LMFDB - Embedded newform 784.2.w.f.19.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(19,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	784.19
Dual form			784.2.w.f.619.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.610438 + 1.27568i) q^{2} +(0.204601 - 0.763582i) q^{3} +(-1.25473 - 1.55745i) q^{4} +(3.81370 - 1.02188i) q^{5} +(0.849192 + 0.727125i) q^{6} +(2.75275 - 0.649913i) q^{8} +(2.05688 + 1.18754i) q^{9} +(-1.02443 + 5.48886i) q^{10} +(-1.16815 + 4.35958i) q^{11} +(-1.44596 + 0.639434i) q^{12} +(-1.34913 + 1.34913i) q^{13} -3.12115i q^{15} +(-0.851298 + 3.90836i) q^{16} +(-0.989178 + 0.571102i) q^{17} +(-2.77052 + 1.89901i) q^{18} +(3.01629 - 0.808212i) q^{19} +(-6.37669 - 4.65746i) q^{20} +(-4.84836 - 4.15144i) q^{22} +(-1.02392 + 1.77348i) q^{23} +(0.0669534 - 2.23492i) q^{24} +(9.16994 - 5.29427i) q^{25} +(-0.897503 - 2.54463i) q^{26} +(3.00457 - 3.00457i) q^{27} +(5.30239 + 5.30239i) q^{29} +(3.98159 + 1.90527i) q^{30} +(-2.07171 - 3.58830i) q^{31} +(-4.46616 - 3.47180i) q^{32} +(3.08989 + 1.78395i) q^{33} +(-0.124713 - 1.61050i) q^{34} +(-0.731298 - 4.69353i) q^{36} +(-0.803695 - 2.99943i) q^{37} +(-0.810234 + 4.34119i) q^{38} +(0.754139 + 1.30621i) q^{39} +(9.83402 - 5.29154i) q^{40} +8.08732 q^{41} +(-3.82205 - 3.82205i) q^{43} +(8.25554 - 3.65078i) q^{44} +(9.05785 + 2.42704i) q^{45} +(-1.63736 - 2.38879i) q^{46} +(-0.814305 + 1.41042i) q^{47} +(2.81018 + 1.44969i) q^{48} +(1.15613 + 14.9298i) q^{50} +(0.233696 + 0.872167i) q^{51} +(3.79400 + 0.408407i) q^{52} +(-2.92499 - 0.783749i) q^{53} +(1.99877 + 5.66697i) q^{54} +17.8198i q^{55} -2.46854i q^{57} +(-10.0010 + 3.52739i) q^{58} +(-6.97383 - 1.86863i) q^{59} +(-4.86103 + 3.91620i) q^{60} +(-1.68972 - 6.30611i) q^{61} +(5.84218 - 0.452405i) q^{62} +(7.15523 - 3.57809i) q^{64} +(-3.76654 + 6.52383i) q^{65} +(-4.16194 + 2.85273i) q^{66} +(0.616236 + 0.165120i) q^{67} +(2.13062 + 0.824015i) q^{68} +(1.14470 + 1.14470i) q^{69} -2.40482 q^{71} +(6.43387 + 1.93221i) q^{72} +(-1.47966 - 2.56284i) q^{73} +(4.31693 + 0.805706i) q^{74} +(-2.16643 - 8.08521i) q^{75} +(-5.04338 - 3.68363i) q^{76} +(-2.12666 + 0.164684i) q^{78} +(1.06303 + 0.613742i) q^{79} +(0.747273 + 15.7752i) q^{80} +(1.88313 + 3.26167i) q^{81} +(-4.93681 + 10.3169i) q^{82} +(2.29910 + 2.29910i) q^{83} +(-3.18883 + 3.18883i) q^{85} +(7.20885 - 2.54260i) q^{86} +(5.13369 - 2.96394i) q^{87} +(-0.382263 + 12.7600i) q^{88} +(-4.36654 + 7.56307i) q^{89} +(-8.62539 + 10.0734i) q^{90} +(4.04685 - 0.630538i) q^{92} +(-3.16383 + 0.847747i) q^{93} +(-1.30216 - 1.89977i) q^{94} +(10.6773 - 6.16455i) q^{95} +(-3.56478 + 2.69995i) q^{96} -8.42967i q^{97} +(-7.57992 + 7.57992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.610438	+	1.27568i	−0.431645	+	0.902044i
$2$	−0.610438	+	1.27568i	−0.431645	+	0.902044i
$3$	0.204601	−	0.763582i	0.118127	−	0.440854i	−0.881375	−	0.472417i	$-0.843382\pi$
$3$	0.204601	−	0.763582i	0.118127	−	0.440854i	0.999502	+	0.0315627i	$0.0100484\pi$
$4$	−1.25473	−	1.55745i	−0.627366	−	0.778725i
$5$	3.81370	−	1.02188i	1.70554	−	0.456998i	0.731214	−	0.682148i	$-0.238954\pi$
$5$	3.81370	−	1.02188i	1.70554	−	0.456998i	0.974324	+	0.225150i	$0.0722873\pi$
$6$	0.849192	+	0.727125i	0.346681	+	0.296848i
$7$		0			0
$7$		0			0
$8$	2.75275	−	0.649913i	0.973243	−	0.229779i
$9$	2.05688	+	1.18754i	0.685627	+	0.395847i
$10$	−1.02443	+	5.48886i	−0.323955	+	1.73573i
$11$	−1.16815	+	4.35958i	−0.352209	+	1.31446i	0.531751	+	0.846901i	$0.321534\pi$
$11$	−1.16815	+	4.35958i	−0.352209	+	1.31446i	−0.883960	+	0.467562i	$0.845132\pi$
$12$	−1.44596	+	0.639434i	−0.417413	+	0.184589i
$13$	−1.34913	+	1.34913i	−0.374182	+	0.374182i	−0.868998	−	0.494816i	$-0.835236\pi$
$13$	−1.34913	+	1.34913i	−0.374182	+	0.374182i	0.494816	+	0.868998i	$0.335236\pi$
$14$		0			0
$15$		−	3.12115i		−	0.805877i
$16$	−0.851298	+	3.90836i	−0.212825	+	0.977090i
$17$	−0.989178	+	0.571102i	−0.239911	+	0.138513i	−0.615136	−	0.788421i	$-0.710899\pi$
$17$	−0.989178	+	0.571102i	−0.239911	+	0.138513i	0.375225	+	0.926934i	$0.377565\pi$
$18$	−2.77052	+	1.89901i	−0.653018	+	0.447600i
$19$	3.01629	−	0.808212i	0.691984	−	0.185416i	0.104346	−	0.994541i	$-0.466725\pi$
$19$	3.01629	−	0.808212i	0.691984	−	0.185416i	0.587637	+	0.809125i	$0.300058\pi$
$20$	−6.37669	−	4.65746i	−1.42587	−	1.04144i
$21$		0			0
$22$	−4.84836	−	4.15144i	−1.03367	−	0.885089i
$23$	−1.02392	+	1.77348i	−0.213502	+	0.369796i	−0.952808	−	0.303573i	$-0.901820\pi$
$23$	−1.02392	+	1.77348i	−0.213502	+	0.369796i	0.739306	+	0.673369i	$0.235154\pi$
$24$	0.0669534	−	2.23492i	0.0136668	−	0.456201i
$25$	9.16994	−	5.29427i	1.83399	−	1.05885i
$26$	−0.897503	−	2.54463i	−0.176015	−	0.499042i
$27$	3.00457	−	3.00457i	0.578229	−	0.578229i
$28$		0			0
$29$	5.30239	+	5.30239i	0.984630	+	0.984630i	0.999884	−	0.0152539i	$-0.00485565\pi$
$29$	5.30239	+	5.30239i	0.984630	+	0.984630i	−0.0152539	+	0.999884i	$0.504856\pi$
$30$	3.98159	+	1.90527i	0.726936	+	0.347853i
$31$	−2.07171	−	3.58830i	−0.372089	−	0.644478i	0.617797	−	0.786337i	$-0.288025\pi$
$31$	−2.07171	−	3.58830i	−0.372089	−	0.644478i	−0.989887	+	0.141860i	$0.954692\pi$
$32$	−4.46616	−	3.47180i	−0.789514	−	0.613733i
$33$	3.08989	+	1.78395i	0.537881	+	0.310546i
$34$	−0.124713	−	1.61050i	−0.0213882	−	0.276198i
$35$		0			0
$36$	−0.731298	−	4.69353i	−0.121883	−	0.782255i
$37$	−0.803695	−	2.99943i	−0.132127	−	0.493103i	0.867867	−	0.496797i	$-0.165491\pi$
$37$	−0.803695	−	2.99943i	−0.132127	−	0.493103i	−0.999993	+	0.00369416i	$0.998824\pi$
$38$	−0.810234	+	4.34119i	−0.131437	+	0.704234i
$39$	0.754139	+	1.30621i	0.120759	+	0.209161i
$40$	9.83402	−	5.29154i	1.55489	−	0.836666i
$41$	8.08732			1.26303			0.631514	−	0.775365i	$-0.282434\pi$
$41$	8.08732			1.26303			0.631514	+	0.775365i	$0.282434\pi$
$42$		0			0
$43$	−3.82205	−	3.82205i	−0.582858	−	0.582858i	0.352830	−	0.935688i	$-0.385220\pi$
$43$	−3.82205	−	3.82205i	−0.582858	−	0.582858i	−0.935688	+	0.352830i	$0.885220\pi$
$44$	8.25554	−	3.65078i	1.24457	−	0.550375i
$45$	9.05785	+	2.42704i	1.35026	+	0.361802i
$46$	−1.63736	−	2.38879i	−0.241415	−	0.352208i
$47$	−0.814305	+	1.41042i	−0.118779	+	0.205731i	−0.919284	−	0.393595i	$-0.871231\pi$
$47$	−0.814305	+	1.41042i	−0.118779	+	0.205731i	0.800505	+	0.599326i	$0.204565\pi$
$48$	2.81018	+	1.44969i	0.405614	+	0.209245i
$49$		0			0
$50$	1.15613	+	14.9298i	0.163501	+	2.11139i
$51$	0.233696	+	0.872167i	0.0327240	+	0.122128i
$52$	3.79400	+	0.408407i	0.526134	+	0.0566358i
$53$	−2.92499	−	0.783749i	−0.401779	−	0.107656i	0.0522704	−	0.998633i	$-0.483354\pi$
$53$	−2.92499	−	0.783749i	−0.401779	−	0.107656i	−0.454049	+	0.890977i	$0.650021\pi$
$54$	1.99877	+	5.66697i	0.271998	+	0.771177i
$55$			17.8198i			2.40283i
$56$		0			0
$57$		−	2.46854i		−	0.326966i
$58$	−10.0010	+	3.52739i	−1.31319	+	0.463169i
$59$	−6.97383	−	1.86863i	−0.907915	−	0.243275i	−0.225503	−	0.974243i	$-0.572403\pi$
$59$	−6.97383	−	1.86863i	−0.907915	−	0.243275i	−0.682412	+	0.730967i	$0.739069\pi$
$60$	−4.86103	+	3.91620i	−0.627556	+	0.505580i
$61$	−1.68972	−	6.30611i	−0.216346	−	0.807414i	−0.985688	−	0.168578i	$-0.946083\pi$
$61$	−1.68972	−	6.30611i	−0.216346	−	0.807414i	0.769342	−	0.638837i	$-0.220584\pi$
$62$	5.84218	−	0.452405i	0.741958	−	0.0574555i
$63$		0			0
$64$	7.15523	−	3.57809i	0.894403	−	0.447261i
$65$	−3.76654	+	6.52383i	−0.467181	+	0.809182i
$66$	−4.16194	+	2.85273i	−0.512300	+	0.351147i
$67$	0.616236	+	0.165120i	0.0752852	+	0.0201726i	0.296265	−	0.955106i	$-0.404259\pi$
$67$	0.616236	+	0.165120i	0.0752852	+	0.0201726i	−0.220980	+	0.975278i	$0.570926\pi$
$68$	2.13062	+	0.824015i	0.258375	+	0.0999265i
$69$	1.14470	+	1.14470i	0.137806	+	0.137806i
$70$		0			0
$71$	−2.40482			−0.285400			−0.142700	−	0.989766i	$-0.545578\pi$
$71$	−2.40482			−0.285400			−0.142700	+	0.989766i	$0.545578\pi$
$72$	6.43387	+	1.93221i	0.758239	+	0.227713i
$73$	−1.47966	−	2.56284i	−0.173181	−	0.299958i	0.766349	−	0.642424i	$-0.222071\pi$
$73$	−1.47966	−	2.56284i	−0.173181	−	0.299958i	−0.939530	+	0.342466i	$0.888738\pi$
$74$	4.31693	+	0.805706i	0.501832	+	0.0936614i
$75$	−2.16643	−	8.08521i	−0.250157	−	0.933600i
$76$	−5.04338	−	3.68363i	−0.578515	−	0.422541i
$77$		0			0
$78$	−2.12666	+	0.164684i	−0.240797	+	0.0186468i
$79$	1.06303	+	0.613742i	0.119601	+	0.0690514i	0.558607	−	0.829433i	$-0.311336\pi$
$79$	1.06303	+	0.613742i	0.119601	+	0.0690514i	−0.439006	+	0.898484i	$0.644669\pi$
$80$	0.747273	+	15.7752i	0.0835476	+	1.76373i
$81$	1.88313	+	3.26167i	0.209236	+	0.362408i
$82$	−4.93681	+	10.3169i	−0.545179	+	1.13931i
