LMFDB - Embedded newform 804.2.e.a.535.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.4
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35079 + 0.418775i) q^{2} -1.00000 q^{3} +(1.64926 - 1.13135i) q^{4} +1.44885i q^{5} +(1.35079 - 0.418775i) q^{6} +2.69839 q^{7} +(-1.75401 + 2.21888i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.35079 + 0.418775i) q^{2} -1.00000 q^{3} +(1.64926 - 1.13135i) q^{4} +1.44885i q^{5} +(1.35079 - 0.418775i) q^{6} +2.69839 q^{7} +(-1.75401 + 2.21888i) q^{8} +1.00000 q^{9} +(-0.606742 - 1.95709i) q^{10} -3.96281 q^{11} +(-1.64926 + 1.13135i) q^{12} +2.95030i q^{13} +(-3.64496 + 1.13002i) q^{14} -1.44885i q^{15} +(1.44009 - 3.73177i) q^{16} -2.16410 q^{17} +(-1.35079 + 0.418775i) q^{18} +6.52411i q^{19} +(1.63916 + 2.38953i) q^{20} -2.69839 q^{21} +(5.35291 - 1.65952i) q^{22} -5.27567i q^{23} +(1.75401 - 2.21888i) q^{24} +2.90083 q^{25} +(-1.23551 - 3.98524i) q^{26} -1.00000 q^{27} +(4.45034 - 3.05283i) q^{28} +1.48281 q^{29} +(0.606742 + 1.95709i) q^{30} +4.41014 q^{31} +(-0.382482 + 5.64391i) q^{32} +3.96281 q^{33} +(2.92324 - 0.906269i) q^{34} +3.90957i q^{35} +(1.64926 - 1.13135i) q^{36} -6.67597 q^{37} +(-2.73213 - 8.81269i) q^{38} -2.95030i q^{39} +(-3.21483 - 2.54130i) q^{40} +0.555830i q^{41} +(3.64496 - 1.13002i) q^{42} -10.5214 q^{43} +(-6.53568 + 4.48333i) q^{44} +1.44885i q^{45} +(2.20931 + 7.12631i) q^{46} +10.0095i q^{47} +(-1.44009 + 3.73177i) q^{48} +0.281330 q^{49} +(-3.91841 + 1.21479i) q^{50} +2.16410 q^{51} +(3.33783 + 4.86581i) q^{52} -3.34580i q^{53} +(1.35079 - 0.418775i) q^{54} -5.74152i q^{55} +(-4.73302 + 5.98742i) q^{56} -6.52411i q^{57} +(-2.00296 + 0.620963i) q^{58} +7.97794i q^{59} +(-1.63916 - 2.38953i) q^{60} +0.843705i q^{61} +(-5.95716 + 1.84685i) q^{62} +2.69839 q^{63} +(-1.84687 - 7.78390i) q^{64} -4.27455 q^{65} +(-5.35291 + 1.65952i) q^{66} +(1.85078 + 7.97337i) q^{67} +(-3.56915 + 2.44835i) q^{68} +5.27567i q^{69} +(-1.63723 - 5.28100i) q^{70} +13.4338i q^{71} +(-1.75401 + 2.21888i) q^{72} -8.46368 q^{73} +(9.01782 - 2.79573i) q^{74} -2.90083 q^{75} +(7.38106 + 10.7599i) q^{76} -10.6932 q^{77} +(1.23551 + 3.98524i) q^{78} -12.5364 q^{79} +(5.40679 + 2.08647i) q^{80} +1.00000 q^{81} +(-0.232767 - 0.750808i) q^{82} +8.13775i q^{83} +(-4.45034 + 3.05283i) q^{84} -3.13545i q^{85} +(14.2122 - 4.40612i) q^{86} -1.48281 q^{87} +(6.95082 - 8.79300i) q^{88} +3.50640 q^{89} +(-0.606742 - 1.95709i) q^{90} +7.96108i q^{91} +(-5.96863 - 8.70092i) q^{92} -4.41014 q^{93} +(-4.19172 - 13.5207i) q^{94} -9.45246 q^{95} +(0.382482 - 5.64391i) q^{96} +8.55060i q^{97} +(-0.380018 + 0.117814i) q^{98} -3.96281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.35079	+	0.418775i	−0.955151	+	0.296118i
$2$	−1.35079	+	0.418775i	−0.955151	+	0.296118i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.64926	−	1.13135i	0.824628	−	0.565676i
$5$			1.44885i			0.647946i	0.946066	+	0.323973i	$0.105019\pi$
$5$			1.44885i			0.647946i	−0.946066	+	0.323973i	$0.894981\pi$
$6$	1.35079	−	0.418775i	0.551457	−	0.170964i
$7$	2.69839			1.01990			0.509949	−	0.860205i	$-0.329664\pi$
$7$	2.69839			1.01990			0.509949	+	0.860205i	$0.329664\pi$
$8$	−1.75401	+	2.21888i	−0.620137	+	0.784493i
$9$	1.00000			0.333333
$10$	−0.606742	−	1.95709i	−0.191869	−	0.618886i
$11$	−3.96281			−1.19483			−0.597416	−	0.801932i	$-0.703806\pi$
$11$	−3.96281			−1.19483			−0.597416	+	0.801932i	$0.703806\pi$
$12$	−1.64926	+	1.13135i	−0.476099	+	0.326593i
$13$			2.95030i			0.818267i	0.912474	+	0.409134i	$0.134169\pi$
$13$			2.95030i			0.818267i	−0.912474	+	0.409134i	$0.865831\pi$
$14$	−3.64496	+	1.13002i	−0.974156	+	0.302010i
$15$		−	1.44885i		−	0.374092i
$16$	1.44009	−	3.73177i	0.360022	−	0.932944i
$17$	−2.16410			−0.524871			−0.262435	−	0.964950i	$-0.584526\pi$
$17$	−2.16410			−0.524871			−0.262435	+	0.964950i	$0.584526\pi$
$18$	−1.35079	+	0.418775i	−0.318384	+	0.0987061i
$19$			6.52411i			1.49673i	0.663285	+	0.748366i	$0.269162\pi$
$19$			6.52411i			1.49673i	−0.663285	+	0.748366i	$0.730838\pi$
$20$	1.63916	+	2.38953i	0.366527	+	0.534314i
$21$	−2.69839			−0.588838
$22$	5.35291	−	1.65952i	1.14124	−	0.353812i
$23$		−	5.27567i		−	1.10005i	−0.835147	−	0.550026i	$-0.814618\pi$
$23$		−	5.27567i		−	1.10005i	0.835147	−	0.550026i	$-0.185382\pi$
$24$	1.75401	−	2.21888i	0.358036	−	0.452927i
$25$	2.90083			0.580166
$26$	−1.23551	−	3.98524i	−0.242304	−	0.781569i
$27$	−1.00000			−0.192450
$28$	4.45034	−	3.05283i	0.841036	−	0.576931i
$29$	1.48281			0.275351			0.137675	−	0.990477i	$-0.456037\pi$
$29$	1.48281			0.275351			0.137675	+	0.990477i	$0.456037\pi$
$30$	0.606742	+	1.95709i	0.110775	+	0.357314i
$31$	4.41014			0.792084			0.396042	−	0.918232i	$-0.370383\pi$
$31$	4.41014			0.792084			0.396042	+	0.918232i	$0.370383\pi$
$32$	−0.382482	+	5.64391i	−0.0676139	+	0.997712i
$33$	3.96281			0.689836
$34$	2.92324	−	0.906269i	0.501331	−	0.155424i
$35$			3.90957i			0.660838i
$36$	1.64926	−	1.13135i	0.274876	−	0.188559i
$37$	−6.67597			−1.09752			−0.548762	−	0.835979i	$-0.684901\pi$
$37$	−6.67597			−1.09752			−0.548762	+	0.835979i	$0.684901\pi$
$38$	−2.73213	−	8.81269i	−0.443210	−	1.42961i
$39$		−	2.95030i		−	0.472427i
$40$	−3.21483	−	2.54130i	−0.508309	−	0.401815i
$41$			0.555830i			0.0868060i	0.999058	+	0.0434030i	$0.0138199\pi$
$41$			0.555830i			0.0868060i	−0.999058	+	0.0434030i	$0.986180\pi$
$42$	3.64496	−	1.13002i	0.562429	−	0.174366i
$43$	−10.5214			−1.60451			−0.802253	−	0.596984i	$-0.796365\pi$
$43$	−10.5214			−1.60451			−0.802253	+	0.596984i	$0.796365\pi$
$44$	−6.53568	+	4.48333i	−0.985291	+	0.675887i
$45$			1.44885i			0.215982i
$46$	2.20931	+	7.12631i	0.325746	+	1.05072i
$47$			10.0095i			1.46003i	0.683429	+	0.730017i	$0.260488\pi$
$47$			10.0095i			1.46003i	−0.683429	+	0.730017i	$0.739512\pi$
$48$	−1.44009	+	3.73177i	−0.207859	+	0.538635i
$49$	0.281330			0.0401900
$50$	−3.91841	+	1.21479i	−0.554146	+	0.171798i
$51$	2.16410			0.303034
$52$	3.33783	+	4.86581i	0.462874	+	0.674766i
$53$		−	3.34580i		−	0.459581i	−0.973240	−	0.229790i	$-0.926196\pi$
$53$		−	3.34580i		−	0.459581i	0.973240	−	0.229790i	$-0.0738041\pi$
$54$	1.35079	−	0.418775i	0.183819	−	0.0569880i
$55$		−	5.74152i		−	0.774186i
$56$	−4.73302	+	5.98742i	−0.632476	+	0.800102i
$57$		−	6.52411i		−	0.864139i
$58$	−2.00296	+	0.620963i	−0.263002	+	0.0815364i
$59$			7.97794i			1.03864i	0.854580	+	0.519320i	$0.173815\pi$
$59$			7.97794i			1.03864i	−0.854580	+	0.519320i	$0.826185\pi$
$60$	−1.63916	−	2.38953i	−0.211615	−	0.308486i
$61$			0.843705i			0.108025i	0.998540	+	0.0540127i	$0.0172011\pi$
$61$			0.843705i			0.108025i	−0.998540	+	0.0540127i	$0.982799\pi$
$62$	−5.95716	+	1.84685i	−0.756560	+	0.234551i
$63$	2.69839			0.339966
$64$	−1.84687	−	7.78390i	−0.230859	−	0.972987i
$65$	−4.27455			−0.530193
$66$	−5.35291	+	1.65952i	−0.658898	+	0.204273i
$67$	1.85078	+	7.97337i	0.226108	+	0.974102i
$67$	1.85078	+	7.97337i	0.226108	+	0.974102i
$68$	−3.56915	+	2.44835i	−0.432823	+	0.296907i
$69$			5.27567i			0.635116i
$70$	−1.63723	−	5.28100i	−0.195686	−	0.631200i
$71$			13.4338i			1.59429i	0.603786	+	0.797147i	$0.293658\pi$
$71$			13.4338i			1.59429i	−0.603786	+	0.797147i	$0.706342\pi$
$72$	−1.75401	+	2.21888i	−0.206712	+	0.261498i
$73$	−8.46368			−0.990599			−0.495299	−	0.868722i	$-0.664942\pi$
$73$	−8.46368			−0.990599			−0.495299	+	0.868722i	$0.664942\pi$
$74$	9.01782	−	2.79573i	1.04830	−	0.324997i
$75$	−2.90083			−0.334959
$76$	7.38106	+	10.7599i	0.846665	+	1.23425i
$77$	−10.6932			−1.21861
$78$	1.23551	+	3.98524i	0.139894	+	0.451239i
$79$	−12.5364			−1.41045			−0.705225	−	0.708984i	$-0.749154\pi$
$79$	−12.5364			−1.41045			−0.705225	+	0.708984i	$0.749154\pi$
