LMFDB - Embedded newform 980.2.c.d.979.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(979,980)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			979.12
Character	$\chi$	$=$	980.979
Dual form			980.2.c.d.979.9

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.739583 + 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} +(1.01538 - 2.99483i) 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} +(2.85904 + 3.43888i) 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} +(2.19493 + 0.744179i) 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} +(-6.25976 + 0.902985i) 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} +(-0.730128 + 7.03327i) 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} +(-2.52037 + 2.09541i) 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} +(3.54115 - 8.21342i) 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} +(2.50073 - 7.37581i) 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	$0.0678581\pi$
$3$			0.732905i			0.423143i	−0.977363	+	0.211572i	$0.932142\pi$
$4$	−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
$10$	1.01538	−	2.99483i	0.321092	−	0.947048i
$11$		−	2.69053i		−	0.811226i	−0.914045	−	0.405613i	$-0.867058\pi$
$11$		−	2.69053i		−	0.811226i	0.914045	−	0.405613i	$-0.132942\pi$
$12$	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	$-0.379369\pi$
$19$	3.22529			0.739933			0.369966	+	0.929045i	$0.379369\pi$
$20$	2.85904	+	3.43888i	0.639301	+	0.768957i
$21$		0			0
$22$	3.24320	+	1.98987i	0.691452	+	0.424242i
$23$	4.91239			1.02430			0.512152	−	0.858895i	$-0.328848\pi$
$23$	4.91239			1.02430			0.512152	+	0.858895i	$0.328848\pi$
$24$	−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	$0.659684\pi$
$30$	2.19493	+	0.744179i	0.400737	+	0.135868i
$31$	7.63489			1.37127			0.685634	−	0.727947i	$-0.259525\pi$
$31$	7.63489			1.37127			0.685634	+	0.727947i	$0.259525\pi$
$32$	−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
$40$	−6.25976	+	0.902985i	−0.989755	+	0.142774i
$41$		−	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	$-0.249724\pi$
$43$	9.28165			1.41544			0.707719	+	0.706494i	$0.249724\pi$
$44$	−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	$0.158948\pi$
$47$			6.56574i			0.957712i	−0.877893	+	0.478856i	$0.841052\pi$
$48$	−2.36796	−	1.72834i	−0.341786	−	0.249465i
$49$		0			0
$50$	−0.730128	+	7.03327i	−0.103256	+	0.994655i
$51$			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	$-0.665561\pi$
$59$	−7.63489			−0.993979			−0.496989	+	0.867757i	$0.665561\pi$
$60$	−2.52037	+	2.09541i	−0.325379	+	0.270516i
$61$			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	$-0.440811\pi$
$67$	3.02658			0.369755			0.184878	+	0.982762i	$0.440811\pi$
$68$	−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	$0.367299\pi$
$71$			15.4089i			1.82870i	−0.404922	+	0.914351i	$0.632701\pi$
$72$	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	$-0.758918\pi$
$79$		−	12.2127i		−	1.37404i	0.726638	−	0.687021i	$-0.241082\pi$
$80$	3.54115	−	8.21342i	0.395912	−	0.918288i
$81$	4.45418			0.494909
$82$	0.392372	+	0.240741i	0.0433303	+	0.0265854i
$83$		−	5.26172i		−	0.577549i	−0.957397	−	0.288774i	$-0.906752\pi$
$83$		−	5.26172i		−	0.577549i	0.957397	−	0.288774i	$-0.0932477\pi$
$84$		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	$0.919081\pi$
$90$	2.50073	−	7.37581i	0.263601	−	0.777479i
$91$		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
$100$	−7.93800	−	6.08179i	−0.793800	−	0.608179i
$101$			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	$-0.770471\pi$
$103$		−	13.4006i		−	1.32040i	0.751090	−	0.660200i	$-0.229529\pi$
$104$	−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	$-0.415480\pi$
