LMFDB - Embedded newform 784.2.j.a.195.25

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)

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);

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")

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			195.25
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39250 - 0.246844i) q^{2} +(-1.22906 - 1.22906i) q^{3} +(1.87814 - 0.687462i) q^{4} +(0.535151 + 0.535151i) q^{5} +(-2.01486 - 1.40809i) q^{6} +(2.44562 - 1.42090i) q^{8} +0.0211916i q^{9} +(0.877298 + 0.613101i) q^{10} +(3.23833 + 3.23833i) q^{11} +(-3.15328 - 1.46341i) q^{12} +(2.89529 - 2.89529i) q^{13} -1.31547i q^{15} +(3.05479 - 2.58230i) q^{16} +2.63765i q^{17} +(0.00523102 + 0.0295094i) q^{18} +(-3.93855 - 3.93855i) q^{19} +(1.37298 + 0.637190i) q^{20} +(5.30875 + 3.71003i) q^{22} -2.02285 q^{23} +(-4.75219 - 1.25944i) q^{24} -4.42723i q^{25} +(3.31702 - 4.74639i) q^{26} +(-3.66114 + 3.66114i) q^{27} +(-0.209526 - 0.209526i) q^{29} +(-0.324715 - 1.83179i) q^{30} +6.66105 q^{31} +(3.61639 - 4.34991i) q^{32} -7.96022i q^{33} +(0.651087 + 3.67293i) q^{34} +(0.0145684 + 0.0398007i) q^{36} +(2.79777 - 2.79777i) q^{37} +(-6.45665 - 4.51224i) q^{38} -7.11699 q^{39} +(2.06917 + 0.548378i) q^{40} +5.04472 q^{41} +(-3.79454 - 3.79454i) q^{43} +(8.30826 + 3.85580i) q^{44} +(-0.0113407 + 0.0113407i) q^{45} +(-2.81683 + 0.499328i) q^{46} -5.07985 q^{47} +(-6.92833 - 0.580727i) q^{48} +(-1.09283 - 6.16493i) q^{50} +(3.24183 - 3.24183i) q^{51} +(3.44735 - 7.42816i) q^{52} +(-7.85735 + 7.85735i) q^{53} +(-4.19443 + 6.00189i) q^{54} +3.46599i q^{55} +9.68145i q^{57} +(-0.343486 - 0.240046i) q^{58} +(-3.83007 + 3.83007i) q^{59} +(-0.904334 - 2.47063i) q^{60} +(4.28096 - 4.28096i) q^{61} +(9.27554 - 1.64424i) q^{62} +(3.96208 - 6.94996i) q^{64} +3.09883 q^{65} +(-1.96493 - 11.0846i) q^{66} +(-6.76419 + 6.76419i) q^{67} +(1.81328 + 4.95386i) q^{68} +(2.48621 + 2.48621i) q^{69} -7.25507 q^{71} +(0.0301112 + 0.0518266i) q^{72} +6.59265 q^{73} +(3.20530 - 4.58652i) q^{74} +(-5.44134 + 5.44134i) q^{75} +(-10.1047 - 4.68953i) q^{76} +(-9.91044 + 1.75679i) q^{78} +15.0822i q^{79} +(3.01669 + 0.252857i) q^{80} +9.06313 q^{81} +(7.02479 - 1.24526i) q^{82} +(8.00548 + 8.00548i) q^{83} +(-1.41154 + 1.41154i) q^{85} +(-6.22057 - 4.34725i) q^{86} +0.515042i q^{87} +(12.5211 + 3.31837i) q^{88} +7.85072 q^{89} +(-0.0129926 + 0.0185914i) q^{90} +(-3.79919 + 1.39063i) q^{92} +(-8.18685 - 8.18685i) q^{93} +(-7.07372 + 1.25393i) q^{94} -4.21543i q^{95} +(-9.79108 + 0.901551i) q^{96} +8.79532i q^{97} +(-0.0686254 + 0.0686254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.39250	−	0.246844i	0.984649	−	0.174545i
$2$	1.39250	−	0.246844i	0.984649	−	0.174545i
$3$	−1.22906	−	1.22906i	−0.709600	−	0.709600i	0.256851	−	0.966451i	$-0.417315\pi$
$3$	−1.22906	−	1.22906i	−0.709600	−	0.709600i	−0.966451	+	0.256851i	$0.917315\pi$
$4$	1.87814	−	0.687462i	0.939068	−	0.343731i
$5$	0.535151	+	0.535151i	0.239327	+	0.239327i	0.816571	−	0.577245i	$-0.195872\pi$
$5$	0.535151	+	0.535151i	0.239327	+	0.239327i	−0.577245	+	0.816571i	$0.695872\pi$
$6$	−2.01486	−	1.40809i	−0.822564	−	0.574850i
$7$		0			0
$7$		0			0
$8$	2.44562	−	1.42090i	0.864656	−	0.502364i
$9$			0.0211916i			0.00706387i
$10$	0.877298	+	0.613101i	0.277426	+	0.193880i
$11$	3.23833	+	3.23833i	0.976393	+	0.976393i	0.999728	−	0.0233344i	$-0.00742824\pi$
$11$	3.23833	+	3.23833i	0.976393	+	0.976393i	−0.0233344	+	0.999728i	$0.507428\pi$
$12$	−3.15328	−	1.46341i	−0.910274	−	0.422451i
$13$	2.89529	−	2.89529i	0.803010	−	0.803010i	−0.180555	−	0.983565i	$-0.557789\pi$
$13$	2.89529	−	2.89529i	0.803010	−	0.803010i	0.983565	+	0.180555i	$0.0577895\pi$
$14$		0			0
$15$		−	1.31547i		−	0.339652i
$16$	3.05479	−	2.58230i	0.763698	−	0.645574i
$17$			2.63765i			0.639723i	0.947464	+	0.319862i	$0.103636\pi$
$17$			2.63765i			0.639723i	−0.947464	+	0.319862i	$0.896364\pi$
$18$	0.00523102	+	0.0295094i	0.00123296	+	0.00695543i
$19$	−3.93855	−	3.93855i	−0.903565	−	0.903565i	0.0921778	−	0.995743i	$-0.470617\pi$
$19$	−3.93855	−	3.93855i	−0.903565	−	0.903565i	−0.995743	+	0.0921778i	$0.970617\pi$
$20$	1.37298	+	0.637190i	0.307008	+	0.142480i
$21$		0			0
$22$	5.30875	+	3.71003i	1.13183	+	0.790980i
$23$	−2.02285			−0.421794			−0.210897	−	0.977508i	$-0.567638\pi$
$23$	−2.02285			−0.421794			−0.210897	+	0.977508i	$0.567638\pi$
$24$	−4.75219	−	1.25944i	−0.970037	−	0.257082i
$25$		−	4.42723i		−	0.885446i
$26$	3.31702	−	4.74639i	0.650522	−	0.930844i
$27$	−3.66114	+	3.66114i	−0.704587	+	0.704587i
$28$		0			0
$29$	−0.209526	−	0.209526i	−0.0389080	−	0.0389080i	0.687385	−	0.726293i	$-0.258758\pi$
$29$	−0.209526	−	0.209526i	−0.0389080	−	0.0389080i	−0.726293	+	0.687385i	$0.758758\pi$
$30$	−0.324715	−	1.83179i	−0.0592846	−	0.334438i
$31$	6.66105			1.19636			0.598180	−	0.801362i	$-0.295891\pi$
$31$	6.66105			1.19636			0.598180	+	0.801362i	$0.295891\pi$
$32$	3.61639	−	4.34991i	0.639293	−	0.768963i
$33$		−	7.96022i		−	1.38570i
$34$	0.651087	+	3.67293i	0.111660	+	0.629903i
$35$		0			0
$36$	0.0145684	+	0.0398007i	0.00242807	+	0.00663346i
$37$	2.79777	−	2.79777i	0.459951	−	0.459951i	−0.438688	−	0.898639i	$-0.644557\pi$
$37$	2.79777	−	2.79777i	0.459951	−	0.459951i	0.898639	+	0.438688i	$0.144557\pi$
$38$	−6.45665	−	4.51224i	−1.04741	−	0.731982i
$39$	−7.11699			−1.13963
$40$	2.06917	+	0.548378i	0.327164	+	0.0867061i
$41$	5.04472			0.787853			0.393926	−	0.919142i	$-0.371117\pi$
$41$	5.04472			0.787853			0.393926	+	0.919142i	$0.371117\pi$
$42$		0			0
$43$	−3.79454	−	3.79454i	−0.578662	−	0.578662i	0.355873	−	0.934534i	$-0.384184\pi$
$43$	−3.79454	−	3.79454i	−0.578662	−	0.578662i	−0.934534	+	0.355873i	$0.884184\pi$
$44$	8.30826	+	3.85580i	1.25252	+	0.581283i
$45$	−0.0113407	+	0.0113407i	−0.00169057	+	0.00169057i
$46$	−2.81683	+	0.499328i	−0.415319	+	0.0736220i
$47$	−5.07985			−0.740973			−0.370486	−	0.928838i	$-0.620809\pi$
$47$	−5.07985			−0.740973			−0.370486	+	0.928838i	$0.620809\pi$
$48$	−6.92833	−	0.580727i	−1.00002	−	0.0838208i
$49$		0			0
$50$	−1.09283	−	6.16493i	−0.154550	−	0.871853i
$51$	3.24183	−	3.24183i	0.453948	−	0.453948i
$52$	3.44735	−	7.42816i	0.478061	−	1.03010i
$53$	−7.85735	+	7.85735i	−1.07929	+	1.07929i	−0.0827165	+	0.996573i	$0.526360\pi$
$53$	−7.85735	+	7.85735i	−1.07929	+	1.07929i	−0.996573	+	0.0827165i	$0.973640\pi$
$54$	−4.19443	+	6.00189i	−0.570789	+	0.816754i
$55$			3.46599i			0.467354i
$56$		0			0
$57$			9.68145i			1.28234i
$58$	−0.343486	−	0.240046i	−0.0451020	−	0.0315196i
$59$	−3.83007	+	3.83007i	−0.498633	+	0.498633i	−0.911012	−	0.412379i	$-0.864698\pi$
$59$	−3.83007	+	3.83007i	−0.498633	+	0.498633i	0.412379	+	0.911012i	$0.364698\pi$
$60$	−0.904334	−	2.47063i	−0.116749	−	0.318957i
$61$	4.28096	−	4.28096i	0.548121	−	0.548121i	−0.377776	−	0.925897i	$-0.623311\pi$
$61$	4.28096	−	4.28096i	0.548121	−	0.548121i	0.925897	+	0.377776i	$0.123311\pi$
$62$	9.27554	−	1.64424i	1.17799	−	0.208818i
$63$		0			0
$64$	3.96208	−	6.94996i	0.495261	−	0.868745i
$65$	3.09883			0.384363
$66$	−1.96493	−	11.0846i	−0.241866	−	1.36443i
$67$	−6.76419	+	6.76419i	−0.826377	+	0.826377i	−0.987014	−	0.160636i	$-0.948645\pi$
$67$	−6.76419	+	6.76419i	−0.826377	+	0.826377i	0.160636	+	0.987014i	$0.448645\pi$
$68$	1.81328	+	4.95386i	0.219893	+	0.600744i
$69$	2.48621	+	2.48621i	0.299305	+	0.299305i
$70$		0			0
$71$	−7.25507			−0.861018			−0.430509	−	0.902586i	$-0.641666\pi$
$71$	−7.25507			−0.861018			−0.430509	+	0.902586i	$0.641666\pi$
$72$	0.0301112	+	0.0518266i	0.00354864	+	0.00610782i
$73$	6.59265			0.771612			0.385806	−	0.922580i	$-0.373923\pi$
$73$	6.59265			0.771612			0.385806	+	0.922580i	$0.373923\pi$
$74$	3.20530	−	4.58652i	0.372608	−	0.533173i
$75$	−5.44134	+	5.44134i	−0.628312	+	0.628312i
$76$	−10.1047	−	4.68953i	−1.15909	−	0.537926i
$77$		0			0
$78$	−9.91044	+	1.75679i	−1.12214	+	0.198917i
$79$			15.0822i			1.69687i	0.529296	+	0.848437i	$0.322456\pi$
$79$			15.0822i			1.69687i	−0.529296	+	0.848437i	$0.677544\pi$
$80$	3.01669	+	0.252857i	0.337276	+	0.0282702i
$81$	9.06313			1.00701
$82$	7.02479	−	1.24526i	0.775759	−	0.137516i
