LMFDB - Embedded newform 112.2.w.c.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(37,112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("112.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	112.37
Dual form			112.2.w.c.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.945375 - 1.05179i) q^{2} +(-0.0543752 - 0.0145698i) q^{3} +(-0.212530 - 1.98868i) q^{4} +(1.25781 - 0.337028i) q^{5} +(-0.0667293 + 0.0434174i) q^{6} +(0.230738 + 2.63567i) q^{7} +(-2.29259 - 1.65651i) q^{8} +(-2.59533 - 1.49842i) q^{9} +O(q^{10})$	\(q+(0.945375 - 1.05179i) q^{2} +(-0.0543752 - 0.0145698i) q^{3} +(-0.212530 - 1.98868i) q^{4} +(1.25781 - 0.337028i) q^{5} +(-0.0667293 + 0.0434174i) q^{6} +(0.230738 + 2.63567i) q^{7} +(-2.29259 - 1.65651i) q^{8} +(-2.59533 - 1.49842i) q^{9} +(0.834616 - 1.64157i) q^{10} +(-0.402875 + 1.50355i) q^{11} +(-0.0174182 + 0.111231i) q^{12} +(1.59615 - 1.59615i) q^{13} +(2.99031 + 2.24901i) q^{14} -0.0733039 q^{15} +(-3.90966 + 0.845308i) q^{16} +(1.46910 + 2.54455i) q^{17} +(-4.02958 + 1.31318i) q^{18} +(2.05021 + 7.65147i) q^{19} +(-0.937562 - 2.42974i) q^{20} +(0.0258547 - 0.146677i) q^{21} +(1.20055 + 1.84516i) q^{22} +(-3.91784 - 2.26197i) q^{23} +(0.100525 + 0.123475i) q^{24} +(-2.86164 + 1.65217i) q^{25} +(-0.169855 - 3.18777i) q^{26} +(0.238706 + 0.238706i) q^{27} +(5.19246 - 1.01902i) q^{28} +(2.06234 - 2.06234i) q^{29} +(-0.0692997 + 0.0771004i) q^{30} +(-3.14025 - 5.43908i) q^{31} +(-2.80701 + 4.91128i) q^{32} +(0.0438128 - 0.0758861i) q^{33} +(4.06519 + 0.860373i) q^{34} +(1.17852 + 3.23740i) q^{35} +(-2.42828 + 5.47973i) q^{36} +(5.24787 - 1.40616i) q^{37} +(9.98597 + 5.07713i) q^{38} +(-0.110046 + 0.0635352i) q^{39} +(-3.44193 - 1.31090i) q^{40} -7.34101i q^{41} +(-0.129831 - 0.165858i) q^{42} +(-1.99391 - 1.99391i) q^{43} +(3.07570 + 0.481638i) q^{44} +(-3.76943 - 1.01002i) q^{45} +(-6.08295 + 1.98235i) q^{46} +(0.979430 - 1.69642i) q^{47} +(0.224904 + 0.0109992i) q^{48} +(-6.89352 + 1.21630i) q^{49} +(-0.967587 + 4.57177i) q^{50} +(-0.0428089 - 0.159765i) q^{51} +(-3.51345 - 2.83499i) q^{52} +(3.00493 - 11.2146i) q^{53} +(0.476736 - 0.0254021i) q^{54} +2.02696i q^{55} +(3.83702 - 6.42474i) q^{56} -0.445921i q^{57} +(-0.219466 - 4.11884i) q^{58} +(0.793411 - 2.96105i) q^{59} +(0.0155793 + 0.145778i) q^{60} +(2.60480 + 9.72123i) q^{61} +(-8.68949 - 1.83908i) q^{62} +(3.35049 - 7.18618i) q^{63} +(2.51197 + 7.59540i) q^{64} +(1.46970 - 2.54559i) q^{65} +(-0.0383967 - 0.117823i) q^{66} +(-2.11517 - 0.566758i) q^{67} +(4.74806 - 3.46236i) q^{68} +(0.180077 + 0.180077i) q^{69} +(4.51921 + 1.82100i) q^{70} -7.26378i q^{71} +(3.46790 + 7.73444i) q^{72} +(-12.2392 + 7.06631i) q^{73} +(3.48222 - 6.84902i) q^{74} +(0.179674 - 0.0481435i) q^{75} +(14.7806 - 5.70337i) q^{76} +(-4.05583 - 0.714920i) q^{77} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 + 1.66547i) q^{79} +(-4.63270 + 2.38090i) q^{80} +(4.48574 + 7.76954i) q^{81} +(-7.72121 - 6.94001i) q^{82} +(8.82731 - 8.82731i) q^{83} +(-0.297188 - 0.0202433i) q^{84} +(2.70543 + 2.70543i) q^{85} +(-3.98217 + 0.212184i) q^{86} +(-0.142188 + 0.0820924i) q^{87} +(3.41427 - 2.77967i) q^{88} +(11.5526 + 6.66987i) q^{89} +(-4.62586 + 3.00981i) q^{90} +(4.57521 + 3.83862i) q^{91} +(-3.66566 + 8.27206i) q^{92} +(0.0915056 + 0.341503i) q^{93} +(-0.858354 - 2.63391i) q^{94} +(5.15752 + 8.93309i) q^{95} +(0.224188 - 0.226154i) q^{96} -9.69578 q^{97} +(-5.23767 + 8.40041i) q^{98} +(3.29854 - 3.29854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.945375	−	1.05179i	0.668481	−	0.743729i
$2$	0.945375	−	1.05179i	0.668481	−	0.743729i
$3$	−0.0543752	−	0.0145698i	−0.0313935	−	0.00841187i	0.243088	−	0.970004i	$-0.421840\pi$
$3$	−0.0543752	−	0.0145698i	−0.0313935	−	0.00841187i	−0.274482	+	0.961592i	$0.588506\pi$
$4$	−0.212530	−	1.98868i	−0.106265	−	0.994338i
$5$	1.25781	−	0.337028i	0.562508	−	0.150724i	0.0336497	−	0.999434i	$-0.489287\pi$
$5$	1.25781	−	0.337028i	0.562508	−	0.150724i	0.528858	+	0.848710i	$0.322620\pi$
$6$	−0.0667293	+	0.0434174i	−0.0272421	+	0.0177251i
$7$	0.230738	+	2.63567i	0.0872109	+	0.996190i
$7$	0.230738	+	2.63567i	0.0872109	+	0.996190i
$8$	−2.29259	−	1.65651i	−0.810554	−	0.585664i
$9$	−2.59533	−	1.49842i	−0.865111	−	0.499472i
$10$	0.834616	−	1.64157i	0.263929	−	0.519109i
$11$	−0.402875	+	1.50355i	−0.121472	+	0.453338i	−0.999689	−	0.0249229i	$-0.992066\pi$
$11$	−0.402875	+	1.50355i	−0.121472	+	0.453338i	0.878218	+	0.478261i	$0.158733\pi$
$12$	−0.0174182	+	0.111231i	−0.00502820	+	0.0321097i
$13$	1.59615	−	1.59615i	0.442691	−	0.442691i	−0.450224	−	0.892916i	$-0.648656\pi$
$13$	1.59615	−	1.59615i	0.442691	−	0.442691i	0.892916	+	0.450224i	$0.148656\pi$
$14$	2.99031	+	2.24901i	0.799194	+	0.601073i
$15$	−0.0733039			−0.0189270
$16$	−3.90966	+	0.845308i	−0.977415	+	0.211327i
$17$	1.46910	+	2.54455i	0.356309	+	0.617145i	0.987341	−	0.158612i	$-0.0507018\pi$
$17$	1.46910	+	2.54455i	0.356309	+	0.617145i	−0.631032	+	0.775757i	$0.717368\pi$
$18$	−4.02958	+	1.31318i	−0.949782	+	0.309520i
$19$	2.05021	+	7.65147i	0.470350	+	1.75537i	0.638514	+	0.769610i	$0.279549\pi$
$19$	2.05021	+	7.65147i	0.470350	+	1.75537i	−0.168165	+	0.985759i	$0.553784\pi$
$20$	−0.937562	−	2.42974i	−0.209645	−	0.543306i
$21$	0.0258547	−	0.146677i	0.00564196	−	0.0320075i
$22$	1.20055	+	1.84516i	0.255959	+	0.393390i
$23$	−3.91784	−	2.26197i	−0.816927	−	0.471653i	0.0324286	−	0.999474i	$-0.489676\pi$
$23$	−3.91784	−	2.26197i	−0.816927	−	0.471653i	−0.849356	+	0.527821i	$0.823009\pi$
$24$	0.100525	+	0.123475i	0.0205196	+	0.0252043i
$25$	−2.86164	+	1.65217i	−0.572328	+	0.330434i
$26$	−0.169855	−	3.18777i	−0.0333114	−	0.625173i
$27$	0.238706	+	0.238706i	0.0459390	+	0.0459390i
$28$	5.19246	−	1.01902i	0.981282	−	0.192577i
$29$	2.06234	−	2.06234i	0.382968	−	0.382968i	−0.489203	−	0.872170i	$-0.662712\pi$
$29$	2.06234	−	2.06234i	0.382968	−	0.382968i	0.872170	+	0.489203i	$0.162712\pi$
$30$	−0.0692997	+	0.0771004i	−0.0126523	+	0.0140765i
$31$	−3.14025	−	5.43908i	−0.564006	−	0.976887i	−0.997141	−	0.0755580i	$-0.975926\pi$
$31$	−3.14025	−	5.43908i	−0.564006	−	0.976887i	0.433136	−	0.901329i	$-0.357407\pi$
$32$	−2.80701	+	4.91128i	−0.496214	+	0.868200i
$33$	0.0438128	−	0.0758861i	0.00762684	−	0.0132101i
$34$	4.06519	+	0.860373i	0.697174	+	0.147553i
$35$	1.17852	+	3.23740i	0.199206	+	0.547220i
$36$	−2.42828	+	5.47973i	−0.404713	+	0.913289i
$37$	5.24787	−	1.40616i	0.862745	−	0.231172i	0.199797	−	0.979837i	$-0.435972\pi$
$37$	5.24787	−	1.40616i	0.862745	−	0.231172i	0.662948	+	0.748666i	$0.269305\pi$
$38$	9.98597	+	5.07713i	1.61994	+	0.823619i
$39$	−0.110046	+	0.0635352i	−0.0176215	+	0.0101738i
$40$	−3.44193	−	1.31090i	−0.544216	−	0.207271i
$41$		−	7.34101i		−	1.14647i	−0.819390	−	0.573236i	$-0.805688\pi$
$41$		−	7.34101i		−	1.14647i	0.819390	−	0.573236i	$-0.194312\pi$
$42$	−0.129831	−	0.165858i	−0.0200334	−	0.0255925i
$43$	−1.99391	−	1.99391i	−0.304068	−	0.304068i	0.538535	−	0.842603i	$-0.318978\pi$
$43$	−1.99391	−	1.99391i	−0.304068	−	0.304068i	−0.842603	+	0.538535i	$0.818978\pi$
$44$	3.07570	+	0.481638i	0.463679	+	0.0726097i
$45$	−3.76943	−	1.01002i	−0.561914	−	0.150564i
$46$	−6.08295	+	1.98235i	−0.896882	+	0.292281i
$47$	0.979430	−	1.69642i	0.142865	−	0.247449i	−0.785710	−	0.618596i	$-0.787702\pi$
$47$	0.979430	−	1.69642i	0.142865	−	0.247449i	0.928574	+	0.371147i	$0.121035\pi$
$48$	0.224904	+	0.0109992i	0.0324622	+	0.00158759i
$49$	−6.89352	+	1.21630i	−0.984789	+	0.173757i
$50$	−0.967587	+	4.57177i	−0.136837	+	0.646545i
$51$	−0.0428089	−	0.159765i	−0.00599444	−	0.0223716i
$52$	−3.51345	−	2.83499i	−0.487228	−	0.393142i
$53$	3.00493	−	11.2146i	0.412759	−	1.54044i	−0.376522	−	0.926408i	$-0.622880\pi$
$53$	3.00493	−	11.2146i	0.412759	−	1.54044i	0.789282	−	0.614031i	$-0.210453\pi$
$54$	0.476736	−	0.0254021i	0.0648756	−	0.00345679i
$55$			2.02696i			0.273315i
$56$	3.83702	−	6.42474i	0.512743	−	0.858542i
$57$		−	0.445921i		−	0.0590637i
$58$	−0.219466	−	4.11884i	−0.0288173	−	0.540831i
$59$	0.793411	−	2.96105i	0.103293	−	0.385496i	−0.894853	−	0.446362i	$-0.852719\pi$
$59$	0.793411	−	2.96105i	0.103293	−	0.385496i	0.998146	+	0.0608657i	$0.0193861\pi$
$60$	0.0155793	+	0.145778i	0.00201128	+	0.0188198i
$61$	2.60480	+	9.72123i	0.333510	+	1.24468i	0.905476	+	0.424398i	$0.139514\pi$
$61$	2.60480	+	9.72123i	0.333510	+	1.24468i	−0.571966	+	0.820277i	$0.693819\pi$
$62$	−8.68949	−	1.83908i	−1.10357	−	0.233563i
$63$	3.35049	−	7.18618i	0.422122	−	0.905374i
$64$	2.51197	+	7.59540i	0.313996	+	0.949424i
$65$	1.46970	−	2.54559i	0.182293	−	0.315742i
$66$	−0.0383967	−	0.117823i	−0.00472631	−	0.0145030i
$67$	−2.11517	−	0.566758i	−0.258409	−	0.0692405i	0.127289	−	0.991866i	$-0.459373\pi$
$67$	−2.11517	−	0.566758i	−0.258409	−	0.0692405i	−0.385698	+	0.922625i	$0.626039\pi$
$68$	4.74806	−	3.46236i	0.575787	−	0.419872i
$69$	0.180077	+	0.180077i	0.0216787	+	0.0216787i
$70$	4.51921	+	1.82100i	0.540149	+	0.217651i
$71$		−	7.26378i		−	0.862052i	−0.902340	−	0.431026i	$-0.858152\pi$
$71$		−	7.26378i		−	0.862052i	0.902340	−	0.431026i	$-0.141848\pi$
$72$	3.46790	+	7.73444i	0.408696	+	0.911513i
$73$	−12.2392	+	7.06631i	−1.43249	+	0.827049i	−0.997310	−	0.0732936i	$-0.976649\pi$
$73$	−12.2392	+	7.06631i	−1.43249	+	0.827049i	−0.435181	+	0.900343i	$0.643316\pi$
$74$	3.48222	−	6.84902i	0.404800	−	0.796182i
$75$	0.179674	−	0.0481435i	0.0207469	−	0.00555913i
$76$	14.7806	−	5.70337i	1.69545	−	0.654221i
$77$	−4.05583	−	0.714920i	−0.462204	−	0.0814727i
$78$	−0.0372092	+	0.175810i	−0.00421311	+	0.0199066i
$79$	−0.961559	+	1.66547i	−0.108184	+	0.187380i	−0.915035	−	0.403376i	$-0.867837\pi$
