LMFDB - Embedded newform 980.2.c.d.979.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(979,980)] 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("980.979"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.23
Character	$\chi$	$=$	980.979
Dual form			980.2.c.d.979.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.739583 + 1.20541i) q^{2} -0.732905i q^{3} +(-0.906034 + 1.78300i) q^{4} +(-2.18048 + 0.495485i) q^{5} +(0.883452 - 0.542044i) q^{6} +(-2.81934 + 0.226536i) q^{8} +2.46285 q^{9} +(-2.20991 - 2.26192i) q^{10} +2.69053i q^{11} +(1.30677 + 0.664037i) q^{12} -3.95118 q^{13} +(0.363144 + 1.59809i) q^{15} +(-2.35821 - 3.23092i) q^{16} +1.41902 q^{17} +(1.82148 + 2.96875i) q^{18} -3.22529 q^{19} +(1.09214 - 4.33673i) q^{20} +(-3.24320 + 1.98987i) q^{22} -4.91239 q^{23} +(0.166030 + 2.06631i) q^{24} +(4.50899 - 2.16079i) q^{25} +(-2.92222 - 4.76279i) q^{26} -4.00375i q^{27} -5.17926 q^{29} +(-1.65778 + 1.61965i) q^{30} -7.63489 q^{31} +(2.15050 - 5.23214i) q^{32} +1.97191 q^{33} +(1.04948 + 1.71050i) q^{34} +(-2.23142 + 4.39127i) q^{36} +4.47981i q^{37} +(-2.38537 - 3.88780i) q^{38} +2.89584i q^{39} +(6.03527 - 1.89090i) q^{40} -0.325509i q^{41} -9.28165 q^{43} +(-4.79723 - 2.43771i) q^{44} +(-5.37020 + 1.22031i) q^{45} +(-3.63312 - 5.92146i) q^{46} -6.56574i q^{47} +(-2.36796 + 1.72834i) q^{48} +(5.93942 + 3.83710i) q^{50} -1.04001i q^{51} +(3.57990 - 7.04496i) q^{52} +1.61591i q^{53} +(4.82617 - 2.96111i) q^{54} +(-1.33312 - 5.86665i) q^{55} +2.36383i q^{57} +(-3.83049 - 6.24314i) q^{58} +7.63489 q^{59} +(-3.17841 - 0.800432i) q^{60} +14.3001i q^{61} +(-5.64664 - 9.20319i) q^{62} +(7.89736 - 1.27737i) q^{64} +(8.61546 - 1.95775i) q^{65} +(1.45839 + 2.37696i) q^{66} -3.02658 q^{67} +(-1.28568 + 2.53012i) q^{68} +3.60032i q^{69} -15.4089i q^{71} +(-6.94361 + 0.557925i) q^{72} -1.41902 q^{73} +(-5.40001 + 3.31319i) q^{74} +(-1.58366 - 3.30466i) q^{75} +(2.92222 - 5.75071i) q^{76} +(-3.49068 + 2.14171i) q^{78} +12.2127i q^{79} +(6.74290 + 5.87651i) q^{80} +4.45418 q^{81} +(0.392372 - 0.240741i) q^{82} +5.26172i q^{83} +(-3.09414 + 0.703103i) q^{85} +(-6.86455 - 11.1882i) q^{86} +3.79591i q^{87} +(-0.609503 - 7.58553i) q^{88} +4.74501i q^{89} +(-5.44268 - 5.57078i) q^{90} +(4.45079 - 8.75882i) q^{92} +5.59565i q^{93} +(7.91442 - 4.85591i) q^{94} +(7.03269 - 1.59809i) q^{95} +(-3.83467 - 1.57611i) q^{96} +8.35134 q^{97} +6.62638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{4} - 8 q^{9} - 36 q^{16} + 52 q^{25} + 52 q^{30} - 28 q^{36} + 52 q^{44} + 44 q^{46} + 36 q^{50} - 8 q^{60} + 36 q^{64} + 8 q^{65} - 28 q^{74} - 144 q^{81} + 20 q^{85} - 16 q^{86}+O(q^{100}) $ 32 * q - 12 * q^4 - 8 * q^9 - 36 * q^16 + 52 * q^25 + 52 * q^30 - 28 * q^36 + 52 * q^44 + 44 * q^46 + 36 * q^50 - 8 * q^60 + 36 * q^64 + 8 * q^65 - 28 * q^74 - 144 * q^81 + 20 * q^85 - 16 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.739583	+	1.20541i	0.522964	+	0.852355i
$2$	0.739583	+	1.20541i	0.522964	+	0.852355i
$3$		−	0.732905i		−	0.423143i	−0.977363	−	0.211572i	$-0.932142\pi$
$3$		−	0.732905i		−	0.423143i	0.977363	−	0.211572i	$-0.0678581\pi$
$4$	−0.906034	+	1.78300i	−0.453017	+	0.891502i
$5$	−2.18048	+	0.495485i	−0.975140	+	0.221588i
$5$	−2.18048	+	0.495485i	−0.975140	+	0.221588i
$6$	0.883452	−	0.542044i	0.360668	−	0.221289i
$7$		0			0
$7$		0			0
$8$	−2.81934	+	0.226536i	−0.996787	+	0.0800926i
$9$	2.46285			0.820950
$10$	−2.20991	−	2.26192i	−0.698835	−	0.715283i
$11$			2.69053i			0.811226i	0.914045	+	0.405613i	$0.132942\pi$
$11$			2.69053i			0.811226i	−0.914045	+	0.405613i	$0.867058\pi$
$12$	1.30677	+	0.664037i	0.377233	+	0.191691i
$13$	−3.95118			−1.09586			−0.547930	−	0.836524i	$-0.684584\pi$
$13$	−3.95118			−1.09586			−0.547930	+	0.836524i	$0.684584\pi$
$14$		0			0
$15$	0.363144	+	1.59809i	0.0937633	+	0.412624i
$16$	−2.35821	−	3.23092i	−0.589551	−	0.807731i
$17$	1.41902			0.344163			0.172081	−	0.985083i	$-0.444951\pi$
$17$	1.41902			0.344163			0.172081	+	0.985083i	$0.444951\pi$
$18$	1.82148	+	2.96875i	0.429327	+	0.699740i
$19$	−3.22529			−0.739933			−0.369966	−	0.929045i	$-0.620631\pi$
$19$	−3.22529			−0.739933			−0.369966	+	0.929045i	$0.620631\pi$
$20$	1.09214	−	4.33673i	0.244209	−	0.969723i
$21$		0			0
$22$	−3.24320	+	1.98987i	−0.691452	+	0.424242i
$23$	−4.91239			−1.02430			−0.512152	−	0.858895i	$-0.671152\pi$
$23$	−4.91239			−1.02430			−0.512152	+	0.858895i	$0.671152\pi$
$24$	0.166030	+	2.06631i	0.0338906	+	0.421784i
$25$	4.50899	−	2.16079i	0.901798	−	0.432158i
$26$	−2.92222	−	4.76279i	−0.573095	−	0.934061i
$27$		−	4.00375i		−	0.770522i
$28$		0			0
$29$	−5.17926			−0.961765			−0.480882	−	0.876785i	$-0.659684\pi$
$29$	−5.17926			−0.961765			−0.480882	+	0.876785i	$0.659684\pi$
$30$	−1.65778	+	1.61965i	−0.302667	+	0.295707i
$31$	−7.63489			−1.37127			−0.685634	−	0.727947i	$-0.740475\pi$
$31$	−7.63489			−1.37127			−0.685634	+	0.727947i	$0.740475\pi$
$32$	2.15050	−	5.23214i	0.380159	−	0.924921i
$33$	1.97191			0.343265
$34$	1.04948	+	1.71050i	0.179985	+	0.293349i
$35$		0			0
$36$	−2.23142	+	4.39127i	−0.371904	+	0.731878i
$37$			4.47981i			0.736475i	0.929732	+	0.368238i	$0.120039\pi$
$37$			4.47981i			0.736475i	−0.929732	+	0.368238i	$0.879961\pi$
$38$	−2.38537	−	3.88780i	−0.386958	−	0.630685i
$39$			2.89584i			0.463705i
$40$	6.03527	−	1.89090i	0.954260	−	0.298978i
$41$		−	0.325509i		−	0.0508359i	−0.999677	−	0.0254180i	$-0.991908\pi$
$41$		−	0.325509i		−	0.0508359i	0.999677	−	0.0254180i	$-0.00809166\pi$
$42$		0			0
$43$	−9.28165			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$43$	−9.28165			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$44$	−4.79723	−	2.43771i	−0.723210	−	0.367499i
$45$	−5.37020	+	1.22031i	−0.800541	+	0.181913i
$46$	−3.63312	−	5.92146i	−0.535675	−	0.873071i
$47$		−	6.56574i		−	0.957712i	−0.877893	−	0.478856i	$-0.841052\pi$
$47$		−	6.56574i		−	0.957712i	0.877893	−	0.478856i	$-0.158948\pi$
$48$	−2.36796	+	1.72834i	−0.341786	+	0.249465i
$49$		0			0
$50$	5.93942	+	3.83710i	0.839960	+	0.542648i
$51$		−	1.04001i		−	0.145630i
$52$	3.57990	−	7.04496i	0.496443	−	0.976961i
$53$			1.61591i			0.221962i	0.993823	+	0.110981i	$0.0353993\pi$
$53$			1.61591i			0.221962i	−0.993823	+	0.110981i	$0.964601\pi$
$54$	4.82617	−	2.96111i	0.656758	−	0.402956i
$55$	−1.33312	−	5.86665i	−0.179758	−	0.791059i
$56$		0			0
$57$			2.36383i			0.313097i
$58$	−3.83049	−	6.24314i	−0.502969	−	0.819765i
$59$	7.63489			0.993979			0.496989	−	0.867757i	$-0.334439\pi$
$59$	7.63489			0.993979			0.496989	+	0.867757i	$0.334439\pi$
$60$	−3.17841	−	0.800432i	−0.410331	−	0.103335i
$61$			14.3001i			1.83093i	0.402392	+	0.915467i	$0.368179\pi$
$61$			14.3001i			1.83093i	−0.402392	+	0.915467i	$0.631821\pi$
$62$	−5.64664	−	9.20319i	−0.717124	−	1.16881i
$63$		0			0
$64$	7.89736	−	1.27737i	0.987170	−	0.159671i
$65$	8.61546	−	1.95775i	1.06862	−	0.242829i
$66$	1.45839	+	2.37696i	0.179515	+	0.292583i
$67$	−3.02658			−0.369755			−0.184878	−	0.982762i	$-0.559189\pi$
$67$	−3.02658			−0.369755			−0.184878	+	0.982762i	$0.559189\pi$
$68$	−1.28568	+	2.53012i	−0.155911	+	0.306822i
$69$			3.60032i			0.433427i
$70$		0			0
$71$		−	15.4089i		−	1.82870i	−0.404922	−	0.914351i	$-0.632701\pi$
$71$		−	15.4089i		−	1.82870i	0.404922	−	0.914351i	$-0.367299\pi$
$72$	−6.94361	+	0.557925i	−0.818313	+	0.0657520i
$73$	−1.41902			−0.166084			−0.0830418	−	0.996546i	$-0.526463\pi$
$73$	−1.41902			−0.166084			−0.0830418	+	0.996546i	$0.526463\pi$
$74$	−5.40001	+	3.31319i	−0.627738	+	0.385150i
$75$	−1.58366	−	3.30466i	−0.182865	−	0.381589i
$76$	2.92222	−	5.75071i	0.335202	−	0.659652i
$77$		0			0
$78$	−3.49068	+	2.14171i	−0.395241	+	0.242501i
