LMFDB - Embedded newform 740.2.bp.a.169.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(169,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.169"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.bp (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.15
Character	$\chi$	$=$	740.169
Dual form			740.2.bp.a.289.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.583105 + 1.60207i) q^{3} +(-1.38719 + 1.75377i) q^{5} +(0.0792084 + 0.0139666i) q^{7} +(0.0715239 - 0.0600157i) q^{9} +(1.18626 + 2.05465i) q^{11} +(3.75018 + 3.14678i) q^{13} +(-3.61853 - 1.19974i) q^{15} +(-4.04619 + 3.39516i) q^{17} +(-1.65640 - 4.55091i) q^{19} +(0.0238114 + 0.135041i) q^{21} +(-1.11475 + 1.93081i) q^{23} +(-1.15141 - 4.86562i) q^{25} +(4.56728 + 2.63692i) q^{27} +(-7.71310 + 4.45316i) q^{29} +8.47122i q^{31} +(-2.59998 + 3.09854i) q^{33} +(-0.134371 + 0.119539i) q^{35} +(1.01674 - 5.99719i) q^{37} +(-2.85460 + 7.84294i) q^{39} +(-3.20670 - 2.69074i) q^{41} -5.46918 q^{43} +(0.00603632 + 0.208690i) q^{45} +(-1.08101 - 0.624120i) q^{47} +(-6.57177 - 2.39193i) q^{49} +(-7.79862 - 4.50254i) q^{51} +(10.0249 - 1.76766i) q^{53} +(-5.24895 - 0.769780i) q^{55} +(6.32502 - 5.30732i) q^{57} +(-0.0395489 + 0.00697353i) q^{59} +(6.95139 - 8.28434i) q^{61} +(0.00650351 - 0.00375480i) q^{63} +(-10.7209 + 2.21177i) q^{65} +(1.49255 + 0.263177i) q^{67} +(-3.74331 - 0.660047i) q^{69} +(11.6356 - 4.23500i) q^{71} +12.8456i q^{73} +(7.12366 - 4.68180i) q^{75} +(0.0652649 + 0.179314i) q^{77} +(16.9092 + 2.98155i) q^{79} +(-1.51268 + 8.57884i) q^{81} +(4.82941 + 5.75547i) q^{83} +(-0.341481 - 11.8058i) q^{85} +(-11.6318 - 9.76025i) q^{87} +(-1.10202 + 0.194316i) q^{89} +(0.253096 + 0.301628i) q^{91} +(-13.5715 + 4.93961i) q^{93} +(10.2790 + 3.40805i) q^{95} +(-7.09258 + 12.2847i) q^{97} +(0.208157 + 0.0757630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{5} + 6 q^{9} + 12 q^{11} + 3 q^{15} + 6 q^{19} - 12 q^{21} - 33 q^{25} - 48 q^{35} + 24 q^{39} + 30 q^{41} - 27 q^{45} + 6 q^{49} - 3 q^{55} - 42 q^{59} + 48 q^{61} - 18 q^{65} - 108 q^{69}+ \cdots + 90 q^{99}+O(q^{100}) $ 120 * q + 3 * q^5 + 6 * q^9 + 12 * q^11 + 3 * q^15 + 6 * q^19 - 12 * q^21 - 33 * q^25 - 48 * q^35 + 24 * q^39 + 30 * q^41 - 27 * q^45 + 6 * q^49 - 3 * q^55 - 42 * q^59 + 48 * q^61 - 18 * q^65 - 108 * q^69 - 18 * q^71 - 12 * q^75 - 48 * q^79 + 108 * q^81 - 33 * q^85 - 84 * q^89 - 30 * q^91 + 99 * q^95 + 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$	$1$

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
$3$	0.583105	+	1.60207i	0.336656	+	0.924954i	0.986336	+	0.164747i	$0.0526806\pi$
$3$	0.583105	+	1.60207i	0.336656	+	0.924954i	−0.649680	+	0.760208i	$0.725097\pi$
$4$		0			0
$5$	−1.38719	+	1.75377i	−0.620370	+	0.784309i
$5$	−1.38719	+	1.75377i	−0.620370	+	0.784309i
$6$		0			0
$7$	0.0792084	+	0.0139666i	0.0299379	+	0.00527887i	0.188597	−	0.982055i	$-0.439606\pi$
$7$	0.0792084	+	0.0139666i	0.0299379	+	0.00527887i	−0.158659	+	0.987333i	$0.550717\pi$
$8$		0			0
$9$	0.0715239	−	0.0600157i	0.0238413	−	0.0200052i
$10$		0			0
$11$	1.18626	+	2.05465i	0.357669	+	0.619502i	0.987571	−	0.157173i	$-0.0502381\pi$
$11$	1.18626	+	2.05465i	0.357669	+	0.619502i	−0.629902	+	0.776675i	$0.716905\pi$
$12$		0			0
$13$	3.75018	+	3.14678i	1.04011	+	0.872758i	0.992020	−	0.126084i	$-0.0402410\pi$
$13$	3.75018	+	3.14678i	1.04011	+	0.872758i	0.0480934	+	0.998843i	$0.484685\pi$
$14$		0			0
$15$	−3.61853	−	1.19974i	−0.934301	−	0.309772i
$16$		0			0
$17$	−4.04619	+	3.39516i	−0.981345	+	0.823446i	−0.984292	−	0.176549i	$-0.943506\pi$
$17$	−4.04619	+	3.39516i	−0.981345	+	0.823446i	0.00294680	+	0.999996i	$0.499062\pi$
$18$		0			0
$19$	−1.65640	−	4.55091i	−0.380004	−	1.04405i	−0.971354	−	0.237637i	$-0.923627\pi$
$19$	−1.65640	−	4.55091i	−0.380004	−	1.04405i	0.591351	−	0.806415i	$-0.298595\pi$
$20$		0			0
$21$	0.0238114	+	0.135041i	0.00519607	+	0.0294684i
$22$		0			0
$23$	−1.11475	+	1.93081i	−0.232442	+	0.402602i	−0.958526	−	0.285004i	$-0.908005\pi$
$23$	−1.11475	+	1.93081i	−0.232442	+	0.402602i	0.726084	+	0.687606i	$0.241338\pi$
$24$		0			0
$25$	−1.15141	−	4.86562i	−0.230281	−	0.973124i
$26$		0			0
$27$	4.56728	+	2.63692i	0.878973	+	0.507475i
$28$		0			0
$29$	−7.71310	+	4.45316i	−1.43229	+	0.826931i	−0.997295	−	0.0735032i	$-0.976582\pi$
$29$	−7.71310	+	4.45316i	−1.43229	+	0.826931i	−0.434992	+	0.900434i	$0.643249\pi$
$30$		0			0
$31$			8.47122i			1.52148i	0.649059	+	0.760738i	$0.275163\pi$
$31$			8.47122i			1.52148i	−0.649059	+	0.760738i	$0.724837\pi$
$32$		0			0
$33$	−2.59998	+	3.09854i	−0.452599	+	0.539387i
$34$		0			0
$35$	−0.134371	+	0.119539i	−0.0227129	+	0.0202057i
$36$		0			0
$37$	1.01674	−	5.99719i	0.167152	−	0.985931i
$37$	1.01674	−	5.99719i	0.167152	−	0.985931i
$38$		0			0
$39$	−2.85460	+	7.84294i	−0.457101	+	1.25588i
$40$		0			0
$41$	−3.20670	−	2.69074i	−0.500802	−	0.420223i	0.357077	−	0.934075i	$-0.383773\pi$
$41$	−3.20670	−	2.69074i	−0.500802	−	0.420223i	−0.857879	+	0.513852i	$0.828218\pi$
$42$		0			0
$43$	−5.46918			−0.834042			−0.417021	−	0.908897i	$-0.636926\pi$
$43$	−5.46918			−0.834042			−0.417021	+	0.908897i	$0.636926\pi$
$44$		0			0
$45$	0.00603632	+	0.208690i	0.000899841	+	0.0311096i
$46$		0			0
$47$	−1.08101	−	0.624120i	−0.157681	−	0.0910373i	0.419083	−	0.907948i	$-0.362352\pi$
$47$	−1.08101	−	0.624120i	−0.157681	−	0.0910373i	−0.576764	+	0.816911i	$0.695685\pi$
$48$		0			0
$49$	−6.57177	−	2.39193i	−0.938824	−	0.341704i
$50$		0			0
$51$	−7.79862	−	4.50254i	−1.09203	−	0.630481i
$52$		0			0
$53$	10.0249	−	1.76766i	1.37703	−	0.242807i	0.564356	−	0.825531i	$-0.309124\pi$
$53$	10.0249	−	1.76766i	1.37703	−	0.242807i	0.812670	+	0.582724i	$0.198013\pi$
$54$		0			0
$55$	−5.24895	−	0.769780i	−0.707768	−	0.103797i
$56$		0			0
$57$	6.32502	−	5.30732i	0.837769	−	0.702972i
$58$		0			0
$59$	−0.0395489	+	0.00697353i	−0.00514882	+	0.000907876i	−0.176222	−	0.984350i	$-0.556388\pi$
$59$	−0.0395489	+	0.00697353i	−0.00514882	+	0.000907876i	0.171073	+	0.985258i	$0.445277\pi$
$60$		0			0
$61$	6.95139	−	8.28434i	0.890034	−	1.06070i	−0.107751	−	0.994178i	$-0.534365\pi$
$61$	6.95139	−	8.28434i	0.890034	−	1.06070i	0.997785	−	0.0665230i	$-0.0211906\pi$
$62$		0			0
$63$	0.00650351	−	0.00375480i	0.000819365	−	0.000473060i
$64$		0			0
$65$	−10.7209	+	2.21177i	−1.32977	+	0.274336i
$66$		0			0
$67$	1.49255	+	0.263177i	0.182344	+	0.0321522i	0.264074	−	0.964502i	$-0.414934\pi$
$67$	1.49255	+	0.263177i	0.182344	+	0.0321522i	−0.0817305	+	0.996654i	$0.526045\pi$
$68$		0			0
$69$	−3.74331	−	0.660047i	−0.450642	−	0.0794603i
$70$		0			0
$71$	11.6356	−	4.23500i	1.38089	−	0.502602i	0.458440	−	0.888725i	$-0.348408\pi$
$71$	11.6356	−	4.23500i	1.38089	−	0.502602i	0.922447	+	0.386123i	$0.126186\pi$
$72$		0			0
$73$			12.8456i			1.50346i	0.659470	+	0.751731i	$0.270781\pi$
$73$			12.8456i			1.50346i	−0.659470	+	0.751731i	$0.729219\pi$
$74$		0			0
