LMFDB - Embedded newform 416.2.bd.a.83.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.15
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877210 - 1.10928i) q^{2} +(-1.94716 - 0.806541i) q^{3} +(-0.461004 + 1.94614i) q^{4} +(-0.00996722 + 0.0240630i) q^{5} +(0.813391 + 2.86746i) q^{6} -2.96755i q^{7} +(2.56322 - 1.19579i) q^{8} +(1.01961 + 1.01961i) q^{9} +O(q^{10})$	\(q+(-0.877210 - 1.10928i) q^{2} +(-1.94716 - 0.806541i) q^{3} +(-0.461004 + 1.94614i) q^{4} +(-0.00996722 + 0.0240630i) q^{5} +(0.813391 + 2.86746i) q^{6} -2.96755i q^{7} +(2.56322 - 1.19579i) q^{8} +(1.01961 + 1.01961i) q^{9} +(0.0354360 - 0.0100519i) q^{10} +(-4.21937 - 1.74772i) q^{11} +(2.46730 - 3.41764i) q^{12} +(-1.90143 + 3.06342i) q^{13} +(-3.29184 + 2.60316i) q^{14} +(0.0388156 - 0.0388156i) q^{15} +(-3.57495 - 1.79436i) q^{16} +0.268171 q^{17} +(0.236622 - 2.02545i) q^{18} +(1.32058 + 3.18817i) q^{19} +(-0.0422351 - 0.0304908i) q^{20} +(-2.39345 + 5.77830i) q^{21} +(1.76256 + 6.21358i) q^{22} +(0.593999 + 0.593999i) q^{23} +(-5.95546 + 0.261067i) q^{24} +(3.53505 + 3.53505i) q^{25} +(5.06615 - 0.578050i) q^{26} +(1.25663 + 3.03377i) q^{27} +(5.77528 + 1.36805i) q^{28} +(-1.36076 + 3.28517i) q^{29} +(-0.0771068 - 0.00900793i) q^{30} +(-3.68370 - 3.68370i) q^{31} +(1.14553 + 5.53965i) q^{32} +(6.80619 + 6.80619i) q^{33} +(-0.235242 - 0.297477i) q^{34} +(0.0714081 + 0.0295782i) q^{35} +(-2.45436 + 1.51427i) q^{36} +(2.06714 + 0.856238i) q^{37} +(2.37814 - 4.26159i) q^{38} +(6.17317 - 4.43141i) q^{39} +(0.00322627 + 0.0735974i) q^{40} -11.1368 q^{41} +(8.50931 - 2.41378i) q^{42} +(1.83875 + 4.43912i) q^{43} +(5.34646 - 7.40580i) q^{44} +(-0.0346977 + 0.0143723i) q^{45} +(0.137849 - 1.17997i) q^{46} +(3.17617 + 3.17617i) q^{47} +(5.51378 + 6.37726i) q^{48} -1.80635 q^{49} +(0.820379 - 7.02235i) q^{50} +(-0.522173 - 0.216291i) q^{51} +(-5.08530 - 5.11271i) q^{52} +(0.167087 + 0.403384i) q^{53} +(2.26297 - 4.05521i) q^{54} +(0.0841108 - 0.0841108i) q^{55} +(-3.54858 - 7.60647i) q^{56} -7.27299i q^{57} +(4.83784 - 1.37232i) q^{58} +(1.69544 - 4.09314i) q^{59} +(0.0576466 + 0.0934349i) q^{60} +(-4.09323 + 9.88192i) q^{61} +(-0.854876 + 7.31764i) q^{62} +(3.02576 - 3.02576i) q^{63} +(5.14015 - 6.13016i) q^{64} +(-0.0547632 - 0.0762879i) q^{65} +(1.57951 - 13.5204i) q^{66} +(-13.8508 + 5.73720i) q^{67} +(-0.123628 + 0.521899i) q^{68} +(-0.677528 - 1.63570i) q^{69} +(-0.0298294 - 0.105158i) q^{70} -8.21571 q^{71} +(3.83274 + 1.39424i) q^{72} +10.2218i q^{73} +(-0.863510 - 3.04414i) q^{74} +(-4.03216 - 9.73449i) q^{75} +(-6.81343 + 1.10028i) q^{76} +(-5.18645 + 12.5212i) q^{77} +(-10.3308 - 2.96050i) q^{78} -1.80629 q^{79} +(0.0788100 - 0.0681393i) q^{80} -11.2466i q^{81} +(9.76934 + 12.3539i) q^{82} +(-5.60506 - 13.5318i) q^{83} +(-10.1420 - 7.32182i) q^{84} +(-0.00267292 + 0.00645300i) q^{85} +(3.31126 - 5.93373i) q^{86} +(5.29924 - 5.29924i) q^{87} +(-12.9051 + 0.565715i) q^{88} -0.316072 q^{89} +(0.0463801 + 0.0258820i) q^{90} +(9.09086 + 5.64258i) q^{91} +(-1.42984 + 0.882171i) q^{92} +(4.20171 + 10.1438i) q^{93} +(0.737093 - 6.30943i) q^{94} -0.0898794 q^{95} +(2.23742 - 11.7105i) q^{96} +(8.51081 - 8.51081i) q^{97} +(1.58455 + 2.00374i) q^{98} +(-2.52013 - 6.08413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.877210	−	1.10928i	−0.620281	−	0.784379i
$2$	−0.877210	−	1.10928i	−0.620281	−	0.784379i
$3$	−1.94716	−	0.806541i	−1.12420	−	0.465657i	−0.258391	−	0.966040i	$-0.583192\pi$
$3$	−1.94716	−	0.806541i	−1.12420	−	0.465657i	−0.865804	+	0.500384i	$0.833192\pi$
$4$	−0.461004	+	1.94614i	−0.230502	+	0.973072i
$5$	−0.00996722	+	0.0240630i	−0.00445748	+	0.0107613i	−0.926093	−	0.377296i	$-0.876854\pi$
$5$	−0.00996722	+	0.0240630i	−0.00445748	+	0.0107613i	0.921635	+	0.388058i	$0.126854\pi$
$6$	0.813391	+	2.86746i	0.332066	+	1.17063i
$7$		−	2.96755i		−	1.12163i	−0.827942	−	0.560814i	$-0.810488\pi$
$7$		−	2.96755i		−	1.12163i	0.827942	−	0.560814i	$-0.189512\pi$
$8$	2.56322	−	1.19579i	0.906234	−	0.422777i
$9$	1.01961	+	1.01961i	0.339872	+	0.339872i
$10$	0.0354360	−	0.0100519i	0.0112058	−	0.00317868i
$11$	−4.21937	−	1.74772i	−1.27219	−	0.526958i	−0.358559	−	0.933507i	$-0.616732\pi$
$11$	−4.21937	−	1.74772i	−1.27219	−	0.526958i	−0.913629	+	0.406549i	$0.866732\pi$
$12$	2.46730	−	3.41764i	0.712247	−	0.986588i
$13$	−1.90143	+	3.06342i	−0.527362	+	0.849641i
$13$	−1.90143	+	3.06342i	−0.527362	+	0.849641i
$14$	−3.29184	+	2.60316i	−0.879782	+	0.695725i
$15$	0.0388156	−	0.0388156i	0.0100221	−	0.0100221i
$16$	−3.57495	−	1.79436i	−0.893738	−	0.448590i
$17$	0.268171			0.0650410			0.0325205	−	0.999471i	$-0.489647\pi$
$17$	0.268171			0.0650410			0.0325205	+	0.999471i	$0.489647\pi$
$18$	0.236622	−	2.02545i	0.0557723	−	0.477404i
$19$	1.32058	+	3.18817i	0.302962	+	0.731416i	0.999898	+	0.0142821i	$0.00454630\pi$
$19$	1.32058	+	3.18817i	0.302962	+	0.731416i	−0.696936	+	0.717134i	$0.745454\pi$
$20$	−0.0422351	−	0.0304908i	−0.00944406	−	0.00681795i
$21$	−2.39345	+	5.77830i	−0.522294	+	1.26093i
$22$	1.76256	+	6.21358i	0.375780	+	1.32474i
$23$	0.593999	+	0.593999i	0.123857	+	0.123857i	0.766318	−	0.642461i	$-0.222087\pi$
$23$	0.593999	+	0.593999i	0.123857	+	0.123857i	−0.642461	+	0.766318i	$0.722087\pi$
$24$	−5.95546	+	0.261067i	−1.21565	+	0.0532901i
$25$	3.53505	+	3.53505i	0.707011	+	0.707011i
$26$	5.06615	−	0.578050i	0.993553	−	0.113365i
$27$	1.25663	+	3.03377i	0.241838	+	0.583850i
$28$	5.77528	+	1.36805i	1.09142	+	0.258538i
$29$	−1.36076	+	3.28517i	−0.252687	+	0.610040i	−0.998419	−	0.0562056i	$-0.982100\pi$
$29$	−1.36076	+	3.28517i	−0.252687	+	0.610040i	0.745732	+	0.666246i	$0.232100\pi$
$30$	−0.0771068	−	0.00900793i	−0.0140777	−	0.00164462i
$31$	−3.68370	−	3.68370i	−0.661613	−	0.661613i	0.294147	−	0.955760i	$-0.404964\pi$
$31$	−3.68370	−	3.68370i	−0.661613	−	0.661613i	−0.955760	+	0.294147i	$0.904964\pi$
$32$	1.14553	+	5.53965i	0.202504	+	0.979281i
$33$	6.80619	+	6.80619i	1.18481	+	1.18481i
$34$	−0.235242	−	0.297477i	−0.0403437	−	0.0510168i
$35$	0.0714081	+	0.0295782i	0.0120702	+	0.00499963i
$36$	−2.45436	+	1.51427i	−0.409060	+	0.252378i
$37$	2.06714	+	0.856238i	0.339836	+	0.140765i	0.546073	−	0.837737i	$-0.316122\pi$
$37$	2.06714	+	0.856238i	0.339836	+	0.140765i	−0.206238	+	0.978502i	$0.566122\pi$
$38$	2.37814	−	4.26159i	0.385786	−	0.691321i
$39$	6.17317	−	4.43141i	0.988498	−	0.709593i
$40$	0.00322627	+	0.0735974i	0.000510117	+	0.0116368i
$41$	−11.1368			−1.73928			−0.869640	−	0.493686i	$-0.835649\pi$
$41$	−11.1368			−1.73928			−0.869640	+	0.493686i	$0.835649\pi$
$42$	8.50931	−	2.41378i	1.31302	−	0.372454i
$43$	1.83875	+	4.43912i	0.280406	+	0.676960i	0.999845	−	0.0175955i	$-0.00560110\pi$
$43$	1.83875	+	4.43912i	0.280406	+	0.676960i	−0.719439	+	0.694555i	$0.755601\pi$
$44$	5.34646	−	7.40580i	0.806010	−	1.11647i
$45$	−0.0346977	+	0.0143723i	−0.00517243	+	0.00214249i
$46$	0.137849	−	1.17997i	0.0203247	−	0.173977i
$47$	3.17617	+	3.17617i	0.463292	+	0.463292i	0.899733	−	0.436441i	$-0.143761\pi$
$47$	3.17617	+	3.17617i	0.463292	+	0.463292i	−0.436441	+	0.899733i	$0.643761\pi$
$48$	5.51378	+	6.37726i	0.795846	+	0.920478i
$49$	−1.80635			−0.258050
$50$	0.820379	−	7.02235i	0.116019	−	0.993110i
$51$	−0.522173	−	0.216291i	−0.0731188	−	0.0302868i
