LMFDB - Embedded newform 936.2.s.f.529.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.529"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.12
Character	$\chi$	$=$	936.529
Dual form			936.2.s.f.913.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.348515 - 1.69663i) q^{3} +(1.65071 + 2.85912i) q^{5} +1.86626 q^{7} +(-2.75708 - 1.18260i) q^{9} +(0.938166 + 1.62495i) q^{11} +(0.230589 + 3.59817i) q^{13} +(5.42615 - 1.80420i) q^{15} +(-2.21681 - 3.83963i) q^{17} +(3.24988 + 5.62896i) q^{19} +(0.650419 - 3.16634i) q^{21} +3.76346 q^{23} +(-2.94970 + 5.10903i) q^{25} +(-2.96731 + 4.26557i) q^{27} +(-0.668020 - 1.15705i) q^{29} +(1.73294 + 3.00154i) q^{31} +(3.08390 - 1.02540i) q^{33} +(3.08066 + 5.33585i) q^{35} +(-0.457982 + 0.793248i) q^{37} +(6.18511 + 0.862792i) q^{39} +2.32732 q^{41} -3.74484 q^{43} +(-1.16995 - 9.83493i) q^{45} +(5.05850 - 8.76158i) q^{47} -3.51708 q^{49} +(-7.28700 + 2.42293i) q^{51} -9.98182 q^{53} +(-3.09728 + 5.36465i) q^{55} +(10.6829 - 3.55206i) q^{57} +(-1.46596 + 2.53912i) q^{59} +14.3492 q^{61} +(-5.14542 - 2.20703i) q^{63} +(-9.90695 + 6.59882i) q^{65} +8.96043 q^{67} +(1.31162 - 6.38518i) q^{69} +(-1.03307 - 1.78932i) q^{71} +2.56896 q^{73} +(7.64009 + 6.78510i) q^{75} +(1.75086 + 3.03258i) q^{77} +(7.05149 - 12.2135i) q^{79} +(6.20293 + 6.52102i) q^{81} +(1.35281 - 2.34313i) q^{83} +(7.31863 - 12.6762i) q^{85} +(-2.19589 + 0.730133i) q^{87} +(4.60157 - 7.97016i) q^{89} +(0.430338 + 6.71512i) q^{91} +(5.69645 - 1.89407i) q^{93} +(-10.7292 + 18.5836i) q^{95} -10.3552 q^{97} +(-0.664931 - 5.58959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.348515	−	1.69663i	0.201215	−	0.979547i
$3$	0.348515	−	1.69663i	0.201215	−	0.979547i
$4$		0			0
$5$	1.65071	+	2.85912i	0.738221	+	1.27864i	0.953296	+	0.302038i	$0.0976670\pi$
$5$	1.65071	+	2.85912i	0.738221	+	1.27864i	−0.215075	+	0.976597i	$0.569000\pi$
$6$		0			0
$7$	1.86626			0.705380			0.352690	−	0.935740i	$-0.385267\pi$
$7$	1.86626			0.705380			0.352690	+	0.935740i	$0.385267\pi$
$8$		0			0
$9$	−2.75708	−	1.18260i	−0.919025	−	0.394199i
$10$		0			0
$11$	0.938166	+	1.62495i	0.282868	+	0.489941i	0.972090	−	0.234609i	$-0.0753809\pi$
$11$	0.938166	+	1.62495i	0.282868	+	0.489941i	−0.689222	+	0.724550i	$0.742048\pi$
$12$		0			0
$13$	0.230589	+	3.59817i	0.0639538	+	0.997953i
$13$	0.230589	+	3.59817i	0.0639538	+	0.997953i
$14$		0			0
$15$	5.42615	−	1.80420i	1.40102	−	0.465841i
$16$		0			0
$17$	−2.21681	−	3.83963i	−0.537655	−	0.931246i	−0.999030	−	0.0440408i	$-0.985977\pi$
$17$	−2.21681	−	3.83963i	−0.537655	−	0.931246i	0.461374	−	0.887206i	$-0.347357\pi$
$18$		0			0
$19$	3.24988	+	5.62896i	0.745574	+	1.29137i	0.949926	+	0.312475i	$0.101158\pi$
$19$	3.24988	+	5.62896i	0.745574	+	1.29137i	−0.204352	+	0.978898i	$0.565509\pi$
$20$		0			0
$21$	0.650419	−	3.16634i	0.141933	−	0.690953i
$22$		0			0
$23$	3.76346			0.784735			0.392367	−	0.919809i	$-0.371656\pi$
$23$	3.76346			0.784735			0.392367	+	0.919809i	$0.371656\pi$
$24$		0			0
$25$	−2.94970	+	5.10903i	−0.589939	+	1.02181i
$26$		0			0
$27$	−2.96731	+	4.26557i	−0.571058	+	0.820909i
$28$		0			0
$29$	−0.668020	−	1.15705i	−0.124048	−	0.214858i	0.797312	−	0.603567i	$-0.206254\pi$
$29$	−0.668020	−	1.15705i	−0.124048	−	0.214858i	−0.921361	+	0.388709i	$0.872921\pi$
$30$		0			0
$31$	1.73294	+	3.00154i	0.311245	+	0.539093i	0.978632	−	0.205618i	$-0.0659206\pi$
$31$	1.73294	+	3.00154i	0.311245	+	0.539093i	−0.667387	+	0.744711i	$0.732587\pi$
$32$		0			0
$33$	3.08390	−	1.02540i	0.536838	−	0.178499i
$34$		0			0
$35$	3.08066	+	5.33585i	0.520726	+	0.901924i
$36$		0			0
$37$	−0.457982	+	0.793248i	−0.0752917	+	0.130409i	−0.901213	−	0.433376i	$-0.857322\pi$
$37$	−0.457982	+	0.793248i	−0.0752917	+	0.130409i	0.825921	+	0.563785i	$0.190655\pi$
$38$		0			0
$39$	6.18511	+	0.862792i	0.990410	+	0.138157i
$40$		0			0
$41$	2.32732			0.363466			0.181733	−	0.983348i	$-0.441829\pi$
$41$	2.32732			0.363466			0.181733	+	0.983348i	$0.441829\pi$
$42$		0			0
$43$	−3.74484			−0.571082			−0.285541	−	0.958366i	$-0.592173\pi$
$43$	−3.74484			−0.571082			−0.285541	+	0.958366i	$0.592173\pi$
$44$		0			0
$45$	−1.16995	−	9.83493i	−0.174406	−	1.46610i
$46$		0			0
$47$	5.05850	−	8.76158i	0.737858	−	1.27801i	−0.215600	−	0.976482i	$-0.569171\pi$
$47$	5.05850	−	8.76158i	0.737858	−	1.27801i	0.953458	−	0.301525i	$-0.0974958\pi$
$48$		0			0
$49$	−3.51708			−0.502439
$50$		0			0
$51$	−7.28700	+	2.42293i	−1.02038	+	0.339278i
$52$		0			0
$53$	−9.98182			−1.37111			−0.685554	−	0.728022i	$-0.740440\pi$
$53$	−9.98182			−1.37111			−0.685554	+	0.728022i	$0.740440\pi$
$54$		0			0
$55$	−3.09728	+	5.36465i	−0.417638	+	0.723370i
$56$		0			0
$57$	10.6829	−	3.55206i	1.41498	−	0.470482i
$58$		0			0
$59$	−1.46596	+	2.53912i	−0.190852	+	0.330565i	−0.945533	−	0.325527i	$-0.894458\pi$
$59$	−1.46596	+	2.53912i	−0.190852	+	0.330565i	0.754681	+	0.656092i	$0.227792\pi$
$60$		0			0
$61$	14.3492			1.83723			0.918614	−	0.395156i	$-0.129310\pi$
$61$	14.3492			1.83723			0.918614	+	0.395156i	$0.129310\pi$
$62$		0			0
$63$	−5.14542	−	2.20703i	−0.648262	−	0.278060i
$64$		0			0
$65$	−9.90695	+	6.59882i	−1.22881	+	0.818483i
$66$		0			0
$67$	8.96043			1.09469			0.547345	−	0.836907i	$-0.315638\pi$
$67$	8.96043			1.09469			0.547345	+	0.836907i	$0.315638\pi$
$68$		0			0
$69$	1.31162	−	6.38518i	0.157900	−	0.768685i
$70$		0			0
$71$	−1.03307	−	1.78932i	−0.122602	−	0.212354i	0.798191	−	0.602405i	$-0.205791\pi$
$71$	−1.03307	−	1.78932i	−0.122602	−	0.212354i	−0.920793	+	0.390051i	$0.872457\pi$
$72$		0			0
$73$	2.56896			0.300674			0.150337	−	0.988635i	$-0.451964\pi$
$73$	2.56896			0.300674			0.150337	+	0.988635i	$0.451964\pi$
$74$		0			0
$75$	7.64009	+	6.78510i	0.882202	+	0.783476i
$76$		0			0
$77$	1.75086	+	3.03258i	0.199529	+	0.345595i
$78$		0			0
$79$	7.05149	−	12.2135i	0.793355	−	1.37413i	−0.130524	−	0.991445i	$-0.541666\pi$
$79$	7.05149	−	12.2135i	0.793355	−	1.37413i	0.923879	−	0.382685i	$-0.125001\pi$
$80$		0			0
$81$	6.20293	+	6.52102i	0.689214	+	0.724558i
$82$		0			0
$83$	1.35281	−	2.34313i	0.148490	−	0.257192i	−0.782179	−	0.623053i	$-0.785892\pi$
$83$	1.35281	−	2.34313i	0.148490	−	0.257192i	0.930670	+	0.365861i	$0.119225\pi$
$84$		0			0
$85$	7.31863	−	12.6762i	0.793817	−	1.37493i
$86$		0			0
$87$	−2.19589	+	0.730133i	−0.235424	+	0.0782785i
$88$		0			0
$89$	4.60157	−	7.97016i	0.487766	−	0.844835i	−0.512135	−	0.858905i	$-0.671145\pi$