$107$	5.42894			0.524836			0.262418	+	0.964954i	$0.415480\pi$
$108$	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	$0.359553\pi$
$110$	−8.05768	−	2.73192i	−0.768270	−	0.260478i
$111$	−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
$120$	−0.661802	−	4.58781i	−0.0604140	−	0.418808i
$121$	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	$-0.524283\pi$
$127$	−1.71773			−0.152424			−0.0762121	+	0.997092i	$0.524283\pi$
$128$	−7.38051	+	8.57485i	−0.652351	+	0.757917i
$129$			6.80257i			0.598933i
$130$	−4.01196	+	11.8331i	−0.351872	+	1.03783i
$131$	14.1435			1.23572			0.617860	−	0.786288i	$-0.288000\pi$
$131$	14.1435			1.23572			0.617860	+	0.786288i	$0.288000\pi$
$132$	−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	$-0.403102\pi$
$139$	7.06762			0.599468			0.299734	+	0.954023i	$0.403102\pi$
$140$		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	$0.382818\pi$
$150$	−5.15472	−	0.535114i	−0.420881	−	0.0436919i
$151$			0.300332i			0.0244407i	0.999925	+	0.0122204i	$0.00388996\pi$
$151$			0.300332i			0.0244407i	−0.999925	+	0.0122204i	$0.996110\pi$
$152$	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
$160$	7.28158	+	10.3430i	0.575659	+	0.817690i
$161$		0			0
$162$	−3.29424	+	5.36912i	−0.258820	+	0.421838i
$163$	−10.7192			−0.839589			−0.419795	−	0.907619i	$-0.637898\pi$
$163$	−10.7192			−0.839589			−0.419795	+	0.907619i	$0.637898\pi$
$164$	−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	$-0.829010\pi$
$167$		−	13.2256i		−	1.02343i	0.859155	−	0.511715i	$-0.170990\pi$
$168$		0			0
$169$	2.61180			0.200908
$170$	1.44085	−	4.24972i	0.110508	−	0.325938i
$171$	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	$-0.990411\pi$
$179$		−	0.805971i		−	0.0602411i	0.999546	−	0.0301206i	$-0.00958912\pi$
$180$	7.04139	+	8.46944i	0.524834	+	0.631275i
$181$			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
$190$	3.27491	−	9.65920i	0.237587	−	0.700752i
$191$			17.4602i			1.26338i	0.775223	+	0.631688i	$0.217638\pi$
$191$			17.4602i			1.26338i	−0.775223	+	0.631688i	$0.782362\pi$
$192$	−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	$-0.314588\pi$
$199$	15.5203			1.10021			0.550103	+	0.835097i	$0.314588\pi$
$200$	13.2019	−	5.07056i	0.933513	−	0.358543i
$201$			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	$-0.837897\pi$
$211$		−	14.1636i		−	0.975063i	0.873105	−	0.487531i	$-0.162103\pi$
$212$	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
$220$	9.25241	−	7.69234i	0.623798	−	0.518618i
$221$	−5.60679			−0.377154
$222$	2.42825	−	3.95770i	0.162974	−	0.265623i
$223$		−	3.03443i		−	0.203201i	−0.994825	−	0.101600i	$-0.967604\pi$
$223$		−	3.03443i		−	0.203201i	0.994825	−	0.101600i	$-0.0323963\pi$
$224$		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	$-0.836856\pi$
$227$		−	14.7768i		−	0.980769i	0.871506	−	0.490385i	$-0.163144\pi$
$228$	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	$-0.0681550\pi$
$230$	4.98796	−	14.7118i	0.328896	−	0.970066i
$231$		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	$-0.966740\pi$
$239$		−	3.22490i		−	0.208601i	0.994546	−	0.104301i	$-0.0332604\pi$
$240$	6.01966	+	2.59532i	0.388567	+	0.167527i
$241$			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
$250$	−1.89285	−	15.6977i	−0.119715	−	0.992808i
$251$	−15.1647			−0.957189			−0.478594	−	0.878036i	$-0.658854\pi$
$251$	−15.1647			−0.957189			−0.478594	+	0.878036i	$0.658854\pi$
$252$		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
$260$	−11.2966	−	13.5876i	−0.700584	−	0.842668i
$261$	−12.7557			−0.789561
$262$	−10.4603	+	17.0487i	−0.646237	+	1.05327i
$263$	4.70042			0.289840			0.144920	−	0.989443i	$-0.453707\pi$
$263$	4.70042			0.289840			0.144920	+	0.989443i	$0.453707\pi$
