LMFDB - Embedded newform 416.2.bd.a.83.8

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			83.8
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28670 + 0.586855i) q^{2} +(-0.191326 - 0.0792497i) q^{3} +(1.31120 - 1.51021i) q^{4} +(-1.64053 + 3.96058i) q^{5} +(0.292687 - 0.0103097i) q^{6} +2.32652i q^{7} +(-0.800850 + 2.71268i) q^{8} +(-2.09100 - 2.09100i) q^{9} +O(q^{10})$	\(q+(-1.28670 + 0.586855i) q^{2} +(-0.191326 - 0.0792497i) q^{3} +(1.31120 - 1.51021i) q^{4} +(-1.64053 + 3.96058i) q^{5} +(0.292687 - 0.0103097i) q^{6} +2.32652i q^{7} +(-0.800850 + 2.71268i) q^{8} +(-2.09100 - 2.09100i) q^{9} +(-0.213419 - 6.05884i) q^{10} +(-4.50478 - 1.86594i) q^{11} +(-0.370551 + 0.185030i) q^{12} +(3.60278 - 0.141384i) q^{13} +(-1.36533 - 2.99353i) q^{14} +(0.627750 - 0.627750i) q^{15} +(-0.561496 - 3.96039i) q^{16} +2.56133 q^{17} +(3.91760 + 1.46338i) q^{18} +(-0.0705605 - 0.170348i) q^{19} +(3.83027 + 7.67067i) q^{20} +(0.184376 - 0.445123i) q^{21} +(6.89135 - 0.242743i) q^{22} +(-4.61958 - 4.61958i) q^{23} +(0.368202 - 0.455539i) q^{24} +(-9.45935 - 9.45935i) q^{25} +(-4.55273 + 2.29623i) q^{26} +(0.472100 + 1.13975i) q^{27} +(3.51354 + 3.05054i) q^{28} +(-1.87131 + 4.51774i) q^{29} +(-0.439329 + 1.17613i) q^{30} +(-0.159899 - 0.159899i) q^{31} +(3.04665 + 4.76633i) q^{32} +(0.714005 + 0.714005i) q^{33} +(-3.29566 + 1.50313i) q^{34} +(-9.21436 - 3.81671i) q^{35} +(-5.89957 + 0.416133i) q^{36} +(-2.92642 - 1.21216i) q^{37} +(0.190760 + 0.177778i) q^{38} +(-0.700509 - 0.258469i) q^{39} +(-9.42998 - 7.62206i) q^{40} -4.82421 q^{41} +(0.0239857 + 0.680942i) q^{42} +(-0.0449925 - 0.108621i) q^{43} +(-8.72465 + 4.35656i) q^{44} +(11.7119 - 4.85122i) q^{45} +(8.65504 + 3.23300i) q^{46} +(-4.53070 - 4.53070i) q^{47} +(-0.206432 + 0.802224i) q^{48} +1.58732 q^{49} +(17.7226 + 6.62009i) q^{50} +(-0.490048 - 0.202984i) q^{51} +(4.51045 - 5.62635i) q^{52} +(2.15934 + 5.21310i) q^{53} +(-1.27632 - 1.18946i) q^{54} +(14.7804 - 14.7804i) q^{55} +(-6.31110 - 1.86319i) q^{56} +0.0381839i q^{57} +(-0.243441 - 6.91117i) q^{58} +(3.31700 - 8.00795i) q^{59} +(-0.124930 - 1.77114i) q^{60} +(-5.92923 + 14.3144i) q^{61} +(0.299579 + 0.111904i) q^{62} +(4.86474 - 4.86474i) q^{63} +(-6.71728 - 4.34490i) q^{64} +(-5.35049 + 14.5010i) q^{65} +(-1.33773 - 0.499694i) q^{66} +(-12.9206 + 5.35190i) q^{67} +(3.35842 - 3.86815i) q^{68} +(0.517744 + 1.24994i) q^{69} +(14.0960 - 0.496522i) q^{70} -7.05985 q^{71} +(7.34678 - 3.99763i) q^{72} +1.70448i q^{73} +(4.47680 - 0.157692i) q^{74} +(1.06017 + 2.55947i) q^{75} +(-0.349781 - 0.116799i) q^{76} +(4.34115 - 10.4805i) q^{77} +(1.05303 - 0.0785249i) q^{78} +2.98362 q^{79} +(16.6066 + 4.27328i) q^{80} +8.61586i q^{81} +(6.20732 - 2.83111i) q^{82} +(3.02767 + 7.30944i) q^{83} +(-0.430477 - 0.862093i) q^{84} +(-4.20193 + 10.1443i) q^{85} +(0.121637 + 0.113359i) q^{86} +(0.716059 - 0.716059i) q^{87} +(8.66936 - 10.7257i) q^{88} -2.26277 q^{89} +(-12.2227 + 13.1153i) q^{90} +(0.328933 + 8.38193i) q^{91} +(-13.0338 + 0.919351i) q^{92} +(0.0179208 + 0.0432646i) q^{93} +(8.48853 + 3.17080i) q^{94} +0.790434 q^{95} +(-0.205173 - 1.15337i) q^{96} +(-4.35308 + 4.35308i) q^{97} +(-2.04240 + 0.931525i) q^{98} +(5.51780 + 13.3212i) 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 $

$2$	−1.28670	+	0.586855i	−0.909836	+	0.414969i
$2$	−1.28670	+	0.586855i	−0.909836	+	0.414969i
$3$	−0.191326	−	0.0792497i	−0.110462	−	0.0457548i	0.326768	−	0.945105i	$-0.394040\pi$
$3$	−0.191326	−	0.0792497i	−0.110462	−	0.0457548i	−0.437230	+	0.899350i	$0.644040\pi$
$4$	1.31120	−	1.51021i	0.655601	−	0.755107i
$5$	−1.64053	+	3.96058i	−0.733666	+	1.77123i	−0.103692	+	0.994609i	$0.533066\pi$
$5$	−1.64053	+	3.96058i	−0.733666	+	1.77123i	−0.629974	+	0.776617i	$0.716934\pi$
$6$	0.292687	−	0.0103097i	0.119489	−	0.00420892i
$7$			2.32652i			0.879341i	0.898159	+	0.439670i	$0.144905\pi$
$7$			2.32652i			0.879341i	−0.898159	+	0.439670i	$0.855095\pi$
$8$	−0.800850	+	2.71268i	−0.283143	+	0.959078i
$9$	−2.09100	−	2.09100i	−0.696998	−	0.696998i
$10$	−0.213419	−	6.05884i	−0.0674889	−	1.91597i
$11$	−4.50478	−	1.86594i	−1.35824	−	0.562603i	−0.419668	−	0.907678i	$-0.637853\pi$
$11$	−4.50478	−	1.86594i	−1.35824	−	0.562603i	−0.938575	+	0.345075i	$0.887853\pi$
$12$	−0.370551	+	0.185030i	−0.106969	+	0.0534137i
$13$	3.60278	−	0.141384i	0.999231	−	0.0392129i
$13$	3.60278	−	0.141384i	0.999231	−	0.0392129i
$14$	−1.36533	−	2.99353i	−0.364899	−	0.800056i
$15$	0.627750	−	0.627750i	0.162084	−	0.162084i
$16$	−0.561496	−	3.96039i	−0.140374	−	0.990099i
$17$	2.56133			0.621213			0.310607	−	0.950539i	$-0.399468\pi$
$17$	2.56133			0.621213			0.310607	+	0.950539i	$0.399468\pi$
$18$	3.91760	+	1.46338i	0.923387	+	0.344921i
$19$	−0.0705605	−	0.170348i	−0.0161877	−	0.0390805i	0.915579	−	0.402138i	$-0.131733\pi$
$19$	−0.0705605	−	0.170348i	−0.0161877	−	0.0390805i	−0.931767	+	0.363058i	$0.881733\pi$
$20$	3.83027	+	7.67067i	0.856473	+	1.71521i
$21$	0.184376	−	0.445123i	0.0402341	−	0.0971337i
$22$	6.89135	−	0.242743i	1.46924	−	0.0517530i
$23$	−4.61958	−	4.61958i	−0.963249	−	0.963249i	0.0360995	−	0.999348i	$-0.488507\pi$
$23$	−4.61958	−	4.61958i	−0.963249	−	0.963249i	−0.999348	+	0.0360995i	$0.988507\pi$
$24$	0.368202	−	0.455539i	0.0751590	−	0.0929864i
$25$	−9.45935	−	9.45935i	−1.89187	−	1.89187i
$26$	−4.55273	+	2.29623i	−0.892864	+	0.450327i
$27$	0.472100	+	1.13975i	0.0908556	+	0.219345i
$28$	3.51354	+	3.05054i	0.663997	+	0.576497i
$29$	−1.87131	+	4.51774i	−0.347493	+	0.838923i	0.649421	+	0.760429i	$0.275011\pi$
$29$	−1.87131	+	4.51774i	−0.347493	+	0.838923i	−0.996915	+	0.0784940i	$0.974989\pi$
$30$	−0.439329	+	1.17613i	−0.0802101	+	0.214730i
$31$	−0.159899	−	0.159899i	−0.0287186	−	0.0287186i	0.692602	−	0.721320i	$-0.256464\pi$
$31$	−0.159899	−	0.159899i	−0.0287186	−	0.0287186i	−0.721320	+	0.692602i	$0.756464\pi$
$32$	3.04665	+	4.76633i	0.538578	+	0.842576i
$33$	0.714005	+	0.714005i	0.124292	+	0.124292i
$34$	−3.29566	+	1.50313i	−0.565202	+	0.257784i
$35$	−9.21436	−	3.81671i	−1.55751	−	0.645142i
$36$	−5.89957	+	0.416133i	−0.983262	+	0.0693555i
$37$	−2.92642	−	1.21216i	−0.481101	−	0.199278i	0.128934	−	0.991653i	$-0.458844\pi$
$37$	−2.92642	−	1.21216i	−0.481101	−	0.199278i	−0.610035	+	0.792375i	$0.708844\pi$
$38$	0.190760	+	0.177778i	0.0309453	+	0.0288395i
$39$	−0.700509	−	0.258469i	−0.112171	−	0.0413881i
$40$	−9.42998	−	7.62206i	−1.49101	−	1.20515i
$41$	−4.82421			−0.753415			−0.376708	−	0.926332i	$-0.622944\pi$
$41$	−4.82421			−0.753415			−0.376708	+	0.926332i	$0.622944\pi$
$42$	0.0239857	+	0.680942i	0.00370108	+	0.105072i
$43$	−0.0449925	−	0.108621i	−0.00686129	−	0.0165646i	0.920412	−	0.390950i	$-0.127854\pi$
$43$	−0.0449925	−	0.108621i	−0.00686129	−	0.0165646i	−0.927273	+	0.374386i	$0.877854\pi$
$44$	−8.72465	+	4.35656i	−1.31529	+	0.656776i
$45$	11.7119	−	4.85122i	1.74591	−	0.723178i
$46$	8.65504	+	3.23300i	1.27612	+	0.476679i
$47$	−4.53070	−	4.53070i	−0.660871	−	0.660871i	0.294715	−	0.955585i	$-0.404775\pi$
$47$	−4.53070	−	4.53070i	−0.660871	−	0.660871i	−0.955585	+	0.294715i	$0.904775\pi$
$48$	−0.206432	+	0.802224i	−0.0297958	+	0.115791i
$49$	1.58732			0.226760
$50$	17.7226	+	6.62009i	2.50636	+	0.936222i