$89$	4.60157	−	7.97016i	0.487766	−	0.844835i	0.999901	+	0.0140698i	$0.00447869\pi$
$90$		0			0
$91$	0.430338	+	6.71512i	0.0451117	+	0.703936i
$92$		0			0
$93$	5.69645	−	1.89407i	0.590694	−	0.196406i
$94$		0			0
$95$	−10.7292	+	18.5836i	−1.10080	+	1.90664i
$96$		0			0
$97$	−10.3552			−1.05141			−0.525703	−	0.850668i	$-0.676198\pi$
$97$	−10.3552			−1.05141			−0.525703	+	0.850668i	$0.676198\pi$
$98$		0			0
$99$	−0.664931	−	5.58959i	−0.0668281	−	0.561775i
$100$		0			0
$101$	−7.33258	−	12.7004i	−0.729619	−	1.26374i	−0.957045	−	0.289941i	$-0.906364\pi$
$101$	−7.33258	−	12.7004i	−0.729619	−	1.26374i	0.227426	−	0.973795i	$-0.426969\pi$
$102$		0			0
$103$	−3.71350	−	6.43197i	−0.365902	−	0.633760i	0.623019	−	0.782207i	$-0.285906\pi$
$103$	−3.71350	−	6.43197i	−0.365902	−	0.633760i	−0.988920	+	0.148447i	$0.952573\pi$
$104$		0			0
$105$	10.1266	−	3.36710i	0.988255	−	0.328595i
$106$		0			0
$107$	4.77286	−	8.26684i	0.461410	−	0.799185i	−0.537622	−	0.843186i	$-0.680677\pi$
$107$	4.77286	−	8.26684i	0.461410	−	0.799185i	0.999031	+	0.0440009i	$0.0140105\pi$
$108$		0			0
$109$	9.07781			0.869497			0.434748	−	0.900552i	$-0.356837\pi$
$109$	9.07781			0.869497			0.434748	+	0.900552i	$0.356837\pi$
$110$		0			0
$111$	1.18623	+	1.05348i	0.112592	+	0.0999921i
$112$		0			0
$113$	−6.40794	+	11.0989i	−0.602808	+	1.04409i	0.389586	+	0.920990i	$0.372618\pi$
$113$	−6.40794	+	11.0989i	−0.602808	+	1.04409i	−0.992394	+	0.123104i	$0.960715\pi$
$114$		0			0
$115$	6.21238	+	10.7602i	0.579308	+	1.00339i
$116$		0			0
$117$	3.61944	−	10.1931i	0.334617	−	0.942354i
$118$		0			0
$119$	−4.13714	−	7.16574i	−0.379251	−	0.656882i
$120$		0			0
$121$	3.73969	−	6.47733i	0.339972	−	0.588848i
$122$		0			0
$123$	0.811104	−	3.94858i	0.0731348	−	0.356032i
$124$		0			0
$125$	−2.96928			−0.265581
$126$		0			0
$127$	−1.84439	+	3.19458i	−0.163663	+	0.283473i	−0.936180	−	0.351522i	$-0.885664\pi$
$127$	−1.84439	+	3.19458i	−0.163663	+	0.283473i	0.772516	+	0.634995i	$0.218998\pi$
$128$		0			0
$129$	−1.30513	+	6.35358i	−0.114910	+	0.559402i
$130$		0			0
$131$	−8.37547	−	14.5067i	−0.731768	−	1.26746i	−0.956127	−	0.292953i	$-0.905362\pi$
$131$	−8.37547	−	14.5067i	−0.731768	−	1.26746i	0.224359	−	0.974507i	$-0.427971\pi$
$132$		0			0
$133$	6.06512	+	10.5051i	0.525913	+	0.910908i
$134$		0			0
$135$	−17.0939	−	1.44265i	−1.47121	−	0.124163i
$136$		0			0
$137$	−2.09939			−0.179363			−0.0896814	−	0.995971i	$-0.528585\pi$
$137$	−2.09939			−0.179363			−0.0896814	+	0.995971i	$0.528585\pi$
$138$		0			0
$139$	−3.92420	+	6.79692i	−0.332846	+	0.576507i	−0.983069	−	0.183237i	$-0.941342\pi$
$139$	−3.92420	+	6.79692i	−0.332846	+	0.576507i	0.650222	+	0.759744i	$0.274676\pi$
$140$		0			0
$141$	−13.1022	−	11.6359i	−1.10340	−	0.979921i
$142$		0			0
$143$	−5.63052	+	3.75038i	−0.470848	+	0.313622i
$144$		0			0
$145$	2.20542	−	3.81990i	0.183150	−	0.317225i
$146$		0			0
$147$	−1.22575	+	5.96716i	−0.101098	+	0.492163i
$148$		0			0
$149$	−9.51840	+	16.4864i	−0.779778	+	1.35061i	0.152292	+	0.988336i	$0.451335\pi$
$149$	−9.51840	+	16.4864i	−0.779778	+	1.35061i	−0.932070	+	0.362279i	$0.881999\pi$
$150$		0			0
$151$	−9.78217	+	16.9432i	−0.796062	+	1.37882i	0.126101	+	0.992017i	$0.459754\pi$
$151$	−9.78217	+	16.9432i	−0.796062	+	1.37882i	−0.922163	+	0.386802i	$0.873580\pi$
$152$		0			0
$153$	1.57118	+	13.2077i	0.127022	+	1.06778i
$154$		0			0
$155$	−5.72117	+	9.90936i	−0.459536	+	0.795939i
$156$		0			0
$157$	−10.9030	−	18.8845i	−0.870152	−	1.50715i	−0.861839	−	0.507182i	$-0.830687\pi$
$157$	−10.9030	−	18.8845i	−0.870152	−	1.50715i	−0.00831272	−	0.999965i	$-0.502646\pi$
$158$		0			0
$159$	−3.47881	+	16.9354i	−0.275888	+	1.34307i
$160$		0			0
$161$	7.02359			0.553536
$162$		0			0
$163$	5.93328	+	10.2767i	0.464731	+	0.804937i	0.999189	−	0.0402575i	$-0.0128178\pi$
$163$	5.93328	+	10.2767i	0.464731	+	0.804937i	−0.534459	+	0.845195i	$0.679484\pi$
$164$		0			0
$165$	8.02236	+	7.12459i	0.624540	+	0.554649i
$166$		0			0
$167$	−14.2224			−1.10056			−0.550279	−	0.834981i	$-0.685479\pi$
$167$	−14.2224			−1.10056			−0.550279	+	0.834981i	$0.685479\pi$
$168$		0			0
$169$	−12.8937	+	1.65939i	−0.991820	+	0.127646i
$170$		0			0
$171$	−2.30337	−	19.3628i	−0.176143	−	1.48071i
$172$		0			0
$173$	−17.8530			−1.35734			−0.678669	−	0.734444i	$-0.737443\pi$
$173$	−17.8530			−1.35734			−0.678669	+	0.734444i	$0.737443\pi$
$174$		0			0
$175$	−5.50490	+	9.53477i	−0.416131	+	0.720761i
$176$		0			0
$177$	3.79702	+	3.37211i	0.285402	+	0.253463i
$178$		0			0
$179$	−3.04421	+	5.27273i	−0.227535	+	0.394102i	−0.957077	−	0.289834i	$-0.906400\pi$
$179$	−3.04421	+	5.27273i	−0.227535	+	0.394102i	0.729542	+	0.683936i	$0.239733\pi$
$180$		0			0
$181$	−5.73434			−0.426230			−0.213115	−	0.977027i	$-0.568361\pi$
$181$	−5.73434			−0.426230			−0.213115	+	0.977027i	$0.568361\pi$
$182$		0			0
$183$	5.00091	−	24.3452i	0.369678	−	1.79965i
$184$		0			0
$185$	−3.02398			−0.222328
$186$		0			0
$187$	4.15947	−	7.20442i	0.304171	−	0.526839i
$188$		0			0
$189$	−5.53776	+	7.96066i	−0.402813	+	0.579053i
$190$		0			0
$191$	12.2730			0.888043			0.444021	−	0.896016i	$-0.353551\pi$
$191$	12.2730			0.888043			0.444021	+	0.896016i	$0.353551\pi$
$192$		0			0
$193$	−24.8533			−1.78898			−0.894490	−	0.447089i	$-0.852461\pi$
$193$	−24.8533			−1.78898			−0.894490	+	0.447089i	$0.852461\pi$
$194$		0			0
$195$	7.74301	+	19.1082i	0.554488	+	1.36836i
$196$		0			0
$197$	−3.80810	+	6.59582i	−0.271316	+	0.469932i	−0.969199	−	0.246279i	$-0.920792\pi$
$197$	−3.80810	+	6.59582i	−0.271316	+	0.469932i	0.697883	+	0.716211i	$0.254125\pi$
$198$		0			0
$199$	11.5276	+	19.9664i	0.817172	+	1.41538i	0.907757	+	0.419495i	$0.137793\pi$
$199$	11.5276	+	19.9664i	0.817172	+	1.41538i	−0.0905851	+	0.995889i	$0.528874\pi$
$200$		0			0
$201$	3.12284	−	15.2025i	0.220268	−	1.07230i
$202$		0			0
$203$	−1.24670	−	2.15935i	−0.0875011	−	0.151556i
$204$		0			0
$205$	3.84173	+	6.65407i	0.268318	+	0.464740i
$206$		0			0
$207$	−10.3761	−	4.45065i	−0.721191	−	0.309342i
$208$		0			0
$209$	−6.09786	+	10.5618i	−0.421798	+	0.730575i
$210$		0			0
$211$	19.7639			1.36061			0.680303	−	0.732931i	$-0.261848\pi$
$211$	19.7639			1.36061			0.680303	+	0.732931i	$0.261848\pi$
$212$		0			0
$213$	−3.39585	+	1.12912i	−0.232680	+	0.0773661i
$214$		0			0
$215$	−6.18164	−	10.7069i	−0.421585	−	0.730206i
$216$		0			0
$217$	3.23412	+	5.60166i	0.219546	+	0.380265i