$83$	2.29910	+	2.29910i	0.252359	+	0.252359i	0.821937	−	0.569578i	$-0.192893\pi$
$83$	2.29910	+	2.29910i	0.252359	+	0.252359i	−0.569578	+	0.821937i	$0.692893\pi$
$84$		0			0
$85$	−3.18883	+	3.18883i	−0.345877	+	0.345877i
$86$	7.20885	−	2.54260i	0.777351	−	0.274176i
$87$	5.13369	−	2.96394i	0.550389	−	0.317767i
$88$	−0.382263	+	12.7600i	−0.0407493	+	1.36022i
$89$	−4.36654	+	7.56307i	−0.462852	+	0.801684i	−0.999102	−	0.0423758i	$-0.986507\pi$
$89$	−4.36654	+	7.56307i	−0.462852	+	0.801684i	0.536249	+	0.844060i	$0.319841\pi$
$90$	−8.62539	+	10.0734i	−0.909196	+	1.06183i
$91$		0			0
$92$	4.04685	−	0.630538i	0.421913	−	0.0657381i
$93$	−3.16383	+	0.847747i	−0.328074	+	0.0879073i
$94$	−1.30216	−	1.89977i	−0.134308	−	0.195946i
$95$	10.6773	−	6.16455i	1.09547	−	0.632470i
$96$	−3.56478	+	2.69995i	−0.363829	+	0.275562i
$97$		−	8.42967i		−	0.855903i	−0.903802	−	0.427952i	$-0.859235\pi$
$97$		−	8.42967i		−	0.855903i	0.903802	−	0.427952i	$-0.140765\pi$
$98$		0			0
$99$	−7.57992	+	7.57992i	−0.761810	+	0.761810i
$100$	−19.7514	−	7.63884i	−1.97514	−	0.763884i
$101$	3.81352	−	14.2323i	0.379460	−	1.41616i	−0.467258	−	0.884121i	$-0.654758\pi$
$101$	3.81352	−	14.2323i	0.379460	−	1.41616i	0.846718	−	0.532042i	$-0.178575\pi$
$102$	−1.25526	−	0.234281i	−0.124290	−	0.0231973i
$103$	−6.87358	−	3.96846i	−0.677274	−	0.391024i	0.121553	−	0.992585i	$-0.461213\pi$
$103$	−6.87358	−	3.96846i	−0.677274	−	0.391024i	−0.798827	+	0.601561i	$0.794546\pi$
$104$	−2.83700	+	4.59064i	−0.278191	+	0.450149i
$105$		0			0
$106$	2.78534	−	3.25293i	0.270536	−	0.315953i
$107$	8.96762	−	2.40287i	0.866932	−	0.232294i	0.202172	−	0.979350i	$-0.435200\pi$
$107$	8.96762	−	2.40287i	0.866932	−	0.232294i	0.664761	+	0.747056i	$0.268533\pi$
$108$	−8.44938	−	0.909537i	−0.813042	−	0.0875202i
$109$	0.227686	−	0.849736i	0.0218084	−	0.0813900i	−0.954164	−	0.299284i	$-0.903252\pi$
$109$	0.227686	−	0.849736i	0.0218084	−	0.0813900i	0.975972	+	0.217894i	$0.0699188\pi$
$110$	−22.7325	−	10.8779i	−2.16745	−	1.03717i
$111$	−2.45475			−0.232994
$112$		0			0
$113$	1.91230			0.179894			0.0899469	−	0.995947i	$-0.471330\pi$
$113$	1.91230			0.179894			0.0899469	+	0.995947i	$0.471330\pi$
$114$	3.14908	+	1.50689i	0.294938	+	0.141133i
$115$	−2.09264	+	7.80983i	−0.195140	+	0.728271i
$116$	1.60513	−	14.9113i	0.149033	−	1.38448i
$117$	−4.37715	+	1.17285i	−0.404668	+	0.108430i
$118$	6.64087	−	7.75571i	0.611342	−	0.713971i
$119$		0			0
$120$	−2.02847	−	8.59173i	−0.185174	−	0.784314i
$121$	−8.11511	−	4.68526i	−0.737737	−	0.425933i
$122$	9.07606	+	1.69395i	0.821708	+	0.153363i
$123$	1.65468	−	6.17533i	0.149197	−	0.556811i
$124$	−2.98916	+	7.72893i	−0.268435	+	0.694079i
$125$	15.6022	−	15.6022i	1.39550	−	1.39550i
$126$		0			0
$127$			11.9607i			1.06134i	0.847578	+	0.530671i	$0.178060\pi$
$127$			11.9607i			1.06134i	−0.847578	+	0.530671i	$0.821940\pi$
$128$	0.196687	+	11.3120i	0.0173848	+	0.999849i
$129$	−3.70045	+	2.13645i	−0.325806	+	0.188104i
$130$	−6.02310	−	8.78730i	−0.528261	−	0.770697i
$131$	5.36296	−	1.43700i	0.468564	−	0.125551i	−0.0168089	−	0.999859i	$-0.505351\pi$
$131$	5.36296	−	1.43700i	0.468564	−	0.125551i	0.485372	+	0.874307i	$0.338684\pi$
$132$	−1.09857	−	7.05073i	−0.0956185	−	0.613687i
$133$		0			0
$134$	−0.586814	+	0.685325i	−0.0506930	+	0.0592031i
$135$	8.38821	−	14.5288i	0.721943	−	1.25044i
$136$	−2.35179	+	2.21498i	−0.201664	+	0.189933i
$137$	−12.4195	+	7.17038i	−1.06107	+	0.612607i	−0.925727	−	0.378192i	$-0.876546\pi$
$137$	−12.4195	+	7.17038i	−1.06107	+	0.612607i	−0.135339	+	0.990799i	$0.543212\pi$
$138$	−2.15904	+	0.761506i	−0.183790	+	0.0648237i
$139$	−14.6088	+	14.6088i	−1.23910	+	1.23910i	−0.278731	+	0.960369i	$0.589914\pi$
$139$	−14.6088	+	14.6088i	−1.23910	+	1.23910i	−0.960369	+	0.278731i	$0.910086\pi$
$140$		0			0
$141$	0.910361	+	0.910361i	0.0766663	+	0.0766663i
$142$	1.46799	−	3.06779i	0.123191	−	0.257443i
$143$	−4.30567	−	7.45764i	−0.360058	−	0.623639i
$144$	−6.39236	+	7.02808i	−0.532696	+	0.585674i
$145$	25.6401	+	14.8033i	2.12930	+	1.22935i
$146$	4.17262	−	0.323118i	0.345328	−	0.0267414i
$147$		0			0
$148$	−3.66304	+	5.01519i	−0.301100	+	0.412246i
$149$	−3.05093	−	11.3862i	−0.249942	−	0.932797i	−0.970835	−	0.239750i	$-0.922934\pi$
$149$	−3.05093	−	11.3862i	−0.249942	−	0.932797i	0.720892	−	0.693047i	$-0.243732\pi$
$150$	11.6366	+	2.17185i	0.950127	+	0.177331i
$151$	6.85381	+	11.8712i	0.557755	+	0.966061i	0.997683	+	0.0680276i	$0.0216706\pi$
$151$	6.85381	+	11.8712i	0.557755	+	0.966061i	−0.439928	+	0.898033i	$0.644996\pi$
$152$	7.77781	−	4.18513i	0.630863	−	0.339458i
$153$	−2.71283			−0.219319
$154$		0			0
$155$	−11.5677	−	11.5677i	−0.929138	−	0.929138i
$156$	1.08811	−	2.81347i	0.0871185	−	0.225258i
$157$	−2.01291	−	0.539359i	−0.160648	−	0.0430455i	0.177599	−	0.984103i	$-0.443167\pi$
$157$	−2.01291	−	0.539359i	−0.160648	−	0.0430455i	−0.338247	+	0.941058i	$0.609834\pi$
$158$	−1.43186	+	0.981441i	−0.113912	+	0.0780792i
$159$	−1.19691	+	2.07311i	−0.0949214	+	0.164409i
$160$	−20.5804	−	8.67652i	−1.62702	−	0.685939i
$161$		0			0
$162$	−5.31039	+	0.411225i	−0.417224	+	0.0323089i
$163$	0.466826	+	1.74222i	0.0365647	+	0.136461i	0.981795	−	0.189942i	$-0.0608300\pi$
$163$	0.466826	+	1.74222i	0.0365647	+	0.136461i	−0.945231	+	0.326403i	$0.894163\pi$
$164$	−10.1474	−	12.5956i	−0.792380	−	0.983551i
$165$	13.6069	+	3.64596i	1.05930	+	0.283837i
$166$	−4.33638	+	1.52946i	−0.336568	+	0.118709i
$167$		−	21.6002i		−	1.67147i	−0.549132	−	0.835735i	$-0.685042\pi$
$167$		−	21.6002i		−	1.67147i	0.549132	−	0.835735i	$-0.314958\pi$
$168$		0			0
$169$			9.35968i			0.719976i
$170$	−2.12135	−	6.01452i	−0.162700	−	0.461293i
$171$	7.16393	+	1.91957i	0.547839	+	0.146793i
$172$	−1.15701	+	10.7483i	−0.0882208	+	0.819551i
$173$	2.27429	+	8.48775i	0.172911	+	0.645312i	0.996898	+	0.0787035i	$0.0250780\pi$
$173$	2.27429	+	8.48775i	0.172911	+	0.645312i	−0.823987	+	0.566608i	$0.808255\pi$
$174$	0.647244	+	8.35825i	0.0490674	+	0.633637i
$175$		0			0
$176$	−16.0444	−	8.27684i	−1.20939	−	0.623890i
$177$	−2.85371	+	4.94277i	−0.214498	+	0.371521i
$178$	−6.98257	−	10.1871i	−0.523366	−	0.763556i
$179$	−1.68719	−	0.452081i	−0.126106	−	0.0337901i	0.195214	−	0.980761i	$-0.437460\pi$
$179$	−1.68719	−	0.452081i	−0.126106	−	0.0337901i	−0.321320	+	0.946971i	$0.604127\pi$
$180$	−7.58517	−	17.1524i	−0.565365	−	1.27847i
$181$	−5.29547	−	5.29547i	−0.393609	−	0.393609i	0.482362	−	0.875972i	$-0.339779\pi$
$181$	−5.29547	−	5.29547i	−0.393609	−	0.393609i	−0.875972	+	0.482362i	$0.839779\pi$
$182$		0			0
$183$	−5.16095			−0.381508
$184$	−1.66598	+	5.54739i	−0.122818	+	0.408959i
$185$	−6.13010	−	10.6176i	−0.450694	−	0.780625i
$186$	0.849868	−	4.55354i	0.0623154	−	0.333882i
$187$	−1.33426	−	4.97953i	−0.0975709	−	0.364140i
$188$	3.21839	−	0.501456i	0.234725	−	0.0365725i
$189$		0			0
$190$	1.34617	+	17.3839i	0.0976617	+	1.26116i
$191$	−23.5567	−	13.6004i	−1.70450	−	0.984093i	−0.941076	−	0.338195i	$-0.890184\pi$
$191$	−23.5567	−	13.6004i	−1.70450	−	0.984093i	−0.763423	−	0.645899i	$-0.776483\pi$
$192$	−1.26820	−	6.19568i	−0.0915243	−	0.447135i
$193$	−2.88165	−	4.99117i	−0.207426	−	0.359272i	0.743477	−	0.668762i	$-0.233175\pi$
$193$	−2.88165	−	4.99117i	−0.207426	−	0.359272i	−0.950903	+	0.309489i	$0.899842\pi$
$194$	10.7536	+	5.14579i	0.772062	+	0.369446i
$195$	4.21084	+	4.21084i	0.301545	+	0.301545i
$196$		0			0
$197$	12.7740	−	12.7740i	0.910107	−	0.910107i	−0.0861731	−	0.996280i	$-0.527464\pi$
$197$	12.7740	−	12.7740i	0.910107	−	0.910107i	0.996280	+	0.0861731i	$0.0274638\pi$
$198$	−5.04250	−	14.2966i	−0.358355	−	1.01602i
$199$	4.76949	−	2.75367i	0.338100	−	0.195202i	−0.321331	−	0.946967i	$-0.604130\pi$
$199$	4.76949	−	2.75367i	0.338100	−	0.195202i	0.659432	+	0.751764i	$0.270797\pi$
$200$	21.8017	−	20.5334i	1.54161	−	1.45193i
$201$	0.252165	−	0.436763i	0.0177863	−	0.0308069i
$202$	15.8279	+	13.5528i	1.11365	+	0.953569i
$203$		0			0
$204$	1.06513	−	1.45831i	0.0745740	−	0.102102i
$205$	30.8426	−	8.26425i	2.15414	−	0.577201i
$206$	9.25839	−	6.34601i	0.645063	−	0.442147i
$207$	−4.21216	+	2.43189i	−0.292765	+	0.169028i
$208$	−4.12438	−	6.42141i	−0.285975	−	0.445245i
$209$			14.0939i			0.974893i
$210$		0			0
$211$	19.3846	−	19.3846i	1.33449	−	1.33449i	0.433192	−	0.901302i	$-0.357387\pi$
$211$	19.3846	−	19.3846i	1.33449	−	1.33449i	0.901302	−	0.433192i	$-0.142613\pi$
$212$	2.44943	+	5.53892i	0.168227	+	0.380415i
$213$	−0.492029	+	1.83628i	−0.0337133	+	0.125820i
$214$	−2.40888	+	12.9066i	−0.164668	+	0.882279i
$215$	−18.4818	−	10.6705i	−1.26045	−	0.727722i
$216$	6.31810	−	10.2235i	0.429892	−	0.695622i
