LMFDB - Embedded newform 936.2.g.f.469.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.13
Character	$\chi$	$=$	936.469
Dual form			936.2.g.f.469.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.229270 - 1.39551i) q^{2} +(-1.89487 - 0.639895i) q^{4} +1.61588i q^{5} -1.38556 q^{7} +(-1.32741 + 2.49759i) q^{8} +(2.25497 + 0.370474i) q^{10} -1.47970i q^{11} -1.00000i q^{13} +(-0.317667 + 1.93355i) q^{14} +(3.18107 + 2.42504i) q^{16} +7.02308 q^{17} +8.02537i q^{19} +(1.03400 - 3.06189i) q^{20} +(-2.06493 - 0.339252i) q^{22} -2.42604 q^{23} +2.38892 q^{25} +(-1.39551 - 0.229270i) q^{26} +(2.62545 + 0.886611i) q^{28} -7.74359i q^{29} +9.19604 q^{31} +(4.11348 - 3.88321i) q^{32} +(1.61018 - 9.80075i) q^{34} -2.23890i q^{35} +8.58159i q^{37} +(11.1995 + 1.83998i) q^{38} +(-4.03582 - 2.14495i) q^{40} +9.35947 q^{41} +8.19056i q^{43} +(-0.946855 + 2.80385i) q^{44} +(-0.556219 + 3.38556i) q^{46} +8.31410 q^{47} -5.08023 q^{49} +(0.547708 - 3.33375i) q^{50} +(-0.639895 + 1.89487i) q^{52} -4.07306i q^{53} +2.39103 q^{55} +(1.83921 - 3.46055i) q^{56} +(-10.8062 - 1.77537i) q^{58} +10.8609i q^{59} -1.38219i q^{61} +(2.10838 - 12.8331i) q^{62} +(-4.47594 - 6.63068i) q^{64} +1.61588 q^{65} -3.44800i q^{67} +(-13.3078 - 4.49404i) q^{68} +(-3.12439 - 0.513312i) q^{70} -13.4495 q^{71} +8.58159 q^{73} +(11.9757 + 1.96750i) q^{74} +(5.13540 - 15.2070i) q^{76} +2.05021i q^{77} -7.01990 q^{79} +(-3.91858 + 5.14024i) q^{80} +(2.14585 - 13.0612i) q^{82} -10.6471i q^{83} +11.3485i q^{85} +(11.4300 + 1.87785i) q^{86} +(3.69570 + 1.96418i) q^{88} +4.76398 q^{89} +1.38556i q^{91} +(4.59704 + 1.55241i) q^{92} +(1.90617 - 11.6024i) q^{94} -12.9681 q^{95} -9.47337 q^{97} +(-1.16475 + 7.08949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * 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 $

$2$	0.229270	−	1.39551i	0.162118	−	0.986771i
$2$	0.229270	−	1.39551i	0.162118	−	0.986771i
$3$		0			0
$3$		0			0
$4$	−1.89487	−	0.639895i	−0.947435	−	0.319948i
$5$			1.61588i			0.722645i	0.932441	+	0.361323i	$0.117675\pi$
$5$			1.61588i			0.722645i	−0.932441	+	0.361323i	$0.882325\pi$
$6$		0			0
$7$	−1.38556			−0.523691			−0.261845	−	0.965110i	$-0.584331\pi$
$7$	−1.38556			−0.523691			−0.261845	+	0.965110i	$0.584331\pi$
$8$	−1.32741	+	2.49759i	−0.469312	+	0.883032i
$9$		0			0
$10$	2.25497	+	0.370474i	0.713086	+	0.117154i
$11$		−	1.47970i		−	0.446147i	−0.974802	−	0.223074i	$-0.928391\pi$
$11$		−	1.47970i		−	0.446147i	0.974802	−	0.223074i	$-0.0716090\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.317667	+	1.93355i	−0.0849000	+	0.516763i
$15$		0			0
$16$	3.18107	+	2.42504i	0.795267	+	0.606259i
$17$	7.02308			1.70335			0.851674	−	0.524073i	$-0.175588\pi$
$17$	7.02308			1.70335			0.851674	+	0.524073i	$0.175588\pi$
$18$		0			0
$19$			8.02537i			1.84115i	0.390570	+	0.920573i	$0.372278\pi$
$19$			8.02537i			1.84115i	−0.390570	+	0.920573i	$0.627722\pi$
$20$	1.03400	−	3.06189i	0.231209	−	0.684660i
$21$		0			0
$22$	−2.06493	−	0.339252i	−0.440245	−	0.0723287i
$23$	−2.42604			−0.505865			−0.252932	−	0.967484i	$-0.581395\pi$
$23$	−2.42604			−0.505865			−0.252932	+	0.967484i	$0.581395\pi$
$24$		0			0
$25$	2.38892			0.477784
$26$	−1.39551	−	0.229270i	−0.273681	−	0.0449636i
$27$		0			0
$28$	2.62545	+	0.886611i	0.496163	+	0.167554i
$29$		−	7.74359i		−	1.43795i	−0.695037	−	0.718974i	$-0.744612\pi$
$29$		−	7.74359i		−	1.43795i	0.695037	−	0.718974i	$-0.255388\pi$
$30$		0			0
$31$	9.19604			1.65166			0.825828	−	0.563922i	$-0.190708\pi$
$31$	9.19604			1.65166			0.825828	+	0.563922i	$0.190708\pi$
$32$	4.11348	−	3.88321i	0.727167	−	0.686461i
$33$		0			0
$34$	1.61018	−	9.80075i	0.276144	−	1.68081i
$35$		−	2.23890i		−	0.378443i
$36$		0			0
$37$			8.58159i			1.41080i	0.708807	+	0.705402i	$0.249234\pi$
$37$			8.58159i			1.41080i	−0.708807	+	0.705402i	$0.750766\pi$
$38$	11.1995	+	1.83998i	1.81679	+	0.298484i
$39$		0			0
$40$	−4.03582	−	2.14495i	−0.638119	−	0.339146i
$41$	9.35947			1.46170			0.730852	−	0.682536i	$-0.239123\pi$
$41$	9.35947			1.46170			0.730852	+	0.682536i	$0.239123\pi$
$42$		0			0
$43$			8.19056i			1.24905i	0.781005	+	0.624525i	$0.214707\pi$
$43$			8.19056i			1.24905i	−0.781005	+	0.624525i	$0.785293\pi$
$44$	−0.946855	+	2.80385i	−0.142744	+	0.422696i
$45$		0			0
$46$	−0.556219	+	3.38556i	−0.0820100	+	0.499173i
$47$	8.31410			1.21274			0.606368	−	0.795184i	$-0.292626\pi$
$47$	8.31410			1.21274			0.606368	+	0.795184i	$0.292626\pi$
$48$		0			0
$49$	−5.08023			−0.725748
$50$	0.547708	−	3.33375i	0.0774576	−	0.471463i
$51$		0			0
$52$	−0.639895	+	1.89487i	−0.0887375	+	0.262771i
$53$		−	4.07306i		−	0.559478i	−0.960076	−	0.279739i	$-0.909752\pi$
$53$		−	4.07306i		−	0.559478i	0.960076	−	0.279739i	$-0.0902479\pi$
$54$		0			0
$55$	2.39103			0.322406
$56$	1.83921	−	3.46055i	0.245774	−	0.462436i
$57$		0			0
$58$	−10.8062	−	1.77537i	−1.41893	−	0.233118i
$59$			10.8609i			1.41397i	0.707228	+	0.706986i	$0.249946\pi$
$59$			10.8609i			1.41397i	−0.707228	+	0.706986i	$0.750054\pi$
$60$		0			0
$61$		−	1.38219i		−	0.176972i	−0.996077	−	0.0884859i	$-0.971797\pi$
$61$		−	1.38219i		−	0.176972i	0.996077	−	0.0884859i	$-0.0282028\pi$
$62$	2.10838	−	12.8331i	0.267764	−	1.62981i
$63$		0			0
$64$	−4.47594	−	6.63068i	−0.559493	−	0.828835i
$65$	1.61588			0.200426
$66$		0			0
$67$		−	3.44800i		−	0.421240i	−0.977568	−	0.210620i	$-0.932452\pi$
$67$		−	3.44800i		−	0.421240i	0.977568	−	0.210620i	$-0.0675483\pi$
$68$	−13.3078	−	4.49404i	−1.61381	−	0.544982i
$69$		0			0
$70$	−3.12439	−	0.513312i	−0.373437	−	0.0613526i
$71$	−13.4495			−1.59616			−0.798079	−	0.602552i	$-0.794150\pi$
$71$	−13.4495			−1.59616			−0.798079	+	0.602552i	$0.794150\pi$
$72$		0			0
$73$	8.58159			1.00440			0.502200	−	0.864752i	$-0.332524\pi$
$73$	8.58159			1.00440			0.502200	+	0.864752i	$0.332524\pi$
$74$	11.9757	+	1.96750i	1.39214	+	0.228718i
$75$		0			0
$76$	5.13540	−	15.2070i	0.589071	−	1.74437i
$77$			2.05021i			0.233643i
$78$		0			0
$79$	−7.01990			−0.789800			−0.394900	−	0.918724i	$-0.629221\pi$
$79$	−7.01990			−0.789800			−0.394900	+	0.918724i	$0.629221\pi$
$80$	−3.91858	+	5.14024i	−0.438111	+	0.574696i
$81$		0			0
$82$	2.14585	−	13.0612i	0.236969	−	1.44237i
$83$		−	10.6471i		−	1.16867i	−0.811513	−	0.584334i	$-0.801356\pi$
$83$		−	10.6471i		−	1.16867i	0.811513	−	0.584334i	$-0.198644\pi$
$84$		0			0
$85$			11.3485i			1.23092i
$86$	11.4300	+	1.87785i	1.23253	+	0.202494i
