LMFDB - Embedded newform 200.2.k.h.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(43,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("200.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.k (of order $4$, degree $2$, 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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	200.107
Dual form			200.2.k.h.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26007 + 0.642040i) q^{2} +(1.61803 - 1.61803i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-1.00000 + 3.07768i) q^{6} +(1.17557 - 1.17557i) q^{7} +(-0.442463 + 2.79360i) q^{8} -2.23607i q^{9} +1.23607 q^{11} +(-0.715921 - 4.52015i) q^{12} +(-3.07768 - 3.07768i) q^{13} +(-0.726543 + 2.23607i) q^{14} +(-1.23607 - 3.80423i) q^{16} +(1.00000 + 1.00000i) q^{17} +(1.43564 + 2.81761i) q^{18} -2.00000i q^{19} -3.80423i q^{21} +(-1.55754 + 0.793604i) q^{22} +(2.62866 + 2.62866i) q^{23} +(3.80423 + 5.23607i) q^{24} +(5.85410 + 1.90211i) q^{26} +(1.23607 + 1.23607i) q^{27} +(-0.520147 - 3.28408i) q^{28} +1.45309 q^{29} +5.25731i q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 - 2.00000i) q^{33} +(-1.90211 - 0.618034i) q^{34} +(-3.61803 - 2.62866i) q^{36} +(3.07768 - 3.07768i) q^{37} +(1.28408 + 2.52015i) q^{38} -9.95959 q^{39} -7.70820 q^{41} +(2.44246 + 4.79360i) q^{42} +(-2.38197 + 2.38197i) q^{43} +(1.45309 - 2.00000i) q^{44} +(-5.00000 - 1.62460i) q^{46} +(-7.33094 + 7.33094i) q^{47} +(-8.15537 - 4.15537i) q^{48} +4.23607i q^{49} +3.23607 q^{51} +(-8.59783 + 1.36176i) q^{52} +(-0.726543 - 0.726543i) q^{53} +(-2.35114 - 0.763932i) q^{54} +(2.76393 + 3.80423i) q^{56} +(-3.23607 - 3.23607i) q^{57} +(-1.83099 + 0.932938i) q^{58} +8.47214i q^{59} -9.95959i q^{61} +(-3.37540 - 6.62460i) q^{62} +(-2.62866 - 2.62866i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(-1.23607 + 3.80423i) q^{66} +(2.38197 + 2.38197i) q^{67} +(2.79360 - 0.442463i) q^{68} +8.50651 q^{69} +7.05342i q^{71} +(6.24669 + 0.989378i) q^{72} +(-8.70820 + 8.70820i) q^{73} +(-1.90211 + 5.85410i) q^{74} +(-3.23607 - 2.35114i) q^{76} +(1.45309 - 1.45309i) q^{77} +(12.5498 - 6.39445i) q^{78} +12.3107 q^{79} +10.7082 q^{81} +(9.71290 - 4.94897i) q^{82} +(4.38197 - 4.38197i) q^{83} +(-6.15537 - 4.47214i) q^{84} +(1.47214 - 4.53077i) q^{86} +(2.35114 - 2.35114i) q^{87} +(-0.546915 + 3.45309i) q^{88} -6.47214i q^{89} -7.23607 q^{91} +(7.34342 - 1.16308i) q^{92} +(8.50651 + 8.50651i) q^{93} +(4.53077 - 13.9443i) q^{94} +12.9443 q^{96} +(0.236068 + 0.236068i) q^{97} +(-2.71972 - 5.33776i) q^{98} -2.76393i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{3} - 8 q^{6} - 4 q^{8} - 8 q^{11} - 12 q^{12} + 8 q^{16} + 8 q^{17} - 10 q^{18} - 12 q^{22} + 20 q^{26} - 8 q^{27} + 20 q^{28} + 32 q^{32} + 16 q^{33} - 20 q^{36} + 4 q^{38} - 8 q^{41}+ \cdots + 6 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^3 - 8 * q^6 - 4 * q^8 - 8 * q^11 - 12 * q^12 + 8 * q^16 + 8 * q^17 - 10 * q^18 - 12 * q^22 + 20 * q^26 - 8 * q^27 + 20 * q^28 + 32 * q^32 + 16 * q^33 - 20 * q^36 + 4 * q^38 - 8 * q^41 + 20 * q^42 - 28 * q^43 - 40 * q^46 - 16 * q^48 + 8 * q^51 - 20 * q^52 + 40 * q^56 - 8 * q^57 - 20 * q^58 - 40 * q^62 + 8 * q^66 + 28 * q^67 + 4 * q^68 + 20 * q^72 - 16 * q^73 - 8 * q^76 + 40 * q^78 + 32 * q^81 + 28 * q^82 + 44 * q^83 - 24 * q^86 - 16 * q^88 - 40 * q^91 - 20 * q^92 + 32 * q^96 - 16 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.26007	+	0.642040i	−0.891007	+	0.453990i
$2$	−1.26007	+	0.642040i	−0.891007	+	0.453990i
$3$	1.61803	−	1.61803i	0.934172	−	0.934172i	−0.0637909	−	0.997963i	$-0.520319\pi$
$3$	1.61803	−	1.61803i	0.934172	−	0.934172i	0.997963	+	0.0637909i	$0.0203191\pi$
$4$	1.17557	−	1.61803i	0.587785	−	0.809017i
$5$		0			0
$5$		0			0
$6$	−1.00000	+	3.07768i	−0.408248	+	1.25646i
$7$	1.17557	−	1.17557i	0.444324	−	0.444324i	−0.449138	−	0.893462i	$-0.648269\pi$
$7$	1.17557	−	1.17557i	0.444324	−	0.444324i	0.893462	+	0.449138i	$0.148269\pi$
$8$	−0.442463	+	2.79360i	−0.156434	+	0.987688i
$9$		−	2.23607i		−	0.745356i
$10$		0			0
$11$	1.23607			0.372689			0.186344	−	0.982485i	$-0.440336\pi$
$11$	1.23607			0.372689			0.186344	+	0.982485i	$0.440336\pi$
$12$	−0.715921	−	4.52015i	−0.206669	−	1.30485i
$13$	−3.07768	−	3.07768i	−0.853596	−	0.853596i	0.136978	−	0.990574i	$-0.456261\pi$
$13$	−3.07768	−	3.07768i	−0.853596	−	0.853596i	−0.990574	+	0.136978i	$0.956261\pi$
$14$	−0.726543	+	2.23607i	−0.194177	+	0.597614i
$15$		0			0
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$	1.43564	+	2.81761i	0.338385	+	0.664117i
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$		−	3.80423i		−	0.830150i
$22$	−1.55754	+	0.793604i	−0.332068	+	0.169197i
$23$	2.62866	+	2.62866i	0.548113	+	0.548113i	0.925895	−	0.377782i	$-0.123313\pi$
$23$	2.62866	+	2.62866i	0.548113	+	0.548113i	−0.377782	+	0.925895i	$0.623313\pi$
$24$	3.80423	+	5.23607i	0.776534	+	1.06881i
$25$		0			0
$26$	5.85410	+	1.90211i	1.14808	+	0.373035i
$27$	1.23607	+	1.23607i	0.237881	+	0.237881i
$28$	−0.520147	−	3.28408i	−0.0982985	−	0.620633i
$29$	1.45309			0.269831			0.134916	−	0.990857i	$-0.456924\pi$
$29$	1.45309			0.269831			0.134916	+	0.990857i	$0.456924\pi$
$30$		0			0
$31$			5.25731i			0.944241i	0.881534	+	0.472120i	$0.156511\pi$
$31$			5.25731i			0.944241i	−0.881534	+	0.472120i	$0.843489\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$	−1.90211	−	0.618034i	−0.326210	−	0.105992i
$35$		0			0
$36$	−3.61803	−	2.62866i	−0.603006	−	0.438109i
$37$	3.07768	−	3.07768i	0.505968	−	0.505968i	−0.407318	−	0.913286i	$-0.633536\pi$
$37$	3.07768	−	3.07768i	0.505968	−	0.505968i	0.913286	+	0.407318i	$0.133536\pi$
$38$	1.28408	+	2.52015i	0.208305	+	0.408822i
$39$	−9.95959			−1.59481
$40$		0			0
$41$	−7.70820			−1.20382			−0.601910	−	0.798564i	$-0.705593\pi$
$41$	−7.70820			−1.20382			−0.601910	+	0.798564i	$0.705593\pi$
$42$	2.44246	+	4.79360i	0.376880	+	0.739669i
$43$	−2.38197	+	2.38197i	−0.363246	+	0.363246i	−0.865007	−	0.501760i	$-0.832686\pi$
$43$	−2.38197	+	2.38197i	−0.363246	+	0.363246i	0.501760	+	0.865007i	$0.332686\pi$
$44$	1.45309	−	2.00000i	0.219061	−	0.301511i
$45$		0			0
$46$	−5.00000	−	1.62460i	−0.737210	−	0.239534i
$47$	−7.33094	+	7.33094i	−1.06933	+	1.06933i	−0.0719165	+	0.997411i	$0.522912\pi$
$47$	−7.33094	+	7.33094i	−1.06933	+	1.06933i	−0.997411	+	0.0719165i	$0.977088\pi$
$48$	−8.15537	−	4.15537i	−1.17713	−	0.599776i
$49$			4.23607i			0.605153i
$50$		0			0
$51$	3.23607			0.453140
$52$	−8.59783	+	1.36176i	−1.19230	+	0.188842i
$53$	−0.726543	−	0.726543i	−0.0997983	−	0.0997983i	0.655445	−	0.755243i	$-0.272481\pi$
$53$	−0.726543	−	0.726543i	−0.0997983	−	0.0997983i	−0.755243	+	0.655445i	$0.772481\pi$
$54$	−2.35114	−	0.763932i	−0.319950	−	0.103958i
$55$		0			0
$56$	2.76393	+	3.80423i	0.369346	+	0.508361i
$57$	−3.23607	−	3.23607i	−0.428628	−	0.428628i
$58$	−1.83099	+	0.932938i	−0.240421	+	0.122501i
$59$			8.47214i			1.10298i	0.834182	+	0.551489i	$0.185940\pi$
$59$			8.47214i			1.10298i	−0.834182	+	0.551489i	$0.814060\pi$
$60$		0			0
$61$		−	9.95959i		−	1.27520i	−0.770370	−	0.637598i	$-0.779928\pi$
$61$		−	9.95959i		−	1.27520i	0.770370	−	0.637598i	$-0.220072\pi$
$62$	−3.37540	−	6.62460i	−0.428676	−	0.841325i
$63$	−2.62866	−	2.62866i	−0.331179	−	0.331179i
$64$	−7.60845	−	2.47214i	−0.951057	−	0.309017i
$65$		0			0
$66$	−1.23607	+	3.80423i	−0.152149	+	0.468268i
$67$	2.38197	+	2.38197i	0.291003	+	0.291003i	0.837477	−	0.546473i	$-0.184030\pi$
$67$	2.38197	+	2.38197i	0.291003	+	0.291003i	−0.546473	+	0.837477i	$0.684030\pi$
$68$	2.79360	−	0.442463i	0.338774	−	0.0536566i
$69$	8.50651			1.02406
$70$		0			0
$71$			7.05342i			0.837087i	0.908197	+	0.418544i	$0.137459\pi$
$71$			7.05342i			0.837087i	−0.908197	+	0.418544i	$0.862541\pi$
$72$	6.24669	+	0.989378i	0.736179	+	0.116599i
$73$	−8.70820	+	8.70820i	−1.01922	+	1.01922i	−0.0194065	+	0.999812i	$0.506178\pi$
$73$	−8.70820	+	8.70820i	−1.01922	+	1.01922i	−0.999812	+	0.0194065i	$0.993822\pi$
$74$	−1.90211	+	5.85410i	−0.221116	+	0.680526i
$75$		0			0
