LMFDB - Embedded newform 784.2.j.a.195.19

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			195.19
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.945273 + 1.05188i) q^{2} +(-1.68113 - 1.68113i) q^{3} +(-0.212918 + 1.98863i) q^{4} +(-0.611867 - 0.611867i) q^{5} +(0.179226 - 3.35748i) q^{6} +(-2.29308 + 1.65584i) q^{8} +2.65240i q^{9} +(0.0652315 - 1.22199i) q^{10} +(1.48838 + 1.48838i) q^{11} +(3.70110 - 2.98521i) q^{12} +(-0.336492 + 0.336492i) q^{13} +2.05725i q^{15} +(-3.90933 - 0.846832i) q^{16} +0.0564247i q^{17} +(-2.79001 + 2.50724i) q^{18} +(5.78189 + 5.78189i) q^{19} +(1.34706 - 1.08650i) q^{20} +(-0.158677 + 2.97253i) q^{22} +7.19628 q^{23} +(6.63864 + 1.07128i) q^{24} -4.25124i q^{25} +(-0.672027 - 0.0358736i) q^{26} +(-0.584366 + 0.584366i) q^{27} +(4.81700 + 4.81700i) q^{29} +(-2.16399 + 1.94467i) q^{30} +3.69909 q^{31} +(-2.80462 - 4.91265i) q^{32} -5.00432i q^{33} +(-0.0593522 + 0.0533367i) q^{34} +(-5.27465 - 0.564743i) q^{36} +(-2.39386 + 2.39386i) q^{37} +(-0.616410 + 11.5473i) q^{38} +1.13137 q^{39} +(2.41621 + 0.389906i) q^{40} -4.95983 q^{41} +(4.99825 + 4.99825i) q^{43} +(-3.27674 + 2.64294i) q^{44} +(1.62291 - 1.62291i) q^{45} +(6.80244 + 7.56964i) q^{46} +11.0075 q^{47} +(5.14846 + 7.99573i) q^{48} +(4.47181 - 4.01858i) q^{50} +(0.0948572 - 0.0948572i) q^{51} +(-0.597514 - 0.740805i) q^{52} +(-2.65409 + 2.65409i) q^{53} +(-1.16707 - 0.0622996i) q^{54} -1.82138i q^{55} -19.4402i q^{57} +(-0.513543 + 9.62030i) q^{58} +(-6.21901 + 6.21901i) q^{59} +(-4.09113 - 0.438027i) q^{60} +(-4.55283 + 4.55283i) q^{61} +(3.49665 + 3.89102i) q^{62} +(2.51641 - 7.59393i) q^{64} +0.411776 q^{65} +(5.26396 - 4.73045i) q^{66} +(7.65741 - 7.65741i) q^{67} +(-0.112208 - 0.0120138i) q^{68} +(-12.0979 - 12.0979i) q^{69} -13.1246 q^{71} +(-4.39194 - 6.08215i) q^{72} +5.39185 q^{73} +(-4.78092 - 0.255211i) q^{74} +(-7.14689 + 7.14689i) q^{75} +(-12.7291 + 10.2670i) q^{76} +(1.06946 + 1.19007i) q^{78} +5.76911i q^{79} +(1.87384 + 2.91014i) q^{80} +9.92198 q^{81} +(-4.68840 - 5.21717i) q^{82} +(4.52860 + 4.52860i) q^{83} +(0.0345244 - 0.0345244i) q^{85} +(-0.532866 + 9.98228i) q^{86} -16.1960i q^{87} +(-5.87748 - 0.948455i) q^{88} -2.56436 q^{89} +(3.24121 + 0.173020i) q^{90} +(-1.53222 + 14.3108i) q^{92} +(-6.21866 - 6.21866i) q^{93} +(10.4051 + 11.5786i) q^{94} -7.07548i q^{95} +(-3.54388 + 12.9737i) q^{96} -9.06313i q^{97} +(-3.94777 + 3.94777i) 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 $

$2$	0.945273	+	1.05188i	0.668409	+	0.743794i
$2$	0.945273	+	1.05188i	0.668409	+	0.743794i
$3$	−1.68113	−	1.68113i	−0.970601	−	0.970601i	0.0289791	−	0.999580i	$-0.490774\pi$
$3$	−1.68113	−	1.68113i	−0.970601	−	0.970601i	−0.999580	+	0.0289791i	$0.990774\pi$
$4$	−0.212918	+	1.98863i	−0.106459	+	0.994317i
$5$	−0.611867	−	0.611867i	−0.273635	−	0.273635i	0.556927	−	0.830562i	$-0.311980\pi$
$5$	−0.611867	−	0.611867i	−0.273635	−	0.273635i	−0.830562	+	0.556927i	$0.811980\pi$
$6$	0.179226	−	3.35748i	0.0731688	−	1.37069i
$7$		0			0
$7$		0			0
$8$	−2.29308	+	1.65584i	−0.810725	+	0.585427i
$9$			2.65240i			0.884132i
$10$	0.0652315	−	1.22199i	0.0206280	−	0.386428i
$11$	1.48838	+	1.48838i	0.448763	+	0.448763i	0.894943	−	0.446180i	$-0.147216\pi$
$11$	1.48838	+	1.48838i	0.448763	+	0.448763i	−0.446180	+	0.894943i	$0.647216\pi$
$12$	3.70110	−	2.98521i	1.06841	−	0.861756i
$13$	−0.336492	+	0.336492i	−0.0933261	+	0.0933261i	−0.752228	−	0.658902i	$-0.771021\pi$
$13$	−0.336492	+	0.336492i	−0.0933261	+	0.0933261i	0.658902	+	0.752228i	$0.271021\pi$
$14$		0			0
$15$			2.05725i			0.531181i
$16$	−3.90933	−	0.846832i	−0.977333	−	0.211708i
$17$			0.0564247i			0.0136850i	0.999977	+	0.00684250i	$0.00217805\pi$
$17$			0.0564247i			0.0136850i	−0.999977	+	0.00684250i	$0.997822\pi$
$18$	−2.79001	+	2.50724i	−0.657612	+	0.590962i
$19$	5.78189	+	5.78189i	1.32646	+	1.32646i	0.908440	+	0.418016i	$0.137274\pi$
$19$	5.78189	+	5.78189i	1.32646	+	1.32646i	0.418016	+	0.908440i	$0.362726\pi$
$20$	1.34706	−	1.08650i	0.301211	−	0.242949i
$21$		0			0
$22$	−0.158677	+	2.97253i	−0.0338300	+	0.633745i
$23$	7.19628			1.50053			0.750264	−	0.661139i	$-0.229927\pi$
$23$	7.19628			1.50053			0.750264	+	0.661139i	$0.229927\pi$
$24$	6.63864	+	1.07128i	1.35511	+	0.218675i
$25$		−	4.25124i		−	0.850248i
$26$	−0.672027	−	0.0358736i	−0.131795	−	0.00703539i
$27$	−0.584366	+	0.584366i	−0.112461	+	0.112461i
$28$		0			0
$29$	4.81700	+	4.81700i	0.894494	+	0.894494i	0.994942	−	0.100448i	$-0.0320277\pi$
$29$	4.81700	+	4.81700i	0.894494	+	0.894494i	−0.100448	+	0.994942i	$0.532028\pi$
$30$	−2.16399	+	1.94467i	−0.395089	+	0.355046i
$31$	3.69909			0.664377			0.332188	−	0.943213i	$-0.392213\pi$
$31$	3.69909			0.664377			0.332188	+	0.943213i	$0.392213\pi$
$32$	−2.80462	−	4.91265i	−0.495791	−	0.868442i
$33$		−	5.00432i		−	0.871140i
$34$	−0.0593522	+	0.0533367i	−0.0101788	+	0.00914717i
$35$		0			0
$36$	−5.27465	−	0.564743i	−0.879108	−	0.0941239i
$37$	−2.39386	+	2.39386i	−0.393548	+	0.393548i	−0.875950	−	0.482402i	$-0.839765\pi$
$37$	−2.39386	+	2.39386i	−0.393548	+	0.393548i	0.482402	+	0.875950i	$0.339765\pi$
$38$	−0.616410	+	11.5473i	−0.0999949	+	1.87322i
$39$	1.13137			0.181165
$40$	2.41621	+	0.389906i	0.382036	+	0.0616495i
$41$	−4.95983			−0.774596			−0.387298	−	0.921955i	$-0.626592\pi$
$41$	−4.95983			−0.774596			−0.387298	+	0.921955i	$0.626592\pi$
$42$		0			0
$43$	4.99825	+	4.99825i	0.762225	+	0.762225i	0.976724	−	0.214499i	$-0.0688118\pi$
$43$	4.99825	+	4.99825i	0.762225	+	0.762225i	−0.214499	+	0.976724i	$0.568812\pi$
$44$	−3.27674	+	2.64294i	−0.493988	+	0.398438i
$45$	1.62291	−	1.62291i	0.241930	−	0.241930i
$46$	6.80244	+	7.56964i	1.00297	+	1.11608i
$47$	11.0075			1.60561			0.802807	−	0.596239i	$-0.203339\pi$
$47$	11.0075			1.60561			0.802807	+	0.596239i	$0.203339\pi$
$48$	5.14846	+	7.99573i	0.743116	+	1.15408i
$49$		0			0
$50$	4.47181	−	4.01858i	0.632409	−	0.568313i
$51$	0.0948572	−	0.0948572i	0.0132827	−	0.0132827i
$52$	−0.597514	−	0.740805i	−0.0828603	−	0.102731i
$53$	−2.65409	+	2.65409i	−0.364567	+	0.364567i	−0.865491	−	0.500924i	$-0.832994\pi$
$53$	−2.65409	+	2.65409i	−0.364567	+	0.364567i	0.500924	+	0.865491i	$0.332994\pi$
$54$	−1.16707	−	0.0622996i	−0.158818	−	0.00847790i
$55$		−	1.82138i		−	0.245595i
$56$		0			0
$57$		−	19.4402i		−	2.57492i
$58$	−0.513543	+	9.62030i	−0.0674315	+	1.26321i
$59$	−6.21901	+	6.21901i	−0.809646	+	0.809646i	−0.984580	−	0.174934i	$-0.944029\pi$
$59$	−6.21901	+	6.21901i	−0.809646	+	0.809646i	0.174934	+	0.984580i	$0.444029\pi$
$60$	−4.09113	−	0.438027i	−0.528162	−	0.0565490i
$61$	−4.55283	+	4.55283i	−0.582931	+	0.582931i	−0.935708	−	0.352777i	$-0.885237\pi$
$61$	−4.55283	+	4.55283i	−0.582931	+	0.582931i	0.352777	+	0.935708i	$0.385237\pi$
$62$	3.49665	+	3.89102i	0.444075	+	0.494160i
$63$		0			0
$64$	2.51641	−	7.59393i	0.314551	−	0.949241i
$65$	0.411776			0.0510746
$66$	5.26396	−	4.73045i	0.647949	−	0.582278i
$67$	7.65741	−	7.65741i	0.935501	−	0.935501i	−0.0625413	−	0.998042i	$-0.519921\pi$
$67$	7.65741	−	7.65741i	0.935501	−	0.935501i	0.998042	+	0.0625413i	$0.0199205\pi$
$68$	−0.112208	−	0.0120138i	−0.0136072	−	0.00145689i
$69$	−12.0979	−	12.0979i	−1.45641	−	1.45641i
$70$		0			0
$71$	−13.1246			−1.55760			−0.778800	−	0.627272i	$-0.784171\pi$
$71$	−13.1246			−1.55760			−0.778800	+	0.627272i	$0.784171\pi$
$72$	−4.39194	−	6.08215i	−0.517595	−	0.716788i
$73$	5.39185			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$73$	5.39185			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$74$	−4.78092	−	0.255211i	−0.555770	−	0.0296677i
$75$	−7.14689	+	7.14689i	−0.825251	+	0.825251i
$76$	−12.7291	+	10.2670i	−1.46013	+	1.17770i
$77$		0			0
$78$	1.06946	+	1.19007i	0.121092	+	0.134749i
$79$			5.76911i			0.649075i	0.945873	+	0.324538i	$0.105209\pi$
$79$			5.76911i			0.649075i	−0.945873	+	0.324538i	$0.894791\pi$
$80$	1.87384	+	2.91014i	0.209502	+	0.325363i
$81$	9.92198			1.10244
$82$	−4.68840	−	5.21717i	−0.517747	−	0.576140i
$83$	4.52860	+	4.52860i	0.497079	+	0.497079i	0.910527	−	0.413449i	$-0.135676\pi$
$83$	4.52860	+	4.52860i	0.497079	+	0.497079i	−0.413449	+	0.910527i	$0.635676\pi$
