LMFDB - Embedded newform 693.2.j.f.232.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(232,693)] 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("693.232"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(693, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 11 x^{16} - 12 x^{15} + 83 x^{14} - 88 x^{13} + 337 x^{12} - 336 x^{11} + 966 x^{10} + \cdots + 4 $ x^18 - x^17 + 11x^16 - 12x^15 + 83x^14 - 88x^13 + 337x^12 - 336x^11 + 966x^10 - 828x^9 + 1343x^8 - 646x^7 + 895x^6 - 371x^5 + 373x^4 - 60x^3 + 42*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			232.8
Root			$-1.06106 + 1.83781i$ of defining polynomial
Character	$\chi$	$=$	693.232
Dual form			693.2.j.f.463.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06106 - 1.83781i) q^{2} +(0.729277 - 1.57104i) q^{3} +(-1.25170 - 2.16800i) q^{4} +(-1.40091 - 2.42645i) q^{5} +(-2.11346 - 3.00724i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.06826 q^{8} +(-1.93631 - 2.29144i) q^{9} -5.94581 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-4.31885 + 0.385388i) q^{12} +(1.06913 + 1.85179i) q^{13} +(1.06106 + 1.83781i) q^{14} +(-4.83370 + 0.431330i) q^{15} +(1.36990 - 2.37274i) q^{16} -5.05008 q^{17} +(-6.26577 + 1.12722i) q^{18} +6.01747 q^{19} +(-3.50704 + 6.07436i) q^{20} +(0.995919 + 1.41709i) q^{21} +(1.06106 + 1.83781i) q^{22} +(-1.46024 - 2.52920i) q^{23} +(-0.779059 + 1.67828i) q^{24} +(-1.42511 + 2.46837i) q^{25} +4.53764 q^{26} +(-5.01204 + 1.37092i) q^{27} +2.50339 q^{28} +(3.45024 - 5.97598i) q^{29} +(-4.33614 + 9.34108i) q^{30} +(4.39779 + 7.61719i) q^{31} +(-3.97536 - 6.88553i) q^{32} +(0.995919 + 1.41709i) q^{33} +(-5.35843 + 9.28108i) q^{34} +2.80183 q^{35} +(-2.54418 + 7.06612i) q^{36} -0.741470 q^{37} +(6.38490 - 11.0590i) q^{38} +(3.68891 - 0.329176i) q^{39} +(1.49654 + 2.59209i) q^{40} +(2.12725 + 3.68451i) q^{41} +(3.66107 - 0.326692i) q^{42} +(5.13093 - 8.88704i) q^{43} +2.50339 q^{44} +(-2.84747 + 7.90847i) q^{45} -6.19760 q^{46} +(-2.88192 + 4.99164i) q^{47} +(-2.72862 - 3.88255i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(3.02426 + 5.23817i) q^{50} +(-3.68290 + 7.93385i) q^{51} +(2.67645 - 4.63575i) q^{52} -0.104080 q^{53} +(-2.79859 + 10.6658i) q^{54} +2.80183 q^{55} +(0.534131 - 0.925143i) q^{56} +(4.38840 - 9.45367i) q^{57} +(-7.32182 - 12.6818i) q^{58} +(-5.68816 - 9.85218i) q^{59} +(6.98545 + 9.93957i) q^{60} +(0.0230249 - 0.0398803i) q^{61} +18.6653 q^{62} +(2.95260 - 0.531174i) q^{63} -11.3928 q^{64} +(2.99551 - 5.18838i) q^{65} +(3.66107 - 0.326692i) q^{66} +(3.58204 + 6.20427i) q^{67} +(6.32116 + 10.9486i) q^{68} +(-5.03839 + 0.449595i) q^{69} +(2.97290 - 5.14922i) q^{70} +8.69642 q^{71} +(2.06849 + 2.44786i) q^{72} -9.81166 q^{73} +(-0.786744 + 1.36268i) q^{74} +(2.83859 + 4.03902i) q^{75} +(-7.53205 - 13.0459i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(3.30920 - 7.12880i) q^{78} +(2.06177 - 3.57108i) q^{79} -7.67646 q^{80} +(-1.50140 + 8.87388i) q^{81} +9.02857 q^{82} +(-0.869243 + 1.50557i) q^{83} +(1.82567 - 3.93292i) q^{84} +(7.07471 + 12.2538i) q^{85} +(-10.8885 - 18.8594i) q^{86} +(-6.87231 - 9.77859i) q^{87} +(0.534131 - 0.925143i) q^{88} -8.96044 q^{89} +(11.5129 + 13.6245i) q^{90} -2.13826 q^{91} +(-3.65555 + 6.33159i) q^{92} +(15.1741 - 1.35404i) q^{93} +(6.11578 + 10.5928i) q^{94} +(-8.42995 - 14.6011i) q^{95} +(-13.7166 + 1.22398i) q^{96} +(6.28753 - 10.8903i) q^{97} -2.12212 q^{98} +(2.95260 - 0.531174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} + q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} - 9 q^{7} - 12 q^{8} - 5 q^{9} - 26 q^{10} - 9 q^{11} - 5 q^{12} + 8 q^{13} - q^{14} + 16 q^{15} + 5 q^{16} - 28 q^{17} - 16 q^{18} - 24 q^{19} - 19 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) $ 18 * q - q^2 + q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 - 9 * q^7 - 12 * q^8 - 5 * q^9 - 26 * q^10 - 9 * q^11 - 5 * q^12 + 8 * q^13 - q^14 + 16 * q^15 + 5 * q^16 - 28 * q^17 - 16 * q^18 - 24 * q^19 - 19 * q^20 + q^21 - q^22 + 19 * q^23 - 6 * q^24 + q^25 - 20 * q^26 - 14 * q^27 + 6 * q^28 + 12 * q^29 + 2 * q^30 + 3 * q^31 - 4 * q^32 + q^33 + 12 * q^35 - 8 * q^36 - 38 * q^37 + 20 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 - 4 * q^42 + 32 * q^43 + 6 * q^44 + 22 * q^45 - 4 * q^46 - 8 * q^47 - 21 * q^48 - 9 * q^49 + 18 * q^50 - 3 * q^51 + 4 * q^52 + 30 * q^53 + 35 * q^54 + 12 * q^55 + 6 * q^56 + 18 * q^57 + 3 * q^58 - 8 * q^59 - 5 * q^60 + 2 * q^61 + 24 * q^62 + 10 * q^63 - 68 * q^64 + 20 * q^65 - 4 * q^66 + 49 * q^67 + 46 * q^68 - q^69 + 13 * q^70 - 18 * q^71 + 27 * q^72 - 70 * q^73 - 19 * q^74 - 34 * q^75 + 25 * q^76 - 9 * q^77 + 2 * q^78 + 21 * q^79 - 52 * q^80 + 19 * q^81 - 20 * q^82 + 16 * q^83 - 11 * q^84 + 52 * q^85 - 31 * q^86 - 28 * q^87 + 6 * q^88 + 38 * q^89 + 20 * q^90 - 16 * q^91 + 32 * q^92 + 18 * q^93 - 50 * q^94 - 4 * q^95 + 18 * q^96 + 24 * q^97 + 2 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.06106	−	1.83781i	0.750283	−	1.29953i	−0.197403	−	0.980322i	$-0.563251\pi$
$2$	1.06106	−	1.83781i	0.750283	−	1.29953i	0.947686	−	0.319205i	$-0.103416\pi$
$3$	0.729277	−	1.57104i	0.421048	−	0.907038i
$3$	0.729277	−	1.57104i	0.421048	−	0.907038i
$4$	−1.25170	−	2.16800i	−0.625849	−	1.08400i
$5$	−1.40091	−	2.42645i	−0.626507	−	1.08514i	−0.988247	−	0.152863i	$-0.951151\pi$
$5$	−1.40091	−	2.42645i	−0.626507	−	1.08514i	0.361740	−	0.932279i	$-0.382183\pi$
$6$	−2.11346	−	3.00724i	−0.862816	−	1.22770i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.06826			−0.377688
$9$	−1.93631	−	2.29144i	−0.645437	−	0.763814i
$10$	−5.94581			−1.88023
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−4.31885	+	0.385388i	−1.24674	+	0.111252i
$13$	1.06913	+	1.85179i	0.296523	+	0.513593i	0.975338	−	0.220716i	$-0.0708395\pi$
$13$	1.06913	+	1.85179i	0.296523	+	0.513593i	−0.678815	+	0.734309i	$0.737506\pi$
$14$	1.06106	+	1.83781i	0.283580	+	0.491175i
$15$	−4.83370	+	0.431330i	−1.24806	+	0.111369i
$16$	1.36990	−	2.37274i	0.342476	−	0.593185i
$17$	−5.05008			−1.22482			−0.612412	−	0.790539i	$-0.709800\pi$
$17$	−5.05008			−1.22482			−0.612412	+	0.790539i	$0.709800\pi$
$18$	−6.26577	+	1.12722i	−1.47686	+	0.265687i
$19$	6.01747			1.38050			0.690251	−	0.723570i	$-0.257500\pi$
$19$	6.01747			1.38050			0.690251	+	0.723570i	$0.257500\pi$
$20$	−3.50704	+	6.07436i	−0.784197	+	1.35827i
$21$	0.995919	+	1.41709i	0.217327	+	0.309234i
$22$	1.06106	+	1.83781i	0.226219	+	0.391822i
$23$	−1.46024	−	2.52920i	−0.304480	−	0.527376i	0.672665	−	0.739947i	$-0.265149\pi$
$23$	−1.46024	−	2.52920i	−0.304480	−	0.527376i	−0.977146	+	0.212572i	$0.931816\pi$
$24$	−0.779059	+	1.67828i	−0.159025	+	0.342577i
$25$	−1.42511	+	2.46837i	−0.285022	+	0.493673i
$26$	4.53764			0.889905
$27$	−5.01204	+	1.37092i	−0.964568	+	0.263834i
$28$	2.50339			0.473097
$29$	3.45024	−	5.97598i	0.640693	−	1.10971i	−0.344586	−	0.938755i	$-0.611981\pi$
$29$	3.45024	−	5.97598i	0.640693	−	1.10971i	0.985278	−	0.170958i	$-0.0546861\pi$
$30$	−4.33614	+	9.34108i	−0.791667	+	1.70544i
$31$	4.39779	+	7.61719i	0.789866	+	1.36809i	0.926049	+	0.377404i	$0.123183\pi$
$31$	4.39779	+	7.61719i	0.789866	+	1.36809i	−0.136183	+	0.990684i	$0.543483\pi$
$32$	−3.97536	−	6.88553i	−0.702751	−	1.21720i
$33$	0.995919	+	1.41709i	0.173367	+	0.246684i
$34$	−5.35843	+	9.28108i	−0.918964	+	1.59169i
$35$	2.80183			0.473595
$36$	−2.54418	+	7.06612i	−0.424029	+	1.17769i
$37$	−0.741470			−0.121897			−0.0609484	−	0.998141i	$-0.519413\pi$
$37$	−0.741470			−0.121897			−0.0609484	+	0.998141i	$0.519413\pi$
$38$	6.38490	−	11.0590i	1.03577	−	1.79400i
$39$	3.68891	−	0.329176i	0.590699	−	0.0527104i
$40$	1.49654	+	2.59209i	0.236624	+	0.409845i
$41$	2.12725	+	3.68451i	0.332221	+	0.575424i	0.982947	−	0.183889i	$-0.0588686\pi$
$41$	2.12725	+	3.68451i	0.332221	+	0.575424i	−0.650726	+	0.759313i	$0.725535\pi$
$42$	3.66107	−	0.326692i	0.564916	−	0.0504097i
$43$	5.13093	−	8.88704i	0.782460	−	1.35526i	−0.148045	−	0.988981i	$-0.547298\pi$
$43$	5.13093	−	8.88704i	0.782460	−	1.35526i	0.930505	−	0.366280i	$-0.119369\pi$
$44$	2.50339			0.377401
$45$	−2.84747	+	7.90847i	−0.424475	+	1.17893i
$46$	−6.19760			−0.913786
$47$	−2.88192	+	4.99164i	−0.420372	+	0.728105i	−0.995976	−	0.0896236i	$-0.971434\pi$
$47$	−2.88192	+	4.99164i	−0.420372	+	0.728105i	0.575604	+	0.817728i	$0.304767\pi$
$48$	−2.72862	−	3.88255i	−0.393843	−	0.560398i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	3.02426	+	5.23817i	0.427695	+	0.740789i
$51$	−3.68290	+	7.93385i	−0.515709	+	1.11096i
$52$	2.67645	−	4.63575i	0.371157	−	0.642863i
$53$	−0.104080			−0.0142965			−0.00714824	−	0.999974i	$-0.502275\pi$
$53$	−0.104080			−0.0142965			−0.00714824	+	0.999974i	$0.502275\pi$
$54$	−2.79859	+	10.6658i	−0.380840	+	1.45143i
$55$	2.80183			0.377798
$56$	0.534131	−	0.925143i	0.0713763	−	0.123627i
$57$	4.38840	−	9.45367i	0.581258	−	1.25217i
$58$	−7.32182	−	12.6818i	−0.961402	−	1.66520i
$59$	−5.68816	−	9.85218i	−0.740535	−	1.28264i	−0.952252	−	0.305313i	$-0.901239\pi$
