LMFDB - Embedded newform 112.2.w.c.53.8

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			53.8
Character	$\chi$	$=$	112.53
Dual form			112.2.w.c.93.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438190 + 1.34461i) q^{2} +(0.0145698 + 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(-0.337028 + 1.25781i) q^{5} +(-0.0667293 + 0.0434174i) q^{6} +(-0.230738 + 2.63567i) q^{7} +(-2.29259 - 1.65651i) q^{8} +(2.59533 - 1.49842i) q^{9} +O(q^{10})$	\(q+(0.438190 + 1.34461i) q^{2} +(0.0145698 + 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(-0.337028 + 1.25781i) 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} +(-1.83895 + 0.0979855i) q^{10} +(1.50355 - 0.402875i) q^{11} +(-0.0876199 - 0.0707001i) q^{12} +(1.59615 - 1.59615i) q^{13} +(-3.64507 + 0.844671i) q^{14} -0.0733039 q^{15} +(1.22277 - 3.80852i) q^{16} +(1.46910 - 2.54455i) q^{17} +(3.15204 + 2.83313i) q^{18} +(-7.65147 - 2.05021i) q^{19} +(-0.937562 - 2.42974i) q^{20} +(-0.146677 + 0.0258547i) q^{21} +(1.20055 + 1.84516i) q^{22} +(3.91784 - 2.26197i) q^{23} +(0.0566703 - 0.148795i) q^{24} +(2.86164 + 1.65217i) q^{25} +(2.84562 + 1.44679i) q^{26} +(0.238706 + 0.238706i) q^{27} +(-2.73299 - 4.53109i) q^{28} +(2.06234 - 2.06234i) q^{29} +(-0.0321210 - 0.0985654i) q^{30} +(-3.14025 + 5.43908i) q^{31} +(5.65680 - 0.0246987i) q^{32} +(0.0438128 + 0.0758861i) q^{33} +(4.06519 + 0.860373i) q^{34} +(-3.23740 - 1.17852i) q^{35} +(-2.42828 + 5.47973i) q^{36} +(-1.40616 + 5.24787i) q^{37} +(-0.596064 - 11.1867i) q^{38} +(0.110046 + 0.0635352i) q^{39} +(2.85623 - 2.32535i) q^{40} -7.34101i q^{41} +(-0.0990370 - 0.185895i) q^{42} +(-1.99391 - 1.99391i) q^{43} +(-1.95496 + 2.42282i) q^{44} +(1.01002 + 3.76943i) q^{45} +(4.75824 + 4.27682i) 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} +(0.159765 + 0.0428089i) q^{51} +(-0.698448 + 4.46023i) q^{52} +(-11.2146 + 3.00493i) q^{53} +(-0.216369 + 0.425567i) q^{54} +2.02696i q^{55} +(4.89500 - 5.66030i) q^{56} -0.445921i q^{57} +(3.67676 + 1.86936i) q^{58} +(-2.96105 + 0.793411i) q^{59} +(0.118457 - 0.0863809i) q^{60} +(-9.72123 - 2.60480i) 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} +(-0.0828392 + 0.0921640i) q^{66} +(0.566758 + 2.11517i) q^{67} +(0.624456 + 5.84312i) q^{68} +(0.180077 + 0.180077i) q^{69} +(0.166059 - 4.86947i) q^{70} -7.26378i q^{71} +(-8.43218 - 0.863930i) q^{72} +(12.2392 + 7.06631i) q^{73} +(-7.67253 + 0.408819i) q^{74} +(-0.0481435 + 0.179674i) q^{75} +(14.7806 - 5.70337i) q^{76} +(0.714920 + 4.05583i) q^{77} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 - 1.66547i) q^{79} +(4.37827 + 2.82159i) q^{80} +(4.48574 - 7.76954i) q^{81} +(9.87083 - 3.21676i) q^{82} +(8.82731 - 8.82731i) q^{83} +(0.206560 - 0.214624i) q^{84} +(2.70543 + 2.70543i) q^{85} +(1.80733 - 3.55475i) q^{86} +(0.142188 + 0.0820924i) q^{87} +(-4.11440 - 1.56702i) q^{88} +(-11.5526 + 6.66987i) q^{89} +(-4.62586 + 3.00981i) q^{90} +(3.83862 + 4.57521i) q^{91} +(-3.66566 + 8.27206i) q^{92} +(-0.341503 - 0.0915056i) q^{93} +(-1.85186 + 2.06031i) q^{94} +(5.15752 - 8.93309i) q^{95} +(0.0837613 + 0.307230i) q^{96} -9.69578 q^{97} +(-1.38522 - 9.80210i) 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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.438190	+	1.34461i	0.309847	+	0.950786i
$2$	0.438190	+	1.34461i	0.309847	+	0.950786i
$3$	0.0145698	+	0.0543752i	0.00841187	+	0.0313935i	0.970004	−	0.243088i	$-0.0781604\pi$
$3$	0.0145698	+	0.0543752i	0.00841187	+	0.0313935i	−0.961592	+	0.274482i	$0.911494\pi$
$4$	−1.61598	+	1.17839i	−0.807989	+	0.589197i
$5$	−0.337028	+	1.25781i	−0.150724	+	0.562508i	0.848710	+	0.528858i	$0.177380\pi$
$5$	−0.337028	+	1.25781i	−0.150724	+	0.562508i	−0.999434	+	0.0336497i	$0.989287\pi$
$6$	−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
$10$	−1.83895	+	0.0979855i	−0.581526	+	0.0309857i
$11$	1.50355	−	0.402875i	0.453338	−	0.121472i	−0.0249229	−	0.999689i	$-0.507934\pi$
$11$	1.50355	−	0.402875i	0.453338	−	0.121472i	0.478261	+	0.878218i	$0.341267\pi$
$12$	−0.0876199	−	0.0707001i	−0.0252937	−	0.0204094i
$13$	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	$0.148656\pi$
$14$	−3.64507	+	0.844671i	−0.974186	+	0.225748i
$15$	−0.0733039			−0.0189270
$16$	1.22277	−	3.80852i	0.305693	−	0.952130i
$17$	1.46910	−	2.54455i	0.356309	−	0.617145i	−0.631032	−	0.775757i	$-0.717368\pi$
$17$	1.46910	−	2.54455i	0.356309	−	0.617145i	0.987341	+	0.158612i	$0.0507018\pi$
$18$	3.15204	+	2.83313i	0.742943	+	0.667775i
$19$	−7.65147	−	2.05021i	−1.75537	−	0.470350i	−0.769610	−	0.638514i	$-0.779549\pi$
$19$	−7.65147	−	2.05021i	−1.75537	−	0.470350i	−0.985759	+	0.168165i	$0.946216\pi$
$20$	−0.937562	−	2.42974i	−0.209645	−	0.543306i
$21$	−0.146677	+	0.0258547i	−0.0320075	+	0.00564196i
$22$	1.20055	+	1.84516i	0.255959	+	0.393390i
$23$	3.91784	−	2.26197i	0.816927	−	0.471653i	−0.0324286	−	0.999474i	$-0.510324\pi$
$23$	3.91784	−	2.26197i	0.816927	−	0.471653i	0.849356	+	0.527821i	$0.176991\pi$
$24$	0.0566703	−	0.148795i	0.0115678	−	0.0303727i
$25$	2.86164	+	1.65217i	0.572328	+	0.330434i
$26$	2.84562	+	1.44679i	0.558072	+	0.283738i
$27$	0.238706	+	0.238706i	0.0459390	+	0.0459390i
$28$	−2.73299	−	4.53109i	−0.516487	−	0.856295i
$29$	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	$0.162712\pi$
$30$	−0.0321210	−	0.0985654i	−0.00586447	−	0.0179955i
$31$	−3.14025	+	5.43908i	−0.564006	+	0.976887i	0.433136	+	0.901329i	$0.357407\pi$
$31$	−3.14025	+	5.43908i	−0.564006	+	0.976887i	−0.997141	+	0.0755580i	$0.975926\pi$
$32$	5.65680	−	0.0246987i	0.999990	−	0.00436615i
$33$	0.0438128	+	0.0758861i	0.00762684	+	0.0132101i
$34$	4.06519	+	0.860373i	0.697174	+	0.147553i
$35$	−3.23740	−	1.17852i	−0.547220	−	0.199206i
$36$	−2.42828	+	5.47973i	−0.404713	+	0.913289i
$37$	−1.40616	+	5.24787i	−0.231172	+	0.862745i	0.748666	+	0.662948i	$0.230695\pi$
$37$	−1.40616	+	5.24787i	−0.231172	+	0.862745i	−0.979837	+	0.199797i	$0.935972\pi$
$38$	−0.596064	−	11.1867i	−0.0966944	−	1.81472i
$39$	0.110046	+	0.0635352i	0.0176215	+	0.0101738i
$40$	2.85623	−	2.32535i	0.451610	−	0.367670i
$41$		−	7.34101i		−	1.14647i	−0.819390	−	0.573236i	$-0.805688\pi$
$41$		−	7.34101i		−	1.14647i	0.819390	−	0.573236i	$-0.194312\pi$
$42$	−0.0990370	−	0.185895i	−0.0152817	−	0.0286842i
$43$	−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	$0.818978\pi$
$44$	−1.95496	+	2.42282i	−0.294721	+	0.365253i
$45$	1.01002	+	3.76943i	0.150564	+	0.561914i
$46$	4.75824	+	4.27682i	0.701564	+	0.630583i
$47$	0.979430	+	1.69642i	0.142865	+	0.247449i	0.928574	−	0.371147i	$-0.121035\pi$
$47$	0.979430	+	1.69642i	0.142865	+	0.247449i	−0.785710	+	0.618596i	$0.787702\pi$
$48$	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
$51$	0.159765	+	0.0428089i	0.0223716	+	0.00599444i
$52$	−0.698448	+	4.46023i	−0.0968573	+	0.618523i
$53$	−11.2146	+	3.00493i	−1.54044	+	0.412759i	−0.926408	−	0.376522i	$-0.877120\pi$
$53$	−11.2146	+	3.00493i	−1.54044	+	0.412759i	−0.614031	+	0.789282i	$0.710453\pi$
$54$	−0.216369	+	0.425567i	−0.0294441	+	0.0579123i
$55$			2.02696i			0.273315i
$56$	4.89500	−	5.66030i	0.654122	−	0.756389i
$57$		−	0.445921i		−	0.0590637i
$58$	3.67676	+	1.86936i	0.482782	+	0.245459i
$59$	−2.96105	+	0.793411i	−0.385496	+	0.103293i	−0.446362	−	0.894853i	$-0.647281\pi$
$59$	−2.96105	+	0.793411i	−0.385496	+	0.103293i	0.0608657	+	0.998146i	$0.480614\pi$
$60$	0.118457	−	0.0863809i	0.0152928	−	0.0111517i
$61$	−9.72123	−	2.60480i	−1.24468	−	0.333510i	−0.424398	−	0.905476i	$-0.639514\pi$
$61$	−9.72123	−	2.60480i	−1.24468	−	0.333510i	−0.820277	+	0.571966i	$0.806181\pi$
$62$	−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
$66$	−0.0828392	+	0.0921640i	−0.0101968	+	0.0113446i
$67$	0.566758	+	2.11517i	0.0692405	+	0.258409i	0.991866	−	0.127289i	$-0.0406274\pi$
$67$	0.566758	+	2.11517i	0.0692405	+	0.258409i	−0.922625	+	0.385698i	$0.873961\pi$
$68$	0.624456	+	5.84312i	0.0757264	+	0.708583i
$69$	0.180077	+	0.180077i	0.0216787	+	0.0216787i
$70$	0.166059	−	4.86947i	0.0198478	−	0.582013i
$71$		−	7.26378i		−	0.862052i	−0.902340	−	0.431026i	$-0.858152\pi$
$71$		−	7.26378i		−	0.862052i	0.902340	−	0.431026i	$-0.141848\pi$
$72$	−8.43218	−	0.863930i	−0.993742	−	0.101815i
$73$	12.2392	+	7.06631i	1.43249	+	0.827049i	0.997310	−	0.0732936i	$-0.0233510\pi$
$73$	12.2392	+	7.06631i	1.43249	+	0.827049i	0.435181	+	0.900343i	$0.356684\pi$
$74$	−7.67253	+	0.408819i	−0.891914	+	0.0475242i
$75$	−0.0481435	+	0.179674i	−0.00555913	+	0.0207469i
$76$	14.7806	−	5.70337i	1.69545	−	0.654221i
$77$	0.714920	+	4.05583i	0.0814727	+	0.462204i
