LMFDB - Embedded newform 200.2.k.h.107.3

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			107.3
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	200.107
Dual form			200.2.k.h.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642040 - 1.26007i) 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} +(-2.79360 + 0.442463i) q^{8} -2.23607i q^{9} +1.23607 q^{11} +(-4.52015 - 0.715921i) 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} +(-2.81761 - 1.43564i) q^{18} -2.00000i q^{19} +3.80423i q^{21} +(0.793604 - 1.55754i) 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} +(3.28408 + 0.520147i) 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} +(-2.52015 - 1.28408i) q^{38} +9.95959 q^{39} -7.70820 q^{41} +(4.79360 + 2.44246i) 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} +(4.15537 + 8.15537i) q^{48} +4.23607i q^{49} +3.23607 q^{51} +(1.36176 - 8.59783i) 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} +(-0.932938 + 1.83099i) q^{58} +8.47214i q^{59} +9.95959i q^{61} +(-6.62460 - 3.37540i) 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} +(0.442463 - 2.79360i) q^{68} -8.50651 q^{69} -7.05342i q^{71} +(0.989378 + 6.24669i) 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} +(6.39445 - 12.5498i) q^{78} -12.3107 q^{79} +10.7082 q^{81} +(-4.94897 + 9.71290i) 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} +(-3.45309 + 0.546915i) q^{88} -6.47214i q^{89} -7.23607 q^{91} +(-1.16308 + 7.34342i) q^{92} +(-8.50651 - 8.50651i) q^{93} +(-4.53077 - 13.9443i) q^{94} +12.9443 q^{96} +(0.236068 + 0.236068i) q^{97} +(5.33776 + 2.71972i) 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 $

$2$	0.642040	−	1.26007i	0.453990	−	0.891007i
$2$	0.642040	−	1.26007i	0.453990	−	0.891007i
$3$	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	−0.893462	−	0.449138i	$-0.851731\pi$
$7$	−1.17557	+	1.17557i	−0.444324	+	0.444324i	0.449138	+	0.893462i	$0.351731\pi$
$8$	−2.79360	+	0.442463i	−0.987688	+	0.156434i
$9$		−	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	$0.440336\pi$
$12$	−4.52015	−	0.715921i	−1.30485	−	0.206669i
$13$	3.07768	+	3.07768i	0.853596	+	0.853596i	0.990574	−	0.136978i	$-0.0437390\pi$
$13$	3.07768	+	3.07768i	0.853596	+	0.853596i	−0.136978	+	0.990574i	$0.543739\pi$
$14$	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	$0.695139\pi$
$18$	−2.81761	−	1.43564i	−0.664117	−	0.338385i
$19$		−	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
$22$	0.793604	−	1.55754i	0.169197	−	0.332068i
$23$	−2.62866	−	2.62866i	−0.548113	−	0.548113i	0.377782	−	0.925895i	$-0.376687\pi$
$23$	−2.62866	−	2.62866i	−0.548113	−	0.548113i	−0.925895	+	0.377782i	$0.876687\pi$
$24$	−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
$28$	3.28408	+	0.520147i	0.620633	+	0.0982985i
$29$	−1.45309			−0.269831			−0.134916	−	0.990857i	$-0.543076\pi$
$29$	−1.45309			−0.269831			−0.134916	+	0.990857i	$0.543076\pi$
$30$		0			0
$31$		−	5.25731i		−	0.944241i	−0.881534	−	0.472120i	$-0.843489\pi$
$31$		−	5.25731i		−	0.944241i	0.881534	−	0.472120i	$-0.156511\pi$
$32$	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	−0.913286	−	0.407318i	$-0.866464\pi$
$37$	−3.07768	+	3.07768i	−0.505968	+	0.505968i	0.407318	+	0.913286i	$0.366464\pi$
$38$	−2.52015	−	1.28408i	−0.408822	−	0.208305i
$39$	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	$0.705593\pi$
$42$	4.79360	+	2.44246i	0.739669	+	0.376880i
$43$	−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	$-0.477088\pi$
$47$	7.33094	−	7.33094i	1.06933	−	1.06933i	0.997411	−	0.0719165i	$-0.0229115\pi$
$48$	4.15537	+	8.15537i	0.599776	+	1.17713i
$49$			4.23607i			0.605153i
$50$		0			0
$51$	3.23607			0.453140
$52$	1.36176	−	8.59783i	0.188842	−	1.19230i
$53$	0.726543	+	0.726543i	0.0997983	+	0.0997983i	0.755243	−	0.655445i	$-0.227519\pi$
$53$	0.726543	+	0.726543i	0.0997983	+	0.0997983i	−0.655445	+	0.755243i	$0.727519\pi$
$54$	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
$58$	−0.932938	+	1.83099i	−0.122501	+	0.240421i
$59$			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	$0.220072\pi$
$61$			9.95959i			1.27520i	−0.770370	+	0.637598i	$0.779928\pi$
$62$	−6.62460	−	3.37540i	−0.841325	−	0.428676i
$63$	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	$0.684030\pi$
$68$	0.442463	−	2.79360i	0.0536566	−	0.338774i
$69$	−8.50651			−1.02406
$70$		0			0
$71$		−	7.05342i		−	0.837087i	−0.908197	−	0.418544i	$-0.862541\pi$
$71$		−	7.05342i		−	0.837087i	0.908197	−	0.418544i	$-0.137459\pi$
$72$	0.989378	+	6.24669i	0.116599	+	0.736179i
$73$	−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
$78$	6.39445	−	12.5498i	0.724029	−	1.42099i
