LMFDB - Embedded newform 280.2.n.b.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(139,280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			139.6
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20452 - 0.741038i) q^{2} +2.57969 q^{3} +(0.901725 + 1.78519i) q^{4} +(0.460102 - 2.18822i) q^{5} +(-3.10728 - 1.91165i) q^{6} +(2.31487 + 1.28116i) q^{7} +(0.236748 - 2.81850i) q^{8} +3.65479 q^{9} +O(q^{10})$	\(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} +(-2.17576 + 2.29480i) q^{10} -3.59890 q^{11} +(2.32617 + 4.60522i) q^{12} -1.33525i q^{13} +(-1.83892 - 3.25858i) 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} +(4.32127 - 1.15180i) 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} +(-0.199723 + 5.28773i) q^{28} -1.88494i q^{29} +(-5.61277 + 5.91986i) 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} +(-6.05857 - 1.81486i) q^{40} -0.606622i q^{41} +(-4.74384 - 8.40613i) 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} +(4.02045 + 5.81687i) 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} +(4.15898 - 6.22116i) q^{56} +13.9020i q^{57} +(-1.39682 + 2.27045i) q^{58} +1.39031i q^{59} +(11.1475 - 2.97129i) 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} +(-7.97659 + 2.52468i) 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} +(5.95278 + 6.67566i) q^{80} -6.60690 q^{81} +(-0.449530 + 0.730687i) q^{82} +13.5735 q^{83} +(-0.515222 + 13.6407i) 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} +(-7.95192 + 8.38699i) 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} +(-0.0821172 - 9.89915i) q^{98} -13.1532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 12 * q^4 + 40 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$10$	−2.17576	+	2.29480i	−0.688034	+	0.725678i
$11$	−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	$-0.940718\pi$
$13$		−	1.33525i		−	0.370332i	0.982707	−	0.185166i	$-0.0592824\pi$
$14$	−1.83892	−	3.25858i	−0.491472	−	0.870893i
$15$	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	$0.787877\pi$
$20$	4.32127	−	1.15180i	0.966265	−	0.257551i
$21$	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	$-0.653939\pi$
$23$	−4.45993			−0.929960			−0.464980	+	0.885321i	$0.653939\pi$
$24$	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
$28$	−0.199723	+	5.28773i	−0.0377440	+	0.999287i
$29$		−	1.88494i		−	0.350025i	−0.984566	−	0.175013i	$-0.944003\pi$
$29$		−	1.88494i		−	0.350025i	0.984566	−	0.175013i	$-0.0559967\pi$
$30$	−5.61277	+	5.91986i	−1.02475	+	1.08081i
$31$	7.70769			1.38434			0.692171	−	0.721734i	$-0.256654\pi$
$31$	7.70769			1.38434			0.692171	+	0.721734i	$0.256654\pi$
$32$	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	$-0.624794\pi$
$37$	−4.64826			−0.764168			−0.382084	+	0.924128i	$0.624794\pi$
$38$	3.99346	−	6.49116i	0.647825	−	1.05301i
$39$		−	3.44453i		−	0.551567i
$40$	−6.05857	−	1.81486i	−0.957944	−	0.286954i
$41$		−	0.606622i		−	0.0947385i	−0.998877	−	0.0473693i	$-0.984916\pi$
$41$		−	0.606622i		−	0.0947385i	0.998877	−	0.0473693i	$-0.0150837\pi$
$42$	−4.74384	−	8.40613i	−0.731991	−	1.29709i
$43$		−	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	$0.168428\pi$
$47$			6.92126i			1.00957i	−0.863245	+	0.504784i	$0.831572\pi$
$48$	−6.12362	+	8.30529i	−0.883869	+	1.19877i
$49$	3.71728	+	5.93143i	0.531040	+	0.847347i
$50$	4.02045	+	5.81687i	0.568577	+	0.822630i
$51$	7.44256			1.04217
$52$	2.38368	−	1.20403i	0.330556	−	0.166969i
$53$	−6.31531			−0.867474			−0.433737	−	0.901039i	$-0.642805\pi$
$53$	−6.31531			−0.867474			−0.433737	+	0.901039i	$0.642805\pi$
$54$	−2.03460	−	1.25172i	−0.276874	−	0.170337i
$55$	−1.65586	+	7.87519i	−0.223277	+	1.06189i
$56$	4.15898	−	6.22116i	0.555767	−	0.831338i
$57$			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	$0.971153\pi$
$60$	11.1475	−	2.97129i	1.43914	−	0.383592i
$61$	−3.80122			−0.486696			−0.243348	−	0.969939i	$-0.578246\pi$
$61$	−3.80122			−0.486696			−0.243348	+	0.969939i	$0.578246\pi$
$62$	−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
$70$	−7.97659	+	2.52468i	−0.953385	+	0.301757i
$71$			8.19810i			0.972935i	0.873699	+	0.486467i	$0.161715\pi$
