LMFDB - Embedded newform 980.2.x.m.263.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$980 = 2^{2} \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	980.x (of order $12$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.3
Character	$\chi$	$=$	980.263
Dual form			980.2.x.m.667.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15974 + 0.809319i) q^{2} +(0.147892 + 0.551941i) q^{3} +(0.690004 - 1.87720i) q^{4} +(-1.15064 - 1.91729i) q^{5} +(-0.618214 - 0.520418i) q^{6} +(0.719030 + 2.73551i) q^{8} +(2.31531 - 1.33674i) q^{9} +(2.88615 + 1.29233i) q^{10} +(3.42960 + 1.98008i) q^{11} +(1.13815 + 0.103218i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(0.888062 - 0.918641i) q^{15} +(-3.04779 - 2.59056i) q^{16} +(0.155552 + 0.580528i) q^{17} +(-1.60331 + 3.42410i) q^{18} +(-1.00269 - 1.73671i) q^{19} +(-4.39310 + 0.837053i) q^{20} +(-5.57997 + 0.479259i) q^{22} +(-2.39119 - 0.640717i) q^{23} +(-1.40350 + 0.801422i) q^{24} +(-2.35203 + 4.41225i) q^{25} +(4.03632 + 0.718322i) q^{26} +(2.29237 + 2.29237i) q^{27} -7.25964i q^{29} +(-0.286450 + 1.78411i) q^{30} +(2.83005 + 1.63393i) q^{31} +(5.63124 + 0.537745i) q^{32} +(-0.585677 + 2.18578i) q^{33} +(-0.650233 - 0.547372i) q^{34} +(-0.911768 - 5.26867i) q^{36} +(-9.29977 - 2.49187i) q^{37} +(2.56841 + 1.20264i) q^{38} +(0.828248 - 1.43457i) q^{39} +(4.41742 - 4.52619i) q^{40} +3.35439 q^{41} +(3.31777 - 3.31777i) q^{43} +(6.08345 - 5.07179i) q^{44} +(-5.22703 - 2.90101i) q^{45} +(3.29171 - 1.19217i) q^{46} +(3.24611 - 12.1147i) q^{47} +(0.979091 - 2.06532i) q^{48} +(-0.843164 - 7.02062i) q^{50} +(-0.297413 + 0.171711i) q^{51} +(-5.26244 + 2.43360i) q^{52} +(2.90777 - 0.779134i) q^{53} +(-4.51381 - 0.803298i) q^{54} +(-0.149853 - 8.85392i) q^{55} +(0.810271 - 0.810271i) q^{57} +(5.87537 + 8.41932i) q^{58} +(7.41735 - 12.8472i) q^{59} +(-1.11171 - 2.30094i) q^{60} +(2.11676 + 3.66633i) q^{61} +(-4.60450 + 0.395476i) q^{62} +(-6.96599 + 3.93382i) q^{64} +(-1.57153 + 6.28888i) q^{65} +(-1.08976 - 3.00894i) q^{66} +(3.67445 - 0.984566i) q^{67} +(1.19710 + 0.108564i) q^{68} -1.41455i q^{69} +4.86004i q^{71} +(5.32145 + 5.37238i) q^{72} +(-9.44944 + 2.53197i) q^{73} +(12.8021 - 4.63656i) q^{74} +(-2.78315 - 0.645648i) q^{75} +(-3.95201 + 0.683915i) q^{76} +(0.200469 + 2.33405i) q^{78} +(-3.45719 - 5.98803i) q^{79} +(-1.45994 + 8.82432i) q^{80} +(3.08400 - 5.34165i) q^{81} +(-3.89023 + 2.71477i) q^{82} +(-5.46792 + 5.46792i) q^{83} +(0.934058 - 0.966221i) q^{85} +(-1.16262 + 6.53289i) q^{86} +(4.00690 - 1.07364i) q^{87} +(-2.95054 + 10.8054i) q^{88} +(3.35292 - 1.93581i) q^{89} +(8.40985 - 0.865911i) q^{90} +(-2.85269 + 4.04665i) q^{92} +(-0.483291 + 1.80367i) q^{93} +(6.03997 + 16.6770i) q^{94} +(-2.17604 + 3.92078i) q^{95} +(0.536012 + 3.18764i) q^{96} +(-1.11914 + 1.11914i) q^{97} +10.5874 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100})$ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−1.15974	+	0.809319i	−0.820062	+	0.572275i
