LMFDB - Embedded newform 936.2.j.a.755.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(755,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.755"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			755.37
Character	$\chi$	$=$	936.755
Dual form			936.2.j.a.755.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01985 - 0.979751i) q^{2} +(0.0801759 - 1.99839i) q^{4} -2.22260 q^{5} +0.534598i q^{7} +(-1.87616 - 2.11661i) q^{8} +(-2.26672 + 2.17760i) q^{10} -2.35523i q^{11} +1.00000i q^{13} +(0.523773 + 0.545208i) q^{14} +(-3.98714 - 0.320446i) q^{16} -4.78791i q^{17} -4.25343 q^{19} +(-0.178199 + 4.44164i) q^{20} +(-2.30754 - 2.40198i) q^{22} -2.55292 q^{23} -0.0600300 q^{25} +(0.979751 + 1.01985i) q^{26} +(1.06834 + 0.0428618i) q^{28} -8.32790 q^{29} -0.284086i q^{31} +(-4.38023 + 3.57960i) q^{32} +(-4.69096 - 4.88293i) q^{34} -1.18820i q^{35} +6.30002i q^{37} +(-4.33784 + 4.16730i) q^{38} +(4.16996 + 4.70438i) q^{40} -4.33386i q^{41} -0.666197 q^{43} +(-4.70668 - 0.188833i) q^{44} +(-2.60359 + 2.50122i) q^{46} -1.10114 q^{47} +6.71421 q^{49} +(-0.0612214 + 0.0588145i) q^{50} +(1.99839 + 0.0801759i) q^{52} -1.42724 q^{53} +5.23475i q^{55} +(1.13153 - 1.00299i) q^{56} +(-8.49319 + 8.15927i) q^{58} -3.21354i q^{59} -4.98877i q^{61} +(-0.278334 - 0.289724i) q^{62} +(-0.960049 + 7.94219i) q^{64} -2.22260i q^{65} +0.658322 q^{67} +(-9.56811 - 0.383874i) q^{68} +(-1.16414 - 1.21178i) q^{70} +12.3352 q^{71} +14.1390 q^{73} +(6.17245 + 6.42505i) q^{74} +(-0.341022 + 8.50001i) q^{76} +1.25910 q^{77} -11.8382i q^{79} +(8.86184 + 0.712224i) q^{80} +(-4.24610 - 4.41987i) q^{82} -14.7707i q^{83} +10.6416i q^{85} +(-0.679419 + 0.652707i) q^{86} +(-4.98510 + 4.41879i) q^{88} -1.91146i q^{89} -0.534598 q^{91} +(-0.204682 + 5.10173i) q^{92} +(-1.12300 + 1.07885i) q^{94} +9.45368 q^{95} -7.69682 q^{97} +(6.84746 - 6.57825i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.01985	−	0.979751i	0.721141	−	0.692789i
$2$	1.01985	−	0.979751i	0.721141	−	0.692789i
$3$		0			0
$3$		0			0
$4$	0.0801759	−	1.99839i	0.0400879	−	0.999196i
$5$	−2.22260			−0.993979			−0.496989	−	0.867757i	$-0.665561\pi$
$5$	−2.22260			−0.993979			−0.496989	+	0.867757i	$0.665561\pi$
$6$		0			0
$7$			0.534598i			0.202059i	0.994883	+	0.101029i	$0.0322136\pi$
$7$			0.534598i			0.202059i	−0.994883	+	0.101029i	$0.967786\pi$
$8$	−1.87616	−	2.11661i	−0.663323	−	0.748334i
$9$		0			0
$10$	−2.26672	+	2.17760i	−0.716799	+	0.688617i
$11$		−	2.35523i		−	0.710129i	−0.934842	−	0.355065i	$-0.884459\pi$
$11$		−	2.35523i		−	0.710129i	0.934842	−	0.355065i	$-0.115541\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.523773	+	0.545208i	0.139984	+	0.145713i
$15$		0			0
$16$	−3.98714	−	0.320446i	−0.996786	−	0.0801114i
$17$		−	4.78791i		−	1.16124i	−0.814176	−	0.580619i	$-0.802811\pi$
$17$		−	4.78791i		−	1.16124i	0.814176	−	0.580619i	$-0.197189\pi$
$18$		0			0
$19$	−4.25343			−0.975803			−0.487901	−	0.872899i	$-0.662237\pi$
$19$	−4.25343			−0.975803			−0.487901	+	0.872899i	$0.662237\pi$
$20$	−0.178199	+	4.44164i	−0.0398466	+	0.993180i
$21$		0			0
$22$	−2.30754	−	2.40198i	−0.491969	−	0.512103i
$23$	−2.55292			−0.532320			−0.266160	−	0.963929i	$-0.585755\pi$
$23$	−2.55292			−0.532320			−0.266160	+	0.963929i	$0.585755\pi$
$24$		0			0
$25$	−0.0600300			−0.0120060
$26$	0.979751	+	1.01985i	0.192145	+	0.200008i
$27$		0			0
$28$	1.06834	+	0.0428618i	0.201897	+	0.00810013i
$29$	−8.32790			−1.54645			−0.773226	−	0.634130i	$-0.781358\pi$
$29$	−8.32790			−1.54645			−0.773226	+	0.634130i	$0.781358\pi$
$30$		0			0
$31$		−	0.284086i		−	0.0510234i	−0.999675	−	0.0255117i	$-0.991878\pi$
$31$		−	0.284086i		−	0.0510234i	0.999675	−	0.0255117i	$-0.00812150\pi$
$32$	−4.38023	+	3.57960i	−0.774323	+	0.632790i
$33$		0			0
$34$	−4.69096	−	4.88293i	−0.804492	−	0.837416i
$35$		−	1.18820i		−	0.200842i
$36$		0			0
$37$			6.30002i			1.03572i	0.855467	+	0.517858i	$0.173270\pi$
$37$			6.30002i			1.03572i	−0.855467	+	0.517858i	$0.826730\pi$
$38$	−4.33784	+	4.16730i	−0.703691	+	0.676025i
$39$		0			0
$40$	4.16996	+	4.70438i	0.659329	+	0.743828i
$41$		−	4.33386i		−	0.676835i	−0.940996	−	0.338417i	$-0.890108\pi$
$41$		−	4.33386i		−	0.676835i	0.940996	−	0.338417i	$-0.109892\pi$
$42$		0			0
$43$	−0.666197			−0.101594			−0.0507970	−	0.998709i	$-0.516176\pi$
$43$	−0.666197			−0.101594			−0.0507970	+	0.998709i	$0.516176\pi$
$44$	−4.70668	−	0.188833i	−0.709558	−	0.0284676i
$45$		0			0
$46$	−2.60359	+	2.50122i	−0.383878	+	0.368785i
$47$	−1.10114			−0.160618			−0.0803092	−	0.996770i	$-0.525591\pi$
$47$	−1.10114			−0.160618			−0.0803092	+	0.996770i	$0.525591\pi$
$48$		0			0
$49$	6.71421			0.959172
$50$	−0.0612214	+	0.0588145i	−0.00865802	+	0.00831762i
$51$		0			0
$52$	1.99839	+	0.0801759i	0.277127	+	0.0111184i
$53$	−1.42724			−0.196047			−0.0980233	−	0.995184i	$-0.531252\pi$
$53$	−1.42724			−0.196047			−0.0980233	+	0.995184i	$0.531252\pi$
$54$		0			0
$55$			5.23475i			0.705853i
$56$	1.13153	−	1.00299i	0.151207	−	0.134030i
$57$		0			0
$58$	−8.49319	+	8.15927i	−1.11521	+	1.07136i
$59$		−	3.21354i		−	0.418368i	−0.977876	−	0.209184i	$-0.932919\pi$
$59$		−	3.21354i		−	0.418368i	0.977876	−	0.209184i	$-0.0670807\pi$
$60$		0			0
$61$		−	4.98877i		−	0.638747i	−0.947629	−	0.319373i	$-0.896528\pi$
$61$		−	4.98877i		−	0.638747i	0.947629	−	0.319373i	$-0.103472\pi$
$62$	−0.278334	−	0.289724i	−0.0353484	−	0.0367950i
$63$		0			0
$64$	−0.960049	+	7.94219i	−0.120006	+	0.992773i
$65$		−	2.22260i		−	0.275680i
$66$		0			0
$67$	0.658322			0.0804268			0.0402134	−	0.999191i	$-0.487196\pi$
$67$	0.658322			0.0804268			0.0402134	+	0.999191i	$0.487196\pi$
$68$	−9.56811	−	0.383874i	−1.16030	−	0.0465516i
$69$		0			0
$70$	−1.16414	−	1.21178i	−0.139141	−	0.144836i
$71$	12.3352			1.46391			0.731957	−	0.681350i	$-0.238607\pi$
$71$	12.3352			1.46391			0.731957	+	0.681350i	$0.238607\pi$
$72$		0			0
$73$	14.1390			1.65485			0.827423	−	0.561579i	$-0.189806\pi$
$73$	14.1390			1.65485			0.827423	+	0.561579i	$0.189806\pi$
$74$	6.17245	+	6.42505i	0.717532	+	0.746897i
$75$		0			0
$76$	−0.341022	+	8.50001i	−0.0391179	+	0.975018i
$77$	1.25910			0.143488
$78$		0			0
$79$		−	11.8382i		−	1.33190i	−0.745998	−	0.665948i	$-0.768027\pi$
$79$		−	11.8382i		−	1.33190i	0.745998	−	0.665948i	$-0.231973\pi$
$80$	8.86184	+	0.712224i	0.990784	+	0.0796291i
$81$		0			0
$82$	−4.24610	−	4.41987i	−0.468903	−	0.488093i
$83$		−	14.7707i		−	1.62130i	−0.585531	−	0.810650i	$-0.699114\pi$
