LMFDB - Embedded newform 864.2.y.c.385.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.2
Character	$\chi$	$=$	864.385
Dual form			864.2.y.c.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41286 - 1.00191i) q^{3} +(0.727972 + 4.12853i) q^{5} +(0.397562 + 0.333594i) q^{7} +(0.992364 + 2.83112i) q^{9} +O(q^{10})$	\(q+(-1.41286 - 1.00191i) q^{3} +(0.727972 + 4.12853i) q^{5} +(0.397562 + 0.333594i) q^{7} +(0.992364 + 2.83112i) q^{9} +(0.338741 - 1.92110i) q^{11} +(2.95390 + 1.07513i) q^{13} +(3.10788 - 6.56241i) q^{15} +(-2.23260 - 3.86698i) q^{17} +(-4.33300 + 7.50498i) q^{19} +(-0.227470 - 0.869642i) q^{21} +(2.88631 - 2.42190i) q^{23} +(-11.8164 + 4.30081i) q^{25} +(1.43444 - 4.99423i) q^{27} +(-5.46203 + 1.98802i) q^{29} +(-4.70771 + 3.95024i) q^{31} +(-2.40336 + 2.37486i) q^{33} +(-1.08784 + 1.88419i) q^{35} +(3.15428 + 5.46337i) q^{37} +(-3.09628 - 4.47855i) q^{39} +(4.69808 + 1.70996i) q^{41} +(-0.710244 + 4.02799i) q^{43} +(-10.9659 + 6.15798i) q^{45} +(1.88530 + 1.58196i) q^{47} +(-1.16877 - 6.62841i) q^{49} +(-0.719994 + 7.70037i) q^{51} -0.351690 q^{53} +8.17791 q^{55} +(13.6412 - 6.26224i) q^{57} +(0.704805 + 3.99715i) q^{59} +(2.53188 + 2.12450i) q^{61} +(-0.549917 + 1.45659i) q^{63} +(-2.28836 + 12.9780i) q^{65} +(8.82272 + 3.21121i) q^{67} +(-6.50449 + 0.530001i) q^{69} +(-5.42150 - 9.39031i) q^{71} +(-5.54175 + 9.59859i) q^{73} +(21.0039 + 5.76245i) q^{75} +(0.775537 - 0.650753i) q^{77} +(-6.53196 + 2.37744i) q^{79} +(-7.03043 + 5.61899i) q^{81} +(-14.7555 + 5.37055i) q^{83} +(14.3397 - 12.0324i) q^{85} +(9.70891 + 2.66365i) q^{87} +(5.41326 - 9.37604i) q^{89} +(0.815702 + 1.41284i) q^{91} +(10.6091 - 0.864457i) q^{93} +(-34.1389 - 12.4255i) q^{95} +(-0.783229 + 4.44191i) q^{97} +(5.77501 - 0.947413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−1.41286	−	1.00191i	−0.815717	−	0.578451i
$3$	−1.41286	−	1.00191i	−0.815717	−	0.578451i
$4$		0			0
$5$	0.727972	+	4.12853i	0.325559	+	1.84634i	0.505719	+	0.862698i	$0.331227\pi$
$5$	0.727972	+	4.12853i	0.325559	+	1.84634i	−0.180160	+	0.983637i	$0.557662\pi$
$6$		0			0
$7$	0.397562	+	0.333594i	0.150264	+	0.126087i	0.714821	−	0.699308i	$-0.246508\pi$
$7$	0.397562	+	0.333594i	0.150264	+	0.126087i	−0.564556	+	0.825394i	$0.690953\pi$
$8$		0			0
$9$	0.992364	+	2.83112i	0.330788	+	0.943705i
$10$		0			0
$11$	0.338741	−	1.92110i	0.102134	−	0.579233i	−0.890192	−	0.455586i	$-0.849430\pi$
$11$	0.338741	−	1.92110i	0.102134	−	0.579233i	0.992326	−	0.123647i	$-0.0394591\pi$
$12$		0			0
$13$	2.95390	+	1.07513i	0.819266	+	0.298188i	0.717446	−	0.696614i	$-0.245311\pi$
$13$	2.95390	+	1.07513i	0.819266	+	0.298188i	0.101820	+	0.994803i	$0.467533\pi$
$14$		0			0
$15$	3.10788	−	6.56241i	0.802452	−	1.69441i
$16$		0			0
$17$	−2.23260	−	3.86698i	−0.541486	−	0.937880i	−0.998819	−	0.0485852i	$-0.984529\pi$
$17$	−2.23260	−	3.86698i	−0.541486	−	0.937880i	0.457334	−	0.889295i	$-0.348805\pi$
$18$		0			0
$19$	−4.33300	+	7.50498i	−0.994059	+	1.72176i	−0.402770	+	0.915301i	$0.631953\pi$
$19$	−4.33300	+	7.50498i	−0.994059	+	1.72176i	−0.591289	+	0.806460i	$0.701381\pi$
$20$		0			0
$21$	−0.227470	−	0.869642i	−0.0496381	−	0.189772i
$22$		0			0
$23$	2.88631	−	2.42190i	0.601838	−	0.505002i	−0.290198	−	0.956967i	$-0.593721\pi$
$23$	2.88631	−	2.42190i	0.601838	−	0.505002i	0.892036	+	0.451965i	$0.149277\pi$
$24$		0			0
$25$	−11.8164	+	4.30081i	−2.36327	+	0.860161i
$26$		0			0
$27$	1.43444	−	4.99423i	0.276058	−	0.961141i
$28$		0			0
$29$	−5.46203	+	1.98802i	−1.01427	+	0.369166i	−0.795073	−	0.606514i	$-0.792567\pi$
$29$	−5.46203	+	1.98802i	−1.01427	+	0.369166i	−0.219201	+	0.975680i	$0.570345\pi$
$30$		0			0
$31$	−4.70771	+	3.95024i	−0.845530	+	0.709484i	−0.958801	−	0.284080i	$-0.908312\pi$
$31$	−4.70771	+	3.95024i	−0.845530	+	0.709484i	0.113270	+	0.993564i	$0.463867\pi$
$32$		0			0
$33$	−2.40336	+	2.37486i	−0.418371	+	0.413410i
$34$		0			0
$35$	−1.08784	+	1.88419i	−0.183878	+	0.318487i
$36$		0			0
$37$	3.15428	+	5.46337i	0.518560	+	0.898173i	0.999767	+	0.0215660i	$0.00686519\pi$
$37$	3.15428	+	5.46337i	0.518560	+	0.898173i	−0.481207	+	0.876607i	$0.659801\pi$
$38$		0			0
$39$	−3.09628	−	4.47855i	−0.495801	−	0.717143i
$40$		0			0
$41$	4.69808	+	1.70996i	0.733716	+	0.267051i	0.681737	−	0.731597i	$-0.261225\pi$
$41$	4.69808	+	1.70996i	0.733716	+	0.267051i	0.0519793	+	0.998648i	$0.483447\pi$
$42$		0			0
$43$	−0.710244	+	4.02799i	−0.108311	+	0.614263i	0.881535	+	0.472119i	$0.156511\pi$
$43$	−0.710244	+	4.02799i	−0.108311	+	0.614263i	−0.989846	+	0.142144i	$0.954600\pi$
$44$		0			0
$45$	−10.9659	+	6.15798i	−1.63471	+	0.917977i
$46$		0			0
$47$	1.88530	+	1.58196i	0.275000	+	0.230752i	0.769848	−	0.638227i	$-0.220332\pi$
$47$	1.88530	+	1.58196i	0.275000	+	0.230752i	−0.494848	+	0.868979i	$0.664776\pi$
$48$		0			0
$49$	−1.16877	−	6.62841i	−0.166967	−	0.946915i
$50$		0			0
$51$	−0.719994	+	7.70037i	−0.100819	+	1.07827i
$52$		0			0
$53$	−0.351690			−0.0483084			−0.0241542	−	0.999708i	$-0.507689\pi$
$53$	−0.351690			−0.0483084			−0.0241542	+	0.999708i	$0.507689\pi$
$54$		0			0
$55$	8.17791			1.10271
$56$		0			0
$57$	13.6412	−	6.26224i	1.80683	−	0.829455i
$58$		0			0
$59$	0.704805	+	3.99715i	0.0917578	+	0.520384i	0.995693	+	0.0927142i	$0.0295543\pi$
$59$	0.704805	+	3.99715i	0.0917578	+	0.520384i	−0.903935	+	0.427670i	$0.859335\pi$
$60$		0			0
$61$	2.53188	+	2.12450i	0.324174	+	0.272014i	0.790321	−	0.612693i	$-0.209914\pi$
$61$	2.53188	+	2.12450i	0.324174	+	0.272014i	−0.466147	+	0.884707i	$0.654358\pi$
$62$		0			0
$63$	−0.549917	+	1.45659i	−0.0692830	+	0.183513i
$64$		0			0
$65$	−2.28836	+	12.9780i	−0.283837	+	1.60972i
$66$		0			0
$67$	8.82272	+	3.21121i	1.07787	+	0.392311i	0.819113	−	0.573632i	$-0.194466\pi$
$67$	8.82272	+	3.21121i	1.07787	+	0.392311i	0.258753	+	0.965943i	$0.416688\pi$
$68$		0			0
$69$	−6.50449	+	0.530001i	−0.783048	+	0.0638046i
$70$		0			0
$71$	−5.42150	−	9.39031i	−0.643414	−	1.11443i	−0.984665	−	0.174453i	$-0.944184\pi$
$71$	−5.42150	−	9.39031i	−0.643414	−	1.11443i	0.341252	−	0.939972i	$-0.389149\pi$
$72$		0			0
$73$	−5.54175	+	9.59859i	−0.648613	+	1.12343i	0.334842	+	0.942274i	$0.391317\pi$
$73$	−5.54175	+	9.59859i	−0.648613	+	1.12343i	−0.983454	+	0.181156i	$0.942016\pi$
$74$		0			0
$75$	21.0039	+	5.76245i	2.42532	+	0.665391i
$76$		0			0
$77$	0.775537	−	0.650753i	0.0883807	−	0.0741602i
$78$		0			0
$79$	−6.53196	+	2.37744i	−0.734902	+	0.267483i	−0.682238	−	0.731130i	$-0.738993\pi$
$79$	−6.53196	+	2.37744i	−0.734902	+	0.267483i	−0.0526639	+	0.998612i	$0.516771\pi$
$80$		0			0
$81$	−7.03043	+	5.61899i	−0.781159	+	0.624333i
$82$		0			0
$83$	−14.7555	+	5.37055i	−1.61962	+	0.589495i	−0.983310	−	0.181937i	$-0.941763\pi$
