LMFDB - Embedded newform 1764.2.j.g.589.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(589,1764)] 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("1764.589"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.6
Root			$-1.73040 + 0.0755709i$ of defining polynomial
Character	$\chi$	$=$	1764.589
Dual form			1764.2.j.g.1177.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930647 + 1.46079i) q^{3} +(-0.483929 + 0.838189i) q^{5} +(-1.26779 + 2.71895i) q^{9} +(-0.364122 - 0.630678i) q^{11} +(1.81066 - 3.13615i) q^{13} +(-1.67478 + 0.0731419i) q^{15} -6.99897 q^{17} +0.696101 q^{19} +(-3.21898 + 5.57544i) q^{23} +(2.03163 + 3.51888i) q^{25} +(-5.15168 + 0.678412i) q^{27} +(3.34727 + 5.79764i) q^{29} +(-4.58310 + 7.93816i) q^{31} +(0.582416 - 1.11884i) q^{33} -1.70901 q^{37} +(6.26634 - 0.273666i) q^{39} +(-3.62444 + 6.27771i) q^{41} +(-0.348050 - 0.602841i) q^{43} +(-1.66548 - 2.37843i) q^{45} +(-3.83120 - 6.63583i) q^{47} +(-6.51357 - 10.2240i) q^{51} -4.11275 q^{53} +0.704836 q^{55} +(0.647824 + 1.01685i) q^{57} +(2.38809 - 4.13629i) q^{59} +(-2.46287 - 4.26582i) q^{61} +(1.75246 + 3.03535i) q^{65} +(2.91035 - 5.04087i) q^{67} +(-11.1403 + 0.486523i) q^{69} +0.304424 q^{71} -10.6776 q^{73} +(-3.24960 + 6.24261i) q^{75} +(1.61945 + 2.80497i) q^{79} +(-5.78541 - 6.89413i) q^{81} +(0.618759 + 1.07172i) q^{83} +(3.38700 - 5.86646i) q^{85} +(-5.35399 + 10.2852i) q^{87} +11.5736 q^{89} +(-15.8612 + 0.692698i) q^{93} +(-0.336863 + 0.583464i) q^{95} +(1.32933 + 2.30247i) q^{97} +(2.17641 - 0.190462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 2 q^{5} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} - 4 q^{17} - 14 q^{19} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} - q^{31} - q^{33} - 20 q^{37} + 22 q^{39} - 33 q^{41} + 7 q^{43}+ \cdots + 7 q^{99}+O(q^{100}) $ 14 * q - 3 * q^3 - 2 * q^5 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 - 4 * q^17 - 14 * q^19 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 - q^31 - q^33 - 20 * q^37 + 22 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 7 * q^51 + 30 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 - 42 * q^73 + 43 * q^75 - 10 * q^79 + 7 * q^81 - 25 * q^83 + 8 * q^85 - 26 * q^87 + 12 * q^89 - 38 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.930647	+	1.46079i	0.537309	+	0.843385i
$3$	0.930647	+	1.46079i	0.537309	+	0.843385i
$4$		0			0
$5$	−0.483929	+	0.838189i	−0.216419	+	0.374850i	−0.953711	−	0.300725i	$-0.902771\pi$
$5$	−0.483929	+	0.838189i	−0.216419	+	0.374850i	0.737291	+	0.675575i	$0.236105\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.26779	+	2.71895i	−0.422597	+	0.906318i
$10$		0			0
$11$	−0.364122	−	0.630678i	−0.109787	−	0.190156i	0.805897	−	0.592056i	$-0.201683\pi$
$11$	−0.364122	−	0.630678i	−0.109787	−	0.190156i	−0.915684	+	0.401899i	$0.868350\pi$
$12$		0			0
$13$	1.81066	−	3.13615i	0.502187	−	0.869813i	−0.497810	−	0.867286i	$-0.665862\pi$
$13$	1.81066	−	3.13615i	0.502187	−	0.869813i	0.999997	−	0.00252677i	$-0.000804296\pi$
$14$		0			0
$15$	−1.67478	+	0.0731419i	−0.432427	+	0.0188851i
$16$		0			0
$17$	−6.99897			−1.69750			−0.848749	−	0.528795i	$-0.822644\pi$
$17$	−6.99897			−1.69750			−0.848749	+	0.528795i	$0.822644\pi$
$18$		0			0
$19$	0.696101			0.159697			0.0798483	−	0.996807i	$-0.474556\pi$
$19$	0.696101			0.159697			0.0798483	+	0.996807i	$0.474556\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.21898	+	5.57544i	−0.671204	+	1.16256i	0.306359	+	0.951916i	$0.400889\pi$
$23$	−3.21898	+	5.57544i	−0.671204	+	1.16256i	−0.977563	+	0.210643i	$0.932444\pi$
$24$		0			0
$25$	2.03163	+	3.51888i	0.406325	+	0.703776i
$26$		0			0
$27$	−5.15168	+	0.678412i	−0.991440	+	0.130560i
$28$		0			0
$29$	3.34727	+	5.79764i	0.621573	+	1.07660i	0.989193	+	0.146619i	$0.0468393\pi$
$29$	3.34727	+	5.79764i	0.621573	+	1.07660i	−0.367620	+	0.929976i	$0.619827\pi$
$30$		0			0
$31$	−4.58310	+	7.93816i	−0.823149	+	1.42574i	0.0801762	+	0.996781i	$0.474452\pi$
$31$	−4.58310	+	7.93816i	−0.823149	+	1.42574i	−0.903326	+	0.428956i	$0.858882\pi$
$32$		0			0
$33$	0.582416	−	1.11884i	0.101386	−	0.194765i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.70901			−0.280960			−0.140480	−	0.990084i	$-0.544865\pi$
$37$	−1.70901			−0.280960			−0.140480	+	0.990084i	$0.544865\pi$
$38$		0			0
$39$	6.26634	−	0.273666i	1.00342	−	0.0438217i
$40$		0			0
$41$	−3.62444	+	6.27771i	−0.566042	+	0.980413i	0.430910	+	0.902395i	$0.358193\pi$
$41$	−3.62444	+	6.27771i	−0.566042	+	0.980413i	−0.996952	+	0.0780185i	$0.975141\pi$
$42$		0			0
$43$	−0.348050	−	0.602841i	−0.0530772	−	0.0919324i	0.838266	−	0.545261i	$-0.183570\pi$
$43$	−0.348050	−	0.602841i	−0.0530772	−	0.0919324i	−0.891343	+	0.453329i	$0.850236\pi$
$44$		0			0
$45$	−1.66548	−	2.37843i	−0.248274	−	0.354555i
$46$		0			0
$47$	−3.83120	−	6.63583i	−0.558838	−	0.967936i	−0.997594	−	0.0693294i	$-0.977914\pi$
$47$	−3.83120	−	6.63583i	−0.558838	−	0.967936i	0.438756	−	0.898606i	$-0.355419\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6.51357	−	10.2240i	−0.912082	−	1.43165i
$52$		0			0
$53$	−4.11275			−0.564929			−0.282465	−	0.959278i	$-0.591152\pi$
$53$	−4.11275			−0.564929			−0.282465	+	0.959278i	$0.591152\pi$
$54$		0			0
$55$	0.704836			0.0950401
$56$		0			0
$57$	0.647824	+	1.01685i	0.0858064	+	0.134686i
$58$		0			0
$59$	2.38809	−	4.13629i	0.310903	−	0.538500i	−0.667655	−	0.744471i	$-0.732702\pi$
$59$	2.38809	−	4.13629i	0.310903	−	0.538500i	0.978558	+	0.205971i	$0.0660353\pi$
$60$		0			0
$61$	−2.46287	−	4.26582i	−0.315338	−	0.546182i	0.664171	−	0.747581i	$-0.268785\pi$
$61$	−2.46287	−	4.26582i	−0.315338	−	0.546182i	−0.979509	+	0.201399i	$0.935451\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.75246	+	3.03535i	0.217366	+	0.376489i
$66$		0			0
$67$	2.91035	−	5.04087i	0.355556	−	0.615841i	−0.631657	−	0.775248i	$-0.717625\pi$
$67$	2.91035	−	5.04087i	0.355556	−	0.615841i	0.987213	+	0.159407i	$0.0509583\pi$
$68$		0			0
$69$	−11.1403	+	0.486523i	−1.34113	+	0.0585704i
$70$		0			0
$71$	0.304424			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$71$	0.304424			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$72$		0			0
$73$	−10.6776			−1.24972			−0.624858	−	0.780739i	$-0.714843\pi$
$73$	−10.6776			−1.24972			−0.624858	+	0.780739i	$0.714843\pi$
$74$		0			0
$75$	−3.24960	+	6.24261i	−0.375232	+	0.720834i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.61945	+	2.80497i	0.182203	+	0.315584i	0.942630	−	0.333839i	$-0.108344\pi$
$79$	1.61945	+	2.80497i	0.182203	+	0.315584i	−0.760428	+	0.649423i	$0.775011\pi$
