LMFDB - Embedded newform 280.2.n.b.139.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [280,2,Mod(139,280)] 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("280.139"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.n (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.34
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20452 - 0.741038i) q^{2} +2.57969 q^{3} +(0.901725 - 1.78519i) q^{4} +(-0.460102 + 2.18822i) q^{5} +(3.10728 - 1.91165i) q^{6} +(-2.31487 - 1.28116i) q^{7} +(-0.236748 - 2.81850i) q^{8} +3.65479 q^{9} +(1.06735 + 2.97670i) q^{10} -3.59890 q^{11} +(2.32617 - 4.60522i) q^{12} +1.33525i q^{13} +(-3.73769 + 0.172236i) q^{14} +(-1.18692 + 5.64492i) q^{15} +(-2.37378 - 3.21949i) q^{16} +2.88506 q^{17} +(4.40225 - 2.70834i) q^{18} +5.38901i q^{19} +(3.49150 + 2.79454i) q^{20} +(-5.97165 - 3.30498i) q^{21} +(-4.33494 + 2.66693i) q^{22} +4.45993 q^{23} +(-0.610736 - 7.27085i) q^{24} +(-4.57661 - 2.01361i) q^{25} +(0.989473 + 1.60834i) q^{26} +1.68914 q^{27} +(-4.37448 + 2.97723i) q^{28} +1.88494i q^{29} +(2.75344 + 7.67896i) q^{30} -7.70769 q^{31} +(-5.24503 - 2.11887i) q^{32} -9.28405 q^{33} +(3.47511 - 2.13794i) q^{34} +(3.86853 - 4.47599i) q^{35} +(3.29561 - 6.52448i) q^{36} +4.64826 q^{37} +(3.99346 + 6.49116i) q^{38} +3.44453i q^{39} +(6.27643 + 0.778741i) q^{40} -0.606622i q^{41} +(-9.64207 + 0.444314i) q^{42} -12.1167i q^{43} +(-3.24522 + 6.42472i) q^{44} +(-1.68157 + 7.99747i) q^{45} +(5.37207 - 3.30498i) q^{46} -6.92126i q^{47} +(-6.12362 - 8.30529i) q^{48} +(3.71728 + 5.93143i) q^{49} +(-7.00477 + 0.966017i) q^{50} +7.44256 q^{51} +(2.38368 + 1.20403i) q^{52} +6.31531 q^{53} +(2.03460 - 1.25172i) q^{54} +(1.65586 - 7.87519i) q^{55} +(-3.06290 + 6.82779i) q^{56} +13.9020i q^{57} +(1.39682 + 2.27045i) q^{58} +1.39031i q^{59} +(9.00697 + 7.20904i) q^{60} +3.80122 q^{61} +(-9.28405 + 5.71169i) q^{62} +(-8.46037 - 4.68235i) q^{63} +(-7.88790 + 1.33455i) q^{64} +(-2.92183 - 0.614353i) q^{65} +(-11.1828 + 6.87983i) q^{66} +13.6816i q^{67} +(2.60153 - 5.15038i) q^{68} +11.5052 q^{69} +(1.34283 - 8.25814i) q^{70} -8.19810i q^{71} +(-0.865264 - 10.3010i) q^{72} -11.4433 q^{73} +(5.59890 - 3.44453i) q^{74} +(-11.8062 - 5.19448i) q^{75} +(9.62040 + 4.85941i) q^{76} +(8.33101 + 4.61076i) q^{77} +(2.55253 + 4.14900i) q^{78} -10.3062i q^{79} +(8.13715 - 3.71307i) q^{80} -6.60690 q^{81} +(-0.449530 - 0.730687i) q^{82} +13.5735 q^{83} +(-11.2848 + 7.68033i) q^{84} +(-1.32742 + 6.31315i) q^{85} +(-8.97897 - 14.5948i) q^{86} +4.86257i q^{87} +(0.852034 + 10.1435i) q^{88} +7.04915i q^{89} +(3.90095 + 10.8792i) q^{90} +(1.71067 - 3.09094i) q^{91} +(4.02163 - 7.96181i) q^{92} -19.8834 q^{93} +(-5.12891 - 8.33677i) q^{94} +(-11.7923 - 2.47950i) q^{95} +(-13.5305 - 5.46603i) q^{96} +6.26335 q^{97} +(8.87294 + 4.38986i) q^{98} -13.1532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65}+ \cdots - 128 q^{99}+O(q^{100}) $ 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.20452	−	0.741038i	0.851723	−	0.523993i
$2$	1.20452	−	0.741038i	0.851723	−	0.523993i
$3$	2.57969			1.48938			0.744692	−	0.667409i	$-0.232597\pi$
$3$	2.57969			1.48938			0.744692	+	0.667409i	$0.232597\pi$
$4$	0.901725	−	1.78519i	0.450862	−	0.892593i
$5$	−0.460102	+	2.18822i	−0.205764	+	0.978602i
$5$	−0.460102	+	2.18822i	−0.205764	+	0.978602i
$6$	3.10728	−	1.91165i	1.26854	−	0.780426i
$7$	−2.31487	−	1.28116i	−0.874940	−	0.484231i
$7$	−2.31487	−	1.28116i	−0.874940	−	0.484231i
$8$	−0.236748	−	2.81850i	−0.0837031	−	0.996491i
$9$	3.65479			1.21826
$10$	1.06735	+	2.97670i	0.337527	+	0.941316i
$11$	−3.59890			−1.08511			−0.542555	−	0.840020i	$-0.682543\pi$
$11$	−3.59890			−1.08511			−0.542555	+	0.840020i	$0.682543\pi$
$12$	2.32617	−	4.60522i	0.671507	−	1.32941i
$13$			1.33525i			0.370332i	0.982707	+	0.185166i	$0.0592824\pi$
$13$			1.33525i			0.370332i	−0.982707	+	0.185166i	$0.940718\pi$
$14$	−3.73769	+	0.172236i	−0.998940	+	0.0460319i
$15$	−1.18692	+	5.64492i	−0.306461	+	1.45751i
$16$	−2.37378	−	3.21949i	−0.593446	−	0.804874i
$17$	2.88506			0.699730			0.349865	−	0.936800i	$-0.386227\pi$
$17$	2.88506			0.699730			0.349865	+	0.936800i	$0.386227\pi$
$18$	4.40225	−	2.70834i	1.03762	−	0.638361i
$19$			5.38901i			1.23632i	0.786051	+	0.618162i	$0.212123\pi$
$19$			5.38901i			1.23632i	−0.786051	+	0.618162i	$0.787877\pi$
$20$	3.49150	+	2.79454i	0.780722	+	0.624878i
$21$	−5.97165	−	3.30498i	−1.30312	−	0.721206i
$22$	−4.33494	+	2.66693i	−0.924213	+	0.568590i
$23$	4.45993			0.929960			0.464980	−	0.885321i	$-0.346061\pi$
$23$	4.45993			0.929960			0.464980	+	0.885321i	$0.346061\pi$
$24$	−0.610736	−	7.27085i	−0.124666	−	1.48416i
$25$	−4.57661	−	2.01361i	−0.915322	−	0.402722i
$26$	0.989473	+	1.60834i	0.194052	+	0.315421i
$27$	1.68914			0.325075
$28$	−4.37448	+	2.97723i	−0.826699	+	0.562644i
$29$			1.88494i			0.350025i	0.984566	+	0.175013i	$0.0559967\pi$
$29$			1.88494i			0.350025i	−0.984566	+	0.175013i	$0.944003\pi$
$30$	2.75344	+	7.67896i	0.502707	+	1.40198i
$31$	−7.70769			−1.38434			−0.692171	−	0.721734i	$-0.743346\pi$
$31$	−7.70769			−1.38434			−0.692171	+	0.721734i	$0.743346\pi$
$32$	−5.24503	−	2.11887i	−0.927200	−	0.374567i
$33$	−9.28405			−1.61615
$34$	3.47511	−	2.13794i	0.595976	−	0.366654i
$35$	3.86853	−	4.47599i	0.653901	−	0.756580i
$36$	3.29561	−	6.52448i	0.549269	−	1.08741i
$37$	4.64826			0.764168			0.382084	−	0.924128i	$-0.375206\pi$
$37$	4.64826			0.764168			0.382084	+	0.924128i	$0.375206\pi$
$38$	3.99346	+	6.49116i	0.647825	+	1.05301i
$39$			3.44453i			0.551567i
$40$	6.27643	+	0.778741i	0.992391	+	0.123130i
$41$		−	0.606622i		−	0.0947385i	−0.998877	−	0.0473693i	$-0.984916\pi$
$41$		−	0.606622i		−	0.0947385i	0.998877	−	0.0473693i	$-0.0150837\pi$
$42$	−9.64207	+	0.444314i	−1.48780	+	0.0685591i
$43$		−	12.1167i		−	1.84779i	−0.382652	−	0.923893i	$-0.624989\pi$
$43$		−	12.1167i		−	1.84779i	0.382652	−	0.923893i	$-0.375011\pi$
$44$	−3.24522	+	6.42472i	−0.489236	+	0.968563i
$45$	−1.68157	+	7.99747i	−0.250674	+	1.19219i
$46$	5.37207	−	3.30498i	0.792068	−	0.487293i
$47$		−	6.92126i		−	1.00957i	−0.863245	−	0.504784i	$-0.831572\pi$
$47$		−	6.92126i		−	1.00957i	0.863245	−	0.504784i	$-0.168428\pi$
$48$	−6.12362	−	8.30529i	−0.883869	−	1.19877i
$49$	3.71728	+	5.93143i	0.531040	+	0.847347i
$50$	−7.00477	+	0.966017i	−0.990624	+	0.136615i
$51$	7.44256			1.04217
$52$	2.38368	+	1.20403i	0.330556	+	0.166969i
$53$	6.31531			0.867474			0.433737	−	0.901039i	$-0.357195\pi$
$53$	6.31531			0.867474			0.433737	+	0.901039i	$0.357195\pi$
$54$	2.03460	−	1.25172i	0.276874	−	0.170337i
$55$	1.65586	−	7.87519i	0.223277	−	1.06189i
$56$	−3.06290	+	6.82779i	−0.409297	+	0.912401i
$57$			13.9020i			1.84136i
$58$	1.39682	+	2.27045i	0.183411	+	0.298125i
$59$			1.39031i			0.181002i	0.995896	+	0.0905012i	$0.0288469\pi$
$59$			1.39031i			0.181002i	−0.995896	+	0.0905012i	$0.971153\pi$
$60$	9.00697	+	7.20904i	1.16279	+	0.930683i
$61$	3.80122			0.486696			0.243348	−	0.969939i	$-0.421754\pi$
$61$	3.80122			0.486696			0.243348	+	0.969939i	$0.421754\pi$
$62$	−9.28405	+	5.71169i	−1.17908	+	0.725386i
$63$	−8.46037	−	4.68235i	−1.06591	−	0.589920i
$64$	−7.88790	+	1.33455i	−0.985988	+	0.166819i
$65$	−2.92183	−	0.614353i	−0.362408	−	0.0762011i
$66$	−11.1828	+	6.87983i	−1.37651	+	0.846849i
$67$			13.6816i			1.67148i	0.549127	+	0.835739i	$0.314960\pi$
$67$			13.6816i			1.67148i	−0.549127	+	0.835739i	$0.685040\pi$
$68$	2.60153	−	5.15038i	0.315482	−	0.624575i
$69$	11.5052			1.38507
$70$	1.34283	−	8.25814i	0.160499	−	0.987036i
$71$		−	8.19810i		−	0.972935i	−0.873699	−	0.486467i	$-0.838285\pi$
$71$		−	8.19810i		−	0.972935i	0.873699	−	0.486467i	$-0.161715\pi$
$72$	−0.865264	−	10.3010i	−0.101972	−	1.21399i
$73$	−11.4433			−1.33934			−0.669671	−	0.742658i	$-0.733565\pi$
$73$	−11.4433			−1.33934			−0.669671	+	0.742658i	$0.733565\pi$
$74$	5.59890	−	3.44453i	0.650859	−	0.400419i
$75$	−11.8062	−	5.19448i	−1.36327	−	0.599807i
$76$	9.62040	+	4.85941i	1.10354	+	0.557412i
$77$	8.33101	+	4.61076i	0.949407	+	0.525444i
$78$	2.55253	+	4.14900i	0.289017	+	0.469782i
$79$		−	10.3062i		−	1.15954i	−0.814782	−	0.579768i	$-0.803143\pi$
