LMFDB - Embedded newform 980.2.k.j.883.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(687,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("980.687");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			883.9
Character	$\chi$	$=$	980.883
Dual form			980.2.k.j.687.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.121020 - 1.40903i) q^{2} +(0.404049 - 0.404049i) q^{3} +(-1.97071 + 0.341041i) q^{4} +(2.23575 - 0.0378402i) q^{5} +(-0.618214 - 0.520418i) q^{6} +(0.719030 + 2.73551i) q^{8} +2.67349i q^{9} +O(q^{10})$	\(q+(-0.121020 - 1.40903i) q^{2} +(0.404049 - 0.404049i) q^{3} +(-1.97071 + 0.341041i) q^{4} +(2.23575 - 0.0378402i) q^{5} +(-0.618214 - 0.520418i) q^{6} +(0.719030 + 2.73551i) q^{8} +2.67349i q^{9} +(-0.323888 - 3.14565i) q^{10} -3.96016i q^{11} +(-0.658466 + 0.934060i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(0.888062 - 0.918641i) q^{15} +(3.76738 - 1.34418i) q^{16} +(0.424976 - 0.424976i) q^{17} +(3.76702 - 0.323546i) q^{18} +2.00538 q^{19} +(-4.39310 + 0.837053i) q^{20} +(-5.57997 + 0.479259i) q^{22} +(1.75047 - 1.75047i) q^{23} +(1.39580 + 0.814755i) q^{24} +(4.99714 - 0.169202i) q^{25} +(-2.64025 + 3.13640i) q^{26} +(2.29237 + 2.29237i) q^{27} -7.25964i q^{29} +(-1.40186 - 1.14013i) q^{30} -3.26786i q^{31} +(-2.34992 - 5.14567i) q^{32} +(-1.60010 - 1.60010i) q^{33} +(-0.650233 - 0.547372i) q^{34} +(-0.911768 - 5.26867i) q^{36} +(6.80791 - 6.80791i) q^{37} +(-0.242691 - 2.82563i) q^{38} -1.65650 q^{39} +(1.71108 + 6.08869i) q^{40} +3.35439 q^{41} +(3.31777 - 3.31777i) q^{43} +(1.35058 + 7.80432i) q^{44} +(0.101165 + 5.97725i) q^{45} +(-2.67830 - 2.25462i) q^{46} +(8.86854 + 8.86854i) q^{47} +(0.979091 - 2.06532i) q^{48} +(-0.843164 - 7.02062i) q^{50} -0.343422i q^{51} +(4.73879 + 3.34061i) q^{52} +(-2.12863 - 2.12863i) q^{53} +(2.95258 - 3.50743i) q^{54} +(-0.149853 - 8.85392i) q^{55} +(0.810271 - 0.810271i) q^{57} +(-10.2290 + 0.878562i) q^{58} -14.8347 q^{59} +(-1.43682 + 2.11324i) q^{60} -4.23352 q^{61} +(-4.60450 + 0.395476i) q^{62} +(-6.96599 + 3.93382i) q^{64} +(-4.66056 - 4.50543i) q^{65} +(-2.06094 + 2.44823i) q^{66} +(-2.68988 - 2.68988i) q^{67} +(-0.692570 + 0.982438i) q^{68} -1.41455i q^{69} +4.86004i q^{71} +(-7.31335 + 1.92232i) q^{72} +(6.91747 + 6.91747i) q^{73} +(-10.4164 - 8.76863i) q^{74} +(1.95072 - 2.08745i) q^{75} +(-3.95201 + 0.683915i) q^{76} +(0.200469 + 2.33405i) q^{78} +6.91439 q^{79} +(8.37205 - 3.14781i) q^{80} -6.16801 q^{81} +(-0.405948 - 4.72642i) q^{82} +(-5.46792 + 5.46792i) q^{83} +(0.934058 - 0.966221i) q^{85} +(-5.07634 - 4.27330i) q^{86} +(-2.93325 - 2.93325i) q^{87} +(10.8330 - 2.84748i) q^{88} +3.87162i q^{89} +(8.40985 - 0.865911i) q^{90} +(-2.85269 + 4.04665i) q^{92} +(-1.32037 - 1.32037i) q^{93} +(11.4227 - 13.5693i) q^{94} +(4.48352 - 0.0758839i) q^{95} +(-3.02858 - 1.12962i) q^{96} +(-1.11914 + 1.11914i) q^{97} +10.5874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8}+O(q^{10}) $ 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8	$ 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37} + 12 q^{38} + 2 q^{40} + 20 q^{41} - 12 q^{45} + 28 q^{46} - 6 q^{48} - 14 q^{50} + 48 q^{52} + 24 q^{53} - 8 q^{57} - 30 q^{58} + 10 q^{60} - 20 q^{61} - 28 q^{62} - 4 q^{65} + 44 q^{66} - 12 q^{68} - 44 q^{72} - 12 q^{73} - 56 q^{76} + 32 q^{78} + 52 q^{80} + 52 q^{81} - 34 q^{82} + 8 q^{85} - 64 q^{86} - 16 q^{88} + 16 q^{90} + 22 q^{92} - 12 q^{93} - 48 q^{96} + 12 q^{97}+O(q^{100}) $ 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.121020	−	1.40903i	−0.0855740	−	0.996332i
$2$	−0.121020	−	1.40903i	−0.0855740	−	0.996332i
$3$	0.404049	−	0.404049i	0.233278	−	0.233278i	−0.580782	−	0.814059i	$-0.697253\pi$
$3$	0.404049	−	0.404049i	0.233278	−	0.233278i	0.814059	+	0.580782i	$0.197253\pi$
$4$	−1.97071	+	0.341041i	−0.985354	+	0.170520i
$5$	2.23575	−	0.0378402i	0.999857	−	0.0169227i
$5$	2.23575	−	0.0378402i	0.999857	−	0.0169227i
$6$	−0.618214	−	0.520418i	−0.252385	−	0.212460i
$7$		0			0
$7$		0			0
$8$	0.719030	+	2.73551i	0.254216	+	0.967148i
$9$			2.67349i			0.891163i
$10$	−0.323888	−	3.14565i	−0.102422	−	0.994741i
$11$		−	3.96016i		−	1.19403i	−0.802229	−	0.597017i	$-0.796353\pi$
$11$		−	3.96016i		−	1.19403i	0.802229	−	0.597017i	$-0.203647\pi$
$12$	−0.658466	+	0.934060i	−0.190083	+	0.269640i
$13$	−2.04987	−	2.04987i	−0.568532	−	0.568532i	0.363185	−	0.931717i	$-0.381689\pi$
$13$	−2.04987	−	2.04987i	−0.568532	−	0.568532i	−0.931717	+	0.363185i	$0.881689\pi$
$14$		0			0
$15$	0.888062	−	0.918641i	0.229297	−	0.237192i
$16$	3.76738	−	1.34418i	0.941846	−	0.336046i
$17$	0.424976	−	0.424976i	0.103072	−	0.103072i	−0.653690	−	0.756762i	$-0.726780\pi$
$17$	0.424976	−	0.424976i	0.103072	−	0.103072i	0.756762	+	0.653690i	$0.226780\pi$
$18$	3.76702	−	0.323546i	0.887894	−	0.0762604i
$19$	2.00538			0.460065			0.230033	−	0.973183i	$-0.426117\pi$
$19$	2.00538			0.460065			0.230033	+	0.973183i	$0.426117\pi$
$20$	−4.39310	+	0.837053i	−0.982327	+	0.187171i
$21$		0			0
$22$	−5.57997	+	0.479259i	−1.18965	+	0.102178i
$23$	1.75047	−	1.75047i	0.364999	−	0.364999i	−0.500651	−	0.865649i	$-0.666906\pi$
$23$	1.75047	−	1.75047i	0.364999	−	0.364999i	0.865649	+	0.500651i	$0.166906\pi$
$24$	1.39580	+	0.814755i	0.284917	+	0.166311i
$25$	4.99714	−	0.169202i	0.999427	−	0.0338405i
$26$	−2.64025	+	3.13640i	−0.517795	+	0.615098i
$27$	2.29237	+	2.29237i	0.441166	+	0.441166i
$28$		0			0
$29$		−	7.25964i		−	1.34808i	−0.738694	−	0.674041i	$-0.764557\pi$
$29$		−	7.25964i		−	1.34808i	0.738694	−	0.674041i	$-0.235443\pi$
$30$	−1.40186	−	1.14013i	−0.255944	−	0.208158i
$31$		−	3.26786i		−	0.586925i	−0.955971	−	0.293462i	$-0.905192\pi$
$31$		−	3.26786i		−	0.586925i	0.955971	−	0.293462i	$-0.0948075\pi$
$32$	−2.34992	−	5.14567i	−0.415411	−	0.909634i
$33$	−1.60010	−	1.60010i	−0.278542	−	0.278542i
$34$	−0.650233	−	0.547372i	−0.111514	−	0.0938735i
$35$		0			0
$36$	−0.911768	−	5.26867i	−0.151961	−	0.878111i
$37$	6.80791	−	6.80791i	1.11921	−	1.11921i	0.127356	−	0.991857i	$-0.459351\pi$
$37$	6.80791	−	6.80791i	1.11921	−	1.11921i	0.991857	−	0.127356i	$-0.0406491\pi$
$38$	−0.242691	−	2.82563i	−0.0393696	−	0.458377i
$39$	−1.65650			−0.265252
$40$	1.71108	+	6.08869i	0.270546	+	0.962707i
$41$	3.35439			0.523868			0.261934	−	0.965086i	$-0.415640\pi$
$41$	3.35439			0.523868			0.261934	+	0.965086i	$0.415640\pi$
$42$		0			0
$43$	3.31777	−	3.31777i	0.505955	−	0.505955i	−0.407327	−	0.913282i	$-0.633539\pi$
$43$	3.31777	−	3.31777i	0.505955	−	0.505955i	0.913282	+	0.407327i	$0.133539\pi$
$44$	1.35058	+	7.80432i	0.203607	+	1.17655i
$45$	0.101165	+	5.97725i	0.0150808	+	0.891035i
$46$	−2.67830	−	2.25462i	−0.394894	−	0.332425i
$47$	8.86854	+	8.86854i	1.29361	+	1.29361i	0.932538	+	0.361072i	$0.117589\pi$
$47$	8.86854	+	8.86854i	1.29361	+	1.29361i	0.361072	+	0.932538i	$0.382411\pi$
$48$	0.979091	−	2.06532i	0.141320	−	0.298104i
$49$		0			0
$50$	−0.843164	−	7.02062i	−0.119241	−	0.992865i
$51$		−	0.343422i		−	0.0480888i
$52$	4.73879	+	3.34061i	0.657151	+	0.463259i
$53$	−2.12863	−	2.12863i	−0.292390	−	0.292390i	0.545633	−	0.838024i	$-0.316289\pi$
$53$	−2.12863	−	2.12863i	−0.292390	−	0.292390i	−0.838024	+	0.545633i	$0.816289\pi$
$54$	2.95258	−	3.50743i	0.401796	−	0.477300i
$55$	−0.149853	−	8.85392i	−0.0202062	−	1.19386i
$56$		0			0
$57$	0.810271	−	0.810271i	0.107323	−	0.107323i
$58$	−10.2290	+	0.878562i	−1.34314	+	0.115361i
$59$	−14.8347			−1.93131			−0.965657	−	0.259819i	$-0.916337\pi$
$59$	−14.8347			−1.93131			−0.965657	+	0.259819i	$0.916337\pi$
$60$	−1.43682	+	2.11324i	−0.185492	+	0.272818i
$61$	−4.23352			−0.542046			−0.271023	−	0.962573i	$-0.587362\pi$
$61$	−4.23352			−0.542046			−0.271023	+	0.962573i	$0.587362\pi$
$62$	−4.60450	+	0.395476i	−0.584772	+	0.0502255i
$63$		0			0
$64$	−6.96599	+	3.93382i	−0.870749	+	0.491728i
$65$	−4.66056	−	4.50543i	−0.578071	−	0.558829i
$66$	−2.06094	+	2.44823i	−0.253684	+	0.301356i
$67$	−2.68988	−	2.68988i	−0.328622	−	0.328622i	0.523441	−	0.852062i	$-0.324648\pi$
$67$	−2.68988	−	2.68988i	−0.328622	−	0.328622i	−0.852062	+	0.523441i	$0.824648\pi$
$68$	−0.692570	+	0.982438i	−0.0839865	+	0.119138i
$69$		−	1.41455i		−	0.170292i
$70$		0			0
$71$			4.86004i			0.576781i	0.957513	+	0.288390i	$0.0931201\pi$
$71$			4.86004i			0.576781i	−0.957513	+	0.288390i	$0.906880\pi$
$72$	−7.31335	+	1.92232i	−0.861886	+	0.226547i
$73$	6.91747	+	6.91747i	0.809629	+	0.809629i	0.984578	−	0.174949i	$-0.0559759\pi$
$73$	6.91747	+	6.91747i	0.809629	+	0.809629i	−0.174949	+	0.984578i	$0.555976\pi$