$52$	−5.08530	−	5.11271i	−0.705204	−	0.709005i
$53$	0.167087	+	0.403384i	0.0229512	+	0.0554090i	0.934940	−	0.354807i	$-0.115453\pi$
$53$	0.167087	+	0.403384i	0.0229512	+	0.0554090i	−0.911988	+	0.410216i	$0.865453\pi$
$54$	2.26297	−	4.05521i	0.307952	−	0.551844i
$55$	0.0841108	−	0.0841108i	0.0113415	−	0.0113415i
$56$	−3.54858	−	7.60647i	−0.474199	−	1.01646i
$57$		−	7.27299i		−	0.963331i
$58$	4.83784	−	1.37232i	0.635240	−	0.180194i
$59$	1.69544	−	4.09314i	0.220727	−	0.532882i	−0.774262	−	0.632865i	$-0.781879\pi$
$59$	1.69544	−	4.09314i	0.220727	−	0.532882i	0.994989	+	0.0999830i	$0.0318788\pi$
$60$	0.0576466	+	0.0934349i	0.00744214	+	0.0120624i
$61$	−4.09323	+	9.88192i	−0.524084	+	1.26525i	0.411262	+	0.911517i	$0.365088\pi$
$61$	−4.09323	+	9.88192i	−0.524084	+	1.26525i	−0.935346	+	0.353733i	$0.884912\pi$
$62$	−0.854876	+	7.31764i	−0.108569	+	0.929342i
$63$	3.02576	−	3.02576i	0.381209	−	0.381209i
$64$	5.14015	−	6.13016i	0.642519	−	0.766270i
$65$	−0.0547632	−	0.0762879i	−0.00679254	−	0.00946235i
$66$	1.57951	−	13.5204i	0.194424	−	1.66425i
$67$	−13.8508	+	5.73720i	−1.69215	+	0.700910i	−0.999787	−	0.0206421i	$-0.993429\pi$
$67$	−13.8508	+	5.73720i	−1.69215	+	0.700910i	−0.692360	+	0.721552i	$0.743429\pi$
$68$	−0.123628	+	0.521899i	−0.0149921	+	0.0632896i
$69$	−0.677528	−	1.63570i	−0.0815648	−	0.196915i
$70$	−0.0298294	−	0.105158i	−0.00356530	−	0.0125688i
$71$	−8.21571			−0.975026			−0.487513	−	0.873116i	$-0.662096\pi$
$71$	−8.21571			−0.975026			−0.487513	+	0.873116i	$0.662096\pi$
$72$	3.83274	+	1.39424i	0.451693	+	0.164313i
$73$			10.2218i			1.19637i	0.801357	+	0.598186i	$0.204112\pi$
$73$			10.2218i			1.19637i	−0.801357	+	0.598186i	$0.795888\pi$
$74$	−0.863510	−	3.04414i	−0.100381	−	0.353874i
$75$	−4.03216	−	9.73449i	−0.465594	−	1.12404i
$76$	−6.81343	+	1.10028i	−0.781554	+	0.126211i
$77$	−5.18645	+	12.5212i	−0.591051	+	1.42692i
$78$	−10.3308	−	2.96050i	−1.16974	−	0.335211i
$79$	−1.80629			−0.203224			−0.101612	−	0.994824i	$-0.532400\pi$
$79$	−1.80629			−0.203224			−0.101612	+	0.994824i	$0.532400\pi$
$80$	0.0788100	−	0.0681393i	0.00881123	−	0.00761820i
$81$		−	11.2466i		−	1.24963i
$82$	9.76934	+	12.3539i	1.07884	+	1.36426i
$83$	−5.60506	−	13.5318i	−0.615235	−	1.48531i	−0.857179	−	0.515018i	$-0.827785\pi$
$83$	−5.60506	−	13.5318i	−0.615235	−	1.48531i	0.241945	−	0.970290i	$-0.422215\pi$
$84$	−10.1420	−	7.32182i	−1.10658	−	0.798876i
$85$	−0.00267292	+	0.00645300i	−0.000289919	+	0.000699926i
$86$	3.31126	−	5.93373i	0.357063	−	0.639850i
$87$	5.29924	−	5.29924i	0.568139	−	0.568139i
$88$	−12.9051	+	0.565715i	−1.37569	+	0.0603055i
$89$	−0.316072			−0.0335035			−0.0167518	−	0.999860i	$-0.505333\pi$
$89$	−0.316072			−0.0335035			−0.0167518	+	0.999860i	$0.505333\pi$
$90$	0.0463801	+	0.0258820i	0.00488889	+	0.00272820i
$91$	9.09086	+	5.64258i	0.952981	+	0.591503i
$92$	−1.42984	+	0.882171i	−0.149071	+	0.0919727i
$93$	4.20171	+	10.1438i	0.435697	+	1.05187i
$94$	0.737093	−	6.30943i	0.0760253	−	0.650768i
$95$	−0.0898794			−0.00922144
$96$	2.23742	−	11.7105i	0.228355	−	1.19520i
$97$	8.51081	−	8.51081i	0.864141	−	0.864141i	−0.127675	−	0.991816i	$-0.540751\pi$
$97$	8.51081	−	8.51081i	0.864141	−	0.864141i	0.991816	+	0.127675i	$0.0407514\pi$
$98$	1.58455	+	2.00374i	0.160063	+	0.202409i
$99$	−2.52013	−	6.08413i	−0.253283	−	0.611478i
$100$	−8.50940	+	5.25005i	−0.850940	+	0.525005i
$101$	−6.38965	−	15.4260i	−0.635794	−	1.53494i	−0.832232	−	0.554427i	$-0.812938\pi$
$101$	−6.38965	−	15.4260i	−0.635794	−	1.53494i	0.196438	−	0.980516i	$-0.437062\pi$
$102$	0.218128	+	0.768969i	0.0215979	+	0.0761392i
$103$	−3.66386	+	3.66386i	−0.361011	+	0.361011i	−0.864185	−	0.503174i	$-0.832165\pi$
$103$	−3.66386	+	3.66386i	−0.361011	+	0.361011i	0.503174	+	0.864185i	$0.332165\pi$
$104$	−1.21055	+	10.1259i	−0.118704	+	0.992930i
$105$	−0.115187	−	0.115187i	−0.0112411	−	0.0112411i
$106$	0.300895	−	0.539199i	0.0292255	−	0.0523716i
$107$	1.31915	−	0.546410i	0.127527	−	0.0528234i	−0.318007	−	0.948088i	$-0.603014\pi$
$107$	1.31915	−	0.546410i	0.127527	−	0.0528234i	0.445534	+	0.895265i	$0.353014\pi$
$108$	−6.48347	+	1.04700i	−0.623872	+	0.100748i
$109$	−0.990292	+	0.410192i	−0.0948528	+	0.0392893i	−0.429605	−	0.903017i	$-0.641347\pi$
$109$	−0.990292	+	0.410192i	−0.0948528	+	0.0392893i	0.334753	+	0.942306i	$0.391347\pi$
$110$	−0.167085	−	0.0195196i	−0.0159310	−	0.00186112i
$111$	−3.33447	−	3.33447i	−0.316494	−	0.316494i
$112$	−5.32485	+	10.6088i	−0.503151	+	1.00244i
$113$		−	9.61963i		−	0.904939i	−0.891780	−	0.452469i	$-0.850543\pi$
$113$		−	9.61963i		−	0.904939i	0.891780	−	0.452469i	$-0.149457\pi$
$114$	−8.06778	+	6.37994i	−0.755617	+	0.597536i
$115$	−0.0202139	+	0.00837288i	−0.00188496	+	0.000780775i
$116$	−5.76609	−	4.16271i	−0.535368	−	0.386498i
$117$	−5.06224	+	1.18479i	−0.468004	+	0.109534i
$118$	−6.02770	+	1.70984i	−0.554894	+	0.157403i
$119$		−	0.795811i		−	0.0729518i
$120$	0.0530773	−	0.145908i	0.00484527	−	0.0133195i
$121$	6.97039	+	6.97039i	0.633672	+	0.633672i
$122$	14.5524	−	4.12799i	1.31752	−	0.373731i
$123$	21.6852	+	8.98231i	1.95529	+	0.809908i
$124$	8.86722	−	5.47082i	0.796300	−	0.491294i
$125$	−0.240614	+	0.0996655i	−0.0215211	+	0.00891435i
$126$	−6.01064	−	0.702186i	−0.535470	−	0.0625557i
$127$	11.4366			1.01483			0.507417	−	0.861701i	$-0.330601\pi$
$127$	11.4366			1.01483			0.507417	+	0.861701i	$0.330601\pi$
$128$	−11.3091	−	0.324428i	−0.999589	−	0.0286757i
$129$		−	10.1267i		−	0.891608i
$130$	−0.0365858	+	0.127668i	−0.00320879	+	0.0111973i
$131$	−8.63610	−	3.57719i	−0.754540	−	0.312541i	−0.0279474	−	0.999609i	$-0.508897\pi$
$131$	−8.63610	−	3.57719i	−0.754540	−	0.312541i	−0.726592	+	0.687069i	$0.758897\pi$
$132$	−16.3835	+	10.1081i	−1.42600	+	0.879801i
$133$	9.46104	−	3.91889i	0.820376	−	0.339811i
$134$	18.5142	+	10.3317i	1.59939	+	0.892524i
$135$	−0.0855268			−0.00736097
$136$	0.687380	−	0.320677i	0.0589424	−	0.0274979i
$137$		−	16.0392i		−	1.37032i	−0.728391	−	0.685162i	$-0.759732\pi$
$137$		−	16.0392i		−	1.37032i	0.728391	−	0.685162i	$-0.240268\pi$
$138$	−1.22011	+	2.18642i	−0.103863	+	0.186120i
$139$	−13.5185	+	5.59954i	−1.14662	+	0.474947i	−0.873400	−	0.487004i	$-0.838090\pi$
$139$	−13.5185	+	5.59954i	−1.14662	+	0.474947i	−0.273224	+	0.961951i	$0.588090\pi$
$140$	−0.0904829	+	0.125335i	−0.00764720	+	0.0105927i
$141$	−3.62281	−	8.74624i	−0.305096	−	0.736566i
$142$	7.20691	+	9.11353i	0.604790	+	0.764790i
$143$	13.3768	−	9.60256i	1.11863	−	0.803006i
$144$	−1.81551	−	5.47463i	−0.151293	−	0.456219i
$145$	−0.0654880	−	0.0654880i	−0.00543848	−	0.00543848i
$146$	11.3389	−	8.96668i	0.938410	−	0.742088i
$147$	3.51725	+	1.45689i	0.290098	+	0.120163i
$148$	−2.61932	+	3.62822i	−0.215307	+	0.298238i
$149$	15.2610	+	6.32130i	1.25023	+	0.517861i	0.906896	−	0.421354i	$-0.138445\pi$
$149$	15.2610	+	6.32130i	1.25023	+	0.517861i	0.343331	+	0.939215i	$0.388445\pi$
$150$	−7.26123	+	13.0120i	−0.592877	+	1.06242i
$151$	0.214554			0.0174602			0.00873009	−	0.999962i	$-0.497221\pi$
$151$	0.214554			0.0174602			0.00873009	+	0.999962i	$0.497221\pi$
$152$	7.19733	+	6.59282i	0.583781	+	0.534748i
$153$	0.273431	+	0.273431i	0.0221056	+	0.0221056i
$154$	18.4391	−	5.23050i	1.48587	−	0.421485i
$155$	0.125357	−	0.0519247i	0.0100689	−	0.00417069i
$156$	5.77829	+	14.0568i	0.462634	+	1.12544i