$2$	−1.15974	+	0.809319i	−0.820062	+	0.572275i
$3$	0.147892	+	0.551941i	0.0853856	+	0.318663i	0.995387	−	0.0959419i	$-0.0305863\pi$
$3$	0.147892	+	0.551941i	0.0853856	+	0.318663i	−0.910001	+	0.414605i	$0.863920\pi$
$4$	0.690004	−	1.87720i	0.345002	−	0.938602i
$5$	−1.15064	−	1.91729i	−0.514584	−	0.857440i
$5$	−1.15064	−	1.91729i	−0.514584	−	0.857440i
$6$	−0.618214	−	0.520418i	−0.252385	−	0.212460i
$7$		0			0
$7$		0			0
$8$	0.719030	+	2.73551i	0.254216	+	0.967148i
$9$	2.31531	−	1.33674i	0.771770	−	0.445581i
$10$	2.88615	+	1.29233i	0.912682	+	0.408670i
$11$	3.42960	+	1.98008i	1.03406	+	0.597017i	0.918146	−	0.396242i	$-0.129686\pi$
$11$	3.42960	+	1.98008i	1.03406	+	0.597017i	0.115917	+	0.993259i	$0.463019\pi$
$12$	1.13815	+	0.103218i	0.328556	+	0.0297965i
$13$	−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
$16$	−3.04779	−	2.59056i	−0.761947	−	0.647639i
$17$	0.155552	+	0.580528i	0.0377269	+	0.140799i	0.982220	−	0.187731i	$-0.0601134\pi$
$17$	0.155552	+	0.580528i	0.0377269	+	0.140799i	−0.944493	+	0.328530i	$0.893447\pi$
$18$	−1.60331	+	3.42410i	−0.377904	+	0.807069i
$19$	−1.00269	−	1.73671i	−0.230033	−	0.398428i	0.727785	−	0.685805i	$-0.240550\pi$
$19$	−1.00269	−	1.73671i	−0.230033	−	0.398428i	−0.957817	+	0.287377i	$0.907217\pi$
$20$	−4.39310	+	0.837053i	−0.982327	+	0.187171i
$21$		0			0
$22$	−5.57997	+	0.479259i	−1.18965	+	0.102178i
$23$	−2.39119	−	0.640717i	−0.498597	−	0.133599i	0.000751542	−	1.00000i	$-0.499761\pi$
$23$	−2.39119	−	0.640717i	−0.498597	−	0.133599i	−0.499349	+	0.866401i	$0.666427\pi$
$24$	−1.40350	+	0.801422i	−0.286488	+	0.163590i
$25$	−2.35203	+	4.41225i	−0.470407	+	0.882450i
$26$	4.03632	+	0.718322i	0.791588	+	0.140874i
$27$	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	$-0.235443\pi$
$30$	−0.286450	+	1.78411i	−0.0522983	+	0.325733i
$31$	2.83005	+	1.63393i	0.508292	+	0.293462i	0.732131	−	0.681164i	$-0.238526\pi$
$31$	2.83005	+	1.63393i	0.508292	+	0.293462i	−0.223840	+	0.974626i	$0.571859\pi$
$32$	5.63124	+	0.537745i	0.995471	+	0.0950609i
$33$	−0.585677	+	2.18578i	−0.101953	+	0.380495i
$34$	−0.650233	−	0.547372i	−0.111514	−	0.0938735i
$35$		0			0
$36$	−0.911768	−	5.26867i	−0.151961	−	0.878111i
$37$	−9.29977	−	2.49187i	−1.52887	−	0.409660i	−0.606222	−	0.795295i	$-0.707316\pi$
$37$	−9.29977	−	2.49187i	−1.52887	−	0.409660i	−0.922651	+	0.385635i	$0.873982\pi$
$38$	2.56841	+	1.20264i	0.416651	+	0.195094i
$39$	0.828248	−	1.43457i	0.132626	−	0.229715i
$40$	4.41742	−	4.52619i	0.698456	−	0.715653i
$41$	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	$0.133539\pi$
$44$	6.08345	−	5.07179i	0.917115	−	0.764602i
$45$	−5.22703	−	2.90101i	−0.779200	−	0.432457i
$46$	3.29171	−	1.19217i	0.485336	−	0.175776i
$47$	3.24611	−	12.1147i	0.473494	−	1.76710i	−0.153572	−	0.988137i	$-0.549078\pi$
$47$	3.24611	−	12.1147i	0.473494	−	1.76710i	0.627066	−	0.778966i	$-0.284256\pi$