$264$	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	$-0.269057\pi$
$270$	11.9905	+	4.06534i	0.729722	+	0.247409i
$271$	26.3914			1.60316			0.801582	−	0.597885i	$-0.203992\pi$
$271$	26.3914			1.60316			0.801582	+	0.597885i	$0.203992\pi$
$272$	−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	$-0.924063\pi$
$283$		−	7.95057i		−	0.472612i	0.971679	−	0.236306i	$-0.0759368\pi$
$284$	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
$290$	−5.25893	+	15.5110i	−0.308815	+	0.910837i
$291$			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
$300$	4.45738	−	5.81780i	0.257347	−	0.335891i
$301$		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	$-0.821299\pi$
$307$		−	18.6560i		−	1.06475i	0.846508	−	0.532376i	$-0.178701\pi$
$308$		0			0
$309$	9.82137			0.558718
$310$	7.75234	−	22.8652i	0.440303	−	1.29866i
$311$	−8.18305			−0.464018			−0.232009	−	0.972714i	$-0.574530\pi$
$311$	−8.18305			−0.464018			−0.232009	+	0.972714i	$0.574530\pi$
$312$	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
$320$	−17.8530	+	1.12776i	−0.998011	+	0.0630436i
$321$			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
$330$	2.00224	−	5.90552i	0.110220	−	0.325088i
$331$			19.5213i			1.07299i	0.843904	+	0.536495i	$0.180252\pi$
$331$			19.5213i			1.07299i	−0.843904	+	0.536495i	$0.819748\pi$
$332$	−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
$340$	4.05703	+	4.87983i	0.220023	+	0.264646i
$341$		−	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	$-0.335733\pi$
$347$	18.3842			0.986916			0.493458	+	0.869770i	$0.335733\pi$
$348$	−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	$0.0428064\pi$
$359$			5.08073i			0.268151i	−0.990971	+	0.134075i	$0.957194\pi$
$360$	−15.4169	+	2.22392i	−0.812540	+	0.117211i
$361$	−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	$-0.884981\pi$
$367$		−	13.5453i		−	0.707061i	0.935423	−	0.353530i	$-0.115019\pi$
$368$	−11.5844	+	15.8716i	−0.603880	+	0.827363i
$369$		−	0.801679i		−	0.0417338i
$370$	13.4162	+	4.54872i	0.697478	+	0.236476i
$371$		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	$0.136985\pi$
$379$			16.2436i			0.834379i	−0.908820	+	0.417189i	$0.863015\pi$
$380$	9.22124	+	11.0914i	0.473040	+	0.568976i
$381$		−	1.25894i		−	0.0644972i
$382$	−21.0467	−	12.9133i	−1.07684	−	0.660700i
$383$		−	9.88716i		−	0.505211i	−0.967569	−	0.252605i	$-0.918713\pi$
$383$		−	9.88716i		−	0.505211i	0.967569	−	0.252605i	$-0.0812874\pi$
$384$	−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	$0.800683\pi$
$390$	−8.67254	−	2.94038i	−0.439151	−	0.148892i
$391$	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
$400$	−3.65177	+	19.6638i	−0.182588	+	0.983189i
$401$	−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	$-0.0577643\pi$
$410$	−0.974843	−	0.330516i	−0.0481441	−	0.0163230i
$411$	−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	$-0.644283\pi$
$419$	−17.9278			−0.875831			−0.437915	+	0.899016i	$0.644283\pi$
$420$		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
$430$	9.42442	−	27.7969i	0.454486	−	1.34049i
$431$			32.6737i			1.57384i	0.617058	+	0.786918i	$0.288324\pi$
$431$			32.6737i			1.57384i	−0.617058	+	0.786918i	$0.711676\pi$
$432$	−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	$-0.644615\pi$
$439$	−18.3900			−0.877708			−0.438854	+	0.898558i	$0.644615\pi$
$440$	2.42951	+	16.8421i	0.115822	+	0.802915i
$441$		0			0
$442$	4.14669	−	6.75849i	0.197238	−	0.321469i
$443$	3.38433			0.160795			0.0803973	−	0.996763i	$-0.474381\pi$
$443$	3.38433			0.160795			0.0803973	+	0.996763i	$0.474381\pi$
$444$	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	$0.590609\pi$
$450$	−1.79819	+	17.3219i	−0.0847677	+	0.816562i
