LMFDB - Embedded newform 867.2.h.k.712.3

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			712.3
Root			$0.467712 + 1.12916i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.k.688.3

$q$-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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.86422	+	1.86422i	1.31820	+	1.31820i	0.915198	+	0.403004i	$0.132034\pi$
$2$	1.86422	+	1.86422i	1.31820	+	1.31820i	0.403004	+	0.915198i	$0.367966\pi$
$3$	−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	−0.791169	−	0.611597i	$-0.790527\pi$
$5$	−2.05304	+	0.850396i	−0.918146	+	0.380309i	−0.126977	+	0.991906i	$0.540527\pi$
$6$	1.00891	−	2.43572i	0.411885	−	0.994379i
$7$	−2.13807	−	0.885616i	−0.808113	−	0.334731i	−0.0599122	−	0.998204i	$-0.519082\pi$
$7$	−2.13807	−	0.885616i	−0.808113	−	0.334731i	−0.748201	+	0.663472i	$0.769082\pi$
$8$	−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	−0.995565	−	0.0940788i	$-0.970009\pi$
$11$	−0.746474	+	1.80215i	−0.225070	+	0.543368i	0.770494	+	0.637447i	$0.220009\pi$
$12$	4.57379	−	1.89452i	1.32034	−	0.546902i
$13$		−	1.32218i		−	0.366706i	−0.983047	−	0.183353i	$-0.941305\pi$
$13$		−	1.32218i		−	0.366706i	0.983047	−	0.183353i	$-0.0586952\pi$
$14$	−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	0.0340987	−	0.999418i	$-0.489144\pi$
$19$	−4.20773	−	4.20773i	−0.965320	−	0.965320i	−0.999418	+	0.0340987i	$0.989144\pi$
$20$	−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	0.610361	+	0.792123i	$0.291024\pi$
$23$	−1.82887	+	4.41527i	−0.381345	+	0.920648i	−0.991706	+	0.128525i	$0.958976\pi$
$24$	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	−0.397459	−	0.917620i	$-0.630108\pi$
$29$	−0.159667	+	0.0661363i	−0.0296494	+	0.0122812i	0.367809	+	0.929901i	$0.380108\pi$
$30$			5.85860i			1.06963i
$31$	−0.170058	−	0.410556i	−0.0305433	−	0.0737381i	0.907872	−	0.419248i	$-0.137706\pi$
$31$	−0.170058	−	0.410556i	−0.0305433	−	0.0737381i	−0.938415	+	0.345510i	$0.887706\pi$
$32$	−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	0.998231	+	0.0594480i	$0.0189340\pi$
$37$	2.03414	+	4.91086i	0.334411	+	0.807340i	−0.663820	+	0.747892i	$0.731066\pi$
$38$		−	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	0.653492	−	0.756933i	$-0.273303\pi$
$41$	3.71604	+	1.53924i	0.580348	+	0.240388i	−0.0731438	+	0.997321i	$0.523303\pi$
$42$	−4.31423	+	4.31423i	−0.665700	+	0.665700i
$43$	−5.89351	+	5.89351i	−0.898751	+	0.898751i	−0.995326	−	0.0965746i	$-0.969211\pi$
$43$	−5.89351	+	5.89351i	−0.898751	+	0.898751i	0.0965746	+	0.995326i	$0.469211\pi$
$44$	−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	$-0.944371\pi$
$47$		−	2.38404i		−	0.347749i	0.984768	−	0.173874i	$-0.0556286\pi$
$48$	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	0.741540	−	0.670909i	$-0.234096\pi$
$53$	0.514201	+	0.514201i	0.0706309	+	0.0706309i	−0.670909	+	0.741540i	$0.734096\pi$
$54$	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	−0.0890557	+	0.996027i	$0.528385\pi$
$59$	−8.33468	+	8.33468i	−1.08508	+	1.08508i	−0.996027	+	0.0890557i	$0.971615\pi$
$60$	−7.77906	+	7.77906i	−1.00427	+	1.00427i
$61$	8.02576	+	3.32438i	1.02759	+	0.425643i	0.831843	−	0.555011i	$-0.187286\pi$
$61$	8.02576	+	3.32438i	1.02759	+	0.425643i	0.195750	+	0.980654i	$0.437286\pi$
$62$	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	0.999753	−	0.0222399i	$-0.00707976\pi$
$71$	2.33484	+	5.63681i	0.277095	+	0.668966i	−0.722658	+	0.691206i	$0.757080\pi$
$72$		−	7.77906i		−	0.916771i
$73$	−9.75327	+	4.03994i	−1.14153	+	0.472839i	−0.871686	−	0.490064i	$-0.836973\pi$
$73$	−9.75327	+	4.03994i	−1.14153	+	0.472839i	−0.269848	+	0.962903i	$0.586973\pi$