$51$	−0.490048	−	0.202984i	−0.0686204	−	0.0284235i
$52$	4.51045	−	5.62635i	0.625487	−	0.780235i
$53$	2.15934	+	5.21310i	0.296608	+	0.716075i	0.999986	+	0.00525901i	$0.00167400\pi$
$53$	2.15934	+	5.21310i	0.296608	+	0.716075i	−0.703378	+	0.710816i	$0.748326\pi$
$54$	−1.27632	−	1.18946i	−0.173685	−	0.161865i
$55$	14.7804	−	14.7804i	1.99299	−	1.99299i
$56$	−6.31110	−	1.86319i	−0.843356	−	0.248979i
$57$			0.0381839i			0.00505758i
$58$	−0.243441	−	6.91117i	−0.0319654	−	0.907481i
$59$	3.31700	−	8.00795i	0.431837	−	1.04255i	−0.546858	−	0.837225i	$-0.684176\pi$
$59$	3.31700	−	8.00795i	0.431837	−	1.04255i	0.978695	−	0.205321i	$-0.0658237\pi$
$60$	−0.124930	−	1.77114i	−0.0161284	−	0.228654i
$61$	−5.92923	+	14.3144i	−0.759160	+	1.83277i	−0.262157	+	0.965025i	$0.584434\pi$
$61$	−5.92923	+	14.3144i	−0.759160	+	1.83277i	−0.497002	+	0.867749i	$0.665566\pi$
$62$	0.299579	+	0.111904i	0.0380466	+	0.0142119i
$63$	4.86474	−	4.86474i	0.612899	−	0.612899i
$64$	−6.71728	−	4.34490i	−0.839660	−	0.543112i
$65$	−5.35049	+	14.5010i	−0.663647	+	1.79863i
$66$	−1.33773	−	0.499694i	−0.164663	−	0.0615081i
$67$	−12.9206	+	5.35190i	−1.57851	+	0.653839i	−0.988176	−	0.153322i	$-0.951003\pi$
$67$	−12.9206	+	5.35190i	−1.57851	+	0.653839i	−0.590331	+	0.807161i	$0.701003\pi$
$68$	3.35842	−	3.86815i	0.407268	−	0.469083i
$69$	0.517744	+	1.24994i	0.0623290	+	0.150476i
$70$	14.0960	−	0.496522i	1.68479	−	0.0593457i
$71$	−7.05985			−0.837850			−0.418925	−	0.908021i	$-0.637593\pi$
$71$	−7.05985			−0.837850			−0.418925	+	0.908021i	$0.637593\pi$
$72$	7.34678	−	3.99763i	0.865826	−	0.471125i
$73$			1.70448i			0.199494i	0.995013	+	0.0997471i	$0.0318034\pi$
$73$			1.70448i			0.199494i	−0.995013	+	0.0997471i	$0.968197\pi$
$74$	4.47680	−	0.157692i	0.520417	−	0.0183313i
$75$	1.06017	+	2.55947i	0.122417	+	0.295542i
$76$	−0.349781	−	0.116799i	−0.0401227	−	0.0133978i
$77$	4.34115	−	10.4805i	0.494719	−	1.19436i
$78$	1.05303	−	0.0785249i	0.119232	−	0.00889120i
$79$	2.98362			0.335684			0.167842	−	0.985814i	$-0.446320\pi$
$79$	2.98362			0.335684			0.167842	+	0.985814i	$0.446320\pi$
$80$	16.6066	+	4.27328i	1.85668	+	0.477768i
$81$			8.61586i			0.957318i
$82$	6.20732	−	2.83111i	0.685484	−	0.312644i
$83$	3.02767	+	7.30944i	0.332330	+	0.802316i	0.998406	+	0.0564322i	$0.0179725\pi$
$83$	3.02767	+	7.30944i	0.332330	+	0.802316i	−0.666076	+	0.745884i	$0.732028\pi$
$84$	−0.430477	−	0.862093i	−0.0469688	−	0.0940621i
$85$	−4.20193	+	10.1443i	−0.455763	+	1.10031i
$86$	0.121637	+	0.113359i	0.0131165	+	0.0122239i
$87$	0.716059	−	0.716059i	0.0767696	−	0.0767696i
$88$	8.66936	−	10.7257i	0.924157	−	1.14336i
$89$	−2.26277			−0.239853			−0.119927	−	0.992783i	$-0.538266\pi$
$89$	−2.26277			−0.239853			−0.119927	+	0.992783i	$0.538266\pi$
$90$	−12.2227	+	13.1153i	−1.28839	+	1.38247i
$91$	0.328933	+	8.38193i	0.0344815	+	0.878665i
$92$	−13.0338	+	0.919351i	−1.35886	+	0.0958490i
$93$	0.0179208	+	0.0432646i	0.00185830	+	0.00448633i
$94$	8.48853	+	3.17080i	0.875525	+	0.327043i
$95$	0.790434			0.0810968
$96$	−0.205173	−	1.15337i	−0.0209404	−	0.117715i
$97$	−4.35308	+	4.35308i	−0.441988	+	0.441988i	−0.892680	−	0.450691i	$-0.851177\pi$
$97$	−4.35308	+	4.35308i	−0.441988	+	0.441988i	0.450691	+	0.892680i	$0.351177\pi$
$98$	−2.04240	+	0.931525i	−0.206314	+	0.0940983i
$99$	5.51780	+	13.3212i	0.554560	+	1.33883i
$100$	−26.6888	+	1.88252i	−2.66888	+	0.188252i
$101$	0.560805	+	1.35390i	0.0558022	+	0.134718i	0.949322	−	0.314306i	$-0.101772\pi$
$101$	0.560805	+	1.35390i	0.0558022	+	0.134718i	−0.893520	+	0.449024i	$0.851772\pi$
$102$	0.749668	−	0.0264065i	0.0742282	−	0.00261464i
$103$	9.41156	−	9.41156i	0.927348	−	0.927348i	−0.0701858	−	0.997534i	$-0.522359\pi$
$103$	9.41156	−	9.41156i	0.927348	−	0.927348i	0.997534	+	0.0701858i	$0.0223592\pi$
$104$	−2.50175	+	9.88642i	−0.245317	+	0.969443i
$105$	1.46047	+	1.46047i	0.142527	+	0.142527i
$106$	−5.83776	−	5.44049i	−0.567013	−	0.528427i
$107$	4.51391	−	1.86972i	0.436376	−	0.180753i	−0.153670	−	0.988122i	$-0.549109\pi$
$107$	4.51391	−	1.86972i	0.436376	−	0.180753i	0.590047	+	0.807369i	$0.299109\pi$
$108$	2.34028	+	0.781470i	0.225194	+	0.0751970i
$109$	−4.33327	+	1.79490i	−0.415052	+	0.171920i	−0.580430	−	0.814310i	$-0.697116\pi$
$109$	−4.33327	+	1.79490i	−0.415052	+	0.171920i	0.165378	+	0.986230i	$0.447116\pi$
$110$	−10.3440	+	27.6920i	−0.986265	+	2.64033i
$111$	0.463836	+	0.463836i	0.0440254	+	0.0440254i
$112$	9.21393	−	1.30633i	0.870634	−	0.123437i
$113$			8.95770i			0.842669i	0.906905	+	0.421335i	$0.138438\pi$
$113$			8.95770i			0.842669i	−0.906905	+	0.421335i	$0.861562\pi$
$114$	−0.0224084	−	0.0491313i	−0.00209874	−	0.00460156i
$115$	25.8748	−	10.7177i	2.41283	−	0.999428i
$116$	4.36909	+	8.74975i	0.405660	+	0.812393i
$117$	−7.82903	−	7.23776i	−0.723794	−	0.669131i
$118$	0.431513	+	12.2504i	0.0397240	+	1.12774i
$119$			5.95897i			0.546258i
$120$	1.20015	+	2.20562i	0.109558	+	0.201345i
$121$	9.03315	+	9.03315i	0.821195	+	0.821195i
$122$	−0.771342	−	21.8980i	−0.0698340	−	1.98255i
$123$	0.922996	+	0.382317i	0.0832237	+	0.0344724i
$124$	−0.451140	+	0.0318217i	−0.0405136	+	0.00285767i
$125$	33.1799	−	13.7436i	2.96770	−	1.22926i
$126$	−3.40457	+	9.11436i	−0.303303	+	0.811972i
$127$	−7.24395			−0.642796			−0.321398	−	0.946944i	$-0.604153\pi$
$127$	−7.24395			−0.642796			−0.321398	+	0.946944i	$0.604153\pi$
$128$	11.1930	+	1.64852i	0.989327	+	0.145710i
$129$			0.0243477i			0.00214370i
$130$	−1.62552	−	21.7985i	−0.142568	−	1.91185i
$131$	18.2859	+	7.57426i	1.59765	+	0.661767i	0.991080	−	0.133267i	$-0.0425467\pi$
$131$	18.2859	+	7.57426i	1.59765	+	0.661767i	0.606566	+	0.795033i	$0.292547\pi$
$132$	2.01451	−	0.142096i	0.175340	−	0.0123678i
$133$	0.396318	−	0.164160i	0.0343651	−	0.0142345i
$134$	13.4842	−	14.4688i	1.16486	−	1.24992i
$135$	−5.28856			−0.455167
$136$	−2.05124	+	6.94806i	−0.175892	+	0.595792i
$137$		−	3.00133i		−	0.256421i	−0.991747	−	0.128210i	$-0.959077\pi$
$137$		−	3.00133i		−	0.256421i	0.991747	−	0.128210i	$-0.0409233\pi$
$138$	−1.39972	−	1.30447i	−0.119152	−	0.111043i
$139$	−10.0852	+	4.17744i	−0.855419	+	0.354326i	−0.766914	−	0.641750i	$-0.778209\pi$
$139$	−10.0852	+	4.17744i	−0.855419	+	0.354326i	−0.0885046	+	0.996076i	$0.528209\pi$
$140$	−17.8460	+	8.91118i	−1.50826	+	0.753132i
$141$	0.507783	+	1.22590i	0.0427630	+	0.103239i
$142$	9.08392	−	4.14311i	0.762306	−	0.347682i
$143$	−16.4935	−	6.08567i	−1.37926	−	0.508909i
$144$	−7.10708	+	9.45525i	−0.592257	+	0.787938i
$145$	−14.8229	−	14.8229i	−1.23098	−	1.23098i
$146$	−1.00028	−	2.19316i	−0.0827840	−	0.181507i
$147$	−0.303695	−	0.125794i	−0.0250483	−	0.0103754i
$148$	−5.66776	+	2.83013i	−0.465887	+	0.232635i
$149$	11.9295	+	4.94138i	0.977307	+	0.404814i	0.813427	−	0.581667i	$-0.197599\pi$
$149$	11.9295	+	4.94138i	0.977307	+	0.404814i	0.163879	+	0.986480i	$0.447599\pi$
$150$	−2.86615	−	2.67111i	−0.234020	−	0.218095i
$151$	−17.8933			−1.45614			−0.728069	−	0.685504i	$-0.759582\pi$
$151$	−17.8933			−1.45614			−0.728069	+	0.685504i	$0.759582\pi$
$152$	0.518608	−	0.0549849i	0.0420647	−	0.00445987i
$153$	−5.35572	−	5.35572i	−0.432985	−	0.432985i
$154$	0.564746	+	16.0328i	0.0455085	+	1.29196i
$155$	0.895609	−	0.370973i	0.0719370	−	0.0297973i
$156$	−1.30885	+	0.719014i	−0.104792	+	0.0575672i
