LMFDB - Embedded newform 1512.2.j.d.323.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.26
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0811990 + 1.41188i) q^{2} +(-1.98681 + 0.229287i) q^{4} +1.27819 q^{5} -1.00000i q^{7} +(-0.485052 - 2.78653i) q^{8} +O(q^{10})$	\(q+(0.0811990 + 1.41188i) q^{2} +(-1.98681 + 0.229287i) q^{4} +1.27819 q^{5} -1.00000i q^{7} +(-0.485052 - 2.78653i) q^{8} +(0.103788 + 1.80466i) q^{10} -2.84853i q^{11} -0.223683i q^{13} +(1.41188 - 0.0811990i) q^{14} +(3.89486 - 0.911099i) q^{16} -0.397844i q^{17} -4.64862 q^{19} +(-2.53953 + 0.293073i) q^{20} +(4.02179 - 0.231298i) q^{22} -7.36177 q^{23} -3.36622 q^{25} +(0.315814 - 0.0181628i) q^{26} +(0.229287 + 1.98681i) q^{28} -10.6317 q^{29} -7.67558i q^{31} +(1.60262 + 5.42509i) q^{32} +(0.561708 - 0.0323045i) q^{34} -1.27819i q^{35} +4.74489i q^{37} +(-0.377464 - 6.56330i) q^{38} +(-0.619991 - 3.56172i) q^{40} +1.97843i q^{41} +7.62888 q^{43} +(0.653130 + 5.65950i) q^{44} +(-0.597768 - 10.3939i) q^{46} -11.0724 q^{47} -1.00000 q^{49} +(-0.273334 - 4.75270i) q^{50} +(0.0512875 + 0.444416i) q^{52} +0.295366 q^{53} -3.64098i q^{55} +(-2.78653 + 0.485052i) q^{56} +(-0.863279 - 15.0106i) q^{58} -7.25779i q^{59} -9.45592i q^{61} +(10.8370 - 0.623249i) q^{62} +(-7.52945 + 2.70322i) q^{64} -0.285910i q^{65} -3.52321 q^{67} +(0.0912202 + 0.790441i) q^{68} +(1.80466 - 0.103788i) q^{70} +8.37710 q^{71} +10.6704 q^{73} +(-6.69921 + 0.385280i) q^{74} +(9.23595 - 1.06587i) q^{76} -2.84853 q^{77} -5.22135i q^{79} +(4.97838 - 1.16456i) q^{80} +(-2.79331 + 0.160647i) q^{82} +9.11868i q^{83} -0.508521i q^{85} +(0.619457 + 10.7711i) q^{86} +(-7.93751 + 1.38169i) q^{88} +8.94887i q^{89} -0.223683 q^{91} +(14.6265 - 1.68795i) q^{92} +(-0.899068 - 15.6329i) q^{94} -5.94184 q^{95} +0.228078 q^{97} +(-0.0811990 - 1.41188i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0811990	+	1.41188i	0.0574164	+	0.998350i
$2$	0.0811990	+	1.41188i	0.0574164	+	0.998350i
$3$		0			0
$3$		0			0
$4$	−1.98681	+	0.229287i	−0.993407	+	0.114643i
$5$	1.27819			0.571625			0.285813	−	0.958285i	$-0.407736\pi$
$5$	1.27819			0.571625			0.285813	+	0.958285i	$0.407736\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.485052	−	2.78653i	−0.171492	−	0.985186i
$9$		0			0
$10$	0.103788	+	1.80466i	0.0328207	+	0.570682i
$11$		−	2.84853i		−	0.858865i	−0.903099	−	0.429433i	$-0.858714\pi$
$11$		−	2.84853i		−	0.858865i	0.903099	−	0.429433i	$-0.141286\pi$
$12$		0			0
$13$		−	0.223683i		−	0.0620385i	−0.999519	−	0.0310192i	$-0.990125\pi$
$13$		−	0.223683i		−	0.0620385i	0.999519	−	0.0310192i	$-0.00987531\pi$
$14$	1.41188	−	0.0811990i	0.377341	−	0.0217013i
$15$		0			0
$16$	3.89486	−	0.911099i	0.973714	−	0.227775i
$17$		−	0.397844i		−	0.0964913i	−0.998836	−	0.0482456i	$-0.984637\pi$
$17$		−	0.397844i		−	0.0964913i	0.998836	−	0.0482456i	$-0.0153630\pi$
$18$		0			0
$19$	−4.64862			−1.06647			−0.533234	−	0.845968i	$-0.679023\pi$
$19$	−4.64862			−1.06647			−0.533234	+	0.845968i	$0.679023\pi$
$20$	−2.53953	+	0.293073i	−0.567857	+	0.0655330i
$21$		0			0
$22$	4.02179	−	0.231298i	0.857448	−	0.0493129i
$23$	−7.36177			−1.53503			−0.767517	−	0.641028i	$-0.778508\pi$
$23$	−7.36177			−1.53503			−0.767517	+	0.641028i	$0.778508\pi$
$24$		0			0
$25$	−3.36622			−0.673244
$26$	0.315814	−	0.0181628i	0.0619361	−	0.00356202i
$27$		0			0
$28$	0.229287	+	1.98681i	0.0433311	+	0.375472i
$29$	−10.6317			−1.97425			−0.987124	−	0.159957i	$-0.948864\pi$
$29$	−10.6317			−1.97425			−0.987124	+	0.159957i	$0.948864\pi$
$30$		0			0
$31$		−	7.67558i		−	1.37857i	−0.724488	−	0.689287i	$-0.757924\pi$
$31$		−	7.67558i		−	1.37857i	0.724488	−	0.689287i	$-0.242076\pi$
$32$	1.60262	+	5.42509i	0.283306	+	0.959030i
$33$		0			0
$34$	0.561708	−	0.0323045i	0.0963321	−	0.00554018i
$35$		−	1.27819i		−	0.216054i
$36$		0			0
$37$			4.74489i			0.780055i	0.920803	+	0.390027i	$0.127534\pi$
$37$			4.74489i			0.780055i	−0.920803	+	0.390027i	$0.872466\pi$
$38$	−0.377464	−	6.56330i	−0.0612327	−	1.06471i
$39$		0			0
$40$	−0.619991	−	3.56172i	−0.0980292	−	0.563157i
$41$			1.97843i			0.308979i	0.987994	+	0.154490i	$0.0493733\pi$
$41$			1.97843i			0.308979i	−0.987994	+	0.154490i	$0.950627\pi$
$42$		0			0
$43$	7.62888			1.16339			0.581697	−	0.813406i	$-0.302389\pi$
$43$	7.62888			1.16339			0.581697	+	0.813406i	$0.302389\pi$
$44$	0.653130	+	5.65950i	0.0984631	+	0.853202i
$45$		0			0
$46$	−0.597768	−	10.3939i	−0.0881361	−	1.53250i
$47$	−11.0724			−1.61508			−0.807538	−	0.589815i	$-0.799201\pi$
$47$	−11.0724			−1.61508			−0.807538	+	0.589815i	$0.799201\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.273334	−	4.75270i	−0.0386552	−	0.672134i
$51$		0			0
$52$	0.0512875	+	0.444416i	0.00711229	+	0.0616294i
$53$	0.295366			0.0405717			0.0202858	−	0.999794i	$-0.493542\pi$
$53$	0.295366			0.0405717			0.0202858	+	0.999794i	$0.493542\pi$
$54$		0			0
$55$		−	3.64098i		−	0.490949i
$56$	−2.78653	+	0.485052i	−0.372365	+	0.0648179i
$57$		0			0
$58$	−0.863279	−	15.0106i	−0.113354	−	1.97099i
$59$		−	7.25779i		−	0.944884i	−0.881362	−	0.472442i	$-0.843373\pi$
$59$		−	7.25779i		−	0.944884i	0.881362	−	0.472442i	$-0.156627\pi$
$60$		0			0
$61$		−	9.45592i		−	1.21071i	−0.795957	−	0.605354i	$-0.793032\pi$
$61$		−	9.45592i		−	1.21071i	0.795957	−	0.605354i	$-0.206968\pi$
$62$	10.8370	−	0.623249i	1.37630	−	0.0791527i
$63$		0			0
$64$	−7.52945	+	2.70322i	−0.941181	+	0.337903i
$65$		−	0.285910i		−	0.0354628i
$66$		0			0
$67$	−3.52321			−0.430428			−0.215214	−	0.976567i	$-0.569045\pi$
$67$	−3.52321			−0.430428			−0.215214	+	0.976567i	$0.569045\pi$
$68$	0.0912202	+	0.790441i	0.0110621	+	0.0958551i
$69$		0			0
$70$	1.80466	−	0.103788i	0.215698	−	0.0124050i
$71$	8.37710			0.994179			0.497089	−	0.867699i	$-0.334402\pi$
$71$	8.37710			0.994179			0.497089	+	0.867699i	$0.334402\pi$
$72$		0			0
$73$	10.6704			1.24887			0.624437	−	0.781076i	$-0.285329\pi$
$73$	10.6704			1.24887			0.624437	+	0.781076i	$0.285329\pi$
$74$	−6.69921	+	0.385280i	−0.778768	+	0.0447879i
$75$		0			0
$76$	9.23595	−	1.06587i	1.05944	−	0.122263i
$77$	−2.84853			−0.324621
$78$		0			0
$79$		−	5.22135i		−	0.587448i	−0.955890	−	0.293724i	$-0.905105\pi$
$79$		−	5.22135i		−	0.587448i	0.955890	−	0.293724i	$-0.0948947\pi$
$80$	4.97838	−	1.16456i	0.556600	−	0.130202i
$81$		0			0
$82$	−2.79331	+	0.160647i	−0.308470	+	0.0177405i
$83$			9.11868i			1.00091i	0.865764	+	0.500453i	$0.166833\pi$
$83$			9.11868i			1.00091i	−0.865764	+	0.500453i	$0.833167\pi$
$84$		0			0
