LMFDB - Embedded newform 867.2.h.i.733.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.688"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-8,0,0,0,0,0,32,0,0,0,0,0,0,8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} + 296x^{10} + 1057x^{8} + 1184x^{6} + 512x^{4} - 512x^{2} + 256 $ x^16 - 8x^14 + 32x^12 + 296x^10 + 1057x^8 + 1184x^6 + 512x^4 - 512*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			733.1
Root			$-0.467712 - 1.12916i$ of defining polynomial
Character	$\chi$	$=$	867.733
Dual form			867.2.h.i.757.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86422 - 1.86422i) q^{2} +(-0.923880 + 0.382683i) q^{3} +4.95063i q^{4} +(0.850396 + 2.05304i) q^{5} +(2.43572 + 1.00891i) q^{6} +(0.885616 - 2.13807i) q^{7} +(5.50062 - 5.50062i) q^{8} +(0.707107 - 0.707107i) q^{9} +(2.24199 - 5.41264i) q^{10} +(-1.80215 - 0.746474i) q^{11} +(-1.89452 - 4.57379i) q^{12} -1.32218i q^{13} +(-5.63681 + 2.33484i) q^{14} +(-1.57133 - 1.57133i) q^{15} -10.6075 q^{16} -2.63640 q^{18} +(4.20773 + 4.20773i) q^{19} +(-10.1638 + 4.21000i) q^{20} +2.31423i q^{21} +(1.96801 + 4.75119i) q^{22} +(-4.41527 - 1.82887i) q^{23} +(-2.97692 + 7.18691i) q^{24} +(0.0437455 - 0.0437455i) q^{25} +(-2.46483 + 2.46483i) q^{26} +(-0.382683 + 0.923880i) q^{27} +(10.5848 + 4.38436i) q^{28} +(0.0661363 + 0.159667i) q^{29} +5.85860i q^{30} +(-0.410556 + 0.170058i) q^{31} +(8.77343 + 8.77343i) q^{32} +1.95063 q^{33} +5.14265 q^{35} +(3.50062 + 3.50062i) q^{36} +(4.91086 - 2.03414i) q^{37} -15.6883i q^{38} +(0.505976 + 1.22153i) q^{39} +(15.9707 + 6.61528i) q^{40} +(-1.53924 + 3.71604i) q^{41} +(4.31423 - 4.31423i) q^{42} +(5.89351 - 5.89351i) q^{43} +(3.69552 - 8.92177i) q^{44} +(2.05304 + 0.850396i) q^{45} +(4.82163 + 11.6405i) q^{46} -2.38404i q^{47} +(9.80004 - 4.05931i) q^{48} +(1.16274 + 1.16274i) q^{49} -0.163102 q^{50} +6.54562 q^{52} +(-0.514201 - 0.514201i) q^{53} +(2.43572 - 1.00891i) q^{54} -4.33468i q^{55} +(-6.88926 - 16.6321i) q^{56} +(-5.49767 - 2.27721i) q^{57} +(0.174362 - 0.420947i) q^{58} +(8.33468 - 8.33468i) q^{59} +(7.77906 - 7.77906i) q^{60} +(-3.32438 + 8.02576i) q^{61} +(1.08239 + 0.448342i) q^{62} +(-0.885616 - 2.13807i) q^{63} -11.4963i q^{64} +(2.71448 - 1.12438i) q^{65} +(-3.63640 - 3.63640i) q^{66} +14.1866 q^{67} +4.77906 q^{69} +(-9.58704 - 9.58704i) q^{70} +(5.63681 - 2.33484i) q^{71} -7.77906i q^{72} +(4.03994 + 9.75327i) q^{73} +(-12.9470 - 5.36283i) q^{74} +(-0.0236749 + 0.0571563i) q^{75} +(-20.8309 + 20.8309i) q^{76} +(-3.19202 + 3.19202i) q^{77} +(1.33396 - 3.22046i) q^{78} +(-0.645118 - 0.267217i) q^{79} +(-9.02056 - 21.7776i) q^{80} -1.00000i q^{81} +(9.79700 - 4.05805i) q^{82} +(-6.03142 - 6.03142i) q^{83} -11.4569 q^{84} -21.9736 q^{86} +(-0.122204 - 0.122204i) q^{87} +(-14.0190 + 5.80687i) q^{88} +5.40297i q^{89} +(-2.24199 - 5.41264i) q^{90} +(-2.82691 - 1.17094i) q^{91} +(9.05404 - 21.8584i) q^{92} +(0.314226 - 0.314226i) q^{93} +(-4.44438 + 4.44438i) q^{94} +(-5.06039 + 12.2169i) q^{95} +(-11.4630 - 4.74815i) q^{96} +(-1.80471 - 4.35696i) q^{97} -4.33519i q^{98} +(-1.80215 + 0.746474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 32 q^{8} + 8 q^{15} - 24 q^{16} - 8 q^{18} + 32 q^{25} + 40 q^{26} + 16 q^{32} - 24 q^{33} + 16 q^{35} + 48 q^{42} + 48 q^{43} + 32 q^{49} + 120 q^{50} - 32 q^{52} + 16 q^{53} + 56 q^{59}+ \cdots - 48 q^{94}+O(q^{100}) $ 16 * q - 8 * q^2 + 32 * q^8 + 8 * q^15 - 24 * q^16 - 8 * q^18 + 32 * q^25 + 40 * q^26 + 16 * q^32 - 24 * q^33 + 16 * q^35 + 48 * q^42 + 48 * q^43 + 32 * q^49 + 120 * q^50 - 32 * q^52 + 16 * q^53 + 56 * q^59 + 24 * q^60 - 24 * q^66 - 16 * q^67 - 24 * q^69 - 64 * q^70 - 64 * q^76 - 40 * q^77 + 16 * q^83 - 96 * q^84 - 16 * q^86 + 8 * q^87 - 16 * q^93 - 48 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.86422	−	1.86422i	−1.31820	−	1.31820i	−0.915198	−	0.403004i	$-0.867966\pi$
$2$	−1.86422	−	1.86422i	−1.31820	−	1.31820i	−0.403004	−	0.915198i	$-0.632034\pi$
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$4$			4.95063i			2.47532i
$5$	0.850396	+	2.05304i	0.380309	+	0.918146i	0.991906	+	0.126977i	$0.0405274\pi$
$5$	0.850396	+	2.05304i	0.380309	+	0.918146i	−0.611597	+	0.791169i	$0.709473\pi$
$6$	2.43572	+	1.00891i	0.994379	+	0.411885i
$7$	0.885616	−	2.13807i	0.334731	−	0.808113i	−0.663472	−	0.748201i	$-0.730918\pi$
$7$	0.885616	−	2.13807i	0.334731	−	0.808113i	0.998204	−	0.0599122i	$-0.0190821\pi$
$8$	5.50062	−	5.50062i	1.94476	−	1.94476i
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$	2.24199	−	5.41264i	0.708979	−	1.71163i
$11$	−1.80215	−	0.746474i	−0.543368	−	0.225070i	0.0940788	−	0.995565i	$-0.470009\pi$
$11$	−1.80215	−	0.746474i	−0.543368	−	0.225070i	−0.637447	+	0.770494i	$0.720009\pi$
$12$	−1.89452	−	4.57379i	−0.546902	−	1.32034i
$13$		−	1.32218i		−	0.366706i	−0.983047	−	0.183353i	$-0.941305\pi$
$13$		−	1.32218i		−	0.366706i	0.983047	−	0.183353i	$-0.0586952\pi$
$14$	−5.63681	+	2.33484i	−1.50650	+	0.624013i
$15$	−1.57133	−	1.57133i	−0.405715	−	0.405715i
$16$	−10.6075			−2.65187
$17$		0			0
$17$		0			0
$18$	−2.63640			−0.621407
$19$	4.20773	+	4.20773i	0.965320	+	0.965320i	0.999418	−	0.0340987i	$-0.0108560\pi$
$19$	4.20773	+	4.20773i	0.965320	+	0.965320i	−0.0340987	+	0.999418i	$0.510856\pi$
$20$	−10.1638	+	4.21000i	−2.27270	+	0.941384i
$21$			2.31423i			0.505006i
$22$	1.96801	+	4.75119i	0.419581	+	1.01296i
$23$	−4.41527	−	1.82887i	−0.920648	−	0.381345i	−0.128525	−	0.991706i	$-0.541024\pi$
$23$	−4.41527	−	1.82887i	−0.920648	−	0.381345i	−0.792123	+	0.610361i	$0.791024\pi$
$24$	−2.97692	+	7.18691i	−0.607661	+	1.46702i
$25$	0.0437455	−	0.0437455i	0.00874910	−	0.00874910i
$26$	−2.46483	+	2.46483i	−0.483393	+	0.483393i
$27$	−0.382683	+	0.923880i	−0.0736475	+	0.177801i
$28$	10.5848	+	4.38436i	2.00033	+	0.828566i
$29$	0.0661363	+	0.159667i	0.0122812	+	0.0296494i	0.929901	−	0.367809i	$-0.119892\pi$
$29$	0.0661363	+	0.159667i	0.0122812	+	0.0296494i	−0.917620	+	0.397459i	$0.869892\pi$
$30$			5.85860i			1.06963i
$31$	−0.410556	+	0.170058i	−0.0737381	+	0.0305433i	−0.419248	−	0.907872i	$-0.637706\pi$
$31$	−0.410556	+	0.170058i	−0.0737381	+	0.0305433i	0.345510	+	0.938415i	$0.387706\pi$
$32$	8.77343	+	8.77343i	1.55094	+	1.55094i
$33$	1.95063			0.339561
$34$		0			0
$35$	5.14265			0.869267
$36$	3.50062	+	3.50062i	0.583437	+	0.583437i
$37$	4.91086	−	2.03414i	0.807340	−	0.334411i	0.0594480	−	0.998231i	$-0.481066\pi$
$37$	4.91086	−	2.03414i	0.807340	−	0.334411i	0.747892	+	0.663820i	$0.231066\pi$
$38$		−	15.6883i		−	2.54497i
$39$	0.505976	+	1.22153i	0.0810210	+	0.195602i
$40$	15.9707	+	6.61528i	2.52519	+	1.04597i
$41$	−1.53924	+	3.71604i	−0.240388	+	0.580348i	−0.997321	−	0.0731438i	$-0.976697\pi$
$41$	−1.53924	+	3.71604i	−0.240388	+	0.580348i	0.756933	+	0.653492i	$0.226697\pi$
$42$	4.31423	−	4.31423i	0.665700	−	0.665700i
$43$	5.89351	−	5.89351i	0.898751	−	0.898751i	−0.0965746	−	0.995326i	$-0.530789\pi$
$43$	5.89351	−	5.89351i	0.898751	−	0.898751i	0.995326	+	0.0965746i	$0.0307886\pi$
$44$	3.69552	−	8.92177i	0.557120	−	1.34501i
$45$	2.05304	+	0.850396i	0.306049	+	0.126770i
$46$	4.82163	+	11.6405i	0.710911	+	1.71629i
$47$		−	2.38404i		−	0.347749i	−0.984768	−	0.173874i	$-0.944371\pi$
$47$		−	2.38404i		−	0.347749i	0.984768	−	0.173874i	$-0.0556286\pi$
$48$	9.80004	−	4.05931i	1.41451	−	0.585911i
$49$	1.16274	+	1.16274i	0.166105	+	0.166105i
$50$	−0.163102			−0.0230662
$51$		0			0
$52$	6.54562			0.907714
$53$	−0.514201	−	0.514201i	−0.0706309	−	0.0706309i	0.670909	−	0.741540i	$-0.265904\pi$
$53$	−0.514201	−	0.514201i	−0.0706309	−	0.0706309i	−0.741540	+	0.670909i	$0.765904\pi$
$54$	2.43572	−	1.00891i	0.331460	−	0.137295i
$55$		−	4.33468i		−	0.584488i
$56$	−6.88926	−	16.6321i	−0.920616	−	2.22256i
$57$	−5.49767	−	2.27721i	−0.728184	−	0.301624i
$58$	0.174362	−	0.420947i	0.0228948	−	0.0552730i
$59$	8.33468	−	8.33468i	1.08508	−	1.08508i	0.0890557	−	0.996027i	$-0.471615\pi$
$59$	8.33468	−	8.33468i	1.08508	−	1.08508i	0.996027	−	0.0890557i	$-0.0283849\pi$
$60$	7.77906	−	7.77906i	1.00427	−	1.00427i
$61$	−3.32438	+	8.02576i	−0.425643	+	1.02759i	0.555011	+	0.831843i	$0.312714\pi$
$61$	−3.32438	+	8.02576i	−0.425643	+	1.02759i	−0.980654	+	0.195750i	$0.937286\pi$
$62$	1.08239	+	0.448342i	0.137464	+	0.0569394i
$63$	−0.885616	−	2.13807i	−0.111577	−	0.269371i
$64$		−	11.4963i		−	1.43703i
$65$	2.71448	−	1.12438i	0.336690	−	0.139462i
$66$	−3.63640	−	3.63640i	−0.447611	−	0.447611i
$67$	14.1866			1.73317			0.866583	−	0.499034i	$-0.166312\pi$
$67$	14.1866			1.73317			0.866583	+	0.499034i	$0.166312\pi$
$68$		0			0
$69$	4.77906			0.575331
$70$	−9.58704	−	9.58704i	−1.14587	−	1.14587i
$71$	5.63681	−	2.33484i	0.668966	−	0.277095i	−0.0222399	−	0.999753i	$-0.507080\pi$
