LMFDB - Embedded newform 867.2.h.k.688.3

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			688.3
Root			$0.467712 - 1.12916i$ of defining polynomial
Character	$\chi$	$=$	867.688
Dual form			867.2.h.k.712.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.86422 - 1.86422i) q^{2} +(-0.382683 + 0.923880i) q^{3} -4.95063i q^{4} +(-2.05304 - 0.850396i) q^{5} +(1.00891 + 2.43572i) q^{6} +(-2.13807 + 0.885616i) q^{7} +(-5.50062 - 5.50062i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-5.41264 + 2.24199i) q^{10} +(-0.746474 - 1.80215i) q^{11} +(4.57379 + 1.89452i) q^{12} +1.32218i q^{13} +(-2.33484 + 5.63681i) q^{14} +(1.57133 - 1.57133i) q^{15} -10.6075 q^{16} -2.63640 q^{18} +(-4.20773 + 4.20773i) q^{19} +(-4.21000 + 10.1638i) q^{20} -2.31423i q^{21} +(-4.75119 - 1.96801i) q^{22} +(-1.82887 - 4.41527i) q^{23} +(7.18691 - 2.97692i) q^{24} +(-0.0437455 - 0.0437455i) q^{25} +(2.46483 + 2.46483i) q^{26} +(0.923880 - 0.382683i) q^{27} +(4.38436 + 10.5848i) q^{28} +(-0.159667 - 0.0661363i) q^{29} -5.85860i q^{30} +(-0.170058 + 0.410556i) q^{31} +(-8.77343 + 8.77343i) q^{32} +1.95063 q^{33} +5.14265 q^{35} +(-3.50062 + 3.50062i) q^{36} +(2.03414 - 4.91086i) q^{37} +15.6883i q^{38} +(-1.22153 - 0.505976i) q^{39} +(6.61528 + 15.9707i) q^{40} +(3.71604 - 1.53924i) q^{41} +(-4.31423 - 4.31423i) q^{42} +(-5.89351 - 5.89351i) q^{43} +(-8.92177 + 3.69552i) q^{44} +(0.850396 + 2.05304i) q^{45} +(-11.6405 - 4.82163i) q^{46} +2.38404i q^{47} +(4.05931 - 9.80004i) q^{48} +(-1.16274 + 1.16274i) q^{49} -0.163102 q^{50} +6.54562 q^{52} +(0.514201 - 0.514201i) q^{53} +(1.00891 - 2.43572i) q^{54} +4.33468i q^{55} +(16.6321 + 6.88926i) q^{56} +(-2.27721 - 5.49767i) q^{57} +(-0.420947 + 0.174362i) q^{58} +(-8.33468 - 8.33468i) q^{59} +(-7.77906 - 7.77906i) q^{60} +(8.02576 - 3.32438i) q^{61} +(0.448342 + 1.08239i) q^{62} +(2.13807 + 0.885616i) q^{63} +11.4963i q^{64} +(1.12438 - 2.71448i) q^{65} +(3.63640 - 3.63640i) q^{66} +14.1866 q^{67} +4.77906 q^{69} +(9.58704 - 9.58704i) q^{70} +(2.33484 - 5.63681i) q^{71} +7.77906i q^{72} +(-9.75327 - 4.03994i) q^{73} +(-5.36283 - 12.9470i) q^{74} +(0.0571563 - 0.0236749i) q^{75} +(20.8309 + 20.8309i) q^{76} +(3.19202 + 3.19202i) q^{77} +(-3.22046 + 1.33396i) q^{78} +(-0.267217 - 0.645118i) q^{79} +(21.7776 + 9.02056i) q^{80} +1.00000i q^{81} +(4.05805 - 9.79700i) q^{82} +(6.03142 - 6.03142i) q^{83} -11.4569 q^{84} -21.9736 q^{86} +(0.122204 - 0.122204i) q^{87} +(-5.80687 + 14.0190i) q^{88} -5.40297i q^{89} +(5.41264 + 2.24199i) q^{90} +(-1.17094 - 2.82691i) q^{91} +(-21.8584 + 9.05404i) q^{92} +(-0.314226 - 0.314226i) q^{93} +(4.44438 + 4.44438i) q^{94} +(12.2169 - 5.06039i) q^{95} +(-4.74815 - 11.4630i) q^{96} +(4.35696 + 1.80471i) q^{97} +4.33519i q^{98} +(-0.746474 + 1.80215i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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	0.403004	−	0.915198i	$-0.367966\pi$
$2$	1.86422	−	1.86422i	1.31820	−	1.31820i	0.915198	−	0.403004i	$-0.132034\pi$
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		−	4.95063i		−	2.47532i
$5$	−2.05304	−	0.850396i	−0.918146	−	0.380309i	−0.126977	−	0.991906i	$-0.540527\pi$
$5$	−2.05304	−	0.850396i	−0.918146	−	0.380309i	−0.791169	+	0.611597i	$0.790527\pi$
$6$	1.00891	+	2.43572i	0.411885	+	0.994379i
$7$	−2.13807	+	0.885616i	−0.808113	+	0.334731i	−0.748201	−	0.663472i	$-0.769082\pi$
$7$	−2.13807	+	0.885616i	−0.808113	+	0.334731i	−0.0599122	+	0.998204i	$0.519082\pi$
$8$	−5.50062	−	5.50062i	−1.94476	−	1.94476i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−5.41264	+	2.24199i	−1.71163	+	0.708979i
$11$	−0.746474	−	1.80215i	−0.225070	−	0.543368i	0.770494	−	0.637447i	$-0.220009\pi$
$11$	−0.746474	−	1.80215i	−0.225070	−	0.543368i	−0.995565	+	0.0940788i	$0.970009\pi$
$12$	4.57379	+	1.89452i	1.32034	+	0.546902i
$13$			1.32218i			0.366706i	0.983047	+	0.183353i	$0.0586952\pi$
$13$			1.32218i			0.366706i	−0.983047	+	0.183353i	$0.941305\pi$
$14$	−2.33484	+	5.63681i	−0.624013	+	1.50650i
$15$	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	$-0.989144\pi$
$19$	−4.20773	+	4.20773i	−0.965320	+	0.965320i	0.0340987	+	0.999418i	$0.489144\pi$
$20$	−4.21000	+	10.1638i	−0.941384	+	2.27270i
$21$		−	2.31423i		−	0.505006i
$22$	−4.75119	−	1.96801i	−1.01296	−	0.419581i
$23$	−1.82887	−	4.41527i	−0.381345	−	0.920648i	−0.991706	−	0.128525i	$-0.958976\pi$
$23$	−1.82887	−	4.41527i	−0.381345	−	0.920648i	0.610361	−	0.792123i	$-0.291024\pi$
$24$	7.18691	−	2.97692i	1.46702	−	0.607661i
$25$	−0.0437455	−	0.0437455i	−0.00874910	−	0.00874910i
$26$	2.46483	+	2.46483i	0.483393	+	0.483393i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	4.38436	+	10.5848i	0.828566	+	2.00033i
$29$	−0.159667	−	0.0661363i	−0.0296494	−	0.0122812i	0.367809	−	0.929901i	$-0.380108\pi$
$29$	−0.159667	−	0.0661363i	−0.0296494	−	0.0122812i	−0.397459	+	0.917620i	$0.630108\pi$
$30$		−	5.85860i		−	1.06963i
$31$	−0.170058	+	0.410556i	−0.0305433	+	0.0737381i	−0.938415	−	0.345510i	$-0.887706\pi$
$31$	−0.170058	+	0.410556i	−0.0305433	+	0.0737381i	0.907872	+	0.419248i	$0.137706\pi$
$32$	−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
$37$	2.03414	−	4.91086i	0.334411	−	0.807340i	−0.663820	−	0.747892i	$-0.731066\pi$
$37$	2.03414	−	4.91086i	0.334411	−	0.807340i	0.998231	−	0.0594480i	$-0.0189340\pi$
$38$			15.6883i			2.54497i
$39$	−1.22153	−	0.505976i	−0.195602	−	0.0810210i
$40$	6.61528	+	15.9707i	1.04597	+	2.52519i
$41$	3.71604	−	1.53924i	0.580348	−	0.240388i	−0.0731438	−	0.997321i	$-0.523303\pi$
$41$	3.71604	−	1.53924i	0.580348	−	0.240388i	0.653492	+	0.756933i	$0.273303\pi$
$42$	−4.31423	−	4.31423i	−0.665700	−	0.665700i
$43$	−5.89351	−	5.89351i	−0.898751	−	0.898751i	0.0965746	−	0.995326i	$-0.469211\pi$
$43$	−5.89351	−	5.89351i	−0.898751	−	0.898751i	−0.995326	+	0.0965746i	$0.969211\pi$
$44$	−8.92177	+	3.69552i	−1.34501	+	0.557120i
$45$	0.850396	+	2.05304i	0.126770	+	0.306049i
$46$	−11.6405	−	4.82163i	−1.71629	−	0.710911i
$47$			2.38404i			0.347749i	0.984768	+	0.173874i	$0.0556286\pi$
$47$			2.38404i			0.347749i	−0.984768	+	0.173874i	$0.944371\pi$
$48$	4.05931	−	9.80004i	0.585911	−	1.41451i
$49$	−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	$-0.734096\pi$
$53$	0.514201	−	0.514201i	0.0706309	−	0.0706309i	0.741540	+	0.670909i	$0.234096\pi$
$54$	1.00891	−	2.43572i	0.137295	−	0.331460i
$55$			4.33468i			0.584488i
$56$	16.6321	+	6.88926i	2.22256	+	0.920616i
$57$	−2.27721	−	5.49767i	−0.301624	−	0.728184i
$58$	−0.420947	+	0.174362i	−0.0552730	+	0.0228948i
$59$	−8.33468	−	8.33468i	−1.08508	−	1.08508i	−0.996027	−	0.0890557i	$-0.971615\pi$
$59$	−8.33468	−	8.33468i	−1.08508	−	1.08508i	−0.0890557	−	0.996027i	$-0.528385\pi$
$60$	−7.77906	−	7.77906i	−1.00427	−	1.00427i
$61$	8.02576	−	3.32438i	1.02759	−	0.425643i	0.195750	−	0.980654i	$-0.437286\pi$
$61$	8.02576	−	3.32438i	1.02759	−	0.425643i	0.831843	+	0.555011i	$0.187286\pi$
$62$	0.448342	+	1.08239i	0.0569394	+	0.137464i
$63$	2.13807	+	0.885616i	0.269371	+	0.111577i
$64$			11.4963i			1.43703i
$65$	1.12438	−	2.71448i	0.139462	−	0.336690i
$66$	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
$71$	2.33484	−	5.63681i	0.277095	−	0.668966i	−0.722658	−	0.691206i	$-0.757080\pi$
$71$	2.33484	−	5.63681i	0.277095	−	0.668966i	0.999753	+	0.0222399i	$0.00707976\pi$
$72$			7.77906i			0.916771i
$73$	−9.75327	−	4.03994i	−1.14153	−	0.472839i	−0.269848	−	0.962903i	$-0.586973\pi$
$73$	−9.75327	−	4.03994i	−1.14153	−	0.472839i	−0.871686	+	0.490064i	$0.836973\pi$
$74$	−5.36283	−	12.9470i	−0.623416	−	1.50506i
$75$	0.0571563	−	0.0236749i	0.00659984	−	0.00273374i
$76$	20.8309	+	20.8309i	2.38947	+	2.38947i