$59$	−5.68816	−	9.85218i	−0.740535	−	1.28264i	0.211717	−	0.977331i	$-0.432094\pi$
$60$	6.98545	+	9.93957i	0.901818	+	1.28319i
$61$	0.0230249	−	0.0398803i	0.00294803	−	0.00510615i	−0.864548	−	0.502551i	$-0.832395\pi$
$61$	0.0230249	−	0.0398803i	0.00294803	−	0.00510615i	0.867496	+	0.497445i	$0.165728\pi$
$62$	18.6653			2.37049
$63$	2.95260	−	0.531174i	0.371993	−	0.0669216i
$64$	−11.3928			−1.42410
$65$	2.99551	−	5.18838i	0.371548	−	0.643539i
$66$	3.66107	−	0.326692i	0.450647	−	0.0402130i
$67$	3.58204	+	6.20427i	0.437616	+	0.757973i	0.997505	−	0.0705947i	$-0.0224897\pi$
$67$	3.58204	+	6.20427i	0.437616	+	0.757973i	−0.559889	+	0.828567i	$0.689156\pi$
$68$	6.32116	+	10.9486i	0.766554	+	1.32771i
$69$	−5.03839	+	0.449595i	−0.606551	+	0.0541249i
$70$	2.97290	−	5.14922i	0.355330	−	0.615450i
$71$	8.69642			1.03208			0.516038	−	0.856566i	$-0.327406\pi$
$71$	8.69642			1.03208			0.516038	+	0.856566i	$0.327406\pi$
$72$	2.06849	+	2.44786i	0.243774	+	0.288483i
$73$	−9.81166			−1.14837			−0.574184	−	0.818726i	$-0.694681\pi$
$73$	−9.81166			−1.14837			−0.574184	+	0.818726i	$0.694681\pi$
$74$	−0.786744	+	1.36268i	−0.0914571	+	0.158408i
$75$	2.83859	+	4.03902i	0.327772	+	0.466386i
$76$	−7.53205	−	13.0459i	−0.863986	−	1.49647i
$77$	−0.500000	−	0.866025i	−0.0569803	−	0.0986928i
$78$	3.30920	−	7.12880i	0.374693	−	0.807178i
$79$	2.06177	−	3.57108i	0.231967	−	0.401778i	−0.726420	−	0.687251i	$-0.758817\pi$
$79$	2.06177	−	3.57108i	0.231967	−	0.401778i	0.958387	+	0.285473i	$0.0921506\pi$
$80$	−7.67646			−0.858254
$81$	−1.50140	+	8.87388i	−0.166822	+	0.985987i
$82$	9.02857			0.997039
$83$	−0.869243	+	1.50557i	−0.0954118	+	0.165258i	−0.909780	−	0.415090i	$-0.863750\pi$
$83$	−0.869243	+	1.50557i	−0.0954118	+	0.165258i	0.814369	+	0.580348i	$0.197083\pi$
$84$	1.82567	−	3.93292i	0.199197	−	0.429117i
$85$	7.07471	+	12.2538i	0.767360	+	1.32911i
$86$	−10.8885	−	18.8594i	−1.17413	−	2.03366i
$87$	−6.87231	−	9.77859i	−0.736789	−	1.04838i
$88$	0.534131	−	0.925143i	0.0569386	−	0.0986206i
$89$	−8.96044			−0.949805			−0.474903	−	0.880038i	$-0.657517\pi$
$89$	−8.96044			−0.949805			−0.474903	+	0.880038i	$0.657517\pi$
$90$	11.5129	+	13.6245i	1.21357	+	1.43615i
$91$	−2.13826			−0.224150
$92$	−3.65555	+	6.33159i	−0.381117	+	0.660114i
$93$	15.1741	−	1.35404i	1.57348	−	0.140408i
$94$	6.11578	+	10.5928i	0.630795	+	1.09257i
$95$	−8.42995	−	14.6011i	−0.864895	−	1.49804i
$96$	−13.7166	+	1.22398i	−1.39994	+	0.124922i
$97$	6.28753	−	10.8903i	0.638402	−	1.10574i	−0.347382	−	0.937724i	$-0.612929\pi$
$97$	6.28753	−	10.8903i	0.638402	−	1.10574i	0.985784	−	0.168020i	$-0.0537375\pi$
$98$	−2.12212			−0.214367
$99$	2.95260	−	0.531174i	0.296748	−	0.0533850i
$100$	7.13523			0.713523
$101$	8.95551	−	15.5114i	0.891107	−	1.54344i	0.0525570	−	0.998618i	$-0.483263\pi$
$101$	8.95551	−	15.5114i	0.891107	−	1.54344i	0.838550	−	0.544825i	$-0.183404\pi$
$102$	10.6731	+	15.1868i	1.05680	+	1.50371i
$103$	6.97310	+	12.0778i	0.687080	+	1.19006i	0.972778	+	0.231738i	$0.0744411\pi$
$103$	6.97310	+	12.0778i	0.687080	+	1.19006i	−0.285699	+	0.958320i	$0.592226\pi$
$104$	−1.14211	−	1.97819i	−0.111993	−	0.193978i
$105$	2.04331	−	4.40177i	0.199406	−	0.429569i
$106$	−0.110435	+	0.191279i	−0.0107264	+	0.0185787i
$107$	18.9455			1.83153			0.915764	−	0.401717i	$-0.131586\pi$
$107$	18.9455			1.83153			0.915764	+	0.401717i	$0.131586\pi$
$108$	9.24572	+	9.15015i	0.889670	+	0.880473i
$109$	−0.769989			−0.0737516			−0.0368758	−	0.999320i	$-0.511741\pi$
$109$	−0.769989			−0.0737516			−0.0368758	+	0.999320i	$0.511741\pi$
$110$	2.97290	−	5.14922i	0.283455	−	0.490959i
$111$	−0.540737	+	1.16488i	−0.0513244	+	0.110565i
$112$	1.36990	+	2.37274i	0.129444	+	0.224203i
$113$	6.47873	+	11.2215i	0.609467	+	1.05563i	0.991328	+	0.131409i	$0.0419500\pi$
$113$	6.47873	+	11.2215i	0.609467	+	1.05563i	−0.381861	+	0.924220i	$0.624717\pi$
$114$	−12.7177	−	18.0960i	−1.19112	−	1.69484i
$115$	−4.09133	+	7.08639i	−0.381518	+	0.660809i
$116$	−17.2746			−1.60391
$117$	2.17309	−	6.03548i	0.200902	−	0.557980i
$118$	−24.1419			−2.22244
$119$	2.52504	−	4.37349i	0.231470	−	0.400917i
$120$	5.16366	−	0.460774i	0.471375	−	0.0420627i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.0488616	−	0.0846307i	−0.00442372	−	0.00766211i
$123$	7.33986	−	0.654964i	0.661813	−	0.0590561i
$124$	11.0094	−	19.0688i	0.988673	−	1.71243i
$125$	−6.02330			−0.538740
$126$	2.15669	−	5.98993i	0.192133	−	0.533625i
$127$	−20.5528			−1.82377			−0.911883	−	0.410451i	$-0.865371\pi$
$127$	−20.5528			−1.82377			−0.911883	+	0.410451i	$0.865371\pi$
$128$	−4.13770	+	7.16671i	−0.365724	+	0.633453i
$129$	−10.2200	−	14.5420i	−0.899820	−	1.28035i
$130$	−6.35684	−	11.0104i	−0.557532	−	0.965673i
$131$	1.79015	+	3.10064i	0.156406	+	0.270904i	0.933570	−	0.358394i	$-0.116676\pi$
$131$	1.79015	+	3.10064i	0.156406	+	0.270904i	−0.777164	+	0.629298i	$0.783342\pi$
$132$	1.82567	−	3.93292i	0.158904	−	0.342317i
$133$	−3.00874	+	5.21128i	−0.260890	+	0.451876i
$134$	15.2030			1.31334
$135$	10.3479	+	10.2409i	0.890606	+	0.881400i
$136$	5.39481			0.462601
$137$	−5.83625	+	10.1087i	−0.498625	+	0.863643i	−0.999999	−	0.00158730i	$-0.999495\pi$
$137$	−5.83625	+	10.1087i	−0.498625	+	0.863643i	0.501374	+	0.865231i	$0.332828\pi$
$138$	−4.51976	+	9.73665i	−0.384748	+	0.828839i
$139$	4.31979	+	7.48209i	0.366400	+	0.634623i	0.989000	−	0.147917i	$-0.0472570\pi$
$139$	4.31979	+	7.48209i	0.366400	+	0.634623i	−0.622600	+	0.782540i	$0.713924\pi$
$140$	−3.50704	−	6.07436i	−0.296399	−	0.513378i
$141$	5.74032	+	8.16789i	0.483422	+	0.687860i
$142$	9.22743	−	15.9824i	0.774349	−	1.34121i
$143$	−2.13826			−0.178810
$144$	−8.08955	+	1.45531i	−0.674130	+	0.121276i
$145$	−19.3339			−1.60559
$146$	−10.4108	+	18.0320i	−0.861601	+	1.49234i
$147$	−1.72520	+	0.153946i	−0.142292	+	0.0126973i
$148$	0.928095	+	1.60751i	0.0762890	+	0.132136i
$149$	8.09454	+	14.0201i	0.663130	+	1.14858i	0.979789	+	0.200036i	$0.0641058\pi$
$149$	8.09454	+	14.0201i	0.663130	+	1.14858i	−0.316658	+	0.948540i	$0.602561\pi$
$150$	10.4349	−	0.931145i	0.852004	−	0.0760277i
$151$	0.688349	−	1.19225i	0.0560170	−	0.0970243i	−0.836657	−	0.547727i	$-0.815493\pi$
$151$	0.688349	−	1.19225i	0.0560170	−	0.0970243i	0.892674	+	0.450703i	$0.148827\pi$
$152$	−6.42824			−0.521399
$153$	9.77851	+	11.5719i	0.790546	+	0.935537i
$154$	−2.12212			−0.171005
$155$	12.3218	−	21.3420i	0.989713	−	1.71423i
$156$	−5.33106	−	7.58555i	−0.426826	−	0.607330i
$157$	−4.05547	−	7.02429i	−0.323662	−	0.560599i	0.657579	−	0.753386i	$-0.271581\pi$
$157$	−4.05547	−	7.02429i	−0.323662	−	0.560599i	−0.981241	+	0.192787i	$0.938247\pi$
$158$	−4.37531	−	7.57826i	−0.348081	−	0.602894i
$159$	−0.0759031	+	0.163513i	−0.00601951	+	0.0129675i
$160$	−11.1383	+	19.2920i	−0.880557	+	1.52517i
$161$	2.92047			0.230166
$162$	14.7154	+	12.1750i	1.15615	+	0.956559i
$163$	−7.48325			−0.586133			−0.293067	−	0.956092i	$-0.594676\pi$
$163$	−7.48325			−0.586133			−0.293067	+	0.956092i	$0.594676\pi$
$164$	5.32535	−	9.22378i	0.415840	−	0.720256i
$165$	2.04331	−	4.40177i	0.159071	−	0.342677i
$166$	1.84464	+	3.19501i	0.143172	+	0.247981i
$167$	1.83558	+	3.17932i	0.142042	+	0.246023i	0.928265	−	0.371919i	$-0.121300\pi$
$167$	1.83558	+	3.17932i	0.142042	+	0.246023i	−0.786224	+	0.617942i	$0.787967\pi$
$168$	−1.06390	−	1.51383i	−0.0820819	−	0.116794i
$169$	4.21393	−	7.29873i	0.324148	−	0.561441i
$170$	30.0268			2.30295
$171$	−11.6517	−	13.7887i	−0.891027	−	1.05445i
$172$	−25.6895			−1.95881
$173$	−5.23743	+	9.07149i	−0.398194	+	0.689693i	−0.993503	−	0.113804i	$-0.963696\pi$
$173$	−5.23743	+	9.07149i	−0.398194	+	0.689693i	0.595309	+	0.803497i	$0.297030\pi$
$174$	−25.2631	+	2.25433i	−1.91519	+	0.170900i
$175$	−1.42511	−	2.46837i	−0.107728	−	0.186591i
$176$	1.36990	+	2.37274i	0.103260	+	0.178852i
$177$	−19.6264	+	1.75134i	−1.47521	+	0.131639i
$178$	−9.50757	+	16.4676i	−0.712622	+	1.23430i
$179$	0.0404602			0.00302413			0.00151207	−	0.999999i	$-0.499519\pi$
$179$	0.0404602			0.00302413			0.00151207	+	0.999999i	$0.499519\pi$
$180$	20.7098	−	3.72569i	1.54361	−	0.277697i
$181$	24.7567			1.84015			0.920076	−	0.391739i	$-0.128127\pi$
$181$	24.7567			1.84015			0.920076	+	0.391739i	$0.128127\pi$
$182$	−2.26882	+	3.92971i	−0.168176	+	0.291290i
$183$	−0.0458618	−	0.0652567i	−0.00339020	−	0.00482391i
$184$	1.55992	+	2.70186i	0.114999	+	0.199183i
$185$	1.03873	+	1.79914i	0.0763693	+	0.132275i
$186$	13.6121	−	29.3238i	0.998091	−	2.15013i
$187$	2.52504	−	4.37349i	0.184649	−	0.319822i
$188$	14.4292			1.05236
$189$	1.31877	−	5.02602i	0.0959264	−	0.365589i
$190$	−35.7787			−2.59566
$191$	7.62190	−	13.2015i	0.551502	−	0.955229i	−0.446665	−	0.894701i	$-0.647388\pi$
$191$	7.62190	−	13.2015i	0.551502	−	0.955229i	0.998167	−	0.0605275i	$-0.0192783\pi$
$192$	−8.30849	+	17.8985i	−0.599614	+	1.29171i
$193$	4.55677	+	7.89255i	0.328003	+	0.568119i	0.982116	−	0.188279i	$-0.0602909\pi$
$193$	4.55677	+	7.89255i	0.328003	+	0.568119i	−0.654112	+	0.756398i	$0.726958\pi$