$78$	−0.0372092	+	0.175810i	−0.00421311	+	0.0199066i
$79$	−0.961559	−	1.66547i	−0.108184	−	0.187380i	0.806851	−	0.590755i	$-0.201170\pi$
$79$	−0.961559	−	1.66547i	−0.108184	−	0.187380i	−0.915035	+	0.403376i	$0.867837\pi$
$80$	4.37827	+	2.82159i	0.489506	+	0.315463i
$81$	4.48574	−	7.76954i	0.498416	−	0.863282i
$82$	9.87083	−	3.21676i	1.09005	−	0.355231i
$83$	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	$0.00974454\pi$
$84$	0.206560	−	0.214624i	0.0225375	−	0.0234174i
$85$	2.70543	+	2.70543i	0.293445	+	0.293445i
$86$	1.80733	−	3.55475i	0.194889	−	0.383318i
$87$	0.142188	+	0.0820924i	0.0152442	+	0.00880123i
$88$	−4.11440	−	1.56702i	−0.438596	−	0.167044i
$89$	−11.5526	+	6.66987i	−1.22457	+	0.707005i	−0.965888	−	0.258959i	$-0.916621\pi$
$89$	−11.5526	+	6.66987i	−1.22457	+	0.707005i	−0.258680	+	0.965963i	$0.583287\pi$
$90$	−4.62586	+	3.00981i	−0.487608	+	0.317262i
$91$	3.83862	+	4.57521i	0.402397	+	0.479612i
$92$	−3.66566	+	8.27206i	−0.382172	+	0.862422i
$93$	−0.341503	−	0.0915056i	−0.0354123	−	0.00948869i
$94$	−1.85186	+	2.06031i	−0.191005	+	0.212505i
$95$	5.15752	−	8.93309i	0.529151	−	0.916516i
$96$	0.0837613	+	0.307230i	0.00854886	+	0.0313565i
$97$	−9.69578			−0.984458			−0.492229	−	0.870466i	$-0.663818\pi$
$97$	−9.69578			−0.984458			−0.492229	+	0.870466i	$0.663818\pi$
$98$	−1.38522	−	9.80210i	−0.139928	−	0.990162i
$99$	3.29854	−	3.29854i	0.331516	−	0.331516i
$100$	−6.57125	+	0.702272i	−0.657125	+	0.0702272i
$101$	10.2081	−	2.73526i	1.01575	−	0.272168i	0.287718	−	0.957715i	$-0.407103\pi$
$101$	10.2081	−	2.73526i	1.01575	−	0.272168i	0.728029	+	0.685547i	$0.240437\pi$
$102$	0.0124460	+	0.233581i	0.00123234	+	0.0231279i
$103$	2.96542	−	1.71209i	0.292192	−	0.168697i	−0.346738	−	0.937962i	$-0.612711\pi$
$103$	2.96542	−	1.71209i	0.292192	−	0.168697i	0.638930	+	0.769265i	$0.279377\pi$
$104$	−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
$107$	2.96534	−	11.0668i	0.286670	−	1.06987i	−0.660940	−	0.750439i	$-0.729842\pi$
$107$	2.96534	−	11.0668i	0.286670	−	1.06987i	0.947610	−	0.319429i	$-0.103491\pi$
$108$	−0.667034	−	0.104454i	−0.0641854	−	0.0100511i
$109$	−0.811511	−	3.02860i	−0.0777287	−	0.290087i	0.916110	−	0.400928i	$-0.131312\pi$
$109$	−0.811511	−	3.02860i	−0.0777287	−	0.290087i	−0.993838	+	0.110841i	$0.964646\pi$
$110$	−2.72548	+	0.888193i	−0.259864	+	0.0846859i
$111$	−0.305841			−0.0290292
$112$	9.75586	+	4.10160i	0.921843	+	0.387565i
$113$	4.67963			0.440223			0.220111	−	0.975475i	$-0.429358\pi$
$113$	4.67963			0.440223			0.220111	+	0.975475i	$0.429358\pi$
$114$	0.599592	−	0.195398i	0.0561570	−	0.0183007i
$115$	1.52469	+	5.69024i	0.142178	+	0.530617i
$116$	−0.902448	+	5.76296i	−0.0837902	+	0.535077i
$117$	1.75084	−	6.53422i	0.161865	−	0.604089i
$118$	−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
$122$	−0.757302	−	14.2127i	−0.0685629	−	1.28676i
$123$	0.399168	−	0.106957i	0.0359918	−	0.00964398i
$124$	−1.33480	−	12.4899i	−0.119868	−	1.12162i
$125$	−7.64645	+	7.64645i	−0.683919	+	0.683919i
$126$	−8.19450	+	7.65403i	−0.730024	+	0.681875i
$127$	5.63308			0.499855			0.249928	−	0.968265i	$-0.419593\pi$
$127$	5.63308			0.499855			0.249928	+	0.968265i	$0.419593\pi$
$128$	−9.11216	+	6.70586i	−0.805409	+	0.592719i
$129$	0.0793683	−	0.137470i	0.00698799	−	0.0121035i
$130$	−2.77883	+	3.09163i	−0.243720	+	0.271154i
$131$	−2.00524	−	0.537304i	−0.175199	−	0.0469444i	0.170153	−	0.985418i	$-0.445574\pi$
$131$	−2.00524	−	0.537304i	−0.175199	−	0.0469444i	−0.345352	+	0.938473i	$0.612240\pi$
$132$	−0.160224	−	0.0710014i	−0.0139457	−	0.00617988i
$133$	7.16916	−	19.6937i	0.621645	−	1.70766i
$134$	−2.59574	+	1.68892i	−0.224238	+	0.145900i
$135$	−0.380697	+	0.219795i	−0.0327652	+	0.0189170i
$136$	−7.58312	+	3.40005i	−0.650247	+	0.291552i
$137$	−2.68685	−	1.55125i	−0.229553	−	0.132532i	0.380813	−	0.924652i	$-0.375644\pi$
$137$	−2.68685	−	1.55125i	−0.229553	−	0.132532i	−0.610366	+	0.792120i	$0.708978\pi$
$138$	−0.163226	+	0.321042i	−0.0138947	+	0.0273289i
$139$	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	$0.473035\pi$
$140$	6.62033	−	1.91047i	0.559520	−	0.161464i
$141$	−0.0779732	+	0.0779732i	−0.00656653	+	0.00656653i
$142$	9.76698	−	3.18292i	0.819627	−	0.267104i
$143$	1.75684	−	3.04294i	0.146914	−	0.254463i
$144$	−2.53325	−	11.7166i	−0.211104	−	0.976383i
$145$	1.89896	+	3.28910i	0.157700	+	0.273145i
$146$	−4.13836	+	19.5534i	−0.342493	+	1.61825i
$147$	−0.0343005	−	0.392558i	−0.00282906	−	0.0323776i
$148$	−3.91173	−	10.1375i	−0.321543	−	0.833294i
$149$	−3.89339	+	14.5303i	−0.318959	+	1.19037i	0.601288	+	0.799032i	$0.294654\pi$
$149$	−3.89339	+	14.5303i	−0.318959	+	1.19037i	−0.920247	+	0.391338i	$0.872012\pi$
$150$	−0.262688	+	0.0139969i	−0.0214484	+	0.00114284i
$151$	−15.7545	−	9.09588i	−1.28209	−	0.740212i	−0.304856	−	0.952398i	$-0.598608\pi$
$151$	−15.7545	−	9.09588i	−1.28209	−	0.740212i	−0.977229	+	0.212186i	$0.931942\pi$
$152$	14.1455	+	17.3750i	1.14735	+	1.40930i
$153$		−	8.80528i		−	0.711865i
$154$	−5.14025	+	2.73852i	−0.414213	+	0.220676i
$155$	−5.78295	−	5.78295i	−0.464498	−	0.464498i
$156$	−0.252702	+	0.0270063i	−0.0202323	+	0.00216224i
$157$	−2.51651	−	9.39175i	−0.200840	−	0.749544i	−0.990678	−	0.136228i	$-0.956502\pi$
$157$	−2.51651	−	9.39175i	−0.200840	−	0.749544i	0.789838	−	0.613316i	$-0.210165\pi$
$158$	1.81807	−	2.02272i	0.144638	−	0.160919i
$159$	−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
$163$	12.5602	+	3.36548i	0.983787	+	0.263605i	0.714639	−	0.699494i	$-0.246591\pi$
$163$	12.5602	+	3.36548i	0.983787	+	0.263605i	0.269148	+	0.963099i	$0.413258\pi$
$164$	8.65060	+	11.8629i	0.675498	+	0.926337i
$165$	−0.110216	+	0.0295323i	−0.00858031	+	0.00229909i
$166$	15.7374	+	8.00129i	1.22146	+	0.621020i
$167$			16.5417i			1.28004i	0.768360	+	0.640018i	$0.221073\pi$
$167$			16.5417i			1.28004i	−0.768360	+	0.640018i	$0.778927\pi$
$168$	0.379099	+	0.183697i	0.0292481	+	0.0141725i
$169$			7.90463i			0.608049i
$170$	−2.45227	+	4.82325i	−0.188080	+	0.369926i
$171$	−22.9302	+	6.14412i	−1.75351	+	0.469853i
$172$	5.57172	+	0.872502i	0.424840	+	0.0665276i
$173$	20.8703	+	5.59219i	1.58674	+	0.425166i	0.941005	−	0.338393i	$-0.109883\pi$
$173$	20.8703	+	5.59219i	1.58674	+	0.425166i	0.645738	+	0.763559i	$0.276550\pi$
$174$	−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
$178$	−14.0306	−	12.6111i	−1.05164	−	0.945239i
$179$	4.91053	+	18.3264i	0.367031	+	1.36978i	0.864647	+	0.502379i	$0.167542\pi$
$179$	4.91053	+	18.3264i	0.367031	+	1.36978i	−0.497617	+	0.867397i	$0.665791\pi$
$180$	−6.07404	−	4.90112i	−0.452732	−	0.365308i
$181$	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	$0.640048\pi$
$182$	−4.46985	+	7.16628i	−0.331327	+	0.531200i
$183$		−	0.566545i		−	0.0418802i
$184$	−12.7290	−	1.30417i	−0.938394	−	0.0961444i
$185$	−6.12689	−	3.53736i	−0.450458	−	0.260072i
$186$	−0.0266038	−	0.499287i	−0.00195068	−	0.0366095i
$187$	1.18373	−	4.41773i	0.0865627	−	0.323057i
$188$	−3.58179	−	1.58723i	−0.261229	−	0.115760i
$189$	−0.684230	+	0.574072i	−0.0497704	+	0.0417576i
$190$	14.2716	+	3.02049i	1.03537	+	0.219129i
$191$	−12.9567	−	22.4417i	−0.937515	−	1.62382i	−0.770086	−	0.637940i	$-0.779787\pi$
$191$	−12.9567	−	22.4417i	−0.937515	−	1.62382i	−0.167429	−	0.985884i	$-0.553546\pi$
$192$	−0.376402	+	0.247252i	−0.0271645	+	0.0178439i
$193$	−6.27389	+	10.8667i	−0.451604	+	0.782202i	−0.998486	−	0.0550082i	$-0.982481\pi$
$193$	−6.27389	+	10.8667i	−0.451604	+	0.782202i	0.546881	+	0.837210i	$0.315815\pi$
$194$	−4.24860	−	13.0371i	−0.305032	−	0.936009i
$195$	−0.117004	+	0.117004i	−0.00837881	+	0.00837881i
$196$	12.5731	−	6.15777i	0.898076	−	0.439841i
$197$	−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	$0.887612\pi$
$198$	5.88066	+	2.98988i	0.417920	+	0.212481i
$199$	−16.6783	−	9.62922i	−1.18229	−	0.682597i	−0.225749	−	0.974186i	$-0.572483\pi$
$199$	−16.6783	−	9.62922i	−1.18229	−	0.682597i	−0.956544	+	0.291589i	$0.905816\pi$
$200$	−3.82374	−	8.52807i	−0.270380	−	0.603026i
$201$	−0.106755	+	0.0616352i	−0.00752993	+	0.00434741i
$202$	8.15097	+	12.5274i	0.573501	+	0.881427i
$203$	4.95980	+	5.91152i	0.348109	+	0.414907i
$204$	−0.308623	+	0.119088i	−0.0216079	+	0.00833782i
$205$	9.23356	+	2.47413i	0.644900	+	0.172800i
$206$	3.60151	+	3.23713i	0.250929	+	0.225541i
$207$	6.77874	−	11.7411i	0.471155	−	0.816064i
$208$	−4.12723	−	8.03068i	−0.286172	−	0.556828i
$209$	−12.3304			−0.852909
$210$	0.267198	−	0.0619176i	0.0184384	−	0.00427272i
$211$	−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	$0.387873\pi$
$212$	14.5815	−	18.0711i	1.00146	−	1.24113i
