LMFDB - Embedded newform 784.2.j.a.587.8

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			587.8
Character	$\chi$	$=$	784.587
Dual form			784.2.j.a.195.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07857 + 0.914706i) q^{2} +(1.91404 - 1.91404i) q^{3} +(0.326624 - 1.97315i) q^{4} +(0.329897 - 0.329897i) q^{5} +(-0.313640 + 3.81521i) q^{6} +(1.45257 + 2.42694i) q^{8} -4.32709i q^{9} +(-0.0540578 + 0.657575i) q^{10} +(1.41679 - 1.41679i) q^{11} +(-3.15151 - 4.40186i) q^{12} +(-4.51607 - 4.51607i) q^{13} -1.26287i q^{15} +(-3.78663 - 1.28896i) q^{16} -5.40476i q^{17} +(3.95802 + 4.66707i) q^{18} +(-1.39438 + 1.39438i) q^{19} +(-0.543183 - 0.758687i) q^{20} +(-0.232159 + 2.82405i) q^{22} -1.90249 q^{23} +(7.42553 + 1.86500i) q^{24} +4.78234i q^{25} +(9.00178 + 0.740017i) q^{26} +(-2.54010 - 2.54010i) q^{27} +(-1.12415 + 1.12415i) q^{29} +(1.15516 + 1.36209i) q^{30} +0.868151 q^{31} +(5.26316 - 2.07343i) q^{32} -5.42358i q^{33} +(4.94377 + 5.82941i) q^{34} +(-8.53799 - 1.41333i) q^{36} +(5.78856 + 5.78856i) q^{37} +(0.228487 - 2.77939i) q^{38} -17.2879 q^{39} +(1.27984 + 0.321444i) q^{40} +3.24226 q^{41} +(6.35727 - 6.35727i) q^{43} +(-2.33278 - 3.25830i) q^{44} +(-1.42749 - 1.42749i) q^{45} +(2.05197 - 1.74022i) q^{46} +2.98532 q^{47} +(-9.71488 + 4.78065i) q^{48} +(-4.37443 - 5.15808i) q^{50} +(-10.3449 - 10.3449i) q^{51} +(-10.3859 + 7.43582i) q^{52} +(-4.96313 - 4.96313i) q^{53} +(5.06313 + 0.416229i) q^{54} -0.934789i q^{55} +5.33780i q^{57} +(0.184206 - 2.24074i) q^{58} +(-6.07138 - 6.07138i) q^{59} +(-2.49183 - 0.412484i) q^{60} +(-0.343846 - 0.343846i) q^{61} +(-0.936361 + 0.794103i) q^{62} +(-3.78011 + 7.05059i) q^{64} -2.97967 q^{65} +(4.96099 + 5.84971i) q^{66} +(-2.82013 - 2.82013i) q^{67} +(-10.6644 - 1.76533i) q^{68} +(-3.64144 + 3.64144i) q^{69} -12.1916 q^{71} +(10.5016 - 6.28538i) q^{72} +15.5822 q^{73} +(-11.5382 - 0.948530i) q^{74} +(9.15358 + 9.15358i) q^{75} +(2.29588 + 3.20676i) q^{76} +(18.6462 - 15.8133i) q^{78} +1.23703i q^{79} +(-1.67442 + 0.823975i) q^{80} +3.25756 q^{81} +(-3.49701 + 2.96572i) q^{82} +(9.03560 - 9.03560i) q^{83} +(-1.78301 - 1.78301i) q^{85} +(-1.04172 + 12.6718i) q^{86} +4.30333i q^{87} +(5.49645 + 1.38049i) q^{88} +2.32727 q^{89} +(2.84539 + 0.233913i) q^{90} +(-0.621399 + 3.75390i) q^{92} +(1.66167 - 1.66167i) q^{93} +(-3.21987 + 2.73069i) q^{94} +0.920003i q^{95} +(6.10528 - 14.0425i) q^{96} +4.69704i q^{97} +(-6.13058 - 6.13058i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.07857	+	0.914706i	−0.762664	+	0.646795i
$2$	−1.07857	+	0.914706i	−0.762664	+	0.646795i
$3$	1.91404	−	1.91404i	1.10507	−	1.10507i	0.111282	−	0.993789i	$-0.464504\pi$
$3$	1.91404	−	1.91404i	1.10507	−	1.10507i	0.993789	−	0.111282i	$-0.0354957\pi$
$4$	0.326624	−	1.97315i	0.163312	−	0.986574i
$5$	0.329897	−	0.329897i	0.147534	−	0.147534i	−0.629481	−	0.777016i	$-0.716733\pi$
$5$	0.329897	−	0.329897i	0.147534	−	0.147534i	0.777016	+	0.629481i	$0.216733\pi$
$6$	−0.313640	+	3.81521i	−0.128043	+	1.55755i
$7$		0			0
$7$		0			0
$8$	1.45257	+	2.42694i	0.513559	+	0.858054i
$9$		−	4.32709i		−	1.44236i
$10$	−0.0540578	+	0.657575i	−0.0170946	+	0.207943i
$11$	1.41679	−	1.41679i	0.427178	−	0.427178i	−0.460488	−	0.887666i	$-0.652325\pi$
$11$	1.41679	−	1.41679i	0.427178	−	0.427178i	0.887666	+	0.460488i	$0.152325\pi$
$12$	−3.15151	−	4.40186i	−0.909763	−	1.27071i
$13$	−4.51607	−	4.51607i	−1.25253	−	1.25253i	−0.954581	−	0.297952i	$-0.903696\pi$
$13$	−4.51607	−	4.51607i	−1.25253	−	1.25253i	−0.297952	−	0.954581i	$-0.596304\pi$
$14$		0			0
$15$		−	1.26287i		−	0.326072i
$16$	−3.78663	−	1.28896i	−0.946658	−	0.322239i
$17$		−	5.40476i		−	1.31085i	−0.755262	−	0.655424i	$-0.772490\pi$
$17$		−	5.40476i		−	1.31085i	0.755262	−	0.655424i	$-0.227510\pi$
$18$	3.95802	+	4.66707i	0.932914	+	1.10004i
$19$	−1.39438	+	1.39438i	−0.319893	+	0.319893i	−0.848726	−	0.528833i	$-0.822630\pi$
$19$	−1.39438	+	1.39438i	−0.319893	+	0.319893i	0.528833	+	0.848726i	$0.322630\pi$
$20$	−0.543183	−	0.758687i	−0.121459	−	0.169648i
$21$		0			0
$22$	−0.232159	+	2.82405i	−0.0494966	+	0.602090i
$23$	−1.90249			−0.396697			−0.198348	−	0.980132i	$-0.563558\pi$
$23$	−1.90249			−0.396697			−0.198348	+	0.980132i	$0.563558\pi$
$24$	7.42553	+	1.86500i	1.51573	+	0.380691i
$25$			4.78234i			0.956467i
$26$	9.00178	+	0.740017i	1.76539	+	0.145129i
$27$	−2.54010	−	2.54010i	−0.488843	−	0.488843i
$28$		0			0
$29$	−1.12415	+	1.12415i	−0.208749	+	0.208749i	−0.803736	−	0.594986i	$-0.797157\pi$
$29$	−1.12415	+	1.12415i	−0.208749	+	0.208749i	0.594986	+	0.803736i	$0.297157\pi$
$30$	1.15516	+	1.36209i	0.210902	+	0.248683i
$31$	0.868151			0.155924			0.0779622	−	0.996956i	$-0.475159\pi$
$31$	0.868151			0.155924			0.0779622	+	0.996956i	$0.475159\pi$
$32$	5.26316	−	2.07343i	0.930405	−	0.366534i
$33$		−	5.42358i		−	0.944125i
$34$	4.94377	+	5.82941i	0.847849	+	0.999736i
$35$		0			0
$36$	−8.53799	−	1.41333i	−1.42300	−	0.235555i
$37$	5.78856	+	5.78856i	0.951633	+	0.951633i	0.998883	−	0.0472499i	$-0.0150457\pi$
$37$	5.78856	+	5.78856i	0.951633	+	0.951633i	−0.0472499	+	0.998883i	$0.515046\pi$
$38$	0.228487	−	2.77939i	0.0370656	−	0.450876i
$39$	−17.2879			−2.76828
$40$	1.27984	+	0.321444i	0.202360	+	0.0508248i
$41$	3.24226			0.506356			0.253178	−	0.967420i	$-0.418524\pi$
$41$	3.24226			0.506356			0.253178	+	0.967420i	$0.418524\pi$
$42$		0			0
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	−0.0300731	−	0.999548i	$-0.509574\pi$
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	0.999548	+	0.0300731i	$0.00957401\pi$
$44$	−2.33278	−	3.25830i	−0.351680	−	0.491207i
$45$	−1.42749	−	1.42749i	−0.212798	−	0.212798i
$46$	2.05197	−	1.74022i	0.302546	−	0.256582i
$47$	2.98532			0.435454			0.217727	−	0.976010i	$-0.430136\pi$
$47$	2.98532			0.435454			0.217727	+	0.976010i	$0.430136\pi$
$48$	−9.71488	+	4.78065i	−1.40222	+	0.690028i
$49$		0			0
$50$	−4.37443	−	5.15808i	−0.618638	−	0.729463i
$51$	−10.3449	−	10.3449i	−1.44858	−	1.44858i
$52$	−10.3859	+	7.43582i	−1.44027	+	1.03116i
$53$	−4.96313	−	4.96313i	−0.681738	−	0.681738i	0.278654	−	0.960392i	$-0.410112\pi$
$53$	−4.96313	−	4.96313i	−0.681738	−	0.681738i	−0.960392	+	0.278654i	$0.910112\pi$
$54$	5.06313	+	0.416229i	0.689004	+	0.0566416i
$55$		−	0.934789i		−	0.126047i
$56$		0			0
$57$			5.33780i			0.707009i
$58$	0.184206	−	2.24074i	0.0241875	−	0.294224i
$59$	−6.07138	−	6.07138i	−0.790427	−	0.790427i	0.191137	−	0.981563i	$-0.438783\pi$
$59$	−6.07138	−	6.07138i	−0.790427	−	0.790427i	−0.981563	+	0.191137i	$0.938783\pi$
$60$	−2.49183	−	0.412484i	−0.321694	−	0.0532514i
$61$	−0.343846	−	0.343846i	−0.0440250	−	0.0440250i	0.684752	−	0.728777i	$-0.259911\pi$
$61$	−0.343846	−	0.343846i	−0.0440250	−	0.0440250i	−0.728777	+	0.684752i	$0.759911\pi$
$62$	−0.936361	+	0.794103i	−0.118918	+	0.100851i
$63$		0			0
$64$	−3.78011	+	7.05059i	−0.472513	+	0.881323i
$65$	−2.97967			−0.369583
$66$	4.96099	+	5.84971i	0.610655	+	0.720050i
$67$	−2.82013	−	2.82013i	−0.344534	−	0.344534i	0.513535	−	0.858069i	$-0.328336\pi$
$67$	−2.82013	−	2.82013i	−0.344534	−	0.344534i	−0.858069	+	0.513535i	$0.828336\pi$
$68$	−10.6644	−	1.76533i	−1.29325	−	0.214077i
$69$	−3.64144	+	3.64144i	−0.438378	+	0.438378i
$70$		0			0
$71$	−12.1916			−1.44687			−0.723437	−	0.690390i	$-0.757439\pi$
$71$	−12.1916			−1.44687			−0.723437	+	0.690390i	$0.757439\pi$
$72$	10.5016	−	6.28538i	1.23763	−	0.740739i
$73$	15.5822			1.82376			0.911878	−	0.410460i	$-0.134632\pi$
$73$	15.5822			1.82376			0.911878	+	0.410460i	$0.134632\pi$
$74$	−11.5382	−	0.948530i	−1.34129	−	0.110264i
$75$	9.15358	+	9.15358i	1.05696	+	1.05696i
$76$	2.29588	+	3.20676i	0.263356	+	0.367841i
$77$		0			0
$78$	18.6462	−	15.8133i	2.11126	−	1.79051i
$79$			1.23703i			0.139177i	0.997576	+	0.0695885i	$0.0221686\pi$
$79$			1.23703i			0.139177i	−0.997576	+	0.0695885i	$0.977831\pi$
$80$	−1.67442	+	0.823975i	−0.187206	+	0.0921232i
$81$	3.25756			0.361951
$82$	−3.49701	+	2.96572i	−0.386180	+	0.327509i
$83$	9.03560	−	9.03560i	0.991786	−	0.991786i	−0.00818066	−	0.999967i	$-0.502604\pi$
