LMFDB - Embedded newform 289.2.d.b.179.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,2,Mod(110,289)] 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("289.110"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.30767661842$
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:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			179.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	289.179
Dual form			289.2.d.b.155.1

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

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	0.235147	−	0.971960i	$-0.424443\pi$
$2$	1.70711	−	1.70711i	1.20711	−	1.20711i	0.971960	−	0.235147i	$-0.0755571\pi$
$3$	−1.00000	−	0.414214i	−0.577350	−	0.239146i	0.0748477	−	0.997195i	$-0.476153\pi$
$3$	−1.00000	−	0.414214i	−0.577350	−	0.239146i	−0.652198	+	0.758049i	$0.726153\pi$
$4$		−	3.82843i		−	1.91421i
$5$	−0.292893	+	0.707107i	−0.130986	+	0.316228i	−0.975742	−	0.218924i	$-0.929745\pi$
$5$	−0.292893	+	0.707107i	−0.130986	+	0.316228i	0.844756	+	0.535151i	$0.179745\pi$
$6$	−2.41421	+	1.00000i	−0.985599	+	0.408248i
$7$	−1.00000	−	2.41421i	−0.377964	−	0.912487i	−0.992347	−	0.123479i	$-0.960595\pi$
$7$	−1.00000	−	2.41421i	−0.377964	−	0.912487i	0.614383	−	0.789008i	$-0.289405\pi$
$8$	−3.12132	−	3.12132i	−1.10355	−	1.10355i
$9$	−1.29289	−	1.29289i	−0.430964	−	0.430964i
$10$	0.707107	+	1.70711i	0.223607	+	0.539835i
$11$	2.41421	−	1.00000i	0.727913	−	0.301511i	0.0122188	−	0.999925i	$-0.496111\pi$
$11$	2.41421	−	1.00000i	0.727913	−	0.301511i	0.715694	+	0.698414i	$0.246111\pi$
$12$	−1.58579	+	3.82843i	−0.457777	+	1.10517i
$13$			1.41421i			0.392232i	0.980581	+	0.196116i	$0.0628330\pi$
$13$			1.41421i			0.392232i	−0.980581	+	0.196116i	$0.937167\pi$
$14$	−5.82843	−	2.41421i	−1.55771	−	0.645226i
$15$	0.585786	−	0.585786i	0.151249	−	0.151249i
$16$	−3.00000			−0.750000
$17$		0			0
$17$		0			0
$18$	−4.41421			−1.04044
$19$	−0.585786	+	0.585786i	−0.134389	+	0.134389i	−0.771101	−	0.636713i	$-0.780294\pi$
$19$	−0.585786	+	0.585786i	−0.134389	+	0.134389i	0.636713	+	0.771101i	$0.280294\pi$
$20$	2.70711	+	1.12132i	0.605327	+	0.250735i
$21$			2.82843i			0.617213i
$22$	2.41421	−	5.82843i	0.514712	−	1.24262i
$23$	4.41421	−	1.82843i	0.920427	−	0.381253i	0.128388	−	0.991724i	$-0.459020\pi$
$23$	4.41421	−	1.82843i	0.920427	−	0.381253i	0.792039	+	0.610471i	$0.209020\pi$
$24$	1.82843	+	4.41421i	0.373226	+	0.901048i
$25$	3.12132	+	3.12132i	0.624264	+	0.624264i
$26$	2.41421	+	2.41421i	0.473466	+	0.473466i
$27$	2.00000	+	4.82843i	0.384900	+	0.929231i
$28$	−9.24264	+	3.82843i	−1.74669	+	0.723505i
$29$	−0.121320	+	0.292893i	−0.0225286	+	0.0543889i	−0.934744	−	0.355323i	$-0.884371\pi$
$29$	−0.121320	+	0.292893i	−0.0225286	+	0.0543889i	0.912215	+	0.409712i	$0.134371\pi$
$30$		−	2.00000i		−	0.365148i
$31$	7.24264	+	3.00000i	1.30082	+	0.538816i	0.922191	−	0.386734i	$-0.126397\pi$
$31$	7.24264	+	3.00000i	1.30082	+	0.538816i	0.378625	+	0.925550i	$0.376397\pi$
$32$	1.12132	−	1.12132i	0.198223	−	0.198223i
$33$	−2.82843			−0.492366
$34$		0			0
$35$	2.00000			0.338062
$36$	−4.94975	+	4.94975i	−0.824958	+	0.824958i
$37$	−8.53553	−	3.53553i	−1.40323	−	0.581238i	−0.452644	−	0.891691i	$-0.649519\pi$
$37$	−8.53553	−	3.53553i	−1.40323	−	0.581238i	−0.950589	+	0.310453i	$0.899519\pi$
$38$			2.00000i			0.324443i
$39$	0.585786	−	1.41421i	0.0938009	−	0.226455i
$40$	3.12132	−	1.29289i	0.493524	−	0.204424i
$41$	0.464466	+	1.12132i	0.0725374	+	0.175121i	0.955990	−	0.293400i	$-0.0947869\pi$
$41$	0.464466	+	1.12132i	0.0725374	+	0.175121i	−0.883452	+	0.468521i	$0.844787\pi$
$42$	4.82843	+	4.82843i	0.745042	+	0.745042i
$43$	0.585786	+	0.585786i	0.0893316	+	0.0893316i	0.750360	−	0.661029i	$-0.229880\pi$
$43$	0.585786	+	0.585786i	0.0893316	+	0.0893316i	−0.661029	+	0.750360i	$0.729880\pi$
$44$	−3.82843	−	9.24264i	−0.577157	−	1.39338i
$45$	1.29289	−	0.535534i	0.192733	−	0.0798327i
$46$	4.41421	−	10.6569i	0.650840	−	1.57127i
$47$			5.17157i			0.754351i	0.926142	+	0.377176i	$0.123105\pi$
$47$			5.17157i			0.754351i	−0.926142	+	0.377176i	$0.876895\pi$
$48$	3.00000	+	1.24264i	0.433013	+	0.179360i
$49$	0.121320	−	0.121320i	0.0173315	−	0.0173315i
$50$	10.6569			1.50711
$51$		0			0
$52$	5.41421			0.750816
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	11.6569	+	4.82843i	1.58630	+	0.657066i
$55$			2.00000i			0.269680i
$56$	−4.41421	+	10.6569i	−0.589874	+	1.42408i
$57$	0.828427	−	0.343146i	0.109728	−	0.0454508i
$58$	0.292893	+	0.707107i	0.0384588	+	0.0928477i
$59$	−4.24264	−	4.24264i	−0.552345	−	0.552345i	0.374772	−	0.927117i	$-0.377721\pi$
$59$	−4.24264	−	4.24264i	−0.552345	−	0.552345i	−0.927117	+	0.374772i	$0.877721\pi$
$60$	−2.24264	−	2.24264i	−0.289524	−	0.289524i
$61$	−1.46447	−	3.53553i	−0.187506	−	0.452679i	0.801973	−	0.597361i	$-0.203784\pi$
$61$	−1.46447	−	3.53553i	−0.187506	−	0.452679i	−0.989478	+	0.144682i	$0.953784\pi$
$62$	17.4853	−	7.24264i	2.22063	−	0.919816i
$63$	−1.82843	+	4.41421i	−0.230360	+	0.556139i
$64$		−	9.82843i		−	1.22855i
$65$	−1.00000	−	0.414214i	−0.124035	−	0.0513769i
$66$	−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	$0.477201\pi$
$68$		0			0
$69$	−5.17157			−0.622584
$70$	3.41421	−	3.41421i	0.408077	−	0.408077i
$71$	5.00000	+	2.07107i	0.593391	+	0.245791i	0.659109	−	0.752048i	$-0.270934\pi$
$71$	5.00000	+	2.07107i	0.593391	+	0.245791i	−0.0657178	+	0.997838i	$0.520934\pi$
$72$			8.07107i			0.951184i
$73$	−4.94975	+	11.9497i	−0.579324	+	1.39861i	0.314097	+	0.949391i	$0.398298\pi$
$73$	−4.94975	+	11.9497i	−0.579324	+	1.39861i	−0.893421	+	0.449221i	$0.851702\pi$
$74$	−20.6066	+	8.53553i	−2.39547	+	0.992236i
$75$	−1.82843	−	4.41421i	−0.211129	−	0.509709i
$76$	2.24264	+	2.24264i	0.257249	+	0.257249i
$77$	−4.82843	−	4.82843i	−0.550250	−	0.550250i
$78$	−1.41421	−	3.41421i	−0.160128	−	0.386584i
$79$	−4.41421	+	1.82843i	−0.496638	+	0.205714i	−0.616920	−	0.787026i	$-0.711620\pi$
$79$	−4.41421	+	1.82843i	−0.496638	+	0.205714i	0.120283	+	0.992740i	$0.461620\pi$
$80$	0.878680	−	2.12132i	0.0982394	−	0.237171i
$81$		−	0.171573i		−	0.0190637i
$82$	2.70711	+	1.12132i	0.298950	+	0.123829i
$83$	−8.24264	+	8.24264i	−0.904747	+	0.904747i	−0.995842	−	0.0910949i	$-0.970963\pi$
$83$	−8.24264	+	8.24264i	−0.904747	+	0.904747i	0.0910949	+	0.995842i	$0.470963\pi$
$84$	10.8284			1.18148
$85$		0			0
$86$	2.00000			0.215666
$87$	0.242641	−	0.242641i	0.0260138	−	0.0260138i
$88$	−10.6569	−	4.41421i	−1.13602	−	0.470557i
$89$		−	6.58579i		−	0.698092i	−0.937106	−	0.349046i	$-0.886506\pi$
$89$		−	6.58579i		−	0.698092i	0.937106	−	0.349046i	$-0.113494\pi$
$90$	1.29289	−	3.12132i	0.136283	−	0.329016i
$91$	3.41421	−	1.41421i	0.357907	−	0.148250i
$92$	−7.00000	−	16.8995i	−0.729800	−	1.76189i
$93$	−6.00000	−	6.00000i	−0.622171	−	0.622171i
$94$	8.82843	+	8.82843i	0.910583	+	0.910583i
$95$	−0.242641	−	0.585786i	−0.0248944	−	0.0601004i
$96$	−1.58579	+	0.656854i	−0.161849	+	0.0670399i
$97$	3.94975	−	9.53553i	0.401036	−	0.968187i	−0.586379	−	0.810037i	$-0.699447\pi$
$97$	3.94975	−	9.53553i	0.401036	−	0.968187i	0.987415	−	0.158150i	$-0.0505529\pi$
$98$		−	0.414214i		−	0.0418419i
$99$	−4.41421	−	1.82843i	−0.443645	−	0.183764i
$100$	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	$0.676557\pi$
$102$		0			0
$103$	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
$105$	−2.00000	−	0.828427i	−0.195180	−	0.0808462i
$106$		−	3.41421i		−	0.331618i
$107$	0.171573	−	0.414214i	0.0165866	−	0.0400435i	−0.915369	−	0.402615i	$-0.868101\pi$
$107$	0.171573	−	0.414214i	0.0165866	−	0.0400435i	0.931956	+	0.362572i	$0.118101\pi$
$108$	18.4853	−	7.65685i	1.77875	−	0.736781i
$109$	5.94975	+	14.3640i	0.569882	+	1.37582i	0.901654	+	0.432458i	$0.142354\pi$
$109$	5.94975	+	14.3640i	0.569882	+	1.37582i	−0.331772	+	0.943360i	$0.607646\pi$
$110$	3.41421	+	3.41421i	0.325532	+	0.325532i