$83$	−14.7555	+	5.37055i	−1.61962	+	0.589495i	−0.636313	+	0.771431i	$0.719541\pi$
$84$		0			0
$85$	14.3397	−	12.0324i	1.55536	−	1.30510i
$86$		0			0
$87$	9.70891	+	2.66365i	1.04090	+	0.285574i
$88$		0			0
$89$	5.41326	−	9.37604i	0.573805	−	0.993859i	−0.422366	−	0.906425i	$-0.638800\pi$
$89$	5.41326	−	9.37604i	0.573805	−	0.993859i	0.996170	−	0.0874333i	$-0.0278665\pi$
$90$		0			0
$91$	0.815702	+	1.41284i	0.0855088	+	0.148106i
$92$		0			0
$93$	10.6091	−	0.864457i	1.10012	−	0.0896401i
$94$		0			0
$95$	−34.1389	−	12.4255i	−3.50257	−	1.27483i
$96$		0			0
$97$	−0.783229	+	4.44191i	−0.0795249	+	0.451008i	0.918879	+	0.394538i	$0.129096\pi$
$97$	−0.783229	+	4.44191i	−0.0795249	+	0.451008i	−0.998404	+	0.0564696i	$0.982016\pi$
$98$		0			0
$99$	5.77501	−	0.947413i	0.580410	−	0.0952186i
$100$		0			0
$101$	6.86487	+	5.76031i	0.683080	+	0.573172i	0.916905	−	0.399107i	$-0.130680\pi$
$101$	6.86487	+	5.76031i	0.683080	+	0.573172i	−0.233824	+	0.972279i	$0.575124\pi$
$102$		0			0
$103$	0.998230	+	5.66124i	0.0983585	+	0.557819i	0.993666	+	0.112371i	$0.0358445\pi$
$103$	0.998230	+	5.66124i	0.0983585	+	0.557819i	−0.895308	+	0.445448i	$0.853044\pi$
$104$		0			0
$105$	3.42475	−	1.57219i	0.334222	−	0.153430i
$106$		0			0
$107$	−8.67132			−0.838288			−0.419144	−	0.907920i	$-0.637670\pi$
$107$	−8.67132			−0.838288			−0.419144	+	0.907920i	$0.637670\pi$
$108$		0			0
$109$	−4.60033			−0.440631			−0.220316	−	0.975429i	$-0.570709\pi$
$109$	−4.60033			−0.440631			−0.220316	+	0.975429i	$0.570709\pi$
$110$		0			0
$111$	1.01723	−	10.8793i	0.0965509	−	1.03262i
$112$		0			0
$113$	1.65469	+	9.38424i	0.155661	+	0.882795i	0.958179	+	0.286168i	$0.0923815\pi$
$113$	1.65469	+	9.38424i	0.155661	+	0.882795i	−0.802519	+	0.596627i	$0.796507\pi$
$114$		0			0
$115$	12.1001	+	10.1532i	1.12834	+	0.946787i
$116$		0			0
$117$	−0.112478	+	9.42977i	−0.0103986	+	0.871782i
$118$		0			0
$119$	0.402404	−	2.28215i	0.0368883	−	0.209204i
$120$		0			0
$121$	6.76075	+	2.46071i	0.614613	+	0.223701i
$122$		0			0
$123$	−4.92452	−	7.12298i	−0.444029	−	0.642257i
$124$		0			0
$125$	−15.8774	−	27.5005i	−1.42012	−	2.45972i
$126$		0			0
$127$	5.48402	−	9.49860i	0.486628	−	0.842865i	−0.513254	−	0.858237i	$-0.671560\pi$
$127$	5.48402	−	9.49860i	0.486628	−	0.842865i	0.999882	+	0.0153723i	$0.00489334\pi$
$128$		0			0
$129$	5.03915	−	4.97940i	0.443672	−	0.438412i
$130$		0			0
$131$	8.42835	−	7.07222i	0.736388	−	0.617903i	−0.195477	−	0.980708i	$-0.562625\pi$
$131$	8.42835	−	7.07222i	0.736388	−	0.617903i	0.931865	+	0.362805i	$0.118181\pi$
$132$		0			0
$133$	−4.22625	+	1.53823i	−0.366463	+	0.133381i
$134$		0			0
$135$	21.6631	+	2.28647i	1.86446	+	0.196788i
$136$		0			0
$137$	9.90506	−	3.60515i	0.846246	−	0.308008i	0.117737	−	0.993045i	$-0.462436\pi$
$137$	9.90506	−	3.60515i	0.846246	−	0.308008i	0.728509	+	0.685036i	$0.240214\pi$
$138$		0			0
$139$	2.19888	−	1.84508i	0.186506	−	0.156497i	−0.544754	−	0.838596i	$-0.683377\pi$
$139$	2.19888	−	1.84508i	0.186506	−	0.156497i	0.731260	+	0.682099i	$0.238932\pi$
$140$		0			0
$141$	−1.07870	−	4.12399i	−0.0908430	−	0.347303i
$142$		0			0
$143$	3.06605	−	5.31055i	0.256396	−	0.444090i
$144$		0			0
$145$	−12.1838	−	21.1030i	−1.01181	−	1.75251i
$146$		0			0
$147$	−4.98974	+	10.5360i	−0.411547	+	0.868997i
$148$		0			0
$149$	−8.06624	−	2.93587i	−0.660812	−	0.240516i	−0.0102250	−	0.999948i	$-0.503255\pi$
$149$	−8.06624	−	2.93587i	−0.660812	−	0.240516i	−0.650587	+	0.759432i	$0.725477\pi$
$150$		0			0
$151$	2.12108	−	12.0292i	0.172611	−	0.978926i	−0.768254	−	0.640145i	$-0.778874\pi$
$151$	2.12108	−	12.0292i	0.172611	−	0.978926i	0.940865	−	0.338781i	$-0.110015\pi$
$152$		0			0
$153$	8.73231	−	10.1582i	0.705966	−	0.821242i
$154$		0			0
$155$	−19.7358	−	16.5603i	−1.58522	−	1.33015i
$156$		0			0
$157$	−0.0191440	−	0.108571i	−0.00152786	−	0.00866490i	0.984034	−	0.177979i	$-0.0569559\pi$
$157$	−0.0191440	−	0.108571i	−0.00152786	−	0.00866490i	−0.985562	+	0.169314i	$0.945845\pi$
$158$		0			0
$159$	0.496890	+	0.352361i	0.0394059	+	0.0279440i
$160$		0			0
$161$	1.95542			0.154109
$162$		0			0
$163$	−17.6960			−1.38606			−0.693028	−	0.720911i	$-0.743724\pi$
$163$	−17.6960			−1.38606			−0.693028	+	0.720911i	$0.743724\pi$
$164$		0			0
$165$	−11.5543	−	8.19351i	−0.899498	−	0.637864i
$166$		0			0
$167$	3.68830	+	20.9174i	0.285409	+	1.61864i	0.703820	+	0.710379i	$0.251476\pi$
$167$	3.68830	+	20.9174i	0.285409	+	1.61864i	−0.418410	+	0.908258i	$0.637413\pi$
$168$		0			0
$169$	−2.38894	−	2.00455i	−0.183764	−	0.154197i
$170$		0			0
$171$	−25.5474	−	4.81956i	−1.95366	−	0.368561i
$172$		0			0
$173$	1.86740	−	10.5906i	0.141976	−	0.805185i	−0.827770	−	0.561068i	$-0.810391\pi$
$173$	1.86740	−	10.5906i	0.141976	−	0.805185i	0.969746	−	0.244117i	$-0.0784982\pi$
$174$		0			0
$175$	−6.13246	−	2.23203i	−0.463570	−	0.168726i
$176$		0			0
$177$	3.00898	−	6.35357i	0.226169	−	0.477564i
$178$		0			0
$179$	5.06826	+	8.77849i	0.378820	+	0.656135i	0.990891	−	0.134668i	$-0.0429967\pi$
$179$	5.06826	+	8.77849i	0.378820	+	0.656135i	−0.612071	+	0.790803i	$0.709663\pi$
$180$		0			0
$181$	10.2707	−	17.7894i	0.763417	−	1.32228i	−0.177663	−	0.984091i	$-0.556854\pi$
$181$	10.2707	−	17.7894i	0.763417	−	1.32228i	0.941080	−	0.338185i	$-0.109813\pi$
$182$		0			0
$183$	−1.44865	−	5.53833i	−0.107087	−	0.409405i
$184$		0			0
$185$	−20.2595	+	16.9997i	−1.48951	+	1.24984i
$186$		0			0
$187$	−8.18512	+	2.97914i	−0.598555	+	0.217856i
$188$		0			0
$189$	2.23632	−	1.50700i	0.162669	−	0.109618i
$190$		0			0
$191$	11.0639	−	4.02693i	0.800556	−	0.291379i	0.0908393	−	0.995866i	$-0.471045\pi$
$191$	11.0639	−	4.02693i	0.800556	−	0.291379i	0.709717	+	0.704487i	$0.248823\pi$
$192$		0			0
$193$	9.34887	−	7.84463i	0.672946	−	0.564669i	−0.240990	−	0.970528i	$-0.577472\pi$
$193$	9.34887	−	7.84463i	0.672946	−	0.564669i	0.913936	+	0.405859i	$0.133028\pi$
$194$		0			0
$195$	16.2359	−	16.0433i	1.16267	−	1.14889i
$196$		0			0
$197$	7.72454	−	13.3793i	0.550351	−	0.953235i	−0.447898	−	0.894085i	$-0.647827\pi$
$197$	7.72454	−	13.3793i	0.550351	−	0.953235i	0.998249	−	0.0591509i	$-0.0188393\pi$
$198$		0			0
$199$	11.2621	+	19.5066i	0.798350	+	1.38278i	0.920690	+	0.390294i	$0.127627\pi$
$199$	11.2621	+	19.5066i	0.798350	+	1.38278i	−0.122340	+	0.992488i	$0.539040\pi$
$200$		0			0
$201$	−9.24796	−	13.3765i	−0.652301	−	0.943508i
$202$		0			0
$203$	−2.83469	−	1.03174i	−0.198956	−	0.0724140i
$204$		0			0
$205$	−3.63956	+	20.6410i	−0.254198	+	1.44163i
$206$		0			0
$207$	9.72096	+	5.76807i	0.675653	+	0.400909i
$208$		0			0
$209$	12.9500	+	10.8664i	0.895773	+	0.751643i
$210$		0			0
$211$	−0.165731	−	0.939910i	−0.0114094	−	0.0647060i	0.978571	−	0.205907i	$-0.0660146\pi$