$83$	9.03560	−	9.03560i	0.991786	−	0.991786i	0.999967	+	0.00818066i	$0.00260402\pi$
$84$		0			0
$85$	−1.78301	−	1.78301i	−0.193395	−	0.193395i
$86$	−1.04172	+	12.6718i	−0.112332	+	1.36643i
$87$			4.30333i			0.461366i
$88$	5.49645	+	1.38049i	0.585924	+	0.147161i
$89$	2.32727			0.246691			0.123345	−	0.992364i	$-0.460638\pi$
$89$	2.32727			0.246691			0.123345	+	0.992364i	$0.460638\pi$
$90$	2.84539	+	0.233913i	0.299930	+	0.0246566i
$91$		0			0
$92$	−0.621399	+	3.75390i	−0.0647854	+	0.391371i
$93$	1.66167	−	1.66167i	0.172308	−	0.172308i
$94$	−3.21987	+	2.73069i	−0.332105	+	0.281649i
$95$			0.920003i			0.0943904i
$96$	6.10528	−	14.0425i	0.623117	−	1.43321i
$97$			4.69704i			0.476912i	0.971153	+	0.238456i	$0.0766414\pi$
$97$			4.69704i			0.476912i	−0.971153	+	0.238456i	$0.923359\pi$
$98$		0			0
$99$	−6.13058	−	6.13058i	−0.616146	−	0.616146i
$100$	9.43626	+	1.56203i	0.943626	+	0.156203i
$101$	−3.92074	+	3.92074i	−0.390129	+	0.390129i	−0.874733	−	0.484605i	$-0.838963\pi$
$101$	−3.92074	+	3.92074i	−0.390129	+	0.390129i	0.484605	+	0.874733i	$0.338963\pi$
$102$	20.6203	+	1.69515i	2.04171	+	0.167845i
$103$			1.10634i			0.109011i	0.998513	+	0.0545053i	$0.0173582\pi$
$103$			1.10634i			0.109011i	−0.998513	+	0.0545053i	$0.982642\pi$
$104$	4.40036	−	17.5201i	0.431491	−	1.71799i
$105$		0			0
$106$	9.89289	+	0.813273i	0.960882	+	0.0789921i
$107$	−4.37182	+	4.37182i	−0.422640	+	0.422640i	−0.886112	−	0.463472i	$-0.846603\pi$
$107$	−4.37182	+	4.37182i	−0.422640	+	0.422640i	0.463472	+	0.886112i	$0.346603\pi$
$108$	−5.84166	+	4.18234i	−0.562114	+	0.402446i
$109$	7.70382	−	7.70382i	0.737892	−	0.737892i	−0.234278	−	0.972170i	$-0.575273\pi$
$109$	7.70382	−	7.70382i	0.737892	−	0.737892i	0.972170	+	0.234278i	$0.0752725\pi$
$110$	0.855057	+	1.00823i	0.0815265	+	0.0961314i
$111$	22.1591			2.10324
$112$		0			0
$113$	−2.81872			−0.265163			−0.132582	−	0.991172i	$-0.542327\pi$
$113$	−2.81872			−0.265163			−0.132582	+	0.991172i	$0.542327\pi$
$114$	−4.88252	−	5.75719i	−0.457290	−	0.539210i
$115$	−0.627625	+	0.627625i	−0.0585264	+	0.0585264i
$116$	1.85094	+	2.58529i	0.171855	+	0.240038i
$117$	−19.5414	+	19.5414i	−1.80661	+	1.80661i
$118$	12.1019	+	0.994875i	1.11407	+	0.0915857i
$119$		0			0
$120$	3.06491	−	1.83440i	0.279787	−	0.167457i
$121$			6.98541i			0.635037i
$122$	0.685380	+	0.0563437i	0.0620514	+	0.00510112i
$123$	6.20582	−	6.20582i	0.559560	−	0.559560i
$124$	0.283559	−	1.71299i	0.0254643	−	0.153831i
$125$	3.22716	+	3.22716i	0.288646	+	0.288646i
$126$		0			0
$127$			9.34725i			0.829434i	0.909950	+	0.414717i	$0.136119\pi$
$127$			9.34725i			0.829434i	−0.909950	+	0.414717i	$0.863881\pi$
$128$	−2.37211	−	11.0622i	−0.209667	−	0.977773i
$129$		−	24.3361i		−	2.14268i
$130$	3.21378	−	2.72553i	0.281868	−	0.239045i
$131$	13.1186	−	13.1186i	1.14618	−	1.14618i	0.158879	−	0.987298i	$-0.449212\pi$
$131$	13.1186	−	13.1186i	1.14618	−	1.14618i	0.987298	−	0.158879i	$-0.0507879\pi$
$132$	−10.7015	−	1.77147i	−0.931449	−	0.154187i
$133$		0			0
$134$	5.62131	+	0.462116i	0.485607	+	0.0399207i
$135$	−1.67594			−0.144242
$136$	13.1170	−	7.85077i	1.12478	−	0.673198i
$137$			15.1891i			1.29769i	0.760921	+	0.648844i	$0.224747\pi$
$137$			15.1891i			1.29769i	−0.760921	+	0.648844i	$0.775253\pi$
$138$	0.596697	−	7.25840i	0.0507943	−	0.617876i
$139$	1.13113	+	1.13113i	0.0959413	+	0.0959413i	0.753448	−	0.657507i	$-0.228389\pi$
$139$	1.13113	+	1.13113i	0.0959413	+	0.0959413i	−0.657507	+	0.753448i	$0.728389\pi$
$140$		0			0
$141$	5.71402	−	5.71402i	0.481207	−	0.481207i
$142$	13.1495	−	11.1517i	1.10348	−	0.935831i
$143$	−12.7967			−1.07011
$144$	−5.57743	+	16.3851i	−0.464786	+	1.36543i
$145$			0.741706i			0.0615954i
$146$	−16.8065	+	14.2531i	−1.39091	+	1.17960i
$147$		0			0
$148$	13.3124	−	9.53101i	1.09427	−	0.783444i
$149$	7.18420	+	7.18420i	0.588553	+	0.588553i	0.937239	−	0.348687i	$-0.113372\pi$
$149$	7.18420	+	7.18420i	0.588553	+	0.588553i	−0.348687	+	0.937239i	$0.613372\pi$
$150$	−18.2456	−	1.49993i	−1.48975	−	0.122469i
$151$	11.6780			0.950342			0.475171	−	0.879894i	$-0.342386\pi$
$151$	11.6780			0.950342			0.475171	+	0.879894i	$0.342386\pi$
$152$	−5.40951	−	1.35865i	−0.438770	−	0.110201i
$153$	−23.3869			−1.89072
$154$		0			0
$155$	0.286400	−	0.286400i	0.0230042	−	0.0230042i
$156$	−5.64664	+	34.1115i	−0.452093	+	2.73111i
$157$	1.57484	+	1.57484i	0.125686	+	0.125686i	0.767152	−	0.641466i	$-0.221673\pi$
$157$	1.57484	+	1.57484i	0.125686	+	0.125686i	−0.641466	+	0.767152i	$0.721673\pi$
$158$	−1.13152	−	1.33423i	−0.0900190	−	0.106145i
$159$	−18.9992			−1.50674
$160$	1.05228	−	2.42032i	0.0831902	−	0.191343i
$161$		0			0
$162$	−3.51350	+	2.97971i	−0.276047	+	0.234108i
$163$	10.3761	+	10.3761i	0.812720	+	0.812720i	0.985041	−	0.172321i	$-0.0551266\pi$
$163$	10.3761	+	10.3761i	0.812720	+	0.812720i	−0.172321	+	0.985041i	$0.555127\pi$
$164$	1.05900	−	6.39747i	0.0826941	−	0.499558i
$165$	−1.78922	−	1.78922i	−0.139291	−	0.139291i
$166$	−1.48060	+	18.0104i	−0.114917	+	1.39788i
$167$		−	5.94995i		−	0.460421i	−0.973141	−	0.230210i	$-0.926059\pi$
$167$		−	5.94995i		−	0.460421i	0.973141	−	0.230210i	$-0.0739415\pi$
$168$		0			0
$169$			27.7898i			2.13768i
$170$	3.55404	+	0.292170i	0.272582	+	0.0224084i
$171$	6.03361	+	6.03361i	0.461402	+	0.461402i
$172$	−10.4674	−	14.6203i	−0.798132	−	1.11479i
$173$	6.49471	+	6.49471i	0.493784	+	0.493784i	0.909496	−	0.415713i	$-0.136468\pi$
$173$	6.49471	+	6.49471i	0.493784	+	0.493784i	−0.415713	+	0.909496i	$0.636468\pi$
$174$	−3.93629	−	4.64144i	−0.298409	−	0.351867i
$175$		0			0
$176$	−7.19105	+	3.53868i	−0.542045	+	0.266738i
$177$	−23.2417			−1.74696
$178$	−2.51013	+	2.12877i	−0.188142	+	0.159558i
$179$	−2.69029	−	2.69029i	−0.201082	−	0.201082i	0.599382	−	0.800463i	$-0.295413\pi$
$179$	−2.69029	−	2.69029i	−0.201082	−	0.201082i	−0.800463	+	0.599382i	$0.795413\pi$
$180$	−3.28291	+	2.35040i	−0.244694	+	0.175189i
$181$	5.13439	−	5.13439i	0.381636	−	0.381636i	−0.490055	−	0.871691i	$-0.663023\pi$
$181$	5.13439	−	5.13439i	0.381636	−	0.381636i	0.871691	+	0.490055i	$0.163023\pi$
$182$		0			0
$183$	−1.31627			−0.0973015
$184$	−2.76349	−	4.61724i	−0.203727	−	0.340387i
$185$	3.81925			0.280797
$186$	−0.272287	+	3.31217i	−0.0199650	+	0.242860i
$187$	−7.65741	−	7.65741i	−0.559965	−	0.559965i
$188$	0.975077	−	5.89048i	0.0711148	−	0.429607i
$189$		0			0
$190$	−0.841533	−	0.992287i	−0.0610512	−	0.0719881i
$191$			17.5976i			1.27332i	0.771145	+	0.636660i	$0.219685\pi$
$191$			17.5976i			1.27332i	−0.771145	+	0.636660i	$0.780315\pi$
$192$	6.25983	+	20.7304i	0.451764	+	1.49609i
$193$	−6.57937			−0.473593			−0.236797	−	0.971559i	$-0.576097\pi$
$193$	−6.57937			−0.473593			−0.236797	+	0.971559i	$0.576097\pi$
$194$	−4.29642	−	5.06609i	−0.308465	−	0.363724i
$195$	−5.70321	+	5.70321i	−0.408415	+	0.408415i
$196$		0			0
$197$	14.8776	+	14.8776i	1.05998	+	1.05998i	0.998082	+	0.0619015i	$0.0197165\pi$
$197$	14.8776	+	14.8776i	1.05998	+	1.05998i	0.0619015	+	0.998082i	$0.480284\pi$
$198$	12.2199	+	1.00457i	0.868433	+	0.0713920i
$199$			7.42845i			0.526589i	0.964716	+	0.263294i	$0.0848090\pi$
$199$			7.42845i			0.526589i	−0.964716	+	0.263294i	$0.915191\pi$
$200$	−11.6065	+	6.94666i	−0.820701	+	0.491203i
$201$	−10.7957			−0.761470
$202$	0.642465	−	7.81512i	0.0452037	−	0.549870i
$203$		0			0
$204$	−23.7910	+	17.0332i	−1.66570	+	1.19256i
$205$	1.06961	−	1.06961i	0.0747049	−	0.0747049i
$206$	−1.01197	−	1.19326i	−0.0705075	−	0.0831384i
$207$			8.23225i			0.572181i
$208$	11.2797	+	22.9217i	0.782106	+	1.58934i
$209$			3.95109i			0.273303i
$210$		0			0
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	0.319820	−	0.947478i	$-0.396378\pi$
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	−0.947478	+	0.319820i	$0.896378\pi$
$212$	−11.4141	+	8.17192i	−0.783922	+	0.561249i
$213$	−23.3352	+	23.3352i	−1.59890	+	1.59890i
$214$	0.716379	−	8.71424i	0.0489707	−	0.595693i
$215$		−	4.19448i		−	0.286061i
$216$	2.47502	−	9.85435i	0.168404	−	0.670504i
$217$		0			0
$218$	−1.26237	+	15.3558i	−0.0854985	+	1.04003i
$219$	29.8249	−	29.8249i	2.01538	−	2.01538i
