LMFDB - Embedded newform 784.2.j.a.195.9

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			195.9
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.795020 + 1.16959i) q^{2} +(-0.648349 - 0.648349i) q^{3} +(-0.735886 - 1.85970i) q^{4} +(-2.23699 - 2.23699i) q^{5} +(1.27375 - 0.242853i) q^{6} +(2.76013 + 0.617811i) q^{8} -2.15929i q^{9} +(4.39482 - 0.837912i) q^{10} +(0.873801 + 0.873801i) q^{11} +(-0.728622 + 1.68284i) q^{12} +(0.430348 - 0.430348i) q^{13} +2.90070i q^{15} +(-2.91694 + 2.73705i) q^{16} -5.93673i q^{17} +(2.52548 + 1.71668i) q^{18} +(0.146719 + 0.146719i) q^{19} +(-2.51396 + 5.80630i) q^{20} +(-1.71668 + 0.327300i) q^{22} +3.54208 q^{23} +(-1.38897 - 2.19008i) q^{24} +5.00828i q^{25} +(0.161196 + 0.845467i) q^{26} +(-3.34502 + 3.34502i) q^{27} +(1.84275 + 1.84275i) q^{29} +(-3.39264 - 2.30612i) q^{30} -7.20354 q^{31} +(-0.882198 - 5.58764i) q^{32} -1.13306i q^{33} +(6.94355 + 4.71982i) q^{34} +(-4.01562 + 1.58899i) q^{36} +(-8.19631 + 8.19631i) q^{37} +(-0.288247 + 0.0549568i) q^{38} -0.558032 q^{39} +(-4.79235 - 7.55643i) q^{40} -9.61218 q^{41} +(-7.30761 - 7.30761i) q^{43} +(0.981987 - 2.26802i) q^{44} +(-4.83031 + 4.83031i) q^{45} +(-2.81603 + 4.14279i) q^{46} +5.75263 q^{47} +(3.66576 + 0.116635i) q^{48} +(-5.85763 - 3.98168i) q^{50} +(-3.84907 + 3.84907i) q^{51} +(-1.11700 - 0.483630i) q^{52} +(-3.64830 + 3.64830i) q^{53} +(-1.25295 - 6.57166i) q^{54} -3.90937i q^{55} -0.190251i q^{57} +(-3.62028 + 0.690239i) q^{58} +(1.00885 - 1.00885i) q^{59} +(5.39443 - 2.13459i) q^{60} +(-0.939971 + 0.939971i) q^{61} +(5.72696 - 8.42519i) q^{62} +(7.23662 + 3.41048i) q^{64} -1.92537 q^{65} +(1.32521 + 0.900803i) q^{66} +(-5.78442 + 5.78442i) q^{67} +(-11.0405 + 4.36876i) q^{68} +(-2.29651 - 2.29651i) q^{69} +13.7963 q^{71} +(1.33403 - 5.95991i) q^{72} -2.25309 q^{73} +(-3.07010 - 16.1026i) q^{74} +(3.24711 - 3.24711i) q^{75} +(0.164885 - 0.380823i) q^{76} +(0.443647 - 0.652669i) q^{78} +1.70380i q^{79} +(12.6479 + 0.402424i) q^{80} -2.14038 q^{81} +(7.64188 - 11.2423i) q^{82} +(7.78261 + 7.78261i) q^{83} +(-13.2804 + 13.2804i) q^{85} +(14.3566 - 2.73722i) q^{86} -2.38949i q^{87} +(1.87196 + 2.95165i) q^{88} +6.10947 q^{89} +(-1.80929 - 9.48968i) q^{90} +(-2.60657 - 6.58720i) q^{92} +(4.67041 + 4.67041i) q^{93} +(-4.57345 + 6.72822i) q^{94} -0.656421i q^{95} +(-3.05077 + 4.19471i) q^{96} -10.6315i q^{97} +(1.88679 - 1.88679i) 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 $

$2$	−0.795020	+	1.16959i	−0.562164	+	0.827026i
$2$	−0.795020	+	1.16959i	−0.562164	+	0.827026i
$3$	−0.648349	−	0.648349i	−0.374325	−	0.374325i	0.494725	−	0.869050i	$-0.335269\pi$
$3$	−0.648349	−	0.648349i	−0.374325	−	0.374325i	−0.869050	+	0.494725i	$0.835269\pi$
$4$	−0.735886	−	1.85970i	−0.367943	−	0.929848i
$5$	−2.23699	−	2.23699i	−1.00041	−	1.00041i	−1.00000		0.000413829i	$-0.999868\pi$
$5$	−2.23699	−	2.23699i	−1.00041	−	1.00041i	−0.000413829	−	1.00000i	$-0.500132\pi$
$6$	1.27375	−	0.242853i	0.520008	−	0.0991442i
$7$		0			0
$7$		0			0
$8$	2.76013	+	0.617811i	0.975853	+	0.218429i
$9$		−	2.15929i		−	0.719762i
$10$	4.39482	−	0.837912i	1.38976	−	0.264971i
$11$	0.873801	+	0.873801i	0.263461	+	0.263461i	0.826459	−	0.562998i	$-0.190352\pi$
$11$	0.873801	+	0.873801i	0.263461	+	0.263461i	−0.562998	+	0.826459i	$0.690352\pi$
$12$	−0.728622	+	1.68284i	−0.210335	+	0.485795i
$13$	0.430348	−	0.430348i	0.119357	−	0.119357i	−0.644905	−	0.764262i	$-0.723103\pi$
$13$	0.430348	−	0.430348i	0.119357	−	0.119357i	0.764262	+	0.644905i	$0.223103\pi$
$14$		0			0
$15$			2.90070i			0.748959i
$16$	−2.91694	+	2.73705i	−0.729236	+	0.684262i
$17$		−	5.93673i		−	1.43987i	−0.694042	−	0.719934i	$-0.744172\pi$
$17$		−	5.93673i		−	1.43987i	0.694042	−	0.719934i	$-0.255828\pi$
$18$	2.52548	+	1.71668i	0.595262	+	0.404625i
$19$	0.146719	+	0.146719i	0.0336598	+	0.0336598i	0.723736	−	0.690077i	$-0.242423\pi$
$19$	0.146719	+	0.146719i	0.0336598	+	0.0336598i	−0.690077	+	0.723736i	$0.742423\pi$
$20$	−2.51396	+	5.80630i	−0.562138	+	1.29833i
$21$		0			0
$22$	−1.71668	+	0.327300i	−0.365997	+	0.0697807i
$23$	3.54208			0.738575			0.369287	−	0.929315i	$-0.379602\pi$
$23$	3.54208			0.738575			0.369287	+	0.929315i	$0.379602\pi$
$24$	−1.38897	−	2.19008i	−0.283522	−	0.447049i
$25$			5.00828i			1.00166i
$26$	0.161196	+	0.845467i	0.0316131	+	0.165810i
$27$	−3.34502	+	3.34502i	−0.643749	+	0.643749i
$28$		0			0
$29$	1.84275	+	1.84275i	0.342190	+	0.342190i	0.857190	−	0.515000i	$-0.172208\pi$
$29$	1.84275	+	1.84275i	0.342190	+	0.342190i	−0.515000	+	0.857190i	$0.672208\pi$
$30$	−3.39264	−	2.30612i	−0.619408	−	0.421038i
$31$	−7.20354			−1.29379			−0.646897	−	0.762578i	$-0.723934\pi$
$31$	−7.20354			−1.29379			−0.646897	+	0.762578i	$0.723934\pi$
$32$	−0.882198	−	5.58764i	−0.155952	−	0.987765i
$33$		−	1.13306i		−	0.197240i
$34$	6.94355	+	4.71982i	1.19081	+	0.809443i
$35$		0			0
$36$	−4.01562	+	1.58899i	−0.669270	+	0.264831i
$37$	−8.19631	+	8.19631i	−1.34747	+	1.34747i	−0.459061	+	0.888405i	$0.651814\pi$
$37$	−8.19631	+	8.19631i	−1.34747	+	1.34747i	−0.888405	+	0.459061i	$0.848186\pi$
$38$	−0.288247	+	0.0549568i	−0.0467598	+	0.00891517i
$39$	−0.558032			−0.0893566
$40$	−4.79235	−	7.55643i	−0.757737	−	1.19478i
$41$	−9.61218			−1.50117			−0.750585	−	0.660774i	$-0.770228\pi$
$41$	−9.61218			−1.50117			−0.750585	+	0.660774i	$0.770228\pi$
$42$		0			0
$43$	−7.30761	−	7.30761i	−1.11440	−	1.11440i	−0.992548	−	0.121852i	$-0.961117\pi$
$43$	−7.30761	−	7.30761i	−1.11440	−	1.11440i	−0.121852	−	0.992548i	$-0.538883\pi$
$44$	0.981987	−	2.26802i	0.148040	−	0.341917i
$45$	−4.83031	+	4.83031i	−0.720060	+	0.720060i
$46$	−2.81603	+	4.14279i	−0.415200	+	0.610820i
$47$	5.75263			0.839107			0.419553	−	0.907731i	$-0.362187\pi$
$47$	5.75263			0.839107			0.419553	+	0.907731i	$0.362187\pi$
$48$	3.66576	+	0.116635i	0.529107	+	0.0168348i
$49$		0			0
$50$	−5.85763	−	3.98168i	−0.828395	−	0.563095i
$51$	−3.84907	+	3.84907i	−0.538978	+	0.538978i
$52$	−1.11700	−	0.483630i	−0.154901	−	0.0670674i
$53$	−3.64830	+	3.64830i	−0.501133	+	0.501133i	−0.911790	−	0.410657i	$-0.865299\pi$
$53$	−3.64830	+	3.64830i	−0.501133	+	0.501133i	0.410657	+	0.911790i	$0.365299\pi$
$54$	−1.25295	−	6.57166i	−0.170504	−	0.894290i
$55$		−	3.90937i		−	0.527140i
$56$		0			0
$57$		−	0.190251i		−	0.0251993i
$58$	−3.62028	+	0.690239i	−0.475366	+	0.0906328i
$59$	1.00885	−	1.00885i	0.131341	−	0.131341i	−0.638380	−	0.769721i	$-0.720395\pi$
$59$	1.00885	−	1.00885i	0.131341	−	0.131341i	0.769721	+	0.638380i	$0.220395\pi$
$60$	5.39443	−	2.13459i	0.696418	−	0.275574i
$61$	−0.939971	+	0.939971i	−0.120351	+	0.120351i	−0.764717	−	0.644366i	$-0.777121\pi$
$61$	−0.939971	+	0.939971i	−0.120351	+	0.120351i	0.644366	+	0.764717i	$0.277121\pi$
$62$	5.72696	−	8.42519i	0.727324	−	1.07000i
$63$		0			0
$64$	7.23662	+	3.41048i	0.904577	+	0.426309i
$65$	−1.92537			−0.238813
$66$	1.32521	+	0.900803i	0.163122	+	0.110881i
$67$	−5.78442	+	5.78442i	−0.706680	+	0.706680i	−0.965836	−	0.259156i	$-0.916556\pi$
$67$	−5.78442	+	5.78442i	−0.706680	+	0.706680i	0.259156	+	0.965836i	$0.416556\pi$
$68$	−11.0405	+	4.36876i	−1.33886	+	0.529790i
$69$	−2.29651	−	2.29651i	−0.276467	−	0.276467i
$70$		0			0
$71$	13.7963			1.63732			0.818661	−	0.574277i	$-0.194717\pi$
$71$	13.7963			1.63732			0.818661	+	0.574277i	$0.194717\pi$
$72$	1.33403	−	5.95991i	0.157217	−	0.702382i
$73$	−2.25309			−0.263704			−0.131852	−	0.991269i	$-0.542092\pi$
$73$	−2.25309			−0.263704			−0.131852	+	0.991269i	$0.542092\pi$
$74$	−3.07010	−	16.1026i	−0.356892	−	1.87189i
$75$	3.24711	−	3.24711i	0.374944	−	0.374944i
$76$	0.164885	−	0.380823i	0.0189136	−	0.0436833i
$77$		0			0
$78$	0.443647	−	0.652669i	0.0502331	−	0.0739002i
$79$			1.70380i			0.191693i	0.995396	+	0.0958465i	$0.0305558\pi$
$79$			1.70380i			0.191693i	−0.995396	+	0.0958465i	$0.969444\pi$
$80$	12.6479	+	0.402424i	1.41408	+	0.0449924i
$81$	−2.14038			−0.237820
$82$	7.64188	−	11.2423i	0.843904	−	1.24151i
$83$	7.78261	+	7.78261i	0.854253	+	0.854253i	0.990654	−	0.136401i	$-0.0435536\pi$
$83$	7.78261	+	7.78261i	0.854253	+	0.854253i	−0.136401	+	0.990654i	$0.543554\pi$