$218$		0			0
$219$	0.895319	−	4.35856i	0.0605000	−	0.294524i
$220$		0			0
$221$	13.3045	−	8.86183i	0.894955	−	0.596111i
$222$		0			0
$223$	2.78358	+	4.82131i	0.186402	+	0.322859i	0.944048	−	0.329807i	$-0.106984\pi$
$223$	2.78358	+	4.82131i	0.186402	+	0.322859i	−0.757646	+	0.652666i	$0.773651\pi$
$224$		0			0
$225$	14.1745	−	10.5977i	0.944964	−	0.706511i
$226$		0			0
$227$	8.50166			0.564275			0.282138	−	0.959374i	$-0.408957\pi$
$227$	8.50166			0.564275			0.282138	+	0.959374i	$0.408957\pi$
$228$		0			0
$229$	−7.46686	−	12.9330i	−0.493424	−	0.854635i	0.506547	−	0.862212i	$-0.330922\pi$
$229$	−7.46686	−	12.9330i	−0.493424	−	0.854635i	−0.999971	+	0.00757686i	$0.997588\pi$
$230$		0			0
$231$	5.75536	−	1.91366i	0.378675	−	0.125909i
$232$		0			0
$233$	−24.2714			−1.59007			−0.795037	−	0.606561i	$-0.792549\pi$
$233$	−24.2714			−1.59007			−0.795037	+	0.606561i	$0.792549\pi$
$234$		0			0
$235$	33.4005			2.17881
$236$		0			0
$237$	−18.2643	−	16.2203i	−1.18639	−	1.05362i
$238$		0			0
$239$	−6.45026	−	11.1722i	−0.417232	−	0.722668i	0.578428	−	0.815734i	$-0.303667\pi$
$239$	−6.45026	−	11.1722i	−0.417232	−	0.722668i	−0.995660	+	0.0930660i	$0.970333\pi$
$240$		0			0
$241$	−9.61902			−0.619615			−0.309808	−	0.950799i	$-0.600265\pi$
$241$	−9.61902			−0.619615			−0.309808	+	0.950799i	$0.600265\pi$
$242$		0			0
$243$	13.2255	−	8.25137i	0.848419	−	0.529326i
$244$		0			0
$245$	−5.80568	−	10.0557i	−0.370911	−	0.642437i
$246$		0			0
$247$	−19.5046	+	12.9916i	−1.24105	+	0.826636i
$248$		0			0
$249$	−3.50395	−	3.11183i	−0.222054	−	0.197204i
$250$		0			0
$251$	−6.13449	−	10.6253i	−0.387206	−	0.670660i	0.604867	−	0.796327i	$-0.293226\pi$
$251$	−6.13449	−	10.6253i	−0.387206	−	0.670660i	−0.992073	+	0.125667i	$0.959893\pi$
$252$		0			0
$253$	3.53075	+	6.11544i	0.221976	+	0.384474i
$254$		0			0
$255$	−18.9562	−	16.8348i	−1.18708	−	1.05424i
$256$		0			0
$257$	18.7126			1.16726			0.583629	−	0.812021i	$-0.301632\pi$
$257$	18.7126			1.16726			0.583629	+	0.812021i	$0.301632\pi$
$258$		0			0
$259$	−0.854713	+	1.48041i	−0.0531093	+	0.0919879i
$260$		0			0
$261$	0.473463	+	3.98006i	0.0293067	+	0.246360i
$262$		0			0
$263$	−10.3025	−	17.8444i	−0.635277	−	1.10033i	−0.986456	−	0.164024i	$-0.947553\pi$
$263$	−10.3025	−	17.8444i	−0.635277	−	1.10033i	0.351179	−	0.936308i	$-0.385781\pi$
$264$		0			0
$265$	−16.4771	−	28.5392i	−1.01218	−	1.75315i
$266$		0			0
$267$	−11.9187	−	10.5849i	−0.729410	−	0.647783i
$268$		0			0
$269$	8.82631	+	15.2876i	0.538150	+	0.932103i	0.999004	+	0.0446269i	$0.0142099\pi$
$269$	8.82631	+	15.2876i	0.538150	+	0.932103i	−0.460854	+	0.887476i	$0.652457\pi$
$270$		0			0
$271$	7.84835	−	13.5937i	0.476753	−	0.825761i	−0.522892	−	0.852399i	$-0.675147\pi$
$271$	7.84835	−	13.5937i	0.476753	−	0.825761i	0.999645	+	0.0266382i	$0.00848020\pi$
$272$		0			0
$273$	11.5430	+	1.61019i	0.698615	+	0.0974534i
$274$		0			0
$275$	−11.0692			−0.667499
$276$		0			0
$277$	8.98946			0.540124			0.270062	−	0.962843i	$-0.412956\pi$
$277$	8.98946			0.540124			0.270062	+	0.962843i	$0.412956\pi$
$278$		0			0
$279$	−1.22823	−	10.3248i	−0.0735323	−	0.618132i
$280$		0			0
$281$	9.17862	−	15.8978i	0.547551	−	0.948385i	−0.450891	−	0.892579i	$-0.648894\pi$
$281$	9.17862	−	15.8978i	0.547551	−	0.948385i	0.998442	−	0.0558064i	$-0.0177729\pi$
$282$		0			0
$283$	−3.03135			−0.180195			−0.0900974	−	0.995933i	$-0.528718\pi$
$283$	−3.03135			−0.180195			−0.0900974	+	0.995933i	$0.528718\pi$
$284$		0			0
$285$	27.7901	+	24.6801i	1.64614	+	1.46193i
$286$		0			0
$287$	4.34338			0.256381
$288$		0			0
$289$	−1.32849	+	2.30101i	−0.0781465	+	0.135354i
$290$		0			0
$291$	−3.60892	+	17.5688i	−0.211559	+	1.02990i
$292$		0			0
$293$	−1.47905	+	2.56180i	−0.0864073	+	0.149662i	−0.905990	−	0.423299i	$-0.860872\pi$
$293$	−1.47905	+	2.56180i	−0.0864073	+	0.149662i	0.819583	+	0.572961i	$0.194205\pi$
$294$		0			0
$295$	−9.67951			−0.563563
$296$		0			0
$297$	−9.71517	−	0.819914i	−0.563732	−	0.0475762i
$298$		0			0
$299$	0.867811	+	13.5416i	0.0501868	+	0.783128i
$300$		0			0
$301$	−6.98883			−0.402830
$302$		0			0
$303$	−24.1033	+	8.01436i	−1.38470	+	0.460413i
$304$		0			0
$305$	23.6864	+	41.0261i	1.35628	+	2.34914i
$306$		0			0
$307$	7.39083			0.421817			0.210909	−	0.977506i	$-0.432358\pi$
$307$	7.39083			0.421817			0.210909	+	0.977506i	$0.432358\pi$
$308$		0			0
$309$	−12.2068	+	4.05878i	−0.694423	+	0.230896i
$310$		0			0
$311$	−7.06555	−	12.2379i	−0.400651	−	0.693947i	0.593154	−	0.805089i	$-0.297883\pi$
$311$	−7.06555	−	12.2379i	−0.400651	−	0.693947i	−0.993805	+	0.111142i	$0.964549\pi$
$312$		0			0
$313$	5.69278	−	9.86019i	0.321775	−	0.557331i	−0.659079	−	0.752073i	$-0.729054\pi$
$313$	5.69278	−	9.86019i	0.321775	−	0.557331i	0.980854	+	0.194743i	$0.0623872\pi$
$314$		0			0
$315$	−2.18343	−	18.3545i	−0.123023	−	1.03416i
$316$		0			0
$317$	5.58479	−	9.67314i	0.313673	−	0.543298i	−0.665482	−	0.746414i	$-0.731774\pi$
$317$	5.58479	−	9.67314i	0.313673	−	0.543298i	0.979155	+	0.203117i	$0.0651071\pi$
$318$		0			0
$319$	1.25343	−	2.17100i	0.0701785	−	0.121553i
$320$		0			0
$321$	−12.3623	−	10.9789i	−0.689997	−	0.612781i
$322$		0			0
$323$	14.4087	−	24.9567i	0.801724	−	1.38863i
$324$		0			0
$325$	−19.0633	−	9.43543i	−1.05744	−	0.523383i
$326$		0			0
$327$	3.16375	−	15.4016i	0.174956	−	0.851713i
$328$		0			0
$329$	9.44047	−	16.3514i	0.520470	−	0.901480i
$330$		0			0
$331$	−17.0316			−0.936139			−0.468069	−	0.883692i	$-0.655050\pi$
$331$	−17.0316			−0.936139			−0.468069	+	0.883692i	$0.655050\pi$
$332$		0			0
$333$	2.20078	−	1.64544i	0.120602	−	0.0901693i
$334$		0			0
$335$	14.7911	+	25.6189i	0.808123	+	1.39971i
$336$		0			0
$337$	15.2871	+	26.4780i	0.832739	+	1.44235i	0.895858	+	0.444340i	$0.146562\pi$
$337$	15.2871	+	26.4780i	0.832739	+	1.44235i	−0.0631194	+	0.998006i	$0.520105\pi$
$338$		0			0
$339$	16.5974	+	14.7400i	0.901445	+	0.800566i
$340$		0			0
$341$	−3.25157	+	5.63189i	−0.176083	+	0.304984i
$342$		0			0
$343$	−19.6276			−1.05979
$344$		0			0
$345$	20.4211	−	6.79001i	1.09943	−	0.365562i
$346$		0			0
$347$	14.4392	−	25.0094i	0.775137	−	1.34258i	−0.159581	−	0.987185i	$-0.551014\pi$
$347$	14.4392	−	25.0094i	0.775137	−	1.34258i	0.934718	−	0.355391i	$-0.115652\pi$
$348$		0			0
$349$	13.4698	+	23.3304i	0.721022	+	1.24885i	0.960590	+	0.277968i	$0.0896608\pi$
$349$	13.4698	+	23.3304i	0.721022	+	1.24885i	−0.239568	+	0.970880i	$0.577006\pi$