$74$	−10.4164	−	8.76863i	−1.21088	−	1.01933i
$75$	1.95072	−	2.08745i	0.225250	−	0.241038i
$76$	−3.95201	+	0.683915i	−0.453327	+	0.0784504i
$77$		0			0
$78$	0.200469	+	2.33405i	0.0226987	+	0.264279i
$79$	6.91439			0.777929			0.388965	−	0.921253i	$-0.372833\pi$
$79$	6.91439			0.777929			0.388965	+	0.921253i	$0.372833\pi$
$80$	8.37205	−	3.14781i	0.936024	−	0.351936i
$81$	−6.16801			−0.685334
$82$	−0.405948	−	4.72642i	−0.0448295	−	0.521946i
$83$	−5.46792	+	5.46792i	−0.600182	+	0.600182i	−0.940361	−	0.340179i	$-0.889512\pi$
$83$	−5.46792	+	5.46792i	−0.600182	+	0.600182i	0.340179	+	0.940361i	$0.389512\pi$
$84$		0			0
$85$	0.934058	−	0.966221i	0.101313	−	0.104801i
$86$	−5.07634	−	4.27330i	−0.547396	−	0.460802i
$87$	−2.93325	−	2.93325i	−0.314478	−	0.314478i
$88$	10.8330	−	2.84748i	1.15481	−	0.303542i
$89$			3.87162i			0.410391i	0.978721	+	0.205195i	$0.0657830\pi$
$89$			3.87162i			0.410391i	−0.978721	+	0.205195i	$0.934217\pi$
$90$	8.40985	−	0.865911i	0.886476	−	0.0912750i
$91$		0			0
$92$	−2.85269	+	4.04665i	−0.297413	+	0.421893i
$93$	−1.32037	−	1.32037i	−0.136916	−	0.136916i
$94$	11.4227	−	13.5693i	1.17817	−	1.39956i
$95$	4.48352	−	0.0758839i	0.459999	−	0.00778552i
$96$	−3.02858	−	1.12962i	−0.309103	−	0.115291i
$97$	−1.11914	+	1.11914i	−0.113632	+	0.113632i	−0.761636	−	0.648005i	$-0.775604\pi$
$97$	−1.11914	+	1.11914i	−0.113632	+	0.113632i	0.648005	+	0.761636i	$0.275604\pi$
$98$		0			0
$99$	10.5874			1.06408
$100$	−9.79019	+	2.03767i	−0.979019	+	0.203767i
$101$	−17.8653			−1.77767			−0.888833	−	0.458232i	$-0.848483\pi$
$101$	−17.8653			−1.77767			−0.888833	+	0.458232i	$0.848483\pi$
$102$	−0.483891	+	0.0415610i	−0.0479124	+	0.00411515i
$103$	−7.93139	+	7.93139i	−0.781503	+	0.781503i	−0.980084	−	0.198581i	$-0.936367\pi$
$103$	−7.93139	+	7.93139i	−0.781503	+	0.781503i	0.198581	+	0.980084i	$0.436367\pi$
$104$	4.13352	−	7.08135i	0.405325	−	0.694384i
$105$		0			0
$106$	−2.74169	+	3.25691i	−0.266297	+	0.316339i
$107$	5.56023	+	5.56023i	0.537527	+	0.537527i	0.922802	−	0.385275i	$-0.125893\pi$
$107$	5.56023	+	5.56023i	0.537527	+	0.537527i	−0.385275	+	0.922802i	$0.625893\pi$
$108$	−5.29938	−	3.73580i	−0.509933	−	0.359477i
$109$			0.404298i			0.0387248i	0.999813	+	0.0193624i	$0.00616362\pi$
$109$			0.404298i			0.0387248i	−0.999813	+	0.0193624i	$0.993836\pi$
$110$	−12.4573	+	1.28265i	−1.18775	+	0.122296i
$111$		−	5.50146i		−	0.522175i
$112$		0			0
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	0.518834	−	0.854875i	$-0.326366\pi$
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	−0.854875	+	0.518834i	$0.826366\pi$
$114$	−1.23975	−	1.04363i	−0.116113	−	0.0977452i
$115$	3.84738	−	3.97985i	0.358770	−	0.371123i
$116$	2.47583	+	14.3066i	0.229875	+	1.32834i
$117$	5.48031	−	5.48031i	0.506654	−	0.506654i
$118$	1.79530	+	20.9025i	0.165270	+	1.92423i
$119$		0			0
$120$	3.15149	+	1.76877i	0.287691	+	0.161466i
$121$	−4.68288			−0.425716
$122$	0.512340	+	5.96513i	0.0463851	+	0.540058i
$123$	1.35534	−	1.35534i	0.122207	−	0.122207i
$124$	1.11447	+	6.43999i	0.100083	+	0.578329i
$125$	11.1659	−	0.567387i	0.998711	−	0.0507486i
$126$		0			0
$127$	4.80151	+	4.80151i	0.426065	+	0.426065i	0.887286	−	0.461221i	$-0.152588\pi$
$127$	4.80151	+	4.80151i	0.426065	+	0.426065i	−0.461221	+	0.887286i	$0.652588\pi$
$128$	6.38588	+	9.33919i	0.564438	+	0.825476i
$129$		−	2.68108i		−	0.236056i
$130$	−5.78424	+	7.11210i	−0.507311	+	0.623772i
$131$		−	15.1917i		−	1.32731i	−0.748041	−	0.663653i	$-0.769005\pi$
$131$		−	15.1917i		−	1.32731i	0.748041	−	0.663653i	$-0.230995\pi$
$132$	3.69903	+	2.60763i	0.321959	+	0.226965i
$133$		0			0
$134$	−3.46459	+	4.11565i	−0.299295	+	0.355538i
$135$	5.21190	+	5.03841i	0.448569	+	0.433637i
$136$	1.46810	+	0.856955i	0.125888	+	0.0734832i
$137$	3.23692	−	3.23692i	0.276549	−	0.276549i	−0.555181	−	0.831730i	$-0.687351\pi$
$137$	3.23692	−	3.23692i	0.276549	−	0.276549i	0.831730	+	0.555181i	$0.187351\pi$
$138$	−1.99314	+	0.171189i	−0.169668	+	0.0145726i
$139$	11.1198			0.943167			0.471583	−	0.881821i	$-0.343683\pi$
$139$	11.1198			0.943167			0.471583	+	0.881821i	$0.343683\pi$
$140$		0			0
$141$	7.16665			0.603541
$142$	6.84792	−	0.588162i	0.574665	−	0.0493574i
$143$	−8.11782	+	8.11782i	−0.678846	+	0.678846i
$144$	3.59366	+	10.0721i	0.299472	+	0.839338i
$145$	−0.274707	−	16.2307i	−0.0228131	−	1.34789i
$146$	8.90975	−	10.5841i	0.737376	−	0.875942i
$147$		0			0
$148$	−11.0946	+	15.7382i	−0.911973	+	1.29367i
$149$		−	4.89788i		−	0.401250i	−0.979668	−	0.200625i	$-0.935703\pi$
$149$		−	4.89788i		−	0.401250i	0.979668	−	0.200625i	$-0.0642972\pi$
$150$	−3.17735	−	2.49599i	−0.259430	−	0.203797i
$151$			14.7376i			1.19933i	0.800251	+	0.599666i	$0.204700\pi$
$151$			14.7376i			1.19933i	−0.800251	+	0.599666i	$0.795300\pi$
$152$	1.44193	+	5.48572i	0.116956	+	0.444951i
$153$	1.13617	+	1.13617i	0.0918538	+	0.0918538i
$154$		0			0
$155$	−0.123656	−	7.30611i	−0.00993233	−	0.586841i
$156$	3.26447	−	0.564932i	0.261367	−	0.0452308i
$157$	−7.86056	+	7.86056i	−0.627341	+	0.627341i	−0.947398	−	0.320057i	$-0.896298\pi$
$157$	−7.86056	+	7.86056i	−0.627341	+	0.627341i	0.320057	+	0.947398i	$0.396298\pi$
$158$	−0.836779	−	9.74255i	−0.0665705	−	0.775076i
$159$	−1.72015			−0.136416
$160$	−5.44854	−	11.4155i	−0.430745	−	0.902474i
$161$		0			0
$162$	0.746452	+	8.69088i	0.0586468	+	0.682820i
$163$	−12.9842	+	12.9842i	−1.01700	+	1.01700i	−0.0171472	+	0.999853i	$0.505458\pi$
$163$	−12.9842	+	12.9842i	−1.01700	+	1.01700i	−0.999853	+	0.0171472i	$0.994542\pi$
$164$	−6.61052	+	1.14398i	−0.516195	+	0.0893301i
$165$	−3.63797	−	3.51687i	−0.283215	−	0.273788i
$166$	8.36616	+	7.04271i	0.649340	+	0.546620i
$167$	13.1233	+	13.1233i	1.01551	+	1.01551i	0.999878	+	0.0156336i	$0.00497655\pi$
$167$	13.1233	+	13.1233i	1.01551	+	1.01551i	0.0156336	+	0.999878i	$0.495023\pi$
$168$		0			0
$169$		−	4.59606i		−	0.353543i
$170$	−1.47447	−	1.19918i	−0.113087	−	0.0919730i
$171$			5.36135i			0.409993i
$172$	−5.40686	+	7.66985i	−0.412269	+	0.584820i
$173$	5.48367	+	5.48367i	0.416916	+	0.416916i	0.884139	−	0.467224i	$-0.154746\pi$
$173$	5.48367	+	5.48367i	0.416916	+	0.416916i	−0.467224	+	0.884139i	$0.654746\pi$
$174$	−3.77805	+	4.48801i	−0.286413	+	0.340235i
$175$		0			0
$176$	−5.32318	−	14.9194i	−0.401250	−	1.12460i
$177$	−5.99395	+	5.99395i	−0.450533	+	0.450533i
$178$	5.45521	−	0.468543i	0.408885	−	0.0351188i
$179$	−5.12869			−0.383336			−0.191668	−	0.981460i	$-0.561390\pi$
$179$	−5.12869			−0.383336			−0.191668	+	0.981460i	$0.561390\pi$
$180$	−2.23785	−	11.7449i	−0.166800	−	0.875414i
$181$	−18.1294			−1.34755			−0.673774	−	0.738938i	$-0.735328\pi$
$181$	−18.1294			−1.34755			−0.673774	+	0.738938i	$0.735328\pi$
$182$		0			0
$183$	−1.71055	+	1.71055i	−0.126447	+	0.126447i
$184$	6.04707	+	3.52979i	0.445796	+	0.260219i
$185$	14.9632	−	15.4784i	1.10011	−	1.13799i
$186$	−1.70065	+	2.02023i	−0.124698	+	0.148131i
$187$	−1.68297	−	1.68297i	−0.123071	−	0.123071i
$188$	−20.5018	−	14.4528i	−1.49525	−	1.05408i
$189$		0			0
$190$	−0.649518	−	6.30821i	−0.0471210	−	0.457646i
$191$		−	15.6837i		−	1.13483i	−0.823431	−	0.567416i	$-0.807943\pi$
$191$		−	15.6837i		−	1.13483i	0.823431	−	0.567416i	$-0.192057\pi$
$192$	−1.22514	+	4.40406i	−0.0884172	+	0.317836i
$193$	5.48865	+	5.48865i	0.395082	+	0.395082i	0.876494	−	0.481412i	$-0.159876\pi$
$193$	5.48865	+	5.48865i	0.395082	+	0.395082i	−0.481412	+	0.876494i	$0.659876\pi$
$194$	1.71234	+	1.44146i	0.122939	+	0.103491i
$195$	−3.70351	+	0.0626822i	−0.265214	+	0.00448876i
$196$		0			0
$197$	4.22983	−	4.22983i	0.301363	−	0.301363i	−0.540184	−	0.841547i	$-0.681645\pi$
$197$	4.22983	−	4.22983i	0.301363	−	0.301363i	0.841547	+	0.540184i	$0.181645\pi$
$198$	−1.28129	−	14.9180i	−0.0910575	−	1.06018i
$199$	14.0881			0.998677			0.499338	−	0.866407i	$-0.333577\pi$
$199$	14.0881			0.998677			0.499338	+	0.866407i	$0.333577\pi$
$200$	4.05595	+	13.5480i	0.286799	+	0.957991i
$201$	−2.17369			−0.153320
$202$	2.16206	+	25.1727i	0.152122	+	1.77114i
$203$		0			0
$204$	0.117121	+	0.676785i	0.00820011	+	0.0473845i
$205$	7.49957	−	0.126931i	0.523793	−	0.00886523i
$206$	12.1354	+	10.2157i	0.845513	+	0.711760i
$207$	4.67987	+	4.67987i	0.325273	+	0.325273i
$208$	−10.4780	−	4.96725i	−0.726522	−	0.344416i
$209$		−	7.94162i		−	0.549333i
$210$		0			0
$211$			17.2435i			1.18709i	0.804799	+	0.593547i	$0.202273\pi$
$211$			17.2435i			1.18709i	−0.804799	+	0.593547i	$0.797727\pi$
$212$	4.92087	+	3.46897i	0.337967	+	0.238250i