$84$		0			0
$85$	−13.2804	+	13.2804i	−1.44046	+	1.44046i
$86$	14.3566	−	2.73722i	1.54811	−	0.295162i
$87$		−	2.38949i		−	0.256180i
$88$	1.87196	+	2.95165i	0.199552	+	0.314647i
$89$	6.10947			0.647603			0.323801	−	0.946125i	$-0.395039\pi$
$89$	6.10947			0.647603			0.323801	+	0.946125i	$0.395039\pi$
$90$	−1.80929	−	9.48968i	−0.190716	−	1.00030i
$91$		0			0
$92$	−2.60657	−	6.58720i	−0.271753	−	0.686763i
$93$	4.67041	+	4.67041i	0.484299	+	0.484299i
$94$	−4.57345	+	6.72822i	−0.471716	+	0.693963i
$95$		−	0.656421i		−	0.0673474i
$96$	−3.05077	+	4.19471i	−0.311368	+	0.428121i
$97$		−	10.6315i		−	1.07946i	−0.841837	−	0.539732i	$-0.818526\pi$
$97$		−	10.6315i		−	1.07946i	0.841837	−	0.539732i	$-0.181474\pi$
$98$		0			0
$99$	1.88679	−	1.88679i	0.189629	−	0.189629i
$100$	9.31388	−	3.68552i	0.931388	−	0.368552i
$101$	0.901752	+	0.901752i	0.0897277	+	0.0897277i	0.750546	−	0.660818i	$-0.229791\pi$
$101$	0.901752	+	0.901752i	0.0897277	+	0.0897277i	−0.660818	+	0.750546i	$0.729791\pi$
$102$	−1.44175	−	7.56194i	−0.142755	−	0.748743i
$103$			9.82187i			0.967778i	0.875129	+	0.483889i	$0.160776\pi$
$103$			9.82187i			0.967778i	−0.875129	+	0.483889i	$0.839224\pi$
$104$	1.45369	−	0.921943i	0.142546	−	0.0904039i
$105$		0			0
$106$	−1.36655	−	7.16750i	−0.132731	−	0.696169i
$107$	−7.34736	−	7.34736i	−0.710296	−	0.710296i	0.256301	−	0.966597i	$-0.417496\pi$
$107$	−7.34736	−	7.34736i	−0.710296	−	0.710296i	−0.966597	+	0.256301i	$0.917496\pi$
$108$	8.68227	+	3.75917i	0.835452	+	0.361726i
$109$	0.0287071	+	0.0287071i	0.00274964	+	0.00274964i	0.708480	−	0.705731i	$-0.249381\pi$
$109$	0.0287071	+	0.0287071i	0.00274964	+	0.00274964i	−0.705731	+	0.708480i	$0.749381\pi$
$110$	4.57237	+	3.10803i	0.435958	+	0.296339i
$111$	10.6281			1.00878
$112$		0			0
$113$	−11.0778			−1.04211			−0.521055	−	0.853523i	$-0.674461\pi$
$113$	−11.0778			−1.04211			−0.521055	+	0.853523i	$0.674461\pi$
$114$	0.222516	+	0.151253i	0.0208405	+	0.0141662i
$115$	−7.92361	−	7.92361i	−0.738881	−	0.738881i
$116$	2.07090	−	4.78300i	0.192278	−	0.444091i
$117$	−0.929245	−	0.929245i	−0.0859088	−	0.0859088i
$118$	0.377885	+	1.98199i	0.0347871	+	0.182457i
$119$		0			0
$120$	−1.79209	+	8.00632i	−0.163594	+	0.730874i
$121$		−	9.47294i		−	0.861177i
$122$	−0.352086	−	1.84668i	−0.0318764	−	0.167190i
$123$	6.23205	+	6.23205i	0.561925	+	0.561925i
$124$	5.30098	+	13.3964i	0.476042	+	1.20303i
$125$	0.0185146	−	0.0185146i	0.00165600	−	0.00165600i
$126$		0			0
$127$		−	18.0882i		−	1.60506i	−0.596609	−	0.802532i	$-0.703486\pi$
$127$		−	18.0882i		−	1.60506i	0.596609	−	0.802532i	$-0.296514\pi$
$128$	−9.74212	+	5.75249i	−0.861090	+	0.508453i
$129$			9.47577i			0.834295i
$130$	1.53071	−	2.25190i	0.134252	−	0.197505i
$131$	−1.94710	−	1.94710i	−0.170119	−	0.170119i	0.616913	−	0.787032i	$-0.288383\pi$
$131$	−1.94710	−	1.94710i	−0.170119	−	0.170119i	−0.787032	+	0.616913i	$0.788383\pi$
$132$	−2.10714	+	0.833800i	−0.183403	+	0.0725730i
$133$		0			0
$134$	−2.16668	−	11.3641i	−0.187172	−	0.981713i
$135$	14.9656			1.28803
$136$	3.66778	−	16.3861i	0.314509	−	1.40510i
$137$			1.95344i			0.166894i	0.996512	+	0.0834468i	$0.0265929\pi$
$137$			1.95344i			0.166894i	−0.996512	+	0.0834468i	$0.973407\pi$
$138$	4.51174	−	0.860204i	0.384065	−	0.0732254i
$139$	−5.22260	+	5.22260i	−0.442975	+	0.442975i	−0.893011	−	0.450035i	$-0.851411\pi$
$139$	−5.22260	+	5.22260i	−0.442975	+	0.442975i	0.450035	+	0.893011i	$0.351411\pi$
$140$		0			0
$141$	−3.72971	−	3.72971i	−0.314098	−	0.314098i
$142$	−10.9684	+	16.1361i	−0.920444	+	1.35411i
$143$	0.752078			0.0628919
$144$	5.91007	+	6.29852i	0.492506	+	0.524877i
$145$		−	8.24443i		−	0.684662i
$146$	1.79125	−	2.63520i	0.148245	−	0.218090i
$147$		0			0
$148$	21.2742	+	9.21111i	1.74873	+	0.757148i
$149$	5.39707	−	5.39707i	0.442145	−	0.442145i	−0.450587	−	0.892732i	$-0.648785\pi$
$149$	5.39707	−	5.39707i	0.442145	−	0.442145i	0.892732	+	0.450587i	$0.148785\pi$
$150$	1.21627	+	6.37931i	0.0993083	+	0.520869i
$151$	14.1062			1.14795			0.573973	−	0.818874i	$-0.305401\pi$
$151$	14.1062			1.14795			0.573973	+	0.818874i	$0.305401\pi$
$152$	0.314320	+	0.495610i	0.0254947	+	0.0401992i
$153$	−12.8191			−1.03636
$154$		0			0
$155$	16.1143	+	16.1143i	1.29433	+	1.29433i
$156$	0.410648	+	1.03777i	0.0328781	+	0.0830881i
$157$	−10.3352	+	10.3352i	−0.824840	+	0.824840i	−0.986798	−	0.161958i	$-0.948219\pi$
$157$	−10.3352	+	10.3352i	−0.824840	+	0.824840i	0.161958	+	0.986798i	$0.448219\pi$
$158$	−1.99275	−	1.35456i	−0.158535	−	0.107763i
$159$	4.73075			0.375173
$160$	−10.5260	+	14.4730i	−0.832157	+	1.14419i
$161$		0			0
$162$	1.70165	−	2.50337i	0.133694	−	0.196683i
$163$	−0.295188	+	0.295188i	−0.0231209	+	0.0231209i	−0.718573	−	0.695452i	$-0.755204\pi$
$163$	−0.295188	+	0.295188i	−0.0231209	+	0.0231209i	0.695452	+	0.718573i	$0.255204\pi$
$164$	7.07347	+	17.8757i	0.552345	+	1.39586i
$165$	−2.53464	+	2.53464i	−0.197321	+	0.197321i
$166$	−15.2898	+	2.91514i	−1.18672	+	0.226259i
$167$			3.16944i			0.245259i	0.992453	+	0.122629i	$0.0391326\pi$
$167$			3.16944i			0.245259i	−0.992453	+	0.122629i	$0.960867\pi$
$168$		0			0
$169$			12.6296i			0.971508i
$170$	−4.97446	−	26.0909i	−0.381524	−	2.00108i
$171$	0.316809	−	0.316809i	0.0242270	−	0.0242270i
$172$	−8.21238	+	18.9675i	−0.626188	+	1.44626i
$173$	−16.1699	+	16.1699i	−1.22937	+	1.22937i	−0.265170	+	0.964202i	$0.585428\pi$
$173$	−16.1699	+	16.1699i	−1.22937	+	1.22937i	−0.964202	+	0.265170i	$0.914572\pi$
$174$	2.79472	+	1.89969i	0.211867	+	0.144015i
$175$		0			0
$176$	−4.94047	−	0.157192i	−0.372402	−	0.0118488i
$177$	−1.30817			−0.0983281
$178$	−4.85715	+	7.14558i	−0.364059	+	0.535584i
$179$	9.72629	−	9.72629i	0.726977	−	0.726977i	−0.243039	−	0.970016i	$-0.578144\pi$
$179$	9.72629	−	9.72629i	0.726977	−	0.726977i	0.970016	+	0.243039i	$0.0781444\pi$
$180$	12.5375	+	5.42835i	0.934488	+	0.404606i
$181$	−5.01349	−	5.01349i	−0.372650	−	0.372650i	0.495792	−	0.868441i	$-0.334878\pi$
$181$	−5.01349	−	5.01349i	−0.372650	−	0.372650i	−0.868441	+	0.495792i	$0.834878\pi$
$182$		0			0
$183$	1.21886			0.0901007
$184$	9.77660	+	2.18834i	0.720740	+	0.161326i
$185$	36.6702			2.69605
$186$	−9.17553	+	1.74940i	−0.672783	+	0.128272i
$187$	5.18752	−	5.18752i	0.379349	−	0.379349i
$188$	−4.23328	−	10.6981i	−0.308743	−	0.780242i
$189$		0			0
$190$	0.767744	+	0.521868i	0.0556980	+	0.0378603i
$191$		−	5.37259i		−	0.388747i	−0.980928	−	0.194373i	$-0.937733\pi$
$191$		−	5.37259i		−	0.388747i	0.980928	−	0.194373i	$-0.0622673\pi$
$192$	−2.48068	−	6.90303i	−0.179027	−	0.498184i
$193$	−0.0718573			−0.00517240			−0.00258620	−	0.999997i	$-0.500823\pi$
$193$	−0.0718573			−0.00517240			−0.00258620	+	0.999997i	$0.500823\pi$
$194$	12.4345	+	8.45224i	0.892744	+	0.606836i
$195$	1.24831	+	1.24831i	0.0893936	+	0.0893936i
$196$		0			0
$197$	2.60367	−	2.60367i	0.185504	−	0.185504i	−0.608245	−	0.793749i	$-0.708126\pi$
$197$	2.60367	−	2.60367i	0.185504	−	0.185504i	0.793749	+	0.608245i	$0.208126\pi$
$198$	0.706735	+	3.70680i	0.0502255	+	0.263431i
$199$			10.4137i			0.738211i	0.929387	+	0.369106i	$0.120336\pi$
$199$			10.4137i			0.738211i	−0.929387	+	0.369106i	$0.879664\pi$
$200$	−3.09417	+	13.8235i	−0.218791	+	0.977468i
$201$	7.50065			0.529055
$202$	−1.77159	+	0.337770i	−0.124649	+	0.0237654i
$203$		0			0
$204$	9.99059	+	4.32563i	0.699481	+	0.302855i
$205$	21.5024	+	21.5024i	1.50179	+	1.50179i
$206$	−11.4876	−	7.80859i	−0.800377	−	0.544050i
$207$		−	7.64837i		−	0.531598i
$208$	−0.0774175	+	2.43319i	−0.00536794	+	0.168711i
$209$			0.256407i			0.0177361i
$210$		0			0
$211$	2.30105	−	2.30105i	0.158411	−	0.158411i	−0.623451	−	0.781862i	$-0.714270\pi$
$211$	2.30105	−	2.30105i	0.158411	−	0.158411i	0.781862	+	0.623451i	$0.214270\pi$
$212$	9.46947	+	4.10000i	0.650366	+	0.281589i
$213$	−8.94484	−	8.94484i	−0.612890	−	0.612890i
$214$	14.4347	−	2.75211i	0.986736	−	0.188130i
$215$			32.6942i			2.22972i
$216$	−11.2993	+	7.16609i	−0.768818	+	0.487591i
$217$		0			0
$218$	−0.0563983	+	0.0107528i	−0.00381977	+	0.000728274i
$219$	1.46079	+	1.46079i	0.0987111	+	0.0987111i