$217$		0			0
$218$	0.945005	+	0.809166i	0.0640038	+	0.0548036i
$219$	−2.25968	+	0.605480i	−0.152695	+	0.0409145i
$220$	27.7535	−	22.3591i	1.87114	−	1.50745i
$221$	0.564040	−	2.10503i	0.0379414	−	0.141599i
$222$	1.49847	−	3.13148i	0.100571	−	0.210171i
$223$	−22.1379			−1.48247			−0.741233	−	0.671248i	$-0.765759\pi$
$223$	−22.1379			−1.48247			−0.741233	+	0.671248i	$0.765759\pi$
$224$		0			0
$225$	25.1486			1.67658
$226$	−1.16734	+	2.43948i	−0.0776502	+	0.162272i
$227$	−2.22844	+	8.31664i	−0.147907	+	0.551995i	0.851702	+	0.524026i	$0.175571\pi$
$227$	−2.22844	+	8.31664i	−0.147907	+	0.551995i	−0.999609	+	0.0279688i	$0.991096\pi$
$228$	−3.84463	+	3.09736i	−0.254617	+	0.205128i
$229$	−24.4498	+	6.55130i	−1.61569	+	0.432922i	−0.949731	−	0.313067i	$-0.898643\pi$
$229$	−24.4498	+	6.55130i	−1.61569	+	0.432922i	−0.665957	+	0.745990i	$0.731977\pi$
$230$	−8.68544	−	7.43696i	−0.572701	−	0.490379i
$231$		0			0
$232$	18.0422	+	11.1501i	1.18453	+	0.732037i
$233$	−13.4837	−	7.78481i	−0.883346	−	0.510000i	−0.0115857	−	0.999933i	$-0.503688\pi$
$233$	−13.4837	−	7.78481i	−0.883346	−	0.510000i	−0.871760	+	0.489933i	$0.837021\pi$
$234$	1.17579	−	6.29981i	0.0768638	−	0.411832i
$235$	−1.66424	+	6.21103i	−0.108563	+	0.405163i
$236$	5.83998	+	13.2060i	0.380151	+	0.859639i
$237$	0.686140	−	0.686140i	0.0445696	−	0.0445696i
$238$		0			0
$239$		−	11.6230i		−	0.751832i	−0.926654	−	0.375916i	$-0.877328\pi$
$239$		−	11.6230i		−	0.751832i	0.926654	−	0.375916i	$-0.122672\pi$
$240$	12.1986	+	2.65703i	0.787415	+	0.171510i
$241$	−2.43625	+	1.40657i	−0.156933	+	0.0906051i	−0.576410	−	0.817161i	$-0.695547\pi$
$241$	−2.43625	+	1.40657i	−0.156933	+	0.0906051i	0.419477	+	0.907766i	$0.362213\pi$
$242$	10.9307	−	7.49224i	0.702650	−	0.481619i
$243$	15.1888	−	4.06982i	0.974361	−	0.261079i
$244$	−7.70131	+	10.5441i	−0.493026	+	0.675018i
$245$		0			0
$246$	6.86769	+	5.88050i	0.437868	+	0.374927i
$247$	−2.97899	+	5.15975i	−0.189548	+	0.328307i
$248$	−8.03496	−	8.53125i	−0.510221	−	0.541735i
$249$	2.22595	−	1.28515i	0.141064	−	0.0814432i
$250$	10.3793	+	29.4276i	0.656443	+	1.86117i
$251$	1.99507	−	1.99507i	0.125928	−	0.125928i	−0.641334	−	0.767262i	$-0.721619\pi$
$251$	1.99507	−	1.99507i	0.125928	−	0.125928i	0.767262	+	0.641334i	$0.221619\pi$
$252$		0			0
$253$	−6.53554	−	6.53554i	−0.410886	−	0.410886i
$254$	−15.2581	−	7.30127i	−0.957377	−	0.458123i
$255$	1.78250	+	3.08737i	0.111624	+	0.193339i
$256$	−14.5506	−	6.65436i	−0.909411	−	0.415898i
$257$	−12.9550	−	7.47955i	−0.808108	−	0.466561i	0.0381904	−	0.999270i	$-0.487841\pi$
$257$	−12.9550	−	7.47955i	−0.808108	−	0.466561i	−0.846298	+	0.532709i	$0.821174\pi$
$258$	−0.466544	−	6.02477i	−0.0290458	−	0.375086i
$259$		0			0
$260$	14.8865	−	2.31947i	0.923224	−	0.143847i
$261$	4.60958	+	17.2032i	0.285326	+	1.06485i
$262$	−1.44060	+	7.71863i	−0.0890003	+	0.476858i
$263$	−7.39409	−	12.8069i	−0.455939	−	0.789710i	0.542802	−	0.839860i	$-0.317363\pi$
$263$	−7.39409	−	12.8069i	−0.455939	−	0.789710i	−0.998742	+	0.0501505i	$0.984030\pi$
$264$	9.66510	+	2.90260i	0.594846	+	0.178643i
$265$	−11.9559			−0.734447
$266$		0			0
$267$	4.88162	+	4.88162i	0.298750	+	0.298750i
$268$	−0.516044	−	1.16694i	−0.0315224	−	0.0712820i
$269$	23.1455	+	6.20182i	1.41121	+	0.378132i	0.882356	−	0.470583i	$-0.155956\pi$
$269$	23.1455	+	6.20182i	1.41121	+	0.378132i	0.528851	+	0.848715i	$0.322623\pi$
$270$	13.4137	+	19.5696i	0.816330	+	1.19097i
$271$	−7.37718	+	12.7776i	−0.448131	+	0.776186i	−0.998264	−	0.0588906i	$-0.981244\pi$
$271$	−7.37718	+	12.7776i	−0.448131	+	0.776186i	0.550133	+	0.835077i	$0.314577\pi$
$272$	−1.38999	−	4.35224i	−0.0842805	−	0.263894i
$273$		0			0
$274$	−1.56582	−	20.2204i	−0.0945946	−	1.22156i
$275$	12.3690	+	46.1616i	0.745877	+	2.78365i
$276$	0.346522	−	3.21911i	0.0208582	−	0.193767i
$277$	−17.7680	−	4.76091i	−1.06757	−	0.286055i	−0.318077	−	0.948065i	$-0.603037\pi$
$277$	−17.7680	−	4.76091i	−1.06757	−	0.286055i	−0.749496	+	0.662009i	$0.769704\pi$
$278$	−9.71841	−	27.5539i	−0.582871	−	1.65257i
$279$		−	9.84094i		−	0.589162i
$280$		0			0
$281$			31.9694i			1.90713i	0.301185	+	0.953566i	$0.402618\pi$
$281$			31.9694i			1.90713i	−0.301185	+	0.953566i	$0.597382\pi$
$282$	−1.71705	+	0.605613i	−0.102249	+	0.0360637i
$283$	3.17648	+	0.851136i	0.188822	+	0.0505948i	0.351991	−	0.936003i	$-0.385505\pi$
$283$	3.17648	+	0.851136i	0.188822	+	0.0505948i	−0.163169	+	0.986598i	$0.552171\pi$
$284$	3.01740	+	3.74539i	0.179050	+	0.222248i
$285$	−2.52255	−	9.41428i	−0.149423	−	0.557654i
$286$	12.1419	−	0.940243i	0.717967	−	0.0555977i
$287$		0			0
$288$	−5.06347	−	12.4448i	−0.298368	−	0.733318i
$289$	−7.84768	+	13.5926i	−0.461628	+	0.799564i
$290$	−34.5361	+	23.6722i	−2.02803	+	1.39008i
$291$	−6.43674	−	1.72472i	−0.377329	−	0.101105i
$292$	−2.13493	+	5.52018i	−0.124937	+	0.323044i
$293$	−6.98254	−	6.98254i	−0.407925	−	0.407925i	0.473090	−	0.881014i	$-0.343139\pi$
$293$	−6.98254	−	6.98254i	−0.407925	−	0.407925i	−0.881014	+	0.473090i	$0.843139\pi$
$294$		0			0
$295$	−28.5056			−1.65966
$296$	−4.16174	−	7.73434i	−0.241896	−	0.449549i
$297$	9.58888	+	16.6084i	0.556403	+	0.963719i
$298$	16.3876	+	3.05857i	0.949310	+	0.177178i
$299$	−1.01126	−	3.77406i	−0.0584824	−	0.218259i
$300$	−9.87403	+	13.5189i	−0.570077	+	0.780513i
$301$		0			0
$302$	−19.3276	+	1.49669i	−1.11218	+	0.0861248i
$303$	−10.0872	−	5.82388i	−0.579497	−	0.334573i
$304$	0.591024	+	12.4768i	0.0338976	+	0.715592i
$305$	−12.8881	−	22.3229i	−0.737973	−	1.27821i
$306$	1.65601	−	3.46071i	0.0946680	−	0.197836i
$307$	23.3885	+	23.3885i	1.33485	+	1.33485i	0.900967	+	0.433888i	$0.142859\pi$
$307$	23.3885	+	23.3885i	1.33485	+	1.33485i	0.433888	+	0.900967i	$0.357141\pi$
$308$		0			0
$309$	−4.43659	+	4.43659i	−0.252389	+	0.252389i
$310$	21.8180	−	7.69533i	1.23918	−	0.437065i
$311$	−21.8118	+	12.5931i	−1.23684	+	0.714087i	−0.968446	−	0.249223i	$-0.919825\pi$
$311$	−21.8118	+	12.5931i	−1.23684	+	0.714087i	−0.268390	+	0.963310i	$0.586491\pi$
$312$	2.92487	+	3.10553i	0.165588	+	0.175816i
$313$	−4.22602	+	7.31969i	−0.238869	+	0.413733i	−0.960390	−	0.278659i	$-0.910110\pi$
$313$	−4.22602	+	7.31969i	−0.238869	+	0.413733i	0.721521	+	0.692393i	$0.243443\pi$
$314$	1.91681	−	2.23859i	0.108172	−	0.126331i
$315$		0			0
$316$	−0.377948	−	2.42570i	−0.0212612	−	0.136456i
$317$	18.4857	−	4.95323i	1.03826	−	0.278201i	0.300868	−	0.953666i	$-0.402724\pi$
$317$	18.4857	−	4.95323i	1.03826	−	0.278201i	0.737393	+	0.675464i	$0.236057\pi$
$318$	−1.91399	−	2.79239i	−0.107331	−	0.156589i
$319$	−29.3102	+	16.9222i	−1.64106	+	0.947464i
$320$	23.6315	−	20.9575i	1.32104	−	1.17156i
$321$		−	7.33914i		−	0.409631i
$322$		0			0
$323$	−2.52207	+	2.52207i	−0.140332	+	0.140332i
$324$	2.71707	−	7.02540i	0.150948	−	0.390300i
$325$	−5.22880	+	19.5141i	−0.290041	+	1.08245i
$326$	−2.50749	−	0.467994i	−0.138877	−	0.0259198i
$327$	−0.602258	−	0.347714i	−0.0333050	−	0.0192286i
$328$	22.2623	−	5.25606i	1.22923	−	0.290217i
$329$		0			0
$330$	−12.9573	+	15.1325i	−0.713273	+	0.833014i
$331$	−13.9616	+	3.74100i	−0.767399	+	0.205624i	−0.621222	−	0.783635i	$-0.713364\pi$
$331$	−13.9616	+	3.74100i	−0.767399	+	0.205624i	−0.146177	+	0.989258i	$0.546697\pi$
$332$	0.695979	−	6.46549i	0.0381968	−	0.354840i
$333$	1.90884	−	7.12389i	0.104604	−	0.390387i
$334$	27.5549	+	13.1856i	1.50774	+	0.721482i
$335$	2.51887			0.137621
$336$		0			0
$337$	−13.7159			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$337$	−13.7159			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$338$	−11.9400	−	5.71350i	−0.649449	−	0.310774i
$339$	0.391258	−	1.46020i	0.0212502	−	0.0793069i
$340$	8.96757	+	0.965317i	0.486335	+	0.0523517i
$341$	18.0635	−	4.84011i	0.978196	−	0.262107i
$342$	−6.82189	+	7.96712i	−0.368886	+	0.430812i
$343$		0			0
$344$	−13.0052	−	8.03715i	−0.701191	−	0.433334i
$345$	5.53529	+	3.19580i	0.298010	+	0.172056i
$346$	−12.2160	−	2.27998i	−0.656736	−	0.122572i
$347$	−2.43191	+	9.07603i	−0.130552	+	0.487227i	−0.999977	−	0.00683892i	$-0.997823\pi$
$347$	−2.43191	+	9.07603i	−0.130552	+	0.487227i	0.869425	+	0.494066i	$0.164490\pi$
$348$	−11.0576	−	4.27651i	−0.592748	−	0.229245i
$349$	8.35069	−	8.35069i	0.447002	−	0.447002i	−0.447355	−	0.894357i	$-0.647634\pi$
$349$	8.35069	−	8.35069i	0.447002	−	0.447002i	0.894357	+	0.447355i	$0.147634\pi$
$350$		0			0
$351$			8.10712i			0.432726i
$352$	20.3527	−	15.4150i	1.08480	−	0.821624i
$353$	−16.9374	+	9.77882i	−0.901488	+	0.520474i	−0.877683	−	0.479242i	$-0.840911\pi$
$353$	−16.9374	+	9.77882i	−0.901488	+	0.520474i	−0.0238051	+	0.999717i	$0.507578\pi$
