LMFDB - Embedded newform 336.2.bq.b.109.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.22
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.816979 - 1.15436i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.665089 - 1.88618i) q^{4} +(0.397602 + 0.106537i) q^{5} +(0.490371 - 1.32647i) q^{6} +(0.990173 - 2.45348i) q^{7} +(-2.72069 - 0.773215i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.816979 - 1.15436i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.665089 - 1.88618i) q^{4} +(0.397602 + 0.106537i) q^{5} +(0.490371 - 1.32647i) q^{6} +(0.990173 - 2.45348i) q^{7} +(-2.72069 - 0.773215i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.447815 - 0.371937i) q^{10} +(0.789156 + 2.94517i) q^{11} +(-1.13060 - 1.64977i) q^{12} +(-1.20445 - 1.20445i) q^{13} +(-2.02324 - 3.14746i) q^{14} +0.411628 q^{15} +(-3.11531 + 2.50895i) q^{16} +(-0.646807 + 1.12030i) q^{17} +(0.130346 - 1.40819i) q^{18} +(-0.527534 + 1.96878i) q^{19} +(-0.0634931 - 0.820804i) q^{20} +(0.321426 - 2.62615i) q^{21} +(4.04451 + 1.49517i) q^{22} +(7.20198 - 4.15807i) q^{23} +(-2.82810 - 0.0427024i) q^{24} +(-4.18339 - 2.41528i) q^{25} +(-2.37438 + 0.406358i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-5.28624 - 0.235857i) q^{28} +(1.73431 + 1.73431i) q^{29} +(0.336292 - 0.475167i) q^{30} +(-2.95454 + 5.11741i) q^{31} +(0.351081 + 5.64595i) q^{32} +(1.52453 + 2.64057i) q^{33} +(0.764803 + 1.66191i) q^{34} +(0.655082 - 0.870018i) q^{35} +(-1.51907 - 1.30093i) q^{36} +(5.97426 + 1.60080i) q^{37} +(1.84170 + 2.21742i) q^{38} +(-1.47515 - 0.851677i) q^{39} +(-0.999375 - 0.597286i) q^{40} +0.372651i q^{41} +(-2.76893 - 2.51656i) q^{42} +(-4.89445 + 4.89445i) q^{43} +(5.03025 - 3.44729i) q^{44} +(0.397602 - 0.106537i) q^{45} +(1.08397 - 11.7107i) q^{46} +(6.21903 + 10.7717i) q^{47} +(-2.35980 + 3.22976i) q^{48} +(-5.03912 - 4.85874i) q^{49} +(-6.20584 + 2.85590i) q^{50} +(-0.334812 + 1.24953i) q^{51} +(-1.47074 + 3.07288i) q^{52} +(-1.93373 - 7.21678i) q^{53} +(-0.238563 - 1.39395i) q^{54} +1.25508i q^{55} +(-4.59102 + 5.90953i) q^{56} +2.03823i q^{57} +(3.41890 - 0.585119i) q^{58} +(2.13287 + 7.95999i) q^{59} +(-0.273769 - 0.776403i) q^{60} +(-1.08642 + 4.05457i) q^{61} +(3.49353 + 7.59142i) q^{62} +(-0.369225 - 2.61986i) q^{63} +(6.80428 + 4.20735i) q^{64} +(-0.350574 - 0.607212i) q^{65} +(4.29367 + 0.397432i) q^{66} +(6.46115 - 1.73126i) q^{67} +(2.54327 + 0.474890i) q^{68} +(5.88039 - 5.88039i) q^{69} +(-0.469125 - 1.46699i) q^{70} +4.39987i q^{71} +(-2.74279 + 0.690720i) q^{72} +(-6.66771 - 3.84961i) q^{73} +(6.72874 - 5.58862i) q^{74} +(-4.66596 - 1.25024i) q^{75} +(4.06433 - 0.314395i) q^{76} +(8.00731 + 0.980050i) q^{77} +(-2.18831 + 1.00705i) q^{78} +(-6.20951 - 10.7552i) q^{79} +(-1.50595 + 0.665667i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.430173 + 0.304448i) q^{82} +(7.59322 + 7.59322i) q^{83} +(-5.16716 + 1.14036i) q^{84} +(-0.376526 + 0.376526i) q^{85} +(1.65129 + 9.64861i) q^{86} +(2.12408 + 1.22634i) q^{87} +(0.130203 - 8.62308i) q^{88} +(-1.31387 + 0.758565i) q^{89} +(0.201851 - 0.546014i) q^{90} +(-4.14771 + 1.76248i) q^{91} +(-12.6328 - 10.8187i) q^{92} +(-1.52938 + 5.70773i) q^{93} +(17.5152 + 1.62124i) q^{94} +(-0.419497 + 0.726590i) q^{95} +(1.80040 + 5.36270i) q^{96} -10.4656 q^{97} +(-9.72558 + 1.84746i) q^{98} +(2.15601 + 2.15601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.816979	−	1.15436i	0.577692	−	0.816255i
$2$	0.816979	−	1.15436i	0.577692	−	0.816255i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.665089	−	1.88618i	−0.332545	−	0.943088i
$5$	0.397602	+	0.106537i	0.177813	+	0.0476449i	0.346627	−	0.938003i	$-0.387327\pi$
$5$	0.397602	+	0.106537i	0.177813	+	0.0476449i	−0.168814	+	0.985648i	$0.553994\pi$
$6$	0.490371	−	1.32647i	0.200193	−	0.541531i
$7$	0.990173	−	2.45348i	0.374250	−	0.927328i
$7$	0.990173	−	2.45348i	0.374250	−	0.927328i
$8$	−2.72069	−	0.773215i	−0.961908	−	0.273373i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	0.447815	−	0.371937i	0.141612	−	0.117617i
$11$	0.789156	+	2.94517i	0.237940	+	0.888002i	0.976802	+	0.214146i	$0.0686968\pi$
$11$	0.789156	+	2.94517i	0.237940	+	0.888002i	−0.738862	+	0.673857i	$0.764637\pi$
$12$	−1.13060	−	1.64977i	−0.326377	−	0.476247i
$13$	−1.20445	−	1.20445i	−0.334055	−	0.334055i	0.520069	−	0.854124i	$-0.325906\pi$
$13$	−1.20445	−	1.20445i	−0.334055	−	0.334055i	−0.854124	+	0.520069i	$0.825906\pi$
$14$	−2.02324	−	3.14746i	−0.540735	−	0.841193i
$15$	0.411628			0.106282
$16$	−3.11531	+	2.50895i	−0.778828	+	0.627237i
$17$	−0.646807	+	1.12030i	−0.156874	+	0.271713i	−0.933740	−	0.357953i	$-0.883475\pi$
$17$	−0.646807	+	1.12030i	−0.156874	+	0.271713i	0.776866	+	0.629666i	$0.216808\pi$
$18$	0.130346	−	1.40819i	0.0307227	−	0.331914i
$19$	−0.527534	+	1.96878i	−0.121025	+	0.451670i	−0.999667	−	0.0258109i	$-0.991783\pi$
$19$	−0.527534	+	1.96878i	−0.121025	+	0.451670i	0.878642	+	0.477481i	$0.158450\pi$
$20$	−0.0634931	−	0.820804i	−0.0141975	−	0.183537i
$21$	0.321426	−	2.62615i	0.0701410	−	0.573074i
$22$	4.04451	+	1.49517i	0.862292	+	0.318772i
$23$	7.20198	−	4.15807i	1.50172	−	0.867017i	0.501719	−	0.865031i	$-0.332701\pi$
$23$	7.20198	−	4.15807i	1.50172	−	0.867017i	0.999998	−	0.00198570i	$-0.000632068\pi$
$24$	−2.82810	−	0.0427024i	−0.577284	−	0.00871660i
$25$	−4.18339	−	2.41528i	−0.836678	−	0.483056i
$26$	−2.37438	+	0.406358i	−0.465655	+	0.0796933i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−5.28624	−	0.235857i	−0.999006	−	0.0445728i
$29$	1.73431	+	1.73431i	0.322052	+	0.322052i	0.849554	−	0.527502i	$-0.176871\pi$
$29$	1.73431	+	1.73431i	0.322052	+	0.322052i	−0.527502	+	0.849554i	$0.676871\pi$
$30$	0.336292	−	0.475167i	0.0613982	−	0.0867531i
$31$	−2.95454	+	5.11741i	−0.530651	+	0.919115i	0.468709	+	0.883352i	$0.344719\pi$
$31$	−2.95454	+	5.11741i	−0.530651	+	0.919115i	−0.999360	+	0.0357621i	$0.988614\pi$
$32$	0.351081	+	5.64595i	0.0620629	+	0.998072i
$33$	1.52453	+	2.64057i	0.265387	+	0.459664i
$34$	0.764803	+	1.66191i	0.131163	+	0.285015i
$35$	0.655082	−	0.870018i	0.110729	−	0.147060i
$36$	−1.51907	−	1.30093i	−0.253179	−	0.216822i
$37$	5.97426	+	1.60080i	0.982162	+	0.263170i	0.713955	−	0.700192i	$-0.246902\pi$
$37$	5.97426	+	1.60080i	0.982162	+	0.263170i	0.268207	+	0.963361i	$0.413569\pi$
$38$	1.84170	+	2.21742i	0.298763	+	0.359713i
$39$	−1.47515	−	0.851677i	−0.236213	−	0.136377i
$40$	−0.999375	−	0.597286i	−0.158015	−	0.0944392i
$41$			0.372651i			0.0581984i	0.999577	+	0.0290992i	$0.00926386\pi$
$41$			0.372651i			0.0581984i	−0.999577	+	0.0290992i	$0.990736\pi$
$42$	−2.76893	−	2.51656i	−0.427254	−	0.388313i
$43$	−4.89445	+	4.89445i	−0.746396	+	0.746396i	−0.973800	−	0.227404i	$-0.926976\pi$
$43$	−4.89445	+	4.89445i	−0.746396	+	0.746396i	0.227404	+	0.973800i	$0.426976\pi$
$44$	5.03025	−	3.44729i	0.758339	−	0.519698i
$45$	0.397602	−	0.106537i	0.0592710	−	0.0158816i
$46$	1.08397	−	11.7107i	0.159823	−	1.72665i
$47$	6.21903	+	10.7717i	0.907139	+	1.57121i	0.818021	+	0.575189i	$0.195071\pi$
$47$	6.21903	+	10.7717i	0.907139	+	1.57121i	0.0891179	+	0.996021i	$0.471595\pi$
$48$	−2.35980	+	3.22976i	−0.340607	+	0.466176i
$49$	−5.03912	−	4.85874i	−0.719874	−	0.694105i
$50$	−6.20584	+	2.85590i	−0.877639	+	0.403885i
$51$	−0.334812	+	1.24953i	−0.0468830	+	0.174970i
$52$	−1.47074	+	3.07288i	−0.203955	+	0.426131i
$53$	−1.93373	−	7.21678i	−0.265618	−	0.991301i	−0.961871	−	0.273504i	$-0.911817\pi$
$53$	−1.93373	−	7.21678i	−0.265618	−	0.991301i	0.696253	−	0.717797i	$-0.254849\pi$
$54$	−0.238563	−	1.39395i	−0.0324644	−	0.189692i
$55$			1.25508i			0.169235i
$56$	−4.59102	+	5.90953i	−0.613500	+	0.789694i
$57$			2.03823i			0.269971i
$58$	3.41890	−	0.585119i	0.448924	−	0.0768299i
$59$	2.13287	+	7.95999i	0.277677	+	1.03630i	0.954026	+	0.299722i	$0.0968941\pi$
$59$	2.13287	+	7.95999i	0.277677	+	1.03630i	−0.676350	+	0.736580i	$0.736439\pi$
$60$	−0.273769	−	0.776403i	−0.0353435	−	0.100233i
$61$	−1.08642	+	4.05457i	−0.139102	+	0.519134i	0.860846	+	0.508866i	$0.169935\pi$
$61$	−1.08642	+	4.05457i	−0.139102	+	0.519134i	−0.999947	+	0.0102681i	$0.996732\pi$
$62$	3.49353	+	7.59142i	0.443679	+	0.964111i
$63$	−0.369225	−	2.61986i	−0.0465179	−	0.330071i
$64$	6.80428	+	4.20735i	0.850535	+	0.525919i
$65$	−0.350574	−	0.607212i	−0.0434833	−	0.0753154i
$66$	4.29367	+	0.397432i	0.528515	+	0.0489205i
$67$	6.46115	−	1.73126i	0.789355	−	0.211507i	0.158450	−	0.987367i	$-0.449350\pi$
$67$	6.46115	−	1.73126i	0.789355	−	0.211507i	0.630905	+	0.775860i	$0.282684\pi$
$68$	2.54327	+	0.474890i	0.308417	+	0.0575889i
$69$	5.88039	−	5.88039i	0.707916	−	0.707916i
$70$	−0.469125	−	1.46699i	−0.0560712	−	0.175338i
$71$			4.39987i			0.522169i	0.965316	+	0.261084i	$0.0840800\pi$
$71$			4.39987i			0.522169i	−0.965316	+	0.261084i	$0.915920\pi$
$72$	−2.74279	+	0.690720i	−0.323241	+	0.0814021i
$73$	−6.66771	−	3.84961i	−0.780397	−	0.450562i	0.0561741	−	0.998421i	$-0.482110\pi$
$73$	−6.66771	−	3.84961i	−0.780397	−	0.450562i	−0.836571	+	0.547859i	$0.815443\pi$
$74$	6.72874	−	5.58862i	0.782200	−	0.649664i
$75$	−4.66596	−	1.25024i	−0.538779	−	0.144365i
$76$	4.06433	−	0.314395i	0.466210	−	0.0360636i
$77$	8.00731	+	0.980050i	0.912518	+	0.111687i
$78$	−2.18831	+	1.00705i	−0.247777	+	0.114026i