$87$		0			0
$88$	3.69570	+	1.96418i	0.393962	+	0.209382i
$89$	4.76398			0.504981			0.252490	−	0.967599i	$-0.418750\pi$
$89$	4.76398			0.504981			0.252490	+	0.967599i	$0.418750\pi$
$90$		0			0
$91$			1.38556i			0.145246i
$92$	4.59704	+	1.55241i	0.479274	+	0.161850i
$93$		0			0
$94$	1.90617	−	11.6024i	0.196607	−	1.19669i
$95$	−12.9681			−1.33050
$96$		0			0
$97$	−9.47337			−0.961875			−0.480938	−	0.876755i	$-0.659704\pi$
$97$	−9.47337			−0.961875			−0.480938	+	0.876755i	$0.659704\pi$
$98$	−1.16475	+	7.08949i	−0.117657	+	0.716147i
$99$		0			0
$100$	−4.52669	−	1.52866i	−0.452669	−	0.152866i
$101$			6.74133i			0.670788i	0.942078	+	0.335394i	$0.108869\pi$
$101$			6.74133i			0.670788i	−0.942078	+	0.335394i	$0.891131\pi$
$102$		0			0
$103$	−7.53160			−0.742110			−0.371055	−	0.928611i	$-0.621004\pi$
$103$	−7.53160			−0.742110			−0.371055	+	0.928611i	$0.621004\pi$
$104$	2.49759	+	1.32741i	0.244909	+	0.130164i
$105$		0			0
$106$	−5.68398	−	0.933831i	−0.552077	−	0.0907017i
$107$		−	1.76846i		−	0.170964i	−0.996340	−	0.0854819i	$-0.972757\pi$
$107$		−	1.76846i		−	0.170964i	0.996340	−	0.0854819i	$-0.0272430\pi$
$108$		0			0
$109$			1.02842i			0.0985051i	0.998786	+	0.0492525i	$0.0156839\pi$
$109$			1.02842i			0.0985051i	−0.998786	+	0.0492525i	$0.984316\pi$
$110$	0.548191	−	3.33669i	0.0522680	−	0.318141i
$111$		0			0
$112$	−4.40755	−	3.36003i	−0.416474	−	0.317493i
$113$	−6.28028			−0.590799			−0.295400	−	0.955374i	$-0.595453\pi$
$113$	−6.28028			−0.590799			−0.295400	+	0.955374i	$0.595453\pi$
$114$		0			0
$115$		−	3.92020i		−	0.365561i
$116$	−4.95509	+	14.6731i	−0.460068	+	1.36236i
$117$		0			0
$118$	15.1565	+	2.49009i	1.39527	+	0.229231i
$119$	−9.73087			−0.892027
$120$		0			0
$121$	8.81048			0.800953
$122$	−1.92886	−	0.316896i	−0.174631	−	0.0286904i
$123$		0			0
$124$	−17.4253	−	5.88450i	−1.56484	−	0.528444i
$125$			11.9396i			1.06791i
$126$		0			0
$127$	−2.25301			−0.199922			−0.0999611	−	0.994991i	$-0.531872\pi$
$127$	−2.25301			−0.199922			−0.0999611	+	0.994991i	$0.531872\pi$
$128$	−10.2794	+	4.72598i	−0.908575	+	0.417722i
$129$		0			0
$130$	0.370474	−	2.25497i	0.0324927	−	0.197774i
$131$			0.720508i			0.0629510i	0.999505	+	0.0314755i	$0.0100206\pi$
$131$			0.720508i			0.0629510i	−0.999505	+	0.0314755i	$0.989979\pi$
$132$		0			0
$133$		−	11.1196i		−	0.964192i
$134$	−4.81170	−	0.790524i	−0.415668	−	0.0682908i
$135$		0			0
$136$	−9.32254	+	17.5408i	−0.799401	+	1.50411i
$137$	18.6308			1.59174			0.795870	−	0.605468i	$-0.207014\pi$
$137$	18.6308			1.59174			0.795870	+	0.605468i	$0.207014\pi$
$138$		0			0
$139$			12.1973i			1.03456i	0.855816	+	0.517280i	$0.173056\pi$
$139$			12.1973i			1.03456i	−0.855816	+	0.517280i	$0.826944\pi$
$140$	−1.43266	+	4.24242i	−0.121082	+	0.358550i
$141$		0			0
$142$	−3.08356	+	18.7688i	−0.258767	+	1.57504i
$143$	−1.47970			−0.123739
$144$		0			0
$145$	12.5127			1.03913
$146$	1.96750	−	11.9757i	0.162832	−	0.991112i
$147$		0			0
$148$	5.49132	−	16.2610i	0.451384	−	1.33665i
$149$		−	17.0258i		−	1.39481i	−0.716679	−	0.697403i	$-0.754339\pi$
$149$		−	17.0258i		−	1.39481i	0.716679	−	0.697403i	$-0.245661\pi$
$150$		0			0
$151$	14.6652			1.19344			0.596718	−	0.802451i	$-0.296471\pi$
$151$	14.6652			1.19344			0.596718	+	0.802451i	$0.296471\pi$
$152$	−20.0441	−	10.6530i	−1.62579	−	0.864072i
$153$		0			0
$154$	2.86108	+	0.470052i	0.230552	+	0.0378779i
$155$			14.8597i			1.19356i
$156$		0			0
$157$			2.49714i			0.199293i	0.995023	+	0.0996466i	$0.0317712\pi$
$157$			2.49714i			0.199293i	−0.995023	+	0.0996466i	$0.968229\pi$
$158$	−1.60945	+	9.79631i	−0.128041	+	0.779352i
$159$		0			0
$160$	6.27481	+	6.64690i	0.496068	+	0.525484i
$161$	3.36142			0.264917
$162$		0			0
$163$		−	10.0942i		−	0.790641i	−0.918543	−	0.395320i	$-0.870634\pi$
$163$		−	10.0942i		−	0.790641i	0.918543	−	0.395320i	$-0.129366\pi$
$164$	−17.7350	−	5.98908i	−1.38487	−	0.467669i
$165$		0			0
$166$	−14.8581	−	2.44106i	−1.15321	−	0.189463i
$167$	−7.22273			−0.558912			−0.279456	−	0.960159i	$-0.590154\pi$
$167$	−7.22273			−0.558912			−0.279456	+	0.960159i	$0.590154\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	15.8369	+	2.60187i	1.21463	+	0.199554i
$171$		0			0
$172$	5.24110	−	15.5201i	0.399630	−	1.18339i
$173$		−	2.45274i		−	0.186478i	−0.995644	−	0.0932392i	$-0.970278\pi$
$173$		−	2.45274i		−	0.186478i	0.995644	−	0.0932392i	$-0.0297221\pi$
$174$		0			0
$175$	−3.30998			−0.250211
$176$	3.58834	−	4.70703i	0.270481	−	0.354806i
$177$		0			0
$178$	1.09224	−	6.64815i	0.0818667	−	0.498300i
$179$			8.77357i			0.655767i	0.944718	+	0.327884i	$0.106335\pi$
$179$			8.77357i			0.655767i	−0.944718	+	0.327884i	$0.893665\pi$
$180$		0			0
$181$			20.3247i			1.51072i	0.655307	+	0.755362i	$0.272539\pi$
$181$			20.3247i			1.51072i	−0.655307	+	0.755362i	$0.727461\pi$
$182$	1.93355	+	0.317667i	0.143324	+	0.0235470i
$183$		0			0
$184$	3.22037	−	6.05927i	0.237408	−	0.446695i
$185$	−13.8669			−1.01951
$186$		0			0
$187$		−	10.3921i		−	0.759944i
$188$	−15.7541	−	5.32015i	−1.14899	−	0.388012i
$189$		0			0
$190$	−2.97319	+	18.0970i	−0.215698	+	1.31290i
$191$	0.514593			0.0372347			0.0186173	−	0.999827i	$-0.494074\pi$
$191$	0.514593			0.0372347			0.0186173	+	0.999827i	$0.494074\pi$
$192$		0			0
$193$	−22.9585			−1.65259			−0.826294	−	0.563238i	$-0.809555\pi$
$193$	−22.9585			−1.65259			−0.826294	+	0.563238i	$0.809555\pi$
$194$	−2.17196	+	13.2201i	−0.155938	+	0.949151i
$195$		0			0
$196$	9.62639	+	3.25082i	0.687599	+	0.232201i
$197$			7.71400i			0.549600i	0.961501	+	0.274800i	$0.0886116\pi$
$197$			7.71400i			0.549600i	−0.961501	+	0.274800i	$0.911388\pi$
$198$		0			0
$199$	−4.24879			−0.301189			−0.150594	−	0.988596i	$-0.548119\pi$
$199$	−4.24879			−0.301189			−0.150594	+	0.988596i	$0.548119\pi$
$200$	−3.17109	+	5.96655i	−0.224230	+	0.421898i
$201$		0			0
$202$	9.40757	+	1.54559i	0.661914	+	0.108747i
$203$			10.7292i			0.753040i
$204$		0			0
$205$			15.1238i			1.05629i
$206$	−1.72677	+	10.5104i	−0.120310	+	0.732293i
$207$		0			0
$208$	2.42504	−	3.18107i	0.168146	−	0.220567i
$209$	11.8752			0.821422
$210$		0			0
$211$			6.38535i			0.439585i	0.975547	+	0.219793i	$0.0705381\pi$
$211$			6.38535i			0.439585i	−0.975547	+	0.219793i	$0.929462\pi$
$212$	−2.60633	+	7.71792i	−0.179004	+	0.530069i
$213$		0			0
$214$	−2.46790	−	0.405456i	−0.168702	−	0.0277164i
$215$	−13.2350			−0.902620
$216$		0			0
$217$	−12.7416			−0.864958