$79$	−0.961559	+	1.66547i	−0.108184	+	0.187380i	0.806851	+	0.590755i	$0.201170\pi$
$80$	−4.63270	+	2.38090i	−0.517952	+	0.266193i
$81$	4.48574	+	7.76954i	0.498416	+	0.863282i
$82$	−7.72121	−	6.94001i	−0.852665	−	0.766396i
$83$	8.82731	−	8.82731i	0.968923	−	0.968923i	−0.0306086	−	0.999531i	$-0.509745\pi$
$83$	8.82731	−	8.82731i	0.968923	−	0.968923i	0.999531	+	0.0306086i	$0.00974454\pi$
$84$	−0.297188	−	0.0202433i	−0.0324258	−	0.00220873i
$85$	2.70543	+	2.70543i	0.293445	+	0.293445i
$86$	−3.98217	+	0.212184i	−0.429408	+	0.0228803i
$87$	−0.142188	+	0.0820924i	−0.0152442	+	0.00880123i
$88$	3.41427	−	2.77967i	0.363963	−	0.296313i
$89$	11.5526	+	6.66987i	1.22457	+	0.707005i	0.965888	−	0.258959i	$-0.0833793\pi$
$89$	11.5526	+	6.66987i	1.22457	+	0.707005i	0.258680	+	0.965963i	$0.416713\pi$
$90$	−4.62586	+	3.00981i	−0.487608	+	0.317262i
$91$	4.57521	+	3.83862i	0.479612	+	0.402397i
$92$	−3.66566	+	8.27206i	−0.382172	+	0.862422i
$93$	0.0915056	+	0.341503i	0.00948869	+	0.0354123i
$94$	−0.858354	−	2.63391i	−0.0885325	−	0.271667i
$95$	5.15752	+	8.93309i	0.529151	+	0.916516i
$96$	0.224188	−	0.226154i	0.0228811	−	0.0230818i
$97$	−9.69578			−0.984458			−0.492229	−	0.870466i	$-0.663818\pi$
$97$	−9.69578			−0.984458			−0.492229	+	0.870466i	$0.663818\pi$
$98$	−5.23767	+	8.40041i	−0.529084	+	0.848569i
$99$	3.29854	−	3.29854i	0.331516	−	0.331516i
$100$	3.89381	+	5.33974i	0.389381	+	0.533974i
$101$	−2.73526	+	10.2081i	−0.272168	+	1.01575i	0.685547	+	0.728029i	$0.259563\pi$
$101$	−2.73526	+	10.2081i	−0.272168	+	1.01575i	−0.957715	+	0.287718i	$0.907103\pi$
$102$	−0.208510	−	0.106012i	−0.0206456	−	0.0104967i
$103$	−2.96542	−	1.71209i	−0.292192	−	0.168697i	0.346738	−	0.937962i	$-0.387289\pi$
$103$	−2.96542	−	1.71209i	−0.292192	−	0.168697i	−0.638930	+	0.769265i	$0.720623\pi$
$104$	−6.30334	+	1.01529i	−0.618094	+	0.0995570i
$105$	−0.0169140	−	0.193205i	−0.00165064	−	0.0188549i
$106$	−8.95459	−	13.7625i	−0.869747	−	1.33674i
$107$	−11.0668	+	2.96534i	−1.06987	+	0.286670i	−0.750439	−	0.660940i	$-0.770158\pi$
$107$	−11.0668	+	2.96534i	−1.06987	+	0.286670i	−0.319429	+	0.947610i	$0.603491\pi$
$108$	0.423977	−	0.525441i	0.0407972	−	0.0505606i
$109$	3.02860	+	0.811511i	0.290087	+	0.0777287i	0.400928	−	0.916110i	$-0.368688\pi$
$109$	3.02860	+	0.811511i	0.290087	+	0.0777287i	−0.110841	+	0.993838i	$0.535354\pi$
$110$	2.13194	+	1.91624i	0.203272	+	0.182706i
$111$	−0.305841			−0.0290292
$112$	−3.13006	−	10.1095i	−0.295763	−	0.955261i
$113$	4.67963			0.440223			0.220111	−	0.975475i	$-0.429358\pi$
$113$	4.67963			0.440223			0.220111	+	0.975475i	$0.429358\pi$
$114$	−0.469016	−	0.421563i	−0.0439274	−	0.0394830i
$115$	−5.69024	−	1.52469i	−0.530617	−	0.142178i
$116$	−4.53964	−	3.66302i	−0.421495	−	0.340103i
$117$	−6.53422	+	1.75084i	−0.604089	+	0.161865i
$118$	−2.36434	−	3.63381i	−0.217655	−	0.334519i
$119$	−6.36763	+	4.45919i	−0.583719	+	0.408773i
$120$	0.168056	+	0.121428i	0.0153413	+	0.0110848i
$121$	7.42792	+	4.28851i	0.675265	+	0.389865i
$122$	12.6872	+	6.45051i	1.14865	+	0.584002i
$123$	−0.106957	+	0.399168i	−0.00964398	+	0.0359918i
$124$	−10.1492	+	7.40091i	−0.911421	+	0.664621i
$125$	−7.64645	+	7.64645i	−0.683919	+	0.683919i
$126$	−4.39090	−	10.3177i	−0.391172	−	0.919170i
$127$	5.63308			0.499855			0.249928	−	0.968265i	$-0.419593\pi$
$127$	5.63308			0.499855			0.249928	+	0.968265i	$0.419593\pi$
$128$	10.3635	+	4.53844i	0.916015	+	0.401145i
$129$	0.0793683	+	0.137470i	0.00698799	+	0.0121035i
$130$	−1.28801	−	3.95235i	−0.112966	−	0.346644i
$131$	0.537304	+	2.00524i	0.0469444	+	0.175199i	0.985418	−	0.170153i	$-0.0544262\pi$
$131$	0.537304	+	2.00524i	0.0469444	+	0.175199i	−0.938473	+	0.345352i	$0.887760\pi$
$132$	−0.160224	−	0.0710014i	−0.0139457	−	0.00617988i
$133$	−19.6937	+	7.16916i	−1.70766	+	0.621645i
$134$	−2.59574	+	1.68892i	−0.224238	+	0.145900i
$135$	0.380697	+	0.219795i	0.0327652	+	0.0189170i
$136$	0.847027	−	8.26720i	0.0726319	−	0.708906i
$137$	2.68685	−	1.55125i	0.229553	−	0.132532i	−0.380813	−	0.924652i	$-0.624356\pi$
$137$	2.68685	−	1.55125i	0.229553	−	0.132532i	0.610366	+	0.792120i	$0.291022\pi$
$138$	0.359644	−	0.0191631i	0.0306149	−	0.00163127i
$139$	12.7451	+	12.7451i	1.08103	+	1.08103i	0.996414	+	0.0846114i	$0.0269649\pi$
$139$	12.7451	+	12.7451i	1.08103	+	1.08103i	0.0846114	+	0.996414i	$0.473035\pi$
$140$	6.18766	−	3.03174i	0.522953	−	0.256229i
$141$	−0.0779732	+	0.0779732i	−0.00656653	+	0.00656653i
$142$	−7.63998	−	6.86700i	−0.641133	−	0.576266i
$143$	1.75684	+	3.04294i	0.146914	+	0.254463i
$144$	11.4135	+	3.66444i	0.951124	+	0.305370i
$145$	1.89896	−	3.28910i	0.157700	−	0.273145i
$146$	−4.13836	+	19.5534i	−0.342493	+	1.61825i
$147$	0.392558	+	0.0343005i	0.0323776	+	0.00282906i
$148$	−3.91173	−	10.1375i	−0.321543	−	0.833294i
$149$	14.5303	−	3.89339i	1.19037	−	0.318959i	0.391338	−	0.920247i	$-0.372012\pi$
$149$	14.5303	−	3.89339i	1.19037	−	0.318959i	0.799032	+	0.601288i	$0.205346\pi$
$150$	0.119222	−	0.234493i	0.00973446	−	0.0191463i
$151$	15.7545	−	9.09588i	1.28209	−	0.740212i	0.304856	−	0.952398i	$-0.401392\pi$
$151$	15.7545	−	9.09588i	1.28209	−	0.740212i	0.977229	+	0.212186i	$0.0680584\pi$
$152$	7.97444	−	20.9379i	0.646812	−	1.69829i
$153$		−	8.80528i		−	0.711865i
$154$	−4.58623	+	3.59002i	−0.369569	+	0.289292i
$155$	−5.78295	−	5.78295i	−0.464498	−	0.464498i
$156$	0.149739	+	0.205343i	0.0119887	+	0.0164406i
$157$	9.39175	+	2.51651i	0.749544	+	0.200840i	0.613316	−	0.789838i	$-0.289835\pi$
$157$	9.39175	+	2.51651i	0.749544	+	0.200840i	0.136228	+	0.990678i	$0.456502\pi$
$158$	0.842692	+	2.58585i	0.0670410	+	0.205719i
$159$	−0.326788	+	0.566013i	−0.0259159	+	0.0448877i
$160$	−1.87543	+	7.12348i	−0.148266	+	0.563161i
$161$	5.05781	−	10.8481i	0.398611	−	0.854948i
$162$	12.4126	+	2.62706i	0.975230	+	0.206402i
$163$	−3.36548	−	12.5602i	−0.263605	−	0.983787i	−0.963099	−	0.269148i	$-0.913258\pi$
$163$	−3.36548	−	12.5602i	−0.263605	−	0.983787i	0.699494	−	0.714639i	$-0.253409\pi$
$164$	−14.5989	+	1.56019i	−1.13998	+	0.121830i
$165$	0.0295323	−	0.110216i	0.00229909	−	0.00858031i
$166$	−0.939366	−	17.6296i	−0.0729090	−	1.36832i
$167$			16.5417i			1.28004i	0.768360	+	0.640018i	$0.221073\pi$
$167$			16.5417i			1.28004i	−0.768360	+	0.640018i	$0.778927\pi$
$168$	−0.302246	+	0.293442i	−0.0233188	+	0.0226395i
$169$			7.90463i			0.608049i
$170$	5.40319	−	0.287901i	0.414406	−	0.0220810i
$171$	6.14412	−	22.9302i	0.469853	−	1.75351i
$172$	−3.54147	+	4.38900i	−0.270035	+	0.334658i
$173$	−5.59219	−	20.8703i	−0.425166	−	1.58674i	−0.763559	−	0.645738i	$-0.776550\pi$
$173$	−5.59219	−	20.8703i	−0.425166	−	1.58674i	0.338393	−	0.941005i	$-0.390117\pi$
$174$	−0.0480771	+	0.227160i	−0.00364472	+	0.0172210i
$175$	−5.01486	−	7.16112i	−0.379088	−	0.541330i
$176$	0.304142	−	6.21893i	0.0229256	−	0.468770i
$177$	−0.0862837	+	0.149448i	−0.00648548	+	0.0112332i
$178$	17.9368	−	5.84534i	1.34442	−	0.438127i
$179$	−18.3264	−	4.91053i	−1.36978	−	0.367031i	−0.502379	−	0.864647i	$-0.667542\pi$
$179$	−18.3264	−	4.91053i	−1.36978	−	0.367031i	−0.867397	+	0.497617i	$0.834209\pi$
$180$	−1.20748	+	7.71084i	−0.0899999	+	0.574732i
$181$	6.44222	+	6.44222i	0.478846	+	0.478846i	0.904763	−	0.425916i	$-0.140048\pi$
$181$	6.44222	+	6.44222i	0.478846	+	0.478846i	−0.425916	+	0.904763i	$0.640048\pi$
$182$	8.36272	−	1.18322i	0.619886	−	0.0877064i
$183$		−	0.566545i		−	0.0418802i
$184$	5.23505	+	11.6757i	0.385933	+	0.860745i
$185$	6.12689	−	3.53736i	0.450458	−	0.260072i
$186$	0.445698	+	0.226604i	0.0326801	+	0.0166154i
$187$	−4.41773	+	1.18373i	−0.323057	+	0.0865627i
$188$	−3.58179	−	1.58723i	−0.261229	−	0.115760i
$189$	−0.574072	+	0.684230i	−0.0417576	+	0.0497704i
$190$	14.2716	+	3.02049i	1.03537	+	0.219129i
$191$	−12.9567	+	22.4417i	−0.937515	+	1.62382i	−0.167429	+	0.985884i	$0.553546\pi$
$191$	−12.9567	+	22.4417i	−0.937515	+	1.62382i	−0.770086	+	0.637940i	$0.779787\pi$
$192$	−0.0259253	−	0.449600i	−0.00187100	−	0.0324471i
$193$	−6.27389	−	10.8667i	−0.451604	−	0.782202i	0.546881	−	0.837210i	$-0.315815\pi$
$193$	−6.27389	−	10.8667i	−0.451604	−	0.782202i	−0.998486	+	0.0550082i	$0.982481\pi$
$194$	−9.16616	+	10.1979i	−0.658092	+	0.732170i
$195$	−0.117004	+	0.117004i	−0.00837881	+	0.00837881i
$196$	3.88391	+	13.4505i	0.277422	+	0.960748i
$197$	−8.31651	−	8.31651i	−0.592527	−	0.592527i	0.345786	−	0.938313i	$-0.387612\pi$
$197$	−8.31651	−	8.31651i	−0.592527	−	0.592527i	−0.938313	+	0.345786i	$0.887612\pi$
$198$	−0.351017	−	6.58774i	−0.0249457	−	0.468170i
$199$	16.6783	−	9.62922i	1.18229	−	0.682597i	0.225749	−	0.974186i	$-0.427517\pi$
$199$	16.6783	−	9.62922i	1.18229	−	0.682597i	0.956544	+	0.291589i	$0.0941838\pi$
$200$	9.29740	+	0.952578i	0.657426	+	0.0673574i
$201$	0.106755	+	0.0616352i	0.00752993	+	0.00434741i
$202$	8.15097	+	12.5274i	0.573501	+	0.881427i
$203$	5.91152	+	4.95980i	0.414907	+	0.348109i
$204$	−0.308623	+	0.119088i	−0.0216079	+	0.00833782i
$205$	−2.47413	−	9.23356i	−0.172800	−	0.644900i
$206$	−4.60419	+	1.50044i	−0.320789	+	0.104541i
$207$	6.77874	+	11.7411i	0.471155	+	0.816064i
$208$	−4.89116	+	7.58963i	−0.339141	+	0.526246i
$209$	−12.3304			−0.852909
$210$	−0.219201	−	0.164861i	−0.0151263	−	0.0113765i
$211$	−8.62222	+	8.62222i	−0.593578	+	0.593578i	−0.938596	−	0.345018i	$-0.887873\pi$
$211$	−8.62222	+	8.62222i	−0.593578	+	0.593578i	0.345018	+	0.938596i	$0.387873\pi$
$212$	−22.9408	−	3.59240i	−1.57558	−	0.246727i
$213$	−0.105832	+	0.394969i	−0.00725147	+	0.0270628i
$214$	−7.34336	+	14.4433i	−0.501982	+	0.987325i
$215$	−3.17995	−	1.83595i	−0.216871	−	0.125211i
$216$	−0.151838	−	0.942675i	−0.0103312	−	0.0641409i