$79$			12.2127i			1.37404i	0.726638	+	0.687021i	$0.241082\pi$
$79$			12.2127i			1.37404i	−0.726638	+	0.687021i	$0.758918\pi$
$80$	6.74290	+	5.87651i	0.753879	+	0.657014i
$81$	4.45418			0.494909
$82$	0.392372	−	0.240741i	0.0433303	−	0.0265854i
$83$			5.26172i			0.577549i	0.957397	+	0.288774i	$0.0932477\pi$
$83$			5.26172i			0.577549i	−0.957397	+	0.288774i	$0.906752\pi$
$84$		0			0
$85$	−3.09414	+	0.703103i	−0.335607	+	0.0762622i
$86$	−6.86455	−	11.1882i	−0.740223	−	1.20645i
$87$			3.79591i			0.406964i
$88$	−0.609503	−	7.58553i	−0.0649732	−	0.808620i
$89$			4.74501i			0.502970i	0.967861	+	0.251485i	$0.0809189\pi$
$89$			4.74501i			0.502970i	−0.967861	+	0.251485i	$0.919081\pi$
$90$	−5.44268	−	5.57078i	−0.573709	−	0.587212i
$91$		0			0
$92$	4.45079	−	8.75882i	0.464027	−	0.913170i
$93$			5.59565i			0.580242i
$94$	7.91442	−	4.85591i	0.816310	−	0.500849i
$95$	7.03269	−	1.59809i	0.721538	−	0.163960i
$96$	−3.83467	−	1.57611i	−0.391374	−	0.160862i
$97$	8.35134			0.847950			0.423975	−	0.905674i	$-0.360634\pi$
$97$	8.35134			0.847950			0.423975	+	0.905674i	$0.360634\pi$
$98$		0			0
$99$			6.62638i			0.665976i
$100$	−0.232594	+	9.99729i	−0.0232594	+	0.999729i
$101$			0.279354i			0.0277967i	0.999903	+	0.0138984i	$0.00442413\pi$
$101$			0.279354i			0.0277967i	−0.999903	+	0.0138984i	$0.995576\pi$
$102$	1.25364	−	0.769171i	0.124128	−	0.0761593i
$103$			13.4006i			1.32040i	0.751090	+	0.660200i	$0.229529\pi$
$103$			13.4006i			1.32040i	−0.751090	+	0.660200i	$0.770471\pi$
$104$	11.1397	−	0.895084i	1.09234	−	0.0877703i
$105$		0			0
$106$	−1.94784	+	1.19510i	−0.189191	+	0.116078i
$107$	−5.42894			−0.524836			−0.262418	−	0.964954i	$-0.584520\pi$
$107$	−5.42894			−0.524836			−0.262418	+	0.964954i	$0.584520\pi$
$108$	7.13870	+	3.62753i	0.686922	+	0.349060i
$109$	8.91703			0.854096			0.427048	−	0.904229i	$-0.359553\pi$
$109$	8.91703			0.854096			0.427048	+	0.904229i	$0.359553\pi$
$110$	6.08578	−	5.94583i	0.580256	−	0.566913i
$111$	3.28327			0.311634
$112$		0			0
$113$			1.05161i			0.0989268i	0.998776	+	0.0494634i	$0.0157511\pi$
$113$			1.05161i			0.0989268i	−0.998776	+	0.0494634i	$0.984249\pi$
$114$	−2.84939	+	1.74825i	−0.266870	+	0.163739i
$115$	10.7114	−	2.43402i	0.998841	−	0.226973i
$116$	4.69259	−	9.23464i	0.435696	−	0.857415i
$117$	−9.73116			−0.899646
$118$	5.64664	+	9.20319i	0.519815	+	0.847222i
$119$		0			0
$120$	−1.38585	−	4.42328i	−0.126510	−	0.403789i
$121$	3.76104			0.341912
$122$	−17.2375	+	10.5761i	−1.56061	+	0.957513i
$123$	−0.238567			−0.0215109
$124$	6.91747	−	13.6130i	0.621207	−	1.22249i
$125$	−8.76112	+	6.94570i	−0.783618	+	0.621243i
$126$		0			0
$127$	1.71773			0.152424			0.0762121	−	0.997092i	$-0.475717\pi$
$127$	1.71773			0.152424			0.0762121	+	0.997092i	$0.475717\pi$
$128$	7.38051	+	8.57485i	0.652351	+	0.757917i
$129$			6.80257i			0.598933i
$130$	8.73175	+	8.93726i	0.765825	+	0.783850i
$131$	−14.1435			−1.23572			−0.617860	−	0.786288i	$-0.712000\pi$
$131$	−14.1435			−1.23572			−0.617860	+	0.786288i	$0.712000\pi$
$132$	−1.78661	+	3.51591i	−0.155505	+	0.306021i
$133$		0			0
$134$	−2.23841	−	3.64827i	−0.193369	−	0.315163i
$135$	1.98380	+	8.73010i	0.170738	+	0.751367i
$136$	−4.00070	+	0.321459i	−0.343057	+	0.0275649i
$137$			14.8710i			1.27052i	0.772300	+	0.635259i	$0.219106\pi$
$137$			14.8710i			1.27052i	−0.772300	+	0.635259i	$0.780894\pi$
$138$	−4.33987	+	2.66274i	−0.369434	+	0.226667i
$139$	−7.06762			−0.599468			−0.299734	−	0.954023i	$-0.596898\pi$
$139$	−7.06762			−0.599468			−0.299734	+	0.954023i	$0.596898\pi$
$140$		0			0
$141$	−4.81207			−0.405249
$142$	18.5741	−	11.3962i	1.55870	−	0.956346i
$143$		−	10.6308i		−	0.888990i
$144$	−5.80791	−	7.95728i	−0.483992	−	0.663107i
$145$	11.2933	−	2.56625i	0.937856	−	0.213115i
$146$	−1.04948	−	1.71050i	−0.0868557	−	0.141562i
$147$		0			0
$148$	−7.98751	−	4.05885i	−0.656569	−	0.333636i
$149$	8.78577			0.719758			0.359879	−	0.932999i	$-0.382818\pi$
$149$	8.78577			0.719758			0.359879	+	0.932999i	$0.382818\pi$
$150$	2.81223	−	4.35303i	0.229618	−	0.355423i
$151$		−	0.300332i		−	0.0244407i	−0.999925	−	0.0122204i	$-0.996110\pi$
$151$		−	0.300332i		−	0.0244407i	0.999925	−	0.0122204i	$-0.00388996\pi$
$152$	9.09320	−	0.730645i	0.737556	−	0.0592632i
$153$	3.49483			0.282540
$154$		0			0
$155$	16.6477	−	3.78298i	1.33718	−	0.303856i
$156$	−5.16329	−	2.62373i	−0.413394	−	0.210066i
$157$	19.2348			1.53511			0.767553	−	0.640985i	$-0.221474\pi$
$157$	19.2348			1.53511			0.767553	+	0.640985i	$0.221474\pi$
$158$	−14.7214	+	9.03234i	−1.17117	+	0.718575i
$159$	1.18431			0.0939218
$160$	−2.09668	+	12.4741i	−0.165757	+	0.986167i
$161$		0			0
$162$	3.29424	+	5.36912i	0.258820	+	0.421838i
$163$	10.7192			0.839589			0.419795	−	0.907619i	$-0.362102\pi$
$163$	10.7192			0.839589			0.419795	+	0.907619i	$0.362102\pi$
$164$	0.580384	+	0.294922i	0.0453203	+	0.0230295i
$165$	−4.29970	+	0.977050i	−0.334731	+	0.0760633i
$166$	−6.34254	+	3.89148i	−0.492276	+	0.302037i
$167$			13.2256i			1.02343i	0.859155	+	0.511715i	$0.170990\pi$
$167$			13.2256i			1.02343i	−0.859155	+	0.511715i	$0.829010\pi$
$168$		0			0
$169$	2.61180			0.200908
$170$	−3.13590	−	3.20971i	−0.240513	−	0.246174i
$171$	−7.94341			−0.607448
$172$	8.40948	−	16.5492i	0.641217	−	1.26187i
$173$	−11.2541			−0.855632			−0.427816	−	0.903866i	$-0.640717\pi$
$173$	−11.2541			−0.855632			−0.427816	+	0.903866i	$0.640717\pi$
$174$	−4.57563	+	2.80739i	−0.346878	+	0.212828i
$175$		0			0
$176$	8.69290	−	6.34483i	0.655252	−	0.478259i
$177$		−	5.59565i		−	0.420595i
$178$	−5.71969	+	3.50933i	−0.428709	+	0.263035i
$179$			0.805971i			0.0602411i	0.999546	+	0.0301206i	$0.00958912\pi$
$179$			0.805971i			0.0602411i	−0.999546	+	0.0301206i	$0.990411\pi$
$180$	2.68977	−	10.6807i	0.200483	−	0.796094i
$181$			0.0667108i			0.00495857i	0.999997	+	0.00247929i	$0.000789182\pi$
$181$			0.0667108i			0.00495857i	−0.999997	+	0.00247929i	$0.999211\pi$
$182$		0			0
$183$	10.4806			0.774747
$184$	13.8497	−	1.11283i	1.02101	−	0.0820393i
$185$	−2.21968	−	9.76813i	−0.163194	−	0.718167i
$186$	−6.74507	+	4.13845i	−0.494572	+	0.303446i
$187$			3.81791i			0.279194i
$188$	11.7067	+	5.94878i	0.853802	+	0.433860i
$189$		0			0
$190$	7.12761	+	7.29536i	0.517091	+	0.529261i
$191$		−	17.4602i		−	1.26338i	−0.775223	−	0.631688i	$-0.782362\pi$
$191$		−	17.4602i		−	1.26338i	0.775223	−	0.631688i	$-0.217638\pi$
$192$	−0.936188	−	5.78802i	−0.0675635	−	0.417714i
$193$		−	17.1967i		−	1.23785i	−0.785452	−	0.618923i	$-0.787569\pi$
$193$		−	17.1967i		−	1.23785i	0.785452	−	0.618923i	$-0.212431\pi$
$194$	6.17651	+	10.0668i	0.443447	+	0.722754i
$195$	−1.43485	−	6.31432i	−0.102751	−	0.452178i
$196$		0			0
$197$		−	11.9392i		−	0.850635i	−0.905044	−	0.425318i	$-0.860162\pi$
$197$		−	11.9392i		−	0.850635i	0.905044	−	0.425318i	$-0.139838\pi$
$198$	−7.98751	+	4.90076i	−0.567648	+	0.348282i
$199$	−15.5203			−1.10021			−0.550103	−	0.835097i	$-0.685412\pi$
$199$	−15.5203			−1.10021			−0.550103	+	0.835097i	$0.685412\pi$
$200$	−12.2229	+	7.11346i	−0.864288	+	0.502997i
$201$			2.21820i			0.156459i
$202$	−0.336736	+	0.206605i	−0.0236927	+	0.0145367i
$203$		0			0
$204$	1.85433	+	0.942281i	0.129829	+	0.0659728i
$205$	0.161285	+	0.709766i	0.0112646	+	0.0495722i
$206$	−16.1532	+	9.91086i	−1.12545	+	0.690522i
$207$	−12.0985			−0.840903
$208$	9.31769	+	12.7659i	0.646066	+	0.885159i
$209$		−	8.67775i		−	0.600253i
$210$		0			0
$211$			14.1636i			0.975063i	0.873105	+	0.487531i	$0.162103\pi$
$211$			14.1636i			0.975063i	−0.873105	+	0.487531i	$0.837897\pi$
$212$	−2.88117	−	1.46407i	−0.197880	−	0.100553i
$213$	−11.2933			−0.773803
$214$	−4.01516	−	6.54411i	−0.274470	−	0.447346i
$215$	20.2384	−	4.59892i	1.38025	−	0.313644i
$216$	0.906994	+	11.2879i	0.0617132	+	0.768047i
