LMFDB - Embedded newform 936.2.s.f.913.17

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			913.17
Character	$\chi$	$=$	936.913
Dual form			936.2.s.f.529.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31464 + 1.12771i) q^{3} +(0.766914 - 1.32833i) q^{5} -3.51479 q^{7} +(0.456560 + 2.96506i) q^{9} +(-3.19399 + 5.53215i) q^{11} +(-3.46170 - 1.00830i) q^{13} +(2.50619 - 0.881428i) q^{15} +(-0.550501 + 0.953495i) q^{17} +(-1.13796 + 1.97100i) q^{19} +(-4.62069 - 3.96365i) q^{21} -3.32815 q^{23} +(1.32369 + 2.29269i) q^{25} +(-2.74350 + 4.41285i) q^{27} +(0.714825 - 1.23811i) q^{29} +(-1.93596 + 3.35318i) q^{31} +(-10.4376 + 3.67091i) q^{33} +(-2.69554 + 4.66881i) q^{35} +(1.81670 + 3.14662i) q^{37} +(-3.41383 - 5.22932i) q^{39} +11.9875 q^{41} +12.5528 q^{43} +(4.28873 + 1.66748i) q^{45} +(-1.23298 - 2.13558i) q^{47} +5.35375 q^{49} +(-1.79897 + 0.632701i) q^{51} -6.18395 q^{53} +(4.89903 + 8.48537i) q^{55} +(-3.71871 + 1.30788i) q^{57} +(-2.42804 - 4.20550i) q^{59} +3.09918 q^{61} +(-1.60471 - 10.4215i) q^{63} +(-3.99418 + 3.82501i) q^{65} -7.60626 q^{67} +(-4.37533 - 3.75318i) q^{69} +(2.43267 - 4.21351i) q^{71} -5.40814 q^{73} +(-0.845310 + 4.50679i) q^{75} +(11.2262 - 19.4444i) q^{77} +(2.39185 + 4.14281i) q^{79} +(-8.58311 + 2.70745i) q^{81} +(-3.19592 - 5.53550i) q^{83} +(0.844373 + 1.46250i) q^{85} +(2.33597 - 0.821562i) q^{87} +(-4.25286 - 7.36618i) q^{89} +(12.1671 + 3.54395i) q^{91} +(-6.32649 + 2.22503i) q^{93} +(1.74543 + 3.02318i) q^{95} -3.52623 q^{97} +(-17.8614 - 6.94460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

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

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
$3$	1.31464	+	1.12771i	0.759008	+	0.651081i
$3$	1.31464	+	1.12771i	0.759008	+	0.651081i
$4$		0			0
$5$	0.766914	−	1.32833i	0.342974	−	0.594049i	−0.642009	−	0.766697i	$-0.721899\pi$
$5$	0.766914	−	1.32833i	0.342974	−	0.594049i	0.984984	+	0.172648i	$0.0552323\pi$
$6$		0			0
$7$	−3.51479			−1.32847			−0.664233	−	0.747526i	$-0.731242\pi$
$7$	−3.51479			−1.32847			−0.664233	+	0.747526i	$0.731242\pi$
$8$		0			0
$9$	0.456560	+	2.96506i	0.152187	+	0.988352i
$10$		0			0
$11$	−3.19399	+	5.53215i	−0.963024	+	1.66801i	−0.248192	+	0.968711i	$0.579837\pi$
$11$	−3.19399	+	5.53215i	−0.963024	+	1.66801i	−0.714832	+	0.699296i	$0.753497\pi$
$12$		0			0
$13$	−3.46170	−	1.00830i	−0.960102	−	0.279651i
$13$	−3.46170	−	1.00830i	−0.960102	−	0.279651i
$14$		0			0
$15$	2.50619	−	0.881428i	0.647094	−	0.227584i
$16$		0			0
$17$	−0.550501	+	0.953495i	−0.133516	+	0.231256i	−0.925030	−	0.379895i	$-0.875960\pi$
$17$	−0.550501	+	0.953495i	−0.133516	+	0.231256i	0.791514	+	0.611152i	$0.209293\pi$
$18$		0			0
$19$	−1.13796	+	1.97100i	−0.261065	+	0.452179i	−0.966525	−	0.256571i	$-0.917407\pi$
$19$	−1.13796	+	1.97100i	−0.261065	+	0.452179i	0.705460	+	0.708750i	$0.250741\pi$
$20$		0			0
$21$	−4.62069	−	3.96365i	−1.00832	−	0.864939i
$22$		0			0
$23$	−3.32815			−0.693968			−0.346984	−	0.937871i	$-0.612794\pi$
$23$	−3.32815			−0.693968			−0.346984	+	0.937871i	$0.612794\pi$
$24$		0			0
$25$	1.32369	+	2.29269i	0.264737	+	0.458538i
$26$		0			0
$27$	−2.74350	+	4.41285i	−0.527986	+	0.849253i
$28$		0			0
$29$	0.714825	−	1.23811i	0.132740	−	0.229912i	−0.791992	−	0.610531i	$-0.790956\pi$
$29$	0.714825	−	1.23811i	0.132740	−	0.229912i	0.924732	+	0.380620i	$0.124289\pi$
$30$		0			0
$31$	−1.93596	+	3.35318i	−0.347708	+	0.602248i	−0.985842	−	0.167677i	$-0.946373\pi$
$31$	−1.93596	+	3.35318i	−0.347708	+	0.602248i	0.638134	+	0.769926i	$0.279707\pi$
$32$		0			0
$33$	−10.4376	+	3.67091i	−1.81695	+	0.639024i
$34$		0			0
$35$	−2.69554	+	4.66881i	−0.455630	+	0.789174i
$36$		0			0
$37$	1.81670	+	3.14662i	0.298664	+	0.517302i	0.975831	−	0.218528i	$-0.0701256\pi$
$37$	1.81670	+	3.14662i	0.298664	+	0.517302i	−0.677166	+	0.735830i	$0.736792\pi$
$38$		0			0
$39$	−3.41383	−	5.22932i	−0.546650	−	0.837361i
$40$		0			0
$41$	11.9875			1.87213			0.936065	−	0.351827i	$-0.114439\pi$
$41$	11.9875			1.87213			0.936065	+	0.351827i	$0.114439\pi$
$42$		0			0
$43$	12.5528			1.91428			0.957142	−	0.289619i	$-0.0935287\pi$
$43$	12.5528			1.91428			0.957142	+	0.289619i	$0.0935287\pi$
$44$		0			0
$45$	4.28873	+	1.66748i	0.639325	+	0.248573i
$46$		0			0
$47$	−1.23298	−	2.13558i	−0.179848	−	0.311506i	0.761980	−	0.647600i	$-0.224227\pi$
$47$	−1.23298	−	2.13558i	−0.179848	−	0.311506i	−0.941828	+	0.336094i	$0.890894\pi$
$48$		0			0
$49$	5.35375			0.764821
$50$		0			0
$51$	−1.79897	+	0.632701i	−0.251906	+	0.0885958i
$52$		0			0
$53$	−6.18395			−0.849431			−0.424716	−	0.905327i	$-0.639626\pi$
$53$	−6.18395			−0.849431			−0.424716	+	0.905327i	$0.639626\pi$
$54$		0			0
$55$	4.89903	+	8.48537i	0.660585	+	1.14417i
$56$		0			0
$57$	−3.71871	+	1.30788i	−0.492556	+	0.173232i
$58$		0			0
$59$	−2.42804	−	4.20550i	−0.316104	−	0.547509i	0.663567	−	0.748117i	$-0.269042\pi$
$59$	−2.42804	−	4.20550i	−0.316104	−	0.547509i	−0.979672	+	0.200608i	$0.935708\pi$
$60$		0			0
$61$	3.09918			0.396809			0.198405	−	0.980120i	$-0.436424\pi$
$61$	3.09918			0.396809			0.198405	+	0.980120i	$0.436424\pi$
$62$		0			0
$63$	−1.60471	−	10.4215i	−0.202175	−	1.31299i
$64$		0			0
$65$	−3.99418	+	3.82501i	−0.495417	+	0.474434i
$66$		0			0
$67$	−7.60626			−0.929252			−0.464626	−	0.885507i	$-0.653811\pi$
$67$	−7.60626			−0.929252			−0.464626	+	0.885507i	$0.653811\pi$
$68$		0			0
$69$	−4.37533	−	3.75318i	−0.526727	−	0.451829i
$70$		0			0
$71$	2.43267	−	4.21351i	0.288705	−	0.500051i	−0.684796	−	0.728735i	$-0.740109\pi$
$71$	2.43267	−	4.21351i	0.288705	−	0.500051i	0.973501	+	0.228683i	$0.0734421\pi$
$72$		0			0
$73$	−5.40814			−0.632975			−0.316487	−	0.948597i	$-0.602504\pi$
$73$	−5.40814			−0.632975			−0.316487	+	0.948597i	$0.602504\pi$
$74$		0			0
$75$	−0.845310	+	4.50679i	−0.0976080	+	0.520400i
$76$		0			0
$77$	11.2262	−	19.4444i	1.27934	−	2.21589i
$78$		0			0
$79$	2.39185	+	4.14281i	0.269104	+	0.466102i	0.968631	−	0.248505i	$-0.0799391\pi$
$79$	2.39185	+	4.14281i	0.269104	+	0.466102i	−0.699527	+	0.714607i	$0.746606\pi$
$80$		0			0
$81$	−8.58311	+	2.70745i	−0.953678	+	0.300828i
$82$		0			0
$83$	−3.19592	−	5.53550i	−0.350798	−	0.607600i	0.635591	−	0.772026i	$-0.280756\pi$
$83$	−3.19592	−	5.53550i	−0.350798	−	0.607600i	−0.986390	+	0.164425i	$0.947423\pi$
$84$		0			0
$85$	0.844373	+	1.46250i	0.0915851	+	0.158630i
$86$		0			0
$87$	2.33597	−	0.821562i	0.250442	−	0.0880807i