$80$		0			0
$81$	−5.78541	−	6.89413i	−0.642823	−	0.766015i
$82$		0			0
$83$	0.618759	+	1.07172i	0.0679176	+	0.117637i	0.897985	−	0.440027i	$-0.145031\pi$
$83$	0.618759	+	1.07172i	0.0679176	+	0.117637i	−0.830067	+	0.557664i	$0.811698\pi$
$84$		0			0
$85$	3.38700	−	5.86646i	0.367372	−	0.636307i
$86$		0			0
$87$	−5.35399	+	10.2852i	−0.574008	+	1.10269i
$88$		0			0
$89$	11.5736			1.22680			0.613399	−	0.789773i	$-0.289802\pi$
$89$	11.5736			1.22680			0.613399	+	0.789773i	$0.289802\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−15.8612	+	0.692698i	−1.64473	+	0.0718295i
$94$		0			0
$95$	−0.336863	+	0.583464i	−0.0345614	+	0.0598622i
$96$		0			0
$97$	1.32933	+	2.30247i	0.134973	+	0.233780i	0.925587	−	0.378534i	$-0.123572\pi$
$97$	1.32933	+	2.30247i	0.134973	+	0.233780i	−0.790614	+	0.612315i	$0.790238\pi$
$98$		0			0
$99$	2.17641	−	0.190462i	0.218738	−	0.0191422i
$100$		0			0
$101$	−0.806969	−	1.39771i	−0.0802964	−	0.139077i	0.823081	−	0.567924i	$-0.192253\pi$
$101$	−0.806969	−	1.39771i	−0.0802964	−	0.139077i	−0.903377	+	0.428847i	$0.858920\pi$
$102$		0			0
$103$	−5.42007	+	9.38783i	−0.534055	+	0.925010i	0.465153	+	0.885230i	$0.345999\pi$
$103$	−5.42007	+	9.38783i	−0.534055	+	0.925010i	−0.999208	+	0.0397803i	$0.987334\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.95259			−0.962153			−0.481077	−	0.876679i	$-0.659754\pi$
$107$	−9.95259			−0.962153			−0.481077	+	0.876679i	$0.659754\pi$
$108$		0			0
$109$	18.5567			1.77741			0.888705	−	0.458480i	$-0.151606\pi$
$109$	18.5567			1.77741			0.888705	+	0.458480i	$0.151606\pi$
$110$		0			0
$111$	−1.59049	−	2.49650i	−0.150962	−	0.236957i
$112$		0			0
$113$	5.75824	−	9.97356i	0.541689	−	0.938234i	−0.457118	−	0.889406i	$-0.651118\pi$
$113$	5.75824	−	9.97356i	0.541689	−	0.938234i	0.998807	−	0.0488275i	$-0.0155485\pi$
$114$		0			0
$115$	−3.11551	−	5.39623i	−0.290523	−	0.503201i
$116$		0			0
$117$	6.23152	+	8.89909i	0.576104	+	0.822721i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.23483	−	9.06699i	0.475894	−	0.824272i
$122$		0			0
$123$	−12.5435	+	0.547804i	−1.13101	+	0.0493938i
$124$		0			0
$125$	−8.77193			−0.784586
$126$		0			0
$127$	9.06977			0.804812			0.402406	−	0.915461i	$-0.368174\pi$
$127$	9.06977			0.804812			0.402406	+	0.915461i	$0.368174\pi$
$128$		0			0
$129$	0.556710	−	1.06946i	0.0490156	−	0.0941607i
$130$		0			0
$131$	−6.54255	+	11.3320i	−0.571625	+	0.990084i	0.424774	+	0.905299i	$0.360354\pi$
$131$	−6.54255	+	11.3320i	−0.571625	+	0.990084i	−0.996399	+	0.0847847i	$0.972980\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.92441	−	4.64638i	0.165626	−	0.399897i
$136$		0			0
$137$	10.0382	+	17.3867i	0.857623	+	1.48545i	0.874190	+	0.485584i	$0.161393\pi$
$137$	10.0382	+	17.3867i	0.857623	+	1.48545i	−0.0165668	+	0.999863i	$0.505274\pi$
$138$		0			0
$139$	0.337832	−	0.585143i	0.0286546	−	0.0496312i	−0.851343	−	0.524610i	$-0.824211\pi$
$139$	0.337832	−	0.585143i	0.0286546	−	0.0496312i	0.879997	+	0.474979i	$0.157544\pi$
$140$		0			0
$141$	6.12804	−	11.7722i	0.516074	−	0.991397i
$142$		0			0
$143$	−2.63720			−0.220534
$144$		0			0
$145$	−6.47936			−0.538082
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.7544	+	18.6271i	−0.881034	+	1.52599i	−0.0308402	+	0.999524i	$0.509818\pi$
$149$	−10.7544	+	18.6271i	−0.881034	+	1.52599i	−0.850193	+	0.526471i	$0.823515\pi$
$150$		0			0
$151$	−7.08523	−	12.2720i	−0.576588	−	0.998680i	−0.995867	−	0.0908223i	$-0.971050\pi$
$151$	−7.08523	−	12.2720i	−0.576588	−	0.998680i	0.419279	−	0.907857i	$-0.362283\pi$
$152$		0			0
$153$	8.87324	−	19.0299i	0.717359	−	1.53847i
$154$		0			0
$155$	−4.43579	−	7.68301i	−0.356291	−	0.617114i
$156$		0			0
$157$	7.99845	−	13.8537i	0.638346	−	1.10565i	−0.347450	−	0.937699i	$-0.612952\pi$
$157$	7.99845	−	13.8537i	0.638346	−	1.10565i	0.985796	−	0.167949i	$-0.0537143\pi$
$158$		0			0
$159$	−3.82752	−	6.00784i	−0.303542	−	0.476453i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	20.1808			1.58068			0.790340	−	0.612669i	$-0.209904\pi$
$163$	20.1808			1.58068			0.790340	+	0.612669i	$0.209904\pi$
$164$		0			0
$165$	0.655953	+	1.02961i	0.0510659	+	0.0801554i
$166$		0			0
$167$	−12.2299	+	21.1828i	−0.946378	+	1.63917i	−0.193410	+	0.981118i	$0.561955\pi$
$167$	−12.2299	+	21.1828i	−0.946378	+	1.63917i	−0.752968	+	0.658057i	$0.771379\pi$
$168$		0			0
$169$	−0.0569772	−	0.0986874i	−0.00438286	−	0.00759134i
$170$		0			0
$171$	−0.882511	+	1.89267i	−0.0674873	+	0.144736i
$172$		0			0
$173$	−9.87800	−	17.1092i	−0.751010	−	1.30079i	−0.947333	−	0.320249i	$-0.896233\pi$
$173$	−9.87800	−	17.1092i	−0.751010	−	1.30079i	0.196323	−	0.980539i	$-0.437100\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.26471	−	0.360940i	0.621214	−	0.0271299i
$178$		0			0
$179$	12.6488			0.945415			0.472707	−	0.881219i	$-0.343277\pi$
$179$	12.6488			0.945415			0.472707	+	0.881219i	$0.343277\pi$
$180$		0			0
$181$	12.5654			0.933975			0.466988	−	0.884264i	$-0.345339\pi$
$181$	12.5654			0.933975			0.466988	+	0.884264i	$0.345339\pi$
$182$		0			0
$183$	3.93938	−	7.56770i	0.291208	−	0.559421i
$184$		0			0
$185$	0.827040	−	1.43248i	0.0608052	−	0.105318i
$186$		0			0
$187$	2.54848	+	4.41409i	0.186363	+	0.322790i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.70316	+	6.41407i	0.267951	+	0.464105i	0.968333	−	0.249663i	$-0.0803200\pi$
$191$	3.70316	+	6.41407i	0.267951	+	0.464105i	−0.700381	+	0.713769i	$0.746987\pi$
$192$		0			0
$193$	0.813937	−	1.40978i	0.0585885	−	0.101478i	−0.835244	−	0.549880i	$-0.814673\pi$
$193$	0.813937	−	1.40978i	0.0585885	−	0.101478i	0.893832	+	0.448402i	$0.148007\pi$
$194$		0			0
$195$	−2.80308	+	5.38481i	−0.200732	+	0.385614i
$196$		0			0
$197$	−8.27125			−0.589302			−0.294651	−	0.955605i	$-0.595203\pi$
$197$	−8.27125			−0.589302			−0.294651	+	0.955605i	$0.595203\pi$
$198$		0			0
$199$	−10.6882			−0.757667			−0.378834	−	0.925465i	$-0.623675\pi$
$199$	−10.6882			−0.757667			−0.378834	+	0.925465i	$0.623675\pi$
$200$		0			0
$201$	10.0721	−	0.439876i	0.710434	−	0.0310264i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.50794	−	6.07593i	−0.245005	−	0.424361i
$206$		0			0
$207$	−11.0783	−	15.8207i	−0.769998	−	1.09962i
$208$		0			0
$209$	−0.253466	−	0.439015i	−0.0175326	−	0.0303673i
$210$		0			0
$211$	−11.2725	+	19.5246i	−0.776034	+	1.34413i	0.158178	+	0.987411i	$0.449438\pi$
$211$	−11.2725	+	19.5246i	−0.776034	+	1.34413i	−0.934211	+	0.356720i	$0.883895\pi$
$212$		0			0
$213$	0.283311	+	0.444699i	0.0194122	+	0.0304702i
$214$		0			0
$215$	0.673726			0.0459478