$354$	−4.56339	−	6.65767i	−0.242541	−	0.353851i
$355$	−9.17127	+	2.45743i	−0.486760	+	0.130427i
$356$	17.2579	−	2.68895i	0.914669	−	0.142514i
$357$		0			0
$358$	1.60663	−	1.87635i	0.0849133	−	0.0991681i
$359$	8.80385	−	15.2487i	0.464650	−	0.804797i	−0.534536	−	0.845146i	$-0.679514\pi$
$359$	8.80385	−	15.2487i	0.464650	−	0.804797i	0.999186	+	0.0403489i	$0.0128469\pi$
$360$	26.5113	+	0.794222i	1.39727	+	0.0418592i
$361$	−8.00970	+	4.62440i	−0.421563	+	0.243390i
$362$	9.98789	−	3.52278i	0.524952	−	0.185153i
$363$	−5.23794	+	5.23794i	−0.274920	+	0.274920i
$364$		0			0
$365$	−8.26189	−	8.26189i	−0.432447	−	0.432447i
$366$	3.15044	−	6.58373i	0.164676	−	0.344137i
$367$	−16.4811	−	28.5462i	−0.860309	−	1.49010i	−0.871631	−	0.490163i	$-0.836937\pi$
$367$	−16.4811	−	28.5462i	−0.860309	−	1.49010i	0.0113220	−	0.999936i	$-0.496396\pi$
$368$	−6.05974	−	5.51160i	−0.315886	−	0.287312i
$369$	16.6347	+	9.60402i	0.865966	+	0.499966i
$370$	17.2868	−	1.33865i	0.898697	−	0.0695931i
$371$		0			0
$372$	5.29009	+	3.86382i	0.274278	+	0.200330i
$373$	3.47655	+	12.9747i	0.180009	+	0.671802i	0.995644	+	0.0932356i	$0.0297210\pi$
$373$	3.47655	+	12.9747i	0.180009	+	0.671802i	−0.815635	+	0.578566i	$0.803612\pi$
$374$	7.16679	+	1.33760i	0.370586	+	0.0691657i
$375$	−8.72133	−	15.1058i	−0.450368	−	0.780059i
$376$	−1.32493	+	4.41175i	−0.0683279	+	0.227519i
$377$	−14.3073			−0.736861
$378$		0			0
$379$	0.617225	+	0.617225i	0.0317047	+	0.0317047i	0.722781	−	0.691077i	$-0.242863\pi$
$379$	0.617225	+	0.617225i	0.0317047	+	0.0317047i	−0.691077	+	0.722781i	$0.742863\pi$
$380$	−22.9981	−	8.89453i	−1.17978	−	0.456280i
$381$	9.13298	+	2.44718i	0.467897	+	0.125373i
$382$	31.7297	−	21.7486i	1.62343	−	1.11275i
$383$	−0.214398	+	0.371348i	−0.0109552	+	0.0189750i	−0.871451	−	0.490483i	$-0.836821\pi$
$383$	−0.214398	+	0.371348i	−0.0109552	+	0.0189750i	0.860496	+	0.509457i	$0.170154\pi$
$384$	8.67788	+	2.16426i	0.442841	+	0.110444i
$385$		0			0
$386$	8.12622	−	0.629276i	0.413614	−	0.0320293i
$387$	−3.32267	−	12.4004i	−0.168901	−	0.630346i
$388$	−13.1288	+	10.5770i	−0.666513	+	0.536964i
$389$	10.1095	+	2.70883i	0.512571	+	0.137343i	0.505828	−	0.862634i	$-0.331187\pi$
$389$	10.1095	+	2.70883i	0.512571	+	0.137343i	0.00674269	+	0.999977i	$0.497854\pi$
$390$	−7.94216	+	2.80124i	−0.402167	+	0.141846i
$391$		−	2.33905i		−	0.118291i
$392$		0			0
$393$		−	4.38907i		−	0.221399i
$394$	8.49781	+	24.0932i	0.428113	+	1.21380i
$395$	4.68126	+	1.25434i	0.235540	+	0.0631126i
$396$	21.3161	+	2.29458i	1.07117	+	0.115307i
$397$	−7.22485	−	26.9635i	−0.362605	−	1.35326i	−0.870639	−	0.491922i	$-0.836294\pi$
$397$	−7.22485	−	26.9635i	−0.362605	−	1.35326i	0.508034	−	0.861337i	$-0.330372\pi$
$398$	0.601327	+	7.76530i	0.0301418	+	0.389239i
$399$		0			0
$400$	12.8856	+	40.3465i	0.644278	+	2.01732i
$401$	−13.1880	+	22.8422i	−0.658575	+	1.14069i	0.322410	+	0.946600i	$0.395507\pi$
$401$	−13.1880	+	22.8422i	−0.658575	+	1.14069i	−0.980985	+	0.194085i	$0.937826\pi$
$402$	0.403239	+	0.588299i	0.0201117	+	0.0293417i
$403$	7.63610	+	2.04609i	0.380381	+	0.101923i
$404$	−26.9510	+	11.9183i	−1.34086	+	0.592958i
$405$	10.5147	+	10.5147i	0.522480	+	0.522480i
$406$		0			0
$407$	14.0151			0.694702
$408$	1.21014	+	2.24897i	0.0599108	+	0.111341i
$409$	8.91434	+	15.4401i	0.440786	+	0.763463i	0.997748	−	0.0670744i	$-0.0213665\pi$
$409$	8.91434	+	15.4401i	0.440786	+	0.763463i	−0.556962	+	0.830538i	$0.688033\pi$
$410$	−8.28494	+	44.3902i	−0.409164	+	2.19228i
$411$	2.93414	+	10.9503i	0.144730	+	0.540141i
$412$	2.44382	+	15.6846i	0.120398	+	0.772725i
$413$		0			0
$414$	−0.531059	−	6.85789i	−0.0261001	−	0.337047i
$415$	11.1175	+	6.41868i	0.545735	+	0.315081i
$416$	10.7094	−	1.34153i	0.525070	−	0.0657740i
$417$	8.16602	+	14.1440i	0.399892	+	0.692633i
$418$	−17.9793	−	8.60342i	−0.879396	−	0.420807i
$419$	−19.6171	−	19.6171i	−0.958358	−	0.958358i	0.0408093	−	0.999167i	$-0.487006\pi$
$419$	−19.6171	−	19.6171i	−0.958358	−	0.958358i	−0.999167	+	0.0408093i	$0.987006\pi$
$420$		0			0
$421$	−5.25405	+	5.25405i	−0.256067	+	0.256067i	−0.823452	−	0.567385i	$-0.807955\pi$
$421$	−5.25405	+	5.25405i	−0.256067	+	0.256067i	0.567385	+	0.823452i	$0.307955\pi$
$422$	12.8955	+	36.5618i	0.627745	+	1.77980i
$423$	−3.34986	+	1.93404i	−0.162876	+	0.0940363i
$424$	−8.56113	−	0.256473i	−0.415765	−	0.0124554i
$425$	−6.04714	+	10.4740i	−0.293329	+	0.508061i
$426$	−2.04215	−	1.74861i	−0.0989427	−	0.0847202i
$427$		0			0
$428$	−14.9943	−	10.9517i	−0.724777	−	0.529369i
$429$	−6.57546	+	1.76189i	−0.317466	+	0.0850648i
$430$	24.8942	−	17.0633i	1.20050	−	0.822865i
$431$	23.2543	−	13.4259i	1.12012	−	0.646701i	0.178687	−	0.983906i	$-0.442815\pi$
$431$	23.2543	−	13.4259i	1.12012	−	0.646701i	0.941431	+	0.337205i	$0.109482\pi$
$432$	9.18515	+	14.3007i	0.441921	+	0.688043i
$433$			18.6517i			0.896344i	0.893947	+	0.448172i	$0.147925\pi$
$433$			18.6517i			0.896344i	−0.893947	+	0.448172i	$0.852075\pi$
$434$		0			0
$435$	16.5496	−	16.5496i	0.793491	−	0.793491i
$436$	−1.60911	+	0.711581i	−0.0770622	+	0.0340785i
$437$	−1.65509	+	6.17686i	−0.0791735	+	0.295479i
$438$	0.606995	−	3.25224i	0.0290033	−	0.155398i
$439$	17.5460	+	10.1302i	0.837427	+	0.483488i	0.856389	−	0.516332i	$-0.172703\pi$
$439$	17.5460	+	10.1302i	0.837427	+	0.483488i	−0.0189621	+	0.999820i	$0.506036\pi$
$440$	11.5813	+	49.0535i	0.552119	+	2.33853i
$441$		0			0
$442$	2.34103	+	2.00452i	0.111352	+	0.0953454i
$443$	34.1538	−	9.15149i	1.62270	−	0.434800i	0.670904	−	0.741544i	$-0.265906\pi$
$443$	34.1538	−	9.15149i	1.62270	−	0.434800i	0.951792	+	0.306744i	$0.0992394\pi$
$444$	3.08005	+	3.82314i	0.146173	+	0.181438i
$445$	−8.92414	+	33.3053i	−0.423045	+	1.57882i
$446$	13.5138	−	28.2410i	0.639898	−	1.33725i
$447$	−9.31855			−0.440752
$448$		0			0
$449$	14.0702			0.664012			0.332006	−	0.943277i	$-0.392275\pi$
$449$	14.0702			0.664012			0.332006	+	0.943277i	$0.392275\pi$
$450$	−15.3517	+	32.0817i	−0.723685	+	1.51234i
$451$	−9.44718	+	35.2573i	−0.444850	+	1.66020i
$452$	−2.39942	−	2.97831i	−0.112859	−	0.140088i
$453$	10.4669	−	2.80460i	0.491777	−	0.131771i
$454$	−9.24907	−	7.91957i	−0.434080	−	0.371684i
$455$		0			0
$456$	−1.60434	−	6.79527i	−0.0751300	−	0.318218i
$457$	−4.61613	−	2.66512i	−0.215933	−	0.124669i	0.388133	−	0.921604i	$-0.373120\pi$
$457$	−4.61613	−	2.66512i	−0.215933	−	0.124669i	−0.604066	+	0.796934i	$0.706454\pi$
$458$	6.56770	−	35.1893i	0.306888	−	1.64429i
$459$	−1.25614	+	4.68797i	−0.0586314	+	0.218816i
$460$	14.7891	−	6.54006i	0.689546	−	0.304932i
$461$	2.32075	−	2.32075i	0.108088	−	0.108088i	−0.650995	−	0.759082i	$-0.725648\pi$
$461$	2.32075	−	2.32075i	0.108088	−	0.108088i	0.759082	+	0.650995i	$0.225648\pi$
$462$		0			0
$463$		−	15.2932i		−	0.710736i	−0.934727	−	0.355368i	$-0.884356\pi$
$463$		−	15.2932i		−	0.710736i	0.934727	−	0.355368i	$-0.115644\pi$
$464$	−25.2376	+	16.2098i	−1.17163	+	0.752519i
$465$	−11.1996	+	6.46610i	−0.519370	+	0.299858i
$466$	18.1619	−	12.4488i	0.841334	−	0.576678i
$467$	29.0012	−	7.77086i	1.34202	−	0.359592i	0.484835	−	0.874606i	$-0.338880\pi$
$467$	29.0012	−	7.77086i	1.34202	−	0.359592i	0.857182	+	0.515014i	$0.172213\pi$
$468$	7.31882	+	5.34558i	0.338312	+	0.247099i
$469$		0			0
$470$	−6.90739	−	5.91449i	−0.318614	−	0.272815i
$471$	−0.823689	+	1.42667i	−0.0379536	+	0.0657375i
$472$	−20.4116	−	0.611489i	−0.939522	−	0.0281461i
$473$	21.1273	−	12.1978i	0.971433	−	0.560857i
$474$	0.456451	+	1.29414i	0.0209655	+	0.0594419i
$475$	23.3803	−	23.3803i	1.07276	−	1.07276i
$476$		0			0
$477$	−5.08563	−	5.08563i	−0.232855	−	0.232855i
$478$	14.8273	+	7.09514i	0.678185	+	0.324524i
$479$	17.2367	+	29.8548i	0.787564	+	1.36410i	0.927456	+	0.373933i	$0.121991\pi$
$479$	17.2367	+	29.8548i	0.787564	+	1.36410i	−0.139892	+	0.990167i	$0.544676\pi$
$480$	−10.8360	+	13.9396i	−0.494593	+	0.636251i
$481$	5.13092	+	2.96234i	0.233950	+	0.135071i
$482$	−0.307157	−	3.96651i	−0.0139906	−	0.180669i
$483$		0			0
$484$	2.88523	+	18.5176i	0.131147	+	0.841710i
$485$	−8.61409	−	32.1482i	−0.391146	−	1.45978i
$486$	−4.08001	+	21.8604i	−0.185073	+	0.991610i
$487$	7.45142	+	12.9062i	0.337656	+	0.584837i	0.983991	−	0.178216i	$-0.0570326\pi$
$487$	7.45142	+	12.9062i	0.337656	+	0.584837i	−0.646335	+	0.763053i	$0.723699\pi$
$488$	−8.74978	−	16.2610i	−0.396084	−	0.736099i
$489$	1.42584			0.0644787
$490$		0			0
$491$	30.5248	+	30.5248i	1.37756	+	1.37756i	0.848719	+	0.528844i	$0.177374\pi$
$491$	30.5248	+	30.5248i	1.37756	+	1.37756i	0.528844	+	0.848719i	$0.322626\pi$
$492$	−11.6939	+	5.17131i	−0.527204	+	0.233141i
$493$	−8.27322	−	2.21680i	−0.372607	−	0.0998398i