$218$	1.43517	+	0.235787i	0.0972020	+	0.0159695i
$219$		0			0
$220$	−4.53069	−	1.53001i	−0.305459	−	0.103153i
$221$		−	7.02308i		−	0.472423i
$222$		0			0
$223$	17.3498			1.16183			0.580914	−	0.813965i	$-0.302695\pi$
$223$	17.3498			1.16183			0.580914	+	0.813965i	$0.302695\pi$
$224$	−5.69945	+	5.38040i	−0.380811	+	0.359493i
$225$		0			0
$226$	−1.43988	+	8.76417i	−0.0957795	+	0.582984i
$227$		−	8.84746i		−	0.587226i	−0.955924	−	0.293613i	$-0.905142\pi$
$227$		−	8.84746i		−	0.587226i	0.955924	−	0.293613i	$-0.0948578\pi$
$228$		0			0
$229$		−	8.01094i		−	0.529378i	−0.964334	−	0.264689i	$-0.914731\pi$
$229$		−	8.01094i		−	0.529378i	0.964334	−	0.264689i	$-0.0852693\pi$
$230$	−5.47067	−	0.898786i	−0.360725	−	0.0592642i
$231$		0			0
$232$	19.3403	+	10.2790i	1.26975	+	0.674846i
$233$	14.3800			0.942068			0.471034	−	0.882115i	$-0.343881\pi$
$233$	14.3800			0.942068			0.471034	+	0.882115i	$0.343881\pi$
$234$		0			0
$235$			13.4346i			0.876378i
$236$	6.94985	−	20.5800i	0.452397	−	1.33965i
$237$		0			0
$238$	−2.23100	+	13.5795i	−0.144614	+	0.880227i
$239$	−25.4651			−1.64720			−0.823600	−	0.567172i	$-0.808038\pi$
$239$	−25.4651			−1.64720			−0.823600	+	0.567172i	$0.808038\pi$
$240$		0			0
$241$	18.8109			1.21172			0.605859	−	0.795572i	$-0.292830\pi$
$241$	18.8109			1.21172			0.605859	+	0.795572i	$0.292830\pi$
$242$	2.01998	−	12.2951i	0.129849	−	0.790357i
$243$		0			0
$244$	−0.884459	+	2.61908i	−0.0566217	+	0.167669i
$245$		−	8.20907i		−	0.524458i
$246$		0			0
$247$	8.02537			0.510642
$248$	−12.2070	+	22.9680i	−0.775142	+	1.45847i
$249$		0			0
$250$	16.6618	+	2.73740i	1.05379	+	0.173129i
$251$		−	20.0393i		−	1.26487i	−0.774615	−	0.632434i	$-0.782056\pi$
$251$		−	20.0393i		−	1.26487i	0.774615	−	0.632434i	$-0.217944\pi$
$252$		0			0
$253$			3.58982i			0.225690i
$254$	−0.516547	+	3.14408i	−0.0324111	+	0.197277i
$255$		0			0
$256$	4.23838	+	15.4284i	0.264899	+	0.964276i
$257$	13.3034			0.829841			0.414920	−	0.909858i	$-0.363809\pi$
$257$	13.3034			0.829841			0.414920	+	0.909858i	$0.363809\pi$
$258$		0			0
$259$		−	11.8903i		−	0.738826i
$260$	−3.06189	−	1.03400i	−0.189890	−	0.0641258i
$261$		0			0
$262$	1.00547	+	0.165191i	0.0621183	+	0.0102055i
$263$	−12.2893			−0.757790			−0.378895	−	0.925440i	$-0.623696\pi$
$263$	−12.2893			−0.757790			−0.378895	+	0.925440i	$0.623696\pi$
$264$		0			0
$265$	6.58159			0.404304
$266$	−15.5175	−	2.54939i	−0.951437	−	0.156313i
$267$		0			0
$268$	−2.20636	+	6.53351i	−0.134775	+	0.399098i
$269$		−	9.03003i		−	0.550570i	−0.961363	−	0.275285i	$-0.911228\pi$
$269$		−	9.03003i		−	0.550570i	0.961363	−	0.275285i	$-0.0887723\pi$
$270$		0			0
$271$	−7.08209			−0.430206			−0.215103	−	0.976591i	$-0.569009\pi$
$271$	−7.08209			−0.430206			−0.215103	+	0.976591i	$0.569009\pi$
$272$	22.3409	+	17.0312i	1.35462	+	1.03267i
$273$		0			0
$274$	4.27149	−	25.9994i	0.258050	−	1.57068i
$275$		−	3.53489i		−	0.213162i
$276$		0			0
$277$		−	25.6608i		−	1.54181i	−0.636953	−	0.770903i	$-0.719805\pi$
$277$		−	25.6608i		−	1.54181i	0.636953	−	0.770903i	$-0.280195\pi$
$278$	17.0214	+	2.79647i	1.02087	+	0.167721i
$279$		0			0
$280$	5.59186	+	2.97195i	0.334177	+	0.177608i
$281$	4.50739			0.268888			0.134444	−	0.990921i	$-0.457075\pi$
$281$	4.50739			0.268888			0.134444	+	0.990921i	$0.457075\pi$
$282$		0			0
$283$			17.5489i			1.04318i	0.853197	+	0.521588i	$0.174660\pi$
$283$			17.5489i			1.04318i	−0.853197	+	0.521588i	$0.825340\pi$
$284$	25.4850	+	8.60625i	1.51226	+	0.510687i
$285$		0			0
$286$	−0.339252	+	2.06493i	−0.0200604	+	0.122102i
$287$	−12.9681			−0.765481
$288$		0			0
$289$	32.3237			1.90139
$290$	2.86880	−	17.4616i	0.168462	−	1.02538i
$291$		0			0
$292$	−16.2610	−	5.49132i	−0.951603	−	0.321355i
$293$			30.7749i			1.79789i	0.438061	+	0.898945i	$0.355665\pi$
$293$			30.7749i			1.79789i	−0.438061	+	0.898945i	$0.644335\pi$
$294$		0			0
$295$	−17.5500			−1.02180
$296$	−21.4333	−	11.3913i	−1.24579	−	0.662108i
$297$		0			0
$298$	−23.7596	−	3.90350i	−1.37635	−	0.226124i
$299$			2.42604i			0.140302i
$300$		0			0
$301$		−	11.3485i		−	0.654116i
$302$	3.36229	−	20.4653i	0.193478	−	1.17765i
$303$		0			0
$304$	−19.4618	+	25.5293i	−1.11621	+	1.46420i
$305$	2.23346			0.127888
$306$		0			0
$307$		−	22.1839i		−	1.26610i	−0.774110	−	0.633051i	$-0.781802\pi$
$307$		−	22.1839i		−	1.26610i	0.774110	−	0.633051i	$-0.218198\pi$
$308$	1.31192	−	3.88488i	0.0747536	−	0.221362i
$309$		0			0
$310$	20.7368	+	3.40689i	1.17777	+	0.193498i
$311$	14.8795			0.843740			0.421870	−	0.906656i	$-0.361374\pi$
$311$	14.8795			0.843740			0.421870	+	0.906656i	$0.361374\pi$
$312$		0			0
$313$	−22.2093			−1.25534			−0.627671	−	0.778479i	$-0.715992\pi$
$313$	−22.2093			−1.25534			−0.627671	+	0.778479i	$0.715992\pi$
$314$	3.48477	+	0.572519i	0.196657	+	0.0323091i
$315$		0			0
$316$	13.3018	+	4.49200i	0.748285	+	0.252695i
$317$			9.62245i			0.540451i	0.962797	+	0.270225i	$0.0870982\pi$
$317$			9.62245i			0.540451i	−0.962797	+	0.270225i	$0.912902\pi$
$318$		0			0
$319$	−11.4582			−0.641537
$320$	10.7144	−	7.23260i	0.598954	−	0.404315i
$321$		0			0
$322$	0.770673	−	4.69088i	0.0429479	−	0.261412i
$323$			56.3628i			3.13611i
$324$		0			0
$325$		−	2.38892i		−	0.132513i
$326$	−14.0865	−	2.31430i	−0.780181	−	0.128177i
$327$		0			0
$328$	−12.4239	+	23.3762i	−0.685995	+	1.29073i
$329$	−11.5196			−0.635099
$330$		0			0
$331$		−	3.02387i		−	0.166207i	−0.996541	−	0.0831034i	$-0.973517\pi$
$331$		−	3.02387i		−	0.166207i	0.996541	−	0.0831034i	$-0.0264832\pi$
$332$	−6.81302	+	20.1748i	−0.373913	+	1.10724i
$333$		0			0
$334$	−1.65596	+	10.0794i	−0.0906099	+	0.551518i
$335$	5.57157			0.304407
$336$		0			0
$337$	7.68559			0.418661			0.209330	−	0.977845i	$-0.432872\pi$
$337$	7.68559			0.418661			0.209330	+	0.977845i	$0.432872\pi$
$338$	−0.229270	+	1.39551i	−0.0124707	+	0.0759055i
$339$		0			0
$340$	7.26184	−	21.5039i	0.393829	−	1.16621i
$341$		−	13.6074i		−	0.736882i
$342$		0			0
$343$	16.7378			0.903758
$344$	−20.4567	−	10.8723i	−1.10295	−	0.586194i
$345$		0			0
$346$	−3.42281	−	0.562340i	−0.184012	−	0.0302316i
$347$		−	32.9632i		−	1.76956i	−0.466013	−	0.884778i	$-0.654310\pi$
$347$		−	32.9632i		−	1.76956i	0.466013	−	0.884778i	$-0.345690\pi$
$348$		0			0
$349$		−	20.4696i		−	1.09571i	−0.836573	−	0.547856i	$-0.815444\pi$
$349$		−	20.4696i		−	1.09571i	0.836573	−	0.547856i	$-0.184556\pi$
$350$	−0.758880	+	4.61910i	−0.0405638	+	0.246901i