$79$		−	10.3062i		−	1.15954i	0.814782	−	0.579768i	$-0.196857\pi$
$80$	8.13715	−	3.71307i	0.909761	−	0.415133i
$81$	−6.60690			−0.734100
$82$	−0.449530	−	0.730687i	−0.0496423	−	0.0806909i
$83$	13.5735			1.48989			0.744943	−	0.667129i	$-0.232477\pi$
$83$	13.5735			1.48989			0.744943	+	0.667129i	$0.232477\pi$
$84$	−11.2848	+	7.68033i	−1.23127	+	0.837993i
$85$	−1.32742	+	6.31315i	−0.143979	+	0.684757i
$86$	−8.97897	−	14.5948i	−0.968227	−	1.57380i
$87$			4.86257i			0.521322i
$88$	0.852034	+	10.1435i	0.0908271	+	1.08130i
$89$			7.04915i			0.747208i	0.927588	+	0.373604i	$0.121878\pi$
$89$			7.04915i			0.747208i	−0.927588	+	0.373604i	$0.878122\pi$
$90$	3.90095	+	10.8792i	0.411196	+	1.14677i
$91$	1.71067	−	3.09094i	0.179327	−	0.324019i
$92$	4.02163	−	7.96181i	0.419284	−	0.830076i
$93$	−19.8834			−2.06182
$94$	−5.12891	−	8.33677i	−0.529007	−	0.859873i
$95$	−11.7923	−	2.47950i	−1.20987	−	0.254391i
$96$	−13.5305	−	5.46603i	−1.38096	−	0.557874i
$97$	6.26335			0.635946			0.317973	−	0.948100i	$-0.396998\pi$
$97$	6.26335			0.635946			0.317973	+	0.948100i	$0.396998\pi$
$98$	8.87294	+	4.38986i	0.896303	+	0.443443i
$99$	−13.1532			−1.32195
$100$	−7.72151	+	6.35439i	−0.772151	+	0.635439i
$101$	4.83035			0.480638			0.240319	−	0.970694i	$-0.422748\pi$
$101$	4.83035			0.480638			0.240319	+	0.970694i	$0.422748\pi$
$102$	8.96469	−	5.51522i	0.887637	−	0.546088i
$103$			13.4501i			1.32528i	0.748938	+	0.662640i	$0.230564\pi$
$103$			13.4501i			1.32528i	−0.748938	+	0.662640i	$0.769436\pi$
$104$	3.76341	−	0.316119i	0.369033	−	0.0309980i
$105$	9.97959	−	11.5467i	0.973908	−	1.12684i
$106$	7.60690	−	4.67988i	0.738847	−	0.454551i
$107$		−	8.42571i		−	0.814544i	−0.913307	−	0.407272i	$-0.866480\pi$
$107$		−	8.42571i		−	0.814544i	0.913307	−	0.407272i	$-0.133520\pi$
$108$	1.52314	−	3.01543i	0.146564	−	0.290160i
$109$			12.1174i			1.16064i	0.814388	+	0.580320i	$0.197073\pi$
$109$			12.1174i			1.16064i	−0.814388	+	0.580320i	$0.802927\pi$
$110$	−3.84130	−	10.7129i	−0.366254	−	1.02143i
$111$	11.9910			1.13814
$112$	1.37034	+	10.4939i	0.129485	+	0.991581i
$113$			10.3315i			0.971907i	0.873985	+	0.485953i	$0.161528\pi$
$113$			10.3315i			0.971907i	−0.873985	+	0.485953i	$0.838472\pi$
$114$	10.3019	+	16.7452i	0.964860	+	1.56833i
$115$	−2.05202	+	9.75931i	−0.191352	+	0.910061i
$116$	3.36498	+	1.69970i	0.312430	+	0.157813i
$117$			4.88006i			0.451162i
$118$	1.03027	+	1.67465i	0.0948440	+	0.154164i
$119$	−6.67855	−	3.69621i	−0.612222	−	0.338831i
$120$	16.1912	+	2.00891i	1.47805	+	0.183387i
$121$	1.95211			0.177465
$122$	4.57863	−	2.81685i	0.414530	−	0.255025i
$123$		−	1.56490i		−	0.141102i
$124$	−6.95022	+	13.7597i	−0.624148	+	1.23565i
$125$	6.51193	−	9.08817i	0.582445	−	0.812870i
$126$	−13.6605	+	0.629484i	−1.21697	+	0.0560789i
$127$	9.65843			0.857047			0.428524	−	0.903531i	$-0.359034\pi$
$127$	9.65843			0.857047			0.428524	+	0.903531i	$0.359034\pi$
$128$	−8.51216	+	7.45272i	−0.752376	+	0.658734i
$129$		−	31.2574i		−	2.75206i
$130$	−3.97465	+	1.42519i	−0.348600	+	0.124997i
$131$		−	20.2931i		−	1.77302i	−0.462711	−	0.886509i	$-0.653123\pi$
$131$		−	20.2931i		−	1.77302i	0.462711	−	0.886509i	$-0.346877\pi$
$132$	−8.37166	+	16.5738i	−0.728659	+	1.44256i
$133$	6.90416	−	12.4749i	0.598667	−	1.08171i
$134$	10.1386	+	16.4798i	0.875843	+	1.42364i
$135$	−0.777178	+	3.69621i	−0.0668888	+	0.318119i
$136$	−0.683033	−	8.13155i	−0.0585696	−	0.697275i
$137$		−	12.2326i		−	1.04510i	−0.852608	−	0.522551i	$-0.824981\pi$
$137$		−	12.2326i		−	1.04510i	0.852608	−	0.522551i	$-0.175019\pi$
$138$	13.8583	−	8.52581i	1.17969	−	0.725766i
$139$			0.177061i			0.0150181i	0.999972	+	0.00750907i	$0.00239023\pi$
$139$			0.177061i			0.0150181i	−0.999972	+	0.00750907i	$0.997610\pi$
$140$	−4.50213	−	10.9422i	−0.380500	−	0.924781i
$141$		−	17.8547i		−	1.50363i
$142$	−6.07510	−	9.87475i	−0.509811	−	0.828671i
$143$		−	4.80545i		−	0.401852i
$144$	−8.67567	−	11.7666i	−0.722973	−	0.980547i
$145$	−4.12467	−	0.867267i	−0.342535	−	0.0720226i
$146$	−13.7837	+	8.47995i	−1.14075	+	0.701806i
$147$	9.58942	+	15.3012i	0.790922	+	1.26202i
$148$	4.19145	−	8.29800i	0.344535	−	0.682092i
$149$		−	0.279108i		−	0.0228654i	−0.999935	−	0.0114327i	$-0.996361\pi$
$149$		−	0.279108i		−	0.0228654i	0.999935	−	0.0114327i	$-0.00363923\pi$
$150$	−18.0701	+	2.49202i	−1.47542	+	0.203473i
$151$			4.75356i			0.386839i	0.981116	+	0.193420i	$0.0619579\pi$
$151$			4.75356i			0.386839i	−0.981116	+	0.193420i	$0.938042\pi$
$152$	15.1889	−	1.27584i	1.23199	−	0.103484i
$153$	10.5443			0.852455
$154$	13.4516	−	0.619860i	1.08396	−	0.0499497i
$155$	3.54632	−	16.8661i	0.284848	−	1.35472i
$156$	6.14914	+	3.10602i	0.492325	+	0.248681i
$157$		−	2.97219i		−	0.237206i	−0.992942	−	0.118603i	$-0.962158\pi$
$157$		−	2.97219i		−	0.237206i	0.992942	−	0.118603i	$-0.0378416\pi$
$158$	−7.63727	−	12.4140i	−0.607588	−	0.987602i
$159$	16.2915			1.29200
$160$	7.04981	−	10.5024i	0.557337	−	0.830287i
$161$	−10.3242	−	5.71387i	−0.813659	−	0.450316i
$162$	−7.95813	+	4.89596i	−0.625249	+	0.384663i
$163$			8.42571i			0.659953i	0.943989	+	0.329976i	$0.107041\pi$
$163$			8.42571i			0.659953i	−0.943989	+	0.329976i	$0.892959\pi$
$164$	−1.08293	−	0.547007i	−0.0845630	−	0.0427140i
$165$	4.27161	−	20.3155i	0.332544	−	1.58156i
$166$	16.3495	−	10.0585i	1.26897	−	0.780690i
$167$		−	13.4501i		−	1.04080i	−0.853922	−	0.520401i	$-0.825782\pi$
$167$		−	13.4501i		−	1.04080i	0.853922	−	0.520401i	$-0.174218\pi$
$168$	−7.90131	+	17.6136i	−0.609600	+	1.35892i
$169$	11.2171			0.862854
$170$	3.07938	+	8.58797i	0.236178	+	0.658667i
$171$			19.6957i			1.50617i
$172$	−21.6306	−	10.9260i	−1.64932	−	0.833097i
$173$			10.5918i			0.805276i	0.915359	+	0.402638i	$0.131907\pi$
$173$			10.5918i			0.805276i	−0.915359	+	0.402638i	$0.868093\pi$
$174$	3.60335	+	5.85705i	0.273169	+	0.444022i
$175$	8.01453	+	10.5246i	0.605842	+	0.795585i
$176$	8.54302	+	11.5867i	0.643955	+	0.873377i
$177$			3.58655i			0.269582i
$178$	5.22369	+	8.49083i	0.391532	+	0.636414i
$179$	−1.93943			−0.144959			−0.0724797	−	0.997370i	$-0.523091\pi$
$179$	−1.93943			−0.144959			−0.0724797	+	0.997370i	$0.523091\pi$
$180$	12.7607	+	10.2134i	0.951124	+	0.761265i
$181$	−11.9947			−0.891561			−0.445780	−	0.895142i	$-0.647074\pi$
$181$	−11.9947			−0.891561			−0.445780	+	0.895142i	$0.647074\pi$
$182$	−0.229978	−	4.99076i	−0.0170471	−	0.369940i
$183$	9.80596			0.724877
$184$	−1.05588	−	12.5703i	−0.0778406	−	0.926697i
$185$	−2.13867	+	10.1714i	−0.157238	+	0.747816i
$186$	−23.9499	+	14.7344i	−1.75609	+	1.08038i
$187$	−10.3831			−0.759285
$188$	−12.3557	−	6.24107i	−0.901135	−	0.455177i
$189$	−3.91015	−	2.16405i	−0.284422	−	0.157412i
$190$	−16.0415	+	5.75198i	−1.16377	+	0.417293i
$191$			10.3062i			0.745729i	0.927886	+	0.372864i	$0.121624\pi$
$191$			10.3062i			0.745729i	−0.927886	+	0.372864i	$0.878376\pi$
$192$	−20.3483	+	3.44272i	−1.46851	+	0.248457i
$193$		−	7.97366i		−	0.573957i	−0.957937	−	0.286978i	$-0.907349\pi$
$193$		−	7.97366i		−	0.573957i	0.957937	−	0.286978i	$-0.0926508\pi$
$194$	7.54431	−	4.64138i	0.541650	−	0.333232i
$195$	−7.53740	−	1.58484i	−0.539764	−	0.113493i
$196$	13.9407	−	1.28753i	0.995762	−	0.0919662i
$197$	−9.16007			−0.652628			−0.326314	−	0.945261i	$-0.605807\pi$
$197$	−9.16007			−0.652628			−0.326314	+	0.945261i	$0.605807\pi$
$198$	−15.8433	+	9.74704i	−1.12593	+	0.692692i
$199$	−18.1246			−1.28482			−0.642408	−	0.766362i	$-0.722065\pi$
$199$	−18.1246			−1.28482			−0.642408	+	0.766362i	$0.722065\pi$
$200$	−4.59186	+	13.3759i	−0.324693	+	0.945819i
$201$			35.2943i			2.48947i
$202$	5.81825	−	3.57948i	0.409370	−	0.251851i
$203$	2.41491	−	4.36341i	0.169493	−	0.306251i
$204$	6.71114	−	13.2864i	0.469874	−	0.930231i
$205$	1.32742	+	0.279108i	0.0927113	+	0.0194938i
$206$	9.96706	+	16.2009i	0.694438	+	1.12877i
$207$	16.3001			1.13294
$208$	4.29884	−	3.16960i	0.298071	−	0.219772i
$209$		−	19.3945i		−	1.34155i
$210$	3.46408	−	21.3034i	0.239044	−	1.47007i
$211$	9.48714			0.653122			0.326561	−	0.945176i	$-0.394110\pi$
$211$	9.48714			0.653122			0.326561	+	0.945176i	$0.394110\pi$
$212$	5.69467	−	11.2740i	0.391112	−	0.774302i
$213$		−	21.1485i		−	1.44907i
$214$	−6.24377	−	10.1489i	−0.426816	−	0.693766i