$79$	−6.20951	−	10.7552i	−0.698624	−	1.21005i	−0.968944	−	0.247282i	$-0.920463\pi$
$79$	−6.20951	−	10.7552i	−0.698624	−	1.21005i	0.270320	−	0.962771i	$-0.412871\pi$
$80$	−1.50595	+	0.665667i	−0.168370	+	0.0744238i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.430173	+	0.304448i	0.0475047	+	0.0336207i
$83$	7.59322	+	7.59322i	0.833464	+	0.833464i	0.987989	−	0.154525i	$-0.0493848\pi$
$83$	7.59322	+	7.59322i	0.833464	+	0.833464i	−0.154525	+	0.987989i	$0.549385\pi$
$84$	−5.16716	+	1.14036i	−0.563784	+	0.124423i
$85$	−0.376526	+	0.376526i	−0.0408399	+	0.0408399i
$86$	1.65129	+	9.64861i	0.178063	+	1.04044i
$87$	2.12408	+	1.22634i	0.227725	+	0.131477i
$88$	0.130203	−	8.62308i	0.0138796	−	0.919223i
$89$	−1.31387	+	0.758565i	−0.139270	+	0.0804077i	−0.568016	−	0.823017i	$-0.692289\pi$
$89$	−1.31387	+	0.758565i	−0.139270	+	0.0804077i	0.428746	+	0.903425i	$0.358956\pi$
$90$	0.201851	−	0.546014i	0.0212769	−	0.0575550i
$91$	−4.14771	+	1.76248i	−0.434799	+	0.184758i
$92$	−12.6328	−	10.8187i	−1.31706	−	1.12793i
$93$	−1.52938	+	5.70773i	−0.158590	+	0.591864i
$94$	17.5152	+	1.62124i	1.80655	+	0.167219i
$95$	−0.419497	+	0.726590i	−0.0430395	+	0.0745466i
$96$	1.80040	+	5.36270i	0.183752	+	0.547328i
$97$	−10.4656			−1.06262			−0.531309	−	0.847178i	$-0.678300\pi$
$97$	−10.4656			−1.06262			−0.531309	+	0.847178i	$0.678300\pi$
$98$	−9.72558	+	1.84746i	−0.982432	+	0.186622i
$99$	2.15601	+	2.15601i	0.216688	+	0.216688i
$100$	−1.77332	+	9.49698i	−0.177332	+	0.949698i
$101$	−3.60959	−	13.4712i	−0.359168	−	1.34043i	−0.875158	−	0.483838i	$-0.839242\pi$
$101$	−3.60959	−	13.4712i	−0.359168	−	1.34043i	0.515990	−	0.856595i	$-0.327424\pi$
$102$	1.16888	+	1.40734i	0.115736	+	0.139347i
$103$	9.79175	−	5.65327i	0.964809	−	0.557033i	0.0671595	−	0.997742i	$-0.478606\pi$
$103$	9.79175	−	5.65327i	0.964809	−	0.557033i	0.897650	+	0.440709i	$0.145273\pi$
$104$	2.34564	+	4.20824i	0.230009	+	0.412652i
$105$	0.407583	−	1.00992i	0.0397760	−	0.0985582i
$106$	−9.91057	−	3.66374i	−0.962600	−	0.355854i
$107$	−1.63213	−	0.437329i	−0.157784	−	0.0422782i	0.179062	−	0.983838i	$-0.442694\pi$
$107$	−1.63213	−	0.437329i	−0.157784	−	0.0422782i	−0.336846	+	0.941560i	$0.609360\pi$
$108$	−1.80402	−	0.863438i	−0.173592	−	0.0830844i
$109$	6.04087	−	1.61865i	0.578610	−	0.155038i	0.0423676	−	0.999102i	$-0.486510\pi$
$109$	6.04087	−	1.61865i	0.578610	−	0.155038i	0.536242	+	0.844064i	$0.319843\pi$
$110$	1.44881	+	1.02538i	0.138139	+	0.0977657i
$111$	6.18501			0.587055
$112$	3.07096	+	10.1276i	0.290178	+	0.956973i
$113$	−15.9492			−1.50037			−0.750187	−	0.661226i	$-0.770036\pi$
$113$	−15.9492			−1.50037			−0.750187	+	0.661226i	$0.770036\pi$
$114$	2.35285	+	1.66520i	0.220365	+	0.155960i
$115$	3.30651	−	0.885977i	0.308334	−	0.0826178i
$116$	2.11774	−	4.42467i	0.196627	−	0.410820i
$117$	−1.64531	−	0.440860i	−0.152109	−	0.0407575i
$118$	10.9312	+	4.04105i	1.00630	+	0.372009i
$119$	2.10819	+	2.69622i	0.193257	+	0.247162i
$120$	−1.11991	−	0.318277i	−0.102233	−	0.0290546i
$121$	1.47502	−	0.851601i	0.134092	−	0.0774183i
$122$	3.79284	+	4.56661i	0.343388	+	0.413442i
$123$	0.0964492	+	0.359953i	0.00869654	+	0.0324559i
$124$	11.6174	+	2.16924i	1.04327	+	0.194804i
$125$	−2.86133	−	2.86133i	−0.255925	−	0.255925i
$126$	−3.32591	−	1.71416i	−0.296296	−	0.152709i
$127$	−2.95707			−0.262397			−0.131199	−	0.991356i	$-0.541883\pi$
$127$	−2.95707			−0.262397			−0.131199	+	0.991356i	$0.541883\pi$
$128$	10.4157	−	4.41726i	0.920631	−	0.390434i
$129$	−3.46090	+	5.99445i	−0.304715	+	0.527782i
$130$	−0.987352	−	0.0913915i	−0.0865965	−	0.00801556i
$131$	−4.54516	+	16.9628i	−0.397112	+	1.48204i	0.421040	+	0.907042i	$0.361665\pi$
$131$	−4.54516	+	16.9628i	−0.397112	+	1.48204i	−0.818153	+	0.575001i	$0.805002\pi$
$132$	3.96662	−	4.63175i	0.345250	−	0.403142i
$133$	4.30802	+	3.24373i	0.373552	+	0.281267i
$134$	3.28013	−	8.87288i	0.283360	−	0.766500i
$135$	0.356480	−	0.205814i	0.0306809	−	0.0177137i
$136$	2.62599	−	2.54787i	0.225177	−	0.218478i
$137$	−1.64029	−	0.947019i	−0.140139	−	0.0809093i	0.428291	−	0.903641i	$-0.359116\pi$
$137$	−1.64029	−	0.947019i	−0.140139	−	0.0809093i	−0.568430	+	0.822731i	$0.692449\pi$
$138$	−1.98392	−	11.5922i	−0.168883	−	0.986797i
$139$	−7.57484	+	7.57484i	−0.642489	+	0.642489i	−0.951167	−	0.308677i	$-0.900114\pi$
$139$	−7.57484	+	7.57484i	−0.642489	+	0.642489i	0.308677	+	0.951167i	$0.400114\pi$
$140$	−2.07669	−	0.656959i	−0.175513	−	0.0555232i
$141$	8.79503	+	8.79503i	0.740675	+	0.740675i
$142$	5.07903	+	3.59460i	0.426223	+	0.301652i
$143$	2.59682	−	4.49782i	0.217157	−	0.376127i
$144$	−1.44347	+	3.73047i	−0.120289	+	0.310873i
$145$	0.504796	+	0.874332i	0.0419210	+	0.0726093i
$146$	−9.89121	+	4.55188i	−0.818602	+	0.376717i
$147$	−6.12495	−	3.38896i	−0.505177	−	0.279517i
$148$	−0.954029	−	12.3332i	−0.0784207	−	1.01378i
$149$	−3.20814	−	0.859620i	−0.262821	−	0.0704228i	0.125002	−	0.992156i	$-0.460106\pi$
$149$	−3.20814	−	0.859620i	−0.262821	−	0.0704228i	−0.387823	+	0.921734i	$0.626773\pi$
$150$	−5.25523	+	4.36478i	−0.429087	+	0.356383i
$151$	−18.6433	−	10.7637i	−1.51717	−	0.875940i	−0.999796	−	0.0201829i	$-0.993575\pi$
$151$	−18.6433	−	10.7637i	−1.51717	−	0.875940i	−0.517377	−	0.855758i	$-0.673092\pi$
$152$	2.95755	−	4.94854i	0.239889	−	0.401380i
$153$			1.29361i			0.104582i
$154$	7.67314	−	8.44263i	0.618319	−	0.680327i
$155$	−1.71993	+	1.71993i	−0.138148	+	0.138148i
$156$	−0.625307	+	3.34883i	−0.0500646	+	0.268121i
$157$	−10.1598	+	2.72230i	−0.810836	+	0.217263i	−0.640336	−	0.768095i	$-0.721205\pi$
$157$	−10.1598	+	2.72230i	−0.810836	+	0.217263i	−0.170500	+	0.985358i	$0.554538\pi$
$158$	−17.4884	−	1.61876i	−1.39130	−	0.128782i
$159$	−3.73568	−	6.47039i	−0.296259	−	0.513135i
$160$	−0.461913	+	2.28224i	−0.0365174	+	0.180427i
$161$	−3.07052	−	21.7871i	−0.241991	−	1.71706i
$162$	−0.591214	−	1.28470i	−0.0464502	−	0.100936i
$163$	4.07021	−	15.1902i	0.318803	−	1.18979i	−0.601593	−	0.798803i	$-0.705467\pi$
$163$	4.07021	−	15.1902i	0.318803	−	1.18979i	0.920396	−	0.390987i	$-0.127866\pi$
$164$	0.702886	−	0.247846i	0.0548861	−	0.0193535i
$165$	0.324839	+	1.21231i	0.0252887	+	0.0943786i
$166$	14.9688	−	2.56180i	1.16180	−	0.198834i
$167$		−	21.3137i		−	1.64930i	−0.565641	−	0.824651i	$-0.691371\pi$
$167$		−	21.3137i		−	1.64930i	0.565641	−	0.824651i	$-0.308629\pi$
$168$	−2.90508	+	6.89641i	−0.224132	+	0.532070i
$169$		−	10.0986i		−	0.776814i
$170$	0.127032	+	0.742259i	0.00974291	+	0.0569287i
$171$	0.527534	+	1.96878i	0.0403415	+	0.150557i
$172$	12.4870	+	5.97654i	0.952127	+	0.455707i
$173$	−0.282160	+	1.05303i	−0.0214522	+	0.0800607i	−0.975822	−	0.218566i	$-0.929862\pi$
$173$	−0.282160	+	1.05303i	−0.0214522	+	0.0800607i	0.954370	+	0.298627i	$0.0965287\pi$
$174$	3.15097	−	1.45006i	0.238874	−	0.109929i
$175$	−10.0681	+	7.87231i	−0.761078	+	0.595091i
$176$	−9.84775	−	7.19518i	−0.742302	−	0.542357i
$177$	4.12040	+	7.13674i	0.309708	+	0.536430i
$178$	−0.197751	+	2.13641i	−0.0148221	+	0.160131i
$179$	−4.18886	+	1.12240i	−0.313090	+	0.0838922i	−0.411942	−	0.911210i	$-0.635150\pi$
$179$	−4.18886	+	1.12240i	−0.313090	+	0.0838922i	0.0988524	+	0.995102i	$0.468483\pi$
$180$	−0.465389	−	0.679091i	−0.0346880	−	0.0506164i
$181$	−7.75354	+	7.75354i	−0.576316	+	0.576316i	−0.933886	−	0.357570i	$-0.883605\pi$
$181$	−7.75354	+	7.75354i	−0.576316	+	0.576316i	0.357570	+	0.933886i	$0.383605\pi$
$182$	−1.35406	+	6.22786i	−0.100370	+	0.461640i
$183$			4.19760i			0.310295i
$184$	−22.8094	+	5.74412i	−1.68153	+	0.423462i
$185$	2.20483	+	1.27296i	0.162103	+	0.0935900i
$186$	5.33930	+	6.42856i	0.391496	+	0.471365i
$187$	−3.80991	−	1.02086i	−0.278608	−	0.0746529i
$188$	16.1811	−	18.8943i	1.18012	−	1.37801i
$189$	−1.03471	−	2.43503i	−0.0752643	−	0.177122i
$190$	0.496025	+	1.07786i	0.0359855	+	0.0781961i
$191$	−4.41802	−	7.65223i	−0.319677	−	0.553696i	0.660744	−	0.750611i	$-0.270241\pi$
$191$	−4.41802	−	7.65223i	−0.319677	−	0.553696i	−0.980421	+	0.196915i	$0.936908\pi$
$192$	7.66137	+	2.30291i	0.552912	+	0.166198i
$193$	10.1233	−	17.5342i	0.728694	−	1.26214i	−0.228741	−	0.973487i	$-0.573461\pi$
$193$	10.1233	−	17.5342i	0.728694	−	1.26214i	0.957435	−	0.288648i	$-0.0932059\pi$
$194$	−8.55015	+	12.0810i	−0.613865	+	0.867367i
$195$	−0.495786	−	0.495786i	−0.0355040	−	0.0355040i
$196$	−5.81296	+	12.7361i	−0.415212	+	0.909725i
$197$	5.11666	−	5.11666i	0.364547	−	0.364547i	−0.500937	−	0.865484i	$-0.667011\pi$
$197$	5.11666	−	5.11666i	0.364547	−	0.364547i	0.865484	+	0.500937i	$0.167011\pi$
$198$	4.25023	−	0.727395i	0.302051	−	0.0516937i
$199$	−22.0702	−	12.7422i	−1.56452	−	0.903273i	−0.996790	−	0.0800553i	$-0.974490\pi$
$199$	−22.0702	−	12.7422i	−1.56452	−	0.903273i	−0.567725	−	0.823218i	$-0.692176\pi$
$200$	9.51416	+	9.80588i	0.672753	+	0.693381i
$201$	5.79290	−	3.34454i	0.408600	−	0.235905i
$202$	−18.4995	−	6.83891i	−1.30162	−	0.481184i
$203$	5.97234	−	2.53782i	0.419176	−	0.178120i
$204$	2.57952	−	0.199538i	0.180603	−	0.0139705i
$205$	−0.0397012	+	0.148167i	−0.00277285	+	0.0103484i
$206$	1.47376	−	15.9218i	0.102681	−	1.10932i
$207$	4.15807	−	7.20198i	0.289006	−	0.500572i
$208$	6.77416	+	0.730337i	0.469703	+	0.0506397i
$209$	−6.21471			−0.429880
$210$	−0.832824	−	1.29558i	−0.0574703	−	0.0894036i
