LMFDB - Embedded newform 17.2.d.a.15.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [17,2,Mod(2,17)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.135745683436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			15.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	17.15
Dual form			17.2.d.a.8.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70711 - 1.70711i) q^{2} +(0.414214 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 + 0.292893i) q^{5} +(1.00000 - 2.41421i) q^{6} +(-2.41421 - 1.00000i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.29289 - 1.29289i) q^{9} +(1.70711 + 0.707107i) q^{10} +(-1.00000 + 2.41421i) q^{11} +(-3.82843 + 1.58579i) q^{12} -1.41421i q^{13} +(2.41421 + 5.82843i) q^{14} +(-0.585786 - 0.585786i) q^{15} -3.00000 q^{16} +(2.82843 - 3.00000i) q^{17} -4.41421 q^{18} +(0.585786 + 0.585786i) q^{19} +(-1.12132 - 2.70711i) q^{20} -2.82843i q^{21} +(5.82843 - 2.41421i) q^{22} +(-1.82843 + 4.41421i) q^{23} +(4.41421 + 1.82843i) q^{24} +(-3.12132 + 3.12132i) q^{25} +(-2.41421 + 2.41421i) q^{26} +(4.82843 + 2.00000i) q^{27} +(3.82843 - 9.24264i) q^{28} +(-0.292893 + 0.121320i) q^{29} +2.00000i q^{30} +(-3.00000 - 7.24264i) q^{31} +(-1.12132 - 1.12132i) q^{32} -2.82843 q^{33} +(-9.94975 + 0.292893i) q^{34} +2.00000 q^{35} +(4.94975 + 4.94975i) q^{36} +(3.53553 + 8.53553i) q^{37} -2.00000i q^{38} +(1.41421 - 0.585786i) q^{39} +(-1.29289 + 3.12132i) q^{40} +(1.12132 + 0.464466i) q^{41} +(-4.82843 + 4.82843i) q^{42} +(-0.585786 + 0.585786i) q^{43} +(-9.24264 - 3.82843i) q^{44} +(-0.535534 + 1.29289i) q^{45} +(10.6569 - 4.41421i) q^{46} -5.17157i q^{47} +(-1.24264 - 3.00000i) q^{48} +(-0.121320 - 0.121320i) q^{49} +10.6569 q^{50} +(4.17157 + 1.58579i) q^{51} +5.41421 q^{52} +(-1.00000 - 1.00000i) q^{53} +(-4.82843 - 11.6569i) q^{54} -2.00000i q^{55} +(-10.6569 + 4.41421i) q^{56} +(-0.343146 + 0.828427i) q^{57} +(0.707107 + 0.292893i) q^{58} +(4.24264 - 4.24264i) q^{59} +(2.24264 - 2.24264i) q^{60} +(-3.53553 - 1.46447i) q^{61} +(-7.24264 + 17.4853i) q^{62} +(-4.41421 + 1.82843i) q^{63} +9.82843i q^{64} +(0.414214 + 1.00000i) q^{65} +(4.82843 + 4.82843i) q^{66} +1.17157 q^{67} +(11.4853 + 10.8284i) q^{68} -5.17157 q^{69} +(-3.41421 - 3.41421i) q^{70} +(-2.07107 - 5.00000i) q^{71} -8.07107i q^{72} +(-11.9497 + 4.94975i) q^{73} +(8.53553 - 20.6066i) q^{74} +(-4.41421 - 1.82843i) q^{75} +(-2.24264 + 2.24264i) q^{76} +(4.82843 - 4.82843i) q^{77} +(-3.41421 - 1.41421i) q^{78} +(1.82843 - 4.41421i) q^{79} +(2.12132 - 0.878680i) q^{80} +0.171573i q^{81} +(-1.12132 - 2.70711i) q^{82} +(8.24264 + 8.24264i) q^{83} +10.8284 q^{84} +(-1.12132 + 2.94975i) q^{85} +2.00000 q^{86} +(-0.242641 - 0.242641i) q^{87} +(4.41421 + 10.6569i) q^{88} +6.58579i q^{89} +(3.12132 - 1.29289i) q^{90} +(-1.41421 + 3.41421i) q^{91} +(-16.8995 - 7.00000i) q^{92} +(6.00000 - 6.00000i) q^{93} +(-8.82843 + 8.82843i) q^{94} +(-0.585786 - 0.242641i) q^{95} +(0.656854 - 1.58579i) q^{96} +(9.53553 - 3.94975i) q^{97} +0.414214i q^{98} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 8 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 4 q^{14} - 8 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} + 4 q^{20} + 12 q^{22} + 4 q^{23} + 12 q^{24} - 4 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 + 8 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 4 * q^14 - 8 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 + 4 * q^20 + 12 * q^22 + 4 * q^23 + 12 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^29 - 12 * q^31 + 4 * q^32 - 20 * q^34 + 8 * q^35 - 8 * q^40 - 4 * q^41 - 8 * q^42 - 8 * q^43 - 20 * q^44 + 12 * q^45 + 20 * q^46 + 12 * q^48 + 8 * q^49 + 20 * q^50 + 28 * q^51 + 16 * q^52 - 4 * q^53 - 8 * q^54 - 20 * q^56 - 24 * q^57 - 8 * q^60 - 12 * q^62 - 12 * q^63 - 4 * q^65 + 8 * q^66 + 16 * q^67 + 12 * q^68 - 32 * q^69 - 8 * q^70 + 20 * q^71 - 28 * q^73 + 20 * q^74 - 12 * q^75 + 8 * q^76 + 8 * q^77 - 8 * q^78 - 4 * q^79 + 4 * q^82 + 16 * q^83 + 32 * q^84 + 4 * q^85 + 8 * q^86 + 16 * q^87 + 12 * q^88 + 4 * q^90 - 28 * q^92 + 24 * q^93 - 24 * q^94 - 8 * q^95 - 20 * q^96 + 24 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.971960	−	0.235147i	$-0.924443\pi$
$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.235147	−	0.971960i	$-0.575557\pi$
$3$	0.414214	+	1.00000i	0.239146	+	0.577350i	0.997195	−	0.0748477i	$-0.0238471\pi$
$3$	0.414214	+	1.00000i	0.239146	+	0.577350i	−0.758049	+	0.652198i	$0.773847\pi$
$4$			3.82843i			1.91421i
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	−0.535151	−	0.844756i	$-0.679745\pi$
$5$	−0.707107	+	0.292893i	−0.316228	+	0.130986i	0.218924	+	0.975742i	$0.429745\pi$
$6$	1.00000	−	2.41421i	0.408248	−	0.985599i
$7$	−2.41421	−	1.00000i	−0.912487	−	0.377964i	−0.123479	−	0.992347i	$-0.539405\pi$
$7$	−2.41421	−	1.00000i	−0.912487	−	0.377964i	−0.789008	+	0.614383i	$0.789405\pi$
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	1.29289	−	1.29289i	0.430964	−	0.430964i
$10$	1.70711	+	0.707107i	0.539835	+	0.223607i
$11$	−1.00000	+	2.41421i	−0.301511	+	0.727913i	0.698414	+	0.715694i	$0.253889\pi$
$11$	−1.00000	+	2.41421i	−0.301511	+	0.727913i	−0.999925	+	0.0122188i	$0.996111\pi$
$12$	−3.82843	+	1.58579i	−1.10517	+	0.457777i
$13$		−	1.41421i		−	0.392232i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$		−	1.41421i		−	0.392232i	0.980581	−	0.196116i	$-0.0628330\pi$
$14$	2.41421	+	5.82843i	0.645226	+	1.55771i
$15$	−0.585786	−	0.585786i	−0.151249	−	0.151249i
$16$	−3.00000			−0.750000
$17$	2.82843	−	3.00000i	0.685994	−	0.727607i
$17$	2.82843	−	3.00000i	0.685994	−	0.727607i
$18$	−4.41421			−1.04044
$19$	0.585786	+	0.585786i	0.134389	+	0.134389i	0.771101	−	0.636713i	$-0.219706\pi$
$19$	0.585786	+	0.585786i	0.134389	+	0.134389i	−0.636713	+	0.771101i	$0.719706\pi$
$20$	−1.12132	−	2.70711i	−0.250735	−	0.605327i
$21$		−	2.82843i		−	0.617213i
$22$	5.82843	−	2.41421i	1.24262	−	0.514712i
$23$	−1.82843	+	4.41421i	−0.381253	+	0.920427i	0.610471	+	0.792039i	$0.290980\pi$
$23$	−1.82843	+	4.41421i	−0.381253	+	0.920427i	−0.991724	+	0.128388i	$0.959020\pi$
$24$	4.41421	+	1.82843i	0.901048	+	0.373226i
$25$	−3.12132	+	3.12132i	−0.624264	+	0.624264i
$26$	−2.41421	+	2.41421i	−0.473466	+	0.473466i
$27$	4.82843	+	2.00000i	0.929231	+	0.384900i
$28$	3.82843	−	9.24264i	0.723505	−	1.74669i
$29$	−0.292893	+	0.121320i	−0.0543889	+	0.0225286i	−0.409712	−	0.912215i	$-0.634371\pi$
$29$	−0.292893	+	0.121320i	−0.0543889	+	0.0225286i	0.355323	+	0.934744i	$0.384371\pi$
$30$			2.00000i			0.365148i
$31$	−3.00000	−	7.24264i	−0.538816	−	1.30082i	−0.925550	−	0.378625i	$-0.876397\pi$
$31$	−3.00000	−	7.24264i	−0.538816	−	1.30082i	0.386734	−	0.922191i	$-0.373603\pi$
$32$	−1.12132	−	1.12132i	−0.198223	−	0.198223i
$33$	−2.82843			−0.492366
$34$	−9.94975	+	0.292893i	−1.70637	+	0.0502308i
$35$	2.00000			0.338062
$36$	4.94975	+	4.94975i	0.824958	+	0.824958i
$37$	3.53553	+	8.53553i	0.581238	+	1.40323i	0.891691	+	0.452644i	$0.149519\pi$
$37$	3.53553	+	8.53553i	0.581238	+	1.40323i	−0.310453	+	0.950589i	$0.600481\pi$
$38$		−	2.00000i		−	0.324443i
$39$	1.41421	−	0.585786i	0.226455	−	0.0938009i
$40$	−1.29289	+	3.12132i	−0.204424	+	0.493524i
$41$	1.12132	+	0.464466i	0.175121	+	0.0725374i	0.468521	−	0.883452i	$-0.344787\pi$
$41$	1.12132	+	0.464466i	0.175121	+	0.0725374i	−0.293400	+	0.955990i	$0.594787\pi$
$42$	−4.82843	+	4.82843i	−0.745042	+	0.745042i
$43$	−0.585786	+	0.585786i	−0.0893316	+	0.0893316i	−0.750360	−	0.661029i	$-0.770120\pi$
$43$	−0.585786	+	0.585786i	−0.0893316	+	0.0893316i	0.661029	+	0.750360i	$0.270120\pi$
$44$	−9.24264	−	3.82843i	−1.39338	−	0.577157i
$45$	−0.535534	+	1.29289i	−0.0798327	+	0.192733i
$46$	10.6569	−	4.41421i	1.57127	−	0.650840i
$47$		−	5.17157i		−	0.754351i	−0.926142	−	0.377176i	$-0.876895\pi$
$47$		−	5.17157i		−	0.754351i	0.926142	−	0.377176i	$-0.123105\pi$
$48$	−1.24264	−	3.00000i	−0.179360	−	0.433013i
$49$	−0.121320	−	0.121320i	−0.0173315	−	0.0173315i
$50$	10.6569			1.50711
$51$	4.17157	+	1.58579i	0.584137	+	0.222055i
$52$	5.41421			0.750816
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	0.635083	−	0.772444i	$-0.280966\pi$
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	−0.772444	+	0.635083i	$0.780966\pi$
$54$	−4.82843	−	11.6569i	−0.657066	−	1.58630i
$55$		−	2.00000i		−	0.269680i
$56$	−10.6569	+	4.41421i	−1.42408	+	0.589874i
$57$	−0.343146	+	0.828427i	−0.0454508	+	0.109728i
$58$	0.707107	+	0.292893i	0.0928477	+	0.0384588i
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	−0.374772	−	0.927117i	$-0.622279\pi$
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	0.927117	+	0.374772i	$0.122279\pi$
$60$	2.24264	−	2.24264i	0.289524	−	0.289524i
$61$	−3.53553	−	1.46447i	−0.452679	−	0.187506i	0.144682	−	0.989478i	$-0.453784\pi$
$61$	−3.53553	−	1.46447i	−0.452679	−	0.187506i	−0.597361	+	0.801973i	$0.703784\pi$
$62$	−7.24264	+	17.4853i	−0.919816	+	2.22063i
$63$	−4.41421	+	1.82843i	−0.556139	+	0.230360i
$64$			9.82843i			1.22855i
$65$	0.414214	+	1.00000i	0.0513769	+	0.124035i
$66$	4.82843	+	4.82843i	0.594338	+	0.594338i
$67$	1.17157			0.143130			0.0715652	−	0.997436i	$-0.477201\pi$
$67$	1.17157			0.143130			0.0715652	+	0.997436i	$0.477201\pi$