$217$	13.6110	−	9.53167i	0.923977	−	0.647052i
$218$	3.71670	−	2.41827i	0.251727	−	0.163786i
$219$	0.768464	−	0.205909i	0.0519280	−	0.0139141i
$220$	4.03096	−	0.430790i	0.271767	−	0.0290439i
$221$	6.40638	+	1.71658i	0.430940	+	0.115470i
$222$	−0.289135	+	0.321681i	−0.0194055	+	0.0215898i
$223$	−22.4402			−1.50271			−0.751354	−	0.659899i	$-0.770599\pi$
$223$	−22.4402			−1.50271			−0.751354	+	0.659899i	$0.770599\pi$
$224$	−13.5922	−	6.26513i	−0.908168	−	0.418607i
$225$	9.90254			0.660169
$226$	4.42401	−	4.92200i	0.294281	−	0.327406i
$227$	−2.25930	−	0.605377i	−0.149955	−	0.0401803i	0.183061	−	0.983102i	$-0.441400\pi$
$227$	−2.25930	−	0.605377i	−0.149955	−	0.0401803i	−0.333016	+	0.942921i	$0.608066\pi$
$228$	−0.886793	+	0.0947718i	−0.0587293	+	0.00627642i
$229$	−18.9832	+	5.08653i	−1.25444	+	0.336127i	−0.824052	−	0.566514i	$-0.808292\pi$
$229$	−18.9832	+	5.08653i	−1.25444	+	0.336127i	−0.430393	+	0.902642i	$0.641625\pi$
$230$	−6.98307	+	4.54353i	−0.460450	+	0.299592i
$231$	0.210120	+	0.0979664i	0.0138249	+	0.00644572i
$232$	−8.14440	+	1.31183i	−0.534706	+	0.0861256i
$233$	−3.35515	−	1.93710i	−0.219803	−	0.126903i	0.386056	−	0.922475i	$-0.373837\pi$
$233$	−3.35515	−	1.93710i	−0.219803	−	0.126903i	−0.605859	+	0.795572i	$0.707171\pi$
$234$	−4.33577	+	8.52784i	−0.283438	+	0.557482i
$235$	0.660191	−	2.46387i	0.0430661	−	0.160725i
$236$	−6.05719	−	0.948524i	−0.394290	−	0.0617437i
$237$	0.0765505	−	0.0765505i	0.00497249	−	0.00497249i
$238$	−1.32966	+	10.9130i	−0.0861894	+	0.707386i
$239$	−6.56774			−0.424832			−0.212416	−	0.977179i	$-0.568133\pi$
$239$	−6.56774			−0.424832			−0.212416	+	0.977179i	$0.568133\pi$
$240$	0.286593	−	0.0619643i	0.0184995	−	0.00399978i
$241$	6.62647	+	11.4774i	0.426849	+	0.739323i	0.996591	−	0.0824998i	$-0.0262904\pi$
$241$	6.62647	+	11.4774i	0.426849	+	0.739323i	−0.569742	+	0.821823i	$0.692957\pi$
$242$	11.5328	−	3.75837i	0.741356	−	0.241597i
$243$	−0.392830	−	1.46606i	−0.0252001	−	0.0940479i
$244$	18.7788	−	7.24615i	1.20219	−	0.463887i
$245$	−8.26078	+	3.85318i	−0.527762	+	0.246171i
$246$	0.318728	+	0.489860i	0.0203213	+	0.0312324i
$247$	15.4853	+	8.94045i	0.985306	+	0.568867i
$248$	−1.81055	+	17.6714i	−0.114970	+	1.12214i
$249$	−0.608598	+	0.351374i	−0.0385683	+	0.0222674i
$250$	0.813704	+	15.2712i	0.0514632	+	0.965838i
$251$	−3.80916	−	3.80916i	−0.240432	−	0.240432i	0.576597	−	0.817029i	$-0.304380\pi$
$251$	−3.80916	−	3.80916i	−0.240432	−	0.240432i	−0.817029	+	0.576597i	$0.804380\pi$
$252$	−15.0031	−	5.13575i	−0.945104	−	0.323522i
$253$	4.97939	−	4.97939i	0.313052	−	0.313052i
$254$	5.32538	−	5.92483i	0.334144	−	0.371757i
$255$	−0.107691	−	0.186526i	−0.00674385	−	0.0116807i
$256$	14.5709	−	6.60974i	0.910682	−	0.413109i
$257$	11.8190	−	20.4712i	0.737251	−	1.27696i	−0.216477	−	0.976288i	$-0.569457\pi$
$257$	11.8190	−	20.4712i	0.737251	−	1.27696i	0.953729	−	0.300669i	$-0.0972099\pi$
$258$	0.219622	+	0.0464818i	0.0136731	+	0.00289383i
$259$	4.91707	+	13.5072i	0.305532	+	0.839297i
$260$	−5.37471	−	2.38174i	−0.333325	−	0.147709i
$261$	−8.44271	+	2.26222i	−0.522591	+	0.140028i
$262$	2.61705	+	1.33058i	0.161682	+	0.0822033i
$263$	−15.4301	+	8.90857i	−0.951460	+	0.549326i	−0.893534	−	0.448995i	$-0.851782\pi$
$263$	−15.4301	+	8.90857i	−0.951460	+	0.549326i	−0.0579260	+	0.998321i	$0.518449\pi$
$264$	−0.226151	+	0.101400i	−0.0139186	+	0.00624071i
$265$		−	15.1185i		−	0.928722i
$266$	−11.0775	+	27.4912i	−0.679204	+	1.68559i
$267$	−0.530993	−	0.530993i	−0.0324963	−	0.0324963i
$268$	−0.677560	+	4.32684i	−0.0413886	+	0.264304i
$269$	−6.16728	−	1.65252i	−0.376026	−	0.100756i	0.0658559	−	0.997829i	$-0.479022\pi$
$269$	−6.16728	−	1.65252i	−0.376026	−	0.100756i	−0.441882	+	0.897073i	$0.645689\pi$
$270$	0.591080	−	0.192624i	0.0359720	−	0.0117228i
$271$	3.98703	−	6.90574i	0.242195	−	0.419494i	−0.719144	−	0.694861i	$-0.755466\pi$
$271$	3.98703	−	6.90574i	0.242195	−	0.419494i	0.961339	+	0.275367i	$0.0887993\pi$
$272$	−7.89461	−	8.70650i	−0.478681	−	0.527909i
$273$	−0.192850	−	0.275386i	−0.0116718	−	0.0166671i
$274$	0.908486	−	4.29252i	0.0548836	−	0.259320i
$275$	−1.33124	−	4.96824i	−0.0802765	−	0.299596i
$276$	0.319843	−	0.396387i	0.0192523	−	0.0238597i
$277$	3.31607	−	12.3757i	0.199243	−	0.743586i	−0.791884	−	0.610671i	$-0.790900\pi$
$277$	3.31607	−	12.3757i	0.199243	−	0.743586i	0.991127	−	0.132915i	$-0.0424337\pi$
$278$	25.4541	−	1.35628i	1.52664	−	0.0813444i
$279$			18.8216i			1.12682i
$280$	2.66091	−	9.37426i	0.159020	−	0.560219i
$281$			13.0438i			0.778126i	0.921211	+	0.389063i	$0.127201\pi$
$281$			13.0438i			0.778126i	−0.921211	+	0.389063i	$0.872799\pi$
$282$	0.00829759	+	0.155726i	0.000494115	+	0.00927332i
$283$	−4.98843	+	18.6171i	−0.296531	+	1.10667i	0.643462	+	0.765478i	$0.277497\pi$
$283$	−4.98843	+	18.6171i	−0.296531	+	1.10667i	−0.939994	+	0.341192i	$0.889169\pi$
$284$	−14.4453	+	1.54377i	−0.857171	+	0.0916061i
$285$	−0.150288	−	0.560883i	−0.00890229	−	0.0332238i
$286$	4.86141	+	1.02889i	0.287461	+	0.0608395i
$287$	19.3485	−	1.69385i	1.14210	−	0.0999850i
$288$	14.6443	−	8.54034i	0.862922	−	0.503244i
$289$	4.18350	−	7.24603i	0.246088	−	0.426237i
$290$	−1.66421	−	5.10674i	−0.0977259	−	0.299878i
$291$	0.527210	+	0.141265i	0.0309056	+	0.00828113i
$292$	16.6538	+	22.8380i	0.974590	+	1.33649i
$293$	12.7021	+	12.7021i	0.742067	+	0.742067i	0.972975	−	0.230908i	$-0.0741698\pi$
$293$	12.7021	+	12.7021i	0.742067	+	0.742067i	−0.230908	+	0.972975i	$0.574170\pi$
$294$	0.407191	−	0.380462i	0.0237479	−	0.0221890i
$295$		−	3.99183i		−	0.232413i
$296$	−14.3605	−	5.46938i	−0.834690	−	0.317901i
$297$	−0.455076	+	0.262738i	−0.0264062	+	0.0152456i
$298$	9.64158	−	18.9636i	0.558522	−	1.09853i
$299$	−9.86389	+	2.64302i	−0.570443	+	0.152850i
$300$	−0.133928	−	0.347081i	−0.00773233	−	0.0200387i
$301$	4.79521	−	5.71536i	0.276391	−	0.329428i
$302$	5.32697	−	25.1695i	0.306533	−	1.44834i
$303$	0.297460	−	0.515217i	0.0170887	−	0.0295984i
$304$	−14.4835	−	28.1816i	−0.830684	−	1.61633i
$305$	6.55265	+	11.3495i	0.375204	+	0.649872i
$306$	−9.26132	−	8.32430i	−0.529434	−	0.475868i
$307$	15.5180	−	15.5180i	0.885657	−	0.885657i	−0.108446	−	0.994102i	$-0.534587\pi$
$307$	15.5180	−	15.5180i	0.885657	−	0.885657i	0.994102	+	0.108446i	$0.0345873\pi$
$308$	−0.559757	+	8.21767i	−0.0318951	+	0.468245i
$309$	0.136300	+	0.136300i	0.00775386	+	0.00775386i
$310$	−11.5495	+	0.615398i	−0.655968	+	0.0349523i
$311$	3.14576	−	1.81621i	0.178380	−	0.102988i	−0.408151	−	0.912914i	$-0.633826\pi$
$311$	3.14576	−	1.81621i	0.178380	−	0.102988i	0.586531	+	0.809927i	$0.300493\pi$
$312$	0.357538	+	0.0366320i	0.0202416	+	0.00207388i
$313$	3.24479	+	1.87338i	0.183406	+	0.105890i	0.588892	−	0.808212i	$-0.299564\pi$
$313$	3.24479	+	1.87338i	0.183406	+	0.105890i	−0.405486	+	0.914101i	$0.632898\pi$
$314$	11.5256	−	7.49912i	0.650426	−	0.423200i
$315$	1.79232	−	10.1680i	0.100986	−	0.572904i
$316$	3.51644	+	1.55827i	0.197815	+	0.0876593i
$317$	6.36774	+	23.7647i	0.357648	+	1.33476i	0.877119	+	0.480272i	$0.159462\pi$
$317$	6.36774	+	23.7647i	0.357648	+	1.33476i	−0.519472	+	0.854488i	$0.673871\pi$
$318$	0.286390	+	0.878807i	0.0160600	+	0.0492810i
$319$	2.26997	+	3.93171i	0.127094	+	0.220133i
$320$	5.71943	+	8.70693i	0.319726	+	0.486732i
$321$	0.644963			0.0359983
$322$	−6.62838	−	15.5753i	−0.369385	−	0.867975i
$323$	−16.4576	+	16.4576i	−0.915727	+	0.915727i
$324$	14.4977	−	10.5720i	0.805430	−	0.587331i
$325$	−1.93049	+	7.20470i	−0.107084	+	0.399645i
$326$	−16.3923	−	8.33427i	−0.907886	−	0.461593i
$327$	−0.152857	−	0.0882521i	−0.00845302	−	0.00488035i
$328$	−12.1604	+	16.8299i	−0.671448	+	0.929278i
$329$	4.69721	+	2.19003i	0.258965	+	0.120740i
$330$	−0.0880053	−	0.135257i	−0.00484453	−	0.00744568i
$331$	9.79479	−	2.62451i	0.538370	−	0.144256i	0.0206195	−	0.999787i	$-0.493436\pi$
$331$	9.79479	−	2.62451i	0.538370	−	0.144256i	0.517751	+	0.855532i	$0.326769\pi$
$332$	−19.4307	−	15.6786i	−1.06640	−	0.860474i
$333$	−15.7270	−	4.21403i	−0.861833	−	0.230928i
$334$	17.3984	+	15.6381i	0.952000	+	0.855680i
$335$	−2.85149			−0.155793
$336$	0.0229040	+	0.595312i	0.00124951	+	0.0324769i
$337$	−5.30745			−0.289115			−0.144558	−	0.989496i	$-0.546176\pi$
$337$	−5.30745			−0.289115			−0.144558	+	0.989496i	$0.546176\pi$
$338$	8.31402	+	7.47284i	0.452223	+	0.406469i
$339$	−0.254456	−	0.0681812i	−0.0138201	−	0.00370309i
$340$	4.80523	−	5.95520i	0.260600	−	0.322966i
$341$	9.44306	−	2.53026i	0.511370	−	0.137021i
$342$	−18.3093	−	28.1400i	−0.990051	−	1.52163i
$343$	−4.79637	−	17.8884i	−0.258980	−	0.965883i
$344$	1.26830	+	7.87414i	0.0683819	+	0.424545i
$345$	0.287193	+	0.165811i	0.0154620	+	0.00892696i
$346$	−27.2380	−	13.8485i	−1.46432	−	0.744499i
$347$	1.06753	−	3.98409i	0.0573082	−	0.213877i	−0.931334	−	0.364166i	$-0.881354\pi$
$347$	1.06753	−	3.98409i	0.0573082	−	0.213877i	0.988642	+	0.150290i	$0.0480206\pi$
$348$	0.193474	+	0.265319i	0.0103713	+	0.0142226i
$349$	11.4637	−	11.4637i	0.613639	−	0.613639i	−0.330253	−	0.943892i	$-0.607134\pi$
$349$	11.4637	−	11.4637i	0.613639	−	0.613639i	0.943892	+	0.330253i	$0.107134\pi$
$350$	−12.2729	−	1.49536i	−0.656016	−	0.0799303i
$351$	0.762020			0.0406736
$352$	−6.25349	−	6.19912i	−0.333312	−	0.330414i
$353$	1.93371	+	3.34929i	0.102921	+	0.178265i	0.912887	−	0.408212i	$-0.133848\pi$
$353$	1.93371	+	3.34929i	0.102921	+	0.178265i	−0.809966	+	0.586477i	$0.800514\pi$
$354$	0.0756174	+	0.232037i	0.00401902	+	0.0123326i
$355$	−2.44810	−	9.13642i	−0.129932	−	0.484911i
$356$	10.8089	−	24.3918i	0.572873	−	1.29276i
$357$	0.411210	−	0.149694i	0.0217636	−	0.00792265i
$358$	−22.4901	+	14.6332i	−1.18864	+	0.773389i