$157$	2.09186	−	5.05019i	0.166948	−	0.403049i	−0.818158	−	0.574993i	$-0.805005\pi$
$157$	2.09186	−	5.05019i	0.166948	−	0.403049i	0.985107	+	0.171944i	$0.0550048\pi$
$158$	−3.83903	+	1.75095i	−0.305417	+	0.139298i
$159$		−	1.16853i		−	0.0926703i
$160$	−23.8756	+	4.24723i	−1.88753	+	0.335773i
$161$	10.7475	−	10.7475i	0.847024	−	0.847024i
$162$	−5.05626	−	11.0860i	−0.397258	−	0.871002i
$163$	−3.91829	−	9.45958i	−0.306904	−	0.740932i	−0.999802	−	0.0198962i	$-0.993666\pi$
$163$	−3.91829	−	9.45958i	−0.306904	−	0.740932i	0.692898	−	0.721036i	$-0.256334\pi$
$164$	−6.32552	+	7.28560i	−0.493940	+	0.568909i
$165$	−3.99922	+	1.65653i	−0.311339	+	0.128961i
$166$	−8.18529	−	7.62827i	−0.635302	−	0.592069i
$167$			12.7318i			0.985215i	0.870251	+	0.492608i	$0.163956\pi$
$167$			12.7318i			0.985215i	−0.870251	+	0.492608i	$0.836044\pi$
$168$	1.05982	+	0.856629i	0.0817668	+	0.0660904i
$169$	12.9600	−	1.01875i	0.996925	−	0.0783655i
$170$	−0.546635	−	15.5187i	−0.0419250	−	1.19023i
$171$	−0.208655	+	0.503739i	−0.0159563	+	0.0385219i
$172$	−0.223036	−	0.0744765i	−0.0170063	−	0.00567878i
$173$	−4.83781	+	11.6795i	−0.367812	+	0.887976i	0.626297	+	0.779585i	$0.284570\pi$
$173$	−4.83781	+	11.6795i	−0.367812	+	0.887976i	−0.994108	+	0.108391i	$0.965430\pi$
$174$	−0.501131	+	1.34158i	−0.0379907	+	0.101705i
$175$	22.0073	−	22.0073i	1.66360	−	1.66360i
$176$	−4.86045	+	18.8884i	−0.366370	+	1.42377i
$177$	−1.26925	+	1.26925i	−0.0954030	+	0.0954030i
$178$	2.91151	−	1.32792i	0.218227	−	0.0995317i
$179$	−5.90646	−	2.44654i	−0.441470	−	0.182863i	0.150866	−	0.988554i	$-0.451794\pi$
$179$	−5.90646	−	2.44654i	−0.441470	−	0.182863i	−0.592335	+	0.805692i	$0.701794\pi$
$180$	8.03027	−	24.0484i	0.598541	−	1.79246i
$181$	−9.02909	+	3.73997i	−0.671127	+	0.277990i	−0.692112	−	0.721790i	$-0.743320\pi$
$181$	−9.02909	+	3.73997i	−0.671127	+	0.277990i	0.0209854	+	0.999780i	$0.493320\pi$
$182$	−5.34221	−	10.5920i	−0.395991	−	0.785131i
$183$	2.26883	−	2.26883i	0.167717	−	0.167717i
$184$	16.2310	−	8.83186i	1.19657	−	0.651093i
$185$	9.60174	−	9.60174i	0.705934	−	0.705934i
$186$	−0.0484488	−	0.0451517i	−0.00355244	−	0.00331069i
$187$	−11.5382	−	4.77929i	−0.843758	−	0.349496i
$188$	−12.7830	+	0.901664i	−0.932296	+	0.0657606i
$189$	−2.65165	+	1.09835i	−0.192879	+	0.0798930i
$190$	−1.01705	+	0.463870i	−0.0737848	+	0.0336527i
$191$		−	8.66872i		−	0.627247i	−0.949547	−	0.313623i	$-0.898457\pi$
$191$		−	8.66872i		−	0.627247i	0.949547	−	0.313623i	$-0.101543\pi$
$192$	0.940856	+	1.36363i	0.0679005	+	0.0984118i
$193$	−4.48756	−	4.48756i	−0.323022	−	0.323022i	0.526904	−	0.849925i	$-0.323353\pi$
$193$	−4.48756	−	4.48756i	−0.323022	−	0.323022i	−0.849925	+	0.526904i	$0.823353\pi$
$194$	3.04649	−	8.15574i	0.218725	−	0.585548i
$195$	2.17289	−	2.35040i	0.155604	−	0.168315i
$196$	2.08130	−	2.39719i	0.148664	−	0.171228i
$197$	7.19629	−	17.3734i	0.512715	−	1.23780i	−0.429584	−	0.903027i	$-0.641340\pi$
$197$	7.19629	−	17.3734i	0.512715	−	1.23780i	0.942298	−	0.334775i	$-0.108660\pi$
$198$	−14.9174	−	13.9022i	−1.06013	−	0.987986i
$199$	−14.8598	+	14.8598i	−1.05338	+	1.05338i	−0.0548906	+	0.998492i	$0.517481\pi$
$199$	−14.8598	+	14.8598i	−1.05338	+	1.05338i	−0.998492	+	0.0548906i	$0.982519\pi$
$200$	33.2357	−	18.0847i	2.35012	−	1.27878i
$201$	2.89619			0.204281
$202$	−1.51613	−	1.41296i	−0.106675	−	0.0994154i
$203$	−10.5106	−	4.35363i	−0.737699	−	0.305565i
$204$	−0.949102	+	0.473924i	−0.0664504	+	0.0331813i
$205$	7.91425	−	19.1067i	0.552755	−	1.33447i
$206$	−6.58665	+	17.6331i	−0.458913	+	1.22856i
$207$			19.3190i			1.34277i
$208$	−2.58288	−	14.1890i	−0.179091	−	0.983833i
$209$			0.899043i			0.0621881i
$210$	−2.73628	−	1.02211i	−0.188821	−	0.0705320i
$211$	−5.67194	+	13.6933i	−0.390472	+	0.942683i	0.599365	+	0.800476i	$0.295420\pi$
$211$	−5.67194	+	13.6933i	−0.390472	+	0.942683i	−0.989837	+	0.142207i	$0.954580\pi$
$212$	10.7042	+	3.57437i	0.735170	+	0.245489i
$213$	1.35073	+	0.559491i	0.0925505	+	0.0383357i
$214$	−4.71080	+	5.05479i	−0.322024	+	0.345538i
$215$	0.504016			0.0343736
$216$	−3.46986	+	0.367888i	−0.236094	+	0.0250316i
$217$	0.372007	−	0.372007i	0.0252535	−	0.0252535i
$218$	4.52228	−	4.85250i	0.306288	−	0.328653i
$219$	0.135080	−	0.326111i	0.00912783	−	0.0220365i
$220$	−2.94148	−	41.7018i	−0.198315	−	2.81153i
$221$	9.22789	−	0.362131i	0.620735	−	0.0243596i
$222$	−0.869023	−	0.324614i	−0.0583250	−	0.0217867i
$223$	10.5465	+	10.5465i	0.706243	+	0.706243i	0.965743	−	0.259500i	$-0.0835578\pi$
$223$	10.5465	+	10.5465i	0.706243	+	0.706243i	−0.259500	+	0.965743i	$0.583558\pi$
$224$	−11.0889	+	7.08809i	−0.740911	+	0.473593i
$225$			39.5589i			2.63726i
$226$	−5.25687	−	11.5259i	−0.349682	−	0.766690i
$227$	−17.1891	+	7.11995i	−1.14088	+	0.472567i	−0.871465	−	0.490457i	$-0.836830\pi$
$227$	−17.1891	+	7.11995i	−1.14088	+	0.472567i	−0.269413	+	0.963025i	$0.586830\pi$
$228$	0.0576658	+	0.0500668i	0.00381901	+	0.00331575i
$229$	−0.0656877	−	0.0272087i	−0.00434076	−	0.00179800i	0.380512	−	0.924776i	$-0.375748\pi$
$229$	−0.0656877	−	0.0272087i	−0.00434076	−	0.00179800i	−0.384853	+	0.922978i	$0.625748\pi$
$230$	−27.0034	+	28.9752i	−1.78055	+	1.91057i
$231$	−1.66115	+	1.66115i	−0.109295	+	0.109295i
$232$	−10.7565	−	8.69429i	−0.706202	−	0.570808i
$233$	−4.56426	+	4.56426i	−0.299014	+	0.299014i	−0.840628	−	0.541613i	$-0.817814\pi$
$233$	−4.56426	+	4.56426i	−0.299014	+	0.299014i	0.541613	+	0.840628i	$0.317814\pi$
$234$	14.3211	+	4.71833i	0.936202	+	0.308447i
$235$	25.3770	−	10.5115i	1.65541	−	0.685693i
$236$	−7.74446	−	15.5094i	−0.504121	−	1.00958i
$237$	−0.570844	−	0.236451i	−0.0370803	−	0.0153592i
$238$	−3.49705	−	7.66742i	−0.226680	−	0.497005i
$239$	15.8475	−	15.8475i	1.02509	−	1.02509i	0.0254124	−	0.999677i	$-0.491910\pi$
$239$	15.8475	−	15.8475i	1.02509	−	1.02509i	0.999677	−	0.0254124i	$-0.00808990\pi$
$240$	−2.83862	−	2.13366i	−0.183232	−	0.137727i
$241$	7.85180	−	7.85180i	0.505779	−	0.505779i	−0.407449	−	0.913228i	$-0.633582\pi$
$241$	7.85180	−	7.85180i	0.505779	−	0.505779i	0.913228	+	0.407449i	$0.133582\pi$
$242$	−16.9241	−	6.32182i	−1.08792	−	0.406382i
$243$	2.09910	−	5.06768i	0.134658	−	0.325092i
$244$	13.8434	+	27.7235i	0.886235	+	1.77482i
$245$	−2.60404	+	6.28670i	−0.166366	+	0.401643i
$246$	−1.41199	+	0.0497362i	−0.0900249	+	0.00317107i
$247$	−0.278298	−	0.603750i	−0.0177077	−	0.0384157i
$248$	0.561808	−	0.305699i	0.0356749	−	0.0194119i
$249$		−	1.63843i		−	0.103831i
$250$	−34.6272	+	37.1557i	−2.19001	+	2.34993i
$251$	−21.9212	+	9.08008i	−1.38366	+	0.573129i	−0.945457	−	0.325748i	$-0.894384\pi$
$251$	−21.9212	+	9.08008i	−1.38366	+	0.573129i	−0.438200	+	0.898878i	$0.644384\pi$
$252$	−0.968141	−	13.7255i	−0.0609871	−	0.864622i
$253$	12.1903	+	29.4301i	0.766399	+	1.85025i
$254$	9.32080	−	4.25115i	0.584839	−	0.266741i
$255$	1.60787	−	1.60787i	0.100689	−	0.100689i
$256$	−15.3694	+	4.44749i	−0.960590	+	0.277968i
$257$		−	9.77918i		−	0.610008i	−0.952351	−	0.305004i	$-0.901342\pi$
$257$		−	9.77918i		−	0.610008i	0.952351	−	0.305004i	$-0.0986578\pi$
$258$	−0.0142886	−	0.0313283i	−0.000889568	−	0.00195041i
$259$	2.82012	−	6.80837i	0.175234	−	0.423051i
$260$	14.8841	+	27.0942i	0.923073	+	1.68031i
$261$	13.3595	−	5.53367i	0.826930	−	0.342526i
$262$	−27.9735	+	0.985347i	−1.72821	+	0.0608749i