$76$	−3.23607	−	2.35114i	−0.371202	−	0.269694i
$77$	1.45309	−	1.45309i	0.165594	−	0.165594i
$78$	12.5498	−	6.39445i	1.42099	−	0.724029i
$79$	12.3107			1.38507			0.692533	−	0.721386i	$-0.256495\pi$
$79$	12.3107			1.38507			0.692533	+	0.721386i	$0.256495\pi$
$80$		0			0
$81$	10.7082			1.18980
$82$	9.71290	−	4.94897i	1.07261	−	0.546522i
$83$	4.38197	−	4.38197i	0.480983	−	0.480983i	−0.424462	−	0.905446i	$-0.639537\pi$
$83$	4.38197	−	4.38197i	0.480983	−	0.480983i	0.905446	+	0.424462i	$0.139537\pi$
$84$	−6.15537	−	4.47214i	−0.671606	−	0.487950i
$85$		0			0
$86$	1.47214	−	4.53077i	0.158745	−	0.488565i
$87$	2.35114	−	2.35114i	0.252069	−	0.252069i
$88$	−0.546915	+	3.45309i	−0.0583013	+	0.368100i
$89$		−	6.47214i		−	0.686045i	−0.939327	−	0.343023i	$-0.888549\pi$
$89$		−	6.47214i		−	0.686045i	0.939327	−	0.343023i	$-0.111451\pi$
$90$		0			0
$91$	−7.23607			−0.758546
$92$	7.34342	−	1.16308i	0.765605	−	0.121260i
$93$	8.50651	+	8.50651i	0.882084	+	0.882084i
$94$	4.53077	−	13.9443i	0.467313	−	1.43824i
$95$		0			0
$96$	12.9443			1.32112
$97$	0.236068	+	0.236068i	0.0239691	+	0.0239691i	0.718990	−	0.695021i	$-0.244605\pi$
$97$	0.236068	+	0.236068i	0.0239691	+	0.0239691i	−0.695021	+	0.718990i	$0.744605\pi$
$98$	−2.71972	−	5.33776i	−0.274734	−	0.539195i
$99$		−	2.76393i		−	0.277786i
$100$		0			0
$101$			12.3107i			1.22496i	0.790485	+	0.612482i	$0.209829\pi$
$101$			12.3107i			1.22496i	−0.790485	+	0.612482i	$0.790171\pi$
$102$	−4.07768	+	2.07768i	−0.403751	+	0.205721i
$103$	7.33094	+	7.33094i	0.722339	+	0.722339i	0.969081	−	0.246742i	$-0.0793601\pi$
$103$	7.33094	+	7.33094i	0.722339	+	0.722339i	−0.246742	+	0.969081i	$0.579360\pi$
$104$	9.95959	−	7.23607i	0.976618	−	0.709555i
$105$		0			0
$106$	1.38197	+	0.449028i	0.134228	+	0.0436135i
$107$	−12.0902	−	12.0902i	−1.16880	−	1.16880i	−0.982491	−	0.186310i	$-0.940347\pi$
$107$	−12.0902	−	12.0902i	−1.16880	−	1.16880i	−0.186310	−	0.982491i	$-0.559653\pi$
$108$	3.45309	−	0.546915i	0.332273	−	0.0526269i
$109$	−6.71040			−0.642739			−0.321370	−	0.946954i	$-0.604143\pi$
$109$	−6.71040			−0.642739			−0.321370	+	0.946954i	$0.604143\pi$
$110$		0			0
$111$		−	9.95959i		−	0.945323i
$112$	−5.92522	−	3.01905i	−0.559881	−	0.285273i
$113$	4.70820	−	4.70820i	0.442911	−	0.442911i	−0.450078	−	0.892989i	$-0.648604\pi$
$113$	4.70820	−	4.70820i	0.442911	−	0.442911i	0.892989	+	0.450078i	$0.148604\pi$
$114$	6.15537	+	2.00000i	0.576503	+	0.187317i
$115$		0			0
$116$	1.70820	−	2.35114i	0.158603	−	0.218298i
$117$	−6.88191	+	6.88191i	−0.636233	+	0.636233i
$118$	−5.43945	−	10.6755i	−0.500742	−	0.982761i
$119$	2.35114			0.215529
$120$		0			0
$121$	−9.47214			−0.861103
$122$	6.39445	+	12.5498i	0.578927	+	1.13621i
$123$	−12.4721	+	12.4721i	−1.12457	+	1.12457i
$124$	8.50651	+	6.18034i	0.763907	+	0.555011i
$125$		0			0
$126$	5.00000	+	1.62460i	0.445435	+	0.144731i
$127$	8.78402	−	8.78402i	0.779456	−	0.779456i	−0.200282	−	0.979738i	$-0.564186\pi$
$127$	8.78402	−	8.78402i	0.779456	−	0.779456i	0.979738	+	0.200282i	$0.0641859\pi$
$128$	11.1744	−	1.76985i	0.987688	−	0.156434i
$129$			7.70820i			0.678670i
$130$		0			0
$131$	0.291796			0.0254943			0.0127472	−	0.999919i	$-0.495942\pi$
$131$	0.291796			0.0254943			0.0127472	+	0.999919i	$0.495942\pi$
$132$	−0.884927	−	5.58721i	−0.0770230	−	0.486304i
$133$	−2.35114	−	2.35114i	−0.203870	−	0.203870i
$134$	−4.53077	−	1.47214i	−0.391399	−	0.127173i
$135$		0			0
$136$	−3.23607	+	2.35114i	−0.277491	+	0.201609i
$137$	−3.47214	−	3.47214i	−0.296645	−	0.296645i	0.543054	−	0.839698i	$-0.317268\pi$
$137$	−3.47214	−	3.47214i	−0.296645	−	0.296645i	−0.839698	+	0.543054i	$0.817268\pi$
$138$	−10.7188	+	5.46151i	−0.912447	+	0.464915i
$139$		−	5.41641i		−	0.459414i	−0.973260	−	0.229707i	$-0.926223\pi$
$139$		−	5.41641i		−	0.459414i	0.973260	−	0.229707i	$-0.0737767\pi$
$140$		0			0
$141$			23.7234i			1.99787i
$142$	−4.52858	−	8.88783i	−0.380030	−	0.745850i
$143$	−3.80423	−	3.80423i	−0.318125	−	0.318125i
$144$	−8.50651	+	2.76393i	−0.708876	+	0.230328i
$145$		0			0
$146$	5.38197	−	16.5640i	0.445415	−	1.37085i
$147$	6.85410	+	6.85410i	0.565317	+	0.565317i
$148$	−1.36176	−	8.59783i	−0.111936	−	0.706737i
$149$	−13.2088			−1.08211			−0.541053	−	0.840988i	$-0.681974\pi$
$149$	−13.2088			−1.08211			−0.541053	+	0.840988i	$0.681974\pi$
$150$		0			0
$151$		−	14.6619i		−	1.19317i	−0.802551	−	0.596583i	$-0.796525\pi$
$151$		−	14.6619i		−	1.19317i	0.802551	−	0.596583i	$-0.203475\pi$
$152$	5.58721	+	0.884927i	0.453182	+	0.0717771i
$153$	2.23607	−	2.23607i	0.180775	−	0.180775i
$154$	−0.898056	+	2.76393i	−0.0723674	+	0.222724i
$155$		0			0
$156$	−11.7082	+	16.1150i	−0.937407	+	1.29023i
$157$	−9.78808	+	9.78808i	−0.781174	+	0.781174i	−0.980029	−	0.198855i	$-0.936278\pi$
$157$	−9.78808	+	9.78808i	−0.781174	+	0.781174i	0.198855	+	0.980029i	$0.436278\pi$
$158$	−15.5124	+	7.90398i	−1.23410	+	0.628807i
$159$	−2.35114			−0.186458
$160$		0			0
$161$	6.18034			0.487079
$162$	−13.4931	+	6.87509i	−1.06012	+	0.540158i
$163$	7.14590	−	7.14590i	0.559710	−	0.559710i	−0.369515	−	0.929225i	$-0.620476\pi$
$163$	7.14590	−	7.14590i	0.559710	−	0.559710i	0.929225	+	0.369515i	$0.120476\pi$
$164$	−9.06154	+	12.4721i	−0.707587	+	0.973910i
$165$		0			0
$166$	−2.70820	+	8.33499i	−0.210197	+	0.646921i
$167$	0.277515	−	0.277515i	0.0214747	−	0.0214747i	−0.696288	−	0.717763i	$-0.745166\pi$
$167$	0.277515	−	0.277515i	0.0214747	−	0.0214747i	0.717763	+	0.696288i	$0.245166\pi$
$168$	10.6275	+	1.68323i	0.819930	+	0.129864i
$169$			5.94427i			0.457252i
$170$		0			0
$171$	−4.47214			−0.341993
$172$	1.05393	+	6.65427i	0.0803616	+	0.507383i
$173$	−6.32688	−	6.32688i	−0.481024	−	0.481024i	0.424435	−	0.905459i	$-0.360473\pi$
$173$	−6.32688	−	6.32688i	−0.481024	−	0.481024i	−0.905459	+	0.424435i	$0.860473\pi$
$174$	−1.45309	+	4.47214i	−0.110158	+	0.339032i
$175$		0			0
$176$	−1.52786	−	4.70228i	−0.115167	−	0.354448i
$177$	13.7082	+	13.7082i	1.03037	+	1.03037i
$178$	4.15537	+	8.15537i	0.311458	+	0.611271i
$179$		−	16.4721i		−	1.23119i	−0.788065	−	0.615593i	$-0.788917\pi$
$179$		−	16.4721i		−	1.23119i	0.788065	−	0.615593i	$-0.211083\pi$
$180$		0			0
$181$		−	9.40456i		−	0.699036i	−0.936930	−	0.349518i	$-0.886345\pi$
$181$		−	9.40456i		−	0.699036i	0.936930	−	0.349518i	$-0.113655\pi$
$182$	9.11798	−	4.64584i	0.675869	−	0.344373i
$183$	−16.1150	−	16.1150i	−1.19125	−	1.19125i
$184$	−8.50651	+	6.18034i	−0.627108	+	0.455621i
$185$		0			0
$186$	−16.1803	−	5.25731i	−1.18640	−	0.385485i
$187$	1.23607	+	1.23607i	0.0903902	+	0.0903902i
$188$	3.24367	+	20.4797i	0.236569	+	1.49364i
$189$	2.90617			0.211393
$190$		0			0
$191$		−	12.8658i		−	0.930934i	−0.885065	−	0.465467i	$-0.845886\pi$
$191$		−	12.8658i		−	0.930934i	0.885065	−	0.465467i	$-0.154114\pi$
$192$	−16.3107	+	8.31073i	−1.17713	+	0.599776i
$193$	7.47214	−	7.47214i	0.537856	−	0.537856i	−0.385043	−	0.922899i	$-0.625813\pi$
$193$	7.47214	−	7.47214i	0.537856	−	0.537856i	0.922899	+	0.385043i	$0.125813\pi$
$194$	−0.449028	−	0.145898i	−0.0322383	−	0.0104749i
$195$		0			0
$196$	6.85410	+	4.97980i	0.489579	+	0.355700i
$197$	2.17963	−	2.17963i	0.155292	−	0.155292i	−0.625185	−	0.780477i	$-0.714976\pi$
$197$	2.17963	−	2.17963i	0.155292	−	0.155292i	0.780477	+	0.625185i	$0.214976\pi$
$198$	1.77455	+	3.48276i	0.126112	+	0.247509i
$199$	18.1231			1.28471			0.642355	−	0.766407i	$-0.277957\pi$
$199$	18.1231			1.28471			0.642355	+	0.766407i	$0.277957\pi$
$200$		0			0
$201$	7.70820			0.543695
$202$	−7.90398	−	15.5124i	−0.556122	−	1.09145i
$203$	1.70820	−	1.70820i	0.119892	−	0.119892i
$204$	3.80423	−	5.23607i	0.266349	−	0.366598i
$205$		0			0
$206$	−13.9443	−	4.53077i	−0.971543	−	0.315674i
$207$	5.87785	−	5.87785i	0.408539	−	0.408539i
$208$	−7.90398	+	15.5124i	−0.548042	+	1.07559i
$209$		−	2.47214i		−	0.171001i
$210$		0			0
$211$	15.7082			1.08140			0.540699	−	0.841216i	$-0.318160\pi$
$211$	15.7082			1.08140			0.540699	+	0.841216i	$0.318160\pi$
$212$	−2.02967	+	0.321469i	−0.139398	+	0.0220785i
$213$	11.4127	+	11.4127i	0.781984	+	0.781984i