$74$	−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	−0.938199	−	0.346097i	$-0.887507\pi$
$79$	−0.267217	+	0.645118i	−0.0300642	+	0.0725814i	0.908134	+	0.418679i	$0.137507\pi$
$80$	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	0.955859	−	0.293825i	$-0.0949283\pi$
$83$	6.03142	+	6.03142i	0.662034	+	0.662034i	−0.293825	+	0.955859i	$0.594928\pi$
$84$	−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	$0.0924442\pi$
$89$			5.40297i			0.572713i	−0.958123	+	0.286357i	$0.907556\pi$
$90$	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	−0.150363	−	0.988631i	$-0.548044\pi$
$97$	4.35696	−	1.80471i	0.442383	−	0.183241i	0.592745	+	0.805390i	$0.298044\pi$
$98$		−	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	−0.601920	−	0.798556i	$-0.705598\pi$
$107$	−4.78804	+	1.98327i	−0.462878	+	0.191730i	0.139043	+	0.990286i	$0.455598\pi$
$108$	−1.89452	+	4.57379i	−0.182301	+	0.440113i
$109$	−18.4548	−	7.64423i	−1.76765	−	0.732185i	−0.995284	−	0.0970083i	$-0.969073\pi$
$109$	−18.4548	−	7.64423i	−1.76765	−	0.732185i	−0.772367	−	0.635177i	$-0.780927\pi$
$110$	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	−0.214696	−	0.976681i	$-0.568876\pi$
$113$	6.67291	−	16.1098i	0.627735	−	1.51549i	0.842431	−	0.538805i	$-0.181124\pi$
$114$	−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	−0.945060	−	0.326897i	$-0.893997\pi$
$127$	−6.96634	+	6.96634i	−0.618163	+	0.618163i	0.326897	+	0.945060i	$0.393997\pi$
$128$	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	−0.0538952	−	0.998547i	$-0.517164\pi$
$131$	7.02840	−	2.91126i	0.614074	−	0.254358i	0.667969	+	0.744189i	$0.267164\pi$
$132$			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	0.971317	−	0.237789i	$-0.0764228\pi$
$139$	1.37174	+	3.31168i	0.116350	+	0.280893i	−0.854967	+	0.518682i	$0.826423\pi$
$140$			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	$0.160149\pi$
$149$			11.7711i			0.964327i	−0.876081	+	0.482163i	$0.839851\pi$
$150$	0.0624166	+	0.150687i	0.00509630	+	0.0123035i
$151$	−11.3871	−	11.3871i	−0.926666	−	0.926666i	0.0708230	−	0.997489i	$-0.477437\pi$
$151$	−11.3871	−	11.3871i	−0.926666	−	0.926666i	−0.997489	+	0.0708230i	$0.977437\pi$
$152$	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	$-0.917069\pi$
$157$		−	6.45535i		−	0.515193i	0.966253	−	0.257597i	$-0.0829306\pi$
$158$	−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	−0.316330	−	0.948649i	$-0.602451\pi$
$163$	−15.4585	−	6.40313i	−1.21081	−	0.501532i	−0.894475	+	0.447117i	$0.852451\pi$
$164$	−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	0.898332	−	0.439317i	$-0.144779\pi$
$167$	−0.614202	−	1.48281i	−0.0475284	−	0.114744i	−0.945861	+	0.324573i	$0.894779\pi$
$168$	−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	−0.950255	−	0.311474i	$-0.899177\pi$
$173$	−6.55764	−	15.8316i	−0.498568	−	1.20365i	0.451686	−	0.892177i	$-0.350823\pi$
$174$			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	−0.936368	−	0.351019i	$-0.885835\pi$
$179$	−7.83144	+	7.83144i	−0.585350	+	0.585350i	0.351019	+	0.936368i	$0.385835\pi$
$180$	10.1638	+	4.21000i	0.757567	+	0.313795i
$181$	−7.53868	+	18.2000i	−0.560346	+	1.35279i	0.349145	+	0.937069i	$0.386472\pi$
$181$	−7.53868	+	18.2000i	−0.560346	+	1.35279i	−0.909490	+	0.415725i	$0.863528\pi$
$182$	−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	$0.0185459\pi$
$191$			1.60953i			0.116461i	−0.998303	+	0.0582307i	$0.981454\pi$
$192$	−10.6212	+	4.39942i	−0.766516	+	0.317501i
$193$	1.71214	−	4.13347i	0.123242	−	0.297534i	−0.850202	−	0.526456i	$-0.823520\pi$
$193$	1.71214	−	4.13347i	0.123242	−	0.297534i	0.973445	+	0.228923i	$0.0735203\pi$
$194$	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	0.612513	−	0.790461i	$-0.290159\pi$