$157$	−7.17191	+	17.3145i	−0.572381	+	1.38185i	0.327141	+	0.944975i	$0.393915\pi$
$157$	−7.17191	+	17.3145i	−0.572381	+	1.38185i	−0.899522	+	0.436875i	$0.856085\pi$
$158$	1.58450	+	2.00368i	0.126056	+	0.159405i
$159$		−	0.920216i		−	0.0729779i
$160$	−0.144718	−	0.0276499i	−0.0114410	−	0.00218592i
$161$	1.76272	−	1.76272i	0.138922	−	0.138922i
$162$	−12.4757	+	9.86566i	−0.980181	+	0.775119i
$163$	−4.63693	−	11.1945i	−0.363192	−	0.876824i	−0.994829	−	0.101560i	$-0.967617\pi$
$163$	−4.63693	−	11.1945i	−0.363192	−	0.876824i	0.631637	−	0.775264i	$-0.282383\pi$
$164$	5.13412	−	21.6739i	0.400908	−	1.69244i
$165$	−0.231616	+	0.0959386i	−0.0180313	+	0.00746881i
$166$	−10.0937	+	18.0878i	−0.783426	+	1.40389i
$167$			22.1889i			1.71703i	0.512788	+	0.858515i	$0.328613\pi$
$167$			22.1889i			1.71703i	−0.512788	+	0.858515i	$0.671387\pi$
$168$	0.774730	+	17.6731i	0.0597717	+	1.36351i
$169$	−5.76914	−	11.6498i	−0.443780	−	0.896136i
$170$	0.00950290	−	0.00269562i	0.000728839	−	0.000206745i
$171$	−1.90422	+	4.59719i	−0.145619	+	0.351556i
$172$	−9.48684	+	1.53201i	−0.723365	+	0.116814i
$173$	−0.663233	+	1.60119i	−0.0504247	+	0.121736i	−0.947085	−	0.320984i	$-0.895986\pi$
$173$	−0.663233	+	1.60119i	−0.0504247	+	0.121736i	0.896660	+	0.442720i	$0.145986\pi$
$174$	−10.5269	−	1.22979i	−0.798042	−	0.0932305i
$175$	10.4904	−	10.4904i	0.793003	−	0.793003i
$176$	11.9480	+	13.8191i	0.900614	+	1.04165i
$177$	−6.60258	+	6.60258i	−0.496280	+	0.496280i
$178$	0.277261	+	0.350612i	0.0207816	+	0.0262795i
$179$	−9.91253	−	4.10590i	−0.740897	−	0.306890i	−0.0198758	−	0.999802i	$-0.506327\pi$
$179$	−9.91253	−	4.10590i	−0.740897	−	0.306890i	−0.721021	+	0.692913i	$0.756327\pi$
$180$	−0.0119747	−	0.0741524i	−0.000892541	−	0.00552699i
$181$	−10.4244	+	4.31792i	−0.774839	+	0.320949i	−0.734831	−	0.678251i	$-0.762738\pi$
$181$	−10.4244	+	4.31792i	−0.774839	+	0.320949i	−0.0400082	+	0.999199i	$0.512738\pi$
$182$	−1.71539	−	15.0340i	−0.127153	−	1.11440i
$183$	15.9404	−	15.9404i	1.17835	−	1.17835i
$184$	2.23285	+	0.812246i	0.164608	+	0.0598796i
$185$	−0.0412073	+	0.0412073i	−0.00302962	+	0.00302962i
$186$	7.56657	−	13.5592i	0.554807	−	0.994205i
$187$	−1.13151	−	0.468688i	−0.0827444	−	0.0342739i
$188$	−7.64551	+	4.71706i	−0.557606	+	0.344027i
$189$	9.00287	−	3.72911i	0.654862	−	0.271253i
$190$	0.0788432	+	0.0997015i	0.00571988	+	0.00723310i
$191$			18.5536i			1.34249i	0.741236	+	0.671244i	$0.234240\pi$
$191$			18.5536i			1.34249i	−0.741236	+	0.671244i	$0.765760\pi$
$192$	−14.9529	+	7.79067i	−1.07914	+	0.562244i
$193$	−14.2878	−	14.2878i	−1.02846	−	1.02846i	−0.999583	−	0.0288750i	$-0.990808\pi$
$193$	−14.2878	−	14.2878i	−1.02846	−	1.02846i	−0.0288750	−	0.999583i	$-0.509192\pi$
$194$	−16.9066	−	1.97510i	−1.21383	−	0.141804i
$195$	0.0451036	+	0.192714i	0.00322993	+	0.0138005i
$196$	0.832733	−	3.51541i	0.0594810	−	0.251101i
$197$	7.76230	−	18.7399i	0.553041	−	1.33516i	−0.362142	−	0.932123i	$-0.617955\pi$
$197$	7.76230	−	18.7399i	0.553041	−	1.33516i	0.915184	−	0.403037i	$-0.132045\pi$
$198$	−4.53832	+	8.13260i	−0.322525	+	0.577958i
$199$	−3.43778	+	3.43778i	−0.243698	+	0.243698i	−0.818378	−	0.574680i	$-0.805126\pi$
$199$	−3.43778	+	3.43778i	−0.243698	+	0.243698i	0.574680	+	0.818378i	$0.305126\pi$
$200$	13.2883	+	4.83391i	0.939625	+	0.341809i
$201$	31.5971			2.22869
$202$	−11.5067	+	20.6197i	−0.809606	+	1.45080i
$203$	9.74889	+	4.03812i	0.684238	+	0.283421i
$204$	0.661657	−	0.916512i	0.0463253	−	0.0641687i
$205$	0.111003	−	0.267986i	0.00775280	−	0.0187169i
$206$	7.27822	+	0.850271i	0.507098	+	0.0592412i
$207$			1.21130i			0.0841911i
$208$	12.2944	−	7.53974i	0.852463	−	0.522787i
$209$		−	15.7601i		−	1.09015i
$210$	−0.0267315	+	0.228818i	−0.00184465	+	0.0157900i
$211$	3.04036	−	7.34007i	0.209307	−	0.505312i	−0.784008	−	0.620751i	$-0.786828\pi$
$211$	3.04036	−	7.34007i	0.209307	−	0.505312i	0.993314	+	0.115440i	$0.0368277\pi$
$212$	−0.862071	+	0.139214i	−0.0592072	+	0.00956124i
$213$	15.9973	+	6.62631i	1.09612	+	0.454027i
$214$	−1.76329	−	0.983991i	−0.120536	−	0.0672642i
$215$	−0.125146			−0.00853488
$216$	6.84878	+	6.27354i	0.466000	+	0.426860i
$217$	−10.9316	+	10.9316i	−0.742084	+	0.742084i
$218$	1.32371	+	0.738686i	0.0896531	+	0.0500301i
$219$	8.24432	−	19.9035i	0.557099	−	1.34496i
$220$	0.124916	+	0.202467i	0.00842186	+	0.0136503i
$221$	−0.509908	+	0.821522i	−0.0343001	+	0.0552615i
$222$	−0.773829	+	6.62389i	−0.0519360	+	0.444566i
$223$	10.3641	+	10.3641i	0.694032	+	0.694032i	0.963117	−	0.269084i	$-0.0867210\pi$
$223$	10.3641	+	10.3641i	0.694032	+	0.694032i	−0.269084	+	0.963117i	$0.586721\pi$
$224$	16.4392	−	3.39943i	1.09839	−	0.227134i
$225$			7.20879i			0.480586i
$226$	−10.6709	+	8.43844i	−0.709815	+	0.561317i
$227$	−19.8036	+	8.20293i	−1.31441	+	0.544448i	−0.926169	−	0.377109i	$-0.876918\pi$
$227$	−19.8036	+	8.20293i	−1.31441	+	0.544448i	−0.388244	+	0.921557i	$0.626918\pi$
$228$	14.1543	+	3.35288i	0.937390	+	0.222050i
$229$	14.0168	+	5.80594i	0.926255	+	0.383667i	0.794257	−	0.607582i	$-0.207861\pi$
$229$	14.0168	+	5.80594i	0.926255	+	0.383667i	0.131999	+	0.991250i	$0.457861\pi$
$230$	0.0270197	+	0.0150781i	0.00178163	+	0.000994221i
$231$	20.1977	−	20.1977i	1.32891	−	1.32891i
$232$	0.440461	+	10.0478i	0.0289177	+	0.659669i
$233$	−9.87813	+	9.87813i	−0.647138	+	0.647138i	−0.952300	−	0.305163i	$-0.901289\pi$
$233$	−9.87813	+	9.87813i	−0.647138	+	0.647138i	0.305163	+	0.952300i	$0.401289\pi$
$234$	5.75491	+	4.57613i	0.376210	+	0.299151i
$235$	−0.108086	+	0.0447706i	−0.00705074	+	0.00292051i
$236$	7.18424	+	5.18652i	0.467654	+	0.337614i
$237$	3.51715	+	1.45685i	0.228463	+	0.0946325i
$238$	−0.882777	+	0.698093i	−0.0572219	+	0.0452507i
$239$	−11.4619	+	11.4619i	−0.741406	+	0.741406i	−0.972849	−	0.231443i	$-0.925655\pi$
$239$	−11.4619	+	11.4619i	−0.741406	+	0.741406i	0.231443	+	0.972849i	$0.425655\pi$
$240$	−0.208413	+	0.0691147i	−0.0134530	+	0.00446133i
$241$	−3.34883	+	3.34883i	−0.215717	+	0.215717i	−0.806691	−	0.590974i	$-0.798744\pi$
$241$	−3.34883	+	3.34883i	−0.215717	+	0.215717i	0.590974	+	0.806691i	$0.298744\pi$
$242$	1.61762	−	13.8466i	0.103984	−	0.890094i
$243$	−5.30098	+	12.7977i	−0.340058	+	0.820973i
$244$	−17.3446	−	12.5216i	−1.11038	−	0.801614i
$245$	0.0180043	−	0.0434661i	0.00115025	−	0.00277695i
$246$	−9.05860	−	31.9344i	−0.577555	−	2.03606i
$247$	−12.2777	−	2.01657i	−0.781212	−	0.128311i
$248$	−13.8471	−	5.03718i	−0.879291	−	0.319861i
$249$			30.8693i			1.95626i
$250$	0.321626	+	0.179480i	0.0203414	+	0.0113513i
$251$	−17.5824	+	7.28285i	−1.10979	+	0.459690i	−0.860865	−	0.508833i	$-0.830077\pi$
$251$	−17.5824	+	7.28285i	−1.10979	+	0.459690i	−0.248924	+	0.968523i	$0.580077\pi$
$252$	4.49367	+	7.28344i	0.283075	+	0.458814i
$253$	−1.46816	−	3.54444i	−0.0923022	−	0.222837i
$254$	−10.0323	−	12.6864i	−0.629482	−	0.796014i
$255$	0.0104092	−	0.0104092i	0.000651851	−	0.000651851i
$256$	9.56054	+	12.8295i	0.597534	+	0.801844i
$257$			28.3298i			1.76717i	0.468275	+	0.883583i	$0.344876\pi$
$257$			28.3298i			1.76717i	−0.468275	+	0.883583i	$0.655124\pi$
$258$	−11.2334	+	8.88326i	−0.699359	+	0.553048i
$259$	2.54093	−	6.13434i	0.157886	−	0.381169i
$260$	0.173713	−	0.0714080i	0.0107732	−	0.00442854i
$261$	−4.73705	+	1.96215i	−0.293216	+	0.121454i
$262$	3.60757	+	12.7178i	0.222877	+	0.785709i