$220$	−1.84448	−	0.305325i	−0.124355	−	0.0205850i
$221$	−24.4083	+	24.4083i	−1.64188	+	1.64188i
$222$	−23.9001	+	20.2690i	−1.60407	+	1.36037i
$223$	−6.72926			−0.450624			−0.225312	−	0.974287i	$-0.572340\pi$
$223$	−6.72926			−0.450624			−0.225312	+	0.974287i	$0.572340\pi$
$224$		0			0
$225$	20.6936			1.37957
$226$	3.04019	−	2.57830i	0.202230	−	0.171506i
$227$	5.46476	−	5.46476i	0.362709	−	0.362709i	−0.502101	−	0.864809i	$-0.667439\pi$
$227$	5.46476	−	5.46476i	0.362709	−	0.362709i	0.864809	+	0.502101i	$0.167439\pi$
$228$	10.5323	+	1.74345i	0.697517	+	0.115463i
$229$	−10.7782	+	10.7782i	−0.712242	+	0.712242i	−0.967004	−	0.254762i	$-0.918003\pi$
$229$	−10.7782	+	10.7782i	−0.712242	+	0.712242i	0.254762	+	0.967004i	$0.418003\pi$
$230$	0.102845	−	1.25103i	0.00678137	−	0.0824905i
$231$		0			0
$232$	−4.36115	−	1.09535i	−0.286323	−	0.0719130i
$233$		−	14.7748i		−	0.967931i	−0.875087	−	0.483965i	$-0.839196\pi$
$233$		−	14.7748i		−	0.967931i	0.875087	−	0.483965i	$-0.160804\pi$
$234$	3.20212	−	38.9515i	0.209329	−	2.54634i
$235$	0.984847	−	0.984847i	0.0642443	−	0.0642443i
$236$	−13.9628	+	9.99668i	−0.908901	+	0.650729i
$237$	2.36773	+	2.36773i	0.153800	+	0.153800i
$238$		0			0
$239$		−	28.5488i		−	1.84667i	−0.383998	−	0.923334i	$-0.625453\pi$
$239$		−	28.5488i		−	1.84667i	0.383998	−	0.923334i	$-0.374547\pi$
$240$	−1.62778	+	4.78203i	−0.105073	+	0.308678i
$241$			22.9545i			1.47863i	0.673361	+	0.739314i	$0.264850\pi$
$241$			22.9545i			1.47863i	−0.673361	+	0.739314i	$0.735150\pi$
$242$	−6.38960	−	7.53425i	−0.410739	−	0.484320i
$243$	13.8554	−	13.8554i	0.888825	−	0.888825i
$244$	−0.790768	+	0.566151i	−0.0506238	+	0.0362441i
$245$		0			0
$246$	−1.01690	+	12.3699i	−0.0648354	+	0.788677i
$247$	12.5943			0.801353
$248$	1.26105	+	2.10695i	0.0800765	+	0.133792i
$249$		−	34.5890i		−	2.19199i
$250$	−6.43262	−	0.528812i	−0.406835	−	0.0334450i
$251$	−10.2808	−	10.2808i	−0.648918	−	0.648918i	0.303813	−	0.952732i	$-0.401740\pi$
$251$	−10.2808	−	10.2808i	−0.648918	−	0.648918i	−0.952732	+	0.303813i	$0.901740\pi$
$252$		0			0
$253$	−2.69543	+	2.69543i	−0.169460	+	0.169460i
$254$	−8.54999	−	10.0817i	−0.536474	−	0.632580i
$255$	−6.82551			−0.427430
$256$	12.6772	+	9.76161i	0.792324	+	0.610100i
$257$		−	2.51508i		−	0.156886i	−0.996919	−	0.0784431i	$-0.975005\pi$
$257$		−	2.51508i		−	0.156886i	0.996919	−	0.0784431i	$-0.0249949\pi$
$258$	22.2604	+	26.2482i	1.38587	+	1.63414i
$259$		0			0
$260$	−0.973233	+	5.87934i	−0.0603574	+	0.364621i
$261$	4.86430	+	4.86430i	0.301092	+	0.301092i
$262$	−2.14965	+	26.1490i	−0.132806	+	1.61549i
$263$	9.09561			0.560859			0.280430	−	0.959875i	$-0.409523\pi$
$263$	9.09561			0.560859			0.280430	+	0.959875i	$0.409523\pi$
$264$	13.1627	−	7.87811i	0.810110	−	0.484864i
$265$	−3.27464			−0.201159
$266$		0			0
$267$	4.45449	−	4.45449i	0.272611	−	0.272611i
$268$	−6.48567	+	4.64342i	−0.396175	+	0.283642i
$269$	4.03108	+	4.03108i	0.245780	+	0.245780i	0.819236	−	0.573456i	$-0.194398\pi$
$269$	4.03108	+	4.03108i	0.245780	+	0.245780i	−0.573456	+	0.819236i	$0.694398\pi$
$270$	1.80762	−	1.53300i	0.110008	−	0.0932951i
$271$	11.5201			0.699798			0.349899	−	0.936787i	$-0.386216\pi$
$271$	11.5201			0.699798			0.349899	+	0.936787i	$0.386216\pi$
$272$	−6.96650	+	20.4658i	−0.422406	+	1.24092i
$273$		0			0
$274$	−13.8935	−	16.3824i	−0.839338	−	0.989700i
$275$	6.77557	+	6.77557i	0.408582	+	0.408582i
$276$	5.99572	+	8.37449i	0.360900	+	0.504085i
$277$	14.7749	+	14.7749i	0.887740	+	0.887740i	0.994306	−	0.106566i	$-0.0339855\pi$
$277$	14.7749	+	14.7749i	0.887740	+	0.887740i	−0.106566	+	0.994306i	$0.533985\pi$
$278$	−2.25466	−	0.185350i	−0.135225	−	0.0111166i
$279$		−	3.75657i		−	0.224900i
$280$		0			0
$281$		−	19.8360i		−	1.18331i	−0.806190	−	0.591657i	$-0.798474\pi$
$281$		−	19.8360i		−	1.18331i	0.806190	−	0.591657i	$-0.201526\pi$
$282$	−0.936316	+	11.3896i	−0.0557568	+	0.678242i
$283$	14.3870	+	14.3870i	0.855221	+	0.855221i	0.990771	−	0.135550i	$-0.0432801\pi$
$283$	14.3870	+	14.3870i	0.855221	+	0.855221i	−0.135550	+	0.990771i	$0.543280\pi$
$284$	−3.98206	+	24.0558i	−0.236292	+	1.42745i
$285$	1.76092	+	1.76092i	0.104308	+	0.104308i
$286$	13.8021	−	11.7052i	0.816134	−	0.692142i
$287$		0			0
$288$	−8.97192	−	22.7742i	−0.528675	−	1.34198i
$289$	−12.2114			−0.718320
$290$	−0.678444	−	0.799982i	−0.0398396	−	0.0469765i
$291$	8.99032	+	8.99032i	0.527022	+	0.527022i
$292$	5.08952	−	30.7460i	0.297841	−	1.79927i
$293$	−6.75509	+	6.75509i	−0.394636	+	0.394636i	−0.876336	−	0.481700i	$-0.840020\pi$
$293$	−6.75509	+	6.75509i	−0.394636	+	0.394636i	0.481700	+	0.876336i	$0.340020\pi$
$294$		0			0
$295$	−4.00586			−0.233230
$296$	−5.64024	+	22.4568i	−0.327833	+	1.30527i
$297$	−7.19759			−0.417646
$298$	−14.3201	−	1.17722i	−0.829541	−	0.0681948i
$299$	8.59178	+	8.59178i	0.496876	+	0.496876i
$300$	21.0512	−	15.0716i	1.21539	−	0.870159i
$301$		0			0
$302$	−12.5955	+	10.6819i	−0.724791	+	0.614676i
$303$			15.0089i			0.862239i
$304$	7.07731	−	3.48271i	0.405911	−	0.199747i
$305$	−0.226867			−0.0129904
$306$	25.2244	−	21.3921i	1.44198	−	1.22291i
$307$	2.36930	−	2.36930i	0.135223	−	0.135223i	−0.636255	−	0.771479i	$-0.719517\pi$
$307$	2.36930	−	2.36930i	0.135223	−	0.135223i	0.771479	+	0.636255i	$0.219517\pi$
$308$		0			0
$309$	2.11757	+	2.11757i	0.120464	+	0.120464i
$310$	−0.0469303	+	0.570874i	−0.00266546	+	0.0324235i
$311$		−	15.1541i		−	0.859312i	−0.902993	−	0.429656i	$-0.858635\pi$
$311$		−	15.1541i		−	0.859312i	0.902993	−	0.429656i	$-0.141365\pi$
$312$	−25.1118	−	41.9567i	−1.42167	−	2.37533i
$313$	6.65582			0.376209			0.188105	−	0.982149i	$-0.439766\pi$
$313$	6.65582			0.376209			0.188105	+	0.982149i	$0.439766\pi$
$314$	−3.13909	−	0.258058i	−0.177149	−	0.0145630i
$315$		0			0
$316$	2.44085	+	0.404045i	0.137308	+	0.0227293i
$317$	18.7482	−	18.7482i	1.05301	−	1.05301i	0.0544922	−	0.998514i	$-0.482646\pi$
$317$	18.7482	−	18.7482i	1.05301	−	1.05301i	0.998514	−	0.0544922i	$-0.0173540\pi$
$318$	20.4920	−	17.3787i	1.14913	−	0.974551i
$319$			3.18537i			0.178346i
$320$	1.07892	+	3.57301i	0.0603135	+	0.199737i
$321$			16.7357i			0.934094i
$322$		0			0
$323$	7.53630	+	7.53630i	0.419331	+	0.419331i
$324$	1.06400	−	6.42765i	0.0591110	−	0.357092i
$325$	21.5974	−	21.5974i	1.19801	−	1.19801i
$326$	−20.6825	−	1.70026i	−1.14550	−	0.0941687i
$327$		−	29.4908i		−	1.63085i
$328$	4.70960	+	7.86879i	0.260044	+	0.434481i
$329$		0			0
$330$	3.56641	+	0.293187i	0.196325	+	0.0161394i
$331$	6.70801	−	6.70801i	0.368705	−	0.368705i	−0.498300	−	0.867005i	$-0.666042\pi$
$331$	6.70801	−	6.70801i	0.368705	−	0.368705i	0.867005	+	0.498300i	$0.166042\pi$
$332$	−14.8773	−	20.7798i	−0.816500	−	1.14044i
$333$	25.0476	−	25.0476i	1.37260	−	1.37260i
$334$	5.44246	+	6.41743i	0.297798	+	0.351146i
$335$	−1.86071			−0.101661
$336$		0			0
$337$	−16.0354			−0.873502			−0.436751	−	0.899582i	$-0.643871\pi$
$337$	−16.0354			−0.873502			−0.436751	+	0.899582i	$0.643871\pi$
$338$	−25.4195	−	29.9732i	−1.38264	−	1.63033i
$339$	−5.39515	+	5.39515i	−0.293024	+	0.293024i
$340$	−4.10052	+	2.93577i	−0.222382	+	0.159215i
$341$	1.22999	−	1.22999i	0.0666075	−	0.0666075i
$342$	−12.0267	−	0.988686i	−0.650327	−	0.0534620i
$343$		0			0
$344$	24.6631	+	6.19438i	1.32974	+	0.333979i
$345$			2.40260i			0.129352i
$346$	−12.9457	−	1.06424i	−0.695968	−	0.0572140i
$347$	2.24473	−	2.24473i	0.120504	−	0.120504i	−0.644283	−	0.764787i	$-0.722844\pi$
$347$	2.24473	−	2.24473i	0.120504	−	0.120504i	0.764787	+	0.644283i	$0.222844\pi$
$348$	8.49112	+	1.40557i	0.455172	+	0.0753466i
$349$	−2.21348	−	2.21348i	−0.118485	−	0.118485i	0.645378	−	0.763863i	$-0.276700\pi$
$349$	−2.21348	−	2.21348i	−0.118485	−	0.118485i	−0.763863	+	0.645378i	$0.776700\pi$
$350$		0			0
$351$			22.9426i			1.22458i
$352$	4.51918	−	10.3944i	0.240873	−	0.554024i
$353$		−	8.21881i		−	0.437443i	−0.975787	−	0.218722i	$-0.929811\pi$
$353$		−	8.21881i		−	0.437443i	0.975787	−	0.218722i	$-0.0701887\pi$
$354$	25.0678	−	21.2594i	1.33234	−	1.12992i
$355$	−4.02196	+	4.02196i	−0.213464	+	0.213464i