$84$		0			0
$85$	0.0345244	−	0.0345244i	0.00374469	−	0.00374469i
$86$	−0.532866	+	9.98228i	−0.0574604	+	1.07642i
$87$		−	16.1960i		−	1.73639i
$88$	−5.87748	−	0.948455i	−0.626542	−	0.101106i
$89$	−2.56436			−0.271821			−0.135911	−	0.990721i	$-0.543396\pi$
$89$	−2.56436			−0.271821			−0.135911	+	0.990721i	$0.543396\pi$
$90$	3.24121	+	0.173020i	0.341654	+	0.0182379i
$91$		0			0
$92$	−1.53222	+	14.3108i	−0.159745	+	1.49200i
$93$	−6.21866	−	6.21866i	−0.644845	−	0.644845i
$94$	10.4051	+	11.5786i	1.07321	+	1.19425i
$95$		−	7.07548i		−	0.725929i
$96$	−3.54388	+	12.9737i	−0.361695	+	1.32413i
$97$		−	9.06313i		−	0.920222i	−0.887861	−	0.460111i	$-0.847810\pi$
$97$		−	9.06313i		−	0.920222i	0.887861	−	0.460111i	$-0.152190\pi$
$98$		0			0
$99$	−3.94777	+	3.94777i	−0.396766	+	0.396766i
$100$	8.45416	+	0.905165i	0.845416	+	0.0905165i
$101$	−6.78762	−	6.78762i	−0.675394	−	0.675394i	0.283561	−	0.958954i	$-0.408484\pi$
$101$	−6.78762	−	6.78762i	−0.675394	−	0.675394i	−0.958954	+	0.283561i	$0.908484\pi$
$102$	0.189445	+	0.0101128i	0.0187578	+	0.00100132i
$103$		−	1.37379i		−	0.135363i	−0.997707	−	0.0676816i	$-0.978440\pi$
$103$		−	1.37379i		−	0.135363i	0.997707	−	0.0676816i	$-0.0215602\pi$
$104$	0.214426	−	1.32878i	0.0210262	−	0.130297i
$105$		0			0
$106$	−5.30063	−	0.282954i	−0.514843	−	0.0274829i
$107$	−9.89377	−	9.89377i	−0.956467	−	0.956467i	0.0426244	−	0.999091i	$-0.486428\pi$
$107$	−9.89377	−	9.89377i	−0.956467	−	0.956467i	−0.999091	+	0.0426244i	$0.986428\pi$
$108$	−1.03767	−	1.28651i	−0.0998497	−	0.123795i
$109$	1.96846	+	1.96846i	0.188544	+	0.188544i	0.795066	−	0.606522i	$-0.207436\pi$
$109$	1.96846	+	1.96846i	0.188544	+	0.188544i	−0.606522	+	0.795066i	$0.707436\pi$
$110$	1.91588	−	1.72170i	0.182672	−	0.164158i
$111$	8.04879			0.763957
$112$		0			0
$113$	6.74317			0.634344			0.317172	−	0.948368i	$-0.397267\pi$
$113$	6.74317			0.634344			0.317172	+	0.948368i	$0.397267\pi$
$114$	20.4488	−	18.3763i	1.91521	−	1.72110i
$115$	−4.40316	−	4.40316i	−0.410597	−	0.410597i
$116$	−10.6049	+	8.55362i	−0.984637	+	0.794184i
$117$	−0.892510	−	0.892510i	−0.0825126	−	0.0825126i
$118$	−12.4203	−	0.663012i	−1.14338	−	0.0610352i
$119$		0			0
$120$	−3.40648	−	4.71744i	−0.310968	−	0.430642i
$121$		−	6.56945i		−	0.597223i
$122$	−9.09272	−	0.485380i	−0.823216	−	0.0439443i
$123$	8.33813	+	8.33813i	0.751824	+	0.751824i
$124$	−0.787604	+	7.35614i	−0.0707289	+	0.660601i
$125$	−5.66052	+	5.66052i	−0.506293	+	0.506293i
$126$		0			0
$127$			8.62463i			0.765312i	0.923891	+	0.382656i	$0.124991\pi$
$127$			8.62463i			0.765312i	−0.923891	+	0.382656i	$0.875009\pi$
$128$	10.3666	−	4.53137i	0.916288	−	0.400520i
$129$		−	16.8054i		−	1.47963i
$130$	0.389241	+	0.433141i	0.0341387	+	0.0379890i
$131$	−3.80852	−	3.80852i	−0.332752	−	0.332752i	0.520879	−	0.853631i	$-0.325604\pi$
$131$	−3.80852	−	3.80852i	−0.332752	−	0.332752i	−0.853631	+	0.520879i	$0.825604\pi$
$132$	9.95176	+	1.06551i	0.866189	+	0.0927407i
$133$		0			0
$134$	15.2930	+	0.816361i	1.32112	+	0.0705228i
$135$	0.715108			0.0615467
$136$	−0.0934301	−	0.129386i	−0.00801156	−	0.0110948i
$137$		−	10.7615i		−	0.919413i	−0.888071	−	0.459707i	$-0.847955\pi$
$137$		−	10.7615i		−	0.919413i	0.888071	−	0.459707i	$-0.152045\pi$
$138$	1.28976	−	24.1614i	0.109792	−	2.05675i
$139$	13.2045	−	13.2045i	1.11999	−	1.11999i	0.128251	−	0.991742i	$-0.459064\pi$
$139$	13.2045	−	13.2045i	1.11999	−	1.11999i	0.991742	−	0.128251i	$-0.0409362\pi$
$140$		0			0
$141$	−18.5051	−	18.5051i	−1.55841	−	1.55841i
$142$	−12.4063	−	13.8055i	−1.04111	−	1.15853i
$143$	−1.00166			−0.0837626
$144$	2.24613	−	10.3691i	0.187178	−	0.864092i
$145$		−	5.89472i		−	0.489530i
$146$	5.09677	+	5.67160i	0.421812	+	0.469385i
$147$		0			0
$148$	−4.25082	−	5.27021i	−0.349415	−	0.433209i
$149$	2.85563	−	2.85563i	0.233942	−	0.233942i	−0.580394	−	0.814336i	$-0.697101\pi$
$149$	2.85563	−	2.85563i	0.233942	−	0.233942i	0.814336	+	0.580394i	$0.197101\pi$
$150$	−14.2734	−	0.761934i	−1.16542	−	0.0622116i
$151$	−7.89738			−0.642680			−0.321340	−	0.946964i	$-0.604133\pi$
$151$	−7.89738			−0.642680			−0.321340	+	0.946964i	$0.604133\pi$
$152$	−22.8322	−	3.68445i	−1.85193	−	0.298848i
$153$	−0.149661			−0.0120993
$154$		0			0
$155$	−2.26335	−	2.26335i	−0.181797	−	0.181797i
$156$	−0.240890	+	2.24989i	−0.0192866	+	0.180135i
$157$	−11.4262	+	11.4262i	−0.911912	+	0.911912i	−0.996423	−	0.0845104i	$-0.973067\pi$
$157$	−11.4262	+	11.4262i	−0.911912	+	0.911912i	0.0845104	+	0.996423i	$0.473067\pi$
$158$	−6.06843	+	5.45338i	−0.482778	+	0.433848i
$159$	8.92373			0.707698
$160$	−1.28983	+	4.72194i	−0.101970	+	0.373302i
$161$		0			0
$162$	9.37898	+	10.4368i	0.736882	+	0.819990i
$163$	2.18896	−	2.18896i	0.171453	−	0.171453i	−0.616165	−	0.787617i	$-0.711314\pi$
$163$	2.18896	−	2.18896i	0.171453	−	0.171453i	0.787617	+	0.616165i	$0.211314\pi$
$164$	1.05604	−	9.86330i	0.0824627	−	0.770194i
$165$	−3.06198	+	3.06198i	−0.238374	+	0.238374i
$166$	−0.482797	+	9.04433i	−0.0374723	+	0.701976i
$167$			5.62954i			0.435627i	0.975990	+	0.217813i	$0.0698924\pi$
$167$			5.62954i			0.435627i	−0.975990	+	0.217813i	$0.930108\pi$
$168$		0			0
$169$			12.7735i			0.982580i
$170$	0.0689506	+	0.00368066i	0.00528827	+	0.000282294i
$171$	−15.3359	+	15.3359i	−1.17276	+	1.17276i
$172$	−11.0039	+	8.87547i	−0.839040	+	0.676748i
$173$	−1.24249	+	1.24249i	−0.0944648	+	0.0944648i	−0.752760	−	0.658295i	$-0.771278\pi$
$173$	−1.24249	+	1.24249i	−0.0944648	+	0.0944648i	0.658295	+	0.752760i	$0.271278\pi$
$174$	17.0363	−	15.3096i	1.29152	−	1.16062i
$175$		0			0
$176$	−4.55816	−	7.07898i	−0.343584	−	0.533598i
$177$	20.9099			1.57169
$178$	−2.42402	−	2.69740i	−0.181688	−	0.202179i
$179$	−5.41675	+	5.41675i	−0.404867	+	0.404867i	−0.879944	−	0.475077i	$-0.842420\pi$
$179$	−5.41675	+	5.41675i	−0.404867	+	0.404867i	0.475077	+	0.879944i	$0.342420\pi$
$180$	2.88183	+	3.57293i	0.214799	+	0.266310i
$181$	−0.00448004	−	0.00448004i	−0.000332999	−	0.000332999i	0.706940	−	0.707273i	$-0.250075\pi$
$181$	−0.00448004	−	0.00448004i	−0.000332999	−	0.000332999i	−0.707273	+	0.706940i	$0.750075\pi$
$182$		0			0
$183$	15.3078			1.13159
$184$	−16.5016	+	11.9159i	−1.21652	+	0.878449i
$185$	2.92945			0.215377
$186$	0.662975	−	12.4196i	0.0486117	−	0.910652i
$187$	−0.0839813	+	0.0839813i	−0.00614132	+	0.00614132i
$188$	−2.34370	+	21.8900i	−0.170932	+	1.59649i
$189$		0			0
$190$	7.44259	−	6.68826i	0.539942	−	0.485218i
$191$			15.4015i			1.11441i	0.830375	+	0.557206i	$0.188126\pi$
$191$			15.4015i			1.11441i	−0.830375	+	0.557206i	$0.811874\pi$
$192$	−16.9968	+	8.53597i	−1.22664	+	0.616031i
$193$	−1.55065			−0.111618			−0.0558091	−	0.998441i	$-0.517774\pi$
$193$	−1.55065			−0.111618			−0.0558091	+	0.998441i	$0.517774\pi$
$194$	9.53336	−	8.56713i	0.684455	−	0.615084i
$195$	−0.692250	−	0.692250i	−0.0495730	−	0.0495730i
$196$		0			0
$197$	1.05178	−	1.05178i	0.0749363	−	0.0749363i	−0.668645	−	0.743582i	$-0.733126\pi$
$197$	1.05178	−	1.05178i	0.0749363	−	0.0749363i	0.743582	+	0.668645i	$0.233126\pi$
$198$	−7.88432	−	0.420874i	−0.560314	−	0.0299102i
$199$		−	12.6591i		−	0.897378i	−0.893688	−	0.448689i	$-0.851891\pi$
$199$		−	12.6591i		−	0.897378i	0.893688	−	0.448689i	$-0.148109\pi$
$200$	7.03936	+	9.74842i	0.497758	+	0.689317i
$201$	−25.7462			−1.81600
$202$	0.723633	−	13.5559i	0.0509146	−	0.953793i
$203$		0			0
$204$	0.168440	+	0.208833i	0.0117931	+	0.0146212i
$205$	3.03476	+	3.03476i	0.211957	+	0.211957i
$206$	1.44506	−	1.29860i	0.100682	−	0.0904780i
$207$			19.0874i			1.32666i
$208$	1.60041	−	1.03051i	0.110969	−	0.0714528i
$209$			17.2113i			1.19053i
$210$		0			0
$211$	0.830513	−	0.830513i	0.0571749	−	0.0571749i	−0.677941	−	0.735116i	$-0.737128\pi$
$211$	0.830513	−	0.830513i	0.0571749	−	0.0571749i	0.735116	+	0.677941i	$0.237128\pi$
$212$	−4.71291	−	5.84311i	−0.323684	−	0.401307i
$213$	22.0641	+	22.0641i	1.51181	+	1.51181i
$214$	1.05478	−	19.7594i	0.0721033	−	1.35073i
$215$		−	6.11652i		−	0.417143i
$216$	0.372382	−	2.30761i	0.0253374	−	0.157013i
$217$		0			0
$218$	−0.209859	+	3.93132i	−0.0142134	+	0.266263i
