LMFDB - Embedded newform 2646.2.t.c.1979.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1979,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("2646.1979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.t (of order $6$, degree $2$, not 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1979.5
Character	$\chi$	$=$	2646.1979
Dual form			2646.2.t.c.2285.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.16972 q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.16972 q^{5} +1.00000i q^{8} +(1.01301 - 0.584859i) q^{10} +5.76436i q^{11} +(0.571028 - 0.329683i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.83946 + 4.91809i) q^{17} +(3.16853 + 1.82935i) q^{19} +(-0.584859 + 1.01301i) q^{20} +(-2.88218 - 4.99209i) q^{22} -0.580945i q^{23} -3.63176 q^{25} +(-0.329683 + 0.571028i) q^{26} +(-6.53449 - 3.77269i) q^{29} +(2.75231 + 1.58905i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.91809 - 2.83946i) q^{34} +(5.29511 - 9.17140i) q^{37} -3.65870 q^{38} -1.16972i q^{40} +(2.64145 + 4.57513i) q^{41} +(2.37970 - 4.12177i) q^{43} +(4.99209 + 2.88218i) q^{44} +(0.290473 + 0.503113i) q^{46} +(-2.67305 - 4.62986i) q^{47} +(3.14519 - 1.81588i) q^{50} -0.659367i q^{52} +(-4.14347 + 2.39223i) q^{53} -6.74269i q^{55} +7.54538 q^{58} +(0.514856 - 0.891757i) q^{59} +(-10.1334 + 5.85054i) q^{61} -3.17809 q^{62} -1.00000 q^{64} +(-0.667943 + 0.385637i) q^{65} +(-4.26100 + 7.38027i) q^{67} +5.67892 q^{68} -8.34154i q^{71} +(-0.899038 + 0.519060i) q^{73} +10.5902i q^{74} +(3.16853 - 1.82935i) q^{76} +(0.631283 + 1.09341i) q^{79} +(0.584859 + 1.01301i) q^{80} +(-4.57513 - 2.64145i) q^{82} +(-6.21900 + 10.7716i) q^{83} +(-3.32137 - 5.75278i) q^{85} +4.75941i q^{86} -5.76436 q^{88} +(-7.83957 + 13.5785i) q^{89} +(-0.503113 - 0.290473i) q^{92} +(4.62986 + 2.67305i) q^{94} +(-3.70629 - 2.13983i) q^{95} +(-12.5887 - 7.26808i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 48 q^{44} + 48 q^{50} + 96 q^{53} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 48 q^{92} - 192 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 48 * q^44 + 48 * q^50 + 96 * q^53 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 48 * q^92 - 192 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.16972			−0.523114			−0.261557	−	0.965188i	$-0.584236\pi$
$5$	−1.16972			−0.523114			−0.261557	+	0.965188i	$0.584236\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.01301	−	0.584859i	0.320341	−	0.184949i
$11$			5.76436i			1.73802i	0.494794	+	0.869010i	$0.335244\pi$
$11$			5.76436i			1.73802i	−0.494794	+	0.869010i	$0.664756\pi$
$12$		0			0
$13$	0.571028	−	0.329683i	0.158375	−	0.0914377i	−0.418718	−	0.908116i	$-0.637520\pi$
$13$	0.571028	−	0.329683i	0.158375	−	0.0914377i	0.577093	+	0.816679i	$0.304187\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.83946	+	4.91809i	0.688670	+	1.19281i	0.972268	+	0.233868i	$0.0751384\pi$
$17$	2.83946	+	4.91809i	0.688670	+	1.19281i	−0.283598	+	0.958943i	$0.591528\pi$
$18$		0			0
$19$	3.16853	+	1.82935i	0.726910	+	0.419682i	0.817291	−	0.576226i	$-0.195475\pi$
$19$	3.16853	+	1.82935i	0.726910	+	0.419682i	−0.0903806	+	0.995907i	$0.528808\pi$
$20$	−0.584859	+	1.01301i	−0.130779	+	0.226515i
$21$		0			0
$22$	−2.88218	−	4.99209i	−0.614483	−	1.06432i
$23$		−	0.580945i		−	0.121135i	−0.998164	−	0.0605677i	$-0.980709\pi$
$23$		−	0.580945i		−	0.121135i	0.998164	−	0.0605677i	$-0.0192911\pi$
$24$		0			0
$25$	−3.63176			−0.726352
$26$	−0.329683	+	0.571028i	−0.0646562	+	0.111988i
$27$		0			0
$28$		0			0
$29$	−6.53449	−	3.77269i	−1.21342	−	0.700571i	−0.249920	−	0.968266i	$-0.580404\pi$
$29$	−6.53449	−	3.77269i	−1.21342	−	0.700571i	−0.963503	+	0.267696i	$0.913738\pi$
$30$		0			0
$31$	2.75231	+	1.58905i	0.494329	+	0.285401i	0.726369	−	0.687305i	$-0.241207\pi$
$31$	2.75231	+	1.58905i	0.494329	+	0.285401i	−0.232040	+	0.972706i	$0.574540\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−4.91809	−	2.83946i	−0.843445	−	0.486963i
$35$		0			0
$36$		0			0
$37$	5.29511	−	9.17140i	0.870511	−	1.50777i	0.00904243	−	0.999959i	$-0.497122\pi$
$37$	5.29511	−	9.17140i	0.870511	−	1.50777i	0.861469	−	0.507811i	$-0.169545\pi$
$38$	−3.65870			−0.593520
$39$		0			0
$40$		−	1.16972i		−	0.184949i
$41$	2.64145	+	4.57513i	0.412525	+	0.714514i	0.995165	−	0.0982159i	$-0.0313136\pi$
$41$	2.64145	+	4.57513i	0.412525	+	0.714514i	−0.582640	+	0.812730i	$0.697980\pi$
$42$		0			0
$43$	2.37970	−	4.12177i	0.362902	−	0.628564i	−0.625535	−	0.780196i	$-0.715119\pi$
$43$	2.37970	−	4.12177i	0.362902	−	0.628564i	0.988437	+	0.151632i	$0.0484528\pi$
$44$	4.99209	+	2.88218i	0.752585	+	0.434505i
$45$		0			0
$46$	0.290473	+	0.503113i	0.0428279	+	0.0741800i
$47$	−2.67305	−	4.62986i	−0.389904	−	0.675334i	0.602532	−	0.798095i	$-0.294159\pi$
$47$	−2.67305	−	4.62986i	−0.389904	−	0.675334i	−0.992436	+	0.122761i	$0.960825\pi$
$48$		0			0
$49$		0			0
$50$	3.14519	−	1.81588i	0.444798	−	0.256804i
$51$		0			0
$52$		−	0.659367i		−	0.0914377i
$53$	−4.14347	+	2.39223i	−0.569150	+	0.328599i	−0.756810	−	0.653635i	$-0.773243\pi$
$53$	−4.14347	+	2.39223i	−0.569150	+	0.328599i	0.187660	+	0.982234i	$0.439910\pi$
$54$		0			0
$55$		−	6.74269i		−	0.909183i
$56$		0			0
$57$		0			0
$58$	7.54538			0.990756
$59$	0.514856	−	0.891757i	0.0670286	−	0.116097i	−0.830563	−	0.556924i	$-0.811981\pi$
$59$	0.514856	−	0.891757i	0.0670286	−	0.116097i	0.897592	+	0.440827i	$0.145315\pi$
$60$		0			0
$61$	−10.1334	+	5.85054i	−1.29745	+	0.749085i	−0.979964	−	0.199176i	$-0.936173\pi$
$61$	−10.1334	+	5.85054i	−1.29745	+	0.749085i	−0.317490	+	0.948262i	$0.602840\pi$
$62$	−3.17809			−0.403618
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.667943	+	0.385637i	−0.0828481	+	0.0478324i
$66$		0			0
$67$	−4.26100	+	7.38027i	−0.520564	+	0.901644i	0.479150	+	0.877733i	$0.340945\pi$
$67$	−4.26100	+	7.38027i	−0.520564	+	0.901644i	−0.999714	+	0.0239107i	$0.992388\pi$
$68$	5.67892			0.688670
$69$		0			0
$70$		0			0
$71$		−	8.34154i		−	0.989959i	−0.868905	−	0.494979i	$-0.835176\pi$
$71$		−	8.34154i		−	0.989959i	0.868905	−	0.494979i	$-0.164824\pi$
$72$		0			0
$73$	−0.899038	+	0.519060i	−0.105224	+	0.0607514i	−0.551689	−	0.834050i	$-0.686016\pi$
$73$	−0.899038	+	0.519060i	−0.105224	+	0.0607514i	0.446464	+	0.894801i	$0.352683\pi$
$74$			10.5902i			1.23109i
$75$		0			0
$76$	3.16853	−	1.82935i	0.363455	−	0.209841i
$77$		0			0
$78$		0			0
$79$	0.631283	+	1.09341i	0.0710249	+	0.123019i	0.899351	−	0.437228i	$-0.144040\pi$
$79$	0.631283	+	1.09341i	0.0710249	+	0.123019i	−0.828326	+	0.560247i	$0.810706\pi$
$80$	0.584859	+	1.01301i	0.0653893	+	0.113258i
$81$		0			0
$82$	−4.57513	−	2.64145i	−0.505238	−	0.291699i
$83$	−6.21900	+	10.7716i	−0.682624	+	1.18234i	0.291553	+	0.956555i	$0.405828\pi$
$83$	−6.21900	+	10.7716i	−0.682624	+	1.18234i	−0.974177	+	0.225785i	$0.927505\pi$