$351$		0			0
$352$	−5.74599	−	6.08672i	−0.306263	−	0.324423i
$353$	−15.1387			−0.805753			−0.402877	−	0.915254i	$-0.631990\pi$
$353$	−15.1387			−0.805753			−0.402877	+	0.915254i	$0.631990\pi$
$354$		0			0
$355$		−	21.7328i		−	1.15346i
$356$	−9.02712	−	3.04845i	−0.478436	−	0.161567i
$357$		0			0
$358$	12.2436	+	2.01152i	0.647092	+	0.106312i
$359$	−22.8971			−1.20846			−0.604230	−	0.796810i	$-0.706519\pi$
$359$	−22.8971			−1.20846			−0.604230	+	0.796810i	$0.706519\pi$
$360$		0			0
$361$	−45.4066			−2.38982
$362$	28.3633	+	4.65985i	1.49074	+	0.244916i
$363$		0			0
$364$	0.886611	−	2.62545i	0.0464710	−	0.137611i
$365$			13.8669i			0.725825i
$366$		0			0
$367$	−23.2970			−1.21609			−0.608046	−	0.793902i	$-0.708047\pi$
$367$	−23.2970			−1.21609			−0.608046	+	0.793902i	$0.708047\pi$
$368$	−7.71741	−	5.88325i	−0.402298	−	0.306685i
$369$		0			0
$370$	−3.17926	+	19.3513i	−0.165282	+	1.00602i
$371$			5.64345i			0.292993i
$372$		0			0
$373$			8.34133i			0.431898i	0.976405	+	0.215949i	$0.0692844\pi$
$373$			8.34133i			0.431898i	−0.976405	+	0.215949i	$0.930716\pi$
$374$	−14.5022	−	2.38259i	−0.749890	−	0.123201i
$375$		0			0
$376$	−11.0363	+	20.7652i	−0.569151	+	1.07088i
$377$	−7.74359			−0.398815
$378$		0			0
$379$		−	5.95652i		−	0.305966i	−0.988229	−	0.152983i	$-0.951112\pi$
$379$		−	5.95652i		−	0.305966i	0.988229	−	0.152983i	$-0.0488880\pi$
$380$	24.5728	+	8.29821i	1.26056	+	0.425689i
$381$		0			0
$382$	0.117981	−	0.718118i	0.00603643	−	0.0367421i
$383$	18.1470			0.927267			0.463634	−	0.886027i	$-0.346545\pi$
$383$	18.1470			0.927267			0.463634	+	0.886027i	$0.346545\pi$
$384$		0			0
$385$	−3.31290			−0.168841
$386$	−5.26370	+	32.0387i	−0.267915	+	1.63073i
$387$		0			0
$388$	17.9508	+	6.06197i	0.911315	+	0.307750i
$389$		−	0.172915i		−	0.00876713i	−0.999990	−	0.00438357i	$-0.998605\pi$
$389$		−	0.172915i		−	0.00876713i	0.999990	−	0.00438357i	$-0.00139534\pi$
$390$		0			0
$391$	−17.0383			−0.861664
$392$	6.74358	−	12.6884i	0.340602	−	0.640859i
$393$		0			0
$394$	10.7649	+	1.76859i	0.542329	+	0.0891002i
$395$		−	11.3433i		−	0.570746i
$396$		0			0
$397$		−	38.9446i		−	1.95457i	−0.211920	−	0.977287i	$-0.567972\pi$
$397$		−	38.9446i		−	1.95457i	0.211920	−	0.977287i	$-0.432028\pi$
$398$	−0.974120	+	5.92921i	−0.0488282	+	0.297204i
$399$		0			0
$400$	7.59931	+	5.79322i	0.379966	+	0.289661i
$401$	5.51185			0.275249			0.137624	−	0.990485i	$-0.456053\pi$
$401$	5.51185			0.275249			0.137624	+	0.990485i	$0.456053\pi$
$402$		0			0
$403$		−	9.19604i		−	0.458087i
$404$	4.31375	−	12.7740i	0.214617	−	0.635528i
$405$		0			0
$406$	14.9726	+	2.45988i	0.743079	+	0.122082i
$407$	12.6982			0.629427
$408$		0			0
$409$	20.0099			0.989424			0.494712	−	0.869057i	$-0.335273\pi$
$409$	20.0099			0.989424			0.494712	+	0.869057i	$0.335273\pi$
$410$	21.1054	+	3.46744i	1.04232	+	0.171245i
$411$		0			0
$412$	14.2714	+	4.81943i	0.703101	+	0.237437i
$413$		−	15.0484i		−	0.740484i
$414$		0			0
$415$	17.2044			0.844533
$416$	−3.88321	−	4.11348i	−0.190390	−	0.201680i
$417$		0			0
$418$	2.72262	−	16.5719i	0.133168	−	0.810556i
$419$		−	7.04824i		−	0.344329i	−0.985068	−	0.172164i	$-0.944924\pi$
$419$		−	7.04824i		−	0.344329i	0.985068	−	0.172164i	$-0.0550760\pi$
$420$		0			0
$421$		−	8.21644i		−	0.400445i	−0.979750	−	0.200222i	$-0.935834\pi$
$421$		−	8.21644i		−	0.400445i	0.979750	−	0.200222i	$-0.0641664\pi$
$422$	8.91078	+	1.46397i	0.433770	+	0.0712649i
$423$		0			0
$424$	10.1728	+	5.40664i	0.494037	+	0.262570i
$425$	16.7776			0.813831
$426$		0			0
$427$			1.91511i			0.0926785i
$428$	−1.13163	+	3.35101i	−0.0546995	+	0.161977i
$429$		0			0
$430$	−3.03439	+	18.4695i	−0.146331	+	0.890679i
$431$	14.3766			0.692499			0.346249	−	0.938143i	$-0.387455\pi$
$431$	14.3766			0.692499			0.346249	+	0.938143i	$0.387455\pi$
$432$		0			0
$433$	−17.3512			−0.833846			−0.416923	−	0.908942i	$-0.636891\pi$
$433$	−17.3512			−0.833846			−0.416923	+	0.908942i	$0.636891\pi$
$434$	−2.92127	+	17.7810i	−0.140226	+	0.853515i
$435$		0			0
$436$	0.658083	−	1.94873i	0.0315165	−	0.0933272i
$437$		−	19.4699i		−	0.931372i
$438$		0			0
$439$	−15.4286			−0.736367			−0.368183	−	0.929753i	$-0.620020\pi$
$439$	−15.4286			−0.736367			−0.368183	+	0.929753i	$0.620020\pi$
$440$	−3.17389	+	5.97182i	−0.151309	+	0.284695i
$441$		0			0
$442$	−9.80075	−	1.61018i	−0.466174	−	0.0765886i
$443$		−	15.6442i		−	0.743278i	−0.928377	−	0.371639i	$-0.878796\pi$
$443$		−	15.6442i		−	0.743278i	0.928377	−	0.371639i	$-0.121204\pi$
$444$		0			0
$445$			7.69803i			0.364922i
$446$	3.97779	−	24.2117i	0.188354	−	1.14646i
$447$		0			0
$448$	6.20167	+	9.18718i	0.293001	+	0.434054i
$449$	−6.10007			−0.287880			−0.143940	−	0.989586i	$-0.545977\pi$
$449$	−6.10007			−0.287880			−0.143940	+	0.989586i	$0.545977\pi$
$450$		0			0
$451$		−	13.8492i		−	0.652135i
$452$	11.9003	+	4.01872i	0.559744	+	0.189025i
$453$		0			0
$454$	−12.3467	−	2.02846i	−0.579458	−	0.0952003i
$455$	−2.23890			−0.104961
$456$		0			0
$457$	−10.1476			−0.474684			−0.237342	−	0.971426i	$-0.576276\pi$
$457$	−10.1476			−0.474684			−0.237342	+	0.971426i	$0.576276\pi$
$458$	−11.1793	−	1.83667i	−0.522375	−	0.0858220i
$459$		0			0
$460$	−2.50852	+	7.42828i	−0.116960	+	0.346345i
$461$		−	19.8398i		−	0.924029i	−0.886872	−	0.462015i	$-0.847127\pi$
$461$		−	19.8398i		−	0.924029i	0.886872	−	0.462015i	$-0.152873\pi$
$462$		0			0
$463$	28.1588			1.30865			0.654324	−	0.756214i	$-0.272953\pi$
$463$	28.1588			1.30865			0.654324	+	0.756214i	$0.272953\pi$
$464$	18.7785	−	24.6329i	0.871770	−	1.14355i
$465$		0			0
$466$	3.29691	−	20.0674i	0.152727	−	0.929605i
$467$			12.6982i			0.587603i	0.955866	+	0.293801i	$0.0949204\pi$
$467$			12.6982i			0.587603i	−0.955866	+	0.293801i	$0.905080\pi$
$468$		0			0
$469$			4.77740i			0.220600i
$470$	18.7481	+	3.08016i	0.864784	+	0.142077i
$471$		0			0
$472$	−27.1262	−	14.4169i	−1.24858	−	0.663594i
$473$	12.1196			0.557260
$474$		0			0
$475$			19.1720i			0.879670i
$476$	18.4387	+	6.22674i	0.845138	+	0.285402i
$477$		0			0
$478$	−5.83838	+	35.5367i	−0.267041	+	1.62541i
$479$	36.8272			1.68268			0.841339	−	0.540508i	$-0.181768\pi$
$479$	36.8272			1.68268			0.841339	+	0.540508i	$0.181768\pi$
$480$		0			0
$481$	8.58159			0.391287
$482$	4.31278	−	26.2507i	0.196442	−	1.19569i
$483$		0			0
$484$	−16.6947	−	5.63779i	−0.758851	−	0.256263i
$485$		−	15.3079i		−	0.695095i
$486$		0			0
