LMFDB - Embedded newform 980.2.k.j.687.9

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			687.9
Character	$\chi$	$=$	980.687
Dual form			980.2.k.j.883.9

$q$-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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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	0.814059	−	0.580782i	$-0.197253\pi$
$3$	0.404049	+	0.404049i	0.233278	+	0.233278i	−0.580782	+	0.814059i	$0.697253\pi$
$4$	−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	$0.203647\pi$
$11$			3.96016i			1.19403i	−0.802229	+	0.597017i	$0.796353\pi$
$12$	−0.658466	−	0.934060i	−0.190083	−	0.269640i
$13$	−2.04987	+	2.04987i	−0.568532	+	0.568532i	−0.931717	−	0.363185i	$-0.881689\pi$
$13$	−2.04987	+	2.04987i	−0.568532	+	0.568532i	0.363185	+	0.931717i	$0.381689\pi$
$14$		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	0.756762	−	0.653690i	$-0.226780\pi$
$17$	0.424976	+	0.424976i	0.103072	+	0.103072i	−0.653690	+	0.756762i	$0.726780\pi$
$18$	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	0.865649	−	0.500651i	$-0.166906\pi$
$23$	1.75047	+	1.75047i	0.364999	+	0.364999i	−0.500651	+	0.865649i	$0.666906\pi$
$24$	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	$0.235443\pi$
$29$			7.25964i			1.34808i	−0.738694	+	0.674041i	$0.764557\pi$
$30$	−1.40186	+	1.14013i	−0.255944	+	0.208158i
$31$			3.26786i			0.586925i	0.955971	+	0.293462i	$0.0948075\pi$
$31$			3.26786i			0.586925i	−0.955971	+	0.293462i	$0.905192\pi$
$32$	−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	0.991857	+	0.127356i	$0.0406491\pi$
$37$	6.80791	+	6.80791i	1.11921	+	1.11921i	0.127356	+	0.991857i	$0.459351\pi$
$38$	−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	0.913282	−	0.407327i	$-0.133539\pi$
$43$	3.31777	+	3.31777i	0.505955	+	0.505955i	−0.407327	+	0.913282i	$0.633539\pi$
$44$	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	0.361072	−	0.932538i	$-0.382411\pi$
$47$	8.86854	−	8.86854i	1.29361	−	1.29361i	0.932538	−	0.361072i	$-0.117589\pi$
$48$	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	−0.838024	−	0.545633i	$-0.816289\pi$
$53$	−2.12863	+	2.12863i	−0.292390	+	0.292390i	0.545633	+	0.838024i	$0.316289\pi$
$54$	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	−0.852062	−	0.523441i	$-0.824648\pi$
$67$	−2.68988	+	2.68988i	−0.328622	+	0.328622i	0.523441	+	0.852062i	$0.324648\pi$
$68$	−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	$-0.906880\pi$
$71$		−	4.86004i		−	0.576781i	0.957513	−	0.288390i	$-0.0931201\pi$
$72$	−7.31335	−	1.92232i	−0.861886	−	0.226547i
$73$	6.91747	−	6.91747i	0.809629	−	0.809629i	−0.174949	−	0.984578i	$-0.555976\pi$
$73$	6.91747	−	6.91747i	0.809629	−	0.809629i	0.984578	+	0.174949i	$0.0559759\pi$
$74$	−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	0.340179	−	0.940361i	$-0.389512\pi$
$83$	−5.46792	−	5.46792i	−0.600182	−	0.600182i	−0.940361	+	0.340179i	$0.889512\pi$
$84$		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	$-0.934217\pi$
$89$		−	3.87162i		−	0.410391i	0.978721	−	0.205195i	$-0.0657830\pi$
$90$	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	0.648005	−	0.761636i	$-0.275604\pi$
$97$	−1.11914	−	1.11914i	−0.113632	−	0.113632i	−0.761636	+	0.648005i	$0.775604\pi$
$98$		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	0.198581	−	0.980084i	$-0.436367\pi$
$103$	−7.93139	−	7.93139i	−0.781503	−	0.781503i	−0.980084	+	0.198581i	$0.936367\pi$
$104$	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	−0.385275	−	0.922802i	$-0.625893\pi$