$71$			8.19810i			0.972935i	−0.873699	+	0.486467i	$0.838285\pi$
$72$	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	$0.196857\pi$
$79$			10.3062i			1.15954i	−0.814782	+	0.579768i	$0.803143\pi$
$80$	5.95278	+	6.67566i	0.665541	+	0.746361i
$81$	−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	$0.232477\pi$
$84$	−0.515222	+	13.6407i	−0.0562153	+	1.48832i
$85$	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	$0.878122\pi$
$90$	−7.95192	+	8.38699i	−0.838206	+	0.884066i
$91$	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	$0.396998\pi$
$98$	−0.0821172	−	9.89915i	−0.00829509	−	0.999966i
$99$	−13.1532			−1.32195
$100$	−0.532176	−	9.98583i	−0.0532176	−	0.998583i
$101$	−4.83035			−0.480638			−0.240319	−	0.970694i	$-0.577252\pi$
$101$	−4.83035			−0.480638			−0.240319	+	0.970694i	$0.577252\pi$
$102$	−8.96469	−	5.51522i	−0.887637	−	0.546088i
$103$		−	13.4501i		−	1.32528i	−0.748938	−	0.662640i	$-0.769436\pi$
$103$		−	13.4501i		−	1.32528i	0.748938	−	0.662640i	$-0.230564\pi$
$104$	−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	$-0.802927\pi$
$109$		−	12.1174i		−	1.16064i	0.814388	−	0.580320i	$-0.197073\pi$
$110$	7.83034	−	8.25875i	0.746593	−	0.787441i
$111$	−11.9910			−1.13814
$112$	−9.61968	+	4.41154i	−0.908975	+	0.416851i
$113$			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
$120$	−15.6292	−	4.68176i	−1.42675	−	0.427384i
$121$	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
$126$	−6.72086	−	11.9094i	−0.598742	−	1.06098i
$127$	−9.65843			−0.857047			−0.428524	−	0.903531i	$-0.640966\pi$
$127$	−9.65843			−0.857047			−0.428524	+	0.903531i	$0.640966\pi$
$128$	8.51216	+	7.45272i	0.752376	+	0.658734i
$129$		−	31.2574i		−	2.75206i
$130$	3.06413	+	2.90518i	0.268742	+	0.254801i
$131$		−	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	$0.997610\pi$
$140$	11.4788	+	2.86993i	0.970138	+	0.242554i
$141$			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	$0.00363923\pi$
$149$			0.279108i			0.0228654i	−0.999935	+	0.0114327i	$0.996361\pi$
$150$	10.3715	+	15.0057i	0.846829	+	1.22521i
$151$		−	4.75356i		−	0.386839i	−0.981116	−	0.193420i	$-0.938042\pi$
$151$		−	4.75356i		−	0.386839i	0.981116	−	0.193420i	$-0.0619579\pi$
$152$	15.1889	+	1.27584i	1.23199	+	0.103484i
$153$	10.5443			0.852455
$154$	6.61810	+	11.7273i	0.533302	+	0.945015i
$155$	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	$0.0378416\pi$
$157$			2.97219i			0.237206i	−0.992942	+	0.118603i	$0.962158\pi$
$158$	7.63727	−	12.4140i	0.607588	−	0.987602i
$159$	−16.2915			−1.29200
$160$	−2.22331	−	12.4522i	−0.175768	−	0.984432i
$161$	−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	$0.174218\pi$
$167$			13.4501i			1.04080i	−0.853922	+	0.520401i	$0.825782\pi$
$168$	10.7289	−	16.0487i	0.827750	−	1.23818i
$169$	11.2171			0.862854
$170$	−6.27719	+	6.62063i	−0.481438	+	0.507779i
$171$			19.6957i			1.50617i
$172$	21.6306	−	10.9260i	1.64932	−	0.833097i
$173$		−	10.5918i		−	0.805276i	−0.915359	−	0.402638i	$-0.868093\pi$
$173$		−	10.5918i		−	0.805276i	0.915359	−	0.402638i	$-0.131907\pi$
$174$	−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	$0.523091\pi$
$180$	15.7933	−	4.20960i	1.17716	−	0.313765i
$181$	11.9947			0.891561			0.445780	−	0.895142i	$-0.352926\pi$
$181$	11.9947			0.891561			0.445780	+	0.895142i	$0.352926\pi$
$182$	−4.35103	+	2.45542i	−0.322520	+	0.182008i
$183$	−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
$190$	−12.3667	−	11.7252i	−0.897174	−	0.850634i
$191$		−	10.3062i		−	0.745729i	−0.927886	−	0.372864i	$-0.878376\pi$
$191$		−	10.3062i		−	0.745729i	0.927886	−	0.372864i	$-0.121624\pi$
$192$	−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
$196$	−7.23674	+	11.9846i	−0.516910	+	0.856040i
$197$	9.16007			0.652628			0.326314	−	0.945261i	$-0.394193\pi$
$197$	9.16007			0.652628			0.326314	+	0.945261i	$0.394193\pi$
$198$	15.8433	+	9.74704i	1.12593	+	0.692692i
$199$	18.1246			1.28482			0.642408	−	0.766362i	$-0.277935\pi$
$199$	18.1246			1.28482			0.642408	+	0.766362i	$0.277935\pi$
$200$	−6.75886	+	12.4225i	−0.477924	+	0.878401i
$201$			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
