LMFDB - Embedded newform 784.2.j.a.195.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(195,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.195"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == 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:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			195.27
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40999 - 0.109187i) q^{2} +(-0.558981 - 0.558981i) q^{3} +(1.97616 - 0.307905i) q^{4} +(2.79182 + 2.79182i) q^{5} +(-0.849192 - 0.727125i) q^{6} +(2.75275 - 0.649913i) q^{8} -2.37508i q^{9} +(4.24128 + 3.63162i) q^{10} +(-3.19144 - 3.19144i) q^{11} +(-1.27675 - 0.932521i) q^{12} +(1.34913 - 1.34913i) q^{13} -3.12115i q^{15} +(3.81039 - 1.21694i) q^{16} +1.14220i q^{17} +(-0.259327 - 3.34885i) q^{18} +(2.20808 + 2.20808i) q^{19} +(6.37669 + 4.65746i) q^{20} +(-4.84836 - 4.15144i) q^{22} +2.04784 q^{23} +(-1.90202 - 1.17544i) q^{24} +10.5885i q^{25} +(1.75496 - 2.04957i) q^{26} +(-3.00457 + 3.00457i) q^{27} +(5.30239 + 5.30239i) q^{29} +(-0.340788 - 4.40080i) q^{30} -4.14341 q^{31} +(5.23975 - 2.13191i) q^{32} +3.56790i q^{33} +(0.124713 + 1.61050i) q^{34} +(-0.731298 - 4.69353i) q^{36} +(-2.19573 + 2.19573i) q^{37} +(3.35446 + 2.87228i) q^{38} -1.50828 q^{39} +(9.49962 + 5.87074i) q^{40} -8.08732 q^{41} +(-3.82205 - 3.82205i) q^{43} +(-7.28943 - 5.32412i) q^{44} +(6.63080 - 6.63080i) q^{45} +(2.88743 - 0.223596i) q^{46} -1.62861 q^{47} +(-2.81018 - 1.44969i) q^{48} +(1.15613 + 14.9298i) q^{50} +(0.638470 - 0.638470i) q^{51} +(2.25069 - 3.08150i) q^{52} +(2.14124 - 2.14124i) q^{53} +(-3.90836 + 4.56447i) q^{54} -17.8198i q^{55} -2.46854i q^{57} +(8.05528 + 6.89738i) q^{58} +(-5.10520 + 5.10520i) q^{59} +(-0.961016 - 6.16788i) q^{60} +(4.61639 - 4.61639i) q^{61} +(-5.84218 + 0.452405i) q^{62} +(7.15523 - 3.57809i) q^{64} +7.53307 q^{65} +(0.389567 + 5.03071i) q^{66} +(-0.451116 + 0.451116i) q^{67} +(0.351690 + 2.25718i) q^{68} +(-1.14470 - 1.14470i) q^{69} -2.40482 q^{71} +(-1.54360 - 6.53800i) q^{72} -2.95932 q^{73} +(-2.85622 + 3.33571i) q^{74} +(5.91879 - 5.91879i) q^{75} +(5.04338 + 3.68363i) q^{76} +(-2.12666 + 0.164684i) q^{78} -1.22748i q^{79} +(14.0354 + 7.24046i) q^{80} -3.76625 q^{81} +(-11.4031 + 0.883027i) q^{82} +(-2.29910 - 2.29910i) q^{83} +(-3.18883 + 3.18883i) q^{85} +(-5.80638 - 4.97175i) q^{86} -5.92787i q^{87} +(-10.8594 - 6.71106i) q^{88} -8.73308 q^{89} +(8.62539 - 10.0734i) q^{90} +(4.04685 - 0.630538i) q^{92} +(2.31609 + 2.31609i) q^{93} +(-2.29633 + 0.177822i) q^{94} +12.3291i q^{95} +(-4.12062 - 1.73722i) q^{96} +8.42967i q^{97} +(-7.57992 + 7.57992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Character values

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

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

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 $

$2$	1.40999	−	0.109187i	0.997015	−	0.0772066i
$2$	1.40999	−	0.109187i	0.997015	−	0.0772066i
$3$	−0.558981	−	0.558981i	−0.322728	−	0.322728i	0.527085	−	0.849813i	$-0.323285\pi$
$3$	−0.558981	−	0.558981i	−0.322728	−	0.322728i	−0.849813	+	0.527085i	$0.823285\pi$
$4$	1.97616	−	0.307905i	0.988078	−	0.153952i
$5$	2.79182	+	2.79182i	1.24854	+	1.24854i	0.956365	+	0.292176i	$0.0943794\pi$
$5$	2.79182	+	2.79182i	1.24854	+	1.24854i	0.292176	+	0.956365i	$0.405621\pi$
$6$	−0.849192	−	0.727125i	−0.346681	−	0.296848i
$7$		0			0
$7$		0			0
$8$	2.75275	−	0.649913i	0.973243	−	0.229779i
$9$		−	2.37508i		−	0.791694i
$10$	4.24128	+	3.63162i	1.34121	+	1.14842i
$11$	−3.19144	−	3.19144i	−0.962254	−	0.962254i	0.0370591	−	0.999313i	$-0.488201\pi$
$11$	−3.19144	−	3.19144i	−0.962254	−	0.962254i	−0.999313	+	0.0370591i	$0.988201\pi$
$12$	−1.27675	−	0.932521i	−0.368565	−	0.269196i
$13$	1.34913	−	1.34913i	0.374182	−	0.374182i	−0.494816	−	0.868998i	$-0.664764\pi$
$13$	1.34913	−	1.34913i	0.374182	−	0.374182i	0.868998	+	0.494816i	$0.164764\pi$
$14$		0			0
$15$		−	3.12115i		−	0.805877i
$16$	3.81039	−	1.21694i	0.952597	−	0.304234i
$17$			1.14220i			0.277025i	0.990361	+	0.138513i	$0.0442322\pi$
$17$			1.14220i			0.277025i	−0.990361	+	0.138513i	$0.955768\pi$
$18$	−0.259327	−	3.34885i	−0.0611240	−	0.789331i
$19$	2.20808	+	2.20808i	0.506567	+	0.506567i	0.913471	−	0.406904i	$-0.133392\pi$
$19$	2.20808	+	2.20808i	0.506567	+	0.506567i	−0.406904	+	0.913471i	$0.633392\pi$
$20$	6.37669	+	4.65746i	1.42587	+	1.04144i
$21$		0			0
$22$	−4.84836	−	4.15144i	−1.03367	−	0.885089i
$23$	2.04784			0.427003			0.213502	−	0.976943i	$-0.431513\pi$
$23$	2.04784			0.427003			0.213502	+	0.976943i	$0.431513\pi$
$24$	−1.90202	−	1.17544i	−0.388248	−	0.239936i
$25$			10.5885i			2.11771i
$26$	1.75496	−	2.04957i	0.344176	−	0.401954i
$27$	−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	$0.504856\pi$
$30$	−0.340788	−	4.40080i	−0.0622190	−	0.803472i
$31$	−4.14341			−0.744179			−0.372089	−	0.928197i	$-0.621359\pi$
$31$	−4.14341			−0.744179			−0.372089	+	0.928197i	$0.621359\pi$
$32$	5.23975	−	2.13191i	0.926265	−	0.376872i
$33$			3.56790i			0.621092i
$34$	0.124713	+	1.61050i	0.0213882	+	0.276198i
$35$		0			0
$36$	−0.731298	−	4.69353i	−0.121883	−	0.782255i
$37$	−2.19573	+	2.19573i	−0.360977	+	0.360977i	−0.864172	−	0.503196i	$-0.832157\pi$
$37$	−2.19573	+	2.19573i	−0.360977	+	0.360977i	0.503196	+	0.864172i	$0.332157\pi$
$38$	3.35446	+	2.87228i	0.544165	+	0.465945i
$39$	−1.50828			−0.241518
$40$	9.49962	+	5.87074i	1.50202	+	0.928245i
$41$	−8.08732			−1.26303			−0.631514	−	0.775365i	$-0.717566\pi$
$41$	−8.08732			−1.26303			−0.631514	+	0.775365i	$0.717566\pi$
$42$		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	$0.885220\pi$
$44$	−7.28943	−	5.32412i	−1.09892	−	0.802641i
$45$	6.63080	−	6.63080i	0.988462	−	0.988462i
$46$	2.88743	−	0.223596i	0.425729	−	0.0329675i
$47$	−1.62861			−0.237557			−0.118779	−	0.992921i	$-0.537898\pi$
$47$	−1.62861			−0.237557			−0.118779	+	0.992921i	$0.537898\pi$
$48$	−2.81018	−	1.44969i	−0.405614	−	0.209245i
$49$		0			0
$50$	1.15613	+	14.9298i	0.163501	+	2.11139i
$51$	0.638470	−	0.638470i	0.0894037	−	0.0894037i
$52$	2.25069	−	3.08150i	0.312115	−	0.427327i
$53$	2.14124	−	2.14124i	0.294122	−	0.294122i	−0.544584	−	0.838706i	$-0.683312\pi$
$53$	2.14124	−	2.14124i	0.294122	−	0.294122i	0.838706	+	0.544584i	$0.183312\pi$
$54$	−3.90836	+	4.56447i	−0.531860	+	0.621146i
$55$		−	17.8198i		−	2.40283i
$56$		0			0
$57$		−	2.46854i		−	0.326966i
$58$	8.05528	+	6.89738i	1.05771	+	0.905671i
$59$	−5.10520	+	5.10520i	−0.664640	+	0.664640i	−0.956470	−	0.291830i	$-0.905736\pi$
$59$	−5.10520	+	5.10520i	−0.664640	+	0.664640i	0.291830	+	0.956470i	$0.405736\pi$
$60$	−0.961016	−	6.16788i	−0.124067	−	0.796270i
$61$	4.61639	−	4.61639i	0.591068	−	0.591068i	−0.346852	−	0.937920i	$-0.612749\pi$
$61$	4.61639	−	4.61639i	0.591068	−	0.591068i	0.937920	+	0.346852i	$0.112749\pi$
$62$	−5.84218	+	0.452405i	−0.741958	+	0.0574555i
$63$		0			0
$64$	7.15523	−	3.57809i	0.894403	−	0.447261i
$65$	7.53307			0.934363
$66$	0.389567	+	5.03071i	0.0479524	+	0.619238i
$67$	−0.451116	+	0.451116i	−0.0551126	+	0.0551126i	−0.734126	−	0.679013i	$-0.762408\pi$
$67$	−0.451116	+	0.451116i	−0.0551126	+	0.0551126i	0.679013	+	0.734126i	$0.262408\pi$
$68$	0.351690	+	2.25718i	0.0426487	+	0.273723i
$69$	−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	$0.545578\pi$
$72$	−1.54360	−	6.53800i	−0.181915	−	0.770510i
$73$	−2.95932			−0.346362			−0.173181	−	0.984890i	$-0.555405\pi$
$73$	−2.95932			−0.346362			−0.173181	+	0.984890i	$0.555405\pi$
$74$	−2.85622	+	3.33571i	−0.332029	+	0.387769i
$75$	5.91879	−	5.91879i	0.683443	−	0.683443i