$213$	1.96369	+	1.96369i	0.134550	+	0.134550i
$214$	7.16160	−	8.50740i	0.489557	−	0.581554i
$215$	7.29215	−	7.54324i	0.497320	−	0.514444i
$216$	−4.62250	+	7.91907i	−0.314522	+	0.538824i
$217$		0			0
$218$	0.569667	−	0.0489282i	0.0385827	−	0.00331383i
$219$	5.59000			0.377737
$220$	3.31486	+	17.3974i	0.223488	+	1.17293i
$221$	−1.74229			−0.117199
$222$	−7.75170	+	0.665786i	−0.520260	+	0.0446846i
$223$	−11.5356	+	11.5356i	−0.772484	+	0.772484i	−0.978540	−	0.206056i	$-0.933937\pi$
$223$	−11.5356	+	11.5356i	−0.772484	+	0.772484i	0.206056	+	0.978540i	$0.433937\pi$
$224$		0			0
$225$	0.452361	+	13.3598i	0.0301574	+	0.890653i
$226$	−4.60097	+	5.46558i	−0.306052	+	0.363565i
$227$	8.54837	+	8.54837i	0.567375	+	0.567375i	0.931392	−	0.364017i	$-0.118595\pi$
$227$	8.54837	+	8.54837i	0.567375	+	0.567375i	−0.364017	+	0.931392i	$0.618595\pi$
$228$	−1.32047	+	1.87314i	−0.0874504	+	0.124052i
$229$		−	2.19386i		−	0.144975i	−0.997369	−	0.0724873i	$-0.976906\pi$
$229$		−	2.19386i		−	0.144975i	0.997369	−	0.0724873i	$-0.0230937\pi$
$230$	−6.07332	−	4.93941i	−0.400463	−	0.325695i
$231$		0			0
$232$	19.8588	−	5.21990i	1.30379	−	0.342703i
$233$	0.796972	+	0.796972i	0.0522113	+	0.0522113i	0.732730	−	0.680519i	$-0.238246\pi$
$233$	0.796972	+	0.796972i	0.0522113	+	0.0522113i	−0.680519	+	0.732730i	$0.738246\pi$
$234$	−8.38512	−	7.05867i	−0.548152	−	0.461439i
$235$	20.1634	+	19.4922i	1.31532	+	1.27153i
$236$	29.2349	−	5.05924i	1.90303	−	0.329328i
$237$	2.79375	−	2.79375i	0.181474	−	0.181474i
$238$		0			0
$239$	19.8536			1.28422			0.642111	−	0.766612i	$-0.278059\pi$
$239$	19.8536			1.28422			0.642111	+	0.766612i	$0.278059\pi$
$240$	2.11085	−	4.65459i	0.136255	−	0.300453i
$241$	8.65488			0.557510			0.278755	−	0.960362i	$-0.410078\pi$
$241$	8.65488			0.557510			0.278755	+	0.960362i	$0.410078\pi$
$242$	0.566722	+	6.59830i	0.0364303	+	0.424155i
$243$	−9.36928	+	9.36928i	−0.601040	+	0.601040i
$244$	8.34302	−	1.44380i	0.534107	−	0.0924299i
$245$		0			0
$246$	−2.07373	−	1.74568i	−0.132216	−	0.111301i
$247$	−4.11076	−	4.11076i	−0.261562	−	0.261562i
$248$	8.93925	−	2.34969i	0.567643	−	0.149205i
$249$			4.41861i			0.280018i
$250$	−2.15076	−	15.6644i	−0.136026	−	0.990705i
$251$		−	1.55623i		−	0.0982283i	−0.998793	−	0.0491141i	$-0.984360\pi$
$251$		−	1.55623i		−	0.0982283i	0.998793	−	0.0491141i	$-0.0156398\pi$
$252$		0			0
$253$	−6.93215	−	6.93215i	−0.435821	−	0.435821i
$254$	6.18437	−	7.34653i	0.388042	−	0.460962i
$255$	−0.0129952	−	0.767806i	−0.000813790	−	0.0480819i
$256$	12.3863	−	10.1281i	0.774147	−	0.633006i
$257$	−12.5808	+	12.5808i	−0.784768	+	0.784768i	−0.980631	−	0.195863i	$-0.937249\pi$
$257$	−12.5808	+	12.5808i	−0.784768	+	0.784768i	0.195863	+	0.980631i	$0.437249\pi$
$258$	−3.77771	+	0.324464i	−0.235190	+	0.0202003i
$259$		0			0
$260$	10.7211	+	7.28944i	0.664897	+	0.452072i
$261$	19.4086			1.20136
$262$	−21.4055	+	1.83850i	−1.32244	+	0.113583i
$263$	13.5787	−	13.5787i	0.837300	−	0.837300i	−0.151203	−	0.988503i	$-0.548315\pi$
$263$	13.5787	−	13.5787i	0.837300	−	0.837300i	0.988503	+	0.151203i	$0.0483146\pi$
$264$	3.22656	−	5.52760i	0.198581	−	0.340200i
$265$	−4.83964	−	4.67854i	−0.297297	−	0.287401i
$266$		0			0
$267$	1.56432	+	1.56432i	0.0957350	+	0.0957350i
$268$	6.21834	+	4.38362i	0.379845	+	0.267772i
$269$			14.3480i			0.874810i	0.899265	+	0.437405i	$0.144102\pi$
$269$			14.3480i			0.874810i	−0.899265	+	0.437405i	$0.855898\pi$
$270$	6.46851	−	7.95345i	0.393661	−	0.484032i
$271$		−	20.6758i		−	1.25596i	−0.778228	−	0.627981i	$-0.783881\pi$
$271$		−	20.6758i		−	1.25596i	0.778228	−	0.627981i	$-0.216119\pi$
$272$	1.02980	−	2.17229i	0.0624409	−	0.131715i
$273$		0			0
$274$	−4.95263	−	4.16917i	−0.299199	−	0.251869i
$275$	−0.670069	−	19.7895i	−0.0404067	−	1.19335i
$276$	0.482420	+	2.78767i	0.0290383	+	0.167798i
$277$	3.44621	−	3.44621i	0.207062	−	0.207062i	−0.595955	−	0.803018i	$-0.703226\pi$
$277$	3.44621	−	3.44621i	0.207062	−	0.207062i	0.803018	+	0.595955i	$0.203226\pi$
$278$	−1.34571	−	15.6681i	−0.0807106	−	0.939707i
$279$	8.73658			0.523045
$280$		0			0
$281$	−9.71163			−0.579347			−0.289674	−	0.957125i	$-0.593547\pi$
$281$	−9.71163			−0.579347			−0.289674	+	0.957125i	$0.593547\pi$
$282$	−0.867308	−	10.0980i	−0.0516474	−	0.601327i
$283$	1.00261	−	1.00261i	0.0595989	−	0.0595989i	−0.676679	−	0.736278i	$-0.736582\pi$
$283$	1.00261	−	1.00261i	0.0595989	−	0.0595989i	0.736278	+	0.676679i	$0.236582\pi$
$284$	−1.65747	−	9.57772i	−0.0983528	−	0.568333i
$285$	1.78090	−	1.84222i	0.105491	−	0.109124i
$286$	12.4206	+	10.4558i	0.734447	+	0.618264i
$287$		0			0
$288$	13.7569	−	6.28248i	0.810632	−	0.370199i
$289$			16.6388i			0.978752i
$290$	−22.8363	+	2.35131i	−1.34099	+	0.138074i
$291$			0.904377i			0.0530155i
$292$	−15.9915	−	11.2732i	−0.935830	−	0.659713i
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	0.860880	−	0.508809i	$-0.169914\pi$
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	−0.508809	+	0.860880i	$0.669914\pi$
$294$		0			0
$295$	−33.1667	+	0.561349i	−1.93104	+	0.0326830i
$296$	23.5182	+	13.7280i	1.36697	+	0.797923i
$297$	9.07814	−	9.07814i	0.526767	−	0.526767i
$298$	−6.90124	+	0.592741i	−0.399778	+	0.0343366i
$299$	−7.17648			−0.415027
$300$	−3.13240	+	4.77904i	−0.180849	+	0.275918i
$301$		0			0
$302$	20.7657	−	1.78355i	1.19493	−	0.102632i
$303$	−7.21846	+	7.21846i	−0.414690	+	0.414690i
$304$	7.55502	−	2.69559i	0.433310	−	0.154603i
$305$	−9.46507	+	0.160197i	−0.541969	+	0.00917286i
$306$	1.46339	−	1.73839i	0.0836566	−	0.0993772i
$307$	−11.0030	−	11.0030i	−0.627975	−	0.627975i	0.319583	−	0.947558i	$-0.396457\pi$
$307$	−11.0030	−	11.0030i	−0.627975	−	0.627975i	−0.947558	+	0.319583i	$0.896457\pi$
$308$		0			0
$309$			6.40934i			0.364615i
$310$	−10.2795	+	1.05842i	−0.583838	+	0.0601142i
$311$		−	25.3983i		−	1.44021i	−0.693866	−	0.720104i	$-0.744094\pi$
$311$		−	25.3983i		−	1.44021i	0.693866	−	0.720104i	$-0.255906\pi$
$312$	−1.19107	−	4.53136i	−0.0674311	−	0.256538i
$313$	18.3469	+	18.3469i	1.03703	+	1.03703i	0.999287	+	0.0377426i	$0.0120167\pi$
$313$	18.3469	+	18.3469i	1.03703	+	1.03703i	0.0377426	+	0.999287i	$0.487983\pi$
$314$	12.0270	+	10.1245i	0.678724	+	0.571356i
$315$		0			0
$316$	−13.6262	+	2.35809i	−0.766536	+	0.132653i
$317$	0.151543	−	0.151543i	0.00851151	−	0.00851151i	−0.702838	−	0.711350i	$-0.748084\pi$
$317$	0.151543	−	0.151543i	0.00851151	−	0.00851151i	0.711350	+	0.702838i	$0.248084\pi$
$318$	0.208172	+	2.42373i	0.0116737	+	0.135916i
$319$	−28.7494			−1.60966
$320$	−15.4253	+	9.05863i	−0.862303	+	0.506393i
$321$	4.49321			0.250786
$322$		0			0
$323$	0.852238	−	0.852238i	0.0474198	−	0.0474198i
$324$	12.1553	−	2.10354i	0.675297	−	0.116863i
$325$	−10.5903	−	9.89664i	−0.587445	−	0.548967i
$326$	19.8664	+	16.7237i	1.10030	+	0.926241i
$327$	0.163356	+	0.163356i	0.00903363	+	0.00903363i
$328$	2.41191	+	9.17595i	0.133175	+	0.506657i
$329$		0			0
$330$	−4.51509	+	5.55160i	−0.248548	+	0.305606i
$331$			2.12541i			0.116823i	0.998293	+	0.0584115i	$0.0186036\pi$
$331$			2.12541i			0.116823i	−0.998293	+	0.0584115i	$0.981396\pi$
$332$	8.91089	−	12.6404i	0.489048	−	0.693735i
$333$	18.2009	+	18.2009i	0.997401	+	0.997401i
$334$	16.9029	−	20.0793i	0.924885	−	1.09869i
$335$	−6.11569	−	5.91212i	−0.334136	−	0.323013i
$336$		0			0
$337$	−22.4528	+	22.4528i	−1.22308	+	1.22308i	−0.256552	+	0.966530i	$0.582586\pi$
$337$	−22.4528	+	22.4528i	−1.22308	+	1.22308i	−0.966530	+	0.256552i	$0.917414\pi$
$338$	−6.47597	+	0.556215i	−0.352246	+	0.0302541i
$339$	−2.88666			−0.156782
$340$	−1.51124	+	2.22269i	−0.0819583	+	0.120542i
$341$	−12.9412			−0.700808
$342$	7.55429	−	0.648831i	0.408489	−	0.0350848i
$343$		0			0
$344$	11.4613	+	6.69020i	0.617955	+	0.360711i
$345$	−0.0535270	−	3.16258i	−0.00288180	−	0.170268i
$346$	7.06300	−	8.39026i	0.379709	−	0.451063i
$347$	−12.9149	−	12.9149i	−0.693306	−	0.693306i	0.269651	−	0.962958i	$-0.413092\pi$
$347$	−12.9149	−	12.9149i	−0.693306	−	0.693306i	−0.962958	+	0.269651i	$0.913092\pi$
$348$	6.78094	+	4.78023i	0.363497	+	0.256247i
$349$			21.6072i			1.15661i	0.815821	+	0.578304i	$0.196285\pi$
$349$			21.6072i			1.15661i	−0.815821	+	0.578304i	$0.803715\pi$
$350$		0			0
$351$		−	9.39811i		−	0.501634i
$352$	−20.3777	+	9.30605i	−1.08613	+	0.496014i
$353$	−11.9996	−	11.9996i	−0.638675	−	0.638675i	0.311554	−	0.950229i	$-0.399151\pi$
$353$	−11.9996	−	11.9996i	−0.638675	−	0.638675i	−0.950229	+	0.311554i	$0.899151\pi$
$354$	9.17102	+	7.72024i	0.487434	+	0.410326i
$355$	0.183905	+	10.8658i	0.00976066	+	0.576698i