$214$	22.9969	+	7.47214i	1.57203	+	0.510785i
$215$		0			0
$216$	−4.00000	+	2.90617i	−0.272166	+	0.197740i
$217$	6.18034	+	6.18034i	0.419549	+	0.419549i
$218$	8.45559	−	4.30834i	0.572685	−	0.291798i
$219$			28.1803i			1.90425i
$220$		0			0
$221$		−	6.15537i		−	0.414055i
$222$	6.39445	+	12.5498i	0.429168	+	0.842289i
$223$	1.73060	+	1.73060i	0.115890	+	0.115890i	0.762673	−	0.646784i	$-0.223886\pi$
$223$	1.73060	+	1.73060i	0.115890	+	0.115890i	−0.646784	+	0.762673i	$0.723886\pi$
$224$	9.40456			0.628369
$225$		0			0
$226$	−2.90983	+	8.95554i	−0.193559	+	0.595713i
$227$	11.6180	+	11.6180i	0.771116	+	0.771116i	0.978302	−	0.207186i	$-0.0664304\pi$
$227$	11.6180	+	11.6180i	0.771116	+	0.771116i	−0.207186	+	0.978302i	$0.566430\pi$
$228$	−9.04029	+	1.43184i	−0.598708	+	0.0948260i
$229$	−21.3723			−1.41232			−0.706160	−	0.708053i	$-0.749574\pi$
$229$	−21.3723			−1.41232			−0.706160	+	0.708053i	$0.749574\pi$
$230$		0			0
$231$		−	4.70228i		−	0.309387i
$232$	−0.642937	+	4.05934i	−0.0422109	+	0.266509i
$233$	3.47214	−	3.47214i	0.227467	−	0.227467i	−0.584167	−	0.811634i	$-0.698579\pi$
$233$	3.47214	−	3.47214i	0.227467	−	0.227467i	0.811634	+	0.584167i	$0.198579\pi$
$234$	4.25325	−	13.0902i	0.278044	−	0.855731i
$235$		0			0
$236$	13.7082	+	9.95959i	0.892328	+	0.648314i
$237$	19.9192	−	19.9192i	1.29389	−	1.29389i
$238$	−2.96261	+	1.50953i	−0.192038	+	0.0978480i
$239$	−29.3238			−1.89680			−0.948398	−	0.317083i	$-0.897297\pi$
$239$	−29.3238			−1.89680			−0.948398	+	0.317083i	$0.897297\pi$
$240$		0			0
$241$	6.76393			0.435703			0.217852	−	0.975982i	$-0.430095\pi$
$241$	6.76393			0.435703			0.217852	+	0.975982i	$0.430095\pi$
$242$	11.9356	−	6.08149i	0.767249	−	0.390933i
$243$	13.6180	−	13.6180i	0.873597	−	0.873597i
$244$	−16.1150	−	11.7082i	−1.03165	−	0.749541i
$245$		0			0
$246$	7.70820	−	23.7234i	0.491457	−	1.51255i
$247$	−6.15537	+	6.15537i	−0.391657	+	0.391657i
$248$	−14.6868	−	2.32617i	−0.932616	−	0.147712i
$249$		−	14.1803i		−	0.898643i
$250$		0			0
$251$	−22.1803			−1.40001			−0.700005	−	0.714138i	$-0.746819\pi$
$251$	−22.1803			−1.40001			−0.700005	+	0.714138i	$0.746819\pi$
$252$	−7.34342	+	1.16308i	−0.462592	+	0.0732674i
$253$	3.24920	+	3.24920i	0.204275	+	0.204275i
$254$	−5.42882	+	16.7082i	−0.340635	+	1.04837i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	−18.7082	−	18.7082i	−1.16699	−	1.16699i	−0.982913	−	0.184073i	$-0.941072\pi$
$257$	−18.7082	−	18.7082i	−1.16699	−	1.16699i	−0.184073	−	0.982913i	$-0.558928\pi$
$258$	−4.94897	−	9.71290i	−0.308110	−	0.604699i
$259$		−	7.23607i		−	0.449627i
$260$		0			0
$261$		−	3.24920i		−	0.201120i
$262$	−0.367684	+	0.187345i	−0.0227156	+	0.0115742i
$263$	−16.3925	−	16.3925i	−1.01080	−	1.01080i	−0.999941	−	0.0108623i	$-0.996542\pi$
$263$	−16.3925	−	16.3925i	−1.01080	−	1.01080i	−0.0108623	−	0.999941i	$-0.503458\pi$
$264$	4.70228	+	6.47214i	0.289405	+	0.398332i
$265$		0			0
$266$	4.47214	+	1.45309i	0.274204	+	0.0890944i
$267$	−10.4721	−	10.4721i	−0.640884	−	0.640884i
$268$	6.65427	−	1.05393i	0.406474	−	0.0643792i
$269$	17.9111			1.09206			0.546029	−	0.837766i	$-0.316139\pi$
$269$	17.9111			1.09206			0.546029	+	0.837766i	$0.316139\pi$
$270$		0			0
$271$			31.6749i			1.92411i	0.272851	+	0.962056i	$0.412033\pi$
$271$			31.6749i			1.92411i	−0.272851	+	0.962056i	$0.587967\pi$
$272$	2.56816	−	5.04029i	0.155717	−	0.305613i
$273$	−11.7082	+	11.7082i	−0.708613	+	0.708613i
$274$	6.60440	+	2.14590i	0.398986	+	0.129638i
$275$		0			0
$276$	10.0000	−	13.7638i	0.601929	−	0.828485i
$277$	−2.17963	+	2.17963i	−0.130961	+	0.130961i	−0.769549	−	0.638588i	$-0.779519\pi$
$277$	−2.17963	+	2.17963i	−0.130961	+	0.130961i	0.638588	+	0.769549i	$0.279519\pi$
$278$	3.47755	+	6.82507i	0.208569	+	0.409341i
$279$	11.7557			0.703796
$280$		0			0
$281$	3.70820			0.221213			0.110606	−	0.993864i	$-0.464721\pi$
$281$	3.70820			0.221213			0.110606	+	0.993864i	$0.464721\pi$
$282$	−15.2314	−	29.8932i	−0.907015	−	1.78012i
$283$	−15.6180	+	15.6180i	−0.928396	+	0.928396i	−0.997602	−	0.0692066i	$-0.977953\pi$
$283$	−15.6180	+	15.6180i	−0.928396	+	0.928396i	0.0692066	+	0.997602i	$0.477953\pi$
$284$	11.4127	+	8.29180i	0.677218	+	0.492028i
$285$		0			0
$286$	7.23607	+	2.35114i	0.427878	+	0.139026i
$287$	−9.06154	+	9.06154i	−0.534886	+	0.534886i
$288$	8.94427	−	8.94427i	0.527046	−	0.527046i
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$	0.763932			0.0447825
$292$	3.85306	+	24.3273i	0.225483	+	1.42365i
$293$	0.726543	+	0.726543i	0.0424451	+	0.0424451i	0.728011	−	0.685566i	$-0.240445\pi$
$293$	0.726543	+	0.726543i	0.0424451	+	0.0424451i	−0.685566	+	0.728011i	$0.740445\pi$
$294$	−13.0373	−	4.23607i	−0.760349	−	0.247053i
$295$		0			0
$296$	7.23607	+	9.95959i	0.420588	+	0.578890i
$297$	1.52786	+	1.52786i	0.0886557	+	0.0886557i
$298$	16.6440	−	8.48057i	0.964164	−	0.491266i
$299$		−	16.1803i		−	0.935733i
$300$		0			0
$301$			5.60034i			0.322798i
$302$	9.41350	+	18.4750i	0.541686	+	1.06312i
$303$	19.9192	+	19.9192i	1.14433	+	1.14433i
$304$	−7.60845	+	2.47214i	−0.436375	+	0.141787i
$305$		0			0
$306$	−1.38197	+	4.25325i	−0.0790017	+	0.243142i
$307$	−6.56231	−	6.56231i	−0.374531	−	0.374531i	0.494594	−	0.869124i	$-0.335317\pi$
$307$	−6.56231	−	6.56231i	−0.374531	−	0.374531i	−0.869124	+	0.494594i	$0.835317\pi$
$308$	−0.642937	−	4.05934i	−0.0366347	−	0.231303i
$309$	23.7234			1.34958
$310$		0			0
$311$			8.16348i			0.462909i	0.972846	+	0.231454i	$0.0743484\pi$
$311$			8.16348i			0.462909i	−0.972846	+	0.231454i	$0.925652\pi$
$312$	4.40676	−	27.8232i	0.249483	−	1.57518i
$313$	6.23607	−	6.23607i	0.352483	−	0.352483i	−0.508549	−	0.861033i	$-0.669818\pi$
$313$	6.23607	−	6.23607i	0.352483	−	0.352483i	0.861033	+	0.508549i	$0.169818\pi$
$314$	6.04937	−	18.6180i	0.341385	−	1.05068i
$315$		0			0
$316$	14.4721	−	19.9192i	0.814121	−	1.12054i
$317$	−10.6861	+	10.6861i	−0.600193	+	0.600193i	−0.940364	−	0.340171i	$-0.889515\pi$
$317$	−10.6861	+	10.6861i	−0.600193	+	0.600193i	0.340171	+	0.940364i	$0.389515\pi$
$318$	2.96261	−	1.50953i	0.166135	−	0.0846500i
$319$	1.79611			0.100563
$320$		0			0
$321$	−39.1246			−2.18372
$322$	−7.78768	+	3.96802i	−0.433991	+	0.221129i
$323$	2.00000	−	2.00000i	0.111283	−	0.111283i
$324$	12.5882	−	17.3262i	0.699347	−	0.962569i
$325$		0			0
$326$	−4.41641	+	13.5923i	−0.244602	+	0.752808i
$327$	−10.8576	+	10.8576i	−0.600429	+	0.600429i
$328$	3.41060	−	21.5337i	0.188319	−	1.18900i
$329$			17.2361i			0.950255i
$330$		0			0
$331$	28.0689			1.54281			0.771403	−	0.636347i	$-0.219555\pi$
$331$	28.0689			1.54281			0.771403	+	0.636347i	$0.219555\pi$
$332$	−1.93886	−	12.2415i	−0.106409	−	0.671838i
$333$	−6.88191	−	6.88191i	−0.377126	−	0.377126i
$334$	−0.171513	+	0.527864i	−0.00938480	+	0.0288834i
$335$		0			0
$336$	−14.4721	+	4.70228i	−0.789520	+	0.256531i
$337$	2.05573	+	2.05573i	0.111983	+	0.111983i	0.760878	−	0.648895i	$-0.224769\pi$
$337$	2.05573	+	2.05573i	0.111983	+	0.111983i	−0.648895	+	0.760878i	$0.724769\pi$
$338$	−3.81646	−	7.49022i	−0.207588	−	0.407414i
$339$		−	15.2361i		−	0.827510i
$340$		0			0
$341$			6.49839i			0.351908i
$342$	5.63522	−	2.87129i	0.304718	−	0.155261i
$343$	13.2088	+	13.2088i	0.713208	+	0.713208i
$344$	−5.60034	−	7.70820i	−0.301950	−	0.415599i
$345$		0			0
$346$	12.0344	+	3.91023i	0.646976	+	0.210215i
$347$	3.03444	+	3.03444i	0.162897	+	0.162897i	0.783849	−	0.620952i	$-0.213254\pi$
$347$	3.03444	+	3.03444i	0.162897	+	0.162897i	−0.620952	+	0.783849i	$0.713254\pi$
$348$	−1.04029	−	6.56816i	−0.0557656	−	0.352090i
$349$	−15.5599			−0.832904			−0.416452	−	0.909158i	$-0.636727\pi$
$349$	−15.5599			−0.832904			−0.416452	+	0.909158i	$0.636727\pi$
$350$		0			0
$351$		−	7.60845i		−	0.406109i
$352$	4.94427	+	4.94427i	0.263531	+	0.263531i
$353$	−4.41641	+	4.41641i	−0.235062	+	0.235062i	−0.814802	−	0.579740i	$-0.803154\pi$
$353$	−4.41641	+	4.41641i	−0.235062	+	0.235062i	0.579740	+	0.814802i	$0.303154\pi$
$354$	−26.0746	−	8.47214i	−1.38585	−	0.450289i
$355$		0			0
$356$	−10.4721	−	7.60845i	−0.555022	−	0.403247i