$359$	−13.6977	−	7.90839i	−0.722938	−	0.417389i	0.0928949	−	0.995676i	$-0.470388\pi$
$359$	−13.6977	−	7.90839i	−0.722938	−	0.417389i	−0.815833	+	0.578287i	$0.803721\pi$
$360$	6.96867	+	8.55965i	0.367281	+	0.451133i
$361$	−37.8872	+	21.8742i	−1.99407	+	1.15127i
$362$	12.8662	−	0.685555i	0.676232	−	0.0360320i
$363$	−0.341412	−	0.341412i	−0.0179195	−	0.0179195i
$364$	6.66141	−	9.91443i	0.349153	−	0.519657i
$365$	−13.0130	+	13.0130i	−0.681132	+	0.681132i
$366$	−0.595887	−	0.535597i	−0.0311475	−	0.0279961i
$367$	2.37345	+	4.11093i	0.123893	+	0.214589i	0.921300	−	0.388853i	$-0.127129\pi$
$367$	2.37345	+	4.11093i	0.123893	+	0.214589i	−0.797407	+	0.603442i	$0.793795\pi$
$368$	17.2295	+	5.53175i	0.898150	+	0.288362i
$369$	−10.9999	+	19.0523i	−0.572631	+	0.991826i
$370$	2.07164	−	9.78834i	0.107700	−	0.508872i
$371$	30.2513	+	5.33238i	1.57057	+	0.276844i
$372$	0.659692	−	0.254555i	0.0342034	−	0.0131980i
$373$	22.0083	−	5.89711i	1.13955	−	0.305341i	0.360779	−	0.932651i	$-0.382511\pi$
$373$	22.0083	−	5.89711i	1.13955	−	0.305341i	0.778769	+	0.627310i	$0.215844\pi$
$374$	−2.93138	+	5.76560i	−0.151578	+	0.298132i
$375$	0.527184	−	0.304370i	0.0272237	−	0.0157176i
$376$	−5.05557	+	2.26677i	−0.260721	+	0.116900i
$377$		−	6.58360i		−	0.339073i
$378$	0.176953	+	1.25066i	0.00910148	+	0.0643269i
$379$	20.1030	+	20.1030i	1.03262	+	1.03262i	0.999450	+	0.0331705i	$0.0105604\pi$
$379$	20.1030	+	20.1030i	1.03262	+	1.03262i	0.0331705	+	0.999450i	$0.489440\pi$
$380$	16.6689	−	12.1552i	0.855096	−	0.623549i
$381$	−0.306300	−	0.0820728i	−0.0156922	−	0.00420472i
$382$	11.3550	+	34.8436i	0.580973	+	1.78275i
$383$	11.7252	−	20.3087i	0.599131	−	1.03773i	−0.393819	−	0.919188i	$-0.628846\pi$
$383$	11.7252	−	20.3087i	0.599131	−	1.03773i	0.992950	−	0.118537i	$-0.0378204\pi$
$384$	−0.497394	−	0.397773i	−0.0253825	−	0.0202987i
$385$	−5.34239	+	0.467697i	−0.272273	+	0.0238360i
$386$	−17.3607	−	3.67428i	−0.883635	−	0.187016i
$387$	2.18715	+	8.16255i	0.111179	+	0.414926i
$388$	2.06065	+	19.2818i	0.104614	+	0.978883i
$389$	2.77356	−	10.3510i	0.140625	−	0.524819i	−0.859286	−	0.511495i	$-0.829092\pi$
$389$	2.77356	−	10.3510i	0.140625	−	0.524819i	0.999911	−	0.0133242i	$-0.00424136\pi$
$390$	0.0124511	+	0.233676i	0.000630484	+	0.0118326i
$391$		−	13.2922i		−	0.672216i
$392$	17.8188	+	8.63068i	0.899988	+	0.435915i
$393$		−	0.116864i		−	0.00589500i
$394$	−16.6095	+	0.885009i	−0.836773	+	0.0445861i
$395$	−0.648145	+	2.41891i	−0.0326117	+	0.121709i
$396$	−7.26077	−	5.85869i	−0.364867	−	0.294410i
$397$	1.71548	+	6.40226i	0.0860975	+	0.321320i	0.995520	−	0.0945536i	$-0.0301424\pi$
$397$	1.71548	+	6.40226i	0.0860975	+	0.321320i	−0.909422	+	0.415874i	$0.863476\pi$
$398$	5.63932	−	26.6453i	0.282674	−	1.33561i
$399$	1.17530	−	0.102891i	0.0588387	−	0.00515100i
$400$	9.79145	−	8.87838i	0.489572	−	0.443919i
$401$	−15.8657	+	27.4802i	−0.792294	+	1.37229i	0.132250	+	0.991216i	$0.457780\pi$
$401$	−15.8657	+	27.4802i	−0.792294	+	1.37229i	−0.924543	+	0.381077i	$0.875553\pi$
$402$	0.165751	−	0.0540159i	0.00826691	−	0.00269407i
$403$	−13.6939	−	3.66926i	−0.682140	−	0.182779i
$404$	20.8820	+	3.27001i	1.03892	+	0.162689i
$405$	8.26075	+	8.26075i	0.410480	+	0.410480i
$406$	10.8053	−	1.52882i	0.536257	−	0.0758739i
$407$			8.45695i			0.419196i
$408$	−0.166509	+	0.437189i	−0.00824340	+	0.0216441i
$409$	−1.11952	+	0.646353i	−0.0553565	+	0.0319601i	−0.527423	−	0.849603i	$-0.676842\pi$
$409$	−1.11952	+	0.646353i	−0.0553565	+	0.0319601i	0.472066	+	0.881563i	$0.343508\pi$
$410$	−12.0508	−	6.12692i	−0.595145	−	0.302587i
$411$	−0.168699	+	0.0452028i	−0.00832131	+	0.00222969i
$412$	−2.77454	+	6.26113i	−0.136692	+	0.308464i
$413$	7.98742	+	1.40794i	0.393035	+	0.0692803i
$414$	18.7577	+	3.96995i	0.921889	+	0.195112i
$415$	8.12799	−	14.0781i	0.398987	−	0.691066i
$416$	3.35873	+	12.3195i	0.164675	+	0.604015i
$417$	−0.507324	−	0.878710i	−0.0248437	−	0.0430306i
$418$	−11.6568	+	12.9690i	−0.570154	+	0.634333i
$419$	17.2788	−	17.2788i	0.844124	−	0.844124i	−0.145269	−	0.989392i	$-0.546405\pi$
$419$	17.2788	−	17.2788i	0.844124	−	0.844124i	0.989392	+	0.145269i	$0.0464046\pi$
$420$	−0.380627	+	0.0746984i	−0.0185727	+	0.00364491i
$421$	3.36245	+	3.36245i	0.163876	+	0.163876i	0.784281	−	0.620405i	$-0.213032\pi$
$421$	3.36245	+	3.36245i	0.163876	+	0.163876i	−0.620405	+	0.784281i	$0.713032\pi$
$422$	0.917541	+	17.2200i	0.0446652	+	0.838257i
$423$	−5.08389	+	2.93519i	−0.247187	+	0.142714i
$424$	−25.4661	+	20.7327i	−1.23674	+	1.00687i
$425$	−8.40806	−	4.85440i	−0.407851	−	0.235473i
$426$	0.315374	+	0.484707i	0.0152799	+	0.0234841i
$427$	−25.0209	+	9.10844i	−1.21085	+	0.440788i
$428$	8.24913	+	21.3780i	0.398737	+	1.03335i
$429$	−0.0511936	−	0.191057i	−0.00247165	−	0.00922432i
$430$	−4.93728	+	1.60899i	−0.238097	+	0.0775923i
$431$	−5.58722	−	9.67735i	−0.269127	−	0.466141i	0.699510	−	0.714623i	$-0.253402\pi$
$431$	−5.58722	−	9.67735i	−0.269127	−	0.466141i	−0.968637	+	0.248482i	$0.920068\pi$
$432$	−1.13504	−	0.731480i	−0.0546097	−	0.0351934i
$433$	−17.3943			−0.835916			−0.417958	−	0.908466i	$-0.637254\pi$
$433$	−17.3943			−0.835916			−0.417958	+	0.908466i	$0.637254\pi$
$434$	2.84221	−	23.3270i	0.136430	−	1.11973i
$435$	−0.151178	+	0.151178i	−0.00724842	+	0.00724842i
$436$	0.970163	−	6.19537i	0.0464624	−	0.296705i
$437$	9.27500	−	34.6148i	0.443684	−	1.65585i
$438$	0.509913	−	1.00293i	0.0243646	−	0.0479216i
$439$	−32.5115	−	18.7705i	−1.55169	−	0.895867i	−0.998005	−	0.0631399i	$-0.979889\pi$
$439$	−32.5115	−	18.7705i	−1.55169	−	0.895867i	−0.553683	−	0.832727i	$-0.686778\pi$
$440$	3.35767	−	4.64699i	0.160071	−	0.221536i
$441$	19.7135	+	7.17265i	0.938738	+	0.341555i
$442$	7.86192	−	5.11536i	0.373953	−	0.243313i
$443$	6.88186	−	1.84399i	0.326967	−	0.0876106i	−0.0916015	−	0.995796i	$-0.529199\pi$
$443$	6.88186	−	1.84399i	0.326967	−	0.0876106i	0.418569	+	0.908185i	$0.362532\pi$
$444$	0.0650006	+	0.608219i	0.00308479	+	0.0288648i
$445$	16.7788	+	4.49587i	0.795392	+	0.213125i
$446$	−21.2144	+	23.6024i	−1.00453	+	1.11761i
$447$	−0.846815			−0.0400530
$448$	−19.4394	+	8.37326i	−0.918423	+	0.395600i
$449$	−7.84005			−0.369995			−0.184997	−	0.982739i	$-0.559228\pi$
$449$	−7.84005			−0.369995			−0.184997	+	0.982739i	$0.559228\pi$
$450$	9.36161	−	10.4154i	0.441311	−	0.490987i
$451$	11.0376	+	2.95751i	0.519739	+	0.139264i
$452$	−0.994564	−	9.30627i	−0.0467803	−	0.437730i
$453$	−0.989180	+	0.265050i	−0.0464757	+	0.0124531i
$454$	−2.77262	+	1.80400i	−0.130125	+	0.0846660i
$455$	7.04845	+	3.28627i	0.330436	+	0.154063i
$456$	−0.738672	+	1.02232i	−0.0345915	+	0.0478743i
$457$	−22.2821	−	12.8646i	−1.04231	−	0.601780i	−0.121826	−	0.992551i	$-0.538875\pi$
$457$	−22.2821	−	12.8646i	−1.04231	−	0.601780i	−0.920488	+	0.390771i	$0.872208\pi$
$458$	−12.5963	+	24.7750i	−0.588585	+	1.15766i
$459$	−0.256718	+	0.958084i	−0.0119826	+	0.0447195i
$460$	−1.82277	+	11.6401i	−0.0849873	+	0.542721i
$461$	−13.1661	+	13.1661i	−0.613207	+	0.613207i	−0.943780	−	0.330573i	$-0.892758\pi$
$461$	−13.1661	+	13.1661i	−0.613207	+	0.613207i	0.330573	+	0.943780i	$0.392758\pi$
$462$	0.301683	−	0.128387i	0.0140355	−	0.00597312i
$463$	6.88821			0.320122			0.160061	−	0.987107i	$-0.448831\pi$
$463$	6.88821			0.320122			0.160061	+	0.987107i	$0.448831\pi$
$464$	−6.31975	+	9.80638i	−0.293387	+	0.455250i
$465$	0.230193	+	0.398705i	0.0106749	+	0.0184895i
$466$	−5.20930	+	1.69763i	−0.241316	+	0.0786414i
$467$	10.2399	+	38.2159i	0.473847	+	1.76842i	0.625749	+	0.780025i	$0.284794\pi$
$467$	10.2399	+	38.2159i	0.473847	+	1.76842i	−0.151902	+	0.988396i	$0.548540\pi$
$468$	4.87057	+	12.6223i	0.225142	+	0.583468i
$469$	1.00574	−	5.70567i	0.0464406	−	0.263463i
$470$	−1.96735	−	3.02366i	−0.0907469	−	0.139471i
$471$	−0.474013	−	0.273672i	−0.0218414	−	0.0126101i
$472$	−6.72397	+	5.47419i	−0.309496	+	0.251970i
$473$	3.80124	−	2.19465i	0.174781	−	0.100910i
$474$	−0.00814619	−	0.152884i	−0.000374167	−	0.00702220i
$475$	−18.5085	−	18.5085i	−0.849227	−	0.849227i
$476$	10.2212	+	11.7154i	0.468487	+	0.536976i
$477$	−24.6029	+	24.6029i	−1.12649	+	1.12649i
$478$	−6.20898	+	6.90790i	−0.283992	+	0.315960i
$479$	0.261991	+	0.453782i	0.0119707	+	0.0207338i	0.871949	−	0.489597i	$-0.162856\pi$
$479$	0.261991	+	0.453782i	0.0119707	+	0.0207338i	−0.859978	+	0.510331i	$0.829523\pi$
$480$	0.205765	−	0.360016i	0.00939183	−	0.0164324i
$481$	6.13193	−	10.6208i	0.279592	−	0.484267i
$482$	18.3363	+	3.88077i	0.835197	+	0.176764i
$483$	−0.433073	+	0.516175i	−0.0197055	+	0.0234868i
$484$	6.94980	−	15.6832i	0.315900	−	0.712871i
$485$	−12.1954	+	3.26775i	−0.553765	+	0.148381i
$486$	−1.91336	−	0.972804i	−0.0867920	−	0.0441273i
$487$	2.46586	−	1.42366i	0.111739	−	0.0645124i	−0.443089	−	0.896478i	$-0.646117\pi$
$487$	2.46586	−	1.42366i	0.111739	−	0.0645124i	0.554828	+	0.831965i	$0.312784\pi$
$488$	10.1316	−	26.6017i	0.458634	−	1.20420i
$489$			0.731995i			0.0331019i
$490$	−3.75680	+	12.3313i	−0.169715	+	0.557072i
$491$	−17.4826	−	17.4826i	−0.788977	−	0.788977i	0.192349	−	0.981327i	$-0.438389\pi$
$491$	−17.4826	−	17.4826i	−0.788977	−	0.788977i	−0.981327	+	0.192349i	$0.938389\pi$
$492$	0.816548	+	0.127867i	0.0368128	+	0.00576469i
$493$	8.27753	+	2.21796i	0.372801	+	0.0998918i
$494$	24.0429	−	7.83523i	1.08174	−	0.352524i
$495$	3.03722	−	5.26063i	0.136513	−	0.236448i
$496$	16.8750	+	18.6105i	0.757711	+	0.835635i
$497$	19.1449	−	1.67603i	0.858767	−	0.0751803i
$498$	−0.205781	+	0.972299i	−0.00922128	+	0.0435698i
$499$	0.350599	+	1.30845i	0.0156949	+	0.0585743i	0.973329	−	0.229413i	$-0.0736806\pi$
$499$	0.350599	+	1.30845i	0.0156949	+	0.0585743i	−0.957634	+	0.287987i	$0.907014\pi$