$356$	0.760144	−	4.59206i	0.0402875	−	0.243379i
$357$		0			0
$358$	5.36250	+	0.440840i	0.283417	+	0.0232991i
$359$	−30.6637			−1.61837			−0.809184	−	0.587555i	$-0.800091\pi$
$359$	−30.6637			−1.61837			−0.809184	+	0.587555i	$0.800091\pi$
$360$	1.39092	−	5.53797i	0.0733078	−	0.291877i
$361$			15.1114i			0.795337i
$362$	−0.841336	+	10.2342i	−0.0442196	+	0.537900i
$363$	13.3703	+	13.3703i	0.701761	+	0.701761i
$364$		0			0
$365$	5.14051	−	5.14051i	0.269067	−	0.269067i
$366$	1.41969	−	1.20400i	0.0742083	−	0.0629341i
$367$	−17.8234			−0.930372			−0.465186	−	0.885213i	$-0.654013\pi$
$367$	−17.8234			−0.930372			−0.465186	+	0.885213i	$0.654013\pi$
$368$	7.20404	+	2.45223i	0.375536	+	0.127831i
$369$		−	14.0296i		−	0.730350i
$370$	−4.11933	+	3.49349i	−0.214154	+	0.181618i
$371$		0			0
$372$	−2.73599	−	3.82147i	−0.141854	−	0.198134i
$373$	−1.75647	−	1.75647i	−0.0909468	−	0.0909468i	0.660170	−	0.751116i	$-0.270484\pi$
$373$	−1.75647	−	1.75647i	−0.0909468	−	0.0909468i	−0.751116	+	0.660170i	$0.770484\pi$
$374$	15.2633	+	1.25477i	0.789248	+	0.0648824i
$375$	12.3538			0.637948
$376$	4.33637	+	7.24520i	0.223631	+	0.373643i
$377$	10.1535			0.522931
$378$		0			0
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	−0.720489	−	0.693466i	$-0.756083\pi$
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	0.693466	+	0.720489i	$0.256083\pi$
$380$	1.81530	+	0.300495i	0.0931231	+	0.0154151i
$381$	17.8910	+	17.8910i	0.916584	+	0.916584i
$382$	−16.0967	−	18.9803i	−0.823577	−	0.971115i
$383$	−23.7855			−1.21538			−0.607692	−	0.794173i	$-0.707904\pi$
$383$	−23.7855			−1.21538			−0.607692	+	0.794173i	$0.707904\pi$
$384$	−25.7139	−	16.6332i	−1.31221	−	0.848812i
$385$		0			0
$386$	7.09630	−	6.01819i	0.361192	−	0.306318i
$387$	−27.5085	−	27.5085i	−1.39833	−	1.39833i
$388$	9.26797	+	1.53417i	0.470510	+	0.0778856i
$389$	17.1439	+	17.1439i	0.869229	+	0.869229i	0.992387	−	0.123158i	$-0.0393023\pi$
$389$	17.1439	+	17.1439i	0.869229	+	0.869229i	−0.123158	+	0.992387i	$0.539302\pi$
$390$	0.934545	−	11.3681i	0.0473225	−	0.575645i
$391$			10.2825i			0.520009i
$392$		0			0
$393$		−	50.2190i		−	2.53321i
$394$	−29.6551	−	2.43788i	−1.49400	−	0.122819i
$395$	0.408093	+	0.408093i	0.0205334	+	0.0205334i
$396$	−14.0989	+	10.0942i	−0.708498	+	0.507250i
$397$	−2.98427	−	2.98427i	−0.149776	−	0.149776i	0.628242	−	0.778018i	$-0.283775\pi$
$397$	−2.98427	−	2.98427i	−0.149776	−	0.149776i	−0.778018	+	0.628242i	$0.783775\pi$
$398$	−6.79485	−	8.01209i	−0.340595	−	0.401610i
$399$		0			0
$400$	6.16422	−	18.1090i	0.308211	−	0.905448i
$401$	18.0233			0.900039			0.450019	−	0.893019i	$-0.351417\pi$
$401$	18.0233			0.900039			0.450019	+	0.893019i	$0.351417\pi$
$402$	11.6439	−	9.87489i	0.580745	−	0.492515i
$403$	−3.92063	−	3.92063i	−0.195300	−	0.195300i
$404$	6.45560	+	9.01682i	0.321178	+	0.448604i
$405$	1.07466	−	1.07466i	0.0534002	−	0.0534002i
$406$		0			0
$407$	16.4023			0.813034
$408$	10.0799	−	40.1332i	0.499028	−	1.98689i
$409$	−27.9686			−1.38296			−0.691478	−	0.722397i	$-0.743040\pi$
$409$	−27.9686			−1.38296			−0.691478	+	0.722397i	$0.743040\pi$
$410$	−0.175270	+	2.13203i	−0.00865596	+	0.105294i
$411$	29.0724	+	29.0724i	1.43404	+	1.43404i
$412$	2.18297	+	0.361356i	0.107547	+	0.0178027i
$413$		0			0
$414$	−7.53009	−	8.87905i	−0.370084	−	0.436382i
$415$		−	5.96163i		−	0.292645i
$416$	−33.1326	−	14.4051i	−1.62446	−	0.706266i
$417$	4.33006			0.212044
$418$	−3.61409	−	4.26153i	−0.176771	−	0.208438i
$419$	−10.4669	+	10.4669i	−0.511342	+	0.511342i	−0.914937	−	0.403596i	$-0.867760\pi$
$419$	−10.4669	+	10.4669i	−0.511342	+	0.511342i	0.403596	+	0.914937i	$0.367760\pi$
$420$		0			0
$421$	12.3722	+	12.3722i	0.602984	+	0.602984i	0.941103	−	0.338119i	$-0.109791\pi$
$421$	12.3722	+	12.3722i	0.602984	+	0.602984i	−0.338119	+	0.941103i	$0.609791\pi$
$422$	18.1732	+	1.49398i	0.884659	+	0.0727260i
$423$		−	12.9177i		−	0.628082i
$424$	4.83596	−	19.2545i	0.234855	−	0.935081i
$425$	25.8474			1.25378
$426$	3.82377	−	46.5134i	0.185262	−	2.25358i
$427$		0			0
$428$	7.19831	+	10.0542i	0.347943	+	0.485988i
$429$	−24.4933	+	24.4933i	−1.18255	+	1.18255i
$430$	3.83672	+	4.52404i	0.185023	+	0.218169i
$431$		−	13.6357i		−	0.656809i	−0.944537	−	0.328405i	$-0.893489\pi$
$431$		−	13.6357i		−	0.656809i	0.944537	−	0.328405i	$-0.106511\pi$
$432$	6.34436	+	12.8925i	0.305243	+	0.620292i
$433$			19.1575i			0.920649i	0.887751	+	0.460325i	$0.152267\pi$
$433$			19.1575i			0.920649i	−0.887751	+	0.460325i	$0.847733\pi$
$434$		0			0
$435$	1.41965	+	1.41965i	0.0680672	+	0.0680672i
$436$	−12.6845	−	17.7170i	−0.607479	−	0.848492i
$437$	2.65280	−	2.65280i	0.126901	−	0.126901i
$438$	−4.88720	+	59.4493i	−0.233519	+	2.84060i
$439$		−	8.57235i		−	0.409136i	−0.978852	−	0.204568i	$-0.934421\pi$
$439$		−	8.57235i		−	0.409136i	0.978852	−	0.204568i	$-0.0655789\pi$
$440$	2.26868	−	1.35784i	0.108155	−	0.0647326i
$441$		0			0
$442$	3.99961	−	48.6524i	0.190242	−	2.31416i
$443$	−14.8101	+	14.8101i	−0.703650	+	0.703650i	−0.965192	−	0.261542i	$-0.915769\pi$
$443$	−14.8101	+	14.8101i	−0.703650	+	0.703650i	0.261542	+	0.965192i	$0.415769\pi$
$444$	7.23768	−	43.7231i	0.343485	−	2.07501i
$445$	0.767760	−	0.767760i	0.0363953	−	0.0363953i
$446$	7.25797	−	6.15530i	0.343675	−	0.291462i
$447$	27.5017			1.30079
$448$		0			0
$449$	−24.4270			−1.15278			−0.576391	−	0.817174i	$-0.695539\pi$
$449$	−24.4270			−1.15278			−0.576391	+	0.817174i	$0.695539\pi$
$450$	−22.3195	+	18.9286i	−1.05215	+	0.892301i
$451$	4.59361	−	4.59361i	0.216305	−	0.216305i
$452$	−0.920663	+	5.56176i	−0.0433044	+	0.261603i
$453$	22.3521	−	22.3521i	1.05019	−	1.05019i
$454$	−0.895471	+	10.8928i	−0.0420265	+	0.511223i
$455$		0			0
$456$	−12.9545	+	7.75350i	−0.606652	+	0.363091i
$457$		−	3.61171i		−	0.168949i	−0.996426	−	0.0844743i	$-0.973079\pi$
$457$		−	3.61171i		−	0.168949i	0.996426	−	0.0844743i	$-0.0269211\pi$
$458$	1.76614	−	21.4839i	0.0825265	−	1.00388i
$459$	−13.7286	+	13.7286i	−0.640798	+	0.640798i
$460$	1.03340	+	1.44340i	0.0481826	+	0.0672987i
$461$	−25.2872	−	25.2872i	−1.17774	−	1.17774i	−0.980318	−	0.197423i	$-0.936743\pi$
$461$	−25.2872	−	25.2872i	−1.17774	−	1.17774i	−0.197423	−	0.980318i	$-0.563257\pi$
$462$		0			0
$463$			8.01165i			0.372333i	0.982518	+	0.186166i	$0.0596064\pi$
$463$			8.01165i			0.372333i	−0.982518	+	0.186166i	$0.940394\pi$
$464$	5.70572	−	2.80776i	0.264881	−	0.130347i
$465$		−	1.09636i		−	0.0508425i
$466$	13.5146	+	15.9357i	0.626053	+	0.738206i
$467$	−13.1038	+	13.1038i	−0.606373	+	0.606373i	−0.941996	−	0.335623i	$-0.891053\pi$
$467$	−13.1038	+	13.1038i	−0.606373	+	0.606373i	0.335623	+	0.941996i	$0.391053\pi$
$468$	32.1755	+	44.9409i	1.48731	+	2.07739i
$469$		0			0
$470$	−0.161380	+	1.96307i	−0.00744390	+	0.0905498i
$471$	6.02861			0.277784
$472$	5.91582	−	23.5540i	0.272298	−	1.08416i
$473$		−	18.0138i		−	0.828277i
$474$	−4.71954	−	0.387983i	−0.216775	−	0.0178206i
$475$	−6.66840	−	6.66840i	−0.305967	−	0.305967i
$476$		0			0
$477$	−21.4759	+	21.4759i	−0.983314	+	0.983314i
$478$	26.1138	+	30.7918i	1.19442	+	1.40839i
$479$	−27.3765			−1.25086			−0.625432	−	0.780279i	$-0.715077\pi$
$479$	−27.3765			−1.25086			−0.625432	+	0.780279i	$0.715077\pi$
$480$	−2.61847	−	6.64669i	−0.119516	−	0.303379i
$481$		−	52.2831i		−	2.38390i
$482$	−20.9966	−	24.7580i	−0.956369	−	1.12770i
$483$		0			0
$484$	13.7833	+	2.28160i	0.626512	+	0.103709i
$485$	1.54954	+	1.54954i	0.0703609	+	0.0703609i
$486$	−2.27039	+	27.6176i	−0.102987	+	1.25276i
$487$	19.3602			0.877296			0.438648	−	0.898659i	$-0.355458\pi$
$487$	19.3602			0.877296			0.438648	+	0.898659i	$0.355458\pi$
$488$	0.335036	−	1.33395i	0.0151664	−	0.0603853i
$489$	39.7206			1.79623
$490$		0			0
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	−0.979148	−	0.203149i	$-0.934882\pi$
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	0.203149	+	0.979148i	$0.434882\pi$
$492$	−10.2180	−	14.2720i	−0.460665	−	0.643430i
$493$	6.07576	+	6.07576i	0.273638	+	0.273638i
$494$	−13.5838	+	11.5200i	−0.611163	+	0.518311i
$495$	−4.04491			−0.181805
$496$	−3.28737	−	1.11901i	−0.147607	−	0.0502449i