$194$	−13.3429	−	23.1106i	−0.957964	−	1.65924i
$195$	−5.96658	−	8.48983i	−0.427275	−	0.607969i
$196$	−1.25170	+	2.16800i	−0.0894069	+	0.154857i
$197$	16.1817			1.15290			0.576448	−	0.817134i	$-0.304439\pi$
$197$	16.1817			1.15290			0.576448	+	0.817134i	$0.304439\pi$
$198$	2.15669	−	5.98993i	0.153269	−	0.425686i
$199$	6.96657			0.493847			0.246924	−	0.969035i	$-0.420580\pi$
$199$	6.96657			0.493847			0.246924	+	0.969035i	$0.420580\pi$
$200$	1.52239	−	2.63686i	0.107650	−	0.186454i
$201$	12.3594	−	1.10288i	0.871768	−	0.0777912i
$202$	−19.0047	−	32.9171i	−1.33716	−	2.31604i
$203$	3.45024	+	5.97598i	0.242159	+	0.419432i
$204$	21.8105	−	1.94624i	1.52704	−	0.136264i
$205$	5.96019	−	10.3234i	0.416278	−	0.721014i
$206$	29.5955			2.06202
$207$	−2.96805	+	8.24337i	−0.206294	+	0.572954i
$208$	5.85841			0.406208
$209$	−3.00874	+	5.21128i	−0.208119	+	0.360472i
$210$	−5.92155	−	8.42575i	−0.408625	−	0.581432i
$211$	−3.78568	−	6.55698i	−0.260617	−	0.451401i	0.705789	−	0.708422i	$-0.250593\pi$
$211$	−3.78568	−	6.55698i	−0.260617	−	0.451401i	−0.966406	+	0.257020i	$0.917259\pi$
$212$	0.130277	+	0.225646i	0.00894743	+	0.0154974i
$213$	6.34210	−	13.6624i	0.434554	−	0.936132i
$214$	20.1023	−	34.8182i	1.37416	−	2.38012i
$215$	−28.7520			−1.96087
$216$	5.35418	−	1.46450i	0.364306	−	0.0996468i
$217$	−8.79557			−0.597082
$218$	−0.817005	+	1.41509i	−0.0553346	+	0.0958423i
$219$	−7.15542	+	15.4145i	−0.483518	+	1.04161i
$220$	−3.50704	−	6.07436i	−0.236444	−	0.409534i
$221$	−5.39918	−	9.35166i	−0.363188	−	0.629061i
$222$	1.56707	+	2.22977i	0.105175	+	0.149653i
$223$	−7.68146	+	13.3047i	−0.514388	+	0.890947i	0.485472	+	0.874252i	$0.338648\pi$
$223$	−7.68146	+	13.3047i	−0.514388	+	0.890947i	−0.999861	+	0.0166948i	$0.994686\pi$
$224$	7.95072			0.531230
$225$	8.41557	−	1.51396i	0.561038	−	0.100931i
$226$	27.4973			1.82909
$227$	−4.35046	+	7.53521i	−0.288750	+	0.500130i	−0.973512	−	0.228637i	$-0.926573\pi$
$227$	−4.35046	+	7.53521i	−0.288750	+	0.500130i	0.684762	+	0.728767i	$0.259906\pi$
$228$	−25.9885	+	2.31906i	−1.72113	+	0.153583i
$229$	−0.0843452	−	0.146090i	−0.00557369	−	0.00965392i	0.863225	−	0.504819i	$-0.168441\pi$
$229$	−0.0843452	−	0.146090i	−0.00557369	−	0.00965392i	−0.868799	+	0.495165i	$0.835108\pi$
$230$	8.68229	+	15.0382i	0.572493	+	0.991587i
$231$	−1.72520	+	0.153946i	−0.113510	+	0.0101289i
$232$	−3.68576	+	6.38392i	−0.241982	+	0.419125i
$233$	5.06133			0.331579			0.165789	−	0.986161i	$-0.446983\pi$
$233$	5.06133			0.331579			0.165789	+	0.986161i	$0.446983\pi$
$234$	−8.78628	−	10.3977i	−0.574377	−	0.679721i
$235$	16.1493			1.05346
$236$	−14.2397	+	24.6639i	−0.926925	+	1.60548i
$237$	−4.10670	−	5.84342i	−0.266759	−	0.379571i
$238$	−5.35843	−	9.28108i	−0.347336	−	0.601603i
$239$	−11.4432	−	19.8202i	−0.740197	−	1.28206i	−0.952405	−	0.304835i	$-0.901399\pi$
$239$	−11.4432	−	19.8202i	−0.740197	−	1.28206i	0.212208	−	0.977225i	$-0.431935\pi$
$240$	−5.59826	+	12.0600i	−0.361366	+	0.778469i
$241$	−9.33780	+	16.1735i	−0.601501	+	1.04183i	0.391093	+	0.920351i	$0.372097\pi$
$241$	−9.33780	+	16.1735i	−0.601501	+	1.04183i	−0.992594	+	0.121479i	$0.961236\pi$
$242$	−2.12212			−0.136415
$243$	12.8463	+	8.83027i	0.824088	+	0.566462i
$244$	−0.115281			−0.00738009
$245$	−1.40091	+	2.42645i	−0.0895010	+	0.155020i
$246$	6.58433	−	14.1842i	0.419801	−	0.904353i
$247$	6.43345	+	11.1431i	0.409351	+	0.709017i
$248$	−4.69799	−	8.13716i	−0.298323	−	0.516710i
$249$	1.73139	+	2.46359i	0.109722	+	0.156124i
$250$	−6.39108	+	11.0697i	−0.404207	+	0.700108i
$251$	8.17564			0.516042			0.258021	−	0.966139i	$-0.416930\pi$
$251$	8.17564			0.516042			0.258021	+	0.966139i	$0.416930\pi$
$252$	−4.84735	−	5.73638i	−0.305354	−	0.361358i
$253$	2.92047			0.183609
$254$	−21.8077	+	37.7721i	−1.36834	+	2.37003i
$255$	24.4105	−	2.17825i	1.52865	−	0.136407i
$256$	−2.61208	−	4.52426i	−0.163255	−	0.282766i
$257$	7.60802	+	13.1775i	0.474575	+	0.821988i	0.999576	−	0.0291135i	$-0.00926841\pi$
$257$	7.60802	+	13.1775i	0.474575	+	0.821988i	−0.525001	+	0.851102i	$0.675935\pi$
$258$	−37.5694	+	3.35247i	−2.33897	+	0.208716i
$259$	0.370735	−	0.642132i	0.0230363	−	0.0399001i
$260$	−14.9979			−0.930130
$261$	−20.3743	+	3.66535i	−1.26114	+	0.226880i
$262$	7.59784			0.469396
$263$	5.45685	−	9.45154i	0.336484	−	0.582807i	−0.647285	−	0.762248i	$-0.724096\pi$
$263$	5.45685	−	9.45154i	0.336484	−	0.582807i	0.983769	+	0.179441i	$0.0574290\pi$
$264$	−1.06390	−	1.51383i	−0.0654787	−	0.0931695i
$265$	0.145807	+	0.252545i	0.00895685	+	0.0155137i
$266$	6.38490	+	11.0590i	0.391483	+	0.678069i
$267$	−6.53464	+	14.0772i	−0.399914	+	0.861510i
$268$	8.96726	−	15.5317i	0.547762	−	0.948752i
$269$	7.65604			0.466797			0.233399	−	0.972381i	$-0.425015\pi$
$269$	7.65604			0.466797			0.233399	+	0.972381i	$0.425015\pi$
$270$	29.8007	−	8.15123i	1.81361	−	0.496068i
$271$	3.90715			0.237343			0.118671	−	0.992934i	$-0.462136\pi$
$271$	3.90715			0.237343			0.118671	+	0.992934i	$0.462136\pi$
$272$	−6.91811	+	11.9825i	−0.419472	+	0.726547i
$273$	−1.55938	+	3.35928i	−0.0943781	+	0.203313i
$274$	12.3852	+	21.4518i	0.748219	+	1.29595i
$275$	−1.42511	−	2.46837i	−0.0859375	−	0.148848i
$276$	7.28126	+	10.3605i	0.438280	+	0.623628i
$277$	6.46312	−	11.1944i	0.388331	−	0.672609i	−0.603894	−	0.797065i	$-0.706385\pi$
$277$	6.46312	−	11.1944i	0.388331	−	0.672609i	0.992225	+	0.124455i	$0.0397183\pi$
$278$	18.3342			1.09961
$279$	8.93886	−	24.8265i	0.535155	−	1.48632i
$280$	−2.99309			−0.178871
$281$	−10.0417	+	17.3927i	−0.599036	+	1.03756i	0.393928	+	0.919141i	$0.371116\pi$
$281$	−10.0417	+	17.3927i	−0.599036	+	1.03756i	−0.992964	+	0.118419i	$0.962217\pi$
$282$	21.1019	−	1.88300i	1.25660	−	0.112131i
$283$	−1.89157	−	3.27630i	−0.112442	−	0.194756i	0.804312	−	0.594207i	$-0.202534\pi$
$283$	−1.89157	−	3.27630i	−0.112442	−	0.194756i	−0.916754	+	0.399451i	$0.869201\pi$
$284$	−10.8853	−	18.8539i	−0.645923	−	1.11877i
$285$	−29.0866	+	2.59551i	−1.72294	+	0.153745i
$286$	−2.26882	+	3.92971i	−0.134158	+	0.232369i
$287$	−4.25451			−0.251136
$288$	−8.08024	+	22.4418i	−0.476133	+	1.32240i
$289$	8.50326			0.500192
$290$	−20.5144	+	35.5321i	−1.20465	+	2.08651i
$291$	−12.5237	−	17.8200i	−0.734155	−	1.04463i
$292$	12.2812	+	21.2717i	0.718705	+	1.24483i
$293$	14.2922	+	24.7548i	0.834957	+	1.44619i	0.894065	+	0.447937i	$0.147841\pi$
$293$	14.2922	+	24.7548i	0.834957	+	1.44619i	−0.0591077	+	0.998252i	$0.518826\pi$
$294$	−1.54761	+	3.33393i	−0.0902586	+	0.194439i
$295$	−15.9372	+	27.6041i	−0.927901	+	1.60717i
$296$	0.792085			0.0460390
$297$	1.31877	−	5.02602i	0.0765228	−	0.291639i
$298$	34.3552			1.99014
$299$	3.12236	−	5.40809i	0.180571	−	0.312758i
$300$	5.20356	−	11.2097i	0.300428	−	0.647193i
$301$	5.13093	+	8.88704i	0.295742	+	0.512240i
$302$	−1.46076	−	2.53011i	−0.0840572	−	0.145591i
$303$	−17.8379	−	25.3815i	−1.02476	−	1.45813i
$304$	8.24335	−	14.2779i	0.472789	−	0.818894i
$305$	−0.129023			−0.00738786
$306$	31.6426	−	5.69252i	1.80889	−	0.325420i
$307$	−27.2873			−1.55737			−0.778683	−	0.627418i	$-0.784112\pi$
$307$	−27.2873			−1.55737			−0.778683	+	0.627418i	$0.784112\pi$
$308$	−1.25170	+	2.16800i	−0.0713221	+	0.123533i
$309$	24.0599	−	2.14696i	1.36872	−	0.122136i
$310$	−26.1484	−	45.2904i	−1.48513	−	2.57232i
$311$	12.4984	+	21.6478i	0.708718	+	1.22754i	0.965333	+	0.261021i	$0.0840593\pi$
$311$	12.4984	+	21.6478i	0.708718	+	1.22754i	−0.256615	+	0.966514i	$0.582607\pi$
$312$	−3.94073	+	0.351647i	−0.223100	+	0.0199081i
$313$	−13.3603	+	23.1408i	−0.755170	+	1.30799i	0.190119	+	0.981761i	$0.439113\pi$
$313$	−13.3603	+	23.1408i	−0.755170	+	1.30799i	−0.945290	+	0.326232i	$0.894221\pi$
$314$	−17.2124			−0.971352
$315$	−5.42520	−	6.42022i	−0.305676	−	0.361738i
$316$	−10.3228			−0.580704
$317$	5.68400	−	9.84498i	0.319245	−	0.552949i	−0.661085	−	0.750311i	$-0.729904\pi$
$317$	5.68400	−	9.84498i	0.319245	−	0.552949i	0.980331	+	0.197361i	$0.0632373\pi$
$318$	0.219969	+	0.312993i	0.0123352	+	0.0175518i
$319$	3.45024	+	5.97598i	0.193176	+	0.334591i
$320$	15.9603	+	27.6440i	0.892207	+	1.54535i
$321$	13.8165	−	29.7640i	0.771161	−	1.66127i
$322$	3.09880	−	5.36728i	0.172689	−	0.299107i
$323$	−30.3887			−1.69087
$324$	21.1179	−	7.85237i	1.17322	−	0.436243i
$325$	−6.09451			−0.338063
$326$	−7.94018	+	13.7528i	−0.439766	+	0.761697i
$327$	−0.561535	+	1.20968i	−0.0310530	+	0.0668955i
$328$	−2.27247	−	3.93603i	−0.125476	−	0.217331i
$329$	−2.88192	−	4.99164i	−0.158885	−	0.275198i
$330$	−5.92155	−	8.42575i	−0.325970	−	0.463822i
$331$	−7.80810	+	13.5240i	−0.429172	+	0.743348i	−0.996800	−	0.0799375i	$-0.974528\pi$
$331$	−7.80810	+	13.5240i	−0.429172	+	0.743348i	0.567628	+	0.823285i	$0.307861\pi$
$332$	4.35212			0.238853
$333$	1.43572	+	1.69903i	0.0786767	+	0.0931065i
$334$	7.79066			0.426286
$335$	10.0362	−	17.3833i	0.548339	−	0.949751i
$336$	4.72670	−	0.421782i	0.257863	−	0.0230101i
$337$	7.02855	+	12.1738i	0.382870	+	0.663149i	0.991471	−	0.130326i	$-0.0416026\pi$
$337$	7.02855	+	12.1738i	0.382870	+	0.663149i	−0.608602	+	0.793476i	$0.708269\pi$