$77$	3.19202	+	3.19202i	0.363765	+	0.363765i
$78$	−3.22046	+	1.33396i	−0.364645	+	0.151041i
$79$	−0.267217	−	0.645118i	−0.0300642	−	0.0725814i	0.908134	−	0.418679i	$-0.137507\pi$
$79$	−0.267217	−	0.645118i	−0.0300642	−	0.0725814i	−0.938199	+	0.346097i	$0.887507\pi$
$80$	21.7776	+	9.02056i	2.43481	+	1.00853i
$81$			1.00000i			0.111111i
$82$	4.05805	−	9.79700i	0.448136	−	1.08190i
$83$	6.03142	−	6.03142i	0.662034	−	0.662034i	−0.293825	−	0.955859i	$-0.594928\pi$
$83$	6.03142	−	6.03142i	0.662034	−	0.662034i	0.955859	+	0.293825i	$0.0949283\pi$
$84$	−11.4569			−1.25005
$85$		0			0
$86$	−21.9736			−2.36947
$87$	0.122204	−	0.122204i	0.0131016	−	0.0131016i
$88$	−5.80687	+	14.0190i	−0.619014	+	1.49443i
$89$		−	5.40297i		−	0.572713i	−0.958123	−	0.286357i	$-0.907556\pi$
$89$		−	5.40297i		−	0.572713i	0.958123	−	0.286357i	$-0.0924442\pi$
$90$	5.41264	+	2.24199i	0.570542	+	0.236326i
$91$	−1.17094	−	2.82691i	−0.122748	−	0.296340i
$92$	−21.8584	+	9.05404i	−2.27889	+	0.943949i
$93$	−0.314226	−	0.314226i	−0.0325837	−	0.0325837i
$94$	4.44438	+	4.44438i	0.458403	+	0.458403i
$95$	12.2169	−	5.06039i	1.25342	−	0.519185i
$96$	−4.74815	−	11.4630i	−0.484606	−	1.16994i
$97$	4.35696	+	1.80471i	0.442383	+	0.183241i	0.592745	−	0.805390i	$-0.298044\pi$
$97$	4.35696	+	1.80471i	0.442383	+	0.183241i	−0.150363	+	0.988631i	$0.548044\pi$
$98$			4.33519i			0.437921i
$99$	−0.746474	+	1.80215i	−0.0750235	+	0.181123i
$100$	−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
$105$	−1.96801	+	4.75119i	−0.192058	+	0.463669i
$106$		−	1.91717i		−	0.186212i
$107$	−4.78804	−	1.98327i	−0.462878	−	0.191730i	0.139043	−	0.990286i	$-0.455598\pi$
$107$	−4.78804	−	1.98327i	−0.462878	−	0.191730i	−0.601920	+	0.798556i	$0.705598\pi$
$108$	−1.89452	−	4.57379i	−0.182301	−	0.440113i
$109$	−18.4548	+	7.64423i	−1.76765	+	0.732185i	−0.772367	+	0.635177i	$0.780927\pi$
$109$	−18.4548	+	7.64423i	−1.76765	+	0.732185i	−0.995284	+	0.0970083i	$0.969073\pi$
$110$	8.08079	+	8.08079i	0.770473	+	0.770473i
$111$	3.75861	+	3.75861i	0.356751	+	0.356751i
$112$	22.6795	−	9.39416i	2.14301	−	0.887665i
$113$	6.67291	+	16.1098i	0.627735	+	1.51549i	0.842431	+	0.538805i	$0.181124\pi$
$113$	6.67291	+	16.1098i	0.627735	+	1.51549i	−0.214696	+	0.976681i	$0.568876\pi$
$114$	−14.4941	−	6.00364i	−1.35749	−	0.562293i
$115$			10.6200i			0.990318i
$116$	−0.327416	+	0.790453i	−0.0303998	+	0.0733917i
$117$	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
$122$	8.76441	−	21.1592i	0.793493	−	1.91566i
$123$			4.02222i			0.362671i
$124$	2.03251	+	0.841894i	0.182525	+	0.0756043i
$125$	4.30459	+	10.3922i	0.385014	+	0.929506i
$126$	5.63681	−	2.33484i	0.502167	−	0.208004i
$127$	−6.96634	−	6.96634i	−0.618163	−	0.618163i	0.326897	−	0.945060i	$-0.393997\pi$
$127$	−6.96634	−	6.96634i	−0.618163	−	0.618163i	−0.945060	+	0.326897i	$0.893997\pi$
$128$	3.88467	+	3.88467i	0.343359	+	0.343359i
$129$	7.70024	−	3.18954i	0.677968	−	0.280824i
$130$	−2.96431	−	7.15647i	−0.259987	−	0.627664i
$131$	7.02840	+	2.91126i	0.614074	+	0.254358i	0.667969	−	0.744189i	$-0.267164\pi$
$131$	7.02840	+	2.91126i	0.614074	+	0.254358i	−0.0538952	+	0.998547i	$0.517164\pi$
$132$		−	9.65685i		−	0.840521i
$133$	5.26997	−	12.7228i	0.456965	−	1.10321i
$134$	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
$139$	1.37174	−	3.31168i	0.116350	−	0.280893i	−0.854967	−	0.518682i	$-0.826423\pi$
$139$	1.37174	−	3.31168i	0.116350	−	0.280893i	0.971317	+	0.237789i	$0.0764228\pi$
$140$		−	25.4594i		−	2.15171i
$141$	−2.20257	−	0.912334i	−0.185490	−	0.0768324i
$142$	−6.15559	−	14.8609i	−0.516566	−	1.24710i
$143$	2.38276	−	0.986972i	0.199257	−	0.0825348i
$144$	7.50062	+	7.50062i	0.625052	+	0.625052i
$145$	0.271560	+	0.271560i	0.0225519	+	0.0225519i
$146$	−25.7136	+	10.6509i	−2.12807	+	0.881476i
$147$	−0.629268	−	1.51919i	−0.0519012	−	0.125301i
$148$	−24.3119	−	10.0703i	−1.99842	−	0.827773i
$149$		−	11.7711i		−	0.964327i	−0.876081	−	0.482163i	$-0.839851\pi$
$149$		−	11.7711i		−	0.964327i	0.876081	−	0.482163i	$-0.160149\pi$
$150$	0.0624166	−	0.150687i	0.00509630	−	0.0123035i
$151$	−11.3871	+	11.3871i	−0.926666	+	0.926666i	−0.997489	−	0.0708230i	$-0.977437\pi$
$151$	−11.3871	+	11.3871i	−0.926666	+	0.926666i	0.0708230	+	0.997489i	$0.477437\pi$
$152$	46.2903			3.75464
$153$		0			0
$154$	11.9013			0.959031
$155$	0.698270	−	0.698270i	0.0560864	−	0.0560864i
$156$	−2.50490	+	6.04736i	−0.200553	+	0.484177i
$157$			6.45535i			0.515193i	0.966253	+	0.257597i	$0.0829306\pi$
$157$			6.45535i			0.515193i	−0.966253	+	0.257597i	$0.917069\pi$
$158$	−1.70079	−	0.704491i	−0.135308	−	0.0560463i
$159$	0.278284	+	0.671836i	0.0220693	+	0.0532801i
$160$	25.4731	−	10.5513i	2.01382	−	0.834153i
$161$	7.82047	+	7.82047i	0.616340	+	0.616340i
$162$	1.86422	+	1.86422i	0.146467	+	0.146467i
$163$	−15.4585	+	6.40313i	−1.21081	+	0.501532i	−0.894475	−	0.447117i	$-0.852451\pi$
$163$	−15.4585	+	6.40313i	−1.21081	+	0.501532i	−0.316330	+	0.948649i	$0.602451\pi$
$164$	−7.62019	−	18.3968i	−0.595037	−	1.43655i
$165$	−4.00472	−	1.65881i	−0.311767	−	0.129138i
$166$		−	22.4878i		−	1.74539i
$167$	−0.614202	+	1.48281i	−0.0475284	+	0.114744i	−0.945861	−	0.324573i	$-0.894779\pi$
$167$	−0.614202	+	1.48281i	−0.0475284	+	0.114744i	0.898332	+	0.439317i	$0.144779\pi$
$168$	−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
$173$	−6.55764	+	15.8316i	−0.498568	+	1.20365i	0.451686	+	0.892177i	$0.350823\pi$
$173$	−6.55764	+	15.8316i	−0.498568	+	1.20365i	−0.950255	+	0.311474i	$0.899177\pi$
$174$		−	0.455630i		−	0.0345412i
$175$	0.132273	+	0.0547891i	0.00999886	+	0.00414166i
$176$	7.91821	+	19.1163i	0.596858	+	1.44094i
$177$	10.8898	−	4.51069i	0.818526	−	0.339045i
$178$	−10.0723	−	10.0723i	−0.754952	−	0.754952i
$179$	−7.83144	−	7.83144i	−0.585350	−	0.585350i	0.351019	−	0.936368i	$-0.385835\pi$
$179$	−7.83144	−	7.83144i	−0.585350	−	0.585350i	−0.936368	+	0.351019i	$0.885835\pi$
$180$	10.1638	−	4.21000i	0.757567	−	0.313795i
$181$	−7.53868	−	18.2000i	−0.560346	−	1.35279i	−0.909490	−	0.415725i	$-0.863528\pi$
$181$	−7.53868	−	18.2000i	−0.560346	−	1.35279i	0.349145	−	0.937069i	$-0.386472\pi$
$182$	−7.45287	−	3.08708i	−0.552443	−	0.228830i
$183$			8.68702i			0.642163i
$184$	−14.2269	+	34.3467i	−1.04882	+	2.53207i
$185$	−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
$190$	13.3412	−	32.2086i	0.967875	−	2.33666i
$191$		−	1.60953i		−	0.116461i	−0.998303	−	0.0582307i	$-0.981454\pi$
$191$		−	1.60953i		−	0.116461i	0.998303	−	0.0582307i	$-0.0185459\pi$
$192$	−10.6212	−	4.39942i	−0.766516	−	0.317501i
$193$	1.71214	+	4.13347i	0.123242	+	0.297534i	0.973445	−	0.228923i	$-0.0735203\pi$
$193$	1.71214	+	4.13347i	0.123242	+	0.297534i	−0.850202	+	0.526456i	$0.823520\pi$
$194$	11.4867	−	4.75796i	0.824698	−	0.341601i
$195$	2.07757	+	2.07757i	0.148778	+	0.148778i
$196$	5.75628	+	5.75628i	0.411163	+	0.411163i
$197$	6.83095	−	2.82947i	0.486685	−	0.201591i	−0.125828	−	0.992052i	$-0.540159\pi$
$197$	6.83095	−	2.82947i	0.486685	−	0.201591i	0.612513	+	0.790461i	$0.290159\pi$
$198$	1.96801	+	4.75119i	0.139860	+	0.337653i
$199$	6.64876	+	2.75401i	0.471318	+	0.195226i	0.605684	−	0.795705i	$-0.292900\pi$
$199$	6.64876	+	2.75401i	0.471318	+	0.195226i	−0.134366	+	0.990932i	$0.542900\pi$
$200$			0.481255i			0.0340299i
$201$	−5.42896	+	13.1067i	−0.382930	+	0.924474i
$202$	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
$207$	−1.82887	+	4.41527i	−0.127115	+	0.306883i
$208$		−	14.0250i		−	0.972458i
$209$	10.7239	+	4.44199i	0.741789	+	0.307259i
$210$	5.18847	+	12.5261i	0.358038	+	0.864381i
$211$	12.3971	−	5.13503i	0.853449	−	0.353510i	0.0873068	−	0.996181i	$-0.472174\pi$