$494$	−4.76372	−	6.94995i	−0.214330	−	0.312693i
$495$	−21.1618	+	36.6533i	−0.951151	+	1.64744i
$496$	15.7880	−	5.04226i	0.708903	−	0.226404i
$497$		0			0
$498$	0.280643	+	3.62411i	0.0125759	+	0.162400i
$499$	2.86434	+	10.6899i	0.128225	+	0.478544i	0.999934	−	0.0114806i	$-0.00365448\pi$
$499$	2.86434	+	10.6899i	0.128225	+	0.478544i	−0.871709	+	0.490025i	$0.836988\pi$
$500$	−43.8762	−	4.72307i	−1.96220	−	0.211222i
$501$	−16.4935	−	4.41942i	−0.736875	−	0.197445i
$502$	1.32721	+	3.76294i	0.0592363	+	0.167948i
$503$			25.6811i			1.14507i	0.819882	+	0.572533i	$0.194039\pi$
$503$			25.6811i			1.14507i	−0.819882	+	0.572533i	$0.805961\pi$
$504$		0			0
$505$		−	58.1745i		−	2.58873i
$506$	12.3268	−	4.34773i	0.547994	−	0.193280i
$507$	7.14688	+	1.91500i	0.317404	+	0.0850482i
$508$	18.6282	−	15.0075i	0.826493	−	0.665849i
$509$	−3.97493	−	14.8346i	−0.176186	−	0.657534i	−0.996347	−	0.0854009i	$-0.972783\pi$
$509$	−3.97493	−	14.8346i	−0.176186	−	0.657534i	0.820161	−	0.572133i	$-0.193884\pi$
$510$	−5.02661	+	0.389249i	−0.222582	+	0.0172362i
$511$		0			0
$512$	17.3711	−	14.4998i	0.767700	−	0.640809i
$513$	6.63431	−	11.4910i	0.292912	−	0.507338i
$514$	17.4497	−	11.9606i	0.769674	−	0.527560i
$515$	−30.2691	−	8.11057i	−1.33381	−	0.357394i
$516$	7.97049	+	3.08258i	0.350881	+	0.135703i
$517$	−5.19760	−	5.19760i	−0.228590	−	0.228590i
$518$		0			0
$519$	6.94641			0.304914
$520$	−6.12840	+	20.4064i	−0.268748	+	0.894879i
$521$	−14.9189	−	25.8403i	−0.653609	−	1.13208i	−0.982241	−	0.187626i	$-0.939921\pi$
$521$	−14.9189	−	25.8403i	−0.653609	−	1.13208i	0.328632	−	0.944458i	$-0.393412\pi$
$522$	−24.7597	−	4.62112i	−1.08370	−	0.202261i
$523$	−9.32633	−	34.8063i	−0.407812	−	1.52198i	−0.798810	−	0.601583i	$-0.794537\pi$
$523$	−9.32633	−	34.8063i	−0.407812	−	1.52198i	0.390998	−	0.920392i	$-0.372130\pi$
$524$	−8.96712	−	6.54948i	−0.391731	−	0.286116i
$525$		0			0
$526$	20.8512	−	1.61467i	0.909157	−	0.0704030i
$527$	4.09857	+	2.36631i	0.178537	+	0.103078i
$528$	−9.60274	+	10.5577i	−0.417906	+	0.459467i
$529$	9.40318	+	16.2868i	0.408834	+	0.708121i
$530$	7.29835	−	15.2520i	0.317020	−	0.662504i
$531$	−12.1253	−	12.1253i	−0.526191	−	0.526191i
$532$		0			0
$533$	−10.9109	+	10.9109i	−0.472602	+	0.472602i
$534$	−9.20733	+	3.24747i	−0.398440	+	0.140532i
$535$	31.7444	−	18.3276i	1.37243	−	0.792372i
$536$	1.80365	+	0.0540336i	0.0779060	+	0.00233390i
$537$	−0.690401	+	1.19581i	−0.0297930	+	0.0516030i
$538$	−22.0405	+	25.7405i	−0.950231	+	1.10975i
$539$		0			0
$540$	−33.1528	+	5.16554i	−1.42667	+	0.222289i
$541$	−13.0674	+	3.50141i	−0.561813	+	0.150537i	−0.528539	−	0.848909i	$-0.677260\pi$
$541$	−13.0674	+	3.50141i	−0.561813	+	0.150537i	−0.0332740	+	0.999446i	$0.510593\pi$
$542$	−11.7969	−	17.2109i	−0.506721	−	0.739271i
$543$	−5.12698	+	2.96007i	−0.220020	+	0.127029i
$544$	6.40058	+	0.883590i	0.274423	+	0.0378836i
$545$		−	3.47331i		−	0.148780i
$546$		0			0
$547$	−19.9064	+	19.9064i	−0.851134	+	0.851134i	−0.990273	−	0.139139i	$-0.955567\pi$
$547$	−19.9064	+	19.9064i	−0.851134	+	0.851134i	0.139139	+	0.990273i	$0.455567\pi$
$548$	26.7506	+	10.3458i	1.14273	+	0.441950i
$549$	4.01321	−	14.9775i	0.171280	−	0.639225i
$550$	−66.4380	−	12.3999i	−2.83293	−	0.528734i
$551$	20.2790	+	11.7081i	0.863914	+	0.498781i
$552$	3.89503	+	2.40712i	0.165783	+	0.102454i
$553$		0			0
$554$	16.9196	−	19.7600i	0.718847	−	0.839523i
$555$	−9.36167	+	2.50845i	−0.397381	+	0.106478i
$556$	41.0825	+	4.42234i	1.74229	+	0.187549i
$557$	3.45569	−	12.8968i	0.146422	−	0.546456i	−0.853265	−	0.521477i	$-0.825381\pi$
$557$	3.45569	−	12.8968i	0.146422	−	0.546456i	0.999688	−	0.0249794i	$-0.00795201\pi$
$558$	12.5539	+	6.00728i	0.531450	+	0.254309i
$559$	10.3129			0.436190
$560$		0			0
$561$	−4.07527			−0.172058
$562$	−40.7827	−	19.5153i	−1.72032	−	0.823203i
$563$	−6.53907	+	24.4041i	−0.275589	+	1.02851i	0.679857	+	0.733345i	$0.262042\pi$
$563$	−6.53907	+	24.4041i	−0.275589	+	1.02851i	−0.955446	+	0.295167i	$0.904625\pi$
$564$	0.275583	−	2.56010i	0.0116041	−	0.107800i
$565$	7.29293	−	1.95413i	0.306816	−	0.0822110i
$566$	−3.02482	+	3.53262i	−0.127143	+	0.148487i
$567$		0			0
$568$	−6.61986	+	1.56292i	−0.277763	+	0.0655788i
$569$	10.8718	+	6.27682i	0.455768	+	0.263138i	0.710263	−	0.703936i	$-0.248576\pi$
$569$	10.8718	+	6.27682i	0.455768	+	0.263138i	−0.254495	+	0.967074i	$0.581909\pi$
$570$	13.5495	+	2.52886i	0.567526	+	0.105922i
$571$	10.2203	−	38.1427i	0.427706	−	1.59622i	−0.330235	−	0.943899i	$-0.607128\pi$
$571$	10.2203	−	38.1427i	0.427706	−	1.59622i	0.757942	−	0.652322i	$-0.226205\pi$
$572$	−6.21244	+	16.0632i	−0.259755	+	0.671636i
$573$	−15.2048	+	15.2048i	−0.635188	+	0.635188i
$574$		0			0
$575$			21.6836i			0.904268i
$576$	18.9666	+	1.13742i	0.790274	+	0.0473924i
$577$	20.1944	−	11.6592i	0.840702	−	0.485380i	−0.0168006	−	0.999859i	$-0.505348\pi$
$577$	20.1944	−	11.6592i	0.840702	−	0.485380i	0.857503	+	0.514479i	$0.172015\pi$
$578$	−12.5493	−	18.3086i	−0.521982	−	0.761537i
$579$	−4.40076	+	1.17918i	−0.182889	+	0.0490050i
$580$	−9.11603	−	58.5074i	−0.378523	−	2.42939i
$581$		0			0
$582$	6.12943	−	7.15841i	0.254073	−	0.296725i
$583$	6.83364	−	11.8362i	0.283020	−	0.490206i
$584$	−5.73875	−	6.09321i	−0.237471	−	0.252139i
$585$	−15.4946	+	8.94583i	−0.640624	+	0.369865i
$586$	13.1699	−	4.64510i	0.544044	−	0.191887i
$587$	24.2488	−	24.2488i	1.00085	−	1.00085i	0.000853494	−	1.00000i	$-0.499728\pi$
$587$	24.2488	−	24.2488i	1.00085	−	1.00085i	1.00000		0.000853494i	$-0.000271676\pi$
$588$		0			0
$589$	−9.14897	−	9.14897i	−0.376977	−	0.376977i
$590$	17.4009	−	36.3641i	0.716384	−	1.49709i
$591$	−7.14040	−	12.3675i	−0.293717	−	0.508732i
$592$	12.4070	−	0.587721i	0.509926	−	0.0241552i
$593$	−33.2134	−	19.1758i	−1.36391	−	0.787454i	−0.373768	−	0.927522i	$-0.621934\pi$
$593$	−33.2134	−	19.1758i	−1.36391	−	0.787454i	−0.990142	+	0.140068i	$0.955268\pi$
$594$	−27.0405	+	2.09395i	−1.10948	+	0.0859160i
$595$		0			0
$596$	−13.9054	+	19.0384i	−0.569587	+	0.779841i
$597$	−1.12681	−	4.20530i	−0.0461171	−	0.172112i
$598$	5.43181	+	1.01379i	0.222123	+	0.0414568i
$599$	−0.398968	−	0.691033i	−0.0163014	−	0.0282348i	0.857760	−	0.514051i	$-0.171856\pi$
$599$	−0.398968	−	0.691033i	−0.0163014	−	0.0282348i	−0.874061	+	0.485816i	$0.838522\pi$
$600$	−11.2183	−	20.8486i	−0.457986	−	0.851139i
$601$	−4.37578			−0.178492			−0.0892459	−	0.996010i	$-0.528446\pi$
$601$	−4.37578			−0.178492			−0.0892459	+	0.996010i	$0.528446\pi$
$602$		0			0
$603$	1.07144	+	1.07144i	0.0436323	+	0.0436323i
$604$	9.88902	−	25.5696i	0.402379	−	1.04041i
$605$	−35.7363	−	9.57552i	−1.45289	−	0.389300i
$606$	13.5871	−	9.31301i	0.551936	−	0.378315i
$607$	3.27685	−	5.67568i	0.133003	−	0.230369i	−0.791830	−	0.610742i	$-0.790871\pi$
$607$	3.27685	−	5.67568i	0.133003	−	0.230369i	0.924833	+	0.380373i	$0.124205\pi$
$608$	−16.2772	−	6.86233i	−0.660127	−	0.278304i
$609$		0			0
$610$	36.3444	−	2.81443i	1.47154	−	0.113953i
$611$	−0.804235	−	3.00145i	−0.0325359	−	0.121425i
$612$	3.40387	+	4.22509i	0.137593	+	0.170789i
$613$	−18.1595	−	4.86583i	−0.733457	−	0.196529i	−0.127289	−	0.991866i	$-0.540627\pi$
$613$	−18.1595	−	4.86583i	−0.733457	−	0.196529i	−0.606168	+	0.795337i	$0.707294\pi$
$614$	−44.1136	+	15.5591i	−1.78028	+	0.627914i
$615$		−	25.2417i		−	1.01785i
$616$		0			0
$617$		−	22.2202i		−	0.894552i	−0.894396	−	0.447276i	$-0.852394\pi$
$617$		−	22.2202i		−	0.894552i	0.894396	−	0.447276i	$-0.147606\pi$
$618$	−2.95142	−	8.36794i	−0.118723	−	0.336608i
$619$	8.23929	+	2.20771i	0.331165	+	0.0887354i	0.420570	−	0.907260i	$-0.361830\pi$
$619$	8.23929	+	2.20771i	0.331165	+	0.0887354i	−0.0894053	+	0.995995i	$0.528497\pi$
$620$	−3.50174	+	32.5304i	−0.140633	+	1.30645i
$621$	2.25210	+	8.40496i	0.0903738	+	0.337280i
$622$	−2.74999	−	35.5123i	−0.110264	−	1.42391i
$623$		0			0
$624$	−5.74713	+	1.83548i	−0.230069	+	0.0734779i
$625$	17.0872	−	29.5959i	0.683489	−	1.18384i
$626$	−6.75787	−	9.85928i	−0.270099	−	0.394056i
$627$	10.7618	+	2.88362i	0.429785	+	0.115161i
$628$	1.68564	+	3.81176i	0.0672645	+	0.152106i
$629$	2.50798	+	2.50798i	0.0999997	+	0.0999997i
$630$		0			0
$631$	45.0684			1.79415			0.897073	−	0.441882i	$-0.145689\pi$
$631$	45.0684			1.79415			0.897073	+	0.441882i	$0.145689\pi$
$632$	3.32514	+	0.998598i	0.132267	+	0.0397221i
$633$	−10.8356	−	18.7679i	−0.430678	−	0.745956i
$634$	−4.96563	+	26.6055i	−0.197210	+	1.05664i
$635$	12.2224	+	45.6146i	0.485031	+	1.81016i
$636$	4.73058	−	0.737070i	0.187580	−	0.0292267i
$637$		0			0
$638$	−3.69537	−	47.7205i	−0.146301	−	1.88927i
$639$	−4.94643	−	2.85582i	−0.195678	−	0.112975i