$215$	26.5141	+	5.57494i	1.80825	+	0.380208i
$216$	−0.399901	−	4.76085i	−0.0272098	−	0.323935i
$217$	17.8423	+	9.87475i	1.21122	+	0.670342i
$218$	8.97949	+	14.5957i	0.608168	+	0.988544i
$219$	−29.5202			−1.99479
$220$	−12.5656	−	10.0573i	−0.847170	−	0.678062i
$221$			3.85229i			0.259133i
$222$	14.4434	−	8.88582i	0.969379	−	0.596377i
$223$			28.0127i			1.87587i	0.346816	+	0.937933i	$0.387263\pi$
$223$			28.0127i			1.87587i	−0.346816	+	0.937933i	$0.612737\pi$
$224$	9.42698	+	11.6246i	0.629867	+	0.776703i
$225$	−16.7265	−	7.35931i	−1.11510	−	0.490621i
$226$	7.65604	+	12.4445i	0.509272	+	0.827795i
$227$	1.85392			0.123049			0.0615245	−	0.998106i	$-0.480404\pi$
$227$	1.85392			0.123049			0.0615245	+	0.998106i	$0.480404\pi$
$228$	24.8176	+	12.5358i	1.64359	+	0.830200i
$229$	−20.2457			−1.33788			−0.668938	−	0.743318i	$-0.733251\pi$
$229$	−20.2457			−1.33788			−0.668938	+	0.743318i	$0.733251\pi$
$230$	4.76032	+	13.2759i	0.313886	+	0.875386i
$231$	21.4914	+	11.8943i	1.41403	+	0.782588i
$232$	5.31272	−	0.446257i	0.348797	−	0.0292982i
$233$		−	2.35785i		−	0.154468i	−0.997013	−	0.0772339i	$-0.975391\pi$
$233$		−	2.35785i		−	0.154468i	0.997013	−	0.0772339i	$-0.0246088\pi$
$234$	3.61631	+	5.87812i	0.236406	+	0.384265i
$235$	15.1452	+	3.18448i	0.987966	+	0.207733i
$236$	2.48196	+	1.25367i	0.161562	+	0.0816072i
$237$		−	26.5867i		−	1.72699i
$238$	−10.7835	+	0.496911i	−0.698989	+	0.0322099i
$239$		−	5.34718i		−	0.345880i	−0.984932	−	0.172940i	$-0.944673\pi$
$239$		−	5.34718i		−	0.345880i	0.984932	−	0.172940i	$-0.0553267\pi$
$240$	20.9913	−	9.57855i	1.35498	−	0.618293i
$241$		−	9.70134i		−	0.624919i	−0.949931	−	0.312459i	$-0.898847\pi$
$241$		−	9.70134i		−	0.624919i	0.949931	−	0.312459i	$-0.101153\pi$
$242$	2.35136	−	1.44659i	0.151151	−	0.0929904i
$243$	−22.1112			−1.41843
$244$	3.42765	−	6.78589i	0.219433	−	0.434422i
$245$	−14.6896	+	5.40517i	−0.938484	+	0.345323i
$246$	−1.15965	−	1.88494i	−0.0739364	−	0.120180i
$247$	−7.19569			−0.457851
$248$	1.82478	+	21.7241i	0.115874	+	1.37948i
$249$	35.0154			2.21901
$250$	1.10905	−	15.7724i	0.0701427	−	0.997537i
$251$			14.7270i			0.929563i	0.885425	+	0.464782i	$0.153867\pi$
$251$			14.7270i			0.929563i	−0.885425	+	0.464782i	$0.846133\pi$
$252$	−15.9878	+	10.8811i	−1.00714	+	0.685448i
$253$	−16.0509			−1.00911
$254$	11.6338	−	7.15727i	0.729967	−	0.449087i
$255$	−3.42434	+	16.2860i	−0.214440	+	1.01987i
$256$	−4.73029	+	15.2848i	−0.295643	+	0.955298i
$257$	−11.2700			−0.703006			−0.351503	−	0.936187i	$-0.614329\pi$
$257$	−11.2700			−0.703006			−0.351503	+	0.936187i	$0.614329\pi$
$258$	−23.1629	−	37.6501i	−1.44206	−	2.34399i
$259$	−10.7601	−	5.95514i	−0.668602	−	0.370034i
$260$	−3.73142	+	4.66203i	−0.231413	+	0.289127i
$261$			6.88907i			0.426423i
$262$	−15.0380	−	24.4434i	−0.929049	−	1.51012i
$263$	−14.2659			−0.879672			−0.439836	−	0.898078i	$-0.644963\pi$
$263$	−14.2659			−0.879672			−0.439836	+	0.898078i	$0.644963\pi$
$264$	2.19798	+	26.1671i	0.135276	+	1.61047i
$265$	−2.90569	+	13.8193i	−0.178495	+	0.848912i
$266$	−0.928180	−	20.1425i	−0.0569104	−	1.23501i
$267$			18.1846i			1.11288i
$268$	24.4243	+	12.3371i	1.49195	+	0.753607i
$269$	19.6473			1.19792			0.598959	−	0.800780i	$-0.295581\pi$
$269$	19.6473			1.19792			0.598959	+	0.800780i	$0.295581\pi$
$270$	1.80291	+	5.02807i	0.109722	+	0.305999i
$271$	−21.4339			−1.30202			−0.651008	−	0.759071i	$-0.725654\pi$
$271$	−21.4339			−1.30202			−0.651008	+	0.759071i	$0.725654\pi$
$272$	−6.84852	−	9.28844i	−0.415252	−	0.563195i
$273$	4.41298	−	7.97366i	0.267086	−	0.482588i
$274$	−9.06482	−	14.7344i	−0.547626	−	0.890136i
$275$	16.4708	+	7.24679i	0.993226	+	0.436998i
$276$	10.3746	−	20.5390i	0.624475	−	1.23630i
$277$	−20.3225			−1.22106			−0.610530	−	0.791993i	$-0.709043\pi$
$277$	−20.3225			−1.22106			−0.610530	+	0.791993i	$0.709043\pi$
$278$	0.131209	+	0.213273i	0.00786940	+	0.0127913i
$279$	−28.1700			−1.68649
$280$	−13.5315	−	9.84377i	−0.808659	−	0.588278i
$281$	6.60360			0.393938			0.196969	−	0.980410i	$-0.436890\pi$
$281$	6.60360			0.393938			0.196969	+	0.980410i	$0.436890\pi$
$282$	−13.2310	−	21.5063i	−0.787894	−	1.28068i
$283$	−26.0188			−1.54666			−0.773330	−	0.634004i	$-0.781410\pi$
$283$	−26.0188			−1.54666			−0.773330	+	0.634004i	$0.781410\pi$
$284$	−14.6351	−	7.39243i	−0.868435	−	0.438660i
$285$	−30.4206	−	6.39632i	−1.80196	−	0.378886i
$286$	−3.56102	−	5.78825i	−0.210568	−	0.342266i
$287$	−0.777178	+	1.40425i	−0.0458753	+	0.0828905i
$288$	−19.1695	−	7.74403i	−1.12957	−	0.456321i
$289$	−8.67642			−0.510377
$290$	−5.61092	+	2.01190i	−0.329485	+	0.118143i
$291$	16.1575			0.947168
$292$	−10.3187	+	20.4285i	−0.603859	+	1.19549i
$293$			23.5795i			1.37753i	0.724984	+	0.688765i	$0.241847\pi$
$293$			23.5795i			1.37753i	−0.724984	+	0.688765i	$0.758153\pi$
$294$	22.8894	+	11.3245i	1.33494	+	0.660456i
$295$	−3.04230	−	0.639683i	−0.177129	−	0.0372438i
$296$	−1.10047	−	13.1011i	−0.0639633	−	0.761487i
$297$	−6.07906			−0.352743
$298$	−0.206830	−	0.336191i	−0.0119813	−	0.0194750i
$299$			5.95514i			0.344394i
$300$	−19.9191	+	16.3923i	−1.15003	+	0.946412i
$301$	−15.5234	+	28.0487i	−0.894755	+	1.61670i
$302$	3.52257	+	5.72575i	0.202701	+	0.329480i
$303$	12.4608			0.715854
$304$	17.3499	−	12.7924i	0.995085	−	0.733692i
$305$	−1.74895	+	8.31790i	−0.100145	+	0.476282i
$306$	12.7008	−	7.81372i	0.726055	−	0.446680i
$307$	8.34981			0.476549			0.238274	−	0.971198i	$-0.423418\pi$
$307$	8.34981			0.476549			0.238274	+	0.971198i	$0.423418\pi$
$308$	15.7433	−	10.7148i	0.897060	−	0.610531i
$309$			34.6971i			1.97385i
$310$	−8.22683	−	22.9435i	−0.467252	−	1.30310i
$311$	−3.79343			−0.215105			−0.107553	−	0.994199i	$-0.534301\pi$
$311$	−3.79343			−0.215105			−0.107553	+	0.994199i	$0.534301\pi$
$312$	9.70842	−	0.815487i	0.549631	−	0.0461679i
$313$	21.8977			1.23773			0.618867	−	0.785496i	$-0.287592\pi$
$313$	21.8977			1.23773			0.618867	+	0.785496i	$0.287592\pi$
$314$	−2.20250	−	3.58005i	−0.124294	−	0.202034i
$315$	14.1386	−	16.3588i	0.796622	−	0.921713i
$316$	−18.3984	−	9.29333i	−1.03499	−	0.522791i
$317$	26.3887			1.48213			0.741067	−	0.671431i	$-0.234320\pi$
$317$	26.3887			1.48213			0.741067	+	0.671431i	$0.234320\pi$
$318$	19.6234	−	12.0726i	1.10043	−	0.677000i
$319$		−	6.78374i		−	0.379816i
$320$	0.708951	−	17.8745i	0.0396315	−	0.999214i
$321$		−	21.7357i		−	1.21317i
$322$	−16.6699	+	0.768159i	−0.928974	+	0.0428078i
$323$			15.5476i			0.865094i
$324$	−5.95761	+	11.7946i	−0.330978	+	0.655253i
$325$	2.68868	−	6.11093i	0.149141	−	0.338974i
$326$	6.24377	+	10.1489i	0.345811	+	0.562097i
$327$			31.2592i			1.72864i
$328$	−1.70977	+	0.143617i	−0.0944060	+	0.00792991i
$329$	−8.86720	+	16.0218i	−0.488865	+	0.883312i
$330$	−9.90936	−	27.6358i	−0.545492	−	1.52130i
$331$	−7.51497			−0.413060			−0.206530	−	0.978440i	$-0.566217\pi$
$331$	−7.51497			−0.413060			−0.206530	+	0.978440i	$0.566217\pi$
$332$	12.2396	−	24.2312i	0.671733	−	1.32986i
$333$	16.9884			0.930957
$334$	−9.96706	−	16.2009i	−0.545373	−	0.886475i
$335$	−29.9384	−	6.29495i	−1.63571	−	0.343930i
$336$	3.53504	+	27.0710i	0.192852	+	1.47684i
$337$			4.69960i			0.256004i	0.991774	+	0.128002i	$0.0408563\pi$
$337$			4.69960i			0.256004i	−0.991774	+	0.128002i	$0.959144\pi$
$338$	13.5112	−	8.31230i	0.734912	−	0.452129i
$339$			26.6521i			1.44754i
$340$	10.0732	+	8.06242i	0.546295	+	0.437246i
$341$	27.7392			1.50216
$342$	14.5953	+	23.7238i	0.789221	+	1.28284i
$343$	−1.00596	−	18.4929i	−0.0543166	−	0.998524i
$344$	−34.1510	+	2.86862i	−1.84130	+	0.154665i
$345$	−5.29358	+	25.1760i	−0.284997	+	1.35543i
$346$	7.84889	+	12.7580i	0.421959	+	0.685872i
$347$		−	9.75889i		−	0.523885i	−0.965084	−	0.261942i	$-0.915637\pi$
$347$		−	9.75889i		−	0.523885i	0.965084	−	0.261942i	$-0.0843630\pi$
$348$	8.68059	+	4.38470i	0.465329	+	0.235044i
$349$	−6.30167			−0.337321			−0.168660	−	0.985674i	$-0.553944\pi$
$349$	−6.30167			−0.337321			−0.168660	+	0.985674i	$0.553944\pi$
$350$	17.4528	+	6.73799i	0.932890	+	0.360161i
$351$			2.25543i			0.120386i
$352$	18.8764	+	7.62562i	1.00611	+	0.406447i
$353$	−2.43058			−0.129367			−0.0646833	−	0.997906i	$-0.520604\pi$