$220$	−7.27025	+	2.87685i	−0.490160	+	0.193957i
$221$	−2.55486	−	2.55486i	−0.171859	−	0.171859i
$222$	−8.44959	+	12.4306i	−0.567099	+	0.834286i
$223$	−21.9153			−1.46756			−0.733778	−	0.679390i	$-0.762245\pi$
$223$	−21.9153			−1.46756			−0.733778	+	0.679390i	$0.762245\pi$
$224$		0			0
$225$	10.8143			0.720954
$226$	8.80706	−	12.9565i	0.585837	−	0.861852i
$227$	−8.19350	−	8.19350i	−0.543822	−	0.543822i	0.380825	−	0.924647i	$-0.375640\pi$
$227$	−8.19350	−	8.19350i	−0.543822	−	0.543822i	−0.924647	+	0.380825i	$0.875640\pi$
$228$	−0.353809	+	0.140003i	−0.0234316	+	0.00927192i
$229$	−15.3658	−	15.3658i	−1.01540	−	1.01540i	−0.999880	−	0.0155235i	$-0.995059\pi$
$229$	−15.3658	−	15.3658i	−1.01540	−	1.01540i	−0.0155235	−	0.999880i	$-0.504941\pi$
$230$	15.5668	−	2.96795i	1.02645	−	0.195701i
$231$		0			0
$232$	3.94775	+	6.22469i	0.259182	+	0.408671i
$233$		−	12.4965i		−	0.818670i	−0.912384	−	0.409335i	$-0.865761\pi$
$233$		−	12.4965i		−	0.818670i	0.912384	−	0.409335i	$-0.134239\pi$
$234$	1.82561	−	0.348068i	0.119344	−	0.0227539i
$235$	−12.8686	−	12.8686i	−0.839454	−	0.839454i
$236$	−2.61855	−	1.13375i	−0.170453	−	0.0738011i
$237$	1.10466	−	1.10466i	0.0717554	−	0.0717554i
$238$		0			0
$239$		−	7.70978i		−	0.498704i	−0.968413	−	0.249352i	$-0.919782\pi$
$239$		−	7.70978i		−	0.498704i	0.968413	−	0.249352i	$-0.0802176\pi$
$240$	−7.93937	−	8.46119i	−0.512484	−	0.546168i
$241$			10.9758i			0.707014i	0.935432	+	0.353507i	$0.115011\pi$
$241$			10.9758i			0.707014i	−0.935432	+	0.353507i	$0.884989\pi$
$242$	11.0795	+	7.53118i	0.712215	+	0.484123i
$243$	11.4228	+	11.4228i	0.732771	+	0.732771i
$244$	2.43977	+	1.05635i	0.156191	+	0.0676259i
$245$		0			0
$246$	−12.2435	+	2.33434i	−0.780620	+	0.148832i
$247$	0.126281			0.00803507
$248$	−19.8827	−	4.45042i	−1.26255	−	0.282602i
$249$		−	10.0917i		−	0.639535i
$250$	0.00693505	+	0.0363741i	0.000438611	+	0.00230050i
$251$	18.8899	−	18.8899i	1.19232	−	1.19232i	0.215903	−	0.976415i	$-0.430731\pi$
$251$	18.8899	−	18.8899i	1.19232	−	1.19232i	0.976415	−	0.215903i	$-0.0692694\pi$
$252$		0			0
$253$	3.09507	+	3.09507i	0.194586	+	0.194586i
$254$	21.1557	+	14.3804i	1.32743	+	0.902309i
$255$	17.2207			1.07840
$256$	1.01712	−	15.9676i	0.0635703	−	0.997977i
$257$		−	17.6400i		−	1.10035i	−0.835048	−	0.550177i	$-0.814560\pi$
$257$		−	17.6400i		−	1.10035i	0.835048	−	0.550177i	$-0.185440\pi$
$258$	−11.0828	−	7.53343i	−0.689983	−	0.469011i
$259$		0			0
$260$	1.41685	+	3.58061i	0.0878696	+	0.222060i
$261$	3.97902	−	3.97902i	0.246295	−	0.246295i
$262$	3.82529	−	0.729326i	0.236327	−	0.0450579i
$263$	−7.18147			−0.442829			−0.221414	−	0.975180i	$-0.571067\pi$
$263$	−7.18147			−0.442829			−0.221414	+	0.975180i	$0.571067\pi$
$264$	0.700015	−	3.12738i	0.0430829	−	0.192477i
$265$	16.3225			1.00268
$266$		0			0
$267$	−3.96107	−	3.96107i	−0.242414	−	0.242414i
$268$	15.0140	+	6.50060i	0.917123	+	0.397087i
$269$	13.0641	−	13.0641i	0.796534	−	0.796534i	−0.186013	−	0.982547i	$-0.559557\pi$
$269$	13.0641	−	13.0641i	0.796534	−	0.796534i	0.982547	+	0.186013i	$0.0595566\pi$
$270$	−11.8979	+	17.5036i	−0.724085	+	1.06523i
$271$	−0.985661			−0.0598746			−0.0299373	−	0.999552i	$-0.509531\pi$
$271$	−0.985661			−0.0598746			−0.0299373	+	0.999552i	$0.509531\pi$
$272$	16.2491	+	17.3171i	0.985248	+	1.05000i
$273$		0			0
$274$	−2.28473	−	1.55302i	−0.138025	−	0.0938216i
$275$	−4.37624	+	4.37624i	−0.263897	+	0.263897i
$276$	−2.58084	+	5.96077i	−0.155348	+	0.358796i
$277$	−0.0617858	+	0.0617858i	−0.00371235	+	0.00371235i	−0.708961	−	0.705248i	$-0.750836\pi$
$277$	−0.0617858	+	0.0617858i	−0.00371235	+	0.00371235i	0.705248	+	0.708961i	$0.250836\pi$
$278$	−1.95623	−	10.2604i	−0.117327	−	0.615377i
$279$			15.5545i			0.931224i
$280$		0			0
$281$		−	13.9541i		−	0.832431i	−0.909266	−	0.416215i	$-0.863356\pi$
$281$		−	13.9541i		−	0.832431i	0.909266	−	0.416215i	$-0.136644\pi$
$282$	7.32743	−	1.39704i	0.436342	−	0.0831925i
$283$	9.34386	−	9.34386i	0.555435	−	0.555435i	−0.372569	−	0.928004i	$-0.621523\pi$
$283$	9.34386	−	9.34386i	0.555435	−	0.555435i	0.928004	+	0.372569i	$0.121523\pi$
$284$	−10.1525	−	25.6570i	−0.602441	−	1.52246i
$285$	−0.425590	+	0.425590i	−0.0252098	+	0.0252098i
$286$	−0.597917	+	0.879623i	−0.0353556	+	0.0520132i
$287$		0			0
$288$	−12.0653	+	1.90492i	−0.710956	+	0.112248i
$289$	−18.2448			−1.07322
$290$	9.64261	+	6.55448i	0.566233	+	0.384893i
$291$	−6.89291	+	6.89291i	−0.404070	+	0.404070i
$292$	1.65802	+	4.19007i	0.0970282	+	0.245205i
$293$	−1.11946	−	1.11946i	−0.0653995	−	0.0653995i	0.673651	−	0.739050i	$-0.264725\pi$
$293$	−1.11946	−	1.11946i	−0.0653995	−	0.0653995i	−0.739050	+	0.673651i	$0.764725\pi$
$294$		0			0
$295$	−4.51357			−0.262790
$296$	−27.6867	+	17.5591i	−1.60925	+	1.02060i
$297$	−5.84576			−0.339206
$298$	2.02159	+	10.6031i	0.117107	+	0.614224i
$299$	1.52433	−	1.52433i	0.0881542	−	0.0881542i
$300$	−8.42815	−	3.64914i	−0.486599	−	0.210683i
$301$		0			0
$302$	−11.2147	+	16.4985i	−0.645334	+	0.949381i
$303$		−	1.16930i		−	0.0671745i
$304$	−0.829551	−	0.0263941i	−0.0475780	−	0.00151381i
$305$	4.20542			0.240802
$306$	10.1914	−	14.9931i	0.582606	−	0.857099i
$307$	15.8597	+	15.8597i	0.905158	+	0.905158i	0.995877	−	0.0907183i	$-0.0289163\pi$
$307$	15.8597	+	15.8597i	0.905158	+	0.905158i	−0.0907183	+	0.995877i	$0.528916\pi$
$308$		0			0
$309$	6.36800	−	6.36800i	0.362263	−	0.362263i
$310$	−31.6583	+	6.03593i	−1.79807	+	0.342818i
$311$			28.5431i			1.61853i	0.587441	+	0.809267i	$0.300135\pi$
$311$			28.5431i			1.61853i	−0.587441	+	0.809267i	$0.699865\pi$
$312$	−1.54024	−	0.344758i	−0.0871989	−	0.0195181i
$313$	−0.0623260			−0.00352288			−0.00176144	−	0.999998i	$-0.500561\pi$
$313$	−0.0623260			−0.00352288			−0.00176144	+	0.999998i	$0.500561\pi$
$314$	−3.87127	−	20.3047i	−0.218468	−	1.14586i
$315$		0			0
$316$	3.16856	−	1.25381i	0.178245	−	0.0705321i
$317$	−16.0496	−	16.0496i	−0.901435	−	0.901435i	0.0941256	−	0.995560i	$-0.469994\pi$
$317$	−16.0496	−	16.0496i	−0.901435	−	0.901435i	−0.995560	+	0.0941256i	$0.969994\pi$
$318$	−3.76104	+	5.53304i	−0.210909	+	0.310277i
$319$			3.22039i			0.180307i
$320$	−8.55906	−	23.8175i	−0.478466	−	1.33144i
$321$			9.52731i			0.531762i
$322$		0			0
$323$	0.871034	−	0.871034i	0.0484656	−	0.0484656i
$324$	1.57508	+	3.98046i	0.0875042	+	0.221137i
$325$	2.15530	+	2.15530i	0.119555	+	0.119555i
$326$	−0.110569	−	0.579930i	−0.00612384	−	0.0321193i
$327$		−	0.0372244i		−	0.00205852i
$328$	−26.5308	−	5.93851i	−1.46492	−	0.327899i
$329$		0			0
$330$	−0.949402	−	4.97958i	−0.0522629	−	0.274117i
$331$	−11.3645	−	11.3645i	−0.624651	−	0.624651i	0.322066	−	0.946717i	$-0.395623\pi$
$331$	−11.3645	−	11.3645i	−0.624651	−	0.624651i	−0.946717	+	0.322066i	$0.895623\pi$
$332$	8.74618	−	20.2004i	0.480009	−	1.10864i
$333$	17.6982	+	17.6982i	0.969855	+	0.969855i
$334$	−3.70695	−	2.51977i	−0.202835	−	0.137876i
$335$	25.8794			1.41394
$336$		0			0
$337$	−15.2905			−0.832928			−0.416464	−	0.909152i	$-0.636731\pi$
$337$	−15.2905			−0.832928			−0.416464	+	0.909152i	$0.636731\pi$
$338$	−14.7715	−	10.0408i	−0.803462	−	0.546147i
$339$	7.18227	+	7.18227i	0.390087	+	0.390087i
$340$	34.4704	+	14.9247i	1.86942	+	0.809405i
$341$	−6.29446	−	6.29446i	−0.340864	−	0.340864i
$342$	0.118668	+	0.622407i	0.00641681	+	0.0336559i
$343$		0			0
$344$	−15.6552	−	24.6847i	−0.844073	−	1.33091i
$345$			10.2745i			0.553162i
$346$	−6.05676	−	31.7675i	−0.325613	−	1.70783i
$347$	−19.4891	−	19.4891i	−1.04623	−	1.04623i	−0.998878	−	0.0473539i	$-0.984921\pi$
$347$	−19.4891	−	19.4891i	−1.04623	−	1.04623i	−0.0473539	−	0.998878i	$-0.515079\pi$
$348$	−4.44372	+	1.75839i	−0.238208	+	0.0942596i
$349$	17.0806	−	17.0806i	0.914304	−	0.914304i	−0.0823032	−	0.996607i	$-0.526228\pi$
$349$	17.0806	−	17.0806i	0.914304	−	0.914304i	0.996607	+	0.0823032i	$0.0262276\pi$
$350$		0			0
$351$			2.87905i			0.153672i
$352$	4.11162	−	5.65335i	0.219150	−	0.301325i
$353$		−	23.4335i		−	1.24724i	−0.781727	−	0.623621i	$-0.785661\pi$
$353$		−	23.4335i		−	1.24724i	0.781727	−	0.623621i	$-0.214339\pi$
$354$	1.04002	−	1.53002i	0.0552765	−	0.0813199i