$263$	10.7169	+	10.7169i	0.660835	+	0.660835i	0.955577	−	0.294742i	$-0.0952338\pi$
$263$	10.7169	+	10.7169i	0.660835	+	0.660835i	−0.294742	+	0.955577i	$0.595234\pi$
$264$	25.5846	+	9.30694i	1.57462	+	0.572802i
$265$	−0.0113720			−0.000698578
$266$	−12.6465	−	7.05725i	−0.775405	−	0.432708i
$267$	0.615443	+	0.254925i	0.0376645	+	0.0156011i
$268$	−4.78012	−	29.6006i	−0.291993	−	1.80814i
$269$	−11.6979	−	4.84543i	−0.713233	−	0.295431i	−0.00359137	−	0.999994i	$-0.501143\pi$
$269$	−11.6979	−	4.84543i	−0.713233	−	0.295431i	−0.709642	+	0.704563i	$0.751143\pi$
$270$	0.0750250	+	0.0948731i	0.00456587	+	0.00577380i
$271$	10.1650	+	10.1650i	0.617478	+	0.617478i	0.944884	−	0.327406i	$-0.106174\pi$
$271$	10.1650	+	10.1650i	0.617478	+	0.617478i	−0.327406	+	0.944884i	$0.606174\pi$
$272$	−0.958698	−	0.481196i	−0.0581296	−	0.0291768i
$273$	−13.1504	−	18.3192i	−0.795899	−	1.10873i
$274$	−17.7920	+	14.0698i	−1.07485	+	0.849986i
$275$	−8.73742	−	21.0940i	−0.526886	−	1.27202i
$276$	3.49564	−	0.564503i	0.210413	−	0.0339791i
$277$	−5.10546	+	2.11475i	−0.306758	+	0.127063i	−0.530752	−	0.847527i	$-0.678090\pi$
$277$	−5.10546	+	2.11475i	−0.306758	+	0.127063i	0.223994	+	0.974590i	$0.428090\pi$
$278$	18.0700	+	10.0838i	1.08377	+	0.604787i
$279$		−	7.51192i		−	0.449727i
$280$	0.218404	−	0.00957410i	0.0130521	−	0.000572162i
$281$	4.91247			0.293053			0.146527	−	0.989207i	$-0.453191\pi$
$281$	4.91247			0.293053			0.146527	+	0.989207i	$0.453191\pi$
$282$	−6.52406	+	11.6910i	−0.388502	+	0.696189i
$283$	18.3084	−	7.58361i	1.08832	−	0.450799i	0.234902	−	0.972019i	$-0.424523\pi$
$283$	18.3084	−	7.58361i	1.08832	−	0.450799i	0.853422	+	0.521220i	$0.174523\pi$
$284$	3.78748	−	15.9890i	0.224746	−	0.948770i
$285$	0.175010	+	0.0724915i	0.0103667	+	0.00429402i
$286$	−22.3862	−	6.41521i	−1.32373	−	0.379339i
$287$			33.0491i			1.95083i
$288$	−4.48031	+	6.81631i	−0.264005	+	0.401655i
$289$	−16.9281			−0.995770
$290$	−0.0151978	+	0.130091i	−0.000892444	+	0.00763922i
$291$	−23.4362	+	9.70761i	−1.37386	+	0.569070i
$292$	−19.8931	−	4.71230i	−1.16416	−	0.275766i
$293$	20.7746	+	8.60511i	1.21366	+	0.502716i	0.895390	−	0.445283i	$-0.146897\pi$
$293$	20.7746	+	8.60511i	1.21366	+	0.502716i	0.318274	+	0.947999i	$0.396897\pi$
$294$	−1.46927	−	5.17962i	−0.0856894	−	0.302081i
$295$	0.0815946	+	0.0815946i	0.00475062	+	0.00475062i
$296$	6.32241	−	0.277153i	0.367483	−	0.0161092i
$297$		−	14.9968i		−	0.870205i
$298$	−6.37499	−	22.4738i	−0.369293	−	1.30187i
$299$	−2.94912	+	0.690224i	−0.170552	+	0.0399167i
$300$	20.8036	−	3.35952i	1.20109	−	0.193962i
$301$	13.1733	−	5.45657i	0.759297	−	0.314511i
$302$	−0.188209	−	0.238001i	−0.0108302	−	0.0136954i
$303$			35.1904i			2.02164i
$304$	0.999707	−	13.7671i	0.0573371	−	0.789600i
$305$	−0.196991	−	0.196991i	−0.0112797	−	0.0112797i
$306$	0.0634551	−	0.543168i	0.00362749	−	0.0310509i
$307$	8.84131	−	3.66219i	0.504600	−	0.209012i	−0.115837	−	0.993268i	$-0.536955\pi$
$307$	8.84131	−	3.66219i	0.504600	−	0.209012i	0.620437	+	0.784256i	$0.286955\pi$
$308$	−21.9771	−	15.8659i	−1.25226	−	0.904043i
$309$	10.0892	−	4.17908i	0.573954	−	0.237739i
$310$	−0.167564	−	0.0935075i	−0.00951698	−	0.00531087i
$311$	−11.3087	−	11.3087i	−0.641257	−	0.641257i	0.309607	−	0.950864i	$-0.399802\pi$
$311$	−11.3087	−	11.3087i	−0.641257	−	0.641257i	−0.950864	+	0.309607i	$0.899802\pi$
$312$	10.5241	−	18.7405i	0.595811	−	1.06097i
$313$	−1.65788	+	1.65788i	−0.0937087	+	0.0937087i	−0.752407	−	0.658698i	$-0.771107\pi$
$313$	−1.65788	+	1.65788i	−0.0937087	+	0.0937087i	0.658698	+	0.752407i	$0.271107\pi$
$314$	25.4979	−	7.23282i	1.43893	−	0.408172i
$315$	0.0426504	+	0.102967i	0.00240308	+	0.00580154i
$316$	0.832708	−	3.51530i	0.0468435	−	0.197751i
$317$	−6.72640	−	16.2390i	−0.377792	−	0.912071i	−0.992379	−	0.123222i	$-0.960677\pi$
$317$	−6.72640	−	16.2390i	−0.377792	−	0.912071i	0.614587	−	0.788849i	$-0.289323\pi$
$318$	−1.02078	+	0.807223i	−0.0572424	+	0.0452668i
$319$	11.4831	−	11.4831i	0.642931	−	0.642931i
$320$	0.0962770	+	0.184788i	0.00538205	+	0.0103300i
$321$	−3.00930			−0.167963
$322$	−3.50163	−	0.409074i	−0.195138	−	0.0227968i
$323$	0.354142	+	0.854974i	0.0197050	+	0.0475720i
$324$	21.8876	+	5.18474i	1.21598	+	0.288041i
$325$	−17.5510	+	4.10772i	−0.973556	+	0.227855i
$326$	−8.35032	+	14.9636i	−0.462481	+	0.828758i
$327$	2.25910			0.124928
$328$	−28.5461	+	13.3174i	−1.57619	+	0.735328i
$329$	9.42544	−	9.42544i	0.519642	−	0.519642i
$330$	0.309599	+	0.172769i	0.0170429	+	0.00951062i
$331$	4.07077	−	9.82772i	0.223750	−	0.540180i	−0.771643	−	0.636055i	$-0.780565\pi$
$331$	4.07077	−	9.82772i	0.223750	−	0.540180i	0.995393	+	0.0958752i	$0.0305650\pi$
$332$	28.9188	−	4.67003i	1.58712	−	0.256301i
$333$	1.23465	+	2.98072i	0.0676586	+	0.163342i
$334$	24.6137	−	19.4644i	1.34680	−	1.06504i
$335$		−	0.390476i		−	0.0213340i
$336$	18.9248	−	16.3624i	1.03243	−	0.892644i
$337$	−6.73096			−0.366659			−0.183329	−	0.983052i	$-0.558687\pi$
$337$	−6.73096			−0.366659			−0.183329	+	0.983052i	$0.558687\pi$
$338$	−7.86211	+	16.6189i	−0.427642	+	0.903948i
$339$	−7.75863	+	18.7310i	−0.421391	+	1.01733i
$340$	−0.0113262	−	0.00817675i	−0.000614252	−	0.000443446i
$341$	9.10483	+	21.9810i	0.493054	+	1.19034i
$342$	6.76997	−	1.92039i	0.366078	−	0.103843i
$343$		−	15.4124i		−	0.832192i
$344$	10.0214	+	9.17967i	0.540317	+	0.494935i
$345$	0.0461128			0.00248263
$346$	2.35796	−	0.668866i	0.126765	−	0.0359585i
$347$	5.50962	+	13.3014i	0.295772	+	0.714056i	0.999992	+	0.00407413i	$0.00129684\pi$
$347$	5.50962	+	13.3014i	0.295772	+	0.714056i	−0.704220	+	0.709982i	$0.748703\pi$
$348$	7.87012	+	12.7561i	0.421883	+	0.683797i
$349$	29.0284	−	12.0240i	1.55386	−	0.643629i	0.569848	−	0.821750i	$-0.307002\pi$
$349$	29.0284	−	12.0240i	1.55386	−	0.643629i	0.984009	+	0.178121i	$0.0570020\pi$
$350$	−20.8392	−	2.43451i	−1.11390	−	0.130130i
$351$	−11.6831	−	1.91891i	−0.623599	−	0.102424i
$352$	4.84833	−	25.3759i	0.258417	−	1.35254i
$353$	5.36936	−	5.36936i	0.285782	−	0.285782i	−0.549627	−	0.835410i	$-0.685230\pi$
$353$	5.36936	−	5.36936i	0.285782	−	0.285782i	0.835410	+	0.549627i	$0.185230\pi$
$354$	13.1160	+	1.53226i	0.697105	+	0.0814386i
$355$	0.0818879	−	0.197695i	0.00434616	−	0.0104925i
$356$	0.145710	−	0.615121i	0.00772263	−	0.0326013i
$357$	−0.641854	+	1.54957i	−0.0339705	+	0.0820121i
$358$	4.14077	+	14.5975i	0.218847	+	0.771502i
$359$			12.2132i			0.644587i	0.946640	+	0.322293i	$0.104454\pi$
$359$			12.2132i			0.644587i	−0.946640	+	0.322293i	$0.895546\pi$
$360$	−0.0717515	+	0.0783306i	−0.00378163	+	0.00412838i
$361$	5.01455	−	5.01455i	0.263924	−	0.263924i
$362$	13.9342	+	7.77584i	0.732364	+	0.408689i
$363$	−7.95058	−	19.1944i	−0.417297	−	1.00744i
$364$	−15.1722	+	15.0909i	−0.795240	+	0.790976i
$365$	−0.245968	−	0.101883i	−0.0128745	−	0.00533281i
$366$	−31.6654	−	3.69927i	−1.65518	−	0.193364i
$367$	−30.7403			−1.60463			−0.802316	−	0.596900i	$-0.796399\pi$
$367$	−30.7403			−1.60463			−0.802316	+	0.596900i	$0.796399\pi$
$368$	−1.05767	−	3.18936i	−0.0551347	−	0.166257i
$369$	−11.3553	−	11.3553i	−0.591132	−	0.591132i
$370$	0.0818579	+	0.00956297i	0.00425559	+	0.000497155i
$371$	1.19706	−	0.495839i	0.0621483	−	0.0257427i
$372$	−21.6784	+	3.50079i	−1.12397	+	0.181507i