$83$		−	14.7707i		−	1.62130i	0.585531	−	0.810650i	$-0.300886\pi$
$84$		0			0
$85$			10.6416i			1.15425i
$86$	−0.679419	+	0.652707i	−0.0732636	+	0.0703832i
$87$		0			0
$88$	−4.98510	+	4.41879i	−0.531413	+	0.471045i
$89$		−	1.91146i		−	0.202614i	−0.994855	−	0.101307i	$-0.967697\pi$
$89$		−	1.91146i		−	0.202614i	0.994855	−	0.101307i	$-0.0323025\pi$
$90$		0			0
$91$	−0.534598			−0.0560411
$92$	−0.204682	+	5.10173i	−0.0213396	+	0.531892i
$93$		0			0
$94$	−1.12300	+	1.07885i	−0.115828	+	0.111275i
$95$	9.45368			0.969927
$96$		0			0
$97$	−7.69682			−0.781493			−0.390747	−	0.920498i	$-0.627783\pi$
$97$	−7.69682			−0.781493			−0.390747	+	0.920498i	$0.627783\pi$
$98$	6.84746	−	6.57825i	0.691698	−	0.664504i
$99$		0			0
$100$	−0.00481296	+	0.119964i	−0.000481296	+	0.0119964i
$101$	−1.87035			−0.186106			−0.0930532	−	0.995661i	$-0.529663\pi$
$101$	−1.87035			−0.186106			−0.0930532	+	0.995661i	$0.529663\pi$
$102$		0			0
$103$			0.952030i			0.0938063i	0.998899	+	0.0469031i	$0.0149352\pi$
$103$			0.952030i			0.0938063i	−0.998899	+	0.0469031i	$0.985065\pi$
$104$	2.11661	−	1.87616i	0.207550	−	0.183973i
$105$		0			0
$106$	−1.45557	+	1.39834i	−0.141377	+	0.135819i
$107$		−	16.5895i		−	1.60377i	−0.597481	−	0.801883i	$-0.703832\pi$
$107$		−	16.5895i		−	1.60377i	0.597481	−	0.801883i	$-0.296168\pi$
$108$		0			0
$109$			9.32470i			0.893144i	0.894748	+	0.446572i	$0.147355\pi$
$109$			9.32470i			0.893144i	−0.894748	+	0.446572i	$0.852645\pi$
$110$	5.12875	+	5.33864i	0.489007	+	0.509020i
$111$		0			0
$112$	0.171310	−	2.13152i	0.0161872	−	0.201410i
$113$			3.63306i			0.341770i	0.985291	+	0.170885i	$0.0546626\pi$
$113$			3.63306i			0.341770i	−0.985291	+	0.170885i	$0.945337\pi$
$114$		0			0
$115$	5.67413			0.529115
$116$	−0.667697	+	16.6424i	−0.0619941	+	1.54521i
$117$		0			0
$118$	−3.14847	−	3.27732i	−0.289840	−	0.301702i
$119$	2.55960			0.234638
$120$		0			0
$121$	5.45288			0.495717
$122$	−4.88776	−	5.08779i	−0.442517	−	0.460626i
$123$		0			0
$124$	−0.567715	−	0.0227768i	−0.0509824	−	0.00204542i
$125$	11.2464			1.00591
$126$		0			0
$127$		−	13.2516i		−	1.17589i	−0.808902	−	0.587943i	$-0.799938\pi$
$127$		−	13.2516i		−	1.17589i	0.808902	−	0.587943i	$-0.200062\pi$
$128$	6.80226	+	9.04042i	0.601241	+	0.799068i
$129$		0			0
$130$	−2.17760	−	2.26672i	−0.190988	−	0.198804i
$131$		−	10.2828i		−	0.898409i	−0.893429	−	0.449204i	$-0.851708\pi$
$131$		−	10.2828i		−	0.898409i	0.893429	−	0.449204i	$-0.148292\pi$
$132$		0			0
$133$		−	2.27387i		−	0.197170i
$134$	0.671387	−	0.644991i	0.0579990	−	0.0557188i
$135$		0			0
$136$	−10.1341	+	8.98288i	−0.868993	+	0.770275i
$137$			19.8206i			1.69339i	0.532081	+	0.846694i	$0.321410\pi$
$137$			19.8206i			1.69339i	−0.532081	+	0.846694i	$0.678590\pi$
$138$		0			0
$139$	−21.6113			−1.83304			−0.916522	−	0.399983i	$-0.869016\pi$
$139$	−21.6113			−1.83304			−0.916522	+	0.399983i	$0.869016\pi$
$140$	−2.37449	−	0.0952649i	−0.200681	−	0.00805135i
$141$		0			0
$142$	12.5800	−	12.0854i	1.05569	−	1.01418i
$143$	2.35523			0.196954
$144$		0			0
$145$	18.5096			1.53714
$146$	14.4196	−	13.8527i	1.19338	−	1.14646i
$147$		0			0
$148$	12.5899	+	0.505109i	1.03488	+	0.0415197i
$149$	3.98437			0.326413			0.163206	−	0.986592i	$-0.447816\pi$
$149$	3.98437			0.326413			0.163206	+	0.986592i	$0.447816\pi$
$150$		0			0
$151$		−	6.03988i		−	0.491518i	−0.969331	−	0.245759i	$-0.920963\pi$
$151$		−	6.03988i		−	0.491518i	0.969331	−	0.245759i	$-0.0790372\pi$
$152$	7.98011	+	9.00283i	0.647272	+	0.730226i
$153$		0			0
$154$	1.28409	−	1.23361i	0.103475	−	0.0994068i
$155$			0.631411i			0.0507162i
$156$		0			0
$157$		−	9.13676i		−	0.729193i	−0.931166	−	0.364597i	$-0.881207\pi$
$157$		−	9.13676i		−	0.729193i	0.931166	−	0.364597i	$-0.118793\pi$
$158$	−11.5984	−	12.0731i	−0.922723	−	0.960485i
$159$		0			0
$160$	9.73553	−	7.95604i	0.769661	−	0.628980i
$161$		−	1.36478i		−	0.107560i
$162$		0			0
$163$	21.7664			1.70487			0.852437	−	0.522829i	$-0.175124\pi$
$163$	21.7664			1.70487			0.852437	+	0.522829i	$0.175124\pi$
$164$	−8.66075	−	0.347471i	−0.676291	−	0.0271329i
$165$		0			0
$166$	−14.4717	−	15.0639i	−1.12322	−	1.16919i
$167$	−14.7137			−1.13858			−0.569291	−	0.822136i	$-0.692782\pi$
$167$	−14.7137			−1.13858			−0.569291	+	0.822136i	$0.692782\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	10.4261	+	10.8528i	0.799648	+	0.832374i
$171$		0			0
$172$	−0.0534129	+	1.33132i	−0.00407270	+	0.101512i
$173$	−14.1757			−1.07776			−0.538881	−	0.842382i	$-0.681153\pi$
$173$	−14.1757			−1.07776			−0.538881	+	0.842382i	$0.681153\pi$
$174$		0			0
$175$		−	0.0320919i		−	0.00242592i
$176$	−0.754724	+	9.39065i	−0.0568894	+	0.707847i
$177$		0			0
$178$	−1.87276	−	1.94940i	−0.140369	−	0.146114i
$179$			17.7742i			1.32851i	0.747506	+	0.664255i	$0.231251\pi$
$179$			17.7742i			1.32851i	−0.747506	+	0.664255i	$0.768749\pi$
$180$		0			0
$181$			15.3188i			1.13864i	0.822117	+	0.569318i	$0.192793\pi$
$181$			15.3188i			1.13864i	−0.822117	+	0.569318i	$0.807207\pi$
$182$	−0.545208	+	0.523773i	−0.0404135	+	0.0388246i
$183$		0			0
$184$	4.78968	+	5.40352i	0.353100	+	0.398353i
$185$		−	14.0024i		−	1.02948i
$186$		0			0
$187$	−11.2766			−0.824629
$188$	−0.0882852	+	2.20052i	−0.00643886	+	0.160489i
$189$		0			0
$190$	9.64131	−	9.26226i	0.699454	−	0.671955i
$191$	−3.40080			−0.246073			−0.123037	−	0.992402i	$-0.539263\pi$
$191$	−3.40080			−0.246073			−0.123037	+	0.992402i	$0.539263\pi$
$192$		0			0
$193$	9.94428			0.715805			0.357902	−	0.933759i	$-0.383492\pi$
$193$	9.94428			0.715805			0.357902	+	0.933759i	$0.383492\pi$
$194$	−7.84958	+	7.54096i	−0.563567	+	0.541410i
$195$		0			0
$196$	0.538317	−	13.4176i	0.0384512	−	0.958401i
$197$	0.736457			0.0524704			0.0262352	−	0.999656i	$-0.491648\pi$
$197$	0.736457			0.0524704			0.0262352	+	0.999656i	$0.491648\pi$
$198$		0			0
$199$		−	14.0332i		−	0.994789i	−0.867524	−	0.497395i	$-0.834290\pi$
$199$		−	14.0332i		−	0.994789i	0.867524	−	0.497395i	$-0.165710\pi$
$200$	0.112626	+	0.127060i	0.00796385	+	0.00898449i
$201$		0			0
$202$	−1.90747	+	1.83247i	−0.134209	+	0.128932i
$203$		−	4.45208i		−	0.312475i
$204$		0			0
$205$			9.63245i			0.672760i
$206$	0.932752	+	0.970925i	0.0649879	+	0.0676475i
$207$		0			0
$208$	0.320446	−	3.98714i	0.0222189	−	0.276459i
$209$			10.0178i			0.692946i
$210$		0			0
$211$	−1.55071			−0.106756			−0.0533778	−	0.998574i	$-0.516999\pi$
$211$	−1.55071			−0.106756			−0.0533778	+	0.998574i	$0.516999\pi$
$212$	−0.114430	+	2.85219i	−0.00785911	+	0.195889i