$76$	5.04338	+	3.68363i	0.578515	+	0.422541i
$77$		0			0
$78$	−2.12666	+	0.164684i	−0.240797	+	0.0186468i
$79$		−	1.22748i		−	0.138103i	−0.997613	−	0.0690514i	$-0.978003\pi$
$79$		−	1.22748i		−	0.138103i	0.997613	−	0.0690514i	$-0.0219972\pi$
$80$	14.0354	+	7.24046i	1.56920	+	0.809508i
$81$	−3.76625			−0.418473
$82$	−11.4031	+	0.883027i	−1.25926	+	0.0975141i
$83$	−2.29910	−	2.29910i	−0.252359	−	0.252359i	0.569578	−	0.821937i	$-0.307107\pi$
$83$	−2.29910	−	2.29910i	−0.252359	−	0.252359i	−0.821937	+	0.569578i	$0.807107\pi$
$84$		0			0
$85$	−3.18883	+	3.18883i	−0.345877	+	0.345877i
$86$	−5.80638	−	4.97175i	−0.626119	−	0.536118i
$87$		−	5.92787i		−	0.635534i
$88$	−10.8594	−	6.71106i	−1.15761	−	0.715401i
$89$	−8.73308			−0.925705			−0.462852	−	0.886435i	$-0.653174\pi$
$89$	−8.73308			−0.925705			−0.462852	+	0.886435i	$0.653174\pi$
$90$	8.62539	−	10.0734i	0.909196	−	1.06183i
$91$		0			0
$92$	4.04685	−	0.630538i	0.421913	−	0.0657381i
$93$	2.31609	+	2.31609i	0.240167	+	0.240167i
$94$	−2.29633	+	0.177822i	−0.236848	+	0.0183410i
$95$			12.3291i			1.26494i
$96$	−4.12062	−	1.73722i	−0.420559	−	0.177304i
$97$			8.42967i			0.855903i	0.903802	+	0.427952i	$0.140765\pi$
$97$			8.42967i			0.855903i	−0.903802	+	0.427952i	$0.859235\pi$
$98$		0			0
$99$	−7.57992	+	7.57992i	−0.761810	+	0.761810i
$100$	3.26026	+	20.9246i	0.326026	+	2.09246i
$101$	−10.4187	−	10.4187i	−1.03670	−	1.03670i	−0.999300	−	0.0374034i	$-0.988091\pi$
$101$	−10.4187	−	10.4187i	−1.03670	−	1.03670i	−0.0374034	−	0.999300i	$-0.511909\pi$
$102$	0.830526	−	0.969951i	0.0822343	−	0.0960394i
$103$		−	7.93693i		−	0.782049i	−0.920380	−	0.391024i	$-0.872121\pi$
$103$		−	7.93693i		−	0.782049i	0.920380	−	0.391024i	$-0.127879\pi$
$104$	2.83700	−	4.59064i	0.278191	−	0.450149i
$105$		0			0
$106$	2.78534	−	3.25293i	0.270536	−	0.315953i
$107$	−6.56475	−	6.56475i	−0.634639	−	0.634639i	0.314589	−	0.949228i	$-0.398133\pi$
$107$	−6.56475	−	6.56475i	−0.634639	−	0.634639i	−0.949228	+	0.314589i	$0.898133\pi$
$108$	−5.01237	+	6.86261i	−0.482316	+	0.660355i
$109$	0.622050	+	0.622050i	0.0595816	+	0.0595816i	0.736270	−	0.676688i	$-0.236585\pi$
$109$	0.622050	+	0.622050i	0.0595816	+	0.0595816i	−0.676688	+	0.736270i	$0.736585\pi$
$110$	−1.94569	−	25.1258i	−0.185514	−	2.39565i
$111$	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	$0.471330\pi$
$114$	−0.269532	−	3.48063i	−0.0252440	−	0.325990i
$115$	5.71719	+	5.71719i	0.533131	+	0.533131i
$116$	12.1110	+	8.84573i	1.12448	+	0.821305i
$117$	−3.20430	−	3.20430i	−0.296238	−	0.296238i
$118$	−6.64087	+	7.75571i	−0.611342	+	0.713971i
$119$		0			0
$120$	−2.02847	−	8.59173i	−0.185174	−	0.784314i
$121$			9.37052i			0.851865i
$122$	6.00503	−	7.01313i	0.543670	−	0.634939i
$123$	4.52066	+	4.52066i	0.407614	+	0.407614i
$124$	−8.18803	+	1.27578i	−0.735307	+	0.114568i
$125$	−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	$0.821940\pi$
$128$	9.69813	−	5.82634i	0.857202	−	0.514980i
$129$			4.27291i			0.376209i
$130$	10.6216	−	0.822511i	0.931574	−	0.0721390i
$131$	3.92596	+	3.92596i	0.343012	+	0.343012i	0.857499	−	0.514486i	$-0.172017\pi$
$131$	3.92596	+	3.92596i	0.343012	+	0.343012i	−0.514486	+	0.857499i	$0.672017\pi$
$132$	1.09857	+	7.05073i	0.0956185	+	0.613687i
$133$		0			0
$134$	−0.586814	+	0.685325i	−0.0506930	+	0.0592031i
$135$	−16.7764			−1.44389
$136$	0.742333	+	3.14420i	0.0636546	+	0.269613i
$137$		−	14.3408i		−	1.22521i	−0.790388	−	0.612607i	$-0.790121\pi$
$137$		−	14.3408i		−	1.22521i	0.790388	−	0.612607i	$-0.209879\pi$
$138$	−1.73901	−	1.48903i	−0.148034	−	0.126755i
$139$	14.6088	−	14.6088i	1.23910	−	1.23910i	0.278731	−	0.960369i	$-0.410086\pi$
$139$	14.6088	−	14.6088i	1.23910	−	1.23910i	0.960369	−	0.278731i	$-0.0899137\pi$
$140$		0			0
$141$	0.910361	+	0.910361i	0.0766663	+	0.0766663i
$142$	−3.39078	+	0.262574i	−0.284548	+	0.0220347i
$143$	−8.61134			−0.720116
$144$	−2.89032	−	9.04998i	−0.240860	−	0.754165i
$145$			29.6067i			2.45870i
$146$	−4.17262	+	0.323118i	−0.345328	+	0.0267414i
$147$		0			0
$148$	−3.66304	+	5.01519i	−0.301100	+	0.412246i
$149$	−8.33531	+	8.33531i	−0.682855	+	0.682855i	−0.960643	−	0.277788i	$-0.910399\pi$
$149$	−8.33531	+	8.33531i	−0.682855	+	0.682855i	0.277788	+	0.960643i	$0.410399\pi$
$150$	7.69919	−	8.99170i	0.628636	−	0.734169i
$151$	−13.7076			−1.11551			−0.557755	−	0.830005i	$-0.688337\pi$
$151$	−13.7076			−1.11551			−0.557755	+	0.830005i	$0.688337\pi$
$152$	7.51333	+	4.64321i	0.609411	+	0.376614i
$153$	2.71283			0.219319
$154$		0			0
$155$	−11.5677	−	11.5677i	−0.929138	−	0.929138i
$156$	−2.98059	+	0.464406i	−0.238638	+	0.0371822i
$157$	−1.47356	+	1.47356i	−0.117603	+	0.117603i	−0.763459	−	0.645856i	$-0.776500\pi$
$157$	−1.47356	+	1.47356i	−0.117603	+	0.117603i	0.645856	+	0.763459i	$0.276500\pi$
$158$	−0.134025	−	1.73074i	−0.0106624	−	0.137691i
$159$	−2.39383			−0.189843
$160$	20.5804	+	8.67652i	1.62702	+	0.685939i
$161$		0			0
$162$	−5.31039	+	0.411225i	−0.417224	+	0.0323089i
$163$	1.27539	−	1.27539i	0.0998965	−	0.0998965i	−0.655392	−	0.755289i	$-0.727497\pi$
$163$	1.27539	−	1.27539i	0.0998965	−	0.0998965i	0.755289	+	0.655392i	$0.227497\pi$
$164$	−15.9818	+	2.49012i	−1.24797	+	0.194446i
$165$	−9.96094	+	9.96094i	−0.775458	+	0.775458i
$166$	−3.49274	−	2.99068i	−0.271090	−	0.232122i
$167$			21.6002i			1.67147i	0.549132	+	0.835735i	$0.314958\pi$
$167$			21.6002i			1.67147i	−0.549132	+	0.835735i	$0.685042\pi$
$168$		0			0
$169$			9.35968i			0.719976i
$170$	−4.14805	+	4.84441i	−0.318141	+	0.371549i
$171$	5.24436	−	5.24436i	0.401046	−	0.401046i
$172$	−8.72981	−	6.37615i	−0.665642	−	0.486177i
$173$	−6.21347	+	6.21347i	−0.472401	+	0.472401i	−0.902691	−	0.430290i	$-0.858411\pi$
$173$	−6.21347	+	6.21347i	−0.472401	+	0.472401i	0.430290	+	0.902691i	$0.358411\pi$
$174$	−0.647244	−	8.35825i	−0.0490674	−	0.633637i
$175$		0			0
$176$	−16.0444	−	8.27684i	−1.20939	−	0.623890i
$177$	5.70741			0.428995
$178$	−12.3136	+	0.953535i	−0.922942	+	0.0714705i
$179$	1.23511	−	1.23511i	0.0923162	−	0.0923162i	−0.659441	−	0.751757i	$-0.729207\pi$
$179$	1.23511	−	1.23511i	0.0923162	−	0.0923162i	0.751757	+	0.659441i	$0.229207\pi$
$180$	11.0619	−	15.1452i	0.824502	−	1.12885i
$181$	5.29547	+	5.29547i	0.393609	+	0.393609i	0.875972	−	0.482362i	$-0.160221\pi$
$181$	5.29547	+	5.29547i	0.393609	+	0.393609i	−0.482362	+	0.875972i	$0.660221\pi$
$182$		0			0
$183$	−5.16095			−0.381508
$184$	5.63718	−	1.33092i	0.415578	−	0.0981164i
$185$	−12.2602			−0.901388
$186$	3.51855	+	3.01278i	0.257993	+	0.220908i
$187$	3.64527	−	3.64527i	0.266569	−	0.266569i
$188$	−3.21839	+	0.501456i	−0.234725	+	0.0365725i
$189$		0			0
$190$	1.34617	+	17.3839i	0.0976617	+	1.26116i
$191$			27.2009i			1.96819i	0.177653	+	0.984093i	$0.443150\pi$
$191$			27.2009i			1.96819i	−0.177653	+	0.984093i	$0.556850\pi$
$192$	−5.99972	−	1.99955i	−0.432992	−	0.144305i
$193$	5.76331			0.414852			0.207426	−	0.978251i	$-0.433491\pi$
$193$	5.76331			0.414852			0.207426	+	0.978251i	$0.433491\pi$
$194$	0.920407	+	11.8858i	0.0660814	+	0.853349i
$195$	−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	$0.0274638\pi$
$198$	−9.86000	+	11.5153i	−0.700720	+	0.818353i
$199$		−	5.50734i		−	0.390405i	−0.980763	−	0.195202i	$-0.937464\pi$
$199$		−	5.50734i		−	0.390405i	0.980763	−	0.195202i	$-0.0625364\pi$
$200$	6.88163	+	29.1476i	0.486604	+	2.06104i
$201$	0.504330			0.0355727
$202$	−15.8279	−	13.5528i	−1.11365	−	0.953569i
$203$		0			0
$204$	1.06513	−	1.45831i	0.0745740	−	0.102102i
$205$	−22.5784	−	22.5784i	−1.57694	−	1.57694i
$206$	−0.866606	−	11.1910i	−0.0603793	−	0.779714i