$84$		0			0
$85$	−3.32137	−	5.75278i	−0.360253	−	0.623976i
$86$			4.75941i			0.513220i
$87$		0			0
$88$	−5.76436			−0.614483
$89$	−7.83957	+	13.5785i	−0.830993	+	1.43932i	0.0662589	+	0.997802i	$0.478894\pi$
$89$	−7.83957	+	13.5785i	−0.830993	+	1.43932i	−0.897252	+	0.441519i	$0.854440\pi$
$90$		0			0
$91$		0			0
$92$	−0.503113	−	0.290473i	−0.0524532	−	0.0302839i
$93$		0			0
$94$	4.62986	+	2.67305i	0.477533	+	0.275704i
$95$	−3.70629	−	2.13983i	−0.380257	−	0.219541i
$96$		0			0
$97$	−12.5887	−	7.26808i	−1.27819	−	0.737962i	−0.301672	−	0.953412i	$-0.597545\pi$
$97$	−12.5887	−	7.26808i	−1.27819	−	0.737962i	−0.976515	+	0.215450i	$0.930878\pi$
$98$		0			0
$99$		0			0
$100$	−1.81588	+	3.14519i	−0.181588	+	0.314519i
$101$	11.7853			1.17268			0.586340	−	0.810065i	$-0.300568\pi$
$101$	11.7853			1.17268			0.586340	+	0.810065i	$0.300568\pi$
$102$		0			0
$103$			14.1817i			1.39737i	0.715430	+	0.698684i	$0.246231\pi$
$103$			14.1817i			1.39737i	−0.715430	+	0.698684i	$0.753769\pi$
$104$	0.329683	+	0.571028i	0.0323281	+	0.0559939i
$105$		0			0
$106$	2.39223	−	4.14347i	0.232354	−	0.402450i
$107$	−7.42305	−	4.28570i	−0.717613	−	0.414314i	0.0962602	−	0.995356i	$-0.469312\pi$
$107$	−7.42305	−	4.28570i	−0.717613	−	0.414314i	−0.813874	+	0.581042i	$0.802645\pi$
$108$		0			0
$109$	5.51634	+	9.55458i	0.528369	+	0.915163i	0.999453	+	0.0330740i	$0.0105297\pi$
$109$	5.51634	+	9.55458i	0.528369	+	0.915163i	−0.471084	+	0.882089i	$0.656137\pi$
$110$	3.37134	+	5.83934i	0.321445	+	0.556759i
$111$		0			0
$112$		0			0
$113$	−15.5623	+	8.98489i	−1.46398	+	0.845227i	−0.999192	−	0.0401964i	$-0.987202\pi$
$113$	−15.5623	+	8.98489i	−1.46398	+	0.845227i	−0.464785	+	0.885424i	$0.653868\pi$
$114$		0			0
$115$			0.679543i			0.0633677i
$116$	−6.53449	+	3.77269i	−0.606712	+	0.350285i
$117$		0			0
$118$			1.02971i			0.0947927i
$119$		0			0
$120$		0			0
$121$	−22.2279			−2.02072
$122$	5.85054	−	10.1334i	0.529683	−	0.917438i
$123$		0			0
$124$	2.75231	−	1.58905i	0.247164	−	0.142700i
$125$	10.0967			0.903079
$126$		0			0
$127$	21.6367			1.91994			0.959971	−	0.280099i	$-0.0903672\pi$
$127$	21.6367			1.91994			0.959971	+	0.280099i	$0.0903672\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.385637	−	0.667943i	0.0338226	−	0.0585824i
$131$	9.95053			0.869381			0.434691	−	0.900580i	$-0.356858\pi$
$131$	9.95053			0.869381			0.434691	+	0.900580i	$0.356858\pi$
$132$		0			0
$133$		0			0
$134$		−	8.52200i		−	0.736189i
$135$		0			0
$136$	−4.91809	+	2.83946i	−0.421722	+	0.243482i
$137$			3.68762i			0.315055i	0.987515	+	0.157527i	$0.0503523\pi$
$137$			3.68762i			0.315055i	−0.987515	+	0.157527i	$0.949648\pi$
$138$		0			0
$139$	−7.66159	+	4.42342i	−0.649848	+	0.375190i	−0.788398	−	0.615166i	$-0.789089\pi$
$139$	−7.66159	+	4.42342i	−0.649848	+	0.375190i	0.138550	+	0.990355i	$0.455756\pi$
$140$		0			0
$141$		0			0
$142$	4.17077	+	7.22398i	0.350003	+	0.606223i
$143$	1.90041	+	3.29161i	0.158921	+	0.275259i
$144$		0			0
$145$	7.64351	+	4.41298i	0.634759	+	0.366478i
$146$	0.519060	−	0.899038i	0.0429577	−	0.0744049i
$147$		0			0
$148$	−5.29511	−	9.17140i	−0.435256	−	0.753885i
$149$		−	7.05595i		−	0.578046i	−0.957322	−	0.289023i	$-0.906670\pi$
$149$		−	7.05595i		−	0.578046i	0.957322	−	0.289023i	$-0.0933305\pi$
$150$		0			0
$151$	−16.2021			−1.31851			−0.659254	−	0.751920i	$-0.729128\pi$
$151$	−16.2021			−1.31851			−0.659254	+	0.751920i	$0.729128\pi$
$152$	−1.82935	+	3.16853i	−0.148380	+	0.257002i
$153$		0			0
$154$		0			0
$155$	−3.21943	−	1.85874i	−0.258590	−	0.149297i
$156$		0			0
$157$	11.0879	+	6.40163i	0.884914	+	0.510905i	0.872275	−	0.489015i	$-0.162644\pi$
$157$	11.0879	+	6.40163i	0.884914	+	0.510905i	0.0126385	+	0.999920i	$0.495977\pi$
$158$	−1.09341	−	0.631283i	−0.0869874	−	0.0502222i
$159$		0			0
$160$	−1.01301	−	0.584859i	−0.0800852	−	0.0462372i
$161$		0			0
$162$		0			0
$163$	−6.42036	+	11.1204i	−0.502881	+	0.871016i	0.497113	+	0.867686i	$0.334393\pi$
$163$	−6.42036	+	11.1204i	−0.502881	+	0.871016i	−0.999994	+	0.00333001i	$0.998940\pi$
$164$	5.28290			0.412525
$165$		0			0
$166$		−	12.4380i		−	0.965376i
$167$	−12.3584	−	21.4054i	−0.956322	−	1.65640i	−0.731313	−	0.682042i	$-0.761092\pi$
$167$	−12.3584	−	21.4054i	−0.956322	−	1.65640i	−0.225009	−	0.974357i	$-0.572241\pi$
$168$		0			0
$169$	−6.28262	+	10.8818i	−0.483278	+	0.837063i
$170$	5.75278	+	3.32137i	0.441218	+	0.254737i
$171$		0			0
$172$	−2.37970	−	4.12177i	−0.181451	−	0.314282i
$173$	6.38534	+	11.0597i	0.485468	+	0.840856i	0.999861	−	0.0166992i	$-0.00531575\pi$
$173$	6.38534	+	11.0597i	0.485468	+	0.840856i	−0.514392	+	0.857555i	$0.671982\pi$
$174$		0			0
$175$		0			0
$176$	4.99209	−	2.88218i	0.376293	−	0.217253i
$177$		0			0
$178$		−	15.6791i		−	1.17520i
$179$	0.380000	−	0.219393i	0.0284025	−	0.0163982i	−0.485732	−	0.874108i	$-0.661447\pi$
$179$	0.380000	−	0.219393i	0.0284025	−	0.0163982i	0.514134	+	0.857710i	$0.328113\pi$
$180$		0			0
$181$			14.8740i			1.10557i	0.833323	+	0.552787i	$0.186436\pi$
$181$			14.8740i			1.10557i	−0.833323	+	0.552787i	$0.813564\pi$
$182$		0			0
$183$		0			0
$184$	0.580945			0.0428279
$185$	−6.19379	+	10.7280i	−0.455377	+	0.788736i
$186$		0			0
$187$	−28.3496	+	16.3677i	−2.07313	+	1.19692i
$188$	−5.34610			−0.389904
$189$		0			0
$190$	4.27965			0.310479
$191$	6.43026	−	3.71251i	0.465277	−	0.268628i	−0.248983	−	0.968508i	$-0.580096\pi$
$191$	6.43026	−	3.71251i	0.465277	−	0.268628i	0.714261	+	0.699880i	$0.246763\pi$
$192$		0			0
$193$	1.91154	−	3.31088i	0.137595	−	0.238322i	−0.788991	−	0.614405i	$-0.789396\pi$
$193$	1.91154	−	3.31088i	0.137595	−	0.238322i	0.926586	+	0.376083i	$0.122729\pi$
$194$	14.5362			1.04364
$195$		0			0
$196$		0			0
$197$		−	8.80043i		−	0.627005i	−0.949587	−	0.313502i	$-0.898498\pi$
$197$		−	8.80043i		−	0.627005i	0.949587	−	0.313502i	$-0.101502\pi$
$198$		0			0
$199$	−14.5174	+	8.38165i	−1.02911	+	0.594159i	−0.916731	−	0.399506i	$-0.869182\pi$
$199$	−14.5174	+	8.38165i	−1.02911	+	0.594159i	−0.112383	+	0.993665i	$0.535848\pi$
$200$		−	3.63176i		−	0.256804i
$201$		0			0
$202$	−10.2064	+	5.89265i	−0.718117	+	0.414605i
$203$		0			0
$204$		0			0
$205$	−3.08975	−	5.35161i	−0.215798	−	0.373773i
$206$	−7.09087	−	12.2817i	−0.494044	−	0.855710i
$207$		0			0
$208$	−0.571028	−	0.329683i	−0.0395937	−	0.0228594i
$209$	−10.5450	+	18.2645i	−0.729416	+	1.26338i
$210$		0			0
$211$	−7.61019	−	13.1812i	−0.523907	−	0.907434i	−0.999613	−	0.0278293i	$-0.991141\pi$
$211$	−7.61019	−	13.1812i	−0.523907	−	0.907434i	0.475705	−	0.879605i	$-0.342193\pi$
$212$			4.78447i			0.328599i
$213$		0			0
$214$	8.57140			0.585929
$215$	−2.78359	+	4.82131i	−0.189839	+	0.328811i
$216$		0			0
$217$		0			0
$218$	−9.55458	−	5.51634i	−0.647118	−	0.373614i
$219$		0			0
$220$	−5.83934	−	3.37134i	−0.393688	−	0.227296i