$85$		−	0.508521i		−	0.0551569i
$86$	0.619457	+	10.7711i	0.0667978	+	1.16147i
$87$		0			0
$88$	−7.93751	+	1.38169i	−0.846142	+	0.147288i
$89$			8.94887i			0.948578i	0.880369	+	0.474289i	$0.157295\pi$
$89$			8.94887i			0.948578i	−0.880369	+	0.474289i	$0.842705\pi$
$90$		0			0
$91$	−0.223683			−0.0234483
$92$	14.6265	−	1.68795i	1.52491	−	0.175981i
$93$		0			0
$94$	−0.899068	−	15.6329i	−0.0927318	−	1.61241i
$95$	−5.94184			−0.609620
$96$		0			0
$97$	0.228078			0.0231578			0.0115789	−	0.999933i	$-0.496314\pi$
$97$	0.228078			0.0231578			0.0115789	+	0.999933i	$0.496314\pi$
$98$	−0.0811990	−	1.41188i	−0.00820234	−	0.142621i
$99$		0			0
$100$	6.68805	−	0.771829i	0.668805	−	0.0771829i
$101$	−6.36504			−0.633346			−0.316673	−	0.948535i	$-0.602566\pi$
$101$	−6.36504			−0.633346			−0.316673	+	0.948535i	$0.602566\pi$
$102$		0			0
$103$		−	11.6557i		−	1.14847i	−0.818690	−	0.574236i	$-0.805299\pi$
$103$		−	11.6557i		−	1.14847i	0.818690	−	0.574236i	$-0.194701\pi$
$104$	−0.623298	+	0.108498i	−0.0611194	+	0.0106391i
$105$		0			0
$106$	0.0239834	+	0.417022i	0.00232948	+	0.0405047i
$107$			9.01403i			0.871419i	0.900087	+	0.435709i	$0.143502\pi$
$107$			9.01403i			0.871419i	−0.900087	+	0.435709i	$0.856498\pi$
$108$		0			0
$109$			5.45206i			0.522213i	0.965310	+	0.261106i	$0.0840873\pi$
$109$			5.45206i			0.522213i	−0.965310	+	0.261106i	$0.915913\pi$
$110$	5.14062	−	0.295644i	0.490139	−	0.0281885i
$111$		0			0
$112$	−0.911099	−	3.89486i	−0.0860908	−	0.368029i
$113$		−	7.00229i		−	0.658720i	−0.944204	−	0.329360i	$-0.893167\pi$
$113$		−	7.00229i		−	0.658720i	0.944204	−	0.329360i	$-0.106833\pi$
$114$		0			0
$115$	−9.40976			−0.877465
$116$	21.1231	−	2.43769i	1.96123	−	0.226334i
$117$		0			0
$118$	10.2471	−	0.589326i	0.943326	−	0.0542518i
$119$	−0.397844			−0.0364703
$120$		0			0
$121$	2.88586			0.262351
$122$	13.3506	−	0.767812i	1.20871	−	0.0695144i
$123$		0			0
$124$	1.75991	+	15.2499i	0.158044	+	1.36948i
$125$	−10.6936			−0.956469
$126$		0			0
$127$		−	9.48046i		−	0.841255i	−0.907234	−	0.420627i	$-0.861810\pi$
$127$		−	9.48046i		−	0.841255i	0.907234	−	0.420627i	$-0.138190\pi$
$128$	−4.42801	−	10.4112i	−0.391385	−	0.920227i
$129$		0			0
$130$	0.403671	−	0.0232156i	0.0354043	−	0.00203614i
$131$		−	6.34169i		−	0.554076i	−0.960859	−	0.277038i	$-0.910647\pi$
$131$		−	6.34169i		−	0.554076i	0.960859	−	0.277038i	$-0.0893528\pi$
$132$		0			0
$133$			4.64862i			0.403087i
$134$	−0.286081	−	4.97435i	−0.0247136	−	0.429718i
$135$		0			0
$136$	−1.10860	+	0.192975i	−0.0950618	+	0.0165475i
$137$		−	11.3108i		−	0.966349i	−0.875524	−	0.483174i	$-0.839484\pi$
$137$		−	11.3108i		−	0.966349i	0.875524	−	0.483174i	$-0.160516\pi$
$138$		0			0
$139$	21.7583			1.84551			0.922757	−	0.385382i	$-0.125930\pi$
$139$	21.7583			1.84551			0.922757	+	0.385382i	$0.125930\pi$
$140$	0.293073	+	2.53953i	0.0247692	+	0.214630i
$141$		0			0
$142$	0.680212	+	11.8275i	0.0570821	+	0.992539i
$143$	−0.637168			−0.0532827
$144$		0			0
$145$	−13.5893			−1.12853
$146$	0.866424	+	15.0653i	0.0717057	+	1.24681i
$147$		0			0
$148$	−1.08794	−	9.42721i	−0.0894280	−	0.774912i
$149$	−2.42505			−0.198668			−0.0993340	−	0.995054i	$-0.531671\pi$
$149$	−2.42505			−0.198668			−0.0993340	+	0.995054i	$0.531671\pi$
$150$		0			0
$151$		−	20.0398i		−	1.63082i	−0.578887	−	0.815408i	$-0.696513\pi$
$151$		−	20.0398i		−	1.63082i	0.578887	−	0.815408i	$-0.303487\pi$
$152$	2.25483	+	12.9535i	0.182891	+	1.05067i
$153$		0			0
$154$	−0.231298	−	4.02179i	−0.0186385	−	0.324085i
$155$		−	9.81087i		−	0.788028i
$156$		0			0
$157$			15.5990i			1.24494i	0.782644	+	0.622470i	$0.213871\pi$
$157$			15.5990i			1.24494i	−0.782644	+	0.622470i	$0.786129\pi$
$158$	7.37193	−	0.423969i	0.586479	−	0.0337291i
$159$		0			0
$160$	2.04846	+	6.93431i	0.161945	+	0.548206i
$161$			7.36177i			0.580189i
$162$		0			0
$163$	12.8755			1.00848			0.504242	−	0.863562i	$-0.331772\pi$
$163$	12.8755			1.00848			0.504242	+	0.863562i	$0.331772\pi$
$164$	−0.453628	−	3.93078i	−0.0354224	−	0.306942i
$165$		0			0
$166$	−12.8745	+	0.740428i	−0.999255	+	0.0574684i
$167$	−1.55771			−0.120539			−0.0602697	−	0.998182i	$-0.519196\pi$
$167$	−1.55771			−0.120539			−0.0602697	+	0.998182i	$0.519196\pi$
$168$		0			0
$169$	12.9500			0.996151
$170$	0.717971	−	0.0412914i	0.0550659	−	0.00316691i
$171$		0			0
$172$	−15.1572	+	1.74920i	−1.15572	+	0.133375i
$173$	−2.60553			−0.198095			−0.0990474	−	0.995083i	$-0.531580\pi$
$173$	−2.60553			−0.198095			−0.0990474	+	0.995083i	$0.531580\pi$
$174$		0			0
$175$			3.36622i			0.254462i
$176$	−2.59530	−	11.0946i	−0.195628	−	0.836289i
$177$		0			0
$178$	−12.6347	+	0.726639i	−0.947013	+	0.0544639i
$179$		−	18.9293i		−	1.41484i	−0.706793	−	0.707420i	$-0.749859\pi$
$179$		−	18.9293i		−	1.41484i	0.706793	−	0.707420i	$-0.250141\pi$
$180$		0			0
$181$			15.6813i			1.16558i	0.812621	+	0.582792i	$0.198040\pi$
$181$			15.6813i			1.16558i	−0.812621	+	0.582792i	$0.801960\pi$
$182$	−0.0181628	−	0.315814i	−0.00134632	−	0.0234097i
$183$		0			0
$184$	3.57084	+	20.5138i	0.263246	+	1.51229i
$185$			6.06488i			0.445899i
$186$		0			0
$187$	−1.13327			−0.0828730
$188$	21.9988	−	2.53875i	1.60443	−	0.185158i
$189$		0			0
$190$	−0.482472	−	8.38917i	−0.0350022	−	0.608614i
$191$	−3.86888			−0.279943			−0.139971	−	0.990156i	$-0.544701\pi$
$191$	−3.86888			−0.279943			−0.139971	+	0.990156i	$0.544701\pi$
$192$		0			0
$193$	−12.1061			−0.871419			−0.435710	−	0.900087i	$-0.643503\pi$
$193$	−12.1061			−0.871419			−0.435710	+	0.900087i	$0.643503\pi$
$194$	0.0185197	+	0.322019i	0.00132964	+	0.0231196i
$195$		0			0
$196$	1.98681	−	0.229287i	0.141915	−	0.0163776i
$197$	5.20058			0.370526			0.185263	−	0.982689i	$-0.440686\pi$
$197$	5.20058			0.370526			0.185263	+	0.982689i	$0.440686\pi$
$198$		0			0
$199$			15.5030i			1.09898i	0.835501	+	0.549489i	$0.185177\pi$
$199$			15.5030i			1.09898i	−0.835501	+	0.549489i	$0.814823\pi$
$200$	1.63279	+	9.38006i	0.115456	+	0.663271i
$201$		0			0
$202$	−0.516835	−	8.98668i	−0.0363644	−	0.632301i
$203$			10.6317i			0.746196i
$204$		0			0
$205$			2.52882i			0.176620i
$206$	16.4565	−	0.946433i	1.14658	−	0.0659411i
$207$		0			0
$208$	−0.203797	−	0.871213i	−0.0141308	−	0.0604077i
$209$			13.2418i			0.915952i
$210$		0			0
$211$	−9.04096			−0.622406			−0.311203	−	0.950344i	$-0.600732\pi$
$211$	−9.04096			−0.622406			−0.311203	+	0.950344i	$0.600732\pi$
$212$	−0.586837	+	0.0677235i	−0.0403042	+	0.00465127i
$213$		0			0
$214$	−12.7267	+	0.731930i	−0.869981	+	0.0500337i