$213$	0.394969	−	0.105832i	0.0270628	−	0.00725147i
$214$	16.1800	−	0.862124i	1.10604	−	0.0589336i
$215$	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
$219$	−0.205909	+	0.768464i	−0.0139141	+	0.0519280i
$220$	−2.38856	−	3.27552i	−0.161036	−	0.220835i
$221$	−1.71658	−	6.40638i	−0.115470	−	0.430940i
$222$	−0.134017	−	0.411239i	−0.00899461	−	0.0276005i
$223$	−22.4402			−1.50271			−0.751354	−	0.659899i	$-0.770599\pi$
$223$	−22.4402			−1.50271			−0.751354	+	0.659899i	$0.770599\pi$
$224$	−1.24014	+	14.9152i	−0.0828606	+	0.996561i
$225$	9.90254			0.660169
$226$	2.05057	+	6.29230i	0.136402	+	0.418558i
$227$	0.605377	+	2.25930i	0.0401803	+	0.149955i	0.983102	−	0.183061i	$-0.0586005\pi$
$227$	0.605377	+	2.25930i	0.0401803	+	0.149955i	−0.942921	+	0.333016i	$0.891934\pi$
$228$	0.525471	+	0.720599i	0.0348002	+	0.0477229i
$229$	5.08653	−	18.9832i	0.336127	−	1.25444i	−0.566514	−	0.824052i	$-0.691708\pi$
$229$	5.08653	−	18.9832i	0.336127	−	1.25444i	0.902642	−	0.430393i	$-0.141625\pi$
$230$	−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	$-0.626163\pi$
$233$	3.35515	−	1.93710i	0.219803	−	0.126903i	0.605859	+	0.795572i	$0.292829\pi$
$234$	9.55321	−	0.509028i	0.624513	−	0.0332762i
$235$	−2.46387	+	0.660191i	−0.160725	+	0.0430661i
$236$	3.85004	−	4.77142i	0.250616	−	0.310593i
$237$	0.0765505	−	0.0765505i	0.00497249	−	0.00497249i
$238$	−3.20566	+	10.5160i	−0.207792	+	0.681650i
$239$	−6.56774			−0.424832			−0.212416	−	0.977179i	$-0.568133\pi$
$239$	−6.56774			−0.424832			−0.212416	+	0.977179i	$0.568133\pi$
$240$	−0.0896339	+	0.279179i	−0.00578585	+	0.0180209i
$241$	6.62647	−	11.4774i	0.426849	−	0.739323i	−0.569742	−	0.821823i	$-0.692957\pi$
$241$	6.62647	−	11.4774i	0.426849	−	0.739323i	0.996591	+	0.0824998i	$0.0262904\pi$
$242$	−9.02124	−	8.10851i	−0.579907	−	0.521235i
$243$	1.46606	+	0.392830i	0.0940479	+	0.0252001i
$244$	18.7788	−	7.24615i	1.20219	−	0.463887i
$245$	3.85318	−	8.26078i	0.246171	−	0.527762i
$246$	0.318728	+	0.489860i	0.0203213	+	0.0312324i
$247$	−15.4853	+	8.94045i	−0.985306	+	0.568867i
$248$	16.2092	−	7.26774i	1.02928	−	0.461502i
$249$	0.608598	+	0.351374i	0.0385683	+	0.0222674i
$250$	−13.6321	−	6.93093i	−0.862172	−	0.438350i
$251$	−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	$0.804380\pi$
$252$	−13.8825	−	7.66452i	−0.874514	−	0.482819i
$253$	4.97939	−	4.97939i	0.313052	−	0.313052i
$254$	2.46836	+	7.57433i	0.154879	+	0.475256i
$255$	−0.107691	+	0.186526i	−0.00674385	+	0.0116807i
$256$	−13.0097	−	9.31391i	−0.813103	−	0.582119i
$257$	11.8190	+	20.4712i	0.737251	+	1.27696i	0.953729	+	0.300669i	$0.0972099\pi$
$257$	11.8190	+	20.4712i	0.737251	+	1.27696i	−0.216477	+	0.976288i	$0.569457\pi$
$258$	0.219622	+	0.0464818i	0.0136731	+	0.00289383i
$259$	−13.5072	−	4.91707i	−0.839297	−	0.305532i
$260$	−5.37471	−	2.38174i	−0.333325	−	0.147709i
$261$	2.26222	−	8.44271i	0.140028	−	0.522591i
$262$	−0.156212	−	2.93172i	−0.00965083	−	0.181122i
$263$	15.4301	+	8.90857i	0.951460	+	0.549326i	0.893534	−	0.448995i	$-0.148218\pi$
$263$	15.4301	+	8.90857i	0.951460	+	0.549326i	0.0579260	+	0.998321i	$0.481551\pi$
$264$	0.0252608	−	0.246552i	0.00155470	−	0.0151742i
$265$		−	15.1185i		−	0.928722i
$266$	29.6219	+	1.01017i	1.81624	+	0.0619372i
$267$	−0.530993	−	0.530993i	−0.0324963	−	0.0324963i
$268$	−3.40837	−	2.75021i	−0.208200	−	0.167996i
$269$	1.65252	+	6.16728i	0.100756	+	0.376026i	0.997829	−	0.0658559i	$-0.0209778\pi$
$269$	1.65252	+	6.16728i	0.100756	+	0.376026i	−0.897073	+	0.441882i	$0.854311\pi$
$270$	−0.462358	−	0.415578i	−0.0281382	−	0.0252913i
$271$	3.98703	+	6.90574i	0.242195	+	0.419494i	0.961339	−	0.275367i	$-0.0887993\pi$
$271$	3.98703	+	6.90574i	0.242195	+	0.419494i	−0.719144	+	0.694861i	$0.755466\pi$
$272$	−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
$275$	4.96824	+	1.33124i	0.299596	+	0.0802765i
$276$	−0.503202	−	0.0787988i	−0.0302892	−	0.00474313i
$277$	−12.3757	+	3.31607i	−0.743586	+	0.199243i	−0.610671	−	0.791884i	$-0.709100\pi$
$277$	−12.3757	+	3.31607i	−0.743586	+	0.199243i	−0.132915	+	0.991127i	$0.542434\pi$
$278$	−11.5525	+	22.7220i	−0.692871	+	1.36278i
$279$			18.8216i			1.12682i
$280$	5.46981	+	8.06464i	0.326884	+	0.481954i
$281$			13.0438i			0.778126i	0.921211	+	0.389063i	$0.127201\pi$
$281$			13.0438i			0.778126i	−0.921211	+	0.389063i	$0.872799\pi$
$282$	−0.139011	−	0.0706768i	−0.00827799	−	0.00420874i
$283$	18.6171	−	4.98843i	1.10667	−	0.296531i	0.341192	−	0.939994i	$-0.389169\pi$
$283$	18.6171	−	4.98843i	1.10667	−	0.296531i	0.765478	+	0.643462i	$0.222503\pi$
$284$	8.55960	+	11.7381i	0.507919	+	0.696529i
$285$	0.560883	+	0.150288i	0.0332238	+	0.00890229i
$286$	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
$290$	−3.59046	+	3.99462i	−0.210839	+	0.234572i
$291$	−0.141265	−	0.527210i	−0.00828113	−	0.0309056i
$292$	−28.1052	+	3.00361i	−1.64473	+	0.175773i
$293$	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	$0.574170\pi$
$294$	0.512809	−	0.218136i	0.0299076	−	0.0127219i
$295$		−	3.99183i		−	0.232413i
$296$	11.9169	−	9.70191i	0.692655	−	0.563912i
$297$	0.455076	+	0.262738i	0.0264062	+	0.0152456i
$298$	−21.2437	+	1.13194i	−1.23062	+	0.0655715i
$299$	2.64302	−	9.86389i	0.152850	−	0.570443i
$300$	−0.133928	−	0.347081i	−0.00773233	−	0.0200387i
$301$	5.71536	−	4.79521i	0.329428	−	0.276391i
$302$	5.32697	−	25.1695i	0.306533	−	1.44834i
$303$	0.297460	+	0.515217i	0.0170887	+	0.0295984i
$304$	−17.1643	+	26.6339i	−0.984438	+	1.52756i
$305$	6.55265	−	11.3495i	0.375204	−	0.649872i
$306$	11.8397	−	3.85839i	0.676831	−	0.220569i
$307$	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	$0.0345873\pi$
$308$	−5.93466	−	5.71167i	−0.338159	−	0.325453i
$309$	0.136300	+	0.136300i	0.00775386	+	0.00775386i
$310$	5.24181	−	10.3099i	0.297715	−	0.585561i
$311$	−3.14576	−	1.81621i	−0.178380	−	0.102988i	0.408151	−	0.912914i	$-0.366174\pi$
$311$	−3.14576	−	1.81621i	−0.178380	−	0.102988i	−0.586531	+	0.809927i	$0.699507\pi$
$312$	−0.147045	−	0.327953i	−0.00832477	−	0.0185667i
$313$	−3.24479	+	1.87338i	−0.183406	+	0.105890i	−0.588892	−	0.808212i	$-0.700436\pi$
$313$	−3.24479	+	1.87338i	−0.183406	+	0.105890i	0.405486	+	0.914101i	$0.367102\pi$
$314$	11.5256	−	7.49912i	0.650426	−	0.423200i
$315$	−10.1680	+	1.79232i	−0.572904	+	0.100986i
$316$	3.51644	+	1.55827i	0.197815	+	0.0876593i
$317$	−23.7647	−	6.36774i	−1.33476	−	0.357648i	−0.480272	−	0.877119i	$-0.659462\pi$
$317$	−23.7647	−	6.36774i	−1.33476	−	0.357648i	−0.854488	+	0.519472i	$0.826129\pi$
$318$	0.617874	−	0.687425i	0.0346486	−	0.0385489i
$319$	2.26997	−	3.93171i	0.127094	−	0.220133i
$320$	−10.4001	+	0.599704i	−0.581385	+	0.0335245i
$321$	0.644963			0.0359983
$322$	−12.3702	+	11.5543i	−0.689364	+	0.643897i
$323$	−16.4576	+	16.4576i	−0.915727	+	0.915727i
$324$	1.90671	+	17.8414i	0.105929	+	0.991188i
$325$	7.20470	−	1.93049i	0.399645	−	0.107084i
$326$	0.978459	+	18.3633i	0.0541919	+	1.01705i
$327$	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
$331$	−2.62451	+	9.79479i	−0.144256	+	0.538370i	0.855532	+	0.517751i	$0.173231\pi$
$331$	−2.62451	+	9.79479i	−0.144256	+	0.538370i	−0.999787	+	0.0206195i	$0.993436\pi$
$332$	−3.86269	+	24.6668i	−0.211993	+	1.35377i
$333$	4.21403	+	15.7270i	0.230928	+	0.861833i
$334$	−22.2422	+	7.24842i	−1.21704	+	0.396616i
$335$	−2.85149			−0.155793
$336$	−0.0808843	+	0.590236i	−0.00441260	+	0.0322000i
$337$	−5.30745			−0.289115			−0.144558	−	0.989496i	$-0.546176\pi$
$337$	−5.30745			−0.289115			−0.144558	+	0.989496i	$0.546176\pi$
$338$	−10.6287	+	3.46373i	−0.578124	+	0.188402i
$339$	0.0681812	+	0.254456i	0.00370309	+	0.0138201i
$340$	−7.55997	−	1.18385i	−0.409997	−	0.0642034i
$341$	−2.53026	+	9.44306i	−0.137021	+	0.511370i
$342$	−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
$346$	1.62584	+	30.5130i	0.0874056	+	1.64039i
$347$	−3.98409	+	1.06753i	−0.213877	+	0.0573082i	−0.364166	−	0.931334i	$-0.618646\pi$
$347$	−3.98409	+	1.06753i	−0.213877	+	0.0573082i	0.150290	+	0.988642i	$0.451979\pi$
$348$	−0.326510	+	0.0348942i	−0.0175028	+	0.00187053i
$349$	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	$0.107134\pi$
$350$	−11.8264	−	3.60512i	−0.632148	−	0.192702i
$351$	0.762020			0.0406736
$352$	8.49534	−	2.31612i	0.452803	−	0.123450i
$353$	1.93371	−	3.34929i	0.102921	−	0.178265i	−0.809966	−	0.586477i	$-0.800514\pi$
$353$	1.93371	−	3.34929i	0.102921	−	0.178265i	0.912887	+	0.408212i	$0.133848\pi$
$354$	0.163141	−	0.181505i	0.00867085	−	0.00964688i
$355$	9.13642	+	2.44810i	0.484911	+	0.129932i
$356$	10.8089	−	24.3918i	0.572873	−	1.29276i
