		0			0
$907$	−12.4729	−	12.4729i	−0.414156	−	0.414156i	0.469028	−	0.883183i	$-0.344604\pi$
$907$	−12.4729	−	12.4729i	−0.414156	−	0.414156i	−0.883183	+	0.469028i	$0.844604\pi$
$908$	10.9291	−	9.21225i	0.362695	−	0.305719i
$909$		0			0
$910$	19.6305	+	12.3927i	0.650744	+	0.410814i
$911$	41.2168			1.36557			0.682786	−	0.730618i	$-0.260768\pi$
$911$	41.2168			1.36557			0.682786	+	0.730618i	$0.260768\pi$
$912$		0			0
$913$		−	46.0725i		−	1.52478i
$914$	−22.3063	−	24.2886i	−0.737827	−	0.803394i
$915$		0			0
$916$	29.1557	−	24.5757i	0.963332	−	0.812003i
$917$	−15.5899	−	15.5899i	−0.514825	−	0.514825i
$918$		0			0
$919$	−36.4592			−1.20268			−0.601339	−	0.798994i	$-0.705366\pi$
$919$	−36.4592			−1.20268			−0.601339	+	0.798994i	$0.705366\pi$
$920$	−6.74719	+	0.931895i	−0.222448	+	0.0307237i
$921$		0			0
$922$	0.593719	−	13.9558i	0.0195531	−	0.459611i
$923$	−43.9678	+	43.9678i	−1.44722	+	1.44722i
$924$		0			0
$925$	52.1596	+	13.6413i	1.71500	+	0.448523i
$926$	−0.170205	−	0.185331i	−0.00559329	−	0.00609035i
$927$		0			0
$928$	2.09279	−	9.69571i	0.0686992	−	0.318277i
$929$			23.1770i			0.760413i	0.924902	+	0.380206i	$0.124147\pi$
$929$			23.1770i			0.760413i	−0.924902	+	0.380206i	$0.875853\pi$
$930$		0			0
$931$	0.263908	+	0.263908i	0.00864924	+	0.00864924i
$932$	23.6076	+	2.01230i	0.773292	+	0.0659152i
$933$		0			0
$934$	−2.19820	+	51.6705i	−0.0719274	+	1.69071i
$935$	12.6411	+	46.6174i	0.413407	+	1.52455i
$936$		0			0
$937$	33.1100			1.08166			0.540829	−	0.841133i	$-0.318111\pi$
$937$	33.1100			1.08166			0.540829	+	0.841133i	$0.318111\pi$
$938$	0.889515	−	20.9087i	0.0290437	−	0.682695i
$939$		0			0
$940$	−23.2438	−	16.0949i	−0.758130	−	0.524959i
$941$	11.7810	+	11.7810i	0.384050	+	0.384050i	0.872559	−	0.488509i	$-0.162459\pi$
$941$	11.7810	+	11.7810i	0.384050	+	0.384050i	−0.488509	+	0.872559i	$0.662459\pi$
$942$		0			0
$943$	−8.52517			−0.277618
$944$	−7.34953	−	10.3971i	−0.239207	−	0.338397i
$945$		0			0
$946$	−16.3841	+	15.0470i	−0.532694	+	0.489219i
$947$	3.78760	+	3.78760i	0.123080	+	0.123080i	0.765964	−	0.642884i	$-0.222262\pi$
$947$	3.78760	+	3.78760i	0.123080	+	0.123080i	−0.642884	+	0.765964i	$0.722262\pi$
$948$		0			0
$949$	19.9794	+	19.9794i	0.648559	+	0.648559i
$950$	0.613153	−	0.324753i	0.0198933	−	0.0105364i
$951$		0			0
$952$	−14.1213	−	18.2763i	−0.457675	−	0.592337i
$953$			33.8756i			1.09734i	0.836039	+	0.548670i	$0.184866\pi$
$953$			33.8756i			1.09734i	−0.836039	+	0.548670i	$0.815134\pi$
$954$		0			0
$955$	9.18286	+	5.26506i	0.297150	+	0.170373i
$956$	4.22314	−	49.5443i	0.136586	−	1.60238i
$957$		0			0
$958$	6.45248	+	7.02589i	0.208470	+	0.226996i
$959$	41.4375			1.33809
$960$		0			0