$210$	−20.5771	+	6.51289i	−1.41996	+	0.449432i
$211$	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
$220$	−15.5518	+	4.14523i	−1.04850	+	0.279472i
$221$		−	3.85229i		−	0.259133i
$222$	14.4434	+	8.88582i	0.969379	+	0.596377i
$223$		−	28.0127i		−	1.87587i	−0.346816	−	0.937933i	$-0.612737\pi$
$223$		−	28.0127i		−	1.87587i	0.346816	−	0.937933i	$-0.387263\pi$
$224$	14.8562	+	1.81478i	0.992621	+	0.121255i
$225$	−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	$-0.266749\pi$
$229$	20.2457			1.33788			0.668938	+	0.743318i	$0.266749\pi$
$230$	9.70372	−	10.2346i	0.639845	−	0.674852i
$231$	−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
$238$	−5.30540	−	9.40122i	−0.343898	−	0.609390i
$239$			5.34718i			0.345880i	0.984932	+	0.172940i	$0.0553267\pi$
$239$			5.34718i			0.345880i	−0.984932	+	0.172940i	$0.944673\pi$
$240$	15.3563	+	17.2211i	0.991245	+	1.11162i
$241$		−	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
$250$	14.5784	−	6.12127i	0.922020	−	0.387143i
$251$			14.7270i			0.929563i	0.885425	+	0.464782i	$0.153867\pi$
$251$			14.7270i			0.929563i	−0.885425	+	0.464782i	$0.846133\pi$
$252$	−0.729943	+	19.3255i	−0.0459821	+	1.21739i
$253$	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
$260$	−1.53795	−	5.76998i	−0.0953796	−	0.357839i
$261$		−	6.88907i		−	0.426423i
$262$	−15.0380	+	24.4434i	−0.929049	+	1.51012i
$263$	14.2659			0.879672			0.439836	−	0.898078i	$-0.355037\pi$
$263$	14.2659			0.879672			0.439836	+	0.898078i	$0.355037\pi$
$264$	−2.19798	+	26.1671i	−0.135276	+	1.61047i
$265$	−2.90569	+	13.8193i	−0.178495	+	0.848912i
$266$	17.5606	−	9.90997i	1.07671	−	0.607619i
$267$			18.1846i			1.11288i
$268$	−24.4243	+	12.3371i	−1.49195	+	0.753607i
$269$	−19.6473			−1.19792			−0.598959	−	0.800780i	$-0.704419\pi$
$269$	−19.6473			−1.19792			−0.598959	+	0.800780i	$0.704419\pi$
$270$	−3.67516	+	3.87624i	−0.223663	+	0.235900i
$271$	21.4339			1.30202			0.651008	−	0.759071i	$-0.274346\pi$
$271$	21.4339			1.30202			0.651008	+	0.759071i	$0.274346\pi$
$272$	−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	$-0.290957\pi$
$277$	20.3225			1.22106			0.610530	+	0.791993i	$0.290957\pi$
$278$	0.131209	−	0.213273i	0.00786940	−	0.0127913i
$279$	28.1700			1.68649
$280$	−11.6997	−	11.9631i	−0.699192	−	0.714934i
$281$	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
$290$	4.32556	+	4.10118i	0.254006	+	0.240830i
$291$	16.1575			0.947168
$292$	−10.3187	−	20.4285i	−0.603859	−	1.19549i
$293$		−	23.5795i		−	1.37753i	−0.724984	−	0.688765i	$-0.758153\pi$
$293$		−	23.5795i		−	1.37753i	0.724984	−	0.688765i	$-0.241847\pi$
$294$	−0.211837	−	25.5367i	−0.0123546	−	1.48933i
$295$	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
$300$	−1.37285	−	25.7603i	−0.0792614	−	1.48727i
$301$	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	$0.423418\pi$
$308$	0.718783	−	19.0300i	0.0409564	−	1.08434i
$309$		−	34.6971i		−	1.97385i
$310$	−16.7700	+	17.6876i	−0.952475	+	1.00459i
$311$	3.79343			0.215105			0.107553	−	0.994199i	$-0.465699\pi$
$311$	3.79343			0.215105			0.107553	+	0.994199i	$0.465699\pi$
$312$	−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	$-0.765680\pi$
$317$	−26.3887			−1.48213			−0.741067	+	0.671431i	$0.765680\pi$
$318$	19.6234	+	12.0726i	1.10043	+	0.677000i
$319$			6.78374i			0.379816i
$320$	−6.54953	+	16.6464i	−0.366130	+	0.930564i
$321$		−	21.7357i		−	1.21317i
$322$	8.20146	+	14.5331i	0.457050	+	0.809896i
$323$			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
$330$	20.1998	−	21.3050i	1.11196	−	1.17280i
$331$	−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
$336$	−24.8158	+	11.3804i	−1.35381	+	0.620851i
$337$			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
$340$	12.4671	−	3.32303i	0.676125	−	0.180216i
$341$	−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	$-0.446056\pi$
$349$	6.30167			0.337321			0.168660	+	0.985674i	$0.446056\pi$
$350$	1.85451	+	18.6161i	0.0991279	+	0.995075i
$351$		−	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	$0.0670487\pi$
$359$			7.92321i			0.418171i	−0.977897	+	0.209086i	$0.932951\pi$
$360$	−22.1428	−	6.63291i	−1.16703	−	0.349585i