$211$	10.4900	+	10.4900i	0.722158	+	0.722158i	0.969044	−	0.246886i	$-0.0794075\pi$
$211$	10.4900	+	10.4900i	0.722158	+	0.722158i	−0.246886	+	0.969044i	$0.579407\pi$
$212$	−12.3260	+	8.44716i	−0.846554	+	0.580153i
$213$	1.13877	+	4.24995i	0.0780272	+	0.291202i
$214$	−1.83825	+	1.52678i	−0.125660	+	0.104368i
$215$	−2.46748	+	1.42460i	−0.168281	+	0.0971570i
$216$	−2.47056	+	1.37707i	−0.168100	+	0.0936978i
$217$	9.62996	+	12.3160i	0.653724	+	0.836066i
$218$	3.06677	−	8.29573i	0.207708	−	0.561858i
$219$	−7.43687	−	1.99270i	−0.502537	−	0.134654i
$220$	2.36730	−	0.834741i	0.159603	−	0.0562782i
$221$	2.12840	−	0.570303i	0.143172	−	0.0383627i
$222$	5.05302	−	7.13972i	0.339137	−	0.479187i
$223$	0.587287			0.0393276			0.0196638	−	0.999807i	$-0.493740\pi$
$223$	0.587287			0.0393276			0.0196638	+	0.999807i	$0.493740\pi$
$224$	14.1998	+	4.72910i	0.948767	+	0.315976i
$225$	−4.83056			−0.322037
$226$	−13.0302	+	18.4111i	−0.866754	+	1.22469i
$227$	−15.5693	+	4.17178i	−1.03337	+	0.276891i	−0.735363	−	0.677673i	$-0.762988\pi$
$227$	−15.5693	+	4.17178i	−1.03337	+	0.276891i	−0.298007	+	0.954564i	$0.596322\pi$
$228$	3.84447	−	1.35561i	0.254606	−	0.0897773i
$229$	9.08809	+	2.43515i	0.600558	+	0.160919i	0.546274	−	0.837607i	$-0.316046\pi$
$229$	9.08809	+	2.43515i	0.600558	+	0.160919i	0.0542837	+	0.998526i	$0.482712\pi$
$230$	1.67862	−	4.54073i	0.110685	−	0.299407i
$231$	7.98813	−	1.12579i	0.525580	−	0.0740715i
$232$	−3.37751	−	6.05949i	−0.221745	−	0.397825i
$233$	−9.33291	+	5.38836i	−0.611419	+	0.353003i	−0.773521	−	0.633771i	$-0.781506\pi$
$233$	−9.33291	+	5.38836i	−0.611419	+	0.353003i	0.162102	+	0.986774i	$0.448173\pi$
$234$	−1.85310	+	1.53911i	−0.121141	+	0.100615i
$235$	1.32512	+	4.94540i	0.0864410	+	0.322602i
$236$	13.5954	−	9.31708i	0.884985	−	0.606490i
$237$	−8.78157	−	8.78157i	−0.570424	−	0.570424i
$238$	4.83475	−	0.230849i	0.313390	−	0.0149637i
$239$	16.1356			1.04373			0.521864	−	0.853029i	$-0.325237\pi$
$239$	16.1356			1.04373			0.521864	+	0.853029i	$0.325237\pi$
$240$	−1.28235	+	1.03275i	−0.0827753	+	0.0666640i
$241$	−7.33343	+	12.7019i	−0.472388	+	0.818200i	−0.999501	−	0.0315953i	$-0.989941\pi$
$241$	−7.33343	+	12.7019i	−0.472388	+	0.818200i	0.527113	+	0.849795i	$0.323275\pi$
$242$	0.222005	−	2.39844i	0.0142710	−	0.154177i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	8.37019	−	0.647474i	0.535846	−	0.0414503i
$245$	−1.48593	−	2.46870i	−0.0949324	−	0.157719i
$246$	0.494313	+	0.182738i	0.0315162	+	0.0116509i
$247$	3.00669	−	1.73592i	0.191311	−	0.110454i
$248$	11.9952	−	11.6384i	0.761698	−	0.739038i
$249$	9.29975	+	5.36921i	0.589348	+	0.340260i
$250$	−5.64065	+	0.965355i	−0.356746	+	0.0610544i
$251$	21.1241	−	21.1241i	1.33334	−	1.33334i	0.430976	−	0.902363i	$-0.358169\pi$
$251$	21.1241	−	21.1241i	1.33334	−	1.33334i	0.902363	−	0.430976i	$-0.141831\pi$
$252$	−4.69595	+	2.43886i	−0.295817	+	0.153634i
$253$	17.9297	+	17.9297i	1.12723	+	1.12723i
$254$	−2.41586	+	3.41352i	−0.151585	+	0.214183i
$255$	−0.266244	+	0.461148i	−0.0166728	+	0.0288782i
$256$	3.41035	−	15.6323i	0.213147	−	0.977020i
$257$	2.21199	+	3.83129i	0.137980	+	0.238989i	0.926732	−	0.375723i	$-0.122606\pi$
$257$	2.21199	+	3.83129i	0.137980	+	0.238989i	−0.788752	+	0.614712i	$0.789272\pi$
$258$	4.09226	+	8.89246i	0.254773	+	0.553620i
$259$	9.84307	−	13.0726i	0.611619	−	0.812295i
$260$	−0.912145	+	1.06509i	−0.0565688	+	0.0660543i
$261$	2.36911	+	0.634800i	0.146644	+	0.0392931i
$262$	15.8678	+	19.1050i	0.980317	+	1.18031i
$263$	−12.5233	−	7.23032i	−0.772219	−	0.445841i	0.0614469	−	0.998110i	$-0.480429\pi$
$263$	−12.5233	−	7.23032i	−0.772219	−	0.445841i	−0.833665	+	0.552270i	$0.813762\pi$
$264$	−2.10605	−	8.36295i	−0.129618	−	0.514704i
$265$		−	3.07542i		−	0.188922i
$266$	7.26399	−	2.32294i	0.445384	−	0.142429i
$267$	−1.07277	+	1.07277i	−0.0656526	+	0.0656526i
$268$	−7.56269	−	11.0354i	−0.461965	−	0.674095i
$269$	0.660397	−	0.176953i	0.0402651	−	0.0107890i	−0.238630	−	0.971111i	$-0.576698\pi$
$269$	0.660397	−	0.176953i	0.0402651	−	0.0107890i	0.278895	+	0.960321i	$0.410032\pi$
$270$	0.0536539	−	0.579652i	0.00326527	−	0.0352765i
$271$	5.00366	+	8.66659i	0.303951	+	0.526458i	0.977027	−	0.213115i	$-0.0683609\pi$
$271$	5.00366	+	8.66659i	0.303951	+	0.526458i	−0.673076	+	0.739573i	$0.735028\pi$
$272$	−0.795775	−	5.11290i	−0.0482510	−	0.310015i
$273$	−3.55022	+	2.77594i	−0.214869	+	0.168007i
$274$	−2.43328	+	1.11978i	−0.147000	+	0.0676486i
$275$	3.81207	−	14.2268i	0.229876	−	0.857910i
$276$	−15.0024	−	7.18046i	−0.903040	−	0.432213i
$277$	7.53342	+	28.1151i	0.452639	+	1.68927i	0.694937	+	0.719071i	$0.255432\pi$
$277$	7.53342	+	28.1151i	0.452639	+	1.68927i	−0.242298	+	0.970202i	$0.577901\pi$
$278$	2.55560	+	14.9326i	0.153274	+	0.895596i
$279$			5.90908i			0.353767i
$280$	−2.45498	+	1.86053i	−0.146713	+	0.111188i
$281$			15.2029i			0.906927i	0.891275	+	0.453463i	$0.149812\pi$
$281$			15.2029i			0.906927i	−0.891275	+	0.453463i	$0.850188\pi$
$282$	17.3380	−	2.96726i	1.03246	−	0.176698i
$283$	−5.35743	−	19.9942i	−0.318466	−	1.18853i	−0.920719	−	0.390226i	$-0.872397\pi$
$283$	−5.35743	−	19.9942i	−0.318466	−	1.18853i	0.602253	−	0.798305i	$-0.294270\pi$
$284$	8.29893	−	2.92631i	0.492451	−	0.173644i
$285$	−0.217148	+	0.810406i	−0.0128627	+	0.0480043i
$286$	−3.07055	−	6.67229i	−0.181566	−	0.394540i
$287$	0.914292	+	0.368989i	0.0539690	+	0.0217807i
$288$	3.12702	+	4.71399i	0.184261	+	0.277775i
$289$	7.66328	+	13.2732i	0.450781	+	0.780776i
$290$	1.42170	+	0.131596i	0.0834851	+	0.00772756i
$291$	−10.1090	+	2.70869i	−0.592598	+	0.158786i
$292$	−2.82641	+	15.1368i	−0.165403	+	0.885814i
$293$	−5.67023	+	5.67023i	−0.331258	+	0.331258i	−0.853064	−	0.521806i	$-0.825259\pi$
$293$	−5.67023	+	5.67023i	−0.331258	+	0.331258i	0.521806	+	0.853064i	$0.325259\pi$
$294$	−8.91603	+	4.30168i	−0.519993	+	0.250879i
$295$			3.39214i			0.197498i
$296$	−15.0163	−	8.97465i	−0.872806	−	0.521641i
$297$	2.64057	+	1.52453i	0.153221	+	0.0884624i
$298$	−3.61330	+	3.00106i	−0.209313	+	0.173847i
$299$	−13.6826	−	3.66625i	−0.791287	−	0.212025i
$300$	0.745108	+	9.63235i	0.0430188	+	0.556124i
$301$	7.16207	+	16.8548i	0.412815	+	0.971493i
$302$	−27.6564	+	12.7274i	−1.59145	+	0.732377i
$303$	−6.97320	−	12.0779i	−0.400600	−	0.693859i
$304$	−3.29614	−	7.45693i	−0.189047	−	0.427684i
$305$	−0.863924	+	1.49636i	−0.0494682	+	0.0856814i
$306$	1.49329	+	1.05686i	0.0853659	+	0.0604164i
$307$	21.8596	+	21.8596i	1.24759	+	1.24759i	0.956780	+	0.290812i	$0.0939255\pi$
$307$	21.8596	+	21.8596i	1.24759	+	1.24759i	0.290812	+	0.956780i	$0.406075\pi$
$308$	−3.47703	−	15.7550i	−0.198122	−	0.897725i
$309$	7.99493	−	7.99493i	0.454816	−	0.454816i
$310$	0.580268	+	3.39056i	0.0329570	+	0.192571i
$311$	21.3785	+	12.3429i	1.21226	+	0.699901i	0.963252	−	0.268600i	$-0.0865609\pi$
$311$	21.3785	+	12.3429i	1.21226	+	0.699901i	0.249012	+	0.968500i	$0.419894\pi$
$312$	3.35488	+	3.45775i	0.189933	+	0.195757i
$313$	−2.55699	+	1.47628i	−0.144529	+	0.0834441i	−0.570521	−	0.821283i	$-0.693259\pi$
$313$	−2.55699	+	1.47628i	−0.144529	+	0.0834441i	0.425992	+	0.904727i	$0.359925\pi$
$314$	−5.15780	+	13.9521i	−0.291071	+	0.787360i
$315$	0.132308	−	1.08100i	0.00745472	−	0.0609074i
$316$	−16.1563	+	18.8654i	−0.908862	+	1.06126i
$317$	−1.61944	+	6.04382i	−0.0909566	+	0.339454i	−0.996375	−	0.0850649i	$-0.972890\pi$
$317$	−1.61944	+	6.04382i	−0.0909566	+	0.339454i	0.905419	+	0.424519i	$0.139557\pi$
$318$	−10.5211	−	0.973858i	−0.589995	−	0.0546113i
$319$	−3.73919	+	6.47646i	−0.209354	+	0.362612i
$320$	2.25716	+	2.39776i	0.126179	+	0.134039i
$321$	−1.68971			−0.0943103
$322$	−27.6587	−	14.2551i	−1.54136	−	0.794408i
$323$	−1.86442	−	1.86442i	−0.103739	−	0.103739i
$324$	−1.96602	−	0.367103i	−0.109223	−	0.0203946i
$325$	2.12960	+	7.94779i	0.118129	+	0.440864i
$326$	−14.2097	−	17.1086i	−0.787002	−	0.947556i
$327$	5.41609	−	3.12698i	0.299511	−	0.172923i
$328$	0.288139	−	1.01387i	0.0159098	−	0.0559815i
$329$	32.5860	−	4.59244i	1.79652	−	0.253189i
$330$	1.66483	+	0.615456i	0.0916460	+	0.0338797i
$331$	1.13542	+	0.304235i	0.0624083	+	0.0167223i	0.289888	−	0.957061i	$-0.406382\pi$
$331$	1.13542	+	0.304235i	0.0624083	+	0.0167223i	−0.227480	+	0.973783i	$0.573049\pi$
$332$	9.27197	−	19.3723i	0.508865	−	1.06319i
$333$	5.97426	−	1.60080i	0.327387	−	0.0877232i
$334$	−24.6036	−	17.4128i	−1.34625	−	0.952788i
$335$	2.75341			0.150435
$336$	5.58754	+	8.98773i	0.304825	+	0.490321i
$337$	10.4061			0.566858			0.283429	−	0.958993i	$-0.408528\pi$
$337$	10.4061			0.566858			0.283429	+	0.958993i	$0.408528\pi$
$338$	−11.6574	−	8.25034i	−0.634079	−	0.448759i
$339$	−15.4057	+	4.12795i	−0.836725	+	0.224200i
$340$	0.960616	+	0.459770i	0.0520967	+	0.0249345i
$341$	−17.4032	−	4.66319i	−0.942439	−	0.252526i
$342$	2.70367	+	0.999492i	0.146198	+	0.0540463i
$343$	−16.9104	+	7.55238i	−0.913076	+	0.407790i
$344$	17.1007	−	9.53180i	0.922009	−	0.513920i
$345$	2.96454	−	1.71158i	0.159605	−	0.0921482i
$346$	0.985061	+	1.18602i	0.0529572	+	0.0637609i
$347$	7.69810	+	28.7297i	0.413255	+	1.54229i	0.788304	+	0.615285i	$0.210959\pi$
$347$	7.69810	+	28.7297i	0.413255	+	1.54229i	−0.375049	+	0.927005i	$0.622374\pi$
$348$	0.900387	−	4.82201i	0.0482658	−	0.258487i
$349$	−20.5022	−	20.5022i	−1.09746	−	1.09746i	−0.994707	−	0.102752i	$-0.967235\pi$