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−9.93705	−	15.5976i	−0.671484	−	1.05399i
$220$		0			0
$221$	−12.6727	+	21.9498i	−0.852461	+	1.47651i
$222$		0			0
$223$	3.70093	+	6.41020i	0.247832	+	0.429258i	0.962924	−	0.269772i	$-0.0869484\pi$
$223$	3.70093	+	6.41020i	0.247832	+	0.429258i	−0.715092	+	0.699031i	$0.753615\pi$
$224$		0			0
$225$	−12.1433	+	1.06269i	−0.809556	+	0.0708458i
$226$		0			0
$227$	0.299086	+	0.518033i	0.0198511	+	0.0343831i	0.875780	−	0.482710i	$-0.160347\pi$
$227$	0.299086	+	0.518033i	0.0198511	+	0.0343831i	−0.855929	+	0.517093i	$0.827014\pi$
$228$		0			0
$229$	2.01858	−	3.49629i	0.133392	−	0.231041i	−0.791590	−	0.611052i	$-0.790747\pi$
$229$	2.01858	−	3.49629i	0.133392	−	0.231041i	0.924982	+	0.380011i	$0.124080\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.1951			0.733414			0.366707	−	0.930336i	$-0.380485\pi$
$233$	11.1951			0.733414			0.366707	+	0.930336i	$0.380485\pi$
$234$		0			0
$235$	7.41611			0.483774
$236$		0			0
$237$	−2.59033	+	4.97611i	−0.168260	+	0.323233i
$238$		0			0
$239$	−12.8171	+	22.1999i	−0.829069	+	1.43599i	0.0697006	+	0.997568i	$0.477796\pi$
$239$	−12.8171	+	22.1999i	−0.829069	+	1.43599i	−0.898769	+	0.438421i	$0.855538\pi$
$240$		0			0
$241$	3.29590	+	5.70866i	0.212307	+	0.367727i	0.952436	−	0.304738i	$-0.0985688\pi$
$241$	3.29590	+	5.70866i	0.212307	+	0.367727i	−0.740129	+	0.672465i	$0.765236\pi$
$242$		0			0
$243$	4.68668	−	14.8672i	0.300651	−	0.953734i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.26040	−	2.18308i	0.0801975	−	0.138906i
$248$		0			0
$249$	−0.989711	+	1.90127i	−0.0627204	+	0.120488i
$250$		0			0
$251$	25.0438			1.58075			0.790374	−	0.612624i	$-0.209886\pi$
$251$	25.0438			1.58075			0.790374	+	0.612624i	$0.209886\pi$
$252$		0			0
$253$	4.68840			0.294757
$254$		0			0
$255$	11.7217	−	0.511918i	0.734044	−	0.0320575i
$256$		0			0
$257$	9.07036	−	15.7103i	0.565794	−	0.979984i	−0.431182	−	0.902265i	$-0.641903\pi$
$257$	9.07036	−	15.7103i	0.565794	−	0.979984i	0.996975	−	0.0777184i	$-0.0247635\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−20.0072	+	1.75086i	−1.23841	+	0.108376i
$262$		0			0
$263$	−6.40438	−	11.0927i	−0.394911	−	0.684006i	0.598179	−	0.801363i	$-0.295891\pi$
$263$	−6.40438	−	11.0927i	−0.394911	−	0.684006i	−0.993090	+	0.117357i	$0.962558\pi$
$264$		0			0
$265$	1.99028	−	3.44726i	0.122262	−	0.211763i
$266$		0			0
$267$	10.7709	+	16.9065i	0.659170	+	1.03466i
$268$		0			0
$269$	28.8825			1.76099			0.880497	−	0.474052i	$-0.157209\pi$
$269$	28.8825			1.76099			0.880497	+	0.474052i	$0.157209\pi$
$270$		0			0
$271$	−9.19159			−0.558349			−0.279175	−	0.960240i	$-0.590061\pi$
$271$	−9.19159			−0.558349			−0.279175	+	0.960240i	$0.590061\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.47952	−	2.56260i	0.0892183	−	0.154531i
$276$		0			0
$277$	1.95778	+	3.39098i	0.117632	+	0.203744i	0.918829	−	0.394656i	$-0.129136\pi$
$277$	1.95778	+	3.39098i	0.117632	+	0.203744i	−0.801197	+	0.598401i	$0.795803\pi$
$278$		0			0
$279$	−15.7731	−	22.5252i	−0.944309	−	1.34855i
$280$		0			0
$281$	7.64654	+	13.2442i	0.456154	+	0.790082i	0.998754	−	0.0499093i	$-0.0158932\pi$
$281$	7.64654	+	13.2442i	0.456154	+	0.790082i	−0.542600	+	0.839991i	$0.682560\pi$
$282$		0			0
$283$	−12.4890	+	21.6315i	−0.742392	+	1.28586i	0.209011	+	0.977913i	$0.432975\pi$
$283$	−12.4890	+	21.6315i	−0.742392	+	1.28586i	−0.951403	+	0.307947i	$0.900358\pi$
$284$		0			0
$285$	−1.16582	+	0.0509141i	−0.0690570	+	0.00301589i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	31.9855			1.88150
$290$		0			0
$291$	−2.12628	+	4.08466i	−0.124645	+	0.239447i
$292$		0			0
$293$	−4.08092	+	7.06835i	−0.238410	+	0.412938i	−0.960258	−	0.279114i	$-0.909959\pi$
$293$	−4.08092	+	7.06835i	−0.238410	+	0.412938i	0.721848	+	0.692051i	$0.243293\pi$
$294$		0			0
$295$	2.31133	+	4.00334i	0.134571	+	0.233084i
$296$		0			0
$297$	2.30370	+	3.00202i	0.133674	+	0.174195i
$298$		0			0
$299$	11.6570	+	20.1904i	0.674139	+	1.16764i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.29075	−	2.47959i	0.0741519	−	0.142448i
$304$		0			0
$305$	4.76742			0.272981
$306$		0			0
$307$	18.0692			1.03126			0.515631	−	0.856811i	$-0.327558\pi$
$307$	18.0692			1.03126			0.515631	+	0.856811i	$0.327558\pi$
$308$		0			0
$309$	−18.7578	+	0.819199i	−1.06709	+	0.0466026i
$310$		0			0
$311$	5.00384	−	8.66691i	0.283742	−	0.491456i	−0.688561	−	0.725178i	$-0.741757\pi$
$311$	5.00384	−	8.66691i	0.283742	−	0.491456i	0.972303	+	0.233723i	$0.0750907\pi$
$312$		0			0
$313$	−1.49532	−	2.58998i	−0.0845207	−	0.146394i	0.820666	−	0.571408i	$-0.193603\pi$
$313$	−1.49532	−	2.58998i	−0.0845207	−	0.146394i	−0.905187	+	0.425014i	$0.860269\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.9246	+	20.6541i	0.669754	+	1.16005i	0.977973	+	0.208732i	$0.0669336\pi$
$317$	11.9246	+	20.6541i	0.669754	+	1.16005i	−0.308219	+	0.951315i	$0.599733\pi$
$318$		0			0
$319$	2.43763	−	4.22210i	0.136481	−	0.236392i
$320$		0			0
$321$	−9.26235	−	14.5386i	−0.516974	−	0.811466i
$322$		0			0
$323$	−4.87199			−0.271085
$324$		0			0
$325$	14.7143			0.816204
$326$		0			0
$327$	17.2697	+	27.1074i	0.955019	+	1.49904i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.01886	+	13.8891i	0.440757	+	0.763413i	0.997746	−	0.0671069i	$-0.0213768\pi$
$331$	8.01886	+	13.8891i	0.440757	+	0.763413i	−0.556989	+	0.830520i	$0.688044\pi$
$332$		0			0
$333$	2.16667	−	4.64672i	0.118733	−	0.254639i
$334$		0			0
$335$	2.81680	+	4.87884i	0.153898	+	0.266560i
$336$		0			0
$337$	16.8985	−	29.2691i	0.920520	−	1.59439i	0.121907	−	0.992542i	$-0.461099\pi$
$337$	16.8985	−	29.2691i	0.920520	−	1.59439i	0.798613	−	0.601845i	$-0.205568\pi$
$338$		0			0
$339$	19.9281	−	0.870311i	1.08235	−	0.0472688i
$340$		0			0
$341$	6.67523			0.361484
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.98329	−	9.57308i	0.268291	−	0.515397i
$346$		0			0
$347$	−17.6637	+	30.5944i	−0.948237	+	1.64240i	−0.199102	+	0.979979i	$0.563802\pi$
$347$	−17.6637	+	30.5944i	−0.948237	+	1.64240i	−0.749136	+	0.662417i	$0.769531\pi$
$348$		0			0
$349$	−5.75344	−	9.96526i	−0.307975	−	0.533428i	0.669944	−	0.742411i	$-0.266318\pi$
$349$	−5.75344	−	9.96526i	−0.307975	−	0.533428i	−0.977919	+	0.208983i	$0.932985\pi$
$350$		0			0
$351$	−7.20033	+	17.3848i	−0.384325	+	0.927933i
$352$		0			0
$353$	−12.4432	−	21.5522i	−0.662283	−	1.14711i	−0.980014	−	0.198926i	$-0.936254\pi$
$353$	−12.4432	−	21.5522i	−0.662283	−	1.14711i	0.317732	−	0.948181i	$-0.397079\pi$
$354$		0			0
$355$	−0.147320	+	0.255165i	−0.00781891	+	0.0135427i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.4536			−0.973944			−0.486972	−	0.873417i	$-0.661899\pi$