$68$	11.4853	+	10.8284i	1.39279	+	1.31314i
$69$	−5.17157			−0.622584
$70$	−3.41421	−	3.41421i	−0.408077	−	0.408077i
$71$	−2.07107	−	5.00000i	−0.245791	−	0.593391i	0.752048	−	0.659109i	$-0.229066\pi$
$71$	−2.07107	−	5.00000i	−0.245791	−	0.593391i	−0.997838	+	0.0657178i	$0.979066\pi$
$72$		−	8.07107i		−	0.951184i
$73$	−11.9497	+	4.94975i	−1.39861	+	0.579324i	−0.949391	−	0.314097i	$-0.898298\pi$
$73$	−11.9497	+	4.94975i	−1.39861	+	0.579324i	−0.449221	+	0.893421i	$0.648298\pi$
$74$	8.53553	−	20.6066i	0.992236	−	2.39547i
$75$	−4.41421	−	1.82843i	−0.509709	−	0.211129i
$76$	−2.24264	+	2.24264i	−0.257249	+	0.257249i
$77$	4.82843	−	4.82843i	0.550250	−	0.550250i
$78$	−3.41421	−	1.41421i	−0.386584	−	0.160128i
$79$	1.82843	−	4.41421i	0.205714	−	0.496638i	−0.787026	−	0.616920i	$-0.788380\pi$
$79$	1.82843	−	4.41421i	0.205714	−	0.496638i	0.992740	+	0.120283i	$0.0383801\pi$
$80$	2.12132	−	0.878680i	0.237171	−	0.0982394i
$81$			0.171573i			0.0190637i
$82$	−1.12132	−	2.70711i	−0.123829	−	0.298950i
$83$	8.24264	+	8.24264i	0.904747	+	0.904747i	0.995842	−	0.0910949i	$-0.0290366\pi$
$83$	8.24264	+	8.24264i	0.904747	+	0.904747i	−0.0910949	+	0.995842i	$0.529037\pi$
$84$	10.8284			1.18148
$85$	−1.12132	+	2.94975i	−0.121624	+	0.319945i
$86$	2.00000			0.215666
$87$	−0.242641	−	0.242641i	−0.0260138	−	0.0260138i
$88$	4.41421	+	10.6569i	0.470557	+	1.13602i
$89$			6.58579i			0.698092i	0.937106	+	0.349046i	$0.113494\pi$
$89$			6.58579i			0.698092i	−0.937106	+	0.349046i	$0.886506\pi$
$90$	3.12132	−	1.29289i	0.329016	−	0.136283i
$91$	−1.41421	+	3.41421i	−0.148250	+	0.357907i
$92$	−16.8995	−	7.00000i	−1.76189	−	0.729800i
$93$	6.00000	−	6.00000i	0.622171	−	0.622171i
$94$	−8.82843	+	8.82843i	−0.910583	+	0.910583i
$95$	−0.585786	−	0.242641i	−0.0601004	−	0.0248944i
$96$	0.656854	−	1.58579i	0.0670399	−	0.161849i
$97$	9.53553	−	3.94975i	0.968187	−	0.401036i	0.158150	−	0.987415i	$-0.449447\pi$
$97$	9.53553	−	3.94975i	0.968187	−	0.401036i	0.810037	+	0.586379i	$0.199447\pi$
$98$			0.414214i			0.0418419i
$99$	1.82843	+	4.41421i	0.183764	+	0.443645i
$100$	−11.9497	−	11.9497i	−1.19497	−	1.19497i
$101$	−10.5858			−1.05333			−0.526663	−	0.850074i	$-0.676557\pi$
$101$	−10.5858			−1.05333			−0.526663	+	0.850074i	$0.676557\pi$
$102$	−4.41421	−	9.82843i	−0.437072	−	0.973159i
$103$	12.4853			1.23021			0.615106	−	0.788445i	$-0.289113\pi$
$103$	12.4853			1.23021			0.615106	+	0.788445i	$0.289113\pi$
$104$	−4.41421	−	4.41421i	−0.432849	−	0.432849i
$105$	0.828427	+	2.00000i	0.0808462	+	0.195180i
$106$			3.41421i			0.331618i
$107$	0.414214	−	0.171573i	0.0400435	−	0.0165866i	−0.362572	−	0.931956i	$-0.618101\pi$
$107$	0.414214	−	0.171573i	0.0400435	−	0.0165866i	0.402615	+	0.915369i	$0.368101\pi$
$108$	−7.65685	+	18.4853i	−0.736781	+	1.77875i
$109$	14.3640	+	5.94975i	1.37582	+	0.569882i	0.943360	−	0.331772i	$-0.107646\pi$
$109$	14.3640	+	5.94975i	1.37582	+	0.569882i	0.432458	+	0.901654i	$0.357646\pi$
$110$	−3.41421	+	3.41421i	−0.325532	+	0.325532i
$111$	−7.07107	+	7.07107i	−0.671156	+	0.671156i
$112$	7.24264	+	3.00000i	0.684365	+	0.283473i
$113$	5.05025	−	12.1924i	0.475088	−	1.14696i	−0.486799	−	0.873514i	$-0.661835\pi$
$113$	5.05025	−	12.1924i	0.475088	−	1.14696i	0.961886	−	0.273449i	$-0.0881645\pi$
$114$	2.00000	−	0.828427i	0.187317	−	0.0775893i
$115$		−	3.65685i		−	0.341003i
$116$	−0.464466	−	1.12132i	−0.0431246	−	0.104112i
$117$	−1.82843	−	1.82843i	−0.169038	−	0.169038i
$118$	−14.4853			−1.33348
$119$	−9.82843	+	4.41421i	−0.900970	+	0.404650i
$120$	−3.65685			−0.333824
$121$	2.94975	+	2.94975i	0.268159	+	0.268159i
$122$	3.53553	+	8.53553i	0.320092	+	0.772771i
$123$			1.31371i			0.118453i
$124$	27.7279	−	11.4853i	2.49004	−	1.03141i
$125$	2.75736	−	6.65685i	0.246626	−	0.595407i
$126$	10.6569	+	4.41421i	0.949388	+	0.393249i
$127$	−3.75736	+	3.75736i	−0.333412	+	0.333412i	−0.853881	−	0.520469i	$-0.825757\pi$
$127$	−3.75736	+	3.75736i	−0.333412	+	0.333412i	0.520469	+	0.853881i	$0.325757\pi$
$128$	14.5355	−	14.5355i	1.28477	−	1.28477i
$129$	−0.828427	−	0.343146i	−0.0729389	−	0.0302123i
$130$	1.00000	−	2.41421i	0.0877058	−	0.211741i
$131$	−14.0711	+	5.82843i	−1.22939	+	0.509232i	−0.900385	−	0.435094i	$-0.856715\pi$
$131$	−14.0711	+	5.82843i	−1.22939	+	0.509232i	−0.329010	+	0.944326i	$0.606715\pi$
$132$		−	10.8284i		−	0.942494i
$133$	−0.828427	−	2.00000i	−0.0718337	−	0.173422i
$134$	−2.00000	−	2.00000i	−0.172774	−	0.172774i
$135$	−4.00000			−0.344265
$136$	−0.535534	−	18.1924i	−0.0459217	−	1.55998i
$137$	−16.7279			−1.42916			−0.714581	−	0.699552i	$-0.753383\pi$
$137$	−16.7279			−1.42916			−0.714581	+	0.699552i	$0.753383\pi$
$138$	8.82843	+	8.82843i	0.751526	+	0.751526i
$139$	−8.17157	−	19.7279i	−0.693104	−	1.67330i	−0.738432	−	0.674328i	$-0.764433\pi$
$139$	−8.17157	−	19.7279i	−0.693104	−	1.67330i	0.0453279	−	0.998972i	$-0.485567\pi$
$140$			7.65685i			0.647122i
$141$	5.17157	−	2.14214i	0.435525	−	0.180400i
$142$	−5.00000	+	12.0711i	−0.419591	+	1.01298i
$143$	3.41421	+	1.41421i	0.285511	+	0.118262i
$144$	−3.87868	+	3.87868i	−0.323223	+	0.323223i
$145$	0.171573	−	0.171573i	0.0142484	−	0.0142484i
$146$	28.8492	+	11.9497i	2.38758	+	0.988968i
$147$	0.0710678	−	0.171573i	0.00586157	−	0.0141511i
$148$	−32.6777	+	13.5355i	−2.68609	+	1.11261i
$149$			16.9706i			1.39028i	0.718873	+	0.695141i	$0.244658\pi$
$149$			16.9706i			1.39028i	−0.718873	+	0.695141i	$0.755342\pi$
$150$	4.41421	+	10.6569i	0.360419	+	0.870129i
$151$	5.07107	+	5.07107i	0.412678	+	0.412678i	0.882670	−	0.469993i	$-0.155743\pi$
$151$	5.07107	+	5.07107i	0.412678	+	0.412678i	−0.469993	+	0.882670i	$0.655743\pi$
$152$	3.65685			0.296610
$153$	−0.221825	−	7.53553i	−0.0179335	−	0.609212i
$154$	−16.4853			−1.32842
$155$	4.24264	+	4.24264i	0.340777	+	0.340777i
$156$	2.24264	+	5.41421i	0.179555	+	0.433484i
$157$		−	9.65685i		−	0.770701i	−0.922770	−	0.385350i	$-0.874081\pi$
$157$		−	9.65685i		−	0.770701i	0.922770	−	0.385350i	$-0.125919\pi$
$158$	−10.6569	+	4.41421i	−0.847814	+	0.351176i
$159$	0.585786	−	1.41421i	0.0464559	−	0.112154i
$160$	1.12132	+	0.464466i	0.0886482	+	0.0367193i
$161$	8.82843	−	8.82843i	0.695778	−	0.695778i
$162$	0.292893	−	0.292893i	0.0230119	−	0.0230119i
$163$	−7.82843	−	3.24264i	−0.613170	−	0.253983i	0.0544134	−	0.998518i	$-0.482671\pi$
$163$	−7.82843	−	3.24264i	−0.613170	−	0.253983i	−0.667583	+	0.744535i	$0.732671\pi$
$164$	−1.77817	+	4.29289i	−0.138852	+	0.335219i
$165$	2.00000	−	0.828427i	0.155700	−	0.0644930i
$166$		−	28.1421i		−	2.18425i
$167$	0.757359	+	1.82843i	0.0586062	+	0.141488i	0.950470	−	0.310816i	$-0.100602\pi$
$167$	0.757359	+	1.82843i	0.0586062	+	0.141488i	−0.891864	+	0.452304i	$0.850602\pi$
$168$	−8.82843	−	8.82843i	−0.681128	−	0.681128i
$169$	11.0000			0.846154
$170$	6.94975	−	3.12132i	0.533021	−	0.239394i
$171$	1.51472			0.115833
$172$	−2.24264	−	2.24264i	−0.171000	−	0.171000i
$173$	1.12132	+	2.70711i	0.0852524	+	0.205818i	0.960756	−	0.277393i	$-0.0894705\pi$
$173$	1.12132	+	2.70711i	0.0852524	+	0.205818i	−0.875504	+	0.483211i	$0.839470\pi$
$174$			0.828427i			0.0628029i
$175$	10.6569	−	4.41421i	0.805582	−	0.333683i
$176$	3.00000	−	7.24264i	0.226134	−	0.545935i
$177$	6.00000	+	2.48528i	0.450988	+	0.186805i
$178$	11.2426	−	11.2426i	0.842672	−	0.842672i
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	−0.847656	−	0.530546i	$-0.821987\pi$
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	0.530546	+	0.847656i	$0.321987\pi$
$180$	−4.94975	−	2.05025i	−0.368932	−	0.152817i
$181$	−4.46447	+	10.7782i	−0.331841	+	0.801135i	0.666605	+	0.745411i	$0.267747\pi$
$181$	−4.46447	+	10.7782i	−0.331841	+	0.801135i	−0.998446	+	0.0557243i	$0.982253\pi$
$182$	8.24264	−	3.41421i	0.610985	−	0.253078i
$183$		−	4.14214i		−	0.306195i
$184$	8.07107	+	19.4853i	0.595007	+	1.43647i
$185$	−5.00000	−	5.00000i	−0.367607	−	0.367607i
$186$	−20.4853			−1.50205
$187$	4.41421	+	9.82843i	0.322799	+	0.718726i
$188$	19.7990			1.44399
$189$	−9.65685	−	9.65685i	−0.702433	−	0.702433i
$190$	0.585786	+	1.41421i	0.0424974	+	0.102598i
$191$			20.0000i			1.44715i	0.690246	+	0.723575i	$0.257502\pi$
$191$			20.0000i			1.44715i	−0.690246	+	0.723575i	$0.742498\pi$
$192$	−9.82843	+	4.07107i	−0.709306	+	0.293804i
$193$	0.878680	−	2.12132i	0.0632487	−	0.152696i	−0.889095	−	0.457722i	$-0.848665\pi$
$193$	0.878680	−	2.12132i	0.0632487	−	0.152696i	0.952344	+	0.305027i	$0.0986653\pi$
$194$	−23.0208	−	9.53553i	−1.65280	−	0.684611i
$195$	−0.828427	+	0.828427i	−0.0593249	+	0.0593249i
$196$	0.464466	−	0.464466i	0.0331761	−	0.0331761i
$197$	−4.29289	−	1.77817i	−0.305856	−	0.126690i	0.224476	−	0.974480i	$-0.427933\pi$
$197$	−4.29289	−	1.77817i	−0.305856	−	0.126690i	−0.530332	+	0.847790i	$0.677933\pi$
$198$	4.41421	−	10.6569i	0.313704	−	0.757350i
$199$	10.6569	−	4.41421i	0.755444	−	0.312915i	0.0284836	−	0.999594i	$-0.490932\pi$
$199$	10.6569	−	4.41421i	0.755444	−	0.312915i	0.726961	+	0.686679i	$0.240932\pi$
$200$			19.4853i			1.37782i
$201$	0.485281	+	1.17157i	0.0342291	+	0.0826364i
$202$	18.0711	+	18.0711i	1.27148	+	1.27148i
$203$	0.828427			0.0581442
$204$	−6.07107	+	15.9706i	−0.425060	+	1.11816i
$205$	−0.928932			−0.0648794
$206$	−21.3137	−	21.3137i	−1.48500	−	1.48500i
$207$	3.34315	+	8.07107i	0.232365	+	0.560978i