$353$	−2.43058			−0.129367			−0.0646833	+	0.997906i	$0.520604\pi$
$354$	2.65777	+	4.32007i	0.141259	+	0.229609i
$355$	17.9392	+	3.77196i	0.952116	+	0.200195i
$356$	12.5841	+	6.35639i	0.666953	+	0.336888i
$357$	−17.2286	−	9.53507i	−0.911833	−	0.504650i
$358$	−2.33607	+	1.43719i	−0.123465	+	0.0759577i
$359$		−	7.92321i		−	0.418171i	−0.977897	−	0.209086i	$-0.932951\pi$
$359$		−	7.92321i		−	0.418171i	0.977897	−	0.209086i	$-0.0670487\pi$
$360$	22.9390	+	2.84613i	1.20899	+	0.150004i
$361$	−10.0415			−0.528498
$362$	−14.4479	+	8.88855i	−0.759362	+	0.467172i
$363$	5.03584			0.264313
$364$	−3.97536	−	5.84104i	−0.208365	−	0.306154i
$365$	5.26511	−	25.0406i	0.275588	−	1.31068i
$366$	11.8114	−	7.26659i	0.617394	−	0.379831i
$367$			15.9826i			0.834287i	0.908841	+	0.417143i	$0.136969\pi$
$367$			15.9826i			0.834287i	−0.908841	+	0.417143i	$0.863031\pi$
$368$	−10.5869	−	14.3587i	−0.551881	−	0.748501i
$369$		−	2.21707i		−	0.115416i
$370$	4.96133	+	13.8365i	0.257927	+	0.719324i
$371$	−14.6191	−	8.09089i	−0.758988	−	0.420058i
$372$	−17.9294	+	35.4956i	−0.929595	+	1.84036i
$373$	20.9336			1.08390			0.541951	−	0.840410i	$-0.317686\pi$
$373$	20.9336			1.08390			0.541951	+	0.840410i	$0.317686\pi$
$374$	−12.5066	+	7.69425i	−0.646700	+	0.397860i
$375$	16.7987	−	23.4446i	0.867483	−	1.21068i
$376$	−19.5076	+	1.63859i	−1.00603	+	0.0845041i
$377$	−2.51688			−0.129626
$378$	−6.31349	+	0.290930i	−0.324731	+	0.0149638i
$379$	13.1532			0.675636			0.337818	−	0.941211i	$-0.390311\pi$
$379$	13.1532			0.675636			0.337818	+	0.941211i	$0.390311\pi$
$380$	−15.0598	+	18.8157i	−0.772552	+	0.965226i
$381$	24.9157			1.27647
$382$	7.63727	+	12.4140i	0.390757	+	0.635154i
$383$		−	22.4872i		−	1.14904i	−0.818490	−	0.574521i	$-0.805188\pi$
$383$		−	22.4872i		−	1.14904i	0.818490	−	0.574521i	$-0.194812\pi$
$384$	−21.9587	+	19.2257i	−1.12058	+	0.981107i
$385$	−13.9225	+	16.1087i	−0.709554	+	0.820973i
$386$	−5.90879	−	9.60442i	−0.300749	−	0.488852i
$387$		−	44.2841i		−	2.25109i
$388$	5.64781	−	11.1812i	0.286724	−	0.567642i
$389$			7.58914i			0.384785i	0.981318	+	0.192392i	$0.0616246\pi$
$389$			7.58914i			0.384785i	−0.981318	+	0.192392i	$0.938375\pi$
$390$	−10.2534	+	3.67654i	−0.519199	+	0.186169i
$391$	12.8672			0.650721
$392$	15.8377	−	11.8814i	0.799923	−	0.600102i
$393$		−	52.3499i		−	2.64070i
$394$	−11.0335	+	6.78796i	−0.555858	+	0.341973i
$395$	22.5522	+	4.74189i	1.13472	+	0.238590i
$396$	−11.8606	+	23.4810i	−0.596017	+	1.17996i
$397$		−	4.23587i		−	0.212592i	−0.994335	−	0.106296i	$-0.966101\pi$
$397$		−	4.23587i		−	0.212592i	0.994335	−	0.106296i	$-0.0338992\pi$
$398$	−21.8314	+	13.4310i	−1.09431	+	0.673235i
$399$	17.8106	−	32.1813i	0.891644	−	1.61108i
$400$	4.38109	+	19.5143i	0.219054	+	0.975713i
$401$	−6.90753			−0.344946			−0.172473	−	0.985014i	$-0.555176\pi$
$401$	−6.90753			−0.344946			−0.172473	+	0.985014i	$0.555176\pi$
$402$	26.1545	+	42.5126i	1.30447	+	2.12034i
$403$		−	10.2917i		−	0.512667i
$404$	4.35565	−	8.62308i	0.216702	−	0.429014i
$405$	3.03985	−	14.4573i	0.151051	−	0.718391i
$406$	−0.324655	−	7.04534i	−0.0161123	−	0.349654i
$407$	−16.7286			−0.829207
$408$	−1.76201	−	20.9769i	−0.0872326	−	1.03851i
$409$		−	3.86544i		−	0.191134i	−0.995423	−	0.0955668i	$-0.969534\pi$
$409$		−	3.86544i		−	0.191134i	0.995423	−	0.0955668i	$-0.0304664\pi$
$410$	1.80573	−	0.647480i	0.0891789	−	0.0319768i
$411$		−	31.5563i		−	1.55656i
$412$	24.0110	+	12.1283i	1.18294	+	0.597519i
$413$	1.78120	−	3.21838i	0.0876470	−	0.158366i
$414$	19.6338	−	12.0790i	0.964946	−	0.593650i
$415$	−6.24520	+	29.7018i	−0.306565	+	1.45800i
$416$	2.82923	−	7.00345i	0.138714	−	0.343372i
$417$			0.456763i			0.0223678i
$418$	−14.3721	−	23.3611i	−0.702962	−	1.14263i
$419$			12.9925i			0.634726i	0.948304	+	0.317363i	$0.102797\pi$
$419$			12.9925i			0.634726i	−0.948304	+	0.317363i	$0.897203\pi$
$420$	−11.6141	−	28.2273i	−0.566710	−	1.37735i
$421$			20.4156i			0.994997i	0.867465	+	0.497499i	$0.165748\pi$
$421$			20.4156i			0.994997i	−0.867465	+	0.497499i	$0.834252\pi$
$422$	11.4274	−	7.03033i	0.556279	−	0.342231i
$423$		−	25.2957i		−	1.22992i
$424$	−1.49514	−	17.7997i	−0.0726103	−	0.864430i
$425$	−13.2038	−	5.80939i	−0.640479	−	0.281797i
$426$	−15.6719	−	25.4738i	−0.759304	−	1.23421i
$427$	−8.79934	−	4.86995i	−0.425830	−	0.235674i
$428$	−15.0415	−	7.59767i	−0.727057	−	0.367247i
$429$		−	12.3966i		−	0.598511i
$430$	36.0679	−	12.9328i	1.73935	−	0.623677i
$431$			3.54463i			0.170739i	0.996349	+	0.0853695i	$0.0272071\pi$
$431$			3.54463i			0.170739i	−0.996349	+	0.0853695i	$0.972793\pi$
$432$	−4.00966	−	5.43818i	−0.192915	−	0.261645i
$433$	24.1539			1.16076			0.580382	−	0.814344i	$-0.302903\pi$
$433$	24.1539			1.16076			0.580382	+	0.814344i	$0.302903\pi$
$434$	28.8090	−	1.32754i	1.38287	−	0.0637239i
$435$	−10.6404	−	2.23728i	−0.510167	−	0.107269i
$436$	21.6319	+	10.9266i	1.03598	+	0.523289i
$437$			24.0346i			1.14973i
$438$	−35.5577	+	21.8756i	−1.69901	+	1.04526i
$439$	−8.10213			−0.386694			−0.193347	−	0.981130i	$-0.561934\pi$
$439$	−8.10213			−0.386694			−0.193347	+	0.981130i	$0.561934\pi$
$440$	−22.5883	−	2.80262i	−1.07685	−	0.133609i
$441$	13.5859	+	21.6781i	0.646946	+	1.03229i
$442$	2.85469	+	4.64015i	0.135784	+	0.220709i
$443$			26.0995i			1.24002i	0.784592	+	0.620012i	$0.212872\pi$
$443$			26.0995i			1.24002i	−0.784592	+	0.620012i	$0.787128\pi$
$444$	10.8126	−	21.4063i	0.513144	−	1.01590i
$445$	−15.4251	−	3.24333i	−0.731219	−	0.153749i
$446$	20.7584	+	33.7417i	0.982941	+	1.59772i
$447$		−	0.720012i		−	0.0340554i
$448$	19.9693	+	7.01631i	0.943459	+	0.331490i
$449$	14.9898			0.707414			0.353707	−	0.935356i	$-0.384921\pi$
$449$	14.9898			0.707414			0.353707	+	0.935356i	$0.384921\pi$
$450$	−25.6009	+	3.53058i	−1.20684	+	0.166433i
$451$			2.18318i			0.102802i
$452$	18.4437	+	9.31618i	0.867518	+	0.438196i
$453$			12.2627i			0.576152i
$454$	2.23308	−	1.37383i	0.104804	−	0.0644769i
$455$	5.97658	+	5.16546i	0.280186	+	0.242161i
$456$	39.1827	−	3.29127i	1.83490	−	0.154128i
$457$		−	38.8078i		−	1.81535i	−0.419670	−	0.907677i	$-0.637854\pi$
$457$		−	38.8078i		−	1.81535i	0.419670	−	0.907677i	$-0.362146\pi$
$458$	−24.3863	+	15.0029i	−1.13950	+	0.701038i
$459$	4.87328			0.227465
$460$	15.5718	+	12.4635i	0.726041	+	0.581112i
$461$	−28.0610			−1.30693			−0.653466	−	0.756956i	$-0.726686\pi$
$461$	−28.0610			−1.30693			−0.653466	+	0.756956i	$0.726686\pi$
$462$	34.7009	−	1.59904i	1.61443	−	0.0743942i
$463$	9.44403			0.438901			0.219451	−	0.975624i	$-0.429573\pi$
$463$	9.44403			0.438901			0.219451	+	0.975624i	$0.429573\pi$
$464$	6.06857	−	4.47445i	0.281726	−	0.207721i
$465$	9.14841	−	43.5093i	0.424247	−	2.01770i
$466$	−1.74726	−	2.84007i	−0.0809401	−	0.131564i
$467$	−19.1643			−0.886818			−0.443409	−	0.896319i	$-0.646231\pi$
$467$	−19.1643			−0.886818			−0.443409	+	0.896319i	$0.646231\pi$
$468$	8.71182	+	4.40047i	0.402704	+	0.203412i
$469$	17.5283	−	31.6713i	0.809382	−	1.46244i
$470$	20.6025	−	7.38743i	0.950323	−	0.340757i
$471$		−	7.66731i		−	0.353291i
$472$	3.91858	−	0.329152i	0.180367	−	0.0151505i
$473$			43.6070i			2.00505i
$474$	−19.7018	−	32.0241i	−0.904932	−	1.47092i
$475$	10.8514	−	24.6634i	0.497895	−	1.13164i
$476$	−12.6207	+	8.58950i	−0.578467	+	0.393699i
$477$	23.0811			1.05681
$478$	−3.96247	−	6.44077i	−0.181239	−	0.294594i
$479$	19.8597			0.907414			0.453707	−	0.891151i	$-0.350101\pi$
$479$	19.8597			0.907414			0.453707	+	0.891151i	$0.350101\pi$
$480$	18.1863	−	27.0929i	0.830088	−	1.23661i
$481$			6.20660i			0.282996i
$482$	−7.18907	−	11.6854i	−0.327453	−	0.532257i
$483$	−26.6332	−	14.7400i	−1.21185	−	0.670693i
$484$	1.76027	−	3.48489i	0.0800123	−	0.158404i
$485$	−2.88178	+	13.7056i	−0.130855	+	0.622338i
$486$	−26.6333	+	16.3852i	−1.20811	+	0.743248i
$487$	2.59554			0.117615			0.0588075	−	0.998269i	$-0.481270\pi$
$487$	2.59554			0.117615			0.0588075	+	0.998269i	$0.481270\pi$
$488$	−0.899932	−	10.7137i	−0.0407380	−	0.484988i
$489$			21.7357i			0.982922i
$490$	−13.6884	+	17.3962i	−0.618381	+	0.785879i
$491$	16.6118			0.749679			0.374839	−	0.927090i	$-0.377698\pi$
$491$	16.6118			0.749679			0.374839	+	0.927090i	$0.377698\pi$
$492$	−2.79363	−	1.41111i	−0.125947	−	0.0636176i