$359$	−18.4536			−0.973944			−0.486972	+	0.873417i	$0.661899\pi$
$360$		0			0
$361$	−18.5154			−0.974497
$362$		0			0
$363$	18.1167	−	0.791202i	0.950881	−	0.0415273i
$364$		0			0
$365$	5.16718	−	8.94982i	0.270463	−	0.468455i
$366$		0			0
$367$	9.10688	+	15.7736i	0.475375	+	0.823374i	0.999602	−	0.0282046i	$-0.00897899\pi$
$367$	9.10688	+	15.7736i	0.475375	+	0.823374i	−0.524227	+	0.851579i	$0.675646\pi$
$368$		0			0
$369$	−12.4738	−	17.8135i	−0.649358	−	0.927334i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	9.09995	−	15.7616i	0.471177	−	0.816103i	−0.528279	−	0.849071i	$-0.677162\pi$
$373$	9.09995	−	15.7616i	0.471177	−	0.816103i	0.999456	+	0.0329676i	$0.0104958\pi$
$374$		0			0
$375$	−8.16357	−	12.8139i	−0.421565	−	0.661708i
$376$		0			0
$377$	24.2431			1.24858
$378$		0			0
$379$	−24.1061			−1.23825			−0.619124	−	0.785293i	$-0.712512\pi$
$379$	−24.1061			−1.23825			−0.619124	+	0.785293i	$0.712512\pi$
$380$		0			0
$381$	8.44076	+	13.2490i	0.432433	+	0.678767i
$382$		0			0
$383$	3.21847	−	5.57455i	0.164456	−	0.284846i	−0.772006	−	0.635615i	$-0.780746\pi$
$383$	3.21847	−	5.57455i	0.164456	−	0.284846i	0.936462	+	0.350769i	$0.114080\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.08035	−	0.182055i	0.105750	−	0.00925440i
$388$		0			0
$389$	−16.9299	−	29.3234i	−0.858379	−	1.48676i	−0.873475	−	0.486869i	$-0.838139\pi$
$389$	−16.9299	−	29.3234i	−0.858379	−	1.48676i	0.0150964	−	0.999886i	$-0.495194\pi$
$390$		0			0
$391$	22.5295	−	39.0223i	1.13937	−	1.97344i
$392$		0			0
$393$	−22.6425	+	0.988853i	−1.14216	+	0.0498810i
$394$		0			0
$395$	−3.13480			−0.157729
$396$		0			0
$397$	1.61726			0.0811679			0.0405840	−	0.999176i	$-0.487078\pi$
$397$	1.61726			0.0811679			0.0405840	+	0.999176i	$0.487078\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.87691	+	4.98296i	−0.143666	+	0.248837i	−0.928874	−	0.370395i	$-0.879222\pi$
$401$	−2.87691	+	4.98296i	−0.143666	+	0.248837i	0.785208	+	0.619232i	$0.212556\pi$
$402$		0			0
$403$	16.5969	+	28.7466i	0.826749	+	1.43197i
$404$		0			0
$405$	8.57831	−	1.51300i	0.426260	−	0.0751813i
$406$		0			0
$407$	0.622289	+	1.07784i	0.0308457	+	0.0534263i
$408$		0			0
$409$	2.88631	−	4.99923i	0.142719	−	0.247196i	−0.785801	−	0.618480i	$-0.787749\pi$
$409$	2.88631	−	4.99923i	0.142719	−	0.247196i	0.928520	+	0.371284i	$0.121082\pi$
$410$		0			0
$411$	−16.0562	+	30.8446i	−0.791995	+	1.52145i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.19774			−0.0587948
$416$		0			0
$417$	1.16917	−	0.0510606i	0.0572546	−	0.00250045i
$418$		0			0
$419$	−9.29032	+	16.0913i	−0.453862	+	0.786111i	−0.998622	−	0.0524804i	$-0.983287\pi$
$419$	−9.29032	+	16.0913i	−0.453862	+	0.786111i	0.544760	+	0.838592i	$0.316621\pi$
$420$		0			0
$421$	−8.05788	−	13.9567i	−0.392717	−	0.680206i	0.600090	−	0.799933i	$-0.295131\pi$
$421$	−8.05788	−	13.9567i	−0.392717	−	0.680206i	−0.992807	+	0.119727i	$0.961798\pi$
$422$		0			0
$423$	22.8997	−	2.00399i	1.11342	−	0.0974375i
$424$		0			0
$425$	−14.2193	−	24.6285i	−0.689737	−	1.19466i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.45431	−	3.85239i	−0.118495	−	0.185995i
$430$		0			0
$431$	−3.65327			−0.175972			−0.0879860	−	0.996122i	$-0.528043\pi$
$431$	−3.65327			−0.175972			−0.0879860	+	0.996122i	$0.528043\pi$
$432$		0			0
$433$	12.6697			0.608865			0.304432	−	0.952534i	$-0.401533\pi$
$433$	12.6697			0.608865			0.304432	+	0.952534i	$0.401533\pi$
$434$		0			0
$435$	−6.03000	−	9.46496i	−0.289116	−	0.453810i
$436$		0			0
$437$	−2.24073	+	3.88107i	−0.107189	+	0.185657i
$438$		0			0
$439$	−5.85810	−	10.1465i	−0.279592	−	0.484267i	0.691692	−	0.722193i	$-0.256866\pi$
$439$	−5.85810	−	10.1465i	−0.279592	−	0.484267i	−0.971283	+	0.237926i	$0.923532\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.8735	+	25.7617i	0.706661	+	1.22397i	0.966089	+	0.258210i	$0.0831328\pi$
$443$	14.8735	+	25.7617i	0.706661	+	1.22397i	−0.259428	+	0.965763i	$0.583534\pi$
$444$		0			0
$445$	−5.60079	+	9.70085i	−0.265503	+	0.459865i
$446$		0			0
$447$	−37.2188	+	1.62544i	−1.76039	+	0.0768806i
$448$		0			0
$449$	11.0193			0.520034			0.260017	−	0.965604i	$-0.416272\pi$
$449$	11.0193			0.520034			0.260017	+	0.965604i	$0.416272\pi$
$450$		0			0
$451$	5.27895			0.248576
$452$		0			0
$453$	11.3329	−	21.7709i	0.532466	−	1.02289i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.258224	−	0.447257i	−0.0120792	−	0.0209218i	0.859923	−	0.510424i	$-0.170512\pi$
$457$	−0.258224	−	0.447257i	−0.0120792	−	0.0209218i	−0.872002	+	0.489503i	$0.837178\pi$
$458$		0			0
$459$	36.0564	−	4.74818i	1.68297	−	0.221626i
$460$		0			0
$461$	−3.54962	−	6.14813i	−0.165322	−	0.286347i	0.771447	−	0.636293i	$-0.219533\pi$
$461$	−3.54962	−	6.14813i	−0.165322	−	0.286347i	−0.936770	+	0.349946i	$0.886200\pi$
$462$		0			0
$463$	−4.91148	+	8.50693i	−0.228256	+	0.395351i	−0.957291	−	0.289125i	$-0.906636\pi$
$463$	−4.91148	+	8.50693i	−0.228256	+	0.395351i	0.729035	+	0.684476i	$0.239969\pi$
$464$		0			0
$465$	7.09508	−	13.6299i	0.329027	−	0.632072i
$466$		0			0
$467$	9.59208			0.443868			0.221934	−	0.975062i	$-0.428763\pi$
$467$	9.59208			0.443868			0.221934	+	0.975062i	$0.428763\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	27.6811	−	1.20890i	1.27548	−	0.0557032i
$472$		0			0
$473$	−0.253466	+	0.439015i	−0.0116544	+	0.0201859i
$474$		0			0
$475$	1.41422	+	2.44950i	0.0648887	+	0.112391i
$476$		0			0
$477$	5.21411	−	11.1824i	0.238738	−	0.512005i
$478$		0			0
$479$	−8.13621	−	14.0923i	−0.371753	−	0.643895i	0.618082	−	0.786113i	$-0.287910\pi$
$479$	−8.13621	−	14.0923i	−0.371753	−	0.643895i	−0.989835	+	0.142218i	$0.954576\pi$
$480$		0			0
$481$	−3.09444	+	5.35973i	−0.141094	+	0.244383i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.57321			−0.116843
$486$		0			0
$487$	19.0102			0.861436			0.430718	−	0.902487i	$-0.358260\pi$
$487$	19.0102			0.861436			0.430718	+	0.902487i	$0.358260\pi$
$488$		0			0
$489$	18.7812	+	29.4798i	0.849314	+	1.33312i
$490$		0			0
$491$	2.55413	−	4.42387i	0.115266	−	0.199647i	−0.802620	−	0.596491i	$-0.796561\pi$
$491$	2.55413	−	4.42387i	0.115266	−	0.199647i	0.917886	+	0.396844i	$0.129895\pi$
$492$		0			0
$493$	−23.4274	−	40.5775i	−1.05512	−	1.82752i
$494$		0			0
$495$	−0.893585	+	1.91642i	−0.0401637	+	0.0861365i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.2638	−	24.7056i	0.638536	−	1.10598i	−0.347219	−	0.937784i	$-0.612874\pi$
$499$	14.2638	−	24.7056i	0.638536	−	1.10598i	0.985754	−	0.168192i	$-0.0537928\pi$
$500$		0			0
$501$	−42.3253	+	1.84845i	−1.89095	+	0.0825826i