$361$	−10.0415			−0.528498
$362$	−14.4479	−	8.88855i	−0.759362	−	0.467172i
$363$	5.03584			0.264313
$364$	7.06046	+	0.266680i	0.370069	+	0.0139778i
$365$	−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	$-0.863031\pi$
$367$		−	15.9826i		−	0.834287i	0.908841	−	0.417143i	$-0.136969\pi$
$368$	10.5869	−	14.3587i	0.551881	−	0.748501i
$369$		−	2.21707i		−	0.115416i
$370$	10.1135	−	10.6668i	0.525774	−	0.554540i
$371$	−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	$-0.682314\pi$
$373$	−20.9336			−1.08390			−0.541951	+	0.840410i	$0.682314\pi$
$374$	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
$378$	−3.10620	−	5.50421i	−0.159766	−	0.283106i
$379$	13.1532			0.675636			0.337818	−	0.941211i	$-0.390311\pi$
$379$	13.1532			0.675636			0.337818	+	0.941211i	$0.390311\pi$
$380$	6.20709	+	23.2874i	0.318417	+	1.19462i
$381$	−24.9157			−1.27647
$382$	−7.63727	+	12.4140i	−0.390757	+	0.635154i
$383$			22.4872i			1.14904i	0.818490	+	0.574521i	$0.194812\pi$
$383$			22.4872i			1.14904i	−0.818490	+	0.574521i	$0.805188\pi$
$384$	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	$-0.938375\pi$
$389$		−	7.58914i		−	0.384785i	0.981318	−	0.192392i	$-0.0616246\pi$
$390$	7.90450	+	7.49446i	0.400260	+	0.379497i
$391$	−12.8672			−0.650721
$392$	17.5978	−	9.07291i	0.888823	−	0.458251i
$393$		−	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	$0.0338992\pi$
$397$			4.23587i			0.212592i	−0.994335	+	0.106296i	$0.966101\pi$
$398$	−21.8314	−	13.4310i	−1.09431	−	0.673235i
$399$	−17.8106	+	32.1813i	−0.891644	+	1.61108i
$400$	17.3467	−	9.95451i	0.867335	−	0.497725i
$401$	−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
$406$	−6.14225	+	3.46626i	−0.304835	+	0.172028i
$407$	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	$-0.0304664\pi$
$410$	1.39207	+	1.31986i	0.0687497	+	0.0651833i
$411$		−	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	$0.897203\pi$
$420$	29.6118	+	7.40353i	1.44491	+	0.361255i
$421$		−	20.4156i		−	0.994997i	−0.867465	−	0.497499i	$-0.834252\pi$
$421$		−	20.4156i		−	0.994997i	0.867465	−	0.497499i	$-0.165748\pi$
$422$	−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
$430$	27.8054	+	26.3631i	1.34090	+	1.27134i
$431$		−	3.54463i		−	0.170739i	−0.996349	−	0.0853695i	$-0.972793\pi$
$431$		−	3.54463i		−	0.170739i	0.996349	−	0.0853695i	$-0.0272071\pi$
$432$	−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	$0.302903\pi$
$434$	−14.1738	−	25.1162i	−0.680366	−	1.20561i
$435$	−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	$-0.438066\pi$
$439$	8.10213			0.386694			0.193347	+	0.981130i	$0.438066\pi$
$440$	21.8042	+	6.53149i	1.03948	+	0.311377i
$441$	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
$448$	−16.5497	−	13.1949i	−0.781901	−	0.623402i
$449$	14.9898			0.707414			0.353707	−	0.935356i	$-0.384921\pi$
$449$	14.9898			0.707414			0.353707	+	0.935356i	$0.384921\pi$
$450$	14.6939	+	21.2594i	0.692676	+	1.00218i
$451$			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
$460$	−19.2726	+	5.13697i	−0.898588	+	0.239512i
$461$	28.0610			1.30693			0.653466	−	0.756956i	$-0.273314\pi$
$461$	28.0610			1.30693			0.653466	+	0.756956i	$0.273314\pi$
$462$	17.0726	+	30.2528i	0.794291	+	1.40749i
$463$	−9.44403			−0.438901			−0.219451	−	0.975624i	$-0.570427\pi$
$463$	−9.44403			−0.438901			−0.219451	+	0.975624i	$0.570427\pi$
$464$	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
$470$	−15.8829	−	15.0590i	−0.732622	−	0.694618i
$471$			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
$476$	−0.576212	+	15.2554i	−0.0264106	+	0.699232i
$477$	−23.0811			−1.05681
$478$	3.96247	−	6.44077i	0.181239	−	0.294594i
$479$	−19.8597			−0.907414			−0.453707	−	0.891151i	$-0.649899\pi$
$479$	−19.8597			−0.907414			−0.453707	+	0.891151i	$0.649899\pi$
$480$	−5.73544	−	32.1227i	−0.261786	−	1.46620i
$481$			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	$-0.518730\pi$
$487$	−2.59554			−0.117615			−0.0588075	+	0.998269i	$0.518730\pi$
$488$	−0.899932	+	10.7137i	−0.0407380	+	0.484988i
$489$			21.7357i			0.982922i
$490$	−21.6993	−	4.37493i	−0.980275	−	0.197639i