$355$	−30.8623	−	30.8623i	−1.63800	−	1.63800i
$356$	−4.49587	−	11.3618i	−0.238281	−	0.602172i
$357$		0			0
$358$	3.64318	+	19.1084i	0.192548	+	1.00991i
$359$	8.71557			0.459990			0.229995	−	0.973192i	$-0.426129\pi$
$359$	8.71557			0.459990			0.229995	+	0.973192i	$0.426129\pi$
$360$	−16.3165	+	10.3481i	−0.859955	+	0.545391i
$361$		−	18.9569i		−	0.997734i
$362$	9.84956	−	1.87791i	0.517681	−	0.0987006i
$363$	−6.14177	+	6.14177i	−0.322360	+	0.322360i
$364$		0			0
$365$	5.04015	+	5.04015i	0.263814	+	0.263814i
$366$	−0.969018	+	1.42557i	−0.0506514	+	0.0745156i
$367$	−2.82816			−0.147629			−0.0738143	−	0.997272i	$-0.523517\pi$
$367$	−2.82816			−0.147629			−0.0738143	+	0.997272i	$0.523517\pi$
$368$	−10.3321	+	9.69485i	−0.538595	+	0.505379i
$369$			20.7555i			1.08049i
$370$	−29.1535	+	42.8891i	−1.51562	+	2.22970i
$371$		0			0
$372$	5.24865	−	12.1224i	0.272130	−	0.628519i
$373$	−10.0112	+	10.0112i	−0.518359	+	0.518359i	−0.917075	−	0.398716i	$-0.869456\pi$
$373$	−10.0112	+	10.0112i	−0.518359	+	0.518359i	0.398716	+	0.917075i	$0.369456\pi$
$374$	1.94309	+	10.1915i	0.100475	+	0.526988i
$375$	−0.0240079			−0.00123976
$376$	15.8780	+	3.55404i	0.818845	+	0.183285i
$377$	1.58605			0.0816855
$378$		0			0
$379$	−10.2443	−	10.2443i	−0.526215	−	0.526215i	0.393227	−	0.919442i	$-0.371359\pi$
$379$	−10.2443	−	10.2443i	−0.526215	−	0.526215i	−0.919442	+	0.393227i	$0.871359\pi$
$380$	−1.22074	+	0.483051i	−0.0626228	+	0.0247800i
$381$	−11.7274	+	11.7274i	−0.600815	+	0.600815i
$382$	6.28373	+	4.27131i	0.321503	+	0.218539i
$383$	−6.41444			−0.327763			−0.163881	−	0.986480i	$-0.552401\pi$
$383$	−6.41444			−0.327763			−0.163881	+	0.986480i	$0.552401\pi$
$384$	10.0459	+	2.58667i	0.512653	+	0.132001i
$385$		0			0
$386$	0.0571280	−	0.0840436i	0.00290774	−	0.00427771i
$387$	−15.7792	+	15.7792i	−0.802104	+	0.802104i
$388$	−19.7713	+	7.82356i	−1.00374	+	0.397181i
$389$	12.0260	−	12.0260i	0.609743	−	0.609743i	−0.333136	−	0.942879i	$-0.608107\pi$
$389$	12.0260	−	12.0260i	0.609743	−	0.609743i	0.942879	+	0.333136i	$0.108107\pi$
$390$	−2.45245	+	0.467582i	−0.124185	+	0.0236769i
$391$		−	21.0284i		−	1.06345i
$392$		0			0
$393$			2.52480i			0.127359i
$394$	0.975258	+	5.11520i	0.0491328	+	0.257700i
$395$	3.81140	−	3.81140i	0.191772	−	0.191772i
$396$	−4.89731	−	2.12039i	−0.246099	−	0.106554i
$397$	7.82453	−	7.82453i	0.392702	−	0.392702i	−0.482947	−	0.875649i	$-0.660434\pi$
$397$	7.82453	−	7.82453i	0.392702	−	0.392702i	0.875649	+	0.482947i	$0.160434\pi$
$398$	−12.1798	−	8.27914i	−0.610519	−	0.414996i
$399$		0			0
$400$	−13.7079	−	14.6089i	−0.685395	−	0.730443i
$401$	15.1860			0.758352			0.379176	−	0.925325i	$-0.376208\pi$
$401$	15.1860			0.758352			0.379176	+	0.925325i	$0.376208\pi$
$402$	−5.96317	+	8.77270i	−0.297416	+	0.437542i
$403$	−3.10003	+	3.10003i	−0.154423	+	0.154423i
$404$	1.01340	−	2.34057i	0.0504185	−	0.116448i
$405$	4.78802	+	4.78802i	0.237918	+	0.237918i
$406$		0			0
$407$	−14.3239			−0.710009
$408$	−13.0019	+	8.24594i	−0.643692	+	0.408235i
$409$	5.31069			0.262596			0.131298	−	0.991343i	$-0.458085\pi$
$409$	5.31069			0.262596			0.131298	+	0.991343i	$0.458085\pi$
$410$	−42.2438	+	8.05416i	−2.08627	+	0.397767i
$411$	1.26651	−	1.26651i	0.0624724	−	0.0624724i
$412$	18.2657	−	7.22778i	0.899887	−	0.356087i
$413$		0			0
$414$	8.94546	+	6.08061i	0.439646	+	0.298846i
$415$		−	34.8193i		−	1.70921i
$416$	−2.78428	−	2.02498i	−0.136511	−	0.0992828i
$417$	6.77214			0.331633
$418$	−0.299892	−	0.203849i	−0.0146682	−	0.00997058i
$419$	−7.73525	−	7.73525i	−0.377891	−	0.377891i	0.492450	−	0.870341i	$-0.336102\pi$
$419$	−7.73525	−	7.73525i	−0.377891	−	0.377891i	−0.870341	+	0.492450i	$0.836102\pi$
$420$		0			0
$421$	4.79155	−	4.79155i	0.233526	−	0.233526i	−0.580637	−	0.814163i	$-0.697196\pi$
$421$	4.79155	−	4.79155i	0.233526	−	0.233526i	0.814163	+	0.580637i	$0.197196\pi$
$422$	0.861907	+	4.52067i	0.0419570	+	0.220063i
$423$		−	12.4216i		−	0.603957i
$424$	−12.3237	+	7.81582i	−0.598494	+	0.379570i
$425$	29.7328			1.44225
$426$	17.5731	−	3.35047i	0.851421	−	0.162331i
$427$		0			0
$428$	−8.25704	+	19.0707i	−0.399119	+	0.921816i
$429$	−0.487609	−	0.487609i	−0.0235420	−	0.0235420i
$430$	−38.2388	−	25.9925i	−1.84404	−	1.25347i
$431$		−	2.54672i		−	0.122671i	−0.998117	−	0.0613356i	$-0.980464\pi$
$431$		−	2.54672i		−	0.122671i	0.998117	−	0.0613356i	$-0.0195360\pi$
$432$	0.601752	−	18.9127i	0.0289518	−	0.909938i
$433$			19.0390i			0.914954i	0.889221	+	0.457477i	$0.151247\pi$
$433$			19.0390i			0.914954i	−0.889221	+	0.457477i	$0.848753\pi$
$434$		0			0
$435$	−5.34527	+	5.34527i	−0.256286	+	0.256286i
$436$	0.0322613	−	0.0745116i	0.00154504	−	0.00356846i
$437$	0.519692	+	0.519692i	0.0248603	+	0.0248603i
$438$	−2.86988	+	0.547169i	−0.137128	+	0.0261448i
$439$		−	17.5885i		−	0.839454i	−0.907650	−	0.419727i	$-0.862126\pi$
$439$		−	17.5885i		−	0.839454i	0.907650	−	0.419727i	$-0.137874\pi$
$440$	2.41525	−	10.7904i	0.115143	−	0.514411i
$441$		0			0
$442$	5.01931	−	0.956977i	0.238744	−	0.0455187i
$443$	19.1147	+	19.1147i	0.908169	+	0.908169i	0.996124	−	0.0879557i	$-0.0280334\pi$
$443$	19.1147	+	19.1147i	0.908169	+	0.908169i	−0.0879557	+	0.996124i	$0.528033\pi$
$444$	−7.82110	−	19.7651i	−0.371173	−	0.938012i
$445$	−13.6668	−	13.6668i	−0.647871	−	0.647871i
$446$	17.4231	−	25.6319i	0.825007	−	1.21371i
$447$	−6.99837			−0.331012
$448$		0			0
$449$	−4.60299			−0.217228			−0.108614	−	0.994084i	$-0.534641\pi$
$449$	−4.60299			−0.217228			−0.108614	+	0.994084i	$0.534641\pi$
$450$	−8.59759	+	12.6483i	−0.405294	+	0.596247i
$451$	−8.39913	−	8.39913i	−0.395500	−	0.395500i
$452$	8.15198	+	20.6013i	0.383437	+	0.969004i
$453$	−9.14574	−	9.14574i	−0.429704	−	0.429704i
$454$	16.0970	−	3.06905i	0.755472	−	0.144037i
$455$		0			0
$456$	0.117539	−	0.525117i	0.00550427	−	0.0245909i
$457$		−	25.7807i		−	1.20597i	−0.797753	−	0.602985i	$-0.793978\pi$
$457$		−	25.7807i		−	1.20597i	0.797753	−	0.602985i	$-0.206022\pi$
$458$	30.1879	−	5.75559i	1.41059	−	0.268941i
$459$	19.8585	+	19.8585i	0.926915	+	0.926915i
$460$	−8.90464	+	20.5664i	−0.415181	+	0.958913i
$461$	−4.40686	+	4.40686i	−0.205248	+	0.205248i	−0.802244	−	0.596996i	$-0.796361\pi$
$461$	−4.40686	+	4.40686i	−0.205248	+	0.205248i	0.596996	+	0.802244i	$0.296361\pi$
$462$		0			0
$463$			31.0375i			1.44244i	0.692708	+	0.721218i	$0.256417\pi$
$463$			31.0375i			1.44244i	−0.692708	+	0.721218i	$0.743583\pi$
$464$	−10.4189	−	0.331501i	−0.483684	−	0.0153895i
$465$		−	20.8953i		−	0.968998i
$466$	14.6157	+	9.93494i	0.677061	+	0.460227i
$467$	−25.7640	−	25.7640i	−1.19221	−	1.19221i	−0.976444	−	0.215769i	$-0.930774\pi$
$467$	−25.7640	−	25.7640i	−1.19221	−	1.19221i	−0.215769	−	0.976444i	$-0.569226\pi$
$468$	−1.04430	+	2.41193i	−0.0482726	+	0.111492i
$469$		0			0
$470$	25.2818	−	4.82020i	1.16616	−	0.222339i
$471$	13.4017			0.617516
$472$	3.40782	−	2.16127i	0.156858	−	0.0994806i
$473$		−	12.7708i		−	0.587202i
$474$	0.413773	+	2.17023i	0.0190052	+	0.0996819i
$475$	−0.734812	+	0.734812i	−0.0337155	+	0.0337155i
$476$		0			0
$477$	7.87773	+	7.87773i	0.360697	+	0.360697i
$478$	9.01728	+	6.12943i	0.412441	+	0.280353i
$479$	9.53799			0.435802			0.217901	−	0.975971i	$-0.430079\pi$
$479$	9.53799			0.435802			0.217901	+	0.975971i	$0.430079\pi$
$480$	16.2081	−	2.55900i	0.739795	−	0.116802i
$481$			7.05454i			0.321659i
$482$	−12.8372	−	8.72599i	−0.584719	−	0.397458i
$483$		0			0
$484$	−17.6168	+	6.97100i	−0.800764	+	0.316864i
$485$	−23.7826	+	23.7826i	−1.07991	+	1.07991i
$486$	−22.4413	+	4.27864i	−1.01796	+	0.194083i
$487$	2.79085			0.126465			0.0632327	−	0.997999i	$-0.479859\pi$
$487$	2.79085			0.126465			0.0632327	+	0.997999i	$0.479859\pi$
$488$	−3.17517	+	2.01372i	−0.143733	+	0.0911567i
$489$	0.382770			0.0173094
$490$		0			0
$491$	−14.9085	−	14.9085i	−0.672809	−	0.672809i	0.285554	−	0.958363i	$-0.407823\pi$
$491$	−14.9085	−	14.9085i	−0.672809	−	0.672809i	−0.958363	+	0.285554i	$0.907823\pi$
$492$	7.00364	−	16.1758i	0.315749	−	0.729261i
$493$	10.9399	−	10.9399i	0.492708	−	0.492708i
$494$	−0.100396	+	0.147697i	−0.00451703	+	0.00664521i
$495$	−8.44146			−0.379415