$357$	−0.149694	+	0.411210i	−0.00792265	+	0.0217636i
$358$	−22.4901	+	14.6332i	−1.18864	+	0.773389i
$359$	13.6977	−	7.90839i	0.722938	−	0.417389i	−0.0928949	−	0.995676i	$-0.529612\pi$
$359$	13.6977	−	7.90839i	0.722938	−	0.417389i	0.815833	+	0.578287i	$0.196279\pi$
$360$	3.92854	−	10.3149i	0.207052	−	0.543642i
$361$	37.8872	+	21.8742i	1.99407	+	1.15127i
$362$	−5.83939	+	11.4852i	−0.306911	+	0.603650i
$363$	−0.341412	−	0.341412i	−0.0179195	−	0.0179195i
$364$	−11.5945	−	2.87003i	−0.607719	−	0.150430i
$365$	−13.0130	+	13.0130i	−0.681132	+	0.681132i
$366$	0.761784	−	0.248254i	0.0398191	−	0.0129765i
$367$	2.37345	−	4.11093i	0.123893	−	0.214589i	−0.797407	−	0.603442i	$-0.793795\pi$
$367$	2.37345	−	4.11093i	0.123893	−	0.214589i	0.921300	+	0.388853i	$0.127129\pi$
$368$	−3.82412	−	17.6871i	−0.199346	−	0.922002i
$369$	−10.9999	−	19.0523i	−0.572631	−	0.991826i
$370$	2.07164	−	9.78834i	0.107700	−	0.508872i
$371$	−5.33238	−	30.2513i	−0.276844	−	1.57057i
$372$	0.659692	−	0.254555i	0.0342034	−	0.0131980i
$373$	−5.89711	+	22.0083i	−0.305341	+	1.13955i	0.627310	+	0.778769i	$0.284156\pi$
$373$	−5.89711	+	22.0083i	−0.305341	+	1.13955i	−0.932651	+	0.360779i	$0.882511\pi$
$374$	6.45885	−	0.344150i	0.333979	−	0.0177956i
$375$	−0.527184	−	0.304370i	−0.0272237	−	0.0157176i
$376$	0.564703	−	5.51164i	0.0291223	−	0.284241i
$377$		−	6.58360i		−	0.339073i
$378$	−1.07173	−	0.668472i	−0.0551238	−	0.0343825i
$379$	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	$0.489440\pi$
$380$	2.19226	+	20.5133i	0.112461	+	1.05231i
$381$	0.0820728	+	0.306300i	0.00420472	+	0.0156922i
$382$	24.4979	−	27.2555i	1.25342	−	1.39451i
$383$	11.7252	+	20.3087i	0.599131	+	1.03773i	0.992950	+	0.118537i	$0.0378204\pi$
$383$	11.7252	+	20.3087i	0.599131	+	1.03773i	−0.393819	+	0.919188i	$0.628846\pi$
$384$	−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
$387$	−8.16255	−	2.18715i	−0.414926	−	0.111179i
$388$	15.6682	−	11.4255i	0.795431	−	0.580040i
$389$	−10.3510	+	2.77356i	−0.524819	+	0.140625i	−0.511495	−	0.859286i	$-0.670908\pi$
$389$	−10.3510	+	2.77356i	−0.524819	+	0.140625i	−0.0133242	+	0.999911i	$0.504241\pi$
$390$	−0.208595	−	0.106055i	−0.0105626	−	0.00537030i
$391$		−	13.2922i		−	0.672216i
$392$	13.7892	+	14.2077i	0.696461	+	0.717595i
$393$		−	0.116864i		−	0.00589500i
$394$	7.53829	−	14.8267i	0.379774	−	0.746959i
$395$	2.41891	−	0.648145i	0.121709	−	0.0326117i
$396$	−1.44339	+	9.21735i	−0.0725330	+	0.463189i
$397$	−6.40226	−	1.71548i	−0.321320	−	0.0860975i	0.0945536	−	0.995520i	$-0.469858\pi$
$397$	−6.40226	−	1.71548i	−0.321320	−	0.0860975i	−0.415874	+	0.909422i	$0.636524\pi$
$398$	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	−0.924543	−	0.381077i	$-0.875553\pi$
$401$	−15.8657	−	27.4802i	−0.792294	−	1.37229i	0.132250	−	0.991216i	$-0.457780\pi$
$402$	−0.129655	−	0.116537i	−0.00646659	−	0.00581232i
$403$	3.66926	+	13.6939i	0.182779	+	0.682140i
$404$	−13.2729	+	16.4493i	−0.660351	+	0.818384i
$405$	8.26075	+	8.26075i	0.410480	+	0.410480i
$406$	−5.77538	+	9.25939i	−0.286627	+	0.459536i
$407$			8.45695i			0.419196i
$408$	−0.295363	−	0.362795i	−0.0146226	−	0.0179610i
$409$	1.11952	+	0.646353i	0.0553565	+	0.0319601i	0.527423	−	0.849603i	$-0.323158\pi$
$409$	1.11952	+	0.646353i	0.0553565	+	0.0319601i	−0.472066	+	0.881563i	$0.656492\pi$
$410$	0.719312	+	13.4997i	0.0355243	+	0.666704i
$411$	0.0452028	−	0.168699i	0.00222969	−	0.00832131i
$412$	−2.77454	+	6.26113i	−0.136692	+	0.308464i
$413$	−1.40794	−	7.98742i	−0.0692803	−	0.393035i
$414$	18.7577	+	3.96995i	0.921889	+	0.195112i
$415$	8.12799	+	14.0781i	0.398987	+	0.691066i
$416$	8.98966	−	9.06851i	0.440754	−	0.444620i
$417$	−0.507324	+	0.878710i	−0.0248437	+	0.0430306i
$418$	−5.40305	−	16.5796i	−0.264272	−	0.810935i
$419$	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	$0.0464046\pi$
$420$	0.200339	+	0.332146i	0.00977553	+	0.0162071i
$421$	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	$0.713032\pi$
$422$	−15.3717	−	7.81539i	−0.748284	−	0.380447i
$423$	5.08389	+	2.93519i	0.247187	+	0.142714i
$424$	30.6881	+	11.6879i	1.49035	+	0.567616i
$425$	8.40806	−	4.85440i	0.407851	−	0.235473i
$426$	0.315374	+	0.484707i	0.0152799	+	0.0234841i
$427$	9.10844	−	25.0209i	0.440788	−	1.21085i
$428$	8.24913	+	21.3780i	0.398737	+	1.03335i
$429$	0.191057	+	0.0511936i	0.00922432	+	0.00247165i
$430$	3.86207	+	3.47132i	0.186245	+	0.167402i
$431$	−5.58722	+	9.67735i	−0.269127	+	0.466141i	−0.968637	−	0.248482i	$-0.920068\pi$
$431$	−5.58722	+	9.67735i	−0.269127	+	0.466141i	0.699510	+	0.714623i	$0.253402\pi$
$432$	1.20100	−	0.617234i	0.0577832	−	0.0296967i
$433$	−17.3943			−0.835916			−0.417958	−	0.908466i	$-0.637254\pi$
$433$	−17.3943			−0.835916			−0.417958	+	0.908466i	$0.637254\pi$
$434$	6.85221	−	22.4783i	0.328916	−	1.07899i
$435$	−0.151178	+	0.151178i	−0.00724842	+	0.00724842i
$436$	4.88027	+	3.93787i	0.233723	+	0.188590i
$437$	−34.6148	+	9.27500i	−1.65585	+	0.443684i
$438$	−1.12352	+	0.0598648i	−0.0536836	+	0.00286045i
$439$	32.5115	−	18.7705i	1.55169	−	0.895867i	0.553683	−	0.832727i	$-0.313222\pi$
$439$	32.5115	−	18.7705i	1.55169	−	0.895867i	0.998005	−	0.0631399i	$-0.0201114\pi$
$440$	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
$443$	−1.84399	+	6.88186i	−0.0876106	+	0.326967i	−0.995796	−	0.0916015i	$-0.970801\pi$
$443$	−1.84399	+	6.88186i	−0.0876106	+	0.326967i	0.908185	+	0.418569i	$0.137468\pi$
$444$	0.494233	−	0.360402i	0.0234553	−	0.0171039i
$445$	−4.49587	−	16.7788i	−0.213125	−	0.795392i
$446$	−9.83309	−	30.1734i	−0.465610	−	1.42875i
$447$	−0.846815			−0.0400530
$448$	−20.5986	+	4.86816i	−0.973191	+	0.229999i
$449$	−7.84005			−0.369995			−0.184997	−	0.982739i	$-0.559228\pi$
$449$	−7.84005			−0.369995			−0.184997	+	0.982739i	$0.559228\pi$
$450$	4.33920	+	13.3151i	0.204552	+	0.627680i
$451$	−2.95751	−	11.0376i	−0.139264	−	0.519739i
$452$	−7.56218	+	5.51445i	−0.355695	+	0.259378i
$453$	0.265050	−	0.989180i	0.0124531	−	0.0464757i
$454$	−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	$-0.461125\pi$
$457$	22.2821	−	12.8646i	1.04231	−	0.601780i	0.920488	+	0.390771i	$0.127792\pi$
$458$	27.7539	−	1.47883i	1.29686	−	0.0691010i
$459$	0.958084	−	0.256718i	0.0447195	−	0.0119826i
$460$	−9.16922	−	7.39861i	−0.427517	−	0.344962i
$461$	−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	$0.392758\pi$
$462$	−0.223800	−	0.239603i	−0.0104121	−	0.0111473i
$463$	6.88821			0.320122			0.160061	−	0.987107i	$-0.448831\pi$
$463$	6.88821			0.320122			0.160061	+	0.987107i	$0.448831\pi$
$464$	−5.33270	−	10.3763i	−0.247564	−	0.481705i
$465$	0.230193	−	0.398705i	0.0106749	−	0.0184895i
$466$	4.07484	+	3.66257i	0.188764	+	0.169665i
$467$	−38.2159	−	10.2399i	−1.76842	−	0.473847i	−0.780025	−	0.625749i	$-0.784794\pi$
$467$	−38.2159	−	10.2399i	−1.76842	−	0.473847i	−0.988396	+	0.151902i	$0.951460\pi$
$468$	4.87057	+	12.6223i	0.225142	+	0.583468i
$469$	−5.70567	+	1.00574i	−0.263463	+	0.0464406i
$470$	−1.96735	−	3.02366i	−0.0907469	−	0.139471i
$471$	0.474013	−	0.273672i	0.0218414	−	0.0126101i
$472$	8.10278	+	3.08603i	0.372960	+	0.142046i
$473$	−3.80124	−	2.19465i	−0.174781	−	0.100910i
$474$	0.136475	+	0.0693872i	0.00626848	+	0.00318706i
$475$	−18.5085	−	18.5085i	−0.849227	−	0.849227i
$476$	−15.5446	+	0.297628i	−0.712487	+	0.0136418i
$477$	−24.6029	+	24.6029i	−1.12649	+	1.12649i
$478$	−2.87792	−	8.83109i	−0.131633	−	0.403924i
$479$	0.261991	−	0.453782i	0.0119707	−	0.0207338i	−0.859978	−	0.510331i	$-0.829523\pi$
$479$	0.261991	−	0.453782i	0.0119707	−	0.0207338i	0.871949	+	0.489597i	$0.162856\pi$
$480$	−0.414665	+	0.00181051i	−0.0189268	+	8.26379e-5i
$481$	6.13193	+	10.6208i	0.279592	+	0.484267i
$482$	18.3363	+	3.88077i	0.835197	+	0.176764i
$483$	−0.516175	+	0.433073i	−0.0234868	+	0.0197055i
$484$	6.94980	−	15.6832i	0.315900	−	0.712871i
$485$	3.26775	−	12.1954i	0.148381	−	0.553765i
$486$	0.114209	+	2.14342i	0.00518063	+	0.0972277i
$487$	−2.46586	−	1.42366i	−0.111739	−	0.0645124i	0.443089	−	0.896478i	$-0.353883\pi$
$487$	−2.46586	−	1.42366i	−0.111739	−	0.0645124i	−0.554828	+	0.831965i	$0.687216\pi$
$488$	17.9720	+	22.0750i	0.813552	+	0.999289i
$489$			0.731995i			0.0331019i
$490$	12.7960	+	1.56125i	0.578064	+	0.0705301i
$491$	−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	$0.938389\pi$
$492$	−0.519010	+	0.643218i	−0.0233988	+	0.0289985i
$493$	−2.21796	−	8.27753i	−0.0998918	−	0.372801i
$494$	−18.8070	−	16.9042i	−0.846166	−	0.760554i
$495$	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
$499$	−1.30845	−	0.350599i	−0.0585743	−	0.0156949i	0.229413	−	0.973329i	$-0.426319\pi$