$88$		0			0
$89$	−4.25286	−	7.36618i	−0.450803	−	0.780813i	0.547633	−	0.836718i	$-0.315529\pi$
$89$	−4.25286	−	7.36618i	−0.450803	−	0.780813i	−0.998436	+	0.0559053i	$0.982196\pi$
$90$		0			0
$91$	12.1671	+	3.54395i	1.27546	+	0.371507i
$92$		0			0
$93$	−6.32649	+	2.22503i	−0.656026	+	0.230725i
$94$		0			0
$95$	1.74543	+	3.02318i	0.179077	+	0.310171i
$96$		0			0
$97$	−3.52623			−0.358035			−0.179017	−	0.983846i	$-0.557292\pi$
$97$	−3.52623			−0.358035			−0.179017	+	0.983846i	$0.557292\pi$
$98$		0			0
$99$	−17.8614	−	6.94460i	−1.79514	−	0.697958i
$100$		0			0
$101$	7.43406	−	12.8762i	0.739717	−	1.28123i	−0.212906	−	0.977073i	$-0.568293\pi$
$101$	7.43406	−	12.8762i	0.739717	−	1.28123i	0.952623	−	0.304154i	$-0.0983739\pi$
$102$		0			0
$103$	−5.76469	+	9.98474i	−0.568012	+	0.983826i	0.428750	+	0.903423i	$0.358954\pi$
$103$	−5.76469	+	9.98474i	−0.568012	+	0.983826i	−0.996762	+	0.0804029i	$0.974379\pi$
$104$		0			0
$105$	−8.80872	+	3.09804i	−0.859643	+	0.302337i
$106$		0			0
$107$	4.41074	+	7.63962i	0.426402	+	0.738550i	0.996550	−	0.0829919i	$-0.0264476\pi$
$107$	4.41074	+	7.63962i	0.426402	+	0.738550i	−0.570148	+	0.821542i	$0.693114\pi$
$108$		0			0
$109$	−9.26955			−0.887862			−0.443931	−	0.896061i	$-0.646416\pi$
$109$	−9.26955			−0.887862			−0.443931	+	0.896061i	$0.646416\pi$
$110$		0			0
$111$	−1.16015	+	6.18539i	−0.110117	+	0.587091i
$112$		0			0
$113$	3.36243	+	5.82389i	0.316310	+	0.547866i	0.979715	−	0.200395i	$-0.0642226\pi$
$113$	3.36243	+	5.82389i	0.316310	+	0.547866i	−0.663405	+	0.748261i	$0.730889\pi$
$114$		0			0
$115$	−2.55241	+	4.42090i	−0.238013	+	0.412251i
$116$		0			0
$117$	1.40918	−	10.7245i	0.130279	−	0.991477i
$118$		0			0
$119$	1.93489	−	3.35133i	0.177371	−	0.307216i
$120$		0			0
$121$	−14.9031	−	25.8130i	−1.35483	−	2.34664i
$122$		0			0
$123$	15.7592	+	13.5184i	1.42096	+	1.21891i
$124$		0			0
$125$	11.7298			1.04914
$126$		0			0
$127$	7.61299	+	13.1861i	0.675544	+	1.17008i	0.976310	+	0.216378i	$0.0694245\pi$
$127$	7.61299	+	13.1861i	0.675544	+	1.17008i	−0.300766	+	0.953698i	$0.597242\pi$
$128$		0			0
$129$	16.5024	+	14.1559i	1.45296	+	1.24635i
$130$		0			0
$131$	5.89951	−	10.2183i	0.515443	−	0.892773i	−0.484396	−	0.874849i	$-0.660961\pi$
$131$	5.89951	−	10.2183i	0.515443	−	0.892773i	0.999839	−	0.0179247i	$-0.00570593\pi$
$132$		0			0
$133$	3.99968	−	6.92765i	0.346817	−	0.600704i
$134$		0			0
$135$	3.75771	+	7.02855i	0.323412	+	0.604922i
$136$		0			0
$137$	−14.0053			−1.19655			−0.598277	−	0.801289i	$-0.704148\pi$
$137$	−14.0053			−1.19655			−0.598277	+	0.801289i	$0.704148\pi$
$138$		0			0
$139$	4.14354	+	7.17682i	0.351450	+	0.608730i	0.986504	−	0.163738i	$-0.0523553\pi$
$139$	4.14354	+	7.17682i	0.351450	+	0.608730i	−0.635054	+	0.772468i	$0.719022\pi$
$140$		0			0
$141$	0.787382	−	4.19795i	0.0663095	−	0.353531i
$142$		0			0
$143$	16.6347	−	15.9301i	1.39106	−	1.33215i
$144$		0			0
$145$	−1.09642	−	1.89905i	−0.0910526	−	0.157708i
$146$		0			0
$147$	7.03826	+	6.03745i	0.580506	+	0.497961i
$148$		0			0
$149$	−1.96851	−	3.40955i	−0.161266	−	0.279321i	0.774057	−	0.633116i	$-0.218224\pi$
$149$	−1.96851	−	3.40955i	−0.161266	−	0.279321i	−0.935323	+	0.353795i	$0.884891\pi$
$150$		0			0
$151$	10.1395	+	17.5621i	0.825138	+	1.42918i	0.901814	+	0.432125i	$0.142236\pi$
$151$	10.1395	+	17.5621i	0.825138	+	1.42918i	−0.0766753	+	0.997056i	$0.524430\pi$
$152$		0			0
$153$	−3.07850	−	1.19694i	−0.248882	−	0.0967666i
$154$		0			0
$155$	2.96943	+	5.14320i	0.238510	+	0.413111i
$156$		0			0
$157$	−11.7247	+	20.3078i	−0.935735	+	1.62074i	−0.162416	+	0.986722i	$0.551929\pi$
$157$	−11.7247	+	20.3078i	−0.935735	+	1.62074i	−0.773319	+	0.634017i	$0.781405\pi$
$158$		0			0
$159$	−8.12968	−	6.97368i	−0.644725	−	0.553049i
$160$		0			0
$161$	11.6978			0.921913
$162$		0			0
$163$	−1.54310	+	2.67272i	−0.120865	+	0.209344i	−0.920109	−	0.391663i	$-0.871900\pi$
$163$	−1.54310	+	2.67272i	−0.120865	+	0.209344i	0.799244	+	0.601006i	$0.205233\pi$
$164$		0			0
$165$	−3.12853	+	16.6799i	−0.243556	+	1.29853i
$166$		0			0
$167$	−19.5069			−1.50949			−0.754744	−	0.656019i	$-0.772239\pi$
$167$	−19.5069			−1.50949			−0.754744	+	0.656019i	$0.772239\pi$
$168$		0			0
$169$	10.9667	+	6.98083i	0.843591	+	0.536987i
$170$		0			0
$171$	−6.36367	−	2.47423i	−0.486642	−	0.189209i
$172$		0			0
$173$	−10.7005			−0.813543			−0.406771	−	0.913530i	$-0.633345\pi$
$173$	−10.7005			−0.813543			−0.406771	+	0.913530i	$0.633345\pi$
$174$		0			0
$175$	−4.65248	−	8.05833i	−0.351694	−	0.609153i
$176$		0			0
$177$	1.55056	−	8.26684i	0.116547	−	0.621373i
$178$		0			0
$179$	1.14067	+	1.97569i	0.0852574	+	0.147670i	0.905501	−	0.424344i	$-0.139495\pi$
$179$	1.14067	+	1.97569i	0.0852574	+	0.147670i	−0.820243	+	0.572015i	$0.806162\pi$
$180$		0			0
$181$	10.2756			0.763780			0.381890	−	0.924208i	$-0.375273\pi$
$181$	10.2756			0.763780			0.381890	+	0.924208i	$0.375273\pi$
$182$		0			0
$183$	4.07431	+	3.49496i	0.301182	+	0.258355i
$184$		0			0
$185$	5.57302			0.409737
$186$		0			0
$187$	−3.51659	−	6.09091i	−0.257158	−	0.445411i
$188$		0			0
$189$	9.64282	−	15.5102i	0.701412	−	1.12820i
$190$		0			0
$191$	23.6279			1.70965			0.854826	−	0.518914i	$-0.173664\pi$
$191$	23.6279			1.70965			0.854826	+	0.518914i	$0.173664\pi$
$192$		0			0
$193$	11.0395			0.794640			0.397320	−	0.917680i	$-0.369940\pi$
$193$	11.0395			0.794640			0.397320	+	0.917680i	$0.369940\pi$
$194$		0			0
$195$	−9.56439	+	0.524262i	−0.684920	+	0.0375432i
$196$		0			0
$197$	4.47677	+	7.75399i	0.318957	+	0.552449i	0.980271	−	0.197660i	$-0.0633342\pi$
$197$	4.47677	+	7.75399i	0.318957	+	0.552449i	−0.661314	+	0.750109i	$0.730001\pi$
$198$		0			0
$199$	11.6750	−	20.2217i	0.827620	−	1.43348i	−0.0722797	−	0.997384i	$-0.523027\pi$
$199$	11.6750	−	20.2217i	0.827620	−	1.43348i	0.899900	−	0.436096i	$-0.143639\pi$
$200$		0			0
$201$	−9.99949	−	8.57762i	−0.705310	−	0.605018i
$202$		0			0
$203$	−2.51246	+	4.35171i	−0.176340	+	0.305430i
$204$		0			0
$205$	9.19337	−	15.9234i	0.642093	−	1.11214i
$206$		0			0
$207$	−1.51950	−	9.86816i	−0.105613	−	0.685884i
$208$		0			0
$209$	−7.26925	−	12.5907i	−0.502825	−	0.870918i
$210$		0			0
$211$	−0.171961			−0.0118383			−0.00591913	−	0.999982i	$-0.501884\pi$
$211$	−0.171961			−0.0118383			−0.00591913	+	0.999982i	$0.501884\pi$
$212$		0			0
$213$	7.94968	−	2.79591i	0.544703	−	0.191573i
$214$		0			0
$215$	9.62691	−	16.6743i	0.656550	−	1.13718i
$216$		0			0