$373$	−13.5003	−	32.5925i	−0.699017	−	1.68758i	−0.725773	−	0.687935i	$-0.758518\pi$
$373$	−13.5003	−	32.5925i	−0.699017	−	1.68758i	0.0267554	−	0.999642i	$-0.491482\pi$
$374$	0.472669	+	1.66630i	0.0244411	+	0.0861625i
$375$	0.548899			0.0283450
$376$	11.9393	+	4.34316i	0.615720	+	0.223982i
$377$	−7.47647	−	10.4151i	−0.385058	−	0.536405i
$378$	−12.0340	−	6.71549i	−0.618964	−	0.345407i
$379$	−29.3794	−	12.1693i	−1.50912	−	0.625097i	−0.533743	−	0.845647i	$-0.679215\pi$
$379$	−29.3794	−	12.1693i	−1.50912	−	0.625097i	−0.975376	+	0.220549i	$0.929215\pi$
$380$	0.0414348	−	0.174918i	0.00212556	−	0.00897312i
$381$	−22.2689	−	9.22408i	−1.14087	−	0.472564i
$382$	20.5811	−	16.2754i	1.05302	−	0.832721i
$383$	−11.6463	−	11.6463i	−0.595097	−	0.595097i	0.343907	−	0.939004i	$-0.388249\pi$
$383$	−11.6463	−	11.6463i	−0.595097	−	0.595097i	−0.939004	+	0.343907i	$0.888249\pi$
$384$	21.7589	+	9.75294i	1.11038	+	0.497702i
$385$	−0.249603	−	0.249603i	−0.0127209	−	0.0127209i
$386$	−3.31576	+	28.3826i	−0.168768	+	1.44463i
$387$	−2.65138	+	6.40101i	−0.134777	+	0.325381i
$388$	12.6397	+	20.4868i	0.641685	+	1.04006i
$389$	−6.53556	−	15.7782i	−0.331366	−	0.799989i	−0.998484	−	0.0550369i	$-0.982472\pi$
$389$	−6.53556	−	15.7782i	−0.331366	−	0.799989i	0.667118	−	0.744952i	$-0.267528\pi$
$390$	0.174208	−	0.219083i	0.00882138	−	0.0110937i
$391$	0.159293	+	0.159293i	0.00805581	+	0.00805581i
$392$	−4.63006	+	2.16002i	−0.233853	+	0.109097i
$393$	13.9307	+	13.9307i	0.702713	+	0.702713i
$394$	−27.5969	+	7.82823i	−1.39031	+	0.394380i
$395$	0.0180037	−	0.0434648i	0.000905866	−	0.00218695i
$396$	13.0024	−	2.09973i	0.653395	−	0.105515i
$397$	−4.08975	−	9.87354i	−0.205259	−	0.495539i	0.787406	−	0.616434i	$-0.211423\pi$
$397$	−4.08975	−	9.87354i	−0.205259	−	0.495539i	−0.992665	+	0.120896i	$0.961423\pi$
$398$	6.82912	+	0.797805i	0.342313	+	0.0399904i
$399$	−21.5829			−1.08050
$400$	−6.29448	−	18.9808i	−0.314724	−	0.949040i
$401$	17.9244	−	17.9244i	0.895104	−	0.895104i	−0.0998942	−	0.994998i	$-0.531850\pi$
$401$	17.9244	−	17.9244i	0.895104	−	0.895104i	0.994998	+	0.0998942i	$0.0318504\pi$
$402$	−27.7173	−	35.0500i	−1.38241	−	1.74814i
$403$	18.2891	−	4.28045i	0.911043	−	0.213224i
$404$	32.9668	−	5.32374i	1.64016	−	0.264866i
$405$	0.270628	+	0.112098i	0.0134476	+	0.00557018i
$406$	−4.07242	−	14.3565i	−0.202111	−	0.712503i
$407$	−7.22557	−	7.22557i	−0.358158	−	0.358158i
$408$	−1.59708	+	0.0700107i	−0.0790673	+	0.00346605i
$409$		−	7.38002i		−	0.364919i	−0.983213	−	0.182459i	$-0.941594\pi$
$409$		−	7.38002i		−	0.364919i	0.983213	−	0.182459i	$-0.0584058\pi$
$410$	−0.394644	+	0.111946i	−0.0194901	+	0.00552862i
$411$	−12.9363	+	31.2310i	−0.638100	+	1.54051i
$412$	−5.44134	−	8.81945i	−0.268076	−	0.434503i
$413$	−12.1466	−	5.03129i	−0.597695	−	0.247574i
$414$	1.34367	−	1.06256i	0.0660378	−	0.0522222i
$415$	0.381483			0.0187262
$416$	−19.1485	−	7.02400i	−0.938830	−	0.344380i
$417$	30.8390			1.51019
$418$	−17.4823	+	13.8249i	−0.855089	+	0.676198i
$419$	12.6984	+	5.25983i	0.620356	+	0.256960i	0.670649	−	0.741775i	$-0.266016\pi$
$419$	12.6984	+	5.25983i	0.620356	+	0.256960i	−0.0502934	+	0.998734i	$0.516016\pi$
$420$	0.277273	−	0.171069i	0.0135295	−	0.00834732i
$421$	−3.06061	+	7.38897i	−0.149165	+	0.360116i	−0.980746	−	0.195287i	$-0.937436\pi$
$421$	−3.06061	+	7.38897i	−0.149165	+	0.360116i	0.831581	+	0.555403i	$0.187436\pi$
$422$	−10.8092	+	3.06618i	−0.526185	+	0.149259i
$423$			6.47694i			0.314920i
$424$	0.910644	+	0.834158i	0.0442248	+	0.0405103i
$425$	0.947999	+	0.947999i	0.0459847	+	0.0459847i
$426$	−6.68259	−	23.5582i	−0.323773	−	1.14140i
$427$	29.3251	+	12.1468i	1.41914	+	0.587827i
$428$	0.455258	+	2.81915i	0.0220057	+	0.136269i
$429$	−33.7918	+	7.90877i	−1.63148	+	0.381839i
$430$	0.109779	+	0.138822i	0.00529402	+	0.00669458i
$431$	−9.74838	+	9.74838i	−0.469563	+	0.469563i	−0.901773	−	0.432210i	$-0.857734\pi$
$431$	−9.74838	+	9.74838i	−0.469563	+	0.469563i	0.432210	+	0.901773i	$0.357734\pi$
$432$	0.951294	−	13.1004i	0.0457691	−	0.630295i
$433$	−4.81238			−0.231268			−0.115634	−	0.993292i	$-0.536890\pi$
$433$	−4.81238			−0.231268			−0.115634	+	0.993292i	$0.536890\pi$
$434$	21.7155	+	2.53689i	1.04238	+	0.121774i
$435$	0.0746970	+	0.180335i	0.00358145	+	0.00864638i
$436$	−0.341764	−	2.11635i	−0.0163675	−	0.101355i
$437$	−1.10934	+	2.67819i	−0.0530671	+	0.128115i
$438$	−29.3106	+	8.31434i	−1.40051	+	0.397274i
$439$	20.4045	+	20.4045i	0.973852	+	0.973852i	0.999667	−	0.0258147i	$-0.00821800\pi$
$439$	20.4045	+	20.4045i	0.973852	+	0.973852i	−0.0258147	+	0.999667i	$0.508218\pi$
$440$	0.115015	−	0.316174i	0.00548312	−	0.0150730i
$441$	−1.84178	−	1.84178i	−0.0877037	−	0.0877037i
$442$	1.35859	−	0.155016i	0.0646217	−	0.00737337i
$443$	−2.21608	−	5.35010i	−0.105289	−	0.254191i	0.862451	−	0.506141i	$-0.168928\pi$
$443$	−2.21608	−	5.35010i	−0.105289	−	0.254191i	−0.967740	+	0.251950i	$0.918928\pi$
$444$	8.02656	−	4.95215i	0.380924	−	0.235019i
$445$	0.00315036	−	0.00760563i	0.000149341	−	0.000360542i
$446$	2.40520	−	20.5882i	0.113889	−	0.974880i
$447$	−24.6172	−	24.6172i	−1.16435	−	1.16435i
$448$	−18.1915	−	15.2536i	−0.859470	−	0.720667i
$449$	−24.3563	−	24.3563i	−1.14944	−	1.14944i	−0.986662	−	0.162783i	$-0.947953\pi$
$449$	−24.3563	−	24.3563i	−1.14944	−	1.14944i	−0.162783	−	0.986662i	$-0.552047\pi$
$450$	7.99656	−	6.32362i	0.376962	−	0.298098i
$451$	46.9904	+	19.4641i	2.21269	+	0.916527i
$452$	18.7212	+	4.43469i	0.880570	+	0.208590i
$453$	−0.417772	−	0.173047i	−0.0196286	−	0.00813045i
$454$	26.4713	+	14.7721i	1.24236	+	0.693288i
$455$	−0.226388	+	0.162513i	−0.0106132	+	0.00761871i
$456$	−8.69700	−	18.6422i	−0.407274	−	0.873003i
$457$	16.9751			0.794063			0.397031	−	0.917805i	$-0.370040\pi$
$457$	16.9751			0.794063			0.397031	+	0.917805i	$0.370040\pi$
$458$	−5.85525	−	20.6416i	−0.273598	−	0.964517i
$459$	0.336992	+	0.813570i	0.0157294	+	0.0379742i
$460$	−0.00697612	−	0.0431991i	−0.000325263	−	0.00201417i
$461$	−27.4151	+	11.3557i	−1.27685	+	0.528888i	−0.915040	−	0.403364i	$-0.867841\pi$
$461$	−27.4151	+	11.3557i	−1.27685	+	0.528888i	−0.361809	+	0.932252i	$0.617841\pi$
$462$	−40.1226	−	4.68728i	−1.86667	−	0.218072i
$463$	12.0839	+	12.0839i	0.561585	+	0.561585i	0.929758	−	0.368172i	$-0.120016\pi$
$463$	12.0839	+	12.0839i	0.561585	+	0.561585i	−0.368172	+	0.929758i	$0.620016\pi$
$464$	10.7594	−	9.30261i	0.499494	−	0.431863i
$465$	−0.285971			−0.0132616
$466$	19.6228	+	2.29241i	0.909009	+	0.106194i
$467$	8.83362	+	3.65900i	0.408771	+	0.169319i	0.577587	−	0.816329i	$-0.303994\pi$
$467$	8.83362	+	3.65900i	0.408771	+	0.169319i	−0.168816	+	0.985648i	$0.553994\pi$
$468$	0.0279463	−	10.3980i	0.00129182	−	0.480649i
$469$	17.0254	+	41.1030i	0.786161	+	1.89796i
$470$	0.144477	+	0.0806242i	0.00666423	+	0.00371892i
$471$	27.9298	−	27.9298i	1.28694	−	1.28694i
$472$	−0.548791	−	12.5190i	−0.0252602	−	0.576234i
$473$		−	21.9439i		−	1.00898i
$474$	−1.46922	−	5.17946i	−0.0674836	−	0.237901i
$475$	−6.60202	+	15.9387i	−0.302921	+	0.731317i
$476$	1.54876	+	0.366872i	0.0709874	+	0.0168156i
$477$	−0.240932	+	0.581660i	−0.0110315	+	0.0266324i
$478$	22.7689	+	2.65995i	1.04142	+	0.121663i
$479$	−22.4193	+	22.4193i	−1.02437	+	1.02437i	−0.0246703	+	0.999696i	$0.507854\pi$
$479$	−22.4193	+	22.4193i	−1.02437	+	1.02437i	−0.999696	+	0.0246703i	$0.992146\pi$