$499$	−1.30845	−	0.350599i	−0.0585743	−	0.0156949i	−0.287987	+	0.957634i	$0.592986\pi$
$500$	3.34596	−	21.3670i	0.149636	−	0.955563i
$501$	−0.899458	+	0.241009i	−0.0401848	+	0.0107675i
$502$	3.45271	−	6.79098i	0.154102	−	0.303096i
$503$		−	15.4389i		−	0.688388i	−0.938899	−	0.344194i	$-0.888152\pi$
$503$		−	15.4389i		−	0.688388i	0.938899	−	0.344194i	$-0.111848\pi$
$504$	4.22266	−	22.0251i	0.188092	−	0.981076i
$505$			13.7617i			0.612388i
$506$	8.87728	+	4.51344i	0.394643	+	0.200647i
$507$	−0.429816	+	0.115169i	−0.0190888	+	0.00511482i
$508$	−9.10294	+	6.63800i	−0.403878	+	0.294513i
$509$	8.34301	+	2.23550i	0.369797	+	0.0990869i	0.438932	−	0.898520i	$-0.355357\pi$
$509$	8.34301	+	2.23550i	0.369797	+	0.0990869i	−0.0691342	+	0.997607i	$0.522024\pi$
$510$	−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
$514$	−22.3469	+	24.8623i	−0.985677	+	1.09663i
$515$	1.15404	+	4.30694i	0.0508532	+	0.189787i
$516$	0.0337363	+	0.315675i	0.00148516	+	0.0138968i
$517$	2.15607	+	2.15607i	0.0948239	+	0.0948239i
$518$	0.692836	−	20.3166i	0.0304415	−	0.892660i
$519$			1.21631i			0.0533899i
$520$	0.847372	−	8.27056i	0.0371597	−	0.362688i
$521$	−3.08690	−	1.78222i	−0.135240	−	0.0780807i	0.430854	−	0.902422i	$-0.358213\pi$
$521$	−3.08690	−	1.78222i	−0.135240	−	0.0780807i	−0.566093	+	0.824341i	$0.691546\pi$
$522$	12.3435	−	0.657703i	0.540259	−	0.0287869i
$523$	−5.23389	+	19.5332i	−0.228862	+	0.854125i	0.751958	+	0.659211i	$0.229110\pi$
$523$	−5.23389	+	19.5332i	−0.228862	+	0.854125i	−0.980820	+	0.194914i	$0.937557\pi$
$524$	3.87359	−	1.49470i	0.169218	−	0.0652962i
$525$	−0.462452	−	0.168348i	−0.0201831	−	0.00734731i
$526$	−5.21728	+	24.6512i	−0.227484	+	1.07484i
$527$	9.22668	+	15.9811i	0.401920	+	0.696147i
$528$	0.342587	−	0.0740707i	0.0149092	−	0.00322351i
$529$	−1.26700	+	2.19451i	−0.0550869	+	0.0954133i
$530$	20.3286	−	6.62478i	0.883016	−	0.287762i
$531$	−6.49605	+	6.49605i	−0.281905	+	0.281905i
$532$	11.6218	+	40.2727i	0.503867	+	1.74604i
$533$	−11.7173	−	11.7173i	−0.507534	−	0.507534i
$534$	0.481305	−	0.946658i	0.0208281	−	0.0409659i
$535$	12.9205	+	7.45964i	0.558601	+	0.322508i
$536$	2.20445	−	5.78806i	0.0952177	−	0.250006i
$537$	−0.924954	+	0.534022i	−0.0399147	+	0.0230448i
$538$	−7.56850	+	4.92444i	−0.326301	+	0.212308i
$539$	−10.8548	+	0.948458i	−0.467549	+	0.0408530i
$540$	0.356192	−	0.803796i	0.0153281	−	0.0345899i
$541$	7.11973	+	1.90773i	0.306101	+	0.0820195i	0.408600	−	0.912714i	$-0.366017\pi$
$541$	7.11973	+	1.90773i	0.306101	+	0.0820195i	−0.102499	+	0.994733i	$0.532684\pi$
$542$	−7.53849	+	8.38706i	−0.323806	+	0.360255i
$543$	−0.256435	+	0.444159i	−0.0110047	+	0.0190607i
$544$	8.24755	−	14.4303i	0.353611	−	0.618695i
$545$	4.08289			0.174892
$546$	−0.454793	−	0.138637i	−0.0194633	−	0.00593314i
$547$	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	$0.0685893\pi$
$548$	6.16987	−	0.659376i	0.263564	−	0.0281671i
$549$	−29.1329	+	7.80613i	−1.24336	+	0.333158i
$550$	0.387035	+	7.26370i	0.0165032	+	0.309725i
$551$	−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
$555$	0.103077	−	0.384689i	0.00437538	−	0.0163291i
$556$	−35.6146	−	5.57705i	−1.51039	−	0.236520i
$557$	3.86313	+	14.4174i	0.163686	+	0.610884i	0.998204	+	0.0599038i	$0.0190794\pi$
$557$	3.86313	+	14.4174i	0.163686	+	0.610884i	−0.834518	+	0.550980i	$0.814254\pi$
$558$	−25.3078	+	8.24745i	−1.07137	+	0.349142i
$559$	−6.36514			−0.269217
$560$	−8.44702	+	10.8886i	−0.356952	+	0.460129i
$561$	0.257462			0.0108700
$562$	−17.5388	+	5.71565i	−0.739831	+	0.241100i
$563$	−2.06799	−	7.71786i	−0.0871556	−	0.325269i	0.908558	−	0.417759i	$-0.137184\pi$
$563$	−2.06799	−	7.71786i	−0.0871556	−	0.325269i	−0.995714	+	0.0924895i	$0.970518\pi$
$564$	0.0341198	−	0.217886i	0.00143670	−	0.00917467i
$565$	−1.57717	+	5.88607i	−0.0663519	+	0.247629i
$566$	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	$-0.571837\pi$
$569$	12.1275	−	7.00179i	0.508409	−	0.293530i	0.732180	+	0.681112i	$0.238503\pi$
$570$	0.0436938	+	0.820026i	0.00183013	+	0.0343471i
$571$	1.82494	−	0.488992i	0.0763715	−	0.0204637i	−0.220431	−	0.975403i	$-0.570746\pi$
$571$	1.82494	−	0.488992i	0.0763715	−	0.0204637i	0.296802	+	0.954939i	$0.404080\pi$
$572$	0.746764	+	6.98757i	0.0312238	+	0.292165i
$573$	1.03149	−	1.03149i	0.0430913	−	0.0430913i
$574$	6.20074	+	26.7585i	0.258814	+	1.11688i
$575$	14.9486			0.623400
$576$	17.9004	+	15.9486i	0.745852	+	0.664525i
$577$	−8.81809	+	15.2734i	−0.367102	+	0.635839i	−0.989111	−	0.147171i	$-0.952983\pi$
$577$	−8.81809	+	15.2734i	−0.367102	+	0.635839i	0.622009	+	0.783010i	$0.286317\pi$
$578$	−7.90995	+	8.80034i	−0.329011	+	0.366046i
$579$	−0.682288	−	0.182818i	−0.0283549	−	0.00759767i
$580$	−6.94453	−	3.07738i	−0.288356	−	0.127781i
$581$	21.2291	+	25.3027i	0.880730	+	1.04973i
$582$	0.646993	−	0.420966i	0.0268187	−	0.0174496i
$583$	−15.6511	+	9.03615i	−0.648201	+	0.374239i
$584$	−16.3541	−	36.4745i	−0.676739	−	1.50933i
$585$	7.62870	+	4.40443i	0.315408	+	0.182101i
$586$	−11.5135	+	22.6454i	−0.475620	+	0.935475i
$587$	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	$0.568285\pi$
$588$	0.518017	+	0.593945i	0.0213626	+	0.0244939i
$589$	35.1788	−	35.1788i	1.44952	−	1.44952i
$590$	5.36747	−	1.74918i	0.220975	−	0.0720127i
$591$	0.331042	−	0.573382i	0.0136172	−	0.0235858i
$592$	18.2672	+	11.7724i	0.750777	+	0.483841i
$593$	−3.95463	−	6.84963i	−0.162397	−	0.281281i	0.773331	−	0.634003i	$-0.218589\pi$
$593$	−3.95463	−	6.84963i	−0.162397	−	0.281281i	−0.935728	+	0.352722i	$0.885256\pi$
$594$	−0.153872	+	0.727031i	−0.00631344	+	0.0298305i
$595$	−7.75486	+	6.50637i	−0.317918	+	0.266735i
$596$	−10.8308	−	28.0686i	−0.443648	−	1.14974i
$597$	0.280591	−	1.04718i	0.0114838	−	0.0428582i
$598$	14.4213	−	0.768415i	0.589730	−	0.0314228i
$599$	−18.5333	−	10.7002i	−0.757251	−	0.437199i	0.0710572	−	0.997472i	$-0.477363\pi$
$599$	−18.5333	−	10.7002i	−0.757251	−	0.437199i	−0.828308	+	0.560273i	$0.810696\pi$
$600$	0.408004	−	0.332169i	0.0166567	−	0.0135607i
$601$			0.974684i			0.0397582i	0.999802	+	0.0198791i	$0.00632813\pi$
$601$			0.974684i			0.0397582i	−0.999802	+	0.0198791i	$0.993672\pi$
$602$	8.95213	+	5.58374i	0.364862	+	0.227576i
$603$	4.64033	+	4.64033i	0.188969	+	0.188969i
$604$	36.1775	−	3.86630i	1.47204	−	0.157318i
$605$	−2.89070	−	10.7882i	−0.117524	−	0.438604i
$606$	−0.562424	+	0.625733i	−0.0228469	+	0.0254186i
$607$	−3.01261	−	5.21800i	−0.122278	−	0.211792i	0.798388	−	0.602144i	$-0.205687\pi$
$607$	−3.01261	−	5.21800i	−0.122278	−	0.211792i	−0.920666	+	0.390352i	$0.872353\pi$
$608$	−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
$611$	4.27106	+	1.14443i	0.172788	+	0.0462985i
$612$	10.3761	+	14.2291i	0.419429	+	0.575179i
$613$	1.58990	−	0.426012i	0.0642155	−	0.0172065i	−0.226568	−	0.973995i	$-0.572751\pi$
$613$	1.58990	−	0.426012i	0.0642155	−	0.0172065i	0.290784	+	0.956789i	$0.406084\pi$
$614$	27.6655	+	14.0659i	1.11649	+	0.567652i
$615$			0.538124i			0.0216993i
$616$	5.07949	−	10.4826i	0.204658	−	0.422357i
$617$		−	34.0864i		−	1.37227i	−0.727476	−	0.686134i	$-0.759307\pi$
$617$		−	34.0864i		−	1.37227i	0.727476	−	0.686134i	$-0.240693\pi$
$618$	−0.123546	+	0.242997i	−0.00496975	+	0.00977478i
$619$	32.3004	−	8.65485i	1.29826	−	0.347868i	0.457469	−	0.889226i	$-0.348756\pi$
$619$	32.3004	−	8.65485i	1.29826	−	0.347868i	0.840792	+	0.541358i	$0.182090\pi$
$620$	16.1597	+	2.53053i	0.648990	+	0.101628i
$621$	1.47516	+	0.395268i	0.0591961	+	0.0158615i
$622$	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
$626$	−3.94081	−	3.54210i	−0.157506	−	0.141571i
$627$	−0.179651	−	0.670466i	−0.00717456	−	0.0267758i
$628$	15.1338	+	12.2114i	0.603905	+	0.487289i
$629$	11.2877	+	11.2877i	0.450070	+	0.450070i
$630$	−6.86551	−	12.8867i	−0.273528	−	0.513419i
$631$			4.58799i			0.182645i	0.995821	+	0.0913225i	$0.0291094\pi$
$631$			4.58799i			0.182645i	−0.995821	+	0.0913225i	$0.970891\pi$
$632$	−0.554399	+	5.41107i	−0.0220528	+	0.215241i
$633$	−0.594458	−	0.343211i	−0.0236276	−	0.0136414i
$634$	−1.85132	−	34.7447i	−0.0735252	−	1.37989i
$635$	−1.89851	+	7.08533i	−0.0753400	+	0.281173i
$636$	1.19507	+	0.529580i	0.0473875	+	0.0209992i
$637$	−12.9445	+	9.06167i	−0.512878	+	0.359037i
$638$	6.28131	+	1.32940i	0.248680	+	0.0526315i
$639$	−10.8842	−	18.8519i	−0.430571	−	0.745770i
$640$	−5.36361	−	13.7214i	−0.212015	−	0.542386i
$641$	24.9135	−	43.1515i	0.984025	−	1.70438i	0.337835	−	0.941205i	$-0.390305\pi$
$641$	24.9135	−	43.1515i	0.984025	−	1.70438i	0.646190	−	0.763177i	$-0.276361\pi$
$642$	0.282617	+	0.867227i	0.0111540	+	0.0342267i