$502$		0			0
$503$	4.05885			0.180975			0.0904877	−	0.995898i	$-0.471157\pi$
$503$	4.05885			0.180975			0.0904877	+	0.995898i	$0.471157\pi$
$504$		0			0
$505$	1.56206			0.0695108
$506$		0			0
$507$	0.0911355	−	0.175075i	0.00404747	−	0.00777534i
$508$		0			0
$509$	−8.63023	+	14.9480i	−0.382528	+	0.662558i	−0.991423	−	0.130693i	$-0.958280\pi$
$509$	−8.63023	+	14.9480i	−0.382528	+	0.662558i	0.608895	+	0.793251i	$0.291613\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3.58609	+	0.472243i	−0.158330	+	0.0208500i
$514$		0			0
$515$	−5.24585	−	9.08608i	−0.231160	−	0.400380i
$516$		0			0
$517$	−2.79005	+	4.83250i	−0.122706	+	0.212533i
$518$		0			0
$519$	15.7999	−	30.3523i	0.693541	−	1.33232i
$520$		0			0
$521$	34.1050			1.49417			0.747083	−	0.664730i	$-0.231454\pi$
$521$	34.1050			1.49417			0.747083	+	0.664730i	$0.231454\pi$
$522$		0			0
$523$	18.8969			0.826306			0.413153	−	0.910662i	$-0.364428\pi$
$523$	18.8969			0.826306			0.413153	+	0.910662i	$0.364428\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	32.0770	−	55.5589i	1.39729	−	2.42019i
$528$		0			0
$529$	−9.22366	−	15.9758i	−0.401029	−	0.694602i
$530$		0			0
$531$	8.21878	+	11.7371i	0.356665	+	0.509345i
$532$		0			0
$533$	13.1252	+	22.7336i	0.568517	+	0.984701i
$534$		0			0
$535$	4.81634	−	8.34215i	0.208229	−	0.360663i
$536$		0			0
$537$	11.7716	+	18.4772i	0.507980	+	0.797349i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.12823			−0.0485066			−0.0242533	−	0.999706i	$-0.507721\pi$
$541$	−1.12823			−0.0485066			−0.0242533	+	0.999706i	$0.507721\pi$
$542$		0			0
$543$	11.6939	+	18.3553i	0.501834	+	0.787701i
$544$		0			0
$545$	−8.98012	+	15.5540i	−0.384666	+	0.666261i
$546$		0			0
$547$	15.8427	+	27.4404i	0.677386	+	1.17327i	0.975765	+	0.218819i	$0.0702205\pi$
$547$	15.8427	+	27.4404i	0.677386	+	1.17327i	−0.298380	+	0.954447i	$0.596446\pi$
$548$		0			0
$549$	14.7210	−	1.28826i	0.628276	−	0.0549816i
$550$		0			0
$551$	2.33004	+	4.03575i	0.0992630	+	0.171929i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.86222	−	0.125000i	0.121495	−	0.00530597i
$556$		0			0
$557$	27.6271			1.17060			0.585298	−	0.810818i	$-0.300977\pi$
$557$	27.6271			1.17060			0.585298	+	0.810818i	$0.300977\pi$
$558$		0			0
$559$	−2.52080			−0.106619
$560$		0			0
$561$	−4.07631	+	7.83074i	−0.172102	+	0.330614i
$562$		0			0
$563$	−0.920685	+	1.59467i	−0.0388022	+	0.0672074i	−0.884774	−	0.466020i	$-0.845688\pi$
$563$	−0.920685	+	1.59467i	−0.0388022	+	0.0672074i	0.845972	+	0.533227i	$0.179021\pi$
$564$		0			0
$565$	5.57315	+	9.65298i	0.234464	+	0.406104i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.75524	+	9.96837i	0.241272	+	0.417896i	0.961077	−	0.276281i	$-0.0891020\pi$
$569$	5.75524	+	9.96837i	0.241272	+	0.417896i	−0.719805	+	0.694177i	$0.755769\pi$
$570$		0			0
$571$	4.35262	−	7.53896i	0.182152	−	0.315496i	−0.760461	−	0.649383i	$-0.775027\pi$
$571$	4.35262	−	7.53896i	0.182152	−	0.315496i	0.942613	+	0.333887i	$0.108361\pi$
$572$		0			0
$573$	−5.92324	+	11.3788i	−0.247447	+	0.475354i
$574$		0			0
$575$	−26.1591			−1.09091
$576$		0			0
$577$	14.4872			0.603108			0.301554	−	0.953449i	$-0.402495\pi$
$577$	14.4872			0.603108			0.301554	+	0.953449i	$0.402495\pi$
$578$		0			0
$579$	2.81688	−	0.123020i	0.117065	−	0.00511254i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.49754	+	2.59382i	0.0620218	+	0.107425i
$584$		0			0
$585$	−10.4747	+	0.916663i	−0.433077	+	0.0378994i
$586$		0			0
$587$	−14.3695	−	24.8886i	−0.593091	−	1.02726i	−0.993813	−	0.111065i	$-0.964574\pi$
$587$	−14.3695	−	24.8886i	−0.593091	−	1.02726i	0.400722	−	0.916200i	$-0.368759\pi$
$588$		0			0
$589$	−3.19030	+	5.52576i	−0.131454	+	0.227685i
$590$		0			0
$591$	−7.69761	−	12.0825i	−0.316637	−	0.497009i
$592$		0			0
$593$	−13.6466			−0.560397			−0.280199	−	0.959942i	$-0.590400\pi$
$593$	−13.6466			−0.560397			−0.280199	+	0.959942i	$0.590400\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.94696	−	15.6132i	−0.407102	−	0.639006i
$598$		0			0
$599$	−2.64585	+	4.58275i	−0.108106	+	0.187246i	−0.915003	−	0.403447i	$-0.867812\pi$
$599$	−2.64585	+	4.58275i	−0.108106	+	0.187246i	0.806897	+	0.590693i	$0.201145\pi$
$600$		0			0
$601$	17.0522	+	29.5353i	0.695574	+	1.20477i	0.969987	+	0.243158i	$0.0781834\pi$
$601$	17.0522	+	29.5353i	0.695574	+	1.20477i	−0.274412	+	0.961612i	$0.588483\pi$
$602$		0			0
$603$	10.0162	+	14.3039i	0.407890	+	0.582499i
$604$		0			0
$605$	5.06657	+	8.77555i	0.205985	+	0.356777i
$606$		0			0
$607$	4.52232	−	7.83289i	0.183555	−	0.317927i	−0.759533	−	0.650468i	$-0.774573\pi$
$607$	4.52232	−	7.83289i	0.183555	−	0.317927i	0.943089	+	0.332541i	$0.107906\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−27.7480			−1.12256
$612$		0			0
$613$	−11.9578			−0.482970			−0.241485	−	0.970405i	$-0.577634\pi$
$613$	−11.9578			−0.482970			−0.241485	+	0.970405i	$0.577634\pi$
$614$		0			0
$615$	5.61098	−	10.7789i	0.226256	−	0.434647i
$616$		0			0
$617$	5.13220	−	8.88923i	0.206615	−	0.357867i	−0.744031	−	0.668145i	$-0.767089\pi$
$617$	5.13220	−	8.88923i	0.206615	−	0.357867i	0.950646	+	0.310278i	$0.100422\pi$
$618$		0			0
$619$	21.7803	+	37.7245i	0.875423	+	1.51628i	0.856312	+	0.516460i	$0.172750\pi$
$619$	21.7803	+	37.7245i	0.875423	+	1.51628i	0.0191114	+	0.999817i	$0.493916\pi$
$620$		0			0
$621$	12.8007	−	30.9066i	0.513674	−	1.24024i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.91314	+	10.2419i	−0.236526	+	0.409674i
$626$		0			0
$627$	0.405420	−	0.778827i	0.0161909	−	0.0311034i
$628$		0			0
$629$	11.9613			0.476929
$630$		0			0
$631$	19.3703			0.771119			0.385559	−	0.922683i	$-0.374008\pi$
$631$	19.3703			0.771119			0.385559	+	0.922683i	$0.374008\pi$
$632$		0			0
$633$	−39.0121	+	1.70375i	−1.55059	+	0.0677181i
$634$		0			0
$635$	−4.38912	+	7.60218i	−0.174177	+	0.301684i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.385946	+	0.827715i	−0.0152678	+	0.0327439i
$640$		0			0
$641$	−2.25008	−	3.89725i	−0.0888728	−	0.153932i	0.818162	−	0.574988i	$-0.194993\pi$
$641$	−2.25008	−	3.89725i	−0.0888728	−	0.153932i	−0.907035	+	0.421055i	$0.861660\pi$
$642$		0			0
$643$	−20.9045	+	36.2077i	−0.824394	+	1.42789i	0.0779869	+	0.996954i	$0.475151\pi$
$643$	−20.9045	+	36.2077i	−0.824394	+	1.42789i	−0.902381	+	0.430939i	$0.858183\pi$
$644$		0			0
$645$	0.627001	+	0.984170i	0.0246882	+	0.0387517i
$646$		0			0
$647$	−23.8761			−0.938667			−0.469334	−	0.883021i	$-0.655506\pi$
$647$	−23.8761			−0.938667			−0.469334	+	0.883021i	$0.655506\pi$
$648$		0			0
$649$	−3.47822			−0.136532