$500$	16.8314	+	13.5812i	0.752724	+	0.607370i
$501$	0.241009	−	0.899458i	0.0107675	−	0.0401848i
$502$	−7.60752	+	0.405355i	−0.339540	+	0.0180919i
$503$		−	15.4389i		−	0.688388i	−0.938899	−	0.344194i	$-0.888152\pi$
$503$		−	15.4389i		−	0.688388i	0.938899	−	0.344194i	$-0.111848\pi$
$504$	−19.5853	+	10.9249i	−0.872397	+	0.486633i
$505$			13.7617i			0.612388i
$506$	−0.529886	−	9.94467i	−0.0235563	−	0.442095i
$507$	0.115169	−	0.429816i	0.00511482	−	0.0190888i
$508$	−1.19720	−	11.2024i	−0.0531172	−	0.497025i
$509$	−2.23550	−	8.34301i	−0.0990869	−	0.369797i	0.898520	−	0.438932i	$-0.144643\pi$
$509$	−2.23550	−	8.34301i	−0.0990869	−	0.369797i	−0.997607	+	0.0691342i	$0.977976\pi$
$510$	−0.297994	−	0.0630687i	−0.0131954	−	0.00279273i
$511$	−21.4485	−	30.6281i	−0.948827	−	1.35491i
$512$	6.82291	−	21.5742i	0.301533	−	0.953456i
$513$	−1.33706	+	2.31585i	−0.0590325	+	0.102247i
$514$	−10.3580	−	31.7841i	−0.456871	−	1.40194i
$515$	−4.30694	−	1.15404i	−0.189787	−	0.0508532i
$516$	0.256515	−	0.187054i	0.0112924	−	0.00823461i
$517$	2.15607	+	2.15607i	0.0948239	+	0.0948239i
$518$	18.8552	+	7.59765i	0.828451	+	0.333822i
$519$			1.21631i			0.0533899i
$520$	−7.58620	+	3.40144i	−0.332677	+	0.149163i
$521$	3.08690	−	1.78222i	0.135240	−	0.0780807i	−0.430854	−	0.902422i	$-0.641787\pi$
$521$	3.08690	−	1.78222i	0.135240	−	0.0780807i	0.566093	+	0.824341i	$0.308454\pi$
$522$	−5.60215	+	11.0186i	−0.245200	+	0.482272i
$523$	19.5332	−	5.23389i	0.854125	−	0.228862i	0.194914	−	0.980820i	$-0.437557\pi$
$523$	19.5332	−	5.23389i	0.854125	−	0.228862i	0.659211	+	0.751958i	$0.270890\pi$
$524$	3.87359	−	1.49470i	0.169218	−	0.0652962i
$525$	0.168348	+	0.462452i	0.00734731	+	0.0201831i
$526$	−5.21728	+	24.6512i	−0.227484	+	1.07484i
$527$	9.22668	−	15.9811i	0.401920	−	0.696147i
$528$	−0.107146	+	0.333724i	−0.00466294	+	0.0145235i
$529$	−1.26700	−	2.19451i	−0.0550869	−	0.0954133i
$530$	−15.9015	−	14.2927i	−0.690717	−	0.620833i
$531$	−6.49605	+	6.49605i	−0.281905	+	0.281905i
$532$	18.4426	+	37.6407i	0.799590	+	1.63193i
$533$	−11.7173	−	11.7173i	−0.507534	−	0.507534i
$534$	−1.06048	+	0.0565062i	−0.0458916	+	0.00244526i
$535$	−12.9205	+	7.45964i	−0.558601	+	0.322508i
$536$	3.91039	+	4.80314i	0.168903	+	0.207464i
$537$	0.924954	+	0.534022i	0.0399147	+	0.0230448i
$538$	−7.56850	+	4.92444i	−0.326301	+	0.212308i
$539$	0.948458	−	10.8548i	0.0408530	−	0.467549i
$540$	0.356192	−	0.803796i	0.0153281	−	0.0345899i
$541$	−1.90773	−	7.11973i	−0.0820195	−	0.306101i	0.912714	−	0.408600i	$-0.133983\pi$
$541$	−1.90773	−	7.11973i	−0.0820195	−	0.306101i	−0.994733	+	0.102499i	$0.967316\pi$
$542$	−3.49416	−	10.7220i	−0.150087	−	0.460551i
$543$	−0.256435	−	0.444159i	−0.0110047	−	0.0190607i
$544$	−16.6208	+	0.0725695i	−0.712611	+	0.00311139i
$545$	4.08289			0.174892
$546$	−0.471964	−	0.0575050i	−0.0201982	−	0.00246099i
$547$	17.8464	−	17.8464i	0.763058	−	0.763058i	−0.213816	−	0.976874i	$-0.568589\pi$
$547$	17.8464	−	17.8464i	0.763058	−	0.763058i	0.976874	+	0.213816i	$0.0685893\pi$
$548$	−3.65597	−	5.01358i	−0.156175	−	0.214169i
$549$	7.80613	−	29.1329i	0.333158	−	1.24336i
$550$	−6.48407	−	3.29667i	−0.276482	−	0.140570i
$551$	20.0082	+	11.5517i	0.852378	+	0.492121i
$552$	−0.114544	−	0.711142i	−0.00487533	−	0.0302682i
$553$	−4.61150	−	2.15006i	−0.196101	−	0.0914301i
$554$	−9.88177	−	15.1875i	−0.419836	−	0.645257i
$555$	−0.384689	+	0.103077i	−0.0163291	+	0.00437538i
$556$	22.6372	−	28.0546i	0.960029	−	1.18978i
$557$	−14.4174	−	3.86313i	−0.610884	−	0.163686i	−0.0599038	−	0.998204i	$-0.519079\pi$
$557$	−14.4174	−	3.86313i	−0.610884	−	0.163686i	−0.550980	+	0.834518i	$0.685746\pi$
$558$	19.7964	+	17.7935i	0.838049	+	0.753258i
$559$	−6.36514			−0.269217
$560$	−7.34421	−	11.6609i	−0.310350	−	0.492764i
$561$	0.257462			0.0108700
$562$	13.7193	+	12.3313i	0.578715	+	0.520163i
$563$	7.71786	+	2.06799i	0.325269	+	0.0871556i	0.417759	−	0.908558i	$-0.362816\pi$
$563$	7.71786	+	2.06799i	0.325269	+	0.0871556i	−0.0924895	+	0.995714i	$0.529482\pi$
$564$	0.171635	+	0.138492i	0.00722714	+	0.00583156i
$565$	5.88607	−	1.57717i	0.247629	−	0.0663519i
$566$	14.8653	+	22.8469i	0.624837	+	0.960327i
$567$	−19.4429	+	13.6157i	−0.816525	+	0.571805i
$568$	−12.0325	+	16.6529i	−0.504873	+	0.698740i
$569$	−12.1275	−	7.00179i	−0.508409	−	0.293530i	0.223770	−	0.974642i	$-0.428163\pi$
$569$	−12.1275	−	7.00179i	−0.508409	−	0.293530i	−0.732180	+	0.681112i	$0.761497\pi$
$570$	−0.732010	−	0.372173i	−0.0306605	−	0.0155886i
$571$	−0.488992	+	1.82494i	−0.0204637	+	0.0763715i	−0.975403	−	0.220431i	$-0.929254\pi$
$571$	−0.488992	+	1.82494i	−0.0204637	+	0.0763715i	0.954939	+	0.296802i	$0.0959203\pi$
$572$	5.67803	−	4.14050i	0.237411	−	0.173123i
$573$	1.03149	−	1.03149i	0.0430913	−	0.0430913i
$574$	16.5100	−	21.9519i	0.689114	−	0.916254i
$575$	14.9486			0.623400
$576$	4.86167	−	23.4765i	0.202570	−	0.978189i
$577$	−8.81809	−	15.2734i	−0.367102	−	0.635839i	0.622009	−	0.783010i	$-0.286317\pi$
$577$	−8.81809	−	15.2734i	−0.367102	−	0.635839i	−0.989111	+	0.147171i	$0.952983\pi$
$578$	−3.66634	−	11.2504i	−0.152500	−	0.467954i
$579$	0.182818	+	0.682288i	0.00759767	+	0.0283549i
$580$	−6.94453	−	3.07738i	−0.288356	−	0.127781i
$581$	25.3027	+	21.2291i	1.04973	+	0.880730i
$582$	0.646993	−	0.420966i	0.0268187	−	0.0174496i
$583$	15.6511	+	9.03615i	0.648201	+	0.374239i
$584$	39.7649	+	4.07417i	1.64548	+	0.168590i
$585$	−7.62870	+	4.40443i	−0.315408	+	0.182101i
$586$	25.3683	−	1.35171i	1.04795	−	0.0558386i
$587$	18.5150	+	18.5150i	0.764194	+	0.764194i	0.977078	−	0.212883i	$-0.0682854\pi$
$587$	18.5150	+	18.5150i	0.764194	+	0.764194i	−0.212883	+	0.977078i	$0.568285\pi$
$588$	−0.0152178	−	0.787960i	−0.000627574	−	0.0324949i
$589$	35.1788	−	35.1788i	1.44952	−	1.44952i
$590$	−4.19857	−	3.77378i	−0.172852	−	0.155364i
$591$	0.331042	+	0.573382i	0.0136172	+	0.0235858i
$592$	−19.3288	+	9.93369i	−0.794407	+	0.408272i
$593$	−3.95463	+	6.84963i	−0.162397	+	0.281281i	−0.935728	−	0.352722i	$-0.885256\pi$
$593$	−3.95463	+	6.84963i	−0.162397	+	0.281281i	0.773331	+	0.634003i	$0.218589\pi$
$594$	−0.153872	+	0.727031i	−0.00631344	+	0.0298305i
$595$	−6.50637	+	7.75486i	−0.266735	+	0.317918i
$596$	−10.8308	−	28.0686i	−0.443648	−	1.14974i
$597$	−1.04718	+	0.280591i	−0.0428582	+	0.0114838i
$598$	−6.54517	+	12.8734i	−0.267652	+	0.526432i
$599$	18.5333	−	10.7002i	0.757251	−	0.437199i	−0.0710572	−	0.997472i	$-0.522637\pi$
$599$	18.5333	−	10.7002i	0.757251	−	0.437199i	0.828308	+	0.560273i	$0.189304\pi$
$600$	−0.491669	−	0.187258i	−0.0200723	−	0.00764476i
$601$			0.974684i			0.0397582i	0.999802	+	0.0198791i	$0.00632813\pi$
$601$			0.974684i			0.0397582i	−0.999802	+	0.0198791i	$0.993672\pi$
$602$	−1.47809	−	10.4467i	−0.0602422	−	0.425777i
$603$	4.64033	+	4.64033i	0.188969	+	0.188969i
$604$	−21.4371	−	29.3975i	−0.872262	−	1.19617i
$605$	10.7882	+	2.89070i	0.438604	+	0.117524i
$606$	−0.260689	−	0.799939i	−0.0105897	−	0.0324953i
$607$	−3.01261	+	5.21800i	−0.122278	+	0.211792i	−0.920666	−	0.390352i	$-0.872353\pi$
$607$	−3.01261	+	5.21800i	−0.122278	+	0.211792i	0.798388	+	0.602144i	$0.205687\pi$
$608$	−43.3335	−	11.4086i	−1.75741	−	0.462681i
$609$	−0.249177	−	0.355819i	−0.0100972	−	0.0144185i
$610$	18.1321	+	3.83754i	0.734146	+	0.155378i
$611$	−1.14443	−	4.27106i	−0.0462985	−	0.172788i
$612$	−17.5108	+	1.87139i	−0.707834	+	0.0756465i
$613$	−0.426012	+	1.58990i	−0.0172065	+	0.0642155i	−0.973995	−	0.226568i	$-0.927249\pi$
$613$	−0.426012	+	1.58990i	−0.0172065	+	0.0642155i	0.956789	+	0.290784i	$0.0939160\pi$
$614$	−1.65136	−	30.9920i	−0.0666434	−	1.25073i
$615$			0.538124i			0.0216993i
$616$	8.11409	+	8.35753i	0.326926	+	0.336734i
$617$		−	34.0864i		−	1.37227i	−0.727476	−	0.686134i	$-0.759307\pi$
$617$		−	34.0864i		−	1.37227i	0.727476	−	0.686134i	$-0.240693\pi$
$618$	0.272215	−	0.0145045i	0.0109501	−	0.000583458i
$619$	−8.65485	+	32.3004i	−0.347868	+	1.29826i	0.541358	+	0.840792i	$0.317910\pi$
$619$	−8.65485	+	32.3004i	−0.347868	+	1.29826i	−0.889226	+	0.457469i	$0.848756\pi$
$620$	−10.2714	+	12.7295i	−0.412508	+	0.511228i
$621$	−0.395268	−	1.47516i	−0.0158615	−	0.0591961i
$622$	1.06366	−	5.02568i	0.0426487	−	0.201512i
$623$	−14.9140	+	31.9877i	−0.597515	+	1.28156i
$624$	0.376537	−	0.341424i	0.0150735	−	0.0136679i
$625$	1.22016	−	2.11337i	0.0488063	−	0.0845349i
$626$	5.03795	−	1.64179i	0.201357	−	0.0656193i
$627$	0.670466	+	0.179651i	0.0267758	+	0.00717456i
$628$	3.00849	−	19.2120i	0.120052	−	0.766642i
$629$	11.2877	+	11.2877i	0.450070	+	0.450070i
$630$	−9.00024	−	11.4978i	−0.358578	−	0.458081i
$631$			4.58799i			0.182645i	0.995821	+	0.0913225i	$0.0291094\pi$
$631$			4.58799i			0.182645i	−0.995821	+	0.0913225i	$0.970891\pi$
$632$	4.96333	−	2.22541i	0.197430	−	0.0885222i
$633$	0.594458	−	0.343211i	0.0236276	−	0.0136414i
$634$	31.0154	+	15.7691i	1.23178	+	0.626269i
$635$	7.08533	−	1.89851i	0.281173	−	0.0753400i
$636$	1.19507	+	0.529580i	0.0473875	+	0.0209992i
$637$	−9.06167	+	12.9445i	−0.359037	+	0.512878i
$638$	6.28131	+	1.32940i	0.248680	+	0.0526315i
$639$	−10.8842	+	18.8519i	−0.430571	+	0.745770i
$640$	14.5649	+	2.21567i	0.575728	+	0.0875822i
$641$	24.9135	+	43.1515i	0.984025	+	1.70438i	0.646190	+	0.763177i	$0.276361\pi$
$641$	24.9135	+	43.1515i	0.984025	+	1.70438i	0.337835	+	0.941205i	$0.390305\pi$
$642$	0.609732	−	0.678367i	0.0240642	−	0.0267730i
$643$	−31.1050	+	31.1050i	−1.22666	+	1.22666i	−0.261443	+	0.965219i	$0.584198\pi$
$643$	−31.1050	+	31.1050i	−1.22666	+	1.22666i	−0.965219	+	0.261443i	$0.915802\pi$
$644$	−22.6482	−	7.75279i	−0.892465	−	0.305503i
$645$	0.146161	+	0.146161i	0.00575509	+	0.00575509i
$646$	1.75135	+	32.8686i	0.0689061	+	1.29320i