$208$			4.24264i			0.294174i
$209$	−2.00000	+	0.828427i	−0.138343	+	0.0573035i
$210$	2.00000	−	4.82843i	0.138013	−	0.333193i
$211$	−19.7279	−	8.17157i	−1.35813	−	0.562554i	−0.419583	−	0.907717i	$-0.637824\pi$
$211$	−19.7279	−	8.17157i	−1.35813	−	0.562554i	−0.938543	+	0.345163i	$0.887824\pi$
$212$	3.82843	−	3.82843i	0.262937	−	0.262937i
$213$	4.14214	−	4.14214i	0.283814	−	0.283814i
$214$	−1.00000	−	0.414214i	−0.0683586	−	0.0283151i
$215$	0.242641	−	0.585786i	0.0165480	−	0.0399503i
$216$	21.3137	−	8.82843i	1.45021	−	0.600698i
$217$			20.4853i			1.39063i
$218$	−14.3640	−	34.6777i	−0.972850	−	2.34867i
$219$	−9.89949	−	9.89949i	−0.668946	−	0.668946i
$220$	7.65685			0.516225
$221$	−4.24264	−	4.00000i	−0.285391	−	0.269069i
$222$	24.1421			1.62031
$223$	3.41421	+	3.41421i	0.228633	+	0.228633i	0.812121	−	0.583489i	$-0.198313\pi$
$223$	3.41421	+	3.41421i	0.228633	+	0.228633i	−0.583489	+	0.812121i	$0.698313\pi$
$224$	1.58579	+	3.82843i	0.105955	+	0.255798i
$225$			8.07107i			0.538071i
$226$	−29.4350	+	12.1924i	−1.95799	+	0.811026i
$227$	6.65685	−	16.0711i	0.441831	−	1.06667i	−0.533475	−	0.845816i	$-0.679114\pi$
$227$	6.65685	−	16.0711i	0.441831	−	1.06667i	0.975306	−	0.220858i	$-0.0708859\pi$
$228$	−3.17157	−	1.31371i	−0.210043	−	0.0870025i
$229$	−12.1421	+	12.1421i	−0.802375	+	0.802375i	−0.983466	−	0.181091i	$-0.942037\pi$
$229$	−12.1421	+	12.1421i	−0.802375	+	0.802375i	0.181091	+	0.983466i	$0.442037\pi$
$230$	−6.24264	+	6.24264i	−0.411628	+	0.411628i
$231$	6.82843	+	2.82843i	0.449278	+	0.186097i
$232$	−0.535534	+	1.29289i	−0.0351595	+	0.0848826i
$233$	8.12132	−	3.36396i	0.532045	−	0.220380i	−0.100453	−	0.994942i	$-0.532029\pi$
$233$	8.12132	−	3.36396i	0.532045	−	0.220380i	0.632499	+	0.774561i	$0.282029\pi$
$234$			6.24264i			0.408094i
$235$	1.51472	+	3.65685i	0.0988093	+	0.238547i
$236$	16.2426	+	16.2426i	1.05731	+	1.05731i
$237$	5.17157			0.335930
$238$	24.3137	+	9.24264i	1.57602	+	0.599111i
$239$	14.8284			0.959171			0.479586	−	0.877495i	$-0.340787\pi$
$239$	14.8284			0.959171			0.479586	+	0.877495i	$0.340787\pi$
$240$	1.75736	+	1.75736i	0.113437	+	0.113437i
$241$	−1.36396	−	3.29289i	−0.0878605	−	0.212114i	0.873842	−	0.486211i	$-0.161621\pi$
$241$	−1.36396	−	3.29289i	−0.0878605	−	0.212114i	−0.961702	+	0.274097i	$0.911621\pi$
$242$		−	10.0711i		−	0.647393i
$243$	14.3137	−	5.92893i	0.918225	−	0.380341i
$244$	5.60660	−	13.5355i	0.358926	−	0.866524i
$245$	0.121320	+	0.0502525i	0.00775087	+	0.00321052i
$246$	2.24264	−	2.24264i	0.142986	−	0.142986i
$247$	0.828427	−	0.828427i	0.0527116	−	0.0527116i
$248$	−31.9706	−	13.2426i	−2.03013	−	0.840909i
$249$	−4.82843	+	11.6569i	−0.305989	+	0.738723i
$250$	−16.0711	+	6.65685i	−1.01642	+	0.421016i
$251$		−	20.4853i		−	1.29302i	−0.762906	−	0.646510i	$-0.776228\pi$
$251$		−	20.4853i		−	1.29302i	0.762906	−	0.646510i	$-0.223772\pi$
$252$	−7.00000	−	16.8995i	−0.440959	−	1.06457i
$253$	−8.82843	−	8.82843i	−0.555038	−	0.555038i
$254$	12.8284			0.804927
$255$	−3.41421	+	0.100505i	−0.213806	+	0.00629387i
$256$	−29.9706			−1.87316
$257$	−4.34315	−	4.34315i	−0.270918	−	0.270918i	0.558552	−	0.829470i	$-0.311357\pi$
$257$	−4.34315	−	4.34315i	−0.270918	−	0.270918i	−0.829470	+	0.558552i	$0.811357\pi$
$258$	0.828427	+	2.00000i	0.0515756	+	0.124515i
$259$		−	24.1421i		−	1.50012i
$260$	−3.82843	+	1.58579i	−0.237429	+	0.0983463i
$261$	−0.221825	+	0.535534i	−0.0137306	+	0.0331487i
$262$	33.9706	+	14.0711i	2.09871	+	0.869313i
$263$	−7.41421	+	7.41421i	−0.457180	+	0.457180i	−0.897729	−	0.440549i	$-0.854784\pi$
$263$	−7.41421	+	7.41421i	−0.457180	+	0.457180i	0.440549	+	0.897729i	$0.354784\pi$
$264$	−8.82843	+	8.82843i	−0.543352	+	0.543352i
$265$	1.00000	+	0.414214i	0.0614295	+	0.0254449i
$266$	−2.00000	+	4.82843i	−0.122628	+	0.296050i
$267$	−6.58579	+	2.72792i	−0.403044	+	0.166946i
$268$			4.48528i			0.273982i
$269$	10.1213	+	24.4350i	0.617108	+	1.48983i	0.855047	+	0.518550i	$0.173528\pi$
$269$	10.1213	+	24.4350i	0.617108	+	1.48983i	−0.237939	+	0.971280i	$0.576472\pi$
$270$	6.82843	+	6.82843i	0.415565	+	0.415565i
$271$	22.1421			1.34504			0.672519	−	0.740079i	$-0.265212\pi$
$271$	22.1421			1.34504			0.672519	+	0.740079i	$0.265212\pi$
$272$	−8.48528	+	9.00000i	−0.514496	+	0.545705i
$273$	−4.00000			−0.242091
$274$	28.5563	+	28.5563i	1.72515	+	1.72515i
$275$	−4.41421	−	10.6569i	−0.266187	−	0.642632i
$276$		−	19.7990i		−	1.19176i
$277$	−18.4350	+	7.63604i	−1.10765	+	0.458805i	−0.860129	−	0.510077i	$-0.829617\pi$
$277$	−18.4350	+	7.63604i	−1.10765	+	0.458805i	−0.247525	+	0.968882i	$0.579617\pi$
$278$	−19.7279	+	47.6274i	−1.18320	+	2.85650i
$279$	−13.2426	−	5.48528i	−0.792816	−	0.328395i
$280$	6.24264	−	6.24264i	0.373069	−	0.373069i
$281$	−1.34315	+	1.34315i	−0.0801254	+	0.0801254i	−0.746034	−	0.665908i	$-0.768044\pi$
$281$	−1.34315	+	1.34315i	−0.0801254	+	0.0801254i	0.665908	+	0.746034i	$0.268044\pi$
$282$	−12.4853	−	5.17157i	−0.743488	−	0.307963i
$283$	−7.14214	+	17.2426i	−0.424556	+	1.02497i	0.556431	+	0.830894i	$0.312170\pi$
$283$	−7.14214	+	17.2426i	−0.424556	+	1.02497i	−0.980987	+	0.194075i	$0.937830\pi$
$284$	19.1421	−	7.92893i	1.13588	−	0.470496i
$285$		−	0.686292i		−	0.0406524i
$286$	−3.41421	−	8.24264i	−0.201887	−	0.487398i
$287$	−2.24264	−	2.24264i	−0.132379	−	0.132379i
$288$	−2.89949			−0.170854
$289$	−1.00000	−	16.9706i	−0.0588235	−	0.998268i
$290$	−0.585786			−0.0343986
$291$	7.89949	+	7.89949i	0.463077	+	0.463077i
$292$	−18.9497	−	45.7487i	−1.10895	−	2.67724i
$293$		−	12.3431i		−	0.721094i	−0.932741	−	0.360547i	$-0.882590\pi$
$293$		−	12.3431i		−	0.721094i	0.932741	−	0.360547i	$-0.117410\pi$
$294$	−0.414214	+	0.171573i	−0.0241574	+	0.0100063i
$295$	−1.75736	+	4.24264i	−0.102317	+	0.247016i
$296$	37.6777	+	15.6066i	2.18997	+	0.907115i
$297$	−9.65685	+	9.65685i	−0.560348	+	0.560348i
$298$	28.9706	−	28.9706i	1.67822	−	1.67822i
$299$	6.24264	+	2.58579i	0.361021	+	0.149540i
$300$	7.00000	−	16.8995i	0.404145	−	0.975693i
$301$	2.00000	−	0.828427i	0.115278	−	0.0477497i
$302$		−	17.3137i		−	0.996292i
$303$	−4.38478	−	10.5858i	−0.251899	−	0.608138i
$304$	−1.75736	−	1.75736i	−0.100791	−	0.100791i
$305$	2.92893			0.167710
$306$	−12.4853	+	13.2426i	−0.713736	+	0.757031i
$307$	−26.1421			−1.49201			−0.746005	−	0.665940i	$-0.768031\pi$
$307$	−26.1421			−1.49201			−0.746005	+	0.665940i	$0.768031\pi$
$308$	18.4853	+	18.4853i	1.05330	+	1.05330i
$309$	5.17157	+	12.4853i	0.294201	+	0.710263i
$310$		−	14.4853i		−	0.822709i
$311$	23.7279	−	9.82843i	1.34549	−	0.557319i	0.410455	−	0.911881i	$-0.365370\pi$
$311$	23.7279	−	9.82843i	1.34549	−	0.557319i	0.935032	+	0.354562i	$0.115370\pi$
$312$	2.58579	−	6.24264i	0.146391	−	0.353420i
$313$	−9.12132	−	3.77817i	−0.515568	−	0.213555i	0.109701	−	0.993965i	$-0.465011\pi$
$313$	−9.12132	−	3.77817i	−0.515568	−	0.213555i	−0.625269	+	0.780410i	$0.715011\pi$
$314$	−16.4853	+	16.4853i	−0.930318	+	0.930318i
$315$	2.58579	−	2.58579i	0.145693	−	0.145693i
$316$	16.8995	+	7.00000i	0.950671	+	0.393781i
$317$	7.36396	−	17.7782i	0.413601	−	0.998522i	−0.570562	−	0.821255i	$-0.693274\pi$
$317$	7.36396	−	17.7782i	0.413601	−	0.998522i	0.984163	−	0.177267i	$-0.0567256\pi$
$318$	−3.41421	+	1.41421i	−0.191460	+	0.0793052i
$319$		−	0.828427i		−	0.0463830i
$320$	−2.87868	−	6.94975i	−0.160923	−	0.388503i
$321$	0.343146	+	0.343146i	0.0191525	+	0.0191525i
$322$	−30.1421			−1.67976
$323$	3.41421	−	0.100505i	0.189972	−	0.00559225i
$324$	−0.656854			−0.0364919
$325$	4.41421	+	4.41421i	0.244857	+	0.244857i
$326$	7.82843	+	18.8995i	0.433576	+	1.04675i
$327$			16.8284i			0.930614i
$328$	4.94975	−	2.05025i	0.273304	−	0.113206i
$329$	−5.17157	+	12.4853i	−0.285118	+	0.688336i
$330$	−4.82843	−	2.00000i	−0.265796	−	0.110096i
$331$	−15.4142	+	15.4142i	−0.847242	+	0.847242i	−0.989788	−	0.142546i	$-0.954471\pi$
$331$	−15.4142	+	15.4142i	−0.847242	+	0.847242i	0.142546	+	0.989788i	$0.454471\pi$
$332$	−31.5563	+	31.5563i	−1.73188	+	1.73188i
$333$	15.6066	+	6.46447i	0.855237	+	0.354251i
$334$	1.82843	−	4.41421i	0.100047	−	0.241535i
$335$	−0.828427	+	0.343146i	−0.0452618	+	0.0187481i
$336$			8.48528i			0.462910i
$337$	−2.15076	−	5.19239i	−0.117159	−	0.282847i	0.854411	−	0.519597i	$-0.173918\pi$
$337$	−2.15076	−	5.19239i	−0.117159	−	0.282847i	−0.971571	+	0.236750i	$0.923918\pi$
$338$	−18.7782	−	18.7782i	−1.02140	−	1.02140i
$339$	14.2843			0.775815
$340$	−11.2929	−	4.29289i	−0.612443	−	0.232815i
$341$	20.4853			1.10934
$342$	−2.58579	−	2.58579i	−0.139823	−	0.139823i
$343$	7.17157	+	17.3137i	0.387229	+	0.934852i
$344$			3.65685i			0.197164i
$345$	3.65685	−	1.51472i	0.196878	−	0.0815497i
$346$	2.70711	−	6.53553i	0.145535	−	0.351352i
$347$	15.4853	+	6.41421i	0.831293	+	0.344333i	0.757415	−	0.652934i	$-0.226462\pi$
$347$	15.4853	+	6.41421i	0.831293	+	0.344333i	0.0738788	+	0.997267i	$0.476462\pi$
$348$	0.928932	−	0.928932i	0.0497960	−	0.0497960i
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$	−25.7279	−	10.6569i	−1.37522	−	0.569633i
$351$	2.82843	−	6.82843i	0.150970	−	0.364474i
$352$	3.82843	−	1.58579i	0.204056	−	0.0845227i
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$	−6.00000	−	14.4853i	−0.318896	−	0.769884i
$355$	2.92893	+	2.92893i	0.155452	+	0.155452i