$491$	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	$0.407482\pi$
$500$	−22.0960	−	3.42998i	−0.988165	−	0.153393i
$501$			34.6971i			1.55015i
$502$	10.9133	−	17.7390i	0.487085	−	0.791730i
$503$			7.66175i			0.341621i	0.985304	+	0.170810i	$0.0546385\pi$
$503$			7.66175i			0.341621i	−0.985304	+	0.170810i	$0.945361\pi$
$504$	15.2002	−	22.7370i	0.677070	−	1.01279i
$505$	−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	$-0.558934\pi$
$509$	−8.30655			−0.368181			−0.184091	+	0.982909i	$0.558934\pi$
$510$	−16.1932	+	17.0792i	−0.717046	+	0.756278i
$511$	−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
$518$	8.54777	+	15.1467i	0.375568	+	0.665509i
$519$		−	27.3234i		−	1.19936i
$520$	−2.42329	+	8.08973i	−0.106268	+	0.354758i
$521$		−	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
$530$	13.7406	−	14.4923i	0.596852	−	0.629507i
$531$			5.08127i			0.220508i
$532$	−28.4957	−	1.07631i	−1.23544	−	0.0466639i
$533$	−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
$540$	7.29923	−	1.94556i	0.314109	−	0.0837236i
$541$			23.9613i			1.03018i	0.857137	+	0.515088i	$0.172241\pi$
$541$			23.9613i			1.03018i	−0.857137	+	0.515088i	$0.827759\pi$
$542$	−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
$546$	−11.2243	+	6.33423i	−0.480356	+	0.271080i
$547$			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
$550$	−14.4692	−	20.9344i	−0.616969	−	0.892644i
$551$	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	$-0.556752\pi$
$557$	−8.37113			−0.354696			−0.177348	+	0.984148i	$0.556752\pi$
$558$	−33.9312	−	20.8750i	−1.43642	−	0.883710i
$559$	−16.1789			−0.684295
$560$	5.22738	+	23.0797i	0.220897	+	0.975297i
$561$	−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	$0.273234\pi$
$570$	−31.9022	−	30.2473i	−1.33624	−	1.26692i
$571$	−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
$574$	−1.97673	+	1.11553i	−0.0825071	+	0.0465614i
$575$	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
$580$	−2.17109	−	8.14535i	−0.0901495	−	0.338217i
$581$	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	$0.597689\pi$
$588$	−18.6685	+	30.9164i	−0.769877	+	1.27497i
$589$			41.5368i			1.71150i
$590$	−3.19047	−	3.02497i	−0.131350	−	0.124536i
$591$	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	$-0.551115\pi$
$599$		−	48.3192i		−	1.97427i	0.159893	−	0.987134i	$-0.448885\pi$
$600$	−17.4358	+	32.0461i	−0.711812	+	1.30828i
$601$		−	7.63740i		−	0.311536i	−0.987794	−	0.155768i	$-0.950215\pi$
$601$		−	7.63740i		−	0.311536i	0.987794	−	0.155768i	$-0.0497852\pi$
$602$	−39.4834	+	22.2817i	−1.60922	+	0.908135i
$603$			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	$0.283007\pi$
$607$			38.2619i			1.55300i	−0.630116	+	0.776501i	$0.716993\pi$
$608$	11.4186	+	28.2656i	0.463087	+	1.14632i
$609$	6.22971	−	11.2562i	0.252440	−	0.456125i
$610$	8.27052	−	8.72302i	0.334864	−	0.353185i
$611$	9.24163			0.373876
$612$	9.50804	+	18.8235i	0.384340	+	0.760896i
$613$	17.0330			0.687955			0.343977	−	0.938978i	$-0.388226\pi$
$613$	17.0330			0.687955			0.343977	+	0.938978i	$0.388226\pi$
$614$	−10.0575	−	6.18753i	−0.405887	−	0.249708i
$615$	−3.42434	−	0.720012i	−0.138083	−	0.0290337i
$616$	−14.9678	+	22.3894i	−0.603069	+	0.902094i
$617$		−	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	$0.637794\pi$
$620$	33.3070	−	8.87775i	1.33764	−	0.356539i
$621$	−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
$630$	−29.1527	+	9.22717i	−1.16147	+	0.367619i
$631$			1.44976i			0.0577141i	0.999584	+	0.0288571i	$0.00918676\pi$
$631$			1.44976i			0.0577141i	−0.999584	+	0.0288571i	$0.990813\pi$
$632$	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
$640$	20.2247	−	15.1975i	0.799450	−	0.600733i
$641$	−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	$0.636122\pi$
$644$	0.890749	−	23.5829i	0.0351004	−	0.929298i
$645$	−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	$0.316158\pi$
$647$			42.6208i			1.67560i	−0.545979	+	0.837799i	$0.683842\pi$
$648$	−1.56417	+	18.6216i	−0.0614465	+	0.731524i
$649$		−	5.00358i		−	0.196408i
$650$	7.76699	−	5.36831i	0.304647	−	0.210563i
$651$	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	$-0.564813\pi$