$350$		0			0
$351$	−16.0325	−	9.69328i	−0.855750	−	0.517389i
$352$		0			0
$353$	14.1482	+	24.5054i	0.753032	+	1.30429i	0.946347	+	0.323153i	$0.104743\pi$
$353$	14.1482	+	24.5054i	0.753032	+	1.30429i	−0.193314	+	0.981137i	$0.561924\pi$
$354$		0			0
$355$	3.41059	−	5.90732i	0.181015	−	0.313528i
$356$		0			0
$357$	−13.5994	+	4.52181i	−0.719758	+	0.239320i
$358$		0			0
$359$	18.9967			1.00261			0.501304	−	0.865271i	$-0.332854\pi$
$359$	18.9967			1.00261			0.501304	+	0.865271i	$0.332854\pi$
$360$		0			0
$361$	−11.6235	+	20.1324i	−0.611762	+	1.05960i
$362$		0			0
$363$	−9.68626	−	8.60229i	−0.508397	−	0.451503i
$364$		0			0
$365$	4.24061	+	7.34494i	0.221963	+	0.384452i
$366$		0			0
$367$	−12.9955	−	22.5089i	−0.678361	−	1.17496i	−0.975474	−	0.220113i	$-0.929357\pi$
$367$	−12.9955	−	22.5089i	−0.678361	−	1.17496i	0.297113	−	0.954842i	$-0.403976\pi$
$368$		0			0
$369$	−6.41659	−	2.75228i	−0.334034	−	0.143278i
$370$		0			0
$371$	−18.6287			−0.967152
$372$		0			0
$373$	15.7252	−	27.2369i	0.814222	−	1.41027i	−0.0956638	−	0.995414i	$-0.530497\pi$
$373$	15.7252	−	27.2369i	0.814222	−	1.41027i	0.909885	−	0.414860i	$-0.136169\pi$
$374$		0			0
$375$	−1.03484	+	5.03776i	−0.0534388	+	0.260149i
$376$		0			0
$377$	4.00921	−	2.67045i	0.206485	−	0.137535i
$378$		0			0
$379$	5.08601	−	8.80922i	0.261251	−	0.452499i	−0.705324	−	0.708885i	$-0.749198\pi$
$379$	5.08601	−	8.80922i	0.261251	−	0.452499i	0.966575	+	0.256386i	$0.0825318\pi$
$380$		0			0
$381$	4.77721	+	4.24260i	0.244744	+	0.217355i
$382$		0			0
$383$	14.3383	−	24.8346i	0.732651	−	1.26899i	−0.223095	−	0.974797i	$-0.571616\pi$
$383$	14.3383	−	24.8346i	0.732651	−	1.26899i	0.955746	−	0.294193i	$-0.0950507\pi$
$384$		0			0
$385$	−5.78034	+	10.0118i	−0.294593	+	0.510250i
$386$		0			0
$387$	10.3248	+	4.42863i	0.524839	+	0.225120i
$388$		0			0
$389$	−7.19376	+	12.4600i	−0.364738	+	0.631745i	−0.988734	−	0.149683i	$-0.952175\pi$
$389$	−7.19376	+	12.4600i	−0.364738	+	0.631745i	0.623996	+	0.781428i	$0.285508\pi$
$390$		0			0
$391$	−8.34287	−	14.4503i	−0.421917	−	0.730782i
$392$		0			0
$393$	−27.5315	+	9.15422i	−1.38878	+	0.461770i
$394$		0			0
$395$	46.5599			2.34268
$396$		0			0
$397$	−0.0814812	−	0.141130i	−0.00408942	−	0.00708309i	0.863973	−	0.503537i	$-0.167968\pi$
$397$	−0.0814812	−	0.141130i	−0.00408942	−	0.00708309i	−0.868063	+	0.496454i	$0.834635\pi$
$398$		0			0
$399$	19.9370	−	6.62906i	0.998099	−	0.331868i
$400$		0			0
$401$	−9.65865			−0.482330			−0.241165	−	0.970484i	$-0.577529\pi$
$401$	−9.65865			−0.482330			−0.241165	+	0.970484i	$0.577529\pi$
$402$		0			0
$403$	−10.4005	+	6.92754i	−0.518084	+	0.345085i
$404$		0			0
$405$	−8.40511	+	28.4992i	−0.417653	+	1.41614i
$406$		0			0
$407$	−1.71865			−0.0851904
$408$		0			0
$409$	−11.1303	+	19.2782i	−0.550358	+	0.953247i	0.447891	+	0.894088i	$0.352175\pi$
$409$	−11.1303	+	19.2782i	−0.550358	+	0.953247i	−0.998249	+	0.0591591i	$0.981158\pi$
$410$		0			0
$411$	−0.731667	+	3.56187i	−0.0360905	+	0.175694i
$412$		0			0
$413$	−2.73586	+	4.73865i	−0.134623	+	0.233174i
$414$		0			0
$415$	8.93239			0.438474
$416$		0			0
$417$	10.1642	+	9.02673i	0.497742	+	0.442041i
$418$		0			0
$419$	14.3294			0.700038			0.350019	−	0.936743i	$-0.386175\pi$
$419$	14.3294			0.700038			0.350019	+	0.936743i	$0.386175\pi$
$420$		0			0
$421$	0.334370	−	0.579145i	0.0162962	−	0.0282258i	−0.857762	−	0.514047i	$-0.828146\pi$
$421$	0.334370	−	0.579145i	0.0162962	−	0.0282258i	0.874058	+	0.485821i	$0.161479\pi$
$422$		0			0
$423$	−24.3081	+	18.1742i	−1.18190	+	0.883658i
$424$		0			0
$425$	26.1557			1.26874
$426$		0			0
$427$	26.7793			1.29594
$428$		0			0
$429$	4.40067	+	10.8599i	0.212466	+	0.524323i
$430$		0			0
$431$	−19.1537	+	33.1752i	−0.922601	+	1.59799i	−0.127228	+	0.991874i	$0.540608\pi$
$431$	−19.1537	+	33.1752i	−0.922601	+	1.59799i	−0.795374	+	0.606119i	$0.792725\pi$
$432$		0			0
$433$	2.75906	+	4.77883i	0.132592	+	0.229656i	0.924675	−	0.380757i	$-0.124337\pi$
$433$	2.75906	+	4.77883i	0.132592	+	0.229656i	−0.792083	+	0.610413i	$0.791003\pi$
$434$		0			0
$435$	−5.71231	−	5.07306i	−0.273884	−	0.243234i
$436$		0			0
$437$	12.2308	+	21.1844i	0.585078	+	1.01339i
$438$		0			0
$439$	15.0911	+	26.1385i	0.720257	+	1.24752i	0.960897	+	0.276907i	$0.0893095\pi$
$439$	15.0911	+	26.1385i	0.720257	+	1.24752i	−0.240639	+	0.970615i	$0.577357\pi$
$440$		0			0
$441$	9.69684	+	4.15929i	0.461754	+	0.198061i
$442$		0			0
$443$	−11.2133	+	19.4221i	−0.532762	+	0.922770i	0.466507	+	0.884518i	$0.345512\pi$
$443$	−11.2133	+	19.4221i	−0.532762	+	0.922770i	−0.999268	+	0.0382523i	$0.987821\pi$
$444$		0			0
$445$	30.3835			1.44031
$446$		0			0
$447$	24.6539	+	21.8949i	1.16609	+	1.03559i
$448$		0			0
$449$	−9.68866	−	16.7813i	−0.457236	−	0.791956i	0.541577	−	0.840651i	$-0.317827\pi$
$449$	−9.68866	−	16.7813i	−0.457236	−	0.791956i	−0.998814	+	0.0486945i	$0.984494\pi$
$450$		0			0
$451$	2.18341	+	3.78178i	0.102813	+	0.178077i
$452$		0			0
$453$	25.3371	+	22.5016i	1.19044	+	1.05722i
$454$		0			0
$455$	−18.4889	+	12.3151i	−0.866775	+	0.577341i
$456$		0			0
$457$	−19.1187	−	33.1146i	−0.894335	−	1.54903i	−0.834626	−	0.550818i	$-0.814316\pi$
$457$	−19.1187	−	33.1146i	−0.894335	−	1.54903i	−0.0597094	−	0.998216i	$-0.519017\pi$
$458$		0			0
$459$	22.9562	+	1.93739i	1.07150	+	0.0904296i
$460$		0			0
$461$	−40.1158			−1.86838			−0.934189	−	0.356780i	$-0.883875\pi$
$461$	−40.1158			−1.86838			−0.934189	+	0.356780i	$0.883875\pi$
$462$		0			0
$463$	8.04452	+	13.9335i	0.373861	+	0.647546i	0.990156	−	0.139970i	$-0.0447005\pi$
$463$	8.04452	+	13.9335i	0.373861	+	0.647546i	−0.616295	+	0.787515i	$0.711367\pi$
$464$		0			0
$465$	14.8186	+	13.1602i	0.687194	+	0.610292i
$466$		0			0
$467$	7.11182			0.329096			0.164548	−	0.986369i	$-0.447383\pi$
$467$	7.11182			0.329096			0.164548	+	0.986369i	$0.447383\pi$
$468$		0			0
$469$	16.7225			0.772173
$470$		0			0
$471$	−35.8398	+	11.9167i	−1.65141	+	0.549094i
$472$		0			0
$473$	−3.51328	−	6.08518i	−0.161541	−	0.279797i
$474$		0			0
$475$	−38.3447			−1.75937
$476$		0			0
$477$	27.5206	+	11.8045i	1.26008	+	0.540490i
$478$		0			0
$479$	9.17751	+	15.8959i	0.419331	+	0.726303i	0.995872	−	0.0907654i	$-0.0289313\pi$
$479$	9.17751	+	15.8959i	0.419331	+	0.726303i	−0.576541	+	0.817068i	$0.695598\pi$
$480$		0			0
$481$	−2.95985	−	1.46498i	−0.134957	−	0.0667974i
$482$		0			0
$483$	2.44782	−	11.9164i	0.111380	−	0.542215i