$349$	−20.5022	−	20.5022i	−1.09746	−	1.09746i	−0.102752	−	0.994707i	$-0.532765\pi$
$350$	0.862027	+	18.0537i	0.0460773	+	0.965013i
$351$	−1.70335			−0.0909183
$352$	−16.3512	+	5.48953i	−0.871523	+	0.292593i
$353$	−6.46519	+	11.1980i	−0.344107	+	0.596012i	−0.985191	−	0.171459i	$-0.945152\pi$
$353$	−6.46519	+	11.1980i	−0.344107	+	0.596012i	0.641084	+	0.767471i	$0.278485\pi$
$354$	11.6046	+	1.07415i	0.616779	+	0.0570904i
$355$	−0.468750	+	1.74940i	−0.0248787	+	0.0928484i
$356$	2.30463	+	1.97368i	0.122145	+	0.104605i
$357$	2.73418	+	2.05871i	0.144708	+	0.108958i
$358$	−2.12656	+	5.75243i	−0.112392	+	0.304025i
$359$	6.40168	−	3.69601i	0.337868	−	0.195068i	−0.321461	−	0.946923i	$-0.604174\pi$
$359$	6.40168	−	3.69601i	0.337868	−	0.195068i	0.659329	+	0.751855i	$0.270841\pi$
$360$	−1.16413	−	0.0175775i	−0.0613549	−	0.000926417i
$361$	12.8567	+	7.42280i	0.676667	+	0.390674i
$362$	2.61589	+	15.2849i	0.137488	+	0.803354i
$363$	1.20435	−	1.20435i	0.0632118	−	0.0632118i
$364$	6.08295	+	6.65111i	0.318833	+	0.348613i
$365$	−2.24097	−	2.24097i	−0.117298	−	0.117298i
$366$	4.84553	+	3.42935i	0.253280	+	0.179255i
$367$	−1.81825	+	3.14931i	−0.0949120	+	0.164392i	−0.909572	−	0.415547i	$-0.863590\pi$
$367$	−1.81825	+	3.14931i	−0.0949120	+	0.164392i	0.814660	+	0.579939i	$0.196924\pi$
$368$	−12.0040	+	31.0231i	−0.625754	+	1.61719i
$369$	0.186326	+	0.322725i	0.00969973	+	0.0168004i
$370$	3.27076	−	1.50519i	0.170039	−	0.0782509i
$371$	−19.6209	−	2.40149i	−1.01867	−	0.124679i
$372$	11.7830	−	0.911468i	0.610918	−	0.0472574i
$373$	17.0347	+	4.56443i	0.882023	+	0.236337i	0.671280	−	0.741204i	$-0.265745\pi$
$373$	17.0347	+	4.56443i	0.882023	+	0.236337i	0.210743	+	0.977541i	$0.432412\pi$
$374$	−4.29106	+	3.56398i	−0.221886	+	0.184289i
$375$	−3.50440	−	2.02327i	−0.180967	−	0.104481i
$376$	−8.59121	−	34.1150i	−0.443058	−	1.75935i
$377$		−	4.17778i		−	0.215166i
$378$	−3.65624	−	0.794938i	−0.188057	−	0.0408872i
$379$	26.7390	−	26.7390i	1.37349	−	1.37349i	0.518281	−	0.855211i	$-0.326572\pi$
$379$	26.7390	−	26.7390i	1.37349	−	1.37349i	0.855211	−	0.518281i	$-0.173428\pi$
$380$	1.64948	+	0.307998i	0.0846165	+	0.0157999i
$381$	−2.85631	+	0.765345i	−0.146333	+	0.0392098i
$382$	−12.4429	−	1.15174i	−0.636632	−	0.0589280i
$383$	4.45873	+	7.72276i	0.227831	+	0.394614i	0.957165	−	0.289543i	$-0.0935034\pi$
$383$	4.45873	+	7.72276i	0.227831	+	0.394614i	−0.729334	+	0.684158i	$0.760170\pi$
$384$	8.91757	−	6.96254i	0.455073	−	0.355306i
$385$	3.07931	+	1.24275i	0.156936	+	0.0633362i
$386$	−11.9701	−	26.0110i	−0.609264	−	1.32393i
$387$	−1.79149	+	6.68594i	−0.0910666	+	0.339865i
$388$	6.96053	+	19.7399i	0.353368	+	1.00214i
$389$	2.40002	+	8.95701i	0.121686	+	0.454138i	0.999700	−	0.0244968i	$-0.00779836\pi$
$389$	2.40002	+	8.95701i	0.121686	+	0.454138i	−0.878014	+	0.478635i	$0.841132\pi$
$390$	−0.977363	+	0.167268i	−0.0494907	+	0.00846995i
$391$			10.7579i			0.544048i
$392$	9.95301	+	17.1154i	0.502703	+	0.864459i
$393$			17.5611i			0.885842i
$394$	−1.72626	−	10.0867i	−0.0869675	−	0.508159i
$395$	−1.32309	−	4.93783i	−0.0665717	−	0.248449i
$396$	2.63268	−	5.50056i	0.132297	−	0.276414i
$397$	7.09341	−	26.4730i	0.356008	−	1.32864i	−0.523203	−	0.852208i	$-0.675263\pi$
$397$	7.09341	−	26.4730i	0.356008	−	1.32864i	0.879211	−	0.476432i	$-0.158070\pi$
$398$	−32.7400	+	15.0668i	−1.64111	+	0.755230i
$399$	5.00076	+	2.01820i	0.250351	+	0.101037i
$400$	19.0924	−	2.97155i	0.954619	−	0.148578i
$401$	5.68256	+	9.84248i	0.283773	+	0.491510i	0.972311	−	0.233691i	$-0.0750803\pi$
$401$	5.68256	+	9.84248i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$402$	0.871890	−	9.41951i	0.0434859	−	0.469802i
$403$	9.72228	−	2.60508i	0.484301	−	0.129768i
$404$	−23.0083	+	15.7679i	−1.14471	+	0.784480i
$405$	0.291065	−	0.291065i	0.0144631	−	0.0144631i
$406$	1.94973	−	8.96757i	0.0967633	−	0.445053i
$407$			18.8585i			0.934781i
$408$	1.87708	−	3.14071i	0.0929291	−	0.155488i
$409$	−34.1307	−	19.7054i	−1.68766	−	0.974369i	−0.956307	−	0.292365i	$-0.905558\pi$
$409$	−34.1307	−	19.7054i	−1.68766	−	0.974369i	−0.731349	−	0.682003i	$-0.761109\pi$
$410$	0.138603	+	0.166879i	0.00684510	+	0.00824156i
$411$	−1.82950	−	0.490213i	−0.0902426	−	0.0241804i
$412$	−17.1754	−	14.7090i	−0.846173	−	0.724661i
$413$	21.6416	+	2.64881i	1.06491	+	0.130339i
$414$	−4.91662	−	10.6838i	−0.241639	−	0.525079i
$415$	2.21012	+	3.82804i	0.108490	+	0.187911i
$416$	6.37742	−	7.22314i	0.312679	−	0.354143i
$417$	−5.35622	+	9.27724i	−0.262295	+	0.454309i
$418$	−5.07729	+	7.17400i	−0.248338	+	0.350892i
$419$	−21.1877	−	21.1877i	−1.03509	−	1.03509i	−0.999362	−	0.0357241i	$-0.988626\pi$
$419$	−21.1877	−	21.1877i	−1.03509	−	1.03509i	−0.0357241	−	0.999362i	$-0.511374\pi$
$420$	−2.17597	−	0.0970854i	−0.106176	−	0.00473728i
$421$	1.08504	−	1.08504i	0.0528818	−	0.0528818i	−0.680171	−	0.733053i	$-0.738095\pi$
$421$	1.08504	−	1.08504i	0.0528818	−	0.0528818i	0.733053	+	0.680171i	$0.238095\pi$
$422$	20.6792	−	3.53909i	1.00665	−	0.172280i
$423$	10.7717	+	6.21903i	0.523737	+	0.302380i
$424$	−0.319045	+	21.1298i	−0.0154942	+	1.02615i
$425$	5.41169	−	3.12444i	0.262505	−	0.151558i
$426$	5.83632	+	2.15757i	0.282771	+	0.104535i
$427$	8.87205	+	6.68023i	0.429349	+	0.323279i
$428$	0.260635	+	3.36935i	0.0125983	+	0.162864i
$429$	1.34421	−	5.01667i	0.0648991	−	0.242207i
$430$	−0.371381	+	4.01223i	−0.0179096	+	0.193487i
$431$	−8.16801	+	14.1474i	−0.393439	+	0.681456i	−0.992901	−	0.118947i	$-0.962048\pi$
$431$	−8.16801	+	14.1474i	−0.393439	+	0.681456i	0.599462	+	0.800404i	$0.295381\pi$
$432$	−0.428764	+	3.97695i	−0.0206289	+	0.191341i
$433$	40.2761			1.93554			0.967772	−	0.251826i	$-0.0810311\pi$
$433$	40.2761			1.93554			0.967772	+	0.251826i	$0.0810311\pi$
$434$	22.0846	−	1.05449i	1.06009	−	0.0506172i
$435$	0.713889	+	0.713889i	0.0342283	+	0.0342283i
$436$	−7.07076	−	10.3176i	−0.338628	−	0.494123i
$437$	4.38704	+	16.3727i	0.209861	+	0.783210i
$438$	−8.37606	+	6.95682i	−0.400224	+	0.332410i
$439$	12.5934	−	7.27082i	0.601051	−	0.347017i	−0.168404	−	0.985718i	$-0.553861\pi$
$439$	12.5934	−	7.27082i	0.601051	−	0.347017i	0.769455	+	0.638701i	$0.220528\pi$
$440$	0.970447	−	3.41468i	0.0462642	−	0.162789i
$441$	−6.79337	−	1.68823i	−0.323494	−	0.0803919i
$442$	1.08052	−	2.92286i	0.0513953	−	0.139026i
$443$	−10.4694	−	2.80527i	−0.497417	−	0.133283i	0.00138373	−	0.999999i	$-0.499560\pi$
$443$	−10.4694	−	2.80527i	−0.497417	−	0.133283i	−0.498801	+	0.866716i	$0.666226\pi$
$444$	−4.11358	−	11.6660i	−0.195222	−	0.553644i
$445$	−0.603214	+	0.161631i	−0.0285951	+	0.00766203i
$446$	0.479801	−	0.677940i	0.0227192	−	0.0321014i
$447$	−3.32132			−0.157093
$448$	17.0601	−	12.5281i	0.806012	−	0.591899i
$449$	−8.62693			−0.407130			−0.203565	−	0.979061i	$-0.565253\pi$
$449$	−8.62693			−0.407130			−0.203565	+	0.979061i	$0.565253\pi$
$450$	−3.94647	+	5.57620i	−0.186038	+	0.262865i
$451$	−1.09752	+	0.294080i	−0.0516803	+	0.0138477i
$452$	10.6076	+	30.0830i	0.498941	+	1.41498i
$453$	−20.7939	−	5.57172i	−0.976985	−	0.261782i
$454$	−7.90406	+	21.3808i	−0.370956	+	1.00345i
$455$	−1.83691	+	0.258881i	−0.0861157	+	0.0121365i
$456$	1.57599	−	5.54540i	0.0738026	−	0.259687i
$457$	6.81343	−	3.93373i	0.318719	−	0.184012i	−0.332103	−	0.943243i	$-0.607758\pi$
$457$	6.81343	−	3.93373i	0.318719	−	0.184012i	0.650821	+	0.759231i	$0.274425\pi$
$458$	10.2358	−	8.50145i	0.478288	−	0.397247i
$459$	0.334812	+	1.24953i	0.0156277	+	0.0583233i
$460$	−3.87023	−	5.64741i	−0.180451	−	0.263312i
$461$	−20.7449	−	20.7449i	−0.966185	−	0.966185i	0.0332621	−	0.999447i	$-0.489410\pi$
$461$	−20.7449	−	20.7449i	−0.966185	−	0.966185i	−0.999447	+	0.0332621i	$0.989410\pi$
$462$	5.22657	−	10.1409i	0.243162	−	0.471798i
$463$	32.5211			1.51138			0.755692	−	0.654927i	$-0.227301\pi$
$463$	32.5211			1.51138			0.755692	+	0.654927i	$0.227301\pi$
$464$	−9.75419	−	1.05162i	−0.452827	−	0.0488202i
$465$	−1.21617	+	2.10647i	−0.0563986	+	0.0976852i
$466$	−1.40470	+	15.1757i	−0.0650713	+	0.703001i
$467$	−7.46491	+	27.8594i	−0.345435	+	1.28918i	0.546669	+	0.837349i	$0.315896\pi$
$467$	−7.46491	+	27.8594i	−0.345435	+	1.28918i	−0.892103	+	0.451831i	$0.850771\pi$
$468$	0.262740	+	3.39656i	0.0121452	+	0.157006i
$469$	2.15004	−	17.5665i	0.0992798	−	0.811147i
$470$	6.79136	+	2.51063i	0.313262	+	0.115807i
$471$	−9.10898	+	5.25907i	−0.419720	+	0.242325i
$472$	0.351902	−	23.3058i	0.0161976	−	1.07274i
$473$	−18.2775	−	10.5525i	−0.840399	−	0.485204i
$474$	−17.3114	+	2.96272i	−0.795141	+	0.136082i
$475$	6.96204	−	6.96204i	0.319440	−	0.319440i
$476$	3.68341	−	5.76964i	0.168829	−	0.264451i
$477$	−5.28305	−	5.28305i	−0.241894	−	0.241894i
$478$	13.1825	−	18.6263i	0.602953	−	0.851948i
$479$	13.6339	−	23.6146i	0.622948	−	1.07898i	−0.365986	−	0.930620i	$-0.619268\pi$
$479$	13.6339	−	23.6146i	0.622948	−	1.07898i	0.988934	−	0.148357i	$-0.0473984\pi$
$480$	0.144515	+	2.32403i	0.00659617	+	0.106077i
$481$	−5.26763	−	9.12380i	−0.240183	−	0.416009i
$482$	8.67126	+	18.8426i	0.394965	+	0.858257i
$483$	−8.60481	−	20.2500i	−0.391533	−	0.921408i
$484$	−2.58729	−	2.21575i	−0.117604	−	0.100716i
$485$	−4.16113	−	1.11497i	−0.188947	−	0.0506283i
$486$	−0.903575	−	1.08791i	−0.0409870	−	0.0493487i
$487$	−15.0100	−	8.66601i	−0.680167	−	0.392695i	0.119751	−	0.992804i	$-0.461790\pi$