$217$		0			0
$218$	6.59488	+	10.7487i	0.446662	+	0.727993i
$219$			1.04001i			0.0702771i
$220$	11.6681	+	2.93843i	0.786664	+	0.198109i
$221$	−5.60679			−0.377154
$222$	2.42825	+	3.95770i	0.162974	+	0.265623i
$223$			3.03443i			0.203201i	0.994825	+	0.101600i	$0.0323963\pi$
$223$			3.03443i			0.203201i	−0.994825	+	0.101600i	$0.967604\pi$
$224$		0			0
$225$	11.1050	−	5.32171i	0.740331	−	0.354780i
$226$	−1.26762	+	0.777750i	−0.0843207	+	0.0517352i
$227$			14.7768i			0.980769i	0.871506	+	0.490385i	$0.163144\pi$
$227$			14.7768i			0.980769i	−0.871506	+	0.490385i	$0.836856\pi$
$228$	−4.21473	−	2.14171i	−0.279127	−	0.141838i
$229$		−	6.43090i		−	0.424966i	−0.977165	−	0.212483i	$-0.931845\pi$
$229$		−	6.43090i		−	0.424966i	0.977165	−	0.212483i	$-0.0681550\pi$
$230$	10.8559	+	11.1115i	0.715820	+	0.732668i
$231$		0			0
$232$	14.6021	−	1.17329i	0.958675	−	0.0770303i
$233$		−	17.4706i		−	1.14454i	−0.820065	−	0.572270i	$-0.806063\pi$
$233$		−	17.4706i		−	1.14454i	0.820065	−	0.572270i	$-0.193937\pi$
$234$	−7.19700	−	11.7300i	−0.470483	−	0.766817i
$235$	3.25323	+	14.3165i	0.212217	+	0.933904i
$236$	−6.91747	+	13.6130i	−0.450289	+	0.886134i
$237$	8.95079			0.581416
$238$		0			0
$239$			3.22490i			0.208601i	0.994546	+	0.104301i	$0.0332604\pi$
$239$			3.22490i			0.208601i	−0.994546	+	0.104301i	$0.966740\pi$
$240$	4.30692	−	4.94190i	0.278011	−	0.318999i
$241$			20.4872i			1.31970i	0.751399	+	0.659848i	$0.229379\pi$
$241$			20.4872i			1.31970i	−0.751399	+	0.659848i	$0.770621\pi$
$242$	2.78160	+	4.53360i	0.178808	+	0.291431i
$243$		−	15.2757i		−	0.979940i
$244$	−25.4971	−	12.9563i	−1.63228	−	0.829444i
$245$		0			0
$246$	−0.176440	−	0.287572i	−0.0112494	−	0.0183349i
$247$	12.7437			0.810862
$248$	21.5254	−	1.72958i	1.36686	−	0.109828i
$249$	3.85634			0.244386
$250$	−14.8520	−	5.42383i	−0.939323	−	0.343033i
$251$	15.1647			0.957189			0.478594	−	0.878036i	$-0.341146\pi$
$251$	15.1647			0.957189			0.478594	+	0.878036i	$0.341146\pi$
$252$		0			0
$253$		−	13.2170i		−	0.830943i
$254$	1.27041	+	2.07058i	0.0797124	+	0.129919i
$255$	0.515308	+	2.26771i	0.0322698	+	0.142010i
$256$	−4.87773	+	15.2384i	−0.304858	+	0.952398i
$257$	4.73155			0.295146			0.147573	−	0.989051i	$-0.452854\pi$
$257$	4.73155			0.295146			0.147573	+	0.989051i	$0.452854\pi$
$258$	−8.19989	+	5.03106i	−0.510503	+	0.313220i
$259$		0			0
$260$	−4.31522	+	17.1352i	−0.267619	+	1.06268i
$261$	−12.7557			−0.789561
$262$	−10.4603	−	17.0487i	−0.646237	−	1.05327i
$263$	−4.70042			−0.289840			−0.144920	−	0.989443i	$-0.546293\pi$
$263$	−4.70042			−0.289840			−0.144920	+	0.989443i	$0.546293\pi$
$264$	−5.55947	+	0.446708i	−0.342162	+	0.0274930i
$265$	−0.800660	−	3.52346i	−0.0491842	−	0.216444i
$266$		0			0
$267$	3.47764			0.212828
$268$	2.74218	−	5.39640i	0.167505	−	0.329638i
$269$		−	24.5411i		−	1.49630i	−0.663530	−	0.748149i	$-0.730943\pi$
$269$		−	24.5411i		−	1.49630i	0.663530	−	0.748149i	$-0.269057\pi$
$270$	−9.05618	+	8.84793i	−0.551141	+	0.538468i
$271$	−26.3914			−1.60316			−0.801582	−	0.597885i	$-0.796008\pi$
$271$	−26.3914			−1.60316			−0.801582	+	0.597885i	$0.796008\pi$
$272$	−3.34634	−	4.58474i	−0.202902	−	0.277991i
$273$		0			0
$274$	−17.9257	+	10.9984i	−1.08293	+	0.664435i
$275$	5.81368	+	12.1316i	0.350578	+	0.731562i
$276$	−6.41938	−	3.26201i	−0.386401	−	0.196350i
$277$			24.0701i			1.44623i	0.690727	+	0.723115i	$0.257290\pi$
$277$			24.0701i			1.44623i	−0.690727	+	0.723115i	$0.742710\pi$
$278$	−5.22709	−	8.51939i	−0.313500	−	0.510959i
$279$	−18.8036			−1.12574
$280$		0			0
$281$	−7.78577			−0.464460			−0.232230	−	0.972661i	$-0.574602\pi$
$281$	−7.78577			−0.464460			−0.232230	+	0.972661i	$0.574602\pi$
$282$	−3.55892	−	5.80052i	−0.211931	−	0.345416i
$283$			7.95057i			0.472612i	0.971679	+	0.236306i	$0.0759368\pi$
$283$			7.95057i			0.472612i	−0.971679	+	0.236306i	$0.924063\pi$
$284$	27.4742	+	13.9610i	1.63029	+	0.828433i
$285$	−1.17125	−	5.15429i	−0.0693786	−	0.305314i
$286$	12.8145	−	7.86234i	0.757734	−	0.464910i
$287$		0			0
$288$	5.29637	−	12.8860i	0.312091	−	0.759314i
$289$	−14.9864			−0.881552
$290$	11.4457	+	11.7151i	0.672115	+	0.687934i
$291$		−	6.12074i		−	0.358804i
$292$	1.28568	−	2.53012i	0.0752386	−	0.148064i
$293$	−2.11501			−0.123560			−0.0617801	−	0.998090i	$-0.519678\pi$
$293$	−2.11501			−0.123560			−0.0617801	+	0.998090i	$0.519678\pi$
$294$		0			0
$295$	−16.6477	+	3.78298i	−0.969269	+	0.220254i
$296$	−1.01484	−	12.6301i	−0.0589863	−	0.734110i
$297$	10.7722			0.625068
$298$	6.49781	+	10.5905i	0.376408	+	0.613489i
$299$	19.4097			1.12249
$300$	7.32707	+	0.170469i	0.423029	+	0.00984206i
$301$		0			0
$302$	0.362024	−	0.222121i	0.0208321	−	0.0127816i
$303$	0.204740			0.0117620
$304$	7.60590	+	10.4207i	0.436229	+	0.597667i
$305$	−7.08547	−	31.1810i	−0.405713	−	1.78542i
$306$	2.58472	+	4.21271i	0.147758	+	0.240824i
$307$			18.6560i			1.06475i	0.846508	+	0.532376i	$0.178701\pi$
$307$			18.6560i			1.06475i	−0.846508	+	0.532376i	$0.821299\pi$
$308$		0			0
$309$	9.82137			0.558718
$310$	16.8724	+	17.2695i	0.958290	+	0.980844i
$311$	8.18305			0.464018			0.232009	−	0.972714i	$-0.425470\pi$
$311$	8.18305			0.464018			0.232009	+	0.972714i	$0.425470\pi$
$312$	−0.656012	−	8.16436i	−0.0371394	−	0.462216i
$313$	23.3743			1.32119			0.660597	−	0.750741i	$-0.270303\pi$
$313$	23.3743			1.32119			0.660597	+	0.750741i	$0.270303\pi$
$314$	14.2258	+	23.1859i	0.802806	+	1.30846i
$315$		0			0
$316$	−21.7754	−	11.0652i	−1.22496	−	0.622464i
$317$			26.2078i			1.47198i	0.676994	+	0.735988i	$0.263282\pi$
$317$			26.2078i			1.47198i	−0.676994	+	0.735988i	$0.736718\pi$
$318$	0.875895	+	1.42758i	0.0491178	+	0.0800547i
$319$		−	13.9350i		−	0.780209i
$320$	−16.5871	+	6.69830i	−0.927249	+	0.374446i
$321$			3.97890i			0.222081i
$322$		0			0
$323$	−4.57675			−0.254657
$324$	−4.03564	+	7.94182i	−0.224202	+	0.441212i
$325$	−17.8158	+	8.53767i	−0.988243	+	0.473585i
$326$	7.92771	+	12.9210i	0.439075	+	0.715628i
$327$		−	6.53534i		−	0.361405i
$328$	0.0737395	+	0.917720i	0.00407158	+	0.0506726i
$329$		0			0
$330$	−4.35773	−	4.46030i	−0.239885	−	0.245531i
$331$		−	19.5213i		−	1.07299i	−0.843904	−	0.536495i	$-0.819748\pi$
$331$		−	19.5213i		−	1.07299i	0.843904	−	0.536495i	$-0.180252\pi$
$332$	−9.38167	−	4.76729i	−0.514886	−	0.261639i
$333$			11.0331i			0.604610i
$334$	−15.9423	+	9.78146i	−0.872326	+	0.535218i
$335$	6.59940	−	1.49963i	0.360564	−	0.0819333i
$336$		0			0
$337$			31.7520i			1.72964i	0.502082	+	0.864820i	$0.332567\pi$
$337$			31.7520i			1.72964i	−0.502082	+	0.864820i	$0.667433\pi$
$338$	1.93164	+	3.14829i	0.105068	+	0.171245i
$339$	0.770728			0.0418602
$340$	1.54976	−	6.15390i	0.0840476	−	0.333742i
$341$		−	20.5419i		−	1.11241i
$342$	−5.87481	−	9.57508i	−0.317674	−	0.517761i
$343$		0			0
$344$	26.1681	−	2.10263i	1.41089	−	0.113366i
$345$	−1.78391	−	7.85042i	−0.0960422	−	0.422653i
$346$	−8.32333	−	13.5658i	−0.447465	−	0.729302i
$347$	−18.3842			−0.986916			−0.493458	−	0.869770i	$-0.664267\pi$
$347$	−18.3842			−0.986916			−0.493458	+	0.869770i	$0.664267\pi$
$348$	−6.76812	−	3.43922i	−0.362809	−	0.184362i
$349$			2.37390i			0.127072i	0.997980	+	0.0635360i	$0.0202378\pi$
$349$			2.37390i			0.127072i	−0.997980	+	0.0635360i	$0.979762\pi$
$350$		0			0
$351$			15.8195i			0.844384i
$352$	14.0773	+	5.78600i	0.750320	+	0.308395i
$353$	−2.15421			−0.114657			−0.0573284	−	0.998355i	$-0.518258\pi$
$353$	−2.15421			−0.114657			−0.0573284	+	0.998355i	$0.518258\pi$
$354$	6.74507	−	4.13845i	0.358496	−	0.219956i
$355$	7.63489	+	33.5988i	0.405218	+	1.78324i
$356$	−8.46037	−	4.29914i	−0.448399	−	0.227854i
$357$		0			0
$358$	−0.971527	+	0.596083i	−0.0513468	+	0.0315039i