$487$	−0.484527			−0.0219560			−0.0109780	−	0.999940i	$-0.503494\pi$
$487$	−0.484527			−0.0219560			−0.0109780	+	0.999940i	$0.503494\pi$
$488$	3.45216	+	1.83474i	0.156272	+	0.0830550i
$489$		0			0
$490$	−11.4558	−	1.88209i	−0.517520	−	0.0850244i
$491$			3.26565i			0.147377i	0.997281	+	0.0736883i	$0.0234770\pi$
$491$			3.26565i			0.147377i	−0.997281	+	0.0736883i	$0.976523\pi$
$492$		0			0
$493$		−	54.3838i		−	2.44932i
$494$	1.83998	−	11.1995i	0.0827845	−	0.503887i
$495$		0			0
$496$	29.2532	+	22.3007i	1.31351	+	1.00133i
$497$	18.6350			0.835894
$498$		0			0
$499$			0.338708i			0.0151627i	0.999971	+	0.00758133i	$0.00241323\pi$
$499$			0.338708i			0.0151627i	−0.999971	+	0.00758133i	$0.997587\pi$
$500$	7.64012	−	22.6241i	0.341676	−	1.01178i
$501$		0			0
$502$	−27.9649	−	4.59440i	−1.24813	−	0.205058i
$503$	−39.7613			−1.77287			−0.886435	−	0.462853i	$-0.846826\pi$
$503$	−39.7613			−1.77287			−0.886435	+	0.462853i	$0.846826\pi$
$504$		0			0
$505$	−10.8932			−0.484742
$506$	5.00962	+	0.823039i	0.222705	+	0.0365886i
$507$		0			0
$508$	4.26916	+	1.44169i	0.189413	+	0.0639646i
$509$			33.4538i			1.48281i	0.671055	+	0.741407i	$0.265841\pi$
$509$			33.4538i			1.48281i	−0.671055	+	0.741407i	$0.734159\pi$
$510$		0			0
$511$	−11.8903			−0.525995
$512$	22.5022	−	2.37741i	0.994465	−	0.105068i
$513$		0			0
$514$	3.05006	−	18.5649i	0.134533	−	0.818863i
$515$		−	12.1702i		−	0.536283i
$516$		0			0
$517$		−	12.3024i		−	0.541059i
$518$	−16.5929	−	2.72609i	−0.729052	−	0.119777i
$519$		0			0
$520$	−2.14495	+	4.03582i	−0.0940622	+	0.176982i
$521$	−16.5479			−0.724979			−0.362489	−	0.931988i	$-0.618073\pi$
$521$	−16.5479			−0.724979			−0.362489	+	0.931988i	$0.618073\pi$
$522$		0			0
$523$		−	28.4449i		−	1.24381i	−0.783093	−	0.621905i	$-0.786359\pi$
$523$		−	28.4449i		−	1.24381i	0.783093	−	0.621905i	$-0.213641\pi$
$524$	0.461050	−	1.36527i	0.0201410	−	0.0596420i
$525$		0			0
$526$	−2.81757	+	17.1498i	−0.122852	+	0.747765i
$527$	64.5845			2.81334
$528$		0			0
$529$	−17.1143			−0.744101
$530$	1.50896	−	9.18465i	0.0655451	−	0.398956i
$531$		0			0
$532$	−7.11538	+	21.0702i	−0.308491	+	0.913509i
$533$		−	9.35947i		−	0.405404i
$534$		0			0
$535$	2.85763			0.123546
$536$	8.61170	+	4.57693i	0.371969	+	0.197693i
$537$		0			0
$538$	−12.6014	−	2.07032i	−0.543287	−	0.0892576i
$539$			7.51724i			0.323790i
$540$		0			0
$541$		−	13.0052i		−	0.559138i	−0.960126	−	0.279569i	$-0.909808\pi$
$541$		−	13.0052i		−	0.559138i	0.960126	−	0.279569i	$-0.0901916\pi$
$542$	−1.62371	+	9.88310i	−0.0697444	+	0.424515i
$543$		0			0
$544$	28.8893	−	27.2721i	1.23862	−	1.16928i
$545$	−1.66181			−0.0711842
$546$		0			0
$547$		−	23.3847i		−	0.999859i	−0.866066	−	0.499930i	$-0.833359\pi$
$547$		−	23.3847i		−	0.999859i	0.866066	−	0.499930i	$-0.166641\pi$
$548$	−35.3030	−	11.9218i	−1.50807	−	0.509273i
$549$		0			0
$550$	−4.93296	−	0.810445i	−0.210342	−	0.0345575i
$551$	62.1452			2.64747
$552$		0			0
$553$	9.72646			0.413611
$554$	−35.8097	−	5.88325i	−1.52141	−	0.249955i
$555$		0			0
$556$	7.80499	−	23.1123i	0.331005	−	0.980179i
$557$		−	6.92263i		−	0.293321i	−0.989187	−	0.146661i	$-0.953147\pi$
$557$		−	6.92263i		−	0.293321i	0.989187	−	0.146661i	$-0.0468525\pi$
$558$		0			0
$559$	8.19056			0.346424
$560$	5.42941	−	7.12209i	0.229435	−	0.300963i
$561$		0			0
$562$	1.03341	−	6.29008i	0.0435917	−	0.265331i
$563$		−	21.7430i		−	0.916360i	−0.888859	−	0.458180i	$-0.848501\pi$
$563$		−	21.7430i		−	0.916360i	0.888859	−	0.458180i	$-0.151499\pi$
$564$		0			0
$565$		−	10.1482i		−	0.426938i
$566$	24.4897	+	4.02345i	1.02938	+	0.169118i
$567$		0			0
$568$	17.8530	−	33.5913i	0.749096	−	1.40946i
$569$	−19.2824			−0.808362			−0.404181	−	0.914679i	$-0.632443\pi$
$569$	−19.2824			−0.808362			−0.404181	+	0.914679i	$0.632443\pi$
$570$		0			0
$571$			37.4334i			1.56654i	0.621683	+	0.783269i	$0.286449\pi$
$571$			37.4334i			1.56654i	−0.621683	+	0.783269i	$0.713551\pi$
$572$	2.80385	+	0.946855i	0.117235	+	0.0395900i
$573$		0			0
$574$	−2.97319	+	18.0970i	−0.124099	+	0.755355i
$575$	−5.79562			−0.241694
$576$		0			0
$577$	−6.89178			−0.286909			−0.143454	−	0.989657i	$-0.545821\pi$
$577$	−6.89178			−0.286909			−0.143454	+	0.989657i	$0.545821\pi$
$578$	7.41085	−	45.1078i	0.308251	−	1.87624i
$579$		0			0
$580$	−23.7100	−	8.00685i	−0.984505	−	0.332466i
$581$			14.7521i			0.612021i
$582$		0			0
$583$	−6.02692			−0.249609
$584$	−11.3913	+	21.4333i	−0.471377	+	0.886917i
$585$		0			0
$586$	42.9466	+	7.05577i	1.77411	+	0.291471i
$587$		−	20.4244i		−	0.843007i	−0.906827	−	0.421503i	$-0.861503\pi$
$587$		−	20.4244i		−	0.843007i	0.906827	−	0.421503i	$-0.138497\pi$
$588$		0			0
$589$			73.8016i			3.04094i
$590$	−4.02369	+	24.4911i	−0.165653	+	1.00828i
$591$		0			0
$592$	−20.8107	+	27.2986i	−0.855314	+	1.12197i
$593$	14.2116			0.583599			0.291799	−	0.956480i	$-0.405746\pi$
$593$	14.2116			0.583599			0.291799	+	0.956480i	$0.405746\pi$
$594$		0			0
$595$		−	15.7240i		−	0.644619i
$596$	−10.8947	+	32.2616i	−0.446265	+	1.32149i
$597$		0			0
$598$	3.38556	+	0.556219i	0.138446	+	0.0227455i
$599$	30.0038			1.22592			0.612960	−	0.790114i	$-0.289979\pi$
$599$	30.0038			1.22592			0.612960	+	0.790114i	$0.289979\pi$
$600$		0			0
$601$	4.34999			0.177440			0.0887199	−	0.996057i	$-0.471722\pi$
$601$	4.34999			0.177440			0.0887199	+	0.996057i	$0.471722\pi$
$602$	−15.8369	−	2.60187i	−0.645463	−	0.106044i
$603$		0			0
$604$	−27.7886	−	9.38419i	−1.13070	−	0.381837i
$605$			14.2367i			0.578805i
$606$		0			0
$607$	−15.0209			−0.609681			−0.304841	−	0.952403i	$-0.598603\pi$
$607$	−15.0209			−0.609681			−0.304841	+	0.952403i	$0.598603\pi$
$608$	31.1642	+	33.0122i	1.26387	+	1.33882i
$609$		0			0
$610$	0.512067	−	3.11681i	0.0207330	−	0.126196i
$611$		−	8.31410i		−	0.336352i
$612$		0			0
$613$		−	2.19625i		−	0.0887055i	−0.999016	−	0.0443528i	$-0.985877\pi$
$613$		−	2.19625i		−	0.0887055i	0.999016	−	0.0443528i	$-0.0141226\pi$
$614$	−30.9578	−	5.08611i	−1.24935	−	0.205259i
$615$		0			0
$616$	−5.12059	−	2.72148i	−0.206315	−	0.109652i
$617$	−35.3729			−1.42406			−0.712030	−	0.702149i	$-0.752224\pi$
$617$	−35.3729			−1.42406			−0.712030	+	0.702149i	$0.752224\pi$
$618$		0			0
$619$			25.4878i			1.02444i	0.858854	+	0.512221i	$0.171177\pi$
$619$			25.4878i			1.02444i	−0.858854	+	0.512221i	$0.828823\pi$
$620$	9.50867	−	28.1573i	0.381877	−	1.13082i
$621$		0			0
$622$	3.41143	−	20.7645i	0.136786	−	0.832579i
$623$	−6.60076			−0.264454