$211$	12.3971	−	5.13503i	0.853449	−	0.353510i	0.766142	+	0.642671i	$0.222174\pi$
$212$	−2.54562	−	2.54562i	−0.174834	−	0.174834i
$213$	4.31423	+	4.31423i	0.295606	+	0.295606i
$214$	−12.6232	+	5.22871i	−0.862906	+	0.357427i
$215$	7.08777	+	17.1114i	0.483382	+	1.16699i
$216$	−7.18691	−	2.97692i	−0.489007	−	0.202554i
$217$		−	1.02840i		−	0.0698125i
$218$	−20.1533	+	48.6544i	−1.36495	+	3.29529i
$219$	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	−0.00691960	+	0.999976i	$0.502203\pi$
$223$	−15.0362	+	15.0362i	−1.00690	+	1.00690i	−0.999976	+	0.00691960i	$0.997797\pi$
$224$	10.9883	−	26.5281i	0.734186	−	1.77248i
$225$			0.0618655i			0.00412437i
$226$	42.4721	+	17.5925i	2.82520	+	1.17024i
$227$	1.89583	+	4.57694i	0.125831	+	0.303782i	0.974223	−	0.225585i	$-0.0724294\pi$
$227$	1.89583	+	4.57694i	0.125831	+	0.303782i	−0.848393	+	0.529367i	$0.822429\pi$
$228$	−27.2169	+	11.2736i	−1.80248	+	0.746613i
$229$	1.29996	+	1.29996i	0.0859039	+	0.0859039i	0.748753	−	0.662849i	$-0.230653\pi$
$229$	1.29996	+	1.29996i	0.0859039	+	0.0859039i	−0.662849	+	0.748753i	$0.730653\pi$
$230$	19.7980	+	19.7980i	1.30544	+	1.30544i
$231$	−4.17058	+	1.72751i	−0.274404	+	0.113662i
$232$	0.514478	+	1.24206i	0.0337771	+	0.0815452i
$233$	−1.38120	−	0.572112i	−0.0904855	−	0.0374803i	0.336982	−	0.941511i	$-0.390594\pi$
$233$	−1.38120	−	0.572112i	−0.0904855	−	0.0374803i	−0.427467	+	0.904031i	$0.640594\pi$
$234$		−	3.48580i		−	0.227874i
$235$	2.02738	−	4.89453i	0.132252	−	0.319284i
$236$	−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
$241$	−4.40677	+	10.6389i	−0.283865	+	0.685311i	−0.999919	−	0.0127340i	$-0.995947\pi$
$241$	−4.40677	+	10.6389i	−0.283865	+	0.685311i	0.716054	+	0.698045i	$0.245947\pi$
$242$		−	18.9690i		−	1.21938i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	−16.4578	−	39.7326i	−1.05360	−	2.54362i
$245$	3.37593	−	1.39835i	0.215680	−	0.0893376i
$246$	7.49830	+	7.49830i	0.478074	+	0.478074i
$247$	−5.56337	−	5.56337i	−0.353989	−	0.353989i
$248$	3.19374	−	1.32289i	0.202803	−	0.0840036i
$249$	3.26418	+	7.88043i	0.206859	+	0.499402i
$250$	27.3980	+	11.3486i	1.73280	+	0.717751i
$251$		−	0.940179i		−	0.0593436i	−0.999560	−	0.0296718i	$-0.990554\pi$
$251$		−	0.940179i		−	0.0593436i	0.999560	−	0.0296718i	$-0.00944621\pi$
$252$	4.38436	−	10.5848i	0.276189	−	0.666778i
$253$	−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	$-0.771412\pi$
$257$	−1.52392	+	1.52392i	−0.0950596	+	0.0950596i	0.657978	+	0.753037i	$0.271412\pi$
$258$	8.40892	−	20.3009i	0.523517	−	1.26388i
$259$			12.3012i			0.764360i
$260$	−13.4384	−	5.56637i	−0.833414	−	0.345211i
$261$	0.0661363	+	0.159667i	0.00409373	+	0.00988314i
$262$	18.5297	−	7.67526i	1.14477	−	0.474179i
$263$	−9.29326	−	9.29326i	−0.573047	−	0.573047i	0.359932	−	0.932979i	$-0.382800\pi$
$263$	−9.29326	−	9.29326i	−0.573047	−	0.573047i	−0.932979	+	0.359932i	$0.882800\pi$
$264$	−10.7297	−	10.7297i	−0.660367	−	0.660367i
$265$	−1.49295	+	0.618399i	−0.0917111	+	0.0379880i
$266$	−13.8938	−	33.5426i	−0.851883	−	2.05663i
$267$	4.99169	+	2.06763i	0.305486	+	0.126537i
$268$		−	70.2325i		−	4.29013i
$269$	5.80697	−	14.0193i	0.354057	−	0.854770i	−0.642053	−	0.766660i	$-0.721917\pi$
$269$	5.80697	−	14.0193i	0.354057	−	0.854770i	0.996111	−	0.0881101i	$-0.0280827\pi$
$270$	−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
$275$	−0.0461810	+	0.111491i	−0.00278482	+	0.00672315i
$276$		−	23.6594i		−	1.42413i
$277$	−24.8547	−	10.2951i	−1.49337	−	0.618575i	−0.521325	−	0.853358i	$-0.674562\pi$
$277$	−24.8547	−	10.2951i	−1.49337	−	0.618575i	−0.972048	+	0.234783i	$0.924562\pi$
$278$	−3.61647	−	8.73093i	−0.216901	−	0.523646i
$279$	0.410556	−	0.170058i	0.0245794	−	0.0101811i
$280$	−28.2878	−	28.2878i	−1.69052	−	1.69052i
$281$	15.7217	+	15.7217i	0.937880	+	0.937880i	0.998180	−	0.0603001i	$-0.0192058\pi$
$281$	15.7217	+	15.7217i	0.937880	+	0.937880i	−0.0603001	+	0.998180i	$0.519206\pi$
$282$	−5.80687	+	2.40528i	−0.345794	+	0.143232i
$283$	−9.16820	−	22.1340i	−0.544993	−	1.31573i	−0.921162	−	0.389179i	$-0.872759\pi$
$283$	−9.16820	−	22.1340i	−0.544993	−	1.31573i	0.376169	−	0.926551i	$-0.377241\pi$
$284$	−27.9058	−	11.5589i	−1.65590	−	0.685897i
$285$			13.2234i			0.783289i
$286$	2.60206	−	6.28193i	0.153863	−	0.371458i
$287$	−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
$292$	−20.0002	+	48.2849i	−1.17043	+	2.82566i
$293$		−	7.44387i		−	0.434875i	−0.976074	−	0.217438i	$-0.930230\pi$
$293$		−	7.44387i		−	0.434875i	0.976074	−	0.217438i	$-0.0697699\pi$
$294$	−4.00520	−	1.65901i	−0.233588	−	0.0967552i
$295$	10.0236	+	24.1992i	0.583598	+	1.40893i
$296$	−38.2019	+	15.8237i	−2.22044	+	0.919735i
$297$	−1.37930	−	1.37930i	−0.0800354	−	0.0800354i
$298$	−21.9439	−	21.9439i	−1.27118	−	1.27118i
$299$	5.83778	−	2.41809i	0.337608	−	0.139842i
$300$	−0.117206	−	0.282960i	−0.00676687	−	0.0163367i
$301$	17.8201	+	7.38132i	1.02713	+	0.425452i
$302$			42.4560i			2.44307i
$303$	−2.72135	+	6.56992i	−0.156338	+	0.377432i
$304$	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
$309$	3.52966	−	8.52135i	0.200795	−	0.484763i
$310$		−	2.60346i		−	0.147867i
$311$	9.57282	+	3.96519i	0.542825	+	0.224846i	0.637210	−	0.770690i	$-0.280088\pi$
$311$	9.57282	+	3.96519i	0.542825	+	0.224846i	−0.0943849	+	0.995536i	$0.530088\pi$
$312$	3.93602	+	9.50238i	0.222833	+	0.537967i
$313$	16.0997	−	6.66872i	0.910009	−	0.376938i	0.121949	−	0.992536i	$-0.461086\pi$
$313$	16.0997	−	6.66872i	0.910009	−	0.376938i	0.788060	+	0.615598i	$0.211086\pi$
$314$	12.0342	+	12.0342i	0.679129	+	0.679129i
$315$	−3.63640	−	3.63640i	−0.204888	−	0.204888i
$316$	−3.19374	+	1.32289i	−0.179662	+	0.0744184i
$317$	−5.42466	−	13.0963i	−0.304679	−	0.735561i	−0.999860	−	0.0167260i	$-0.994676\pi$
$317$	−5.42466	−	13.0963i	−0.304679	−	0.735561i	0.695181	−	0.718835i	$-0.255324\pi$
$318$	1.77123	+	0.733668i	0.0993258	+	0.0411421i
$319$			0.337113i			0.0188747i
$320$	9.77636	−	23.6022i	0.546515	−	1.31940i
$321$	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
$326$	−16.8812	+	40.7549i	−0.934966	+	2.25721i
$327$		−	19.9753i		−	1.10464i
$328$	−28.9073	−	11.9738i	−1.59614	−	0.661143i
$329$	−2.11135	−	5.09724i	−0.116402	−	0.281020i
$330$	−10.5581	+	4.37329i	−0.581202	+	0.240742i
$331$	7.67104	+	7.67104i	0.421638	+	0.421638i	0.885768	−	0.464129i	$-0.153633\pi$
$331$	7.67104	+	7.67104i	0.421638	+	0.421638i	−0.464129	+	0.885768i	$0.653633\pi$
$332$	−29.8593	−	29.8593i	−1.63874	−	1.63874i
$333$	−4.91086	+	2.03414i	−0.269113	+	0.111470i
$334$	1.61928	+	3.90930i	0.0886033	+	0.213907i
$335$	−29.1256	−	12.0642i	−1.59130	−	0.659138i
$336$			24.5481i			1.33921i
$337$	3.75707	−	9.07037i	0.204661	−	0.494095i	−0.787906	−	0.615795i	$-0.788835\pi$
$337$	3.75707	−	9.07037i	0.204661	−	0.494095i	0.992567	+	0.121701i	$0.0388348\pi$
$338$	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
$343$	7.65558	−	18.4822i	0.413363	−	0.997945i
$344$			64.8359i			3.49572i
$345$	−9.81158	−	4.06409i	−0.528238	−	0.218803i
$346$	17.2886	+	41.7384i	0.929441	+	2.24387i
$347$	−24.0642	+	9.96773i	−1.29184	+	0.535096i	−0.919532	−	0.393015i	$-0.871432\pi$
$347$	−24.0642	+	9.96773i	−1.29184	+	0.535096i	−0.372303	+	0.928111i	$0.621432\pi$
$348$	−0.604986	−	0.604986i	−0.0324307	−	0.0324307i
$349$	13.1952	+	13.1952i	0.706325	+	0.706325i	0.965760	−	0.259436i	$-0.0835365\pi$
$349$	13.1952	+	13.1952i	0.706325	+	0.706325i	−0.259436	+	0.965760i	$0.583537\pi$
$350$	0.348724	−	0.144446i	0.0186401	−	0.00772097i
$351$	0.505976	+	1.22153i	0.0270070	+	0.0652007i
$352$	22.3602	+	9.26189i	1.19180	+	0.493660i
$353$			11.8339i			0.629857i	0.949115	+	0.314929i	$0.101981\pi$
$353$			11.8339i			0.629857i	−0.949115	+	0.314929i	$0.898019\pi$