$213$		0			0
$214$	−16.2536	−	16.9187i	−1.11107	−	1.15654i
$215$	1.48069			0.100982
$216$		0			0
$217$	0.151872			0.0103097
$218$	9.13588	+	9.50976i	0.618760	+	0.644082i
$219$		0			0
$220$	10.4611	+	0.419700i	0.705286	+	0.0282962i
$221$	4.78791			0.322069
$222$		0			0
$223$		−	3.64245i		−	0.243917i	−0.992535	−	0.121958i	$-0.961083\pi$
$223$		−	3.64245i		−	0.243917i	0.992535	−	0.121958i	$-0.0389174\pi$
$224$	−1.91365	−	2.34166i	−0.127861	−	0.156459i
$225$		0			0
$226$	3.55950	+	3.70517i	0.236774	+	0.246464i
$227$			12.9635i			0.860417i	0.902730	+	0.430208i	$0.141560\pi$
$227$			12.9635i			0.860417i	−0.902730	+	0.430208i	$0.858440\pi$
$228$		0			0
$229$			3.85891i			0.255004i	0.991838	+	0.127502i	$0.0406959\pi$
$229$			3.85891i			0.255004i	−0.991838	+	0.127502i	$0.959304\pi$
$230$	5.78674	−	5.55923i	0.381566	−	0.366565i
$231$		0			0
$232$	15.6245	+	17.6269i	1.02580	+	1.15726i
$233$			17.6243i			1.15461i	0.816529	+	0.577304i	$0.195895\pi$
$233$			17.6243i			1.15461i	−0.816529	+	0.577304i	$0.804105\pi$
$234$		0			0
$235$	2.44741			0.159651
$236$	−6.42192	−	0.257649i	−0.418031	−	0.0167715i
$237$		0			0
$238$	2.61040	−	2.50777i	0.169207	−	0.162555i
$239$	−19.4649			−1.25908			−0.629540	−	0.776968i	$-0.716757\pi$
$239$	−19.4649			−1.25908			−0.629540	+	0.776968i	$0.716757\pi$
$240$		0			0
$241$	9.66859			0.622809			0.311404	−	0.950278i	$-0.399201\pi$
$241$	9.66859			0.622809			0.311404	+	0.950278i	$0.399201\pi$
$242$	5.56111	−	5.34247i	0.357482	−	0.343427i
$243$		0			0
$244$	−9.96953	−	0.399979i	−0.638233	−	0.0256060i
$245$	−14.9230			−0.953397
$246$		0			0
$247$		−	4.25343i		−	0.270639i
$248$	−0.601299	+	0.532991i	−0.0381825	+	0.0338450i
$249$		0			0
$250$	11.4697	−	11.0187i	0.725405	−	0.696885i
$251$		−	10.1660i		−	0.641670i	−0.947135	−	0.320835i	$-0.896036\pi$
$251$		−	10.1660i		−	0.641670i	0.947135	−	0.320835i	$-0.103964\pi$
$252$		0			0
$253$			6.01271i			0.378016i
$254$	−12.9832	−	13.5146i	−0.814641	−	0.847979i
$255$		0			0
$256$	15.7946	+	2.55533i	0.987164	+	0.159708i
$257$			11.2601i			0.702386i	0.936303	+	0.351193i	$0.114224\pi$
$257$			11.2601i			0.702386i	−0.936303	+	0.351193i	$0.885776\pi$
$258$		0			0
$259$	−3.36797			−0.209276
$260$	−4.44164	−	0.178199i	−0.275459	−	0.0110514i
$261$		0			0
$262$	−10.0745	−	10.4868i	−0.622407	−	0.647879i
$263$	29.3228			1.80812			0.904061	−	0.427404i	$-0.140572\pi$
$263$	29.3228			1.80812			0.904061	+	0.427404i	$0.140572\pi$
$264$		0			0
$265$	3.17219			0.194866
$266$	−2.22783	−	2.31900i	−0.136597	−	0.142187i
$267$		0			0
$268$	0.0527815	−	1.31559i	0.00322414	−	0.0803621i
$269$	−1.81250			−0.110510			−0.0552551	−	0.998472i	$-0.517597\pi$
$269$	−1.81250			−0.110510			−0.0552551	+	0.998472i	$0.517597\pi$
$270$		0			0
$271$		−	28.5969i		−	1.73714i	−0.495566	−	0.868570i	$-0.665039\pi$
$271$		−	28.5969i		−	1.73714i	0.495566	−	0.868570i	$-0.334961\pi$
$272$	−1.53426	+	19.0901i	−0.0930284	+	1.15751i
$273$		0			0
$274$	19.4192	+	20.2140i	1.17316	+	1.22117i
$275$			0.141385i			0.00852581i
$276$		0			0
$277$		−	18.6565i		−	1.12096i	−0.828168	−	0.560480i	$-0.810617\pi$
$277$		−	18.6565i		−	1.12096i	0.828168	−	0.560480i	$-0.189383\pi$
$278$	−22.0402	+	21.1737i	−1.32188	+	1.26991i
$279$		0			0
$280$	−2.51495	+	2.22925i	−0.150297	+	0.133223i
$281$			10.2308i			0.610317i	0.952302	+	0.305159i	$0.0987095\pi$
$281$			10.2308i			0.610317i	−0.952302	+	0.305159i	$0.901291\pi$
$282$		0			0
$283$	−6.27100			−0.372772			−0.186386	−	0.982477i	$-0.559678\pi$
$283$	−6.27100			−0.372772			−0.186386	+	0.982477i	$0.559678\pi$
$284$	0.988983	−	24.6505i	0.0586853	−	1.46274i
$285$		0			0
$286$	2.40198	−	2.30754i	0.142032	−	0.136448i
$287$	2.31687			0.136761
$288$		0			0
$289$	−5.92404			−0.348473
$290$	18.8770	−	18.1348i	1.10850	−	1.06491i
$291$		0			0
$292$	1.13361	−	28.2553i	0.0663394	−	1.65352i
$293$	−14.3609			−0.838971			−0.419486	−	0.907762i	$-0.637790\pi$
$293$	−14.3609			−0.838971			−0.419486	+	0.907762i	$0.637790\pi$
$294$		0			0
$295$			7.14243i			0.415849i
$296$	13.3347	−	11.8198i	0.775061	−	0.687014i
$297$		0			0
$298$	4.06345	−	3.90369i	0.235389	−	0.226135i
$299$		−	2.55292i		−	0.147639i
$300$		0			0
$301$		−	0.356147i		−	0.0205280i
$302$	−5.91757	−	6.15975i	−0.340518	−	0.354454i
$303$		0			0
$304$	16.9590	+	1.36299i	0.972667	+	0.0781729i
$305$			11.0881i			0.634901i
$306$		0			0
$307$	20.5030			1.17017			0.585083	−	0.810973i	$-0.301062\pi$
$307$	20.5030			1.17017			0.585083	+	0.810973i	$0.301062\pi$
$308$	0.100950	−	2.51618i	0.00575213	−	0.143373i
$309$		0			0
$310$	0.618626	+	0.643943i	0.0351356	+	0.0365735i
$311$	21.8586			1.23949			0.619744	−	0.784804i	$-0.287236\pi$
$311$	21.8586			1.23949			0.619744	+	0.784804i	$0.287236\pi$
$312$		0			0
$313$	−16.6056			−0.938605			−0.469302	−	0.883038i	$-0.655495\pi$
$313$	−16.6056			−0.938605			−0.469302	+	0.883038i	$0.655495\pi$
$314$	−8.95175	−	9.31810i	−0.505177	−	0.525851i
$315$		0			0
$316$	−23.6573	−	0.949134i	−1.33083	−	0.0533930i
$317$	24.8968			1.39834			0.699171	−	0.714954i	$-0.253553\pi$
$317$	24.8968			1.39834			0.699171	+	0.714954i	$0.253553\pi$
$318$		0			0
$319$			19.6141i			1.09818i
$320$	2.13381	−	17.6523i	0.119284	−	0.986796i
$321$		0			0
$322$	−1.33715	−	1.39187i	−0.0745164	−	0.0775659i
$323$			20.3650i			1.13314i
$324$		0			0
$325$		−	0.0600300i		−	0.00332987i
$326$	22.1984	−	21.3256i	1.22945	−	1.18112i
$327$		0			0
$328$	−9.17307	+	8.13101i	−0.506498	+	0.448960i
$329$		−	0.588669i		−	0.0324544i
$330$		0			0
$331$	−29.5671			−1.62515			−0.812577	−	0.582854i	$-0.801936\pi$
$331$	−29.5671			−1.62515			−0.812577	+	0.582854i	$0.801936\pi$
$332$	−29.5177	−	1.18426i	−1.62000	−	0.0649945i
$333$		0			0
$334$	−15.0058	+	14.4158i	−0.821078	+	0.788797i
$335$	−1.46319			−0.0799425
$336$		0			0
$337$	0.297033			0.0161804			0.00809022	−	0.999967i	$-0.497425\pi$
$337$	0.297033			0.0161804			0.00809022	+	0.999967i	$0.497425\pi$
$338$	−1.01985	+	0.979751i	−0.0554724	+	0.0532914i
$339$		0			0
$340$	21.2661	+	0.853201i	1.15332	+	0.0462713i
$341$	−0.669089			−0.0362332
$342$		0			0
$343$			7.33158i			0.395868i
$344$	1.24989	+	1.41008i	0.0673896	+	0.0760262i
$345$		0			0
$346$	−14.4571	+	13.8887i	−0.777218	+	0.746661i
$347$		−	7.16773i		−	0.384784i	−0.981318	−	0.192392i	$-0.938375\pi$
$347$		−	7.16773i		−	0.384784i	0.981318	−	0.192392i	$-0.0616245\pi$
$348$		0			0
$349$			3.32515i			0.177991i	0.996032	+	0.0889955i	$0.0283657\pi$
$349$			3.32515i			0.177991i	−0.996032	+	0.0889955i	$0.971634\pi$