$357$	3.80423	−	3.80423i	0.201341	−	0.201341i
$358$	10.5758	+	20.7561i	0.558946	+	1.09699i
$359$	1.79611			0.0947952			0.0473976	−	0.998876i	$-0.484907\pi$
$359$	1.79611			0.0947952			0.0473976	+	0.998876i	$0.484907\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	6.03810	+	11.8504i	0.317356	+	0.622845i
$363$	−15.3262	+	15.3262i	−0.804419	+	0.804419i
$364$	−8.50651	+	11.7082i	−0.445862	+	0.613677i
$365$		0			0
$366$	30.6525	+	9.95959i	1.60223	+	0.520596i
$367$	24.0009	−	24.0009i	1.25284	−	1.25284i	0.298396	−	0.954442i	$-0.403548\pi$
$367$	24.0009	−	24.0009i	1.25284	−	1.25284i	0.954442	−	0.298396i	$-0.0964516\pi$
$368$	6.75080	−	13.2492i	0.351910	−	0.690662i
$369$			17.2361i			0.897274i
$370$		0			0
$371$	−1.70820			−0.0886855
$372$	23.7638	−	3.76382i	1.23210	−	0.195145i
$373$	−15.0454	−	15.0454i	−0.779021	−	0.779021i	0.200644	−	0.979664i	$-0.435697\pi$
$373$	−15.0454	−	15.0454i	−0.779021	−	0.779021i	−0.979664	+	0.200644i	$0.935697\pi$
$374$	−2.35114	−	0.763932i	−0.121575	−	0.0395020i
$375$		0			0
$376$	−17.2361	−	23.7234i	−0.888882	−	1.22344i
$377$	−4.47214	−	4.47214i	−0.230327	−	0.230327i
$378$	−3.66199	+	1.86588i	−0.188352	+	0.0959703i
$379$			35.8885i			1.84347i	0.387820	+	0.921735i	$0.373228\pi$
$379$			35.8885i			1.84347i	−0.387820	+	0.921735i	$0.626772\pi$
$380$		0			0
$381$		−	28.4257i		−	1.45629i
$382$	8.26033	+	16.2118i	0.422635	+	0.829468i
$383$	11.1352	+	11.1352i	0.568980	+	0.568980i	0.931843	−	0.362862i	$-0.118201\pi$
$383$	11.1352	+	11.1352i	0.568980	+	0.568980i	−0.362862	+	0.931843i	$0.618201\pi$
$384$	15.2169	−	20.9443i	0.776534	−	1.06881i
$385$		0			0
$386$	−4.61803	+	14.2128i	−0.235052	+	0.723415i
$387$	5.32624	+	5.32624i	0.270748	+	0.270748i
$388$	0.659481	−	0.104451i	0.0334801	−	0.00530272i
$389$	23.7234			1.20282			0.601412	−	0.798939i	$-0.294605\pi$
$389$	23.7234			1.20282			0.601412	+	0.798939i	$0.294605\pi$
$390$		0			0
$391$			5.25731i			0.265874i
$392$	−11.8339	−	1.87431i	−0.597702	−	0.0946667i
$393$	0.472136	−	0.472136i	0.0238161	−	0.0238161i
$394$	−1.34708	+	4.14590i	−0.0678651	+	0.208867i
$395$		0			0
$396$	−4.47214	−	3.24920i	−0.224733	−	0.163278i
$397$	−7.22494	+	7.22494i	−0.362609	+	0.362609i	−0.864773	−	0.502164i	$-0.832538\pi$
$397$	−7.22494	+	7.22494i	−0.362609	+	0.362609i	0.502164	+	0.864773i	$0.332538\pi$
$398$	−22.8364	+	11.6357i	−1.14469	+	0.583246i
$399$	−7.60845			−0.380899
$400$		0			0
$401$	−3.88854			−0.194185			−0.0970923	−	0.995275i	$-0.530954\pi$
$401$	−3.88854			−0.194185			−0.0970923	+	0.995275i	$0.530954\pi$
$402$	−9.71290	+	4.94897i	−0.484436	+	0.246832i
$403$	16.1803	−	16.1803i	0.806000	−	0.806000i
$404$	19.9192	+	14.4721i	0.991017	+	0.720016i
$405$		0			0
$406$	−1.05573	+	3.24920i	−0.0523949	+	0.161255i
$407$	3.80423	−	3.80423i	0.188568	−	0.188568i
$408$	−1.43184	+	9.04029i	−0.0708867	+	0.447561i
$409$			27.5967i			1.36457i	0.731086	+	0.682286i	$0.239014\pi$
$409$			27.5967i			1.36457i	−0.731086	+	0.682286i	$0.760986\pi$
$410$		0			0
$411$	−11.2361			−0.554234
$412$	20.4797	−	3.24367i	1.00896	−	0.159804i
$413$	9.95959	+	9.95959i	0.490080	+	0.490080i
$414$	−3.63271	+	11.1803i	−0.178538	+	0.549484i
$415$		0			0
$416$		−	24.6215i		−	1.20717i
$417$	−8.76393	−	8.76393i	−0.429172	−	0.429172i
$418$	1.58721	+	3.11507i	0.0776329	+	0.152363i
$419$			24.8328i			1.21316i	0.795022	+	0.606581i	$0.207460\pi$
$419$			24.8328i			1.21316i	−0.795022	+	0.606581i	$0.792540\pi$
$420$		0			0
$421$		−	3.46120i		−	0.168689i	−0.996437	−	0.0843443i	$-0.973120\pi$
$421$		−	3.46120i		−	0.168689i	0.996437	−	0.0843443i	$-0.0268795\pi$
$422$	−19.7935	+	10.0853i	−0.963532	+	0.490944i
$423$	16.3925	+	16.3925i	0.797029	+	0.797029i
$424$	2.35114	−	1.70820i	0.114182	−	0.0829577i
$425$		0			0
$426$	−21.7082	−	7.05342i	−1.05177	−	0.341739i
$427$	−11.7082	−	11.7082i	−0.566600	−	0.566600i
$428$	−33.7752	+	5.34946i	−1.63258	+	0.258576i
$429$	−12.3107			−0.594368
$430$		0			0
$431$		−	11.7557i		−	0.566252i	−0.959083	−	0.283126i	$-0.908628\pi$
$431$		−	11.7557i		−	0.566252i	0.959083	−	0.283126i	$-0.0913715\pi$
$432$	3.17442	−	6.23015i	0.152729	−	0.299748i
$433$	−23.1803	+	23.1803i	−1.11398	+	1.11398i	−0.121369	+	0.992608i	$0.538728\pi$
$433$	−23.1803	+	23.1803i	−1.11398	+	1.11398i	−0.992608	+	0.121369i	$0.961272\pi$
$434$	−11.7557	−	3.81966i	−0.564292	−	0.183350i
$435$		0			0
$436$	−7.88854	+	10.8576i	−0.377793	+	0.519987i
$437$	5.25731	−	5.25731i	0.251491	−	0.251491i
$438$	−18.0929	−	35.5093i	−0.864512	−	1.69670i
$439$	−11.2007			−0.534579			−0.267290	−	0.963616i	$-0.586128\pi$
$439$	−11.2007			−0.534579			−0.267290	+	0.963616i	$0.586128\pi$
$440$		0			0
$441$	9.47214			0.451054
$442$	3.95199	+	7.75621i	0.187977	+	0.368926i
$443$	−10.0902	+	10.0902i	−0.479398	+	0.479398i	−0.904939	−	0.425541i	$-0.860084\pi$
$443$	−10.0902	+	10.0902i	−0.479398	+	0.479398i	0.425541	+	0.904939i	$0.360084\pi$
$444$	−16.1150	−	11.7082i	−0.764782	−	0.555647i
$445$		0			0
$446$	−3.29180	−	1.06957i	−0.155871	−	0.0506456i
$447$	−21.3723	+	21.3723i	−1.01087	+	1.01087i
$448$	−11.8504	+	6.03810i	−0.559881	+	0.285273i
$449$		−	31.5967i		−	1.49114i	−0.666426	−	0.745571i	$-0.732177\pi$
$449$		−	31.5967i		−	1.49114i	0.666426	−	0.745571i	$-0.267823\pi$
$450$		0			0
$451$	−9.52786			−0.448650
$452$	−2.08321	−	13.1529i	−0.0979859	−	0.618658i
$453$	−23.7234	−	23.7234i	−1.11462	−	1.11462i
$454$	−22.0988	−	7.18034i	−1.03715	−	0.336990i
$455$		0			0
$456$	10.4721	−	7.60845i	0.490403	−	0.356298i
$457$	21.6525	+	21.6525i	1.01286	+	1.01286i	0.999916	+	0.0129439i	$0.00412028\pi$
$457$	21.6525	+	21.6525i	1.01286	+	1.01286i	0.0129439	+	0.999916i	$0.495880\pi$
$458$	26.9306	−	13.7218i	1.25839	−	0.641180i
$459$			2.47214i			0.115389i
$460$		0			0
$461$		−	6.49839i		−	0.302660i	−0.988483	−	0.151330i	$-0.951644\pi$
$461$		−	6.49839i		−	0.302660i	0.988483	−	0.151330i	$-0.0483557\pi$
$462$	3.01905	+	5.92522i	0.140459	+	0.275666i
$463$	−17.2905	−	17.2905i	−0.803559	−	0.803559i	0.180091	−	0.983650i	$-0.442361\pi$
$463$	−17.2905	−	17.2905i	−0.803559	−	0.803559i	−0.983650	+	0.180091i	$0.942361\pi$
$464$	−1.79611	−	5.52786i	−0.0833824	−	0.256625i
$465$		0			0
$466$	−2.14590	+	6.60440i	−0.0994068	+	0.305943i
$467$	2.67376	+	2.67376i	0.123727	+	0.123727i	0.766259	−	0.642532i	$-0.222116\pi$
$467$	2.67376	+	2.67376i	0.123727	+	0.123727i	−0.642532	+	0.766259i	$0.722116\pi$
$468$	3.04499	+	19.2253i	0.140755	+	0.888691i
$469$	5.60034			0.258600
$470$		0			0
$471$			31.6749i			1.45950i
$472$	−23.6678	−	3.74861i	−1.08940	−	0.172544i
$473$	−2.94427	+	2.94427i	−0.135378	+	0.135378i
$474$	−12.3107	+	37.8885i	−0.565451	+	1.74028i
$475$		0			0
$476$	2.76393	−	3.80423i	0.126685	−	0.174366i
$477$	−1.62460	+	1.62460i	−0.0743853	+	0.0743853i
$478$	36.9501	−	18.8270i	1.69006	−	0.861127i
$479$	7.60845			0.347639			0.173820	−	0.984778i	$-0.444389\pi$
$479$	7.60845			0.347639			0.173820	+	0.984778i	$0.444389\pi$
$480$		0			0
$481$	−18.9443			−0.863784
$482$	−8.52305	+	4.34271i	−0.388214	+	0.197805i
$483$	10.0000	−	10.0000i	0.455016	−	0.455016i
$484$	−11.1352	+	15.3262i	−0.506144	+	0.696647i
$485$		0			0
$486$	−8.41641	+	25.9030i	−0.381776	+	1.17499i
$487$	−9.33905	+	9.33905i	−0.423193	+	0.423193i	−0.886302	−	0.463109i	$-0.846734\pi$
$487$	−9.33905	+	9.33905i	−0.423193	+	0.423193i	0.463109	+	0.886302i	$0.346734\pi$
$488$	27.8232	+	4.40676i	1.25950	+	0.199484i
$489$		−	23.1246i		−	1.04573i
$490$		0			0
$491$	−10.7639			−0.485769			−0.242885	−	0.970055i	$-0.578094\pi$
$491$	−10.7639			−0.485769			−0.242885	+	0.970055i	$0.578094\pi$
$492$	5.51846	+	34.8422i	0.248792	+	1.57081i
$493$	1.45309	+	1.45309i	0.0654437	+	0.0654437i
$494$	3.80423	−	11.7082i	0.171160	−	0.526777i
$495$		0			0
$496$	20.0000	−	6.49839i	0.898027	−	0.291787i
$497$	8.29180	+	8.29180i	0.371938	+	0.371938i
$498$	9.10434	+	17.8683i	0.407975	+	0.800696i
$499$		−	23.8885i		−	1.06940i	−0.845043	−	0.534699i	$-0.820425\pi$
$499$		−	23.8885i		−	1.06940i	0.845043	−	0.534699i	$-0.179575\pi$
$500$		0			0
$501$		−	0.898056i		−	0.0401222i