$111$	7.07107	+	7.07107i	0.671156	+	0.671156i
$112$	3.00000	+	7.24264i	0.283473	+	0.684365i
$113$	−12.1924	+	5.05025i	−1.14696	+	0.475088i	−0.873514	−	0.486799i	$-0.838165\pi$
$113$	−12.1924	+	5.05025i	−1.14696	+	0.475088i	−0.273449	+	0.961886i	$0.588165\pi$
$114$	0.828427	−	2.00000i	0.0775893	−	0.187317i
$115$			3.65685i			0.341003i
$116$	1.12132	+	0.464466i	0.104112	+	0.0431246i
$117$	1.82843	−	1.82843i	0.169038	−	0.169038i
$118$	−14.4853			−1.33348
$119$		0			0
$120$	−3.65685			−0.333824
$121$	−2.94975	+	2.94975i	−0.268159	+	0.268159i
$122$	−8.53553	−	3.53553i	−0.772771	−	0.320092i
$123$		−	1.31371i		−	0.118453i
$124$	11.4853	−	27.7279i	1.03141	−	2.49004i
$125$	−6.65685	+	2.75736i	−0.595407	+	0.246626i
$126$	4.41421	+	10.6569i	0.393249	+	0.949388i
$127$	3.75736	+	3.75736i	0.333412	+	0.333412i	0.853881	−	0.520469i	$-0.174243\pi$
$127$	3.75736	+	3.75736i	0.333412	+	0.333412i	−0.520469	+	0.853881i	$0.674243\pi$
$128$	−14.5355	−	14.5355i	−1.28477	−	1.28477i
$129$	−0.343146	−	0.828427i	−0.0302123	−	0.0729389i
$130$	−2.41421	+	1.00000i	−0.211741	+	0.0877058i
$131$	−5.82843	+	14.0711i	−0.509232	+	1.22939i	0.435094	+	0.900385i	$0.356715\pi$
$131$	−5.82843	+	14.0711i	−0.509232	+	1.22939i	−0.944326	+	0.329010i	$0.893285\pi$
$132$			10.8284i			0.942494i
$133$	2.00000	+	0.828427i	0.173422	+	0.0718337i
$134$	2.00000	−	2.00000i	0.172774	−	0.172774i
$135$	−4.00000			−0.344265
$136$		0			0
$137$	−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
$139$	19.7279	+	8.17157i	1.67330	+	0.693104i	0.998972	−	0.0453279i	$-0.0144333\pi$
$139$	19.7279	+	8.17157i	1.67330	+	0.693104i	0.674328	+	0.738432i	$0.264433\pi$
$140$		−	7.65685i		−	0.647122i
$141$	2.14214	−	5.17157i	0.180400	−	0.435525i
$142$	12.0711	−	5.00000i	1.01298	−	0.419591i
$143$	1.41421	+	3.41421i	0.118262	+	0.285511i
$144$	3.87868	+	3.87868i	0.323223	+	0.323223i
$145$	−0.171573	−	0.171573i	−0.0142484	−	0.0142484i
$146$	11.9497	+	28.8492i	0.988968	+	2.38758i
$147$	−0.171573	+	0.0710678i	−0.0141511	+	0.00586157i
$148$	−13.5355	+	32.6777i	−1.11261	+	2.68609i
$149$		−	16.9706i		−	1.39028i	−0.718873	−	0.695141i	$-0.755342\pi$
$149$		−	16.9706i		−	1.39028i	0.718873	−	0.695141i	$-0.244658\pi$
$150$	−10.6569	−	4.41421i	−0.870129	−	0.360419i
$151$	−5.07107	+	5.07107i	−0.412678	+	0.412678i	−0.882670	−	0.469993i	$-0.844257\pi$
$151$	−5.07107	+	5.07107i	−0.412678	+	0.412678i	0.469993	+	0.882670i	$0.344257\pi$
$152$	3.65685			0.296610
$153$		0			0
$154$	−16.4853			−1.32842
$155$	−4.24264	+	4.24264i	−0.340777	+	0.340777i
$156$	−5.41421	−	2.24264i	−0.433484	−	0.179555i
$157$			9.65685i			0.770701i	0.922770	+	0.385350i	$0.125919\pi$
$157$			9.65685i			0.770701i	−0.922770	+	0.385350i	$0.874081\pi$
$158$	−4.41421	+	10.6569i	−0.351176	+	0.847814i
$159$	−1.41421	+	0.585786i	−0.112154	+	0.0464559i
$160$	0.464466	+	1.12132i	0.0367193	+	0.0886482i
$161$	−8.82843	−	8.82843i	−0.695778	−	0.695778i
$162$	−0.292893	−	0.292893i	−0.0230119	−	0.0230119i
$163$	−3.24264	−	7.82843i	−0.253983	−	0.613170i	0.744535	−	0.667583i	$-0.232671\pi$
$163$	−3.24264	−	7.82843i	−0.253983	−	0.613170i	−0.998518	+	0.0544134i	$0.982671\pi$
$164$	4.29289	−	1.77817i	0.335219	−	0.138852i
$165$	0.828427	−	2.00000i	0.0644930	−	0.155700i
$166$			28.1421i			2.18425i
$167$	−1.82843	−	0.757359i	−0.141488	−	0.0586062i	0.310816	−	0.950470i	$-0.399398\pi$
$167$	−1.82843	−	0.757359i	−0.141488	−	0.0586062i	−0.452304	+	0.891864i	$0.649398\pi$
$168$	8.82843	−	8.82843i	0.681128	−	0.681128i
$169$	11.0000			0.846154
$170$		0			0
$171$	1.51472			0.115833
$172$	2.24264	−	2.24264i	0.171000	−	0.171000i
$173$	−2.70711	−	1.12132i	−0.205818	−	0.0852524i	0.277393	−	0.960756i	$-0.410530\pi$
$173$	−2.70711	−	1.12132i	−0.205818	−	0.0852524i	−0.483211	+	0.875504i	$0.660530\pi$
$174$		−	0.828427i		−	0.0628029i
$175$	4.41421	−	10.6569i	0.333683	−	0.805582i
$176$	−7.24264	+	3.00000i	−0.545935	+	0.226134i
$177$	2.48528	+	6.00000i	0.186805	+	0.450988i
$178$	−11.2426	−	11.2426i	−0.842672	−	0.842672i
$179$	4.24264	+	4.24264i	0.317110	+	0.317110i	0.847656	−	0.530546i	$-0.178013\pi$
$179$	4.24264	+	4.24264i	0.317110	+	0.317110i	−0.530546	+	0.847656i	$0.678013\pi$
$180$	−2.05025	−	4.94975i	−0.152817	−	0.368932i
$181$	10.7782	−	4.46447i	0.801135	−	0.331841i	0.0557243	−	0.998446i	$-0.482253\pi$
$181$	10.7782	−	4.46447i	0.801135	−	0.331841i	0.745411	+	0.666605i	$0.232253\pi$
$182$	3.41421	−	8.24264i	0.253078	−	0.610985i
$183$			4.14214i			0.306195i
$184$	−19.4853	−	8.07107i	−1.43647	−	0.595007i
$185$	5.00000	−	5.00000i	0.367607	−	0.367607i
$186$	−20.4853			−1.50205
$187$		0			0
$188$	19.7990			1.44399
$189$	9.65685	−	9.65685i	0.702433	−	0.702433i
$190$	−1.41421	−	0.585786i	−0.102598	−	0.0424974i
$191$		−	20.0000i		−	1.44715i	−0.690246	−	0.723575i	$-0.742498\pi$
$191$		−	20.0000i		−	1.44715i	0.690246	−	0.723575i	$-0.257502\pi$
$192$	−4.07107	+	9.82843i	−0.293804	+	0.709306i
$193$	−2.12132	+	0.878680i	−0.152696	+	0.0632487i	−0.457722	−	0.889095i	$-0.651335\pi$
$193$	−2.12132	+	0.878680i	−0.152696	+	0.0632487i	0.305027	+	0.952344i	$0.401335\pi$
$194$	−9.53553	−	23.0208i	−0.684611	−	1.65280i
$195$	0.828427	+	0.828427i	0.0593249	+	0.0593249i
$196$	−0.464466	−	0.464466i	−0.0331761	−	0.0331761i
$197$	−1.77817	−	4.29289i	−0.126690	−	0.305856i	0.847790	−	0.530332i	$-0.177933\pi$
$197$	−1.77817	−	4.29289i	−0.126690	−	0.305856i	−0.974480	+	0.224476i	$0.927933\pi$
$198$	−10.6569	+	4.41421i	−0.757350	+	0.313704i
$199$	4.41421	−	10.6569i	0.312915	−	0.755444i	−0.686679	−	0.726961i	$-0.740932\pi$
$199$	4.41421	−	10.6569i	0.312915	−	0.755444i	0.999594	−	0.0284836i	$-0.00906783\pi$
$200$		−	19.4853i		−	1.37782i
$201$	−1.17157	−	0.485281i	−0.0826364	−	0.0342291i
$202$	−18.0711	+	18.0711i	−1.27148	+	1.27148i
$203$	0.828427			0.0581442
$204$		0			0
$205$	−0.928932			−0.0648794
$206$	21.3137	−	21.3137i	1.48500	−	1.48500i
$207$	−8.07107	−	3.34315i	−0.560978	−	0.232365i
$208$		−	4.24264i		−	0.294174i
$209$	−0.828427	+	2.00000i	−0.0573035	+	0.138343i
$210$	−4.82843	+	2.00000i	−0.333193	+	0.138013i
$211$	−8.17157	−	19.7279i	−0.562554	−	1.35813i	−0.907717	−	0.419583i	$-0.862176\pi$
$211$	−8.17157	−	19.7279i	−0.562554	−	1.35813i	0.345163	−	0.938543i	$-0.387824\pi$
$212$	−3.82843	−	3.82843i	−0.262937	−	0.262937i
$213$	−4.14214	−	4.14214i	−0.283814	−	0.283814i
$214$	−0.414214	−	1.00000i	−0.0283151	−	0.0683586i
$215$	−0.585786	+	0.242641i	−0.0399503	+	0.0165480i
$216$	8.82843	−	21.3137i	0.600698	−	1.45021i
$217$		−	20.4853i		−	1.39063i
$218$	34.6777	+	14.3640i	2.34867	+	0.972850i
$219$	9.89949	−	9.89949i	0.668946	−	0.668946i
$220$	7.65685			0.516225
$221$		0			0
$222$	24.1421			1.62031
$223$	−3.41421	+	3.41421i	−0.228633	+	0.228633i	−0.812121	−	0.583489i	$-0.801687\pi$
$223$	−3.41421	+	3.41421i	−0.228633	+	0.228633i	0.583489	+	0.812121i	$0.301687\pi$
$224$	−3.82843	−	1.58579i	−0.255798	−	0.105955i
$225$		−	8.07107i		−	0.538071i
$226$	−12.1924	+	29.4350i	−0.811026	+	1.95799i
$227$	−16.0711	+	6.65685i	−1.06667	+	0.441831i	−0.845816	−	0.533475i	$-0.820886\pi$
$227$	−16.0711	+	6.65685i	−1.06667	+	0.441831i	−0.220858	+	0.975306i	$0.570886\pi$
$228$	−1.31371	−	3.17157i	−0.0870025	−	0.210043i
$229$	12.1421	+	12.1421i	0.802375	+	0.802375i	0.983466	−	0.181091i	$-0.0579630\pi$
$229$	12.1421	+	12.1421i	0.802375	+	0.802375i	−0.181091	+	0.983466i	$0.557963\pi$
$230$	6.24264	+	6.24264i	0.411628	+	0.411628i
$231$	2.82843	+	6.82843i	0.186097	+	0.449278i
$232$	1.29289	−	0.535534i	0.0848826	−	0.0351595i
$233$	3.36396	−	8.12132i	0.220380	−	0.532045i	−0.774561	−	0.632499i	$-0.782029\pi$
$233$	3.36396	−	8.12132i	0.220380	−	0.532045i	0.994942	+	0.100453i	$0.0320293\pi$
$234$		−	6.24264i		−	0.408094i
$235$	−3.65685	−	1.51472i	−0.238547	−	0.0988093i
$236$	−16.2426	+	16.2426i	−1.05731	+	1.05731i
$237$	5.17157			0.335930