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.16674	−	7.21700i	0.163057	−	0.282423i	−0.772907	−	0.634520i	$-0.781198\pi$
$653$	4.16674	−	7.21700i	0.163057	−	0.282423i	0.935964	+	0.352097i	$0.114531\pi$
$654$		0			0
$655$	−6.33226	−	10.9678i	−0.247422	−	0.428547i
$656$		0			0
$657$	13.5369	−	29.0318i	0.528126	−	1.13264i
$658$		0			0
$659$	−20.2488	−	35.0719i	−0.788781	−	1.36621i	−0.926714	−	0.375767i	$-0.877379\pi$
$659$	−20.2488	−	35.0719i	−0.788781	−	1.36621i	0.137933	−	0.990442i	$-0.455954\pi$
$660$		0			0
$661$	3.88559	−	6.73004i	0.151132	−	0.261768i	−0.780512	−	0.625141i	$-0.785042\pi$
$661$	3.88559	−	6.73004i	0.151132	−	0.261768i	0.931644	+	0.363373i	$0.118375\pi$
$662$		0			0
$663$	−43.8579	+	1.91538i	−1.70330	+	0.0743873i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−43.0992			−1.66881
$668$		0			0
$669$	−5.91967	+	11.3719i	−0.228868	+	0.439663i
$670$		0			0
$671$	−1.79357	+	3.10656i	−0.0692400	+	0.119927i
$672$		0			0
$673$	−22.7830	−	39.4614i	−0.878221	−	1.52112i	−0.853291	−	0.521435i	$-0.825397\pi$
$673$	−22.7830	−	39.4614i	−0.878221	−	1.52112i	−0.0249302	−	0.999689i	$-0.507936\pi$
$674$		0			0
$675$	−12.8535	−	16.7498i	−0.494733	−	0.644702i
$676$		0			0
$677$	−6.54521	−	11.3366i	−0.251553	−	0.435702i	0.712401	−	0.701773i	$-0.247608\pi$
$677$	−6.54521	−	11.3366i	−0.251553	−	0.435702i	−0.963954	+	0.266071i	$0.914275\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.478391	+	0.919007i	−0.0183320	+	0.0352164i
$682$		0			0
$683$	25.3011			0.968121			0.484060	−	0.875035i	$-0.339161\pi$
$683$	25.3011			0.968121			0.484060	+	0.875035i	$0.339161\pi$
$684$		0			0
$685$	−19.4311			−0.742425
$686$		0			0
$687$	6.98592	−	0.305092i	0.266529	−	0.0116400i
$688$		0			0
$689$	−7.44679	+	12.8982i	−0.283700	+	0.491383i
$690$		0			0
$691$	12.2016	+	21.1337i	0.464170	+	0.803965i	0.999164	−	0.0408905i	$-0.0130195\pi$
$691$	12.2016	+	21.1337i	0.464170	+	0.803965i	−0.534994	+	0.844856i	$0.679686\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.326974	+	0.566335i	0.0124028	+	0.0214823i
$696$		0			0
$697$	25.3673	−	43.9375i	0.960855	−	1.66425i
$698$		0			0
$699$	10.4187	+	16.3536i	0.394070	+	0.618551i
$700$		0			0
$701$	−18.4137			−0.695476			−0.347738	−	0.937592i	$-0.613050\pi$
$701$	−18.4137			−0.695476			−0.347738	+	0.937592i	$0.613050\pi$
$702$		0			0
$703$	−1.18965			−0.0448683
$704$		0			0
$705$	6.90178	+	10.8333i	0.259936	+	0.408008i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	6.66501	+	11.5441i	0.250310	+	0.433549i	0.963611	−	0.267308i	$-0.0861342\pi$
$709$	6.66501	+	11.5441i	0.250310	+	0.433549i	−0.713301	+	0.700858i	$0.752801\pi$
$710$		0			0
$711$	−9.67971	+	0.847090i	−0.363018	+	0.0317684i
$712$		0			0
$713$	−29.5058	−	51.1056i	−1.10500	−	1.91392i
$714$		0			0
$715$	1.27622	−	2.21047i	0.0477278	−	0.0826671i
$716$		0			0
$717$	−44.3574	+	1.93720i	−1.65656	+	0.0723460i
$718$		0			0
$719$	15.6941			0.585291			0.292646	−	0.956221i	$-0.405464\pi$
$719$	15.6941			0.585291			0.292646	+	0.956221i	$0.405464\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−5.27182	+	10.1274i	−0.196061	+	0.376640i
$724$		0			0
$725$	−13.6008	+	23.5573i	−0.505121	+	0.874896i
$726$		0			0
$727$	−12.8388	−	22.2374i	−0.476163	−	0.824739i	0.523464	−	0.852048i	$-0.324640\pi$
$727$	−12.8388	−	22.2374i	−0.476163	−	0.824739i	−0.999627	+	0.0273090i	$0.991306\pi$
$728$		0			0
$729$	26.0795	−	6.98992i	0.965908	−	0.258886i
$730$		0			0
$731$	2.43599	+	4.21926i	0.0900985	+	0.156055i
$732$		0			0
$733$	−0.586541	+	1.01592i	−0.0216644	+	0.0375238i	−0.876654	−	0.481121i	$-0.840230\pi$
$733$	−0.586541	+	1.01592i	−0.0216644	+	0.0375238i	0.854990	+	0.518645i	$0.173563\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.23889			−0.156141
$738$		0			0
$739$	−23.2229			−0.854266			−0.427133	−	0.904189i	$-0.640476\pi$
$739$	−23.2229			−0.854266			−0.427133	+	0.904189i	$0.640476\pi$
$740$		0			0
$741$	4.36200	−	0.190499i	0.160242	−	0.00699817i
$742$		0			0
$743$	11.7846	−	20.4115i	0.432335	−	0.748826i	−0.564739	−	0.825269i	$-0.691023\pi$
$743$	11.7846	−	20.4115i	0.432335	−	0.748826i	0.997074	+	0.0764439i	$0.0243566\pi$
$744$		0			0
$745$	−10.4087	−	18.0284i	−0.381346	−	0.660510i
$746$		0			0
$747$	−3.69842	+	0.323656i	−0.135318	+	0.0118419i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−22.0531	+	38.1971i	−0.804728	+	1.39383i	0.111746	+	0.993737i	$0.464356\pi$
$751$	−22.0531	+	38.1971i	−0.804728	+	1.39383i	−0.916474	+	0.400093i	$0.868978\pi$
$752$		0			0
$753$	23.3069	+	36.5836i	0.849351	+	1.33318i
$754$		0			0
$755$	13.7150			0.499139
$756$		0			0
$757$	−2.71020			−0.0985040			−0.0492520	−	0.998786i	$-0.515684\pi$
$757$	−2.71020			−0.0985040			−0.0492520	+	0.998786i	$0.515684\pi$
$758$		0			0
$759$	4.36325	+	6.84875i	0.158376	+	0.248594i
$760$		0			0
$761$	−14.5248	+	25.1577i	−0.526524	+	0.911966i	0.472999	+	0.881063i	$0.343172\pi$
$761$	−14.5248	+	25.1577i	−0.526524	+	0.911966i	−0.999522	+	0.0309029i	$0.990162\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.6566	+	16.6465i	0.421445	+	0.601857i
$766$		0			0
$767$	−8.64804	−	14.9788i	−0.312263	−	0.540855i
$768$		0			0
$769$	−5.25175	+	9.09629i	−0.189383	+	0.328021i	−0.945045	−	0.326941i	$-0.893982\pi$
$769$	−5.25175	+	9.09629i	−0.189383	+	0.328021i	0.755662	+	0.654962i	$0.227315\pi$
$770$		0			0
$771$	31.3907	−	1.37091i	1.13051	−	0.0493722i
$772$		0			0
$773$	23.8460			0.857682			0.428841	−	0.903380i	$-0.358922\pi$
$773$	23.8460			0.857682			0.428841	+	0.903380i	$0.358922\pi$
$774$		0			0
$775$	−37.2446			−1.33787
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.52297	+	4.36992i	−0.0903949	+	0.156569i
$780$		0			0
$781$	−0.110847	−	0.191993i	−0.00396643	−	0.00687007i
$782$		0			0
$783$	−21.1772	−	27.5968i	−0.756813	−	0.986227i
$784$		0			0
$785$	7.74136	+	13.4084i	0.276301	+	0.478567i
$786$		0			0
$787$	2.19788	−	3.80684i	0.0783460	−	0.135699i	−0.824190	−	0.566313i	$-0.808369\pi$
$787$	2.19788	−	3.80684i	0.0783460	−	0.135699i	0.902536	+	0.430613i	$0.141703\pi$
$788$		0			0
$789$	10.2439	−	19.6788i	0.364691	−	0.700585i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−17.8377			−0.633435
$794$		0			0
$795$	6.88795	−	0.300814i	0.244291	−	0.0106688i
$796$		0			0
$797$	−2.56236	+	4.43813i	−0.0907633	+	0.157207i	−0.907833	−	0.419333i	$-0.862264\pi$
$797$	−2.56236	+	4.43813i	−0.0907633	+	0.157207i	0.817069	+	0.576540i	$0.195597\pi$
$798$		0			0
$799$	26.8144	+	46.4440i	0.948627	+	1.64307i
$800$		0			0
$801$	−14.6729	+	31.4680i	−0.518442	+	1.11187i
$802$		0			0