$496$	21.0123	−	19.7164i	0.943481	−	0.885294i
$497$		0			0
$498$	11.8032	+	8.02310i	0.528912	+	0.359524i
$499$	−10.0031	+	10.0031i	−0.447802	+	0.447802i	−0.894623	−	0.446822i	$-0.852556\pi$
$499$	−10.0031	+	10.0031i	−0.447802	+	0.447802i	0.446822	+	0.894623i	$0.352556\pi$
$500$	−0.0480563	−	0.0208070i	−0.00214914	−	0.000930516i
$501$	2.05490	−	2.05490i	0.0918064	−	0.0918064i
$502$	7.07559	+	37.1112i	0.315799	+	1.65636i
$503$			0.855211i			0.0381320i	0.999818	+	0.0190660i	$0.00606926\pi$
$503$			0.855211i			0.0381320i	−0.999818	+	0.0190660i	$0.993931\pi$
$504$		0			0
$505$		−	4.03443i		−	0.179530i
$506$	−6.08062	+	1.15932i	−0.270316	+	0.0515383i
$507$	8.18839	−	8.18839i	0.363659	−	0.363659i
$508$	−33.6385	+	13.3108i	−1.49247	+	0.590572i
$509$	−12.8599	+	12.8599i	−0.570006	+	0.570006i	−0.932130	−	0.362124i	$-0.882052\pi$
$509$	−12.8599	+	12.8599i	−0.570006	+	0.570006i	0.362124	+	0.932130i	$0.382052\pi$
$510$	−13.6908	+	20.1412i	−0.606239	+	0.891867i
$511$		0			0
$512$	17.8670	+	13.8842i	0.789616	+	0.613601i
$513$	−0.981559			−0.0433369
$514$	20.6316	+	14.0242i	0.910021	+	0.618580i
$515$	21.9715	−	21.9715i	0.968178	−	0.968178i
$516$	17.6221	−	6.97308i	0.775768	−	0.306973i
$517$	5.02665	+	5.02665i	0.221072	+	0.221072i
$518$		0			0
$519$	20.9674			0.920368
$520$	−5.31428	−	1.18952i	−0.233046	−	0.0521637i
$521$	−0.947626			−0.0415163			−0.0207581	−	0.999785i	$-0.506608\pi$
$521$	−0.947626			−0.0415163			−0.0207581	+	0.999785i	$0.506608\pi$
$522$	1.49042	+	7.81723i	0.0652341	+	0.342151i
$523$	18.9225	−	18.9225i	0.827425	−	0.827425i	−0.159735	−	0.987160i	$-0.551064\pi$
$523$	18.9225	−	18.9225i	0.827425	−	0.827425i	0.987160	+	0.159735i	$0.0510640\pi$
$524$	−2.18817	+	5.05385i	−0.0955906	+	0.220779i
$525$		0			0
$526$	5.70942	−	8.39939i	0.248942	−	0.366231i
$527$			42.7655i			1.86289i
$528$	3.10123	+	3.30506i	0.134964	+	0.143834i
$529$	−10.4537			−0.454507
$530$	−12.9767	+	19.0906i	−0.563671	+	0.829243i
$531$	−2.17839	−	2.17839i	−0.0945341	−	0.0945341i
$532$		0			0
$533$	−4.13658	+	4.13658i	−0.179175	+	0.179175i
$534$	7.78196	−	1.48370i	0.336758	−	0.0642060i
$535$			32.8720i			1.42118i
$536$	−19.5394	+	12.3921i	−0.843975	+	0.535256i
$537$	−12.6121			−0.544251
$538$	4.89344	+	25.6659i	0.210971	+	1.10654i
$539$		0			0
$540$	−11.0130	−	27.8314i	−0.473922	−	1.19767i
$541$	14.6136	+	14.6136i	0.628289	+	0.628289i	0.947637	−	0.319348i	$-0.103464\pi$
$541$	14.6136	+	14.6136i	0.628289	+	0.628289i	−0.319348	+	0.947637i	$0.603464\pi$
$542$	0.783620	−	1.15282i	0.0336594	−	0.0495178i
$543$			6.50098i			0.278984i
$544$	−33.1723	+	5.23738i	−1.42225	+	0.224551i
$545$		−	0.128435i		−	0.00550156i
$546$		0			0
$547$	3.84440	−	3.84440i	0.164375	−	0.164375i	−0.620127	−	0.784502i	$-0.712919\pi$
$547$	3.84440	−	3.84440i	0.164375	−	0.164375i	0.784502	+	0.620127i	$0.212919\pi$
$548$	3.63281	−	1.43751i	0.155186	−	0.0614073i
$549$	2.02967	+	2.02967i	0.0866241	+	0.0866241i
$550$	−1.63921	−	8.59761i	−0.0698962	−	0.366603i
$551$			0.540734i			0.0230360i
$552$	−4.91984	−	7.75746i	−0.209402	−	0.330179i
$553$		0			0
$554$	−0.0231432	−	0.121385i	−0.000983259	−	0.00515716i
$555$	−23.7751	−	23.7751i	−1.00920	−	1.00920i
$556$	13.5557	+	5.86922i	0.574889	+	0.248910i
$557$	−8.79685	−	8.79685i	−0.372735	−	0.372735i	0.495738	−	0.868472i	$-0.334898\pi$
$557$	−8.79685	−	8.79685i	−0.372735	−	0.372735i	−0.868472	+	0.495738i	$0.834898\pi$
$558$	−18.1924	−	12.3661i	−0.770146	−	0.523501i
$559$	−6.28964			−0.266023
$560$		0			0
$561$	−6.72665			−0.284000
$562$	16.3206	+	11.0938i	0.688442	+	0.467963i
$563$	2.57121	+	2.57121i	0.108363	+	0.108363i	0.759210	−	0.650846i	$-0.225586\pi$
$563$	2.57121	+	2.57121i	0.108363	+	0.108363i	−0.650846	+	0.759210i	$0.725586\pi$
$564$	−4.19149	+	9.68077i	−0.176494	+	0.407634i
$565$	24.7809	+	24.7809i	1.04254	+	1.04254i
$566$	3.49994	+	18.3571i	0.147113	+	0.771605i
$567$		0			0
$568$	38.0796	+	8.52352i	1.59779	+	0.357639i
$569$		−	16.2826i		−	0.682601i	−0.939954	−	0.341300i	$-0.889133\pi$
$569$		−	16.2826i		−	0.682601i	0.939954	−	0.341300i	$-0.110867\pi$
$570$	−0.159414	−	0.836119i	−0.00667710	−	0.0350212i
$571$	5.51686	+	5.51686i	0.230874	+	0.230874i	0.813057	−	0.582184i	$-0.197802\pi$
$571$	5.51686	+	5.51686i	0.230874	+	0.230874i	−0.582184	+	0.813057i	$0.697802\pi$
$572$	−0.553443	−	1.39864i	−0.0231406	−	0.0584799i
$573$	−3.48331	+	3.48331i	−0.145517	+	0.145517i
$574$		0			0
$575$			17.7397i			0.739798i
$576$	7.36420	−	15.6259i	0.306841	−	0.651081i
$577$			36.6237i			1.52467i	0.647185	+	0.762333i	$0.275946\pi$
$577$			36.6237i			1.52467i	−0.647185	+	0.762333i	$0.724054\pi$
$578$	14.5050	−	21.3389i	0.603327	−	0.887583i
$579$	0.0465886	+	0.0465886i	0.00193616	+	0.00193616i
$580$	−15.3321	+	6.06696i	−0.636632	+	0.251917i
$581$		0			0
$582$	−2.58188	−	13.5419i	−0.107023	−	0.561329i
$583$	−6.37578			−0.264058
$584$	−6.21882	−	1.39199i	−0.257337	−	0.0576008i
$585$			4.15743i			0.171889i
$586$	2.19930	−	0.419316i	0.0908523	−	0.0173218i
$587$	−26.7399	+	26.7399i	−1.10367	+	1.10367i	−0.109709	+	0.993964i	$0.534992\pi$
$587$	−26.7399	+	26.7399i	−1.10367	+	1.10367i	−0.993964	+	0.109709i	$0.965008\pi$
$588$		0			0
$589$	−1.05690	−	1.05690i	−0.0435488	−	0.0435488i
$590$	3.58838	−	5.27903i	0.147731	−	0.217334i
$591$	−3.37617			−0.138877
$592$	1.47448	−	46.3419i	0.0606006	−	1.90464i
$593$			5.66759i			0.232740i	0.993206	+	0.116370i	$0.0371258\pi$
$593$			5.66759i			0.232740i	−0.993206	+	0.116370i	$0.962874\pi$
$594$	4.64750	−	6.83715i	0.190689	−	0.280532i
$595$		0			0
$596$	−14.0085	−	6.06529i	−0.573812	−	0.248444i
$597$	6.75174	−	6.75174i	0.276331	−	0.276331i
$598$	0.570969	+	2.99471i	0.0233487	+	0.122463i
$599$	−10.2103			−0.417183			−0.208591	−	0.978003i	$-0.566888\pi$
$599$	−10.2103			−0.417183			−0.208591	+	0.978003i	$0.566888\pi$
$600$	10.9685	−	6.95634i	0.447789	−	0.283992i
$601$	2.00211			0.0816677			0.0408339	−	0.999166i	$-0.486999\pi$
$601$	2.00211			0.0816677			0.0408339	+	0.999166i	$0.486999\pi$
$602$		0			0
$603$	12.4902	+	12.4902i	0.508642	+	0.508642i
$604$	−10.3806	−	26.2333i	−0.422379	−	1.06742i
$605$	−21.1909	+	21.1909i	−0.861533	+	0.861533i
$606$	1.36760	+	0.929617i	0.0555551	+	0.0377631i
$607$	28.4425			1.15445			0.577223	−	0.816587i	$-0.304136\pi$
$607$	28.4425			1.15445			0.577223	+	0.816587i	$0.304136\pi$
$608$	0.690380	−	0.949251i	0.0279986	−	0.0384972i
$609$		0			0
$610$	−3.34339	+	4.91862i	−0.135370	+	0.199149i
$611$	2.47563	−	2.47563i	0.100153	−	0.100153i
$612$	9.43340	+	23.8397i	0.381323	+	0.963661i
$613$	−11.3192	+	11.3192i	−0.457178	+	0.457178i	−0.897728	−	0.440550i	$-0.854783\pi$
$613$	−11.3192	+	11.3192i	−0.457178	+	0.457178i	0.440550	+	0.897728i	$0.354783\pi$
$614$	−31.1581	+	5.94056i	−1.25744	+	0.239742i
$615$		−	27.8821i		−	1.12431i
$616$		0			0
$617$		−	41.5070i		−	1.67101i	−0.549485	−	0.835504i	$-0.685176\pi$
$617$		−	41.5070i		−	1.67101i	0.549485	−	0.835504i	$-0.314824\pi$
$618$	2.38527	+	12.5106i	0.0959495	+	0.503252i
$619$	12.6764	−	12.6764i	0.509507	−	0.509507i	−0.404868	−	0.914375i	$-0.632683\pi$
$619$	12.6764	−	12.6764i	0.509507	−	0.509507i	0.914375	+	0.404868i	$0.132683\pi$
$620$	18.1094	−	41.8259i	0.727290	−	1.67977i
$621$	−11.8483	+	11.8483i	−0.475457	+	0.475457i
$622$	−33.3838	−	22.6924i	−1.33857	−	0.909881i
$623$		0			0
$624$	1.62775	−	1.52736i	0.0651621	−	0.0611434i
$625$	24.9585			0.998342
$626$	0.0495504	−	0.0728960i	0.00198043	−	0.00291351i
$627$	0.166241	−	0.166241i	0.00663904	−	0.00663904i
$628$	26.8259	+	11.6148i	1.07047	+	0.463482i
$629$	48.6593	+	48.6593i	1.94017	+	1.94017i
$630$		0			0
$631$	−21.0724			−0.838880			−0.419440	−	0.907783i	$-0.637774\pi$
$631$	−21.0724			−0.838880			−0.419440	+	0.907783i	$0.637774\pi$
$632$	−1.05263	+	4.70272i	−0.0418713	+	0.187064i
$633$	−2.98377			−0.118594
$634$	31.5312	−	6.01171i	1.25226	−	0.238755i
$635$	−40.4631	+	40.4631i	−1.60573	+	1.60573i
$636$	−3.48129	−	8.79776i	−0.138042	−	0.348854i
$637$		0			0
$638$	−3.76654	−	2.56027i	−0.149119	−	0.101362i
$639$		−	29.7902i		−	1.17848i
$640$	34.6613	+	8.92478i	1.37011	+	0.352783i