$238$		0			0
$239$	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
$241$	3.29289	+	1.36396i	0.212114	+	0.0878605i	0.486211	−	0.873842i	$-0.338379\pi$
$241$	3.29289	+	1.36396i	0.212114	+	0.0878605i	−0.274097	+	0.961702i	$0.588379\pi$
$242$			10.0711i			0.647393i
$243$	5.92893	−	14.3137i	0.380341	−	0.918225i
$244$	−13.5355	+	5.60660i	−0.866524	+	0.358926i
$245$	0.0502525	+	0.121320i	0.00321052	+	0.00775087i
$246$	−2.24264	−	2.24264i	−0.142986	−	0.142986i
$247$	−0.828427	−	0.828427i	−0.0527116	−	0.0527116i
$248$	−13.2426	−	31.9706i	−0.840909	−	2.03013i
$249$	11.6569	−	4.82843i	0.738723	−	0.305989i
$250$	−6.65685	+	16.0711i	−0.421016	+	1.01642i
$251$			20.4853i			1.29302i	0.762906	+	0.646510i	$0.223772\pi$
$251$			20.4853i			1.29302i	−0.762906	+	0.646510i	$0.776228\pi$
$252$	16.8995	+	7.00000i	1.06457	+	0.440959i
$253$	8.82843	−	8.82843i	0.555038	−	0.555038i
$254$	12.8284			0.804927
$255$		0			0
$256$	−29.9706			−1.87316
$257$	4.34315	−	4.34315i	0.270918	−	0.270918i	−0.558552	−	0.829470i	$-0.688643\pi$
$257$	4.34315	−	4.34315i	0.270918	−	0.270918i	0.829470	+	0.558552i	$0.188643\pi$
$258$	−2.00000	−	0.828427i	−0.124515	−	0.0515756i
$259$			24.1421i			1.50012i
$260$	−1.58579	+	3.82843i	−0.0983463	+	0.237429i
$261$	0.535534	−	0.221825i	0.0331487	−	0.0137306i
$262$	14.0711	+	33.9706i	0.869313	+	2.09871i
$263$	7.41421	+	7.41421i	0.457180	+	0.457180i	0.897729	−	0.440549i	$-0.145216\pi$
$263$	7.41421	+	7.41421i	0.457180	+	0.457180i	−0.440549	+	0.897729i	$0.645216\pi$
$264$	8.82843	+	8.82843i	0.543352	+	0.543352i
$265$	0.414214	+	1.00000i	0.0254449	+	0.0614295i
$266$	4.82843	−	2.00000i	0.296050	−	0.122628i
$267$	−2.72792	+	6.58579i	−0.166946	+	0.403044i
$268$		−	4.48528i		−	0.273982i
$269$	−24.4350	−	10.1213i	−1.48983	−	0.617108i	−0.518550	−	0.855047i	$-0.673528\pi$
$269$	−24.4350	−	10.1213i	−1.48983	−	0.617108i	−0.971280	+	0.237939i	$0.923528\pi$
$270$	−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	$0.265212\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$	−28.5563	+	28.5563i	−1.72515	+	1.72515i
$275$	10.6569	+	4.41421i	0.642632	+	0.266187i
$276$			19.7990i			1.19176i
$277$	−7.63604	+	18.4350i	−0.458805	+	1.10765i	0.510077	+	0.860129i	$0.329617\pi$
$277$	−7.63604	+	18.4350i	−0.458805	+	1.10765i	−0.968882	+	0.247525i	$0.920383\pi$
$278$	47.6274	−	19.7279i	2.85650	−	1.18320i
$279$	−5.48528	−	13.2426i	−0.328395	−	0.792816i
$280$	−6.24264	−	6.24264i	−0.373069	−	0.373069i
$281$	1.34315	+	1.34315i	0.0801254	+	0.0801254i	0.746034	−	0.665908i	$-0.231956\pi$
$281$	1.34315	+	1.34315i	0.0801254	+	0.0801254i	−0.665908	+	0.746034i	$0.731956\pi$
$282$	−5.17157	−	12.4853i	−0.307963	−	0.743488i
$283$	17.2426	−	7.14214i	1.02497	−	0.424556i	0.194075	−	0.980987i	$-0.437830\pi$
$283$	17.2426	−	7.14214i	1.02497	−	0.424556i	0.830894	+	0.556431i	$0.187830\pi$
$284$	7.92893	−	19.1421i	0.470496	−	1.13588i
$285$			0.686292i			0.0406524i
$286$	8.24264	+	3.41421i	0.487398	+	0.201887i
$287$	2.24264	−	2.24264i	0.132379	−	0.132379i
$288$	−2.89949			−0.170854
$289$		0			0
$290$	−0.585786			−0.0343986
$291$	−7.89949	+	7.89949i	−0.463077	+	0.463077i
$292$	45.7487	+	18.9497i	2.67724	+	1.10895i
$293$			12.3431i			0.721094i	0.932741	+	0.360547i	$0.117410\pi$
$293$			12.3431i			0.721094i	−0.932741	+	0.360547i	$0.882590\pi$
$294$	−0.171573	+	0.414214i	−0.0100063	+	0.0241574i
$295$	4.24264	−	1.75736i	0.247016	−	0.102317i
$296$	15.6066	+	37.6777i	0.907115	+	2.18997i
$297$	9.65685	+	9.65685i	0.560348	+	0.560348i
$298$	−28.9706	−	28.9706i	−1.67822	−	1.67822i
$299$	2.58579	+	6.24264i	0.149540	+	0.361021i
$300$	−16.8995	+	7.00000i	−0.975693	+	0.404145i
$301$	0.828427	−	2.00000i	0.0477497	−	0.115278i
$302$			17.3137i			0.996292i
$303$	10.5858	+	4.38478i	0.608138	+	0.251899i
$304$	1.75736	−	1.75736i	0.100791	−	0.100791i
$305$	2.92893			0.167710
$306$		0			0
$307$	−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
$309$	−12.4853	−	5.17157i	−0.710263	−	0.294201i
$310$			14.4853i			0.822709i
$311$	9.82843	−	23.7279i	0.557319	−	1.34549i	−0.354562	−	0.935032i	$-0.615370\pi$
$311$	9.82843	−	23.7279i	0.557319	−	1.34549i	0.911881	−	0.410455i	$-0.134630\pi$
$312$	−6.24264	+	2.58579i	−0.353420	+	0.146391i
$313$	−3.77817	−	9.12132i	−0.213555	−	0.515568i	0.780410	−	0.625269i	$-0.215011\pi$
$313$	−3.77817	−	9.12132i	−0.213555	−	0.515568i	−0.993965	+	0.109701i	$0.965011\pi$
$314$	16.4853	+	16.4853i	0.930318	+	0.930318i
$315$	−2.58579	−	2.58579i	−0.145693	−	0.145693i
$316$	7.00000	+	16.8995i	0.393781	+	0.950671i
$317$	−17.7782	+	7.36396i	−0.998522	+	0.413601i	−0.821255	−	0.570562i	$-0.806726\pi$
$317$	−17.7782	+	7.36396i	−0.998522	+	0.413601i	−0.177267	+	0.984163i	$0.556726\pi$
$318$	−1.41421	+	3.41421i	−0.0793052	+	0.191460i
$319$			0.828427i			0.0463830i
$320$	6.94975	+	2.87868i	0.388503	+	0.160923i
$321$	−0.343146	+	0.343146i	−0.0191525	+	0.0191525i
$322$	−30.1421			−1.67976
$323$		0			0
$324$	−0.656854			−0.0364919
$325$	−4.41421	+	4.41421i	−0.244857	+	0.244857i
$326$	−18.8995	−	7.82843i	−1.04675	−	0.433576i
$327$		−	16.8284i		−	0.930614i
$328$	2.05025	−	4.94975i	0.113206	−	0.273304i
$329$	12.4853	−	5.17157i	0.688336	−	0.285118i
$330$	−2.00000	−	4.82843i	−0.110096	−	0.265796i
$331$	15.4142	+	15.4142i	0.847242	+	0.847242i	0.989788	−	0.142546i	$-0.0455290\pi$
$331$	15.4142	+	15.4142i	0.847242	+	0.847242i	−0.142546	+	0.989788i	$0.545529\pi$
$332$	31.5563	+	31.5563i	1.73188	+	1.73188i
$333$	6.46447	+	15.6066i	0.354251	+	0.855237i
$334$	−4.41421	+	1.82843i	−0.241535	+	0.100047i
$335$	−0.343146	+	0.828427i	−0.0187481	+	0.0452618i
$336$		−	8.48528i		−	0.462910i
$337$	5.19239	+	2.15076i	0.282847	+	0.117159i	0.519597	−	0.854411i	$-0.326082\pi$
$337$	5.19239	+	2.15076i	0.282847	+	0.117159i	−0.236750	+	0.971571i	$0.576082\pi$
$338$	18.7782	−	18.7782i	1.02140	−	1.02140i
$339$	14.2843			0.775815
$340$		0			0
$341$	20.4853			1.10934
$342$	2.58579	−	2.58579i	0.139823	−	0.139823i
$343$	−17.3137	−	7.17157i	−0.934852	−	0.387229i
$344$		−	3.65685i		−	0.197164i
$345$	1.51472	−	3.65685i	0.0815497	−	0.196878i
$346$	−6.53553	+	2.70711i	−0.351352	+	0.145535i
$347$	6.41421	+	15.4853i	0.344333	+	0.831293i	0.997267	+	0.0738788i	$0.0235378\pi$
$347$	6.41421	+	15.4853i	0.344333	+	0.831293i	−0.652934	+	0.757415i	$0.726462\pi$
$348$	−0.928932	−	0.928932i	−0.0497960	−	0.0497960i
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	0.622240	−	0.782826i	$-0.286223\pi$
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	−0.782826	+	0.622240i	$0.786223\pi$
$350$	−10.6569	−	25.7279i	−0.569633	−	1.37522i
$351$	−6.82843	+	2.82843i	−0.364474	+	0.150970i
$352$	1.58579	−	3.82843i	0.0845227	−	0.204056i
$353$		−	14.0000i		−	0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$		−	14.0000i		−	0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$	14.4853	+	6.00000i	0.769884	+	0.318896i
$355$	−2.92893	+	2.92893i	−0.155452	+	0.155452i
$356$	−25.2132			−1.33630
$357$		0			0
$358$	14.4853			0.765571
$359$	20.3848	−	20.3848i	1.07587	−	1.07587i	0.0789921	−	0.996875i	$-0.474830\pi$
$359$	20.3848	−	20.3848i	1.07587	−	1.07587i	0.996875	−	0.0789921i	$-0.0251702\pi$
$360$	−5.70711	−	2.36396i	−0.300791	−	0.124592i
$361$			18.3137i			0.963879i
$362$	10.7782	−	26.0208i	0.566488	−	1.36762i
$363$	4.17157	−	1.72792i	0.218951	−	0.0906924i
$364$	−5.41421	−	13.0711i	−0.283782	−	0.685110i
$365$	−7.00000	−	7.00000i	−0.366397	−	0.366397i
$366$	7.07107	+	7.07107i	0.369611	+	0.369611i
$367$	−1.68629	−	4.07107i	−0.0880237	−	0.212508i	0.873737	−	0.486398i	$-0.161690\pi$
$367$	−1.68629	−	4.07107i	−0.0880237	−	0.212508i	−0.961761	+	0.273890i	$0.911690\pi$
$368$	−13.2426	+	5.48528i	−0.690320	+	0.285940i
$369$	0.849242	−	2.05025i	0.0442098	−	0.106732i
$370$		−	17.0711i		−	0.887483i
$371$	−3.41421	−	1.41421i	−0.177257	−	0.0734223i