$647$	−25.4255	+	14.6794i	−0.999579	+	0.577107i	−0.908124	−	0.418702i	$-0.862485\pi$
$647$	−25.4255	+	14.6794i	−0.999579	+	0.577107i	−0.0914555	+	0.995809i	$0.529152\pi$
$648$	2.58631	−	25.2431i	0.101600	−	0.991641i
$649$	4.13245	+	2.38587i	0.162213	+	0.0936536i
$650$	5.75280	+	8.84162i	0.225643	+	0.346797i
$651$	−0.878977	+	0.319977i	−0.0344498	+	0.0125409i
$652$	−24.2628	+	9.36227i	−0.950205	+	0.366655i
$653$	−3.93761	−	14.6954i	−0.154091	−	0.575075i	−0.999181	−	0.0404516i	$-0.987120\pi$
$653$	−3.93761	−	14.6954i	−0.154091	−	0.575075i	0.845091	−	0.534623i	$-0.179546\pi$
$654$	−0.237330	+	0.0773424i	−0.00928034	+	0.00302433i
$655$	1.35165	+	2.34112i	0.0528132	+	0.0914752i
$656$	6.20541	+	28.7008i	0.242281	+	1.12058i
$657$	42.3531			1.65235
$658$	6.74407	−	2.87008i	0.262911	−	0.111888i
$659$	−8.45620	+	8.45620i	−0.329407	+	0.329407i	−0.852361	−	0.522954i	$-0.824830\pi$
$659$	−8.45620	+	8.45620i	−0.329407	+	0.329407i	0.522954	+	0.852361i	$0.324830\pi$
$660$	−0.225461	−	0.0353059i	−0.00877604	−	0.00137428i
$661$	−3.50720	+	13.0890i	−0.136414	+	0.509105i	0.863574	+	0.504222i	$0.168221\pi$
$661$	−3.50720	+	13.0890i	−0.136414	+	0.509105i	−0.999988	+	0.00488232i	$0.998446\pi$
$662$	6.49932	−	12.7832i	0.252603	−	0.496834i
$663$	−0.323338	−	0.186679i	−0.0125574	−	0.00725001i
$664$	−34.8599	+	5.61492i	−1.35283	+	0.217901i
$665$	−22.3547	+	15.6547i	−0.866876	+	0.607065i
$666$	−19.3002	+	12.5577i	−0.747867	+	0.486599i
$667$	−12.7449	+	3.41498i	−0.493484	+	0.132229i
$668$	32.8961	−	3.51562i	1.27279	−	0.136023i
$669$	1.22019	+	0.326949i	0.0471753	+	0.0126406i
$670$	−2.69573	+	2.99917i	−0.104145	+	0.115868i
$671$	−15.6658			−0.604771
$672$	0.647797	+	0.538703i	0.0249893	+	0.0207809i
$673$	−15.5552			−0.599610			−0.299805	−	0.954000i	$-0.596922\pi$
$673$	−15.5552			−0.599610			−0.299805	+	0.954000i	$0.596922\pi$
$674$	−5.01753	+	5.58233i	−0.193268	+	0.215023i
$675$	−1.07747	−	0.288708i	−0.0414720	−	0.0111124i
$676$	15.7197	−	1.67997i	0.604606	−	0.0646144i
$677$	−39.5868	+	10.6072i	−1.52144	+	0.407669i	−0.920217	−	0.391410i	$-0.871988\pi$
$677$	−39.5868	+	10.6072i	−1.52144	+	0.407669i	−0.601226	+	0.799079i	$0.705321\pi$
$678$	−0.312269	+	0.203178i	−0.0119926	+	0.00780299i
$679$	−2.23719	−	25.5549i	−0.0858555	−	0.980707i
$680$	−1.72088	−	10.6840i	−0.0659929	−	0.409713i
$681$	0.114030	+	0.0658350i	0.00436962	+	0.00252280i
$682$	6.26593	−	12.3242i	0.239935	−	0.471917i
$683$	3.19786	−	11.9346i	0.122363	−	0.456664i	−0.877369	−	0.479816i	$-0.840704\pi$
$683$	3.19786	−	11.9346i	0.122363	−	0.456664i	0.999732	+	0.0231521i	$0.00737021\pi$
$684$	−46.9065	−	7.34531i	−1.79351	−	0.280855i
$685$	2.85672	−	2.85672i	0.109150	−	0.109150i
$686$	−23.3492	−	11.8665i	−0.891478	−	0.453064i
$687$	1.10632			0.0422089
$688$	9.48097	+	6.11004i	0.361459	+	0.232943i
$689$	−13.1038	−	22.6964i	−0.499214	−	0.864664i
$690$	0.445904	−	0.145314i	0.0169753	−	0.00553199i
$691$	−1.44023	−	5.37500i	−0.0547888	−	0.204475i	0.933106	−	0.359603i	$-0.117088\pi$
$691$	−1.44023	−	5.37500i	−0.0547888	−	0.204475i	−0.987894	+	0.155128i	$0.950421\pi$
$692$	−40.3158	+	15.5566i	−1.53258	+	0.591375i
$693$	9.45497	+	7.93277i	0.359165	+	0.301341i
$694$	−3.18121	−	4.88928i	−0.120757	−	0.185594i
$695$	20.3263	+	11.7354i	0.771021	+	0.445149i
$696$	0.461966	+	0.0473314i	0.0175108	+	0.00179409i
$697$	18.6796	−	10.7847i	0.707540	−	0.408498i
$698$	−1.21992	−	22.8950i	−0.0461748	−	0.866587i
$699$	0.154214	+	0.154214i	0.00583290	+	0.00583290i
$700$	−13.1753	+	11.4949i	−0.497981	+	0.434466i
$701$	22.0458	−	22.0458i	0.832657	−	0.832657i	−0.155223	−	0.987880i	$-0.549609\pi$
$701$	22.0458	−	22.0458i	0.832657	−	0.832657i	0.987880	+	0.155223i	$0.0496095\pi$
$702$	0.720395	−	0.801486i	0.0271896	−	0.0302502i
$703$	21.5184	+	37.2710i	0.811583	+	1.40570i
$704$	−12.4321	+	0.716872i	−0.468552	+	0.0270181i
$705$	−0.0717960	+	0.124354i	−0.00270399	+	0.00468346i
$706$	5.35084	+	1.13247i	0.201381	+	0.0426212i
$707$	−27.5364	−	4.85384i	−1.03561	−	0.182547i
$708$	0.315541	+	0.139828i	0.0118588	+	0.00525506i
$709$	−11.9661	+	3.20632i	−0.449398	+	0.120416i	−0.476417	−	0.879219i	$-0.658065\pi$
$709$	−11.9661	+	3.20632i	−0.449398	+	0.120416i	0.0270200	+	0.999635i	$0.491398\pi$
$710$	−11.9240	−	6.06246i	−0.447499	−	0.227520i
$711$	4.99113	−	2.88163i	0.187182	−	0.108070i
$712$	−15.4366	−	34.4282i	−0.578511	−	1.29025i
$713$			28.4126i			1.06406i
$714$	0.231301	−	0.574024i	0.00865623	−	0.0214823i
$715$	3.23532	+	3.23532i	0.120994	+	0.120994i
$716$	−5.87055	+	37.4888i	−0.219393	+	1.40102i
$717$	0.357122	+	0.0956906i	0.0133370	+	0.00357363i
$718$	−21.2675	+	6.93076i	−0.793695	+	0.258654i
$719$	−7.64439	+	13.2405i	−0.285088	+	0.493786i	−0.972630	−	0.232358i	$-0.925356\pi$
$719$	−7.64439	+	13.2405i	−0.285088	+	0.493786i	0.687543	+	0.726144i	$0.258689\pi$
$720$	15.5910	+	0.762491i	0.581042	+	0.0284164i
$721$	3.82826	−	8.21091i	0.142572	−	0.305790i
$722$	−12.8106	+	60.5288i	−0.476760	+	2.25265i
$723$	−0.193093	−	0.720631i	−0.00718119	−	0.0268006i
$724$	11.4423	−	14.1807i	0.425250	−	0.527020i
$725$	−2.49434	+	9.30902i	−0.0926376	+	0.345728i
$726$	−0.681856	+	0.0363317i	−0.0253061	+	0.00134839i
$727$			23.7860i			0.882173i	0.897465	+	0.441086i	$0.145407\pi$
$727$			23.7860i			0.882173i	−0.897465	+	0.441086i	$0.854593\pi$
$728$	−4.13038	−	16.3793i	−0.153082	−	0.607056i
$729$		−	26.8290i		−	0.993668i
$730$	1.38479	+	25.9892i	0.0512534	+	0.961902i
$731$	2.14436	−	8.00285i	0.0793119	−	0.295996i
$732$	−1.12667	+	0.120408i	−0.0416431	+	0.00445041i
$733$	5.32874	+	19.8871i	0.196822	+	0.734548i	0.991788	+	0.127894i	$0.0408219\pi$
$733$	5.32874	+	19.8871i	0.196822	+	0.734548i	−0.794966	+	0.606654i	$0.792511\pi$
$734$	6.56764	+	1.39000i	0.242416	+	0.0513059i
$735$	0.505322	−	0.0891596i	0.0186391	−	0.00328870i
$736$	22.1066	−	12.8923i	0.814860	−	0.475215i
$737$	1.70430	−	2.95194i	0.0627787	−	0.108736i
$738$	9.64008	+	29.5812i	0.354856	+	1.08890i
$739$	26.3224	+	7.05306i	0.968284	+	0.259451i	0.708103	−	0.706109i	$-0.249551\pi$
$739$	26.3224	+	7.05306i	0.968284	+	0.259451i	0.260181	+	0.965560i	$0.416218\pi$
$740$	−8.33681	−	11.4326i	−0.306467	−	0.420271i
$741$	−0.711756	−	0.711756i	−0.0261470	−	0.0261470i
$742$	34.2074	−	26.7769i	1.25579	−	0.983011i
$743$			12.8386i			0.471002i	0.971874	+	0.235501i	$0.0756731\pi$
$743$			12.8386i			0.471002i	−0.971874	+	0.235501i	$0.924327\pi$
$744$	0.355918	−	0.934508i	0.0130486	−	0.0342607i
$745$	16.9641	−	9.79426i	0.621518	−	0.358834i
$746$	14.6036	−	28.7232i	0.534676	−	1.05163i
$747$	−36.1368	+	9.68282i	−1.32218	+	0.354276i
$748$	3.29295	+	8.53386i	0.120402	+	0.312029i
$749$	−10.3692	−	28.4842i	−0.378882	−	1.04079i
$750$	0.178253	−	0.842232i	0.00650889	−	0.0307539i
$751$	7.23318	−	12.5282i	0.263942	−	0.457162i	−0.703344	−	0.710850i	$-0.748310\pi$
$751$	7.23318	−	12.5282i	0.263942	−	0.457162i	0.967286	+	0.253688i	$0.0816438\pi$
$752$	−2.39524	+	7.46036i	−0.0873455	+	0.272051i
$753$	0.151625	+	0.262622i	0.00552552	+	0.00957048i
$754$	−6.92458	−	6.22398i	−0.252178	−	0.226664i
$755$	16.7506	−	16.7506i	0.609616	−	0.609616i
$756$	1.48272	+	0.996224i	0.0539260	+	0.0362323i
$757$	−2.16062	−	2.16062i	−0.0785291	−	0.0785291i	0.666751	−	0.745280i	$-0.267684\pi$
$757$	−2.16062	−	2.16062i	−0.0785291	−	0.0785291i	−0.745280	+	0.666751i	$0.767684\pi$
$758$	40.1490	−	2.13928i	1.45828	−	0.0777020i
$759$	−0.343304	+	0.198207i	−0.0124611	+	0.00719444i
$760$	2.97363	−	29.0234i	0.107865	−	1.05279i
$761$	2.04136	+	1.17858i	0.0739994	+	0.0427236i	0.536543	−	0.843873i	$-0.319730\pi$
$761$	2.04136	+	1.17858i	0.0739994	+	0.0427236i	−0.462544	+	0.886596i	$0.653063\pi$
$762$	−0.375892	+	0.244574i	−0.0136171	+	0.00885998i
$763$	−1.44006	+	8.16964i	−0.0521337	+	0.295761i
$764$	47.3829	+	20.9972i	1.71425	+	0.759651i
$765$	−2.96763	−	11.0753i	−0.107295	−	0.400430i
$766$	−10.2758	−	31.5318i	−0.371278	−	1.13929i
$767$	−3.45987	−	5.99267i	−0.124929	−	0.216383i
$768$	−0.888598	+	0.147111i	−0.0320645	+	0.00530840i
$769$	7.96868			0.287358			0.143679	−	0.989624i	$-0.454107\pi$
$769$	7.96868			0.287358			0.143679	+	0.989624i	$0.454107\pi$
$770$	−4.55865	+	6.06123i	−0.164282	+	0.218432i
$771$	−0.940923	+	0.940923i	−0.0338865	+	0.0338865i
$772$	−20.2769	+	14.7862i	−0.729783	+	0.532168i
$773$	−5.69575	+	21.2568i	−0.204862	+	0.764555i	0.784630	+	0.619965i	$0.212853\pi$
$773$	−5.69575	+	21.2568i	−0.204862	+	0.764555i	−0.989492	+	0.144590i	$0.953814\pi$
$774$	10.6530	+	5.41625i	0.382914	+	0.194683i
$775$	17.9725	+	10.3764i	0.645592	+	0.372733i
$776$	22.2285	+	16.0611i	0.797956	+	0.576561i
$777$	−0.0705694	−	0.806097i	−0.00253166	−	0.0289186i
$778$	−8.26509	−	12.7028i	−0.296318	−	0.455418i
$779$	56.1695	−	15.0506i	2.01248	−	0.539243i
$780$	0.257549	+	0.207816i	0.00922174	+	0.00744099i
$781$	10.9215	+	2.92640i	0.390801	+	0.104715i
$782$	−13.9806	−	12.5661i	−0.499947	−	0.449364i
$783$	0.984588			0.0351863
$784$	25.9232	−	10.5825i	0.925828	−	0.377945i
$785$	12.6611			0.451896
$786$	−0.122916	−	0.110480i	−0.00438428	−	0.00394070i
$787$	−27.7816	−	7.44405i	−0.990306	−	0.265352i	−0.272927	−	0.962035i	$-0.587992\pi$
$787$	−27.7816	−	7.44405i	−0.990306	−	0.265352i	−0.717379	+	0.696683i	$0.754658\pi$
$788$	−14.7713	+	18.3064i	−0.526207	+	0.652137i
$789$	0.968810	−	0.259592i	0.0344905	−	0.00924171i
$790$	1.93145	+	2.96849i	0.0687178	+	0.105614i
$791$	1.07977	+	12.3340i	0.0383922	+	0.438545i
$792$	−13.0263	+	2.09815i	−0.462868	+	0.0745547i
$793$	19.6741	+	11.3589i	0.698649	+	0.403365i
$794$	8.35562	+	4.24821i	0.296530	+	0.150764i
$795$	−0.220273	+	0.822071i	−0.00781229	+	0.0291558i