$71$	5.63681	−	2.33484i	0.668966	−	0.277095i	0.691206	+	0.722658i	$0.257080\pi$
$72$		−	7.77906i		−	0.916771i
$73$	4.03994	+	9.75327i	0.472839	+	1.14153i	0.962903	+	0.269848i	$0.0869734\pi$
$73$	4.03994	+	9.75327i	0.472839	+	1.14153i	−0.490064	+	0.871686i	$0.663027\pi$
$74$	−12.9470	−	5.36283i	−1.50506	−	0.623416i
$75$	−0.0236749	+	0.0571563i	−0.00273374	+	0.00659984i
$76$	−20.8309	+	20.8309i	−2.38947	+	2.38947i
$77$	−3.19202	+	3.19202i	−0.363765	+	0.363765i
$78$	1.33396	−	3.22046i	0.151041	−	0.364645i
$79$	−0.645118	−	0.267217i	−0.0725814	−	0.0300642i	0.346097	−	0.938199i	$-0.387507\pi$
$79$	−0.645118	−	0.267217i	−0.0725814	−	0.0300642i	−0.418679	+	0.908134i	$0.637507\pi$
$80$	−9.02056	−	21.7776i	−1.00853	−	2.43481i
$81$		−	1.00000i		−	0.111111i
$82$	9.79700	−	4.05805i	1.08190	−	0.448136i
$83$	−6.03142	−	6.03142i	−0.662034	−	0.662034i	0.293825	−	0.955859i	$-0.405072\pi$
$83$	−6.03142	−	6.03142i	−0.662034	−	0.662034i	−0.955859	+	0.293825i	$0.905072\pi$
$84$	−11.4569			−1.25005
$85$		0			0
$86$	−21.9736			−2.36947
$87$	−0.122204	−	0.122204i	−0.0131016	−	0.0131016i
$88$	−14.0190	+	5.80687i	−1.49443	+	0.619014i
$89$			5.40297i			0.572713i	0.958123	+	0.286357i	$0.0924442\pi$
$89$			5.40297i			0.572713i	−0.958123	+	0.286357i	$0.907556\pi$
$90$	−2.24199	−	5.41264i	−0.236326	−	0.570542i
$91$	−2.82691	−	1.17094i	−0.296340	−	0.122748i
$92$	9.05404	−	21.8584i	0.943949	−	2.27889i
$93$	0.314226	−	0.314226i	0.0325837	−	0.0325837i
$94$	−4.44438	+	4.44438i	−0.458403	+	0.458403i
$95$	−5.06039	+	12.2169i	−0.519185	+	1.25342i
$96$	−11.4630	−	4.74815i	−1.16994	−	0.484606i
$97$	−1.80471	−	4.35696i	−0.183241	−	0.442383i	0.805390	−	0.592745i	$-0.201956\pi$
$97$	−1.80471	−	4.35696i	−0.183241	−	0.442383i	−0.988631	+	0.150363i	$0.951956\pi$
$98$		−	4.33519i		−	0.437921i
$99$	−1.80215	+	0.746474i	−0.181123	+	0.0750235i
$100$	0.216568	+	0.216568i	0.0216568	+	0.0216568i
$101$	7.11123			0.707594			0.353797	−	0.935322i	$-0.384890\pi$
$101$	7.11123			0.707594			0.353797	+	0.935322i	$0.384890\pi$
$102$		0			0
$103$	−9.22344			−0.908813			−0.454406	−	0.890795i	$-0.650149\pi$
$103$	−9.22344			−0.908813			−0.454406	+	0.890795i	$0.650149\pi$
$104$	−7.27281	−	7.27281i	−0.713158	−	0.713158i
$105$	−4.75119	+	1.96801i	−0.463669	+	0.192058i
$106$			1.91717i			0.186212i
$107$	1.98327	+	4.78804i	0.191730	+	0.462878i	0.990286	−	0.139043i	$-0.0444025\pi$
$107$	1.98327	+	4.78804i	0.191730	+	0.462878i	−0.798556	+	0.601920i	$0.794402\pi$
$108$	−4.57379	−	1.89452i	−0.440113	−	0.182301i
$109$	7.64423	−	18.4548i	0.732185	−	1.76765i	0.0970083	−	0.995284i	$-0.469073\pi$
$109$	7.64423	−	18.4548i	0.732185	−	1.76765i	0.635177	−	0.772367i	$-0.280927\pi$
$110$	−8.08079	+	8.08079i	−0.770473	+	0.770473i
$111$	−3.75861	+	3.75861i	−0.356751	+	0.356751i
$112$	−9.39416	+	22.6795i	−0.887665	+	2.14301i
$113$	16.1098	+	6.67291i	1.51549	+	0.627735i	0.976681	−	0.214696i	$-0.0688760\pi$
$113$	16.1098	+	6.67291i	1.51549	+	0.627735i	0.538805	+	0.842431i	$0.318876\pi$
$114$	6.00364	+	14.4941i	0.562293	+	1.35749i
$115$		−	10.6200i		−	0.990318i
$116$	−0.790453	+	0.327416i	−0.0733917	+	0.0303998i
$117$	−0.934922	−	0.934922i	−0.0864335	−	0.0864335i
$118$	−31.0753			−2.86072
$119$		0			0
$120$	−17.2866			−1.57804
$121$	−5.08766	−	5.08766i	−0.462515	−	0.462515i
$122$	21.1592	−	8.76441i	1.91566	−	0.793493i
$123$		−	4.02222i		−	0.362671i
$124$	−0.841894	−	2.03251i	−0.0756043	−	0.182525i
$125$	10.3922	+	4.30459i	0.929506	+	0.385014i
$126$	−2.33484	+	5.63681i	−0.208004	+	0.502167i
$127$	6.96634	−	6.96634i	0.618163	−	0.618163i	−0.326897	−	0.945060i	$-0.606003\pi$
$127$	6.96634	−	6.96634i	0.618163	−	0.618163i	0.945060	+	0.326897i	$0.106003\pi$
$128$	−3.88467	+	3.88467i	−0.343359	+	0.343359i
$129$	−3.18954	+	7.70024i	−0.280824	+	0.677968i
$130$	−7.15647	−	2.96431i	−0.627664	−	0.259987i
$131$	−2.91126	−	7.02840i	−0.254358	−	0.614074i	0.744189	−	0.667969i	$-0.232836\pi$
$131$	−2.91126	−	7.02840i	−0.254358	−	0.614074i	−0.998547	+	0.0538952i	$0.982836\pi$
$132$			9.65685i			0.840521i
$133$	12.7228	−	5.26997i	1.10321	−	0.456965i
$134$	−26.4469	−	26.4469i	−2.28466	−	2.28466i
$135$	−2.22219			−0.191256
$136$		0			0
$137$	22.0723			1.88577			0.942883	−	0.333125i	$-0.108103\pi$
$137$	22.0723			1.88577			0.942883	+	0.333125i	$0.108103\pi$
$138$	−8.90921	−	8.90921i	−0.758403	−	0.758403i
$139$	3.31168	−	1.37174i	0.280893	−	0.116350i	−0.237789	−	0.971317i	$-0.576423\pi$
$139$	3.31168	−	1.37174i	0.280893	−	0.116350i	0.518682	+	0.854967i	$0.326423\pi$
$140$			25.4594i			2.15171i
$141$	0.912334	+	2.20257i	0.0768324	+	0.185490i
$142$	−14.8609	−	6.15559i	−1.24710	−	0.516566i
$143$	−0.986972	+	2.38276i	−0.0825348	+	0.199257i
$144$	−7.50062	+	7.50062i	−0.625052	+	0.625052i
$145$	−0.271560	+	0.271560i	−0.0225519	+	0.0225519i
$146$	10.6509	−	25.7136i	0.881476	−	2.12807i
$147$	−1.51919	−	0.629268i	−0.125301	−	0.0519012i
$148$	10.0703	+	24.3119i	0.827773	+	1.99842i
$149$			11.7711i			0.964327i	0.876081	+	0.482163i	$0.160149\pi$
$149$			11.7711i			0.964327i	−0.876081	+	0.482163i	$0.839851\pi$
$150$	0.150687	−	0.0624166i	0.0123035	−	0.00509630i
$151$	11.3871	+	11.3871i	0.926666	+	0.926666i	0.997489	−	0.0708230i	$-0.0225626\pi$
$151$	11.3871	+	11.3871i	0.926666	+	0.926666i	−0.0708230	+	0.997489i	$0.522563\pi$
$152$	46.2903			3.75464
$153$		0			0
$154$	11.9013			0.959031
$155$	−0.698270	−	0.698270i	−0.0560864	−	0.0560864i
$156$	−6.04736	+	2.50490i	−0.484177	+	0.200553i
$157$		−	6.45535i		−	0.515193i	−0.966253	−	0.257597i	$-0.917069\pi$
$157$		−	6.45535i		−	0.515193i	0.966253	−	0.257597i	$-0.0829306\pi$
$158$	0.704491	+	1.70079i	0.0560463	+	0.135308i
$159$	0.671836	+	0.278284i	0.0532801	+	0.0220693i
$160$	−10.5513	+	25.4731i	−0.834153	+	2.01382i
$161$	−7.82047	+	7.82047i	−0.616340	+	0.616340i
$162$	−1.86422	+	1.86422i	−0.146467	+	0.146467i
$163$	6.40313	−	15.4585i	0.501532	−	1.21081i	−0.447117	−	0.894475i	$-0.647549\pi$
$163$	6.40313	−	15.4585i	0.501532	−	1.21081i	0.948649	−	0.316330i	$-0.102451\pi$
$164$	−18.3968	−	7.62019i	−1.43655	−	0.595037i
$165$	1.65881	+	4.00472i	0.129138	+	0.311767i
$166$			22.4878i			1.74539i
$167$	−1.48281	+	0.614202i	−0.114744	+	0.0475284i	−0.439317	−	0.898332i	$-0.644779\pi$
$167$	−1.48281	+	0.614202i	−0.114744	+	0.0475284i	0.324573	+	0.945861i	$0.394779\pi$
$168$	12.7297	+	12.7297i	0.982117	+	0.982117i
$169$	11.2518			0.865526
$170$		0			0
$171$	5.95063			0.455056
$172$	29.1766	+	29.1766i	2.22469	+	2.22469i
$173$	−15.8316	+	6.55764i	−1.20365	+	0.498568i	−0.892177	−	0.451686i	$-0.850823\pi$
$173$	−15.8316	+	6.55764i	−1.20365	+	0.498568i	−0.311474	+	0.950255i	$0.600823\pi$
$174$			0.455630i			0.0345412i
$175$	−0.0547891	−	0.132273i	−0.00414166	−	0.00999886i
$176$	19.1163	+	7.91821i	1.44094	+	0.596858i
$177$	−4.51069	+	10.8898i	−0.339045	+	0.818526i
$178$	10.0723	−	10.0723i	0.754952	−	0.754952i
$179$	7.83144	−	7.83144i	0.585350	−	0.585350i	−0.351019	−	0.936368i	$-0.614165\pi$
$179$	7.83144	−	7.83144i	0.585350	−	0.585350i	0.936368	+	0.351019i	$0.114165\pi$
$180$	−4.21000	+	10.1638i	−0.313795	+	0.757567i
$181$	−18.2000	−	7.53868i	−1.35279	−	0.560346i	−0.415725	−	0.909490i	$-0.636472\pi$
$181$	−18.2000	−	7.53868i	−1.35279	−	0.560346i	−0.937069	+	0.349145i	$0.886472\pi$
$182$	3.08708	+	7.45287i	0.228830	+	0.552443i
$183$		−	8.68702i		−	0.642163i
$184$	−34.3467	+	14.2269i	−2.53207	+	1.04882i
$185$	8.35235	+	8.35235i	0.614077	+	0.614077i
$186$	−1.17157			−0.0859039
$187$		0			0
$188$	11.8025			0.860788
$189$	1.63640	+	1.63640i	0.119031	+	0.119031i
$190$	32.2086	−	13.3412i	2.33666	−	0.967875i
$191$			1.60953i			0.116461i	0.998303	+	0.0582307i	$0.0185459\pi$
$191$			1.60953i			0.116461i	−0.998303	+	0.0582307i	$0.981454\pi$
$192$	4.39942	+	10.6212i	0.317501	+	0.766516i
$193$	4.13347	+	1.71214i	0.297534	+	0.123242i	0.526456	−	0.850202i	$-0.323520\pi$
$193$	4.13347	+	1.71214i	0.297534	+	0.123242i	−0.228923	+	0.973445i	$0.573520\pi$
$194$	−4.75796	+	11.4867i	−0.341601	+	0.824698i
$195$	−2.07757	+	2.07757i	−0.148778	+	0.148778i
$196$	−5.75628	+	5.75628i	−0.411163	+	0.411163i
$197$	−2.82947	+	6.83095i	−0.201591	+	0.486685i	−0.992052	−	0.125828i	$-0.959841\pi$
$197$	−2.82947	+	6.83095i	−0.201591	+	0.486685i	0.790461	+	0.612513i	$0.209841\pi$
$198$	4.75119	+	1.96801i	0.337653	+	0.139860i
$199$	−2.75401	−	6.64876i	−0.195226	−	0.471318i	0.795705	−	0.605684i	$-0.207100\pi$
$199$	−2.75401	−	6.64876i	−0.195226	−	0.471318i	−0.990932	+	0.134366i	$0.957100\pi$
$200$		−	0.481255i		−	0.0340299i
$201$	−13.1067	+	5.42896i	−0.924474	+	0.382930i
$202$	−13.2569	−	13.2569i	−0.932753	−	0.932753i
$203$	0.399950			0.0280710
$204$		0			0
$205$	−8.93813			−0.624266
$206$	17.1945	+	17.1945i	1.19800	+	1.19800i
$207$	−4.41527	+	1.82887i	−0.306883	+	0.127115i