$107$	5.56023	−	5.56023i	0.537527	−	0.537527i	0.922802	+	0.385275i	$0.125893\pi$
$108$	−5.29938	+	3.73580i	−0.509933	+	0.359477i
$109$		−	0.404298i		−	0.0387248i	−0.999813	−	0.0193624i	$-0.993836\pi$
$109$		−	0.404298i		−	0.0387248i	0.999813	−	0.0193624i	$-0.00616362\pi$
$110$	−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	−0.854875	−	0.518834i	$-0.826366\pi$
$113$	−3.57217	+	3.57217i	−0.336041	+	0.336041i	0.518834	+	0.854875i	$0.326366\pi$
$114$	−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	−0.461221	−	0.887286i	$-0.652588\pi$
$127$	4.80151	−	4.80151i	0.426065	−	0.426065i	0.887286	+	0.461221i	$0.152588\pi$
$128$	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	$0.230995\pi$
$131$			15.1917i			1.32731i	−0.748041	+	0.663653i	$0.769005\pi$
$132$	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	0.831730	−	0.555181i	$-0.187351\pi$
$137$	3.23692	+	3.23692i	0.276549	+	0.276549i	−0.555181	+	0.831730i	$0.687351\pi$
$138$	−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	$0.0642972\pi$
$149$			4.89788i			0.401250i	−0.979668	+	0.200625i	$0.935703\pi$
$150$	−3.17735	+	2.49599i	−0.259430	+	0.203797i
$151$		−	14.7376i		−	1.19933i	−0.800251	−	0.599666i	$-0.795300\pi$
$151$		−	14.7376i		−	1.19933i	0.800251	−	0.599666i	$-0.204700\pi$
$152$	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	0.320057	−	0.947398i	$-0.396298\pi$
$157$	−7.86056	−	7.86056i	−0.627341	−	0.627341i	−0.947398	+	0.320057i	$0.896298\pi$
$158$	−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	−0.999853	−	0.0171472i	$-0.994542\pi$
$163$	−12.9842	−	12.9842i	−1.01700	−	1.01700i	−0.0171472	−	0.999853i	$-0.505458\pi$
$164$	−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	0.0156336	−	0.999878i	$-0.495023\pi$
$167$	13.1233	−	13.1233i	1.01551	−	1.01551i	0.999878	−	0.0156336i	$-0.00497655\pi$
$168$		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	−0.467224	−	0.884139i	$-0.654746\pi$
$173$	5.48367	−	5.48367i	0.416916	−	0.416916i	0.884139	+	0.467224i	$0.154746\pi$
$174$	−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	$0.192057\pi$
$191$			15.6837i			1.13483i	−0.823431	+	0.567416i	$0.807943\pi$
$192$	−1.22514	−	4.40406i	−0.0884172	−	0.317836i
$193$	5.48865	−	5.48865i	0.395082	−	0.395082i	−0.481412	−	0.876494i	$-0.659876\pi$
$193$	5.48865	−	5.48865i	0.395082	−	0.395082i	0.876494	+	0.481412i	$0.159876\pi$
$194$	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	0.841547	−	0.540184i	$-0.181645\pi$
$197$	4.22983	+	4.22983i	0.301363	+	0.301363i	−0.540184	+	0.841547i	$0.681645\pi$
$198$	−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	$-0.797727\pi$
$211$		−	17.2435i		−	1.18709i	0.804799	−	0.593547i	$-0.202273\pi$
$212$	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	0.206056	−	0.978540i	$-0.433937\pi$
$223$	−11.5356	−	11.5356i	−0.772484	−	0.772484i	−0.978540	+	0.206056i	$0.933937\pi$
$224$		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	−0.364017	−	0.931392i	$-0.618595\pi$
$227$	8.54837	−	8.54837i	0.567375	−	0.567375i	0.931392	+	0.364017i	$0.118595\pi$
$228$	−1.32047	−	1.87314i	−0.0874504	−	0.124052i
$229$			2.19386i			0.144975i	0.997369	+	0.0724873i	$0.0230937\pi$
$229$			2.19386i			0.144975i	−0.997369	+	0.0724873i	$0.976906\pi$
$230$	−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	−0.680519	−	0.732730i	$-0.738246\pi$
$233$	0.796972	−	0.796972i	0.0522113	−	0.0522113i	0.732730	+	0.680519i	$0.238246\pi$
$234$	−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	$0.0156398\pi$