$493$			5.43818i			0.244923i
$494$	−8.66734	+	5.33228i	−0.389962	+	0.239911i
$495$	6.05183	−	28.7821i	0.272009	−	1.29366i
$496$	18.2964	+	24.8149i	0.821532	+	1.11422i
$497$	−10.5030	+	18.9776i	−0.471125	+	0.851260i
$498$	42.1766	−	25.9477i	1.88998	−	1.16275i
$499$	12.8033			0.573155			0.286578	−	0.958057i	$-0.407482\pi$
$499$	12.8033			0.573155			0.286578	+	0.958057i	$0.407482\pi$
$500$	−10.3521	−	19.8200i	−0.462960	−	0.886379i
$501$		−	34.6971i		−	1.55015i
$502$	10.9133	+	17.7390i	0.487085	+	0.791730i
$503$		−	7.66175i		−	0.341621i	−0.985304	−	0.170810i	$-0.945361\pi$
$503$		−	7.66175i		−	0.341621i	0.985304	−	0.170810i	$-0.0546385\pi$
$504$	−11.1942	+	24.9541i	−0.498631	+	1.11154i
$505$	−2.22246	+	10.5699i	−0.0988980	+	0.470353i
$506$	−19.3336	+	11.8943i	−0.859481	+	0.528767i
$507$	28.9366			1.28512
$508$	8.70925	−	17.2421i	0.386410	−	0.764995i
$509$	8.30655			0.368181			0.184091	−	0.982909i	$-0.441066\pi$
$509$	8.30655			0.368181			0.184091	+	0.982909i	$0.441066\pi$
$510$	7.94384	+	22.1543i	0.351759	+	0.981008i
$511$	26.4899	+	14.6607i	1.17184	+	0.648551i
$512$	5.62888	+	21.9161i	0.248764	+	0.968564i
$513$			9.10281i			0.401899i
$514$	−13.5750	+	8.35154i	−0.598766	+	0.368370i
$515$	−29.4318	−	6.18843i	−1.29692	−	0.272695i
$516$	−55.8003	−	28.1856i	−2.45647	−	1.24080i
$517$			24.9089i			1.09549i
$518$	−17.3737	+	0.800595i	−0.763358	+	0.0351761i
$519$			27.3234i			1.19936i
$520$	−1.03982	+	8.38062i	−0.0455990	+	0.367514i
$521$		−	19.9456i		−	0.873833i	−0.899502	−	0.436916i	$-0.856071\pi$
$521$		−	19.9456i		−	0.873833i	0.899502	−	0.436916i	$-0.143929\pi$
$522$	5.10506	+	8.29800i	0.223443	+	0.363194i
$523$	21.9379			0.959276			0.479638	−	0.877467i	$-0.340768\pi$
$523$	21.9379			0.959276			0.479638	+	0.877467i	$0.340768\pi$
$524$	−36.2270	−	18.2988i	−1.58258	−	0.799387i
$525$	20.6750	+	27.1502i	0.902330	+	1.18493i
$526$	−17.1835	+	10.5716i	−0.749237	+	0.460942i
$527$	−22.2372			−0.968666
$528$	22.0383	+	29.8899i	0.959095	+	1.30079i
$529$	−3.10900			−0.135174
$530$	6.74067	+	18.7988i	0.292796	+	0.816567i
$531$			5.08127i			0.220508i
$532$	−16.0443	−	23.5741i	−0.695611	−	1.02207i
$533$	0.809994			0.0350847
$534$	13.4755	+	21.9037i	0.583141	+	0.947865i
$535$	18.4373	+	3.87669i	0.797114	+	0.167604i
$536$	38.5617	−	3.23910i	1.66561	−	0.139908i
$537$	−5.00311			−0.215900
$538$	23.6655	−	14.5594i	1.02029	−	0.627701i
$539$	−13.3781	−	21.3466i	−0.576237	−	0.919465i
$540$	5.89763	+	4.72037i	0.253794	+	0.203133i
$541$		−	23.9613i		−	1.03018i	−0.857137	−	0.515088i	$-0.827759\pi$
$541$		−	23.9613i		−	1.03018i	0.857137	−	0.515088i	$-0.172241\pi$
$542$	−25.8175	+	15.8833i	−1.10896	+	0.682247i
$543$	−30.9426			−1.32788
$544$	−15.1322	−	6.11308i	−0.648790	−	0.262096i
$545$	−26.5156	−	5.57526i	−1.13580	−	0.238818i
$546$	−0.593272	−	12.8746i	−0.0253897	−	0.550982i
$547$			8.98695i			0.384254i	0.981370	+	0.192127i	$0.0615386\pi$
$547$			8.98695i			0.384254i	−0.981370	+	0.192127i	$0.938461\pi$
$548$	−21.8375	−	11.0304i	−0.932851	−	0.471197i
$549$	13.8926			0.592923
$550$	25.2095	−	3.47660i	1.07494	−	0.148243i
$551$	−10.1580			−0.432745
$552$	−2.72384	−	32.4275i	−0.115934	−	1.38021i
$553$	−13.2038	+	23.8575i	−0.561483	+	1.01452i
$554$	−24.4788	+	15.0597i	−1.04000	+	0.639827i
$555$	−5.51710	+	26.2390i	−0.234188	+	1.11379i
$556$	0.316087	+	0.159660i	0.0134051	+	0.00677111i
$557$	8.37113			0.354696			0.177348	−	0.984148i	$-0.443248\pi$
$557$	8.37113			0.354696			0.177348	+	0.984148i	$0.443248\pi$
$558$	−33.9312	+	20.8750i	−1.43642	+	0.883710i
$559$	16.1789			0.684295
$560$	−23.5935	−	1.82967i	−0.997007	−	0.0773177i
$561$	−26.7851			−1.13087
$562$	7.95415	−	4.89352i	0.335526	−	0.206421i
$563$	26.2152			1.10484			0.552420	−	0.833566i	$-0.313705\pi$
$563$	26.2152			1.10484			0.552420	+	0.833566i	$0.313705\pi$
$564$	−31.8739	−	16.1000i	−1.34213	−	0.677932i
$565$	−22.6076	−	4.75355i	−0.951110	−	0.199983i
$566$	−31.3402	+	19.2810i	−1.31733	+	0.810439i
$567$	15.2941	+	8.46447i	0.642293	+	0.355474i
$568$	−23.1063	+	1.94088i	−0.969521	+	0.0814377i
$569$	31.1843			1.30732			0.653658	−	0.756790i	$-0.273234\pi$
$569$	31.1843			1.30732			0.653658	+	0.756790i	$0.273234\pi$
$570$	−41.3820	+	14.8383i	−1.73330	+	0.621508i
$571$	−45.6053			−1.90852			−0.954261	−	0.298974i	$-0.903356\pi$
$571$	−45.6053			−1.90852			−0.954261	+	0.298974i	$0.903356\pi$
$572$	−8.57862	−	4.33319i	−0.358690	−	0.181180i
$573$			26.5867i			1.11068i
$574$	0.104482	+	2.26737i	0.00436099	+	0.0946381i
$575$	−20.4114	−	8.98056i	−0.851213	−	0.374515i
$576$	−28.8286	+	4.87749i	−1.20119	+	0.203229i
$577$	−24.1057			−1.00353			−0.501766	−	0.865003i	$-0.667316\pi$
$577$	−24.1057			−1.00353			−0.501766	+	0.865003i	$0.667316\pi$
$578$	−10.4509	+	6.42956i	−0.434700	+	0.267434i
$579$		−	20.5696i		−	0.854841i
$580$	−5.26755	+	6.58128i	−0.218723	+	0.273273i
$581$	−31.4209	−	17.3898i	−1.30356	−	0.721449i
$582$	19.4620	−	11.9733i	0.806724	−	0.496309i
$583$	−22.7282			−0.941306
$584$	2.70919	+	32.2531i	0.112107	+	1.33464i
$585$	−10.6786	−	2.24533i	−0.441508	−	0.0928329i
$586$	17.4733	+	28.4020i	0.721817	+	1.17327i
$587$	−14.6387			−0.604205			−0.302103	−	0.953275i	$-0.597689\pi$
$587$	−14.6387			−0.604205			−0.302103	+	0.953275i	$0.597689\pi$
$588$	35.9626	−	3.32142i	1.48307	−	0.136973i
$589$		−	41.5368i		−	1.71150i
$590$	−4.13853	+	1.48395i	−0.170380	+	0.0610932i
$591$	−23.6301			−0.972013
$592$	−11.0340	−	14.9650i	−0.453493	−	0.615059i
$593$	−9.32979			−0.383129			−0.191564	−	0.981480i	$-0.561356\pi$
$593$	−9.32979			−0.383129			−0.191564	+	0.981480i	$0.561356\pi$
$594$	−7.32233	+	4.50482i	−0.300439	+	0.184835i
$595$	11.1609	−	12.9135i	0.457554	−	0.529402i
$596$	−0.498260	−	0.251679i	−0.0204095	−	0.0103092i
$597$	−46.7557			−1.91358
$598$	4.41298	+	7.17307i	0.180460	+	0.293329i
$599$			48.3192i			1.97427i	0.159893	+	0.987134i	$0.448885\pi$
$599$			48.3192i			1.97427i	−0.159893	+	0.987134i	$0.551115\pi$
$600$	−11.8456	+	34.5057i	−0.483593	+	1.40869i
$601$		−	7.63740i		−	0.311536i	−0.987794	−	0.155768i	$-0.950215\pi$
$601$		−	7.63740i		−	0.311536i	0.987794	−	0.155768i	$-0.0497852\pi$
$602$	2.08693	+	45.2886i	0.0850571	+	1.84583i
$603$			50.0034i			2.03630i
$604$	8.48599	+	4.28640i	0.345290	+	0.174411i
$605$	−0.898172	+	4.27165i	−0.0365159	+	0.173667i
$606$	15.0093	−	9.23393i	0.609709	−	0.375103i
$607$		−	38.2619i		−	1.55300i	−0.630116	−	0.776501i	$-0.716993\pi$
$607$		−	38.2619i		−	1.55300i	0.630116	−	0.776501i	$-0.283007\pi$
$608$	11.4186	−	28.2656i	0.463087	−	1.14632i
$609$	6.22971	−	11.2562i	0.252440	−	0.456125i
$610$	4.05724	+	11.3151i	0.164273	+	0.458135i
$611$	9.24163			0.373876
$612$	9.50804	−	18.8235i	0.384340	−	0.760896i
$613$	−17.0330			−0.687955			−0.343977	−	0.938978i	$-0.611774\pi$
$613$	−17.0330			−0.687955			−0.343977	+	0.938978i	$0.611774\pi$
$614$	10.0575	−	6.18753i	0.405887	−	0.249708i
$615$	3.42434	+	0.720012i	0.138083	+	0.0290337i
$616$	11.0231	−	24.5726i	0.444132	−	0.990056i
$617$		−	5.71269i		−	0.229984i	−0.993366	−	0.114992i	$-0.963316\pi$
$617$		−	5.71269i		−	0.229984i	0.993366	−	0.114992i	$-0.0366843\pi$
$618$	25.7119	+	41.7933i	1.03428	+	1.68117i
$619$			45.1694i			1.81551i	0.419497	+	0.907757i	$0.362206\pi$
$619$			45.1694i			1.81551i	−0.419497	+	0.907757i	$0.637794\pi$
$620$	−26.9114	−	21.5395i	−1.08079	−	0.865045i
$621$	7.53346			0.302307
$622$	−4.56925	+	2.81107i	−0.183210	+	0.112714i
$623$	9.03106	−	16.3179i	0.361822	−	0.653763i
$624$	11.0897	−	8.17658i	0.443942	−	0.327325i
$625$	16.8908	+	18.4310i	0.675630	+	0.737241i
$626$	26.3762	−	16.2271i	1.05421	−	0.648564i
$627$		−	50.0319i		−	1.99808i
$628$	−5.30591	−	2.68009i	−0.211729	−	0.106947i
$629$	13.4105			0.534712
$630$	4.90776	−	30.1817i	0.195530	−	1.20247i
$631$		−	1.44976i		−	0.0577141i	−0.999584	−	0.0288571i	$-0.990813\pi$
$631$		−	1.44976i		−	0.0577141i	0.999584	−	0.0288571i	$-0.00918676\pi$
$632$	−29.0480	+	2.43997i	−1.15547	+	0.0970567i
$633$	24.4739			0.972749
$634$	31.7856	−	19.5550i	1.26237	−	0.776628i
$635$	−4.44387	+	21.1348i	−0.176349	+	0.838708i
$636$	14.6905	−	29.0834i	0.582515	−	1.15323i
$637$	−7.91995	+	4.96351i	−0.313800	+	0.196661i