$83$	8.00548	+	8.00548i	0.878715	+	0.878715i	0.993402	−	0.114687i	$-0.0365864\pi$
$83$	8.00548	+	8.00548i	0.878715	+	0.878715i	−0.114687	+	0.993402i	$0.536586\pi$
$84$		0			0
$85$	−1.41154	+	1.41154i	−0.153103	+	0.153103i
$86$	−6.22057	−	4.34725i	−0.670781	−	0.468776i
$87$			0.515042i			0.0552183i
$88$	12.5211	+	3.31837i	1.33475	+	0.353739i
$89$	7.85072			0.832174			0.416087	−	0.909325i	$-0.363401\pi$
$89$	7.85072			0.832174			0.416087	+	0.909325i	$0.363401\pi$
$90$	−0.0129926	+	0.0185914i	−0.00136954	+	0.00195970i
$91$		0			0
$92$	−3.79919	+	1.39063i	−0.396093	+	0.144984i
$93$	−8.18685	−	8.18685i	−0.848936	−	0.848936i
$94$	−7.07372	+	1.25393i	−0.729598	+	0.129333i
$95$		−	4.21543i		−	0.432494i
$96$	−9.79108	+	0.901551i	−0.999298	+	0.0920142i
$97$			8.79532i			0.893029i	0.894776	+	0.446514i	$0.147335\pi$
$97$			8.79532i			0.893029i	−0.894776	+	0.446514i	$0.852665\pi$
$98$		0			0
$99$	−0.0686254	+	0.0686254i	−0.00689712	+	0.00689712i
$100$	−3.04355	−	8.31494i	−0.304355	−	0.831494i
$101$	−1.63115	−	1.63115i	−0.162305	−	0.162305i	0.621282	−	0.783587i	$-0.286612\pi$
$101$	−1.63115	−	1.63115i	−0.162305	−	0.162305i	−0.783587	+	0.621282i	$0.786612\pi$
$102$	3.71404	−	5.31449i	0.367745	−	0.526213i
$103$			13.6263i			1.34264i	0.741168	+	0.671319i	$0.234272\pi$
$103$			13.6263i			1.34264i	−0.741168	+	0.671319i	$0.765728\pi$
$104$	2.96685	−	11.1947i	0.290924	−	1.09773i
$105$		0			0
$106$	−9.00185	+	12.8809i	−0.874337	+	1.25111i
$107$	−3.34081	−	3.34081i	−0.322968	−	0.322968i	0.526937	−	0.849905i	$-0.323341\pi$
$107$	−3.34081	−	3.34081i	−0.322968	−	0.322968i	−0.849905	+	0.526937i	$0.823341\pi$
$108$	−4.35923	+	9.39302i	−0.419467	+	0.903844i
$109$	−5.82662	−	5.82662i	−0.558089	−	0.558089i	0.370674	−	0.928763i	$-0.379127\pi$
$109$	−5.82662	−	5.82662i	−0.558089	−	0.558089i	−0.928763	+	0.370674i	$0.879127\pi$
$110$	0.855558	+	4.82640i	0.0815743	+	0.460180i
$111$	−6.87728			−0.652763
$112$		0			0
$113$	18.4851			1.73893			0.869467	−	0.493990i	$-0.164462\pi$
$113$	18.4851			1.73893			0.869467	+	0.493990i	$0.164462\pi$
$114$	2.38981	+	13.4815i	0.223826	+	1.26265i
$115$	−1.08253	−	1.08253i	−0.100946	−	0.100946i
$116$	−0.537560	−	0.249477i	−0.0499112	−	0.0231634i
$117$	0.0613559	+	0.0613559i	0.00567236	+	0.00567236i
$118$	−4.38796	+	6.27882i	−0.403945	+	0.578012i
$119$		0			0
$120$	−1.86915	−	3.21713i	−0.170629	−	0.293682i
$121$			9.97357i			0.906688i
$122$	4.90453	−	7.01799i	0.444035	−	0.635379i
$123$	−6.20028	−	6.20028i	−0.559060	−	0.559060i
$124$	12.5104	−	4.57922i	1.12346	−	0.411226i
$125$	5.04499	−	5.04499i	0.451237	−	0.451237i
$126$		0			0
$127$		−	13.0667i		−	1.15948i	−0.814802	−	0.579739i	$-0.803154\pi$
$127$		−	13.0667i		−	1.15948i	0.814802	−	0.579739i	$-0.196846\pi$
$128$	3.80166	−	10.6559i	0.336023	−	0.941854i
$129$			9.32745i			0.821236i
$130$	4.31514	−	0.764928i	0.378463	−	0.0670886i
$131$	−6.07560	−	6.07560i	−0.530828	−	0.530828i	0.389991	−	0.920819i	$-0.372478\pi$
$131$	−6.07560	−	6.07560i	−0.530828	−	0.530828i	−0.920819	+	0.389991i	$0.872478\pi$
$132$	−5.47235	−	14.9504i	−0.476307	−	1.30126i
$133$		0			0
$134$	−7.74946	+	11.0889i	−0.669452	+	0.957932i
$135$	−3.91853			−0.337253
$136$	3.74783	+	6.45067i	0.321374	+	0.553141i
$137$			23.0868i			1.97244i	0.165434	+	0.986221i	$0.447098\pi$
$137$			23.0868i			1.97244i	−0.165434	+	0.986221i	$0.552902\pi$
$138$	4.07577	+	2.84835i	0.346952	+	0.242468i
$139$	−6.09369	+	6.09369i	−0.516860	+	0.516860i	−0.916620	−	0.399760i	$-0.869093\pi$
$139$	−6.09369	+	6.09369i	−0.516860	+	0.516860i	0.399760	+	0.916620i	$0.369093\pi$
$140$		0			0
$141$	6.24346	+	6.24346i	0.525794	+	0.525794i
$142$	−10.1027	+	1.79087i	−0.847801	+	0.150286i
$143$	18.7518			1.56811
$144$	0.0547230	+	0.0647360i	0.00456025	+	0.00539466i
$145$		−	0.224256i		−	0.0186235i
$146$	9.18030	−	1.62736i	0.759767	−	0.134681i
$147$		0			0
$148$	3.33124	−	7.17796i	0.273826	−	0.590025i
$149$	−8.54257	+	8.54257i	−0.699835	+	0.699835i	−0.964375	−	0.264540i	$-0.914780\pi$
$149$	−8.54257	+	8.54257i	−0.699835	+	0.699835i	0.264540	+	0.964375i	$0.414780\pi$
$150$	−6.23393	+	8.92025i	−0.508998	+	0.728336i
$151$	1.62736			0.132433			0.0662165	−	0.997805i	$-0.478907\pi$
$151$	1.62736			0.132433			0.0662165	+	0.997805i	$0.478907\pi$
$152$	−15.2285	−	4.03589i	−1.23519	−	0.327354i
$153$	−0.0558960			−0.00451892
$154$		0			0
$155$	3.56466	+	3.56466i	0.286321	+	0.286321i
$156$	−13.3667	+	4.89266i	−1.07019	+	0.391727i
$157$	−17.0092	+	17.0092i	−1.35748	+	1.35748i	−0.480468	+	0.877012i	$0.659533\pi$
$157$	−17.0092	+	17.0092i	−1.35748	+	1.35748i	−0.877012	+	0.480468i	$0.840467\pi$
$158$	3.72294	+	21.0020i	0.296181	+	1.67083i
$159$	19.3143			1.53173
$160$	4.26317	−	0.392548i	0.337033	−	0.0310336i
$161$		0			0
$162$	12.6204	−	2.23718i	0.991556	−	0.175769i
$163$	6.44786	−	6.44786i	0.505035	−	0.505035i	−0.407963	−	0.912998i	$-0.633761\pi$
$163$	6.44786	−	6.44786i	0.505035	−	0.505035i	0.912998	+	0.407963i	$0.133761\pi$
$164$	9.47467	−	3.46805i	0.739847	−	0.270809i
$165$	4.25992	−	4.25992i	0.331634	−	0.331634i
$166$	13.1238	+	9.17156i	1.01860	+	0.711851i
$167$			3.18749i			0.246656i	0.992366	+	0.123328i	$0.0393566\pi$
$167$			3.18749i			0.246656i	−0.992366	+	0.123328i	$0.960643\pi$
$168$		0			0
$169$		−	3.76544i		−	0.289649i
$170$	−1.61714	+	2.31400i	−0.124029	+	0.177476i
$171$	0.0834642	−	0.0834642i	0.00638266	−	0.00638266i
$172$	−9.73526	−	4.51806i	−0.742307	−	0.344499i
$173$	−13.6245	+	13.6245i	−1.03585	+	1.03585i	−0.0365212	+	0.999333i	$0.511628\pi$
$173$	−13.6245	+	13.6245i	−1.03585	+	1.03585i	−0.999333	+	0.0365212i	$0.988372\pi$
$174$	0.127135	+	0.717198i	0.00963807	+	0.0543706i
$175$		0			0
$176$	18.2547	+	1.53010i	1.37600	+	0.115336i
$177$	9.41480			0.707660
$178$	10.9322	−	1.93790i	0.819400	−	0.145252i
$179$	5.14697	−	5.14697i	0.384703	−	0.384703i	−0.488090	−	0.872793i	$-0.662306\pi$
$179$	5.14697	−	5.14697i	0.384703	−	0.384703i	0.872793	+	0.488090i	$0.162306\pi$
$180$	−0.0135031	+	0.0290957i	−0.00100646	+	0.00216866i
$181$	−5.59617	−	5.59617i	−0.415960	−	0.415960i	0.467849	−	0.883809i	$-0.345029\pi$
$181$	−5.59617	−	5.59617i	−0.415960	−	0.415960i	−0.883809	+	0.467849i	$0.845029\pi$
$182$		0			0
$183$	−10.5231			−0.777894
$184$	−4.94712	+	2.87427i	−0.364706	+	0.211894i
$185$	2.99446			0.220157
$186$	−13.4211	−	9.37935i	−0.984082	−	0.687727i
$187$	−8.54157	+	8.54157i	−0.624622	+	0.624622i
$188$	−9.54065	+	3.49221i	−0.695824	+	0.254695i
$189$		0			0
$190$	−1.04055	−	5.87001i	−0.0754897	−	0.425855i
$191$		−	4.76585i		−	0.344845i	−0.985023	−	0.172422i	$-0.944841\pi$
$191$		−	4.76585i		−	0.344845i	0.985023	−	0.172422i	$-0.0551594\pi$
$192$	−13.4116	+	3.67228i	−0.967898	+	0.265024i
$193$	−5.34099			−0.384453			−0.192226	−	0.981351i	$-0.561571\pi$
$193$	−5.34099			−0.384453			−0.192226	+	0.981351i	$0.561571\pi$
$194$	2.17107	+	12.2475i	0.155874	+	0.879320i
$195$	−3.80866	−	3.80866i	−0.272744	−	0.272744i
$196$		0			0
$197$	−11.6754	+	11.6754i	−0.831838	+	0.831838i	−0.987768	−	0.155930i	$-0.950163\pi$
$197$	−11.6754	+	11.6754i	−0.831838	+	0.831838i	0.155930	+	0.987768i	$0.450163\pi$
$198$	−0.0786215	+	0.112501i	−0.00558738	+	0.00799510i
$199$			10.4260i			0.739080i	0.929215	+	0.369540i	$0.120485\pi$
$199$			10.4260i			0.739080i	−0.929215	+	0.369540i	$0.879515\pi$
$200$	−6.29065	−	10.8273i	−0.444816	−	0.765606i
$201$	16.6272			1.17279
$202$	−2.67402	−	1.86874i	−0.188143	−	0.131484i
$203$		0			0
$204$	3.85997	−	8.31724i	0.270252	−	0.582324i
$205$	2.69968	+	2.69968i	0.188554	+	0.188554i
$206$	3.36357	+	18.9747i	0.234351	+	1.32203i
$207$		−	0.0428675i		−	0.00297950i
$208$	1.36801	−	16.3210i	0.0948547	−	1.13166i
$209$		−	25.5086i		−	1.76447i
$210$		0			0
$211$	−0.716512	+	0.716512i	−0.0493267	+	0.0493267i	−0.731340	−	0.682013i	$-0.761105\pi$
$211$	−0.716512	+	0.716512i	−0.0493267	+	0.0493267i	0.682013	+	0.731340i	$0.261105\pi$
$212$	−9.35554	+	20.1588i	−0.642541	+	1.38451i
$213$	8.91694	+	8.91694i	0.610979	+	0.610979i
$214$	−5.47675	−	3.82743i	−0.374383	−	0.261638i
$215$		−	4.06130i		−	0.276978i
$216$	−3.75163	+	14.1559i	−0.255266	+	0.963185i
