LMFDB - Embedded newform 720.2.u.a.179.13

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			179.13
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +O(q^{10})$	\(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +(0.956594 + 3.01412i) q^{10} +(-3.34421 + 3.34421i) q^{11} +(2.90349 - 2.90349i) q^{13} +(1.86224 + 1.71025i) q^{14} +(-3.94229 + 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 - 0.0693845i) q^{19} +(-4.05458 - 1.88690i) q^{20} +(-0.284286 - 6.68237i) q^{22} -1.07695 q^{23} +(-2.52593 - 4.31505i) q^{25} +(0.246821 + 5.80172i) q^{26} +(-3.56280 + 0.303692i) q^{28} +(1.23988 - 1.23988i) q^{29} -8.56612i q^{31} +(3.06600 - 4.75391i) q^{32} +(-4.36907 + 4.75733i) q^{34} +(-3.46816 - 1.98849i) q^{35} +(-7.62458 - 7.62458i) q^{37} +(0.00589828 + 0.138644i) q^{38} +(5.84397 - 2.41826i) q^{40} -7.91601 q^{41} +(2.35179 - 2.35179i) q^{43} +(7.23230 + 6.09619i) q^{44} +(1.03020 - 1.12175i) q^{46} -6.32188i q^{47} +3.80356 q^{49} +(6.91085 + 1.49673i) q^{50} +(-6.27919 - 5.29279i) q^{52} +(3.61429 - 3.61429i) q^{53} +(2.76772 + 10.2067i) q^{55} +(3.09182 - 4.00152i) q^{56} +(0.105400 + 2.47751i) q^{58} +(-2.25080 + 2.25080i) q^{59} +(4.29893 + 4.29893i) q^{61} +(8.92248 + 8.19429i) q^{62} +(2.01876 + 7.74110i) q^{64} +(-2.40297 - 8.86160i) q^{65} +(5.85271 + 5.85271i) q^{67} +(-0.775822 - 9.10164i) q^{68} +(5.38883 - 1.71026i) q^{70} -15.1431i q^{71} +6.88118 q^{73} +(15.2354 - 0.648155i) q^{74} +(-0.150054 - 0.126482i) q^{76} +(5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-3.07143 + 8.40038i) q^{80} +(7.57239 - 8.24532i) q^{82} +(-6.88840 + 6.88840i) q^{83} +(5.07987 - 8.85986i) q^{85} +(0.199923 + 4.69933i) q^{86} +(-13.2682 + 1.70161i) q^{88} -6.31609 q^{89} +(-5.19103 - 5.19103i) q^{91} +(0.182935 + 2.14612i) q^{92} +(6.58487 + 6.04746i) q^{94} +(-0.0574238 - 0.211766i) q^{95} -4.56728i q^{97} +(-3.63845 + 3.96179i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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
$5$	1.11222	−	1.93984i	0.497400	−	0.867521i
$5$	1.11222	−	1.93984i	0.497400	−	0.867521i
$6$		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
$10$	0.956594	+	3.01412i	0.302502	+	0.953149i
$11$	−3.34421	+	3.34421i	−1.00832	+	1.00832i	−0.00835103	+	0.999965i	$0.502658\pi$
$11$	−3.34421	+	3.34421i	−1.00832	+	1.00832i	−0.999965	+	0.00835103i	$0.997342\pi$
$12$		0			0
$13$	2.90349	−	2.90349i	0.805282	−	0.805282i	−0.178634	−	0.983916i	$-0.557168\pi$
$13$	2.90349	−	2.90349i	0.805282	−	0.805282i	0.983916	+	0.178634i	$0.0571677\pi$
$14$	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	−0.699103	−	0.715021i	$-0.746417\pi$
$19$	0.0693845	−	0.0693845i	0.0159179	−	0.0159179i	0.715021	+	0.699103i	$0.246417\pi$
$20$	−4.05458	−	1.88690i	−0.906632	−	0.421923i
$21$		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	$-0.697946\pi$
$29$	1.23988	−	1.23988i	0.230239	−	0.230239i	0.812792	+	0.582553i	$0.197946\pi$
$30$		0			0
$31$		−	8.56612i		−	1.53852i	−0.638935	−	0.769261i	$-0.720625\pi$
$31$		−	8.56612i		−	1.53852i	0.638935	−	0.769261i	$-0.279375\pi$
$32$	3.06600	−	4.75391i	0.541998	−	0.840380i
$33$		0			0
$34$	−4.36907	+	4.75733i	−0.749289	+	0.815875i
$35$	−3.46816	−	1.98849i	−0.586225	−	0.336117i
$36$		0			0
$37$	−7.62458	−	7.62458i	−1.25347	−	1.25347i	−0.954153	−	0.299321i	$-0.903240\pi$
$37$	−7.62458	−	7.62458i	−1.25347	−	1.25347i	−0.299321	−	0.954153i	$-0.596760\pi$
$38$	0.00589828	+	0.138644i	0.000956828	+	0.0224910i
$39$		0			0
$40$	5.84397	−	2.41826i	0.924013	−	0.382361i
$41$	−7.91601			−1.23627			−0.618137	−	0.786071i	$-0.712112\pi$
$41$	−7.91601			−1.23627			−0.618137	+	0.786071i	$0.712112\pi$
$42$		0			0
$43$	2.35179	−	2.35179i	0.358645	−	0.358645i	−0.504668	−	0.863313i	$-0.668385\pi$
$43$	2.35179	−	2.35179i	0.358645	−	0.358645i	0.863313	+	0.504668i	$0.168385\pi$
$44$	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	$-0.847466\pi$
$47$		−	6.32188i		−	0.922141i	0.887364	−	0.461070i	$-0.152534\pi$
$48$		0			0
$49$	3.80356			0.543365
$50$	6.91085	+	1.49673i	0.977341	+	0.211670i
$51$		0			0
$52$	−6.27919	−	5.29279i	−0.870766	−	0.733978i
$53$	3.61429	−	3.61429i	0.496461	−	0.496461i	−0.413874	−	0.910334i	$-0.635824\pi$
$53$	3.61429	−	3.61429i	0.496461	−	0.496461i	0.910334	+	0.413874i	$0.135824\pi$
$54$		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	$-0.816436\pi$
$59$	−2.25080	+	2.25080i	−0.293030	+	0.293030i	0.545246	+	0.838276i	$0.316436\pi$
$60$		0			0
$61$	4.29893	+	4.29893i	0.550421	+	0.550421i	0.926562	−	0.376141i	$-0.122749\pi$
$61$	4.29893	+	4.29893i	0.550421	+	0.550421i	−0.376141	+	0.926562i	$0.622749\pi$