$354$	11.8920	−	28.7099i	0.632053	−	1.52591i
$355$	−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	$-0.628288\pi$
$359$	9.99796	−	9.99796i	0.527672	−	0.527672i	0.919878	+	0.392206i	$0.128288\pi$
$360$	6.61528	−	15.9707i	0.348656	−	0.841730i
$361$		−	16.4100i		−	0.863685i
$362$	−47.9825	−	19.8750i	−2.52191	−	1.04461i
$363$	2.75342	+	6.64735i	0.144517	+	0.348895i
$364$	−13.9950	+	5.79691i	−0.733536	+	0.303840i
$365$	16.5883	+	16.5883i	0.868271	+	0.868271i
$366$	16.1945	+	16.1945i	0.846501	+	0.846501i
$367$	3.44017	−	1.42497i	0.179576	−	0.0743827i	−0.291084	−	0.956697i	$-0.594016\pi$
$367$	3.44017	−	1.42497i	0.179576	−	0.0743827i	0.470660	+	0.882315i	$0.344016\pi$
$368$	19.3997	+	46.8350i	1.01128	+	2.44144i
$369$	−3.71604	−	1.53924i	−0.193449	−	0.0801294i
$370$			31.1412i			1.61896i
$371$	−0.644011	+	1.55478i	−0.0334354	+	0.0807202i
$372$	−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
$377$	0.0874440	−	0.211108i	0.00450359	−	0.0108726i
$378$			6.10124i			0.313814i
$379$	33.3992	+	13.8344i	1.71560	+	0.710626i	0.999926	+	0.0121949i	$0.00388185\pi$
$379$	33.3992	+	13.8344i	1.71560	+	0.710626i	0.715677	+	0.698431i	$0.246118\pi$
$380$	−25.0521	−	60.4812i	−1.28515	−	3.10262i
$381$	9.10196	−	3.77016i	0.466308	−	0.193151i
$382$	−3.00052	−	3.00052i	−0.153520	−	0.153520i
$383$	11.5606	+	11.5606i	0.590720	+	0.590720i	0.937826	−	0.347106i	$-0.112836\pi$
$383$	11.5606	+	11.5606i	0.590720	+	0.590720i	−0.347106	+	0.937826i	$0.612836\pi$
$384$	−5.07556	+	2.10237i	−0.259011	+	0.107286i
$385$	−3.83886	−	9.26782i	−0.195646	−	0.472332i
$386$	10.8975	+	4.51389i	0.554668	+	0.229751i
$387$			8.33468i			0.423675i
$388$	8.93447	−	21.5697i	0.453579	−	1.09504i
$389$	−11.6342	+	11.6342i	−0.589880	+	0.589880i	−0.937599	−	0.347719i	$-0.886956\pi$
$389$	−11.6342	+	11.6342i	−0.589880	+	0.589880i	0.347719	+	0.937599i	$0.386956\pi$
$390$	7.74611			0.392240
$391$		0			0
$392$	12.7916			0.646071
$393$	−5.37930	+	5.37930i	−0.271350	+	0.271350i
$394$	7.45963	−	18.0091i	0.375811	−	0.907288i
$395$			1.55169i			0.0780740i
$396$	8.92177	+	3.69552i	0.448336	+	0.185707i
$397$	−13.9529	−	33.6852i	−0.700275	−	1.69061i	−0.722978	−	0.690871i	$-0.757227\pi$
$397$	−13.9529	−	33.6852i	−0.700275	−	1.69061i	0.0227033	−	0.999742i	$-0.492773\pi$
$398$	17.5288	−	7.26068i	0.878641	−	0.363945i
$399$	9.73764	+	9.73764i	0.487492	+	0.487492i
$400$	0.464030	+	0.464030i	0.0232015	+	0.0232015i
$401$	−8.94230	+	3.70402i	−0.446557	+	0.184970i	−0.594618	−	0.804008i	$-0.702697\pi$
$401$	−8.94230	+	3.70402i	−0.446557	+	0.184970i	0.148061	+	0.988978i	$0.452697\pi$
$402$	14.3129	+	34.5545i	0.713865	+	1.72342i
$403$	−0.542829	−	0.224847i	−0.0270402	−	0.0112004i
$404$		−	35.2051i		−	1.75152i
$405$	0.850396	−	2.05304i	0.0422565	−	0.102016i
$406$	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
$411$	−8.44671	+	20.3922i	−0.416645	+	1.00587i
$412$			45.6619i			2.24960i
$413$	25.2014	+	10.4388i	1.24008	+	0.513658i
$414$	4.82163	+	11.6405i	0.236970	+	0.572097i
$415$	−17.5118	+	7.25363i	−0.859621	+	0.356067i
$416$	−11.6000	−	11.6000i	−0.568739	−	0.568739i
$417$	2.53465	+	2.53465i	0.124122	+	0.124122i
$418$	28.2726	−	11.7109i	1.38286	−	0.572798i
$419$	10.0746	+	24.3222i	0.492177	+	1.18822i	0.953610	+	0.301045i	$0.0973353\pi$
$419$	10.0746	+	24.3222i	0.492177	+	1.18822i	−0.461434	+	0.887175i	$0.652665\pi$
$420$	23.5214	+	9.74288i	1.14773	+	0.475404i
$421$		−	6.61089i		−	0.322195i	−0.986938	−	0.161098i	$-0.948497\pi$
$421$		−	6.61089i		−	0.322195i	0.986938	−	0.161098i	$-0.0515034\pi$
$422$	13.5380	−	32.6837i	0.659020	−	1.59102i
$423$	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
$428$	−9.81845	+	23.7038i	−0.474593	+	1.14577i
$429$			2.57908i			0.124519i
$430$	45.1126	+	18.6862i	2.17552	+	0.901131i
$431$	10.7634	+	25.9852i	0.518457	+	1.25167i	0.938851	+	0.344324i	$0.111892\pi$
$431$	10.7634	+	25.9852i	0.518457	+	1.25167i	−0.420394	+	0.907342i	$0.638108\pi$
$432$	−9.80004	+	4.05931i	−0.471505	+	0.195304i
$433$	12.1267	+	12.1267i	0.582770	+	0.582770i	0.935664	−	0.352893i	$-0.114802\pi$
$433$	12.1267	+	12.1267i	0.582770	+	0.582770i	−0.352893	+	0.935664i	$0.614802\pi$
$434$	−1.91717	−	1.91717i	−0.0920270	−	0.0920270i
$435$	−0.354811	+	0.146967i	−0.0170119	+	0.00704655i
$436$	37.8438	+	91.3630i	1.81239	+	4.37549i
$437$	26.2737	+	10.8829i	1.25684	+	0.520600i
$438$		−	27.8322i		−	1.32987i
$439$	−3.14756	+	7.59888i	−0.150225	+	0.362675i	−0.981021	−	0.193902i	$-0.937886\pi$
$439$	−3.14756	+	7.59888i	−0.150225	+	0.362675i	0.830796	+	0.556577i	$0.187886\pi$
$440$	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
$445$	−4.59466	+	11.0925i	−0.217808	+	0.525835i
$446$			56.0614i			2.65458i
$447$	10.8751	+	4.50461i	0.514374	+	0.213061i
$448$	−10.1813	−	24.5797i	−0.481019	−	1.16128i
$449$	28.5710	−	11.8345i	1.34835	−	0.558504i	0.412516	−	0.910950i	$-0.364650\pi$
$449$	28.5710	−	11.8345i	1.34835	−	0.558504i	0.935832	+	0.352446i	$0.114650\pi$
$450$	0.115331	+	0.115331i	0.00543675	+	0.00543675i
$451$	−5.54786	−	5.54786i	−0.261239	−	0.261239i
$452$	79.7539	−	33.0351i	3.75131	−	1.55384i
$453$	−6.16263	−	14.8779i	−0.289546	−	0.699025i
$454$	12.0667	+	4.99817i	0.566316	+	0.234576i
$455$			6.79951i			0.318766i
$456$	−17.7145	+	42.7667i	−0.829559	+	2.00273i
$457$	−10.9840	+	10.9840i	−0.513810	+	0.513810i	−0.915692	−	0.401881i	$-0.868356\pi$
$457$	−10.9840	+	10.9840i	−0.513810	+	0.513810i	0.401881	+	0.915692i	$0.368356\pi$
$458$	4.84683			0.226478
$459$		0			0
$460$	52.5756			2.45135
$461$	27.5087	−	27.5087i	1.28121	−	1.28121i	0.341230	−	0.939980i	$-0.389156\pi$
$461$	27.5087	−	27.5087i	1.28121	−	1.28121i	0.939980	−	0.341230i	$-0.110844\pi$
$462$	−4.55442	+	10.9953i	−0.211891	+	0.511549i
$463$			22.7572i			1.05762i	0.848742	+	0.528808i	$0.177361\pi$
$463$			22.7572i			1.05762i	−0.848742	+	0.528808i	$0.822639\pi$
$464$	1.69367	+	0.701539i	0.0786265	+	0.0325681i
$465$	0.377901	+	0.912334i	0.0175248	+	0.0423085i
$466$	−3.64141	+	1.50832i	−0.168685	+	0.0698715i
$467$	−8.87780	−	8.87780i	−0.410815	−	0.410815i	0.471207	−	0.882023i	$-0.343818\pi$
$467$	−8.87780	−	8.87780i	−0.410815	−	0.410815i	−0.882023	+	0.471207i	$0.843818\pi$
$468$	−4.62845	−	4.62845i	−0.213950	−	0.213950i
$469$	−30.3318	+	12.5639i	−1.40059	+	0.580145i
$470$	−5.34500	−	12.9040i	−0.246546	−	0.595216i
$471$	−5.96397	−	2.47036i	−0.274805	−	0.113828i
$472$			91.6918i			4.22046i
$473$	−6.22162	+	15.0203i	−0.286070	+	0.690635i
$474$	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
$479$	14.2518	−	34.4070i	0.651183	−	1.57209i	−0.159880	−	0.987136i	$-0.551111\pi$
$479$	14.2518	−	34.4070i	0.651183	−	1.57209i	0.811063	−	0.584959i	$-0.198889\pi$
$480$			27.5719i			1.25848i
$481$	6.49303	+	2.68950i	0.296057	+	0.122631i
$482$	11.6180	+	28.0484i	0.529187	+	1.27757i
$483$	−10.2179	+	4.23241i	−0.464932	+	0.192581i
$484$	−25.1871	−	25.1871i	−1.14487	−	1.14487i
$485$	−7.41029	−	7.41029i	−0.336484	−	0.336484i
$486$	−2.43572	+	1.00891i	−0.110487	+	0.0457650i
$487$	0.629467	+	1.51967i	0.0285239	+	0.0688627i	0.937500	−	0.347986i	$-0.113134\pi$
$487$	0.629467	+	1.51967i	0.0285239	+	0.0688627i	−0.908976	+	0.416849i	$0.863134\pi$
$488$	−62.4329	−	25.8605i	−2.82620	−	1.17065i
$489$		−	16.7322i		−	0.756656i
$490$	3.68663	−	8.90031i	0.166545	−	0.402075i
$491$	3.04142	−	3.04142i	0.137257	−	0.137257i	−0.635140	−	0.772397i	$-0.719058\pi$
$491$	3.04142	−	3.04142i	0.137257	−	0.137257i	0.772397	+	0.635140i	$0.219058\pi$
$492$	19.9125			0.897725
$493$		0			0
$494$	−20.7427			−0.933258
$495$	3.06508	−	3.06508i	0.137765	−	0.137765i
$496$	1.80389	−	4.35497i	0.0809969	−	0.195544i