$251$			1.55623i			0.0982283i	−0.998793	+	0.0491141i	$0.984360\pi$
$252$		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	0.195863	−	0.980631i	$-0.437249\pi$
$257$	−12.5808	−	12.5808i	−0.784768	−	0.784768i	−0.980631	+	0.195863i	$0.937249\pi$
$258$	−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	0.988503	−	0.151203i	$-0.0483146\pi$
$263$	13.5787	+	13.5787i	0.837300	+	0.837300i	−0.151203	+	0.988503i	$0.548315\pi$
$264$	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	$-0.855898\pi$
$269$		−	14.3480i		−	0.874810i	0.899265	−	0.437405i	$-0.144102\pi$
$270$	6.46851	+	7.95345i	0.393661	+	0.484032i
$271$			20.6758i			1.25596i	0.778228	+	0.627981i	$0.216119\pi$
$271$			20.6758i			1.25596i	−0.778228	+	0.627981i	$0.783881\pi$
$272$	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	0.803018	−	0.595955i	$-0.203226\pi$
$277$	3.44621	+	3.44621i	0.207062	+	0.207062i	−0.595955	+	0.803018i	$0.703226\pi$
$278$	−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	0.736278	−	0.676679i	$-0.236582\pi$
$283$	1.00261	+	1.00261i	0.0595989	+	0.0595989i	−0.676679	+	0.736278i	$0.736582\pi$
$284$	−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	−0.508809	−	0.860880i	$-0.669914\pi$
$293$	6.02648	−	6.02648i	0.352071	−	0.352071i	0.860880	+	0.508809i	$0.169914\pi$
$294$		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	−0.947558	−	0.319583i	$-0.896457\pi$
$307$	−11.0030	+	11.0030i	−0.627975	+	0.627975i	0.319583	+	0.947558i	$0.396457\pi$
$308$		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	$0.255906\pi$
$311$			25.3983i			1.44021i	−0.693866	+	0.720104i	$0.744094\pi$
$312$	−1.19107	+	4.53136i	−0.0674311	+	0.256538i
$313$	18.3469	−	18.3469i	1.03703	−	1.03703i	0.0377426	−	0.999287i	$-0.487983\pi$
$313$	18.3469	−	18.3469i	1.03703	−	1.03703i	0.999287	−	0.0377426i	$-0.0120167\pi$
$314$	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	0.711350	−	0.702838i	$-0.248084\pi$
$317$	0.151543	+	0.151543i	0.00851151	+	0.00851151i	−0.702838	+	0.711350i	$0.748084\pi$
$318$	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	$-0.981396\pi$
$331$		−	2.12541i		−	0.116823i	0.998293	−	0.0584115i	$-0.0186036\pi$
$332$	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	−0.966530	−	0.256552i	$-0.917414\pi$
$337$	−22.4528	−	22.4528i	−1.22308	−	1.22308i	−0.256552	−	0.966530i	$-0.582586\pi$
$338$	−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	−0.962958	−	0.269651i	$-0.913092\pi$
$347$	−12.9149	+	12.9149i	−0.693306	+	0.693306i	0.269651	+	0.962958i	$0.413092\pi$
$348$	6.78094	−	4.78023i	0.363497	−	0.256247i
$349$		−	21.6072i		−	1.15661i	−0.815821	−	0.578304i	$-0.803715\pi$
$349$		−	21.6072i		−	1.15661i	0.815821	−	0.578304i	$-0.196285\pi$
$350$		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	−0.950229	−	0.311554i	$-0.899151\pi$
$353$	−11.9996	+	11.9996i	−0.638675	+	0.638675i	0.311554	+	0.950229i	$0.399151\pi$
$354$	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	−0.181059	−	0.983472i	$-0.557953\pi$
$367$	15.3720	−	15.3720i	0.802413	−	0.802413i	0.983472	+	0.181059i	$0.0579525\pi$
$368$	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	−0.715998	−	0.698102i	$-0.754028\pi$
$373$	−0.345634	+	0.345634i	−0.0178963	+	0.0178963i	0.698102	+	0.715998i	$0.254028\pi$
$374$	−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	0.607476	−	0.794338i	$-0.292182\pi$
$383$	−3.65697	−	3.65697i	−0.186862	−	0.186862i	−0.794338	+	0.607476i	$0.792182\pi$