$356$	−25.2132			−1.33630
$357$	−8.48528	−	8.00000i	−0.449089	−	0.423405i
$358$	14.4853			0.765571
$359$	−20.3848	−	20.3848i	−1.07587	−	1.07587i	−0.996875	−	0.0789921i	$-0.974830\pi$
$359$	−20.3848	−	20.3848i	−1.07587	−	1.07587i	−0.0789921	−	0.996875i	$-0.525170\pi$
$360$	2.36396	+	5.70711i	0.124592	+	0.300791i
$361$		−	18.3137i		−	0.963879i
$362$	26.0208	−	10.7782i	1.36762	−	0.566488i
$363$	−1.72792	+	4.17157i	−0.0906924	+	0.218951i
$364$	−13.0711	−	5.41421i	−0.685110	−	0.283782i
$365$	7.00000	−	7.00000i	0.366397	−	0.366397i
$366$	−7.07107	+	7.07107i	−0.369611	+	0.369611i
$367$	−4.07107	−	1.68629i	−0.212508	−	0.0880237i	0.273890	−	0.961761i	$-0.411690\pi$
$367$	−4.07107	−	1.68629i	−0.212508	−	0.0880237i	−0.486398	+	0.873737i	$0.661690\pi$
$368$	5.48528	−	13.2426i	0.285940	−	0.690320i
$369$	2.05025	−	0.849242i	0.106732	−	0.0442098i
$370$			17.0711i			0.887483i
$371$	1.41421	+	3.41421i	0.0734223	+	0.177257i
$372$	22.9706	+	22.9706i	1.19097	+	1.19097i
$373$	11.5563			0.598365			0.299183	−	0.954196i	$-0.403286\pi$
$373$	11.5563			0.598365			0.299183	+	0.954196i	$0.403286\pi$
$374$	9.24264	−	24.3137i	0.477926	−	1.25723i
$375$	7.79899			0.402738
$376$	−16.1421	−	16.1421i	−0.832467	−	0.832467i
$377$	0.171573	+	0.414214i	0.00883645	+	0.0213331i
$378$			32.9706i			1.69582i
$379$	−2.41421	+	1.00000i	−0.124010	+	0.0513665i	−0.443826	−	0.896113i	$-0.646379\pi$
$379$	−2.41421	+	1.00000i	−0.124010	+	0.0513665i	0.319816	+	0.947480i	$0.396379\pi$
$380$	0.928932	−	2.24264i	0.0476532	−	0.115045i
$381$	−5.31371	−	2.20101i	−0.272230	−	0.112761i
$382$	34.1421	−	34.1421i	1.74686	−	1.74686i
$383$	−15.8995	+	15.8995i	−0.812426	+	0.812426i	−0.984997	−	0.172571i	$-0.944793\pi$
$383$	−15.8995	+	15.8995i	−0.812426	+	0.812426i	0.172571	+	0.984997i	$0.444793\pi$
$384$	20.5563	+	8.51472i	1.04901	+	0.434515i
$385$	−2.00000	+	4.82843i	−0.101929	+	0.246079i
$386$	−5.12132	+	2.12132i	−0.260668	+	0.107972i
$387$			1.51472i			0.0769975i
$388$	15.1213	+	36.5061i	0.767669	+	1.85332i
$389$	−8.58579	−	8.58579i	−0.435317	−	0.435317i	0.455116	−	0.890432i	$-0.349598\pi$
$389$	−8.58579	−	8.58579i	−0.435317	−	0.435317i	−0.890432	+	0.455116i	$0.849598\pi$
$390$	2.82843			0.143223
$391$	8.07107	+	17.9706i	0.408171	+	0.908810i
$392$	−0.757359			−0.0382524
$393$	−11.6569	−	11.6569i	−0.588011	−	0.588011i
$394$	4.29289	+	10.3640i	0.216273	+	0.522129i
$395$			3.65685i			0.183996i
$396$	−16.8995	+	7.00000i	−0.849232	+	0.351763i
$397$	6.80761	−	16.4350i	0.341664	−	0.824850i	−0.655884	−	0.754862i	$-0.727704\pi$
$397$	6.80761	−	16.4350i	0.341664	−	0.824850i	0.997548	−	0.0699884i	$-0.0222962\pi$
$398$	−25.7279	−	10.6569i	−1.28962	−	0.534180i
$399$	1.65685	−	1.65685i	0.0829465	−	0.0829465i
$400$	9.36396	−	9.36396i	0.468198	−	0.468198i
$401$	−0.535534	−	0.221825i	−0.0267433	−	0.0110774i	0.369272	−	0.929321i	$-0.379607\pi$
$401$	−0.535534	−	0.221825i	−0.0267433	−	0.0110774i	−0.396015	+	0.918244i	$0.629607\pi$
$402$	1.17157	−	2.82843i	0.0584327	−	0.141069i
$403$	−10.2426	+	4.24264i	−0.510222	+	0.211341i
$404$		−	40.5269i		−	2.01629i
$405$	−0.0502525	−	0.121320i	−0.00249707	−	0.00602846i
$406$	−1.41421	−	1.41421i	−0.0701862	−	0.0701862i
$407$	−24.1421			−1.19668
$408$	17.9706	−	8.07107i	0.889675	−	0.399577i
$409$	−3.31371			−0.163852			−0.0819262	−	0.996638i	$-0.526107\pi$
$409$	−3.31371			−0.163852			−0.0819262	+	0.996638i	$0.526107\pi$
$410$	1.58579	+	1.58579i	0.0783164	+	0.0783164i
$411$	−6.92893	−	16.7279i	−0.341779	−	0.825128i
$412$			47.7990i			2.35489i
$413$	−14.4853	+	6.00000i	−0.712774	+	0.295241i
$414$	8.07107	−	19.4853i	0.396671	−	0.957649i
$415$	−8.24264	−	3.41421i	−0.404615	−	0.167597i
$416$	−1.58579	+	1.58579i	−0.0777496	+	0.0777496i
$417$	16.3431	−	16.3431i	0.800327	−	0.800327i
$418$	4.82843	+	2.00000i	0.236166	+	0.0978232i
$419$	−5.10051	+	12.3137i	−0.249176	+	0.601564i	−0.998135	−	0.0610528i	$-0.980554\pi$
$419$	−5.10051	+	12.3137i	−0.249176	+	0.601564i	0.748959	+	0.662617i	$0.230554\pi$
$420$	−7.65685	+	3.17157i	−0.373616	+	0.154757i
$421$		−	14.5858i		−	0.710868i	−0.934701	−	0.355434i	$-0.884333\pi$
$421$		−	14.5858i		−	0.710868i	0.934701	−	0.355434i	$-0.115667\pi$
$422$	19.7279	+	47.6274i	0.960340	+	2.31847i
$423$	−6.68629	−	6.68629i	−0.325099	−	0.325099i
$424$	−6.24264			−0.303169
$425$	0.535534	+	18.1924i	0.0259772	+	0.882460i
$426$	−14.1421			−0.685189
$427$	7.07107	+	7.07107i	0.342193	+	0.342193i
$428$	0.656854	+	1.58579i	0.0317502	+	0.0766519i
$429$			4.00000i			0.193122i
$430$	−1.41421	+	0.585786i	−0.0681994	+	0.0282491i
$431$	2.79899	−	6.75736i	0.134823	−	0.325491i	−0.842021	−	0.539445i	$-0.818634\pi$
$431$	2.79899	−	6.75736i	0.134823	−	0.325491i	0.976844	+	0.213954i	$0.0686343\pi$
$432$	−14.4853	−	6.00000i	−0.696923	−	0.288675i
$433$	14.7279	−	14.7279i	0.707779	−	0.707779i	−0.258289	−	0.966068i	$-0.583159\pi$
$433$	14.7279	−	14.7279i	0.707779	−	0.707779i	0.966068	+	0.258289i	$0.0831587\pi$
$434$	34.9706	−	34.9706i	1.67864	−	1.67864i
$435$	0.242641	+	0.100505i	0.0116337	+	0.00481885i
$436$	−22.7782	+	54.9914i	−1.09088	+	2.63361i
$437$	−3.65685	+	1.51472i	−0.174931	+	0.0724588i
$438$			33.7990i			1.61498i
$439$	−4.07107	−	9.82843i	−0.194301	−	0.469085i	0.796462	−	0.604689i	$-0.206703\pi$
$439$	−4.07107	−	9.82843i	−0.194301	−	0.469085i	−0.990763	+	0.135604i	$0.956703\pi$
$440$	−6.24264	−	6.24264i	−0.297606	−	0.297606i
$441$	−0.313708			−0.0149385
$442$	0.414214	+	14.0711i	0.0197021	+	0.669292i
$443$	−23.7990			−1.13072			−0.565362	−	0.824843i	$-0.691264\pi$
$443$	−23.7990			−1.13072			−0.565362	+	0.824843i	$0.691264\pi$
$444$	−27.0711	−	27.0711i	−1.28474	−	1.28474i
$445$	−1.92893	−	4.65685i	−0.0914402	−	0.220756i
$446$		−	11.6569i		−	0.551968i
$447$	−16.9706	+	7.02944i	−0.802680	+	0.332481i
$448$	9.82843	−	23.7279i	0.464350	−	1.12104i
$449$	11.1924	+	4.63604i	0.528201	+	0.218788i	0.630815	−	0.775933i	$-0.282721\pi$
$449$	11.1924	+	4.63604i	0.528201	+	0.218788i	−0.102614	+	0.994721i	$0.532721\pi$
$450$	13.7782	−	13.7782i	0.649509	−	0.649509i
$451$	−2.24264	+	2.24264i	−0.105602	+	0.105602i
$452$	46.6777	+	19.3345i	2.19553	+	0.909419i
$453$	−2.97056	+	7.17157i	−0.139569	+	0.336950i
$454$	−38.7990	+	16.0711i	−1.82093	+	0.754253i
$455$		−	2.82843i		−	0.132599i
$456$	1.51472	+	3.65685i	0.0709332	+	0.171248i
$457$	9.31371	+	9.31371i	0.435677	+	0.435677i	0.890554	−	0.454877i	$-0.150317\pi$
$457$	9.31371	+	9.31371i	0.435677	+	0.435677i	−0.454877	+	0.890554i	$0.650317\pi$
$458$	41.4558			1.93710
$459$	19.6569	−	8.82843i	0.917503	−	0.412076i
$460$	14.0000			0.652753
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	0.981782	−	0.190013i	$-0.0608529\pi$
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	−0.190013	+	0.981782i	$0.560853\pi$
$462$	−6.82843	−	16.4853i	−0.317687	−	0.766965i
$463$			14.6274i			0.679794i	0.940463	+	0.339897i	$0.110392\pi$
$463$			14.6274i			0.679794i	−0.940463	+	0.339897i	$0.889608\pi$
$464$	0.878680	−	0.363961i	0.0407917	−	0.0168965i
$465$	−2.48528	+	6.00000i	−0.115252	+	0.278243i
$466$	−19.6066	−	8.12132i	−0.908258	−	0.376213i
$467$	23.0711	−	23.0711i	1.06760	−	1.06760i	0.0700588	−	0.997543i	$-0.477681\pi$
$467$	23.0711	−	23.0711i	1.06760	−	1.06760i	0.997543	−	0.0700588i	$-0.0223187\pi$
$468$	7.00000	−	7.00000i	0.323575	−	0.323575i
$469$	−2.82843	−	1.17157i	−0.130605	−	0.0540982i
$470$	3.65685	−	8.82843i	0.168678	−	0.407225i
$471$	9.65685	−	4.00000i	0.444964	−	0.184310i
$472$		−	26.4853i		−	1.21908i
$473$	−0.828427	−	2.00000i	−0.0380911	−	0.0919601i
$474$	−8.82843	−	8.82843i	−0.405503	−	0.405503i
$475$	−3.65685			−0.167788
$476$	−16.8995	−	37.6274i	−0.774587	−	1.72465i
$477$	−2.58579			−0.118395
$478$	−25.3137	−	25.3137i	−1.15782	−	1.15782i
$479$	1.97056	+	4.75736i	0.0900373	+	0.217369i	0.962483	−	0.271342i	$-0.0874673\pi$
$479$	1.97056	+	4.75736i	0.0900373	+	0.217369i	−0.872446	+	0.488711i	$0.837467\pi$
$480$			1.31371i			0.0599623i
$481$	12.0711	−	5.00000i	0.550393	−	0.227980i
$482$	−3.29289	+	7.94975i	−0.149987	+	0.362101i
$483$	12.4853	+	5.17157i	0.568100	+	0.235315i
$484$	−11.2929	+	11.2929i	−0.513313	+	0.513313i
$485$	−5.58579	+	5.58579i	−0.253637	+	0.253637i
$486$	−34.5563	−	14.3137i	−1.56751	−	0.649283i
$487$	10.0711	−	24.3137i	0.456364	−	1.10176i	−0.513495	−	0.858092i	$-0.671650\pi$
$487$	10.0711	−	24.3137i	0.456364	−	1.10176i	0.969859	−	0.243667i	$-0.0783504\pi$
$488$	−15.6066	+	6.46447i	−0.706478	+	0.292633i
$489$		−	9.17157i		−	0.414753i
$490$	−0.121320	−	0.292893i	−0.00548069	−	0.0132316i
$491$	26.2426	+	26.2426i	1.18431	+	1.18431i	0.978615	+	0.205698i	$0.0659466\pi$
$491$	26.2426	+	26.2426i	1.18431	+	1.18431i	0.205698	+	0.978615i	$0.434053\pi$
$492$	−5.02944			−0.226745
$493$	−0.464466	+	1.22183i	−0.0209185	+	0.0550282i
$494$	−2.82843			−0.127257
$495$	−2.58579	−	2.58579i	−0.116222	−	0.116222i
$496$	9.00000	+	21.7279i	0.404112	+	0.975613i
$497$			14.1421i			0.634361i
$498$	28.1421	−	11.6569i	1.26108	−	0.522356i
$499$	−8.21320	+	19.8284i	−0.367673	+	0.887642i	0.626457	+	0.779456i	$0.284504\pi$
$499$	−8.21320	+	19.8284i	−0.367673	+	0.887642i	−0.994131	+	0.108186i	$0.965496\pi$
$500$	25.4853	+	10.5563i	1.13974	+	0.472094i
$501$	−1.51472	+	1.51472i	−0.0676726	+	0.0676726i