$451$	−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
$460$	14.0447	+	16.8931i	0.654839	+	0.787646i
$461$		−	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	$-0.613707\pi$
$463$	−15.0481			−0.699342			−0.349671	+	0.936873i	$0.613707\pi$
$464$	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	$0.0379894\pi$
$467$			5.14599i			0.238128i	−0.992887	+	0.119064i	$0.962011\pi$
$468$	8.81676	+	17.3507i	0.407555	+	0.802036i
$469$		0			0
$470$	19.6633	+	6.66674i	0.906999	+	0.307514i
$471$			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	$-0.866111\pi$
$479$	−39.9567			−1.82567			−0.912834	+	0.408331i	$0.866111\pi$
$480$	−7.58047	+	5.33671i	−0.346000	+	0.243586i
$481$		−	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	$-0.589334\pi$
$487$	−12.2249			−0.553964			−0.276982	+	0.960875i	$0.589334\pi$
$488$	−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	$0.173284\pi$
$491$			22.9515i			1.03579i	−0.855445	+	0.517894i	$0.826716\pi$
$492$	−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	$-0.969978\pi$
$499$		−	4.20745i		−	0.188351i	0.995556	−	0.0941756i	$-0.0300215\pi$
$500$	20.3221	+	9.32807i	0.908831	+	0.417164i
$501$	9.69314			0.433058
$502$	11.2156	−	18.2797i	0.500576	−	0.815864i
$503$			43.1904i			1.92576i	0.269924	+	0.962882i	$0.413001\pi$
$503$			43.1904i			1.92576i	−0.269924	+	0.962882i	$0.586999\pi$
$504$		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	$-0.310486\pi$
$510$	3.11464	+	1.05600i	0.137919	+	0.0467606i
$511$		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
$520$	24.7334	−	3.56785i	1.08463	−	0.156461i
$521$		−	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	$0.113511\pi$
$523$			15.9671i			0.698193i	−0.937087	+	0.349097i	$0.886489\pi$
$524$	−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
$530$	4.83937	+	1.64077i	0.210209	+	0.0712704i
$531$	−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
$540$	−13.7684	+	11.4469i	−0.592498	+	0.492596i
$541$	−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	$-0.384567\pi$
$547$	16.5936			0.709493			0.354747	+	0.934963i	$0.384567\pi$
$548$	26.5151	−	13.4736i	1.13267	−	0.575566i
$549$			35.2189i			1.50311i
$550$	18.9232	+	1.96443i	0.806890	+	0.0837637i
$551$	−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	$-0.831590\pi$
$563$		−	23.9524i		−	1.00947i	0.863273	−	0.504737i	$-0.168410\pi$
$564$	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	$0.438491\pi$
$570$	7.07928	+	2.40020i	0.296518	+	0.100533i
$571$		−	24.7258i		−	1.03474i	−0.855761	−	0.517372i	$-0.826910\pi$
$571$		−	24.7258i		−	1.03474i	0.855761	−	0.517372i	$-0.173090\pi$
$572$	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
$580$	−14.8077	−	17.8109i	−0.614857	−	0.739555i
$581$		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	$0.0947382\pi$
$587$			14.2100i			0.586508i	−0.956035	+	0.293254i	$0.905262\pi$
$588$		0			0
$589$	24.6248			1.01465
$590$	−7.75234	+	22.8652i	−0.319159	+	0.941345i
$591$	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	$-0.859132\pi$
$599$		−	20.9621i		−	0.856488i	0.903663	−	0.428244i	$-0.140868\pi$
$600$	3.71624	+	9.67572i	0.151715	+	0.395010i
$601$			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	$0.0207203\pi$
$607$			3.20526i			0.130097i	−0.997882	+	0.0650487i	$0.979280\pi$
$608$	−6.93600	−	16.8752i	−0.281292	−	0.684380i
$609$		0			0
$610$	42.8262	+	14.5200i	1.73398	+	0.587899i
$611$		−	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	$-0.327469\pi$
$619$	25.6693			1.03174			0.515868	+	0.856668i	$0.327469\pi$
$620$	21.8285	+	26.2555i	0.876653	+	1.05445i
$621$			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	$-0.988904\pi$
$631$		−	1.75095i		−	0.0697043i	0.999392	−	0.0348521i	$-0.0110960\pi$