$197$	6.83095	+	2.82947i	0.486685	+	0.201591i	−0.125828	+	0.992052i	$0.540159\pi$
$198$	1.96801	−	4.75119i	0.139860	−	0.337653i
$199$	6.64876	−	2.75401i	0.471318	−	0.195226i	−0.134366	−	0.990932i	$-0.542900\pi$
$199$	6.64876	−	2.75401i	0.471318	−	0.195226i	0.605684	+	0.795705i	$0.292900\pi$
$200$		−	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	0.766142	−	0.642671i	$-0.222174\pi$
$211$	12.3971	+	5.13503i	0.853449	+	0.353510i	0.0873068	+	0.996181i	$0.472174\pi$
$212$	−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	−0.999976	−	0.00691960i	$-0.997797\pi$
$223$	−15.0362	−	15.0362i	−1.00690	−	1.00690i	−0.00691960	−	0.999976i	$-0.502203\pi$
$224$	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	−0.848393	−	0.529367i	$-0.822429\pi$
$227$	1.89583	−	4.57694i	0.125831	−	0.303782i	0.974223	+	0.225585i	$0.0724294\pi$
$228$	−27.2169	−	11.2736i	−1.80248	−	0.746613i
$229$	1.29996	−	1.29996i	0.0859039	−	0.0859039i	−0.662849	−	0.748753i	$-0.730653\pi$
$229$	1.29996	−	1.29996i	0.0859039	−	0.0859039i	0.748753	+	0.662849i	$0.230653\pi$
$230$	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	−0.427467	−	0.904031i	$-0.640594\pi$
$233$	−1.38120	+	0.572112i	−0.0904855	+	0.0374803i	0.336982	+	0.941511i	$0.390594\pi$
$234$			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	0.716054	−	0.698045i	$-0.245947\pi$
$241$	−4.40677	−	10.6389i	−0.283865	−	0.685311i	−0.999919	+	0.0127340i	$0.995947\pi$
$242$			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	$0.00944621\pi$
$251$			0.940179i			0.0593436i	−0.999560	+	0.0296718i	$0.990554\pi$
$252$	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	0.657978	−	0.753037i	$-0.271412\pi$
$257$	−1.52392	−	1.52392i	−0.0950596	−	0.0950596i	−0.753037	+	0.657978i	$0.771412\pi$
$258$	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	−0.932979	−	0.359932i	$-0.882800\pi$
$263$	−9.29326	+	9.29326i	−0.573047	+	0.573047i	0.359932	+	0.932979i	$0.382800\pi$
$264$	−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	0.996111	+	0.0881101i	$0.0280827\pi$
$269$	5.80697	+	14.0193i	0.354057	+	0.854770i	−0.642053	+	0.766660i	$0.721917\pi$
$270$	−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	−0.972048	−	0.234783i	$-0.924562\pi$
$277$	−24.8547	+	10.2951i	−1.49337	+	0.618575i	−0.521325	+	0.853358i	$0.674562\pi$
$278$	−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	−0.0603001	−	0.998180i	$-0.519206\pi$
$281$	15.7217	−	15.7217i	0.937880	−	0.937880i	0.998180	+	0.0603001i	$0.0192058\pi$
$282$	−5.80687	−	2.40528i	−0.345794	−	0.143232i
$283$	−9.16820	+	22.1340i	−0.544993	+	1.31573i	0.376169	+	0.926551i	$0.377241\pi$
$283$	−9.16820	+	22.1340i	−0.544993	+	1.31573i	−0.921162	+	0.389179i	$0.872759\pi$
$284$	−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	$0.0697699\pi$
$293$			7.44387i			0.434875i	−0.976074	+	0.217438i	$0.930230\pi$
$294$	−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	−0.0943849	−	0.995536i	$-0.530088\pi$
$311$	9.57282	−	3.96519i	0.542825	−	0.224846i	0.637210	+	0.770690i	$0.280088\pi$
$312$	3.93602	−	9.50238i	0.222833	−	0.537967i
$313$	16.0997	+	6.66872i	0.910009	+	0.376938i	0.788060	−	0.615598i	$-0.211086\pi$
$313$	16.0997	+	6.66872i	0.910009	+	0.376938i	0.121949	+	0.992536i	$0.461086\pi$
$314$	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	0.695181	+	0.718835i	$0.255324\pi$
$317$	−5.42466	+	13.0963i	−0.304679	+	0.735561i	−0.999860	+	0.0167260i	$0.994676\pi$
$318$	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	−0.464129	−	0.885768i	$-0.653633\pi$
$331$	7.67104	−	7.67104i	0.421638	−	0.421638i	0.885768	+	0.464129i	$0.153633\pi$