$207$		−	4.86378i		−	0.338056i
$208$	3.49891	−	6.78253i	0.242606	−	0.470284i
$209$		−	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	$-0.142613\pi$
$212$	3.57213	−	4.89073i	0.245335	−	0.335897i
$213$	1.34425	+	1.34425i	0.0921064	+	0.0921064i
$214$	−9.97303	−	8.53947i	−0.681743	−	0.583746i
$215$		−	21.3410i		−	1.45544i
$216$	−6.31810	+	10.2235i	−0.429892	+	0.695622i
$217$		0			0
$218$	0.945005	+	0.809166i	0.0640038	+	0.0548036i
$219$	1.65420	+	1.65420i	0.111781	+	0.111781i
$220$	−5.48681	−	35.2148i	−0.369921	−	2.37418i
$221$	1.54099	+	1.54099i	0.103658	+	0.103658i
$222$	3.46117	−	0.268025i	0.232299	−	0.0179887i
$223$	22.1379			1.48247			0.741233	−	0.671248i	$-0.234241\pi$
$223$	22.1379			1.48247			0.741233	+	0.671248i	$0.234241\pi$
$224$		0			0
$225$	25.1486			1.67658
$226$	2.69632	−	0.208797i	0.179357	−	0.0138890i
$227$	6.08820	+	6.08820i	0.404088	+	0.404088i	0.879671	−	0.475583i	$-0.157763\pi$
$227$	6.08820	+	6.08820i	0.404088	+	0.404088i	−0.475583	+	0.879671i	$0.657763\pi$
$228$	−0.760075	−	4.87823i	−0.0503372	−	0.323068i
$229$	−17.8985	−	17.8985i	−1.18277	−	1.18277i	−0.979025	−	0.203741i	$-0.934690\pi$
$229$	−17.8985	−	17.8985i	−1.18277	−	1.18277i	−0.203741	−	0.979025i	$-0.565310\pi$
$230$	8.68544	+	7.43696i	0.572701	+	0.490379i
$231$		0			0
$232$	18.0422	+	11.1501i	1.18453	+	0.732037i
$233$			15.5696i			1.02000i	0.860174	+	0.510000i	$0.170355\pi$
$233$			15.5696i			1.02000i	−0.860174	+	0.510000i	$0.829645\pi$
$234$	−4.86790	−	4.16817i	−0.318225	−	0.272482i
$235$	−4.54679	−	4.54679i	−0.296600	−	0.296600i
$236$	−8.51676	+	11.6606i	−0.554394	+	0.759039i
$237$	−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	$-0.122672\pi$
$240$	−3.79824	−	11.8928i	−0.245175	−	0.767676i
$241$			2.81314i			0.181210i	0.995887	+	0.0906051i	$0.0288801\pi$
$241$			2.81314i			0.181210i	−0.995887	+	0.0906051i	$0.971120\pi$
$242$	1.02314	+	13.2124i	0.0657696	+	0.849323i
$243$	11.1190	+	11.1190i	0.713282	+	0.713282i
$244$	7.70131	−	10.5441i	0.493026	−	0.675018i
$245$		0			0
$246$	6.86769	+	5.88050i	0.437868	+	0.374927i
$247$	5.95797			0.379097
$248$	−11.4058	+	2.69286i	−0.724267	+	0.170997i
$249$			2.57031i			0.162886i
$250$	−20.2954	+	23.7025i	−1.28360	+	1.49908i
$251$	−1.99507	+	1.99507i	−0.125928	+	0.125928i	−0.767262	−	0.641334i	$-0.778381\pi$
$251$	−1.99507	+	1.99507i	−0.125928	+	0.125928i	0.641334	+	0.767262i	$0.278381\pi$
$252$		0			0
$253$	−6.53554	−	6.53554i	−0.410886	−	0.410886i
$254$	1.30595	+	16.8645i	0.0819426	+	1.05817i
$255$	3.56499			0.223248
$256$	13.0381	−	9.27399i	0.814884	−	0.579625i
$257$		−	14.9591i		−	0.933123i	−0.884489	−	0.466561i	$-0.845493\pi$
$257$		−	14.9591i		−	0.933123i	0.884489	−	0.466561i	$-0.154507\pi$
$258$	0.466544	+	6.02477i	0.0290458	+	0.375086i
$259$		0			0
$260$	14.8865	−	2.31947i	0.923224	−	0.143847i
$261$	12.5936	−	12.5936i	0.779525	−	0.779525i
$262$	5.96423	+	5.10691i	0.368471	+	0.315506i
$263$	14.7882			0.911878			0.455939	−	0.890011i	$-0.349303\pi$
$263$	14.7882			0.911878			0.455939	+	0.890011i	$0.349303\pi$
$264$	2.31882	+	9.82153i	0.142714	+	0.604473i
$265$	11.9559			0.734447
$266$		0			0
$267$	4.88162	+	4.88162i	0.298750	+	0.298750i
$268$	−0.752575	+	1.03038i	−0.0459708	+	0.0629402i
$269$	16.9437	−	16.9437i	1.03308	−	1.03308i	0.0336411	−	0.999434i	$-0.489290\pi$
$269$	16.9437	−	16.9437i	1.03308	−	1.03308i	0.999434	−	0.0336411i	$-0.0107103\pi$
$270$	−23.6546	+	1.83176i	−1.43958	+	0.111477i
$271$	−14.7544			−0.896263			−0.448131	−	0.893968i	$-0.647910\pi$
$271$	−14.7544			−0.896263			−0.448131	+	0.893968i	$0.647910\pi$
$272$	1.38999	+	4.35224i	0.0842805	+	0.263894i
$273$		0			0
$274$	−1.56582	−	20.2204i	−0.0945946	−	1.22156i
$275$	33.7926	−	33.7926i	2.03777	−	2.03777i
$276$	−2.61457	−	1.90965i	−0.157378	−	0.114947i
$277$	13.0070	−	13.0070i	0.781518	−	0.781518i	−0.198569	−	0.980087i	$-0.563629\pi$
$277$	13.0070	−	13.0070i	0.781518	−	0.781518i	0.980087	+	0.198569i	$0.0636294\pi$
$278$	19.0032	−	22.1933i	1.13973	−	1.33107i
$279$			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	$0.597382\pi$
$282$	1.38300	+	1.18420i	0.0823566	+	0.0705183i
$283$	2.32535	−	2.32535i	0.138227	−	0.138227i	−0.634607	−	0.772835i	$-0.718838\pi$
$283$	2.32535	−	2.32535i	0.138227	−	0.138227i	0.772835	+	0.634607i	$0.218838\pi$
$284$	−4.75230	+	0.740455i	−0.281997	+	0.0439379i
$285$	6.89173	−	6.89173i	0.408231	−	0.408231i
$286$	−12.1419	+	0.940243i	−0.717967	+	0.0555977i
$287$		0			0
$288$	−5.06347	−	12.4448i	−0.298368	−	0.733318i
$289$	15.6954			0.923257
$290$	3.23265	+	41.7452i	0.189828	+	2.45136i
$291$	4.71202	−	4.71202i	0.276224	−	0.276224i
$292$	−5.84808	+	0.911187i	−0.342233	+	0.0533232i
$293$	6.98254	+	6.98254i	0.407925	+	0.407925i	0.881014	−	0.473090i	$-0.156861\pi$
$293$	6.98254	+	6.98254i	0.407925	+	0.407925i	−0.473090	+	0.881014i	$0.656861\pi$
$294$		0			0
$295$	−28.5056			−1.65966
$296$	−4.61727	+	7.47134i	−0.268373	+	0.434263i
$297$	19.1778			1.11281
$298$	−10.8426	+	12.6628i	−0.628096	+	0.733538i
$299$	2.76280	−	2.76280i	0.159777	−	0.159777i
$300$	9.87403	−	13.5189i	0.570077	−	0.780513i
$301$		0			0
$302$	−19.3276	+	1.49669i	−1.11218	+	0.0861248i
$303$			11.6478i			0.669146i
$304$	11.1007	+	5.72654i	0.636669	+	0.328440i
$305$	25.7763			1.47595
$306$	3.82507	−	0.296205i	0.218665	−	0.0169329i
$307$	−23.3885	−	23.3885i	−1.33485	−	1.33485i	−0.900967	−	0.433888i	$-0.857141\pi$
$307$	−23.3885	−	23.3885i	−1.33485	−	1.33485i	−0.433888	−	0.900967i	$-0.642859\pi$
$308$		0			0
$309$	−4.43659	+	4.43659i	−0.252389	+	0.252389i
$310$	−17.5734	−	15.0473i	−0.998100	−	0.854629i
$311$			25.1861i			1.42817i	0.700057	+	0.714087i	$0.253158\pi$
$311$			25.1861i			1.42817i	−0.700057	+	0.714087i	$0.746842\pi$
$312$	−4.15191	+	0.980249i	−0.235055	+	0.0554957i
$313$	−8.45205			−0.477738			−0.238869	−	0.971052i	$-0.576777\pi$
$313$	−8.45205			−0.477738			−0.238869	+	0.971052i	$0.576777\pi$
$314$	−1.91681	+	2.23859i	−0.108172	+	0.126331i
$315$		0			0
$316$	−0.377948	−	2.42570i	−0.0212612	−	0.136456i
$317$	−13.5325	−	13.5325i	−0.760060	−	0.760060i	0.216273	−	0.976333i	$-0.430610\pi$
$317$	−13.5325	−	13.5325i	−0.760060	−	0.760060i	−0.976333	+	0.216273i	$0.930610\pi$
$318$	−3.37528	+	0.261374i	−0.189276	+	0.0146571i
$319$		−	33.8445i		−	1.89493i
$320$	29.9655	+	9.98673i	1.67512	+	0.558275i
$321$			7.33914i			0.409631i
$322$		0			0
$323$	−2.52207	+	2.52207i	−0.140332	+	0.140332i
$324$	−7.44271	+	1.15965i	−0.413484	+	0.0644248i
$325$	14.2853	+	14.2853i	0.792408	+	0.792408i
$326$	1.65904	−	1.93755i	0.0918856	−	0.107311i
$327$		−	0.695428i		−	0.0384572i
$328$	−22.2623	+	5.25606i	−1.22923	+	0.290217i
$329$		0			0
$330$	−12.9573	+	15.1325i	−0.713273	+	0.833014i
$331$	10.2206	+	10.2206i	0.561775	+	0.561775i	0.929811	−	0.368036i	$-0.119970\pi$
$331$	10.2206	+	10.2206i	0.561775	+	0.561775i	−0.368036	+	0.929811i	$0.619970\pi$
$332$	−5.25129	−	3.83548i	−0.288202	−	0.210499i
$333$	5.21505	+	5.21505i	0.285783	+	0.285783i
$334$	2.35845	+	30.4561i	0.129049	+	1.66648i
$335$	−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	$0.621868\pi$
$338$	1.02195	+	13.1971i	0.0555869	+	0.717827i
$339$	−1.06894	−	1.06894i	−0.0580567	−	0.0580567i
$340$	−5.31978	+	7.28349i	−0.288505	+	0.395003i
$341$	13.2234	+	13.2234i	0.716089	+	0.716089i
$342$	6.82189	−	7.96712i	0.368886	−	0.430812i
$343$		0			0
$344$	−13.0052	−	8.03715i	−0.701191	−	0.433334i
$345$		−	6.39160i		−	0.344112i
$346$	−8.08251	+	9.43937i	−0.434519	+	0.507463i
$347$	−6.64411	−	6.64411i	−0.356675	−	0.356675i	0.505911	−	0.862586i	$-0.331156\pi$