$502$	−34.9706	+	34.9706i	−1.56081	+	1.56081i
$503$	−19.7279	−	8.17157i	−0.879625	−	0.364352i	−0.103273	−	0.994653i	$-0.532932\pi$
$503$	−19.7279	−	8.17157i	−0.879625	−	0.364352i	−0.776351	+	0.630301i	$0.782932\pi$
$504$	−8.07107	+	19.4853i	−0.359514	+	0.867943i
$505$	7.48528	−	3.10051i	0.333091	−	0.137971i
$506$			30.1421i			1.33998i
$507$	4.55635	+	11.0000i	0.202355	+	0.488527i
$508$	−14.3848	−	14.3848i	−0.638221	−	0.638221i
$509$	−36.9706			−1.63869			−0.819346	−	0.573300i	$-0.805663\pi$
$509$	−36.9706			−1.63869			−0.819346	+	0.573300i	$0.805663\pi$
$510$	6.00000	+	5.65685i	0.265684	+	0.250490i
$511$	33.7990			1.49518
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	1.65685	+	4.00000i	0.0731519	+	0.176604i
$514$			14.8284i			0.654054i
$515$	−8.82843	+	3.65685i	−0.389027	+	0.161140i
$516$	1.31371	−	3.17157i	0.0578328	−	0.139621i
$517$	12.4853	+	5.17157i	0.549102	+	0.227446i
$518$	−41.2132	+	41.2132i	−1.81080	+	1.81080i
$519$	−2.24264	+	2.24264i	−0.0984410	+	0.0984410i
$520$	4.41421	+	1.82843i	0.193576	+	0.0801818i
$521$	7.12132	−	17.1924i	0.311991	−	0.753212i	−0.687640	−	0.726051i	$-0.741353\pi$
$521$	7.12132	−	17.1924i	0.311991	−	0.753212i	0.999631	−	0.0271607i	$-0.00864660\pi$
$522$	1.29289	−	0.535534i	0.0565884	−	0.0234397i
$523$		−	1.17157i		−	0.0512293i	−0.999672	−	0.0256147i	$-0.991846\pi$
$523$		−	1.17157i		−	0.0512293i	0.999672	−	0.0256147i	$-0.00815429\pi$
$524$	−22.3137	−	53.8701i	−0.974779	−	2.35332i
$525$	8.82843	+	8.82843i	0.385304	+	0.385304i
$526$	25.3137			1.10373
$527$	−30.2132	−	11.4853i	−1.31611	−	0.500307i
$528$	8.48528			0.369274
$529$	0.121320	+	0.121320i	0.00527480	+	0.00527480i
$530$	−1.00000	−	2.41421i	−0.0434372	−	0.104867i
$531$		−	10.9706i		−	0.476082i
$532$	7.65685	−	3.17157i	0.331967	−	0.137505i
$533$	0.656854	−	1.58579i	0.0284515	−	0.0686880i
$534$	15.8995	+	6.58579i	0.688038	+	0.284995i
$535$	−0.242641	+	0.242641i	−0.0104903	+	0.0104903i
$536$	3.65685	−	3.65685i	0.157952	−	0.157952i
$537$	−6.00000	−	2.48528i	−0.258919	−	0.107248i
$538$	24.4350	−	58.9914i	1.05347	−	2.54330i
$539$	0.414214	−	0.171573i	0.0178414	−	0.00739017i
$540$		−	15.3137i		−	0.658997i
$541$	−7.05025	−	17.0208i	−0.303114	−	0.731782i	−0.999895	−	0.0144979i	$-0.995385\pi$
$541$	−7.05025	−	17.0208i	−0.303114	−	0.731782i	0.696781	−	0.717284i	$-0.254615\pi$
$542$	−37.7990	−	37.7990i	−1.62361	−	1.62361i
$543$	−12.6274			−0.541894
$544$	−6.53553	+	0.192388i	−0.280209	+	0.00824857i
$545$	−11.8995			−0.509718
$546$	6.82843	+	6.82843i	0.292230	+	0.292230i
$547$	3.10051	+	7.48528i	0.132568	+	0.320048i	0.976199	−	0.216875i	$-0.0695866\pi$
$547$	3.10051	+	7.48528i	0.132568	+	0.320048i	−0.843631	+	0.536923i	$0.819587\pi$
$548$		−	64.0416i		−	2.73572i
$549$	−6.46447	+	2.67767i	−0.275897	+	0.114280i
$550$	−10.6569	+	25.7279i	−0.454410	+	1.09704i
$551$	−0.242641	−	0.100505i	−0.0103368	−	0.00428166i
$552$	−16.1421	+	16.1421i	−0.687055	+	0.687055i
$553$	−8.82843	+	8.82843i	−0.375423	+	0.375423i
$554$	44.5061	+	18.4350i	1.89088	+	0.783229i
$555$	2.92893	−	7.07107i	0.124326	−	0.300150i
$556$	75.5269	−	31.2843i	3.20305	−	1.32675i
$557$			19.7574i			0.837146i	0.908183	+	0.418573i	$0.137470\pi$
$557$			19.7574i			0.837146i	−0.908183	+	0.418573i	$0.862530\pi$
$558$	13.2426	+	31.9706i	0.560606	+	1.35342i
$559$	0.828427	+	0.828427i	0.0350387	+	0.0350387i
$560$	−6.00000			−0.253546
$561$	−8.00000	+	8.48528i	−0.337760	+	0.358249i
$562$	4.58579			0.193440
$563$	24.5858	+	24.5858i	1.03617	+	1.03617i	0.999321	+	0.0368464i	$0.0117312\pi$
$563$	24.5858	+	24.5858i	1.03617	+	1.03617i	0.0368464	+	0.999321i	$0.488269\pi$
$564$	8.20101	+	19.7990i	0.345325	+	0.833688i
$565$			10.1005i			0.424931i
$566$	41.6274	−	17.2426i	1.74973	−	0.724762i
$567$	0.171573	−	0.414214i	0.00720538	−	0.0173953i
$568$	−22.0711	−	9.14214i	−0.926081	−	0.383595i
$569$	8.51472	−	8.51472i	0.356956	−	0.356956i	−0.505734	−	0.862690i	$-0.668778\pi$
$569$	8.51472	−	8.51472i	0.356956	−	0.356956i	0.862690	+	0.505734i	$0.168778\pi$
$570$	−1.17157	+	1.17157i	−0.0490718	+	0.0490718i
$571$	−3.92893	−	1.62742i	−0.164421	−	0.0681053i	0.298955	−	0.954267i	$-0.403362\pi$
$571$	−3.92893	−	1.62742i	−0.164421	−	0.0681053i	−0.463376	+	0.886162i	$0.653362\pi$
$572$	−5.41421	+	13.0711i	−0.226380	+	0.546529i
$573$	−20.0000	+	8.28427i	−0.835512	+	0.346080i
$574$			7.65685i			0.319591i
$575$	−8.07107	−	19.4853i	−0.336587	−	0.812592i
$576$	12.7071	+	12.7071i	0.529463	+	0.529463i
$577$	−27.0711			−1.12698			−0.563492	−	0.826122i	$-0.690542\pi$
$577$	−27.0711			−1.12698			−0.563492	+	0.826122i	$0.690542\pi$
$578$	−27.2635	+	30.6777i	−1.13401	+	1.27602i
$579$	2.48528			0.103285
$580$	0.656854	+	0.656854i	0.0272744	+	0.0272744i
$581$	−11.6569	−	28.1421i	−0.483608	−	1.16753i
$582$		−	26.9706i		−	1.11797i
$583$	3.41421	−	1.41421i	0.141402	−	0.0585707i
$584$	−21.8492	+	52.7487i	−0.904128	+	2.18276i
$585$	1.82843	+	0.757359i	0.0755962	+	0.0313130i
$586$	−21.0711	+	21.0711i	−0.870438	+	0.870438i
$587$	32.0416	−	32.0416i	1.32250	−	1.32250i	0.410753	−	0.911747i	$-0.365266\pi$
$587$	32.0416	−	32.0416i	1.32250	−	1.32250i	0.911747	−	0.410753i	$-0.134734\pi$
$588$	0.656854	+	0.272078i	0.0270882	+	0.0112203i
$589$	2.48528	−	6.00000i	0.102404	−	0.247226i
$590$	10.2426	−	4.24264i	0.421683	−	0.174667i
$591$		−	5.02944i		−	0.206883i
$592$	−10.6066	−	25.6066i	−0.435929	−	1.05242i
$593$	9.14214	+	9.14214i	0.375423	+	0.375423i	0.869448	−	0.494025i	$-0.164475\pi$
$593$	9.14214	+	9.14214i	0.375423	+	0.375423i	−0.494025	+	0.869448i	$0.664475\pi$
$594$	32.9706			1.35280
$595$	5.65685	−	6.00000i	0.231908	−	0.245976i
$596$	−64.9706			−2.66130
$597$	8.82843	+	8.82843i	0.361323	+	0.361323i
$598$	−6.24264	−	15.0711i	−0.255281	−	0.616302i
$599$		−	10.6274i		−	0.434224i	−0.976147	−	0.217112i	$-0.930336\pi$
$599$		−	10.6274i		−	0.434224i	0.976147	−	0.217112i	$-0.0696638\pi$
$600$	−19.4853	+	8.07107i	−0.795483	+	0.329500i
$601$	−3.22183	+	7.77817i	−0.131421	+	0.317278i	−0.975868	−	0.218360i	$-0.929929\pi$
$601$	−3.22183	+	7.77817i	−0.131421	+	0.317278i	0.844447	+	0.535639i	$0.179929\pi$
$602$	−4.82843	−	2.00000i	−0.196792	−	0.0815139i
$603$	1.51472	−	1.51472i	0.0616841	−	0.0616841i
$604$	−19.4142	+	19.4142i	−0.789953	+	0.789953i
$605$	−2.94975	−	1.22183i	−0.119924	−	0.0496743i
$606$	−10.5858	+	25.5563i	−0.430018	+	1.03816i
$607$	15.1421	−	6.27208i	0.614600	−	0.254576i	−0.0535937	−	0.998563i	$-0.517068\pi$
$607$	15.1421	−	6.27208i	0.614600	−	0.254576i	0.668194	+	0.743987i	$0.267068\pi$
$608$		−	1.31371i		−	0.0532779i
$609$	0.343146	+	0.828427i	0.0139050	+	0.0335696i
$610$	−5.00000	−	5.00000i	−0.202444	−	0.202444i
$611$	−7.31371			−0.295881
$612$	28.8492	−	0.849242i	1.16616	−	0.0343286i
$613$	5.31371			0.214619			0.107309	−	0.994226i	$-0.465776\pi$
$613$	5.31371			0.214619			0.107309	+	0.994226i	$0.465776\pi$
$614$	44.6274	+	44.6274i	1.80102	+	1.80102i
$615$	−0.384776	−	0.928932i	−0.0155157	−	0.0374582i
$616$		−	30.1421i		−	1.21446i
$617$	−2.70711	+	1.12132i	−0.108984	+	0.0451427i	−0.436509	−	0.899700i	$-0.643785\pi$
$617$	−2.70711	+	1.12132i	−0.108984	+	0.0451427i	0.327525	+	0.944842i	$0.393785\pi$
$618$	12.4853	−	30.1421i	0.502232	−	1.21249i
$619$	26.3137	+	10.8995i	1.05764	+	0.438088i	0.842612	−	0.538521i	$-0.181017\pi$
$619$	26.3137	+	10.8995i	1.05764	+	0.438088i	0.215025	+	0.976609i	$0.431017\pi$
$620$	−16.2426	+	16.2426i	−0.652320	+	0.652320i
$621$	−17.6569	+	17.6569i	−0.708545	+	0.708545i
$622$	−57.2843	−	23.7279i	−2.29689	−	0.951403i
$623$	6.58579	−	15.8995i	0.263854	−	0.637000i
$624$	−4.24264	+	1.75736i	−0.169842	+	0.0703507i
$625$		−	16.5563i		−	0.662254i
$626$	9.12132	+	22.0208i	0.364561	+	0.880129i
$627$	−1.65685	−	1.65685i	−0.0661684	−	0.0661684i
$628$	36.9706			1.47529
$629$	35.6066	+	13.5355i	1.41973	+	0.539697i
$630$	−8.82843			−0.351733
$631$	−20.7279	−	20.7279i	−0.825166	−	0.825166i	0.161678	−	0.986844i	$-0.448309\pi$
$631$	−20.7279	−	20.7279i	−0.825166	−	0.825166i	−0.986844	+	0.161678i	$0.948309\pi$
$632$	−8.07107	−	19.4853i	−0.321050	−	0.775083i
$633$		−	23.1127i		−	0.918647i
$634$	−42.9203	+	17.7782i	−1.70458	+	0.706062i
$635$	1.55635	−	3.75736i	0.0617618	−	0.149106i
$636$	5.41421	+	2.24264i	0.214688	+	0.0889265i
$637$	−0.171573	+	0.171573i	−0.00679796	+	0.00679796i
$638$	−1.41421	+	1.41421i	−0.0559893	+	0.0559893i
$639$	−9.14214	−	3.78680i	−0.361657	−	0.149803i
$640$	−6.02082	+	14.5355i	−0.237994	+	0.574567i
$641$	−38.2635	+	15.8492i	−1.51132	+	0.626007i	−0.975829	−	0.218536i	$-0.929872\pi$
$641$	−38.2635	+	15.8492i	−1.51132	+	0.626007i	−0.535487	+	0.844544i	$0.679872\pi$
$642$		−	1.17157i		−	0.0462383i
$643$	11.0416	+	26.6569i	0.435439	+	1.05124i	0.977506	+	0.210908i	$0.0676421\pi$
$643$	11.0416	+	26.6569i	0.435439	+	1.05124i	−0.542066	+	0.840336i	$0.682358\pi$
$644$	33.7990	+	33.7990i	1.33187	+	1.33187i
$645$	0.686292			0.0270227
$646$	−6.00000	−	5.65685i	−0.236067	−	0.222566i
$647$	−2.82843			−0.111197			−0.0555985	−	0.998453i	$-0.517707\pi$
$647$	−2.82843			−0.111197			−0.0555985	+	0.998453i	$0.517707\pi$
$648$	0.535534	+	0.535534i	0.0210378	+	0.0210378i
$649$	6.00000	+	14.4853i	0.235521	+	0.568597i
$650$		−	15.0711i		−	0.591136i
$651$	−20.4853	+	8.48528i	−0.802881	+	0.332564i