$263$	−15.7939	−	15.7939i	−0.973893	−	0.973893i	0.0257743	−	0.999668i	$-0.491795\pi$
$263$	−15.7939	−	15.7939i	−0.973893	−	0.973893i	−0.999668	+	0.0257743i	$0.991795\pi$
$264$	−2.50868	+	1.36506i	−0.154399	+	0.0840135i
$265$	−24.1894			−1.48594
$266$	−0.413605	+	0.443806i	−0.0253597	+	0.0272115i
$267$	0.432926	+	0.179324i	0.0264947	+	0.0109744i
$268$	−8.85905	+	26.5304i	−0.541153	+	1.62060i
$269$	−12.2947	−	5.09265i	−0.749624	−	0.310504i	−0.0250356	−	0.999687i	$-0.507970\pi$
$269$	−12.2947	−	5.09265i	−0.749624	−	0.310504i	−0.724588	+	0.689182i	$0.757970\pi$
$270$	6.80480	−	3.10362i	0.414127	−	0.188880i
$271$	7.54371	+	7.54371i	0.458248	+	0.458248i	0.898080	−	0.439832i	$-0.144962\pi$
$271$	7.54371	+	7.54371i	0.458248	+	0.458248i	−0.439832	+	0.898080i	$0.644962\pi$
$272$	−1.43817	−	10.1439i	−0.0872021	−	0.615062i
$273$	0.601332	−	1.62975i	0.0363943	−	0.0986367i
$274$	1.76134	+	3.86182i	0.106407	+	0.233301i
$275$	24.9617	+	60.2629i	1.50525	+	3.63399i
$276$	2.56655	+	0.857026i	0.154488	+	0.0515869i
$277$	7.84978	−	3.25149i	0.471648	−	0.195363i	−0.134183	−	0.990957i	$-0.542841\pi$
$277$	7.84978	−	3.25149i	0.471648	−	0.195363i	0.605831	+	0.795594i	$0.292841\pi$
$278$	10.5251	−	11.2937i	0.631256	−	0.677351i
$279$			0.668694i			0.0400337i
$280$	17.7328	−	21.9390i	1.05974	−	1.31111i
$281$	−21.5160			−1.28353			−0.641767	−	0.766899i	$-0.721799\pi$
$281$	−21.5160			−1.28353			−0.641767	+	0.766899i	$0.721799\pi$
$282$	−1.37279	−	1.27937i	−0.0817484	−	0.0761853i
$283$	−11.0164	+	4.56316i	−0.654860	+	0.271252i	−0.685274	−	0.728286i	$-0.740317\pi$
$283$	−11.0164	+	4.56316i	−0.654860	+	0.271252i	0.0304139	+	0.999537i	$0.490317\pi$
$284$	−9.25689	+	10.6619i	−0.549295	+	0.632667i
$285$	−0.151230	−	0.0626417i	−0.00895811	−	0.00371057i
$286$	24.7937	−	1.84888i	1.46608	−	0.109326i
$287$		−	11.2236i		−	0.662509i
$288$	3.59583	−	16.3369i	0.211886	−	0.962662i
$289$	−10.4396			−0.614094
$290$	27.7716	+	10.3738i	1.63081	+	0.609170i
$291$	1.17784	−	0.487876i	0.0690460	−	0.0285998i
$292$	2.57413	+	2.23492i	0.150640	+	0.130789i
$293$	18.8819	+	7.82115i	1.10309	+	0.456916i	0.858554	−	0.512723i	$-0.171363\pi$
$293$	18.8819	+	7.82115i	1.10309	+	0.456916i	0.244540	+	0.969639i	$0.421363\pi$
$294$	0.464588	−	0.0163648i	0.0270953	−	0.000954414i
$295$	26.2745	+	26.2745i	1.52976	+	1.52976i
$296$	5.63184	−	6.96769i	0.327344	−	0.404989i
$297$		−	6.01523i		−	0.349039i
$298$	−18.2496	+	0.642831i	−1.05717	+	0.0372382i
$299$	−17.2965	−	15.9902i	−1.00028	−	0.924736i
$300$	5.25544	+	1.75490i	0.303423	+	0.101319i
$301$	0.252710	−	0.104676i	0.0145659	−	0.00603341i
$302$	23.0234	−	10.5008i	1.32485	−	0.604252i
$303$		−	0.303480i		−	0.0174345i
$304$	−0.635026	+	0.375097i	−0.0364213	+	0.0215133i
$305$	−46.9664	−	46.9664i	−2.68929	−	2.68929i
$306$	10.0343	+	3.74819i	0.573620	+	0.214270i
$307$	21.2471	−	8.80082i	1.21263	−	0.502289i	0.317573	−	0.948234i	$-0.397132\pi$
$307$	21.2471	−	8.80082i	1.21263	−	0.502289i	0.895061	+	0.445944i	$0.147132\pi$
$308$	−10.1356	−	20.2981i	−0.577530	−	1.15659i
$309$	−2.54654	+	1.05481i	−0.144867	+	0.0600060i
$310$	−0.934674	+	1.00292i	−0.0530859	+	0.0569623i
$311$	11.8743	+	11.8743i	0.673327	+	0.673327i	0.958482	−	0.285154i	$-0.0920448\pi$
$311$	11.8743	+	11.8743i	0.673327	+	0.673327i	−0.285154	+	0.958482i	$0.592045\pi$
$312$	1.26215	−	1.69326i	0.0714549	−	0.0958621i
$313$	−3.88264	+	3.88264i	−0.219460	+	0.219460i	−0.808271	−	0.588811i	$-0.799596\pi$
$313$	−3.88264	+	3.88264i	−0.219460	+	0.219460i	0.588811	+	0.808271i	$0.299596\pi$
$314$	0.272133	+	7.72571i	0.0153573	+	0.435987i
$315$	11.2865	+	27.2479i	0.635920	+	1.53525i
$316$	3.91213	−	4.50591i	0.220075	−	0.253477i
$317$	−4.73155	−	11.4230i	−0.265750	−	0.641578i	0.733524	−	0.679664i	$-0.237874\pi$
$317$	−4.73155	−	11.4230i	−0.265750	−	0.641578i	−0.999274	+	0.0380851i	$0.987874\pi$
$318$	0.685756	+	1.50355i	0.0384553	+	0.0843147i
$319$	16.8597	−	16.8597i	0.943960	−	0.943960i
$320$	28.2282	−	19.4764i	1.57800	−	1.08876i
$321$	−1.01180			−0.0564733
$322$	−7.52162	+	20.1361i	−0.419164	+	1.12214i
$323$	−0.180729	−	0.436317i	−0.0100560	−	0.0242773i
$324$	13.0118	+	11.2971i	0.722878	+	0.627619i
$325$	−35.4173	−	32.7425i	−1.96460	−	1.81623i
$326$	10.5931	+	9.87220i	0.586696	+	0.546770i
$327$	0.971312			0.0537136
$328$	3.86347	−	13.0866i	0.213324	−	0.722584i
$329$	10.5408	−	10.5408i	0.581131	−	0.581131i
$330$	4.17366	−	4.47843i	0.229752	−	0.246529i
$331$	−10.7883	+	26.0453i	−0.592979	+	1.43158i	0.287633	+	0.957741i	$0.407132\pi$
$331$	−10.7883	+	26.0453i	−0.592979	+	1.43158i	−0.880612	+	0.473837i	$0.842868\pi$
$332$	15.0087	+	5.01173i	0.823710	+	0.275054i
$333$	3.58451	+	8.65376i	0.196430	+	0.474223i
$334$	−7.47171	−	16.3820i	−0.408834	−	0.896384i
$335$		−	59.9532i		−	3.27559i
$336$	−1.86639	−	0.480266i	−0.101820	−	0.0262007i
$337$	14.1585			0.771261			0.385631	−	0.922653i	$-0.373984\pi$
$337$	14.1585			0.771261			0.385631	+	0.922653i	$0.373984\pi$
$338$	−16.0778	+	8.91648i	−0.874518	+	0.484993i
$339$	0.709895	−	1.71384i	0.0385562	−	0.0930829i
$340$	9.81056	+	19.6471i	0.532052	+	1.06551i
$341$	0.421947	+	1.01867i	0.0228497	+	0.0551640i
$342$	−0.0271443	−	0.770612i	−0.00146780	−	0.0416699i
$343$			19.9785i			1.07874i
$344$	0.330688	−	0.0350608i	0.0178295	−	0.00189035i
$345$	−5.79988			−0.312255
$346$	−0.629357	−	17.8671i	−0.0338345	−	0.960542i
$347$	−10.4077	−	25.1264i	−0.558714	−	1.34885i	−0.910785	−	0.412881i	$-0.864523\pi$
$347$	−10.4077	−	25.1264i	−0.558714	−	1.34885i	0.352071	−	0.935973i	$-0.385477\pi$
$348$	−0.142504	−	2.02030i	−0.00763903	−	0.108299i
$349$	−21.4212	+	8.87296i	−1.14665	+	0.474959i	−0.873410	−	0.486986i	$-0.838096\pi$
$349$	−21.4212	+	8.87296i	−1.14665	+	0.474959i	−0.273243	+	0.961945i	$0.588096\pi$
$350$	−15.4018	+	41.2320i	−0.823259	+	2.20394i
$351$	1.86201	+	4.03952i	0.0993869	+	0.215613i
$352$	−4.83082	−	27.1562i	−0.257484	−	1.44743i
$353$	−6.05890	+	6.05890i	−0.322483	+	0.322483i	−0.849719	−	0.527236i	$-0.823228\pi$
$353$	−6.05890	+	6.05890i	−0.322483	+	0.322483i	0.527236	+	0.849719i	$0.323228\pi$
$354$	0.888284	−	2.37802i	0.0472118	−	0.126390i
$355$	11.5819	−	27.9611i	0.614702	−	1.48402i
$356$	−2.96695	+	3.41727i	−0.157248	+	0.181115i
$357$	0.472247	−	1.14010i	0.0249940	−	0.0603407i
$358$	9.03562	−	0.318274i	0.477547	−	0.0168213i
$359$			32.4711i			1.71376i	0.515518	+	0.856879i	$0.327599\pi$
$359$			32.4711i			1.71376i	−0.515518	+	0.856879i	$0.672401\pi$
$360$	3.78036	+	35.6557i	0.199242	+	1.87922i
$361$	13.4110	−	13.4110i	0.705842	−	0.705842i
$362$	9.42292	−	10.1110i	0.495258	−	0.531422i
$363$	−1.01240	−	2.44415i	−0.0531372	−	0.128285i
$364$	13.0898	+	10.4936i	0.686092	+	0.550016i
$365$	−6.75073	−	2.79624i	−0.353349	−	0.146362i
$366$	−1.58783	+	4.25078i	−0.0829973	+	0.222192i
$367$	10.1818			0.531486			0.265743	−	0.964044i	$-0.414383\pi$
$367$	10.1818			0.531486			0.265743	+	0.964044i	$0.414383\pi$
$368$	−15.7015	+	20.8892i	−0.818496	+	1.08893i
$369$	10.0874	+	10.0874i	0.525129	+	0.525129i
$370$	−6.71975	+	17.9894i	−0.349343	+	0.935225i
$371$	−12.1284	+	5.02374i	−0.629674	+	0.260819i
$372$	0.0888366	+	0.0296644i	0.00460596	+	0.00153803i
$373$	12.5195	+	30.2247i	0.648235	+	1.56498i	0.815305	+	0.579032i	$0.196569\pi$