$217$	6.80449	−	11.7857i	0.461919	−	0.800066i
$218$		0			0
$219$	−7.10976	−	6.09879i	−0.480433	−	0.412118i
$220$		0			0
$221$	2.86707	−	2.74564i	0.192860	−	0.184692i
$222$		0			0
$223$	0.813127	−	1.40838i	0.0544510	−	0.0943119i	−0.837515	−	0.546414i	$-0.815992\pi$
$223$	0.813127	−	1.40838i	0.0544510	−	0.0943119i	0.891966	+	0.452102i	$0.149326\pi$
$224$		0			0
$225$	−6.19362	+	4.97156i	−0.412908	+	0.331437i
$226$		0			0
$227$	−22.5389			−1.49596			−0.747979	−	0.663722i	$-0.768976\pi$
$227$	−22.5389			−1.49596			−0.747979	+	0.663722i	$0.768976\pi$
$228$		0			0
$229$	−12.0818	+	20.9263i	−0.798389	+	1.38285i	0.122276	+	0.992496i	$0.460981\pi$
$229$	−12.0818	+	20.9263i	−0.798389	+	1.38285i	−0.920665	+	0.390354i	$0.872353\pi$
$230$		0			0
$231$	36.6859	−	12.9025i	2.41376	−	0.848921i
$232$		0			0
$233$	16.4919			1.08042			0.540211	−	0.841530i	$-0.318344\pi$
$233$	16.4919			1.08042			0.540211	+	0.841530i	$0.318344\pi$
$234$		0			0
$235$	−3.78235			−0.246733
$236$		0			0
$237$	−1.52744	+	8.14360i	−0.0992180	+	0.528984i
$238$		0			0
$239$	−5.24014	+	9.07618i	−0.338956	+	0.587089i	−0.984237	−	0.176856i	$-0.943407\pi$
$239$	−5.24014	+	9.07618i	−0.338956	+	0.587089i	0.645280	+	0.763946i	$0.276741\pi$
$240$		0			0
$241$	23.1800			1.49315			0.746577	−	0.665299i	$-0.231696\pi$
$241$	23.1800			1.49315			0.746577	+	0.665299i	$0.231696\pi$
$242$		0			0
$243$	−14.3369	−	6.11989i	−0.919713	−	0.392591i
$244$		0			0
$245$	4.10587	−	7.11157i	0.262314	−	0.454341i
$246$		0			0
$247$	5.92662	−	5.67561i	0.377102	−	0.361130i
$248$		0			0
$249$	2.04093	−	10.8813i	0.129338	−	0.689572i
$250$		0			0
$251$	−10.1392	+	17.5616i	−0.639979	+	1.10848i	0.345458	+	0.938434i	$0.387724\pi$
$251$	−10.1392	+	17.5616i	−0.639979	+	1.10848i	−0.985437	+	0.170042i	$0.945610\pi$
$252$		0			0
$253$	10.6301	−	18.4119i	0.668308	−	1.15754i
$254$		0			0
$255$	−0.539219	+	2.87486i	−0.0337672	+	0.180031i
$256$		0			0
$257$	−0.725978			−0.0452853			−0.0226426	−	0.999744i	$-0.507208\pi$
$257$	−0.725978			−0.0452853			−0.0226426	+	0.999744i	$0.507208\pi$
$258$		0			0
$259$	−6.38534	−	11.0597i	−0.396765	−	0.687218i
$260$		0			0
$261$	3.99743	+	1.55422i	0.247435	+	0.0962040i
$262$		0			0
$263$	4.81064	−	8.33227i	0.296637	−	0.513790i	−0.678728	−	0.734390i	$-0.737468\pi$
$263$	4.81064	−	8.33227i	0.296637	−	0.513790i	0.975364	+	0.220600i	$0.0708017\pi$
$264$		0			0
$265$	−4.74256	+	8.21435i	−0.291333	+	0.504604i
$266$		0			0
$267$	2.71589	−	14.4799i	0.166210	−	0.886153i
$268$		0			0
$269$	−6.12405	+	10.6072i	−0.373390	+	0.646731i	−0.990085	−	0.140472i	$-0.955138\pi$
$269$	−6.12405	+	10.6072i	−0.373390	+	0.646731i	0.616695	+	0.787202i	$0.288471\pi$
$270$		0			0
$271$	2.64462	+	4.58062i	0.160650	+	0.278253i	0.935102	−	0.354379i	$-0.115308\pi$
$271$	2.64462	+	4.58062i	0.160650	+	0.278253i	−0.774452	+	0.632632i	$0.781974\pi$
$272$		0			0
$273$	11.9989	+	18.3800i	0.726205	+	1.11241i
$274$		0			0
$275$	−16.9114			−1.01979
$276$		0			0
$277$	5.92911			0.356246			0.178123	−	0.984008i	$-0.442998\pi$
$277$	5.92911			0.356246			0.178123	+	0.984008i	$0.442998\pi$
$278$		0			0
$279$	−10.8262	−	4.20929i	−0.648150	−	0.252004i
$280$		0			0
$281$	16.2879	+	28.2115i	0.971654	+	1.68295i	0.690561	+	0.723275i	$0.257364\pi$
$281$	16.2879	+	28.2115i	0.971654	+	1.68295i	0.281094	+	0.959680i	$0.409303\pi$
$282$		0			0
$283$	18.5480			1.10256			0.551281	−	0.834320i	$-0.314139\pi$
$283$	18.5480			1.10256			0.551281	+	0.834320i	$0.314139\pi$
$284$		0			0
$285$	−1.11464	+	5.94272i	−0.0660254	+	0.352016i
$286$		0			0
$287$	−42.1335			−2.48706
$288$		0			0
$289$	7.89390	+	13.6726i	0.464347	+	0.804273i
$290$		0			0
$291$	−4.63573	−	3.97655i	−0.271751	−	0.233110i
$292$		0			0
$293$	8.99242	+	15.5753i	0.525343	+	0.909920i	0.999564	+	0.0295149i	$0.00939624\pi$
$293$	8.99242	+	15.5753i	0.525343	+	0.909920i	−0.474222	+	0.880406i	$0.657270\pi$
$294$		0			0
$295$	−7.44840			−0.433663
$296$		0			0
$297$	−15.6498	−	29.2720i	−0.908096	−	1.69854i
$298$		0			0
$299$	11.5211	+	3.35576i	0.666280	+	0.194069i
$300$		0			0
$301$	−44.1205			−2.54306
$302$		0			0
$303$	24.2937	−	8.54411i	1.39563	−	0.490846i
$304$		0			0
$305$	2.37680	−	4.11675i	0.136095	−	0.235724i
$306$		0			0
$307$	14.0831			0.803768			0.401884	−	0.915691i	$-0.368356\pi$
$307$	14.0831			0.803768			0.401884	+	0.915691i	$0.368356\pi$
$308$		0			0
$309$	−18.8384	+	6.62547i	−1.07168	+	0.376910i
$310$		0			0
$311$	15.3440	−	26.5767i	0.870081	−	1.50702i	0.00816904	−	0.999967i	$-0.497400\pi$
$311$	15.3440	−	26.5767i	0.870081	−	1.50702i	0.861912	−	0.507058i	$-0.169267\pi$
$312$		0			0
$313$	−5.48343	−	9.49757i	−0.309942	−	0.536835i	0.668408	−	0.743795i	$-0.266976\pi$
$313$	−5.48343	−	9.49757i	−0.309942	−	0.536835i	−0.978349	+	0.206961i	$0.933643\pi$
$314$		0			0
$315$	−15.0740	−	5.86083i	−0.849322	−	0.330221i
$316$		0			0
$317$	−1.15353	−	1.99797i	−0.0647885	−	0.112217i	0.831812	−	0.555058i	$-0.187304\pi$
$317$	−1.15353	−	1.99797i	−0.0647885	−	0.112217i	−0.896600	+	0.442841i	$0.853971\pi$
$318$		0			0
$319$	4.56629	+	7.90904i	0.255663	+	0.442821i
$320$		0			0
$321$	−2.81671	+	15.0174i	−0.157213	+	0.838188i
$322$		0			0
$323$	−1.25289	−	2.17007i	−0.0697128	−	0.120746i
$324$		0			0
$325$	−2.27049	−	9.27127i	−0.125944	−	0.514278i
$326$		0			0
$327$	−12.1861	−	10.4533i	−0.673894	−	0.578070i
$328$		0			0
$329$	4.33365	+	7.50611i	0.238922	+	0.413825i
$330$		0			0
$331$	−33.6498			−1.84956			−0.924780	−	0.380502i	$-0.875751\pi$
$331$	−33.6498			−1.84956			−0.924780	+	0.380502i	$0.875751\pi$
$332$		0			0
$333$	−8.50048	+	6.82325i	−0.465823	+	0.373912i
$334$		0			0
$335$	−5.83334	+	10.1036i	−0.318710	+	0.552021i
$336$		0			0
$337$	6.88906	−	11.9322i	0.375271	−	0.649988i	−0.615097	−	0.788452i	$-0.710883\pi$
$337$	6.88906	−	11.9322i	0.375271	−	0.649988i	0.990368	+	0.138464i	$0.0442164\pi$
$338$		0			0
$339$	−2.14725	+	11.4481i	−0.116623	+	0.621778i
$340$		0			0
$341$	−12.3669	−	21.4200i	−0.669703	−	1.15996i
$342$		0			0
$343$	5.78622			0.312427
$344$		0			0
$345$	−8.34097	+	2.93353i	−0.449063	+	0.157936i
$346$		0			0
$347$	−3.16260	−	5.47778i	−0.169777	−	0.294063i	0.768564	−	0.639773i	$-0.220971\pi$
$347$	−3.16260	−	5.47778i	−0.169777	−	0.294063i	−0.938341	+	0.345710i	$0.887638\pi$
$348$		0			0
$349$	−6.66685	+	11.5473i	−0.356868	+	0.618114i	−0.987436	−	0.158021i	$-0.949489\pi$
$349$	−6.66685	+	11.5473i	−0.356868	+	0.618114i	0.630568	+	0.776134i	$0.282822\pi$