$480$	0.259490	+	0.170560i	0.0118440	+	0.00778498i
$481$	−6.55354	+	4.70445i	−0.298816	+	0.214505i
$482$	6.65242	+	0.777162i	0.303010	+	0.0353988i
$483$	−4.85401	+	2.01060i	−0.220865	+	0.0914853i
$484$	−16.7788	+	10.3520i	−0.762671	+	0.470546i
$485$	0.119966	+	0.289625i	0.00544740	+	0.0131512i
$486$	18.8463	−	5.34601i	0.854886	−	0.242500i
$487$	−25.6151			−1.16073			−0.580365	−	0.814357i	$-0.697090\pi$
$487$	−25.6151			−1.16073			−0.580365	+	0.814357i	$0.697090\pi$
$488$	1.32493	+	30.2242i	0.0599766	+	1.36818i
$489$			25.5375i			1.15484i
$490$	−0.0640096	+	0.0181572i	−0.00289166	+	0.000820257i
$491$	−4.59810	−	11.1008i	−0.207509	−	0.500972i	0.785520	−	0.618836i	$-0.212395\pi$
$491$	−4.59810	−	11.1008i	−0.207509	−	0.500972i	−0.993030	+	0.117864i	$0.962395\pi$
$492$	−27.4778	+	38.0617i	−1.23880	+	1.71595i
$493$	−0.364917	+	0.880987i	−0.0164350	+	0.0396776i
$494$	8.53319	+	15.3884i	0.383926	+	0.692355i
$495$	0.171521			0.00770931
$496$	6.55917	+	19.7790i	0.294515	+	0.888101i
$497$			24.3805i			1.09362i
$498$	34.2427	−	27.0789i	1.53445	−	1.21343i
$499$	10.5089	+	25.3708i	0.470444	+	1.13575i	0.963968	+	0.266019i	$0.0857084\pi$
$499$	10.5089	+	25.3708i	0.470444	+	1.13575i	−0.493524	+	0.869732i	$0.664292\pi$
$500$	−0.0830394	−	0.514215i	−0.00371363	−	0.0229964i
$501$	17.8963	−	43.2055i	0.799547	−	1.93028i
$502$	23.5022	+	13.1152i	1.04895	+	0.585359i
$503$	21.8546	−	21.8546i	0.974450	−	0.974450i	−0.0252319	−	0.999682i	$-0.508032\pi$
$503$	21.8546	−	21.8546i	0.974450	−	0.974450i	0.999682	+	0.0252319i	$0.00803242\pi$
$504$	4.13748	−	11.3738i	0.184298	−	0.506631i
$505$	0.434883			0.0193520
$506$	−2.64390	+	4.73782i	−0.117536	+	0.210622i
$507$	1.83743	+	27.3370i	0.0816030	+	1.21408i
$508$	−5.27232	+	22.2572i	−0.233921	+	0.987506i
$509$	16.2627	+	39.2615i	0.720829	+	1.74024i	0.670976	+	0.741479i	$0.265875\pi$
$509$	16.2627	+	39.2615i	0.720829	+	1.74024i	0.0498536	+	0.998757i	$0.484125\pi$
$510$	−0.0206778	−	0.00241567i	−0.000915629	−	0.000106967i
$511$	30.3337			1.34189
$512$	5.84491	−	21.8595i	0.258311	−	0.966062i
$513$	−8.01269	+	8.01269i	−0.353769	+	0.353769i
$514$	31.4257	−	24.8512i	1.38613	−	1.09614i
$515$	−0.0516450	−	0.124682i	−0.00227575	−	0.00549415i
$516$	19.7081	+	4.66846i	0.867599	+	0.205518i
$517$	−7.85039	−	18.9525i	−0.345260	−	0.833530i
$518$	−9.03363	+	2.56251i	−0.396915	+	0.112590i
$519$	2.58285	−	2.58285i	0.113374	−	0.113374i
$520$	−0.231595	−	0.130057i	−0.0101561	−	0.00570337i
$521$	2.55737	+	2.55737i	0.112040	+	0.112040i	0.760904	−	0.648864i	$-0.224756\pi$
$521$	2.55737	+	2.55737i	0.112040	+	0.112040i	−0.648864	+	0.760904i	$0.724756\pi$
$522$	6.33197	+	3.53350i	0.277143	+	0.154657i
$523$	21.3029	−	8.82393i	0.931509	−	0.385844i	0.135258	−	0.990810i	$-0.456814\pi$
$523$	21.3029	−	8.82393i	0.931509	−	0.385844i	0.796251	+	0.604967i	$0.206814\pi$
$524$	10.9430	−	15.1580i	0.478047	−	0.662180i
$525$	−28.8876	+	11.9656i	−1.26076	+	0.522223i
$526$	2.48708	−	21.2891i	0.108442	−	0.928248i
$527$	−0.987863	−	0.987863i	−0.0430320	−	0.0430320i
$528$	−12.1190	−	36.5446i	−0.527413	−	1.59040i
$529$		−	22.2943i		−	0.969319i
$530$	0.00997565	+	0.0126148i	0.000433315	+	0.000547950i
$531$	5.90212	−	2.44474i	0.256130	−	0.106093i
$532$	3.26515	+	20.2192i	0.141562	+	0.876612i
$533$	21.1759	−	34.1168i	0.917229	−	1.47776i
$534$	−0.257090	−	0.906321i	−0.0111254	−	0.0392204i
$535$			0.0371889i			0.00160782i
$536$	−28.6421	+	31.2684i	−1.23715	+	1.35059i
$537$	15.9897	+	15.9897i	0.690008	+	0.690008i
$538$	4.88658	+	17.2267i	0.210675	+	0.742696i
$539$	7.62165	+	3.15699i	0.328288	+	0.135981i
$540$	0.0394282	−	0.166447i	0.00169672	−	0.00716276i
$541$	−9.37221	+	3.88210i	−0.402943	+	0.166904i	−0.574945	−	0.818192i	$-0.694976\pi$
$541$	−9.37221	+	3.88210i	−0.402943	+	0.166904i	0.172002	+	0.985097i	$0.444976\pi$
$542$	2.35898	−	20.1926i	0.101327	−	0.867347i
$543$	23.7806			1.02052
$544$	0.307199	+	1.48557i	0.0131711	+	0.0636935i
$545$		−	0.0279179i		−	0.00119587i
$546$	−8.78543	+	30.6573i	−0.375982	+	1.31201i
$547$	0.663968	+	0.275024i	0.0283892	+	0.0117592i	0.396833	−	0.917891i	$-0.370109\pi$
$547$	0.663968	+	0.275024i	0.0283892	+	0.0117592i	−0.368444	+	0.929650i	$0.620109\pi$
$548$	31.2146	+	7.39415i	1.33342	+	0.315862i
$549$	−14.2493	+	5.90224i	−0.608144	+	0.251901i
$550$	−15.7346	+	28.1961i	−0.670925	+	1.20229i
$551$	−12.2707			−0.522748
$552$	−3.69261	−	3.38246i	−0.157168	−	0.143967i
$553$			5.36026i			0.227941i
$554$	6.82442	+	3.80831i	0.289942	+	0.161799i
$555$	0.113473	−	0.0470019i	0.00481665	−	0.00199512i
$556$	−4.66543	−	28.8903i	−0.197858	−	1.22522i
$557$	2.47229	+	5.96863i	0.104754	+	0.252899i	0.967562	−	0.252633i	$-0.0812964\pi$
$557$	2.47229	+	5.96863i	0.104754	+	0.252899i	−0.862808	+	0.505532i	$0.831296\pi$
$558$	−8.33282	+	6.58953i	−0.352756	+	0.278957i
$559$	−17.0952	−	2.80782i	−0.723048	−	0.118758i
$560$	−0.202207	−	0.233873i	−0.00854479	−	0.00988292i
$561$	1.82522	+	1.82522i	0.0770610	+	0.0770610i
$562$	−4.30927	−	5.44930i	−0.181775	−	0.229865i
$563$	−17.8075	−	7.37612i	−0.750497	−	0.310866i	−0.0255529	−	0.999673i	$-0.508135\pi$
$563$	−17.8075	−	7.37612i	−0.750497	−	0.310866i	−0.724945	+	0.688807i	$0.758135\pi$
$564$	18.6916	−	3.01846i	0.787057	−	0.127100i
$565$	0.231477	+	0.0958810i	0.00973832	+	0.00403374i
$566$	−24.4727	−	13.6568i	−1.02866	−	0.574037i
$567$	−33.3749			−1.40162
$568$	−21.0586	+	9.82431i	−0.883601	+	0.412219i
$569$	−3.04769	−	3.04769i	−0.127766	−	0.127766i	0.640332	−	0.768098i	$-0.278797\pi$
$569$	−3.04769	−	3.04769i	−0.127766	−	0.127766i	−0.768098	+	0.640332i	$0.778797\pi$
$570$	−0.0731071	−	0.257725i	−0.00306212	−	0.0107949i
$571$	29.9921	−	12.4231i	1.25513	−	0.519893i	0.346720	−	0.937969i	$-0.387296\pi$
$571$	29.9921	−	12.4231i	1.25513	−	0.519893i	0.908412	+	0.418076i	$0.137296\pi$
$572$	12.5212	+	30.4601i	0.523537	+	1.27360i
$573$	14.9642	−	36.1268i	0.625139	−	1.50922i
$574$	36.6607	−	28.9910i	1.53019	−	1.21006i
$575$			4.19963i			0.175137i
$576$	11.4914	−	1.00943i	0.478807	−	0.0420594i
$577$	−11.2926	+	11.2926i	−0.470118	+	0.470118i	−0.901953	−	0.431834i	$-0.857866\pi$
$577$	−11.2926	+	11.2926i	−0.470118	+	0.470118i	0.431834	+	0.901953i	$0.357866\pi$
$578$	14.8495	+	18.7780i	0.617657	+	0.781061i
$579$	16.2970	+	39.3444i	0.677279	+	1.63510i
$580$	0.157639	−	0.0972588i	0.00654561	−	0.00403845i
$581$	−40.1563	+	16.6333i	−1.66596	+	0.690065i
$582$	31.3270	+	17.4817i	1.29854	+	0.724641i
$583$		−	1.99405i		−	0.0825850i
$584$	12.2232	+	26.2007i	0.505799	+	1.08419i
$585$	0.0219469	−	0.133622i	0.000907393	−	0.00552458i
$586$	−8.67819	−	30.5933i	−0.358493	−	1.26380i
$587$	−16.2027	+	39.1168i	−0.668758	+	1.61452i	0.114934	+	0.993373i	$0.463334\pi$
$587$	−16.2027	+	39.1168i	−0.668758	+	1.61452i	−0.783691	+	0.621151i	$0.786666\pi$
$588$	−4.45679	+	6.17344i	−0.183795	+	0.254588i
$589$	6.87963	−	16.6089i	0.283470	−	0.684358i
$590$	0.0189356	−	0.162087i	0.000779567	−	0.00667301i
$591$	−30.2289	+	30.2289i	−1.24345	+	1.24345i
$592$	−5.85352	−	6.77020i	−0.240578	−	0.278254i
$593$	2.04495	−	2.04495i	0.0839759	−	0.0839759i	−0.663871	−	0.747847i	$-0.731088\pi$
$593$	2.04495	−	2.04495i	0.0839759	−	0.0839759i	0.747847	+	0.663871i	$0.231088\pi$
$594$	−16.6357	+	13.1554i	−0.682571	+	0.539772i