$502$	27.9489	−	14.2407i	1.24742	−	0.635592i
$503$	5.53483	+	5.53483i	0.246786	+	0.246786i	0.819650	−	0.572864i	$-0.194168\pi$
$503$	5.53483	+	5.53483i	0.246786	+	0.246786i	−0.572864	+	0.819650i	$0.694168\pi$
$504$	8.50651	−	6.18034i	0.378910	−	0.275294i
$505$		0			0
$506$	−6.18034	−	2.00811i	−0.274750	−	0.0892716i
$507$	9.61803	+	9.61803i	0.427152	+	0.427152i
$508$	−3.88661	−	24.5391i	−0.172440	−	1.08875i
$509$	9.06154			0.401646			0.200823	−	0.979628i	$-0.435638\pi$
$509$	9.06154			0.401646			0.200823	+	0.979628i	$0.435638\pi$
$510$		0			0
$511$			20.4742i			0.905726i
$512$	10.2726	−	20.1612i	0.453990	−	0.891007i
$513$	2.47214	−	2.47214i	0.109147	−	0.109147i
$514$	35.5851	+	11.5623i	1.56959	+	0.509991i
$515$		0			0
$516$	12.4721	+	9.06154i	0.549055	+	0.398912i
$517$	−9.06154	+	9.06154i	−0.398526	+	0.398526i
$518$	4.64584	+	9.11798i	0.204127	+	0.400621i
$519$	−20.4742			−0.898718
$520$		0			0
$521$	8.47214			0.371171			0.185586	−	0.982628i	$-0.440582\pi$
$521$	8.47214			0.371171			0.185586	+	0.982628i	$0.440582\pi$
$522$	2.08611	+	4.09423i	0.0913067	+	0.179199i
$523$	16.7426	−	16.7426i	0.732105	−	0.732105i	−0.238932	−	0.971036i	$-0.576797\pi$
$523$	16.7426	−	16.7426i	0.732105	−	0.732105i	0.971036	+	0.238932i	$0.0767972\pi$
$524$	0.343027	−	0.472136i	0.0149852	−	0.0206254i
$525$		0			0
$526$	31.1803	+	10.1311i	1.35953	+	0.441737i
$527$	−5.25731	+	5.25731i	−0.229012	+	0.229012i
$528$	−10.0806	−	5.13632i	−0.438701	−	0.223529i
$529$		−	9.18034i		−	0.399145i
$530$		0			0
$531$	18.9443			0.822111
$532$	−6.56816	+	1.04029i	−0.284766	+	0.0451025i
$533$	23.7234	+	23.7234i	1.02758	+	1.02758i
$534$	19.9192	+	6.47214i	0.861987	+	0.280077i
$535$		0			0
$536$	−7.70820	+	5.60034i	−0.332944	+	0.241898i
$537$	−26.6525	−	26.6525i	−1.15014	−	1.15014i
$538$	−22.5693	+	11.4996i	−0.973030	+	0.495784i
$539$			5.23607i			0.225533i
$540$		0			0
$541$		−	2.90617i		−	0.124946i	−0.998047	−	0.0624730i	$-0.980101\pi$
$541$		−	2.90617i		−	0.124946i	0.998047	−	0.0624730i	$-0.0198987\pi$
$542$	−20.3365	−	39.9127i	−0.873529	−	1.71440i
$543$	−15.2169	−	15.2169i	−0.653020	−	0.653020i
$544$			8.00000i			0.342997i
$545$		0			0
$546$	7.23607	−	22.2703i	0.309675	−	0.953082i
$547$	8.56231	+	8.56231i	0.366098	+	0.366098i	0.866052	−	0.499954i	$-0.166650\pi$
$547$	8.56231	+	8.56231i	0.366098	+	0.366098i	−0.499954	+	0.866052i	$0.666650\pi$
$548$	−9.69977	+	1.53629i	−0.414354	+	0.0656272i
$549$	−22.2703			−0.950474
$550$		0			0
$551$		−	2.90617i		−	0.123807i
$552$	−3.76382	+	23.7638i	−0.160199	+	1.01146i
$553$	14.4721	−	14.4721i	0.615418	−	0.615418i
$554$	1.34708	−	4.14590i	0.0572321	−	0.176142i
$555$		0			0
$556$	−8.76393	−	6.36737i	−0.371674	−	0.270037i
$557$	17.1845	−	17.1845i	0.728132	−	0.728132i	−0.242116	−	0.970247i	$-0.577841\pi$
$557$	17.1845	−	17.1845i	0.728132	−	0.728132i	0.970247	+	0.242116i	$0.0778413\pi$
$558$	−14.8131	+	7.54763i	−0.627087	+	0.319517i
$559$	14.6619			0.620131
$560$		0			0
$561$	4.00000			0.168880
$562$	−4.67261	+	2.38081i	−0.197102	+	0.100429i
$563$	−11.3262	+	11.3262i	−0.477344	+	0.477344i	−0.904281	−	0.426937i	$-0.859593\pi$
$563$	−11.3262	+	11.3262i	−0.477344	+	0.477344i	0.426937	+	0.904281i	$0.359593\pi$
$564$	38.3853	+	27.8885i	1.61631	+	1.17432i
$565$		0			0
$566$	9.65248	−	29.7073i	0.405724	−	1.24869i
$567$	12.5882	−	12.5882i	0.528657	−	0.528657i
$568$	−19.7045	−	3.12088i	−0.826781	−	0.130949i
$569$			13.1246i			0.550212i	0.961414	+	0.275106i	$0.0887130\pi$
$569$			13.1246i			0.550212i	−0.961414	+	0.275106i	$0.911287\pi$
$570$		0			0
$571$	−8.65248			−0.362095			−0.181047	−	0.983474i	$-0.557949\pi$
$571$	−8.65248			−0.362095			−0.181047	+	0.983474i	$0.557949\pi$
$572$	−10.6275	+	1.68323i	−0.444358	+	0.0703794i
$573$	−20.8172	−	20.8172i	−0.869653	−	0.869653i
$574$	5.60034	−	17.2361i	0.233754	−	0.719420i
$575$		0			0
$576$	−5.52786	+	17.0130i	−0.230328	+	0.708876i
$577$	−21.7639	−	21.7639i	−0.906044	−	0.906044i	0.0899059	−	0.995950i	$-0.471343\pi$
$577$	−21.7639	−	21.7639i	−0.906044	−	0.906044i	−0.995950	+	0.0899059i	$0.971343\pi$
$578$	9.63059	+	18.9011i	0.400580	+	0.786182i
$579$		−	24.1803i		−	1.00490i
$580$		0			0
$581$		−	10.3026i		−	0.427425i
$582$	−0.962611	+	0.490475i	−0.0399015	+	0.0203308i
$583$	−0.898056	−	0.898056i	−0.0371937	−	0.0371937i
$584$	−20.4742	−	28.1803i	−0.847229	−	1.16611i
$585$		0			0
$586$	−1.38197	−	0.449028i	−0.0570885	−	0.0185492i
$587$	−5.90983	−	5.90983i	−0.243925	−	0.243925i	0.574547	−	0.818472i	$-0.305178\pi$
$587$	−5.90983	−	5.90983i	−0.243925	−	0.243925i	−0.818472	+	0.574547i	$0.805178\pi$
$588$	19.1477	−	3.03269i	0.789636	−	0.125066i
$589$	10.5146			0.433247
$590$		0			0
$591$		−	7.05342i		−	0.290139i
$592$	−15.5124	−	7.90398i	−0.637557	−	0.324851i
$593$	6.41641	−	6.41641i	0.263490	−	0.263490i	−0.562980	−	0.826470i	$-0.690345\pi$
$593$	6.41641	−	6.41641i	0.263490	−	0.263490i	0.826470	+	0.562980i	$0.190345\pi$
$594$	−2.90617	−	0.944272i	−0.119242	−	0.0387439i
$595$		0			0
$596$	−15.5279	+	21.3723i	−0.636046	+	0.875442i
$597$	29.3238	−	29.3238i	1.20014	−	1.20014i
$598$	10.3884	+	20.3884i	0.424814	+	0.833744i
$599$	−27.5276			−1.12475			−0.562374	−	0.826883i	$-0.690112\pi$
$599$	−27.5276			−1.12475			−0.562374	+	0.826883i	$0.690112\pi$
$600$		0			0
$601$	−4.29180			−0.175066			−0.0875330	−	0.996162i	$-0.527898\pi$
$601$	−4.29180			−0.175066			−0.0875330	+	0.996162i	$0.527898\pi$
$602$	−3.59564	−	7.05684i	−0.146547	−	0.287615i
$603$	5.32624	−	5.32624i	0.216901	−	0.216901i
$604$	−23.7234	−	17.2361i	−0.965292	−	0.701326i
$605$		0			0
$606$	−37.8885	−	12.3107i	−1.53912	−	0.500089i
$607$	6.08985	−	6.08985i	0.247180	−	0.247180i	−0.572633	−	0.819812i	$-0.694078\pi$
$607$	6.08985	−	6.08985i	0.247180	−	0.247180i	0.819812	+	0.572633i	$0.194078\pi$
$608$	8.00000	−	8.00000i	0.324443	−	0.324443i
$609$		−	5.52786i		−	0.224000i
$610$		0			0
$611$	45.1246			1.82555
$612$	−0.989378	−	6.24669i	−0.0399933	−	0.252507i
$613$	27.3561	+	27.3561i	1.10490	+	1.10490i	0.993810	+	0.111094i	$0.0354353\pi$
$613$	27.3561	+	27.3561i	1.10490	+	1.10490i	0.111094	+	0.993810i	$0.464565\pi$
$614$	12.4822	+	4.05573i	0.503743	+	0.163676i
$615$		0			0
$616$	3.41641	+	4.70228i	0.137651	+	0.189460i
$617$	30.8885	+	30.8885i	1.24353	+	1.24353i	0.958528	+	0.284998i	$0.0919929\pi$
$617$	30.8885	+	30.8885i	1.24353	+	1.24353i	0.284998	+	0.958528i	$0.408007\pi$
$618$	−29.8932	+	15.2314i	−1.20248	+	0.612695i
$619$		−	27.3050i		−	1.09748i	−0.835994	−	0.548739i	$-0.815108\pi$
$619$		−	27.3050i		−	1.09748i	0.835994	−	0.548739i	$-0.184892\pi$
$620$		0			0
$621$			6.49839i			0.260772i
$622$	−5.24128	−	10.2866i	−0.210156	−	0.412455i
$623$	−7.60845	−	7.60845i	−0.304826	−	0.304826i
$624$	12.3107	+	37.8885i	0.492824	+	1.51676i
$625$		0			0
$626$	−3.85410	+	11.8617i	−0.154041	+	0.474089i
$627$	−4.00000	−	4.00000i	−0.159745	−	0.159745i
$628$	4.33087	+	27.3440i	0.172820	+	1.09115i
$629$	6.15537			0.245431
$630$		0			0
$631$		−	28.0827i		−	1.11795i	−0.829183	−	0.558977i	$-0.811194\pi$
$631$		−	28.0827i		−	1.11795i	0.829183	−	0.558977i	$-0.188806\pi$
$632$	−5.44705	+	34.3913i	−0.216672	+	1.36801i
$633$	25.4164	−	25.4164i	1.01021	−	1.01021i
$634$	6.60440	−	20.3262i	0.262294	−	0.807258i
$635$		0			0
$636$	−2.76393	+	3.80423i	−0.109597	+	0.150847i
$637$	13.0373	−	13.0373i	0.516556	−	0.516556i
$638$	−2.26323	+	1.15317i	−0.0896023	+	0.0456546i
$639$	15.7719			0.623928
$640$		0			0
$641$	−7.34752			−0.290210			−0.145105	−	0.989416i	$-0.546352\pi$
$641$	−7.34752			−0.290210			−0.145105	+	0.989416i	$0.546352\pi$
$642$	49.2999	−	25.1195i	1.94571	−	0.991389i
$643$	−8.56231	+	8.56231i	−0.337664	+	0.337664i	−0.855488	−	0.517823i	$-0.826742\pi$
$643$	−8.56231	+	8.56231i	−0.337664	+	0.337664i	0.517823	+	0.855488i	$0.326742\pi$
$644$	7.26543	−	10.0000i	0.286298	−	0.394055i
$645$		0			0
$646$	−1.23607	+	3.80423i	−0.0486324	+	0.149675i
$647$	22.8909	−	22.8909i	0.899933	−	0.899933i	−0.0954968	−	0.995430i	$-0.530444\pi$
$647$	22.8909	−	22.8909i	0.899933	−	0.899933i	0.995430	+	0.0954968i	$0.0304440\pi$
