LMFDB - Embedded newform 804.2.e.b.535.31

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			535.31
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.32

$q$-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	$-0.894981\pi$
$5$		−	1.44885i		−	0.647946i	0.946066	−	0.323973i	$-0.105019\pi$
$6$	1.35079	−	0.418775i	0.551457	−	0.170964i
$7$	−2.69839			−1.01990			−0.509949	−	0.860205i	$-0.670336\pi$
$7$	−2.69839			−1.01990			−0.509949	+	0.860205i	$0.670336\pi$
$8$	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	$-0.296194\pi$
$11$	3.96281			1.19483			0.597416	+	0.801932i	$0.296194\pi$
$12$	1.64926	−	1.13135i	0.476099	−	0.326593i
$13$		−	2.95030i		−	0.818267i	−0.912474	−	0.409134i	$-0.865831\pi$
$13$		−	2.95030i		−	0.818267i	0.912474	−	0.409134i	$-0.134169\pi$
$14$	−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	$-0.629617\pi$
$31$	−4.41014			−0.792084			−0.396042	+	0.918232i	$0.629617\pi$
$32$	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	$-0.986180\pi$
$41$		−	0.555830i		−	0.0868060i	0.999058	−	0.0434030i	$-0.0138199\pi$
$42$	−3.64496	+	1.13002i	−0.562429	+	0.174366i
$43$	10.5214			1.60451			0.802253	−	0.596984i	$-0.203635\pi$
$43$	10.5214			1.60451			0.802253	+	0.596984i	$0.203635\pi$
$44$	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	$0.0738041\pi$
$53$			3.34580i			0.459581i	−0.973240	+	0.229790i	$0.926196\pi$
$54$	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	$-0.982799\pi$
$61$		−	0.843705i		−	0.108025i	0.998540	−	0.0540127i	$-0.0172011\pi$
$62$	−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	$-0.250846\pi$
$79$	12.5364			1.41045			0.705225	+	0.708984i	$0.250846\pi$
$80$	−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	$-0.857070\pi$
$97$		−	8.55060i		−	0.868182i	0.900869	−	0.434091i	$-0.142930\pi$
$98$	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	$0.266018\pi$
$101$			14.9096i			1.48356i	−0.670644	+	0.741779i	$0.733982\pi$
$102$	−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	$-0.940420\pi$
$109$		−	3.88557i		−	0.372170i	0.982534	−	0.186085i	$-0.0595800\pi$
$110$	−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	$-0.835122\pi$
$113$		−	10.5265i		−	0.990252i	0.868821	−	0.495126i	$-0.164878\pi$
$114$	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
$134$	0.839040	+	11.5454i	0.0724820	+	0.997370i
$135$		−	1.44885i		−	0.124697i
$136$	−3.79586	+	4.80188i	−0.325492	+	0.411757i
$137$			9.32069i			0.796320i	0.917316	+	0.398160i	$0.130351\pi$
$137$			9.32069i			0.796320i	−0.917316	+	0.398160i	$0.869649\pi$
$138$	−2.20931	−	7.12631i	−0.188069	−	0.606631i
$139$	−6.89205			−0.584576			−0.292288	−	0.956330i	$-0.594417\pi$
$139$	−6.89205			−0.584576			−0.292288	+	0.956330i	$0.594417\pi$
$140$	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	$-0.873176\pi$
$179$	−24.6622			−1.84334			−0.921671	+	0.387972i	$0.873176\pi$
$180$	−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	$-0.641651\pi$
$191$	−11.8983			−0.860932			−0.430466	+	0.902607i	$0.641651\pi$
$192$	−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	$-0.900113\pi$
$197$		−	8.66502i		−	0.617357i	0.951166	−	0.308679i	$-0.0998868\pi$
$198$	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	$0.000676388\pi$
$229$			0.0643122i			0.00424987i	−0.999998	+	0.00212494i	$0.999324\pi$
$230$	−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	$-0.950010\pi$
$233$		−	4.77483i		−	0.312809i	0.987693	−	0.156405i	$-0.0499904\pi$
$234$	−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	$-0.640655\pi$
$239$	−13.2223			−0.855278			−0.427639	+	0.903950i	$0.640655\pi$
$240$	−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	$-0.376768\pi$
$251$	11.9629			0.755091			0.377546	+	0.925991i	$0.376768\pi$
$252$	−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
$268$	5.96828	+	15.2440i	0.364571	+	0.931176i
$269$	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	$-0.516362\pi$
$271$	−1.69169			−0.102763			−0.0513816	+	0.998679i	$0.516362\pi$
$272$	−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	$0.274817\pi$
$281$			25.4809i			1.52006i	−0.649886	+	0.760032i	$0.725183\pi$