$48$	0.979091	−	2.06532i	0.141320	−	0.298104i
$49$		0			0
$50$	−0.843164	−	7.02062i	−0.119241	−	0.992865i
$51$	−0.297413	+	0.171711i	−0.0416461	+	0.0240444i
$52$	−5.26244	+	2.43360i	−0.729770	+	0.337480i
$53$	2.90777	−	0.779134i	0.399413	−	0.107022i	−0.0535205	−	0.998567i	$-0.517044\pi$
$53$	2.90777	−	0.779134i	0.399413	−	0.107022i	0.452933	+	0.891544i	$0.350378\pi$
$54$	−4.51381	−	0.803298i	−0.614252	−	0.109315i
$55$	−0.149853	−	8.85392i	−0.0202062	−	1.19386i
$56$		0			0
$57$	0.810271	−	0.810271i	0.107323	−	0.107323i
$58$	5.87537	+	8.41932i	0.771474	+	1.10551i
$59$	7.41735	−	12.8472i	0.965657	−	1.67257i	0.257818	−	0.966193i	$-0.416996\pi$
$59$	7.41735	−	12.8472i	0.965657	−	1.67257i	0.707839	−	0.706374i	$-0.249670\pi$
$60$	−1.11171	−	2.30094i	−0.143521	−	0.297050i
$61$	2.11676	+	3.66633i	0.271023	+	0.469426i	0.969124	−	0.246574i	$-0.0793047\pi$
$61$	2.11676	+	3.66633i	0.271023	+	0.469426i	−0.698101	+	0.715999i	$0.745971\pi$
$62$	−4.60450	+	0.395476i	−0.584772	+	0.0502255i
$63$		0			0
$64$	−6.96599	+	3.93382i	−0.870749	+	0.491728i
$65$	−1.57153	+	6.28888i	−0.194925	+	0.780039i
$66$	−1.08976	−	3.00894i	−0.134140	−	0.370375i
$67$	3.67445	−	0.984566i	0.448906	−	0.120284i	−0.0272817	−	0.999628i	$-0.508685\pi$
$67$	3.67445	−	0.984566i	0.448906	−	0.120284i	0.476187	+	0.879344i	$0.342018\pi$
$68$	1.19710	+	0.108564i	0.145170	+	0.0131653i
$69$		−	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	$0.906880\pi$
$72$	5.32145	+	5.37238i	0.627139	+	0.633142i
$73$	−9.44944	+	2.53197i	−1.10597	+	0.296345i	−0.765195	−	0.643799i	$-0.777357\pi$
$73$	−9.44944	+	2.53197i	−1.10597	+	0.296345i	−0.340779	+	0.940143i	$0.610691\pi$
$74$	12.8021	−	4.63656i	1.48821	−	0.538990i
$75$	−2.78315	−	0.645648i	−0.321370	−	0.0745530i
$76$	−3.95201	+	0.683915i	−0.453327	+	0.0784504i
$77$		0			0
$78$	0.200469	+	2.33405i	0.0226987	+	0.264279i
$79$	−3.45719	−	5.98803i	−0.388965	−	0.673706i	0.603346	−	0.797480i	$-0.293834\pi$
$79$	−3.45719	−	5.98803i	−0.388965	−	0.673706i	−0.992311	+	0.123773i	$0.960500\pi$
$80$	−1.45994	+	8.82432i	−0.163226	+	0.986589i
$81$	3.08400	−	5.34165i	0.342667	−	0.593517i
$82$	−3.89023	+	2.71477i	−0.429604	+	0.299796i
$83$	−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
$86$	−1.16262	+	6.53289i	−0.125369	+	0.704460i
$87$	4.00690	−	1.07364i	0.429584	−	0.115107i
$88$	−2.95054	+	10.8054i	−0.314528	+	1.15186i
$89$	3.35292	−	1.93581i	0.355409	−	0.205195i	−0.311656	−	0.950195i	$-0.600884\pi$
$89$	3.35292	−	1.93581i	0.355409	−	0.205195i	0.667065	+	0.745000i	$0.267550\pi$
$90$	8.40985	−	0.865911i	0.886476	−	0.0912750i
$91$		0			0
$92$	−2.85269	+	4.04665i	−0.297413	+	0.421893i
$93$	−0.483291	+	1.80367i	−0.0501149	+	0.187031i
$94$	6.03997	+	16.6770i	0.622975	+	1.72010i
$95$	−2.17604	+	3.92078i	−0.223257	+	0.402264i
$96$	0.536012	+	3.18764i	0.0547065	+	0.325337i
$97$	−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
$100$	6.65977	+	7.45972i	0.665977	+	0.745972i