$372$	−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	$0.403286\pi$
$374$		0			0
$375$	7.79899			0.402738
$376$	16.1421	−	16.1421i	0.832467	−	0.832467i
$377$	−0.414214	−	0.171573i	−0.0213331	−	0.00883645i
$378$		−	32.9706i		−	1.69582i
$379$	−1.00000	+	2.41421i	−0.0513665	+	0.124010i	−0.947480	−	0.319816i	$-0.896379\pi$
$379$	−1.00000	+	2.41421i	−0.0513665	+	0.124010i	0.896113	+	0.443826i	$0.146379\pi$
$380$	−2.24264	+	0.928932i	−0.115045	+	0.0476532i
$381$	−2.20101	−	5.31371i	−0.112761	−	0.272230i
$382$	−34.1421	−	34.1421i	−1.74686	−	1.74686i
$383$	15.8995	+	15.8995i	0.812426	+	0.812426i	0.984997	−	0.172571i	$-0.0552074\pi$
$383$	15.8995	+	15.8995i	0.812426	+	0.812426i	−0.172571	+	0.984997i	$0.555207\pi$
$384$	8.51472	+	20.5563i	0.434515	+	1.04901i
$385$	4.82843	−	2.00000i	0.246079	−	0.101929i
$386$	−2.12132	+	5.12132i	−0.107972	+	0.260668i
$387$		−	1.51472i		−	0.0769975i
$388$	−36.5061	−	15.1213i	−1.85332	−	0.767669i
$389$	8.58579	−	8.58579i	0.435317	−	0.435317i	−0.455116	−	0.890432i	$-0.650402\pi$
$389$	8.58579	−	8.58579i	0.435317	−	0.435317i	0.890432	+	0.455116i	$0.150402\pi$
$390$	2.82843			0.143223
$391$		0			0
$392$	−0.757359			−0.0382524
$393$	11.6569	−	11.6569i	0.588011	−	0.588011i
$394$	−10.3640	−	4.29289i	−0.522129	−	0.216273i
$395$		−	3.65685i		−	0.183996i
$396$	−7.00000	+	16.8995i	−0.351763	+	0.849232i
$397$	−16.4350	+	6.80761i	−0.824850	+	0.341664i	−0.754862	−	0.655884i	$-0.772296\pi$
$397$	−16.4350	+	6.80761i	−0.824850	+	0.341664i	−0.0699884	+	0.997548i	$0.522296\pi$
$398$	−10.6569	−	25.7279i	−0.534180	−	1.28962i
$399$	−1.65685	−	1.65685i	−0.0829465	−	0.0829465i
$400$	−9.36396	−	9.36396i	−0.468198	−	0.468198i
$401$	−0.221825	−	0.535534i	−0.0110774	−	0.0267433i	0.918244	−	0.396015i	$-0.129607\pi$
$401$	−0.221825	−	0.535534i	−0.0110774	−	0.0267433i	−0.929321	+	0.369272i	$0.879607\pi$
$402$	−2.82843	+	1.17157i	−0.141069	+	0.0584327i
$403$	−4.24264	+	10.2426i	−0.211341	+	0.510222i
$404$			40.5269i			2.01629i
$405$	0.121320	+	0.0502525i	0.00602846	+	0.00249707i
$406$	1.41421	−	1.41421i	0.0701862	−	0.0701862i
$407$	−24.1421			−1.19668
$408$		0			0
$409$	−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
$411$	16.7279	+	6.92893i	0.825128	+	0.341779i
$412$		−	47.7990i		−	2.35489i
$413$	−6.00000	+	14.4853i	−0.295241	+	0.712774i
$414$	−19.4853	+	8.07107i	−0.957649	+	0.396671i
$415$	−3.41421	−	8.24264i	−0.167597	−	0.404615i
$416$	1.58579	+	1.58579i	0.0777496	+	0.0777496i
$417$	−16.3431	−	16.3431i	−0.800327	−	0.800327i
$418$	2.00000	+	4.82843i	0.0978232	+	0.236166i
$419$	12.3137	−	5.10051i	0.601564	−	0.249176i	−0.0610528	−	0.998135i	$-0.519446\pi$
$419$	12.3137	−	5.10051i	0.601564	−	0.249176i	0.662617	+	0.748959i	$0.269446\pi$
$420$	−3.17157	+	7.65685i	−0.154757	+	0.373616i
$421$			14.5858i			0.710868i	0.934701	+	0.355434i	$0.115667\pi$
$421$			14.5858i			0.710868i	−0.934701	+	0.355434i	$0.884333\pi$
$422$	−47.6274	−	19.7279i	−2.31847	−	0.960340i
$423$	6.68629	−	6.68629i	0.325099	−	0.325099i
$424$	−6.24264			−0.303169
$425$		0			0
$426$	−14.1421			−0.685189
$427$	−7.07107	+	7.07107i	−0.342193	+	0.342193i
$428$	−1.58579	−	0.656854i	−0.0766519	−	0.0317502i
$429$		−	4.00000i		−	0.193122i
$430$	−0.585786	+	1.41421i	−0.0282491	+	0.0681994i
$431$	−6.75736	+	2.79899i	−0.325491	+	0.134823i	−0.539445	−	0.842021i	$-0.681366\pi$
$431$	−6.75736	+	2.79899i	−0.325491	+	0.134823i	0.213954	+	0.976844i	$0.431366\pi$
$432$	−6.00000	−	14.4853i	−0.288675	−	0.696923i
$433$	−14.7279	−	14.7279i	−0.707779	−	0.707779i	0.258289	−	0.966068i	$-0.416841\pi$
$433$	−14.7279	−	14.7279i	−0.707779	−	0.707779i	−0.966068	+	0.258289i	$0.916841\pi$
$434$	−34.9706	−	34.9706i	−1.67864	−	1.67864i
$435$	0.100505	+	0.242641i	0.00481885	+	0.0116337i
$436$	54.9914	−	22.7782i	2.63361	−	1.09088i
$437$	−1.51472	+	3.65685i	−0.0724588	+	0.174931i
$438$		−	33.7990i		−	1.61498i
$439$	9.82843	+	4.07107i	0.469085	+	0.194301i	0.604689	−	0.796462i	$-0.293297\pi$
$439$	9.82843	+	4.07107i	0.469085	+	0.194301i	−0.135604	+	0.990763i	$0.543297\pi$
$440$	6.24264	−	6.24264i	0.297606	−	0.297606i
$441$	−0.313708			−0.0149385
$442$		0			0
$443$	−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
$445$	4.65685	+	1.92893i	0.220756	+	0.0914402i
$446$			11.6569i			0.551968i
$447$	−7.02944	+	16.9706i	−0.332481	+	0.802680i
$448$	−23.7279	+	9.82843i	−1.12104	+	0.464350i
$449$	4.63604	+	11.1924i	0.218788	+	0.528201i	0.994721	−	0.102614i	$-0.0327206\pi$
$449$	4.63604	+	11.1924i	0.218788	+	0.528201i	−0.775933	+	0.630815i	$0.782721\pi$
$450$	−13.7782	−	13.7782i	−0.649509	−	0.649509i
$451$	2.24264	+	2.24264i	0.105602	+	0.105602i
$452$	19.3345	+	46.6777i	0.909419	+	2.19553i
$453$	7.17157	−	2.97056i	0.336950	−	0.139569i
$454$	−16.0711	+	38.7990i	−0.754253	+	1.82093i
$455$			2.82843i			0.132599i
$456$	−3.65685	−	1.51472i	−0.171248	−	0.0709332i
$457$	−9.31371	+	9.31371i	−0.435677	+	0.435677i	−0.890554	−	0.454877i	$-0.849683\pi$
$457$	−9.31371	+	9.31371i	−0.435677	+	0.435677i	0.454877	+	0.890554i	$0.349683\pi$
$458$	41.4558			1.93710
$459$		0			0
$460$	14.0000			0.652753
$461$	−17.0000	+	17.0000i	−0.791769	+	0.791769i	−0.981782	−	0.190013i	$-0.939147\pi$
$461$	−17.0000	+	17.0000i	−0.791769	+	0.791769i	0.190013	+	0.981782i	$0.439147\pi$
$462$	16.4853	+	6.82843i	0.766965	+	0.317687i
$463$		−	14.6274i		−	0.679794i	−0.940463	−	0.339897i	$-0.889608\pi$
$463$		−	14.6274i		−	0.679794i	0.940463	−	0.339897i	$-0.110392\pi$
$464$	0.363961	−	0.878680i	0.0168965	−	0.0407917i
$465$	6.00000	−	2.48528i	0.278243	−	0.115252i
$466$	−8.12132	−	19.6066i	−0.376213	−	0.908258i
$467$	−23.0711	−	23.0711i	−1.06760	−	1.06760i	−0.997543	−	0.0700588i	$-0.977681\pi$
$467$	−23.0711	−	23.0711i	−1.06760	−	1.06760i	−0.0700588	−	0.997543i	$-0.522319\pi$
$468$	−7.00000	−	7.00000i	−0.323575	−	0.323575i
$469$	−1.17157	−	2.82843i	−0.0540982	−	0.130605i
$470$	−8.82843	+	3.65685i	−0.407225	+	0.168678i
$471$	4.00000	−	9.65685i	0.184310	−	0.444964i
$472$			26.4853i			1.21908i
$473$	2.00000	+	0.828427i	0.0919601	+	0.0380911i
$474$	8.82843	−	8.82843i	0.405503	−	0.405503i
$475$	−3.65685			−0.167788
$476$		0			0
$477$	−2.58579			−0.118395
$478$	25.3137	−	25.3137i	1.15782	−	1.15782i
$479$	−4.75736	−	1.97056i	−0.217369	−	0.0900373i	0.271342	−	0.962483i	$-0.412533\pi$
$479$	−4.75736	−	1.97056i	−0.217369	−	0.0900373i	−0.488711	+	0.872446i	$0.662533\pi$
$480$		−	1.31371i		−	0.0599623i
$481$	5.00000	−	12.0711i	0.227980	−	0.550393i
$482$	7.94975	−	3.29289i	0.362101	−	0.149987i
$483$	5.17157	+	12.4853i	0.235315	+	0.568100i
$484$	11.2929	+	11.2929i	0.513313	+	0.513313i
$485$	5.58579	+	5.58579i	0.253637	+	0.253637i
$486$	−14.3137	−	34.5563i	−0.649283	−	1.56751i
$487$	−24.3137	+	10.0711i	−1.10176	+	0.456364i	−0.858092	−	0.513495i	$-0.828350\pi$
$487$	−24.3137	+	10.0711i	−1.10176	+	0.456364i	−0.243667	+	0.969859i	$0.578350\pi$
$488$	−6.46447	+	15.6066i	−0.292633	+	0.706478i
$489$			9.17157i			0.414753i
$490$	0.292893	+	0.121320i	0.0132316	+	0.00548069i
$491$	−26.2426	+	26.2426i	−1.18431	+	1.18431i	−0.205698	+	0.978615i	$0.565947\pi$
$491$	−26.2426	+	26.2426i	−1.18431	+	1.18431i	−0.978615	+	0.205698i	$0.934053\pi$
$492$	−5.02944			−0.226745
$493$		0			0
$494$	−2.82843			−0.127257
$495$	2.58579	−	2.58579i	0.116222	−	0.116222i
$496$	−21.7279	−	9.00000i	−0.975613	−	0.404112i
$497$		−	14.1421i		−	0.634361i
$498$	11.6569	−	28.1421i	0.522356	−	1.26108i
$499$	19.8284	−	8.21320i	0.887642	−	0.367673i	0.108186	−	0.994131i	$-0.465496\pi$
$499$	19.8284	−	8.21320i	0.887642	−	0.367673i	0.779456	+	0.626457i	$0.215496\pi$
$500$	10.5563	+	25.4853i	0.472094	+	1.13974i
$501$	1.51472	+	1.51472i	0.0676726	+	0.0676726i
$502$	34.9706	+	34.9706i	1.56081	+	1.56081i
$503$	−8.17157	−	19.7279i	−0.364352	−	0.879625i	−0.994653	−	0.103273i	$-0.967068\pi$