$221$	3.24282	+	1.87224i	0.218136	+	0.125941i
$222$		0			0
$223$	13.2581	+	7.65455i	0.887825	+	0.512586i	0.873231	−	0.487307i	$-0.162021\pi$
$223$	13.2581	+	7.65455i	0.887825	+	0.512586i	0.0145948	+	0.999893i	$0.495354\pi$
$224$		0			0
$225$		0			0
$226$	8.98489	−	15.5623i	0.597666	−	1.03519i
$227$	−5.48572			−0.364100			−0.182050	−	0.983289i	$-0.558273\pi$
$227$	−5.48572			−0.364100			−0.182050	+	0.983289i	$0.558273\pi$
$228$		0			0
$229$		−	19.2534i		−	1.27230i	−0.771566	−	0.636150i	$-0.780526\pi$
$229$		−	19.2534i		−	1.27230i	0.771566	−	0.636150i	$-0.219474\pi$
$230$	−0.339771	−	0.588501i	−0.0224039	−	0.0388046i
$231$		0			0
$232$	3.77269	−	6.53449i	0.247689	−	0.429010i
$233$	2.52528	+	1.45797i	0.165436	+	0.0955147i	0.580432	−	0.814309i	$-0.302884\pi$
$233$	2.52528	+	1.45797i	0.165436	+	0.0955147i	−0.414996	+	0.909823i	$0.636217\pi$
$234$		0			0
$235$	3.12672	+	5.41563i	0.203964	+	0.353277i
$236$	−0.514856	−	0.891757i	−0.0335143	−	0.0580484i
$237$		0			0
$238$		0			0
$239$	−7.39276	+	4.26821i	−0.478198	+	0.276088i	−0.719665	−	0.694321i	$-0.755705\pi$
$239$	−7.39276	+	4.26821i	−0.478198	+	0.276088i	0.241467	+	0.970409i	$0.422371\pi$
$240$		0			0
$241$			1.58168i			0.101885i	0.998702	+	0.0509424i	$0.0162225\pi$
$241$			1.58168i			0.101885i	−0.998702	+	0.0509424i	$0.983778\pi$
$242$	19.2499	−	11.1139i	1.23743	−	0.714431i
$243$		0			0
$244$			11.7011i			0.749085i
$245$		0			0
$246$		0			0
$247$	2.41243			0.153499
$248$	−1.58905	+	2.75231i	−0.100904	+	0.174772i
$249$		0			0
$250$	−8.74402	+	5.04837i	−0.553021	+	0.319287i
$251$	0.524263			0.0330912			0.0165456	−	0.999863i	$-0.494733\pi$
$251$	0.524263			0.0330912			0.0165456	+	0.999863i	$0.494733\pi$
$252$		0			0
$253$	3.34878			0.210536
$254$	−18.7379	+	10.8183i	−1.17572	+	0.678802i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.35574			−0.146947			−0.0734737	−	0.997297i	$-0.523408\pi$
$257$	−2.35574			−0.146947			−0.0734737	+	0.997297i	$0.523408\pi$
$258$		0			0
$259$		0			0
$260$			0.771274i			0.0478324i
$261$		0			0
$262$	−8.61741	+	4.97526i	−0.532385	+	0.307373i
$263$		−	4.45656i		−	0.274803i	−0.990515	−	0.137402i	$-0.956125\pi$
$263$		−	4.45656i		−	0.274803i	0.990515	−	0.137402i	$-0.0438751\pi$
$264$		0			0
$265$	4.84670	−	2.79824i	0.297730	−	0.171895i
$266$		0			0
$267$		0			0
$268$	4.26100	+	7.38027i	0.260282	+	0.450822i
$269$	−4.76668	−	8.25613i	−0.290630	−	0.503385i	0.683329	−	0.730110i	$-0.260531\pi$
$269$	−4.76668	−	8.25613i	−0.290630	−	0.503385i	−0.973959	+	0.226725i	$0.927198\pi$
$270$		0			0
$271$	−10.6509	−	6.14930i	−0.646996	−	0.373543i	0.140308	−	0.990108i	$-0.455191\pi$
$271$	−10.6509	−	6.14930i	−0.646996	−	0.373543i	−0.787304	+	0.616564i	$0.788524\pi$
$272$	2.83946	−	4.91809i	0.172167	−	0.298203i
$273$		0			0
$274$	−1.84381	−	3.19357i	−0.111389	−	0.192931i
$275$		−	20.9348i		−	1.26241i
$276$		0			0
$277$	−17.0452			−1.02415			−0.512073	−	0.858942i	$-0.671122\pi$
$277$	−17.0452			−1.02415			−0.512073	+	0.858942i	$0.671122\pi$
$278$	4.42342	−	7.66159i	0.265299	−	0.459512i
$279$		0			0
$280$		0			0
$281$	−8.31719	−	4.80193i	−0.496162	−	0.286459i	0.230965	−	0.972962i	$-0.425812\pi$
$281$	−8.31719	−	4.80193i	−0.496162	−	0.286459i	−0.727127	+	0.686503i	$0.759145\pi$
$282$		0			0
$283$	24.1345	+	13.9340i	1.43464	+	0.828292i	0.997470	−	0.0710843i	$-0.0226459\pi$
$283$	24.1345	+	13.9340i	1.43464	+	0.828292i	0.437174	+	0.899377i	$0.355979\pi$
$284$	−7.22398	−	4.17077i	−0.428665	−	0.247490i
$285$		0			0
$286$	−3.29161	−	1.90041i	−0.194637	−	0.112374i
$287$		0			0
$288$		0			0
$289$	−7.62505	+	13.2070i	−0.448532	+	0.776881i
$290$	−8.82597			−0.518279
$291$		0			0
$292$			1.03812i			0.0607514i
$293$	−0.271017	−	0.469416i	−0.0158330	−	0.0274236i	0.858000	−	0.513649i	$-0.171707\pi$
$293$	−0.271017	−	0.469416i	−0.0158330	−	0.0274236i	−0.873833	+	0.486226i	$0.838373\pi$
$294$		0			0
$295$	−0.602237	+	1.04311i	−0.0350636	+	0.0607319i
$296$	9.17140	+	5.29511i	0.533077	+	0.307772i
$297$		0			0
$298$	3.52798	+	6.11064i	0.204370	+	0.353980i
$299$	−0.191528	−	0.331736i	−0.0110763	−	0.0191848i
$300$		0			0
$301$		0			0
$302$	14.0314	−	8.10105i	0.807418	−	0.466163i
$303$		0			0
$304$		−	3.65870i		−	0.209841i
$305$	11.8533	−	6.84349i	0.678717	−	0.391857i
$306$		0			0
$307$		−	13.6813i		−	0.780832i	−0.920639	−	0.390416i	$-0.872331\pi$
$307$		−	13.6813i		−	0.780832i	0.920639	−	0.390416i	$-0.127669\pi$
$308$		0			0
$309$		0			0
$310$	3.71747			0.211138
$311$	−10.5307	+	18.2397i	−0.597140	+	1.03428i	0.396101	+	0.918207i	$0.370363\pi$
$311$	−10.5307	+	18.2397i	−0.597140	+	1.03428i	−0.993241	+	0.116070i	$0.962970\pi$
$312$		0			0
$313$	28.7669	−	16.6086i	1.62600	−	0.938771i	0.640730	−	0.767767i	$-0.278632\pi$
$313$	28.7669	−	16.6086i	1.62600	−	0.938771i	0.985270	−	0.171005i	$-0.0547014\pi$
$314$	−12.8033			−0.722529
$315$		0			0
$316$	1.26257			0.0710249
$317$	−6.15398	+	3.55300i	−0.345642	+	0.199556i	−0.662764	−	0.748828i	$-0.730617\pi$
$317$	−6.15398	+	3.55300i	−0.345642	+	0.199556i	0.317122	+	0.948385i	$0.397283\pi$
$318$		0			0
$319$	21.7471	−	37.6672i	1.21761	−	2.10896i
$320$	1.16972			0.0653893
$321$		0			0
$322$		0			0
$323$			20.7775i			1.15609i
$324$		0			0
$325$	−2.07384	+	1.19733i	−0.115036	+	0.0664159i
$326$		−	12.8407i		−	0.711181i
$327$		0			0
$328$	−4.57513	+	2.64145i	−0.252619	+	0.145850i
$329$		0			0
$330$		0			0
$331$	−3.48612	−	6.03814i	−0.191615	−	0.331886i	0.754171	−	0.656678i	$-0.228039\pi$
$331$	−3.48612	−	6.03814i	−0.191615	−	0.331886i	−0.945786	+	0.324792i	$0.894706\pi$
$332$	6.21900	+	10.7716i	0.341312	+	0.591170i
$333$		0			0
$334$	21.4054	+	12.3584i	1.17125	+	0.676222i
$335$	4.98418	−	8.63284i	0.272315	−	0.471663i
$336$		0			0
$337$	3.96019	+	6.85926i	0.215726	+	0.373648i	0.953497	−	0.301403i	$-0.0974550\pi$
$337$	3.96019	+	6.85926i	0.215726	+	0.373648i	−0.737771	+	0.675051i	$0.764122\pi$
$338$		−	12.5652i		−	0.683459i
$339$		0			0
$340$	−6.64274			−0.360253
$341$	−9.15983	+	15.8653i	−0.496033	+	0.859154i
$342$		0			0
$343$		0			0
$344$	4.12177	+	2.37970i	0.222231	+	0.128305i
$345$		0			0
$346$	−11.0597	−	6.38534i	−0.594575	−	0.343278i
$347$	−7.74291	−	4.47037i	−0.415661	−	0.239982i	0.277558	−	0.960709i	$-0.410475\pi$
$347$	−7.74291	−	4.47037i	−0.415661	−	0.239982i	−0.693219	+	0.720727i	$0.743808\pi$
$348$		0			0
$349$	1.32673	+	0.765989i	0.0710183	+	0.0410025i	0.535089	−	0.844796i	$-0.320278\pi$
$349$	1.32673	+	0.765989i	0.0710183	+	0.0410025i	−0.464070	+	0.885798i	$0.653612\pi$
$350$		0			0
$351$		0			0
$352$	−2.88218	+	4.99209i	−0.153621	+	0.266079i
$353$	−5.96988			−0.317745			−0.158872	−	0.987299i	$-0.550786\pi$
$353$	−5.96988			−0.317745			−0.158872	+	0.987299i	$0.550786\pi$
$354$		0			0
$355$			9.75726i			0.517861i
