LMFDB - Embedded newform 1512.2.j.c.323.15

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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.15
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.154052 - 1.40580i) q^{2} +(-1.95254 + 0.433131i) q^{4} -0.162025 q^{5} -1.00000i q^{7} +(0.909686 + 2.67815i) q^{8} +O(q^{10})$	\(q+(-0.154052 - 1.40580i) q^{2} +(-1.95254 + 0.433131i) q^{4} -0.162025 q^{5} -1.00000i q^{7} +(0.909686 + 2.67815i) q^{8} +(0.0249602 + 0.227774i) q^{10} -2.40352i q^{11} +4.76784i q^{13} +(-1.40580 + 0.154052i) q^{14} +(3.62480 - 1.69141i) q^{16} +2.74335i q^{17} -1.86073 q^{19} +(0.316360 - 0.0701781i) q^{20} +(-3.37887 + 0.370267i) q^{22} +1.32970 q^{23} -4.97375 q^{25} +(6.70262 - 0.734494i) q^{26} +(0.433131 + 1.95254i) q^{28} -3.96112 q^{29} +8.01692i q^{31} +(-2.93618 - 4.83517i) q^{32} +(3.85659 - 0.422617i) q^{34} +0.162025i q^{35} +6.09436i q^{37} +(0.286648 + 2.61581i) q^{38} +(-0.147392 - 0.433927i) q^{40} +3.16889i q^{41} -1.70927 q^{43} +(1.04104 + 4.69296i) q^{44} +(-0.204843 - 1.86929i) q^{46} +12.1502 q^{47} -1.00000 q^{49} +(0.766214 + 6.99208i) q^{50} +(-2.06510 - 9.30938i) q^{52} +8.22731 q^{53} +0.389431i q^{55} +(2.67815 - 0.909686i) q^{56} +(0.610217 + 5.56853i) q^{58} -5.45449i q^{59} +4.28553i q^{61} +(11.2702 - 1.23502i) q^{62} +(-6.34494 + 4.87255i) q^{64} -0.772509i q^{65} -4.61226 q^{67} +(-1.18823 - 5.35648i) q^{68} +(0.227774 - 0.0249602i) q^{70} +13.9767 q^{71} -6.37815 q^{73} +(8.56744 - 0.938846i) q^{74} +(3.63314 - 0.805940i) q^{76} -2.40352 q^{77} +9.75258i q^{79} +(-0.587307 + 0.274050i) q^{80} +(4.45482 - 0.488173i) q^{82} +16.4983i q^{83} -0.444491i q^{85} +(0.263316 + 2.40289i) q^{86} +(6.43699 - 2.18645i) q^{88} -2.35048i q^{89} +4.76784 q^{91} +(-2.59629 + 0.575935i) q^{92} +(-1.87176 - 17.0807i) q^{94} +0.301485 q^{95} +14.4569 q^{97} +(0.154052 + 1.40580i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

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 $

$2$	−0.154052	−	1.40580i	−0.108931	−	0.994049i
$2$	−0.154052	−	1.40580i	−0.108931	−	0.994049i
$3$		0			0
$3$		0			0
$4$	−1.95254	+	0.433131i	−0.976268	+	0.216566i
$5$	−0.162025			−0.0724598			−0.0362299	−	0.999343i	$-0.511535\pi$
$5$	−0.162025			−0.0724598			−0.0362299	+	0.999343i	$0.511535\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.909686	+	2.67815i	0.321623	+	0.946868i
$9$		0			0
$10$	0.0249602	+	0.227774i	0.00789311	+	0.0720286i
$11$		−	2.40352i		−	0.724689i	−0.932044	−	0.362345i	$-0.881976\pi$
$11$		−	2.40352i		−	0.724689i	0.932044	−	0.362345i	$-0.118024\pi$
$12$		0			0
$13$			4.76784i			1.32236i	0.750227	+	0.661181i	$0.229944\pi$
$13$			4.76784i			1.32236i	−0.750227	+	0.661181i	$0.770056\pi$
$14$	−1.40580	+	0.154052i	−0.375715	+	0.0411720i
$15$		0			0
$16$	3.62480	−	1.69141i	0.906199	−	0.422852i
$17$			2.74335i			0.665359i	0.943040	+	0.332680i	$0.107953\pi$
$17$			2.74335i			0.665359i	−0.943040	+	0.332680i	$0.892047\pi$
$18$		0			0
$19$	−1.86073			−0.426881			−0.213440	−	0.976956i	$-0.568467\pi$
$19$	−1.86073			−0.426881			−0.213440	+	0.976956i	$0.568467\pi$
$20$	0.316360	−	0.0701781i	0.0707402	−	0.0156923i
$21$		0			0
$22$	−3.37887	+	0.370267i	−0.720377	+	0.0789411i
$23$	1.32970			0.277262			0.138631	−	0.990344i	$-0.455730\pi$
$23$	1.32970			0.277262			0.138631	+	0.990344i	$0.455730\pi$
$24$		0			0
$25$	−4.97375			−0.994750
$26$	6.70262	−	0.734494i	1.31449	−	0.144046i
$27$		0			0
$28$	0.433131	+	1.95254i	0.0818541	+	0.368995i
$29$	−3.96112			−0.735561			−0.367780	−	0.929913i	$-0.619882\pi$
$29$	−3.96112			−0.735561			−0.367780	+	0.929913i	$0.619882\pi$
$30$		0			0
$31$			8.01692i			1.43988i	0.694036	+	0.719941i	$0.255831\pi$
$31$			8.01692i			1.43988i	−0.694036	+	0.719941i	$0.744169\pi$
$32$	−2.93618	−	4.83517i	−0.519049	−	0.854745i
$33$		0			0
$34$	3.85659	−	0.422617i	0.661400	−	0.0724782i
$35$			0.162025i			0.0273872i
$36$		0			0
$37$			6.09436i			1.00191i	0.865474	+	0.500953i	$0.167017\pi$
$37$			6.09436i			1.00191i	−0.865474	+	0.500953i	$0.832983\pi$
$38$	0.286648	+	2.61581i	0.0465005	+	0.424340i
$39$		0			0
$40$	−0.147392	−	0.433927i	−0.0233047	−	0.0686098i
$41$			3.16889i			0.494898i	0.968901	+	0.247449i	$0.0795922\pi$
$41$			3.16889i			0.494898i	−0.968901	+	0.247449i	$0.920408\pi$
$42$		0			0
$43$	−1.70927			−0.260662			−0.130331	−	0.991471i	$-0.541604\pi$
$43$	−1.70927			−0.260662			−0.130331	+	0.991471i	$0.541604\pi$
$44$	1.04104	+	4.69296i	0.156943	+	0.707491i
$45$		0			0
$46$	−0.204843	−	1.86929i	−0.0302024	−	0.275612i
$47$	12.1502			1.77229			0.886144	−	0.463410i	$-0.153374\pi$
$47$	12.1502			1.77229			0.886144	+	0.463410i	$0.153374\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.766214	+	6.99208i	0.108359	+	0.988830i
$51$		0			0
$52$	−2.06510	−	9.30938i	−0.286378	−	1.29098i
$53$	8.22731			1.13011			0.565054	−	0.825054i	$-0.308855\pi$
$53$	8.22731			1.13011			0.565054	+	0.825054i	$0.308855\pi$
$54$		0			0
$55$			0.389431i			0.0525108i
$56$	2.67815	−	0.909686i	0.357882	−	0.121562i
$57$		0			0
$58$	0.610217	+	5.56853i	0.0801254	+	0.731184i
$59$		−	5.45449i		−	0.710114i	−0.934845	−	0.355057i	$-0.884461\pi$
$59$		−	5.45449i		−	0.710114i	0.934845	−	0.355057i	$-0.115539\pi$
$60$		0			0
$61$			4.28553i			0.548706i	0.961629	+	0.274353i	$0.0884636\pi$
$61$			4.28553i			0.548706i	−0.961629	+	0.274353i	$0.911536\pi$
$62$	11.2702	−	1.23502i	1.43131	−	0.156848i
$63$		0			0
$64$	−6.34494	+	4.87255i	−0.793118	+	0.609068i
$65$		−	0.772509i		−	0.0958180i
$66$		0			0
$67$	−4.61226			−0.563477			−0.281738	−	0.959491i	$-0.590911\pi$
$67$	−4.61226			−0.563477			−0.281738	+	0.959491i	$0.590911\pi$
$68$	−1.18823	−	5.35648i	−0.144094	−	0.649569i
$69$		0			0
$70$	0.227774	−	0.0249602i	0.0272242	−	0.00298332i
$71$	13.9767			1.65873			0.829363	−	0.558710i	$-0.188703\pi$
$71$	13.9767			1.65873			0.829363	+	0.558710i	$0.188703\pi$
$72$		0			0
$73$	−6.37815			−0.746506			−0.373253	−	0.927730i	$-0.621758\pi$
$73$	−6.37815			−0.746506			−0.373253	+	0.927730i	$0.621758\pi$
$74$	8.56744	−	0.938846i	0.995944	−	0.109139i
$75$		0			0
$76$	3.63314	−	0.805940i	0.416750	−	0.0924476i
$77$	−2.40352			−0.273907
$78$		0			0
$79$			9.75258i			1.09725i	0.836068	+	0.548625i	$0.184849\pi$
$79$			9.75258i			1.09725i	−0.836068	+	0.548625i	$0.815151\pi$
$80$	−0.587307	+	0.274050i	−0.0656630	+	0.0306398i
$81$		0			0
$82$	4.45482	−	0.488173i	0.491953	−	0.0539097i
$83$			16.4983i			1.81093i	0.424426	+	0.905463i	$0.360476\pi$
