LMFDB - Embedded newform 1008.2.bf.i.31.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(31,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.14
Character	$\chi$	$=$	1008.31
Dual form			1008.2.bf.i.943.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33729 - 1.10075i) q^{3} +1.09736i q^{5} +(-1.10288 - 2.40492i) q^{7} +(0.576701 - 2.94405i) q^{9} -0.100798i q^{11} +(4.27107 + 2.46590i) q^{13} +(1.20792 + 1.46750i) q^{15} +(3.23648 + 1.86858i) q^{17} +(2.54669 + 4.41100i) q^{19} +(-4.12209 - 2.00210i) q^{21} -9.20757i q^{23} +3.79579 q^{25} +(-2.46944 - 4.57186i) q^{27} +(-3.96297 - 6.86407i) q^{29} +(-2.41787 - 4.18787i) q^{31} +(-0.110953 - 0.134796i) q^{33} +(2.63908 - 1.21026i) q^{35} +(-2.77437 - 4.80534i) q^{37} +(8.42601 - 1.40374i) q^{39} +(-3.91138 - 2.25823i) q^{41} +(1.73626 - 1.00243i) q^{43} +(3.23069 + 0.632852i) q^{45} +(3.17534 - 5.49984i) q^{47} +(-4.56733 + 5.30467i) q^{49} +(6.38495 - 1.06371i) q^{51} +(-6.53502 + 11.3190i) q^{53} +0.110612 q^{55} +(8.26109 + 3.09553i) q^{57} +(1.44382 + 2.50077i) q^{59} +(8.21186 + 4.74112i) q^{61} +(-7.71624 + 1.86000i) q^{63} +(-2.70599 + 4.68692i) q^{65} +(10.8779 - 6.28036i) q^{67} +(-10.1352 - 12.3132i) q^{69} +14.5863i q^{71} +(5.92115 + 3.41858i) q^{73} +(5.07608 - 4.17822i) q^{75} +(-0.242411 + 0.111167i) q^{77} +(-2.31531 - 1.33675i) q^{79} +(-8.33483 - 3.39567i) q^{81} +(0.112583 + 0.195000i) q^{83} +(-2.05051 + 3.55159i) q^{85} +(-12.8553 - 4.81703i) q^{87} +(-4.90756 + 2.83338i) q^{89} +(1.21985 - 12.9912i) q^{91} +(-7.84319 - 2.93894i) q^{93} +(-4.84048 + 2.79465i) q^{95} +(6.47632 - 3.73911i) q^{97} +(-0.296753 - 0.0581302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.33729	−	1.10075i	0.772086	−	0.635518i
$3$	1.33729	−	1.10075i	0.772086	−	0.635518i
$4$		0			0
$5$			1.09736i			0.490756i	0.969427	+	0.245378i	$0.0789121\pi$
$5$			1.09736i			0.490756i	−0.969427	+	0.245378i	$0.921088\pi$
$6$		0			0
$7$	−1.10288	−	2.40492i	−0.416848	−	0.908976i
$7$	−1.10288	−	2.40492i	−0.416848	−	0.908976i
$8$		0			0
$9$	0.576701	−	2.94405i	0.192234	−	0.981349i
$10$		0			0
$11$		−	0.100798i		−	0.0303917i	−0.999885	−	0.0151958i	$-0.995163\pi$
$11$		−	0.100798i		−	0.0303917i	0.999885	−	0.0151958i	$-0.00483717\pi$
$12$		0			0
$13$	4.27107	+	2.46590i	1.18458	+	0.683918i	0.957070	−	0.289857i	$-0.0936078\pi$
$13$	4.27107	+	2.46590i	1.18458	+	0.683918i	0.227511	+	0.973775i	$0.426941\pi$
$14$		0			0
$15$	1.20792	+	1.46750i	0.311884	+	0.378906i
$16$		0			0
$17$	3.23648	+	1.86858i	0.784961	+	0.453197i	0.838185	−	0.545385i	$-0.183617\pi$
$17$	3.23648	+	1.86858i	0.784961	+	0.453197i	−0.0532247	+	0.998583i	$0.516950\pi$
$18$		0			0
$19$	2.54669	+	4.41100i	0.584252	+	1.01195i	0.994968	+	0.100191i	$0.0319453\pi$
$19$	2.54669	+	4.41100i	0.584252	+	1.01195i	−0.410716	+	0.911763i	$0.634721\pi$
$20$		0			0
$21$	−4.12209	−	2.00210i	−0.899513	−	0.436893i
$22$		0			0
$23$		−	9.20757i		−	1.91991i	−0.280151	−	0.959956i	$-0.590385\pi$
$23$		−	9.20757i		−	1.91991i	0.280151	−	0.959956i	$-0.409615\pi$
$24$		0			0
$25$	3.79579			0.759158
$26$		0			0
$27$	−2.46944	−	4.57186i	−0.475244	−	0.879854i
$28$		0			0
$29$	−3.96297	−	6.86407i	−0.735905	−	1.27463i	−0.954325	−	0.298770i	$-0.903424\pi$
$29$	−3.96297	−	6.86407i	−0.735905	−	1.27463i	0.218420	−	0.975855i	$-0.429910\pi$
$30$		0			0
$31$	−2.41787	−	4.18787i	−0.434262	−	0.752164i	0.562973	−	0.826475i	$-0.309657\pi$
$31$	−2.41787	−	4.18787i	−0.434262	−	0.752164i	−0.997235	+	0.0743115i	$0.976324\pi$
$32$		0			0
$33$	−0.110953	−	0.134796i	−0.0193145	−	0.0234650i
$34$		0			0
$35$	2.63908	−	1.21026i	0.446086	−	0.204571i
$36$		0			0
$37$	−2.77437	−	4.80534i	−0.456103	−	0.789993i	0.542648	−	0.839960i	$-0.317422\pi$
$37$	−2.77437	−	4.80534i	−0.456103	−	0.789993i	−0.998751	+	0.0499669i	$0.984088\pi$
$38$		0			0
$39$	8.42601	−	1.40374i	1.34924	−	0.224779i
$40$		0			0
$41$	−3.91138	−	2.25823i	−0.610854	−	0.352677i	0.162446	−	0.986718i	$-0.448062\pi$
$41$	−3.91138	−	2.25823i	−0.610854	−	0.352677i	−0.773300	+	0.634041i	$0.781395\pi$
$42$		0			0
$43$	1.73626	−	1.00243i	0.264777	−	0.152869i	−0.361735	−	0.932281i	$-0.617815\pi$
$43$	1.73626	−	1.00243i	0.264777	−	0.152869i	0.626512	+	0.779412i	$0.284482\pi$
$44$		0			0
$45$	3.23069	+	0.632852i	0.481603	+	0.0943399i
$46$		0			0
$47$	3.17534	−	5.49984i	0.463170	−	0.802235i	−0.535947	−	0.844252i	$-0.680045\pi$
$47$	3.17534	−	5.49984i	0.463170	−	0.802235i	0.999117	+	0.0420174i	$0.0133785\pi$
$48$		0			0
$49$	−4.56733	+	5.30467i	−0.652475	+	0.757810i
$50$		0			0
$51$	6.38495	−	1.06371i	0.894072	−	0.148949i
$52$		0			0
$53$	−6.53502	+	11.3190i	−0.897655	+	1.55478i	−0.0671703	+	0.997742i	$0.521397\pi$
$53$	−6.53502	+	11.3190i	−0.897655	+	1.55478i	−0.830484	+	0.557042i	$0.811936\pi$
$54$		0			0
$55$	0.110612			0.0149149
$56$		0			0
$57$	8.26109	+	3.09553i	1.09421	+	0.410013i
$58$		0			0
$59$	1.44382	+	2.50077i	0.187969	+	0.325572i	0.944573	−	0.328301i	$-0.106476\pi$
$59$	1.44382	+	2.50077i	0.187969	+	0.325572i	−0.756604	+	0.653874i	$0.773143\pi$
$60$		0			0
$61$	8.21186	+	4.74112i	1.05142	+	0.607038i	0.923047	−	0.384687i	$-0.125691\pi$
$61$	8.21186	+	4.74112i	1.05142	+	0.607038i	0.128374	+	0.991726i	$0.459024\pi$
$62$		0			0
$63$	−7.71624	+	1.86000i	−0.972155	+	0.234337i
$64$		0			0
$65$	−2.70599	+	4.68692i	−0.335637	+	0.581341i
$66$		0			0
$67$	10.8779	−	6.28036i	1.32895	−	0.767268i	0.343810	−	0.939039i	$-0.388282\pi$
$67$	10.8779	−	6.28036i	1.32895	−	0.767268i	0.985137	+	0.171771i	$0.0549489\pi$
$68$		0			0
$69$	−10.1352	−	12.3132i	−1.22014	−	1.48234i
$70$		0			0
$71$			14.5863i			1.73107i	0.500848	+	0.865535i	$0.333022\pi$
$71$			14.5863i			1.73107i	−0.500848	+	0.865535i	$0.666978\pi$
$72$		0			0
$73$	5.92115	+	3.41858i	0.693018	+	0.400114i	0.804742	−	0.593625i	$-0.202304\pi$
$73$	5.92115	+	3.41858i	0.693018	+	0.400114i	−0.111724	+	0.993739i	$0.535637\pi$
$74$		0			0
$75$	5.07608	−	4.17822i	0.586135	−	0.482459i
$76$		0			0
$77$	−0.242411	+	0.111167i	−0.0276253	+	0.0126687i
$78$		0			0
$79$	−2.31531	−	1.33675i	−0.260493	−	0.150396i	0.364066	−	0.931373i	$-0.381388\pi$
$79$	−2.31531	−	1.33675i	−0.260493	−	0.150396i	−0.624559	+	0.780977i	$0.714721\pi$
$80$		0			0
$81$	−8.33483	−	3.39567i	−0.926092	−	0.377297i
$82$		0			0
$83$	0.112583	+	0.195000i	0.0123576	+	0.0214040i	0.872138	−	0.489260i	$-0.162733\pi$
$83$	0.112583	+	0.195000i	0.0123576	+	0.0214040i	−0.859780	+	0.510664i	$0.829400\pi$
$84$		0			0
$85$	−2.05051	+	3.55159i	−0.222409	+	0.385224i
$86$		0			0
$87$	−12.8553	−	4.81703i	−1.37823	−	0.516439i