$217$		0			0
$218$	−9.55186	−	6.67533i	−0.646933	−	0.452110i
$219$	−8.10278	−	8.10278i	−0.547535	−	0.547535i
$220$	2.38274	+	6.50960i	0.160644	+	0.438877i
$221$	7.63676	+	7.63676i	0.513704	+	0.513704i
$222$	−9.57664	+	1.69761i	−0.642742	+	0.113936i
$223$	−12.9181			−0.865062			−0.432531	−	0.901619i	$-0.642379\pi$
$223$	−12.9181			−0.865062			−0.432531	+	0.901619i	$0.642379\pi$
$224$		0			0
$225$	0.0938201			0.00625467
$226$	25.7406	−	4.56294i	1.71224	−	0.303522i
$227$	−10.9984	−	10.9984i	−0.729990	−	0.729990i	0.240628	−	0.970617i	$-0.422647\pi$
$227$	−10.9984	−	10.9984i	−0.729990	−	0.729990i	−0.970617	+	0.240628i	$0.922647\pi$
$228$	6.65563	+	18.1831i	0.440780	+	1.20420i
$229$	−9.79182	−	9.79182i	−0.647062	−	0.647062i	0.305220	−	0.952282i	$-0.401270\pi$
$229$	−9.79182	−	9.79182i	−0.647062	−	0.647062i	−0.952282	+	0.305220i	$0.901270\pi$
$230$	−1.77464	−	1.24021i	−0.117017	−	0.0817771i
$231$		0			0
$232$	−0.810136	−	0.214705i	−0.0531881	−	0.0140961i
$233$			12.3002i			0.805812i	0.915241	+	0.402906i	$0.132000\pi$
$233$			12.3002i			0.805812i	−0.915241	+	0.402906i	$0.868000\pi$
$234$	0.100584	+	0.0702930i	0.00657536	+	0.00459520i
$235$	−2.71849	−	2.71849i	−0.177334	−	0.177334i
$236$	−4.56037	+	9.82643i	−0.296855	+	0.639646i
$237$	18.5369	−	18.5369i	1.20410	−	1.20410i
$238$		0			0
$239$			7.20218i			0.465870i	0.972492	+	0.232935i	$0.0748329\pi$
$239$			7.20218i			0.465870i	−0.972492	+	0.232935i	$0.925167\pi$
$240$	−3.39693	−	4.01848i	−0.219271	−	0.259392i
$241$		−	23.9465i		−	1.54253i	−0.636514	−	0.771265i	$-0.719624\pi$
$241$		−	23.9465i		−	1.54253i	0.636514	−	0.771265i	$-0.280376\pi$
$242$	2.46191	+	13.8882i	0.158258	+	0.892770i
$243$	−0.155723	−	0.155723i	−0.00998964	−	0.00998964i
$244$	5.09723	−	10.9832i	0.326317	−	0.703130i
$245$		0			0
$246$	−10.1644	−	7.10341i	−0.648059	−	0.452897i
$247$	−22.8065			−1.45114
$248$	16.2904	−	9.46468i	1.03444	−	0.601008i
$249$		−	19.6785i		−	1.24707i
$250$	5.77984	−	8.27049i	0.365549	−	0.523072i
$251$	6.11266	−	6.11266i	0.385828	−	0.385828i	−0.487369	−	0.873196i	$-0.662043\pi$
$251$	6.11266	−	6.11266i	0.385828	−	0.385828i	0.873196	+	0.487369i	$0.162043\pi$
$252$		0			0
$253$	−6.55066	−	6.55066i	−0.411837	−	0.411837i
$254$	−3.22543	−	18.1954i	−0.202381	−	1.14168i
$255$	3.46974			0.217283
$256$	2.66350	−	15.7767i	0.166469	−	0.986047i
$257$		−	22.7840i		−	1.42123i	−0.703583	−	0.710613i	$-0.748418\pi$
$257$		−	22.7840i		−	1.42123i	0.703583	−	0.710613i	$-0.251582\pi$
$258$	2.30242	+	12.9885i	0.143343	+	0.808630i
$259$		0			0
$260$	5.82003	−	2.13033i	0.360943	−	0.132118i
$261$	0.00444020	−	0.00444020i	0.000274841	−	0.000274841i
$262$	−9.96002	−	6.96057i	−0.615332	−	0.430026i
$263$	10.5758			0.652130			0.326065	−	0.945347i	$-0.394277\pi$
$263$	10.5758			0.652130			0.326065	+	0.945347i	$0.394277\pi$
$264$	−11.3107	−	19.4677i	−0.696125	−	1.19815i
$265$	−8.40973			−0.516605
$266$		0			0
$267$	−9.64903	−	9.64903i	−0.590511	−	0.590511i
$268$	−8.05394	+	17.3542i	−0.491973	+	1.06008i
$269$	7.32471	−	7.32471i	0.446595	−	0.446595i	−0.447626	−	0.894221i	$-0.647730\pi$
$269$	7.32471	−	7.32471i	0.446595	−	0.446595i	0.894221	+	0.447626i	$0.147730\pi$
$270$	−5.45656	+	0.967264i	−0.332076	+	0.0588658i
$271$	24.6645			1.49826			0.749131	−	0.662422i	$-0.230471\pi$
$271$	24.6645			1.49826			0.749131	+	0.662422i	$0.230471\pi$
$272$	6.81118	+	8.05746i	0.412989	+	0.488555i
$273$		0			0
$274$	5.69884	+	32.1485i	0.344280	+	1.94216i
$275$	14.3368	−	14.3368i	0.864543	−	0.864543i
$276$	6.37862	+	2.96027i	0.383948	+	0.178187i
$277$	7.58476	−	7.58476i	0.455724	−	0.455724i	−0.441525	−	0.897249i	$-0.645562\pi$
$277$	7.58476	−	7.58476i	0.455724	−	0.455724i	0.897249	+	0.441525i	$0.145562\pi$
$278$	−6.98130	+	9.98968i	−0.418710	+	0.599141i
$279$			0.141158i			0.00845093i
$280$		0			0
$281$		−	6.46396i		−	0.385608i	−0.981237	−	0.192804i	$-0.938242\pi$
$281$		−	6.46396i		−	0.385608i	0.981237	−	0.192804i	$-0.0617581\pi$
$282$	10.2352	+	7.15288i	0.609497	+	0.425948i
$283$	13.9329	−	13.9329i	0.828224	−	0.828224i	−0.159047	−	0.987271i	$-0.550842\pi$
$283$	13.9329	−	13.9329i	0.828224	−	0.828224i	0.987271	+	0.159047i	$0.0508421\pi$
$284$	−13.6260	+	4.98759i	−0.808555	+	0.295959i
$285$	−5.18103	+	5.18103i	−0.306898	+	0.306898i
$286$	26.1120	−	4.62877i	1.54403	−	0.273705i
$287$		0			0
$288$	0.0921817	+	0.0766371i	0.00543186	+	0.00451588i
$289$	10.0428			0.590754
$290$	−0.0553562	−	0.312277i	−0.00325063	−	0.0183376i
$291$	10.8100	−	10.8100i	0.633693	−	0.633693i
$292$	12.3819	−	4.53220i	0.724596	−	0.265227i
$293$	−2.96394	−	2.96394i	−0.173155	−	0.173155i	0.615209	−	0.788364i	$-0.289072\pi$
$293$	−2.96394	−	2.96394i	−0.173155	−	0.173155i	−0.788364	+	0.615209i	$0.789072\pi$
$294$		0			0
$295$	−4.09933			−0.238672
$296$	2.86692	−	10.8176i	0.166637	−	0.628763i
$297$	−23.7120			−1.37591
$298$	−9.78689	+	14.0042i	−0.566939	+	0.811244i
$299$	−5.85675	+	5.85675i	−0.338704	+	0.338704i
$300$	−6.47886	+	13.9603i	−0.374057	+	0.805998i
$301$		0			0
$302$	2.26611	−	0.401705i	0.130400	−	0.0231155i
$303$			4.00957i			0.230344i
$304$	−22.2019	−	1.86095i	−1.27337	−	0.106733i
$305$	4.58192			0.262360
$306$	−0.0778354	+	0.0137976i	−0.00444955	+	0.000788755i
$307$	−8.60981	−	8.60981i	−0.491388	−	0.491388i	0.417356	−	0.908743i	$-0.362957\pi$
$307$	−8.60981	−	8.60981i	−0.491388	−	0.491388i	−0.908743	+	0.417356i	$0.862957\pi$
$308$		0			0
$309$	16.7476	−	16.7476i	0.952736	−	0.952736i
$310$	5.84372	+	4.08389i	0.331901	+	0.231950i
$311$		−	5.76192i		−	0.326728i	−0.986566	−	0.163364i	$-0.947765\pi$
$311$		−	5.76192i		−	0.326728i	0.986566	−	0.163364i	$-0.0522346\pi$
$312$	−17.4054	+	10.1125i	−0.985389	+	0.572510i
$313$	−8.03237			−0.454016			−0.227008	−	0.973893i	$-0.572894\pi$
$313$	−8.03237			−0.454016			−0.227008	+	0.973893i	$0.572894\pi$
$314$	−19.4867	+	27.8840i	−1.09970	+	1.57358i
$315$		0			0
$316$	10.3684	+	28.3263i	0.583269	+	1.59348i
$317$	−6.59717	−	6.59717i	−0.370534	−	0.370534i	0.497138	−	0.867672i	$-0.334384\pi$
$317$	−6.59717	−	6.59717i	−0.370534	−	0.370534i	−0.867672	+	0.497138i	$0.834384\pi$
$318$	26.8953	−	4.76763i	1.50821	−	0.267355i
$319$		−	1.35703i		−	0.0759791i
$320$	5.83958	−	1.59896i	0.326443	−	0.0893847i
$321$			8.21213i			0.458356i
$322$		0			0
$323$	10.3885	−	10.3885i	0.578031	−	0.578031i
$324$	17.0218	−	6.23056i	0.945655	−	0.346142i
$325$	−12.8181	−	12.8181i	−0.711021	−	0.711021i
$326$	7.38706	−	10.5703i	0.409131	−	0.585434i
$327$			14.3226i			0.792040i
$328$	12.3374	−	7.16804i	0.681222	−	0.395789i
$329$		0			0
$330$	4.88042	−	6.98349i	0.268658	−	0.384428i
$331$	−3.63131	−	3.63131i	−0.199595	−	0.199595i	0.600231	−	0.799826i	$-0.295075\pi$
$331$	−3.63131	−	3.63131i	−0.199595	−	0.199595i	−0.799826	+	0.600231i	$0.795075\pi$
$332$	20.5388	+	9.53191i	1.12722	+	0.523132i
$333$	0.0592893	+	0.0592893i	0.00324904	+	0.00324904i
$334$	0.786813	+	4.43860i	0.0430525	+	0.242869i
$335$	−7.23972			−0.395548
$336$		0			0
$337$	1.50446			0.0819532			0.0409766	−	0.999160i	$-0.486953\pi$
$337$	1.50446			0.0819532			0.0409766	+	0.999160i	$0.486953\pi$
$338$	−0.929475	−	5.24339i	−0.0505568	−	0.285203i
$339$	−22.7194	−	22.7194i	−1.23395	−	1.23395i
$340$	−1.68068	+	3.62144i	−0.0911478	+	0.196400i
$341$	21.5707	+	21.5707i	1.16812	+	1.16812i
$342$	0.0956216	−	0.136827i	0.00517062	−	0.00739875i
$343$		0			0
$344$	−14.6716	−	3.88833i	−0.791042	−	0.209644i
$345$			2.66100i			0.143263i
$346$	−15.6091	+	22.3354i	−0.839150	+	1.20076i
$347$	6.14205	+	6.14205i	0.329723	+	0.329723i	0.852481	−	0.522758i	$-0.175097\pi$
$347$	6.14205	+	6.14205i	0.329723	+	0.329723i	−0.522758	+	0.852481i	$0.675097\pi$
$348$	0.354072	+	0.967318i	0.0189802	+	0.0518537i
$349$	−15.6677	+	15.6677i	−0.838672	+	0.838672i	−0.988684	−	0.150012i	$-0.952069\pi$
$349$	−15.6677	+	15.6677i	−0.838672	+	0.838672i	0.150012	+	0.988684i	$0.452069\pi$
$350$		0			0
$351$			21.2002i			1.13158i
$352$	25.7975	−	2.37540i	1.37501	−	0.126609i
$353$		−	24.8767i		−	1.32405i	−0.749480	−	0.662027i	$-0.769697\pi$
$353$		−	24.8767i		−	1.32405i	0.749480	−	0.662027i	$-0.230303\pi$
$354$	13.1101	−	2.32399i	0.696796	−	0.123518i