$652$	12.4142	−	29.9706i	0.486178	−	1.17374i
$653$	8.77817	+	3.63604i	0.343517	+	0.142289i	0.547770	−	0.836629i	$-0.315477\pi$
$653$	8.77817	+	3.63604i	0.343517	+	0.142289i	−0.204254	+	0.978918i	$0.565477\pi$
$654$	28.7279	−	28.7279i	1.12335	−	1.12335i
$655$	8.24264	−	8.24264i	0.322067	−	0.322067i
$656$	−3.36396	−	1.39340i	−0.131341	−	0.0544031i
$657$	−9.05025	+	21.8492i	−0.353084	+	0.852420i
$658$	30.1421	−	12.4853i	1.17506	−	0.486727i
$659$			8.48528i			0.330540i	0.986248	+	0.165270i	$0.0528495\pi$
$659$			8.48528i			0.330540i	−0.986248	+	0.165270i	$0.947151\pi$
$660$	3.17157	+	7.65685i	0.123453	+	0.298043i
$661$	0.857864	+	0.857864i	0.0333671	+	0.0333671i	0.723593	−	0.690226i	$-0.242489\pi$
$661$	0.857864	+	0.857864i	0.0333671	+	0.0333671i	−0.690226	+	0.723593i	$0.742489\pi$
$662$	52.6274			2.04542
$663$	2.24264	−	5.89949i	0.0870969	−	0.229117i
$664$	51.4558			1.99687
$665$	1.17157	+	1.17157i	0.0454316	+	0.0454316i
$666$	−15.6066	−	37.6777i	−0.604744	−	1.45998i
$667$		−	1.51472i		−	0.0586501i
$668$	−7.00000	+	2.89949i	−0.270838	+	0.112185i
$669$	−2.00000	+	4.82843i	−0.0773245	+	0.186678i
$670$	2.00000	+	0.828427i	0.0772667	+	0.0320049i
$671$	7.07107	−	7.07107i	0.272976	−	0.272976i
$672$	−3.17157	+	3.17157i	−0.122346	+	0.122346i
$673$	4.12132	+	1.70711i	0.158865	+	0.0658041i	0.460699	−	0.887556i	$-0.347599\pi$
$673$	4.12132	+	1.70711i	0.158865	+	0.0658041i	−0.301834	+	0.953361i	$0.597599\pi$
$674$	−5.19239	+	12.5355i	−0.200003	+	0.482851i
$675$	−21.3137	+	8.82843i	−0.820365	+	0.339806i
$676$			42.1127i			1.61972i
$677$	−14.5772	−	35.1924i	−0.560246	−	1.35255i	−0.909570	−	0.415551i	$-0.863589\pi$
$677$	−14.5772	−	35.1924i	−0.560246	−	1.35255i	0.349324	−	0.937002i	$-0.386411\pi$
$678$	−24.3848	−	24.3848i	−0.936492	−	0.936492i
$679$	−26.9706			−1.03504
$680$	5.70711	+	12.7071i	0.218858	+	0.487295i
$681$	18.8284			0.721507
$682$	−34.9706	−	34.9706i	−1.33909	−	1.33909i
$683$	−9.10051	−	21.9706i	−0.348221	−	0.840680i	−0.996830	−	0.0795585i	$-0.974649\pi$
$683$	−9.10051	−	21.9706i	−0.348221	−	0.840680i	0.648609	−	0.761122i	$-0.275351\pi$
$684$			5.79899i			0.221730i
$685$	11.8284	−	4.89949i	0.451941	−	0.187200i
$686$	17.3137	−	41.7990i	0.661040	−	1.59589i
$687$	−17.1716	−	7.11270i	−0.655136	−	0.271366i
$688$	1.75736	−	1.75736i	0.0669987	−	0.0669987i
$689$	−1.41421	+	1.41421i	−0.0538772	+	0.0538772i
$690$	−8.82843	−	3.65685i	−0.336092	−	0.139214i
$691$	−7.62742	+	18.4142i	−0.290161	+	0.700510i	−0.999993	−	0.00386139i	$-0.998771\pi$
$691$	−7.62742	+	18.4142i	−0.290161	+	0.700510i	0.709832	+	0.704371i	$0.248771\pi$
$692$	−10.3640	+	4.29289i	−0.393979	+	0.163191i
$693$		−	12.4853i		−	0.474277i
$694$	−15.4853	−	37.3848i	−0.587813	−	1.41911i
$695$	11.5563	+	11.5563i	0.438357	+	0.438357i
$696$	−1.51472			−0.0574153
$697$	4.56497	−	2.05025i	0.172911	−	0.0776589i
$698$	−10.2426			−0.387690
$699$	6.72792	+	6.72792i	0.254473	+	0.254473i
$700$	16.8995	+	40.7990i	0.638741	+	1.54206i
$701$			37.6985i			1.42385i	0.702254	+	0.711926i	$0.252177\pi$
$701$			37.6985i			1.42385i	−0.702254	+	0.711926i	$0.747823\pi$
$702$	−16.4853	+	6.82843i	−0.622197	+	0.257722i
$703$	−2.92893	+	7.07107i	−0.110467	+	0.266690i
$704$	−23.7279	−	9.82843i	−0.894280	−	0.370423i
$705$	−3.02944	+	3.02944i	−0.114095	+	0.114095i
$706$	23.8995	−	23.8995i	0.899469	−	0.899469i
$707$	25.5563	+	10.5858i	0.961145	+	0.398119i
$708$	−9.51472	+	22.9706i	−0.357585	+	0.863287i
$709$	22.4350	−	9.29289i	0.842565	−	0.349002i	0.0807007	−	0.996738i	$-0.474284\pi$
$709$	22.4350	−	9.29289i	0.842565	−	0.349002i	0.761864	+	0.647736i	$0.224284\pi$
$710$		−	10.0000i		−	0.375293i
$711$	−3.34315	−	8.07107i	−0.125378	−	0.302689i
$712$	20.5563	+	20.5563i	0.770382	+	0.770382i
$713$	37.4558			1.40273
$714$	0.828427	+	28.1421i	0.0310031	+	1.05319i
$715$	−2.82843			−0.105777
$716$	−16.2426	−	16.2426i	−0.607016	−	0.607016i
$717$	6.14214	+	14.8284i	0.229382	+	0.553778i
$718$			69.5980i			2.59737i
$719$	−31.3848	+	13.0000i	−1.17045	+	0.484818i	−0.881343	−	0.472477i	$-0.843360\pi$
$719$	−31.3848	+	13.0000i	−1.17045	+	0.484818i	−0.289112	+	0.957295i	$0.593360\pi$
$720$	1.60660	−	3.87868i	0.0598745	−	0.144550i
$721$	−30.1421	−	12.4853i	−1.12255	−	0.464976i
$722$	−31.2635	+	31.2635i	−1.16351	+	1.16351i
$723$	2.72792	−	2.72792i	0.101453	−	0.101453i
$724$	−41.2635	−	17.0919i	−1.53354	−	0.635215i
$725$	0.535534	−	1.29289i	0.0198892	−	0.0480168i
$726$	10.0711	−	4.17157i	0.373772	−	0.154822i
$727$			43.1127i			1.59896i	0.600692	+	0.799481i	$0.294892\pi$
$727$			43.1127i			1.59896i	−0.600692	+	0.799481i	$0.705108\pi$
$728$	6.24264	+	15.0711i	0.231368	+	0.558571i
$729$	12.2218	+	12.2218i	0.452660	+	0.452660i
$730$	−23.8995			−0.884560
$731$	0.100505	+	3.41421i	0.00371731	+	0.126279i
$732$	15.8579			0.586124
$733$	−25.4853	−	25.4853i	−0.941320	−	0.941320i	0.0570509	−	0.998371i	$-0.481830\pi$
$733$	−25.4853	−	25.4853i	−0.941320	−	0.941320i	−0.998371	+	0.0570509i	$0.981830\pi$
$734$	4.07107	+	9.82843i	0.150266	+	0.362774i
$735$			0.142136i			0.00524275i
$736$	7.00000	−	2.89949i	0.258023	−	0.106877i
$737$	−1.17157	+	2.82843i	−0.0431554	+	0.104186i
$738$	−4.94975	−	2.05025i	−0.182203	−	0.0754708i
$739$	15.7574	−	15.7574i	0.579644	−	0.579644i	−0.355161	−	0.934805i	$-0.615574\pi$
$739$	15.7574	−	15.7574i	0.579644	−	0.579644i	0.934805	+	0.355161i	$0.115574\pi$
$740$	19.1421	−	19.1421i	0.703679	−	0.703679i
$741$	1.17157	+	0.485281i	0.0430388	+	0.0178273i
$742$	3.41421	−	8.24264i	0.125340	−	0.302597i
$743$	47.1421	−	19.5269i	1.72948	−	0.716373i	0.730020	−	0.683426i	$-0.239511\pi$
$743$	47.1421	−	19.5269i	1.72948	−	0.716373i	0.999457	−	0.0329473i	$-0.0104893\pi$
$744$		−	37.4558i		−	1.37320i
$745$	−4.97056	−	12.0000i	−0.182107	−	0.439646i
$746$	−19.7279	−	19.7279i	−0.722291	−	0.722291i
$747$	21.3137			0.779828
$748$	−37.6274	+	16.8995i	−1.37579	+	0.617907i
$749$	−1.17157			−0.0428083
$750$	−13.3137	−	13.3137i	−0.486148	−	0.486148i
$751$	18.2132	+	43.9706i	0.664609	+	1.60451i	0.790498	+	0.612464i	$0.209822\pi$
$751$	18.2132	+	43.9706i	0.664609	+	1.60451i	−0.125889	+	0.992044i	$0.540178\pi$
$752$			15.5147i			0.565764i
$753$	20.4853	−	8.48528i	0.746525	−	0.309221i
$754$	0.414214	−	1.00000i	0.0150848	−	0.0364179i
$755$	−5.07107	−	2.10051i	−0.184555	−	0.0764452i
$756$	36.9706	−	36.9706i	1.34461	−	1.34461i
$757$	−1.79899	+	1.79899i	−0.0653854	+	0.0653854i	−0.739043	−	0.673658i	$-0.764722\pi$
$757$	−1.79899	+	1.79899i	−0.0653854	+	0.0653854i	0.673658	+	0.739043i	$0.264722\pi$
$758$	5.82843	+	2.41421i	0.211698	+	0.0876882i
$759$	5.17157	−	12.4853i	0.187716	−	0.453187i
$760$	−2.58579	+	1.07107i	−0.0937963	+	0.0388517i
$761$		−	37.6985i		−	1.36657i	−0.730152	−	0.683285i	$-0.760551\pi$
$761$		−	37.6985i		−	1.36657i	0.730152	−	0.683285i	$-0.239449\pi$
$762$	5.31371	+	12.8284i	0.192495	+	0.464725i
$763$	−28.7279	−	28.7279i	−1.04002	−	1.04002i
$764$	−76.5685			−2.77015
$765$	2.36396	+	5.26346i	0.0854692	+	0.190301i
$766$	54.2843			1.96137
$767$	−6.00000	−	6.00000i	−0.216647	−	0.216647i
$768$	−12.4142	−	29.9706i	−0.447959	−	1.08147i
$769$			12.7279i			0.458981i	0.973311	+	0.229490i	$0.0737059\pi$
$769$			12.7279i			0.458981i	−0.973311	+	0.229490i	$0.926294\pi$
$770$	11.6569	−	4.82843i	0.420084	−	0.174004i
$771$	2.54416	−	6.14214i	0.0916255	−	0.221204i
$772$	8.12132	+	3.36396i	0.292293	+	0.121072i
$773$	−0.585786	+	0.585786i	−0.0210693	+	0.0210693i	−0.717563	−	0.696494i	$-0.754742\pi$
$773$	−0.585786	+	0.585786i	−0.0210693	+	0.0210693i	0.696494	+	0.717563i	$0.254742\pi$
$774$	2.58579	−	2.58579i	0.0929442	−	0.0929442i
$775$	31.9706	+	13.2426i	1.14842	+	0.475690i
$776$	17.4350	−	42.0919i	0.625881	−	1.51101i
$777$	24.1421	−	10.0000i	0.866094	−	0.358748i
$778$			29.3137i			1.05095i
$779$	0.384776	+	0.928932i	0.0137860	+	0.0332824i
$780$	−3.17157	−	3.17157i	−0.113561	−	0.113561i
$781$	14.1421			0.506045
$782$	16.8995	−	44.4558i	0.604325	−	1.58974i
$783$	−1.65685			−0.0592111
$784$	0.363961	+	0.363961i	0.0129986	+	0.0129986i
$785$	2.82843	+	6.82843i	0.100951	+	0.243717i
$786$			39.7990i			1.41958i
$787$	−19.0000	+	7.87006i	−0.677277	+	0.280537i	−0.694688	−	0.719311i	$-0.744458\pi$
$787$	−19.0000	+	7.87006i	−0.677277	+	0.280537i	0.0174112	+	0.999848i	$0.494458\pi$
$788$	6.80761	−	16.4350i	0.242511	−	0.585474i
$789$	−10.4853	−	4.34315i	−0.373286	−	0.154620i
$790$	6.24264	−	6.24264i	0.222103	−	0.222103i
$791$	−24.3848	+	24.3848i	−0.867023	+	0.867023i
$792$	19.4853	+	8.07107i	0.692379	+	0.286793i
$793$	−2.07107	+	5.00000i	−0.0735458	+	0.177555i
$794$	−39.6777	+	16.4350i	−1.40811	+	0.583257i
$795$			1.17157i			0.0415514i
$796$	16.8995	+	40.7990i	0.598987	+	1.44608i
$797$	−17.8284	−	17.8284i	−0.631515	−	0.631515i	0.316933	−	0.948448i	$-0.397347\pi$
$797$	−17.8284	−	17.8284i	−0.631515	−	0.631515i	−0.948448	+	0.316933i	$0.897347\pi$
$798$	−5.65685			−0.200250
$799$	−15.5147	−	14.6274i	−0.548871	−	0.517481i
$800$	7.00000			0.247487
$801$	8.51472	+	8.51472i	0.300853	+	0.300853i
$802$	0.535534	+	1.29289i	0.0189104	+	0.0456536i
$803$		−	33.7990i		−	1.19274i
$804$	−4.48528	+	1.85786i	−0.158184	+	0.0655218i
$805$	−3.65685	+	8.82843i	−0.128887	+	0.311161i
$806$	24.7279	+	10.2426i	0.871004	+	0.360782i