$356$	7.83957	+	13.5785i	0.415496	+	0.719661i
$357$		0			0
$358$	−0.219393	+	0.380000i	−0.0115953	+	0.0200836i
$359$	−23.7156	−	13.6922i	−1.25166	−	0.722646i	−0.280221	−	0.959935i	$-0.590408\pi$
$359$	−23.7156	−	13.6922i	−1.25166	−	0.722646i	−0.971439	+	0.237289i	$0.923741\pi$
$360$		0			0
$361$	−2.80696	−	4.86179i	−0.147735	−	0.255884i
$362$	−7.43699	−	12.8812i	−0.390879	−	0.677023i
$363$		0			0
$364$		0			0
$365$	1.05162	−	0.607154i	0.0550444	−	0.0317799i
$366$		0			0
$367$		−	15.7696i		−	0.823165i	−0.911372	−	0.411583i	$-0.864976\pi$
$367$		−	15.7696i		−	0.823165i	0.911372	−	0.411583i	$-0.135024\pi$
$368$	−0.503113	+	0.290473i	−0.0262266	+	0.0151419i
$369$		0			0
$370$		−	12.3876i		−	0.644000i
$371$		0			0
$372$		0			0
$373$	−16.4224			−0.850321			−0.425161	−	0.905118i	$-0.639782\pi$
$373$	−16.4224			−0.850321			−0.425161	+	0.905118i	$0.639782\pi$
$374$	16.3677	−	28.3496i	0.846352	−	1.46592i
$375$		0			0
$376$	4.62986	−	2.67305i	0.238767	−	0.137852i
$377$	−4.97517			−0.256234
$378$		0			0
$379$	−9.75267			−0.500961			−0.250480	−	0.968122i	$-0.580589\pi$
$379$	−9.75267			−0.500961			−0.250480	+	0.968122i	$0.580589\pi$
$380$	−3.70629	+	2.13983i	−0.190128	+	0.109771i
$381$		0			0
$382$	−3.71251	+	6.43026i	−0.189949	+	0.329001i
$383$	−28.2466			−1.44333			−0.721667	−	0.692240i	$-0.756624\pi$
$383$	−28.2466			−1.44333			−0.721667	+	0.692240i	$0.756624\pi$
$384$		0			0
$385$		0			0
$386$			3.82307i			0.194589i
$387$		0			0
$388$	−12.5887	+	7.26808i	−0.639094	+	0.368981i
$389$			6.18449i			0.313566i	0.987633	+	0.156783i	$0.0501123\pi$
$389$			6.18449i			0.313566i	−0.987633	+	0.156783i	$0.949888\pi$
$390$		0			0
$391$	2.85714	−	1.64957i	0.144492	−	0.0834223i
$392$		0			0
$393$		0			0
$394$	4.40021	+	7.62140i	0.221680	+	0.383960i
$395$	−0.738424	−	1.27899i	−0.0371541	−	0.0643529i
$396$		0			0
$397$	19.4575	+	11.2338i	0.976545	+	0.563808i	0.901225	−	0.433351i	$-0.142669\pi$
$397$	19.4575	+	11.2338i	0.976545	+	0.563808i	0.0753197	+	0.997159i	$0.476002\pi$
$398$	8.38165	−	14.5174i	0.420134	−	0.727693i
$399$		0			0
$400$	1.81588	+	3.14519i	0.0907939	+	0.157260i
$401$		−	0.631535i		−	0.0315373i	−0.999876	−	0.0157687i	$-0.994980\pi$
$401$		−	0.631535i		−	0.0315373i	0.999876	−	0.0157687i	$-0.00501953\pi$
$402$		0			0
$403$	2.09553			0.104386
$404$	5.89265	−	10.2064i	0.293170	−	0.507786i
$405$		0			0
$406$		0			0
$407$	52.8673	+	30.5230i	2.62054	+	1.51297i
$408$		0			0
$409$	6.95912	+	4.01785i	0.344107	+	0.198670i	0.662086	−	0.749427i	$-0.269671\pi$
$409$	6.95912	+	4.01785i	0.344107	+	0.198670i	−0.317980	+	0.948097i	$0.603004\pi$
$410$	5.35161	+	3.08975i	0.264297	+	0.152592i
$411$		0			0
$412$	12.2817	+	7.09087i	0.605078	+	0.349342i
$413$		0			0
$414$		0			0
$415$	7.27448	−	12.5998i	0.357090	−	0.618498i
$416$	0.659367			0.0323281
$417$		0			0
$418$		−	21.0901i		−	1.03155i
$419$	14.0455	+	24.3275i	0.686168	+	1.18848i	0.973068	+	0.230518i	$0.0740420\pi$
$419$	14.0455	+	24.3275i	0.686168	+	1.18848i	−0.286900	+	0.957961i	$0.592625\pi$
$420$		0			0
$421$	−20.4254	+	35.3779i	−0.995474	+	1.72421i	−0.415439	+	0.909621i	$0.636372\pi$
$421$	−20.4254	+	35.3779i	−0.995474	+	1.72421i	−0.580035	+	0.814591i	$0.696961\pi$
$422$	13.1812	+	7.61019i	0.641653	+	0.370458i
$423$		0			0
$424$	−2.39223	−	4.14347i	−0.116177	−	0.201225i
$425$	−10.3122	−	17.8613i	−0.500216	−	0.866400i
$426$		0			0
$427$		0			0
$428$	−7.42305	+	4.28570i	−0.358807	+	0.207157i
$429$		0			0
$430$		−	5.56717i		−	0.268473i
$431$	−2.90971	+	1.67992i	−0.140156	+	0.0809191i	−0.568438	−	0.822726i	$-0.692452\pi$
$431$	−2.90971	+	1.67992i	−0.140156	+	0.0809191i	0.428282	+	0.903645i	$0.359119\pi$
$432$		0			0
$433$			12.7148i			0.611033i	0.952187	+	0.305517i	$0.0988292\pi$
$433$			12.7148i			0.611033i	−0.952187	+	0.305517i	$0.901171\pi$
$434$		0			0
$435$		0			0
$436$	11.0327			0.528369
$437$	1.06275	−	1.84074i	0.0508383	−	0.0880546i
$438$		0			0
$439$	−14.7749	+	8.53028i	−0.705167	+	0.407128i	−0.809269	−	0.587438i	$-0.800136\pi$
$439$	−14.7749	+	8.53028i	−0.705167	+	0.407128i	0.104102	+	0.994567i	$0.466803\pi$
$440$	6.74269			0.321445
$441$		0			0
$442$	−3.74449			−0.178107
$443$	−4.25849	+	2.45864i	−0.202327	+	0.116814i	−0.597740	−	0.801690i	$-0.703935\pi$
$443$	−4.25849	+	2.45864i	−0.202327	+	0.116814i	0.395413	+	0.918503i	$0.370601\pi$
$444$		0			0
$445$	9.17009	−	15.8831i	0.434704	−	0.752930i
$446$	−15.3091			−0.724906
$447$		0			0
$448$		0			0
$449$		−	4.88329i		−	0.230457i	−0.993339	−	0.115228i	$-0.963240\pi$
$449$		−	4.88329i		−	0.230457i	0.993339	−	0.115228i	$-0.0367600\pi$
$450$		0			0
$451$	−26.3727	+	15.2263i	−1.24184	+	0.716977i
$452$			17.9698i			0.845227i
$453$		0			0
$454$	4.75077	−	2.74286i	0.222965	−	0.128729i
$455$		0			0
$456$		0			0
$457$	6.06523	+	10.5053i	0.283719	+	0.491416i	0.972298	−	0.233745i	$-0.0750982\pi$
$457$	6.06523	+	10.5053i	0.283719	+	0.491416i	−0.688578	+	0.725162i	$0.741765\pi$
$458$	9.62669	+	16.6739i	0.449826	+	0.779121i
$459$		0			0
$460$	0.588501	+	0.339771i	0.0274390	+	0.0158419i
$461$	−3.32024	+	5.75083i	−0.154639	+	0.267843i	−0.932928	−	0.360064i	$-0.882755\pi$
$461$	−3.32024	+	5.75083i	−0.154639	+	0.267843i	0.778288	+	0.627907i	$0.216088\pi$
$462$		0			0
$463$	3.64017	+	6.30496i	0.169173	+	0.293016i	0.938129	−	0.346285i	$-0.112557\pi$
$463$	3.64017	+	6.30496i	0.169173	+	0.293016i	−0.768956	+	0.639301i	$0.779224\pi$
$464$			7.54538i			0.350285i
$465$		0			0
$466$	−2.91594			−0.135078
$467$	17.1931	−	29.7794i	0.795604	−	1.37803i	−0.126851	−	0.991922i	$-0.540487\pi$
$467$	17.1931	−	29.7794i	0.795604	−	1.37803i	0.922455	−	0.386104i	$-0.126180\pi$
$468$		0			0
$469$		0			0
$470$	−5.41563	−	3.12672i	−0.249804	−	0.144225i
$471$		0			0
$472$	0.891757	+	0.514856i	0.0410464	+	0.0236982i
$473$	23.7594	+	13.7175i	1.09246	+	0.630731i
$474$		0			0
$475$	−11.5073	−	6.64376i	−0.527992	−	0.304836i
$476$		0			0
$477$		0			0
$478$	4.26821	−	7.39276i	0.195223	−	0.338137i
$479$	−21.3806			−0.976903			−0.488452	−	0.872591i	$-0.662438\pi$
$479$	−21.3806			−0.976903			−0.488452	+	0.872591i	$0.662438\pi$
$480$		0			0
$481$		−	6.98284i		−	0.318390i
$482$	−0.790838	−	1.36977i	−0.0360217	−	0.0623914i
$483$		0			0
$484$	−11.1139	+	19.2499i	−0.505179	+	0.874996i
$485$	14.7252	+	8.50161i	0.668638	+	0.386038i
$486$		0			0
$487$	1.42429	+	2.46694i	0.0645408	+	0.111788i	0.896490	−	0.443064i	$-0.146108\pi$
$487$	1.42429	+	2.46694i	0.0645408	+	0.111788i	−0.831949	+	0.554851i	$0.812775\pi$
$488$	−5.85054	−	10.1334i	−0.264842	−	0.458719i
$489$		0			0
$490$		0			0
$491$	0.159838	−	0.0922824i	0.00721338	−	0.00416464i	−0.496389	−	0.868100i	$-0.665341\pi$
$491$	0.159838	−	0.0922824i	0.00721338	−	0.00416464i	0.503602	+	0.863936i	$0.332008\pi$
$492$		0			0
$493$		−	42.8496i		−	1.92985i
$494$	−2.08922	+	1.20621i	−0.0939985	+	0.0542701i