$350$	−0.0314421	−	0.0327288i	−0.00168065	−	0.00174943i
$351$		0			0
$352$	8.43079	+	10.3165i	0.449363	+	0.549869i
$353$		−	2.31174i		−	0.123041i	−0.998106	−	0.0615207i	$-0.980405\pi$
$353$		−	2.31174i		−	0.123041i	0.998106	−	0.0615207i	$-0.0195950\pi$
$354$		0			0
$355$	−27.4162			−1.45510
$356$	−3.81985	−	0.153253i	−0.202452	−	0.00812239i
$357$		0			0
$358$	17.4143	+	18.1270i	0.920376	+	0.958042i
$359$	30.0147			1.58411			0.792057	−	0.610448i	$-0.209010\pi$
$359$	30.0147			1.58411			0.792057	+	0.610448i	$0.209010\pi$
$360$		0			0
$361$	−0.908366			−0.0478087
$362$	15.0086	+	15.6228i	0.788835	+	0.821118i
$363$		0			0
$364$	−0.0428618	+	1.06834i	−0.00224657	+	0.0559960i
$365$	−31.4254			−1.64488
$366$		0			0
$367$		−	26.3530i		−	1.37562i	−0.725893	−	0.687808i	$-0.758573\pi$
$367$		−	26.3530i		−	1.37562i	0.725893	−	0.687808i	$-0.241427\pi$
$368$	10.1789	+	0.818072i	0.530609	+	0.0426449i
$369$		0			0
$370$	−13.7189	−	14.2803i	−0.713212	−	0.742400i
$371$		−	0.763000i		−	0.0396130i
$372$		0			0
$373$		−	22.9710i		−	1.18939i	−0.803951	−	0.594696i	$-0.797273\pi$
$373$		−	22.9710i		−	1.18939i	0.803951	−	0.594696i	$-0.202727\pi$
$374$	−11.5004	+	11.0483i	−0.594673	+	0.571293i
$375$		0			0
$376$	2.06592	+	2.33069i	0.106542	+	0.120196i
$377$		−	8.32790i		−	0.428909i
$378$		0			0
$379$	−16.2876			−0.836637			−0.418318	−	0.908301i	$-0.637380\pi$
$379$	−16.2876			−0.836637			−0.418318	+	0.908301i	$0.637380\pi$
$380$	0.757957	−	18.8922i	0.0388824	−	0.969148i
$381$		0			0
$382$	−3.46830	+	3.33194i	−0.177453	+	0.170477i
$383$	−11.6718			−0.596404			−0.298202	−	0.954503i	$-0.596387\pi$
$383$	−11.6718			−0.596404			−0.298202	+	0.954503i	$0.596387\pi$
$384$		0			0
$385$	−2.79848			−0.142624
$386$	10.1416	−	9.74292i	0.516196	−	0.495901i
$387$		0			0
$388$	−0.617099	+	15.3813i	−0.0313285	+	0.780865i
$389$	−10.0270			−0.508387			−0.254193	−	0.967153i	$-0.581810\pi$
$389$	−10.0270			−0.508387			−0.254193	+	0.967153i	$0.581810\pi$
$390$		0			0
$391$			12.2231i			0.618150i
$392$	−12.5969	−	14.2113i	−0.636241	−	0.717781i
$393$		0			0
$394$	0.751074	−	0.721545i	0.0378386	−	0.0363509i
$395$			26.3115i			1.32388i
$396$		0			0
$397$		−	18.9924i		−	0.953201i	−0.879120	−	0.476601i	$-0.841869\pi$
$397$		−	18.9924i		−	0.953201i	0.879120	−	0.476601i	$-0.158131\pi$
$398$	−13.7491	−	14.3117i	−0.689178	−	0.717383i
$399$		0			0
$400$	0.239348	+	0.0192364i	0.0119674	+	0.000961818i
$401$		−	23.9527i		−	1.19614i	−0.801444	−	0.598070i	$-0.795935\pi$
$401$		−	23.9527i		−	1.19614i	0.801444	−	0.598070i	$-0.204065\pi$
$402$		0			0
$403$	0.284086			0.0141513
$404$	−0.149957	+	3.73769i	−0.00746062	+	0.185957i
$405$		0			0
$406$	−4.36193	−	4.54044i	−0.216479	−	0.225338i
$407$	14.8380			0.735492
$408$		0			0
$409$	−19.3336			−0.955985			−0.477993	−	0.878364i	$-0.658635\pi$
$409$	−19.3336			−0.955985			−0.477993	+	0.878364i	$0.658635\pi$
$410$	9.43740	+	9.82363i	0.466080	+	0.485154i
$411$		0			0
$412$	1.90253	+	0.0763298i	0.0937309	+	0.00376050i
$413$	1.71795			0.0845349
$414$		0			0
$415$			32.8295i			1.61154i
$416$	−3.57960	−	4.38023i	−0.175504	−	0.214759i
$417$		0			0
$418$	9.81495	+	10.2166i	0.480065	+	0.499712i
$419$			1.67129i			0.0816477i	0.999166	+	0.0408239i	$0.0129982\pi$
$419$			1.67129i			0.0816477i	−0.999166	+	0.0408239i	$0.987002\pi$
$420$		0			0
$421$			18.7410i			0.913380i	0.889626	+	0.456690i	$0.150965\pi$
$421$			18.7410i			0.913380i	−0.889626	+	0.456690i	$0.849035\pi$
$422$	−1.58149	+	1.51931i	−0.0769858	+	0.0739591i
$423$		0			0
$424$	2.67773	+	3.02091i	0.130042	+	0.146708i
$425$			0.287418i			0.0139418i
$426$		0			0
$427$	2.66699			0.129065
$428$	−33.1523	−	1.33008i	−1.60248	−	0.0642917i
$429$		0			0
$430$	1.51008	−	1.45071i	0.0728225	−	0.0699594i
$431$	−17.7512			−0.855043			−0.427522	−	0.904005i	$-0.640613\pi$
$431$	−17.7512			−0.855043			−0.427522	+	0.904005i	$0.640613\pi$
$432$		0			0
$433$	−35.1148			−1.68751			−0.843754	−	0.536729i	$-0.819660\pi$
$433$	−35.1148			−1.68751			−0.843754	+	0.536729i	$0.819660\pi$
$434$	0.154886	−	0.148797i	0.00743477	−	0.00714246i
$435$		0			0
$436$	18.6344	+	0.747615i	0.892426	+	0.0358043i
$437$	10.8586			0.519440
$438$		0			0
$439$		−	2.03379i		−	0.0970674i	−0.998822	−	0.0485337i	$-0.984545\pi$
$439$		−	2.03379i		−	0.0970674i	0.998822	−	0.0485337i	$-0.0154548\pi$
$440$	11.0799	−	9.82122i	0.528214	−	0.468208i
$441$		0			0
$442$	4.88293	−	4.69096i	0.232257	−	0.223126i
$443$		−	5.40321i		−	0.256714i	−0.991728	−	0.128357i	$-0.959030\pi$
$443$		−	5.40321i		−	0.256714i	0.991728	−	0.128357i	$-0.0409704\pi$
$444$		0			0
$445$			4.24842i			0.201394i
$446$	−3.56870	−	3.71475i	−0.168983	−	0.175898i
$447$		0			0
$448$	−4.24587	−	0.513240i	−0.200599	−	0.0242483i
$449$			23.2885i			1.09905i	0.835477	+	0.549525i	$0.185191\pi$
$449$			23.2885i			1.09905i	−0.835477	+	0.549525i	$0.814809\pi$
$450$		0			0
$451$	−10.2072			−0.480640
$452$	7.26028	+	0.291284i	0.341495	+	0.0137008i
$453$		0			0
$454$	12.7010	+	13.2208i	0.596087	+	0.620482i
$455$	1.18820			0.0557036
$456$		0			0
$457$	21.0679			0.985515			0.492758	−	0.870167i	$-0.335989\pi$
$457$	21.0679			0.985515			0.492758	+	0.870167i	$0.335989\pi$
$458$	3.78077	+	3.93550i	0.176664	+	0.183894i
$459$		0			0
$460$	0.454928	−	11.3391i	0.0212111	−	0.528690i
$461$	21.7196			1.01158			0.505792	−	0.862655i	$-0.331200\pi$
$461$	21.7196			1.01158			0.505792	+	0.862655i	$0.331200\pi$
$462$		0			0
$463$			31.7599i			1.47601i	0.674798	+	0.738003i	$0.264231\pi$
$463$			31.7599i			1.47601i	−0.674798	+	0.738003i	$0.735769\pi$
$464$	33.2045	+	2.66864i	1.54148	+	0.123888i
$465$		0			0
$466$	17.2674	+	17.9741i	0.799899	+	0.832635i
$467$			40.1071i			1.85594i	0.372660	+	0.927968i	$0.378446\pi$
$467$			40.1071i			1.85594i	−0.372660	+	0.927968i	$0.621554\pi$
$468$		0			0
$469$			0.351937i			0.0162510i
$470$	2.49598	−	2.39785i	0.115131	−	0.110605i
$471$		0			0
$472$	−6.80181	+	6.02912i	−0.313079	+	0.277513i
$473$			1.56905i			0.0721449i
$474$		0			0
$475$	0.255333			0.0117155
$476$	0.205218	−	5.11509i	0.00940617	−	0.234450i
$477$		0			0
$478$	−19.8512	+	19.0708i	−0.907974	+	0.872277i
$479$	−40.3160			−1.84208			−0.921042	−	0.389463i	$-0.872661\pi$
$479$	−40.3160			−1.84208			−0.921042	+	0.389463i	$0.872661\pi$
$480$		0			0
$481$	−6.30002			−0.287256
$482$	9.86048	−	9.47281i	0.449133	−	0.431475i
$483$		0			0
$484$	0.437190	−	10.8970i	0.0198723	−	0.495318i
$485$	17.1070			0.776788
$486$		0			0