$503$	−8.17157	−	19.7279i	−0.364352	−	0.879625i	0.630301	−	0.776351i	$-0.282932\pi$
$504$	19.4853	−	8.07107i	0.867943	−	0.359514i
$505$	3.10051	−	7.48528i	0.137971	−	0.333091i
$506$		−	30.1421i		−	1.33998i
$507$	−11.0000	−	4.55635i	−0.488527	−	0.202355i
$508$	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	$0.805663\pi$
$510$		0			0
$511$	33.7990			1.49518
$512$	−22.0919	+	22.0919i	−0.976333	+	0.976333i
$513$	−4.00000	−	1.65685i	−0.176604	−	0.0731519i
$514$		−	14.8284i		−	0.654054i
$515$	−3.65685	+	8.82843i	−0.161140	+	0.389027i
$516$	−3.17157	+	1.31371i	−0.139621	+	0.0578328i
$517$	5.17157	+	12.4853i	0.227446	+	0.549102i
$518$	41.2132	+	41.2132i	1.81080	+	1.81080i
$519$	2.24264	+	2.24264i	0.0984410	+	0.0984410i
$520$	1.82843	+	4.41421i	0.0801818	+	0.193576i
$521$	−17.1924	+	7.12132i	−0.753212	+	0.311991i	−0.726051	−	0.687640i	$-0.758647\pi$
$521$	−17.1924	+	7.12132i	−0.753212	+	0.311991i	−0.0271607	+	0.999631i	$0.508647\pi$
$522$	0.535534	−	1.29289i	0.0234397	−	0.0565884i
$523$			1.17157i			0.0512293i	0.999672	+	0.0256147i	$0.00815429\pi$
$523$			1.17157i			0.0512293i	−0.999672	+	0.0256147i	$0.991846\pi$
$524$	53.8701	+	22.3137i	2.35332	+	0.974779i
$525$	−8.82843	+	8.82843i	−0.385304	+	0.385304i
$526$	25.3137			1.10373
$527$		0			0
$528$	8.48528			0.369274
$529$	−0.121320	+	0.121320i	−0.00527480	+	0.00527480i
$530$	2.41421	+	1.00000i	0.104867	+	0.0434372i
$531$			10.9706i			0.476082i
$532$	3.17157	−	7.65685i	0.137505	−	0.331967i
$533$	−1.58579	+	0.656854i	−0.0686880	+	0.0284515i
$534$	6.58579	+	15.8995i	0.284995	+	0.688038i
$535$	0.242641	+	0.242641i	0.0104903	+	0.0104903i
$536$	−3.65685	−	3.65685i	−0.157952	−	0.157952i
$537$	−2.48528	−	6.00000i	−0.107248	−	0.258919i
$538$	−58.9914	+	24.4350i	−2.54330	+	1.05347i
$539$	0.171573	−	0.414214i	0.00739017	−	0.0178414i
$540$			15.3137i			0.658997i
$541$	17.0208	+	7.05025i	0.731782	+	0.303114i	0.717284	−	0.696781i	$-0.245385\pi$
$541$	17.0208	+	7.05025i	0.731782	+	0.303114i	0.0144979	+	0.999895i	$0.495385\pi$
$542$	37.7990	−	37.7990i	1.62361	−	1.62361i
$543$	−12.6274			−0.541894
$544$		0			0
$545$	−11.8995			−0.509718
$546$	−6.82843	+	6.82843i	−0.292230	+	0.292230i
$547$	−7.48528	−	3.10051i	−0.320048	−	0.132568i	0.216875	−	0.976199i	$-0.430413\pi$
$547$	−7.48528	−	3.10051i	−0.320048	−	0.132568i	−0.536923	+	0.843631i	$0.680413\pi$
$548$			64.0416i			2.73572i
$549$	−2.67767	+	6.46447i	−0.114280	+	0.275897i
$550$	25.7279	−	10.6569i	1.09704	−	0.454410i
$551$	−0.100505	−	0.242641i	−0.00428166	−	0.0103368i
$552$	16.1421	+	16.1421i	0.687055	+	0.687055i
$553$	8.82843	+	8.82843i	0.375423	+	0.375423i
$554$	18.4350	+	44.5061i	0.783229	+	1.89088i
$555$	−7.07107	+	2.92893i	−0.300150	+	0.124326i
$556$	31.2843	−	75.5269i	1.32675	−	3.20305i
$557$		−	19.7574i		−	0.837146i	−0.908183	−	0.418573i	$-0.862530\pi$
$557$		−	19.7574i		−	0.837146i	0.908183	−	0.418573i	$-0.137470\pi$
$558$	−31.9706	−	13.2426i	−1.35342	−	0.560606i
$559$	−0.828427	+	0.828427i	−0.0350387	+	0.0350387i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	4.58579			0.193440
$563$	−24.5858	+	24.5858i	−1.03617	+	1.03617i	−0.0368464	+	0.999321i	$0.511731\pi$
$563$	−24.5858	+	24.5858i	−1.03617	+	1.03617i	−0.999321	+	0.0368464i	$0.988269\pi$
$564$	−19.7990	−	8.20101i	−0.833688	−	0.345325i
$565$		−	10.1005i		−	0.424931i
$566$	17.2426	−	41.6274i	0.724762	−	1.74973i
$567$	−0.414214	+	0.171573i	−0.0173953	+	0.00720538i
$568$	−9.14214	−	22.0711i	−0.383595	−	0.926081i
$569$	−8.51472	−	8.51472i	−0.356956	−	0.356956i	0.505734	−	0.862690i	$-0.331222\pi$
$569$	−8.51472	−	8.51472i	−0.356956	−	0.356956i	−0.862690	+	0.505734i	$0.831222\pi$
$570$	1.17157	+	1.17157i	0.0490718	+	0.0490718i
$571$	−1.62742	−	3.92893i	−0.0681053	−	0.164421i	0.886162	−	0.463376i	$-0.153362\pi$
$571$	−1.62742	−	3.92893i	−0.0681053	−	0.164421i	−0.954267	+	0.298955i	$0.903362\pi$
$572$	13.0711	−	5.41421i	0.546529	−	0.226380i
$573$	−8.28427	+	20.0000i	−0.346080	+	0.835512i
$574$		−	7.65685i		−	0.319591i
$575$	19.4853	+	8.07107i	0.812592	+	0.336587i
$576$	−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	$0.690542\pi$
$578$		0			0
$579$	2.48528			0.103285
$580$	−0.656854	+	0.656854i	−0.0272744	+	0.0272744i
$581$	28.1421	+	11.6569i	1.16753	+	0.483608i
$582$			26.9706i			1.11797i
$583$	1.41421	−	3.41421i	0.0585707	−	0.141402i
$584$	52.7487	−	21.8492i	2.18276	−	0.904128i
$585$	0.757359	+	1.82843i	0.0313130	+	0.0755962i
$586$	21.0711	+	21.0711i	0.870438	+	0.870438i
$587$	−32.0416	−	32.0416i	−1.32250	−	1.32250i	−0.911747	−	0.410753i	$-0.865266\pi$
$587$	−32.0416	−	32.0416i	−1.32250	−	1.32250i	−0.410753	−	0.911747i	$-0.634734\pi$
$588$	0.272078	+	0.656854i	0.0112203	+	0.0270882i
$589$	−6.00000	+	2.48528i	−0.247226	+	0.102404i
$590$	4.24264	−	10.2426i	0.174667	−	0.421683i
$591$			5.02944i			0.206883i
$592$	25.6066	+	10.6066i	1.05242	+	0.435929i
$593$	−9.14214	+	9.14214i	−0.375423	+	0.375423i	−0.869448	−	0.494025i	$-0.835525\pi$
$593$	−9.14214	+	9.14214i	−0.375423	+	0.375423i	0.494025	+	0.869448i	$0.335525\pi$
$594$	32.9706			1.35280
$595$		0			0
$596$	−64.9706			−2.66130
$597$	−8.82843	+	8.82843i	−0.361323	+	0.361323i
$598$	15.0711	+	6.24264i	0.616302	+	0.255281i
$599$			10.6274i			0.434224i	0.976147	+	0.217112i	$0.0696638\pi$
$599$			10.6274i			0.434224i	−0.976147	+	0.217112i	$0.930336\pi$
$600$	−8.07107	+	19.4853i	−0.329500	+	0.795483i
$601$	7.77817	−	3.22183i	0.317278	−	0.131421i	−0.218360	−	0.975868i	$-0.570071\pi$
$601$	7.77817	−	3.22183i	0.317278	−	0.131421i	0.535639	+	0.844447i	$0.320071\pi$
$602$	−2.00000	−	4.82843i	−0.0815139	−	0.196792i
$603$	−1.51472	−	1.51472i	−0.0616841	−	0.0616841i
$604$	19.4142	+	19.4142i	0.789953	+	0.789953i
$605$	−1.22183	−	2.94975i	−0.0496743	−	0.119924i
$606$	25.5563	−	10.5858i	1.03816	−	0.430018i
$607$	6.27208	−	15.1421i	0.254576	−	0.614600i	−0.743987	−	0.668194i	$-0.767068\pi$
$607$	6.27208	−	15.1421i	0.254576	−	0.614600i	0.998563	+	0.0535937i	$0.0170676\pi$
$608$			1.31371i			0.0532779i
$609$	−0.828427	−	0.343146i	−0.0335696	−	0.0139050i
$610$	5.00000	−	5.00000i	0.202444	−	0.202444i
$611$	−7.31371			−0.295881
$612$		0			0
$613$	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
$615$	0.928932	+	0.384776i	0.0374582	+	0.0155157i
$616$			30.1421i			1.21446i
$617$	−1.12132	+	2.70711i	−0.0451427	+	0.108984i	−0.944842	−	0.327525i	$-0.893785\pi$
$617$	−1.12132	+	2.70711i	−0.0451427	+	0.108984i	0.899700	+	0.436509i	$0.143785\pi$
$618$	−30.1421	+	12.4853i	−1.21249	+	0.502232i
$619$	10.8995	+	26.3137i	0.438088	+	1.05764i	0.976609	+	0.215025i	$0.0689833\pi$
$619$	10.8995	+	26.3137i	0.438088	+	1.05764i	−0.538521	+	0.842612i	$0.681017\pi$
$620$	16.2426	+	16.2426i	0.652320	+	0.652320i
$621$	17.6569	+	17.6569i	0.708545	+	0.708545i
$622$	−23.7279	−	57.2843i	−0.951403	−	2.29689i
$623$	−15.8995	+	6.58579i	−0.637000	+	0.263854i
$624$	−1.75736	+	4.24264i	−0.0703507	+	0.169842i
$625$			16.5563i			0.662254i
$626$	−22.0208	−	9.12132i	−0.880129	−	0.364561i
$627$	1.65685	−	1.65685i	0.0661684	−	0.0661684i
$628$	36.9706			1.47529
$629$		0			0
$630$	−8.82843			−0.351733
$631$	20.7279	−	20.7279i	0.825166	−	0.825166i	−0.161678	−	0.986844i	$-0.551691\pi$
$631$	20.7279	−	20.7279i	0.825166	−	0.825166i	0.986844	+	0.161678i	$0.0516906\pi$
$632$	19.4853	+	8.07107i	0.775083	+	0.321050i
$633$			23.1127i			0.918647i
$634$	−17.7782	+	42.9203i	−0.706062	+	1.70458i
$635$	−3.75736	+	1.55635i	−0.149106	+	0.0617618i
$636$	2.24264	+	5.41421i	0.0889265	+	0.214688i
$637$	0.171573	+	0.171573i	0.00679796	+	0.00679796i
$638$	1.41421	+	1.41421i	0.0559893	+	0.0559893i
$639$	−3.78680	−	9.14214i	−0.149803	−	0.361657i
$640$	14.5355	−	6.02082i	0.574567	−	0.237994i
$641$	−15.8492	+	38.2635i	−0.626007	+	1.51132i	0.218536	+	0.975829i	$0.429872\pi$
$641$	−15.8492	+	38.2635i	−0.626007	+	1.51132i	−0.844544	+	0.535487i	$0.820128\pi$