$75$	7.12366	−	4.68180i	0.822570	−	0.540607i
$76$		0			0
$77$	0.0652649	+	0.179314i	0.00743762	+	0.0204347i
$78$		0			0
$79$	16.9092	+	2.98155i	1.90243	+	0.335451i	0.996183	−	0.0872879i	$-0.0278200\pi$
$79$	16.9092	+	2.98155i	1.90243	+	0.335451i	0.906252	+	0.422739i	$0.138931\pi$
$80$		0			0
$81$	−1.51268	+	8.57884i	−0.168076	+	0.953204i
$82$		0			0
$83$	4.82941	+	5.75547i	0.530097	+	0.631745i	0.962937	−	0.269726i	$-0.0869331\pi$
$83$	4.82941	+	5.75547i	0.530097	+	0.631745i	−0.432840	+	0.901471i	$0.642489\pi$
$84$		0			0
$85$	−0.341481	−	11.8058i	−0.0370389	−	1.28052i
$86$		0			0
$87$	−11.6318	−	9.76025i	−1.24706	−	1.04641i
$88$		0			0
$89$	−1.10202	+	0.194316i	−0.116814	+	0.0205974i	−0.231749	−	0.972776i	$-0.574445\pi$
$89$	−1.10202	+	0.194316i	−0.116814	+	0.0205974i	0.114936	+	0.993373i	$0.463334\pi$
$90$		0			0
$91$	0.253096	+	0.301628i	0.0265317	+	0.0316192i
$92$		0			0
$93$	−13.5715	+	4.93961i	−1.40730	+	0.512214i
$94$		0			0
$95$	10.2790	+	3.40805i	1.05460	+	0.349658i
$96$		0			0
$97$	−7.09258	+	12.2847i	−0.720142	+	1.24732i	0.240800	+	0.970575i	$0.422590\pi$
$97$	−7.09258	+	12.2847i	−0.720142	+	1.24732i	−0.960942	+	0.276749i	$0.910743\pi$
$98$		0			0
$99$	0.208157	+	0.0757630i	0.0209206	+	0.00761447i
$100$		0			0
$101$	−5.15022	+	8.92044i	−0.512466	+	0.887617i	0.487430	+	0.873162i	$0.337935\pi$
$101$	−5.15022	+	8.92044i	−0.512466	+	0.887617i	−0.999896	+	0.0144548i	$0.995399\pi$
$102$		0			0
$103$	3.61083	+	6.25414i	0.355786	+	0.616239i	0.987252	−	0.159164i	$-0.0508799\pi$
$103$	3.61083	+	6.25414i	0.355786	+	0.616239i	−0.631466	+	0.775403i	$0.717547\pi$
$104$		0			0
$105$	−0.269862	−	0.145568i	−0.0263358	−	0.0142060i
$106$		0			0
$107$	5.12605	−	6.10899i	0.495554	−	0.590578i	−0.459067	−	0.888402i	$-0.651816\pi$
$107$	5.12605	−	6.10899i	0.495554	−	0.590578i	0.954621	+	0.297823i	$0.0962607\pi$
$108$		0			0
$109$	5.36181	−	14.7315i	0.513568	−	1.41102i	−0.363925	−	0.931428i	$-0.618563\pi$
$109$	5.36181	−	14.7315i	0.513568	−	1.41102i	0.877493	−	0.479589i	$-0.159214\pi$
$110$		0			0
$111$	10.2008	−	1.86810i	0.968214	−	0.177312i
$112$		0			0
$113$	2.01058	+	0.731790i	0.189139	+	0.0688410i	0.434853	−	0.900501i	$-0.356800\pi$
$113$	2.01058	+	0.731790i	0.189139	+	0.0688410i	−0.245714	+	0.969342i	$0.579022\pi$
$114$		0			0
$115$	−1.83982	−	4.63343i	−0.171564	−	0.432069i
$116$		0			0
$117$	0.457083			0.0422574
$118$		0			0
$119$	−0.367911	+	0.212413i	−0.0337263	+	0.0194719i
$120$		0			0
$121$	2.68560	−	4.65159i	0.244145	−	0.422872i
$122$		0			0
$123$	2.44090	−	6.70633i	0.220089	−	0.604689i
$124$		0			0
$125$	10.1304	+	4.73024i	0.906090	+	0.423086i
$126$		0			0
$127$	5.24797	−	0.925359i	0.465682	−	0.0821124i	0.0641163	−	0.997942i	$-0.479577\pi$
$127$	5.24797	−	0.925359i	0.465682	−	0.0821124i	0.401566	+	0.915830i	$0.368466\pi$
$128$		0			0
$129$	−3.18910	−	8.76199i	−0.280785	−	0.771450i
$130$		0			0
$131$	7.54891	+	8.99644i	0.659551	+	0.786023i	0.987321	−	0.158735i	$-0.0507415\pi$
$131$	7.54891	+	8.99644i	0.659551	+	0.786023i	−0.327770	+	0.944758i	$0.606297\pi$
$132$		0			0
$133$	−0.0676398	−	0.383605i	−0.00586512	−	0.0332627i
$134$		0			0
$135$	−10.9602	+	4.35204i	−0.943306	+	0.374564i
$136$		0			0
$137$	−8.88650	+	5.13062i	−0.759225	+	0.438339i	−0.829017	−	0.559223i	$-0.811100\pi$
$137$	−8.88650	+	5.13062i	−0.759225	+	0.438339i	0.0697927	+	0.997562i	$0.477766\pi$
$138$		0			0
$139$	9.55309	−	8.01599i	0.810283	−	0.679908i	−0.140393	−	0.990096i	$-0.544836\pi$
$139$	9.55309	−	8.01599i	0.810283	−	0.679908i	0.950675	+	0.310188i	$0.100392\pi$
$140$		0			0
$141$	0.369542	−	2.09577i	0.0311210	−	0.176496i
$142$		0			0
$143$	−2.01686	+	11.4382i	−0.168659	+	0.956511i
$144$		0			0
$145$	2.88973	−	19.7044i	0.239979	−	1.63636i
$146$		0			0
$147$		−	11.9232i		−	0.983406i
$148$		0			0
$149$	−8.41838			−0.689660			−0.344830	−	0.938665i	$-0.612063\pi$
$149$	−8.41838			−0.689660			−0.344830	+	0.938665i	$0.612063\pi$
$150$		0			0
$151$	10.8015	−	3.93144i	0.879017	−	0.319936i	0.137204	−	0.990543i	$-0.456188\pi$
$151$	10.8015	−	3.93144i	0.879017	−	0.319936i	0.741813	+	0.670607i	$0.233966\pi$
$152$		0			0
$153$	−0.0856367	+	0.485670i	−0.00692331	+	0.0392641i
$154$		0			0
$155$	−14.8566	−	11.7512i	−1.19331	−	0.943879i
$156$		0			0
$157$	−5.44329	−	6.48707i	−0.434422	−	0.517724i	0.503771	−	0.863838i	$-0.331946\pi$
$157$	−5.44329	−	6.48707i	−0.434422	−	0.517724i	−0.938193	+	0.346113i	$0.887501\pi$
$158$		0			0
$159$	8.67748	+	15.0298i	0.688169	+	1.19194i
$160$		0			0
$161$	−0.115265	+	0.137367i	−0.00908413	+	0.0108261i
$162$		0			0
$163$	3.03781	+	17.2283i	0.237939	+	1.34942i	0.836334	+	0.548220i	$0.184694\pi$
$163$	3.03781	+	17.2283i	0.237939	+	1.34942i	−0.598395	+	0.801202i	$0.704194\pi$
$164$		0			0
$165$	−1.82745	−	8.85804i	−0.142267	−	0.689597i
$166$		0			0
$167$	13.2056	−	4.80643i	1.02188	−	0.371933i	0.223894	−	0.974613i	$-0.428123\pi$
$167$	13.2056	−	4.80643i	1.02188	−	0.371933i	0.797982	+	0.602681i	$0.205901\pi$
$168$		0			0
$169$	1.90423	+	10.7994i	0.146480	+	0.830727i
$170$		0			0
$171$	−0.391598	−	0.226089i	−0.0299463	−	0.0172895i
$172$		0			0
$173$	−3.11090	+	8.54714i	−0.236518	+	0.649827i	0.763474	+	0.645838i	$0.223492\pi$
$173$	−3.11090	+	8.54714i	−0.236518	+	0.649827i	−0.999992	+	0.00398872i	$0.998730\pi$
$174$		0			0
$175$	−0.0232449	−	0.401479i	−0.00175715	−	0.0303490i
$176$		0			0
$177$	−0.0342332	−	0.0592936i	−0.00257312	−	0.00445678i
$178$		0			0
$179$		−	8.50177i		−	0.635452i	−0.948183	−	0.317726i	$-0.897081\pi$
$179$		−	8.50177i		−	0.635452i	0.948183	−	0.317726i	$-0.102919\pi$
$180$		0			0
$181$	1.55177	+	1.30209i	0.115342	+	0.0967833i	0.698634	−	0.715479i	$-0.253791\pi$
$181$	1.55177	+	1.30209i	0.115342	+	0.0967833i	−0.583293	+	0.812262i	$0.698236\pi$
$182$		0			0
$183$	17.3255	+	6.30595i	1.28073	+	0.466149i
$184$		0			0
$185$	9.10726	+	10.1024i	0.669579	+	0.742741i
$186$		0			0
$187$	−11.7757	−	4.28600i	−0.861123	−	0.313423i
$188$		0			0
$189$	0.324938	+	0.272655i	0.0236357	+	0.0198327i
$190$		0			0
$191$		−	5.28657i		−	0.382523i	−0.981539	−	0.191262i	$-0.938742\pi$
$191$		−	5.28657i		−	0.382523i	0.981539	−	0.191262i	$-0.0612579\pi$
$192$		0			0
$193$	−7.00497	−	12.1330i	−0.504229	−	0.873349i	−0.999988	−	0.00488961i	$-0.998444\pi$
$193$	−7.00497	−	12.1330i	−0.504229	−	0.873349i	0.495760	−	0.868460i	$-0.334890\pi$
$194$		0			0
$195$	−9.79483	−	15.8860i	−0.701423	−	1.13762i
$196$		0			0
$197$	4.44150	−	12.2029i	0.316444	−	0.869422i	−0.674874	−	0.737933i	$-0.735802\pi$
$197$	4.44150	−	12.2029i	0.316444	−	0.869422i	0.991318	−	0.131489i	$-0.0419759\pi$
$198$		0			0
$199$	18.1499	+	10.4789i	1.28662	+	0.742828i	0.978049	−	0.208375i	$-0.0668176\pi$
$199$	18.1499	+	10.4789i	1.28662	+	0.742828i	0.308566	+	0.951203i	$0.400151\pi$
$200$		0			0
$201$	0.448686	+	2.54462i	0.0316479	+	0.179484i
$202$		0			0
$203$	−0.673137	+	0.245002i	−0.0472450	+	0.0171958i
$204$		0			0