$653$	−10.3346			−0.404424			−0.202212	+	0.979342i	$0.564813\pi$
$654$	−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
$658$	22.5535	−	12.7276i	0.879227	−	0.496175i
$659$	−24.5798			−0.957493			−0.478746	−	0.877953i	$-0.658909\pi$
$659$	−24.5798			−0.957493			−0.478746	+	0.877953i	$0.658909\pi$
$660$	−40.1188	+	10.6934i	−1.56162	+	0.416240i
$661$	−27.2497			−1.05989			−0.529946	−	0.848031i	$-0.677788\pi$
$661$	−27.2497			−1.05989			−0.529946	+	0.848031i	$0.677788\pi$
$662$	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
$670$	−31.3966	−	29.7679i	−1.21295	−	1.15003i
$671$	13.6802			0.528119
$672$	38.3243	+	4.68156i	1.47839	+	0.180595i
$673$		−	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	$-0.997216\pi$
$677$		−	0.455107i		−	0.0174912i	0.999962	−	0.00874559i	$-0.00278384\pi$
$678$	19.7502	−	32.1029i	0.758502	−	1.23290i
$679$	14.4989	+	8.02432i	0.556415	+	0.307945i
$680$	−17.4794	−	5.23597i	−0.670303	−	0.200790i
$681$	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
$686$	12.4923	−	23.0205i	0.476957	−	0.878927i
$687$	52.2277			1.99261
$688$	39.0098	+	28.7625i	1.48723	+	1.09656i
$689$			8.43253i			0.321254i
$690$	25.0326	−	26.4022i	0.952974	−	1.00511i
$691$		−	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
$700$	11.5615	−	23.7977i	0.436983	−	0.899470i
$701$			33.6356i			1.27040i	0.772349	+	0.635199i	$0.219082\pi$
$701$			33.6356i			1.27040i	−0.772349	+	0.635199i	$0.780918\pi$
$702$	−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	$0.0859099\pi$
$709$			14.1991i			0.533258i	−0.963799	+	0.266629i	$0.914090\pi$
$710$	−18.8130	−	17.8371i	−0.706038	−	0.669413i
$711$			37.6669i			1.41262i
$712$	19.8680	+	1.66887i	0.744586	+	0.0625437i
$713$	−34.3758			−1.28738
$714$	−13.6863	−	24.2522i	−0.512196	−	0.907616i
$715$	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	$-0.730344\pi$
$719$	−35.5086			−1.32425			−0.662123	+	0.749395i	$0.730344\pi$
$720$	21.7561	+	24.3981i	0.810803	+	0.909264i
$721$	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	$-0.913759\pi$
$727$		−	14.4322i		−	0.535261i	0.963522	−	0.267630i	$-0.0862406\pi$
$728$	−8.30683	−	5.55329i	−0.307871	−	0.205819i
$729$	−37.2192			−1.37849
$730$	24.8979	−	26.2601i	0.921513	−	0.971931i
$731$		−	34.9575i		−	1.29295i
$732$	−8.84227	−	17.5055i	−0.326820	−	0.647021i
$733$			20.7489i			0.766378i	0.923670	+	0.383189i	$0.125174\pi$
$733$			20.7489i			0.766378i	−0.923670	+	0.383189i	$0.874826\pi$
$734$	−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	$0.409185\pi$
$740$	−20.0864	+	5.35388i	−0.738389	+	0.196812i
$741$	18.5626			0.681916
$742$	11.6134	+	20.5790i	0.426340	+	0.755477i
$743$	−30.8617			−1.13221			−0.566103	−	0.824334i	$-0.691550\pi$
$743$	−30.8617			−1.13221			−0.566103	+	0.824334i	$0.691550\pi$
$744$	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
$750$	37.6077	−	15.7910i	1.37324	−	0.576604i
$751$			10.9371i			0.399099i	0.979888	+	0.199550i	$0.0639479\pi$
$751$			10.9371i			0.399099i	−0.979888	+	0.199550i	$0.936052\pi$
$752$	−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
$756$	−0.337360	+	8.93173i	−0.0122697	+	0.324844i
$757$	−28.1387			−1.02272			−0.511359	−	0.859367i	$-0.670858\pi$
$757$	−28.1387			−1.02272			−0.511359	+	0.859367i	$0.670858\pi$
$758$	−15.8433	−	9.74704i	−0.575454	−	0.354028i
$759$	41.4062			1.50295
$760$	9.78028	−	32.6497i	0.354768	−	1.18433i
$761$			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	$0.953123\pi$
$770$	28.7070	−	9.08609i	1.03453	−	0.327440i
$771$	−29.0732			−1.04705
$772$	14.2345	−	7.19005i	0.512310	−	0.258776i
$773$			8.13686i			0.292662i	0.989236	+	0.146331i	$0.0467465\pi$
$773$			8.13686i			0.292662i	−0.989236	+	0.146331i	$0.953253\pi$
$774$	−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
$780$	−3.96743	−	14.8848i	−0.142057	−	0.532960i
$781$		−	29.5042i		−	1.05574i
$782$	15.4987	+	9.53507i	0.554234	+	0.340974i
$783$		−	3.18394i		−	0.113785i
$784$	−27.9202	−	2.11216i	−0.997151	−	0.0754343i
$785$	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
$790$	−23.6506	−	22.4237i	−0.841449	−	0.797800i