$803$	3.88794	+	6.73410i	0.137202	+	0.237641i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	26.8794	+	42.1911i	0.946199	+	1.48520i
$808$		0			0
$809$	32.9223			1.15749			0.578744	−	0.815510i	$-0.303543\pi$
$809$	32.9223			1.15749			0.578744	+	0.815510i	$0.303543\pi$
$810$		0			0
$811$	−31.8830			−1.11956			−0.559781	−	0.828640i	$-0.689115\pi$
$811$	−31.8830			−1.11956			−0.559781	+	0.828640i	$0.689115\pi$
$812$		0			0
$813$	−8.55412	−	13.4269i	−0.300006	−	0.470903i
$814$		0			0
$815$	−9.76605	+	16.9153i	−0.342090	+	0.592517i
$816$		0			0
$817$	−0.242278	−	0.419638i	−0.00847624	−	0.0146813i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.1139	−	29.6421i	−0.597278	−	1.03452i	−0.993221	−	0.116241i	$-0.962916\pi$
$821$	−17.1139	−	29.6421i	−0.597278	−	1.03452i	0.395943	−	0.918275i	$-0.370418\pi$
$822$		0			0
$823$	−19.1866	+	33.2321i	−0.668802	+	1.15840i	0.309437	+	0.950920i	$0.399859\pi$
$823$	−19.1866	+	33.2321i	−0.668802	+	1.15840i	−0.978239	+	0.207480i	$0.933474\pi$
$824$		0			0
$825$	5.12032	−	0.223617i	0.178267	−	0.00778535i
$826$		0			0
$827$	9.23903			0.321273			0.160636	−	0.987014i	$-0.448645\pi$
$827$	9.23903			0.321273			0.160636	+	0.987014i	$0.448645\pi$
$828$		0			0
$829$	−41.6448			−1.44638			−0.723191	−	0.690648i	$-0.757326\pi$
$829$	−41.6448			−1.44638			−0.723191	+	0.690648i	$0.757326\pi$
$830$		0			0
$831$	−3.13149	+	6.01571i	−0.108630	+	0.208683i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−11.8368	−	20.5019i	−0.409629	−	0.709499i
$836$		0			0
$837$	18.2253	−	44.0041i	0.629959	−	1.52100i
$838$		0			0
$839$	−15.4241	−	26.7154i	−0.532500	−	0.922318i	−0.999280	−	0.0379439i	$-0.987919\pi$
$839$	−15.4241	−	26.7154i	−0.532500	−	0.922318i	0.466780	−	0.884374i	$-0.345414\pi$
$840$		0			0
$841$	−7.90845	+	13.6978i	−0.272705	+	0.472339i
$842$		0			0
$843$	−12.2307	+	23.4956i	−0.421248	+	0.809232i
$844$		0			0
$845$	0.110292			0.00379415
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−43.2218	+	1.88761i	−1.48337	+	0.0647825i
$850$		0			0
$851$	5.50128	−	9.52849i	0.188581	−	0.326632i
$852$		0			0
$853$	−11.4171	−	19.7750i	−0.390913	−	0.677082i	0.601657	−	0.798755i	$-0.294507\pi$
$853$	−11.4171	−	19.7750i	−0.390913	−	0.677082i	−0.992570	+	0.121673i	$0.961174\pi$
$854$		0			0
$855$	−1.15934	−	1.65563i	−0.0396485	−	0.0566212i
$856$		0			0
$857$	26.6720	+	46.1973i	0.911100	+	1.57807i	0.812513	+	0.582942i	$0.198099\pi$
$857$	26.6720	+	46.1973i	0.911100	+	1.57807i	0.0985862	+	0.995129i	$0.468568\pi$
$858$		0			0
$859$	11.5878	−	20.0707i	0.395372	−	0.684804i	−0.597777	−	0.801663i	$-0.703949\pi$
$859$	11.5878	−	20.0707i	0.395372	−	0.684804i	0.993149	+	0.116859i	$0.0372825\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.16911			−0.312120			−0.156060	−	0.987748i	$-0.549879\pi$
$863$	−9.16911			−0.312120			−0.156060	+	0.987748i	$0.549879\pi$
$864$		0			0
$865$	19.1210			0.650133
$866$		0			0
$867$	29.7672	+	46.7240i	1.01095	+	1.58683i
$868$		0			0
$869$	1.17936	−	2.04270i	0.0400069	−	0.0692940i
$870$		0			0
$871$	−10.5393	−	18.2546i	−0.357111	−	0.618534i
$872$		0			0
$873$	−7.94562	+	0.695336i	−0.268919	+	0.0235336i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.6190	+	32.2490i	−0.628718	+	1.08897i	0.359091	+	0.933303i	$0.383087\pi$
$877$	−18.6190	+	32.2490i	−0.628718	+	1.08897i	−0.987809	+	0.155670i	$0.950247\pi$
$878$		0			0
$879$	−14.1232	+	0.616797i	−0.476365	+	0.0208041i
$880$		0			0
$881$	7.15345			0.241006			0.120503	−	0.992713i	$-0.461549\pi$
$881$	7.15345			0.241006			0.120503	+	0.992713i	$0.461549\pi$
$882$		0			0
$883$	−39.8688			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$883$	−39.8688			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$884$		0			0
$885$	−3.69699	+	7.10206i	−0.124273	+	0.238733i
$886$		0			0
$887$	10.6755	−	18.4904i	0.358447	−	0.620848i	−0.629255	−	0.777199i	$-0.716640\pi$
$887$	10.6755	−	18.4904i	0.358447	−	0.620848i	0.987702	+	0.156351i	$0.0499731\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.24138	+	6.15903i	−0.0750891	+	0.206335i
$892$		0			0
$893$	−2.66690	−	4.61921i	−0.0892445	−	0.154576i
$894$		0			0
$895$	−6.12111	+	10.6021i	−0.204606	+	0.354388i
$896$		0			0
$897$	−18.6454	+	35.8185i	−0.622552	+	1.19594i
$898$		0			0
$899$	−61.3635			−2.04659
$900$		0			0
$901$	28.7850			0.958967
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.08073	+	10.5321i	−0.202130	+	0.350100i
$906$		0			0
$907$	11.3012	+	19.5742i	0.375250	+	0.649951i	0.990364	−	0.138486i	$-0.0442237\pi$
$907$	11.3012	+	19.5742i	0.375250	+	0.649951i	−0.615115	+	0.788438i	$0.710890\pi$
$908$		0			0
$909$	4.82338	−	0.422103i	0.159981	−	0.0140003i
$910$		0			0
$911$	12.7594	+	22.0999i	0.422738	+	0.732203i	0.996206	−	0.0870243i	$-0.0277358\pi$
$911$	12.7594	+	22.0999i	0.422738	+	0.732203i	−0.573468	+	0.819228i	$0.694402\pi$
$912$		0			0
$913$	0.450607	−	0.780475i	0.0149129	−	0.0258300i
$914$		0			0
$915$	4.43678	+	6.96418i	0.146675	+	0.230229i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−11.4265			−0.376926			−0.188463	−	0.982080i	$-0.560351\pi$
$919$	−11.4265			−0.376926			−0.188463	+	0.982080i	$0.560351\pi$
$920$		0			0
$921$	16.8160	+	26.3952i	0.554106	+	0.869751i
$922$		0			0
$923$	0.551208	−	0.954721i	0.0181432	−	0.0314250i
$924$		0			0
$925$	−3.47207	−	6.01381i	−0.114161	−	0.197733i
$926$		0			0
$927$	−18.6535	−	26.6387i	−0.612663	−	0.874930i
$928$		0			0
$929$	−6.79851	−	11.7754i	−0.223052	−	0.386337i	0.732681	−	0.680572i	$-0.238269\pi$
$929$	−6.79851	−	11.7754i	−0.223052	−	0.386337i	−0.955733	+	0.294235i	$0.904935\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	17.3173	−	0.756290i	0.566944	−	0.0247598i
$934$		0			0
$935$	−4.93312			−0.161330
$936$		0			0
$937$	−11.1455			−0.364109			−0.182054	−	0.983288i	$-0.558275\pi$
$937$	−11.1455			−0.364109			−0.182054	+	0.983288i	$0.558275\pi$
$938$		0			0
$939$	2.39178	−	4.59470i	0.0780529	−	0.149942i
$940$		0			0
$941$	−20.7310	+	35.9072i	−0.675813	+	1.17054i	0.300418	+	0.953808i	$0.402874\pi$
$941$	−20.7310	+	35.9072i	−0.675813	+	1.17054i	−0.976231	+	0.216734i	$0.930460\pi$
$942$		0			0
$943$	−23.3340	−	40.4156i	−0.759859	−	1.31611i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.2784	−	36.8552i	−0.691454	−	1.19763i	−0.971362	−	0.237606i	$-0.923637\pi$
$947$	−21.2784	−	36.8552i	−0.691454	−	1.19763i	0.279908	−	0.960027i	$-0.409696\pi$
$948$		0			0
$949$	−19.3335	+	33.4865i	−0.627590	+	1.08702i
$950$		0			0
$951$	−19.0735	+	36.6410i	−0.618502	+	1.18816i
$952$		0			0
$953$	21.2114			0.687106			0.343553	−	0.939133i	$-0.388370\pi$
$953$	21.2114			0.687106			0.343553	+	0.939133i	$0.388370\pi$