$796$	−22.6940	−	31.1212i	−0.804369	−	1.10306i
$797$	−22.0411	+	22.0411i	−0.780736	+	0.780736i	−0.979955	−	0.199219i	$-0.936160\pi$
$797$	−22.0411	+	22.0411i	−0.780736	+	0.780736i	0.199219	+	0.979955i	$0.436160\pi$
$798$	1.00288	−	1.33344i	0.0355016	−	0.0472034i
$799$	5.75552			0.203616
$800$	−0.0816127	−	18.6920i	−0.00288544	−	0.660861i
$801$	−19.9885	−	34.6210i	−0.706258	−	1.22327i
$802$	13.9044	+	42.6664i	0.490980	+	1.50660i
$803$	−5.69369	−	21.2491i	−0.200926	−	0.749866i
$804$	0.0998836	−	0.225401i	0.00352262	−	0.00794928i
$805$	2.70563	−	15.3494i	0.0953611	−	0.540995i
$806$	−16.8051	+	10.9343i	−0.591936	+	0.385143i
$807$	0.311270	+	0.179712i	0.0109572	+	0.00632616i
$808$	23.1807	−	18.8721i	0.815493	−	0.663918i
$809$	25.9855	−	15.0027i	0.913600	−	0.527467i	0.0320125	−	0.999487i	$-0.489808\pi$
$809$	25.9855	−	15.0027i	0.913600	−	0.527467i	0.881588	+	0.472020i	$0.156475\pi$
$810$	16.4981	−	0.879076i	0.579684	−	0.0308876i
$811$	−20.2976	−	20.2976i	−0.712746	−	0.712746i	0.254363	−	0.967109i	$-0.418134\pi$
$811$	−20.2976	−	20.2976i	−0.712746	−	0.712746i	−0.967109	+	0.254363i	$0.918134\pi$
$812$	8.60705	−	12.8102i	0.302048	−	0.449550i
$813$	−0.317411	+	0.317411i	−0.0111321	+	0.0111321i
$814$	8.89495	+	7.99500i	0.311768	+	0.280224i
$815$	−8.46625	−	14.6640i	−0.296560	−	0.513657i
$816$	0.302419	+	0.588440i	0.0105868	+	0.0205995i
$817$	11.1684	−	19.3443i	0.390733	−	0.676770i
$818$	−0.378535	+	1.78854i	−0.0132351	+	0.0625349i
$819$	−6.12233	−	16.8181i	−0.213932	−	0.587671i
$820$	−17.8367	+	6.88265i	−0.622886	+	0.240352i
$821$	−53.0609	+	14.2176i	−1.85184	+	0.496199i	−0.999635	−	0.0270111i	$-0.991401\pi$
$821$	−53.0609	+	14.2176i	−1.85184	+	0.496199i	−0.852204	+	0.523210i	$0.824734\pi$
$822$	−0.111940	+	0.220170i	−0.00390436	+	0.00767931i
$823$	20.1906	−	11.6571i	0.703800	−	0.406339i	−0.104961	−	0.994476i	$-0.533472\pi$
$823$	20.1906	−	11.6571i	0.703800	−	0.406339i	0.808761	+	0.588137i	$0.200138\pi$
$824$	3.96242	+	8.83736i	0.138037	+	0.307864i
$825$			0.289545i			0.0100807i
$826$	9.03198	−	7.07007i	0.314263	−	0.245999i
$827$	4.26358	+	4.26358i	0.148259	+	0.148259i	0.777340	−	0.629081i	$-0.216568\pi$
$827$	4.26358	+	4.26358i	0.148259	+	0.148259i	−0.629081	+	0.777340i	$0.716568\pi$
$828$	21.9086	−	15.9761i	0.761376	−	0.555206i
$829$	−40.5325	−	10.8606i	−1.40775	−	0.377206i	−0.526630	−	0.850095i	$-0.676545\pi$
$829$	−40.5325	−	10.8606i	−1.40775	−	0.377206i	−0.881122	+	0.472889i	$0.843211\pi$
$830$	−7.12321	−	21.8580i	−0.247250	−	0.758703i
$831$	−0.360624	+	0.624619i	−0.0125099	+	0.0216678i
$832$	16.1328	+	8.11390i	0.559305	+	0.281299i
$833$	−13.2222	−	15.7541i	−0.458122	−	0.545846i
$834$	−1.40383	−	0.297113i	−0.0486107	−	0.0102882i
$835$	5.57502	+	20.8063i	0.192932	+	0.720030i
$836$	2.62058	+	24.5211i	0.0906346	+	0.848080i
$837$	0.548743	−	2.04794i	0.0189673	−	0.0707871i
$838$	−1.83874	−	34.5086i	−0.0635181	−	1.19208i
$839$		−	46.6970i		−	1.61216i	−0.591806	−	0.806081i	$-0.701585\pi$
$839$		−	46.6970i		−	1.61216i	0.591806	−	0.806081i	$-0.298415\pi$
$840$	−0.281268	+	0.470958i	−0.00970468	+	0.0162496i
$841$			20.4935i			0.706672i
$842$	6.71538	−	0.357819i	0.231427	−	0.0123312i
$843$	0.190045	−	0.709257i	0.00654549	−	0.0244281i
$844$	18.9793	+	15.3143i	0.653294	+	0.527140i
$845$	2.66408	+	9.94249i	0.0916472	+	0.342032i
$846$	−1.71898	+	8.12205i	−0.0590999	+	0.279242i
$847$	−9.58920	+	20.5671i	−0.329489	+	0.706693i
$848$	−2.26851	+	46.3853i	−0.0779010	+	1.59288i
$849$	0.542493	−	0.939626i	0.0186183	−	0.0322479i
$850$	−13.0546	+	4.25430i	−0.447769	+	0.145921i
$851$	−23.7410	−	6.36139i	−0.813832	−	0.218066i
$852$	0.807958	+	0.126522i	0.0276802	+	0.00433457i
$853$	−14.9036	−	14.9036i	−0.510289	−	0.510289i	0.404326	−	0.914615i	$-0.367506\pi$
$853$	−14.9036	−	14.9036i	−0.510289	−	0.510289i	−0.914615	+	0.404326i	$0.867506\pi$
$854$	−14.0740	+	34.9277i	−0.481602	+	1.19520i
$855$		−	30.9125i		−	1.05718i
$856$	30.2838	+	11.5339i	1.03508	+	0.394221i
$857$	12.5881	−	7.26772i	0.430000	−	0.248261i	−0.269347	−	0.963043i	$-0.586808\pi$
$857$	12.5881	−	7.26772i	0.430000	−	0.248261i	0.699347	+	0.714783i	$0.253474\pi$
$858$	−0.249349	−	0.126776i	−0.00851265	−	0.00432805i
$859$	37.9861	−	10.1784i	1.29607	−	0.347281i	0.456107	−	0.889925i	$-0.349243\pi$
$859$	37.9861	−	10.1784i	1.29607	−	0.347281i	0.839963	+	0.542644i	$0.182577\pi$
$860$	−2.97527	+	6.71409i	−0.101456	+	0.228949i
$861$	−1.07676	−	0.189800i	−0.0366957	−	0.00646835i
$862$	−15.4606	−	3.27214i	−0.526589	−	0.111449i
$863$	6.49230	−	11.2450i	0.221000	−	0.382784i	−0.734112	−	0.679029i	$-0.762401\pi$
$863$	6.49230	−	11.2450i	0.221000	−	0.382784i	0.955112	+	0.296245i	$0.0957345\pi$
$864$	−1.84240	+	0.502303i	−0.0626799	+	0.0170887i
$865$	−14.0678	−	24.3661i	−0.478319	−	0.828473i
$866$	−16.4441	+	18.2952i	−0.558795	+	0.621695i
$867$	−0.333052	+	0.333052i	−0.0113110	+	0.0113110i
$868$	−21.8482	−	25.0422i	−0.741575	−	0.849986i
$869$	−2.11673	−	2.11673i	−0.0718052	−	0.0718052i
$870$	0.0160877	+	0.301927i	0.000545425	+	0.0102363i
$871$	−4.28075	+	2.47149i	−0.145048	+	0.0837434i
$872$	−5.59907	−	6.87736i	−0.189609	−	0.232897i
$873$	25.1638	+	14.5283i	0.851665	+	0.491709i
$874$	−27.6392	−	42.4793i	−0.934909	−	1.43689i
$875$	−21.9179	−	18.3892i	−0.740959	−	0.621668i
$876$	−0.572809	−	1.48446i	−0.0193534	−	0.0501554i
$877$	5.80637	+	21.6697i	0.196067	+	0.731733i	0.991988	+	0.126332i	$0.0403205\pi$
$877$	5.80637	+	21.6697i	0.196067	+	0.731733i	−0.795921	+	0.605401i	$0.793013\pi$
$878$	−50.4782	+	16.4501i	−1.70356	+	0.555164i
$879$	−0.505614	−	0.875749i	−0.0170539	−	0.0295383i
$880$	−1.71340	−	7.92472i	−0.0577588	−	0.267142i
$881$	−8.65332			−0.291538			−0.145769	−	0.989319i	$-0.546566\pi$
$881$	−8.65332			−0.291538			−0.145769	+	0.989319i	$0.546566\pi$
$882$	26.1808	−	13.9536i	0.881553	−	0.469843i
$883$	30.6837	−	30.6837i	1.03259	−	1.03259i	0.0331374	−	0.999451i	$-0.489450\pi$
$883$	30.6837	−	30.6837i	1.03259	−	1.03259i	0.999451	−	0.0331374i	$-0.0105499\pi$
$884$	2.05218	−	13.1050i	0.0690222	−	0.440770i
$885$	−0.0581601	+	0.217056i	−0.00195503	+	0.00729627i
$886$	4.56645	−	8.98155i	0.153413	−	0.301741i
$887$	24.7803	+	14.3069i	0.832042	+	0.480380i	0.854551	−	0.519367i	$-0.173832\pi$
$887$	24.7803	+	14.3069i	0.832042	+	0.480380i	−0.0225091	+	0.999747i	$0.507165\pi$
$888$	0.701170	+	0.506628i	0.0235297	+	0.0170013i
$889$	1.29977	+	14.8470i	0.0435929	+	0.497951i
$890$	20.5910	−	13.3975i	0.690211	−	0.449086i
$891$	−13.4891	+	3.61439i	−0.451902	+	0.121087i
$892$	4.76923	+	44.6263i	0.159686	+	1.49420i
$893$	14.9882	+	4.01607i	0.501560	+	0.134393i
$894$	−0.800558	+	0.890672i	−0.0267747	+	0.0297885i
$895$	−24.7060			−0.825830
$896$	−9.57056	+	28.3620i	−0.319730	+	0.947509i
$897$	0.574859			0.0191940
$898$	−7.41179	+	8.24610i	−0.247335	+	0.275176i
$899$	−17.6935	−	4.74096i	−0.590112	−	0.158120i
$900$	−2.10459	−	19.6929i	−0.0701530	−	0.656431i
$901$	32.9506	−	8.82909i	1.09774	−	0.294140i
$902$	13.5453	−	8.81328i	0.451011	−	0.293450i
$903$	−0.344012	+	0.240908i	−0.0114480	+	0.00801692i
$904$	−10.7285	−	7.75184i	−0.356824	−	0.257822i
$905$	10.2743	+	5.93185i	0.341528	+	0.197182i
$906$	−0.656369	+	1.29098i	−0.0218064	+	0.0428900i
$907$	4.82227	−	17.9969i	0.160121	−	0.597579i	−0.838492	−	0.544915i	$-0.816562\pi$
$907$	4.82227	−	17.9969i	0.160121	−	0.597579i	0.998612	−	0.0526640i	$-0.0167712\pi$
$908$	−0.723729	+	4.62167i	−0.0240178	+	0.153376i
$909$	22.3949	−	22.3949i	0.742793	−	0.742793i
$910$	10.1199	−	4.30674i	0.335472	−	0.142767i
$911$	−12.2041			−0.404341			−0.202170	−	0.979350i	$-0.564799\pi$
$911$	−12.2041			−0.404341			−0.202170	+	0.979350i	$0.564799\pi$
$912$	0.376941	+	1.74340i	0.0124818	+	0.0577298i
$913$	9.71601	+	16.8286i	0.321553	+	0.556946i
$914$	−34.5958	+	11.2743i	−1.14433	+	0.372920i
$915$	−0.190942	−	0.712603i	−0.00631233	−	0.0235579i
$916$	14.1500	+	36.6704i	0.467528	+	1.21162i
$917$	−5.16119	+	1.87884i	−0.170437	+	0.0620448i
$918$	0.765009	+	1.17576i	0.0252491	+	0.0388059i
$919$	−3.57056	−	2.06146i	−0.117782	−	0.0680014i	0.439952	−	0.898021i	$-0.354996\pi$
$919$	−3.57056	−	2.06146i	−0.117782	−	0.0680014i	−0.557734	+	0.830020i	$0.688329\pi$
$920$	10.5197	+	12.9214i	0.346825	+	0.426007i
$921$	−1.06989	+	0.617699i	−0.0352539	+	0.0203539i
$922$	1.40109	+	26.2949i	0.0461423	+	0.865978i
$923$	−11.5941	−	11.5941i	−0.381623	−	0.381623i
$924$	0.150166	−	0.438681i	0.00494012	−	0.0144316i
$925$	−12.6943	+	12.6943i	−0.417386	+	0.417386i
$926$	6.51195	−	7.24496i	0.213996	−	0.238084i
$927$	5.13083	+	8.88686i	0.168519	+	0.291883i
$928$	4.33973	+	15.9178i	0.142459	+	0.522526i
$929$	−22.7002	+	39.3180i	−0.744771	+	1.28998i	0.205531	+	0.978651i	$0.434108\pi$
$929$	−22.7002	+	39.3180i	−0.744771	+	1.28998i	−0.950302	+	0.311330i	$0.899225\pi$
$930$	0.636973	+	0.134812i	0.0208872	+	0.00442064i
$931$	−23.4396	−	50.2519i	−0.768203	−	1.64694i
$932$	−3.13919	+	7.08400i	−0.102827	+	0.232044i
$933$	−0.197513	+	0.0529235i	−0.00646629	+	0.00173264i
$934$	49.8757	+	25.3581i	1.63198	+	0.829743i
$935$	−5.15770	+	2.97780i	−0.168675	+	0.0973845i
$936$	17.8806	+	6.81003i	0.584445	+	0.222593i
$937$			8.69727i			0.284127i	0.989858	+	0.142064i	$0.0453738\pi$
$937$			8.69727i			0.284127i	−0.989858	+	0.142064i	$0.954626\pi$
$938$	−5.05037	−	6.45182i	−0.164900	−	0.210659i
$939$	−0.149141	−	0.149141i	−0.00486704	−	0.00486704i
$940$	−5.04014	−	0.789260i	−0.164391	−	0.0257428i
$941$	−11.6093	−	3.11071i	−0.378454	−	0.101406i	0.0645772	−	0.997913i	$-0.479430\pi$
$941$	−11.6093	−	3.11071i	−0.378454	−	0.101406i	−0.443031	+	0.896506i	$0.646097\pi$
$942$	−0.735966	+	0.239841i	−0.0239791	+	0.00781443i