$347$	−6.64411	−	6.64411i	−0.356675	−	0.356675i	−0.862586	+	0.505911i	$0.831156\pi$
$348$	−1.82522	−	11.7144i	−0.0978420	−	0.627958i
$349$	−8.35069	+	8.35069i	−0.447002	+	0.447002i	−0.894357	−	0.447355i	$-0.852366\pi$
$349$	−8.35069	+	8.35069i	−0.447002	+	0.447002i	0.447355	+	0.894357i	$0.352366\pi$
$350$		0			0
$351$			8.10712i			0.432726i
$352$	−23.5262	−	9.91845i	−1.25395	−	0.528655i
$353$			19.5576i			1.04095i	0.853877	+	0.520474i	$0.174245\pi$
$353$			19.5576i			1.04095i	−0.853877	+	0.520474i	$0.825755\pi$
$354$	8.04741	−	0.623173i	0.427715	−	0.0331213i
$355$	−6.71383	−	6.71383i	−0.356333	−	0.356333i
$356$	−17.2579	+	2.68895i	−0.914669	+	0.142514i
$357$		0			0
$358$	1.60663	−	1.87635i	0.0849133	−	0.0991681i
$359$	−17.6077			−0.929299			−0.464650	−	0.885495i	$-0.653820\pi$
$359$	−17.6077			−0.929299			−0.464650	+	0.885495i	$0.653820\pi$
$360$	13.9435	−	22.5624i	0.734886	−	1.18914i
$361$		−	9.24881i		−	0.486779i
$362$	8.04477	+	6.88838i	0.422824	+	0.362045i
$363$	5.23794	−	5.23794i	0.274920	−	0.274920i
$364$		0			0
$365$	−8.26189	−	8.26189i	−0.432447	−	0.432447i
$366$	−7.27690	+	0.563506i	−0.380369	+	0.0294549i
$367$	−32.9623			−1.72062			−0.860309	−	0.509773i	$-0.829729\pi$
$367$	−32.9623			−1.72062			−0.860309	+	0.509773i	$0.829729\pi$
$368$	7.80306	−	2.49208i	0.406762	−	0.129909i
$369$			19.2080i			0.999931i
$370$	−17.2868	+	1.33865i	−0.898697	+	0.0695931i
$371$		0			0
$372$	5.29009	+	3.86382i	0.274278	+	0.200330i
$373$	9.49811	−	9.49811i	0.491793	−	0.491793i	−0.417078	−	0.908871i	$-0.636946\pi$
$373$	9.49811	−	9.49811i	0.491793	−	0.491793i	0.908871	+	0.417078i	$0.136946\pi$
$374$	4.74179	−	5.53782i	0.245192	−	0.286354i
$375$	17.4427			0.900735
$376$	−4.48315	+	1.05845i	−0.231201	+	0.0545856i
$377$	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	$0.742863\pi$
$380$	3.79619	+	24.3642i	0.194740	+	1.24986i
$381$	6.68581	−	6.68581i	0.342524	−	0.342524i
$382$	2.96997	+	38.3530i	0.151957	+	1.96231i
$383$	−0.428796			−0.0219104			−0.0109552	−	0.999940i	$-0.503487\pi$
$383$	−0.428796			−0.0219104			−0.0109552	+	0.999940i	$0.503487\pi$
$384$	−8.67788	−	2.16426i	−0.442841	−	0.110444i
$385$		0			0
$386$	8.12622	−	0.629276i	0.413614	−	0.0320293i
$387$	−9.07769	+	9.07769i	−0.461445	+	0.461445i
$388$	2.59553	+	16.6583i	0.131768	+	0.845700i
$389$	−7.40065	+	7.40065i	−0.375228	+	0.375228i	−0.869377	−	0.494149i	$-0.835480\pi$
$389$	−7.40065	+	7.40065i	−0.375228	+	0.375228i	0.494149	+	0.869377i	$0.335480\pi$
$390$	−6.39702	−	5.47749i	−0.323926	−	0.277363i
$391$			2.33905i			0.118291i
$392$		0			0
$393$		−	4.38907i		−	0.221399i
$394$	16.6164	−	19.4059i	0.837124	−	0.977657i
$395$	3.42692	−	3.42692i	0.172427	−	0.172427i
$396$	−12.6452	+	17.3130i	−0.635446	+	0.870011i
$397$	19.7386	−	19.7386i	0.990654	−	0.990654i	−0.00930231	−	0.999957i	$-0.502961\pi$
$397$	19.7386	−	19.7386i	0.990654	−	0.990654i	0.999957	+	0.00930231i	$0.00296106\pi$
$398$	−0.601327	−	7.76530i	−0.0301418	−	0.389239i
$399$		0			0
$400$	12.8856	+	40.3465i	0.644278	+	2.01732i
$401$	26.3759			1.31715			0.658575	−	0.752515i	$-0.271160\pi$
$401$	26.3759			1.31715			0.658575	+	0.752515i	$0.271160\pi$
$402$	0.711101	−	0.0550661i	0.0354665	−	0.00274645i
$403$	−5.59001	+	5.59001i	−0.278458	+	0.278458i
$404$	−23.7970	−	17.3811i	−1.18395	−	0.864741i
$405$	−10.5147	−	10.5147i	−0.522480	−	0.522480i
$406$		0			0
$407$	14.0151			0.694702
$408$	1.34260	−	2.17250i	0.0664684	−	0.107555i
$409$	17.8287			0.881572			0.440786	−	0.897612i	$-0.354700\pi$
$409$	17.8287			0.881572			0.440786	+	0.897612i	$0.354700\pi$
$410$	−34.3006	−	29.3701i	−1.69398	−	1.45048i
$411$	−8.01621	+	8.01621i	−0.395410	+	0.395410i
$412$	−2.44382	−	15.6846i	−0.120398	−	0.772725i
$413$		0			0
$414$	−0.531059	−	6.85789i	−0.0261001	−	0.337047i
$415$		−	12.8374i		−	0.630161i
$416$	4.19288	−	9.94535i	0.205573	−	0.487611i
$417$	−16.3320			−0.799784
$418$	−1.53886	−	19.8722i	−0.0752681	−	0.971983i
$419$	19.6171	+	19.6171i	0.958358	+	0.958358i	0.999167	−	0.0408093i	$-0.0129936\pi$
$419$	19.6171	+	19.6171i	0.958358	+	0.958358i	−0.0408093	+	0.999167i	$0.512994\pi$
$420$		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	$0.307955\pi$
$422$	25.2157	−	29.4487i	1.22748	−	1.43354i
$423$			3.86808i			0.188073i
$424$	4.50268	−	7.28592i	0.218669	−	0.353836i
$425$	−12.0943			−0.586659
$426$	2.04215	+	1.74861i	0.0989427	+	0.0847202i
$427$		0			0
$428$	−14.9943	−	10.9517i	−0.724777	−	0.529369i
$429$	4.81357	+	4.81357i	0.232401	+	0.232401i
$430$	−2.33015	−	30.0906i	−0.112370	−	1.45110i
$431$			26.8517i			1.29340i	0.762744	+	0.646701i	$0.223852\pi$
$431$			26.8517i			1.29340i	−0.762744	+	0.646701i	$0.776148\pi$
$432$	−7.79221	+	15.1049i	−0.374903	+	0.726736i
$433$		−	18.6517i		−	0.896344i	−0.893947	−	0.448172i	$-0.852075\pi$
$433$		−	18.6517i		−	0.896344i	0.893947	−	0.448172i	$-0.147925\pi$
$434$		0			0
$435$	16.5496	−	16.5496i	0.793491	−	0.793491i
$436$	1.42080	+	1.03774i	0.0680440	+	0.0496985i
$437$	4.52178	+	4.52178i	0.216306	+	0.216306i
$438$	2.51303	+	2.15179i	0.120077	+	0.102817i
$439$			20.2604i			0.966977i	0.875351	+	0.483488i	$0.160630\pi$
$439$			20.2604i			0.966977i	−0.875351	+	0.483488i	$0.839370\pi$
$440$	−11.5813	−	49.0535i	−0.552119	−	2.33853i
$441$		0			0
$442$	2.34103	+	2.00452i	0.111352	+	0.0953454i
$443$	−25.0023	−	25.0023i	−1.18790	−	1.18790i	−0.977648	−	0.210248i	$-0.932573\pi$
$443$	−25.0023	−	25.0023i	−1.18790	−	1.18790i	−0.210248	−	0.977648i	$-0.567427\pi$
$444$	4.85096	−	0.755828i	0.230217	−	0.0358700i
$445$	−24.3812	−	24.3812i	−1.15578	−	1.15578i
$446$	31.2143	−	2.41717i	1.47804	−	0.114456i
$447$	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	$0.392275\pi$
$450$	35.4594	−	2.74589i	1.67157	−	0.129443i
$451$	25.8102	+	25.8102i	1.21535	+	1.21535i
$452$	3.77900	−	0.588805i	0.177749	−	0.0276951i
$453$	7.66230	+	7.66230i	0.360006	+	0.360006i
$454$	9.24907	+	7.91957i	0.434080	+	0.371684i
$455$		0			0
$456$	−1.60434	−	6.79527i	−0.0751300	−	0.318218i
$457$			5.33024i			0.249338i	0.992198	+	0.124669i	$0.0397870\pi$
$457$			5.33024i			0.249338i	−0.992198	+	0.124669i	$0.960213\pi$
$458$	−27.1910	−	23.2825i	−1.27055	−	1.08792i
$459$	−3.43183	−	3.43183i	−0.160184	−	0.160184i
$460$	13.0584	+	9.53772i	0.608852	+	0.444699i
$461$	−2.32075	+	2.32075i	−0.108088	+	0.108088i	−0.759082	−	0.650995i	$-0.774352\pi$
$461$	−2.32075	+	2.32075i	−0.108088	+	0.108088i	0.650995	+	0.759082i	$0.274352\pi$
$462$		0			0
$463$		−	15.2932i		−	0.710736i	−0.934727	−	0.355368i	$-0.884356\pi$
$463$		−	15.2932i		−	0.710736i	0.934727	−	0.355368i	$-0.115644\pi$
$464$	26.6569	+	13.7515i	1.23751	+	0.638398i
$465$			12.9322i			0.599717i
$466$	1.69999	+	21.9530i	0.0787507	+	1.01696i
$467$	21.2304	+	21.2304i	0.982424	+	0.982424i	0.999848	−	0.0174238i	$-0.00554645\pi$
$467$	21.2304	+	21.2304i	0.982424	+	0.982424i	−0.0174238	+	0.999848i	$0.505546\pi$
$468$	−7.31882	−	5.34558i	−0.338312	−	0.247099i
$469$		0			0
$470$	−6.90739	−	5.91449i	−0.318614	−	0.272815i
$471$	1.64738			0.0759072
$472$	−10.7354	+	17.3712i	−0.494136	+	0.799577i
$473$			24.3957i			1.12171i
$474$	−0.892535	+	1.04237i	−0.0409955	+	0.0478776i
$475$	−23.3803	+	23.3803i	−1.07276	+	1.07276i
$476$		0			0
$477$	−5.08563	−	5.08563i	−0.232855	−	0.232855i
$478$	−1.26908	−	16.3884i	−0.0580464	−	0.749588i
$479$	34.4733			1.57513			0.787564	−	0.616233i	$-0.211342\pi$
$479$	34.4733			1.57513			0.787564	+	0.616233i	$0.211342\pi$
$480$	−6.65402	−	16.3540i	−0.303713	−	0.746456i
$481$			5.92467i			0.270142i
$482$	0.307157	+	3.96651i	0.0139906	+	0.180669i
$483$		0			0