$495$		0			0
$496$		−	3.17809i		−	0.142700i
$497$		0			0
$498$		0			0
$499$	10.8331			0.484954			0.242477	−	0.970157i	$-0.422040\pi$
$499$	10.8331			0.484954			0.242477	+	0.970157i	$0.422040\pi$
$500$	5.04837	−	8.74402i	0.225770	−	0.391045i
$501$		0			0
$502$	−0.454025	+	0.262131i	−0.0202641	+	0.0116995i
$503$	17.6633			0.787570			0.393785	−	0.919203i	$-0.371166\pi$
$503$	17.6633			0.787570			0.393785	+	0.919203i	$0.371166\pi$
$504$		0			0
$505$	−13.7855			−0.613446
$506$	−2.90013	+	1.67439i	−0.128926	+	0.0744357i
$507$		0			0
$508$	10.8183	−	18.7379i	0.479986	−	0.831359i
$509$	7.11256			0.315259			0.157629	−	0.987498i	$-0.449615\pi$
$509$	7.11256			0.315259			0.157629	+	0.987498i	$0.449615\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	2.04013	−	1.17787i	0.0899865	−	0.0519537i
$515$		−	16.5887i		−	0.730983i
$516$		0			0
$517$	26.6882	−	15.4084i	1.17374	−	0.677662i
$518$		0			0
$519$		0			0
$520$	−0.385637	−	0.667943i	−0.0169113	−	0.0292912i
$521$	−19.2668	−	33.3711i	−0.844095	−	1.46202i	−0.886404	−	0.462912i	$-0.846805\pi$
$521$	−19.2668	−	33.3711i	−0.844095	−	1.46202i	0.0423090	−	0.999105i	$-0.486529\pi$
$522$		0			0
$523$	19.6786	+	11.3615i	0.860486	+	0.496802i	0.864175	−	0.503191i	$-0.167841\pi$
$523$	19.6786	+	11.3615i	0.860486	+	0.496802i	−0.00368891	+	0.999993i	$0.501174\pi$
$524$	4.97526	−	8.61741i	0.217345	−	0.376453i
$525$		0			0
$526$	2.22828	+	3.85949i	0.0971576	+	0.168282i
$527$			18.0481i			0.786188i
$528$		0			0
$529$	22.6625			0.985326
$530$	−2.79824	+	4.84670i	−0.121548	+	0.210527i
$531$		0			0
$532$		0			0
$533$	3.01669	+	1.74168i	0.130667	+	0.0754407i
$534$		0			0
$535$	8.68288	+	5.01307i	0.375394	+	0.216734i
$536$	−7.38027	−	4.26100i	−0.318779	−	0.184047i
$537$		0			0
$538$	8.25613	+	4.76668i	0.355947	+	0.205506i
$539$		0			0
$540$		0			0
$541$	10.6657	−	18.4735i	0.458553	−	0.794237i	−0.540332	−	0.841452i	$-0.681701\pi$
$541$	10.6657	−	18.4735i	0.458553	−	0.794237i	0.998885	+	0.0472149i	$0.0150346\pi$
$542$	12.2986			0.528270
$543$		0			0
$544$			5.67892i			0.243482i
$545$	−6.45257	−	11.1762i	−0.276398	−	0.478735i
$546$		0			0
$547$	−4.51312	+	7.81695i	−0.192967	+	0.334229i	−0.946232	−	0.323488i	$-0.895144\pi$
$547$	−4.51312	+	7.81695i	−0.192967	+	0.334229i	0.753265	+	0.657717i	$0.228478\pi$
$548$	3.19357	+	1.84381i	0.136423	+	0.0787637i
$549$		0			0
$550$	10.4674	+	18.1300i	0.446331	+	0.773068i
$551$	−13.8031	−	23.9077i	−0.588033	−	1.01850i
$552$		0			0
$553$		0			0
$554$	14.7616	−	8.52259i	0.627159	−	0.362090i
$555$		0			0
$556$			8.84684i			0.375190i
$557$	2.10247	−	1.21386i	0.0890843	−	0.0514329i	−0.454796	−	0.890596i	$-0.650288\pi$
$557$	2.10247	−	1.21386i	0.0890843	−	0.0514329i	0.543880	+	0.839163i	$0.316955\pi$
$558$		0			0
$559$		−	3.13820i		−	0.132732i
$560$		0			0
$561$		0			0
$562$	9.60387			0.405115
$563$	−3.06573	+	5.31001i	−0.129205	+	0.223790i	−0.923369	−	0.383914i	$-0.874576\pi$
$563$	−3.06573	+	5.31001i	−0.129205	+	0.223790i	0.794164	+	0.607704i	$0.207909\pi$
$564$		0			0
$565$	18.2035	−	10.5098i	0.765827	−	0.442150i
$566$	−27.8681			−1.17138
$567$		0			0
$568$	8.34154			0.350003
$569$	27.8290	−	16.0671i	1.16665	−	0.673566i	0.213762	−	0.976886i	$-0.431428\pi$
$569$	27.8290	−	16.0671i	1.16665	−	0.673566i	0.952889	+	0.303319i	$0.0980949\pi$
$570$		0			0
$571$	−1.95523	+	3.38656i	−0.0818239	+	0.141723i	−0.904033	−	0.427462i	$-0.859408\pi$
$571$	−1.95523	+	3.38656i	−0.0818239	+	0.141723i	0.822210	+	0.569185i	$0.192741\pi$
$572$	3.80083			0.158921
$573$		0			0
$574$		0			0
$575$			2.10985i			0.0879869i
$576$		0			0
$577$	13.2404	−	7.64437i	0.551207	−	0.318239i	−0.198402	−	0.980121i	$-0.563575\pi$
$577$	13.2404	−	7.64437i	0.551207	−	0.318239i	0.749609	+	0.661881i	$0.230242\pi$
$578$		−	15.2501i		−	0.634320i
$579$		0			0
$580$	7.64351	−	4.41298i	0.317380	−	0.183239i
$581$		0			0
$582$		0			0
$583$	−13.7897	−	23.8845i	−0.571111	−	0.989194i
$584$	−0.519060	−	0.899038i	−0.0214789	−	0.0372025i
$585$		0			0
$586$	0.469416	+	0.271017i	0.0193914	+	0.0111956i
$587$	11.6794	−	20.2293i	0.482061	−	0.834955i	−0.517727	−	0.855546i	$-0.673222\pi$
$587$	11.6794	−	20.2293i	0.482061	−	0.834955i	0.999788	+	0.0205915i	$0.00655493\pi$
$588$		0			0
$589$	5.81384	+	10.0699i	0.239555	+	0.414922i
$590$		−	1.20447i		−	0.0495874i
$591$		0			0
$592$	−10.5902			−0.435256
$593$	5.26150	−	9.11319i	0.216064	−	0.374234i	−0.737537	−	0.675306i	$-0.764011\pi$
$593$	5.26150	−	9.11319i	0.216064	−	0.374234i	0.953601	+	0.301073i	$0.0973447\pi$
$594$		0			0
$595$		0			0
$596$	−6.11064	−	3.52798i	−0.250301	−	0.144512i
$597$		0			0
$598$	0.331736	+	0.191528i	0.0135657	+	0.00783216i
$599$	−29.4740	−	17.0169i	−1.20428	−	0.695290i	−0.242774	−	0.970083i	$-0.578057\pi$
$599$	−29.4740	−	17.0169i	−1.20428	−	0.695290i	−0.961503	+	0.274793i	$0.911391\pi$
$600$		0			0
$601$	35.2808	+	20.3694i	1.43913	+	0.830885i	0.997790	−	0.0664531i	$-0.0211683\pi$
$601$	35.2808	+	20.3694i	1.43913	+	0.830885i	0.441345	+	0.897338i	$0.354502\pi$
$602$		0			0
$603$		0			0
$604$	−8.10105	+	14.0314i	−0.329627	+	0.570931i
$605$	26.0004			1.05707
$606$		0			0
$607$		−	40.6777i		−	1.65106i	−0.564362	−	0.825528i	$-0.690878\pi$
$607$		−	40.6777i		−	1.65106i	0.564362	−	0.825528i	$-0.309122\pi$
$608$	1.82935	+	3.16853i	0.0741899	+	0.128501i
$609$		0			0
$610$	−6.84349	+	11.8533i	−0.277085	+	0.479925i
$611$	−3.05277	−	1.76252i	−0.123502	−	0.0713039i
$612$		0			0
$613$	14.0710	+	24.3717i	0.568323	+	0.984365i	0.996732	+	0.0807797i	$0.0257410\pi$
$613$	14.0710	+	24.3717i	0.568323	+	0.984365i	−0.428409	+	0.903585i	$0.640926\pi$
$614$	6.84064	+	11.8483i	0.276066	+	0.478160i
$615$		0			0
$616$		0			0
$617$	−3.75514	+	2.16803i	−0.151176	+	0.0872817i	−0.573680	−	0.819080i	$-0.694485\pi$
$617$	−3.75514	+	2.16803i	−0.151176	+	0.0872817i	0.422504	+	0.906361i	$0.361151\pi$
$618$		0			0
$619$		−	4.34298i		−	0.174559i	−0.996184	−	0.0872797i	$-0.972183\pi$
$619$		−	4.34298i		−	0.174559i	0.996184	−	0.0872797i	$-0.0278174\pi$
$620$	−3.21943	+	1.85874i	−0.129295	+	0.0746486i
$621$		0			0
$622$		−	21.0614i		−	0.844484i
$623$		0			0
$624$		0			0
$625$	6.34845			0.253938
$626$	−16.6086	+	28.7669i	−0.663812	+	1.14976i
$627$		0			0
$628$	11.0879	−	6.40163i	0.442457	−	0.255453i
$629$	60.1410			2.39798
$630$		0			0
$631$	34.8449			1.38715			0.693577	−	0.720383i	$-0.256034\pi$
$631$	34.8449			1.38715			0.693577	+	0.720383i	$0.256034\pi$
$632$	−1.09341	+	0.631283i	−0.0434937	+	0.0251111i
$633$		0			0
$634$	3.55300	−	6.15398i	0.141108	−	0.244406i
$635$	−25.3088			−1.00435
$636$		0			0
$637$		0			0
$638$			43.4943i			1.72196i
$639$		0			0
$640$	−1.01301	+	0.584859i	−0.0400426	+	0.0231186i
$641$		−	22.7218i		−	0.897458i	−0.893668	−	0.448729i	$-0.851877\pi$