$359$		−	5.08073i		−	0.268151i	−0.990971	−	0.134075i	$-0.957194\pi$
$359$		−	5.08073i		−	0.268151i	0.990971	−	0.134075i	$-0.0428064\pi$
$360$	14.8640	−	4.65700i	0.783400	−	0.245446i
$361$	−8.59749			−0.452499
$362$	−0.0804139	+	0.0493381i	−0.00422646	+	0.00259316i
$363$		−	2.75648i		−	0.144678i
$364$		0			0
$365$	3.09414	−	0.703103i	0.161955	−	0.0368021i
$366$	7.75127	+	12.6334i	0.405165	+	0.660360i
$367$			13.5453i			0.707061i	0.935423	+	0.353530i	$0.115019\pi$
$367$			13.5453i			0.707061i	−0.935423	+	0.353530i	$0.884981\pi$
$368$	11.5844	+	15.8716i	0.603880	+	0.827363i
$369$		−	0.801679i		−	0.0417338i
$370$	10.1330	−	9.89997i	0.526788	−	0.514675i
$371$		0			0
$372$	−9.97707	−	5.06985i	−0.517287	−	0.262860i
$373$		−	7.13400i		−	0.369384i	−0.982796	−	0.184692i	$-0.940871\pi$
$373$		−	7.13400i		−	0.369384i	0.982796	−	0.184692i	$-0.0591288\pi$
$374$	−4.60216	+	2.82367i	−0.237972	+	0.146008i
$375$	5.09054	+	6.42107i	0.262874	+	0.331583i
$376$	1.48738	+	18.5111i	0.0767057	+	0.954635i
$377$	20.4642			1.05396
$378$		0			0
$379$		−	16.2436i		−	0.834379i	−0.908820	−	0.417189i	$-0.863015\pi$
$379$		−	16.2436i		−	0.834379i	0.908820	−	0.417189i	$-0.136985\pi$
$380$	−3.52246	+	13.9872i	−0.180698	+	0.717530i
$381$		−	1.25894i		−	0.0644972i
$382$	21.0467	−	12.9133i	1.07684	−	0.660700i
$383$			9.88716i			0.505211i	0.967569	+	0.252605i	$0.0812874\pi$
$383$			9.88716i			0.505211i	−0.967569	+	0.252605i	$0.918713\pi$
$384$	6.28456	−	5.40921i	0.320707	−	0.276038i
$385$		0			0
$386$	20.7291	−	12.7184i	1.05508	−	0.647349i
$387$	−22.8593			−1.16200
$388$	−7.56659	+	14.8905i	−0.384135	+	0.755949i
$389$	−31.9623			−1.62055			−0.810276	−	0.586048i	$-0.800683\pi$
$389$	−31.9623			−1.62055			−0.810276	+	0.586048i	$0.800683\pi$
$390$	6.55016	−	6.39954i	0.331680	−	0.324053i
$391$	−6.97078			−0.352527
$392$		0			0
$393$			10.3658i			0.522886i
$394$	14.3917	−	8.83005i	0.725043	−	0.444852i
$395$	−6.05124	−	26.6297i	−0.304471	−	1.33988i
$396$	−11.8149	−	6.00372i	−0.593719	−	0.301698i
$397$	−17.4757			−0.877079			−0.438539	−	0.898712i	$-0.644504\pi$
$397$	−17.4757			−0.877079			−0.438539	+	0.898712i	$0.644504\pi$
$398$	−11.4786	−	18.7084i	−0.575369	−	0.937766i
$399$		0			0
$400$	−17.6145	−	9.47260i	−0.880724	−	0.473630i
$401$	−17.3585			−0.866843			−0.433422	−	0.901191i	$-0.642694\pi$
$401$	−17.3585			−0.866843			−0.433422	+	0.901191i	$0.642694\pi$
$402$	−2.67384	+	1.64054i	−0.133359	+	0.0818227i
$403$	30.1668			1.50272
$404$	−0.498089	−	0.253104i	−0.0247808	−	0.0125924i
$405$	−9.71225	+	2.20698i	−0.482606	+	0.109666i
$406$		0			0
$407$	−12.0531			−0.597448
$408$	0.235599	+	2.93213i	0.0116639	+	0.145162i
$409$		−	7.29987i		−	0.360955i	−0.983579	−	0.180478i	$-0.942236\pi$
$409$		−	7.29987i		−	0.360955i	0.983579	−	0.180478i	$-0.0577643\pi$
$410$	−0.736276	+	0.719345i	−0.0363621	+	0.0355259i
$411$	10.8990			0.537610
$412$	−23.8933	−	12.1414i	−1.17714	−	0.598164i
$413$		0			0
$414$	−8.94784	−	14.5837i	−0.439762	−	0.716748i
$415$	−2.60710	−	11.4731i	−0.127978	−	0.563191i
$416$	−8.49702	+	20.6731i	−0.416601	+	1.01358i
$417$			5.17990i			0.253661i
$418$	10.4603	−	6.41792i	0.511628	−	0.313911i
$419$	17.9278			0.875831			0.437915	−	0.899016i	$-0.355717\pi$
$419$	17.9278			0.875831			0.437915	+	0.899016i	$0.355717\pi$
$420$		0			0
$421$	12.6334			0.615716			0.307858	−	0.951432i	$-0.400388\pi$
$421$	12.6334			0.615716			0.307858	+	0.951432i	$0.400388\pi$
$422$	−17.0730	+	10.4752i	−0.831099	+	0.509923i
$423$		−	16.1704i		−	0.786234i
$424$	−0.366062	−	4.55580i	−0.0177775	−	0.221249i
$425$	6.39834	−	3.06620i	0.310365	−	0.148733i
$426$	−8.35232	−	13.6130i	−0.404671	−	0.659554i
$427$		0			0
$428$	4.91881	−	9.67983i	0.237759	−	0.467892i
$429$	−7.79135			−0.376170
$430$	20.5116	+	20.9944i	0.989157	+	1.01244i
$431$		−	32.6737i		−	1.57384i	−0.617058	−	0.786918i	$-0.711676\pi$
$431$		−	32.6737i		−	1.57384i	0.617058	−	0.786918i	$-0.288324\pi$
$432$	−12.9358	+	9.44167i	−0.622375	+	0.454263i
$433$	−23.5884			−1.13359			−0.566794	−	0.823860i	$-0.691816\pi$
$433$	−23.5884			−1.13359			−0.566794	+	0.823860i	$0.691816\pi$
$434$		0			0
$435$	−1.88082	−	8.27690i	−0.0901783	−	0.396847i
$436$	−8.07913	+	15.8991i	−0.386920	+	0.761429i
$437$	15.8439			0.757917
$438$	−1.25364	+	0.769171i	−0.0599010	+	0.0367524i
$439$	18.3900			0.877708			0.438854	−	0.898558i	$-0.355385\pi$
$439$	18.3900			0.877708			0.438854	+	0.898558i	$0.355385\pi$
$440$	5.08753	+	16.2381i	0.242538	+	0.774121i
$441$		0			0
$442$	−4.14669	−	6.75849i	−0.197238	−	0.321469i
$443$	−3.38433			−0.160795			−0.0803973	−	0.996763i	$-0.525619\pi$
$443$	−3.38433			−0.160795			−0.0803973	+	0.996763i	$0.525619\pi$
$444$	−2.97476	+	5.85409i	−0.141176	+	0.277823i
$445$	−2.35108	−	10.3464i	−0.111452	−	0.490466i
$446$	−3.65774	+	2.24422i	−0.173199	+	0.106267i
$447$		−	6.43914i		−	0.304561i
$448$		0			0
$449$	−11.9013			−0.561658			−0.280829	−	0.959758i	$-0.590609\pi$
$449$	−11.9013			−0.561658			−0.280829	+	0.959758i	$0.590609\pi$
$450$	14.6279	+	9.45020i	0.689565	+	0.445487i
$451$	0.875792			0.0412394
$452$	−1.87502	−	0.952791i	−0.0881934	−	0.0448155i
$453$	−0.220115			−0.0103419
$454$	−17.8121	+	10.9287i	−0.835963	+	0.512907i
$455$		0			0
$456$	−0.535494	−	6.66445i	−0.0250768	−	0.312092i
$457$		−	21.0704i		−	0.985631i	−0.870134	−	0.492816i	$-0.835968\pi$
$457$		−	21.0704i		−	0.985631i	0.870134	−	0.492816i	$-0.164032\pi$
$458$	7.75188	−	4.75619i	0.362222	−	0.222242i
$459$		−	5.68140i		−	0.265185i
$460$	−5.36500	+	21.3037i	−0.250145	+	0.993292i
$461$		−	29.6708i		−	1.38191i	−0.722899	−	0.690954i	$-0.757191\pi$
$461$		−	29.6708i		−	1.38191i	0.722899	−	0.690954i	$-0.242809\pi$
$462$		0			0
$463$	15.0481			0.699342			0.349671	−	0.936873i	$-0.386293\pi$
$463$	15.0481			0.699342			0.349671	+	0.936873i	$0.386293\pi$
$464$	12.2138	+	16.7338i	0.567010	+	0.776847i
$465$	−2.77257	−	12.2012i	−0.128575	−	0.565818i
$466$	21.0593	−	12.9210i	0.975554	−	0.598553i
$467$		−	5.14599i		−	0.238128i	−0.992887	−	0.119064i	$-0.962011\pi$
$467$		−	5.14599i		−	0.238128i	0.992887	−	0.119064i	$-0.0379894\pi$
$468$	8.81676	−	17.3507i	0.407555	−	0.802036i
$469$		0			0
$470$	−14.8512	+	14.5097i	−0.685035	+	0.669283i
$471$		−	14.0973i		−	0.649570i
$472$	−21.5254	+	1.72958i	−0.990785	+	0.0796104i
$473$		−	24.9726i		−	1.14824i
$474$	6.61985	+	10.7894i	0.304060	+	0.495573i
$475$	−14.5428	+	6.96919i	−0.667270	+	0.319768i
$476$		0			0
$477$			3.97974i			0.182220i
$478$	−3.88733	+	2.38508i	−0.177802	+	0.109091i
$479$	39.9567			1.82567			0.912834	−	0.408331i	$-0.133889\pi$
$479$	39.9567			1.82567			0.912834	+	0.408331i	$0.133889\pi$
$480$	9.14236	+	1.53667i	0.417290	+	0.0701389i
$481$		−	17.7005i		−	0.807074i
$482$	−24.6955	+	15.1520i	−1.12485	+	0.690153i
$483$		0			0
$484$	−3.40763	+	6.70594i	−0.154892	+	0.304816i
$485$	−18.2099	+	4.13797i	−0.826870	+	0.187895i
$486$	18.4136	−	11.2977i	0.835256	−	0.512473i
$487$	12.2249			0.553964			0.276982	−	0.960875i	$-0.410666\pi$
$487$	12.2249			0.553964			0.276982	+	0.960875i	$0.410666\pi$
$488$	−3.23948	−	40.3167i	−0.146644	−	1.82505i
$489$		−	7.85613i		−	0.355266i
$490$		0			0
$491$		−	22.9515i		−	1.03579i	−0.855445	−	0.517894i	$-0.826716\pi$
$491$		−	22.9515i		−	1.03579i	0.855445	−	0.517894i	$-0.173284\pi$
$492$	0.216150	−	0.425366i	0.00974479	−	0.0191770i
$493$	−7.34947			−0.331003
$494$	9.42503	+	15.3614i	0.424052	+	0.691142i
$495$	−3.28327	−	14.4487i	−0.147572	−	0.649420i
$496$	18.0047	+	24.6678i	0.808433	+	1.10762i
$497$		0			0
$498$	2.85209	+	4.64848i	0.127805	+	0.208303i
$499$			4.20745i			0.188351i	0.995556	+	0.0941756i	$0.0300215\pi$
$499$			4.20745i			0.188351i	−0.995556	+	0.0941756i	$0.969978\pi$
$500$	−4.44635	−	21.9142i	−0.198847	−	0.980031i