$208$			14.0250i			0.972458i
$209$	−4.44199	−	10.7239i	−0.307259	−	0.741789i
$210$	12.5261	+	5.18847i	0.864381	+	0.358038i
$211$	−5.13503	+	12.3971i	−0.353510	+	0.853449i	0.642671	+	0.766142i	$0.277826\pi$
$211$	−5.13503	+	12.3971i	−0.353510	+	0.853449i	−0.996181	+	0.0873068i	$0.972174\pi$
$212$	2.54562	−	2.54562i	0.174834	−	0.174834i
$213$	−4.31423	+	4.31423i	−0.295606	+	0.295606i
$214$	5.22871	−	12.6232i	0.357427	−	0.862906i
$215$	17.1114	+	7.08777i	1.16699	+	0.483382i
$216$	2.97692	+	7.18691i	0.202554	+	0.489007i
$217$			1.02840i			0.0698125i
$218$	−48.6544	+	20.1533i	−3.29529	+	1.36495i
$219$	−7.46483	−	7.46483i	−0.504427	−	0.504427i
$220$	21.4594			1.44679
$221$		0			0
$222$	14.0137			0.940541
$223$	15.0362	+	15.0362i	1.00690	+	1.00690i	0.999976	+	0.00691960i	$0.00220259\pi$
$223$	15.0362	+	15.0362i	1.00690	+	1.00690i	0.00691960	+	0.999976i	$0.497797\pi$
$224$	26.5281	−	10.9883i	1.77248	−	0.734186i
$225$		−	0.0618655i		−	0.00412437i
$226$	−17.5925	−	42.4721i	−1.17024	−	2.82520i
$227$	4.57694	+	1.89583i	0.303782	+	0.125831i	0.529367	−	0.848393i	$-0.322429\pi$
$227$	4.57694	+	1.89583i	0.303782	+	0.125831i	−0.225585	+	0.974223i	$0.572429\pi$
$228$	11.2736	−	27.2169i	0.746613	−	1.80248i
$229$	−1.29996	+	1.29996i	−0.0859039	+	0.0859039i	−0.748753	−	0.662849i	$-0.769347\pi$
$229$	−1.29996	+	1.29996i	−0.0859039	+	0.0859039i	0.662849	+	0.748753i	$0.269347\pi$
$230$	−19.7980	+	19.7980i	−1.30544	+	1.30544i
$231$	1.72751	−	4.17058i	0.113662	−	0.274404i
$232$	1.24206	+	0.514478i	0.0815452	+	0.0337771i
$233$	0.572112	+	1.38120i	0.0374803	+	0.0904855i	0.941511	−	0.336982i	$-0.109406\pi$
$233$	0.572112	+	1.38120i	0.0374803	+	0.0904855i	−0.904031	+	0.427467i	$0.859406\pi$
$234$			3.48580i			0.227874i
$235$	4.89453	−	2.02738i	0.319284	−	0.132252i
$236$	41.2619	+	41.2619i	2.68592	+	2.68592i
$237$	0.698270			0.0453575
$238$		0			0
$239$	−10.0250			−0.648463			−0.324231	−	0.945978i	$-0.605106\pi$
$239$	−10.0250			−0.648463			−0.324231	+	0.945978i	$0.605106\pi$
$240$	16.6678	+	16.6678i	1.07590	+	1.07590i
$241$	−10.6389	+	4.40677i	−0.685311	+	0.283865i	−0.698045	−	0.716054i	$-0.745947\pi$
$241$	−10.6389	+	4.40677i	−0.685311	+	0.283865i	0.0127340	+	0.999919i	$0.495947\pi$
$242$			18.9690i			1.21938i
$243$	0.382683	+	0.923880i	0.0245492	+	0.0592669i
$244$	−39.7326	−	16.4578i	−2.54362	−	1.05360i
$245$	−1.39835	+	3.37593i	−0.0893376	+	0.215680i
$246$	−7.49830	+	7.49830i	−0.478074	+	0.478074i
$247$	5.56337	−	5.56337i	0.353989	−	0.353989i
$248$	−1.32289	+	3.19374i	−0.0840036	+	0.202803i
$249$	7.88043	+	3.26418i	0.499402	+	0.206859i
$250$	−11.3486	−	27.3980i	−0.717751	−	1.73280i
$251$			0.940179i			0.0593436i	0.999560	+	0.0296718i	$0.00944621\pi$
$251$			0.940179i			0.0593436i	−0.999560	+	0.0296718i	$0.990554\pi$
$252$	10.5848	−	4.38436i	0.666778	−	0.276189i
$253$	6.59178	+	6.59178i	0.414421	+	0.414421i
$254$	−25.9736			−1.62973
$255$		0			0
$256$	−8.50875			−0.531797
$257$	1.52392	+	1.52392i	0.0950596	+	0.0950596i	0.753037	−	0.657978i	$-0.228588\pi$
$257$	1.52392	+	1.52392i	0.0950596	+	0.0950596i	−0.657978	+	0.753037i	$0.728588\pi$
$258$	20.3009	−	8.40892i	1.26388	−	0.523517i
$259$		−	12.3012i		−	0.764360i
$260$	5.56637	+	13.4384i	0.345211	+	0.833414i
$261$	0.159667	+	0.0661363i	0.00988314	+	0.00409373i
$262$	−7.67526	+	18.5297i	−0.474179	+	1.14477i
$263$	9.29326	−	9.29326i	0.573047	−	0.573047i	−0.359932	−	0.932979i	$-0.617200\pi$
$263$	9.29326	−	9.29326i	0.573047	−	0.573047i	0.932979	+	0.359932i	$0.117200\pi$
$264$	10.7297	−	10.7297i	0.660367	−	0.660367i
$265$	0.618399	−	1.49295i	0.0379880	−	0.0917111i
$266$	−33.5426	−	13.8938i	−2.05663	−	0.851883i
$267$	−2.06763	−	4.99169i	−0.126537	−	0.305486i
$268$			70.2325i			4.29013i
$269$	14.0193	−	5.80697i	0.854770	−	0.354057i	0.0881101	−	0.996111i	$-0.471917\pi$
$269$	14.0193	−	5.80697i	0.854770	−	0.354057i	0.766660	+	0.642053i	$0.221917\pi$
$270$	4.14265	+	4.14265i	0.252114	+	0.252114i
$271$	−11.8360			−0.718985			−0.359493	−	0.933148i	$-0.617050\pi$
$271$	−11.8360			−0.718985			−0.359493	+	0.933148i	$0.617050\pi$
$272$		0			0
$273$	3.05982			0.185189
$274$	−41.1477	−	41.1477i	−2.48582	−	2.48582i
$275$	−0.111491	+	0.0461810i	−0.00672315	+	0.00278482i
$276$			23.6594i			1.42413i
$277$	10.2951	+	24.8547i	0.618575	+	1.49337i	0.853358	+	0.521325i	$0.174562\pi$
$277$	10.2951	+	24.8547i	0.618575	+	1.49337i	−0.234783	+	0.972048i	$0.575438\pi$
$278$	−8.73093	−	3.61647i	−0.523646	−	0.216901i
$279$	−0.170058	+	0.410556i	−0.0101811	+	0.0245794i
$280$	28.2878	−	28.2878i	1.69052	−	1.69052i
$281$	−15.7217	+	15.7217i	−0.937880	+	0.937880i	−0.998180	−	0.0603001i	$-0.980794\pi$
$281$	−15.7217	+	15.7217i	−0.937880	+	0.937880i	0.0603001	+	0.998180i	$0.480794\pi$
$282$	2.40528	−	5.80687i	0.143232	−	0.345794i
$283$	−22.1340	−	9.16820i	−1.31573	−	0.544993i	−0.389179	−	0.921162i	$-0.627241\pi$
$283$	−22.1340	−	9.16820i	−1.31573	−	0.544993i	−0.926551	+	0.376169i	$0.877241\pi$
$284$	11.5589	+	27.9058i	0.685897	+	1.65590i
$285$		−	13.2234i		−	0.783289i
$286$	6.28193	−	2.60206i	0.371458	−	0.153863i
$287$	6.58197	+	6.58197i	0.388522	+	0.388522i
$288$	12.4075			0.731120
$289$		0			0
$290$	1.01250			0.0594558
$291$	3.33468	+	3.33468i	0.195482	+	0.195482i
$292$	−48.2849	+	20.0002i	−2.82566	+	1.17043i
$293$			7.44387i			0.434875i	0.976074	+	0.217438i	$0.0697699\pi$
$293$			7.44387i			0.434875i	−0.976074	+	0.217438i	$0.930230\pi$
$294$	1.65901	+	4.00520i	0.0967552	+	0.233588i
$295$	24.1992	+	10.0236i	1.40893	+	0.583598i
$296$	15.8237	−	38.2019i	0.919735	−	2.22044i
$297$	1.37930	−	1.37930i	0.0800354	−	0.0800354i
$298$	21.9439	−	21.9439i	1.27118	−	1.27118i
$299$	−2.41809	+	5.83778i	−0.139842	+	0.337608i
$300$	−0.282960	−	0.117206i	−0.0163367	−	0.00676687i
$301$	−7.38132	−	17.8201i	−0.425452	−	1.02713i
$302$		−	42.4560i		−	2.44307i
$303$	−6.56992	+	2.72135i	−0.377432	+	0.156338i
$304$	−44.6335	−	44.6335i	−2.55990	−	2.55990i
$305$	−19.3042			−1.10536
$306$		0			0
$307$	−14.2184			−0.811486			−0.405743	−	0.913987i	$-0.632987\pi$
$307$	−14.2184			−0.811486			−0.405743	+	0.913987i	$0.632987\pi$
$308$	−15.8025	−	15.8025i	−0.900432	−	0.900432i
$309$	8.52135	−	3.52966i	0.484763	−	0.200795i
$310$			2.60346i			0.147867i
$311$	−3.96519	−	9.57282i	−0.224846	−	0.542825i	0.770690	−	0.637210i	$-0.219912\pi$
$311$	−3.96519	−	9.57282i	−0.224846	−	0.542825i	−0.995536	+	0.0943849i	$0.969912\pi$
$312$	9.50238	+	3.93602i	0.537967	+	0.222833i
$313$	−6.66872	+	16.0997i	−0.376938	+	0.910009i	0.615598	+	0.788060i	$0.288914\pi$
$313$	−6.66872	+	16.0997i	−0.376938	+	0.910009i	−0.992536	+	0.121949i	$0.961086\pi$
$314$	−12.0342	+	12.0342i	−0.679129	+	0.679129i
$315$	3.63640	−	3.63640i	0.204888	−	0.204888i
$316$	1.32289	−	3.19374i	0.0744184	−	0.179662i
$317$	−13.0963	−	5.42466i	−0.735561	−	0.304679i	−0.0167260	−	0.999860i	$-0.505324\pi$
$317$	−13.0963	−	5.42466i	−0.735561	−	0.304679i	−0.718835	+	0.695181i	$0.755324\pi$
$318$	−0.733668	−	1.77123i	−0.0411421	−	0.0993258i
$319$		−	0.337113i		−	0.0188747i
$320$	23.6022	−	9.77636i	1.31940	−	0.546515i
$321$	−3.66461	−	3.66461i	−0.204539	−	0.204539i
$322$	29.1582			1.62492
$323$		0			0
$324$	4.95063			0.275035
$325$	−0.0578394	−	0.0578394i	−0.00320835	−	0.00320835i
$326$	−40.7549	+	16.8812i	−2.25721	+	0.934966i
$327$			19.9753i			1.10464i
$328$	11.9738	+	28.9073i	0.661143	+	1.59614i
$329$	−5.09724	−	2.11135i	−0.281020	−	0.116402i
$330$	4.37329	−	10.5581i	0.240742	−	0.581202i
$331$	−7.67104	+	7.67104i	−0.421638	+	0.421638i	−0.885768	−	0.464129i	$-0.846367\pi$
$331$	−7.67104	+	7.67104i	−0.421638	+	0.421638i	0.464129	+	0.885768i	$0.346367\pi$
$332$	29.8593	−	29.8593i	1.63874	−	1.63874i
$333$	2.03414	−	4.91086i	0.111470	−	0.269113i
$334$	3.90930	+	1.61928i	0.213907	+	0.0886033i
$335$	12.0642	+	29.1256i	0.659138	+	1.59130i
$336$		−	24.5481i		−	1.33921i
$337$	9.07037	−	3.75707i	0.494095	−	0.204661i	−0.121701	−	0.992567i	$-0.538835\pi$
$337$	9.07037	−	3.75707i	0.494095	−	0.204661i	0.615795	+	0.787906i	$0.288835\pi$
$338$	−20.9759	−	20.9759i	−1.14094	−	1.14094i
$339$	−17.4372			−0.947057
$340$		0			0
$341$	0.866827			0.0469413
$342$	−11.0933	−	11.0933i	−0.599856	−	0.599856i
$343$	18.4822	−	7.65558i	0.997945	−	0.413363i
$344$		−	64.8359i		−	3.49572i
$345$	4.06409	+	9.81158i	0.218803	+	0.528238i
$346$	41.7384	+	17.2886i	2.24387	+	0.929441i
$347$	9.96773	−	24.0642i	0.535096	−	1.29184i	−0.393015	−	0.919532i	$-0.628568\pi$
$347$	9.96773	−	24.0642i	0.535096	−	1.29184i	0.928111	−	0.372303i	$-0.121432\pi$
$348$	0.604986	−	0.604986i	0.0324307	−	0.0324307i
$349$	−13.1952	+	13.1952i	−0.706325	+	0.706325i	−0.965760	−	0.259436i	$-0.916463\pi$
$349$	−13.1952	+	13.1952i	−0.706325	+	0.706325i	0.259436	+	0.965760i	$0.416463\pi$