$211$	−0.165731	−	0.939910i	−0.0114094	−	0.0647060i	−0.989981	+	0.141201i	$0.954903\pi$
$212$		0			0
$213$	−1.74839	+	18.6991i	−0.119797	+	1.28124i
$214$		0			0
$215$	−17.1467			−1.16940
$216$		0			0
$217$	−3.18938			−0.216509
$218$		0			0
$219$	17.4466	−	8.00918i	1.17893	−	0.541210i
$220$		0			0
$221$	−2.43737	−	13.8230i	−0.163956	−	0.929838i
$222$		0			0
$223$	17.4485	+	14.6411i	1.16844	+	0.980439i	0.999986	−	0.00527080i	$-0.00167776\pi$
$223$	17.4485	+	14.6411i	1.16844	+	0.980439i	0.168455	+	0.985709i	$0.446122\pi$
$224$		0			0
$225$	−23.9022	−	29.1855i	−1.59348	−	1.94570i
$226$		0			0
$227$	2.00294	−	11.3593i	0.132940	−	0.753940i	−0.843332	−	0.537393i	$-0.819409\pi$
$227$	2.00294	−	11.3593i	0.132940	−	0.753940i	0.976272	−	0.216547i	$-0.0694796\pi$
$228$		0			0
$229$	8.50727	+	3.09639i	0.562176	+	0.204615i	0.607448	−	0.794359i	$-0.292193\pi$
$229$	8.50727	+	3.09639i	0.562176	+	0.204615i	−0.0452721	+	0.998975i	$0.514415\pi$
$230$		0			0
$231$	−1.74772	+	0.142409i	−0.114992	+	0.00936980i
$232$		0			0
$233$	7.28232	+	12.6134i	0.477081	+	0.826328i	0.999655	−	0.0262656i	$-0.00836158\pi$
$233$	7.28232	+	12.6134i	0.477081	+	0.826328i	−0.522574	+	0.852594i	$0.675028\pi$
$234$		0			0
$235$	−5.15872	+	8.93516i	−0.336517	+	0.582865i
$236$		0			0
$237$	11.6107	+	3.18542i	0.754198	+	0.206915i
$238$		0			0
$239$	18.6745	−	15.6697i	1.20795	−	1.01359i	0.208585	−	0.978004i	$-0.433114\pi$
$239$	18.6745	−	15.6697i	1.20795	−	1.01359i	0.999367	−	0.0355874i	$-0.0113302\pi$
$240$		0			0
$241$	14.5341	−	5.29000i	0.936226	−	0.340759i	0.171552	−	0.985175i	$-0.445122\pi$
$241$	14.5341	−	5.29000i	0.936226	−	0.340759i	0.764675	+	0.644417i	$0.222900\pi$
$242$		0			0
$243$	15.5627	−	0.895034i	0.998350	−	0.0574165i
$244$		0			0
$245$	26.5148	−	9.65058i	1.69397	−	0.616553i
$246$		0			0
$247$	−20.8681	+	17.5104i	−1.32781	+	1.11416i
$248$		0			0
$249$	26.2282	+	7.19576i	1.66215	+	0.456012i
$250$		0			0
$251$	−0.451297	+	0.781669i	−0.0284856	+	0.0493385i	−0.879917	−	0.475128i	$-0.842402\pi$
$251$	−0.451297	+	0.781669i	−0.0284856	+	0.0493385i	0.851431	+	0.524466i	$0.175735\pi$
$252$		0			0
$253$	−3.67500	−	6.36529i	−0.231045	−	0.400182i
$254$		0			0
$255$	−32.3154	+	2.63313i	−2.02367	+	0.164893i
$256$		0			0
$257$	−5.29741	−	1.92810i	−0.330443	−	0.120271i	0.171470	−	0.985189i	$-0.445148\pi$
$257$	−5.29741	−	1.92810i	−0.330443	−	0.120271i	−0.501913	+	0.864918i	$0.667370\pi$
$258$		0			0
$259$	−0.568527	+	3.22428i	−0.0353265	+	0.200347i
$260$		0			0
$261$	−11.0486	−	13.4908i	−0.683893	−	0.835060i
$262$		0			0
$263$	13.9613	+	11.7149i	0.860890	+	0.722373i	0.962160	−	0.272486i	$-0.0878459\pi$
$263$	13.9613	+	11.7149i	0.860890	+	0.722373i	−0.101269	+	0.994859i	$0.532290\pi$
$264$		0			0
$265$	−0.256020	−	1.45196i	−0.0157272	−	0.0891934i
$266$		0			0
$267$	−17.0421	+	7.82348i	−1.04296	+	0.478789i
$268$		0			0
$269$	4.83550			0.294826			0.147413	−	0.989075i	$-0.452905\pi$
$269$	4.83550			0.294826			0.147413	+	0.989075i	$0.452905\pi$
$270$		0			0
$271$	−4.27563			−0.259726			−0.129863	−	0.991532i	$-0.541454\pi$
$271$	−4.27563			−0.259726			−0.129863	+	0.991532i	$0.541454\pi$
$272$		0			0
$273$	0.263056	−	2.81340i	0.0159209	−	0.170275i
$274$		0			0
$275$	4.25958	+	24.1573i	0.256862	+	1.45674i
$276$		0			0
$277$	10.1248	+	8.49569i	0.608338	+	0.510456i	0.894114	−	0.447840i	$-0.147807\pi$
$277$	10.1248	+	8.49569i	0.608338	+	0.510456i	−0.285775	+	0.958297i	$0.592251\pi$
$278$		0			0
$279$	−15.8554	−	9.40800i	−0.949235	−	0.563242i
$280$		0			0
$281$	2.17961	−	12.3612i	0.130025	−	0.737407i	−0.848171	−	0.529723i	$-0.822296\pi$
$281$	2.17961	−	12.3612i	0.130025	−	0.737407i	0.978196	−	0.207685i	$-0.0665928\pi$
$282$		0			0
$283$	5.46661	+	1.98968i	0.324956	+	0.118274i	0.499347	−	0.866402i	$-0.333573\pi$
$283$	5.46661	+	1.98968i	0.324956	+	0.118274i	−0.174391	+	0.984677i	$0.555796\pi$
$284$		0			0
$285$	35.7843	+	51.7595i	2.11968	+	3.06597i
$286$		0			0
$287$	1.29734	+	2.24706i	0.0765798	+	0.132640i
$288$		0			0
$289$	−1.46902	+	2.54442i	−0.0864131	+	0.149672i
$290$		0			0
$291$	5.55698	−	5.49109i	0.325756	−	0.321894i
$292$		0			0
$293$	−9.34704	+	7.84310i	−0.546060	+	0.458199i	−0.873604	−	0.486637i	$-0.838223\pi$
$293$	−9.34704	+	7.84310i	−0.546060	+	0.458199i	0.327544	+	0.944836i	$0.393779\pi$
$294$		0			0
$295$	−15.9893	+	5.81962i	−0.930931	+	0.338831i
$296$		0			0
$297$	−9.10851	−	4.44745i	−0.528529	−	0.258067i
$298$		0			0
$299$	11.1298	−	4.05090i	0.643651	−	0.234270i
$300$		0			0
$301$	−1.62608	+	1.36444i	−0.0937256	+	0.0786451i
$302$		0			0
$303$	−3.92783	−	15.0165i	−0.225648	−	0.862675i
$304$		0			0
$305$	−6.92792	+	11.9995i	−0.396692	+	0.687090i
$306$		0			0
$307$	3.85183	+	6.67156i	0.219835	+	0.380766i	0.954757	−	0.297385i	$-0.0961147\pi$
$307$	3.85183	+	6.67156i	0.219835	+	0.380766i	−0.734922	+	0.678151i	$0.762781\pi$
$308$		0			0
$309$	4.26168	−	8.99870i	0.242438	−	0.511918i
$310$		0			0
$311$	3.87776	+	1.41139i	0.219887	+	0.0800325i	0.449615	−	0.893223i	$-0.351561\pi$
$311$	3.87776	+	1.41139i	0.219887	+	0.0800325i	−0.229727	+	0.973255i	$0.573783\pi$
$312$		0			0
$313$	−4.84848	+	27.4971i	−0.274052	+	1.55423i	0.467904	+	0.883779i	$0.345009\pi$
$313$	−4.84848	+	27.4971i	−0.274052	+	1.55423i	−0.741956	+	0.670448i	$0.766102\pi$
$314$		0			0
$315$	−6.41390	−	1.20999i	−0.361382	−	0.0681754i
$316$		0			0
$317$	−6.52651	−	5.47639i	−0.366565	−	0.307585i	0.440836	−	0.897588i	$-0.354682\pi$
$317$	−6.52651	−	5.47639i	−0.366565	−	0.307585i	−0.807401	+	0.590003i	$0.799127\pi$
$318$		0			0
$319$	1.96896	+	11.1665i	0.110241	+	0.625205i
$320$		0			0
$321$	12.2514	+	8.68786i	0.683806	+	0.484909i
$322$		0			0
$323$	38.6955			2.15307
$324$		0			0
$325$	−39.5284			−2.19264
$326$		0			0
$327$	6.49963	+	4.60910i	0.359430	+	0.254884i
$328$		0			0
$329$	0.221793	+	1.25785i	0.0122279	+	0.0693476i
$330$		0			0
$331$	−18.1887	−	15.2621i	−0.999739	−	0.838881i	−0.0127909	−	0.999918i	$-0.504072\pi$
$331$	−18.1887	−	15.2621i	−0.999739	−	0.838881i	−0.986948	+	0.161037i	$0.948516\pi$
$332$		0			0
$333$	−12.3372	+	14.3518i	−0.676077	+	0.786473i
$334$		0			0
$335$	−6.83488	+	38.7625i	−0.373429	+	2.11782i
$336$		0			0
$337$	−1.61521	−	0.587888i	−0.0879860	−	0.0320243i	0.297652	−	0.954674i	$-0.403796\pi$
$337$	−1.61521	−	0.587888i	−0.0879860	−	0.0320243i	−0.385638	+	0.922650i	$0.626019\pi$
$338$		0			0
$339$	7.06428	−	14.9165i	0.383679	−	0.810152i
$340$		0			0
$341$	5.99410	+	10.3821i	0.324599	+	0.562222i
$342$		0			0
$343$	3.56297	−	6.17124i	0.192382	−	0.333216i
$344$		0			0
$345$	−6.92321	−	26.4682i	−0.372733	−	1.42500i
$346$		0			0
$347$	10.0591	−	8.44059i	0.540001	−	0.453114i	−0.331537	−	0.943442i	$-0.607567\pi$