$215$	9.75118			0.665025
$216$		0			0
$217$	−7.67558			−0.521052
$218$	−7.69766	+	0.442702i	−0.521351	+	0.0299835i
$219$		0			0
$220$	0.834827	+	7.23394i	0.0562840	+	0.487712i
$221$	−0.0889909			−0.00598617
$222$		0			0
$223$		−	10.2327i		−	0.685231i	−0.939476	−	0.342616i	$-0.888687\pi$
$223$		−	10.2327i		−	0.685231i	0.939476	−	0.342616i	$-0.111313\pi$
$224$	5.42509	−	1.60262i	0.362479	−	0.107080i
$225$		0			0
$226$	9.88640	−	0.568579i	0.657633	−	0.0378213i
$227$			10.9987i			0.730007i	0.931006	+	0.365003i	$0.118932\pi$
$227$			10.9987i			0.730007i	−0.931006	+	0.365003i	$0.881068\pi$
$228$		0			0
$229$			24.1988i			1.59910i	0.600600	+	0.799550i	$0.294928\pi$
$229$			24.1988i			1.59910i	−0.600600	+	0.799550i	$0.705072\pi$
$230$	−0.764063	−	13.2855i	−0.0503808	−	0.876017i
$231$		0			0
$232$	5.15691	+	29.6254i	0.338568	+	1.94500i
$233$		−	21.5448i		−	1.41144i	−0.708489	−	0.705722i	$-0.750623\pi$
$233$		−	21.5448i		−	1.41144i	0.708489	−	0.705722i	$-0.249377\pi$
$234$		0			0
$235$	−14.1527			−0.923219
$236$	1.66411	+	14.4199i	0.108325	+	0.938655i
$237$		0			0
$238$	−0.0323045	−	0.561708i	−0.00209399	−	0.0364101i
$239$	−20.5708			−1.33061			−0.665307	−	0.746570i	$-0.731699\pi$
$239$	−20.5708			−1.33061			−0.665307	+	0.746570i	$0.731699\pi$
$240$		0			0
$241$	−11.0840			−0.713984			−0.356992	−	0.934107i	$-0.616198\pi$
$241$	−11.0840			−0.713984			−0.356992	+	0.934107i	$0.616198\pi$
$242$	0.234329	+	4.07449i	0.0150632	+	0.261918i
$243$		0			0
$244$	2.16812	+	18.7872i	0.138799	+	1.20272i
$245$	−1.27819			−0.0816608
$246$		0			0
$247$			1.03982i			0.0661620i
$248$	−21.3882	+	3.72306i	−1.35815	+	0.236414i
$249$		0			0
$250$	−0.868314	−	15.0982i	−0.0549170	−	0.954891i
$251$			20.7016i			1.30667i	0.757068	+	0.653336i	$0.226631\pi$
$251$			20.7016i			1.30667i	−0.757068	+	0.653336i	$0.773369\pi$
$252$		0			0
$253$			20.9702i			1.31839i
$254$	13.3853	−	0.769804i	0.839867	−	0.0483018i
$255$		0			0
$256$	14.3398	−	7.09720i	0.896237	−	0.443575i
$257$		−	10.6516i		−	0.664427i	−0.943204	−	0.332213i	$-0.892205\pi$
$257$		−	10.6516i		−	0.664427i	0.943204	−	0.332213i	$-0.107795\pi$
$258$		0			0
$259$	4.74489			0.294833
$260$	0.0655553	+	0.568050i	0.00406557	+	0.0352290i
$261$		0			0
$262$	8.95371	−	0.514939i	0.553162	−	0.0318130i
$263$	6.36313			0.392367			0.196184	−	0.980567i	$-0.437145\pi$
$263$	6.36313			0.392367			0.196184	+	0.980567i	$0.437145\pi$
$264$		0			0
$265$	0.377535			0.0231918
$266$	−6.56330	+	0.377464i	−0.402422	+	0.0231438i
$267$		0			0
$268$	6.99996	−	0.807824i	0.427590	−	0.0493457i
$269$	14.3840			0.877007			0.438503	−	0.898730i	$-0.355509\pi$
$269$	14.3840			0.877007			0.438503	+	0.898730i	$0.355509\pi$
$270$		0			0
$271$		−	12.9317i		−	0.785548i	−0.919635	−	0.392774i	$-0.871515\pi$
$271$		−	12.9317i		−	0.785548i	0.919635	−	0.392774i	$-0.128485\pi$
$272$	−0.362475	−	1.54954i	−0.0219783	−	0.0939549i
$273$		0			0
$274$	15.9695	−	0.918427i	0.964755	−	0.0554842i
$275$			9.58880i			0.578226i
$276$		0			0
$277$			13.5242i			0.812593i	0.913741	+	0.406297i	$0.133180\pi$
$277$			13.5242i			0.812593i	−0.913741	+	0.406297i	$0.866820\pi$
$278$	1.76675	+	30.7201i	0.105963	+	1.84247i
$279$		0			0
$280$	−3.56172	+	0.619991i	−0.212853	+	0.0370515i
$281$		−	20.7882i		−	1.24012i	−0.784554	−	0.620061i	$-0.787108\pi$
$281$		−	20.7882i		−	1.24012i	0.784554	−	0.620061i	$-0.212892\pi$
$282$		0			0
$283$	−17.6119			−1.04692			−0.523459	−	0.852051i	$-0.675359\pi$
$283$	−17.6119			−1.04692			−0.523459	+	0.852051i	$0.675359\pi$
$284$	−16.6437	+	1.92076i	−0.987624	+	0.113976i
$285$		0			0
$286$	−0.0517374	−	0.899605i	−0.00305930	−	0.0531948i
$287$	1.97843			0.116783
$288$		0			0
$289$	16.8417			0.990689
$290$	−1.10344	−	19.1865i	−0.0647961	−	1.12667i
$291$		0			0
$292$	−21.2000	+	2.44657i	−1.24064	+	0.143175i
$293$	2.42581			0.141718			0.0708588	−	0.997486i	$-0.477426\pi$
$293$	2.42581			0.141718			0.0708588	+	0.997486i	$0.477426\pi$
$294$		0			0
$295$		−	9.27687i		−	0.540120i
$296$	13.2218	−	2.30152i	0.768499	−	0.133773i
$297$		0			0
$298$	−0.196912	−	3.42388i	−0.0114068	−	0.198340i
$299$			1.64670i			0.0952312i
$300$		0			0
$301$		−	7.62888i		−	0.439721i
$302$	28.2938	−	1.62721i	1.62813	−	0.0936355i
$303$		0			0
$304$	−18.1057	+	4.23536i	−1.03843	+	0.242914i
$305$		−	12.0865i		−	0.692071i
$306$		0			0
$307$	−5.15871			−0.294423			−0.147212	−	0.989105i	$-0.547030\pi$
$307$	−5.15871			−0.294423			−0.147212	+	0.989105i	$0.547030\pi$
$308$	5.65950	−	0.653130i	0.322480	−	0.0372156i
$309$		0			0
$310$	13.8518	−	0.796633i	0.786728	−	0.0452457i
$311$	−31.1304			−1.76524			−0.882620	−	0.470086i	$-0.844223\pi$
$311$	−31.1304			−1.76524			−0.882620	+	0.470086i	$0.844223\pi$
$312$		0			0
$313$	−21.8080			−1.23266			−0.616330	−	0.787488i	$-0.711381\pi$
$313$	−21.8080			−1.23266			−0.616330	+	0.787488i	$0.711381\pi$
$314$	−22.0240	+	1.26663i	−1.24289	+	0.0714799i
$315$		0			0
$316$	1.19719	+	10.3739i	0.0673470	+	0.583575i
$317$	0.309869			0.0174040			0.00870199	−	0.999962i	$-0.497230\pi$
$317$	0.309869			0.0174040			0.00870199	+	0.999962i	$0.497230\pi$
$318$		0			0
$319$			30.2846i			1.69561i
$320$	−9.62409	+	3.45524i	−0.538003	+	0.193154i
$321$		0			0
$322$	−10.3939	+	0.597768i	−0.579231	+	0.0333123i
$323$			1.84943i			0.102905i
$324$		0			0
$325$			0.752966i			0.0417670i
$326$	1.04547	+	18.1786i	0.0579035	+	1.00682i
$327$		0			0
$328$	5.51295	−	0.959644i	0.304402	−	0.0529875i
$329$			11.0724i			0.610441i
$330$		0			0
$331$	28.5893			1.57141			0.785706	−	0.618600i	$-0.212300\pi$
$331$	28.5893			1.57141			0.785706	+	0.618600i	$0.212300\pi$
$332$	−2.09079	−	18.1171i	−0.114747	−	0.994306i
$333$		0			0
$334$	−0.126485	−	2.19930i	−0.00692093	−	0.120341i
$335$	−4.50334			−0.246044
$336$		0			0
$337$	26.7103			1.45500			0.727502	−	0.686106i	$-0.240681\pi$
$337$	26.7103			1.45500			0.727502	+	0.686106i	$0.240681\pi$
$338$	1.05152	+	18.2838i	0.0571954	+	0.994508i
$339$		0			0
$340$	0.116597	+	1.01034i	0.00632337	+	0.0547932i
$341$	−21.8641			−1.18401
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−3.70041	−	21.2581i	−0.199513	−	1.14616i
$345$		0			0
$346$	−0.211566	−	3.67870i	−0.0113739	−	0.197768i
$347$		−	11.0302i		−	0.592132i	−0.955168	−	0.296066i	$-0.904325\pi$
$347$		−	11.0302i		−	0.592132i	0.955168	−	0.296066i	$-0.0956748\pi$
$348$		0			0
$349$		−	9.30132i		−	0.497888i	−0.968518	−	0.248944i	$-0.919916\pi$
$349$		−	9.30132i		−	0.497888i	0.968518	−	0.248944i	$-0.0800836\pi$