$80$	5.40679	+	2.08647i	0.604497	+	0.233275i
$81$	1.00000			0.111111
$82$	−0.232767	−	0.750808i	−0.0257049	−	0.0829129i
$83$			8.13775i			0.893234i	0.894725	+	0.446617i	$0.147371\pi$
$83$			8.13775i			0.893234i	−0.894725	+	0.446617i	$0.852629\pi$
$84$	−4.45034	+	3.05283i	−0.485572	+	0.333091i
$85$		−	3.13545i		−	0.340088i
$86$	14.2122	−	4.40612i	1.53255	−	0.475124i
$87$	−1.48281			−0.158974
$88$	6.95082	−	8.79300i	0.740960	−	0.937337i
$89$	3.50640			0.371677			0.185839	−	0.982580i	$-0.440500\pi$
$89$	3.50640			0.371677			0.185839	+	0.982580i	$0.440500\pi$
$90$	−0.606742	−	1.95709i	−0.0639562	−	0.206295i
$91$			7.96108i			0.834548i
$92$	−5.96863	−	8.70092i	−0.622273	−	0.907134i
$93$	−4.41014			−0.457310
$94$	−4.19172	−	13.5207i	−0.432343	−	1.39455i
$95$	−9.45246			−0.969802
$96$	0.382482	−	5.64391i	0.0390369	−	0.576029i
$97$			8.55060i			0.868182i	0.900869	+	0.434091i	$0.142930\pi$
$97$			8.55060i			0.868182i	−0.900869	+	0.434091i	$0.857070\pi$
$98$	−0.380018	+	0.117814i	−0.0383876	+	0.0119010i
$99$	−3.96281			−0.398277
$100$	4.78421	−	3.28186i	0.478421	−	0.328186i
$101$		−	14.9096i		−	1.48356i	−0.670644	−	0.741779i	$-0.733982\pi$
$101$		−	14.9096i		−	1.48356i	0.670644	−	0.741779i	$-0.266018\pi$
$102$	−2.92324	+	0.906269i	−0.289444	+	0.0897340i
$103$		−	9.31724i		−	0.918055i	−0.888422	−	0.459027i	$-0.848198\pi$
$103$		−	9.31724i		−	0.918055i	0.888422	−	0.459027i	$-0.151802\pi$
$104$	−6.54638	−	5.17487i	−0.641925	−	0.507438i
$105$		−	3.90957i		−	0.381535i
$106$	1.40114	+	4.51947i	0.136090	+	0.438969i
$107$		−	8.13306i		−	0.786253i	−0.919484	−	0.393127i	$-0.871393\pi$
$107$		−	8.13306i		−	0.786253i	0.919484	−	0.393127i	$-0.128607\pi$
$108$	−1.64926	+	1.13135i	−0.158700	+	0.108864i
$109$			3.88557i			0.372170i	0.982534	+	0.186085i	$0.0595800\pi$
$109$			3.88557i			0.372170i	−0.982534	+	0.186085i	$0.940420\pi$
$110$	2.40440	+	7.75557i	0.229251	+	0.739465i
$111$	6.67597			0.633655
$112$	3.88593	−	10.0698i	0.367186	−	0.951507i
$113$			10.5265i			0.990252i	0.868821	+	0.495126i	$0.164878\pi$
$113$			10.5265i			0.990252i	−0.868821	+	0.495126i	$0.835122\pi$
$114$	2.73213	+	8.81269i	0.255887	+	0.825384i
$115$	7.64365			0.712774
$116$	2.44553	−	1.67758i	0.227062	−	0.155759i
$117$			2.95030i			0.272756i
$118$	−3.34096	−	10.7765i	−0.307560	−	0.992057i
$119$	−5.83959			−0.535314
$120$	3.21483	+	2.54130i	0.293472	+	0.231988i
$121$	4.70385			0.427622
$122$	−0.353322	−	1.13967i	−0.0319883	−	0.103181i
$123$		−	0.555830i		−	0.0501175i
$124$	7.27345	−	4.98942i	0.653175	−	0.448063i
$125$			11.4471i			1.02386i
$126$	−3.64496	+	1.13002i	−0.324719	+	0.100670i
$127$			1.37164i			0.121713i	0.998147	+	0.0608567i	$0.0193833\pi$
$127$			1.37164i			0.121713i	−0.998147	+	0.0608567i	$0.980617\pi$
$128$	5.75443	+	9.74097i	0.508625	+	0.860988i
$129$	10.5214			0.926362
$130$	5.77401	−	1.79007i	0.506414	−	0.157000i
$131$			12.0496i			1.05278i	0.850245	+	0.526388i	$0.176454\pi$
$131$			12.0496i			1.05278i	−0.850245	+	0.526388i	$0.823546\pi$
$132$	6.53568	−	4.48333i	0.568858	−	0.390224i
$133$			17.6046i			1.52651i
$134$	−5.83905	−	9.99527i	−0.504417	−	0.863460i
$135$		−	1.44885i		−	0.124697i
$136$	3.79586	−	4.80188i	0.325492	−	0.411757i
$137$		−	9.32069i		−	0.796320i	−0.917316	−	0.398160i	$-0.869649\pi$
$137$		−	9.32069i		−	0.796320i	0.917316	−	0.398160i	$-0.130351\pi$
$138$	−2.20931	−	7.12631i	−0.188069	−	0.606631i
$139$	6.89205			0.584576			0.292288	−	0.956330i	$-0.405583\pi$
$139$	6.89205			0.584576			0.292288	+	0.956330i	$0.405583\pi$
$140$	4.42310	+	6.44788i	0.373820	+	0.544945i
$141$		−	10.0095i		−	0.842951i
$142$	−5.62571	−	18.1462i	−0.472100	−	1.52279i
$143$		−	11.6915i		−	0.977692i
$144$	1.44009	−	3.73177i	0.120007	−	0.310981i
$145$			2.14837i			0.178412i
$146$	11.4326	−	3.54437i	0.946171	−	0.293334i
$147$	−0.281330			−0.0232037
$148$	−11.0104	+	7.55287i	−0.905048	+	0.620842i
$149$	−8.35907			−0.684802			−0.342401	−	0.939554i	$-0.611240\pi$
$149$	−8.35907			−0.684802			−0.342401	+	0.939554i	$0.611240\pi$
$150$	3.91841	−	1.21479i	0.319937	−	0.0991875i
$151$		−	19.1949i		−	1.56206i	−0.624496	−	0.781028i	$-0.714696\pi$
$151$		−	19.1949i		−	1.56206i	0.624496	−	0.781028i	$-0.285304\pi$
$152$	−14.4762	−	11.4434i	−1.17418	−	0.928180i
$153$	−2.16410			−0.174957
$154$	14.4443	−	4.47805i	1.16395	−	0.360851i
$155$			6.38963i			0.513228i
$156$	−3.33783	−	4.86581i	−0.267240	−	0.389576i
$157$	−10.3625			−0.827014			−0.413507	−	0.910501i	$-0.635696\pi$
$157$	−10.3625			−0.827014			−0.413507	+	0.910501i	$0.635696\pi$
$158$	16.9340	−	5.24991i	1.34719	−	0.417660i
$159$			3.34580i			0.265339i
$160$	−8.17718	−	0.554159i	−0.646463	−	0.0438101i
$161$		−	14.2358i		−	1.12194i
$162$	−1.35079	+	0.418775i	−0.106128	+	0.0329020i
$163$			2.48121i			0.194343i	0.995268	+	0.0971716i	$0.0309796\pi$
$163$			2.48121i			0.194343i	−0.995268	+	0.0971716i	$0.969020\pi$
$164$	0.628839	+	0.916705i	0.0491040	+	0.0715827i
$165$			5.74152i			0.446977i
$166$	−3.40788	−	10.9924i	−0.264503	−	0.853174i
$167$			12.4615i			0.964300i	0.876089	+	0.482150i	$0.160144\pi$
$167$			12.4615i			0.964300i	−0.876089	+	0.482150i	$0.839856\pi$
$168$	4.73302	−	5.98742i	0.365160	−	0.461939i
$169$	4.29570			0.330439
$170$	1.31305	+	4.23533i	0.100706	+	0.324835i
$171$			6.52411i			0.498911i
$172$	−17.3526	+	11.9035i	−1.32312	+	0.907630i
$173$	11.2618			0.856221			0.428111	−	0.903726i	$-0.359179\pi$
$173$	11.2618			0.856221			0.428111	+	0.903726i	$0.359179\pi$
$174$	2.00296	−	0.620963i	0.151844	−	0.0470751i
$175$	7.82758			0.591710
$176$	−5.70679	+	14.7883i	−0.430166	+	1.11471i
$177$		−	7.97794i		−	0.599659i
$178$	−4.73640	+	1.46839i	−0.355008	+	0.110060i
$179$	24.6622			1.84334			0.921671	−	0.387972i	$-0.126824\pi$
$179$	24.6622			1.84334			0.921671	+	0.387972i	$0.126824\pi$
$180$	1.63916	+	2.38953i	0.122176	+	0.178105i
$181$	23.7830			1.76778			0.883888	−	0.467699i	$-0.154917\pi$
$181$	23.7830			1.76778			0.883888	+	0.467699i	$0.154917\pi$
$182$	−3.33390	−	10.7537i	−0.247125	−	0.797120i
$183$		−	0.843705i		−	0.0623685i
$184$	11.7061	+	9.25359i	0.862984	+	0.682184i
$185$		−	9.67249i		−	0.711136i
$186$	5.95716	−	1.84685i	0.436800	−	0.135418i
$187$	8.57590			0.627132
$188$	11.3243	+	16.5082i	0.825906	+	1.20399i
$189$	−2.69839			−0.196279
$190$	12.7683	−	3.95845i	0.926307	−	0.287176i
$191$	11.8983			0.860932			0.430466	−	0.902607i	$-0.358349\pi$
$191$	11.8983			0.860932			0.430466	+	0.902607i	$0.358349\pi$
$192$	1.84687	+	7.78390i	0.133287	+	0.561754i
$193$	−19.2001			−1.38205			−0.691026	−	0.722830i	$-0.742841\pi$
$193$	−19.2001			−1.38205			−0.691026	+	0.722830i	$0.742841\pi$
$194$	−3.58077	−	11.5500i	−0.257084	−	0.829245i
$195$	4.27455			0.306107
$196$	0.463986	−	0.318283i	0.0331418	−	0.0227345i
$197$			8.66502i			0.617357i	0.951166	+	0.308679i	$0.0998868\pi$
$197$			8.66502i			0.617357i	−0.951166	+	0.308679i	$0.900113\pi$
$198$	5.35291	−	1.65952i	0.380415	−	0.117937i
$199$			3.96638i			0.281169i	0.990069	+	0.140585i	$0.0448982\pi$
$199$			3.96638i			0.281169i	−0.990069	+	0.140585i	$0.955102\pi$
$200$	−5.08810	+	6.43660i	−0.359783	+	0.455136i
$201$	−1.85078	−	7.97337i	−0.130544	−	0.562398i
$202$	6.24375	+	20.1397i	0.439309	+	1.41702i
$203$	4.00120			0.280829
$204$	3.56915	−	2.44835i	0.249890	−	0.171419i
$205$	−0.805314			−0.0562456
$206$	3.90182	+	12.5856i	0.271853	+	0.876881i
$207$		−	5.27567i		−	0.366684i
$208$	11.0099	+	4.24870i	0.763397	+	0.294594i
$209$		−	25.8538i		−	1.78834i
$210$	1.63723	+	5.28100i	0.112980	+	0.364424i
$211$		−	16.2868i		−	1.12123i	−0.828077	−	0.560615i	$-0.810565\pi$
$211$		−	16.2868i		−	1.12123i	0.828077	−	0.560615i	$-0.189435\pi$