$350$		0			0
$351$	13.9466	−	12.5097i	0.744415	−	0.667717i
$352$		0			0
$353$	12.6247	−	21.8666i	0.671945	−	1.16384i	−0.305407	−	0.952222i	$-0.598792\pi$
$353$	12.6247	−	21.8666i	0.671945	−	1.16384i	0.977352	−	0.211621i	$-0.0678742\pi$
$354$		0			0
$355$	−3.73130	−	6.46279i	−0.198037	−	0.343010i
$356$		0			0
$357$	6.32301	−	2.22381i	0.334649	−	0.117697i
$358$		0			0
$359$	1.22423			0.0646123			0.0323062	−	0.999478i	$-0.489715\pi$
$359$	1.22423			0.0646123			0.0323062	+	0.999478i	$0.489715\pi$
$360$		0			0
$361$	6.91010	+	11.9687i	0.363690	+	0.629929i
$362$		0			0
$363$	9.51719	−	50.7412i	0.499523	−	2.66322i
$364$		0			0
$365$	−4.14758	+	7.18381i	−0.217094	+	0.376018i
$366$		0			0
$367$	7.09999	−	12.2975i	0.370617	−	0.641927i	−0.619044	−	0.785356i	$-0.712480\pi$
$367$	7.09999	−	12.2975i	0.370617	−	0.641927i	0.989661	+	0.143430i	$0.0458131\pi$
$368$		0			0
$369$	5.47301	+	35.5436i	0.284913	+	1.85032i
$370$		0			0
$371$	21.7353			1.12844
$372$		0			0
$373$	8.38836	+	14.5291i	0.434333	+	0.752287i	0.997241	−	0.0742329i	$-0.0236508\pi$
$373$	8.38836	+	14.5291i	0.434333	+	0.752287i	−0.562908	+	0.826520i	$0.690317\pi$
$374$		0			0
$375$	15.4204	+	13.2277i	0.796306	+	0.683076i
$376$		0			0
$377$	−3.72289	+	3.56522i	−0.191739	+	0.183618i
$378$		0			0
$379$	18.3934	+	31.8583i	0.944807	+	1.63645i	0.756138	+	0.654413i	$0.227084\pi$
$379$	18.3934	+	31.8583i	0.944807	+	1.63645i	0.188669	+	0.982041i	$0.439583\pi$
$380$		0			0
$381$	−4.86168	+	25.9202i	−0.249071	+	1.32793i
$382$		0			0
$383$	−7.66299	−	13.2727i	−0.391561	−	0.678203i	0.601095	−	0.799178i	$-0.294731\pi$
$383$	−7.66299	−	13.2727i	−0.391561	−	0.678203i	−0.992656	+	0.120975i	$0.961398\pi$
$384$		0			0
$385$	−17.2191	−	29.8243i	−0.877565	−	1.51999i
$386$		0			0
$387$	5.73111	+	37.2197i	0.291329	+	1.89199i
$388$		0			0
$389$	4.10671	+	7.11304i	0.208219	+	0.360645i	0.951153	−	0.308718i	$-0.0999001\pi$
$389$	4.10671	+	7.11304i	0.208219	+	0.360645i	−0.742935	+	0.669364i	$0.766567\pi$
$390$		0			0
$391$	1.83215	−	3.17338i	0.0926558	−	0.160485i
$392$		0			0
$393$	19.2789	−	6.78042i	0.972493	−	0.342027i
$394$		0			0
$395$	7.33737			0.369183
$396$		0			0
$397$	−12.3499	+	21.3906i	−0.619822	+	1.07356i	0.369695	+	0.929153i	$0.379462\pi$
$397$	−12.3499	+	21.3906i	−0.619822	+	1.07356i	−0.989518	+	0.144411i	$0.953871\pi$
$398$		0			0
$399$	13.0705	−	4.59691i	0.654343	−	0.230133i
$400$		0			0
$401$	13.8473			0.691501			0.345750	−	0.938327i	$-0.387624\pi$
$401$	13.8473			0.691501			0.345750	+	0.938327i	$0.387624\pi$
$402$		0			0
$403$	10.0827	−	9.65566i	0.502255	−	0.480983i
$404$		0			0
$405$	−2.98610	+	13.4776i	−0.148381	+	0.669708i
$406$		0			0
$407$	−23.2101			−1.15048
$408$		0			0
$409$	−9.32539	−	16.1521i	−0.461111	−	0.798668i	0.537906	−	0.843005i	$-0.319216\pi$
$409$	−9.32539	−	16.1521i	−0.461111	−	0.798668i	−0.999017	+	0.0443375i	$0.985882\pi$
$410$		0			0
$411$	−18.4120	−	15.7939i	−0.908195	−	0.779054i
$412$		0			0
$413$	8.53407	+	14.7814i	0.419934	+	0.727347i
$414$		0			0
$415$	−9.80399			−0.481259
$416$		0			0
$417$	−2.64607	+	14.1076i	−0.129579	+	0.690853i
$418$		0			0
$419$	−15.7552			−0.769693			−0.384846	−	0.922981i	$-0.625746\pi$
$419$	−15.7552			−0.769693			−0.384846	+	0.922981i	$0.625746\pi$
$420$		0			0
$421$	−7.16989	−	12.4186i	−0.349439	−	0.605246i	0.636711	−	0.771103i	$-0.280295\pi$
$421$	−7.16989	−	12.4186i	−0.349439	−	0.605246i	−0.986150	+	0.165856i	$0.946961\pi$
$422$		0			0
$423$	5.76918	−	4.63086i	0.280507	−	0.225160i
$424$		0			0
$425$	−2.91476			−0.141387
$426$		0			0
$427$	−10.8930			−0.527148
$428$		0			0
$429$	39.8331	−	2.18341i	1.92316	−	0.105416i
$430$		0			0
$431$	4.49274	+	7.78165i	0.216408	+	0.374829i	0.953707	−	0.300737i	$-0.0972327\pi$
$431$	4.49274	+	7.78165i	0.216408	+	0.374829i	−0.737300	+	0.675566i	$0.763899\pi$
$432$		0			0
$433$	−13.8669	+	24.0182i	−0.666401	+	1.15424i	0.312503	+	0.949917i	$0.398833\pi$
$433$	−13.8669	+	24.0182i	−0.666401	+	1.15424i	−0.978904	+	0.204323i	$0.934501\pi$
$434$		0			0
$435$	0.700176	−	3.73301i	0.0335709	−	0.178984i
$436$		0			0
$437$	3.78730	−	6.55979i	0.181171	−	0.313797i
$438$		0			0
$439$	−2.97597	+	5.15453i	−0.142035	+	0.246012i	−0.928263	−	0.371925i	$-0.878698\pi$
$439$	−2.97597	+	5.15453i	−0.142035	+	0.246012i	0.786228	+	0.617937i	$0.212031\pi$
$440$		0			0
$441$	2.44431	+	15.8742i	0.116396	+	0.755913i
$442$		0			0
$443$	−5.66685	−	9.81526i	−0.269240	−	0.466337i	0.699426	−	0.714705i	$-0.253439\pi$
$443$	−5.66685	−	9.81526i	−0.269240	−	0.466337i	−0.968666	+	0.248368i	$0.920106\pi$
$444$		0			0
$445$	−13.0463			−0.618455
$446$		0			0
$447$	1.25709	−	6.70223i	0.0594585	−	0.317005i
$448$		0			0
$449$	6.47394	−	11.2132i	0.305524	−	0.529183i	−0.671854	−	0.740684i	$-0.734502\pi$
$449$	6.47394	−	11.2132i	0.305524	−	0.529183i	0.977378	+	0.211501i	$0.0678350\pi$
$450$		0			0
$451$	−38.2879	+	66.3166i	−1.80291	+	3.12273i
$452$		0			0
$453$	−6.47509	+	34.5222i	−0.304226	+	1.62199i
$454$		0			0
$455$	14.0387	−	13.4441i	0.658144	−	0.630270i
$456$		0			0
$457$	9.67396	−	16.7558i	0.452529	−	0.783803i	−0.546013	−	0.837776i	$-0.683855\pi$
$457$	9.67396	−	16.7558i	0.452529	−	0.783803i	0.998542	+	0.0539733i	$0.0171886\pi$
$458$		0			0
$459$	−2.69733	−	5.04519i	−0.125901	−	0.235489i
$460$		0			0
$461$	34.7972			1.62067			0.810334	−	0.585969i	$-0.199286\pi$
$461$	34.7972			1.62067			0.810334	+	0.585969i	$0.199286\pi$
$462$		0			0
$463$	13.0277	−	22.5647i	0.605450	−	1.04867i	−0.386530	−	0.922277i	$-0.626326\pi$
$463$	13.0277	−	22.5647i	0.605450	−	1.04867i	0.991980	−	0.126394i	$-0.0403402\pi$
$464$		0			0
$465$	−1.89628	+	10.1101i	−0.0879380	+	0.468844i
$466$		0			0
$467$	−39.3170			−1.81937			−0.909686	−	0.415296i	$-0.863678\pi$
$467$	−39.3170			−1.81937			−0.909686	+	0.415296i	$0.863678\pi$
$468$		0			0
$469$	26.7344			1.23448
$470$		0			0
$471$	−38.3150	+	13.4754i	−1.76546	+	0.620916i
$472$		0			0
$473$	−40.0935	+	69.4440i	−1.84350	+	3.19304i
$474$		0			0
$475$	−6.02520			−0.276455
$476$		0			0
$477$	−2.82335	−	18.3358i	−0.129272	−	0.839537i
$478$		0			0
$479$	−12.3647	+	21.4163i	−0.564957	+	0.978534i	0.432097	+	0.901827i	$0.357774\pi$
$479$	−12.3647	+	21.4163i	−0.564957	+	0.978534i	−0.997054	+	0.0767069i	$0.975559\pi$
$480$		0			0
$481$	−3.11615	−	12.7244i	−0.142084	−	0.580184i
$482$		0			0
$483$	15.3784	+	13.1916i	0.699739	+	0.600240i
$484$		0			0