$356$	−1.32038	−	7.62983i	−0.0699799	−	0.404380i
$357$		0			0
$358$	0.620673	+	7.22645i	0.0328036	+	0.381930i
$359$	−8.87981			−0.468658			−0.234329	−	0.972157i	$-0.575289\pi$
$359$	−8.87981			−0.468658			−0.234329	+	0.972157i	$0.575289\pi$
$360$	−16.2781	+	4.57456i	−0.857929	+	0.241100i
$361$	−14.9785			−0.788340
$362$	2.19402	+	25.5448i	0.115315	+	1.34260i
$363$	−1.89211	+	1.89211i	−0.0993101	+	0.0993101i
$364$		0			0
$365$	15.7275	+	15.2040i	0.823214	+	0.795812i
$366$	2.61722	+	2.20320i	0.136804	+	0.115163i
$367$	15.3720	+	15.3720i	0.802413	+	0.802413i	0.983472	−	0.181059i	$-0.0579525\pi$
$367$	15.3720	+	15.3720i	0.802413	+	0.802413i	−0.181059	+	0.983472i	$0.557953\pi$
$368$	4.24174	−	8.94765i	0.221116	−	0.466429i
$369$			8.96792i			0.466851i
$370$	−23.6203	−	19.2103i	−1.22796	−	0.998695i
$371$		0			0
$372$	3.05237	+	2.15177i	0.158258	+	0.111564i
$373$	−0.345634	−	0.345634i	−0.0178963	−	0.0178963i	0.698102	−	0.715998i	$-0.254028\pi$
$373$	−0.345634	−	0.345634i	−0.0178963	−	0.0178963i	−0.715998	+	0.698102i	$0.754028\pi$
$374$	−2.16768	+	2.57503i	−0.112088	+	0.133152i
$375$	4.28233	−	4.74084i	0.221139	−	0.244816i
$376$	−17.8832	+	30.6367i	−0.922256	+	1.57997i
$377$	−14.8813	+	14.8813i	−0.766427	+	0.766427i
$378$		0			0
$379$	−27.8315			−1.42961			−0.714805	−	0.699324i	$-0.753484\pi$
$379$	−27.8315			−1.42961			−0.714805	+	0.699324i	$0.753484\pi$
$380$	−8.80983	+	1.67861i	−0.451935	+	0.0861107i
$381$	3.88009			0.198783
$382$	−22.0987	+	1.89804i	−1.13067	+	0.0971122i
$383$	−3.65697	+	3.65697i	−0.186862	+	0.186862i	−0.794338	−	0.607476i	$-0.792182\pi$
$383$	−3.65697	+	3.65697i	−0.186862	+	0.186862i	0.607476	+	0.794338i	$0.292182\pi$
$384$	6.35370	+	1.19328i	0.324236	+	0.0608944i
$385$		0			0
$386$	7.06942	−	8.39789i	0.359824	−	0.427441i
$387$	8.87001	+	8.87001i	0.450888	+	0.450888i
$388$	1.82383	−	2.58718i	0.0925910	−	0.131344i
$389$		−	12.2252i		−	0.619841i	−0.950762	−	0.309921i	$-0.899698\pi$
$389$		−	12.2252i		−	0.619841i	0.950762	−	0.309921i	$-0.100302\pi$
$390$	0.536519	+	5.21075i	0.0271677	+	0.263857i
$391$		−	1.48782i		−	0.0752422i
$392$		0			0
$393$	−6.13820	−	6.13820i	−0.309631	−	0.309631i
$394$	−6.47184	−	5.44805i	−0.326047	−	0.274469i
$395$	15.4588	−	0.261642i	0.777818	−	0.0131646i
$396$	−20.8648	+	3.61075i	−1.04849	+	0.181447i
$397$	12.3653	−	12.3653i	0.620597	−	0.620597i	−0.325087	−	0.945684i	$-0.605394\pi$
$397$	12.3653	−	12.3653i	0.620597	−	0.620597i	0.945684	+	0.325087i	$0.105394\pi$
$398$	−1.70494	−	19.8505i	−0.0854608	−	0.995013i
$399$		0			0
$400$	18.5987	−	7.35452i	0.929934	−	0.367726i
$401$	−31.1224			−1.55418			−0.777089	−	0.629391i	$-0.783305\pi$
$401$	−31.1224			−1.55418			−0.777089	+	0.629391i	$0.783305\pi$
$402$	0.263060	+	3.06279i	0.0131202	+	0.152758i
$403$	−6.69868	+	6.69868i	−0.333685	+	0.333685i
$404$	35.2073	−	6.09280i	1.75163	−	0.303128i
$405$	−13.7901	+	0.233399i	−0.685236	+	0.0115977i
$406$		0			0
$407$	−26.9604	−	26.9604i	−1.33638	−	1.33638i
$408$	0.939434	−	0.246931i	0.0465089	−	0.0122249i
$409$			5.12060i			0.253197i	0.991954	+	0.126599i	$0.0404061\pi$
$409$			5.12060i			0.253197i	−0.991954	+	0.126599i	$0.959594\pi$
$410$	−1.08645	−	10.5517i	−0.0536558	−	0.521113i
$411$		−	2.61575i		−	0.129025i
$412$	12.9255	−	18.3354i	0.636795	−	0.903319i
$413$		0			0
$414$	6.02770	−	7.16041i	0.296245	−	0.351915i
$415$	−12.0180	+	12.4318i	−0.589939	+	0.610252i
$416$	−5.73092	+	15.3650i	−0.280982	+	0.753330i
$417$	4.49293	−	4.49293i	0.220020	−	0.220020i
$418$	−11.1899	+	0.961094i	−0.547318	+	0.0470087i
$419$	−14.0529			−0.686531			−0.343266	−	0.939238i	$-0.611533\pi$
$419$	−14.0529			−0.686531			−0.343266	+	0.939238i	$0.611533\pi$
$420$		0			0
$421$	37.5305			1.82913			0.914563	−	0.404443i	$-0.132535\pi$
$421$	37.5305			1.82913			0.914563	+	0.404443i	$0.132535\pi$
$422$	24.2966	−	2.08681i	1.18274	−	0.101584i
$423$	−23.7099	+	23.7099i	−1.15282	+	1.15282i
$424$	4.29234	−	7.35345i	0.208455	−	0.357115i
$425$	2.05176	−	2.19557i	0.0995248	−	0.106501i
$426$	2.52925	−	3.00454i	0.122543	−	0.145571i
$427$		0			0
$428$	−12.8538	−	9.06132i	−0.621314	−	0.437995i
$429$			6.55999i			0.316719i
$430$	−11.5111	−	9.36194i	−0.555115	−	0.451473i
$431$		−	24.2687i		−	1.16898i	−0.811400	−	0.584492i	$-0.801294\pi$
$431$		−	24.2687i		−	1.16898i	0.811400	−	0.584492i	$-0.198706\pi$
$432$	11.7176	+	5.55486i	0.563763	+	0.267259i
$433$	−0.0253628	−	0.0253628i	−0.00121886	−	0.00121886i	0.706497	−	0.707716i	$-0.250274\pi$
$433$	−0.0253628	−	0.0253628i	−0.00121886	−	0.00121886i	−0.707716	+	0.706497i	$0.750274\pi$
$434$		0			0
$435$	−6.66901	−	6.44702i	−0.319754	−	0.309111i
$436$	−0.137882	−	0.796754i	−0.00660336	−	0.0381576i
$437$	3.51036	−	3.51036i	0.167923	−	0.167923i
$438$	−0.676501	−	7.87645i	−0.0323245	−	0.376351i
$439$	−15.2590			−0.728274			−0.364137	−	0.931345i	$-0.618636\pi$
$439$	−15.2590			−0.728274			−0.364137	+	0.931345i	$0.618636\pi$
$440$	24.1122	−	6.77616i	1.14950	−	0.323041i
$441$		0			0
$442$	0.210852	+	2.45494i	0.0100292	+	0.116769i
$443$	8.45422	−	8.45422i	0.401672	−	0.401672i	−0.477150	−	0.878822i	$-0.658330\pi$
$443$	8.45422	−	8.45422i	0.401672	−	0.401672i	0.878822	+	0.477150i	$0.158330\pi$
$444$	1.87622	+	10.8418i	0.0890415	+	0.514527i
$445$	0.146503	+	8.65596i	0.00694490	+	0.410332i
$446$	17.6501	+	14.8580i	0.835755	+	0.703546i
$447$	−1.97898	−	1.97898i	−0.0936027	−	0.0936027i
$448$		0			0
$449$			13.7142i			0.647213i	0.946192	+	0.323607i	$0.104895\pi$
$449$			13.7142i			0.647213i	−0.946192	+	0.323607i	$0.895105\pi$
$450$	18.7695	−	2.25419i	0.884805	−	0.106263i
$451$		−	13.2839i		−	0.625516i
$452$	8.25795	+	5.82144i	0.388421	+	0.273818i
$453$	5.95472	+	5.95472i	0.279777	+	0.279777i
$454$	11.0104	−	13.0794i	0.516741	−	0.613847i
$455$		0			0
$456$	2.79911	+	1.63389i	0.131080	+	0.0765140i
$457$	−9.86469	+	9.86469i	−0.461451	+	0.461451i	−0.899131	−	0.437680i	$-0.855800\pi$
$457$	−9.86469	+	9.86469i	−0.461451	+	0.461451i	0.437680	+	0.899131i	$0.355800\pi$
$458$	−3.09121	+	0.265501i	−0.144443	+	0.0124061i
$459$	1.94840			0.0909437
$460$	−6.22476	+	9.15524i	−0.290231	+	0.426865i
$461$	27.6588			1.28820			0.644100	−	0.764941i	$-0.277232\pi$
$461$	27.6588			1.28820			0.644100	+	0.764941i	$0.277232\pi$
$462$		0			0
$463$	−4.03783	+	4.03783i	−0.187654	+	0.187654i	−0.794681	−	0.607027i	$-0.792362\pi$
$463$	−4.03783	+	4.03783i	−0.187654	+	0.187654i	0.607027	+	0.794681i	$0.292362\pi$
$464$	−9.75829	−	27.3499i	−0.453017	−	1.26969i
$465$	−3.00199	−	2.90206i	−0.139214	−	0.134580i
$466$	1.02650	−	1.21940i	0.0475519	−	0.0564878i
$467$	8.68402	+	8.68402i	0.401849	+	0.401849i	0.878884	−	0.477035i	$-0.158289\pi$
$467$	8.68402	+	8.68402i	0.401849	+	0.401849i	−0.477035	+	0.878884i	$0.658289\pi$
$468$	−8.93108	+	12.6691i	−0.412839	+	0.585629i
$469$		0			0
$470$	25.0249	−	30.7697i	1.15431	−	1.41930i
$471$			6.35211i			0.292690i
$472$	−10.6666	−	40.5804i	−0.490970	−	1.86787i
$473$	−13.1389	−	13.1389i	−0.604127	−	0.604127i
$474$	−4.27457	−	3.59837i	−0.196337	−	0.165278i
$475$	10.0211	−	0.339315i	0.459802	−	0.0155688i
$476$		0			0
$477$	5.69088	−	5.69088i	0.260568	−	0.260568i
$478$	−2.40268	−	27.9742i	−0.109896	−	1.27951i
$479$	24.0844			1.10045			0.550223	−	0.835018i	$-0.314543\pi$
$479$	24.0844			1.10045			0.550223	+	0.835018i	$0.314543\pi$
$480$	−6.81389	−	2.41094i	−0.311010	−	0.110044i
$481$	−27.9107			−1.27262
$482$	−1.04741	−	12.1950i	−0.0477084	−	0.555465i
$483$		0			0
$484$	9.22859	−	1.59705i	0.419481	−	0.0725932i
$485$	−2.45977	+	2.54447i	−0.111693	+	0.115538i
$486$	14.3354	+	12.0677i	0.650268	+	0.547401i
$487$	−2.42674	−	2.42674i	−0.109966	−	0.109966i	0.649983	−	0.759949i	$-0.274776\pi$
$487$	−2.42674	−	2.42674i	−0.109966	−	0.109966i	−0.759949	+	0.649983i	$0.774776\pi$
$488$	−3.04403	−	11.5808i	−0.137797	−	0.524239i
$489$			10.4925i			0.474487i
$490$		0			0
$491$			3.54370i			0.159925i	0.996798	+	0.0799626i	$0.0254801\pi$
$491$			3.54370i			0.159925i	−0.996798	+	0.0799626i	$0.974520\pi$
$492$	−2.20875	+	3.13320i	−0.0995782	+	0.141256i
$493$	−3.08518	−	3.08518i	−0.138949	−	0.138949i
$494$	−5.29469	+	6.28966i	−0.238219	+	0.282985i
$495$	23.6709	−	0.400631i	1.06393	−	0.0180070i
$496$	−4.39260	−	12.3113i	−0.197234	−	0.552792i
$497$		0			0
$498$	6.22594	−	0.534740i	0.278991	−	0.0239623i
$499$	−30.3293			−1.35773			−0.678864	−	0.734264i	$-0.737527\pi$
$499$	−30.3293			−1.35773			−0.678864	+	0.734264i	$0.737527\pi$
$500$	−21.8113	+	4.92619i	−0.975431	+	0.220306i
$501$	10.6049			0.473793