$624$		0			0
$625$	−7.34848			−0.293939
$626$	−5.09192	+	30.9932i	−0.203514	+	1.23874i
$627$		0			0
$628$	1.59791	−	4.73175i	0.0637634	−	0.188817i
$629$			60.2692i			2.40309i
$630$		0			0
$631$	3.58602			0.142757			0.0713786	−	0.997449i	$-0.477260\pi$
$631$	3.58602			0.142757			0.0713786	+	0.997449i	$0.477260\pi$
$632$	9.31832	−	17.5329i	0.370663	−	0.697419i
$633$		0			0
$634$	13.4282	+	2.20614i	0.533301	+	0.0876170i
$635$		−	3.64060i		−	0.144473i
$636$		0			0
$637$			5.08023i			0.201286i
$638$	−2.62703	+	15.9900i	−0.104005	+	0.633050i
$639$		0			0
$640$	−7.63664	−	16.6102i	−0.301865	−	0.656578i
$641$	−40.1221			−1.58473			−0.792363	−	0.610050i	$-0.791149\pi$
$641$	−40.1221			−1.58473			−0.792363	+	0.610050i	$0.791149\pi$
$642$		0			0
$643$		−	25.3341i		−	0.999078i	−0.866292	−	0.499539i	$-0.833503\pi$
$643$		−	25.3341i		−	0.999078i	0.866292	−	0.499539i	$-0.166497\pi$
$644$	−6.36945	−	2.15096i	−0.250992	−	0.0847595i
$645$		0			0
$646$	78.6546	+	12.9223i	3.09463	+	0.508422i
$647$	−0.825159			−0.0324404			−0.0162202	−	0.999868i	$-0.505163\pi$
$647$	−0.825159			−0.0324404			−0.0162202	+	0.999868i	$0.505163\pi$
$648$		0			0
$649$	16.0709			0.630839
$650$	−3.33375	−	0.547708i	−0.130760	−	0.0214829i
$651$		0			0
$652$	−6.45925	+	19.1272i	−0.252964	+	0.749081i
$653$		−	37.6019i		−	1.47148i	−0.677265	−	0.735739i	$-0.736835\pi$
$653$		−	37.6019i		−	1.47148i	0.677265	−	0.735739i	$-0.263165\pi$
$654$		0			0
$655$	−1.16426			−0.0454913
$656$	29.7731	+	22.6971i	1.16244	+	0.886172i
$657$		0			0
$658$	−2.64111	+	16.0757i	−0.102961	+	0.626697i
$659$		−	16.9728i		−	0.661165i	−0.943777	−	0.330583i	$-0.892755\pi$
$659$		−	16.9728i		−	0.661165i	0.943777	−	0.330583i	$-0.107245\pi$
$660$		0			0
$661$			41.0591i			1.59701i	0.601985	+	0.798507i	$0.294377\pi$
$661$			41.0591i			1.59701i	−0.601985	+	0.798507i	$0.705623\pi$
$662$	−4.21982	−	0.693282i	−0.164008	−	0.0269452i
$663$		0			0
$664$	26.5921	+	14.1331i	1.03197	+	0.548470i
$665$	17.9680			0.696769
$666$		0			0
$667$			18.7863i			0.727408i
$668$	13.6861	+	4.62179i	0.529533	+	0.178823i
$669$		0			0
$670$	1.27739	−	7.77516i	0.0493501	−	0.300380i
$671$	−2.04524			−0.0789554
$672$		0			0
$673$	14.8665			0.573062			0.286531	−	0.958071i	$-0.407498\pi$
$673$	14.8665			0.573062			0.286531	+	0.958071i	$0.407498\pi$
$674$	1.76208	−	10.7253i	0.0678726	−	0.413122i
$675$		0			0
$676$	1.89487	+	0.639895i	0.0728796	+	0.0246114i
$677$		−	24.2997i		−	0.933913i	−0.884280	−	0.466957i	$-0.845350\pi$
$677$		−	24.2997i		−	0.933913i	0.884280	−	0.466957i	$-0.154650\pi$
$678$		0			0
$679$	13.1259			0.503725
$680$	−28.3439	−	15.0641i	−1.08694	−	0.577684i
$681$		0			0
$682$	−18.9892	−	3.11977i	−0.727134	−	0.119462i
$683$			5.98111i			0.228861i	0.993431	+	0.114430i	$0.0365043\pi$
$683$			5.98111i			0.228861i	−0.993431	+	0.114430i	$0.963496\pi$
$684$		0			0
$685$			30.1053i			1.15026i
$686$	3.83749	−	23.3577i	0.146516	−	0.891803i
$687$		0			0
$688$	−19.8624	+	26.0547i	−0.757248	+	0.993328i
$689$	−4.07306			−0.155171
$690$		0			0
$691$		−	20.6198i		−	0.784414i	−0.919877	−	0.392207i	$-0.871712\pi$
$691$		−	20.6198i		−	0.784414i	0.919877	−	0.392207i	$-0.128288\pi$
$692$	−1.56950	+	4.64763i	−0.0596634	+	0.176676i
$693$		0			0
$694$	−46.0003	−	7.55747i	−1.74615	−	0.286878i
$695$	−19.7094			−0.747620
$696$		0			0
$697$	65.7323			2.48979
$698$	−28.5654	−	4.69306i	−1.08122	−	0.177635i
$699$		0			0
$700$	6.27198	+	2.11804i	0.237059	+	0.0800544i
$701$			11.9063i			0.449694i	0.974394	+	0.224847i	$0.0721882\pi$
$701$			11.9063i			0.449694i	−0.974394	+	0.224847i	$0.927812\pi$
$702$		0			0
$703$	−68.8705			−2.59750
$704$	−9.81144	+	6.62306i	−0.369783	+	0.249616i
$705$		0			0
$706$	−3.47086	+	21.1262i	−0.130627	+	0.795094i
$707$		−	9.34049i		−	0.351285i
$708$		0			0
$709$			14.4805i			0.543828i	0.962322	+	0.271914i	$0.0876566\pi$
$709$			14.4805i			0.543828i	−0.962322	+	0.271914i	$0.912343\pi$
$710$	−30.3282	−	4.98268i	−1.13820	−	0.186997i
$711$		0			0
$712$	−6.32377	+	11.8985i	−0.236993	+	0.445914i
$713$	−22.3100			−0.835515
$714$		0			0
$715$		−	2.39103i		−	0.0894194i
$716$	5.61416	−	16.6248i	0.209811	−	0.621297i
$717$		0			0
$718$	−5.24961	+	31.9530i	−0.195914	+	1.19247i
$719$	−25.6663			−0.957191			−0.478595	−	0.878036i	$-0.658854\pi$
$719$	−25.6663			−0.957191			−0.478595	+	0.878036i	$0.658854\pi$
$720$		0			0
$721$	10.4355			0.388636
$722$	−10.4104	+	63.3652i	−0.387434	+	2.35821i
$723$		0			0
$724$	13.0057	−	38.5127i	0.483353	−	1.43131i
$725$		−	18.4988i		−	0.687028i
$726$		0			0
$727$	36.6958			1.36097			0.680486	−	0.732761i	$-0.261769\pi$
$727$	36.6958			1.36097			0.680486	+	0.732761i	$0.261769\pi$
$728$	−3.46055	−	1.83921i	−0.128257	−	0.0681656i
$729$		0			0
$730$	19.3513	+	3.17926i	0.716223	+	0.117670i
$731$			57.5230i			2.12756i
$732$		0			0
$733$		−	9.04187i		−	0.333969i	−0.985960	−	0.166985i	$-0.946597\pi$
$733$		−	9.04187i		−	0.333969i	0.985960	−	0.166985i	$-0.0534030\pi$
$734$	−5.34130	+	32.5111i	−0.197151	+	1.20001i
$735$		0			0
$736$	−9.97947	+	9.42083i	−0.367848	+	0.347256i
$737$	−5.10202			−0.187935
$738$		0			0
$739$			25.6800i			0.944653i	0.881424	+	0.472327i	$0.156586\pi$
$739$			25.6800i			0.944653i	−0.881424	+	0.472327i	$0.843414\pi$
$740$	26.2759	+	8.87334i	0.965921	+	0.326190i
$741$		0			0
$742$	7.87547	+	1.29387i	0.289117	+	0.0474996i
$743$	10.0377			0.368249			0.184124	−	0.982903i	$-0.441055\pi$
$743$	10.0377			0.368249			0.184124	+	0.982903i	$0.441055\pi$
$744$		0			0
$745$	27.5117			1.00795
$746$	11.6404	+	1.91242i	0.426184	+	0.0700186i
$747$		0			0
$748$	−6.64984	+	19.6916i	−0.243142	+	0.719997i
$749$			2.45031i			0.0895322i
$750$		0			0
$751$	22.3094			0.814083			0.407041	−	0.913410i	$-0.366560\pi$
$751$	22.3094			0.814083			0.407041	+	0.913410i	$0.366560\pi$
$752$	26.4477	+	20.1620i	0.964448	+	0.735232i
$753$		0			0
$754$	−1.77537	+	10.8062i	−0.0646553	+	0.393539i
$755$			23.6972i			0.862431i
$756$		0			0
$757$		−	14.9903i		−	0.544833i	−0.962179	−	0.272416i	$-0.912177\pi$
$757$		−	14.9903i		−	0.544833i	0.962179	−	0.272416i	$-0.0878228\pi$
$758$	−8.31236	−	1.36565i	−0.301918	−	0.0496027i
$759$		0			0
$760$	17.2140	−	32.3890i	0.624418	−	1.17487i
$761$	−44.0511			−1.59685			−0.798426	−	0.602093i	$-0.794334\pi$
$761$	−44.0511			−1.59685			−0.798426	+	0.602093i	$0.794334\pi$
$762$		0			0
$763$		−	1.42494i		−	0.0515862i