$641$		−	22.7218i		−	0.897458i	0.893668	−	0.448729i	$-0.148123\pi$
$642$		0			0
$643$	6.64900	−	3.83880i	0.262211	−	0.151387i	−0.363132	−	0.931738i	$-0.618293\pi$
$643$	6.64900	−	3.83880i	0.262211	−	0.151387i	0.625343	+	0.780350i	$0.284959\pi$
$644$		0			0
$645$		0			0
$646$	−10.3887	−	17.9938i	−0.408739	−	0.707957i
$647$	7.51498	+	13.0163i	0.295444	+	0.511724i	0.975088	−	0.221818i	$-0.0711990\pi$
$647$	7.51498	+	13.0163i	0.295444	+	0.511724i	−0.679644	+	0.733542i	$0.737866\pi$
$648$		0			0
$649$	5.14041	+	2.96782i	0.201779	+	0.116497i
$650$	1.19733	−	2.07384i	0.0469632	−	0.0813426i
$651$		0			0
$652$	6.42036	+	11.1204i	0.251441	+	0.435508i
$653$			48.1556i			1.88448i	0.334944	+	0.942238i	$0.391283\pi$
$653$			48.1556i			1.88448i	−0.334944	+	0.942238i	$0.608717\pi$
$654$		0			0
$655$	−11.6393			−0.454786
$656$	2.64145	−	4.57513i	0.103131	−	0.178629i
$657$		0			0
$658$		0			0
$659$	38.5699	+	22.2684i	1.50247	+	0.867452i	0.999996	+	0.00286104i	$0.000910700\pi$
$659$	38.5699	+	22.2684i	1.50247	+	0.867452i	0.502476	+	0.864591i	$0.332423\pi$
$660$		0			0
$661$	25.3356	+	14.6275i	0.985441	+	0.568944i	0.903908	−	0.427726i	$-0.140685\pi$
$661$	25.3356	+	14.6275i	0.985441	+	0.568944i	0.0815323	+	0.996671i	$0.474019\pi$
$662$	6.03814	+	3.48612i	0.234679	+	0.135492i
$663$		0			0
$664$	−10.7716	−	6.21900i	−0.418020	−	0.241344i
$665$		0			0
$666$		0			0
$667$	−2.19173	+	3.79618i	−0.0848639	+	0.146989i
$668$	−24.7168			−0.956322
$669$		0			0
$670$			9.96835i			0.385111i
$671$	−33.7247	−	58.4128i	−1.30193	−	2.25500i
$672$		0			0
$673$	−7.96391	+	13.7939i	−0.306986	+	0.531716i	−0.977702	−	0.209999i	$-0.932654\pi$
$673$	−7.96391	+	13.7939i	−0.306986	+	0.531716i	0.670715	+	0.741715i	$0.265987\pi$
$674$	−6.85926	−	3.96019i	−0.264209	−	0.152541i
$675$		0			0
$676$	6.28262	+	10.8818i	0.241639	+	0.418531i
$677$	16.2659	+	28.1734i	0.625150	+	1.08279i	0.988512	+	0.151143i	$0.0482955\pi$
$677$	16.2659	+	28.1734i	0.625150	+	1.08279i	−0.363362	+	0.931648i	$0.618371\pi$
$678$		0			0
$679$		0			0
$680$	5.75278	−	3.32137i	0.220609	−	0.127369i
$681$		0			0
$682$		−	18.3197i		−	0.701496i
$683$	−15.2586	+	8.80957i	−0.583855	+	0.337089i	−0.762664	−	0.646795i	$-0.776109\pi$
$683$	−15.2586	+	8.80957i	−0.583855	+	0.337089i	0.178809	+	0.983884i	$0.442776\pi$
$684$		0			0
$685$		−	4.31348i		−	0.164810i
$686$		0			0
$687$		0			0
$688$	−4.75941			−0.181451
$689$	−1.57736	+	2.73207i	−0.0600926	+	0.104083i
$690$		0			0
$691$	−15.9146	+	9.18832i	−0.605421	+	0.349540i	−0.771171	−	0.636628i	$-0.780329\pi$
$691$	−15.9146	+	9.18832i	−0.605421	+	0.349540i	0.165750	+	0.986168i	$0.446996\pi$
$692$	12.7707			0.485468
$693$		0			0
$694$	8.94074			0.339386
$695$	8.96191	−	5.17416i	0.339945	−	0.196267i
$696$		0			0
$697$	−15.0006	+	25.9818i	−0.568187	+	0.984129i
$698$	−1.53198			−0.0579862
$699$		0			0
$700$		0			0
$701$			28.1696i			1.06395i	0.846760	+	0.531975i	$0.178550\pi$
$701$			28.1696i			1.06395i	−0.846760	+	0.531975i	$0.821450\pi$
$702$		0			0
$703$	33.5554	−	19.3732i	1.26557	−	0.730675i
$704$		−	5.76436i		−	0.217253i
$705$		0			0
$706$	5.17007	−	2.98494i	0.194578	−	0.112340i
$707$		0			0
$708$		0			0
$709$	16.5812	+	28.7196i	0.622722	+	1.07859i	0.988977	+	0.148071i	$0.0473064\pi$
$709$	16.5812	+	28.7196i	0.622722	+	1.07859i	−0.366255	+	0.930514i	$0.619360\pi$
$710$	−4.87863	−	8.45003i	−0.183092	−	0.317124i
$711$		0			0
$712$	−13.5785	−	7.83957i	−0.508877	−	0.293800i
$713$	0.923148	−	1.59894i	0.0345722	−	0.0598808i
$714$		0			0
$715$	−2.22295	−	3.85026i	−0.0831337	−	0.143992i
$716$		−	0.438786i		−	0.0163982i
$717$		0			0
$718$	27.3844			1.02198
$719$	17.8533	−	30.9227i	0.665814	−	1.15322i	−0.313250	−	0.949671i	$-0.601418\pi$
$719$	17.8533	−	30.9227i	0.665814	−	1.15322i	0.979064	−	0.203553i	$-0.0652489\pi$
$720$		0			0
$721$		0			0
$722$	4.86179	+	2.80696i	0.180937	+	0.104464i
$723$		0			0
$724$	12.8812	+	7.43699i	0.478727	+	0.276393i
$725$	23.7317	+	13.7015i	0.881372	+	0.508861i
$726$		0			0
$727$	10.0523	+	5.80367i	0.372817	+	0.215246i	0.674689	−	0.738103i	$-0.264278\pi$
$727$	10.0523	+	5.80367i	0.372817	+	0.215246i	−0.301871	+	0.953349i	$0.597611\pi$
$728$		0			0
$729$		0			0
$730$	−0.607154	+	1.05162i	−0.0224718	+	0.0389223i
$731$	27.0283			0.999678
$732$		0			0
$733$		−	3.76160i		−	0.138938i	−0.997584	−	0.0694689i	$-0.977870\pi$
$733$		−	3.76160i		−	0.138938i	0.997584	−	0.0694689i	$-0.0221305\pi$
$734$	7.88479	+	13.6569i	0.291033	+	0.504084i
$735$		0			0
$736$	0.290473	−	0.503113i	0.0107070	−	0.0185450i
$737$	−42.5426	−	24.5620i	−1.56708	−	0.904752i
$738$		0			0
$739$	3.44781	+	5.97178i	0.126830	+	0.219675i	0.922447	−	0.386125i	$-0.126187\pi$
$739$	3.44781	+	5.97178i	0.126830	+	0.219675i	−0.795617	+	0.605800i	$0.792853\pi$
$740$	6.19379	+	10.7280i	0.227688	+	0.394368i
$741$		0			0
$742$		0			0
$743$	12.9943	−	7.50227i	0.476715	−	0.275232i	−0.242331	−	0.970194i	$-0.577912\pi$
$743$	12.9943	−	7.50227i	0.476715	−	0.275232i	0.719047	+	0.694962i	$0.244579\pi$
$744$		0			0
$745$			8.25348i			0.302384i
$746$	14.2222	−	8.21122i	0.520713	−	0.300634i
$747$		0			0
$748$			32.7353i			1.19692i
$749$		0			0
$750$		0			0
$751$	−2.56672			−0.0936611			−0.0468305	−	0.998903i	$-0.514912\pi$
$751$	−2.56672			−0.0936611			−0.0468305	+	0.998903i	$0.514912\pi$
$752$	−2.67305	+	4.62986i	−0.0974761	+	0.168833i
$753$		0			0
$754$	4.30862	−	2.48759i	0.156911	−	0.0905925i
$755$	18.9519			0.689730
$756$		0			0
$757$	−8.74001			−0.317661			−0.158831	−	0.987306i	$-0.550772\pi$
$757$	−8.74001			−0.317661			−0.158831	+	0.987306i	$0.550772\pi$
$758$	8.44606	−	4.87633i	0.306775	−	0.177116i
$759$		0			0
$760$	2.13983	−	3.70629i	0.0776196	−	0.134441i
$761$	22.2680			0.807215			0.403608	−	0.914932i	$-0.367756\pi$
$761$	22.2680			0.807215			0.403608	+	0.914932i	$0.367756\pi$
$762$		0			0
$763$		0			0
$764$		−	7.42503i		−	0.268628i
$765$		0			0
$766$	24.4623	−	14.1233i	0.883858	−	0.510296i
$767$		−	0.678958i		−	0.0245158i
$768$		0			0
$769$	−19.3368	+	11.1641i	−0.697304	+	0.402589i	−0.806342	−	0.591449i	$-0.798556\pi$
$769$	−19.3368	+	11.1641i	−0.697304	+	0.402589i	0.109039	+	0.994038i	$0.465223\pi$
$770$		0			0
$771$		0			0
$772$	−1.91154	−	3.31088i	−0.0687977	−	0.119161i
$773$	13.2482	+	22.9465i	0.476504	+	0.825329i	0.999638	−	0.0269220i	$-0.00857057\pi$
$773$	13.2482	+	22.9465i	0.476504	+	0.825329i	−0.523134	+	0.852251i	$0.675237\pi$
$774$		0			0
$775$	−9.99571	−	5.77103i	−0.359057	−	0.207301i
$776$	7.26808	−	12.5887i	0.260909	−	0.451907i
$777$		0			0
$778$	−3.09224	−	5.35592i	−0.110862	−	0.192019i
$779$			19.3285i			0.692517i
$780$		0			0
$781$	48.0837			1.72057
$782$	−1.64957	+	2.85714i	−0.0589885	+	0.102171i
$783$		0			0
$784$		0			0
$785$	−12.9698	−	7.48810i	−0.462911	−	0.267262i
$786$		0			0