$502$	−2.19277	+	0.188335i	−0.0978679	+	0.00840579i
$503$	−6.85172	+	6.85172i	−0.305503	+	0.305503i	−0.843162	−	0.537659i	$-0.819309\pi$
$503$	−6.85172	+	6.85172i	−0.305503	+	0.305503i	0.537659	+	0.843162i	$0.319309\pi$
$504$		0			0
$505$	−39.9423	+	0.676027i	−1.77741	+	0.0300828i
$506$	−8.92865	+	10.6065i	−0.396927	+	0.471517i
$507$	−1.85703	−	1.85703i	−0.0824738	−	0.0824738i
$508$	−11.0999	−	7.82486i	−0.492478	−	0.347172i
$509$			9.51419i			0.421709i	0.977517	+	0.210854i	$0.0676246\pi$
$509$			9.51419i			0.421709i	−0.977517	+	0.210854i	$0.932375\pi$
$510$	−1.08029	+	0.111230i	−0.0478359	+	0.00492537i
$511$		0			0
$512$	−15.7698	−	16.2270i	−0.696931	−	0.717138i
$513$	4.59706	+	4.59706i	0.202965	+	0.202965i
$514$	19.2492	+	16.2041i	0.849045	+	0.714733i
$515$	−17.4325	+	18.0327i	−0.768166	+	0.794616i
$516$	0.914358	+	5.28363i	0.0402523	+	0.232599i
$517$	35.1209	−	35.1209i	1.54461	−	1.54461i
$518$		0			0
$519$	4.43134			0.194514
$520$	8.97354	−	15.9885i	0.393516	−	0.701143i
$521$	4.60813			0.201886			0.100943	−	0.994892i	$-0.467814\pi$
$521$	4.60813			0.201886			0.100943	+	0.994892i	$0.467814\pi$
$522$	−2.34883	−	27.3472i	−0.102805	−	1.19695i
$523$	−24.3039	+	24.3039i	−1.06273	+	1.06273i	−0.0648374	+	0.997896i	$0.520653\pi$
$523$	−24.3039	+	24.3039i	−1.06273	+	1.06273i	−0.997896	+	0.0648374i	$0.979347\pi$
$524$	5.18099	+	29.9384i	0.226333	+	1.30787i
$525$		0			0
$526$	−20.7761	−	17.4895i	−0.905880	−	0.762578i
$527$	−1.38876	−	1.38876i	−0.0604954	−	0.0604954i
$528$	−8.17901	−	3.87736i	−0.355946	−	0.168740i
$529$			16.8717i			0.733552i
$530$	−6.00650	+	7.38537i	−0.260905	+	0.320800i
$531$		−	39.6604i		−	1.72112i
$532$		0			0
$533$	−6.87606	−	6.87606i	−0.297835	−	0.297835i
$534$	2.01486	−	2.39349i	0.0871914	−	0.103576i
$535$	12.6417	+	12.2209i	0.546547	+	0.528354i
$536$	5.42409	−	9.29230i	0.234285	−	0.401366i
$537$	−2.07224	+	2.07224i	−0.0894238	+	0.0894238i
$538$	20.2166	−	1.73639i	0.871601	−	0.0748610i
$539$		0			0
$540$	−11.9894	−	8.15177i	−0.515943	−	0.350796i
$541$	−15.5727			−0.669524			−0.334762	−	0.942303i	$-0.608656\pi$
$541$	−15.5727			−0.669524			−0.334762	+	0.942303i	$0.608656\pi$
$542$	−29.1327	+	2.50218i	−1.25136	+	0.107478i
$543$	−7.32517	+	7.32517i	−0.314353	+	0.314353i
$544$	−3.18545	−	1.18813i	−0.136575	−	0.0509405i
$545$	0.0152987	+	0.903909i	0.000655326	+	0.0387192i
$546$		0			0
$547$	−6.09970	−	6.09970i	−0.260804	−	0.260804i	0.564577	−	0.825381i	$-0.309039\pi$
$547$	−6.09970	−	6.09970i	−0.260804	−	0.260804i	−0.825381	+	0.564577i	$0.809039\pi$
$548$	−5.27510	+	7.48294i	−0.225341	+	0.319655i
$549$		−	11.3183i		−	0.483051i
$550$	−27.8028	+	3.33906i	−1.18551	+	0.142378i
$551$		−	14.5583i		−	0.620205i
$552$	3.86952	−	1.01711i	0.164698	−	0.0432909i
$553$		0			0
$554$	−5.27285	−	4.43873i	−0.224022	−	0.188584i
$555$	−0.208176	−	12.2999i	−0.00883659	−	0.522100i
$556$	−21.9138	+	3.79229i	−0.929354	+	0.160829i
$557$	−9.22254	+	9.22254i	−0.390771	+	0.390771i	−0.874962	−	0.484191i	$-0.839114\pi$
$557$	−9.22254	+	9.22254i	−0.390771	+	0.390771i	0.484191	+	0.874962i	$0.339114\pi$
$558$	−1.05730	−	12.3101i	−0.0447591	−	0.521127i
$559$	−13.6020			−0.575303
$560$		0			0
$561$	−1.36001			−0.0574196
$562$	1.17530	+	13.6839i	0.0495771	+	0.577222i
$563$	14.7504	−	14.7504i	0.621656	−	0.621656i	−0.324299	−	0.945955i	$-0.605128\pi$
$563$	14.7504	−	14.7504i	0.621656	−	0.621656i	0.945955	+	0.324299i	$0.105128\pi$
$564$	−14.1234	+	2.44412i	−0.594701	+	0.102916i
$565$	−8.12163	−	7.85129i	−0.341680	−	0.330306i
$566$	−1.53404	−	1.29137i	−0.0644804	−	0.0542801i
$567$		0			0
$568$	−13.2947	+	3.49451i	−0.557832	+	0.146627i
$569$		−	7.99934i		−	0.335350i	−0.985842	−	0.167675i	$-0.946374\pi$
$569$		−	7.99934i		−	0.335350i	0.985842	−	0.167675i	$-0.0536259\pi$
$570$	−2.81126	−	2.28639i	−0.117751	−	0.0957663i
$571$		−	32.8653i		−	1.37537i	−0.726010	−	0.687684i	$-0.758627\pi$
$571$		−	32.8653i		−	1.37537i	0.726010	−	0.687684i	$-0.241373\pi$
$572$	13.2293	−	18.7664i	0.553147	−	0.784661i
$573$	−6.33698	−	6.33698i	−0.264731	−	0.264731i
$574$		0			0
$575$	8.45116	−	9.04353i	0.352438	−	0.377141i
$576$	−10.5170	−	18.6235i	−0.438210	−	0.775979i
$577$	27.4180	−	27.4180i	1.14143	−	1.14143i	0.153237	−	0.988189i	$-0.451030\pi$
$577$	27.4180	−	27.4180i	1.14143	−	1.14143i	0.988189	−	0.153237i	$-0.0489699\pi$
$578$	23.4445	−	2.01363i	0.975162	−	0.0837558i
$579$	4.43537			0.184328
$580$	6.07671	+	31.8924i	0.252321	+	1.32426i
$581$		0			0
$582$	1.27429	−	0.109448i	0.0528211	−	0.00453675i
$583$	−8.42974	+	8.42974i	−0.349124	+	0.349124i
$584$	−13.9489	+	23.8967i	−0.577210	+	0.988851i
$585$	12.0452	−	12.4600i	0.498008	−	0.515156i
$586$	7.76214	−	9.22079i	0.320651	−	0.380907i
$587$	6.10922	+	6.10922i	0.252155	+	0.252155i	0.821854	−	0.569699i	$-0.192940\pi$
$587$	6.10922	+	6.10922i	0.252155	+	0.252155i	−0.569699	+	0.821854i	$0.692940\pi$
$588$		0			0
$589$		−	6.55329i		−	0.270023i
$590$	4.80478	+	46.6648i	0.197810	+	1.92116i
$591$		−	3.41812i		−	0.140603i
$592$	16.4969	−	34.7991i	0.678019	−	1.43023i
$593$	−30.3332	−	30.3332i	−1.24564	−	1.24564i	−0.957628	−	0.288007i	$-0.907007\pi$
$593$	−30.3332	−	30.3332i	−1.24564	−	1.24564i	−0.288007	−	0.957628i	$-0.592993\pi$
$594$	−13.8900	−	11.6927i	−0.569913	−	0.479757i
$595$		0			0
$596$	1.67038	+	9.65229i	0.0684212	+	0.395373i
$597$	5.69227	−	5.69227i	0.232969	−	0.232969i
$598$	0.868498	+	10.1118i	0.0355155	+	0.413504i
$599$	10.0319			0.409893			0.204946	−	0.978773i	$-0.434298\pi$
$599$	10.0319			0.409893			0.204946	+	0.978773i	$0.434298\pi$
$600$	7.11287	+	3.83527i	0.290382	+	0.156574i
$601$	−24.3587			−0.993613			−0.496806	−	0.867861i	$-0.665494\pi$
$601$	−24.3587			−0.993613			−0.496806	+	0.867861i	$0.665494\pi$
$602$		0			0
$603$	7.19138	−	7.19138i	0.292855	−	0.292855i
$604$	−5.02613	−	29.0436i	−0.204510	−	1.18177i
$605$	−10.4697	+	0.177201i	−0.425655	+	0.00720425i
$606$	11.0446	+	9.29742i	0.448655	+	0.377682i
$607$	17.7002	+	17.7002i	0.718430	+	0.718430i	0.968284	−	0.249853i	$-0.0803824\pi$
$607$	17.7002	+	17.7002i	0.718430	+	0.718430i	−0.249853	+	0.968284i	$0.580382\pi$
$608$	−4.71247	−	10.3190i	−0.191116	−	0.418491i
$609$		0			0
$610$	1.37118	+	13.3171i	0.0555177	+	0.539196i
$611$		−	36.3587i		−	1.47092i
$612$	−2.62654	−	1.85158i	−0.106172	−	0.0748456i
$613$	−6.62581	−	6.62581i	−0.267614	−	0.267614i	0.560524	−	0.828138i	$-0.310600\pi$
$613$	−6.62581	−	6.62581i	−0.267614	−	0.267614i	−0.828138	+	0.560524i	$0.810600\pi$
$614$	−14.1719	+	16.8351i	−0.571933	+	0.679410i
$615$	2.97891	−	3.08148i	0.120121	−	0.124257i
$616$		0			0
$617$	−16.6913	+	16.6913i	−0.671965	+	0.671965i	−0.958169	−	0.286204i	$-0.907606\pi$
$617$	−16.6913	+	16.6913i	−0.671965	+	0.671965i	0.286204	+	0.958169i	$0.407606\pi$
$618$	9.03093	−	0.775658i	0.363277	−	0.0312015i
$619$	−29.7851			−1.19716			−0.598582	−	0.801061i	$-0.704269\pi$
$619$	−29.7851			−1.19716			−0.598582	+	0.801061i	$0.704269\pi$
$620$	2.73537	+	14.3560i	0.109855	+	0.576552i
$621$	8.02545			0.322050
$622$	−35.7869	+	3.07371i	−1.43492	+	0.123244i
$623$		0			0
$624$	−6.24065	+	2.22663i	−0.249826	+	0.0891367i
$625$	24.9427	−	1.69105i	0.997710	−	0.0676422i
$626$	23.6310	−	28.0717i	0.944483	−	1.12197i
$627$	−3.20880	−	3.20880i	−0.128147	−	0.128147i
$628$	12.8101	−	18.1716i	0.511179	−	0.725128i
$629$		−	5.78640i		−	0.230719i
$630$		0			0
$631$			9.29850i			0.370167i	0.982723	+	0.185084i	$0.0592556\pi$
$631$			9.29850i			0.370167i	−0.982723	+	0.185084i	$0.940744\pi$
$632$	4.97165	+	18.9143i	0.197762	+	0.752372i
$633$	6.96724	+	6.96724i	0.276923	+	0.276923i
$634$	−0.231868	−	0.195188i	−0.00920865	−	0.00775192i
$635$	10.9167	+	10.5533i	0.433214	+	0.418794i
$636$	3.38991	−	0.586639i	0.134418	−	0.0232618i
$637$		0			0
$638$	3.47925	+	40.5086i	0.137745	+	1.60375i
$639$	−12.9933			−0.514005
$640$	14.6306	+	20.6384i	0.578326	+	0.815806i
$641$	−2.74348			−0.108361			−0.0541805	−	0.998531i	$-0.517255\pi$
$641$	−2.74348			−0.108361			−0.0541805	+	0.998531i	$0.517255\pi$
$642$	−0.543768	−	6.33105i	−0.0214608	−	0.249866i
$643$	4.45513	−	4.45513i	0.175693	−	0.175693i	−0.613782	−	0.789475i	$-0.710353\pi$
$643$	4.45513	−	4.45513i	0.175693	−	0.175693i	0.789475	+	0.613782i	$0.210353\pi$
$644$		0			0
$645$	−0.101453	−	5.99422i	−0.00399470	−	0.236022i
$646$	−1.30396	−	1.09769i	−0.0513037	−	0.0431879i
$647$	−15.2682	−	15.2682i	−0.600256	−	0.600256i	0.340125	−	0.940380i	$-0.389531\pi$
$647$	−15.2682	−	15.2682i	−0.600256	−	0.600256i	−0.940380	+	0.340125i	$0.889531\pi$