$83$			16.4983i			1.81093i	−0.424426	+	0.905463i	$0.639524\pi$
$84$		0			0
$85$		−	0.444491i		−	0.0482118i
$86$	0.263316	+	2.40289i	0.0283941	+	0.259111i
$87$		0			0
$88$	6.43699	−	2.18645i	0.686185	−	0.233076i
$89$		−	2.35048i		−	0.249150i	−0.992210	−	0.124575i	$-0.960243\pi$
$89$		−	2.35048i		−	0.249150i	0.992210	−	0.124575i	$-0.0397567\pi$
$90$		0			0
$91$	4.76784			0.499806
$92$	−2.59629	+	0.575935i	−0.270682	+	0.0600454i
$93$		0			0
$94$	−1.87176	−	17.0807i	−0.193057	−	1.76174i
$95$	0.301485			0.0309317
$96$		0			0
$97$	14.4569			1.46788			0.733938	−	0.679217i	$-0.237680\pi$
$97$	14.4569			1.46788			0.733938	+	0.679217i	$0.237680\pi$
$98$	0.154052	+	1.40580i	0.0155616	+	0.142007i
$99$		0			0
$100$	9.71142	−	2.15428i	0.971142	−	0.215428i
$101$	−0.453215			−0.0450966			−0.0225483	−	0.999746i	$-0.507178\pi$
$101$	−0.453215			−0.0450966			−0.0225483	+	0.999746i	$0.507178\pi$
$102$		0			0
$103$			8.93542i			0.880434i	0.897892	+	0.440217i	$0.145098\pi$
$103$			8.93542i			0.880434i	−0.897892	+	0.440217i	$0.854902\pi$
$104$	−12.7690	+	4.33724i	−1.25210	+	0.425301i
$105$		0			0
$106$	−1.26743	−	11.5659i	−0.123104	−	1.12338i
$107$			14.9379i			1.44411i	0.691838	+	0.722053i	$0.256801\pi$
$107$			14.9379i			1.44411i	−0.691838	+	0.722053i	$0.743199\pi$
$108$		0			0
$109$		−	4.33798i		−	0.415503i	−0.978182	−	0.207751i	$-0.933385\pi$
$109$		−	4.33798i		−	0.415503i	0.978182	−	0.207751i	$-0.0666145\pi$
$110$	0.547461	−	0.0599924i	0.0521983	−	0.00572005i
$111$		0			0
$112$	−1.69141	−	3.62480i	−0.159823	−	0.342511i
$113$		−	0.451095i		−	0.0424354i	−0.999775	−	0.0212177i	$-0.993246\pi$
$113$		−	0.451095i		−	0.0424354i	0.999775	−	0.0212177i	$-0.00675431\pi$
$114$		0			0
$115$	−0.215445			−0.0200903
$116$	7.73422	−	1.71568i	0.718105	−	0.159297i
$117$		0			0
$118$	−7.66791	+	0.840273i	−0.705888	+	0.0773534i
$119$	2.74335			0.251482
$120$		0			0
$121$	5.22308			0.474826
$122$	6.02459	−	0.660193i	0.545440	−	0.0597710i
$123$		0			0
$124$	−3.47238	−	15.6533i	−0.311829	−	1.40571i
$125$	1.61600			0.144539
$126$		0			0
$127$		−	0.196751i		−	0.0174589i	−0.999962	−	0.00872943i	$-0.997221\pi$
$127$		−	0.196751i		−	0.0174589i	0.999962	−	0.00872943i	$-0.00277870\pi$
$128$	7.82727	+	8.16908i	0.691839	+	0.722052i
$129$		0			0
$130$	−1.08599	+	0.119006i	−0.0952478	+	0.0104375i
$131$		−	4.69097i		−	0.409852i	−0.978778	−	0.204926i	$-0.934305\pi$
$131$		−	4.69097i		−	0.409852i	0.978778	−	0.204926i	$-0.0656953\pi$
$132$		0			0
$133$			1.86073i			0.161346i
$134$	0.710526	+	6.48390i	0.0613801	+	0.560124i
$135$		0			0
$136$	−7.34708	+	2.49558i	−0.630007	+	0.213995i
$137$		−	11.1485i		−	0.952479i	−0.879316	−	0.476240i	$-0.841999\pi$
$137$		−	11.1485i		−	0.952479i	0.879316	−	0.476240i	$-0.158001\pi$
$138$		0			0
$139$	6.93228			0.587988			0.293994	−	0.955807i	$-0.405015\pi$
$139$	6.93228			0.587988			0.293994	+	0.955807i	$0.405015\pi$
$140$	−0.0701781	−	0.316360i	−0.00593113	−	0.0267373i
$141$		0			0
$142$	−2.15313	−	19.6484i	−0.180687	−	1.64886i
$143$	11.4596			0.958301
$144$		0			0
$145$	0.641800			0.0532986
$146$	0.982564	+	8.96639i	0.0813176	+	0.742064i
$147$		0			0
$148$	−2.63966	−	11.8995i	−0.216978	−	0.978129i
$149$	−16.2542			−1.33160			−0.665799	−	0.746132i	$-0.731909\pi$
$149$	−16.2542			−1.33160			−0.665799	+	0.746132i	$0.731909\pi$
$150$		0			0
$151$			0.426011i			0.0346683i	0.999850	+	0.0173341i	$0.00551791\pi$
$151$			0.426011i			0.0346683i	−0.999850	+	0.0173341i	$0.994482\pi$
$152$	−1.69268	−	4.98331i	−0.137294	−	0.404200i
$153$		0			0
$154$	0.370267	+	3.37887i	0.0298369	+	0.272277i
$155$		−	1.29894i		−	0.104333i
$156$		0			0
$157$			14.0451i			1.12092i	0.828180	+	0.560462i	$0.189376\pi$
$157$			14.0451i			1.12092i	−0.828180	+	0.560462i	$0.810624\pi$
$158$	13.7102	−	1.50240i	1.09072	−	0.119525i
$159$		0			0
$160$	0.475735	+	0.783418i	0.0376102	+	0.0619346i
$161$		−	1.32970i		−	0.104795i
$162$		0			0
$163$	−4.72962			−0.370453			−0.185226	−	0.982696i	$-0.559302\pi$
$163$	−4.72962			−0.370453			−0.185226	+	0.982696i	$0.559302\pi$
$164$	−1.37255	−	6.18737i	−0.107178	−	0.483153i
$165$		0			0
$166$	23.1933	−	2.54159i	1.80015	−	0.197266i
$167$	−11.7344			−0.908036			−0.454018	−	0.890993i	$-0.650010\pi$
$167$	−11.7344			−0.908036			−0.454018	+	0.890993i	$0.650010\pi$
$168$		0			0
$169$	−9.73231			−0.748639
$170$	−0.624864	+	0.0684745i	−0.0479249	+	0.00525175i
$171$		0			0
$172$	3.33742	−	0.740339i	0.254476	−	0.0564503i
$173$	−18.2577			−1.38810			−0.694052	−	0.719925i	$-0.744176\pi$
$173$	−18.2577			−1.38810			−0.694052	+	0.719925i	$0.744176\pi$
$174$		0			0
$175$			4.97375i			0.375980i
$176$	−4.06534	−	8.71227i	−0.306436	−	0.656712i
$177$		0			0
$178$	−3.30430	+	0.362095i	−0.247667	+	0.0271402i
$179$		−	14.5950i		−	1.09088i	−0.838148	−	0.545442i	$-0.816362\pi$
$179$		−	14.5950i		−	1.09088i	0.838148	−	0.545442i	$-0.183638\pi$
$180$		0			0
$181$		−	3.82026i		−	0.283958i	−0.989870	−	0.141979i	$-0.954653\pi$
$181$		−	3.82026i		−	0.283958i	0.989870	−	0.141979i	$-0.0453465\pi$
$182$	−0.734494	−	6.70262i	−0.0544443	−	0.496831i
$183$		0			0
$184$	1.20961	+	3.56114i	0.0891738	+	0.262531i
$185$		−	0.987438i		−	0.0725979i
$186$		0			0
$187$	6.59369			0.482178
$188$	−23.7237	+	5.26263i	−1.73023	+	0.383816i
$189$		0			0
$190$	−0.0464442	−	0.423827i	−0.00336942	−	0.0307476i
$191$	21.4447			1.55168			0.775840	−	0.630929i	$-0.217326\pi$
$191$	21.4447			1.55168			0.775840	+	0.630929i	$0.217326\pi$
$192$		0			0
$193$	−17.5991			−1.26681			−0.633407	−	0.773819i	$-0.718344\pi$
$193$	−17.5991			−1.26681			−0.633407	+	0.773819i	$0.718344\pi$
$194$	−2.22711	−	20.3235i	−0.159897	−	1.45914i
$195$		0			0
$196$	1.95254	−	0.433131i	0.139467	−	0.0309379i
$197$	−19.1329			−1.36316			−0.681581	−	0.731743i	$-0.738707\pi$
$197$	−19.1329			−1.36316			−0.681581	+	0.731743i	$0.738707\pi$
$198$		0			0
$199$		−	13.3125i		−	0.943699i	−0.881679	−	0.471850i	$-0.843586\pi$
$199$		−	13.3125i		−	0.943699i	0.881679	−	0.471850i	$-0.156414\pi$
$200$	−4.52455	−	13.3204i	−0.319934	−	0.941896i
$201$		0			0
$202$	0.0698185	+	0.637128i	0.00491241	+	0.0448282i
$203$			3.96112i			0.278016i
$204$		0			0
$205$		−	0.513440i		−	0.0358602i
$206$	12.5614	−	1.37652i	0.875194	−	0.0959065i
$207$		0			0
$208$	8.06436	+	17.2824i	0.559163	+	1.19832i
$209$			4.47230i			0.309356i
$210$		0			0
$211$	−23.9337			−1.64766			−0.823830	−	0.566836i	$-0.808167\pi$
$211$	−23.9337			−1.64766			−0.823830	+	0.566836i	$0.808167\pi$
$212$	−16.0641	+	3.56350i	−1.10329	+	0.244742i