$961$	−42.3785			−1.36705
$962$	42.3538	+	46.1176i	1.36554	+	1.48689i
$963$		0			0
$964$	−3.20016	+	37.5430i	−0.103070	+	1.20918i
$965$	18.5983	−	32.4375i	0.598700	−	1.04420i
$966$		0			0
$967$		−	39.8455i		−	1.28134i	−0.767814	−	0.640672i	$-0.778656\pi$
$967$		−	39.8455i		−	1.28134i	0.767814	−	0.640672i	$-0.221344\pi$
$968$	19.6582	+	25.4422i	0.631838	+	0.817743i
$969$		0			0
$970$	−14.0877	+	3.18405i	−0.452328	+	0.102234i
$971$	−10.4598	−	10.4598i	−0.335670	−	0.335670i	0.519065	−	0.854735i	$-0.326280\pi$
$971$	−10.4598	−	10.4598i	−0.335670	−	0.335670i	−0.854735	+	0.519065i	$0.826280\pi$
$972$		0			0
$973$	14.0406	+	14.0406i	0.450122	+	0.450122i
$974$	−28.6527	+	26.3143i	−0.918092	+	0.843164i
$975$		0			0
$976$	−19.8580	+	14.0373i	−0.635639	+	0.449322i
$977$	32.8272			1.05024			0.525118	−	0.851030i	$-0.324021\pi$
$977$	32.8272			1.05024			0.525118	+	0.851030i	$0.324021\pi$
$978$		0			0
$979$	21.1223	+	21.1223i	0.675071	+	0.675071i
$980$	−9.68352	+	13.9847i	−0.309329	+	0.446723i
$981$		0			0
$982$	−0.166852	+	3.92199i	−0.00532447	+	0.125156i
$983$	4.96088			0.158227			0.0791137	−	0.996866i	$-0.474791\pi$
$983$	4.96088			0.158227			0.0791137	+	0.996866i	$0.474791\pi$
$984$		0			0
$985$	−6.56354	−	24.2048i	−0.209132	−	0.771229i
$986$	−0.481396	+	11.3156i	−0.0153308	+	0.360362i
$987$		0			0
$988$	0.802916	+	0.0684404i	0.0255442	+	0.00217738i
$989$	2.53277	+	2.53277i	0.0805373	+	0.0805373i
$990$		0			0
$991$		−	53.9675i		−	1.71433i	−0.515039	−	0.857166i	$-0.672223\pi$
$991$		−	53.9675i		−	1.71433i	0.515039	−	0.857166i	$-0.327777\pi$
$992$	−40.7226	+	26.2638i	−1.29294	+	0.833875i
$993$		0			0
$994$	25.8986	+	28.2001i	0.821452	+	0.894452i
$995$	−4.55312	−	2.61057i	−0.144344	−	0.0827606i
$996$		0			0
$997$	−3.14670	+	3.14670i	−0.0996570	+	0.0996570i	−0.755177	−	0.655520i	$-0.772449\pi$
$997$	−3.14670	+	3.14670i	−0.0996570	+	0.0996570i	0.655520	+	0.755177i	$0.272449\pi$
$998$	−0.853485	+	20.0618i	−0.0270166	+	0.635046i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.539.14	yes	96
3.2	odd	2	inner	720.2.u.a.539.35	yes	96
4.3	odd	2		2880.2.u.a.719.42		96
5.4	even	2	inner	720.2.u.a.539.36	yes	96
12.11	even	2		2880.2.u.a.719.7		96
15.14	odd	2	inner	720.2.u.a.539.13	yes	96
16.3	odd	4	inner	720.2.u.a.179.13	✓	96
16.13	even	4		2880.2.u.a.2159.31		96
20.19	odd	2		2880.2.u.a.719.18		96
48.29	odd	4		2880.2.u.a.2159.18		96
48.35	even	4	inner	720.2.u.a.179.36	yes	96
60.59	even	2		2880.2.u.a.719.31		96
80.19	odd	4	inner	720.2.u.a.179.35	yes	96
80.29	even	4		2880.2.u.a.2159.7		96
240.29	odd	4		2880.2.u.a.2159.42		96
240.179	even	4	inner	720.2.u.a.179.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.13	✓	96	16.3	odd	4	inner