$338$	−8.94246	−	15.4888i	−0.486406	−	0.842479i
$339$	22.3541	−	1.99475i	1.21411	−	0.108340i
$340$	17.7108	−	30.6760i	0.960503	−	1.66364i
$341$	−8.79557			−0.476307
$342$	−37.7041	+	6.78298i	−2.03881	+	0.366782i
$343$	1.00000			0.0539949
$344$	−5.48119	+	9.49369i	−0.295526	+	0.511866i
$345$	8.14926	+	11.5956i	0.438742	+	0.624284i
$346$	11.1144	+	19.2508i	0.597516	+	1.03493i
$347$	2.30820	+	3.99792i	0.123911	+	0.214619i	0.921307	−	0.388837i	$-0.127123\pi$
$347$	2.30820	+	3.99792i	0.123911	+	0.214619i	−0.797396	+	0.603456i	$0.793790\pi$
$348$	−12.5980	+	27.1390i	−0.675322	+	1.45480i
$349$	−7.36666	+	12.7594i	−0.394328	+	0.682997i	−0.993015	−	0.117986i	$-0.962356\pi$
$349$	−7.36666	+	12.7594i	−0.394328	+	0.682997i	0.598687	+	0.800983i	$0.295689\pi$
$350$	−6.04852			−0.323307
$351$	−7.89717	−	7.81554i	−0.421520	−	0.417163i
$352$	7.95072			0.423775
$353$	−5.43262	+	9.40958i	−0.289149	+	0.500822i	−0.973607	−	0.228231i	$-0.926706\pi$
$353$	−5.43262	+	9.40958i	−0.289149	+	0.500822i	0.684458	+	0.729053i	$0.260039\pi$
$354$	−17.6061	+	37.9278i	−0.935755	+	2.01584i
$355$	−12.1829	−	21.1015i	−0.646603	−	1.11995i
$356$	11.2158	+	19.4263i	0.594434	+	1.02959i
$357$	−5.02947	−	7.15641i	−0.266188	−	0.378758i
$358$	0.0429307	−	0.0743581i	0.00226896	−	0.00392995i
$359$	−16.8844			−0.891124			−0.445562	−	0.895251i	$-0.646996\pi$
$359$	−16.8844			−0.891124			−0.445562	+	0.895251i	$0.646996\pi$
$360$	3.04184	−	8.44833i	0.160319	−	0.445266i
$361$	17.2100			0.905787
$362$	26.2684	−	45.4981i	1.38063	−	2.39133i
$363$	−1.72520	+	0.153946i	−0.0905493	+	0.00808007i
$364$	2.67645	+	4.63575i	0.140284	+	0.242979i
$365$	13.7453	+	23.8075i	0.719461	+	1.24614i
$366$	−0.168592	+	0.0150441i	−0.00881242	+	0.000786367i
$367$	2.79805	−	4.84637i	0.146057	−	0.252978i	−0.783710	−	0.621127i	$-0.786675\pi$
$367$	2.79805	−	4.84637i	0.146057	−	0.252978i	0.929767	+	0.368149i	$0.120008\pi$
$368$	−8.00153			−0.417109
$369$	4.32381	−	12.0088i	0.225089	−	0.625155i
$370$	4.40864			0.229194
$371$	0.0520400	−	0.0901359i	0.00270178	−	0.00467962i
$372$	−21.9289	−	31.2026i	−1.13696	−	1.61778i
$373$	14.3655	+	24.8817i	0.743816	+	1.28833i	0.950746	+	0.309972i	$0.100320\pi$
$373$	14.3655	+	24.8817i	0.743816	+	1.28833i	−0.206929	+	0.978356i	$0.566347\pi$
$374$	−5.35843	−	9.28108i	−0.277078	−	0.479913i
$375$	−4.39265	+	9.46282i	−0.226836	+	0.488658i
$376$	3.07865	−	5.33238i	0.158769	−	0.274996i
$377$	14.7550			0.759921
$378$	−7.83757	−	7.75655i	−0.403121	−	0.398954i
$379$	−8.81739			−0.452919			−0.226459	−	0.974021i	$-0.572715\pi$
$379$	−8.81739			−0.452919			−0.226459	+	0.974021i	$0.572715\pi$
$380$	−21.1035	+	36.5523i	−1.08259	+	1.87509i
$381$	−14.9887	+	32.2892i	−0.767893	+	1.65423i
$382$	−16.1746	−	28.0152i	−0.827564	−	1.43338i
$383$	0.977789	+	1.69358i	0.0499627	+	0.0865379i	0.889925	−	0.456107i	$-0.150756\pi$
$383$	0.977789	+	1.69358i	0.0499627	+	0.0865379i	−0.839962	+	0.542645i	$0.817423\pi$
$384$	8.24163	+	11.7270i	0.420579	+	0.598440i
$385$	−1.40091	+	2.42645i	−0.0713971	+	0.123663i
$386$	19.3400			0.984381
$387$	−30.2992	+	5.45084i	−1.54019	+	0.277082i
$388$	−31.4803			−1.59817
$389$	−17.6267	+	30.5303i	−0.893709	+	1.54795i	−0.0583154	+	0.998298i	$0.518573\pi$
$389$	−17.6267	+	30.5303i	−0.893709	+	1.54795i	−0.835394	+	0.549652i	$0.814760\pi$
$390$	−21.9336	+	1.95722i	−1.11065	+	0.0991077i
$391$	7.37430	+	12.7727i	0.372935	+	0.645942i
$392$	0.534131	+	0.925143i	0.0269777	+	0.0467268i
$393$	6.17673	−	0.551174i	0.311575	−	0.0278030i
$394$	17.1697	−	29.7388i	0.864997	−	1.49822i
$395$	−11.5534			−0.581315
$396$	−4.84735	−	5.73638i	−0.243588	−	0.288264i
$397$	31.2947			1.57063			0.785317	−	0.619094i	$-0.212500\pi$
$397$	31.2947			1.57063			0.785317	+	0.619094i	$0.212500\pi$
$398$	7.39195	−	12.8032i	0.370525	−	0.641768i
$399$	5.99291	+	8.52730i	0.300021	+	0.426899i
$400$	3.90453	+	6.76284i	0.195226	+	0.338142i
$401$	−1.22730	−	2.12574i	−0.0612883	−	0.106154i	0.833753	−	0.552137i	$-0.186188\pi$
$401$	−1.22730	−	2.12574i	−0.0612883	−	0.106154i	−0.895042	+	0.445983i	$0.852854\pi$
$402$	11.0872	−	23.8845i	0.552980	−	1.19125i
$403$	−9.40360	+	16.2875i	−0.468427	+	0.811339i
$404$	−44.8384			−2.23079
$405$	23.6354	−	8.78846i	1.17445	−	0.436702i
$406$	14.6436			0.726751
$407$	0.370735	−	0.642132i	0.0183766	−	0.0318293i
$408$	3.93431	−	8.47544i	0.194777	−	0.419597i
$409$	−9.79818	−	16.9709i	−0.484489	−	0.839159i	0.515352	−	0.856978i	$-0.327661\pi$
$409$	−9.79818	−	16.9709i	−0.484489	−	0.839159i	−0.999841	+	0.0178192i	$0.994328\pi$
$410$	−12.6482	−	21.9074i	−0.624652	−	1.08193i
$411$	11.6249	+	16.5410i	0.573413	+	0.815907i
$412$	17.4564	−	30.2354i	0.860016	−	1.48959i
$413$	11.3763			0.559792
$414$	12.0005	+	14.2014i	0.589791	+	0.697962i
$415$	4.87093			0.239105
$416$	8.50035	−	14.7230i	0.416764	−	0.721856i
$417$	14.9050	−	1.33003i	0.729899	−	0.0651318i
$418$	6.38490	+	11.0590i	0.312296	+	0.540912i
$419$	−16.5001	−	28.5790i	−0.806083	−	1.39618i	−0.915557	−	0.402188i	$-0.868250\pi$
$419$	−16.5001	−	28.5790i	−0.806083	−	1.39618i	0.109474	−	0.993990i	$-0.465083\pi$
$420$	−12.1006	+	1.07979i	−0.590451	+	0.0526883i
$421$	−15.2219	+	26.3652i	−0.741871	+	1.28496i	0.209771	+	0.977751i	$0.432728\pi$
$421$	−15.2219	+	26.3652i	−0.741871	+	1.28496i	−0.951642	+	0.307208i	$0.900605\pi$
$422$	−16.0673			−0.782145
$423$	17.0183	−	3.06160i	0.827460	−	0.148860i
$424$	0.111185			0.00539961
$425$	7.19692	−	12.4654i	0.349102	−	0.604662i
$426$	−18.3795	−	26.1522i	−0.890492	−	1.26708i
$427$	0.0230249	+	0.0398803i	0.00111425	+	0.00192994i
$428$	−23.7140	−	41.0738i	−1.14626	−	1.98538i
$429$	−1.55938	+	3.35928i	−0.0752877	+	0.162188i
$430$	−30.5076	+	52.8406i	−1.47120	+	2.54820i
$431$	−15.2681			−0.735437			−0.367719	−	0.929937i	$-0.619861\pi$
$431$	−15.2681			−0.735437			−0.367719	+	0.929937i	$0.619861\pi$
$432$	−3.61317	+	13.7703i	−0.173839	+	0.662524i
$433$	11.2140			0.538910			0.269455	−	0.963013i	$-0.413156\pi$
$433$	11.2140			0.538910			0.269455	+	0.963013i	$0.413156\pi$
$434$	−9.33263	+	16.1646i	−0.447981	+	0.775925i
$435$	−14.0998	+	30.3743i	−0.676033	+	1.45634i
$436$	0.963793	+	1.66934i	0.0461573	+	0.0799469i
$437$	−8.78693	−	15.2194i	−0.420336	−	0.728043i
$438$	20.7366	+	29.5060i	0.990831	+	1.40985i
$439$	0.194695	−	0.337222i	0.00929229	−	0.0160947i	−0.861342	−	0.508026i	$-0.830375\pi$
$439$	0.194695	−	0.337222i	0.00929229	−	0.0160947i	0.870634	+	0.491931i	$0.163709\pi$
$440$	−2.99309			−0.142690
$441$	−1.01629	+	2.82261i	−0.0483948	+	0.134410i
$442$	−22.9154			−1.08998
$443$	−14.4989	+	25.1128i	−0.688862	+	1.19314i	0.283345	+	0.959018i	$0.408556\pi$
$443$	−14.4989	+	25.1128i	−0.688862	+	1.19314i	−0.972206	+	0.234125i	$0.924777\pi$
$444$	3.20229	−	0.285753i	0.151974	−	0.0135612i
$445$	12.5528	+	21.7421i	0.595060	+	1.03067i
$446$	16.3010	+	28.2341i	0.771874	+	1.33692i
$447$	27.9293	−	2.49224i	1.32101	−	0.117879i
$448$	5.69639	−	9.86644i	0.269129	−	0.466145i
$449$	−18.3299			−0.865039			−0.432520	−	0.901624i	$-0.642375\pi$
$449$	−18.3299			−0.865039			−0.432520	+	0.901624i	$0.642375\pi$
$450$	6.14705	−	17.0726i	0.289775	−	0.804812i
$451$	−4.25451			−0.200337
$452$	16.2188	−	28.0918i	0.762869	−	1.32133i
$453$	−1.37108	−	1.95090i	−0.0644189	−	0.0916615i
$454$	9.23219	+	15.9906i	0.433288	+	0.750477i
$455$	2.99551	+	5.18838i	0.140432	+	0.243235i
$456$	−4.68797	+	10.0990i	−0.219534	+	0.472929i
$457$	11.7525	−	20.3560i	0.549759	−	0.952211i	−0.448531	−	0.893767i	$-0.648053\pi$
$457$	11.7525	−	20.3560i	0.549759	−	0.952211i	0.998291	−	0.0584442i	$-0.0186140\pi$
$458$	−0.357982			−0.0167274
$459$	25.3112	−	6.92325i	1.18143	−	0.323150i
$460$	20.4844			0.955091
$461$	3.00969	−	5.21294i	0.140175	−	0.242791i	−0.787387	−	0.616459i	$-0.788567\pi$
$461$	3.00969	−	5.21294i	0.140175	−	0.242791i	0.927563	+	0.373668i	$0.121900\pi$
$462$	−1.54761	+	3.33393i	−0.0720015	+	0.155108i
$463$	−2.01195	−	3.48480i	−0.0935034	−	0.161953i	0.815480	−	0.578786i	$-0.196473\pi$
$463$	−2.01195	−	3.48480i	−0.0935034	−	0.161953i	−0.908983	+	0.416833i	$0.863140\pi$
$464$	−9.45298	−	16.3730i	−0.438844	−	0.760099i
$465$	−24.5431	−	34.9223i	−1.13816	−	1.61948i
$466$	5.37037	−	9.30176i	0.248778	−	0.430896i
$467$	−21.4469			−0.992445			−0.496223	−	0.868195i	$-0.665280\pi$
$467$	−21.4469			−0.992445			−0.496223	+	0.868195i	$0.665280\pi$
$468$	−15.8050	+	2.84332i	−0.730586	+	0.131433i
$469$	−7.16408			−0.330806
$470$	17.1354	−	29.6793i	0.790395	−	1.36900i
$471$	−13.9930	+	1.24865i	−0.644762	+	0.0575347i
$472$	6.07645	+	10.5247i	0.279691	+	0.484439i
$473$	5.13093	+	8.88704i	0.235921	+	0.408626i
$474$	−15.0965	+	1.34712i	−0.693407	+	0.0618755i
$475$	−8.57557	+	14.8533i	−0.393474	+	0.681517i
$476$	−12.6423			−0.579460
$477$	0.201531	+	0.238493i	0.00922748	+	0.0109198i
$478$	−48.5676			−2.22143
$479$	14.5650	−	25.2274i	0.665493	−	1.15267i	−0.313659	−	0.949536i	$-0.601555\pi$
$479$	14.5650	−	25.2274i	0.665493	−	1.15267i	0.979151	−	0.203132i	$-0.0651120\pi$