$213$		0			0
$214$	20.9997	−	2.30122i	1.43551	−	0.157308i
$215$	0.276945			0.0188875
$216$		0			0
$217$	8.01692			0.544224
$218$	−6.09832	+	0.668273i	−0.413030	+	0.0452611i
$219$		0			0
$220$	−0.168674	−	0.760377i	−0.0113720	−	0.0512646i
$221$	−13.0798			−0.879845
$222$		0			0
$223$			13.9928i			0.937024i	0.883457	+	0.468512i	$0.155210\pi$
$223$			13.9928i			0.937024i	−0.883457	+	0.468512i	$0.844790\pi$
$224$	−4.83517	+	2.93618i	−0.323063	+	0.196182i
$225$		0			0
$226$	−0.634148	+	0.0694919i	−0.0421829	+	0.00462253i
$227$		−	10.8975i		−	0.723292i	−0.932316	−	0.361646i	$-0.882215\pi$
$227$		−	10.8975i		−	0.723292i	0.932316	−	0.361646i	$-0.117785\pi$
$228$		0			0
$229$			11.1299i			0.735485i	0.929928	+	0.367743i	$0.119869\pi$
$229$			11.1299i			0.735485i	−0.929928	+	0.367743i	$0.880131\pi$
$230$	0.0331897	+	0.302872i	0.00218846	+	0.0199708i
$231$		0			0
$232$	−3.60337	−	10.6085i	−0.236573	−	0.696479i
$233$			13.7778i			0.902613i	0.892369	+	0.451307i	$0.149042\pi$
$233$			13.7778i			0.902613i	−0.892369	+	0.451307i	$0.850958\pi$
$234$		0			0
$235$	−1.96863			−0.128420
$236$	2.36251	+	10.6501i	0.153786	+	0.693261i
$237$		0			0
$238$	−0.422617	−	3.85659i	−0.0273942	−	0.249986i
$239$	−7.99259			−0.516998			−0.258499	−	0.966012i	$-0.583228\pi$
$239$	−7.99259			−0.516998			−0.258499	+	0.966012i	$0.583228\pi$
$240$		0			0
$241$	−5.18318			−0.333878			−0.166939	−	0.985967i	$-0.553388\pi$
$241$	−5.18318			−0.333878			−0.166939	+	0.985967i	$0.553388\pi$
$242$	−0.804624	−	7.34260i	−0.0517232	−	0.472000i
$243$		0			0
$244$	−1.85620	−	8.36765i	−0.118831	−	0.535684i
$245$	0.162025			0.0103514
$246$		0			0
$247$		−	8.87166i		−	0.564490i
$248$	−21.4705	+	7.29288i	−1.36338	+	0.463098i
$249$		0			0
$250$	−0.248947	−	2.27176i	−0.0157448	−	0.143679i
$251$		−	7.88280i		−	0.497558i	−0.968560	−	0.248779i	$-0.919971\pi$
$251$		−	7.88280i		−	0.497558i	0.968560	−	0.248779i	$-0.0800293\pi$
$252$		0			0
$253$		−	3.19597i		−	0.200929i
$254$	−0.276593	+	0.0303099i	−0.0173550	+	0.00190181i
$255$		0			0
$256$	10.2783	−	12.2620i	0.642392	−	0.766376i
$257$		−	28.1394i		−	1.75529i	−0.479312	−	0.877645i	$-0.659114\pi$
$257$		−	28.1394i		−	1.75529i	0.479312	−	0.877645i	$-0.340886\pi$
$258$		0			0
$259$	6.09436			0.378685
$260$	0.334598	+	1.50835i	0.0207509	+	0.0935441i
$261$		0			0
$262$	−6.59455	+	0.722651i	−0.407413	+	0.0446455i
$263$	30.5298			1.88255			0.941274	−	0.337645i	$-0.109630\pi$
$263$	30.5298			1.88255			0.941274	+	0.337645i	$0.109630\pi$
$264$		0			0
$265$	−1.33303			−0.0818874
$266$	2.61581	−	0.286648i	0.160386	−	0.0175755i
$267$		0			0
$268$	9.00560	−	1.99771i	0.550104	−	0.122030i
$269$	−13.2495			−0.807839			−0.403920	−	0.914795i	$-0.632352\pi$
$269$	−13.2495			−0.807839			−0.403920	+	0.914795i	$0.632352\pi$
$270$		0			0
$271$		−	7.06832i		−	0.429370i	−0.976683	−	0.214685i	$-0.931128\pi$
$271$		−	7.06832i		−	0.429370i	0.976683	−	0.214685i	$-0.0688725\pi$
$272$	4.64012	+	9.94407i	0.281348	+	0.602948i
$273$		0			0
$274$	−15.6725	+	1.71744i	−0.946811	+	0.103754i
$275$			11.9545i			0.720884i
$276$		0			0
$277$			10.3435i			0.621481i	0.950495	+	0.310740i	$0.100577\pi$
$277$			10.3435i			0.621481i	−0.950495	+	0.310740i	$0.899423\pi$
$278$	−1.06793	−	9.74539i	−0.0640502	−	0.584490i
$279$		0			0
$280$	−0.433927	+	0.147392i	−0.0259321	+	0.00880835i
$281$			27.0638i			1.61449i	0.590217	+	0.807245i	$0.299042\pi$
$281$			27.0638i			1.61449i	−0.590217	+	0.807245i	$0.700958\pi$
$282$		0			0
$283$	17.2246			1.02390			0.511948	−	0.859017i	$-0.328924\pi$
$283$	17.2246			1.02390			0.511948	+	0.859017i	$0.328924\pi$
$284$	−27.2900	+	6.05373i	−1.61936	+	0.359223i
$285$		0			0
$286$	−1.76537	−	16.1099i	−0.104389	−	0.952598i
$287$	3.16889			0.187054
$288$		0			0
$289$	9.47405			0.557297
$290$	−0.0988703	−	0.902241i	−0.00580587	−	0.0529814i
$291$		0			0
$292$	12.4536	−	2.76257i	0.728790	−	0.161667i
$293$	0.199121			0.0116328			0.00581639	−	0.999983i	$-0.498149\pi$
$293$	0.199121			0.0116328			0.00581639	+	0.999983i	$0.498149\pi$
$294$		0			0
$295$			0.883763i			0.0514547i
$296$	−16.3216	+	5.54395i	−0.948673	+	0.322236i
$297$		0			0
$298$	2.50399	+	22.8501i	0.145052	+	1.32367i
$299$			6.33981i			0.366641i
$300$		0			0
$301$			1.70927i			0.0985209i
$302$	0.598886	−	0.0656277i	0.0344620	−	0.00377645i
$303$		0			0
$304$	−6.74476	+	3.14725i	−0.386839	+	0.180507i
$305$		−	0.694363i		−	0.0397591i
$306$		0			0
$307$	10.0504			0.573606			0.286803	−	0.957990i	$-0.407407\pi$
$307$	10.0504			0.573606			0.286803	+	0.957990i	$0.407407\pi$
$308$	4.69296	−	1.04104i	0.267406	−	0.0593188i
$309$		0			0
$310$	−1.82605	+	0.200104i	−0.103713	+	0.0113651i
$311$	−9.74569			−0.552627			−0.276314	−	0.961068i	$-0.589113\pi$
$311$	−9.74569			−0.552627			−0.276314	+	0.961068i	$0.589113\pi$
$312$		0			0
$313$	3.46199			0.195683			0.0978415	−	0.995202i	$-0.468806\pi$
$313$	3.46199			0.195683			0.0978415	+	0.995202i	$0.468806\pi$
$314$	19.7446	−	2.16368i	1.11425	−	0.122103i
$315$		0			0
$316$	−4.22414	−	19.0423i	−0.237627	−	1.07121i
$317$	−27.5983			−1.55008			−0.775039	−	0.631914i	$-0.782270\pi$
$317$	−27.5983			−1.55008			−0.775039	+	0.631914i	$0.782270\pi$
$318$		0			0
$319$			9.52063i			0.533053i
$320$	1.02804	−	0.789474i	0.0574691	−	0.0441330i
$321$		0			0
$322$	−1.86929	+	0.204843i	−0.104172	+	0.0114154i
$323$		−	5.10462i		−	0.284029i
$324$		0			0
$325$		−	23.7140i		−	1.31542i
$326$	0.728606	+	6.64890i	0.0403538	+	0.368248i
$327$		0			0
$328$	−8.48676	+	2.88270i	−0.468603	+	0.159170i
$329$		−	12.1502i		−	0.669862i
$330$		0			0
$331$	−13.5802			−0.746434			−0.373217	−	0.927744i	$-0.621745\pi$
$331$	−13.5802			−0.746434			−0.373217	+	0.927744i	$0.621745\pi$
$332$	−7.14593	−	32.2136i	−0.392184	−	1.76795i
$333$		0			0
$334$	1.80771	+	16.4962i	0.0989132	+	0.902632i
$335$	0.747301			0.0408294
$336$		0			0
$337$	−0.0989875			−0.00539219			−0.00269610	−	0.999996i	$-0.500858\pi$
$337$	−0.0989875			−0.00539219			−0.00269610	+	0.999996i	$0.500858\pi$
$338$	1.49928	+	13.6817i	0.0815500	+	0.744184i
$339$		0			0
$340$	0.192523	+	0.867884i	0.0104410	+	0.0470676i
$341$	19.2688			1.04347
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−1.55490	−	4.57769i	−0.0838347	−	0.246812i
$345$		0			0
$346$	2.81262	+	25.6666i	0.151208	+	1.37984i
$347$			5.82609i			0.312761i	0.987697	+	0.156380i	$0.0499826\pi$
$347$			5.82609i			0.312761i	−0.987697	+	0.156380i	$0.950017\pi$
$348$		0			0
$349$			30.1726i			1.61510i	0.589798	+	0.807551i	$0.299207\pi$