$807$	−20.2426	+	20.2426i	−0.712575	+	0.712575i
$808$	−33.0416	+	33.0416i	−1.16240	+	1.16240i
$809$	−32.6066	−	13.5061i	−1.14639	−	0.474849i	−0.273067	−	0.961995i	$-0.588038\pi$
$809$	−32.6066	−	13.5061i	−1.14639	−	0.474849i	−0.873321	+	0.487146i	$0.838038\pi$
$810$	−0.121320	+	0.292893i	−0.00426276	+	0.0102912i
$811$	−50.9411	+	21.1005i	−1.78878	+	0.740939i	−0.798481	+	0.602020i	$0.794363\pi$
$811$	−50.9411	+	21.1005i	−1.78878	+	0.740939i	−0.990304	+	0.138919i	$0.955637\pi$
$812$			3.17157i			0.111300i
$813$	9.17157	+	22.1421i	0.321661	+	0.776559i
$814$	41.2132	+	41.2132i	1.44452	+	1.44452i
$815$	6.48528			0.227169
$816$	−12.5147	−	4.75736i	−0.438103	−	0.166541i
$817$	−0.686292			−0.0240103
$818$	5.65685	+	5.65685i	0.197787	+	0.197787i
$819$	2.58579	+	6.24264i	0.0903547	+	0.218136i
$820$		−	3.55635i		−	0.124193i
$821$	35.5061	−	14.7071i	1.23917	−	0.513282i	0.335716	−	0.941963i	$-0.391022\pi$
$821$	35.5061	−	14.7071i	1.23917	−	0.513282i	0.903456	+	0.428682i	$0.141022\pi$
$822$	−16.7279	+	40.3848i	−0.583453	+	1.40858i
$823$	9.00000	+	3.72792i	0.313720	+	0.129947i	0.533987	−	0.845492i	$-0.320693\pi$
$823$	9.00000	+	3.72792i	0.313720	+	0.129947i	−0.220267	+	0.975440i	$0.570693\pi$
$824$	38.9706	−	38.9706i	1.35760	−	1.35760i
$825$	8.82843	−	8.82843i	0.307366	−	0.307366i
$826$	34.9706	+	14.4853i	1.21678	+	0.504007i
$827$	−17.9289	+	43.2843i	−0.623450	+	1.50514i	0.224177	+	0.974549i	$0.428031\pi$
$827$	−17.9289	+	43.2843i	−0.623450	+	1.50514i	−0.847627	+	0.530593i	$0.821969\pi$
$828$	−30.8995	+	12.7990i	−1.07383	+	0.444796i
$829$		−	53.9411i		−	1.87345i	−0.350062	−	0.936726i	$-0.613840\pi$
$829$		−	53.9411i		−	1.87345i	0.350062	−	0.936726i	$-0.386160\pi$
$830$	8.24264	+	19.8995i	0.286106	+	0.690722i
$831$	−15.2721	−	15.2721i	−0.529783	−	0.529783i
$832$	13.8995			0.481878
$833$	−0.707107	+	0.0208153i	−0.0244998	+	0.000721207i
$834$	−55.7990			−1.93216
$835$	−1.07107	−	1.07107i	−0.0370658	−	0.0370658i
$836$	−3.17157	−	7.65685i	−0.109691	−	0.264818i
$837$		−	40.9706i		−	1.41615i
$838$	29.7279	−	12.3137i	1.02693	−	0.425370i
$839$	−6.41421	+	15.4853i	−0.221443	+	0.534611i	−0.995086	−	0.0990102i	$-0.968432\pi$
$839$	−6.41421	+	15.4853i	−0.221443	+	0.534611i	0.773643	+	0.633622i	$0.218432\pi$
$840$	8.82843	+	3.65685i	0.304610	+	0.126173i
$841$	−20.4350	+	20.4350i	−0.704656	+	0.704656i
$842$	−24.8995	+	24.8995i	−0.858093	+	0.858093i
$843$	−1.89949	−	0.786797i	−0.0654221	−	0.0270987i
$844$	31.2843	−	75.5269i	1.07685	−	2.59974i
$845$	−7.77817	+	3.22183i	−0.267577	+	0.110834i
$846$			22.8284i			0.784857i
$847$	−4.17157	−	10.0711i	−0.143337	−	0.346046i
$848$	3.00000	+	3.00000i	0.103020	+	0.103020i
$849$	−20.2010			−0.693297
$850$	30.1421	−	31.9706i	1.03387	−	1.09658i
$851$	−44.1421			−1.51317
$852$	15.8579	+	15.8579i	0.543281	+	0.543281i
$853$	−7.33452	−	17.7071i	−0.251129	−	0.606280i	0.747166	−	0.664637i	$-0.231414\pi$
$853$	−7.33452	−	17.7071i	−0.251129	−	0.606280i	−0.998296	+	0.0583572i	$0.981414\pi$
$854$		−	24.1421i		−	0.826127i
$855$	−1.07107	+	0.443651i	−0.0366297	+	0.0151725i
$856$	0.757359	−	1.82843i	0.0258860	−	0.0624944i
$857$	−8.53553	−	3.53553i	−0.291568	−	0.120772i	0.232105	−	0.972691i	$-0.425439\pi$
$857$	−8.53553	−	3.53553i	−0.291568	−	0.120772i	−0.523673	+	0.851919i	$0.675439\pi$
$858$	6.82843	−	6.82843i	0.233119	−	0.233119i
$859$	24.7279	−	24.7279i	0.843706	−	0.843706i	−0.145633	−	0.989339i	$-0.546522\pi$
$859$	24.7279	−	24.7279i	0.843706	−	0.843706i	0.989339	+	0.145633i	$0.0465218\pi$
$860$	2.24264	+	0.928932i	0.0764734	+	0.0316763i
$861$	1.31371	−	3.17157i	0.0447711	−	0.108087i
$862$	−16.3137	+	6.75736i	−0.555647	+	0.230157i
$863$			10.6274i			0.361761i	0.983505	+	0.180881i	$0.0578948\pi$
$863$			10.6274i			0.361761i	−0.983505	+	0.180881i	$0.942105\pi$
$864$	−3.17157	−	7.65685i	−0.107899	−	0.260491i
$865$	−1.58579	−	1.58579i	−0.0539184	−	0.0539184i
$866$	−50.2843			−1.70873
$867$	16.5563	−	8.02944i	0.562283	−	0.272694i
$868$	−78.4264			−2.66197
$869$	8.82843	+	8.82843i	0.299484	+	0.299484i
$870$	−0.242641	−	0.585786i	−0.00822629	−	0.0198600i
$871$		−	1.65685i		−	0.0561404i
$872$	63.4056	−	26.2635i	2.14718	−	0.889393i
$873$	7.22183	−	17.4350i	0.244422	−	0.590086i
$874$	8.82843	+	3.65685i	0.298626	+	0.123695i
$875$	−13.3137	+	13.3137i	−0.450085	+	0.450085i
$876$	37.8995	−	37.8995i	1.28051	−	1.28051i
$877$	46.4056	+	19.2218i	1.56701	+	0.649075i	0.986288	−	0.165031i	$-0.0527723\pi$
$877$	46.4056	+	19.2218i	1.56701	+	0.649075i	0.580717	+	0.814105i	$0.302772\pi$
$878$	−9.82843	+	23.7279i	−0.331693	+	0.800779i
$879$	12.3431	−	5.11270i	0.416324	−	0.172447i
$880$			6.00000i			0.202260i
$881$	12.8787	+	31.0919i	0.433894	+	1.04751i	0.978020	+	0.208509i	$0.0668611\pi$
$881$	12.8787	+	31.0919i	0.433894	+	1.04751i	−0.544127	+	0.839003i	$0.683139\pi$
$882$	0.535534	+	0.535534i	0.0180324	+	0.0180324i
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	15.3137	−	16.2426i	0.515056	−	0.546299i
$885$	−4.97056			−0.167084
$886$	40.6274	+	40.6274i	1.36490	+	1.36490i
$887$	16.8579	+	40.6985i	0.566032	+	1.36652i	0.904875	+	0.425678i	$0.139965\pi$
$887$	16.8579	+	40.6985i	0.566032	+	1.36652i	−0.338843	+	0.940843i	$0.610035\pi$
$888$			44.1421i			1.48131i
$889$	12.8284	−	5.31371i	0.430252	−	0.178216i
$890$	−4.65685	+	11.2426i	−0.156098	+	0.376854i
$891$	−0.414214	−	0.171573i	−0.0138767	−	0.00574791i
$892$	−13.0711	+	13.0711i	−0.437652	+	0.437652i
$893$	3.02944	−	3.02944i	0.101376	−	0.101376i
$894$	40.9706	+	16.9706i	1.37026	+	0.567581i
$895$	1.75736	−	4.24264i	0.0587420	−	0.141816i
$896$	−49.6274	+	20.5563i	−1.65794	+	0.686739i
$897$			7.31371i			0.244198i
$898$	−11.1924	−	27.0208i	−0.373495	−	0.901696i
$899$	1.75736	+	1.75736i	0.0586112	+	0.0586112i
$900$	−30.8995			−1.02998
$901$	−5.82843	+	0.171573i	−0.194173	+	0.00571592i
$902$	7.65685			0.254945
$903$	1.65685	+	1.65685i	0.0551367	+	0.0551367i
$904$	−22.2929	−	53.8198i	−0.741451	−	1.79002i
$905$		−	8.92893i		−	0.296808i
$906$	17.3137	−	7.17157i	0.575209	−	0.238260i
$907$	5.14214	−	12.4142i	0.170742	−	0.412207i	−0.815226	−	0.579143i	$-0.803387\pi$
$907$	5.14214	−	12.4142i	0.170742	−	0.412207i	0.985968	+	0.166936i	$0.0533873\pi$
$908$	61.5269	+	25.4853i	2.04184	+	0.845759i
$909$	−13.6863	+	13.6863i	−0.453946	+	0.453946i
$910$	−4.82843	+	4.82843i	−0.160061	+	0.160061i
$911$	5.24264	+	2.17157i	0.173696	+	0.0719474i	0.467837	−	0.883815i	$-0.345033\pi$
$911$	5.24264	+	2.17157i	0.173696	+	0.0719474i	−0.294141	+	0.955762i	$0.595033\pi$
$912$	1.02944	−	2.48528i	0.0340881	−	0.0822959i
$913$	−28.1421	+	11.6569i	−0.931369	+	0.385786i
$914$		−	31.7990i		−	1.05182i
$915$	1.21320	+	2.92893i	0.0401073	+	0.0968275i
$916$	−46.4853	−	46.4853i	−1.53592	−	1.53592i
$917$	39.7990			1.31428
$918$	−48.6274	−	18.4853i	−1.60494	−	0.610105i
$919$	19.3137			0.637100			0.318550	−	0.947906i	$-0.396804\pi$
$919$	19.3137			0.637100			0.318550	+	0.947906i	$0.396804\pi$
$920$	−11.4142	−	11.4142i	−0.376315	−	0.376315i
$921$	−10.8284	−	26.1421i	−0.356809	−	0.861413i
$922$		−	58.0416i		−	1.91150i
$923$	−7.07107	+	2.92893i	−0.232747	+	0.0964070i
$924$	−10.8284	+	26.1421i	−0.356229	+	0.860013i
$925$	−37.6777	−	15.6066i	−1.23883	−	0.513142i
$926$	24.9706	−	24.9706i	0.820584	−	0.820584i
$927$	16.1421	−	16.1421i	0.530177	−	0.530177i
$928$	0.464466	+	0.192388i	0.0152468	+	0.00631545i
$929$	6.63604	−	16.0208i	0.217721	−	0.525626i	−0.776850	−	0.629686i	$-0.783183\pi$
$929$	6.63604	−	16.0208i	0.217721	−	0.525626i	0.994571	+	0.104060i	$0.0331835\pi$
$930$	14.4853	−	6.00000i	0.474991	−	0.196748i
$931$		−	0.142136i		−	0.00465831i
$932$	12.8787	+	31.0919i	0.421855	+	1.01845i
$933$	19.6569	+	19.6569i	0.643537	+	0.643537i
$934$	−78.7696			−2.57742
$935$	−6.00000	−	5.65685i	−0.196221	−	0.184999i
$936$	−11.4142			−0.373085
$937$	19.4853	+	19.4853i	0.636556	+	0.636556i	0.949704	−	0.313148i	$-0.101384\pi$
$937$	19.4853	+	19.4853i	0.636556	+	0.636556i	−0.313148	+	0.949704i	$0.601384\pi$
$938$	2.82843	+	6.82843i	0.0923514	+	0.222956i
$939$		−	10.6863i		−	0.348734i
$940$	−14.0000	+	5.79899i	−0.456630	+	0.189142i
$941$	−15.2635	+	36.8492i	−0.497574	+	1.20125i	0.453212	+	0.891403i	$0.350278\pi$
$941$	−15.2635	+	36.8492i	−0.497574	+	1.20125i	−0.950786	+	0.309848i	$0.899722\pi$
$942$	−23.3137	−	9.65685i	−0.759602	−	0.314637i
$943$	−4.10051	+	4.10051i	−0.133531	+	0.133531i
$944$	−12.7279	+	12.7279i	−0.414259	+	0.414259i
$945$	9.65685	+	4.00000i	0.314137	+	0.130120i
$946$	−2.00000	+	4.82843i	−0.0650256	+	0.156986i
$947$	28.3137	−	11.7279i	0.920072	−	0.381106i	0.128168	−	0.991752i	$-0.459090\pi$
$947$	28.3137	−	11.7279i	0.920072	−	0.381106i	0.791904	+	0.610646i	$0.209090\pi$
$948$			19.7990i			0.643041i
$949$	7.00000	+	16.8995i	0.227230	+	0.548581i
$950$	6.24264	+	6.24264i	0.202538	+	0.202538i
$951$	20.8284			0.675408
$952$	−16.8995	+	44.4558i	−0.547716	+	1.44082i
$953$	49.6985			1.60989			0.804946	−	0.593348i	$-0.202194\pi$
$953$	49.6985			1.60989			0.804946	+	0.593348i	$0.202194\pi$
$954$	4.41421	+	4.41421i	0.142915	+	0.142915i
$955$	−5.85786	−	14.1421i	−0.189556	−	0.457629i
$956$			56.7696i			1.83606i
$957$	0.828427	−	0.343146i	0.0267792	−	0.0110923i
$958$	4.75736	−	11.4853i	0.153703	−	0.371073i