$332$	−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	0.992567	−	0.121701i	$-0.0388348\pi$
$337$	3.75707	+	9.07037i	0.204661	+	0.494095i	−0.787906	+	0.615795i	$0.788835\pi$
$338$	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	−0.372303	−	0.928111i	$-0.621432\pi$
$347$	−24.0642	−	9.96773i	−1.29184	−	0.535096i	−0.919532	+	0.393015i	$0.871432\pi$
$348$	−0.604986	+	0.604986i	−0.0324307	+	0.0324307i
$349$	13.1952	−	13.1952i	0.706325	−	0.706325i	−0.259436	−	0.965760i	$-0.583537\pi$
$349$	13.1952	−	13.1952i	0.706325	−	0.706325i	0.965760	+	0.259436i	$0.0835365\pi$
$350$	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	$-0.898019\pi$
$353$		−	11.8339i		−	0.629857i	0.949115	−	0.314929i	$-0.101981\pi$
$354$	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	0.919878	−	0.392206i	$-0.128288\pi$
$359$	9.99796	+	9.99796i	0.527672	+	0.527672i	−0.392206	+	0.919878i	$0.628288\pi$
$360$	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	0.470660	−	0.882315i	$-0.344016\pi$
$367$	3.44017	+	1.42497i	0.179576	+	0.0743827i	−0.291084	+	0.956697i	$0.594016\pi$
$368$	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	0.715677	−	0.698431i	$-0.246118\pi$
$379$	33.3992	−	13.8344i	1.71560	−	0.710626i	0.999926	−	0.0121949i	$-0.00388185\pi$
$380$	−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	−0.347106	−	0.937826i	$-0.612836\pi$
$383$	11.5606	−	11.5606i	0.590720	−	0.590720i	0.937826	+	0.347106i	$0.112836\pi$
$384$	−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	0.347719	−	0.937599i	$-0.386956\pi$
$389$	−11.6342	−	11.6342i	−0.589880	−	0.589880i	−0.937599	+	0.347719i	$0.886956\pi$
$390$	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	0.0227033	+	0.999742i	$0.492773\pi$
$397$	−13.9529	+	33.6852i	−0.700275	+	1.69061i	−0.722978	+	0.690871i	$0.757227\pi$
$398$	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	0.148061	−	0.988978i	$-0.452697\pi$
$401$	−8.94230	−	3.70402i	−0.446557	−	0.184970i	−0.594618	+	0.804008i	$0.702697\pi$
$402$	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	−0.461434	−	0.887175i	$-0.652665\pi$
$419$	10.0746	−	24.3222i	0.492177	−	1.18822i	0.953610	−	0.301045i	$-0.0973353\pi$
$420$	23.5214	−	9.74288i	1.14773	−	0.475404i
$421$			6.61089i			0.322195i	0.986938	+	0.161098i	$0.0515034\pi$
$421$			6.61089i			0.322195i	−0.986938	+	0.161098i	$0.948497\pi$
$422$	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	−0.420394	−	0.907342i	$-0.638108\pi$
$431$	10.7634	−	25.9852i	0.518457	−	1.25167i	0.938851	−	0.344324i	$-0.111892\pi$
$432$	−9.80004	−	4.05931i	−0.471505	−	0.195304i
$433$	12.1267	−	12.1267i	0.582770	−	0.582770i	−0.352893	−	0.935664i	$-0.614802\pi$
$433$	12.1267	−	12.1267i	0.582770	−	0.582770i	0.935664	+	0.352893i	$0.114802\pi$
$434$	−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	0.830796	−	0.556577i	$-0.187886\pi$
$439$	−3.14756	−	7.59888i	−0.150225	−	0.362675i	−0.981021	+	0.193902i	$0.937886\pi$
$440$	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	0.935832	−	0.352446i	$-0.114650\pi$
$449$	28.5710	+	11.8345i	1.34835	+	0.558504i	0.412516	+	0.910950i	$0.364650\pi$
$450$	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	0.401881	−	0.915692i	$-0.368356\pi$
$457$	−10.9840	−	10.9840i	−0.513810	−	0.513810i	−0.915692	+	0.401881i	$0.868356\pi$
$458$	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	$0.110844\pi$
$461$	27.5087	+	27.5087i	1.28121	+	1.28121i	0.341230	+	0.939980i	$0.389156\pi$
$462$	−4.55442	−	10.9953i	−0.211891	−	0.511549i
$463$		−	22.7572i		−	1.05762i	−0.848742	−	0.528808i	$-0.822639\pi$
$463$		−	22.7572i		−	1.05762i	0.848742	−	0.528808i	$-0.177361\pi$
$464$	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	−0.882023	−	0.471207i	$-0.843818\pi$