$88$		0			0
$89$	−4.90756	+	2.83338i	−0.520200	+	0.300338i	−0.737016	−	0.675875i	$-0.763766\pi$
$89$	−4.90756	+	2.83338i	−0.520200	+	0.300338i	0.216817	+	0.976212i	$0.430433\pi$
$90$		0			0
$91$	1.21985	−	12.9912i	0.127875	−	1.36185i
$92$		0			0
$93$	−7.84319	−	2.93894i	−0.813301	−	0.304754i
$94$		0			0
$95$	−4.84048	+	2.79465i	−0.496623	+	0.286725i
$96$		0			0
$97$	6.47632	−	3.73911i	0.657571	−	0.379649i	−0.133780	−	0.991011i	$-0.542712\pi$
$97$	6.47632	−	3.73911i	0.657571	−	0.379649i	0.791351	+	0.611362i	$0.209378\pi$
$98$		0			0
$99$	−0.296753	−	0.0581302i	−0.0298248	−	0.00584231i
$100$		0			0
$101$			1.69404i			0.168564i	0.996442	+	0.0842818i	$0.0268596\pi$
$101$			1.69404i			0.168564i	−0.996442	+	0.0842818i	$0.973140\pi$
$102$		0			0
$103$	−5.92861			−0.584164			−0.292082	−	0.956393i	$-0.594348\pi$
$103$	−5.92861			−0.584164			−0.292082	+	0.956393i	$0.594348\pi$
$104$		0			0
$105$	2.19703	−	4.52343i	0.214408	−	0.441442i
$106$		0			0
$107$	4.25250	−	2.45518i	0.411104	−	0.237351i	−0.280160	−	0.959953i	$-0.590387\pi$
$107$	4.25250	−	2.45518i	0.411104	−	0.237351i	0.691264	+	0.722602i	$0.257054\pi$
$108$		0			0
$109$	−5.22573	+	9.05124i	−0.500535	+	0.866951i	0.499465	+	0.866334i	$0.333530\pi$
$109$	−5.22573	+	9.05124i	−0.500535	+	0.866951i	−1.00000		0.000617375i	$0.999803\pi$
$110$		0			0
$111$	−8.99961	−	3.37227i	−0.854206	−	0.320081i
$112$		0			0
$113$	−5.15634	+	8.93104i	−0.485068	+	0.840162i	−0.999853	−	0.0171575i	$-0.994538\pi$
$113$	−5.15634	+	8.93104i	−0.485068	+	0.840162i	0.514785	+	0.857319i	$0.327872\pi$
$114$		0			0
$115$	10.1041			0.942209
$116$		0			0
$117$	9.72287	−	11.1521i	0.898879	−	1.03102i
$118$		0			0
$119$	0.924363	−	9.84430i	0.0847362	−	0.902425i
$120$		0			0
$121$	10.9898			0.999076
$122$		0			0
$123$	−7.71640	+	1.28553i	−0.695764	+	0.115912i
$124$		0			0
$125$			9.65219i			0.863318i
$126$		0			0
$127$			8.87104i			0.787177i	0.919287	+	0.393589i	$0.128767\pi$
$127$			8.87104i			0.787177i	−0.919287	+	0.393589i	$0.871233\pi$
$128$		0			0
$129$	1.21846	−	3.25172i	0.107279	−	0.286298i
$130$		0			0
$131$	−5.89886			−0.515386			−0.257693	−	0.966227i	$-0.582962\pi$
$131$	−5.89886			−0.515386			−0.257693	+	0.966227i	$0.582962\pi$
$132$		0			0
$133$	7.79945	−	10.9894i	0.676298	−	0.952902i
$134$		0			0
$135$	5.01699	−	2.70988i	0.431794	−	0.233229i
$136$		0			0
$137$	−17.4326			−1.48937			−0.744683	−	0.667418i	$-0.767400\pi$
$137$	−17.4326			−1.48937			−0.744683	+	0.667418i	$0.767400\pi$
$138$		0			0
$139$	−8.09773	+	14.0257i	−0.686840	+	1.18964i	0.286014	+	0.958225i	$0.407669\pi$
$139$	−8.09773	+	14.0257i	−0.686840	+	1.18964i	−0.972855	+	0.231417i	$0.925664\pi$
$140$		0			0
$141$	−1.80760	−	10.8501i	−0.152227	−	0.913747i
$142$		0			0
$143$	0.248558	−	0.430514i	0.0207854	−	0.0360014i
$144$		0			0
$145$	7.53238	−	4.34882i	0.625530	−	0.361150i
$146$		0			0
$147$	−0.268742	+	12.1214i	−0.0221655	+	0.999754i
$148$		0			0
$149$	10.4411			0.855370			0.427685	−	0.903928i	$-0.359329\pi$
$149$	10.4411			0.855370			0.427685	+	0.903928i	$0.359329\pi$
$150$		0			0
$151$			8.91419i			0.725427i	0.931901	+	0.362713i	$0.118150\pi$
$151$			8.91419i			0.725427i	−0.931901	+	0.362713i	$0.881850\pi$
$152$		0			0
$153$	7.36767	−	8.45073i	0.595641	−	0.683201i
$154$		0			0
$155$	4.59562	−	2.65328i	0.369129	−	0.213117i
$156$		0			0
$157$	5.54621	−	3.20210i	0.442635	−	0.255556i	−0.262079	−	0.965046i	$-0.584408\pi$
$157$	5.54621	−	3.20210i	0.442635	−	0.255556i	0.704715	+	0.709491i	$0.251075\pi$
$158$		0			0
$159$	3.72014	+	22.3302i	0.295026	+	1.77090i
$160$		0			0
$161$	−22.1435	+	10.1548i	−1.74515	+	0.800311i
$162$		0			0
$163$	−7.19404	+	4.15348i	−0.563481	+	0.325326i	−0.754541	−	0.656253i	$-0.772141\pi$
$163$	−7.19404	+	4.15348i	−0.563481	+	0.325326i	0.191061	+	0.981578i	$0.438807\pi$
$164$		0			0
$165$	0.147920	−	0.121756i	0.0115156	−	0.00947869i
$166$		0			0
$167$	−7.92799	+	13.7317i	−0.613487	+	1.06259i	0.377161	+	0.926148i	$0.376900\pi$
$167$	−7.92799	+	13.7317i	−0.613487	+	1.06259i	−0.990648	+	0.136442i	$0.956433\pi$
$168$		0			0
$169$	5.66135	+	9.80575i	0.435488	+	0.754288i
$170$		0			0
$171$	14.4549	−	4.95376i	1.10539	−	0.378823i
$172$		0			0
$173$	−3.20209	−	1.84873i	−0.243450	−	0.140556i	0.373311	−	0.927706i	$-0.378222\pi$
$173$	−3.20209	−	1.84873i	−0.243450	−	0.140556i	−0.616762	+	0.787150i	$0.711556\pi$
$174$		0			0
$175$	−4.18629	−	9.12859i	−0.316454	−	0.690057i
$176$		0			0
$177$	4.68352	+	1.75497i	0.352035	+	0.131912i
$178$		0			0
$179$	7.20657	+	4.16072i	0.538645	+	0.310987i	0.744529	−	0.667590i	$-0.232674\pi$
$179$	7.20657	+	4.16072i	0.538645	+	0.310987i	−0.205885	+	0.978576i	$0.566007\pi$
$180$		0			0
$181$		−	25.2442i		−	1.87638i	−0.346115	−	0.938192i	$-0.612499\pi$
$181$		−	25.2442i		−	1.87638i	0.346115	−	0.938192i	$-0.387501\pi$
$182$		0			0
$183$	16.2004	−	2.69894i	1.19757	−	0.199511i
$184$		0			0
$185$	5.27321	−	3.04449i	0.387694	−	0.223835i
$186$		0			0
$187$	0.188349	−	0.326230i	0.0137734	−	0.0238563i
$188$		0			0
$189$	−8.27148	+	10.9810i	−0.601662	+	0.798751i
$190$		0			0
$191$	−3.65606	−	2.11082i	−0.264543	−	0.152734i	0.361862	−	0.932232i	$-0.382141\pi$
$191$	−3.65606	−	2.11082i	−0.264543	−	0.152734i	−0.626405	+	0.779498i	$0.715474\pi$
$192$		0			0
$193$	11.6625	+	20.2001i	0.839487	+	1.45403i	0.890324	+	0.455327i	$0.150478\pi$
$193$	11.6625	+	20.2001i	0.839487	+	1.45403i	−0.0508376	+	0.998707i	$0.516189\pi$
$194$		0			0
$195$	1.54042	+	9.24640i	0.110312	+	0.662149i
$196$		0			0
$197$	14.9348			1.06406			0.532030	−	0.846725i	$-0.321429\pi$
$197$	14.9348			1.06406			0.532030	+	0.846725i	$0.321429\pi$
$198$		0			0
$199$	−6.05559	+	10.4886i	−0.429269	+	0.743516i	−0.996808	−	0.0798303i	$-0.974562\pi$
$199$	−6.05559	+	10.4886i	−0.429269	+	0.743516i	0.567539	+	0.823346i	$0.307895\pi$
$200$		0			0
$201$	7.63383	−	20.3725i	0.538449	−	1.43697i
$202$		0			0
$203$	−12.1369	+	17.1009i	−0.851843	+	1.20025i
$204$		0			0
$205$	2.47811	−	4.29220i	0.173078	−	0.299781i
$206$		0			0
$207$	−27.1075	−	5.31002i	−1.88410	−	0.369072i
$208$		0			0
$209$	0.444619	−	0.256701i	0.0307550	−	0.0177564i
$210$		0			0
$211$	−0.912360	−	0.526751i	−0.0628095	−	0.0362631i	0.468266	−	0.883587i	$-0.344879\pi$
$211$	−0.912360	−	0.526751i	−0.0628095	−	0.0362631i	−0.531076	+	0.847324i	$0.678212\pi$
$212$		0			0
$213$	16.0558	+	19.5061i	1.10013	+	1.33654i
$214$		0			0
$215$	1.10003	+	1.90531i	0.0750213	+	0.129941i
$216$		0			0
$217$	−7.40490	+	10.4335i	−0.502678	+	0.708272i
$218$		0			0
$219$	11.6813	−	1.94607i	0.789350	−	0.131503i
$220$		0			0