$487$	−15.0100	−	8.66601i	−0.680167	−	0.392695i	−0.799918	+	0.600109i	$0.795124\pi$
$488$	6.09085	−	10.1912i	0.275720	−	0.461333i
$489$		−	15.7261i		−	0.711157i
$490$	−4.06373	−	0.301581i	−0.183581	−	0.0136240i
$491$	3.51159	−	3.51159i	0.158476	−	0.158476i	−0.623415	−	0.781891i	$-0.714255\pi$
$491$	3.51159	−	3.51159i	0.158476	−	0.158476i	0.781891	+	0.623415i	$0.214255\pi$
$492$	0.614788	−	0.421321i	0.0277168	−	0.0189946i
$493$	−3.06471	+	0.821186i	−0.138027	+	0.0369843i
$494$	0.452538	−	4.88901i	0.0203606	−	0.219967i
$495$	0.627540	+	1.08693i	0.0282058	+	0.0488540i
$496$	−3.63501	−	23.3551i	−0.163217	−	1.04868i
$497$	10.7950	+	4.35663i	0.484221	+	0.195422i
$498$	13.7957	−	6.34871i	0.618200	−	0.284493i
$499$	5.33845	−	19.9234i	0.238982	−	0.891892i	−0.737332	−	0.675531i	$-0.763915\pi$
$499$	5.33845	−	19.9234i	0.238982	−	0.891892i	0.976313	−	0.216361i	$-0.0694188\pi$
$500$	−3.49393	+	7.30002i	−0.156253	+	0.326467i
$501$	−5.51639	−	20.5874i	−0.246454	−	0.919779i
$502$	−7.12683	−	41.6427i	−0.318086	−	1.85860i
$503$			27.4099i			1.22215i	0.791575	+	0.611073i	$0.209262\pi$
$503$			27.4099i			1.22215i	−0.791575	+	0.611073i	$0.790738\pi$
$504$	−1.02117	+	7.41331i	−0.0454866	+	0.330215i
$505$		−	5.74073i		−	0.255459i
$506$	35.3455	−	6.04911i	1.57130	−	0.268916i
$507$	−2.61371	−	9.75449i	−0.116079	−	0.433212i
$508$	1.96671	+	5.57754i	0.0872588	+	0.247464i
$509$	7.66627	−	28.6109i	0.339801	−	1.26816i	−0.558768	−	0.829324i	$-0.688726\pi$
$509$	7.66627	−	28.6109i	0.339801	−	1.26816i	0.898569	−	0.438832i	$-0.144608\pi$
$510$	0.314814	+	0.684089i	0.0139402	+	0.0302920i
$511$	−16.0471	+	12.5473i	−0.709882	+	0.555061i
$512$	−15.2591	−	16.7081i	−0.674364	−	0.738399i
$513$	1.01912	+	1.76516i	0.0449951	+	0.0779338i
$514$	6.22984	+	0.576647i	0.274786	+	0.0254348i
$515$	4.49550	−	1.20457i	0.198096	−	0.0530795i
$516$	13.6084	+	2.54101i	0.599076	+	0.111862i
$517$	−26.8166	+	26.8166i	−1.17939	+	1.17939i
$518$	−7.04894	−	22.0425i	−0.309713	−	0.968493i
$519$			1.09018i			0.0478537i
$520$	0.484297	+	1.92310i	0.0212378	+	0.0843336i
$521$	20.4143	+	11.7862i	0.894367	+	0.516363i	0.875368	−	0.483456i	$-0.160619\pi$
$521$	20.4143	+	11.7862i	0.894367	+	0.516363i	0.0189987	+	0.999820i	$0.493952\pi$
$522$	2.66830	−	2.21618i	0.116788	−	0.0969995i
$523$	−25.0899	−	6.72282i	−1.09710	−	0.293968i	−0.335520	−	0.942033i	$-0.608912\pi$
$523$	−25.0899	−	6.72282i	−1.09710	−	0.293968i	−0.761585	+	0.648065i	$0.775579\pi$
$524$	35.0177	−	2.70878i	1.52975	−	0.118334i
$525$	−7.68755	+	10.2099i	−0.335512	+	0.445596i
$526$	−18.5776	+	8.54934i	−0.810024	+	0.372769i
$527$	−3.82203	−	6.61995i	−0.166490	−	0.288370i
$528$	−11.3744	−	4.40122i	−0.495009	−	0.191539i
$529$	23.0790	−	39.9740i	1.00344	−	1.73800i
$530$	−3.55014	−	2.51256i	−0.154208	−	0.109138i
$531$	5.82712	+	5.82712i	0.252875	+	0.252875i
$532$	3.25302	−	10.2830i	0.141036	−	0.445826i
$533$	0.448841	−	0.448841i	0.0194415	−	0.0194415i
$534$	0.361932	+	2.11480i	0.0156623	+	0.0915163i
$535$	−0.602348	−	0.347766i	−0.0260418	−	0.0150352i
$536$	−18.9174	−	0.285640i	−0.817107	−	0.0123378i
$537$	−3.75563	+	2.16831i	−0.162067	+	0.0935696i
$538$	0.335264	−	0.906903i	0.0144543	−	0.0390993i
$539$	10.3332	−	18.6754i	0.445081	−	0.804405i
$540$	−0.625292	−	0.535500i	−0.0269083	−	0.0230442i
$541$	0.344467	−	1.28557i	0.0148098	−	0.0552708i	−0.958126	−	0.286349i	$-0.907558\pi$
$541$	0.344467	−	1.28557i	0.0148098	−	0.0552708i	0.972935	+	0.231078i	$0.0742252\pi$
$542$	14.0922	+	1.30441i	0.605314	+	0.0560292i
$543$	−5.48258	+	9.49611i	−0.235280	+	0.407517i
$544$	−6.55225	−	3.25852i	−0.280925	−	0.139708i
$545$	2.57431			0.110271
$546$	0.303968	+	6.36611i	0.0130086	+	0.272444i
$547$	−22.2083	−	22.2083i	−0.949560	−	0.949560i	0.0492275	−	0.998788i	$-0.484324\pi$
$547$	−22.2083	−	22.2083i	−0.949560	−	0.949560i	−0.998788	+	0.0492275i	$0.984324\pi$
$548$	−0.695308	+	3.72372i	−0.0297021	+	0.159069i
$549$	1.08642	+	4.05457i	0.0463672	+	0.173045i
$550$	−13.3085	−	16.0235i	−0.567476	−	0.683245i
$551$	−4.32938	+	2.49957i	−0.184438	+	0.106485i
$552$	−20.5455	+	11.4519i	−0.874475	+	0.487425i
$553$	−32.5361	+	4.58540i	−1.38358	+	0.194991i
$554$	38.6096	+	14.2732i	1.64036	+	0.606410i
$555$	2.45917	+	0.658933i	0.104386	+	0.0279702i
$556$	19.3254	+	9.24953i	0.819580	+	0.392267i
$557$	−39.0344	+	10.4592i	−1.65394	+	0.443172i	−0.960713	−	0.277545i	$-0.910479\pi$
$557$	−39.0344	+	10.4592i	−1.65394	+	0.443172i	−0.693229	+	0.720717i	$0.743812\pi$
$558$	6.82120	+	4.82760i	0.288764	+	0.204368i
$559$	11.7903			0.498675
$560$	0.142047	+	4.35395i	0.00600260	+	0.183988i
$561$	−3.94431			−0.166529
$562$	17.5496	+	12.4204i	0.740284	+	0.523924i
$563$	36.0706	−	9.66509i	1.52020	−	0.407335i	0.600389	−	0.799708i	$-0.295012\pi$
$563$	36.0706	−	9.66509i	1.52020	−	0.407335i	0.919806	+	0.392373i	$0.128346\pi$
$564$	10.7395	−	22.4385i	0.452214	−	0.944829i
$565$	−6.34143	−	1.69918i	−0.266786	−	0.0714851i
$566$	−27.4574	−	10.1504i	−1.15412	−	0.426655i
$567$	−1.62969	−	2.08425i	−0.0684405	−	0.0875304i
$568$	3.40204	−	11.9707i	0.142747	−	0.502278i
$569$	−22.9441	+	13.2468i	−0.961868	+	0.555335i	−0.896747	−	0.442543i	$-0.854076\pi$
$569$	−22.9441	+	13.2468i	−0.961868	+	0.555335i	−0.0651204	+	0.997877i	$0.520743\pi$
$570$	0.758094	+	0.912752i	0.0317531	+	0.0382310i
$571$	7.62497	+	28.4568i	0.319095	+	1.19088i	0.920116	+	0.391645i	$0.128094\pi$
$571$	7.62497	+	28.4568i	0.319095	+	1.19088i	−0.601021	+	0.799233i	$0.705239\pi$
$572$	−10.2108	−	1.90660i	−0.426935	−	0.0797190i
$573$	−6.24802	−	6.24802i	−0.261015	−	0.261015i
$574$	1.17290	−	0.753965i	0.0489561	−	0.0314699i
$575$	−40.1716			−1.67527
$576$	7.99635	+	0.241534i	0.333181	+	0.0100639i
$577$	11.5473	−	20.0005i	0.480719	−	0.832630i	−0.519036	−	0.854752i	$-0.673709\pi$
$577$	11.5473	−	20.0005i	0.480719	−	0.832630i	0.999755	+	0.0221221i	$0.00704226\pi$
$578$	21.5828	+	1.99775i	0.897725	+	0.0830954i
$579$	5.24023	−	19.5568i	0.217777	−	0.812753i
$580$	1.31341	−	1.53364i	0.0545363	−	0.0636810i
$581$	26.1484	−	11.1112i	1.08482	−	0.460970i
$582$	−5.13202	+	13.8823i	−0.212729	+	0.575440i
$583$	19.7286	−	11.3903i	0.817076	−	0.471739i
$584$	15.1642	+	15.6291i	0.627499	+	0.646739i
$585$	−0.607212	−	0.350574i	−0.0251051	−	0.0144944i
$586$	1.91302	+	11.1779i	0.0790261	+	0.461757i
$587$	−23.1784	+	23.1784i	−0.956675	+	0.956675i	−0.999100	−	0.0424243i	$-0.986492\pi$
$587$	−23.1784	+	23.1784i	−0.956675	+	0.956675i	0.0424243	+	0.999100i	$0.486492\pi$
$588$	−2.31854	+	13.8067i	−0.0956148	+	0.569378i
$589$	−8.51645	−	8.51645i	−0.350914	−	0.350914i
$590$	3.91575	+	2.77131i	0.161209	+	0.114093i
$591$	3.61803	−	6.26660i	0.148826	−	0.257774i
$592$	−22.6280	+	10.0021i	−0.930005	+	0.411085i
$593$	18.3372	+	31.7609i	0.753018	+	1.30427i	0.946354	+	0.323133i	$0.104736\pi$
$593$	18.3372	+	31.7609i	0.753018	+	1.30427i	−0.193336	+	0.981133i	$0.561931\pi$
$594$	3.91715	−	1.80265i	0.160723	−	0.0739637i
$595$	0.550972	+	1.29662i	0.0225877	+	0.0531564i
$596$	0.512309	+	6.62285i	0.0209850	+	0.271282i
$597$	−24.6161	−	6.59587i	−1.00747	−	0.269951i
$598$	−15.4106	+	12.7994i	−0.630186	+	0.523407i
$599$	−5.19514	−	2.99942i	−0.212268	−	0.122553i	0.390097	−	0.920774i	$-0.372441\pi$
$599$	−5.19514	−	2.99942i	−0.212268	−	0.122553i	−0.602365	+	0.798221i	$0.705775\pi$
$600$	11.7279	+	7.00931i	0.478791	+	0.286154i
$601$		−	6.18407i		−	0.252253i	−0.992014	−	0.126127i	$-0.959745\pi$
$601$		−	6.18407i		−	0.252253i	0.992014	−	0.126127i	$-0.0402546\pi$
$602$	25.3077	+	5.50240i	1.03147	+	0.224261i
$603$	4.72989	−	4.72989i	0.192616	−	0.192616i
$604$	−7.90281	+	42.3234i	−0.321561	+	1.72212i
$605$	0.677197	−	0.181454i	0.0275320	−	0.00737717i
$606$	−19.6392	−	1.81785i	−0.797789	−	0.0738451i
$607$	−15.0189	−	26.0136i	−0.609600	−	1.05586i	−0.991306	−	0.131574i	$-0.957997\pi$
$607$	−15.0189	−	26.0136i	−0.609600	−	1.05586i	0.381707	−	0.924284i	$-0.375336\pi$
$608$	−11.3009	−	2.28723i	−0.458310	−	0.0927593i
$609$	5.11200	−	3.99710i	0.207149	−	0.161971i
$610$	1.02153	+	2.21977i	0.0413605	+	0.0898761i
$611$	5.48344	−	20.4645i	0.221836	−	0.827905i
$612$	2.43998	−	0.860368i	0.0986304	−	0.0347783i
$613$	9.40236	+	35.0901i	0.379758	+	1.41728i	0.846267	+	0.532759i	$0.178845\pi$
$613$	9.40236	+	35.0901i	0.379758	+	1.41728i	−0.466509	+	0.884517i	$0.654488\pi$
$614$	43.0926	−	7.37497i	1.73908	−	0.297630i
$615$			0.153394i			0.00618543i
$616$	−21.0276	−	8.85778i	−0.847227	−	0.356890i
$617$		−	24.5325i		−	0.987641i	−0.869564	−	0.493821i	$-0.835600\pi$
$617$		−	24.5325i		−	0.987641i	0.869564	−	0.493821i	$-0.164400\pi$
$618$	−2.69732	−	15.7607i	−0.108502	−	0.633989i
$619$	−0.697411	−	2.60277i	−0.0280313	−	0.104614i	0.950493	−	0.310746i	$-0.100579\pi$
$619$	−0.697411	−	2.60277i	−0.0280313	−	0.104614i	−0.978524	+	0.206132i	$0.933912\pi$
$620$	4.38799	+	2.10018i	0.176226	+	0.0843452i
$621$	2.15237	−	8.03277i	0.0863718	−	0.322344i
$622$	31.7139	−	14.5946i	1.27161	−	0.585189i
$623$	0.560162	+	3.97467i	0.0224424	+	0.159242i
$624$	6.73236	−	1.04783i	0.269510	−	0.0419468i
$625$	11.2436	+	19.4744i	0.449743	+	0.778978i
$626$	−0.384852	+	4.15777i	−0.0153818	+	0.166178i
$627$	−6.00295	+	1.60848i	−0.239735	+	0.0642367i
$628$	11.8919	+	17.3525i	0.474537	+	0.692440i