$350$	−4.75270	+	0.273334i	−0.254043	+	0.0146103i
$351$		0			0
$352$	15.4536	−	4.56512i	0.823677	−	0.243322i
$353$			18.4585i			0.982446i	0.871034	+	0.491223i	$0.163450\pi$
$353$			18.4585i			0.982446i	−0.871034	+	0.491223i	$0.836550\pi$
$354$		0			0
$355$	10.7076			0.568298
$356$	−2.05186	−	17.7797i	−0.108748	−	0.942324i
$357$		0			0
$358$	26.7259	−	1.53704i	1.41251	−	0.0812350i
$359$	7.70098			0.406442			0.203221	−	0.979133i	$-0.434859\pi$
$359$	7.70098			0.406442			0.203221	+	0.979133i	$0.434859\pi$
$360$		0			0
$361$	2.60971			0.137353
$362$	−22.1402	+	1.27331i	−1.16366	+	0.0669236i
$363$		0			0
$364$	0.444416	−	0.0512875i	0.0232937	−	0.00268819i
$365$	13.6388			0.713888
$366$		0			0
$367$		−	36.0127i		−	1.87985i	−0.341386	−	0.939923i	$-0.610896\pi$
$367$		−	36.0127i		−	1.87985i	0.341386	−	0.939923i	$-0.389104\pi$
$368$	−28.6730	+	6.70730i	−1.49468	+	0.349642i
$369$		0			0
$370$	−8.56289	+	0.492462i	−0.445164	+	0.0256019i
$371$		−	0.295366i		−	0.0153346i
$372$		0			0
$373$			32.8248i			1.69960i	0.527103	+	0.849801i	$0.323278\pi$
$373$			32.8248i			1.69960i	−0.527103	+	0.849801i	$0.676722\pi$
$374$	−0.0920205	−	1.60004i	−0.00475827	−	0.0827363i
$375$		0			0
$376$	5.37070	+	30.8535i	0.276973	+	1.59115i
$377$			2.37812i			0.122479i
$378$		0			0
$379$	−27.8200			−1.42902			−0.714509	−	0.699626i	$-0.753350\pi$
$379$	−27.8200			−1.42902			−0.714509	+	0.699626i	$0.753350\pi$
$380$	11.8053	−	1.36238i	0.605601	−	0.0698888i
$381$		0			0
$382$	−0.314150	−	5.46240i	−0.0160733	−	0.279481i
$383$	−11.9047			−0.608301			−0.304151	−	0.952624i	$-0.598373\pi$
$383$	−11.9047			−0.608301			−0.304151	+	0.952624i	$0.598373\pi$
$384$		0			0
$385$	−3.64098			−0.185561
$386$	−0.983007	−	17.0924i	−0.0500337	−	0.869982i
$387$		0			0
$388$	−0.453148	+	0.0522952i	−0.0230051	+	0.00265489i
$389$	−24.8388			−1.25938			−0.629688	−	0.776848i	$-0.716817\pi$
$389$	−24.8388			−1.25938			−0.629688	+	0.776848i	$0.716817\pi$
$390$		0			0
$391$			2.92883i			0.148117i
$392$	0.485052	+	2.78653i	0.0244988	+	0.140741i
$393$		0			0
$394$	0.422282	+	7.34260i	0.0212743	+	0.369915i
$395$		−	6.67390i		−	0.335800i
$396$		0			0
$397$			4.49543i			0.225619i	0.993617	+	0.112810i	$0.0359850\pi$
$397$			4.49543i			0.225619i	−0.993617	+	0.112810i	$0.964015\pi$
$398$	−21.8884	+	1.25883i	−1.09716	+	0.0630993i
$399$		0			0
$400$	−13.1109	+	3.06696i	−0.655547	+	0.153348i
$401$			14.8094i			0.739545i	0.929122	+	0.369772i	$0.120564\pi$
$401$			14.8094i			0.739545i	−0.929122	+	0.369772i	$0.879436\pi$
$402$		0			0
$403$	−1.71689			−0.0855246
$404$	12.6462	−	1.45942i	0.629170	−	0.0726088i
$405$		0			0
$406$	−15.0106	+	0.863279i	−0.744965	+	0.0428438i
$407$	13.5160			0.669962
$408$		0			0
$409$	−33.4088			−1.65196			−0.825980	−	0.563699i	$-0.809378\pi$
$409$	−33.4088			−1.65196			−0.825980	+	0.563699i	$0.809378\pi$
$410$	−3.57039	+	0.205338i	−0.176329	+	0.0101409i
$411$		0			0
$412$	2.67250	+	23.1577i	0.131665	+	1.14090i
$413$	−7.25779			−0.357133
$414$		0			0
$415$			11.6554i			0.572143i
$416$	1.21350	−	0.358479i	0.0594967	−	0.0175759i
$417$		0			0
$418$	−18.6958	+	1.07522i	−0.914441	+	0.0525906i
$419$		−	6.31558i		−	0.308536i	−0.988029	−	0.154268i	$-0.950698\pi$
$419$		−	6.31558i		−	0.308536i	0.988029	−	0.154268i	$-0.0493020\pi$
$420$		0			0
$421$		−	10.6716i		−	0.520104i	−0.965595	−	0.260052i	$-0.916260\pi$
$421$		−	10.6716i		−	0.520104i	0.965595	−	0.260052i	$-0.0837397\pi$
$422$	−0.734117	−	12.7648i	−0.0357363	−	0.621379i
$423$		0			0
$424$	−0.143268	−	0.823045i	−0.00695771	−	0.0399706i
$425$			1.33923i			0.0649622i
$426$		0			0
$427$	−9.45592			−0.457604
$428$	−2.06680	−	17.9092i	−0.0999023	−	0.865673i
$429$		0			0
$430$	0.791786	+	13.7675i	0.0381833	+	0.663928i
$431$	35.8686			1.72773			0.863865	−	0.503723i	$-0.168037\pi$
$431$	35.8686			1.72773			0.863865	+	0.503723i	$0.168037\pi$
$432$		0			0
$433$	4.43908			0.213328			0.106664	−	0.994295i	$-0.465983\pi$
$433$	4.43908			0.213328			0.106664	+	0.994295i	$0.465983\pi$
$434$	−0.623249	−	10.8370i	−0.0299169	−	0.520192i
$435$		0			0
$436$	−1.25008	−	10.8322i	−0.0598682	−	0.518770i
$437$	34.2221			1.63706
$438$		0			0
$439$		−	18.7939i		−	0.896985i	−0.893787	−	0.448493i	$-0.851961\pi$
$439$		−	18.7939i		−	0.896985i	0.893787	−	0.448493i	$-0.148039\pi$
$440$	−10.1457	+	1.76606i	−0.483676	+	0.0841938i
$441$		0			0
$442$	−0.00722597	−	0.125644i	−0.000343704	−	0.00597630i
$443$		−	30.9630i		−	1.47109i	−0.677473	−	0.735547i	$-0.736925\pi$
$443$		−	30.9630i		−	1.47109i	0.677473	−	0.735547i	$-0.263075\pi$
$444$		0			0
$445$			11.4384i			0.542232i
$446$	14.4473	−	0.830883i	0.684101	−	0.0393435i
$447$		0			0
$448$	2.70322	+	7.52945i	0.127715	+	0.355733i
$449$			24.6744i			1.16446i	0.813025	+	0.582229i	$0.197819\pi$
$449$			24.6744i			1.16446i	−0.813025	+	0.582229i	$0.802181\pi$
$450$		0			0
$451$	5.63563			0.265372
$452$	1.60553	+	13.9122i	0.0755178	+	0.654377i
$453$		0			0
$454$	−15.5288	+	0.893080i	−0.728803	+	0.0419143i
$455$	−0.285910			−0.0134037
$456$		0			0
$457$	13.3915			0.626429			0.313214	−	0.949682i	$-0.398594\pi$
$457$	13.3915			0.626429			0.313214	+	0.949682i	$0.398594\pi$
$458$	−34.1658	+	1.96492i	−1.59646	+	0.0918145i
$459$		0			0
$460$	18.6954	−	2.15753i	0.871679	−	0.100595i
$461$	−12.3835			−0.576759			−0.288379	−	0.957516i	$-0.593116\pi$
$461$	−12.3835			−0.576759			−0.288379	+	0.957516i	$0.593116\pi$
$462$		0			0
$463$		−	3.34707i		−	0.155551i	−0.996971	−	0.0777757i	$-0.975218\pi$
$463$		−	3.34707i		−	0.155551i	0.996971	−	0.0777757i	$-0.0247818\pi$
$464$	−41.4087	+	9.68649i	−1.92235	+	0.449684i
$465$		0			0
$466$	30.4186	−	1.74941i	1.40912	−	0.0810400i
$467$			3.05078i			0.141173i	0.997506	+	0.0705866i	$0.0224871\pi$
$467$			3.05078i			0.141173i	−0.997506	+	0.0705866i	$0.977513\pi$
$468$		0			0
$469$			3.52321i			0.162687i
$470$	−1.14918	−	19.9819i	−0.0530079	−	0.921696i
$471$		0			0
$472$	−20.2240	+	3.52041i	−0.930886	+	0.162040i
$473$		−	21.7311i		−	0.999198i
$474$		0			0
$475$	15.6483			0.717993
$476$	0.790441	−	0.0912202i	0.0362298	−	0.00418107i
$477$		0			0
$478$	−1.67033	−	29.0435i	−0.0763990	−	1.32842i
$479$	−20.4934			−0.936368			−0.468184	−	0.883631i	$-0.655092\pi$
$479$	−20.4934			−0.936368			−0.468184	+	0.883631i	$0.655092\pi$
$480$		0			0
$481$	1.06135			0.0483934
$482$	−0.900011	−	15.6493i	−0.0409944	−	0.712807i
$483$		0			0
$484$	−5.73366	+	0.661688i	−0.260621	+	0.0300767i
$485$	0.291528			0.0132376
$486$		0			0
$487$		−	21.9186i		−	0.993226i	−0.867972	−	0.496613i	$-0.834577\pi$