$638$	−5.02701	−	8.17113i	−0.199021	−	0.323498i
$639$		−	29.9623i		−	1.18529i
$640$	−12.3917	−	22.0555i	−0.489826	−	0.871820i
$641$	−8.82070			−0.348397			−0.174198	−	0.984711i	$-0.555733\pi$
$641$	−8.82070			−0.348397			−0.174198	+	0.984711i	$0.555733\pi$
$642$	−16.1070	−	26.1810i	−0.635692	−	1.03328i
$643$	−21.0328			−0.829451			−0.414726	−	0.909946i	$-0.636122\pi$
$643$	−21.0328			−0.829451			−0.414726	+	0.909946i	$0.636122\pi$
$644$	−19.5099	+	13.2783i	−0.768797	+	0.523237i
$645$	68.3981	+	14.3816i	2.69317	+	0.566275i
$646$	11.5214	+	18.7274i	0.453303	+	0.736820i
$647$		−	42.6208i		−	1.67560i	−0.545979	−	0.837799i	$-0.683842\pi$
$647$		−	42.6208i		−	1.67560i	0.545979	−	0.837799i	$-0.316158\pi$
$648$	1.56417	+	18.6216i	0.0614465	+	0.731524i
$649$		−	5.00358i		−	0.196408i
$650$	−1.28988	−	9.35314i	−0.0505931	−	0.366860i
$651$	46.0276	+	25.4738i	1.80396	+	0.998395i
$652$	15.0415	+	7.59767i	0.589069	+	0.297548i
$653$	10.3346			0.404424			0.202212	−	0.979342i	$-0.435187\pi$
$653$	10.3346			0.404424			0.202212	+	0.979342i	$0.435187\pi$
$654$	23.1643	+	37.6523i	0.905795	+	1.47232i
$655$	44.4058	+	9.33691i	1.73508	+	0.364823i
$656$	−1.95302	+	1.43999i	−0.0762525	+	0.0562222i
$657$	−41.8230			−1.63167
$658$	1.19209	+	25.8695i	0.0464724	+	1.00850i
$659$	−24.5798			−0.957493			−0.478746	−	0.877953i	$-0.658909\pi$
$659$	−24.5798			−0.957493			−0.478746	+	0.877953i	$0.658909\pi$
$660$	−32.4152	−	25.9446i	−1.26176	−	1.00989i
$661$	27.2497			1.05989			0.529946	−	0.848031i	$-0.322212\pi$
$661$	27.2497			1.05989			0.529946	+	0.848031i	$0.322212\pi$
$662$	−9.05191	+	5.56888i	−0.351813	+	0.216441i
$663$			9.93770i			0.385948i
$664$	−3.21350	−	38.2569i	−0.124708	−	1.48466i
$665$	24.1212	+	20.8475i	0.935379	+	0.808433i
$666$	20.4628	−	12.5890i	0.792917	−	0.487815i
$667$			8.40673i			0.325510i
$668$	−24.0110	−	12.1283i	−0.929013	−	0.469259i
$669$			72.2639i			2.79388i
$670$	−40.7262	+	14.6031i	−1.57339	+	0.564168i
$671$	−13.6802			−0.528119
$672$	24.3187	+	29.9879i	0.938113	+	1.15681i
$673$		−	30.4582i		−	1.17408i	−0.809559	−	0.587038i	$-0.800294\pi$
$673$		−	30.4582i		−	1.17408i	0.809559	−	0.587038i	$-0.199706\pi$
$674$	3.48258	+	5.66075i	0.134144	+	0.218044i
$675$	−7.73055	−	3.40127i	−0.297549	−	0.130915i
$676$	10.1147	−	20.0246i	0.389028	−	0.770178i
$677$			0.455107i			0.0174912i	0.999962	+	0.00874559i	$0.00278384\pi$
$677$			0.455107i			0.0174912i	−0.999962	+	0.00874559i	$0.997216\pi$
$678$	19.7502	+	32.1029i	0.758502	+	1.23290i
$679$	−14.4989	−	8.02432i	−0.556415	−	0.307945i
$680$	18.1079	+	2.24672i	0.694406	+	0.0861577i
$681$	4.78254			0.183267
$682$	33.4124	−	20.5558i	1.27943	−	0.787124i
$683$			1.03207i			0.0394911i	0.999805	+	0.0197456i	$0.00628562\pi$
$683$			1.03207i			0.0394911i	−0.999805	+	0.0197456i	$0.993714\pi$
$684$	35.1605	+	17.7601i	1.34439	+	0.679074i
$685$	26.7676	+	5.62824i	1.02274	+	0.215044i
$686$	−14.9157	−	21.5296i	−0.569482	−	0.822004i
$687$	−52.2277			−1.99261
$688$	−39.0098	+	28.7625i	−1.48723	+	1.09656i
$689$			8.43253i			0.321254i
$690$	12.2801	+	34.2476i	0.467497	+	1.30379i
$691$		−	10.9090i		−	0.414999i	−0.978235	−	0.207500i	$-0.933467\pi$
$691$		−	10.9090i		−	0.414999i	0.978235	−	0.207500i	$-0.0665326\pi$
$692$	18.9083	+	9.55085i	0.718784	+	0.363069i
$693$	30.4481	+	16.8513i	1.15663	+	0.640129i
$694$	−7.23171	−	11.7548i	−0.274512	−	0.446204i
$695$	−0.387449	−	0.0814662i	−0.0146968	−	0.00309019i
$696$	13.7052	−	1.15120i	0.519493	−	0.0436363i
$697$		−	1.75014i		−	0.0662914i
$698$	−7.59048	+	4.66978i	−0.287304	+	0.176754i
$699$		−	6.08251i		−	0.230062i
$700$	26.0153	−	4.81714i	0.983285	−	0.182071i
$701$		−	33.6356i		−	1.27040i	−0.772349	−	0.635199i	$-0.780918\pi$
$701$		−	33.6356i		−	1.27040i	0.772349	−	0.635199i	$-0.219082\pi$
$702$	1.67136	+	2.71671i	0.0630814	+	0.102535i
$703$			25.0495i			0.944760i
$704$	28.3878	−	4.80292i	1.06991	−	0.181017i
$705$	39.0700	+	8.21497i	1.47146	+	0.309394i
$706$	−2.92767	+	1.80115i	−0.110184	+	0.0677872i
$707$	−11.1817	−	6.18843i	−0.420530	−	0.232740i
$708$	6.40267	+	3.23409i	0.240627	+	0.121544i
$709$		−	14.1991i		−	0.533258i	−0.963799	−	0.266629i	$-0.914090\pi$
$709$		−	14.1991i		−	0.533258i	0.963799	−	0.266629i	$-0.0859099\pi$
$710$	24.4033	−	8.75026i	0.915839	−	0.328392i
$711$		−	37.6669i		−	1.41262i
$712$	19.8680	−	1.66887i	0.744586	−	0.0625437i
$713$	−34.3758			−1.28738
$714$	−27.8180	+	1.28187i	−1.04106	+	0.0479729i
$715$	10.5154	+	2.21100i	0.393253	+	0.0826866i
$716$	−1.74883	+	3.46224i	−0.0653568	+	0.129390i
$717$		−	13.7941i		−	0.515148i
$718$	−5.87140	−	9.54365i	−0.219119	−	0.356166i
$719$	35.5086			1.32425			0.662123	−	0.749395i	$-0.269656\pi$
$719$	35.5086			1.32425			0.662123	+	0.749395i	$0.269656\pi$
$720$	29.7395	−	13.5705i	1.10833	−	0.505741i
$721$	17.2317	−	31.1354i	0.641742	−	1.15954i
$722$	−12.0951	+	7.44111i	−0.450134	+	0.276929i
$723$		−	25.0264i		−	0.930743i
$724$	−10.8159	+	21.4128i	−0.401971	+	0.795801i
$725$	3.79554	−	8.62666i	0.140963	−	0.320386i
$726$	6.06576	−	3.73175i	0.225122	−	0.138498i
$727$			14.4322i			0.535261i	0.963522	+	0.267630i	$0.0862406\pi$
$727$			14.4322i			0.535261i	−0.963522	+	0.267630i	$0.913759\pi$
$728$	−9.11682	−	4.08974i	−0.337892	−	0.151576i
$729$	−37.2192			−1.37849
$730$	−12.2141	−	34.0634i	−0.452064	−	1.26074i
$731$		−	34.9575i		−	1.29295i
$732$	8.84227	−	17.5055i	0.326820	−	0.647021i
$733$		−	20.7489i		−	0.766378i	−0.923670	−	0.383189i	$-0.874826\pi$
$733$		−	20.7489i		−	0.766378i	0.923670	−	0.383189i	$-0.125174\pi$
$734$	11.8437	+	19.2514i	0.437160	+	0.710581i
$735$	−37.8946	+	13.9436i	−1.39776	+	0.514319i
$736$	−23.3925	−	9.45003i	−0.862259	−	0.348333i
$737$		−	49.2389i		−	1.81374i
$738$	−1.64294	−	2.67051i	−0.0604774	−	0.0983027i
$739$	15.3022			0.562901			0.281450	−	0.959576i	$-0.409185\pi$
$739$	15.3022			0.562901			0.281450	+	0.959576i	$0.409185\pi$
$740$	16.2294	+	12.9897i	0.596603	+	0.477512i
$741$	−18.5626			−0.681916
$742$	−23.6047	+	1.08772i	−0.866555	+	0.0399315i
$743$	30.8617			1.13221			0.566103	−	0.824334i	$-0.308450\pi$
$743$	30.8617			1.13221			0.566103	+	0.824334i	$0.308450\pi$
$744$	4.70737	+	56.0415i	0.172580	+	2.05458i
$745$	0.610750	+	0.128418i	0.0223762	+	0.00470488i
$746$	25.2149	−	15.5126i	0.923184	−	0.567957i
$747$	49.6082			1.81507
$748$	−9.36267	+	18.5357i	−0.342333	+	0.677733i
$749$	−10.7946	+	19.5045i	−0.394428	+	0.712677i
$750$	2.86101	−	40.6880i	0.104469	−	1.48571i
$751$		−	10.9371i		−	0.399099i	−0.979888	−	0.199550i	$-0.936052\pi$
$751$		−	10.9371i		−	0.399099i	0.979888	−	0.199550i	$-0.0639479\pi$
$752$	−22.2829	+	16.4296i	−0.812575	+	0.599125i
$753$			37.9912i			1.38448i
$754$	−3.03162	+	1.86510i	−0.110405	+	0.0679230i
$755$	−10.4018	−	2.18712i	−0.378562	−	0.0795976i
$756$	−7.38912	+	5.02897i	−0.268740	+	0.182902i
$757$	28.1387			1.02272			0.511359	−	0.859367i	$-0.329142\pi$
$757$	28.1387			1.02272			0.511359	+	0.859367i	$0.329142\pi$
$758$	15.8433	−	9.74704i	0.575454	−	0.354028i
$759$	−41.4062			−1.50295
$760$	−4.19665	+	33.8238i	−0.152228	+	1.22692i
$761$			46.8922i			1.69984i	0.526911	+	0.849921i	$0.323350\pi$
$761$			46.8922i			1.69984i	−0.526911	+	0.849921i	$0.676650\pi$
$762$	30.0114	−	18.4635i	1.08720	−	0.668862i
$763$	15.5243	−	28.0503i	0.562018	−	1.01549i
$764$	18.3984	+	9.29333i	0.665632	+	0.336221i
$765$	−4.85145	+	23.0732i	−0.175404	+	0.834214i
$766$	−16.6639	−	27.0862i	−0.602090	−	0.978665i
$767$	−1.85641			−0.0670311
$768$	−12.2027	+	39.4299i	−0.440326	+	1.42281i
$769$			8.13831i			0.293475i	0.989175	+	0.146738i	$0.0468773\pi$
$769$			8.13831i			0.293475i	−0.989175	+	0.146738i	$0.953123\pi$
$770$	−4.83272	+	29.7202i	−0.174159	+	1.07104i
$771$	−29.0732			−1.04705
$772$	−14.2345	−	7.19005i	−0.512310	−	0.258776i
$773$		−	8.13686i		−	0.292662i	−0.989236	−	0.146331i	$-0.953253\pi$
$773$		−	8.13686i		−	0.292662i	0.989236	−	0.146331i	$-0.0467465\pi$
$774$	−32.8162	−	53.3410i	−1.17955	−	1.91730i
$775$	35.2751	+	15.5203i	1.26712	+	0.557505i
$776$	−1.48284	−	17.6532i	−0.0532307	−	0.633715i
$777$	−27.7578	−	15.3624i	−0.995804	−	0.551123i
$778$	5.62384	+	9.14125i	0.201624	+	0.327730i
$779$	3.26910			0.117128