$62$	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	$-0.0812722\pi$
$67$	5.85271	+	5.85271i	0.715022	+	0.715022i	−0.252559	+	0.967581i	$0.581272\pi$
$68$	−0.775822	−	9.10164i	−0.0940822	−	1.10374i
$69$		0			0
$70$	5.38883	−	1.71026i	0.644088	−	0.204415i
$71$		−	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	$-0.368075\pi$
$73$	6.88118			0.805381			0.402691	+	0.915336i	$0.368075\pi$
$74$	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	$0.260357\pi$
$79$			12.9721i			1.45947i	−0.683730	+	0.729735i	$0.739643\pi$
$80$	−3.07143	+	8.40038i	−0.343396	+	0.939191i
$81$		0			0
$82$	7.57239	−	8.24532i	0.836231	−	0.910544i
$83$	−6.88840	+	6.88840i	−0.756100	+	0.756100i	−0.975610	−	0.219510i	$-0.929554\pi$
$83$	−6.88840	+	6.88840i	−0.756100	+	0.756100i	0.219510	+	0.975610i	$0.429554\pi$
$84$		0			0
$85$	5.07987	−	8.85986i	0.550989	−	0.960987i
$86$	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	$-0.608653\pi$
$89$	−6.31609			−0.669504			−0.334752	+	0.942306i	$0.608653\pi$
$90$		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
$100$	−8.16986	+	5.76658i	−0.816986	+	0.576658i
$101$	6.24690	+	6.24690i	0.621589	+	0.621589i	0.945938	−	0.324348i	$-0.105145\pi$
$101$	6.24690	+	6.24690i	0.621589	+	0.621589i	−0.324348	+	0.945938i	$0.605145\pi$
$102$		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	0.750277	−	0.661124i	$-0.229920\pi$
$107$	0.922209	+	0.922209i	0.0891533	+	0.0891533i	−0.661124	+	0.750277i	$0.729920\pi$
$108$		0			0
$109$	−2.28662	−	2.28662i	−0.219019	−	0.219019i	0.589066	−	0.808085i	$-0.299496\pi$
$109$	−2.28662	−	2.28662i	−0.219019	−	0.219019i	−0.808085	+	0.589066i	$0.799496\pi$
$110$	−13.2789	−	6.88080i	−1.26609	−	0.656058i
$111$		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
$115$	−1.19781	+	2.08911i	−0.111696	+	0.194811i
$116$	−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
$125$	−11.1799	+	0.100608i	−0.999960	+	0.00899866i
$126$		0			0
$127$	−0.00277854			−0.000246555			−0.000123278	−	1.00000i	$-0.500039\pi$
$127$	−0.00277854			−0.000246555			−0.000123278		1.00000i	$0.500039\pi$
$128$	−9.99426	−	5.30233i	−0.883376	−	0.468665i
$129$		0			0
$130$	11.5289	+	5.97400i	1.01115	+	0.523955i
$131$	−8.71989	−	8.71989i	−0.761860	−	0.761860i	0.214798	−	0.976658i	$-0.431091\pi$
$131$	−8.71989	−	8.71989i	−0.761860	−	0.761860i	−0.976658	+	0.214798i	$0.931091\pi$
$132$		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	$-0.544876\pi$
$137$		−	23.1771i		−	1.98016i	0.140516	−	0.990078i	$-0.455124\pi$
$138$		0			0
$139$	−7.85331	−	7.85331i	−0.666109	−	0.666109i	0.290704	−	0.956813i	$-0.406111\pi$
$139$	−7.85331	−	7.85331i	−0.666109	−	0.666109i	−0.956813	+	0.290704i	$0.906111\pi$
$140$	−3.37350	+	7.24902i	−0.285113	+	0.612654i
$141$		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	0.992495	+	0.122285i	$0.0390222\pi$
$149$	13.6076	+	13.6076i	1.11478	+	1.11478i	0.122285	+	0.992495i	$0.460978\pi$
$150$		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
$155$	−16.6169	−	9.52742i	−1.33470	−	0.765261i
$156$		0			0
$157$	5.76894	−	5.76894i	0.460411	−	0.460411i	−0.438379	−	0.898790i	$-0.644447\pi$
$157$	5.76894	−	5.76894i	0.460411	−	0.460411i	0.898790	+	0.438379i	$0.144447\pi$
$158$	−13.5117	−	12.4090i	−1.07493	−	0.987204i
$159$		0			0
$160$	−5.81173	−	11.2349i	−0.459458	−	0.888200i
$161$			1.92544i			0.151746i
$162$		0			0
$163$	10.4511	+	10.4511i	0.818594	+	0.818594i	0.985904	−	0.167311i	$-0.0535083\pi$
$163$	10.4511	+	10.4511i	0.818594	+	0.818594i	−0.167311	+	0.985904i	$0.553508\pi$
$164$	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
$170$	4.36908	+	13.7665i	0.335093	+	1.05584i
$171$		0			0
$172$	−5.08607	−	4.28711i	−0.387810	−	0.326889i
$173$	6.21995	+	6.21995i	0.472894	+	0.472894i	0.902850	−	0.429956i	$-0.141471\pi$
$173$	6.21995	+	6.21995i	0.472894	+	0.472894i	−0.429956	+	0.902850i	$0.641471\pi$
$174$		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	0.852179	+	0.523251i	$0.175281\pi$
$179$	18.4020	+	18.4020i	1.37543	+	1.37543i	0.523251	+	0.852179i	$0.324719\pi$
$180$		0			0
$181$	−18.5731	+	18.5731i	−1.38053	+	1.38053i	−0.536851	+	0.843677i	$0.680386\pi$
$181$	−18.5731	+	18.5731i	−1.38053	+	1.38053i	−0.843677	+	0.536851i	$0.819614\pi$
$182$	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
$190$	0.275506	+	0.142761i	0.0199873	+	0.0103569i
$191$	−4.73383			−0.342528			−0.171264	−	0.985225i	$-0.554785\pi$
$191$	−4.73383			−0.342528			−0.171264	+	0.985225i	$0.554785\pi$
$192$		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	−0.930734	−	0.365698i	$-0.880830\pi$
$197$	−7.93066	+	7.93066i	−0.565036	+	0.565036i	0.365698	+	0.930734i	$0.380830\pi$