$487$		−	21.9186i		−	0.993226i	0.867972	−	0.496613i	$-0.165423\pi$
$488$	−26.3492	+	4.58662i	−1.19277	+	0.207627i
$489$		0			0
$490$	−0.103788	−	1.80466i	−0.00468866	−	0.0815261i
$491$			10.2880i			0.464291i	0.972681	+	0.232146i	$0.0745746\pi$
$491$			10.2880i			0.464291i	−0.972681	+	0.232146i	$0.925425\pi$
$492$		0			0
$493$			4.22974i			0.190498i
$494$	−1.46810	+	0.0844322i	−0.0660529	+	0.00379878i
$495$		0			0
$496$	−6.99321	−	29.8953i	−0.314004	−	1.34234i
$497$		−	8.37710i		−	0.375764i
$498$		0			0
$499$	−1.87931			−0.0841294			−0.0420647	−	0.999115i	$-0.513394\pi$
$499$	−1.87931			−0.0841294			−0.0420647	+	0.999115i	$0.513394\pi$
$500$	21.2463	−	2.45191i	0.950163	−	0.109653i
$501$		0			0
$502$	−29.2281	+	1.68095i	−1.30452	+	0.0750243i
$503$	14.5489			0.648702			0.324351	−	0.945937i	$-0.394854\pi$
$503$	14.5489			0.648702			0.324351	+	0.945937i	$0.394854\pi$
$504$		0			0
$505$	−8.13576			−0.362036
$506$	−29.6075	+	1.70276i	−1.31621	+	0.0756970i
$507$		0			0
$508$	2.17374	+	18.8359i	0.0964442	+	0.835708i
$509$	25.7122			1.13967			0.569837	−	0.821758i	$-0.307006\pi$
$509$	25.7122			1.13967			0.569837	+	0.821758i	$0.307006\pi$
$510$		0			0
$511$		−	10.6704i		−	0.472030i
$512$	11.1848	+	19.6698i	0.494302	+	0.869290i
$513$		0			0
$514$	15.0387	−	0.864897i	0.663331	−	0.0381490i
$515$		−	14.8983i		−	0.656496i
$516$		0			0
$517$			31.5401i			1.38713i
$518$	0.385280	+	6.69921i	0.0169282	+	0.294347i
$519$		0			0
$520$	−0.796695	+	0.138681i	−0.0349374	+	0.00608158i
$521$		−	8.03293i		−	0.351929i	−0.984397	−	0.175965i	$-0.943696\pi$
$521$		−	8.03293i		−	0.351929i	0.984397	−	0.175965i	$-0.0563044\pi$
$522$		0			0
$523$	17.2938			0.756206			0.378103	−	0.925764i	$-0.376577\pi$
$523$	17.2938			0.756206			0.378103	+	0.925764i	$0.376577\pi$
$524$	1.45406	+	12.5998i	0.0635211	+	0.550423i
$525$		0			0
$526$	0.516680	+	8.98398i	0.0225283	+	0.391720i
$527$	−3.05368			−0.133020
$528$		0			0
$529$	31.1956			1.35633
$530$	0.0306555	+	0.533034i	0.00133159	+	0.0231535i
$531$		0			0
$532$	−1.06587	−	9.23595i	−0.0462112	−	0.400429i
$533$	0.442542			0.0191686
$534$		0			0
$535$			11.5217i			0.498125i
$536$	1.70894	+	9.81751i	0.0738150	+	0.424052i
$537$		0			0
$538$	1.16796	+	20.3085i	0.0503545	+	0.875560i
$539$			2.84853i			0.122695i
$540$		0			0
$541$			6.58504i			0.283113i	0.989930	+	0.141557i	$0.0452107\pi$
$541$			6.58504i			0.283113i	−0.989930	+	0.141557i	$0.954789\pi$
$542$	18.2581	−	1.05004i	0.784252	−	0.0451033i
$543$		0			0
$544$	2.15834	−	0.637593i	0.0925380	−	0.0273366i
$545$			6.96879i			0.298510i
$546$		0			0
$547$	−33.4478			−1.43012			−0.715062	−	0.699061i	$-0.753602\pi$
$547$	−33.4478			−1.43012			−0.715062	+	0.699061i	$0.753602\pi$
$548$	2.59342	+	22.4725i	0.110785	+	0.959978i
$549$		0			0
$550$	−13.5382	+	0.778600i	−0.577272	+	0.0331996i
$551$	49.4226			2.10547
$552$		0			0
$553$	−5.22135			−0.222035
$554$	−19.0946	+	1.09816i	−0.811253	+	0.0466561i
$555$		0			0
$556$	−43.2297	+	4.98888i	−1.83335	+	0.211576i
$557$	−5.92223			−0.250933			−0.125467	−	0.992098i	$-0.540043\pi$
$557$	−5.92223			−0.250933			−0.125467	+	0.992098i	$0.540043\pi$
$558$		0			0
$559$		−	1.70645i		−	0.0721751i
$560$	−1.16456	−	4.97838i	−0.0492117	−	0.210375i
$561$		0			0
$562$	29.3505	−	1.68798i	1.23808	−	0.0712033i
$563$			23.1453i			0.975459i	0.872995	+	0.487730i	$0.162175\pi$
$563$			23.1453i			0.975459i	−0.872995	+	0.487730i	$0.837825\pi$
$564$		0			0
$565$		−	8.95028i		−	0.376541i
$566$	−1.43007	−	24.8659i	−0.0601102	−	1.04519i
$567$		0			0
$568$	−4.06333	−	23.3430i	−0.170494	−	0.979451i
$569$			1.41139i			0.0591686i	0.999562	+	0.0295843i	$0.00941835\pi$
$569$			1.41139i			0.0591686i	−0.999562	+	0.0295843i	$0.990582\pi$
$570$		0			0
$571$	−6.82194			−0.285489			−0.142745	−	0.989760i	$-0.545593\pi$
$571$	−6.82194			−0.285489			−0.142745	+	0.989760i	$0.545593\pi$
$572$	1.26593	−	0.146094i	0.0529314	−	0.00610850i
$573$		0			0
$574$	0.160647	+	2.79331i	0.00670527	+	0.116591i
$575$	24.7813			1.03345
$576$		0			0
$577$	6.97587			0.290409			0.145205	−	0.989402i	$-0.453616\pi$
$577$	6.97587			0.290409			0.145205	+	0.989402i	$0.453616\pi$
$578$	1.36753	+	23.7785i	0.0568818	+	0.989055i
$579$		0			0
$580$	26.9994	−	3.11584i	1.12109	−	0.129378i
$581$	9.11868			0.378307
$582$		0			0
$583$		−	0.841360i		−	0.0348456i
$584$	−5.17569	−	29.7333i	−0.214172	−	1.23037i
$585$		0			0
$586$	0.196974	+	3.42496i	0.00813691	+	0.141484i
$587$			40.3481i			1.66534i	0.553766	+	0.832672i	$0.313190\pi$
$587$			40.3481i			1.66534i	−0.553766	+	0.832672i	$0.686810\pi$
$588$		0			0
$589$			35.6809i			1.47020i
$590$	13.0978	−	0.753272i	0.539229	−	0.0310117i
$591$		0			0
$592$	4.32306	+	18.4807i	0.177677	+	0.759550i
$593$		−	6.40544i		−	0.263040i	−0.991314	−	0.131520i	$-0.958014\pi$
$593$		−	6.40544i		−	0.263040i	0.991314	−	0.131520i	$-0.0419858\pi$
$594$		0			0
$595$	−0.508521			−0.0208473
$596$	4.81813	−	0.556032i	0.197358	−	0.0227760i
$597$		0			0
$598$	−2.32495	+	0.133710i	−0.0950741	+	0.00546783i
$599$	2.80603			0.114651			0.0573257	−	0.998356i	$-0.481743\pi$
$599$	2.80603			0.114651			0.0573257	+	0.998356i	$0.481743\pi$
$600$		0			0
$601$	11.6165			0.473847			0.236924	−	0.971528i	$-0.423861\pi$
$601$	11.6165			0.473847			0.236924	+	0.971528i	$0.423861\pi$
$602$	10.7711	−	0.619457i	0.438996	−	0.0252472i
$603$		0			0
$604$	4.59486	+	39.8153i	0.186962	+	1.62006i
$605$	3.68868			0.149966
$606$		0			0
$607$			38.5388i			1.56424i	0.623126	+	0.782122i	$0.285862\pi$
$607$			38.5388i			1.56424i	−0.623126	+	0.782122i	$0.714138\pi$
$608$	−7.44999	−	25.2192i	−0.302137	−	1.02277i
$609$		0			0
$610$	17.0647	−	0.981412i	0.690929	−	0.0397362i
$611$			2.47671i			0.100197i
$612$		0			0
$613$		−	15.8274i		−	0.639261i	−0.947542	−	0.319631i	$-0.896441\pi$
$613$		−	15.8274i		−	0.639261i	0.947542	−	0.319631i	$-0.103559\pi$
$614$	−0.418882	−	7.28348i	−0.0169047	−	0.293937i
$615$		0			0
$616$	1.38169	+	7.93751i	0.0556698	+	0.319811i
$617$			23.9040i			0.962339i	0.876628	+	0.481170i	$0.159788\pi$
$617$			23.9040i			0.962339i	−0.876628	+	0.481170i	$0.840212\pi$
$618$		0			0
$619$	−31.4193			−1.26285			−0.631424	−	0.775437i	$-0.717529\pi$
$619$	−31.4193			−1.26285			−0.631424	+	0.775437i	$0.717529\pi$
$620$	2.24950	+	19.4924i	0.0903421	+	0.782832i
$621$		0			0
$622$	−2.52775	−	43.9523i	−0.101354	−	1.76233i
$623$	8.94887			0.358529
$624$		0			0
$625$	3.16256			0.126502
$626$	−1.77079	−	30.7902i	−0.0707748	−	1.23063i