$497$			14.1196i			0.633352i
$498$	20.7760	+	8.60570i	0.930995	+	0.385631i
$499$	0.572218	+	1.38146i	0.0256160	+	0.0618425i	0.936170	−	0.351548i	$-0.114345\pi$
$499$	0.572218	+	1.38146i	0.0256160	+	0.0618425i	−0.910554	+	0.413390i	$0.864345\pi$
$500$	51.4479	−	21.3104i	2.30082	−	0.953032i
$501$	−1.13490	−	1.13490i	−0.0507034	−	0.0507034i
$502$	−1.75270	−	1.75270i	−0.0782269	−	0.0782269i
$503$	1.55838	−	0.645504i	0.0694849	−	0.0287816i	−0.347670	−	0.937617i	$-0.613027\pi$
$503$	1.55838	−	0.645504i	0.0694849	−	0.0287816i	0.417155	+	0.908835i	$0.363027\pi$
$504$	−6.88926	−	16.6321i	−0.306872	−	0.740854i
$505$	−14.5996	−	6.04736i	−0.649675	−	0.269104i
$506$			24.5770i			1.09258i
$507$	−4.30589	+	10.3953i	−0.191231	+	0.461674i
$508$	−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
$513$	−2.27721	+	5.49767i	−0.100541	+	0.242728i
$514$			5.68185i			0.250616i
$515$	18.9361	+	7.84358i	0.834423	+	0.345629i
$516$	−15.7902	−	38.1210i	−0.695127	−	1.67818i
$517$	4.29640	−	1.77963i	0.188955	−	0.0782679i
$518$	22.9322	+	22.9322i	1.00758	+	1.00758i
$519$	−12.1169	−	12.1169i	−0.531875	−	0.531875i
$520$	−21.1161	+	8.74658i	−0.926003	+	0.383563i
$521$	−5.12653	−	12.3765i	−0.224597	−	0.542226i	0.770906	−	0.636948i	$-0.219804\pi$
$521$	−5.12653	−	12.3765i	−0.224597	−	0.542226i	−0.995504	+	0.0947226i	$0.969804\pi$
$522$	0.420947	+	0.174362i	0.0184243	+	0.00763162i
$523$		−	4.40904i		−	0.192794i	−0.995343	−	0.0963969i	$-0.969268\pi$
$523$		−	4.40904i		−	0.192794i	0.995343	−	0.0963969i	$-0.0307318\pi$
$524$	14.4126	−	34.7950i	0.629616	−	1.52003i
$525$	−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
$530$	−1.63035	+	3.93602i	−0.0708179	+	0.170970i
$531$			11.7870i			0.511513i
$532$	−62.9861	−	26.0897i	−2.73079	−	1.13113i
$533$	2.03514	+	4.91327i	0.0881519	+	0.212818i
$534$	13.1601	−	5.45110i	0.569494	−	0.235892i
$535$	8.14347	+	8.14347i	0.352073	+	0.352073i
$536$	−78.0350	−	78.0350i	−3.37060	−	3.37060i
$537$	10.2323	−	4.23835i	0.441555	−	0.182898i
$538$	−15.3095	−	36.9605i	−0.660041	−	1.59348i
$539$	2.96338	+	1.22747i	0.127642	+	0.0528709i
$540$			11.0012i			0.473418i
$541$	8.84592	−	21.3559i	0.380316	−	0.918163i	−0.611589	−	0.791176i	$-0.709469\pi$
$541$	8.84592	−	21.3559i	0.380316	−	0.918163i	0.991904	−	0.126987i	$-0.0405308\pi$
$542$	−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
$547$	−3.62966	+	8.76278i	−0.155193	+	0.374669i	−0.982284	−	0.187399i	$-0.939994\pi$
$547$	−3.62966	+	8.76278i	−0.155193	+	0.374669i	0.827091	+	0.562068i	$0.189994\pi$
$548$		−	109.272i		−	4.66786i
$549$	−8.02576	−	3.32438i	−0.342531	−	0.141881i
$550$	0.121752	+	0.293935i	0.00519151	+	0.0125334i
$551$	0.950120	−	0.393552i	0.0404765	−	0.0167659i
$552$	−26.2878	−	26.2878i	−1.11888	−	1.11888i
$553$	1.14265	+	1.14265i	0.0485906	+	0.0485906i
$554$	−65.5270	+	27.1422i	−2.78398	+	1.15316i
$555$	−4.52026	−	10.9129i	−0.191874	−	0.463225i
$556$	−16.3949	−	6.79099i	−0.695299	−	0.288002i
$557$		−	38.1670i		−	1.61719i	−0.588368	−	0.808593i	$-0.700229\pi$
$557$		−	38.1670i		−	1.61719i	0.588368	−	0.808593i	$-0.299771\pi$
$558$	0.448342	−	1.08239i	0.0189798	−	0.0458213i
$559$	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	$-0.655949\pi$
$563$	9.77111	−	9.77111i	0.411803	−	0.411803i	0.882366	+	0.470563i	$0.155949\pi$
$564$	−4.51663	+	10.9041i	−0.190184	+	0.459146i
$565$		−	38.7487i		−	1.63017i
$566$	−58.3542	−	24.1711i	−2.45281	−	1.01599i
$567$	−0.885616	−	2.13807i	−0.0371924	−	0.0897903i
$568$	−43.8491	+	18.1629i	−1.83987	+	0.762097i
$569$	−9.15817	−	9.15817i	−0.383930	−	0.383930i	0.488586	−	0.872516i	$-0.337513\pi$
$569$	−9.15817	−	9.15817i	−0.383930	−	0.383930i	−0.872516	+	0.488586i	$0.837513\pi$
$570$	24.6514	+	24.6514i	1.03253	+	1.03253i
$571$	6.01797	−	2.49273i	0.251844	−	0.104317i	−0.253190	−	0.967417i	$-0.581480\pi$
$571$	6.01797	−	2.49273i	0.251844	−	0.104317i	0.505034	+	0.863099i	$0.331480\pi$
$572$	−4.88614	−	11.7962i	−0.204300	−	0.493223i
$573$	1.48701	+	0.615940i	0.0621208	+	0.0257313i
$574$			24.5405i			1.02430i
$575$	−0.113144	+	0.273153i	−0.00471842	+	0.0113913i
$576$	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
$581$	−7.55405	+	18.2371i	−0.313395	+	0.756602i
$582$			12.4331i			0.515370i
$583$	−1.31050	−	0.542829i	−0.0542755	−	0.0224817i
$584$	31.4269	+	75.8713i	1.30045	+	3.13958i
$585$	−2.71448	+	1.12438i	−0.112230	+	0.0464872i
$586$	−13.8770	−	13.8770i	−0.573254	−	0.573254i
$587$	10.5901	+	10.5901i	0.437098	+	0.437098i	0.891034	−	0.453936i	$-0.149981\pi$
$587$	10.5901	+	10.5901i	0.437098	+	0.437098i	−0.453936	+	0.891034i	$0.649981\pi$
$588$	−7.52094	+	3.11528i	−0.310158	+	0.128472i
$589$	−1.01195	−	2.44307i	−0.0416968	−	0.100665i
$590$	63.7988	+	26.4263i	2.62656	+	1.08795i
$591$			7.39376i			0.304139i
$592$	−21.5772	+	52.0919i	−0.886816	+	2.14096i
$593$	32.7886	−	32.7886i	1.34647	−	1.34647i	0.456999	−	0.889467i	$-0.348924\pi$
$593$	32.7886	−	32.7886i	1.34647	−	1.34647i	0.889467	−	0.456999i	$-0.151076\pi$
$594$	−5.14265			−0.211006
$595$		0			0
$596$	−58.2744			−2.38701
$597$	−5.08874	+	5.08874i	−0.208268	+	0.208268i
$598$	6.37506	−	15.3908i	0.260696	−	0.629375i
$599$		−	28.7068i		−	1.17293i	−0.809975	−	0.586464i	$-0.800520\pi$
$599$		−	28.7068i		−	1.17293i	0.809975	−	0.586464i	$-0.199480\pi$
$600$	−0.444622	−	0.184168i	−0.0181516	−	0.00751864i
$601$	−7.95547	−	19.2062i	−0.324511	−	0.783438i	−0.998981	−	0.0451358i	$-0.985628\pi$
$601$	−7.95547	−	19.2062i	−0.324511	−	0.783438i	0.674470	−	0.738302i	$-0.264372\pi$
$602$	46.9810	−	19.4602i	1.91480	−	0.793137i
$603$	−10.0314	−	10.0314i	−0.408511	−	0.408511i
$604$	56.3731	+	56.3731i	2.29379	+	2.29379i
$605$	−14.7717	+	6.11863i	−0.600554	+	0.248758i
$606$	7.17458	+	17.3210i	0.291448	+	0.703617i
$607$	−15.8963	−	6.58447i	−0.645211	−	0.267255i	0.0359891	−	0.999352i	$-0.488542\pi$
$607$	−15.8963	−	6.58447i	−0.645211	−	0.267255i	−0.681201	+	0.732097i	$0.738542\pi$
$608$		−	73.8325i		−	2.99430i
$609$	−0.153054	+	0.369506i	−0.00620207	+	0.0149731i
$610$	−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
$615$	3.42048	−	8.25776i	0.137927	−	0.332985i
$616$		−	35.1162i		−	1.41487i
$617$	35.3658	+	14.6490i	1.42377	+	0.589745i	0.955805	−	0.294001i	$-0.0949868\pi$
$617$	35.3658	+	14.6490i	1.42377	+	0.589745i	0.467966	+	0.883746i	$0.344987\pi$
$618$	−9.30561	−	22.4657i	−0.374326	−	0.903704i
$619$	−8.56660	+	3.54840i	−0.344321	+	0.142622i	−0.548141	−	0.836386i	$-0.684664\pi$
$619$	−8.56660	+	3.54840i	−0.344321	+	0.142622i	0.203820	+	0.979008i	$0.434664\pi$
$620$	−3.45688	−	3.45688i	−0.138832	−	0.138832i
$621$	−3.37930	−	3.37930i	−0.135607	−	0.135607i
$622$	25.2378	−	10.4539i	1.01195	−	0.419161i
$623$	4.78495	+	11.5519i	0.191705	+	0.462817i
$624$	12.9574	+	5.36713i	0.518711	+	0.214857i
$625$		−	24.6868i		−	0.987474i
$626$	17.5814	−	42.4453i	0.702695	−	1.69646i
$627$	−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	$-0.514691\pi$
$631$	23.9340	−	23.9340i	0.952798	−	0.952798i	0.998935	+	0.0461372i	$0.0146911\pi$
$632$	−2.07869	+	5.01841i	−0.0826860	+	0.199622i
$633$			13.4185i			0.533337i
$634$	−34.5271	−	14.3016i	−1.37125	−	0.567989i
$635$	8.37801	+	20.2263i	0.332471	+	0.802656i
$636$	3.32601	−	1.37768i	0.131885	−	0.0546285i
$637$	−1.53735	−	1.53735i	−0.0609119	−	0.0609119i
$638$	0.628452	+	0.628452i	0.0248807	+	0.0248807i
$639$	−5.63681	+	2.33484i	−0.222989	+	0.0923649i
$640$	−4.67186	−	11.2789i	−0.184672	−	0.445837i
$641$	9.85925	+	4.08383i	0.389417	+	0.161302i	0.568797	−	0.822478i	$-0.307409\pi$
$641$	9.85925	+	4.08383i	0.389417	+	0.161302i	−0.179380	+	0.983780i	$0.557409\pi$
$642$		−	13.6633i		−	0.539247i