720.2.u.a.179.14	yes	96	240.179	even	4	inner
720.2.u.a.179.35	yes	96	80.19	odd	4	inner
720.2.u.a.179.36	yes	96	48.35	even	4	inner
720.2.u.a.539.13	yes	96	15.14	odd	2	inner
720.2.u.a.539.14	yes	96	1.1	even	1	trivial
720.2.u.a.539.35	yes	96	3.2	odd	2	inner
720.2.u.a.539.36	yes	96	5.4	even	2	inner
2880.2.u.a.719.7		96	12.11	even	2
2880.2.u.a.719.18		96	20.19	odd	2
2880.2.u.a.719.31		96	60.59	even	2
2880.2.u.a.719.42		96	4.3	odd	2
2880.2.u.a.2159.7		96	80.29	even	4
2880.2.u.a.2159.18		96	48.29	odd	4
2880.2.u.a.2159.31		96	16.13	even	4
2880.2.u.a.2159.42		96	240.29	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.956592 - 1.04160i) q^{2} +(-0.169864 + 1.99277i) q^{4} +(1.93984 + 1.11222i) q^{5} -1.78786i q^{7} +(2.23816 - 1.72934i) q^{8} +O(q^{10})\)	\(q+(-0.956592 - 1.04160i) q^{2} +(-0.169864 + 1.99277i) q^{4} +(1.93984 + 1.11222i) q^{5} -1.78786i q^{7} +(2.23816 - 1.72934i) q^{8} +(-0.697143 - 3.08448i) q^{10} +(3.34421 + 3.34421i) q^{11} +(-2.90349 - 2.90349i) q^{13} +(-1.86224 + 1.71025i) q^{14} +(-3.94229 - 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 + 0.0693845i) q^{19} +(-2.54591 + 3.67673i) q^{20} +(0.284286 - 6.68237i) q^{22} -1.07695 q^{23} +(2.52593 + 4.31505i) q^{25} +(-0.246821 + 5.80172i) q^{26} +(3.56280 + 0.303692i) q^{28} +(-1.23988 - 1.23988i) q^{29} +8.56612i q^{31} +(3.06600 + 4.75391i) q^{32} +(-4.36907 - 4.75733i) q^{34} +(1.98849 - 3.46816i) q^{35} +(7.62458 - 7.62458i) q^{37} +(0.00589828 - 0.138644i) q^{38} +(6.26508 - 0.865308i) q^{40} +7.91601 q^{41} +(-2.35179 - 2.35179i) q^{43} +(-7.23230 + 6.09619i) q^{44} +(1.03020 + 1.12175i) q^{46} +6.32188i q^{47} +3.80356 q^{49} +(2.07827 - 6.75876i) q^{50} +(6.27919 - 5.29279i) q^{52} +(3.61429 + 3.61429i) q^{53} +(2.76772 + 10.2067i) q^{55} +(-3.09182 - 4.00152i) q^{56} +(-0.105400 + 2.47751i) q^{58} +(2.25080 + 2.25080i) q^{59} +(4.29893 - 4.29893i) q^{61} +(8.92248 - 8.19429i) q^{62} +(2.01876 - 7.74110i) q^{64} +(-2.40297 - 8.86160i) q^{65} +(-5.85271 + 5.85271i) q^{67} +(-0.775822 + 9.10164i) q^{68} +(-5.51461 + 1.24639i) q^{70} -15.1431i q^{71} -6.88118 q^{73} +(-15.2354 - 0.648155i) q^{74} +(-0.150054 + 0.126482i) q^{76} +(5.97897 - 5.97897i) q^{77} -12.9721i q^{79} +(-6.89443 - 5.69797i) q^{80} +(-7.57239 - 8.24532i) q^{82} +(-6.88840 - 6.88840i) q^{83} +(8.85986 + 5.07987i) q^{85} +(-0.199923 + 4.69933i) q^{86} +(13.2682 + 1.70161i) q^{88} +6.31609 q^{89} +(-5.19103 + 5.19103i) q^{91} +(0.182935 - 2.14612i) q^{92} +(6.58487 - 6.04746i) q^{94} +(0.0574238 + 0.211766i) q^{95} -4.56728i q^{97} +(-3.63845 - 3.96179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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