$198$		0			0
$199$	−2.34717			−0.166386			−0.0831932	−	0.996533i	$-0.526512\pi$
$199$	−2.34717			−0.166386			−0.0831932	+	0.996533i	$0.526512\pi$
$200$	1.80875	−	14.0260i	0.127898	−	0.991787i
$201$		0			0
$202$	−12.4825	+	0.531040i	−0.878266	+	0.0373638i
$203$	−2.21672	−	2.21672i	−0.155583	−	0.155583i
$204$		0			0
$205$	−8.80435	+	15.3558i	−0.614922	+	1.07249i
$206$	−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	−0.802813	−	0.596231i	$-0.796664\pi$
$211$	−3.00077	+	3.00077i	−0.206581	+	0.206581i	0.596231	+	0.802813i	$0.296664\pi$
$212$	−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
$220$	19.8695	−	7.24919i	1.33960	−	0.488740i
$221$	13.2612	−	13.2612i	0.892042	−	0.892042i
$222$		0			0
$223$	24.6842			1.65298			0.826489	−	0.562952i	$-0.190335\pi$
$223$	24.6842			1.65298			0.826489	+	0.562952i	$0.190335\pi$
$224$	−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	−0.854640	−	0.519221i	$-0.826222\pi$
$227$	−5.05360	+	5.05360i	−0.335419	+	0.335419i	0.519221	+	0.854640i	$0.326222\pi$
$228$		0			0
$229$	−13.4816	+	13.4816i	−0.890886	+	0.890886i	−0.994606	−	0.103720i	$-0.966925\pi$
$229$	−13.4816	+	13.4816i	−0.890886	+	0.890886i	0.103720	+	0.994606i	$0.466925\pi$
$230$	−1.03021	−	3.24606i	−0.0679298	−	0.214039i
$231$		0			0
$232$	4.91921	−	0.630877i	0.322962	−	0.0414191i
$233$			11.8466i			0.776096i	0.921639	+	0.388048i	$0.126851\pi$
$233$			11.8466i			0.776096i	−0.921639	+	0.388048i	$0.873149\pi$
$234$		0			0
$235$	−12.2634	−	7.03132i	−0.799977	−	0.458673i
$236$	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	$-0.202651\pi$
$239$	24.8620			1.60819			0.804093	+	0.594503i	$0.202651\pi$
$240$		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
$245$	4.23039	−	7.37828i	0.270270	−	0.471381i
$246$		0			0
$247$		−	0.402914i		−	0.0256368i
$248$	14.8138	−	19.1724i	0.940674	−	1.21745i
$249$		0			0
$250$	10.5898	−	11.7412i	0.669758	−	0.742580i
$251$	−21.6723	+	21.6723i	−1.36795	+	1.36795i	−0.504582	+	0.863364i	$0.668353\pi$
$251$	−21.6723	+	21.6723i	−1.36795	+	1.36795i	−0.863364	+	0.504582i	$0.831647\pi$
$252$		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
$260$	−17.2510	+	6.29384i	−1.06986	+	0.390328i
$261$		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	$-0.644533\pi$
$269$	7.54542	−	7.54542i	0.460053	−	0.460053i	0.898673	+	0.438620i	$0.144533\pi$
$270$		0			0
$271$			4.45852i			0.270836i	0.990789	+	0.135418i	$0.0432377\pi$
$271$			4.45852i			0.270836i	−0.990789	+	0.135418i	$0.956762\pi$
$272$	−18.0057	+	3.09207i	−1.09176	+	0.187485i
$273$		0			0
$274$	24.1413	+	22.1711i	1.45843	+	1.33940i
$275$	22.8777	+	5.98318i	1.37957	+	0.360800i
$276$		0			0
$277$	5.28152	+	5.28152i	0.317336	+	0.317336i	0.847743	−	0.530407i	$-0.177961\pi$
$277$	5.28152	+	5.28152i	0.317336	+	0.317336i	−0.530407	+	0.847743i	$0.677961\pi$
$278$	15.6924	−	0.667599i	0.941169	−	0.0400399i
$279$		0			0
$280$	−4.32352	−	10.4482i	−0.258380	−	0.624399i
$281$	26.3280			1.57060			0.785298	−	0.619118i	$-0.212510\pi$
$281$	26.3280			1.57060			0.785298	+	0.619118i	$0.212510\pi$
$282$		0			0
$283$	13.6186	−	13.6186i	0.809540	−	0.809540i	−0.175024	−	0.984564i	$-0.556000\pi$
$283$	13.6186	−	13.6186i	0.809540	−	0.809540i	0.984564	+	0.175024i	$0.0560005\pi$
$284$	−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
$290$	4.92319	+	2.55108i	0.289100	+	0.149804i
$291$		0			0
$292$	−1.16886	−	13.7126i	−0.0684024	−	0.802471i
$293$	−9.23746	+	9.23746i	−0.539658	+	0.539658i	−0.923429	−	0.383770i	$-0.874625\pi$
$293$	−9.23746	+	9.23746i	−0.539658	+	0.539658i	0.383770	+	0.923429i	$0.374625\pi$
$294$		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	$-0.219489\pi$
$307$	2.37148	+	2.37148i	0.135348	+	0.135348i	−0.636187	+	0.771535i	$0.719489\pi$
$308$	10.8991	−	12.9303i	0.621035	−	0.736775i
$309$		0			0
$310$	25.8193	−	8.19430i	1.46644	−	0.465405i
$311$		−	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	$-0.295389\pi$
$313$	21.2104			1.19888			0.599442	+	0.800418i	$0.295389\pi$
$314$	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	0.723082	−	0.690763i	$-0.242725\pi$
$317$	0.575423	+	0.575423i	0.0323190	+	0.0323190i	−0.690763	+	0.723082i	$0.742725\pi$
$318$		0			0
$319$			8.29280i			0.464308i
$320$	17.2618	+	4.69375i	0.964962	+	0.262388i
$321$		0			0
$322$	−2.00554	−	1.84186i	−0.111764	−	0.102643i
$323$	0.316902	−	0.316902i	0.0176329	−	0.0176329i
$324$		0			0
$325$	−19.8627	−	5.19468i	−1.10178	−	0.288149i
$326$	−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	0.842901	−	0.538068i	$-0.180846\pi$
$331$	5.54595	+	5.54595i	0.304833	+	0.304833i	−0.538068	+	0.842901i	$0.680846\pi$