$212$	−3.78527	−	5.51808i	−0.259974	−	0.378983i
$213$		−	13.4338i		−	0.920466i
$214$	3.40592	+	10.9860i	0.232824	+	0.750991i
$215$		−	15.2440i		−	1.03963i
$216$	1.75401	−	2.21888i	0.119345	−	0.150976i
$217$	11.9003			0.807845
$218$	−1.62718	−	5.24858i	−0.110206	−	0.355479i
$219$	8.46368			0.571922
$220$	−6.49567	−	9.46923i	−0.437938	−	0.638415i
$221$		−	6.38475i		−	0.429484i
$222$	−9.01782	+	2.79573i	−0.605237	+	0.187637i
$223$			10.7707i			0.721258i	0.932709	+	0.360629i	$0.117438\pi$
$223$			10.7707i			0.721258i	−0.932709	+	0.360629i	$0.882562\pi$
$224$	−1.03209	+	15.2295i	−0.0689592	+	1.01756i
$225$	2.90083			0.193389
$226$	−4.40824	−	14.2191i	−0.293232	−	0.945840i
$227$		−	23.5814i		−	1.56515i	−0.622554	−	0.782577i	$-0.713905\pi$
$227$		−	23.5814i		−	1.56515i	0.622554	−	0.782577i	$-0.286095\pi$
$228$	−7.38106	−	10.7599i	−0.488822	−	0.712593i
$229$		−	0.0643122i		−	0.00424987i	−0.999998	−	0.00212494i	$-0.999324\pi$
$229$		−	0.0643122i		−	0.00424987i	0.999998	−	0.00212494i	$-0.000676388\pi$
$230$	−10.3250	+	3.20097i	−0.680807	+	0.211066i
$231$	10.6932			0.703562
$232$	−2.60087	+	3.29018i	−0.170755	+	0.216011i
$233$			4.77483i			0.312809i	0.987693	+	0.156405i	$0.0499904\pi$
$233$			4.77483i			0.312809i	−0.987693	+	0.156405i	$0.950010\pi$
$234$	−1.23551	−	3.98524i	−0.0807680	−	0.260523i
$235$	−14.5023			−0.946023
$236$	9.02585	+	13.1577i	0.587533	+	0.856491i
$237$	12.5364			0.814324
$238$	7.88804	−	2.44547i	0.511306	−	0.158516i
$239$	13.2223			0.855278			0.427639	−	0.903950i	$-0.359345\pi$
$239$	13.2223			0.855278			0.427639	+	0.903950i	$0.359345\pi$
$240$	−5.40679	−	2.08647i	−0.349007	−	0.134681i
$241$	26.9947			1.73888			0.869439	−	0.494040i	$-0.164480\pi$
$241$	26.9947			1.73888			0.869439	+	0.494040i	$0.164480\pi$
$242$	−6.35390	+	1.96985i	−0.408444	+	0.126627i
$243$	−1.00000			−0.0641500
$244$	0.954527	+	1.39149i	0.0611073	+	0.0890807i
$245$			0.407606i			0.0260410i
$246$	0.232767	+	0.750808i	0.0148407	+	0.0478698i
$247$	−19.2481			−1.22473
$248$	−7.73544	+	9.78558i	−0.491201	+	0.621385i
$249$		−	8.13775i		−	0.515709i
$250$	−4.79377	−	15.4626i	−0.303184	−	0.977943i
$251$	−11.9629			−0.755091			−0.377546	−	0.925991i	$-0.623232\pi$
$251$	−11.9629			−0.755091			−0.377546	+	0.925991i	$0.623232\pi$
$252$	4.45034	−	3.05283i	0.280345	−	0.192310i
$253$			20.9065i			1.31438i
$254$	−0.574408	−	1.85280i	−0.0360416	−	0.116255i
$255$			3.13545i			0.196350i
$256$	−11.8523	−	10.7482i	−0.740768	−	0.671761i
$257$	1.46492			0.0913791			0.0456896	−	0.998956i	$-0.485451\pi$
$257$	1.46492			0.0913791			0.0456896	+	0.998956i	$0.485451\pi$
$258$	−14.2122	+	4.40612i	−0.884816	+	0.274313i
$259$	−18.0144			−1.11936
$260$	−7.04983	+	4.83602i	−0.437212	+	0.299917i
$261$	1.48281			0.0917836
$262$	−5.04605	−	16.2764i	−0.311746	−	1.00556i
$263$		−	0.0327787i		−	0.00202122i	−0.999999	−	0.00101061i	$-0.999678\pi$
$263$		−	0.0327787i		−	0.00202122i	0.999999	−	0.00101061i	$-0.000321688\pi$
$264$	−6.95082	+	8.79300i	−0.427793	+	0.541172i
$265$	4.84756			0.297784
$266$	−7.37236	−	23.7801i	−0.452029	−	1.45805i
$267$	−3.50640			−0.214588
$268$	12.0731	+	11.0562i	0.737481	+	0.675368i
$269$	13.8847			0.846562			0.423281	−	0.905998i	$-0.360878\pi$
$269$	13.8847			0.846562			0.423281	+	0.905998i	$0.360878\pi$
$270$	0.606742	+	1.95709i	0.0369251	+	0.119105i
$271$	1.69169			0.102763			0.0513816	−	0.998679i	$-0.483638\pi$
$271$	1.69169			0.102763			0.0513816	+	0.998679i	$0.483638\pi$
$272$	−3.11649	+	8.07592i	−0.188965	+	0.489675i
$273$		−	7.96108i		−	0.481827i
$274$	3.90327	+	12.5903i	0.235805	+	0.760606i
$275$	−11.4954			−0.693201
$276$	5.96863	+	8.70092i	0.359269	+	0.523734i
$277$	−0.841553			−0.0505640			−0.0252820	−	0.999680i	$-0.508048\pi$
$277$	−0.841553			−0.0505640			−0.0252820	+	0.999680i	$0.508048\pi$
$278$	−9.30970	+	2.88621i	−0.558358	+	0.173104i
$279$	4.41014			0.264028
$280$	−8.67488	−	6.85744i	−0.518423	−	0.409810i
$281$		−	25.4809i		−	1.52006i	−0.649886	−	0.760032i	$-0.725183\pi$
$281$		−	25.4809i		−	1.52006i	0.649886	−	0.760032i	$-0.274817\pi$
$282$	4.19172	+	13.5207i	0.249613	+	0.805146i
$283$		−	1.94265i		−	0.115478i	−0.998332	−	0.0577392i	$-0.981611\pi$
$283$		−	1.94265i		−	0.115478i	0.998332	−	0.0577392i	$-0.0183892\pi$
$284$	15.1983	+	22.1557i	0.901853	+	1.31470i
$285$	9.45246			0.559915
$286$	4.89610	+	15.7927i	0.289512	+	0.933843i
$287$			1.49985i			0.0885332i
$288$	−0.382482	+	5.64391i	−0.0225380	+	0.332571i
$289$	−12.3167			−0.724511
$290$	−0.899682	−	2.90199i	−0.0528312	−	0.170411i
$291$		−	8.55060i		−	0.501245i
$292$	−13.9588	+	9.57539i	−0.816875	+	0.560357i
$293$	−23.0061			−1.34403			−0.672016	−	0.740536i	$-0.734571\pi$
$293$	−23.0061			−1.34403			−0.672016	+	0.740536i	$0.734571\pi$
$294$	0.380018	−	0.117814i	0.0221631	−	0.00687105i
$295$	−11.5588			−0.672982
$296$	11.7097	−	14.8132i	0.680615	−	0.861000i
$297$	3.96281			0.229945
$298$	11.2913	−	3.50057i	0.654089	−	0.202782i
$299$	15.5648			0.900137
$300$	−4.78421	+	3.28186i	−0.276217	+	0.189478i
$301$	−28.3910			−1.63643
$302$	8.03832	+	25.9282i	0.462553	+	1.49200i
$303$			14.9096i			0.856533i
$304$	24.3465	+	9.39529i	1.39637	+	0.538857i
$305$	−1.22240			−0.0699946
$306$	2.92324	−	0.906269i	0.167110	−	0.0518079i
$307$		−	28.0965i		−	1.60355i	−0.597626	−	0.801775i	$-0.703889\pi$
$307$		−	28.0965i		−	1.60355i	0.597626	−	0.801775i	$-0.296111\pi$
$308$	−17.6358	+	12.0978i	−1.00490	+	0.689335i
$309$			9.31724i			0.530039i
$310$	−2.67582	−	8.63104i	−0.151976	−	0.490210i
$311$	21.5109			1.21977			0.609885	−	0.792490i	$-0.291216\pi$
$311$	21.5109			1.21977			0.609885	+	0.792490i	$0.291216\pi$
$312$	6.54638	+	5.17487i	0.370616	+	0.292970i
$313$			35.2883i			1.99461i	0.0733438	+	0.997307i	$0.476633\pi$
$313$			35.2883i			1.99461i	−0.0733438	+	0.997307i	$0.523367\pi$
$314$	13.9975	−	4.33953i	0.789924	−	0.244894i
$315$			3.90957i			0.220279i
$316$	−20.6756	+	14.1830i	−1.16310	+	0.797857i
$317$	17.5449			0.985418			0.492709	−	0.870194i	$-0.336007\pi$
$317$	17.5449			0.985418			0.492709	+	0.870194i	$0.336007\pi$
$318$	−1.40114	−	4.51947i	−0.0785718	−	0.253439i
$319$	−5.87609			−0.328998
$320$	11.2777	−	2.67584i	0.630443	−	0.149584i
$321$			8.13306i			0.453943i
$322$	5.96160	+	19.2296i	0.332227	+	1.07162i
$323$		−	14.1188i		−	0.785591i
$324$	1.64926	−	1.13135i	0.0916253	−	0.0628528i
$325$			8.55834i			0.474731i
$326$	−1.03907	−	3.35159i	−0.0575486	−	0.185627i
$327$		−	3.88557i		−	0.214873i
$328$	−1.23332	−	0.974933i	−0.0680987	−	0.0538317i
$329$			27.0096i			1.48908i
$330$	−2.40440	−	7.75557i	−0.132358	−	0.426930i
$331$	12.3828			0.680623			0.340311	−	0.940313i	$-0.389468\pi$
$331$	12.3828			0.680623			0.340311	+	0.940313i	$0.389468\pi$
$332$	9.20665	+	13.4212i	0.505281	+	0.736586i
$333$	−6.67597			−0.365841
$334$	−5.21856	−	16.8329i	−0.285547	−	0.921053i
$335$	−11.5522	+	2.68150i	−0.631165	+	0.146506i
$336$	−3.88593	+	10.0698i	−0.211995	+	0.549353i
$337$		−	5.69001i		−	0.309955i	−0.987918	−	0.154977i	$-0.950470\pi$
$337$		−	5.69001i		−	0.309955i	0.987918	−	0.154977i	$-0.0495305\pi$
$338$	−5.80258	+	1.79893i	−0.315619	+	0.0978490i
$339$		−	10.5265i		−	0.571722i
$340$	−3.54730	−	5.17117i	−0.192379	−	0.280446i
$341$	−17.4765			−0.946407
$342$	−2.73213	−	8.81269i	−0.147737	−	0.476535i
$343$	−18.1296			−0.978907
$344$	18.4548	−	23.3459i	0.995014	−	1.25872i
$345$	−7.64365			−0.411521
$346$	−15.2123	+	4.71617i	−0.817821	+	0.253543i
$347$	−32.2136			−1.72932			−0.864660	−	0.502358i	$-0.832466\pi$
$347$	−32.2136			−1.72932			−0.864660	+	0.502358i	$0.832466\pi$
$348$	−2.44553	+	1.67758i	−0.131094	+	0.0899276i
$349$	0.815507			0.0436531			0.0218265	−	0.999762i	$-0.493052\pi$