$640$	12.3096	+	42.9396i	0.486579	+	1.69734i
$641$	−14.4649	−	25.0540i	−0.571329	−	0.989572i	−0.996430	−	0.0844254i	$-0.973095\pi$
$641$	−14.4649	−	25.0540i	−0.571329	−	0.989572i	0.425100	−	0.905146i	$-0.360239\pi$
$642$	9.36241	+	4.48009i	0.369505	+	0.176815i
$643$	−27.4126	−	27.4126i	−1.08105	−	1.08105i	−0.996412	−	0.0846366i	$-0.973027\pi$
$643$	−27.4126	−	27.4126i	−1.08105	−	1.08105i	−0.0846366	−	0.996412i	$-0.526973\pi$
$644$		0			0
$645$	−11.9292	+	11.9292i	−0.469712	+	0.469712i
$646$	−1.67780	−	4.75693i	−0.0660120	−	0.187159i
$647$	25.8281	−	14.9119i	1.01541	−	0.586247i	0.102638	−	0.994719i	$-0.467272\pi$
$647$	25.8281	−	14.9119i	1.01541	−	0.586247i	0.912771	+	0.408472i	$0.133938\pi$
$648$	7.30358	+	7.75469i	0.286912	+	0.304633i
$649$	16.2929	−	28.2201i	0.639553	−	1.10774i
$650$	−21.7020	−	18.5825i	−0.851222	−	0.728864i
$651$		0			0
$652$	2.12768	−	2.91308i	0.0833263	−	0.114085i
$653$	−12.5980	+	3.37562i	−0.492997	+	0.132098i	−0.496748	−	0.867895i	$-0.665473\pi$
$653$	−12.5980	+	3.37562i	−0.492997	+	0.132098i	0.00375078	+	0.999993i	$0.498806\pi$
$654$	0.811214	−	0.556032i	0.0317210	−	0.0217426i
$655$	18.9843	−	10.9606i	0.741776	−	0.428265i
$656$	−6.88472	+	31.6082i	−0.268803	+	1.23409i
$657$		−	7.02862i		−	0.274213i
$658$		0			0
$659$	−15.1555	+	15.1555i	−0.590375	+	0.590375i	−0.937733	−	0.347358i	$-0.887079\pi$
$659$	−15.1555	+	15.1555i	−0.590375	+	0.590375i	0.347358	+	0.937733i	$0.387079\pi$
$660$	−11.3946	−	25.7668i	−0.443535	−	1.00297i
$661$	−0.571930	+	2.13447i	−0.0222455	+	0.0830213i	−0.976156	−	0.217069i	$-0.930350\pi$
$661$	−0.571930	+	2.13447i	−0.0222455	+	0.0830213i	0.953911	+	0.300091i	$0.0970169\pi$
$662$	3.75036	−	20.0942i	0.145762	−	0.780984i
$663$	−1.49196	−	0.861381i	−0.0579428	−	0.0334533i
$664$	7.82305	+	4.83463i	0.303593	+	0.187620i
$665$		0			0
$666$	7.92259	+	6.78377i	0.306994	+	0.262866i
$667$	−14.8329	+	3.97446i	−0.574332	+	0.153892i
$668$	−33.6412	+	27.1024i	−1.30162	+	1.04862i
$669$	−4.52945	+	16.9041i	−0.175118	+	0.653551i
$670$	−1.53761	+	3.21328i	−0.0594032	+	0.124140i
$671$	29.4658			1.13752
$672$		0			0
$673$	−50.4864			−1.94611			−0.973054	−	0.230577i	$-0.925939\pi$
$673$	−50.4864			−1.94611			−0.973054	+	0.230577i	$0.925939\pi$
$674$	8.37270	−	17.4971i	0.322504	−	0.673964i
$675$	11.6447	−	43.4587i	0.448205	−	1.67273i
$676$	14.5772	−	11.7439i	0.560663	−	0.451688i
$677$	−28.6211	+	7.66899i	−1.10000	+	0.294743i	−0.762763	−	0.646678i	$-0.776158\pi$
$677$	−28.6211	+	7.66899i	−1.10000	+	0.294743i	−0.337234	+	0.941421i	$0.609491\pi$
$678$	1.62391	+	1.39048i	0.0623658	+	0.0534010i
$679$		0			0
$680$	−6.70558	+	10.8505i	−0.257147	+	0.416098i
$681$	5.89450	+	3.40319i	0.225878	+	0.130410i
$682$	−4.85222	+	25.9979i	−0.185801	+	0.995512i
$683$	−0.972755	+	3.63037i	−0.0372214	+	0.138912i	−0.982036	−	0.188693i	$-0.939575\pi$
$683$	−0.972755	+	3.63037i	−0.0372214	+	0.138912i	0.944815	+	0.327605i	$0.106242\pi$
$684$	−5.99917	−	13.5660i	−0.229384	−	0.518709i
$685$	−40.0368	+	40.0368i	−1.52973	+	1.52973i
$686$		0			0
$687$			20.0098i			0.763423i
$688$	18.1917	−	11.6843i	0.693551	−	0.445458i
$689$	5.00358	−	2.88882i	0.190621	−	0.110055i
$690$	−7.45578	+	5.11043i	−0.283837	+	0.194551i
$691$	−13.8605	+	3.71391i	−0.527278	+	0.141284i	−0.512631	−	0.858609i	$-0.671329\pi$
$691$	−13.8605	+	3.71391i	−0.527278	+	0.141284i	−0.0146470	+	0.999893i	$0.504662\pi$
$692$	10.3656	−	14.1919i	0.394042	−	0.539496i
$693$		0			0
$694$	−10.0936	−	8.64270i	−0.383148	−	0.328072i
$695$	−40.7851	+	70.6418i	−1.54707	+	2.67960i
$696$	12.2054	−	11.4954i	0.462646	−	0.435732i
$697$	−7.99980	+	4.61869i	−0.303014	+	0.174945i
$698$	5.55525	+	15.7504i	0.210269	+	0.596162i
$699$	−8.70312	+	8.70312i	−0.329182	+	0.329182i
$700$		0			0
$701$	12.9519	+	12.9519i	0.489187	+	0.489187i	0.908050	−	0.418863i	$-0.137571\pi$
$701$	12.9519	+	12.9519i	0.489187	+	0.489187i	−0.418863	+	0.908050i	$0.637571\pi$
$702$	−10.3421	−	4.94889i	−0.390338	−	0.186784i
$703$	−4.84835	−	8.39758i	−0.182859	−	0.316721i
$704$	7.24063	+	35.3735i	0.272891	+	1.33319i
$705$	4.40212	+	2.54157i	0.165794	+	0.0957210i
$706$	−2.13543	−	27.5761i	−0.0803681	−	1.03784i
$707$		0			0
$708$	11.2787	−	1.75734i	0.423881	−	0.0660448i
$709$	−0.167036	−	0.623389i	−0.00627319	−	0.0234119i	0.962718	−	0.270506i	$-0.0871910\pi$
$709$	−0.167036	−	0.623389i	−0.00627319	−	0.0234119i	−0.968991	+	0.247094i	$0.920524\pi$
$710$	2.46358	−	13.1997i	0.0924566	−	0.495377i
$711$	1.45769	+	2.52479i	0.0546676	+	0.0946870i
$712$	−7.10464	+	23.6571i	−0.266258	+	0.886587i
$713$	8.48503			0.317767
$714$		0			0
$715$	−24.0413	−	24.0413i	−0.899094	−	0.899094i
$716$	1.41287	+	3.19495i	0.0528016	+	0.119401i
$717$	−8.87514	−	2.37809i	−0.331448	−	0.0888113i
$718$	14.0783	+	20.5393i	0.525398	+	0.766521i
$719$	15.4833	−	26.8178i	0.577429	−	1.00014i	−0.418344	−	0.908289i	$-0.637389\pi$
$719$	15.4833	−	26.8178i	0.577429	−	1.00014i	0.995773	−	0.0918476i	$-0.0292772\pi$
$720$	−17.1967	+	33.3352i	−0.640883	+	1.24233i
$721$		0			0
$722$	−1.00985	−	13.0407i	−0.0375826	−	0.485326i
$723$	0.575572	+	2.14806i	0.0214057	+	0.0798873i
$724$	−1.60303	+	14.8918i	−0.0595763	+	0.553450i
$725$	76.6949	+	20.5503i	2.84838	+	0.763221i
$726$	−3.48451	−	9.87938i	−0.129322	−	0.366658i
$727$			16.7744i			0.622128i	0.950389	+	0.311064i	$0.100685\pi$
$727$			16.7744i			0.622128i	−0.950389	+	0.311064i	$0.899315\pi$
$728$		0			0
$729$		−	1.13181i		−	0.0419187i
$730$	15.5829	−	5.49618i	0.576750	−	0.203423i
$731$	5.96348	+	1.59791i	0.220567	+	0.0591008i
$732$	6.47560	+	8.03792i	0.239345	+	0.297090i
$733$	−7.88067	−	29.4110i	−0.291079	−	1.08632i	−0.944282	−	0.329139i	$-0.893242\pi$
$733$	−7.88067	−	29.4110i	−0.291079	−	1.08632i	0.653203	−	0.757183i	$-0.273425\pi$
$734$	46.4766	−	3.59904i	1.71548	−	0.132843i
$735$		0			0
$736$	10.7301	−	4.36581i	0.395518	−	0.160926i
$737$	−1.43971	+	2.49365i	−0.0530323	+	0.0918546i
$738$	−22.4061	+	15.3579i	−0.824780	+	0.565331i
$739$	24.9711	+	6.69098i	0.918577	+	0.246132i	0.686977	−	0.726679i	$-0.258937\pi$
$739$	24.9711	+	6.69098i	0.918577	+	0.246132i	0.231600	+	0.972811i	$0.425604\pi$
$740$	−8.84482	+	22.8696i	−0.325142	+	0.840704i
$741$	3.33039	+	3.33039i	0.122345	+	0.122345i
$742$		0			0
$743$	16.7597			0.614855			0.307427	−	0.951572i	$-0.400532\pi$
$743$	16.7597			0.614855			0.307427	+	0.951572i	$0.400532\pi$
$744$	−8.15827	+	4.38985i	−0.299097	+	0.160940i
$745$	−23.2707	−	40.3060i	−0.852572	−	1.47670i
$746$	−18.6738	−	3.48525i	−0.683695	−	0.127604i
$747$	1.99870	+	7.45925i	0.0731286	+	0.272920i
$748$	−6.08123	+	8.32602i	−0.222352	+	0.304430i
$749$		0			0
$750$	24.5940	−	1.90450i	0.898046	−	0.0695427i
$751$	−19.4065	−	11.2044i	−0.708154	−	0.408853i	0.102223	−	0.994761i	$-0.467404\pi$
$751$	−19.4065	−	11.2044i	−0.708154	−	0.408853i	−0.810377	+	0.585909i	$0.800738\pi$
$752$	−4.81921	−	4.38328i	−0.175738	−	0.159842i
$753$	−1.11521	−	1.93159i	−0.0406404	−	0.0703912i
$754$	8.73369	−	18.2515i	0.318062	−	0.664681i
$755$	38.2692	+	38.2692i	1.39276	+	1.39276i
$756$		0			0
$757$	10.1520	−	10.1520i	0.368982	−	0.368982i	−0.498124	−	0.867106i	$-0.665978\pi$
$757$	10.1520	−	10.1520i	0.368982	−	0.368982i	0.867106	+	0.498124i	$0.165978\pi$
$758$	−1.16416	+	0.410605i	−0.0422842	+	0.0149139i
$759$	−6.32760	+	3.65324i	−0.229677	+	0.132604i
$760$	25.3855	−	23.9088i	0.920830	−	0.867262i
$761$	−10.0149	+	17.3464i	−0.363041	+	0.628805i	−0.988460	−	0.151484i	$-0.951595\pi$
$761$	−10.0149	+	17.3464i	−0.363041	+	0.628805i	0.625419	+	0.780289i	$0.284928\pi$
$762$	−8.69694	+	10.1569i	−0.315057	+	0.367947i
$763$		0			0
$764$	8.37527	+	53.7532i	0.303007	+	1.94472i
$765$	−10.3459	+	2.77218i	−0.374057	+	0.100228i
$766$	−0.342845	−	0.500188i	−0.0123875	−	0.0180725i
$767$	11.9297	−	6.88759i	0.430755	−	0.248696i
$768$	−8.05821	+	9.74907i	−0.290776	+	0.351789i
$769$			50.7365i			1.82960i	0.403902	+	0.914802i	$0.367654\pi$
$769$			50.7365i			1.82960i	−0.403902	+	0.914802i	$0.632346\pi$
$770$		0			0
$771$	−8.36185	+	8.36185i	−0.301144	+	0.301144i
$772$	−4.15780	+	10.7506i	−0.149642	+	0.386923i
$773$	7.73070	−	28.8514i	0.278054	−	1.03771i	−0.675713	−	0.737165i	$-0.736164\pi$
$773$	7.73070	−	28.8514i	0.278054	−	1.03771i	0.953767	−	0.300547i	$-0.0971692\pi$
$774$	17.8472	+	3.33098i	0.641504	+	0.119730i
$775$	−37.9949	−	21.9363i	−1.36482	−	0.787977i
$776$	−5.47855	−	23.2047i	−0.196669	−	0.833002i
$777$		0			0
$778$	−9.62681	+	11.2429i	−0.345138	+	0.403078i
$779$	24.3937	−	6.53627i	0.873994	−	0.234186i
$780$	1.27470	−	11.8417i	0.0456415	−	0.423999i
$781$	2.80918	−	10.4840i	0.100520	−	0.375148i