$355$	−3.88255	−	3.88255i	−0.206065	−	0.206065i
$356$	14.7447	−	5.39707i	0.781468	−	0.286044i
$357$		0			0
$358$	5.89668	−	8.43768i	0.311649	−	0.445945i
$359$	8.65728			0.456914			0.228457	−	0.973554i	$-0.426632\pi$
$359$	8.65728			0.456914			0.228457	+	0.973554i	$0.426632\pi$
$360$	−0.0116210	+	0.0438490i	−0.000612481	+	0.00231105i
$361$			12.0243i			0.632859i
$362$	−9.17407	−	6.41131i	−0.482179	−	0.336971i
$363$	12.2581	−	12.2581i	0.643386	−	0.643386i
$364$		0			0
$365$	3.52806	+	3.52806i	0.184667	+	0.184667i
$366$	−14.6535	+	2.59757i	−0.765952	+	0.135777i
$367$	−23.9341			−1.24935			−0.624676	−	0.780884i	$-0.714769\pi$
$367$	−23.9341			−1.24935			−0.624676	+	0.780884i	$0.714769\pi$
$368$	−6.17939	+	5.22360i	−0.322123	+	0.272299i
$369$			0.106906i			0.00556529i
$370$	4.16980	−	0.739164i	0.216778	−	0.0384273i
$371$		0			0
$372$	−21.0042	−	9.74787i	−1.08901	−	0.505403i
$373$	1.67321	−	1.67321i	0.0866353	−	0.0866353i	−0.662461	−	0.749096i	$-0.730488\pi$
$373$	1.67321	−	1.67321i	0.0866353	−	0.0866353i	0.749096	+	0.662461i	$0.230488\pi$
$374$	−9.78574	+	14.0026i	−0.506009	+	0.724058i
$375$	−12.4012			−0.640396
$376$	−12.4234	+	7.21796i	−0.640687	+	0.372238i
$377$	−1.21328			−0.0624870
$378$		0			0
$379$	−5.34619	−	5.34619i	−0.274615	−	0.274615i	0.556340	−	0.830955i	$-0.312205\pi$
$379$	−5.34619	−	5.34619i	−0.274615	−	0.274615i	−0.830955	+	0.556340i	$0.812205\pi$
$380$	−2.89795	−	7.91716i	−0.148662	−	0.406142i
$381$	−16.0598	+	16.0598i	−0.822766	+	0.822766i
$382$	−1.17642	−	6.63647i	−0.0601909	−	0.339551i
$383$	−25.1400			−1.28459			−0.642296	−	0.766457i	$-0.722018\pi$
$383$	−25.1400			−1.28459			−0.642296	+	0.766457i	$0.722018\pi$
$384$	−17.7692	+	8.42424i	−0.906781	+	0.429898i
$385$		0			0
$386$	−7.43735	+	1.31839i	−0.378551	+	0.0671043i
$387$	0.0804124	−	0.0804124i	0.00408759	−	0.00408759i
$388$	6.04645	+	16.5188i	0.306962	+	0.838615i
$389$	4.45094	−	4.45094i	0.225672	−	0.225672i	−0.585210	−	0.810882i	$-0.698988\pi$
$389$	4.45094	−	4.45094i	0.225672	−	0.225672i	0.810882	+	0.585210i	$0.198988\pi$
$390$	−6.24372	−	4.36343i	−0.316163	−	0.220951i
$391$		−	5.33557i		−	0.269831i
$392$		0			0
$393$			14.9346i			0.753350i
$394$	−13.3761	+	19.1401i	−0.673876	+	0.964262i
$395$	−8.07122	+	8.07122i	−0.406107	+	0.406107i
$396$	−0.0817105	+	0.176065i	−0.00410611	+	0.00884762i
$397$	−12.7682	+	12.7682i	−0.640816	+	0.640816i	−0.950756	−	0.309940i	$-0.899691\pi$
$397$	−12.7682	+	12.7682i	−0.640816	+	0.640816i	0.309940	+	0.950756i	$0.399691\pi$
$398$	2.57360	+	14.5183i	0.129003	+	0.727735i
$399$		0			0
$400$	−11.4324	−	13.5243i	−0.571620	−	0.676213i
$401$	15.7766			0.787848			0.393924	−	0.919143i	$-0.371117\pi$
$401$	15.7766			0.787848			0.393924	+	0.919143i	$0.371117\pi$
$402$	23.1535	−	4.10433i	1.15479	−	0.204705i
$403$	19.2857	−	19.2857i	0.960688	−	0.960688i
$404$	−4.18487	−	1.94217i	−0.208205	−	0.0966264i
$405$	4.85014	+	4.85014i	0.241005	+	0.241005i
$406$		0			0
$407$	18.1202			0.898186
$408$	3.32196	−	12.5346i	0.164462	−	0.620556i
$409$	29.9701			1.48193			0.740963	−	0.671546i	$-0.234370\pi$
$409$	29.9701			1.48193			0.740963	+	0.671546i	$0.234370\pi$
$410$	4.42572	+	3.09292i	0.218571	+	0.152748i
$411$	28.3752	−	28.3752i	1.39964	−	1.39964i
$412$	9.36756	+	25.5920i	0.461507	+	1.26083i
$413$		0			0
$414$	−0.0105816	−	0.0596931i	−0.000520056	−	0.00293376i
$415$			8.56827i			0.420600i
$416$	−2.12378	−	23.0648i	−0.104127	−	1.13084i
$417$	14.9791			0.733527
$418$	−6.29665	−	35.5209i	−0.307979	−	1.73738i
$419$	19.0681	+	19.0681i	0.931537	+	0.931537i	0.997802	−	0.0662653i	$-0.0211084\pi$
$419$	19.0681	+	19.0681i	0.931537	+	0.931537i	−0.0662653	+	0.997802i	$0.521108\pi$
$420$		0			0
$421$	1.12116	−	1.12116i	0.0546418	−	0.0546418i	−0.679258	−	0.733900i	$-0.737698\pi$
$421$	1.12116	−	1.12116i	0.0546418	−	0.0546418i	0.733900	+	0.679258i	$0.237698\pi$
$422$	−0.820880	+	1.17461i	−0.0399598	+	0.0571793i
$423$		−	0.107650i		−	0.00523413i
$424$	−8.05155	+	30.3806i	−0.391018	+	1.47541i
$425$	11.6775			0.566440
$426$	14.6180	+	10.2158i	0.708243	+	0.494956i
$427$		0			0
$428$	−8.57117	−	3.97781i	−0.414303	−	0.192275i
$429$	−23.0472	−	23.0472i	−1.11273	−	1.11273i
$430$	−1.00251	−	5.65537i	−0.0483452	−	0.272726i
$431$			16.4410i			0.791933i	0.918265	+	0.395966i	$0.129590\pi$
$431$			16.4410i			0.791933i	−0.918265	+	0.395966i	$0.870410\pi$
$432$	−1.72988	+	20.6382i	−0.0832287	+	0.992955i
$433$			34.3709i			1.65176i	0.563847	+	0.825879i	$0.309321\pi$
$433$			34.3709i			1.65176i	−0.563847	+	0.825879i	$0.690679\pi$
$434$		0			0
$435$	−0.275625	+	0.275625i	−0.0132152	+	0.0132152i
$436$	−14.9488	−	6.93760i	−0.715916	−	0.332251i
$437$	7.96710	+	7.96710i	0.381118	+	0.381118i
$438$	−13.2833	−	9.28304i	−0.634700	−	0.443561i
$439$			9.66830i			0.461443i	0.973020	+	0.230721i	$0.0741086\pi$
$439$			9.66830i			0.461443i	−0.973020	+	0.230721i	$0.925891\pi$
$440$	4.92482	+	8.47648i	0.234782	+	0.404100i
$441$		0			0
$442$	12.5193	+	8.74913i	0.595483	+	0.416154i
$443$	24.5950	+	24.5950i	1.16854	+	1.16854i	0.982551	+	0.185992i	$0.0595499\pi$
$443$	24.5950	+	24.5950i	1.16854	+	1.16854i	0.185992	+	0.982551i	$0.440450\pi$
$444$	−12.9165	+	4.72787i	−0.612988	+	0.224375i
$445$	4.20132	+	4.20132i	0.199161	+	0.199161i
$446$	−17.9886	+	3.18876i	−0.851783	+	0.150992i
$447$	20.9987			0.993205
$448$		0			0
$449$	−35.5072			−1.67569			−0.837844	−	0.545910i	$-0.816184\pi$
$449$	−35.5072			−1.67569			−0.837844	+	0.545910i	$0.816184\pi$
$450$	0.130645	−	0.0231589i	0.00615866	−	0.00109172i
$451$	16.3365	+	16.3365i	0.769254	+	0.769254i
$452$	34.7176	−	12.7078i	1.63298	−	0.597726i
$453$	−2.00013	−	2.00013i	−0.0939745	−	0.0939745i
$454$	−18.0302	−	12.6004i	−0.846200	−	0.591368i
$455$		0			0
$456$	13.7564	+	23.6771i	0.644201	+	1.10878i
$457$		−	30.1215i		−	1.40902i	−0.709692	−	0.704512i	$-0.751166\pi$
$457$		−	30.1215i		−	1.40902i	0.709692	−	0.704512i	$-0.248834\pi$
$458$	−16.0522	−	11.2181i	−0.750070	−	0.524188i
$459$	−9.65680	−	9.65680i	−0.450741	−	0.450741i
$460$	−2.77734	−	1.28894i	−0.129494	−	0.0600972i
$461$	−2.37946	+	2.37946i	−0.110822	+	0.110822i	−0.760344	−	0.649521i	$-0.774969\pi$
$461$	−2.37946	+	2.37946i	−0.110822	+	0.110822i	0.649521	+	0.760344i	$0.274969\pi$
$462$		0			0
$463$			1.23324i			0.0573136i	0.999589	+	0.0286568i	$0.00912299\pi$
$463$			1.23324i			0.0573136i	−0.999589	+	0.0286568i	$0.990877\pi$
$464$	−1.18112	−	0.0990003i	−0.0548320	−	0.00459597i
$465$		−	8.76239i		−	0.406346i
$466$	3.03623	+	17.1281i	0.140651	+	0.793443i
$467$	−22.5465	−	22.5465i	−1.04333	−	1.04333i	−0.999018	−	0.0443082i	$-0.985892\pi$
$467$	−22.5465	−	22.5465i	−1.04333	−	1.04333i	−0.0443082	−	0.999018i	$-0.514108\pi$
$468$	0.157415	+	0.0730549i	0.00727649	+	0.00337696i
$469$		0			0
$470$	−4.45654	−	3.11446i	−0.205565	−	0.143659i
$471$	41.8107			1.92654
$472$	−3.92474	+	14.8090i	−0.180651	+	0.681641i
$473$		−	24.5759i		−	1.13000i
$474$	21.2370	−	30.3885i	0.975448	−	1.39579i
$475$	−17.4368	+	17.4368i	−0.800057	+	0.800057i
$476$		0			0
$477$	−0.166510	−	0.166510i	−0.00762396	−	0.00762396i
$478$	1.77781	+	10.0291i	0.0813153	+	0.458719i
$479$	−13.2922			−0.607337			−0.303668	−	0.952778i	$-0.598211\pi$
$479$	−13.2922			−0.607337			−0.303668	+	0.952778i	$0.598211\pi$
$480$	−5.72217	−	4.75724i	−0.261180	−	0.217137i
$481$		−	16.2007i		−	0.738690i
$482$	−5.91105	−	33.3456i	−0.269241	−	1.51885i
$483$		0			0
$484$	6.85645	+	18.7317i	0.311657	+	0.851442i
$485$	−4.70682	+	4.70682i	−0.213726	+	0.213726i
$486$	−0.255284	−	0.178406i	−0.0115799	−	0.00809265i
$487$	−1.28409			−0.0581876			−0.0290938	−	0.999577i	$-0.509262\pi$
$487$	−1.28409			−0.0581876			−0.0290938	+	0.999577i	$0.509262\pi$
$488$	4.38677	−	16.5524i	0.198580	−	0.749293i
$489$	−15.8497			−0.716746
$490$		0			0
$491$	7.08341	+	7.08341i	0.319670	+	0.319670i	0.848640	−	0.528970i	$-0.177422\pi$
$491$	7.08341	+	7.08341i	0.319670	+	0.319670i	−0.528970	+	0.848640i	$0.677422\pi$
$492$	−15.9074	−	7.38251i	−0.717162	−	0.332829i
$493$	0.552656	−	0.552656i	0.0248904	−	0.0248904i
$494$	−31.7581	+	5.62964i	−1.42887	+	0.253290i