$373$	12.5195	+	30.2247i	0.648235	+	1.56498i	−0.167070	+	0.985945i	$0.553431\pi$
$374$	17.6510	−	0.621745i	0.912711	−	0.0321496i
$375$	−7.43734			−0.384063
$376$	15.9188	−	8.66194i	0.820947	−	0.446705i
$377$	−6.10317	+	16.5410i	−0.314329	+	0.851904i
$378$	2.76731	−	2.96938i	0.142335	−	0.152728i
$379$	−6.17240	−	2.55669i	−0.317055	−	0.131328i	0.218480	−	0.975841i	$-0.429890\pi$
$379$	−6.17240	−	2.55669i	−0.317055	−	0.131328i	−0.535535	+	0.844513i	$0.679890\pi$
$380$	1.03642	−	1.19372i	0.0531672	−	0.0612368i
$381$	1.38595	+	0.574081i	0.0710045	+	0.0294110i
$382$	5.08728	+	11.1541i	0.260288	+	0.570691i
$383$	23.7782	+	23.7782i	1.21501	+	1.21501i	0.969359	+	0.245650i	$0.0790013\pi$
$383$	23.7782	+	23.7782i	1.21501	+	1.21501i	0.245650	+	0.969359i	$0.420999\pi$
$384$	−2.01086	−	1.20244i	−0.102616	−	0.0613619i
$385$	34.3869	+	34.3869i	1.75252	+	1.75252i
$386$	8.40770	+	3.14060i	0.427940	+	0.159853i
$387$	−0.133048	+	0.321206i	−0.00676321	+	0.0163278i
$388$	0.866315	+	12.2819i	0.0439805	+	0.623517i
$389$	−1.39984	−	3.37951i	−0.0709747	−	0.171348i	0.884411	−	0.466709i	$-0.154560\pi$
$389$	−1.39984	−	3.37951i	−0.0709747	−	0.171348i	−0.955386	+	0.295360i	$0.904560\pi$
$390$	−1.41652	+	4.29943i	−0.0717282	+	0.217710i
$391$	−11.8323	−	11.8323i	−0.598383	−	0.598383i
$392$	−1.27120	+	4.30589i	−0.0642054	+	0.217480i
$393$	−2.89830	−	2.89830i	−0.146200	−	0.146200i
$394$	0.936176	+	26.5775i	0.0471639	+	1.33896i
$395$	−4.89471	+	11.8169i	−0.246280	+	0.594572i
$396$	27.3528	+	9.13367i	1.37453	+	0.458984i
$397$	−2.42766	−	5.86090i	−0.121841	−	0.294150i	0.851177	−	0.524878i	$-0.175889\pi$
$397$	−2.42766	−	5.86090i	−0.121841	−	0.294150i	−0.973018	+	0.230728i	$0.925889\pi$
$398$	10.3996	−	27.8407i	0.521284	−	1.39553i
$399$	−0.0888354			−0.00444733
$400$	−32.1514	+	42.7741i	−1.60757	+	2.13871i
$401$	8.87139	−	8.87139i	0.443016	−	0.443016i	−0.450008	−	0.893024i	$-0.648579\pi$
$401$	8.87139	−	8.87139i	0.443016	−	0.443016i	0.893024	+	0.450008i	$0.148579\pi$
$402$	−3.72653	+	1.69964i	−0.185862	+	0.0847705i
$403$	−0.598686	−	0.553472i	−0.0298227	−	0.0275704i
$404$	2.78001	+	0.928305i	0.138311	+	0.0461849i
$405$	−34.1238	−	14.1346i	−1.69563	−	0.702352i
$406$	16.0789	−	0.566370i	0.797985	−	0.0281085i
$407$	10.9211	+	10.9211i	0.541337	+	0.541337i
$408$	0.943087	−	1.16678i	0.0466898	−	0.0577644i
$409$		−	35.0222i		−	1.73173i	−0.500273	−	0.865867i	$-0.666767\pi$
$409$		−	35.0222i		−	1.73173i	0.500273	−	0.865867i	$-0.333233\pi$
$410$	1.02958	+	29.2291i	0.0508471	+	1.44352i
$411$	−0.237854	+	0.574231i	−0.0117325	+	0.0283247i
$412$	−1.87301	−	26.5539i	−0.0922767	−	1.30822i
$413$	18.6306	+	7.71706i	0.916753	+	0.379732i
$414$	−11.3375	−	24.8578i	−0.557206	−	1.22170i
$415$	−33.9166			−1.66490
$416$	11.6503	+	16.7413i	0.571203	+	0.820809i
$417$	2.26063			0.110703
$418$	−0.527608	−	1.15680i	−0.0258061	−	0.0565809i
$419$	−14.1285	−	5.85222i	−0.690222	−	0.285899i	0.00987052	−	0.999951i	$-0.496858\pi$
$419$	−14.1285	−	5.85222i	−0.690222	−	0.285899i	−0.700093	+	0.714052i	$0.746858\pi$
$420$	4.12060	−	0.290651i	0.201065	−	0.0141823i
$421$	−13.0624	+	31.5354i	−0.636621	+	1.53694i	0.194532	+	0.980896i	$0.437681\pi$
$421$	−13.0624	+	31.5354i	−0.636621	+	1.53694i	−0.831153	+	0.556044i	$0.812319\pi$
$422$	−0.737871	−	20.9478i	−0.0359190	−	1.01972i
$423$			18.9474i			0.921252i
$424$	−15.8708	+	1.68268i	−0.770754	+	0.0817183i
$425$	−24.2285	−	24.2285i	−1.17525	−	1.17525i
$426$	−2.06633	+	0.0727850i	−0.100114	+	0.00352644i
$427$	−33.3028	−	13.7945i	−1.61163	−	0.667560i
$428$	3.09497	−	9.26856i	0.149601	−	0.448013i
$429$	2.67335	+	2.47145i	0.129071	+	0.119323i
$430$	−0.648518	+	0.295784i	−0.0312743	+	0.0142640i
$431$	3.07644	−	3.07644i	0.148187	−	0.148187i	−0.629121	−	0.777308i	$-0.716585\pi$
$431$	3.07644	−	3.07644i	0.148187	−	0.148187i	0.777308	+	0.629121i	$0.216585\pi$
$432$	4.24877	−	2.50966i	0.204419	−	0.120746i
$433$	29.6773			1.42620			0.713099	−	0.701064i	$-0.247291\pi$
$433$	29.6773			1.42620			0.713099	+	0.701064i	$0.247291\pi$
$434$	−0.260348	+	0.696975i	−0.0124971	+	0.0334559i
$435$	1.66130	+	4.01072i	0.0796530	+	0.192299i
$436$	−2.97111	+	8.89765i	−0.142290	+	0.426120i
$437$	−0.460977	+	1.11290i	−0.0220515	+	0.0532370i
$438$	0.0175727	+	0.498879i	0.000839656	+	0.0238374i
$439$	−9.15150	−	9.15150i	−0.436777	−	0.436777i	0.454149	−	0.890926i	$-0.349944\pi$
$439$	−9.15150	−	9.15150i	−0.436777	−	0.436777i	−0.890926	+	0.454149i	$0.849944\pi$
$440$	28.2577	+	51.9315i	1.34713	+	2.47574i
$441$	−3.31907	−	3.31907i	−0.158051	−	0.158051i
$442$	−11.6610	+	5.88139i	−0.554659	+	0.279749i
$443$	5.83248	+	14.0809i	0.277110	+	0.669002i	0.999753	−	0.0222192i	$-0.00707317\pi$
$443$	5.83248	+	14.0809i	0.277110	+	0.669002i	−0.722644	+	0.691221i	$0.757073\pi$
$444$	1.30868	−	0.0923089i	0.0621070	−	0.00438079i
$445$	3.71214	−	8.96189i	0.175972	−	0.424834i
$446$	−19.7594	−	7.38090i	−0.935634	−	0.349496i
$447$	−1.89083	−	1.89083i	−0.0894330	−	0.0894330i
$448$	10.1085	−	15.6279i	0.477581	−	0.738347i
$449$	−3.53778	−	3.53778i	−0.166958	−	0.166958i	0.618683	−	0.785641i	$-0.287667\pi$
$449$	−3.53778	−	3.53778i	−0.166958	−	0.166958i	−0.785641	+	0.618683i	$0.787667\pi$
$450$	−23.2153	−	50.9005i	−1.09438	−	2.39947i
$451$	21.7320	+	9.00170i	1.02332	+	0.423874i
$452$	13.5280	+	11.7454i	0.636306	+	0.552455i
$453$	3.42345	+	1.41804i	0.160848	+	0.0666254i
$454$	17.9388	−	19.2487i	0.841911	−	0.903388i
$455$	−33.7369	−	12.4480i	−1.58161	−	0.583572i
$456$	−0.103581	−	0.0305795i	−0.00485061	−	0.00143202i
$457$	30.9796			1.44916			0.724582	−	0.689188i	$-0.242033\pi$
$457$	30.9796			1.44916			0.724582	+	0.689188i	$0.242033\pi$
$458$	0.100488	−	0.00353962i	0.00469550	−	0.000165396i
$459$	1.20920	+	2.91927i	0.0564407	+	0.136260i
$460$	17.7411	−	53.1295i	0.827181	−	2.47717i
$461$	2.30493	−	0.954733i	0.107351	−	0.0444663i	−0.328361	−	0.944552i	$-0.606496\pi$
$461$	2.30493	−	0.954733i	0.107351	−	0.0444663i	0.435713	+	0.900086i	$0.356496\pi$
$462$	1.16255	−	3.11225i	0.0540866	−	0.144795i
$463$	8.19990	+	8.19990i	0.381082	+	0.381082i	0.871492	−	0.490410i	$-0.163153\pi$
$463$	8.19990	+	8.19990i	0.381082	+	0.381082i	−0.490410	+	0.871492i	$0.663153\pi$
$464$	18.9428	+	4.87443i	0.879395	+	0.226290i
$465$	−0.200753			−0.00930968
$466$	3.19428	−	8.55139i	0.147972	−	0.396136i
$467$	24.9018	+	10.3146i	1.15232	+	0.477305i	0.875309	−	0.483563i	$-0.160658\pi$
$467$	24.9018	+	10.3146i	1.15232	+	0.477305i	0.277006	+	0.960868i	$0.410658\pi$
$468$	−21.1960	+	2.33334i	−0.979786	+	0.107859i
$469$	−12.4513	−	30.0601i	−0.574948	−	1.38805i
$470$	−26.4839	+	28.4177i	−1.22161	+	1.31081i
$471$	−0.800453	+	0.800453i	−0.0368829	+	0.0368829i
$472$	19.0666	+	15.4111i	0.877611	+	0.709355i
$473$			0.573270i			0.0263590i
$474$	0.873268	−	0.0307603i	0.0401105	−	0.00141287i
$475$	−0.943926	+	2.27884i	−0.0433103	+	0.104560i
$476$	8.99933	+	7.81342i	0.412483	+	0.358127i
$477$	6.38541	−	15.4157i	0.292368	−	0.705838i
$478$	−11.0908	+	29.6912i	−0.507282	+	1.35804i
$479$	−12.5195	+	12.5195i	−0.572029	+	0.572029i	−0.932695	−	0.360666i	$-0.882549\pi$
$479$	−12.5195	+	12.5195i	−0.572029	+	0.572029i	0.360666	+	0.932695i	$0.382549\pi$
$480$	4.90460	+	1.07953i	0.223863	+	0.0492734i