$349$			30.1726i			1.61510i	−0.589798	+	0.807551i	$0.700793\pi$
$350$	6.99208	−	0.766214i	0.373743	−	0.0409559i
$351$		0			0
$352$	−11.6214	+	7.05718i	−0.619424	+	0.376149i
$353$		−	16.0333i		−	0.853364i	−0.904402	−	0.426682i	$-0.859682\pi$
$353$		−	16.0333i		−	0.853364i	0.904402	−	0.426682i	$-0.140318\pi$
$354$		0			0
$355$	−2.26457			−0.120191
$356$	1.01806	+	4.58939i	0.0539573	+	0.243237i
$357$		0			0
$358$	−20.5177	+	2.24839i	−1.08439	+	0.118831i
$359$	−16.0001			−0.844451			−0.422225	−	0.906491i	$-0.638751\pi$
$359$	−16.0001			−0.844451			−0.422225	+	0.906491i	$0.638751\pi$
$360$		0			0
$361$	−15.5377			−0.817773
$362$	−5.37052	+	0.588518i	−0.282268	+	0.0309318i
$363$		0			0
$364$	−9.30938	+	2.06510i	−0.487944	+	0.108241i
$365$	1.03342			0.0540917
$366$		0			0
$367$			13.0471i			0.681053i	0.940235	+	0.340527i	$0.110605\pi$
$367$			13.0471i			0.681053i	−0.940235	+	0.340527i	$0.889395\pi$
$368$	4.81990	−	2.24907i	0.251255	−	0.117241i
$369$		0			0
$370$	−1.38814	+	0.152116i	−0.0721659	+	0.00790816i
$371$		−	8.22731i		−	0.427141i
$372$		0			0
$373$		−	0.319142i		−	0.0165245i	−0.999966	−	0.00826227i	$-0.997370\pi$
$373$		−	0.319142i		−	0.0165245i	0.999966	−	0.00826227i	$-0.00262999\pi$
$374$	−1.01577	−	9.26940i	−0.0525242	−	0.479309i
$375$		0			0
$376$	11.0529	+	32.5400i	0.570008	+	1.67812i
$377$		−	18.8860i		−	0.972677i
$378$		0			0
$379$	13.4802			0.692431			0.346215	−	0.938155i	$-0.387467\pi$
$379$	13.4802			0.692431			0.346215	+	0.938155i	$0.387467\pi$
$380$	−0.588660	+	0.130582i	−0.0301976	+	0.00669873i
$381$		0			0
$382$	−3.30358	−	30.1469i	−0.169026	−	1.54245i
$383$	5.80894			0.296823			0.148411	−	0.988926i	$-0.452584\pi$
$383$	5.80894			0.296823			0.148411	+	0.988926i	$0.452584\pi$
$384$		0			0
$385$	0.389431			0.0198472
$386$	2.71118	+	24.7408i	0.137995	+	1.25928i
$387$		0			0
$388$	−28.2276	+	6.26173i	−1.43304	+	0.317891i
$389$	−32.7958			−1.66282			−0.831408	−	0.555663i	$-0.812465\pi$
$389$	−32.7958			−1.66282			−0.831408	+	0.555663i	$0.812465\pi$
$390$		0			0
$391$			3.64783i			0.184479i
$392$	−0.909686	−	2.67815i	−0.0459461	−	0.135267i
$393$		0			0
$394$	2.94745	+	26.8970i	0.148491	+	1.35505i
$395$		−	1.58016i		−	0.0795066i
$396$		0			0
$397$		−	26.2294i		−	1.31641i	−0.752837	−	0.658207i	$-0.771315\pi$
$397$		−	26.2294i		−	1.31641i	0.752837	−	0.658207i	$-0.228685\pi$
$398$	−18.7147	+	2.05082i	−0.938084	+	0.102798i
$399$		0			0
$400$	−18.0288	+	8.41264i	−0.901441	+	0.420632i
$401$			20.9069i			1.04404i	0.852933	+	0.522020i	$0.174821\pi$
$401$			20.9069i			1.04404i	−0.852933	+	0.522020i	$0.825179\pi$
$402$		0			0
$403$	−38.2234			−1.90404
$404$	0.884918	−	0.196301i	0.0440263	−	0.00976636i
$405$		0			0
$406$	5.56853	−	0.610217i	0.276361	−	0.0302845i
$407$	14.6479			0.726071
$408$		0			0
$409$	33.7856			1.67059			0.835295	−	0.549801i	$-0.185297\pi$
$409$	33.7856			1.67059			0.835295	+	0.549801i	$0.185297\pi$
$410$	−0.721792	+	0.0790962i	−0.0356468	+	0.00390628i
$411$		0			0
$412$	−3.87021	−	17.4467i	−0.190672	−	0.859539i
$413$	−5.45449			−0.268398
$414$		0			0
$415$		−	2.67314i		−	0.131219i
$416$	23.0533	−	13.9993i	1.13028	−	0.686370i
$417$		0			0
$418$	6.28716	−	0.688966i	0.307515	−	0.0336984i
$419$			12.4203i			0.606771i	0.952868	+	0.303385i	$0.0981170\pi$
$419$			12.4203i			0.606771i	−0.952868	+	0.303385i	$0.901883\pi$
$420$		0			0
$421$			21.3631i			1.04118i	0.853808	+	0.520588i	$0.174287\pi$
$421$			21.3631i			1.04118i	−0.853808	+	0.520588i	$0.825713\pi$
$422$	3.68702	+	33.6459i	0.179481	+	1.63786i
$423$		0			0
$424$	7.48427	+	22.0340i	0.363468	+	1.07006i
$425$		−	13.6447i		−	0.661866i
$426$		0			0
$427$	4.28553			0.207391
$428$	−6.47009	−	29.1669i	−0.312743	−	1.40983i
$429$		0			0
$430$	−0.0426638	−	0.389329i	−0.00205743	−	0.0187751i
$431$	−21.3649			−1.02911			−0.514557	−	0.857456i	$-0.672043\pi$
$431$	−21.3649			−1.02911			−0.514557	+	0.857456i	$0.672043\pi$
$432$		0			0
$433$	21.5834			1.03723			0.518617	−	0.855007i	$-0.326447\pi$
$433$	21.5834			1.03723			0.518617	+	0.855007i	$0.326447\pi$
$434$	−1.23502	−	11.2702i	−0.0592828	−	0.540985i
$435$		0			0
$436$	1.87891	+	8.47006i	0.0899836	+	0.405642i
$437$	−2.47422			−0.118358
$438$		0			0
$439$			13.4860i			0.643650i	0.946799	+	0.321825i	$0.104296\pi$
$439$			13.4860i			0.643650i	−0.946799	+	0.321825i	$0.895704\pi$
$440$	−1.04295	+	0.354260i	−0.0497208	+	0.0168887i
$441$		0			0
$442$	2.01497	+	18.3876i	0.0958424	+	0.874609i
$443$			4.29225i			0.203931i	0.994788	+	0.101965i	$0.0325131\pi$
$443$			4.29225i			0.203931i	−0.994788	+	0.101965i	$0.967487\pi$
$444$		0			0
$445$			0.380836i			0.0180534i
$446$	19.6710	−	2.15561i	0.931448	−	0.102071i
$447$		0			0
$448$	4.87255	+	6.34494i	0.230206	+	0.299770i
$449$			33.7152i			1.59112i	0.605876	+	0.795559i	$0.292823\pi$
$449$			33.7152i			1.59112i	−0.605876	+	0.795559i	$0.707177\pi$
$450$		0			0
$451$	7.61650			0.358647
$452$	0.195383	+	0.880778i	0.00919005	+	0.0414283i
$453$		0			0
$454$	−15.3197	+	1.67878i	−0.718988	+	0.0787889i
$455$	−0.772509			−0.0362158
$456$		0			0
$457$	−31.2919			−1.46377			−0.731886	−	0.681427i	$-0.761360\pi$
$457$	−31.2919			−1.46377			−0.731886	+	0.681427i	$0.761360\pi$
$458$	15.6464	−	1.71458i	0.731108	−	0.0801171i
$459$		0			0
$460$	0.420664	−	0.0933159i	0.0196136	−	0.00435088i
$461$	−30.9245			−1.44030			−0.720149	−	0.693820i	$-0.755927\pi$
$461$	−30.9245			−1.44030			−0.720149	+	0.693820i	$0.755927\pi$
$462$		0			0
$463$		−	12.0160i		−	0.558432i	−0.960228	−	0.279216i	$-0.909925\pi$
$463$		−	12.0160i		−	0.558432i	0.960228	−	0.279216i	$-0.0900746\pi$
$464$	−14.3582	+	6.69986i	−0.666564	+	0.311033i
$465$		0			0
$466$	19.3688	−	2.12249i	0.897242	−	0.0983225i
$467$			7.24380i			0.335203i	0.985855	+	0.167601i	$0.0536022\pi$
$467$			7.24380i			0.335203i	−0.985855	+	0.167601i	$0.946398\pi$
$468$		0			0
$469$			4.61226i			0.212974i
$470$	0.303271	+	2.76750i	0.0139889	+	0.127655i
$471$		0			0
$472$	14.6079	−	4.96187i	0.672384	−	0.228389i
$473$			4.10828i			0.188899i
$474$		0			0
$475$	9.25480			0.424639
$476$	−5.35648	+	1.18823i	−0.245514	+	0.0544623i
$477$		0			0
$478$	1.23127	+	11.2360i	0.0563171	+	0.513921i
$479$	31.8562			1.45555			0.727773	−	0.685818i	$-0.240555\pi$
$479$	31.8562			1.45555			0.727773	+	0.685818i	$0.240555\pi$
$480$		0			0
$481$	−29.0569			−1.32488
$482$	0.798477	+	7.28650i	0.0363696	+	0.331891i
$483$		0			0
$484$	−10.1983	+	2.26228i	−0.463557	+	0.102831i
$485$	−2.34238			−0.106362