$632$	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
$640$	11.8443	−	22.3542i	0.468188	−	0.883629i
$641$	−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	$0.242515\pi$
$643$			35.0077i			1.38057i	−0.723538	+	0.690285i	$0.757485\pi$
$644$		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	$-0.841888\pi$
$647$		−	24.2431i		−	0.953094i	0.879149	−	0.476547i	$-0.158112\pi$
$648$	12.5578	+	1.00903i	0.493319	+	0.0396385i
$649$			20.5419i			0.806341i
$650$	2.88486	−	27.7897i	0.113154	−	1.09000i
$651$		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	$-0.927203\pi$
$659$		−	11.6398i		−	0.453422i	0.973962	−	0.226711i	$-0.0727973\pi$
$660$	5.63776	+	6.78114i	0.219449	+	0.263956i
$661$		−	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
$670$	3.07314	−	9.06409i	0.118726	−	0.350176i
$671$	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
$680$	−8.88272	+	1.28135i	−0.340637	+	0.0491376i
$681$	10.8300			0.415006
$682$	24.7615	+	15.1925i	0.948166	+	0.581750i
$683$	−11.1730			−0.427525			−0.213762	−	0.976886i	$-0.568572\pi$
$683$	−11.1730			−0.427525			−0.213762	+	0.976886i	$0.568572\pi$
$684$	−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
$690$	10.7823	+	3.65570i	0.410477	+	0.139170i
$691$	−35.4114			−1.34711			−0.673556	−	0.739136i	$-0.735234\pi$
$691$	−35.4114			−1.34711			−0.673556	+	0.739136i	$0.735234\pi$
$692$	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	$0.596459\pi$
$710$	46.1471	+	15.6459i	1.73187	+	0.587182i
$711$		−	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	$-0.265514\pi$
$719$	36.0284			1.34363			0.671817	+	0.740717i	$0.265514\pi$
$720$	8.72131	−	20.2284i	0.325024	−	0.753869i
$721$		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	$-0.596279\pi$
$727$		−	51.4779i		−	1.90921i	0.297878	−	0.954604i	$-0.403721\pi$
$728$		0			0
$729$	2.16686			0.0802541
$730$	−1.44085	+	4.24972i	−0.0533281	+	0.157289i
$731$	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	$-0.891143\pi$
$739$		−	18.2331i		−	0.670714i	0.942091	−	0.335357i	$-0.108857\pi$
$740$	−15.4055	+	12.8079i	−0.566318	+	0.470830i
$741$		−	9.33993i		−	0.343111i
$742$		0			0
$743$	−29.1171			−1.06820			−0.534102	−	0.845420i	$-0.679350\pi$
$743$	−29.1171			−1.06820			−0.534102	+	0.845420i	$0.679350\pi$
$744$	−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
$750$	11.5049	−	1.38728i	0.420100	−	0.0506564i
$751$		−	43.0360i		−	1.57041i	−0.619239	−	0.785203i	$-0.712559\pi$
$751$		−	43.0360i		−	1.57041i	0.619239	−	0.785203i	$-0.287441\pi$
$752$	−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
$760$	−20.1896	+	2.91239i	−0.732352	+	0.105643i
$761$			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
$780$	9.95844	−	8.27932i	0.356569	−	0.296447i
$781$	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	$0.309726\pi$
$787$			46.3779i			1.65319i	−0.562794	+	0.826597i	$0.690274\pi$
$788$	−21.2877	+	10.8173i	−0.758343	+	0.385352i
$789$			3.44496i			0.122644i
$790$	−36.5751	−	12.4006i	−1.30128	−	0.441194i
$791$		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
$800$	−21.0022	−	18.9449i	−0.742539	−	0.669803i
$801$			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	$0.401506\pi$
$810$	4.52270	−	13.3395i	0.158911	−	0.468702i
$811$	16.4459			0.577493			0.288746	−	0.957406i	$-0.406762\pi$
$811$	16.4459			0.577493			0.288746	+	0.957406i	$0.406762\pi$
$812$		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
$820$	1.11939	−	0.930643i	0.0390906	−	0.0324995i
$821$	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	$-0.364402\pi$
$823$	23.7093			0.826453			0.413226	+	0.910628i	$0.364402\pi$
$824$	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	$-0.545567\pi$