$487$		−	6.50924i		−	0.294962i	−0.989065	−	0.147481i	$-0.952883\pi$
$487$		−	6.50924i		−	0.294962i	0.989065	−	0.147481i	$-0.0471165\pi$
$488$	−10.5593	+	9.35973i	−0.477996	+	0.423695i
$489$		0			0
$490$	−15.2192	+	14.6208i	−0.687533	+	0.660502i
$491$			30.1527i			1.36077i	0.732854	+	0.680386i	$0.238188\pi$
$491$			30.1527i			1.36077i	−0.732854	+	0.680386i	$0.761812\pi$
$492$		0			0
$493$			39.8732i			1.79580i
$494$	−4.16730	−	4.33784i	−0.187496	−	0.195169i
$495$		0			0
$496$	−0.0910342	+	1.13269i	−0.00408755	+	0.0508594i
$497$			6.59435i			0.295797i
$498$		0			0
$499$	−25.4542			−1.13949			−0.569744	−	0.821822i	$-0.692957\pi$
$499$	−25.4542			−1.13949			−0.569744	+	0.821822i	$0.692957\pi$
$500$	0.901693	−	22.4748i	0.0403250	−	1.00510i
$501$		0			0
$502$	−9.96012	−	10.3677i	−0.444542	−	0.462735i
$503$	−28.7136			−1.28028			−0.640138	−	0.768260i	$-0.721123\pi$
$503$	−28.7136			−1.28028			−0.640138	+	0.768260i	$0.721123\pi$
$504$		0			0
$505$	4.15704			0.184986
$506$	5.89096	+	6.13205i	0.261885	+	0.272603i
$507$		0			0
$508$	−26.4818	−	1.06246i	−1.17494	−	0.0471388i
$509$	11.0695			0.490645			0.245323	−	0.969441i	$-0.421106\pi$
$509$	11.0695			0.490645			0.245323	+	0.969441i	$0.421106\pi$
$510$		0			0
$511$			7.55869i			0.334377i
$512$	18.6117	−	12.8688i	0.822528	−	0.568724i
$513$		0			0
$514$	11.0321	+	11.4836i	0.486605	+	0.506519i
$515$		−	2.11599i		−	0.0932414i
$516$		0			0
$517$			2.59345i			0.114060i
$518$	−3.43482	+	3.29978i	−0.150917	+	0.144984i
$519$		0			0
$520$	−4.70438	+	4.16996i	−0.206301	+	0.182865i
$521$			13.6152i			0.596493i	0.954489	+	0.298246i	$0.0964017\pi$
$521$			13.6152i			0.596493i	−0.954489	+	0.298246i	$0.903598\pi$
$522$		0			0
$523$	30.2130			1.32112			0.660561	−	0.750772i	$-0.270318\pi$
$523$	30.2130			1.32112			0.660561	+	0.750772i	$0.270318\pi$
$524$	−20.5490	−	0.824429i	−0.897687	−	0.0360153i
$525$		0			0
$526$	29.9048	−	28.7290i	1.30391	−	1.25265i
$527$	−1.36018			−0.0592503
$528$		0			0
$529$	−16.4826			−0.716635
$530$	3.23515	−	3.10796i	0.140526	−	0.135001i
$531$		0			0
$532$	−4.54409	−	0.182310i	−0.197011	−	0.00790413i
$533$	4.33386			0.187720
$534$		0			0
$535$			36.8719i			1.59411i
$536$	−1.23512	−	1.39341i	−0.0533489	−	0.0601861i
$537$		0			0
$538$	−1.84848	+	1.77580i	−0.0796934	+	0.0765602i
$539$		−	15.8135i		−	0.681136i
$540$		0			0
$541$			21.4574i			0.922527i	0.887263	+	0.461264i	$0.152604\pi$
$541$			21.4574i			0.922527i	−0.887263	+	0.461264i	$0.847396\pi$
$542$	−28.0179	−	29.1645i	−1.20347	−	1.25272i
$543$		0			0
$544$	17.1388	+	20.9721i	0.734820	+	0.899173i
$545$		−	20.7251i		−	0.887766i
$546$		0			0
$547$	−5.45515			−0.233245			−0.116623	−	0.993176i	$-0.537207\pi$
$547$	−5.45515			−0.233245			−0.116623	+	0.993176i	$0.537207\pi$
$548$	39.6093	+	1.58913i	1.69203	+	0.0678844i
$549$		0			0
$550$	0.138522	+	0.144191i	0.00590658	+	0.00614831i
$551$	35.4221			1.50903
$552$		0			0
$553$	6.32865			0.269122
$554$	−18.2787	−	19.0268i	−0.776589	−	0.808370i
$555$		0			0
$556$	−1.73270	+	43.1878i	−0.0734830	+	1.83157i
$557$	−35.6007			−1.50845			−0.754225	−	0.656616i	$-0.771987\pi$
$557$	−35.6007			−1.50845			−0.754225	+	0.656616i	$0.771987\pi$
$558$		0			0
$559$		−	0.666197i		−	0.0281771i
$560$	−0.380753	+	4.73752i	−0.0160898	+	0.200197i
$561$		0			0
$562$	10.0236	+	10.4338i	0.422821	+	0.440125i
$563$		−	17.7813i		−	0.749392i	−0.927148	−	0.374696i	$-0.877747\pi$
$563$		−	17.7813i		−	0.749392i	0.927148	−	0.374696i	$-0.122253\pi$
$564$		0			0
$565$		−	8.07486i		−	0.339712i
$566$	−6.39546	+	6.14402i	−0.268821	+	0.258252i
$567$		0			0
$568$	−23.1427	−	26.1087i	−0.971048	−	1.09550i
$569$		−	7.00142i		−	0.293515i	−0.989173	−	0.146757i	$-0.953116\pi$
$569$		−	7.00142i		−	0.293515i	0.989173	−	0.146757i	$-0.0468837\pi$
$570$		0			0
$571$	32.3791			1.35502			0.677511	−	0.735513i	$-0.263059\pi$
$571$	32.3791			1.35502			0.677511	+	0.735513i	$0.263059\pi$
$572$	0.188833	−	4.70668i	0.00789549	−	0.196796i
$573$		0			0
$574$	2.36285	−	2.26996i	0.0986236	−	0.0947461i
$575$	0.153252			0.00639104
$576$		0			0
$577$	43.8685			1.82627			0.913135	−	0.407657i	$-0.133654\pi$
$577$	43.8685			1.82627			0.913135	+	0.407657i	$0.133654\pi$
$578$	−6.04161	+	5.80408i	−0.251298	+	0.241418i
$579$		0			0
$580$	1.48403	−	36.9895i	0.0616208	−	1.53591i
$581$	7.89641			0.327598
$582$		0			0
$583$			3.36148i			0.139218i
$584$	−26.5271	−	29.9267i	−1.09770	−	1.23838i
$585$		0			0
$586$	−14.6459	+	14.0701i	−0.605016	+	0.581230i
$587$		−	18.5529i		−	0.765758i	−0.923798	−	0.382879i	$-0.874933\pi$
$587$		−	18.5529i		−	0.765758i	0.923798	−	0.382879i	$-0.125067\pi$
$588$		0			0
$589$			1.20834i			0.0497888i
$590$	6.99781	+	7.28419i	0.288095	+	0.299885i
$591$		0			0
$592$	2.01881	−	25.1191i	0.0829727	−	1.03239i
$593$		−	23.1700i		−	0.951479i	−0.879586	−	0.475739i	$-0.842181\pi$
$593$		−	23.1700i		−	0.951479i	0.879586	−	0.475739i	$-0.157819\pi$
$594$		0			0
$595$	−5.68899			−0.233226
$596$	0.319451	−	7.96234i	0.0130852	−	0.326150i
$597$		0			0
$598$	−2.50122	−	2.60359i	−0.102283	−	0.106469i
$599$	−41.7546			−1.70605			−0.853024	−	0.521871i	$-0.825234\pi$
$599$	−41.7546			−1.70605			−0.853024	+	0.521871i	$0.825234\pi$
$600$		0			0
$601$	−44.9068			−1.83179			−0.915894	−	0.401420i	$-0.868517\pi$
$601$	−44.9068			−1.83179			−0.915894	+	0.401420i	$0.868517\pi$
$602$	−0.348936	−	0.363216i	−0.0142216	−	0.0148036i
$603$		0			0
$604$	−12.0700	−	0.484252i	−0.491123	−	0.0197039i
$605$	−12.1196			−0.492732
$606$		0			0
$607$		−	48.1964i		−	1.95623i	−0.208066	−	0.978115i	$-0.566717\pi$
$607$		−	48.1964i		−	1.95623i	0.208066	−	0.978115i	$-0.433283\pi$
$608$	18.6310	−	15.2256i	0.755587	−	0.617479i
$609$		0			0
$610$	10.8635	+	11.3081i	0.439852	+	0.457853i
$611$		−	1.10114i		−	0.0445475i
$612$		0			0
$613$		−	27.5841i		−	1.11411i	−0.830475	−	0.557056i	$-0.811931\pi$
$613$		−	27.5841i		−	1.11411i	0.830475	−	0.557056i	$-0.188069\pi$
$614$	20.9099	−	20.0878i	0.843855	−	0.810678i
$615$		0			0
$616$	−2.36228	−	2.66502i	−0.0951788	−	0.107377i
$617$		−	23.8625i		−	0.960668i	−0.877086	−	0.480334i	$-0.840515\pi$
$617$		−	23.8625i		−	0.960668i	0.877086	−	0.480334i	$-0.159485\pi$
$618$		0			0
$619$	−20.4340			−0.821312			−0.410656	−	0.911790i	$-0.634700\pi$
$619$	−20.4340			−0.821312			−0.410656	+	0.911790i	$0.634700\pi$
$620$	1.26181	+	0.0506239i	0.0506754	+	0.00203311i
$621$		0			0
$622$	22.2924	−	21.4160i	0.893846	−	0.858703i
$623$	1.02186			0.0409401
$624$		0			0