$79$	−12.3107			−1.38507			−0.692533	−	0.721386i	$-0.743505\pi$
$79$	−12.3107			−1.38507			−0.692533	+	0.721386i	$0.743505\pi$
$80$		0			0
$81$	10.7082			1.18980
$82$	−4.94897	+	9.71290i	−0.546522	+	1.07261i
$83$	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
$88$	−3.45309	+	0.546915i	−0.368100	+	0.0583013i
$89$		−	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
$92$	−1.16308	+	7.34342i	−0.121260	+	0.765605i
$93$	−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	$0.744605\pi$
$98$	5.33776	+	2.71972i	0.539195	+	0.274734i
$99$		−	2.76393i		−	0.277786i
$100$		0			0
$101$		−	12.3107i		−	1.22496i	−0.790485	−	0.612482i	$-0.790171\pi$
$101$		−	12.3107i		−	1.22496i	0.790485	−	0.612482i	$-0.209829\pi$
$102$	2.07768	−	4.07768i	0.205721	−	0.403751i
$103$	−7.33094	−	7.33094i	−0.722339	−	0.722339i	0.246742	−	0.969081i	$-0.420640\pi$
$103$	−7.33094	−	7.33094i	−0.722339	−	0.722339i	−0.969081	+	0.246742i	$0.920640\pi$
$104$	−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	$-0.559653\pi$
$108$	0.546915	−	3.45309i	0.0526269	−	0.332273i
$109$	6.71040			0.642739			0.321370	−	0.946954i	$-0.395857\pi$
$109$	6.71040			0.642739			0.321370	+	0.946954i	$0.395857\pi$
$110$		0			0
$111$			9.95959i			0.945323i
$112$	−3.01905	−	5.92522i	−0.285273	−	0.559881i
$113$	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
$118$	10.6755	+	5.43945i	0.982761	+	0.500742i
$119$	−2.35114			−0.215529
$120$		0			0
$121$	−9.47214			−0.861103
$122$	12.5498	+	6.39445i	1.13621	+	0.578927i
$123$	−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	−0.979738	−	0.200282i	$-0.935814\pi$
$127$	−8.78402	+	8.78402i	−0.779456	+	0.779456i	0.200282	+	0.979738i	$0.435814\pi$
$128$	1.76985	−	11.1744i	0.156434	−	0.987688i
$129$			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	$0.495942\pi$
$132$	−5.58721	−	0.884927i	−0.486304	−	0.0770230i
$133$	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	$0.817268\pi$
$138$	−5.46151	+	10.7188i	−0.464915	+	0.912447i
$139$		−	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
$142$	−8.88783	−	4.52858i	−0.745850	−	0.380030i
$143$	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
$148$	8.59783	+	1.36176i	0.706737	+	0.111936i
$149$	13.2088			1.08211			0.541053	−	0.840988i	$-0.318026\pi$
$149$	13.2088			1.08211			0.541053	+	0.840988i	$0.318026\pi$
$150$		0			0
$151$			14.6619i			1.19317i	0.802551	+	0.596583i	$0.203475\pi$
$151$			14.6619i			1.19317i	−0.802551	+	0.596583i	$0.796525\pi$
$152$	0.884927	+	5.58721i	0.0717771	+	0.453182i
$153$	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	−0.198855	−	0.980029i	$-0.563722\pi$
$157$	9.78808	−	9.78808i	0.781174	−	0.781174i	0.980029	+	0.198855i	$0.0637223\pi$
$158$	−7.90398	+	15.5124i	−0.628807	+	1.23410i
$159$	2.35114			0.186458
$160$		0			0
$161$	6.18034			0.487079
$162$	6.87509	−	13.4931i	0.540158	−	1.06012i
$163$	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	−0.717763	−	0.696288i	$-0.754834\pi$
$167$	−0.277515	+	0.277515i	−0.0214747	+	0.0214747i	0.696288	+	0.717763i	$0.254834\pi$
$168$	−1.68323	−	10.6275i	−0.129864	−	0.819930i
$169$			5.94427i			0.457252i
$170$		0			0
$171$	−4.47214			−0.341993
$172$	6.65427	+	1.05393i	0.507383	+	0.0803616i
$173$	6.32688	+	6.32688i	0.481024	+	0.481024i	0.905459	−	0.424435i	$-0.139527\pi$
$173$	6.32688	+	6.32688i	0.481024	+	0.481024i	−0.424435	+	0.905459i	$0.639527\pi$
$174$	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
$178$	−8.15537	−	4.15537i	−0.611271	−	0.311458i
$179$		−	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	$0.113655\pi$
$181$			9.40456i			0.699036i	−0.936930	+	0.349518i	$0.886345\pi$
$182$	−4.64584	+	9.11798i	−0.344373	+	0.675869i
$183$	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
$188$	−20.4797	−	3.24367i	−1.49364	−	0.236569i
$189$	−2.90617			−0.211393
$190$		0			0
$191$			12.8658i			0.930934i	0.885065	+	0.465467i	$0.154114\pi$
$191$			12.8658i			0.930934i	−0.885065	+	0.465467i	$0.845886\pi$
$192$	8.31073	−	16.3107i	0.599776	−	1.17713i
$193$	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	−0.780477	−	0.625185i	$-0.785024\pi$
$197$	−2.17963	+	2.17963i	−0.155292	+	0.155292i	0.625185	+	0.780477i	$0.285024\pi$
$198$	−3.48276	−	1.77455i	−0.247509	−	0.126112i
$199$	−18.1231			−1.28471			−0.642355	−	0.766407i	$-0.722043\pi$
$199$	−18.1231			−1.28471			−0.642355	+	0.766407i	$0.722043\pi$
$200$		0			0
$201$	7.70820			0.543695
$202$	−15.5124	−	7.90398i	−1.09145	−	0.556122i
$203$	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
$208$	−15.5124	+	7.90398i	−1.07559	+	0.548042i
$209$		−	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	$0.318160\pi$
$212$	0.321469	−	2.02967i	0.0220785	−	0.139398i