$827$	−8.20536			−0.285328			−0.142664	+	0.989771i	$0.545567\pi$
$828$	−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	$0.874513\pi$
$830$	−15.7579	−	5.34266i	−0.546966	−	0.185446i
$831$	−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	$-0.520067\pi$
$839$	−3.64977			−0.126004			−0.0630020	+	0.998013i	$0.520067\pi$
$840$		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
$850$	−1.03606	+	9.98034i	−0.0355367	+	0.342323i
$851$			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	$-0.360140\pi$
$859$	24.9348			0.850763			0.425382	+	0.905014i	$0.360140\pi$
$860$	26.5366	+	31.9184i	0.904891	+	1.08841i
$861$		0			0
$862$	−39.3852	−	24.1649i	−1.34147	−	0.823060i
$863$	5.96709			0.203122			0.101561	−	0.994829i	$-0.467616\pi$
$863$	5.96709			0.203122			0.101561	+	0.994829i	$0.467616\pi$
$864$	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
$870$	−11.3681	−	3.85430i	−0.385415	−	0.130673i
$871$	−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
$880$	−22.0985	−	9.52757i	−0.744939	−	0.321174i
$881$			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	$-0.580043\pi$
$883$	−14.7876			−0.497642			−0.248821	+	0.968549i	$0.580043\pi$
$884$	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	$-0.960357\pi$
$887$		−	7.39916i		−	0.248439i	0.992255	−	0.124220i	$-0.0396428\pi$
$888$	−9.25667	−	0.743780i	−0.310633	−	0.0249596i
$889$		0			0
$890$	14.2105	+	4.81800i	0.476336	+	0.161500i
$891$		−	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
$900$	−19.5501	−	14.9785i	−0.651670	−	0.499285i
$901$			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	$-0.400560\pi$
$907$	18.5122			0.614686			0.307343	+	0.951599i	$0.400560\pi$
$908$	−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	$0.0574912\pi$
$911$			10.8437i			0.359267i	−0.983734	+	0.179634i	$0.942509\pi$
$912$	−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	$-0.914369\pi$
$919$		−	16.1145i		−	0.531567i	0.964033	−	0.265784i	$-0.0856307\pi$
$920$	−30.7504	+	4.43582i	−1.01381	+	0.146245i
$921$	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	$0.699669\pi$
$930$	16.7580	+	5.68173i	0.549517	+	0.186311i
$931$		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
$940$	−22.5788	+	18.7717i	−0.736439	+	0.612266i
$941$		−	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	$-0.423580\pi$
$947$	14.6346			0.475560			0.237780	+	0.971319i	$0.423580\pi$
$948$	−8.10971	−	15.9593i	−0.263391	−	0.518334i
$949$	5.60679			0.182004
$950$	−2.35488	+	22.6844i	−0.0764022	+	0.735978i
$951$	−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
$960$	−0.826540	−	13.0845i	−0.0266765	−	0.422301i
$961$	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	$-0.545647\pi$
$967$	−8.88824			−0.285827			−0.142913	+	0.989735i	$0.545647\pi$
$968$	10.6036	+	0.852011i	0.340814	+	0.0273847i
$969$			3.35432i			0.107756i
$970$	8.47980	−	25.0108i	0.272270	−	0.803049i
$971$	8.74211			0.280548			0.140274	−	0.990113i	$-0.455202\pi$
$971$	8.74211			0.280548			0.140274	+	0.990113i	$0.455202\pi$
$972$	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	$0.0561535\pi$
$983$			11.0047i			0.350996i	−0.984480	+	0.175498i	$0.943846\pi$
$984$	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
$990$	−19.8449	−	6.72831i	−0.630711	−	0.213840i
$991$		−	36.5808i		−	1.16203i	−0.813894	−	0.581013i	$-0.802656\pi$
$991$		−	36.5808i		−	1.16203i	0.813894	−	0.581013i	$-0.197344\pi$
$992$	−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

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

)

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	980.2.c.d.979.12

Level	$980$
Weight	$2$
Character	980.979
Analytic conductor	$7.825$
Analytic rank	$0$
Dimension	$32$
Inner twists	$8$