$467$	−8.87780	+	8.87780i	−0.410815	+	0.410815i	0.471207	+	0.882023i	$0.343818\pi$
$468$	−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	0.811063	+	0.584959i	$0.198889\pi$
$479$	14.2518	+	34.4070i	0.651183	+	1.57209i	−0.159880	+	0.987136i	$0.551111\pi$
$480$		−	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	−0.908976	−	0.416849i	$-0.863134\pi$
$487$	0.629467	−	1.51967i	0.0285239	−	0.0688627i	0.937500	+	0.347986i	$0.113134\pi$
$488$	−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	0.772397	−	0.635140i	$-0.219058\pi$
$491$	3.04142	+	3.04142i	0.137257	+	0.137257i	−0.635140	+	0.772397i	$0.719058\pi$
$492$	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	−0.910554	−	0.413390i	$-0.864345\pi$
$499$	0.572218	−	1.38146i	0.0256160	−	0.0618425i	0.936170	+	0.351548i	$0.114345\pi$
$500$	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	0.417155	−	0.908835i	$-0.363027\pi$
$503$	1.55838	+	0.645504i	0.0694849	+	0.0287816i	−0.347670	+	0.937617i	$0.613027\pi$
$504$	−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	−0.995504	−	0.0947226i	$-0.969804\pi$
$521$	−5.12653	+	12.3765i	−0.224597	+	0.542226i	0.770906	+	0.636948i	$0.219804\pi$
$522$	0.420947	−	0.174362i	0.0184243	−	0.00763162i
$523$			4.40904i			0.192794i	0.995343	+	0.0963969i	$0.0307318\pi$
$523$			4.40904i			0.192794i	−0.995343	+	0.0963969i	$0.969268\pi$
$524$	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	0.991904	+	0.126987i	$0.0405308\pi$
$541$	8.84592	+	21.3559i	0.380316	+	0.918163i	−0.611589	+	0.791176i	$0.709469\pi$
$542$	−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	0.827091	−	0.562068i	$-0.189994\pi$
$547$	−3.62966	−	8.76278i	−0.155193	−	0.374669i	−0.982284	+	0.187399i	$0.939994\pi$
$548$			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	$0.299771\pi$
$557$			38.1670i			1.61719i	−0.588368	+	0.808593i	$0.700229\pi$
$558$	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	0.882366	−	0.470563i	$-0.155949\pi$
$563$	9.77111	+	9.77111i	0.411803	+	0.411803i	−0.470563	+	0.882366i	$0.655949\pi$
$564$	−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	−0.872516	−	0.488586i	$-0.837513\pi$
$569$	−9.15817	+	9.15817i	−0.383930	+	0.383930i	0.488586	+	0.872516i	$0.337513\pi$
$570$	24.6514	−	24.6514i	1.03253	−	1.03253i
$571$	6.01797	+	2.49273i	0.251844	+	0.104317i	0.505034	−	0.863099i	$-0.331480\pi$
$571$	6.01797	+	2.49273i	0.251844	+	0.104317i	−0.253190	+	0.967417i	$0.581480\pi$
$572$	−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	−0.453936	−	0.891034i	$-0.649981\pi$
$587$	10.5901	−	10.5901i	0.437098	−	0.437098i	0.891034	+	0.453936i	$0.149981\pi$
$588$	−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	0.889467	+	0.456999i	$0.151076\pi$
$593$	32.7886	+	32.7886i	1.34647	+	1.34647i	0.456999	+	0.889467i	$0.348924\pi$
$594$	−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	$0.199480\pi$
$599$			28.7068i			1.17293i	−0.809975	+	0.586464i	$0.800520\pi$
$600$	−0.444622	+	0.184168i	−0.0181516	+	0.00751864i
$601$	−7.95547	+	19.2062i	−0.324511	+	0.783438i	0.674470	+	0.738302i	$0.264372\pi$
$601$	−7.95547	+	19.2062i	−0.324511	+	0.783438i	−0.998981	+	0.0451358i	$0.985628\pi$
$602$	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	−0.681201	−	0.732097i	$-0.738542\pi$
$607$	−15.8963	+	6.58447i	−0.645211	+	0.267255i	0.0359891	+	0.999352i	$0.488542\pi$
$608$			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	0.467966	−	0.883746i	$-0.344987\pi$
$617$	35.3658	−	14.6490i	1.42377	−	0.589745i	0.955805	+	0.294001i	$0.0949868\pi$
$618$	−9.30561	+	22.4657i	−0.374326	+	0.903704i
$619$	−8.56660	−	3.54840i	−0.344321	−	0.142622i	0.203820	−	0.979008i	$-0.434664\pi$