$495$	−0.0734499			−0.00330133
$496$	20.3481	−	17.2008i	0.913657	−	0.772338i
$497$		0			0
$498$	−4.85751	−	27.4023i	−0.217670	−	1.22793i
$499$	16.0586	−	16.0586i	0.718882	−	0.718882i	−0.249494	−	0.968376i	$-0.580264\pi$
$499$	16.0586	−	16.0586i	0.718882	−	0.718882i	0.968376	+	0.249494i	$0.0802643\pi$
$500$	6.00693	−	12.9434i	0.268638	−	0.578847i
$501$	3.91763	−	3.91763i	0.175027	−	0.175027i
$502$	7.00303	−	10.0208i	0.312561	−	0.447249i
$503$		−	36.0928i		−	1.60930i	−0.593751	−	0.804649i	$-0.702354\pi$
$503$		−	36.0928i		−	1.60930i	0.593751	−	0.804649i	$-0.297646\pi$
$504$		0			0
$505$		−	1.74582i		−	0.0776880i
$506$	−10.7388	−	7.50483i	−0.477398	−	0.333631i
$507$	−4.62796	+	4.62796i	−0.205535	+	0.205535i
$508$	−8.98284	−	24.5410i	−0.398549	−	1.08883i
$509$	3.84953	−	3.84953i	0.170627	−	0.170627i	−0.616628	−	0.787255i	$-0.711502\pi$
$509$	3.84953	−	3.84953i	0.170627	−	0.170627i	0.787255	+	0.616628i	$0.211502\pi$
$510$	4.83163	−	0.856484i	0.213948	−	0.0379257i
$511$		0			0
$512$	−0.185456	−	22.6267i	−0.00819607	−	0.999966i
$513$	28.8392			1.27328
$514$	−5.62408	−	31.7268i	−0.248068	−	1.39941i
$515$	−7.29212	+	7.29212i	−0.321329	+	0.321329i
$516$	6.41227	+	17.5182i	0.282284	+	0.771197i
$517$	−16.4502	−	16.4502i	−0.723481	−	0.723481i
$518$		0			0
$519$	33.4908			1.47008
$520$	7.57856	−	4.40314i	0.332342	−	0.193090i
$521$	5.15722			0.225942			0.112971	−	0.993598i	$-0.463963\pi$
$521$	5.15722			0.225942			0.112971	+	0.993598i	$0.463963\pi$
$522$	0.00508696	−	0.00727903i	0.000222650	−	0.000318594i
$523$	−5.43529	+	5.43529i	−0.237669	+	0.237669i	−0.815884	−	0.578215i	$-0.803749\pi$
$523$	−5.43529	+	5.43529i	−0.237669	+	0.237669i	0.578215	+	0.815884i	$0.303749\pi$
$524$	−15.5875	−	7.23406i	−0.680945	−	0.316021i
$525$		0			0
$526$	14.7268	−	2.61056i	0.642119	−	0.113826i
$527$			17.5695i			0.765339i
$528$	−20.5556	−	24.3168i	−0.894570	−	1.05825i
$529$	−18.9081			−0.822090
$530$	−11.7106	+	2.07589i	−0.508675	+	0.0901709i
$531$	−0.0811654	−	0.0811654i	−0.00352228	−	0.00352228i
$532$		0			0
$533$	14.6059	−	14.6059i	0.632653	−	0.632653i
$534$	−15.8181	−	11.0545i	−0.684517	−	0.478375i
$535$		−	3.57567i		−	0.154590i
$536$	−6.93138	+	26.1539i	−0.299390	+	1.12967i
$537$	−12.6519			−0.545970
$538$	8.39163	−	12.0077i	0.361789	−	0.517691i
$539$		0			0
$540$	−7.35952	+	2.69384i	−0.316704	+	0.115924i
$541$	−5.52727	−	5.52727i	−0.237636	−	0.237636i	0.578235	−	0.815871i	$-0.303742\pi$
$541$	−5.52727	−	5.52727i	−0.237636	−	0.237636i	−0.815871	+	0.578235i	$0.803742\pi$
$542$	34.3454	−	6.08828i	1.47526	−	0.261514i
$543$			13.7561i			0.590330i
$544$	11.4735	+	9.53875i	0.491924	+	0.408971i
$545$		−	6.23624i		−	0.267131i
$546$		0			0
$547$	3.45431	−	3.45431i	0.147696	−	0.147696i	−0.629392	−	0.777088i	$-0.716696\pi$
$547$	3.45431	−	3.45431i	0.147696	−	0.147696i	0.777088	+	0.629392i	$0.216696\pi$
$548$	15.8713	+	43.3602i	0.677990	+	1.85226i
$549$	0.0907205	+	0.0907205i	0.00387186	+	0.00387186i
$550$	16.4251	−	23.5030i	0.700370	−	1.00217i
$551$			1.65046i			0.0703118i
$552$	9.61298	+	2.54766i	0.409156	+	0.108436i
$553$		0			0
$554$	8.68956	−	12.4341i	0.369184	−	0.528273i
$555$	−3.68038	−	3.68038i	−0.156223	−	0.156223i
$556$	−7.25560	+	15.6340i	−0.307706	+	0.663027i
$557$	−20.4236	−	20.4236i	−0.865374	−	0.865374i	0.126582	−	0.991956i	$-0.459599\pi$
$557$	−20.4236	−	20.4236i	−0.865374	−	0.865374i	−0.991956	+	0.126582i	$0.959599\pi$
$558$	0.0348441	+	0.196564i	0.00147507	+	0.00832120i
$559$	−21.9726			−0.929342
$560$		0			0
$561$	20.9963			0.886463
$562$	−1.59559	−	9.00109i	−0.0673059	−	0.379688i
$563$	−0.664824	−	0.664824i	−0.0280190	−	0.0280190i	0.692959	−	0.720977i	$-0.256307\pi$
$563$	−0.664824	−	0.664824i	−0.0280190	−	0.0280190i	−0.720977	+	0.692959i	$0.756307\pi$
$564$	16.0182	+	7.43392i	0.674488	+	0.313025i
$565$	9.89233	+	9.89233i	0.416173	+	0.416173i
$566$	15.9624	−	22.8409i	0.670948	−	0.960073i
$567$		0			0
$568$	−17.7431	+	10.3087i	−0.744485	+	0.432545i
$569$			13.2954i			0.557371i	0.960382	+	0.278686i	$0.0898987\pi$
$569$			13.2954i			0.557371i	−0.960382	+	0.278686i	$0.910101\pi$
$570$	−5.93570	+	8.49351i	−0.248619	+	0.355754i
$571$	5.78684	+	5.78684i	0.242172	+	0.242172i	0.817748	−	0.575576i	$-0.195222\pi$
$571$	5.78684	+	5.78684i	0.242172	+	0.242172i	−0.575576	+	0.817748i	$0.695222\pi$
$572$	35.2185	−	12.8912i	1.47256	−	0.539007i
$573$	−5.85753	+	5.85753i	−0.244702	+	0.244702i
$574$		0			0
$575$			8.95562i			0.373475i
$576$	0.147281	+	0.0839629i	0.00613670	+	0.00349846i
$577$		−	26.6018i		−	1.10745i	−0.832701	−	0.553724i	$-0.813206\pi$
$577$		−	26.6018i		−	1.10745i	0.832701	−	0.553724i	$-0.186794\pi$
$578$	13.9847	−	2.47901i	0.581686	−	0.103113i
$579$	6.56441	+	6.56441i	0.272808	+	0.272808i
$580$	−0.154168	−	0.421183i	−0.00640146	−	0.0174887i
$581$		0			0
$582$	12.3846	−	17.7213i	0.513358	−	0.734573i
$583$	−50.8894			−2.10762
$584$	16.1231	−	9.36750i	0.667179	−	0.387630i
$585$			0.0656693i			0.00271509i
$586$	−4.85894	−	3.39567i	−0.200721	−	0.140274i
$587$	9.30074	−	9.30074i	0.383883	−	0.383883i	−0.488616	−	0.872499i	$-0.662498\pi$
$587$	9.30074	−	9.30074i	0.383883	−	0.383883i	0.872499	+	0.488616i	$0.162498\pi$
$588$		0			0
$589$	−26.2349	−	26.2349i	−1.08099	−	1.08099i
$590$	−5.70833	+	1.01189i	−0.235008	+	0.0416590i
$591$	28.6996			1.18054
$592$	1.32194	−	15.7713i	0.0543313	−	0.648196i
$593$			14.1060i			0.579266i	0.957138	+	0.289633i	$0.0935332\pi$
$593$			14.1060i			0.579266i	−0.957138	+	0.289633i	$0.906467\pi$
$594$	−33.0190	+	5.85316i	−1.35479	+	0.240158i
$595$		0			0
$596$	−10.1714	+	21.9168i	−0.416638	+	0.897748i
$597$	12.8142	−	12.8142i	0.524451	−	0.524451i
$598$	−6.70984	+	9.60125i	−0.274386	+	0.392624i
$599$	29.4793			1.20449			0.602247	−	0.798310i	$-0.294272\pi$
$599$	29.4793			1.20449			0.602247	+	0.798310i	$0.294272\pi$
$600$	−5.57583	+	21.0390i	−0.227632	+	0.858915i
$601$	23.6858			0.966164			0.483082	−	0.875575i	$-0.339517\pi$
$601$	23.6858			0.966164			0.483082	+	0.875575i	$0.339517\pi$
$602$		0			0
$603$	−0.143344	−	0.143344i	−0.00583742	−	0.00583742i
$604$	3.05641	−	1.11875i	0.124364	−	0.0455214i
$605$	−5.33736	+	5.33736i	−0.216995	+	0.216995i
$606$	0.989738	+	5.58334i	0.0402053	+	0.226808i
$607$	−5.72600			−0.232411			−0.116206	−	0.993225i	$-0.537073\pi$
$607$	−5.72600			−0.232411			−0.116206	+	0.993225i	$0.537073\pi$
$608$	−31.3757	+	2.88903i	−1.27245	+	0.117166i
$609$		0			0
$610$	6.38034	−	1.13102i	0.258333	−	0.0457936i
$611$	−14.7077	+	14.7077i	−0.595008	+	0.595008i
$612$	−0.104980	+	0.0384264i	−0.00424358	+	0.00155329i
$613$	−1.59218	+	1.59218i	−0.0643077	+	0.0643077i	−0.738529	−	0.674221i	$-0.764479\pi$
$613$	−1.59218	+	1.59218i	−0.0643077	+	0.0643077i	0.674221	+	0.738529i	$0.264479\pi$
$614$	−14.1145	−	9.86392i	−0.569614	−	0.398075i
$615$		−	6.63616i		−	0.267596i
$616$		0			0
$617$			12.2572i			0.493457i	0.969085	+	0.246729i	$0.0793556\pi$
$617$			12.2572i			0.493457i	−0.969085	+	0.246729i	$0.920644\pi$
$618$	19.1870	−	27.4551i	0.771816	−	1.10441i
$619$	−5.28135	+	5.28135i	−0.212275	+	0.212275i	−0.805233	−	0.592958i	$-0.797960\pi$
$619$	−5.28135	+	5.28135i	−0.212275	+	0.212275i	0.592958	+	0.805233i	$0.297960\pi$
$620$	9.14549	+	4.24435i	0.367292	+	0.170457i
$621$	7.40595	−	7.40595i	0.297190	−	0.297190i
$622$	−1.42229	−	8.02350i	−0.0570288	−	0.321713i
$623$		0			0
$624$	−21.7409	+	18.3782i	−0.870334	+	0.735716i
$625$	−16.7365			−0.669459
$626$	−11.1851	+	1.98274i	−0.447047	+	0.0792462i
$627$	−31.3517	+	31.3517i	−1.25207	+	1.25207i
$628$	−20.2524	+	43.6387i	−0.808158	+	1.74137i
$629$	7.37954	+	7.37954i	0.294241	+	0.294241i
$630$		0			0
$631$	−10.1046			−0.402257			−0.201129	−	0.979565i	$-0.564461\pi$
$631$	−10.1046			−0.402257			−0.201129	+	0.979565i	$0.564461\pi$
$632$	21.4302	+	36.8852i	0.852449	+	1.46721i
$633$	1.76128			0.0700045
$634$	−10.8151	−	7.55811i	−0.429521	−	0.300171i
$635$	6.99263	−	6.99263i	0.277494	−	0.277494i
$636$	36.2750	−	13.2779i	1.43840	−	0.526502i
$637$		0			0
$638$	−0.334974	−	1.88967i	−0.0132618	−	0.0748127i
$639$		−	0.153747i		−	0.00608212i
$640$	7.73695	−	3.66803i	0.305830	−	0.144991i