$205$	9.16723	−	1.89124i	0.640267	−	0.132090i
$206$		0			0
$207$	0.0361474	+	0.205002i	0.00251242	+	0.0142486i
$208$		0			0
$209$	7.38565	−	8.80187i	0.510876	−	0.608838i
$210$		0			0
$211$	−6.37504	−	11.0419i	−0.438876	−	0.760156i	0.558727	−	0.829352i	$-0.311290\pi$
$211$	−6.37504	−	11.0419i	−0.438876	−	0.760156i	−0.997603	+	0.0691959i	$0.977957\pi$
$212$		0			0
$213$	13.5695	+	16.1715i	0.929768	+	1.10805i
$214$		0			0
$215$	7.58679	−	9.59167i	0.517415	−	0.654146i
$216$		0			0
$217$	−0.118314	+	0.670992i	−0.00803167	+	0.0455499i
$218$		0			0
$219$	−20.5795	+	7.49032i	−1.39063	+	0.506149i
$220$		0			0
$221$	−25.8577			−1.73938
$222$		0			0
$223$		−	21.6797i		−	1.45178i	−0.687811	−	0.725890i	$-0.741428\pi$
$223$		−	21.6797i		−	1.45178i	0.687811	−	0.725890i	$-0.258572\pi$
$224$		0			0
$225$	−0.374367	−	0.278906i	−0.0249578	−	0.0185937i
$226$		0			0
$227$	3.15501	−	17.8930i	0.209406	−	1.18760i	−0.680949	−	0.732331i	$-0.738433\pi$
$227$	3.15501	−	17.8930i	0.209406	−	1.18760i	0.890355	−	0.455267i	$-0.150456\pi$
$228$		0			0
$229$	4.25230	−	24.1160i	0.281000	−	1.59363i	−0.438234	−	0.898861i	$-0.644396\pi$
$229$	4.25230	−	24.1160i	0.281000	−	1.59363i	0.719234	−	0.694768i	$-0.244493\pi$
$230$		0			0
$231$	−0.249217	+	0.209117i	−0.0163972	+	0.0137589i
$232$		0			0
$233$	0.952643	−	0.550009i	0.0624097	−	0.0360323i	−0.468470	−	0.883479i	$-0.655195\pi$
$233$	0.952643	−	0.550009i	0.0624097	−	0.0360323i	0.530880	+	0.847447i	$0.321861\pi$
$234$		0			0
$235$	2.59413	−	1.03006i	0.169222	−	0.0671939i
$236$		0			0
$237$	5.08320	+	28.8283i	0.330189	+	1.87260i
$238$		0			0
$239$	17.9038	+	21.3369i	1.15810	+	1.38017i	0.911628	+	0.411017i	$0.134826\pi$
$239$	17.9038	+	21.3369i	1.15810	+	1.38017i	0.246470	+	0.969150i	$0.420729\pi$
$240$		0			0
$241$	−2.91049	−	7.99649i	−0.187481	−	0.515099i	0.809969	−	0.586473i	$-0.199484\pi$
$241$	−2.91049	−	7.99649i	−0.187481	−	0.515099i	−0.997450	+	0.0713736i	$0.977262\pi$
$242$		0			0
$243$	0.955215	−	0.168430i	0.0612771	−	0.0108048i
$244$		0			0
$245$	13.3112	−	8.20730i	0.850420	−	0.524345i
$246$		0			0
$247$	8.10891	−	22.2791i	0.515958	−	1.41758i
$248$		0			0
$249$	−6.40460	+	11.0931i	−0.405875	+	0.702996i
$250$		0			0
$251$	12.3125	−	7.10865i	0.777161	−	0.448694i	−0.0582625	−	0.998301i	$-0.518556\pi$
$251$	12.3125	−	7.10865i	0.777161	−	0.448694i	0.835423	+	0.549607i	$0.185223\pi$
$252$		0			0
$253$	−5.28954			−0.332550
$254$		0			0
$255$	18.7146	−	7.43110i	1.17195	−	0.465353i
$256$		0			0
$257$	−9.09685	−	3.31098i	−0.567446	−	0.206533i	0.0423351	−	0.999103i	$-0.486520\pi$
$257$	−9.09685	−	3.31098i	−0.567446	−	0.206533i	−0.609781	+	0.792570i	$0.708743\pi$
$258$		0			0
$259$	0.164295	−	0.460827i	0.0102088	−	0.0286344i
$260$		0			0
$261$	−0.284412	+	0.781415i	−0.0176046	+	0.0483683i
$262$		0			0
$263$	−18.0445	+	21.5046i	−1.11267	+	1.32603i	−0.172624	+	0.984988i	$0.555225\pi$
$263$	−18.0445	+	21.5046i	−1.11267	+	1.32603i	−0.940048	+	0.341043i	$0.889220\pi$
$264$		0			0
$265$	−10.8064	+	20.0334i	−0.663831	+	1.23064i
$266$		0			0
$267$	−0.953901	−	1.65220i	−0.0583778	−	0.101113i
$268$		0			0
$269$	4.12941	−	7.15235i	0.251775	−	0.436086i	−0.712240	−	0.701936i	$-0.752319\pi$
$269$	4.12941	−	7.15235i	0.251775	−	0.436086i	0.964014	+	0.265850i	$0.0856525\pi$
$270$		0			0
$271$	−28.1820	−	10.2574i	−1.71193	−	0.623093i	−0.714840	−	0.699288i	$-0.753501\pi$
$271$	−28.1820	−	10.2574i	−1.71193	−	0.623093i	−0.997093	+	0.0761948i	$0.975723\pi$
$272$		0			0
$273$	−0.335647	+	0.581358i	−0.0203143	+	0.0351854i
$274$		0			0
$275$	8.63131	−	8.13761i	0.520488	−	0.490716i
$276$		0			0
$277$	−22.6189	+	8.23259i	−1.35904	+	0.494649i	−0.915756	−	0.401735i	$-0.868407\pi$
$277$	−22.6189	+	8.23259i	−1.35904	+	0.494649i	−0.443280	+	0.896383i	$0.646185\pi$
$278$		0			0
$279$	0.508406	+	0.605895i	0.0304375	+	0.0362740i
$280$		0			0
$281$	−6.32774	+	1.11575i	−0.377481	+	0.0665602i	−0.359170	−	0.933272i	$-0.616940\pi$
$281$	−6.32774	+	1.11575i	−0.377481	+	0.0665602i	−0.0183115	+	0.999832i	$0.505829\pi$
$282$		0			0
$283$	−10.1239	−	8.49499i	−0.601805	−	0.504975i	0.290220	−	0.956960i	$-0.406271\pi$
$283$	−10.1239	−	8.49499i	−0.601805	−	0.504975i	−0.892025	+	0.451985i	$0.850716\pi$
$284$		0			0
$285$	0.533805	+	18.4549i	0.0316199	+	1.09317i
$286$		0			0
$287$	−0.216417	−	0.257915i	−0.0127747	−	0.0152243i
$288$		0			0
$289$	1.89254	−	10.7332i	0.111326	−	0.631362i
$290$		0			0
$291$	−23.8167	−	4.19952i	−1.39616	−	0.246180i
$292$		0			0
$293$	8.73125	+	23.9889i	0.510085	+	1.40145i	0.881149	+	0.472839i	$0.156771\pi$
$293$	8.73125	+	23.9889i	0.510085	+	1.40145i	−0.371064	+	0.928607i	$0.621007\pi$
$294$		0			0
$295$	0.0426318	−	0.0790331i	0.00248212	−	0.00460149i
$296$		0			0
$297$			12.5122i			0.726033i
$298$		0			0
$299$	−10.2564	+	3.73301i	−0.593141	+	0.215886i
$300$		0			0
$301$	−0.433205	−	0.0763857i	−0.0249695	−	0.00440280i
$302$		0			0
$303$	−17.2943	−	3.04945i	−0.993530	−	0.175186i
$304$		0			0
$305$	4.88591	+	23.6831i	0.279767	+	1.35609i
$306$		0			0
$307$	−3.29602	+	1.90296i	−0.188114	+	0.108607i	−0.591099	−	0.806599i	$-0.701306\pi$
$307$	−3.29602	+	1.90296i	−0.188114	+	0.108607i	0.402986	+	0.915206i	$0.367972\pi$
$308$		0			0
$309$	−7.91407	+	9.43162i	−0.450216	+	0.536546i
$310$		0			0
$311$	−20.1434	+	3.55182i	−1.14223	+	0.201405i	−0.712579	−	0.701592i	$-0.752473\pi$
$311$	−20.1434	+	3.55182i	−1.14223	+	0.201405i	−0.429647	+	0.902997i	$0.641362\pi$
$312$		0			0
$313$	6.58564	−	5.52601i	0.372242	−	0.312348i	−0.437406	−	0.899264i	$-0.644103\pi$
$313$	6.58564	−	5.52601i	0.372242	−	0.312348i	0.809648	+	0.586916i	$0.199658\pi$
$314$		0			0
$315$	−0.00243655	+	0.0166143i	−0.000137284	+	0.000936108i
$316$		0			0
$317$	14.7726	−	2.60480i	0.829710	−	0.146300i	0.257366	−	0.966314i	$-0.417145\pi$
$317$	14.7726	−	2.60480i	0.829710	−	0.146300i	0.572344	+	0.820014i	$0.306034\pi$
$318$		0			0
$319$	−18.2994	−	10.5652i	−1.02457	−	0.591536i
$320$		0			0
$321$	12.7760	+	4.65010i	0.713089	+	0.259543i
$322$		0			0
$323$	22.1532	+	12.7901i	1.23263	+	0.711662i
$324$		0			0
$325$	10.9930	−	21.8702i	0.609784	−	1.21314i
$326$		0			0
$327$	26.7273			1.47802
$328$		0			0
$329$	−0.0769080	−	0.0645335i	−0.00424008	−	0.00355785i
$330$		0			0
$331$	−5.20508	+	14.3008i	−0.286097	+	0.786045i	0.710506	+	0.703691i	$0.248466\pi$
$331$	−5.20508	+	14.3008i	−0.286097	+	0.786045i	−0.996603	+	0.0823541i	$0.973756\pi$
$332$		0			0
$333$	−0.287204	−	0.489963i	−0.0157387	−	0.0268498i
$334$		0			0
$335$	−2.53200	+	2.25251i	−0.138338	+	0.123068i
$336$		0			0
$337$	−10.2878	+	12.2606i	−0.560414	+	0.667875i	−0.969634	−	0.244561i	$-0.921356\pi$
$337$	−10.2878	+	12.2606i	−0.560414	+	0.667875i	0.409220	+	0.912436i	$0.365801\pi$
$338$		0			0
$339$			3.64779i			0.198121i
$340$		0			0
$341$	−17.4054	+	10.0490i	−0.942557	+	0.544186i
$342$		0			0
$343$	−0.974715	−	0.562752i	−0.0526297	−	0.0303857i
$344$		0			0