$213$	−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
$218$	4.30834	−	8.45559i	0.291798	−	0.572685i
$219$			28.1803i			1.90425i
$220$		0			0
$221$			6.15537i			0.414055i
$222$	12.5498	+	6.39445i	0.842289	+	0.429168i
$223$	−1.73060	−	1.73060i	−0.115890	−	0.115890i	0.646784	−	0.762673i	$-0.276114\pi$
$223$	−1.73060	−	1.73060i	−0.115890	−	0.115890i	−0.762673	+	0.646784i	$0.776114\pi$
$224$	−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	$0.566430\pi$
$228$	−1.43184	+	9.04029i	−0.0948260	+	0.598708i
$229$	21.3723			1.41232			0.706160	−	0.708053i	$-0.250426\pi$
$229$	21.3723			1.41232			0.706160	+	0.708053i	$0.250426\pi$
$230$		0			0
$231$			4.70228i			0.309387i
$232$	4.05934	−	0.642937i	0.266509	−	0.0422109i
$233$	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
$238$	−1.50953	+	2.96261i	−0.0978480	+	0.192038i
$239$	29.3238			1.89680			0.948398	−	0.317083i	$-0.102703\pi$
$239$	29.3238			1.89680			0.948398	+	0.317083i	$0.102703\pi$
$240$		0			0
$241$	6.76393			0.435703			0.217852	−	0.975982i	$-0.430095\pi$
$241$	6.76393			0.435703			0.217852	+	0.975982i	$0.430095\pi$
$242$	−6.08149	+	11.9356i	−0.390933	+	0.767249i
$243$	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
$248$	2.32617	+	14.6868i	0.147712	+	0.932616i
$249$		−	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	$0.746819\pi$
$252$	1.16308	−	7.34342i	0.0732674	−	0.462592i
$253$	−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	$-0.558928\pi$
$258$	9.71290	+	4.94897i	0.604699	+	0.308110i
$259$		−	7.23607i		−	0.449627i
$260$		0			0
$261$			3.24920i			0.201120i
$262$	0.187345	−	0.367684i	0.0115742	−	0.0227156i
$263$	16.3925	+	16.3925i	1.01080	+	1.01080i	0.999941	+	0.0108623i	$0.00345764\pi$
$263$	16.3925	+	16.3925i	1.01080	+	1.01080i	0.0108623	+	0.999941i	$0.496542\pi$
$264$	−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
$268$	1.05393	−	6.65427i	0.0643792	−	0.406474i
$269$	−17.9111			−1.09206			−0.546029	−	0.837766i	$-0.683861\pi$
$269$	−17.9111			−1.09206			−0.546029	+	0.837766i	$0.683861\pi$
$270$		0			0
$271$		−	31.6749i		−	1.92411i	−0.272851	−	0.962056i	$-0.587967\pi$
$271$		−	31.6749i		−	1.92411i	0.272851	−	0.962056i	$-0.412033\pi$
$272$	−5.04029	+	2.56816i	−0.305613	+	0.155717i
$273$	−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	−0.638588	−	0.769549i	$-0.720481\pi$
$277$	2.17963	−	2.17963i	0.130961	−	0.130961i	0.769549	+	0.638588i	$0.220481\pi$
$278$	−6.82507	−	3.47755i	−0.409341	−	0.208569i
$279$	−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	$0.464721\pi$
$282$	−29.8932	−	15.2314i	−1.78012	−	0.907015i
$283$	−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
$292$	24.3273	+	3.85306i	1.42365	+	0.225483i
$293$	−0.726543	−	0.726543i	−0.0424451	−	0.0424451i	0.685566	−	0.728011i	$-0.259555\pi$
$293$	−0.726543	−	0.726543i	−0.0424451	−	0.0424451i	−0.728011	+	0.685566i	$0.759555\pi$
$294$	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
$298$	8.48057	−	16.6440i	0.491266	−	0.964164i
$299$		−	16.1803i		−	0.935733i
$300$		0			0
$301$		−	5.60034i		−	0.322798i
$302$	18.4750	+	9.41350i	1.06312	+	0.541686i
$303$	−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	$0.835317\pi$
$308$	4.05934	+	0.642937i	0.231303	+	0.0366347i
$309$	−23.7234			−1.34958
$310$		0			0
$311$		−	8.16348i		−	0.462909i	−0.972846	−	0.231454i	$-0.925652\pi$
$311$		−	8.16348i		−	0.462909i	0.972846	−	0.231454i	$-0.0743484\pi$
$312$	−27.8232	+	4.40676i	−1.57518	+	0.249483i
$313$	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	−0.340171	−	0.940364i	$-0.610485\pi$
$317$	10.6861	−	10.6861i	0.600193	−	0.600193i	0.940364	+	0.340171i	$0.110485\pi$
$318$	1.50953	−	2.96261i	0.0846500	−	0.166135i
$319$	−1.79611			−0.100563
$320$		0			0
$321$	−39.1246			−2.18372
$322$	3.96802	−	7.78768i	0.221129	−	0.433991i
$323$	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
$328$	21.5337	−	3.41060i	1.18900	−	0.188319i
$329$			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	$0.219555\pi$
$332$	−12.2415	−	1.93886i	−0.671838	−	0.106409i
$333$	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	$0.724769\pi$
$338$	7.49022	+	3.81646i	0.407414	+	0.207588i
$339$		−	15.2361i		−	0.827510i
$340$		0			0
$341$		−	6.49839i		−	0.351908i
$342$	−2.87129	+	5.63522i	−0.155261	+	0.304718i
$343$	−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	$0.713254\pi$
$348$	6.56816	+	1.04029i	0.352090	+	0.0557656i
$349$	15.5599			0.832904			0.416452	−	0.909158i	$-0.363273\pi$
$349$	15.5599			0.832904			0.416452	+	0.909158i	$0.363273\pi$
$350$		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
$358$	−20.7561	−	10.5758i	−1.09699	−	0.558946i