$485$	−2.70432	+	4.68401i	−0.122797	+	0.212690i
$486$		0			0
$487$	15.5768	−	26.9798i	0.705853	−	1.22257i	−0.260530	−	0.965466i	$-0.583897\pi$
$487$	15.5768	−	26.9798i	0.705853	−	1.22257i	0.966383	−	0.257107i	$-0.0827694\pi$
$488$		0			0
$489$	−5.04266	+	1.77351i	−0.228037	+	0.0802009i
$490$		0			0
$491$	−1.64887			−0.0744124			−0.0372062	−	0.999308i	$-0.511846\pi$
$491$	−1.64887			−0.0744124			−0.0372062	+	0.999308i	$0.511846\pi$
$492$		0			0
$493$	0.787023	+	1.36316i	0.0354457	+	0.0613938i
$494$		0			0
$495$	−22.9229	+	18.4000i	−1.03031	+	0.827018i
$496$		0			0
$497$	−8.55032	+	14.8096i	−0.383534	+	0.664301i
$498$		0			0
$499$	−21.3882	+	37.0455i	−0.957468	+	1.65838i	−0.228850	+	0.973462i	$0.573496\pi$
$499$	−21.3882	+	37.0455i	−0.957468	+	1.65838i	−0.728618	+	0.684921i	$0.759837\pi$
$500$		0			0
$501$	−25.6445	−	21.9980i	−1.14571	−	0.982799i
$502$		0			0
$503$	−19.6416	+	34.0203i	−0.875777	+	1.51689i	−0.0198439	+	0.999803i	$0.506317\pi$
$503$	−19.6416	+	34.0203i	−0.875777	+	1.51689i	−0.855933	+	0.517087i	$0.827016\pi$
$504$		0			0
$505$	−11.4026	−	19.7498i	−0.507408	−	0.878856i
$506$		0			0
$507$	6.54493	+	21.5445i	0.290670	+	0.956823i
$508$		0			0
$509$	12.0577			0.534448			0.267224	−	0.963634i	$-0.413894\pi$
$509$	12.0577			0.534448			0.267224	+	0.963634i	$0.413894\pi$
$510$		0			0
$511$	19.0085			0.840885
$512$		0			0
$513$	−5.57574	−	10.4291i	−0.246175	−	0.460455i
$514$		0			0
$515$	8.84205	+	15.3149i	0.389627	+	0.674854i
$516$		0			0
$517$	15.7525			0.692792
$518$		0			0
$519$	−14.0673	−	12.0670i	−0.617486	−	0.529682i
$520$		0			0
$521$	16.6196			0.728116			0.364058	−	0.931376i	$-0.381391\pi$
$521$	16.6196			0.728116			0.364058	+	0.931376i	$0.381391\pi$
$522$		0			0
$523$	−0.621458	−	1.07640i	−0.0271745	−	0.0470676i	0.852118	−	0.523349i	$-0.175318\pi$
$523$	−0.621458	−	1.07640i	−0.0271745	−	0.0470676i	−0.879293	+	0.476282i	$0.841984\pi$
$524$		0			0
$525$	2.97109	−	15.8404i	0.129669	−	0.691333i
$526$		0			0
$527$	−2.13149	−	3.69185i	−0.0928492	−	0.160820i
$528$		0			0
$529$	−11.9234			−0.518409
$530$		0			0
$531$	11.3610	−	9.11935i	0.493025	−	0.395746i
$532$		0			0
$533$	−41.4970	−	12.0869i	−1.79744	−	0.523543i
$534$		0			0
$535$	13.5306			0.584980
$536$		0			0
$537$	−0.728433	+	3.88366i	−0.0314342	+	0.167592i
$538$		0			0
$539$	−17.0998	+	29.6178i	−0.736542	+	1.27573i
$540$		0			0
$541$	−41.8105			−1.79757			−0.898787	−	0.438386i	$-0.855550\pi$
$541$	−41.8105			−1.79757			−0.898787	+	0.438386i	$0.855550\pi$
$542$		0			0
$543$	13.5087	+	11.5879i	0.579715	+	0.497283i
$544$		0			0
$545$	−7.10895	+	12.3131i	−0.304514	+	0.527433i
$546$		0			0
$547$	−0.266912	−	0.462305i	−0.0114123	−	0.0197668i	0.860263	−	0.509851i	$-0.170299\pi$
$547$	−0.266912	−	0.462305i	−0.0114123	−	0.0197668i	−0.871675	+	0.490084i	$0.836966\pi$
$548$		0			0
$549$	1.41496	+	9.18924i	0.0603891	+	0.392187i
$550$		0			0
$551$	1.62688	+	2.81784i	0.0693075	+	0.120044i
$552$		0			0
$553$	−8.40685	−	14.5611i	−0.357496	−	0.619201i
$554$		0			0
$555$	7.32652	+	6.28473i	0.310994	+	0.266772i
$556$		0			0
$557$	3.96368	+	6.86530i	0.167947	+	0.290892i	0.937698	−	0.347452i	$-0.112953\pi$
$557$	3.96368	+	6.86530i	0.167947	+	0.290892i	−0.769751	+	0.638344i	$0.779620\pi$
$558$		0			0
$559$	−43.4540	−	12.6569i	−1.83791	−	0.535331i
$560$		0			0
$561$	2.24570	−	11.9730i	0.0948136	−	0.505502i
$562$		0			0
$563$	−15.5866	−	26.9968i	−0.656897	−	1.13778i	−0.981415	−	0.191899i	$-0.938535\pi$
$563$	−15.5866	−	26.9968i	−0.656897	−	1.13778i	0.324518	−	0.945880i	$-0.394798\pi$
$564$		0			0
$565$	10.3148			0.433945
$566$		0			0
$567$	30.1678	−	9.51612i	1.26693	−	0.399640i
$568$		0			0
$569$	−10.5253	+	18.2304i	−0.441244	+	0.764257i	−0.997782	−	0.0665652i	$-0.978796\pi$
$569$	−10.5253	+	18.2304i	−0.441244	+	0.764257i	0.556538	+	0.830822i	$0.312129\pi$
$570$		0			0
$571$	−2.80025	+	4.85017i	−0.117187	+	0.202973i	−0.918652	−	0.395068i	$-0.870721\pi$
$571$	−2.80025	+	4.85017i	−0.117187	+	0.202973i	0.801465	+	0.598042i	$0.204054\pi$
$572$		0			0
$573$	31.0622	+	26.6453i	1.29764	+	1.11312i
$574$		0			0
$575$	−4.40543	−	7.63043i	−0.183719	−	0.318211i
$576$		0			0
$577$	−30.6676			−1.27671			−0.638355	−	0.769742i	$-0.720385\pi$
$577$	−30.6676			−1.27671			−0.638355	+	0.769742i	$0.720385\pi$
$578$		0			0
$579$	14.5130	+	12.4493i	0.603138	+	0.517375i
$580$		0			0
$581$	11.2330	+	19.4561i	0.466023	+	0.807176i
$582$		0			0
$583$	19.7515	−	34.2106i	0.818023	−	1.41686i
$584$		0			0
$585$	−13.1650	−	10.0966i	−0.544304	−	0.417443i
$586$		0			0
$587$	15.7329	−	27.2501i	0.649364	−	1.12473i	−0.333911	−	0.942605i	$-0.608368\pi$
$587$	15.7329	−	27.2501i	0.649364	−	1.12473i	0.983275	−	0.182127i	$-0.0582983\pi$
$588$		0			0
$589$	−4.40608	−	7.63155i	−0.181549	−	0.314452i
$590$		0			0
$591$	−2.85888	+	15.2422i	−0.117599	+	0.626980i
$592$		0			0
$593$	0.583862			0.0239763			0.0119882	−	0.999928i	$-0.496184\pi$
$593$	0.583862			0.0239763			0.0119882	+	0.999928i	$0.496184\pi$
$594$		0			0
$595$	−2.96779	−	5.14037i	−0.121668	−	0.210735i
$596$		0			0
$597$	38.1526	−	13.4183i	1.56148	−	0.549175i
$598$		0			0
$599$	−12.5346	+	21.7106i	−0.512150	+	0.887069i	0.487751	+	0.872983i	$0.337817\pi$
$599$	−12.5346	+	21.7106i	−0.512150	+	0.887069i	−0.999901	+	0.0140866i	$0.995516\pi$
$600$		0			0
$601$	−7.76215	+	13.4444i	−0.316625	+	0.548410i	−0.979782	−	0.200071i	$-0.935883\pi$
$601$	−7.76215	+	13.4444i	−0.316625	+	0.548410i	0.663157	+	0.748480i	$0.269216\pi$
$602$		0			0
$603$	−3.47271	−	22.5530i	−0.141420	−	0.918428i
$604$		0			0
$605$	−45.7177			−1.85869
$606$		0			0
$607$	−15.4441	−	26.7500i	−0.626858	−	1.08575i	−0.988178	−	0.153308i	$-0.951007\pi$
$607$	−15.4441	−	26.7500i	−0.626858	−	1.08575i	0.361321	−	0.932442i	$-0.382326\pi$
$608$		0			0
$609$	−8.21043	+	2.88762i	−0.332703	+	0.117012i
$610$		0			0
$611$	2.11490	+	8.63592i	0.0855595	+	0.349372i
$612$		0			0
$613$	15.1558	+	26.2506i	0.612138	+	1.06025i	0.990879	+	0.134751i	$0.0430235\pi$
$613$	15.1558	+	26.2506i	0.612138	+	1.06025i	−0.378742	+	0.925502i	$0.623643\pi$
$614$		0			0
$615$	30.0429	−	10.5661i	1.21144	−	0.426067i
$616$		0			0
$617$	−5.97492	−	10.3489i	−0.240541	−	0.416630i	0.720327	−	0.693634i	$-0.243992\pi$
$617$	−5.97492	−	10.3489i	−0.240541	−	0.416630i	−0.960869	+	0.277005i	$0.910658\pi$
$618$		0			0
$619$	−11.3093	−	19.5884i	−0.454561	−	0.787323i	0.544102	−	0.839019i	$-0.316870\pi$