$350$	−0.144446	+	0.348724i	−0.00772097	+	0.0186401i
$351$	1.22153	+	0.505976i	0.0652007	+	0.0270070i
$352$	−9.26189	−	22.3602i	−0.493660	−	1.19180i
$353$		−	11.8339i		−	0.629857i	−0.949115	−	0.314929i	$-0.898019\pi$
$353$		−	11.8339i		−	0.629857i	0.949115	−	0.314929i	$-0.101981\pi$
$354$	28.7099	−	11.8920i	1.52591	−	0.632053i
$355$	9.58704	+	9.58704i	0.508827	+	0.508827i
$356$	−26.7481			−1.41765
$357$		0			0
$358$	−29.1991			−1.54322
$359$	−9.99796	−	9.99796i	−0.527672	−	0.527672i	0.392206	−	0.919878i	$-0.371712\pi$
$359$	−9.99796	−	9.99796i	−0.527672	−	0.527672i	−0.919878	+	0.392206i	$0.871712\pi$
$360$	15.9707	−	6.61528i	0.841730	−	0.348656i
$361$			16.4100i			0.863685i
$362$	19.8750	+	47.9825i	1.04461	+	2.52191i
$363$	6.64735	+	2.75342i	0.348895	+	0.144517i
$364$	5.79691	−	13.9950i	0.303840	−	0.733536i
$365$	−16.5883	+	16.5883i	−0.868271	+	0.868271i
$366$	−16.1945	+	16.1945i	−0.846501	+	0.846501i
$367$	−1.42497	+	3.44017i	−0.0743827	+	0.179576i	−0.956697	−	0.291084i	$-0.905984\pi$
$367$	−1.42497	+	3.44017i	−0.0743827	+	0.179576i	0.882315	+	0.470660i	$0.155984\pi$
$368$	46.8350	+	19.3997i	2.44144	+	1.01128i
$369$	1.53924	+	3.71604i	0.0801294	+	0.193449i
$370$		−	31.1412i		−	1.61896i
$371$	−1.55478	+	0.644011i	−0.0807202	+	0.0334354i
$372$	1.55562	+	1.55562i	0.0806550	+	0.0806550i
$373$	−1.53618			−0.0795403			−0.0397701	−	0.999209i	$-0.512663\pi$
$373$	−1.53618			−0.0795403			−0.0397701	+	0.999209i	$0.512663\pi$
$374$		0			0
$375$	−11.2484			−0.580867
$376$	−13.1137	−	13.1137i	−0.676289	−	0.676289i
$377$	0.211108	−	0.0874440i	0.0108726	−	0.00450359i
$378$		−	6.10124i		−	0.313814i
$379$	−13.8344	−	33.3992i	−0.710626	−	1.71560i	−0.698431	−	0.715677i	$-0.746118\pi$
$379$	−13.8344	−	33.3992i	−0.710626	−	1.71560i	−0.0121949	−	0.999926i	$-0.503882\pi$
$380$	−60.4812	−	25.0521i	−3.10262	−	1.28515i
$381$	−3.77016	+	9.10196i	−0.193151	+	0.466308i
$382$	3.00052	−	3.00052i	0.153520	−	0.153520i
$383$	−11.5606	+	11.5606i	−0.590720	+	0.590720i	−0.937826	−	0.347106i	$-0.887164\pi$
$383$	−11.5606	+	11.5606i	−0.590720	+	0.590720i	0.347106	+	0.937826i	$0.387164\pi$
$384$	2.10237	−	5.07556i	0.107286	−	0.259011i
$385$	−9.26782	−	3.83886i	−0.472332	−	0.195646i
$386$	−4.51389	−	10.8975i	−0.229751	−	0.554668i
$387$		−	8.33468i		−	0.423675i
$388$	21.5697	−	8.93447i	1.09504	−	0.453579i
$389$	11.6342	+	11.6342i	0.589880	+	0.589880i	0.937599	−	0.347719i	$-0.113044\pi$
$389$	11.6342	+	11.6342i	0.589880	+	0.589880i	−0.347719	+	0.937599i	$0.613044\pi$
$390$	7.74611			0.392240
$391$		0			0
$392$	12.7916			0.646071
$393$	5.37930	+	5.37930i	0.271350	+	0.271350i
$394$	18.0091	−	7.45963i	0.907288	−	0.375811i
$395$		−	1.55169i		−	0.0780740i
$396$	−3.69552	−	8.92177i	−0.185707	−	0.448336i
$397$	−33.6852	−	13.9529i	−1.69061	−	0.700275i	−0.690871	−	0.722978i	$-0.742773\pi$
$397$	−33.6852	−	13.9529i	−1.69061	−	0.700275i	−0.999742	+	0.0227033i	$0.992773\pi$
$398$	−7.26068	+	17.5288i	−0.363945	+	0.878641i
$399$	−9.73764	+	9.73764i	−0.487492	+	0.487492i
$400$	−0.464030	+	0.464030i	−0.0232015	+	0.0232015i
$401$	3.70402	−	8.94230i	0.184970	−	0.446557i	−0.804008	−	0.594618i	$-0.797303\pi$
$401$	3.70402	−	8.94230i	0.184970	−	0.446557i	0.988978	+	0.148061i	$0.0473033\pi$
$402$	34.5545	+	14.3129i	1.72342	+	0.713865i
$403$	0.224847	+	0.542829i	0.0112004	+	0.0270402i
$404$			35.2051i			1.75152i
$405$	2.05304	−	0.850396i	0.102016	−	0.0422565i
$406$	−0.745595	−	0.745595i	−0.0370032	−	0.0370032i
$407$	−10.3685			−0.513949
$408$		0			0
$409$	−2.52228			−0.124719			−0.0623593	−	0.998054i	$-0.519862\pi$
$409$	−2.52228			−0.124719			−0.0623593	+	0.998054i	$0.519862\pi$
$410$	16.6626	+	16.6626i	0.822909	+	0.822909i
$411$	−20.3922	+	8.44671i	−1.00587	+	0.416645i
$412$		−	45.6619i		−	2.24960i
$413$	−10.4388	−	25.2014i	−0.513658	−	1.24008i
$414$	11.6405	+	4.82163i	0.572097	+	0.236970i
$415$	7.25363	−	17.5118i	0.356067	−	0.859621i
$416$	11.6000	−	11.6000i	0.568739	−	0.568739i
$417$	−2.53465	+	2.53465i	−0.124122	+	0.124122i
$418$	−11.7109	+	28.2726i	−0.572798	+	1.38286i
$419$	24.3222	+	10.0746i	1.18822	+	0.492177i	0.887175	−	0.461434i	$-0.152665\pi$
$419$	24.3222	+	10.0746i	1.18822	+	0.492177i	0.301045	+	0.953610i	$0.402665\pi$
$420$	−9.74288	−	23.5214i	−0.475404	−	1.14773i
$421$			6.61089i			0.322195i	0.986938	+	0.161098i	$0.0515034\pi$
$421$			6.61089i			0.322195i	−0.986938	+	0.161098i	$0.948497\pi$
$422$	32.6837	−	13.5380i	1.59102	−	0.659020i
$423$	−1.68577	−	1.68577i	−0.0819651	−	0.0819651i
$424$	−5.65685			−0.274721
$425$		0			0
$426$	16.0853			0.779337
$427$	14.2155	+	14.2155i	0.687936	+	0.687936i
$428$	−23.7038	+	9.81845i	−1.14577	+	0.474593i
$429$		−	2.57908i		−	0.124519i
$430$	−18.6862	−	45.1126i	−0.901131	−	2.17552i
$431$	25.9852	+	10.7634i	1.25167	+	0.518457i	0.907342	−	0.420394i	$-0.138108\pi$
$431$	25.9852	+	10.7634i	1.25167	+	0.518457i	0.344324	+	0.938851i	$0.388108\pi$
$432$	4.05931	−	9.80004i	0.195304	−	0.471505i
$433$	−12.1267	+	12.1267i	−0.582770	+	0.582770i	−0.935664	−	0.352893i	$-0.885198\pi$
$433$	−12.1267	+	12.1267i	−0.582770	+	0.582770i	0.352893	+	0.935664i	$0.385198\pi$
$434$	1.91717	−	1.91717i	0.0920270	−	0.0920270i
$435$	0.146967	−	0.354811i	0.00704655	−	0.0170119i
$436$	91.3630	+	37.8438i	4.37549	+	1.81239i
$437$	−10.8829	−	26.2737i	−0.520600	−	1.25684i
$438$			27.8322i			1.32987i
$439$	−7.59888	+	3.14756i	−0.362675	+	0.150225i	−0.556577	−	0.830796i	$-0.687886\pi$
$439$	−7.59888	+	3.14756i	−0.362675	+	0.150225i	0.193902	+	0.981021i	$0.437886\pi$
$440$	−23.8434	−	23.8434i	−1.13669	−	1.13669i
$441$	1.64436			0.0783028
$442$		0			0
$443$	−18.4658			−0.877339			−0.438669	−	0.898649i	$-0.644550\pi$
$443$	−18.4658			−0.877339			−0.438669	+	0.898649i	$0.644550\pi$
$444$	−18.6075	−	18.6075i	−0.883072	−	0.883072i
$445$	−11.0925	+	4.59466i	−0.525835	+	0.217808i
$446$		−	56.0614i		−	2.65458i
$447$	−4.50461	−	10.8751i	−0.213061	−	0.514374i
$448$	−24.5797	−	10.1813i	−1.16128	−	0.481019i
$449$	−11.8345	+	28.5710i	−0.558504	+	1.34835i	0.352446	+	0.935832i	$0.385350\pi$
$449$	−11.8345	+	28.5710i	−0.558504	+	1.34835i	−0.910950	+	0.412516i	$0.864650\pi$
$450$	−0.115331	+	0.115331i	−0.00543675	+	0.00543675i
$451$	5.54786	−	5.54786i	0.261239	−	0.261239i
$452$	−33.0351	+	79.7539i	−1.55384	+	3.75131i
$453$	−14.8779	−	6.16263i	−0.699025	−	0.289546i
$454$	−4.99817	−	12.0667i	−0.234576	−	0.566316i
$455$		−	6.79951i		−	0.318766i
$456$	−42.7667	+	17.7145i	−2.00273	+	0.829559i
$457$	10.9840	+	10.9840i	0.513810	+	0.513810i	0.915692	−	0.401881i	$-0.131644\pi$
$457$	10.9840	+	10.9840i	0.513810	+	0.513810i	−0.401881	+	0.915692i	$0.631644\pi$
$458$	4.84683			0.226478
$459$		0			0
$460$	52.5756			2.45135
$461$	−27.5087	−	27.5087i	−1.28121	−	1.28121i	−0.939980	−	0.341230i	$-0.889156\pi$
$461$	−27.5087	−	27.5087i	−1.28121	−	1.28121i	−0.341230	−	0.939980i	$-0.610844\pi$
$462$	−10.9953	+	4.55442i	−0.511549	+	0.211891i
$463$		−	22.7572i		−	1.05762i	−0.848742	−	0.528808i	$-0.822639\pi$
$463$		−	22.7572i		−	1.05762i	0.848742	−	0.528808i	$-0.177361\pi$
$464$	−0.701539	−	1.69367i	−0.0325681	−	0.0786265i
$465$	0.912334	+	0.377901i	0.0423085	+	0.0175248i
$466$	1.50832	−	3.64141i	0.0698715	−	0.168685i
$467$	8.87780	−	8.87780i	0.410815	−	0.410815i	−0.471207	−	0.882023i	$-0.656182\pi$
$467$	8.87780	−	8.87780i	0.410815	−	0.410815i	0.882023	+	0.471207i	$0.156182\pi$
$468$	4.62845	−	4.62845i	0.213950	−	0.213950i
$469$	12.5639	−	30.3318i	0.580145	−	1.40059i
$470$	−12.9040	−	5.34500i	−0.595216	−	0.246546i
$471$	2.47036	+	5.96397i	0.113828	+	0.274805i
$472$		−	91.6918i		−	4.22046i
$473$	−15.0203	+	6.22162i	−0.690635	+	0.286070i
$474$	−1.30173	−	1.30173i	−0.0597904	−	0.0597904i
$475$	0.368139			0.0168914
$476$		0			0
$477$	−0.727190			−0.0332957
$478$	18.6888	+	18.6888i	0.854805	+	0.854805i
$479$	34.4070	−	14.2518i	1.57209	−	0.651183i	0.584959	−	0.811063i	$-0.301111\pi$
$479$	34.4070	−	14.2518i	1.57209	−	0.651183i	0.987136	+	0.159880i	$0.0511108\pi$
$480$		−	27.5719i		−	1.25848i
$481$	−2.68950	−	6.49303i	−0.122631	−	0.296057i
$482$	28.0484	+	11.6180i	1.27757	+	0.529187i
$483$	4.23241	−	10.2179i	0.192581	−	0.464932i
$484$	25.1871	−	25.1871i	1.14487	−	1.14487i
$485$	7.41029	−	7.41029i	0.336484	−	0.336484i
$486$	1.00891	−	2.43572i	0.0457650	−	0.110487i
$487$	1.51967	+	0.629467i	0.0688627	+	0.0285239i	0.416849	−	0.908976i	$-0.363134\pi$
$487$	1.51967	+	0.629467i	0.0688627	+	0.0285239i	−0.347986	+	0.937500i	$0.613134\pi$
$488$	25.8605	+	62.4329i	1.17065	+	2.82620i
$489$			16.7322i			0.756656i
$490$	8.90031	−	3.68663i	0.402075	−	0.166545i
$491$	−3.04142	−	3.04142i	−0.137257	−	0.137257i	0.635140	−	0.772397i	$-0.280942\pi$
$491$	−3.04142	−	3.04142i	−0.137257	−	0.137257i	−0.772397	+	0.635140i	$0.780942\pi$