$782$	2.98388	+	1.42784i	0.106703	+	0.0510596i
$783$	31.8628			1.13868
$784$		0			0
$785$	−8.22781			−0.293663
$786$	5.59905	+	2.67925i	0.199712	+	0.0955658i
$787$	9.92221	−	37.0302i	0.353688	−	1.31998i	−0.528438	−	0.848972i	$-0.677222\pi$
$787$	9.92221	−	37.0302i	0.353688	−	1.31998i	0.882127	−	0.471012i	$-0.156111\pi$
$788$	−35.9227	−	3.86691i	−1.27969	−	0.137753i
$789$	−11.2920	+	3.02568i	−0.402005	+	0.107717i
$790$	−4.45775	+	5.20610i	−0.158600	+	0.185225i
$791$		0			0
$792$	−15.9393	+	25.7919i	−0.566379	+	0.916475i
$793$	10.7874	+	6.22812i	0.383073	+	0.221167i
$794$	38.8072	+	7.24293i	1.37722	+	0.257042i
$795$	−2.44620	+	9.12933i	−0.0867577	+	0.323784i
$796$	−10.2731	−	3.97313i	−0.364121	−	0.140824i
$797$	−18.8328	+	18.8328i	−0.667092	+	0.667092i	−0.957042	−	0.289949i	$-0.906361\pi$
$797$	−18.8328	+	18.8328i	−0.667092	+	0.667092i	0.289949	+	0.957042i	$0.406361\pi$
$798$		0			0
$799$		−	1.86021i		−	0.0658094i
$800$	−59.3351	−	8.19111i	−2.09781	−	0.289600i
$801$	−17.9629	+	10.3709i	−0.634688	+	0.366437i
$802$	−21.0890	−	30.7674i	−0.744678	−	1.08643i
$803$	12.9014	−	3.45692i	0.455280	−	0.121992i
$804$	−0.996635	+	0.155285i	−0.0351486	+	0.00547650i
$805$		0			0
$806$	−7.27152	+	8.49223i	−0.256128	+	0.299126i
$807$	9.47120	−	16.4046i	0.333402	−	0.577469i
$808$	1.24793	−	41.6563i	0.0439021	−	1.46546i
$809$	17.1772	−	9.91725i	0.603918	−	0.348672i	−0.166663	−	0.986014i	$-0.553299\pi$
$809$	17.1772	−	9.91725i	0.603918	−	0.348672i	0.770581	+	0.637342i	$0.219966\pi$
$810$	−19.8320	+	6.99486i	−0.696826	+	0.245774i
$811$	−3.89894	+	3.89894i	−0.136910	+	0.136910i	−0.772240	−	0.635330i	$-0.780864\pi$
$811$	−3.89894	+	3.89894i	−0.136910	+	0.136910i	0.635330	+	0.772240i	$0.280864\pi$
$812$		0			0
$813$	8.24740	+	8.24740i	0.289249	+	0.289249i
$814$	−8.55534	+	17.8788i	−0.299865	+	0.626652i
$815$	3.56067	+	6.16726i	0.124725	+	0.216030i
$816$	−3.60769	+	0.170896i	−0.126294	+	0.00598256i
$817$	−14.6174	−	8.43938i	−0.511400	−	0.295257i
$818$	−25.1383	+	1.94665i	−0.878940	+	0.0680631i
$819$		0			0
$820$	−51.5704	−	37.6664i	−1.80092	−	1.31537i
$821$	−5.00859	−	18.6923i	−0.174801	−	0.652366i	−0.996585	−	0.0825677i	$-0.973688\pi$
$821$	−5.00859	−	18.6923i	−0.174801	−	0.652366i	0.821784	−	0.569798i	$-0.192979\pi$
$822$	−15.7603	−	2.94148i	−0.549702	−	0.102596i
$823$	20.0886	+	34.7944i	0.700243	+	1.21286i	0.968381	+	0.249476i	$0.0802583\pi$
$823$	20.0886	+	34.7944i	0.700243	+	1.21286i	−0.268138	+	0.963381i	$0.586408\pi$
$824$	−21.5004	−	6.45695i	−0.749001	−	0.224938i
$825$	37.7789			1.31529
$826$		0			0
$827$	11.2802	+	11.2802i	0.392250	+	0.392250i	0.875489	−	0.483239i	$-0.160540\pi$
$827$	11.2802	+	11.2802i	0.392250	+	0.392250i	−0.483239	+	0.875489i	$0.660540\pi$
$828$	9.07267	+	3.50885i	0.315297	+	0.121941i
$829$	40.7143	+	10.9094i	1.41407	+	0.378898i	0.883375	−	0.468668i	$-0.155266\pi$
$829$	40.7143	+	10.9094i	1.41407	+	0.378898i	0.530691	+	0.847565i	$0.321933\pi$
$830$	−14.9747	+	10.2642i	−0.519780	+	0.356274i
$831$	−7.27069	+	12.5932i	−0.252217	+	0.436853i
$832$	−4.82603	+	14.4807i	−0.167312	+	0.502027i
$833$		0			0
$834$	−23.0281	+	1.78324i	−0.797396	+	0.0617486i
$835$	−22.0727	−	82.3765i	−0.763858	−	2.85076i
$836$	21.9505	−	17.6840i	0.759173	−	0.611614i
$837$	−17.0059	−	4.55671i	−0.587809	−	0.157503i
$838$	37.0002	−	13.0502i	1.27815	−	0.450811i
$839$		−	27.4328i		−	0.947087i	−0.880771	−	0.473543i	$-0.842975\pi$
$839$		−	27.4328i		−	0.947087i	0.880771	−	0.473543i	$-0.157025\pi$
$840$		0			0
$841$			27.2308i			0.938992i
$842$	−3.49523	−	9.90977i	−0.120454	−	0.341513i
$843$	24.4112	+	6.54097i	0.840767	+	0.225283i
$844$	−54.5131	−	5.86808i	−1.87642	−	0.201988i
$845$	9.56445	+	35.6950i	0.329027	+	1.22795i
$846$	−0.422343	−	5.45396i	−0.0145204	−	0.187511i
$847$		0			0
$848$	5.55322	−	10.7647i	0.190698	−	0.369662i
$849$	1.29982	−	2.25136i	0.0446098	−	0.0772665i
$850$	−9.67003	−	14.1079i	−0.331679	−	0.483898i
$851$	6.14234	+	1.64584i	0.210557	+	0.0564185i
$852$	3.47727	−	1.53772i	0.119129	−	0.0526816i
$853$	8.95019	+	8.95019i	0.306449	+	0.306449i	0.843530	−	0.537082i	$-0.180473\pi$
$853$	8.95019	+	8.95019i	0.306449	+	0.306449i	−0.537082	+	0.843530i	$0.680473\pi$
$854$		0			0
$855$	29.2826			1.00144
$856$	23.1239	−	12.4427i	0.790360	−	0.425281i
$857$	26.8241	+	46.4607i	0.916294	+	1.58707i	0.804995	+	0.593281i	$0.202168\pi$
$857$	26.8241	+	46.4607i	0.916294	+	1.58707i	0.111299	+	0.993787i	$0.464499\pi$
$858$	1.76630	−	9.46372i	0.0603004	−	0.323086i
$859$	3.41188	+	12.7333i	0.116412	+	0.434455i	0.999389	−	0.0349617i	$-0.0111309\pi$
$859$	3.41188	+	12.7333i	0.116412	+	0.434455i	−0.882977	+	0.469417i	$0.844464\pi$
$860$	6.57099	+	42.1731i	0.224069	+	1.43809i
$861$		0			0
$862$	2.93185	+	37.8607i	0.0998591	+	1.28954i
$863$	6.64111	+	3.83425i	0.226066	+	0.130519i	0.608756	−	0.793358i	$-0.291669\pi$
$863$	6.64111	+	3.83425i	0.226066	+	0.130519i	−0.382690	+	0.923877i	$0.625002\pi$
$864$	−23.8501	+	2.98764i	−0.811398	+	0.101642i
$865$	17.3469	+	30.0457i	0.589812	+	1.02158i
$866$	−23.7937	−	11.3857i	−0.808541	−	0.386902i
$867$	8.77341	+	8.77341i	0.297961	+	0.297961i
$868$		0			0
$869$	−3.91744	+	3.91744i	−0.132890	+	0.132890i
$870$	11.0095	+	31.2145i	0.373257	+	1.05827i
$871$	−1.05415	+	0.608615i	−0.0357186	+	0.0206221i
$872$	0.0745077	−	2.48708i	0.00252315	−	0.0842233i
$873$	10.0106	−	17.3388i	0.338807	−	0.586830i
$874$	−6.86939	−	5.88195i	−0.232361	−	0.198960i
$875$		0			0
$876$	3.77830	+	2.75962i	0.127657	+	0.0932391i
$877$	14.8501	−	3.97908i	0.501453	−	0.134364i	0.000778781	−	1.00000i	$-0.499752\pi$
$877$	14.8501	−	3.97908i	0.501453	−	0.134364i	0.500674	+	0.865636i	$0.333085\pi$
$878$	−23.6337	+	16.1993i	−0.797598	+	0.546700i
$879$	−6.76038	+	3.90311i	−0.228022	+	0.131649i
$880$	−69.6464	−	15.1700i	−2.34778	−	0.511380i
$881$		−	21.5605i		−	0.726392i	−0.931713	−	0.363196i	$-0.881686\pi$
$881$		−	21.5605i		−	0.726392i	0.931713	−	0.363196i	$-0.118314\pi$
$882$		0			0
$883$	3.61325	−	3.61325i	0.121596	−	0.121596i	−0.643690	−	0.765286i	$-0.722598\pi$
$883$	3.61325	−	3.61325i	0.121596	−	0.121596i	0.765286	+	0.643690i	$0.222598\pi$
$884$	−3.98619	+	1.76278i	−0.134070	+	0.0592886i
$885$	−5.83228	+	21.7664i	−0.196050	+	0.731668i
$886$	−9.17439	+	49.1558i	−0.308220	+	1.65142i
$887$	31.1537	+	17.9866i	1.04604	+	0.603930i	0.921537	−	0.388290i	$-0.126934\pi$
$887$	31.1537	+	17.9866i	1.04604	+	0.603930i	0.124500	+	0.992220i	$0.460267\pi$
$888$	−6.75730	+	1.59537i	−0.226760	+	0.0535372i
$889$		0			0
$890$	−37.0394	−	31.7152i	−1.24156	−	1.06310i
$891$	−16.4193	+	4.39954i	−0.550067	+	0.147390i
$892$	27.7772	+	34.4787i	0.930048	+	1.15443i
$893$	−1.31626	+	4.91235i	−0.0440470	+	0.164386i
$894$	5.68840	−	11.8875i	0.190248	−	0.397578i
$895$	−6.89640			−0.230521
$896$		0			0
$897$	−3.08871			−0.103129
$898$	−8.58896	+	17.9491i	−0.286617	+	0.598968i
$899$	8.04158	−	30.0116i	0.268202	−	1.00094i
$900$	−31.5548	−	39.1677i	−1.05183	−	1.30559i
$901$	3.34094	−	0.895202i	0.111303	−	0.0298235i
$902$	−39.2103	−	33.5740i	−1.30556	−	1.11789i
$903$		0			0
$904$	5.26407	−	1.24283i	0.175080	−	0.0413358i
$905$	−25.6067	−	14.7840i	−0.851194	−	0.491437i
$906$	−2.81161	+	15.0645i	−0.0934096	+	0.500483i
$907$	4.95935	−	18.5085i	0.164672	−	0.614566i	−0.833409	−	0.552656i	$-0.813614\pi$
$907$	4.95935	−	18.5085i	0.164672	−	0.614566i	0.998082	−	0.0619098i	$-0.0197191\pi$
$908$	15.7488	−	6.96447i	0.522644	−	0.231124i
$909$	24.7454	−	24.7454i	0.820752	−	0.820752i
$910$		0			0
$911$		−	16.9566i		−	0.561797i	−0.959737	−	0.280899i	$-0.909368\pi$
$911$		−	16.9566i		−	0.561797i	0.959737	−	0.280899i	$-0.0906325\pi$
$912$	9.64796	+	2.10147i	0.319476	+	0.0695865i
$913$	−12.7088	+	7.33743i	−0.420600	+	0.242833i
$914$	6.21771	−	4.26182i	0.205664	−	0.140969i
$915$	−19.6823	+	5.27386i	−0.650677	+	0.174348i
$916$	40.8813	+	29.8592i	1.35075	+	0.986576i
$917$		0			0
$918$	−5.21356	−	4.46414i	−0.172073	−	0.147339i
$919$	19.0403	−	32.9788i	0.628083	−	1.08787i	−0.359853	−	0.933009i	$-0.617173\pi$
$919$	19.0403	−	32.9788i	0.628083	−	1.08787i	0.987936	−	0.154863i	$-0.0494935\pi$
$920$	−0.684792	+	22.8585i	−0.0225769	+	0.753623i
$921$	22.6444	−	13.0737i	0.746158	−	0.430794i
$922$	1.54386	+	4.37720i	0.0508444	+	0.144156i
$923$	3.24442	−	3.24442i	0.106791	−	0.106791i
$924$		0			0
$925$	−23.2496	−	23.2496i	−0.764443	−	0.764443i
$926$	19.5093	+	9.33555i	0.641115	+	0.306785i
$927$	−9.42543	−	16.3253i	−0.309572	−	0.536194i
$928$	−5.27252	−	42.0902i	−0.173079	−	1.38168i
$929$	3.92408	+	2.26557i	0.128745	+	0.0743309i	0.562989	−	0.826464i	$-0.309651\pi$
