LMFDB - Embedded newform 784.2.j.a.587.7

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			587.7
Character	$\chi$	$=$	784.587
Dual form			784.2.j.a.195.7

$q$-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	$0.535496\pi$
$3$	−1.91404	+	1.91404i	−1.10507	+	1.10507i	−0.993789	+	0.111282i	$0.964504\pi$
$4$	0.326624	−	1.97315i	0.163312	−	0.986574i
$5$	−0.329897	+	0.329897i	−0.147534	+	0.147534i	−0.777016	−	0.629481i	$-0.783267\pi$
$5$	−0.329897	+	0.329897i	−0.147534	+	0.147534i	0.629481	+	0.777016i	$0.283267\pi$
$6$	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	$0.0963035\pi$
$13$	4.51607	+	4.51607i	1.25253	+	1.25253i	0.297952	+	0.954581i	$0.403696\pi$
$14$		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	$0.227510\pi$
$17$			5.40476i			1.31085i	−0.755262	+	0.655424i	$0.772490\pi$
$18$	3.95802	+	4.66707i	0.932914	+	1.10004i
$19$	1.39438	−	1.39438i	0.319893	−	0.319893i	−0.528833	−	0.848726i	$-0.677370\pi$
$19$	1.39438	−	1.39438i	0.319893	−	0.319893i	0.848726	+	0.528833i	$0.177370\pi$
$20$	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	$-0.524841\pi$
$31$	−0.868151			−0.155924			−0.0779622	+	0.996956i	$0.524841\pi$
$32$	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	$-0.581476\pi$
$41$	−3.24226			−0.506356			−0.253178	+	0.967420i	$0.581476\pi$
$42$		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	$-0.569864\pi$
$47$	−2.98532			−0.435454			−0.217727	+	0.976010i	$0.569864\pi$
$48$	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	0.981563	−	0.191137i	$-0.0612173\pi$
$59$	6.07138	+	6.07138i	0.790427	+	0.790427i	−0.191137	+	0.981563i	$0.561217\pi$
$60$	−2.49183	−	0.412484i	−0.321694	−	0.0532514i
$61$	0.343846	+	0.343846i	0.0440250	+	0.0440250i	0.728777	−	0.684752i	$-0.240089\pi$
$61$	0.343846	+	0.343846i	0.0440250	+	0.0440250i	−0.684752	+	0.728777i	$0.740089\pi$
$62$	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	$-0.865368\pi$
$73$	−15.5822			−1.82376			−0.911878	+	0.410460i	$0.865368\pi$
$74$	−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	−0.999967	−	0.00818066i	$-0.997396\pi$
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	0.00818066	+	0.999967i	$0.497396\pi$
$84$		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	$-0.539362\pi$
$89$	−2.32727			−0.246691			−0.123345	+	0.992364i	$0.539362\pi$
$90$	−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	$-0.923359\pi$
$97$		−	4.69704i		−	0.476912i	0.971153	−	0.238456i	$-0.0766414\pi$
$98$		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	−0.484605	−	0.874733i	$-0.661037\pi$
$101$	3.92074	−	3.92074i	0.390129	−	0.390129i	0.874733	+	0.484605i	$0.161037\pi$
$102$	20.6203	+	1.69515i	2.04171	+	0.167845i
$103$		−	1.10634i		−	0.109011i	−0.998513	−	0.0545053i	$-0.982642\pi$
$103$		−	1.10634i		−	0.109011i	0.998513	−	0.0545053i	$-0.0173582\pi$
$104$	−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	$0.550788\pi$
$131$	−13.1186	+	13.1186i	−1.14618	+	1.14618i	−0.987298	+	0.158879i	$0.949212\pi$
$132$	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	0.657507	−	0.753448i	$-0.271611\pi$
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	−0.753448	+	0.657507i	$0.771611\pi$
$140$		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	0.641466	−	0.767152i	$-0.278327\pi$
$157$	−1.57484	−	1.57484i	−0.125686	−	0.125686i	−0.767152	+	0.641466i	$0.778327\pi$
$158$	−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	$0.0739415\pi$
$167$			5.94995i			0.460421i	−0.973141	+	0.230210i	$0.926059\pi$
$168$		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	0.415713	−	0.909496i	$-0.363532\pi$
$173$	−6.49471	−	6.49471i	−0.493784	−	0.493784i	−0.909496	+	0.415713i	$0.863532\pi$
$174$	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	−0.871691	−	0.490055i	$-0.836977\pi$
$181$	−5.13439	+	5.13439i	−0.381636	+	0.381636i	0.490055	+	0.871691i	$0.336977\pi$
$182$		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	$-0.915191\pi$
$199$		−	7.42845i		−	0.526589i	0.964716	−	0.263294i	$-0.0848090\pi$