$219$	−9.06440	−	9.06440i	−0.612515	−	0.612515i
$220$	3.62206	+	0.387804i	0.244199	+	0.0261458i
$221$	−0.0189865	−	0.0189865i	−0.00127717	−	0.00127717i
$222$	7.60830	+	8.46639i	0.510636	+	0.568227i
$223$	−4.19686			−0.281043			−0.140521	−	0.990078i	$-0.544878\pi$
$223$	−4.19686			−0.281043			−0.140521	+	0.990078i	$0.544878\pi$
$224$		0			0
$225$	11.2760			0.751731
$226$	6.37414	+	7.09303i	0.424001	+	0.471822i
$227$	9.09470	+	9.09470i	0.603636	+	0.603636i	0.941276	−	0.337639i	$-0.109628\pi$
$227$	9.09470	+	9.09470i	0.603636	+	0.603636i	−0.337639	+	0.941276i	$0.609628\pi$
$228$	38.6595	+	4.13917i	2.56028	+	0.274123i
$229$	14.3071	+	14.3071i	0.945438	+	0.945438i	0.998587	−	0.0531488i	$-0.0169258\pi$
$229$	14.3071	+	14.3071i	0.945438	+	0.945438i	−0.0531488	+	0.998587i	$0.516926\pi$
$230$	0.469424	−	8.79380i	0.0309529	−	0.579846i
$231$		0			0
$232$	−19.0219	−	3.06958i	−1.24885	−	0.201528i
$233$		−	22.9311i		−	1.50226i	−0.660152	−	0.751132i	$-0.729508\pi$
$233$		−	22.9311i		−	1.50226i	0.660152	−	0.751132i	$-0.270492\pi$
$234$	0.0951510	−	1.78248i	0.00622022	−	0.116525i
$235$	−6.73514	−	6.73514i	−0.439352	−	0.439352i
$236$	−11.0432	−	13.6915i	−0.718851	−	0.891239i
$237$	9.69862	−	9.69862i	0.629993	−	0.629993i
$238$		0			0
$239$			5.12967i			0.331811i	0.986142	+	0.165905i	$0.0530546\pi$
$239$			5.12967i			0.331811i	−0.986142	+	0.165905i	$0.946945\pi$
$240$	1.74215	−	8.04249i	0.112455	−	0.519141i
$241$			16.9504i			1.09187i	0.837827	+	0.545936i	$0.183826\pi$
$241$			16.9504i			1.09187i	−0.837827	+	0.545936i	$0.816174\pi$
$242$	6.91030	−	6.20993i	0.444211	−	0.399189i
$243$	−14.9270	−	14.9270i	−0.957570	−	0.957570i
$244$	−8.08454	−	10.0233i	−0.517560	−	0.641676i
$245$		0			0
$246$	−0.888933	+	16.6525i	−0.0566763	+	1.06173i
$247$	−3.89112			−0.247586
$248$	−8.48231	+	6.12510i	−0.538627	+	0.388944i
$249$		−	15.2263i		−	0.964931i
$250$	−11.3050	−	0.603472i	−0.714988	−	0.0381669i
$251$	−1.63771	+	1.63771i	−0.103371	+	0.103371i	−0.756901	−	0.653530i	$-0.773288\pi$
$251$	−1.63771	+	1.63771i	−0.103371	+	0.103371i	0.653530	+	0.756901i	$0.273288\pi$
$252$		0			0
$253$	10.7108	+	10.7108i	0.673381	+	0.673381i
$254$	−9.07210	+	8.15263i	−0.569234	+	0.511541i
$255$	−0.116080			−0.00726921
$256$	14.5658	+	6.62110i	0.910359	+	0.413818i
$257$		−	8.09393i		−	0.504885i	−0.967612	−	0.252443i	$-0.918766\pi$
$257$		−	8.09393i		−	0.504885i	0.967612	−	0.252443i	$-0.0812339\pi$
$258$	17.6773	−	15.8857i	1.10054	−	0.989000i
$259$		0			0
$260$	−0.0876746	+	0.818873i	−0.00543735	+	0.0507843i
$261$	−12.7766	+	12.7766i	−0.790851	+	0.790851i
$262$	0.406028	−	7.60621i	0.0250845	−	0.469913i
$263$	−14.8366			−0.914863			−0.457431	−	0.889245i	$-0.651231\pi$
$263$	−14.8366			−0.914863			−0.457431	+	0.889245i	$0.651231\pi$
$264$	8.28634	+	11.4753i	0.509989	+	0.706255i
$265$	3.24790			0.199517
$266$		0			0
$267$	4.31102	+	4.31102i	0.263830	+	0.263830i
$268$	13.5974	+	16.8582i	0.830592	+	1.02978i
$269$	−0.171356	+	0.171356i	−0.0104478	+	0.0104478i	−0.712311	−	0.701864i	$-0.752352\pi$
$269$	−0.171356	+	0.171356i	−0.0104478	+	0.0104478i	0.701864	+	0.712311i	$0.252352\pi$
$270$	0.675972	+	0.752211i	0.0411384	+	0.0457781i
$271$	22.4289			1.36246			0.681229	−	0.732070i	$-0.261446\pi$
$271$	22.4289			1.36246			0.681229	+	0.732070i	$0.261446\pi$
$272$	0.0477822	−	0.220583i	0.00289722	−	0.0133748i
$273$		0			0
$274$	11.3198	−	10.1725i	0.683854	−	0.614544i
$275$	6.32745	−	6.32745i	0.381560	−	0.381560i
$276$	26.6341	−	21.4824i	1.60318	−	1.29309i
$277$	13.7619	−	13.7619i	0.826875	−	0.826875i	−0.160208	−	0.987083i	$-0.551217\pi$
$277$	13.7619	−	13.7619i	0.826875	−	0.826875i	0.987083	+	0.160208i	$0.0512166\pi$
$278$	26.3715	+	1.40774i	1.58166	+	0.0844307i
$279$			9.81146i			0.587397i
$280$		0			0
$281$		−	12.3856i		−	0.738865i	−0.929258	−	0.369432i	$-0.879552\pi$
$281$		−	12.3856i		−	0.738865i	0.929258	−	0.369432i	$-0.120448\pi$
$282$	1.97284	−	36.9576i	0.117481	−	2.20079i
$283$	2.67193	−	2.67193i	0.158830	−	0.158830i	−0.623218	−	0.782048i	$-0.714175\pi$
$283$	2.67193	−	2.67193i	0.158830	−	0.158830i	0.782048	+	0.623218i	$0.214175\pi$
$284$	2.79446	−	26.1000i	0.165821	−	1.54875i
$285$	−11.8948	+	11.8948i	−0.704588	+	0.704588i
$286$	−0.946838	−	1.05362i	−0.0559877	−	0.0623021i
$287$		0			0
$288$	13.0303	−	7.43896i	0.767818	−	0.438345i
$289$	16.9968			0.999813
$290$	6.20056	−	5.57212i	0.364109	−	0.327206i
$291$	−15.2363	+	15.2363i	−0.893168	+	0.893168i
$292$	−1.14802	+	10.7224i	−0.0671829	+	0.627482i
$293$	2.83797	+	2.83797i	0.165796	+	0.165796i	0.785129	−	0.619333i	$-0.212597\pi$
$293$	2.83797	+	2.83797i	0.165796	+	0.165796i	−0.619333	+	0.785129i	$0.712597\pi$
$294$		0			0
$295$	7.61041			0.443095
$296$	1.52546	−	9.45316i	0.0886658	−	0.549454i
$297$	−1.73952			−0.100937
$298$	5.70314	+	0.304441i	0.330374	+	0.0176358i
$299$	−2.42149	+	2.42149i	−0.140038	+	0.140038i
$300$	−12.6908	−	15.7342i	−0.732706	−	0.908417i
$301$		0			0
$302$	−7.46518	−	8.30713i	−0.429573	−	0.478022i
$303$			22.8218i			1.31108i
$304$	−17.7070	−	27.4996i	−1.01557	−	1.57721i
$305$	5.57145			0.319021
$306$	−0.141470	−	0.157426i	−0.00808731	−	0.00899942i
$307$	17.5282	+	17.5282i	1.00038	+	1.00038i	1.00000		0.000384595i	$0.000122420\pi$
$307$	17.5282	+	17.5282i	1.00038	+	1.00038i	0.000384595		1.00000i	$0.499878\pi$
$308$		0			0
$309$	−2.30951	+	2.30951i	−0.131384	+	0.131384i
$310$	0.241297	−	4.52027i	0.0137048	−	0.256734i
$311$			22.4197i			1.27130i	0.771976	+	0.635651i	$0.219268\pi$
$311$			22.4197i			1.27130i	−0.771976	+	0.635651i	$0.780732\pi$
$312$	−2.59433	+	1.87337i	−0.146875	+	0.106059i
$313$	7.73860			0.437412			0.218706	−	0.975791i	$-0.429816\pi$
$313$	7.73860			0.437412			0.218706	+	0.975791i	$0.429816\pi$
$314$	−22.8200	−	1.21816i	−1.28781	−	0.0687446i
$315$		0			0
$316$	−11.4726	−	1.22835i	−0.645387	−	0.0690999i
$317$	−2.29043	−	2.29043i	−0.128643	−	0.128643i	0.639853	−	0.768497i	$-0.278995\pi$
$317$	−2.29043	−	2.29043i	−0.128643	−	0.128643i	−0.768497	+	0.639853i	$0.778995\pi$
$318$	8.43537	+	9.38673i	0.473032	+	0.526382i
$319$			14.3390i			0.802832i
$320$	−6.18617	+	3.10676i	−0.345818	+	0.173673i
$321$			33.2654i			1.85669i
$322$		0			0
$323$	−0.326241	+	0.326241i	−0.0181525	+	0.0181525i
$324$	−2.11257	+	19.7312i	−0.117365	+	1.09618i
$325$	1.43051	+	1.43051i	0.0793503	+	0.0793503i
$326$	4.37170	+	0.233366i	0.242126	+	0.0129250i
$327$		−	6.61847i		−	0.366002i
$328$	11.3733	−	8.21268i	0.627985	−	0.453469i
$329$		0			0
$330$	−6.11524	−	0.326439i	−0.336633	−	0.0179699i
$331$	2.94412	+	2.94412i	0.161824	+	0.161824i	0.783374	−	0.621550i	$-0.213497\pi$
$331$	2.94412	+	2.94412i	0.161824	+	0.161824i	−0.621550	+	0.783374i	$0.713497\pi$
$332$	−9.96996	+	8.04152i	−0.547173	+	0.441336i
$333$	−6.34947	−	6.34947i	−0.347949	−	0.347949i
$334$	−5.92162	+	5.32145i	−0.324016	+	0.291177i
$335$	−9.37062			−0.511972
$336$		0			0
$337$	−6.10926			−0.332793			−0.166396	−	0.986059i	$-0.553213\pi$
$337$	−6.10926			−0.332793			−0.166396	+	0.986059i	$0.553213\pi$
$338$	−13.4363	+	12.0745i	−0.730837	+	0.656766i
$339$	−11.3362	−	11.3362i	−0.615695	−	0.615695i
$340$	0.0613055	+	0.0760072i	0.00332476	+	0.00412207i
$341$	5.50565	+	5.50565i	0.298148	+	0.298148i
$342$	−30.6281	−	1.63496i	−1.65618	−	0.0884087i
$343$		0			0
$344$	−19.7376	−	3.18508i	−1.06418	−	0.171728i
$345$			14.8046i			0.797051i
$346$	−2.48145	−	0.132463i	−0.133403	−	0.00712123i
$347$	−21.9718	−	21.9718i	−1.17951	−	1.17951i	−0.979869	−	0.199640i	$-0.936023\pi$
$347$	−21.9718	−	21.9718i	−1.17951	−	1.17951i	−0.199640	−	0.979869i	$-0.563977\pi$
$348$	32.2079	+	3.44842i	1.72653	+	0.184855i
$349$	−5.02028	+	5.02028i	−0.268730	+	0.268730i	−0.828588	−	0.559859i	$-0.810855\pi$
$349$	−5.02028	+	5.02028i	−0.268730	+	0.268730i	0.559859	+	0.828588i	$0.310855\pi$
$350$		0			0
$351$		−	0.393269i		−	0.0209911i
$352$	3.13755	−	11.4862i	0.167232	−	0.612218i
$353$		−	22.5953i		−	1.20263i	−0.799012	−	0.601314i	$-0.794644\pi$
$353$		−	22.5953i		−	1.20263i	0.799012	−	0.601314i	$-0.205356\pi$
$354$	19.7656	+	21.9948i	1.05053	+	1.16901i
$355$	8.03049	+	8.03049i	0.426214	+	0.426214i