$627$		0			0
$628$	−3.57665	−	30.9924i	−0.142724	−	1.23673i
$629$	1.88772			0.0752685
$630$		0			0
$631$			6.94219i			0.276364i	0.990407	+	0.138182i	$0.0441260\pi$
$631$			6.94219i			0.276364i	−0.990407	+	0.138182i	$0.955874\pi$
$632$	−14.5494	+	2.53263i	−0.578746	+	0.100743i
$633$		0			0
$634$	0.0251610	+	0.437498i	0.000999273	+	0.0173753i
$635$		−	12.1179i		−	0.480883i
$636$		0			0
$637$			0.223683i			0.00886264i
$638$	−42.7583	+	2.45908i	−1.69282	+	0.0973559i
$639$		0			0
$640$	−5.65985	−	13.3075i	−0.223725	−	0.526025i
$641$		−	31.1823i		−	1.23163i	−0.787892	−	0.615814i	$-0.788827\pi$
$641$		−	31.1823i		−	1.23163i	0.787892	−	0.615814i	$-0.211173\pi$
$642$		0			0
$643$	22.6881			0.894733			0.447366	−	0.894351i	$-0.352362\pi$
$643$	22.6881			0.894733			0.447366	+	0.894351i	$0.352362\pi$
$644$	−1.68795	−	14.6265i	−0.0665147	−	0.576363i
$645$		0			0
$646$	−2.61117	+	0.150172i	−0.102735	+	0.00590842i
$647$	37.7608			1.48453			0.742266	−	0.670106i	$-0.233751\pi$
$647$	37.7608			1.48453			0.742266	+	0.670106i	$0.233751\pi$
$648$		0			0
$649$	−20.6741			−0.811528
$650$	−1.06310	+	0.0611401i	−0.0416981	+	0.00239811i
$651$		0			0
$652$	−25.5811	+	2.95217i	−1.00183	+	0.115616i
$653$	47.8848			1.87388			0.936939	−	0.349494i	$-0.113647\pi$
$653$	47.8848			1.87388			0.936939	+	0.349494i	$0.113647\pi$
$654$		0			0
$655$		−	8.10591i		−	0.316724i
$656$	1.80255	+	7.70571i	0.0703777	+	0.300857i
$657$		0			0
$658$	−15.6329	+	0.899068i	−0.609434	+	0.0350493i
$659$			7.00120i			0.272728i	0.990659	+	0.136364i	$0.0435417\pi$
$659$			7.00120i			0.272728i	−0.990659	+	0.136364i	$0.956458\pi$
$660$		0			0
$661$		−	41.8042i		−	1.62599i	−0.582267	−	0.812997i	$-0.697834\pi$
$661$		−	41.8042i		−	1.62599i	0.582267	−	0.812997i	$-0.302166\pi$
$662$	2.32142	+	40.3647i	0.0902247	+	1.56882i
$663$		0			0
$664$	25.4094	−	4.42304i	0.986078	−	0.171647i
$665$			5.94184i			0.230415i
$666$		0			0
$667$	78.2677			3.03054
$668$	3.09488	−	0.357163i	0.119745	−	0.0138190i
$669$		0			0
$670$	−0.365667	−	6.35818i	−0.0141269	−	0.245638i
$671$	−26.9355			−1.03983
$672$		0			0
$673$	22.2519			0.857747			0.428874	−	0.903364i	$-0.358911\pi$
$673$	22.2519			0.857747			0.428874	+	0.903364i	$0.358911\pi$
$674$	2.16885	+	37.7118i	0.0835410	+	1.45260i
$675$		0			0
$676$	−25.7292	+	2.96925i	−0.989583	+	0.114202i
$677$	29.2219			1.12309			0.561544	−	0.827447i	$-0.310207\pi$
$677$	29.2219			1.12309			0.561544	+	0.827447i	$0.310207\pi$
$678$		0			0
$679$		−	0.228078i		−	0.00875283i
$680$	−1.41701	+	0.246660i	−0.0543398	+	0.00945896i
$681$		0			0
$682$	−1.77535	−	30.8695i	−0.0679815	−	1.18206i
$683$		−	35.0080i		−	1.33954i	−0.742567	−	0.669772i	$-0.766392\pi$
$683$		−	35.0080i		−	1.33954i	0.742567	−	0.669772i	$-0.233608\pi$
$684$		0			0
$685$		−	14.4574i		−	0.552390i
$686$	−1.41188	+	0.0811990i	−0.0539059	+	0.00310019i
$687$		0			0
$688$	29.7134	−	6.95067i	1.13281	−	0.264992i
$689$		−	0.0660684i		−	0.00251700i
$690$		0			0
$691$	1.33849			0.0509185			0.0254593	−	0.999676i	$-0.491895\pi$
$691$	1.33849			0.0509185			0.0254593	+	0.999676i	$0.491895\pi$
$692$	5.17670	−	0.597413i	0.196789	−	0.0227102i
$693$		0			0
$694$	15.5733	−	0.895640i	0.591155	−	0.0339980i
$695$	27.8113			1.05494
$696$		0			0
$697$	0.787107			0.0298138
$698$	13.1324	−	0.755258i	0.497067	−	0.0285869i
$699$		0			0
$700$	−0.771829	−	6.68805i	−0.0291724	−	0.252785i
$701$	−23.0621			−0.871044			−0.435522	−	0.900178i	$-0.643436\pi$
$701$	−23.0621			−0.871044			−0.435522	+	0.900178i	$0.643436\pi$
$702$		0			0
$703$		−	22.0572i		−	0.831903i
$704$	7.70022	+	21.4479i	0.290213	+	0.808348i
$705$		0			0
$706$	−26.0612	+	1.49881i	−0.980825	+	0.0564085i
$707$			6.36504i			0.239382i
$708$		0			0
$709$		−	46.8150i		−	1.75818i	−0.476660	−	0.879088i	$-0.658153\pi$
$709$		−	46.8150i		−	1.75818i	0.476660	−	0.879088i	$-0.341847\pi$
$710$	0.869443	+	15.1178i	0.0326296	+	0.567360i
$711$		0			0
$712$	24.9363	−	4.34067i	0.934526	−	0.162674i
$713$			56.5058i			2.11616i
$714$		0			0
$715$	−0.814424			−0.0304577
$716$	4.34023	+	37.6090i	0.162202	+	1.40551i
$717$		0			0
$718$	0.625312	+	10.8729i	0.0233364	+	0.405772i
$719$	−34.8849			−1.30099			−0.650493	−	0.759512i	$-0.725438\pi$
$719$	−34.8849			−1.30099			−0.650493	+	0.759512i	$0.725438\pi$
$720$		0			0
$721$	−11.6557			−0.434082
$722$	0.211906	+	3.68460i	0.00788633	+	0.137127i
$723$		0			0
$724$	−3.59552	−	31.1559i	−0.133626	−	1.15790i
$725$	35.7885			1.32915
$726$		0			0
$727$			16.4491i			0.610063i	0.952342	+	0.305032i	$0.0986671\pi$
$727$			16.4491i			0.610063i	−0.952342	+	0.305032i	$0.901333\pi$
$728$	0.108498	+	0.623298i	0.00402120	+	0.0231010i
$729$		0			0
$730$	1.10746	+	19.2564i	0.0409888	+	0.712710i
$731$		−	3.03510i		−	0.112257i
$732$		0			0
$733$		−	35.9855i		−	1.32915i	−0.747220	−	0.664577i	$-0.768612\pi$
$733$		−	35.9855i		−	1.32915i	0.747220	−	0.664577i	$-0.231388\pi$
$734$	50.8456	−	2.92419i	1.87675	−	0.107934i
$735$		0			0
$736$	−11.7981	−	39.9382i	−0.434885	−	1.47214i
$737$			10.0360i			0.369680i
$738$		0			0
$739$	−5.44866			−0.200432			−0.100216	−	0.994966i	$-0.531953\pi$
$739$	−5.44866			−0.200432			−0.100216	+	0.994966i	$0.531953\pi$
$740$	−1.39060	−	12.0498i	−0.0511193	−	0.442959i
$741$		0			0
$742$	0.417022	−	0.0239834i	0.0153093	−	0.000880459i
$743$	31.2115			1.14504			0.572520	−	0.819891i	$-0.305966\pi$
$743$	31.2115			1.14504			0.572520	+	0.819891i	$0.305966\pi$
$744$		0			0
$745$	−3.09969			−0.113564
$746$	−46.3447	+	2.66534i	−1.69680	+	0.0975850i
$747$		0			0
$748$	2.25160	−	0.259844i	0.0823266	−	0.00950083i
$749$	9.01403			0.329365
$750$		0			0
$751$		−	23.1812i		−	0.845894i	−0.906154	−	0.422947i	$-0.860996\pi$
$751$		−	23.1812i		−	0.845894i	0.906154	−	0.422947i	$-0.139004\pi$
$752$	−43.1254	+	10.0881i	−1.57262	+	0.367874i
$753$		0			0
$754$	−3.35762	+	0.193101i	−0.122277	+	0.00703232i
$755$		−	25.6147i		−	0.932216i
$756$		0			0
$757$		−	39.3962i		−	1.43188i	−0.698162	−	0.715940i	$-0.745998\pi$
$757$		−	39.3962i		−	1.43188i	0.698162	−	0.715940i	$-0.254002\pi$
$758$	−2.25896	−	39.2785i	−0.0820490	−	1.42666i
$759$		0			0
$760$	2.88210	+	16.5571i	0.104545	+	0.600589i
$761$		−	17.1356i		−	0.621166i	−0.950546	−	0.310583i	$-0.899476\pi$
$761$		−	17.1356i		−	0.621166i	0.950546	−	0.310583i	$-0.100524\pi$
$762$		0			0
$763$	5.45206			0.197378
$764$	7.68675	−	0.887083i	0.278097	−	0.0320935i
$765$		0			0
$766$	−0.966649	−	16.8080i	−0.0349265	−	0.607298i
$767$	−1.62344			−0.0586192
$768$		0			0