$359$	−1.79611			−0.0947952			−0.0473976	−	0.998876i	$-0.515093\pi$
$359$	−1.79611			−0.0947952			−0.0473976	+	0.998876i	$0.515093\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	11.8504	+	6.03810i	0.622845	+	0.317356i
$363$	−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	$0.596452\pi$
$367$	−24.0009	+	24.0009i	−1.25284	+	1.25284i	−0.954442	+	0.298396i	$0.903548\pi$
$368$	13.2492	−	6.75080i	0.690662	−	0.351910i
$369$			17.2361i			0.897274i
$370$		0			0
$371$	−1.70820			−0.0886855
$372$	−3.76382	+	23.7638i	−0.195145	+	1.23210i
$373$	15.0454	+	15.0454i	0.779021	+	0.779021i	0.979664	−	0.200644i	$-0.0643033\pi$
$373$	15.0454	+	15.0454i	0.779021	+	0.779021i	−0.200644	+	0.979664i	$0.564303\pi$
$374$	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
$378$	−1.86588	+	3.66199i	−0.0959703	+	0.188352i
$379$			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
$382$	16.2118	+	8.26033i	0.829468	+	0.422635i
$383$	−11.1352	−	11.1352i	−0.568980	−	0.568980i	0.362862	−	0.931843i	$-0.381799\pi$
$383$	−11.1352	−	11.1352i	−0.568980	−	0.568980i	−0.931843	+	0.362862i	$0.881799\pi$
$384$	−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
$388$	0.104451	−	0.659481i	0.00530272	−	0.0334801i
$389$	−23.7234			−1.20282			−0.601412	−	0.798939i	$-0.705395\pi$
$389$	−23.7234			−1.20282			−0.601412	+	0.798939i	$0.705395\pi$
$390$		0			0
$391$		−	5.25731i		−	0.265874i
$392$	−1.87431	−	11.8339i	−0.0946667	−	0.597702i
$393$	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	−0.502164	−	0.864773i	$-0.667462\pi$
$397$	7.22494	−	7.22494i	0.362609	−	0.362609i	0.864773	+	0.502164i	$0.167462\pi$
$398$	−11.6357	+	22.8364i	−0.583246	+	1.14469i
$399$	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	$0.530954\pi$
$402$	4.94897	−	9.71290i	0.246832	−	0.484436i
$403$	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
$408$	−9.04029	+	1.43184i	−0.447561	+	0.0708867i
$409$			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
$412$	−3.24367	+	20.4797i	−0.159804	+	1.00896i
$413$	−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
$418$	−3.11507	−	1.58721i	−0.152363	−	0.0776329i
$419$			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	$0.0268795\pi$
$421$			3.46120i			0.168689i	−0.996437	+	0.0843443i	$0.973120\pi$
$422$	10.0853	−	19.7935i	0.490944	−	0.963532i
$423$	−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
$428$	−5.34946	+	33.7752i	−0.258576	+	1.63258i
$429$	12.3107			0.594368
$430$		0			0
$431$			11.7557i			0.566252i	0.959083	+	0.283126i	$0.0913715\pi$
$431$			11.7557i			0.566252i	−0.959083	+	0.283126i	$0.908628\pi$
$432$	−6.23015	+	3.17442i	−0.299748	+	0.152729i
$433$	−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
$438$	35.5093	+	18.0929i	1.69670	+	0.864512i
$439$	11.2007			0.534579			0.267290	−	0.963616i	$-0.413872\pi$
$439$	11.2007			0.534579			0.267290	+	0.963616i	$0.413872\pi$
$440$		0			0
$441$	9.47214			0.451054
$442$	7.75621	+	3.95199i	0.368926	+	0.187977i
$443$	−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
$448$	−6.03810	+	11.8504i	−0.285273	+	0.559881i
$449$		−	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
$452$	−13.1529	−	2.08321i	−0.618658	−	0.0979859i
$453$	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	$0.495880\pi$
$458$	13.7218	−	26.9306i	0.641180	−	1.25839i
$459$			2.47214i			0.115389i
$460$		0			0
$461$			6.49839i			0.302660i	0.988483	+	0.151330i	$0.0483557\pi$
$461$			6.49839i			0.302660i	−0.988483	+	0.151330i	$0.951644\pi$
$462$	5.92522	+	3.01905i	0.275666	+	0.140459i
$463$	17.2905	+	17.2905i	0.803559	+	0.803559i	0.983650	−	0.180091i	$-0.0576392\pi$
$463$	17.2905	+	17.2905i	0.803559	+	0.803559i	−0.180091	+	0.983650i	$0.557639\pi$
$464$	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	$0.722116\pi$
$468$	−19.2253	−	3.04499i	−0.888691	−	0.140755i
$469$	−5.60034			−0.258600
$470$		0			0
$471$		−	31.6749i		−	1.45950i
$472$	−3.74861	−	23.6678i	−0.172544	−	1.08940i
$473$	−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
$478$	18.8270	−	36.9501i	0.861127	−	1.69006i
$479$	−7.60845			−0.347639			−0.173820	−	0.984778i	$-0.555611\pi$
$479$	−7.60845			−0.347639			−0.173820	+	0.984778i	$0.555611\pi$
$480$		0			0
$481$	−18.9443			−0.863784
$482$	4.34271	−	8.52305i	0.197805	−	0.388214i
$483$	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	−0.463109	−	0.886302i	$-0.653266\pi$
$487$	9.33905	−	9.33905i	0.423193	−	0.423193i	0.886302	+	0.463109i	$0.153266\pi$
$488$	−4.40676	−	27.8232i	−0.199484	−	1.25950i
$489$		−	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	$0.578094\pi$
$492$	34.8422	+	5.51846i	1.57081	+	0.248792i
$493$	−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