$481$	−10.7146	−	3.95341i	−0.488545	−	0.180260i
$482$	−5.49506	+	14.7108i	−0.250293	+	0.670058i
$483$	−2.90802	+	1.20454i	−0.132319	+	0.0548085i
$484$	25.4863	−	1.79770i	1.15847	−	0.0817139i
$485$	−10.0994	−	24.3821i	−0.458590	−	1.10713i
$486$	0.273075	+	7.75247i	0.0123870	+	0.351659i
$487$	22.0115			0.997435			0.498717	−	0.866765i	$-0.333805\pi$
$487$	22.0115			0.997435			0.498717	+	0.866765i	$0.333805\pi$
$488$	−34.0821	−	27.5478i	−1.54282	−	1.24703i
$489$			2.12039i			0.0958871i
$490$	−0.338763	−	9.61730i	−0.0153038	−	0.434465i
$491$	−8.71333	−	21.0358i	−0.393227	−	0.949334i	−0.989232	−	0.146354i	$-0.953246\pi$
$491$	−8.71333	−	21.0358i	−0.393227	−	0.949334i	0.596005	−	0.802981i	$-0.296754\pi$
$492$	1.78762	−	0.892626i	0.0805920	−	0.0402427i
$493$	−4.79303	+	11.5714i	−0.215867	+	0.521150i
$494$	0.712401	+	0.613526i	0.0320524	+	0.0276038i
$495$	−61.8116			−2.77823
$496$	−0.543479	+	0.723043i	−0.0244029	+	0.0324656i
$497$		−	16.4249i		−	0.736756i
$498$	0.961519	+	2.10817i	0.0430867	+	0.0944692i
$499$	−15.2983	−	36.9332i	−0.684844	−	1.65336i	−0.754920	−	0.655817i	$-0.772324\pi$
$499$	−15.2983	−	36.9332i	−0.684844	−	1.65336i	0.0700758	−	0.997542i	$-0.477676\pi$
$500$	22.7498	−	68.1294i	1.01740	−	3.04684i
$501$	1.00899	−	2.43592i	0.0450784	−	0.108829i
$502$	22.8774	−	24.5479i	1.02107	−	1.09563i
$503$	3.35083	−	3.35083i	0.149406	−	0.149406i	−0.628447	−	0.777853i	$-0.716309\pi$
$503$	3.35083	−	3.35083i	0.149406	−	0.149406i	0.777853	+	0.628447i	$0.216309\pi$
$504$	9.30056	+	17.0924i	0.414280	+	0.761356i
$505$	−6.28226			−0.279557
$506$	−32.9565	−	30.7138i	−1.46509	−	1.36539i
$507$	−2.56032	−	0.832165i	−0.113708	−	0.0369577i
$508$	−9.49828	+	10.9399i	−0.421418	+	0.485380i
$509$	−0.974136	−	2.35177i	−0.0431778	−	0.104241i	0.900819	−	0.434194i	$-0.142967\pi$
$509$	−0.974136	−	2.35177i	−0.0431778	−	0.104241i	−0.943997	+	0.329954i	$0.892967\pi$
$510$	−1.12526	+	3.01244i	−0.0498276	+	0.133393i
$511$	−3.96550			−0.175423
$512$	17.1659	−	14.7422i	0.758631	−	0.651521i
$513$	0.160843	−	0.160843i	0.00710137	−	0.00710137i
$514$	5.73896	+	12.5829i	0.253135	+	0.555007i
$515$	21.8353	+	52.7151i	0.962179	+	2.32291i
$516$	0.0367703	+	0.0319248i	0.00161872	+	0.00140541i
$517$	11.9558	+	28.8639i	0.525815	+	1.26943i
$518$	0.366873	+	10.4153i	0.0161195	+	0.457624i
$519$	1.85119	−	1.85119i	0.0812584	−	0.0812584i
$520$	−35.0518	−	26.1273i	−1.53712	−	1.14576i
$521$	7.76097	+	7.76097i	0.340014	+	0.340014i	0.856373	−	0.516358i	$-0.172713\pi$
$521$	7.76097	+	7.76097i	0.340014	+	0.340014i	−0.516358	+	0.856373i	$0.672713\pi$
$522$	−13.9422	+	14.9603i	−0.610233	+	0.654792i
$523$	26.1513	−	10.8322i	1.14352	−	0.473659i	0.271161	−	0.962534i	$-0.412592\pi$
$523$	26.1513	−	10.8322i	1.14352	−	0.473659i	0.872354	+	0.488875i	$0.162592\pi$
$524$	35.4153	−	17.6842i	1.54712	−	0.772539i
$525$	−5.95464	+	2.46649i	−0.259882	+	0.107647i
$526$	29.5908	+	11.0533i	1.29022	+	0.481947i
$527$	−0.409552	−	0.409552i	−0.0178404	−	0.0178404i
$528$	2.42683	−	3.22865i	0.105614	−	0.140509i
$529$			19.6810i			0.855696i
$530$	31.1245	−	14.1957i	1.35196	−	0.616620i
$531$	−23.6804	+	9.80875i	−1.02764	+	0.425663i
$532$	0.271736	−	0.813772i	0.0117812	−	0.0352815i
$533$	−17.3806	+	0.682067i	−0.752836	+	0.0295436i
$534$	−0.662284	+	0.0233285i	−0.0286598	+	0.00100952i
$535$			20.9450i			0.905533i
$536$	−4.17052	−	39.3357i	−0.180139	−	1.69904i
$537$	0.936171	+	0.936171i	0.0403988	+	0.0403988i
$538$	18.8083	−	0.662510i	0.810884	−	0.0285628i
$539$	−7.15052	−	2.96184i	−0.307995	−	0.127576i
$540$	−6.93438	+	7.98686i	−0.298408	+	0.343700i
$541$	35.9223	−	14.8795i	1.54442	−	0.639720i	0.562124	−	0.827053i	$-0.309984\pi$
$541$	35.9223	−	14.8795i	1.54442	−	0.639720i	0.982296	+	0.187333i	$0.0599843\pi$
$542$	−14.1336	−	5.27944i	−0.607089	−	0.226771i
$543$	2.02389			0.0868534
$544$	7.80348	+	12.2081i	0.334571	+	0.523419i
$545$		−	20.1069i		−	0.861283i
$546$	0.182690	+	2.44989i	0.00781839	+	0.104846i
$547$	4.11077	+	1.70274i	0.175764	+	0.0728037i	0.468830	−	0.883288i	$-0.344676\pi$
$547$	4.11077	+	1.70274i	0.175764	+	0.0728037i	−0.293066	+	0.956092i	$0.594676\pi$
$548$	−4.53265	−	3.93535i	−0.193625	−	0.168110i
$549$	42.3294	−	17.5334i	1.80657	−	0.748307i
$550$	−67.4838	−	62.8915i	−2.87752	−	2.68170i
$551$	0.901628			0.0384107
$552$	−3.80534	+	0.403457i	−0.161966	+	0.0171723i
$553$			6.94145i			0.295180i
$554$	−8.19218	+	8.79038i	−0.348052	+	0.373467i
$555$	−2.59800	+	1.07613i	−0.110279	+	0.0456790i
$556$	−6.91496	+	20.7083i	−0.293259	+	0.878229i
$557$	−13.4720	−	32.5243i	−0.570827	−	1.37810i	−0.900852	−	0.434127i	$-0.857057\pi$
$557$	−13.4720	−	32.5243i	−0.570827	−	1.37810i	0.330024	−	0.943972i	$-0.392943\pi$
$558$	−0.392426	−	0.860410i	−0.0166127	−	0.0364241i
$559$	−0.177455	−	0.384978i	−0.00750556	−	0.0162828i
$560$	−9.94187	+	38.6356i	−0.420120	+	1.63265i
$561$	1.82880	+	1.82880i	0.0772121	+	0.0772121i
$562$	27.6846	−	12.6267i	1.16781	−	0.532627i
$563$	1.00613	+	0.416753i	0.0424033	+	0.0175640i	0.403784	−	0.914854i	$-0.367695\pi$
$563$	1.00613	+	0.416753i	0.0424033	+	0.0175640i	−0.361381	+	0.932418i	$0.617695\pi$
$564$	2.51717	+	0.840538i	0.105992	+	0.0353930i
$565$	−35.4777	−	14.6953i	−1.49256	−	0.618238i
$566$	11.4970	−	12.3365i	0.483254	−	0.518541i
$567$	−20.0450			−0.841809
$568$	5.65388	−	19.1511i	0.237231	−	0.803563i
$569$	−1.24621	−	1.24621i	−0.0522439	−	0.0522439i	0.680502	−	0.732746i	$-0.261762\pi$
$569$	−1.24621	−	1.24621i	−0.0522439	−	0.0522439i	−0.732746	+	0.680502i	$0.761762\pi$
$570$	0.231350	−	0.00814915i	0.00969018	−	0.000341330i
$571$	−11.6347	+	4.81925i	−0.486897	+	0.201679i	−0.612607	−	0.790388i	$-0.709879\pi$
$571$	−11.6347	+	4.81925i	−0.486897	+	0.201679i	0.125710	+	0.992067i	$0.459879\pi$
$572$	−30.8170	+	16.9292i	−1.28853	+	0.707847i
$573$	−0.686994	+	1.65855i	−0.0286996	+	0.0692869i
$574$	6.58663	+	14.4414i	0.274921	+	0.602774i
$575$			87.3964i			3.64468i
$576$	4.96063	+	23.1310i	0.206693	+	0.963790i
$577$	−18.7925	+	18.7925i	−0.782343	+	0.782343i	−0.980226	−	0.197882i	$-0.936594\pi$
$577$	−18.7925	+	18.7925i	−0.782343	+	0.782343i	0.197882	+	0.980226i	$0.436594\pi$
$578$	13.4327	−	6.12653i	0.558725	−	0.254830i
$579$	0.502948	+	1.21422i	0.0209018	+	0.0504614i
$580$	−41.8217	+	2.94994i	−1.73655	+	0.122490i
$581$	−17.0055	+	7.04393i	−0.705509	+	0.292231i
$582$	−1.22921	+	1.31897i	−0.0509525	+	0.0546731i
$583$		−	27.5131i		−	1.13948i
$584$	−4.62371	−	1.36503i	−0.191331	−	0.0564854i
$585$	41.5095	−	19.1338i	1.71620	−	0.791084i
$586$	−28.8853	+	1.01746i	−1.19324	+	0.0420311i
$587$	14.6802	−	35.4410i	0.605915	−	1.46281i	−0.261490	−	0.965206i	$-0.584214\pi$
$587$	14.6802	−	35.4410i	0.605915	−	1.46281i	0.867405	−	0.497602i	$-0.165786\pi$
$588$	−0.588182	+	0.293702i	−0.0242562	+	0.0121121i
$589$	−0.0159559	+	0.0385209i	−0.000657451	+	0.00158723i
$590$	−49.2268	−	18.3881i	−2.02663	−	0.757027i
$591$	−2.75367	+	2.75367i	−0.113271	+	0.113271i
$592$	−3.15747	+	12.2704i	−0.129771	+	0.504311i
$593$	−7.05458	+	7.05458i	−0.289697	+	0.289697i	−0.836960	−	0.547263i	$-0.815670\pi$
$593$	−7.05458	+	7.05458i	−0.289697	+	0.289697i	0.547263	+	0.836960i	$0.315670\pi$
$594$	3.53007	+	7.73981i	0.144840	+	0.317568i
$595$	−23.6010	−	9.77585i	−0.967546	−	0.400771i