$484$		0			0
$485$	−17.0934	−	29.6066i	−0.776170	−	1.34437i
$486$		0			0
$487$	−14.3769	−	24.9015i	−0.651479	−	1.12839i	−0.982764	−	0.184864i	$-0.940816\pi$
$487$	−14.3769	−	24.9015i	−0.651479	−	1.12839i	0.331285	−	0.943531i	$-0.392518\pi$
$488$		0			0
$489$	19.5036	−	6.48496i	0.881985	−	0.293260i
$490$		0			0
$491$	24.5019			1.10575			0.552877	−	0.833263i	$-0.313530\pi$
$491$	24.5019			1.10575			0.552877	+	0.833263i	$0.313530\pi$
$492$		0			0
$493$	−2.96175	+	5.12990i	−0.133390	+	0.231039i
$494$		0			0
$495$	14.8837	−	11.1279i	0.668971	−	0.500162i
$496$		0			0
$497$	−1.92797	−	3.33934i	−0.0864813	−	0.149790i
$498$		0			0
$499$	−16.7052	−	28.9342i	−0.747827	−	1.29527i	−0.948862	−	0.315690i	$-0.897764\pi$
$499$	−16.7052	−	28.9342i	−0.747827	−	1.29527i	0.201036	−	0.979584i	$-0.435569\pi$
$500$		0			0
$501$	−4.95670	+	24.1300i	−0.221449	+	1.07805i
$502$		0			0
$503$	−9.85083	−	17.0621i	−0.439227	−	0.760763i	0.558403	−	0.829570i	$-0.311414\pi$
$503$	−9.85083	−	17.0621i	−0.439227	−	0.760763i	−0.997630	+	0.0688067i	$0.978081\pi$
$504$		0			0
$505$	24.2079	−	41.9294i	1.07724	−	1.86583i
$506$		0			0
$507$	−1.67826	+	22.4540i	−0.0745340	+	0.997218i
$508$		0			0
$509$	−6.06570			−0.268857			−0.134429	−	0.990923i	$-0.542920\pi$
$509$	−6.06570			−0.268857			−0.134429	+	0.990923i	$0.542920\pi$
$510$		0			0
$511$	4.79434			0.212089
$512$		0			0
$513$	−33.6541	−	2.84025i	−1.48587	−	0.125400i
$514$		0			0
$515$	12.2598	−	21.2346i	0.540232	−	0.935710i
$516$		0			0
$517$	18.9829			0.834865
$518$		0			0
$519$	−6.22203	+	30.2898i	−0.273117	+	1.32958i
$520$		0			0
$521$	20.0607			0.878876			0.439438	−	0.898273i	$-0.355178\pi$
$521$	20.0607			0.878876			0.439438	+	0.898273i	$0.355178\pi$
$522$		0			0
$523$	15.6061	−	27.0306i	0.682408	−	1.18196i	−0.291836	−	0.956468i	$-0.594266\pi$
$523$	15.6061	−	27.0306i	0.682408	−	1.18196i	0.974244	−	0.225497i	$-0.0724004\pi$
$524$		0			0
$525$	14.2584	+	12.6628i	0.622287	+	0.552648i
$526$		0			0
$527$	7.68320	−	13.3077i	0.334685	−	0.579692i
$528$		0			0
$529$	−8.83640			−0.384191
$530$		0			0
$531$	7.04452	−	5.26690i	0.305706	−	0.228564i
$532$		0			0
$533$	0.536653	+	8.37408i	0.0232450	+	0.362722i
$534$		0			0
$535$	31.5145			1.36249
$536$		0			0
$537$	7.88490	+	7.00251i	0.340258	+	0.302181i
$538$		0			0
$539$	−3.29960	−	5.71508i	−0.142124	−	0.246166i
$540$		0			0
$541$	23.6592			1.01719			0.508594	−	0.861007i	$-0.330166\pi$
$541$	23.6592			1.01719			0.508594	+	0.861007i	$0.330166\pi$
$542$		0			0
$543$	−1.99850	+	9.72902i	−0.0857638	+	0.417512i
$544$		0			0
$545$	14.9848	+	25.9545i	0.641880	+	1.11177i
$546$		0			0
$547$	−13.4497	+	23.2955i	−0.575066	+	0.996044i	0.420968	+	0.907075i	$0.361690\pi$
$547$	−13.4497	+	23.2955i	−0.575066	+	0.996044i	−0.996034	+	0.0889686i	$0.971643\pi$
$548$		0			0
$549$	−39.5618	−	16.9693i	−1.68846	−	0.724234i
$550$		0			0
$551$	4.34198	−	7.52052i	0.184974	−	0.320385i
$552$		0			0
$553$	13.1599	−	22.7936i	0.559616	−	0.969284i
$554$		0			0
$555$	−1.05390	+	5.13057i	−0.0447357	+	0.217780i
$556$		0			0
$557$	9.16528	−	15.8747i	0.388346	−	0.672634i	−0.603882	−	0.797074i	$-0.706380\pi$
$557$	9.16528	−	15.8747i	0.388346	−	0.672634i	0.992227	+	0.124440i	$0.0397134\pi$
$558$		0			0
$559$	−0.863517	−	13.4746i	−0.0365229	−	0.569913i
$560$		0			0
$561$	−10.7736	−	9.56791i	−0.454860	−	0.403958i
$562$		0			0
$563$	−5.71682	+	9.90183i	−0.240935	+	0.417312i	−0.960981	−	0.276614i	$-0.910788\pi$
$563$	−5.71682	+	9.90183i	−0.240935	+	0.417312i	0.720046	+	0.693927i	$0.244121\pi$
$564$		0			0
$565$	−42.3106			−1.78002
$566$		0			0
$567$	11.5763	+	12.1699i	0.486158	+	0.511088i
$568$		0			0
$569$	0.701197	+	1.21451i	0.0293957	+	0.0509148i	0.880349	−	0.474327i	$-0.157308\pi$
$569$	0.701197	+	1.21451i	0.0293957	+	0.0509148i	−0.850953	+	0.525241i	$0.823975\pi$
$570$		0			0
$571$	−20.3941	−	35.3237i	−0.853468	−	1.47825i	−0.878059	−	0.478552i	$-0.841162\pi$
$571$	−20.3941	−	35.3237i	−0.853468	−	1.47825i	0.0245910	−	0.999698i	$-0.492172\pi$
$572$		0			0
$573$	4.27732	−	20.8227i	0.178688	−	0.869880i
$574$		0			0
$575$	−11.1011	+	19.2276i	−0.462946	+	0.801846i
$576$		0			0
$577$	−11.7497			−0.489146			−0.244573	−	0.969631i	$-0.578648\pi$
$577$	−11.7497			−0.489146			−0.244573	+	0.969631i	$0.578648\pi$
$578$		0			0
$579$	−8.66174	+	42.1667i	−0.359969	+	1.75239i
$580$		0			0
$581$	2.52469	−	4.37290i	0.104742	−	0.181418i
$582$		0			0
$583$	−9.36461	−	16.2200i	−0.387842	−	0.671763i
$584$		0			0
$585$	35.1180	−	6.47751i	1.45195	−	0.267812i
$586$		0			0
$587$	7.12235	+	12.3363i	0.293971	+	0.509173i	0.974745	−	0.223321i	$-0.0716897\pi$
$587$	7.12235	+	12.3363i	0.293971	+	0.509173i	−0.680774	+	0.732494i	$0.738356\pi$
$588$		0			0
$589$	−11.2637	+	19.5093i	−0.464113	+	0.803867i
$590$		0			0
$591$	9.86345	+	8.75965i	0.405728	+	0.360324i
$592$		0			0
$593$	−26.9551			−1.10691			−0.553457	−	0.832878i	$-0.686692\pi$
$593$	−26.9551			−1.10691			−0.553457	+	0.832878i	$0.686692\pi$
$594$		0			0
$595$	13.6585	−	23.6571i	0.559942	−	0.969848i
$596$		0			0
$597$	37.8931	−	12.5995i	1.55086	−	0.515662i
$598$		0			0
$599$	−14.1367	−	24.4855i	−0.577609	−	1.00045i	−0.995753	−	0.0920675i	$-0.970652\pi$
$599$	−14.1367	−	24.4855i	−0.577609	−	1.00045i	0.418144	−	0.908381i	$-0.362681\pi$
$600$		0			0
$601$	14.6530	+	25.3797i	0.597708	+	1.03526i	0.993159	+	0.116774i	$0.0372552\pi$
$601$	14.6530	+	25.3797i	0.597708	+	1.03526i	−0.395450	+	0.918487i	$0.629411\pi$
$602$		0			0
$603$	−24.7046	−	10.5966i	−1.00605	−	0.431526i
$604$		0			0
$605$	24.6926			1.00390
$606$		0			0
$607$	15.2475	−	26.4094i	0.618877	−	1.07193i	−0.370814	−	0.928707i	$-0.620921\pi$
$607$	15.2475	−	26.4094i	0.618877	−	1.07193i	0.989691	−	0.143219i	$-0.0457453\pi$
$608$		0			0
$609$	−4.09810	+	1.36262i	−0.166063	+	0.0552161i
$610$		0			0
$611$	32.6921	+	16.1810i	1.32258	+	0.654614i
$612$		0			0
$613$	−1.13510	+	1.96606i	−0.0458464	+	0.0794083i	−0.888038	−	0.459770i	$-0.847932\pi$
$613$	−1.13510	+	1.96606i	−0.0458464	+	0.0794083i	0.842192	+	0.539178i	$0.181265\pi$
$614$		0			0
$615$	12.6284	−	4.19893i	0.509225	−	0.169317i
$616$		0			0
$617$	2.49748	−	4.32577i	0.100545	−	0.174149i	−0.811364	−	0.584541i	$-0.801275\pi$
$617$	2.49748	−	4.32577i	0.100545	−	0.174149i	0.911909	+	0.410392i	$0.134608\pi$
$618$		0			0
$619$	−20.1821	+	34.9564i	−0.811187	+	1.40502i	0.100848	+	0.994902i	$0.467845\pi$