$347$	10.0591	−	8.44059i	0.540001	−	0.453114i	0.871538	+	0.490328i	$0.163123\pi$
$348$		0			0
$349$	23.5026	−	8.55426i	1.25807	−	0.457899i	0.374947	−	0.927046i	$-0.377661\pi$
$349$	23.5026	−	8.55426i	1.25807	−	0.457899i	0.883120	+	0.469147i	$0.155439\pi$
$350$		0			0
$351$	9.60667	−	13.2103i	0.512766	−	0.705113i
$352$		0			0
$353$	10.7188	−	3.90132i	0.570503	−	0.207646i	−0.0406297	−	0.999174i	$-0.512936\pi$
$353$	10.7188	−	3.90132i	0.570503	−	0.207646i	0.611133	+	0.791528i	$0.290714\pi$
$354$		0			0
$355$	34.8215	−	29.2187i	1.84813	−	1.55077i
$356$		0			0
$357$	−2.85504	+	2.82119i	−0.151105	+	0.149313i
$358$		0			0
$359$	−9.25877	+	16.0367i	−0.488659	+	0.846383i	−0.999915	−	0.0130459i	$-0.995847\pi$
$359$	−9.25877	+	16.0367i	−0.488659	+	0.846383i	0.511256	+	0.859429i	$0.329181\pi$
$360$		0			0
$361$	−28.0498	−	48.5837i	−1.47631	−	2.55704i
$362$		0			0
$363$	−7.08661	−	10.2503i	−0.371950	−	0.538001i
$364$		0			0
$365$	−43.6623	−	15.8918i	−2.28539	−	0.831814i
$366$		0			0
$367$	−0.166601	+	0.944840i	−0.00869649	+	0.0493203i	−0.988847	−	0.148934i	$-0.952416\pi$
$367$	−0.166601	+	0.944840i	−0.00869649	+	0.0493203i	0.980151	+	0.198254i	$0.0635270\pi$
$368$		0			0
$369$	−0.178891	+	14.9977i	−0.00931272	+	0.780749i
$370$		0			0
$371$	−0.139819	−	0.117322i	−0.00725902	−	0.00609104i
$372$		0			0
$373$	4.20802	+	23.8649i	0.217883	+	1.23568i	0.875833	+	0.482615i	$0.160313\pi$
$373$	4.20802	+	23.8649i	0.217883	+	1.23568i	−0.657950	+	0.753062i	$0.728576\pi$
$374$		0			0
$375$	−5.12033	+	54.7622i	−0.264413	+	2.82791i
$376$		0			0
$377$	−18.2717			−0.941041
$378$		0			0
$379$	5.31265			0.272892			0.136446	−	0.990647i	$-0.456432\pi$
$379$	5.31265			0.272892			0.136446	+	0.990647i	$0.456432\pi$
$380$		0			0
$381$	−17.2649	+	7.92575i	−0.884507	+	0.406048i
$382$		0			0
$383$	−4.84186	−	27.4596i	−0.247408	−	1.40312i	−0.814834	−	0.579694i	$-0.803172\pi$
$383$	−4.84186	−	27.4596i	−0.247408	−	1.40312i	0.567426	−	0.823424i	$-0.307939\pi$
$384$		0			0
$385$	3.25122	+	2.72810i	0.165698	+	0.139037i
$386$		0			0
$387$	−12.1085	+	1.98645i	−0.615511	+	0.100977i
$388$		0			0
$389$	−1.25121	+	7.09595i	−0.0634388	+	0.359779i	0.936519	+	0.350616i	$0.114028\pi$
$389$	−1.25121	+	7.09595i	−0.0634388	+	0.359779i	−0.999958	+	0.00916295i	$0.997083\pi$
$390$		0			0
$391$	−15.8094	−	5.75416i	−0.799518	−	0.291001i
$392$		0			0
$393$	−18.9938	+	1.54766i	−0.958111	+	0.0780692i
$394$		0			0
$395$	−14.5704	−	25.2367i	−0.733117	−	1.26980i
$396$		0			0
$397$	15.5495	−	26.9326i	0.780408	−	1.35171i	−0.151296	−	0.988488i	$-0.548345\pi$
$397$	15.5495	−	26.9326i	0.780408	−	1.35171i	0.931704	−	0.363218i	$-0.118322\pi$
$398$		0			0
$399$	7.51228	+	2.06100i	0.376084	+	0.103179i
$400$		0			0
$401$	−16.7755	+	14.0763i	−0.837729	+	0.702938i	−0.957052	−	0.289917i	$-0.906372\pi$
$401$	−16.7755	+	14.0763i	−0.837729	+	0.702938i	0.119323	+	0.992856i	$0.461928\pi$
$402$		0			0
$403$	−18.1532	+	6.60722i	−0.904274	+	0.329129i
$404$		0			0
$405$	−28.3161	−	24.9349i	−1.40704	−	1.23902i
$406$		0			0
$407$	11.5642	−	4.20901i	0.573214	−	0.208633i
$408$		0			0
$409$	−22.6272	+	18.9865i	−1.11884	+	0.938821i	−0.998545	−	0.0539169i	$-0.982829\pi$
$409$	−22.6272	+	18.9865i	−1.11884	+	0.938821i	−0.120298	+	0.992738i	$0.538385\pi$
$410$		0			0
$411$	−17.6065	−	4.83037i	−0.868465	−	0.238265i
$412$		0			0
$413$	−1.05322	+	1.82423i	−0.0518256	+	0.0897645i
$414$		0			0
$415$	−32.9141	−	57.0088i	−1.61569	−	2.79845i
$416$		0			0
$417$	−4.95531	+	0.403771i	−0.242663	+	0.0197727i
$418$		0			0
$419$	−27.2766	−	9.92788i	−1.33255	−	0.485009i	−0.425091	−	0.905150i	$-0.639758\pi$
$419$	−27.2766	−	9.92788i	−1.33255	−	0.485009i	−0.907458	+	0.420142i	$0.861980\pi$
$420$		0			0
$421$	−1.24724	+	7.07345i	−0.0607867	+	0.344739i	0.939212	+	0.343337i	$0.111557\pi$
$421$	−1.24724	+	7.07345i	−0.0607867	+	0.344739i	−0.999999	+	0.00140168i	$0.999554\pi$
$422$		0			0
$423$	−2.60780	+	6.90739i	−0.126795	+	0.335849i
$424$		0			0
$425$	43.0124	+	36.0917i	2.08641	+	1.75070i
$426$		0			0
$427$	0.297858	+	1.68924i	0.0144144	+	0.0817480i
$428$		0			0
$429$	−9.65258	+	4.43118i	−0.466031	+	0.213940i
$430$		0			0
$431$	−0.998962			−0.0481183			−0.0240592	−	0.999711i	$-0.507659\pi$
$431$	−0.998962			−0.0481183			−0.0240592	+	0.999711i	$0.507659\pi$
$432$		0			0
$433$	−0.707797			−0.0340145			−0.0170073	−	0.999855i	$-0.505414\pi$
$433$	−0.707797			−0.0340145			−0.0170073	+	0.999855i	$0.505414\pi$
$434$		0			0
$435$	−3.92917	+	42.0226i	−0.188389	+	2.01483i
$436$		0			0
$437$	5.66994	+	32.1558i	0.271230	+	1.53822i
$438$		0			0
$439$	23.6003	+	19.8030i	1.12638	+	0.945147i	0.998909	−	0.0466953i	$-0.0148690\pi$
$439$	23.6003	+	19.8030i	1.12638	+	0.945147i	0.127473	+	0.991842i	$0.459313\pi$
$440$		0			0
$441$	17.6059	−	9.88671i	0.838378	−	0.470795i
$442$		0			0
$443$	−1.09002	+	6.18183i	−0.0517885	+	0.293707i	−0.999691	−	0.0248529i	$-0.992088\pi$
$443$	−1.09002	+	6.18183i	−0.0517885	+	0.293707i	0.947903	+	0.318560i	$0.103199\pi$
$444$		0			0
$445$	42.6500	+	15.5233i	2.02180	+	0.735876i
$446$		0			0
$447$	8.45502	+	12.2296i	0.399909	+	0.578440i
$448$		0			0
$449$	−8.67608	−	15.0274i	−0.409449	−	0.709187i	0.585379	−	0.810760i	$-0.300946\pi$
$449$	−8.67608	−	15.0274i	−0.409449	−	0.709187i	−0.994828	+	0.101573i	$0.967612\pi$
$450$		0			0
$451$	4.87643	−	8.44623i	0.229622	−	0.397718i
$452$		0			0
$453$	−15.0490	+	14.8705i	−0.707063	+	0.698679i
$454$		0			0
$455$	−5.23913	+	4.39616i	−0.245614	+	0.206095i
$456$		0			0
$457$	−22.1808	+	8.07315i	−1.03757	+	0.377646i	−0.803960	−	0.594684i	$-0.797277\pi$
$457$	−22.1808	+	8.07315i	−1.03757	+	0.377646i	−0.233614	+	0.972330i	$0.575055\pi$
$458$		0			0
$459$	−22.5151	+	5.60319i	−1.05092	+	0.261534i
$460$		0			0
$461$	24.2975	−	8.84357i	1.13165	−	0.411886i	0.292758	−	0.956187i	$-0.405427\pi$
$461$	24.2975	−	8.84357i	1.13165	−	0.411886i	0.838890	+	0.544300i	$0.183205\pi$
$462$		0			0
$463$	29.6083	−	24.8444i	1.37602	−	1.15461i	0.405357	−	0.914159i	$-0.367147\pi$
$463$	29.6083	−	24.8444i	1.37602	−	1.15461i	0.970660	−	0.240456i	$-0.0772971\pi$
$464$		0			0
$465$	11.2921	+	43.1708i	0.523658	+	2.00200i
$466$		0			0
$467$	16.6902	−	28.9083i	0.772331	−	1.33772i	−0.163952	−	0.986468i	$-0.552424\pi$
$467$	16.6902	−	28.9083i	0.772331	−	1.33772i	0.936283	−	0.351248i	$-0.114242\pi$
$468$		0			0
$469$	2.43634	+	4.21986i	0.112500	+	0.194855i
$470$		0			0
$471$	−0.0817302	+	0.172576i	−0.00376593	+	0.00795190i
$472$		0			0
$473$	7.49758	+	2.72890i	0.344739	+	0.125475i
$474$		0			0
$475$	18.9229	−	107.317i	0.868242	−	4.92404i
$476$		0			0
$477$	−0.349005	−	0.995675i	−0.0159798	−	0.0455888i
$478$		0			0
$479$	0.360818	+	0.302762i	0.0164862	+	0.0138336i	0.650993	−	0.759083i	$-0.274353\pi$