$221$	9.21547	+	15.9617i	0.619900	+	1.07370i
$222$		0			0
$223$	−5.36823	−	9.29804i	−0.359483	−	0.622643i	0.628392	−	0.777897i	$-0.283714\pi$
$223$	−5.36823	−	9.29804i	−0.359483	−	0.622643i	−0.987875	+	0.155254i	$0.950380\pi$
$224$		0			0
$225$	2.18904	−	11.1750i	0.145936	−	0.744999i
$226$		0			0
$227$	1.51369			0.100467			0.0502334	−	0.998738i	$-0.484003\pi$
$227$	1.51369			0.100467			0.0502334	+	0.998738i	$0.484003\pi$
$228$		0			0
$229$			14.4501i			0.954893i	0.878661	+	0.477446i	$0.158438\pi$
$229$			14.4501i			0.954893i	−0.878661	+	0.477446i	$0.841562\pi$
$230$		0			0
$231$	−0.201807	+	0.415497i	−0.0132779	+	0.0273377i
$232$		0			0
$233$	−9.37435	−	16.2368i	−0.614134	−	1.06371i	−0.990536	−	0.137254i	$-0.956172\pi$
$233$	−9.37435	−	16.2368i	−0.614134	−	1.06371i	0.376402	−	0.926456i	$-0.377161\pi$
$234$		0			0
$235$	6.03533	+	3.48450i	0.393702	+	0.227304i
$236$		0			0
$237$	−4.56767	+	0.760958i	−0.296702	+	0.0494296i
$238$		0			0
$239$	−20.4105	−	11.7840i	−1.32025	−	0.762244i	−0.336478	−	0.941691i	$-0.609236\pi$
$239$	−20.4105	−	11.7840i	−1.32025	−	0.762244i	−0.983768	+	0.179447i	$0.942569\pi$
$240$		0			0
$241$			14.8848i			0.958815i	0.877592	+	0.479407i	$0.159148\pi$
$241$			14.8848i			0.958815i	−0.877592	+	0.479407i	$0.840852\pi$
$242$		0			0
$243$	−14.8839	+	4.63355i	−0.954802	+	0.297243i
$244$		0			0
$245$	−5.82116	−	5.01202i	−0.371900	−	0.320206i
$246$		0			0
$247$			25.1196i			1.59832i
$248$		0			0
$249$	0.365203	+	0.136846i	0.0231438	+	0.00867226i
$250$		0			0
$251$	6.87937			0.434222			0.217111	−	0.976147i	$-0.430337\pi$
$251$	6.87937			0.434222			0.217111	+	0.976147i	$0.430337\pi$
$252$		0			0
$253$	−0.928103			−0.0583493
$254$		0			0
$255$	1.16728	+	7.00662i	0.0730978	+	0.438772i
$256$		0			0
$257$		−	17.9963i		−	1.12258i	−0.827619	−	0.561290i	$-0.810305\pi$
$257$		−	17.9963i		−	1.12258i	0.827619	−	0.561290i	$-0.189695\pi$
$258$		0			0
$259$	−8.49670	+	11.9718i	−0.527960	+	0.743894i
$260$		0			0
$261$	−22.4936	+	7.70866i	−1.39232	+	0.477154i
$262$		0			0
$263$			8.87717i			0.547390i	0.961817	+	0.273695i	$0.0882458\pi$
$263$			8.87717i			0.547390i	−0.961817	+	0.273695i	$0.911754\pi$
$264$		0			0
$265$	−12.4211	−	7.17130i	−0.763020	−	0.440530i
$266$		0			0
$267$	−3.44400	+	9.19105i	−0.210769	+	0.562483i
$268$		0			0
$269$	9.95646	+	5.74836i	0.607056	+	0.350484i	0.771812	−	0.635850i	$-0.219350\pi$
$269$	9.95646	+	5.74836i	0.607056	+	0.350484i	−0.164756	+	0.986334i	$0.552684\pi$
$270$		0			0
$271$	−12.3583	−	21.4052i	−0.750713	−	1.30027i	−0.947478	−	0.319822i	$-0.896377\pi$
$271$	−12.3583	−	21.4052i	−0.750713	−	1.30027i	0.196765	−	0.980451i	$-0.436956\pi$
$272$		0			0
$273$	−12.6687	−	18.7158i	−0.766747	−	1.13273i
$274$		0			0
$275$		−	0.382607i		−	0.0230721i
$276$		0			0
$277$	1.03433			0.0621466			0.0310733	−	0.999517i	$-0.490107\pi$
$277$	1.03433			0.0621466			0.0310733	+	0.999517i	$0.490107\pi$
$278$		0			0
$279$	−13.7237	+	4.70317i	−0.821615	+	0.281571i
$280$		0			0
$281$	−1.51917	−	2.63128i	−0.0906262	−	0.156969i	0.817149	−	0.576427i	$-0.195554\pi$
$281$	−1.51917	−	2.63128i	−0.0906262	−	0.156969i	−0.907775	+	0.419458i	$0.862220\pi$
$282$		0			0
$283$	7.02389	+	12.1657i	0.417527	+	0.723177i	0.995690	−	0.0927436i	$-0.0295637\pi$
$283$	7.02389	+	12.1657i	0.417527	+	0.723177i	−0.578163	+	0.815921i	$0.696230\pi$
$284$		0			0
$285$	−3.39692	+	9.06542i	−0.201216	+	0.536989i
$286$		0			0
$287$	−1.11712	+	11.8971i	−0.0659415	+	0.702265i
$288$		0			0
$289$	−1.51681	−	2.62720i	−0.0892244	−	0.154541i
$290$		0			0
$291$	4.54492	−	12.1291i	0.266428	−	0.711020i
$292$		0			0
$293$	−0.747160	−	0.431373i	−0.0436496	−	0.0252011i	0.478016	−	0.878351i	$-0.341356\pi$
$293$	−0.747160	−	0.431373i	−0.0436496	−	0.0252011i	−0.521666	+	0.853150i	$0.674689\pi$
$294$		0			0
$295$	−2.74425	+	1.58440i	−0.159777	+	0.0922470i
$296$		0			0
$297$	−0.460833	+	0.248914i	−0.0267402	+	0.0144435i
$298$		0			0
$299$	22.7050	−	39.3262i	1.31306	−	2.27429i
$300$		0			0
$301$	−4.32564	−	3.07001i	−0.249326	−	0.176953i
$302$		0			0
$303$	1.86472	+	2.26543i	0.107125	+	0.130146i
$304$		0			0
$305$	−5.20274	+	9.01141i	−0.297908	+	0.515992i
$306$		0			0
$307$	−0.799801			−0.0456471			−0.0228235	−	0.999740i	$-0.507266\pi$
$307$	−0.799801			−0.0456471			−0.0228235	+	0.999740i	$0.507266\pi$
$308$		0			0
$309$	−7.92829	+	6.52592i	−0.451025	+	0.371246i
$310$		0			0
$311$	−13.1501	−	22.7767i	−0.745674	−	1.29155i	−0.949879	−	0.312618i	$-0.898794\pi$
$311$	−13.1501	−	22.7767i	−0.745674	−	1.29155i	0.204205	−	0.978928i	$-0.434539\pi$
$312$		0			0
$313$	−6.76366	−	3.90500i	−0.382305	−	0.220724i	0.296516	−	0.955028i	$-0.404175\pi$
$313$	−6.76366	−	3.90500i	−0.382305	−	0.220724i	−0.678821	+	0.734304i	$0.737509\pi$
$314$		0			0
$315$	−2.04109	−	8.46753i	−0.115003	−	0.477091i
$316$		0			0
$317$	−6.66835	+	11.5499i	−0.374532	+	0.648708i	−0.990257	−	0.139253i	$-0.955530\pi$
$317$	−6.66835	+	11.5499i	−0.374532	+	0.648708i	0.615725	+	0.787961i	$0.288863\pi$
$318$		0			0
$319$	−0.691883	+	0.399459i	−0.0387380	+	0.0223654i
$320$		0			0
$321$	2.98429	−	7.96423i	0.166567	−	0.444520i
$322$		0			0
$323$			19.0348i			1.05913i
$324$		0			0
$325$	16.2121	+	9.36005i	0.899285	+	0.519202i
$326$		0			0
$327$	2.97481	+	17.8564i	0.164507	+	0.987460i
$328$		0			0
$329$	−16.7287	−	1.57080i	−0.922284	−	0.0866009i
$330$		0			0
$331$	12.6057	+	7.27788i	0.692870	+	0.400029i	0.804686	−	0.593700i	$-0.202334\pi$
$331$	12.6057	+	7.27788i	0.692870	+	0.400029i	−0.111816	+	0.993729i	$0.535667\pi$
$332$		0			0
$333$	−15.7471	+	5.39662i	−0.862938	+	0.295733i
$334$		0			0
$335$	6.89184	+	11.9370i	0.376542	+	0.652189i
$336$		0			0
$337$	7.67592	−	13.2951i	0.418134	−	0.724229i	−0.577618	−	0.816307i	$-0.696018\pi$
$337$	7.67592	−	13.2951i	0.418134	−	0.724229i	0.995752	+	0.0920783i	$0.0293510\pi$
$338$		0			0
$339$	2.93531	+	17.6193i	0.159424	+	0.956946i
$340$		0			0
$341$	−0.422128	+	0.243716i	−0.0228595	+	0.0131979i
$342$		0			0
$343$	17.7945	+	5.13369i	0.960814	+	0.277193i
$344$		0			0
$345$	13.5121	−	11.1220i	0.727466	−	0.598791i
$346$		0			0
$347$	−20.1653	+	11.6424i	−1.08253	+	0.624999i	−0.931578	−	0.363542i	$-0.881567\pi$
$347$	−20.1653	+	11.6424i	−1.08253	+	0.624999i	−0.150952	+	0.988541i	$0.548234\pi$
$348$		0			0
$349$	12.0364	−	6.94922i	0.644294	−	0.371983i	−0.141973	−	0.989871i	$-0.545345\pi$
$349$	12.0364	−	6.94922i	0.644294	−	0.371983i	0.786267	+	0.617887i	$0.212011\pi$
$350$		0			0
$351$	0.726602	−	25.6161i	0.0387831	−	1.36729i
$352$		0			0
$353$			26.6932i			1.42074i	0.703830	+	0.710368i	$0.251471\pi$