$498$	−17.8683	−	9.10434i	−0.800696	−	0.407975i
$499$		−	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
$502$	−14.2407	+	27.9489i	−0.635592	+	1.24742i
$503$	−5.53483	−	5.53483i	−0.246786	−	0.246786i	0.572864	−	0.819650i	$-0.305832\pi$
$503$	−5.53483	−	5.53483i	−0.246786	−	0.246786i	−0.819650	+	0.572864i	$0.805832\pi$
$504$	−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
$508$	24.5391	+	3.88661i	1.08875	+	0.172440i
$509$	−9.06154			−0.401646			−0.200823	−	0.979628i	$-0.564362\pi$
$509$	−9.06154			−0.401646			−0.200823	+	0.979628i	$0.564362\pi$
$510$		0			0
$511$		−	20.4742i		−	0.905726i
$512$	−20.1612	+	10.2726i	−0.891007	+	0.453990i
$513$	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
$518$	−9.11798	−	4.64584i	−0.400621	−	0.204127i
$519$	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	$0.440582\pi$
$522$	4.09423	+	2.08611i	0.179199	+	0.0913067i
$523$	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
$528$	5.13632	+	10.0806i	0.223529	+	0.438701i
$529$		−	9.18034i		−	0.399145i
$530$		0			0
$531$	18.9443			0.822111
$532$	1.04029	−	6.56816i	0.0451025	−	0.284766i
$533$	−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
$538$	−11.4996	+	22.5693i	−0.495784	+	0.973030i
$539$			5.23607i			0.225533i
$540$		0			0
$541$			2.90617i			0.124946i	0.998047	+	0.0624730i	$0.0198987\pi$
$541$			2.90617i			0.124946i	−0.998047	+	0.0624730i	$0.980101\pi$
$542$	−39.9127	−	20.3365i	−1.71440	−	0.873529i
$543$	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	$0.666650\pi$
$548$	−1.53629	+	9.69977i	−0.0656272	+	0.414354i
$549$	22.2703			0.950474
$550$		0			0
$551$			2.90617i			0.123807i
$552$	23.7638	−	3.76382i	1.01146	−	0.160199i
$553$	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	−0.970247	−	0.242116i	$-0.922159\pi$
$557$	−17.1845	+	17.1845i	−0.728132	+	0.728132i	0.242116	+	0.970247i	$0.422159\pi$
$558$	−7.54763	+	14.8131i	−0.319517	+	0.627087i
$559$	−14.6619			−0.620131
$560$		0			0
$561$	4.00000			0.168880
$562$	2.38081	−	4.67261i	0.100429	−	0.197102i
$563$	−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
$568$	3.12088	+	19.7045i	0.130949	+	0.826781i
$569$			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	$0.557949\pi$
$572$	1.68323	−	10.6275i	0.0703794	−	0.444358i
$573$	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	$0.971343\pi$
$578$	−18.9011	−	9.63059i	−0.786182	−	0.400580i
$579$		−	24.1803i		−	1.00490i
$580$		0			0
$581$			10.3026i			0.427425i
$582$	0.490475	−	0.962611i	0.0203308	−	0.0399015i
$583$	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	$0.805178\pi$
$588$	3.03269	−	19.1477i	0.125066	−	0.789636i
$589$	−10.5146			−0.433247
$590$		0			0
$591$			7.05342i			0.290139i
$592$	−7.90398	−	15.5124i	−0.324851	−	0.637557i
$593$	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
$598$	−20.3884	−	10.3884i	−0.833744	−	0.424814i
$599$	27.5276			1.12475			0.562374	−	0.826883i	$-0.309888\pi$
$599$	27.5276			1.12475			0.562374	+	0.826883i	$0.309888\pi$
$600$		0			0
$601$	−4.29180			−0.175066			−0.0875330	−	0.996162i	$-0.527898\pi$
$601$	−4.29180			−0.175066			−0.0875330	+	0.996162i	$0.527898\pi$
$602$	−7.05684	−	3.59564i	−0.287615	−	0.146547i
$603$	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	−0.819812	−	0.572633i	$-0.805922\pi$
$607$	−6.08985	+	6.08985i	−0.247180	+	0.247180i	0.572633	+	0.819812i	$0.305922\pi$
$608$	8.00000	−	8.00000i	0.324443	−	0.324443i
$609$		−	5.52786i		−	0.224000i
$610$		0			0
$611$	45.1246			1.82555
$612$	−6.24669	−	0.989378i	−0.252507	−	0.0399933i
$613$	−27.3561	−	27.3561i	−1.10490	−	1.10490i	−0.993810	−	0.111094i	$-0.964565\pi$
$613$	−27.3561	−	27.3561i	−1.10490	−	1.10490i	−0.111094	−	0.993810i	$-0.535435\pi$
$614$	−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	$0.408007\pi$
$618$	−15.2314	+	29.8932i	−0.612695	+	1.20248i
$619$		−	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
$622$	−10.2866	−	5.24128i	−0.412455	−	0.210156i
$623$	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
$628$	−27.3440	−	4.33087i	−1.09115	−	0.172820i
$629$	−6.15537			−0.245431
$630$		0			0
$631$			28.0827i			1.11795i	0.829183	+	0.558977i	$0.188806\pi$
$631$			28.0827i			1.11795i	−0.829183	+	0.558977i	$0.811194\pi$
$632$	34.3913	−	5.44705i	1.36801	−	0.216672i
$633$	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
$638$	−1.15317	+	2.26323i	−0.0456546	+	0.0896023i
$639$	−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	$0.546352\pi$
$642$	−25.1195	+	49.2999i	−0.991389	+	1.94571i
$643$	−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	−0.995430	−	0.0954968i	$-0.969556\pi$
$647$	−22.8909	+	22.8909i	−0.899933	+	0.899933i	0.0954968	+	0.995430i	$0.469556\pi$