$480$	22.1856	+	31.5679i	1.01263	+	1.44087i
$481$	−0.792727	−	1.37304i	−0.0361452	−	0.0626054i
$482$	19.8159	+	34.3222i	0.902591	+	1.56333i
$483$	2.12983	−	4.58817i	0.0969108	−	0.208769i
$484$	−1.25170	+	2.16800i	−0.0568953	+	0.0985456i
$485$	−35.2331			−1.59985
$486$	29.8590	−	14.2395i	1.35443	−	0.645918i
$487$	31.4283			1.42415			0.712075	−	0.702103i	$-0.247755\pi$
$487$	31.4283			1.42415			0.712075	+	0.702103i	$0.247755\pi$
$488$	−0.0245966	+	0.0426026i	−0.00111344	+	0.00192853i
$489$	−5.45736	+	11.7565i	−0.246790	+	0.531645i
$490$	2.97290	+	5.14922i	0.134302	+	0.232618i
$491$	−10.8876	−	18.8579i	−0.491350	−	0.851044i	0.508600	−	0.861003i	$-0.330163\pi$
$491$	−10.8876	−	18.8579i	−0.491350	−	0.851044i	−0.999950	+	0.00995924i	$0.996830\pi$
$492$	−10.6072	−	15.0930i	−0.478211	−	0.680446i
$493$	−17.4240	+	30.1792i	−0.784735	+	1.35920i
$494$	27.3051			1.22852
$495$	−5.42520	−	6.42022i	−0.243845	−	0.288567i
$496$	24.0982			1.08204
$497$	−4.34821	+	7.53132i	−0.195044	+	0.337826i
$498$	6.36473	−	0.567949i	0.285210	−	0.0254504i
$499$	8.67997	+	15.0341i	0.388569	+	0.673021i	0.992257	−	0.124200i	$-0.0396363\pi$
$499$	8.67997	+	15.0341i	0.388569	+	0.673021i	−0.603689	+	0.797220i	$0.706303\pi$
$500$	7.53934	+	13.0585i	0.337170	+	0.583995i
$501$	6.33348	−	0.565161i	0.282959	−	0.0252496i
$502$	8.67484	−	15.0253i	0.387177	−	0.670610i
$503$	27.9201			1.24489			0.622447	−	0.782662i	$-0.286139\pi$
$503$	27.9201			1.24489			0.622447	+	0.782662i	$0.286139\pi$
$504$	−3.15415	+	0.567433i	−0.140497	+	0.0252755i
$505$	−50.1836			−2.23314
$506$	3.09880	−	5.36728i	0.137758	−	0.238604i
$507$	−8.39346	−	11.9430i	−0.372767	−	0.530408i
$508$	25.7259	+	44.5585i	1.14140	+	1.97696i
$509$	8.05421	+	13.9503i	0.356996	+	0.618336i	0.987458	−	0.157885i	$-0.0504675\pi$
$509$	8.05421	+	13.9503i	0.356996	+	0.618336i	−0.630461	+	0.776221i	$0.717134\pi$
$510$	21.8978	−	47.1732i	0.969653	−	2.08886i
$511$	4.90583	−	8.49715i	0.217021	−	0.375892i
$512$	−27.6371			−1.22140
$513$	−30.1598	+	8.24947i	−1.33159	+	0.364223i
$514$	32.2903			1.42426
$515$	19.5374	−	33.8398i	0.860921	−	1.49116i
$516$	−18.7348	+	40.3591i	−0.824752	+	1.77671i
$517$	−2.88192	−	4.99164i	−0.126747	−	0.219532i
$518$	−0.786744	−	1.36268i	−0.0345675	−	0.0598727i
$519$	10.4321	+	14.8438i	0.457919	+	0.651571i
$520$	−3.20000	+	5.54255i	−0.140329	+	0.243057i
$521$	−0.993343			−0.0435191			−0.0217596	−	0.999763i	$-0.506927\pi$
$521$	−0.993343			−0.0435191			−0.0217596	+	0.999763i	$0.506927\pi$
$522$	−14.8822	+	41.3333i	−0.651376	+	1.80911i
$523$	−37.4772			−1.63876			−0.819381	−	0.573249i	$-0.805683\pi$
$523$	−37.4772			−1.63876			−0.819381	+	0.573249i	$0.805683\pi$
$524$	4.48146	−	7.76211i	0.195773	−	0.339089i
$525$	−4.91719	+	0.438781i	−0.214604	+	0.0191500i
$526$	−11.5801	−	20.0573i	−0.504916	−	0.874540i
$527$	−22.2092	−	38.4674i	−0.967446	−	1.67567i
$528$	4.72670	−	0.421782i	0.205703	−	0.0183557i
$529$	7.23542	−	12.5321i	0.314583	−	0.544874i
$530$	0.618840			0.0268807
$531$	−11.5616	+	32.1109i	−0.501732	+	1.39350i
$532$	15.0641			0.653112
$533$	−4.54862	+	7.87844i	−0.197022	+	0.341253i
$534$	18.9375	+	26.9462i	0.819507	+	1.16607i
$535$	−26.5409	−	45.9703i	−1.14747	−	1.98747i
$536$	−3.82656	−	6.62780i	−0.165282	−	0.286277i
$537$	0.0295066	−	0.0635644i	0.00127331	−	0.00274301i
$538$	8.12352	−	14.0703i	0.350230	−	0.606616i
$539$	1.00000			0.0430730
$540$	9.24995	−	35.2528i	0.398054	−	1.51704i
$541$	−25.5455			−1.09829			−0.549144	−	0.835728i	$-0.685046\pi$
$541$	−25.5455			−1.09829			−0.549144	+	0.835728i	$0.685046\pi$
$542$	4.14573	−	7.18061i	0.178074	−	0.308434i
$543$	18.0545	−	38.8937i	0.774793	−	1.66909i
$544$	20.0759	+	34.7724i	0.860746	+	1.49086i
$545$	1.07869	+	1.86834i	0.0462059	+	0.0800310i
$546$	4.51912	+	6.43025i	0.193401	+	0.275189i
$547$	15.2477	−	26.4098i	0.651946	−	1.12920i	−0.330704	−	0.943734i	$-0.607286\pi$
$547$	15.2477	−	26.4098i	0.651946	−	1.12920i	0.982650	−	0.185469i	$-0.0593804\pi$
$548$	29.2209			1.24825
$549$	−0.135967	+	0.0244604i	−0.00580291	+	0.00104395i
$550$	−6.04852			−0.257910
$551$	20.7617	−	35.9603i	0.884478	−	1.53196i
$552$	5.38232	−	0.480286i	0.229087	−	0.0204423i
$553$	2.06177	+	3.57108i	0.0876752	+	0.151858i
$554$	−13.7155	−	23.7560i	−0.582716	−	1.00929i
$555$	3.58404	−	0.319818i	0.152134	−	0.0135755i
$556$	10.8141	−	18.7306i	0.458621	−	0.794356i
$557$	−16.7664			−0.710416			−0.355208	−	0.934787i	$-0.615590\pi$
$557$	−16.7664			−0.710416			−0.355208	+	0.934787i	$0.615590\pi$
$558$	−36.1418	−	42.7703i	−1.53000	−	1.81061i
$559$	21.9425			0.928070
$560$	3.83823	−	6.64801i	0.162195	−	0.280930i
$561$	−5.02947	−	7.15641i	−0.212344	−	0.302144i
$562$	21.3096	+	36.9094i	0.898892	+	1.55693i
$563$	−18.3411	−	31.7678i	−0.772987	−	1.33885i	−0.935919	−	0.352215i	$-0.885429\pi$
$563$	−18.3411	−	31.7678i	−0.772987	−	1.33885i	0.162933	−	0.986637i	$-0.447905\pi$
$564$	10.5229	−	22.6688i	0.443092	−	0.954527i
$565$	18.1523	−	31.4406i	0.763671	−	1.32272i
$566$	−8.02829			−0.337454
$567$	−6.93431	−	5.73719i	−0.291214	−	0.240939i
$568$	−9.29007			−0.389803
$569$	−0.591951	+	1.02529i	−0.0248159	+	0.0429824i	−0.878167	−	0.478355i	$-0.841233\pi$
$569$	−0.591951	+	1.02529i	−0.0248159	+	0.0429824i	0.853351	+	0.521337i	$0.174567\pi$
$570$	−26.0926	+	56.2097i	−1.09290	+	2.35437i
$571$	−2.98082	−	5.16292i	−0.124743	−	0.216062i	0.796889	−	0.604125i	$-0.206477\pi$
$571$	−2.98082	−	5.16292i	−0.124743	−	0.216062i	−0.921633	+	0.388064i	$0.873144\pi$
$572$	2.67645	+	4.63575i	0.111908	+	0.193830i
$573$	−15.1816	−	21.6019i	−0.634220	−	0.902430i
$574$	−4.51429	+	7.81897i	−0.188423	+	0.326358i
$575$	8.32400			0.347135
$576$	22.0600	+	26.1059i	0.919165	+	1.08774i
$577$	−38.2415			−1.59201			−0.796007	−	0.605287i	$-0.793058\pi$
$577$	−38.2415			−1.59201			−0.796007	+	0.605287i	$0.793058\pi$
$578$	9.02247	−	15.6274i	0.375285	−	0.650013i
$579$	15.7226	−	1.40299i	0.653410	−	0.0583064i
$580$	24.2002	+	41.9160i	1.00486	+	1.74047i
$581$	−0.869243	−	1.50557i	−0.0360623	−	0.0624617i
$582$	−46.0382	+	4.10817i	−1.90834	+	0.170289i
$583$	0.0520400	−	0.0901359i	0.00215528	−	0.00373305i
$584$	10.4814			0.433725
$585$	−17.6891	+	3.18228i	−0.731355	+	0.131571i
$586$	60.6594			2.50582
$587$	−11.1719	+	19.3503i	−0.461113	+	0.798671i	−0.999017	−	0.0443353i	$-0.985883\pi$
$587$	−11.1719	+	19.3503i	−0.461113	+	0.798671i	0.537904	+	0.843006i	$0.319216\pi$
$588$	2.49318	+	3.54754i	0.102817	+	0.146298i
$589$	26.4636	+	45.8362i	1.09041	+	1.88865i
$590$	33.8207	+	58.5792i	1.39238	+	2.41167i
$591$	11.8009	−	25.4220i	0.485424	−	1.04572i
$592$	−1.01574	+	1.75932i	−0.0417467	+	0.0723074i
$593$	−48.0729			−1.97412			−0.987058	−	0.160361i	$-0.948734\pi$
$593$	−48.0729			−1.97412			−0.987058	+	0.160361i	$0.948734\pi$
$594$	−7.83757	−	7.75655i	−0.321579	−	0.318255i
$595$	−14.1494			−0.580070
$596$	20.2638	−	35.0980i	0.830038	−	1.43767i
$597$	5.08056	−	10.9447i	0.207933	−	0.447938i
$598$	−6.62603	−	11.4766i	−0.270959	−	0.469314i
$599$	−16.7061	−	28.9358i	−0.682593	−	1.18229i	−0.974187	−	0.225743i	$-0.927519\pi$
$599$	−16.7061	−	28.9358i	−0.682593	−	1.18229i	0.291594	−	0.956542i	$-0.405814\pi$
$600$	−3.03236	−	4.31474i	−0.123796	−	0.176149i
$601$	16.0092	−	27.7287i	0.653027	−	1.13108i	−0.329357	−	0.944205i	$-0.606832\pi$
$601$	16.0092	−	27.7287i	0.653027	−	1.13108i	0.982384	−	0.186871i	$-0.0598347\pi$
$602$	21.7769			0.887561
$603$	7.28078	−	20.2214i	0.296496	−	0.823480i
$604$	−3.44642			−0.140233
$605$	−1.40091	+	2.42645i	−0.0569552	+	0.0986493i
$606$	−65.5736	+	5.85139i	−2.66374	+	0.237696i
$607$	−13.0888	−	22.6706i	−0.531260	−	0.920169i	−0.999334	−	0.0364803i	$-0.988385\pi$
$607$	−13.0888	−	22.6706i	−0.531260	−	0.920169i	0.468074	−	0.883689i	$-0.344948\pi$
$608$	−23.9216	−	41.4335i	−0.970150	−	1.68035i
$609$	11.9047	−	1.06230i	0.482401	−	0.0430466i
$610$	−0.136902	+	0.237120i	−0.00554298	+	0.00960073i
$611$	−12.3246			−0.498599
$612$	12.8483	−	35.6844i	0.519361	−	1.44246i
$613$	14.8814			0.601053			0.300527	−	0.953773i	$-0.402838\pi$
$613$	14.8814			0.601053			0.300527	+	0.953773i	$0.402838\pi$
$614$	−28.9534	+	50.1488i	−1.16846	+	2.02384i
$615$	−11.8717	−	16.8923i	−0.478715	−	0.681162i
$616$	0.534131	+	0.925143i	0.0215208	+	0.0372751i
$617$	3.84958	+	6.66767i	0.154978	+	0.268430i	0.933051	−	0.359744i	$-0.117136\pi$
$617$	3.84958	+	6.66767i	0.154978	+	0.268430i	−0.778073	+	0.628174i	$0.783803\pi$
$618$	21.5833	−	46.4956i	0.868208	−	1.87033i
$619$	9.41521	−	16.3076i	0.378429	−	0.655459i	−0.612405	−	0.790545i	$-0.709798\pi$
$619$	9.41521	−	16.3076i	0.378429	−	0.655459i	0.990834	+	0.135086i	$0.0431310\pi$
$620$	−61.6928			−2.47764
$621$	10.7861	+	10.6746i	0.432832	+	0.428357i
$622$	53.0461			2.12695
$623$	4.48022	−	7.75997i	0.179496	−	0.310897i
$624$	4.27240	−	9.20378i	0.171033	−	0.368446i
$625$	15.5637	+	26.9571i	0.622547	+	1.07828i
$626$	28.3522	+	49.1075i	1.13318	+	1.96273i
$627$	5.99291	+	8.52730i	0.239334	+	0.340548i
$628$	−10.1525	+	17.5846i	−0.405127	+	0.701700i