$356$	0.545998	−	5.09957i	0.0289378	−	0.270276i
$357$		0			0
$358$	−10.8181	−	0.577483i	−0.571755	−	0.0305209i
$359$	−11.6106			−0.612782			−0.306391	−	0.951906i	$-0.599121\pi$
$359$	−11.6106			−0.612782			−0.306391	+	0.951906i	$0.599121\pi$
$360$	−1.03419	+	6.40874i	−0.0545063	+	0.337770i
$361$			47.8604i			2.51897i
$362$	0.000477620	−	0.00894735i	2.51032e−5	−	0.000470262i
$363$	−11.0441	+	11.0441i	−0.579665	+	0.579665i
$364$		0			0
$365$	−3.29909	−	3.29909i	−0.172682	−	0.172682i
$366$	14.4701	+	16.1020i	0.756362	+	0.841667i
$367$	34.2580			1.78825			0.894126	−	0.447816i	$-0.147798\pi$
$367$	34.2580			1.78825			0.894126	+	0.447816i	$0.147798\pi$
$368$	−28.1326	−	6.09404i	−1.46651	−	0.317674i
$369$		−	13.1554i		−	0.684845i
$370$	2.76913	+	3.08144i	0.143960	+	0.160196i
$371$		0			0
$372$	13.6907	−	11.0426i	0.709830	−	0.572531i
$373$	−17.7221	+	17.7221i	−0.917617	+	0.917617i	−0.996856	−	0.0792383i	$-0.974751\pi$
$373$	−17.7221	+	17.7221i	−0.917617	+	0.917617i	0.0792383	+	0.996856i	$0.474751\pi$
$374$	−0.167724	−	0.00895330i	−0.00867279	−	0.000462964i
$375$	19.0322			0.982816
$376$	−25.2411	+	18.2267i	−1.30171	+	0.939970i
$377$	−3.24176			−0.166959
$378$		0			0
$379$	−19.0292	−	19.0292i	−0.977466	−	0.977466i	0.0222852	−	0.999752i	$-0.492906\pi$
$379$	−19.0292	−	19.0292i	−0.977466	−	0.977466i	−0.999752	+	0.0222852i	$0.992906\pi$
$380$	14.0706	+	1.50650i	0.721804	+	0.0772817i
$381$	14.4991	−	14.4991i	0.742812	−	0.742812i
$382$	−16.2006	+	14.5586i	−0.828892	+	0.744882i
$383$	−22.7286			−1.16138			−0.580690	−	0.814125i	$-0.697217\pi$
$383$	−22.7286			−1.16138			−0.580690	+	0.814125i	$0.697217\pi$
$384$	−25.0454	−	9.80982i	−1.27810	−	0.500605i
$385$		0			0
$386$	−1.46579	−	1.63110i	−0.0746066	−	0.0830209i
$387$	−13.2573	+	13.2573i	−0.673908	+	0.673908i
$388$	18.0233	+	1.92970i	0.914992	+	0.0979659i
$389$	−19.0824	+	19.0824i	−0.967517	+	0.967517i	−0.999489	−	0.0319722i	$-0.989821\pi$
$389$	−19.0824	+	19.0824i	−0.967517	+	0.967517i	0.0319722	+	0.999489i	$0.489821\pi$
$390$	0.0738011	−	1.38253i	0.00373707	−	0.0700072i
$391$			0.406048i			0.0205347i
$392$		0			0
$393$			12.8052i			0.645938i
$394$	2.10057	+	0.112131i	0.105825	+	0.00564908i
$395$	3.52993	−	3.52993i	0.177610	−	0.177610i
$396$	−7.01012	−	8.69123i	−0.352272	−	0.436751i
$397$	17.8975	−	17.8975i	0.898248	−	0.898248i	−0.0970328	−	0.995281i	$-0.530935\pi$
$397$	17.8975	−	17.8975i	0.898248	−	0.898248i	0.995281	+	0.0970328i	$0.0309352\pi$
$398$	13.3159	−	11.9663i	0.667464	−	0.599815i
$399$		0			0
$400$	−3.60009	+	16.6195i	−0.180004	+	0.830975i
$401$	−3.51654			−0.175607			−0.0878037	−	0.996138i	$-0.527985\pi$
$401$	−3.51654			−0.175607			−0.0878037	+	0.996138i	$0.527985\pi$
$402$	−24.3372	−	27.0820i	−1.21383	−	1.35073i
$403$	−1.24472	+	1.24472i	−0.0620037	+	0.0620037i
$404$	14.9433	−	12.0529i	0.743457	−	0.599654i
$405$	−6.07093	−	6.07093i	−0.301667	−	0.301667i
$406$		0			0
$407$	−7.12595			−0.353220
$408$	−0.0604468	+	0.374583i	−0.00299256	+	0.0185446i
$409$	−18.6724			−0.923292			−0.461646	−	0.887064i	$-0.652741\pi$
$409$	−18.6724			−0.923292			−0.461646	+	0.887064i	$0.652741\pi$
$410$	−0.323537	+	6.06088i	−0.0159784	+	0.299326i
$411$	−18.0914	+	18.0914i	−0.892383	+	0.892383i
$412$	2.73196	+	0.292504i	0.134594	+	0.0144106i
$413$		0			0
$414$	−20.0777	+	18.0428i	−0.986765	+	0.886754i
$415$		−	5.54180i		−	0.272036i
$416$	2.59680	+	0.709336i	0.127319	+	0.0347781i
$417$	−44.3970			−2.17413
$418$	−18.1043	+	16.2694i	−0.885508	+	0.795760i
$419$	−2.28986	−	2.28986i	−0.111867	−	0.111867i	0.648958	−	0.760825i	$-0.275205\pi$
$419$	−2.28986	−	2.28986i	−0.111867	−	0.111867i	−0.760825	+	0.648958i	$0.775205\pi$
$420$		0			0
$421$	−0.821840	+	0.821840i	−0.0400540	+	0.0400540i	−0.726850	−	0.686796i	$-0.759017\pi$
$421$	−0.821840	+	0.821840i	−0.0400540	+	0.0400540i	0.686796	+	0.726850i	$0.259017\pi$
$422$	1.65866	+	0.0885415i	0.0807425	+	0.00431013i
$423$			29.1964i			1.41958i
$424$	1.69129	−	10.4808i	0.0821364	−	0.508991i
$425$	0.239875			0.0116356
$426$	−2.35227	+	44.0655i	−0.113968	+	2.13498i
$427$		0			0
$428$	21.7816	−	17.5685i	1.05286	−	0.849207i
$429$	1.68391	+	1.68391i	0.0813001	+	0.0813001i
$430$	6.43387	−	5.78178i	0.310269	−	0.278822i
$431$		−	20.4370i		−	0.984414i	−0.870478	−	0.492207i	$-0.836190\pi$
$431$		−	20.4370i		−	0.984414i	0.870478	−	0.492207i	$-0.163810\pi$
$432$	2.77934	−	1.78962i	0.133721	−	0.0861032i
$433$		−	34.7460i		−	1.66979i	−0.550413	−	0.834893i	$-0.685530\pi$
$433$		−	34.7460i		−	1.66979i	0.550413	−	0.834893i	$-0.314470\pi$
$434$		0			0
$435$	−9.90979	+	9.90979i	−0.475138	+	0.475138i
$436$	−4.33366	+	3.49542i	−0.207545	+	0.167400i
$437$	41.6080	+	41.6080i	1.99038	+	1.99038i
$438$	0.966361	−	18.1030i	0.0461745	−	0.864996i
$439$		−	32.6135i		−	1.55656i	−0.627919	−	0.778278i	$-0.716093\pi$
$439$		−	32.6135i		−	1.55656i	0.627919	−	0.778278i	$-0.283907\pi$
$440$	3.01591	+	4.17656i	0.143778	+	0.199110i
$441$		0			0
$442$	0.00202416	−	0.0379189i	9.62793e−5	−	0.00180362i
$443$	−9.76396	−	9.76396i	−0.463900	−	0.463900i	0.436032	−	0.899931i	$-0.356384\pi$
$443$	−9.76396	−	9.76396i	−0.463900	−	0.463900i	−0.899931	+	0.436032i	$0.856384\pi$
$444$	−1.71373	+	16.0061i	−0.0813301	+	0.759616i
$445$	1.56904	+	1.56904i	0.0743798	+	0.0743798i
$446$	−3.96718	−	4.41461i	−0.187852	−	0.209038i
$447$	−9.60138			−0.454130
$448$		0			0
$449$	−17.6685			−0.833830			−0.416915	−	0.908946i	$-0.636889\pi$
$449$	−17.6685			−0.833830			−0.416915	+	0.908946i	$0.636889\pi$
$450$	10.6589	+	11.8610i	0.502464	+	0.559133i
$451$	−7.38211	−	7.38211i	−0.347610	−	0.347610i
$452$	−1.43574	+	13.4097i	−0.0675317	+	0.630740i
$453$	13.2765	+	13.2765i	0.623786	+	0.623786i
$454$	−0.969591	+	18.1635i	−0.0455052	+	0.852457i
$455$		0			0
$456$	32.1898	+	44.5779i	1.50743	+	2.08755i
$457$		−	4.05357i		−	0.189618i	−0.995495	−	0.0948090i	$-0.969776\pi$
$457$		−	4.05357i		−	0.189618i	0.995495	−	0.0948090i	$-0.0302240\pi$
$458$	−1.52529	+	28.5735i	−0.0712719	+	1.33515i
$459$	−0.0329727	−	0.0329727i	−0.00153903	−	0.00153903i
$460$	9.69379	−	7.81876i	0.451975	−	0.364552i
$461$	−2.39386	+	2.39386i	−0.111493	+	0.111493i	−0.760653	−	0.649159i	$-0.775121\pi$
$461$	−2.39386	+	2.39386i	−0.111493	+	0.111493i	0.649159	+	0.760653i	$0.275121\pi$
$462$		0			0
$463$			30.7630i			1.42968i	0.699289	+	0.714839i	$0.253500\pi$
$463$			30.7630i			1.42968i	−0.699289	+	0.714839i	$0.746500\pi$
$464$	−14.7521	−	22.9104i	−0.684847	−	1.06359i
$465$			7.60998i			0.352904i
$466$	24.1208	−	21.6761i	1.11737	−	1.00413i
$467$	5.08862	+	5.08862i	0.235473	+	0.235473i	0.814973	−	0.579500i	$-0.196752\pi$
$467$	5.08862	+	5.08862i	0.235473	+	0.235473i	−0.579500	+	0.814973i	$0.696752\pi$
$468$	1.96491	−	1.58484i	0.0908279	−	0.0732595i
$469$		0			0
$470$	0.718038	−	13.4511i	0.0331206	−	0.620455i
$471$	38.4179			1.77021
$472$	3.96300	−	24.5583i	0.182412	−	1.13039i
$473$			14.8786i			0.684117i
$474$	19.3697	+	1.03398i	0.889678	+	0.0474921i
$475$	24.5802	−	24.5802i	1.12782	−	1.12782i
$476$		0			0
$477$	−7.03969	−	7.03969i	−0.322325	−	0.322325i
$478$	−5.39581	+	4.84894i	−0.246799	+	0.221785i
$479$	2.85508			0.130452			0.0652259	−	0.997871i	$-0.479223\pi$
$479$	2.85508			0.130452			0.0652259	+	0.997871i	$0.479223\pi$
$480$	10.1066	−	5.76981i	0.461300	−	0.263355i
$481$		−	1.61103i		−	0.0734567i
$482$	−17.8299	+	16.0228i	−0.812128	+	0.729817i
$483$		0			0
$484$	13.0642	+	1.39876i	0.593829	+	0.0635798i
$485$	−5.54543	+	5.54543i	−0.251805	+	0.251805i
$486$	1.59138	−	29.8116i	0.0721865	−	1.35228i
$487$	33.2105			1.50491			0.752457	−	0.658642i	$-0.228869\pi$
$487$	33.2105			1.50491			0.752457	+	0.658642i	$0.228869\pi$
$488$	2.90125	−	17.9788i	0.131333	−	0.813860i
$489$	−7.35986			−0.332824
$490$		0			0
$491$	−23.0686	−	23.0686i	−1.04107	−	1.04107i	−0.999120	−	0.0419533i	$-0.986642\pi$
$491$	−23.0686	−	23.0686i	−1.04107	−	1.04107i	−0.0419533	−	0.999120i	$-0.513358\pi$
$492$	−18.3568	+	14.8061i	−0.827589	+	0.667513i
$493$	−0.271798	+	0.271798i	−0.0122411	+	0.0122411i
$494$	−3.67817	−	4.09300i	−0.165489	−	0.184153i
$495$	4.83102			0.217138