$501$	9.69314			0.433058
$502$	11.2156	+	18.2797i	0.500576	+	0.815864i
$503$		−	43.1904i		−	1.92576i	−0.269924	−	0.962882i	$-0.586999\pi$
$503$		−	43.1904i		−	1.92576i	0.269924	−	0.962882i	$-0.413001\pi$
$504$		0			0
$505$	−0.138416	−	0.609125i	−0.00615942	−	0.0271057i
$506$	15.9319	−	9.77503i	0.708258	−	0.434553i
$507$		−	1.91420i		−	0.0850127i
$508$	−1.55632	+	3.06273i	−0.0690507	+	0.135886i
$509$		−	37.3582i		−	1.65587i	−0.560821	−	0.827937i	$-0.689514\pi$
$509$		−	37.3582i		−	1.65587i	0.560821	−	0.827937i	$-0.310486\pi$
$510$	−2.35241	+	2.29832i	−0.104167	+	0.101771i
$511$		0			0
$512$	−21.9760	+	5.39037i	−0.971211	+	0.238223i
$513$			12.9133i			0.570135i
$514$	3.49937	+	5.70346i	0.154351	+	0.251569i
$515$	−6.63980	−	29.2198i	−0.292585	−	1.28758i
$516$	−12.1290	−	6.16335i	−0.533950	−	0.271327i
$517$	17.6653			0.776921
$518$		0			0
$519$			8.24817i			0.362055i
$520$	−23.8464	+	7.47128i	−1.04573	+	0.327637i
$521$		−	16.1208i		−	0.706265i	−0.935573	−	0.353132i	$-0.885117\pi$
$521$		−	16.1208i		−	0.706265i	0.935573	−	0.353132i	$-0.114883\pi$
$522$	−9.43393	−	15.3759i	−0.412912	−	0.672986i
$523$		−	15.9671i		−	0.698193i	−0.937087	−	0.349097i	$-0.886489\pi$
$523$		−	15.9671i		−	0.698193i	0.937087	−	0.349097i	$-0.113511\pi$
$524$	12.8145	−	25.2178i	0.559802	−	1.10165i
$525$		0			0
$526$	−3.47635	−	5.66594i	−0.151576	−	0.247047i
$527$	−10.8341			−0.471939
$528$	−4.65016	−	6.37107i	−0.202372	−	0.277265i
$529$	1.13161			0.0492004
$530$	3.65507	−	3.57102i	0.158766	−	0.155115i
$531$	18.8036			0.816007
$532$		0			0
$533$			1.28614i			0.0557090i
$534$	2.57200	+	4.19199i	0.111302	+	0.181405i
$535$	11.8377	−	2.68996i	0.511789	−	0.116297i
$536$	8.53296	−	0.685630i	0.368568	−	0.0296147i
$537$	0.590701			0.0254906
$538$	29.5822	−	18.1502i	1.27538	−	0.782511i
$539$		0			0
$540$	−17.3632	−	4.37264i	−0.747193	−	0.188169i
$541$	−14.6337			−0.629153			−0.314576	−	0.949232i	$-0.601862\pi$
$541$	−14.6337			−0.629153			−0.314576	+	0.949232i	$0.601862\pi$
$542$	−19.5186	−	31.8125i	−0.838397	−	1.36646i
$543$	0.0488927			0.00209818
$544$	3.05160	−	7.42451i	0.130836	−	0.318323i
$545$	−19.4434	+	4.41826i	−0.832864	+	0.189257i
$546$		0			0
$547$	−16.5936			−0.709493			−0.354747	−	0.934963i	$-0.615433\pi$
$547$	−16.5936			−0.709493			−0.354747	+	0.934963i	$0.615433\pi$
$548$	−26.5151	−	13.4736i	−1.13267	−	0.575566i
$549$			35.2189i			1.50311i
$550$	−10.3238	+	15.9802i	−0.440210	+	0.681398i
$551$	16.7046			0.711641
$552$	−0.815602	−	10.1505i	−0.0347143	−	0.432035i
$553$		0			0
$554$	−29.0143	+	17.8018i	−1.23270	+	0.756327i
$555$	−7.15911	+	1.62681i	−0.303887	+	0.0690544i
$556$	6.40350	−	12.6016i	0.271569	−	0.534427i
$557$			24.7755i			1.04977i	0.851173	+	0.524886i	$0.175892\pi$
$557$			24.7755i			1.04977i	−0.851173	+	0.524886i	$0.824108\pi$
$558$	−13.9068	−	22.6661i	−0.588723	−	0.959531i
$559$	36.6734			1.55112
$560$		0			0
$561$	2.79817			0.118139
$562$	−5.75822	−	9.38506i	−0.242896	−	0.395885i
$563$			23.9524i			1.00947i	0.863273	+	0.504737i	$0.168410\pi$
$563$			23.9524i			1.00947i	−0.863273	+	0.504737i	$0.831590\pi$
$564$	4.35990	−	8.57993i	0.183585	−	0.361280i
$565$	−0.521055	−	2.29301i	−0.0219210	−	0.0964675i
$566$	−9.58371	+	5.88011i	−0.402833	+	0.247159i
$567$		0			0
$568$	3.49068	+	43.4430i	0.146466	+	1.82283i
$569$	9.16157			0.384073			0.192036	−	0.981388i	$-0.438491\pi$
$569$	9.16157			0.384073			0.192036	+	0.981388i	$0.438491\pi$
$570$	5.34681	−	5.22386i	0.223953	−	0.218803i
$571$			24.7258i			1.03474i	0.855761	+	0.517372i	$0.173090\pi$
$571$			24.7258i			1.03474i	−0.855761	+	0.517372i	$0.826910\pi$
$572$	18.9547	+	9.63184i	0.792536	+	0.402727i
$573$	−12.7967			−0.534589
$574$		0			0
$575$	−22.1499	+	10.6147i	−0.923716	+	0.442662i
$576$	19.4500	−	3.14596i	0.810417	−	0.131082i
$577$	9.50367			0.395643			0.197822	−	0.980238i	$-0.436613\pi$
$577$	9.50367			0.395643			0.197822	+	0.980238i	$0.436613\pi$
$578$	−11.0837	−	18.0648i	−0.461020	−	0.751395i
$579$	−12.6036			−0.523786
$580$	−5.65646	+	22.4611i	−0.234872	+	0.932645i
$581$		0			0
$582$	7.37801	−	4.52679i	0.305828	−	0.187642i
$583$	−4.34766			−0.180062
$584$	4.00070	−	0.321459i	0.165550	−	0.0133021i
$585$	21.2186	−	4.82165i	0.877281	−	0.199351i
$586$	−1.56422	−	2.54946i	−0.0646175	−	0.105317i
$587$		−	14.2100i		−	0.586508i	−0.956035	−	0.293254i	$-0.905262\pi$
$587$		−	14.2100i		−	0.586508i	0.956035	−	0.293254i	$-0.0947382\pi$
$588$		0			0
$589$	24.6248			1.01465
$590$	−16.8724	−	17.2695i	−0.694627	−	0.710976i
$591$	−8.75033			−0.359940
$592$	14.4739	−	10.5643i	0.594874	−	0.434190i
$593$	17.7571			0.729196			0.364598	−	0.931165i	$-0.381206\pi$
$593$	17.7571			0.729196			0.364598	+	0.931165i	$0.381206\pi$
$594$	7.96695	+	12.9850i	0.326888	+	0.532779i
$595$		0			0
$596$	−7.96020	+	15.6651i	−0.326063	+	0.641666i
$597$			11.3749i			0.465545i
$598$	14.3551	+	23.3967i	0.587024	+	0.956763i
$599$			20.9621i			0.856488i	0.903663	+	0.428244i	$0.140868\pi$
$599$			20.9621i			0.856488i	−0.903663	+	0.428244i	$0.859132\pi$
$600$	5.21349	+	8.95821i	0.212840	+	0.365717i
$601$			20.7196i			0.845169i	0.906324	+	0.422585i	$0.138877\pi$
$601$			20.7196i			0.845169i	−0.906324	+	0.422585i	$0.861123\pi$
$602$		0			0
$603$	−7.45401			−0.303551
$604$	0.535494	+	0.272111i	0.0217889	+	0.0110721i
$605$	−8.20087	+	1.86354i	−0.333413	+	0.0757636i
$606$	0.151422	+	0.246796i	0.00615110	+	0.0100254i
$607$		−	3.20526i		−	0.130097i	−0.997882	−	0.0650487i	$-0.979280\pi$
$607$		−	3.20526i		−	0.130097i	0.997882	−	0.0650487i	$-0.0207203\pi$
$608$	−6.93600	+	16.8752i	−0.281292	+	0.684380i
$609$		0			0
$610$	32.3456	−	31.6018i	1.30964	−	1.27952i
$611$			25.9424i			1.04952i
$612$	−3.16643	+	6.23129i	−0.127995	+	0.251885i
$613$		−	4.79556i		−	0.193691i	−0.995299	−	0.0968454i	$-0.969125\pi$
$613$		−	4.79556i		−	0.193691i	0.995299	−	0.0968454i	$-0.0308753\pi$
$614$	−22.4881	+	13.7976i	−0.907547	+	0.556827i
$615$	0.520191	−	0.118207i	0.0209761	−	0.00476655i
$616$		0			0
$617$		−	8.95961i		−	0.360700i	−0.983602	−	0.180350i	$-0.942277\pi$
$617$		−	8.95961i		−	0.360700i	0.983602	−	0.180350i	$-0.0577231\pi$
$618$	7.26372	+	11.8388i	0.292190	+	0.476226i
$619$	−25.6693			−1.03174			−0.515868	−	0.856668i	$-0.672531\pi$
$619$	−25.6693			−1.03174			−0.515868	+	0.856668i	$0.672531\pi$
$620$	−8.33834	+	33.1105i	−0.334876	+	1.32975i
$621$			19.6680i			0.789250i
$622$	6.05205	+	9.86394i	0.242665	+	0.395508i
$623$		0			0
$624$	9.35623	−	6.82898i	0.374549	−	0.273378i
$625$	15.6620	−	19.4860i	0.626478	−	0.779439i
$626$	17.2872	+	28.1756i	0.690937	+	1.12613i
$627$	−6.35997			−0.253993
$628$	−17.4274	+	34.2958i	−0.695429	+	1.36855i
$629$			6.35693i			0.253467i
$630$		0			0
$631$			1.75095i			0.0697043i	0.999392	+	0.0348521i	$0.0110960\pi$
$631$			1.75095i			0.0697043i	−0.999392	+	0.0348521i	$0.988904\pi$
$632$	−2.76663	−	34.4319i	−0.110051	−	1.36963i
$633$	10.3806			0.412591
$634$	−31.5912	+	19.3828i	−1.25465	+	0.769791i
$635$	−3.74548	+	0.851112i	−0.148635	+	0.0337753i
$636$	−1.07302	+	2.11163i	−0.0425482	+	0.0837315i
$637$		0			0
$638$	16.7974	−	10.3061i	0.665014	−	0.408021i
$639$		−	37.9499i		−	1.50127i
$640$	−20.3418	−	15.0404i	−0.804079	−	0.594523i
$641$	−40.7774			−1.61061			−0.805306	−	0.592859i	$-0.797999\pi$
$641$	−40.7774			−1.61061			−0.805306	+	0.592859i	$0.797999\pi$
$642$	−4.79621	+	2.94273i	−0.189291	+	0.116140i
$643$		−	35.0077i		−	1.38057i	−0.723538	−	0.690285i	$-0.757485\pi$
$643$		−	35.0077i		−	1.38057i	0.723538	−	0.690285i	$-0.242515\pi$
$644$		0			0
$645$	−3.37057	−	14.8329i	−0.132716	−	0.584043i
$646$	−3.38489	−	5.51687i	−0.133177	−	0.217058i
$647$			24.2431i			0.953094i	0.879149	+	0.476547i	$0.158112\pi$