$641$	−22.2785			−0.879947			−0.439973	−	0.898011i	$-0.645012\pi$
$641$	−22.2785			−0.879947			−0.439973	+	0.898011i	$0.645012\pi$
$642$	2.02711	+	11.4354i	0.0800038	+	0.451320i
$643$	−2.94059	−	2.94059i	−0.115965	−	0.115965i	0.646743	−	0.762708i	$-0.276131\pi$
$643$	−2.94059	−	2.94059i	−0.115965	−	0.115965i	−0.762708	+	0.646743i	$0.776131\pi$
$644$		0			0
$645$	−4.99159	+	4.99159i	−0.196544	+	0.196544i
$646$	11.9017	−	17.0304i	0.468266	−	0.670051i
$647$			15.7728i			0.620092i	0.950722	+	0.310046i	$0.100344\pi$
$647$			15.7728i			0.620092i	−0.950722	+	0.310046i	$0.899656\pi$
$648$	22.1649	−	12.8778i	0.870721	−	0.505888i
$649$	−24.8061			−0.973724
$650$	−21.0134	−	14.6852i	−0.824212	−	0.576001i
$651$		0			0
$652$	7.67730	−	16.5426i	0.300666	−	0.647859i
$653$	8.69876	+	8.69876i	0.340409	+	0.340409i	0.856521	−	0.516112i	$-0.172621\pi$
$653$	8.69876	+	8.69876i	0.340409	+	0.340409i	−0.516112	+	0.856521i	$0.672621\pi$
$654$	3.53544	+	19.9442i	0.138247	+	0.779881i
$655$		−	6.50272i		−	0.254082i
$656$	15.4106	−	13.0270i	0.601681	−	0.508617i
$657$			0.139709i			0.00545056i
$658$		0			0
$659$	22.1996	−	22.1996i	0.864775	−	0.864775i	−0.127114	−	0.991888i	$-0.540571\pi$
$659$	22.1996	−	22.1996i	0.864775	−	0.864775i	0.991888	+	0.127114i	$0.0405713\pi$
$660$	5.07217	−	10.9292i	0.197434	−	0.425420i
$661$	0.693821	+	0.693821i	0.0269865	+	0.0269865i	0.720471	−	0.693485i	$-0.243926\pi$
$661$	0.693821	+	0.693821i	0.0269865	+	0.0269865i	−0.693485	+	0.720471i	$0.743926\pi$
$662$	−5.95298	−	4.16025i	−0.231369	−	0.161693i
$663$		−	18.7721i		−	0.729049i
$664$	30.9533	+	8.20334i	1.20122	+	0.318351i
$665$		0			0
$666$	0.0971959	+	0.0679254i	0.00376626	+	0.00263206i
$667$	0.423840	+	0.423840i	0.0164112	+	0.0164112i
$668$	2.19128	+	5.98654i	0.0847832	+	0.231626i
$669$	15.8772	+	15.8772i	0.613848	+	0.613848i
$670$	−10.0813	+	1.78708i	−0.389476	+	0.0690409i
$671$	27.7264			1.07036
$672$		0			0
$673$	−28.5560			−1.10075			−0.550376	−	0.834917i	$-0.685516\pi$
$673$	−28.5560			−1.10075			−0.550376	+	0.834917i	$0.685516\pi$
$674$	2.09497	−	0.371367i	0.0806952	−	0.0143045i
$675$	16.2087	+	16.2087i	0.623874	+	0.623874i
$676$	−2.58859	−	7.07200i	−0.0995613	−	0.272000i
$677$	5.22505	+	5.22505i	0.200815	+	0.200815i	0.800349	−	0.599534i	$-0.204647\pi$
$677$	5.22505	+	5.22505i	0.200815	+	0.200815i	−0.599534	+	0.800349i	$0.704647\pi$
$678$	−37.2450	−	26.0287i	−1.43039	−	0.999627i
$679$		0			0
$680$	−1.44643	+	5.45774i	−0.0554679	+	0.209295i
$681$			27.0355i			1.03600i
$682$	35.3618	+	24.7127i	1.35407	+	0.946297i
$683$	1.39461	+	1.39461i	0.0533633	+	0.0533633i	0.733285	−	0.679922i	$-0.237986\pi$
$683$	1.39461	+	1.39461i	0.0533633	+	0.0533633i	−0.679922	+	0.733285i	$0.737986\pi$
$684$	0.0993786	−	0.214136i	0.00379984	−	0.00818768i
$685$	−12.3549	+	12.3549i	−0.472058	+	0.472058i
$686$		0			0
$687$			24.0695i			0.918310i
$688$	−21.3901	−	1.79290i	−0.815491	−	0.0683538i
$689$			45.4986i			1.73336i
$690$	0.656850	+	3.70545i	0.0250059	+	0.141064i
$691$	−0.158334	−	0.158334i	−0.00602332	−	0.00602332i	0.704089	−	0.710112i	$-0.251356\pi$
$691$	−0.158334	−	0.158334i	−0.00602332	−	0.00602332i	−0.710112	+	0.704089i	$0.751356\pi$
$692$	−16.2224	+	34.9551i	−0.616682	+	1.32879i
$693$		0			0
$694$	10.0690	+	7.03671i	0.382213	+	0.267110i
$695$	−6.52208			−0.247397
$696$	0.731823	+	1.25959i	0.0277397	+	0.0477448i
$697$			13.3062i			0.504008i
$698$	−17.9498	+	25.6848i	−0.679412	+	0.972184i
$699$	15.1177	−	15.1177i	0.571804	−	0.571804i
$700$		0			0
$701$	18.2761	+	18.2761i	0.690279	+	0.690279i	0.962293	−	0.272014i	$-0.0876898\pi$
$701$	18.2761	+	18.2761i	0.690279	+	0.690279i	−0.272014	+	0.962293i	$0.587690\pi$
$702$	5.23313	+	29.5213i	0.197512	+	1.11421i
$703$	−22.0383			−0.831191
$704$	35.3368	−	9.67572i	1.33181	−	0.364667i
$705$			6.68238i			0.251673i
$706$	−6.14066	−	34.6409i	−0.231107	−	1.30373i
$707$		0			0
$708$	17.6823	−	6.47232i	0.664541	−	0.243245i
$709$	1.21878	−	1.21878i	0.0457723	−	0.0457723i	−0.683850	−	0.729622i	$-0.739696\pi$
$709$	1.21878	−	1.21878i	0.0457723	−	0.0457723i	0.729622	+	0.683850i	$0.239696\pi$
$710$	−6.36486	−	4.44809i	−0.238869	−	0.166934i
$711$	−0.319615			−0.0119865
$712$	19.1998	−	11.1551i	0.719545	−	0.418055i
$713$	−13.4743			−0.504617
$714$		0			0
$715$	10.0351	+	10.0351i	0.375290	+	0.375290i
$716$	6.12837	−	13.2051i	0.229028	−	0.493497i
$717$	8.85193	−	8.85193i	0.330581	−	0.330581i
$718$	12.0553	−	2.13700i	0.449900	−	0.0797520i
$719$	51.0128			1.90246			0.951229	−	0.308486i	$-0.0998224\pi$
$719$	51.0128			1.90246			0.951229	+	0.308486i	$0.0998224\pi$
$720$	−0.00535844	+	0.0639285i	−0.000199697	+	0.00238248i
$721$		0			0
$722$	2.96813	+	16.7439i	0.110462	+	0.623144i
$723$	−29.4318	+	29.4318i	−1.09458	+	1.09458i
$724$	−14.3575	−	6.66322i	−0.533593	−	0.247636i
$725$	−0.927620	+	0.927620i	−0.0344509	+	0.0344509i
$726$	14.0437	−	20.0954i	0.521209	−	0.745809i
$727$			31.5017i			1.16833i	0.811634	+	0.584166i	$0.198578\pi$
$727$			31.5017i			1.16833i	−0.811634	+	0.584166i	$0.801422\pi$
$728$		0			0
$729$		−	26.8066i		−	0.992837i
$730$	5.78372	+	4.04196i	0.214065	+	0.149600i
$731$	10.0087	−	10.0087i	0.370183	−	0.370183i
$732$	−19.7639	+	7.23427i	−0.730495	+	0.267386i
$733$	−29.5288	+	29.5288i	−1.09067	+	1.09067i	−0.0952142	+	0.995457i	$0.530354\pi$
$733$	−29.5288	+	29.5288i	−1.09067	+	1.09067i	−0.995457	+	0.0952142i	$0.969646\pi$
$734$	−33.3284	+	5.90799i	−1.23017	+	0.218068i
$735$		0			0
$736$	−7.31541	+	8.79923i	−0.269650	+	0.324344i
$737$	−43.8094			−1.61374
$738$	0.0263890	+	0.148867i	0.000971393	+	0.00547986i
$739$	12.7370	−	12.7370i	0.468539	−	0.468539i	−0.432902	−	0.901441i	$-0.642510\pi$
$739$	12.7370	−	12.7370i	0.468539	−	0.468539i	0.901441	+	0.432902i	$0.142510\pi$
$740$	5.62400	−	2.05858i	0.206743	−	0.0756748i
$741$	28.0306	+	28.0306i	1.02973	+	1.02973i
$742$		0			0
$743$	−23.0128			−0.844256			−0.422128	−	0.906536i	$-0.638717\pi$
$743$	−23.0128			−0.844256			−0.422128	+	0.906536i	$0.638717\pi$
$744$	−31.6546	−	8.38920i	−1.16051	−	0.307563i
$745$	−9.14312			−0.334978
$746$	1.91693	−	2.74297i	0.0701836	−	0.100427i
$747$	−0.169649	+	0.169649i	−0.00620713	+	0.00620713i
$748$	−10.1702	+	21.9142i	−0.371860	+	0.801264i
$749$		0			0
$750$	−17.2687	+	3.06116i	−0.630565	+	0.111778i
$751$		−	0.461609i		−	0.0168443i	−0.999965	−	0.00842217i	$-0.997319\pi$
$751$		−	0.461609i		−	0.0168443i	0.999965	−	0.00842217i	$-0.00268089\pi$
$752$	−15.5179	+	13.1177i	−0.565879	+	0.478353i
$753$	−15.0257			−0.547566
$754$	−1.68950	+	0.299490i	−0.0615278	+	0.0109068i
$755$	0.870885	+	0.870885i	0.0316947	+	0.0316947i
$756$		0			0
$757$	−5.23204	+	5.23204i	−0.190162	+	0.190162i	−0.795766	−	0.605604i	$-0.792931\pi$
$757$	−5.23204	+	5.23204i	−0.190162	+	0.190162i	0.605604	+	0.795766i	$0.292931\pi$
$758$	−8.76427	−	6.12492i	−0.318332	−	0.222467i
$759$			16.1023i			0.584478i
$760$	−5.98971	−	10.3093i	−0.217270	−	0.373959i
$761$	21.2103			0.768874			0.384437	−	0.923151i	$-0.374396\pi$
$761$	21.2103			0.768874			0.384437	+	0.923151i	$0.374396\pi$
$762$	−18.3990	+	26.3275i	−0.666526	+	0.953746i
$763$		0			0
$764$	−3.27634	−	8.95091i	−0.118534	−	0.323833i
$765$	−0.0299128	−	0.0299128i	−0.00108150	−	0.00108150i
$766$	−35.0075	+	6.20565i	−1.26487	+	0.224219i
$767$			22.1784i			0.800814i
$768$	−22.6642	+	16.1170i	−0.817825	+	0.581572i
$769$		−	10.8533i		−	0.391379i	−0.980666	−	0.195689i	$-0.937306\pi$
$769$		−	10.8533i		−	0.391379i	0.980666	−	0.195689i	$-0.0626944\pi$
$770$		0			0
$771$	−28.0029	+	28.0029i	−1.00850	+	1.00850i
$772$	−10.0311	+	3.67173i	−0.361028	+	0.132148i
$773$	34.4036	+	34.4036i	1.23741	+	1.23741i	0.961055	+	0.276357i	$0.0891271\pi$
$773$	34.4036	+	34.4036i	1.23741	+	1.23741i	0.276357	+	0.961055i	$0.410873\pi$
$774$	0.0921253	−	0.131824i	0.00331137	−	0.00473831i
$775$		−	29.4900i		−	1.05931i
$776$	12.4973	+	21.5100i	0.448626	+	0.772163i
$777$		0			0
$778$	5.09927	−	7.29665i	0.182818	−	0.261597i
$779$	−19.8689	−	19.8689i	−0.711876	−	0.711876i
$780$	−9.77150	−	4.53488i	−0.349876	−	0.162375i
$781$	−23.4943	−	23.4943i	−0.840693	−	0.840693i