$497$		0			0
$498$	31.6388	+	37.3066i	1.41777	+	1.67175i
$499$	−2.14113	−	2.14113i	−0.0958501	−	0.0958501i	0.657556	−	0.753406i	$-0.271590\pi$
$499$	−2.14113	−	2.14113i	−0.0958501	−	0.0958501i	−0.753406	+	0.657556i	$0.771590\pi$
$500$	7.42174	−	5.31360i	0.331910	−	0.237631i
$501$	−11.3884	−	11.3884i	−0.508798	−	0.508798i
$502$	20.4925	+	1.68464i	0.914624	+	0.0751893i
$503$			34.5673i			1.54128i	0.637272	+	0.770639i	$0.280063\pi$
$503$			34.5673i			1.54128i	−0.637272	+	0.770639i	$0.719937\pi$
$504$		0			0
$505$			2.58688i			0.115115i
$506$	0.441681	−	5.37274i	0.0196351	−	0.238847i
$507$	53.1908	+	53.1908i	2.36228	+	2.36228i
$508$	18.4435	+	3.05304i	0.818299	+	0.135457i
$509$	11.1496	+	11.1496i	0.494199	+	0.494199i	0.909626	−	0.415427i	$-0.136368\pi$
$509$	11.1496	+	11.1496i	0.494199	+	0.494199i	−0.415427	+	0.909626i	$0.636368\pi$
$510$	7.36179	−	6.24334i	0.325985	−	0.276460i
$511$		0			0
$512$	−22.6022	+	1.06733i	−0.998887	+	0.0471698i
$513$	7.08374			0.312755
$514$	2.30056	+	2.71269i	0.101473	+	0.119651i
$515$	0.364977	+	0.364977i	0.0160828	+	0.0160828i
$516$	−48.0188	−	7.94876i	−2.11391	−	0.349925i
$517$	4.22957	−	4.22957i	0.186016	−	0.186016i
$518$		0			0
$519$	24.8623			1.09133
$520$	−4.32817	−	7.23150i	−0.189803	−	0.317122i
$521$	15.4419			0.676522			0.338261	−	0.941052i	$-0.390161\pi$
$521$	15.4419			0.676522			0.338261	+	0.941052i	$0.390161\pi$
$522$	−9.69589	−	0.797078i	−0.424377	−	0.0348872i
$523$	−1.44190	−	1.44190i	−0.0630500	−	0.0630500i	0.674879	−	0.737929i	$-0.264196\pi$
$523$	−1.44190	−	1.44190i	−0.0630500	−	0.0630500i	−0.737929	+	0.674879i	$0.764196\pi$
$524$	−21.6001	−	30.1698i	−0.943604	−	1.31797i
$525$		0			0
$526$	−9.81025	+	8.31981i	−0.427747	+	0.362761i
$527$		−	4.69215i		−	0.204393i
$528$	−6.99076	+	20.5371i	−0.304234	+	0.893764i
$529$	−19.3805			−0.842632
$530$	3.53193	−	2.99533i	0.153417	−	0.130109i
$531$	−26.2714	+	26.2714i	−1.14008	+	1.14008i
$532$		0			0
$533$	−14.6423	−	14.6423i	−0.634228	−	0.634228i
$534$	−0.729926	+	8.87903i	−0.0315870	+	0.384233i
$535$			2.88450i			0.124708i
$536$	2.74788	−	10.9407i	0.118690	−	0.472568i
$537$	−10.2987			−0.444420
$538$	−8.03506	−	0.660545i	−0.346416	−	0.0284781i
$539$		0			0
$540$	−0.547403	+	3.30688i	−0.0235565	+	0.142306i
$541$	14.7742	−	14.7742i	0.635190	−	0.635190i	−0.314175	−	0.949365i	$-0.601728\pi$
$541$	14.7742	−	14.7742i	0.635190	−	0.635190i	0.949365	+	0.314175i	$0.101728\pi$
$542$	−12.4253	+	10.5375i	−0.533711	+	0.452626i
$543$		−	19.6548i		−	0.843469i
$544$	−11.2064	−	28.4461i	−0.480470	−	1.21962i
$545$		−	5.08293i		−	0.217729i
$546$		0			0
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	0.928945	−	0.370217i	$-0.120717\pi$
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	−0.370217	+	0.928945i	$0.620717\pi$
$548$	29.9703	+	4.96111i	1.28027	+	0.211928i
$549$	−1.48785	+	1.48785i	−0.0635000	+	0.0635000i
$550$	−13.5056	−	1.11026i	−0.575880	−	0.0473418i
$551$		−	3.13499i		−	0.133555i
$552$	−14.1270	−	3.54814i	−0.601285	−	0.151019i
$553$		0			0
$554$	−29.4505	−	2.42106i	−1.25123	−	0.102861i
$555$	7.31020	−	7.31020i	0.310301	−	0.310301i
$556$	2.60134	−	1.86244i	0.110322	−	0.0789849i
$557$	8.55871	−	8.55871i	0.362644	−	0.362644i	−0.502141	−	0.864786i	$-0.667454\pi$
$557$	8.55871	−	8.55871i	0.362644	−	0.362644i	0.864786	+	0.502141i	$0.167454\pi$
$558$	3.43615	+	4.05172i	0.145464	+	0.171523i
$559$	−57.4198			−2.42860
$560$		0			0
$561$	−29.3132			−1.23760
$562$	18.1441	+	21.3945i	0.765362	+	0.902471i
$563$	−19.9147	+	19.9147i	−0.839306	+	0.839306i	−0.988768	−	0.149462i	$-0.952246\pi$
$563$	−19.9147	+	19.9147i	−0.839306	+	0.839306i	0.149462	+	0.988768i	$0.452246\pi$
$564$	−9.40827	−	13.1409i	−0.396160	−	0.553334i
$565$	−0.929888	+	0.929888i	−0.0391207	+	0.0391207i
$566$	−28.6773	−	2.35750i	−1.20540	−	0.0990932i
$567$		0			0
$568$	−17.7091	−	29.5883i	−0.743056	−	1.24150i
$569$			23.5879i			0.988857i	0.869218	+	0.494428i	$0.164623\pi$
$569$			23.5879i			0.988857i	−0.869218	+	0.494428i	$0.835377\pi$
$570$	−3.51000	−	0.288550i	−0.147018	−	0.0120860i
$571$	−15.9348	+	15.9348i	−0.666849	+	0.666849i	−0.956985	−	0.290136i	$-0.906299\pi$
$571$	−15.9348	+	15.9348i	−0.666849	+	0.666849i	0.290136	+	0.956985i	$0.406299\pi$
$572$	−4.17969	+	25.2497i	−0.174762	+	1.05574i
$573$	33.6826	+	33.6826i	1.40711	+	1.40711i
$574$		0			0
$575$		−	9.09835i		−	0.379427i
$576$	30.5085	+	16.3569i	1.27119	+	0.681536i
$577$		−	18.8093i		−	0.783040i	−0.920170	−	0.391520i	$-0.871949\pi$
$577$		−	18.8093i		−	0.783040i	0.920170	−	0.391520i	$-0.128051\pi$
$578$	13.1709	−	11.1699i	0.547837	−	0.464606i
$579$	−12.5932	+	12.5932i	−0.523354	+	0.523354i
$580$	1.46350	+	0.242259i	0.0607684	+	0.0100593i
$581$		0			0
$582$	−17.9202	−	1.47318i	−0.742816	−	0.0610653i
$583$	−14.0634			−0.582448
$584$	22.6341	+	37.8171i	0.936608	+	1.56488i
$585$			12.8933i			0.533073i
$586$	1.10691	−	13.4648i	0.0457260	−	0.556224i
$587$	12.6185	+	12.6185i	0.520820	+	0.520820i	0.917819	−	0.396999i	$-0.129948\pi$
$587$	12.6185	+	12.6185i	0.520820	+	0.520820i	−0.396999	+	0.917819i	$0.629948\pi$
$588$		0			0
$589$	−1.21053	+	1.21053i	−0.0498791	+	0.0498791i
$590$	4.32060	−	3.66418i	0.177876	−	0.150852i
$591$	56.9525			2.34271
$592$	−14.4580	−	29.3803i	−0.594218	−	1.20752i
$593$			25.4334i			1.04442i	0.852816	+	0.522212i	$0.174893\pi$
$593$			25.4334i			1.04442i	−0.852816	+	0.522212i	$0.825107\pi$
$594$	7.76310	−	6.58368i	0.318524	−	0.270132i
$595$		0			0
$596$	16.5220	−	11.8290i	0.676769	−	0.484533i
$597$	14.2183	+	14.2183i	0.581918	+	0.581918i
$598$	−17.1258	−	1.40788i	−0.700326	−	0.0575723i
$599$	−42.2006			−1.72427			−0.862135	−	0.506678i	$-0.830873\pi$
$599$	−42.2006			−1.72427			−0.862135	+	0.506678i	$0.830873\pi$
$600$	−8.91905	+	35.5114i	−0.364118	+	1.44975i
$601$	−29.8695			−1.21840			−0.609202	−	0.793015i	$-0.708510\pi$
$601$	−29.8695			−1.21840			−0.609202	+	0.793015i	$0.708510\pi$
$602$		0			0
$603$	−12.2030	+	12.2030i	−0.496944	+	0.496944i
$604$	3.81431	−	23.0424i	0.155202	−	0.937583i
$605$	2.30446	+	2.30446i	0.0936898	+	0.0936898i
$606$	−13.7287	−	16.1882i	−0.557692	−	0.657599i
$607$	−29.4275			−1.19442			−0.597212	−	0.802083i	$-0.703725\pi$
$607$	−29.4275			−1.19442			−0.597212	+	0.802083i	$0.703725\pi$
$608$	−4.44771	+	10.2300i	−0.180378	+	0.414882i
$609$		0			0
$610$	0.244692	−	0.207517i	0.00990730	−	0.00840212i
$611$	−13.4819	−	13.4819i	−0.545420	−	0.545420i
$612$	−7.63872	+	46.1458i	−0.308777	+	1.86533i
$613$	16.2429	+	16.2429i	0.656045	+	0.656045i	0.954442	−	0.298397i	$-0.0964518\pi$
$613$	16.2429	+	16.2429i	0.656045	+	0.656045i	−0.298397	+	0.954442i	$0.596452\pi$
$614$	−0.388241	+	4.72268i	−0.0156681	+	0.190592i
$615$		−	4.09456i		−	0.165108i
$616$		0			0
$617$			31.2064i			1.25632i	0.778084	+	0.628161i	$0.216192\pi$
$617$			31.2064i			1.25632i	−0.778084	+	0.628161i	$0.783808\pi$
$618$	−4.22090	−	0.346991i	−0.169790	−	0.0139580i
$619$	−12.9637	−	12.9637i	−0.521053	−	0.521053i	0.396836	−	0.917890i	$-0.370108\pi$
$619$	−12.9637	−	12.9637i	−0.521053	−	0.521053i	−0.917890	+	0.396836i	$0.870108\pi$
$620$	−0.471565	−	0.658655i	−0.0189385	−	0.0264522i
$621$	4.83252	+	4.83252i	0.193922	+	0.193922i
$622$	13.8616	+	16.3448i	0.555799	+	0.655366i
$623$		0			0
$624$	65.4628	+	22.2833i	2.62061	+	0.892046i
$625$	−21.7824			−0.871297
$626$	−7.17877	+	6.08812i	−0.286921	+	0.243330i
$627$	7.56254	+	7.56254i	0.302019	+	0.302019i
$628$	3.62177	−	2.59301i	0.144524	−	0.103472i
$629$	31.2858	−	31.2858i	1.24745	−	1.24745i
$630$		0			0
$631$	8.10970			0.322842			0.161421	−	0.986886i	$-0.448392\pi$
$631$	8.10970			0.322842			0.161421	+	0.986886i	$0.448392\pi$
$632$	−3.00221	+	1.79687i	−0.119421	+	0.0714757i
$633$	−34.9016			−1.38722
$634$	−3.07214	+	37.3704i	−0.122010	+	1.48417i
$635$	3.08363	+	3.08363i	0.122370	+	0.122370i
$636$	−6.20561	+	37.4883i	−0.246068	+	1.48651i
$637$		0			0
$638$	−2.91368	−	3.43564i	−0.115354	−	0.136018i
$639$			52.7541i			2.08692i
$640$	−4.43195	−	2.86684i	−0.175188	−	0.113322i
$641$	28.0870			1.10937			0.554685	−	0.832060i	$-0.312839\pi$