$648$	−4.43498	−	16.8726i	−0.174223	−	0.662819i
$649$			58.7478i			2.30605i
$650$	−12.6630	+	16.1197i	−0.496683	+	0.632268i
$651$		0			0
$652$	21.1599	−	30.0162i	0.828686	−	1.17552i
$653$	20.6170	+	20.6170i	0.806806	+	0.806806i	0.984149	−	0.177343i	$-0.0567502\pi$
$653$	20.6170	+	20.6170i	0.806806	+	0.806806i	−0.177343	+	0.984149i	$0.556750\pi$
$654$	0.210404	−	0.249943i	0.00822745	−	0.00977353i
$655$	−0.574858	−	33.9648i	−0.0224615	−	1.32712i
$656$	12.6373	−	4.50891i	0.493402	−	0.176044i
$657$	−18.4938	+	18.4938i	−0.721511	+	0.721511i
$658$		0			0
$659$	8.28576			0.322768			0.161384	−	0.986892i	$-0.448404\pi$
$659$	8.28576			0.322768			0.161384	+	0.986892i	$0.448404\pi$
$660$	8.36877	+	5.69003i	0.325754	+	0.221484i
$661$	−20.9563			−0.815105			−0.407553	−	0.913182i	$-0.633618\pi$
$661$	−20.9563			−0.815105			−0.407553	+	0.913182i	$0.633618\pi$
$662$	2.99476	−	0.257217i	0.116395	−	0.00999702i
$663$	−0.703971	+	0.703971i	−0.0273400	+	0.0273400i
$664$	−18.8891	−	11.0259i	−0.733040	−	0.427889i
$665$		0			0
$666$	23.4428	−	27.8482i	0.908391	−	1.07909i
$667$	−12.7078	−	12.7078i	−0.492048	−	0.492048i
$668$	−30.3378	−	21.3866i	−1.17380	−	0.827473i
$669$			9.32193i			0.360407i
$670$	−7.59021	+	9.33265i	−0.293235	+	0.360552i
$671$			16.7654i			0.647221i
$672$		0			0
$673$	29.0523	+	29.0523i	1.11988	+	1.11988i	0.991758	+	0.128125i	$0.0408958\pi$
$673$	29.0523	+	29.0523i	1.11988	+	1.11988i	0.128125	+	0.991758i	$0.459104\pi$
$674$	34.3538	+	28.9194i	1.32326	+	1.11393i
$675$	11.8431	+	11.0674i	0.455843	+	0.425984i
$676$	1.56744	+	9.05750i	0.0602863	+	0.348365i
$677$	27.6916	−	27.6916i	1.06427	−	1.06427i	0.0664868	−	0.997787i	$-0.478821\pi$
$677$	27.6916	−	27.6916i	1.06427	−	1.06427i	0.997787	−	0.0664868i	$-0.0211790\pi$
$678$	0.349344	+	4.06738i	0.0134165	+	0.156207i
$679$		0			0
$680$	3.31472	+	1.86038i	0.127114	+	0.0713424i
$681$	6.90792			0.264712
$682$	1.56615	+	18.2345i	0.0599709	+	0.698237i
$683$	−8.39874	+	8.39874i	−0.321369	+	0.321369i	−0.849292	−	0.527923i	$-0.822971\pi$
$683$	−8.39874	+	8.39874i	−0.321369	+	0.321369i	0.527923	+	0.849292i	$0.322971\pi$
$684$	−1.82844	−	10.5657i	−0.0699121	−	0.403988i
$685$	7.11444	−	7.35942i	0.271829	−	0.281189i
$686$		0			0
$687$	−0.886428	−	0.886428i	−0.0338193	−	0.0338193i
$688$	8.03961	−	16.9590i	0.306507	−	0.646555i
$689$			8.72685i			0.332467i
$690$	−4.44968	+	0.458157i	−0.169397	+	0.0174417i
$691$			7.90757i			0.300818i	0.988624	+	0.150409i	$0.0480591\pi$
$691$			7.90757i			0.300818i	−0.988624	+	0.150409i	$0.951941\pi$
$692$	−12.6769	−	8.93656i	−0.481902	−	0.339717i
$693$		0			0
$694$	−16.6344	+	19.7603i	−0.631434	+	0.750092i
$695$	24.8610	−	0.420775i	0.943032	−	0.0159609i
$696$	5.91483	−	10.1330i	0.224201	−	0.384091i
$697$	1.42554	−	1.42554i	0.0539960	−	0.0539960i
$698$	30.4451	−	2.61491i	1.15237	−	0.0989757i
$699$	0.644031			0.0243595
$700$		0			0
$701$	29.1974			1.10277			0.551386	−	0.834250i	$-0.314099\pi$
$701$	29.1974			1.10277			0.551386	+	0.834250i	$0.314099\pi$
$702$	−13.2422	+	1.13736i	−0.499794	+	0.0429269i
$703$	13.6524	−	13.6524i	0.514911	−	0.514911i
$704$	15.5786	+	27.5864i	0.587140	+	1.03970i
$705$	16.0228	−	0.271188i	0.603454	−	0.0102135i
$706$	−15.4556	+	18.3600i	−0.581678	+	0.690986i
$707$		0			0
$708$	9.76814	−	13.8565i	0.367109	−	0.520759i
$709$		−	27.2663i		−	1.02401i	−0.858983	−	0.512003i	$-0.828903\pi$
$709$		−	27.2663i		−	1.02401i	0.858983	−	0.512003i	$-0.171097\pi$
$710$	15.2880	−	1.57411i	0.573747	−	0.0590752i
$711$			18.4855i			0.693262i
$712$	−10.5908	+	2.78381i	−0.396908	+	0.104328i
$713$	−5.72029	−	5.72029i	−0.214227	−	0.214227i
$714$		0			0
$715$	−17.8422	+	18.4566i	−0.667261	+	0.690237i
$716$	10.1071	−	1.74909i	0.377722	−	0.0653666i
$717$	8.02182	−	8.02182i	0.299580	−	0.299580i
$718$	1.07463	+	12.5119i	0.0401050	+	0.466939i
$719$	−35.9490			−1.34067			−0.670335	−	0.742058i	$-0.733850\pi$
$719$	−35.9490			−1.34067			−0.670335	+	0.742058i	$0.733850\pi$
$720$	8.41564	+	22.3826i	0.313632	+	0.834150i
$721$		0			0
$722$	1.81269	+	21.1050i	0.0674615	+	0.785448i
$723$	3.49700	−	3.49700i	0.130055	−	0.130055i
$724$	35.7278	−	6.18286i	1.32781	−	0.229784i
$725$	−1.22835	−	36.2774i	−0.0456197	−	1.34731i
$726$	2.89502	+	2.43705i	0.107444	+	0.0904475i
$727$	−5.64012	−	5.64012i	−0.209180	−	0.209180i	0.594739	−	0.803919i	$-0.297256\pi$
$727$	−5.64012	−	5.64012i	−0.209180	−	0.209180i	−0.803919	+	0.594739i	$0.797256\pi$
$728$		0			0
$729$		−	10.9327i		−	0.404916i
$730$	19.5194	−	24.0004i	0.722447	−	0.888295i
$731$		−	2.81994i		−	0.104299i
$732$	2.78762	−	3.95436i	0.103034	−	0.146157i
$733$	11.3775	+	11.3775i	0.420236	+	0.420236i	0.885285	−	0.465049i	$-0.153963\pi$
$733$	11.3775	+	11.3775i	0.420236	+	0.420236i	−0.465049	+	0.885285i	$0.653963\pi$
$734$	19.7993	−	23.5199i	0.730804	−	0.868136i
$735$		0			0
$736$	−13.1208	−	4.89388i	−0.483640	−	0.180391i
$737$	−10.6524	+	10.6524i	−0.392385	+	0.392385i
$738$	12.6360	−	1.08530i	0.465139	−	0.0399504i
$739$	22.9087			0.842710			0.421355	−	0.906896i	$-0.361555\pi$
$739$	22.9087			0.842710			0.421355	+	0.906896i	$0.361555\pi$
$740$	−24.2093	+	35.6064i	−0.889950	+	1.30892i
$741$	−3.32190			−0.122033
$742$		0			0
$743$	21.3493	−	21.3493i	0.783229	−	0.783229i	−0.197145	−	0.980374i	$-0.563167\pi$
$743$	21.3493	−	21.3493i	0.783229	−	0.783229i	0.980374	+	0.197145i	$0.0631669\pi$
$744$	2.66250	−	4.56128i	0.0976121	−	0.167225i
$745$	−0.185337	−	10.9504i	−0.00679021	−	0.401192i
$746$	−0.445179	+	0.528836i	−0.0162992	+	0.0193621i
$747$	−14.6184	−	14.6184i	−0.534860	−	0.534860i
$748$	3.89061	+	2.74269i	0.142255	+	0.100283i
$749$		0			0
$750$	−7.19821	−	5.46018i	−0.262841	−	0.199378i
$751$			36.6934i			1.33896i	0.742829	+	0.669481i	$0.233484\pi$
$751$			36.6934i			1.33896i	−0.742829	+	0.669481i	$0.766516\pi$
$752$	45.3321	+	21.4902i	1.65309	+	0.783669i
$753$	−0.628792	−	0.628792i	−0.0229145	−	0.0229145i
$754$	22.7691	+	19.1672i	0.829202	+	0.698030i
$755$	0.557675	+	32.9496i	0.0202959	+	1.19916i
$756$		0			0
$757$	23.2904	−	23.2904i	0.846504	−	0.846504i	−0.143191	−	0.989695i	$-0.545736\pi$
$757$	23.2904	−	23.2904i	0.846504	−	0.846504i	0.989695	+	0.143191i	$0.0457363\pi$
$758$	3.36817	+	39.2153i	0.122337	+	1.42437i
$759$	−5.60186			−0.203335
$760$	3.43136	+	12.2101i	0.124469	+	0.442908i
$761$	−7.61920			−0.276196			−0.138098	−	0.990419i	$-0.544099\pi$
$761$	−7.61920			−0.276196			−0.138098	+	0.990419i	$0.544099\pi$
$762$	−0.469568	−	5.46715i	−0.0170107	−	0.198054i
$763$		0			0
$764$	5.34878	+	30.9080i	0.193512	+	1.11821i
$765$	2.58318	+	2.49719i	0.0933951	+	0.0902863i
$766$	5.59533	+	4.71020i	0.202168	+	0.170186i
$767$	30.4092	+	30.4092i	1.09801	+	1.09801i
$768$	0.912440	−	9.09694i	0.0329248	−	0.328258i
$769$			30.3461i			1.09431i	0.837031	+	0.547155i	$0.184289\pi$
$769$			30.3461i			1.09431i	−0.837031	+	0.547155i	$0.815711\pi$
$770$		0			0
$771$			10.1665i			0.366138i
$772$	−12.6884	−	8.94468i	−0.456665	−	0.321926i
$773$	18.5284	+	18.5284i	0.666420	+	0.666420i	0.956885	−	0.290465i	$-0.0938101\pi$
$773$	18.5284	+	18.5284i	0.666420	+	0.666420i	−0.290465	+	0.956885i	$0.593810\pi$
$774$	11.4246	−	13.5715i	0.410650	−	0.487819i
$775$	−0.552929	−	16.3299i	−0.0198618	−	0.586588i
$776$	−3.86612	−	2.25673i	−0.138786	−	0.0810117i
$777$		0			0
$778$	−17.2256	+	1.47949i	−0.617568	+	0.0530423i
$779$	6.72682			0.241013
$780$	7.27716	−	1.38657i	0.260564	−	0.0496473i
$781$	19.2465			0.688695
$782$	−2.09637	+	0.180056i	−0.0749662	+	0.00643878i
$783$	16.6418	−	16.6418i	0.594728	−	0.594728i
$784$		0			0
$785$	−17.2768	+	17.8717i	−0.616635	+	0.637868i
$786$	−7.90603	+	9.39172i	−0.281999	+	0.334992i
$787$	7.88453	+	7.88453i	0.281053	+	0.281053i	0.833529	−	0.552476i	$-0.186317\pi$
$787$	7.88453	+	7.88453i	0.281053	+	0.281053i	−0.552476	+	0.833529i	$0.686317\pi$
$788$	−6.89322	+	9.77831i	−0.245561	+	0.348338i
$789$		−	10.9729i		−	0.390647i
$790$	−2.23949	−	21.7502i	−0.0796773	−	0.773838i
$791$		0			0
$792$	7.61269	+	28.9620i	0.270505	+	1.02912i
$793$	8.67816	+	8.67816i	0.308170	+	0.308170i
$794$	−18.9195	−	15.9266i	−0.671427	−	0.565213i
$795$	−3.84581	+	0.0650907i	−0.136397	+	0.00230853i
$796$	−27.7635	+	4.80460i	−0.984050	+	0.170295i
$797$	−9.45111	+	9.45111i	−0.334775	+	0.334775i	−0.854397	−	0.519621i	$-0.826073\pi$
$797$	−9.45111	+	9.45111i	−0.334775	+	0.334775i	0.519621	+	0.854397i	$0.326073\pi$
$798$		0			0
$799$	7.53784			0.266670
$800$	−12.6135	−	25.3160i	−0.445955	−	0.895055i
$801$	−10.3507			−0.365725