$643$	−15.0447	+	36.3211i	−0.593305	+	1.43237i	0.286987	+	0.957934i	$0.407346\pi$
$643$	−15.0447	+	36.3211i	−0.593305	+	1.43237i	−0.880293	+	0.474431i	$0.842654\pi$
$644$	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
$649$	−8.79870	+	21.2419i	−0.345379	+	0.833819i
$650$		−	0.215651i		−	0.00845852i
$651$	0.950120	+	0.393552i	0.0372381	+	0.0154245i
$652$	31.6995	+	76.5295i	1.24145	+	2.99712i
$653$	−37.8346	+	15.6716i	−1.48058	+	0.613277i	−0.969244	−	0.246102i	$-0.920850\pi$
$653$	−37.8346	+	15.6716i	−1.48058	+	0.613277i	−0.511339	+	0.859379i	$0.670850\pi$
$654$	−37.2384	−	37.2384i	−1.45614	−	1.45614i
$655$	−11.9538	−	11.9538i	−0.467075	−	0.467075i
$656$	−39.4179	+	16.3274i	−1.53901	+	0.637479i
$657$	4.03994	+	9.75327i	0.157613	+	0.380511i
$658$	−13.4384	−	5.56637i	−0.523883	−	0.217000i
$659$		−	10.8164i		−	0.421349i	−0.977556	−	0.210674i	$-0.932434\pi$
$659$		−	10.8164i		−	0.421349i	0.977556	−	0.210674i	$-0.0675660\pi$
$660$	−8.21215	+	19.8259i	−0.319657	+	0.771721i
$661$	14.1983	−	14.1983i	0.552248	−	0.552248i	−0.374841	−	0.927089i	$-0.622303\pi$
$661$	14.1983	−	14.1983i	0.552248	−	0.552248i	0.927089	+	0.374841i	$0.122303\pi$
$662$	28.6010			1.11161
$663$		0			0
$664$	−66.3531			−2.57500
$665$	−21.6389	+	21.6389i	−0.839121	+	0.839121i
$666$	−5.36283	+	12.9470i	−0.207805	+	0.501687i
$667$			0.825928i			0.0319801i
$668$	7.34086	+	3.04069i	0.284027	+	0.117648i
$669$	−8.13751	−	19.6457i	−0.314614	−	0.759546i
$670$	−76.7867	+	31.8061i	−2.96653	+	1.22878i
$671$	−11.9820	−	11.9820i	−0.462562	−	0.462562i
$672$	20.3037	+	20.3037i	0.783233	+	0.783233i
$673$	25.3238	−	10.4895i	0.976161	−	0.404339i	0.163159	−	0.986600i	$-0.447832\pi$
$673$	25.3238	−	10.4895i	0.976161	−	0.404339i	0.813002	+	0.582261i	$0.197832\pi$
$674$	−9.90516	−	23.9132i	−0.381532	−	0.921101i
$675$	−0.0571563	−	0.0236749i	−0.00219995	−	0.000911247i
$676$		−	55.7037i		−	2.14245i
$677$	8.69682	−	20.9960i	0.334246	−	0.806941i	−0.664000	−	0.747733i	$-0.731142\pi$
$677$	8.69682	−	20.9960i	0.334246	−	0.806941i	0.998246	−	0.0592081i	$-0.0188575\pi$
$678$	−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
$683$	14.2383	−	34.3743i	0.544814	−	1.31530i	−0.376478	−	0.926425i	$-0.622865\pi$
$683$	14.2383	−	34.3743i	0.544814	−	1.31530i	0.921292	−	0.388871i	$-0.127135\pi$
$684$		−	29.4594i		−	1.12641i
$685$	−45.3153	−	18.7702i	−1.73141	−	0.717173i
$686$	−20.1832	−	48.7266i	−0.770599	−	1.86039i
$687$	−1.69848	+	0.703535i	−0.0648012	+	0.0268415i
$688$	62.5153	+	62.5153i	2.38337	+	2.38337i
$689$	0.679866	+	0.679866i	0.0259008	+	0.0259008i
$690$	−25.8673	+	10.7146i	−0.984752	+	0.407897i
$691$	6.90974	+	16.6816i	0.262859	+	0.634597i	0.999113	−	0.0421076i	$-0.0134072\pi$
$691$	6.90974	+	16.6816i	0.262859	+	0.634597i	−0.736254	+	0.676705i	$0.763407\pi$
$692$	78.3762	+	32.4645i	2.97942	+	1.23411i
$693$		−	4.51420i		−	0.171480i
$694$	−26.2790	+	63.4430i	−0.997536	+	2.40827i
$695$	−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
$700$	0.271240	−	0.654832i	0.0102519	−	0.0247503i
$701$		−	9.99896i		−	0.377656i	−0.982010	−	0.188828i	$-0.939531\pi$
$701$		−	9.99896i		−	0.377656i	0.982010	−	0.188828i	$-0.0604688\pi$
$702$	3.22046	+	1.33396i	0.121548	+	0.0503470i
$703$	12.1044	+	29.2227i	0.456528	+	1.10216i
$704$	20.7179	−	8.58165i	0.780837	−	0.323433i
$705$	3.74611	+	3.74611i	0.141087	+	0.141087i
$706$	22.0611	+	22.0611i	0.830279	+	0.830279i
$707$	−15.2043	+	6.29782i	−0.571816	+	0.236854i
$708$	−22.3308	−	53.9113i	−0.839242	−	2.02611i
$709$	1.01068	+	0.418638i	0.0379570	+	0.0157223i	0.401581	−	0.915823i	$-0.368461\pi$
$709$	1.01068	+	0.418638i	0.0379570	+	0.0157223i	−0.363624	+	0.931546i	$0.618461\pi$
$710$			35.7447i			1.34147i
$711$	−0.267217	+	0.645118i	−0.0100214	+	0.0241938i
$712$	−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
$717$	3.83640	−	9.26189i	0.143273	−	0.345891i
$718$		−	37.2768i		−	1.39116i
$719$	−39.2481	−	16.2571i	−1.46371	−	0.606287i	−0.498292	−	0.867009i	$-0.666039\pi$
$719$	−39.2481	−	16.2571i	−1.46371	−	0.606287i	−0.965414	+	0.260722i	$0.916039\pi$
$720$	−9.02056	−	21.7776i	−0.336176	−	0.811602i
$721$	19.7203	−	8.16843i	0.734423	−	0.304208i
$722$	−30.5919	−	30.5919i	−1.13851	−	1.13851i
$723$	−8.14265	−	8.14265i	−0.302829	−	0.302829i
$724$	−90.1014	+	37.3212i	−3.34859	+	1.38703i
$725$	0.00409155	+	0.00987788i	0.000151956	+	0.000366855i
$726$	17.5251	+	7.25914i	0.650418	+	0.269412i
$727$			45.2169i			1.67700i	0.544900	+	0.838501i	$0.316568\pi$
$727$			45.2169i			1.67700i	−0.544900	+	0.838501i	$0.683432\pi$
$728$	−9.10883	+	21.9907i	−0.337596	+	0.815028i
$729$	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	$-0.619396\pi$
$733$	15.2728	−	15.2728i	0.564114	−	0.564114i	0.930473	+	0.366359i	$0.119396\pi$
$734$	3.75679	−	9.06969i	0.138666	−	0.334769i
$735$			3.65408i			0.134783i
$736$	54.7826	+	22.6917i	2.01931	+	0.836426i
$737$	−10.5899	−	25.5663i	−0.390084	−	0.941747i
$738$	−9.79700	+	4.05805i	−0.360632	+	0.149379i
$739$	13.4646	+	13.4646i	0.495305	+	0.495305i	0.909973	−	0.414668i	$-0.136102\pi$
$739$	13.4646	+	13.4646i	0.495305	+	0.495305i	−0.414668	+	0.909973i	$0.636102\pi$
$740$	41.3494	+	41.3494i	1.52003	+	1.52003i
$741$	7.26890	−	3.01088i	0.267030	−	0.110607i
$742$	1.69787	+	4.09903i	0.0623309	+	0.150480i
$743$	−24.4221	−	10.1160i	−0.895959	−	0.371118i	−0.113294	−	0.993562i	$-0.536140\pi$
$743$	−24.4221	−	10.1160i	−0.895959	−	0.371118i	−0.782665	+	0.622443i	$0.786140\pi$
$744$			3.45688i			0.126735i
$745$	−10.0101	+	24.1665i	−0.366742	+	0.885393i
$746$	−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
$751$	−1.77828	+	4.29314i	−0.0648902	+	0.156659i	−0.952998	−	0.302976i	$-0.902020\pi$
$751$	−1.77828	+	4.29314i	−0.0648902	+	0.156659i	0.888108	+	0.459635i	$0.152020\pi$
$752$		−	25.2887i		−	0.922185i
$753$	0.868612	+	0.359791i	0.0316540	+	0.0131115i
$754$	−0.230538	−	0.556567i	−0.00839569	−	0.0202690i
$755$	33.0616	−	13.6945i	1.20323	−	0.498396i
$756$	8.10124	+	8.10124i	0.294639	+	0.294639i
$757$	7.35913	+	7.35913i	0.267472	+	0.267472i	0.828081	−	0.560609i	$-0.189433\pi$
$757$	7.35913	+	7.35913i	0.267472	+	0.267472i	−0.560609	+	0.828081i	$0.689433\pi$
$758$	88.0539	−	36.4731i	3.19826	−	1.32476i
$759$	−3.56744	−	8.61257i	−0.129490	−	0.312616i
$760$	−95.0357	−	39.3651i	−3.44731	−	1.42792i
$761$		−	38.6365i		−	1.40057i	−0.713862	−	0.700286i	$-0.753056\pi$
$761$		−	38.6365i		−	1.40057i	0.713862	−	0.700286i	$-0.246944\pi$
$762$	9.93966	−	23.9965i	0.360076	−	0.869300i
$763$	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
$768$	3.25616	−	7.86106i	0.117496	−	0.283661i
$769$			0.178098i			0.00642238i	0.999995	+	0.00321119i	$0.00102215\pi$
$769$			0.178098i			0.00642238i	−0.999995	+	0.00321119i	$0.998978\pi$
$770$	−24.4337	−	10.1208i	−0.880531	−	0.364728i
$771$	−0.824740	−	1.99110i	−0.0297023	−	0.0717077i
$772$	20.4633	−	8.47617i	0.736490	−	0.305064i
$773$	2.93841	+	2.93841i	0.105687	+	0.105687i	0.757973	−	0.652286i	$-0.226190\pi$
$773$	2.93841	+	2.93841i	0.105687	+	0.105687i	−0.652286	+	0.757973i	$0.726190\pi$
$774$	15.5377	+	15.5377i	0.558490	+	0.558490i
$775$	0.0253993	−	0.0105207i	0.000912368	−	0.000377915i
$776$	−14.0390	−	33.8931i	−0.503970	−	1.21669i
$777$	−11.3648	−	4.70747i	−0.407711	−	0.168880i
$778$			43.3776i			1.55516i
$779$	−9.15942	+	22.1128i	−0.328170	+	0.792273i
$780$	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
$785$	5.48960	−	13.2531i	0.195932	−	0.473023i
$786$			20.0564i			0.715389i
$787$	−1.60630	−	0.665353i	−0.0572586	−	0.0237173i	0.353870	−	0.935294i	$-0.384865\pi$
$787$	−1.60630	−	0.665353i	−0.0572586	−	0.0237173i	−0.411129	+	0.911577i	$0.634865\pi$
$788$	−14.0077	−	33.8175i	−0.499002	−	1.20470i