$648$	−4.73799	+	29.9145i	−0.186126	+	1.17515i
$649$			10.4721i			0.411067i
$650$		0			0
$651$	20.0000			0.783862
$652$	−3.16180	−	19.9628i	−0.123826	−	0.781804i
$653$	−11.2412	−	11.2412i	−0.439901	−	0.439901i	0.452078	−	0.891979i	$-0.350683\pi$
$653$	−11.2412	−	11.2412i	−0.439901	−	0.439901i	−0.891979	+	0.452078i	$0.850683\pi$
$654$	6.71040	−	20.6525i	0.262397	−	0.807576i
$655$		0			0
$656$	9.52786	+	29.3238i	0.372001	+	1.14490i
$657$	19.4721	+	19.4721i	0.759680	+	0.759680i
$658$	−11.0662	−	21.7187i	−0.431407	−	0.846684i
$659$			18.0000i			0.701180i	0.936529	+	0.350590i	$0.114019\pi$
$659$			18.0000i			0.701180i	−0.936529	+	0.350590i	$0.885981\pi$
$660$		0			0
$661$		−	2.35114i		−	0.0914488i	−0.998954	−	0.0457244i	$-0.985440\pi$
$661$		−	2.35114i		−	0.0914488i	0.998954	−	0.0457244i	$-0.0145596\pi$
$662$	−35.3689	+	18.0213i	−1.37465	+	0.700419i
$663$	−9.95959	−	9.95959i	−0.386799	−	0.386799i
$664$	10.3026	+	14.1803i	0.399819	+	0.550304i
$665$		0			0
$666$	13.0902	+	4.25325i	0.507234	+	0.164810i
$667$	3.81966	+	3.81966i	0.147898	+	0.147898i
$668$	−0.122790	−	0.775266i	−0.00475089	−	0.0299959i
$669$	5.60034			0.216522
$670$		0			0
$671$		−	12.3107i		−	0.475251i
$672$	15.2169	−	15.2169i	0.587005	−	0.587005i
$673$	30.7082	−	30.7082i	1.18371	−	1.18371i	0.204940	−	0.978775i	$-0.434300\pi$
$673$	30.7082	−	30.7082i	1.18371	−	1.18371i	0.978775	−	0.204940i	$-0.0656998\pi$
$674$	−3.91023	−	1.27051i	−0.150616	−	0.0489382i
$675$		0			0
$676$	9.61803	+	6.98791i	0.369924	+	0.268766i
$677$	−8.33499	+	8.33499i	−0.320340	+	0.320340i	−0.848897	−	0.528558i	$-0.822733\pi$
$677$	−8.33499	+	8.33499i	−0.320340	+	0.320340i	0.528558	+	0.848897i	$0.322733\pi$
$678$	9.78216	+	19.1986i	0.375682	+	0.737316i
$679$	0.555029			0.0213001
$680$		0			0
$681$	37.5967			1.44071
$682$	−4.17223	−	8.18845i	−0.159763	−	0.313552i
$683$	−1.79837	+	1.79837i	−0.0688129	+	0.0688129i	−0.740676	−	0.671863i	$-0.765494\pi$
$683$	−1.79837	+	1.79837i	−0.0688129	+	0.0688129i	0.671863	+	0.740676i	$0.265494\pi$
$684$	−5.25731	+	7.23607i	−0.201018	+	0.276678i
$685$		0			0
$686$	−25.1246	−	8.16348i	−0.959262	−	0.311683i
$687$	−34.5811	+	34.5811i	−1.31935	+	1.31935i
$688$	12.0058	+	6.11727i	0.457717	+	0.233219i
$689$			4.47214i			0.170375i
$690$		0			0
$691$	−31.1246			−1.18404			−0.592018	−	0.805925i	$-0.701669\pi$
$691$	−31.1246			−1.18404			−0.592018	+	0.805925i	$0.701669\pi$
$692$	−17.6748	+	2.79941i	−0.671895	+	0.106418i
$693$	−3.24920	−	3.24920i	−0.123427	−	0.123427i
$694$	−5.77185	−	1.87539i	−0.219096	−	0.0711888i
$695$		0			0
$696$	5.52786	+	7.60845i	0.209533	+	0.288398i
$697$	−7.70820	−	7.70820i	−0.291969	−	0.291969i
$698$	19.6067	−	9.99009i	0.742123	−	0.378131i
$699$		−	11.2361i		−	0.424987i
$700$		0			0
$701$			40.3934i			1.52564i	0.646612	+	0.762819i	$0.276185\pi$
$701$			40.3934i			1.52564i	−0.646612	+	0.762819i	$0.723815\pi$
$702$	4.88493	+	9.58721i	0.184370	+	0.361846i
$703$	−6.15537	−	6.15537i	−0.232154	−	0.232154i
$704$	−9.40456	−	3.05573i	−0.354448	−	0.115167i
$705$		0			0
$706$	2.72949	−	8.40051i	0.102726	−	0.316157i
$707$	14.4721	+	14.4721i	0.544281	+	0.544281i
$708$	38.2953	−	6.06538i	1.43923	−	0.227951i
$709$	−13.7638			−0.516911			−0.258456	−	0.966023i	$-0.583214\pi$
$709$	−13.7638			−0.516911			−0.258456	+	0.966023i	$0.583214\pi$
$710$		0			0
$711$		−	27.5276i		−	1.03237i
$712$	18.0806	+	2.86368i	0.677599	+	0.107321i
$713$	−13.8197	+	13.8197i	−0.517550	+	0.517550i
$714$	−2.35114	+	7.23607i	−0.0879892	+	0.270803i
$715$		0			0
$716$	−26.6525	−	19.3642i	−0.996050	−	0.723673i
$717$	−47.4468	+	47.4468i	−1.77193	+	1.77193i
$718$	−2.26323	+	1.15317i	−0.0844631	+	0.0430361i
$719$	44.5407			1.66109			0.830543	−	0.556954i	$-0.188030\pi$
$719$	44.5407			1.66109			0.830543	+	0.556954i	$0.188030\pi$
$720$		0			0
$721$	17.2361			0.641905
$722$	−18.9011	+	9.63059i	−0.703426	+	0.358414i
$723$	10.9443	−	10.9443i	0.407022	−	0.407022i
$724$	−15.2169	−	11.0557i	−0.565532	−	0.410883i
$725$		0			0
$726$	9.47214	−	29.1522i	0.351544	−	1.08194i
$727$	5.87785	−	5.87785i	0.217997	−	0.217997i	−0.589657	−	0.807654i	$-0.700737\pi$
$727$	5.87785	−	5.87785i	0.217997	−	0.217997i	0.807654	+	0.589657i	$0.200737\pi$
$728$	3.20170	−	20.2147i	0.118663	−	0.749207i
$729$		−	11.9443i		−	0.442380i
$730$		0			0
$731$	−4.76393			−0.176200
$732$	−45.0188	+	7.13028i	−1.66394	+	0.263543i
$733$	1.28157	+	1.28157i	0.0473359	+	0.0473359i	0.730379	−	0.683043i	$-0.239344\pi$
$733$	1.28157	+	1.28157i	0.0473359	+	0.0473359i	−0.683043	+	0.730379i	$0.739344\pi$
$734$	−14.8334	+	45.6525i	−0.547510	+	1.68506i
$735$		0			0
$736$			21.0292i			0.775148i
$737$	2.94427	+	2.94427i	0.108454	+	0.108454i
$738$	−11.0662	−	21.7187i	−0.407354	−	0.799477i
$739$			17.4164i			0.640673i	0.947304	+	0.320336i	$0.103796\pi$
$739$			17.4164i			0.640673i	−0.947304	+	0.320336i	$0.896204\pi$
$740$		0			0
$741$			19.9192i			0.731750i
$742$	2.15246	−	1.09673i	0.0790194	−	0.0402624i
$743$	−13.4863	−	13.4863i	−0.494765	−	0.494765i	0.415039	−	0.909804i	$-0.363768\pi$
$743$	−13.4863	−	13.4863i	−0.494765	−	0.494765i	−0.909804	+	0.415039i	$0.863768\pi$
$744$	−27.5276	+	20.0000i	−1.00921	+	0.733236i
$745$		0			0
$746$	28.6180	+	9.29856i	1.04778	+	0.340445i
$747$	−9.79837	−	9.79837i	−0.358504	−	0.358504i
$748$	3.45309	−	0.546915i	0.126257	−	0.0199972i
$749$	−28.4257			−1.03865
$750$		0			0
$751$		−	7.05342i		−	0.257383i	−0.991685	−	0.128692i	$-0.958922\pi$
$751$		−	7.05342i		−	0.257383i	0.991685	−	0.128692i	$-0.0410777\pi$
$752$	36.9501	+	18.8270i	1.34743	+	0.686550i
$753$	−35.8885	+	35.8885i	−1.30785	+	1.30785i
$754$	8.50651	+	2.76393i	0.309789	+	0.100656i
$755$		0			0
$756$	3.41641	−	4.70228i	0.124254	−	0.171020i
$757$	−38.0018	+	38.0018i	−1.38120	+	1.38120i	−0.538701	+	0.842497i	$0.681085\pi$
$757$	−38.0018	+	38.0018i	−1.38120	+	1.38120i	−0.842497	+	0.538701i	$0.818915\pi$
$758$	−23.0419	−	45.2222i	−0.836918	−	1.64254i
$759$	10.5146			0.381657
$760$		0			0
$761$	−14.9443			−0.541729			−0.270865	−	0.962617i	$-0.587310\pi$
$761$	−14.9443			−0.541729			−0.270865	+	0.962617i	$0.587310\pi$
$762$	18.2504	+	35.8185i	0.661143	+	1.29757i
$763$	−7.88854	+	7.88854i	−0.285584	+	0.285584i
$764$	−20.8172	−	15.1246i	−0.753141	−	0.547189i
$765$		0			0
$766$	−21.1803	−	6.88191i	−0.765277	−	0.248654i
$767$	26.0746	−	26.0746i	0.941498	−	0.941498i
$768$	−5.72737	+	36.1612i	−0.206669	+	1.30485i
$769$			2.47214i			0.0891475i	0.999006	+	0.0445738i	$0.0141930\pi$
$769$			2.47214i			0.0891475i	−0.999006	+	0.0445738i	$0.985807\pi$
$770$		0			0
$771$	−60.5410			−2.18033
$772$	−3.30615	−	20.8742i	−0.118991	−	0.751279i
$773$	−4.18774	−	4.18774i	−0.150623	−	0.150623i	0.627773	−	0.778396i	$-0.283966\pi$
$773$	−4.18774	−	4.18774i	−0.150623	−	0.150623i	−0.778396	+	0.627773i	$0.783966\pi$
$774$	−10.1311	−	3.29180i	−0.364155	−	0.118321i
$775$		0			0
$776$	−0.763932	+	0.555029i	−0.0274236	+	0.0199244i
$777$	−11.7082	−	11.7082i	−0.420029	−	0.420029i
$778$	−29.8932	+	15.2314i	−1.07172	+	0.546071i
$779$			15.4164i			0.552350i
$780$		0			0
$781$			8.71851i			0.311973i
$782$	−3.37540	−	6.62460i	−0.120704	−	0.236895i
$783$	1.79611	+	1.79611i	0.0641878	+	0.0641878i
$784$	16.1150	−	5.23607i	0.575534	−	0.187002i
$785$		0			0
$786$	−0.291796	+	0.898056i	−0.0104080	+	0.0320326i
$787$	−11.1459	−	11.1459i	−0.397308	−	0.397308i	0.479974	−	0.877283i	$-0.340646\pi$
$787$	−11.1459	−	11.1459i	−0.397308	−	0.397308i	−0.877283	+	0.479974i	$0.840646\pi$
$788$	−0.964406	−	6.08902i	−0.0343555	−	0.216912i
$789$	−53.0472			−1.88853
$790$		0			0
$791$		−	11.0697i		−	0.393591i
$792$	7.72133	+	1.22294i	0.274366	+	0.0434552i
$793$	−30.6525	+	30.6525i	−1.08850	+	1.08850i
$794$	4.46526	−	13.7426i	0.158466	−	0.487708i
$795$		0			0
$796$	21.3050	−	29.3238i	0.755134	−	1.03935i
$797$	19.7477	−	19.7477i	0.699498	−	0.699498i	−0.264804	−	0.964302i	$-0.585307\pi$
$797$	19.7477	−	19.7477i	0.699498	−	0.699498i	0.964302	+	0.264804i	$0.0853072\pi$
$798$	9.58721	−	4.88493i	0.339384	−	0.172925i