$479$	0.360818	+	0.302762i	0.0164862	+	0.0138336i	−0.634507	+	0.772917i	$0.718797\pi$
$480$		0			0
$481$	3.44359	+	19.5296i	0.157014	+	0.890471i
$482$		0			0
$483$	−2.76274	−	1.95915i	−0.125709	−	0.0891444i
$484$		0			0
$485$	−18.9088			−0.858602
$486$		0			0
$487$	40.2500			1.82390			0.911952	−	0.410297i	$-0.134575\pi$
$487$	40.2500			1.82390			0.911952	+	0.410297i	$0.134575\pi$
$488$		0			0
$489$	25.0020	+	17.7297i	1.13063	+	0.801766i
$490$		0			0
$491$	6.83036	+	38.7369i	0.308250	+	1.74817i	0.607800	+	0.794090i	$0.292052\pi$
$491$	6.83036	+	38.7369i	0.308250	+	1.74817i	−0.299550	+	0.954080i	$0.596837\pi$
$492$		0			0
$493$	19.8822	+	16.6831i	0.895448	+	0.751370i
$494$		0			0
$495$	8.11546	+	23.1526i	0.364763	+	1.04063i
$496$		0			0
$497$	0.977170	−	5.54181i	0.0438321	−	0.248584i
$498$		0			0
$499$	−8.47651	−	3.08520i	−0.379461	−	0.138112i	0.145246	−	0.989396i	$-0.453603\pi$
$499$	−8.47651	−	3.08520i	−0.379461	−	0.138112i	−0.524706	+	0.851283i	$0.675825\pi$
$500$		0			0
$501$	15.7462	−	33.2488i	0.703490	−	1.48544i
$502$		0			0
$503$	20.4344	+	35.3934i	0.911123	+	1.57811i	0.812480	+	0.582989i	$0.198117\pi$
$503$	20.4344	+	35.3934i	0.911123	+	1.57811i	0.0986432	+	0.995123i	$0.468550\pi$
$504$		0			0
$505$	−18.7842	+	32.5352i	−0.835886	+	1.44780i
$506$		0			0
$507$	1.36686	+	5.22565i	0.0607044	+	0.232079i
$508$		0			0
$509$	−17.5491	+	14.7254i	−0.777849	+	0.652693i	−0.942706	−	0.333624i	$-0.891728\pi$
$509$	−17.5491	+	14.7254i	−0.777849	+	0.652693i	0.164857	+	0.986318i	$0.447284\pi$
$510$		0			0
$511$	−5.40522	+	1.96734i	−0.239113	+	0.0870299i
$512$		0			0
$513$	31.2662	+	32.4055i	1.38044	+	1.43074i
$514$		0			0
$515$	−22.6459	+	8.24245i	−0.997900	+	0.363206i
$516$		0			0
$517$	3.67773	−	3.08598i	0.161746	−	0.135721i
$518$		0			0
$519$	−13.2491	+	13.0920i	−0.581573	+	0.574677i
$520$		0			0
$521$	12.9117	−	22.3638i	0.565674	−	0.979776i	−0.431313	−	0.902202i	$-0.641949\pi$
$521$	12.9117	−	22.3638i	0.565674	−	0.979776i	0.996987	−	0.0775733i	$-0.0247172\pi$
$522$		0			0
$523$	−3.07404	−	5.32440i	−0.134418	−	0.232820i	0.790957	−	0.611872i	$-0.209583\pi$
$523$	−3.07404	−	5.32440i	−0.134418	−	0.232820i	−0.925375	+	0.379053i	$0.876250\pi$
$524$		0			0
$525$	6.42804	+	9.29771i	0.280543	+	0.405785i
$526$		0			0
$527$	25.7860	+	9.38532i	1.12325	+	0.408831i
$528$		0			0
$529$	−1.52873	+	8.66984i	−0.0664664	+	0.376950i
$530$		0			0
$531$	−10.6170	+	5.96201i	−0.460737	+	0.258729i
$532$		0			0
$533$	12.0392	+	10.1021i	0.521477	+	0.437571i
$534$		0			0
$535$	−6.31248	−	35.7998i	−0.272912	−	1.54776i
$536$		0			0
$537$	1.63447	−	17.4807i	0.0705325	−	0.754349i
$538$		0			0
$539$	−13.1297			−0.565537
$540$		0			0
$541$	−13.6685			−0.587656			−0.293828	−	0.955858i	$-0.594929\pi$
$541$	−13.6685			−0.587656			−0.293828	+	0.955858i	$0.594929\pi$
$542$		0			0
$543$	−32.3345	+	14.8437i	−1.38760	+	0.637004i
$544$		0			0
$545$	−3.34891	−	18.9926i	−0.143451	−	0.813553i
$546$		0			0
$547$	6.25867	+	5.25165i	0.267601	+	0.224544i	0.766707	−	0.641997i	$-0.221894\pi$
$547$	6.25867	+	5.25165i	0.267601	+	0.224544i	−0.499106	+	0.866541i	$0.666338\pi$
$548$		0			0
$549$	−3.50215	+	9.27631i	−0.149468	+	0.395903i
$550$		0			0
$551$	8.74697	−	49.6065i	0.372634	−	2.11331i
$552$		0			0
$553$	−3.38995	−	1.23384i	−0.144156	−	0.0524683i
$554$		0			0
$555$	45.6560	−	3.72016i	1.93799	−	0.157912i
$556$		0			0
$557$	2.07607	+	3.59586i	0.0879658	+	0.152361i	0.906651	−	0.421881i	$-0.138630\pi$
$557$	2.07607	+	3.59586i	0.0879658	+	0.152361i	−0.818685	+	0.574242i	$0.805297\pi$
$558$		0			0
$559$	−6.42862	+	11.1347i	−0.271902	+	0.470947i
$560$		0			0
$561$	14.5493	+	3.99161i	0.614271	+	0.168526i
$562$		0			0
$563$	−10.3029	+	8.64514i	−0.434215	+	0.364349i	−0.833539	−	0.552460i	$-0.813689\pi$
$563$	−10.3029	+	8.64514i	−0.434215	+	0.364349i	0.399325	+	0.916810i	$0.369245\pi$
$564$		0			0
$565$	−37.5385	+	13.6629i	−1.57926	+	0.574803i
$566$		0			0
$567$	−4.66949	−	0.111411i	−0.196100	−	0.00467880i
$568$		0			0
$569$	−6.59146	+	2.39909i	−0.276328	+	0.100575i	−0.476467	−	0.879192i	$-0.658083\pi$
$569$	−6.59146	+	2.39909i	−0.276328	+	0.100575i	0.200139	+	0.979768i	$0.435861\pi$
$570$		0			0
$571$	−34.4590	+	28.9145i	−1.44206	+	1.21003i	−0.503937	+	0.863740i	$0.668116\pi$
$571$	−34.4590	+	28.9145i	−1.44206	+	1.21003i	−0.938126	+	0.346294i	$0.887440\pi$
$572$		0			0
$573$	−19.6664	−	5.39550i	−0.821576	−	0.225400i
$574$		0			0
$575$	−23.6896	+	41.0316i	−0.987924	+	1.71114i
$576$		0			0
$577$	1.53173	+	2.65303i	0.0637667	+	0.110447i	0.896146	−	0.443759i	$-0.146355\pi$
$577$	1.53173	+	2.65303i	0.0637667	+	0.110447i	−0.832380	+	0.554206i	$0.813022\pi$
$578$		0			0
$579$	−21.0683	+	1.71669i	−0.875567	+	0.0713433i
$580$		0			0
$581$	−7.65779	−	2.78721i	−0.317699	−	0.115633i
$582$		0			0
$583$	−0.119132	+	0.675631i	−0.00493394	+	0.0279818i
$584$		0			0
$585$	−39.0130	+	6.40024i	−1.61299	+	0.264617i
$586$		0			0
$587$	18.5779	+	15.5887i	0.766790	+	0.643413i	0.939885	−	0.341492i	$-0.110932\pi$
$587$	18.5779	+	15.5887i	0.766790	+	0.643413i	−0.173095	+	0.984905i	$0.555377\pi$
$588$		0			0
$589$	−9.24795	−	52.4477i	−0.381055	−	2.16107i
$590$		0			0
$591$	−24.3185	+	11.1638i	−1.00033	+	0.459219i
$592$		0			0
$593$	16.6619			0.684222			0.342111	−	0.939660i	$-0.388858\pi$
$593$	16.6619			0.684222			0.342111	+	0.939660i	$0.388858\pi$
$594$		0			0
$595$	9.71485			0.398270
$596$		0			0
$597$	3.63193	−	38.8437i	0.148645	−	1.58977i
$598$		0			0
$599$	−2.92340	−	16.5794i	−0.119447	−	0.677417i	−0.984452	−	0.175654i	$-0.943796\pi$
$599$	−2.92340	−	16.5794i	−0.119447	−	0.677417i	0.865005	−	0.501763i	$-0.167315\pi$
$600$		0			0
$601$	22.6863	+	19.0361i	0.925394	+	0.776498i	0.974985	−	0.222272i	$-0.0713472\pi$
$601$	22.6863	+	19.0361i	0.925394	+	0.776498i	−0.0495905	+	0.998770i	$0.515792\pi$
$602$		0			0
$603$	−0.335948	+	28.1648i	−0.0136809	+	1.14696i
$604$		0			0
$605$	−5.23749	+	29.7033i	−0.212934	+	1.20761i
$606$		0			0
$607$	−13.9075	−	5.06190i	−0.564487	−	0.205456i	0.0439846	−	0.999032i	$-0.485995\pi$
$607$	−13.9075	−	5.06190i	−0.564487	−	0.205456i	−0.608471	+	0.793576i	$0.708217\pi$
$608$		0			0
$609$	2.97131	+	4.29780i	0.120404	+	0.174156i
$610$		0			0
$611$	3.86819	+	6.69991i	0.156490	+	0.271049i
$612$		0			0
$613$	1.19319	−	2.06666i	0.0481925	−	0.0834718i	−0.840923	−	0.541155i	$-0.817987\pi$
$613$	1.19319	−	2.06666i	0.0481925	−	0.0834718i	0.889115	+	0.457683i	$0.151321\pi$
$614$		0			0
$615$	25.8225	−	25.5164i	1.04126	−	1.02892i
$616$		0			0
$617$	−1.94666	+	1.63345i	−0.0783698	+	0.0657600i	−0.681131	−	0.732162i	$-0.738512\pi$
$617$	−1.94666	+	1.63345i	−0.0783698	+	0.0657600i	0.602761	+	0.797922i	$0.294067\pi$