$787$	−21.3968	−	12.3534i	−0.762712	−	0.440352i	0.0675564	−	0.997715i	$-0.478480\pi$
$787$	−21.3968	−	12.3534i	−0.762712	−	0.440352i	−0.830269	+	0.557363i	$0.811813\pi$
$788$	−7.62140	−	4.40021i	−0.271501	−	0.156751i
$789$		0			0
$790$	1.27899	+	0.738424i	0.0455043	+	0.0262719i
$791$		0			0
$792$		0			0
$793$	−3.85765	+	6.68165i	−0.136989	+	0.237272i
$794$	−22.4676			−0.797346
$795$		0			0
$796$			16.7633i			0.594159i
$797$	5.22781	+	9.05484i	0.185179	+	0.320739i	0.943637	−	0.330983i	$-0.107380\pi$
$797$	5.22781	+	9.05484i	0.185179	+	0.320739i	−0.758458	+	0.651722i	$0.774047\pi$
$798$		0			0
$799$	15.1800	−	26.2926i	0.537031	−	0.930164i
$800$	−3.14519	−	1.81588i	−0.111199	−	0.0642010i
$801$		0			0
$802$	0.315767	+	0.546925i	0.0111501	+	0.0193126i
$803$	−2.99205	−	5.18238i	−0.105587	−	0.182882i
$804$		0			0
$805$		0			0
$806$	−1.81478	+	1.04776i	−0.0639229	+	0.0369059i
$807$		0			0
$808$			11.7853i			0.414605i
$809$	−27.1354	+	15.6666i	−0.954031	+	0.550810i	−0.894331	−	0.447406i	$-0.852348\pi$
$809$	−27.1354	+	15.6666i	−0.954031	+	0.550810i	−0.0597000	+	0.998216i	$0.519014\pi$
$810$		0			0
$811$		−	12.4653i		−	0.437717i	−0.975757	−	0.218858i	$-0.929767\pi$
$811$		−	12.4653i		−	0.437717i	0.975757	−	0.218858i	$-0.0702333\pi$
$812$		0			0
$813$		0			0
$814$	−61.0459			−2.13966
$815$	7.51001	−	13.0077i	0.263064	−	0.455641i
$816$		0			0
$817$	15.0803	−	8.70663i	0.527594	−	0.304606i
$818$	−8.03570			−0.280962
$819$		0			0
$820$	−6.17951			−0.215798
$821$	31.9428	−	18.4422i	1.11481	−	0.643637i	0.174741	−	0.984615i	$-0.444091\pi$
$821$	31.9428	−	18.4422i	1.11481	−	0.643637i	0.940071	+	0.340977i	$0.110758\pi$
$822$		0			0
$823$	−7.35560	+	12.7403i	−0.256400	+	0.444098i	−0.965275	−	0.261236i	$-0.915870\pi$
$823$	−7.35560	+	12.7403i	−0.256400	+	0.444098i	0.708875	+	0.705334i	$0.249203\pi$
$824$	−14.1817			−0.494044
$825$		0			0
$826$		0			0
$827$		−	44.3837i		−	1.54337i	−0.636004	−	0.771686i	$-0.719414\pi$
$827$		−	44.3837i		−	1.54337i	0.636004	−	0.771686i	$-0.280586\pi$
$828$		0			0
$829$	−47.7610	+	27.5748i	−1.65881	+	0.957712i	−0.685540	+	0.728035i	$0.740434\pi$
$829$	−47.7610	+	27.5748i	−1.65881	+	0.957712i	−0.973267	+	0.229677i	$0.926233\pi$
$830$			14.5490i			0.505002i
$831$		0			0
$832$	−0.571028	+	0.329683i	−0.0197968	+	0.0114297i
$833$		0			0
$834$		0			0
$835$	14.4559	+	25.0383i	0.500266	+	0.866486i
$836$	10.5450	+	18.2645i	0.364708	+	0.631692i
$837$		0			0
$838$	−24.3275	−	14.0455i	−0.840381	−	0.485194i
$839$	3.89752	−	6.75071i	0.134557	−	0.233060i	−0.790871	−	0.611983i	$-0.790372\pi$
$839$	3.89752	−	6.75071i	0.134557	−	0.233060i	0.925428	+	0.378923i	$0.123705\pi$
$840$		0			0
$841$	13.9664	+	24.1904i	0.481598	+	0.834153i
$842$		−	40.8509i		−	1.40781i
$843$		0			0
$844$	−15.2204			−0.523907
$845$	7.34890	−	12.7287i	0.252810	−	0.437879i
$846$		0			0
$847$		0			0
$848$	4.14347	+	2.39223i	0.142287	+	0.0821497i
$849$		0			0
$850$	17.8613	+	10.3122i	0.612637	+	0.353706i
$851$	−5.32808	−	3.07617i	−0.182644	−	0.105450i
$852$		0			0
$853$	21.3756	+	12.3412i	0.731887	+	0.422555i	0.819112	−	0.573633i	$-0.194467\pi$
$853$	21.3756	+	12.3412i	0.731887	+	0.422555i	−0.0872249	+	0.996189i	$0.527800\pi$
$854$		0			0
$855$		0			0
$856$	4.28570	−	7.42305i	0.146482	−	0.253715i
$857$	30.0402			1.02615			0.513077	−	0.858342i	$-0.328505\pi$
$857$	30.0402			1.02615			0.513077	+	0.858342i	$0.328505\pi$
$858$		0			0
$859$		−	47.9959i		−	1.63760i	−0.574081	−	0.818799i	$-0.694640\pi$
$859$		−	47.9959i		−	1.63760i	0.574081	−	0.818799i	$-0.305360\pi$
$860$	2.78359	+	4.82131i	0.0949195	+	0.164405i
$861$		0			0
$862$	1.67992	−	2.90971i	0.0572184	−	0.0991052i
$863$	36.8446	+	21.2722i	1.25420	+	0.724115i	0.971942	−	0.235222i	$-0.0755817\pi$
$863$	36.8446	+	21.2722i	1.25420	+	0.724115i	0.282263	+	0.959337i	$0.408915\pi$
$864$		0			0
$865$	−7.46905	−	12.9368i	−0.253955	−	0.439864i
$866$	−6.35739	−	11.0113i	−0.216033	−	0.374180i
$867$		0			0
$868$		0			0
$869$	−6.30284	+	3.63895i	−0.213809	+	0.123443i
$870$		0			0
$871$			5.61913i			0.190397i
$872$	−9.55458	+	5.51634i	−0.323559	+	0.186807i
$873$		0			0
$874$			2.12550i			0.0718963i
$875$		0			0
$876$		0			0
$877$	33.6012			1.13463			0.567317	−	0.823500i	$-0.307982\pi$
$877$	33.6012			1.13463			0.567317	+	0.823500i	$0.307982\pi$
$878$	8.53028	−	14.7749i	0.287883	−	0.498628i
$879$		0			0
$880$	−5.83934	+	3.37134i	−0.196844	+	0.113648i
$881$	−36.1880			−1.21921			−0.609603	−	0.792707i	$-0.708671\pi$
$881$	−36.1880			−1.21921			−0.609603	+	0.792707i	$0.708671\pi$
$882$		0			0
$883$	2.99025			0.100630			0.0503149	−	0.998733i	$-0.483977\pi$
$883$	2.99025			0.100630			0.0503149	+	0.998733i	$0.483977\pi$
$884$	3.24282	−	1.87224i	0.109068	−	0.0629704i
$885$		0			0
$886$	2.45864	−	4.25849i	0.0825997	−	0.143067i
$887$	5.86981			0.197089			0.0985445	−	0.995133i	$-0.468581\pi$
$887$	5.86981			0.197089			0.0985445	+	0.995133i	$0.468581\pi$
$888$		0			0
$889$		0			0
$890$			18.3402i			0.614765i
$891$		0			0
$892$	13.2581	−	7.65455i	0.443913	−	0.256293i
$893$		−	19.5598i		−	0.654543i
$894$		0			0
$895$	−0.444493	+	0.256628i	−0.0148578	+	0.00857814i
$896$		0			0
$897$		0			0
$898$	2.44165	+	4.22906i	0.0814788	+	0.141125i
$899$	−11.9899	−	20.7672i	−0.399887	−	0.692625i
$900$		0			0
$901$	−23.5304	−	13.5853i	−0.783912	−	0.452592i
$902$	15.2263	−	26.3727i	0.506980	−	0.878114i
$903$		0			0
$904$	−8.98489	−	15.5623i	−0.298833	−	0.517594i
$905$		−	17.3984i		−	0.578341i
$906$		0			0
$907$	14.2532			0.473271			0.236636	−	0.971598i	$-0.423955\pi$
$907$	14.2532			0.473271			0.236636	+	0.971598i	$0.423955\pi$
$908$	−2.74286	+	4.75077i	−0.0910250	+	0.157660i
$909$		0			0
$910$		0			0
$911$	−24.3461	−	14.0562i	−0.806623	−	0.465704i	0.0391589	−	0.999233i	$-0.487532\pi$
$911$	−24.3461	−	14.0562i	−0.806623	−	0.465704i	−0.845782	+	0.533529i	$0.820865\pi$
$912$		0			0
$913$	−62.0915	−	35.8486i	−2.05493	−	1.18641i
$914$	−10.5053	−	6.06523i	−0.347484	−	0.200620i
$915$		0			0
$916$	−16.6739	−	9.62669i	−0.550922	−	0.318075i
$917$		0			0
$918$		0			0
$919$	1.20114	−	2.08044i	0.0396220	−	0.0686273i	−0.845534	−	0.533921i	$-0.820718\pi$
$919$	1.20114	−	2.08044i	0.0396220	−	0.0686273i	0.885156	+	0.465294i	$0.154051\pi$
$920$	−0.679543			−0.0224039
$921$		0			0
$922$		−	6.64048i		−	0.218693i
$923$	−2.75007	−	4.76326i	−0.0905195	−	0.156784i
$924$		0			0
$925$	−19.2306	+	33.3083i	−0.632297	+	1.09517i
$926$	−6.30496	−	3.64017i	−0.207194	−	0.119623i
$927$		0			0
$928$	−3.77269	−	6.53449i	−0.123845	−	0.214505i
$929$	11.1786	+	19.3619i	0.366758	+	0.635243i	0.989057	−	0.147537i	$-0.0471344\pi$
$929$	11.1786	+	19.3619i	0.366758	+	0.635243i	−0.622299	+	0.782780i	$0.713801\pi$
$930$		0			0
$931$		0			0
$932$	2.52528	−	1.45797i	0.0827182	−	0.0477574i
$933$		0			0
$934$			34.3863i			1.12515i
$935$	33.1611	−	19.1456i	1.08448	−	0.626127i