$345$	6.35025	−	5.64929i	0.341886	−	0.304148i
$346$		0			0
$347$	−1.92108	+	3.32740i	−0.103129	+	0.178624i	−0.912972	−	0.408022i	$-0.866219\pi$
$347$	−1.92108	+	3.32740i	−0.103129	+	0.178624i	0.809843	+	0.586646i	$0.199552\pi$
$348$		0			0
$349$	1.25828	+	7.13607i	0.0673543	+	0.381985i	0.999787	+	0.0206413i	$0.00657080\pi$
$349$	1.25828	+	7.13607i	0.0673543	+	0.381985i	−0.932433	+	0.361344i	$0.882318\pi$
$350$		0			0
$351$	8.83032	+	24.2611i	0.471328	+	1.29496i
$352$		0			0
$353$	13.0242	−	10.9286i	0.693208	−	0.581671i	−0.226624	−	0.973982i	$-0.572769\pi$
$353$	13.0242	−	10.9286i	0.693208	−	0.581671i	0.919832	+	0.392312i	$0.128325\pi$
$354$		0			0
$355$	−8.71354	+	26.2808i	−0.462467	+	1.39484i
$356$		0			0
$357$	−0.554831	−	0.465559i	−0.0293648	−	0.0246400i
$358$		0			0
$359$	1.00440	+	1.73968i	0.0530104	+	0.0918166i	0.891313	−	0.453389i	$-0.149785\pi$
$359$	1.00440	+	1.73968i	0.0530104	+	0.0918166i	−0.838303	+	0.545205i	$0.816452\pi$
$360$		0			0
$361$	−3.41232	+	2.86327i	−0.179596	+	0.150699i
$362$		0			0
$363$	9.01814	+	1.59014i	0.473330	+	0.0834608i
$364$		0			0
$365$	−22.5282	−	17.8193i	−1.17918	−	0.932703i
$366$		0			0
$367$	1.11071	+	3.05166i	0.0579787	+	0.159295i	0.965300	−	0.261142i	$-0.0840990\pi$
$367$	1.11071	+	3.05166i	0.0579787	+	0.159295i	−0.907322	+	0.420437i	$0.861877\pi$
$368$		0			0
$369$	−0.390842			−0.0203464
$370$		0			0
$371$	0.818744			0.0425071
$372$		0			0
$373$	−3.39200	−	9.31944i	−0.175631	−	0.482542i	0.820375	−	0.571826i	$-0.193765\pi$
$373$	−3.39200	−	9.31944i	−0.175631	−	0.482542i	−0.996006	+	0.0892833i	$0.971542\pi$
$374$		0			0
$375$	−1.67109	+	18.9878i	−0.0862948	+	0.980526i
$376$		0			0
$377$	−42.9386	−	7.57124i	−2.21145	−	0.389939i
$378$		0			0
$379$	13.0928	−	10.9862i	0.672532	−	0.564322i	−0.241281	−	0.970455i	$-0.577568\pi$
$379$	13.0928	−	10.9862i	0.672532	−	0.564322i	0.913814	+	0.406133i	$0.133123\pi$
$380$		0			0
$381$	4.54261	+	7.86803i	0.232725	+	0.403091i
$382$		0			0
$383$	7.45459	+	6.25514i	0.380912	+	0.319623i	0.813060	−	0.582180i	$-0.197800\pi$
$383$	7.45459	+	6.25514i	0.380912	+	0.319623i	−0.432149	+	0.901802i	$0.642244\pi$
$384$		0			0
$385$	−0.405010	−	0.134283i	−0.0206412	−	0.00684369i
$386$		0			0
$387$	−0.391177	+	0.328236i	−0.0198846	+	0.0166852i
$388$		0			0
$389$	−2.97958	−	8.18632i	−0.151071	−	0.415063i	0.840954	−	0.541106i	$-0.181994\pi$
$389$	−2.97958	−	8.18632i	−0.151071	−	0.415063i	−0.992025	+	0.126043i	$0.959772\pi$
$390$		0			0
$391$	−2.04490	−	11.5972i	−0.103415	−	0.586496i
$392$		0			0
$393$	−10.0111	+	17.3397i	−0.504993	+	0.874674i
$394$		0			0
$395$	−28.6852	+	25.5189i	−1.44331	+	1.28399i
$396$		0			0
$397$	20.4266	+	11.7933i	1.02518	+	0.591890i	0.915601	−	0.402088i	$-0.131715\pi$
$397$	20.4266	+	11.7933i	1.02518	+	0.591890i	0.109582	+	0.993978i	$0.465049\pi$
$398$		0			0
$399$	0.575119	−	0.332045i	0.0287920	−	0.0166231i
$400$		0			0
$401$		−	30.5230i		−	1.52424i	−0.647434	−	0.762122i	$-0.724158\pi$
$401$		−	30.5230i		−	1.52424i	0.647434	−	0.762122i	$-0.275842\pi$
$402$		0			0
$403$	−26.6570	+	31.7686i	−1.32788	+	1.58251i
$404$		0			0
$405$	−12.9469	−	14.5534i	−0.643337	−	0.723163i
$406$		0			0
$407$	13.5283	−	5.02514i	0.670571	−	0.249087i
$408$		0			0
$409$	−3.05621	+	8.39687i	−0.151120	+	0.415198i	−0.992034	−	0.125970i	$-0.959796\pi$
$409$	−3.05621	+	8.39687i	−0.151120	+	0.415198i	0.840914	+	0.541168i	$0.182018\pi$
$410$		0			0
$411$	−13.4014	−	11.2451i	−0.661040	−	0.554679i
$412$		0			0
$413$	−0.00323000			−0.000158938
$414$		0			0
$415$	−16.7931	+	0.485737i	−0.824339	+	0.0238439i
$416$		0			0
$417$	18.4126	+	10.6305i	0.901670	+	0.520579i
$418$		0			0
$419$	31.6082	+	11.5044i	1.54416	+	0.562029i	0.967039	−	0.254628i	$-0.0819531\pi$
$419$	31.6082	+	11.5044i	1.54416	+	0.562029i	0.577123	+	0.816657i	$0.304175\pi$
$420$		0			0
$421$	24.8740	+	14.3610i	1.21229	+	0.699914i	0.963257	−	0.268582i	$-0.0865550\pi$
$421$	24.8740	+	14.3610i	1.21229	+	0.699914i	0.249030	+	0.968496i	$0.419888\pi$
$422$		0			0
$423$	−0.114775	+	0.0202379i	−0.00558055	+	0.000984001i
$424$		0			0
$425$	21.1783	+	15.7780i	1.02730	+	0.765346i
$426$		0			0
$427$	0.666312	−	0.559102i	0.0322451	−	0.0270568i
$428$		0			0
$429$	−19.5008	+	3.43852i	−0.941509	+	0.166013i
$430$		0			0
$431$	−12.3342	+	14.6993i	−0.594118	+	0.708042i	−0.976392	−	0.216007i	$-0.930697\pi$
$431$	−12.3342	+	14.6993i	−0.594118	+	0.708042i	0.382274	+	0.924049i	$0.375141\pi$
$432$		0			0
$433$	−2.31009	+	1.33373i	−0.111016	+	0.0640951i	−0.554480	−	0.832197i	$-0.687083\pi$
$433$	−2.31009	+	1.33373i	−0.111016	+	0.0640951i	0.443464	+	0.896292i	$0.353749\pi$
$434$		0			0
$435$	33.2528	−	6.86018i	1.59435	−	0.328920i
$436$		0			0
$437$	10.6334	+	1.87496i	0.508666	+	0.0896916i
$438$		0			0
$439$	−12.4602	−	2.19707i	−0.594693	−	0.104861i	−0.131803	−	0.991276i	$-0.542077\pi$
$439$	−12.4602	−	2.19707i	−0.594693	−	0.104861i	−0.462891	+	0.886415i	$0.653188\pi$
$440$		0			0
$441$	−0.613592	+	0.223329i	−0.0292187	+	0.0106347i
$442$		0			0
$443$		−	11.4388i		−	0.543472i	−0.962372	−	0.271736i	$-0.912402\pi$
$443$		−	11.4388i		−	0.543472i	0.962372	−	0.271736i	$-0.0875978\pi$
$444$		0			0
$445$	1.18793	−	2.20224i	0.0563131	−	0.104396i
$446$		0			0
$447$	−4.90880	−	13.4868i	−0.232178	−	0.637904i
$448$		0			0
$449$	−6.69110	−	1.17982i	−0.315773	−	0.0556792i	0.0135157	−	0.999909i	$-0.495698\pi$
$449$	−6.69110	−	1.17982i	−0.315773	−	0.0556792i	−0.329288	+	0.944229i	$0.606809\pi$
$450$		0			0
$451$	1.72458	−	9.78056i	0.0812071	−	0.460548i
$452$		0			0
$453$	12.5969	+	15.0124i	0.591852	+	0.705342i
$454$		0			0
$455$	−0.880078	+	0.0254561i	−0.0412587	+	0.00119340i
$456$		0			0
$457$	26.2633	+	22.0375i	1.22855	+	1.03087i	0.998332	+	0.0577323i	$0.0183870\pi$
$457$	26.2633	+	22.0375i	1.22855	+	1.03087i	0.230214	+	0.973140i	$0.426057\pi$
$458$		0			0
$459$	−27.4328	+	4.83714i	−1.28045	+	0.225779i
$460$		0			0
$461$	19.8726	+	23.6832i	0.925557	+	1.10304i	0.994429	+	0.105411i	$0.0336158\pi$
$461$	19.8726	+	23.6832i	0.925557	+	1.10304i	−0.0688713	+	0.997626i	$0.521940\pi$
$462$		0			0
$463$	−1.73394	+	0.631102i	−0.0805829	+	0.0293298i	−0.381997	−	0.924164i	$-0.624764\pi$
$463$	−1.73394	+	0.631102i	−0.0805829	+	0.0293298i	0.301414	+	0.953493i	$0.402541\pi$
$464$		0			0
$465$	10.1633	−	30.6534i	0.471311	−	1.42152i
$466$		0			0
$467$	−18.4199	+	31.9042i	−0.852372	+	1.47635i	0.0266889	+	0.999644i	$0.491504\pi$
$467$	−18.4199	+	31.9042i	−0.852372	+	1.47635i	−0.879061	+	0.476709i	$0.841830\pi$
$468$		0			0
$469$	0.114547	+	0.0416916i	0.00528928	+	0.00192514i
$470$		0			0
$471$	7.21871	−	12.5032i	0.332620	−	0.576115i
$472$		0			0
$473$	−6.48784	−	11.2373i	−0.298311	−	0.516690i
$474$		0			0
$475$	−20.2358	+	13.2993i	−0.928484	+	0.610216i
$476$		0			0
$477$	0.610933	−	0.728082i	0.0279727	−	0.0333366i
$478$		0			0
$479$	−1.74879	+	4.80475i	−0.0799041	+	0.219535i	−0.973212	−	0.229911i	$-0.926156\pi$