$101$	8.93266	−	15.4718i	0.888833	−	1.53950i	0.0475759	−	0.998868i	$-0.484850\pi$
$101$	8.93266	−	15.4718i	0.888833	−	1.53950i	0.841257	−	0.540636i	$-0.181816\pi$
$102$	0.205953	−	0.439843i	0.0203924	−	0.0435509i
$103$	10.8345	+	2.90309i	1.06755	+	0.286050i	0.749487	−	0.662019i	$-0.230300\pi$
$103$	10.8345	+	2.90309i	1.06755	+	0.286050i	0.318066	+	0.948069i	$0.396967\pi$
$104$	4.13352	−	7.08135i	0.405325	−	0.694384i
$105$		0			0
$106$	−2.74169	+	3.25691i	−0.266297	+	0.316339i
$107$	2.03518	−	7.59541i	0.196749	−	0.734276i	−0.795059	−	0.606533i	$-0.792560\pi$
$107$	2.03518	−	7.59541i	0.196749	−	0.734276i	0.991807	−	0.127743i	$-0.0407734\pi$
$108$	5.88498	−	2.72150i	0.566283	−	0.261876i
$109$	−0.350133	−	0.202149i	−0.0335366	−	0.0193624i	0.483138	−	0.875544i	$-0.339497\pi$
$109$	−0.350133	−	0.202149i	−0.0335366	−	0.0193624i	−0.516675	+	0.856182i	$0.672830\pi$
$110$	7.33944	+	10.1470i	0.699788	+	0.967477i
$111$		−	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	$0.826366\pi$
$114$	−0.283937	+	1.59547i	−0.0265932	+	0.149430i
$115$	1.52297	+	5.32185i	0.142017	+	0.496265i
$116$	−13.6278	−	5.00919i	−1.26531	−	0.465091i
$117$	−7.48624	−	2.00593i	−0.692103	−	0.185448i
$118$	1.79530	+	20.9025i	0.165270	+	1.92423i
$119$		0			0
$120$	3.15149	+	1.76877i	0.287691	+	0.161466i
$121$	2.34144	+	4.05549i	0.212858	+	0.368681i
$122$	−5.42213	−	2.53887i	−0.490896	−	0.229858i
$123$	0.496088	+	1.85143i	0.0447308	+	0.166937i
$124$	5.01996	−	4.18516i	0.450806	−	0.375838i
$125$	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	$0.652588\pi$
$128$	4.89504	−	10.1999i	0.432664	−	0.901555i
$129$	2.32188	+	1.34054i	0.204431	+	0.118028i
$130$	−3.26714	−	8.56535i	−0.286547	−	0.751231i
$131$	−13.1564	+	7.59586i	−1.14948	+	0.663653i	−0.948761	−	0.315996i	$-0.897661\pi$
$131$	−13.1564	+	7.59586i	−1.14948	+	0.663653i	−0.200720	+	0.979649i	$0.564328\pi$
$132$	3.69903	+	2.60763i	0.321959	+	0.226965i
$133$		0			0
$134$	−3.46459	+	4.11565i	−0.299295	+	0.355538i
$135$	1.75744	−	7.03284i	0.151257	−	0.605291i
$136$	−1.47619	+	0.842931i	−0.126582	+	0.0722807i
$137$	1.18479	+	4.42171i	0.101224	+	0.377772i	0.997889	−	0.0649361i	$-0.0206844\pi$
$137$	1.18479	+	4.42171i	0.101224	+	0.377772i	−0.896666	+	0.442708i	$0.854018\pi$
$138$	1.14483	+	1.64052i	0.0974540	+	0.139650i
$139$	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
$142$	−3.93332	−	5.63639i	−0.330077	−	0.472996i
$143$	−2.97133	−	11.0891i	−0.248475	−	0.927321i
$144$	−10.5195	−	1.92383i	−0.876624	−	0.160319i
$145$	−13.9189	+	8.35327i	−1.15590	+	0.693701i
$146$	8.90975	−	10.5841i	0.737376	−	0.875942i
$147$		0			0
$148$	−11.0946	+	15.7382i	−0.911973	+	1.29367i
$149$	−4.24169	+	2.44894i	−0.347493	+	0.200625i	−0.663580	−	0.748105i	$-0.730964\pi$
$149$	−4.24169	+	2.44894i	−0.347493	+	0.200625i	0.316088	+	0.948730i	$0.397631\pi$
$150$	3.75027	−	1.50367i	0.306208	−	0.122774i
$151$	−12.7632	−	7.36881i	−1.03865	−	0.599666i	−0.119200	−	0.992870i	$-0.538033\pi$