$619$	−11.3093	−	19.5884i	−0.454561	−	0.787323i	−0.998663	+	0.0516965i	$0.983537\pi$
$620$		0			0
$621$	9.13078	−	14.6866i	0.366406	−	0.589354i
$622$		0			0
$623$	14.9479	+	25.8906i	0.598876	+	1.03728i
$624$		0			0
$625$	2.37728	−	4.11756i	0.0950911	−	0.164703i
$626$		0			0
$627$	4.64216	−	24.7498i	0.185390	−	0.988414i
$628$		0			0
$629$	−4.00039			−0.159506
$630$		0			0
$631$	2.92924	−	5.07359i	0.116611	−	0.201976i	−0.801811	−	0.597577i	$-0.796130\pi$
$631$	2.92924	−	5.07359i	0.116611	−	0.201976i	0.918423	+	0.395601i	$0.129464\pi$
$632$		0			0
$633$	−0.226066	−	0.193921i	−0.00898533	−	0.00770766i
$634$		0			0
$635$	23.3540			0.926777
$636$		0			0
$637$	−18.5331	−	5.39816i	−0.734306	−	0.213883i
$638$		0			0
$639$	13.6039	+	5.28928i	0.538164	+	0.209241i
$640$		0			0
$641$	−13.8853			−0.548437			−0.274218	−	0.961667i	$-0.588419\pi$
$641$	−13.8853			−0.548437			−0.274218	+	0.961667i	$0.588419\pi$
$642$		0			0
$643$	−13.9906	−	24.2324i	−0.551734	−	0.955632i	−0.998150	−	0.0608059i	$-0.980633\pi$
$643$	−13.9906	−	24.2324i	−0.551734	−	0.955632i	0.446415	−	0.894826i	$-0.352700\pi$
$644$		0			0
$645$	31.4596	−	11.0644i	1.23872	−	0.435660i
$646$		0			0
$647$	13.4477	+	23.2920i	0.528682	+	0.915705i	0.999441	+	0.0334425i	$0.0106471\pi$
$647$	13.4477	+	23.2920i	0.528682	+	0.915705i	−0.470758	+	0.882262i	$0.656020\pi$
$648$		0			0
$649$	31.0206			1.21767
$650$		0			0
$651$	22.2363	−	7.82052i	0.871508	−	0.306510i
$652$		0			0
$653$	−19.3964			−0.759039			−0.379519	−	0.925184i	$-0.623911\pi$
$653$	−19.3964			−0.759039			−0.379519	+	0.925184i	$0.623911\pi$
$654$		0			0
$655$	−9.04884	−	15.6730i	−0.353567	−	0.612397i
$656$		0			0
$657$	−2.46914	−	16.0354i	−0.0963303	−	0.625602i
$658$		0			0
$659$	39.8501			1.55234			0.776171	−	0.630523i	$-0.217159\pi$
$659$	39.8501			1.55234			0.776171	+	0.630523i	$0.217159\pi$
$660$		0			0
$661$	11.4745			0.446306			0.223153	−	0.974783i	$-0.428365\pi$
$661$	11.4745			0.446306			0.223153	+	0.974783i	$0.428365\pi$
$662$		0			0
$663$	6.86544	−	0.376322i	0.266632	−	0.0146151i
$664$		0			0
$665$	−6.13482	−	10.6258i	−0.237898	−	0.412052i
$666$		0			0
$667$	−2.37905	+	4.12063i	−0.0921171	+	0.159551i
$668$		0			0
$669$	2.65720	−	0.934542i	0.102733	−	0.0361315i
$670$		0			0
$671$	−9.89875	+	17.1451i	−0.382137	+	0.661881i
$672$		0			0
$673$	18.3543	−	31.7906i	0.707506	−	1.22544i	−0.258273	−	0.966072i	$-0.583154\pi$
$673$	18.3543	−	31.7906i	0.707506	−	1.22544i	0.965779	−	0.259365i	$-0.0835132\pi$
$674$		0			0
$675$	−13.7488	−	0.448768i	−0.529193	−	0.0172731i
$676$		0			0
$677$	−3.57943	−	6.19976i	−0.137569	−	0.238276i	0.789007	−	0.614384i	$-0.210595\pi$
$677$	−3.57943	−	6.19976i	−0.137569	−	0.238276i	−0.926576	+	0.376108i	$0.877262\pi$
$678$		0			0
$679$	12.3940			0.475637
$680$		0			0
$681$	−29.6305	−	25.4172i	−1.13544	−	0.973990i
$682$		0			0
$683$	13.2982	−	23.0331i	0.508841	−	0.881338i	−0.491107	−	0.871099i	$-0.663408\pi$
$683$	13.2982	−	23.0331i	0.508841	−	0.881338i	0.999948	−	0.0102387i	$-0.00325912\pi$
$684$		0			0
$685$	−10.7409	+	18.6037i	−0.410387	+	0.710812i
$686$		0			0
$687$	−39.4820	+	13.8859i	−1.50633	+	0.529779i
$688$		0			0
$689$	21.4070	+	6.23525i	0.815540	+	0.237544i
$690$		0			0
$691$	15.5581	−	26.9474i	0.591858	−	1.02513i	−0.402124	−	0.915585i	$-0.631728\pi$
$691$	15.5581	−	26.9474i	0.591858	−	1.02513i	0.993982	−	0.109543i	$-0.0349387\pi$
$692$		0			0
$693$	62.7790	+	24.4088i	2.38478	+	0.927214i
$694$		0			0
$695$	12.7109			0.482154
$696$		0			0
$697$	−6.59912	+	11.4300i	−0.249959	+	0.432942i
$698$		0			0
$699$	21.6810	+	18.5980i	0.820049	+	0.703442i
$700$		0			0
$701$	−38.5419			−1.45571			−0.727854	−	0.685732i	$-0.759482\pi$
$701$	−38.5419			−1.45571			−0.727854	+	0.685732i	$0.759482\pi$
$702$		0			0
$703$	−8.26933			−0.311884
$704$		0			0
$705$	−4.97243	−	4.26537i	−0.187272	−	0.160643i
$706$		0			0
$707$	−26.1292	+	45.2570i	−0.982688	+	1.70207i
$708$		0			0
$709$	1.84079			0.0691325			0.0345662	−	0.999402i	$-0.488995\pi$
$709$	1.84079			0.0691325			0.0345662	+	0.999402i	$0.488995\pi$
$710$		0			0
$711$	−11.1916	+	8.98341i	−0.419719	+	0.336904i
$712$		0			0
$713$	6.44316	−	11.1599i	0.241298	−	0.417941i
$714$		0			0
$715$	−8.40319	−	34.3134i	−0.314262	−	1.28325i
$716$		0			0
$717$	−17.1242	+	6.02259i	−0.639513	+	0.224918i
$718$		0			0
$719$	9.15519	−	15.8573i	0.341431	−	0.591376i	−0.643268	−	0.765641i	$-0.722422\pi$
$719$	9.15519	−	15.8573i	0.341431	−	0.591376i	0.984699	+	0.174265i	$0.0557551\pi$
$720$		0			0
$721$	20.2617	−	35.0943i	0.754585	−	1.30698i
$722$		0			0
$723$	30.4734	+	26.1402i	1.13332	+	0.972164i
$724$		0			0
$725$	3.78482			0.140565
$726$		0			0
$727$	−11.6183	−	20.1235i	−0.430900	−	0.746340i	0.566051	−	0.824370i	$-0.308470\pi$
$727$	−11.6183	−	20.1235i	−0.430900	−	0.746340i	−0.996951	+	0.0780300i	$0.975137\pi$
$728$		0			0
$729$	−11.9464	−	24.2133i	−0.442461	−	0.896788i
$730$		0			0
$731$	−6.91032	+	11.9690i	−0.255587	+	0.442691i
$732$		0			0
$733$	−9.62013	+	16.6626i	−0.355328	+	0.615446i	−0.987174	−	0.159648i	$-0.948964\pi$
$733$	−9.62013	+	16.6626i	−0.355328	+	0.615446i	0.631846	+	0.775094i	$0.282297\pi$
$734$		0			0
$735$	13.4175	−	4.71895i	0.494912	−	0.174061i
$736$		0			0
$737$	24.2943	−	42.0790i	0.894892	−	1.55000i
$738$		0			0
$739$	−1.98535	−	3.43873i	−0.0730324	−	0.126496i	0.827197	−	0.561913i	$-0.189934\pi$
$739$	−1.98535	−	3.43873i	−0.0730324	−	0.126496i	−0.900229	+	0.435417i	$0.856601\pi$
$740$		0			0
$741$	14.1918	−	0.777907i	0.521348	−	0.0285771i
$742$		0			0
$743$	−5.75177			−0.211012			−0.105506	−	0.994419i	$-0.533646\pi$
$743$	−5.75177			−0.211012			−0.105506	+	0.994419i	$0.533646\pi$
$744$		0			0
$745$	−6.03870			−0.221241
$746$		0			0
$747$	14.9539	−	12.0034i	0.547136	−	0.439181i
$748$		0			0
$749$	−15.5028	−	26.8517i	−0.566460	−	0.981138i
$750$		0			0
$751$	−45.3603			−1.65522			−0.827610	−	0.561304i	$-0.810300\pi$
$751$	−45.3603			−1.65522			−0.827610	+	0.561304i	$0.810300\pi$
$752$		0			0
$753$	−33.1337	+	11.6531i	−1.20746	+	0.424664i
$754$		0			0
$755$	31.1044			1.13200
$756$		0			0
$757$	6.54346	+	11.3336i	0.237826	+	0.411927i	0.960090	−	0.279691i	$-0.0902319\pi$
$757$	6.54346	+	11.3336i	0.237826	+	0.411927i	−0.722264	+	0.691617i	$0.756899\pi$
$758$		0			0
$759$	34.7379	−	12.2174i	1.26091	−	0.443462i
$760$		0			0
$761$	13.5091	+	23.3985i	0.489706	+	0.848195i	0.999930	−	0.0118465i	$-0.00377094\pi$
$761$	13.5091	+	23.3985i	0.489706	+	0.848195i	−0.510224	+	0.860041i	$0.670438\pi$