$479$	−1.74879	+	4.80475i	−0.0799041	+	0.219535i	0.893307	+	0.449446i	$0.148379\pi$
$480$		0			0
$481$	22.6848	−	19.2911i	1.03434	−	0.879597i
$482$		0			0
$483$	−0.287283	−	0.104562i	−0.0130718	−	0.00475776i
$484$		0			0
$485$	−11.7058	−	29.4800i	−0.531532	−	1.33862i
$486$		0			0
$487$	21.6004			0.978808			0.489404	−	0.872057i	$-0.337214\pi$
$487$	21.6004			0.978808			0.489404	+	0.872057i	$0.337214\pi$
$488$		0			0
$489$	−25.8295	+	14.9127i	−1.16805	+	0.674374i
$490$		0			0
$491$	−7.85865	+	13.6116i	−0.354656	+	0.614282i	−0.987059	−	0.160357i	$-0.948735\pi$
$491$	−7.85865	+	13.6116i	−0.354656	+	0.614282i	0.632403	+	0.774639i	$0.282069\pi$
$492$		0			0
$493$	16.0895	−	44.2055i	0.724634	−	1.99092i
$494$		0			0
$495$	−0.421624	+	0.259962i	−0.0189506	+	0.0116844i
$496$		0			0
$497$	0.980782	−	0.172938i	0.0439941	−	0.00775735i
$498$		0			0
$499$	0.344270	+	0.945875i	0.0154117	+	0.0423432i	0.947160	−	0.320762i	$-0.103939\pi$
$499$	0.344270	+	0.945875i	0.0154117	+	0.0423432i	−0.931748	+	0.363105i	$0.881717\pi$
$500$		0			0
$501$	15.4004	+	18.3535i	0.688041	+	0.819976i
$502$		0			0
$503$	−1.90172	−	10.7852i	−0.0847936	−	0.480888i	−0.997401	−	0.0720512i	$-0.977045\pi$
$503$	−1.90172	−	10.7852i	−0.0847936	−	0.480888i	0.912607	−	0.408837i	$-0.134066\pi$
$504$		0			0
$505$	−8.50005	−	21.4066i	−0.378247	−	0.952583i
$506$		0			0
$507$	−16.1911	+	9.34792i	−0.719071	+	0.415156i
$508$		0			0
$509$	5.84423	−	4.90389i	0.259041	−	0.217361i	−0.504013	−	0.863696i	$-0.668144\pi$
$509$	5.84423	−	4.90389i	0.259041	−	0.217361i	0.763054	+	0.646335i	$0.223699\pi$
$510$		0			0
$511$	−0.179409	+	1.01748i	−0.00793657	+	0.0450105i
$512$		0			0
$513$	4.43516	−	25.1531i	0.195817	−	1.11053i
$514$		0			0
$515$	−15.9772	−	2.34313i	−0.704041	−	0.103251i
$516$		0			0
$517$		−	2.96146i		−	0.130245i
$518$		0			0
$519$	−15.5071			−0.680685
$520$		0			0
$521$	−16.1961	+	5.89491i	−0.709565	+	0.258261i	−0.671489	−	0.741014i	$-0.734345\pi$
$521$	−16.1961	+	5.89491i	−0.709565	+	0.258261i	−0.0380760	+	0.999275i	$0.512123\pi$
$522$		0			0
$523$	1.00314	−	5.68911i	0.0438644	−	0.248767i	−0.954989	−	0.296641i	$-0.904133\pi$
$523$	1.00314	−	5.68911i	0.0438644	−	0.248767i	0.998853	+	0.0478740i	$0.0152446\pi$
$524$		0			0
$525$	0.629642	−	0.271344i	0.0274798	−	0.0118424i
$526$		0			0
$527$	−28.7611	−	34.2762i	−1.25285	−	1.49309i
$528$		0			0
$529$	9.01464	+	15.6138i	0.391941	+	0.678862i
$530$		0			0
$531$	−0.00241017	+	0.00287233i	−0.000104592	+	0.000124648i
$532$		0			0
$533$	−3.55854	−	20.1815i	−0.154138	−	0.874158i
$534$		0			0
$535$	3.60294	+	17.4642i	0.155769	+	0.755045i
$536$		0			0
$537$	13.6204	−	4.95742i	0.587764	−	0.213929i
$538$		0			0
$539$	−2.88121	−	16.3402i	−0.124103	−	0.703820i
$540$		0			0
$541$	−18.6176	−	10.7489i	−0.800433	−	0.462130i	0.0431893	−	0.999067i	$-0.486248\pi$
$541$	−18.6176	−	10.7489i	−0.800433	−	0.462130i	−0.843623	+	0.536937i	$0.819581\pi$
$542$		0			0
$543$	−1.18119	+	3.24529i	−0.0506896	+	0.139269i
$544$		0			0
$545$	18.3977	+	29.8387i	0.788071	+	1.27815i
$546$		0			0
$547$	−10.2159	−	17.6945i	−0.436802	−	0.756563i	0.560639	−	0.828060i	$-0.310556\pi$
$547$	−10.2159	−	17.6945i	−0.436802	−	0.756563i	−0.997441	+	0.0714973i	$0.977222\pi$
$548$		0			0
$549$		−	1.00972i		−	0.0430938i
$550$		0			0
$551$	33.0419	+	27.7255i	1.40763	+	1.18114i
$552$		0			0
$553$	1.29771	+	0.472327i	0.0551842	+	0.0200854i
$554$		0			0
$555$	−10.8742	+	20.4812i	−0.461584	+	0.869378i
$556$		0			0
$557$	−39.6227	−	14.4215i	−1.67887	−	0.611057i	−0.685712	−	0.727873i	$-0.740509\pi$
$557$	−39.6227	−	14.4215i	−1.67887	−	0.611057i	−0.993154	+	0.116816i	$0.962731\pi$
$558$		0			0
$559$	−20.5104	−	17.2103i	−0.867498	−	0.727917i
$560$		0			0
$561$		−	21.3646i		−	0.902016i
$562$		0			0
$563$	−9.41619	−	16.3093i	−0.396845	−	0.687356i	0.596490	−	0.802621i	$-0.296562\pi$
$563$	−9.41619	−	16.3093i	−0.396845	−	0.687356i	−0.993335	+	0.115265i	$0.963228\pi$
$564$		0			0
$565$	−4.07244	+	2.51095i	−0.171329	+	0.105637i
$566$		0			0
$567$	−0.239634	+	0.658389i	−0.0100637	+	0.0276497i
$568$		0			0
$569$	−8.64894	−	4.99347i	−0.362582	−	0.209337i	0.307631	−	0.951506i	$-0.400464\pi$
$569$	−8.64894	−	4.99347i	−0.362582	−	0.209337i	−0.670213	+	0.742169i	$0.733797\pi$
$570$		0			0
$571$	−4.48352	−	25.4273i	−0.187629	−	1.06410i	−0.922530	−	0.385925i	$-0.873882\pi$
$571$	−4.48352	−	25.4273i	−0.187629	−	1.06410i	0.734901	−	0.678174i	$-0.237229\pi$
$572$		0			0
$573$	8.46945	−	3.08263i	0.353816	−	0.128779i
$574$		0			0
$575$	10.6781	+	3.20083i	0.445309	+	0.133484i
$576$		0			0
$577$	−7.73305	−	43.8563i	−0.321931	−	1.82576i	−0.530416	−	0.847737i	$-0.677964\pi$
$577$	−7.73305	−	43.8563i	−0.321931	−	1.82576i	0.208485	−	0.978026i	$-0.433147\pi$
$578$		0			0
$579$	15.3532	−	18.2972i	0.638057	−	0.760406i
$580$		0			0
$581$	0.302146	+	0.523331i	0.0125351	+	0.0217114i
$582$		0			0
$583$	15.5240	+	18.5008i	0.642940	+	0.766226i
$584$		0			0
$585$	−0.634062	+	0.801618i	−0.0262152	+	0.0331428i
$586$		0			0
$587$	−3.39032	+	19.2275i	−0.139934	+	0.793603i	0.831363	+	0.555730i	$0.187561\pi$
$587$	−3.39032	+	19.2275i	−0.139934	+	0.793603i	−0.971296	+	0.237873i	$0.923550\pi$
$588$		0			0
$589$	38.5518	−	14.0317i	1.58850	−	0.578166i
$590$		0			0
$591$	22.1398			0.910709
$592$		0			0
$593$		−	15.3790i		−	0.631540i	−0.948836	−	0.315770i	$-0.897737\pi$
$593$		−	15.3790i		−	0.631540i	0.948836	−	0.315770i	$-0.102263\pi$
$594$		0			0
$595$	0.137838	−	0.939888i	0.00565083	−	0.0385316i
$596$		0			0
$597$	−6.20454	+	35.1877i	−0.253935	+	1.44014i
$598$		0			0
$599$	−3.02042	+	17.1296i	−0.123411	+	0.699898i	0.858828	+	0.512264i	$0.171193\pi$
$599$	−3.02042	+	17.1296i	−0.123411	+	0.699898i	−0.982239	+	0.187634i	$0.939918\pi$
$600$		0			0
$601$	3.37731	−	2.83390i	0.137763	−	0.115597i	−0.571302	−	0.820740i	$-0.693561\pi$
$601$	3.37731	−	2.83390i	0.137763	−	0.115597i	0.709065	+	0.705143i	$0.249117\pi$
$602$		0			0
$603$	0.122548	−	0.0707529i	0.00499053	−	0.00288128i
$604$		0			0
$605$	4.43237	+	11.1626i	0.180202	+	0.453822i
$606$		0			0
$607$	5.66111	+	32.1057i	0.229777	+	1.30313i	0.853339	+	0.521357i	$0.174574\pi$
$607$	5.66111	+	32.1057i	0.229777	+	1.30313i	−0.623561	+	0.781775i	$0.714315\pi$
$608$		0			0
$609$	−0.785020	−	0.935550i	−0.0318106	−	0.0379104i
$610$		0			0
$611$	−2.09001	−	5.74225i	−0.0845527	−	0.232307i
$612$		0			0
$613$	5.67013	−	0.999796i	0.229014	−	0.0403814i	−0.0579632	−	0.998319i	$-0.518461\pi$
$613$	5.67013	−	0.999796i	0.229014	−	0.0403814i	0.286977	+	0.957937i	$0.407350\pi$
$614$		0			0
$615$	8.37534	+	13.5837i	0.337726	+	0.547749i
$616$		0			0
$617$	−1.64913	+	4.53095i	−0.0663916	+	0.182409i	−0.968452	−	0.249201i	$-0.919832\pi$
$617$	−1.64913	+	4.53095i	−0.0663916	+	0.182409i	0.902060	+	0.431610i	$0.142054\pi$
$618$		0			0
$619$	3.46095	−	5.99455i	0.139107	−	0.240941i	−0.788052	−	0.615609i	$-0.788910\pi$