$332$	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
$340$	−18.5186	−	8.61807i	−1.00431	−	0.467380i
$341$	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	−0.999997	−	0.00262421i	$-0.999165\pi$
$347$	−18.6768	−	18.6768i	−1.00262	−	1.00262i	−0.00262421	−	0.999997i	$-0.500835\pi$
$348$		0			0
$349$	15.2350	+	15.2350i	0.815511	+	0.815511i	0.985454	−	0.169943i	$-0.0543583\pi$
$349$	15.2350	+	15.2350i	0.815511	+	0.815511i	−0.169943	+	0.985454i	$0.554358\pi$
$350$	2.67595	−	12.3556i	0.143035	−	0.660436i
$351$		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
$355$	−29.3752	−	16.8425i	−1.55907	−	0.893906i
$356$	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
$365$	7.65339	−	13.3484i	0.400597	−	0.698685i
$366$		0			0
$367$	−25.3790			−1.32477			−0.662385	−	0.749163i	$-0.730456\pi$
$367$	−25.3790			−1.32477			−0.662385	+	0.749163i	$0.730456\pi$
$368$	4.24566	−	0.729096i	0.221320	−	0.0380067i
$369$		0			0
$370$	15.6878	−	30.2750i	0.815569	−	1.57392i
$371$	−6.46184	−	6.46184i	−0.335482	−	0.335482i
$372$		0			0
$373$	−2.85715	−	2.85715i	−0.147938	−	0.147938i	0.629259	−	0.777196i	$-0.283359\pi$
$373$	−2.85715	−	2.85715i	−0.147938	−	0.147938i	−0.777196	+	0.629259i	$0.783359\pi$
$374$	−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	0.438440	−	0.898760i	$-0.355531\pi$
$379$	−8.96148	−	8.96148i	−0.460320	−	0.460320i	−0.898760	+	0.438440i	$0.855531\pi$
$380$	−0.412247	+	0.150404i	−0.0211478	+	0.00771555i
$381$		0			0
$382$	4.52834	−	4.93076i	0.231690	−	0.252280i
$383$		−	9.83688i		−	0.502641i	−0.967904	−	0.251321i	$-0.919135\pi$
$383$		−	9.83688i		−	0.502641i	0.967904	−	0.251321i	$-0.0808648\pi$
$384$		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	$-0.149045\pi$
$389$	8.69886	+	8.69886i	0.441050	+	0.441050i	−0.451315	+	0.892365i	$0.649045\pi$
$390$		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
$395$	25.1637	+	14.4278i	1.26612	+	0.725941i
$396$		0			0
$397$	2.52696	−	2.52696i	0.126824	−	0.126824i	−0.640845	−	0.767670i	$-0.721416\pi$
$397$	2.52696	−	2.52696i	0.126824	−	0.126824i	0.767670	+	0.640845i	$0.221416\pi$
$398$	2.24528	−	2.44481i	0.112546	−	0.122547i
$399$		0			0
$400$	12.8792	+	15.3011i	0.643962	+	0.765057i
$401$			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	$-0.857527\pi$
$409$		−	17.5055i		−	0.865591i	0.901492	−	0.432795i	$-0.142473\pi$
$410$	−7.57241	−	23.8598i	−0.373975	−	1.17835i
$411$		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	$-0.213627\pi$
$419$	3.30068	+	3.30068i	0.161249	+	0.161249i	−0.621871	+	0.783120i	$0.713627\pi$
$420$		0			0
$421$	−6.14311	+	6.14311i	−0.299397	+	0.299397i	−0.840778	−	0.541381i	$-0.817902\pi$
$421$	−6.14311	+	6.14311i	−0.299397	+	0.299397i	0.541381	+	0.840778i	$0.317902\pi$
$422$	−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
$430$	9.33830	+	4.83888i	0.450333	+	0.233351i
$431$	−8.73359			−0.420682			−0.210341	−	0.977628i	$-0.567457\pi$
$431$	−8.73359			−0.420682			−0.210341	+	0.977628i	$0.567457\pi$
$432$		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	$0.269884\pi$
$440$	−11.4563	+	27.6306i	−0.546156	+	1.31724i
$441$		0			0
$442$	1.12731	+	26.4984i	0.0536208	+	1.26040i
$443$	15.8575	+	15.8575i	0.753410	+	0.753410i	0.975114	−	0.221704i	$-0.0711618\pi$
$443$	15.8575	+	15.8575i	0.753410	+	0.753410i	−0.221704	+	0.975114i	$0.571162\pi$
$444$		0			0
$445$	−7.02488	+	12.2522i	−0.333011	+	0.580809i
$446$	−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	$-0.683621\pi$
$457$	−23.3185			−1.09079			−0.545397	+	0.838178i	$0.683621\pi$
$458$	−1.14605	−	26.9387i	−0.0535513	−	1.25876i
$459$		0			0
$460$	4.36659	+	2.03210i	0.203593	+	0.0947470i
$461$	−6.98422	+	6.98422i	−0.325288	+	0.325288i	−0.850791	−	0.525504i	$-0.823877\pi$
$461$	−6.98422	+	6.98422i	−0.325288	+	0.325288i	0.525504	+	0.850791i	$0.323877\pi$
$462$		0			0
$463$	−0.177929			−0.00826905			−0.00413453	−	0.999991i	$-0.501316\pi$
$463$	−0.177929			−0.00826905			−0.00413453	+	0.999991i	$0.501316\pi$
$464$	−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	−0.221414	+	0.975180i	$0.571067\pi$
$467$	−25.8586	+	25.8586i	−1.19659	+	1.19659i	−0.975180	+	0.221414i	$0.928933\pi$
$468$		0			0
$469$	10.4638	−	10.4638i	0.483175	−	0.483175i
$470$	19.0549	−	6.04747i	0.878937	−	0.278949i
$471$		0			0
$472$	−8.93008	+	1.14526i	−0.411040	+	0.0527149i
$473$			15.7298i			0.723255i
$474$		0			0
$475$	−0.474658	−	0.124137i	−0.0217788	−	0.00569581i
$476$	−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	$-0.450752\pi$
$479$	6.74528			0.308200			0.154100	+	0.988055i	$0.450752\pi$
$480$		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
$485$	−8.85978	−	5.07982i	−0.402302	−	0.230663i