$629$	−5.65757	+	5.65757i	−0.225582	+	0.225582i
$630$	−1.13977	−	1.03588i	−0.0454094	−	0.0412706i
$631$			23.6243i			0.940467i	0.882542	+	0.470234i	$0.155830\pi$
$631$			23.6243i			0.940467i	−0.882542	+	0.470234i	$0.844170\pi$
$632$	8.57806	+	34.0628i	0.341217	+	1.35494i
$633$	12.8475	+	7.41752i	0.510643	+	0.294820i
$634$	5.65369	+	6.80708i	0.224537	+	0.270344i
$635$	−1.17574	−	0.315037i	−0.0466577	−	0.0125019i
$636$	−9.71972	+	11.3495i	−0.385412	+	0.450038i
$637$	0.217260	+	11.9215i	0.00860814	+	0.472347i
$638$	4.42132	+	9.60750i	0.175042	+	0.380365i
$639$	2.19994	+	3.81040i	0.0870281	+	0.150737i
$640$	4.61193	−	0.646647i	0.182302	−	0.0255610i
$641$	18.1344	−	31.4097i	0.716267	−	1.24061i	−0.246202	−	0.969218i	$-0.579183\pi$
$641$	18.1344	−	31.4097i	0.716267	−	1.24061i	0.962469	−	0.271392i	$-0.0874840\pi$
$642$	−1.38046	+	1.95053i	−0.0544823	+	0.0769813i
$643$	20.3449	+	20.3449i	0.802326	+	0.802326i	0.983459	−	0.181132i	$-0.0579762\pi$
$643$	20.3449	+	20.3449i	0.802326	+	0.802326i	−0.181132	+	0.983459i	$0.557976\pi$
$644$	−39.0521	+	20.2819i	−1.53887	+	0.799219i
$645$	−2.01469	+	2.01469i	−0.0793284	+	0.0793284i
$646$	−3.67540	+	0.629017i	−0.144607	+	0.0247483i
$647$	22.5185	+	13.0010i	0.885292	+	0.511124i	0.872400	−	0.488793i	$-0.162563\pi$
$647$	22.5185	+	13.0010i	0.885292	+	0.511124i	0.0128926	+	0.999917i	$0.495896\pi$
$648$	−2.02997	+	1.96958i	−0.0797446	+	0.0773723i
$649$	−21.7604	+	12.5634i	−0.854169	+	0.493155i
$650$	10.9144	+	4.03485i	0.428100	+	0.158260i
$651$	12.4894	+	9.40395i	0.489500	+	0.368570i
$652$	−31.3585	+	2.42573i	−1.22809	+	0.0949987i
$653$	−0.456236	+	1.70270i	−0.0178539	+	0.0666317i	−0.974278	−	0.225349i	$-0.927648\pi$
$653$	−0.456236	+	1.70270i	−0.0178539	+	0.0666317i	0.956424	+	0.291981i	$0.0943144\pi$
$654$	0.815176	−	8.80679i	0.0318759	−	0.344373i
$655$	−3.61433	+	6.26020i	−0.141224	+	0.244606i
$656$	−0.934963	−	1.16093i	−0.0365042	−	0.0453265i
$657$	−7.69921			−0.300375
$658$	21.3208	−	41.3678i	0.831170	−	1.61269i
$659$	−0.0613024	−	0.0613024i	−0.00238800	−	0.00238800i	0.705912	−	0.708300i	$-0.250537\pi$
$659$	−0.0613024	−	0.0613024i	−0.00238800	−	0.00238800i	−0.708300	+	0.705912i	$0.750537\pi$
$660$	2.07059	−	1.41900i	0.0805977	−	0.0552345i
$661$	−9.26101	−	34.5626i	−0.360212	−	1.34433i	−0.873798	−	0.486290i	$-0.838350\pi$
$661$	−9.26101	−	34.5626i	−0.360212	−	1.34433i	0.513586	−	0.858038i	$-0.328317\pi$
$662$	1.27881	−	1.06213i	0.0497024	−	0.0412808i
$663$	1.90827	−	1.10174i	0.0741111	−	0.0427880i
$664$	−14.7876	−	26.5300i	−0.573869	−	1.02956i
$665$	1.36730	+	1.74868i	0.0530216	+	0.0678108i
$666$	3.03295	−	8.20426i	0.117524	−	0.317909i
$667$	19.7018	+	5.27908i	0.762856	+	0.204407i
$668$	−40.2013	+	14.1755i	−1.55544	+	0.548467i
$669$	0.567275	−	0.152001i	0.0219321	−	0.00587670i
$670$	2.24948	−	3.17842i	0.0869049	−	0.122793i
$671$	−12.7987			−0.494090
$672$	14.9400	+	0.892764i	0.576322	+	0.0344391i
$673$	2.23403			0.0861157			0.0430578	−	0.999073i	$-0.486290\pi$
$673$	2.23403			0.0861157			0.0430578	+	0.999073i	$0.486290\pi$
$674$	8.50159	−	12.0124i	0.327469	−	0.462700i
$675$	−4.66596	+	1.25024i	−0.179593	+	0.0481218i
$676$	−19.0477	+	6.71646i	−0.732604	+	0.258325i
$677$	−40.5851	−	10.8747i	−1.55981	−	0.417950i	−0.627207	−	0.778853i	$-0.715802\pi$
$677$	−40.5851	−	10.8747i	−1.55981	−	0.417950i	−0.932603	+	0.360903i	$0.882469\pi$
$678$	−7.82103	+	21.1562i	−0.300365	+	0.812499i
$679$	−10.3627	+	25.6770i	−0.397685	+	0.985395i
$680$	1.31554	−	0.733273i	0.0504488	−	0.0281197i
$681$	−13.9590	+	8.05926i	−0.534912	+	0.308831i
$682$	−19.6011	+	16.2799i	−0.750564	+	0.623388i
$683$	1.35618	+	5.06135i	0.0518930	+	0.193667i	0.987006	−	0.160682i	$-0.0513692\pi$
$683$	1.35618	+	5.06135i	0.0518930	+	0.193667i	−0.935113	+	0.354349i	$0.884703\pi$
$684$	3.36261	−	2.30444i	0.128573	−	0.0881123i
$685$	−0.551288	−	0.551288i	−0.0210636	−	0.0210636i
$686$	−5.09730	+	25.6908i	−0.194616	+	0.980880i
$687$	9.40868			0.358963
$688$	2.96782	−	27.5276i	0.113147	−	1.04948i
$689$	−6.36318	+	11.0214i	−0.242418	+	0.419880i
$690$	0.446193	−	4.82046i	0.0169863	−	0.183512i
$691$	−6.87455	+	25.6562i	−0.261520	+	0.976007i	0.702826	+	0.711362i	$0.251921\pi$
$691$	−6.87455	+	25.6562i	−0.261520	+	0.976007i	−0.964346	+	0.264645i	$0.914745\pi$
$692$	2.17387	−	0.168159i	0.0826381	−	0.00639245i
$693$	7.42456	−	3.15491i	0.282036	−	0.119845i
$694$	39.4536	+	14.5852i	1.49764	+	0.553647i
$695$	−3.81877	+	2.20477i	−0.144854	+	0.0836317i
$696$	−4.83074	−	4.97886i	−0.183109	−	0.188723i
$697$	−0.417482	−	0.241033i	−0.0158133	−	0.00912979i
$698$	−40.4168	+	6.91703i	−1.52980	+	0.261814i
$699$	−7.62029	+	7.62029i	−0.288226	+	0.288226i
$700$	21.5448	+	13.7544i	0.814315	+	0.519869i
$701$	−6.50004	−	6.50004i	−0.245503	−	0.245503i	0.573619	−	0.819122i	$-0.305539\pi$
$701$	−6.50004	−	6.50004i	−0.245503	−	0.245503i	−0.819122	+	0.573619i	$0.805539\pi$
$702$	−1.39160	+	1.96628i	−0.0525227	+	0.0742125i
$703$	−6.30325	+	10.9175i	−0.237731	+	0.411763i
$704$	−7.02173	+	23.3600i	−0.264641	+	0.880414i
$705$	2.55993	+	4.43392i	0.0964124	+	0.166991i
$706$	7.64463	+	16.6117i	0.287709	+	0.625190i
$707$	−36.6254	−	4.48274i	−1.37744	−	0.168591i
$708$	10.7207	−	12.5184i	0.402909	−	0.470469i
$709$	−23.2071	−	6.21832i	−0.871561	−	0.233534i	−0.204798	−	0.978804i	$-0.565654\pi$
$709$	−23.2071	−	6.21832i	−0.871561	−	0.233534i	−0.666762	+	0.745270i	$0.732320\pi$
$710$	1.63647	+	1.97033i	0.0614158	+	0.0739451i
$711$	−10.7552	−	6.20951i	−0.403351	−	0.232875i
$712$	4.16117	−	1.04791i	0.155947	−	0.0392722i
$713$			49.1407i			1.84033i
$714$	4.61026	−	1.47431i	0.172535	−	0.0551746i
$715$	1.51169	−	1.51169i	0.0565338	−	0.0565338i
$716$	4.90301	+	7.15442i	0.183234	+	0.267373i
$717$	15.5858	−	4.17621i	0.582063	−	0.155963i
$718$	0.963516	−	10.4094i	0.0359581	−	0.388475i
$719$	−1.08329	−	1.87630i	−0.0403997	−	0.0699744i	0.845119	−	0.534579i	$-0.179530\pi$
$719$	−1.08329	−	1.87630i	−0.0403997	−	0.0699744i	−0.885518	+	0.464605i	$0.846196\pi$
$720$	−0.971359	+	1.32946i	−0.0362004	+	0.0495461i
$721$	−4.17465	−	29.6216i	−0.155472	−	1.10316i
$722$	19.0722	−	8.77693i	0.709794	−	0.326644i
$723$	−3.79606	+	14.1671i	−0.141177	+	0.526880i
$724$	19.7813	+	9.46774i	0.735167	+	0.351866i
$725$	−3.06644	−	11.4441i	−0.113885	−	0.425024i
$726$	−0.406321	−	2.37417i	−0.0150800	−	0.0881138i
$727$			35.7827i			1.32711i	0.748129	+	0.663553i	$0.230952\pi$
$727$			35.7827i			1.32711i	−0.748129	+	0.663553i	$0.769048\pi$
$728$	12.6474	−	1.58809i	0.468744	−	0.0588585i
$729$		−	1.00000i		−	0.0370370i
$730$	−4.41771	+	0.756058i	−0.163507	+	0.0279829i
$731$	−2.31750	−	8.64902i	−0.0857157	−	0.319895i
$732$	7.91740	−	2.79178i	0.292636	−	0.103187i
$733$	−3.81736	+	14.2466i	−0.140997	+	0.526209i	0.858904	+	0.512137i	$0.171146\pi$
$733$	−3.81736	+	14.2466i	−0.140997	+	0.526209i	−0.999901	+	0.0140719i	$0.995521\pi$
$734$	2.14995	+	4.67184i	0.0793563	+	0.172441i
$735$	−2.07424	−	1.99999i	−0.0765095	−	0.0737708i
$736$	26.0047	+	39.2022i	0.958546	+	1.44501i
$737$	10.1977	+	17.6629i	0.375637	+	0.650623i
$738$	0.524765	+	0.0485734i	0.0193169	+	0.00178801i
$739$	−31.1031	+	8.33404i	−1.14415	+	0.306573i	−0.780616	−	0.625010i	$-0.785095\pi$
$739$	−31.1031	+	8.33404i	−1.14415	+	0.306573i	−0.363529	+	0.931583i	$0.618428\pi$
$740$	0.934617	−	5.00533i	0.0343572	−	0.184000i
$741$	2.45496	−	2.45496i	0.0901851	−	0.0901851i
$742$	−18.8021	+	20.6876i	−0.690246	+	0.759467i
$743$			27.4237i			1.00608i	0.864264	+	0.503039i	$0.167785\pi$
$743$			27.4237i			1.00608i	−0.864264	+	0.503039i	$0.832215\pi$
$744$	8.57427	−	14.3464i	0.314348	−	0.525965i
$745$	−1.18398	−	0.683573i	−0.0433778	−	0.0250442i
$746$	19.1860	−	15.9351i	0.702449	−	0.583426i
$747$	10.3725	+	2.77931i	0.379511	+	0.101690i
$748$	0.608405	+	7.86513i	0.0222455	+	0.287578i
$749$	−2.68907	+	3.57137i	−0.0982565	+	0.130495i
$750$	−5.19860	+	2.39237i	−0.189826	+	0.0873570i
$751$	10.0593	+	17.4232i	0.367069	+	0.635783i	0.989106	−	0.147205i	$-0.0470278\pi$
$751$	10.0593	+	17.4232i	0.367069	+	0.635783i	−0.622036	+	0.782988i	$0.713694\pi$
$752$	−46.3998	−	17.9539i	−1.69203	−	0.654712i
$753$	14.9370	−	25.8716i	0.544334	−	0.942814i
$754$	−4.82265	−	3.41316i	−0.175631	−	0.124300i
$755$	−6.26589	−	6.26589i	−0.228039	−	0.228039i
$756$	−3.90471	+	3.57116i	−0.142013	+	0.129882i
$757$	−21.9954	+	21.9954i	−0.799436	+	0.799436i	−0.983007	−	0.183571i	$-0.941234\pi$
$757$	−21.9954	+	21.9954i	−0.799436	+	0.799436i	0.183571	+	0.983007i	$0.441234\pi$
$758$	−9.02120	−	52.7117i	−0.327665	−	1.91457i
$759$	21.9593	+	12.6782i	0.797072	+	0.460190i
$760$	1.70313	−	1.65246i	0.0617790	−	0.0599412i
$761$	36.4694	−	21.0556i	1.32201	−	0.763265i	0.337964	−	0.941159i	$-0.390262\pi$
$761$	36.4694	−	21.0556i	1.32201	−	0.763265i	0.984050	+	0.177894i	$0.0569284\pi$
$762$	−1.45006	+	3.92247i	−0.0525302	+	0.142096i
$763$	2.01019	−	16.4239i	0.0727737	−	0.594584i
$764$	−11.4951	+	13.4226i	−0.415877	+	0.485612i
$765$	−0.137818	+	0.514343i	−0.00498282	+	0.0185961i
$766$	12.5575	+	1.16235i	0.453722	+	0.0419975i
$767$	7.01849	−	12.1564i	0.253423	−	0.438941i
$768$	−0.751798	−	15.9823i	−0.0271282	−	0.576713i
$769$	−9.61281			−0.346647			−0.173323	−	0.984865i	$-0.555451\pi$
$769$	−9.61281			−0.346647			−0.173323	+	0.984865i	$0.555451\pi$