$619$	3.46095	−	5.99455i	0.139107	−	0.240941i	0.927159	+	0.374668i	$0.122243\pi$
$620$		0			0
$621$	−10.1828	+	5.87903i	−0.408621	+	0.235918i
$622$		0			0
$623$	−0.0900031			−0.00360590
$624$		0			0
$625$	−22.3485	+	11.2046i	−0.893941	+	0.448184i
$626$		0			0
$627$	18.4078	+	6.69989i	0.735137	+	0.267568i
$628$		0			0
$629$	16.2474	+	27.7177i	0.647828	+	1.10518i
$630$		0			0
$631$	−1.89785	+	5.21429i	−0.0755521	+	0.207578i	−0.971719	−	0.236139i	$-0.924118\pi$
$631$	−1.89785	+	5.21429i	−0.0755521	+	0.207578i	0.896167	+	0.443716i	$0.146340\pi$
$632$		0			0
$633$	13.9726	−	16.6518i	0.555359	−	0.661851i
$634$		0			0
$635$	−5.65707	+	10.4874i	−0.224494	+	0.416179i
$636$		0			0
$637$	−17.1185	−	29.6500i	−0.678258	−	1.17478i
$638$		0			0
$639$	0.578055	−	1.00122i	0.0228675	−	0.0396077i
$640$		0			0
$641$	−21.3012	−	7.75301i	−0.841348	−	0.306226i	−0.114840	−	0.993384i	$-0.536636\pi$
$641$	−21.3012	−	7.75301i	−0.841348	−	0.306226i	−0.726508	+	0.687158i	$0.758858\pi$
$642$		0			0
$643$	4.53745	−	7.85909i	0.178939	−	0.309932i	−0.762578	−	0.646896i	$-0.776067\pi$
$643$	4.53745	−	7.85909i	0.178939	−	0.309932i	0.941518	+	0.336964i	$0.109400\pi$
$644$		0			0
$645$	19.7904	+	6.56160i	0.779246	+	0.258363i
$646$		0			0
$647$	6.56351	−	2.38892i	0.258038	−	0.0939182i	−0.209762	−	0.977752i	$-0.567269\pi$
$647$	6.56351	−	2.38892i	0.258038	−	0.0939182i	0.467800	+	0.883834i	$0.345047\pi$
$648$		0			0
$649$	−0.0612432	−	0.0729869i	−0.00240401	−	0.00286498i
$650$		0			0
$651$	−1.14396	+	0.201712i	−0.0448355	+	0.00790570i
$652$		0			0
$653$	−26.4196	−	22.1686i	−1.03388	−	0.867526i	−0.0425699	−	0.999093i	$-0.513555\pi$
$653$	−26.4196	−	22.1686i	−1.03388	−	0.867526i	−0.991307	+	0.131568i	$0.957999\pi$
$654$		0			0
$655$	−26.2494	+	0.759262i	−1.02565	+	0.0296668i
$656$		0			0
$657$	0.770936	+	0.918766i	0.0300771	+	0.0358445i
$658$		0			0
$659$	4.70805	−	26.7007i	0.183400	−	1.04011i	−0.744595	−	0.667517i	$-0.767357\pi$
$659$	4.70805	−	26.7007i	0.183400	−	1.04011i	0.927994	−	0.372594i	$-0.121532\pi$
$660$		0			0
$661$	22.5175	+	3.97044i	0.875828	+	0.154432i	0.593450	−	0.804871i	$-0.297766\pi$
$661$	22.5175	+	3.97044i	0.875828	+	0.154432i	0.282378	+	0.959303i	$0.408877\pi$
$662$		0			0
$663$	−15.0778	−	41.4258i	−0.585572	−	1.60885i
$664$		0			0
$665$	0.766583	+	0.413508i	0.0297268	+	0.0160352i
$666$		0			0
$667$		−	19.8567i		−	0.768856i
$668$		0			0
$669$	34.7323	−	12.6415i	1.34283	−	0.488750i
$670$		0			0
$671$	25.2676	+	4.45536i	0.975444	+	0.171997i
$672$		0			0
$673$	−28.5452	−	5.03328i	−1.10034	−	0.194019i	−0.406144	−	0.913809i	$-0.633127\pi$
$673$	−28.5452	−	5.03328i	−1.10034	−	0.194019i	−0.694192	+	0.719790i	$0.744238\pi$
$674$		0			0
$675$	7.57146	−	25.2588i	0.291425	−	0.972211i
$676$		0			0
$677$	8.15681	−	4.70934i	0.313492	−	0.180994i	−0.334996	−	0.942219i	$-0.608735\pi$
$677$	8.15681	−	4.70934i	0.313492	−	0.180994i	0.648488	+	0.761225i	$0.275402\pi$
$678$		0			0
$679$	−0.733367	+	0.873993i	−0.0281440	+	0.0335408i
$680$		0			0
$681$	30.5054	−	5.37893i	1.16897	−	0.206121i
$682$		0			0
$683$	1.59763	−	1.34057i	0.0611316	−	0.0512955i	−0.611710	−	0.791082i	$-0.709518\pi$
$683$	1.59763	−	1.34057i	0.0611316	−	0.0512955i	0.672842	+	0.739787i	$0.265074\pi$
$684$		0			0
$685$	3.32934	−	22.7020i	0.127208	−	0.867399i
$686$		0			0
$687$	41.1150	−	7.24968i	1.56863	−	0.276592i
$688$		0			0
$689$	43.1576	+	24.9171i	1.64417	+	0.949265i
$690$		0			0
$691$	−1.09733	−	0.399394i	−0.0417442	−	0.0151937i	0.321064	−	0.947058i	$-0.395960\pi$
$691$	−1.09733	−	0.399394i	−0.0417442	−	0.0151937i	−0.362808	+	0.931864i	$0.618182\pi$
$692$		0			0
$693$	0.0154296	+	0.00890831i	0.000586124	+	0.000338399i
$694$		0			0
$695$	0.806241	+	27.8736i	0.0305825	+	1.05731i
$696$		0			0
$697$	22.1104			0.837490
$698$		0			0
$699$	1.43664	+	1.20549i	0.0543388	+	0.0455957i
$700$		0			0
$701$	9.26395	−	25.4525i	0.349894	−	0.961327i	−0.632509	−	0.774553i	$-0.717975\pi$
$701$	9.26395	−	25.4525i	0.349894	−	0.961327i	0.982403	−	0.186774i	$-0.0598031\pi$
$702$		0			0
$703$	−28.9768	+	5.30661i	−1.09288	+	0.200142i
$704$		0			0
$705$	3.16288	+	3.55533i	0.119121	+	0.133901i
$706$		0			0
$707$	−0.532528	+	0.634643i	−0.0200278	+	0.0238682i
$708$		0			0
$709$		−	0.0901398i		−	0.00338527i	−0.999999	−	0.00169264i	$-0.999461\pi$
$709$		−	0.0901398i		−	0.00338527i	0.999999	−	0.00169264i	$-0.000538783\pi$
$710$		0			0
$711$	1.38835	−	0.801566i	0.0520673	−	0.0300611i
$712$		0			0
$713$	−16.3563	−	9.44334i	−0.612550	−	0.353656i
$714$		0			0
$715$	−17.2622	−	19.4041i	−0.645569	−	0.725671i
$716$		0			0
$717$	−23.7433	+	41.1247i	−0.886711	+	1.53583i
$718$		0			0
$719$	−7.87429	−	44.6573i	−0.293661	−	1.66544i	−0.672594	−	0.740012i	$-0.734820\pi$
$719$	−7.87429	−	44.6573i	−0.293661	−	1.66544i	0.378933	−	0.925424i	$-0.376291\pi$
$720$		0			0
$721$	0.198659	+	0.545811i	0.00739845	+	0.0203271i
$722$		0			0
$723$	11.1138	−	9.32559i	0.413327	−	0.346822i
$724$		0			0
$725$	30.5483	+	32.4016i	1.13454	+	1.20337i
$726$		0			0
$727$	36.0121	+	30.2178i	1.33562	+	1.12072i	0.982729	+	0.185049i	$0.0592445\pi$
$727$	36.0121	+	30.2178i	1.33562	+	1.12072i	0.352887	+	0.935666i	$0.385200\pi$
$728$		0			0
$729$	13.8936	+	24.0644i	0.514578	+	0.891275i
$730$		0			0
$731$	22.1293	−	18.5687i	0.818483	−	0.686789i
$732$		0			0
$733$	−38.7519	−	6.83301i	−1.43133	−	0.252383i	−0.596380	−	0.802702i	$-0.703395\pi$
$733$	−38.7519	−	6.83301i	−1.43133	−	0.252383i	−0.834954	+	0.550319i	$0.814506\pi$
$734$		0			0
$735$	20.9105	+	16.5397i	0.771294	+	0.610076i
$736$		0			0
$737$	1.22981	+	3.37887i	0.0453005	+	0.124462i
$738$		0			0
$739$	−23.2174			−0.854064			−0.427032	−	0.904236i	$-0.640441\pi$
$739$	−23.2174			−0.854064			−0.427032	+	0.904236i	$0.640441\pi$
$740$		0			0
$741$	40.4209			1.48490
$742$		0			0
$743$	5.14467	+	14.1349i	0.188740	+	0.518558i	0.997584	−	0.0694642i	$-0.0221290\pi$
$743$	5.14467	+	14.1349i	0.188740	+	0.518558i	−0.808845	+	0.588022i	$0.799907\pi$
$744$		0			0
$745$	11.6779	−	14.7639i	0.427845	−	0.540907i
$746$		0			0
$747$	0.690837	+	0.121813i	0.0252764	+	0.00445691i
$748$		0			0
$749$	0.491348	−	0.412290i	0.0179535	−	0.0150647i
$750$		0			0
$751$	17.7098	+	30.6743i	0.646241	+	1.11932i	0.984013	+	0.178094i	$0.0569931\pi$
$751$	17.7098	+	30.6743i	0.646241	+	1.11932i	−0.337773	+	0.941228i	$0.609674\pi$
$752$		0			0
$753$	18.5680	+	15.5804i	0.676657	+	0.567783i
$754$		0			0
$755$	−8.08896	+	24.3971i	−0.294387	+	0.887900i
$756$		0			0
$757$	−15.8884	+	13.3320i	−0.577475	+	0.484559i	−0.884117	−	0.467266i	$-0.845239\pi$
$757$	−15.8884	+	13.3320i	−0.577475	+	0.484559i	0.306642	+	0.951825i	$0.400795\pi$
$758$		0			0
$759$	−3.08436	−	8.47420i	−0.111955	−	0.307594i
$760$		0			0
$761$	6.95161	+	39.4245i	0.251996	+	1.42914i	0.803669	+	0.595077i	$0.202879\pi$
$761$	6.95161	+	39.4245i	0.251996	+	1.42914i	−0.551673	+	0.834060i	$0.686010\pi$
$762$		0			0
$763$	0.630448	−	1.09197i	0.0228238	−	0.0395319i