$959$	40.3848	+	16.7279i	1.30409	+	0.540173i
$960$	5.75736	−	5.75736i	0.185818	−	0.185818i
$961$	−21.5355	+	21.5355i	−0.694695	+	0.694695i
$962$	−29.1421	−	12.0711i	−0.939580	−	0.389187i
$963$	0.313708	−	0.757359i	0.0101091	−	0.0244056i
$964$	12.6066	−	5.22183i	0.406031	−	0.168184i
$965$			1.75736i			0.0565714i
$966$	−12.4853	−	30.1421i	−0.401707	−	0.969807i
$967$	−30.8701	−	30.8701i	−0.992714	−	0.992714i	0.00725952	−	0.999974i	$-0.497689\pi$
$967$	−30.8701	−	30.8701i	−0.992714	−	0.992714i	−0.999974	+	0.00725952i	$0.997689\pi$
$968$	18.4142			0.591855
$969$	1.51472	+	3.37258i	0.0486598	+	0.108343i
$970$	19.0711			0.612335
$971$	−36.5858	−	36.5858i	−1.17409	−	1.17409i	−0.981224	−	0.192869i	$-0.938221\pi$
$971$	−36.5858	−	36.5858i	−1.17409	−	1.17409i	−0.192869	−	0.981224i	$-0.561779\pi$
$972$	22.6985	+	54.7990i	0.728054	+	1.75768i
$973$			55.7990i			1.78883i
$974$	−58.6985	+	24.3137i	−1.88082	+	0.779061i
$975$	−2.58579	+	6.24264i	−0.0828114	+	0.199925i
$976$	10.6066	+	4.39340i	0.339509	+	0.140629i
$977$	−27.1421	+	27.1421i	−0.868354	+	0.868354i	−0.992290	−	0.123936i	$-0.960448\pi$
$977$	−27.1421	+	27.1421i	−0.868354	+	0.868354i	0.123936	+	0.992290i	$0.460448\pi$
$978$	−15.6569	+	15.6569i	−0.500651	+	0.500651i
$979$	−15.8995	−	6.58579i	−0.508150	−	0.210483i
$980$	−0.192388	+	0.464466i	−0.00614561	+	0.0148368i
$981$	26.2635	−	10.8787i	0.838528	−	0.347330i
$982$		−	89.5980i		−	2.85919i
$983$	3.72792	+	9.00000i	0.118902	+	0.287055i	0.972114	−	0.234510i	$-0.0753484\pi$
$983$	3.72792	+	9.00000i	0.118902	+	0.287055i	−0.853212	+	0.521565i	$0.825348\pi$
$984$	4.10051	+	4.10051i	0.130719	+	0.130719i
$985$	3.55635			0.113315
$986$	2.87868	−	1.29289i	0.0916758	−	0.0411741i
$987$	−14.6274			−0.465596
$988$	3.17157	+	3.17157i	0.100901	+	0.100901i
$989$	−1.51472	−	3.65685i	−0.0481653	−	0.116281i
$990$			8.82843i			0.280586i
$991$	37.7279	−	15.6274i	1.19847	−	0.496421i	0.307964	−	0.951398i	$-0.400352\pi$
$991$	37.7279	−	15.6274i	1.19847	−	0.496421i	0.890503	+	0.454977i	$0.150352\pi$
$992$	−4.75736	+	11.4853i	−0.151046	+	0.364658i
$993$	−21.7990	−	9.02944i	−0.691770	−	0.286541i
$994$	24.1421	−	24.1421i	0.765742	−	0.765742i
$995$	−6.24264	+	6.24264i	−0.197905	+	0.197905i
$996$	−44.6274	−	18.4853i	−1.41407	−	0.585729i
$997$	−2.87868	+	6.94975i	−0.0911687	+	0.220101i	−0.962886	−	0.269908i	$-0.913007\pi$
$997$	−2.87868	+	6.94975i	−0.0911687	+	0.220101i	0.871717	+	0.490009i	$0.163007\pi$
$998$	47.8701	−	19.8284i	1.51530	−	0.627658i
$999$			48.2843i			1.52765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.2.d.a.15.1	yes	4
3.2	odd	2		153.2.l.c.100.1		4
4.3	odd	2		272.2.v.d.49.1		4
5.2	odd	4		425.2.n.b.49.1		4
5.3	odd	4		425.2.n.a.49.1		4
5.4	even	2		425.2.m.a.151.1		4
7.2	even	3		833.2.v.b.508.1		8
7.3	odd	6		833.2.v.a.814.1		8
7.4	even	3		833.2.v.b.814.1		8
7.5	odd	6		833.2.v.a.508.1		8
7.6	odd	2		833.2.l.a.491.1		4
17.2	even	8		289.2.d.c.179.1		4
17.3	odd	16		289.2.b.b.288.2		4
17.4	even	4		289.2.d.c.155.1		4
17.5	odd	16		289.2.a.f.1.3		4
17.6	odd	16		289.2.c.c.251.2		8
17.7	odd	16		289.2.c.c.38.4		8
17.8	even	8	inner	17.2.d.a.8.1	✓	4
17.9	even	8		289.2.d.a.110.1		4
17.10	odd	16		289.2.c.c.38.3		8
17.11	odd	16		289.2.c.c.251.1		8
17.12	odd	16		289.2.a.f.1.4		4
17.13	even	4		289.2.d.b.155.1		4
17.14	odd	16		289.2.b.b.288.1		4
17.15	even	8		289.2.d.b.179.1		4
17.16	even	2		289.2.d.a.134.1		4
51.5	even	16		2601.2.a.bb.1.1		4
51.8	odd	8		153.2.l.c.127.1		4
51.29	even	16		2601.2.a.bb.1.2		4
68.39	even	16		4624.2.a.bp.1.3		4
68.59	odd	8		272.2.v.d.161.1		4
68.63	even	16		4624.2.a.bp.1.2		4
85.8	odd	8		425.2.n.b.399.1		4
85.29	odd	16		7225.2.a.u.1.1		4
85.39	odd	16		7225.2.a.u.1.2		4
85.42	odd	8		425.2.n.a.399.1		4
85.59	even	8		425.2.m.a.76.1		4
119.25	even	24		833.2.v.b.569.1		8
119.59	odd	24		833.2.v.a.569.1		8
119.76	odd	8		833.2.l.a.246.1		4
119.93	even	24		833.2.v.b.263.1		8
119.110	odd	24		833.2.v.a.263.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	17.8	even	8	inner
17.2.d.a.15.1	yes	4	1.1	even	1	trivial
153.2.l.c.100.1		4	3.2	odd	2
153.2.l.c.127.1		4	51.8	odd	8
272.2.v.d.49.1		4	4.3	odd	2
272.2.v.d.161.1		4	68.59	odd	8
289.2.a.f.1.3		4	17.5	odd	16
289.2.a.f.1.4		4	17.12	odd	16
289.2.b.b.288.1		4	17.14	odd	16
289.2.b.b.288.2		4	17.3	odd	16
289.2.c.c.38.3		8	17.10	odd	16
289.2.c.c.38.4		8	17.7	odd	16
289.2.c.c.251.1		8	17.11	odd	16
289.2.c.c.251.2		8	17.6	odd	16
289.2.d.a.110.1		4	17.9	even	8
289.2.d.a.134.1		4	17.16	even	2
289.2.d.b.155.1		4	17.13	even	4
289.2.d.b.179.1		4	17.15	even	8
289.2.d.c.155.1		4	17.4	even	4
289.2.d.c.179.1		4	17.2	even	8
425.2.m.a.76.1		4	85.59	even	8
425.2.m.a.151.1		4	5.4	even	2
425.2.n.a.49.1		4	5.3	odd	4
425.2.n.a.399.1		4	85.42	odd	8
425.2.n.b.49.1		4	5.2	odd	4
425.2.n.b.399.1		4	85.8	odd	8
833.2.l.a.246.1		4	119.76	odd	8
833.2.l.a.491.1		4	7.6	odd	2
833.2.v.a.263.1		8	119.110	odd	24
833.2.v.a.508.1		8	7.5	odd	6
833.2.v.a.569.1		8	119.59	odd	24
833.2.v.a.814.1		8	7.3	odd	6
833.2.v.b.263.1		8	119.93	even	24
833.2.v.b.508.1		8	7.2	even	3
833.2.v.b.569.1		8	119.25	even	24
833.2.v.b.814.1		8	7.4	even	3
2601.2.a.bb.1.1		4	51.5	even	16
2601.2.a.bb.1.2		4	51.29	even	16
4624.2.a.bp.1.2		4	68.63	even	16
4624.2.a.bp.1.3		4	68.39	even	16
7225.2.a.u.1.1		4	85.29	odd	16
7225.2.a.u.1.2		4	85.39	odd	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 1.70711i) q^{2} +(0.414214 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 + 0.292893i) q^{5} +(1.00000 - 2.41421i) q^{6} +(-2.41421 - 1.00000i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.29289 - 1.29289i) q^{9} +(1.70711 + 0.707107i) q^{10} +(-1.00000 + 2.41421i) q^{11} +(-3.82843 + 1.58579i) q^{12} -1.41421i q^{13} +(2.41421 + 5.82843i) q^{14} +(-0.585786 - 0.585786i) q^{15} -3.00000 q^{16} +(2.82843 - 3.00000i) q^{17} -4.41421 q^{18} +(0.585786 + 0.585786i) q^{19} +(-1.12132 - 2.70711i) q^{20} -2.82843i q^{21} +(5.82843 - 2.41421i) q^{22} +(-1.82843 + 4.41421i) q^{23} +(4.41421 + 1.82843i) q^{24} +(-3.12132 + 3.12132i) q^{25} +(-2.41421 + 2.41421i) q^{26} +(4.82843 + 2.00000i) q^{27} +(3.82843 - 9.24264i) q^{28} +(-0.292893 + 0.121320i) q^{29} +2.00000i q^{30} +(-3.00000 - 7.24264i) q^{31} +(-1.12132 - 1.12132i) q^{32} -2.82843 q^{33} +(-9.94975 + 0.292893i) q^{34} +2.00000 q^{35} +(4.94975 + 4.94975i) q^{36} +(3.53553 + 8.53553i) q^{37} -2.00000i q^{38} +(1.41421 - 0.585786i) q^{39} +(-1.29289 + 3.12132i) q^{40} +(1.12132 + 0.464466i) q^{41} +(-4.82843 + 4.82843i) q^{42} +(-0.585786 + 0.585786i) q^{43} +(-9.24264 - 3.82843i) q^{44} +(-0.535534 + 1.29289i) q^{45} +(10.6569 - 4.41421i) q^{46} -5.17157i q^{47} +(-1.24264 - 3.00000i) q^{48} +(-0.121320 - 0.121320i) q^{49} +10.6569 q^{50} +(4.17157 + 1.58579i) q^{51} +5.41421 q^{52} +(-1.00000 - 1.00000i) q^{53} +(-4.82843 - 11.6569i) q^{54} -2.00000i q^{55} +(-10.6569 + 4.41421i) q^{56} +(-0.343146 + 0.828427i) q^{57} +(0.707107 + 0.292893i) q^{58} +(4.24264 - 4.24264i) q^{59} +(2.24264 - 2.24264i) q^{60} +(-3.53553 - 1.46447i) q^{61} +(-7.24264 + 17.4853i) q^{62} +(-4.41421 + 1.82843i) q^{63} +9.82843i q^{64} +(0.414214 + 1.00000i) q^{65} +(4.82843 + 4.82843i) q^{66} +1.17157 q^{67} +(11.4853 + 10.8284i) q^{68} -5.17157 q^{69} +(-3.41421 - 3.41421i) q^{70} +(-2.07107 - 5.00000i) q^{71} -8.07107i q^{72} +(-11.9497 + 4.94975i) q^{73} +(8.53553 - 20.6066i) q^{74} +(-4.41421 - 1.82843i) q^{75} +(-2.24264 + 2.24264i) q^{76} +(4.82843 - 4.82843i) q^{77} +(-3.41421 - 1.41421i) q^{78} +(1.82843 - 4.41421i) q^{79} +(2.12132 - 0.878680i) q^{80} +0.171573i q^{81} +(-1.12132 - 2.70711i) q^{82} +(8.24264 + 8.24264i) q^{83} +10.8284 q^{84} +(-1.12132 + 2.94975i) q^{85} +2.00000 q^{86} +(-0.242641 - 0.242641i) q^{87} +(4.41421 + 10.6569i) q^{88} +6.58579i q^{89} +(3.12132 - 1.29289i) q^{90} +(-1.41421 + 3.41421i) q^{91} +(-16.8995 - 7.00000i) q^{92} +(6.00000 - 6.00000i) q^{93} +(-8.82843 + 8.82843i) q^{94} +(-0.585786 - 0.242641i) q^{95} +(0.656854 - 1.58579i) q^{96} +(9.53553 - 3.94975i) q^{97} +0.414214i q^{98} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 8 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 4 q^{14} - 8 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} + 4 q^{20} + 12 q^{22} + 4 q^{23} + 12 q^{24} - 4 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 + 8 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 4 * q^14 - 8 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 + 4 * q^20 + 12 * q^22 + 4 * q^23 + 12 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^29 - 12 * q^31 + 4 * q^32 - 20 * q^34 + 8 * q^35 - 8 * q^40 - 4 * q^41 - 8 * q^42 - 8 * q^43 - 20 * q^44 + 12 * q^45 + 20 * q^46 + 12 * q^48 + 8 * q^49 + 20 * q^50 + 28 * q^51 + 16 * q^52 - 4 * q^53 - 8 * q^54 - 20 * q^56 - 24 * q^57 - 8 * q^60 - 12 * q^62 - 12 * q^63 - 4 * q^65 + 8 * q^66 + 16 * q^67 + 12 * q^68 - 32 * q^69 - 8 * q^70 + 20 * q^71 - 28 * q^73 + 20 * q^74 - 12 * q^75 + 8 * q^76 + 8 * q^77 - 8 * q^78 - 4 * q^79 + 4 * q^82 + 16 * q^83 + 32 * q^84 + 4 * q^85 + 8 * q^86 + 16 * q^87 + 12 * q^88 + 4 * q^90 - 28 * q^92 + 24 * q^93 - 24 * q^94 - 8 * q^95 - 20 * q^96 + 24 * q^97 - 4 * q^99

Introduction

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