$282$	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	$-0.708784\pi$
$311$	−21.5109			−1.21977			−0.609885	+	0.792490i	$0.708784\pi$
$312$	−6.54638	−	5.17487i	−0.370616	−	0.292970i
$313$		−	35.2883i		−	1.99461i	−0.0733438	−	0.997307i	$-0.523367\pi$
$313$		−	35.2883i		−	1.99461i	0.0733438	−	0.997307i	$-0.476633\pi$
$314$	−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	$-0.610532\pi$
$331$	−12.3828			−0.680623			−0.340311	+	0.940313i	$0.610532\pi$
$332$	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	$0.0495305\pi$
$337$			5.69001i			0.309955i	−0.987918	+	0.154977i	$0.950470\pi$
$338$	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	$-0.167534\pi$
$347$	32.2136			1.72932			0.864660	+	0.502358i	$0.167534\pi$
$348$	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	$0.0107582\pi$
$353$			1.26977i			0.0675828i	−0.999429	+	0.0337914i	$0.989242\pi$
$354$	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	$-0.818406\pi$
$367$	−32.2468			−1.68327			−0.841635	+	0.540047i	$0.818406\pi$
$368$	−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	$-0.747943\pi$
$373$		−	27.4890i		−	1.42332i	0.702522	−	0.711662i	$-0.252057\pi$
$374$	−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	$-0.724016\pi$
$379$	−25.1952			−1.29419			−0.647095	+	0.762409i	$0.724016\pi$
$380$	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	$-0.330639\pi$
$383$	19.8566			1.01463			0.507313	+	0.861762i	$0.330639\pi$
$384$	−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	$0.0375706\pi$
$401$			4.71619i			0.235515i	−0.993042	+	0.117758i	$0.962429\pi$
$402$	0.839040	+	11.5454i	0.0418475	+	0.575832i
$403$			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	$-0.901941\pi$
$409$		−	12.2642i		−	0.606424i	0.952923	−	0.303212i	$-0.0980590\pi$
$410$	−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	$0.201646\pi$
$433$			24.6358i			1.18392i	−0.805968	+	0.591960i	$0.798354\pi$
$434$	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	$-0.789715\pi$
$443$	−33.2386			−1.57921			−0.789606	+	0.613614i	$0.789715\pi$
$444$	−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	$-0.518879\pi$
$463$	−2.55096			−0.118553			−0.0592766	+	0.998242i	$0.518879\pi$
$464$	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	$-0.560515\pi$
$487$	−8.34042			−0.377940			−0.188970	+	0.981983i	$0.560515\pi$
$488$	−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	$-0.298853\pi$
$499$	26.3904			1.18140			0.590698	+	0.806893i	$0.298853\pi$
$500$	−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	$-0.478295\pi$
$503$	3.05618			0.136268			0.0681342	+	0.997676i	$0.478295\pi$
$504$	−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	$-0.942062\pi$
$521$		−	8.26338i		−	0.362025i	0.983481	−	0.181013i	$-0.0579375\pi$
$522$	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
$536$	14.4457	+	18.0920i	0.623958	+	0.781458i
$537$	−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	$-0.561044\pi$
$541$		−	45.6660i		−	1.96333i	0.190603	−	0.981667i	$-0.438956\pi$
$542$	−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	$-0.838910\pi$
$547$	−40.9128			−1.74930			−0.874652	+	0.484751i	$0.838910\pi$
$548$	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	$-0.490337\pi$
$563$	1.44035			0.0607034			0.0303517	+	0.999539i	$0.490337\pi$
$564$	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	$0.392154\pi$
$577$			45.3105i			1.88630i	−0.332364	+	0.943151i	$0.607846\pi$
$578$	−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	$-0.396487\pi$
$587$	15.4815			0.638989			0.319494	+	0.947588i	$0.396487\pi$
$588$	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	$-0.924394\pi$
$593$		−	11.4597i		−	0.470595i	0.971923	−	0.235298i	$-0.0756065\pi$
$594$	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	$-0.412784\pi$
$599$	13.2447			0.541163			0.270581	+	0.962697i	$0.412784\pi$
$600$	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	$-0.520342\pi$
$631$	−3.20849			−0.127728			−0.0638640	+	0.997959i	$0.520342\pi$
$632$	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	$0.0446341\pi$