$643$	−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	$0.915802\pi$
$644$	−20.9566	−	11.5702i	−0.825806	−	0.455928i
$645$	0.146161	+	0.146161i	0.00575509	+	0.00575509i
$646$	−29.3408	−	14.9176i	−1.15440	−	0.586925i
$647$	25.4255	+	14.6794i	0.999579	+	0.577107i	0.908124	−	0.418702i	$-0.137515\pi$
$647$	25.4255	+	14.6794i	0.999579	+	0.577107i	0.0914555	+	0.995809i	$0.470848\pi$
$648$	−23.1543	+	10.3817i	−0.909586	+	0.407832i
$649$	−4.13245	+	2.38587i	−0.162213	+	0.0936536i
$650$	5.75280	+	8.84162i	0.225643	+	0.346797i
$651$	0.319977	−	0.878977i	0.0125409	−	0.0344498i
$652$	−24.2628	+	9.36227i	−0.950205	+	0.366655i
$653$	14.6954	+	3.93761i	0.575075	+	0.154091i	0.534623	−	0.845091i	$-0.320454\pi$
$653$	14.6954	+	3.93761i	0.575075	+	0.154091i	0.0404516	+	0.999181i	$0.487120\pi$
$654$	0.185646	+	0.166863i	0.00725932	+	0.00652485i
$655$	1.35165	−	2.34112i	0.0528132	−	0.0914752i
$656$	−27.9584	−	8.97638i	−1.09159	−	0.350469i
$657$	42.3531			1.65235
$658$	−5.00301	−	5.35628i	−0.195038	−	0.208810i
$659$	−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	$0.324830\pi$
$660$	0.143306	−	0.177602i	0.00557819	−	0.00691314i
$661$	13.0890	−	3.50720i	0.509105	−	0.136414i	0.00488232	−	0.999988i	$-0.498446\pi$
$661$	13.0890	−	3.50720i	0.509105	−	0.136414i	0.504222	+	0.863574i	$0.331779\pi$
$662$	−14.3203	+	0.763032i	−0.556572	+	0.0296561i
$663$	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
$667$	3.41498	−	12.7449i	0.132229	−	0.493484i
$668$	−19.4927	−	26.7310i	−0.754194	−	1.03426i
$669$	−0.326949	−	1.22019i	−0.0126406	−	0.0471753i
$670$	−1.24949	−	3.83415i	−0.0482722	−	0.148126i
$671$	−15.6658			−0.604771
$672$	−0.829083	+	0.149878i	−0.0319826	+	0.00578166i
$673$	−15.5552			−0.599610			−0.299805	−	0.954000i	$-0.596922\pi$
$673$	−15.5552			−0.599610			−0.299805	+	0.954000i	$0.596922\pi$
$674$	−2.32567	−	7.13647i	−0.0895815	−	0.274887i
$675$	0.288708	+	1.07747i	0.0111124	+	0.0414720i
$676$	−9.31477	−	12.7737i	−0.358261	−	0.491297i
$677$	10.6072	−	39.5868i	0.407669	−	1.52144i	−0.391410	−	0.920217i	$-0.628012\pi$
$677$	10.6072	−	39.5868i	0.407669	−	1.52144i	0.799079	−	0.601226i	$-0.205321\pi$
$678$	−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
$682$	−13.8060	+	0.735632i	−0.528660	+	0.0281688i
$683$	−11.9346	+	3.19786i	−0.456664	+	0.122363i	−0.479816	−	0.877369i	$-0.659296\pi$
$683$	−11.9346	+	3.19786i	−0.456664	+	0.122363i	0.0231521	+	0.999732i	$0.492630\pi$
$684$	29.8145	−	36.9496i	1.13998	−	1.41280i
$685$	2.85672	−	2.85672i	0.109150	−	0.109150i
$686$	26.1547	−	1.38925i	0.998592	−	0.0530420i
$687$	1.10632			0.0422089
$688$	−10.0319	+	5.15574i	−0.382464	+	0.196561i
$689$	−13.1038	+	22.6964i	−0.499214	+	0.864664i
$690$	−0.348797	−	0.313507i	−0.0132785	−	0.0119350i
$691$	5.37500	+	1.44023i	0.204475	+	0.0547888i	0.359603	−	0.933106i	$-0.382912\pi$
$691$	5.37500	+	1.44023i	0.204475	+	0.0547888i	−0.155128	+	0.987894i	$0.549579\pi$
$692$	−40.3158	+	15.5566i	−1.53258	+	0.591375i
$693$	7.93277	+	9.45497i	0.301341	+	0.359165i
$694$	−3.18121	−	4.88928i	−0.120757	−	0.185594i
$695$	−20.3263	+	11.7354i	−0.771021	+	0.445149i
$696$	−0.189993	−	0.423740i	−0.00720166	−	0.0160618i
$697$	−18.6796	−	10.7847i	−0.707540	−	0.408498i
$698$	20.4376	+	10.3910i	0.773574	+	0.393305i
$699$	0.154214	+	0.154214i	0.00583290	+	0.00583290i
$700$	−0.334717	−	17.4817i	−0.0126511	−	0.660746i
$701$	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	$0.0496095\pi$
$702$	0.333910	+	1.02462i	0.0126026	+	0.0386719i
$703$	21.5184	−	37.2710i	0.811583	−	1.40570i
$704$	6.83687	+	10.4081i	0.257674	+	0.392269i
$705$	−0.0717960	−	0.124354i	−0.00270399	−	0.00468346i
$706$	5.35084	+	1.13247i	0.201381	+	0.0426212i
$707$	4.85384	+	27.5364i	0.182547	+	1.03561i
$708$	0.315541	+	0.139828i	0.0118588	+	0.00525506i
$709$	3.20632	−	11.9661i	0.120416	−	0.449398i	−0.879219	−	0.476417i	$-0.841935\pi$
$709$	3.20632	−	11.9661i	0.120416	−	0.449398i	0.999635	+	0.0270200i	$0.00860177\pi$
$710$	0.711745	+	13.3577i	0.0267113	+	0.501306i
$711$	−4.99113	−	2.88163i	−0.187182	−	0.108070i
$712$	37.5340	+	3.84559i	1.40665	+	0.144120i
$713$			28.4126i			1.06406i
$714$	−0.618514	−	0.0210925i	−0.0231473	−	0.000789369i
$715$	3.23532	+	3.23532i	0.120994	+	0.120994i
$716$	−29.5310	−	23.8285i	−1.10363	−	0.890511i
$717$	−0.0956906	−	0.357122i	−0.00357363	−	0.0133370i
$718$	16.6359	+	14.9528i	0.620848	+	0.558033i
$719$	−7.64439	−	13.2405i	−0.285088	−	0.493786i	0.687543	−	0.726144i	$-0.258689\pi$
$719$	−7.64439	−	13.2405i	−0.285088	−	0.493786i	−0.972630	+	0.232358i	$0.925356\pi$
$720$	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
$723$	0.720631	+	0.193093i	0.0268006	+	0.00718119i
$724$	−18.0020	−	2.81901i	−0.669038	−	0.104768i
$725$	9.30902	−	2.49434i	0.345728	−	0.0926376i
$726$	0.309464	−	0.608671i	0.0114853	−	0.0225899i
$727$			23.7860i			0.882173i	0.897465	+	0.441086i	$0.145407\pi$
$727$			23.7860i			0.882173i	−0.897465	+	0.441086i	$0.854593\pi$
$728$	−1.22153	−	16.8478i	−0.0452731	−	0.624421i
$729$		−	26.8290i		−	0.993668i
$730$	−23.1997	−	11.7953i	−0.858658	−	0.436564i
$731$	−8.00285	+	2.14436i	−0.295996	+	0.0793119i
$732$	0.667613	+	0.915524i	0.0246757	+	0.0338387i
$733$	−19.8871	−	5.32874i	−0.734548	−	0.196822i	−0.127894	−	0.991788i	$-0.540822\pi$
$733$	−19.8871	−	5.32874i	−0.734548	−	0.196822i	−0.606654	+	0.794966i	$0.707489\pi$
$734$	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
$738$	20.7980	−	23.1392i	0.765586	−	0.851764i
$739$	−7.05306	−	26.3224i	−0.259451	−	0.968284i	−0.965560	−	0.260181i	$-0.916218\pi$
$739$	−7.05306	−	26.3224i	−0.259451	−	0.968284i	0.706109	−	0.708103i	$-0.250449\pi$
$740$	14.0693	−	1.50359i	0.517199	−	0.0552732i
$741$	−0.711756	−	0.711756i	−0.0261470	−	0.0261470i
$742$	38.3397	−	20.4258i	1.40749	−	0.749855i
$743$			12.8386i			0.471002i	0.971874	+	0.235501i	$0.0756731\pi$
$743$			12.8386i			0.471002i	−0.971874	+	0.235501i	$0.924327\pi$
$744$	0.631349	+	0.775488i	0.0231464	+	0.0284308i
$745$	−16.9641	−	9.79426i	−0.621518	−	0.358834i
$746$	−32.1768	+	1.71449i	−1.17808	+	0.0627719i
$747$	9.68282	−	36.1368i	0.354276	−	1.32218i
$748$	3.29295	+	8.53386i	0.120402	+	0.312029i
$749$	28.4842	+	10.3692i	1.04079	+	0.378882i
$750$	0.178253	−	0.842232i	0.00650889	−	0.0307539i
$751$	7.23318	+	12.5282i	0.263942	+	0.457162i	0.967286	−	0.253688i	$-0.0816438\pi$
$751$	7.23318	+	12.5282i	0.263942	+	0.457162i	−0.703344	+	0.710850i	$0.748310\pi$
$752$	7.65848	−	1.65584i	0.279276	−	0.0603823i
$753$	0.151625	−	0.262622i	0.00552552	−	0.00957048i
$754$	8.85241	−	2.88487i	0.322386	−	0.105061i
$755$	16.7506	−	16.7506i	0.609616	−	0.609616i
$756$	0.429217	−	1.73398i	0.0156105	−	0.0630643i
$757$	−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	$0.767684\pi$
$758$	−18.2218	+	35.8397i	−0.661846	+	1.30176i
$759$	0.343304	+	0.198207i	0.0124611	+	0.00719444i
$760$	−26.6218	+	11.9365i	−0.965676	+	0.432981i
$761$	−2.04136	+	1.17858i	−0.0739994	+	0.0427236i	−0.536543	−	0.843873i	$-0.680270\pi$
$761$	−2.04136	+	1.17858i	−0.0739994	+	0.0427236i	0.462544	+	0.886596i	$0.346937\pi$
$762$	−0.375892	+	0.244574i	−0.0136171	+	0.00885998i
$763$	8.16964	−	1.44006i	0.295761	−	0.0521337i
$764$	47.3829	+	20.9972i	1.71425	+	0.759651i
$765$	11.0753	+	2.96763i	0.400430	+	0.107295i
$766$	−22.1695	+	24.6650i	−0.801016	+	0.891182i
$767$	−3.45987	+	5.99267i	−0.124929	+	0.216383i
$768$	0.316898	−	0.843104i	0.0114351	−	0.0304229i
$769$	7.96868			0.287358			0.143679	−	0.989624i	$-0.454107\pi$
$769$	7.96868			0.287358			0.143679	+	0.989624i	$0.454107\pi$
$770$	−1.71211	−	7.38840i	−0.0617002	−	0.266259i
$771$	−0.940923	+	0.940923i	−0.0338865	+	0.0338865i
$772$	−2.66678	−	24.9535i	−0.0959797	−	0.898095i
$773$	21.2568	−	5.69575i	0.764555	−	0.204862i	0.144590	−	0.989492i	$-0.453814\pi$
$773$	21.2568	−	5.69575i	0.764555	−	0.204862i	0.619965	+	0.784630i	$0.287147\pi$
$774$	−0.635878	−	11.9339i	−0.0228562	−	0.428954i
$775$	−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
$779$	−15.0506	+	56.1695i	−0.539243	+	2.01248i
$780$	0.0511989	−	0.326952i	0.00183322	−	0.0117068i
$781$	−2.92640	−	10.9215i	−0.104715	−	0.390801i
$782$	17.8729	−	5.82452i	0.639134	−	0.208284i
$783$	0.984588			0.0351863
$784$	−13.0615	+	24.7668i	−0.466483	+	0.884530i
$785$	12.6611			0.451896
$786$	0.157137	−	0.0512086i	0.00560489	−	0.00182655i
$787$	7.44405	+	27.7816i	0.265352	+	0.990306i	0.962035	+	0.272927i	$0.0879917\pi$
$787$	7.44405	+	27.7816i	0.265352	+	0.990306i	−0.696683	+	0.717379i	$0.745342\pi$
$788$	23.2394	+	3.63917i	0.827871	+	0.129640i