$595$	0.0191496	+	0.00793202i	0.000785057	+	0.000325181i
$596$	−19.3375	+	26.7859i	−0.792096	+	1.09719i
$597$	9.46664	−	3.92121i	0.387444	−	0.160484i
$598$	3.35265	+	2.66592i	0.137100	+	0.109018i
$599$	−14.5412	+	14.5412i	−0.594136	+	0.594136i	−0.938746	−	0.344610i	$-0.888011\pi$
$599$	−14.5412	+	14.5412i	−0.594136	+	0.594136i	0.344610	+	0.938746i	$0.388011\pi$
$600$	−21.9757	−	20.1300i	−0.897156	−	0.821803i
$601$	−3.65663	+	3.65663i	−0.149157	+	0.149157i	−0.777741	−	0.628584i	$-0.783635\pi$
$601$	−3.65663	+	3.65663i	−0.149157	+	0.149157i	0.628584	+	0.777741i	$0.283635\pi$
$602$	−17.6086	−	9.82634i	−0.717674	−	0.400492i
$603$	−19.9722	−	8.27277i	−0.813332	−	0.336893i
$604$	−0.0989104	+	0.417553i	−0.00402461	+	0.0169900i
$605$	−0.237204	+	0.0982531i	−0.00964372	+	0.00399456i
$606$	39.0360	−	30.8694i	1.58573	−	1.25398i
$607$			26.1390i			1.06095i	0.847701	+	0.530475i	$0.177986\pi$
$607$			26.1390i			1.06095i	−0.847701	+	0.530475i	$0.822014\pi$
$608$	−16.1486	+	10.9677i	−0.654911	+	0.444800i
$609$	−15.7258	−	15.7258i	−0.637240	−	0.637240i
$610$	−0.0457156	+	0.391320i	−0.00185097	+	0.0158441i
$611$	−15.7692	+	3.69070i	−0.637955	+	0.149310i
$612$	−0.658189	+	0.406083i	−0.0266057	+	0.0164149i
$613$	15.4920	−	37.4009i	0.625715	−	1.51061i	−0.219185	−	0.975683i	$-0.570340\pi$
$613$	15.4920	−	37.4009i	0.625715	−	1.51061i	0.844899	−	0.534925i	$-0.179660\pi$
$614$	−11.8181	−	6.59498i	−0.476939	−	0.266152i
$615$	−0.432283	+	0.432283i	−0.0174313	+	0.0174313i
$616$	1.67879	+	38.2964i	0.0676403	+	1.54301i
$617$	−6.84111			−0.275413			−0.137706	−	0.990473i	$-0.543973\pi$
$617$	−6.84111			−0.275413			−0.137706	+	0.990473i	$0.543973\pi$
$618$	−13.4861	−	7.52580i	−0.542491	−	0.302732i
$619$	−23.9314	−	9.91270i	−0.961883	−	0.398425i	−0.154199	−	0.988040i	$-0.549280\pi$
$619$	−23.9314	−	9.91270i	−0.961883	−	0.398425i	−0.807685	+	0.589615i	$0.799280\pi$
$620$	0.0432627	+	0.267901i	0.00173747	+	0.0107592i
$621$	−1.05562	+	2.54849i	−0.0423606	+	0.102267i
$622$	−2.62440	+	22.4646i	−0.105229	+	0.900749i
$623$			0.937958i			0.0375785i
$624$	−30.0203	+	4.76516i	−1.20177	+	0.190759i
$625$			24.9898i			0.999593i
$626$	3.29335	+	0.384743i	0.131629	+	0.0153774i
$627$	−12.7111	+	30.6874i	−0.507634	+	1.22554i
$628$	−30.3903	−	21.9396i	−1.21270	−	0.875487i
$629$	0.554347	+	0.229618i	0.0221033	+	0.00915547i
$630$	0.0768061	−	0.137635i	0.00306003	−	0.00548351i
$631$	−23.9231			−0.952362			−0.476181	−	0.879347i	$-0.657979\pi$
$631$	−23.9231			−0.952362			−0.476181	+	0.879347i	$0.657979\pi$
$632$	−4.62992	+	2.15995i	−0.184168	+	0.0859184i
$633$	−11.8401	+	11.8401i	−0.470604	+	0.470604i
$634$	−12.1131	+	21.7065i	−0.481072	+	0.862073i
$635$	−0.113991	+	0.275199i	−0.00452360	+	0.0109209i
$636$	1.79087	+	0.424224i	0.0710128	+	0.0168216i
$637$	3.43464	−	5.53361i	0.136085	−	0.219249i
$638$	−22.8111	−	2.66488i	−0.903099	−	0.105504i
$639$	−8.37686	−	8.37686i	−0.331384	−	0.331384i
$640$	0.120527	−	0.268896i	0.00476423	−	0.0106291i
$641$			20.1156i			0.794520i	0.917706	+	0.397260i	$0.130039\pi$
$641$			20.1156i			0.794520i	−0.917706	+	0.397260i	$0.869961\pi$
$642$	2.63979	+	3.33816i	0.104184	+	0.131747i
$643$	36.6469	−	15.1797i	1.44521	−	0.598627i	0.484158	−	0.874981i	$-0.339126\pi$
$643$	36.6469	−	15.1797i	1.44521	−	0.598627i	0.961056	+	0.276353i	$0.0891260\pi$
$644$	2.61789	+	4.24313i	0.103159	+	0.167203i
$645$	0.243679	+	0.100935i	0.00959487	+	0.00397432i
$646$	0.637749	−	1.14283i	0.0250919	−	0.0449642i
$647$	34.1698	−	34.1698i	1.34335	−	1.34335i	0.450652	−	0.892699i	$-0.351191\pi$
$647$	34.1698	−	34.1698i	1.34335	−	1.34335i	0.892699	−	0.450652i	$-0.148809\pi$
$648$	−13.4487	−	28.8275i	−0.528313	−	1.13245i
$649$	−14.3073	+	14.3073i	−0.561612	+	0.561612i
$650$	19.9525	+	15.8657i	0.782603	+	0.622303i
$651$	30.1023	−	12.4688i	1.17980	−	0.488690i
$652$	23.9238	−	3.86340i	0.936929	−	0.151303i
$653$	−2.00059	−	0.828670i	−0.0782890	−	0.0324284i	0.343195	−	0.939264i	$-0.388491\pi$
$653$	−2.00059	−	0.828670i	−0.0782890	−	0.0324284i	−0.421484	+	0.906836i	$0.638491\pi$
$654$	−1.98170	−	2.50597i	−0.0774907	−	0.0979912i
$655$	0.172156	−	0.172156i	0.00672669	−	0.00672669i
$656$	39.8136	+	19.9835i	1.55446	+	0.780224i
$657$	−10.4223	+	10.4223i	−0.406613	+	0.406613i
$658$	−18.7236	−	2.18736i	−0.729920	−	0.0852722i
$659$	0.844373	−	2.03850i	0.0328921	−	0.0794085i	−0.906580	−	0.422034i	$-0.861316\pi$
$659$	0.844373	−	2.03850i	0.0328921	−	0.0794085i	0.939472	+	0.342626i	$0.111316\pi$
$660$	−0.0799343	−	0.494987i	−0.00311144	−	0.0192673i
$661$	−16.8604	+	40.7045i	−0.655792	+	1.58322i	0.148449	+	0.988920i	$0.452572\pi$
$661$	−16.8604	+	40.7045i	−0.655792	+	1.58322i	−0.804242	+	0.594303i	$0.797428\pi$
$662$	−14.4726	+	4.10535i	−0.562494	+	0.159559i
$663$	1.65547	−	1.18837i	0.0642930	−	0.0461526i
$664$	−30.5482	−	27.9824i	−1.18550	−	1.08593i
$665$			0.266722i			0.0103430i
$666$	2.22340	−	3.98429i	0.0861550	−	0.154388i
$667$	−2.75967	+	1.14309i	−0.106855	+	0.0442608i
$668$	−43.1828	−	10.2292i	−1.67079	−	0.395779i
$669$	−11.8215	−	28.5397i	−0.457047	−	1.10341i
$670$	−0.433148	+	0.342530i	−0.0167339	+	0.0132331i
$671$	34.5417	−	34.5417i	1.33347	−	1.33347i
$672$	−34.7516	−	6.63964i	−1.34057	−	0.256130i
$673$			26.9636i			1.03937i	0.854357	+	0.519686i	$0.173951\pi$
$673$			26.9636i			1.03937i	−0.854357	+	0.519686i	$0.826049\pi$
$674$	5.90446	+	7.46651i	0.227431	+	0.287599i
$675$	−6.28230	+	15.1668i	−0.241806	+	0.583770i
$676$	25.3317	−	5.85697i	0.974297	−	0.225268i
$677$	13.7619	−	5.70038i	0.528914	−	0.219083i	−0.102214	−	0.994762i	$-0.532593\pi$
$677$	13.7619	−	5.70038i	0.528914	−	0.219083i	0.631127	+	0.775679i	$0.282593\pi$
$678$	27.5839	−	7.82452i	1.05935	−	0.300499i
$679$	−25.2562	−	25.2562i	−0.969245	−	0.969245i
$680$	0.000865191		0.0197367i	3.31786e−5		0.000756868i
$681$	45.1769			1.73118
$682$	16.3962	−	29.3818i	0.627844	−	1.12509i
$683$	33.6598	+	13.9423i	1.28795	+	0.533488i	0.918375	−	0.395711i	$-0.129502\pi$
$683$	33.6598	+	13.9423i	1.28795	+	0.533488i	0.369579	+	0.929199i	$0.379502\pi$
$684$	−8.06893	−	5.82520i	−0.308523	−	0.222732i
$685$	0.385952	+	0.159867i	0.0147465	+	0.00610819i
$686$	−17.0967	+	13.5199i	−0.652755	+	0.516193i
$687$	−22.6102	−	22.6102i	−0.862634	−	0.862634i
$688$	1.39197	−	19.1690i	0.0530682	−	0.730812i
$689$	−1.55344	−	0.255147i	−0.0591813	−	0.00972033i
$690$	−0.0404507	−	0.0511521i	−0.00153993	−	0.00194733i
$691$	−17.6631	−	42.6425i	−0.671936	−	1.62220i	−0.778316	−	0.627873i	$-0.783926\pi$
$691$	−17.6631	−	42.6425i	−0.671936	−	1.62220i	0.106380	−	0.994326i	$-0.466074\pi$
$692$	−2.81039	−	2.02890i	−0.106835	−	0.0771273i
$693$	−18.0550	+	7.47861i	−0.685851	+	0.284089i
$694$	9.92187	−	17.7798i	0.376629	−	0.674913i
$695$		−	0.381107i		−	0.0144562i
$696$	7.24630	−	19.9199i	0.274670	−	0.755062i
$697$	−2.98657			−0.113125
$698$	−38.8020	−	21.6531i	−1.46868	−	0.819582i
$699$	27.2014	−	11.2672i	1.02885	−	0.426165i
$700$	15.5798	+	25.2521i	0.588860	+	0.954438i
$701$	15.8848	+	6.57970i	0.599960	+	0.248512i	0.661929	−	0.749566i	$-0.269738\pi$
$701$	15.8848	+	6.57970i	0.599960	+	0.248512i	−0.0619688	+	0.998078i	$0.519738\pi$
$702$	8.11994	+	14.6431i	0.306468	+	0.552670i
$703$			7.72112i			0.291208i
$704$	−32.4020	+	16.8819i	−1.22120	+	0.636259i
$705$	0.246570			0.00928637