$349$	0.815507			0.0436531			0.0218265	+	0.999762i	$0.493052\pi$
$350$	−10.5734	+	3.27799i	−0.565172	+	0.175216i
$351$		−	2.95030i		−	0.157476i
$352$	1.51570	−	22.3657i	0.0807872	−	1.19210i
$353$		−	1.26977i		−	0.0675828i	−0.999429	−	0.0337914i	$-0.989242\pi$
$353$		−	1.26977i		−	0.0675828i	0.999429	−	0.0337914i	$-0.0107582\pi$
$354$	3.34096	+	10.7765i	0.177570	+	0.572765i
$355$	−19.4635			−1.03302
$356$	5.78295	−	3.96697i	0.306495	−	0.210249i
$357$	5.83959			0.309064
$358$	−33.3135	+	10.3279i	−1.76067	+	0.545848i
$359$		−	13.7173i		−	0.723973i	−0.932183	−	0.361987i	$-0.882099\pi$
$359$		−	13.7173i		−	0.723973i	0.932183	−	0.361987i	$-0.117901\pi$
$360$	−3.21483	−	2.54130i	−0.169436	−	0.133938i
$361$	−23.5640			−1.24021
$362$	−32.1258	+	9.95971i	−1.68849	+	0.523471i
$363$	−4.70385			−0.246888
$364$	9.00678	+	13.1299i	0.472084	+	0.688192i
$365$		−	12.2626i		−	0.641854i
$366$	0.353322	+	1.13967i	0.0184684	+	0.0595713i
$367$	32.2468			1.68327			0.841635	−	0.540047i	$-0.181594\pi$
$367$	32.2468			1.68327			0.841635	+	0.540047i	$0.181594\pi$
$368$	−19.6876	−	7.59743i	−1.02629	−	0.396043i
$369$			0.555830i			0.0289353i
$370$	4.05059	+	13.0655i	0.210580	+	0.679242i
$371$		−	9.02829i		−	0.468725i
$372$	−7.27345	+	4.98942i	−0.377111	+	0.258689i
$373$			27.4890i			1.42332i	0.702522	+	0.711662i	$0.252057\pi$
$373$			27.4890i			1.42332i	−0.702522	+	0.711662i	$0.747943\pi$
$374$	−11.5842	+	3.59137i	−0.599006	+	0.185705i
$375$		−	11.4471i		−	0.591127i
$376$	−22.2099	−	17.5568i	−1.14539	−	0.905422i
$377$			4.37474i			0.225310i
$378$	3.64496	−	1.13002i	0.187476	−	0.0581219i
$379$	25.1952			1.29419			0.647095	−	0.762409i	$-0.275984\pi$
$379$	25.1952			1.29419			0.647095	+	0.762409i	$0.275984\pi$
$380$	−15.5895	+	10.6941i	−0.799726	+	0.548593i
$381$		−	1.37164i		−	0.0702713i
$382$	−16.0721	+	4.98272i	−0.822321	+	0.254938i
$383$	−19.8566			−1.01463			−0.507313	−	0.861762i	$-0.669361\pi$
$383$	−19.8566			−1.01463			−0.507313	+	0.861762i	$0.669361\pi$
$384$	−5.75443	−	9.74097i	−0.293655	−	0.497092i
$385$		−	15.4929i		−	0.789590i
$386$	25.9352	−	8.04051i	1.32007	−	0.409251i
$387$	−10.5214			−0.534835
$388$	9.67373	+	14.1021i	0.491109	+	0.715927i
$389$	17.3543			0.879899			0.439950	−	0.898022i	$-0.354996\pi$
$389$	17.3543			0.879899			0.439950	+	0.898022i	$0.354996\pi$
$390$	−5.77401	+	1.79007i	−0.292378	+	0.0906439i
$391$			11.4171i			0.577385i
$392$	−0.493457	+	0.624239i	−0.0249233	+	0.0315288i
$393$		−	12.0496i		−	0.607820i
$394$	−3.62869	−	11.7046i	−0.182811	−	0.589670i
$395$		−	18.1633i		−	0.913895i
$396$	−6.53568	+	4.48333i	−0.328430	+	0.225296i
$397$	−15.8998			−0.797989			−0.398994	−	0.916953i	$-0.630641\pi$
$397$	−15.8998			−0.797989			−0.398994	+	0.916953i	$0.630641\pi$
$398$	−1.66102	−	5.35774i	−0.0832593	−	0.268559i
$399$		−	17.6046i		−	0.881333i
$400$	4.17745	−	10.8252i	0.208873	−	0.541262i
$401$		−	4.71619i		−	0.235515i	−0.993042	−	0.117758i	$-0.962429\pi$
$401$		−	4.71619i		−	0.235515i	0.993042	−	0.117758i	$-0.0375706\pi$
$402$	5.83905	+	9.99527i	0.291225	+	0.498519i
$403$			13.0113i			0.648137i
$404$	−16.8680	−	24.5897i	−0.839213	−	1.22338i
$405$			1.44885i			0.0719940i
$406$	−5.40478	+	1.67560i	−0.268235	+	0.0831587i
$407$	26.4556			1.31136
$408$	−3.79586	+	4.80188i	−0.187923	+	0.237728i
$409$			12.2642i			0.606424i	0.952923	+	0.303212i	$0.0980590\pi$
$409$			12.2642i			0.606424i	−0.952923	+	0.303212i	$0.901941\pi$
$410$	1.08781	−	0.337245i	0.0537231	−	0.0166554i
$411$			9.32069i			0.459756i
$412$	−10.5411	−	15.3665i	−0.519321	−	0.757053i
$413$			21.5276i			1.05930i
$414$	2.20931	+	7.12631i	0.108582	+	0.350239i
$415$	−11.7904			−0.578767
$416$	−16.6513	−	1.12844i	−0.816395	−	0.0553262i
$417$	−6.89205			−0.337505
$418$	10.8269	+	34.9230i	0.529561	+	1.70814i
$419$		−	22.1411i		−	1.08166i	−0.841131	−	0.540832i	$-0.818110\pi$
$419$		−	22.1411i		−	1.08166i	0.841131	−	0.540832i	$-0.181890\pi$
$420$	−4.42310	−	6.44788i	−0.215825	−	0.314624i
$421$	10.7107			0.522009			0.261004	−	0.965338i	$-0.415946\pi$
$421$	10.7107			0.522009			0.261004	+	0.965338i	$0.415946\pi$
$422$	6.82049	+	22.0000i	0.332016	+	1.07094i
$423$			10.0095i			0.486678i
$424$	7.42393	+	5.86858i	0.360538	+	0.285003i
$425$	−6.27768			−0.304512
$426$	5.62571	+	18.1462i	0.272567	+	0.879184i
$427$			2.27665i			0.110175i
$428$	−9.20135	−	13.4135i	−0.444764	−	0.648366i
$429$			11.6915i			0.564470i
$430$	6.38380	+	20.5914i	0.307854	+	0.993007i
$431$			32.2037i			1.55120i	0.631226	+	0.775599i	$0.282552\pi$
$431$			32.2037i			1.55120i	−0.631226	+	0.775599i	$0.717448\pi$
$432$	−1.44009	+	3.73177i	−0.0692863	+	0.179545i
$433$		−	24.6358i		−	1.18392i	−0.805968	−	0.591960i	$-0.798354\pi$
$433$		−	24.6358i		−	1.18392i	0.805968	−	0.591960i	$-0.201646\pi$
$434$	−16.0748	+	4.98354i	−0.771614	+	0.239218i
$435$		−	2.14837i		−	0.103006i
$436$	4.39595	+	6.40830i	0.210528	+	0.306902i
$437$	34.4190			1.64648
$438$	−11.4326	+	3.54437i	−0.546272	+	0.169357i
$439$		−	23.9175i		−	1.14152i	−0.821116	−	0.570761i	$-0.806648\pi$
$439$		−	23.9175i		−	1.14152i	0.821116	−	0.570761i	$-0.193352\pi$
$440$	12.7398	+	10.0707i	0.607344	+	0.480102i
$441$	0.281330			0.0133967
$442$	2.67377	+	8.62444i	0.127178	+	0.410223i
$443$	33.2386			1.57921			0.789606	−	0.613614i	$-0.210285\pi$
$443$	33.2386			1.57921			0.789606	+	0.613614i	$0.210285\pi$
$444$	11.0104	−	7.55287i	0.522530	−	0.358443i
$445$			5.08025i			0.240827i
$446$	−4.51049	−	14.5489i	−0.213578	−	0.688911i
$447$	8.35907			0.395370
$448$	−4.98359	−	21.0040i	−0.235453	−	0.992347i
$449$	7.52893			0.355312			0.177656	−	0.984093i	$-0.443149\pi$
$449$	7.52893			0.355312			0.177656	+	0.984093i	$0.443149\pi$
$450$	−3.91841	+	1.21479i	−0.184715	+	0.0572660i
$451$		−	2.20265i		−	0.103719i
$452$	11.9092	+	17.3609i	0.560161	+	0.816589i
$453$			19.1949i			0.901853i
$454$	9.87530	+	31.8535i	0.463471	+	1.49496i
$455$	−11.5344			−0.540742
$456$	14.4762	+	11.4434i	0.677911	+	0.535885i
$457$	11.0810			0.518345			0.259173	−	0.965831i	$-0.416550\pi$
$457$	11.0810			0.518345			0.259173	+	0.965831i	$0.416550\pi$
$458$	0.0269323	+	0.0868721i	0.00125846	+	0.00405927i
$459$	2.16410			0.101011
$460$	12.6063	−	8.64766i	0.587774	−	0.403199i
$461$	−8.38194			−0.390386			−0.195193	−	0.980765i	$-0.562533\pi$
$461$	−8.38194			−0.390386			−0.195193	+	0.980765i	$0.562533\pi$
$462$	−14.4443	+	4.47805i	−0.672008	+	0.208338i
$463$	2.55096			0.118553			0.0592766	−	0.998242i	$-0.481121\pi$
$463$	2.55096			0.118553			0.0592766	+	0.998242i	$0.481121\pi$
$464$	2.13538	−	5.53351i	0.0991323	−	0.256887i
$465$		−	6.38963i		−	0.296312i
$466$	−1.99958	−	6.44978i	−0.0926286	−	0.298780i
$467$		−	12.9673i		−	0.600053i	−0.953931	−	0.300026i	$-0.903004\pi$
$467$		−	12.9673i		−	0.600053i	0.953931	−	0.300026i	$-0.0969955\pi$
$468$	3.33783	+	4.86581i	0.154291	+	0.224922i
$469$	4.99412	+	21.5153i	0.230607	+	0.993484i
$470$	19.5895	−	6.07318i	0.903595	−	0.280135i
$471$	10.3625			0.477477
$472$	−17.7021	−	13.9934i	−0.814805	−	0.644099i
$473$	41.6945			1.91711
$474$	−16.9340	+	5.24991i	−0.777802	+	0.241136i
$475$			18.9253i			0.868354i
$476$	−9.63097	+	6.60662i	−0.441435	+	0.302814i
$477$		−	3.34580i		−	0.153194i
$478$	−17.8605	+	5.53716i	−0.816920	+	0.253264i
$479$		−	4.68023i		−	0.213845i	−0.994267	−	0.106922i	$-0.965900\pi$
$479$		−	4.68023i		−	0.213845i	0.994267	−	0.106922i	$-0.0340997\pi$
$480$	8.17718	+	0.554159i	0.373236	+	0.0252938i
$481$		−	19.6962i		−	0.898067i
$482$	−36.4640	+	11.3047i	−1.66089	+	0.514914i
$483$			14.2358i			0.647753i
$484$	7.75785	−	5.32170i	0.352629	−	0.241896i
$485$	−12.3885			−0.562535
$486$	1.35079	−	0.418775i	0.0612730	−	0.0189960i