$936$		0			0
$937$			15.6773i			0.512156i	0.966656	+	0.256078i	$0.0824305\pi$
$937$			15.6773i			0.512156i	−0.966656	+	0.256078i	$0.917570\pi$
$938$		0			0
$939$		0			0
$940$	6.25343			0.203964
$941$	−19.1449	+	33.1599i	−0.624105	+	1.08098i	0.364608	+	0.931161i	$0.381203\pi$
$941$	−19.1449	+	33.1599i	−0.624105	+	1.08098i	−0.988713	+	0.149820i	$0.952130\pi$
$942$		0			0
$943$	2.65790	−	1.53454i	0.0865530	−	0.0499714i
$944$	−1.02971			−0.0335143
$945$		0			0
$946$	−27.4350			−0.891988
$947$	46.4660	−	26.8272i	1.50994	−	0.871766i	0.510011	−	0.860168i	$-0.329641\pi$
$947$	46.4660	−	26.8272i	1.50994	−	0.871766i	0.999933	−	0.0115980i	$-0.00369185\pi$
$948$		0			0
$949$	−0.342251	+	0.592796i	−0.0111099	+	0.0192430i
$950$	13.2875			0.431104
$951$		0			0
$952$		0			0
$953$		−	18.0861i		−	0.585866i	−0.956133	−	0.292933i	$-0.905369\pi$
$953$		−	18.0861i		−	0.585866i	0.956133	−	0.292933i	$-0.0946313\pi$
$954$		0			0
$955$	−7.52160	+	4.34260i	−0.243393	+	0.140523i
$956$			8.53642i			0.276088i
$957$		0			0
$958$	18.5161	−	10.6903i	0.598229	−	0.345388i
$959$		0			0
$960$		0			0
$961$	−10.4499	−	18.0997i	−0.337093	−	0.583862i
$962$	3.49142	+	6.04732i	0.112568	+	0.194973i
$963$		0			0
$964$	1.36977	+	0.790838i	0.0441174	+	0.0254712i
$965$	−2.23596	+	3.87280i	−0.0719781	+	0.124670i
$966$		0			0
$967$	−13.8281	−	23.9509i	−0.444681	−	0.770209i	0.553349	−	0.832949i	$-0.313349\pi$
$967$	−13.8281	−	23.9509i	−0.444681	−	0.770209i	−0.998030	+	0.0627399i	$0.980016\pi$
$968$		−	22.2279i		−	0.714431i
$969$		0			0
$970$	−17.0032			−0.545941
$971$	−3.83935	+	6.64995i	−0.123211	+	0.213407i	−0.921032	−	0.389487i	$-0.872652\pi$
$971$	−3.83935	+	6.64995i	−0.123211	+	0.213407i	0.797821	+	0.602894i	$0.205986\pi$
$972$		0			0
$973$		0			0
$974$	−2.46694	−	1.42429i	−0.0790460	−	0.0456372i
$975$		0			0
$976$	10.1334	+	5.85054i	0.324363	+	0.187271i
$977$	25.5162	+	14.7318i	0.816334	+	0.471311i	0.849151	−	0.528150i	$-0.177114\pi$
$977$	25.5162	+	14.7318i	0.816334	+	0.471311i	−0.0328163	+	0.999461i	$0.510448\pi$
$978$		0			0
$979$	−78.2716	−	45.1901i	−2.50157	−	1.44428i
$980$		0			0
$981$		0			0
$982$	−0.0922824	+	0.159838i	−0.00294485	+	0.00510063i
$983$	−32.9147			−1.04982			−0.524908	−	0.851159i	$-0.675900\pi$
$983$	−32.9147			−1.04982			−0.524908	+	0.851159i	$0.675900\pi$
$984$		0			0
$985$			10.2940i			0.327995i
$986$	21.4248	+	37.1088i	0.682304	+	1.18179i
$987$		0			0
$988$	1.20621	−	2.08922i	0.0383747	−	0.0664670i
$989$	−2.39452	−	1.38248i	−0.0761414	−	0.0439602i
$990$		0			0
$991$	−7.31686	−	12.6732i	−0.232428	−	0.402577i	0.726094	−	0.687595i	$-0.241334\pi$
$991$	−7.31686	−	12.6732i	−0.232428	−	0.402577i	−0.958522	+	0.285019i	$0.908000\pi$
$992$	1.58905	+	2.75231i	0.0504522	+	0.0873858i
$993$		0			0
$994$		0			0
$995$	16.9813	−	9.80417i	0.538344	−	0.310813i
$996$		0			0
$997$		−	14.9004i		−	0.471900i	−0.971765	−	0.235950i	$-0.924180\pi$
$997$		−	14.9004i		−	0.471900i	0.971765	−	0.235950i	$-0.0758202\pi$
$998$	−9.38170	+	5.41653i	−0.296972	+	0.171457i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.t.c.1979.5		48
3.2	odd	2		882.2.t.c.803.16		48
7.2	even	3		2646.2.m.c.1763.18		48
7.3	odd	6		2646.2.l.c.521.7		48
7.4	even	3		2646.2.l.c.521.8		48
7.5	odd	6		2646.2.m.c.1763.17		48
7.6	odd	2	inner	2646.2.t.c.1979.6		48
9.4	even	3		882.2.l.c.509.1		48
9.5	odd	6		2646.2.l.c.1097.7		48
21.2	odd	6		882.2.m.c.587.4	yes	48
21.5	even	6		882.2.m.c.587.9	yes	48
21.11	odd	6		882.2.l.c.227.24		48
21.17	even	6		882.2.l.c.227.13		48
21.20	even	2		882.2.t.c.803.21		48
63.4	even	3		882.2.t.c.815.21		48
63.5	even	6		2646.2.m.c.881.18		48
63.13	odd	6		882.2.l.c.509.12		48
63.23	odd	6		2646.2.m.c.881.17		48
63.31	odd	6		882.2.t.c.815.16		48
63.32	odd	6	inner	2646.2.t.c.2285.6		48
63.40	odd	6		882.2.m.c.293.4	✓	48
63.41	even	6		2646.2.l.c.1097.8		48
63.58	even	3		882.2.m.c.293.9	yes	48
63.59	even	6	inner	2646.2.t.c.2285.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.13		48	21.17	even	6
882.2.l.c.227.24		48	21.11	odd	6
882.2.l.c.509.1		48	9.4	even	3
882.2.l.c.509.12		48	63.13	odd	6
882.2.m.c.293.4	✓	48	63.40	odd	6
882.2.m.c.293.9	yes	48	63.58	even	3
882.2.m.c.587.4	yes	48	21.2	odd	6
882.2.m.c.587.9	yes	48	21.5	even	6
882.2.t.c.803.16		48	3.2	odd	2
882.2.t.c.803.21		48	21.20	even	2
882.2.t.c.815.16		48	63.31	odd	6
882.2.t.c.815.21		48	63.4	even	3
2646.2.l.c.521.7		48	7.3	odd	6
2646.2.l.c.521.8		48	7.4	even	3
2646.2.l.c.1097.7		48	9.5	odd	6
2646.2.l.c.1097.8		48	63.41	even	6
2646.2.m.c.881.17		48	63.23	odd	6
2646.2.m.c.881.18		48	63.5	even	6
2646.2.m.c.1763.17		48	7.5	odd	6
2646.2.m.c.1763.18		48	7.2	even	3
2646.2.t.c.1979.5		48	1.1	even	1	trivial
2646.2.t.c.1979.6		48	7.6	odd	2	inner
2646.2.t.c.2285.5		48	63.59	even	6	inner
2646.2.t.c.2285.6		48	63.32	odd	6	inner

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.16972 q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.16972 q^{5} +1.00000i q^{8} +(1.01301 - 0.584859i) q^{10} +5.76436i q^{11} +(0.571028 - 0.329683i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.83946 + 4.91809i) q^{17} +(3.16853 + 1.82935i) q^{19} +(-0.584859 + 1.01301i) q^{20} +(-2.88218 - 4.99209i) q^{22} -0.580945i q^{23} -3.63176 q^{25} +(-0.329683 + 0.571028i) q^{26} +(-6.53449 - 3.77269i) q^{29} +(2.75231 + 1.58905i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.91809 - 2.83946i) q^{34} +(5.29511 - 9.17140i) q^{37} -3.65870 q^{38} -1.16972i q^{40} +(2.64145 + 4.57513i) q^{41} +(2.37970 - 4.12177i) q^{43} +(4.99209 + 2.88218i) q^{44} +(0.290473 + 0.503113i) q^{46} +(-2.67305 - 4.62986i) q^{47} +(3.14519 - 1.81588i) q^{50} -0.659367i q^{52} +(-4.14347 + 2.39223i) q^{53} -6.74269i q^{55} +7.54538 q^{58} +(0.514856 - 0.891757i) q^{59} +(-10.1334 + 5.85054i) q^{61} -3.17809 q^{62} -1.00000 q^{64} +(-0.667943 + 0.385637i) q^{65} +(-4.26100 + 7.38027i) q^{67} +5.67892 q^{68} -8.34154i q^{71} +(-0.899038 + 0.519060i) q^{73} +10.5902i q^{74} +(3.16853 - 1.82935i) q^{76} +(0.631283 + 1.09341i) q^{79} +(0.584859 + 1.01301i) q^{80} +(-4.57513 - 2.64145i) q^{82} +(-6.21900 + 10.7716i) q^{83} +(-3.32137 - 5.75278i) q^{85} +4.75941i q^{86} -5.76436 q^{88} +(-7.83957 + 13.5785i) q^{89} +(-0.503113 - 0.290473i) q^{92} +(4.62986 + 2.67305i) q^{94} +(-3.70629 - 2.13983i) q^{95} +(-12.5887 - 7.26808i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 48 q^{44} + 48 q^{50} + 96 q^{53} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 48 q^{92} - 192 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 24 * q^16 + 48 * q^25 + 48 * q^44 + 48 * q^50 + 96 * q^53 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 48 * q^92 - 192 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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