$486$		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
$490$	3.63846	+	11.4644i	0.164369	+	0.517908i
$491$	1.96277	−	1.96277i	0.0885786	−	0.0885786i	−0.661429	−	0.750008i	$-0.730050\pi$
$491$	1.96277	−	1.96277i	0.0885786	−	0.0885786i	0.750008	+	0.661429i	$0.230050\pi$
$492$		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	−0.895172	−	0.445720i	$-0.852948\pi$
$499$	−10.0400	+	10.0400i	−0.449452	+	0.449452i	0.445720	+	0.895172i	$0.352948\pi$
$500$	2.09954	+	22.2619i	0.0938945	+	0.995582i
$501$		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	$-0.924189\pi$
$509$	−16.6015	+	16.6015i	−0.735849	+	0.735849i	0.235922	+	0.971772i	$0.424189\pi$
$510$		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
$515$	26.8760	+	15.4096i	1.18430	+	0.679027i
$516$		0			0
$517$	21.1417	+	21.1417i	0.929809	+	0.929809i
$518$	−1.15881	−	27.2387i	−0.0509152	−	1.19680i
$519$		0			0
$520$	9.94649	−	23.9893i	0.436182	−	1.05200i
$521$	−7.96468			−0.348939			−0.174469	−	0.984663i	$-0.555821\pi$
$521$	−7.96468			−0.348939			−0.174469	+	0.984663i	$0.555821\pi$
$522$		0			0
$523$	15.2514	−	15.2514i	0.666897	−	0.666897i	−0.290099	−	0.956997i	$-0.593688\pi$
$523$	15.2514	−	15.2514i	0.666897	−	0.666897i	0.956997	+	0.290099i	$0.0936883\pi$
$524$	−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
$530$	14.3513	+	7.43650i	0.623381	+	0.323021i
$531$		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	0.545414	−	0.838167i	$-0.316372\pi$
$541$	−6.80924	−	6.80924i	−0.292752	−	0.292752i	−0.838167	+	0.545414i	$0.816372\pi$
$542$	−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	0.997819	+	0.0660132i	$0.0210279\pi$
$547$	24.8809	+	24.8809i	1.06383	+	1.06383i	0.0660132	+	0.997819i	$0.478972\pi$
$548$	−46.1868	+	3.93695i	−1.97300	+	0.168178i
$549$		0			0
$550$	−28.1167	+	18.1059i	−1.19890	+	0.772039i
$551$		−	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	0.639310	−	0.768949i	$-0.279220\pi$
$557$	−3.05959	−	3.05959i	−0.129639	−	0.129639i	−0.768949	+	0.639310i	$0.779220\pi$
$558$		0			0
$559$		−	13.6568i		−	0.577621i
$560$	15.0187	+	5.49129i	0.634656	+	0.232049i
$561$		0			0
$562$	−25.1851	+	27.4232i	−1.06237	+	1.15678i
$563$	32.0945	−	32.0945i	1.35262	−	1.35262i	0.469906	−	0.882716i	$-0.344288\pi$
$563$	32.0945	−	32.0945i	1.35262	−	1.35262i	0.882716	−	0.469906i	$-0.155712\pi$
$564$		0			0
$565$	8.38360	−	14.6219i	0.352701	−	0.615150i
$566$	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	$-0.703451\pi$
$569$	−28.4585			−1.19304			−0.596521	+	0.802597i	$0.703451\pi$
$570$		0			0
$571$	−26.7837	−	26.7837i	−1.12086	−	1.12086i	−0.991612	−	0.129250i	$-0.958743\pi$
$571$	−26.7837	−	26.7837i	−1.12086	−	1.12086i	−0.129250	−	0.991612i	$-0.541257\pi$
$572$	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
$580$	−7.36669	+	2.68766i	−0.305885	+	0.111599i
$581$	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	0.404232	−	0.914657i	$-0.367539\pi$
$587$	−12.3666	−	12.3666i	−0.510425	−	0.510425i	−0.914657	+	0.404232i	$0.867539\pi$
$588$		0			0
$589$	−0.594357	−	0.594357i	−0.0244900	−	0.0244900i
$590$	−8.93730	−	4.63109i	−0.367943	−	0.190659i
$591$		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
$595$	−15.8402	−	9.08210i	−0.649385	−	0.372330i
$596$	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	$0.125513\pi$
$601$			18.8361i			0.768342i	−0.923262	+	0.384171i	$0.874487\pi$
$602$	8.40175	−	0.357433i	0.342430	−	0.0145679i
$603$		0			0
$604$	−2.58951	−	30.3792i	−0.105366	−	1.23611i
$605$	−22.0510	−	12.6431i	−0.896499	−	0.514015i
$606$		0			0
$607$	−10.4336			−0.423486			−0.211743	−	0.977325i	$-0.567914\pi$
$607$	−10.4336			−0.423486			−0.211743	+	0.977325i	$0.567914\pi$
$608$	−0.117114	−	0.542581i	−0.00474962	−	0.0220046i
$609$		0			0
$610$	−8.84516	+	17.0698i	−0.358130	+	0.691137i
$611$	−18.3555	−	18.3555i	−0.742583	−	0.742583i
$612$		0			0
$613$	9.35631	+	9.35631i	0.377898	+	0.377898i	0.870343	−	0.492445i	$-0.163897\pi$
$613$	9.35631	+	9.35631i	0.377898	+	0.377898i	−0.492445	+	0.870343i	$0.663897\pi$
$614$	−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	$0.152442\pi$
$617$			22.8927i			0.921626i	−0.887497	+	0.460813i	$0.847558\pi$
$618$		0			0
$619$	32.9542	+	32.9542i	1.32454	+	1.32454i	0.910057	+	0.414484i	$0.136038\pi$
$619$	32.9542	+	32.9542i	1.32454	+	1.32454i	0.414484	+	0.910057i	$0.363962\pi$
$620$	−16.1634	+	34.7320i	−0.649137	+	1.39487i
$621$		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
$635$	−0.00309035	+	0.00538991i	−0.000122637	+	0.000213892i
$636$		0			0
$637$	11.0436	−	11.0436i	0.437562	−	0.437562i
$638$	−8.63778	−	7.93283i	−0.341973	−	0.314064i