$487$	8.34042			0.377940			0.188970	−	0.981983i	$-0.439485\pi$
$487$	8.34042			0.377940			0.188970	+	0.981983i	$0.439485\pi$
$488$	−1.87208	−	1.47987i	−0.0847451	−	0.0669906i
$489$		−	2.48121i		−	0.112204i
$490$	−0.170695	−	0.550589i	−0.00771121	−	0.0248731i
$491$		−	13.4563i		−	0.607276i	−0.952787	−	0.303638i	$-0.901799\pi$
$491$		−	13.4563i		−	0.607276i	0.952787	−	0.303638i	$-0.0982014\pi$
$492$	−0.628839	−	0.916705i	−0.0283502	−	0.0413283i
$493$	−3.20894			−0.144523
$494$	26.0001	−	8.06062i	1.16980	−	0.362664i
$495$		−	5.74152i		−	0.258062i
$496$	6.35099	−	16.4576i	0.285168	−	0.738970i
$497$			36.2496i			1.62602i
$498$	3.40788	+	10.9924i	0.152711	+	0.492580i
$499$	−26.3904			−1.18140			−0.590698	−	0.806893i	$-0.701147\pi$
$499$	−26.3904			−1.18140			−0.590698	+	0.806893i	$0.701147\pi$
$500$	12.9507	+	18.8792i	0.579174	+	0.844305i
$501$		−	12.4615i		−	0.556739i
$502$	16.1593	−	5.00976i	0.721227	−	0.223596i
$503$	−3.05618			−0.136268			−0.0681342	−	0.997676i	$-0.521705\pi$
$503$	−3.05618			−0.136268			−0.0681342	+	0.997676i	$0.521705\pi$
$504$	−4.73302	+	5.98742i	−0.210825	+	0.266701i
$505$	21.6018			0.961266
$506$	−8.75509	−	28.2402i	−0.389211	−	1.25543i
$507$	−4.29570			−0.190779
$508$	1.55181	+	2.26219i	0.0688503	+	0.100368i
$509$	−37.5647			−1.66502			−0.832512	−	0.554007i	$-0.813098\pi$
$509$	−37.5647			−1.66502			−0.832512	+	0.554007i	$0.813098\pi$
$510$	−1.31305	−	4.23533i	−0.0581428	−	0.187544i
$511$	−22.8383			−1.01031
$512$	20.5110	+	9.55507i	0.906466	+	0.422278i
$513$		−	6.52411i		−	0.288046i
$514$	−1.97879	+	0.613471i	−0.0872809	+	0.0270590i
$515$	13.4993			0.594850
$516$	17.3526	−	11.9035i	0.763904	−	0.524020i
$517$		−	39.6657i		−	1.74450i
$518$	24.3336	−	7.54398i	1.06916	−	0.331463i
$519$	−11.2618			−0.494340
$520$	7.49762	−	9.48473i	0.328792	−	0.415933i
$521$			8.26338i			0.362025i	0.983481	+	0.181013i	$0.0579375\pi$
$521$			8.26338i			0.362025i	−0.983481	+	0.181013i	$0.942062\pi$
$522$	−2.00296	+	0.620963i	−0.0876672	+	0.0271788i
$523$		−	10.0503i		−	0.439468i	−0.975560	−	0.219734i	$-0.929481\pi$
$523$		−	10.0503i		−	0.439468i	0.975560	−	0.219734i	$-0.0705190\pi$
$524$	13.6323	+	19.8728i	0.595530	+	0.868148i
$525$	−7.82758			−0.341624
$526$	0.0137269	+	0.0442771i	0.000598521	+	0.00193057i
$527$	−9.54397			−0.415742
$528$	5.70679	−	14.7883i	0.248356	−	0.643578i
$529$	−4.83265			−0.210115
$530$	−6.54803	+	2.03004i	−0.284428	+	0.0881792i
$531$			7.97794i			0.346213i
$532$	19.9170	+	29.0345i	0.863511	+	1.25881i
$533$	−1.63987			−0.0710305
$534$	4.73640	−	1.46839i	0.204964	−	0.0635434i
$535$	11.7836			0.509449
$536$	−20.9383	−	9.87875i	−0.904395	−	0.426697i
$537$	−24.6622			−1.06425
$538$	−18.7552	+	5.81454i	−0.808595	+	0.250683i
$539$	−1.11486			−0.0480203
$540$	−1.63916	−	2.38953i	−0.0705382	−	0.102829i
$541$			45.6660i			1.96333i	0.190603	+	0.981667i	$0.438956\pi$
$541$			45.6660i			1.96333i	−0.190603	+	0.981667i	$0.561044\pi$
$542$	−2.28512	+	0.708439i	−0.0981543	+	0.0304300i
$543$	−23.7830			−1.02063
$544$	0.827728	−	12.2140i	0.0354885	−	0.523670i
$545$	−5.62962			−0.241146
$546$	3.33390	+	10.7537i	0.142678	+	0.460217i
$547$	40.9128			1.74930			0.874652	−	0.484751i	$-0.161090\pi$
$547$	40.9128			1.74930			0.874652	+	0.484751i	$0.161090\pi$
$548$	−10.5450	−	15.3722i	−0.450459	−	0.656668i
$549$			0.843705i			0.0360084i
$550$	15.5279	−	4.81400i	0.662112	−	0.205269i
$551$			9.67400i			0.412126i
$552$	−11.7061	−	9.25359i	−0.498244	−	0.393859i
$553$	−33.8280			−1.43851
$554$	1.13676	−	0.352421i	0.0482963	−	0.0149729i
$555$			9.67249i			0.410574i
$556$	11.3668	−	7.79733i	0.482058	−	0.330680i
$557$	36.4189			1.54312			0.771559	−	0.636158i	$-0.219478\pi$
$557$	36.4189			1.54312			0.771559	+	0.636158i	$0.219478\pi$
$558$	−5.95716	+	1.84685i	−0.252187	+	0.0781836i
$559$		−	31.0415i		−	1.31291i
$560$	14.5896	+	5.63013i	0.616525	+	0.237916i
$561$	−8.57590			−0.362075
$562$	10.6708	+	34.4193i	0.450119	+	1.45189i
$563$	−1.44035			−0.0607034			−0.0303517	−	0.999539i	$-0.509663\pi$
$563$	−1.44035			−0.0607034			−0.0303517	+	0.999539i	$0.509663\pi$
$564$	−11.3243	−	16.5082i	−0.476837	−	0.695121i
$565$	−15.2514			−0.641630
$566$	0.813532	+	2.62411i	0.0341953	+	0.110299i
$567$	2.69839			0.113322
$568$	−29.8079	−	23.5630i	−1.25071	−	0.988681i
$569$	18.7895			0.787696			0.393848	−	0.919176i	$-0.371144\pi$
$569$	18.7895			0.787696			0.393848	+	0.919176i	$0.371144\pi$
$570$	−12.7683	+	3.95845i	−0.534804	+	0.165801i
$571$			24.5716i			1.02829i	0.857704	+	0.514144i	$0.171890\pi$
$571$			24.5716i			1.02829i	−0.857704	+	0.514144i	$0.828110\pi$
$572$	−13.2272	−	19.2823i	−0.553056	−	0.806232i
$573$	−11.8983			−0.497060
$574$	−0.628098	−	2.02598i	−0.0262163	−	0.0845626i
$575$		−	15.3038i		−	0.638213i
$576$	−1.84687	−	7.78390i	−0.0769531	−	0.324329i
$577$		−	45.3105i		−	1.88630i	−0.332364	−	0.943151i	$-0.607846\pi$
$577$		−	45.3105i		−	1.88630i	0.332364	−	0.943151i	$-0.392154\pi$
$578$	16.6372	−	5.15791i	0.692017	−	0.214541i
$579$	19.2001			0.797928
$580$	2.43056	+	3.54321i	0.100924	+	0.147124i
$581$			21.9589i			0.911007i
$582$	3.58077	+	11.5500i	0.148428	+	0.478765i
$583$			13.2588i			0.549122i
$584$	14.8454	−	18.7799i	0.614307	−	0.777118i
$585$	−4.27455			−0.176731
$586$	31.0764	−	9.63438i	1.28375	−	0.397993i
$587$	−15.4815			−0.638989			−0.319494	−	0.947588i	$-0.603513\pi$
$587$	−15.4815			−0.638989			−0.319494	+	0.947588i	$0.603513\pi$
$588$	−0.463986	+	0.318283i	−0.0191344	+	0.0131258i
$589$			28.7722i			1.18554i
$590$	15.6135	−	4.84055i	0.642799	−	0.199282i
$591$		−	8.66502i		−	0.356431i
$592$	−9.61399	+	24.9132i	−0.395133	+	1.02393i
$593$			11.4597i			0.470595i	0.971923	+	0.235298i	$0.0756065\pi$
$593$			11.4597i			0.470595i	−0.971923	+	0.235298i	$0.924394\pi$
$594$	−5.35291	+	1.65952i	−0.219633	+	0.0680911i
$595$		−	8.46069i		−	0.346855i
$596$	−13.7862	+	9.45704i	−0.564706	+	0.387376i
$597$		−	3.96638i		−	0.162333i
$598$	−21.0248	+	6.51815i	−0.859767	+	0.266547i
$599$	−13.2447			−0.541163			−0.270581	−	0.962697i	$-0.587216\pi$
$599$	−13.2447			−0.541163			−0.270581	+	0.962697i	$0.587216\pi$
$600$	5.08810	−	6.43660i	0.207721	−	0.262773i
$601$	15.7272			0.641526			0.320763	−	0.947159i	$-0.396061\pi$
$601$	15.7272			0.641526			0.320763	+	0.947159i	$0.396061\pi$
$602$	38.3502	−	11.8894i	1.56304	−	0.484577i
$603$	1.85078	+	7.97337i	0.0753694	+	0.324701i
$604$	−21.7161	−	31.6572i	−0.883617	−	1.28811i
$605$			6.81517i			0.277076i
$606$	−6.24375	−	20.1397i	−0.253635	−	0.818119i
$607$			11.7838i			0.478289i	0.970984	+	0.239144i	$0.0768669\pi$
$607$			11.7838i			0.478289i	−0.970984	+	0.239144i	$0.923133\pi$
$608$	−36.8215	−	2.49535i	−1.49331	−	0.101200i
$609$	−4.00120			−0.162137
$610$	1.65121	−	0.511911i	0.0668554	−	0.0207267i
$611$	−29.5311			−1.19470
$612$	−3.56915	+	2.44835i	−0.144274	+	0.0989688i
$613$	15.6126			0.630588			0.315294	−	0.948994i	$-0.397897\pi$
$613$	15.6126			0.630588			0.315294	+	0.948994i	$0.397897\pi$
$614$	11.7661	+	37.9524i	0.474841	+	1.53163i
$615$	0.805314			0.0324734
$616$	18.7560	−	23.7270i	0.755703	−	0.955988i
$617$	28.6395			1.15298			0.576491	−	0.817103i	$-0.304421\pi$
$617$	28.6395			1.15298			0.576491	+	0.817103i	$0.304421\pi$
$618$	−3.90182	−	12.5856i	−0.156954	−	0.506268i
$619$		−	7.35717i		−	0.295710i	−0.989009	−	0.147855i	$-0.952763\pi$
$619$		−	7.35717i		−	0.295710i	0.989009	−	0.147855i	$-0.0472368\pi$
$620$	7.22892	+	10.5381i	0.290320	+	0.423222i
$621$			5.27567i			0.211705i
$622$	−29.0566	+	9.00821i	−1.16506	+	0.361196i
$623$	9.46164			0.379073
$624$	−11.0099	−	4.24870i	−0.440748	−	0.170084i
$625$	−2.08102			−0.0832410
$626$	−14.7778	−	47.6670i	−0.590642	−	1.90516i