$629$	3.74448			0.149302
$630$	−17.5556	+	3.15826i	−0.699432	+	0.125828i
$631$	44.6783			1.77862			0.889308	−	0.457309i	$-0.151187\pi$
$631$	44.6783			1.77862			0.889308	+	0.457309i	$0.151187\pi$
$632$	−2.20251	+	3.81485i	−0.0876110	+	0.151747i
$633$	−13.0621	+	1.16558i	−0.519171	+	0.0463276i
$634$	−12.0621	−	20.8922i	−0.479049	−	0.829736i
$635$	28.7927	+	49.8704i	1.14260	+	1.97904i
$636$	0.449505	−	0.0401111i	0.0178240	−	0.00159051i
$637$	1.06913	−	1.85179i	0.0423604	−	0.0733704i
$638$	14.6436			0.579747
$639$	−16.8390	−	19.9273i	−0.666140	−	0.788313i
$640$	23.1862			0.916516
$641$	0.997458	−	1.72765i	0.0393972	−	0.0682380i	−0.845654	−	0.533731i	$-0.820790\pi$
$641$	0.997458	−	1.72765i	0.0393972	−	0.0682380i	0.885052	+	0.465493i	$0.154123\pi$
$642$	−40.0405	−	56.9735i	−1.58027	−	2.24856i
$643$	22.2654	+	38.5648i	0.878061	+	1.52085i	0.853466	+	0.521148i	$0.174496\pi$
$643$	22.2654	+	38.5648i	0.878061	+	1.52085i	0.0245941	+	0.999698i	$0.492171\pi$
$644$	−3.65555	−	6.33159i	−0.144049	−	0.249500i
$645$	−20.9681	+	45.1704i	−0.825619	+	1.77858i
$646$	−32.2442	+	55.8486i	−1.26863	+	2.19733i
$647$	8.30047			0.326325			0.163163	−	0.986599i	$-0.447831\pi$
$647$	8.30047			0.326325			0.163163	+	0.986599i	$0.447831\pi$
$648$	1.60389	−	9.47964i	0.0630068	−	0.372395i
$649$	11.3763			0.446559
$650$	−6.46665	+	11.2006i	−0.253643	+	0.439322i
$651$	−6.41441	+	13.8182i	−0.251400	+	0.541577i
$652$	9.36676	+	16.2237i	0.366831	+	0.635369i
$653$	−17.8599	−	30.9342i	−0.698912	−	1.21055i	−0.968844	−	0.247671i	$-0.920335\pi$
$653$	−17.8599	−	30.9342i	−0.698912	−	1.21055i	0.269932	−	0.962879i	$-0.412999\pi$
$654$	1.62734	+	2.31554i	0.0636341	+	0.0905448i
$655$	5.01570	−	8.68744i	0.195979	−	0.339446i
$656$	11.6565			0.455111
$657$	18.9984	+	22.4828i	0.741199	+	0.877139i
$658$	−12.2316			−0.476836
$659$	19.3960	−	33.5949i	0.755562	−	1.30867i	−0.189533	−	0.981874i	$-0.560697\pi$
$659$	19.3960	−	33.5949i	0.755562	−	1.30867i	0.945095	−	0.326797i	$-0.105969\pi$
$660$	−12.1006	+	1.07979i	−0.471017	+	0.0420307i
$661$	11.4498	+	19.8316i	0.445345	+	0.771360i	0.998076	−	0.0619996i	$-0.0197477\pi$
$661$	11.4498	+	19.8316i	0.445345	+	0.771360i	−0.552731	+	0.833360i	$0.686414\pi$
$662$	16.5697	+	28.6996i	0.644001	+	1.11544i
$663$	−18.6293	+	1.66237i	−0.723502	+	0.0645609i
$664$	0.928580	−	1.60835i	0.0360359	−	0.0624160i
$665$	16.8599			0.653799
$666$	4.64588	−	0.835796i	0.180024	−	0.0323864i
$667$	−20.1526			−0.780314
$668$	4.59519	−	7.95910i	0.177793	−	0.307947i
$669$	15.3002	+	21.7706i	0.591541	+	0.841702i
$670$	−21.2981	−	36.8894i	−0.822818	−	1.42516i
$671$	0.0230249	+	0.0398803i	0.000888866	+	0.00153956i
$672$	5.79828	−	12.4909i	0.223673	−	0.481846i
$673$	−5.32849	+	9.22922i	−0.205398	+	0.355760i	−0.950260	−	0.311459i	$-0.899182\pi$
$673$	−5.32849	+	9.22922i	−0.205398	+	0.355760i	0.744861	+	0.667219i	$0.232516\pi$
$674$	29.8309			1.14904
$675$	3.75879	−	14.3253i	0.144676	−	0.551380i
$676$	−21.0982			−0.811471
$677$	2.20444	−	3.81820i	0.0847236	−	0.146746i	−0.820550	−	0.571575i	$-0.806333\pi$
$677$	2.20444	−	3.81820i	0.0847236	−	0.146746i	0.905273	+	0.424829i	$0.139666\pi$
$678$	20.0531	−	43.1992i	0.770136	−	1.65906i
$679$	6.28753	+	10.8903i	0.241293	+	0.417932i
$680$	−7.55765	−	13.0902i	−0.289823	−	0.501988i
$681$	8.66541	+	12.3300i	0.332059	+	0.472486i
$682$	−9.33263	+	16.1646i	−0.357365	+	0.618974i
$683$	−0.677885			−0.0259386			−0.0129693	−	0.999916i	$-0.504128\pi$
$683$	−0.677885			−0.0259386			−0.0129693	+	0.999916i	$0.504128\pi$
$684$	−15.3095	+	42.5202i	−0.585374	+	1.62580i
$685$	32.7043			1.24957
$686$	1.06106	−	1.83781i	0.0405115	−	0.0701679i
$687$	−0.291024	+	0.0259692i	−0.0111033	+	0.000990788i
$688$	−14.0578	−	24.3488i	−0.535947	−	0.928288i
$689$	−0.111275	−	0.192734i	−0.00423924	−	0.00734257i
$690$	29.9573	−	2.67321i	1.14045	−	0.101767i
$691$	11.4758	−	19.8767i	0.436561	−	0.756145i	−0.560861	−	0.827910i	$-0.689530\pi$
$691$	11.4758	−	19.8767i	0.436561	−	0.756145i	0.997422	+	0.0717648i	$0.0228631\pi$
$692$	26.2227			0.996837
$693$	−1.01629	+	2.82261i	−0.0386057	+	0.107222i
$694$	9.79655			0.371872
$695$	12.1033	−	20.9635i	0.459104	−	0.795191i
$696$	7.34144	+	10.4461i	0.278276	+	0.395959i
$697$	−10.7428	−	18.6071i	−0.406912	−	0.704792i
$698$	15.6329	+	27.0770i	0.591715	+	1.02488i
$699$	3.69111	−	7.95153i	0.139611	−	0.300754i
$700$	−3.56762	+	6.17929i	−0.134843	+	0.233555i
$701$	12.4014			0.468396			0.234198	−	0.972189i	$-0.424754\pi$
$701$	12.4014			0.468396			0.234198	+	0.972189i	$0.424754\pi$
$702$	−22.7429	+	6.22074i	−0.858374	+	0.234787i
$703$	−4.46177			−0.168279
$704$	5.69639	−	9.86644i	0.214691	−	0.371855i
$705$	11.7773	−	25.3711i	0.443559	−	0.955531i
$706$	11.5287	+	19.9683i	0.433888	+	0.751516i
$707$	8.95551	+	15.5114i	0.336807	+	0.583366i
$708$	28.3632	+	40.3579i	1.06595	+	1.51674i
$709$	−4.91787	+	8.51800i	−0.184694	+	0.319900i	−0.943473	−	0.331448i	$-0.892463\pi$
$709$	−4.91787	+	8.51800i	−0.184694	+	0.319900i	0.758779	+	0.651348i	$0.225796\pi$
$710$	−51.7073			−1.94054
$711$	−12.1751	+	2.19031i	−0.456603	+	0.0821431i
$712$	9.57211			0.358730
$713$	12.8436	−	22.2458i	0.480997	−	0.833112i
$714$	−18.4887	+	1.64982i	−0.691922	+	0.0617429i
$715$	2.99551	+	5.18838i	0.112026	+	0.194034i
$716$	−0.0506439	−	0.0877177i	−0.00189265	−	0.00327817i
$717$	−39.4834	+	3.52326i	−1.47454	+	0.131579i
$718$	−17.9154	+	31.0303i	−0.668595	+	1.15804i
$719$	−32.0591			−1.19560			−0.597802	−	0.801644i	$-0.703959\pi$
$719$	−32.0591			−1.19560			−0.597802	+	0.801644i	$0.703959\pi$
$720$	14.8640	+	17.5901i	0.553949	+	0.655546i
$721$	−13.9462			−0.519384
$722$	18.2608	−	31.6286i	0.679597	−	1.17710i
$723$	18.5994	+	26.4650i	0.691719	+	0.984245i
$724$	−30.9879	−	53.6726i	−1.15166	−	1.99473i
$725$	9.83395	+	17.0329i	0.365224	+	0.632586i
$726$	−1.54761	+	3.33393i	−0.0574373	+	0.123734i
$727$	10.5696	−	18.3070i	0.392003	−	0.678969i	−0.600711	−	0.799467i	$-0.705116\pi$
$727$	10.5696	−	18.3070i	0.392003	−	0.678969i	0.992714	+	0.120497i	$0.0384489\pi$
$728$	2.28422			0.0846589
$729$	23.2412	−	13.7422i	0.860784	−	0.508971i
$730$	58.3383			2.15920
$731$	−25.9116	+	44.8802i	−0.958375	+	1.65995i
$732$	−0.0840716	+	0.181110i	−0.00310737	+	0.00669403i
$733$	−8.77178	−	15.1932i	−0.323993	−	0.561173i	0.657315	−	0.753616i	$-0.271692\pi$
$733$	−8.77178	−	15.1932i	−0.323993	−	0.561173i	−0.981308	+	0.192443i	$0.938359\pi$
$734$	−5.93780	−	10.2846i	−0.219168	−	0.379611i
$735$	2.79039	+	3.97044i	0.102925	+	0.146452i
$736$	−11.6099	+	20.1090i	−0.427948	+	0.741228i
$737$	−7.16408			−0.263892
$738$	−17.4821	−	20.6884i	−0.643526	−	0.761552i
$739$	29.3430			1.07940			0.539699	−	0.841858i	$-0.318538\pi$
$739$	29.3430			1.07940			0.539699	+	0.841858i	$0.318538\pi$
$740$	2.60036	−	4.50396i	0.0955912	−	0.165569i
$741$	22.1979	−	1.98081i	0.815462	−	0.0727668i
$742$	−0.110435	−	0.191279i	−0.00405420	−	0.00702208i
$743$	21.5021	+	37.2428i	0.788837	+	1.36631i	0.926680	+	0.375852i	$0.122650\pi$
$743$	21.5021	+	37.2428i	0.788837	+	1.36631i	−0.137843	+	0.990454i	$0.544017\pi$
$744$	−16.2099	+	1.44647i	−0.594284	+	0.0530303i
$745$	22.6795	−	39.2820i	0.830912	−	1.43918i
$746$	60.9706			2.23229
$747$	5.13306	−	0.923439i	0.187809	−	0.0337869i
$748$	−12.6423			−0.462249
$749$	−9.47273	+	16.4073i	−0.346126	+	0.599508i
$750$	12.7300	+	18.1135i	0.464834	+	0.661411i
$751$	0.644498	+	1.11630i	0.0235180	+	0.0407345i	0.877545	−	0.479494i	$-0.159180\pi$
$751$	0.644498	+	1.11630i	0.0235180	+	0.0407345i	−0.854027	+	0.520229i	$0.825847\pi$
$752$	7.89591	+	13.6761i	0.287934	+	0.498716i
$753$	5.96230	−	12.8442i	0.217278	−	0.468069i
$754$	15.6559	−	27.1169i	0.570156	−	0.987538i
$755$	−3.85726			−0.140380
$756$	−12.5471	+	3.43195i	−0.456334	+	0.124819i
$757$	−9.00852			−0.327420			−0.163710	−	0.986508i	$-0.552346\pi$
$757$	−9.00852			−0.327420			−0.163710	+	0.986508i	$0.552346\pi$
$758$	−9.35578	+	16.2047i	−0.339817	+	0.588581i
$759$	2.12983	−	4.58817i	0.0773081	−	0.166540i
$760$	9.00540	+	15.5978i	0.326660	+	0.565792i
$761$	10.5534	+	18.2791i	0.382561	+	0.662615i	0.991428	−	0.130658i	$-0.0417088\pi$
$761$	10.5534	+	18.2791i	0.382561	+	0.662615i	−0.608867	+	0.793273i	$0.708375\pi$
$762$	43.4375	+	61.8071i	1.57357	+	2.23904i
$763$	0.384995	−	0.666830i	0.0139377	−	0.0241409i
$764$	−38.1613			−1.38063
$765$	14.3799	−	39.9384i	0.519907	−	1.44398i
$766$	4.14997			0.149945
$767$	12.1627	−	21.0665i	0.439171	−	0.760667i
$768$	−9.01271	+	0.804239i	−0.325218	+	0.0290205i
$769$	−21.1224	−	36.5851i	−0.761693	−	1.31929i	−0.941977	−	0.335677i	$-0.891035\pi$
$769$	−21.1224	−	36.5851i	−0.761693	−	1.31929i	0.180284	−	0.983615i	$-0.442298\pi$
$770$	2.97290	+	5.14922i	0.107136	+	0.185565i
$771$	26.2506	−	2.34245i	0.945394	−	0.0843612i
$772$	11.4074	−	19.7582i	0.410561	−	0.711112i
$773$	9.47703			0.340865			0.170432	−	0.985369i	$-0.445484\pi$
$773$	9.47703			0.340865			0.170432	+	0.985369i	$0.445484\pi$
$774$	−22.1317	+	61.4678i	−0.795506	+	2.20942i