$642$			1.17157i			0.0462383i
$643$	−26.6569	−	11.0416i	−1.05124	−	0.435439i	−0.210908	−	0.977506i	$-0.567642\pi$
$643$	−26.6569	−	11.0416i	−1.05124	−	0.435439i	−0.840336	+	0.542066i	$0.817642\pi$
$644$	−33.7990	+	33.7990i	−1.33187	+	1.33187i
$645$	0.686292			0.0270227
$646$		0			0
$647$	−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
$649$	−14.4853	−	6.00000i	−0.568597	−	0.235521i
$650$			15.0711i			0.591136i
$651$	−8.48528	+	20.4853i	−0.332564	+	0.802881i
$652$	−29.9706	+	12.4142i	−1.17374	+	0.486178i
$653$	3.63604	+	8.77817i	0.142289	+	0.343517i	0.978918	−	0.204254i	$-0.0654768\pi$
$653$	3.63604	+	8.77817i	0.142289	+	0.343517i	−0.836629	+	0.547770i	$0.815477\pi$
$654$	−28.7279	−	28.7279i	−1.12335	−	1.12335i
$655$	−8.24264	−	8.24264i	−0.322067	−	0.322067i
$656$	−1.39340	−	3.36396i	−0.0544031	−	0.131341i
$657$	21.8492	−	9.05025i	0.852420	−	0.353084i
$658$	12.4853	−	30.1421i	0.486727	−	1.17506i
$659$		−	8.48528i		−	0.330540i	−0.986248	−	0.165270i	$-0.947151\pi$
$659$		−	8.48528i		−	0.330540i	0.986248	−	0.165270i	$-0.0528495\pi$
$660$	−7.65685	−	3.17157i	−0.298043	−	0.123453i
$661$	−0.857864	+	0.857864i	−0.0333671	+	0.0333671i	−0.723593	−	0.690226i	$-0.757511\pi$
$661$	−0.857864	+	0.857864i	−0.0333671	+	0.0333671i	0.690226	+	0.723593i	$0.257511\pi$
$662$	52.6274			2.04542
$663$		0			0
$664$	51.4558			1.99687
$665$	−1.17157	+	1.17157i	−0.0454316	+	0.0454316i
$666$	37.6777	+	15.6066i	1.45998	+	0.604744i
$667$			1.51472i			0.0586501i
$668$	−2.89949	+	7.00000i	−0.112185	+	0.270838i
$669$	4.82843	−	2.00000i	0.186678	−	0.0773245i
$670$	0.828427	+	2.00000i	0.0320049	+	0.0772667i
$671$	−7.07107	−	7.07107i	−0.272976	−	0.272976i
$672$	3.17157	+	3.17157i	0.122346	+	0.122346i
$673$	1.70711	+	4.12132i	0.0658041	+	0.158865i	0.953361	−	0.301834i	$-0.0975988\pi$
$673$	1.70711	+	4.12132i	0.0658041	+	0.158865i	−0.887556	+	0.460699i	$0.847599\pi$
$674$	12.5355	−	5.19239i	0.482851	−	0.200003i
$675$	−8.82843	+	21.3137i	−0.339806	+	0.820365i
$676$		−	42.1127i		−	1.61972i
$677$	35.1924	+	14.5772i	1.35255	+	0.560246i	0.937002	−	0.349324i	$-0.113589\pi$
$677$	35.1924	+	14.5772i	1.35255	+	0.560246i	0.415551	+	0.909570i	$0.363589\pi$
$678$	24.3848	−	24.3848i	0.936492	−	0.936492i
$679$	−26.9706			−1.03504
$680$		0			0
$681$	18.8284			0.721507
$682$	34.9706	−	34.9706i	1.33909	−	1.33909i
$683$	21.9706	+	9.10051i	0.840680	+	0.348221i	0.761122	−	0.648609i	$-0.224649\pi$
$683$	21.9706	+	9.10051i	0.840680	+	0.348221i	0.0795585	+	0.996830i	$0.474649\pi$
$684$		−	5.79899i		−	0.221730i
$685$	4.89949	−	11.8284i	0.187200	−	0.451941i
$686$	−41.7990	+	17.3137i	−1.59589	+	0.661040i
$687$	−7.11270	−	17.1716i	−0.271366	−	0.655136i
$688$	−1.75736	−	1.75736i	−0.0669987	−	0.0669987i
$689$	1.41421	+	1.41421i	0.0538772	+	0.0538772i
$690$	−3.65685	−	8.82843i	−0.139214	−	0.336092i
$691$	18.4142	−	7.62742i	0.700510	−	0.290161i	−0.00386139	−	0.999993i	$-0.501229\pi$
$691$	18.4142	−	7.62742i	0.700510	−	0.290161i	0.704371	+	0.709832i	$0.251229\pi$
$692$	−4.29289	+	10.3640i	−0.163191	+	0.393979i
$693$			12.4853i			0.474277i
$694$	37.3848	+	15.4853i	1.41911	+	0.587813i
$695$	−11.5563	+	11.5563i	−0.438357	+	0.438357i
$696$	−1.51472			−0.0574153
$697$		0			0
$698$	−10.2426			−0.387690
$699$	−6.72792	+	6.72792i	−0.254473	+	0.254473i
$700$	−40.7990	−	16.8995i	−1.54206	−	0.638741i
$701$		−	37.6985i		−	1.42385i	−0.702254	−	0.711926i	$-0.747823\pi$
$701$		−	37.6985i		−	1.42385i	0.702254	−	0.711926i	$-0.252177\pi$
$702$	−6.82843	+	16.4853i	−0.257722	+	0.622197i
$703$	7.07107	−	2.92893i	0.266690	−	0.110467i
$704$	−9.82843	−	23.7279i	−0.370423	−	0.894280i
$705$	3.02944	+	3.02944i	0.114095	+	0.114095i
$706$	−23.8995	−	23.8995i	−0.899469	−	0.899469i
$707$	10.5858	+	25.5563i	0.398119	+	0.961145i
$708$	22.9706	−	9.51472i	0.863287	−	0.357585i
$709$	9.29289	−	22.4350i	0.349002	−	0.842565i	−0.647736	−	0.761864i	$-0.724284\pi$
$709$	9.29289	−	22.4350i	0.349002	−	0.842565i	0.996738	−	0.0807007i	$-0.0257158\pi$
$710$			10.0000i			0.375293i
$711$	8.07107	+	3.34315i	0.302689	+	0.125378i
$712$	−20.5563	+	20.5563i	−0.770382	+	0.770382i
$713$	37.4558			1.40273
$714$		0			0
$715$	−2.82843			−0.105777
$716$	16.2426	−	16.2426i	0.607016	−	0.607016i
$717$	−14.8284	−	6.14214i	−0.553778	−	0.229382i
$718$		−	69.5980i		−	2.59737i
$719$	−13.0000	+	31.3848i	−0.484818	+	1.17045i	0.472477	+	0.881343i	$0.343360\pi$
$719$	−13.0000	+	31.3848i	−0.484818	+	1.17045i	−0.957295	+	0.289112i	$0.906640\pi$
$720$	−3.87868	+	1.60660i	−0.144550	+	0.0598745i
$721$	−12.4853	−	30.1421i	−0.464976	−	1.12255i
$722$	31.2635	+	31.2635i	1.16351	+	1.16351i
$723$	−2.72792	−	2.72792i	−0.101453	−	0.101453i
$724$	−17.0919	−	41.2635i	−0.635215	−	1.53354i
$725$	−1.29289	+	0.535534i	−0.0480168	+	0.0198892i
$726$	4.17157	−	10.0711i	0.154822	−	0.373772i
$727$		−	43.1127i		−	1.59896i	−0.600692	−	0.799481i	$-0.705108\pi$
$727$		−	43.1127i		−	1.59896i	0.600692	−	0.799481i	$-0.294892\pi$
$728$	−15.0711	−	6.24264i	−0.558571	−	0.231368i
$729$	−12.2218	+	12.2218i	−0.452660	+	0.452660i
$730$	−23.8995			−0.884560
$731$		0			0
$732$	15.8579			0.586124
$733$	25.4853	−	25.4853i	0.941320	−	0.941320i	−0.0570509	−	0.998371i	$-0.518170\pi$
$733$	25.4853	−	25.4853i	0.941320	−	0.941320i	0.998371	+	0.0570509i	$0.0181697\pi$
$734$	−9.82843	−	4.07107i	−0.362774	−	0.150266i
$735$		−	0.142136i		−	0.00524275i
$736$	2.89949	−	7.00000i	0.106877	−	0.258023i
$737$	2.82843	−	1.17157i	0.104186	−	0.0431554i
$738$	−2.05025	−	4.94975i	−0.0754708	−	0.182203i
$739$	−15.7574	−	15.7574i	−0.579644	−	0.579644i	0.355161	−	0.934805i	$-0.384426\pi$
$739$	−15.7574	−	15.7574i	−0.579644	−	0.579644i	−0.934805	+	0.355161i	$0.884426\pi$
$740$	−19.1421	−	19.1421i	−0.703679	−	0.703679i
$741$	0.485281	+	1.17157i	0.0178273	+	0.0430388i
$742$	−8.24264	+	3.41421i	−0.302597	+	0.125340i
$743$	19.5269	−	47.1421i	0.716373	−	1.72948i	0.0329473	−	0.999457i	$-0.489511\pi$
$743$	19.5269	−	47.1421i	0.716373	−	1.72948i	0.683426	−	0.730020i	$-0.260489\pi$
$744$			37.4558i			1.37320i
$745$	12.0000	+	4.97056i	0.439646	+	0.182107i
$746$	19.7279	−	19.7279i	0.722291	−	0.722291i
$747$	21.3137			0.779828
$748$		0			0
$749$	−1.17157			−0.0428083
$750$	13.3137	−	13.3137i	0.486148	−	0.486148i
$751$	−43.9706	−	18.2132i	−1.60451	−	0.664609i	−0.612464	−	0.790498i	$-0.709822\pi$
$751$	−43.9706	−	18.2132i	−1.60451	−	0.664609i	−0.992044	+	0.125889i	$0.959822\pi$
$752$		−	15.5147i		−	0.565764i
$753$	8.48528	−	20.4853i	0.309221	−	0.746525i
$754$	−1.00000	+	0.414214i	−0.0364179	+	0.0150848i
$755$	−2.10051	−	5.07107i	−0.0764452	−	0.184555i
$756$	−36.9706	−	36.9706i	−1.34461	−	1.34461i
$757$	1.79899	+	1.79899i	0.0653854	+	0.0653854i	0.739043	−	0.673658i	$-0.235278\pi$
$757$	1.79899	+	1.79899i	0.0653854	+	0.0653854i	−0.673658	+	0.739043i	$0.735278\pi$
$758$	2.41421	+	5.82843i	0.0876882	+	0.211698i
$759$	−12.4853	+	5.17157i	−0.453187	+	0.187716i
$760$	−1.07107	+	2.58579i	−0.0388517	+	0.0937963i
$761$			37.6985i			1.36657i	0.730152	+	0.683285i	$0.239449\pi$
$761$			37.6985i			1.36657i	−0.730152	+	0.683285i	$0.760551\pi$
$762$	−12.8284	−	5.31371i	−0.464725	−	0.192495i
$763$	28.7279	−	28.7279i	1.04002	−	1.04002i
$764$	−76.5685			−2.77015
$765$		0			0
$766$	54.2843			1.96137
$767$	6.00000	−	6.00000i	0.216647	−	0.216647i
$768$	29.9706	+	12.4142i	1.08147	+	0.447959i
$769$		−	12.7279i		−	0.458981i	−0.973311	−	0.229490i	$-0.926294\pi$
$769$		−	12.7279i		−	0.458981i	0.973311	−	0.229490i	$-0.0737059\pi$
$770$	4.82843	−	11.6569i	0.174004	−	0.420084i
$771$	−6.14214	+	2.54416i	−0.221204	+	0.0916255i
$772$	3.36396	+	8.12132i	0.121072	+	0.292293i
$773$	0.585786	+	0.585786i	0.0210693	+	0.0210693i	0.717563	−	0.696494i	$-0.245258\pi$
$773$	0.585786	+	0.585786i	0.0210693	+	0.0210693i	−0.696494	+	0.717563i	$0.745258\pi$