$619$	−8.56660	−	3.54840i	−0.344321	−	0.142622i	−0.548141	+	0.836386i	$0.684664\pi$
$620$	−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	0.998935	−	0.0461372i	$-0.0146911\pi$
$631$	23.9340	+	23.9340i	0.952798	+	0.952798i	−0.0461372	+	0.998935i	$0.514691\pi$
$632$	−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	−0.179380	−	0.983780i	$-0.557409\pi$
$641$	9.85925	−	4.08383i	0.389417	−	0.161302i	0.568797	+	0.822478i	$0.307409\pi$
$642$			13.6633i			0.539247i
$643$	−15.0447	−	36.3211i	−0.593305	−	1.43237i	−0.880293	−	0.474431i	$-0.842654\pi$
$643$	−15.0447	−	36.3211i	−0.593305	−	1.43237i	0.286987	−	0.957934i	$-0.407346\pi$
$644$	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	−0.511339	−	0.859379i	$-0.670850\pi$
$653$	−37.8346	−	15.6716i	−1.48058	−	0.613277i	−0.969244	+	0.246102i	$0.920850\pi$
$654$	−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	$0.0675660\pi$
$659$			10.8164i			0.421349i	−0.977556	+	0.210674i	$0.932434\pi$
$660$	−8.21215	−	19.8259i	−0.319657	−	0.771721i
$661$	14.1983	+	14.1983i	0.552248	+	0.552248i	0.927089	−	0.374841i	$-0.122303\pi$
$661$	14.1983	+	14.1983i	0.552248	+	0.552248i	−0.374841	+	0.927089i	$0.622303\pi$
$662$	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	0.813002	−	0.582261i	$-0.197832\pi$
$673$	25.3238	+	10.4895i	0.976161	+	0.404339i	0.163159	+	0.986600i	$0.447832\pi$
$674$	−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	0.998246	+	0.0592081i	$0.0188575\pi$
$677$	8.69682	+	20.9960i	0.334246	+	0.806941i	−0.664000	+	0.747733i	$0.731142\pi$
$678$	−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	0.921292	+	0.388871i	$0.127135\pi$
$683$	14.2383	+	34.3743i	0.544814	+	1.31530i	−0.376478	+	0.926425i	$0.622865\pi$
$684$			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	−0.736254	−	0.676705i	$-0.763407\pi$
$691$	6.90974	−	16.6816i	0.262859	−	0.634597i	0.999113	+	0.0421076i	$0.0134072\pi$
$692$	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	$0.0604688\pi$
$701$			9.99896i			0.377656i	−0.982010	+	0.188828i	$0.939531\pi$
$702$	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	−0.363624	−	0.931546i	$-0.618461\pi$
$709$	1.01068	−	0.418638i	0.0379570	−	0.0157223i	0.401581	+	0.915823i	$0.368461\pi$
$710$		−	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	−0.965414	−	0.260722i	$-0.916039\pi$
$719$	−39.2481	+	16.2571i	−1.46371	+	0.606287i	−0.498292	+	0.867009i	$0.666039\pi$
$720$	−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	$-0.683432\pi$
$727$		−	45.2169i		−	1.67700i	0.544900	−	0.838501i	$-0.316568\pi$
$728$	−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	0.930473	−	0.366359i	$-0.119396\pi$
$733$	15.2728	+	15.2728i	0.564114	+	0.564114i	−0.366359	+	0.930473i	$0.619396\pi$
$734$	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	−0.414668	−	0.909973i	$-0.636102\pi$
$739$	13.4646	−	13.4646i	0.495305	−	0.495305i	0.909973	+	0.414668i	$0.136102\pi$
$740$	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	−0.782665	−	0.622443i	$-0.786140\pi$
$743$	−24.4221	+	10.1160i	−0.895959	+	0.371118i	−0.113294	+	0.993562i	$0.536140\pi$
$744$		−	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	0.888108	−	0.459635i	$-0.152020\pi$
$751$	−1.77828	−	4.29314i	−0.0648902	−	0.156659i	−0.952998	+	0.302976i	$0.902020\pi$
$752$			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	−0.560609	−	0.828081i	$-0.689433\pi$
$757$	7.35913	−	7.35913i	0.267472	−	0.267472i	0.828081	+	0.560609i	$0.189433\pi$
$758$	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	$0.246944\pi$
$761$			38.6365i			1.40057i	−0.713862	+	0.700286i	$0.753056\pi$
$762$	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	$-0.998978\pi$