$484$	2.88523	+	18.5176i	0.131147	+	0.841710i
$485$	−23.5341	+	23.5341i	−1.06863	+	1.06863i
$486$	16.8917	+	14.4636i	0.766223	+	0.656083i
$487$	−14.9028			−0.675312			−0.337656	−	0.941270i	$-0.609634\pi$
$487$	−14.9028			−0.675312			−0.337656	+	0.941270i	$0.609634\pi$
$488$	9.70750	−	15.7080i	0.439438	−	0.711068i
$489$	−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	$0.322626\pi$
$492$	10.3255	+	7.54160i	0.465508	+	0.340001i
$493$	−6.05642	+	6.05642i	−0.272767	+	0.272767i
$494$	8.40069	−	0.650531i	0.377965	−	0.0292688i
$495$	−42.3236			−1.90230
$496$	−15.7880	+	5.04226i	−0.708903	+	0.226404i
$497$		0			0
$498$	0.280643	+	3.62411i	0.0125759	+	0.162400i
$499$	7.82552	−	7.82552i	0.350318	−	0.350318i	−0.509910	−	0.860228i	$-0.670321\pi$
$499$	7.82552	−	7.82552i	0.350318	−	0.350318i	0.860228	+	0.509910i	$0.170321\pi$
$500$	−26.0284	+	35.6364i	−1.16403	+	1.59371i
$501$	12.0741	−	12.0741i	0.539430	−	0.539430i
$502$	−2.59520	+	3.03087i	−0.115829	+	0.135274i
$503$		−	25.6811i		−	1.14507i	−0.819882	−	0.572533i	$-0.805961\pi$
$503$		−	25.6811i		−	1.14507i	0.819882	−	0.572533i	$-0.194039\pi$
$504$		0			0
$505$		−	58.1745i		−	2.58873i
$506$	−9.92865	−	8.50147i	−0.441382	−	0.377936i
$507$	5.23188	−	5.23188i	0.232356	−	0.232356i
$508$	3.68276	+	23.6362i	0.163396	+	1.04869i
$509$	10.8597	−	10.8597i	0.481348	−	0.481348i	−0.424214	−	0.905562i	$-0.639450\pi$
$509$	10.8597	−	10.8597i	0.481348	−	0.481348i	0.905562	+	0.424214i	$0.139450\pi$
$510$	5.02661	−	0.389249i	0.222582	−	0.0172362i
$511$		0			0
$512$	17.3711	−	14.4998i	0.767700	−	0.640809i
$513$	−13.2686			−0.585824
$514$	−1.63333	−	21.0922i	−0.0720432	−	0.930337i
$515$	22.1585	−	22.1585i	0.976420	−	0.976420i
$516$	1.31565	+	8.44394i	0.0579182	+	0.371724i
$517$	5.19760	+	5.19760i	0.228590	+	0.228590i
$518$		0			0
$519$	6.94641			0.304914
$520$	20.7366	−	4.89584i	0.909362	−	0.214697i
$521$	−29.8378			−1.30722			−0.653609	−	0.756833i	$-0.726746\pi$
$521$	−29.8378			−1.30722			−0.653609	+	0.756833i	$0.726746\pi$
$522$	16.3818	−	19.1320i	0.717014	−	0.837383i
$523$	25.4800	−	25.4800i	1.11416	−	1.11416i	0.121582	−	0.992581i	$-0.461203\pi$
$523$	25.4800	−	25.4800i	1.11416	−	1.11416i	0.992581	−	0.121582i	$-0.0387966\pi$
$524$	8.96712	+	6.54948i	0.391731	+	0.286116i
$525$		0			0
$526$	20.8512	−	1.61467i	0.909157	−	0.0704030i
$527$		−	4.73263i		−	0.206156i
$528$	4.34190	+	13.5951i	0.188957	+	0.591651i
$529$	−18.8064			−0.817668
$530$	16.8578	−	1.30543i	0.732255	−	0.0567042i
$531$	12.1253	+	12.1253i	0.526191	+	0.526191i
$532$		0			0
$533$	−10.9109	+	10.9109i	−0.472602	+	0.472602i
$534$	7.41606	+	6.35004i	0.320924	+	0.274793i
$535$		−	36.6552i		−	1.58474i
$536$	−0.948621	+	1.53499i	−0.0409742	+	0.0663016i
$537$	−1.38080			−0.0595860
$538$	22.0405	−	25.7405i	0.950231	−	1.10975i
$539$		0			0
$540$	−33.1528	+	5.16554i	−1.42667	+	0.222289i
$541$	9.56603	+	9.56603i	0.411276	+	0.411276i	0.882183	−	0.470907i	$-0.156073\pi$
$541$	9.56603	+	9.56603i	0.411276	+	0.411276i	−0.470907	+	0.882183i	$0.656073\pi$
$542$	−20.8035	+	1.61098i	−0.893588	+	0.0691974i
$543$		−	5.92013i		−	0.254057i
$544$	2.43508	+	5.98486i	0.104403	+	0.256599i
$545$			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	$0.455567\pi$
$548$	−4.41559	−	28.3396i	−0.188624	−	1.21061i
$549$	−10.9643	−	10.9643i	−0.467945	−	0.467945i
$550$	43.9577	−	51.3371i	1.87436	−	2.18902i
$551$			23.4162i			0.997562i
$552$	−3.89503	−	2.40712i	−0.165783	−	0.102454i
$553$		0			0
$554$	16.9196	−	19.7600i	0.718847	−	0.839523i
$555$	6.85322	+	6.85322i	0.290903	+	0.290903i
$556$	24.3711	−	33.3673i	1.03357	−	1.41509i
$557$	9.44113	+	9.44113i	0.400034	+	0.400034i	0.878245	−	0.478211i	$-0.158715\pi$
$557$	9.44113	+	9.44113i	0.400034	+	0.400034i	−0.478211	+	0.878245i	$0.658715\pi$
$558$	1.07450	+	13.8757i	0.0454872	+	0.587403i
$559$	−10.3129			−0.436190
$560$		0			0
$561$	−4.07527			−0.172058
$562$	3.49063	+	45.0765i	0.147243	+	1.90144i
$563$	17.8651	+	17.8651i	0.752922	+	0.752922i	0.975024	−	0.222101i	$-0.0712915\pi$
$563$	17.8651	+	17.8651i	0.752922	+	0.752922i	−0.222101	+	0.975024i	$0.571292\pi$
$564$	2.07932	+	1.51871i	0.0875552	+	0.0639493i
$565$	5.33879	+	5.33879i	0.224605	+	0.224605i
$566$	3.02482	−	3.53262i	0.127143	−	0.148487i
$567$		0			0
$568$	−6.61986	+	1.56292i	−0.277763	+	0.0655788i
$569$		−	12.5536i		−	0.526276i	−0.964758	−	0.263138i	$-0.915243\pi$
$569$		−	12.5536i		−	0.526276i	0.964758	−	0.263138i	$-0.0847574\pi$
$570$	8.96480	−	10.4698i	0.375494	−	0.438531i
$571$	27.9224	+	27.9224i	1.16851	+	1.16851i	0.982558	+	0.185957i	$0.0595385\pi$
$571$	27.9224	+	27.9224i	1.16851	+	1.16851i	0.185957	+	0.982558i	$0.440461\pi$
$572$	−17.0174	+	2.65147i	−0.711531	+	0.110864i
$573$	15.2048	−	15.2048i	0.635188	−	0.635188i
$574$		0			0
$575$			21.6836i			0.904268i
$576$	−8.49826	−	16.9942i	−0.354094	−	0.708094i
$577$		−	23.3184i		−	0.970759i	−0.874303	−	0.485380i	$-0.838681\pi$
$577$		−	23.3184i		−	0.970759i	0.874303	−	0.485380i	$-0.161319\pi$
$578$	22.1303	−	1.71372i	0.920501	−	0.0712815i
$579$	−3.22158	−	3.22158i	−0.133884	−	0.133884i
$580$	9.11603	+	58.5074i	0.378523	+	2.42939i
$581$		0			0
$582$	6.12943	−	7.15841i	0.254073	−	0.296725i
$583$	−13.6673			−0.566041
$584$	−8.14625	+	1.92330i	−0.337094	+	0.0795867i
$585$		−	17.8917i		−	0.739729i
$586$	10.6077	+	9.08293i	0.438201	+	0.375212i
$587$	−24.2488	+	24.2488i	−1.00085	+	1.00085i	−0.000853494		1.00000i	$0.500272\pi$
$587$	−24.2488	+	24.2488i	−1.00085	+	1.00085i	−1.00000		0.000853494i	$0.999728\pi$
$588$		0			0
$589$	−9.14897	−	9.14897i	−0.376977	−	0.376977i
$590$	−40.1927	+	3.11243i	−1.65471	+	0.128137i
$591$	−14.2808			−0.587433
$592$	−5.69454	+	11.0387i	−0.234044	+	0.453687i
$593$		−	38.3515i		−	1.57491i	−0.616374	−	0.787454i	$-0.711399\pi$
$593$		−	38.3515i		−	1.57491i	0.616374	−	0.787454i	$-0.288601\pi$
$594$	27.0405	−	2.09395i	1.10948	−	0.0859160i
$595$		0			0
$596$	−13.9054	+	19.0384i	−0.569587	+	0.779841i
$597$	−3.07849	+	3.07849i	−0.125994	+	0.125994i
$598$	3.59387	−	4.19719i	0.146964	−	0.171636i
$599$	0.797936			0.0326028			0.0163014	−	0.999867i	$-0.494811\pi$
$599$	0.797936			0.0326028			0.0163014	+	0.999867i	$0.494811\pi$
$600$	12.4462	−	20.1396i	0.508115	−	0.822196i
$601$	4.37578			0.178492			0.0892459	−	0.996010i	$-0.471554\pi$
$601$	4.37578			0.178492			0.0892459	+	0.996010i	$0.471554\pi$
$602$		0			0
$603$	1.07144	+	1.07144i	0.0436323	+	0.0436323i
$604$	−27.0884	+	4.22064i	−1.10221	+	0.171735i
$605$	−26.1608	+	26.1608i	−1.06359	+	1.06359i
$606$	1.27178	+	16.4232i	0.0516625	+	0.667148i
$607$	6.55371			0.266007			0.133003	−	0.991116i	$-0.457538\pi$
$607$	6.55371			0.266007			0.133003	+	0.991116i	$0.457538\pi$
$608$	16.2772	+	6.86233i	0.660127	+	0.278304i
$609$		0			0
$610$	36.3444	−	2.81443i	1.47154	−	0.113953i
$611$	−2.19721	+	2.19721i	−0.0888896	+	0.0888896i
$612$	5.36097	−	0.835292i	0.216705	−	0.0337647i
$613$	13.2937	−	13.2937i	0.536928	−	0.536928i	−0.385698	−	0.922625i	$-0.626039\pi$
$613$	13.2937	−	13.2937i	0.536928	−	0.536928i	0.922625	+	0.385698i	$0.126039\pi$
$614$	−35.5314	−	30.4239i	−1.43393	−	1.22781i
$615$			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	$-0.147606\pi$
$618$	−5.77114	+	6.73997i	−0.232149	+	0.271121i
$619$	6.03158	−	6.03158i	0.242430	−	0.242430i	−0.575425	−	0.817855i	$-0.695163\pi$
$619$	6.03158	−	6.03158i	0.242430	−	0.242430i	0.817855	+	0.575425i	$0.195163\pi$
$620$	−26.4213	−	19.2978i	−1.06110	−	0.775018i
$621$	−6.15286	+	6.15286i	−0.246906	+	0.246906i
$622$	2.74999	+	35.5123i	0.110264	+	1.42391i
$623$		0			0