$492$	19.9125			0.897725
$493$		0			0
$494$	−20.7427			−0.933258
$495$	−3.06508	−	3.06508i	−0.137765	−	0.137765i
$496$	4.35497	−	1.80389i	0.195544	−	0.0809969i
$497$		−	14.1196i		−	0.633352i
$498$	−8.60570	−	20.7760i	−0.385631	−	0.930995i
$499$	1.38146	+	0.572218i	0.0618425	+	0.0256160i	0.413390	−	0.910554i	$-0.364345\pi$
$499$	1.38146	+	0.572218i	0.0618425	+	0.0256160i	−0.351548	+	0.936170i	$0.614345\pi$
$500$	−21.3104	+	51.4479i	−0.953032	+	2.30082i
$501$	1.13490	−	1.13490i	0.0507034	−	0.0507034i
$502$	1.75270	−	1.75270i	0.0782269	−	0.0782269i
$503$	−0.645504	+	1.55838i	−0.0287816	+	0.0694849i	−0.937617	−	0.347670i	$-0.886973\pi$
$503$	−0.645504	+	1.55838i	−0.0287816	+	0.0694849i	0.908835	+	0.417155i	$0.136973\pi$
$504$	−16.6321	−	6.88926i	−0.740854	−	0.306872i
$505$	6.04736	+	14.5996i	0.269104	+	0.649675i
$506$		−	24.5770i		−	1.09258i
$507$	−10.3953	+	4.30589i	−0.461674	+	0.191231i
$508$	34.4878	+	34.4878i	1.53015	+	1.53015i
$509$	6.91070			0.306312			0.153156	−	0.988202i	$-0.451056\pi$
$509$	6.91070			0.306312			0.153156	+	0.988202i	$0.451056\pi$
$510$		0			0
$511$	24.4310			1.08076
$512$	23.6315	+	23.6315i	1.04438	+	1.04438i
$513$	−5.49767	+	2.27721i	−0.242728	+	0.100541i
$514$		−	5.68185i		−	0.250616i
$515$	−7.84358	−	18.9361i	−0.345629	−	0.834423i
$516$	−38.1210	−	15.7902i	−1.67818	−	0.695127i
$517$	−1.77963	+	4.29640i	−0.0782679	+	0.188955i
$518$	−22.9322	+	22.9322i	−1.00758	+	1.00758i
$519$	12.1169	−	12.1169i	0.531875	−	0.531875i
$520$	8.74658	−	21.1161i	0.383563	−	0.926003i
$521$	−12.3765	−	5.12653i	−0.542226	−	0.224597i	0.0947226	−	0.995504i	$-0.469804\pi$
$521$	−12.3765	−	5.12653i	−0.542226	−	0.224597i	−0.636948	+	0.770906i	$0.719804\pi$
$522$	−0.174362	−	0.420947i	−0.00763162	−	0.0184243i
$523$			4.40904i			0.192794i	0.995343	+	0.0963969i	$0.0307318\pi$
$523$			4.40904i			0.192794i	−0.995343	+	0.0963969i	$0.969268\pi$
$524$	34.7950	−	14.4126i	1.52003	−	0.629616i
$525$	0.101237	+	0.101237i	0.00441834	+	0.00441834i
$526$	−34.6494			−1.51078
$527$		0			0
$528$	−20.6913			−0.900473
$529$	−0.113564	−	0.113564i	−0.00493756	−	0.00493756i
$530$	−3.93602	+	1.63035i	−0.170970	+	0.0708179i
$531$		−	11.7870i		−	0.511513i
$532$	26.0897	+	62.9861i	1.13113	+	2.73079i
$533$	4.91327	+	2.03514i	0.212818	+	0.0881519i
$534$	−5.45110	+	13.1601i	−0.235892	+	0.569494i
$535$	−8.14347	+	8.14347i	−0.352073	+	0.352073i
$536$	78.0350	−	78.0350i	3.37060	−	3.37060i
$537$	−4.23835	+	10.2323i	−0.182898	+	0.441555i
$538$	−36.9605	−	15.3095i	−1.59348	−	0.660041i
$539$	−1.22747	−	2.96338i	−0.0528709	−	0.127642i
$540$		−	11.0012i		−	0.473418i
$541$	21.3559	−	8.84592i	0.918163	−	0.380316i	0.126987	−	0.991904i	$-0.459469\pi$
$541$	21.3559	−	8.84592i	0.918163	−	0.380316i	0.791176	+	0.611589i	$0.209469\pi$
$542$	22.0649	+	22.0649i	0.947768	+	0.947768i
$543$	19.6995			0.845387
$544$		0			0
$545$	44.3890			1.90142
$546$	−5.70418	−	5.70418i	−0.244116	−	0.244116i
$547$	−8.76278	+	3.62966i	−0.374669	+	0.155193i	−0.562068	−	0.827091i	$-0.689994\pi$
$547$	−8.76278	+	3.62966i	−0.374669	+	0.155193i	0.187399	+	0.982284i	$0.439994\pi$
$548$			109.272i			4.66786i
$549$	3.32438	+	8.02576i	0.141881	+	0.342531i
$550$	0.293935	+	0.121752i	0.0125334	+	0.00519151i
$551$	−0.393552	+	0.950120i	−0.0167659	+	0.0404765i
$552$	26.2878	−	26.2878i	1.11888	−	1.11888i
$553$	−1.14265	+	1.14265i	−0.0485906	+	0.0485906i
$554$	27.1422	−	65.5270i	1.15316	−	2.78398i
$555$	−10.9129	−	4.52026i	−0.463225	−	0.191874i
$556$	6.79099	+	16.3949i	0.288002	+	0.695299i
$557$			38.1670i			1.61719i	0.588368	+	0.808593i	$0.299771\pi$
$557$			38.1670i			1.61719i	−0.588368	+	0.808593i	$0.700229\pi$
$558$	1.08239	−	0.448342i	0.0458213	−	0.0189798i
$559$	−7.79227	−	7.79227i	−0.329578	−	0.329578i
$560$	−54.5506			−2.30518
$561$		0			0
$562$	58.6175			2.47263
$563$	−9.77111	−	9.77111i	−0.411803	−	0.411803i	0.470563	−	0.882366i	$-0.344051\pi$
$563$	−9.77111	−	9.77111i	−0.411803	−	0.411803i	−0.882366	+	0.470563i	$0.844051\pi$
$564$	−10.9041	+	4.51663i	−0.459146	+	0.190184i
$565$			38.7487i			1.63017i
$566$	24.1711	+	58.3542i	1.01599	+	2.45281i
$567$	−2.13807	−	0.885616i	−0.0897903	−	0.0371924i
$568$	18.1629	−	43.8491i	0.762097	−	1.83987i
$569$	9.15817	−	9.15817i	0.383930	−	0.383930i	−0.488586	−	0.872516i	$-0.662487\pi$
$569$	9.15817	−	9.15817i	0.383930	−	0.383930i	0.872516	+	0.488586i	$0.162487\pi$
$570$	−24.6514	+	24.6514i	−1.03253	+	1.03253i
$571$	−2.49273	+	6.01797i	−0.104317	+	0.251844i	−0.967417	−	0.253190i	$-0.918520\pi$
$571$	−2.49273	+	6.01797i	−0.104317	+	0.251844i	0.863099	+	0.505034i	$0.168520\pi$
$572$	−11.7962	−	4.88614i	−0.493223	−	0.204300i
$573$	−0.615940	−	1.48701i	−0.0257313	−	0.0621208i
$574$		−	24.5405i		−	1.02430i
$575$	−0.273153	+	0.113144i	−0.0113913	+	0.00471842i
$576$	−8.12908	−	8.12908i	−0.338712	−	0.338712i
$577$	−15.6703			−0.652364			−0.326182	−	0.945307i	$-0.605762\pi$
$577$	−15.6703			−0.652364			−0.326182	+	0.945307i	$0.605762\pi$
$578$		0			0
$579$	−4.47403			−0.185935
$580$	−1.34440	−	1.34440i	−0.0558230	−	0.0558230i
$581$	−18.2371	+	7.55405i	−0.756602	+	0.313395i
$582$		−	12.4331i		−	0.515370i
$583$	0.542829	+	1.31050i	0.0224817	+	0.0542755i
$584$	75.8713	+	31.4269i	3.13958	+	1.30045i
$585$	1.12438	−	2.71448i	0.0464872	−	0.112230i
$586$	13.8770	−	13.8770i	0.573254	−	0.573254i
$587$	−10.5901	+	10.5901i	−0.437098	+	0.437098i	−0.891034	−	0.453936i	$-0.850019\pi$
$587$	−10.5901	+	10.5901i	−0.437098	+	0.437098i	0.453936	+	0.891034i	$0.350019\pi$
$588$	3.11528	−	7.52094i	0.128472	−	0.310158i
$589$	−2.44307	−	1.01195i	−0.100665	−	0.0416968i
$590$	−26.4263	−	63.7988i	−1.08795	−	2.62656i
$591$		−	7.39376i		−	0.304139i
$592$	−52.0919	+	21.5772i	−2.14096	+	0.886816i
$593$	−32.7886	−	32.7886i	−1.34647	−	1.34647i	−0.889467	−	0.456999i	$-0.848924\pi$
$593$	−32.7886	−	32.7886i	−1.34647	−	1.34647i	−0.456999	−	0.889467i	$-0.651076\pi$
$594$	−5.14265			−0.211006
$595$		0			0
$596$	−58.2744			−2.38701
$597$	5.08874	+	5.08874i	0.208268	+	0.208268i
$598$	15.3908	−	6.37506i	0.629375	−	0.260696i
$599$			28.7068i			1.17293i	0.809975	+	0.586464i	$0.199480\pi$
$599$			28.7068i			1.17293i	−0.809975	+	0.586464i	$0.800520\pi$
$600$	0.184168	+	0.444622i	0.00751864	+	0.0181516i
$601$	−19.2062	−	7.95547i	−0.783438	−	0.324511i	−0.0451358	−	0.998981i	$-0.514372\pi$
$601$	−19.2062	−	7.95547i	−0.783438	−	0.324511i	−0.738302	+	0.674470i	$0.764372\pi$
$602$	−19.4602	+	46.9810i	−0.793137	+	1.91480i
$603$	10.0314	−	10.0314i	0.408511	−	0.408511i
$604$	−56.3731	+	56.3731i	−2.29379	+	2.29379i
$605$	6.11863	−	14.7717i	0.248758	−	0.600554i
$606$	17.3210	+	7.17458i	0.703617	+	0.291448i
$607$	6.58447	+	15.8963i	0.267255	+	0.645211i	0.999352	−	0.0359891i	$-0.0114582\pi$
$607$	6.58447	+	15.8963i	0.267255	+	0.645211i	−0.732097	+	0.681201i	$0.761458\pi$
$608$			73.8325i			2.99430i
$609$	−0.369506	+	0.153054i	−0.0149731	+	0.00620207i
$610$	35.9873	+	35.9873i	1.45708	+	1.45708i
$611$	−3.15213			−0.127522
$612$		0			0
$613$	−42.7657			−1.72729			−0.863644	−	0.504102i	$-0.831824\pi$
$613$	−42.7657			−1.72729			−0.863644	+	0.504102i	$0.831824\pi$
$614$	26.5062	+	26.5062i	1.06970	+	1.06970i
$615$	8.25776	−	3.42048i	0.332985	−	0.137927i
$616$			35.1162i			1.41487i
$617$	−14.6490	−	35.3658i	−0.589745	−	1.42377i	−0.883746	−	0.467966i	$-0.844987\pi$
$617$	−14.6490	−	35.3658i	−0.589745	−	1.42377i	0.294001	−	0.955805i	$-0.405013\pi$
$618$	−22.4657	−	9.30561i	−0.903704	−	0.374326i
$619$	3.54840	−	8.56660i	0.142622	−	0.344321i	−0.836386	−	0.548141i	$-0.815336\pi$
$619$	3.54840	−	8.56660i	0.142622	−	0.344321i	0.979008	+	0.203820i	$0.0653358\pi$
$620$	3.45688	−	3.45688i	0.138832	−	0.138832i
$621$	3.37930	−	3.37930i	0.135607	−	0.135607i
$622$	−10.4539	+	25.2378i	−0.419161	+	1.01195i
$623$	11.5519	+	4.78495i	0.462817	+	0.191705i
$624$	−5.36713	−	12.9574i	−0.214857	−	0.518711i
$625$			24.6868i			0.987474i
$626$	42.4453	−	17.5814i	1.69646	−	0.702695i
$627$	8.20773	+	8.20773i	0.327785	+	0.327785i
$628$	31.9581			1.27527
$629$		0			0
$630$	−13.5581			−0.540168
$631$	−23.9340	−	23.9340i	−0.952798	−	0.952798i	0.0461372	−	0.998935i	$-0.485309\pi$
$631$	−23.9340	−	23.9340i	−0.952798	−	0.952798i	−0.998935	+	0.0461372i	$0.985309\pi$
$632$	−5.01841	+	2.07869i	−0.199622	+	0.0826860i
$633$		−	13.4185i		−	0.533337i
$634$	14.3016	+	34.5271i	0.567989	+	1.37125i
$635$	20.2263	+	8.37801i	0.802656	+	0.332471i
$636$	−1.37768	+	3.32601i	−0.0546285	+	0.131885i
$637$	1.53735	−	1.53735i	0.0609119	−	0.0609119i
$638$	−0.628452	+	0.628452i	−0.0248807	+	0.0248807i
$639$	2.33484	−	5.63681i	0.0923649	−	0.222989i
$640$	−11.2789	−	4.67186i	−0.445837	−	0.184672i
$641$	−4.08383	−	9.85925i	−0.161302	−	0.389417i	0.822478	−	0.568797i	$-0.192591\pi$