$762$		0			0
$763$	32.5805			1.17949
$764$		0			0
$765$	−3.95088	+	3.17133i	−0.142844	+	0.114660i
$766$		0			0
$767$	4.16477	+	17.0063i	0.150381	+	0.614063i
$768$		0			0
$769$	46.2575			1.66809			0.834045	−	0.551697i	$-0.186019\pi$
$769$	46.2575			1.66809			0.834045	+	0.551697i	$0.186019\pi$
$770$		0			0
$771$	−0.954400	−	0.818690i	−0.0343719	−	0.0294844i
$772$		0			0
$773$	20.9744	−	36.3287i	0.754397	−	1.30665i	−0.191276	−	0.981536i	$-0.561263\pi$
$773$	20.9744	−	36.3287i	0.754397	−	1.30665i	0.945673	−	0.325118i	$-0.105404\pi$
$774$		0			0
$775$	−10.2504			−0.368205
$776$		0			0
$777$	4.07769	−	21.7403i	0.146286	−	0.779930i
$778$		0			0
$779$	−13.6413	+	23.6273i	−0.488749	+	0.846537i
$780$		0			0
$781$	15.5398	+	26.9158i	0.556059	+	0.963123i
$782$		0			0
$783$	3.50248	+	6.55117i	0.125169	+	0.234120i
$784$		0			0
$785$	17.9837	+	31.1487i	0.641866	+	1.11174i
$786$		0			0
$787$	−20.5108	−	35.5257i	−0.731131	−	1.26636i	−0.956400	−	0.292059i	$-0.905660\pi$
$787$	−20.5108	−	35.5257i	−0.731131	−	1.26636i	0.225270	−	0.974296i	$-0.427674\pi$
$788$		0			0
$789$	15.7206	−	5.52896i	0.559668	−	0.196836i
$790$		0			0
$791$	−11.8182	−	20.4698i	−0.420207	−	0.727821i
$792$		0			0
$793$	−10.7284	−	3.12489i	−0.380977	−	0.110968i
$794$		0			0
$795$	−15.4981	+	5.45071i	−0.549662	+	0.193317i
$796$		0			0
$797$	−8.28106	−	14.3432i	−0.293330	−	0.508063i	0.681265	−	0.732037i	$-0.261430\pi$
$797$	−8.28106	−	14.3432i	−0.293330	−	0.508063i	−0.974595	+	0.223974i	$0.928097\pi$
$798$		0			0
$799$	2.71502			0.0960504
$800$		0			0
$801$	19.8994	−	15.9731i	0.703112	−	0.564381i
$802$		0			0
$803$	17.2735	−	29.9187i	0.609570	−	1.05581i
$804$		0			0
$805$	8.97117	−	15.5385i	0.316192	−	0.547661i
$806$		0			0
$807$	−20.0127	+	7.03849i	−0.704480	+	0.247767i
$808$		0			0
$809$	−25.0672	−	43.4176i	−0.881314	−	1.52648i	−0.849880	−	0.526976i	$-0.823326\pi$
$809$	−25.0672	−	43.4176i	−0.881314	−	1.52648i	−0.0314339	−	0.999506i	$-0.510007\pi$
$810$		0			0
$811$	−15.2618			−0.535914			−0.267957	−	0.963431i	$-0.586349\pi$
$811$	−15.2618			−0.535914			−0.267957	+	0.963431i	$0.586349\pi$
$812$		0			0
$813$	−1.68886	+	9.00423i	−0.0592311	+	0.315792i
$814$		0			0
$815$	2.36684	+	4.09950i	0.0829070	+	0.143599i
$816$		0			0
$817$	−14.2846	+	24.7416i	−0.499753	+	0.865598i
$818$		0			0
$819$	−4.95297	+	37.6943i	−0.173071	+	1.31714i
$820$		0			0
$821$	2.56075	−	4.43535i	0.0893708	−	0.154795i	−0.817875	−	0.575397i	$-0.804848\pi$
$821$	2.56075	−	4.43535i	0.0893708	−	0.154795i	0.907245	+	0.420602i	$0.138181\pi$
$822$		0			0
$823$	7.45156	+	12.9065i	0.259745	+	0.449891i	0.966174	−	0.257893i	$-0.0830282\pi$
$823$	7.45156	+	12.9065i	0.259745	+	0.449891i	−0.706429	+	0.707784i	$0.749695\pi$
$824$		0			0
$825$	−22.2324	−	19.0710i	−0.774032	−	0.663968i
$826$		0			0
$827$	−18.5879			−0.646364			−0.323182	−	0.946337i	$-0.604753\pi$
$827$	−18.5879			−0.646364			−0.323182	+	0.946337i	$0.604753\pi$
$828$		0			0
$829$	−10.4298	−	18.0650i	−0.362243	−	0.627422i	0.626087	−	0.779753i	$-0.284655\pi$
$829$	−10.4298	−	18.0650i	−0.362243	−	0.627422i	−0.988330	+	0.152331i	$0.951322\pi$
$830$		0			0
$831$	7.79465	+	6.68629i	0.270393	+	0.231945i
$832$		0			0
$833$	−2.94724	+	5.10477i	−0.102116	+	0.176870i
$834$		0			0
$835$	−14.9601	+	25.9117i	−0.517716	+	0.896710i
$836$		0			0
$837$	−9.48577	−	17.7425i	−0.327876	−	0.613271i
$838$		0			0
$839$	36.0457			1.24444			0.622219	−	0.782843i	$-0.286231\pi$
$839$	36.0457			1.24444			0.622219	+	0.782843i	$0.286231\pi$
$840$		0			0
$841$	13.4781	+	23.3447i	0.464760	+	0.804989i
$842$		0			0
$843$	−10.4015	+	55.4559i	−0.358247	+	1.91000i
$844$		0			0
$845$	17.6834	−	9.21372i	0.608326	−	0.316962i
$846$		0			0
$847$	52.3814	+	90.7273i	1.79985	+	3.11743i
$848$		0			0
$849$	24.3839	+	20.9166i	0.836853	+	0.717857i
$850$		0			0
$851$	−6.04627	−	10.4724i	−0.207263	−	0.358991i
$852$		0			0
$853$	6.97776	+	12.0858i	0.238914	+	0.413811i	0.960403	−	0.278615i	$-0.0898753\pi$
$853$	6.97776	+	12.0858i	0.238914	+	0.413811i	−0.721489	+	0.692426i	$0.756542\pi$
$854$		0			0
$855$	−8.16699	+	6.55556i	−0.279305	+	0.224195i
$856$		0			0
$857$	8.73939	+	15.1371i	0.298532	+	0.517073i	0.975800	−	0.218664i	$-0.0701697\pi$
$857$	8.73939	+	15.1371i	0.298532	+	0.517073i	−0.677268	+	0.735736i	$0.736836\pi$
$858$		0			0
$859$	−4.17576	+	7.23263i	−0.142475	+	0.246774i	−0.928428	−	0.371512i	$-0.878839\pi$
$859$	−4.17576	+	7.23263i	−0.142475	+	0.246774i	0.785953	+	0.618286i	$0.212173\pi$
$860$		0			0
$861$	−55.3904	−	47.5142i	−1.88770	−	1.61928i
$862$		0			0
$863$	4.11501			0.140077			0.0700384	−	0.997544i	$-0.477688\pi$
$863$	4.11501			0.140077			0.0700384	+	0.997544i	$0.477688\pi$
$864$		0			0
$865$	−8.20635	+	14.2138i	−0.279024	+	0.483284i
$866$		0			0
$867$	−5.04107	+	26.8766i	−0.171204	+	0.912777i
$868$		0			0
$869$	−30.5582			−1.03662
$870$		0			0
$871$	26.3305	+	7.66935i	0.892176	+	0.259866i
$872$		0			0
$873$	−1.60994	−	10.4555i	−0.0544881	−	0.353864i
$874$		0			0
$875$	−41.2276			−1.39375
$876$		0			0
$877$	−5.30991	−	9.19704i	−0.179303	−	0.310562i	0.762339	−	0.647178i	$-0.224051\pi$
$877$	−5.30991	−	9.19704i	−0.179303	−	0.310562i	−0.941642	+	0.336616i	$0.890718\pi$
$878$		0			0
$879$	−5.74258	+	30.6168i	−0.193693	+	1.03268i
$880$		0			0
$881$	15.0048	+	25.9891i	0.505525	+	0.875595i	0.999980	+	0.00639173i	$0.00203456\pi$
$881$	15.0048	+	25.9891i	0.505525	+	0.875595i	−0.494454	+	0.869204i	$0.664632\pi$
$882$		0			0
$883$	21.3674			0.719072			0.359536	−	0.933131i	$-0.382935\pi$
$883$	21.3674			0.719072			0.359536	+	0.933131i	$0.382935\pi$
$884$		0			0
$885$	−9.79197	−	8.39961i	−0.329154	−	0.282350i
$886$		0			0
$887$	40.3161			1.35368			0.676841	−	0.736129i	$-0.263348\pi$
$887$	40.3161			1.35368			0.676841	+	0.736129i	$0.263348\pi$
$888$		0			0
$889$	−26.7581	−	46.3464i	−0.897437	−	1.55441i
$890$		0			0
$891$	12.4363	−	56.1306i	0.416632	−	1.88045i
$892$		0			0
$893$	5.61230			0.187808
$894$		0			0
$895$	3.49917			0.116964
$896$		0			0
$897$	11.3617	+	17.4040i	0.379357	+	0.581102i
$898$		0			0
$899$	2.76774	+	4.79387i	0.0923094	+	0.159884i
$900$		0			0
$901$	3.40427	−	5.89637i	0.113413	−	0.196436i
$902$		0			0
$903$	−58.0025	−	49.7549i	−1.93020	−	1.65574i
$904$		0			0
$905$	7.88051	−	13.6494i	0.261957	−	0.453723i
$906$		0			0
$907$	−7.39556	+	12.8095i	−0.245566	+	0.425332i	−0.962290	−	0.272024i	$-0.912307\pi$