$641$	28.0870			1.10937			0.554685	+	0.832060i	$0.312839\pi$
$642$	−15.3082	−	18.0506i	−0.604167	−	0.712399i
$643$	21.6759	−	21.6759i	0.854812	−	0.854812i	−0.135909	−	0.990721i	$-0.543395\pi$
$643$	21.6759	−	21.6759i	0.854812	−	0.854812i	0.990721	+	0.135909i	$0.0433955\pi$
$644$		0			0
$645$	−8.02841	−	8.02841i	−0.316118	−	0.316118i
$646$	−15.0219	−	1.23492i	−0.591030	−	0.0485873i
$647$		−	46.0198i		−	1.80922i	−0.426236	−	0.904612i	$-0.640161\pi$
$647$		−	46.0198i		−	1.80922i	0.426236	−	0.904612i	$-0.359839\pi$
$648$	4.73182	+	7.90591i	0.185883	+	0.310574i
$649$	−17.2038			−0.675306
$650$	−3.53901	+	43.0495i	−0.138811	+	1.68854i
$651$		0			0
$652$	23.8627	−	17.0845i	0.934536	−	0.669082i
$653$	21.4193	−	21.4193i	0.838202	−	0.838202i	−0.150420	−	0.988622i	$-0.548063\pi$
$653$	21.4193	−	21.4193i	0.838202	−	0.838202i	0.988622	+	0.150420i	$0.0480627\pi$
$654$	26.9754	+	31.8079i	1.05482	+	1.24379i
$655$		−	8.65556i		−	0.338201i
$656$	−12.2773	−	4.17914i	−0.479347	−	0.163168i
$657$		−	67.4255i		−	2.63052i
$658$		0			0
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	0.546096	−	0.837723i	$-0.316113\pi$
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	−0.837723	+	0.546096i	$0.816113\pi$
$660$	−4.11480	+	2.94600i	−0.160169	+	0.114673i
$661$	−7.47069	+	7.47069i	−0.290576	+	0.290576i	−0.837308	−	0.546732i	$-0.815872\pi$
$661$	−7.47069	+	7.47069i	−0.290576	+	0.290576i	0.546732	+	0.837308i	$0.315872\pi$
$662$	−1.09919	+	13.3709i	−0.0427214	+	0.519675i
$663$			93.4368i			3.62879i
$664$	35.0537	+	8.80409i	1.36035	+	0.341665i
$665$		0			0
$666$	−4.10438	+	49.9268i	−0.159041	+	1.93462i
$667$	2.13868	−	2.13868i	0.0828102	−	0.0828102i
$668$	−11.7401	−	1.94340i	−0.454240	−	0.0751923i
$669$	−12.8801	+	12.8801i	−0.497972	+	0.497972i
$670$	2.00690	−	1.70200i	0.0775333	−	0.0657540i
$671$	−0.974316			−0.0376130
$672$		0			0
$673$	17.2027			0.663115			0.331557	−	0.943435i	$-0.392426\pi$
$673$	17.2027			0.663115			0.331557	+	0.943435i	$0.392426\pi$
$674$	17.2953	−	14.6677i	0.666189	−	0.564977i
$675$	12.1476	−	12.1476i	0.467562	−	0.467562i
$676$	54.8334	+	9.07682i	2.10898	+	0.349108i
$677$	14.1608	−	14.1608i	0.544245	−	0.544245i	−0.380525	−	0.924771i	$-0.624257\pi$
$677$	14.1608	−	14.1608i	0.544245	−	0.544245i	0.924771	+	0.380525i	$0.124257\pi$
$678$	0.884065	−	10.7540i	0.0339523	−	0.413006i
$679$		0			0
$680$	1.73733	−	6.91721i	0.0666235	−	0.265263i
$681$		−	20.9195i		−	0.801637i
$682$	−0.201549	+	2.45170i	−0.00771772	+	0.0938806i
$683$	0.681274	−	0.681274i	0.0260682	−	0.0260682i	−0.693953	−	0.720021i	$-0.744132\pi$
$683$	0.681274	−	0.681274i	0.0260682	−	0.0260682i	0.720021	+	0.693953i	$0.244132\pi$
$684$	13.8759	−	9.93449i	0.530560	−	0.379855i
$685$	5.01082	+	5.01082i	0.191453	+	0.191453i
$686$		0			0
$687$			41.2597i			1.57416i
$688$	−32.2669	+	15.8784i	−1.23016	+	0.605359i
$689$			44.8277i			1.70780i
$690$	−2.19767	−	2.59137i	−0.0836640	−	0.0986518i
$691$	−24.5272	+	24.5272i	−0.933058	+	0.933058i	−0.997896	−	0.0648375i	$-0.979347\pi$
$691$	−24.5272	+	24.5272i	−0.933058	+	0.933058i	0.0648375	+	0.997896i	$0.479347\pi$
$692$	14.9364	−	10.6937i	0.567795	−	0.406513i
$693$		0			0
$694$	−0.367829	+	4.47437i	−0.0139626	+	0.169845i
$695$	0.746313			0.0283093
$696$	−10.4439	+	6.25087i	−0.395877	+	0.236939i
$697$		−	17.5237i		−	0.663756i
$698$	4.41207	+	0.362707i	0.166999	+	0.0137287i
$699$	−28.2796	−	28.2796i	−1.06963	−	1.06963i
$700$		0			0
$701$	32.4969	−	32.4969i	1.22739	−	1.22739i	0.262444	−	0.964947i	$-0.415471\pi$
$701$	32.4969	−	32.4969i	1.22739	−	1.22739i	0.964947	−	0.262444i	$-0.0845286\pi$
$702$	−20.9857	−	24.7452i	−0.792055	−	0.933946i
$703$	−16.1429			−0.608842
$704$	4.63358	+	15.3448i	0.174635	+	0.578330i
$705$		−	3.77007i		−	0.141989i
$706$	7.51780	+	8.86456i	0.282936	+	0.333622i
$707$		0			0
$708$	−7.59131	+	45.8594i	−0.285299	+	1.72350i
$709$	−3.32683	−	3.32683i	−0.124942	−	0.124942i	0.641871	−	0.766813i	$-0.278158\pi$
$709$	−3.32683	−	3.32683i	−0.124942	−	0.124942i	−0.766813	+	0.641871i	$0.778158\pi$
$710$	0.659050	−	8.01688i	0.0247337	−	0.300868i
$711$	5.35275			0.200744
$712$	3.38052	+	5.64816i	0.126690	+	0.211674i
$713$	−1.65165			−0.0618547
$714$		0			0
$715$	−4.22157	+	4.22157i	−0.157878	+	0.157878i
$716$	−6.18706	+	4.42964i	−0.231221	+	0.165543i
$717$	−54.6435	−	54.6435i	−2.04070	−	2.04070i
$718$	33.0729	−	28.0483i	1.23427	−	1.04675i
$719$	−18.5510			−0.691834			−0.345917	−	0.938265i	$-0.612432\pi$
$719$	−18.5510			−0.691834			−0.345917	+	0.938265i	$0.612432\pi$
$720$	3.56542	+	7.24537i	0.132875	+	0.270019i
$721$		0			0
$722$	−13.8225	−	16.2987i	−0.514420	−	0.606575i
$723$	43.9358	+	43.9358i	1.63399	+	1.63399i
$724$	−8.45389	−	11.8079i	−0.314186	−	0.438838i
$725$	−5.37606	−	5.37606i	−0.199662	−	0.199662i
$726$	−26.6508	−	2.19090i	−0.989104	−	0.0813121i
$727$			5.96613i			0.221272i	0.993861	+	0.110636i	$0.0352887\pi$
$727$			5.96613i			0.221272i	−0.993861	+	0.110636i	$0.964711\pi$
$728$		0			0
$729$		−	43.2669i		−	1.60248i
$730$	−0.842339	+	10.2465i	−0.0311764	+	0.379238i
$731$	−34.3595	−	34.3595i	−1.27083	−	1.27083i
$732$	−0.429926	+	2.59720i	−0.0158905	+	0.0959952i
$733$	−15.2819	−	15.2819i	−0.564452	−	0.564452i	0.366117	−	0.930569i	$-0.380687\pi$
$733$	−15.2819	−	15.2819i	−0.564452	−	0.564452i	−0.930569	+	0.366117i	$0.880687\pi$
$734$	19.2237	−	16.3031i	0.709561	−	0.601760i
$735$		0			0
$736$	−10.0131	+	3.94468i	−0.369089	+	0.145403i
$737$	−7.99108			−0.294355
$738$	12.8329	+	15.1319i	0.472387	+	0.557012i
$739$	−25.6074	−	25.6074i	−0.941984	−	0.941984i	0.0564227	−	0.998407i	$-0.482031\pi$
$739$	−25.6074	−	25.6074i	−0.941984	−	0.941984i	−0.998407	+	0.0564227i	$0.982031\pi$
$740$	1.24746	−	7.53595i	0.0458575	−	0.277027i
$741$	24.1059	−	24.1059i	0.885552	−	0.885552i
$742$		0			0
$743$	16.2749			0.597067			0.298533	−	0.954399i	$-0.403503\pi$
$743$	16.2749			0.597067			0.298533	+	0.954399i	$0.403503\pi$
$744$	6.44648	+	1.61910i	0.236339	+	0.0593590i
$745$	4.74009			0.173663
$746$	3.50114	+	0.287821i	0.128186	+	0.0105379i
$747$	−39.0979	−	39.0979i	−1.43052	−	1.43052i
$748$	−17.6103	+	12.6081i	−0.643897	+	0.460998i
$749$		0			0
$750$	−13.3245	+	11.3001i	−0.486540	+	0.412622i
$751$		−	18.3033i		−	0.667898i	−0.942591	−	0.333949i	$-0.891619\pi$
$751$		−	18.3033i		−	0.667898i	0.942591	−	0.333949i	$-0.108381\pi$
$752$	−11.3043	−	3.84795i	−0.412226	−	0.140320i
$753$	−39.3557			−1.43420
$754$	−10.9512	+	9.28745i	−0.398820	+	0.338229i
$755$	3.85253	−	3.85253i	0.140208	−	0.140208i
$756$		0			0
$757$	−16.6944	−	16.6944i	−0.606767	−	0.606767i	0.335333	−	0.942100i	$-0.391151\pi$
$757$	−16.6944	−	16.6944i	−0.606767	−	0.606767i	−0.942100	+	0.335333i	$0.891151\pi$
$758$	0.0862034	−	1.04860i	0.00313105	−	0.0380870i
$759$			10.3183i			0.374531i
$760$	−2.23280	+	1.33636i	−0.0809920	+	0.0484751i
$761$	8.86780			0.321458			0.160729	−	0.986999i	$-0.448616\pi$
$761$	8.86780			0.321458			0.160729	+	0.986999i	$0.448616\pi$
$762$	−35.6617	−	2.93167i	−1.29189	−	0.106203i
$763$		0			0
$764$	34.7228	+	5.74781i	1.25623	+	0.207949i
$765$	−7.71526	+	7.71526i	−0.278946	+	0.278946i
$766$	25.6543	−	21.7568i	0.926929	−	0.786104i
$767$			54.8376i			1.98007i
$768$	42.9487	−	5.58053i	1.54978	−	0.201370i
$769$			1.14344i			0.0412335i	0.999787	+	0.0206167i	$0.00656298\pi$
$769$			1.14344i			0.0412335i	−0.999787	+	0.0206167i	$0.993437\pi$
$770$		0			0
$771$	−4.81396	−	4.81396i	−0.173370	−	0.173370i
$772$	−2.14898	+	12.9821i	−0.0773435	+	0.467235i
$773$	3.84402	−	3.84402i	0.138260	−	0.138260i	−0.634590	−	0.772849i	$-0.718831\pi$
$773$	3.84402	−	3.84402i	0.138260	−	0.138260i	0.772849	+	0.634590i	$0.218831\pi$
$774$	54.8320	+	4.50762i	1.97090	+	0.162023i
$775$			4.15179i			0.149137i
$776$	−11.3995	+	6.82276i	−0.409217	+	0.244923i
$777$		0			0
$778$	−34.1725	−	2.80925i	−1.22514	−	0.100716i
$779$	−4.52095	+	4.52095i	−0.161980	+	0.161980i
$780$	9.39048	+	13.1161i	0.336233	+	0.469631i
$781$	−17.2729	+	17.2729i	−0.618073	+	0.618073i
$782$	−9.40548	−	11.0904i	−0.336339	−	0.396592i