$782$	−1.31705	−	7.42980i	−0.0470977	−	0.265689i
$783$	1.53421			0.0548282
$784$		0			0
$785$	−18.2049			−0.649762
$786$	3.68651	+	20.7965i	0.131493	+	0.741786i
$787$	9.48837	+	9.48837i	0.338224	+	0.338224i	0.855699	−	0.517475i	$-0.173128\pi$
$787$	9.48837	+	9.48837i	0.338224	+	0.338224i	−0.517475	+	0.855699i	$0.673128\pi$
$788$	−13.9016	+	29.9544i	−0.495224	+	1.06708i
$789$	−12.9983	−	12.9983i	−0.462751	−	0.462751i
$790$	−9.24688	+	13.2315i	−0.328989	+	0.470757i
$791$		0			0
$792$	−0.0703216	+	0.265341i	−0.00249877	+	0.00942850i
$793$		−	24.7893i		−	0.880293i
$794$	−14.6280	+	20.9315i	−0.519128	+	0.742830i
$795$	10.3361	+	10.3361i	0.366583	+	0.366583i
$796$	7.16749	+	19.5815i	0.254045	+	0.694047i
$797$	6.22856	−	6.22856i	0.220627	−	0.220627i	−0.588135	−	0.808762i	$-0.700138\pi$
$797$	6.22856	−	6.22856i	0.220627	−	0.220627i	0.808762	+	0.588135i	$0.200138\pi$
$798$		0			0
$799$		−	13.3989i		−	0.474017i
$800$	−19.2581	−	16.0106i	−0.680875	−	0.566059i
$801$			0.166369i			0.00587837i
$802$	21.9690	−	3.89437i	0.775754	−	0.137515i
$803$	21.3492	+	21.3492i	0.753396	+	0.753396i
$804$	31.2282	−	11.4306i	1.10133	−	0.403126i
$805$		0			0
$806$	22.0948	−	31.6159i	0.778258	−	1.11362i
$807$	−18.0051			−0.633808
$808$	−6.30687	−	1.67147i	−0.221875	−	0.0588019i
$809$			1.72438i			0.0606260i	0.999540	+	0.0303130i	$0.00965040\pi$
$809$			1.72438i			0.0606260i	−0.999540	+	0.0303130i	$0.990350\pi$
$810$	7.95106	+	5.55661i	0.279372	+	0.195239i
$811$	29.5809	−	29.5809i	1.03872	−	1.03872i	0.0395050	−	0.999219i	$-0.487422\pi$
$811$	29.5809	−	29.5809i	1.03872	−	1.03872i	0.999219	−	0.0395050i	$-0.0125781\pi$
$812$		0			0
$813$	−30.3142	−	30.3142i	−1.06317	−	1.06317i
$814$	25.2325	−	4.47287i	0.884399	−	0.156774i
$815$	6.90115			0.241737
$816$	1.53175	−	18.2745i	0.0536221	−	0.639735i
$817$			29.8899i			1.04572i
$818$	41.7335	−	7.39793i	1.45918	−	0.258663i
$819$		0			0
$820$	6.92631	+	3.21444i	0.241877	+	0.112253i
$821$	−26.6950	+	26.6950i	−0.931662	+	0.931662i	−0.997810	−	0.0661475i	$-0.978929\pi$
$821$	−26.6950	+	26.6950i	−0.931662	+	0.931662i	0.0661475	+	0.997810i	$0.478929\pi$
$822$	32.5083	−	46.5168i	1.13386	−	1.62246i
$823$	−36.7556			−1.28122			−0.640609	−	0.767867i	$-0.721318\pi$
$823$	−36.7556			−1.28122			−0.640609	+	0.767867i	$0.721318\pi$
$824$	19.3616	+	33.3247i	0.674494	+	1.16092i
$825$	−35.2417			−1.22696
$826$		0			0
$827$	25.1791	+	25.1791i	0.875565	+	0.875565i	0.993072	−	0.117507i	$-0.0374904\pi$
$827$	25.1791	+	25.1791i	0.875565	+	0.875565i	−0.117507	+	0.993072i	$0.537490\pi$
$828$	−0.0294698	−	0.0805110i	−0.00102415	−	0.00279795i
$829$	16.6238	−	16.6238i	0.577370	−	0.577370i	−0.356808	−	0.934178i	$-0.616135\pi$
$829$	16.6238	−	16.6238i	0.577370	−	0.577370i	0.934178	+	0.356808i	$0.116135\pi$
$830$	2.11502	+	11.9314i	0.0734136	+	0.414143i
$831$	−18.6443			−0.646764
$832$	−8.65076	−	31.5935i	−0.299911	−	1.09531i
$833$		0			0
$834$	20.8584	−	3.69749i	0.722267	−	0.128034i
$835$	−1.70579	+	1.70579i	−0.0590312	+	0.0590312i
$836$	−17.5362	−	47.9087i	−0.606503	−	1.65696i
$837$	−24.3870	+	24.3870i	−0.842940	+	0.842940i
$838$	31.2592	+	21.8455i	1.07983	+	0.754642i
$839$		−	13.7267i		−	0.473899i	−0.971522	−	0.236949i	$-0.923852\pi$
$839$		−	13.7267i		−	0.473899i	0.971522	−	0.236949i	$-0.0761475\pi$
$840$		0			0
$841$		−	28.9122i		−	0.996972i
$842$	1.28446	−	1.83797i	0.0442656	−	0.0633405i
$843$	−7.94461	+	7.94461i	−0.273627	+	0.273627i
$844$	−0.853133	+	1.83828i	−0.0293660	+	0.0632763i
$845$	2.01508	−	2.01508i	0.0693207	−	0.0693207i
$846$	−0.0265728	−	0.149903i	−0.000913592	−	0.00515379i
$847$		0			0
$848$	−3.71257	+	44.2925i	−0.127490	+	1.52101i
$849$	−34.2488			−1.17542
$850$	16.2609	−	2.88251i	0.557745	−	0.0988693i
$851$	−5.65948	+	5.65948i	−0.194004	+	0.194004i
$852$	22.8773	+	10.6172i	0.783763	+	0.363738i
$853$	2.88131	+	2.88131i	0.0986542	+	0.0986542i	0.754711	−	0.656057i	$-0.227777\pi$
$853$	2.88131	+	2.88131i	0.0986542	+	0.0986542i	−0.656057	+	0.754711i	$0.727777\pi$
$854$		0			0
$855$	0.0893318			0.00305508
$856$	−12.9173	−	3.42338i	−0.441504	−	0.117009i
$857$	15.5048			0.529635			0.264817	−	0.964299i	$-0.414688\pi$
$857$	15.5048			0.529635			0.264817	+	0.964299i	$0.414688\pi$
$858$	−37.7823	−	26.4042i	−1.28987	−	0.901426i
$859$	−17.3380	+	17.3380i	−0.591566	+	0.591566i	−0.938054	−	0.346488i	$-0.887374\pi$
$859$	−17.3380	+	17.3380i	−0.591566	+	0.591566i	0.346488	+	0.938054i	$0.387374\pi$
$860$	−2.79199	−	7.62767i	−0.0952060	−	0.260101i
$861$		0			0
$862$	4.05835	+	22.8941i	0.138228	+	0.779776i
$863$		−	47.0811i		−	1.60266i	−0.598223	−	0.801329i	$-0.704126\pi$
$863$		−	47.0811i		−	1.60266i	0.598223	−	0.801329i	$-0.295874\pi$
$864$	2.68555	+	29.1658i	0.0913642	+	0.992239i
$865$	−14.5824			−0.495815
$866$	8.48424	+	47.8616i	0.288306	+	1.62640i
$867$	−12.3433	−	12.3433i	−0.419199	−	0.419199i
$868$		0			0
$869$	−48.8410	+	48.8410i	−1.65682	+	1.65682i
$870$	−0.315772	+	0.451845i	−0.0107057	+	0.0153190i
$871$			39.1686i			1.32718i
$872$	−22.5287	−	5.97063i	−0.762919	−	0.202191i
$873$	−0.186387			−0.00630824
$874$	13.0608	+	9.12759i	0.441790	+	0.308745i
$875$		0			0
$876$	−20.7885	−	9.64778i	−0.702378	−	0.325968i
$877$	14.3234	+	14.3234i	0.483667	+	0.483667i	0.906301	−	0.422634i	$-0.138894\pi$
$877$	14.3234	+	14.3234i	0.483667	+	0.483667i	−0.422634	+	0.906301i	$0.638894\pi$
$878$	2.38656	+	13.4631i	0.0805425	+	0.454359i
$879$			7.28575i			0.245742i
$880$	8.95021	+	10.5879i	0.301711	+	0.356917i
$881$			29.7191i			1.00126i	0.865660	+	0.500632i	$0.166899\pi$
$881$			29.7191i			1.00126i	−0.865660	+	0.500632i	$0.833101\pi$
$882$		0			0
$883$	−10.1351	+	10.1351i	−0.341074	+	0.341074i	−0.856771	−	0.515697i	$-0.827533\pi$
$883$	−10.1351	+	10.1351i	−0.341074	+	0.341074i	0.515697	+	0.856771i	$0.327533\pi$
$884$	19.5929	+	9.09289i	0.658979	+	0.305827i
$885$	5.03833	+	5.03833i	0.169362	+	0.169362i
$886$	40.3198	+	28.1775i	1.35457	+	0.946642i
$887$		−	34.5097i		−	1.15872i	−0.815070	−	0.579362i	$-0.803302\pi$
$887$		−	34.5097i		−	1.15872i	0.815070	−	0.579362i	$-0.196698\pi$
$888$	−16.8192	+	9.77193i	−0.564415	+	0.327925i
$889$		0			0
$890$	6.88742	+	4.81328i	0.230867	+	0.161342i
$891$	29.3494	+	29.3494i	0.983242	+	0.983242i
$892$	−24.2620	+	8.88073i	−0.812352	+	0.297349i
$893$	20.0072	+	20.0072i	0.669517	+	0.669517i
$894$	29.2408	−	5.18340i	0.977959	−	0.173359i
$895$	5.50881			0.184139
$896$		0			0
$897$	14.3966			0.480689
$898$	−49.4439	+	8.76473i	−1.64996	+	0.292483i
$899$	−1.39566	−	1.39566i	−0.0465480	−	0.0465480i
$900$	0.176207	−	0.0644978i	0.00587356	−	0.00214993i
$901$	−20.7249	−	20.7249i	−0.690447	−	0.690447i
$902$	26.7812	+	18.7160i	0.891715	+	0.623176i
$903$		0			0
$904$	45.2076	−	26.2655i	1.50358	−	0.873579i
$905$		−	5.98959i		−	0.199101i
$906$	−3.27891	−	2.29147i	−0.108935	−	0.0761291i
$907$	5.90330	+	5.90330i	0.196016	+	0.196016i	0.798290	−	0.602274i	$-0.205738\pi$
$907$	5.90330	+	5.90330i	0.196016	+	0.196016i	−0.602274	+	0.798290i	$0.705738\pi$
$908$	−28.2175	−	13.0955i	−0.936430	−	0.434590i
$909$	0.0345667	−	0.0345667i	0.00114650	−	0.00114650i
$910$		0			0
$911$			8.93090i			0.295894i	0.988995	+	0.147947i	$0.0472665\pi$
$911$			8.93090i			0.295894i	−0.988995	+	0.147947i	$0.952734\pi$
$912$	25.0004	+	29.5748i	0.827844	+	0.979319i
$913$			51.8487i			1.71594i
$914$	−7.43530	−	41.9443i	−0.245938	−	1.38739i
$915$	−5.63147	−	5.63147i	−0.186171	−	0.186171i
$916$	−25.1219	−	11.6589i	−0.830050	−	0.385220i
$917$		0			0
$918$	−15.8309	−	11.0634i	−0.522496	−	0.365147i
$919$	53.3261			1.75907			0.879533	−	0.475837i	$-0.157855\pi$
$919$	53.3261			1.75907			0.879533	+	0.475837i	$0.157855\pi$
$920$	−4.18562	−	1.10929i	−0.137996	−	0.0365721i
$921$			21.1640i			0.697377i
$922$	−2.72605	+	3.90076i	−0.0897777	+	0.128465i
$923$	−21.0055	+	21.0055i	−0.691406	+	0.691406i
$924$		0			0
$925$	−12.3864	−	12.3864i	−0.407262	−	0.407262i
$926$	0.304418	+	1.71729i	0.0100038	+	0.0564338i
$927$	−0.288763			−0.00948423
$928$	−1.66915	+	0.153693i	−0.0547925	+	0.00504522i
$929$			38.7764i			1.27221i	0.771601	+	0.636107i	$0.219456\pi$