$496$	−14.4610	−	3.13251i	−0.649317	−	0.140654i
$497$		0			0
$498$	16.0163	−	14.3931i	0.717710	−	0.644968i
$499$	14.6871	−	14.6871i	0.657486	−	0.657486i	−0.297298	−	0.954785i	$-0.596086\pi$
$499$	14.6871	−	14.6871i	0.657486	−	0.657486i	0.954785	+	0.297298i	$0.0960856\pi$
$500$	−10.0515	−	12.4619i	−0.449516	−	0.557315i
$501$	9.46398	−	9.46398i	0.422820	−	0.422820i
$502$	−3.27076	−	0.174597i	−0.145981	−	0.00779266i
$503$		−	0.960903i		−	0.0428445i	−0.999771	−	0.0214223i	$-0.993181\pi$
$503$		−	0.960903i		−	0.0428445i	0.999771	−	0.0214223i	$-0.00681944\pi$
$504$		0			0
$505$			8.30624i			0.369623i
$506$	−1.14188	+	21.3911i	−0.0507629	+	0.950951i
$507$	21.4740	−	21.4740i	0.953694	−	0.953694i
$508$	−17.1512	−	1.83634i	−0.760963	−	0.0814743i
$509$	−1.93431	+	1.93431i	−0.0857366	+	0.0857366i	−0.748674	−	0.662938i	$-0.769309\pi$
$509$	−1.93431	+	1.93431i	−0.0857366	+	0.0857366i	0.662938	+	0.748674i	$0.269309\pi$
$510$	−0.109727	−	0.122103i	−0.00485880	−	0.00540679i
$511$		0			0
$512$	6.80399	+	21.5802i	0.300697	+	0.953720i
$513$	−6.75748			−0.298350
$514$	8.51387	−	7.65097i	0.375531	−	0.337470i
$515$	−0.840574	+	0.840574i	−0.0370401	+	0.0370401i
$516$	33.4198	+	3.57817i	1.47122	+	0.157520i
$517$	16.3834	+	16.3834i	0.720541	+	0.720541i
$518$		0			0
$519$	4.17758			0.183375
$520$	−0.944235	+	0.681835i	−0.0414074	+	0.0299004i
$521$	−39.3498			−1.72394			−0.861972	−	0.506956i	$-0.830771\pi$
$521$	−39.3498			−1.72394			−0.861972	+	0.506956i	$0.830771\pi$
$522$	−25.5168	−	1.36212i	−1.11684	−	0.0596183i
$523$	2.77949	−	2.77949i	0.121538	−	0.121538i	−0.643721	−	0.765260i	$-0.722610\pi$
$523$	2.77949	−	2.77949i	0.121538	−	0.121538i	0.765260	+	0.643721i	$0.222610\pi$
$524$	8.38465	−	6.76285i	0.366285	−	0.295436i
$525$		0			0
$526$	−14.0246	−	15.6064i	−0.611503	−	0.680470i
$527$			0.208720i			0.00909200i
$528$	−4.23782	+	19.5635i	−0.184427	+	0.851394i
$529$	28.7864			1.25158
$530$	3.07015	+	3.41641i	0.133359	+	0.148399i
$531$	−16.4953	−	16.4953i	−0.715834	−	0.715834i
$532$		0			0
$533$	1.66894	−	1.66894i	0.0722900	−	0.0722900i
$534$	−0.459600	+	8.60977i	−0.0198888	+	0.372581i
$535$			12.1073i			0.523446i
$536$	−4.87961	+	30.2384i	−0.210767	+	1.30610i
$537$	18.2125			0.785929
$538$	−0.342225	−	0.0182684i	−0.0147544	−	0.000787607i
$539$		0			0
$540$	−0.152259	+	1.42209i	−0.00655220	+	0.0611970i
$541$	−27.0467	−	27.0467i	−1.16283	−	1.16283i	−0.983854	−	0.178974i	$-0.942722\pi$
$541$	−27.0467	−	27.0467i	−1.16283	−	1.16283i	−0.178974	−	0.983854i	$-0.557278\pi$
$542$	21.2014	+	23.5926i	0.910679	+	1.01339i
$543$			0.0150631i			0.000646418i
$544$	0.277195	−	0.158250i	0.0118846	−	0.00678490i
$545$		−	2.40887i		−	0.103185i
$546$		0			0
$547$	17.4654	−	17.4654i	0.746767	−	0.746767i	−0.227104	−	0.973871i	$-0.572926\pi$
$547$	17.4654	−	17.4654i	0.746767	−	0.746767i	0.973871	+	0.227104i	$0.0729256\pi$
$548$	21.4006	+	2.29131i	0.914188	+	0.0978798i
$549$	−12.0759	−	12.0759i	−0.515388	−	0.515388i
$550$	12.6369	+	0.674574i	0.538840	+	0.0287639i
$551$			55.7026i			2.37301i
$552$	47.7735	+	7.70925i	2.03337	+	0.328128i
$553$		0			0
$554$	27.4847	+	1.46717i	1.16771	+	0.0623340i
$555$	−4.92478	−	4.92478i	−0.209045	−	0.209045i
$556$	23.4475	+	29.0704i	0.994394	+	1.23286i
$557$	−16.3565	−	16.3565i	−0.693048	−	0.693048i	0.269853	−	0.962901i	$-0.413025\pi$
$557$	−16.3565	−	16.3565i	−0.693048	−	0.693048i	−0.962901	+	0.269853i	$0.913025\pi$
$558$	−10.3205	+	9.27451i	−0.436902	+	0.392621i
$559$	−3.36374			−0.142271
$560$		0			0
$561$	0.282367			0.0119215
$562$	13.0282	−	11.7078i	0.549563	−	0.493864i
$563$	12.2087	+	12.2087i	0.514535	+	0.514535i	0.915913	−	0.401378i	$-0.131468\pi$
$563$	12.2087	+	12.2087i	0.514535	+	0.514535i	−0.401378	+	0.915913i	$0.631468\pi$
$564$	40.7400	−	32.8598i	1.71546	−	1.38365i
$565$	−4.12592	−	4.12592i	−0.173579	−	0.173579i
$566$	5.33626	+	0.284856i	0.224300	+	0.0119734i
$567$		0			0
$568$	30.0957	−	21.7322i	1.26279	−	0.911861i
$569$			21.1145i			0.885167i	0.896727	+	0.442583i	$0.145938\pi$
$569$			21.1145i			0.885167i	−0.896727	+	0.442583i	$0.854062\pi$
$570$	−23.7558	−	1.26811i	−0.995021	−	0.0531154i
$571$	9.33006	+	9.33006i	0.390451	+	0.390451i	0.874848	−	0.484397i	$-0.160961\pi$
$571$	9.33006	+	9.33006i	0.390451	+	0.390451i	−0.484397	+	0.874848i	$0.660961\pi$
$572$	0.213270	−	1.99193i	0.00891729	−	0.0832866i
$573$	25.8919	−	25.8919i	1.08165	−	1.08165i
$574$		0			0
$575$		−	30.5931i		−	1.27582i
$576$	20.1421	+	6.67451i	0.839254	+	0.278105i
$577$		−	25.0806i		−	1.04412i	−0.852908	−	0.522061i	$-0.825164\pi$
$577$		−	25.0806i		−	1.04412i	0.852908	−	0.522061i	$-0.174836\pi$
$578$	16.0666	+	17.8787i	0.668284	+	0.743655i
$579$	2.60684	+	2.60684i	0.108337	+	0.108337i
$580$	11.7224	+	1.25509i	0.486748	+	0.0521149i
$581$		0			0
$582$	−30.4293	−	1.62435i	−1.26133	−	0.0673315i
$583$	−7.90058			−0.327209
$584$	−12.3639	+	8.92802i	−0.511623	+	0.369444i
$585$			1.09219i			0.0451567i
$586$	−0.302557	+	5.66786i	−0.0124985	+	0.234137i
$587$	0.705313	−	0.705313i	0.0291114	−	0.0291114i	−0.692401	−	0.721513i	$-0.743447\pi$
$587$	0.705313	−	0.705313i	0.0291114	−	0.0291114i	0.721513	+	0.692401i	$0.243447\pi$
$588$		0			0
$589$	21.3877	+	21.3877i	0.881266	+	0.881266i
$590$	7.19391	+	8.00526i	0.296169	+	0.329572i
$591$	−3.53636			−0.145467
$592$	11.3856	−	7.33120i	0.467945	−	0.301311i
$593$		−	43.0219i		−	1.76670i	−0.468714	−	0.883350i	$-0.655283\pi$
$593$		−	43.0219i		−	1.76670i	0.468714	−	0.883350i	$-0.344717\pi$
$594$	−1.64432	−	1.82977i	−0.0674672	−	0.0750763i
$595$		0			0
$596$	5.07079	+	6.28682i	0.207708	+	0.257518i
$597$	−21.2815	+	21.2815i	−0.870996	+	0.870996i
$598$	−4.83609	−	0.258156i	−0.197763	−	0.0105568i
$599$	23.4964			0.960039			0.480019	−	0.877258i	$-0.340630\pi$
$599$	23.4964			0.960039			0.480019	+	0.877258i	$0.340630\pi$
$600$	4.55428	−	28.2224i	0.185928	−	1.15218i
$601$	42.4771			1.73268			0.866339	−	0.499456i	$-0.166467\pi$
$601$	42.4771			1.73268			0.866339	+	0.499456i	$0.166467\pi$
$602$		0			0
$603$	20.3105	+	20.3105i	0.827107	+	0.827107i
$604$	1.68150	−	15.7050i	0.0684191	−	0.639028i
$605$	−4.01963	+	4.01963i	−0.163421	+	0.163421i
$606$	−24.0058	+	21.5728i	−0.975170	+	0.876335i
$607$	21.1066			0.856689			0.428345	−	0.903615i	$-0.359097\pi$
$607$	21.1066			0.856689			0.428345	+	0.903615i	$0.359097\pi$
$608$	12.1884	−	44.6203i	0.494305	−	1.80959i
$609$		0			0
$610$	5.26655	+	5.86052i	0.213236	+	0.237286i
$611$	−3.70395	+	3.70395i	−0.149846	+	0.149846i
$612$	0.0318655	−	0.297620i	0.00128808	−	0.0120306i
$613$	−7.89607	+	7.89607i	−0.318919	+	0.318919i	−0.848352	−	0.529433i	$-0.822405\pi$
$613$	−7.89607	+	7.89607i	−0.318919	+	0.318919i	0.529433	+	0.848352i	$0.322405\pi$
$614$	−1.86869	+	35.0065i	−0.0754141	+	1.41275i
$615$		−	10.2036i		−	0.411451i
$616$		0			0
$617$			18.9275i			0.761992i	0.924577	+	0.380996i	$0.124419\pi$
$617$			18.9275i			0.761992i	−0.924577	+	0.380996i	$0.875581\pi$
$618$	−4.61246	−	0.246219i	−0.185540	−	0.00990437i
$619$	−6.00291	+	6.00291i	−0.241277	+	0.241277i	−0.817378	−	0.576101i	$-0.804573\pi$
$619$	−6.00291	+	6.00291i	−0.241277	+	0.241277i	0.576101	+	0.817378i	$0.304573\pi$
$620$	4.98289	−	4.01907i	0.200118	−	0.161410i
$621$	−4.20526	+	4.20526i	−0.168751	+	0.168751i
$622$	−23.5829	+	21.1927i	−0.945588	+	0.849750i
$623$		0			0
$624$	−4.42291	−	0.958083i	−0.177058	−	0.0383540i
$625$	−14.3292			−0.573169
$626$	7.31509	+	8.14011i	0.292370	+	0.325344i
$627$	28.9344	−	28.9344i	1.15553	−	1.15553i
$628$	−20.2897	−	25.1554i	−0.809649	−	1.00381i
$629$	−0.135073	−	0.135073i	−0.00538571	−	0.00538571i
$630$		0			0
$631$	8.88067			0.353534			0.176767	−	0.984253i	$-0.443436\pi$
$631$	8.88067			0.353534			0.176767	+	0.984253i	$0.443436\pi$
$632$	−9.55271	−	13.2290i	−0.379986	−	0.526222i
$633$	−2.79240			−0.110988
$634$	0.244184	−	4.57435i	0.00969779	−	0.181671i
$635$	5.27712	−	5.27712i	0.209416	−	0.209416i
$636$	−1.90002	+	17.7460i	−0.0753409	+	0.703676i
$637$		0			0
$638$	−15.0830	+	13.5543i	−0.597142	+	0.536620i
$639$		−	34.8116i		−	1.37713i
$640$	−9.11558	−	3.57039i	−0.360325	−	0.141132i