$486$		0			0
$487$		−	37.3634i		−	1.69310i	−0.532313	−	0.846548i	$-0.678677\pi$
$487$		−	37.3634i		−	1.69310i	0.532313	−	0.846548i	$-0.321323\pi$
$488$	−11.4773	+	3.89849i	−0.519552	+	0.176476i
$489$		0			0
$490$	−0.0249602	−	0.227774i	−0.00112759	−	0.0102898i
$491$		−	23.8389i		−	1.07583i	−0.842998	−	0.537917i	$-0.819211\pi$
$491$		−	23.8389i		−	1.07583i	0.842998	−	0.537917i	$-0.180789\pi$
$492$		0			0
$493$		−	10.8667i		−	0.489412i
$494$	−12.4718	+	1.36669i	−0.561131	+	0.0614905i
$495$		0			0
$496$	13.5599	+	29.0597i	0.608857	+	1.30482i
$497$		−	13.9767i		−	0.626940i
$498$		0			0
$499$	13.0105			0.582428			0.291214	−	0.956658i	$-0.405941\pi$
$499$	13.0105			0.582428			0.291214	+	0.956658i	$0.405941\pi$
$500$	−3.15529	+	0.699938i	−0.141109	+	0.0313022i
$501$		0			0
$502$	−11.0816	+	1.21436i	−0.494597	+	0.0541995i
$503$	34.4474			1.53593			0.767966	−	0.640491i	$-0.221269\pi$
$503$	34.4474			1.53593			0.767966	+	0.640491i	$0.221269\pi$
$504$		0			0
$505$	0.0734321			0.00326769
$506$	−4.49289	+	0.492344i	−0.199733	+	0.0218874i
$507$		0			0
$508$	0.0852191	+	0.384164i	0.00378099	+	0.0170445i
$509$	7.29166			0.323197			0.161599	−	0.986857i	$-0.448335\pi$
$509$	7.29166			0.323197			0.161599	+	0.986857i	$0.448335\pi$
$510$		0			0
$511$			6.37815i			0.282153i
$512$	−18.8213	−	12.5602i	−0.831792	−	0.555088i
$513$		0			0
$514$	−39.5583	+	4.33493i	−1.74484	+	0.191205i
$515$		−	1.44776i		−	0.0637960i
$516$		0			0
$517$		−	29.2033i		−	1.28436i
$518$	−0.938846	−	8.56744i	−0.0412505	−	0.376432i
$519$		0			0
$520$	2.06889	−	0.702741i	0.0907270	−	0.0308172i
$521$		−	20.0013i		−	0.876274i	−0.898908	−	0.438137i	$-0.855638\pi$
$521$		−	20.0013i		−	0.876274i	0.898908	−	0.438137i	$-0.144362\pi$
$522$		0			0
$523$	−14.7421			−0.644629			−0.322314	−	0.946633i	$-0.604461\pi$
$523$	−14.7421			−0.644629			−0.322314	+	0.946633i	$0.604461\pi$
$524$	2.03180	+	9.15928i	0.0887597	+	0.400125i
$525$		0			0
$526$	−4.70316	−	42.9187i	−0.205068	−	1.87134i
$527$	−21.9932			−0.958038
$528$		0			0
$529$	−21.2319			−0.923126
$530$	0.205356	+	1.87397i	0.00892007	+	0.0814001i
$531$		0			0
$532$	−0.805940	−	3.63314i	−0.0349419	−	0.157517i
$533$	−15.1088			−0.654433
$534$		0			0
$535$		−	2.42032i		−	0.104640i
$536$	−4.19571	−	12.3523i	−0.181227	−	0.533538i
$537$		0			0
$538$	2.04111	+	18.6262i	0.0879987	+	0.803032i
$539$			2.40352i			0.103527i
$540$		0			0
$541$		−	36.6011i		−	1.57360i	−0.617206	−	0.786802i	$-0.711735\pi$
$541$		−	36.6011i		−	1.57360i	0.617206	−	0.786802i	$-0.288265\pi$
$542$	−9.93663	+	1.08889i	−0.426815	+	0.0467717i
$543$		0			0
$544$	13.2645	−	8.05497i	0.568712	−	0.345354i
$545$			0.702861i			0.0301073i
$546$		0			0
$547$	41.4335			1.77157			0.885783	−	0.464099i	$-0.153622\pi$
$547$	41.4335			1.77157			0.885783	+	0.464099i	$0.153622\pi$
$548$	4.82875	+	21.7678i	0.206274	+	0.929875i
$549$		0			0
$550$	16.8056	−	1.84161i	0.716594	−	0.0785266i
$551$	7.37057			0.313997
$552$		0			0
$553$	9.75258			0.414722
$554$	14.5409	−	1.59343i	0.617783	−	0.0676985i
$555$		0			0
$556$	−13.5355	+	3.00259i	−0.574034	+	0.127338i
$557$	23.2128			0.983558			0.491779	−	0.870720i	$-0.336347\pi$
$557$	23.2128			0.983558			0.491779	+	0.870720i	$0.336347\pi$
$558$		0			0
$559$		−	8.14954i		−	0.344689i
$560$	0.274050	+	0.587307i	0.0115807	+	0.0248183i
$561$		0			0
$562$	38.0462	−	4.16922i	1.60488	−	0.175868i
$563$		−	36.2689i		−	1.52855i	−0.644890	−	0.764276i	$-0.723097\pi$
$563$		−	36.2689i		−	1.52855i	0.644890	−	0.764276i	$-0.276903\pi$
$564$		0			0
$565$			0.0730886i			0.00307486i
$566$	−2.65348	−	24.2143i	−0.111534	−	1.01780i
$567$		0			0
$568$	12.7144	+	37.4316i	0.533484	+	1.57059i
$569$		−	16.0163i		−	0.671439i	−0.941962	−	0.335719i	$-0.891021\pi$
$569$		−	16.0163i		−	0.671439i	0.941962	−	0.335719i	$-0.108979\pi$
$570$		0			0
$571$	−32.8412			−1.37436			−0.687180	−	0.726487i	$-0.741152\pi$
$571$	−32.8412			−1.37436			−0.687180	+	0.726487i	$0.741152\pi$
$572$	−22.3753	+	4.96351i	−0.935558	+	0.207535i
$573$		0			0
$574$	−0.488173	−	4.45482i	−0.0203759	−	0.185941i
$575$	−6.61360			−0.275806
$576$		0			0
$577$	10.0637			0.418956			0.209478	−	0.977813i	$-0.432823\pi$
$577$	10.0637			0.418956			0.209478	+	0.977813i	$0.432823\pi$
$578$	−1.45949	−	13.3186i	−0.0607069	−	0.553981i
$579$		0			0
$580$	−1.25314	+	0.277983i	−0.0520337	+	0.0115426i
$581$	16.4983			0.684465
$582$		0			0
$583$		−	19.7745i		−	0.818977i
$584$	−5.80211	−	17.0816i	−0.240093	−	0.706842i
$585$		0			0
$586$	−0.0306749	−	0.279924i	−0.00126717	−	0.0115636i
$587$			29.8278i			1.23112i	0.788088	+	0.615562i	$0.211071\pi$
$587$			29.8278i			1.23112i	−0.788088	+	0.615562i	$0.788929\pi$
$588$		0			0
$589$		−	14.9173i		−	0.614657i
$590$	1.24239	−	0.136145i	0.0511485	−	0.00560501i
$591$		0			0
$592$	10.3080	+	22.0908i	0.423658	+	0.907926i
$593$		−	22.8440i		−	0.938091i	−0.883174	−	0.469046i	$-0.844598\pi$
$593$		−	22.8440i		−	0.938091i	0.883174	−	0.469046i	$-0.155402\pi$
$594$		0			0
$595$	−0.444491			−0.0182223
$596$	31.7369	−	7.04020i	1.30000	−	0.288378i
$597$		0			0
$598$	8.91249	−	0.976658i	0.364459	−	0.0399385i
$599$	−8.07805			−0.330060			−0.165030	−	0.986289i	$-0.552772\pi$
$599$	−8.07805			−0.330060			−0.165030	+	0.986289i	$0.552772\pi$
$600$		0			0
$601$	30.9036			1.26058			0.630292	−	0.776358i	$-0.282935\pi$
$601$	30.9036			1.26058			0.630292	+	0.776358i	$0.282935\pi$
$602$	2.40289	−	0.263316i	0.0979346	−	0.0107320i
$603$		0			0
$604$	−0.184519	−	0.831802i	−0.00750796	−	0.0338455i
$605$	−0.846270			−0.0344058
$606$		0			0
$607$		−	21.2157i		−	0.861121i	−0.902562	−	0.430560i	$-0.858316\pi$
$607$		−	21.2157i		−	0.861121i	0.902562	−	0.430560i	$-0.141684\pi$
$608$	5.46344	+	8.99693i	0.221572	+	0.364874i
$609$		0			0
$610$	−0.976134	+	0.106968i	−0.0395225	+	0.00433100i
$611$			57.9302i			2.34360i
$612$		0			0
$613$		−	22.9612i		−	0.927392i	−0.885994	−	0.463696i	$-0.846523\pi$
$613$		−	22.9612i		−	0.927392i	0.885994	−	0.463696i	$-0.153477\pi$
$614$	−1.54828	−	14.1288i	−0.0624835	−	0.570193i
$615$		0			0
$616$	−2.18645	−	6.43699i	−0.0880946	−	0.259354i
$617$			14.9091i			0.600217i	0.953905	+	0.300108i	$0.0970228\pi$
$617$			14.9091i			0.600217i	−0.953905	+	0.300108i	$0.902977\pi$
$618$		0			0
$619$	−24.6832			−0.992100			−0.496050	−	0.868294i	$-0.665217\pi$
$619$	−24.6832			−0.992100			−0.496050	+	0.868294i	$0.665217\pi$
$620$	0.562612	+	2.53623i	0.0225950	+	0.101857i
$621$		0			0
$622$	1.50134	+	13.7005i	0.0601982	+	0.549339i