$775$	−25.0694			−0.900518
$776$	−6.71673	+	11.6337i	−0.241117	+	0.417626i
$777$	−0.738444	−	1.05073i	−0.0264915	−	0.0376947i
$778$	37.4060	+	64.7891i	1.34107	+	2.32280i
$779$	12.8007	+	22.1714i	0.458632	+	0.794374i
$780$	−10.9376	+	23.5622i	−0.391630	+	0.843664i
$781$	−4.34821	+	7.53132i	−0.155591	+	0.269492i
$782$	31.2983			1.11923
$783$	−9.10014	+	34.6819i	−0.325212	+	1.23943i
$784$	−2.73981			−0.0978502
$785$	−11.3627	+	19.6808i	−0.405553	+	0.702439i
$786$	5.54093	−	11.9365i	0.197638	−	0.425760i
$787$	−1.23819	−	2.14460i	−0.0441366	−	0.0764469i	0.843113	−	0.537736i	$-0.180720\pi$
$787$	−1.23819	−	2.14460i	−0.0441366	−	0.0764469i	−0.887250	+	0.461289i	$0.847387\pi$
$788$	−20.2545	−	35.0819i	−0.721538	−	1.24974i
$789$	−10.8692	−	15.4657i	−0.386952	−	0.550593i
$790$	−12.2589	+	21.2330i	−0.436151	+	0.755435i
$791$	−12.9575			−0.460714
$792$	−3.15415	+	0.567433i	−0.112078	+	0.0201629i
$793$	0.0984663			0.00349664
$794$	33.2055	−	57.5136i	1.17842	−	2.04108i
$795$	0.503091	−	0.0448928i	0.0178428	−	0.00159218i
$796$	−8.72004	−	15.1036i	−0.309074	−	0.535331i
$797$	−13.7900	−	23.8850i	−0.488466	−	0.846049i	0.511446	−	0.859316i	$-0.329110\pi$
$797$	−13.7900	−	23.8850i	−0.488466	−	0.846049i	−0.999912	+	0.0132670i	$0.995777\pi$
$798$	22.0304	−	1.96586i	0.779868	−	0.0695907i
$799$	14.5539	−	25.2081i	0.514881	−	0.891800i
$800$	22.6613			0.801199
$801$	17.3502	+	20.5323i	0.613039	+	0.725474i
$802$	−5.20894			−0.183934
$803$	4.90583	−	8.49715i	0.173123	−	0.299858i
$804$	−17.8613	−	25.4148i	−0.629920	−	0.896312i
$805$	−4.09133	−	7.08639i	−0.144200	−	0.249762i
$806$	19.9556	+	34.5641i	0.702905	+	1.21747i
$807$	5.58337	−	12.0279i	0.196544	−	0.423403i
$808$	−9.56684	+	16.5703i	−0.336560	+	0.582940i
$809$	2.11544			0.0743750			0.0371875	−	0.999308i	$-0.488160\pi$
$809$	2.11544			0.0743750			0.0371875	+	0.999308i	$0.488160\pi$
$810$	8.92705	−	52.7624i	0.313664	−	1.85388i
$811$	−25.8869			−0.909011			−0.454505	−	0.890744i	$-0.650184\pi$
$811$	−25.8869			−0.909011			−0.454505	+	0.890744i	$0.650184\pi$
$812$	8.63730	−	14.9602i	0.303110	−	0.525002i
$813$	2.84940	−	6.13828i	0.0999327	−	0.215279i
$814$	−0.786744	−	1.36268i	−0.0275754	−	0.0477619i
$815$	10.4834	+	18.1577i	0.367217	+	0.636038i
$816$	13.7798	+	19.6072i	0.482388	+	0.686389i
$817$	30.8752	−	53.4775i	1.08019	−	1.87094i
$818$	−41.5858			−1.45401
$819$	4.14033	+	4.89969i	0.144675	+	0.171209i
$820$	−29.8414			−1.04211
$821$	−0.809534	+	1.40215i	−0.0282529	+	0.0489355i	−0.879806	−	0.475333i	$-0.842328\pi$
$821$	−0.809534	+	1.40215i	−0.0282529	+	0.0489355i	0.851553	+	0.524268i	$0.175661\pi$
$822$	42.7339	−	3.81331i	1.49052	−	0.133005i
$823$	−24.5348	−	42.4955i	−0.855229	−	1.48130i	−0.876432	−	0.481525i	$-0.840083\pi$
$823$	−24.5348	−	42.4955i	−0.855229	−	1.48130i	0.0212027	−	0.999775i	$-0.493250\pi$
$824$	−7.44910	−	12.9022i	−0.259502	−	0.449470i
$825$	−4.91719	+	0.438781i	−0.171195	+	0.0152764i
$826$	12.0710	−	20.9075i	0.420002	−	0.727465i
$827$	−47.3207			−1.64550			−0.822751	−	0.568402i	$-0.807562\pi$
$827$	−47.3207			−1.64550			−0.822751	+	0.568402i	$0.807562\pi$
$828$	21.5868	−	3.88346i	0.750191	−	0.134960i
$829$	−30.2730			−1.05143			−0.525713	−	0.850662i	$-0.676201\pi$
$829$	−30.2730			−1.05143			−0.525713	+	0.850662i	$0.676201\pi$
$830$	5.16835	−	8.95185i	0.179396	−	0.310723i
$831$	−12.8735	−	18.3176i	−0.446576	−	0.635432i
$832$	−12.1804	−	21.0970i	−0.422278	−	0.731407i
$833$	2.52504	+	4.37349i	0.0874874	+	0.151533i
$834$	13.3707	−	28.8037i	0.462990	−	0.997391i
$835$	5.14298	−	8.90791i	0.177980	−	0.308271i
$836$	15.0641			0.521003
$837$	−32.4845	−	32.1487i	−1.12283	−	1.11122i
$838$	−70.0305			−2.41916
$839$	8.83031	−	15.2946i	0.304856	−	0.528027i	−0.672373	−	0.740212i	$-0.734725\pi$
$839$	8.83031	−	15.2946i	0.304856	−	0.528027i	0.977229	+	0.212186i	$0.0680582\pi$
$840$	−2.18279	+	4.70225i	−0.0753133	+	0.162243i
$841$	−9.30826	−	16.1224i	−0.320975	−	0.555944i
$842$	32.3028	+	55.9500i	1.11323	+	1.92817i
$843$	20.0014	+	28.4599i	0.688884	+	0.980211i
$844$	−9.47704	+	16.4147i	−0.326213	+	0.565018i
$845$	−23.6134			−0.812324
$846$	12.4308	−	34.5250i	0.427381	−	1.18699i
$847$	1.00000			0.0343604
$848$	−0.142579	+	0.246955i	−0.00489620	+	0.00848046i
$849$	−6.52666	+	0.582400i	−0.223995	+	0.0199879i
$850$	−15.2727	−	26.4531i	−0.523850	−	0.907336i
$851$	1.08272	+	1.87533i	0.0371152	+	0.0642854i
$852$	−37.5585	+	3.35149i	−1.28673	+	0.114820i
$853$	21.2035	−	36.7256i	0.725995	−	1.25746i	−0.232568	−	0.972580i	$-0.574713\pi$
$853$	21.2035	−	36.7256i	0.725995	−	1.25746i	0.958563	−	0.284880i	$-0.0919539\pi$
$854$	0.0977231			0.00334402
$855$	−17.1346	+	47.5890i	−0.585989	+	1.62751i
$856$	−20.2387			−0.691746
$857$	−12.7114	+	22.0167i	−0.434212	+	0.752077i	−0.997231	−	0.0743668i	$-0.976306\pi$
$857$	−12.7114	+	22.0167i	−0.434212	+	0.752077i	0.563019	+	0.826444i	$0.309640\pi$
$858$	4.51912	+	6.43025i	0.154280	+	0.219525i
$859$	−16.5188	−	28.6114i	−0.563614	−	0.976208i	−0.997177	−	0.0750850i	$-0.976077\pi$
$859$	−16.5188	−	28.6114i	−0.563614	−	0.976208i	0.433563	−	0.901123i	$-0.357256\pi$
$860$	35.9887	+	62.3343i	1.22721	+	2.12558i
$861$	−3.10271	+	6.68398i	−0.105740	+	0.227790i
$862$	−16.2003	+	28.0598i	−0.551786	+	0.955721i
$863$	−42.8833			−1.45977			−0.729883	−	0.683572i	$-0.760425\pi$
$863$	−42.8833			−1.45977			−0.729883	+	0.683572i	$0.760425\pi$
$864$	29.3642	+	29.0607i	0.998990	+	0.988664i
$865$	29.3487			0.997886
$866$	11.8987	−	20.6092i	0.404335	−	0.700329i
$867$	6.20123	−	13.3589i	0.210605	−	0.453693i
$868$	11.0094	+	19.0688i	0.373683	+	0.647238i
$869$	2.06177	+	3.57108i	0.0699406	+	0.121141i
$870$	40.8615	+	58.1417i	1.38533	+	1.97119i
$871$	−7.65933	+	13.2663i	−0.259526	+	0.449513i
$872$	0.822551			0.0278551
$873$	−37.1291	+	6.67954i	−1.25663	+	0.226068i
$874$	−37.2939			−1.26148
$875$	3.01165	−	5.21633i	0.101812	−	0.176344i
$876$	42.3751	−	3.78129i	1.43172	−	0.127758i
$877$	3.32607	+	5.76093i	0.112313	+	0.194533i	0.916703	−	0.399570i	$-0.130841\pi$
$877$	3.32607	+	5.76093i	0.112313	+	0.194533i	−0.804389	+	0.594103i	$0.797507\pi$
$878$	−0.413166	−	0.715625i	−0.0139437	−	0.0241512i
$879$	49.3136	−	4.40044i	1.66331	−	0.148423i
$880$	3.83823	−	6.64801i	0.129387	−	0.224104i
$881$	19.1569			0.645414			0.322707	−	0.946499i	$-0.395407\pi$
$881$	19.1569			0.645414			0.322707	+	0.946499i	$0.395407\pi$
$882$	4.10908	+	4.86271i	0.138360	+	0.163736i
$883$	−35.8145			−1.20526			−0.602628	−	0.798023i	$-0.705880\pi$
$883$	−35.8145			−1.20526			−0.602628	+	0.798023i	$0.705880\pi$
$884$	−13.5163	+	23.4109i	−0.454602	+	0.787393i
$885$	31.7444	+	45.1690i	1.06708	+	1.51834i
$886$	30.7683	+	53.2923i	1.03368	+	1.79039i
$887$	14.4466	+	25.0222i	0.485068	+	0.840163i	0.999853	−	0.0171569i	$-0.00546149\pi$
$887$	14.4466	+	25.0222i	0.485068	+	0.840163i	−0.514785	+	0.857319i	$0.672128\pi$
$888$	0.577649	−	1.24439i	0.0193846	−	0.0417591i
$889$	10.2764	−	17.7992i	0.344659	−	0.596967i
$890$	53.2771			1.78585
$891$	−6.93431	−	5.73719i	−0.232308	−	0.192203i
$892$	38.4594			1.28772
$893$	−17.3419	+	30.0370i	−0.580324	+	1.00515i
$894$	25.0544	−	53.9732i	0.837945	−	1.80513i
$895$	−0.0566811	−	0.0981746i	−0.00189464	−	0.00328162i
$896$	−4.13770	−	7.16671i	−0.138231	−	0.239423i
$897$	−6.21924	−	8.84934i	−0.207654	−	0.295471i
$898$	−19.4491	+	33.6868i	−0.649024	+	1.12414i
$899$	60.6936			2.02425
$900$	−13.8160	−	16.3500i	−0.460534	−	0.544999i
$901$	0.525612			0.0175107
$902$	−4.51429	+	7.81897i	−0.150309	+	0.260343i
$903$	17.7037	−	1.57977i	0.589143	−	0.0525716i
$904$	−6.92098	−	11.9875i	−0.230189	−	0.398698i
$905$	−34.6820	−	60.0710i	−1.15287	−	1.99683i
$906$	−5.04019	+	0.449756i	−0.167449	+	0.0149421i
$907$	−20.0589	+	34.7431i	−0.666045	+	1.15362i	0.312956	+	0.949768i	$0.398681\pi$
$907$	−20.0589	+	34.7431i	−0.666045	+	1.15362i	−0.979001	+	0.203856i	$0.934652\pi$
$908$	21.7818			0.722855
$909$	−52.8841	+	9.51387i	−1.75406	+	0.315555i
$910$	12.7137			0.421454
$911$	6.52094	−	11.2946i	0.216048	−	0.374207i	−0.737548	−	0.675295i	$-0.764016\pi$
$911$	6.52094	−	11.2946i	0.216048	−	0.374207i	0.953596	+	0.301088i	$0.0973498\pi$
$912$	−16.4194	−	23.3631i	−0.543701	−	0.773631i
$913$	−0.869243	−	1.50557i	−0.0287678	−	0.0498272i
$914$	−24.9403	−	43.1978i	−0.824950	−	1.42886i
$915$	−0.0940938	+	0.202700i	−0.00311064	+	0.00670107i
$916$	−0.211149	+	0.365721i	−0.00697657	+	0.0120838i
$917$	−3.58031			−0.118232
$918$	14.1331	−	53.8632i	0.466461	−	1.77775i
$919$	50.2657			1.65811			0.829056	−	0.559166i	$-0.188878\pi$
$919$	50.2657			1.65811			0.829056	+	0.559166i	$0.188878\pi$
$920$	4.37061	−	7.57013i	0.144095	−	0.249580i
$921$	−19.9000	+	42.8693i	−0.655726	+	1.41259i
$922$	−6.38693	−	11.0625i	−0.210342	−	0.364324i
$923$	9.29760	+	16.1039i	0.306034	+	0.530067i
$924$	2.49318	+	3.54754i	0.0820195	+	0.116705i
$925$	1.05668	−	1.83022i	0.0347433	−	0.0601772i
$926$	−8.53921			−0.280616
$927$	14.1734	−	39.3647i	0.465515	−	1.29291i
$928$	−54.8638			−1.80099