$648$	−29.9145	+	4.73799i	−1.17515	+	0.186126i
$649$			10.4721i			0.411067i
$650$		0			0
$651$	20.0000			0.783862
$652$	−19.9628	−	3.16180i	−0.781804	−	0.123826i
$653$	11.2412	+	11.2412i	0.439901	+	0.439901i	0.891979	−	0.452078i	$-0.149317\pi$
$653$	11.2412	+	11.2412i	0.439901	+	0.439901i	−0.452078	+	0.891979i	$0.649317\pi$
$654$	−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
$658$	21.7187	+	11.0662i	0.846684	+	0.431407i
$659$			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	$0.0145596\pi$
$661$			2.35114i			0.0914488i	−0.998954	+	0.0457244i	$0.985440\pi$
$662$	18.0213	−	35.3689i	0.700419	−	1.37465i
$663$	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
$668$	0.775266	+	0.122790i	0.0299959	+	0.00475089i
$669$	−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	−0.528558	−	0.848897i	$-0.677267\pi$
$677$	8.33499	−	8.33499i	0.320340	−	0.320340i	0.848897	+	0.528558i	$0.177267\pi$
$678$	−19.1986	−	9.78216i	−0.737316	−	0.375682i
$679$	−0.555029			−0.0213001
$680$		0			0
$681$	37.5967			1.44071
$682$	−8.18845	−	4.17223i	−0.313552	−	0.159763i
$683$	−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
$688$	−6.11727	−	12.0058i	−0.233219	−	0.457717i
$689$			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	$0.701669\pi$
$692$	2.79941	−	17.6748i	0.106418	−	0.671895i
$693$	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
$698$	9.99009	−	19.6067i	0.378131	−	0.742123i
$699$		−	11.2361i		−	0.424987i
$700$		0			0
$701$		−	40.3934i		−	1.52564i	−0.646612	−	0.762819i	$-0.723815\pi$
$701$		−	40.3934i		−	1.52564i	0.646612	−	0.762819i	$-0.276185\pi$
$702$	9.58721	+	4.88493i	0.361846	+	0.184370i
$703$	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
$708$	6.06538	−	38.2953i	0.227951	−	1.43923i
$709$	13.7638			0.516911			0.258456	−	0.966023i	$-0.416786\pi$
$709$	13.7638			0.516911			0.258456	+	0.966023i	$0.416786\pi$
$710$		0			0
$711$			27.5276i			1.03237i
$712$	2.86368	+	18.0806i	0.107321	+	0.677599i
$713$	−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
$718$	−1.15317	+	2.26323i	−0.0430361	+	0.0844631i
$719$	−44.5407			−1.66109			−0.830543	−	0.556954i	$-0.811970\pi$
$719$	−44.5407			−1.66109			−0.830543	+	0.556954i	$0.811970\pi$
$720$		0			0
$721$	17.2361			0.641905
$722$	9.63059	−	18.9011i	0.358414	−	0.703426i
$723$	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	−0.807654	−	0.589657i	$-0.799263\pi$
$727$	−5.87785	+	5.87785i	−0.217997	+	0.217997i	0.589657	+	0.807654i	$0.299263\pi$
$728$	20.2147	−	3.20170i	0.749207	−	0.118663i
$729$		−	11.9443i		−	0.442380i
$730$		0			0
$731$	−4.76393			−0.176200
$732$	7.13028	−	45.0188i	0.263543	−	1.66394i
$733$	−1.28157	−	1.28157i	−0.0473359	−	0.0473359i	0.683043	−	0.730379i	$-0.260656\pi$
$733$	−1.28157	−	1.28157i	−0.0473359	−	0.0473359i	−0.730379	+	0.683043i	$0.760656\pi$
$734$	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
$738$	21.7187	+	11.0662i	0.799477	+	0.407354i
$739$			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
$742$	−1.09673	+	2.15246i	−0.0402624	+	0.0790194i
$743$	13.4863	+	13.4863i	0.494765	+	0.494765i	0.909804	−	0.415039i	$-0.136232\pi$
$743$	13.4863	+	13.4863i	0.494765	+	0.494765i	−0.415039	+	0.909804i	$0.636232\pi$
$744$	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
$748$	0.546915	−	3.45309i	0.0199972	−	0.126257i
$749$	28.4257			1.03865
$750$		0			0
$751$			7.05342i			0.257383i	0.991685	+	0.128692i	$0.0410777\pi$
$751$			7.05342i			0.257383i	−0.991685	+	0.128692i	$0.958922\pi$
$752$	18.8270	+	36.9501i	0.686550	+	1.34743i
$753$	−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	$-0.318915\pi$
$757$	38.0018	−	38.0018i	1.38120	−	1.38120i	0.842497	−	0.538701i	$-0.181085\pi$
$758$	45.2222	+	23.0419i	1.64254	+	0.836918i
$759$	−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	$0.587310\pi$
$762$	35.8185	+	18.2504i	1.29757	+	0.661143i
$763$	−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
$768$	−36.1612	+	5.72737i	−1.30485	+	0.206669i
$769$			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
$772$	−20.8742	−	3.30615i	−0.751279	−	0.118991i
$773$	4.18774	+	4.18774i	0.150623	+	0.150623i	0.778396	−	0.627773i	$-0.216034\pi$
$773$	4.18774	+	4.18774i	0.150623	+	0.150623i	−0.627773	+	0.778396i	$0.716034\pi$
$774$	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
$778$	−15.2314	+	29.8932i	−0.546071	+	1.07172i
$779$			15.4164i			0.552350i
$780$		0			0
$781$		−	8.71851i		−	0.311973i
$782$	−6.62460	−	3.37540i	−0.236895	−	0.120704i
$783$	−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	$0.840646\pi$
$788$	6.08902	+	0.964406i	0.216912	+	0.0343555i
$789$	53.0472			1.88853