$624$	−5.74713	+	1.83548i	−0.230069	+	0.0734779i
$625$	−34.1744			−1.36698
$626$	−11.9173	+	0.922851i	−0.476312	+	0.0368845i
$627$	−7.87819	+	7.87819i	−0.314625	+	0.314625i
$628$	−2.45826	+	3.36569i	−0.0980953	+	0.134306i
$629$	−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	$0.145689\pi$
$632$	−0.797758	−	3.37895i	−0.0317331	−	0.134408i
$633$	−21.6713			−0.861356
$634$	−20.5583	−	17.6031i	−0.816473	−	0.699109i
$635$	−33.3922	+	33.3922i	−1.32513	+	1.32513i
$636$	−4.73058	+	0.737070i	−0.187580	+	0.0292267i
$637$		0			0
$638$	−3.69537	−	47.7205i	−0.146301	−	1.88927i
$639$			5.71165i			0.225949i
$640$	43.3416	+	10.8094i	1.71323	+	0.427278i
$641$	28.9298			1.14266			0.571329	−	0.820721i	$-0.306428\pi$
$641$	28.9298			1.14266			0.571329	+	0.820721i	$0.306428\pi$
$642$	0.801336	+	10.3481i	0.0316262	+	0.408408i
$643$	27.4126	+	27.4126i	1.08105	+	1.08105i	0.996412	+	0.0846366i	$0.0269729\pi$
$643$	27.4126	+	27.4126i	1.08105	+	1.08105i	0.0846366	+	0.996412i	$0.473027\pi$
$644$		0			0
$645$	−11.9292	+	11.9292i	−0.469712	+	0.469712i
$646$	−3.28073	+	3.83148i	−0.129079	+	0.150748i
$647$		−	29.8238i		−	1.17249i	−0.810133	−	0.586247i	$-0.800605\pi$
$647$		−	29.8238i		−	1.17249i	0.810133	−	0.586247i	$-0.199395\pi$
$648$	−10.3675	+	2.44774i	−0.407276	+	0.0961562i
$649$	32.5858			1.27911
$650$	21.7020	+	18.5825i	0.851222	+	0.728864i
$651$		0			0
$652$	2.12768	−	2.91308i	0.0833263	−	0.114085i
$653$	9.22237	+	9.22237i	0.360899	+	0.360899i	0.864144	−	0.503245i	$-0.167861\pi$
$653$	9.22237	+	9.22237i	0.360899	+	0.360899i	−0.503245	+	0.864144i	$0.667861\pi$
$654$	−0.0759314	−	0.980548i	−0.00296915	−	0.0383425i
$655$			21.9211i			0.856530i
$656$	−30.8159	+	9.84175i	−1.20316	+	0.384256i
$657$			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	$0.387079\pi$
$660$	−16.6174	+	22.7514i	−0.646830	+	0.885597i
$661$	1.56254	+	1.56254i	0.0607758	+	0.0607758i	0.736841	−	0.676066i	$-0.236316\pi$
$661$	1.56254	+	1.56254i	0.0607758	+	0.0607758i	−0.676066	+	0.736841i	$0.736316\pi$
$662$	15.5269	+	13.2950i	0.603471	+	0.516725i
$663$		−	1.72276i		−	0.0669065i
$664$	−7.82305	−	4.83463i	−0.303593	−	0.187620i
$665$		0			0
$666$	7.92259	+	6.78377i	0.306994	+	0.262866i
$667$	10.8584	+	10.8584i	0.420440	+	0.420440i
$668$	6.65079	+	42.6853i	0.257327	+	1.65154i
$669$	−12.3747	−	12.3747i	−0.478433	−	0.478433i
$670$	−3.55159	+	0.275027i	−0.137210	+	0.0106252i
$671$	−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	$0.925939\pi$
$674$	−19.3393	+	1.49759i	−0.744922	+	0.0576851i
$675$	−31.8140	−	31.8140i	−1.22452	−	1.22452i
$676$	2.88189	+	18.4962i	0.110842	+	0.711392i
$677$	−20.9521	−	20.9521i	−0.805254	−	0.805254i	0.178658	−	0.983911i	$-0.442825\pi$
$677$	−20.9521	−	20.9521i	−0.805254	−	0.805254i	−0.983911	+	0.178658i	$0.942825\pi$
$678$	−1.62391	−	1.39048i	−0.0623658	−	0.0534010i
$679$		0			0
$680$	−6.70558	+	10.8505i	−0.257147	+	0.416098i
$681$		−	6.80638i		−	0.260821i
$682$	20.0888	+	17.2011i	0.769238	+	0.658665i
$683$	−2.65762	−	2.65762i	−0.101691	−	0.101691i	0.654431	−	0.756122i	$-0.272908\pi$
$683$	−2.65762	−	2.65762i	−0.101691	−	0.101691i	−0.756122	+	0.654431i	$0.772908\pi$
$684$	8.74891	−	11.9784i	0.334523	−	0.458007i
$685$	40.0368	−	40.0368i	1.52973	−	1.52973i
$686$		0			0
$687$			20.0098i			0.763423i
$688$	−19.2147	−	9.91232i	−0.732554	−	0.377904i
$689$		−	5.77764i		−	0.220111i
$690$	−0.697877	−	9.01211i	−0.0265677	−	0.343085i
$691$	−10.1466	−	10.1466i	−0.385994	−	0.385994i	0.487262	−	0.873256i	$-0.337996\pi$
$691$	−10.1466	−	10.1466i	−0.385994	−	0.385994i	−0.873256	+	0.487262i	$0.837996\pi$
$692$	−10.3656	+	14.1919i	−0.394042	+	0.539496i
$693$		0			0
$694$	−10.0936	−	8.64270i	−0.383148	−	0.328072i
$695$	81.5702			3.09413
$696$	−3.85260	−	16.3179i	−0.146032	−	0.618529i
$697$		−	9.23738i		−	0.349891i
$698$	−10.8626	+	12.6862i	−0.411156	+	0.480179i
$699$	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	$0.637571\pi$
$702$	0.885188	+	11.4310i	0.0334093	+	0.431434i
$703$	−9.69670			−0.365718
$704$	−34.2547	−	11.4162i	−1.29102	−	0.430264i
$705$			5.08313i			0.191442i
$706$	2.13543	+	27.5761i	0.0803681	+	1.03784i
$707$		0			0
$708$	11.2787	−	1.75734i	0.423881	−	0.0660448i
$709$	−0.456352	+	0.456352i	−0.0171387	+	0.0171387i	−0.715624	−	0.698486i	$-0.753858\pi$
$709$	−0.456352	+	0.456352i	−0.0171387	+	0.0171387i	0.698486	+	0.715624i	$0.253858\pi$
$710$	−10.1995	−	8.73339i	−0.382781	−	0.327758i
$711$	−2.91538			−0.109335
$712$	−24.0400	+	5.67574i	−0.900935	+	0.212707i
$713$	−8.48503			−0.317767
$714$		0			0
$715$	−24.0413	−	24.0413i	−0.899094	−	0.899094i
$716$	2.06047	−	2.82106i	0.0770034	−	0.105428i
$717$	−6.49706	+	6.49706i	−0.242637	+	0.242637i
$718$	−24.8267	+	1.92253i	−0.926525	+	0.0717480i
$719$	30.9666			1.15486			0.577429	−	0.816441i	$-0.304056\pi$
$719$	30.9666			1.15486			0.577429	+	0.816441i	$0.304056\pi$
$720$	17.1967	−	33.3352i	0.640883	−	1.24233i
$721$		0			0
$722$	−1.00985	−	13.0407i	−0.0375826	−	0.485326i
$723$	1.57249	−	1.57249i	0.0584816	−	0.0584816i
$724$	12.0952	+	8.83418i	0.449514	+	0.328320i
$725$	−56.1446	+	56.1446i	−2.08516	+	2.08516i
$726$	6.81354	−	7.95737i	0.252874	−	0.295326i
$727$		−	16.7744i		−	0.622128i	−0.950389	−	0.311064i	$-0.899315\pi$
$727$		−	16.7744i		−	0.622128i	0.950389	−	0.311064i	$-0.100685\pi$
$728$		0			0
$729$		−	1.13181i		−	0.0419187i
$730$	−12.5513	−	10.7471i	−0.464544	−	0.397768i
$731$	4.36557	−	4.36557i	0.161466	−	0.161466i
$732$	−10.1988	+	1.58908i	−0.376960	+	0.0587341i
$733$	21.5304	−	21.5304i	0.795243	−	0.795243i	−0.187098	−	0.982341i	$-0.559908\pi$
$733$	21.5304	−	21.5304i	0.795243	−	0.795243i	0.982341	+	0.187098i	$0.0599083\pi$
$734$	−46.4766	+	3.59904i	−1.71548	+	0.132843i
$735$		0			0
$736$	10.7301	−	4.36581i	0.395518	−	0.160926i
$737$	2.87941			0.106065
$738$	2.09726	+	27.0832i	0.0772013	+	0.996946i
$739$	−18.2801	+	18.2801i	−0.672445	+	0.672445i	−0.958279	−	0.285834i	$-0.907729\pi$
$739$	−18.2801	+	18.2801i	−0.672445	+	0.672445i	0.285834	+	0.958279i	$0.407729\pi$
$740$	−24.2281	+	3.77497i	−0.890642	+	0.138771i
$741$	−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	$0.400532\pi$
$744$	7.88086	+	4.87035i	0.288926	+	0.178556i
$745$	−46.5414			−1.70514
$746$	12.3552	−	14.4293i	0.452356	−	0.528295i
$747$	−5.46055	+	5.46055i	−0.199791	+	0.199791i
$748$	6.08123	−	8.32602i	0.222352	−	0.304430i
$749$		0			0
$750$	24.5940	−	1.90450i	0.898046	−	0.0695427i
$751$			22.4087i			0.817706i	0.912600	+	0.408853i	$0.134071\pi$
$751$			22.4087i			0.817706i	−0.912600	+	0.408853i	$0.865929\pi$
$752$	−6.20564	+	1.98191i	−0.226296	+	0.0722729i
$753$	2.23041			0.0812807
$754$	20.1731	−	1.56216i	0.734662	−	0.0568906i
$755$	−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	$0.165978\pi$
$758$	0.937675	+	0.802889i	0.0340579	+	0.0291623i
$759$			7.30648i			0.265208i
$760$	8.01284	+	33.9389i	0.290656	+	1.23109i
$761$	−20.0298			−0.726081			−0.363041	−	0.931773i	$-0.618261\pi$
$761$	−20.0298			−0.726081			−0.363041	+	0.931773i	$0.618261\pi$
$762$	8.69694	−	10.1569i	0.315057	−	0.367947i
$763$		0			0
$764$	8.37527	+	53.7532i	0.303007	+	1.94472i
$765$	7.57373	+	7.57373i	0.273829	+	0.273829i
$766$	−0.604598	+	0.0468187i	−0.0218450	+	0.00169163i
$767$			13.7752i			0.497393i
$768$	−12.4720	−	2.10408i	−0.450046	−	0.0759246i
$769$		−	50.7365i		−	1.82960i	−0.403902	−	0.914802i	$-0.632346\pi$
$769$		−	50.7365i		−	1.82960i	0.403902	−	0.914802i	$-0.367654\pi$
$770$		0			0
$771$	−8.36185	+	8.36185i	−0.301144	+	0.301144i
$772$	11.3892	−	1.77455i	0.409906	−	0.0638674i