$627$			25.8538i			1.03250i
$628$	−17.0903	+	11.7236i	−0.681979	+	0.467822i
$629$	14.4475			0.576058
$630$	−1.63723	−	5.28100i	−0.0652288	−	0.210400i
$631$	3.20849			0.127728			0.0638640	−	0.997959i	$-0.479658\pi$
$631$	3.20849			0.127728			0.0638640	+	0.997959i	$0.479658\pi$
$632$	21.9889	−	27.8167i	0.874673	−	1.10649i
$633$			16.2868i			0.647342i
$634$	−23.6994	+	7.34735i	−0.941224	+	0.291800i
$635$	−1.98730			−0.0788637
$636$	3.78527	+	5.51808i	0.150096	+	0.218806i
$637$			0.830010i			0.0328862i
$638$	7.93735	−	2.46076i	0.314243	−	0.0974222i
$639$			13.4338i			0.531431i
$640$	−14.1132	+	8.33732i	−0.557874	+	0.329561i
$641$		−	7.07704i		−	0.279526i	−0.990185	−	0.139763i	$-0.955366\pi$
$641$		−	7.07704i		−	0.279526i	0.990185	−	0.139763i	$-0.0446341\pi$
$642$	−3.40592	−	10.9860i	−0.134421	−	0.433585i
$643$			25.8835i			1.02075i	0.859953	+	0.510373i	$0.170493\pi$
$643$			25.8835i			1.02075i	−0.859953	+	0.510373i	$0.829507\pi$
$644$	−16.1057	−	23.4785i	−0.634654	−	0.925183i
$645$			15.2440i			0.600232i
$646$	5.91260	+	19.0715i	0.232628	+	0.750358i
$647$	26.9464			1.05937			0.529686	−	0.848194i	$-0.322310\pi$
$647$	26.9464			1.05937			0.529686	+	0.848194i	$0.322310\pi$
$648$	−1.75401	+	2.21888i	−0.0689042	+	0.0871659i
$649$		−	31.6150i		−	1.24100i
$650$	−3.58401	−	11.5605i	−0.140577	−	0.453440i
$651$	−11.9003			−0.466409
$652$	2.80712	+	4.09215i	0.109935	+	0.160261i
$653$			17.6046i			0.688923i	0.938800	+	0.344461i	$0.111938\pi$
$653$			17.6046i			0.688923i	−0.938800	+	0.344461i	$0.888062\pi$
$654$	1.62718	+	5.24858i	0.0636277	+	0.205236i
$655$	−17.4580			−0.682142
$656$	2.07423	+	0.800444i	0.0809851	+	0.0312521i
$657$	−8.46368			−0.330200
$658$	−11.3109	−	36.4842i	−0.440945	−	1.42230i
$659$		−	14.9244i		−	0.581373i	−0.956818	−	0.290686i	$-0.906116\pi$
$659$		−	14.9244i		−	0.581373i	0.956818	−	0.290686i	$-0.0938836\pi$
$660$	6.49567	+	9.46923i	0.252844	+	0.368589i
$661$		−	43.8582i		−	1.70589i	−0.522003	−	0.852944i	$-0.674815\pi$
$661$		−	43.8582i		−	1.70589i	0.522003	−	0.852944i	$-0.325185\pi$
$662$	−16.7266	+	5.18562i	−0.650098	+	0.201545i
$663$			6.38475i			0.247963i
$664$	−18.0567	−	14.2737i	−0.700736	−	0.553928i
$665$	−25.5065			−0.989098
$666$	9.01782	−	2.79573i	0.349434	−	0.108332i
$667$		−	7.82280i		−	0.302900i
$668$	14.0983	+	20.5522i	0.545481	+	0.795189i
$669$		−	10.7707i		−	0.416419i
$670$	14.4817	−	8.45991i	0.559475	−	0.326835i
$671$		−	3.34344i		−	0.129072i
$672$	1.03209	−	15.2295i	0.0398136	−	0.587490i
$673$		−	28.4231i		−	1.09563i	−0.836600	−	0.547814i	$-0.815460\pi$
$673$		−	28.4231i		−	1.09563i	0.836600	−	0.547814i	$-0.184540\pi$
$674$	2.38283	+	7.68600i	0.0917833	+	0.296054i
$675$	−2.90083			−0.111653
$676$	7.08471	−	4.85995i	0.272489	−	0.186921i
$677$		−	27.2748i		−	1.04826i	−0.851639	−	0.524128i	$-0.824391\pi$
$677$		−	27.2748i		−	1.04826i	0.851639	−	0.524128i	$-0.175609\pi$
$678$	4.40824	+	14.2191i	0.169297	+	0.546081i
$679$			23.0729i			0.885456i
$680$	6.95720	+	5.49963i	0.266797	+	0.210901i
$681$			23.5814i			0.903642i
$682$	23.6071	−	7.31873i	0.903962	−	0.280249i
$683$	−34.6542			−1.32601			−0.663004	−	0.748616i	$-0.730719\pi$
$683$	−34.6542			−1.32601			−0.663004	+	0.748616i	$0.730719\pi$
$684$	7.38106	+	10.7599i	0.282222	+	0.411416i
$685$	13.5043			0.515972
$686$	24.4893	−	7.59222i	0.935005	−	0.289872i
$687$			0.0643122i			0.00245366i
$688$	−15.1518	+	39.2637i	−0.577658	+	1.49691i
$689$	9.87113			0.376060
$690$	10.3250	−	3.20097i	0.393064	−	0.121859i
$691$			32.2346i			1.22626i	0.789982	+	0.613130i	$0.210090\pi$
$691$			32.2346i			1.22626i	−0.789982	+	0.613130i	$0.789910\pi$
$692$	18.5736	−	12.7411i	0.706064	−	0.484343i
$693$	−10.6932			−0.406202
$694$	43.5138	−	13.4903i	1.65176	−	0.512083i
$695$			9.98555i			0.378774i
$696$	2.60087	−	3.29018i	0.0985856	−	0.124714i
$697$		−	1.20287i		−	0.0455619i
$698$	−1.10158	+	0.341513i	−0.0416953	+	0.0129265i
$699$		−	4.77483i		−	0.180601i
$700$	12.9097	−	8.85575i	0.487940	−	0.334716i
$701$			39.2528i			1.48256i	0.671197	+	0.741279i	$0.265781\pi$
$701$			39.2528i			1.48256i	−0.671197	+	0.741279i	$0.734219\pi$
$702$	1.23551	+	3.98524i	0.0466314	+	0.150413i
$703$		−	43.5548i		−	1.64270i
$704$	7.31881	+	30.8461i	0.275838	+	1.16256i
$705$	14.5023			0.546187
$706$	0.531746	+	1.71518i	0.0200125	+	0.0645518i
$707$		−	40.2319i		−	1.51308i
$708$	−9.02585	−	13.1577i	−0.339212	−	0.494495i
$709$	−10.8919			−0.409054			−0.204527	−	0.978861i	$-0.565566\pi$
$709$	−10.8919			−0.409054			−0.204527	+	0.978861i	$0.565566\pi$
$710$	26.2911	−	8.15082i	0.986686	−	0.305895i
$711$	−12.5364			−0.470150
$712$	−6.15027	+	7.78028i	−0.230491	+	0.291578i
$713$		−	23.2664i		−	0.871334i
$714$	−7.88804	+	2.44547i	−0.295203	+	0.0915194i
$715$	16.9392			0.633491
$716$	40.6743	−	27.9017i	1.52007	−	1.04273i
$717$	−13.2223			−0.493795
$718$	5.74447	+	18.5292i	0.214382	+	0.691504i
$719$			5.20499i			0.194113i	0.995279	+	0.0970567i	$0.0309428\pi$
$719$			5.20499i			0.194113i	−0.995279	+	0.0970567i	$0.969057\pi$
$720$	5.40679	+	2.08647i	0.201499	+	0.0777583i
$721$		−	25.1416i		−	0.936321i
$722$	31.8299	−	9.86800i	1.18459	−	0.367249i
$723$	−26.9947			−1.00394
$724$	39.2242	−	26.9069i	1.45776	−	0.999987i
$725$	4.30138			0.159749
$726$	6.35390	−	1.96985i	0.235815	−	0.0731080i
$727$	24.1729			0.896523			0.448262	−	0.893902i	$-0.352043\pi$
$727$	24.1729			0.896523			0.448262	+	0.893902i	$0.352043\pi$
$728$	−17.6647	−	13.9638i	−0.654698	−	0.517535i
$729$	1.00000			0.0370370
$730$	5.13527	+	16.5642i	0.190065	+	0.613068i
$731$	22.7694			0.842158
$732$	−0.954527	−	1.39149i	−0.0352803	−	0.0514308i
$733$			43.1100i			1.59230i	0.605098	+	0.796151i	$0.293134\pi$
$733$			43.1100i			1.59230i	−0.605098	+	0.796151i	$0.706866\pi$
$734$	−43.5586	+	13.5041i	−1.60778	+	0.498447i
$735$		−	0.407606i		−	0.0150348i
$736$	29.7754	+	2.01785i	1.09754	+	0.0743788i
$737$	−7.33427	−	31.5969i	−0.270161	−	1.16389i
$738$	−0.232767	−	0.750808i	−0.00856828	−	0.0276376i
$739$	33.6770			1.23883			0.619414	−	0.785065i	$-0.287370\pi$
$739$	33.6770			1.23883			0.619414	+	0.785065i	$0.287370\pi$
$740$	−10.9430	−	15.9524i	−0.402272	−	0.586422i
$741$	19.2481			0.707097
$742$	3.78082	+	12.1953i	0.138798	+	0.447703i
$743$		−	0.0899782i		−	0.00330098i	−0.999999	−	0.00165049i	$-0.999475\pi$
$743$		−	0.0899782i		−	0.00330098i	0.999999	−	0.00165049i	$-0.000525368\pi$
$744$	7.73544	−	9.78558i	0.283595	−	0.358757i
$745$		−	12.1110i		−	0.443714i
$746$	−11.5117	−	37.1317i	−0.421472	−	1.35949i
$747$			8.13775i			0.297745i
$748$	14.1439	−	9.70236i	0.517151	−	0.354753i
$749$		−	21.9462i		−	0.801897i
$750$	4.79377	+	15.4626i	0.175044	+	0.564616i
$751$			46.3689i			1.69202i	0.533163	+	0.846012i	$0.321003\pi$
$751$			46.3689i			1.69202i	−0.533163	+	0.846012i	$0.678997\pi$
$752$	37.3532	+	14.4146i	1.36213	+	0.525645i
$753$	11.9629			0.435952
$754$	−1.83203	−	5.90934i	−0.0667186	−	0.215206i
$755$	27.8105			1.01213
$756$	−4.45034	+	3.05283i	−0.161857	+	0.111030i
$757$		−	2.66667i		−	0.0969218i	−0.998825	−	0.0484609i	$-0.984568\pi$
$757$		−	2.66667i		−	0.0969218i	0.998825	−	0.0484609i	$-0.0154316\pi$
$758$	−34.0334	+	10.5511i	−1.23615	+	0.383234i
$759$		−	20.9065i		−	0.758856i
$760$	16.5797	−	20.9739i	0.601410	−	0.760803i
$761$	−17.3962			−0.630610			−0.315305	−	0.948990i	$-0.602107\pi$
$761$	−17.3962			−0.630610			−0.315305	+	0.948990i	$0.602107\pi$
$762$	0.574408	+	1.85280i	0.0208086	+	0.0671197i
$763$			10.4848i			0.379575i
$764$	19.6234	−	13.4612i	0.709949	−	0.487009i
$765$		−	3.13545i		−	0.113363i
$766$	26.8221	−	8.31545i	0.969122	−	0.300450i
$767$	−23.5373			−0.849884
$768$	11.8523	+	10.7482i	0.427683	+	0.387841i