$647$			24.2431i			0.953094i	−0.879149	+	0.476547i	$0.841888\pi$
$648$	−12.5578	+	1.00903i	−0.493319	+	0.0396385i
$649$			20.5419i			0.806341i
$650$	−23.4677	−	15.1611i	−0.920478	−	0.594666i
$651$		0			0
$652$	−9.71192	+	19.1123i	−0.380348	+	0.748495i
$653$			43.1911i			1.69020i	0.534608	+	0.845100i	$0.320459\pi$
$653$			43.1911i			1.69020i	−0.534608	+	0.845100i	$0.679541\pi$
$654$	7.87777	−	4.83343i	0.308045	−	0.189002i
$655$	30.8395	−	7.00788i	1.20500	−	0.273820i
$656$	−1.05169	+	0.767617i	−0.0410618	+	0.0299704i
$657$	−3.49483			−0.136346
$658$		0			0
$659$			11.6398i			0.453422i	0.973962	+	0.226711i	$0.0727973\pi$
$659$			11.6398i			0.453422i	−0.973962	+	0.226711i	$0.927203\pi$
$660$	2.15359	−	8.55162i	0.0838283	−	0.332871i
$661$		−	17.0920i		−	0.664801i	−0.943138	−	0.332400i	$-0.892141\pi$
$661$		−	17.0920i		−	0.664801i	0.943138	−	0.332400i	$-0.107859\pi$
$662$	23.5312	−	14.4377i	0.914568	−	0.561135i
$663$			4.10925i			0.159590i
$664$	−1.19197	−	14.8346i	−0.0462574	−	0.575693i
$665$		0			0
$666$	−13.2994	+	8.15989i	−0.515342	+	0.316189i
$667$	25.4426			0.985140
$668$	−23.5814	−	11.9829i	−0.912391	−	0.463631i
$669$	2.22395			0.0859830
$670$	6.68847	+	6.84589i	0.258398	+	0.264480i
$671$	−38.4748			−1.48530
$672$		0			0
$673$			3.77972i			0.145697i	0.997343	+	0.0728487i	$0.0232090\pi$
$673$			3.77972i			0.145697i	−0.997343	+	0.0728487i	$0.976791\pi$
$674$	−38.2742	+	23.4832i	−1.47427	+	0.904540i
$675$	−8.65128	−	18.0529i	−0.332988	−	0.694855i
$676$	−2.36638	+	4.65685i	−0.0910146	+	0.179110i
$677$	−27.7744			−1.06746			−0.533729	−	0.845655i	$-0.679210\pi$
$677$	−27.7744			−1.06746			−0.533729	+	0.845655i	$0.679210\pi$
$678$	0.570017	+	0.929044i	0.0218914	+	0.0356797i
$679$		0			0
$680$	8.56416	−	2.68322i	0.328421	−	0.102897i
$681$	10.8300			0.415006
$682$	24.7615	−	15.1925i	0.948166	−	0.581750i
$683$	11.1730			0.427525			0.213762	−	0.976886i	$-0.431428\pi$
$683$	11.1730			0.427525			0.213762	+	0.976886i	$0.431428\pi$
$684$	7.19700	−	14.1631i	0.275184	−	0.541541i
$685$	−7.36837	−	32.4260i	−0.281531	−	1.23893i
$686$		0			0
$687$	−4.71324			−0.179821
$688$	21.8880	+	29.9883i	0.834473	+	1.14329i
$689$		−	6.38475i		−	0.243240i
$690$	8.14365	−	7.95638i	0.310023	−	0.302894i
$691$	35.4114			1.34711			0.673556	−	0.739136i	$-0.264766\pi$
$691$	35.4114			1.34711			0.673556	+	0.739136i	$0.264766\pi$
$692$	10.1966	−	20.0661i	0.387616	−	0.762797i
$693$		0			0
$694$	−13.5966	−	22.1605i	−0.516122	−	0.841202i
$695$	15.4108	−	3.50190i	0.584565	−	0.132835i
$696$	−0.859910	−	10.7020i	−0.0325948	−	0.405657i
$697$		−	0.461903i		−	0.0174958i
$698$	−2.86153	+	1.75570i	−0.108310	+	0.0664541i
$699$	−12.8043			−0.484304
$700$		0			0
$701$	2.24955			0.0849643			0.0424821	−	0.999097i	$-0.486473\pi$
$701$	2.24955			0.0849643			0.0424821	+	0.999097i	$0.486473\pi$
$702$	−19.0690	+	11.6999i	−0.719715	+	0.441583i
$703$		−	14.4487i		−	0.544942i
$704$	3.43679	+	21.2481i	0.129529	+	0.800818i
$705$	10.4926	−	2.38431i	0.395175	−	0.0897983i
$706$	−1.59321	−	2.59671i	−0.0599614	−	0.0977283i
$707$		0			0
$708$	9.97707	+	5.06985i	0.374961	+	0.190537i
$709$	−15.8920			−0.596837			−0.298418	−	0.954435i	$-0.596459\pi$
$709$	−15.8920			−0.596837			−0.298418	+	0.954435i	$0.596459\pi$
$710$	−34.8538	+	34.0523i	−1.30804	+	1.27796i
$711$			30.0782i			1.12802i
$712$	−1.07492	−	13.3778i	−0.0402842	−	0.501354i
$713$	37.5056			1.40460
$714$		0			0
$715$	5.26739	+	23.1802i	0.196989	+	0.866890i
$716$	−1.43705	−	0.730237i	−0.0537051	−	0.0272902i
$717$	2.36355			0.0882682
$718$	6.12437	−	3.75762i	0.228560	−	0.140233i
$719$	−36.0284			−1.34363			−0.671817	−	0.740717i	$-0.734486\pi$
$719$	−36.0284			−1.34363			−0.671817	+	0.740717i	$0.734486\pi$
$720$	16.6067	+	14.4730i	0.618897	+	0.539375i
$721$		0			0
$722$	−6.35856	−	10.3635i	−0.236641	−	0.385690i
$723$	15.0152			0.558420
$724$	−0.118946	−	0.0604422i	−0.00442058	−	0.00224632i
$725$	−23.3532	+	11.1913i	−0.867317	+	0.415635i
$726$	3.32270	−	2.03865i	0.123317	−	0.0756613i
$727$			51.4779i			1.90921i	0.297878	+	0.954604i	$0.403721\pi$
$727$			51.4779i			1.90921i	−0.297878	+	0.954604i	$0.596279\pi$
$728$		0			0
$729$	2.16686			0.0802541
$730$	3.13590	+	3.20971i	0.116065	+	0.118797i
$731$	−13.1708			−0.487141
$732$	−9.49577	+	18.6869i	−0.350974	+	0.690689i
$733$	−35.9435			−1.32760			−0.663801	−	0.747909i	$-0.731058\pi$
$733$	−35.9435			−1.32760			−0.663801	+	0.747909i	$0.731058\pi$
$734$	−16.3277	+	10.0179i	−0.602667	+	0.369768i
$735$		0			0
$736$	−10.5641	+	25.7024i	−0.389398	+	0.947401i
$737$		−	8.14311i		−	0.299955i
$738$	0.966354	−	0.592909i	0.0355720	−	0.0218253i
$739$			18.2331i			0.670714i	0.942091	+	0.335357i	$0.108857\pi$
$739$			18.2331i			0.670714i	−0.942091	+	0.335357i	$0.891143\pi$
$740$	19.4277	+	4.89256i	0.714177	+	0.179854i
$741$		−	9.33993i		−	0.343111i
$742$		0			0
$743$	29.1171			1.06820			0.534102	−	0.845420i	$-0.320650\pi$
$743$	29.1171			1.06820			0.534102	+	0.845420i	$0.320650\pi$
$744$	−1.26762	−	15.7761i	−0.0464731	−	0.578378i
$745$	−19.1572	+	4.35322i	−0.701865	+	0.159490i
$746$	8.59940	−	5.27618i	0.314846	−	0.193175i
$747$			12.9588i			0.474139i
$748$	−6.80736	−	3.45916i	−0.248902	−	0.126479i
$749$		0			0
$750$	−3.97515	+	10.8851i	−0.145152	+	0.397468i
$751$			43.0360i			1.57041i	0.619239	+	0.785203i	$0.287441\pi$
$751$			43.0360i			1.57041i	−0.619239	+	0.785203i	$0.712559\pi$
$752$	−21.2134	+	15.4834i	−0.773573	+	0.564621i
$753$		−	11.1143i		−	0.405028i
$754$	15.1350	+	24.6678i	0.551183	+	0.898347i
$755$	0.148810	+	0.654869i	0.00541576	+	0.0238331i
$756$		0			0
$757$		−	10.6531i		−	0.387193i	−0.981081	−	0.193597i	$-0.937985\pi$
$757$		−	10.6531i		−	0.387193i	0.981081	−	0.193597i	$-0.0620153\pi$
$758$	19.5802	−	12.0135i	0.711186	−	0.436350i
$759$	−9.68677			−0.351608
$760$	−19.4655	+	6.09871i	−0.706088	+	0.221223i
$761$			14.2373i			0.516101i	0.966131	+	0.258050i	$0.0830800\pi$
$761$			14.2373i			0.516101i	−0.966131	+	0.258050i	$0.916920\pi$
$762$	1.51754	−	0.931088i	0.0549745	−	0.0337297i
$763$		0			0
$764$	31.1316	+	15.8195i	1.12630	+	0.572331i
$765$	−7.62041	+	1.73164i	−0.275516	+	0.0626075i
$766$	−11.9181	+	7.31238i	−0.430619	+	0.264207i
$767$	−30.1668			−1.08926
$768$	11.1683	+	3.57491i	0.403001	+	0.128999i
$769$			35.5770i			1.28294i	0.767149	+	0.641469i	$0.221675\pi$
$769$			35.5770i			1.28294i	−0.767149	+	0.641469i	$0.778325\pi$
$770$		0			0
$771$		−	3.46777i		−	0.124889i
$772$	30.6618	+	15.5808i	1.10354	+	0.560765i
$773$	−11.8854			−0.427487			−0.213743	−	0.976890i	$-0.568566\pi$
$773$	−11.8854			−0.427487			−0.213743	+	0.976890i	$0.568566\pi$
$774$	−16.9064	−	27.5549i	−0.607686	−	0.990439i
$775$	−34.4257	+	16.4974i	−1.23661	+	0.592605i
$776$	−23.5453	+	1.89188i	−0.845226	+	0.0679145i
$777$		0			0
$778$	−23.6388	−	38.5277i	−0.847491	−	1.38129i
$779$			1.04986i			0.0376152i
$780$	12.5585	+	3.16265i	0.449666	+	0.113241i
$781$	41.4582			1.48349
$782$	−5.15547	−	8.40265i	−0.184359	−	0.300478i
$783$			20.7365i			0.741061i
$784$		0			0
$785$	−41.9412	+	9.53058i	−1.49694	+	0.340161i
$786$	−12.4951	+	7.66638i	−0.445685	+	0.273451i
$787$		−	46.3779i		−	1.65319i	−0.562794	−	0.826597i	$-0.690274\pi$
$787$		−	46.3779i		−	1.65319i	0.562794	−	0.826597i	$-0.309726\pi$
$788$	21.2877	+	10.8173i	0.758343	+	0.385352i
$789$			3.44496i			0.122644i
$790$	27.6243	−	26.9891i	0.982828	−	0.960228i
$791$		0			0
$792$	−1.50111	−	18.6820i	−0.0533398	−	0.663836i
$793$		−	56.5021i		−	2.00645i
$794$	−12.9247	−	21.0654i	−0.458681	−	0.747582i
$795$	−2.58236	+	0.586808i	−0.0915870	+	0.0208119i
$796$	14.0619	−	27.6728i	0.498412	−	0.980836i
$797$	−9.09251			−0.322073			−0.161037	−	0.986948i	$-0.551484\pi$