$773$	−21.1207	−	21.1207i	−0.759658	−	0.759658i	0.216602	−	0.976260i	$-0.430503\pi$
$773$	−21.1207	−	21.1207i	−0.759658	−	0.759658i	−0.976260	+	0.216602i	$0.930503\pi$
$774$	−11.8083	+	13.7906i	−0.424441	+	0.495694i
$775$		−	43.8727i		−	1.57595i
$776$	5.47855	+	23.2047i	0.196669	+	0.833002i
$777$		0			0
$778$	−9.62681	+	11.2429i	−0.345138	+	0.403078i
$779$	−17.8574	−	17.8574i	−0.639808	−	0.639808i
$780$	−9.61782	−	7.02475i	−0.344373	−	0.251526i
$781$	7.67483	+	7.67483i	0.274627	+	0.274627i
$782$	0.255393	+	3.29804i	0.00913283	+	0.117938i
$783$	−31.8628			−1.13868
$784$		0			0
$785$	−8.22781			−0.293663
$786$	−0.479227	−	6.18855i	−0.0170935	−	0.220738i
$787$	−27.1080	−	27.1080i	−0.966295	−	0.966295i	0.0331553	−	0.999450i	$-0.489444\pi$
$787$	−27.1080	−	27.1080i	−0.966295	−	0.966295i	−0.999450	+	0.0331553i	$0.989444\pi$
$788$	21.3102	−	29.1765i	0.759144	−	1.03937i
$789$	−8.26631	−	8.26631i	−0.294288	−	0.294288i
$790$	4.45775	−	5.20610i	0.158600	−	0.185225i
$791$		0			0
$792$	−15.9393	+	25.7919i	−0.566379	+	0.916475i
$793$		−	12.4562i		−	0.442334i
$794$	25.6761	−	29.9865i	0.911212	−	1.06418i
$795$	−6.68314	−	6.68314i	−0.237026	−	0.237026i
$796$	−1.69573	−	10.8834i	−0.0601037	−	0.385750i
$797$	18.8328	−	18.8328i	0.667092	−	0.667092i	−0.289949	−	0.957042i	$-0.593639\pi$
$797$	18.8328	−	18.8328i	0.667092	−	0.667092i	0.957042	+	0.289949i	$0.0936385\pi$
$798$		0			0
$799$		−	1.86021i		−	0.0658094i
$800$	22.5738	+	55.4813i	0.798106	+	1.96156i
$801$			20.7418i			0.732875i
$802$	37.1898	−	2.87990i	1.31322	−	0.101693i
$803$	9.44447	+	9.44447i	0.333288	+	0.333288i
$804$	0.996635	−	0.155285i	0.0351486	−	0.00547650i
$805$		0			0
$806$	−7.27152	+	8.49223i	−0.256128	+	0.299126i
$807$	−18.9424			−0.666804
$808$	−35.4514	−	21.9089i	−1.24718	−	0.770752i
$809$			19.8345i			0.697344i	0.937245	+	0.348672i	$0.113367\pi$
$809$			19.8345i			0.697344i	−0.937245	+	0.348672i	$0.886633\pi$
$810$	−15.9737	−	13.6776i	−0.561260	−	0.480582i
$811$	3.89894	−	3.89894i	0.136910	−	0.136910i	−0.635330	−	0.772240i	$-0.719136\pi$
$811$	3.89894	−	3.89894i	0.136910	−	0.136910i	0.772240	+	0.635330i	$0.219136\pi$
$812$		0			0
$813$	8.24740	+	8.24740i	0.289249	+	0.289249i
$814$	19.7612	−	1.53026i	0.692629	−	0.0536356i
$815$	7.12134			0.249450
$816$	1.65584	−	3.20980i	0.0579661	−	0.112365i
$817$		−	16.8788i		−	0.590513i
$818$	25.1383	−	1.94665i	0.878940	−	0.0680631i
$819$		0			0
$820$	−51.5704	−	37.6664i	−1.80092	−	1.31537i
$821$	−13.6837	+	13.6837i	−0.477565	+	0.477565i	−0.904352	−	0.426787i	$-0.859645\pi$
$821$	−13.6837	+	13.6837i	−0.477565	+	0.477565i	0.426787	+	0.904352i	$0.359645\pi$
$822$	−10.4275	+	12.1781i	−0.363702	+	0.424758i
$823$	−40.1771			−1.40049			−0.700243	−	0.713905i	$-0.746925\pi$
$823$	−40.1771			−1.40049			−0.700243	+	0.713905i	$0.746925\pi$
$824$	−5.15831	−	21.8484i	−0.179698	−	0.761123i
$825$	−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	$0.660540\pi$
$828$	−1.49758	−	9.61159i	−0.0520445	−	0.334026i
$829$	29.8049	−	29.8049i	1.03517	−	1.03517i	0.0358090	−	0.999359i	$-0.488599\pi$
$829$	29.8049	−	29.8049i	1.03517	−	1.03517i	0.999359	−	0.0358090i	$-0.0114008\pi$
$830$	−1.40167	−	18.1006i	−0.0486526	−	0.628280i
$831$	−14.5414			−0.504435
$832$	4.82603	−	14.4807i	0.167312	−	0.502027i
$833$		0			0
$834$	−23.0281	+	1.78324i	−0.797396	+	0.0617486i
$835$	−60.3038	+	60.3038i	−2.08690	+	2.08690i
$836$	−4.33956	−	27.8517i	−0.150087	−	0.963270i
$837$	12.4492	−	12.4492i	0.430306	−	0.430306i
$838$	29.8019	+	25.5180i	1.02949	+	0.881506i
$839$			27.4328i			0.947087i	0.880771	+	0.473543i	$0.157025\pi$
$839$			27.4328i			0.947087i	−0.880771	+	0.473543i	$0.842975\pi$
$840$		0			0
$841$			27.2308i			0.938992i
$842$	−6.83450	+	7.98185i	−0.235532	+	0.275073i
$843$	17.8703	−	17.8703i	0.615484	−	0.615484i
$844$	32.3385	−	44.2757i	1.11314	−	1.52403i
$845$	−26.1306	+	26.1306i	−0.898919	+	0.898919i
$846$	0.422343	+	5.45396i	0.0145204	+	0.187511i
$847$		0			0
$848$	5.55322	−	10.7647i	0.190698	−	0.369662i
$849$	−2.59965			−0.0892197
$850$	−17.0528	+	1.32053i	−0.584907	+	0.0452939i
$851$	−4.49651	+	4.49651i	−0.154138	+	0.154138i
$852$	3.07035	+	2.24255i	0.105188	+	0.0768283i
$853$	−8.95019	−	8.95019i	−0.306449	−	0.306449i	0.537082	−	0.843530i	$-0.319527\pi$
$853$	−8.95019	−	8.95019i	−0.306449	−	0.306449i	−0.843530	+	0.537082i	$0.819527\pi$
$854$		0			0
$855$	29.2826			1.00144
$856$	−22.3376	−	13.8046i	−0.763484	−	0.471831i
$857$	53.6482			1.83259			0.916294	−	0.400506i	$-0.131166\pi$
$857$	53.6482			1.83259			0.916294	+	0.400506i	$0.131166\pi$
$858$	7.31268	+	6.26152i	0.249651	+	0.213765i
$859$	−9.32143	+	9.32143i	−0.318043	+	0.318043i	−0.848015	−	0.529972i	$-0.822202\pi$
$859$	−9.32143	+	9.32143i	−0.318043	+	0.318043i	0.529972	+	0.848015i	$0.322202\pi$
$860$	−6.57099	−	42.1731i	−0.224069	−	1.43809i
$861$		0			0
$862$	2.93185	+	37.8607i	0.0998591	+	1.28954i
$863$		−	7.66849i		−	0.261039i	−0.991446	−	0.130519i	$-0.958336\pi$
$863$		−	7.66849i		−	0.261039i	0.991446	−	0.130519i	$-0.0416644\pi$
$864$	−9.33769	+	22.1486i	−0.317675	+	0.753512i
$865$	−34.6938			−1.17962
$866$	−2.03652	−	26.2988i	−0.0692036	−	0.893668i
$867$	−8.77341	−	8.77341i	−0.297961	−	0.297961i
$868$		0			0
$869$	−3.91744	+	3.91744i	−0.132890	+	0.132890i
$870$	21.5278	−	25.1417i	0.729859	−	0.852385i
$871$			1.21723i			0.0412443i
$872$	2.11662	+	1.30807i	0.0716779	+	0.0442968i
$873$	20.0212			0.677613
$874$	6.86939	+	5.88195i	0.232361	+	0.198960i
$875$		0			0
$876$	3.77830	+	2.75962i	0.127657	+	0.0932391i
$877$	−10.8710	−	10.8710i	−0.367089	−	0.367089i	0.499325	−	0.866415i	$-0.333581\pi$
$877$	−10.8710	−	10.8710i	−0.367089	−	0.367089i	−0.866415	+	0.499325i	$0.833581\pi$
$878$	2.21217	+	28.5670i	0.0746570	+	0.964091i
$879$		−	7.80621i		−	0.263297i
$880$	−21.6856	−	67.9005i	−0.731021	−	2.28893i
$881$			21.5605i			0.726392i	0.931713	+	0.363196i	$0.118314\pi$
$881$			21.5605i			0.726392i	−0.931713	+	0.363196i	$0.881686\pi$
$882$		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	$0.222598\pi$
$884$	3.51970	+	2.57075i	0.118380	+	0.0864637i
$885$	15.9341	+	15.9341i	0.535618	+	0.535618i
$886$	−37.9830	−	32.5232i	−1.27606	−	1.09264i
$887$			35.9731i			1.20786i	0.797037	+	0.603930i	$0.206399\pi$
$887$			35.9731i			1.20786i	−0.797037	+	0.603930i	$0.793601\pi$
$888$	6.75730	−	1.59537i	0.226760	−	0.0535372i
$889$		0			0
$890$	−37.0394	−	31.7152i	−1.24156	−	1.06310i
$891$	12.0198	+	12.0198i	0.402677	+	0.402677i
$892$	43.7480	−	6.81637i	1.46479	−	0.228229i
$893$	−3.59609	−	3.59609i	−0.120339	−	0.120339i
$894$	13.1391	−	1.01746i	0.439437	−	0.0340290i
$895$	6.89640			0.230521
$896$		0			0
$897$	−3.08871			−0.103129
$898$	19.8388	−	1.53627i	0.662030	−	0.0512661i
$899$	−21.9700	−	21.9700i	−0.732741	−	0.732741i
$900$	49.6976	−	7.74338i	1.65659	−	0.258113i
$901$	2.44574	+	2.44574i	0.0814793	+	0.0814793i
$902$	39.2103	+	33.5740i	1.30556	+	1.11789i
$903$		0			0
$904$	5.26407	−	1.24283i	0.175080	−	0.0413358i
$905$			29.5680i			0.982874i
$906$	11.6404	+	9.96716i	0.386726	+	0.331137i
$907$	13.5492	+	13.5492i	0.449894	+	0.449894i	0.895319	−	0.445425i	$-0.146948\pi$
$907$	13.5492	+	13.5492i	0.449894	+	0.449894i	−0.445425	+	0.895319i	$0.646948\pi$
$908$	13.9058	+	10.1567i	0.461481	+	0.337061i
$909$	−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	$-0.0906325\pi$
$912$	−3.00406	−	9.40611i	−0.0994742	−	0.311467i
$913$			14.6749i			0.485667i
$914$	0.581991	+	7.51560i	0.0192506	+	0.248594i
$915$	−14.4084	−	14.4084i	−0.476329	−	0.476329i
$916$	−40.8813	−	29.8592i	−1.35075	−	0.986576i
$917$		0			0
$918$	−5.21356	−	4.46414i	−0.172073	−	0.147339i