$780$	−9.62589	+	12.0266i	−0.344662	+	0.430621i
$781$			29.5042i			1.05574i
$782$	15.4987	−	9.53507i	0.554234	−	0.340974i
$783$			3.18394i			0.113785i
$784$	10.2722	−	26.0477i	0.366863	−	0.930275i
$785$	6.50379	+	1.36751i	0.232130	+	0.0488085i
$786$	−38.7933	−	63.0564i	−1.38371	−	2.24915i
$787$	−35.3405			−1.25975			−0.629877	−	0.776695i	$-0.716895\pi$
$787$	−35.3405			−1.25975			−0.629877	+	0.776695i	$0.716895\pi$
$788$	−8.25987	+	16.3524i	−0.294246	+	0.582532i
$789$	−36.8015			−1.31017
$790$	30.6784	−	11.0003i	1.09149	−	0.391374i
$791$	13.2363	−	23.9161i	0.470628	−	0.850360i
$792$	3.11400	+	37.0724i	0.110651	+	1.31731i
$793$			5.07559i			0.180239i
$794$	−3.13894	−	5.10218i	−0.111397	−	0.181070i
$795$	−7.49576	+	35.6494i	−0.265847	+	1.26435i
$796$	−16.3434	+	32.3557i	−0.579276	+	1.14682i
$797$			21.6145i			0.765626i	0.923826	+	0.382813i	$0.125045\pi$
$797$			21.6145i			0.765626i	−0.923826	+	0.382813i	$0.874955\pi$
$798$	−2.39441	−	51.9613i	−0.0847613	−	1.83941i
$799$		−	19.9683i		−	0.706426i
$800$	19.7379	+	20.2587i	0.697840	+	0.716253i
$801$			25.7631i			0.910296i
$802$	−8.32024	+	5.11874i	−0.293798	+	0.180749i
$803$	41.1835			1.45333
$804$	63.0070	+	31.8258i	2.22209	+	1.12241i
$805$	17.2534	−	19.9626i	0.608102	−	0.703590i
$806$	−7.62655	−	12.3966i	−0.268634	−	0.436650i
$807$	50.6839			1.78416
$808$	−1.14358	−	13.6144i	−0.0402309	−	0.478951i
$809$	−6.77039			−0.238034			−0.119017	−	0.992892i	$-0.537974\pi$
$809$	−6.77039			−0.238034			−0.119017	+	0.992892i	$0.537974\pi$
$810$	−7.05190	−	19.6668i	−0.247778	−	0.691020i
$811$			31.6060i			1.10984i	0.831905	+	0.554918i	$0.187250\pi$
$811$			31.6060i			1.10984i	−0.831905	+	0.554918i	$0.812750\pi$
$812$	−5.61192	−	8.24566i	−0.196940	−	0.289366i
$813$	−55.2927			−1.93920
$814$	−20.1499	+	12.3966i	−0.706254	+	0.434499i
$815$	−18.4373	−	3.87669i	−0.645831	−	0.135794i
$816$	−17.6670	−	23.9613i	−0.618470	−	0.838812i
$817$	65.2973			2.28446
$818$	−2.86444	−	4.65599i	−0.100153	−	0.162793i
$819$	6.25212	−	11.2967i	0.218467	−	0.394740i
$820$	1.69523	−	2.11802i	0.0592000	−	0.0739645i
$821$			28.3663i			0.989990i	0.868896	+	0.494995i	$0.164830\pi$
$821$			28.3663i			0.989990i	−0.868896	+	0.494995i	$0.835170\pi$
$822$	−23.3844	−	38.0101i	−0.815625	−	1.32575i
$823$	15.3770			0.536008			0.268004	−	0.963418i	$-0.413636\pi$
$823$	15.3770			0.536008			0.268004	+	0.963418i	$0.413636\pi$
$824$	37.9092	−	3.18429i	1.32063	−	0.110930i
$825$	42.4895	+	18.6944i	1.47929	+	0.650857i
$826$	−0.239460	−	5.19653i	−0.00833189	−	0.180811i
$827$		−	25.3065i		−	0.879994i	−0.897999	−	0.439997i	$-0.854979\pi$
$827$		−	25.3065i		−	0.879994i	0.897999	−	0.439997i	$-0.145021\pi$
$828$	14.6982	−	29.0987i	0.510798	−	1.01125i
$829$	−34.4068			−1.19500			−0.597498	−	0.801870i	$-0.703838\pi$
$829$	−34.4068			−1.19500			−0.597498	+	0.801870i	$0.703838\pi$
$830$	14.4877	+	40.4043i	0.502876	+	1.40245i
$831$	−52.4256			−1.81863
$832$	−1.78196	−	10.5323i	−0.0617784	−	0.365143i
$833$	10.7246	+	17.1125i	0.371585	+	0.592914i
$834$	0.338478	+	0.550178i	0.0117206	+	0.0190511i
$835$	29.4318	+	6.18843i	1.01853	+	0.214160i
$836$	−34.6229	−	17.4885i	−1.19746	−	0.604854i
$837$	−13.0194			−0.450016
$838$	9.62795	+	15.6497i	0.332592	+	0.540610i
$839$	−30.9918			−1.06995			−0.534977	−	0.844867i	$-0.679680\pi$
$839$	−30.9918			−1.06995			−0.534977	+	0.844867i	$0.679680\pi$
$840$	−34.9069	−	25.3938i	−1.20440	−	0.876171i
$841$	25.4470			0.877482
$842$	15.1288	+	24.5910i	0.521372	+	0.847462i
$843$	17.0352			0.586724
$844$	8.55479	−	16.9363i	0.294468	−	0.582972i
$845$	−5.16101	+	24.5455i	−0.177544	+	0.844390i
$846$	−18.7451	−	30.4691i	−0.644469	−	1.04755i
$847$	−4.51890	−	2.50096i	−0.155271	−	0.0859341i
$848$	−14.9912	−	20.3321i	−0.514799	−	0.698207i
$849$	−67.1205			−2.30357
$850$	−20.2092	+	2.78702i	−0.693170	+	0.0955939i
$851$	20.7309			0.710646
$852$	−37.7541	−	19.0701i	−1.29343	−	0.653332i
$853$		−	48.4535i		−	1.65902i	−0.558495	−	0.829508i	$-0.688621\pi$
$853$		−	48.4535i		−	1.65902i	0.558495	−	0.829508i	$-0.311379\pi$
$854$	−14.2078	+	0.654705i	−0.486180	+	0.0224036i
$855$	−43.0985	−	9.06203i	−1.47394	−	0.309915i
$856$	−23.7479	+	1.99477i	−0.811686	+	0.0681799i
$857$	29.2857			1.00038			0.500190	−	0.865916i	$-0.333264\pi$
$857$	29.2857			1.00038			0.500190	+	0.865916i	$0.333264\pi$
$858$	−9.18632	−	14.9319i	−0.313616	−	0.509765i
$859$		−	48.5659i		−	1.65705i	−0.559955	−	0.828523i	$-0.689182\pi$
$859$		−	48.5659i		−	1.65705i	0.559955	−	0.828523i	$-0.310818\pi$
$860$	33.8607	−	42.3055i	1.15464	−	1.44261i
$861$	−2.00488	+	3.62254i	−0.0683260	+	0.123456i
$862$	2.62671	+	4.26957i	0.0894661	+	0.145422i
$863$	8.92660			0.303865			0.151933	−	0.988391i	$-0.451450\pi$
$863$	8.92660			0.303865			0.151933	+	0.988391i	$0.451450\pi$
$864$	−8.85960	−	3.57908i	−0.301410	−	0.121763i
$865$	−23.1771	−	4.87329i	−0.788045	−	0.165697i
$866$	29.0938	−	17.8990i	0.988649	−	0.608232i
$867$	−22.3824			−0.760147
$868$	33.7171	−	22.9476i	1.14443	−	0.778892i
$869$			37.0909i			1.25822i
$870$	−14.4744	+	5.19008i	−0.490729	+	0.175960i
$871$	−18.2684			−0.619003
$872$	34.1530	−	2.86878i	1.15657	−	0.0971492i
$873$	22.8912			0.774749
$874$	17.8106	+	28.9501i	0.602452	+	0.979253i
$875$	−26.7176	+	12.6952i	−0.903221	+	0.429175i
$876$	−26.6191	+	52.6992i	−0.899377	+	1.78054i
$877$	−3.16793			−0.106973			−0.0534867	−	0.998569i	$-0.517033\pi$
$877$	−3.16793			−0.106973			−0.0534867	+	0.998569i	$0.517033\pi$
$878$	−9.75916	+	6.00399i	−0.329356	+	0.202625i
$879$			60.8278i			2.05167i
$880$	−29.2848	+	13.3630i	−0.987191	+	0.450466i
$881$		−	17.9454i		−	0.604595i	−0.953214	−	0.302297i	$-0.902246\pi$
$881$		−	17.9454i		−	0.604595i	0.953214	−	0.302297i	$-0.0977536\pi$
$882$	32.4287	+	16.0440i	1.09193	+	0.540229i
$883$			8.46669i			0.284927i	0.989800	+	0.142463i	$0.0455023\pi$
$883$			8.46669i			0.284927i	−0.989800	+	0.142463i	$0.954498\pi$
$884$	6.87705	+	3.47370i	0.231300	+	0.116833i
$885$	−7.84817	−	1.65018i	−0.263813	−	0.0554702i
$886$	19.3407	+	31.4373i	0.649764	+	1.05616i
$887$		−	20.3807i		−	0.684317i	−0.939642	−	0.342159i	$-0.888842\pi$
$887$		−	20.3807i		−	0.684317i	0.939642	−	0.342159i	$-0.111158\pi$
$888$	−2.83886	−	33.7968i	−0.0952658	−	1.13415i
$889$	−22.3581	−	12.3740i	−0.749865	−	0.415009i
$890$	−20.9832	+	7.52393i	−0.703359	+	0.252203i
$891$	23.7776			0.796580
$892$	50.0078	+	25.2597i	1.67439	+	0.845758i
$893$	37.2987			1.24815
$894$	−0.533556	−	0.867267i	−0.0178448	−	0.0290058i
$895$	0.892334	−	4.24389i	0.0298274	−	0.141858i
$896$	29.2527	−	6.34671i	0.977263	−	0.212029i
$897$			15.3624i			0.512935i
$898$	18.0555	−	11.1080i	0.602520	−	0.370680i
$899$		−	14.5286i		−	0.484555i
$900$	−28.2205	+	23.2239i	−0.940683	+	0.774131i
$901$	18.2201			0.606998
$902$	1.61782	+	2.62967i	0.0538674	+	0.0875586i
$903$	−40.0456	+	72.3569i	−1.33263	+	2.40789i
$904$	29.1194	−	2.44597i	0.968496	−	0.0813516i
$905$	5.51880	−	26.2471i	0.183451	−	0.872483i
$906$	9.08713	+	14.7706i	0.301900	+	0.490722i
$907$			21.3838i			0.710037i	0.934859	+	0.355018i	$0.115525\pi$
$907$			21.3838i			0.710037i	−0.934859	+	0.355018i	$0.884475\pi$
$908$	1.67173	−	3.30960i	0.0554782	−	0.109833i
$909$	17.6539			0.585543
$910$	11.0267	+	1.79302i	0.365532	+	0.0594380i
$911$			26.8804i			0.890586i	0.895385	+	0.445293i	$0.146901\pi$
$911$			26.8804i			0.890586i	−0.895385	+	0.445293i	$0.853099\pi$
$912$	44.7573	−	33.0003i	1.48206	−	1.09275i
$913$	−48.8497			−1.61669
$914$	−28.7581	−	46.7447i	−0.951233	−	1.54618i
$915$	−4.51174	+	21.4576i	−0.149154	+	0.709366i
$916$	−18.2561	+	36.1424i	−0.603198	+	1.19418i
$917$	−25.9986	+	46.9760i	−0.858551	+	1.55128i
$918$	5.86995	−	3.61129i	0.193737	−	0.119190i
$919$			6.12542i			0.202059i	0.994883	+	0.101029i	$0.0322136\pi$
$919$			6.12542i			0.202059i	−0.994883	+	0.101029i	$0.967786\pi$
$920$	27.9925	+	3.47313i	0.922884	+	0.114506i
$921$	21.5399			0.709764
$922$	−33.8000	+	20.7943i	−1.11314	+	0.684823i
$923$	10.9465			0.360309
$924$	40.6129	−	27.6408i	1.33607	−	0.909315i
$925$	−21.2733	−	9.35977i	−0.699460	−	0.307747i
$926$	11.3755	−	6.99839i	0.373822	−	0.229981i
$927$			49.1573i			1.61454i
$928$	3.99396	−	9.88660i	0.131108	−	0.324543i