$623$	−2.35048			−0.0941699
$624$		0			0
$625$	24.6069			0.984276
$626$	−0.533325	−	4.86686i	−0.0213159	−	0.194519i
$627$		0			0
$628$	−6.08338	−	27.4236i	−0.242753	−	1.09432i
$629$	−16.7189			−0.666627
$630$		0			0
$631$		−	11.1068i		−	0.442154i	−0.975256	−	0.221077i	$-0.929043\pi$
$631$		−	11.1068i		−	0.442154i	0.975256	−	0.221077i	$-0.0709573\pi$
$632$	−26.1188	+	8.87179i	−1.03895	+	0.352901i
$633$		0			0
$634$	4.25157	+	38.7977i	0.168851	+	1.54085i
$635$			0.0318786i			0.00126507i
$636$		0			0
$637$		−	4.76784i		−	0.188909i
$638$	13.3841	−	1.46667i	0.529881	−	0.0580660i
$639$		0			0
$640$	−1.26821	−	1.32360i	−0.0501305	−	0.0523197i
$641$			35.4613i			1.40064i	0.713831	+	0.700318i	$0.246959\pi$
$641$			35.4613i			1.40064i	−0.713831	+	0.700318i	$0.753041\pi$
$642$		0			0
$643$	27.6728			1.09131			0.545654	−	0.838011i	$-0.316281\pi$
$643$	27.6728			1.09131			0.545654	+	0.838011i	$0.316281\pi$
$644$	0.575935	+	2.59629i	0.0226950	+	0.102308i
$645$		0			0
$646$	−7.17607	+	0.786376i	−0.282339	+	0.0309395i
$647$	12.7035			0.499426			0.249713	−	0.968320i	$-0.419664\pi$
$647$	12.7035			0.499426			0.249713	+	0.968320i	$0.419664\pi$
$648$		0			0
$649$	−13.1100			−0.514612
$650$	−33.3371	+	3.65319i	−1.30759	+	0.143290i
$651$		0			0
$652$	9.23476	−	2.04855i	0.361661	−	0.0802273i
$653$	42.8339			1.67622			0.838110	−	0.545501i	$-0.183660\pi$
$653$	42.8339			1.67622			0.838110	+	0.545501i	$0.183660\pi$
$654$		0			0
$655$			0.760054i			0.0296978i
$656$	5.35989	+	11.4866i	0.209268	+	0.448476i
$657$		0			0
$658$	−17.0807	+	1.87176i	−0.665876	+	0.0729687i
$659$		−	35.5914i		−	1.38645i	−0.720723	−	0.693223i	$-0.756190\pi$
$659$		−	35.5914i		−	1.38645i	0.720723	−	0.693223i	$-0.243810\pi$
$660$		0			0
$661$			0.388331i			0.0151043i	0.999971	+	0.00755217i	$0.00240395\pi$
$661$			0.388331i			0.0151043i	−0.999971	+	0.00755217i	$0.997596\pi$
$662$	2.09205	+	19.0910i	0.0813098	+	0.741992i
$663$		0			0
$664$	−44.1849	+	15.0083i	−1.71471	+	0.582435i
$665$		−	0.301485i		−	0.0116911i
$666$		0			0
$667$	−5.26711			−0.203943
$668$	22.9119	−	5.08254i	0.886486	−	0.196649i
$669$		0			0
$670$	−0.115123	−	1.05055i	−0.00444759	−	0.0405864i
$671$	10.3004			0.397641
$672$		0			0
$673$	37.9424			1.46257			0.731286	−	0.682070i	$-0.238920\pi$
$673$	37.9424			1.46257			0.731286	+	0.682070i	$0.238920\pi$
$674$	0.0152492	+	0.139156i	0.000587377	+	0.00536010i
$675$		0			0
$676$	19.0027	−	4.21536i	0.730872	−	0.162129i
$677$	−24.1764			−0.929173			−0.464586	−	0.885528i	$-0.653797\pi$
$677$	−24.1764			−0.929173			−0.464586	+	0.885528i	$0.653797\pi$
$678$		0			0
$679$		−	14.4569i		−	0.554805i
$680$	1.19041	−	0.404347i	0.0456502	−	0.0155060i
$681$		0			0
$682$	−2.96840	−	27.0881i	−0.113666	−	1.03726i
$683$		−	17.3036i		−	0.662104i	−0.943613	−	0.331052i	$-0.892596\pi$
$683$		−	17.3036i		−	0.662104i	0.943613	−	0.331052i	$-0.107404\pi$
$684$		0			0
$685$			1.80633i			0.0690164i
$686$	1.40580	−	0.154052i	0.0536736	−	0.00588172i
$687$		0			0
$688$	−6.19577	+	2.89108i	−0.236211	+	0.110221i
$689$			39.2265i			1.49441i
$690$		0			0
$691$	14.6123			0.555877			0.277938	−	0.960599i	$-0.410349\pi$
$691$	14.6123			0.555877			0.277938	+	0.960599i	$0.410349\pi$
$692$	35.6488	−	7.90796i	1.35516	−	0.300616i
$693$		0			0
$694$	8.19030	−	0.897519i	0.310900	−	0.0340693i
$695$	−1.12320			−0.0426055
$696$		0			0
$697$	−8.69336			−0.329285
$698$	42.4165	−	4.64814i	1.60549	−	0.175935i
$699$		0			0
$700$	−2.15428	−	9.71142i	−0.0814243	−	0.367057i
$701$	28.3532			1.07089			0.535443	−	0.844572i	$-0.320145\pi$
$701$	28.3532			1.07089			0.535443	+	0.844572i	$0.320145\pi$
$702$		0			0
$703$		−	11.3400i		−	0.427694i
$704$	11.7113	+	15.2502i	0.441385	+	0.574764i
$705$		0			0
$706$	−22.5395	+	2.46995i	−0.848286	+	0.0929578i
$707$			0.453215i			0.0170449i
$708$		0			0
$709$			22.7293i			0.853618i	0.904342	+	0.426809i	$0.140362\pi$
$709$			22.7293i			0.853618i	−0.904342	+	0.426809i	$0.859638\pi$
$710$	0.348861	+	3.18353i	0.0130925	+	0.119476i
$711$		0			0
$712$	6.29492	−	2.13820i	0.235912	−	0.0801323i
$713$			10.6601i			0.399224i
$714$		0			0
$715$	−1.85674			−0.0694383
$716$	6.32156	+	28.4973i	0.236248	+	1.06500i
$717$		0			0
$718$	2.46484	+	22.4929i	0.0919868	+	0.839426i
$719$	−27.7959			−1.03661			−0.518306	−	0.855195i	$-0.673437\pi$
$719$	−27.7959			−1.03661			−0.518306	+	0.855195i	$0.673437\pi$
$720$		0			0
$721$	8.93542			0.332773
$722$	2.39361	+	21.8428i	0.0890808	+	0.812907i
$723$		0			0
$724$	1.65467	+	7.45920i	0.0614955	+	0.277219i
$725$	19.7016			0.731699
$726$		0			0
$727$		−	24.4253i		−	0.905886i	−0.891540	−	0.452943i	$-0.850374\pi$
$727$		−	24.4253i		−	0.905886i	0.891540	−	0.452943i	$-0.149626\pi$
$728$	4.33724	+	12.7690i	0.160749	+	0.473250i
$729$		0			0
$730$	−0.159200	−	1.45278i	−0.00589226	−	0.0537698i
$731$		−	4.68913i		−	0.173434i
$732$		0			0
$733$		−	17.1266i		−	0.632585i	−0.948662	−	0.316292i	$-0.897562\pi$
$733$		−	17.1266i		−	0.632585i	0.948662	−	0.316292i	$-0.102438\pi$
$734$	18.3416	−	2.00993i	0.677001	−	0.0741878i
$735$		0			0
$736$	−3.90425	−	6.42933i	−0.143913	−	0.236988i
$737$			11.0857i			0.408346i
$738$		0			0
$739$	−7.60957			−0.279923			−0.139961	−	0.990157i	$-0.544698\pi$
$739$	−7.60957			−0.279923			−0.139961	+	0.990157i	$0.544698\pi$
$740$	0.427690	+	1.92801i	0.0157222	+	0.0708750i
$741$		0			0
$742$	−11.5659	+	1.26743i	−0.424599	+	0.0465289i
$743$	−3.75152			−0.137630			−0.0688150	−	0.997629i	$-0.521922\pi$
$743$	−3.75152			−0.137630			−0.0688150	+	0.997629i	$0.521922\pi$
$744$		0			0
$745$	2.63359			0.0964872
$746$	−0.448649	+	0.0491643i	−0.0164262	+	0.00180003i
$747$		0			0
$748$	−12.8744	+	2.85593i	−0.470735	+	0.104423i
$749$	14.9379			0.545821
$750$		0			0
$751$			39.9652i			1.45835i	0.684326	+	0.729176i	$0.260096\pi$
$751$			39.9652i			1.45835i	−0.684326	+	0.729176i	$0.739904\pi$
$752$	44.0420	−	20.5509i	1.60604	−	0.749415i
$753$		0			0
$754$	−26.5499	+	2.90942i	−0.966889	+	0.105955i
$755$		−	0.0690244i		−	0.00251206i
$756$		0			0
$757$		−	26.4627i		−	0.961802i	−0.876775	−	0.480901i	$-0.840310\pi$
$757$		−	26.4627i		−	0.961802i	0.876775	−	0.480901i	$-0.159690\pi$
$758$	−2.07664	−	18.9504i	−0.0754271	−	0.688310i
$759$		0			0
$760$	0.274256	+	0.807420i	0.00994833	+	0.0292882i
$761$			3.50130i			0.126922i	0.997984	+	0.0634610i	$0.0202139\pi$
$761$			3.50130i			0.126922i	−0.997984	+	0.0634610i	$0.979786\pi$
$762$		0			0
$763$	−4.33798			−0.157045
$764$	−41.8715	+	9.28835i	−1.51486	+	0.336041i