$384$	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	$0.100302\pi$
$389$			12.2252i			0.619841i	−0.950762	+	0.309921i	$0.899698\pi$
$390$	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	0.945684	−	0.325087i	$-0.105394\pi$
$397$	12.3653	+	12.3653i	0.620597	+	0.620597i	−0.325087	+	0.945684i	$0.605394\pi$
$398$	−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	$-0.959594\pi$
$409$		−	5.12060i		−	0.253197i	0.991954	−	0.126599i	$-0.0404061\pi$
$410$	−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	$0.198706\pi$
$431$			24.2687i			1.16898i	−0.811400	+	0.584492i	$0.801294\pi$
$432$	11.7176	−	5.55486i	0.563763	−	0.267259i
$433$	−0.0253628	+	0.0253628i	−0.00121886	+	0.00121886i	−0.707716	−	0.706497i	$-0.750274\pi$
$433$	−0.0253628	+	0.0253628i	−0.00121886	+	0.00121886i	0.706497	+	0.707716i	$0.250274\pi$
$434$		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	0.878822	−	0.477150i	$-0.158330\pi$
$443$	8.45422	+	8.45422i	0.401672	+	0.401672i	−0.477150	+	0.878822i	$0.658330\pi$
$444$	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	$-0.895105\pi$
$449$		−	13.7142i		−	0.647213i	0.946192	−	0.323607i	$-0.104895\pi$
$450$	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	0.437680	−	0.899131i	$-0.355800\pi$
$457$	−9.86469	−	9.86469i	−0.461451	−	0.461451i	−0.899131	+	0.437680i	$0.855800\pi$
$458$	−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	0.607027	−	0.794681i	$-0.292362\pi$
$463$	−4.03783	−	4.03783i	−0.187654	−	0.187654i	−0.794681	+	0.607027i	$0.792362\pi$
$464$	−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	−0.477035	−	0.878884i	$-0.658289\pi$
$467$	8.68402	−	8.68402i	0.401849	−	0.401849i	0.878884	+	0.477035i	$0.158289\pi$
$468$	−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	−0.759949	−	0.649983i	$-0.774776\pi$
$487$	−2.42674	+	2.42674i	−0.109966	+	0.109966i	0.649983	+	0.759949i	$0.274776\pi$
$488$	−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	$-0.974520\pi$
$491$		−	3.54370i		−	0.159925i	0.996798	−	0.0799626i	$-0.0254801\pi$
$492$	−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	0.537659	−	0.843162i	$-0.319309\pi$
$503$	−6.85172	−	6.85172i	−0.305503	−	0.305503i	−0.843162	+	0.537659i	$0.819309\pi$
$504$		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	$-0.932375\pi$
$509$		−	9.51419i		−	0.421709i	0.977517	−	0.210854i	$-0.0676246\pi$
$510$	−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	−0.997896	−	0.0648374i	$-0.979347\pi$
$523$	−24.3039	−	24.3039i	−1.06273	−	1.06273i	−0.0648374	−	0.997896i	$-0.520653\pi$
$524$	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	−0.825381	−	0.564577i	$-0.809039\pi$
$547$	−6.09970	+	6.09970i	−0.260804	+	0.260804i	0.564577	+	0.825381i	$0.309039\pi$
$548$	−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	0.484191	−	0.874962i	$-0.339114\pi$
$557$	−9.22254	−	9.22254i	−0.390771	−	0.390771i	−0.874962	+	0.484191i	$0.839114\pi$
$558$	−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	0.945955	−	0.324299i	$-0.105128\pi$
$563$	14.7504	+	14.7504i	0.621656	+	0.621656i	−0.324299	+	0.945955i	$0.605128\pi$
$564$	−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	$0.0536259\pi$
$569$			7.99934i			0.335350i	−0.985842	+	0.167675i	$0.946374\pi$
$570$	−2.81126	+	2.28639i	−0.117751	+	0.0957663i
$571$			32.8653i			1.37537i	0.726010	+	0.687684i	$0.241373\pi$
$571$			32.8653i			1.37537i	−0.726010	+	0.687684i	$0.758627\pi$
$572$	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	0.988189	+	0.153237i	$0.0489699\pi$