$641$	−27.1495			−1.07234			−0.536171	−	0.844109i	$-0.680130\pi$
$641$	−27.1495			−1.07234			−0.536171	+	0.844109i	$0.680130\pi$
$642$	−11.1431	−	7.57440i	−0.439781	−	0.298938i
$643$	−21.2081	−	21.2081i	−0.836367	−	0.836367i	0.152012	−	0.988379i	$-0.451425\pi$
$643$	−21.2081	−	21.2081i	−0.836367	−	0.836367i	−0.988379	+	0.152012i	$0.951425\pi$
$644$		0			0
$645$	21.1972	−	21.1972i	0.834640	−	0.834640i
$646$	0.326264	+	1.71124i	0.0128367	+	0.0673280i
$647$		−	40.2635i		−	1.58292i	−0.611221	−	0.791460i	$-0.709321\pi$
$647$		−	40.2635i		−	1.58292i	0.611221	−	0.791460i	$-0.290679\pi$
$648$	−5.90773	−	1.32235i	−0.232077	−	0.0519468i
$649$	1.76306			0.0692063
$650$	−4.23433	+	0.807314i	−0.166084	+	0.0316654i
$651$		0			0
$652$	0.766185	+	0.331735i	0.0300061	+	0.0129918i
$653$	−16.4619	−	16.4619i	−0.644206	−	0.644206i	0.307381	−	0.951587i	$-0.400547\pi$
$653$	−16.4619	−	16.4619i	−0.644206	−	0.644206i	−0.951587	+	0.307381i	$0.900547\pi$
$654$	0.0435374	+	0.0295942i	0.00170245	+	0.00115722i
$655$			8.71129i			0.340378i
$656$	28.0382	−	26.3090i	1.09471	−	1.02719i
$657$			4.86507i			0.189805i
$658$		0			0
$659$	−21.3113	+	21.3113i	−0.830171	+	0.830171i	−0.987540	−	0.157369i	$-0.949699\pi$
$659$	−21.3113	+	21.3113i	−0.830171	+	0.830171i	0.157369	+	0.987540i	$0.449699\pi$
$660$	6.57887	+	2.84846i	0.256082	+	0.110876i
$661$	−7.73509	−	7.73509i	−0.300860	−	0.300860i	0.540490	−	0.841350i	$-0.318239\pi$
$661$	−7.73509	−	7.73509i	−0.300860	−	0.300860i	−0.841350	+	0.540490i	$0.818239\pi$
$662$	22.3269	−	4.25682i	0.867758	−	0.165446i
$663$			3.31289i			0.128662i
$664$	16.6728	+	26.2892i	0.647031	+	1.02022i
$665$		0			0
$666$	−34.7701	+	6.62923i	−1.34731	+	0.256877i
$667$	6.52716	+	6.52716i	0.252733	+	0.252733i
$668$	5.89420	−	2.33235i	0.228053	−	0.0902412i
$669$	14.2088	+	14.2088i	0.549342	+	0.549342i
$670$	−20.5747	+	30.2684i	−0.794869	+	1.16937i
$671$	−1.64270			−0.0634156
$672$		0			0
$673$	35.4992			1.36839			0.684197	−	0.729297i	$-0.260153\pi$
$673$	35.4992			1.36839			0.684197	+	0.729297i	$0.260153\pi$
$674$	12.1563	−	17.8837i	0.468243	−	0.688853i
$675$	−16.7528	−	16.7528i	−0.644815	−	0.644815i
$676$	23.4872	−	9.29394i	0.903355	−	0.357459i
$677$	21.3384	+	21.3384i	0.820100	+	0.820100i	0.986122	−	0.166022i	$-0.0530924\pi$
$677$	21.3384	+	21.3384i	0.820100	+	0.820100i	−0.166022	+	0.986122i	$0.553092\pi$
$678$	−14.1104	+	2.69027i	−0.541905	+	0.103319i
$679$		0			0
$680$	−44.8605	+	28.4509i	−1.72032	+	1.09104i
$681$			10.6245i			0.407132i
$682$	12.3662	−	2.35772i	0.473525	−	0.0902818i
$683$	23.6590	+	23.6590i	0.905288	+	0.905288i	0.995887	−	0.0905997i	$-0.0288784\pi$
$683$	23.6590	+	23.6590i	0.905288	+	0.905288i	−0.0905997	+	0.995887i	$0.528878\pi$
$684$	−0.822305	−	0.356034i	−0.0314416	−	0.0136133i
$685$	4.36983	−	4.36983i	0.166963	−	0.166963i
$686$		0			0
$687$			19.9249i			0.760180i
$688$	41.3172	+	1.31460i	1.57520	+	0.0501188i
$689$			3.14008i			0.119628i
$690$	−12.0170	−	8.16846i	−0.457479	−	0.310968i
$691$	31.9217	+	31.9217i	1.21436	+	1.21436i	0.969579	+	0.244780i	$0.0787157\pi$
$691$	31.9217	+	31.9217i	1.21436	+	1.21436i	0.244780	+	0.969579i	$0.421284\pi$
$692$	41.9702	+	18.1719i	1.59547	+	0.690790i
$693$		0			0
$694$	38.2886	−	7.30006i	1.45341	−	0.277107i
$695$	23.3658			0.886317
$696$	1.47625	−	6.59529i	0.0559572	−	0.249994i
$697$			57.0649i			2.16149i
$698$	6.39790	+	33.5568i	0.242164	+	1.27014i
$699$	−8.10207	+	8.10207i	−0.306448	+	0.306448i
$700$		0			0
$701$	7.35956	+	7.35956i	0.277967	+	0.277967i	0.832297	−	0.554330i	$-0.187026\pi$
$701$	7.35956	+	7.35956i	0.277967	+	0.277967i	−0.554330	+	0.832297i	$0.687026\pi$
$702$	−3.36731	−	2.28890i	−0.127091	−	0.0863890i
$703$	−2.40512			−0.0907107
$704$	3.34329	+	9.30344i	0.126005	+	0.350637i
$705$			16.6867i			0.628456i
$706$	27.4077	+	18.6301i	1.03150	+	0.701154i
$707$		0			0
$708$	0.962664	+	2.43280i	0.0361791	+	0.0914302i
$709$	4.37885	−	4.37885i	0.164451	−	0.164451i	−0.620084	−	0.784535i	$-0.712902\pi$
$709$	4.37885	−	4.37885i	0.164451	−	0.164451i	0.784535	+	0.620084i	$0.212902\pi$
$710$	60.6324	−	11.5601i	2.27549	−	0.433843i
$711$	3.67900			0.137973
$712$	16.8629	+	3.77450i	0.631965	+	0.141455i
$713$	−25.5155			−0.955563
$714$		0			0
$715$	−1.68239	−	1.68239i	−0.0629179	−	0.0629179i
$716$	−25.2454	−	10.9305i	−0.943465	−	0.408492i
$717$	−4.99863	+	4.99863i	−0.186677	+	0.186677i
$718$	−6.92905	+	10.1936i	−0.258590	+	0.380424i
$719$	−18.1107			−0.675416			−0.337708	−	0.941251i	$-0.609652\pi$
$719$	−18.1107			−0.675416			−0.337708	+	0.941251i	$0.609652\pi$
$720$	0.868948	−	27.3105i	0.0323838	−	1.01780i
$721$		0			0
$722$	22.1719	+	15.0712i	0.825152	+	0.560890i
$723$	7.11616	−	7.11616i	0.264653	−	0.264653i
$724$	−5.63421	+	13.0129i	−0.209394	+	0.483622i
$725$	−9.22899	+	9.22899i	−0.342756	+	0.342756i
$726$	−2.30053	−	12.0662i	−0.0853806	−	0.447819i
$727$		−	39.2154i		−	1.45442i	−0.686415	−	0.727210i	$-0.740817\pi$
$727$		−	39.2154i		−	1.45442i	0.686415	−	0.727210i	$-0.259183\pi$
$728$		0			0
$729$		−	8.39075i		−	0.310768i
$730$	−9.90194	+	1.88789i	−0.366487	+	0.0698741i
$731$	−43.3833	+	43.3833i	−1.60459	+	1.60459i
$732$	−0.896941	−	2.26671i	−0.0331519	−	0.0837800i
$733$	8.67284	−	8.67284i	0.320339	−	0.320339i	−0.528558	−	0.848897i	$-0.677267\pi$
$733$	8.67284	−	8.67284i	0.320339	−	0.320339i	0.848897	+	0.528558i	$0.177267\pi$
$734$	2.24844	−	3.30779i	0.0829915	−	0.122093i
$735$		0			0
$736$	−3.12482	−	19.7919i	−0.115182	−	0.729538i
$737$	−10.1089			−0.372365
$738$	−24.2754	−	16.5010i	−0.893589	−	0.607410i
$739$	−17.5954	+	17.5954i	−0.647257	+	0.647257i	−0.952329	−	0.305072i	$-0.901319\pi$
$739$	−17.5954	+	17.5954i	−0.647257	+	0.647257i	0.305072	+	0.952329i	$0.401319\pi$
$740$	−26.9851	−	68.1954i	−0.991991	−	2.50691i
$741$	−0.0818741	−	0.0818741i	−0.00300772	−	0.00300772i
$742$		0			0
$743$	18.0234			0.661215			0.330608	−	0.943768i	$-0.392746\pi$
$743$	18.0234			0.661215			0.330608	+	0.943768i	$0.392746\pi$
$744$	10.0055	+	15.7764i	0.366819	+	0.578389i
$745$	−24.1464			−0.884657
$746$	−3.74989	−	19.6681i	−0.137293	−	0.720099i
$747$	16.8049	−	16.8049i	0.614859	−	0.614859i
$748$	−13.4646	−	5.82980i	−0.492316	−	0.213158i
$749$		0			0
$750$	0.0190868	−	0.0280794i	0.000696950	−	0.00102532i
$751$			29.9539i			1.09303i	0.837448	+	0.546516i	$0.184046\pi$
$751$			29.9539i			1.09303i	−0.837448	+	0.546516i	$0.815954\pi$
$752$	−16.7801	+	15.7452i	−0.611907	+	0.574169i
$753$	−24.4945			−0.892627
$754$	−1.26094	+	1.85503i	−0.0459207	+	0.0675560i
$755$	−31.5555	−	31.5555i	−1.14842	−	1.14842i
$756$		0			0
$757$	−11.9616	+	11.9616i	−0.434752	+	0.434752i	−0.890241	−	0.455489i	$-0.849464\pi$
$757$	−11.9616	+	11.9616i	−0.434752	+	0.434752i	0.455489	+	0.890241i	$0.349464\pi$
$758$	20.1261	−	3.83722i	0.731012	−	0.139374i
$759$		−	4.01338i		−	0.145676i
$760$	0.405544	−	1.81181i	0.0147106	−	0.0657211i
$761$	29.4876			1.06892			0.534462	−	0.845193i	$-0.320514\pi$
$761$	29.4876			1.06892			0.534462	+	0.845193i	$0.320514\pi$
$762$	−4.39276	−	23.0399i	−0.159133	−	0.834646i
$763$		0			0
$764$	−9.99138	+	3.95361i	−0.361475	+	0.143037i
$765$	28.6763	+	28.6763i	1.03679	+	1.03679i
$766$	5.09961	−	7.50227i	0.184256	−	0.271068i
$767$		−	0.868311i		−	0.0313529i
$768$	−11.0121	+	9.69315i	−0.397363	+	0.349771i
$769$		−	19.9592i		−	0.719746i	−0.933001	−	0.359873i	$-0.882820\pi$
$769$		−	19.9592i		−	0.719746i	0.933001	−	0.359873i	$-0.117180\pi$
$770$		0			0
$771$	−11.4369	+	11.4369i	−0.411890	+	0.411890i
$772$	0.0528787	+	0.133633i	0.00190315	+	0.00480955i
$773$	−6.70148	−	6.70148i	−0.241035	−	0.241035i	0.576243	−	0.817278i	$-0.304518\pi$
$773$	−6.70148	−	6.70148i	−0.241035	−	0.241035i	−0.817278	+	0.576243i	$0.804518\pi$
$774$	−5.91044	−	31.0001i	−0.212446	−	1.11427i
$775$		−	36.0773i		−	1.29594i
$776$	6.56825	−	29.3443i	0.235786	−	1.05340i
$777$		0			0
$778$	4.50459	+	23.6264i	0.161497	+	0.847048i
$779$	−1.41029	−	1.41029i	−0.0505290	−	0.0505290i
$780$	1.40287	−	3.24010i	0.0502307	−	0.116014i
$781$	12.0552	+	12.0552i	0.431371	+	0.431371i
$782$	24.5946	+	16.7180i	0.879501	+	0.597834i