$791$	−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	$-0.874955\pi$
$797$		−	21.6145i		−	0.765626i	0.923826	−	0.382813i	$-0.125045\pi$
$798$	45.3007	−	25.5646i	1.60363	−	0.904978i
$799$			19.9683i			0.706426i
$800$	−28.2711	−	0.864187i	−0.999533	−	0.0305536i
$801$			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	$0.537974\pi$
$810$	14.3750	−	15.1615i	0.505086	−	0.532720i
$811$			31.6060i			1.10984i	0.831905	+	0.554918i	$0.187250\pi$
$811$			31.6060i			1.10984i	−0.831905	+	0.554918i	$0.812750\pi$
$812$	9.96708	+	0.376466i	0.349776	+	0.0132114i
$813$	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
$820$	−0.698710	−	2.62138i	−0.0244000	−	0.0915425i
$821$		−	28.3663i		−	0.989990i	−0.868896	−	0.494995i	$-0.835170\pi$
$821$		−	28.3663i		−	0.989990i	0.868896	−	0.494995i	$-0.164830\pi$
$822$	−23.3844	+	38.0101i	−0.815625	+	1.32575i
$823$	−15.3770			−0.536008			−0.268004	−	0.963418i	$-0.586364\pi$
$823$	−15.3770			−0.536008			−0.268004	+	0.963418i	$0.586364\pi$
$824$	−37.9092	−	3.18429i	−1.32063	−	0.110930i
$825$	42.4895	+	18.6944i	1.47929	+	0.650857i
$826$	4.53043	−	2.55666i	0.157634	−	0.0889577i
$827$		−	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	$-0.296162\pi$
$829$	34.4068			1.19500			0.597498	+	0.801870i	$0.296162\pi$
$830$	−29.5326	+	31.1484i	−1.02509	+	1.08118i
$831$	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	$-0.320320\pi$
$839$	30.9918			1.06995			0.534977	+	0.844867i	$0.320320\pi$
$840$	−30.1816	−	30.8611i	−1.04136	−	1.06481i
$841$	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
$850$	11.5992	+	16.7820i	0.397851	+	0.575619i
$851$	20.7309			0.710646
$852$	−37.7541	+	19.0701i	−1.29343	+	0.653332i
$853$			48.4535i			1.65902i	0.558495	+	0.829508i	$0.311379\pi$
$853$			48.4535i			1.65902i	−0.558495	+	0.829508i	$0.688621\pi$
$854$	6.99014	+	12.3866i	0.239198	+	0.423860i
$855$	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	$-0.310818\pi$
$860$	−13.9561	−	52.3597i	−0.475899	−	1.78545i
$861$	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	$-0.548550\pi$
$863$	−8.92660			−0.303865			−0.151933	+	0.988391i	$0.548550\pi$
$864$	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
$868$	−1.53940	+	40.7562i	−0.0522506	+	1.38336i
$869$		−	37.0909i		−	1.25822i
$870$	11.1586	+	10.5798i	0.378312	+	0.358687i
$871$	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	$-0.482967\pi$
$877$	3.16793			0.106973			0.0534867	+	0.998569i	$0.482967\pi$
$878$	−9.75916	−	6.00399i	−0.329356	−	0.202625i
$879$		−	60.8278i		−	2.05167i
$880$	−21.4235	−	24.0251i	−0.722186	−	0.809885i
$881$		−	17.9454i		−	0.604595i	−0.953214	−	0.302297i	$-0.902246\pi$
$881$		−	17.9454i		−	0.604595i	0.953214	−	0.302297i	$-0.0977536\pi$
$882$	−0.300121	−	36.1793i	−0.0101056	−	1.21822i
$883$			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	$0.111158\pi$
$887$			20.3807i			0.684317i	−0.939642	+	0.342159i	$0.888842\pi$
$888$	−2.83886	+	33.7968i	−0.0952658	+	1.13415i
$889$	−22.3581	−	12.3740i	−0.749865	−	0.415009i
$890$	−16.1764	−	15.3372i	−0.542233	−	0.514105i
$891$	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
$896$	10.1565	+	28.1575i	0.339304	+	0.940677i
$897$			15.3624i			0.512935i
$898$	−18.0555	−	11.1080i	−0.602520	−	0.370680i
$899$		−	14.5286i		−	0.484555i
$900$	−1.94499	−	36.4961i	−0.0648330	−	1.21654i
$901$	−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
$910$	3.37109	+	10.6508i	0.111750	+	0.353069i
$911$		−	26.8804i		−	0.890586i	−0.895385	−	0.445293i	$-0.853099\pi$
$911$		−	26.8804i		−	0.890586i	0.895385	−	0.445293i	$-0.146901\pi$
$912$	−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	$-0.967786\pi$
$919$		−	6.12542i		−	0.202059i	0.994883	−	0.101029i	$-0.0322136\pi$
$920$	27.0208	+	8.09413i	0.890850	+	0.266856i
$921$	21.5399			0.709764
$922$	−33.8000	−	20.7943i	−1.11314	−	0.684823i
$923$	10.9465			0.360309
$924$	1.85423	−	49.0916i	0.0609998	−	1.61499i
$925$	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	$-0.172133\pi$
$930$	−43.2615	+	45.6284i	−1.41860	+	1.49621i
$931$	−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	$0.456324\pi$
$938$	44.5828	−	25.1594i	1.45568	−	0.821485i