$769$	−44.9084			−1.61944			−0.809718	−	0.586819i	$-0.800380\pi$
$769$	−44.9084			−1.61944			−0.809718	+	0.586819i	$0.800380\pi$
$770$	−0.295644	−	5.14062i	−0.0106543	−	0.185255i
$771$		0			0
$772$	24.0526	−	2.77578i	0.865674	−	0.0999024i
$773$	−27.0273			−0.972106			−0.486053	−	0.873929i	$-0.661564\pi$
$773$	−27.0273			−0.972106			−0.486053	+	0.873929i	$0.661564\pi$
$774$		0			0
$775$			25.8377i			0.928117i
$776$	−0.110630	−	0.635545i	−0.00397138	−	0.0228147i
$777$		0			0
$778$	−2.01688	−	35.0694i	−0.0723088	−	1.25730i
$779$		−	9.19699i		−	0.329516i
$780$		0			0
$781$		−	23.8624i		−	0.853866i
$782$	−4.13516	+	0.237818i	−0.147873	+	0.00850437i
$783$		0			0
$784$	−3.89486	+	0.911099i	−0.139102	+	0.0325393i
$785$			19.9386i			0.711639i
$786$		0			0
$787$	−34.1562			−1.21754			−0.608769	−	0.793348i	$-0.708336\pi$
$787$	−34.1562			−1.21754			−0.608769	+	0.793348i	$0.708336\pi$
$788$	−10.3326	+	1.19242i	−0.368083	+	0.0424783i
$789$		0			0
$790$	9.42275	−	0.541914i	0.335246	−	0.0192804i
$791$	−7.00229			−0.248973
$792$		0			0
$793$	−2.11513			−0.0751104
$794$	−6.34702	+	0.365025i	−0.225247	+	0.0129542i
$795$		0			0
$796$	−3.55463	−	30.8015i	−0.125990	−	1.09173i
$797$	46.2712			1.63901			0.819505	−	0.573072i	$-0.194249\pi$
$797$	46.2712			1.63901			0.819505	+	0.573072i	$0.194249\pi$
$798$		0			0
$799$			4.40509i			0.155841i
$800$	−5.39478	−	18.2621i	−0.190734	−	0.645661i
$801$		0			0
$802$	−20.9091	+	1.20251i	−0.738325	+	0.0424620i
$803$		−	30.3949i		−	1.07261i
$804$		0			0
$805$			9.40976i			0.331651i
$806$	−0.139410	−	2.42405i	−0.00491051	−	0.0853835i
$807$		0			0
$808$	3.08738	+	17.7364i	0.108614	+	0.623963i
$809$		−	26.3429i		−	0.926167i	−0.886315	−	0.463084i	$-0.846743\pi$
$809$		−	26.3429i		−	0.926167i	0.886315	−	0.463084i	$-0.153257\pi$
$810$		0			0
$811$	2.96401			0.104080			0.0520402	−	0.998645i	$-0.483428\pi$
$811$	2.96401			0.104080			0.0520402	+	0.998645i	$0.483428\pi$
$812$	−2.43769	−	21.1231i	−0.0855463	−	0.741276i
$813$		0			0
$814$	1.09748	+	19.0829i	0.0384668	+	0.668857i
$815$	16.4573			0.576475
$816$		0			0
$817$	−35.4638			−1.24072
$818$	−2.71276	−	47.1693i	−0.0948496	−	1.64924i
$819$		0			0
$820$	−0.579824	−	5.02429i	−0.0202483	−	0.175456i
$821$	10.3996			0.362949			0.181475	−	0.983396i	$-0.441913\pi$
$821$	10.3996			0.362949			0.181475	+	0.983396i	$0.441913\pi$
$822$		0			0
$823$		−	39.8598i		−	1.38942i	−0.719288	−	0.694712i	$-0.755532\pi$
$823$		−	39.8598i		−	1.38942i	0.719288	−	0.694712i	$-0.244468\pi$
$824$	−32.4790	+	5.65364i	−1.13146	+	0.196954i
$825$		0			0
$826$	−0.589326	−	10.2471i	−0.0205053	−	0.356544i
$827$			27.5060i			0.956477i	0.878230	+	0.478239i	$0.158725\pi$
$827$			27.5060i			0.956477i	−0.878230	+	0.478239i	$0.841275\pi$
$828$		0			0
$829$			38.0086i			1.32009i	0.751225	+	0.660047i	$0.229464\pi$
$829$			38.0086i			1.32009i	−0.751225	+	0.660047i	$0.770536\pi$
$830$	−16.4561	+	0.946410i	−0.571199	+	0.0328504i
$831$		0			0
$832$	0.604665	+	1.68421i	0.0209630	+	0.0583894i
$833$			0.397844i			0.0137845i
$834$		0			0
$835$	−1.99106			−0.0689034
$836$	−3.03616	−	26.3089i	−0.105008	−	0.909913i
$837$		0			0
$838$	8.91684	−	0.512819i	0.308027	−	0.0177150i
$839$	30.9037			1.06691			0.533457	−	0.845827i	$-0.320893\pi$
$839$	30.9037			1.06691			0.533457	+	0.845827i	$0.320893\pi$
$840$		0			0
$841$	84.0320			2.89765
$842$	15.0671	−	0.866526i	0.519246	−	0.0298625i
$843$		0			0
$844$	17.9627	−	2.07297i	0.618302	−	0.0713546i
$845$	16.5526			0.569425
$846$		0			0
$847$		−	2.88586i		−	0.0991592i
$848$	1.15041	−	0.269108i	0.0395052	−	0.00924120i
$849$		0			0
$850$	−1.89083	+	0.108744i	−0.0648551	+	0.00372989i
$851$		−	34.9308i		−	1.19741i
$852$		0			0
$853$		−	25.3302i		−	0.867290i	−0.901084	−	0.433645i	$-0.857227\pi$
$853$		−	25.3302i		−	0.867290i	0.901084	−	0.433645i	$-0.142773\pi$
$854$	−0.767812	−	13.3506i	−0.0262740	−	0.456849i
$855$		0			0
$856$	25.1178	−	4.37228i	0.858509	−	0.149441i
$857$			39.1574i			1.33759i	0.743447	+	0.668795i	$0.233190\pi$
$857$			39.1574i			1.33759i	−0.743447	+	0.668795i	$0.766810\pi$
$858$		0			0
$859$	11.2783			0.384810			0.192405	−	0.981316i	$-0.438371\pi$
$859$	11.2783			0.384810			0.192405	+	0.981316i	$0.438371\pi$
$860$	−19.3738	+	2.23582i	−0.660641	+	0.0762407i
$861$		0			0
$862$	2.91249	+	50.6422i	0.0992000	+	1.72488i
$863$	−15.6543			−0.532878			−0.266439	−	0.963852i	$-0.585847\pi$
$863$	−15.6543			−0.532878			−0.266439	+	0.963852i	$0.585847\pi$
$864$		0			0
$865$	−3.33037			−0.113236
$866$	0.360449	+	6.26745i	0.0122485	+	0.212976i
$867$		0			0
$868$	15.2499	−	1.75991i	0.517617	−	0.0597351i
$869$	−14.8732			−0.504539
$870$		0			0
$871$			0.788081i			0.0267031i
$872$	15.1923	−	2.64454i	0.514476	−	0.0895553i
$873$		0			0
$874$	2.77880	+	48.3175i	0.0939943	+	1.63436i
$875$			10.6936i			0.361511i
$876$		0			0
$877$		−	14.6357i		−	0.494211i	−0.968989	−	0.247106i	$-0.920521\pi$
$877$		−	14.6357i		−	0.494211i	0.968989	−	0.247106i	$-0.0794795\pi$
$878$	26.5348	−	1.52605i	0.895506	−	0.0515016i
$879$		0			0
$880$	−3.31729	−	14.1811i	−0.111826	−	0.478044i
$881$			21.9054i			0.738013i	0.929427	+	0.369007i	$0.120302\pi$
$881$			21.9054i			0.738013i	−0.929427	+	0.369007i	$0.879698\pi$
$882$		0			0
$883$	−36.3852			−1.22446			−0.612230	−	0.790680i	$-0.709727\pi$
$883$	−36.3852			−1.22446			−0.612230	+	0.790680i	$0.709727\pi$
$884$	0.176808	−	0.0204044i	0.00594670	−	0.000686274i
$885$		0			0
$886$	43.7160	−	2.51416i	1.46867	−	0.0844649i
$887$	−10.3554			−0.347700			−0.173850	−	0.984772i	$-0.555621\pi$
$887$	−10.3554			−0.347700			−0.173850	+	0.984772i	$0.555621\pi$
$888$		0			0
$889$	−9.48046			−0.317964
$890$	−16.1496	+	0.928785i	−0.541337	+	0.0311330i
$891$		0			0
$892$	2.34622	+	20.3304i	0.0785571	+	0.680713i
$893$	51.4715			1.72243
$894$		0			0
$895$		−	24.1953i		−	0.808759i
$896$	−10.4112	+	4.42801i	−0.347813	+	0.147929i
$897$		0			0
$898$	−34.8373	+	2.00354i	−1.16254	+	0.0668589i
$899$			81.6040i			2.72165i
$900$		0			0
$901$		−	0.117510i		−	0.00391481i
$902$	0.457608	+	7.95684i	0.0152367	+	0.264934i
$903$		0			0
$904$	−19.5121	+	3.39648i	−0.648962	+	0.112965i
$905$			20.0438i			0.666278i
$906$		0			0
$907$	10.5615			0.350689			0.175344	−	0.984507i	$-0.443896\pi$
$907$	10.5615			0.350689			0.175344	+	0.984507i	$0.443896\pi$
$908$	−2.52185	−	21.8523i	−0.0836904	−	0.725194i
$909$		0			0
$910$	−0.0232156	−	0.403671i	−0.000769590	−	0.0133816i
$911$	−18.4732			−0.612044			−0.306022	−	0.952024i	$-0.598998\pi$