$799$	−14.6619			−0.518700
$800$		0			0
$801$	−14.4721			−0.511348
$802$	4.89985	−	2.49660i	0.173020	−	0.0881580i
$803$	−10.7639	+	10.7639i	−0.379851	+	0.379851i
$804$	9.06154	−	12.4721i	0.319576	−	0.439858i
$805$		0			0
$806$	−10.0000	+	30.7768i	−0.352235	+	1.08407i
$807$	28.9807	−	28.9807i	1.02017	−	1.02017i
$808$	−34.3913	−	5.44705i	−1.20988	−	0.191627i
$809$			12.9443i			0.455096i	0.973767	+	0.227548i	$0.0730709\pi$
$809$			12.9443i			0.455096i	−0.973767	+	0.227548i	$0.926929\pi$
$810$		0			0
$811$	−32.0689			−1.12609			−0.563045	−	0.826426i	$-0.690370\pi$
$811$	−32.0689			−1.12609			−0.563045	+	0.826426i	$0.690370\pi$
$812$	−0.755818	−	4.77205i	−0.0265240	−	0.167466i
$813$	51.2511	+	51.2511i	1.79745	+	1.79745i
$814$	−2.35114	+	7.23607i	−0.0824074	+	0.253624i
$815$		0			0
$816$	−4.00000	−	12.3107i	−0.140028	−	0.430962i
$817$	4.76393	+	4.76393i	0.166669	+	0.166669i
$818$	−17.7182	−	34.7739i	−0.619502	−	1.21584i
$819$			16.1803i			0.565387i
$820$		0			0
$821$			20.4742i			0.714555i	0.933998	+	0.357278i	$0.116295\pi$
$821$			20.4742i			0.714555i	−0.933998	+	0.357278i	$0.883705\pi$
$822$	14.1583	−	7.21400i	0.493826	−	0.251617i
$823$	24.3440	+	24.3440i	0.848577	+	0.848577i	0.989956	−	0.141379i	$-0.0451535\pi$
$823$	24.3440	+	24.3440i	0.848577	+	0.848577i	−0.141379	+	0.989956i	$0.545154\pi$
$824$	−23.7234	+	17.2361i	−0.826444	+	0.600447i
$825$		0			0
$826$	−18.9443	−	6.15537i	−0.659156	−	0.214173i
$827$	−14.8541	−	14.8541i	−0.516528	−	0.516528i	0.399991	−	0.916519i	$-0.369013\pi$
$827$	−14.8541	−	14.8541i	−0.516528	−	0.516528i	−0.916519	+	0.399991i	$0.869013\pi$
$828$	−2.60074	−	16.4204i	−0.0903818	−	0.570648i
$829$	−3.11817			−0.108299			−0.0541493	−	0.998533i	$-0.517245\pi$
$829$	−3.11817			−0.108299			−0.0541493	+	0.998533i	$0.517245\pi$
$830$		0			0
$831$			7.05342i			0.244681i
$832$	15.8080	+	31.0249i	0.548042	+	1.07559i
$833$	−4.23607	+	4.23607i	−0.146771	+	0.146771i
$834$	16.6700	+	5.41641i	0.577235	+	0.187555i
$835$		0			0
$836$	−4.00000	−	2.90617i	−0.138343	−	0.100512i
$837$	−6.49839	+	6.49839i	−0.224617	+	0.224617i
$838$	−15.9436	−	31.2912i	−0.550764	−	1.08094i
$839$	9.40456			0.324682			0.162341	−	0.986735i	$-0.448096\pi$
$839$	9.40456			0.324682			0.162341	+	0.986735i	$0.448096\pi$
$840$		0			0
$841$	−26.8885			−0.927191
$842$	2.22223	+	4.36137i	0.0765830	+	0.150303i
$843$	6.00000	−	6.00000i	0.206651	−	0.206651i
$844$	18.4661	−	25.4164i	0.635629	−	0.874869i
$845$		0			0
$846$	−31.1803	−	10.1311i	−1.07200	−	0.348315i
$847$	−11.1352	+	11.1352i	−0.382609	+	0.382609i
$848$	−1.86588	+	3.66199i	−0.0640744	+	0.125753i
$849$			50.5410i			1.73456i
$850$		0			0
$851$	16.1803			0.554655
$852$	31.8825	−	5.04969i	1.09228	−	0.173000i
$853$	−24.7930	−	24.7930i	−0.848896	−	0.848896i	0.141100	−	0.989995i	$-0.454936\pi$
$853$	−24.7930	−	24.7930i	−0.848896	−	0.848896i	−0.989995	+	0.141100i	$0.954936\pi$
$854$	22.2703	+	7.23607i	0.762075	+	0.247613i
$855$		0			0
$856$	39.1246	−	28.4257i	1.33725	−	0.971570i
$857$	17.8328	+	17.8328i	0.609157	+	0.609157i	0.942726	−	0.333568i	$-0.108253\pi$
$857$	17.8328	+	17.8328i	0.609157	+	0.609157i	−0.333568	+	0.942726i	$0.608253\pi$
$858$	15.5124	−	7.90398i	0.529586	−	0.269837i
$859$		−	7.52786i		−	0.256847i	−0.991719	−	0.128424i	$-0.959008\pi$
$859$		−	7.52786i		−	0.256847i	0.991719	−	0.128424i	$-0.0409917\pi$
$860$		0			0
$861$			29.3238i			0.999351i
$862$	7.54763	+	14.8131i	0.257073	+	0.504535i
$863$	6.22088	+	6.22088i	0.211761	+	0.211761i	0.805015	−	0.593254i	$-0.202157\pi$
$863$	6.22088	+	6.22088i	0.211761	+	0.211761i	−0.593254	+	0.805015i	$0.702157\pi$
$864$			9.88854i			0.336415i
$865$		0			0
$866$	14.3262	−	44.0916i	0.486825	−	1.49829i
$867$	−24.2705	−	24.2705i	−0.824270	−	0.824270i
$868$	17.2654	−	2.73457i	0.586027	−	0.0928175i
$869$	15.2169			0.516198
$870$		0			0
$871$		−	14.6619i		−	0.496799i
$872$	2.96911	−	18.7462i	0.100547	−	0.634826i
$873$	0.527864	−	0.527864i	0.0178655	−	0.0178655i
$874$	−3.24920	+	10.0000i	−0.109906	+	0.338255i
$875$		0			0
$876$	45.5967	+	33.1280i	1.54057	+	1.11929i
$877$	−5.08580	+	5.08580i	−0.171735	+	0.171735i	−0.787741	−	0.616006i	$-0.788750\pi$
$877$	−5.08580	+	5.08580i	−0.171735	+	0.171735i	0.616006	+	0.787741i	$0.288750\pi$
$878$	14.1137	−	7.19128i	0.476313	−	0.242694i
$879$	2.35114			0.0793020
$880$		0			0
$881$	47.1246			1.58767			0.793834	−	0.608134i	$-0.208082\pi$
$881$	47.1246			1.58767			0.793834	+	0.608134i	$0.208082\pi$
$882$	−11.9356	+	6.08149i	−0.401892	+	0.204774i
$883$	−21.7984	+	21.7984i	−0.733574	+	0.733574i	−0.971326	−	0.237752i	$-0.923589\pi$
$883$	−21.7984	+	21.7984i	−0.733574	+	0.733574i	0.237752	+	0.971326i	$0.423589\pi$
$884$	−9.95959	−	7.23607i	−0.334977	−	0.243375i
$885$		0			0
$886$	6.23607	−	19.1926i	0.209505	−	0.644789i
$887$	−28.1482	+	28.1482i	−0.945123	+	0.945123i	−0.998571	−	0.0534473i	$-0.982979\pi$
$887$	−28.1482	+	28.1482i	−0.945123	+	0.945123i	0.0534473	+	0.998571i	$0.482979\pi$
$888$	27.8232	+	4.40676i	0.933684	+	0.147881i
$889$		−	20.6525i		−	0.692662i
$890$		0			0
$891$	13.2361			0.443425
$892$	4.83461	−	0.765727i	0.161875	−	0.0256384i
$893$	14.6619	+	14.6619i	0.490641	+	0.490641i
$894$	13.2088	−	40.6525i	0.441768	−	1.35962i
$895$		0			0
$896$	11.0557	−	15.2169i	0.369346	−	0.508361i
$897$	−26.1803	−	26.1803i	−0.874136	−	0.874136i
$898$	20.2864	+	39.8142i	0.676965	+	1.32862i
$899$			7.63932i			0.254786i
$900$		0			0
$901$		−	1.45309i		−	0.0484093i
$902$	12.0058	−	6.11727i	0.399750	−	0.203683i
$903$	9.06154	+	9.06154i	0.301549	+	0.301549i
$904$	11.0697	+	15.2361i	0.368171	+	0.506744i
$905$		0			0
$906$	45.1246	+	14.6619i	1.49916	+	0.487108i
$907$	23.3262	+	23.3262i	0.774535	+	0.774535i	0.978896	−	0.204361i	$-0.0655115\pi$
$907$	23.3262	+	23.3262i	0.774535	+	0.774535i	−0.204361	+	0.978896i	$0.565512\pi$
$908$	32.4562	−	5.14056i	1.07710	−	0.170595i
$909$	27.5276			0.913034
$910$		0			0
$911$		−	25.1765i		−	0.834135i	−0.908876	−	0.417067i	$-0.863058\pi$
$911$		−	25.1765i		−	0.834135i	0.908876	−	0.417067i	$-0.136942\pi$
$912$	−8.31073	+	16.3107i	−0.275196	+	0.540102i
$913$	5.41641	−	5.41641i	0.179257	−	0.179257i
$914$	−41.1855	−	13.3820i	−1.36229	−	0.442636i
$915$		0			0
$916$	−25.1246	+	34.5811i	−0.830141	+	1.14259i
$917$	0.343027	−	0.343027i	0.0113277	−	0.0113277i
$918$	−1.58721	−	3.11507i	−0.0523857	−	0.102813i
$919$	21.7153			0.716322			0.358161	−	0.933660i	$-0.383404\pi$
$919$	21.7153			0.716322			0.358161	+	0.933660i	$0.383404\pi$
$920$		0			0
$921$	−21.2361			−0.699752
$922$	4.17223	+	8.18845i	0.137405	+	0.269672i
$923$	21.7082	−	21.7082i	0.714534	−	0.714534i
$924$	−7.60845	−	5.52786i	−0.250300	−	0.181853i
$925$		0			0
$926$	32.8885	+	10.6861i	1.08078	+	0.351168i
$927$	16.3925	−	16.3925i	0.538400	−	0.538400i
$928$	5.81234	+	5.81234i	0.190799	+	0.190799i
$929$		−	5.34752i		−	0.175447i	−0.996145	−	0.0877233i	$-0.972041\pi$
$929$		−	5.34752i		−	0.175447i	0.996145	−	0.0877233i	$-0.0279591\pi$
$930$		0			0
$931$	8.47214			0.277663
$932$	−1.53629	−	9.69977i	−0.0503230	−	0.317727i
$933$	13.2088	+	13.2088i	0.432436	+	0.432436i
$934$	−5.08580	−	1.65248i	−0.166412	−	0.0540707i
$935$		0			0
$936$	−16.1803	−	22.2703i	−0.528871	−	0.727928i
$937$	−20.3050	−	20.3050i	−0.663334	−	0.663334i	0.292831	−	0.956164i	$-0.405403\pi$
$937$	−20.3050	−	20.3050i	−0.663334	−	0.663334i	−0.956164	+	0.292831i	$0.905403\pi$
$938$	−7.05684	+	3.59564i	−0.230414	+	0.117402i
$939$		−	20.1803i		−	0.658561i
$940$		0			0
$941$		−	60.8676i		−	1.98423i	−0.125340	−	0.992114i	$-0.540002\pi$
$941$		−	60.8676i		−	1.98423i	0.125340	−	0.992114i	$-0.459998\pi$
$942$	−20.3365	−	39.9127i	−0.662600	−	1.30043i
$943$	−20.2622	−	20.2622i	−0.659828	−	0.659828i
$944$	32.2299	−	10.4721i	1.04899	−	0.340839i
$945$		0			0
$946$	1.81966	−	5.60034i	0.0591623	−	0.182083i
$947$	8.85410	+	8.85410i	0.287720	+	0.287720i	0.836178	−	0.548458i	$-0.184785\pi$
$947$	8.85410	+	8.85410i	0.287720	+	0.287720i	−0.548458	+	0.836178i	$0.684785\pi$
$948$	−8.81351	−	55.6463i	−0.286250	−	1.80731i