$619$	−20.1821	+	34.9564i	−0.811187	+	1.40502i	−0.912034	+	0.410114i	$0.865489\pi$
$620$		0			0
$621$	−11.1673	+	16.0533i	−0.448129	+	0.644196i
$622$		0			0
$623$	8.58773	−	14.8744i	0.344060	−	0.595930i
$624$		0			0
$625$	9.84706	+	17.0556i	0.393882	+	0.682224i
$626$		0			0
$627$	15.7942	+	14.0267i	0.630761	+	0.560174i
$628$		0			0
$629$	4.06103			0.161924
$630$		0			0
$631$	11.3281	+	19.6209i	0.450966	+	0.781096i	0.998446	−	0.0557225i	$-0.0177462\pi$
$631$	11.3281	+	19.6209i	0.450966	+	0.781096i	−0.547480	+	0.836819i	$0.684413\pi$
$632$		0			0
$633$	6.88802	−	33.5320i	0.273774	−	1.33278i
$634$		0			0
$635$	−12.1782			−0.483279
$636$		0			0
$637$	−0.810998	−	12.6550i	−0.0321329	−	0.501411i
$638$		0			0
$639$	0.732192	+	6.15500i	0.0289651	+	0.243488i
$640$		0			0
$641$	16.4220			0.648631			0.324315	−	0.945949i	$-0.394866\pi$
$641$	16.4220			0.648631			0.324315	+	0.945949i	$0.394866\pi$
$642$		0			0
$643$	−0.826871	+	1.43218i	−0.0326086	+	0.0564797i	−0.881869	−	0.471494i	$-0.843715\pi$
$643$	−0.826871	+	1.43218i	−0.0326086	+	0.0564797i	0.849261	+	0.527974i	$0.177048\pi$
$644$		0			0
$645$	−20.3200	+	6.75641i	−0.800100	+	0.266034i
$646$		0			0
$647$	15.5953	−	27.0119i	0.613115	−	1.06195i	−0.377597	−	0.925970i	$-0.623250\pi$
$647$	15.5953	−	27.0119i	0.613115	−	1.06195i	0.990712	−	0.135976i	$-0.0434171\pi$
$648$		0			0
$649$	−5.50126			−0.215943
$650$		0			0
$651$	10.6310	−	3.53483i	0.416664	−	0.138541i
$652$		0			0
$653$	23.0419			0.901701			0.450850	−	0.892600i	$-0.351121\pi$
$653$	23.0419			0.901701			0.450850	+	0.892600i	$0.351121\pi$
$654$		0			0
$655$	27.6510	−	47.8929i	1.08041	−	1.87133i
$656$		0			0
$657$	−7.08280	−	3.03804i	−0.276327	−	0.118525i
$658$		0			0
$659$	38.6980			1.50746			0.753729	−	0.657185i	$-0.228253\pi$
$659$	38.6980			1.50746			0.753729	+	0.657185i	$0.228253\pi$
$660$		0			0
$661$	−3.03481			−0.118040			−0.0590202	−	0.998257i	$-0.518798\pi$
$661$	−3.03481			−0.118040			−0.0590202	+	0.998257i	$0.518798\pi$
$662$		0			0
$663$	−10.3984	−	25.6612i	−0.403841	−	0.996597i
$664$		0			0
$665$	−20.0235	+	34.6818i	−0.776480	+	1.34490i
$666$		0			0
$667$	−2.51407	−	4.35449i	−0.0973450	−	0.168607i
$668$		0			0
$669$	9.15007	−	3.04240i	0.353762	−	0.117626i
$670$		0			0
$671$	13.4619	+	23.3168i	0.519693	+	0.900134i
$672$		0			0
$673$	−4.24403	−	7.35088i	−0.163595	−	0.283355i	0.772560	−	0.634942i	$-0.218976\pi$
$673$	−4.24403	−	7.35088i	−0.163595	−	0.283355i	−0.936156	+	0.351586i	$0.885642\pi$
$674$		0			0
$675$	−13.0403	−	27.7422i	−0.501920	−	1.06780i
$676$		0			0
$677$	−9.65503	+	16.7230i	−0.371073	+	0.642717i	−0.989731	−	0.142943i	$-0.954343\pi$
$677$	−9.65503	+	16.7230i	−0.371073	+	0.642717i	0.618658	+	0.785661i	$0.287677\pi$
$678$		0			0
$679$	−19.3254			−0.741641
$680$		0			0
$681$	2.96295	−	14.4241i	0.113541	−	0.552734i
$682$		0			0
$683$	12.5757	+	21.7818i	0.481196	+	0.833456i	0.999767	−	0.0215787i	$-0.00686923\pi$
$683$	12.5757	+	21.7818i	0.481196	+	0.833456i	−0.518571	+	0.855034i	$0.673536\pi$
$684$		0			0
$685$	−3.46548	−	6.00239i	−0.132409	−	0.229340i
$686$		0			0
$687$	−24.5447	+	8.16113i	−0.936440	+	0.311366i
$688$		0			0
$689$	−2.30169	−	35.9163i	−0.0876876	−	1.36830i
$690$		0			0
$691$	24.1688	+	41.8616i	0.919425	+	1.59249i	0.800291	+	0.599612i	$0.204678\pi$
$691$	24.1688	+	41.8616i	0.919425	+	1.59249i	0.119133	+	0.992878i	$0.461988\pi$
$692$		0			0
$693$	−1.24093	−	10.4316i	−0.0471392	−	0.396264i
$694$		0			0
$695$	−25.9109			−0.982857
$696$		0			0
$697$	−5.15922	−	8.93603i	−0.195419	−	0.338476i
$698$		0			0
$699$	−8.45895	+	41.1795i	−0.319947	+	1.55755i
$700$		0			0
$701$	−5.76955			−0.217913			−0.108956	−	0.994047i	$-0.534751\pi$
$701$	−5.76955			−0.217913			−0.108956	+	0.994047i	$0.534751\pi$
$702$		0			0
$703$	−5.95355			−0.224542
$704$		0			0
$705$	11.6406	−	56.6681i	0.438409	−	2.13424i
$706$		0			0
$707$	−13.6845	−	23.7022i	−0.514658	−	0.891414i
$708$		0			0
$709$	26.2836			0.987102			0.493551	−	0.869717i	$-0.335699\pi$
$709$	26.2836			0.987102			0.493551	+	0.869717i	$0.335699\pi$
$710$		0			0
$711$	−33.8852	+	25.3346i	−1.27079	+	0.950121i
$712$		0			0
$713$	6.52185	+	11.2962i	0.244245	+	0.423045i
$714$		0			0
$715$	−20.0171	−	9.90753i	−0.748598	−	0.370521i
$716$		0			0
$717$	−21.2030	+	7.05000i	−0.791841	+	0.263287i
$718$		0			0
$719$	−21.7139	−	37.6096i	−0.809793	−	1.40260i	−0.913007	−	0.407943i	$-0.866246\pi$
$719$	−21.7139	−	37.6096i	−0.809793	−	1.40260i	0.103215	−	0.994659i	$-0.467087\pi$
$720$		0			0
$721$	−6.93035	−	12.0037i	−0.258100	−	0.447042i
$722$		0			0
$723$	−3.35237	+	16.3199i	−0.124676	+	0.606942i
$724$		0			0
$725$	7.88183			0.292724
$726$		0			0
$727$	14.0746	−	24.3779i	0.521997	−	0.904125i	−0.477675	−	0.878536i	$-0.658521\pi$
$727$	14.0746	−	24.3779i	0.521997	−	0.904125i	0.999673	−	0.0255891i	$-0.00814616\pi$
$728$		0			0
$729$	−9.39019	−	25.3145i	−0.347785	−	0.937574i
$730$		0			0
$731$	8.30159	+	14.3788i	0.307045	+	0.531818i
$732$		0			0
$733$	−2.35921	−	4.08627i	−0.0871394	−	0.150930i	0.819161	−	0.573563i	$-0.194439\pi$
$733$	−2.35921	−	4.08627i	−0.0871394	−	0.150930i	−0.906301	+	0.422633i	$0.861106\pi$
$734$		0			0
$735$	−19.0842	+	6.34549i	−0.703930	+	0.234057i
$736$		0			0
$737$	8.40638	+	14.5603i	0.309653	+	0.536334i
$738$		0			0
$739$	−11.0290	+	19.1028i	−0.405709	+	0.702709i	−0.994404	−	0.105647i	$-0.966309\pi$
$739$	−11.0290	+	19.1028i	−0.405709	+	0.702709i	0.588695	+	0.808355i	$0.299642\pi$
$740$		0			0
$741$	15.2443	+	37.6197i	0.560012	+	1.38200i
$742$		0			0
$743$	24.6938			0.905927			0.452963	−	0.891529i	$-0.350367\pi$
$743$	24.6938			0.905927			0.452963	+	0.891529i	$0.350367\pi$
$744$		0			0
$745$	−62.8485			−2.30259
$746$		0			0
$747$	−6.50078	+	4.86037i	−0.237851	+	0.177832i
$748$		0			0
$749$	8.90740	−	15.4281i	0.325469	−	0.563729i
$750$		0			0
$751$	−8.23189			−0.300386			−0.150193	−	0.988657i	$-0.547989\pi$
$751$	−8.23189			−0.300386			−0.150193	+	0.988657i	$0.547989\pi$
$752$		0			0
$753$	−20.1650	+	6.70488i	−0.734855	+	0.244339i
$754$		0			0
$755$	−64.5902			−2.35068
$756$		0			0
$757$	3.82380	−	6.62301i	0.138978	−	0.240718i	−0.788132	−	0.615506i	$-0.788951\pi$
$757$	3.82380	−	6.62301i	0.138978	−	0.240718i	0.927110	+	0.374789i	$0.122285\pi$
$758$		0			0
$759$	11.6061	−	3.85904i	0.421275	−	0.140074i
$760$		0			0
$761$	−19.4786	+	33.7379i	−0.706098	+	1.22300i	0.260196	+	0.965556i	$0.416213\pi$