$769$			29.7726i			1.07363i	0.843701	+	0.536814i	$0.180372\pi$
$769$			29.7726i			1.07363i	−0.843701	+	0.536814i	$0.819628\pi$
$770$	6.48802	+	20.9276i	0.233812	+	0.754178i
$771$	−1.46492			−0.0527578
$772$	−31.6658	+	21.7220i	−1.13968	+	0.781793i
$773$	−0.713969			−0.0256797			−0.0128398	−	0.999918i	$-0.504087\pi$
$773$	−0.713969			−0.0256797			−0.0128398	+	0.999918i	$0.504087\pi$
$774$	14.2122	−	4.40612i	0.510849	−	0.158375i
$775$	12.7931			0.459541
$776$	−18.9728	−	14.9979i	−0.681083	−	0.538392i
$777$	18.0144			0.646263
$778$	−23.4420	+	7.26755i	−0.840437	+	0.260554i
$779$	−3.62629			−0.129925
$780$	7.04983	−	4.83602i	0.252424	−	0.173157i
$781$		−	53.2354i		−	1.90491i
$782$	−4.78117	−	15.4220i	−0.170974	−	0.551490i
$783$	−1.48281			−0.0529913
$784$	0.405141	−	1.04986i	0.0144693	−	0.0374950i
$785$		−	15.0137i		−	0.535861i
$786$	5.04605	+	16.2764i	0.179987	+	0.580560i
$787$	6.76258			0.241060			0.120530	−	0.992710i	$-0.461541\pi$
$787$	6.76258			0.241060			0.120530	+	0.992710i	$0.461541\pi$
$788$	9.80319	+	14.2908i	0.349224	+	0.509090i
$789$			0.0327787i			0.00116695i
$790$	7.60633	+	24.5348i	0.270621	+	0.872908i
$791$			28.4047i			1.00995i
$792$	6.95082	−	8.79300i	0.246987	−	0.312446i
$793$	−2.48919			−0.0883936
$794$	21.4773	−	6.65844i	0.762200	−	0.236299i
$795$	−4.84756			−0.171925
$796$	4.48737	+	6.54157i	0.159051	+	0.231860i
$797$	−32.7523			−1.16015			−0.580074	−	0.814564i	$-0.696976\pi$
$797$	−32.7523			−1.16015			−0.580074	+	0.814564i	$0.696976\pi$
$798$	7.37236	+	23.7801i	0.260979	+	0.841806i
$799$		−	21.6615i		−	0.766329i
$800$	−1.10952	+	16.3720i	−0.0392273	+	0.578839i
$801$	3.50640			0.123892
$802$	1.97502	+	6.37057i	0.0697404	+	0.224953i
$803$	33.5399			1.18360
$804$	−12.0731	−	11.0562i	−0.425785	−	0.389924i
$805$	20.6256			0.726957
$806$	−5.44878	−	17.5754i	−0.191925	−	0.619069i
$807$	−13.8847			−0.488763
$808$	33.0826	+	26.1516i	1.16384	+	0.920010i
$809$		−	55.7199i		−	1.95901i	−0.201428	−	0.979503i	$-0.564558\pi$
$809$		−	55.7199i		−	1.95901i	0.201428	−	0.979503i	$-0.435442\pi$
$810$	−0.606742	−	1.95709i	−0.0213187	−	0.0687651i
$811$	42.0272			1.47578			0.737888	−	0.674923i	$-0.235823\pi$
$811$	42.0272			1.47578			0.737888	+	0.674923i	$0.235823\pi$
$812$	6.59901	−	4.52677i	0.231580	−	0.158858i
$813$	−1.69169			−0.0593303
$814$	−35.7359	+	11.0789i	−1.25254	+	0.388316i
$815$	−3.59490			−0.125924
$816$	3.11649	−	8.07592i	0.109099	−	0.282714i
$817$		−	68.6431i		−	2.40152i
$818$	−5.13592	−	16.5663i	−0.179573	−	0.579226i
$819$			7.96108i			0.278183i
$820$	−1.32817	+	0.911093i	−0.0463817	+	0.0318168i
$821$	−29.2823			−1.02196			−0.510979	−	0.859593i	$-0.670717\pi$
$821$	−29.2823			−1.02196			−0.510979	+	0.859593i	$0.670717\pi$
$822$	−3.90327	−	12.5903i	−0.136142	−	0.439136i
$823$			2.20991i			0.0770328i	0.999258	+	0.0385164i	$0.0122632\pi$
$823$			2.20991i			0.0770328i	−0.999258	+	0.0385164i	$0.987737\pi$
$824$	20.6738	+	16.3426i	0.720208	+	0.569320i
$825$	11.4954			0.400220
$826$	−9.01522	−	29.0792i	−0.313680	−	1.01180i
$827$			27.6877i			0.962794i	0.876503	+	0.481397i	$0.159870\pi$
$827$			27.6877i			0.962794i	−0.876503	+	0.481397i	$0.840130\pi$
$828$	−5.96863	−	8.70092i	−0.207424	−	0.302378i
$829$	32.3072			1.12208			0.561038	−	0.827790i	$-0.310402\pi$
$829$	32.3072			1.12208			0.561038	+	0.827790i	$0.310402\pi$
$830$	15.9263	−	4.93751i	0.552810	−	0.171384i
$831$	0.841553			0.0291931
$832$	22.9649	−	5.44884i	0.796164	−	0.188905i
$833$	−0.608826			−0.0210946
$834$	9.30970	−	2.88621i	0.322368	−	0.0999414i
$835$	−18.0549			−0.624814
$836$	−29.2497	−	42.6395i	−1.01162	−	1.47472i
$837$	−4.41014			−0.152437
$838$	9.27213	+	29.9079i	0.320300	+	1.03315i
$839$			48.7324i			1.68243i	0.540700	+	0.841215i	$0.318159\pi$
$839$			48.7324i			1.68243i	−0.540700	+	0.841215i	$0.681841\pi$
$840$	8.67488	+	6.85744i	0.299312	+	0.236604i
$841$	−26.8013			−0.924182
$842$	−14.4679	+	4.48538i	−0.498598	+	0.154576i
$843$			25.4809i			0.877609i
$844$	−18.4261	−	26.8611i	−0.634252	−	0.924597i
$845$			6.22383i			0.214106i
$846$	−4.19172	−	13.5207i	−0.144114	−	0.464851i
$847$	12.6928			0.436131
$848$	−12.4858	−	4.81825i	−0.428763	−	0.165459i
$849$			1.94265i			0.0666715i
$850$	8.47981	−	2.62893i	0.290855	−	0.0901717i
$851$			35.2202i			1.20733i
$852$	−15.1983	−	22.1557i	−0.520685	−	0.759042i
$853$	−13.2588			−0.453972			−0.226986	−	0.973898i	$-0.572887\pi$
$853$	−13.2588			−0.453972			−0.226986	+	0.973898i	$0.572887\pi$
$854$	−0.953402	−	3.07527i	−0.0326248	−	0.105234i
$855$	−9.45246			−0.323267
$856$	18.0463	+	14.2655i	0.616810	+	0.487585i
$857$		−	30.1113i		−	1.02858i	−0.857615	−	0.514292i	$-0.828055\pi$
$857$		−	30.1113i		−	1.02858i	0.857615	−	0.514292i	$-0.171945\pi$
$858$	−4.89610	−	15.7927i	−0.167150	−	0.539155i
$859$			16.9557i			0.578520i	0.957251	+	0.289260i	$0.0934092\pi$
$859$			16.9557i			0.578520i	−0.957251	+	0.289260i	$0.906591\pi$
$860$	−17.2463	−	25.1413i	−0.588095	−	0.857310i
$861$		−	1.49985i		−	0.0511147i
$862$	−13.4861	−	43.5004i	−0.459338	−	1.48163i
$863$		−	8.44174i		−	0.287360i	−0.989624	−	0.143680i	$-0.954106\pi$
$863$		−	8.44174i		−	0.287360i	0.989624	−	0.143680i	$-0.0458936\pi$
$864$	0.382482	−	5.64391i	0.0130123	−	0.192010i
$865$			16.3167i			0.554785i
$866$	10.3168	+	33.2777i	0.350580	+	1.13082i
$867$	12.3167			0.418296
$868$	19.6266	−	13.4634i	0.666171	−	0.456978i
$869$	49.6792			1.68525
$870$	0.899682	+	2.90199i	0.0305021	+	0.0983867i
$871$	−23.5239	+	5.46035i	−0.797076	+	0.185017i
$872$	−8.62163	−	6.81535i	−0.291965	−	0.230797i
$873$			8.55060i			0.289394i
$874$	−46.4928	+	14.4138i	−1.57264	+	0.487554i
$875$			30.8889i			1.04423i
$876$	13.9588	−	9.57539i	0.471623	−	0.323523i
$877$	11.1355			0.376019			0.188009	−	0.982167i	$-0.439796\pi$
$877$	11.1355			0.376019			0.188009	+	0.982167i	$0.439796\pi$
$878$	10.0161	+	32.3075i	0.338025	+	1.09033i
$879$	23.0061			0.775977
$880$	−21.4261	−	8.26830i	−0.722272	−	0.278724i
$881$	−23.6744			−0.797612			−0.398806	−	0.917035i	$-0.630575\pi$
$881$	−23.6744			−0.797612			−0.398806	+	0.917035i	$0.630575\pi$
$882$	−0.380018	+	0.117814i	−0.0127959	+	0.00396700i
$883$	−30.0216			−1.01031			−0.505154	−	0.863029i	$-0.668564\pi$
$883$	−30.0216			−1.01031			−0.505154	+	0.863029i	$0.668564\pi$
$884$	−7.22339	−	10.5301i	−0.242949	−	0.354165i
$885$	11.5588			0.388546
$886$	−44.8982	+	13.9195i	−1.50839	+	0.467634i
$887$			42.8508i			1.43879i	0.694602	+	0.719395i	$0.255581\pi$
$887$			42.8508i			1.43879i	−0.694602	+	0.719395i	$0.744419\pi$
$888$	−11.7097	+	14.8132i	−0.392953	+	0.497098i
$889$			3.70123i			0.124135i
$890$	−2.12748	−	6.86234i	−0.0713132	−	0.230026i
$891$	−3.96281			−0.132759
$892$	12.1854	+	17.7636i	0.407998	+	0.594770i
$893$	−65.3030			−2.18528
$894$	−11.2913	+	3.50057i	−0.377638	+	0.117076i
$895$			35.7319i			1.19439i
$896$	15.5277	+	26.2850i	0.518745	+	0.878119i
$897$	−15.5648			−0.519694
$898$	−10.1700	+	3.15293i	−0.339377	+	0.105214i
$899$	6.53939			0.218101
$900$	4.78421	−	3.28186i	0.159474	−	0.109395i
$901$			7.24064i			0.241221i
$902$	0.922412	+	2.97531i	0.0307130	+	0.0990669i
$903$	28.3910			0.944794
$904$	−23.3571	−	18.4637i	−0.776846	−	0.614092i
$905$			34.4580i			1.14542i
$906$	−8.03832	−	25.9282i	−0.267055	−	0.861406i
$907$			46.1216i			1.53144i	0.643173	+	0.765721i	$0.277618\pi$
$907$			46.1216i			1.53144i	−0.643173	+	0.765721i	$0.722382\pi$
$908$	−26.6789	−	38.8918i	−0.885370	−	1.29067i
$909$		−	14.9096i		−	0.494520i
$910$	15.5806	−	4.83032i	0.516491	−	0.160124i
$911$			21.1620i			0.701128i	0.936539	+	0.350564i	$0.114010\pi$
$911$			21.1620i			0.701128i	−0.936539	+	0.350564i	$0.885990\pi$
$912$	−24.3465	−	9.39529i	−0.806193	−	0.311109i