$929$	3.92408	+	2.26557i	0.128745	+	0.0743309i	−0.434244	+	0.900795i	$0.642985\pi$
$930$	−1.41202	−	18.2343i	−0.0463021	−	0.597927i
$931$		0			0
$932$	4.79396	+	30.7680i	0.157031	+	1.00784i
$933$	5.15311	+	19.2317i	0.168705	+	0.629617i
$934$	−7.79030	+	41.7400i	−0.254906	+	1.36577i
$935$	−10.1770	−	17.6270i	−0.332822	−	0.576464i
$936$	−11.2869	+	6.07334i	−0.368925	+	0.198513i
$937$	37.0969			1.21190			0.605952	−	0.795501i	$-0.292792\pi$
$937$	37.0969			1.21190			0.605952	+	0.795501i	$0.292792\pi$
$938$		0			0
$939$	4.72453	+	4.72453i	0.154179	+	0.154179i
$940$	11.7615	−	5.20120i	0.383619	−	0.169645i
$941$	−2.17799	−	0.583589i	−0.0710003	−	0.0190245i	0.223144	−	0.974785i	$-0.428368\pi$
$941$	−2.17799	−	0.583589i	−0.0710003	−	0.0190245i	−0.294144	+	0.955761i	$0.595035\pi$
$942$	−1.31717	−	1.92166i	−0.0429157	−	0.0626111i
$943$	−8.28076	+	14.3427i	−0.269659	+	0.467062i
$944$	13.2401	−	25.6655i	0.430928	−	0.835340i
$945$		0			0
$946$	2.66368	+	34.3977i	0.0866038	+	1.11837i
$947$	−4.22082	−	15.7523i	−0.137158	−	0.511882i	−0.999980	−	0.00637300i	$-0.997971\pi$
$947$	−4.22082	−	15.7523i	−0.137158	−	0.511882i	0.862821	−	0.505509i	$-0.168695\pi$
$948$	−1.92955	−	0.207707i	−0.0626689	−	0.00674601i
$949$	5.45387	+	1.46136i	0.177040	+	0.0474378i
$950$	15.5536	+	44.0980i	0.504626	+	1.43073i
$951$		−	15.1288i		−	0.490585i
$952$		0			0
$953$			27.9419i			0.905126i	0.891733	+	0.452563i	$0.149490\pi$
$953$			27.9419i			0.905126i	−0.891733	+	0.452563i	$0.850510\pi$
$954$	9.59210	−	3.38319i	0.310556	−	0.109535i
$955$	−103.736	−	27.7960i	−3.35682	−	0.899456i
$956$	−18.1023	+	14.5838i	−0.585470	+	0.471674i
$957$	6.92462	+	25.8430i	0.223841	+	0.835387i
$958$	−48.6071	+	3.76403i	−1.57043	+	0.121610i
$959$		0			0
$960$	−11.1678	−	22.3325i	−0.360438	−	0.720779i
$961$	6.91607	−	11.9790i	0.223099	−	0.386419i
$962$	−6.91111	+	4.73710i	−0.222823	+	0.152730i
$963$	21.2988	+	5.70700i	0.686345	+	0.183906i
$964$	5.24750	+	2.02947i	0.169011	+	0.0653648i
$965$	−16.0901	−	16.0901i	−0.517960	−	0.517960i
$966$		0			0
$967$	−47.4478			−1.52582			−0.762910	−	0.646505i	$-0.776230\pi$
$967$	−47.4478			−1.52582			−0.762910	+	0.646505i	$0.776230\pi$
$968$	−25.3838	−	7.62322i	−0.815868	−	0.245020i
$969$	1.40979	+	2.44183i	0.0452890	+	0.0784428i
$970$	46.2693	+	8.63565i	1.48562	+	0.277274i
$971$	8.47546	+	31.6308i	0.271990	+	1.01508i	0.957832	+	0.287330i	$0.0927678\pi$
$971$	8.47546	+	31.6308i	0.271990	+	1.01508i	−0.685841	+	0.727751i	$0.740566\pi$
$972$	−25.3964	−	18.5492i	−0.814590	−	0.594967i
$973$		0			0
$974$	−21.0129	+	1.62719i	−0.673296	+	0.0521385i
$975$	13.8308	+	7.98523i	0.442941	+	0.255732i
$976$	26.0850	−	1.23565i	0.834961	−	0.0395521i
$977$	15.9234	+	27.5802i	0.509435	+	0.882368i	0.999940	+	0.0109296i	$0.00347908\pi$
$977$	15.9234	+	27.5802i	0.509435	+	0.882368i	−0.490505	+	0.871438i	$0.663188\pi$
$978$	−0.870387	+	1.81892i	−0.0278319	+	0.0581626i
$979$	−27.8711	−	27.8711i	−0.890763	−	0.890763i
$980$		0			0
$981$	1.47742	−	1.47742i	0.0471704	−	0.0471704i
$982$	−57.5734	+	20.3064i	−1.83724	+	0.648004i
$983$	−37.4979	+	21.6494i	−1.19600	+	0.690509i	−0.959660	−	0.281162i	$-0.909280\pi$
$983$	−37.4979	+	21.6494i	−1.19600	+	0.690509i	−0.236337	+	0.971671i	$0.575947\pi$
$984$	0.541474	−	18.0745i	0.0172616	−	0.576195i
$985$	35.6626	−	61.7695i	1.13631	−	1.96814i
$986$	7.87822	−	9.20078i	0.250894	−	0.293013i
$987$		0			0
$988$	11.7739	−	1.83449i	0.374577	−	0.0583628i
$989$	10.6918	−	2.86486i	0.339980	−	0.0910973i
$990$	−33.8400	−	49.3703i	−1.07551	−	1.56909i
$991$	−16.4220	+	9.48127i	−0.521663	+	0.301183i	−0.737615	−	0.675222i	$-0.764048\pi$
$991$	−16.4220	+	9.48127i	−0.521663	+	0.301183i	0.215952	+	0.976404i	$0.430715\pi$
$992$	−3.20527	+	23.2185i	−0.101768	+	0.737188i
$993$			11.4262i			0.362601i
$994$		0			0
$995$	15.3755	−	15.3755i	0.487436	−	0.487436i
$996$	−4.79453	−	1.85428i	−0.151920	−	0.0587552i
$997$	−7.83295	+	29.2330i	−0.248072	+	0.925818i	0.723742	+	0.690070i	$0.242420\pi$
$997$	−7.83295	+	29.2330i	−0.248072	+	0.925818i	−0.971814	+	0.235747i	$0.924246\pi$
$998$	−15.3854	−	2.87151i	−0.487015	−	0.0908960i
$999$	−11.4267	−	6.59723i	−0.361526	−	0.208727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.f.19.5		56
7.2	even	3		784.2.j.a.195.28		56
7.3	odd	6	inner	784.2.w.f.227.6		56
7.4	even	3		112.2.v.a.3.6	✓	56
7.5	odd	6		784.2.j.a.195.27		56
7.6	odd	2		112.2.v.a.19.5	yes	56
16.11	odd	4	inner	784.2.w.f.411.6		56
28.11	odd	6		448.2.z.a.367.8		56
28.27	even	2		448.2.z.a.47.8		56
56.11	odd	6		896.2.z.a.479.7		56
56.13	odd	2		896.2.z.b.607.8		56
56.27	even	2		896.2.z.a.607.7		56
56.53	even	6		896.2.z.b.479.8		56
112.11	odd	12		112.2.v.a.59.5	yes	56
112.13	odd	4		896.2.z.a.159.7		56
112.27	even	4		112.2.v.a.75.6	yes	56
112.53	even	12		448.2.z.a.143.8		56
112.59	even	12	inner	784.2.w.f.619.5		56
112.67	odd	12		896.2.z.b.31.8		56
112.69	odd	4		448.2.z.a.271.8		56
112.75	even	12		784.2.j.a.587.28		56
112.83	even	4		896.2.z.b.159.8		56
112.107	odd	12		784.2.j.a.587.27		56
112.109	even	12		896.2.z.a.31.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.6	✓	56	7.4	even	3
112.2.v.a.19.5	yes	56	7.6	odd	2
112.2.v.a.59.5	yes	56	112.11	odd	12
112.2.v.a.75.6	yes	56	112.27	even	4
448.2.z.a.47.8		56	28.27	even	2
448.2.z.a.143.8		56	112.53	even	12
448.2.z.a.271.8		56	112.69	odd	4
448.2.z.a.367.8		56	28.11	odd	6
784.2.j.a.195.27		56	7.5	odd	6
784.2.j.a.195.28		56	7.2	even	3
784.2.j.a.587.27		56	112.107	odd	12
784.2.j.a.587.28		56	112.75	even	12
784.2.w.f.19.5		56	1.1	even	1	trivial
784.2.w.f.227.6		56	7.3	odd	6	inner
784.2.w.f.411.6		56	16.11	odd	4	inner
784.2.w.f.619.5		56	112.59	even	12	inner
896.2.z.a.31.7		56	112.109	even	12
896.2.z.a.159.7		56	112.13	odd	4
896.2.z.a.479.7		56	56.11	odd	6
896.2.z.a.607.7		56	56.27	even	2
896.2.z.b.31.8		56	112.67	odd	12
896.2.z.b.159.8		56	112.83	even	4
896.2.z.b.479.8		56	56.53	even	6
896.2.z.b.607.8		56	56.13	odd	2

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.610438 + 1.27568i) q^{2} +(0.204601 - 0.763582i) q^{3} +(-1.25473 - 1.55745i) q^{4} +(3.81370 - 1.02188i) q^{5} +(0.849192 + 0.727125i) q^{6} +(2.75275 - 0.649913i) q^{8} +(2.05688 + 1.18754i) q^{9} +(-1.02443 + 5.48886i) q^{10} +(-1.16815 + 4.35958i) q^{11} +(-1.44596 + 0.639434i) q^{12} +(-1.34913 + 1.34913i) q^{13} -3.12115i q^{15} +(-0.851298 + 3.90836i) q^{16} +(-0.989178 + 0.571102i) q^{17} +(-2.77052 + 1.89901i) q^{18} +(3.01629 - 0.808212i) q^{19} +(-6.37669 - 4.65746i) q^{20} +(-4.84836 - 4.15144i) q^{22} +(-1.02392 + 1.77348i) q^{23} +(0.0669534 - 2.23492i) q^{24} +(9.16994 - 5.29427i) q^{25} +(-0.897503 - 2.54463i) q^{26} +(3.00457 - 3.00457i) q^{27} +(5.30239 + 5.30239i) q^{29} +(3.98159 + 1.90527i) q^{30} +(-2.07171 - 3.58830i) q^{31} +(-4.46616 - 3.47180i) q^{32} +(3.08989 + 1.78395i) q^{33} +(-0.124713 - 1.61050i) q^{34} +(-0.731298 - 4.69353i) q^{36} +(-0.803695 - 2.99943i) q^{37} +(-0.810234 + 4.34119i) q^{38} +(0.754139 + 1.30621i) q^{39} +(9.83402 - 5.29154i) q^{40} +8.08732 q^{41} +(-3.82205 - 3.82205i) q^{43} +(8.25554 - 3.65078i) q^{44} +(9.05785 + 2.42704i) q^{45} +(-1.63736 - 2.38879i) q^{46} +(-0.814305 + 1.41042i) q^{47} +(2.81018 + 1.44969i) q^{48} +(1.15613 + 14.9298i) q^{50} +(0.233696 + 0.872167i) q^{51} +(3.79400 + 0.408407i) q^{52} +(-2.92499 - 0.783749i) q^{53} +(1.99877 + 5.66697i) q^{54} +17.8198i q^{55} -2.46854i q^{57} +(-10.0010 + 3.52739i) q^{58} +(-6.97383 - 1.86863i) q^{59} +(-4.86103 + 3.91620i) q^{60} +(-1.68972 - 6.30611i) q^{61} +(5.84218 - 0.452405i) q^{62} +(7.15523 - 3.57809i) q^{64} +(-3.76654 + 6.52383i) q^{65} +(-4.16194 + 2.85273i) q^{66} +(0.616236 + 0.165120i) q^{67} +(2.13062 + 0.824015i) q^{68} +(1.14470 + 1.14470i) q^{69} -2.40482 q^{71} +(6.43387 + 1.93221i) q^{72} +(-1.47966 - 2.56284i) q^{73} +(4.31693 + 0.805706i) q^{74} +(-2.16643 - 8.08521i) q^{75} +(-5.04338 - 3.68363i) q^{76} +(-2.12666 + 0.164684i) q^{78} +(1.06303 + 0.613742i) q^{79} +(0.747273 + 15.7752i) q^{80} +(1.88313 + 3.26167i) q^{81} +(-4.93681 + 10.3169i) q^{82} +(2.29910 + 2.29910i) q^{83} +(-3.18883 + 3.18883i) q^{85} +(7.20885 - 2.54260i) q^{86} +(5.13369 - 2.96394i) q^{87} +(-0.382263 + 12.7600i) q^{88} +(-4.36654 + 7.56307i) q^{89} +(-8.62539 + 10.0734i) q^{90} +(4.04685 - 0.630538i) q^{92} +(-3.16383 + 0.847747i) q^{93} +(-1.30216 - 1.89977i) q^{94} +(10.6773 - 6.16455i) q^{95} +(-3.56478 + 2.69995i) q^{96} -8.42967i q^{97} +(-7.57992 + 7.57992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Introduction

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