$954$		0			0
$955$	−7.16826			−0.231960
$956$		0			0
$957$	8.43615	−	0.368428i	0.272702	−	0.0119096i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−26.5096	−	45.9160i	−0.855150	−	1.48116i
$962$		0			0
$963$	12.6178	−	27.0606i	0.406603	−	0.872016i
$964$		0			0
$965$	0.787775	+	1.36447i	0.0253594	+	0.0439237i
$966$		0			0
$967$	−9.83257	+	17.0305i	−0.316194	+	0.547664i	−0.979691	−	0.200515i	$-0.935738\pi$
$967$	−9.83257	+	17.0305i	−0.316194	+	0.547664i	0.663496	+	0.748179i	$0.269072\pi$
$968$		0			0
$969$	−4.53410	−	7.11693i	−0.145656	−	0.228629i
$970$		0			0
$971$	24.5784			0.788757			0.394379	−	0.918948i	$-0.370960\pi$
$971$	24.5784			0.788757			0.394379	+	0.918948i	$0.370960\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	13.6939	+	21.4945i	0.438554	+	0.688375i
$976$		0			0
$977$	23.7359	−	41.1117i	0.759378	−	1.31528i	−0.183790	−	0.982966i	$-0.558837\pi$
$977$	23.7359	−	41.1117i	0.759378	−	1.31528i	0.943168	−	0.332316i	$-0.107830\pi$
$978$		0			0
$979$	−4.21420	−	7.29920i	−0.134686	−	0.233284i
$980$		0			0
$981$	−23.5260	+	50.4548i	−0.751129	+	1.61090i
$982$		0			0
$983$	−13.7720	−	23.8538i	−0.439258	−	0.760817i	0.558374	−	0.829589i	$-0.311425\pi$
$983$	−13.7720	−	23.8538i	−0.439258	−	0.760817i	−0.997632	+	0.0687719i	$0.978092\pi$
$984$		0			0
$985$	4.00269	−	6.93287i	0.127536	−	0.220900i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.48147			0.142502
$990$		0			0
$991$	−38.4671			−1.22195			−0.610973	−	0.791651i	$-0.709222\pi$
$991$	−38.4671			−1.22195			−0.610973	+	0.791651i	$0.709222\pi$
$992$		0			0
$993$	−12.8262	+	24.6397i	−0.407029	+	0.781917i
$994$		0			0
$995$	5.17233	−	8.95874i	0.163974	−	0.284011i
$996$		0			0
$997$	16.2272	+	28.1064i	0.513921	+	0.890138i	0.999870	+	0.0161503i	$0.00514103\pi$
$997$	16.2272	+	28.1064i	0.513921	+	0.890138i	−0.485948	+	0.873988i	$0.661526\pi$
$998$		0			0
$999$	8.80428	−	1.15941i	0.278555	−	0.0366823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.j.g.589.6		14
3.2	odd	2		5292.2.j.h.1765.5		14
7.2	even	3		252.2.l.b.193.1	yes	14
7.3	odd	6		1764.2.i.i.373.3		14
7.4	even	3		252.2.i.b.121.5	yes	14
7.5	odd	6		1764.2.l.i.949.7		14
7.6	odd	2		1764.2.j.h.589.2		14
9.2	odd	6		5292.2.j.h.3529.5		14
9.7	even	3	inner	1764.2.j.g.1177.6		14
21.2	odd	6		756.2.l.b.361.3		14
21.5	even	6		5292.2.l.i.361.5		14
21.11	odd	6		756.2.i.b.37.5		14
21.17	even	6		5292.2.i.i.1549.3		14
21.20	even	2		5292.2.j.g.1765.3		14
28.11	odd	6		1008.2.q.j.625.3		14
28.23	odd	6		1008.2.t.j.193.7		14
63.2	odd	6		756.2.i.b.613.5		14
63.4	even	3		2268.2.k.e.1297.3		14
63.11	odd	6		756.2.l.b.289.3		14
63.16	even	3		252.2.i.b.25.5	✓	14
63.20	even	6		5292.2.j.g.3529.3		14
63.23	odd	6		2268.2.k.f.1621.5		14
63.25	even	3		252.2.l.b.205.1	yes	14
63.32	odd	6		2268.2.k.f.1297.5		14
63.34	odd	6		1764.2.j.h.1177.2		14
63.38	even	6		5292.2.l.i.3313.5		14
63.47	even	6		5292.2.i.i.2125.3		14
63.52	odd	6		1764.2.l.i.961.7		14
63.58	even	3		2268.2.k.e.1621.3		14
63.61	odd	6		1764.2.i.i.1537.3		14
84.11	even	6		3024.2.q.j.2305.5		14
84.23	even	6		3024.2.t.j.1873.3		14
252.11	even	6		3024.2.t.j.289.3		14
252.79	odd	6		1008.2.q.j.529.3		14
252.151	odd	6		1008.2.t.j.961.7		14
252.191	even	6		3024.2.q.j.2881.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.5	✓	14	63.16	even	3
252.2.i.b.121.5	yes	14	7.4	even	3
252.2.l.b.193.1	yes	14	7.2	even	3
252.2.l.b.205.1	yes	14	63.25	even	3
756.2.i.b.37.5		14	21.11	odd	6
756.2.i.b.613.5		14	63.2	odd	6
756.2.l.b.289.3		14	63.11	odd	6
756.2.l.b.361.3		14	21.2	odd	6
1008.2.q.j.529.3		14	252.79	odd	6
1008.2.q.j.625.3		14	28.11	odd	6
1008.2.t.j.193.7		14	28.23	odd	6
1008.2.t.j.961.7		14	252.151	odd	6
1764.2.i.i.373.3		14	7.3	odd	6
1764.2.i.i.1537.3		14	63.61	odd	6
1764.2.j.g.589.6		14	1.1	even	1	trivial
1764.2.j.g.1177.6		14	9.7	even	3	inner
1764.2.j.h.589.2		14	7.6	odd	2
1764.2.j.h.1177.2		14	63.34	odd	6
1764.2.l.i.949.7		14	7.5	odd	6
1764.2.l.i.961.7		14	63.52	odd	6
2268.2.k.e.1297.3		14	63.4	even	3
2268.2.k.e.1621.3		14	63.58	even	3
2268.2.k.f.1297.5		14	63.32	odd	6
2268.2.k.f.1621.5		14	63.23	odd	6
3024.2.q.j.2305.5		14	84.11	even	6
3024.2.q.j.2881.5		14	252.191	even	6
3024.2.t.j.289.3		14	252.11	even	6
3024.2.t.j.1873.3		14	84.23	even	6
5292.2.i.i.1549.3		14	21.17	even	6
5292.2.i.i.2125.3		14	63.47	even	6
5292.2.j.g.1765.3		14	21.20	even	2
5292.2.j.g.3529.3		14	63.20	even	6
5292.2.j.h.1765.5		14	3.2	odd	2
5292.2.j.h.3529.5		14	9.2	odd	6
5292.2.l.i.361.5		14	21.5	even	6
5292.2.l.i.3313.5		14	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930647 + 1.46079i) q^{3} +(-0.483929 + 0.838189i) q^{5} +(-1.26779 + 2.71895i) q^{9} +(-0.364122 - 0.630678i) q^{11} +(1.81066 - 3.13615i) q^{13} +(-1.67478 + 0.0731419i) q^{15} -6.99897 q^{17} +0.696101 q^{19} +(-3.21898 + 5.57544i) q^{23} +(2.03163 + 3.51888i) q^{25} +(-5.15168 + 0.678412i) q^{27} +(3.34727 + 5.79764i) q^{29} +(-4.58310 + 7.93816i) q^{31} +(0.582416 - 1.11884i) q^{33} -1.70901 q^{37} +(6.26634 - 0.273666i) q^{39} +(-3.62444 + 6.27771i) q^{41} +(-0.348050 - 0.602841i) q^{43} +(-1.66548 - 2.37843i) q^{45} +(-3.83120 - 6.63583i) q^{47} +(-6.51357 - 10.2240i) q^{51} -4.11275 q^{53} +0.704836 q^{55} +(0.647824 + 1.01685i) q^{57} +(2.38809 - 4.13629i) q^{59} +(-2.46287 - 4.26582i) q^{61} +(1.75246 + 3.03535i) q^{65} +(2.91035 - 5.04087i) q^{67} +(-11.1403 + 0.486523i) q^{69} +0.304424 q^{71} -10.6776 q^{73} +(-3.24960 + 6.24261i) q^{75} +(1.61945 + 2.80497i) q^{79} +(-5.78541 - 6.89413i) q^{81} +(0.618759 + 1.07172i) q^{83} +(3.38700 - 5.86646i) q^{85} +(-5.35399 + 10.2852i) q^{87} +11.5736 q^{89} +(-15.8612 + 0.692698i) q^{93} +(-0.336863 + 0.583464i) q^{95} +(1.32933 + 2.30247i) q^{97} +(2.17641 - 0.190462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 2 q^{5} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} - 4 q^{17} - 14 q^{19} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} - q^{31} - q^{33} - 20 q^{37} + 22 q^{39} - 33 q^{41} + 7 q^{43}+ \cdots + 7 q^{99}+O(q^{100}) \) 14 * q - 3 * q^3 - 2 * q^5 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 - 4 * q^17 - 14 * q^19 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 - q^31 - q^33 - 20 * q^37 + 22 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 7 * q^51 + 30 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 - 42 * q^73 + 43 * q^75 - 10 * q^79 + 7 * q^81 - 25 * q^83 + 8 * q^85 - 26 * q^87 + 12 * q^89 - 38 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Introduction

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