$770$	3.95031	−	2.53933i	0.142359	−	0.0915113i
$771$	3.12823	+	3.12823i	0.112661	+	0.112661i
$772$	−39.8054	−	7.43263i	−1.43263	−	0.267506i
$773$	−2.00684	−	7.48965i	−0.0721812	−	0.269384i	0.920398	−	0.390982i	$-0.127865\pi$
$773$	−2.00684	−	7.48965i	−0.0721812	−	0.269384i	−0.992579	+	0.121598i	$0.961198\pi$
$774$	6.25436	+	7.53030i	0.224808	+	0.270671i
$775$	24.7200	−	14.2721i	0.887968	−	0.512669i
$776$	28.4735	+	8.09213i	1.02214	+	0.290491i
$777$	6.12423	−	15.1748i	0.219705	−	0.544392i
$778$	12.3004	+	4.54720i	0.440990	+	0.163025i
$779$	−0.733669	−	0.196586i	−0.0262864	−	0.00704343i
$780$	−0.605398	+	1.26488i	−0.0216767	+	0.0452900i
$781$	−12.9584	+	3.47218i	−0.463687	+	0.124245i
$782$	12.4184	+	8.78895i	0.444082	+	0.314292i
$783$	2.45268			0.0876516
$784$	27.8887	+	2.49360i	0.996027	+	0.0890570i
$785$	−4.32956			−0.154529
$786$	20.2719	+	14.3471i	0.723073	+	0.511744i
$787$	26.4420	−	7.08512i	0.942557	−	0.252557i	0.245356	−	0.969433i	$-0.421095\pi$
$787$	26.4420	−	7.08512i	0.942557	−	0.252557i	0.697201	+	0.716876i	$0.254428\pi$
$788$	−13.0540	−	6.24788i	−0.465028	−	0.222572i
$789$	−13.9679	−	3.74269i	−0.497271	−	0.133243i
$790$	−6.78096	−	2.50679i	−0.241256	−	0.0891874i
$791$	−15.7925	+	39.1310i	−0.561515	+	1.39134i
$792$	−4.19878	−	7.53290i	−0.149197	−	0.267670i
$793$	6.19207	−	3.57499i	0.219887	−	0.126952i
$794$	−24.7641	−	29.8162i	−0.878847	−	1.05814i
$795$	−0.795978	−	2.97063i	−0.0282304	−	0.105357i
$796$	−9.35544	+	50.1030i	−0.331595	+	1.77585i
$797$	26.5611	+	26.5611i	0.940844	+	0.940844i	0.998345	−	0.0575015i	$-0.0183134\pi$
$797$	26.5611	+	26.5611i	0.940844	+	0.940844i	−0.0575015	+	0.998345i	$0.518313\pi$
$798$	6.41525	−	4.12384i	0.227097	−	0.145983i
$799$	−16.0900			−0.569225
$800$	12.1678	−	24.4672i	0.430198	−	0.865045i
$801$	−0.758565	+	1.31387i	−0.0268026	+	0.0464234i
$802$	16.0043	+	1.48139i	0.565131	+	0.0523098i
$803$	6.07588	−	22.6755i	0.214413	−	0.800201i
$804$	−10.1612	−	8.70202i	−0.358357	−	0.306897i
$805$	1.10029	−	8.98973i	0.0387802	−	0.316846i
$806$	4.93571	−	13.3513i	0.173853	−	0.470280i
$807$	0.592096	−	0.341847i	0.0208428	−	0.0120336i
$808$	−0.595545	+	39.4419i	−0.0209512	+	1.38756i
$809$	1.37364	+	0.793074i	0.0482948	+	0.0278830i	0.523953	−	0.851747i	$-0.324457\pi$
$809$	1.37364	+	0.793074i	0.0482948	+	0.0278830i	−0.475658	+	0.879630i	$0.657790\pi$
$810$	−0.0981993	−	0.573788i	−0.00345037	−	0.0201608i
$811$	−5.22217	+	5.22217i	−0.183375	+	0.183375i	−0.792825	−	0.609450i	$-0.791390\pi$
$811$	−5.22217	+	5.22217i	−0.183375	+	0.183375i	0.609450	+	0.792825i	$0.291390\pi$
$812$	−8.75891	−	9.57701i	−0.307378	−	0.336087i
$813$	7.07624	+	7.07624i	0.248175	+	0.248175i
$814$	21.7695	+	15.4070i	0.763019	+	0.540015i
$815$	3.23665	−	5.60603i	0.113375	−	0.196371i
$816$	−2.09198	−	4.73272i	−0.0732338	−	0.165678i
$817$	−7.05411	−	12.2181i	−0.246792	−	0.427457i
$818$	−50.6312	+	23.3002i	−1.77028	+	0.814673i
$819$	−2.71079	+	3.60021i	−0.0947225	+	0.125802i
$820$	0.305874	−	0.0236608i	0.0106816	−	0.000826270i
$821$	−2.96363	−	0.794103i	−0.103431	−	0.0277144i	0.206732	−	0.978398i	$-0.433717\pi$
$821$	−2.96363	−	0.794103i	−0.103431	−	0.0277144i	−0.310164	+	0.950683i	$0.600384\pi$
$822$	−2.06055	+	1.71141i	−0.0718698	+	0.0596922i
$823$	3.11834	+	1.80037i	0.108698	+	0.0627570i	0.553364	−	0.832940i	$-0.313344\pi$
$823$	3.11834	+	1.80037i	0.108698	+	0.0627570i	−0.444665	+	0.895697i	$0.646677\pi$
$824$	−31.0115	+	7.80965i	−1.08034	+	0.272062i
$825$		−	14.7287i		−	0.512787i
$826$	20.7384	−	22.8181i	0.721582	−	0.793945i
$827$	21.7802	−	21.7802i	0.757371	−	0.757371i	−0.218472	−	0.975843i	$-0.570107\pi$
$827$	21.7802	−	21.7802i	0.757371	−	0.757371i	0.975843	+	0.218472i	$0.0701073\pi$
$828$	−16.3497	−	3.05288i	−0.568191	−	0.106095i
$829$	1.27876	−	0.342643i	0.0444132	−	0.0119005i	−0.236544	−	0.971621i	$-0.576015\pi$
$829$	1.27876	−	0.342643i	0.0444132	−	0.0119005i	0.280957	+	0.959720i	$0.409348\pi$
$830$	6.22455	+	0.576158i	0.216057	+	0.0199987i
$831$	14.5534	+	25.2073i	0.504853	+	0.874432i
$832$	−3.12788	−	13.2630i	−0.108440	−	0.459811i
$833$	8.70259	−	2.50267i	0.301527	−	0.0867123i
$834$	6.33335	+	13.7623i	0.219306	+	0.476550i
$835$	2.27070	−	8.47437i	0.0785808	−	0.293268i
$836$	4.13333	+	11.7220i	0.142954	+	0.405415i
$837$	1.52938	+	5.70773i	0.0528632	+	0.197288i
$838$	−41.7681	+	7.14829i	−1.44285	+	0.246933i
$839$		−	51.6292i		−	1.78244i	−0.453574	−	0.891219i	$-0.649851\pi$
$839$		−	51.6292i		−	1.78244i	0.453574	−	0.891219i	$-0.350149\pi$
$840$	−1.88979	+	2.43253i	−0.0652040	+	0.0839302i
$841$		−	22.9844i		−	0.792564i
$842$	−0.366072	−	2.13899i	−0.0126157	−	0.0737144i
$843$	3.93479	+	14.6848i	0.135521	+	0.505773i
$844$	12.8091	−	26.7626i	0.440909	−	0.921208i
$845$	1.07588	−	4.01522i	0.0370112	−	0.138128i
$846$	15.9792	−	7.35356i	0.549377	−	0.252821i
$847$	−0.628864	−	4.46215i	−0.0216080	−	0.153321i
$848$	24.1307	+	17.6309i	0.828652	+	0.605447i
$849$	−10.3498	−	17.9263i	−0.355203	−	0.615229i
$850$	0.814513	−	8.79963i	0.0279376	−	0.301825i
$851$	49.6827	−	13.3124i	1.70310	−	0.456345i
$852$	7.25876	−	4.97451i	0.248681	−	0.170424i
$853$	15.6140	−	15.6140i	0.534612	−	0.534612i	−0.387330	−	0.921941i	$-0.626602\pi$
$853$	15.6140	−	15.6140i	0.534612	−	0.534612i	0.921941	+	0.387330i	$0.126602\pi$
$854$	14.9597	−	4.78393i	0.511909	−	0.163703i
$855$			0.838994i			0.0286930i
$856$	4.10237	+	2.45182i	0.140216	+	0.0838016i
$857$	−34.1516	−	19.7174i	−1.16660	−	0.673534i	−0.213720	−	0.976895i	$-0.568558\pi$
$857$	−34.1516	−	19.7174i	−1.16660	−	0.673534i	−0.952876	+	0.303361i	$0.901891\pi$
$858$	−4.69284	−	5.65022i	−0.160211	−	0.192895i
$859$	33.4745	+	8.96946i	1.14213	+	0.306034i	0.779809	−	0.626017i	$-0.215316\pi$
$859$	33.4745	+	8.96946i	1.14213	+	0.306034i	0.362326	+	0.932052i	$0.381983\pi$
$860$	4.32814	+	3.70662i	0.147588	+	0.126395i
$861$	0.978640	+	0.119780i	0.0333520	+	0.00408209i
$862$	9.65809	+	20.9869i	0.328956	+	0.714818i
$863$	−22.4545	−	38.8924i	−0.764361	−	1.32391i	−0.940584	−	0.339562i	$-0.889721\pi$
$863$	−22.4545	−	38.8924i	−0.764361	−	1.32391i	0.176222	−	0.984350i	$-0.443612\pi$
$864$	4.24054	+	3.74404i	0.144266	+	0.127375i
$865$	−0.224375	+	0.388628i	−0.00762897	+	0.0132138i
$866$	32.9047	−	46.4931i	1.11815	−	1.57990i
$867$	10.8375	+	10.8375i	0.368061	+	0.368061i
$868$	16.8254	−	26.3550i	0.571091	−	0.894548i
$869$	26.7756	−	26.7756i	0.908299	−	0.908299i
$870$	1.40732	−	0.240851i	0.0477125	−	0.00816563i
$871$	−9.86736	−	5.69692i	−0.334343	−	0.193033i
$872$	−17.6869	−	0.267060i	−0.598953	−	0.00904378i
$873$	−9.06345	+	5.23278i	−0.306751	+	0.177103i
$874$	22.4840	+	8.31190i	0.760534	+	0.281154i
$875$	−9.85343	+	4.18700i	−0.333107	+	0.141547i
$876$	1.18759	+	15.3526i	0.0401251	+	0.518715i
$877$	5.65136	−	21.0912i	0.190833	−	0.712198i	−0.802474	−	0.596688i	$-0.796483\pi$
$877$	5.65136	−	21.0912i	0.190833	−	0.712198i	0.993306	−	0.115510i	$-0.0368502\pi$
$878$	1.89544	−	20.4774i	0.0639679	−	0.691080i
$879$	−4.00946	+	6.94459i	−0.135236	+	0.234235i
$880$	−3.14893	−	3.90997i	−0.106151	−	0.131805i
$881$	17.2889			0.582479			0.291240	−	0.956650i	$-0.405932\pi$
$881$	17.2889			0.582479			0.291240	+	0.956650i	$0.405932\pi$
$882$	−7.49887	+	6.46274i	−0.252500	+	0.217612i
$883$	−37.9626	−	37.9626i	−1.27754	−	1.27754i	−0.942038	−	0.335505i	$-0.891093\pi$
$883$	−37.9626	−	37.9626i	−1.27754	−	1.27754i	−0.335505	−	0.942038i	$-0.608907\pi$
$884$	−2.49127	−	3.63523i	−0.0837903	−	0.122266i
$885$	0.877951	+	3.27656i	0.0295120	+	0.110140i
$886$	−11.7916	+	9.79362i	−0.396147	+	0.329023i
$887$	−1.97632	+	1.14103i	−0.0663585	+	0.0383121i	−0.532812	−	0.846234i	$-0.678865\pi$
$887$	−1.97632	+	1.14103i	−0.0663585	+	0.0383121i	0.466454	+	0.884546i	$0.345531\pi$
$888$	−16.8275	−	4.78234i	−0.564693	−	0.160485i
$889$	−2.92801	+	7.25510i	−0.0982022	+	0.243328i
$890$	−0.306234	+	0.828375i	−0.0102650	+	0.0277672i
$891$	2.94517	+	0.789156i	0.0986669	+	0.0264377i
$892$	−0.390598	−	1.10773i	−0.0130782	−	0.0370894i
$893$	−24.4878	+	6.56149i	−0.819454	+	0.219572i
$894$	−2.71345	+	3.83399i	−0.0907512	+	0.128228i
$895$	−1.78508			−0.0596685
$896$	−0.524262	−	29.9287i	−0.0175144	−	0.999847i
$897$	−14.1653			−0.472966
$898$	−7.04802	+	9.95857i	−0.235196	+	0.332322i
$899$	−13.9992	+	3.75108i	−0.466901	+	0.125106i
$900$	3.21275	+	9.11129i	0.107092	+	0.303710i
$901$	9.33572	+	2.50150i	0.311018	+	0.0833370i
$902$	−0.557179	+	1.50719i	−0.0185520	+	0.0501840i
$903$	11.2804	+	14.4268i	0.375387	+	0.480093i
$904$	43.3928	+	12.3322i	1.44322	+	0.410161i
$905$	−3.90886	+	2.25678i	−0.129935	+	0.0750180i
$906$	−23.4200	+	19.4517i	−0.778077	+	0.646239i
$907$	9.35030	+	34.8958i	0.310472	+	1.15870i	0.928132	+	0.372251i	$0.121414\pi$
$907$	9.35030	+	34.8958i	0.310472	+	1.15870i	−0.617660	+	0.786445i	$0.711919\pi$
$908$	18.2237	+	26.5918i	0.604774	+	0.882480i
$909$	−9.86159	−	9.86159i	−0.327088	−	0.327088i
$910$	−1.20188	+	2.33195i	−0.0398418	+	0.0773035i
$911$	25.0285			0.829232			0.414616	−	0.909996i	$-0.363916\pi$
$911$	25.0285			0.829232			0.414616	+	0.909996i	$0.363916\pi$
$912$	−5.11382	−	6.34974i	−0.169336	−	0.210261i
$913$	−16.3711	+	28.3556i	−0.541804	+	0.938432i
$914$	1.02549	−	11.0789i	0.0339202	−	0.366458i