$769$		−	0.178098i		−	0.00642238i	0.999995	−	0.00321119i	$-0.00102215\pi$
$770$	−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	−0.652286	−	0.757973i	$-0.726190\pi$
$773$	2.93841	−	2.93841i	0.105687	−	0.105687i	0.757973	+	0.652286i	$0.226190\pi$
$774$	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	−0.411129	−	0.911577i	$-0.634865\pi$
$787$	−1.60630	+	0.665353i	−0.0572586	+	0.0237173i	0.353870	+	0.935294i	$0.384865\pi$
$788$	−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	0.371983	−	0.928240i	$-0.378678\pi$
$797$	−15.7038	−	15.7038i	−0.556257	−	0.556257i	−0.928240	+	0.371983i	$0.878678\pi$
$798$	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	0.329630	−	0.944110i	$-0.393076\pi$
$809$	−2.98289	−	1.23555i	−0.104873	−	0.0434397i	−0.434503	+	0.900670i	$0.643076\pi$
$810$	−2.24199	+	5.41264i	−0.0787754	+	0.190181i
$811$	−23.2966	+	9.64975i	−0.818053	+	0.338848i	−0.752162	−	0.658978i	$-0.770989\pi$
$811$	−23.2966	+	9.64975i	−0.818053	+	0.338848i	−0.0658907	+	0.997827i	$0.520989\pi$
$812$			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	−0.860969	−	0.508658i	$-0.830142\pi$
$821$	−31.8075	+	13.1751i	−1.11009	+	0.459814i	−0.249121	+	0.968472i	$0.580142\pi$
$822$	22.2689	−	53.7620i	0.776719	−	1.87516i
$823$	−16.4445	−	6.81153i	−0.573219	−	0.237435i	0.0771938	−	0.997016i	$-0.475404\pi$
$823$	−16.4445	−	6.81153i	−0.573219	−	0.237435i	−0.650413	+	0.759581i	$0.725404\pi$
$824$	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	−0.910369	−	0.413797i	$-0.864202\pi$
$827$	0.746474	−	1.80215i	0.0259574	−	0.0626668i	0.936327	+	0.351130i	$0.114202\pi$
$828$	21.8584	−	9.05404i	0.759632	−	0.314650i
$829$		−	0.904671i		−	0.0314205i	−0.999877	−	0.0157103i	$-0.994999\pi$
$829$		−	0.904671i		−	0.0314205i	0.999877	−	0.0157103i	$-0.00500094\pi$
$830$	−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	0.678481	+	0.734618i	$0.262639\pi$
$839$	−9.29013	+	22.4284i	−0.320731	+	0.774313i	−0.999212	+	0.0396949i	$0.987361\pi$
$840$	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	0.949831	+	0.312762i	$0.101254\pi$
$853$	14.5843	+	35.2095i	0.499355	+	1.20555i	−0.450476	+	0.892789i	$0.648746\pi$
$854$		−	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	0.272789	−	0.962074i	$-0.412054\pi$
$857$	−6.28260	−	2.60234i	−0.214610	−	0.0888942i	−0.487398	+	0.873180i	$0.662054\pi$
$858$	4.80798	−	4.80798i	0.164142	−	0.164142i
$859$	−15.7736	+	15.7736i	−0.538188	+	0.538188i	−0.922997	−	0.384808i	$-0.874268\pi$
$859$	−15.7736	+	15.7736i	−0.538188	+	0.538188i	0.384808	+	0.922997i	$0.374268\pi$
$860$	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	$-0.997830\pi$
$863$		−	0.400593i		−	0.0136363i	0.999977	−	0.00681816i	$-0.00217031\pi$
$864$	−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	0.379392	−	0.925236i	$-0.376133\pi$
$877$	−0.194781	−	0.0806809i	−0.00657729	−	0.00272440i	−0.385970	+	0.922511i	$0.626133\pi$
$878$	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	0.785273	+	0.619149i	$0.212522\pi$
$881$	19.8216	+	47.8535i	0.667806	+	1.61223i	−0.117467	+	0.993077i	$0.537478\pi$
$882$	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	0.783523	−	0.621363i	$-0.213421\pi$
$887$	−6.25080	−	15.0908i	−0.209881	−	0.506698i	−0.993404	+	0.114665i	$0.963421\pi$
$888$			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	0.598543	+	0.801091i	$0.295747\pi$
$907$	−11.7800	+	28.4394i	−0.391148	+	0.944314i	−0.989690	+	0.143223i	$0.954253\pi$
$908$	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	0.490072	−	0.871682i	$-0.336971\pi$
$911$	6.64723	+	2.75337i	0.220233	+	0.0912234i	−0.269839	+	0.962905i	$0.586971\pi$