$596$	23.1046	−	11.5370i	0.946401	−	0.472575i
$597$	4.02070	−	1.66543i	0.164556	−	0.0681614i
$598$	31.6393	+	10.4241i	1.29383	+	0.426273i
$599$	−6.76802	+	6.76802i	−0.276534	+	0.276534i	−0.831724	−	0.555190i	$-0.812646\pi$
$599$	−6.76802	+	6.76802i	−0.276534	+	0.276534i	0.555190	+	0.831724i	$0.312646\pi$
$600$	−7.79205	+	0.826144i	−0.318109	+	0.0337272i
$601$	12.0563	−	12.0563i	0.491786	−	0.491786i	−0.417083	−	0.908869i	$-0.636947\pi$
$601$	12.0563	−	12.0563i	0.491786	−	0.491786i	0.908869	+	0.417083i	$0.136947\pi$
$602$	−0.263733	+	0.282991i	−0.0107489	+	0.0115338i
$603$	38.2078	+	15.8262i	1.55594	+	0.644492i
$604$	−23.4618	+	27.0228i	−0.954646	+	1.09954i
$605$	−50.5956	+	20.9574i	−2.05701	+	0.852040i
$606$	0.178099	+	0.390488i	0.00723477	+	0.0158625i
$607$		−	26.5243i		−	1.07659i	−0.842757	−	0.538295i	$-0.819069\pi$
$607$		−	26.5243i		−	1.07659i	0.842757	−	0.538295i	$-0.180931\pi$
$608$	0.596962	−	0.855306i	0.0242100	−	0.0346873i
$609$	1.66592	+	1.66592i	0.0675066	+	0.0675066i
$610$	87.9942	+	32.8693i	3.56278	+	1.33084i
$611$	−16.9637	−	15.6825i	−0.686277	−	0.634448i
$612$	−15.1107	+	1.06585i	−0.610815	+	0.0430846i
$613$	1.54983	−	3.74161i	0.0625969	−	0.151122i	−0.889486	−	0.456963i	$-0.848937\pi$
$613$	1.54983	−	3.74161i	0.0625969	−	0.151122i	0.952083	+	0.305840i	$0.0989373\pi$
$614$	−22.1738	+	23.7930i	−0.894863	+	0.960206i
$615$	−3.02840	+	3.02840i	−0.122117	+	0.122117i
$616$	24.9535	+	20.1694i	1.00541	+	0.812649i
$617$	13.0429			0.525088			0.262544	−	0.964920i	$-0.415439\pi$
$617$	13.0429			0.525088			0.262544	+	0.964920i	$0.415439\pi$
$618$	2.65761	−	2.85167i	0.106905	−	0.114711i
$619$	−0.573103	−	0.237387i	−0.0230349	−	0.00954139i	0.371136	−	0.928578i	$-0.378968\pi$
$619$	−0.573103	−	0.237387i	−0.0230349	−	0.00954139i	−0.394171	+	0.919037i	$0.628968\pi$
$620$	0.614075	−	1.83898i	0.0246619	−	0.0738553i
$621$	3.08426	−	7.44606i	0.123767	−	0.298800i
$622$	−22.2471	−	8.31016i	−0.892027	−	0.333207i
$623$		−	5.26437i		−	0.210913i
$624$	−0.630305	+	2.91942i	−0.0252324	+	0.116870i
$625$			87.0708i			3.48283i
$626$	2.71725	−	7.27435i	0.108603	−	0.290741i
$627$	0.0712489	−	0.172010i	0.00284541	−	0.00686942i
$628$	−4.88402	−	9.78098i	−0.194894	−	0.390304i
$629$	−7.49552	−	3.10475i	−0.298866	−	0.123794i
$630$	−30.5129	−	28.4364i	−1.21566	−	1.13293i
$631$	49.9364			1.98794			0.993968	−	0.109672i	$-0.0349801\pi$
$631$	49.9364			1.98794			0.993968	+	0.109672i	$0.0349801\pi$
$632$	−2.38943	+	8.09361i	−0.0950465	+	0.321947i
$633$	2.17038	−	2.17038i	0.0862647	−	0.0862647i
$634$	12.7917	+	11.9212i	0.508024	+	0.473453i
$635$	11.8839	−	28.6902i	0.471598	−	1.13854i
$636$	−1.76473	−	1.53218i	−0.0699760	−	0.0607547i
$637$	5.71875	−	0.224422i	0.226585	−	0.00889191i
$638$	−11.7992	+	31.5875i	−0.467134	+	1.25056i
$639$	14.7621	+	14.7621i	0.583980	+	0.583980i
$640$	−24.8915	+	41.6262i	−0.983921	+	1.64542i
$641$		−	36.5661i		−	1.44427i	−0.691750	−	0.722137i	$-0.743160\pi$
$641$		−	36.5661i		−	1.44427i	0.691750	−	0.722137i	$-0.256840\pi$
$642$	1.30189	−	0.593781i	0.0513814	−	0.0234347i
$643$	−2.28956	+	0.948369i	−0.0902916	+	0.0374000i	−0.427372	−	0.904076i	$-0.640561\pi$
$643$	−2.28956	+	0.948369i	−0.0902916	+	0.0374000i	0.337080	+	0.941476i	$0.390561\pi$
$644$	−2.13889	−	30.3233i	−0.0842839	−	1.19490i
$645$	−0.0964312	−	0.0399431i	−0.00379697	−	0.00157276i
$646$	0.488599	+	0.455349i	0.0192237	+	0.0179155i
$647$	−0.404738	+	0.404738i	−0.0159119	+	0.0159119i	−0.715018	−	0.699106i	$-0.753582\pi$
$647$	−0.404738	+	0.404738i	−0.0159119	+	0.0159119i	0.699106	+	0.715018i	$0.253582\pi$
$648$	−23.3721	−	6.90001i	−0.918143	−	0.271058i
$649$	−29.8847	+	29.8847i	−1.17308	+	1.17308i
$650$	64.7866	+	21.3450i	2.54114	+	0.837221i
$651$	−0.100656	+	0.0416930i	−0.00394501	+	0.00163408i
$652$	−19.4237	−	6.48598i	−0.760690	−	0.254010i
$653$	−0.913311	−	0.378306i	−0.0357406	−	0.0148043i	0.364742	−	0.931109i	$-0.381157\pi$
$653$	−0.913311	−	0.378306i	−0.0357406	−	0.0148043i	−0.400482	+	0.916305i	$0.631157\pi$
$654$	−1.24979	+	0.570019i	−0.0488706	+	0.0222895i
$655$	−59.9970	+	59.9970i	−2.34428	+	2.34428i
$656$	2.70877	+	19.1058i	0.105760	+	0.745956i
$657$	3.56406	−	3.56406i	0.139047	−	0.139047i
$658$	−7.37691	+	19.7487i	−0.287582	+	0.769885i
$659$	3.46976	−	8.37673i	0.135162	−	0.326311i	−0.841778	−	0.539824i	$-0.818491\pi$
$659$	3.46976	−	8.37673i	0.135162	−	0.326311i	0.976940	+	0.213513i	$0.0684906\pi$
$660$	−2.74207	+	8.21173i	−0.106735	+	0.319641i
$661$	−7.21681	+	17.4229i	−0.280701	+	0.677673i	−0.999852	−	0.0171809i	$-0.994531\pi$
$661$	−7.21681	+	17.4229i	−0.280701	+	0.677673i	0.719151	+	0.694854i	$0.244531\pi$
$662$	−1.40347	−	39.8437i	−0.0545473	−	1.54857i
$663$	−1.79423	−	0.662023i	−0.0696822	−	0.0257108i
$664$	−22.2529	+	2.35934i	−0.863580	+	0.0915601i
$665$			1.83896i			0.0713117i
$666$	−9.69069	−	9.03122i	−0.375507	−	0.349953i
$667$	29.5147	−	12.2254i	1.14281	−	0.473369i
$668$	19.2277	+	16.6940i	0.743943	+	0.645908i
$669$	−1.18201	−	2.85361i	−0.0456990	−	0.110327i
$670$	35.1838	+	77.1419i	1.35927	+	2.98025i
$671$	53.4198	−	53.4198i	2.06225	−	2.06225i
$672$	2.68333	−	0.477339i	0.103512	−	0.0184137i
$673$			9.51163i			0.366646i	0.983053	+	0.183323i	$0.0586855\pi$
$673$			9.51163i			0.366646i	−0.983053	+	0.183323i	$0.941315\pi$
$674$	−18.2177	+	8.30897i	−0.701721	+	0.320050i
$675$	6.31553	−	15.2470i	0.243085	−	0.586859i
$676$	15.4547	−	20.9082i	0.594411	−	0.804162i
$677$	−30.3571	+	12.5743i	−1.16672	+	0.483271i	−0.880107	−	0.474775i	$-0.842529\pi$
$677$	−30.3571	+	12.5743i	−1.16672	+	0.483271i	−0.286613	+	0.958047i	$0.592529\pi$
$678$	0.0923513	+	2.62180i	0.00354673	+	0.100690i
$679$	−10.1275	−	10.1275i	−0.388658	−	0.388658i
$680$	−24.1533	−	19.5226i	−0.926235	−	0.748657i
$681$	3.85296			0.147646
$682$	−1.14073	−	1.06310i	−0.0436808	−	0.0407083i
$683$	−0.697843	−	0.289056i	−0.0267022	−	0.0110604i	0.369292	−	0.929313i	$-0.379600\pi$
$683$	−0.697843	−	0.289056i	−0.0267022	−	0.0110604i	−0.395995	+	0.918253i	$0.629600\pi$
$684$	0.487164	+	0.975618i	0.0186272	+	0.0373037i
$685$	11.8870	+	4.92376i	0.454179	+	0.188127i
$686$	−11.7245	−	25.7064i	−0.447644	−	0.981476i
$687$	0.0104115	+	0.0104115i	0.000397222	+	0.000397222i
$688$	−0.404921	+	0.239179i	−0.0154375	+	0.00911860i
$689$	8.51667	+	18.4764i	0.324459	+	0.703893i
$690$	7.46272	−	3.40369i	0.284101	−	0.129576i
$691$	−16.0480	−	38.7432i	−0.610493	−	1.47386i	−0.862460	−	0.506125i	$-0.831078\pi$
$691$	−16.0480	−	38.7432i	−0.610493	−	1.47386i	0.251967	−	0.967736i	$-0.418922\pi$
$692$	11.2952	+	22.6203i	0.429379	+	0.859895i
$693$	−30.9919	+	12.8373i	−1.17728	+	0.487647i
$694$	28.1371	+	26.2223i	1.06807	+	0.995386i
$695$		−	46.7966i		−	1.77510i
$696$	1.36898	+	2.51589i	0.0518912	+	0.0953647i
$697$	−12.3564			−0.468032
$698$	22.3556	−	23.9880i	0.846172	−	0.907960i
$699$	1.23498	−	0.511544i	0.0467111	−	0.0193484i
$700$	−4.37972	−	62.0919i	−0.165538	−	2.34685i
$701$	−25.7316	−	10.6584i	−0.971870	−	0.402562i	−0.160462	−	0.987042i	$-0.551298\pi$
$701$	−25.7316	−	10.6584i	−0.971870	−	0.402562i	−0.811408	+	0.584480i	$0.801298\pi$
$702$	−4.76646	−	4.10492i	−0.179899	−	0.154930i
$703$			0.584041i			0.0220275i
$704$	22.1526	+	32.1069i	0.834906	+	1.21007i
$705$	−5.68830			−0.214234