$789$	−0.259592	+	0.968810i	−0.00924171	+	0.0344905i
$790$	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
$794$	−0.498748	−	9.36029i	−0.0176999	−	0.332184i
$795$	0.822071	−	0.220273i	0.0291558	−	0.00781229i
$796$	38.2988	−	4.09300i	1.35746	−	0.145073i
$797$	−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	$0.436160\pi$
$798$	0.376657	+	1.62541i	0.0133335	+	0.0575390i
$799$	5.75552			0.203616
$800$	16.2285	+	9.27531i	0.573765	+	0.327932i
$801$	−19.9885	+	34.6210i	−0.706258	+	1.22327i
$802$	29.9980	−	33.3748i	1.05927	−	1.17850i
$803$	21.2491	+	5.69369i	0.749866	+	0.200926i
$804$	0.0998836	−	0.225401i	0.00352262	−	0.00794928i
$805$	−15.3494	+	2.70563i	−0.540995	+	0.0953611i
$806$	−16.8051	+	10.9343i	−0.591936	+	0.385143i
$807$	−0.311270	+	0.179712i	−0.0109572	+	0.00632616i
$808$	−27.9341	−	10.6390i	−0.982717	−	0.374279i
$809$	−25.9855	−	15.0027i	−0.913600	−	0.527467i	−0.0320125	−	0.999487i	$-0.510192\pi$
$809$	−25.9855	−	15.0027i	−0.913600	−	0.527467i	−0.881588	+	0.472020i	$0.843525\pi$
$810$	−7.48775	+	14.7273i	−0.263093	+	0.517465i
$811$	−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	$0.918134\pi$
$812$	−14.9810	−	3.70829i	−0.525731	−	0.130136i
$813$	−0.317411	+	0.317411i	−0.0111321	+	0.0111321i
$814$	−11.3713	+	3.70576i	−0.398565	+	0.129887i
$815$	−8.46625	+	14.6640i	−0.296560	+	0.513657i
$816$	0.358395	−	0.556123i	0.0125463	−	0.0194682i
$817$	11.1684	+	19.3443i	0.390733	+	0.676770i
$818$	−0.378535	+	1.78854i	−0.0132351	+	0.0625349i
$819$	16.8181	+	6.12233i	0.587671	+	0.213932i
$820$	−17.8367	+	6.88265i	−0.622886	+	0.240352i
$821$	14.2176	−	53.0609i	0.496199	−	1.85184i	−0.0270111	−	0.999635i	$-0.508599\pi$
$821$	14.2176	−	53.0609i	0.496199	−	1.85184i	0.523210	−	0.852204i	$-0.324734\pi$
$822$	0.246643	−	0.0131420i	0.00860265	−	0.000458379i
$823$	−20.1906	−	11.6571i	−0.703800	−	0.406339i	0.104961	−	0.994476i	$-0.466528\pi$
$823$	−20.1906	−	11.6571i	−0.703800	−	0.406339i	−0.808761	+	0.588137i	$0.799862\pi$
$824$	−9.63458	−	0.987124i	−0.335637	−	0.0343881i
$825$			0.289545i			0.0100807i
$826$	10.1231	−	5.39315i	0.352226	−	0.187652i
$827$	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	$0.716568\pi$
$828$	2.88138	+	26.9614i	0.100135	+	0.936974i
$829$	10.8606	+	40.5325i	0.377206	+	1.40775i	0.850095	+	0.526630i	$0.176545\pi$
$829$	10.8606	+	40.5325i	0.377206	+	1.40775i	−0.472889	+	0.881122i	$0.656789\pi$
$830$	−15.3680	+	17.0979i	−0.533431	+	0.593477i
$831$	−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
$835$	−20.8063	−	5.57502i	−0.720030	−	0.192932i
$836$	19.9256	−	14.5300i	0.689142	−	0.502532i
$837$	−2.04794	+	0.548743i	−0.0707871	+	0.0189673i
$838$	30.8047	+	15.6619i	1.06413	+	0.541032i
$839$		−	46.6970i		−	1.61216i	−0.591806	−	0.806081i	$-0.701585\pi$
$839$		−	46.6970i		−	1.61216i	0.591806	−	0.806081i	$-0.298415\pi$
$840$	−0.358822	+	0.414922i	−0.0123805	+	0.0143162i
$841$			20.4935i			0.706672i
$842$	−3.04781	+	5.99460i	−0.105034	+	0.206587i
$843$	−0.709257	+	0.190045i	−0.0244281	+	0.00654549i
$844$	3.77294	−	24.0937i	0.129870	−	0.829339i
$845$	−9.94249	−	2.66408i	−0.342032	−	0.0916472i
$846$	−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
$850$	10.2116	+	9.17845i	0.350256	+	0.314818i
$851$	6.36139	+	23.7410i	0.218066	+	0.813832i
$852$	−0.513550	+	0.636451i	−0.0175939	+	0.0218045i
$853$	−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	$0.867506\pi$
$854$	37.6347	+	1.28342i	1.28783	+	0.0439177i
$855$		−	30.9125i		−	1.05718i
$856$	−25.1305	+	20.4595i	−0.858944	+	0.699293i
$857$	−12.5881	−	7.26772i	−0.430000	−	0.248261i	0.269347	−	0.963043i	$-0.413192\pi$
$857$	−12.5881	−	7.26772i	−0.430000	−	0.248261i	−0.699347	+	0.714783i	$0.746526\pi$
$858$	0.0148837	+	0.279331i	0.000508121	+	0.00953619i
$859$	−10.1784	+	37.9861i	−0.347281	+	1.29607i	0.542644	+	0.839963i	$0.317423\pi$
$859$	−10.1784	+	37.9861i	−0.347281	+	1.29607i	−0.889925	+	0.456107i	$0.849243\pi$
$860$	−2.97527	+	6.71409i	−0.101456	+	0.228949i
$861$	0.189800	+	1.07676i	0.00646835	+	0.0366957i
$862$	−15.4606	−	3.27214i	−0.526589	−	0.111449i
$863$	6.49230	+	11.2450i	0.221000	+	0.382784i	0.955112	−	0.296245i	$-0.0957345\pi$
$863$	6.49230	+	11.2450i	0.221000	+	0.382784i	−0.734112	+	0.679029i	$0.762401\pi$
$864$	1.35621	+	1.34442i	0.0461392	+	0.0457380i
$865$	−14.0678	+	24.3661i	−0.478319	+	0.828473i
$866$	−7.62201	−	23.3886i	−0.259006	−	0.794778i
$867$	−0.333052	+	0.333052i	−0.0113110	+	0.0113110i
$868$	33.2272	−	0.636191i	1.12780	−	0.0215937i
$869$	−2.11673	−	2.11673i	−0.0718052	−	0.0718052i
$870$	−0.269520	−	0.137031i	−0.00913760	−	0.00464579i
$871$	4.28075	+	2.47149i	0.145048	+	0.0837434i
$872$	−3.15643	+	8.28762i	−0.106890	+	0.280654i
$873$	−25.1638	+	14.5283i	−0.851665	+	0.491709i
$874$	−27.6392	−	42.4793i	−0.934909	−	1.43689i
$875$	−18.3892	−	21.9179i	−0.621668	−	0.740959i
$876$	−0.572809	−	1.48446i	−0.0193534	−	0.0501554i
$877$	−21.6697	−	5.80637i	−0.731733	−	0.196067i	−0.126332	−	0.991988i	$-0.540321\pi$
$877$	−21.6697	−	5.80637i	−0.731733	−	0.196067i	−0.605401	+	0.795921i	$0.706987\pi$
$878$	39.4853	+	35.4904i	1.33256	+	1.19774i
$879$	−0.505614	+	0.875749i	−0.0170539	+	0.0295383i
$880$	7.71971	+	2.47851i	0.260231	+	0.0835505i
$881$	−8.65332			−0.291538			−0.145769	−	0.989319i	$-0.546566\pi$
$881$	−8.65332			−0.291538			−0.145769	+	0.989319i	$0.546566\pi$
$882$	−18.2827	−	23.3641i	−0.615611	−	0.786709i
$883$	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	$-0.0105499\pi$
$884$	10.3232	+	8.32976i	0.347207	+	0.280160i
$885$	0.217056	−	0.0581601i	0.00729627	−	0.00195503i
$886$	−10.0615	+	0.536110i	−0.338022	+	0.0180110i
$887$	−24.7803	+	14.3069i	−0.832042	+	0.480380i	−0.854551	−	0.519367i	$-0.826168\pi$
$887$	−24.7803	+	14.3069i	−0.832042	+	0.480380i	0.0225091	+	0.999747i	$0.492835\pi$
$888$	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
$891$	3.61439	−	13.4891i	0.121087	−	0.451902i
$892$	36.2629	−	26.4434i	1.21417	−	0.885391i
$893$	−4.01607	−	14.9882i	−0.134393	−	0.501560i
$894$	−0.371066	−	1.13864i	−0.0124103	−	0.0380818i
$895$	−24.7060			−0.825830
$896$	−15.5719	−	25.5640i	−0.520221	−	0.854032i
$897$	0.574859			0.0191940
$898$	−3.43543	−	10.5418i	−0.114642	−	0.351786i
$899$	4.74096	+	17.6935i	0.158120	+	0.590112i
$900$	−16.0023	+	11.6691i	−0.533409	+	0.388970i
$901$	−8.82909	+	32.9506i	−0.294140	+	1.09774i
$902$	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
$906$	1.44621	−	0.0770590i	0.0480471	−	0.00256011i
$907$	−17.9969	+	4.82227i	−0.597579	+	0.160121i	−0.544915	−	0.838492i	$-0.683438\pi$
$907$	−17.9969	+	4.82227i	−0.597579	+	0.160121i	−0.0526640	+	0.998612i	$0.516771\pi$
$908$	−3.64062	−	2.93760i	−0.120818	−	0.0974878i
$909$	22.3949	−	22.3949i	0.742793	−	0.742793i
$910$	−7.50733	−	8.03744i	−0.248866	−	0.266439i
$911$	−12.2041			−0.404341			−0.202170	−	0.979350i	$-0.564799\pi$
$911$	−12.2041			−0.404341			−0.202170	+	0.979350i	$0.564799\pi$
$912$	−1.69830	−	0.545260i	−0.0562363	−	0.0180554i
$913$	9.71601	−	16.8286i	0.321553	−	0.556946i
$914$	27.0617	+	24.3237i	0.895123	+	0.804558i
$915$	0.712603	+	0.190942i	0.0235579	+	0.00631233i
$916$	14.1500	+	36.6704i	0.467528	+	1.21162i
$917$	1.87884	−	5.16119i	0.0620448	−	0.170437i
$918$	0.765009	+	1.17576i	0.0252491	+	0.0388059i
$919$	3.57056	−	2.06146i	0.117782	−	0.0680014i	−0.439952	−	0.898021i	$-0.645004\pi$
$919$	3.57056	−	2.06146i	0.117782	−	0.0680014i	0.557734	+	0.830020i	$0.311671\pi$
$920$	5.93042	−	15.5711i	0.195520	−	0.513363i
$921$	1.06989	+	0.617699i	0.0352539	+	0.0203539i
$922$	−23.4726	−	11.9341i	−0.773030	−	0.393028i
$923$	−11.5941	−	11.5941i	−0.381623	−	0.381623i
$924$	0.224106	−	0.405916i	0.00737256	−	0.0133537i
$925$	−12.6943	+	12.6943i	−0.417386	+	0.417386i
$926$	3.01835	+	9.26199i	0.0991890	+	0.304368i
$927$	5.13083	−	8.88686i	0.168519	−	0.291883i
$928$	11.6153	−	11.7172i	0.381292	−	0.384636i
$929$	−22.7002	−	39.3180i	−0.744771	−	1.28998i	−0.950302	−	0.311330i	$-0.899225\pi$
$929$	−22.7002	−	39.3180i	−0.744771	−	1.28998i	0.205531	−	0.978651i	$-0.434108\pi$
$930$	0.636973	+	0.134812i	0.0208872	+	0.00442064i
$931$	50.2519	+	23.4396i	1.64694	+	0.768203i
$932$	−3.13919	+	7.08400i	−0.102827	+	0.232044i
$933$	0.0529235	−	0.197513i	0.00173264	−	0.00646629i
$934$	−2.97709	−	55.8727i	−0.0974133	−	1.82821i
$935$	5.15770	+	2.97780i	0.168675	+	0.0973845i
$936$	−14.8379	+	12.0800i	−0.484994	+	0.394848i
$937$			8.69727i			0.284127i	0.989858	+	0.142064i	$0.0453738\pi$
$937$			8.69727i			0.284127i	−0.989858	+	0.142064i	$0.954626\pi$
$938$	−3.85250	−	7.23122i	−0.125788	−	0.236108i