$641$	−4.08383	−	9.85925i	−0.161302	−	0.389417i	−0.983780	+	0.179380i	$0.942591\pi$
$642$			13.6633i			0.539247i
$643$	−36.3211	+	15.0447i	−1.43237	+	0.593305i	−0.957934	−	0.286987i	$-0.907346\pi$
$643$	−36.3211	+	15.0447i	−1.43237	+	0.593305i	−0.474431	+	0.880293i	$0.657346\pi$
$644$	−38.7163	−	38.7163i	−1.52564	−	1.52564i
$645$	−18.5212			−0.729273
$646$		0			0
$647$	−27.9895			−1.10038			−0.550190	−	0.835039i	$-0.685445\pi$
$647$	−27.9895			−1.10038			−0.550190	+	0.835039i	$0.685445\pi$
$648$	−5.50062	−	5.50062i	−0.216085	−	0.216085i
$649$	−21.2419	+	8.79870i	−0.833819	+	0.345379i
$650$			0.215651i			0.00845852i
$651$	−0.393552	−	0.950120i	−0.0154245	−	0.0372381i
$652$	76.5295	+	31.6995i	2.99712	+	1.24145i
$653$	15.6716	−	37.8346i	0.613277	−	1.48058i	−0.246102	−	0.969244i	$-0.579150\pi$
$653$	15.6716	−	37.8346i	0.613277	−	1.48058i	0.859379	−	0.511339i	$-0.170850\pi$
$654$	37.2384	−	37.2384i	1.45614	−	1.45614i
$655$	11.9538	−	11.9538i	0.467075	−	0.467075i
$656$	16.3274	−	39.4179i	0.637479	−	1.53901i
$657$	9.75327	+	4.03994i	0.380511	+	0.157613i
$658$	5.56637	+	13.4384i	0.217000	+	0.523883i
$659$			10.8164i			0.421349i	0.977556	+	0.210674i	$0.0675660\pi$
$659$			10.8164i			0.421349i	−0.977556	+	0.210674i	$0.932434\pi$
$660$	−19.8259	+	8.21215i	−0.771721	+	0.319657i
$661$	−14.1983	−	14.1983i	−0.552248	−	0.552248i	0.374841	−	0.927089i	$-0.377697\pi$
$661$	−14.1983	−	14.1983i	−0.552248	−	0.552248i	−0.927089	+	0.374841i	$0.877697\pi$
$662$	28.6010			1.11161
$663$		0			0
$664$	−66.3531			−2.57500
$665$	21.6389	+	21.6389i	0.839121	+	0.839121i
$666$	−12.9470	+	5.36283i	−0.501687	+	0.207805i
$667$		−	0.825928i		−	0.0319801i
$668$	−3.04069	−	7.34086i	−0.117648	−	0.284027i
$669$	−19.6457	−	8.13751i	−0.759546	−	0.314614i
$670$	31.8061	−	76.7867i	1.22878	−	2.96653i
$671$	11.9820	−	11.9820i	0.462562	−	0.462562i
$672$	−20.3037	+	20.3037i	−0.783233	+	0.783233i
$673$	−10.4895	+	25.3238i	−0.404339	+	0.976161i	0.582261	+	0.813002i	$0.302168\pi$
$673$	−10.4895	+	25.3238i	−0.404339	+	0.976161i	−0.986600	+	0.163159i	$0.947832\pi$
$674$	−23.9132	−	9.90516i	−0.921101	−	0.381532i
$675$	0.0236749	+	0.0571563i	0.000911247	+	0.00219995i
$676$			55.7037i			2.14245i
$677$	20.9960	−	8.69682i	0.806941	−	0.334246i	0.0592081	−	0.998246i	$-0.481142\pi$
$677$	20.9960	−	8.69682i	0.806941	−	0.334246i	0.747733	+	0.664000i	$0.231142\pi$
$678$	32.5067	+	32.5067i	1.24841	+	1.24841i
$679$	−10.9138			−0.418832
$680$		0			0
$681$	−4.95404			−0.189839
$682$	−1.61596	−	1.61596i	−0.0618781	−	0.0618781i
$683$	34.3743	−	14.2383i	1.31530	−	0.544814i	0.388871	−	0.921292i	$-0.372865\pi$
$683$	34.3743	−	14.2383i	1.31530	−	0.544814i	0.926425	+	0.376478i	$0.122865\pi$
$684$			29.4594i			1.12641i
$685$	18.7702	+	45.3153i	0.717173	+	1.73141i
$686$	−48.7266	−	20.1832i	−1.86039	−	0.770599i
$687$	0.703535	−	1.69848i	0.0268415	−	0.0648012i
$688$	−62.5153	+	62.5153i	−2.38337	+	2.38337i
$689$	−0.679866	+	0.679866i	−0.0259008	+	0.0259008i
$690$	10.7146	−	25.8673i	0.407897	−	0.984752i
$691$	16.6816	+	6.90974i	0.634597	+	0.262859i	0.676705	−	0.736254i	$-0.263407\pi$
$691$	16.6816	+	6.90974i	0.634597	+	0.262859i	−0.0421076	+	0.999113i	$0.513407\pi$
$692$	−32.4645	−	78.3762i	−1.23411	−	2.97942i
$693$			4.51420i			0.171480i
$694$	−63.4430	+	26.2790i	−2.40827	+	0.997536i
$695$	5.63248	+	5.63248i	0.213652	+	0.213652i
$696$	−1.34440			−0.0509592
$697$		0			0
$698$	49.1976			1.86216
$699$	−1.05713	−	1.05713i	−0.0399842	−	0.0399842i
$700$	0.654832	−	0.271240i	0.0247503	−	0.0102519i
$701$			9.99896i			0.377656i	0.982010	+	0.188828i	$0.0604688\pi$
$701$			9.99896i			0.377656i	−0.982010	+	0.188828i	$0.939531\pi$
$702$	−1.33396	−	3.22046i	−0.0503470	−	0.121548i
$703$	29.2227	+	12.1044i	1.10216	+	0.456528i
$704$	−8.58165	+	20.7179i	−0.323433	+	0.780837i
$705$	−3.74611	+	3.74611i	−0.141087	+	0.141087i
$706$	−22.0611	+	22.0611i	−0.830279	+	0.830279i
$707$	6.29782	−	15.2043i	0.236854	−	0.571816i
$708$	−53.9113	−	22.3308i	−2.02611	−	0.839242i
$709$	−0.418638	−	1.01068i	−0.0157223	−	0.0379570i	0.915823	−	0.401581i	$-0.131539\pi$
$709$	−0.418638	−	1.01068i	−0.0157223	−	0.0379570i	−0.931546	+	0.363624i	$0.881539\pi$
$710$		−	35.7447i		−	1.34147i
$711$	−0.645118	+	0.267217i	−0.0241938	+	0.0100214i
$712$	29.7197	+	29.7197i	1.11379	+	1.11379i
$713$	2.12373			0.0795344
$714$		0			0
$715$	−5.73122			−0.214335
$716$	38.7706	+	38.7706i	1.44892	+	1.44892i
$717$	9.26189	−	3.83640i	0.345891	−	0.143273i
$718$			37.2768i			1.39116i
$719$	16.2571	+	39.2481i	0.606287	+	1.46371i	0.867009	+	0.498292i	$0.166039\pi$
$719$	16.2571	+	39.2481i	0.606287	+	1.46371i	−0.260722	+	0.965414i	$0.583961\pi$
$720$	−21.7776	−	9.02056i	−0.811602	−	0.336176i
$721$	−8.16843	+	19.7203i	−0.304208	+	0.734423i
$722$	30.5919	−	30.5919i	1.13851	−	1.13851i
$723$	8.14265	−	8.14265i	0.302829	−	0.302829i
$724$	37.3212	−	90.1014i	1.38703	−	3.34859i
$725$	0.00987788	+	0.00409155i	0.000366855	+	0.000151956i
$726$	−7.25914	−	17.5251i	−0.269412	−	0.650418i
$727$		−	45.2169i		−	1.67700i	−0.544900	−	0.838501i	$-0.683432\pi$
$727$		−	45.2169i		−	1.67700i	0.544900	−	0.838501i	$-0.316568\pi$
$728$	−21.9907	+	9.10883i	−0.815028	+	0.337596i
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$	61.8484			2.28911
$731$		0			0
$732$	43.0062			1.58956
$733$	−15.2728	−	15.2728i	−0.564114	−	0.564114i	0.366359	−	0.930473i	$-0.380604\pi$
$733$	−15.2728	−	15.2728i	−0.564114	−	0.564114i	−0.930473	+	0.366359i	$0.880604\pi$
$734$	9.06969	−	3.75679i	0.334769	−	0.138666i
$735$		−	3.65408i		−	0.134783i
$736$	−22.6917	−	54.7826i	−0.836426	−	2.01931i
$737$	−25.5663	−	10.5899i	−0.941747	−	0.390084i
$738$	4.05805	−	9.79700i	0.149379	−	0.360632i
$739$	−13.4646	+	13.4646i	−0.495305	+	0.495305i	−0.909973	−	0.414668i	$-0.863898\pi$
$739$	−13.4646	+	13.4646i	−0.495305	+	0.495305i	0.414668	+	0.909973i	$0.363898\pi$
$740$	−41.3494	+	41.3494i	−1.52003	+	1.52003i
$741$	−3.01088	+	7.26890i	−0.110607	+	0.267030i
$742$	4.09903	+	1.69787i	0.150480	+	0.0623309i
$743$	10.1160	+	24.4221i	0.371118	+	0.895959i	0.993562	+	0.113294i	$0.0361402\pi$
$743$	10.1160	+	24.4221i	0.371118	+	0.895959i	−0.622443	+	0.782665i	$0.713860\pi$
$744$		−	3.45688i		−	0.126735i
$745$	−24.1665	+	10.0101i	−0.885393	+	0.366742i
$746$	2.86377	+	2.86377i	0.104850	+	0.104850i
$747$	−8.52971			−0.312086
$748$		0			0
$749$	11.9936			0.438236
$750$	20.9696	+	20.9696i	0.765700	+	0.765700i
$751$	−4.29314	+	1.77828i	−0.156659	+	0.0648902i	−0.459635	−	0.888108i	$-0.652020\pi$
$751$	−4.29314	+	1.77828i	−0.156659	+	0.0648902i	0.302976	+	0.952998i	$0.402020\pi$
$752$			25.2887i			0.922185i
$753$	−0.359791	−	0.868612i	−0.0131115	−	0.0316540i
$754$	−0.556567	−	0.230538i	−0.0202690	−	0.00839569i
$755$	−13.6945	+	33.0616i	−0.498396	+	1.20323i
$756$	−8.10124	+	8.10124i	−0.294639	+	0.294639i
$757$	−7.35913	+	7.35913i	−0.267472	+	0.267472i	−0.828081	−	0.560609i	$-0.810567\pi$
$757$	−7.35913	+	7.35913i	−0.267472	+	0.267472i	0.560609	+	0.828081i	$0.310567\pi$
$758$	−36.4731	+	88.0539i	−1.32476	+	3.19826i
$759$	−8.61257	−	3.56744i	−0.312616	−	0.129490i
$760$	39.3651	+	95.0357i	1.42792	+	3.44731i
$761$			38.6365i			1.40057i	0.713862	+	0.700286i	$0.246944\pi$
$761$			38.6365i			1.40057i	−0.713862	+	0.700286i	$0.753056\pi$
$762$	23.9965	−	9.93966i	0.869300	−	0.360076i
$763$	−32.6878	−	32.6878i	−1.18338	−	1.18338i
$764$	−7.96819			−0.288279
$765$		0			0
$766$	43.1031			1.55738
$767$	−11.0199	−	11.0199i	−0.397907	−	0.397907i
$768$	7.86106	−	3.25616i	0.283661	−	0.117496i
$769$		−	0.178098i		−	0.00642238i	−0.999995	−	0.00321119i	$-0.998978\pi$
$769$		−	0.178098i		−	0.00642238i	0.999995	−	0.00321119i	$-0.00102215\pi$
$770$	10.1208	+	24.4337i	0.364728	+	0.880531i
$771$	−1.99110	−	0.824740i	−0.0717077	−	0.0297023i
$772$	−8.47617	+	20.4633i	−0.305064	+	0.736490i
$773$	−2.93841	+	2.93841i	−0.105687	+	0.105687i	−0.757973	−	0.652286i	$-0.773810\pi$
$773$	−2.93841	+	2.93841i	−0.105687	+	0.105687i	0.652286	+	0.757973i	$0.273810\pi$
$774$	−15.5377	+	15.5377i	−0.558490	+	0.558490i
$775$	−0.0105207	+	0.0253993i	−0.000377915	+	0.000912368i
$776$	−33.8931	−	14.0390i	−1.21669	−	0.503970i
$777$	4.70747	+	11.3648i	0.168880	+	0.407711i
$778$		−	43.3776i		−	1.55516i
$779$	−22.1128	+	9.15942i	−0.792273	+	0.328170i
$780$	−10.2853	−	10.2853i	−0.368273	−	0.368273i
$781$	−11.9013			−0.425861
$782$		0			0
$783$	−0.172822			−0.00617617
$784$	−12.3337	−	12.3337i	−0.440490	−	0.440490i
$785$	13.2531	−	5.48960i	0.473023	−	0.195932i
$786$		−	20.0564i		−	0.715389i
$787$	0.665353	+	1.60630i	0.0237173	+	0.0572586i	0.935294	−	0.353870i	$-0.115135\pi$
$787$	0.665353	+	1.60630i	0.0237173	+	0.0572586i	−0.911577	+	0.411129i	$0.865135\pi$
$788$	−33.8175	−	14.0077i	−1.20470	−	0.499002i