$802$	3.76643	+	43.8523i	0.132997	+	1.54848i
$803$	27.3943	−	27.3943i	0.966724	−	0.966724i
$804$	4.28371	−	0.741317i	0.151075	−	0.0261442i
$805$		0			0
$806$	10.2493	+	8.62795i	0.361016	+	0.303906i
$807$	5.79728	+	5.79728i	0.204074	+	0.204074i
$808$	−12.8457	−	48.8707i	−0.451910	−	1.71926i
$809$			32.6478i			1.14784i	0.818913	+	0.573918i	$0.194577\pi$
$809$			32.6478i			1.14784i	−0.818913	+	0.573918i	$0.805423\pi$
$810$	1.99774	+	19.4024i	0.0701936	+	0.681730i
$811$			38.0037i			1.33449i	0.744838	+	0.667245i	$0.232527\pi$
$811$			38.0037i			1.33449i	−0.744838	+	0.667245i	$0.767473\pi$
$812$		0			0
$813$	−8.35402	−	8.35402i	−0.292988	−	0.292988i
$814$	−34.7252	+	41.2507i	−1.21712	+	1.44584i
$815$	−28.5380	+	29.5207i	−0.999644	+	1.03406i
$816$	−0.461623	−	1.29380i	−0.0161600	−	0.0452922i
$817$	6.65338	−	6.65338i	0.232772	−	0.232772i
$818$	7.21506	−	0.619695i	0.252269	−	0.0216671i
$819$		0			0
$820$	−14.7362	+	2.80780i	−0.514610	+	0.0980527i
$821$	−11.5782			−0.404084			−0.202042	−	0.979377i	$-0.564758\pi$
$821$	−11.5782			−0.404084			−0.202042	+	0.979377i	$0.564758\pi$
$822$	−3.68565	+	0.316558i	−0.128552	+	0.0110412i
$823$	−23.7429	+	23.7429i	−0.827626	+	0.827626i	−0.987188	−	0.159562i	$-0.948992\pi$
$823$	−23.7429	+	23.7429i	−0.827626	+	0.827626i	0.159562	+	0.987188i	$0.448992\pi$
$824$	−27.3993	−	15.9935i	−0.954499	−	0.557159i
$825$	−8.26665	−	7.72517i	−0.287808	−	0.268956i
$826$		0			0
$827$	4.77258	+	4.77258i	0.165959	+	0.165959i	0.785200	−	0.619242i	$-0.212560\pi$
$827$	4.77258	+	4.77258i	0.165959	+	0.165959i	−0.619242	+	0.785200i	$0.712560\pi$
$828$	−10.8187	−	7.62663i	−0.375975	−	0.265044i
$829$			33.8016i			1.17398i	0.809595	+	0.586989i	$0.199687\pi$
$829$			33.8016i			1.17398i	−0.809595	+	0.586989i	$0.800313\pi$
$830$	18.9711	+	15.4291i	0.658497	+	0.535553i
$831$		−	2.78487i		−	0.0966061i
$832$	22.3432	+	6.21555i	0.774611	+	0.215485i
$833$		0			0
$834$	−6.87439	−	5.78693i	−0.238041	−	0.200385i
$835$	29.8370	+	28.8438i	1.03255	+	0.998181i
$836$	2.70841	+	15.6506i	0.0936724	+	0.541288i
$837$	7.49113	−	7.49113i	0.258931	−	0.258931i
$838$	1.70069	+	19.8010i	0.0587492	+	0.684013i
$839$	−3.12360			−0.107839			−0.0539193	−	0.998545i	$-0.517171\pi$
$839$	−3.12360			−0.107839			−0.0539193	+	0.998545i	$0.517171\pi$
$840$		0			0
$841$	−23.7024			−0.817325
$842$	−4.54195	−	52.8815i	−0.156526	−	1.82242i
$843$	−3.92397	+	3.92397i	−0.135149	+	0.135149i
$844$	−5.88075	−	33.9820i	−0.202424	−	1.16971i
$845$	−0.173916	−	10.2756i	−0.00598289	−	0.353493i
$846$	36.2773	+	30.5386i	1.24724	+	1.04994i
$847$		0			0
$848$	−10.8807	−	5.15811i	−0.373643	−	0.177130i
$849$		−	0.810205i		−	0.0278062i
$850$	−3.34192	−	2.62527i	−0.114627	−	0.0900461i
$851$		−	23.8341i		−	0.817023i
$852$	−4.53957	−	3.20017i	−0.155523	−	0.109636i
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	0.760202	−	0.649686i	$-0.225100\pi$
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	−0.649686	+	0.760202i	$0.725100\pi$
$854$		0			0
$855$	0.202875	+	11.9866i	0.00693817	+	0.409934i
$856$	−11.2121	+	19.2080i	−0.383220	+	0.656516i
$857$	−27.2569	+	27.2569i	−0.931077	+	0.931077i	−0.997773	−	0.0666962i	$-0.978754\pi$
$857$	−27.2569	+	27.2569i	−0.931077	+	0.931077i	0.0666962	+	0.997773i	$0.478754\pi$
$858$	9.24320	−	0.793890i	0.315558	−	0.0271030i
$859$	13.9595			0.476293			0.238146	−	0.971229i	$-0.423460\pi$
$859$	13.9595			0.476293			0.238146	+	0.971229i	$0.423460\pi$
$860$	−11.7981	+	17.3524i	−0.402313	+	0.591713i
$861$		0			0
$862$	−34.1953	+	2.93700i	−1.16470	+	0.100035i
$863$	29.2518	−	29.2518i	0.995742	−	0.995742i	−0.00424917	−	0.999991i	$-0.501353\pi$
$863$	29.2518	−	29.2518i	0.995742	−	0.995742i	0.999991	+	0.00424917i	$0.00135256\pi$
$864$	6.40889	−	17.1826i	0.218035	−	0.584565i
$865$	12.4676	+	12.0526i	0.423911	+	0.409800i
$866$	−0.0326674	+	0.0388062i	−0.00111008	+	0.00131869i
$867$	6.72289	+	6.72289i	0.228321	+	0.228321i
$868$		0			0
$869$		−	27.3821i		−	0.928873i
$870$	−8.27693	+	10.1770i	−0.280614	+	0.345033i
$871$			11.0278i			0.373664i
$872$	−1.10596	+	0.290703i	−0.0374526	+	0.00984444i
$873$	−2.99202	−	2.99202i	−0.101264	−	0.101264i
$874$	−5.37101	−	4.52136i	−0.181677	−	0.152937i
$875$		0			0
$876$	−11.0163	+	1.90642i	−0.372205	+	0.0644118i
$877$	24.4487	−	24.4487i	0.825574	−	0.825574i	−0.161327	−	0.986901i	$-0.551577\pi$
$877$	24.4487	−	24.4487i	0.825574	−	0.825574i	0.986901	+	0.161327i	$0.0515773\pi$
$878$	1.84665	+	21.5004i	0.0623213	+	0.725602i
$879$	4.86999			0.164261
$880$	−12.4658	−	33.1547i	−0.420224	−	1.11764i
$881$	9.22163			0.310685			0.155342	−	0.987861i	$-0.450352\pi$
$881$	9.22163			0.310685			0.155342	+	0.987861i	$0.450352\pi$
$882$		0			0
$883$	18.1891	−	18.1891i	0.612111	−	0.612111i	−0.331385	−	0.943496i	$-0.607516\pi$
$883$	18.1891	−	18.1891i	0.612111	−	0.612111i	0.943496	+	0.331385i	$0.107516\pi$
$884$	3.43355	−	0.594192i	0.115483	−	0.0199849i
$885$	−13.1741	+	13.6278i	−0.442844	+	0.458092i
$886$	−12.9354	−	10.8891i	−0.434572	−	0.365826i
$887$	−14.2909	−	14.2909i	−0.479843	−	0.479843i	0.425239	−	0.905081i	$-0.360190\pi$
$887$	−14.2909	−	14.2909i	−0.479843	−	0.479843i	−0.905081	+	0.425239i	$0.860190\pi$
$888$	15.0493	−	3.95571i	0.505020	−	0.132745i
$889$		0			0
$890$	12.1787	−	1.25397i	0.408233	−	0.0420332i
$891$			24.4263i			0.818312i
$892$	18.7993	−	26.6675i	0.629446	−	0.892894i
$893$	17.7848	+	17.7848i	0.595145	+	0.595145i
$894$	−2.54894	+	3.02793i	−0.0852494	+	0.101269i
$895$	−11.4664	+	0.194071i	−0.383281	+	0.00648706i
$896$		0			0
$897$	−2.89965	+	2.89965i	−0.0968165	+	0.0968165i
$898$	19.3237	−	1.65969i	0.644839	−	0.0553846i
$899$	−23.7235			−0.791223
$900$	−5.44770	−	26.1740i	−0.181590	−	0.872466i
$901$	−1.80924			−0.0602745
$902$	−18.7174	+	1.60762i	−0.623221	+	0.0535279i
$903$		0			0
$904$	7.20319	−	12.3402i	0.239574	−	0.410428i
$905$	−40.5328	+	0.686020i	−1.34735	+	0.0228041i
$906$	7.66972	−	9.11100i	0.254809	−	0.302693i
$907$	29.8907	+	29.8907i	0.992506	+	0.992506i	0.999972	−	0.00746634i	$-0.00237663\pi$
$907$	29.8907	+	29.8907i	0.992506	+	0.992506i	−0.00746634	+	0.999972i	$0.502377\pi$
$908$	−19.7617	−	13.9310i	−0.655815	−	0.462317i
$909$		−	47.7627i		−	1.58419i
$910$		0			0
$911$			47.4291i			1.57140i	0.618610	+	0.785698i	$0.287696\pi$
$911$			47.4291i			1.57140i	−0.618610	+	0.785698i	$0.712304\pi$
$912$	1.96345	−	4.14175i	0.0650162	−	0.137147i
$913$	21.6538	+	21.6538i	0.716637	+	0.716637i
$914$	15.0934	+	12.7058i	0.499246	+	0.420270i
$915$	−3.75963	+	3.88908i	−0.124289	+	0.128569i
$916$	0.748196	+	4.32346i	0.0247211	+	0.142851i
$917$		0			0
$918$	−0.235796	−	2.74535i	−0.00778242	−	0.0906101i
$919$	31.7004			1.04570			0.522849	−	0.852425i	$-0.324869\pi$
$919$	31.7004			1.04570			0.522849	+	0.852425i	$0.324869\pi$
$920$	13.6533	+	7.66289i	0.450136	+	0.252638i
$921$	−8.89151			−0.292985
$922$	−3.34727	−	38.9720i	−0.110236	−	1.28347i
$923$	9.96245	−	9.96245i	0.327918	−	0.327918i
$924$		0			0
$925$	32.8681	−	35.1720i	1.08070	−	1.15645i
$926$	6.17807	+	5.20075i	0.203024	+	0.170907i
$927$	−21.2045	−	21.2045i	−0.696447	−	0.696447i
$928$	−37.3557	+	17.0596i	−1.22626	+	0.560008i
$929$		−	43.0681i		−	1.41302i	−0.707704	−	0.706509i	$-0.750269\pi$
$929$		−	43.0681i		−	1.41302i	0.707704	−	0.706509i	$-0.249731\pi$
$930$	−3.72578	+	4.58109i	−0.122173	+	0.150220i
$931$		0			0
$932$	−1.84240	−	1.29880i	−0.0603498	−	0.0425436i
$933$	−10.2622	−	10.2622i	−0.335968	−	0.335968i
$934$	11.1851	−	13.2870i	0.365987	−	0.434762i
$935$	−3.82639	−	3.69902i	−0.125136	−	0.120971i
$936$	18.9319	+	11.0509i	0.618809	+	0.361210i
$937$	11.9105	−	11.9105i	0.389100	−	0.389100i	−0.485266	−	0.874366i	$-0.661277\pi$
$937$	11.9105	−	11.9105i	0.389100	−	0.389100i	0.874366	+	0.485266i	$0.161277\pi$
$938$		0			0
$939$	14.8261			0.483832
$940$	−46.3838	−	31.5370i	−1.51287	−	1.02862i
$941$	−28.2528			−0.921015			−0.460507	−	0.887656i	$-0.652332\pi$
$941$	−28.2528			−0.921015			−0.460507	+	0.887656i	$0.652332\pi$
$942$	8.95028	−	0.768732i	0.291616	−	0.0250466i
$943$	5.87177	−	5.87177i	0.191211	−	0.191211i
$944$	−55.8880	+	19.9406i	−1.81900	+	0.649010i
$945$		0			0
$946$	−16.9230	+	20.1031i	−0.550213	+	0.653609i
$947$	17.5438	+	17.5438i	0.570097	+	0.570097i	0.932156	−	0.362058i	$-0.117926\pi$
$947$	17.5438	+	17.5438i	0.570097	+	0.570097i	−0.362058	+	0.932156i	$0.617926\pi$
$948$	−4.55288	+	6.45845i	−0.147871	+	0.209761i
$949$		−	28.3598i		−	0.920600i
$950$	−1.69086	−	14.0790i	−0.0548588	−	0.456783i
$951$		−	0.122462i		−	0.00397109i