$618$		0			0
$619$	−0.0522432	+	0.0190150i	−0.00209983	+	0.000764277i	−0.343070	−	0.939310i	$-0.611467\pi$
$619$	−0.0522432	+	0.0190150i	−0.00209983	+	0.000764277i	0.340970	+	0.940074i	$0.389245\pi$
$620$		0			0
$621$	−7.95531	−	17.8890i	−0.319236	−	0.717861i
$622$		0			0
$623$	5.27990	−	1.92173i	0.211535	−	0.0769923i
$624$		0			0
$625$	53.8146	−	45.1558i	2.15258	−	1.80623i
$626$		0			0
$627$	−7.40954	−	28.3274i	−0.295908	−	1.13129i
$628$		0			0
$629$	14.0845	−	24.3951i	0.561586	−	0.972695i
$630$		0			0
$631$	4.65181	+	8.05717i	0.185186	+	0.320751i	0.943639	−	0.330976i	$-0.107378\pi$
$631$	4.65181	+	8.05717i	0.185186	+	0.320751i	−0.758453	+	0.651727i	$0.774045\pi$
$632$		0			0
$633$	−0.707546	+	1.49401i	−0.0281224	+	0.0593816i
$634$		0			0
$635$	43.2075	+	15.7262i	1.71464	+	0.624077i
$636$		0			0
$637$	3.67399	−	20.8363i	0.145569	−	0.825563i
$638$		0			0
$639$	21.2050	−	24.6675i	0.838855	−	0.975831i
$640$		0			0
$641$	−34.7204	−	29.1339i	−1.37137	−	1.15072i	−0.972283	−	0.233807i	$-0.924882\pi$
$641$	−34.7204	−	29.1339i	−1.37137	−	1.15072i	−0.399090	−	0.916912i	$-0.630674\pi$
$642$		0			0
$643$	−0.0836140	−	0.474199i	−0.00329741	−	0.0187006i	0.983115	−	0.182991i	$-0.0585778\pi$
$643$	−0.0836140	−	0.474199i	−0.00329741	−	0.0187006i	−0.986412	+	0.164290i	$0.947467\pi$
$644$		0			0
$645$	24.2260	+	17.1794i	0.953897	+	0.676439i
$646$		0			0
$647$	10.0044			0.393313			0.196657	−	0.980472i	$-0.436992\pi$
$647$	10.0044			0.393313			0.196657	+	0.980472i	$0.436992\pi$
$648$		0			0
$649$	7.91766			0.310795
$650$		0			0
$651$	4.50616	+	3.19547i	0.176610	+	0.125240i
$652$		0			0
$653$	7.12063	+	40.3831i	0.278652	+	1.58031i	0.727118	+	0.686513i	$0.240859\pi$
$653$	7.12063	+	40.3831i	0.278652	+	1.58031i	−0.448466	+	0.893800i	$0.648029\pi$
$654$		0			0
$655$	35.3335	+	29.6483i	1.38059	+	1.15846i
$656$		0			0
$657$	−32.6741	−	6.16403i	−1.27474	−	0.240482i
$658$		0			0
$659$	−2.60362	+	14.7659i	−0.101423	+	0.575196i	0.891166	+	0.453677i	$0.149888\pi$
$659$	−2.60362	+	14.7659i	−0.101423	+	0.575196i	−0.992589	+	0.121520i	$0.961223\pi$
$660$		0			0
$661$	−35.1577	−	12.7964i	−1.36748	−	0.497721i	−0.449119	−	0.893472i	$-0.648262\pi$
$661$	−35.1577	−	12.7964i	−1.36748	−	0.497721i	−0.918358	+	0.395751i	$0.870484\pi$
$662$		0			0
$663$	−10.4057	+	21.9721i	−0.404125	+	0.853325i
$664$		0			0
$665$	−9.42722	−	16.3284i	−0.365572	−	0.633189i
$666$		0			0
$667$	−10.9503	+	18.9666i	−0.423999	+	0.734388i
$668$		0			0
$669$	−9.98342	−	38.1677i	−0.385981	−	1.47565i
$670$		0			0
$671$	4.93902	−	4.14433i	0.190669	−	0.159990i
$672$		0			0
$673$	−22.2546	+	8.10003i	−0.857854	+	0.312233i	−0.733238	−	0.679972i	$-0.761992\pi$
$673$	−22.2546	+	8.10003i	−0.857854	+	0.312233i	−0.124615	+	0.992205i	$0.539770\pi$
$674$		0			0
$675$	4.52937	+	65.1830i	0.174335	+	2.50889i
$676$		0			0
$677$	−34.2731	+	12.4744i	−1.31722	+	0.479430i	−0.902567	−	0.430549i	$-0.858320\pi$
$677$	−34.2731	+	12.4744i	−1.31722	+	0.479430i	−0.414655	+	0.909979i	$0.636098\pi$
$678$		0			0
$679$	−1.79318	+	1.50465i	−0.0688158	+	0.0577433i
$680$		0			0
$681$	−14.2108	+	14.0423i	−0.544559	+	0.538102i
$682$		0			0
$683$	20.3239	−	35.2020i	0.777671	−	1.34697i	−0.155610	−	0.987819i	$-0.549734\pi$
$683$	20.3239	−	35.2020i	0.777671	−	1.34697i	0.933281	−	0.359147i	$-0.116932\pi$
$684$		0			0
$685$	22.0946	+	38.2689i	0.844190	+	1.46218i
$686$		0			0
$687$	−8.91731	−	12.8983i	−0.340216	−	0.492100i
$688$		0			0
$689$	−1.03886	−	0.378114i	−0.0395774	−	0.0144050i
$690$		0			0
$691$	2.15879	−	12.2431i	0.0821244	−	0.465751i	−0.915816	−	0.401599i	$-0.868455\pi$
$691$	2.15879	−	12.2431i	0.0821244	−	0.465751i	0.997940	−	0.0641519i	$-0.0204342\pi$
$692$		0			0
$693$	2.61197	+	1.54985i	0.0992206	+	0.0588740i
$694$		0			0
$695$	9.21818	+	7.73498i	0.349666	+	0.293404i
$696$		0			0
$697$	−3.87655	−	21.9850i	−0.146835	−	0.832742i
$698$		0			0
$699$	2.34848	−	25.1171i	0.0888278	−	0.950018i
$700$		0			0
$701$	−9.46063			−0.357323			−0.178662	−	0.983911i	$-0.557177\pi$
$701$	−9.46063			−0.357323			−0.178662	+	0.983911i	$0.557177\pi$
$702$		0			0
$703$	−54.6700			−2.06192
$704$		0			0
$705$	16.2408	−	7.45560i	0.611662	−	0.280794i
$706$		0			0
$707$	0.807605	+	4.58016i	0.0303731	+	0.172255i
$708$		0			0
$709$	−4.39107	−	3.68455i	−0.164910	−	0.138376i	0.556598	−	0.830782i	$-0.312106\pi$
$709$	−4.39107	−	3.68455i	−0.164910	−	0.138376i	−0.721508	+	0.692406i	$0.756551\pi$
$710$		0			0
$711$	−13.2129	−	16.1334i	−0.495522	−	0.605051i
$712$		0			0
$713$	−4.02083	+	22.8033i	−0.150581	+	0.853989i
$714$		0			0
$715$	24.1568	+	8.79234i	0.903412	+	0.328815i
$716$		0			0
$717$	−42.0841	+	3.42911i	−1.57166	+	0.128063i
$718$		0			0
$719$	6.05980	+	10.4959i	0.225992	+	0.391430i	0.956617	−	0.291349i	$-0.0941042\pi$
$719$	6.05980	+	10.4959i	0.225992	+	0.391430i	−0.730624	+	0.682780i	$0.760771\pi$
$720$		0			0
$721$	−1.49170	+	2.58370i	−0.0555538	+	0.0962219i
$722$		0			0
$723$	−25.8348	−	7.08782i	−0.960808	−	0.263599i
$724$		0			0
$725$	55.9913	−	46.9823i	2.07947	−	1.74488i
$726$		0			0
$727$	−24.5355	+	8.93020i	−0.909972	+	0.331203i	−0.754242	−	0.656597i	$-0.771995\pi$
$727$	−24.5355	+	8.93020i	−0.909972	+	0.331203i	−0.155730	+	0.987800i	$0.549773\pi$
$728$		0			0
$729$	−22.8848	−	14.3279i	−0.847584	−	0.530662i
$730$		0			0
$731$	17.1619	−	6.24640i	0.634754	−	0.231032i
$732$		0			0
$733$	24.9067	−	20.8992i	0.919950	−	0.771929i	−0.0540360	−	0.998539i	$-0.517209\pi$
$733$	24.9067	−	20.8992i	0.919950	−	0.771929i	0.973986	+	0.226610i	$0.0727641\pi$
$734$		0			0
$735$	−47.1307	−	12.9304i	−1.73844	−	0.476944i
$736$		0			0
$737$	9.15766	−	15.8615i	0.337327	−	0.584267i
$738$		0			0
$739$	4.12762	+	7.14925i	0.151837	+	0.262989i	0.931903	−	0.362708i	$-0.118148\pi$
$739$	4.12762	+	7.14925i	0.151837	+	0.262989i	−0.780066	+	0.625697i	$0.784814\pi$
$740$		0			0
$741$	47.0277	−	3.83193i	1.72760	−	0.140769i
$742$		0			0
$743$	37.8430	+	13.7737i	1.38833	+	0.505309i	0.924692	−	0.380717i	$-0.124323\pi$
$743$	37.8430	+	13.7737i	1.38833	+	0.505309i	0.463635	+	0.886027i	$0.346545\pi$
$744$		0			0
$745$	6.24884	−	35.4389i	0.228940	−	1.29838i
$746$		0			0
$747$	−29.8474	−	36.4449i	−1.09206	−	1.33345i
$748$		0			0
$749$	−3.44739	−	2.89270i	−0.125965	−	0.105697i
$750$		0			0
$751$	−6.81653	−	38.6585i	−0.248739	−	1.41067i	−0.811647	−	0.584148i	$-0.801429\pi$
$751$	−6.81653	−	38.6585i	−0.248739	−	1.41067i	0.562908	−	0.826519i	$-0.309682\pi$
$752$		0			0
$753$	1.42078	−	0.652234i	0.0517761	−	0.0237687i
$754$		0			0
$755$	51.2072			1.86362
$756$		0			0
$757$	−1.39897			−0.0508466			−0.0254233	−	0.999677i	$-0.508093\pi$
$757$	−1.39897			−0.0508466			−0.0254233	+	0.999677i	$0.508093\pi$