$151$	−12.7632	−	7.36881i	−1.03865	−	0.599666i	−0.919451	+	0.393205i	$0.871366\pi$
$152$	4.02981	−	3.99161i	0.326861	−	0.323762i
$153$	1.13617	+	1.13617i	0.0918538	+	0.0918538i
$154$		0			0
$155$	−0.123656	−	7.30611i	−0.00993233	−	0.586841i
$156$	−2.12148	−	2.54465i	−0.169854	−	0.203735i
$157$	−2.87717	−	10.7377i	−0.229623	−	0.856964i	−0.980499	−	0.196522i	$-0.937035\pi$
$157$	−2.87717	−	10.7377i	−0.229623	−	0.856964i	0.750877	−	0.660442i	$-0.229631\pi$
$158$	8.85568	+	4.14660i	0.704520	+	0.329886i
$159$	0.860073	+	1.48969i	0.0682082	+	0.118140i
$160$	−5.44854	−	11.4155i	−0.430745	−	0.902474i
$161$		0			0
$162$	0.746452	+	8.69088i	0.0586468	+	0.682820i
$163$	17.7367	+	4.75254i	1.38925	+	0.372248i	0.874472	−	0.485077i	$-0.161208\pi$
$163$	17.7367	+	4.75254i	1.38925	+	0.372248i	0.514776	+	0.857324i	$0.327875\pi$
$164$	2.31454	−	6.29687i	0.180735	−	0.491703i
$165$	4.86468	−	1.39214i	0.378715	−	0.108378i
$166$	1.91608	−	10.7667i	0.148717	−	0.835655i
$167$	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
$170$	−0.301286	+	1.87652i	−0.0231076	+	0.143922i
$171$	−4.64307	−	2.68068i	−0.355064	−	0.204996i
$172$	−3.93885	−	8.51740i	−0.300335	−	0.649446i
$173$	2.00716	−	7.49083i	0.152602	−	0.569517i	−0.846697	−	0.532075i	$-0.821412\pi$
$173$	2.00716	−	7.49083i	0.152602	−	0.569517i	0.999299	−	0.0374420i	$-0.0119210\pi$
$174$	−3.77805	+	4.48801i	−0.286413	+	0.340235i
$175$		0			0
$176$	−5.32318	−	14.9194i	−0.401250	−	1.12460i
$177$	8.18789	+	2.19394i	0.615439	+	0.164906i
$178$	−2.32184	+	4.95862i	−0.174029	+	0.371665i
$179$	2.56434	−	4.44157i	0.191668	−	0.331979i	−0.754135	−	0.656719i	$-0.771944\pi$
$179$	2.56434	−	4.44157i	0.191668	−	0.331979i	0.945803	+	0.324741i	$0.105277\pi$
$180$	−9.05246	+	7.81049i	−0.674731	+	0.582160i
$181$	−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
$184$	0.0333491	−	7.00181i	0.00245853	−	0.516180i
$185$	5.92309	+	20.6977i	0.435474	+	1.52172i
$186$	−0.899249	−	2.48292i	−0.0659361	−	0.182057i
$187$	−0.616011	+	2.29899i	−0.0450472	+	0.168118i
$188$	−20.5018	−	14.4528i	−1.49525	−	1.05408i
$189$		0			0
$190$	−0.649518	−	6.30821i	−0.0471210	−	0.457646i
$191$	−13.5825	+	7.84185i	−0.982794	+	0.567416i	−0.903112	−	0.429404i	$-0.858724\pi$
$191$	−13.5825	+	7.84185i	−0.982794	+	0.567416i	−0.0796814	+	0.996820i	$0.525390\pi$
$192$	−3.20145	−	3.26304i	−0.231045	−	0.235489i
$193$	−7.49764	+	2.00899i	−0.539692	+	0.144610i	−0.518360	−	0.855162i	$-0.673457\pi$
$193$	−7.49764	+	2.00899i	−0.539692	+	0.144610i	−0.0213318	+	0.999772i	$0.506791\pi$
$194$	0.392173	−	2.20366i	0.0281564	−	0.158214i
$195$	−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	$0.181645\pi$
$198$	−12.2787	+	8.56863i	−0.872610	+	0.608946i
$199$	−7.04403	+	12.2006i	−0.499338	+	0.864879i	−1.00000		0.000763945i	$-0.999757\pi$
$199$	−7.04403	+	12.2006i	−0.499338	+	0.864879i	0.500661	+	0.865643i	$0.333090\pi$