$639$		0			0
$640$	−21.4015	+	13.4899i	−0.845968	+	0.533234i
$641$		−	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	$-0.0812779\pi$
$643$	18.1306	+	18.1306i	0.715001	+	0.715001i	−0.252576	+	0.967577i	$0.581278\pi$
$644$	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
$650$	24.4113	−	15.7198i	0.957489	−	0.616582i
$651$		0			0
$652$	19.0514	−	22.6019i	0.746111	−	0.885160i
$653$	−12.2088	−	12.2088i	−0.477769	−	0.477769i	0.426649	−	0.904417i	$-0.359694\pi$
$653$	−12.2088	−	12.2088i	−0.477769	−	0.477769i	−0.904417	+	0.426649i	$0.859694\pi$
$654$		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	$-0.490290\pi$
$659$	−24.8761	−	24.8761i	−0.969034	−	0.969034i	−0.999535	+	0.0305007i	$0.990290\pi$
$660$		0			0
$661$	−21.1349	+	21.1349i	−0.822052	+	0.822052i	−0.986402	−	0.164350i	$-0.947447\pi$
$661$	−21.1349	+	21.1349i	−0.822052	+	0.822052i	0.164350	+	0.986402i	$0.447447\pi$
$662$	−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
$670$	−12.0421	+	23.2395i	−0.465227	+	0.897818i
$671$	−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	−0.519981	−	0.854178i	$-0.674061\pi$
$677$	8.69556	−	8.69556i	0.334197	−	0.334197i	0.854178	+	0.519981i	$0.174061\pi$
$678$		0			0
$679$	−8.16566			−0.313369
$680$	26.6913	−	11.0450i	1.02357	−	0.423556i
$681$		0			0
$682$	−57.2420	+	2.43523i	−2.19191	+	0.0932498i
$683$	26.4514	+	26.4514i	1.01213	+	1.01213i	0.999925	+	0.0122093i	$0.00388645\pi$
$683$	26.4514	+	26.4514i	1.01213	+	1.01213i	0.0122093	+	0.999925i	$0.496114\pi$
$684$		0			0
$685$	−44.9599	−	25.7781i	−1.71783	−	0.984930i
$686$	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	−0.517301	−	0.855804i	$-0.673063\pi$
$691$	8.89820	−	8.89820i	0.338503	−	0.338503i	0.855804	+	0.517301i	$0.173063\pi$
$692$	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
$700$	10.3098	+	14.6066i	0.389675	+	0.552076i
$701$	15.7989	−	15.7989i	0.596716	−	0.596716i	−0.342721	−	0.939437i	$-0.611349\pi$
$701$	15.7989	−	15.7989i	0.596716	−	0.596716i	0.939437	+	0.342721i	$0.111349\pi$
$702$		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	−0.255922	−	0.966697i	$-0.582379\pi$
$709$	18.9259	−	18.9259i	0.710776	−	0.710776i	0.966697	+	0.255922i	$0.0823790\pi$
$710$	45.6432	−	14.4858i	1.71296	−	0.543643i
$711$		0			0
$712$	−14.1364	−	10.9227i	−0.529785	−	0.409344i
$713$			9.22531i			0.345490i
$714$		0			0
$715$	37.6711	+	21.5990i	1.40882	+	0.807757i
$716$	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	$-0.563811\pi$
$719$	−10.6789			−0.398256			−0.199128	+	0.979973i	$0.563811\pi$
$720$		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
$725$	−8.48197	−	2.21828i	−0.315012	−	0.0823850i
$726$		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
$730$	6.58249	+	20.7407i	0.243629	+	0.767648i
$731$	10.7414	−	10.7414i	0.397285	−	0.397285i
$732$		0			0
$733$	−29.6986	+	29.6986i	−1.09694	+	1.09694i	−0.102175	+	0.994766i	$0.532580\pi$
$733$	−29.6986	+	29.6986i	−1.09694	+	1.09694i	−0.994766	+	0.102175i	$0.967420\pi$
$734$	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	−0.242509	−	0.970149i	$-0.577970\pi$
$739$	19.7806	−	19.7806i	0.727640	−	0.727640i	0.970149	+	0.242509i	$0.0779704\pi$
$740$	16.5277	+	45.3013i	0.607570	+	1.66531i
$741$		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	$-0.654783\pi$
$751$		−	48.4556i		−	1.76817i	0.467326	−	0.884085i	$-0.345217\pi$
$752$	4.27991	+	24.9227i	0.156072	+	0.908837i
$753$		0			0
$754$	7.49944	+	6.88739i	0.273114	+	0.250824i
$755$	16.9554	−	29.5722i	0.617071	−	1.07624i
$756$		0			0
$757$	24.8358	+	24.8358i	0.902672	+	0.902672i	0.995667	−	0.0929947i	$-0.0296440\pi$
$757$	24.8358	+	24.8358i	0.902672	+	0.902672i	−0.0929947	+	0.995667i	$0.529644\pi$
$758$	17.9068	−	0.761803i	0.650403	−	0.0276699i
$759$		0			0
$760$	0.237691	−	0.573271i	0.00862196	−	0.0207947i
$761$	26.2421			0.951274			0.475637	−	0.879642i	$-0.342218\pi$
$761$	26.2421			0.951274			0.475637	+	0.879642i	$0.342218\pi$
$762$		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	$0.348467\pi$
$770$	−12.3019	+	23.7408i	−0.443330	+	0.855559i
$771$		0			0
$772$	−33.3227	+	2.84042i	−1.19931	+	0.102229i
$773$	30.1984	−	30.1984i	1.08616	−	1.08616i	0.0902412	−	0.995920i	$-0.471236\pi$
$773$	30.1984	−	30.1984i	1.08616	−	1.08616i	0.995920	−	0.0902412i	$-0.0287638\pi$
$774$		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	$-0.412108\pi$
$787$	−19.3428	−	19.3428i	−0.689496	−	0.689496i	−0.962120	+	0.272625i	$0.912108\pi$
$788$	17.1511	+	14.4569i	0.610984	+	0.515005i
$789$		0			0
$790$	−39.0994	+	12.4090i	−1.39109	+	0.441492i
$791$		−	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	0.987468	+	0.157820i	$0.0504466\pi$