$625$	−24.6962			−0.987850
$626$	−16.9352	+	16.2694i	−0.676866	+	0.650255i
$627$		0			0
$628$	−18.2588	−	0.732548i	−0.728607	−	0.0292318i
$629$	30.1639			1.20271
$630$		0			0
$631$			43.7874i			1.74315i	0.490265	+	0.871574i	$0.336900\pi$
$631$			43.7874i			1.74315i	−0.490265	+	0.871574i	$0.663100\pi$
$632$	−25.0567	+	22.2103i	−0.996703	+	0.883477i
$633$		0			0
$634$	25.3909	−	24.3926i	1.00840	−	0.968755i
$635$			29.4530i			1.16881i
$636$		0			0
$637$			6.71421i			0.266026i
$638$	19.2170	+	20.0034i	0.760807	+	0.791943i
$639$		0			0
$640$	−15.1187	−	20.0933i	−0.597620	−	0.794257i
$641$			26.4737i			1.04565i	0.852441	+	0.522824i	$0.175122\pi$
$641$			26.4737i			1.04565i	−0.852441	+	0.522824i	$0.824878\pi$
$642$		0			0
$643$	30.3343			1.19627			0.598134	−	0.801396i	$-0.295909\pi$
$643$	30.3343			1.19627			0.598134	+	0.801396i	$0.295909\pi$
$644$	−2.72737	−	0.109423i	−0.107474	−	0.00431186i
$645$		0			0
$646$	19.9526	+	20.7692i	0.785026	+	0.817153i
$647$	−11.4455			−0.449971			−0.224985	−	0.974362i	$-0.572233\pi$
$647$	−11.4455			−0.449971			−0.224985	+	0.974362i	$0.572233\pi$
$648$		0			0
$649$	−7.56864			−0.297095
$650$	−0.0588145	−	0.0612214i	−0.00230689	−	0.00240130i
$651$		0			0
$652$	1.74514	−	43.4978i	0.0683449	−	1.70350i
$653$	−5.80591			−0.227203			−0.113601	−	0.993526i	$-0.536239\pi$
$653$	−5.80591			−0.227203			−0.113601	+	0.993526i	$0.536239\pi$
$654$		0			0
$655$			22.8545i			0.892999i
$656$	−1.38877	+	17.2797i	−0.0542222	+	0.674659i
$657$		0			0
$658$	−0.576749	−	0.600353i	−0.0224840	−	0.0234042i
$659$		−	14.6774i		−	0.571752i	−0.958267	−	0.285876i	$-0.907715\pi$
$659$		−	14.6774i		−	0.571752i	0.958267	−	0.285876i	$-0.0922845\pi$
$660$		0			0
$661$			3.77769i			0.146935i	0.997298	+	0.0734676i	$0.0234065\pi$
$661$			3.77769i			0.146935i	−0.997298	+	0.0734676i	$0.976593\pi$
$662$	−30.1539	+	28.9684i	−1.17196	+	1.12589i
$663$		0			0
$664$	−31.2639	+	27.7123i	−1.21327	+	1.07544i
$665$			5.05392i			0.195983i
$666$		0			0
$667$	21.2605			0.823208
$668$	−1.17969	+	29.4038i	−0.0456434	+	1.13767i
$669$		0			0
$670$	−1.49223	+	1.43356i	−0.0576498	+	0.0553833i
$671$	−11.7497			−0.453593
$672$		0			0
$673$	−37.6779			−1.45238			−0.726188	−	0.687496i	$-0.758710\pi$
$673$	−37.6779			−1.45238			−0.726188	+	0.687496i	$0.758710\pi$
$674$	0.302929	−	0.291019i	0.0116684	−	0.0112096i
$675$		0			0
$676$	−0.0801759	+	1.99839i	−0.00308369	+	0.0768612i
$677$	−34.4215			−1.32292			−0.661462	−	0.749979i	$-0.730064\pi$
$677$	−34.4215			−1.32292			−0.661462	+	0.749979i	$0.730064\pi$
$678$		0			0
$679$		−	4.11470i		−	0.157908i
$680$	22.5241	−	19.9654i	0.863761	−	0.765637i
$681$		0			0
$682$	−0.682368	+	0.655540i	−0.0261292	+	0.0251019i
$683$		−	15.2294i		−	0.582739i	−0.956611	−	0.291369i	$-0.905889\pi$
$683$		−	15.2294i		−	0.582739i	0.956611	−	0.291369i	$-0.0941108\pi$
$684$		0			0
$685$		−	44.0533i		−	1.68319i
$686$	7.18313	+	7.47709i	0.274253	+	0.285477i
$687$		0			0
$688$	2.65622	+	0.213480i	0.101268	+	0.00813884i
$689$		−	1.42724i		−	0.0543736i
$690$		0			0
$691$	0.308783			0.0117467			0.00587334	−	0.999983i	$-0.498130\pi$
$691$	0.308783			0.0117467			0.00587334	+	0.999983i	$0.498130\pi$
$692$	−1.13655	+	28.3287i	−0.0432052	+	1.07690i
$693$		0			0
$694$	−7.02259	−	7.30999i	−0.266574	−	0.277483i
$695$	48.0333			1.82201
$696$		0			0
$697$	−20.7501			−0.785966
$698$	3.25782	+	3.39114i	0.123310	+	0.128357i
$699$		0			0
$700$	−0.0641322	−	0.00257300i	−0.00242397	−	9.72501e-5i
$701$	0.0310215			0.00117166			0.000585832	−	1.00000i	$-0.499814\pi$
$701$	0.0310215			0.00117166			0.000585832		1.00000i	$0.499814\pi$
$702$		0			0
$703$		−	26.7967i		−	1.01065i
$704$	18.7057	+	2.26114i	0.704997	+	0.0852198i
$705$		0			0
$706$	−2.26493	−	2.35762i	−0.0852416	−	0.0887301i
$707$		−	0.999883i		−	0.0376045i
$708$		0			0
$709$		−	23.9935i		−	0.901094i	−0.892753	−	0.450547i	$-0.851229\pi$
$709$		−	23.9935i		−	0.901094i	0.892753	−	0.450547i	$-0.148771\pi$
$710$	−27.9603	+	26.8610i	−1.04933	+	1.00808i
$711$		0			0
$712$	−4.04581	+	3.58621i	−0.151623	+	0.134399i
$713$			0.725249i			0.0271608i
$714$		0			0
$715$	−5.23475			−0.195768
$716$	35.5199	+	1.42507i	1.32744	+	0.0532572i
$717$		0			0
$718$	30.6104	−	29.4069i	1.14237	−	1.09746i
$719$	−28.8021			−1.07414			−0.537069	−	0.843538i	$-0.680468\pi$
$719$	−28.8021			−1.07414			−0.537069	+	0.843538i	$0.680468\pi$
$720$		0			0
$721$	−0.508953			−0.0189544
$722$	−0.926394	+	0.889972i	−0.0344768	+	0.0331213i
$723$		0			0
$724$	30.6130	+	1.22820i	1.13772	+	0.0456456i
$725$	0.499924			0.0185667
$726$		0			0
$727$			11.5476i			0.428277i	0.976803	+	0.214138i	$0.0686943\pi$
$727$			11.5476i			0.428277i	−0.976803	+	0.214138i	$0.931306\pi$
$728$	1.00299	+	1.13153i	0.0371733	+	0.0419374i
$729$		0			0
$730$	−32.0491	+	30.7891i	−1.18619	+	1.13956i
$731$			3.18969i			0.117975i
$732$		0			0
$733$		−	34.4289i		−	1.27166i	−0.771830	−	0.635830i	$-0.780658\pi$
$733$		−	34.4289i		−	1.27166i	0.771830	−	0.635830i	$-0.219342\pi$
$734$	−25.8194	−	26.8760i	−0.953011	−	0.992013i
$735$		0			0
$736$	11.1824	−	9.13843i	0.412188	−	0.336847i
$737$		−	1.55050i		−	0.0571134i
$738$		0			0
$739$	47.2448			1.73793			0.868964	−	0.494876i	$-0.164786\pi$
$739$	47.2448			1.73793			0.868964	+	0.494876i	$0.164786\pi$
$740$	−27.9824	−	1.12266i	−1.02865	−	0.0412697i
$741$		0			0
$742$	−0.747550	−	0.778143i	−0.0274434	−	0.0285665i
$743$	−40.8575			−1.49892			−0.749459	−	0.662051i	$-0.769686\pi$
$743$	−40.8575			−1.49892			−0.749459	+	0.662051i	$0.769686\pi$
$744$		0			0
$745$	−8.85568			−0.324447
$746$	−22.5058	−	23.4269i	−0.823997	−	0.857719i
$747$		0			0
$748$	−0.904113	+	22.5351i	−0.0330577	+	0.823966i
$749$	8.86870			0.324055
$750$		0			0
$751$		−	54.4523i		−	1.98699i	−0.113859	−	0.993497i	$-0.536321\pi$
$751$		−	54.4523i		−	1.98699i	0.113859	−	0.993497i	$-0.463679\pi$
$752$	4.39042	+	0.352857i	0.160102	+	0.0128674i
$753$		0			0
$754$	−8.15927	−	8.49319i	−0.297143	−	0.309304i
$755$			13.4243i			0.488559i
$756$		0			0
$757$		−	10.5247i		−	0.382527i	−0.981539	−	0.191263i	$-0.938742\pi$
$757$		−	10.5247i		−	0.382527i	0.981539	−	0.191263i	$-0.0612585\pi$
$758$	−16.6108	+	15.9578i	−0.603333	+	0.579612i
$759$		0			0
$760$	−17.7366	−	20.0097i	−0.643375	−	0.725829i
$761$			1.22084i			0.0442555i	0.999755	+	0.0221278i	$0.00704406\pi$
$761$			1.22084i			0.0442555i	−0.999755	+	0.0221278i	$0.992956\pi$
$762$		0			0
$763$	−4.98496			−0.180468
$764$	−0.272662	+	6.79613i	−0.00986457	+	0.245875i