$641$	−2.05235			−0.0810628			−0.0405314	−	0.999178i	$-0.512905\pi$
$641$	−2.05235			−0.0810628			−0.0405314	+	0.999178i	$0.512905\pi$
$642$	−34.9914	+	31.4449i	−1.38100	+	1.24103i
$643$	−20.1070	−	20.1070i	−0.792942	−	0.792942i	0.189029	−	0.981971i	$-0.439466\pi$
$643$	−20.1070	−	20.1070i	−0.792942	−	0.792942i	−0.981971	+	0.189029i	$0.939466\pi$
$644$		0			0
$645$	−10.2827	+	10.2827i	−0.404880	+	0.404880i
$646$	−0.651554	−	0.0347808i	−0.0256351	−	0.00136843i
$647$		−	12.3406i		−	0.485157i	−0.970132	−	0.242579i	$-0.922007\pi$
$647$		−	12.3406i		−	0.485157i	0.970132	−	0.242579i	$-0.0779933\pi$
$648$	−22.7519	+	16.4292i	−0.893778	+	0.645399i
$649$	−18.5125			−0.726679
$650$	−0.152507	+	2.85695i	−0.00598183	+	0.112059i
$651$		0			0
$652$	3.88697	+	4.81911i	0.152226	+	0.188731i
$653$	30.1729	+	30.1729i	1.18076	+	1.18076i	0.979548	+	0.201209i	$0.0644870\pi$
$653$	30.1729	+	30.1729i	1.18076	+	1.18076i	0.201209	+	0.979548i	$0.435513\pi$
$654$	6.96186	−	6.25626i	0.272230	−	0.244639i
$655$			4.66061i			0.182105i
$656$	19.3896	+	4.20015i	0.757038	+	0.163988i
$657$			14.3013i			0.557948i
$658$		0			0
$659$	19.4114	−	19.4114i	0.756162	−	0.756162i	−0.219460	−	0.975622i	$-0.570429\pi$
$659$	19.4114	−	19.4114i	0.756162	−	0.756162i	0.975622	+	0.219460i	$0.0704294\pi$
$660$	−5.43720	−	6.74110i	−0.211643	−	0.262397i
$661$	−23.3763	−	23.3763i	−0.909234	−	0.909234i	0.0869762	−	0.996210i	$-0.472280\pi$
$661$	−23.3763	−	23.3763i	−0.909234	−	0.909234i	−0.996210	+	0.0869762i	$0.972280\pi$
$662$	−0.313875	+	5.87987i	−0.0121991	+	0.228528i
$663$			0.0638374i			0.00247924i
$664$	−17.8831	−	2.88581i	−0.693998	−	0.111991i
$665$		0			0
$666$	0.676921	−	12.6809i	0.0262302	−	0.491374i
$667$	34.6644	+	34.6644i	1.34221	+	1.34221i
$668$	−11.1951	−	1.19863i	−0.433151	−	0.0463764i
$669$	7.05548	+	7.05548i	0.272780	+	0.272780i
$670$	−8.85780	−	9.85680i	−0.342206	−	0.380802i
$671$	−13.5527			−0.523196
$672$		0			0
$673$	−2.56169			−0.0987460			−0.0493730	−	0.998780i	$-0.515722\pi$
$673$	−2.56169			−0.0987460			−0.0493730	+	0.998780i	$0.515722\pi$
$674$	−5.77492	−	6.42623i	−0.222442	−	0.247529i
$675$	2.48428	+	2.48428i	0.0956200	+	0.0956200i
$676$	−25.4019	−	2.71972i	−0.976997	−	0.104605i
$677$	−17.0026	−	17.0026i	−0.653463	−	0.653463i	0.300363	−	0.953825i	$-0.402892\pi$
$677$	−17.0026	−	17.0026i	−0.653463	−	0.653463i	−0.953825	+	0.300363i	$0.902892\pi$
$678$	1.20855	−	22.6401i	0.0464142	−	0.869487i
$679$		0			0
$680$	−0.0220003	+	0.136334i	−0.000843674	+	0.00522816i
$681$		−	30.5787i		−	1.17178i
$682$	−0.586961	+	10.9957i	−0.0224759	+	0.421045i
$683$	−10.1770	−	10.1770i	−0.389412	−	0.389412i	0.485066	−	0.874478i	$-0.338796\pi$
$683$	−10.1770	−	10.1770i	−0.389412	−	0.389412i	−0.874478	+	0.485066i	$0.838796\pi$
$684$	−27.2321	−	33.7627i	−1.04125	−	1.29095i
$685$	−6.58458	+	6.58458i	−0.251584	+	0.251584i
$686$		0			0
$687$		−	48.1041i		−	1.83529i
$688$	−15.3071	−	23.7725i	−0.583579	−	0.906317i
$689$		−	1.78616i		−	0.0680472i
$690$	−15.5727	+	13.9944i	−0.592842	+	0.532756i
$691$	−31.1163	−	31.1163i	−1.18372	−	1.18372i	−0.978773	−	0.204947i	$-0.934298\pi$
$691$	−31.1163	−	31.1163i	−1.18372	−	1.18372i	−0.204947	−	0.978773i	$-0.565702\pi$
$692$	−2.20631	−	2.73541i	−0.0838713	−	0.103985i
$693$		0			0
$694$	2.34243	−	43.8812i	0.0889174	−	1.66571i
$695$	−16.1588			−0.612938
$696$	26.8179	+	37.1387i	1.01653	+	1.40774i
$697$		−	0.279857i		−	0.0106003i
$698$	−10.0263	−	0.535215i	−0.379501	−	0.0202582i
$699$	−38.5501	+	38.5501i	−1.45810	+	1.45810i
$700$		0			0
$701$	15.8844	+	15.8844i	0.599946	+	0.599946i	0.940298	−	0.340352i	$-0.110546\pi$
$701$	15.8844	+	15.8844i	0.599946	+	0.599946i	−0.340352	+	0.940298i	$0.610546\pi$
$702$	0.413673	−	0.371747i	0.0156131	−	0.0140307i
$703$	−27.6821			−1.04405
$704$	15.0480	−	7.55727i	0.567143	−	0.284825i
$705$			22.6453i			0.852872i
$706$	23.7677	−	21.3588i	0.894508	−	0.803848i
$707$		0			0
$708$	−4.45210	+	41.5822i	−0.167320	+	1.56275i
$709$	18.5464	−	18.5464i	0.696523	−	0.696523i	−0.267136	−	0.963659i	$-0.586077\pi$
$709$	18.5464	−	18.5464i	0.696523	−	0.696523i	0.963659	+	0.267136i	$0.0860771\pi$
$710$	−0.856135	+	16.0381i	−0.0321302	+	0.601901i
$711$	−15.3020			−0.573869
$712$	5.88027	−	4.24616i	0.220372	−	0.159131i
$713$	26.6197			0.996916
$714$		0			0
$715$	0.612879	+	0.612879i	0.0229204	+	0.0229204i
$716$	−9.61862	−	11.9253i	−0.359465	−	0.445668i
$717$	8.62364	−	8.62364i	0.322056	−	0.322056i
$718$	−10.9751	−	12.2130i	−0.409589	−	0.455783i
$719$	−15.7107			−0.585909			−0.292954	−	0.956126i	$-0.594638\pi$
$719$	−15.7107			−0.585909			−0.292954	+	0.956126i	$0.594638\pi$
$720$	−7.71884	+	4.97017i	−0.287664	+	0.185227i
$721$		0			0
$722$	−50.3436	+	45.2411i	−1.87359	+	1.68370i
$723$	28.4958	−	28.4958i	1.05977	−	1.05977i
$724$	0.00986305	−	0.00795529i	0.000366557	−	0.000295656i
$725$	20.4782	−	20.4782i	0.760541	−	0.760541i
$726$	−22.0568	−	1.17742i	−0.818605	−	0.0436981i
$727$			24.4125i			0.905411i	0.891660	+	0.452705i	$0.149541\pi$
$727$			24.4125i			0.905411i	−0.891660	+	0.452705i	$0.850459\pi$
$728$		0			0
$729$			20.4227i			0.756395i
$730$	0.351718	−	6.58880i	0.0130177	−	0.243863i
$731$	−0.282024	+	0.282024i	−0.0104311	+	0.0104311i
$732$	−3.25931	+	30.4416i	−0.120468	+	1.12516i
$733$	−5.76415	+	5.76415i	−0.212904	+	0.212904i	−0.805500	−	0.592596i	$-0.798103\pi$
$733$	−5.76415	+	5.76415i	−0.212904	+	0.212904i	0.592596	+	0.805500i	$0.298103\pi$
$734$	32.3831	+	36.0354i	1.19528	+	1.33009i
$735$		0			0
$736$	−20.1828	−	35.3528i	−0.743948	−	1.30312i
$737$	22.7942			0.839637
$738$	13.8380	−	12.4355i	0.509384	−	0.457757i
$739$	5.30141	−	5.30141i	0.195016	−	0.195016i	−0.602844	−	0.797859i	$-0.705966\pi$
$739$	5.30141	−	5.30141i	0.195016	−	0.195016i	0.797859	+	0.602844i	$0.205966\pi$
$740$	−0.623732	+	5.82560i	−0.0229289	+	0.214153i
$741$	6.54147	+	6.54147i	0.240307	+	0.240307i
$742$		0			0
$743$	5.21163			0.191196			0.0955980	−	0.995420i	$-0.469524\pi$
$743$	5.21163			0.191196			0.0955980	+	0.995420i	$0.469524\pi$
$744$	24.5569	+	3.96278i	0.900301	+	0.145282i
$745$	−3.49453			−0.128030
$746$	−35.3939	−	1.88937i	−1.29586	−	0.0691746i
$747$	−12.0117	+	12.0117i	−0.439484	+	0.439484i
$748$	−0.149127	−	0.184889i	−0.00545262	−	0.00676022i
$749$		0			0
$750$	17.9906	+	20.0196i	0.656923	+	0.731013i
$751$		−	4.15721i		−	0.151699i	−0.997119	−	0.0758493i	$-0.975833\pi$
$751$		−	4.15721i		−	0.151699i	0.997119	−	0.0758493i	$-0.0241668\pi$
$752$	−43.0321	−	9.32154i	−1.56922	−	0.339921i
$753$	5.50641			0.200665
$754$	−3.06435	−	3.40996i	−0.111597	−	0.124183i
$755$	4.83215	+	4.83215i	0.175860	+	0.175860i
$756$		0			0
$757$	5.25365	−	5.25365i	0.190947	−	0.190947i	−0.605158	−	0.796105i	$-0.706890\pi$
$757$	5.25365	−	5.25365i	0.190947	−	0.190947i	0.796105	+	0.605158i	$0.206890\pi$
$758$	2.02872	−	38.0044i	0.0736864	−	1.38038i
$759$		−	36.0125i		−	1.30717i
$760$	11.7159	+	16.2246i	0.424979	+	0.588529i
$761$	9.49743			0.344282			0.172141	−	0.985072i	$-0.444932\pi$
$761$	9.49743			0.344282			0.172141	+	0.985072i	$0.444932\pi$
$762$	28.9570	+	1.54576i	1.04900	+	0.0559970i
$763$		0			0
$764$	−30.6279	−	3.27925i	−1.10808	−	0.118639i
$765$	0.0915724	+	0.0915724i	0.00331081	+	0.00331081i
$766$	−21.4848	−	23.9079i	−0.776276	−	0.863827i
$767$		−	4.18529i		−	0.151122i
$768$	−13.3560	−	35.6178i	−0.481943	−	1.28525i
$769$		−	21.7626i		−	0.784779i	−0.919799	−	0.392390i	$-0.871648\pi$
$769$		−	21.7626i		−	0.784779i	0.919799	−	0.392390i	$-0.128352\pi$
$770$		0			0
$771$	−13.6069	+	13.6069i	−0.490042	+	0.490042i
$772$	0.330161	−	3.08367i	0.0118828	−	0.110984i
$773$	−27.9293	−	27.9293i	−1.00455	−	1.00455i	−0.999990	−	0.00455925i	$-0.998549\pi$
$773$	−27.9293	−	27.9293i	−1.00455	−	1.00455i	−0.00455925	−	0.999990i	$-0.501451\pi$
$774$	−26.4770	−	1.41337i	−0.951695	−	0.0508026i
$775$		−	15.7257i		−	0.564885i
$776$	15.0071	+	20.7825i	0.538722	+	0.746047i
$777$		0			0
$778$	−38.1106	−	2.03439i	−1.36633	−	0.0729363i
$779$	−28.6772	−	28.6772i	−1.02747	−	1.02747i
$780$	1.52402	−	1.22924i	0.0545688	−	0.0440138i
$781$	−19.5343	−	19.5343i	−0.698994	−	0.698994i
$782$	−0.427115	+	0.383826i	−0.0152736	+	0.0137256i