$783$	5.71091			0.204091
$784$		0			0
$785$	1.03907			0.0370859
$786$	45.9356	+	54.1647i	1.63847	+	1.93199i
$787$	36.0651	−	36.0651i	1.28558	−	1.28558i	0.348142	−	0.937442i	$-0.386813\pi$
$787$	36.0651	−	36.0651i	1.28558	−	1.28558i	0.937442	−	0.348142i	$-0.113187\pi$
$788$	34.2151	−	24.4963i	1.21886	−	0.872645i
$789$	17.4094	−	17.4094i	0.619789	−	0.619789i
$790$	−0.813442	−	0.0668713i	−0.0289410	−	0.00237917i
$791$		0			0
$792$	5.97350	−	23.7836i	0.212259	−	0.845115i
$793$			3.10567i			0.110286i
$794$	5.94847	+	0.489011i	0.211103	+	0.0173544i
$795$	−6.26779	+	6.26779i	−0.222295	+	0.222295i
$796$	14.6574	+	2.42631i	0.519519	+	0.0859982i
$797$	−26.5433	−	26.5433i	−0.940211	−	0.940211i	0.0581002	−	0.998311i	$-0.481496\pi$
$797$	−26.5433	−	26.5433i	−0.940211	−	0.940211i	−0.998311	+	0.0581002i	$0.981496\pi$
$798$		0			0
$799$		−	16.1349i		−	0.570813i
$800$	9.91584	+	25.1702i	0.350578	+	0.889902i
$801$		−	10.0703i		−	0.355817i
$802$	−19.4393	+	16.4860i	−0.686427	+	0.582141i
$803$	22.0767	−	22.0767i	0.779069	−	0.779069i
$804$	−3.52613	+	21.3015i	−0.124357	+	0.751247i
$805$		0			0
$806$	7.81490	+	0.642446i	0.275268	+	0.0226292i
$807$	15.4313			0.543208
$808$	−15.2106	−	3.82029i	−0.535106	−	0.134397i
$809$		−	20.3627i		−	0.715914i	−0.933738	−	0.357957i	$-0.883473\pi$
$809$		−	20.3627i		−	0.715914i	0.933738	−	0.357957i	$-0.116527\pi$
$810$	−0.176097	+	2.14209i	−0.00618741	+	0.0752654i
$811$	−31.8932	−	31.8932i	−1.11992	−	1.11992i	−0.991752	−	0.128171i	$-0.959089\pi$
$811$	−31.8932	−	31.8932i	−1.11992	−	1.11992i	−0.128171	−	0.991752i	$-0.540911\pi$
$812$		0			0
$813$	22.0500	−	22.0500i	0.773327	−	0.773327i
$814$	−17.6911	+	15.0033i	−0.620072	+	0.525867i
$815$	6.84609			0.239808
$816$	25.8383	+	52.5066i	0.904521	+	1.83810i
$817$			17.7289i			0.620256i
$818$	30.1660	−	25.5830i	1.05473	−	0.894490i
$819$		0			0
$820$	−1.76114	−	2.45986i	−0.0615018	−	0.0859022i
$821$	−17.3333	−	17.3333i	−0.604937	−	0.604937i	0.336682	−	0.941618i	$-0.390695\pi$
$821$	−17.3333	−	17.3333i	−0.604937	−	0.604937i	−0.941618	+	0.336682i	$0.890695\pi$
$822$	−57.9494	−	4.76390i	−2.02122	−	0.166160i
$823$	10.3395			0.360413			0.180207	−	0.983629i	$-0.442323\pi$
$823$	10.3395			0.360413			0.180207	+	0.983629i	$0.442323\pi$
$824$	−2.68501	+	1.60703i	−0.0935369	+	0.0559834i
$825$	25.9374			0.903024
$826$		0			0
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.161581	−	0.986859i	$-0.448341\pi$
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.986859	−	0.161581i	$-0.0516594\pi$
$828$	16.2435	+	2.68885i	0.564499	+	0.0934440i
$829$	26.5039	+	26.5039i	0.920520	+	0.920520i	0.997066	−	0.0765465i	$-0.0243894\pi$
$829$	26.5039	+	26.5039i	0.920520	+	0.920520i	−0.0765465	+	0.997066i	$0.524389\pi$
$830$	5.45314	+	6.43003i	0.189281	+	0.223190i
$831$	56.5596			1.96203
$832$	48.9122	−	14.7697i	1.69573	−	0.512048i
$833$		0			0
$834$	−4.67027	+	3.96073i	−0.161718	+	0.137149i
$835$	−1.96287	−	1.96287i	−0.0679279	−	0.0679279i
$836$	7.79609	+	1.29052i	0.269633	+	0.0446336i
$837$	−2.20519	−	2.20519i	−0.0762226	−	0.0762226i
$838$	1.71514	−	20.8634i	0.0592485	−	0.720715i
$839$		−	41.5802i		−	1.43551i	−0.696296	−	0.717754i	$-0.745170\pi$
$839$		−	41.5802i		−	1.43551i	0.696296	−	0.717754i	$-0.254830\pi$
$840$		0			0
$841$			26.4726i			0.912847i
$842$	−24.6612	−	2.02734i	−0.849881	−	0.0698669i
$843$	−37.9668	−	37.9668i	−1.30765	−	1.30765i
$844$	−20.9677	+	15.0118i	−0.721736	+	0.516728i
$845$	9.16776	+	9.16776i	0.315381	+	0.315381i
$846$	11.8159	+	13.9327i	0.406241	+	0.479016i
$847$		0			0
$848$	12.3963	+	25.1908i	0.425691	+	0.865056i
$849$	55.0747			1.89016
$850$	−27.8782	+	23.6428i	−0.956214	+	0.810940i
$851$	−11.0127	−	11.0127i	−0.377510	−	0.377510i
$852$	38.4219	+	53.6656i	1.31631	+	1.83855i
$853$	−3.78632	+	3.78632i	−0.129641	+	0.129641i	−0.768950	−	0.639309i	$-0.779221\pi$
$853$	−3.78632	+	3.78632i	−0.129641	+	0.129641i	0.639309	+	0.768950i	$0.279221\pi$
$854$		0			0
$855$	3.98094			0.136145
$856$	−16.9605	−	4.25980i	−0.579698	−	0.145597i
$857$	19.8789			0.679049			0.339524	−	0.940597i	$-0.389734\pi$
$857$	19.8789			0.679049			0.339524	+	0.940597i	$0.389734\pi$
$858$	4.01354	−	48.8219i	0.137020	−	1.66675i
$859$	9.05536	+	9.05536i	0.308965	+	0.308965i	0.844508	−	0.535543i	$-0.179893\pi$
$859$	9.05536	+	9.05536i	0.308965	+	0.308965i	−0.535543	+	0.844508i	$0.679893\pi$
$860$	−8.27634	−	1.37002i	−0.282221	−	0.0467173i
$861$		0			0
$862$	12.4727	+	14.7071i	0.424821	+	0.500925i
$863$		−	24.2418i		−	0.825199i	−0.910913	−	0.412599i	$-0.864621\pi$
$863$		−	24.2418i		−	0.825199i	0.910913	−	0.412599i	$-0.135379\pi$
$864$	−18.6357	−	8.10225i	−0.633999	−	0.275644i
$865$	4.28517			0.145700
$866$	−17.5235	−	20.6627i	−0.595471	−	0.702146i
$867$	−23.3732	+	23.3732i	−0.793794	+	0.793794i
$868$		0			0
$869$	1.75262	+	1.75262i	0.0594534	+	0.0594534i
$870$	−2.82976	−	0.232629i	−0.0959380	−	0.00788686i
$871$			25.4719i			0.863081i
$872$	29.8870	+	7.50643i	1.01210	+	0.254200i
$873$	20.3245			0.687881
$874$	−0.434695	+	5.28776i	−0.0147038	+	0.178861i
$875$		0			0
$876$	−49.1075	−	68.5905i	−1.65919	−	2.31746i
$877$	−15.3197	+	15.3197i	−0.517308	+	0.517308i	−0.916756	−	0.399448i	$-0.869202\pi$
$877$	−15.3197	+	15.3197i	−0.517308	+	0.517308i	0.399448	+	0.916756i	$0.369202\pi$
$878$	7.84118	+	9.24587i	0.264627	+	0.312033i
$879$			25.8590i			0.872202i
$880$	−1.20490	+	3.53970i	−0.0406172	+	0.119323i
$881$			15.3375i			0.516733i	0.966047	+	0.258367i	$0.0831842\pi$
$881$			15.3375i			0.516733i	−0.966047	+	0.258367i	$0.916816\pi$
$882$		0			0
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.973124	+	0.230282i	$0.0739648\pi$
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.230282	+	0.973124i	$0.426035\pi$
$884$	40.1888	+	56.1335i	1.35170	+	1.88797i
$885$	−7.66737	+	7.66737i	−0.257736	+	0.257736i
$886$	2.42683	−	29.5207i	0.0815309	−	0.991766i
$887$		−	32.3316i		−	1.08559i	−0.839865	−	0.542795i	$-0.817366\pi$
$887$		−	32.3316i		−	1.08559i	0.839865	−	0.542795i	$-0.182634\pi$
$888$	32.1875	+	53.7788i	1.08014	+	1.80470i
$889$		0			0
$890$	−0.125807	+	1.53036i	−0.00421707	+	0.0512977i
$891$	4.61528	−	4.61528i	0.154618	−	0.154618i
$892$	−2.19794	+	13.2778i	−0.0735924	+	0.444575i
$893$	−4.16267	+	4.16267i	−0.139299	+	0.139299i
$894$	−29.6625	+	25.1560i	−0.992062	+	0.841341i
$895$	−1.77504			−0.0593330
$896$		0			0
$897$	32.8900			1.09817
$898$	26.3462	−	22.3435i	0.879185	−	0.745614i
$899$	−0.975931	+	0.975931i	−0.0325491	+	0.0325491i
$900$	6.75903	−	40.8316i	0.225301	−	1.36105i
$901$	−26.8245	+	26.8245i	−0.893654	+	0.893654i
$902$	−0.752722	+	9.15633i	−0.0250629	+	0.304872i
$903$		0			0
$904$	−4.09438	−	6.84088i	−0.136177	−	0.227524i
$905$		−	3.38763i		−	0.112609i
$906$	−3.66269	+	44.5540i	−0.121685	+	1.48021i
$907$	22.3866	−	22.3866i	0.743336	−	0.743336i	−0.229882	−	0.973218i	$-0.573834\pi$
$907$	22.3866	−	22.3866i	0.743336	−	0.743336i	0.973218	+	0.229882i	$0.0738342\pi$
$908$	−8.99786	−	12.5677i	−0.298604	−	0.417074i
$909$	16.9654	+	16.9654i	0.562707	+	0.562707i
$910$		0			0
$911$			7.17911i			0.237854i	0.992903	+	0.118927i	$0.0379455\pi$
$911$			7.17911i			0.237854i	−0.992903	+	0.118927i	$0.962054\pi$
$912$	6.88019	−	20.2123i	0.227826	−	0.669296i
$913$		−	25.6031i		−	0.847339i
$914$	3.30365	+	3.89548i	0.109275	+	0.128851i
$915$	−0.434233	+	0.434233i	−0.0143553	+	0.0143553i
$916$	17.7465	+	24.7874i	0.586362	+	0.818998i
$917$		0			0
$918$	2.24962	−	27.3650i	0.0742484	−	0.903179i
$919$	2.36484			0.0780087			0.0390044	−	0.999239i	$-0.487581\pi$
$919$	2.36484			0.0780087			0.0390044	+	0.999239i	$0.487581\pi$
$920$	−2.43488	−	0.611544i	−0.0802755	−	0.0201620i
$921$		−	9.06988i		−	0.298863i
$922$	50.4043	+	4.14363i	1.65998	+	0.136463i
$923$	55.0580	+	55.0580i	1.81226	+	1.81226i
$924$		0			0
$925$	−27.6828	+	27.6828i	−0.910206	+	0.910206i
$926$	−7.32831	−	8.64112i	−0.240823	−	0.283965i
$927$	4.78722			0.157233
$928$	−3.58574	+	8.24743i	−0.117708	+	0.270735i
$929$			58.4828i			1.91876i	0.282119	+	0.959379i	$0.408963\pi$