$200$	−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	$-0.427660\pi$
$223$	6.72926			0.450624			0.225312	+	0.974287i	$0.427660\pi$
$224$		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	−0.864809	−	0.502101i	$-0.832561\pi$
$227$	−5.46476	+	5.46476i	−0.362709	+	0.362709i	0.502101	+	0.864809i	$0.332561\pi$
$228$	10.5323	+	1.74345i	0.697517	+	0.115463i
$229$	10.7782	−	10.7782i	0.712242	−	0.712242i	−0.254762	−	0.967004i	$-0.581997\pi$
$229$	10.7782	−	10.7782i	0.712242	−	0.712242i	0.967004	+	0.254762i	$0.0819970\pi$
$230$	−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	$-0.735150\pi$
$241$		−	22.9545i		−	1.47863i	0.673361	−	0.739314i	$-0.264850\pi$
$242$	−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	0.952732	−	0.303813i	$-0.0982599\pi$
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	−0.303813	+	0.952732i	$0.598260\pi$
$252$		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	$0.0249949\pi$
$257$			2.51508i			0.156886i	−0.996919	+	0.0784431i	$0.975005\pi$
$258$	−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	0.573456	−	0.819236i	$-0.305602\pi$
$269$	−4.03108	−	4.03108i	−0.245780	−	0.245780i	−0.819236	+	0.573456i	$0.805602\pi$
$270$	1.80762	−	1.53300i	0.110008	−	0.0932951i
$271$	−11.5201			−0.699798			−0.349899	−	0.936787i	$-0.613784\pi$
$271$	−11.5201			−0.699798			−0.349899	+	0.936787i	$0.613784\pi$
$272$	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	0.135550	−	0.990771i	$-0.456720\pi$
$283$	−14.3870	−	14.3870i	−0.855221	−	0.855221i	−0.990771	+	0.135550i	$0.956720\pi$
$284$	−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	−0.481700	−	0.876336i	$-0.659980\pi$
$293$	6.75509	−	6.75509i	0.394636	−	0.394636i	0.876336	+	0.481700i	$0.159980\pi$
$294$		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	−0.771479	−	0.636255i	$-0.780483\pi$
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	0.636255	+	0.771479i	$0.280483\pi$
$308$		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	$0.141365\pi$
$311$			15.1541i			0.859312i	−0.902993	+	0.429656i	$0.858635\pi$
$312$	−25.1118	−	41.9567i	−1.42167	−	2.37533i
$313$	−6.65582			−0.376209			−0.188105	−	0.982149i	$-0.560234\pi$
$313$	−6.65582			−0.376209			−0.188105	+	0.982149i	$0.560234\pi$
$314$	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	0.763863	−	0.645378i	$-0.223300\pi$
$349$	2.21348	+	2.21348i	0.118485	+	0.118485i	−0.645378	+	0.763863i	$0.723300\pi$
$350$		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	$0.0701887\pi$
$353$			8.21881i			0.437443i	−0.975787	+	0.218722i	$0.929811\pi$
$354$	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	$-0.345987\pi$
$367$	17.8234			0.930372			0.465186	+	0.885213i	$0.345987\pi$
$368$	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	$-0.292096\pi$
$383$	23.7855			1.21538			0.607692	+	0.794173i	$0.292096\pi$
$384$	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	0.778018	−	0.628242i	$-0.216225\pi$
$397$	2.98427	+	2.98427i	0.149776	+	0.149776i	−0.628242	+	0.778018i	$0.716225\pi$
$398$	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	$-0.256960\pi$
$409$	27.9686			1.38296			0.691478	+	0.722397i	$0.256960\pi$
$410$	−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	−0.403596	−	0.914937i	$-0.632240\pi$
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	0.914937	+	0.403596i	$0.132240\pi$
$420$		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	$-0.847733\pi$
$433$		−	19.1575i		−	0.920649i	0.887751	−	0.460325i	$-0.152267\pi$
$434$		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	$0.0655789\pi$
$439$			8.57235i			0.409136i	−0.978852	+	0.204568i	$0.934421\pi$
$440$	−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	$0.0632574\pi$
$461$	25.2872	+	25.2872i	1.17774	+	1.17774i	0.197423	+	0.980318i	$0.436743\pi$
$462$		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	−0.335623	−	0.941996i	$-0.608947\pi$
$467$	13.1038	−	13.1038i	0.606373	−	0.606373i	0.941996	+	0.335623i	$0.108947\pi$
$468$	−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	$-0.284923\pi$
$479$	27.3765			1.25086			0.625432	+	0.780279i	$0.284923\pi$