$949$	53.6022			1.74000
$950$		0			0
$951$			34.5811i			1.12137i
$952$	−1.04029	+	6.56816i	−0.0337161	+	0.212875i
$953$	6.81966	−	6.81966i	0.220910	−	0.220910i	−0.587971	−	0.808882i	$-0.700073\pi$
$953$	6.81966	−	6.81966i	0.220910	−	0.220910i	0.808882	+	0.587971i	$0.200073\pi$
$954$	1.00406	−	3.09017i	0.0325075	−	0.100048i
$955$		0			0
$956$	−34.4721	+	47.4468i	−1.11491	+	1.53454i
$957$	2.90617	−	2.90617i	0.0939431	−	0.0939431i
$958$	−9.58721	+	4.88493i	−0.309749	+	0.157825i
$959$	−8.16348			−0.263613
$960$		0			0
$961$	3.36068			0.108409
$962$	23.8712	−	12.1630i	0.769638	−	0.392150i
$963$	−27.0344	+	27.0344i	−0.871173	+	0.871173i
$964$	7.95148	−	10.9443i	0.256100	−	0.352491i
$965$		0			0
$966$	−6.18034	+	19.0211i	−0.198849	+	0.611995i
$967$	−12.0332	+	12.0332i	−0.386962	+	0.386962i	−0.873602	−	0.486640i	$-0.838222\pi$
$967$	−12.0332	+	12.0332i	−0.386962	+	0.386962i	0.486640	+	0.873602i	$0.338222\pi$
$968$	4.19107	−	26.4614i	0.134706	−	0.850502i
$969$		−	6.47214i		−	0.207915i
$970$		0			0
$971$	33.5967			1.07817			0.539085	−	0.842251i	$-0.318770\pi$
$971$	33.5967			1.07817			0.539085	+	0.842251i	$0.318770\pi$
$972$	−6.02548	−	38.0434i	−0.193267	−	1.22024i
$973$	−6.36737	−	6.36737i	−0.204128	−	0.204128i
$974$	5.77185	−	17.7639i	0.184942	−	0.569193i
$975$		0			0
$976$	−37.8885	+	12.3107i	−1.21278	+	0.394057i
$977$	28.2361	+	28.2361i	0.903352	+	0.903352i	0.995725	−	0.0923727i	$-0.0294451\pi$
$977$	28.2361	+	28.2361i	0.903352	+	0.903352i	−0.0923727	+	0.995725i	$0.529445\pi$
$978$	14.8469	+	29.1387i	0.474752	+	0.931753i
$979$		−	8.00000i		−	0.255681i
$980$		0			0
$981$			15.0049i			0.479070i
$982$	13.5633	−	6.91087i	0.432824	−	0.220535i
$983$	0.620541	+	0.620541i	0.0197922	+	0.0197922i	0.716934	−	0.697141i	$-0.245545\pi$
$983$	0.620541	+	0.620541i	0.0197922	+	0.0197922i	−0.697141	+	0.716934i	$0.745545\pi$
$984$	−29.3238	−	40.3607i	−0.934807	−	1.28665i
$985$		0			0
$986$	−2.76393	−	0.898056i	−0.0880215	−	0.0285999i
$987$	27.8885	+	27.8885i	0.887702	+	0.887702i
$988$	2.72353	+	17.1957i	0.0866469	+	0.547067i
$989$	−12.5227			−0.398200
$990$		0			0
$991$			19.3642i			0.615123i	0.951528	+	0.307561i	$0.0995129\pi$
$991$			19.3642i			0.615123i	−0.951528	+	0.307561i	$0.900487\pi$
$992$	−21.0292	+	21.0292i	−0.667679	+	0.667679i
$993$	45.4164	−	45.4164i	1.44125	−	1.44125i
$994$	−15.7719	−	5.12461i	−0.500255	−	0.162543i
$995$		0			0
$996$	−22.9443	−	16.6700i	−0.727017	−	0.528209i
$997$	35.6506	−	35.6506i	1.12907	−	1.12907i	0.138738	−	0.990329i	$-0.455696\pi$
$997$	35.6506	−	35.6506i	1.12907	−	1.12907i	0.990329	−	0.138738i	$-0.0443045\pi$
$998$	15.3374	+	30.1013i	0.485497	+	0.952841i
$999$	7.60845			0.240721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.k.h.107.1		8
4.3	odd	2		800.2.o.g.207.1		8
5.2	odd	4		40.2.k.a.3.2	✓	8
5.3	odd	4	inner	200.2.k.h.43.3		8
5.4	even	2		40.2.k.a.27.4	yes	8
8.3	odd	2	inner	200.2.k.h.107.3		8
8.5	even	2		800.2.o.g.207.2		8
15.2	even	4		360.2.w.c.163.3		8
15.14	odd	2		360.2.w.c.307.1		8
20.3	even	4		800.2.o.g.143.2		8
20.7	even	4		160.2.o.a.143.4		8
20.19	odd	2		160.2.o.a.47.3		8
40.3	even	4	inner	200.2.k.h.43.1		8
40.13	odd	4		800.2.o.g.143.1		8
40.19	odd	2		40.2.k.a.27.2	yes	8
40.27	even	4		40.2.k.a.3.4	yes	8
40.29	even	2		160.2.o.a.47.4		8
40.37	odd	4		160.2.o.a.143.3		8
60.47	odd	4		1440.2.bi.c.1423.1		8
60.59	even	2		1440.2.bi.c.847.4		8
80.19	odd	4		1280.2.n.q.767.3		8
80.27	even	4		1280.2.n.q.1023.4		8
80.29	even	4		1280.2.n.m.767.1		8
80.37	odd	4		1280.2.n.m.1023.2		8
80.59	odd	4		1280.2.n.m.767.2		8
80.67	even	4		1280.2.n.m.1023.1		8
80.69	even	4		1280.2.n.q.767.4		8
80.77	odd	4		1280.2.n.q.1023.3		8
120.29	odd	2		1440.2.bi.c.847.1		8
120.59	even	2		360.2.w.c.307.3		8
120.77	even	4		1440.2.bi.c.1423.4		8
120.107	odd	4		360.2.w.c.163.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.2	✓	8	5.2	odd	4
40.2.k.a.3.4	yes	8	40.27	even	4
40.2.k.a.27.2	yes	8	40.19	odd	2
40.2.k.a.27.4	yes	8	5.4	even	2
160.2.o.a.47.3		8	20.19	odd	2
160.2.o.a.47.4		8	40.29	even	2
160.2.o.a.143.3		8	40.37	odd	4
160.2.o.a.143.4		8	20.7	even	4
200.2.k.h.43.1		8	40.3	even	4	inner
200.2.k.h.43.3		8	5.3	odd	4	inner
200.2.k.h.107.1		8	1.1	even	1	trivial
200.2.k.h.107.3		8	8.3	odd	2	inner
360.2.w.c.163.1		8	120.107	odd	4
360.2.w.c.163.3		8	15.2	even	4
360.2.w.c.307.1		8	15.14	odd	2
360.2.w.c.307.3		8	120.59	even	2
800.2.o.g.143.1		8	40.13	odd	4
800.2.o.g.143.2		8	20.3	even	4
800.2.o.g.207.1		8	4.3	odd	2
800.2.o.g.207.2		8	8.5	even	2
1280.2.n.m.767.1		8	80.29	even	4
1280.2.n.m.767.2		8	80.59	odd	4
1280.2.n.m.1023.1		8	80.67	even	4
1280.2.n.m.1023.2		8	80.37	odd	4
1280.2.n.q.767.3		8	80.19	odd	4
1280.2.n.q.767.4		8	80.69	even	4
1280.2.n.q.1023.3		8	80.77	odd	4
1280.2.n.q.1023.4		8	80.27	even	4
1440.2.bi.c.847.1		8	120.29	odd	2
1440.2.bi.c.847.4		8	60.59	even	2
1440.2.bi.c.1423.1		8	60.47	odd	4
1440.2.bi.c.1423.4		8	120.77	even	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26007 + 0.642040i) q^{2} +(1.61803 - 1.61803i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-1.00000 + 3.07768i) q^{6} +(1.17557 - 1.17557i) q^{7} +(-0.442463 + 2.79360i) q^{8} -2.23607i q^{9} +1.23607 q^{11} +(-0.715921 - 4.52015i) q^{12} +(-3.07768 - 3.07768i) q^{13} +(-0.726543 + 2.23607i) q^{14} +(-1.23607 - 3.80423i) q^{16} +(1.00000 + 1.00000i) q^{17} +(1.43564 + 2.81761i) q^{18} -2.00000i q^{19} -3.80423i q^{21} +(-1.55754 + 0.793604i) q^{22} +(2.62866 + 2.62866i) q^{23} +(3.80423 + 5.23607i) q^{24} +(5.85410 + 1.90211i) q^{26} +(1.23607 + 1.23607i) q^{27} +(-0.520147 - 3.28408i) q^{28} +1.45309 q^{29} +5.25731i q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 - 2.00000i) q^{33} +(-1.90211 - 0.618034i) q^{34} +(-3.61803 - 2.62866i) q^{36} +(3.07768 - 3.07768i) q^{37} +(1.28408 + 2.52015i) q^{38} -9.95959 q^{39} -7.70820 q^{41} +(2.44246 + 4.79360i) q^{42} +(-2.38197 + 2.38197i) q^{43} +(1.45309 - 2.00000i) q^{44} +(-5.00000 - 1.62460i) q^{46} +(-7.33094 + 7.33094i) q^{47} +(-8.15537 - 4.15537i) q^{48} +4.23607i q^{49} +3.23607 q^{51} +(-8.59783 + 1.36176i) q^{52} +(-0.726543 - 0.726543i) q^{53} +(-2.35114 - 0.763932i) q^{54} +(2.76393 + 3.80423i) q^{56} +(-3.23607 - 3.23607i) q^{57} +(-1.83099 + 0.932938i) q^{58} +8.47214i q^{59} -9.95959i q^{61} +(-3.37540 - 6.62460i) q^{62} +(-2.62866 - 2.62866i) q^{63} +(-7.60845 - 2.47214i) q^{64} +(-1.23607 + 3.80423i) q^{66} +(2.38197 + 2.38197i) q^{67} +(2.79360 - 0.442463i) q^{68} +8.50651 q^{69} +7.05342i q^{71} +(6.24669 + 0.989378i) q^{72} +(-8.70820 + 8.70820i) q^{73} +(-1.90211 + 5.85410i) q^{74} +(-3.23607 - 2.35114i) q^{76} +(1.45309 - 1.45309i) q^{77} +(12.5498 - 6.39445i) q^{78} +12.3107 q^{79} +10.7082 q^{81} +(9.71290 - 4.94897i) q^{82} +(4.38197 - 4.38197i) q^{83} +(-6.15537 - 4.47214i) q^{84} +(1.47214 - 4.53077i) q^{86} +(2.35114 - 2.35114i) q^{87} +(-0.546915 + 3.45309i) q^{88} -6.47214i q^{89} -7.23607 q^{91} +(7.34342 - 1.16308i) q^{92} +(8.50651 + 8.50651i) q^{93} +(4.53077 - 13.9443i) q^{94} +12.9443 q^{96} +(0.236068 + 0.236068i) q^{97} +(-2.71972 - 5.33776i) q^{98} -2.76393i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{3} - 8 q^{6} - 4 q^{8} - 8 q^{11} - 12 q^{12} + 8 q^{16} + 8 q^{17} - 10 q^{18} - 12 q^{22} + 20 q^{26} - 8 q^{27} + 20 q^{28} + 32 q^{32} + 16 q^{33} - 20 q^{36} + 4 q^{38} - 8 q^{41}+ \cdots + 6 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^3 - 8 * q^6 - 4 * q^8 - 8 * q^11 - 12 * q^12 + 8 * q^16 + 8 * q^17 - 10 * q^18 - 12 * q^22 + 20 * q^26 - 8 * q^27 + 20 * q^28 + 32 * q^32 + 16 * q^33 - 20 * q^36 + 4 * q^38 - 8 * q^41 + 20 * q^42 - 28 * q^43 - 40 * q^46 - 16 * q^48 + 8 * q^51 - 20 * q^52 + 40 * q^56 - 8 * q^57 - 20 * q^58 - 40 * q^62 + 8 * q^66 + 28 * q^67 + 4 * q^68 + 20 * q^72 - 16 * q^73 - 8 * q^76 + 40 * q^78 + 32 * q^81 + 28 * q^82 + 44 * q^83 - 24 * q^86 - 16 * q^88 - 40 * q^91 - 20 * q^92 + 32 * q^96 - 16 * q^97 + 6 * q^98

Introduction

L-functions

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