$641$			7.07704i			0.279526i	−0.990185	+	0.139763i	$0.955366\pi$
$642$	−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	$-0.677690\pi$
$647$	−26.9464			−1.05937			−0.529686	+	0.848194i	$0.677690\pi$
$648$	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	$-0.888062\pi$
$653$		−	17.6046i		−	0.688923i	0.938800	−	0.344461i	$-0.111938\pi$
$654$	−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	$0.325185\pi$
$661$			43.8582i			1.70589i	−0.522003	+	0.852944i	$0.674815\pi$
$662$	−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
$670$	16.7275	−	1.21564i	0.646242	−	0.0469644i
$671$		−	3.34344i		−	0.129072i
$672$	−1.03209	+	15.2295i	−0.0398136	+	0.587490i
$673$			28.4231i			1.09563i	0.836600	+	0.547814i	$0.184540\pi$
$673$			28.4231i			1.09563i	−0.836600	+	0.547814i	$0.815460\pi$
$674$	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	$0.175609\pi$
$677$			27.2748i			1.04826i	−0.851639	+	0.524128i	$0.824391\pi$
$678$	−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	$-0.269281\pi$
$683$	34.6542			1.32601			0.663004	+	0.748616i	$0.269281\pi$
$684$	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	$-0.734219\pi$
$701$		−	39.2528i		−	1.48256i	0.671197	−	0.741279i	$-0.265781\pi$
$702$	−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	$-0.647957\pi$
$727$	−24.1729			−0.896523			−0.448262	+	0.893902i	$0.647957\pi$
$728$	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	$-0.706866\pi$
$733$		−	43.1100i		−	1.59230i	0.605098	−	0.796151i	$-0.293134\pi$
$734$	−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	$-0.712630\pi$
$739$	−33.6770			−1.23883			−0.619414	+	0.785065i	$0.712630\pi$
$740$	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	$0.0154316\pi$
$757$			2.66667i			0.0969218i	−0.998825	+	0.0484609i	$0.984568\pi$
$758$	−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	$-0.819628\pi$
$769$		−	29.7726i		−	1.07363i	0.843701	−	0.536814i	$-0.180372\pi$
$770$	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	$-0.538459\pi$
$787$	−6.76258			−0.241060			−0.120530	+	0.992710i	$0.538459\pi$
$788$	−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
$804$	5.96828	+	15.2440i	0.210485	+	0.537615i
$805$	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	$0.435442\pi$
$809$			55.7199i			1.95901i	−0.201428	+	0.979503i	$0.564558\pi$
$810$	−0.606742	−	1.95709i	−0.0213187	−	0.0687651i
$811$	−42.0272			−1.47578			−0.737888	−	0.674923i	$-0.764177\pi$
$811$	−42.0272			−1.47578			−0.737888	+	0.674923i	$0.764177\pi$
$812$	−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	$0.171945\pi$
$857$			30.1113i			1.02858i	−0.857615	+	0.514292i	$0.828055\pi$
$858$	−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	$-0.331436\pi$
$883$	30.0216			1.01031			0.505154	+	0.863029i	$0.331436\pi$
$884$	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	$-0.426377\pi$
$919$	13.8987			0.458475			0.229237	+	0.973371i	$0.426377\pi$
$920$	−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	$-0.998058\pi$
$929$		−	0.371925i		−	0.0122025i	0.999981	−	0.00610123i	$-0.00194210\pi$
$930$	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	$-0.930694\pi$
$937$		−	13.2247i		−	0.432031i	0.976390	−	0.216016i	$-0.0693062\pi$
$938$	−2.26406	−	31.1540i	−0.0739242	−	1.01721i
$939$		−	35.2883i		−	1.15159i
$940$	23.9179	−	16.4072i	0.780117	−	0.535142i
$941$		−	53.5930i		−	1.74708i	−0.486751	−	0.873541i	$-0.661818\pi$
$941$		−	53.5930i		−	1.74708i	0.486751	−	0.873541i	$-0.338182\pi$
$942$	−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	$-0.449656\pi$
$983$	9.87634			0.315006			0.157503	+	0.987518i	$0.449656\pi$
$984$	−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	$-0.830734\pi$
$991$	−54.2663			−1.72383			−0.861913	+	0.507056i	$0.830734\pi$
$992$	−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.b.535.31	yes	34
4.3	odd	2		804.2.e.a.535.3	✓	34
67.66	odd	2		804.2.e.a.535.4	yes	34
268.267	even	2	inner	804.2.e.b.535.32	yes	34

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
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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