$919$	−38.0807			−1.25617			−0.628083	−	0.778146i	$-0.716160\pi$
$919$	−38.0807			−1.25617			−0.628083	+	0.778146i	$0.716160\pi$
$920$	19.4537	+	12.0223i	0.641368	+	0.396364i
$921$			26.1475i			0.861589i
$922$	−3.01884	+	3.52563i	−0.0994202	+	0.116110i
$923$	−3.24442	+	3.24442i	−0.106791	+	0.106791i
$924$		0			0
$925$	−23.2496	−	23.2496i	−0.764443	−	0.764443i
$926$	−1.66981	−	21.5633i	−0.0548735	−	0.708614i
$927$	−18.8509			−0.619143
$928$	39.0874	+	16.4790i	1.28311	+	0.540948i
$929$			4.53114i			0.148662i	0.997234	+	0.0743309i	$0.0236821\pi$
$929$			4.53114i			0.148662i	−0.997234	+	0.0743309i	$0.976318\pi$
$930$	1.41202	+	18.2343i	0.0463021	+	0.597927i
$931$		0			0
$932$	4.79396	+	30.7680i	0.157031	+	1.00784i
$933$	14.0786	−	14.0786i	0.460911	−	0.460911i
$934$	32.2527	+	27.6166i	1.05534	+	0.903642i
$935$	20.3539			0.665644
$936$	−10.9031	−	6.73811i	−0.356380	−	0.220242i
$937$	−37.0969			−1.21190			−0.605952	−	0.795501i	$-0.707208\pi$
$937$	−37.0969			−1.21190			−0.605952	+	0.795501i	$0.707208\pi$
$938$		0			0
$939$	4.72453	+	4.72453i	0.154179	+	0.154179i
$940$	−10.3851	−	7.58519i	−0.338726	−	0.247402i
$941$	−1.59440	+	1.59440i	−0.0519758	+	0.0519758i	−0.732617	−	0.680641i	$-0.761701\pi$
$941$	−1.59440	+	1.59440i	−0.0519758	+	0.0519758i	0.680641	+	0.732617i	$0.261701\pi$
$942$	2.32279	−	0.179872i	0.0756806	−	0.00586053i
$943$	−16.5615			−0.539317
$944$	−13.2401	+	25.6655i	−0.430928	+	0.835340i
$945$		0			0
$946$	2.66368	+	34.3977i	0.0866038	+	1.11837i
$947$	−11.5315	+	11.5315i	−0.374724	+	0.374724i	−0.869194	−	0.494471i	$-0.835362\pi$
$947$	−11.5315	+	11.5315i	−0.374724	+	0.374724i	0.494471	+	0.869194i	$0.335362\pi$
$948$	−1.14465	+	1.56719i	−0.0371767	+	0.0508998i
$949$	−3.99251	+	3.99251i	−0.129602	+	0.129602i
$950$	−30.4132	+	35.5188i	−0.986735	+	1.15238i
$951$			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	$0.850510\pi$
$954$	−7.72597	−	6.61541i	−0.250138	−	0.214182i
$955$	−75.9400	+	75.9400i	−2.45736	+	2.45736i
$956$	−3.57879	−	22.9690i	−0.115746	−	0.742869i
$957$	−18.9184	+	18.9184i	−0.611546	+	0.611546i
$958$	48.6071	−	3.76403i	1.57043	−	0.121610i
$959$		0			0
$960$	−11.1678	−	22.3325i	−0.360438	−	0.720779i
$961$	−13.8321			−0.446198
$962$	0.646895	+	8.35375i	0.0208567	+	0.269336i
$963$	−15.5918	+	15.5918i	−0.502439	+	0.502439i
$964$	0.866179	+	5.55920i	0.0278977	+	0.179050i
$965$	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	$0.776230\pi$
$968$	6.09002	+	25.7947i	0.195741	+	0.829072i
$969$	2.81958			0.0905780
$970$	−30.6133	+	35.7526i	−0.982935	+	1.14795i
$971$	−23.1554	+	23.1554i	−0.743091	+	0.743091i	−0.973172	−	0.230080i	$-0.926101\pi$
$971$	−23.1554	+	23.1554i	−0.743091	+	0.743091i	0.230080	+	0.973172i	$0.426101\pi$
$972$	25.3964	+	18.5492i	0.814590	+	0.594967i
$973$		0			0
$974$	−21.0129	+	1.62719i	−0.673296	+	0.0521385i
$975$		−	15.9705i		−	0.511464i
$976$	11.9724	−	23.2081i	0.383227	−	0.742873i
$977$	−31.8468			−1.01887			−0.509435	−	0.860509i	$-0.670146\pi$
$977$	−31.8468			−1.01887			−0.509435	+	0.860509i	$0.670146\pi$
$978$	−2.01042	+	0.155683i	−0.0642863	+	0.00497818i
$979$	27.8711	+	27.8711i	0.890763	+	0.890763i
$980$		0			0
$981$	1.47742	−	1.47742i	0.0471704	−	0.0471704i
$982$	46.3726	+	39.7068i	1.47981	+	1.26709i
$983$			43.2988i			1.38102i	0.723324	+	0.690509i	$0.242614\pi$
$983$			43.2988i			1.38102i	−0.723324	+	0.690509i	$0.757386\pi$
$984$	15.3823	+	9.50619i	0.490368	+	0.303046i
$985$	71.3253			2.27261
$986$	−7.87822	+	9.20078i	−0.250894	+	0.293013i
$987$		0			0
$988$	11.7739	−	1.83449i	0.374577	−	0.0583628i
$989$	−7.82694	−	7.82694i	−0.248882	−	0.248882i
$990$	−59.6759	+	4.62117i	−1.89662	+	0.146870i
$991$		−	18.9625i		−	0.602365i	−0.953567	−	0.301183i	$-0.902619\pi$
$991$		−	18.9625i		−	0.602365i	0.953567	−	0.301183i	$-0.0973813\pi$
$992$	−21.7104	+	8.83339i	−0.689307	+	0.280461i
$993$		−	11.4262i		−	0.362601i
$994$		0			0
$995$	15.3755	−	15.3755i	0.487436	−	0.487436i
$996$	0.791409	+	5.07933i	0.0250767	+	0.160945i
$997$	21.4000	+	21.4000i	0.677746	+	0.677746i	0.959490	−	0.281744i	$-0.0909129\pi$
$997$	21.4000	+	21.4000i	0.677746	+	0.677746i	−0.281744	+	0.959490i	$0.590913\pi$
$998$	10.1795	−	11.8884i	0.322226	−	0.376320i
$999$		−	13.1945i		−	0.417454i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.6	✓	56	7.5	odd	6
112.2.v.a.19.5	yes	56	7.4	even	3
112.2.v.a.59.5	yes	56	112.75	even	12
112.2.v.a.75.6	yes	56	112.11	odd	12
448.2.z.a.47.8		56	28.11	odd	6
448.2.z.a.143.8		56	112.5	odd	12
448.2.z.a.271.8		56	112.53	even	12
448.2.z.a.367.8		56	28.19	even	6
784.2.j.a.195.27		56	1.1	even	1	trivial
784.2.j.a.195.28		56	7.6	odd	2	inner
784.2.j.a.587.27		56	112.27	even	4	inner
784.2.j.a.587.28		56	16.11	odd	4	inner
784.2.w.f.19.5		56	7.3	odd	6
784.2.w.f.227.6		56	7.2	even	3
784.2.w.f.411.6		56	112.59	even	12
784.2.w.f.619.5		56	112.107	odd	12
896.2.z.a.31.7		56	112.61	odd	12
896.2.z.a.159.7		56	112.109	even	12
896.2.z.a.479.7		56	56.19	even	6
896.2.z.a.607.7		56	56.11	odd	6
896.2.z.b.31.8		56	112.19	even	12
896.2.z.b.159.8		56	112.67	odd	12
896.2.z.b.479.8		56	56.5	odd	6
896.2.z.b.607.8		56	56.53	even	6

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40999 - 0.109187i) q^{2} +(-0.558981 - 0.558981i) q^{3} +(1.97616 - 0.307905i) q^{4} +(2.79182 + 2.79182i) q^{5} +(-0.849192 - 0.727125i) q^{6} +(2.75275 - 0.649913i) q^{8} -2.37508i q^{9} +(4.24128 + 3.63162i) q^{10} +(-3.19144 - 3.19144i) q^{11} +(-1.27675 - 0.932521i) q^{12} +(1.34913 - 1.34913i) q^{13} -3.12115i q^{15} +(3.81039 - 1.21694i) q^{16} +1.14220i q^{17} +(-0.259327 - 3.34885i) q^{18} +(2.20808 + 2.20808i) q^{19} +(6.37669 + 4.65746i) q^{20} +(-4.84836 - 4.15144i) q^{22} +2.04784 q^{23} +(-1.90202 - 1.17544i) q^{24} +10.5885i q^{25} +(1.75496 - 2.04957i) q^{26} +(-3.00457 + 3.00457i) q^{27} +(5.30239 + 5.30239i) q^{29} +(-0.340788 - 4.40080i) q^{30} -4.14341 q^{31} +(5.23975 - 2.13191i) q^{32} +3.56790i q^{33} +(0.124713 + 1.61050i) q^{34} +(-0.731298 - 4.69353i) q^{36} +(-2.19573 + 2.19573i) q^{37} +(3.35446 + 2.87228i) q^{38} -1.50828 q^{39} +(9.49962 + 5.87074i) q^{40} -8.08732 q^{41} +(-3.82205 - 3.82205i) q^{43} +(-7.28943 - 5.32412i) q^{44} +(6.63080 - 6.63080i) q^{45} +(2.88743 - 0.223596i) q^{46} -1.62861 q^{47} +(-2.81018 - 1.44969i) q^{48} +(1.15613 + 14.9298i) q^{50} +(0.638470 - 0.638470i) q^{51} +(2.25069 - 3.08150i) q^{52} +(2.14124 - 2.14124i) q^{53} +(-3.90836 + 4.56447i) q^{54} -17.8198i q^{55} -2.46854i q^{57} +(8.05528 + 6.89738i) q^{58} +(-5.10520 + 5.10520i) q^{59} +(-0.961016 - 6.16788i) q^{60} +(4.61639 - 4.61639i) q^{61} +(-5.84218 + 0.452405i) q^{62} +(7.15523 - 3.57809i) q^{64} +7.53307 q^{65} +(0.389567 + 5.03071i) q^{66} +(-0.451116 + 0.451116i) q^{67} +(0.351690 + 2.25718i) q^{68} +(-1.14470 - 1.14470i) q^{69} -2.40482 q^{71} +(-1.54360 - 6.53800i) q^{72} -2.95932 q^{73} +(-2.85622 + 3.33571i) q^{74} +(5.91879 - 5.91879i) q^{75} +(5.04338 + 3.68363i) q^{76} +(-2.12666 + 0.164684i) q^{78} -1.22748i q^{79} +(14.0354 + 7.24046i) q^{80} -3.76625 q^{81} +(-11.4031 + 0.883027i) q^{82} +(-2.29910 - 2.29910i) q^{83} +(-3.18883 + 3.18883i) q^{85} +(-5.80638 - 4.97175i) q^{86} -5.92787i q^{87} +(-10.8594 - 6.71106i) q^{88} -8.73308 q^{89} +(8.62539 - 10.0734i) q^{90} +(4.04685 - 0.630538i) q^{92} +(2.31609 + 2.31609i) q^{93} +(-2.29633 + 0.177822i) q^{94} +12.3291i q^{95} +(-4.12062 - 1.73722i) q^{96} +8.42967i q^{97} +(-7.57992 + 7.57992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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