$764$	−0.975088	−	0.329286i	−0.0352774	−	0.0119131i
$765$		0			0
$766$	4.16056	−	25.3242i	0.150327	−	0.915001i
$767$	10.8609			0.392165
$768$		0			0
$769$	−20.0678			−0.723665			−0.361833	−	0.932243i	$-0.617849\pi$
$769$	−20.0678			−0.723665			−0.361833	+	0.932243i	$0.617849\pi$
$770$	−0.759550	+	4.62317i	−0.0273723	+	0.166608i
$771$		0			0
$772$	43.5034	+	14.6910i	1.56572	+	0.528742i
$773$			17.6836i			0.636034i	0.948085	+	0.318017i	$0.103017\pi$
$773$			17.6836i			0.636034i	−0.948085	+	0.318017i	$0.896983\pi$
$774$		0			0
$775$	21.9686			0.789135
$776$	12.5751	−	23.6606i	0.451420	−	0.849367i
$777$		0			0
$778$	−0.241304	−	0.0396442i	−0.00865116	−	0.00142131i
$779$			75.1132i			2.69121i
$780$		0			0
$781$			19.9012i			0.712122i
$782$	−3.90637	+	23.7770i	−0.139692	+	0.850265i
$783$		0			0
$784$	−16.1606	−	12.3198i	−0.577163	−	0.439991i
$785$	−4.03508			−0.144018
$786$		0			0
$787$			19.5587i			0.697194i	0.937273	+	0.348597i	$0.113342\pi$
$787$			19.5587i			0.697194i	−0.937273	+	0.348597i	$0.886658\pi$
$788$	4.93615	−	14.6170i	0.175843	−	0.520710i
$789$		0			0
$790$	−15.8297	−	2.60069i	−0.563195	−	0.0925284i
$791$	8.70168			0.309396
$792$		0			0
$793$	−1.38219			−0.0490831
$794$	−54.3474	−	8.92884i	−1.92872	−	0.316873i
$795$		0			0
$796$	8.05090	+	2.71878i	0.285357	+	0.0963646i
$797$		−	31.9695i		−	1.13242i	−0.824262	−	0.566209i	$-0.808409\pi$
$797$		−	31.9695i		−	1.13242i	0.824262	−	0.566209i	$-0.191591\pi$
$798$		0			0
$799$	58.3906			2.06571
$800$	9.82676	−	9.27667i	0.347428	−	0.327980i
$801$		0			0
$802$	1.26370	−	7.69181i	0.0446229	−	0.271607i
$803$		−	12.6982i		−	0.448110i
$804$		0			0
$805$			5.43166i			0.191441i
$806$	−12.8331	−	2.10838i	−0.452027	−	0.0742644i
$807$		0			0
$808$	−16.8371	−	8.94854i	−0.592327	−	0.314809i
$809$	9.62022			0.338229			0.169115	−	0.985596i	$-0.445909\pi$
$809$	9.62022			0.338229			0.169115	+	0.985596i	$0.445909\pi$
$810$		0			0
$811$			19.6731i			0.690816i	0.938453	+	0.345408i	$0.112259\pi$
$811$			19.6731i			0.690816i	−0.938453	+	0.345408i	$0.887741\pi$
$812$	6.86555	−	20.3304i	0.240934	−	0.713457i
$813$		0			0
$814$	2.91132	−	17.7204i	0.102042	−	0.621100i
$815$	16.3111			0.571353
$816$		0			0
$817$	−65.7323			−2.29968
$818$	4.58767	−	27.9239i	0.160404	−	0.976336i
$819$		0			0
$820$	9.67766	−	28.6577i	0.337959	−	1.00077i
$821$			24.6282i			0.859532i	0.902940	+	0.429766i	$0.141404\pi$
$821$			24.6282i			0.859532i	−0.902940	+	0.429766i	$0.858596\pi$
$822$		0			0
$823$	−10.6160			−0.370052			−0.185026	−	0.982734i	$-0.559237\pi$
$823$	−10.6160			−0.370052			−0.185026	+	0.982734i	$0.559237\pi$
$824$	9.99755	−	18.8109i	0.348281	−	0.655308i
$825$		0			0
$826$	−21.0001	−	3.45015i	−0.730688	−	0.120046i
$827$		−	19.1241i		−	0.665009i	−0.943102	−	0.332505i	$-0.892106\pi$
$827$		−	19.1241i		−	0.665009i	0.943102	−	0.332505i	$-0.107894\pi$
$828$		0			0
$829$			15.6561i			0.543759i	0.962331	+	0.271879i	$0.0876452\pi$
$829$			15.6561i			0.543759i	−0.962331	+	0.271879i	$0.912355\pi$
$830$	3.94447	−	24.0089i	0.136914	−	0.833361i
$831$		0			0
$832$	−6.63068	+	4.47594i	−0.229878	+	0.155175i
$833$	−35.6789			−1.23620
$834$		0			0
$835$		−	11.6711i		−	0.403895i
$836$	−22.5019	−	7.59886i	−0.778245	−	0.262812i
$837$		0			0
$838$	−9.83585	−	1.61595i	−0.339774	−	0.0558221i
$839$	−10.6255			−0.366834			−0.183417	−	0.983035i	$-0.558716\pi$
$839$	−10.6255			−0.366834			−0.183417	+	0.983035i	$0.558716\pi$
$840$		0			0
$841$	−30.9632			−1.06769
$842$	−11.4661	−	1.88378i	−0.395147	−	0.0649195i
$843$		0			0
$844$	4.08595	−	12.0994i	0.140644	−	0.416479i
$845$		−	1.61588i		−	0.0555881i
$846$		0			0
$847$	−12.2074			−0.419452
$848$	9.87732	−	12.9567i	0.339189	−	0.444934i
$849$		0			0
$850$	3.84659	−	23.4132i	0.131937	−	0.803066i
$851$		−	20.8193i		−	0.713677i
$852$		0			0
$853$		−	2.79803i		−	0.0958027i	−0.998852	−	0.0479013i	$-0.984747\pi$
$853$		−	2.79803i		−	0.0958027i	0.998852	−	0.0479013i	$-0.0152533\pi$
$854$	2.67254	+	0.439077i	0.0914525	+	0.0150249i
$855$		0			0
$856$	4.41690	+	2.34748i	0.150967	+	0.0802354i
$857$	−10.5004			−0.358686			−0.179343	−	0.983787i	$-0.557397\pi$
$857$	−10.5004			−0.358686			−0.179343	+	0.983787i	$0.557397\pi$
$858$		0			0
$859$			53.6535i			1.83063i	0.402733	+	0.915317i	$0.368060\pi$
$859$			53.6535i			1.83063i	−0.402733	+	0.915317i	$0.631940\pi$
$860$	25.0786	+	8.46902i	0.855174	+	0.288791i
$861$		0			0
$862$	3.29614	−	20.0627i	0.112267	−	0.683338i
$863$	−32.0861			−1.09222			−0.546111	−	0.837713i	$-0.683892\pi$
$863$	−32.0861			−1.09222			−0.546111	+	0.837713i	$0.683892\pi$
$864$		0			0
$865$	3.96335			0.134758
$866$	−3.97811	+	24.2137i	−0.135182	+	0.822815i
$867$		0			0
$868$	24.1437	+	8.15331i	0.819491	+	0.276741i
$869$			10.3874i			0.352367i
$870$		0			0
$871$	−3.44800			−0.116831
$872$	−2.56858	−	1.36514i	−0.0869832	−	0.0462296i
$873$		0			0
$874$	−27.1703	−	4.46387i	−0.919051	−	0.150993i
$875$		−	16.5430i		−	0.559257i
$876$		0			0
$877$			45.7566i			1.54509i	0.634960	+	0.772545i	$0.281017\pi$
$877$			45.7566i			1.54509i	−0.634960	+	0.772545i	$0.718983\pi$
$878$	−3.53732	+	21.5307i	−0.119379	+	0.726626i
$879$		0			0
$880$	7.60602	+	5.79833i	0.256399	+	0.195462i
$881$	−38.0557			−1.28213			−0.641065	−	0.767486i	$-0.721507\pi$
$881$	−38.0557			−1.28213			−0.641065	+	0.767486i	$0.721507\pi$
$882$		0			0
$883$		−	29.9690i		−	1.00854i	−0.863547	−	0.504269i	$-0.831762\pi$
$883$		−	29.9690i		−	1.00854i	0.863547	−	0.504269i	$-0.168238\pi$
$884$	−4.49404	+	13.3078i	−0.151151	+	0.447591i
$885$		0			0
$886$	−21.8315	−	3.58675i	−0.733445	−	0.120499i
$887$	51.8916			1.74235			0.871174	−	0.490975i	$-0.163359\pi$
$887$	51.8916			1.74235			0.871174	+	0.490975i	$0.163359\pi$
$888$		0			0
$889$	3.12167			0.104697
$890$	10.7426	+	1.76493i	0.360094	+	0.0591606i
$891$		0			0
$892$	−32.8756	−	11.1020i	−1.10076	−	0.371724i
$893$			66.7237i			2.23282i
$894$		0			0
$895$	−14.1771			−0.473887
$896$	14.2426	−	6.54811i	0.475813	−	0.218757i
$897$		0			0
$898$	−1.39856	+	8.51268i	−0.0466707	+	0.284072i
$899$		−	71.2103i		−	2.37500i
$900$		0			0
$901$		−	28.6054i		−	0.952985i
$902$	−19.3267	−	3.17522i	−0.643508	−	0.105723i
$903$		0			0
$904$	8.33654	−	15.6856i	0.277269	−	0.521695i
$905$	−32.8424			−1.09172
$906$		0			0
$907$		−	7.37653i		−	0.244934i	−0.992473	−	0.122467i	$-0.960919\pi$
$907$		−	7.37653i		−	0.244934i	0.992473	−	0.122467i	$-0.0390805\pi$