$789$	−5.02948	+	12.1422i	−0.179054	+	0.432275i
$790$	−2.89269	+	2.89269i	−0.102917	+	0.102917i
$791$	28.5343	−	28.5343i	1.01456	−	1.01456i
$792$	−5.80687	+	14.0190i	−0.206338	+	0.498144i
$793$	10.6115	+	4.39542i	0.376825	+	0.156086i
$794$	36.7854	+	88.8079i	1.30547	+	3.15167i
$795$			1.61596i			0.0573120i
$796$	32.9156	−	13.6341i	1.16666	−	0.483247i
$797$	15.7038	+	15.7038i	0.556257	+	0.556257i	0.928240	−	0.371983i	$-0.121322\pi$
$797$	15.7038	+	15.7038i	0.556257	+	0.556257i	−0.371983	+	0.928240i	$0.621322\pi$
$798$	36.3062			1.28523
$799$		0			0
$800$	0.767597			0.0271386
$801$	3.82047	+	3.82047i	0.134990	+	0.134990i
$802$	−23.5755	+	9.76530i	−0.832480	+	0.344825i
$803$		−	20.5926i		−	0.726695i
$804$	−26.8768	−	64.8863i	−0.947872	−	2.28836i
$805$	−22.7062	−	9.40523i	−0.800289	−	0.331491i
$806$	0.592788	−	1.43112i	0.0208801	−	0.0504089i
$807$	−10.7299	+	10.7299i	−0.377710	+	0.377710i
$808$	39.1162	−	39.1162i	1.37610	−	1.37610i
$809$	1.23555	−	2.98289i	0.0434397	−	0.104873i	−0.900670	−	0.434503i	$-0.856924\pi$
$809$	1.23555	−	2.98289i	0.0434397	−	0.104873i	0.944110	+	0.329630i	$0.106924\pi$
$810$	−5.41264	−	2.24199i	−0.190181	−	0.0787754i
$811$	9.64975	+	23.2966i	0.338848	+	0.818053i	0.997827	+	0.0658907i	$0.0209889\pi$
$811$	9.64975	+	23.2966i	0.338848	+	0.818053i	−0.658978	+	0.752162i	$0.729011\pi$
$812$			1.98000i			0.0694846i
$813$	10.9350	−	4.52944i	0.383508	−	0.158854i
$814$	19.3292	+	19.3292i	0.677489	+	0.677489i
$815$	37.1821			1.30243
$816$		0			0
$817$	49.5966			1.73516
$818$	4.70208	+	4.70208i	0.164404	+	0.164404i
$819$	−2.82691	+	1.17094i	−0.0987801	+	0.0409161i
$820$		−	44.2494i		−	1.54526i
$821$	13.1751	+	31.8075i	0.459814	+	1.11009i	0.968472	+	0.249121i	$0.0801417\pi$
$821$	13.1751	+	31.8075i	0.459814	+	1.11009i	−0.508658	+	0.860969i	$0.669858\pi$
$822$	53.7620	+	22.2689i	1.87516	+	0.776719i
$823$	6.81153	−	16.4445i	0.237435	−	0.573219i	−0.759581	−	0.650413i	$-0.774596\pi$
$823$	6.81153	−	16.4445i	0.237435	−	0.573219i	0.997016	+	0.0771938i	$0.0245960\pi$
$824$	−50.7347	+	50.7347i	−1.76743	+	1.76743i
$825$	0.0853313	−	0.0853313i	0.00297086	−	0.00297086i
$826$	−27.5208	+	66.4411i	−0.957572	+	2.31178i
$827$	1.80215	+	0.746474i	0.0626668	+	0.0259574i	0.413797	−	0.910369i	$-0.364202\pi$
$827$	1.80215	+	0.746474i	0.0626668	+	0.0259574i	−0.351130	+	0.936327i	$0.614202\pi$
$828$	−9.05404	−	21.8584i	−0.314650	−	0.759632i
$829$		−	0.904671i		−	0.0314205i	−0.999877	−	0.0157103i	$-0.994999\pi$
$829$		−	0.904671i		−	0.0314205i	0.999877	−	0.0157103i	$-0.00500094\pi$
$830$	−46.1682	+	19.1235i	−1.60252	+	0.663787i
$831$	−19.0229	−	19.0229i	−0.659899	−	0.659899i
$832$	−15.2001			−0.526969
$833$		0			0
$834$	9.45029			0.327237
$835$	−2.52196	−	2.52196i	−0.0872759	−	0.0872759i
$836$	53.0902	−	21.9907i	1.83616	−	0.760563i
$837$		−	0.444383i		−	0.0153601i
$838$	−26.5607	−	64.1233i	−0.917525	−	2.21510i
$839$	−22.4284	−	9.29013i	−0.774313	−	0.320731i	−0.0396949	−	0.999212i	$-0.512639\pi$
$839$	−22.4284	−	9.29013i	−0.774313	−	0.320731i	−0.734618	+	0.678481i	$0.762639\pi$
$840$	−15.3092	+	36.9598i	−0.528219	+	1.27523i
$841$	20.4850	−	20.4850i	0.706379	−	0.706379i
$842$	12.3242	−	12.3242i	0.424719	−	0.424719i
$843$	8.50854	−	20.5414i	0.293050	−	0.707485i
$844$	−61.3733	−	25.4216i	−2.11255	−	0.875049i
$845$	9.56852	+	23.1005i	0.329167	+	0.794680i
$846$			6.28531i			0.216093i
$847$	−15.3835	+	6.37204i	−0.528582	+	0.218946i
$848$	5.45438	+	5.45438i	0.187304	+	0.187304i
$849$	23.9577			0.822225
$850$		0			0
$851$	−25.4030			−0.870802
$852$	−21.3581	−	21.3581i	−0.731718	−	0.731718i
$853$	35.2095	−	14.5843i	1.20555	−	0.499355i	0.312762	−	0.949831i	$-0.398746\pi$
$853$	35.2095	−	14.5843i	1.20555	−	0.499355i	0.892789	+	0.450476i	$0.148746\pi$
$854$		−	53.0016i		−	1.81368i
$855$	5.06039	+	12.2169i	0.173062	+	0.417808i
$856$	37.2465	+	15.4280i	1.27306	+	0.527318i
$857$	2.60234	−	6.28260i	0.0888942	−	0.214610i	−0.873180	−	0.487398i	$-0.837946\pi$
$857$	2.60234	−	6.28260i	0.0888942	−	0.214610i	0.962074	+	0.272789i	$0.0879460\pi$
$858$	−4.80798	+	4.80798i	−0.164142	+	0.164142i
$859$	15.7736	−	15.7736i	0.538188	−	0.538188i	−0.384808	−	0.922997i	$-0.625732\pi$
$859$	15.7736	−	15.7736i	0.538188	−	0.538188i	0.922997	+	0.384808i	$0.125732\pi$
$860$	−35.0889	+	84.7122i	−1.19652	+	2.88866i
$861$	−8.59976	−	3.56214i	−0.293079	−	0.121397i
$862$	−28.3768	−	68.5076i	−0.966517	−	2.33338i
$863$		−	0.400593i		−	0.0136363i	−0.999977	−	0.00681816i	$-0.997830\pi$
$863$		−	0.400593i		−	0.0136363i	0.999977	−	0.00681816i	$-0.00217031\pi$
$864$	−11.4630	+	4.74815i	−0.389981	+	0.161535i
$865$	−26.9262	−	26.9262i	−0.915517	−	0.915517i
$866$	45.2135			1.53642
$867$		0			0
$868$	−5.09124			−0.172808
$869$	0.963127	+	0.963127i	0.0326719	+	0.0326719i
$870$	−0.935425	+	0.387466i	−0.0317139	+	0.0131363i
$871$		−	18.7572i		−	0.635563i
$872$	−59.4649	−	143.561i	−2.01374	−	4.86159i
$873$	−4.35696	−	1.80471i	−0.147461	−	0.0610803i
$874$	−28.6918	+	69.2680i	−0.970513	+	2.34303i
$875$	18.4070	−	18.4070i	0.622270	−	0.622270i
$876$	36.9556	−	36.9556i	1.24861	−	1.24861i
$877$	0.0806809	−	0.194781i	0.00272440	−	0.00657729i	−0.922511	−	0.385970i	$-0.873867\pi$
$877$	0.0806809	−	0.194781i	0.00272440	−	0.00657729i	0.925236	+	0.379392i	$0.123867\pi$
$878$	20.0337	+	8.29824i	0.676105	+	0.280052i
$879$	−2.84864	−	6.87723i	−0.0960824	−	0.231963i
$880$			45.9800i			1.54999i
$881$	47.8535	−	19.8216i	1.61223	−	0.667806i	0.619149	−	0.785273i	$-0.287478\pi$
$881$	47.8535	−	19.8216i	1.61223	−	0.667806i	0.993077	+	0.117467i	$0.0374776\pi$
$882$	−3.06544	−	3.06544i	−0.103219	−	0.103219i
$883$	23.5757			0.793385			0.396692	−	0.917952i	$-0.370158\pi$
$883$	23.5757			0.793385			0.396692	+	0.917952i	$0.370158\pi$
$884$		0			0
$885$	−26.1930			−0.880468
$886$	34.4244	+	34.4244i	1.15651	+	1.15651i
$887$	−15.0908	+	6.25080i	−0.506698	+	0.209881i	−0.621363	−	0.783523i	$-0.713421\pi$
$887$	−15.0908	+	6.25080i	−0.506698	+	0.209881i	0.114665	+	0.993404i	$0.463421\pi$
$888$			41.3494i			1.38759i
$889$	−8.72499	−	21.0640i	−0.292627	−	0.706464i
$890$	29.2443	+	12.1134i	0.980271	+	0.406042i
$891$	−0.746474	+	1.80215i	−0.0250078	+	0.0603742i
$892$	−74.4385	+	74.4385i	−2.49238	+	2.49238i
$893$	10.0314	−	10.0314i	0.335689	−	0.335689i
$894$	−11.8760	+	28.6711i	−0.397192	+	0.958906i
$895$	22.7381	+	9.41842i	0.760050	+	0.314823i
$896$	4.86535	+	11.7460i	0.162540	+	0.392406i
$897$		−	6.31877i		−	0.210978i
$898$	75.3247	−	31.2005i	2.51362	−	1.04117i
$899$	−0.0543053	−	0.0543053i	−0.00181118	−	0.00181118i
$900$	0.306273			0.0102091
$901$		0			0
$902$	−20.6849			−0.688731
$903$	13.6389	+	13.6389i	0.453874	+	0.453874i
$904$	125.319	−	51.9090i	4.16806	−	1.72647i
$905$		−	43.7761i		−	1.45517i
$906$	16.2472	+	39.2242i	0.539777	+	1.30314i
$907$	−28.4394	−	11.7800i	−0.944314	−	0.391148i	−0.143223	−	0.989690i	$-0.545747\pi$
$907$	−28.4394	−	11.7800i	−0.944314	−	0.391148i	−0.801091	+	0.598543i	$0.795747\pi$
$908$	−9.38555	+	22.6587i	−0.311470	+	0.751956i
$909$	5.02840	−	5.02840i	0.166782	−	0.166782i
$910$	−12.6758	+	12.6758i	−0.420198	+	0.420198i
$911$	−2.75337	+	6.64723i	−0.0912234	+	0.220233i	−0.962905	−	0.269839i	$-0.913029\pi$
$911$	−2.75337	+	6.64723i	−0.0912234	+	0.220233i	0.871682	+	0.490072i	$0.163029\pi$
$912$	58.3164	+	24.1554i	1.93105	+	0.799867i
$913$	6.36721	+	15.3718i	0.210724	+	0.508733i
$914$		−	40.9532i		−	1.35461i
$915$	17.8348	−	7.38741i	0.589600	−	0.244220i
$916$	−6.43563	−	6.43563i	−0.212639	−	0.212639i
$917$	−17.6054			−0.581383
$918$		0			0
$919$	11.6873			0.385527			0.192764	−	0.981245i	$-0.438255\pi$
$919$	11.6873			0.385527			0.192764	+	0.981245i	$0.438255\pi$
$920$	−58.4165	−	58.4165i	−1.92594	−	1.92594i
$921$	13.1361	−	5.44114i	0.432848	−	0.179292i
$922$			102.565i			3.37779i
$923$	−3.08708	−	7.45287i	−0.101612	−	0.245314i
$924$	20.6470	+	8.55226i	0.679236	+	0.281349i
$925$	0.125843	−	0.303813i	0.00413770	−	0.00998930i
$926$	−42.4244	+	42.4244i	−1.39415	+	1.39415i
$927$	−6.52196	+	6.52196i	−0.214209	+	0.214209i
$928$	−0.820586	+	1.98107i	−0.0269371	+	0.0650318i
$929$	13.1032	+	5.42751i	0.429901	+	0.178071i	0.587132	−	0.809491i	$-0.300257\pi$
$929$	13.1032	+	5.42751i	0.429901	+	0.178071i	−0.157231	+	0.987562i	$0.550257\pi$
$930$	−0.996301	−	2.40528i	−0.0326700	−	0.0788723i
$931$			9.78497i			0.320689i
$932$	−6.83782	+	2.83232i	−0.223980	+	0.0927756i
$933$	7.32672	+	7.32672i	0.239866	+	0.239866i
$934$	−33.1003			−1.08308
$935$		0			0
$936$	−10.2853			−0.336186
$937$	18.0095	+	18.0095i	0.588344	+	0.588344i	0.937183	−	0.348839i	$-0.113424\pi$
$937$	18.0095	+	18.0095i	0.588344	+	0.588344i	−0.348839	+	0.937183i	$0.613424\pi$
$938$	−79.9670	+	33.1234i	−2.61101	+	1.08152i