$774$	−2.58579	−	2.58579i	−0.0929442	−	0.0929442i
$775$	13.2426	+	31.9706i	0.475690	+	1.14842i
$776$	−42.0919	+	17.4350i	−1.51101	+	0.625881i
$777$	10.0000	−	24.1421i	0.358748	−	0.866094i
$778$		−	29.3137i		−	1.05095i
$779$	−0.928932	−	0.384776i	−0.0332824	−	0.0137860i
$780$	3.17157	−	3.17157i	0.113561	−	0.113561i
$781$	14.1421			0.506045
$782$		0			0
$783$	−1.65685			−0.0592111
$784$	−0.363961	+	0.363961i	−0.0129986	+	0.0129986i
$785$	−6.82843	−	2.82843i	−0.243717	−	0.100951i
$786$		−	39.7990i		−	1.41958i
$787$	−7.87006	+	19.0000i	−0.280537	+	0.677277i	−0.999848	−	0.0174112i	$-0.994458\pi$
$787$	−7.87006	+	19.0000i	−0.280537	+	0.677277i	0.719311	+	0.694688i	$0.244458\pi$
$788$	−16.4350	+	6.80761i	−0.585474	+	0.242511i
$789$	−4.34315	−	10.4853i	−0.154620	−	0.373286i
$790$	−6.24264	−	6.24264i	−0.222103	−	0.222103i
$791$	24.3848	+	24.3848i	0.867023	+	0.867023i
$792$	8.07107	+	19.4853i	0.286793	+	0.692379i
$793$	5.00000	−	2.07107i	0.177555	−	0.0735458i
$794$	−16.4350	+	39.6777i	−0.583257	+	1.40811i
$795$		−	1.17157i		−	0.0415514i
$796$	−40.7990	−	16.8995i	−1.44608	−	0.598987i
$797$	17.8284	−	17.8284i	0.631515	−	0.631515i	−0.316933	−	0.948448i	$-0.602653\pi$
$797$	17.8284	−	17.8284i	0.631515	−	0.631515i	0.948448	+	0.316933i	$0.102653\pi$
$798$	−5.65685			−0.200250
$799$		0			0
$800$	7.00000			0.247487
$801$	−8.51472	+	8.51472i	−0.300853	+	0.300853i
$802$	−1.29289	−	0.535534i	−0.0456536	−	0.0189104i
$803$			33.7990i			1.19274i
$804$	−1.85786	+	4.48528i	−0.0655218	+	0.158184i
$805$	8.82843	−	3.65685i	0.311161	−	0.128887i
$806$	10.2426	+	24.7279i	0.360782	+	0.871004i
$807$	20.2426	+	20.2426i	0.712575	+	0.712575i
$808$	33.0416	+	33.0416i	1.16240	+	1.16240i
$809$	−13.5061	−	32.6066i	−0.474849	−	1.14639i	−0.961995	−	0.273067i	$-0.911962\pi$
$809$	−13.5061	−	32.6066i	−0.474849	−	1.14639i	0.487146	−	0.873321i	$-0.338038\pi$
$810$	0.292893	−	0.121320i	0.0102912	−	0.00426276i
$811$	−21.1005	+	50.9411i	−0.740939	+	1.78878i	−0.138919	+	0.990304i	$0.544363\pi$
$811$	−21.1005	+	50.9411i	−0.740939	+	1.78878i	−0.602020	+	0.798481i	$0.705637\pi$
$812$		−	3.17157i		−	0.111300i
$813$	−22.1421	−	9.17157i	−0.776559	−	0.321661i
$814$	−41.2132	+	41.2132i	−1.44452	+	1.44452i
$815$	6.48528			0.227169
$816$		0			0
$817$	−0.686292			−0.0240103
$818$	−5.65685	+	5.65685i	−0.197787	+	0.197787i
$819$	−6.24264	−	2.58579i	−0.218136	−	0.0903547i
$820$			3.55635i			0.124193i
$821$	14.7071	−	35.5061i	0.513282	−	1.23917i	−0.428682	−	0.903456i	$-0.641022\pi$
$821$	14.7071	−	35.5061i	0.513282	−	1.23917i	0.941963	−	0.335716i	$-0.108978\pi$
$822$	40.3848	−	16.7279i	1.40858	−	0.583453i
$823$	3.72792	+	9.00000i	0.129947	+	0.313720i	0.975440	−	0.220267i	$-0.0706929\pi$
$823$	3.72792	+	9.00000i	0.129947	+	0.313720i	−0.845492	+	0.533987i	$0.820693\pi$
$824$	−38.9706	−	38.9706i	−1.35760	−	1.35760i
$825$	−8.82843	−	8.82843i	−0.307366	−	0.307366i
$826$	14.4853	+	34.9706i	0.504007	+	1.21678i
$827$	43.2843	−	17.9289i	1.50514	−	0.623450i	0.530593	−	0.847627i	$-0.321969\pi$
$827$	43.2843	−	17.9289i	1.50514	−	0.623450i	0.974549	+	0.224177i	$0.0719693\pi$
$828$	−12.7990	+	30.8995i	−0.444796	+	1.07383i
$829$			53.9411i			1.87345i	0.350062	+	0.936726i	$0.386160\pi$
$829$			53.9411i			1.87345i	−0.350062	+	0.936726i	$0.613840\pi$
$830$	−19.8995	−	8.24264i	−0.690722	−	0.286106i
$831$	15.2721	−	15.2721i	0.529783	−	0.529783i
$832$	13.8995			0.481878
$833$		0			0
$834$	−55.7990			−1.93216
$835$	1.07107	−	1.07107i	0.0370658	−	0.0370658i
$836$	7.65685	+	3.17157i	0.264818	+	0.109691i
$837$			40.9706i			1.41615i
$838$	12.3137	−	29.7279i	0.425370	−	1.02693i
$839$	15.4853	−	6.41421i	0.534611	−	0.221443i	−0.0990102	−	0.995086i	$-0.531568\pi$
$839$	15.4853	−	6.41421i	0.534611	−	0.221443i	0.633622	+	0.773643i	$0.281568\pi$
$840$	3.65685	+	8.82843i	0.126173	+	0.304610i
$841$	20.4350	+	20.4350i	0.704656	+	0.704656i
$842$	24.8995	+	24.8995i	0.858093	+	0.858093i
$843$	−0.786797	−	1.89949i	−0.0270987	−	0.0654221i
$844$	−75.5269	+	31.2843i	−2.59974	+	1.07685i
$845$	−3.22183	+	7.77817i	−0.110834	+	0.267577i
$846$		−	22.8284i		−	0.784857i
$847$	10.0711	+	4.17157i	0.346046	+	0.143337i
$848$	−3.00000	+	3.00000i	−0.103020	+	0.103020i
$849$	−20.2010			−0.693297
$850$		0			0
$851$	−44.1421			−1.51317
$852$	−15.8579	+	15.8579i	−0.543281	+	0.543281i
$853$	17.7071	+	7.33452i	0.606280	+	0.251129i	0.664637	−	0.747166i	$-0.268586\pi$
$853$	17.7071	+	7.33452i	0.606280	+	0.251129i	−0.0583572	+	0.998296i	$0.518586\pi$
$854$			24.1421i			0.826127i
$855$	−0.443651	+	1.07107i	−0.0151725	+	0.0366297i
$856$	−1.82843	+	0.757359i	−0.0624944	+	0.0258860i
$857$	−3.53553	−	8.53553i	−0.120772	−	0.291568i	0.851919	−	0.523673i	$-0.175439\pi$
$857$	−3.53553	−	8.53553i	−0.120772	−	0.291568i	−0.972691	+	0.232105i	$0.925439\pi$
$858$	−6.82843	−	6.82843i	−0.233119	−	0.233119i
$859$	−24.7279	−	24.7279i	−0.843706	−	0.843706i	0.145633	−	0.989339i	$-0.453478\pi$
$859$	−24.7279	−	24.7279i	−0.843706	−	0.843706i	−0.989339	+	0.145633i	$0.953478\pi$
$860$	0.928932	+	2.24264i	0.0316763	+	0.0764734i
$861$	−3.17157	+	1.31371i	−0.108087	+	0.0447711i
$862$	−6.75736	+	16.3137i	−0.230157	+	0.555647i
$863$		−	10.6274i		−	0.361761i	−0.983505	−	0.180881i	$-0.942105\pi$
$863$		−	10.6274i		−	0.361761i	0.983505	−	0.180881i	$-0.0578948\pi$
$864$	7.65685	+	3.17157i	0.260491	+	0.107899i
$865$	1.58579	−	1.58579i	0.0539184	−	0.0539184i
$866$	−50.2843			−1.70873
$867$		0			0
$868$	−78.4264			−2.66197
$869$	−8.82843	+	8.82843i	−0.299484	+	0.299484i
$870$	0.585786	+	0.242641i	0.0198600	+	0.00822629i
$871$			1.65685i			0.0561404i
$872$	26.2635	−	63.4056i	0.889393	−	2.14718i
$873$	−17.4350	+	7.22183i	−0.590086	+	0.244422i
$874$	3.65685	+	8.82843i	0.123695	+	0.298626i
$875$	13.3137	+	13.3137i	0.450085	+	0.450085i
$876$	−37.8995	−	37.8995i	−1.28051	−	1.28051i
$877$	19.2218	+	46.4056i	0.649075	+	1.56701i	0.814105	+	0.580717i	$0.197228\pi$
$877$	19.2218	+	46.4056i	0.649075	+	1.56701i	−0.165031	+	0.986288i	$0.552772\pi$
$878$	23.7279	−	9.82843i	0.800779	−	0.331693i
$879$	5.11270	−	12.3431i	0.172447	−	0.416324i
$880$		−	6.00000i		−	0.202260i
$881$	−31.0919	−	12.8787i	−1.04751	−	0.433894i	−0.208509	−	0.978020i	$-0.566861\pi$
$881$	−31.0919	−	12.8787i	−1.04751	−	0.433894i	−0.839003	+	0.544127i	$0.816861\pi$
$882$	−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	$0.457022\pi$
$884$		0			0
$885$	−4.97056			−0.167084
$886$	−40.6274	+	40.6274i	−1.36490	+	1.36490i
$887$	−40.6985	−	16.8579i	−1.36652	−	0.566032i	−0.425678	−	0.904875i	$-0.639965\pi$
$887$	−40.6985	−	16.8579i	−1.36652	−	0.566032i	−0.940843	+	0.338843i	$0.889965\pi$
$888$		−	44.1421i		−	1.48131i
$889$	5.31371	−	12.8284i	0.178216	−	0.430252i
$890$	11.2426	−	4.65685i	0.376854	−	0.156098i
$891$	−0.171573	−	0.414214i	−0.00574791	−	0.0138767i
$892$	13.0711	+	13.0711i	0.437652	+	0.437652i
$893$	−3.02944	−	3.02944i	−0.101376	−	0.101376i
$894$	16.9706	+	40.9706i	0.567581	+	1.37026i
$895$	−4.24264	+	1.75736i	−0.141816	+	0.0587420i
$896$	−20.5563	+	49.6274i	−0.686739	+	1.65794i
$897$		−	7.31371i		−	0.244198i
$898$	27.0208	+	11.1924i	0.901696	+	0.373495i
$899$	−1.75736	+	1.75736i	−0.0586112	+	0.0586112i
$900$	−30.8995			−1.02998
$901$		0			0
$902$	7.65685			0.254945
$903$	−1.65685	+	1.65685i	−0.0551367	+	0.0551367i
$904$	53.8198	+	22.2929i	1.79002	+	0.741451i
$905$			8.92893i			0.296808i
$906$	7.17157	−	17.3137i	0.238260	−	0.575209i
$907$	−12.4142	+	5.14214i	−0.412207	+	0.170742i	−0.579143	−	0.815226i	$-0.696613\pi$
$907$	−12.4142	+	5.14214i	−0.412207	+	0.170742i	0.166936	+	0.985968i	$0.446613\pi$
$908$	25.4853	+	61.5269i	0.845759	+	2.04184i
$909$	13.6863	+	13.6863i	0.453946	+	0.453946i
$910$	4.82843	+	4.82843i	0.160061	+	0.160061i
$911$	2.17157	+	5.24264i	0.0719474	+	0.173696i	0.955762	−	0.294141i	$-0.0950334\pi$