$765$		0			0
$766$	−0.894876	−	8.16619i	−0.0323332	−	0.295057i
$767$	26.0061			0.939027
$768$		0			0
$769$	−26.3596			−0.950551			−0.475275	−	0.879837i	$-0.657652\pi$
$769$	−26.3596			−0.950551			−0.475275	+	0.879837i	$0.657652\pi$
$770$	−0.0599924	−	0.547461i	−0.00216198	−	0.0197291i
$771$		0			0
$772$	34.3630	−	7.62274i	1.23675	−	0.274348i
$773$	22.0363			0.792592			0.396296	−	0.918123i	$-0.370295\pi$
$773$	22.0363			0.792592			0.396296	+	0.918123i	$0.370295\pi$
$774$		0			0
$775$		−	39.8741i		−	1.43232i
$776$	13.1512	+	38.7177i	0.472102	+	1.38988i
$777$		0			0
$778$	5.05225	+	46.1043i	0.181132	+	1.65292i
$779$		−	5.89645i		−	0.211262i
$780$		0			0
$781$		−	33.5933i		−	1.20206i
$782$	5.12812	−	0.561955i	0.183381	−	0.0200955i
$783$		0			0
$784$	−3.62480	+	1.69141i	−0.129457	+	0.0604074i
$785$		−	2.27566i		−	0.0812218i
$786$		0			0
$787$	44.0988			1.57195			0.785976	−	0.618257i	$-0.212161\pi$
$787$	44.0988			1.57195			0.785976	+	0.618257i	$0.212161\pi$
$788$	37.3577	−	8.28705i	1.33081	−	0.295214i
$789$		0			0
$790$	−2.22139	+	0.243427i	−0.0790334	+	0.00866073i
$791$	−0.451095			−0.0160391
$792$		0			0
$793$	−20.4327			−0.725587
$794$	−36.8732	+	4.04068i	−1.30858	+	0.143398i
$795$		0			0
$796$	5.76607	+	25.9932i	0.204373	+	0.921304i
$797$	17.4271			0.617298			0.308649	−	0.951176i	$-0.400123\pi$
$797$	17.4271			0.617298			0.308649	+	0.951176i	$0.400123\pi$
$798$		0			0
$799$			33.3322i			1.17921i
$800$	14.6038	+	24.0489i	0.516324	+	0.850257i
$801$		0			0
$802$	29.3909	−	3.22074i	1.03783	−	0.113728i
$803$			15.3300i			0.540985i
$804$		0			0
$805$			0.215445i			0.00759344i
$806$	5.88838	+	53.7344i	0.207409	+	1.89271i
$807$		0			0
$808$	−0.412283	−	1.21378i	−0.0145041	−	0.0427005i
$809$			1.23533i			0.0434319i	0.999764	+	0.0217159i	$0.00691294\pi$
$809$			1.23533i			0.0434319i	−0.999764	+	0.0217159i	$0.993087\pi$
$810$		0			0
$811$	40.7818			1.43204			0.716021	−	0.698078i	$-0.245961\pi$
$811$	40.7818			1.43204			0.716021	+	0.698078i	$0.245961\pi$
$812$	−1.71568	−	7.73422i	−0.0602087	−	0.271418i
$813$		0			0
$814$	−2.25654	−	20.5920i	−0.0790916	−	0.721750i
$815$	0.766317			0.0268429
$816$		0			0
$817$	3.18050			0.111271
$818$	−5.20473	−	47.4957i	−0.181979	−	1.66065i
$819$		0			0
$820$	0.222387	+	1.00251i	0.00776608	+	0.0350091i
$821$	25.2037			0.879614			0.439807	−	0.898092i	$-0.355047\pi$
$821$	25.2037			0.879614			0.439807	+	0.898092i	$0.355047\pi$
$822$		0			0
$823$		−	46.4360i		−	1.61866i	−0.587356	−	0.809329i	$-0.699831\pi$
$823$		−	46.4360i		−	1.61866i	0.587356	−	0.809329i	$-0.300169\pi$
$824$	−23.9304	+	8.12843i	−0.833654	+	0.283167i
$825$		0			0
$826$	0.840273	+	7.66791i	0.0292368	+	0.266801i
$827$		−	24.6612i		−	0.857554i	−0.903410	−	0.428777i	$-0.858945\pi$
$827$		−	24.6612i		−	0.857554i	0.903410	−	0.428777i	$-0.141055\pi$
$828$		0			0
$829$			29.3304i			1.01869i	0.860564	+	0.509343i	$0.170111\pi$
$829$			29.3304i			1.01869i	−0.860564	+	0.509343i	$0.829889\pi$
$830$	−3.75789	+	0.411802i	−0.130438	+	0.0142938i
$831$		0			0
$832$	−23.2315	−	30.2517i	−0.805408	−	1.04879i
$833$		−	2.74335i		−	0.0950513i
$834$		0			0
$835$	1.90127			0.0657961
$836$	−1.93709	−	8.73234i	−0.0669958	−	0.302014i
$837$		0			0
$838$	17.4604	−	1.91337i	0.603160	−	0.0660961i
$839$	10.5258			0.363390			0.181695	−	0.983355i	$-0.441842\pi$
$839$	10.5258			0.363390			0.181695	+	0.983355i	$0.441842\pi$
$840$		0			0
$841$	−13.3096			−0.458950
$842$	30.0322	−	3.29103i	1.03498	−	0.113416i
$843$		0			0
$844$	46.7313	−	10.3664i	1.60856	−	0.356826i
$845$	1.57688			0.0542462
$846$		0			0
$847$		−	5.22308i		−	0.179467i
$848$	29.8223	−	13.9157i	1.02410	−	0.477869i
$849$		0			0
$850$	−19.1817	+	2.10199i	−0.657927	+	0.0720977i
$851$			8.10368i			0.277791i
$852$		0			0
$853$		−	36.6192i		−	1.25382i	−0.779093	−	0.626908i	$-0.784320\pi$
$853$		−	36.6192i		−	1.25382i	0.779093	−	0.626908i	$-0.215680\pi$
$854$	−0.660193	−	6.02459i	−0.0225913	−	0.206157i
$855$		0			0
$856$	−40.0060	+	13.5888i	−1.36738	+	0.464457i
$857$			9.24273i			0.315726i	0.987461	+	0.157863i	$0.0504604\pi$
$857$			9.24273i			0.315726i	−0.987461	+	0.157863i	$0.949540\pi$
$858$		0			0
$859$	−49.5357			−1.69014			−0.845068	−	0.534659i	$-0.820440\pi$
$859$	−49.5357			−1.69014			−0.845068	+	0.534659i	$0.820440\pi$
$860$	−0.540745	+	0.119953i	−0.0184393	+	0.00409038i
$861$		0			0
$862$	3.29131	+	30.0348i	0.112102	+	1.02299i
$863$	−29.0407			−0.988557			−0.494278	−	0.869304i	$-0.664568\pi$
$863$	−29.0407			−0.988557			−0.494278	+	0.869304i	$0.664568\pi$
$864$		0			0
$865$	2.95820			0.100582
$866$	−3.32497	−	30.3420i	−0.112987	−	1.03106i
$867$		0			0
$868$	−15.6533	+	3.47238i	−0.531308	+	0.117860i
$869$	23.4405			0.795166
$870$		0			0
$871$		−	21.9905i		−	0.745120i
$872$	11.6177	−	3.94620i	0.393426	−	0.133635i
$873$		0			0
$874$	0.381157	+	3.47825i	0.0128928	+	0.117653i
$875$		−	1.61600i		−	0.0546307i
$876$		0			0
$877$			15.3569i			0.518564i	0.965802	+	0.259282i	$0.0834859\pi$
$877$			15.3569i			0.518564i	−0.965802	+	0.259282i	$0.916514\pi$
$878$	18.9585	−	2.07753i	0.639820	−	0.0701134i
$879$		0			0
$880$	0.658686	+	1.41161i	0.0222043	+	0.0475852i
$881$		−	52.3468i		−	1.76361i	−0.471616	−	0.881804i	$-0.656329\pi$
$881$		−	52.3468i		−	1.76361i	0.471616	−	0.881804i	$-0.343671\pi$
$882$		0			0
$883$	7.73223			0.260210			0.130105	−	0.991500i	$-0.458469\pi$
$883$	7.73223			0.260210			0.130105	+	0.991500i	$0.458469\pi$
$884$	25.5389	−	5.66528i	0.858965	−	0.190544i
$885$		0			0
$886$	6.03403	−	0.661228i	0.202717	−	0.0222144i
$887$	7.43973			0.249802			0.124901	−	0.992169i	$-0.460139\pi$
$887$	7.43973			0.249802			0.124901	+	0.992169i	$0.460139\pi$
$888$		0			0
$889$	−0.196751			−0.00659883
$890$	0.535378	−	0.0586684i	0.0179459	−	0.00196657i
$891$		0			0
$892$	−6.06070	−	27.3214i	−0.202927	−	0.914787i
$893$	−22.6082			−0.756555
$894$		0			0
$895$			2.36476i			0.0790452i
$896$	8.16908	−	7.82727i	0.272910	−	0.261491i
$897$		0			0
$898$	47.3968	−	5.19388i	1.58165	−	0.173322i
$899$		−	31.7560i		−	1.05912i
$900$		0			0
$901$			22.5704i			0.751928i
$902$	−1.17333	−	10.7073i	−0.0390678	−	0.356513i
$903$		0			0
$904$	1.20810	−	0.410354i	0.0401807	−	0.0136482i
$905$			0.618978i			0.0205755i
$906$		0			0
$907$	−31.5786			−1.04855			−0.524276	−	0.851549i	$-0.675664\pi$
$907$	−31.5786			−1.04855			−0.524276	+	0.851549i	$0.675664\pi$
$908$	4.72004	+	21.2777i	0.156640	+	0.706127i
$909$		0			0
$910$	0.119006	+	1.08599i	0.00394502	+	0.0360003i