$764$		0			0
$765$	−0.732958	−	0.823903i	−0.0265001	−	0.0297883i
$766$		0			0
$767$	−0.170259	−	0.0982993i	−0.00614771	−	0.00354938i
$768$		0			0
$769$	21.2021	−	12.2410i	0.764566	−	0.441422i	−0.0663668	−	0.997795i	$-0.521141\pi$
$769$	21.2021	−	12.2410i	0.764566	−	0.441422i	0.830933	+	0.556373i	$0.187807\pi$
$770$		0			0
$771$		−	16.5044i		−	0.594392i
$772$		0			0
$773$	16.8541	−	20.0859i	0.606200	−	0.722441i	−0.372432	−	0.928059i	$-0.621476\pi$
$773$	16.8541	−	20.0859i	0.606200	−	0.722441i	0.978632	+	0.205618i	$0.0659205\pi$
$774$		0			0
$775$	41.2178	−	9.75381i	1.48059	−	0.350367i
$776$		0			0
$777$	0.834077	−	0.00549912i	0.0299223	−	0.000197280i
$778$		0			0
$779$	−6.93375	+	19.0503i	−0.248427	+	0.682549i
$780$		0			0
$781$	22.5042	+	18.8833i	0.805264	+	0.675697i
$782$		0			0
$783$	−46.9705			−1.67859
$784$		0			0
$785$	18.9277	−	0.547481i	0.675558	−	0.0195404i
$786$		0			0
$787$	11.4299	+	6.59905i	0.407431	+	0.235231i	0.689686	−	0.724109i	$-0.257749\pi$
$787$	11.4299	+	6.59905i	0.407431	+	0.235231i	−0.282254	+	0.959340i	$0.591082\pi$
$788$		0			0
$789$	−44.9737	−	16.3691i	−1.60111	−	0.582755i
$790$		0			0
$791$	0.149034	+	0.0860448i	0.00529904	+	0.00305940i
$792$		0			0
$793$	52.1379	−	9.19332i	1.85147	−	0.326464i
$794$		0			0
$795$	−38.3962	−	5.63096i	−1.36177	−	0.199710i
$796$		0			0
$797$	−26.2544	+	22.0301i	−0.929980	+	0.780345i	−0.975814	−	0.218604i	$-0.929850\pi$
$797$	−26.2544	+	22.0301i	−0.929980	+	0.780345i	0.0458342	+	0.998949i	$0.485405\pi$
$798$		0			0
$799$	6.49295	−	1.14488i	0.229704	−	0.0405030i
$800$		0			0
$801$	−0.0671588	+	0.0800367i	−0.00237294	+	0.00282796i
$802$		0			0
$803$	−26.3932	+	15.2381i	−0.931397	+	0.537742i
$804$		0			0
$805$	−0.0810160	−	0.392702i	−0.00285544	−	0.0138409i
$806$		0			0
$807$	13.8664	+	2.44503i	0.488121	+	0.0860690i
$808$		0			0
$809$	−4.36369	−	0.769436i	−0.153419	−	0.0270519i	0.0964110	−	0.995342i	$-0.469264\pi$
$809$	−4.36369	−	0.769436i	−0.153419	−	0.0270519i	−0.249830	+	0.968290i	$0.580375\pi$
$810$		0			0
$811$	17.7226	−	6.45051i	0.622325	−	0.226508i	−0.0115622	−	0.999933i	$-0.503680\pi$
$811$	17.7226	−	6.45051i	0.622325	−	0.226508i	0.633888	+	0.773425i	$0.281458\pi$
$812$		0			0
$813$		−	51.1306i		−	1.79323i
$814$		0			0
$815$	−34.4284	−	18.5713i	−1.20597	−	0.650523i
$816$		0			0
$817$	9.05913	+	24.8898i	0.316939	+	0.870782i
$818$		0			0
$819$	0.0362048	+	0.00638389i	0.00126510	+	0.000223071i
$820$		0			0
$821$	−3.58965	+	20.3579i	−0.125280	+	0.710497i	0.855862	+	0.517205i	$0.173027\pi$
$821$	−3.58965	+	20.3579i	−0.125280	+	0.710497i	−0.981141	+	0.193292i	$0.938084\pi$
$822$		0			0
$823$	−18.4212	−	21.9536i	−0.642124	−	0.765254i	0.342580	−	0.939489i	$-0.388699\pi$
$823$	−18.4212	−	21.9536i	−0.642124	−	0.765254i	−0.984704	+	0.174235i	$0.944255\pi$
$824$		0			0
$825$	18.0700	+	9.08286i	0.629115	+	0.316225i
$826$		0			0
$827$	−34.5806	−	29.0166i	−1.20249	−	1.00900i	−0.999556	−	0.0298114i	$-0.990509\pi$
$827$	−34.5806	−	29.0166i	−1.20249	−	1.00900i	−0.202930	−	0.979193i	$-0.565046\pi$
$828$		0			0
$829$	20.3443	−	3.58725i	0.706588	−	0.124590i	0.191204	−	0.981550i	$-0.438761\pi$
$829$	20.3443	−	3.58725i	0.706588	−	0.124590i	0.515383	+	0.856960i	$0.327650\pi$
$830$		0			0
$831$	−26.3783	−	31.4365i	−0.915055	−	1.09052i
$832$		0			0
$833$	34.7116	−	12.6340i	1.20269	−	0.437742i
$834$		0			0
$835$	−9.88926	+	29.8269i	−0.342232	+	1.03220i
$836$		0			0
$837$	−22.3379	+	38.6904i	−0.772111	+	1.33734i
$838$		0			0
$839$	21.6041	+	7.86326i	0.745857	+	0.271470i	0.686861	−	0.726789i	$-0.258988\pi$
$839$	21.6041	+	7.86326i	0.745857	+	0.271470i	0.0589956	+	0.998258i	$0.481210\pi$
$840$		0			0
$841$	25.1613	−	43.5806i	0.867630	−	1.50278i
$842$		0			0
$843$	−5.47725	−	9.48687i	−0.188646	−	0.326745i
$844$		0			0
$845$	−21.5813	−	11.6413i	−0.742418	−	0.400473i
$846$		0			0
$847$	0.277688	−	0.330936i	0.00954149	−	0.0113711i
$848$		0			0
$849$	7.70623	−	21.1727i	0.264477	−	0.726645i
$850$		0			0
$851$	10.4460	+	8.64853i	0.358085	+	0.296468i
$852$		0			0
$853$	−6.14681	−	2.23726i	−0.210463	−	0.0766022i	0.234637	−	0.972083i	$-0.424610\pi$
$853$	−6.14681	−	2.23726i	−0.210463	−	0.0766022i	−0.445100	+	0.895481i	$0.646832\pi$
$854$		0			0
$855$	0.939730	−	0.373144i	0.0321381	−	0.0127612i
$856$		0			0
$857$	1.02419			0.0349857			0.0174929	−	0.999847i	$-0.494432\pi$
$857$	1.02419			0.0349857			0.0174929	+	0.999847i	$0.494432\pi$
$858$		0			0
$859$	−38.4347	+	22.1903i	−1.31137	+	0.757122i	−0.982324	−	0.187190i	$-0.940062\pi$
$859$	−38.4347	+	22.1903i	−1.31137	+	0.757122i	−0.329051	+	0.944312i	$0.606729\pi$
$860$		0			0
$861$	0.287004	−	0.497106i	0.00978108	−	0.0169413i
$862$		0			0
$863$	1.00086	−	2.74985i	0.0340698	−	0.0936061i	−0.921491	−	0.388399i	$-0.873028\pi$
$863$	1.00086	−	2.74985i	0.0340698	−	0.0936061i	0.955561	+	0.294793i	$0.0952506\pi$
$864$		0			0
$865$	−10.6743	−	17.3123i	−0.362936	−	0.588636i
$866$		0			0
$867$	18.2988	−	3.22657i	0.621459	−	0.109580i
$868$		0			0
$869$	13.9326	+	38.2795i	0.472631	+	1.29854i
$870$		0			0
$871$	4.76917	+	5.68368i	0.161597	+	0.192584i
$872$		0			0
$873$	0.229986	+	1.30432i	0.00778385	+	0.0441444i
$874$		0			0
$875$	0.736346	+	0.516162i	0.0248930	+	0.0174495i
$876$		0			0
$877$	10.4440	−	6.02986i	0.352670	−	0.203614i	−0.313191	−	0.949690i	$-0.601398\pi$
$877$	10.4440	−	6.02986i	0.352670	−	0.203614i	0.665860	+	0.746076i	$0.268065\pi$
$878$		0			0
$879$	−33.3406	+	27.9761i	−1.12455	+	0.943610i
$880$		0			0
$881$	5.07096	−	28.7588i	0.170845	−	0.968910i	−0.771986	−	0.635639i	$-0.780737\pi$
$881$	5.07096	−	28.7588i	0.170845	−	0.968910i	0.942831	−	0.333271i	$-0.108152\pi$
$882$		0			0
$883$	8.30126	−	47.0788i	0.279360	−	1.58433i	−0.445404	−	0.895330i	$-0.646940\pi$
$883$	8.30126	−	47.0788i	0.279360	−	1.58433i	0.724764	−	0.688997i	$-0.241949\pi$
$884$		0			0
$885$	0.151475	+	0.0222145i	0.00509179	+	0.000746731i
$886$		0			0
$887$		−	55.4993i		−	1.86349i	−0.363119	−	0.931743i	$-0.618288\pi$
$887$		−	55.4993i		−	1.86349i	0.363119	−	0.931743i	$-0.381712\pi$
$888$		0			0
$889$	0.428608			0.0143750
$890$		0			0
$891$	−19.4210	+	7.06866i	−0.650627	+	0.236809i
$892$		0			0
$893$	−1.04974	+	5.95336i	−0.0351282	+	0.199222i
$894$		0			0
$895$	14.9101	+	11.7936i	0.498391	+	0.394215i
$896$		0			0
$897$	−11.9611	−	14.2547i	−0.399369	−	0.475949i
$898$		0			0
$899$	−37.7237	−	65.3394i	−1.25816	−	2.17919i
$900$		0			0
$901$	−34.5612	+	41.1884i	−1.15140	+	1.37218i
$902$		0			0
$903$	−0.130229	−	0.738564i	−0.00433374	−	0.0245779i
$904$		0			0
$905$	−4.43615	+	0.915196i	−0.147463	+	0.0304221i
$906$		0			0
$907$	−12.2383	+	4.45437i	−0.406366	+	0.147905i	−0.537112	−	0.843511i	$-0.680485\pi$
$907$	−12.2383	+	4.45437i	−0.406366	+	0.147905i	0.130747	+	0.991416i	$0.458263\pi$
$908$		0			0
$909$	0.167003	+	0.947119i	0.00553913	+	0.0314139i
$910$		0			0
$911$	−38.8403	−	22.4245i	−1.28684	−	0.742956i	−0.308748	−	0.951144i	$-0.599910\pi$