$797$	32.3328	+	32.3328i	1.14529	+	1.14529i	0.157820	+	0.987468i	$0.449553\pi$
$798$		0			0
$799$		−	28.8741i		−	1.02149i
$800$	−28.2579	−	1.22192i	−0.999066	−	0.0432013i
$801$		0			0
$802$	−11.9967	−	11.0176i	−0.423619	−	0.389046i
$803$	−23.0121	+	23.0121i	−0.812079	+	0.812079i
$804$		0			0
$805$	3.73504	+	2.14151i	0.131643	+	0.0754784i
$806$	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	$-0.477061\pi$
$809$	4.09587			0.144003			0.0720015	+	0.997405i	$0.477061\pi$
$810$		0			0
$811$	1.34586	+	1.34586i	0.0472594	+	0.0472594i	0.730342	−	0.683082i	$-0.239361\pi$
$811$	1.34586	+	1.34586i	0.0472594	+	0.0472594i	−0.683082	+	0.730342i	$0.739361\pi$
$812$	−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
$820$	32.0961	+	14.9367i	1.12084	+	0.521612i
$821$	−16.3658	−	16.3658i	−0.571171	−	0.571171i	0.361285	−	0.932456i	$-0.382338\pi$
$821$	−16.3658	−	16.3658i	−0.571171	−	0.571171i	−0.932456	+	0.361285i	$0.882338\pi$
$822$		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	0.740051	−	0.672551i	$-0.234801\pi$
$827$	1.94113	+	1.94113i	0.0674997	+	0.0674997i	−0.672551	+	0.740051i	$0.734801\pi$
$828$		0			0
$829$	−31.5836	−	31.5836i	−1.09695	−	1.09695i	−0.994766	−	0.102179i	$-0.967419\pi$
$829$	−31.5836	−	31.5836i	−1.09695	−	1.09695i	−0.102179	−	0.994766i	$-0.532581\pi$
$830$	−27.3519	−	14.1731i	−0.949397	−	0.491955i
$831$		0			0
$832$	28.3376	+	16.6147i	0.982430	+	0.576012i
$833$	17.3721			0.601907
$834$		0			0
$835$	−10.4757	+	18.2708i	−0.362526	+	0.632286i
$836$	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
$845$	−7.48866	−	4.29368i	−0.257618	−	0.147707i
$846$		0			0
$847$	−20.3234			−0.698319
$848$	−11.8017	+	16.6954i	−0.405272	+	0.573324i
$849$		0			0
$850$	31.5641	+	6.83606i	1.08264	+	0.234475i
$851$	8.21131	+	8.21131i	0.281480	+	0.281480i
$852$		0			0
$853$	−5.21199	−	5.21199i	−0.178455	−	0.178455i	0.612227	−	0.790682i	$-0.290274\pi$
$853$	−5.21199	−	5.21199i	−0.178455	−	0.178455i	−0.790682	+	0.612227i	$0.790274\pi$
$854$	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	$-0.739608\pi$
$857$		−	42.7298i		−	1.45962i	0.683649	−	0.729811i	$-0.260392\pi$
$858$		0			0
$859$	−12.0244	−	12.0244i	−0.410268	−	0.410268i	0.471564	−	0.881832i	$-0.343690\pi$
$859$	−12.0244	−	12.0244i	−0.410268	−	0.410268i	−0.881832	+	0.471564i	$0.843690\pi$
$860$	−13.9731	+	5.09795i	−0.476479	+	0.173839i
$861$		0			0
$862$	8.35449	−	9.09692i	0.284555	−	0.309842i
$863$		−	2.21809i		−	0.0755047i	−0.999287	−	0.0377523i	$-0.987980\pi$
$863$		−	2.21809i		−	0.0755047i	0.999287	−	0.0377523i	$-0.0120198\pi$
$864$		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
$875$	0.179873	+	19.9881i	0.00608082	+	0.675720i
$876$		0			0
$877$	37.6890	−	37.6890i	1.27267	−	1.27267i	0.327984	−	0.944683i	$-0.393631\pi$
$877$	37.6890	−	37.6890i	1.27267	−	1.27267i	0.944683	−	0.327984i	$-0.106369\pi$
$878$	−26.5201	+	28.8768i	−0.895009	+	0.974545i
$879$		0			0
$880$	−17.8211	−	38.3641i	−0.600749	−	1.29325i
$881$			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	$-0.455600\pi$
$883$	−25.2952	−	25.2952i	−0.851251	−	0.851251i	−0.990287	+	0.139036i	$0.955600\pi$
$884$	−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
$890$	−6.04193	−	19.0375i	−0.202526	−	0.638137i
$891$		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	$-0.655396\pi$
$907$	12.4729	−	12.4729i	0.414156	−	0.414156i	0.883183	+	0.469028i	$0.155396\pi$
$908$	10.9291	+	9.21225i	0.362695	+	0.305719i
$909$		0			0
$910$	10.6807	−	20.6121i	0.354061	−	0.683284i
$911$	−41.2168			−1.36557			−0.682786	−	0.730618i	$-0.739232\pi$
$911$	−41.2168			−1.36557			−0.682786	+	0.730618i	$0.739232\pi$
$912$		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	$0.705366\pi$
$920$	−6.29368	+	2.60435i	−0.207496	+	0.0858630i
$921$		0			0
$922$	−0.593719	−	13.9558i	−0.0195531	−	0.459611i
$923$	−43.9678	−	43.9678i	−1.44722	−	1.44722i
$924$		0			0
$925$	−13.6413	+	52.1596i	−0.448523	+	1.71500i
$926$	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	$-0.681889\pi$
$937$	−33.1100			−1.08166			−0.540829	+	0.841133i	$0.681889\pi$
$938$	0.889515	+	20.9087i	0.0290437	+	0.682695i
$939$		0			0
$940$	−11.9287	+	25.6326i	−0.389072	+	0.836042i
$941$	−11.7810	+	11.7810i	−0.384050	+	0.384050i	−0.872559	−	0.488509i	$-0.837541\pi$
$941$	−11.7810	+	11.7810i	−0.384050	+	0.384050i	0.488509	+	0.872559i	$0.337541\pi$
$942$		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	−0.642884	−	0.765964i	$-0.722262\pi$
$947$	3.78760	−	3.78760i	0.123080	−	0.123080i	0.765964	+	0.642884i	$0.222262\pi$
$948$		0			0
$949$	19.9794	−	19.9794i	0.648559	−	0.648559i