$929$		−	31.3815i		−	1.02959i	−0.857312	−	0.514796i	$-0.827867\pi$
$929$		−	31.3815i		−	1.02959i	0.857312	−	0.514796i	$-0.172133\pi$
$930$	−21.2226	−	59.1870i	−0.695918	−	1.94082i
$931$	−31.9645	+	20.0325i	−1.04760	+	0.656538i
$932$	−4.20920	−	2.12613i	−0.137877	−	0.0696438i
$933$	−9.78585			−0.320374
$934$	−23.0837	+	14.2015i	−0.755323	+	0.464686i
$935$	4.77727	−	22.7204i	0.156233	−	0.743037i
$936$	13.7545	−	1.15535i	0.449579	−	0.0377637i
$937$	8.37400			0.273567			0.136783	−	0.990601i	$-0.456324\pi$
$937$	8.37400			0.273567			0.136783	+	0.990601i	$0.456324\pi$
$938$	−2.35647	−	51.1377i	−0.0769413	−	1.66971i
$939$	56.4893			1.84346
$940$	19.3417	−	24.1655i	0.630858	−	0.788193i
$941$	−43.1607			−1.40700			−0.703499	−	0.710696i	$-0.748380\pi$
$941$	−43.1607			−1.40700			−0.703499	+	0.710696i	$0.748380\pi$
$942$	−5.68177	−	9.23541i	−0.185122	−	0.300906i
$943$		−	2.70550i		−	0.0881030i
$944$	4.47608	−	3.30029i	0.145684	−	0.107415i
$945$	6.53449	−	7.56058i	0.212567	−	0.245946i
$946$	32.3144	+	52.5254i	1.05063	+	1.70775i
$947$			25.4973i			0.828550i	0.910152	+	0.414275i	$0.135965\pi$
$947$			25.4973i			0.828550i	−0.910152	+	0.414275i	$0.864035\pi$
$948$	−47.4622	−	23.9739i	−1.54150	−	0.778636i
$949$		−	15.2798i		−	0.496002i
$950$	−5.20588	−	37.7488i	−0.168901	−	1.22473i
$951$	68.0745			2.20747
$952$	−8.83665	+	19.6986i	−0.286397	+	0.638435i
$953$			29.6337i			0.959929i	0.877288	+	0.479964i	$0.159350\pi$
$953$			29.6337i			0.959929i	−0.877288	+	0.479964i	$0.840650\pi$
$954$	27.8016	−	17.1040i	0.900110	−	0.553762i
$955$	−22.5522	−	4.74189i	−0.729771	−	0.153444i
$956$	−9.54572	−	4.82169i	−0.308731	−	0.155944i
$957$		−	17.4999i		−	0.565692i
$958$	23.9214	−	14.7168i	0.772865	−	0.475479i
$959$	−15.6719	+	28.3169i	−0.506071	+	0.914401i
$960$	1.82887	−	46.1106i	0.0590266	−	1.48821i
$961$	28.4085			0.916403
$962$	4.59932	+	7.47595i	0.148288	+	0.241034i
$963$		−	30.7942i		−	0.992328i
$964$	−17.3187	−	8.74794i	−0.557798	−	0.281752i
$965$	17.4481	+	3.66870i	0.561675	+	0.118100i
$966$	−43.0030	+	1.98161i	−1.38360	+	0.0637573i
$967$	−5.90310			−0.189831			−0.0949154	−	0.995485i	$-0.530258\pi$
$967$	−5.90310			−0.189831			−0.0949154	+	0.995485i	$0.530258\pi$
$968$	−0.462159	−	5.50204i	−0.0148544	−	0.176842i
$969$			40.1080i			1.28846i
$970$	6.68520	+	18.6441i	0.214649	+	0.598626i
$971$			9.06341i			0.290859i	0.989369	+	0.145429i	$0.0464563\pi$
$971$			9.06341i			0.290859i	−0.989369	+	0.145429i	$0.953544\pi$
$972$	−19.9382	+	39.4726i	−0.639517	+	1.26608i
$973$	0.226843	−	0.409874i	0.00727225	−	0.0131400i
$974$	3.12637	−	1.92339i	0.100175	−	0.0616295i
$975$	6.93595	−	15.7643i	0.222128	−	0.504862i
$976$	−9.02327	−	12.2380i	−0.288828	−	0.391729i
$977$		−	20.7277i		−	0.663138i	−0.943431	−	0.331569i	$-0.892422\pi$
$977$		−	20.7277i		−	0.663138i	0.943431	−	0.331569i	$-0.107578\pi$
$978$	16.1070	+	26.1810i	0.515045	+	0.837177i
$979$		−	25.3692i		−	0.810804i
$980$	−3.59674	+	31.0976i	−0.114894	+	0.993378i
$981$			44.2867i			1.41396i
$982$	20.0092	−	12.3100i	0.638518	−	0.392827i
$983$		−	1.55484i		−	0.0495916i	−0.999693	−	0.0247958i	$-0.992106\pi$
$983$		−	1.55484i		−	0.0495916i	0.999693	−	0.0247958i	$-0.00789356\pi$
$984$	−4.41066	+	0.370486i	−0.140607	+	0.0118107i
$985$	4.21457	−	20.0443i	0.134287	−	0.638663i
$986$	4.02990	+	6.55039i	0.128338	+	0.208607i
$987$	−22.8746	+	41.3313i	−0.728107	+	1.31559i
$988$	−6.48854	+	12.8457i	−0.206428	+	0.408675i
$989$		−	54.0398i		−	1.71837i
$990$	−14.0391	−	39.1532i	−0.446193	−	1.24437i
$991$		−	48.1236i		−	1.52870i	−0.644804	−	0.764348i	$-0.723061\pi$
$991$		−	48.1236i		−	1.52870i	0.644804	−	0.764348i	$-0.276939\pi$
$992$	40.4271	+	16.3316i	1.28356	+	0.518529i
$993$	−19.3863			−0.615205
$994$	1.41200	+	30.6419i	0.0447860	+	0.971904i
$995$	8.33915	−	39.6605i	0.264369	−	1.25732i
$996$	31.5742	−	62.5090i	1.00047	−	1.98067i
$997$		−	19.4339i		−	0.615479i	−0.951471	−	0.307739i	$-0.900428\pi$
$997$		−	19.4339i		−	0.615479i	0.951471	−	0.307739i	$-0.0995725\pi$
$998$	15.4218	−	9.48775i	0.488169	−	0.300329i
$999$	7.85156			0.248412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.n.b.139.34	yes	40
4.3	odd	2		1120.2.n.b.559.6		40
5.4	even	2	inner	280.2.n.b.139.7	yes	40
7.6	odd	2	inner	280.2.n.b.139.33	yes	40
8.3	odd	2	inner	280.2.n.b.139.6	yes	40
8.5	even	2		1120.2.n.b.559.5		40
20.19	odd	2		1120.2.n.b.559.33		40
28.27	even	2		1120.2.n.b.559.35		40
35.34	odd	2	inner	280.2.n.b.139.8	yes	40
40.19	odd	2	inner	280.2.n.b.139.35	yes	40
40.29	even	2		1120.2.n.b.559.34		40
56.13	odd	2		1120.2.n.b.559.36		40
56.27	even	2	inner	280.2.n.b.139.5	✓	40
140.139	even	2		1120.2.n.b.559.8		40
280.69	odd	2		1120.2.n.b.559.7		40
280.139	even	2	inner	280.2.n.b.139.36	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.n.b.139.5	✓	40	56.27	even	2	inner
280.2.n.b.139.6	yes	40	8.3	odd	2	inner
280.2.n.b.139.7	yes	40	5.4	even	2	inner
280.2.n.b.139.8	yes	40	35.34	odd	2	inner
280.2.n.b.139.33	yes	40	7.6	odd	2	inner
280.2.n.b.139.34	yes	40	1.1	even	1	trivial
280.2.n.b.139.35	yes	40	40.19	odd	2	inner
280.2.n.b.139.36	yes	40	280.139	even	2	inner
1120.2.n.b.559.5		40	8.5	even	2
1120.2.n.b.559.6		40	4.3	odd	2
1120.2.n.b.559.7		40	280.69	odd	2
1120.2.n.b.559.8		40	140.139	even	2
1120.2.n.b.559.33		40	20.19	odd	2
1120.2.n.b.559.34		40	40.29	even	2
1120.2.n.b.559.35		40	28.27	even	2
1120.2.n.b.559.36		40	56.13	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20452 - 0.741038i) q^{2} +2.57969 q^{3} +(0.901725 - 1.78519i) q^{4} +(-0.460102 + 2.18822i) q^{5} +(3.10728 - 1.91165i) q^{6} +(-2.31487 - 1.28116i) q^{7} +(-0.236748 - 2.81850i) q^{8} +3.65479 q^{9} +(1.06735 + 2.97670i) q^{10} -3.59890 q^{11} +(2.32617 - 4.60522i) q^{12} +1.33525i q^{13} +(-3.73769 + 0.172236i) q^{14} +(-1.18692 + 5.64492i) q^{15} +(-2.37378 - 3.21949i) q^{16} +2.88506 q^{17} +(4.40225 - 2.70834i) q^{18} +5.38901i q^{19} +(3.49150 + 2.79454i) q^{20} +(-5.97165 - 3.30498i) q^{21} +(-4.33494 + 2.66693i) q^{22} +4.45993 q^{23} +(-0.610736 - 7.27085i) q^{24} +(-4.57661 - 2.01361i) q^{25} +(0.989473 + 1.60834i) q^{26} +1.68914 q^{27} +(-4.37448 + 2.97723i) q^{28} +1.88494i q^{29} +(2.75344 + 7.67896i) q^{30} -7.70769 q^{31} +(-5.24503 - 2.11887i) q^{32} -9.28405 q^{33} +(3.47511 - 2.13794i) q^{34} +(3.86853 - 4.47599i) q^{35} +(3.29561 - 6.52448i) q^{36} +4.64826 q^{37} +(3.99346 + 6.49116i) q^{38} +3.44453i q^{39} +(6.27643 + 0.778741i) q^{40} -0.606622i q^{41} +(-9.64207 + 0.444314i) q^{42} -12.1167i q^{43} +(-3.24522 + 6.42472i) q^{44} +(-1.68157 + 7.99747i) q^{45} +(5.37207 - 3.30498i) q^{46} -6.92126i q^{47} +(-6.12362 - 8.30529i) q^{48} +(3.71728 + 5.93143i) q^{49} +(-7.00477 + 0.966017i) q^{50} +7.44256 q^{51} +(2.38368 + 1.20403i) q^{52} +6.31531 q^{53} +(2.03460 - 1.25172i) q^{54} +(1.65586 - 7.87519i) q^{55} +(-3.06290 + 6.82779i) q^{56} +13.9020i q^{57} +(1.39682 + 2.27045i) q^{58} +1.39031i q^{59} +(9.00697 + 7.20904i) q^{60} +3.80122 q^{61} +(-9.28405 + 5.71169i) q^{62} +(-8.46037 - 4.68235i) q^{63} +(-7.88790 + 1.33455i) q^{64} +(-2.92183 - 0.614353i) q^{65} +(-11.1828 + 6.87983i) q^{66} +13.6816i q^{67} +(2.60153 - 5.15038i) q^{68} +11.5052 q^{69} +(1.34283 - 8.25814i) q^{70} -8.19810i q^{71} +(-0.865264 - 10.3010i) q^{72} -11.4433 q^{73} +(5.59890 - 3.44453i) q^{74} +(-11.8062 - 5.19448i) q^{75} +(9.62040 + 4.85941i) q^{76} +(8.33101 + 4.61076i) q^{77} +(2.55253 + 4.14900i) q^{78} -10.3062i q^{79} +(8.13715 - 3.71307i) q^{80} -6.60690 q^{81} +(-0.449530 - 0.730687i) q^{82} +13.5735 q^{83} +(-11.2848 + 7.68033i) q^{84} +(-1.32742 + 6.31315i) q^{85} +(-8.97897 - 14.5948i) q^{86} +4.86257i q^{87} +(0.852034 + 10.1435i) q^{88} +7.04915i q^{89} +(3.90095 + 10.8792i) q^{90} +(1.71067 - 3.09094i) q^{91} +(4.02163 - 7.96181i) q^{92} -19.8834 q^{93} +(-5.12891 - 8.33677i) q^{94} +(-11.7923 - 2.47950i) q^{95} +(-13.5305 - 5.46603i) q^{96} +6.26335 q^{97} +(8.87294 + 4.38986i) q^{98} -13.1532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65}+ \cdots - 128 q^{99}+O(q^{100}) \) 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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