$577$	27.4180	+	27.4180i	1.14143	+	1.14143i	0.153237	+	0.988189i	$0.451030\pi$
$578$	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	−0.569699	−	0.821854i	$-0.692940\pi$
$587$	6.10922	−	6.10922i	0.252155	−	0.252155i	0.821854	+	0.569699i	$0.192940\pi$
$588$		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	−0.288007	+	0.957628i	$0.592993\pi$
$593$	−30.3332	+	30.3332i	−1.24564	+	1.24564i	−0.957628	+	0.288007i	$0.907007\pi$
$594$	−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	−0.249853	−	0.968284i	$-0.580382\pi$
$607$	17.7002	−	17.7002i	0.718430	−	0.718430i	0.968284	+	0.249853i	$0.0803824\pi$
$608$	−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	−0.828138	−	0.560524i	$-0.810600\pi$
$613$	−6.62581	+	6.62581i	−0.267614	+	0.267614i	0.560524	+	0.828138i	$0.310600\pi$
$614$	−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	0.286204	−	0.958169i	$-0.407606\pi$
$617$	−16.6913	−	16.6913i	−0.671965	−	0.671965i	−0.958169	+	0.286204i	$0.907606\pi$
$618$	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	$-0.940744\pi$
$631$		−	9.29850i		−	0.370167i	0.982723	−	0.185084i	$-0.0592556\pi$
$632$	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	0.789475	−	0.613782i	$-0.210353\pi$
$643$	4.45513	+	4.45513i	0.175693	+	0.175693i	−0.613782	+	0.789475i	$0.710353\pi$
$644$		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	−0.940380	−	0.340125i	$-0.889531\pi$
$647$	−15.2682	+	15.2682i	−0.600256	+	0.600256i	0.340125	+	0.940380i	$0.389531\pi$
$648$	−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	−0.177343	−	0.984149i	$-0.556750\pi$
$653$	20.6170	−	20.6170i	0.806806	−	0.806806i	0.984149	+	0.177343i	$0.0567502\pi$
$654$	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	0.128125	−	0.991758i	$-0.459104\pi$
$673$	29.0523	−	29.0523i	1.11988	−	1.11988i	0.991758	−	0.128125i	$-0.0408958\pi$
$674$	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	0.997787	+	0.0664868i	$0.0211790\pi$
$677$	27.6916	+	27.6916i	1.06427	+	1.06427i	0.0664868	+	0.997787i	$0.478821\pi$
$678$	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	0.527923	−	0.849292i	$-0.322971\pi$
$683$	−8.39874	−	8.39874i	−0.321369	−	0.321369i	−0.849292	+	0.527923i	$0.822971\pi$
$684$	−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	$-0.951941\pi$
$691$		−	7.90757i		−	0.300818i	0.988624	−	0.150409i	$-0.0480591\pi$
$692$	−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	$0.171097\pi$
$709$			27.2663i			1.02401i	−0.858983	+	0.512003i	$0.828903\pi$
$710$	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	−0.803919	−	0.594739i	$-0.797256\pi$
$727$	−5.64012	+	5.64012i	−0.209180	+	0.209180i	0.594739	+	0.803919i	$0.297256\pi$
$728$		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	−0.465049	−	0.885285i	$-0.653963\pi$
$733$	11.3775	−	11.3775i	0.420236	−	0.420236i	0.885285	+	0.465049i	$0.153963\pi$
$734$	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	0.980374	−	0.197145i	$-0.0631669\pi$
$743$	21.3493	+	21.3493i	0.783229	+	0.783229i	−0.197145	+	0.980374i	$0.563167\pi$
$744$	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	$-0.766516\pi$
$751$		−	36.6934i		−	1.33896i	0.742829	−	0.669481i	$-0.233484\pi$
$752$	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	0.989695	−	0.143191i	$-0.0457363\pi$
$757$	23.2904	+	23.2904i	0.846504	+	0.846504i	−0.143191	+	0.989695i	$0.545736\pi$
$758$	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	$-0.815711\pi$
$769$		−	30.3461i		−	1.09431i	0.837031	−	0.547155i	$-0.184289\pi$