$765$		0			0
$766$	−11.9035	+	11.4355i	−0.430091	+	0.413182i
$767$	3.21354			0.116034
$768$		0			0
$769$	−6.42116			−0.231553			−0.115777	−	0.993275i	$-0.536936\pi$
$769$	−6.42116			−0.231553			−0.115777	+	0.993275i	$0.536936\pi$
$770$	−2.85403	+	2.74182i	−0.102852	+	0.0988083i
$771$		0			0
$772$	0.797291	−	19.8726i	0.0286951	−	0.715229i
$773$	43.3705			1.55993			0.779964	−	0.625825i	$-0.215238\pi$
$773$	43.3705			1.55993			0.779964	+	0.625825i	$0.215238\pi$
$774$		0			0
$775$			0.0170537i			0.000612587i
$776$	14.4405	+	16.2911i	0.518382	+	0.584818i
$777$		0			0
$778$	−10.2260	+	9.82392i	−0.366618	+	0.352205i
$779$			18.4337i			0.660457i
$780$		0			0
$781$		−	29.0522i		−	1.03957i
$782$	11.9756	+	12.4657i	0.428248	+	0.445773i
$783$		0			0
$784$	−26.7705	−	2.15154i	−0.956089	−	0.0768406i
$785$			20.3074i			0.724803i
$786$		0			0
$787$	4.57163			0.162961			0.0814804	−	0.996675i	$-0.474035\pi$
$787$	4.57163			0.162961			0.0814804	+	0.996675i	$0.474035\pi$
$788$	0.0590461	−	1.47173i	0.00210343	−	0.0524282i
$789$		0			0
$790$	25.7788	+	26.8337i	0.917167	+	0.954702i
$791$	−1.94223			−0.0690576
$792$		0			0
$793$	4.98877			0.177157
$794$	−18.6078	−	19.3693i	−0.660367	−	0.687392i
$795$		0			0
$796$	−28.0439	−	1.12513i	−0.993989	−	0.0398790i
$797$	45.1833			1.60047			0.800237	−	0.599684i	$-0.204707\pi$
$797$	45.1833			1.60047			0.800237	+	0.599684i	$0.204707\pi$
$798$		0			0
$799$			5.27217i			0.186516i
$800$	0.262945	−	0.214884i	0.00929653	−	0.00759728i
$801$		0			0
$802$	−23.4677	−	24.4281i	−0.828672	−	0.862585i
$803$		−	33.3007i		−	1.17515i
$804$		0			0
$805$			3.03338i			0.106912i
$806$	0.289724	−	0.278334i	0.0102051	−	0.00980388i
$807$		0			0
$808$	3.50907	+	3.95879i	0.123449	+	0.139270i
$809$		−	4.51903i		−	0.158881i	−0.996840	−	0.0794403i	$-0.974687\pi$
$809$		−	4.51903i		−	0.158881i	0.996840	−	0.0794403i	$-0.0253133\pi$
$810$		0			0
$811$	51.7819			1.81831			0.909154	−	0.416460i	$-0.136729\pi$
$811$	51.7819			1.81831			0.909154	+	0.416460i	$0.136729\pi$
$812$	−8.89700	−	0.356949i	−0.312223	−	0.0125265i
$813$		0			0
$814$	15.1325	−	14.5375i	0.530393	−	0.509541i
$815$	−48.3781			−1.69461
$816$		0			0
$817$	2.83362			0.0991358
$818$	−19.7173	+	18.9421i	−0.689400	+	0.662296i
$819$		0			0
$820$	19.2494	+	0.772290i	0.672219	+	0.0269695i
$821$	46.7224			1.63062			0.815312	−	0.579022i	$-0.196566\pi$
$821$	46.7224			1.63062			0.815312	+	0.579022i	$0.196566\pi$
$822$		0			0
$823$			0.605003i			0.0210891i	0.999944	+	0.0105445i	$0.00335649\pi$
$823$			0.605003i			0.0210891i	−0.999944	+	0.0105445i	$0.996644\pi$
$824$	2.01507	−	1.78616i	0.0701984	−	0.0622238i
$825$		0			0
$826$	1.75205	−	1.68317i	0.0609616	−	0.0585648i
$827$			7.96743i			0.277055i	0.990359	+	0.138527i	$0.0442369\pi$
$827$			7.96743i			0.277055i	−0.990359	+	0.138527i	$0.955763\pi$
$828$		0			0
$829$		−	11.5924i		−	0.402622i	−0.979527	−	0.201311i	$-0.935480\pi$
$829$		−	11.5924i		−	0.402622i	0.979527	−	0.201311i	$-0.0645202\pi$
$830$	32.1648	+	33.4811i	1.11645	+	1.16215i
$831$		0			0
$832$	−7.94219	−	0.960049i	−0.275346	−	0.0332837i
$833$		−	32.1470i		−	1.11383i
$834$		0			0
$835$	32.7028			1.13173
$836$	20.0195	+	0.803186i	0.692389	+	0.0277788i
$837$		0			0
$838$	1.63745	+	1.70446i	0.0565646	+	0.0588795i
$839$	29.8351			1.03002			0.515012	−	0.857183i	$-0.327788\pi$
$839$	29.8351			1.03002			0.515012	+	0.857183i	$0.327788\pi$
$840$		0			0
$841$	40.3539			1.39152
$842$	18.3615	+	19.1129i	0.632779	+	0.658675i
$843$		0			0
$844$	−0.124330	+	3.09894i	−0.00427961	+	0.106670i
$845$	2.22260			0.0764599
$846$		0			0
$847$			2.91510i			0.100164i
$848$	5.69062	+	0.457353i	0.195417	+	0.0157056i
$849$		0			0
$850$	0.281598	+	0.293122i	0.00965874	+	0.0100540i
$851$		−	16.0834i		−	0.551333i
$852$		0			0
$853$			27.9548i			0.957155i	0.878045	+	0.478578i	$0.158848\pi$
$853$			27.9548i			0.957155i	−0.878045	+	0.478578i	$0.841152\pi$
$854$	2.71992	−	2.61298i	0.0930737	−	0.0894144i
$855$		0			0
$856$	−35.1134	+	31.1245i	−1.20015	+	1.06381i
$857$			5.72159i			0.195446i	0.995214	+	0.0977229i	$0.0311559\pi$
$857$			5.72159i			0.195446i	−0.995214	+	0.0977229i	$0.968844\pi$
$858$		0			0
$859$	18.9201			0.645544			0.322772	−	0.946477i	$-0.395385\pi$
$859$	18.9201			0.645544			0.322772	+	0.946477i	$0.395385\pi$
$860$	0.118716	−	2.95900i	0.00404817	−	0.100901i
$861$		0			0
$862$	−18.1035	+	17.3917i	−0.616607	+	0.592364i
$863$	−14.3411			−0.488176			−0.244088	−	0.969753i	$-0.578489\pi$
$863$	−14.3411			−0.488176			−0.244088	+	0.969753i	$0.578489\pi$
$864$		0			0
$865$	31.5071			1.07127
$866$	−35.8117	+	34.4037i	−1.21693	+	1.16909i
$867$		0			0
$868$	0.0121765	−	0.303499i	0.000413296	−	0.0103014i
$869$	−27.8816			−0.945819
$870$		0			0
$871$			0.658322i			0.0223064i
$872$	19.7367	−	17.4946i	0.668369	−	0.592443i
$873$		0			0
$874$	11.0742	−	10.6388i	0.374589	−	0.359862i
$875$			6.01232i			0.203254i
$876$		0			0
$877$		−	24.2543i		−	0.819011i	−0.912308	−	0.409505i	$-0.865701\pi$
$877$		−	24.2543i		−	0.819011i	0.912308	−	0.409505i	$-0.134299\pi$
$878$	−1.99261	−	2.07415i	−0.0672472	−	0.0699993i
$879$		0			0
$880$	1.67745	−	20.8717i	0.0565469	−	0.703585i
$881$		−	58.3091i		−	1.96448i	−0.187621	−	0.982241i	$-0.560078\pi$
$881$		−	58.3091i		−	1.96448i	0.187621	−	0.982241i	$-0.439922\pi$
$882$		0			0
$883$	39.8809			1.34210			0.671050	−	0.741412i	$-0.265844\pi$
$883$	39.8809			1.34210			0.671050	+	0.741412i	$0.265844\pi$
$884$	0.383874	−	9.56811i	0.0129111	−	0.321810i
$885$		0			0
$886$	−5.29380	−	5.51045i	−0.177849	−	0.185127i
$887$	30.1897			1.01367			0.506836	−	0.862043i	$-0.330815\pi$
$887$	30.1897			1.01367			0.506836	+	0.862043i	$0.330815\pi$
$888$		0			0
$889$	7.08426			0.237598
$890$	4.16240	+	4.33274i	0.139524	+	0.145234i
$891$		0			0
$892$	−7.27905	−	0.292037i	−0.243721	−	0.00977812i
$893$	4.68364			0.156732
$894$		0			0
$895$		−	39.5051i		−	1.32051i
$896$	−4.83299	+	3.63647i	−0.161459	+	0.121486i
$897$		0			0
$898$	22.8169	+	23.7507i	0.761409	+	0.792570i
$899$			2.36584i			0.0789052i
$900$		0			0
$901$			6.83350i			0.227657i
$902$	−10.4098	+	10.0006i	−0.346609	+	0.332982i
$903$		0			0
$904$	7.68976	−	6.81620i	0.255758	−	0.226704i
$905$		−	34.0476i		−	1.13178i
$906$		0			0
$907$	20.4434			0.678810			0.339405	−	0.940640i	$-0.389774\pi$
$907$	20.4434			0.678810			0.339405	+	0.940640i	$0.389774\pi$
$908$	25.9061	+	1.03936i	0.859725	+	0.0344923i
$909$		0			0
$910$	1.21178	−	1.16414i	0.0401702	−	0.0385908i