$706$	4.24030	−	11.3517i	0.159586	−	0.427227i
$707$	−3.14988	+	1.30472i	−0.118463	+	0.0490691i
$708$	0.252597	+	3.58110i	0.00949317	+	0.134586i
$709$	−18.4030	−	7.62278i	−0.691140	−	0.286280i	0.00933488	−	0.999956i	$-0.497029\pi$
$709$	−18.4030	−	7.62278i	−0.691140	−	0.286280i	−0.700475	+	0.713677i	$0.747029\pi$
$710$	1.50670	+	42.7745i	0.0565455	+	1.60530i
$711$	−6.23874	−	6.23874i	−0.233971	−	0.233971i
$712$	1.81214	−	6.13818i	0.0679128	−	0.230038i
$713$			1.47733i			0.0553263i
$714$	0.0614353	+	1.74412i	0.00229916	+	0.0652719i
$715$	51.1609	−	55.3403i	1.91331	−	2.06961i
$716$	−11.4394	+	5.71212i	−0.427509	+	0.213472i
$717$	−4.28794	+	1.77612i	−0.160136	+	0.0663306i
$718$	−19.0558	−	41.7806i	−0.711156	−	1.55924i
$719$			18.7320i			0.698586i	0.937014	+	0.349293i	$0.113578\pi$
$719$			18.7320i			0.698586i	−0.937014	+	0.349293i	$0.886422\pi$
$720$	−25.7889	−	43.6598i	−0.961097	−	1.62710i
$721$	21.8961	+	21.8961i	0.815455	+	0.815455i
$722$	−9.38564	+	25.1262i	−0.349297	+	0.935102i
$723$	−2.12451	+	0.879999i	−0.0790112	+	0.0327275i
$724$	−6.19080	+	18.5397i	−0.230079	+	0.689023i
$725$	60.4362	−	25.0335i	2.24454	−	0.929720i
$726$	2.73702	+	2.55076i	0.101580	+	0.0946675i
$727$	−6.01336	−	6.01336i	−0.223023	−	0.223023i	0.586747	−	0.809770i	$-0.300408\pi$
$727$	−6.01336	−	6.01336i	−0.223023	−	0.223023i	−0.809770	+	0.586747i	$0.800408\pi$
$728$	−23.0009	−	5.82037i	−0.852471	−	0.215717i
$729$	17.4738	−	17.4738i	0.647177	−	0.647177i
$730$	10.3272	−	0.363768i	0.382226	−	0.0134636i
$731$	−0.115241	−	0.278215i	−0.00426232	−	0.0102902i
$732$	−0.451524	−	6.40131i	−0.0166888	−	0.236599i
$733$	−16.3016	−	39.3554i	−0.602112	−	1.45363i	−0.871403	−	0.490567i	$-0.836790\pi$
$733$	−16.3016	−	39.3554i	−0.602112	−	1.45363i	0.269292	−	0.963059i	$-0.413210\pi$
$734$	−13.1009	+	5.97524i	−0.483565	+	0.220550i
$735$	0.996439	−	0.996439i	0.0367542	−	0.0367542i
$736$	7.94417	−	36.0927i	0.292826	−	1.33039i
$737$	68.1910			2.51185
$738$	−18.8993	−	7.05964i	−0.695694	−	0.259869i
$739$	13.8904	+	33.5343i	0.510966	+	1.23358i	0.943322	+	0.331878i	$0.107682\pi$
$739$	13.8904	+	33.5343i	0.510966	+	1.23358i	−0.432357	+	0.901703i	$0.642318\pi$
$740$	−1.91086	−	27.0905i	−0.0702447	−	0.995867i
$741$	0.00539860	+	0.137568i	0.000198322	+	0.00505369i
$742$	12.6574	−	13.5816i	0.464668	−	0.498598i
$743$	4.47141			0.164040			0.0820200	−	0.996631i	$-0.473863\pi$
$743$	4.47141			0.164040			0.0820200	+	0.996631i	$0.473863\pi$
$744$	−0.131715	+	0.0139649i	−0.00482890	+	0.000511979i
$745$	−39.1415	+	39.1415i	−1.43403	+	1.43403i
$746$	−33.8464	−	31.5431i	−1.23920	−	1.15487i
$747$	8.95317	−	21.6149i	0.327579	−	0.790846i
$748$	−22.3467	+	11.1586i	−0.817076	+	0.407998i
$749$	4.34994	+	10.5017i	0.158943	+	0.383724i
$750$	9.56964	−	4.36464i	0.349434	−	0.159374i
$751$			40.1082i			1.46357i	0.681536	+	0.731784i	$0.261312\pi$
$751$			40.1082i			1.46357i	−0.681536	+	0.731784i	$0.738688\pi$
$752$	−15.3994	+	20.4873i	−0.561558	+	0.747096i
$753$	4.91369			0.179065
$754$	−1.85419	−	24.8650i	−0.0675258	−	0.905529i
$755$	29.3545	−	70.8680i	1.06832	−	2.57915i
$756$	−1.81810	+	5.44471i	−0.0661238	+	0.198022i
$757$	−8.33284	−	20.1172i	−0.302862	−	0.731174i	−0.999900	−	0.0141396i	$-0.995499\pi$
$757$	−8.33284	−	20.1172i	−0.302862	−	0.731174i	0.697038	−	0.717034i	$-0.254501\pi$
$758$	9.44244	−	0.332604i	0.342965	−	0.0120807i
$759$		−	6.59681i		−	0.239449i
$760$	−0.633019	+	2.14420i	−0.0229620	+	0.0777781i
$761$	−0.534563			−0.0193779			−0.00968895	−	0.999953i	$-0.503084\pi$
$761$	−0.534563			−0.0193779			−0.00968895	+	0.999953i	$0.503084\pi$
$762$	−2.12021	+	0.0746830i	−0.0768071	+	0.00270548i
$763$	−4.17586	−	10.0814i	−0.151176	−	0.364972i
$764$	−13.0916	−	11.3665i	−0.473639	−	0.411224i
$765$	29.9980	−	12.4256i	1.08458	−	0.449248i
$766$	−44.5498	−	16.6411i	−1.60965	−	0.601267i
$767$	10.8182	−	29.3198i	0.390623	−	1.05868i
$768$	3.29303	+	0.367105i	0.118827	+	0.0132468i
$769$

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)

\(f(q)\)	\(=\)	\(q+(-1.28670 + 0.586855i) q^{2} +(-0.191326 - 0.0792497i) q^{3} +(1.31120 - 1.51021i) q^{4} +(-1.64053 + 3.96058i) q^{5} +(0.292687 - 0.0103097i) q^{6} +2.32652i q^{7} +(-0.800850 + 2.71268i) q^{8} +(-2.09100 - 2.09100i) q^{9} +O(q^{10})\)	\(q+(-1.28670 + 0.586855i) q^{2} +(-0.191326 - 0.0792497i) q^{3} +(1.31120 - 1.51021i) q^{4} +(-1.64053 + 3.96058i) q^{5} +(0.292687 - 0.0103097i) q^{6} +2.32652i q^{7} +(-0.800850 + 2.71268i) q^{8} +(-2.09100 - 2.09100i) q^{9} +(-0.213419 - 6.05884i) q^{10} +(-4.50478 - 1.86594i) q^{11} +(-0.370551 + 0.185030i) q^{12} +(3.60278 - 0.141384i) q^{13} +(-1.36533 - 2.99353i) q^{14} +(0.627750 - 0.627750i) q^{15} +(-0.561496 - 3.96039i) q^{16} +2.56133 q^{17} +(3.91760 + 1.46338i) q^{18} +(-0.0705605 - 0.170348i) q^{19} +(3.83027 + 7.67067i) q^{20} +(0.184376 - 0.445123i) q^{21} +(6.89135 - 0.242743i) q^{22} +(-4.61958 - 4.61958i) q^{23} +(0.368202 - 0.455539i) q^{24} +(-9.45935 - 9.45935i) q^{25} +(-4.55273 + 2.29623i) q^{26} +(0.472100 + 1.13975i) q^{27} +(3.51354 + 3.05054i) q^{28} +(-1.87131 + 4.51774i) q^{29} +(-0.439329 + 1.17613i) q^{30} +(-0.159899 - 0.159899i) q^{31} +(3.04665 + 4.76633i) q^{32} +(0.714005 + 0.714005i) q^{33} +(-3.29566 + 1.50313i) q^{34} +(-9.21436 - 3.81671i) q^{35} +(-5.89957 + 0.416133i) q^{36} +(-2.92642 - 1.21216i) q^{37} +(0.190760 + 0.177778i) q^{38} +(-0.700509 - 0.258469i) q^{39} +(-9.42998 - 7.62206i) q^{40} -4.82421 q^{41} +(0.0239857 + 0.680942i) q^{42} +(-0.0449925 - 0.108621i) q^{43} +(-8.72465 + 4.35656i) q^{44} +(11.7119 - 4.85122i) q^{45} +(8.65504 + 3.23300i) q^{46} +(-4.53070 - 4.53070i) q^{47} +(-0.206432 + 0.802224i) q^{48} +1.58732 q^{49} +(17.7226 + 6.62009i) q^{50} +(-0.490048 - 0.202984i) q^{51} +(4.51045 - 5.62635i) q^{52} +(2.15934 + 5.21310i) q^{53} +(-1.27632 - 1.18946i) q^{54} +(14.7804 - 14.7804i) q^{55} +(-6.31110 - 1.86319i) q^{56} +0.0381839i q^{57} +(-0.243441 - 6.91117i) q^{58} +(3.31700 - 8.00795i) q^{59} +(-0.124930 - 1.77114i) q^{60} +(-5.92923 + 14.3144i) q^{61} +(0.299579 + 0.111904i) q^{62} +(4.86474 - 4.86474i) q^{63} +(-6.71728 - 4.34490i) q^{64} +(-5.35049 + 14.5010i) q^{65} +(-1.33773 - 0.499694i) q^{66} +(-12.9206 + 5.35190i) q^{67} +(3.35842 - 3.86815i) q^{68} +(0.517744 + 1.24994i) q^{69} +(14.0960 - 0.496522i) q^{70} -7.05985 q^{71} +(7.34678 - 3.99763i) q^{72} +1.70448i q^{73} +(4.47680 - 0.157692i) q^{74} +(1.06017 + 2.55947i) q^{75} +(-0.349781 - 0.116799i) q^{76} +(4.34115 - 10.4805i) q^{77} +(1.05303 - 0.0785249i) q^{78} +2.98362 q^{79} +(16.6066 + 4.27328i) q^{80} +8.61586i q^{81} +(6.20732 - 2.83111i) q^{82} +(3.02767 + 7.30944i) q^{83} +(-0.430477 - 0.862093i) q^{84} +(-4.20193 + 10.1443i) q^{85} +(0.121637 + 0.113359i) q^{86} +(0.716059 - 0.716059i) q^{87} +(8.66936 - 10.7257i) q^{88} -2.26277 q^{89} +(-12.2227 + 13.1153i) q^{90} +(0.328933 + 8.38193i) q^{91} +(-13.0338 + 0.919351i) q^{92} +(0.0179208 + 0.0432646i) q^{93} +(8.48853 + 3.17080i) q^{94} +0.790434 q^{95} +(-0.205173 - 1.15337i) q^{96} +(-4.35308 + 4.35308i) q^{97} +(-2.04240 + 0.931525i) q^{98} +(5.51780 + 13.3212i) 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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