$761$	−19.4786	+	33.7379i	−0.706098	+	1.22300i	−0.966294	+	0.257442i	$0.917121\pi$
$762$		0			0
$763$	16.9416			0.613325
$764$		0			0
$765$	−35.1689	+	26.2943i	−1.27153	+	0.950674i
$766$		0			0
$767$	−9.47421	−	4.68928i	−0.342094	−	0.169320i
$768$		0			0
$769$	−20.8158			−0.750637			−0.375318	−	0.926896i	$-0.622467\pi$
$769$	−20.8158			−0.750637			−0.375318	+	0.926896i	$0.622467\pi$
$770$		0			0
$771$	6.52160	−	31.7482i	0.234870	−	1.14338i
$772$		0			0
$773$	−12.2723	−	21.2563i	−0.441405	−	0.764537i	0.556389	−	0.830922i	$-0.312187\pi$
$773$	−12.2723	−	21.2563i	−0.441405	−	0.764537i	−0.997794	+	0.0663855i	$0.978853\pi$
$774$		0			0
$775$	−20.4466			−0.734464
$776$		0			0
$777$	2.21381	+	1.96607i	0.0794201	+	0.0705324i
$778$		0			0
$779$	7.56351	+	13.1004i	0.270991	+	0.469370i
$780$		0			0
$781$	1.93838	−	3.35737i	0.0693606	−	0.120136i
$782$		0			0
$783$	6.91768	+	0.583819i	0.247218	+	0.0208640i
$784$		0			0
$785$	35.9953	−	62.3457i	1.28473	−	2.22521i
$786$		0			0
$787$	−16.2635	+	28.1691i	−0.579730	+	1.00412i	0.415780	+	0.909465i	$0.363508\pi$
$787$	−16.2635	+	28.1691i	−0.579730	+	1.00412i	−0.995510	+	0.0946561i	$0.969825\pi$
$788$		0			0
$789$	−33.8658	+	11.2604i	−1.20565	+	0.400881i
$790$		0			0
$791$	−11.9589	+	20.7134i	−0.425208	+	0.736483i
$792$		0			0
$793$	3.30876	+	51.6309i	0.117498	+	1.83347i
$794$		0			0
$795$	−54.1628	+	18.0091i	−1.92096	+	0.638719i
$796$		0			0
$797$	25.9161	−	44.8880i	0.917995	−	1.59001i	0.115539	−	0.993303i	$-0.463140\pi$
$797$	25.9161	−	44.8880i	0.917995	−	1.59001i	0.802456	−	0.596711i	$-0.203526\pi$
$798$		0			0
$799$	−44.8549			−1.58685
$800$		0			0
$801$	−22.1124	+	16.5325i	−0.781302	+	0.584148i
$802$		0			0
$803$	2.41011	+	4.17443i	0.0850509	+	0.147312i
$804$		0			0
$805$	11.5939	+	20.0812i	0.408632	+	0.707771i
$806$		0			0
$807$	29.0135	−	9.64699i	1.02132	−	0.339590i
$808$		0			0
$809$	−15.9371	+	27.6039i	−0.560319	+	0.970500i	0.437150	+	0.899389i	$0.355988\pi$
$809$	−15.9371	+	27.6039i	−0.560319	+	0.970500i	−0.997468	+	0.0711115i	$0.977345\pi$
$810$		0			0
$811$	−7.14832			−0.251011			−0.125506	−	0.992093i	$-0.540055\pi$
$811$	−7.14832			−0.251011			−0.125506	+	0.992093i	$0.540055\pi$
$812$		0			0
$813$	−20.3282	−	18.0533i	−0.712942	−	0.633158i
$814$		0			0
$815$	−19.5883	+	33.9279i	−0.686148	+	1.18844i
$816$		0			0
$817$	−12.1703	−	21.0795i	−0.425784	−	0.737480i
$818$		0			0
$819$	6.75481	−	19.0230i	0.236032	−	0.664718i
$820$		0			0
$821$	5.17418	+	8.96194i	0.180580	+	0.312774i	0.942078	−	0.335393i	$-0.108869\pi$
$821$	5.17418	+	8.96194i	0.180580	+	0.312774i	−0.761498	+	0.648167i	$0.775536\pi$
$822$		0			0
$823$	−19.4635	+	33.7119i	−0.678457	+	1.17512i	0.296989	+	0.954881i	$0.404018\pi$
$823$	−19.4635	+	33.7119i	−0.678457	+	1.17512i	−0.975446	+	0.220240i	$0.929316\pi$
$824$		0			0
$825$	−3.85779	+	18.7803i	−0.134311	+	0.653847i
$826$		0			0
$827$	19.5838			0.680994			0.340497	−	0.940246i	$-0.389405\pi$
$827$	19.5838			0.680994			0.340497	+	0.940246i	$0.389405\pi$
$828$		0			0
$829$	−8.13898	+	14.0971i	−0.282678	+	0.489613i	−0.972044	−	0.234801i	$-0.924556\pi$
$829$	−8.13898	+	14.0971i	−0.282678	+	0.489613i	0.689365	+	0.724414i	$0.257890\pi$
$830$		0			0
$831$	3.13296	−	15.2517i	0.108681	−	0.529077i
$832$		0			0
$833$	7.79669	+	13.5043i	0.270139	+	0.467895i
$834$		0			0
$835$	−23.4770	−	40.6634i	−0.812455	−	1.40721i
$836$		0			0
$837$	−17.9455	−	1.51451i	−0.620286	−	0.0523491i
$838$		0			0
$839$	51.0299			1.76175			0.880873	−	0.473352i	$-0.156956\pi$
$839$	51.0299			1.76175			0.880873	+	0.473352i	$0.156956\pi$
$840$		0			0
$841$	13.6075	−	23.5689i	0.469224	−	0.812720i
$842$		0			0
$843$	−23.7738	−	21.1133i	−0.818813	−	0.727181i
$844$		0			0
$845$	−26.0281	−	34.1253i	−0.895394	−	1.17395i
$846$		0			0
$847$	6.97923	−	12.0884i	0.239809	−	0.415362i
$848$		0			0
$849$	−1.05647	+	5.14306i	−0.0362579	+	0.176509i
$850$		0			0
$851$	−1.72359	+	2.98535i	−0.0590840	+	0.102337i
$852$		0			0
$853$	16.9863	−	29.4212i	0.581601	−	1.00736i	−0.413689	−	0.910418i	$-0.635760\pi$
$853$	16.9863	−	29.4212i	0.581601	−	1.00736i	0.995290	−	0.0969437i	$-0.0309067\pi$
$854$		0			0
$855$	51.5582	−	38.5480i	1.76325	−	1.31831i
$856$		0			0
$857$	7.27876	−	12.6072i	0.248638	−	0.430653i	−0.714510	−	0.699625i	$-0.753350\pi$
$857$	7.27876	−	12.6072i	0.248638	−	0.430653i	0.963148	+	0.268972i	$0.0866838\pi$
$858$		0			0
$859$	−2.44195	−	4.22958i	−0.0833181	−	0.144311i	0.821355	−	0.570417i	$-0.193218\pi$
$859$	−2.44195	−	4.22958i	−0.0833181	−	0.144311i	−0.904673	+	0.426106i	$0.859885\pi$
$860$		0			0
$861$	1.51373	−	7.36908i	0.0515878	−	0.251138i
$862$		0			0
$863$	44.0094			1.49810			0.749048	−	0.662515i	$-0.230511\pi$
$863$	44.0094			1.49810			0.749048	+	0.662515i	$0.230511\pi$
$864$		0			0
$865$	−29.4701	−	51.0438i	−1.00201	−	1.73554i
$866$		0			0
$867$	3.44096	+	3.05589i	0.116861	+	0.103783i
$868$		0			0
$869$	26.4619			0.897658
$870$		0			0
$871$	2.06617	+	32.2412i	0.0700096	+	1.09245i
$872$		0			0
$873$	28.5499	+	12.2460i	0.966269	+	0.414464i
$874$		0			0
$875$	−5.54145			−0.187335
$876$		0			0
$877$	−0.444327	+	0.769597i	−0.0150039	+	0.0259874i	−0.873430	−	0.486950i	$-0.838109\pi$
$877$	−0.444327	+	0.769597i	−0.0150039	+	0.0259874i	0.858426	+	0.512937i	$0.171443\pi$
$878$		0			0
$879$	3.83094	+	3.40222i	0.129214	+	0.114754i
$880$		0			0
$881$	−18.0334	+	31.2348i	−0.607561	+	1.05233i	0.384080	+	0.923300i	$0.374519\pi$
$881$	−18.0334	+	31.2348i	−0.607561	+	1.05233i	−0.991641	+	0.129027i	$0.958815\pi$
$882$		0			0
$883$	−42.4663			−1.42910			−0.714552	−	0.699582i	$-0.753369\pi$
$883$	−42.4663			−1.42910			−0.714552	+	0.699582i	$0.753369\pi$
$884$		0			0
$885$	−3.37345	+	16.4225i	−0.113397	+	0.552036i
$886$		0			0
$887$	−4.02334			−0.135091			−0.0675453	−	0.997716i	$-0.521517\pi$
$887$	−4.02334			−0.135091			−0.0675453	+	0.997716i	$0.521517\pi$
$888$		0			0
$889$	−3.44211	+	5.96192i	−0.115445	+	0.199956i
$890$		0			0
$891$	−4.77697	+	16.1973i	−0.160034	+	0.542629i
$892$		0			0
$893$	65.7581			2.20051
$894$		0			0
$895$	−20.1005			−0.671884
$896$		0			0
$897$	23.2774	+	3.24708i	0.777210	+	0.108417i
$898$		0			0
$899$	2.31528	−	4.01018i	0.0772189	−	0.133747i
$900$		0			0
$901$	22.1278	+	38.3265i	0.737184	+	1.27684i
$902$		0			0
$903$	−2.43571	+	11.8574i	−0.0810554	+	0.394591i
$904$		0			0
$905$	−9.46573	−	16.3951i	−0.314652	−	0.544993i
$906$		0			0