$783$	−12.3280			−0.440569
$784$		0			0
$785$	46.2396			1.65036
$786$	−2.95298	−	2.00727i	−0.105329	−	0.0715968i
$787$	36.6649	+	36.6649i	1.30696	+	1.30696i	0.923596	+	0.383368i	$0.125236\pi$
$787$	36.6649	+	36.6649i	1.30696	+	1.30696i	0.383368	+	0.923596i	$0.374764\pi$
$788$	−6.75804	−	2.92603i	−0.240745	−	0.104236i
$789$	4.65610	+	4.65610i	0.165762	+	0.165762i
$790$	1.42764	+	7.48792i	0.0507931	+	0.266408i
$791$		0			0
$792$	6.37345	−	4.04210i	0.226471	−	0.143630i
$793$			0.809030i			0.0287295i
$794$	2.93084	+	15.3722i	0.104012	+	0.545538i
$795$	−10.5827	−	10.5827i	−0.375328	−	0.375328i
$796$	19.3664	−	7.66333i	0.686424	−	0.271620i
$797$	−17.7503	+	17.7503i	−0.628747	+	0.628747i	−0.947753	−	0.319006i	$-0.896651\pi$
$797$	−17.7503	+	17.7503i	−0.628747	+	0.628747i	0.319006	+	0.947753i	$0.396651\pi$
$798$		0			0
$799$		−	34.1518i		−	1.20820i
$800$	27.9844	−	4.41829i	0.989400	−	0.156210i
$801$		−	13.1921i		−	0.466120i
$802$	−12.0732	+	17.7614i	−0.426318	+	0.627176i
$803$	−1.96875	−	1.96875i	−0.0694758	−	0.0694758i
$804$	−5.51962	−	13.9489i	−0.194662	−	0.491941i
$805$		0			0
$806$	−1.16118	−	6.09035i	−0.0409008	−	0.214524i
$807$	−16.9402			−0.596325
$808$	1.93184	+	3.04606i	0.0679618	+	0.107160i
$809$		−	11.6172i		−	0.408441i	−0.978925	−	0.204220i	$-0.934534\pi$
$809$		−	11.6172i		−	0.408441i	0.978925	−	0.204220i	$-0.0654659\pi$
$810$	−9.40659	+	1.79345i	−0.330514	+	0.0630154i
$811$	21.2042	−	21.2042i	0.744579	−	0.744579i	−0.228877	−	0.973455i	$-0.573505\pi$
$811$	21.2042	−	21.2042i	0.744579	−	0.744579i	0.973455	+	0.228877i	$0.0735053\pi$
$812$		0			0
$813$	0.639052	+	0.639052i	0.0224125	+	0.0224125i
$814$	11.3878	−	16.7531i	0.399142	−	0.587196i
$815$	1.32067			0.0462609
$816$	0.692429	−	21.7626i	0.0242399	−	0.761845i
$817$		−	2.14434i		−	0.0750209i
$818$	−4.22210	+	6.21133i	−0.147622	+	0.217174i
$819$		0			0
$820$	24.1646	−	55.8112i	0.843865	−	1.94901i
$821$	19.2357	−	19.2357i	0.671330	−	0.671330i	−0.286692	−	0.958023i	$-0.592556\pi$
$821$	19.2357	−	19.2357i	0.671330	−	0.671330i	0.958023	+	0.286692i	$0.0925558\pi$
$822$	0.474398	+	2.48820i	0.0165465	+	0.0867860i
$823$	0.953410			0.0332338			0.0166169	−	0.999862i	$-0.494710\pi$
$823$	0.953410			0.0332338			0.0166169	+	0.999862i	$0.494710\pi$
$824$	−6.06806	+	27.1096i	−0.211391	+	0.944409i
$825$	5.67466			0.197566
$826$		0			0
$827$	0.699424	+	0.699424i	0.0243213	+	0.0243213i	0.719163	−	0.694842i	$-0.244526\pi$
$827$	0.699424	+	0.699424i	0.0243213	+	0.0243213i	−0.694842	+	0.719163i	$0.744526\pi$
$828$	−14.2236	+	5.62833i	−0.494306	+	0.195598i
$829$	29.0071	−	29.0071i	1.00746	−	1.00746i	0.00748452	−	0.999972i	$-0.497618\pi$
$829$	29.0071	−	29.0071i	1.00746	−	1.00746i	0.999972	−	0.00748452i	$-0.00238242\pi$
$830$	40.7243	+	27.6820i	1.41356	+	0.960858i
$831$	0.0801175			0.00277925
$832$	4.58196	−	1.64657i	0.158851	−	0.0570847i
$833$		0			0
$834$	−5.38399	+	7.92063i	−0.186432	+	0.274269i
$835$	7.09002	−	7.09002i	0.245360	−	0.245360i
$836$	0.476840	−	0.188687i	0.0164919	−	0.00652586i
$837$	24.0960	−	24.0960i	0.832878	−	0.832878i
$838$	15.1967	−	2.89740i	0.524963	−	0.100089i
$839$			5.46062i			0.188522i	0.995548	+	0.0942608i	$0.0300488\pi$
$839$			5.46062i			0.188522i	−0.995548	+	0.0942608i	$0.969951\pi$
$840$		0			0
$841$		−	22.2086i		−	0.765813i
$842$	1.79477	+	9.41353i	0.0618520	+	0.324412i
$843$	−9.04712	+	9.04712i	−0.311599	+	0.311599i
$844$	−5.97257	−	2.58595i	−0.205584	−	0.0890120i
$845$	28.2523	−	28.2523i	0.971910	−	0.971910i
$846$	14.5282	+	9.87540i	0.499488	+	0.339523i
$847$		0			0
$848$	0.656311	−	20.6275i	0.0225378	−	0.708351i
$849$	−12.1162			−0.415826
$850$	−23.6382	+	34.7752i	−0.810783	+	1.19278i
$851$	−29.0320	+	29.0320i	−0.995204	+	0.995204i
$852$	−10.0523	+	23.2171i	−0.344386	+	0.795403i
$853$	−35.1393	−	35.1393i	−1.20315	−	1.20315i	−0.973204	−	0.229943i	$-0.926146\pi$
$853$	−35.1393	−	35.1393i	−1.20315	−	1.20315i	−0.229943	−	0.973204i	$-0.573854\pi$
$854$		0			0
$855$	−1.41740			−0.0484741
$856$	−15.7404	−	24.8189i	−0.537995	−	0.848294i
$857$	−44.9561			−1.53567			−0.767836	−	0.640647i	$-0.778666\pi$
$857$	−44.9561			−1.53567			−0.767836	+	0.640647i	$0.778666\pi$
$858$	0.957962	−	0.182644i	0.0327043	−	0.00623536i
$859$	16.2542	−	16.2542i	0.554585	−	0.554585i	−0.373176	−	0.927761i	$-0.621731\pi$
$859$	16.2542	−	16.2542i	0.554585	−	0.554585i	0.927761	+	0.373176i	$0.121731\pi$
$860$	60.8012	−	24.0592i	2.07330	−	0.820411i
$861$		0			0
$862$	2.97862	+	2.02469i	0.101452	+	0.0689614i
$863$			32.6721i			1.11217i	0.831125	+	0.556085i	$0.187697\pi$
$863$			32.6721i			1.11217i	−0.831125	+	0.556085i	$0.812303\pi$
$864$	21.6417	+	15.7398i	0.736267	+	0.535479i
$865$	72.3437			2.45976
$866$	−22.2678	−	15.1364i	−0.756691	−	0.514354i
$867$	11.8290	+	11.8290i	0.401734	+	0.401734i
$868$		0			0
$869$	−1.48879	+	1.48879i	−0.0505036	+	0.0505036i
$870$	−2.00218	−	10.5014i	−0.0678803	−	0.356030i
$871$			4.97863i			0.168695i
$872$	0.0614997	+	0.0969708i	0.00208264	+	0.00328385i
$873$	−22.9564			−0.776957
$874$	−1.02099	+	0.194662i	−0.0345356	+	0.00658452i
$875$		0			0
$876$	1.64165	−	3.79160i	0.0554663	−	0.128106i
$877$	−12.7382	−	12.7382i	−0.430139	−	0.430139i	0.458537	−	0.888675i	$-0.348374\pi$
$877$	−12.7382	−	12.7382i	−0.430139	−	0.430139i	−0.888675	+	0.458537i	$0.848374\pi$
$878$	20.5714	+	13.9832i	0.694250	+	0.471911i
$879$			1.45160i			0.0489612i
$880$	10.7002	+	11.4034i	0.360702	+	0.384409i
$881$		−	21.0017i		−	0.707564i	−0.935328	−	0.353782i	$-0.884895\pi$
$881$		−	21.0017i		−	0.707564i	0.935328	−	0.353782i	$-0.115105\pi$
$882$		0			0
$883$	−29.0326	+	29.0326i	−0.977024	+	0.977024i	−0.999742	−	0.0227184i	$-0.992768\pi$
$883$	−29.0326	+	29.0326i	−0.977024	+	0.977024i	0.0227184	+	0.999742i	$0.492768\pi$
$884$	−2.87118	+	6.63136i	−0.0965683	+	0.223037i
$885$	2.92637	+	2.92637i	0.0983688	+	0.0983688i
$886$	−37.5530	+	7.15982i	−1.26162	+	0.240539i
$887$			38.2378i			1.28390i	0.766747	+	0.641949i	$0.221874\pi$
$887$			38.2378i			1.28390i	−0.766747	+	0.641949i	$0.778126\pi$
$888$	29.3350	+	6.56619i	0.984420	+	0.220347i
$889$		0			0
$890$	26.8500	−	5.11920i	0.900015	−	0.171596i
$891$	−1.87027	−	1.87027i	−0.0626563	−	0.0626563i
$892$	16.1271	+	40.7558i	0.539977	+	1.36460i
$893$	0.844022	+	0.844022i	0.0282441	+	0.0282441i
$894$	5.56385	−	8.18523i	0.186083	−	0.273755i
$895$	−43.5153			−1.45456
$896$		0			0
$897$	−1.97659			−0.0659966
$898$	3.65947	−	5.38361i	0.122118	−	0.179653i
$899$	−13.2743	−	13.2743i	−0.442723	−	0.442723i
$900$	−7.95809	−	20.1113i	−0.265270	−	0.670378i
$901$	21.6590	+	21.6590i	0.721566	+	0.721566i
$902$	16.5010	−	3.14607i	0.549424	−	0.104753i
$903$		0			0
$904$	−30.5761	−	6.84398i	−1.01695	−	0.227627i
$905$			22.4303i			0.745608i
$906$	17.9678	−	3.42573i	0.596941	−	0.113812i
$907$	−37.7115	−	37.7115i	−1.25219	−	1.25219i	−0.954736	−	0.297455i	$-0.903862\pi$
$907$	−37.7115	−	37.7115i	−1.25219	−	1.25219i	−0.297455	−	0.954736i	$-0.596138\pi$
$908$	−9.20795	+	21.2669i	−0.305576	+	0.705767i
$909$	1.94714	−	1.94714i	0.0645826	−	0.0645826i
$910$		0			0
$911$		−	20.1673i		−	0.668171i	−0.942543	−	0.334086i	$-0.891573\pi$
$911$		−	20.1673i		−	0.668171i	0.942543	−	0.334086i	$-0.108427\pi$
$912$	0.520726	+	0.554951i	0.0172430	+	0.0183763i
$913$			13.6009i			0.450124i
$914$	30.1528	+	20.4962i	0.997367	+	0.677953i
$915$	−2.72658	−	2.72658i	−0.0901380	−	0.0901380i
$916$	−17.2683	+	39.8833i	−0.570560	+	1.31778i
$917$		0			0
$918$	−39.0142	+	7.43841i	−1.28766	+	0.245504i
$919$	−13.3938			−0.441821			−0.220911	−	0.975294i	$-0.570903\pi$
$919$	−13.3938			−0.441821			−0.220911	+	0.975294i	$0.570903\pi$
$920$	−16.9749	−	26.7655i	−0.559646	−	0.882432i
$921$		−	20.5652i		−	0.677646i
$922$	−1.65068	−	8.65776i	−0.0543622	−	0.285128i
$923$	5.93723	−	5.93723i	0.195426	−	0.195426i
$924$		0			0
$925$	−41.0494	−	41.0494i	−1.34970	−	1.34970i
$926$	−36.3012	−	24.6755i	−1.19293	−	0.810886i
$927$	21.2082			0.696570
$928$	8.67094	−	11.9223i	0.284638	−	0.391368i
$929$		−	40.1376i		−	1.31687i	−0.752637	−	0.658436i	$-0.771218\pi$