$783$	−5.62978			−0.201192
$784$		0			0
$785$	13.9827			0.499062
$786$	−13.4696	+	12.1044i	−0.480445	+	0.431751i
$787$	−18.9875	−	18.9875i	−0.676830	−	0.676830i	0.282452	−	0.959281i	$-0.408852\pi$
$787$	−18.9875	−	18.9875i	−0.676830	−	0.676830i	−0.959281	+	0.282452i	$0.908852\pi$
$788$	1.86767	+	2.31555i	0.0665328	+	0.0824881i
$789$	24.9422	+	24.9422i	0.887967	+	0.887967i
$790$	7.04981	+	0.376327i	0.250821	+	0.0133891i
$791$		0			0
$792$	2.51568	−	15.5894i	0.0893908	−	0.553946i
$793$		−	3.06398i		−	0.108805i
$794$	35.7441	+	1.90806i	1.26851	+	0.0677145i
$795$	−5.46014	−	5.46014i	−0.193651	−	0.193651i
$796$	25.1743	+	2.69534i	0.892278	+	0.0955340i
$797$	−28.0289	+	28.0289i	−0.992834	+	0.992834i	−0.999975	−	0.00714087i	$-0.997727\pi$
$797$	−28.0289	+	28.0289i	−0.992834	+	0.992834i	0.00714087	+	0.999975i	$0.497727\pi$
$798$		0			0
$799$			0.621097i			0.0219728i
$800$	−20.8848	+	11.9231i	−0.738391	+	0.421545i
$801$		−	6.80169i		−	0.240326i
$802$	−3.32409	−	3.69899i	−0.117378	−	0.130616i
$803$	8.02512	+	8.02512i	0.283200	+	0.283200i
$804$	5.48183	−	51.1998i	0.193329	−	1.80568i
$805$		0			0
$806$	−2.48589	−	0.132700i	−0.0875618	−	0.00467415i
$807$	0.576145			0.0202813
$808$	26.8037	+	4.32535i	0.942952	+	0.152165i
$809$		−	17.0008i		−	0.597715i	−0.954298	−	0.298857i	$-0.903394\pi$
$809$		−	17.0008i		−	0.597715i	0.954298	−	0.298857i	$-0.0966055\pi$
$810$	0.647225	−	12.1246i	0.0227412	−	0.426015i
$811$	−0.379489	+	0.379489i	−0.0133256	+	0.0133256i	−0.713738	−	0.700413i	$-0.752999\pi$
$811$	−0.379489	+	0.379489i	−0.0133256	+	0.0133256i	0.700413	+	0.713738i	$0.252999\pi$
$812$		0			0
$813$	−37.7059	−	37.7059i	−1.32240	−	1.32240i
$814$	−6.73597	−	7.49567i	−0.236095	−	0.262723i
$815$	−2.67870			−0.0938309
$816$	−0.451157	+	0.290500i	−0.0157936	+	0.0101695i
$817$			57.7986i			2.02212i
$818$	−17.6505	−	19.6412i	−0.617136	−	0.686739i
$819$		0			0
$820$	−6.68118	+	5.38887i	−0.233317	+	0.188187i
$821$	22.5223	−	22.5223i	0.786033	−	0.786033i	−0.194809	−	0.980841i	$-0.562409\pi$
$821$	22.5223	−	22.5223i	0.786033	−	0.786033i	0.980841	+	0.194809i	$0.0624086\pi$
$822$	−36.1314	−	1.92874i	−1.26023	−	0.0672724i
$823$	−45.4065			−1.58277			−0.791386	−	0.611316i	$-0.790640\pi$
$823$	−45.4065			−1.58277			−0.791386	+	0.611316i	$0.790640\pi$
$824$	2.27477	+	3.15020i	0.0792453	+	0.109742i
$825$	−21.2746			−0.740685
$826$		0			0
$827$	−5.61746	−	5.61746i	−0.195338	−	0.195338i	0.602660	−	0.797998i	$-0.294108\pi$
$827$	−5.61746	−	5.61746i	−0.195338	−	0.195338i	−0.797998	+	0.602660i	$0.794108\pi$
$828$	−37.9578	−	4.06405i	−1.31913	−	0.141235i
$829$	−37.6519	+	37.6519i	−1.30770	+	1.30770i	−0.384633	+	0.923069i	$0.625672\pi$
$829$	−37.6519	+	37.6519i	−1.30770	+	1.30770i	−0.923069	+	0.384633i	$0.874328\pi$
$830$	5.82933	−	5.23852i	0.202339	−	0.181832i
$831$	−46.2712			−1.60513
$832$	1.70854	+	3.40205i	0.0592331	+	0.117945i
$833$		0			0
$834$	−41.9673	−	46.7005i	−1.45321	−	1.61711i
$835$	3.44452	−	3.44452i	0.119203	−	0.119203i
$836$	−34.2269	−	3.66459i	−1.18376	−	0.126743i
$837$	−2.16163	+	2.16163i	−0.0747167	+	0.0747167i
$838$	0.244123	−	4.57321i	0.00843310	−	0.157979i
$839$		−	42.8593i		−	1.47967i	−0.672790	−	0.739834i	$-0.734904\pi$
$839$		−	42.8593i		−	1.47967i	0.672790	−	0.739834i	$-0.265096\pi$
$840$		0			0
$841$			17.4069i			0.600238i
$842$	−1.64134	−	0.0876168i	−0.0565644	−	0.00301948i
$843$	−20.8218	+	20.8218i	−0.717143	+	0.717143i
$844$	1.47476	+	1.82842i	0.0507632	+	0.0629367i
$845$	7.81571	−	7.81571i	0.268868	−	0.268868i
$846$	−30.7112	+	27.5985i	−1.05587	+	0.948857i
$847$		0			0
$848$	12.6233	−	8.12814i	0.433485	−	0.279122i
$849$	−8.98371			−0.308320
$850$	0.226747	+	0.252320i	0.00777736	+	0.00865452i
$851$	−17.2269	+	17.2269i	−0.590530	+	0.590530i
$852$	−48.5753	+	39.1796i	−1.66416	+	1.34227i
$853$	1.26515	+	1.26515i	0.0433180	+	0.0433180i	0.728434	−	0.685116i	$-0.240249\pi$
$853$	1.26515	+	1.26515i	0.0433180	+	0.0433180i	−0.685116	+	0.728434i	$0.740249\pi$
$854$		0			0
$855$	18.7670			0.641818
$856$	39.0696	+	6.30471i	1.33537	+	0.215490i
$857$	39.3547			1.34433			0.672166	−	0.740401i	$-0.265364\pi$
$857$	39.3547			1.34433			0.672166	+	0.740401i	$0.265364\pi$
$858$	−0.179523	+	3.36304i	−0.00612881	+	0.114812i
$859$	21.1674	−	21.1674i	0.722224	−	0.722224i	−0.246834	−	0.969058i	$-0.579390\pi$
$859$	21.1674	−	21.1674i	0.722224	−	0.722224i	0.969058	+	0.246834i	$0.0793902\pi$
$860$	12.1635	+	1.30232i	0.414773	+	0.0444087i
$861$		0			0
$862$	21.4973	−	19.3185i	0.732201	−	0.657991i
$863$		−	1.64391i		−	0.0559595i	−0.999608	−	0.0279798i	$-0.991093\pi$
$863$		−	1.64391i		−	0.0559595i	0.999608	−	0.0279798i	$-0.00890740\pi$
$864$	4.50971	+	1.23186i	0.153423	+	0.0419088i
$865$	1.52048			0.0516978
$866$	36.5487	−	32.8444i	1.24198	−	1.11610i
$867$	−28.5739	−	28.5739i	−0.970419	−	0.970419i
$868$		0			0
$869$	−8.58662	+	8.58662i	−0.291281	+	0.291281i
$870$	−19.7914	−	1.05649i	−0.670991	−	0.0358183i
$871$			5.15331i			0.174613i
$872$	−7.77327	−	1.25438i	−0.263236	−	0.0424787i
$873$	24.0390			0.813598
$874$	−4.43586	+	83.0978i	−0.150045	+	2.81082i
$875$		0			0
$876$	19.9558	−	16.0958i	0.674242	−	0.543827i
$877$	5.98528	+	5.98528i	0.202109	+	0.202109i	0.800903	−	0.598794i	$-0.204353\pi$
$877$	5.98528	+	5.98528i	0.202109	+	0.202109i	−0.598794	+	0.800903i	$0.704353\pi$
$878$	34.3056	−	30.8286i	1.15776	−	1.04042i
$879$		−	9.54198i		−	0.321843i
$880$	−1.54240	+	7.12037i	−0.0519944	+	0.240028i
$881$			21.6012i			0.727763i	0.931445	+	0.363881i	$0.118549\pi$
$881$			21.6012i			0.727763i	−0.931445	+	0.363881i	$0.881451\pi$
$882$		0			0
$883$	13.8898	−	13.8898i	0.467428	−	0.467428i	−0.433652	−	0.901080i	$-0.642775\pi$
$883$	13.8898	−	13.8898i	0.467428	−	0.467428i	0.901080	+	0.433652i	$0.142775\pi$
$884$	0.0417997	−	0.0337146i	0.00140588	−	0.00113394i
$885$	−12.7941	−	12.7941i	−0.430069	−	0.430069i
$886$	1.04094	−	19.5001i	0.0349711	−	0.655120i
$887$			7.23196i			0.242825i	0.992602	+	0.121413i	$0.0387424\pi$
$887$			7.23196i			0.242825i	−0.992602	+	0.121413i	$0.961258\pi$
$888$	−18.4565	+	13.3275i	−0.619359	+	0.447241i
$889$		0			0
$890$	−0.167277	+	3.13363i	−0.00560713	+	0.105039i
$891$	14.7677	+	14.7677i	0.494736	+	0.494736i
$892$	0.893588	−	8.34603i	0.0299195	−	0.279446i
$893$	63.6443	+	63.6443i	2.12978	+	2.12978i
$894$	−9.07592	−	10.0995i	−0.303544	−	0.337779i
$895$	6.62866			0.221572
$896$		0			0
$897$	8.14168			0.271843
$898$	−16.7016	−	18.5852i	−0.557339	−	0.620197i
$899$	17.8185	+	17.8185i	0.594281	+	0.594281i
$900$	−2.40086	+	22.4238i	−0.0800286	+	0.747459i
$901$	−0.149756	−	0.149756i	−0.00498910	−	0.00498910i
$902$	0.787012	−	14.7432i	0.0262046	−	0.490896i
$903$		0			0
$904$	−15.4626	+	11.1656i	−0.514279	+	0.371362i
$905$			0.00548238i			0.000182240i
$906$	−1.41542	+	26.5153i	−0.0470241	+	0.880912i
$907$	14.6222	+	14.6222i	0.485523	+	0.485523i	0.906890	−	0.421367i	$-0.138450\pi$
$907$	14.6222	+	14.6222i	0.485523	+	0.485523i	−0.421367	+	0.906890i	$0.638450\pi$
$908$	−20.0225	+	16.1496i	−0.664468	+	0.535943i
$909$	18.0035	−	18.0035i	0.597137	−	0.597137i
$910$		0			0
$911$		−	0.154520i		−	0.00511948i	−0.999997	−	0.00255974i	$-0.999185\pi$
$911$		−	0.154520i		−	0.00511948i	0.999997	−	0.00255974i	$-0.000814791\pi$
$912$	−16.4626	+	75.9982i	−0.545131	+	2.51655i
$913$			13.4806i			0.446141i
$914$	4.26388	−	3.83173i	0.141037	−	0.126742i
$915$	−9.36634	−	9.36634i	−0.309642	−	0.309642i
$916$	−31.4978	+	25.4053i	−1.04072	+	0.839415i
$917$		0			0
$918$	0.00351524	−	0.0658516i	0.000116020	−	0.00217343i
$919$	35.9584			1.18616			0.593079	−	0.805144i	$-0.297912\pi$
$919$	35.9584			1.18616			0.593079	+	0.805144i	$0.297912\pi$
$920$	17.3877	+	2.80587i	0.573256	+	0.0925068i
$921$		−	58.9342i		−	1.94195i
$922$	−4.78092	−	0.255211i	−0.157451	−	0.00840493i
$923$	4.41631	−	4.41631i	0.145365	−	0.145365i
$924$		0			0
$925$	10.1769	+	10.1769i	0.334614	+	0.334614i
$926$	−32.3591	+	29.0794i	−1.06339	+	0.955610i
$927$	3.64383			0.119679
$928$	10.1544	−	37.1740i	0.333334	−	1.22030i
$929$			16.1210i			0.528913i	0.964398	+	0.264456i	$0.0851925\pi$