$908$	−5.66145	+	16.7648i	−0.187882	+	0.556359i
$909$		0			0
$910$	−0.513312	+	3.12439i	−0.0170161	+	0.103573i
$911$	−21.2104			−0.702732			−0.351366	−	0.936238i	$-0.614283\pi$
$911$	−21.2104			−0.702732			−0.351366	+	0.936238i	$0.614283\pi$
$912$		0			0
$913$	−15.7545			−0.521398
$914$	−2.32654	+	14.1610i	−0.0769551	+	0.468405i
$915$		0			0
$916$	−5.12617	+	15.1797i	−0.169373	+	0.501551i
$917$		−	0.998304i		−	0.0329669i
$918$		0			0
$919$	−22.2953			−0.735455			−0.367727	−	0.929934i	$-0.619864\pi$
$919$	−22.2953			−0.735455			−0.367727	+	0.929934i	$0.619864\pi$
$920$	9.79107	+	5.20374i	0.322802	+	0.171562i
$921$		0			0
$922$	−27.6865	−	4.54866i	−0.911806	−	0.149802i
$923$			13.4495i			0.442695i
$924$		0			0
$925$			20.5007i			0.674060i
$926$	6.45596	−	39.2957i	0.212156	−	1.29134i
$927$		0			0
$928$	−30.0700	−	31.8531i	−0.987095	−	1.04563i
$929$	−21.6844			−0.711442			−0.355721	−	0.934592i	$-0.615765\pi$
$929$	−21.6844			−0.711442			−0.355721	+	0.934592i	$0.615765\pi$
$930$		0			0
$931$		−	40.7708i		−	1.33621i
$932$	−27.2483	−	9.20172i	−0.892548	−	0.301412i
$933$		0			0
$934$	17.7204	+	2.91132i	0.579830	+	0.0952613i
$935$	16.7924			0.549170
$936$		0			0
$937$	9.75513			0.318686			0.159343	−	0.987223i	$-0.449062\pi$
$937$	9.75513			0.318686			0.159343	+	0.987223i	$0.449062\pi$
$938$	6.66688	+	1.09531i	0.217681	+	0.0357633i
$939$		0			0
$940$	8.59675	−	25.4569i	0.280395	−	0.830311i
$941$			40.2886i			1.31337i	0.754165	+	0.656685i	$0.228042\pi$
$941$			40.2886i			1.31337i	−0.754165	+	0.656685i	$0.771958\pi$
$942$		0			0
$943$	−22.7065			−0.739425
$944$	−26.3381	+	34.5493i	−0.857234	+	1.12448i
$945$		0			0
$946$	2.77866	−	16.9130i	0.0903421	−	0.549888i
$947$			38.5068i			1.25130i	0.780103	+	0.625651i	$0.215166\pi$
$947$			38.5068i			1.25130i	−0.780103	+	0.625651i	$0.784834\pi$
$948$		0			0
$949$		−	8.58159i		−	0.278570i
$950$	26.7546	+	4.39556i	0.868033	+	0.142611i
$951$		0			0
$952$	12.9169	−	24.3038i	0.418639	−	0.787689i
$953$	9.52795			0.308641			0.154320	−	0.988021i	$-0.450681\pi$
$953$	9.52795			0.308641			0.154320	+	0.988021i	$0.450681\pi$
$954$		0			0
$955$			0.831523i			0.0269075i
$956$	48.2530	+	16.2950i	1.56061	+	0.527018i
$957$		0			0
$958$	8.44338	−	51.3926i	0.272793	−	1.66042i
$959$	−25.8141			−0.833580
$960$		0			0
$961$	53.5671			1.72797
$962$	1.96750	−	11.9757i	0.0634348	−	0.386111i
$963$		0			0
$964$	−35.6442	−	12.0370i	−1.14802	−	0.387686i
$965$		−	37.0983i		−	1.19424i
$966$		0			0
$967$	22.3293			0.718062			0.359031	−	0.933326i	$-0.383107\pi$
$967$	22.3293			0.718062			0.359031	+	0.933326i	$0.383107\pi$
$968$	−11.6952	+	22.0050i	−0.375897	+	0.707267i
$969$		0			0
$970$	−21.3622	−	3.50964i	−0.685900	−	0.112688i
$971$		−	59.7660i		−	1.91798i	−0.283438	−	0.958991i	$-0.591475\pi$
$971$		−	59.7660i		−	1.91798i	0.283438	−	0.958991i	$-0.408525\pi$
$972$		0			0
$973$		−	16.9000i		−	0.541790i
$974$	−0.111088	+	0.676160i	−0.00355948	+	0.0216656i
$975$		0			0
$976$	3.35187	−	4.39685i	0.107291	−	0.140740i
$977$	−6.12704			−0.196021			−0.0980107	−	0.995185i	$-0.531248\pi$
$977$	−6.12704			−0.196021			−0.0980107	+	0.995185i	$0.531248\pi$
$978$		0			0
$979$		−	7.04927i		−	0.225296i
$980$	−5.25295	+	15.5551i	−0.167799	+	0.496890i
$981$		0			0
$982$	4.55723	+	0.748716i	0.145427	+	0.0238925i
$983$	16.6436			0.530849			0.265424	−	0.964132i	$-0.414488\pi$
$983$	16.6436			0.530849			0.265424	+	0.964132i	$0.414488\pi$
$984$		0			0
$985$	−12.4649			−0.397166
$986$	−75.8929	−	12.4686i	−2.41692	−	0.397081i
$987$		0			0
$988$	−15.2070	−	5.13540i	−0.483800	−	0.163379i
$989$		−	19.8707i		−	0.631850i
$990$		0			0
$991$	30.5255			0.969673			0.484836	−	0.874605i	$-0.338879\pi$
$991$	30.5255			0.969673			0.484836	+	0.874605i	$0.338879\pi$
$992$	37.8277	−	35.7101i	1.20103	−	1.13380i
$993$		0			0
$994$	4.27245	−	26.0052i	0.135514	−	0.824836i
$995$		−	6.86555i		−	0.217653i
$996$		0			0
$997$		−	22.7042i		−	0.719049i	−0.933136	−	0.359525i	$-0.882939\pi$
$997$		−	22.7042i		−	0.719049i	0.933136	−	0.359525i	$-0.117061\pi$
$998$	0.472669	+	0.0776556i	0.0149621	+	0.00245815i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.f.469.13	yes	24
3.2	odd	2	inner	936.2.g.f.469.12	yes	24
4.3	odd	2		3744.2.g.f.1873.2		24
8.3	odd	2		3744.2.g.f.1873.1		24
8.5	even	2	inner	936.2.g.f.469.14	yes	24
12.11	even	2		3744.2.g.f.1873.21		24
24.5	odd	2	inner	936.2.g.f.469.11	✓	24
24.11	even	2		3744.2.g.f.1873.22		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.g.f.469.11	✓	24	24.5	odd	2	inner
936.2.g.f.469.12	yes	24	3.2	odd	2	inner
936.2.g.f.469.13	yes	24	1.1	even	1	trivial
936.2.g.f.469.14	yes	24	8.5	even	2	inner
3744.2.g.f.1873.1		24	8.3	odd	2
3744.2.g.f.1873.2		24	4.3	odd	2
3744.2.g.f.1873.21		24	12.11	even	2
3744.2.g.f.1873.22		24	24.11	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.229270 - 1.39551i) q^{2} +(-1.89487 - 0.639895i) q^{4} +1.61588i q^{5} -1.38556 q^{7} +(-1.32741 + 2.49759i) q^{8} +(2.25497 + 0.370474i) q^{10} -1.47970i q^{11} -1.00000i q^{13} +(-0.317667 + 1.93355i) q^{14} +(3.18107 + 2.42504i) q^{16} +7.02308 q^{17} +8.02537i q^{19} +(1.03400 - 3.06189i) q^{20} +(-2.06493 - 0.339252i) q^{22} -2.42604 q^{23} +2.38892 q^{25} +(-1.39551 - 0.229270i) q^{26} +(2.62545 + 0.886611i) q^{28} -7.74359i q^{29} +9.19604 q^{31} +(4.11348 - 3.88321i) q^{32} +(1.61018 - 9.80075i) q^{34} -2.23890i q^{35} +8.58159i q^{37} +(11.1995 + 1.83998i) q^{38} +(-4.03582 - 2.14495i) q^{40} +9.35947 q^{41} +8.19056i q^{43} +(-0.946855 + 2.80385i) q^{44} +(-0.556219 + 3.38556i) q^{46} +8.31410 q^{47} -5.08023 q^{49} +(0.547708 - 3.33375i) q^{50} +(-0.639895 + 1.89487i) q^{52} -4.07306i q^{53} +2.39103 q^{55} +(1.83921 - 3.46055i) q^{56} +(-10.8062 - 1.77537i) q^{58} +10.8609i q^{59} -1.38219i q^{61} +(2.10838 - 12.8331i) q^{62} +(-4.47594 - 6.63068i) q^{64} +1.61588 q^{65} -3.44800i q^{67} +(-13.3078 - 4.49404i) q^{68} +(-3.12439 - 0.513312i) q^{70} -13.4495 q^{71} +8.58159 q^{73} +(11.9757 + 1.96750i) q^{74} +(5.13540 - 15.2070i) q^{76} +2.05021i q^{77} -7.01990 q^{79} +(-3.91858 + 5.14024i) q^{80} +(2.14585 - 13.0612i) q^{82} -10.6471i q^{83} +11.3485i q^{85} +(11.4300 + 1.87785i) q^{86} +(3.69570 + 1.96418i) q^{88} +4.76398 q^{89} +1.38556i q^{91} +(4.59704 + 1.55241i) q^{92} +(1.90617 - 11.6024i) q^{94} -12.9681 q^{95} -9.47337 q^{97} +(-1.16475 + 7.08949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more