$911$	−18.4732			−0.612044			−0.306022	+	0.952024i	$0.598998\pi$
$912$		0			0
$913$	25.9749			0.859643
$914$	1.08738	+	18.9072i	0.0359673	+	0.625395i
$915$		0			0
$916$	−5.54845	−	48.0784i	−0.183326	−	1.58856i
$917$	−6.34169			−0.209421
$918$		0			0
$919$		−	27.7252i		−	0.914569i	−0.889320	−	0.457285i	$-0.848822\pi$
$919$		−	27.7252i		−	0.914569i	0.889320	−	0.457285i	$-0.151178\pi$
$920$	4.56423	+	26.2205i	0.150478	+	0.864466i
$921$		0			0
$922$	−1.00553	−	17.4841i	−0.0331154	−	0.575807i
$923$		−	1.87381i		−	0.0616773i
$924$		0			0
$925$		−	15.9723i		−	0.525167i
$926$	4.72566	−	0.271779i	0.155295	−	0.00893120i
$927$		0			0
$928$	−17.0385	−	57.6777i	−0.559317	−	1.89336i
$929$		−	57.6318i		−	1.89084i	−0.325858	−	0.945419i	$-0.605653\pi$
$929$		−	57.6318i		−	1.89084i	0.325858	−	0.945419i	$-0.394347\pi$
$930$		0			0
$931$	4.64862			0.152353
$932$	4.93992	+	42.8054i	0.161813	+	1.40214i
$933$		0			0
$934$	−4.30734	+	0.247720i	−0.140940	+	0.00810565i
$935$	−1.44854			−0.0473723
$936$		0			0
$937$	−44.9081			−1.46708			−0.733542	−	0.679644i	$-0.762134\pi$
$937$	−44.9081			−1.46708			−0.733542	+	0.679644i	$0.762134\pi$
$938$	−4.97435	+	0.286081i	−0.162418	+	0.00934087i
$939$		0			0
$940$	28.1187	−	3.24502i	0.917132	−	0.105841i
$941$	−25.0167			−0.815521			−0.407761	−	0.913089i	$-0.633690\pi$
$941$	−25.0167			−0.815521			−0.407761	+	0.913089i	$0.633690\pi$
$942$		0			0
$943$		−	14.5648i		−	0.474294i
$944$	−6.61257	−	28.2681i	−0.215221	−	0.920047i
$945$		0			0
$946$	30.6817	−	1.76455i	0.997550	−	0.0573703i
$947$		−	39.7909i		−	1.29303i	−0.762901	−	0.646516i	$-0.776225\pi$
$947$		−	39.7909i		−	1.29303i	0.762901	−	0.646516i	$-0.223775\pi$
$948$		0			0
$949$		−	2.38678i		−	0.0774782i
$950$	1.27063	+	22.0935i	0.0412246	+	0.716809i
$951$		0			0
$952$	0.192975	+	1.10860i	0.00625436	+	0.0359300i
$953$			12.4544i			0.403437i	0.979444	+	0.201718i	$0.0646526\pi$
$953$			12.4544i			0.403437i	−0.979444	+	0.201718i	$0.935347\pi$
$954$		0			0
$955$	−4.94518			−0.160022
$956$	40.8703	−	4.71661i	1.32184	−	0.152546i
$957$		0			0
$958$	−1.66405	−	28.9343i	−0.0537629	−	0.934824i
$959$	−11.3108			−0.365246
$960$		0			0
$961$	−27.9145			−0.900466
$962$	0.0861806	+	1.49850i	0.00277857	+	0.0483136i
$963$		0			0
$964$	22.0219	−	2.54142i	0.709277	−	0.0818535i
$965$	−15.4740			−0.498125
$966$		0			0
$967$			6.97106i			0.224174i	0.993698	+	0.112087i	$0.0357536\pi$
$967$			6.97106i			0.224174i	−0.993698	+	0.112087i	$0.964246\pi$
$968$	−1.39979	−	8.04151i	−0.0449910	−	0.258464i
$969$		0			0
$970$	0.0236718	+	0.411602i	0.000760055	+	0.0132158i
$971$		−	9.18374i		−	0.294720i	−0.989083	−	0.147360i	$-0.952922\pi$
$971$		−	9.18374i		−	0.294720i	0.989083	−	0.147360i	$-0.0470776\pi$
$972$		0			0
$973$		−	21.7583i		−	0.697539i
$974$	30.9464	−	1.77977i	0.991587	−	0.0570274i
$975$		0			0
$976$	−8.61529	−	36.8295i	−0.275769	−	1.17888i
$977$		−	39.1316i		−	1.25193i	−0.779851	−	0.625965i	$-0.784705\pi$
$977$		−	39.1316i		−	1.25193i	0.779851	−	0.625965i	$-0.215295\pi$
$978$		0			0
$979$	25.4912			0.814701
$980$	2.53953	−	0.293073i	0.0811224	−	0.00936186i
$981$		0			0
$982$	−14.5254	+	0.835376i	−0.463525	+	0.0266579i
$983$	50.4121			1.60790			0.803948	−	0.594700i	$-0.202729\pi$
$983$	50.4121			1.60790			0.803948	+	0.594700i	$0.202729\pi$
$984$		0			0
$985$	6.64735			0.211802
$986$	−5.97188	+	0.343450i	−0.190183	+	0.0109377i
$987$		0			0
$988$	−0.238416	−	2.06592i	−0.00758503	−	0.0657258i
$989$	−56.1620			−1.78585
$990$		0			0
$991$			55.9071i			1.77595i	0.459894	+	0.887974i	$0.347887\pi$
$991$			55.9071i			1.77595i	−0.459894	+	0.887974i	$0.652113\pi$
$992$	41.6407	−	12.3010i	1.32209	−	0.390558i
$993$		0			0
$994$	11.8275	−	0.680212i	0.375144	−	0.0215750i
$995$			19.8158i			0.628204i
$996$		0			0
$997$		−	11.6669i		−	0.369494i	−0.982786	−	0.184747i	$-0.940853\pi$
$997$		−	11.6669i		−	0.369494i	0.982786	−	0.184747i	$-0.0591466\pi$
$998$	−0.152598	−	2.65336i	−0.00483040	−	0.0839906i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.26	yes	48
3.2	odd	2	inner	1512.2.j.d.323.23	✓	48
4.3	odd	2		6048.2.j.d.5615.33		48
8.3	odd	2	inner	1512.2.j.d.323.24	yes	48
8.5	even	2		6048.2.j.d.5615.15		48
12.11	even	2		6048.2.j.d.5615.16		48
24.5	odd	2		6048.2.j.d.5615.34		48
24.11	even	2	inner	1512.2.j.d.323.25	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.23	✓	48	3.2	odd	2	inner
1512.2.j.d.323.24	yes	48	8.3	odd	2	inner
1512.2.j.d.323.25	yes	48	24.11	even	2	inner
1512.2.j.d.323.26	yes	48	1.1	even	1	trivial
6048.2.j.d.5615.15		48	8.5	even	2
6048.2.j.d.5615.16		48	12.11	even	2
6048.2.j.d.5615.33		48	4.3	odd	2
6048.2.j.d.5615.34		48	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0811990 + 1.41188i) q^{2} +(-1.98681 + 0.229287i) q^{4} +1.27819 q^{5} -1.00000i q^{7} +(-0.485052 - 2.78653i) q^{8} +O(q^{10})\)	\(q+(0.0811990 + 1.41188i) q^{2} +(-1.98681 + 0.229287i) q^{4} +1.27819 q^{5} -1.00000i q^{7} +(-0.485052 - 2.78653i) q^{8} +(0.103788 + 1.80466i) q^{10} -2.84853i q^{11} -0.223683i q^{13} +(1.41188 - 0.0811990i) q^{14} +(3.89486 - 0.911099i) q^{16} -0.397844i q^{17} -4.64862 q^{19} +(-2.53953 + 0.293073i) q^{20} +(4.02179 - 0.231298i) q^{22} -7.36177 q^{23} -3.36622 q^{25} +(0.315814 - 0.0181628i) q^{26} +(0.229287 + 1.98681i) q^{28} -10.6317 q^{29} -7.67558i q^{31} +(1.60262 + 5.42509i) q^{32} +(0.561708 - 0.0323045i) q^{34} -1.27819i q^{35} +4.74489i q^{37} +(-0.377464 - 6.56330i) q^{38} +(-0.619991 - 3.56172i) q^{40} +1.97843i q^{41} +7.62888 q^{43} +(0.653130 + 5.65950i) q^{44} +(-0.597768 - 10.3939i) q^{46} -11.0724 q^{47} -1.00000 q^{49} +(-0.273334 - 4.75270i) q^{50} +(0.0512875 + 0.444416i) q^{52} +0.295366 q^{53} -3.64098i q^{55} +(-2.78653 + 0.485052i) q^{56} +(-0.863279 - 15.0106i) q^{58} -7.25779i q^{59} -9.45592i q^{61} +(10.8370 - 0.623249i) q^{62} +(-7.52945 + 2.70322i) q^{64} -0.285910i q^{65} -3.52321 q^{67} +(0.0912202 + 0.790441i) q^{68} +(1.80466 - 0.103788i) q^{70} +8.37710 q^{71} +10.6704 q^{73} +(-6.69921 + 0.385280i) q^{74} +(9.23595 - 1.06587i) q^{76} -2.84853 q^{77} -5.22135i q^{79} +(4.97838 - 1.16456i) q^{80} +(-2.79331 + 0.160647i) q^{82} +9.11868i q^{83} -0.508521i q^{85} +(0.619457 + 10.7711i) q^{86} +(-7.93751 + 1.38169i) q^{88} +8.94887i q^{89} -0.223683 q^{91} +(14.6265 - 1.68795i) q^{92} +(-0.899068 - 15.6329i) q^{94} -5.94184 q^{95} +0.228078 q^{97} +(-0.0811990 - 1.41188i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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