$939$	56.4893			1.84346
$940$	7.97193	+	29.9086i	0.260016	+	0.975511i
$941$	43.1607			1.40700			0.703499	−	0.710696i	$-0.251620\pi$
$941$	43.1607			1.40700			0.703499	+	0.710696i	$0.251620\pi$
$942$	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
$950$	−31.3472	+	21.6662i	−1.01704	+	0.702946i
$951$	−68.0745			−2.20747
$952$	11.9989	−	17.9484i	0.388887	−	0.581712i
$953$			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
$960$	−16.8957	+	42.9426i	−0.545308	+	1.38597i
$961$	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
$966$	21.1572	+	37.4908i	0.680722	+	1.20625i
$967$	5.90310			0.189831			0.0949154	−	0.995485i	$-0.469742\pi$
$967$	5.90310			0.189831			0.0949154	+	0.995485i	$0.469742\pi$
$968$	0.462159	−	5.50204i	0.0148544	−	0.176842i
$969$			40.1080i			1.28846i
$970$	−13.6275	+	14.3731i	−0.437553	+	0.461492i
$971$			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
$980$	22.8952	+	21.3497i	0.731361	+	0.681991i
$981$		−	44.2867i		−	1.41396i
$982$	−20.0092	−	12.3100i	−0.638518	−	0.392827i
$983$			1.55484i			0.0495916i	0.999693	+	0.0247958i	$0.00789356\pi$
$983$			1.55484i			0.0495916i	−0.999693	+	0.0247958i	$0.992106\pi$
$984$	−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
$990$	28.6182	−	30.1840i	0.909546	−	0.959309i
$991$			48.1236i			1.52870i	0.644804	+	0.764348i	$0.276939\pi$
$991$			48.1236i			1.52870i	−0.644804	+	0.764348i	$0.723061\pi$
$992$	40.4271	−	16.3316i	1.28356	−	0.518529i
$993$	−19.3863			−0.615205
$994$	26.7142	−	15.0756i	0.847322	−	0.478171i
$995$	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	$0.0995725\pi$
$997$			19.4339i			0.615479i	−0.951471	+	0.307739i	$0.900428\pi$
$998$	−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.139.6	yes	40
4.3	odd	2		1120.2.n.b.559.5		40
5.4	even	2	inner	280.2.n.b.139.35	yes	40
7.6	odd	2	inner	280.2.n.b.139.5	✓	40
8.3	odd	2	inner	280.2.n.b.139.34	yes	40
8.5	even	2		1120.2.n.b.559.6		40
20.19	odd	2		1120.2.n.b.559.34		40
28.27	even	2		1120.2.n.b.559.36		40
35.34	odd	2	inner	280.2.n.b.139.36	yes	40
40.19	odd	2	inner	280.2.n.b.139.7	yes	40
40.29	even	2		1120.2.n.b.559.33		40
56.13	odd	2		1120.2.n.b.559.35		40
56.27	even	2	inner	280.2.n.b.139.33	yes	40
140.139	even	2		1120.2.n.b.559.7		40
280.69	odd	2		1120.2.n.b.559.8		40
280.139	even	2	inner	280.2.n.b.139.8	yes	40

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

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

\(f(q)\)	\(=\)	\(q+(-1.20452 - 0.741038i) q^{2} +2.57969 q^{3} +(0.901725 + 1.78519i) q^{4} +(0.460102 - 2.18822i) q^{5} +(-3.10728 - 1.91165i) q^{6} +(2.31487 + 1.28116i) q^{7} +(0.236748 - 2.81850i) q^{8} +3.65479 q^{9} +O(q^{10})\)	\(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} +(-2.17576 + 2.29480i) q^{10} -3.59890 q^{11} +(2.32617 + 4.60522i) q^{12} -1.33525i q^{13} +(-1.83892 - 3.25858i) 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} +(4.32127 - 1.15180i) 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} +(-0.199723 + 5.28773i) q^{28} -1.88494i q^{29} +(-5.61277 + 5.91986i) 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} +(-6.05857 - 1.81486i) q^{40} -0.606622i q^{41} +(-4.74384 - 8.40613i) 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} +(4.02045 + 5.81687i) 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} +(4.15898 - 6.22116i) q^{56} +13.9020i q^{57} +(-1.39682 + 2.27045i) q^{58} +1.39031i q^{59} +(11.1475 - 2.97129i) 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} +(-7.97659 + 2.52468i) 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} +(5.95278 + 6.67566i) q^{80} -6.60690 q^{81} +(-0.449530 + 0.730687i) q^{82} +13.5735 q^{83} +(-0.515222 + 13.6407i) 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} +(-7.95192 + 8.38699i) 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} +(-0.0821172 - 9.89915i) q^{98} -13.1532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 12 * q^4 + 40 * q^9	\( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) \) 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

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