$789$	12.1422	−	5.02948i	0.432275	−	0.179054i
$790$	2.89269	+	2.89269i	0.102917	+	0.102917i
$791$	−28.5343	−	28.5343i	−1.01456	−	1.01456i
$792$	14.0190	−	5.80687i	0.498144	−	0.206338i
$793$	4.39542	+	10.6115i	0.156086	+	0.376825i
$794$	−88.8079	−	36.7854i	−3.15167	−	1.30547i
$795$		−	1.61596i		−	0.0573120i
$796$	13.6341	−	32.9156i	0.483247	−	1.16666i
$797$	−15.7038	+	15.7038i	−0.556257	+	0.556257i	−0.928240	−	0.371983i	$-0.878678\pi$
$797$	−15.7038	+	15.7038i	−0.556257	+	0.556257i	0.371983	+	0.928240i	$0.378678\pi$
$798$	36.3062			1.28523
$799$		0			0
$800$	0.767597			0.0271386
$801$	−3.82047	+	3.82047i	−0.134990	+	0.134990i
$802$	−9.76530	+	23.5755i	−0.344825	+	0.832480i
$803$			20.5926i			0.726695i
$804$	64.8863	+	26.8768i	2.28836	+	0.947872i
$805$	−9.40523	−	22.7062i	−0.331491	−	0.800289i
$806$	−1.43112	+	0.592788i	−0.0504089	+	0.0208801i
$807$	10.7299	+	10.7299i	0.377710	+	0.377710i
$808$	−39.1162	−	39.1162i	−1.37610	−	1.37610i
$809$	−2.98289	+	1.23555i	−0.104873	+	0.0434397i	−0.434503	−	0.900670i	$-0.643076\pi$
$809$	−2.98289	+	1.23555i	−0.104873	+	0.0434397i	0.329630	+	0.944110i	$0.393076\pi$
$810$	−2.24199	−	5.41264i	−0.0787754	−	0.190181i
$811$	−23.2966	−	9.64975i	−0.818053	−	0.338848i	−0.0658907	−	0.997827i	$-0.520989\pi$
$811$	−23.2966	−	9.64975i	−0.818053	−	0.338848i	−0.752162	+	0.658978i	$0.770989\pi$
$812$		−	1.98000i		−	0.0694846i
$813$	4.52944	−	10.9350i	0.158854	−	0.383508i
$814$	−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
$819$	−1.17094	+	2.82691i	−0.0409161	+	0.0987801i
$820$			44.2494i			1.54526i
$821$	−31.8075	−	13.1751i	−1.11009	−	0.459814i	−0.249121	−	0.968472i	$-0.580142\pi$
$821$	−31.8075	−	13.1751i	−1.11009	−	0.459814i	−0.860969	+	0.508658i	$0.830142\pi$
$822$	22.2689	+	53.7620i	0.776719	+	1.87516i
$823$	−16.4445	+	6.81153i	−0.573219	+	0.237435i	−0.650413	−	0.759581i	$-0.725404\pi$
$823$	−16.4445	+	6.81153i	−0.573219	+	0.237435i	0.0771938	+	0.997016i	$0.475404\pi$
$824$	50.7347	+	50.7347i	1.76743	+	1.76743i
$825$	−0.0853313	−	0.0853313i	−0.00297086	−	0.00297086i
$826$	66.4411	−	27.5208i	2.31178	−	0.957572i
$827$	0.746474	+	1.80215i	0.0259574	+	0.0626668i	0.936327	−	0.351130i	$-0.114202\pi$
$827$	0.746474	+	1.80215i	0.0259574	+	0.0626668i	−0.910369	+	0.413797i	$0.864202\pi$
$828$	21.8584	+	9.05404i	0.759632	+	0.314650i
$829$			0.904671i			0.0314205i	0.999877	+	0.0157103i	$0.00500094\pi$
$829$			0.904671i			0.0314205i	−0.999877	+	0.0157103i	$0.994999\pi$
$830$	−19.1235	+	46.1682i	−0.663787	+	1.60252i
$831$	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
$836$	21.9907	−	53.0902i	0.760563	−	1.83616i
$837$			0.444383i			0.0153601i
$838$	64.1233	+	26.5607i	2.21510	+	0.917525i
$839$	−9.29013	−	22.4284i	−0.320731	−	0.774313i	−0.999212	−	0.0396949i	$-0.987361\pi$
$839$	−9.29013	−	22.4284i	−0.320731	−	0.774313i	0.678481	−	0.734618i	$-0.262639\pi$
$840$	36.9598	−	15.3092i	1.27523	−	0.528219i
$841$	−20.4850	−	20.4850i	−0.706379	−	0.706379i
$842$	−12.3242	−	12.3242i	−0.424719	−	0.424719i
$843$	−20.5414	+	8.50854i	−0.707485	+	0.293050i
$844$	−25.4216	−	61.3733i	−0.875049	−	2.11255i
$845$	−23.1005	−	9.56852i	−0.794680	−	0.329167i
$846$		−	6.28531i		−	0.216093i
$847$	−6.37204	+	15.3835i	−0.218946	+	0.528582i
$848$	−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
$853$	14.5843	−	35.2095i	0.499355	−	1.20555i	−0.450476	−	0.892789i	$-0.648746\pi$
$853$	14.5843	−	35.2095i	0.499355	−	1.20555i	0.949831	−	0.312762i	$-0.101254\pi$
$854$			53.0016i			1.81368i
$855$	−12.2169	−	5.06039i	−0.417808	−	0.173062i
$856$	15.4280	+	37.2465i	0.527318	+	1.27306i
$857$	−6.28260	+	2.60234i	−0.214610	+	0.0888942i	−0.487398	−	0.873180i	$-0.662054\pi$
$857$	−6.28260	+	2.60234i	−0.214610	+	0.0888942i	0.272789	+	0.962074i	$0.412054\pi$
$858$	4.80798	+	4.80798i	0.164142	+	0.164142i
$859$	−15.7736	−	15.7736i	−0.538188	−	0.538188i	0.384808	−	0.922997i	$-0.374268\pi$
$859$	−15.7736	−	15.7736i	−0.538188	−	0.538188i	−0.922997	+	0.384808i	$0.874268\pi$
$860$	84.7122	−	35.0889i	2.88866	−	1.19652i
$861$	−3.56214	−	8.59976i	−0.121397	−	0.293079i
$862$	68.5076	+	28.3768i	2.33338	+	0.966517i
$863$			0.400593i			0.0136363i	0.999977	+	0.00681816i	$0.00217031\pi$
$863$			0.400593i			0.0136363i	−0.999977	+	0.00681816i	$0.997830\pi$
$864$	−4.74815	+	11.4630i	−0.161535	+	0.389981i
$865$	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
$870$	−0.387466	+	0.935425i	−0.0131363	+	0.0317139i
$871$			18.7572i			0.635563i
$872$	143.561	+	59.4649i	4.86159	+	2.01374i
$873$	−1.80471	−	4.35696i	−0.0610803	−	0.147461i
$874$	69.2680	−	28.6918i	2.34303	−	0.970513i
$875$	−18.4070	−	18.4070i	−0.622270	−	0.622270i
$876$	−36.9556	−	36.9556i	−1.24861	−	1.24861i
$877$	−0.194781	+	0.0806809i	−0.00657729	+	0.00272440i	−0.385970	−	0.922511i	$-0.626133\pi$
$877$	−0.194781	+	0.0806809i	−0.00657729	+	0.00272440i	0.379392	+	0.925236i	$0.376133\pi$
$878$	8.29824	+	20.0337i	0.280052	+	0.676105i
$879$	6.87723	+	2.84864i	0.231963	+	0.0960824i
$880$		−	45.9800i		−	1.54999i
$881$	19.8216	−	47.8535i	0.667806	−	1.61223i	−0.117467	−	0.993077i	$-0.537478\pi$
$881$	19.8216	−	47.8535i	0.667806	−	1.61223i	0.785273	−	0.619149i	$-0.212522\pi$
$882$	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
$887$	−6.25080	+	15.0908i	−0.209881	+	0.506698i	−0.993404	−	0.114665i	$-0.963421\pi$
$887$	−6.25080	+	15.0908i	−0.209881	+	0.506698i	0.783523	+	0.621363i	$0.213421\pi$
$888$		−	41.3494i		−	1.38759i
$889$	21.0640	+	8.72499i	0.706464	+	0.292627i
$890$	12.1134	+	29.2443i	0.406042	+	0.980271i
$891$	1.80215	−	0.746474i	0.0603742	−	0.0250078i
$892$	74.4385	+	74.4385i	2.49238	+	2.49238i
$893$	−10.0314	−	10.0314i	−0.335689	−	0.335689i
$894$	28.6711	−	11.8760i	0.958906	−	0.397192i
$895$	9.41842	+	22.7381i	0.314823	+	0.760050i
$896$	−11.7460	−	4.86535i	−0.392406	−	0.162540i
$897$			6.31877i			0.210978i
$898$	31.2005	−	75.3247i	1.04117	−	2.51362i
$899$	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
$904$	51.9090	−	125.319i	1.72647	−	4.16806i
$905$			43.7761i			1.45517i
$906$	−39.2242	−	16.2472i	−1.30314	−	0.539777i
$907$	−11.7800	−	28.4394i	−0.391148	−	0.944314i	−0.989690	−	0.143223i	$-0.954253\pi$
$907$	−11.7800	−	28.4394i	−0.391148	−	0.944314i	0.598543	−	0.801091i	$-0.295747\pi$
$908$	22.6587	−	9.38555i	0.751956	−	0.311470i
$909$	−5.02840	−	5.02840i	−0.166782	−	0.166782i
$910$	12.6758	+	12.6758i	0.420198	+	0.420198i
$911$	6.64723	−	2.75337i	0.220233	−	0.0912234i	−0.269839	−	0.962905i	$-0.586971\pi$
$911$	6.64723	−	2.75337i	0.220233	−	0.0912234i	0.490072	+	0.871682i	$0.336971\pi$
$912$	24.1554	+	58.3164i	0.799867	+	1.93105i
$913$	−15.3718	−	6.36721i	−0.508733	−	0.210724i
$914$			40.9532i			1.35461i
$915$	7.38741	−	17.8348i	0.244220	−	0.589600i
$916$	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
$921$	5.44114	−	13.1361i	0.179292	−	0.432848i
$922$		−	102.565i		−	3.37779i
$923$	7.45287	+	3.08708i	0.245314	+	0.101612i
$924$	8.55226	+	20.6470i	0.281349	+	0.679236i
$925$	−0.303813	+	0.125843i	−0.00998930	+	0.00413770i
$926$	42.4244	+	42.4244i	1.39415	+	1.39415i
$927$	6.52196	+	6.52196i	0.214209	+	0.214209i
$928$	1.98107	−	0.820586i	0.0650318	−	0.0269371i
$929$	5.42751	+	13.1032i	0.178071	+	0.429901i	0.987562	−	0.157231i	$-0.0502569\pi$
$929$	5.42751	+	13.1032i	0.178071	+	0.429901i	−0.809491	+	0.587132i	$0.800257\pi$
$930$	2.40528	+	0.996301i	0.0788723	+	0.0326700i
$931$		−	9.78497i		−	0.320689i
$932$	−2.83232	+	6.83782i	−0.0927756	+	0.223980i
$933$	−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	$-0.886576\pi$
$937$	−18.0095	+	18.0095i	−0.588344	+	0.588344i	0.348839	+	0.937183i	$0.386576\pi$