$911$	−38.8403	−	22.4245i	−1.28684	−	0.742956i	−0.978089	+	0.208188i	$0.933243\pi$
$912$		0			0
$913$	−6.09658	+	16.7502i	−0.201767	+	0.554352i
$914$		0			0
$915$	−35.0929	+	21.6373i	−1.16014	+	0.715306i
$916$		0			0
$917$	0.472287	+	0.818026i	0.0155963	+	0.0270136i
$918$		0			0
$919$			14.3337i			0.472826i	0.971653	+	0.236413i	$0.0759719\pi$
$919$			14.3337i			0.472826i	−0.971653	+	0.236413i	$0.924028\pi$
$920$		0			0
$921$	−4.97059	−	4.17082i	−0.163787	−	0.137433i
$922$		0			0
$923$	56.9621	+	20.7325i	1.87493	+	0.682418i
$924$		0			0
$925$	−30.3507	+	1.95810i	−0.997925	+	0.0643820i
$926$		0			0
$927$	0.633608	+	0.230614i	0.0208104	+	0.00757437i
$928$		0			0
$929$	−7.44612	−	6.24803i	−0.244299	−	0.204991i	0.512414	−	0.858739i	$-0.328751\pi$
$929$	−7.44612	−	6.24803i	−0.244299	−	0.204991i	−0.756713	+	0.653747i	$0.773196\pi$
$930$		0			0
$931$			33.8695i			1.11003i
$932$		0			0
$933$	−17.4359	−	30.1999i	−0.570827	−	0.988702i
$934$		0			0
$935$	23.8518	−	14.7063i	0.780036	−	0.480948i
$936$		0			0
$937$	−7.00012	+	19.2327i	−0.228684	+	0.628304i	−0.999966	−	0.00818896i	$-0.997393\pi$
$937$	−7.00012	+	19.2327i	−0.228684	+	0.628304i	0.771283	+	0.636493i	$0.219616\pi$
$938$		0			0
$939$	12.6932	+	7.32840i	0.414225	+	0.239153i
$940$		0			0
$941$	0.836658	+	4.74492i	0.0272743	+	0.154680i	0.995403	−	0.0957718i	$-0.0305319\pi$
$941$	0.836658	+	4.74492i	0.0272743	+	0.154680i	−0.968129	+	0.250452i	$0.919421\pi$
$942$		0			0
$943$	8.76999	−	3.19202i	0.285590	−	0.103946i
$944$		0			0
$945$	−0.928924	+	0.191641i	−0.0302179	+	0.00623408i
$946$		0			0
$947$	−7.60794	−	43.1468i	−0.247225	−	1.40208i	−0.815268	−	0.579083i	$-0.803411\pi$
$947$	−7.60794	−	43.1468i	−0.247225	−	1.40208i	0.568043	−	0.822999i	$-0.307701\pi$
$948$		0			0
$949$	−40.4221	+	48.1732i	−1.31216	+	1.56377i
$950$		0			0
$951$	12.7870	+	22.1478i	0.414648	+	0.718191i
$952$		0			0
$953$	−9.84182	−	11.7290i	−0.318808	−	0.379940i	0.582712	−	0.812679i	$-0.301992\pi$
$953$	−9.84182	−	11.7290i	−0.318808	−	0.379940i	−0.901519	+	0.432739i	$0.857547\pi$
$954$		0			0
$955$	9.27143	+	7.33349i	0.300016	+	0.237306i
$956$		0			0
$957$	6.25564	−	35.4775i	0.202216	−	1.14682i
$958$		0			0
$959$	−0.775542	+	0.282274i	−0.0250436	+	0.00911511i
$960$		0			0
$961$	−40.7616			−1.31489
$962$		0			0
$963$		−	0.744582i		−	0.0239938i
$964$		0			0
$965$	30.9956	+	4.54564i	0.997784	+	0.146329i
$966$		0			0
$967$	−0.214224	+	1.21492i	−0.00688897	+	0.0390693i	−0.988058	−	0.154079i	$-0.950759\pi$
$967$	−0.214224	+	1.21492i	−0.00688897	+	0.0390693i	0.981170	+	0.193149i	$0.0618700\pi$
$968$		0			0
$969$	−7.57304	+	42.9488i	−0.243281	+	1.37972i
$970$		0			0
$971$	−4.90407	+	4.11501i	−0.157379	+	0.132057i	−0.718077	−	0.695964i	$-0.754977\pi$
$971$	−4.90407	+	4.11501i	−0.157379	+	0.132057i	0.560698	+	0.828021i	$0.310533\pi$
$972$		0			0
$973$	0.868641	−	0.501510i	0.0278473	−	0.0160777i
$974$		0			0
$975$	41.4476	+	4.85898i	1.32739	+	0.155612i
$976$		0			0
$977$	2.05979	+	11.6817i	0.0658986	+	0.373730i	0.999866	+	0.0163714i	$0.00521142\pi$
$977$	2.05979	+	11.6817i	0.0658986	+	0.373730i	−0.933967	+	0.357358i	$0.883677\pi$
$978$		0			0
$979$	−1.70653	−	2.03376i	−0.0545409	−	0.0649993i
$980$		0			0
$981$	−0.500621	−	1.37544i	−0.0159836	−	0.0439146i
$982$		0			0
$983$	49.7820	−	8.77790i	1.58780	−	0.279972i	0.691148	−	0.722713i	$-0.257105\pi$
$983$	49.7820	−	8.77790i	1.58780	−	0.279972i	0.896649	+	0.442741i	$0.145994\pi$
$984$		0			0
$985$	15.2399	+	24.7171i	0.485583	+	0.787554i
$986$		0			0
$987$	0.0585416	−	0.160842i	0.00186340	−	0.00511965i
$988$		0			0
$989$	6.09679	−	10.5600i	0.193867	−	0.335787i
$990$		0			0
$991$	−48.5417	+	28.0256i	−1.54198	+	0.890261i	−0.543264	+	0.839562i	$0.682812\pi$
$991$	−48.5417	+	28.0256i	−1.54198	+	0.890261i	−0.998714	+	0.0506996i	$0.983855\pi$
$992$		0			0
$993$	−25.9460			−0.823372
$994$		0			0
$995$	−43.5549	+	17.2946i	−1.38078	+	0.548275i
$996$		0			0
$997$	38.4650	+	14.0001i	1.21820	+	0.443388i	0.869541	−	0.493861i	$-0.164415\pi$
$997$	38.4650	+	14.0001i	1.21820	+	0.443388i	0.348659	+	0.937250i	$0.386637\pi$
$998$		0			0
$999$	20.4578	−	24.7097i	0.647257	−	0.781781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.bp.a.169.15	yes	120
5.4	even	2	inner	740.2.bp.a.169.6	✓	120
37.30	even	18	inner	740.2.bp.a.289.6	yes	120
185.104	even	18	inner	740.2.bp.a.289.15	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.bp.a.169.6	✓	120	5.4	even	2	inner
740.2.bp.a.169.15	yes	120	1.1	even	1	trivial
740.2.bp.a.289.6	yes	120	37.30	even	18	inner
740.2.bp.a.289.15	yes	120	185.104	even	18	inner

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.bp (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.583105 + 1.60207i) q^{3} +(-1.38719 + 1.75377i) q^{5} +(0.0792084 + 0.0139666i) q^{7} +(0.0715239 - 0.0600157i) q^{9} +(1.18626 + 2.05465i) q^{11} +(3.75018 + 3.14678i) q^{13} +(-3.61853 - 1.19974i) q^{15} +(-4.04619 + 3.39516i) q^{17} +(-1.65640 - 4.55091i) q^{19} +(0.0238114 + 0.135041i) q^{21} +(-1.11475 + 1.93081i) q^{23} +(-1.15141 - 4.86562i) q^{25} +(4.56728 + 2.63692i) q^{27} +(-7.71310 + 4.45316i) q^{29} +8.47122i q^{31} +(-2.59998 + 3.09854i) q^{33} +(-0.134371 + 0.119539i) q^{35} +(1.01674 - 5.99719i) q^{37} +(-2.85460 + 7.84294i) q^{39} +(-3.20670 - 2.69074i) q^{41} -5.46918 q^{43} +(0.00603632 + 0.208690i) q^{45} +(-1.08101 - 0.624120i) q^{47} +(-6.57177 - 2.39193i) q^{49} +(-7.79862 - 4.50254i) q^{51} +(10.0249 - 1.76766i) q^{53} +(-5.24895 - 0.769780i) q^{55} +(6.32502 - 5.30732i) q^{57} +(-0.0395489 + 0.00697353i) q^{59} +(6.95139 - 8.28434i) q^{61} +(0.00650351 - 0.00375480i) q^{63} +(-10.7209 + 2.21177i) q^{65} +(1.49255 + 0.263177i) q^{67} +(-3.74331 - 0.660047i) q^{69} +(11.6356 - 4.23500i) q^{71} +12.8456i q^{73} +(7.12366 - 4.68180i) q^{75} +(0.0652649 + 0.179314i) q^{77} +(16.9092 + 2.98155i) q^{79} +(-1.51268 + 8.57884i) q^{81} +(4.82941 + 5.75547i) q^{83} +(-0.341481 - 11.8058i) q^{85} +(-11.6318 - 9.76025i) q^{87} +(-1.10202 + 0.194316i) q^{89} +(0.253096 + 0.301628i) q^{91} +(-13.5715 + 4.93961i) q^{93} +(10.2790 + 3.40805i) q^{95} +(-7.09258 + 12.2847i) q^{97} +(0.208157 + 0.0757630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{5} + 6 q^{9} + 12 q^{11} + 3 q^{15} + 6 q^{19} - 12 q^{21} - 33 q^{25} - 48 q^{35} + 24 q^{39} + 30 q^{41} - 27 q^{45} + 6 q^{49} - 3 q^{55} - 42 q^{59} + 48 q^{61} - 18 q^{65} - 108 q^{69}+ \cdots + 90 q^{99}+O(q^{100}) \) 120 * q + 3 * q^5 + 6 * q^9 + 12 * q^11 + 3 * q^15 + 6 * q^19 - 12 * q^21 - 33 * q^25 - 48 * q^35 + 24 * q^39 + 30 * q^41 - 27 * q^45 + 6 * q^49 - 3 * q^55 - 42 * q^59 + 48 * q^61 - 18 * q^65 - 108 * q^69 - 18 * q^71 - 12 * q^75 - 48 * q^79 + 108 * q^81 - 33 * q^85 - 84 * q^89 - 30 * q^91 + 99 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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