$929$			38.7764i			1.27221i	−0.771601	+	0.636107i	$0.780544\pi$
$930$	−2.16294	−	12.2017i	−0.0709257	−	0.400108i
$931$		0			0
$932$	8.45592	+	23.1014i	0.276983	+	0.756713i
$933$	−7.08176	+	7.08176i	−0.231846	+	0.231846i
$934$	−36.9615	−	25.8306i	−1.20942	−	0.845203i
$935$	−9.14205			−0.298977
$936$	0.237234	+	0.0628724i	0.00775423	+	0.00205505i
$937$	−14.3493			−0.468771			−0.234385	−	0.972144i	$-0.575308\pi$
$937$	−14.3493			−0.468771			−0.234385	+	0.972144i	$0.575308\pi$
$938$		0			0
$939$	9.87228	+	9.87228i	0.322170	+	0.322170i
$940$	−6.97454	−	3.23683i	−0.227485	−	0.105574i
$941$	23.2491	−	23.2491i	0.757898	−	0.757898i	−0.218041	−	0.975940i	$-0.569967\pi$
$941$	23.2491	−	23.2491i	0.757898	−	0.757898i	0.975940	+	0.218041i	$0.0699667\pi$
$942$	58.2216	−	10.3207i	1.89696	−	0.336267i
$943$	−10.2047			−0.332311
$944$	−1.80969	+	21.5904i	−0.0589005	+	0.702709i
$945$		0			0
$946$	−6.06642	−	34.2221i	−0.197236	−	1.11266i
$947$	35.7306	−	35.7306i	1.16109	−	1.16109i	0.176851	−	0.984238i	$-0.443409\pi$
$947$	35.7306	−	35.7306i	1.16109	−	1.16109i	0.984238	−	0.176851i	$-0.0565910\pi$
$948$	22.0714	−	47.5583i	0.716847	−	1.54462i
$949$	19.0877	−	19.0877i	0.619612	−	0.619612i
$950$	−19.9767	+	28.5851i	−0.648130	+	0.927422i
$951$			16.2167i			0.525861i
$952$		0			0
$953$		−	12.5441i		−	0.406345i	−0.979143	−	0.203172i	$-0.934875\pi$
$953$		−	12.5441i		−	0.406345i	0.979143	−	0.203172i	$-0.0651252\pi$
$954$	−0.272968	−	0.190764i	−0.00883765	−	0.00617620i
$955$	2.55045	−	2.55045i	0.0825305	−	0.0825305i
$956$	4.95122	+	13.5267i	0.160134	+	0.437484i
$957$	−1.66787	+	1.66787i	−0.0539147	+	0.0539147i
$958$	−18.5095	+	3.28110i	−0.598013	+	0.106008i
$959$		0			0
$960$	−9.14244	−	5.21199i	−0.295071	−	0.168216i
$961$	13.3695			0.431276
$962$	−3.99905	−	22.5596i	−0.128935	−	0.727351i
$963$	0.0707971	−	0.0707971i	0.00228140	−	0.00228140i
$964$	−16.4623	−	44.9748i	−0.530216	−	1.44854i
$965$	−2.85823	−	2.85823i	−0.0920098	−	0.0920098i
$966$		0			0
$967$	−19.7015			−0.633559			−0.316779	−	0.948499i	$-0.602601\pi$
$967$	−19.7015			−0.633559			−0.316779	+	0.948499i	$0.602601\pi$
$968$	14.1714	+	24.3915i	0.455488	+	0.783973i
$969$	−25.5362			−0.820342
$970$	−5.39241	+	7.71611i	−0.173140	+	0.247749i
$971$	14.0553	−	14.0553i	0.451055	−	0.451055i	−0.444650	−	0.895705i	$-0.646672\pi$
$971$	14.0553	−	14.0553i	0.451055	−	0.451055i	0.895705	+	0.444650i	$0.146672\pi$
$972$	−0.399523	−	0.185415i	−0.0128147	−	0.00594720i
$973$		0			0
$974$	−1.78810	+	0.316969i	−0.0572943	+	0.0101563i
$975$			31.5086i			1.00908i
$976$	2.02274	−	24.1322i	0.0647463	−	0.772452i
$977$	44.0733			1.41003			0.705015	−	0.709193i	$-0.250940\pi$
$977$	44.0733			1.41003			0.705015	+	0.709193i	$0.250940\pi$
$978$	−22.0707	+	3.91239i	−0.705743	+	0.125104i
$979$	25.4232	+	25.4232i	0.812530	+	0.812530i
$980$		0			0
$981$	0.123475	−	0.123475i	0.00394227	−	0.00394227i
$982$	11.6122	+	8.11518i	0.370559	+	0.258966i
$983$		−	45.0025i		−	1.43536i	−0.696375	−	0.717678i	$-0.745205\pi$
$983$		−	45.0025i		−	1.43536i	0.696375	−	0.717678i	$-0.254795\pi$
$984$	−23.9735	−	6.35353i	−0.764247	−	0.202543i
$985$	−12.4962			−0.398162
$986$	0.633156	−	0.905995i	0.0201638	−	0.0288528i
$987$		0			0
$988$	−42.8337	+	15.6786i	−1.36272	+	0.498803i
$989$	7.67579	+	7.67579i	0.244076	+	0.244076i
$990$	−0.102279	+	0.0181307i	−0.00325065	+	0.000576230i
$991$		−	37.1273i		−	1.17939i	−0.807627	−	0.589693i	$-0.799249\pi$
$991$		−	37.1273i		−	1.17939i	0.807627	−	0.589693i	$-0.200751\pi$
$992$	24.0889	−	28.9750i	0.764824	−	0.919957i
$993$			8.92622i			0.283265i
$994$		0			0
$995$	−5.57949	+	5.57949i	−0.176882	+	0.176882i
$996$	−13.5282	−	36.9588i	−0.428657	−	1.17109i
$997$	−40.8093	−	40.8093i	−1.29244	−	1.29244i	−0.933271	−	0.359174i	$-0.883059\pi$
$997$	−40.8093	−	40.8093i	−1.29244	−	1.29244i	−0.359174	−	0.933271i	$-0.616941\pi$
$998$	18.3977	−	26.3257i	0.582370	−	0.833324i
$999$			20.4861i			0.648152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.195.25		56
7.2	even	3		112.2.v.a.3.5	✓	56
7.3	odd	6		112.2.v.a.19.6	yes	56
7.4	even	3		784.2.w.f.19.6		56
7.5	odd	6		784.2.w.f.227.5		56
7.6	odd	2	inner	784.2.j.a.195.26		56
16.11	odd	4	inner	784.2.j.a.587.26		56
28.3	even	6		448.2.z.a.47.4		56
28.23	odd	6		448.2.z.a.367.4		56
56.3	even	6		896.2.z.a.607.11		56
56.37	even	6		896.2.z.b.479.4		56
56.45	odd	6		896.2.z.b.607.4		56
56.51	odd	6		896.2.z.a.479.11		56
112.3	even	12		896.2.z.b.159.4		56
112.11	odd	12		784.2.w.f.411.5		56
112.27	even	4	inner	784.2.j.a.587.25		56
112.37	even	12		448.2.z.a.143.4		56
112.45	odd	12		896.2.z.a.159.11		56
112.51	odd	12		896.2.z.b.31.4		56
112.59	even	12		112.2.v.a.75.5	yes	56
112.75	even	12		784.2.w.f.619.6		56
112.93	even	12		896.2.z.a.31.11		56
112.101	odd	12		448.2.z.a.271.4		56
112.107	odd	12		112.2.v.a.59.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.5	✓	56	7.2	even	3
112.2.v.a.19.6	yes	56	7.3	odd	6
112.2.v.a.59.6	yes	56	112.107	odd	12
112.2.v.a.75.5	yes	56	112.59	even	12
448.2.z.a.47.4		56	28.3	even	6
448.2.z.a.143.4		56	112.37	even	12
448.2.z.a.271.4		56	112.101	odd	12
448.2.z.a.367.4		56	28.23	odd	6
784.2.j.a.195.25		56	1.1	even	1	trivial
784.2.j.a.195.26		56	7.6	odd	2	inner
784.2.j.a.587.25		56	112.27	even	4	inner
784.2.j.a.587.26		56	16.11	odd	4	inner
784.2.w.f.19.6		56	7.4	even	3
784.2.w.f.227.5		56	7.5	odd	6
784.2.w.f.411.5		56	112.11	odd	12
784.2.w.f.619.6		56	112.75	even	12
896.2.z.a.31.11		56	112.93	even	12
896.2.z.a.159.11		56	112.45	odd	12
896.2.z.a.479.11		56	56.51	odd	6
896.2.z.a.607.11		56	56.3	even	6
896.2.z.b.31.4		56	112.51	odd	12
896.2.z.b.159.4		56	112.3	even	12
896.2.z.b.479.4		56	56.37	even	6
896.2.z.b.607.4		56	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.39250 - 0.246844i) q^{2} +(-1.22906 - 1.22906i) q^{3} +(1.87814 - 0.687462i) q^{4} +(0.535151 + 0.535151i) q^{5} +(-2.01486 - 1.40809i) q^{6} +(2.44562 - 1.42090i) q^{8} +0.0211916i q^{9} +(0.877298 + 0.613101i) q^{10} +(3.23833 + 3.23833i) q^{11} +(-3.15328 - 1.46341i) q^{12} +(2.89529 - 2.89529i) q^{13} -1.31547i q^{15} +(3.05479 - 2.58230i) q^{16} +2.63765i q^{17} +(0.00523102 + 0.0295094i) q^{18} +(-3.93855 - 3.93855i) q^{19} +(1.37298 + 0.637190i) q^{20} +(5.30875 + 3.71003i) q^{22} -2.02285 q^{23} +(-4.75219 - 1.25944i) q^{24} -4.42723i q^{25} +(3.31702 - 4.74639i) q^{26} +(-3.66114 + 3.66114i) q^{27} +(-0.209526 - 0.209526i) q^{29} +(-0.324715 - 1.83179i) q^{30} +6.66105 q^{31} +(3.61639 - 4.34991i) q^{32} -7.96022i q^{33} +(0.651087 + 3.67293i) q^{34} +(0.0145684 + 0.0398007i) q^{36} +(2.79777 - 2.79777i) q^{37} +(-6.45665 - 4.51224i) q^{38} -7.11699 q^{39} +(2.06917 + 0.548378i) q^{40} +5.04472 q^{41} +(-3.79454 - 3.79454i) q^{43} +(8.30826 + 3.85580i) q^{44} +(-0.0113407 + 0.0113407i) q^{45} +(-2.81683 + 0.499328i) q^{46} -5.07985 q^{47} +(-6.92833 - 0.580727i) q^{48} +(-1.09283 - 6.16493i) q^{50} +(3.24183 - 3.24183i) q^{51} +(3.44735 - 7.42816i) q^{52} +(-7.85735 + 7.85735i) q^{53} +(-4.19443 + 6.00189i) q^{54} +3.46599i q^{55} +9.68145i q^{57} +(-0.343486 - 0.240046i) q^{58} +(-3.83007 + 3.83007i) q^{59} +(-0.904334 - 2.47063i) q^{60} +(4.28096 - 4.28096i) q^{61} +(9.27554 - 1.64424i) q^{62} +(3.96208 - 6.94996i) q^{64} +3.09883 q^{65} +(-1.96493 - 11.0846i) q^{66} +(-6.76419 + 6.76419i) q^{67} +(1.81328 + 4.95386i) q^{68} +(2.48621 + 2.48621i) q^{69} -7.25507 q^{71} +(0.0301112 + 0.0518266i) q^{72} +6.59265 q^{73} +(3.20530 - 4.58652i) q^{74} +(-5.44134 + 5.44134i) q^{75} +(-10.1047 - 4.68953i) q^{76} +(-9.91044 + 1.75679i) q^{78} +15.0822i q^{79} +(3.01669 + 0.252857i) q^{80} +9.06313 q^{81} +(7.02479 - 1.24526i) q^{82} +(8.00548 + 8.00548i) q^{83} +(-1.41154 + 1.41154i) q^{85} +(-6.22057 - 4.34725i) q^{86} +0.515042i q^{87} +(12.5211 + 3.31837i) q^{88} +7.85072 q^{89} +(-0.0129926 + 0.0185914i) q^{90} +(-3.79919 + 1.39063i) q^{92} +(-8.18685 - 8.18685i) q^{93} +(-7.07372 + 1.25393i) q^{94} -4.21543i q^{95} +(-9.79108 + 0.901551i) q^{96} +8.79532i q^{97} +(-0.0686254 + 0.0686254i) 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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