$790$		0			0
$791$			11.0697i			0.393591i
$792$	1.22294	+	7.72133i	0.0434552	+	0.274366i
$793$	−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	−0.964302	−	0.264804i	$-0.914693\pi$
$797$	−19.7477	+	19.7477i	−0.699498	+	0.699498i	0.264804	+	0.964302i	$0.414693\pi$
$798$	4.88493	−	9.58721i	0.172925	−	0.339384i
$799$	14.6619			0.518700
$800$		0			0
$801$	−14.4721			−0.511348
$802$	−2.49660	+	4.89985i	−0.0881580	+	0.173020i
$803$	−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
$808$	5.44705	+	34.3913i	0.191627	+	1.20988i
$809$			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	$0.690370\pi$
$812$	−4.77205	−	0.755818i	−0.167466	−	0.0265240i
$813$	−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
$818$	34.7739	+	17.7182i	1.21584	+	0.619502i
$819$			16.1803i			0.565387i
$820$		0			0
$821$		−	20.4742i		−	0.714555i	−0.933998	−	0.357278i	$-0.883705\pi$
$821$		−	20.4742i		−	0.714555i	0.933998	−	0.357278i	$-0.116295\pi$
$822$	−7.21400	+	14.1583i	−0.251617	+	0.493826i
$823$	−24.3440	−	24.3440i	−0.848577	−	0.848577i	0.141379	−	0.989956i	$-0.454846\pi$
$823$	−24.3440	−	24.3440i	−0.848577	−	0.848577i	−0.989956	+	0.141379i	$0.954846\pi$
$824$	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	$0.869013\pi$
$828$	16.4204	+	2.60074i	0.570648	+	0.0903818i
$829$	3.11817			0.108299			0.0541493	−	0.998533i	$-0.482755\pi$
$829$	3.11817			0.108299			0.0541493	+	0.998533i	$0.482755\pi$
$830$		0			0
$831$		−	7.05342i		−	0.244681i
$832$	31.0249	+	15.8080i	1.07559	+	0.548042i
$833$	−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
$838$	31.2912	+	15.9436i	1.08094	+	0.550764i
$839$	−9.40456			−0.324682			−0.162341	−	0.986735i	$-0.551904\pi$
$839$	−9.40456			−0.324682			−0.162341	+	0.986735i	$0.551904\pi$
$840$		0			0
$841$	−26.8885			−0.927191
$842$	4.36137	+	2.22223i	0.150303	+	0.0765830i
$843$	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
$848$	−3.66199	+	1.86588i	−0.125753	+	0.0640744i
$849$			50.5410i			1.73456i
$850$		0			0
$851$	16.1803			0.554655
$852$	−5.04969	+	31.8825i	−0.173000	+	1.09228i
$853$	24.7930	+	24.7930i	0.848896	+	0.848896i	0.989995	−	0.141100i	$-0.0450639\pi$
$853$	24.7930	+	24.7930i	0.848896	+	0.848896i	−0.141100	+	0.989995i	$0.545064\pi$
$854$	−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	$0.608253\pi$
$858$	7.90398	−	15.5124i	0.269837	−	0.529586i
$859$		−	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
$862$	14.8131	+	7.54763i	0.504535	+	0.257073i
$863$	−6.22088	−	6.22088i	−0.211761	−	0.211761i	0.593254	−	0.805015i	$-0.297843\pi$
$863$	−6.22088	−	6.22088i	−0.211761	−	0.211761i	−0.805015	+	0.593254i	$0.797843\pi$
$864$			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
$868$	2.73457	−	17.2654i	0.0928175	−	0.586027i
$869$	−15.2169			−0.516198
$870$		0			0
$871$			14.6619i			0.496799i
$872$	−18.7462	+	2.96911i	−0.634826	+	0.100547i
$873$	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	−0.616006	−	0.787741i	$-0.711250\pi$
$877$	5.08580	−	5.08580i	0.171735	−	0.171735i	0.787741	+	0.616006i	$0.211250\pi$
$878$	7.19128	−	14.1137i	0.242694	−	0.476313i
$879$	−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	$0.208082\pi$
$882$	6.08149	−	11.9356i	0.204774	−	0.401892i
$883$	−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	−0.0534473	−	0.998571i	$-0.517021\pi$
$887$	28.1482	−	28.1482i	0.945123	−	0.945123i	0.998571	+	0.0534473i	$0.0170209\pi$
$888$	−4.40676	−	27.8232i	−0.147881	−	0.933684i
$889$		−	20.6525i		−	0.692662i
$890$		0			0
$891$	13.2361			0.443425
$892$	−0.765727	+	4.83461i	−0.0256384	+	0.161875i
$893$	−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
$898$	−39.8142	−	20.2864i	−1.32862	−	0.676965i
$899$			7.63932i			0.254786i
$900$		0			0
$901$			1.45309i			0.0484093i
$902$	−6.11727	+	12.0058i	−0.203683	+	0.399750i
$903$	−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	$0.565512\pi$
$908$	5.14056	−	32.4562i	0.170595	−	1.07710i
$909$	−27.5276			−0.913034
$910$		0			0
$911$			25.1765i			0.834135i	0.908876	+	0.417067i	$0.136942\pi$
$911$			25.1765i			0.834135i	−0.908876	+	0.417067i	$0.863058\pi$
$912$	16.3107	−	8.31073i	0.540102	−	0.275196i
$913$	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
$918$	3.11507	+	1.58721i	0.102813	+	0.0523857i
$919$	−21.7153			−0.716322			−0.358161	−	0.933660i	$-0.616596\pi$
$919$	−21.7153			−0.716322			−0.358161	+	0.933660i	$0.616596\pi$
$920$		0			0
$921$	−21.2361			−0.699752
$922$	8.18845	+	4.17223i	0.269672	+	0.137405i
$923$	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
$932$	−9.69977	−	1.53629i	−0.317727	−	0.0503230i
$933$	−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	$0.905403\pi$