$952$		0			0
$953$	−19.4338	−	19.4338i	−0.629523	−	0.629523i	0.318425	−	0.947948i	$-0.396846\pi$
$953$	−19.4338	−	19.4338i	−0.629523	−	0.629523i	−0.947948	+	0.318425i	$0.896846\pi$
$954$	−8.70731	−	7.32989i	−0.281910	−	0.237314i
$955$	−0.593475	−	35.0648i	−0.0192044	−	1.13467i
$956$	−39.1256	+	6.77088i	−1.26541	+	0.218986i
$957$	−11.6162	+	11.6162i	−0.375497	+	0.375497i
$958$	−2.91470	−	33.9356i	−0.0941696	−	1.09641i
$959$		0			0
$960$	−2.57246	+	9.89272i	−0.0830259	+	0.319286i
$961$	20.3211			0.655520
$962$	3.37775	+	39.3268i	0.108903	+	1.26795i
$963$	−14.8652	+	14.8652i	−0.479024	+	0.479024i
$964$	−17.0562	+	2.95167i	−0.549345	+	0.0950668i
$965$	12.4789	+	12.0636i	0.401711	+	0.388339i
$966$		0			0
$967$	34.9483	+	34.9483i	1.12386	+	1.12386i	0.991155	+	0.132706i	$0.0423665\pi$
$967$	34.9483	+	34.9483i	1.12386	+	1.12386i	0.132706	+	0.991155i	$0.457633\pi$
$968$	−3.36713	−	12.8100i	−0.108224	−	0.411730i
$969$		−	0.688691i		−	0.0221240i
$970$	3.88291	+	3.15795i	0.124673	+	0.101396i
$971$		−	48.7601i		−	1.56479i	−0.622785	−	0.782393i	$-0.713999\pi$
$971$		−	48.7601i		−	1.56479i	0.622785	−	0.782393i	$-0.286001\pi$
$972$	15.2688	−	21.6594i	0.489747	−	0.694726i
$973$		0			0
$974$	−3.12565	+	3.71302i	−0.100152	+	0.118973i
$975$	−8.27774	+	0.280283i	−0.265100	+	0.00897624i
$976$	−15.9493	+	5.69062i	−0.510524	+	0.182152i
$977$	−31.3201	+	31.3201i	−1.00202	+	1.00202i	−0.00202240	+	0.999998i	$0.500644\pi$
$977$	−31.3201	+	31.3201i	−1.00202	+	1.00202i	−0.999998	+	0.00202240i	$0.999356\pi$
$978$	14.7842	−	1.26980i	0.472747	−	0.0406038i
$979$	15.3322			0.490020
$980$		0			0
$981$	−1.08089			−0.0345101
$982$	4.99317	−	0.428859i	0.159339	−	0.0136854i
$983$	4.42508	−	4.42508i	0.141138	−	0.141138i	−0.633008	−	0.774146i	$-0.718180\pi$
$983$	4.42508	−	4.42508i	0.141138	−	0.141138i	0.774146	+	0.633008i	$0.218180\pi$
$984$	4.68206	+	2.73301i	0.149259	+	0.0871251i
$985$	9.29678	−	9.61690i	0.296220	−	0.306420i
$986$	−3.97373	+	4.72046i	−0.126549	+	0.150330i
$987$		0			0
$988$	9.50305	+	6.69918i	0.302332	+	0.213129i
$989$		−	11.6153i		−	0.369346i
$990$	−3.42915	−	33.3044i	−0.108985	−	1.05848i
$991$			27.6555i			0.878507i	0.898363	+	0.439253i	$0.144757\pi$
$991$			27.6555i			0.878507i	−0.898363	+	0.439253i	$0.855243\pi$
$992$	−16.8153	+	7.67920i	−0.533887	+	0.243815i
$993$	0.858769	+	0.858769i	0.0272522	+	0.0272522i
$994$		0			0
$995$	31.4974	−	0.533095i	0.998534	−	0.0169003i
$996$	−1.50693	−	8.70780i	−0.0477488	−	0.275917i
$997$	−6.35088	+	6.35088i	−0.201134	+	0.201134i	−0.800486	−	0.599352i	$-0.795425\pi$
$997$	−6.35088	+	6.35088i	−0.201134	+	0.201134i	0.599352	+	0.800486i	$0.295425\pi$
$998$	3.67046	+	42.7348i	0.116186	+	1.35275i
$999$	31.2125			0.987518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.j.883.9		36
4.3	odd	2	inner	980.2.k.j.883.17		36
5.2	odd	4	inner	980.2.k.j.687.17		36
7.2	even	3		980.2.x.m.263.3		72
7.3	odd	6		140.2.w.b.23.17	yes	72
7.4	even	3		980.2.x.m.863.17		72
7.5	odd	6		140.2.w.b.123.3	yes	72
7.6	odd	2		980.2.k.k.883.9		36
20.7	even	4	inner	980.2.k.j.687.9		36
28.3	even	6		140.2.w.b.23.6	✓	72
28.11	odd	6		980.2.x.m.863.6		72
28.19	even	6		140.2.w.b.123.7	yes	72
28.23	odd	6		980.2.x.m.263.7		72
28.27	even	2		980.2.k.k.883.17		36
35.2	odd	12		980.2.x.m.67.6		72
35.3	even	12		700.2.be.e.107.12		72
35.12	even	12		140.2.w.b.67.6	yes	72
35.17	even	12		140.2.w.b.107.7	yes	72
35.19	odd	6		700.2.be.e.543.16		72
35.24	odd	6		700.2.be.e.443.2		72
35.27	even	4		980.2.k.k.687.17		36
35.32	odd	12		980.2.x.m.667.7		72
35.33	even	12		700.2.be.e.207.13		72
140.3	odd	12		700.2.be.e.107.16		72
140.19	even	6		700.2.be.e.543.12		72
140.27	odd	4		980.2.k.k.687.9		36
140.47	odd	12		140.2.w.b.67.17	yes	72
140.59	even	6		700.2.be.e.443.13		72
140.67	even	12		980.2.x.m.667.3		72
140.87	odd	12		140.2.w.b.107.3	yes	72
140.103	odd	12		700.2.be.e.207.2		72
140.107	even	12		980.2.x.m.67.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.6	✓	72	28.3	even	6
140.2.w.b.23.17	yes	72	7.3	odd	6
140.2.w.b.67.6	yes	72	35.12	even	12
140.2.w.b.67.17	yes	72	140.47	odd	12
140.2.w.b.107.3	yes	72	140.87	odd	12
140.2.w.b.107.7	yes	72	35.17	even	12
140.2.w.b.123.3	yes	72	7.5	odd	6
140.2.w.b.123.7	yes	72	28.19	even	6
700.2.be.e.107.12		72	35.3	even	12
700.2.be.e.107.16		72	140.3	odd	12
700.2.be.e.207.2		72	140.103	odd	12
700.2.be.e.207.13		72	35.33	even	12
700.2.be.e.443.2		72	35.24	odd	6
700.2.be.e.443.13		72	140.59	even	6
700.2.be.e.543.12		72	140.19	even	6
700.2.be.e.543.16		72	35.19	odd	6
980.2.k.j.687.9		36	20.7	even	4	inner
980.2.k.j.687.17		36	5.2	odd	4	inner
980.2.k.j.883.9		36	1.1	even	1	trivial
980.2.k.j.883.17		36	4.3	odd	2	inner
980.2.k.k.687.9		36	140.27	odd	4
980.2.k.k.687.17		36	35.27	even	4
980.2.k.k.883.9		36	7.6	odd	2
980.2.k.k.883.17		36	28.27	even	2
980.2.x.m.67.6		72	35.2	odd	12
980.2.x.m.67.17		72	140.107	even	12
980.2.x.m.263.3		72	7.2	even	3
980.2.x.m.263.7		72	28.23	odd	6
980.2.x.m.667.3		72	140.67	even	12
980.2.x.m.667.7		72	35.32	odd	12
980.2.x.m.863.6		72	28.11	odd	6
980.2.x.m.863.17		72	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.121020 - 1.40903i) q^{2} +(0.404049 - 0.404049i) q^{3} +(-1.97071 + 0.341041i) q^{4} +(2.23575 - 0.0378402i) q^{5} +(-0.618214 - 0.520418i) q^{6} +(0.719030 + 2.73551i) q^{8} +2.67349i q^{9} +O(q^{10})\)	\(q+(-0.121020 - 1.40903i) q^{2} +(0.404049 - 0.404049i) q^{3} +(-1.97071 + 0.341041i) q^{4} +(2.23575 - 0.0378402i) q^{5} +(-0.618214 - 0.520418i) q^{6} +(0.719030 + 2.73551i) q^{8} +2.67349i q^{9} +(-0.323888 - 3.14565i) q^{10} -3.96016i q^{11} +(-0.658466 + 0.934060i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(0.888062 - 0.918641i) q^{15} +(3.76738 - 1.34418i) q^{16} +(0.424976 - 0.424976i) q^{17} +(3.76702 - 0.323546i) q^{18} +2.00538 q^{19} +(-4.39310 + 0.837053i) q^{20} +(-5.57997 + 0.479259i) q^{22} +(1.75047 - 1.75047i) q^{23} +(1.39580 + 0.814755i) q^{24} +(4.99714 - 0.169202i) q^{25} +(-2.64025 + 3.13640i) q^{26} +(2.29237 + 2.29237i) q^{27} -7.25964i q^{29} +(-1.40186 - 1.14013i) q^{30} -3.26786i q^{31} +(-2.34992 - 5.14567i) q^{32} +(-1.60010 - 1.60010i) q^{33} +(-0.650233 - 0.547372i) q^{34} +(-0.911768 - 5.26867i) q^{36} +(6.80791 - 6.80791i) q^{37} +(-0.242691 - 2.82563i) q^{38} -1.65650 q^{39} +(1.71108 + 6.08869i) q^{40} +3.35439 q^{41} +(3.31777 - 3.31777i) q^{43} +(1.35058 + 7.80432i) q^{44} +(0.101165 + 5.97725i) q^{45} +(-2.67830 - 2.25462i) q^{46} +(8.86854 + 8.86854i) q^{47} +(0.979091 - 2.06532i) q^{48} +(-0.843164 - 7.02062i) q^{50} -0.343422i q^{51} +(4.73879 + 3.34061i) q^{52} +(-2.12863 - 2.12863i) q^{53} +(2.95258 - 3.50743i) q^{54} +(-0.149853 - 8.85392i) q^{55} +(0.810271 - 0.810271i) q^{57} +(-10.2290 + 0.878562i) q^{58} -14.8347 q^{59} +(-1.43682 + 2.11324i) q^{60} -4.23352 q^{61} +(-4.60450 + 0.395476i) q^{62} +(-6.96599 + 3.93382i) q^{64} +(-4.66056 - 4.50543i) q^{65} +(-2.06094 + 2.44823i) q^{66} +(-2.68988 - 2.68988i) q^{67} +(-0.692570 + 0.982438i) q^{68} -1.41455i q^{69} +4.86004i q^{71} +(-7.31335 + 1.92232i) q^{72} +(6.91747 + 6.91747i) q^{73} +(-10.4164 - 8.76863i) q^{74} +(1.95072 - 2.08745i) q^{75} +(-3.95201 + 0.683915i) q^{76} +(0.200469 + 2.33405i) q^{78} +6.91439 q^{79} +(8.37205 - 3.14781i) q^{80} -6.16801 q^{81} +(-0.405948 - 4.72642i) q^{82} +(-5.46792 + 5.46792i) q^{83} +(0.934058 - 0.966221i) q^{85} +(-5.07634 - 4.27330i) q^{86} +(-2.93325 - 2.93325i) q^{87} +(10.8330 - 2.84748i) q^{88} +3.87162i q^{89} +(8.40985 - 0.865911i) q^{90} +(-2.85269 + 4.04665i) q^{92} +(-1.32037 - 1.32037i) q^{93} +(11.4227 - 13.5693i) q^{94} +(4.48352 - 0.0758839i) q^{95} +(-3.02858 - 1.12962i) q^{96} +(-1.11914 + 1.11914i) q^{97} +10.5874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8}+O(q^{10}) \) 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8	\( 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37} + 12 q^{38} + 2 q^{40} + 20 q^{41} - 12 q^{45} + 28 q^{46} - 6 q^{48} - 14 q^{50} + 48 q^{52} + 24 q^{53} - 8 q^{57} - 30 q^{58} + 10 q^{60} - 20 q^{61} - 28 q^{62} - 4 q^{65} + 44 q^{66} - 12 q^{68} - 44 q^{72} - 12 q^{73} - 56 q^{76} + 32 q^{78} + 52 q^{80} + 52 q^{81} - 34 q^{82} + 8 q^{85} - 64 q^{86} - 16 q^{88} + 16 q^{90} + 22 q^{92} - 12 q^{93} - 48 q^{96} + 12 q^{97}+O(q^{100}) \) 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Introduction

L-functions

Modular forms

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Database

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