$938$	−33.1234	+	79.9670i	−1.08152	+	2.61101i
$939$			17.4262i			0.568682i
$940$	−24.2310	−	10.0368i	−0.790329	−	0.327365i
$941$	−22.4191	−	54.1244i	−0.730840	−	1.76440i	−0.639779	−	0.768559i	$-0.720974\pi$
$941$	−22.4191	−	54.1244i	−0.730840	−	1.76440i	−0.0910612	−	0.995845i	$-0.529026\pi$
$942$	−15.7234	+	6.51286i	−0.512297	+	0.212200i
$943$	−13.5923	−	13.5923i	−0.442626	−	0.442626i
$944$	88.4099	+	88.4099i	2.87750	+	2.87750i
$945$	4.75119	−	1.96801i	0.154556	−	0.0640193i
$946$	16.4027	+	39.5996i	0.533298	+	1.28750i
$947$	17.5946	+	7.28794i	0.571749	+	0.236826i	0.649777	−	0.760125i	$-0.274862\pi$
$947$	17.5946	+	7.28794i	0.571749	+	0.236826i	−0.0780278	+	0.996951i	$0.524862\pi$
$948$		−	3.45688i		−	0.112274i
$949$	5.34152	−	12.8956i	0.173393	−	0.418608i
$950$	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
$955$	−1.36874	+	3.30442i	−0.0442913	+	0.106929i
$956$			49.6300i			1.60515i
$957$	−0.311451	−	0.129007i	−0.0100678	−	0.00417022i
$958$	−37.5736	−	90.7107i	−1.21395	−	2.93073i
$959$	−47.1921	+	19.5476i	−1.52391	+	0.631225i
$960$	18.0644	+	18.0644i	0.583025	+	0.583025i
$961$	21.7807	+	21.7807i	0.702602	+	0.702602i
$962$	17.1183	−	7.09062i	0.551915	−	0.228611i
$963$	1.98327	+	4.78804i	0.0639101	+	0.154293i
$964$	52.6692	+	21.8163i	1.69636	+	0.702656i
$965$		−	9.94216i		−	0.320049i
$966$	−11.1583	+	26.9386i	−0.359014	+	0.866736i
$967$	37.4986	−	37.4986i	1.20587	−	1.20587i	0.233520	−	0.972352i	$-0.424975\pi$
$967$	37.4986	−	37.4986i	1.20587	−	1.20587i	0.972352	−	0.233520i	$-0.0750245\pi$
$968$	−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	$-0.765458\pi$
$971$	−2.13924	+	2.13924i	−0.0686516	+	0.0686516i	0.671947	+	0.740599i	$0.265458\pi$
$972$	−1.89452	+	4.57379i	−0.0607669	+	0.146704i
$973$			8.29543i			0.265939i
$974$	4.00646	+	1.65953i	0.128375	+	0.0531747i
$975$	0.0313025	+	0.0755708i	0.00100248	+	0.00242020i
$976$	−85.1332	+	35.2633i	−2.72505	+	1.12875i
$977$	7.96654	+	7.96654i	0.254872	+	0.254872i	0.822965	−	0.568093i	$-0.192318\pi$
$977$	7.96654	+	7.96654i	0.254872	+	0.254872i	−0.568093	+	0.822965i	$0.692318\pi$
$978$	−31.1925	−	31.1925i	−0.997425	−	0.997425i
$979$	−9.73695	+	4.03317i	−0.311194	+	0.128901i
$980$	−6.92274	−	16.7130i	−0.221139	−	0.533876i
$981$	18.4548	+	7.64423i	0.589217	+	0.244062i
$982$		−	11.3397i		−	0.361866i
$983$	−18.5058	+	44.6770i	−0.590244	+	1.42498i	0.293022	+	0.956106i	$0.405339\pi$
$983$	−18.5058	+	44.6770i	−0.590244	+	1.42498i	−0.883267	+	0.468871i	$0.844661\pi$
$984$	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
$989$	−15.2430	+	36.7999i	−0.484699	+	1.17017i
$990$		−	11.4280i		−	0.363204i
$991$	−22.2104	−	9.19984i	−0.705536	−	0.292243i	0.000919961	−	1.00000i	$-0.499707\pi$
$991$	−22.2104	−	9.19984i	−0.705536	−	0.292243i	−0.706456	+	0.707757i	$0.749707\pi$
$992$	−2.11000	−	5.09398i	−0.0669924	−	0.161734i
$993$	−10.0227	+	4.15154i	−0.318061	+	0.131745i
$994$	26.3221	+	26.3221i	0.834887	+	0.834887i
$995$	−11.3082	−	11.3082i	−0.358493	−	0.358493i
$996$	39.0131	−	16.1598i	1.23618	−	0.512041i
$997$	10.0798	+	24.3348i	0.319230	+	0.770691i	0.999295	+	0.0375385i	$0.0119517\pi$
$997$	10.0798	+	24.3348i	0.319230	+	0.770691i	−0.680065	+	0.733152i	$0.738048\pi$
$998$	3.64208	+	1.50860i	0.115288	+	0.0477539i
$999$		−	5.31548i		−	0.168174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.k.688.3		16
17.2	even	8	inner	867.2.h.k.712.4		16
17.3	odd	16		51.2.e.a.4.1	✓	8
17.4	even	4		867.2.h.i.757.2		16
17.5	odd	16		51.2.e.a.13.4	yes	8
17.6	odd	16		867.2.d.f.577.8		8
17.7	odd	16		867.2.a.l.1.1		4
17.8	even	8		867.2.h.i.733.2		16
17.9	even	8		867.2.h.i.733.1		16
17.10	odd	16		867.2.a.k.1.1		4
17.11	odd	16		867.2.d.f.577.7		8
17.12	odd	16		867.2.e.g.829.4		8
17.13	even	4		867.2.h.i.757.1		16
17.14	odd	16		867.2.e.g.616.1		8
17.15	even	8	inner	867.2.h.k.712.3		16
17.16	even	2	inner	867.2.h.k.688.4		16
51.5	even	16		153.2.f.b.64.1		8
51.20	even	16		153.2.f.b.55.4		8
51.41	even	16		2601.2.a.be.1.4		4
51.44	even	16		2601.2.a.bf.1.4		4
68.3	even	16		816.2.bd.e.769.4		8
68.39	even	16		816.2.bd.e.625.4		8
204.71	odd	16		2448.2.be.x.1585.1		8
204.107	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	17.3	odd	16
51.2.e.a.13.4	yes	8	17.5	odd	16
153.2.f.b.55.4		8	51.20	even	16
153.2.f.b.64.1		8	51.5	even	16
816.2.bd.e.625.4		8	68.39	even	16
816.2.bd.e.769.4		8	68.3	even	16
867.2.a.k.1.1		4	17.10	odd	16
867.2.a.l.1.1		4	17.7	odd	16
867.2.d.f.577.7		8	17.11	odd	16
867.2.d.f.577.8		8	17.6	odd	16
867.2.e.g.616.1		8	17.14	odd	16
867.2.e.g.829.4		8	17.12	odd	16
867.2.h.i.733.1		16	17.9	even	8
867.2.h.i.733.2		16	17.8	even	8
867.2.h.i.757.1		16	17.13	even	4
867.2.h.i.757.2		16	17.4	even	4
867.2.h.k.688.3		16	1.1	even	1	trivial
867.2.h.k.688.4		16	17.16	even	2	inner
867.2.h.k.712.3		16	17.15	even	8	inner
867.2.h.k.712.4		16	17.2	even	8	inner
2448.2.be.x.1441.1		8	204.107	odd	16
2448.2.be.x.1585.1		8	204.71	odd	16
2601.2.a.be.1.4		4	51.41	even	16
2601.2.a.bf.1.4		4	51.44	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} +(-0.382683 + 0.923880i) q^{3} -4.95063i q^{4} +(-2.05304 - 0.850396i) q^{5} +(1.00891 + 2.43572i) q^{6} +(-2.13807 + 0.885616i) q^{7} +(-5.50062 - 5.50062i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-5.41264 + 2.24199i) q^{10} +(-0.746474 - 1.80215i) q^{11} +(4.57379 + 1.89452i) q^{12} +1.32218i q^{13} +(-2.33484 + 5.63681i) q^{14} +(1.57133 - 1.57133i) q^{15} -10.6075 q^{16} -2.63640 q^{18} +(-4.20773 + 4.20773i) q^{19} +(-4.21000 + 10.1638i) q^{20} -2.31423i q^{21} +(-4.75119 - 1.96801i) q^{22} +(-1.82887 - 4.41527i) q^{23} +(7.18691 - 2.97692i) q^{24} +(-0.0437455 - 0.0437455i) q^{25} +(2.46483 + 2.46483i) q^{26} +(0.923880 - 0.382683i) q^{27} +(4.38436 + 10.5848i) q^{28} +(-0.159667 - 0.0661363i) q^{29} -5.85860i q^{30} +(-0.170058 + 0.410556i) q^{31} +(-8.77343 + 8.77343i) q^{32} +1.95063 q^{33} +5.14265 q^{35} +(-3.50062 + 3.50062i) q^{36} +(2.03414 - 4.91086i) q^{37} +15.6883i q^{38} +(-1.22153 - 0.505976i) q^{39} +(6.61528 + 15.9707i) q^{40} +(3.71604 - 1.53924i) q^{41} +(-4.31423 - 4.31423i) q^{42} +(-5.89351 - 5.89351i) q^{43} +(-8.92177 + 3.69552i) q^{44} +(0.850396 + 2.05304i) q^{45} +(-11.6405 - 4.82163i) q^{46} +2.38404i q^{47} +(4.05931 - 9.80004i) q^{48} +(-1.16274 + 1.16274i) q^{49} -0.163102 q^{50} +6.54562 q^{52} +(0.514201 - 0.514201i) q^{53} +(1.00891 - 2.43572i) q^{54} +4.33468i q^{55} +(16.6321 + 6.88926i) q^{56} +(-2.27721 - 5.49767i) q^{57} +(-0.420947 + 0.174362i) q^{58} +(-8.33468 - 8.33468i) q^{59} +(-7.77906 - 7.77906i) q^{60} +(8.02576 - 3.32438i) q^{61} +(0.448342 + 1.08239i) q^{62} +(2.13807 + 0.885616i) q^{63} +11.4963i q^{64} +(1.12438 - 2.71448i) q^{65} +(3.63640 - 3.63640i) q^{66} +14.1866 q^{67} +4.77906 q^{69} +(9.58704 - 9.58704i) q^{70} +(2.33484 - 5.63681i) q^{71} +7.77906i q^{72} +(-9.75327 - 4.03994i) q^{73} +(-5.36283 - 12.9470i) q^{74} +(0.0571563 - 0.0236749i) q^{75} +(20.8309 + 20.8309i) q^{76} +(3.19202 + 3.19202i) q^{77} +(-3.22046 + 1.33396i) q^{78} +(-0.267217 - 0.645118i) q^{79} +(21.7776 + 9.02056i) q^{80} +1.00000i q^{81} +(4.05805 - 9.79700i) q^{82} +(6.03142 - 6.03142i) q^{83} -11.4569 q^{84} -21.9736 q^{86} +(0.122204 - 0.122204i) q^{87} +(-5.80687 + 14.0190i) q^{88} -5.40297i q^{89} +(5.41264 + 2.24199i) q^{90} +(-1.17094 - 2.82691i) q^{91} +(-21.8584 + 9.05404i) q^{92} +(-0.314226 - 0.314226i) q^{93} +(4.44438 + 4.44438i) q^{94} +(12.2169 - 5.06039i) q^{95} +(-4.74815 - 11.4630i) q^{96} +(4.35696 + 1.80471i) q^{97} +4.33519i q^{98} +(-0.746474 + 1.80215i) 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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