$353$			26.6932i			1.42074i	−0.703830	+	0.710368i	$0.748529\pi$
$354$		0			0
$355$	−16.0064			−0.849534
$356$		0			0
$357$	−9.59996	−	14.1822i	−0.508084	−	0.750601i
$358$		0			0
$359$	−27.9838	+	16.1564i	−1.47693	+	0.852705i	−0.999661	−	0.0260534i	$-0.991706\pi$
$359$	−27.9838	+	16.1564i	−1.47693	+	0.852705i	−0.477267	+	0.878758i	$0.658373\pi$
$360$		0			0
$361$	−3.47131	+	6.01248i	−0.182700	+	0.316446i
$362$		0			0
$363$	14.6966	−	12.0971i	0.771373	−	0.634931i
$364$		0			0
$365$	−3.75143	+	6.49766i	−0.196359	+	0.340103i
$366$		0			0
$367$	−7.83398			−0.408931			−0.204465	−	0.978874i	$-0.565546\pi$
$367$	−7.83398			−0.408931			−0.204465	+	0.978874i	$0.565546\pi$
$368$		0			0
$369$	−8.90404	+	10.2129i	−0.463526	+	0.531665i
$370$		0			0
$371$	34.4287	+	3.23279i	1.78745	+	0.167838i
$372$		0			0
$373$	−19.2030			−0.994293			−0.497146	−	0.867667i	$-0.665619\pi$
$373$	−19.2030			−0.994293			−0.497146	+	0.867667i	$0.665619\pi$
$374$		0			0
$375$	10.6246	+	12.9078i	0.548654	+	0.666556i
$376$		0			0
$377$		−	39.0892i		−	2.01320i
$378$		0			0
$379$		−	17.4093i		−	0.894254i	−0.894470	−	0.447127i	$-0.852447\pi$
$379$		−	17.4093i		−	0.894254i	0.894470	−	0.447127i	$-0.147553\pi$
$380$		0			0
$381$	9.76479	+	11.8632i	0.500265	+	0.607769i
$382$		0			0
$383$	18.3013			0.935151			0.467575	−	0.883953i	$-0.345128\pi$
$383$	18.3013			0.935151			0.467575	+	0.883953i	$0.345128\pi$
$384$		0			0
$385$	−0.121991	−	0.266013i	−0.00621725	−	0.0135573i
$386$		0			0
$387$	−1.94989	−	5.68972i	−0.0991187	−	0.289225i
$388$		0			0
$389$	−2.17302			−0.110176			−0.0550882	−	0.998481i	$-0.517544\pi$
$389$	−2.17302			−0.110176			−0.0550882	+	0.998481i	$0.517544\pi$
$390$		0			0
$391$	17.2051	−	29.8001i	0.870099	−	1.50706i
$392$		0			0
$393$	−7.88850	+	6.49317i	−0.397922	+	0.327537i
$394$		0			0
$395$	1.46690	−	2.54074i	0.0738076	−	0.127839i
$396$		0			0
$397$	5.63167	−	3.25144i	0.282645	−	0.163185i	−0.351975	−	0.936009i	$-0.614490\pi$
$397$	5.63167	−	3.25144i	0.282645	−	0.163185i	0.634620	+	0.772824i	$0.281156\pi$
$398$		0			0
$399$	−1.66644	−	23.2813i	−0.0834262	−	1.16552i
$400$		0			0
$401$	−4.97927			−0.248653			−0.124326	−	0.992241i	$-0.539677\pi$
$401$	−4.97927			−0.248653			−0.124326	+	0.992241i	$0.539677\pi$
$402$		0			0
$403$		−	23.8489i		−	1.18800i
$404$		0			0
$405$	3.72629	−	9.14635i	0.185161	−	0.454486i
$406$		0			0
$407$	−0.484368	+	0.279650i	−0.0240092	+	0.0138617i
$408$		0			0
$409$	−0.175666	+	0.101421i	−0.00868614	+	0.00501494i	−0.504337	−	0.863507i	$-0.668263\pi$
$409$	−0.175666	+	0.101421i	−0.00868614	+	0.00501494i	0.495651	+	0.868522i	$0.334930\pi$
$410$		0			0
$411$	−23.3125	+	19.1889i	−1.14992	+	0.946519i
$412$		0			0
$413$	4.42180	−	6.23031i	0.217583	−	0.306574i
$414$		0			0
$415$	−0.213986	+	0.123545i	−0.0105042	+	0.00606458i
$416$		0			0
$417$	4.60973	+	27.6700i	0.225739	+	1.35501i
$418$		0			0
$419$	5.38038	−	9.31910i	0.262849	−	0.455268i	−0.704149	−	0.710052i	$-0.748671\pi$
$419$	5.38038	−	9.31910i	0.262849	−	0.455268i	0.966998	+	0.254785i	$0.0820046\pi$
$420$		0			0
$421$	0.428103	+	0.741496i	0.0208645	+	0.0361383i	0.876269	−	0.481822i	$-0.160025\pi$
$421$	0.428103	+	0.741496i	0.0208645	+	0.0361383i	−0.855405	+	0.517960i	$0.826691\pi$
$422$		0			0
$423$	−14.3606	−	12.5201i	−0.698235	−	0.608748i
$424$		0			0
$425$	12.2850	+	7.09274i	0.595909	+	0.344048i
$426$		0			0
$427$	2.34537	−	24.9778i	0.113501	−	1.20876i
$428$		0			0
$429$	−0.141494	−	0.849323i	−0.00683141	−	0.0410057i
$430$		0			0
$431$	9.19956	+	5.31137i	0.443127	+	0.255840i	0.704923	−	0.709284i	$-0.250981\pi$
$431$	9.19956	+	5.31137i	0.443127	+	0.255840i	−0.261796	+	0.965123i	$0.584315\pi$
$432$		0			0
$433$			27.8825i			1.33995i	0.742384	+	0.669974i	$0.233695\pi$
$433$			27.8825i			1.33995i	−0.742384	+	0.669974i	$0.766305\pi$
$434$		0			0
$435$	5.28603	−	14.1069i	0.253446	−	0.676375i
$436$		0			0
$437$	40.6146	−	23.4489i	1.94286	−	1.12171i
$438$		0			0
$439$	−1.71469	+	2.96993i	−0.0818377	+	0.141747i	−0.904039	−	0.427449i	$-0.859412\pi$
$439$	−1.71469	+	2.96993i	−0.0818377	+	0.141747i	0.822202	+	0.569196i	$0.192746\pi$
$440$		0			0
$441$	12.9832	+	16.5056i	0.618248	+	0.785983i
$442$		0			0
$443$	−35.8001	−	20.6692i	−1.70092	−	0.982025i	−0.944835	−	0.327547i	$-0.893778\pi$
$443$	−35.8001	−	20.6692i	−1.70092	−	0.982025i	−0.756082	−	0.654477i	$-0.772889\pi$
$444$		0			0
$445$	−3.10925	−	5.38538i	−0.147393	−	0.255291i
$446$		0			0
$447$	13.9628	−	11.4931i	0.660419	−	0.543603i
$448$		0			0
$449$	7.99114			0.377125			0.188563	−	0.982061i	$-0.439617\pi$
$449$	7.99114			0.377125			0.188563	+	0.982061i	$0.439617\pi$
$450$		0			0
$451$	−0.227625	+	0.394258i	−0.0107184	+	0.0185649i
$452$		0			0
$453$	9.81229	+	11.9209i	0.461022	+	0.560092i
$454$		0			0
$455$	14.2561	+	1.33862i	0.668335	+	0.0627555i
$456$		0			0
$457$	−9.99811	+	17.3172i	−0.467692	+	0.810066i	−0.999318	−	0.0369130i	$-0.988248\pi$
$457$	−9.99811	+	17.3172i	−0.467692	+	0.810066i	0.531627	+	0.846979i	$0.321581\pi$
$458$		0			0
$459$	0.550595	−	19.4110i	0.0256996	−	0.906030i
$460$		0			0
$461$	21.1665	−	12.2205i	0.985824	−	0.569166i	0.0818005	−	0.996649i	$-0.473933\pi$
$461$	21.1665	−	12.2205i	0.985824	−	0.569166i	0.904023	+	0.427483i	$0.140600\pi$
$462$		0			0
$463$	19.5574	+	11.2915i	0.908909	+	0.524759i	0.880080	−	0.474826i	$-0.157489\pi$
$463$	19.5574	+	11.2915i	0.908909	+	0.524759i	0.0288289	+	0.999584i	$0.490822\pi$
$464$		0			0
$465$	3.22509	−	8.60684i	0.149560	−	0.399133i
$466$		0			0
$467$	19.8560	+	34.3915i	0.918824	+	1.59145i	0.801204	+	0.598391i	$0.204193\pi$
$467$	19.8560	+	34.3915i	0.918824	+	1.59145i	0.117620	+	0.993059i	$0.462474\pi$
$468$		0			0
$469$	−27.1008	−	19.2341i	−1.25140	−	0.888147i
$470$		0			0
$471$	3.89218	−	10.3871i	0.179342	−	0.478614i
$472$		0			0
$473$	−0.101043	−	0.175011i	−0.00464594	−	0.00804700i
$474$		0			0
$475$	9.66672	+	16.7433i	0.443540	+	0.768233i
$476$		0			0
$477$	29.5549	+	25.7671i	1.35323	+	1.17979i
$478$		0			0
$479$	2.44014			0.111493			0.0557465	−	0.998445i	$-0.482246\pi$
$479$	2.44014			0.111493			0.0557465	+	0.998445i	$0.482246\pi$
$480$		0			0
$481$		−	27.3653i		−	1.24775i
$482$		0			0
$483$	−18.4345	+	37.9544i	−0.838797	+	1.72699i
$484$		0			0
$485$	4.10316	+	7.10689i	0.186315	+	0.322707i
$486$		0			0
$487$	19.1445	+	11.0531i	0.867519	+	0.500862i	0.866523	−	0.499137i	$-0.166350\pi$
$487$	19.1445	+	11.0531i	0.867519	+	0.500862i	0.000996023		1.00000i	$0.499683\pi$
$488$		0			0
$489$	−5.04859	+	13.4732i	−0.228305	+	0.609281i
$490$		0			0