$907$	13.7481	+	23.8125i	0.456500	+	0.790681i	0.998773	−	0.0495215i	$-0.0157696\pi$
$907$	13.7481	+	23.8125i	0.456500	+	0.790681i	−0.542273	+	0.840202i	$0.682436\pi$
$908$		0			0
$909$	5.19701	+	43.6874i	0.172374	+	1.44902i
$910$		0			0
$911$	−3.01144	+	5.21596i	−0.0997734	+	0.172813i	−0.911591	−	0.411099i	$-0.865145\pi$
$911$	−3.01144	+	5.21596i	−0.0997734	+	0.172813i	0.811817	+	0.583911i	$0.198478\pi$
$912$		0			0
$913$	5.07664			0.168012
$914$		0			0
$915$	77.8609	−	25.8888i	2.57400	−	0.855856i
$916$		0			0
$917$	−15.6308	−	27.0733i	−0.516175	−	0.894040i
$918$		0			0
$919$	−9.16320	−	15.8711i	−0.302266	−	0.523540i	0.674383	−	0.738382i	$-0.264410\pi$
$919$	−9.16320	−	15.8711i	−0.302266	−	0.523540i	−0.976649	+	0.214842i	$0.931076\pi$
$920$		0			0
$921$	2.57581	−	12.5395i	0.0848759	−	0.413190i
$922$		0			0
$923$	6.20008	−	4.12975i	0.204078	−	0.135932i
$924$		0			0
$925$	−2.70181	−	4.67968i	−0.0888351	−	0.153867i
$926$		0			0
$927$	2.63196	+	22.1250i	0.0864450	+	0.726680i
$928$		0			0
$929$	−11.1744			−0.366621			−0.183310	−	0.983055i	$-0.558681\pi$
$929$	−11.1744			−0.366621			−0.183310	+	0.983055i	$0.558681\pi$
$930$		0			0
$931$	−11.4301	−	19.7975i	−0.374606	−	0.648836i
$932$		0			0
$933$	−23.2256	+	7.72251i	−0.760371	+	0.252824i
$934$		0			0
$935$	27.4644			0.898181
$936$		0			0
$937$	27.5887			0.901285			0.450642	−	0.892705i	$-0.351195\pi$
$937$	27.5887			0.901285			0.450642	+	0.892705i	$0.351195\pi$
$938$		0			0
$939$	−14.7450	−	13.0949i	−0.481186	−	0.427337i
$940$		0			0
$941$	−16.1229	−	27.9256i	−0.525591	−	0.910350i	−0.999556	−	0.0298061i	$-0.990511\pi$
$941$	−16.1229	−	27.9256i	−0.525591	−	0.910350i	0.473965	−	0.880544i	$-0.342822\pi$
$942$		0			0
$943$	8.75875			0.285224
$944$		0			0
$945$	−31.9017	−	2.69235i	−1.03776	−	0.0875822i
$946$		0			0
$947$	3.31127	+	5.73529i	0.107602	+	0.186372i	0.914798	−	0.403911i	$-0.132350\pi$
$947$	3.31127	+	5.73529i	0.107602	+	0.186372i	−0.807196	+	0.590283i	$0.799016\pi$
$948$		0			0
$949$	0.592372	+	9.24354i	0.0192292	+	0.300058i
$950$		0			0
$951$	−14.4653	−	12.8465i	−0.469070	−	0.416577i
$952$		0			0
$953$	26.5364	+	45.9624i	0.859598	+	1.48887i	0.872313	+	0.488948i	$0.162619\pi$
$953$	26.5364	+	45.9624i	0.859598	+	1.48887i	−0.0127147	+	0.999919i	$0.504047\pi$
$954$		0			0
$955$	20.2592	+	35.0899i	0.655572	+	1.13548i
$956$		0			0
$957$	−3.24654	−	2.88322i	−0.104946	−	0.0932014i
$958$		0			0
$959$	−3.91800			−0.126519
$960$		0			0
$961$	9.49383	−	16.4438i	0.306253	−	0.530445i
$962$		0			0
$963$	−22.9355	+	17.1479i	−0.739085	+	0.552584i
$964$		0			0
$965$	−41.0256	−	71.0585i	−1.32066	−	2.28745i
$966$		0			0
$967$	8.71147	+	15.0887i	0.280142	+	0.485220i	0.971419	−	0.237369i	$-0.0762851\pi$
$967$	8.71147	+	15.0887i	0.280142	+	0.485220i	−0.691278	+	0.722589i	$0.742952\pi$
$968$		0			0
$969$	−37.3205	−	33.1440i	−1.19891	−	1.06474i
$970$		0			0
$971$	−8.14921	−	14.1148i	−0.261520	−	0.452967i	0.705126	−	0.709082i	$-0.250891\pi$
$971$	−8.14921	−	14.1148i	−0.261520	−	0.452967i	−0.966646	+	0.256116i	$0.917557\pi$
$972$		0			0
$973$	−7.32358	+	12.6848i	−0.234783	+	0.406656i
$974$		0			0
$975$	−22.6522	+	29.0549i	−0.725452	+	0.930502i
$976$		0			0
$977$	47.1150			1.50734			0.753671	−	0.657251i	$-0.228281\pi$
$977$	47.1150			1.50734			0.753671	+	0.657251i	$0.228281\pi$
$978$		0			0
$979$	17.2682			0.551893
$980$		0			0
$981$	−25.0282	−	10.7354i	−0.799089	−	0.342755i
$982$		0			0
$983$	3.42744	−	5.93649i	0.109318	−	0.189345i	−0.806176	−	0.591676i	$-0.798467\pi$
$983$	3.42744	−	5.93649i	0.109318	−	0.189345i	0.915494	+	0.402331i	$0.131800\pi$
$984$		0			0
$985$	−25.1443			−0.801163
$986$		0			0
$987$	−24.4520	−	21.7156i	−0.778316	−	0.691216i
$988$		0			0
$989$	−14.0935			−0.448148
$990$		0			0
$991$	−0.988777	+	1.71261i	−0.0314095	+	0.0544029i	−0.881303	−	0.472552i	$-0.843333\pi$
$991$	−0.988777	+	1.71261i	−0.0314095	+	0.0544029i	0.849893	+	0.526955i	$0.176666\pi$
$992$		0			0
$993$	−5.93575	+	28.8962i	−0.188365	+	0.916992i
$994$		0			0
$995$	−38.0576	+	65.9177i	−1.20651	+	2.08973i
$996$		0			0
$997$	−51.9813			−1.64626			−0.823132	−	0.567850i	$-0.807775\pi$
$997$	−51.9813			−1.64626			−0.823132	+	0.567850i	$0.807775\pi$
$998$		0			0
$999$	−2.02468	−	4.30736i	−0.0640581	−	0.136279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.529.12	yes	40
3.2	odd	2		2808.2.s.f.1153.3		40
9.4	even	3		936.2.r.f.841.16	yes	40
9.5	odd	6		2808.2.r.f.2089.3		40
13.3	even	3		936.2.r.f.601.16	✓	40
39.29	odd	6		2808.2.r.f.289.3		40
117.68	odd	6		2808.2.s.f.1225.3		40
117.94	even	3	inner	936.2.s.f.913.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.16	✓	40	13.3	even	3
936.2.r.f.841.16	yes	40	9.4	even	3
936.2.s.f.529.12	yes	40	1.1	even	1	trivial
936.2.s.f.913.12	yes	40	117.94	even	3	inner
2808.2.r.f.289.3		40	39.29	odd	6
2808.2.r.f.2089.3		40	9.5	odd	6
2808.2.s.f.1153.3		40	3.2	odd	2
2808.2.s.f.1225.3		40	117.68	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.348515 - 1.69663i) q^{3} +(1.65071 + 2.85912i) q^{5} +1.86626 q^{7} +(-2.75708 - 1.18260i) q^{9} +(0.938166 + 1.62495i) q^{11} +(0.230589 + 3.59817i) q^{13} +(5.42615 - 1.80420i) q^{15} +(-2.21681 - 3.83963i) q^{17} +(3.24988 + 5.62896i) q^{19} +(0.650419 - 3.16634i) q^{21} +3.76346 q^{23} +(-2.94970 + 5.10903i) q^{25} +(-2.96731 + 4.26557i) q^{27} +(-0.668020 - 1.15705i) q^{29} +(1.73294 + 3.00154i) q^{31} +(3.08390 - 1.02540i) q^{33} +(3.08066 + 5.33585i) q^{35} +(-0.457982 + 0.793248i) q^{37} +(6.18511 + 0.862792i) q^{39} +2.32732 q^{41} -3.74484 q^{43} +(-1.16995 - 9.83493i) q^{45} +(5.05850 - 8.76158i) q^{47} -3.51708 q^{49} +(-7.28700 + 2.42293i) q^{51} -9.98182 q^{53} +(-3.09728 + 5.36465i) q^{55} +(10.6829 - 3.55206i) q^{57} +(-1.46596 + 2.53912i) q^{59} +14.3492 q^{61} +(-5.14542 - 2.20703i) q^{63} +(-9.90695 + 6.59882i) q^{65} +8.96043 q^{67} +(1.31162 - 6.38518i) q^{69} +(-1.03307 - 1.78932i) q^{71} +2.56896 q^{73} +(7.64009 + 6.78510i) q^{75} +(1.75086 + 3.03258i) q^{77} +(7.05149 - 12.2135i) q^{79} +(6.20293 + 6.52102i) q^{81} +(1.35281 - 2.34313i) q^{83} +(7.31863 - 12.6762i) q^{85} +(-2.19589 + 0.730133i) q^{87} +(4.60157 - 7.97016i) q^{89} +(0.430338 + 6.71512i) q^{91} +(5.69645 - 1.89407i) q^{93} +(-10.7292 + 18.5836i) q^{95} -10.3552 q^{97} +(-0.664931 - 5.58959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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