$797$	−9.09251			−0.322073			−0.161037	+	0.986948i	$0.551484\pi$
$798$		0			0
$799$		−	9.31691i		−	0.329609i
$800$	−1.60899	−	28.2385i	−0.0568863	−	0.998381i
$801$			11.6862i			0.412913i
$802$	−12.8381	−	20.9242i	−0.453328	−	0.738858i
$803$		−	3.81791i		−	0.134731i
$804$	−3.95505	−	2.00976i	−0.139484	−	0.0708788i
$805$		0			0
$806$	22.3109	+	36.3634i	0.785867	+	1.28085i
$807$	−17.9863			−0.633149
$808$	−0.0632837	−	0.787593i	−0.00222631	−	0.0277074i
$809$	17.3226			0.609029			0.304515	−	0.952508i	$-0.401506\pi$
$809$	17.3226			0.609029			0.304515	+	0.952508i	$0.401506\pi$
$810$	−9.84334	−	10.0750i	−0.345860	−	0.354000i
$811$	−16.4459			−0.577493			−0.288746	−	0.957406i	$-0.593238\pi$
$811$	−16.4459			−0.577493			−0.288746	+	0.957406i	$0.593238\pi$
$812$		0			0
$813$			19.3424i			0.678368i
$814$	−8.91424	−	14.5289i	−0.312444	−	0.509238i
$815$	−23.3729	+	5.31119i	−0.818717	+	0.186043i
$816$	−3.36018	+	2.45255i	−0.117630	+	0.0858564i
$817$	29.9360			1.04733
$818$	8.79934	−	5.39886i	0.307662	−	0.188767i
$819$		0			0
$820$	−1.41164	−	0.355500i	−0.0492968	−	0.0124146i
$821$	44.9053			1.56721			0.783603	−	0.621261i	$-0.213379\pi$
$821$	44.9053			1.56721			0.783603	+	0.621261i	$0.213379\pi$
$822$	8.06075	+	13.1378i	0.281151	+	0.458235i
$823$	−23.7093			−0.826453			−0.413226	−	0.910628i	$-0.635598\pi$
$823$	−23.7093			−0.826453			−0.413226	+	0.910628i	$0.635598\pi$
$824$	−3.03572	−	37.7809i	−0.105754	−	1.31616i
$825$	8.89130	−	4.26088i	0.309555	−	0.148345i
$826$		0			0
$827$	8.20536			0.285328			0.142664	−	0.989771i	$-0.454433\pi$
$827$	8.20536			0.285328			0.142664	+	0.989771i	$0.454433\pi$
$828$	10.9616	−	21.5717i	0.380943	−	0.749667i
$829$			22.1180i			0.768190i	0.923293	+	0.384095i	$0.125487\pi$
$829$			22.1180i			0.768190i	−0.923293	+	0.384095i	$0.874513\pi$
$830$	11.9016	−	11.6279i	0.413111	−	0.403611i
$831$	17.6411			0.611962
$832$	−31.2039	+	5.04710i	−1.08180	+	0.174977i
$833$		0			0
$834$	−6.24391	+	3.83096i	−0.216209	+	0.132655i
$835$	−6.55311	−	28.8383i	−0.226780	−	0.997989i
$836$	15.4725	+	7.86234i	0.535127	+	0.271925i
$837$			30.5682i			1.05659i
$838$	13.2591	+	21.6104i	0.458028	+	0.746518i
$839$	3.64977			0.126004			0.0630020	−	0.998013i	$-0.479933\pi$
$839$	3.64977			0.126004			0.0630020	+	0.998013i	$0.479933\pi$
$840$		0			0
$841$	−2.17525			−0.0750086
$842$	9.34348	+	15.2285i	0.321998	+	0.524809i
$843$			5.70623i			0.196533i
$844$	−25.2538	−	12.8327i	−0.869270	−	0.441720i
$845$	−5.69498	+	1.29411i	−0.195913	+	0.0445187i
$846$	19.4920	−	11.9594i	0.670150	−	0.411172i
$847$		0			0
$848$	5.22088	−	3.81065i	0.179286	−	0.130858i
$849$	5.82702			0.199983
$850$	8.42814	+	5.44492i	0.289083	+	0.186759i
$851$		−	22.0066i		−	0.754375i
$852$	10.2321	−	20.1360i	0.350546	−	0.689847i
$853$	1.03474			0.0354290			0.0177145	−	0.999843i	$-0.494361\pi$
$853$	1.03474			0.0354290			0.0177145	+	0.999843i	$0.494361\pi$
$854$		0			0
$855$	17.3205	−	3.93584i	0.592347	−	0.134603i
$856$	15.3060	−	1.22985i	0.523150	−	0.0420355i
$857$	48.5127			1.65716			0.828581	−	0.559870i	$-0.189149\pi$
$857$	48.5127			1.65716			0.828581	+	0.559870i	$0.189149\pi$
$858$	−5.76235	−	9.39178i	−0.196723	−	0.320630i
$859$	−24.9348			−0.850763			−0.425382	−	0.905014i	$-0.639860\pi$
$859$	−24.9348			−0.850763			−0.425382	+	0.905014i	$0.639860\pi$
$860$	−10.1368	+	40.2520i	−0.345663	+	1.37258i
$861$		0			0
$862$	39.3852	−	24.1649i	1.34147	−	0.823060i
$863$	−5.96709			−0.203122			−0.101561	−	0.994829i	$-0.532384\pi$
$863$	−5.96709			−0.203122			−0.101561	+	0.994829i	$0.532384\pi$
$864$	−20.9482	−	8.61008i	−0.712672	−	0.292921i
$865$	24.5393	−	5.57623i	0.834361	−	0.189598i
$866$	−17.4456	−	28.4338i	−0.592826	−	0.966218i
$867$			10.9836i			0.373023i
$868$		0			0
$869$	−32.8588			−1.11466
$870$	8.58605	−	8.38862i	0.291094	−	0.284401i
$871$	11.9585			0.405200
$872$	−25.1401	+	2.02003i	−0.851353	+	0.0684068i
$873$	20.5681			0.696124
$874$	11.7179	+	19.0984i	0.396363	+	0.646014i
$875$		0			0
$876$	−1.85433	−	0.942281i	−0.0626522	−	0.0318367i
$877$			33.8298i			1.14235i	0.820828	+	0.571175i	$0.193512\pi$
$877$			33.8298i			1.14235i	−0.820828	+	0.571175i	$0.806488\pi$
$878$	13.6009	+	22.1675i	0.459010	+	0.748118i
$879$			1.55010i			0.0522836i
$880$	−15.8109	+	18.1420i	−0.532986	+	0.611566i
$881$			20.9239i			0.704944i	0.935822	+	0.352472i	$0.114659\pi$
$881$			20.9239i			0.704944i	−0.935822	+	0.352472i	$0.885341\pi$
$882$		0			0
$883$	14.7876			0.497642			0.248821	−	0.968549i	$-0.419957\pi$
$883$	14.7876			0.497642			0.248821	+	0.968549i	$0.419957\pi$
$884$	5.07994	−	9.99693i	0.170857	−	0.336233i
$885$	2.77257	+	12.2012i	0.0931988	+	0.410139i
$886$	−2.50300	−	4.07952i	−0.0840898	−	0.137054i
$887$			7.39916i			0.248439i	0.992255	+	0.124220i	$0.0396428\pi$
$887$			7.39916i			0.248439i	−0.992255	+	0.124220i	$0.960357\pi$
$888$	−9.25667	+	0.743780i	−0.310633	+	0.0249596i
$889$		0			0
$890$	10.7328	−	10.4860i	0.359766	−	0.351493i
$891$			11.9841i			0.401483i
$892$	−5.41041	−	2.74930i	−0.181154	−	0.0920533i
$893$			21.1764i			0.708643i
$894$	7.76181	−	4.76228i	0.259594	−	0.159274i
$895$	−0.399347	−	1.75740i	−0.0133487	−	0.0587435i
$896$		0			0
$897$		−	14.2255i		−	0.474976i
$898$	−8.80201	−	14.3460i	−0.293727	−	0.478732i
$899$	39.5431			1.31884
$900$	−0.572844	+	24.6218i	−0.0190948	+	0.820728i
$901$			2.29301i			0.0763911i
$902$	0.647721	+	1.05569i	0.0215668	+	0.0351506i
$903$		0			0
$904$	−0.238227	−	2.96484i	−0.00792331	−	0.0986090i
$905$	−0.0330542	−	0.145461i	−0.00109876	−	0.00483530i
$906$	−0.162793	−	0.265329i	−0.00540845	−	0.00881498i
$907$	−18.5122			−0.614686			−0.307343	−	0.951599i	$-0.599440\pi$
$907$	−18.5122			−0.614686			−0.307343	+	0.951599i	$0.599440\pi$
$908$	−26.3471	−	13.3883i	−0.874358	−	0.444305i
$909$			0.688006i			0.0228197i
$910$		0			0
$911$		−	10.8437i		−	0.359267i	−0.983734	−	0.179634i	$-0.942509\pi$
$911$		−	10.8437i		−	0.359267i	0.983734	−	0.179634i	$-0.0574912\pi$
$912$	7.63737	−	5.57441i	0.252898	−	0.184587i
$913$	−14.1568			−0.468522
$914$	25.3985	−	15.5833i	0.840107	−	0.515450i
$915$	−22.8527	+	5.19298i	−0.755488	+	0.171675i
$916$	11.4663	+	5.82661i	0.378858	+	0.192517i
$917$		0			0
$918$	6.84842	−	4.20187i	0.226032	−	0.138682i
$919$			16.1145i			0.531567i	0.964033	+	0.265784i	$0.0856307\pi$
$919$			16.1145i			0.531567i	−0.964033	+	0.265784i	$0.914369\pi$
$920$	−29.6476	+	9.28884i	−0.977453	+	0.306244i
$921$	13.6731			0.450543
$922$	35.7656	−	21.9440i	1.17788	−	0.722689i
$923$			60.8834i			2.00400i
$924$		0			0
$925$	9.67993	+	20.1994i	0.318274	+	0.664152i
$926$	11.1293	+	18.1391i	0.365731	+	0.596088i
$927$			33.0037i			1.08398i
$928$	−11.1380	+	27.0986i	−0.365623	+	0.889557i
$929$			49.3541i			1.61925i	0.586944	+	0.809627i	$0.300331\pi$
$929$			49.3541i			1.61925i	−0.586944	+	0.809627i	$0.699669\pi$
$930$	12.6569	−	12.3659i	0.415037	−	0.405494i
$931$		0			0
$932$	31.1502	+	15.8290i	1.02036	+	0.518496i
$933$		−	5.99740i		−	0.196346i
$934$	6.20303	−	3.80589i	0.202969	−	0.124532i
$935$	−1.89172	−	8.32489i	−0.0618659	−	0.272253i
$936$	27.4354	−	2.20446i	0.896756	−	0.0720550i
$937$	31.3085			1.02280			0.511402	−	0.859342i	$-0.329126\pi$
$937$	31.3085			1.02280			0.511402	+	0.859342i	$0.329126\pi$
$938$		0			0
$939$		−	17.1311i		−	0.559054i
$940$	−28.4739	−	7.17068i	−0.928715	−	0.233882i
$941$		−	43.8200i		−	1.42849i	−0.699896	−	0.714245i	$-0.746770\pi$
$941$		−	43.8200i		−	1.42849i	0.699896	−	0.714245i	$-0.253230\pi$
$942$	16.9931	−	10.4261i	0.553664	−	0.339702i
$943$			1.59903i			0.0520715i
$944$	−18.0047	−	24.6678i	−0.586002	−	0.802867i
$945$		0			0
$946$	30.1022	−	18.4693i	0.978708	−	0.600488i
$947$	−14.6346			−0.475560			−0.237780	−	0.971319i	$-0.576420\pi$