$491$	−24.5750	−	14.1884i	−1.10906	−	0.640314i	−0.170472	−	0.985363i	$-0.554529\pi$
$491$	−24.5750	−	14.1884i	−1.10906	−	0.640314i	−0.938585	+	0.345049i	$0.887862\pi$
$492$		0			0
$493$		−	29.6205i		−	1.33404i
$494$		0			0
$495$	0.0637900	−	0.325647i	0.00286715	−	0.0146367i
$496$		0			0
$497$	35.0789	−	16.0868i	1.57350	−	0.721593i
$498$		0			0
$499$			9.08596i			0.406743i	0.979102	+	0.203372i	$0.0651900\pi$
$499$			9.08596i			0.406743i	−0.979102	+	0.203372i	$0.934810\pi$
$500$		0			0
$501$	4.51310	+	27.0900i	0.201631	+	1.21029i
$502$		0			0
$503$	35.9302			1.60205			0.801025	−	0.598631i	$-0.204288\pi$
$503$	35.9302			1.60205			0.801025	+	0.598631i	$0.204288\pi$
$504$		0			0
$505$	−1.85898			−0.0827236
$506$		0			0
$507$	18.3645	+	6.88142i	0.815598	+	0.305615i
$508$		0			0
$509$			15.0086i			0.665243i	0.943060	+	0.332621i	$0.107933\pi$
$509$			15.0086i			0.665243i	−0.943060	+	0.332621i	$0.892067\pi$
$510$		0			0
$511$	1.69113	−	18.0102i	0.0748111	−	0.796724i
$512$		0			0
$513$	13.8776	−	22.5358i	0.612709	−	0.994981i
$514$		0			0
$515$		−	6.50585i		−	0.286682i
$516$		0			0
$517$	−0.554372	−	0.320067i	−0.0243813	−	0.0140765i
$518$		0			0
$519$	−6.31711	+	1.05241i	−0.277291	+	0.0461956i
$520$		0			0
$521$	−9.05431	−	5.22751i	−0.396677	−	0.229021i	0.288372	−	0.957518i	$-0.406886\pi$
$521$	−9.05431	−	5.22751i	−0.396677	−	0.229021i	−0.685049	+	0.728497i	$0.740219\pi$
$522$		0			0
$523$	−13.6688	−	23.6751i	−0.597697	−	1.03524i	−0.993160	−	0.116759i	$-0.962749\pi$
$523$	−13.6688	−	23.6751i	−0.597697	−	1.03524i	0.395463	−	0.918482i	$-0.370584\pi$
$524$		0			0
$525$	−15.6466	−	7.59954i	−0.682873	−	0.331671i
$526$		0			0
$527$		−	18.0719i		−	0.787225i
$528$		0			0
$529$	−61.7794			−2.68606
$530$		0			0
$531$	8.19503	−	2.80847i	0.355634	−	0.121877i
$532$		0			0
$533$	−11.1372	−	19.2901i	−0.482404	−	0.835549i
$534$		0			0
$535$	2.69423	+	4.66654i	0.116482	+	0.201752i
$536$		0			0
$537$	14.2172	−	2.36854i	0.613518	−	0.102210i
$538$		0			0
$539$	0.534699	+	0.460377i	0.0230311	+	0.0198298i
$540$		0			0
$541$	−11.1507	−	19.3135i	−0.479405	−	0.830354i	0.520316	−	0.853974i	$-0.325814\pi$
$541$	−11.1507	−	19.3135i	−0.479405	−	0.830354i	−0.999721	+	0.0236197i	$0.992481\pi$
$542$		0			0
$543$	−27.7875	−	33.7588i	−1.19248	−	1.44873i
$544$		0			0
$545$	−9.93251	−	5.73454i	−0.425462	−	0.245640i
$546$		0			0
$547$	−5.02929	+	2.90366i	−0.215037	+	0.124152i	−0.603650	−	0.797249i	$-0.706288\pi$
$547$	−5.02929	+	2.90366i	−0.215037	+	0.124152i	0.388613	+	0.921401i	$0.372954\pi$
$548$		0			0
$549$	18.6939	−	21.4419i	0.797835	−	0.915118i
$550$		0			0
$551$	20.1849	−	34.9614i	0.859908	−	1.48940i
$552$		0			0
$553$	−0.661272	+	7.04242i	−0.0281201	+	0.299474i
$554$		0			0
$555$	3.70060	−	9.87586i	0.157082	−	0.419207i
$556$		0			0
$557$	−1.23031	+	2.13096i	−0.0521300	+	0.0902919i	−0.890913	−	0.454174i	$-0.849934\pi$
$557$	−1.23031	+	2.13096i	−0.0521300	+	0.0902919i	0.838783	+	0.544466i	$0.183268\pi$
$558$		0			0
$559$	9.88756			0.418199
$560$		0			0
$561$	−0.107220	−	0.643589i	−0.00452682	−	0.0271724i
$562$		0			0
$563$	2.01921	+	3.49737i	0.0850995	+	0.147397i	0.905434	−	0.424488i	$-0.139546\pi$
$563$	2.01921	+	3.49737i	0.0850995	+	0.147397i	−0.820334	+	0.571885i	$0.806213\pi$
$564$		0			0
$565$	−9.80061	−	5.65838i	−0.412315	−	0.238050i
$566$		0			0
$567$	1.02595	+	23.7896i	0.0430858	+	0.999071i
$568$		0			0
$569$	12.6809	−	21.9640i	0.531612	−	0.920780i	−0.467707	−	0.883884i	$-0.654920\pi$
$569$	12.6809	−	21.9640i	0.531612	−	0.920780i	0.999319	−	0.0368960i	$-0.0117470\pi$
$570$		0			0
$571$	26.2507	−	15.1558i	1.09856	−	0.634252i	0.162716	−	0.986673i	$-0.447975\pi$
$571$	26.2507	−	15.1558i	1.09856	−	0.634252i	0.935842	+	0.352421i	$0.114641\pi$
$572$		0			0
$573$	−7.21270	+	1.20161i	−0.301315	+	0.0501980i
$574$		0			0
$575$		−	34.9500i		−	1.45752i
$576$		0			0
$577$	25.7567	+	14.8707i	1.07227	+	0.619073i	0.928800	−	0.370582i	$-0.120842\pi$
$577$	25.7567	+	14.8707i	1.07227	+	0.619073i	0.143467	+	0.989655i	$0.454175\pi$
$578$		0			0
$579$	37.8314	+	14.1759i	1.57222	+	0.589130i
$580$		0			0
$581$	0.344795	−	0.485815i	0.0143045	−	0.0201550i
$582$		0			0
$583$	1.14093	+	0.658716i	0.0472525	+	0.0272812i
$584$		0			0
$585$	12.2380	+	10.6695i	0.505977	+	0.441131i
$586$		0			0
$587$	−18.1453	−	31.4286i	−0.748938	−	1.29720i	−0.948332	−	0.317280i	$-0.897231\pi$
$587$	−18.1453	−	31.4286i	−0.748938	−	1.29720i	0.199394	−	0.979919i	$-0.436103\pi$
$588$		0			0
$589$	12.3151	−	21.3304i	0.507437	−	0.878906i
$590$		0			0
$591$	19.9722	−	16.4395i	0.821546	−	0.676230i
$592$		0			0
$593$	28.4608	−	16.4319i	1.16875	−	0.674776i	0.215362	−	0.976534i	$-0.430907\pi$
$593$	28.4608	−	16.4319i	1.16875	−	0.674776i	0.953384	+	0.301758i	$0.0975735\pi$
$594$		0			0
$595$	10.8028	+	1.01436i	0.442871	+	0.0415848i
$596$		0			0
$597$	3.44721	+	20.6920i	0.141085	+	0.846867i
$598$		0			0
$599$	−29.9350	+	17.2830i	−1.22311	+	0.706164i	−0.965580	−	0.260105i	$-0.916243\pi$
$599$	−29.9350	+	17.2830i	−1.22311	+	0.706164i	−0.257532	+	0.966270i	$0.582909\pi$
$600$		0			0
$601$	−18.6933	+	10.7926i	−0.762514	+	0.440238i	−0.830198	−	0.557469i	$-0.811772\pi$
$601$	−18.6933	+	10.7926i	−0.762514	+	0.440238i	0.0676837	+	0.997707i	$0.478439\pi$
$602$		0			0
$603$	−12.2164	−	35.6470i	−0.497489	−	1.45166i
$604$		0			0
$605$			12.0599i			0.490303i
$606$		0			0
$607$	−26.7002			−1.08373			−0.541864	−	0.840466i	$-0.682281\pi$
$607$	−26.7002			−1.08373			−0.541864	+	0.840466i	$0.682281\pi$
$608$		0			0
$609$	2.59318	+	36.2285i	0.105081	+	1.46805i
$610$		0			0
$611$	27.1242	−	15.6601i	1.09733	−	0.633541i
$612$		0			0
$613$	1.36963	−	2.37228i	0.0553190	−	0.0958153i	−0.837040	−	0.547142i	$-0.815716\pi$
$613$	1.36963	−	2.37228i	0.0553190	−	0.0958153i	0.892359	+	0.451327i	$0.149049\pi$
$614$		0			0
$615$	−1.41069	−	8.46770i	−0.0568845	−	0.341451i
$616$		0			0
$617$	−3.00455	+	5.20403i	−0.120959	+	0.209506i	−0.920146	−	0.391576i	$-0.871930\pi$
$617$	−3.00455	+	5.20403i	−0.120959	+	0.209506i	0.799187	+	0.601082i	$0.205263\pi$
$618$		0			0
$619$	−45.7252			−1.83785			−0.918925	−	0.394432i	$-0.870941\pi$
$619$	−45.7252			−1.83785			−0.918925	+	0.394432i	$0.870941\pi$
$620$		0			0
$621$	−42.0957	+	22.7376i	−1.68924	+	0.912427i
$622$		0			0
$623$	12.2265	+	8.67744i	0.489844	+	0.347654i
$624$		0			0
$625$	8.38699			0.335479
$626$		0			0
$627$	0.312023	−	0.832699i	0.0124610	−	0.0332548i
$628$		0			0
$629$		−	20.7365i		−	0.826818i
$630$		0			0
$631$			16.5841i			0.660204i	0.943945	+	0.330102i	$0.107083\pi$