$939$		−	17.4262i		−	0.568682i
$940$	10.0368	+	24.2310i	0.327365	+	0.790329i
$941$	−54.1244	−	22.4191i	−1.76440	−	0.730840i	−0.995845	−	0.0910612i	$-0.970974\pi$
$941$	−54.1244	−	22.4191i	−1.76440	−	0.730840i	−0.768559	−	0.639779i	$-0.779026\pi$
$942$	6.51286	−	15.7234i	0.212200	−	0.512297i
$943$	13.5923	−	13.5923i	0.442626	−	0.442626i
$944$	−88.4099	+	88.4099i	−2.87750	+	2.87750i
$945$	−1.96801	+	4.75119i	−0.0640193	+	0.154556i
$946$	39.5996	+	16.4027i	1.28750	+	0.533298i
$947$	−7.28794	−	17.5946i	−0.236826	−	0.571749i	0.760125	−	0.649777i	$-0.225138\pi$
$947$	−7.28794	−	17.5946i	−0.236826	−	0.571749i	−0.996951	+	0.0780278i	$0.975138\pi$
$948$			3.45688i			0.112274i
$949$	12.8956	−	5.34152i	0.418608	−	0.173393i
$950$	−0.686292	−	0.686292i	−0.0222662	−	0.0222662i
$951$	14.1753			0.459666
$952$		0			0
$953$	19.8922			0.644371			0.322185	−	0.946677i	$-0.395583\pi$
$953$	19.8922			0.644371			0.322185	+	0.946677i	$0.395583\pi$
$954$	1.35564	+	1.35564i	0.0438905	+	0.0438905i
$955$	−3.30442	+	1.36874i	−0.106929	+	0.0442913i
$956$		−	49.6300i		−	1.60515i
$957$	0.129007	+	0.311451i	0.00417022	+	0.0100678i
$958$	−90.7107	−	37.5736i	−2.93073	−	1.21395i
$959$	19.5476	−	47.1921i	0.631225	−	1.52391i
$960$	−18.0644	+	18.0644i	−0.583025	+	0.583025i
$961$	−21.7807	+	21.7807i	−0.702602	+	0.702602i
$962$	−7.09062	+	17.1183i	−0.228611	+	0.551915i
$963$	4.78804	+	1.98327i	0.154293	+	0.0639101i
$964$	−21.8163	−	52.6692i	−0.702656	−	1.69636i
$965$			9.94216i			0.320049i
$966$	−26.9386	+	11.1583i	−0.866736	+	0.359014i
$967$	−37.4986	−	37.4986i	−1.20587	−	1.20587i	−0.972352	−	0.233520i	$-0.924975\pi$
$967$	−37.4986	−	37.4986i	−1.20587	−	1.20587i	−0.233520	−	0.972352i	$-0.575025\pi$
$968$	−55.9706			−1.79896
$969$		0			0
$970$	−27.6288			−0.887108
$971$	2.13924	+	2.13924i	0.0686516	+	0.0686516i	0.740599	−	0.671947i	$-0.234542\pi$
$971$	2.13924	+	2.13924i	0.0686516	+	0.0686516i	−0.671947	+	0.740599i	$0.734542\pi$
$972$	−4.57379	+	1.89452i	−0.146704	+	0.0607669i
$973$		−	8.29543i		−	0.265939i
$974$	−1.65953	−	4.00646i	−0.0531747	−	0.128375i
$975$	0.0755708	+	0.0313025i	0.00242020	+	0.00100248i
$976$	35.2633	−	85.1332i	1.12875	−	2.72505i
$977$	−7.96654	+	7.96654i	−0.254872	+	0.254872i	−0.822965	−	0.568093i	$-0.807682\pi$
$977$	−7.96654	+	7.96654i	−0.254872	+	0.254872i	0.568093	+	0.822965i	$0.307682\pi$
$978$	31.1925	−	31.1925i	0.997425	−	0.997425i
$979$	4.03317	−	9.73695i	0.128901	−	0.311194i
$980$	−16.7130	−	6.92274i	−0.533876	−	0.221139i
$981$	−7.64423	−	18.4548i	−0.244062	−	0.589217i
$982$			11.3397i			0.361866i
$983$	−44.6770	+	18.5058i	−1.42498	+	0.590244i	−0.956106	−	0.293022i	$-0.905339\pi$
$983$	−44.6770	+	18.5058i	−1.42498	+	0.590244i	−0.468871	+	0.883267i	$0.655339\pi$
$984$	−22.1247	−	22.1247i	−0.705310	−	0.705310i
$985$	−16.4304			−0.523515
$986$		0			0
$987$	5.51722			0.175615
$988$	27.5422	+	27.5422i	0.876234	+	0.876234i
$989$	−36.7999	+	15.2430i	−1.17017	+	0.484699i
$990$			11.4280i			0.363204i
$991$	9.19984	+	22.2104i	0.292243	+	0.705536i	1.00000		0.000919961i	$-0.000292833\pi$
$991$	9.19984	+	22.2104i	0.292243	+	0.705536i	−0.707757	+	0.706456i	$0.750293\pi$
$992$	−5.09398	−	2.11000i	−0.161734	−	0.0669924i
$993$	4.15154	−	10.0227i	0.131745	−	0.318061i
$994$	−26.3221	+	26.3221i	−0.834887	+	0.834887i
$995$	11.3082	−	11.3082i	0.358493	−	0.358493i
$996$	−16.1598	+	39.0131i	−0.512041	+	1.23618i
$997$	24.3348	+	10.0798i	0.770691	+	0.319230i	0.733152	−	0.680065i	$-0.238048\pi$
$997$	24.3348	+	10.0798i	0.770691	+	0.319230i	0.0375385	+	0.999295i	$0.488048\pi$
$998$	−1.50860	−	3.64208i	−0.0477539	−	0.115288i
$999$			5.31548i			0.168174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.i.733.1		16
17.2	even	8		867.2.h.k.688.3		16
17.3	odd	16		867.2.a.k.1.1		4
17.4	even	4		867.2.h.k.712.4		16
17.5	odd	16		867.2.d.f.577.7		8
17.6	odd	16		51.2.e.a.4.1	✓	8
17.7	odd	16		867.2.e.g.829.4		8
17.8	even	8	inner	867.2.h.i.757.2		16
17.9	even	8	inner	867.2.h.i.757.1		16
17.10	odd	16		51.2.e.a.13.4	yes	8
17.11	odd	16		867.2.e.g.616.1		8
17.12	odd	16		867.2.d.f.577.8		8
17.13	even	4		867.2.h.k.712.3		16
17.14	odd	16		867.2.a.l.1.1		4
17.15	even	8		867.2.h.k.688.4		16
17.16	even	2	inner	867.2.h.i.733.2		16
51.14	even	16		2601.2.a.be.1.4		4
51.20	even	16		2601.2.a.bf.1.4		4
51.23	even	16		153.2.f.b.55.4		8
51.44	even	16		153.2.f.b.64.1		8
68.23	even	16		816.2.bd.e.769.4		8
68.27	even	16		816.2.bd.e.625.4		8
204.23	odd	16		2448.2.be.x.1585.1		8
204.95	odd	16		2448.2.be.x.1441.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.1	✓	8	17.6	odd	16
51.2.e.a.13.4	yes	8	17.10	odd	16
153.2.f.b.55.4		8	51.23	even	16
153.2.f.b.64.1		8	51.44	even	16
816.2.bd.e.625.4		8	68.27	even	16
816.2.bd.e.769.4		8	68.23	even	16
867.2.a.k.1.1		4	17.3	odd	16
867.2.a.l.1.1		4	17.14	odd	16
867.2.d.f.577.7		8	17.5	odd	16
867.2.d.f.577.8		8	17.12	odd	16
867.2.e.g.616.1		8	17.11	odd	16
867.2.e.g.829.4		8	17.7	odd	16
867.2.h.i.733.1		16	1.1	even	1	trivial
867.2.h.i.733.2		16	17.16	even	2	inner
867.2.h.i.757.1		16	17.9	even	8	inner
867.2.h.i.757.2		16	17.8	even	8	inner
867.2.h.k.688.3		16	17.2	even	8
867.2.h.k.688.4		16	17.15	even	8
867.2.h.k.712.3		16	17.13	even	4
867.2.h.k.712.4		16	17.4	even	4
2448.2.be.x.1441.1		8	204.95	odd	16
2448.2.be.x.1585.1		8	204.23	odd	16
2601.2.a.be.1.4		4	51.14	even	16
2601.2.a.bf.1.4		4	51.20	even	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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86422 - 1.86422i) q^{2} +(-0.923880 + 0.382683i) q^{3} +4.95063i q^{4} +(0.850396 + 2.05304i) q^{5} +(2.43572 + 1.00891i) q^{6} +(0.885616 - 2.13807i) q^{7} +(5.50062 - 5.50062i) q^{8} +(0.707107 - 0.707107i) q^{9} +(2.24199 - 5.41264i) q^{10} +(-1.80215 - 0.746474i) q^{11} +(-1.89452 - 4.57379i) q^{12} -1.32218i q^{13} +(-5.63681 + 2.33484i) q^{14} +(-1.57133 - 1.57133i) q^{15} -10.6075 q^{16} -2.63640 q^{18} +(4.20773 + 4.20773i) q^{19} +(-10.1638 + 4.21000i) q^{20} +2.31423i q^{21} +(1.96801 + 4.75119i) q^{22} +(-4.41527 - 1.82887i) q^{23} +(-2.97692 + 7.18691i) q^{24} +(0.0437455 - 0.0437455i) q^{25} +(-2.46483 + 2.46483i) q^{26} +(-0.382683 + 0.923880i) q^{27} +(10.5848 + 4.38436i) q^{28} +(0.0661363 + 0.159667i) q^{29} +5.85860i q^{30} +(-0.410556 + 0.170058i) q^{31} +(8.77343 + 8.77343i) q^{32} +1.95063 q^{33} +5.14265 q^{35} +(3.50062 + 3.50062i) q^{36} +(4.91086 - 2.03414i) q^{37} -15.6883i q^{38} +(0.505976 + 1.22153i) q^{39} +(15.9707 + 6.61528i) q^{40} +(-1.53924 + 3.71604i) q^{41} +(4.31423 - 4.31423i) q^{42} +(5.89351 - 5.89351i) q^{43} +(3.69552 - 8.92177i) q^{44} +(2.05304 + 0.850396i) q^{45} +(4.82163 + 11.6405i) q^{46} -2.38404i q^{47} +(9.80004 - 4.05931i) q^{48} +(1.16274 + 1.16274i) q^{49} -0.163102 q^{50} +6.54562 q^{52} +(-0.514201 - 0.514201i) q^{53} +(2.43572 - 1.00891i) q^{54} -4.33468i q^{55} +(-6.88926 - 16.6321i) q^{56} +(-5.49767 - 2.27721i) q^{57} +(0.174362 - 0.420947i) q^{58} +(8.33468 - 8.33468i) q^{59} +(7.77906 - 7.77906i) q^{60} +(-3.32438 + 8.02576i) q^{61} +(1.08239 + 0.448342i) q^{62} +(-0.885616 - 2.13807i) q^{63} -11.4963i q^{64} +(2.71448 - 1.12438i) q^{65} +(-3.63640 - 3.63640i) q^{66} +14.1866 q^{67} +4.77906 q^{69} +(-9.58704 - 9.58704i) q^{70} +(5.63681 - 2.33484i) q^{71} -7.77906i q^{72} +(4.03994 + 9.75327i) q^{73} +(-12.9470 - 5.36283i) q^{74} +(-0.0236749 + 0.0571563i) q^{75} +(-20.8309 + 20.8309i) q^{76} +(-3.19202 + 3.19202i) q^{77} +(1.33396 - 3.22046i) q^{78} +(-0.645118 - 0.267217i) q^{79} +(-9.02056 - 21.7776i) q^{80} -1.00000i q^{81} +(9.79700 - 4.05805i) q^{82} +(-6.03142 - 6.03142i) q^{83} -11.4569 q^{84} -21.9736 q^{86} +(-0.122204 - 0.122204i) q^{87} +(-14.0190 + 5.80687i) q^{88} +5.40297i q^{89} +(-2.24199 - 5.41264i) q^{90} +(-2.82691 - 1.17094i) q^{91} +(9.05404 - 21.8584i) q^{92} +(0.314226 - 0.314226i) q^{93} +(-4.44438 + 4.44438i) q^{94} +(-5.06039 + 12.2169i) q^{95} +(-11.4630 - 4.74815i) q^{96} +(-1.80471 - 4.35696i) q^{97} -4.33519i q^{98} +(-1.80215 + 0.746474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 32 q^{8} + 8 q^{15} - 24 q^{16} - 8 q^{18} + 32 q^{25} + 40 q^{26} + 16 q^{32} - 24 q^{33} + 16 q^{35} + 48 q^{42} + 48 q^{43} + 32 q^{49} + 120 q^{50} - 32 q^{52} + 16 q^{53} + 56 q^{59}+ \cdots - 48 q^{94}+O(q^{100}) \) 16 * q - 8 * q^2 + 32 * q^8 + 8 * q^15 - 24 * q^16 - 8 * q^18 + 32 * q^25 + 40 * q^26 + 16 * q^32 - 24 * q^33 + 16 * q^35 + 48 * q^42 + 48 * q^43 + 32 * q^49 + 120 * q^50 - 32 * q^52 + 16 * q^53 + 56 * q^59 + 24 * q^60 - 24 * q^66 - 16 * q^67 - 24 * q^69 - 64 * q^70 - 64 * q^76 - 40 * q^77 + 16 * q^83 - 96 * q^84 - 16 * q^86 + 8 * q^87 - 16 * q^93 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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