$758$		0			0
$759$	−1.18515	+	12.6753i	−0.0430184	+	0.460084i
$760$		0			0
$761$	−2.84251	−	16.1206i	−0.103041	−	0.584373i	−0.991985	−	0.126357i	$-0.959671\pi$
$761$	−2.84251	−	16.1206i	−0.103041	−	0.584373i	0.888944	−	0.458016i	$-0.151440\pi$
$762$		0			0
$763$	−1.82891	−	1.53464i	−0.0662111	−	0.0555577i
$764$		0			0
$765$	48.2954	+	28.6567i	1.74612	+	1.03609i
$766$		0			0
$767$	−2.21554	+	12.5649i	−0.0799985	+	0.453694i
$768$		0			0
$769$	1.35384	+	0.492757i	0.0488206	+	0.0177693i	0.366315	−	0.930491i	$-0.380619\pi$
$769$	1.35384	+	0.492757i	0.0488206	+	0.0177693i	−0.317494	+	0.948260i	$0.602841\pi$
$770$		0			0
$771$	5.55273	+	8.03165i	0.199977	+	0.289253i
$772$		0			0
$773$	−14.6589	−	25.3900i	−0.527244	−	0.913213i	−0.999496	−	0.0317497i	$-0.989892\pi$
$773$	−14.6589	−	25.3900i	−0.527244	−	0.913213i	0.472252	−	0.881464i	$-0.343441\pi$
$774$		0			0
$775$	38.6389	−	66.9245i	1.38795	−	2.40400i
$776$		0			0
$777$	4.03368	−	3.98585i	0.144707	−	0.142992i
$778$		0			0
$779$	−33.1900	+	27.8497i	−1.18916	+	0.997820i
$780$		0			0
$781$	−19.8762	+	7.23434i	−0.711226	+	0.258865i
$782$		0			0
$783$	2.09367	+	30.1304i	0.0748216	+	1.07677i
$784$		0			0
$785$	0.434302	−	0.158073i	0.0155009	−	0.00564187i
$786$		0			0
$787$	6.89807	−	5.78816i	0.245889	−	0.206326i	−0.511510	−	0.859277i	$-0.670914\pi$
$787$	6.89807	−	5.78816i	0.245889	−	0.206326i	0.757400	+	0.652951i	$0.226469\pi$
$788$		0			0
$789$	−7.98814	−	30.5395i	−0.284385	−	1.08723i
$790$		0			0
$791$	−2.47268	+	4.28281i	−0.0879184	+	0.152279i
$792$		0			0
$793$	5.19481	+	8.99767i	0.184473	+	0.319517i
$794$		0			0
$795$	−1.09301	+	2.30793i	−0.0387651	+	0.0818540i
$796$		0			0
$797$	40.2727	+	14.6581i	1.42653	+	0.519215i	0.935935	−	0.352172i	$-0.114557\pi$
$797$	40.2727	+	14.6581i	1.42653	+	0.519215i	0.490596	+	0.871387i	$0.336779\pi$
$798$		0			0
$799$	1.90827	−	10.8223i	0.0675096	−	0.382866i
$800$		0			0
$801$	31.9166	+	6.02112i	1.12772	+	0.212746i
$802$		0			0
$803$	16.5626	+	13.8977i	0.584482	+	0.490439i
$804$		0			0
$805$	1.42349	+	8.07301i	0.0501714	+	0.284536i
$806$		0			0
$807$	−6.83191	−	4.84473i	−0.240494	−	0.170542i
$808$		0			0
$809$	30.7784			1.08211			0.541056	−	0.840986i	$-0.318025\pi$
$809$	30.7784			1.08211			0.541056	+	0.840986i	$0.318025\pi$
$810$		0			0
$811$	−4.79541			−0.168390			−0.0841948	−	0.996449i	$-0.526832\pi$
$811$	−4.79541			−0.168390			−0.0841948	+	0.996449i	$0.526832\pi$
$812$		0			0
$813$	6.04088	+	4.28378i	0.211863	+	0.150239i
$814$		0			0
$815$	−12.8822	−	73.0584i	−0.451243	−	2.55912i
$816$		0			0
$817$	−27.1525	−	22.7837i	−0.949946	−	0.797100i
$818$		0			0
$819$	−3.19043	+	3.71139i	−0.111483	+	0.129687i
$820$		0			0
$821$	3.97767	−	22.5585i	0.138822	−	0.787297i	−0.833300	−	0.552821i	$-0.813551\pi$
$821$	3.97767	−	22.5585i	0.138822	−	0.787297i	0.972122	−	0.234476i	$-0.0753375\pi$
$822$		0			0
$823$	−35.7064	−	12.9960i	−1.24465	−	0.453014i	−0.366056	−	0.930593i	$-0.619292\pi$
$823$	−35.7064	−	12.9960i	−1.24465	−	0.453014i	−0.878589	+	0.477579i	$0.841514\pi$
$824$		0			0
$825$	18.1851	−	38.3986i	0.633125	−	1.33687i
$826$		0			0
$827$	9.28709	+	16.0857i	0.322944	+	0.559355i	0.981094	−	0.193532i	$-0.0619942\pi$
$827$	9.28709	+	16.0857i	0.322944	+	0.559355i	−0.658150	+	0.752887i	$0.728661\pi$
$828$		0			0
$829$	9.01411	−	15.6129i	0.313073	−	0.542258i	−0.665953	−	0.745994i	$-0.731975\pi$
$829$	9.01411	−	15.6129i	0.313073	−	0.542258i	0.979026	+	0.203735i	$0.0653082\pi$
$830$		0			0
$831$	−5.79302	−	22.1473i	−0.200958	−	0.768282i
$832$		0			0
$833$	−23.0225	+	19.3182i	−0.797683	+	0.669336i
$834$		0			0
$835$	−83.6732	+	30.4545i	−2.89563	+	1.05392i
$836$		0			0
$837$	12.9755	+	29.1778i	0.448499	+	1.00853i
$838$		0			0
$839$	7.55125	−	2.74843i	0.260698	−	0.0948864i	−0.208365	−	0.978051i	$-0.566814\pi$
$839$	7.55125	−	2.74843i	0.260698	−	0.0948864i	0.469063	+	0.883165i	$0.344592\pi$
$840$		0			0
$841$	3.66630	−	3.07639i	0.126424	−	0.106082i
$842$		0			0
$843$	−15.4643	+	15.2809i	−0.532618	+	0.526303i
$844$		0			0
$845$	6.53679	−	11.3221i	0.224872	−	0.389491i
$846$		0			0
$847$	1.86694	+	3.23363i	0.0641487	+	0.111109i
$848$		0			0
$849$	−5.73010	−	8.28819i	−0.196656	−	0.284450i
$850$		0			0
$851$	22.3360	+	8.12964i	0.765668	+	0.278680i
$852$		0			0
$853$	−5.09553	+	28.8982i	−0.174468	+	0.989455i	0.764289	+	0.644874i	$0.223090\pi$
$853$	−5.09553	+	28.8982i	−0.174468	+	0.989455i	−0.938757	+	0.344581i	$0.888021\pi$
$854$		0			0
$855$	1.29993	−	108.982i	0.0444565	−	3.72710i
$856$		0			0
$857$	−16.9257	−	14.2024i	−0.578172	−	0.485144i	0.306174	−	0.951975i	$-0.400951\pi$
$857$	−16.9257	−	14.2024i	−0.578172	−	0.485144i	−0.884346	+	0.466832i	$0.845395\pi$
$858$		0			0
$859$	7.80162	+	44.2452i	0.266188	+	1.50963i	0.765631	+	0.643280i	$0.222427\pi$
$859$	7.80162	+	44.2452i	0.266188	+	1.50963i	−0.499443	+	0.866347i	$0.666462\pi$
$860$		0			0
$861$	0.418382	−	4.47461i	0.0142584	−	0.152494i
$862$		0			0
$863$	−16.5441			−0.563166			−0.281583	−	0.959537i	$-0.590860\pi$
$863$	−16.5441			−0.563166			−0.281583	+	0.959537i	$0.590860\pi$
$864$		0			0
$865$	45.0829			1.53286
$866$		0			0
$867$	4.62480	−	2.12310i	0.157067	−	0.0721041i
$868$		0			0
$869$	2.35465	+	13.3539i	0.0798759	+	0.452999i
$870$		0			0
$871$	22.6090	+	18.9712i	0.766076	+	0.642814i
$872$		0			0
$873$	−13.3528	+	2.19058i	−0.451924	+	0.0741400i
$874$		0			0
$875$	2.86175	−	16.2298i	0.0967448	−	0.548667i
$876$		0			0
$877$	13.8019	+	5.02347i	0.466056	+	0.169631i	0.564365	−	0.825525i	$-0.309121\pi$
$877$	13.8019	+	5.02347i	0.466056	+	0.169631i	−0.0983089	+	0.995156i	$0.531343\pi$
$878$		0			0
$879$	21.0642	−	1.71636i	0.710476	−	0.0578913i
$880$		0			0
$881$	−26.4990	−	45.8975i	−0.892773	−	1.54633i	−0.836537	−	0.547910i	$-0.815424\pi$
$881$	−26.4990	−	45.8975i	−0.892773	−	1.54633i	−0.0562355	−	0.998418i	$-0.517910\pi$
$882$		0			0
$883$	−0.182608	+	0.316287i	−0.00614526	+	0.0106439i	−0.869082	−	0.494669i	$-0.835289\pi$
$883$	−0.182608	+	0.316287i	−0.00614526	+	0.0106439i	0.862936	+	0.505313i	$0.168623\pi$
$884$		0			0
$885$	28.4214	+	7.79744i	0.955374	+	0.262108i
$886$		0			0
$887$	−3.78207	+	3.17354i	−0.126990	+	0.106557i	−0.704071	−	0.710130i	$-0.748636\pi$
$887$	−3.78207	+	3.17354i	−0.126990	+	0.106557i	0.577081	+	0.816687i	$0.304192\pi$
$888$		0			0
$889$	5.34891	−	1.94685i	0.179397	−	0.0652951i
$890$		0			0
$891$	8.41314	+	15.4095i	0.281851	+	0.516239i
$892$		0			0
$893$	−20.0416	+	7.29454i	−0.670666	+	0.244103i
$894$		0			0
$895$	−32.5527	+	27.3150i	−1.08812	+	0.913039i
$896$		0			0
$897$	−19.7835	−	5.42762i	−0.660550	−	0.181223i
$898$		0			0
$899$	17.8605	−	30.9354i	0.595682	−	1.03175i
$900$		0			0