$913$		−	32.2483i		−	1.06726i
$914$	−14.9680	+	4.64042i	−0.495098	+	0.153492i
$915$	1.22240			0.0404114
$916$	−0.0727597	−	0.106067i	−0.00240405	−	0.00350456i
$917$			32.5145i			1.07372i
$918$	−2.92324	+	0.906269i	−0.0964812	+	0.0299113i
$919$	−13.8987			−0.458475			−0.229237	−	0.973371i	$-0.573623\pi$
$919$	−13.8987			−0.458475			−0.229237	+	0.973371i	$0.573623\pi$
$920$	−13.4071	+	16.9604i	−0.442018	+	0.559167i
$921$			28.0965i			0.925810i
$922$	11.3222	−	3.51014i	0.372878	−	0.115600i
$923$	−39.6337			−1.30456
$924$	17.6358	−	12.0978i	0.580177	−	0.397988i
$925$	−19.3659			−0.636746
$926$	−3.44580	+	1.06828i	−0.113236	+	0.0351058i
$927$		−	9.31724i		−	0.306018i
$928$	−0.567147	+	8.36884i	−0.0186175	+	0.274721i
$929$			0.371925i			0.0122025i	0.999981	+	0.00610123i	$0.00194210\pi$
$929$			0.371925i			0.0122025i	−0.999981	+	0.00610123i	$0.998058\pi$
$930$	2.67582	+	8.63104i	0.0877435	+	0.283023i
$931$			1.83543i			0.0601538i
$932$	5.40201	+	7.87491i	0.176949	+	0.257951i
$933$	−21.5109			−0.704234
$934$	5.43036	+	17.5160i	0.177687	+	0.573141i
$935$			12.4252i			0.406348i
$936$	−6.54638	−	5.17487i	−0.213975	−	0.169146i
$937$			13.2247i			0.432031i	0.976390	+	0.216016i	$0.0693062\pi$
$937$			13.2247i			0.432031i	−0.976390	+	0.216016i	$0.930694\pi$
$938$	−15.7561	−	26.9712i	−0.514453	−	0.880641i
$939$		−	35.2883i		−	1.15159i
$940$	−23.9179	+	16.4072i	−0.780117	+	0.535142i
$941$			53.5930i			1.74708i	0.486751	+	0.873541i	$0.338182\pi$
$941$			53.5930i			1.74708i	−0.486751	+	0.873541i	$0.661818\pi$
$942$	−13.9975	+	4.33953i	−0.456063	+	0.141390i
$943$	2.93237			0.0954912
$944$	29.7719	+	11.4889i	0.968992	+	0.373933i
$945$		−	3.90957i		−	0.127178i
$946$	−56.3204	+	17.4606i	−1.83113	+	0.567693i
$947$		−	40.5293i		−	1.31703i	−0.752569	−	0.658513i	$-0.771186\pi$
$947$		−	40.5293i		−	1.31703i	0.752569	−	0.658513i	$-0.228814\pi$
$948$	20.6756	−	14.1830i	0.671514	−	0.460643i
$949$		−	24.9704i		−	0.810574i
$950$	−7.92545	−	25.5641i	−0.257136	−	0.829409i
$951$	−17.5449			−0.568932
$952$	10.2427	−	12.9574i	0.331968	−	0.419950i
$953$	−24.0154			−0.777934			−0.388967	−	0.921252i	$-0.627168\pi$
$953$	−24.0154			−0.777934			−0.388967	+	0.921252i	$0.627168\pi$
$954$	1.40114	+	4.51947i	0.0453634	+	0.146323i
$955$			17.2389i			0.557838i
$956$	21.8069	−	14.9590i	0.705286	−	0.483810i
$957$	5.87609			0.189947
$958$	1.95996	+	6.32199i	0.0633234	+	0.204254i
$959$		−	25.1509i		−	0.812165i
$960$	−11.2777	+	2.67584i	−0.363986	+	0.0863625i
$961$	−11.5507			−0.372602
$962$	8.24825	+	26.6053i	0.265934	+	0.857790i
$963$		−	8.13306i		−	0.262084i
$964$	44.5211	−	30.5404i	1.43393	−	0.983641i
$965$		−	27.8181i		−	0.895495i
$966$	−5.96160	−	19.2296i	−0.191811	−	0.618702i
$967$		−	57.2676i		−	1.84160i	−0.390032	−	0.920801i	$-0.627536\pi$
$967$		−	57.2676i		−	1.84160i	0.390032	−	0.920801i	$-0.372464\pi$
$968$	−8.25061	+	10.4373i	−0.265185	+	0.335467i
$969$			14.1188i			0.453561i
$970$	16.7343	−	5.18801i	0.537306	−	0.166577i
$971$		−	10.9938i		−	0.352809i	−0.984318	−	0.176405i	$-0.943553\pi$
$971$		−	10.9938i		−	0.352809i	0.984318	−	0.176405i	$-0.0564467\pi$
$972$	−1.64926	+	1.13135i	−0.0528999	+	0.0362881i
$973$	18.5975			0.596207
$974$	−11.2661	+	3.49276i	−0.360990	+	0.111915i
$975$		−	8.55834i		−	0.274086i
$976$	3.14852	+	1.21501i	0.100782	+	0.0388915i
$977$	−23.9018			−0.764688			−0.382344	−	0.924020i	$-0.624883\pi$
$977$	−23.9018			−0.764688			−0.382344	+	0.924020i	$0.624883\pi$
$978$	1.03907	+	3.35159i	0.0332257	+	0.107172i
$979$	−13.8952			−0.444092
$980$	0.461145	+	0.672246i	0.0147307	+	0.0214741i
$981$			3.88557i			0.124057i
$982$	5.63517	+	18.1767i	0.179826	+	0.580041i
$983$	−9.87634			−0.315006			−0.157503	−	0.987518i	$-0.550344\pi$
$983$	−9.87634			−0.315006			−0.157503	+	0.987518i	$0.550344\pi$
$984$	1.23332	+	0.974933i	0.0393168	+	0.0310797i
$985$	−12.5543			−0.400014
$986$	4.33460	−	1.34382i	0.138042	−	0.0427961i
$987$		−	27.0096i		−	0.859724i
$988$	−31.7450	+	21.7764i	−1.00994	+	0.692799i
$989$			55.5077i			1.76504i
$990$	2.40440	+	7.75557i	0.0764169	+	0.246488i
$991$	54.2663			1.72383			0.861913	−	0.507056i	$-0.169266\pi$
$991$	54.2663			1.72383			0.861913	+	0.507056i	$0.169266\pi$
$992$	−1.68680	+	24.8904i	−0.0535559	+	0.790272i
$993$	−12.3828			−0.392958
$994$	−15.1804	−	48.9655i	−0.481493	−	1.55309i
$995$	−5.74669			−0.182182
$996$	−9.20665	−	13.4212i	−0.291724	−	0.425268i
$997$	−10.5448			−0.333958			−0.166979	−	0.985960i	$-0.553401\pi$
$997$	−10.5448			−0.333958			−0.166979	+	0.985960i	$0.553401\pi$
$998$	35.6478	−	11.0516i	1.12841	−	0.349833i
$999$	6.67597			0.211218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.4	yes	34
4.3	odd	2		804.2.e.b.535.32	yes	34
67.66	odd	2		804.2.e.b.535.31	yes	34
268.267	even	2	inner	804.2.e.a.535.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.3	✓	34	268.267	even	2	inner
804.2.e.a.535.4	yes	34	1.1	even	1	trivial
804.2.e.b.535.31	yes	34	67.66	odd	2
804.2.e.b.535.32	yes	34	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35079 + 0.418775i) q^{2} -1.00000 q^{3} +(1.64926 - 1.13135i) q^{4} +1.44885i q^{5} +(1.35079 - 0.418775i) q^{6} +2.69839 q^{7} +(-1.75401 + 2.21888i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.35079 + 0.418775i) q^{2} -1.00000 q^{3} +(1.64926 - 1.13135i) q^{4} +1.44885i q^{5} +(1.35079 - 0.418775i) q^{6} +2.69839 q^{7} +(-1.75401 + 2.21888i) q^{8} +1.00000 q^{9} +(-0.606742 - 1.95709i) q^{10} -3.96281 q^{11} +(-1.64926 + 1.13135i) q^{12} +2.95030i q^{13} +(-3.64496 + 1.13002i) q^{14} -1.44885i q^{15} +(1.44009 - 3.73177i) q^{16} -2.16410 q^{17} +(-1.35079 + 0.418775i) q^{18} +6.52411i q^{19} +(1.63916 + 2.38953i) q^{20} -2.69839 q^{21} +(5.35291 - 1.65952i) q^{22} -5.27567i q^{23} +(1.75401 - 2.21888i) q^{24} +2.90083 q^{25} +(-1.23551 - 3.98524i) q^{26} -1.00000 q^{27} +(4.45034 - 3.05283i) q^{28} +1.48281 q^{29} +(0.606742 + 1.95709i) q^{30} +4.41014 q^{31} +(-0.382482 + 5.64391i) q^{32} +3.96281 q^{33} +(2.92324 - 0.906269i) q^{34} +3.90957i q^{35} +(1.64926 - 1.13135i) q^{36} -6.67597 q^{37} +(-2.73213 - 8.81269i) q^{38} -2.95030i q^{39} +(-3.21483 - 2.54130i) q^{40} +0.555830i q^{41} +(3.64496 - 1.13002i) q^{42} -10.5214 q^{43} +(-6.53568 + 4.48333i) q^{44} +1.44885i q^{45} +(2.20931 + 7.12631i) q^{46} +10.0095i q^{47} +(-1.44009 + 3.73177i) q^{48} +0.281330 q^{49} +(-3.91841 + 1.21479i) q^{50} +2.16410 q^{51} +(3.33783 + 4.86581i) q^{52} -3.34580i q^{53} +(1.35079 - 0.418775i) q^{54} -5.74152i q^{55} +(-4.73302 + 5.98742i) q^{56} -6.52411i q^{57} +(-2.00296 + 0.620963i) q^{58} +7.97794i q^{59} +(-1.63916 - 2.38953i) q^{60} +0.843705i q^{61} +(-5.95716 + 1.84685i) q^{62} +2.69839 q^{63} +(-1.84687 - 7.78390i) q^{64} -4.27455 q^{65} +(-5.35291 + 1.65952i) q^{66} +(1.85078 + 7.97337i) q^{67} +(-3.56915 + 2.44835i) q^{68} +5.27567i q^{69} +(-1.63723 - 5.28100i) q^{70} +13.4338i q^{71} +(-1.75401 + 2.21888i) q^{72} -8.46368 q^{73} +(9.01782 - 2.79573i) q^{74} -2.90083 q^{75} +(7.38106 + 10.7599i) q^{76} -10.6932 q^{77} +(1.23551 + 3.98524i) q^{78} -12.5364 q^{79} +(5.40679 + 2.08647i) q^{80} +1.00000 q^{81} +(-0.232767 - 0.750808i) q^{82} +8.13775i q^{83} +(-4.45034 + 3.05283i) q^{84} -3.13545i q^{85} +(14.2122 - 4.40612i) q^{86} -1.48281 q^{87} +(6.95082 - 8.79300i) q^{88} +3.50640 q^{89} +(-0.606742 - 1.95709i) q^{90} +7.96108i q^{91} +(-5.96863 - 8.70092i) q^{92} -4.41014 q^{93} +(-4.19172 - 13.5207i) q^{94} -9.45246 q^{95} +(0.382482 - 5.64391i) q^{96} +8.55060i q^{97} +(-0.380018 + 0.117814i) q^{98} -3.96281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

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