$950$	0.583356	−	0.375656i	0.0189266	−	0.0121879i
$951$		0			0
$952$	14.1213	−	18.2763i	0.457675	−	0.592337i
$953$		−	33.8756i		−	1.09734i	−0.836039	−	0.548670i	$-0.815134\pi$
$953$		−	33.8756i		−	1.09734i	0.836039	−	0.548670i	$-0.184866\pi$
$954$		0			0
$955$	−5.26506	+	9.18286i	−0.170373	+	0.297150i
$956$	−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
$965$	−32.4375	−	18.5983i	−1.04420	−	0.598700i
$966$		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
$970$	13.7663	−	4.36903i	0.442011	−	0.140281i
$971$	10.4598	−	10.4598i	0.335670	−	0.335670i	−0.519065	−	0.854735i	$-0.673720\pi$
$971$	10.4598	−	10.4598i	0.335670	−	0.335670i	0.854735	+	0.519065i	$0.173720\pi$
$972$		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
$980$	−15.4218	−	7.17692i	−0.492632	−	0.229258i
$981$		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	$0.327777\pi$
$991$			53.9675i			1.71433i	−0.515039	+	0.857166i	$0.672223\pi$
$992$	−40.7226	−	26.2638i	−1.29294	−	0.833875i
$993$		0			0
$994$	25.8986	−	28.2001i	0.821452	−	0.894452i
$995$	−2.61057	+	4.55312i	−0.0827606	+	0.144344i
$996$		0			0
$997$	3.14670	+	3.14670i	0.0996570	+	0.0996570i	0.755177	−	0.655520i	$-0.227551\pi$
$997$	3.14670	+	3.14670i	0.0996570	+	0.0996570i	−0.655520	+	0.755177i	$0.727551\pi$
$998$	−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.179.13	✓	96
3.2	odd	2	inner	720.2.u.a.179.36	yes	96
4.3	odd	2		2880.2.u.a.2159.31		96
5.4	even	2	inner	720.2.u.a.179.35	yes	96
12.11	even	2		2880.2.u.a.2159.18		96
15.14	odd	2	inner	720.2.u.a.179.14	yes	96
16.5	even	4		2880.2.u.a.719.42		96
16.11	odd	4	inner	720.2.u.a.539.14	yes	96
20.19	odd	2		2880.2.u.a.2159.7		96
48.5	odd	4		2880.2.u.a.719.7		96
48.11	even	4	inner	720.2.u.a.539.35	yes	96
60.59	even	2		2880.2.u.a.2159.42		96
80.59	odd	4	inner	720.2.u.a.539.36	yes	96
80.69	even	4		2880.2.u.a.719.18		96
240.59	even	4	inner	720.2.u.a.539.13	yes	96
240.149	odd	4		2880.2.u.a.719.31		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.13	✓	96	1.1	even	1	trivial
720.2.u.a.179.14	yes	96	15.14	odd	2	inner
720.2.u.a.179.35	yes	96	5.4	even	2	inner
720.2.u.a.179.36	yes	96	3.2	odd	2	inner
720.2.u.a.539.13	yes	96	240.59	even	4	inner
720.2.u.a.539.14	yes	96	16.11	odd	4	inner
720.2.u.a.539.35	yes	96	48.11	even	4	inner
720.2.u.a.539.36	yes	96	80.59	odd	4	inner
2880.2.u.a.719.7		96	48.5	odd	4
2880.2.u.a.719.18		96	80.69	even	4
2880.2.u.a.719.31		96	240.149	odd	4
2880.2.u.a.719.42		96	16.5	even	4
2880.2.u.a.2159.7		96	20.19	odd	2
2880.2.u.a.2159.18		96	12.11	even	2
2880.2.u.a.2159.31		96	4.3	odd	2
2880.2.u.a.2159.42		96	60.59	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)

\(f(q)\)	\(=\)	\(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +O(q^{10})\)	\(q+(-0.956592 + 1.04160i) q^{2} +(-0.169864 - 1.99277i) q^{4} +(1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(2.23816 + 1.72934i) q^{8} +(0.956594 + 3.01412i) q^{10} +(-3.34421 + 3.34421i) q^{11} +(2.90349 - 2.90349i) q^{13} +(1.86224 + 1.71025i) q^{14} +(-3.94229 + 0.676999i) q^{16} +4.56733 q^{17} +(0.0693845 - 0.0693845i) q^{19} +(-4.05458 - 1.88690i) q^{20} +(-0.284286 - 6.68237i) q^{22} -1.07695 q^{23} +(-2.52593 - 4.31505i) q^{25} +(0.246821 + 5.80172i) q^{26} +(-3.56280 + 0.303692i) q^{28} +(1.23988 - 1.23988i) q^{29} -8.56612i q^{31} +(3.06600 - 4.75391i) q^{32} +(-4.36907 + 4.75733i) q^{34} +(-3.46816 - 1.98849i) q^{35} +(-7.62458 - 7.62458i) q^{37} +(0.00589828 + 0.138644i) q^{38} +(5.84397 - 2.41826i) q^{40} -7.91601 q^{41} +(2.35179 - 2.35179i) q^{43} +(7.23230 + 6.09619i) q^{44} +(1.03020 - 1.12175i) q^{46} -6.32188i q^{47} +3.80356 q^{49} +(6.91085 + 1.49673i) q^{50} +(-6.27919 - 5.29279i) q^{52} +(3.61429 - 3.61429i) q^{53} +(2.76772 + 10.2067i) q^{55} +(3.09182 - 4.00152i) q^{56} +(0.105400 + 2.47751i) q^{58} +(-2.25080 + 2.25080i) q^{59} +(4.29893 + 4.29893i) q^{61} +(8.92248 + 8.19429i) q^{62} +(2.01876 + 7.74110i) q^{64} +(-2.40297 - 8.86160i) q^{65} +(5.85271 + 5.85271i) q^{67} +(-0.775822 - 9.10164i) q^{68} +(5.38883 - 1.71026i) q^{70} -15.1431i q^{71} +6.88118 q^{73} +(15.2354 - 0.648155i) q^{74} +(-0.150054 - 0.126482i) q^{76} +(5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-3.07143 + 8.40038i) q^{80} +(7.57239 - 8.24532i) q^{82} +(-6.88840 + 6.88840i) q^{83} +(5.07987 - 8.85986i) q^{85} +(0.199923 + 4.69933i) q^{86} +(-13.2682 + 1.70161i) q^{88} -6.31609 q^{89} +(-5.19103 - 5.19103i) q^{91} +(0.182935 + 2.14612i) q^{92} +(6.58487 + 6.04746i) q^{94} +(-0.0574238 - 0.211766i) q^{95} -4.56728i q^{97} +(-3.63845 + 3.96179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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