$929$			16.1210i			0.528913i	−0.964398	+	0.264456i	$0.914807\pi$
$930$	−8.00481	+	7.19351i	−0.262488	+	0.235884i
$931$		0			0
$932$	45.6015	+	4.88244i	1.49373	+	0.159929i
$933$	37.6904	−	37.6904i	1.23393	−	1.23393i
$934$	−0.542500	+	10.1628i	−0.0177512	+	0.332536i
$935$	0.102771			0.00336096
$936$	3.52445	+	0.568743i	0.115200	+	0.0185900i
$937$	−8.23172			−0.268919			−0.134459	−	0.990919i	$-0.542930\pi$
$937$	−8.23172			−0.268919			−0.134459	+	0.990919i	$0.542930\pi$
$938$		0			0
$939$	−13.0096	−	13.0096i	−0.424552	−	0.424552i
$940$	14.8278	−	11.9597i	0.483629	−	0.390083i
$941$	16.7749	−	16.7749i	0.546847	−	0.546847i	−0.378680	−	0.925528i	$-0.623622\pi$
$941$	16.7749	−	16.7749i	0.546847	−	0.546847i	0.925528	+	0.378680i	$0.123622\pi$
$942$	36.3154	+	40.4112i	1.18322	+	1.31667i
$943$	−35.6923			−1.16230
$944$	29.5786	−	19.0457i	0.962703	−	0.619885i
$945$		0			0
$946$	−15.6505	+	14.0643i	−0.508842	+	0.457270i
$947$	−23.3813	+	23.3813i	−0.759791	+	0.759791i	−0.976284	−	0.216493i	$-0.930538\pi$
$947$	−23.3813	+	23.3813i	−0.759791	+	0.759791i	0.216493	+	0.976284i	$0.430538\pi$
$948$	17.2220	+	21.3520i	0.559345	+	0.693482i
$949$	−1.81431	+	1.81431i	−0.0588951	+	0.0588951i
$950$	49.0905	+	2.62051i	1.59270	+	0.0850205i
$951$			7.70103i			0.249723i
$952$		0			0
$953$		−	21.4014i		−	0.693259i	−0.938002	−	0.346630i	$-0.887326\pi$
$953$		−	21.4014i		−	0.693259i	0.938002	−	0.346630i	$-0.112674\pi$
$954$	0.750506	−	14.0594i	0.0242985	−	0.455189i
$955$	9.42364	−	9.42364i	0.304942	−	0.304942i
$956$	−10.2010	−	1.09220i	−0.329925	−	0.0353242i
$957$	24.1058	−	24.1058i	0.779229	−	0.779229i
$958$	2.69883	+	3.00321i	0.0871952	+	0.0970293i
$959$		0			0
$960$	15.6226	+	5.17689i	0.504218	+	0.167083i
$961$	−17.3167			−0.558603
$962$	1.69462	−	1.52286i	0.0546366	−	0.0490991i
$963$	26.2422	−	26.2422i	0.845643	−	0.845643i
$964$	−33.7082	−	3.60905i	−1.08567	−	0.116240i
$965$	0.948791	+	0.948791i	0.0305426	+	0.0305426i
$966$		0			0
$967$	−4.85592			−0.156156			−0.0780779	−	0.996947i	$-0.524878\pi$
$967$	−4.85592			−0.156156			−0.0780779	+	0.996947i	$0.524878\pi$
$968$	10.8779	+	15.0643i	0.349630	+	0.484184i
$969$	1.09691			0.0352377
$970$	−11.0751	−	0.591201i	−0.355600	−	0.0189823i
$971$	−43.5659	+	43.5659i	−1.39810	+	1.39810i	−0.592601	+	0.805496i	$0.701899\pi$
$971$	−43.5659	+	43.5659i	−1.39810	+	1.39810i	−0.805496	+	0.592601i	$0.798101\pi$
$972$	32.8627	−	26.5062i	1.05407	−	0.850187i
$973$		0			0
$974$	31.3930	+	34.9336i	1.00590	+	1.11935i
$975$		−	4.80974i		−	0.154035i
$976$	21.6540	−	13.9431i	0.693129	−	0.446306i
$977$	13.9651			0.446783			0.223392	−	0.974729i	$-0.428287\pi$
$977$	13.9651			0.446783			0.223392	+	0.974729i	$0.428287\pi$
$978$	−6.95707	−	7.74171i	−0.222463	−	0.247553i
$979$	−3.81673	−	3.81673i	−0.121983	−	0.121983i
$980$		0			0
$981$	−5.22113	+	5.22113i	−0.166698	+	0.166698i
$982$	2.45936	−	46.0717i	0.0784814	−	1.47021i
$983$		−	56.4387i		−	1.80012i	−0.435770	−	0.900058i	$-0.643524\pi$
$983$		−	56.4387i		−	1.80012i	0.435770	−	0.900058i	$-0.356476\pi$
$984$	−32.9265	−	5.31339i	−1.04966	−	0.169385i
$985$	−1.28710			−0.0410104
$986$	−0.542822	−	0.0289765i	−0.0172870	−	0.000922800i
$987$		0			0
$988$	0.828489	−	7.73801i	0.0263577	−	0.246179i
$989$	35.9688	+	35.9688i	1.14374	+	1.14374i
$990$	4.56663	+	5.08167i	0.145137	+	0.161506i
$991$		−	45.6839i		−	1.45120i	−0.688118	−	0.725598i	$-0.741563\pi$
$991$		−	45.6839i		−	1.45120i	0.688118	−	0.725598i	$-0.258437\pi$
$992$	−10.3745	−	18.1724i	−0.329392	−	0.576973i
$993$		−	9.89891i		−	0.314132i
$994$		0			0
$995$	−7.74566	+	7.74566i	−0.245554	+	0.245554i
$996$	30.2796	+	3.24196i	0.959447	+	0.102726i
$997$	−9.70185	−	9.70185i	−0.307261	−	0.307261i	0.536585	−	0.843846i	$-0.319714\pi$
$997$	−9.70185	−	9.70185i	−0.307261	−	0.307261i	−0.843846	+	0.536585i	$0.819714\pi$
$998$	29.3325	+	1.56580i	0.928504	+	0.0495647i
$999$		−	2.79778i		−	0.0885180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.195.19		56
7.2	even	3		112.2.v.a.3.10	✓	56
7.3	odd	6		112.2.v.a.19.1	yes	56
7.4	even	3		784.2.w.f.19.1		56
7.5	odd	6		784.2.w.f.227.10		56
7.6	odd	2	inner	784.2.j.a.195.20		56
16.11	odd	4	inner	784.2.j.a.587.20		56
28.3	even	6		448.2.z.a.47.2		56
28.23	odd	6		448.2.z.a.367.2		56
56.3	even	6		896.2.z.a.607.13		56
56.37	even	6		896.2.z.b.479.2		56
56.45	odd	6		896.2.z.b.607.2		56
56.51	odd	6		896.2.z.a.479.13		56
112.3	even	12		896.2.z.b.159.2		56
112.11	odd	12		784.2.w.f.411.10		56
112.27	even	4	inner	784.2.j.a.587.19		56
112.37	even	12		448.2.z.a.143.2		56
112.45	odd	12		896.2.z.a.159.13		56
112.51	odd	12		896.2.z.b.31.2		56
112.59	even	12		112.2.v.a.75.10	yes	56
112.75	even	12		784.2.w.f.619.1		56
112.93	even	12		896.2.z.a.31.13		56
112.101	odd	12		448.2.z.a.271.2		56
112.107	odd	12		112.2.v.a.59.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.10	✓	56	7.2	even	3
112.2.v.a.19.1	yes	56	7.3	odd	6
112.2.v.a.59.1	yes	56	112.107	odd	12
112.2.v.a.75.10	yes	56	112.59	even	12
448.2.z.a.47.2		56	28.3	even	6
448.2.z.a.143.2		56	112.37	even	12
448.2.z.a.271.2		56	112.101	odd	12
448.2.z.a.367.2		56	28.23	odd	6
784.2.j.a.195.19		56	1.1	even	1	trivial
784.2.j.a.195.20		56	7.6	odd	2	inner
784.2.j.a.587.19		56	112.27	even	4	inner
784.2.j.a.587.20		56	16.11	odd	4	inner
784.2.w.f.19.1		56	7.4	even	3
784.2.w.f.227.10		56	7.5	odd	6
784.2.w.f.411.10		56	112.11	odd	12
784.2.w.f.619.1		56	112.75	even	12
896.2.z.a.31.13		56	112.93	even	12
896.2.z.a.159.13		56	112.45	odd	12
896.2.z.a.479.13		56	56.51	odd	6
896.2.z.a.607.13		56	56.3	even	6
896.2.z.b.31.2		56	112.51	odd	12
896.2.z.b.159.2		56	112.3	even	12
896.2.z.b.479.2		56	56.37	even	6
896.2.z.b.607.2		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+(0.945273 + 1.05188i) q^{2} +(-1.68113 - 1.68113i) q^{3} +(-0.212918 + 1.98863i) q^{4} +(-0.611867 - 0.611867i) q^{5} +(0.179226 - 3.35748i) q^{6} +(-2.29308 + 1.65584i) q^{8} +2.65240i q^{9} +(0.0652315 - 1.22199i) q^{10} +(1.48838 + 1.48838i) q^{11} +(3.70110 - 2.98521i) q^{12} +(-0.336492 + 0.336492i) q^{13} +2.05725i q^{15} +(-3.90933 - 0.846832i) q^{16} +0.0564247i q^{17} +(-2.79001 + 2.50724i) q^{18} +(5.78189 + 5.78189i) q^{19} +(1.34706 - 1.08650i) q^{20} +(-0.158677 + 2.97253i) q^{22} +7.19628 q^{23} +(6.63864 + 1.07128i) q^{24} -4.25124i q^{25} +(-0.672027 - 0.0358736i) q^{26} +(-0.584366 + 0.584366i) q^{27} +(4.81700 + 4.81700i) q^{29} +(-2.16399 + 1.94467i) q^{30} +3.69909 q^{31} +(-2.80462 - 4.91265i) q^{32} -5.00432i q^{33} +(-0.0593522 + 0.0533367i) q^{34} +(-5.27465 - 0.564743i) q^{36} +(-2.39386 + 2.39386i) q^{37} +(-0.616410 + 11.5473i) q^{38} +1.13137 q^{39} +(2.41621 + 0.389906i) q^{40} -4.95983 q^{41} +(4.99825 + 4.99825i) q^{43} +(-3.27674 + 2.64294i) q^{44} +(1.62291 - 1.62291i) q^{45} +(6.80244 + 7.56964i) q^{46} +11.0075 q^{47} +(5.14846 + 7.99573i) q^{48} +(4.47181 - 4.01858i) q^{50} +(0.0948572 - 0.0948572i) q^{51} +(-0.597514 - 0.740805i) q^{52} +(-2.65409 + 2.65409i) q^{53} +(-1.16707 - 0.0622996i) q^{54} -1.82138i q^{55} -19.4402i q^{57} +(-0.513543 + 9.62030i) q^{58} +(-6.21901 + 6.21901i) q^{59} +(-4.09113 - 0.438027i) q^{60} +(-4.55283 + 4.55283i) q^{61} +(3.49665 + 3.89102i) q^{62} +(2.51641 - 7.59393i) q^{64} +0.411776 q^{65} +(5.26396 - 4.73045i) q^{66} +(7.65741 - 7.65741i) q^{67} +(-0.112208 - 0.0120138i) q^{68} +(-12.0979 - 12.0979i) q^{69} -13.1246 q^{71} +(-4.39194 - 6.08215i) q^{72} +5.39185 q^{73} +(-4.78092 - 0.255211i) q^{74} +(-7.14689 + 7.14689i) q^{75} +(-12.7291 + 10.2670i) q^{76} +(1.06946 + 1.19007i) q^{78} +5.76911i q^{79} +(1.87384 + 2.91014i) q^{80} +9.92198 q^{81} +(-4.68840 - 5.21717i) q^{82} +(4.52860 + 4.52860i) q^{83} +(0.0345244 - 0.0345244i) q^{85} +(-0.532866 + 9.98228i) q^{86} -16.1960i q^{87} +(-5.87748 - 0.948455i) q^{88} -2.56436 q^{89} +(3.24121 + 0.173020i) q^{90} +(-1.53222 + 14.3108i) q^{92} +(-6.21866 - 6.21866i) q^{93} +(10.4051 + 11.5786i) q^{94} -7.07548i q^{95} +(-3.54388 + 12.9737i) q^{96} -9.06313i q^{97} +(-3.94777 + 3.94777i) 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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