$947$	−14.6346			−0.475560			−0.237780	+	0.971319i	$0.576420\pi$
$948$	−8.10971	+	15.9593i	−0.263391	+	0.518334i
$949$	5.60679			0.182004
$950$	−19.1564	−	12.3758i	−0.621514	−	0.401523i
$951$	19.2078			0.622857
$952$		0			0
$953$		−	28.2044i		−	0.913630i	−0.889562	−	0.456815i	$-0.848990\pi$
$953$		−	28.2044i		−	0.913630i	0.889562	−	0.456815i	$-0.151010\pi$
$954$	−4.79723	+	2.94335i	−0.155316	+	0.0952945i
$955$	8.65128	+	38.0716i	0.279949	+	1.23197i
$956$	−5.75001	−	2.92187i	−0.185969	−	0.0945000i
$957$	−10.2130			−0.330140
$958$	29.5513	+	48.1643i	0.954759	+	1.55612i
$959$		0			0
$960$	4.90922	+	12.1568i	0.158444	+	0.392359i
$961$	27.2916			0.880375
$962$	21.3364	−	13.0910i	0.687913	−	0.422071i
$963$	−13.3707			−0.430864
$964$	−36.5287	−	18.5621i	−1.17651	−	0.597844i
$965$	8.52071	+	37.4971i	0.274291	+	1.20707i
$966$		0			0
$967$	8.88824			0.285827			0.142913	−	0.989735i	$-0.454353\pi$
$967$	8.88824			0.285827			0.142913	+	0.989735i	$0.454353\pi$
$968$	−10.6036	+	0.852011i	−0.340814	+	0.0273847i
$969$			3.35432i			0.107756i
$970$	−18.4557	−	18.8901i	−0.592577	−	0.606524i
$971$	−8.74211			−0.280548			−0.140274	−	0.990113i	$-0.544798\pi$
$971$	−8.74211			−0.280548			−0.140274	+	0.990113i	$0.544798\pi$
$972$	27.2367	+	13.8403i	0.873618	+	0.443929i
$973$		0			0
$974$	9.04134	+	14.7360i	0.289703	+	0.472173i
$975$	6.25731	+	13.0573i	0.200394	+	0.418168i
$976$	46.2024	−	33.7225i	1.47890	−	1.07943i
$977$		−	41.9813i		−	1.34310i	−0.740959	−	0.671551i	$-0.765629\pi$
$977$		−	41.9813i		−	1.34310i	0.740959	−	0.671551i	$-0.234371\pi$
$978$	9.46986	−	5.81026i	0.302813	−	0.185792i
$979$	−12.7666			−0.408022
$980$		0			0
$981$	21.9613			0.701170
$982$	27.6661	−	16.9746i	0.882859	−	0.541680i
$983$		−	11.0047i		−	0.350996i	−0.984480	−	0.175498i	$-0.943846\pi$
$983$		−	11.0047i		−	0.350996i	0.984480	−	0.175498i	$-0.0561535\pi$
$984$	0.672602	−	0.0540441i	0.0214418	−	0.00172286i
$985$	5.91572	+	26.0333i	0.188490	+	0.829489i
$986$	−5.43554	−	8.85913i	−0.173103	−	0.282132i
$987$		0			0
$988$	−11.5462	+	22.7221i	−0.367334	+	0.722885i
$989$	45.5951			1.44984
$990$	14.9884	−	14.6437i	0.476361	−	0.465407i
$991$			36.5808i			1.16203i	0.813894	+	0.581013i	$0.197344\pi$
$991$			36.5808i			1.16203i	−0.813894	+	0.581013i	$0.802656\pi$
$992$	−16.4189	+	39.9469i	−0.521299	+	1.26831i
$993$	−14.3073			−0.454028
$994$		0			0
$995$	33.8418	−	7.69010i	1.07286	−	0.243792i
$996$	−3.49398	+	6.87587i	−0.110711	+	0.217870i
$997$	−14.4641			−0.458082			−0.229041	−	0.973417i	$-0.573559\pi$
$997$	−14.4641			−0.458082			−0.229041	+	0.973417i	$0.573559\pi$
$998$	−5.07171	+	3.11176i	−0.160542	+	0.0985010i
$999$	17.9360			0.567471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.c.d.979.23		32
4.3	odd	2	inner	980.2.c.d.979.12		32
5.4	even	2	inner	980.2.c.d.979.10		32
7.2	even	3		140.2.s.b.59.11	yes	32
7.3	odd	6		140.2.s.b.19.1	✓	32
7.4	even	3		980.2.s.e.19.1		32
7.5	odd	6		980.2.s.e.619.11		32
7.6	odd	2	inner	980.2.c.d.979.24		32
20.19	odd	2	inner	980.2.c.d.979.21		32
28.3	even	6		140.2.s.b.19.6	yes	32
28.11	odd	6		980.2.s.e.19.6		32
28.19	even	6		980.2.s.e.619.16		32
28.23	odd	6		140.2.s.b.59.16	yes	32
28.27	even	2	inner	980.2.c.d.979.11		32
35.2	odd	12		700.2.p.e.451.14		32
35.3	even	12		700.2.p.e.551.9		32
35.4	even	6		980.2.s.e.19.16		32
35.9	even	6		140.2.s.b.59.6	yes	32
35.17	even	12		700.2.p.e.551.8		32
35.19	odd	6		980.2.s.e.619.6		32
35.23	odd	12		700.2.p.e.451.3		32
35.24	odd	6		140.2.s.b.19.16	yes	32
35.34	odd	2	inner	980.2.c.d.979.9		32
140.3	odd	12		700.2.p.e.551.3		32
140.19	even	6		980.2.s.e.619.1		32
140.23	even	12		700.2.p.e.451.9		32
140.39	odd	6		980.2.s.e.19.11		32
140.59	even	6		140.2.s.b.19.11	yes	32
140.79	odd	6		140.2.s.b.59.1	yes	32
140.87	odd	12		700.2.p.e.551.14		32
140.107	even	12		700.2.p.e.451.8		32
140.139	even	2	inner	980.2.c.d.979.22		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.1	✓	32	7.3	odd	6
140.2.s.b.19.6	yes	32	28.3	even	6
140.2.s.b.19.11	yes	32	140.59	even	6
140.2.s.b.19.16	yes	32	35.24	odd	6
140.2.s.b.59.1	yes	32	140.79	odd	6
140.2.s.b.59.6	yes	32	35.9	even	6
140.2.s.b.59.11	yes	32	7.2	even	3
140.2.s.b.59.16	yes	32	28.23	odd	6
700.2.p.e.451.3		32	35.23	odd	12
700.2.p.e.451.8		32	140.107	even	12
700.2.p.e.451.9		32	140.23	even	12
700.2.p.e.451.14		32	35.2	odd	12
700.2.p.e.551.3		32	140.3	odd	12
700.2.p.e.551.8		32	35.17	even	12
700.2.p.e.551.9		32	35.3	even	12
700.2.p.e.551.14		32	140.87	odd	12
980.2.c.d.979.9		32	35.34	odd	2	inner
980.2.c.d.979.10		32	5.4	even	2	inner
980.2.c.d.979.11		32	28.27	even	2	inner
980.2.c.d.979.12		32	4.3	odd	2	inner
980.2.c.d.979.21		32	20.19	odd	2	inner
980.2.c.d.979.22		32	140.139	even	2	inner
980.2.c.d.979.23		32	1.1	even	1	trivial
980.2.c.d.979.24		32	7.6	odd	2	inner
980.2.s.e.19.1		32	7.4	even	3
980.2.s.e.19.6		32	28.11	odd	6
980.2.s.e.19.11		32	140.39	odd	6
980.2.s.e.19.16		32	35.4	even	6
980.2.s.e.619.1		32	140.19	even	6
980.2.s.e.619.6		32	35.19	odd	6
980.2.s.e.619.11		32	7.5	odd	6
980.2.s.e.619.16		32	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.739583 + 1.20541i) q^{2} -0.732905i q^{3} +(-0.906034 + 1.78300i) q^{4} +(-2.18048 + 0.495485i) q^{5} +(0.883452 - 0.542044i) q^{6} +(-2.81934 + 0.226536i) q^{8} +2.46285 q^{9} +(-2.20991 - 2.26192i) q^{10} +2.69053i q^{11} +(1.30677 + 0.664037i) q^{12} -3.95118 q^{13} +(0.363144 + 1.59809i) q^{15} +(-2.35821 - 3.23092i) q^{16} +1.41902 q^{17} +(1.82148 + 2.96875i) q^{18} -3.22529 q^{19} +(1.09214 - 4.33673i) q^{20} +(-3.24320 + 1.98987i) q^{22} -4.91239 q^{23} +(0.166030 + 2.06631i) q^{24} +(4.50899 - 2.16079i) q^{25} +(-2.92222 - 4.76279i) q^{26} -4.00375i q^{27} -5.17926 q^{29} +(-1.65778 + 1.61965i) q^{30} -7.63489 q^{31} +(2.15050 - 5.23214i) q^{32} +1.97191 q^{33} +(1.04948 + 1.71050i) q^{34} +(-2.23142 + 4.39127i) q^{36} +4.47981i q^{37} +(-2.38537 - 3.88780i) q^{38} +2.89584i q^{39} +(6.03527 - 1.89090i) q^{40} -0.325509i q^{41} -9.28165 q^{43} +(-4.79723 - 2.43771i) q^{44} +(-5.37020 + 1.22031i) q^{45} +(-3.63312 - 5.92146i) q^{46} -6.56574i q^{47} +(-2.36796 + 1.72834i) q^{48} +(5.93942 + 3.83710i) q^{50} -1.04001i q^{51} +(3.57990 - 7.04496i) q^{52} +1.61591i q^{53} +(4.82617 - 2.96111i) q^{54} +(-1.33312 - 5.86665i) q^{55} +2.36383i q^{57} +(-3.83049 - 6.24314i) q^{58} +7.63489 q^{59} +(-3.17841 - 0.800432i) q^{60} +14.3001i q^{61} +(-5.64664 - 9.20319i) q^{62} +(7.89736 - 1.27737i) q^{64} +(8.61546 - 1.95775i) q^{65} +(1.45839 + 2.37696i) q^{66} -3.02658 q^{67} +(-1.28568 + 2.53012i) q^{68} +3.60032i q^{69} -15.4089i q^{71} +(-6.94361 + 0.557925i) q^{72} -1.41902 q^{73} +(-5.40001 + 3.31319i) q^{74} +(-1.58366 - 3.30466i) q^{75} +(2.92222 - 5.75071i) q^{76} +(-3.49068 + 2.14171i) q^{78} +12.2127i q^{79} +(6.74290 + 5.87651i) q^{80} +4.45418 q^{81} +(0.392372 - 0.240741i) q^{82} +5.26172i q^{83} +(-3.09414 + 0.703103i) q^{85} +(-6.86455 - 11.1882i) q^{86} +3.79591i q^{87} +(-0.609503 - 7.58553i) q^{88} +4.74501i q^{89} +(-5.44268 - 5.57078i) q^{90} +(4.45079 - 8.75882i) q^{92} +5.59565i q^{93} +(7.91442 - 4.85591i) q^{94} +(7.03269 - 1.59809i) q^{95} +(-3.83467 - 1.57611i) q^{96} +8.35134 q^{97} +6.62638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{4} - 8 q^{9} - 36 q^{16} + 52 q^{25} + 52 q^{30} - 28 q^{36} + 52 q^{44} + 44 q^{46} + 36 q^{50} - 8 q^{60} + 36 q^{64} + 8 q^{65} - 28 q^{74} - 144 q^{81} + 20 q^{85} - 16 q^{86}+O(q^{100}) \) 32 * q - 12 * q^4 - 8 * q^9 - 36 * q^16 + 52 * q^25 + 52 * q^30 - 28 * q^36 + 52 * q^44 + 44 * q^46 + 36 * q^50 - 8 * q^60 + 36 * q^64 + 8 * q^65 - 28 * q^74 - 144 * q^81 + 20 * q^85 - 16 * q^86

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