$480$	−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	$-0.719937\pi$
$503$		−	34.5673i		−	1.54128i	0.637272	−	0.770639i	$-0.280063\pi$
$504$		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	0.415427	−	0.909626i	$-0.363632\pi$
$509$	−11.1496	−	11.1496i	−0.494199	−	0.494199i	−0.909626	+	0.415427i	$0.863632\pi$
$510$	−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	$-0.609839\pi$
$521$	−15.4419			−0.676522			−0.338261	+	0.941052i	$0.609839\pi$
$522$	−9.69589	−	0.797078i	−0.424377	−	0.0348872i
$523$	1.44190	+	1.44190i	0.0630500	+	0.0630500i	0.737929	−	0.674879i	$-0.235804\pi$
$523$	1.44190	+	1.44190i	0.0630500	+	0.0630500i	−0.674879	+	0.737929i	$0.735804\pi$
$524$	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	−0.149462	−	0.988768i	$-0.547754\pi$
$563$	19.9147	−	19.9147i	0.839306	−	0.839306i	0.988768	+	0.149462i	$0.0477540\pi$
$564$	−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	$0.128051\pi$
$577$			18.8093i			0.783040i	−0.920170	+	0.391520i	$0.871949\pi$
$578$	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	0.396999	−	0.917819i	$-0.370052\pi$
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	−0.917819	+	0.396999i	$0.870052\pi$
$588$		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	$-0.825107\pi$
$593$		−	25.4334i		−	1.04442i	0.852816	−	0.522212i	$-0.174893\pi$
$594$	−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	$-0.291490\pi$
$601$	29.8695			1.21840			0.609202	+	0.793015i	$0.291490\pi$
$602$		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	$-0.296275\pi$
$607$	29.4275			1.19442			0.597212	+	0.802083i	$0.296275\pi$
$608$	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	0.917890	−	0.396836i	$-0.129892\pi$
$619$	12.9637	+	12.9637i	0.521053	+	0.521053i	−0.396836	+	0.917890i	$0.629892\pi$
$620$	−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	−0.990721	−	0.135909i	$-0.956605\pi$
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	0.135909	+	0.990721i	$0.456605\pi$
$644$		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	$0.359839\pi$
$647$			46.0198i			1.80922i	−0.426236	+	0.904612i	$0.640161\pi$
$648$	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	−0.546732	−	0.837308i	$-0.684128\pi$
$661$	7.47069	−	7.47069i	0.290576	−	0.290576i	0.837308	+	0.546732i	$0.184128\pi$
$662$	−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	−0.924771	−	0.380525i	$-0.875743\pi$
$677$	−14.1608	+	14.1608i	−0.544245	+	0.544245i	0.380525	+	0.924771i	$0.375743\pi$
$678$	−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	−0.0648375	−	0.997896i	$-0.520653\pi$
$691$	24.5272	−	24.5272i	0.933058	−	0.933058i	0.997896	+	0.0648375i	$0.0206529\pi$
$692$	−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	$-0.387568\pi$
$719$	18.5510			0.691834			0.345917	+	0.938265i	$0.387568\pi$
$720$	−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	$-0.964711\pi$
$727$		−	5.96613i		−	0.221272i	0.993861	−	0.110636i	$-0.0352887\pi$
$728$		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	0.930569	−	0.366117i	$-0.119313\pi$
$733$	15.2819	+	15.2819i	0.564452	+	0.564452i	−0.366117	+	0.930569i	$0.619313\pi$
$734$	−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	$-0.551384\pi$
$761$	−8.86780			−0.321458			−0.160729	+	0.986999i	$0.551384\pi$
$762$	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	$-0.993437\pi$
$769$		−	1.14344i		−	0.0412335i	0.999787	−	0.0206167i	$-0.00656298\pi$
$770$		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	−0.772849	−	0.634590i	$-0.781169\pi$
$773$	−3.84402	+	3.84402i	−0.138260	+	0.138260i	0.634590	+	0.772849i	$0.281169\pi$
$774$	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	$0.613187\pi$
$787$	−36.0651	+	36.0651i	−1.28558	+	1.28558i	−0.937442	+	0.348142i	$0.886813\pi$
$788$	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	0.998311	−	0.0581002i	$-0.0185043\pi$
$797$	26.5433	+	26.5433i	0.940211	+	0.940211i	−0.0581002	+	0.998311i	$0.518504\pi$
$798$		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	$0.0409107\pi$