$706$	−10.6662	−	1.24607i	−0.401427	−	0.0468963i
$707$	−45.7774	+	18.9616i	−1.72164	+	0.713125i
$708$	−9.80575	−	15.8934i	−0.368523	−	0.597310i
$709$	29.1944	+	12.0927i	1.09642	+	0.454151i	0.856240	−	0.516578i	$-0.172794\pi$
$709$	29.1944	+	12.0927i	1.09642	+	0.454151i	0.240178	+	0.970729i	$0.422794\pi$
$710$	−0.291132	+	0.0825833i	−0.0109260	+	0.00309930i
$711$	−1.84172	−	1.84172i	−0.0690700	−	0.0690700i
$712$	−0.810160	+	0.377957i	−0.0303620	+	0.0141645i
$713$		−	4.37623i		−	0.163891i
$714$	2.28195	−	0.647306i	0.0853999	−	0.0242248i
$715$	0.0977364	+	0.417598i	0.00365513	+	0.0156173i
$716$	12.5604	−	17.3984i	0.469404	−	0.650207i
$717$	31.5626	−	13.0736i	1.17873	−	0.488244i
$718$	13.5478	−	10.7135i	0.505601	−	0.399825i
$719$		−	4.47179i		−	0.166770i	−0.996517	−	0.0833849i	$-0.973427\pi$
$719$		−	4.47179i		−	0.166770i	0.996517	−	0.0833849i	$-0.0265731\pi$
$720$	0.149832	+	0.0108801i	0.00558390	+	0.000405477i
$721$	10.8727	+	10.8727i	0.404920	+	0.404920i
$722$	−9.96136	−	1.16373i	−0.370724	−	0.0433094i
$723$	9.22169	−	3.81975i	0.342958	−	0.142058i
$724$	−3.59761	−	22.2779i	−0.133704	−	0.827953i
$725$	−16.4236	+	6.80288i	−0.609957	+	0.252653i
$726$	−14.3176	+	25.6569i	−0.531377	+	0.952218i
$727$	23.0378	+	23.0378i	0.854423	+	0.854423i	0.990674	−	0.136251i	$-0.0435053\pi$
$727$	23.0378	+	23.0378i	0.854423	+	0.854423i	−0.136251	+	0.990674i	$0.543505\pi$
$728$	30.0492	+	3.59236i	1.11370	+	0.133142i
$729$	−3.21395	+	3.21395i	−0.119035	+	0.119035i
$730$	0.102748	+	0.362220i	0.00380289	+	0.0134064i
$731$	0.493098	+	1.19044i	0.0182379	+	0.0440302i
$732$	23.6737	+	38.3708i	0.875003	+	1.41823i
$733$	7.97874	+	19.2624i	0.294701	+	0.711472i	0.999997	+	0.00255843i	$0.000814376\pi$
$733$	7.97874	+	19.2624i	0.294701	+	0.711472i	−0.705295	+	0.708914i	$0.749186\pi$
$734$	26.9657	+	34.0996i	0.995323	+	1.25864i
$735$	−0.0701145	+	0.0701145i	−0.00258621	+	0.00258621i
$736$	−2.61010	+	3.97099i	−0.0962096	+	0.146373i
$737$	68.4688			2.52208
$738$	−2.63521	+	22.5571i	−0.0970036	+	0.830340i
$739$	−13.8276	−	33.3829i	−0.508658	−	1.22801i	−0.944656	−	0.328062i	$-0.893605\pi$
$739$	−13.8276	−	33.3829i	−0.508658	−	1.22801i	0.435998	−	0.899948i	$-0.356395\pi$
$740$	−0.0611986	−	0.0991921i	−0.00224970	−	0.00364637i
$741$	22.2802	+	13.8291i	0.818485	+	0.508023i
$742$	−1.60010	−	0.892921i	−0.0587415	−	0.0327802i
$743$	5.31469			0.194977			0.0974885	−	0.995237i	$-0.468919\pi$
$743$	5.31469			0.194977			0.0974885	+	0.995237i	$0.468919\pi$
$744$	22.8998	+	20.9764i	0.839549	+	0.769034i
$745$	−0.304219	+	0.304219i	−0.0111457	+	0.0111457i
$746$	−24.3117	+	43.5661i	−0.890113	+	1.59507i
$747$	8.08222	−	19.5122i	0.295713	−	0.713915i
$748$	1.43377	−	1.98602i	0.0524237	−	0.0726161i
$749$	−1.62150	−	3.91464i	−0.0592483	−	0.143038i
$750$	−0.481499	−	0.608882i	−0.0175819	−	0.0222332i
$751$		−	43.4197i		−	1.58441i	−0.610256	−	0.792204i	$-0.708933\pi$
$751$		−	43.4197i		−	1.58441i	0.610256	−	0.792204i	$-0.291067\pi$
$752$	−5.65546	−	17.0539i	−0.206233	−	0.621890i
$753$	40.1097			1.46168
$754$	−4.99482	+	17.4297i	−0.181901	+	0.634753i
$755$	−0.00213851	+	0.00516282i	−7.78283e−5	+	0.000187894i
$756$	3.10702	+	19.2400i	0.113001	+	0.699752i
$757$	−6.55370	−	15.8220i	−0.238198	−	0.575061i	0.758898	−	0.651209i	$-0.225738\pi$
$757$	−6.55370	−	15.8220i	−0.238198	−	0.575061i	−0.997097	+	0.0761479i	$0.975738\pi$
$758$	12.2727	+	43.2651i	0.445765	+	1.57146i
$759$			8.08574i			0.293494i
$760$	−0.230380	+	0.107477i	−0.00835677	+	0.00389861i
$761$	−8.40562			−0.304703			−0.152352	−	0.988326i	$-0.548685\pi$
$761$	−8.40562			−0.304703			−0.152352	+	0.988326i	$0.548685\pi$
$762$	9.30242	+	32.7939i	0.336991	+	1.18800i
$763$	1.21727	+	2.93874i	0.0440680	+	0.106390i
$764$	−36.1079	−	8.55327i	−1.30634	−	0.309446i
$765$	−0.00930492	+	0.00385423i	−0.000336420	+	0.000139350i
$766$	−2.70275	+	23.1352i	−0.0976542	+	0.835909i
$767$	9.31529	+	12.9767i	0.336355	+	0.468560i
$768$	−8.26840	−	32.6921i	−0.298360	−	1.17967i

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877210 - 1.10928i) q^{2} +(-1.94716 - 0.806541i) q^{3} +(-0.461004 + 1.94614i) q^{4} +(-0.00996722 + 0.0240630i) q^{5} +(0.813391 + 2.86746i) q^{6} -2.96755i q^{7} +(2.56322 - 1.19579i) q^{8} +(1.01961 + 1.01961i) q^{9} +O(q^{10})\)	\(q+(-0.877210 - 1.10928i) q^{2} +(-1.94716 - 0.806541i) q^{3} +(-0.461004 + 1.94614i) q^{4} +(-0.00996722 + 0.0240630i) q^{5} +(0.813391 + 2.86746i) q^{6} -2.96755i q^{7} +(2.56322 - 1.19579i) q^{8} +(1.01961 + 1.01961i) q^{9} +(0.0354360 - 0.0100519i) q^{10} +(-4.21937 - 1.74772i) q^{11} +(2.46730 - 3.41764i) q^{12} +(-1.90143 + 3.06342i) q^{13} +(-3.29184 + 2.60316i) q^{14} +(0.0388156 - 0.0388156i) q^{15} +(-3.57495 - 1.79436i) q^{16} +0.268171 q^{17} +(0.236622 - 2.02545i) q^{18} +(1.32058 + 3.18817i) q^{19} +(-0.0422351 - 0.0304908i) q^{20} +(-2.39345 + 5.77830i) q^{21} +(1.76256 + 6.21358i) q^{22} +(0.593999 + 0.593999i) q^{23} +(-5.95546 + 0.261067i) q^{24} +(3.53505 + 3.53505i) q^{25} +(5.06615 - 0.578050i) q^{26} +(1.25663 + 3.03377i) q^{27} +(5.77528 + 1.36805i) q^{28} +(-1.36076 + 3.28517i) q^{29} +(-0.0771068 - 0.00900793i) q^{30} +(-3.68370 - 3.68370i) q^{31} +(1.14553 + 5.53965i) q^{32} +(6.80619 + 6.80619i) q^{33} +(-0.235242 - 0.297477i) q^{34} +(0.0714081 + 0.0295782i) q^{35} +(-2.45436 + 1.51427i) q^{36} +(2.06714 + 0.856238i) q^{37} +(2.37814 - 4.26159i) q^{38} +(6.17317 - 4.43141i) q^{39} +(0.00322627 + 0.0735974i) q^{40} -11.1368 q^{41} +(8.50931 - 2.41378i) q^{42} +(1.83875 + 4.43912i) q^{43} +(5.34646 - 7.40580i) q^{44} +(-0.0346977 + 0.0143723i) q^{45} +(0.137849 - 1.17997i) q^{46} +(3.17617 + 3.17617i) q^{47} +(5.51378 + 6.37726i) q^{48} -1.80635 q^{49} +(0.820379 - 7.02235i) q^{50} +(-0.522173 - 0.216291i) q^{51} +(-5.08530 - 5.11271i) q^{52} +(0.167087 + 0.403384i) q^{53} +(2.26297 - 4.05521i) q^{54} +(0.0841108 - 0.0841108i) q^{55} +(-3.54858 - 7.60647i) q^{56} -7.27299i q^{57} +(4.83784 - 1.37232i) q^{58} +(1.69544 - 4.09314i) q^{59} +(0.0576466 + 0.0934349i) q^{60} +(-4.09323 + 9.88192i) q^{61} +(-0.854876 + 7.31764i) q^{62} +(3.02576 - 3.02576i) q^{63} +(5.14015 - 6.13016i) q^{64} +(-0.0547632 - 0.0762879i) q^{65} +(1.57951 - 13.5204i) q^{66} +(-13.8508 + 5.73720i) q^{67} +(-0.123628 + 0.521899i) q^{68} +(-0.677528 - 1.63570i) q^{69} +(-0.0298294 - 0.105158i) q^{70} -8.21571 q^{71} +(3.83274 + 1.39424i) q^{72} +10.2218i q^{73} +(-0.863510 - 3.04414i) q^{74} +(-4.03216 - 9.73449i) q^{75} +(-6.81343 + 1.10028i) q^{76} +(-5.18645 + 12.5212i) q^{77} +(-10.3308 - 2.96050i) q^{78} -1.80629 q^{79} +(0.0788100 - 0.0681393i) q^{80} -11.2466i q^{81} +(9.76934 + 12.3539i) q^{82} +(-5.60506 - 13.5318i) q^{83} +(-10.1420 - 7.32182i) q^{84} +(-0.00267292 + 0.00645300i) q^{85} +(3.31126 - 5.93373i) q^{86} +(5.29924 - 5.29924i) q^{87} +(-12.9051 + 0.565715i) q^{88} -0.316072 q^{89} +(0.0463801 + 0.0258820i) q^{90} +(9.09086 + 5.64258i) q^{91} +(-1.42984 + 0.882171i) q^{92} +(4.20171 + 10.1438i) q^{93} +(0.737093 - 6.30943i) q^{94} -0.0898794 q^{95} +(2.23742 - 11.7105i) q^{96} +(8.51081 - 8.51081i) q^{97} +(1.58455 + 2.00374i) q^{98} +(-2.52013 - 6.08413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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