$200$	−13.7609	−	3.26147i	−0.973044	−	0.230621i
$201$	1.08685	+	1.88247i	0.0766601	+	0.132779i
$202$	2.16206	+	25.1727i	0.152122	+	1.77114i
$203$		0			0
$204$	0.117121	+	0.676785i	0.00820011	+	0.0473845i
$205$	−3.85971	−	6.43135i	−0.269574	−	0.449185i
$206$	−14.9147	+	5.40172i	−1.03916	+	0.376356i
$207$	−6.39282	+	1.71295i	−0.444332	+	0.119058i
$208$	0.937263	+	11.5579i	0.0649875	+	0.801395i
$209$		−	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	$0.797727\pi$
$212$	0.543779	−	5.99608i	0.0373469	−	0.411813i
$213$	−2.68246	+	0.718762i	−0.183799	+	0.0492488i
$214$	3.78682	+	10.4558i	0.258862	+	0.714746i
$215$	−10.1787	−	2.54357i	−0.694182	−	0.173470i
$216$	−4.62250	+	7.91907i	−0.314522	+	0.538824i
$217$		0			0
$218$	0.569667	−	0.0489282i	0.0385827	−	0.00331383i
$219$	−2.79500	−	4.84108i	−0.188868	−	0.327130i
$220$	−16.7240	−	5.82794i	−1.12753	−	0.392920i
$221$	0.871146	−	1.50887i	0.0585996	−	0.101498i
$222$	4.45244	+	6.38027i	0.298828	+	0.428216i
$223$	−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
$226$	7.03382	+	1.25177i	0.467882	+	0.0832664i
$227$	−11.6773	+	3.12892i	−0.775049	+	0.207674i	−0.624601	−	0.780944i	$-0.714738\pi$
$227$	−11.6773	+	3.12892i	−0.775049	+	0.207674i	−0.150448	+	0.988618i	$0.548072\pi$
$228$	−0.961953	−	2.08013i	−0.0637069	−	0.137760i
$229$	−1.89994	+	1.09693i	−0.125552	+	0.0724873i	−0.561460	−	0.827504i	$-0.689760\pi$
$229$	−1.89994	+	1.09693i	−0.125552	+	0.0724873i	0.435909	+	0.899991i	$0.356427\pi$
$230$	−6.07332	−	4.93941i	−0.400463	−	0.325695i
$231$		0			0
$232$	19.8588	−	5.21990i	1.30379	−	0.342703i
$233$	0.291712	−	1.08868i	0.0191107	−	0.0713220i	−0.955712	−	0.294304i	$-0.904912\pi$
$233$	0.291712	−	1.08868i	0.0191107	−	0.0713220i	0.974823	+	0.222982i	$0.0715790\pi$
$234$	10.3055	−	3.73239i	0.673694	−	0.243994i
$235$	−26.9625	+	7.71591i	−1.75884	+	0.503330i
$236$	−18.9989	−	22.7885i	−1.23672	−	1.48341i
$237$	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	$0.278059\pi$
$240$	−5.08642	+	0.499246i	−0.328327	+	0.0322262i
$241$	−4.32744	+	7.49535i	−0.278755	+	0.482818i	−0.971076	−	0.238772i	$-0.923255\pi$
$241$	−4.32744	+	7.49535i	−0.278755	+	0.482818i	0.692321	+	0.721590i	$0.256588\pi$
$242$	−5.99765	−	2.80835i	−0.385544	−	0.180528i
$243$	12.7987	+	3.42939i	0.821035	+	0.219996i
$244$	8.34302	−	1.44380i	0.534107	−	0.0924299i
$245$		0			0
$246$	−2.07373	−	1.74568i	−0.132216	−	0.111301i
$247$	−1.50464	+	5.61541i	−0.0957382	+	0.357300i
$248$	−2.43473	+	8.91646i	−0.154606	+	0.566196i
$249$	−3.82663	−	2.20931i	−0.242503	−	0.140009i
$250$	−12.4904	+	9.69483i	−0.789963	+	0.613155i
$251$		−	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
$254$	−9.45447	−	1.68256i	−0.593226	−	0.105573i
$255$	0.671437	+	0.372649i	0.0420470	+	0.0233362i
$256$	2.57802	+	15.7909i	0.161126	+	0.986934i
$257$	17.1857	+	4.60489i	1.07201	+	0.287245i	0.751320	−	0.659938i	$-0.229418\pi$
$257$	17.1857	+	4.60489i	1.07201	+	0.287245i	0.320693	+	0.947183i	$0.396084\pi$