$911$	4.47336			0.148209			0.0741045	−	0.997250i	$-0.476390\pi$
$911$	4.47336			0.148209			0.0741045	+	0.997250i	$0.476390\pi$
$912$		0			0
$913$	−34.7885			−1.15133
$914$	21.4860	−	20.6413i	0.710695	−	0.682754i
$915$		0			0
$916$	7.71162	+	0.309392i	0.254799	+	0.0102226i
$917$	5.49714			0.181532
$918$		0			0
$919$			49.2114i			1.62333i	0.584121	+	0.811667i	$0.301439\pi$
$919$			49.2114i			1.62333i	−0.584121	+	0.811667i	$0.698561\pi$
$920$	−10.6456	−	12.0099i	−0.350974	−	0.395955i
$921$		0			0
$922$	22.1507	−	21.2798i	0.729494	−	0.700814i
$923$			12.3352i			0.406017i
$924$		0			0
$925$		−	0.378190i		−	0.0124348i
$926$	31.1167	+	32.3902i	1.02256	+	1.06441i
$927$		0			0
$928$	36.4782	−	29.8106i	1.19745	−	0.978580i
$929$			10.4660i			0.343379i	0.985151	+	0.171690i	$0.0549226\pi$
$929$			10.4660i			0.343379i	−0.985151	+	0.171690i	$0.945077\pi$
$930$		0			0
$931$	−28.5584			−0.935963
$932$	35.2203	+	1.41304i	1.15368	+	0.0462858i
$933$		0			0
$934$	39.2950	+	40.9031i	1.28577	+	1.33839i
$935$	25.0635			0.819663
$936$		0			0
$937$	56.2534			1.83772			0.918859	−	0.394585i	$-0.129112\pi$
$937$	56.2534			1.83772			0.918859	+	0.394585i	$0.129112\pi$
$938$	0.344811	+	0.358922i	0.0112585	+	0.0117192i
$939$		0			0
$940$	0.196223	−	4.89088i	0.00640009	−	0.159523i
$941$	3.89072			0.126834			0.0634170	−	0.997987i	$-0.479800\pi$
$941$	3.89072			0.126834			0.0634170	+	0.997987i	$0.479800\pi$
$942$		0			0
$943$			11.0640i			0.360293i
$944$	−1.02977	+	12.8129i	−0.0335160	+	0.417023i
$945$		0			0
$946$	1.53728	+	1.60019i	0.0499812	+	0.0520266i
$947$			22.4095i			0.728211i	0.931358	+	0.364105i	$0.118625\pi$
$947$			22.4095i			0.728211i	−0.931358	+	0.364105i	$0.881375\pi$
$948$		0			0
$949$			14.1390i			0.458972i
$950$	0.260401	−	0.250163i	0.00844852	−	0.00811636i
$951$		0			0
$952$	−4.80223	−	5.41767i	−0.155641	−	0.175588i
$953$		−	52.6242i		−	1.70466i	−0.523001	−	0.852332i	$-0.675187\pi$
$953$		−	52.6242i		−	1.70466i	0.523001	−	0.852332i	$-0.324813\pi$
$954$		0			0
$955$	7.55863			0.244592
$956$	−1.56062	+	38.8985i	−0.0504739	+	1.25807i
$957$		0			0
$958$	−41.1161	+	39.4996i	−1.32840	+	1.27618i
$959$	−10.5960			−0.342164
$960$		0			0
$961$	30.9193			0.997397
$962$	−6.42505	+	6.17245i	−0.207152	+	0.199008i
$963$		0			0
$964$	0.775188	−	19.3216i	0.0249671	−	0.622308i
$965$	−22.1022			−0.711495
$966$		0			0
$967$			54.9989i			1.76865i	0.466876	+	0.884323i	$0.345379\pi$
$967$			54.9989i			1.76865i	−0.466876	+	0.884323i	$0.654621\pi$
$968$	−10.2305	−	11.5416i	−0.328820	−	0.370961i
$969$		0			0
$970$	17.4465	−	16.7606i	0.560173	−	0.538150i
$971$		−	38.5659i		−	1.23764i	−0.785533	−	0.618820i	$-0.787611\pi$
$971$		−	38.5659i		−	1.23764i	0.785533	−	0.618820i	$-0.212389\pi$
$972$		0			0
$973$		−	11.5533i		−	0.370383i
$974$	−6.37744	−	6.63843i	−0.204346	−	0.212709i
$975$		0			0
$976$	−1.59863	+	19.8910i	−0.0511709	+	0.636694i
$977$			10.8882i			0.348345i	0.984715	+	0.174172i	$0.0557250\pi$
$977$			10.8882i			0.348345i	−0.984715	+	0.174172i	$0.944275\pi$
$978$		0			0
$979$	−4.50193			−0.143882
$980$	−1.19647	+	29.8221i	−0.0382197	+	0.952631i
$981$		0			0
$982$	29.5421	+	30.7511i	0.942727	+	0.981308i
$983$	27.2804			0.870111			0.435055	−	0.900404i	$-0.356729\pi$
$983$	27.2804			0.870111			0.435055	+	0.900404i	$0.356729\pi$
$984$		0			0
$985$	−1.63685			−0.0521545
$986$	39.0658	+	40.6646i	1.24411	+	1.29502i
$987$		0			0
$988$	−8.50001	−	0.341022i	−0.270421	−	0.0108494i
$989$	1.70075			0.0540806
$990$		0			0
$991$		−	25.6230i		−	0.813941i	−0.913441	−	0.406971i	$-0.866585\pi$
$991$		−	25.6230i		−	0.813941i	0.913441	−	0.406971i	$-0.133415\pi$
$992$	1.01692	+	1.24436i	0.0322871	+	0.0395086i
$993$		0			0
$994$	6.46082	+	6.72523i	0.204925	+	0.213311i
$995$			31.1903i			0.988799i
$996$		0			0
$997$		−	48.5538i		−	1.53771i	−0.639421	−	0.768856i	$-0.720826\pi$
$997$		−	48.5538i		−	1.53771i	0.639421	−	0.768856i	$-0.279174\pi$
$998$	−25.9594	+	24.9388i	−0.821731	+	0.789424i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.j.a.755.37	yes	48
3.2	odd	2	inner	936.2.j.a.755.12	yes	48
4.3	odd	2		3744.2.j.a.2159.13		48
8.3	odd	2	inner	936.2.j.a.755.11	✓	48
8.5	even	2		3744.2.j.a.2159.36		48
12.11	even	2		3744.2.j.a.2159.35		48
24.5	odd	2		3744.2.j.a.2159.14		48
24.11	even	2	inner	936.2.j.a.755.38	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.j.a.755.11	✓	48	8.3	odd	2	inner
936.2.j.a.755.12	yes	48	3.2	odd	2	inner
936.2.j.a.755.37	yes	48	1.1	even	1	trivial
936.2.j.a.755.38	yes	48	24.11	even	2	inner
3744.2.j.a.2159.13		48	4.3	odd	2
3744.2.j.a.2159.14		48	24.5	odd	2
3744.2.j.a.2159.35		48	12.11	even	2
3744.2.j.a.2159.36		48	8.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01985 - 0.979751i) q^{2} +(0.0801759 - 1.99839i) q^{4} -2.22260 q^{5} +0.534598i q^{7} +(-1.87616 - 2.11661i) q^{8} +(-2.26672 + 2.17760i) q^{10} -2.35523i q^{11} +1.00000i q^{13} +(0.523773 + 0.545208i) q^{14} +(-3.98714 - 0.320446i) q^{16} -4.78791i q^{17} -4.25343 q^{19} +(-0.178199 + 4.44164i) q^{20} +(-2.30754 - 2.40198i) q^{22} -2.55292 q^{23} -0.0600300 q^{25} +(0.979751 + 1.01985i) q^{26} +(1.06834 + 0.0428618i) q^{28} -8.32790 q^{29} -0.284086i q^{31} +(-4.38023 + 3.57960i) q^{32} +(-4.69096 - 4.88293i) q^{34} -1.18820i q^{35} +6.30002i q^{37} +(-4.33784 + 4.16730i) q^{38} +(4.16996 + 4.70438i) q^{40} -4.33386i q^{41} -0.666197 q^{43} +(-4.70668 - 0.188833i) q^{44} +(-2.60359 + 2.50122i) q^{46} -1.10114 q^{47} +6.71421 q^{49} +(-0.0612214 + 0.0588145i) q^{50} +(1.99839 + 0.0801759i) q^{52} -1.42724 q^{53} +5.23475i q^{55} +(1.13153 - 1.00299i) q^{56} +(-8.49319 + 8.15927i) q^{58} -3.21354i q^{59} -4.98877i q^{61} +(-0.278334 - 0.289724i) q^{62} +(-0.960049 + 7.94219i) q^{64} -2.22260i q^{65} +0.658322 q^{67} +(-9.56811 - 0.383874i) q^{68} +(-1.16414 - 1.21178i) q^{70} +12.3352 q^{71} +14.1390 q^{73} +(6.17245 + 6.42505i) q^{74} +(-0.341022 + 8.50001i) q^{76} +1.25910 q^{77} -11.8382i q^{79} +(8.86184 + 0.712224i) q^{80} +(-4.24610 - 4.41987i) q^{82} -14.7707i q^{83} +10.6416i q^{85} +(-0.679419 + 0.652707i) q^{86} +(-4.98510 + 4.41879i) q^{88} -1.91146i q^{89} -0.534598 q^{91} +(-0.204682 + 5.10173i) q^{92} +(-1.12300 + 1.07885i) q^{94} +9.45368 q^{95} -7.69682 q^{97} +(6.84746 - 6.57825i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Introduction

L-functions

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Database

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