$770$		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	−0.290465	−	0.956885i	$-0.593810\pi$
$773$	18.5284	−	18.5284i	0.666420	−	0.666420i	0.956885	+	0.290465i	$0.0938101\pi$
$774$	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	−0.552476	−	0.833529i	$-0.686317\pi$
$787$	7.88453	−	7.88453i	0.281053	−	0.281053i	0.833529	+	0.552476i	$0.186317\pi$
$788$	−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	0.519621	−	0.854397i	$-0.326073\pi$
$797$	−9.45111	−	9.45111i	−0.334775	−	0.334775i	−0.854397	+	0.519621i	$0.826073\pi$
$798$		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	$-0.805423\pi$
$809$		−	32.6478i		−	1.14784i	0.818913	−	0.573918i	$-0.194577\pi$
$810$	1.99774	−	19.4024i	0.0701936	−	0.681730i
$811$		−	38.0037i		−	1.33449i	−0.744838	−	0.667245i	$-0.767473\pi$
$811$		−	38.0037i		−	1.33449i	0.744838	−	0.667245i	$-0.232527\pi$
$812$		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	0.159562	−	0.987188i	$-0.448992\pi$
$823$	−23.7429	−	23.7429i	−0.827626	−	0.827626i	−0.987188	+	0.159562i	$0.948992\pi$
$824$	−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	−0.619242	−	0.785200i	$-0.712560\pi$
$827$	4.77258	−	4.77258i	0.165959	−	0.165959i	0.785200	+	0.619242i	$0.212560\pi$
$828$	−10.8187	+	7.62663i	−0.375975	+	0.265044i
$829$		−	33.8016i		−	1.17398i	−0.809595	−	0.586989i	$-0.800313\pi$
$829$		−	33.8016i		−	1.17398i	0.809595	−	0.586989i	$-0.199687\pi$
$830$	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	−0.649686	−	0.760202i	$-0.725100\pi$
$853$	3.22775	−	3.22775i	0.110516	−	0.110516i	0.760202	+	0.649686i	$0.225100\pi$
$854$		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	0.0666962	−	0.997773i	$-0.478754\pi$
$857$	−27.2569	−	27.2569i	−0.931077	−	0.931077i	−0.997773	+	0.0666962i	$0.978754\pi$
$858$	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	0.999991	−	0.00424917i	$-0.00135256\pi$
$863$	29.2518	+	29.2518i	0.995742	+	0.995742i	−0.00424917	+	0.999991i	$0.501353\pi$
$864$	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	0.986901	−	0.161327i	$-0.0515773\pi$
$877$	24.4487	+	24.4487i	0.825574	+	0.825574i	−0.161327	+	0.986901i	$0.551577\pi$
$878$	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	0.943496	−	0.331385i	$-0.107516\pi$
$883$	18.1891	+	18.1891i	0.612111	+	0.612111i	−0.331385	+	0.943496i	$0.607516\pi$
$884$	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	−0.905081	−	0.425239i	$-0.860190\pi$
$887$	−14.2909	+	14.2909i	−0.479843	+	0.479843i	0.425239	+	0.905081i	$0.360190\pi$
$888$	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	−0.00746634	−	0.999972i	$-0.502377\pi$
$907$	29.8907	−	29.8907i	0.992506	−	0.992506i	0.999972	+	0.00746634i	$0.00237663\pi$
$908$	−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	$-0.712304\pi$
$911$		−	47.4291i		−	1.57140i	0.618610	−	0.785698i	$-0.287696\pi$
$912$	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	$0.249731\pi$
$929$			43.0681i			1.41302i	−0.707704	+	0.706509i	$0.750269\pi$
$930$	−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	0.874366	−	0.485266i	$-0.161277\pi$
$937$	11.9105	+	11.9105i	0.389100	+	0.389100i	−0.485266	+	0.874366i	$0.661277\pi$
$938$		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	−0.362058	−	0.932156i	$-0.617926\pi$
$947$	17.5438	−	17.5438i	0.570097	−	0.570097i	0.932156	+	0.362058i	$0.117926\pi$
$948$	−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	−0.947948	−	0.318425i	$-0.896846\pi$
$953$	−19.4338	+	19.4338i	−0.629523	+	0.629523i	0.318425	+	0.947948i	$0.396846\pi$