$631$			16.5841i			0.660204i	−0.943945	+	0.330102i	$0.892917\pi$
$632$		0			0
$633$	−1.79991	+	0.299859i	−0.0715401	+	0.0119183i
$634$		0			0
$635$	−9.73476			−0.386312
$636$		0			0
$637$	−32.5882	+	11.3940i	−1.29119	+	0.451447i
$638$		0			0
$639$	42.9426	+	8.41192i	1.69878	+	0.332770i
$640$		0			0
$641$	33.5325			1.32446			0.662228	−	0.749303i	$-0.269611\pi$
$641$	33.5325			1.32446			0.662228	+	0.749303i	$0.269611\pi$
$642$		0			0
$643$	15.7710	−	27.3162i	0.621949	−	1.07725i	−0.367174	−	0.930152i	$-0.619675\pi$
$643$	15.7710	−	27.3162i	0.621949	−	1.07725i	0.989122	−	0.147094i	$-0.0469921\pi$
$644$		0			0
$645$	3.56832	+	1.33709i	0.140503	+	0.0526481i
$646$		0			0
$647$	−19.1055	+	33.0917i	−0.751114	+	1.30097i	0.196169	+	0.980570i	$0.437150\pi$
$647$	−19.1055	+	33.0917i	−0.751114	+	1.30097i	−0.947283	+	0.320398i	$0.896183\pi$
$648$		0			0
$649$	0.252072	−	0.145534i	0.00989468	−	0.00571270i
$650$		0			0
$651$	1.58214	+	22.1036i	0.0620089	+	0.866307i
$652$		0			0
$653$	−23.6928			−0.927171			−0.463586	−	0.886052i	$-0.653437\pi$
$653$	−23.6928			−0.927171			−0.463586	+	0.886052i	$0.653437\pi$
$654$		0			0
$655$		−	6.47320i		−	0.252929i
$656$		0			0
$657$	13.4792	−	15.4606i	0.525873	−	0.603177i
$658$		0			0
$659$	−17.6819	+	10.2086i	−0.688788	+	0.397672i	−0.803158	−	0.595766i	$-0.796849\pi$
$659$	−17.6819	+	10.2086i	−0.688788	+	0.397672i	0.114370	+	0.993438i	$0.463515\pi$
$660$		0			0
$661$	−17.3778	+	10.0331i	−0.675919	+	0.390242i	−0.798315	−	0.602239i	$-0.794275\pi$
$661$	−17.3778	+	10.0331i	−0.675919	+	0.390242i	0.122397	+	0.992481i	$0.460942\pi$
$662$		0			0
$663$	29.8936	+	11.2015i	1.16097	+	0.435030i
$664$		0			0
$665$	12.0594	+	8.55883i	0.467643	+	0.331897i
$666$		0			0
$667$	−63.2014	+	36.4893i	−2.44717	+	1.41287i
$668$		0			0
$669$	−17.4137	−	6.52513i	−0.673252	−	0.252276i
$670$		0			0
$671$	0.477895	−	0.827738i	0.0184489	−	0.0319545i
$672$		0			0
$673$	−0.955003	−	1.65411i	−0.0368127	−	0.0637614i	0.847032	−	0.531542i	$-0.178387\pi$
$673$	−0.955003	−	1.65411i	−0.0368127	−	0.0637614i	−0.883845	+	0.467780i	$0.845054\pi$
$674$		0			0
$675$	−9.37348	−	17.3538i	−0.360785	−	0.667948i
$676$		0			0
$677$	37.3961	+	21.5907i	1.43725	+	0.829796i	0.997658	−	0.0684014i	$-0.0217898\pi$
$677$	37.3961	+	21.5907i	1.43725	+	0.829796i	0.439592	+	0.898198i	$0.355123\pi$
$678$		0			0
$679$	−16.1349	−	11.4513i	−0.619199	−	0.439460i
$680$		0			0
$681$	2.02424	−	1.66619i	0.0775690	−	0.0638485i
$682$		0			0
$683$	21.2100	+	12.2456i	0.811579	+	0.468565i	0.847504	−	0.530789i	$-0.178104\pi$
$683$	21.2100	+	12.2456i	0.811579	+	0.468565i	−0.0359249	+	0.999354i	$0.511438\pi$
$684$		0			0
$685$		−	19.1299i		−	0.730916i
$686$		0			0
$687$	15.9060	+	19.3241i	0.606851	+	0.737259i
$688$		0			0
$689$	−55.8231	+	32.2295i	−2.12669	+	1.22784i
$690$		0			0
$691$	−5.83616	+	10.1085i	−0.222018	+	0.384547i	−0.955421	−	0.295248i	$-0.904598\pi$
$691$	−5.83616	+	10.1085i	−0.222018	+	0.384547i	0.733403	+	0.679795i	$0.237931\pi$
$692$		0			0
$693$	0.187484	+	0.777780i	0.00712191	+	0.0295454i
$694$		0			0
$695$	−15.3913	−	8.88616i	−0.583824	−	0.337071i
$696$		0			0
$697$	−8.43938	−	14.6174i	−0.319664	−	0.553675i
$698$		0			0
$699$	−30.4089	−	11.3946i	−1.15017	−	0.430983i
$700$		0			0
$701$	32.0967			1.21227			0.606137	−	0.795360i	$-0.292718\pi$
$701$	32.0967			1.21227			0.606137	+	0.795360i	$0.292718\pi$
$702$		0			0
$703$	14.1309	−	24.4755i	0.532958	−	0.923110i
$704$		0			0
$705$	11.9066	−	1.98359i	0.448427	−	0.0747064i
$706$		0			0
$707$	4.07405	−	1.86832i	0.153220	−	0.0702654i
$708$		0			0
$709$	6.81367	−	11.8016i	0.255893	−	0.443220i	−0.709245	−	0.704962i	$-0.750964\pi$
$709$	6.81367	−	11.8016i	0.255893	−	0.443220i	0.965138	+	0.261743i	$0.0842972\pi$
$710$		0			0
$711$	−5.27069	+	6.04549i	−0.197666	+	0.226723i
$712$		0			0
$713$	−38.5601	+	22.2627i	−1.44409	+	0.833744i
$714$		0			0
$715$	0.472431	+	0.272758i	0.0176679	+	0.0102006i
$716$		0			0
$717$	−40.2661	+	6.70819i	−1.50376	+	0.250522i
$718$		0			0
$719$	−17.9410	−	31.0748i	−0.669088	−	1.15889i	−0.978160	−	0.207855i	$-0.933352\pi$
$719$	−17.9410	−	31.0748i	−0.669088	−	1.15889i	0.309072	−	0.951039i	$-0.399982\pi$
$720$		0			0
$721$	6.53853	+	14.2579i	0.243507	+	0.530991i
$722$		0			0
$723$	16.3844	+	19.9053i	0.609344	+	0.740288i
$724$		0			0
$725$	−15.0426	−	26.0546i	−0.558668	−	0.967642i
$726$		0			0
$727$	1.54920	+	2.68329i	0.0574565	+	0.0995176i	0.893323	−	0.449415i	$-0.148368\pi$
$727$	1.54920	+	2.68329i	0.0574565	+	0.0995176i	−0.835866	+	0.548933i	$0.815034\pi$
$728$		0			0
$729$	−14.8037	+	22.5798i	−0.548286	+	0.836291i
$730$		0			0
$731$	7.49247			0.277119
$732$		0			0
$733$		−	38.4588i		−	1.42051i	−0.703946	−	0.710254i	$-0.748580\pi$
$733$		−	38.4588i		−	1.42051i	0.703946	−	0.710254i	$-0.251420\pi$
$734$		0			0
$735$	−13.3016	−	0.294908i	−0.490636	−	0.0108778i
$736$		0			0
$737$	−0.633046	−	1.09647i	−0.0233186	−	0.0403889i
$738$		0			0
$739$	28.0000	+	16.1658i	1.03000	+	0.594668i	0.916983	−	0.398926i	$-0.130617\pi$
$739$	28.0000	+	16.1658i	1.03000	+	0.594668i	0.113012	+	0.993594i	$0.463950\pi$
$740$		0			0
$741$	27.6504	+	33.5922i	1.01576	+	1.23404i
$742$		0			0
$743$	14.1763	+	8.18468i	0.520077	+	0.300267i	0.736966	−	0.675930i	$-0.236258\pi$
$743$	14.1763	+	8.18468i	0.520077	+	0.300267i	−0.216889	+	0.976196i	$0.569591\pi$
$744$		0			0
$745$			11.4577i			0.419778i
$746$		0			0
$747$	0.639016	−	0.218994i	0.0233804	−	0.00801257i
$748$		0			0
$749$	−10.5945	−	7.51917i	−0.387115	−	0.274745i
$750$		0			0
$751$			47.7607i			1.74281i	0.490562	+	0.871406i	$0.336791\pi$
$751$			47.7607i			1.74281i	−0.490562	+	0.871406i	$0.663209\pi$
$752$		0			0
$753$	9.19973	−	7.57247i	0.335257	−	0.275956i
$754$		0			0
$755$	−9.78212			−0.356008
$756$		0			0
$757$	−32.5248			−1.18213			−0.591066	−	0.806623i	$-0.701293\pi$
$757$	−32.5248			−1.18213			−0.591066	+	0.806623i	$0.701293\pi$
$758$		0			0
$759$	−1.24115	+	1.02161i	−0.0450507	+	0.0370821i
$760$		0			0
$761$		−	31.1794i		−	1.13025i	−0.825004	−	0.565127i	$-0.808827\pi$
$761$		−	31.1794i		−	1.13025i	0.825004	−	0.565127i	$-0.191173\pi$
$762$		0			0
$763$	27.5309	+	2.58511i	0.996685	+	0.0935871i
$764$		0			0
$765$	9.27353	+	8.08502i	0.335285	+	0.292314i
$766$		0			0
$767$			14.2413i			0.514222i
$768$		0			0
$769$	−24.4724	−	14.1292i	−0.882498	−	0.509510i	−0.0110165	−	0.999939i	$-0.503507\pi$
$769$	−24.4724	−	14.1292i	−0.882498	−	0.509510i	−0.871481	+	0.490429i	$0.836840\pi$
$770$		0			0
$771$	−19.8094	−	24.0664i	−0.713420	−	0.866728i
$772$		0			0