$912$	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	−0.809491	−	0.587132i	$-0.800257\pi$
$929$	5.42751	−	13.1032i	0.178071	−	0.429901i	0.987562	+	0.157231i	$0.0502569\pi$
$930$	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	0.348839	−	0.937183i	$-0.386576\pi$
$937$	−18.0095	−	18.0095i	−0.588344	−	0.588344i	−0.937183	+	0.348839i	$0.886576\pi$
$938$	−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	−0.0910612	+	0.995845i	$0.529026\pi$
$941$	−22.4191	+	54.1244i	−0.730840	+	1.76440i	−0.639779	+	0.768559i	$0.720974\pi$
$942$	−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	−0.0780278	−	0.996951i	$-0.524862\pi$
$947$	17.5946	−	7.28794i	0.571749	−	0.236826i	0.649777	+	0.760125i	$0.274862\pi$
$948$			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	0.972352	+	0.233520i	$0.0750245\pi$
$967$	37.4986	+	37.4986i	1.20587	+	1.20587i	0.233520	+	0.972352i	$0.424975\pi$
$968$	−55.9706			−1.79896
$969$		0			0
$970$	−27.6288			−0.887108
$971$	−2.13924	−	2.13924i	−0.0686516	−	0.0686516i	0.671947	−	0.740599i	$-0.265458\pi$
$971$	−2.13924	−	2.13924i	−0.0686516	−	0.0686516i	−0.740599	+	0.671947i	$0.765458\pi$
$972$	−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	−0.568093	−	0.822965i	$-0.692318\pi$
$977$	7.96654	−	7.96654i	0.254872	−	0.254872i	0.822965	+	0.568093i	$0.192318\pi$
$978$	−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	−0.883267	−	0.468871i	$-0.844661\pi$
$983$	−18.5058	−	44.6770i	−0.590244	−	1.42498i	0.293022	−	0.956106i	$-0.405339\pi$
$984$	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	−0.706456	−	0.707757i	$-0.749707\pi$
$991$	−22.2104	+	9.19984i	−0.705536	+	0.292243i	0.000919961		1.00000i	$0.499707\pi$
$992$	−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	−0.680065	−	0.733152i	$-0.738048\pi$
$997$	10.0798	−	24.3348i	0.319230	−	0.770691i	0.999295	−	0.0375385i	$-0.0119517\pi$
$998$	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.712.3		16
17.2	even	8		867.2.h.i.757.1		16
17.3	odd	16		867.2.d.f.577.7		8
17.4	even	4		867.2.h.i.733.1		16
17.5	odd	16		867.2.a.l.1.1		4
17.6	odd	16		51.2.e.a.13.4	yes	8
17.7	odd	16		51.2.e.a.4.1	✓	8
17.8	even	8	inner	867.2.h.k.688.3		16
17.9	even	8	inner	867.2.h.k.688.4		16
17.10	odd	16		867.2.e.g.616.1		8
17.11	odd	16		867.2.e.g.829.4		8
17.12	odd	16		867.2.a.k.1.1		4
17.13	even	4		867.2.h.i.733.2		16
17.14	odd	16		867.2.d.f.577.8		8
17.15	even	8		867.2.h.i.757.2		16
17.16	even	2	inner	867.2.h.k.712.4		16
51.5	even	16		2601.2.a.be.1.4		4
51.23	even	16		153.2.f.b.64.1		8
51.29	even	16		2601.2.a.bf.1.4		4
51.41	even	16		153.2.f.b.55.4		8
68.7	even	16		816.2.bd.e.769.4		8
68.23	even	16		816.2.bd.e.625.4		8
204.23	odd	16		2448.2.be.x.1441.1		8
204.143	odd	16		2448.2.be.x.1585.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.1	✓	8	17.7	odd	16
51.2.e.a.13.4	yes	8	17.6	odd	16
153.2.f.b.55.4		8	51.41	even	16
153.2.f.b.64.1		8	51.23	even	16
816.2.bd.e.625.4		8	68.23	even	16
816.2.bd.e.769.4		8	68.7	even	16
867.2.a.k.1.1		4	17.12	odd	16
867.2.a.l.1.1		4	17.5	odd	16
867.2.d.f.577.7		8	17.3	odd	16
867.2.d.f.577.8		8	17.14	odd	16
867.2.e.g.616.1		8	17.10	odd	16
867.2.e.g.829.4		8	17.11	odd	16
867.2.h.i.733.1		16	17.4	even	4
867.2.h.i.733.2		16	17.13	even	4
867.2.h.i.757.1		16	17.2	even	8
867.2.h.i.757.2		16	17.15	even	8
867.2.h.k.688.3		16	17.8	even	8	inner
867.2.h.k.688.4		16	17.9	even	8	inner
867.2.h.k.712.3		16	1.1	even	1	trivial
867.2.h.k.712.4		16	17.16	even	2	inner
2448.2.be.x.1441.1		8	204.23	odd	16
2448.2.be.x.1585.1		8	204.143	odd	16
2601.2.a.be.1.4		4	51.5	even	16
2601.2.a.bf.1.4		4	51.29	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

Related objects

Downloads

Learn more