$929$	−24.1764	+	41.8748i	−0.793202	+	1.37387i	0.130772	+	0.991412i	$0.458254\pi$
$929$	−24.1764	+	41.8748i	−0.793202	+	1.37387i	−0.923974	+	0.382454i	$0.875079\pi$
$930$	−90.2222	+	8.05088i	−2.95850	+	0.263999i
$931$	−3.00874	−	5.21128i	−0.0986073	−	0.170793i
$932$	−6.33525	−	10.9730i	−0.207518	−	0.359432i
$933$	43.1243	−	3.84815i	1.41183	−	0.125983i
$934$	−22.7565	+	39.4154i	−0.744615	+	1.28971i
$935$	−14.1494			−0.462736
$936$	−2.32143	+	6.44748i	−0.0758784	+	0.210742i
$937$	19.1186			0.624577			0.312288	−	0.949987i	$-0.398905\pi$
$937$	19.1186			0.624577			0.312288	+	0.949987i	$0.398905\pi$
$938$	−7.60152	+	13.1662i	−0.248198	+	0.429892i
$939$	26.6116	+	37.8656i	0.868437	+	1.23570i
$940$	−20.2140	−	35.0117i	−0.659308	−	1.14196i
$941$	−4.20501	−	7.28330i	−0.137079	−	0.237429i	0.789310	−	0.613994i	$-0.210438\pi$
$941$	−4.20501	−	7.28330i	−0.137079	−	0.237429i	−0.926390	+	0.376566i	$0.877105\pi$
$942$	−12.5526	+	27.0413i	−0.408986	+	0.881054i
$943$	6.21259	−	10.7605i	0.202310	−	0.350411i
$944$	−31.1689			−1.01446
$945$	−14.0429	+	3.84108i	−0.456815	+	0.124950i
$946$	21.7769			0.708029
$947$	0.653958	−	1.13269i	0.0212508	−	0.0368074i	−0.855204	−	0.518291i	$-0.826568\pi$
$947$	0.653958	−	1.13269i	0.0212508	−	0.0368074i	0.876455	+	0.481483i	$0.159902\pi$
$948$	−7.52819	+	16.2175i	−0.244504	+	0.526721i
$949$	−10.4899	−	18.1691i	−0.340518	−	0.589794i
$950$	18.1984	+	31.5205i	0.590434	+	1.02266i
$951$	−11.3216	−	16.1095i	−0.367128	−	0.522386i
$952$	−2.69740	+	4.67204i	−0.0874234	+	0.151422i
$953$	−28.5913			−0.926162			−0.463081	−	0.886316i	$-0.653256\pi$
$953$	−28.5913			−0.926162			−0.463081	+	0.886316i	$0.653256\pi$
$954$	0.652142	−	0.117320i	0.0211139	−	0.00379839i
$955$	−42.7105			−1.38208
$956$	−28.6468	+	49.6177i	−0.926503	+	1.60475i
$957$	11.9047	−	1.06230i	0.384823	−	0.0343393i
$958$	−30.9087	−	53.5355i	−0.998616	−	1.72965i
$959$	−5.83625	−	10.1087i	−0.188462	−	0.326427i
$960$	55.0692	−	4.91404i	1.77735	−	0.158600i
$961$	−23.1811	+	40.1508i	−0.747776	+	1.29519i
$962$	−3.36452			−0.108477
$963$	−36.6843	−	43.4124i	−1.18214	−	1.39895i
$964$	46.7524			1.50579
$965$	12.7673	−	22.1136i	0.410993	−	0.711861i
$966$	−6.17230	−	8.78255i	−0.198591	−	0.282574i
$967$	−10.9066	−	18.8907i	−0.350731	−	0.607484i	0.635647	−	0.771980i	$-0.280734\pi$
$967$	−10.9066	−	18.8907i	−0.350731	−	0.607484i	−0.986378	+	0.164496i	$0.947400\pi$
$968$	0.534131	+	0.925143i	0.0171676	+	0.0297352i
$969$	−22.1618	+	47.7417i	−0.711938	+	1.53369i
$970$	−37.3844	+	64.7518i	−1.20034	+	2.07905i
$971$	−48.7785			−1.56538			−0.782689	−	0.622413i	$-0.786152\pi$
$971$	−48.7785			−1.56538			−0.782689	+	0.622413i	$0.786152\pi$
$972$	3.06444	−	38.9035i	0.0982918	−	1.24783i
$973$	−8.63958			−0.276972
$974$	33.3473	−	57.7592i	1.06852	−	1.85072i
$975$	−4.44459	+	9.57470i	−0.142341	+	0.306636i
$976$	−0.0630837	−	0.109264i	−0.00201926	−	0.00349746i
$977$	20.2473	+	35.0693i	0.647767	+	1.12197i	0.983655	+	0.180064i	$0.0576305\pi$
$977$	20.2473	+	35.0693i	0.647767	+	1.12197i	−0.335887	+	0.941902i	$0.609036\pi$
$978$	15.8156	+	22.5039i	0.505726	+	0.719595i
$979$	4.48022	−	7.75997i	0.143189	−	0.248010i
$980$	7.01407			0.224056
$981$	1.49094	+	1.76439i	0.0476020	+	0.0563325i
$982$	−46.2096			−1.47461
$983$	15.4692	−	26.7934i	0.493391	−	0.854578i	−0.506580	−	0.862193i	$-0.669091\pi$
$983$	15.4692	−	26.7934i	0.493391	−	0.854578i	0.999971	+	0.00761472i	$0.00242387\pi$
$984$	−7.84090	+	0.699674i	−0.249959	+	0.0223048i
$985$	−22.6691	−	39.2640i	−0.722297	−	1.25106i
$986$	36.9757	+	64.0438i	1.17755	+	2.03957i
$987$	−9.94376	+	0.887321i	−0.316513	+	0.0282437i
$988$	16.1055	−	27.8955i	0.512383	−	0.887474i
$989$	−29.9695			−0.952975
$990$	−17.5556	+	3.15826i	−0.557954	+	0.100376i
$991$	−48.2221			−1.53183			−0.765914	−	0.642944i	$-0.777713\pi$
$991$	−48.2221			−1.53183			−0.765914	+	0.642944i	$0.777713\pi$
$992$	34.9656	−	60.5622i	1.11016	−	1.92285i
$993$	15.5525	+	22.1296i	0.493543	+	0.702261i
$994$	9.22743	+	15.9824i	0.292676	+	0.506930i
$995$	−9.75956	−	16.9041i	−0.309399	−	0.535894i
$996$	3.17390	−	6.83733i	0.100569	−	0.216649i
$997$	−9.78618	+	16.9502i	−0.309931	+	0.536817i	−0.978347	−	0.206971i	$-0.933639\pi$
$997$	−9.78618	+	16.9502i	−0.309931	+	0.536817i	0.668416	+	0.743788i	$0.266973\pi$
$998$	36.8399			1.16615
$999$	3.71628	−	1.01650i	0.117578	−	0.0321605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.j.f.232.8	✓	18
9.2	odd	6		6237.2.a.ba.1.8		9
9.4	even	3	inner	693.2.j.f.463.8	yes	18
9.7	even	3		6237.2.a.bb.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.j.f.232.8	✓	18	1.1	even	1	trivial
693.2.j.f.463.8	yes	18	9.4	even	3	inner
6237.2.a.ba.1.8		9	9.2	odd	6
6237.2.a.bb.1.2		9	9.7	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06106 - 1.83781i) q^{2} +(0.729277 - 1.57104i) q^{3} +(-1.25170 - 2.16800i) q^{4} +(-1.40091 - 2.42645i) q^{5} +(-2.11346 - 3.00724i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.06826 q^{8} +(-1.93631 - 2.29144i) q^{9} -5.94581 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-4.31885 + 0.385388i) q^{12} +(1.06913 + 1.85179i) q^{13} +(1.06106 + 1.83781i) q^{14} +(-4.83370 + 0.431330i) q^{15} +(1.36990 - 2.37274i) q^{16} -5.05008 q^{17} +(-6.26577 + 1.12722i) q^{18} +6.01747 q^{19} +(-3.50704 + 6.07436i) q^{20} +(0.995919 + 1.41709i) q^{21} +(1.06106 + 1.83781i) q^{22} +(-1.46024 - 2.52920i) q^{23} +(-0.779059 + 1.67828i) q^{24} +(-1.42511 + 2.46837i) q^{25} +4.53764 q^{26} +(-5.01204 + 1.37092i) q^{27} +2.50339 q^{28} +(3.45024 - 5.97598i) q^{29} +(-4.33614 + 9.34108i) q^{30} +(4.39779 + 7.61719i) q^{31} +(-3.97536 - 6.88553i) q^{32} +(0.995919 + 1.41709i) q^{33} +(-5.35843 + 9.28108i) q^{34} +2.80183 q^{35} +(-2.54418 + 7.06612i) q^{36} -0.741470 q^{37} +(6.38490 - 11.0590i) q^{38} +(3.68891 - 0.329176i) q^{39} +(1.49654 + 2.59209i) q^{40} +(2.12725 + 3.68451i) q^{41} +(3.66107 - 0.326692i) q^{42} +(5.13093 - 8.88704i) q^{43} +2.50339 q^{44} +(-2.84747 + 7.90847i) q^{45} -6.19760 q^{46} +(-2.88192 + 4.99164i) q^{47} +(-2.72862 - 3.88255i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(3.02426 + 5.23817i) q^{50} +(-3.68290 + 7.93385i) q^{51} +(2.67645 - 4.63575i) q^{52} -0.104080 q^{53} +(-2.79859 + 10.6658i) q^{54} +2.80183 q^{55} +(0.534131 - 0.925143i) q^{56} +(4.38840 - 9.45367i) q^{57} +(-7.32182 - 12.6818i) q^{58} +(-5.68816 - 9.85218i) q^{59} +(6.98545 + 9.93957i) q^{60} +(0.0230249 - 0.0398803i) q^{61} +18.6653 q^{62} +(2.95260 - 0.531174i) q^{63} -11.3928 q^{64} +(2.99551 - 5.18838i) q^{65} +(3.66107 - 0.326692i) q^{66} +(3.58204 + 6.20427i) q^{67} +(6.32116 + 10.9486i) q^{68} +(-5.03839 + 0.449595i) q^{69} +(2.97290 - 5.14922i) q^{70} +8.69642 q^{71} +(2.06849 + 2.44786i) q^{72} -9.81166 q^{73} +(-0.786744 + 1.36268i) q^{74} +(2.83859 + 4.03902i) q^{75} +(-7.53205 - 13.0459i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(3.30920 - 7.12880i) q^{78} +(2.06177 - 3.57108i) q^{79} -7.67646 q^{80} +(-1.50140 + 8.87388i) q^{81} +9.02857 q^{82} +(-0.869243 + 1.50557i) q^{83} +(1.82567 - 3.93292i) q^{84} +(7.07471 + 12.2538i) q^{85} +(-10.8885 - 18.8594i) q^{86} +(-6.87231 - 9.77859i) q^{87} +(0.534131 - 0.925143i) q^{88} -8.96044 q^{89} +(11.5129 + 13.6245i) q^{90} -2.13826 q^{91} +(-3.65555 + 6.33159i) q^{92} +(15.1741 - 1.35404i) q^{93} +(6.11578 + 10.5928i) q^{94} +(-8.42995 - 14.6011i) q^{95} +(-13.7166 + 1.22398i) q^{96} +(6.28753 - 10.8903i) q^{97} -2.12212 q^{98} +(2.95260 - 0.531174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} + q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} - 9 q^{7} - 12 q^{8} - 5 q^{9} - 26 q^{10} - 9 q^{11} - 5 q^{12} + 8 q^{13} - q^{14} + 16 q^{15} + 5 q^{16} - 28 q^{17} - 16 q^{18} - 24 q^{19} - 19 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) \) 18 * q - q^2 + q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 - 9 * q^7 - 12 * q^8 - 5 * q^9 - 26 * q^10 - 9 * q^11 - 5 * q^12 + 8 * q^13 - q^14 + 16 * q^15 + 5 * q^16 - 28 * q^17 - 16 * q^18 - 24 * q^19 - 19 * q^20 + q^21 - q^22 + 19 * q^23 - 6 * q^24 + q^25 - 20 * q^26 - 14 * q^27 + 6 * q^28 + 12 * q^29 + 2 * q^30 + 3 * q^31 - 4 * q^32 + q^33 + 12 * q^35 - 8 * q^36 - 38 * q^37 + 20 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 - 4 * q^42 + 32 * q^43 + 6 * q^44 + 22 * q^45 - 4 * q^46 - 8 * q^47 - 21 * q^48 - 9 * q^49 + 18 * q^50 - 3 * q^51 + 4 * q^52 + 30 * q^53 + 35 * q^54 + 12 * q^55 + 6 * q^56 + 18 * q^57 + 3 * q^58 - 8 * q^59 - 5 * q^60 + 2 * q^61 + 24 * q^62 + 10 * q^63 - 68 * q^64 + 20 * q^65 - 4 * q^66 + 49 * q^67 + 46 * q^68 - q^69 + 13 * q^70 - 18 * q^71 + 27 * q^72 - 70 * q^73 - 19 * q^74 - 34 * q^75 + 25 * q^76 - 9 * q^77 + 2 * q^78 + 21 * q^79 - 52 * q^80 + 19 * q^81 - 20 * q^82 + 16 * q^83 - 11 * q^84 + 52 * q^85 - 31 * q^86 - 28 * q^87 + 6 * q^88 + 38 * q^89 + 20 * q^90 - 16 * q^91 + 32 * q^92 + 18 * q^93 - 50 * q^94 - 4 * q^95 + 18 * q^96 + 24 * q^97 + 2 * q^98 + 10 * q^99

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