$773$	11.2626	+	6.50244i	0.405086	+	0.233876i	0.688676	−	0.725069i	$-0.258192\pi$
$773$	11.2626	+	6.50244i	0.405086	+	0.233876i	−0.283590	+	0.958946i	$0.591526\pi$
$774$		0			0
$775$	−9.17772	−	15.8963i	−0.329673	−	0.571011i
$776$		0			0
$777$	1.81541	+	25.3626i	0.0651276	+	0.909878i
$778$		0			0
$779$		−	23.0041i		−	0.824208i
$780$		0			0
$781$	1.47026			0.0526101
$782$		0			0
$783$	−21.5952	+	35.0685i	−0.771749	+	1.25325i
$784$		0			0
$785$	3.51387	+	6.08621i	0.125416	+	0.217226i
$786$		0			0
$787$	12.1694	+	21.0780i	0.433791	+	0.751348i	0.997196	−	0.0748328i	$-0.0238423\pi$
$787$	12.1694	+	21.0780i	0.433791	+	0.751348i	−0.563405	+	0.826181i	$0.690509\pi$
$788$		0			0
$789$	9.77154	+	11.8714i	0.347876	+	0.422632i
$790$		0			0
$791$	27.1653	+	2.55078i	0.965886	+	0.0906952i
$792$		0			0
$793$	23.3823	+	40.4993i	0.830329	+	1.43817i
$794$		0			0
$795$	−24.5044	+	4.08235i	−0.869081	+	0.144786i
$796$		0			0
$797$	38.8453	+	22.4273i	1.37597	+	0.794416i	0.991672	−	0.128793i	$-0.0411102\pi$
$797$	38.8453	+	22.4273i	1.37597	+	0.794416i	0.384298	+	0.923209i	$0.374444\pi$
$798$		0			0
$799$	20.5538	−	11.8667i	0.727141	−	0.419815i
$800$		0			0
$801$	5.51141	+	16.0821i	0.194736	+	0.568233i
$802$		0			0
$803$	0.344585	−	0.596839i	0.0121601	−	0.0210620i
$804$		0			0
$805$	−11.1435	−	24.2995i	−0.392758	−	0.856445i
$806$		0			0
$807$	19.6422	−	3.27232i	0.691438	−	0.115191i
$808$		0			0
$809$	16.1308	−	27.9394i	0.567130	−	0.982297i	−0.429719	−	0.902963i	$-0.641387\pi$
$809$	16.1308	−	27.9394i	0.567130	−	0.982297i	0.996848	−	0.0793342i	$-0.0252794\pi$
$810$		0			0
$811$	34.7632			1.22070			0.610350	−	0.792132i	$-0.291029\pi$
$811$	34.7632			1.22070			0.610350	+	0.792132i	$0.291029\pi$
$812$		0			0
$813$	−40.0884	−	15.0216i	−1.40596	−	0.526831i
$814$		0			0
$815$	−4.55788	−	7.89448i	−0.159656	−	0.276532i
$816$		0			0
$817$	8.84343	+	5.10576i	0.309392	+	0.178628i
$818$		0			0
$819$	−37.5432	−	11.0833i	−1.31186	−	0.387283i
$820$		0			0
$821$	20.0987	−	34.8119i	0.701448	−	1.21494i	−0.266510	−	0.963832i	$-0.585870\pi$
$821$	20.0987	−	34.8119i	0.701448	−	1.21494i	0.967958	−	0.251112i	$-0.0807963\pi$
$822$		0			0
$823$	2.85246	−	1.64687i	0.0994305	−	0.0574062i	−0.449460	−	0.893300i	$-0.648384\pi$
$823$	2.85246	−	1.64687i	0.0994305	−	0.0574062i	0.548891	+	0.835894i	$0.315050\pi$
$824$		0			0
$825$	−0.421155	−	0.511658i	−0.0146627	−	0.0178136i
$826$		0			0
$827$			21.5704i			0.750075i	0.927010	+	0.375038i	$0.122370\pi$
$827$			21.5704i			0.750075i	−0.927010	+	0.375038i	$0.877630\pi$
$828$		0			0
$829$	−6.97609	−	4.02765i	−0.242290	−	0.139886i	0.373939	−	0.927453i	$-0.378007\pi$
$829$	−6.97609	−	4.02765i	−0.242290	−	0.139886i	−0.616229	+	0.787567i	$0.711340\pi$
$830$		0			0
$831$	1.38320	−	1.13853i	0.0479826	−	0.0394953i
$832$		0			0
$833$	−24.6942	+	8.63401i	−0.855605	+	0.299151i
$834$		0			0
$835$	−15.0687	−	8.69990i	−0.521473	−	0.301072i
$836$		0			0
$837$	−13.1756	+	21.3958i	−0.455414	+	0.739548i
$838$		0			0
$839$	23.8904	+	41.3793i	0.824787	+	1.42857i	0.902082	+	0.431564i	$0.142038\pi$
$839$	23.8904	+	41.3793i	0.824787	+	1.42857i	−0.0772954	+	0.997008i	$0.524628\pi$
$840$		0			0
$841$	−16.9103	+	29.2894i	−0.583113	+	1.00998i
$842$		0			0
$843$	−4.92796	−	1.84657i	−0.169728	−	0.0635991i
$844$		0			0
$845$	−10.7605	+	6.21256i	−0.370172	+	0.213719i
$846$		0			0
$847$	−12.1204	−	26.4297i	−0.416463	−	0.908137i
$848$		0			0
$849$	22.7844	+	8.53760i	0.781959	+	0.293010i
$850$		0			0
$851$	−44.2455	+	25.5452i	−1.51672	+	0.875677i
$852$		0			0
$853$	−23.5845	+	13.6165i	−0.807518	+	0.466221i	−0.846093	−	0.533035i	$-0.821051\pi$
$853$	−23.5845	+	13.6165i	−0.807518	+	0.466221i	0.0385754	+	0.999256i	$0.487718\pi$
$854$		0			0
$855$	5.43608	+	15.8623i	0.185910	+	0.542479i
$856$		0			0
$857$		−	40.4731i		−	1.38253i	−0.722599	−	0.691267i	$-0.757053\pi$
$857$		−	40.4731i		−	1.38253i	0.722599	−	0.691267i	$-0.242947\pi$
$858$		0			0
$859$	−53.7041			−1.83236			−0.916180	−	0.400766i	$-0.868744\pi$
$859$	−53.7041			−1.83236			−0.916180	+	0.400766i	$0.868744\pi$
$860$		0			0
$861$	11.6018	+	17.1396i	0.395389	+	0.584116i
$862$		0			0
$863$	−16.5769	+	9.57068i	−0.564285	+	0.325790i	−0.754863	−	0.655882i	$-0.772297\pi$
$863$	−16.5769	+	9.57068i	−0.564285	+	0.325790i	0.190579	+	0.981672i	$0.438964\pi$
$864$		0			0
$865$	2.02873	−	3.51386i	0.0689788	−	0.119475i
$866$		0			0
$867$	−4.92031	−	1.84370i	−0.167103	−	0.0626154i
$868$		0			0
$869$	−0.134741	+	0.233378i	−0.00457078	+	0.00791682i
$870$		0			0
$871$	61.9470			2.09899
$872$		0			0
$873$	−7.27320	−	21.2229i	−0.246161	−	0.718288i
$874$		0			0
$875$	23.2128	−	10.6452i	0.784736	−	0.359872i
$876$		0			0
$877$	−12.0902			−0.408258			−0.204129	−	0.978944i	$-0.565436\pi$
$877$	−12.0902			−0.408258			−0.204129	+	0.978944i	$0.565436\pi$
$878$		0			0
$879$	−1.47401	+	0.245564i	−0.0497170	+	0.00828268i
$880$		0			0
$881$		−	41.0338i		−	1.38246i	−0.722633	−	0.691232i	$-0.757068\pi$
$881$		−	41.0338i		−	1.38246i	0.722633	−	0.691232i	$-0.242932\pi$
$882$		0			0
$883$			39.1631i			1.31794i	0.752168	+	0.658971i	$0.229008\pi$
$883$			39.1631i			1.31794i	−0.752168	+	0.658971i	$0.770992\pi$
$884$		0			0
$885$	−1.92585	+	5.13953i	−0.0647366	+	0.172764i
$886$		0			0
$887$	33.1869			1.11431			0.557154	−	0.830409i	$-0.311893\pi$
$887$	33.1869			1.11431			0.557154	+	0.830409i	$0.311893\pi$
$888$		0			0
$889$	21.3342	−	9.78366i	0.715525	−	0.328133i
$890$		0			0
$891$	−0.342276	+	0.840133i	−0.0114667	+	0.0281455i
$892$		0			0
$893$	32.3464			1.08243
$894$		0			0
$895$	−4.56582	+	7.90824i	−0.152619	+	0.264343i
$896$		0			0
$897$	−12.9251	−	77.5831i	−0.431556	−	2.59042i
$898$		0			0
$899$	−19.1639	+	33.1928i	−0.639151	+	1.10704i
$900$		0			0
$901$	−42.3009	+	24.4224i	−1.40925	+	0.813629i
$902$		0			0
$903$	−9.16396	+	0.655942i	−0.304957	+	0.0218284i
$904$		0			0
$905$	27.7020			0.920847
$906$		0			0
$907$		−	17.5768i		−	0.583628i	−0.956475	−	0.291814i	$-0.905741\pi$
$907$		−	17.5768i		−	0.583628i	0.956475	−	0.291814i	$-0.0942589\pi$
$908$		0			0
$909$	4.98734	+	0.976957i	0.165420	+	0.0324036i
$910$		0			0
$911$	28.9644	−	16.7226i	0.959635	−	0.554045i	0.0635741	−	0.997977i	$-0.479750\pi$
$911$	28.9644	−	16.7226i	0.959635	−	0.554045i	0.896061	+	0.443932i	$0.146417\pi$
$912$		0			0
$913$	0.0196556	−	0.0113482i	0.000650505	−	0.000375569i
$914$		0			0
$915$	2.96172	+	17.7778i	0.0979114	+	0.587716i
$916$		0			0
$917$	6.50571	+	14.1863i	0.214838	+	0.468473i
$918$		0			0
$919$	−17.9607	+	10.3696i	−0.592470	+	0.342062i	−0.766073	−	0.642753i	$-0.777792\pi$