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.128171	+	0.991752i	$0.459089\pi$
$812$		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	0.0765465	−	0.997066i	$-0.475611\pi$
$829$	−26.5039	−	26.5039i	−0.920520	−	0.920520i	−0.997066	+	0.0765465i	$0.975611\pi$
$830$	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	$0.254830\pi$
$839$			41.5802i			1.43551i	−0.696296	+	0.717754i	$0.745170\pi$
$840$		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	−0.639309	−	0.768950i	$-0.720779\pi$
$853$	3.78632	−	3.78632i	0.129641	−	0.129641i	0.768950	+	0.639309i	$0.220779\pi$
$854$		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	$-0.610266\pi$
$857$	−19.8789			−0.679049			−0.339524	+	0.940597i	$0.610266\pi$
$858$	4.01354	−	48.8219i	0.137020	−	1.66675i
$859$	−9.05536	−	9.05536i	−0.308965	−	0.308965i	0.535543	−	0.844508i	$-0.320107\pi$
$859$	−9.05536	−	9.05536i	−0.308965	−	0.308965i	−0.844508	+	0.535543i	$0.820107\pi$
$860$	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	$-0.916816\pi$
$881$		−	15.3375i		−	0.516733i	0.966047	−	0.258367i	$-0.0831842\pi$
$882$		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	$0.182634\pi$
$887$			32.3316i			1.08559i	−0.839865	+	0.542795i	$0.817366\pi$
$888$	−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	$-0.591037\pi$
$929$		−	58.4828i		−	1.91876i	0.282119	−	0.959379i	$-0.408963\pi$
$930$	−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	$-0.429433\pi$
$937$	13.4613			0.439761			0.219881	+	0.975527i	$0.429433\pi$
$938$		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	0.862350	−	0.506313i	$-0.168992\pi$
$941$	10.9217	+	10.9217i	0.356036	+	0.356036i	−0.506313	+	0.862350i	$0.668992\pi$
$942$	−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	$0.133736\pi$
$971$	41.1611	+	41.1611i	1.32092	+	1.32092i	0.407893	+	0.913030i	$0.366264\pi$
$972$	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	$-0.765196\pi$
$983$		−	42.1732i		−	1.34512i	0.740045	−	0.672558i	$-0.234804\pi$
$984$	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	−0.949626	−	0.313387i	$-0.898536\pi$
$997$	−20.0894	+	20.0894i	−0.636239	+	0.636239i	0.313387	+	0.949626i	$0.398536\pi$
$998$	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.587.7		56
7.2	even	3		112.2.v.a.59.13	yes	56
7.3	odd	6		112.2.v.a.75.7	yes	56
7.4	even	3		784.2.w.f.411.7		56
7.5	odd	6		784.2.w.f.619.13		56
7.6	odd	2	inner	784.2.j.a.587.8		56
16.3	odd	4	inner	784.2.j.a.195.8		56
28.3	even	6		448.2.z.a.271.13		56
28.23	odd	6		448.2.z.a.143.13		56
56.3	even	6		896.2.z.a.159.2		56
56.37	even	6		896.2.z.b.31.13		56
56.45	odd	6		896.2.z.b.159.13		56
56.51	odd	6		896.2.z.a.31.2		56
112.3	even	12		112.2.v.a.19.13	yes	56
112.19	even	12		784.2.w.f.227.7		56
112.37	even	12		896.2.z.a.479.2		56
112.45	odd	12		448.2.z.a.47.13		56
112.51	odd	12		112.2.v.a.3.7	✓	56
112.59	even	12		896.2.z.b.607.13		56
112.67	odd	12		784.2.w.f.19.13		56
112.83	even	4	inner	784.2.j.a.195.7		56
112.93	even	12		448.2.z.a.367.13		56
112.101	odd	12		896.2.z.a.607.2		56
112.107	odd	12		896.2.z.b.479.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	112.51	odd	12
112.2.v.a.19.13	yes	56	112.3	even	12
112.2.v.a.59.13	yes	56	7.2	even	3
112.2.v.a.75.7	yes	56	7.3	odd	6
448.2.z.a.47.13		56	112.45	odd	12
448.2.z.a.143.13		56	28.23	odd	6
448.2.z.a.271.13		56	28.3	even	6
448.2.z.a.367.13		56	112.93	even	12
784.2.j.a.195.7		56	112.83	even	4	inner
784.2.j.a.195.8		56	16.3	odd	4	inner
784.2.j.a.587.7		56	1.1	even	1	trivial
784.2.j.a.587.8		56	7.6	odd	2	inner
784.2.w.f.19.13		56	112.67	odd	12
784.2.w.f.227.7		56	112.19	even	12
784.2.w.f.411.7		56	7.4	even	3
784.2.w.f.619.13		56	7.5	odd	6
896.2.z.a.31.2		56	56.51	odd	6
896.2.z.a.159.2		56	56.3	even	6
896.2.z.a.479.2		56	112.37	even	12
896.2.z.a.607.2		56	112.101	odd	12
896.2.z.b.31.13		56	56.37	even	6
896.2.z.b.159.13		56	56.45	odd	6
896.2.z.b.479.13		56	112.107	odd	12
896.2.z.b.607.13		56	112.59	even	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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more