$938$	−3.59564	+	7.05684i	−0.117402	+	0.230414i
$939$		−	20.1803i		−	0.658561i
$940$		0			0
$941$			60.8676i			1.98423i	0.125340	+	0.992114i	$0.459998\pi$
$941$			60.8676i			1.98423i	−0.125340	+	0.992114i	$0.540002\pi$
$942$	−39.9127	−	20.3365i	−1.30043	−	0.662600i
$943$	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	$0.684785\pi$
$948$	55.6463	+	8.81351i	1.80731	+	0.286250i
$949$	−53.6022			−1.74000
$950$		0			0
$951$		−	34.5811i		−	1.12137i
$952$	6.56816	−	1.04029i	0.212875	−	0.0337161i
$953$	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
$958$	−4.88493	+	9.58721i	−0.157825	+	0.309749i
$959$	8.16348			0.263613
$960$		0			0
$961$	3.36068			0.108409
$962$	−12.1630	+	23.8712i	−0.392150	+	0.769638i
$963$	−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	−0.486640	−	0.873602i	$-0.661778\pi$
$967$	12.0332	−	12.0332i	0.386962	−	0.386962i	0.873602	+	0.486640i	$0.161778\pi$
$968$	26.4614	−	4.19107i	0.850502	−	0.134706i
$969$		−	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	$0.318770\pi$
$972$	−38.0434	−	6.02548i	−1.22024	−	0.193267i
$973$	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	$0.529445\pi$
$978$	−29.1387	−	14.8469i	−0.931753	−	0.474752i
$979$		−	8.00000i		−	0.255681i
$980$		0			0
$981$		−	15.0049i		−	0.479070i
$982$	−6.91087	+	13.5633i	−0.220535	+	0.432824i
$983$	−0.620541	−	0.620541i	−0.0197922	−	0.0197922i	0.697141	−	0.716934i	$-0.254455\pi$
$983$	−0.620541	−	0.620541i	−0.0197922	−	0.0197922i	−0.716934	+	0.697141i	$0.754455\pi$
$984$	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
$988$	−17.1957	−	2.72353i	−0.547067	−	0.0866469i
$989$	12.5227			0.398200
$990$		0			0
$991$		−	19.3642i		−	0.615123i	−0.951528	−	0.307561i	$-0.900487\pi$
$991$		−	19.3642i		−	0.615123i	0.951528	−	0.307561i	$-0.0995129\pi$
$992$	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	$0.544304\pi$
$997$	−35.6506	+	35.6506i	−1.12907	+	1.12907i	−0.990329	+	0.138738i	$0.955696\pi$
$998$	−30.1013	−	15.3374i	−0.952841	−	0.485497i
$999$	−7.60845			−0.240721

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.2	✓	8	40.27	even	4
40.2.k.a.3.4	yes	8	5.2	odd	4
40.2.k.a.27.2	yes	8	5.4	even	2
40.2.k.a.27.4	yes	8	40.19	odd	2
160.2.o.a.47.3		8	40.29	even	2
160.2.o.a.47.4		8	20.19	odd	2
160.2.o.a.143.3		8	20.7	even	4
160.2.o.a.143.4		8	40.37	odd	4
200.2.k.h.43.1		8	5.3	odd	4	inner
200.2.k.h.43.3		8	40.3	even	4	inner
200.2.k.h.107.1		8	8.3	odd	2	inner
200.2.k.h.107.3		8	1.1	even	1	trivial
360.2.w.c.163.1		8	15.2	even	4
360.2.w.c.163.3		8	120.107	odd	4
360.2.w.c.307.1		8	120.59	even	2
360.2.w.c.307.3		8	15.14	odd	2
800.2.o.g.143.1		8	20.3	even	4
800.2.o.g.143.2		8	40.13	odd	4
800.2.o.g.207.1		8	8.5	even	2
800.2.o.g.207.2		8	4.3	odd	2
1280.2.n.m.767.1		8	80.59	odd	4
1280.2.n.m.767.2		8	80.29	even	4
1280.2.n.m.1023.1		8	80.37	odd	4
1280.2.n.m.1023.2		8	80.67	even	4
1280.2.n.q.767.3		8	80.69	even	4
1280.2.n.q.767.4		8	80.19	odd	4
1280.2.n.q.1023.3		8	80.27	even	4
1280.2.n.q.1023.4		8	80.77	odd	4
1440.2.bi.c.847.1		8	60.59	even	2
1440.2.bi.c.847.4		8	120.29	odd	2
1440.2.bi.c.1423.1		8	120.77	even	4
1440.2.bi.c.1423.4		8	60.47	odd	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+(0.642040 - 1.26007i) 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} +(-2.79360 + 0.442463i) q^{8} -2.23607i q^{9} +1.23607 q^{11} +(-4.52015 - 0.715921i) 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} +(-2.81761 - 1.43564i) q^{18} -2.00000i q^{19} +3.80423i q^{21} +(0.793604 - 1.55754i) 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} +(3.28408 + 0.520147i) 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} +(-2.52015 - 1.28408i) q^{38} +9.95959 q^{39} -7.70820 q^{41} +(4.79360 + 2.44246i) 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} +(4.15537 + 8.15537i) q^{48} +4.23607i q^{49} +3.23607 q^{51} +(1.36176 - 8.59783i) 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} +(-0.932938 + 1.83099i) q^{58} +8.47214i q^{59} +9.95959i q^{61} +(-6.62460 - 3.37540i) 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} +(0.442463 - 2.79360i) q^{68} -8.50651 q^{69} -7.05342i q^{71} +(0.989378 + 6.24669i) 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} +(6.39445 - 12.5498i) q^{78} -12.3107 q^{79} +10.7082 q^{81} +(-4.94897 + 9.71290i) 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} +(-3.45309 + 0.546915i) q^{88} -6.47214i q^{89} -7.23607 q^{91} +(-1.16308 + 7.34342i) q^{92} +(-8.50651 - 8.50651i) q^{93} +(-4.53077 - 13.9443i) q^{94} +12.9443 q^{96} +(0.236068 + 0.236068i) q^{97} +(5.33776 + 2.71972i) 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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