$919$	−17.9607	+	10.3696i	−0.592470	+	0.342062i	0.173604	+	0.984816i	$0.444459\pi$
$920$		0			0
$921$	−1.06957	+	0.880381i	−0.0352435	+	0.0290095i
$922$		0			0
$923$	−35.9683	+	62.2989i	−1.18391	+	2.05059i
$924$		0			0
$925$	−10.5309	−	18.2401i	−0.346254	−	0.599730i
$926$		0			0
$927$	−3.41904	+	17.4541i	−0.112296	+	0.573268i
$928$		0			0
$929$	−2.35262	−	1.35829i	−0.0771870	−	0.0445639i	0.460910	−	0.887447i	$-0.347523\pi$
$929$	−2.35262	−	1.35829i	−0.0771870	−	0.0445639i	−0.538097	+	0.842883i	$0.680857\pi$
$930$		0			0
$931$	−35.0305	−	6.63713i	−1.14808	−	0.217523i
$932$		0			0
$933$	−42.6569	−	15.9841i	−1.39653	−	0.523295i
$934$		0			0
$935$	0.357993	+	0.206687i	0.0117076	+	0.00675940i
$936$		0			0
$937$		−	20.7924i		−	0.679258i	−0.940559	−	0.339629i	$-0.889698\pi$
$937$		−	20.7924i		−	0.679258i	0.940559	−	0.339629i	$-0.110302\pi$
$938$		0			0
$939$	−13.3434	+	2.22297i	−0.435446	+	0.0725438i
$940$		0			0
$941$	44.3702	−	25.6172i	1.44643	−	0.835096i	0.448162	−	0.893953i	$-0.352079\pi$
$941$	44.3702	−	25.6172i	1.44643	−	0.835096i	0.998266	+	0.0588569i	$0.0187456\pi$
$942$		0			0
$943$	−20.7929	+	36.0143i	−0.677108	+	1.17279i
$944$		0			0
$945$	−12.0502	−	9.07683i	−0.391992	−	0.295269i
$946$		0			0
$947$	−37.0086	−	21.3669i	−1.20262	−	0.694332i	−0.241481	−	0.970406i	$-0.577633\pi$
$947$	−37.0086	−	21.3669i	−1.20262	−	0.694332i	−0.961136	+	0.276074i	$0.910967\pi$
$948$		0			0
$949$	16.8598	+	29.2020i	0.547291	+	0.947936i
$950$		0			0
$951$	3.79604	+	22.7858i	0.123095	+	0.738880i
$952$		0			0
$953$	5.14510			0.166666			0.0833331	−	0.996522i	$-0.473443\pi$
$953$	5.14510			0.166666			0.0833331	+	0.996522i	$0.473443\pi$
$954$		0			0
$955$	2.31634	−	4.01203i	0.0749551	−	0.129826i
$956$		0			0
$957$	−0.485545	+	1.29578i	−0.0156955	+	0.0418867i
$958$		0			0
$959$	19.2260	+	41.9241i	0.620840	+	1.35380i
$960$		0			0
$961$	3.80783	−	6.59536i	0.122833	−	0.212753i
$962$		0			0
$963$	−4.77575	−	13.9355i	−0.153896	−	0.449064i
$964$		0			0
$965$	−22.1669	+	12.7980i	−0.713576	+	0.411983i
$966$		0			0
$967$	−8.18515	−	4.72570i	−0.263217	−	0.151968i	0.362584	−	0.931951i	$-0.381894\pi$
$967$	−8.18515	−	4.72570i	−0.263217	−	0.151968i	−0.625801	+	0.779983i	$0.715228\pi$
$968$		0			0
$969$	20.9526	+	25.4551i	0.673093	+	0.817736i
$970$		0			0
$971$	−7.24445	−	12.5478i	−0.232485	−	0.402677i	0.726053	−	0.687638i	$-0.241352\pi$
$971$	−7.24445	−	12.5478i	−0.232485	−	0.402677i	−0.958539	+	0.284962i	$0.908019\pi$
$972$		0			0
$973$	42.6615	+	4.00584i	1.36766	+	0.128421i
$974$		0			0
$975$	31.9834	−	5.32832i	1.02429	−	0.170643i
$976$		0			0
$977$	−9.99130	−	17.3054i	−0.319650	−	0.553650i	0.660765	−	0.750593i	$-0.270232\pi$
$977$	−9.99130	−	17.3054i	−0.319650	−	0.553650i	−0.980415	+	0.196943i	$0.936899\pi$
$978$		0			0
$979$	0.285598	+	0.494671i	0.00912776	+	0.0158097i
$980$		0			0
$981$	23.6336	+	20.6047i	0.754562	+	0.657857i
$982$		0			0
$983$	6.64389			0.211907			0.105954	−	0.994371i	$-0.466211\pi$
$983$	6.64389			0.211907			0.105954	+	0.994371i	$0.466211\pi$
$984$		0			0
$985$			16.3889i			0.522194i
$986$		0			0
$987$	−24.1002	+	16.3135i	−0.767119	+	0.519264i
$988$		0			0
$989$	−9.22993	−	15.9867i	−0.293495	−	0.508348i
$990$		0			0
$991$	−0.701316	−	0.404905i	−0.0222780	−	0.0128622i	0.488820	−	0.872385i	$-0.337428\pi$
$991$	−0.701316	−	0.404905i	−0.0222780	−	0.0128622i	−0.511098	+	0.859523i	$0.670761\pi$
$992$		0			0
$993$	24.8686	−	4.14302i	0.789181	−	0.131475i
$994$		0			0
$995$	−11.5098	−	6.64519i	−0.364885	−	0.210667i
$996$		0			0
$997$		−	15.2446i		−	0.482802i	−0.970425	−	0.241401i	$-0.922393\pi$
$997$		−	15.2446i		−	0.482802i	0.970425	−	0.241401i	$-0.0776069\pi$
$998$		0			0
$999$	−15.1182	+	24.5505i	−0.478319	+	0.776743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.i.31.14	yes	32
3.2	odd	2		3024.2.bf.i.1711.6		32
4.3	odd	2	inner	1008.2.bf.i.31.3	✓	32
7.5	odd	6		1008.2.cz.i.607.8	yes	32
9.2	odd	6		3024.2.cz.i.2719.12		32
9.7	even	3		1008.2.cz.i.367.9	yes	32
12.11	even	2		3024.2.bf.i.1711.5		32
21.5	even	6		3024.2.cz.i.1279.11		32
28.19	even	6		1008.2.cz.i.607.9	yes	32
36.7	odd	6		1008.2.cz.i.367.8	yes	32
36.11	even	6		3024.2.cz.i.2719.11		32
63.47	even	6		3024.2.bf.i.2287.12		32
63.61	odd	6	inner	1008.2.bf.i.943.3	yes	32
84.47	odd	6		3024.2.cz.i.1279.12		32
252.47	odd	6		3024.2.bf.i.2287.11		32
252.187	even	6	inner	1008.2.bf.i.943.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.3	✓	32	4.3	odd	2	inner
1008.2.bf.i.31.14	yes	32	1.1	even	1	trivial
1008.2.bf.i.943.3	yes	32	63.61	odd	6	inner
1008.2.bf.i.943.14	yes	32	252.187	even	6	inner
1008.2.cz.i.367.8	yes	32	36.7	odd	6
1008.2.cz.i.367.9	yes	32	9.7	even	3
1008.2.cz.i.607.8	yes	32	7.5	odd	6
1008.2.cz.i.607.9	yes	32	28.19	even	6
3024.2.bf.i.1711.5		32	12.11	even	2
3024.2.bf.i.1711.6		32	3.2	odd	2
3024.2.bf.i.2287.11		32	252.47	odd	6
3024.2.bf.i.2287.12		32	63.47	even	6
3024.2.cz.i.1279.11		32	21.5	even	6
3024.2.cz.i.1279.12		32	84.47	odd	6
3024.2.cz.i.2719.11		32	36.11	even	6
3024.2.cz.i.2719.12		32	9.2	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33729 - 1.10075i) q^{3} +1.09736i q^{5} +(-1.10288 - 2.40492i) q^{7} +(0.576701 - 2.94405i) q^{9} -0.100798i q^{11} +(4.27107 + 2.46590i) q^{13} +(1.20792 + 1.46750i) q^{15} +(3.23648 + 1.86858i) q^{17} +(2.54669 + 4.41100i) q^{19} +(-4.12209 - 2.00210i) q^{21} -9.20757i q^{23} +3.79579 q^{25} +(-2.46944 - 4.57186i) q^{27} +(-3.96297 - 6.86407i) q^{29} +(-2.41787 - 4.18787i) q^{31} +(-0.110953 - 0.134796i) q^{33} +(2.63908 - 1.21026i) q^{35} +(-2.77437 - 4.80534i) q^{37} +(8.42601 - 1.40374i) q^{39} +(-3.91138 - 2.25823i) q^{41} +(1.73626 - 1.00243i) q^{43} +(3.23069 + 0.632852i) q^{45} +(3.17534 - 5.49984i) q^{47} +(-4.56733 + 5.30467i) q^{49} +(6.38495 - 1.06371i) q^{51} +(-6.53502 + 11.3190i) q^{53} +0.110612 q^{55} +(8.26109 + 3.09553i) q^{57} +(1.44382 + 2.50077i) q^{59} +(8.21186 + 4.74112i) q^{61} +(-7.71624 + 1.86000i) q^{63} +(-2.70599 + 4.68692i) q^{65} +(10.8779 - 6.28036i) q^{67} +(-10.1352 - 12.3132i) q^{69} +14.5863i q^{71} +(5.92115 + 3.41858i) q^{73} +(5.07608 - 4.17822i) q^{75} +(-0.242411 + 0.111167i) q^{77} +(-2.31531 - 1.33675i) q^{79} +(-8.33483 - 3.39567i) q^{81} +(0.112583 + 0.195000i) q^{83} +(-2.05051 + 3.55159i) q^{85} +(-12.8553 - 4.81703i) q^{87} +(-4.90756 + 2.83338i) q^{89} +(1.21985 - 12.9912i) q^{91} +(-7.84319 - 2.93894i) q^{93} +(-4.84048 + 2.79465i) q^{95} +(6.47632 - 3.73911i) q^{97} +(-0.296753 - 0.0581302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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