$943$	−16.6051	+	28.7609i	−0.540737	+	0.936584i
$944$	−0.598969	+	12.2474i	−0.0194948	+	0.398618i
$945$	−0.491467	+	1.05411i	−0.0159874	+	0.0342901i
$946$	1.28529	−	6.07288i	0.0417883	−	0.197446i
$947$	−14.8879	−	55.5623i	−0.483791	−	1.80553i	−0.585443	−	0.810713i	$-0.699080\pi$
$947$	−14.8879	−	55.5623i	−0.483791	−	1.80553i	0.101652	−	0.994820i	$-0.467587\pi$
$948$	−0.168503	−	0.135965i	−0.00547273	−	0.00441593i
$949$	−8.25671	+	30.8145i	−0.268024	+	1.00028i
$950$	−36.9645	+	1.96960i	−1.19929	+	0.0639021i
$951$		−	1.38499i		−	0.0449113i
$952$	21.9851	+	0.324923i	0.712540	+	0.0105308i
$953$		−	8.69133i		−	0.281540i	−0.990042	−	0.140770i	$-0.955042\pi$
$953$		−	8.69133i		−	0.281540i	0.990042	−	0.140770i	$-0.0449578\pi$
$954$	2.61814	+	49.1361i	0.0847654	+	1.59084i
$955$	−8.73356	+	32.5941i	−0.282611	+	1.05472i
$956$	1.39585	+	13.0611i	0.0451449	+	0.422427i
$957$	−0.0661460	−	0.246860i	−0.00213820	−	0.00797986i
$958$	0.724965	+	0.153434i	0.0234225	+	0.00495724i
$959$	4.70855	+	6.72371i	0.152047	+	0.217120i
$960$	−0.184137	−	0.556772i	−0.00594299	−	0.0179697i
$961$	−4.22236	+	7.31334i	−0.136205	+	0.235914i
$962$	−5.37390	−	16.4902i	−0.173262	−	0.531664i
$963$	33.1653	+	8.88662i	1.06874	+	0.286367i
$964$	21.4165	−	15.6172i	0.689778	−	0.502996i
$965$	−11.5537	−	11.5537i	−0.371927	−	0.371927i
$966$	0.133491	+	0.943481i	0.00429501	+	0.0303560i
$967$			28.1636i			0.905681i	0.891592	+	0.452840i	$0.149589\pi$
$967$			28.1636i			0.905681i	−0.891592	+	0.452840i	$0.850411\pi$
$968$	−9.92525	−	22.1362i	−0.319009	−	0.711485i
$969$	1.13467	−	0.655102i	0.0364509	−	0.0210449i
$970$	−8.09225	+	15.9163i	−0.259827	+	0.511041i
$971$	10.1276	−	2.71368i	0.325010	−	0.0870862i	−0.0926248	−	0.995701i	$-0.529526\pi$
$971$	10.1276	−	2.71368i	0.325010	−	0.0870862i	0.417635	+	0.908615i	$0.362859\pi$
$972$	−2.83203	+	1.09279i	−0.0908375	+	0.0350514i
$973$	−30.6511	+	36.5327i	−0.982629	+	1.17118i
$974$	0.833765	−	3.93947i	0.0267155	−	0.126229i
$975$	0.209942	−	0.363630i	0.00672352	−	0.0116455i
$976$	−18.4013	−	35.8049i	−0.589011	−	1.14609i
$977$	−17.3812	−	30.1051i	−0.556073	−	0.963147i	−0.997819	−	0.0660068i	$-0.978974\pi$
$977$	−17.3812	−	30.1051i	−0.556073	−	0.963147i	0.441746	−	0.897140i	$-0.354359\pi$
$978$	0.769906	+	0.692010i	0.0246189	+	0.0221280i
$979$	−14.6827	+	14.6827i	−0.469262	+	0.469262i
$980$	9.41840	+	15.6091i	0.300860	+	0.498614i
$981$	−6.64424	−	6.64424i	−0.212134	−	0.212134i
$982$	−34.9156	+	1.86042i	−1.11420	+	0.0593685i
$983$	2.48718	−	1.43597i	0.0793286	−	0.0458004i	−0.459811	−	0.888017i	$-0.652083\pi$
$983$	2.48718	−	1.43597i	0.0793286	−	0.0458004i	0.539140	+	0.842216i	$0.318750\pi$
$984$	0.906434	−	0.737956i	0.0288961	−	0.0235252i
$985$	−13.2635	−	7.65766i	−0.422609	−	0.243993i
$986$	10.1582	−	6.60943i	0.323503	−	0.210487i
$987$	−0.223503	−	0.187520i	−0.00711418	−	0.00596884i
$988$	14.4885	−	32.6954i	0.460942	−	1.04018i
$989$	3.30166	+	12.3220i	0.104987	+	0.391816i
$990$	−2.66176	−	8.16779i	−0.0845964	−	0.259590i
$991$	15.8744	+	27.4952i	0.504266	+	0.873414i	0.999988	+	0.00493273i	$0.00157014\pi$
$991$	15.8744	+	27.4952i	0.504266	+	0.873414i	−0.495722	+	0.868481i	$0.665097\pi$
$992$	35.5276	−	0.155120i	1.12800	−	0.00492506i
$993$	−0.570832			−0.0181148
$994$	16.3363	−	21.7209i	0.518156	−	0.688947i
$995$	17.7327	−	17.7327i	0.562166	−	0.562166i
$996$	0.828115	+	1.13563i	0.0262398	+	0.0359837i
$997$	5.29788	−	19.7719i	0.167785	−	0.626184i	−0.829883	−	0.557937i	$-0.811593\pi$
$997$	5.29788	−	19.7719i	0.167785	−	0.626184i	0.997668	−	0.0682464i	$-0.0217404\pi$
$998$	1.70767	+	0.868222i	0.0540552	+	0.0274831i
$999$	1.58836	+	0.917039i	0.0502534	+	0.0290138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.37.10	✓	48
4.3	odd	2		448.2.ba.c.177.7		48
7.2	even	3		784.2.m.j.197.1		24
7.3	odd	6		784.2.x.o.165.8		48
7.4	even	3	inner	112.2.w.c.53.8	yes	48
7.5	odd	6		784.2.m.k.197.1		24
7.6	odd	2		784.2.x.o.373.10		48
8.3	odd	2		896.2.ba.e.737.6		48
8.5	even	2		896.2.ba.f.737.7		48
16.3	odd	4		448.2.ba.c.401.6		48
16.5	even	4		896.2.ba.f.289.6		48
16.11	odd	4		896.2.ba.e.289.7		48
16.13	even	4	inner	112.2.w.c.93.8	yes	48
28.11	odd	6		448.2.ba.c.305.6		48
56.11	odd	6		896.2.ba.e.865.7		48
56.53	even	6		896.2.ba.f.865.6		48
112.11	odd	12		896.2.ba.e.417.6		48
112.13	odd	4		784.2.x.o.765.8		48
112.45	odd	12		784.2.x.o.557.10		48
112.53	even	12		896.2.ba.f.417.7		48
112.61	odd	12		784.2.m.k.589.1		24
112.67	odd	12		448.2.ba.c.81.7		48
112.93	even	12		784.2.m.j.589.1		24
112.109	even	12	inner	112.2.w.c.109.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.10	✓	48	1.1	even	1	trivial
112.2.w.c.53.8	yes	48	7.4	even	3	inner
112.2.w.c.93.8	yes	48	16.13	even	4	inner
112.2.w.c.109.10	yes	48	112.109	even	12	inner
448.2.ba.c.81.7		48	112.67	odd	12
448.2.ba.c.177.7		48	4.3	odd	2
448.2.ba.c.305.6		48	28.11	odd	6
448.2.ba.c.401.6		48	16.3	odd	4
784.2.m.j.197.1		24	7.2	even	3
784.2.m.j.589.1		24	112.93	even	12
784.2.m.k.197.1		24	7.5	odd	6
784.2.m.k.589.1		24	112.61	odd	12
784.2.x.o.165.8		48	7.3	odd	6
784.2.x.o.373.10		48	7.6	odd	2
784.2.x.o.557.10		48	112.45	odd	12
784.2.x.o.765.8		48	112.13	odd	4
896.2.ba.e.289.7		48	16.11	odd	4
896.2.ba.e.417.6		48	112.11	odd	12
896.2.ba.e.737.6		48	8.3	odd	2
896.2.ba.e.865.7		48	56.11	odd	6
896.2.ba.f.289.6		48	16.5	even	4
896.2.ba.f.417.7		48	112.53	even	12
896.2.ba.f.737.7		48	8.5	even	2
896.2.ba.f.865.6		48	56.53	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.945375 - 1.05179i) q^{2} +(-0.0543752 - 0.0145698i) q^{3} +(-0.212530 - 1.98868i) q^{4} +(1.25781 - 0.337028i) q^{5} +(-0.0667293 + 0.0434174i) q^{6} +(0.230738 + 2.63567i) q^{7} +(-2.29259 - 1.65651i) q^{8} +(-2.59533 - 1.49842i) q^{9} +O(q^{10})\)	\(q+(0.945375 - 1.05179i) q^{2} +(-0.0543752 - 0.0145698i) q^{3} +(-0.212530 - 1.98868i) q^{4} +(1.25781 - 0.337028i) q^{5} +(-0.0667293 + 0.0434174i) q^{6} +(0.230738 + 2.63567i) q^{7} +(-2.29259 - 1.65651i) q^{8} +(-2.59533 - 1.49842i) q^{9} +(0.834616 - 1.64157i) q^{10} +(-0.402875 + 1.50355i) q^{11} +(-0.0174182 + 0.111231i) q^{12} +(1.59615 - 1.59615i) q^{13} +(2.99031 + 2.24901i) q^{14} -0.0733039 q^{15} +(-3.90966 + 0.845308i) q^{16} +(1.46910 + 2.54455i) q^{17} +(-4.02958 + 1.31318i) q^{18} +(2.05021 + 7.65147i) q^{19} +(-0.937562 - 2.42974i) q^{20} +(0.0258547 - 0.146677i) q^{21} +(1.20055 + 1.84516i) q^{22} +(-3.91784 - 2.26197i) q^{23} +(0.100525 + 0.123475i) q^{24} +(-2.86164 + 1.65217i) q^{25} +(-0.169855 - 3.18777i) q^{26} +(0.238706 + 0.238706i) q^{27} +(5.19246 - 1.01902i) q^{28} +(2.06234 - 2.06234i) q^{29} +(-0.0692997 + 0.0771004i) q^{30} +(-3.14025 - 5.43908i) q^{31} +(-2.80701 + 4.91128i) q^{32} +(0.0438128 - 0.0758861i) q^{33} +(4.06519 + 0.860373i) q^{34} +(1.17852 + 3.23740i) q^{35} +(-2.42828 + 5.47973i) q^{36} +(5.24787 - 1.40616i) q^{37} +(9.98597 + 5.07713i) q^{38} +(-0.110046 + 0.0635352i) q^{39} +(-3.44193 - 1.31090i) q^{40} -7.34101i q^{41} +(-0.129831 - 0.165858i) q^{42} +(-1.99391 - 1.99391i) q^{43} +(3.07570 + 0.481638i) q^{44} +(-3.76943 - 1.01002i) q^{45} +(-6.08295 + 1.98235i) q^{46} +(0.979430 - 1.69642i) q^{47} +(0.224904 + 0.0109992i) q^{48} +(-6.89352 + 1.21630i) q^{49} +(-0.967587 + 4.57177i) q^{50} +(-0.0428089 - 0.159765i) q^{51} +(-3.51345 - 2.83499i) q^{52} +(3.00493 - 11.2146i) q^{53} +(0.476736 - 0.0254021i) q^{54} +2.02696i q^{55} +(3.83702 - 6.42474i) q^{56} -0.445921i q^{57} +(-0.219466 - 4.11884i) q^{58} +(0.793411 - 2.96105i) q^{59} +(0.0155793 + 0.145778i) q^{60} +(2.60480 + 9.72123i) q^{61} +(-8.68949 - 1.83908i) q^{62} +(3.35049 - 7.18618i) q^{63} +(2.51197 + 7.59540i) q^{64} +(1.46970 - 2.54559i) q^{65} +(-0.0383967 - 0.117823i) q^{66} +(-2.11517 - 0.566758i) q^{67} +(4.74806 - 3.46236i) q^{68} +(0.180077 + 0.180077i) q^{69} +(4.51921 + 1.82100i) q^{70} -7.26378i q^{71} +(3.46790 + 7.73444i) q^{72} +(-12.2392 + 7.06631i) q^{73} +(3.48222 - 6.84902i) q^{74} +(0.179674 - 0.0481435i) q^{75} +(14.7806 - 5.70337i) q^{76} +(-4.05583 - 0.714920i) q^{77} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 + 1.66547i) q^{79} +(-4.63270 + 2.38090i) q^{80} +(4.48574 + 7.76954i) q^{81} +(-7.72121 - 6.94001i) q^{82} +(8.82731 - 8.82731i) q^{83} +(-0.297188 - 0.0202433i) q^{84} +(2.70543 + 2.70543i) q^{85} +(-3.98217 + 0.212184i) q^{86} +(-0.142188 + 0.0820924i) q^{87} +(3.41427 - 2.77967i) q^{88} +(11.5526 + 6.66987i) q^{89} +(-4.62586 + 3.00981i) q^{90} +(4.57521 + 3.83862i) q^{91} +(-3.66566 + 8.27206i) q^{92} +(0.0915056 + 0.341503i) q^{93} +(-0.858354 - 2.63391i) q^{94} +(5.15752 + 8.93309i) q^{95} +(0.224188 - 0.226154i) q^{96} -9.69578 q^{97} +(-5.23767 + 8.40041i) q^{98} +(3.29854 - 3.29854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24} - 10 q^{26} - 24 q^{27} - 10 q^{28} + 24 q^{29} - 4 q^{30} + 28 q^{31} + 16 q^{32} + 16 q^{33} - 44 q^{34} + 28 q^{35} - 72 q^{36} - 24 q^{37} + 20 q^{38} + 26 q^{40} + 6 q^{42} - 40 q^{43} + 6 q^{44} - 28 q^{45} - 14 q^{46} - 20 q^{47} + 56 q^{48} + 56 q^{50} + 24 q^{51} - 16 q^{52} - 16 q^{53} + 64 q^{54} + 40 q^{56} - 6 q^{58} - 20 q^{59} + 46 q^{60} + 8 q^{61} + 24 q^{62} - 16 q^{63} + 80 q^{64} + 8 q^{65} - 20 q^{66} + 48 q^{67} - 40 q^{69} + 82 q^{70} - 32 q^{72} - 8 q^{74} - 4 q^{75} - 36 q^{76} - 20 q^{77} + 116 q^{78} - 36 q^{79} - 28 q^{80} + 2 q^{82} - 8 q^{83} + 28 q^{84} - 20 q^{86} - 42 q^{88} - 20 q^{90} + 64 q^{91} + 76 q^{92} + 8 q^{93} - 72 q^{94} - 4 q^{95} - 120 q^{96} - 48 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Introduction

L-functions

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