$911$	2.17157	+	5.24264i	0.0719474	+	0.173696i	−0.883815	+	0.467837i	$0.845033\pi$
$912$	−2.48528	+	1.02944i	−0.0822959	+	0.0340881i
$913$	−11.6569	+	28.1421i	−0.385786	+	0.931369i
$914$			31.7990i			1.05182i
$915$	−2.92893	−	1.21320i	−0.0968275	−	0.0401073i
$916$	46.4853	−	46.4853i	1.53592	−	1.53592i
$917$	39.7990			1.31428
$918$		0			0
$919$	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
$921$	26.1421	+	10.8284i	0.861413	+	0.356809i
$922$			58.0416i			1.91150i
$923$	−2.92893	+	7.07107i	−0.0964070	+	0.232747i
$924$	26.1421	−	10.8284i	0.860013	−	0.356229i
$925$	−15.6066	−	37.6777i	−0.513142	−	1.23883i
$926$	−24.9706	−	24.9706i	−0.820584	−	0.820584i
$927$	−16.1421	−	16.1421i	−0.530177	−	0.530177i
$928$	0.192388	+	0.464466i	0.00631545	+	0.0152468i
$929$	−16.0208	+	6.63604i	−0.525626	+	0.217721i	−0.629686	−	0.776850i	$-0.716817\pi$
$929$	−16.0208	+	6.63604i	−0.525626	+	0.217721i	0.104060	+	0.994571i	$0.466817\pi$
$930$	6.00000	−	14.4853i	0.196748	−	0.474991i
$931$			0.142136i			0.00465831i
$932$	−31.0919	−	12.8787i	−1.01845	−	0.421855i
$933$	−19.6569	+	19.6569i	−0.643537	+	0.643537i
$934$	−78.7696			−2.57742
$935$		0			0
$936$	−11.4142			−0.373085
$937$	−19.4853	+	19.4853i	−0.636556	+	0.636556i	−0.949704	−	0.313148i	$-0.898616\pi$
$937$	−19.4853	+	19.4853i	−0.636556	+	0.636556i	0.313148	+	0.949704i	$0.398616\pi$
$938$	−6.82843	−	2.82843i	−0.222956	−	0.0923514i
$939$			10.6863i			0.348734i
$940$	−5.79899	+	14.0000i	−0.189142	+	0.456630i
$941$	36.8492	−	15.2635i	1.20125	−	0.497574i	0.309848	−	0.950786i	$-0.399722\pi$
$941$	36.8492	−	15.2635i	1.20125	−	0.497574i	0.891403	+	0.453212i	$0.149722\pi$
$942$	−9.65685	−	23.3137i	−0.314637	−	0.759602i
$943$	4.10051	+	4.10051i	0.133531	+	0.133531i
$944$	12.7279	+	12.7279i	0.414259	+	0.414259i
$945$	4.00000	+	9.65685i	0.130120	+	0.314137i
$946$	4.82843	−	2.00000i	0.156986	−	0.0650256i
$947$	11.7279	−	28.3137i	0.381106	−	0.920072i	−0.610646	−	0.791904i	$-0.709090\pi$
$947$	11.7279	−	28.3137i	0.381106	−	0.920072i	0.991752	−	0.128168i	$-0.0409098\pi$
$948$		−	19.7990i		−	0.643041i
$949$	−16.8995	−	7.00000i	−0.548581	−	0.227230i
$950$	−6.24264	+	6.24264i	−0.202538	+	0.202538i
$951$	20.8284			0.675408
$952$		0			0
$953$	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
$955$	14.1421	+	5.85786i	0.457629	+	0.189556i
$956$		−	56.7696i		−	1.83606i
$957$	0.343146	−	0.828427i	0.0110923	−	0.0267792i
$958$	−11.4853	+	4.75736i	−0.371073	+	0.153703i
$959$	16.7279	+	40.3848i	0.540173	+	1.30409i
$960$	−5.75736	−	5.75736i	−0.185818	−	0.185818i
$961$	21.5355	+	21.5355i	0.694695	+	0.694695i
$962$	−12.0711	−	29.1421i	−0.389187	−	0.939580i
$963$	−0.757359	+	0.313708i	−0.0244056	+	0.0101091i
$964$	5.22183	−	12.6066i	0.168184	−	0.406031i
$965$		−	1.75736i		−	0.0565714i
$966$	30.1421	+	12.4853i	0.969807	+	0.401707i
$967$	30.8701	−	30.8701i	0.992714	−	0.992714i	−0.00725952	−	0.999974i	$-0.502311\pi$
$967$	30.8701	−	30.8701i	0.992714	−	0.992714i	0.999974	+	0.00725952i	$0.00231080\pi$
$968$	18.4142			0.591855
$969$		0			0
$970$	19.0711			0.612335
$971$	36.5858	−	36.5858i	1.17409	−	1.17409i	0.192869	−	0.981224i	$-0.438221\pi$
$971$	36.5858	−	36.5858i	1.17409	−	1.17409i	0.981224	−	0.192869i	$-0.0617793\pi$
$972$	−54.7990	−	22.6985i	−1.75768	−	0.728054i
$973$		−	55.7990i		−	1.78883i
$974$	−24.3137	+	58.6985i	−0.779061	+	1.88082i
$975$	6.24264	−	2.58579i	0.199925	−	0.0828114i
$976$	4.39340	+	10.6066i	0.140629	+	0.339509i
$977$	27.1421	+	27.1421i	0.868354	+	0.868354i	0.992290	−	0.123936i	$-0.0395519\pi$
$977$	27.1421	+	27.1421i	0.868354	+	0.868354i	−0.123936	+	0.992290i	$0.539552\pi$
$978$	15.6569	+	15.6569i	0.500651	+	0.500651i
$979$	−6.58579	−	15.8995i	−0.210483	−	0.508150i
$980$	0.464466	−	0.192388i	0.0148368	−	0.00614561i
$981$	10.8787	−	26.2635i	0.347330	−	0.838528i
$982$			89.5980i			2.85919i
$983$	−9.00000	−	3.72792i	−0.287055	−	0.118902i	0.234510	−	0.972114i	$-0.424652\pi$
$983$	−9.00000	−	3.72792i	−0.287055	−	0.118902i	−0.521565	+	0.853212i	$0.674652\pi$
$984$	−4.10051	+	4.10051i	−0.130719	+	0.130719i
$985$	3.55635			0.113315
$986$		0			0
$987$	−14.6274			−0.465596
$988$	−3.17157	+	3.17157i	−0.100901	+	0.100901i
$989$	3.65685	+	1.51472i	0.116281	+	0.0481653i
$990$		−	8.82843i		−	0.280586i
$991$	15.6274	−	37.7279i	0.496421	−	1.19847i	−0.454977	−	0.890503i	$-0.650352\pi$
$991$	15.6274	−	37.7279i	0.496421	−	1.19847i	0.951398	−	0.307964i	$-0.0996475\pi$
$992$	11.4853	−	4.75736i	0.364658	−	0.151046i
$993$	−9.02944	−	21.7990i	−0.286541	−	0.691770i
$994$	−24.1421	−	24.1421i	−0.765742	−	0.765742i
$995$	6.24264	+	6.24264i	0.197905	+	0.197905i
$996$	−18.4853	−	44.6274i	−0.585729	−	1.41407i
$997$	6.94975	−	2.87868i	0.220101	−	0.0911687i	−0.269908	−	0.962886i	$-0.586993\pi$
$997$	6.94975	−	2.87868i	0.220101	−	0.0911687i	0.490009	+	0.871717i	$0.336993\pi$
$998$	19.8284	−	47.8701i	0.627658	−	1.51530i
$999$		−	48.2843i		−	1.52765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.b.179.1		4
17.2	even	8	inner	289.2.d.b.155.1		4
17.3	odd	16		289.2.c.c.251.1		8
17.4	even	4		289.2.d.a.110.1		4
17.5	odd	16		289.2.c.c.38.4		8
17.6	odd	16		289.2.a.f.1.3		4
17.7	odd	16		289.2.b.b.288.2		4
17.8	even	8		17.2.d.a.15.1	yes	4
17.9	even	8		289.2.d.a.134.1		4
17.10	odd	16		289.2.b.b.288.1		4
17.11	odd	16		289.2.a.f.1.4		4
17.12	odd	16		289.2.c.c.38.3		8
17.13	even	4		17.2.d.a.8.1	✓	4
17.14	odd	16		289.2.c.c.251.2		8
17.15	even	8		289.2.d.c.155.1		4
17.16	even	2		289.2.d.c.179.1		4
51.8	odd	8		153.2.l.c.100.1		4
51.11	even	16		2601.2.a.bb.1.2		4
51.23	even	16		2601.2.a.bb.1.1		4
51.47	odd	4		153.2.l.c.127.1		4
68.11	even	16		4624.2.a.bp.1.2		4
68.23	even	16		4624.2.a.bp.1.3		4
68.47	odd	4		272.2.v.d.161.1		4
68.59	odd	8		272.2.v.d.49.1		4
85.8	odd	8		425.2.n.a.49.1		4
85.13	odd	4		425.2.n.b.399.1		4
85.42	odd	8		425.2.n.b.49.1		4
85.47	odd	4		425.2.n.a.399.1		4
85.59	even	8		425.2.m.a.151.1		4
85.64	even	4		425.2.m.a.76.1		4
85.74	odd	16		7225.2.a.u.1.2		4
85.79	odd	16		7225.2.a.u.1.1		4
119.13	odd	4		833.2.l.a.246.1		4
119.25	even	24		833.2.v.b.814.1		8
119.30	even	12		833.2.v.b.263.1		8
119.47	odd	12		833.2.v.a.263.1		8
119.59	odd	24		833.2.v.a.814.1		8
119.76	odd	8		833.2.l.a.491.1		4
119.81	even	12		833.2.v.b.569.1		8
119.93	even	24		833.2.v.b.508.1		8
119.110	odd	24		833.2.v.a.508.1		8
119.115	odd	12		833.2.v.a.569.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	17.13	even	4
17.2.d.a.15.1	yes	4	17.8	even	8
153.2.l.c.100.1		4	51.8	odd	8
153.2.l.c.127.1		4	51.47	odd	4
272.2.v.d.49.1		4	68.59	odd	8
272.2.v.d.161.1		4	68.47	odd	4
289.2.a.f.1.3		4	17.6	odd	16
289.2.a.f.1.4		4	17.11	odd	16
289.2.b.b.288.1		4	17.10	odd	16
289.2.b.b.288.2		4	17.7	odd	16
289.2.c.c.38.3		8	17.12	odd	16
289.2.c.c.38.4		8	17.5	odd	16
289.2.c.c.251.1		8	17.3	odd	16
289.2.c.c.251.2		8	17.14	odd	16
289.2.d.a.110.1		4	17.4	even	4
289.2.d.a.134.1		4	17.9	even	8
289.2.d.b.155.1		4	17.2	even	8	inner
289.2.d.b.179.1		4	1.1	even	1	trivial
289.2.d.c.155.1		4	17.15	even	8
289.2.d.c.179.1		4	17.16	even	2
425.2.m.a.76.1		4	85.64	even	4
425.2.m.a.151.1		4	85.59	even	8
425.2.n.a.49.1		4	85.8	odd	8
425.2.n.a.399.1		4	85.47	odd	4
425.2.n.b.49.1		4	85.42	odd	8
425.2.n.b.399.1		4	85.13	odd	4
833.2.l.a.246.1		4	119.13	odd	4
833.2.l.a.491.1		4	119.76	odd	8
833.2.v.a.263.1		8	119.47	odd	12
833.2.v.a.508.1		8	119.110	odd	24
833.2.v.a.569.1		8	119.115	odd	12
833.2.v.a.814.1		8	119.59	odd	24
833.2.v.b.263.1		8	119.30	even	12
833.2.v.b.508.1		8	119.93	even	24
833.2.v.b.569.1		8	119.81	even	12
833.2.v.b.814.1		8	119.25	even	24
2601.2.a.bb.1.1		4	51.23	even	16
2601.2.a.bb.1.2		4	51.11	even	16
4624.2.a.bp.1.2		4	68.11	even	16
4624.2.a.bp.1.3		4	68.23	even	16
7225.2.a.u.1.1		4	85.79	odd	16
7225.2.a.u.1.2		4	85.74	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more