$954$	−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	0.132706	−	0.991155i	$-0.457633\pi$
$967$	34.9483	−	34.9483i	1.12386	−	1.12386i	0.991155	−	0.132706i	$-0.0423665\pi$
$968$	−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	$0.286001\pi$
$971$			48.7601i			1.56479i	−0.622785	+	0.782393i	$0.713999\pi$
$972$	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	−0.999998	−	0.00202240i	$-0.999356\pi$
$977$	−31.3201	−	31.3201i	−1.00202	−	1.00202i	−0.00202240	−	0.999998i	$-0.500644\pi$
$978$	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	0.774146	−	0.633008i	$-0.218180\pi$
$983$	4.42508	+	4.42508i	0.141138	+	0.141138i	−0.633008	+	0.774146i	$0.718180\pi$
$984$	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	$-0.855243\pi$
$991$		−	27.6555i		−	0.878507i	0.898363	−	0.439253i	$-0.144757\pi$
$992$	−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	0.599352	−	0.800486i	$-0.295425\pi$
$997$	−6.35088	−	6.35088i	−0.201134	−	0.201134i	−0.800486	+	0.599352i	$0.795425\pi$
$998$	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.687.9		36
4.3	odd	2	inner	980.2.k.j.687.17		36
5.3	odd	4	inner	980.2.k.j.883.17		36
7.2	even	3		980.2.x.m.67.17		72
7.3	odd	6		140.2.w.b.107.3	yes	72
7.4	even	3		980.2.x.m.667.3		72
7.5	odd	6		140.2.w.b.67.17	yes	72
7.6	odd	2		980.2.k.k.687.9		36
20.3	even	4	inner	980.2.k.j.883.9		36
28.3	even	6		140.2.w.b.107.7	yes	72
28.11	odd	6		980.2.x.m.667.7		72
28.19	even	6		140.2.w.b.67.6	yes	72
28.23	odd	6		980.2.x.m.67.6		72
28.27	even	2		980.2.k.k.687.17		36
35.3	even	12		140.2.w.b.23.6	✓	72
35.12	even	12		700.2.be.e.543.12		72
35.13	even	4		980.2.k.k.883.17		36
35.17	even	12		700.2.be.e.443.13		72
35.18	odd	12		980.2.x.m.863.6		72
35.19	odd	6		700.2.be.e.207.2		72
35.23	odd	12		980.2.x.m.263.7		72
35.24	odd	6		700.2.be.e.107.16		72
35.33	even	12		140.2.w.b.123.7	yes	72
140.3	odd	12		140.2.w.b.23.17	yes	72
140.19	even	6		700.2.be.e.207.13		72
140.23	even	12		980.2.x.m.263.3		72
140.47	odd	12		700.2.be.e.543.16		72
140.59	even	6		700.2.be.e.107.12		72
140.83	odd	4		980.2.k.k.883.9		36
140.87	odd	12		700.2.be.e.443.2		72
140.103	odd	12		140.2.w.b.123.3	yes	72
140.123	even	12		980.2.x.m.863.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.6	✓	72	35.3	even	12
140.2.w.b.23.17	yes	72	140.3	odd	12
140.2.w.b.67.6	yes	72	28.19	even	6
140.2.w.b.67.17	yes	72	7.5	odd	6
140.2.w.b.107.3	yes	72	7.3	odd	6
140.2.w.b.107.7	yes	72	28.3	even	6
140.2.w.b.123.3	yes	72	140.103	odd	12
140.2.w.b.123.7	yes	72	35.33	even	12
700.2.be.e.107.12		72	140.59	even	6
700.2.be.e.107.16		72	35.24	odd	6
700.2.be.e.207.2		72	35.19	odd	6
700.2.be.e.207.13		72	140.19	even	6
700.2.be.e.443.2		72	140.87	odd	12
700.2.be.e.443.13		72	35.17	even	12
700.2.be.e.543.12		72	35.12	even	12
700.2.be.e.543.16		72	140.47	odd	12
980.2.k.j.687.9		36	1.1	even	1	trivial
980.2.k.j.687.17		36	4.3	odd	2	inner
980.2.k.j.883.9		36	20.3	even	4	inner
980.2.k.j.883.17		36	5.3	odd	4	inner
980.2.k.k.687.9		36	7.6	odd	2
980.2.k.k.687.17		36	28.27	even	2
980.2.k.k.883.9		36	140.83	odd	4
980.2.k.k.883.17		36	35.13	even	4
980.2.x.m.67.6		72	28.23	odd	6
980.2.x.m.67.17		72	7.2	even	3
980.2.x.m.263.3		72	140.23	even	12
980.2.x.m.263.7		72	35.23	odd	12
980.2.x.m.667.3		72	7.4	even	3
980.2.x.m.667.7		72	28.11	odd	6
980.2.x.m.863.6		72	35.18	odd	12
980.2.x.m.863.17		72	140.123	even	12

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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