$929$		−	40.1376i		−	1.31687i	0.752637	−	0.658436i	$-0.228782\pi$
$930$	24.4390	+	16.6122i	0.801386	+	0.544736i
$931$		0			0
$932$	−23.2396	+	9.19597i	−0.761239	+	0.301224i
$933$	18.5059	−	18.5059i	0.605857	−	0.605857i
$934$	50.6161	−	9.65042i	1.65621	−	0.315771i
$935$	−23.2089			−0.759013
$936$	−1.99074	−	3.13893i	−0.0650693	−	0.102599i
$937$	3.61135			0.117978			0.0589888	−	0.998259i	$-0.481212\pi$
$937$	3.61135			0.117978			0.0589888	+	0.998259i	$0.481212\pi$
$938$		0			0
$939$	0.0404090	+	0.0404090i	0.00131870	+	0.00131870i
$940$	−14.4619	+	33.4015i	−0.471694	+	1.08944i
$941$	10.0219	−	10.0219i	0.326706	−	0.326706i	−0.524627	−	0.851332i	$-0.675795\pi$
$941$	10.0219	−	10.0219i	0.326706	−	0.326706i	0.851332	+	0.524627i	$0.175795\pi$
$942$	−10.6546	+	15.6745i	−0.347145	+	0.510701i
$943$	−34.0471			−1.10873
$944$	−0.181487	+	5.70401i	−0.00590688	+	0.185650i
$945$		0			0
$946$	14.9366	+	10.1530i	0.485631	+	0.330104i
$947$	31.3429	−	31.3429i	1.01851	−	1.01851i	0.0186811	−	0.999825i	$-0.494053\pi$
$947$	31.3429	−	31.3429i	1.01851	−	1.01851i	0.999825	−	0.0186811i	$-0.00594672\pi$
$948$	−2.86724	−	1.24143i	−0.0931235	−	0.0403197i
$949$	−0.969614	+	0.969614i	−0.0314750	+	0.0314750i
$950$	−0.275239	−	1.44362i	−0.00892993	−	0.0468372i
$951$			20.8115i			0.674858i
$952$		0			0
$953$			54.7099i			1.77223i	0.463467	+	0.886114i	$0.346605\pi$
$953$			54.7099i			1.77223i	−0.463467	+	0.886114i	$0.653395\pi$
$954$	−15.4767	+	2.95077i	−0.501076	+	0.0955347i
$955$	−12.0184	+	12.0184i	−0.388908	+	0.388908i
$956$	−14.3378	+	5.67351i	−0.463719	+	0.183495i
$957$	2.08794	−	2.08794i	0.0674934	−	0.0674934i
$958$	−7.58290	+	11.1556i	−0.244992	+	0.360420i
$959$		0			0
$960$	−9.89278	+	20.9913i	−0.319288	+	0.677491i
$961$	20.8909			0.673901
$962$	−8.25093	−	5.60850i	−0.266021	−	0.180825i
$963$	−15.8651	+	15.8651i	−0.511244	+	0.511244i
$964$	20.4117	−	8.07694i	0.657416	−	0.260141i
$965$	0.160744	+	0.160744i	0.00517454	+	0.00517454i
$966$		0			0
$967$	−57.5321			−1.85011			−0.925054	−	0.379836i	$-0.875980\pi$
$967$	−57.5321			−1.85011			−0.925054	+	0.379836i	$0.875980\pi$
$968$	5.85249	−	26.1465i	0.188106	−	0.840382i
$969$	−1.12947			−0.0362838
$970$	−8.90825	−	46.7235i	−0.286027	−	1.50020i
$971$	−11.5737	+	11.5737i	−0.371418	+	0.371418i	−0.867994	−	0.496575i	$-0.834591\pi$
$971$	−11.5737	+	11.5737i	−0.371418	+	0.371418i	0.496575	+	0.867994i	$0.334591\pi$
$972$	12.8370	−	29.6487i	0.411748	−	0.950984i
$973$		0			0
$974$	−2.21878	+	3.26415i	−0.0710944	+	0.104590i
$975$		−	2.79478i		−	0.0895045i
$976$	0.169096	−	5.31459i	0.00541264	−	0.170116i
$977$	34.7260			1.11098			0.555491	−	0.831522i	$-0.312530\pi$
$977$	34.7260			1.11098			0.555491	+	0.831522i	$0.312530\pi$
$978$	−0.304310	+	0.447684i	−0.00973075	+	0.0143154i
$979$	5.33846	+	5.33846i	0.170618	+	0.170618i
$980$		0			0
$981$	0.0619868	−	0.0619868i	0.00197909	−	0.00197909i
$982$	29.2893	−	5.58427i	0.934659	−	0.178201i
$983$			21.1127i			0.673390i	0.941614	+	0.336695i	$0.109309\pi$
$983$			21.1127i			0.673390i	−0.941614	+	0.336695i	$0.890691\pi$
$984$	13.3510	+	21.0515i	0.425615	+	0.671097i
$985$	−11.6488			−0.371161
$986$	4.09777	+	21.4926i	0.130499	+	0.684465i
$987$		0			0
$988$	−0.0929284	−	0.234844i	−0.00295645	−	0.00747139i
$989$	−25.8842	−	25.8842i	−0.823068	−	0.823068i
$990$	6.71113	−	9.87306i	0.213294	−	0.313786i
$991$			36.3796i			1.15563i	0.816166	+	0.577817i	$0.196095\pi$
$991$			36.3796i			1.15563i	−0.816166	+	0.577817i	$0.803905\pi$
$992$	6.35495	+	40.2508i	0.201770	+	1.27796i
$993$			14.7364i			0.467644i
$994$		0			0
$995$	23.2955	−	23.2955i	0.738516	−	0.738516i
$996$	−18.7675	+	7.42634i	−0.594671	+	0.235313i
$997$	−35.1855	−	35.1855i	−1.11434	−	1.11434i	−0.992557	−	0.121778i	$-0.961140\pi$
$997$	−35.1855	−	35.1855i	−1.11434	−	1.11434i	−0.121778	−	0.992557i	$-0.538860\pi$
$998$	−3.74688	−	19.6523i	−0.118605	−	0.622081i
$999$		−	54.8337i		−	1.73486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.195.9		56
7.2	even	3		784.2.w.f.227.14		56
7.3	odd	6		784.2.w.f.19.4		56
7.4	even	3		112.2.v.a.19.4	yes	56
7.5	odd	6		112.2.v.a.3.14	✓	56
7.6	odd	2	inner	784.2.j.a.195.10		56
16.11	odd	4	inner	784.2.j.a.587.10		56
28.11	odd	6		448.2.z.a.47.9		56
28.19	even	6		448.2.z.a.367.9		56
56.5	odd	6		896.2.z.b.479.9		56
56.11	odd	6		896.2.z.a.607.6		56
56.19	even	6		896.2.z.a.479.6		56
56.53	even	6		896.2.z.b.607.9		56
112.5	odd	12		448.2.z.a.143.9		56
112.11	odd	12		112.2.v.a.75.14	yes	56
112.19	even	12		896.2.z.b.31.9		56
112.27	even	4	inner	784.2.j.a.587.9		56
112.53	even	12		448.2.z.a.271.9		56
112.59	even	12		784.2.w.f.411.14		56
112.61	odd	12		896.2.z.a.31.6		56
112.67	odd	12		896.2.z.b.159.9		56
112.75	even	12		112.2.v.a.59.4	yes	56
112.107	odd	12		784.2.w.f.619.4		56
112.109	even	12		896.2.z.a.159.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.14	✓	56	7.5	odd	6
112.2.v.a.19.4	yes	56	7.4	even	3
112.2.v.a.59.4	yes	56	112.75	even	12
112.2.v.a.75.14	yes	56	112.11	odd	12
448.2.z.a.47.9		56	28.11	odd	6
448.2.z.a.143.9		56	112.5	odd	12
448.2.z.a.271.9		56	112.53	even	12
448.2.z.a.367.9		56	28.19	even	6
784.2.j.a.195.9		56	1.1	even	1	trivial
784.2.j.a.195.10		56	7.6	odd	2	inner
784.2.j.a.587.9		56	112.27	even	4	inner
784.2.j.a.587.10		56	16.11	odd	4	inner
784.2.w.f.19.4		56	7.3	odd	6
784.2.w.f.227.14		56	7.2	even	3
784.2.w.f.411.14		56	112.59	even	12
784.2.w.f.619.4		56	112.107	odd	12
896.2.z.a.31.6		56	112.61	odd	12
896.2.z.a.159.6		56	112.109	even	12
896.2.z.a.479.6		56	56.19	even	6
896.2.z.a.607.6		56	56.11	odd	6
896.2.z.b.31.9		56	112.19	even	12
896.2.z.b.159.9		56	112.67	odd	12
896.2.z.b.479.9		56	56.5	odd	6
896.2.z.b.607.9		56	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.795020 + 1.16959i) q^{2} +(-0.648349 - 0.648349i) q^{3} +(-0.735886 - 1.85970i) q^{4} +(-2.23699 - 2.23699i) q^{5} +(1.27375 - 0.242853i) q^{6} +(2.76013 + 0.617811i) q^{8} -2.15929i q^{9} +(4.39482 - 0.837912i) q^{10} +(0.873801 + 0.873801i) q^{11} +(-0.728622 + 1.68284i) q^{12} +(0.430348 - 0.430348i) q^{13} +2.90070i q^{15} +(-2.91694 + 2.73705i) q^{16} -5.93673i q^{17} +(2.52548 + 1.71668i) q^{18} +(0.146719 + 0.146719i) q^{19} +(-2.51396 + 5.80630i) q^{20} +(-1.71668 + 0.327300i) q^{22} +3.54208 q^{23} +(-1.38897 - 2.19008i) q^{24} +5.00828i q^{25} +(0.161196 + 0.845467i) q^{26} +(-3.34502 + 3.34502i) q^{27} +(1.84275 + 1.84275i) q^{29} +(-3.39264 - 2.30612i) q^{30} -7.20354 q^{31} +(-0.882198 - 5.58764i) q^{32} -1.13306i q^{33} +(6.94355 + 4.71982i) q^{34} +(-4.01562 + 1.58899i) q^{36} +(-8.19631 + 8.19631i) q^{37} +(-0.288247 + 0.0549568i) q^{38} -0.558032 q^{39} +(-4.79235 - 7.55643i) q^{40} -9.61218 q^{41} +(-7.30761 - 7.30761i) q^{43} +(0.981987 - 2.26802i) q^{44} +(-4.83031 + 4.83031i) q^{45} +(-2.81603 + 4.14279i) q^{46} +5.75263 q^{47} +(3.66576 + 0.116635i) q^{48} +(-5.85763 - 3.98168i) q^{50} +(-3.84907 + 3.84907i) q^{51} +(-1.11700 - 0.483630i) q^{52} +(-3.64830 + 3.64830i) q^{53} +(-1.25295 - 6.57166i) q^{54} -3.90937i q^{55} -0.190251i q^{57} +(-3.62028 + 0.690239i) q^{58} +(1.00885 - 1.00885i) q^{59} +(5.39443 - 2.13459i) q^{60} +(-0.939971 + 0.939971i) q^{61} +(5.72696 - 8.42519i) q^{62} +(7.23662 + 3.41048i) q^{64} -1.92537 q^{65} +(1.32521 + 0.900803i) q^{66} +(-5.78442 + 5.78442i) q^{67} +(-11.0405 + 4.36876i) q^{68} +(-2.29651 - 2.29651i) q^{69} +13.7963 q^{71} +(1.33403 - 5.95991i) q^{72} -2.25309 q^{73} +(-3.07010 - 16.1026i) q^{74} +(3.24711 - 3.24711i) q^{75} +(0.164885 - 0.380823i) q^{76} +(0.443647 - 0.652669i) q^{78} +1.70380i q^{79} +(12.6479 + 0.402424i) q^{80} -2.14038 q^{81} +(7.64188 - 11.2423i) q^{82} +(7.78261 + 7.78261i) q^{83} +(-13.2804 + 13.2804i) q^{85} +(14.3566 - 2.73722i) q^{86} -2.38949i q^{87} +(1.87196 + 2.95165i) q^{88} +6.10947 q^{89} +(-1.80929 - 9.48968i) q^{90} +(-2.60657 - 6.58720i) q^{92} +(4.67041 + 4.67041i) q^{93} +(-4.57345 + 6.72822i) q^{94} -0.656421i q^{95} +(-3.05077 + 4.19471i) q^{96} -10.6315i q^{97} +(1.88679 - 1.88679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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