$911$	26.2059			0.868240			0.434120	−	0.900855i	$-0.357059\pi$
$911$	26.2059			0.868240			0.434120	+	0.900855i	$0.357059\pi$
$912$		0			0
$913$	39.6541			1.31236
$914$	4.82056	+	43.9901i	0.159450	+	1.45506i
$915$		0			0
$916$	−4.82071	−	21.7315i	−0.159281	−	0.718031i
$917$	−4.69097			−0.154909
$918$		0			0
$919$		−	37.9577i		−	1.25211i	−0.779779	−	0.626055i	$-0.784668\pi$
$919$		−	37.9577i		−	1.25211i	0.779779	−	0.626055i	$-0.215332\pi$
$920$	−0.195987	−	0.576993i	−0.00646151	−	0.0190229i
$921$		0			0
$922$	4.76397	+	43.4736i	0.156893	+	1.43173i
$923$			66.6386i			2.19344i
$924$		0			0
$925$		−	30.3118i		−	0.996646i
$926$	−16.8921	+	1.85109i	−0.555109	+	0.0608305i
$927$		0			0
$928$	11.6306	+	19.1527i	0.381792	+	0.628717i
$929$		−	33.3343i		−	1.09366i	−0.837243	−	0.546831i	$-0.815834\pi$
$929$		−	33.3343i		−	1.09366i	0.837243	−	0.546831i	$-0.184166\pi$
$930$		0			0
$931$	1.86073			0.0609829
$932$	−5.96759	−	26.9016i	−0.195475	−	0.881192i
$933$		0			0
$934$	10.1833	−	1.11592i	0.333208	−	0.0365140i
$935$	−1.06834			−0.0349385
$936$		0			0
$937$	8.18384			0.267355			0.133677	−	0.991025i	$-0.457321\pi$
$937$	8.18384			0.267355			0.133677	+	0.991025i	$0.457321\pi$
$938$	6.48390	−	0.710526i	0.211707	−	0.0231995i
$939$		0			0
$940$	3.84383	−	0.852677i	0.125372	−	0.0278113i
$941$	43.9315			1.43213			0.716064	−	0.698035i	$-0.245942\pi$
$941$	43.9315			1.43213			0.716064	+	0.698035i	$0.245942\pi$
$942$		0			0
$943$			4.21368i			0.137216i
$944$	−9.22576	−	19.7714i	−0.300273	−	0.643504i
$945$		0			0
$946$	5.77541	−	0.632887i	0.187775	−	0.0205769i
$947$			45.0323i			1.46335i	0.681652	+	0.731676i	$0.261262\pi$
$947$			45.0323i			1.46335i	−0.681652	+	0.731676i	$0.738738\pi$
$948$		0			0
$949$		−	30.4100i		−	0.987150i
$950$	−1.42572	−	13.0104i	−0.0462564	−	0.422112i
$951$		0			0
$952$	2.49558	+	7.34708i	0.0808823	+	0.238120i
$953$			60.2109i			1.95042i	0.221278	+	0.975211i	$0.428977\pi$
$953$			60.2109i			1.95042i	−0.221278	+	0.975211i	$0.571023\pi$
$954$		0			0
$955$	−3.47457			−0.112434
$956$	15.6058	−	3.46184i	0.504728	−	0.111964i
$957$		0			0
$958$	−4.90750	−	44.7834i	−0.158554	−	1.44689i
$959$	−11.1485			−0.360003
$960$		0			0
$961$	−33.2710			−1.07326
$962$	4.47627	+	40.8482i	0.144321	+	1.31700i
$963$		0			0
$964$	10.1203	−	2.24499i	0.325954	−	0.0723064i
$965$	2.85150			0.0917931
$966$		0			0
$967$		−	1.96099i		−	0.0630613i	−0.999503	−	0.0315307i	$-0.989962\pi$
$967$		−	1.96099i		−	0.0630613i	0.999503	−	0.0315307i	$-0.0100382\pi$
$968$	4.75137	+	13.9882i	0.152715	+	0.449597i
$969$		0			0
$970$	0.360847	+	3.29291i	0.0115861	+	0.105729i
$971$			36.5960i			1.17442i	0.809434	+	0.587210i	$0.199774\pi$
$971$			36.5960i			1.17442i	−0.809434	+	0.587210i	$0.800226\pi$
$972$		0			0
$973$		−	6.93228i		−	0.222239i
$974$	−52.5253	+	5.75589i	−1.68302	+	0.184430i
$975$		0			0
$976$	7.24858	+	15.5342i	0.232021	+	0.497236i
$977$		−	18.0891i		−	0.578721i	−0.957220	−	0.289361i	$-0.906557\pi$
$977$		−	18.0891i		−	0.578721i	0.957220	−	0.289361i	$-0.0934427\pi$
$978$		0			0
$979$	−5.64942			−0.180556
$980$	−0.316360	+	0.0701781i	−0.0101057	+	0.00224176i
$981$		0			0
$982$	−33.5126	+	3.67242i	−1.06943	+	0.117192i
$983$	−12.7144			−0.405525			−0.202763	−	0.979228i	$-0.564992\pi$
$983$	−12.7144			−0.405525			−0.202763	+	0.979228i	$0.564992\pi$
$984$		0			0
$985$	3.10001			0.0987744
$986$	−15.2764	+	1.67403i	−0.486500	+	0.0533121i
$987$		0			0
$988$	3.84259	+	17.3222i	0.122249	+	0.551094i
$989$	−2.27282			−0.0722716
$990$		0			0
$991$			58.4330i			1.85619i	0.372348	+	0.928093i	$0.378553\pi$
$991$			58.4330i			1.85619i	−0.372348	+	0.928093i	$0.621447\pi$
$992$	38.7631	−	23.5391i	1.23073	−	0.747369i
$993$		0			0
$994$	−19.6484	+	2.15313i	−0.623209	+	0.0682931i
$995$			2.15696i			0.0683803i
$996$		0			0
$997$			33.7142i			1.06774i	0.845567	+	0.533869i	$0.179263\pi$
$997$			33.7142i			1.06774i	−0.845567	+	0.533869i	$0.820737\pi$
$998$	−2.00428	−	18.2901i	−0.0634445	−	0.578962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.15	✓	32
3.2	odd	2	inner	1512.2.j.c.323.18	yes	32
4.3	odd	2		6048.2.j.c.5615.15		32
8.3	odd	2	inner	1512.2.j.c.323.17	yes	32
8.5	even	2		6048.2.j.c.5615.17		32
12.11	even	2		6048.2.j.c.5615.18		32
24.5	odd	2		6048.2.j.c.5615.16		32
24.11	even	2	inner	1512.2.j.c.323.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.15	✓	32	1.1	even	1	trivial
1512.2.j.c.323.16	yes	32	24.11	even	2	inner
1512.2.j.c.323.17	yes	32	8.3	odd	2	inner
1512.2.j.c.323.18	yes	32	3.2	odd	2	inner
6048.2.j.c.5615.15		32	4.3	odd	2
6048.2.j.c.5615.16		32	24.5	odd	2
6048.2.j.c.5615.17		32	8.5	even	2
6048.2.j.c.5615.18		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.154052 - 1.40580i) q^{2} +(-1.95254 + 0.433131i) q^{4} -0.162025 q^{5} -1.00000i q^{7} +(0.909686 + 2.67815i) q^{8} +O(q^{10})\)	\(q+(-0.154052 - 1.40580i) q^{2} +(-1.95254 + 0.433131i) q^{4} -0.162025 q^{5} -1.00000i q^{7} +(0.909686 + 2.67815i) q^{8} +(0.0249602 + 0.227774i) q^{10} -2.40352i q^{11} +4.76784i q^{13} +(-1.40580 + 0.154052i) q^{14} +(3.62480 - 1.69141i) q^{16} +2.74335i q^{17} -1.86073 q^{19} +(0.316360 - 0.0701781i) q^{20} +(-3.37887 + 0.370267i) q^{22} +1.32970 q^{23} -4.97375 q^{25} +(6.70262 - 0.734494i) q^{26} +(0.433131 + 1.95254i) q^{28} -3.96112 q^{29} +8.01692i q^{31} +(-2.93618 - 4.83517i) q^{32} +(3.85659 - 0.422617i) q^{34} +0.162025i q^{35} +6.09436i q^{37} +(0.286648 + 2.61581i) q^{38} +(-0.147392 - 0.433927i) q^{40} +3.16889i q^{41} -1.70927 q^{43} +(1.04104 + 4.69296i) q^{44} +(-0.204843 - 1.86929i) q^{46} +12.1502 q^{47} -1.00000 q^{49} +(0.766214 + 6.99208i) q^{50} +(-2.06510 - 9.30938i) q^{52} +8.22731 q^{53} +0.389431i q^{55} +(2.67815 - 0.909686i) q^{56} +(0.610217 + 5.56853i) q^{58} -5.45449i q^{59} +4.28553i q^{61} +(11.2702 - 1.23502i) q^{62} +(-6.34494 + 4.87255i) q^{64} -0.772509i q^{65} -4.61226 q^{67} +(-1.18823 - 5.35648i) q^{68} +(0.227774 - 0.0249602i) q^{70} +13.9767 q^{71} -6.37815 q^{73} +(8.56744 - 0.938846i) q^{74} +(3.63314 - 0.805940i) q^{76} -2.40352 q^{77} +9.75258i q^{79} +(-0.587307 + 0.274050i) q^{80} +(4.45482 - 0.488173i) q^{82} +16.4983i q^{83} -0.444491i q^{85} +(0.263316 + 2.40289i) q^{86} +(6.43699 - 2.18645i) q^{88} -2.35048i q^{89} +4.76784 q^{91} +(-2.59629 + 0.575935i) q^{92} +(-1.87176 - 17.0807i) q^{94} +0.301485 q^{95} +14.4569 q^{97} +(0.154052 + 1.40580i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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