$939$	−0.149141	−	0.149141i	−0.00486704	−	0.00486704i
$940$	3.20359	−	3.97026i	0.104490	−	0.129496i
$941$	3.11071	+	11.6093i	0.101406	+	0.378454i	0.997913	−	0.0645772i	$-0.0205699\pi$
$941$	3.11071	+	11.6093i	0.101406	+	0.378454i	−0.896506	+	0.443031i	$0.853903\pi$
$942$	0.575691	+	0.517445i	0.0187570	+	0.0168593i
$943$	−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
$947$	55.5623	+	14.8879i	1.80553	+	0.483791i	0.994820	−	0.101652i	$-0.0324129\pi$
$947$	55.5623	+	14.8879i	1.80553	+	0.483791i	0.810713	+	0.585443i	$0.199080\pi$
$948$	−0.0334972	+	0.213911i	−0.00108794	+	0.00694749i
$949$	30.8145	−	8.25671i	1.00028	−	0.268024i
$950$	16.7765	−	32.9970i	0.544303	−	1.07056i
$951$		−	1.38499i		−	0.0449113i
$952$	−7.21170	−	20.7711i	−0.233733	−	0.673196i
$953$		−	8.69133i		−	0.281540i	−0.990042	−	0.140770i	$-0.955042\pi$
$953$		−	8.69133i		−	0.281540i	0.990042	−	0.140770i	$-0.0449578\pi$
$954$	−43.8621	−	22.3007i	−1.42009	−	0.722010i
$955$	32.5941	−	8.73356i	1.05472	−	0.282611i
$956$	10.6133	−	7.73939i	0.343260	−	0.250310i
$957$	0.246860	+	0.0661460i	0.00797986	+	0.00213820i
$958$	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
$962$	−11.5940	+	12.8990i	−0.373804	+	0.415881i
$963$	−8.88662	−	33.1653i	−0.286367	−	1.06874i
$964$	2.81665	+	26.3558i	0.0907183	+	0.848863i
$965$	−11.5537	−	11.5537i	−0.371927	−	0.371927i
$966$	−0.808499	−	0.504287i	−0.0260130	−	0.0162252i
$967$			28.1636i			0.905681i	0.891592	+	0.452840i	$0.149589\pi$
$967$			28.1636i			0.905681i	−0.891592	+	0.452840i	$0.850411\pi$
$968$	24.1331	+	2.47259i	0.775669	+	0.0794722i
$969$	−1.13467	−	0.655102i	−0.0364509	−	0.0210449i
$970$	17.8300	−	0.950046i	0.572488	−	0.0305041i
$971$	−2.71368	+	10.1276i	−0.0870862	+	0.325010i	−0.995701	−	0.0926248i	$-0.970474\pi$
$971$	−2.71368	+	10.1276i	−0.0870862	+	0.325010i	0.908615	+	0.417635i	$0.137141\pi$
$972$	−2.83203	+	1.09279i	−0.0908375	+	0.0350514i
$973$	−36.5327	+	30.6511i	−1.17118	+	0.982629i
$974$	0.833765	−	3.93947i	0.0267155	−	0.126229i
$975$	0.209942	+	0.363630i	0.00672352	+	0.0116455i
$976$	−21.8073	+	33.8384i	−0.698034	+	1.08314i
$977$	−17.3812	+	30.1051i	−0.556073	+	0.963147i	0.441746	+	0.897140i	$0.354359\pi$
$977$	−17.3812	+	30.1051i	−0.556073	+	0.963147i	−0.997819	+	0.0660068i	$0.978974\pi$
$978$	−0.984251	+	0.320753i	−0.0314729	+	0.0102566i
$979$	−14.6827	+	14.6827i	−0.469262	+	0.469262i
$980$	3.50780	+	17.8898i	0.112053	+	0.571469i
$981$	−6.64424	−	6.64424i	−0.212134	−	0.212134i
$982$	15.8466	−	31.1680i	0.505686	−	0.994611i
$983$	−2.48718	−	1.43597i	−0.0793286	−	0.0458004i	0.459811	−	0.888017i	$-0.347917\pi$
$983$	−2.48718	−	1.43597i	−0.0793286	−	0.0458004i	−0.539140	+	0.842216i	$0.681250\pi$
$984$	−1.09231	−	0.416017i	−0.0348214	−	0.0132621i
$985$	13.2635	−	7.65766i	0.422609	−	0.243993i
$986$	10.1582	−	6.60943i	0.323503	−	0.210487i
$987$	−0.187520	−	0.223503i	−0.00596884	−	0.00711418i
$988$	14.4885	−	32.6954i	0.460942	−	1.04018i
$989$	−12.3220	−	3.30166i	−0.391816	−	0.104987i
$990$	−5.74263	+	6.38905i	−0.182513	+	0.203057i
$991$	15.8744	−	27.4952i	0.504266	−	0.873414i	−0.495722	−	0.868481i	$-0.665097\pi$
$991$	15.8744	−	27.4952i	0.504266	−	0.873414i	0.999988	−	0.00493273i	$-0.00157014\pi$
$992$	−17.6294	+	30.8453i	−0.559735	+	0.979340i
$993$	−0.570832			−0.0181148
$994$	6.13550	+	26.4770i	0.194606	+	0.839799i
$995$	17.7327	−	17.7327i	0.562166	−	0.562166i
$996$	−1.39754	+	0.149355i	−0.0442827	+	0.00473251i
$997$	−19.7719	+	5.29788i	−0.626184	+	0.167785i	−0.557937	−	0.829883i	$-0.688407\pi$
$997$	−19.7719	+	5.29788i	−0.626184	+	0.167785i	−0.0682464	+	0.997668i	$0.521740\pi$
$998$	−0.101931	−	1.91299i	−0.00322656	−	0.0605547i
$999$	−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.53.8	yes	48
4.3	odd	2		448.2.ba.c.305.6		48
7.2	even	3	inner	112.2.w.c.37.10	✓	48
7.3	odd	6		784.2.m.k.197.1		24
7.4	even	3		784.2.m.j.197.1		24
7.5	odd	6		784.2.x.o.373.10		48
7.6	odd	2		784.2.x.o.165.8		48
8.3	odd	2		896.2.ba.e.865.7		48
8.5	even	2		896.2.ba.f.865.6		48
16.3	odd	4		448.2.ba.c.81.7		48
16.5	even	4		896.2.ba.f.417.7		48
16.11	odd	4		896.2.ba.e.417.6		48
16.13	even	4	inner	112.2.w.c.109.10	yes	48
28.23	odd	6		448.2.ba.c.177.7		48
56.37	even	6		896.2.ba.f.737.7		48
56.51	odd	6		896.2.ba.e.737.6		48
112.13	odd	4		784.2.x.o.557.10		48
112.37	even	12		896.2.ba.f.289.6		48
112.45	odd	12		784.2.m.k.589.1		24
112.51	odd	12		448.2.ba.c.401.6		48
112.61	odd	12		784.2.x.o.765.8		48
112.93	even	12	inner	112.2.w.c.93.8	yes	48
112.107	odd	12		896.2.ba.e.289.7		48
112.109	even	12		784.2.m.j.589.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.10	✓	48	7.2	even	3	inner
112.2.w.c.53.8	yes	48	1.1	even	1	trivial
112.2.w.c.93.8	yes	48	112.93	even	12	inner
112.2.w.c.109.10	yes	48	16.13	even	4	inner
448.2.ba.c.81.7		48	16.3	odd	4
448.2.ba.c.177.7		48	28.23	odd	6
448.2.ba.c.305.6		48	4.3	odd	2
448.2.ba.c.401.6		48	112.51	odd	12
784.2.m.j.197.1		24	7.4	even	3
784.2.m.j.589.1		24	112.109	even	12
784.2.m.k.197.1		24	7.3	odd	6
784.2.m.k.589.1		24	112.45	odd	12
784.2.x.o.165.8		48	7.6	odd	2
784.2.x.o.373.10		48	7.5	odd	6
784.2.x.o.557.10		48	112.13	odd	4
784.2.x.o.765.8		48	112.61	odd	12
896.2.ba.e.289.7		48	112.107	odd	12
896.2.ba.e.417.6		48	16.11	odd	4
896.2.ba.e.737.6		48	56.51	odd	6
896.2.ba.e.865.7		48	8.3	odd	2
896.2.ba.f.289.6		48	112.37	even	12
896.2.ba.f.417.7		48	16.5	even	4
896.2.ba.f.737.7		48	56.37	even	6
896.2.ba.f.865.6		48	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.438190 + 1.34461i) q^{2} +(0.0145698 + 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(-0.337028 + 1.25781i) q^{5} +(-0.0667293 + 0.0434174i) q^{6} +(-0.230738 + 2.63567i) q^{7} +(-2.29259 - 1.65651i) q^{8} +(2.59533 - 1.49842i) q^{9} +O(q^{10})\)	\(q+(0.438190 + 1.34461i) q^{2} +(0.0145698 + 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(-0.337028 + 1.25781i) 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} +(-1.83895 + 0.0979855i) q^{10} +(1.50355 - 0.402875i) q^{11} +(-0.0876199 - 0.0707001i) q^{12} +(1.59615 - 1.59615i) q^{13} +(-3.64507 + 0.844671i) q^{14} -0.0733039 q^{15} +(1.22277 - 3.80852i) q^{16} +(1.46910 - 2.54455i) q^{17} +(3.15204 + 2.83313i) q^{18} +(-7.65147 - 2.05021i) q^{19} +(-0.937562 - 2.42974i) q^{20} +(-0.146677 + 0.0258547i) q^{21} +(1.20055 + 1.84516i) q^{22} +(3.91784 - 2.26197i) q^{23} +(0.0566703 - 0.148795i) q^{24} +(2.86164 + 1.65217i) q^{25} +(2.84562 + 1.44679i) q^{26} +(0.238706 + 0.238706i) q^{27} +(-2.73299 - 4.53109i) q^{28} +(2.06234 - 2.06234i) q^{29} +(-0.0321210 - 0.0985654i) q^{30} +(-3.14025 + 5.43908i) q^{31} +(5.65680 - 0.0246987i) q^{32} +(0.0438128 + 0.0758861i) q^{33} +(4.06519 + 0.860373i) q^{34} +(-3.23740 - 1.17852i) q^{35} +(-2.42828 + 5.47973i) q^{36} +(-1.40616 + 5.24787i) q^{37} +(-0.596064 - 11.1867i) q^{38} +(0.110046 + 0.0635352i) q^{39} +(2.85623 - 2.32535i) q^{40} -7.34101i q^{41} +(-0.0990370 - 0.185895i) q^{42} +(-1.99391 - 1.99391i) q^{43} +(-1.95496 + 2.42282i) q^{44} +(1.01002 + 3.76943i) q^{45} +(4.75824 + 4.27682i) 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} +(0.159765 + 0.0428089i) q^{51} +(-0.698448 + 4.46023i) q^{52} +(-11.2146 + 3.00493i) q^{53} +(-0.216369 + 0.425567i) q^{54} +2.02696i q^{55} +(4.89500 - 5.66030i) q^{56} -0.445921i q^{57} +(3.67676 + 1.86936i) q^{58} +(-2.96105 + 0.793411i) q^{59} +(0.118457 - 0.0863809i) q^{60} +(-9.72123 - 2.60480i) 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} +(-0.0828392 + 0.0921640i) q^{66} +(0.566758 + 2.11517i) q^{67} +(0.624456 + 5.84312i) q^{68} +(0.180077 + 0.180077i) q^{69} +(0.166059 - 4.86947i) q^{70} -7.26378i q^{71} +(-8.43218 - 0.863930i) q^{72} +(12.2392 + 7.06631i) q^{73} +(-7.67253 + 0.408819i) q^{74} +(-0.0481435 + 0.179674i) q^{75} +(14.7806 - 5.70337i) q^{76} +(0.714920 + 4.05583i) q^{77} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 - 1.66547i) q^{79} +(4.37827 + 2.82159i) q^{80} +(4.48574 - 7.76954i) q^{81} +(9.87083 - 3.21676i) q^{82} +(8.82731 - 8.82731i) q^{83} +(0.206560 - 0.214624i) q^{84} +(2.70543 + 2.70543i) q^{85} +(1.80733 - 3.55475i) q^{86} +(0.142188 + 0.0820924i) q^{87} +(-4.11440 - 1.56702i) q^{88} +(-11.5526 + 6.66987i) q^{89} +(-4.62586 + 3.00981i) q^{90} +(3.83862 + 4.57521i) q^{91} +(-3.66566 + 8.27206i) q^{92} +(-0.341503 - 0.0915056i) q^{93} +(-1.85186 + 2.06031i) q^{94} +(5.15752 - 8.93309i) q^{95} +(0.0837613 + 0.307230i) q^{96} -9.69578 q^{97} +(-1.38522 - 9.80210i) 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

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