$915$	−0.447200	+	1.66897i	−0.0147840	+	0.0551746i
$916$	−1.45128	−	18.7613i	−0.0479515	−	0.619891i
$917$	37.1173	+	27.9475i	1.22572	+	0.922908i
$918$	1.71595	+	0.634351i	0.0566346	+	0.0209367i
$919$	−17.9381	+	10.3566i	−0.591725	+	0.341632i	−0.765779	−	0.643104i	$-0.777646\pi$
$919$	−17.9381	+	10.3566i	−0.591725	+	0.341632i	0.174054	+	0.984736i	$0.444313\pi$
$920$	−9.68103	−	0.146177i	−0.319174	−	0.00481931i
$921$	26.7724	+	15.4571i	0.882181	+	0.509327i
$922$	−40.8951	+	6.99889i	−1.34681	+	0.230496i
$923$	5.29943	−	5.29943i	0.174433	−	0.174433i
$924$	−7.43625	−	14.3183i	−0.244635	−	0.471036i
$925$	−21.1263	−	21.1263i	−0.694628	−	0.694628i
$926$	26.5691	−	37.5410i	0.873114	−	1.23368i
$927$	5.65327	−	9.79175i	0.185678	−	0.321603i
$928$	−9.18292	+	10.4007i	−0.301444	+	0.341419i
$929$	13.2137	+	22.8868i	0.433527	+	0.750891i	0.997174	−	0.0751245i	$-0.0239354\pi$
$929$	13.2137	+	22.8868i	0.433527	+	0.750891i	−0.563647	+	0.826016i	$0.690602\pi$
$930$	1.43804	+	3.12484i	0.0471551	+	0.102468i
$931$	12.2241	−	7.35778i	0.400629	−	0.241141i
$932$	16.3706	+	14.0198i	0.536237	+	0.459232i
$933$	23.8446	+	6.38915i	0.780638	+	0.209171i
$934$	26.0611	+	31.3778i	0.852745	+	1.02671i
$935$	−1.40607	−	0.811795i	−0.0459834	−	0.0265485i
$936$	4.13550	+	2.47162i	0.135173	+	0.0807875i
$937$		−	16.5431i		−	0.540438i	−0.962799	−	0.270219i	$-0.912904\pi$
$937$		−	16.5431i		−	0.540438i	0.962799	−	0.270219i	$-0.0870962\pi$
$938$	−18.5215	−	16.8334i	−0.604750	−	0.549631i
$939$	−2.08777	+	2.08777i	−0.0681318	+	0.0681318i
$940$	8.44657	−	5.78853i	0.275497	−	0.188801i
$941$	5.64224	−	1.51183i	0.183932	−	0.0492844i	−0.165677	−	0.986180i	$-0.552981\pi$
$941$	5.64224	−	1.51183i	0.183932	−	0.0492844i	0.349609	+	0.936896i	$0.386314\pi$
$942$	−1.37099	+	14.8116i	−0.0446694	+	0.482588i
$943$	1.54951	+	2.68383i	0.0504589	+	0.0873974i
$944$	−26.6158	−	19.4466i	−0.866270	−	0.632933i
$945$	−0.151983	−	1.07841i	−0.00494401	−	0.0350806i
$946$	−27.1137	+	12.4776i	−0.881542	+	0.405681i
$947$	−12.1534	+	45.3570i	−0.394932	+	1.47391i	0.426965	+	0.904268i	$0.359583\pi$
$947$	−12.1534	+	45.3570i	−0.394932	+	1.47391i	−0.821896	+	0.569637i	$0.807084\pi$
$948$	−10.7230	+	22.4041i	−0.348268	+	0.727651i
$949$	3.39428	+	12.6676i	0.110183	+	0.411208i
$950$	−2.34885	−	13.7245i	−0.0762068	−	0.445283i
$951$			6.25702i			0.202898i
$952$	−3.65096	−	8.96565i	−0.118328	−	0.290578i
$953$		−	22.6944i		−	0.735144i	−0.929995	−	0.367572i	$-0.880189\pi$
$953$		−	22.6944i		−	0.735144i	0.929995	−	0.367572i	$-0.119811\pi$
$954$	−10.4147	+	1.78239i	−0.337188	+	0.0577071i
$955$	−0.941366	−	3.51323i	−0.0304619	−	0.113685i
$956$	−10.7316	−	30.4346i	−0.347086	−	0.984326i
$957$	−1.93555	+	7.22356i	−0.0625673	+	0.233504i
$958$	−16.1211	−	35.0310i	−0.520849	−	1.13180i
$959$	−3.94766	+	3.08669i	−0.127477	+	0.0996745i
$960$	2.80083	+	1.73186i	0.0903965	+	0.0558957i
$961$	−1.95861	−	3.39241i	−0.0631810	−	0.109433i
$962$	−14.8357	−	1.37322i	−0.478321	−	0.0442745i
$963$	−1.63213	+	0.437329i	−0.0525948	+	0.0140927i
$964$	28.8354	+	5.38426i	0.928724	+	0.173415i
$965$	5.89310	−	5.89310i	0.189706	−	0.189706i
$966$	−30.4057	−	6.61081i	−0.978289	−	0.212699i
$967$		−	6.69278i		−	0.215225i	−0.994193	−	0.107613i	$-0.965679\pi$
$967$		−	6.69278i		−	0.215225i	0.994193	−	0.107613i	$-0.0343206\pi$
$968$	−4.67153	+	1.17644i	−0.150149	+	0.0378121i
$969$	−2.28344	−	1.31834i	−0.0733546	−	0.0423513i
$970$	−4.68664	+	3.89253i	−0.150479	+	0.124982i
$971$	−20.3403	−	5.45015i	−0.652750	−	0.174904i	−0.0827779	−	0.996568i	$-0.526379\pi$
$971$	−20.3403	−	5.45015i	−0.652750	−	0.174904i	−0.569972	+	0.821664i	$0.693046\pi$
$972$	−1.99404	+	0.154249i	−0.0639590	+	0.00494753i
$973$	11.0843	+	26.0851i	0.355347	+	0.836250i
$974$	−22.2665	+	10.2469i	−0.713466	+	0.328333i
$975$	4.11408	+	7.12579i	0.131756	+	0.228208i
$976$	−6.78817	−	15.3570i	−0.217284	−	0.491566i
$977$	4.18967	−	7.25671i	0.134039	−	0.232163i	−0.791191	−	0.611569i	$-0.790539\pi$
$977$	4.18967	−	7.25671i	0.134039	−	0.232163i	0.925230	+	0.379407i	$0.123872\pi$
$978$	−18.1535	−	12.8479i	−0.580486	−	0.410830i
$979$	−3.27096	−	3.27096i	−0.104540	−	0.104540i
$980$	−3.66812	+	4.44462i	−0.117174	+	0.141978i
$981$	4.42222	−	4.42222i	0.141191	−	0.141191i
$982$	−1.18474	−	6.92253i	−0.0378065	−	0.220907i
$983$	1.10690	+	0.639070i	0.0353047	+	0.0203832i	0.517548	−	0.855654i	$-0.326845\pi$
$983$	1.10690	+	0.639070i	0.0353047	+	0.0203832i	−0.482244	+	0.876037i	$0.660178\pi$
$984$	0.0159131	−	1.05390i	0.000507292	−	0.0335970i
$985$	2.57951	−	1.48928i	0.0821900	−	0.0474524i
$986$	−1.55586	+	4.20866i	−0.0495487	+	0.134031i
$987$	30.2870	−	12.8698i	0.964047	−	0.409651i
$988$	−5.27396	−	4.51661i	−0.167787	−	0.143693i
$989$	−14.8983	+	55.6011i	−0.473738	+	1.76801i
$990$	1.76740	+	0.163594i	0.0561716	+	0.00519936i
$991$	−17.1841	+	29.7638i	−0.545872	+	0.945478i	0.452679	+	0.891673i	$0.350468\pi$
$991$	−17.1841	+	29.7638i	−0.545872	+	0.945478i	−0.998551	+	0.0538050i	$0.982865\pi$
$992$	−29.9299	−	14.8846i	−0.950276	−	0.472585i
$993$	1.17547			0.0373025
$994$	13.8484	−	8.90201i	0.439245	−	0.282355i
$995$	−7.41764	−	7.41764i	−0.235155	−	0.235155i
$996$	3.94211	−	21.1120i	0.124911	−	0.668958i
$997$	−4.21012	−	15.7124i	−0.133336	−	0.497616i	0.866663	−	0.498893i	$-0.166260\pi$
$997$	−4.21012	−	15.7124i	−0.133336	−	0.497616i	−0.999999	+	0.00127739i	$0.999593\pi$
$998$	−18.6373	−	22.4395i	−0.589953	−	0.710308i
$999$	5.35637	−	3.09250i	0.169468	−	0.0978425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.22	yes	120
7.2	even	3	inner	336.2.bq.b.205.1	yes	120
16.5	even	4	inner	336.2.bq.b.277.1	yes	120
112.37	even	12	inner	336.2.bq.b.37.22	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.22	✓	120	112.37	even	12	inner
336.2.bq.b.109.22	yes	120	1.1	even	1	trivial
336.2.bq.b.205.1	yes	120	7.2	even	3	inner
336.2.bq.b.277.1	yes	120	16.5	even	4	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.816979 - 1.15436i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.665089 - 1.88618i) q^{4} +(0.397602 + 0.106537i) q^{5} +(0.490371 - 1.32647i) q^{6} +(0.990173 - 2.45348i) q^{7} +(-2.72069 - 0.773215i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.816979 - 1.15436i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.665089 - 1.88618i) q^{4} +(0.397602 + 0.106537i) q^{5} +(0.490371 - 1.32647i) q^{6} +(0.990173 - 2.45348i) q^{7} +(-2.72069 - 0.773215i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.447815 - 0.371937i) q^{10} +(0.789156 + 2.94517i) q^{11} +(-1.13060 - 1.64977i) q^{12} +(-1.20445 - 1.20445i) q^{13} +(-2.02324 - 3.14746i) q^{14} +0.411628 q^{15} +(-3.11531 + 2.50895i) q^{16} +(-0.646807 + 1.12030i) q^{17} +(0.130346 - 1.40819i) q^{18} +(-0.527534 + 1.96878i) q^{19} +(-0.0634931 - 0.820804i) q^{20} +(0.321426 - 2.62615i) q^{21} +(4.04451 + 1.49517i) q^{22} +(7.20198 - 4.15807i) q^{23} +(-2.82810 - 0.0427024i) q^{24} +(-4.18339 - 2.41528i) q^{25} +(-2.37438 + 0.406358i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-5.28624 - 0.235857i) q^{28} +(1.73431 + 1.73431i) q^{29} +(0.336292 - 0.475167i) q^{30} +(-2.95454 + 5.11741i) q^{31} +(0.351081 + 5.64595i) q^{32} +(1.52453 + 2.64057i) q^{33} +(0.764803 + 1.66191i) q^{34} +(0.655082 - 0.870018i) q^{35} +(-1.51907 - 1.30093i) q^{36} +(5.97426 + 1.60080i) q^{37} +(1.84170 + 2.21742i) q^{38} +(-1.47515 - 0.851677i) q^{39} +(-0.999375 - 0.597286i) q^{40} +0.372651i q^{41} +(-2.76893 - 2.51656i) q^{42} +(-4.89445 + 4.89445i) q^{43} +(5.03025 - 3.44729i) q^{44} +(0.397602 - 0.106537i) q^{45} +(1.08397 - 11.7107i) q^{46} +(6.21903 + 10.7717i) q^{47} +(-2.35980 + 3.22976i) q^{48} +(-5.03912 - 4.85874i) q^{49} +(-6.20584 + 2.85590i) q^{50} +(-0.334812 + 1.24953i) q^{51} +(-1.47074 + 3.07288i) q^{52} +(-1.93373 - 7.21678i) q^{53} +(-0.238563 - 1.39395i) q^{54} +1.25508i q^{55} +(-4.59102 + 5.90953i) q^{56} +2.03823i q^{57} +(3.41890 - 0.585119i) q^{58} +(2.13287 + 7.95999i) q^{59} +(-0.273769 - 0.776403i) q^{60} +(-1.08642 + 4.05457i) q^{61} +(3.49353 + 7.59142i) q^{62} +(-0.369225 - 2.61986i) q^{63} +(6.80428 + 4.20735i) q^{64} +(-0.350574 - 0.607212i) q^{65} +(4.29367 + 0.397432i) q^{66} +(6.46115 - 1.73126i) q^{67} +(2.54327 + 0.474890i) q^{68} +(5.88039 - 5.88039i) q^{69} +(-0.469125 - 1.46699i) q^{70} +4.39987i q^{71} +(-2.74279 + 0.690720i) q^{72} +(-6.66771 - 3.84961i) q^{73} +(6.72874 - 5.58862i) q^{74} +(-4.66596 - 1.25024i) q^{75} +(4.06433 - 0.314395i) q^{76} +(8.00731 + 0.980050i) q^{77} +(-2.18831 + 1.00705i) q^{78} +(-6.20951 - 10.7552i) q^{79} +(-1.50595 + 0.665667i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.430173 + 0.304448i) q^{82} +(7.59322 + 7.59322i) q^{83} +(-5.16716 + 1.14036i) q^{84} +(-0.376526 + 0.376526i) q^{85} +(1.65129 + 9.64861i) q^{86} +(2.12408 + 1.22634i) q^{87} +(0.130203 - 8.62308i) q^{88} +(-1.31387 + 0.758565i) q^{89} +(0.201851 - 0.546014i) q^{90} +(-4.14771 + 1.76248i) q^{91} +(-12.6328 - 10.8187i) q^{92} +(-1.52938 + 5.70773i) q^{93} +(17.5152 + 1.62124i) q^{94} +(-0.419497 + 0.726590i) q^{95} +(1.80040 + 5.36270i) q^{96} -10.4656 q^{97} +(-9.72558 + 1.84746i) q^{98} +(2.15601 + 2.15601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

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