$901$	0.785184	+	1.35998i	0.0261583	+	0.0453075i
$902$		0			0
$903$	3.66447	−	0.298590i	0.121946	−	0.00993645i
$904$		0			0
$905$	80.9210	+	29.4528i	2.68990	+	0.979045i
$906$		0			0
$907$	2.79349	−	15.8427i	0.0927563	−	0.526047i	−0.902656	−	0.430364i	$-0.858385\pi$
$907$	2.79349	−	15.8427i	0.0927563	−	0.526047i	0.995412	−	0.0956833i	$-0.0305036\pi$
$908$		0			0
$909$	−9.49565	+	25.1516i	−0.314951	+	0.834225i
$910$		0			0
$911$	13.6907	+	11.4879i	0.453593	+	0.380610i	0.840767	−	0.541397i	$-0.182104\pi$
$911$	13.6907	+	11.4879i	0.453593	+	0.380610i	−0.387174	+	0.922007i	$0.626549\pi$
$912$		0			0
$913$	5.31907	+	30.1659i	0.176035	+	0.998347i
$914$		0			0
$915$	21.8106	−	10.0125i	0.721036	−	0.331004i
$916$		0			0
$917$	5.71004			0.188562
$918$		0			0
$919$	−15.3478			−0.506277			−0.253138	−	0.967430i	$-0.581463\pi$
$919$	−15.3478			−0.506277			−0.253138	+	0.967430i	$0.581463\pi$
$920$		0			0
$921$	1.24218	−	13.2852i	0.0409312	−	0.437761i
$922$		0			0
$923$	−5.91875	−	33.5669i	−0.194818	−	1.10487i
$924$		0			0
$925$	−60.7690	−	50.9913i	−1.99807	−	1.67658i
$926$		0			0
$927$	−15.0370	+	8.44412i	−0.493881	+	0.277341i
$928$		0			0
$929$	1.61938	−	9.18398i	0.0531303	−	0.301317i	−0.946650	−	0.322263i	$-0.895557\pi$
$929$	1.61938	−	9.18398i	0.0531303	−	0.301317i	0.999781	+	0.0209458i	$0.00666773\pi$
$930$		0			0
$931$	54.8103	+	19.9493i	1.79634	+	0.653813i
$932$		0			0
$933$	−4.06466	−	5.87925i	−0.133071	−	0.192478i
$934$		0			0
$935$	−18.2580	−	31.6238i	−0.597101	−	1.03421i
$936$		0			0
$937$	20.1708	−	34.9368i	0.658951	−	1.14134i	−0.321936	−	0.946761i	$-0.604334\pi$
$937$	20.1708	−	34.9368i	0.658951	−	1.14134i	0.980888	−	0.194576i	$-0.0623329\pi$
$938$		0			0
$939$	34.3998	−	33.9919i	1.12259	−	1.10928i
$940$		0			0
$941$	11.9741	−	10.0474i	0.390343	−	0.327537i	−0.426404	−	0.904533i	$-0.640220\pi$
$941$	11.9741	−	10.0474i	0.390343	−	0.327537i	0.816747	+	0.576996i	$0.195775\pi$
$942$		0			0
$943$	17.7015	−	6.44281i	0.576439	−	0.209807i
$944$		0			0
$945$	7.84966	+	8.13569i	0.255350	+	0.264654i
$946$		0			0
$947$	−42.5083	+	15.4717i	−1.38133	+	0.502764i	−0.922582	−	0.385801i	$-0.873925\pi$
$947$	−42.5083	+	15.4717i	−1.38133	+	0.502764i	−0.458751	+	0.888565i	$0.651703\pi$
$948$		0			0
$949$	−26.6896	+	22.3952i	−0.866380	+	0.726979i
$950$		0			0
$951$	3.73423	+	14.2764i	0.121091	+	0.462942i
$952$		0			0
$953$	−12.5968	+	21.8183i	−0.408051	+	0.706765i	−0.994671	−	0.103097i	$-0.967125\pi$
$953$	−12.5968	+	21.8183i	−0.408051	+	0.706765i	0.586621	+	0.809862i	$0.300458\pi$
$954$		0			0
$955$	24.6795	+	42.7462i	0.798611	+	1.38323i
$956$		0			0
$957$	8.40595	−	17.7495i	0.271726	−	0.573759i
$958$		0			0
$959$	5.14053	+	1.87100i	0.165996	+	0.0604177i
$960$		0			0
$961$	1.17507	−	6.66417i	0.0379056	−	0.214973i
$962$		0			0
$963$	−8.60511	−	24.5495i	−0.277296	−	0.791097i
$964$		0			0
$965$	39.1925	+	32.8864i	1.26165	+	1.05865i
$966$		0			0
$967$	3.84339	+	21.7970i	0.123595	+	0.700943i	0.982132	+	0.188192i	$0.0602626\pi$
$967$	3.84339	+	21.7970i	0.123595	+	0.700943i	−0.858537	+	0.512751i	$0.828626\pi$
$968$		0			0
$969$	−54.6714	−	38.7693i	−1.75630	−	1.24545i
$970$		0			0
$971$	−24.6357			−0.790597			−0.395298	−	0.918553i	$-0.629359\pi$
$971$	−24.6357			−0.790597			−0.395298	+	0.918553i	$0.629359\pi$
$972$		0			0
$973$	1.48970			0.0477575
$974$		0			0
$975$	55.8482	+	39.6038i	1.78857	+	1.26834i
$976$		0			0
$977$	−7.19233	−	40.7897i	−0.230103	−	1.30498i	−0.852685	−	0.522425i	$-0.825027\pi$
$977$	−7.19233	−	40.7897i	−0.230103	−	1.30498i	0.622582	−	0.782554i	$-0.286084\pi$
$978$		0			0
$979$	−16.1786	−	13.5755i	−0.517071	−	0.433874i
$980$		0			0
$981$	−4.56520	−	13.0241i	−0.145756	−	0.415826i
$982$		0			0
$983$	1.79168	−	10.1611i	0.0571456	−	0.324089i	−0.942812	−	0.333326i	$-0.891829\pi$
$983$	1.79168	−	10.1611i	0.0571456	−	0.324089i	0.999957	+	0.00923687i	$0.00294023\pi$
$984$		0			0
$985$	60.8601	+	22.1513i	1.93916	+	0.705798i
$986$		0			0
$987$	0.946887	−	1.99939i	0.0301398	−	0.0636412i
$988$		0			0
$989$	7.70542	+	13.3462i	0.245018	+	0.424384i
$990$		0			0
$991$	−1.68489	+	2.91832i	−0.0535224	+	0.0927035i	−0.891545	−	0.452932i	$-0.850378\pi$
$991$	−1.68489	+	2.91832i	−0.0535224	+	0.0927035i	0.838023	+	0.545635i	$0.183712\pi$
$992$		0			0
$993$	10.4069	+	39.7866i	0.330252	+	1.26259i
$994$		0			0
$995$	−72.3349	+	60.6962i	−2.29317	+	1.92420i
$996$		0			0
$997$	3.06370	−	1.11510i	0.0970283	−	0.0353154i	−0.293050	−	0.956097i	$-0.594670\pi$
$997$	3.06370	−	1.11510i	0.0970283	−	0.0353154i	0.390078	+	0.920782i	$0.372448\pi$
$998$		0			0
$999$	31.8100	−	7.91633i	1.00642	−	0.250462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.385.2	yes	54
4.3	odd	2		864.2.y.b.385.8	yes	54
27.4	even	9	inner	864.2.y.c.193.2	yes	54
108.31	odd	18		864.2.y.b.193.8	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.8	✓	54	108.31	odd	18
864.2.y.b.385.8	yes	54	4.3	odd	2
864.2.y.c.193.2	yes	54	27.4	even	9	inner
864.2.y.c.385.2	yes	54	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41286 - 1.00191i) q^{3} +(0.727972 + 4.12853i) q^{5} +(0.397562 + 0.333594i) q^{7} +(0.992364 + 2.83112i) q^{9} +O(q^{10})\)	\(q+(-1.41286 - 1.00191i) q^{3} +(0.727972 + 4.12853i) q^{5} +(0.397562 + 0.333594i) q^{7} +(0.992364 + 2.83112i) q^{9} +(0.338741 - 1.92110i) q^{11} +(2.95390 + 1.07513i) q^{13} +(3.10788 - 6.56241i) q^{15} +(-2.23260 - 3.86698i) q^{17} +(-4.33300 + 7.50498i) q^{19} +(-0.227470 - 0.869642i) q^{21} +(2.88631 - 2.42190i) q^{23} +(-11.8164 + 4.30081i) q^{25} +(1.43444 - 4.99423i) q^{27} +(-5.46203 + 1.98802i) q^{29} +(-4.70771 + 3.95024i) q^{31} +(-2.40336 + 2.37486i) q^{33} +(-1.08784 + 1.88419i) q^{35} +(3.15428 + 5.46337i) q^{37} +(-3.09628 - 4.47855i) q^{39} +(4.69808 + 1.70996i) q^{41} +(-0.710244 + 4.02799i) q^{43} +(-10.9659 + 6.15798i) q^{45} +(1.88530 + 1.58196i) q^{47} +(-1.16877 - 6.62841i) q^{49} +(-0.719994 + 7.70037i) q^{51} -0.351690 q^{53} +8.17791 q^{55} +(13.6412 - 6.26224i) q^{57} +(0.704805 + 3.99715i) q^{59} +(2.53188 + 2.12450i) q^{61} +(-0.549917 + 1.45659i) q^{63} +(-2.28836 + 12.9780i) q^{65} +(8.82272 + 3.21121i) q^{67} +(-6.50449 + 0.530001i) q^{69} +(-5.42150 - 9.39031i) q^{71} +(-5.54175 + 9.59859i) q^{73} +(21.0039 + 5.76245i) q^{75} +(0.775537 - 0.650753i) q^{77} +(-6.53196 + 2.37744i) q^{79} +(-7.03043 + 5.61899i) q^{81} +(-14.7555 + 5.37055i) q^{83} +(14.3397 - 12.0324i) q^{85} +(9.70891 + 2.66365i) q^{87} +(5.41326 - 9.37604i) q^{89} +(0.815702 + 1.41284i) q^{91} +(10.6091 - 0.864457i) q^{93} +(-34.1389 - 12.4255i) q^{95} +(-0.783229 + 4.44191i) q^{97} +(5.77501 - 0.947413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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