$907$	−7.39556	+	12.8095i	−0.245566	+	0.425332i	0.716725	+	0.697356i	$0.245640\pi$
$908$		0			0
$909$	41.5727	+	16.1637i	1.37888	+	0.536115i
$910$		0			0
$911$	−16.1529	−	27.9777i	−0.535170	−	0.926942i	−0.999155	−	0.0410987i	$-0.986914\pi$
$911$	−16.1529	−	27.9777i	−0.535170	−	0.926942i	0.463985	−	0.885843i	$-0.346419\pi$
$912$		0			0
$913$	40.8310			1.35131
$914$		0			0
$915$	7.76712	−	2.73171i	0.256773	−	0.0903074i
$916$		0			0
$917$	−20.7356	+	35.9150i	−0.684748	+	1.18602i
$918$		0			0
$919$	18.5950	−	32.2075i	0.613392	−	1.06243i	−0.377272	−	0.926103i	$-0.623138\pi$
$919$	18.5950	−	32.2075i	0.613392	−	1.06243i	0.990664	−	0.136324i	$-0.0435289\pi$
$920$		0			0
$921$	18.5143	+	15.8816i	0.610066	+	0.523318i
$922$		0			0
$923$	−12.6696	+	12.1330i	−0.417026	+	0.399364i
$924$		0			0
$925$	−4.80949	+	8.33029i	−0.158135	+	0.273898i
$926$		0			0
$927$	−32.2372	−	12.5340i	−1.05881	−	0.411671i
$928$		0			0
$929$	15.2044			0.498841			0.249421	−	0.968395i	$-0.419760\pi$
$929$	15.2044			0.498841			0.249421	+	0.968395i	$0.419760\pi$
$930$		0			0
$931$	−6.09234	+	10.5522i	−0.199668	+	0.345836i
$932$		0			0
$933$	50.1426	−	17.6352i	1.64159	−	0.577351i
$934$		0			0
$935$	−10.7877			−0.352795
$936$		0			0
$937$	56.1934			1.83576			0.917880	−	0.396859i	$-0.129900\pi$
$937$	56.1934			1.83576			0.917880	+	0.396859i	$0.129900\pi$
$938$		0			0
$939$	3.50173	−	18.6696i	0.114275	−	0.609259i
$940$		0			0
$941$	15.6111	−	27.0393i	0.508909	−	0.881455i	−0.491038	−	0.871138i	$-0.663382\pi$
$941$	15.6111	−	27.0393i	0.508909	−	0.881455i	0.999947	−	0.0103174i	$-0.00328419\pi$
$942$		0			0
$943$	−39.8962			−1.29920
$944$		0			0
$945$	−13.2076	−	24.7039i	−0.429642	−	0.803618i
$946$		0			0
$947$	20.3364	−	35.2236i	0.660843	−	1.14461i	−0.319552	−	0.947569i	$-0.603532\pi$
$947$	20.3364	−	35.2236i	0.660843	−	1.14461i	0.980395	−	0.197044i	$-0.0631343\pi$
$948$		0			0
$949$	18.7213	+	5.45300i	0.607720	+	0.177012i
$950$		0			0
$951$	0.736645	−	3.92745i	0.0238874	−	0.127356i
$952$		0			0
$953$	1.35525	−	2.34736i	0.0439008	−	0.0760384i	−0.843240	−	0.537537i	$-0.819355\pi$
$953$	1.35525	−	2.34736i	0.0439008	−	0.0760384i	0.887141	+	0.461499i	$0.152688\pi$
$954$		0			0
$955$	18.1205	−	31.3857i	0.586367	−	1.01562i
$956$		0			0
$957$	−2.91604	+	15.5470i	−0.0942623	+	0.502562i
$958$		0			0
$959$	49.2257			1.58958
$960$		0			0
$961$	8.00414	+	13.8636i	0.258198	+	0.447212i
$962$		0			0
$963$	−20.6381	+	16.5660i	−0.665054	+	0.533833i
$964$		0			0
$965$	8.46634	−	14.6641i	0.272541	−	0.472055i
$966$		0			0
$967$	−2.04491	+	3.54189i	−0.0657600	+	0.113900i	−0.897031	−	0.441968i	$-0.854280\pi$
$967$	−2.04491	+	3.54189i	−0.0657600	+	0.113900i	0.831271	+	0.555868i	$0.187614\pi$
$968$		0			0
$969$	0.800101	−	4.26576i	0.0257029	−	0.137036i
$970$		0			0
$971$	−6.04999	+	10.4789i	−0.194153	+	0.336283i	−0.946623	−	0.322344i	$-0.895529\pi$
$971$	−6.04999	+	10.4789i	−0.194153	+	0.336283i	0.752469	+	0.658627i	$0.228863\pi$
$972$		0			0
$973$	−14.5637	−	25.2250i	−0.466890	−	0.808677i
$974$		0			0
$975$	7.47039	−	14.7488i	0.239244	−	0.472341i
$976$		0			0
$977$	7.64951			0.244729			0.122365	−	0.992485i	$-0.460952\pi$
$977$	7.64951			0.244729			0.122365	+	0.992485i	$0.460952\pi$
$978$		0			0
$979$	54.3344			1.73654
$980$		0			0
$981$	−4.23211	−	27.4847i	−0.135121	−	0.877520i
$982$		0			0
$983$	25.0980	+	43.4711i	0.800503	+	1.38651i	0.919286	+	0.393591i	$0.128767\pi$
$983$	25.0980	+	43.4711i	0.800503	+	1.38651i	−0.118783	+	0.992920i	$0.537899\pi$
$984$		0			0
$985$	13.7332			0.437576
$986$		0			0
$987$	−2.76748	+	14.7549i	−0.0880899	+	0.469654i
$988$		0			0
$989$	−41.7776			−1.32845
$990$		0			0
$991$	−21.7547	−	37.6803i	−0.691062	−	1.19695i	−0.971490	−	0.237079i	$-0.923810\pi$
$991$	−21.7547	−	37.6803i	−0.691062	−	1.19695i	0.280428	−	0.959875i	$-0.409523\pi$
$992$		0			0
$993$	−44.2374	−	37.9471i	−1.40383	−	1.20421i
$994$		0			0
$995$	−17.9075	−	31.0167i	−0.567705	−	0.983294i
$996$		0			0
$997$	−30.2028			−0.956532			−0.478266	−	0.878215i	$-0.658735\pi$
$997$	−30.2028			−0.956532			−0.478266	+	0.878215i	$0.658735\pi$
$998$		0			0
$999$	−18.8697	−	0.615915i	−0.597011	−	0.0194867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.913.17	yes	40
3.2	odd	2		2808.2.s.f.1225.8		40
9.2	odd	6		2808.2.r.f.289.8		40
9.7	even	3		936.2.r.f.601.11	✓	40
13.9	even	3		936.2.r.f.841.11	yes	40
39.35	odd	6		2808.2.r.f.2089.8		40
117.61	even	3	inner	936.2.s.f.529.17	yes	40
117.74	odd	6		2808.2.s.f.1153.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.11	✓	40	9.7	even	3
936.2.r.f.841.11	yes	40	13.9	even	3
936.2.s.f.529.17	yes	40	117.61	even	3	inner
936.2.s.f.913.17	yes	40	1.1	even	1	trivial
2808.2.r.f.289.8		40	9.2	odd	6
2808.2.r.f.2089.8		40	39.35	odd	6
2808.2.s.f.1153.8		40	117.74	odd	6
2808.2.s.f.1225.8		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.31464 + 1.12771i) q^{3} +(0.766914 - 1.32833i) q^{5} -3.51479 q^{7} +(0.456560 + 2.96506i) q^{9} +(-3.19399 + 5.53215i) q^{11} +(-3.46170 - 1.00830i) q^{13} +(2.50619 - 0.881428i) q^{15} +(-0.550501 + 0.953495i) q^{17} +(-1.13796 + 1.97100i) q^{19} +(-4.62069 - 3.96365i) q^{21} -3.32815 q^{23} +(1.32369 + 2.29269i) q^{25} +(-2.74350 + 4.41285i) q^{27} +(0.714825 - 1.23811i) q^{29} +(-1.93596 + 3.35318i) q^{31} +(-10.4376 + 3.67091i) q^{33} +(-2.69554 + 4.66881i) q^{35} +(1.81670 + 3.14662i) q^{37} +(-3.41383 - 5.22932i) q^{39} +11.9875 q^{41} +12.5528 q^{43} +(4.28873 + 1.66748i) q^{45} +(-1.23298 - 2.13558i) q^{47} +5.35375 q^{49} +(-1.79897 + 0.632701i) q^{51} -6.18395 q^{53} +(4.89903 + 8.48537i) q^{55} +(-3.71871 + 1.30788i) q^{57} +(-2.42804 - 4.20550i) q^{59} +3.09918 q^{61} +(-1.60471 - 10.4215i) q^{63} +(-3.99418 + 3.82501i) q^{65} -7.60626 q^{67} +(-4.37533 - 3.75318i) q^{69} +(2.43267 - 4.21351i) q^{71} -5.40814 q^{73} +(-0.845310 + 4.50679i) q^{75} +(11.2262 - 19.4444i) q^{77} +(2.39185 + 4.14281i) q^{79} +(-8.58311 + 2.70745i) q^{81} +(-3.19592 - 5.53550i) q^{83} +(0.844373 + 1.46250i) q^{85} +(2.33597 - 0.821562i) q^{87} +(-4.25286 - 7.36618i) q^{89} +(12.1671 + 3.54395i) q^{91} +(-6.32649 + 2.22503i) q^{93} +(1.74543 + 3.02318i) q^{95} -3.52623 q^{97} +(-17.8614 - 6.94460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 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

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Database

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