$258$	−3.77771	+	0.324464i	−0.235190	+	0.0202003i
$259$		0			0
$260$	10.7211	+	7.28944i	0.664897	+	0.452072i
$261$	−9.70429	−	16.8083i	−0.600680	−	1.04041i
$262$	9.11057	−	19.4570i	0.562853	−	1.20206i
$263$	4.97016	+	18.5489i	0.306473	+	1.14377i	0.931670	+	0.363306i	$0.118352\pi$
$263$	4.97016	+	18.5489i	0.306473	+	1.14377i	−0.625197	+	0.780467i	$0.714981\pi$
$264$	−6.40032	−	0.0304843i	−0.393913	−	0.00187618i
$265$	−4.83964	−	4.67854i	−0.297297	−	0.287401i
$266$		0			0
$267$	1.56432	+	1.56432i	0.0957350	+	0.0957350i
$268$	0.687156	−	7.57705i	0.0419747	−	0.462842i
$269$	−12.4257	−	7.17398i	−0.757608	−	0.437405i	0.0708284	−	0.997489i	$-0.477436\pi$
$269$	−12.4257	−	7.17398i	−0.757608	−	0.437405i	−0.828436	+	0.560083i	$0.810769\pi$
$270$	3.65363	+	9.57862i	0.222353	+	0.582936i
$271$	−17.9057	+	10.3379i	−1.08770	+	0.627981i	−0.932962	−	0.359975i	$-0.882785\pi$
$271$	−17.9057	+	10.3379i	−1.08770	+	0.627981i	−0.154733	+	0.987956i	$0.549452\pi$
$272$	1.02980	−	2.17229i	0.0624409	−	0.131715i
$273$		0			0
$274$	−4.95263	−	4.16917i	−0.299199	−	0.251869i
$275$	−16.8031	+	10.4750i	−1.01327	+	0.631668i
$276$	−2.65540	−	0.976048i	−0.159837	−	0.0587512i
$277$	1.26140	+	4.70760i	0.0757901	+	0.282853i	0.993411	−	0.114604i	$-0.0365598\pi$
$277$	1.26140	+	4.70760i	0.0757901	+	0.282853i	−0.917621	+	0.397456i	$0.869893\pi$
$278$	−12.8961	+	8.99945i	−0.773455	+	0.539751i
$279$	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	$0.593547\pi$
$282$	−8.31147	+	5.80011i	−0.494941	+	0.345391i
$283$	0.366980	+	1.36959i	0.0218147	+	0.0814136i	0.975975	−	0.217882i	$-0.0699149\pi$
$283$	0.366980	+	1.36959i	0.0218147	+	0.0814136i	−0.954160	+	0.299296i	$0.903248\pi$
$284$	9.12328	+	3.35345i	0.541367	+	0.198991i
$285$	−2.48586	−	0.621194i	−0.147250	−	0.0367963i
$286$	12.4206	+	10.4558i	0.734447	+	0.618264i
$287$		0			0
$288$	13.7569	−	6.28248i	0.810632	−	0.370199i
$289$	14.4096	−	8.31940i	0.847624	−	0.489376i
$290$	9.38184	−	20.9525i	0.550921	−	1.23037i
$291$	−0.783214	−	0.452189i	−0.0459128	−	0.0265078i
$292$	−1.76713	+	19.4856i	−0.103414	+	1.14031i
$293$	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
$296$	0.129701	−	27.2313i	0.00753870	−	1.58279i
$297$	3.32283	+	12.4010i	0.192810	+	0.719578i
$298$	2.93729	−	6.27302i	0.170153	−	0.363386i
$299$	3.58824	+	6.21502i	0.207513	+	0.359424i
$300$	−3.13240	+	4.77904i	−0.180849	+	0.275918i
$301$		0			0
$302$	20.7657	−	1.78355i	1.19493	−	0.102632i
$303$	9.86060	+	2.64214i	0.566477	+	0.151787i
$304$	−1.44306	+	7.89064i	−0.0827651	+	0.452559i
$305$	4.59380	−	8.27709i	0.263040	−	0.473945i
$306$	−2.23719	−	0.398140i	−0.127891	−	0.0227601i
$307$	−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
$310$	6.05638	+	8.37312i	0.343979	+	0.475561i
$311$	21.9956	+	12.6992i	1.24726	+	0.720104i	0.970561	−	0.240854i	$-0.0774275\pi$
$311$	21.9956	+	12.6992i	1.24726	+	0.720104i	0.276695	+	0.960958i	$0.410761\pi$