$929$			58.4828i			1.91876i	−0.282119	+	0.959379i	$0.591037\pi$
$930$	1.00285	+	1.18250i	0.0328847	+	0.0387758i
$931$		0			0
$932$	−29.1529	−	4.82581i	−0.954936	−	0.158075i
$933$	−29.0056	−	29.0056i	−0.949601	−	0.949601i
$934$	2.14723	−	26.1195i	0.0702596	−	0.854657i
$935$	−5.05231			−0.165228
$936$	−75.8112	−	19.0408i	−2.47797	−	0.622367i
$937$	−13.4613			−0.439761			−0.219881	−	0.975527i	$-0.570567\pi$
$937$	−13.4613			−0.439761			−0.219881	+	0.975527i	$0.570567\pi$
$938$		0			0
$939$	12.7395	−	12.7395i	0.415738	−	0.415738i
$940$	−1.62158	−	2.26492i	−0.0528899	−	0.0738737i
$941$	−10.9217	−	10.9217i	−0.356036	−	0.356036i	0.506313	−	0.862350i	$-0.331008\pi$
$941$	−10.9217	−	10.9217i	−0.356036	−	0.356036i	−0.862350	+	0.506313i	$0.831008\pi$
$942$	−6.50227	+	5.51441i	−0.211855	+	0.179669i
$943$	−6.16838			−0.200870
$944$	15.1644	+	30.8159i	0.493558	+	1.00297i
$945$		0			0
$946$	16.4774	+	19.4292i	0.535726	+	0.631697i
$947$	22.0847	+	22.0847i	0.717657	+	0.717657i	0.968125	−	0.250468i	$-0.0805843\pi$
$947$	22.0847	+	22.0847i	0.717657	+	0.717657i	−0.250468	+	0.968125i	$0.580584\pi$
$948$	5.44524	−	3.89852i	0.176853	−	0.126618i
$949$	−70.3703	−	70.3703i	−2.28432	−	2.28432i
$950$	13.2920	+	1.09270i	0.431248	+	0.0354520i
$951$		−	71.7697i		−	2.32729i
$952$		0			0
$953$		−	15.7802i		−	0.511170i	−0.966787	−	0.255585i	$-0.917732\pi$
$953$		−	15.7802i		−	0.511170i	0.966787	−	0.255585i	$-0.0822680\pi$
$954$	3.51911	−	42.8074i	0.113935	−	1.38594i
$955$	5.80540	+	5.80540i	0.187858	+	0.187858i
$956$	−56.3310	−	9.32472i	−1.82187	−	0.301583i
$957$	6.09692	+	6.09692i	0.197085	+	0.197085i
$958$	29.5275	−	25.0415i	0.953989	−	0.809053i
$959$		0			0
$960$	8.90398	+	4.77378i	0.287375	+	0.154073i
$961$	−30.2463			−0.975688
$962$	47.8237	+	56.3909i	1.54190	+	1.81812i
$963$	18.9173	+	18.9173i	0.609600	+	0.609600i
$964$	45.2926	+	7.49748i	1.45878	+	0.241478i
$965$	−2.17051	+	2.17051i	−0.0698712	+	0.0698712i
$966$		0			0
$967$	−44.7046			−1.43760			−0.718801	−	0.695216i	$-0.755309\pi$
$967$	−44.7046			−1.43760			−0.718801	+	0.695216i	$0.755309\pi$
$968$	−16.9532	+	10.1468i	−0.544896	+	0.326129i
$969$	28.8495			0.926780
$970$	−3.08866	−	0.253912i	−0.0991708	−	0.00815262i
$971$	−41.1611	−	41.1611i	−1.32092	−	1.32092i	−0.913030	−	0.407893i	$-0.866264\pi$
$971$	−41.1611	−	41.1611i	−1.32092	−	1.32092i	−0.407893	−	0.913030i	$-0.633736\pi$
$972$	−22.8133	−	31.8643i	−0.731736	−	1.02205i
$973$		0			0
$974$	−20.8814	+	17.7089i	−0.669082	+	0.567431i
$975$		−	82.6764i		−	2.64776i
$976$	0.858817	+	1.74522i	0.0274901	+	0.0558632i
$977$	−20.8688			−0.667653			−0.333827	−	0.942635i	$-0.608340\pi$
$977$	−20.8688			−0.667653			−0.333827	+	0.942635i	$0.608340\pi$
$978$	−42.8414	+	36.3327i	−1.36992	+	1.16179i
$979$	3.29726	−	3.29726i	0.105381	−	0.105381i
$980$		0			0
$981$	−33.3351	−	33.3351i	−1.06431	−	1.06431i
$982$	2.81762	−	34.2743i	0.0899138	−	1.09374i
$983$			42.1732i			1.34512i	0.740045	+	0.672558i	$0.234804\pi$
$983$			42.1732i			1.34512i	−0.740045	+	0.672558i	$0.765196\pi$
$984$	24.0755	+	6.04681i	0.767500	+	0.192765i
$985$	9.81613			0.312768
$986$	−12.1107	−	0.995592i	−0.385682	−	0.0317061i
$987$		0			0
$988$	4.11359	−	24.8503i	0.130871	−	0.790594i
$989$	−12.0946	+	12.0946i	−0.384587	+	0.384587i
$990$	4.36272	−	3.69991i	0.138656	−	0.117591i
$991$		−	17.0880i		−	0.542819i	−0.962464	−	0.271410i	$-0.912510\pi$
$991$		−	17.0880i		−	0.542819i	0.962464	−	0.271410i	$-0.0874898\pi$
$992$	4.56922	−	1.80005i	0.145073	−	0.0571516i
$993$		−	25.6788i		−	0.814891i
$994$		0			0
$995$	2.45062	+	2.45062i	0.0776898	+	0.0776898i
$996$	−68.2492	−	11.2976i	−2.16256	−	0.357978i
$997$	20.0894	−	20.0894i	0.636239	−	0.636239i	−0.313387	−	0.949626i	$-0.601464\pi$
$997$	20.0894	−	20.0894i	0.636239	−	0.636239i	0.949626	+	0.313387i	$0.101464\pi$
$998$	4.26786	+	0.350852i	0.135097	+	0.0111060i
$999$		−	29.4071i		−	0.930398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.587.8		56
7.2	even	3		784.2.w.f.619.13		56
7.3	odd	6		784.2.w.f.411.7		56
7.4	even	3		112.2.v.a.75.7	yes	56
7.5	odd	6		112.2.v.a.59.13	yes	56
7.6	odd	2	inner	784.2.j.a.587.7		56
16.3	odd	4	inner	784.2.j.a.195.7		56
28.11	odd	6		448.2.z.a.271.13		56
28.19	even	6		448.2.z.a.143.13		56
56.5	odd	6		896.2.z.b.31.13		56
56.11	odd	6		896.2.z.a.159.2		56
56.19	even	6		896.2.z.a.31.2		56
56.53	even	6		896.2.z.b.159.13		56
112.3	even	12		784.2.w.f.19.13		56
112.5	odd	12		896.2.z.a.479.2		56
112.11	odd	12		896.2.z.b.607.13		56
112.19	even	12		112.2.v.a.3.7	✓	56
112.51	odd	12		784.2.w.f.227.7		56
112.53	even	12		896.2.z.a.607.2		56
112.61	odd	12		448.2.z.a.367.13		56
112.67	odd	12		112.2.v.a.19.13	yes	56
112.75	even	12		896.2.z.b.479.13		56
112.83	even	4	inner	784.2.j.a.195.8		56
112.109	even	12		448.2.z.a.47.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	112.19	even	12
112.2.v.a.19.13	yes	56	112.67	odd	12
112.2.v.a.59.13	yes	56	7.5	odd	6
112.2.v.a.75.7	yes	56	7.4	even	3
448.2.z.a.47.13		56	112.109	even	12
448.2.z.a.143.13		56	28.19	even	6
448.2.z.a.271.13		56	28.11	odd	6
448.2.z.a.367.13		56	112.61	odd	12
784.2.j.a.195.7		56	16.3	odd	4	inner
784.2.j.a.195.8		56	112.83	even	4	inner
784.2.j.a.587.7		56	7.6	odd	2	inner
784.2.j.a.587.8		56	1.1	even	1	trivial
784.2.w.f.19.13		56	112.3	even	12
784.2.w.f.227.7		56	112.51	odd	12
784.2.w.f.411.7		56	7.3	odd	6
784.2.w.f.619.13		56	7.2	even	3
896.2.z.a.31.2		56	56.19	even	6
896.2.z.a.159.2		56	56.11	odd	6
896.2.z.a.479.2		56	112.5	odd	12
896.2.z.a.607.2		56	112.53	even	12
896.2.z.b.31.13		56	56.5	odd	6
896.2.z.b.159.13		56	56.53	even	6
896.2.z.b.479.13		56	112.75	even	12
896.2.z.b.607.13		56	112.11	odd	12

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+(-1.07857 + 0.914706i) q^{2} +(1.91404 - 1.91404i) q^{3} +(0.326624 - 1.97315i) q^{4} +(0.329897 - 0.329897i) q^{5} +(-0.313640 + 3.81521i) q^{6} +(1.45257 + 2.42694i) q^{8} -4.32709i q^{9} +(-0.0540578 + 0.657575i) q^{10} +(1.41679 - 1.41679i) q^{11} +(-3.15151 - 4.40186i) q^{12} +(-4.51607 - 4.51607i) q^{13} -1.26287i q^{15} +(-3.78663 - 1.28896i) q^{16} -5.40476i q^{17} +(3.95802 + 4.66707i) q^{18} +(-1.39438 + 1.39438i) q^{19} +(-0.543183 - 0.758687i) q^{20} +(-0.232159 + 2.82405i) q^{22} -1.90249 q^{23} +(7.42553 + 1.86500i) q^{24} +4.78234i q^{25} +(9.00178 + 0.740017i) q^{26} +(-2.54010 - 2.54010i) q^{27} +(-1.12415 + 1.12415i) q^{29} +(1.15516 + 1.36209i) q^{30} +0.868151 q^{31} +(5.26316 - 2.07343i) q^{32} -5.42358i q^{33} +(4.94377 + 5.82941i) q^{34} +(-8.53799 - 1.41333i) q^{36} +(5.78856 + 5.78856i) q^{37} +(0.228487 - 2.77939i) q^{38} -17.2879 q^{39} +(1.27984 + 0.321444i) q^{40} +3.24226 q^{41} +(6.35727 - 6.35727i) q^{43} +(-2.33278 - 3.25830i) q^{44} +(-1.42749 - 1.42749i) q^{45} +(2.05197 - 1.74022i) q^{46} +2.98532 q^{47} +(-9.71488 + 4.78065i) q^{48} +(-4.37443 - 5.15808i) q^{50} +(-10.3449 - 10.3449i) q^{51} +(-10.3859 + 7.43582i) q^{52} +(-4.96313 - 4.96313i) q^{53} +(5.06313 + 0.416229i) q^{54} -0.934789i q^{55} +5.33780i q^{57} +(0.184206 - 2.24074i) q^{58} +(-6.07138 - 6.07138i) q^{59} +(-2.49183 - 0.412484i) q^{60} +(-0.343846 - 0.343846i) q^{61} +(-0.936361 + 0.794103i) q^{62} +(-3.78011 + 7.05059i) q^{64} -2.97967 q^{65} +(4.96099 + 5.84971i) q^{66} +(-2.82013 - 2.82013i) q^{67} +(-10.6644 - 1.76533i) q^{68} +(-3.64144 + 3.64144i) q^{69} -12.1916 q^{71} +(10.5016 - 6.28538i) q^{72} +15.5822 q^{73} +(-11.5382 - 0.948530i) q^{74} +(9.15358 + 9.15358i) q^{75} +(2.29588 + 3.20676i) q^{76} +(18.6462 - 15.8133i) q^{78} +1.23703i q^{79} +(-1.67442 + 0.823975i) q^{80} +3.25756 q^{81} +(-3.49701 + 2.96572i) q^{82} +(9.03560 - 9.03560i) q^{83} +(-1.78301 - 1.78301i) q^{85} +(-1.04172 + 12.6718i) q^{86} +4.30333i q^{87} +(5.49645 + 1.38049i) q^{88} +2.32727 q^{89} +(2.84539 + 0.233913i) q^{90} +(-0.621399 + 3.75390i) q^{92} +(1.66167 - 1.66167i) q^{93} +(-3.21987 + 2.73069i) q^{94} +0.920003i q^{95} +(6.10528 - 14.0425i) q^{96} +4.69704i q^{97} +(-6.13058 - 6.13058i) 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

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