$312$	4.51980	+	1.23418i	0.255884	+	0.0698717i
$313$	6.71544	−	25.0624i	0.379579	−	1.41661i	−0.466958	−	0.884280i	$-0.654650\pi$
$313$	6.71544	−	25.0624i	0.379579	−	1.41661i	0.846537	−	0.532330i	$-0.178683\pi$
$314$	12.0270	+	10.1245i	0.678724	+	0.571356i
$315$		0			0
$316$	−13.6262	+	2.35809i	−0.766536	+	0.132653i
$317$	−0.207012	−	0.0554686i	−0.0116269	−	0.00311543i	0.253001	−	0.967466i	$-0.418582\pi$
$317$	−0.207012	−	0.0554686i	−0.0116269	−	0.00311543i	−0.264628	+	0.964351i	$0.585249\pi$
$318$	−2.20310	−	1.03158i	−0.123544	−	0.0578483i
$319$	14.3747	−	24.8977i	0.804828	−	1.39400i
$320$	15.5577	+	8.82942i	0.869701	+	0.493580i
$321$	4.49321			0.250786
$322$		0			0
$323$	0.852238	−	0.852238i	0.0474198	−	0.0474198i
$324$	−7.89939	−	9.47507i	−0.438855	−	0.526393i
$325$	13.8659	−	4.22317i	0.769142	−	0.234259i
$326$	−24.4164	+	8.84296i	−1.35230	+	0.489766i
$327$	0.0597926	−	0.223149i	0.00330654	−	0.0123402i
$328$	2.41191	+	9.17595i	0.133175	+	0.506657i
$329$		0			0
$330$	−4.51509	+	5.55160i	−0.248548	+	0.305606i
$331$	1.84066	−	1.06270i	0.101172	−	0.0584115i	−0.448560	−	0.893753i	$-0.648063\pi$
$331$	1.84066	−	1.06270i	0.101172	−	0.0584115i	0.549732	+	0.835341i	$0.314730\pi$
$332$	6.49151	+	14.0373i	0.356268	+	0.770396i
$333$	−24.8628	+	6.66198i	−1.36248	+	0.365074i
$334$	−25.8406	−	4.59871i	−1.41393	−	0.251630i
$335$	−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	$0.917414\pi$
$338$	3.71968	+	5.33025i	0.202324	+	0.289927i
$339$	1.44333	−	2.49992i	0.0783909	−	0.135777i
$340$	−1.16929	−	2.42011i	−0.0634136	−	0.131249i
$341$	6.47062	+	11.2074i	0.350404	+	0.606917i
$342$	7.55429	−	0.648831i	0.408489	−	0.0350848i
$343$		0			0
$344$	11.4613	+	6.69020i	0.617955	+	0.360711i
$345$	−2.71211	+	1.62765i	−0.146015	+	0.0876296i
$346$	3.73468	+	10.3119i	0.200778	+	0.554369i
$347$	17.6420	−	4.72717i	0.947074	−	0.253768i	0.247954	−	0.968772i	$-0.420242\pi$
$347$	17.6420	−	4.72717i	0.947074	−	0.253768i	0.699120	+	0.715004i	$0.253575\pi$
$348$	0.749326	−	8.26258i	0.0401681	−	0.442921i
$349$			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
$352$	18.2481	+	12.9946i	0.972628	+	0.692612i
$353$	16.3918	−	4.39216i	0.872446	−	0.233771i	0.205301	−	0.978699i	$-0.434183\pi$
$353$	16.3918	−	4.39216i	0.872446	−	0.233771i	0.667145	+	0.744928i	$0.267516\pi$
$354$	−11.2714	+	4.08221i	−0.599070	+	0.216967i
$355$	9.31813	−	5.59218i	0.494555	−	0.296802i
$356$	−1.32038	−	7.62983i	−0.0699799	−	0.404380i
$357$		0			0
$358$	0.620673	+	7.22645i	0.0328036	+	0.381930i
$359$	4.43990	+	7.69014i	0.234329	+	0.405870i	0.959078	−	0.283144i	$-0.0913773\pi$
$359$	4.43990	+	7.69014i	0.234329	+	0.405870i	−0.724748	+	0.689014i	$0.758044\pi$
$360$	4.17734	−	16.3845i	0.220165	−	0.863538i
$361$	7.48923	−	12.9717i	0.394170	−	0.682723i
$362$	21.0254	−	14.6725i	1.10507	−	0.771168i
$363$	−1.89211	+	1.89211i	−0.0993101	+	0.0993101i
$364$		0			0
$365$	15.7275	+	15.2040i	0.823214	+	0.795812i
$366$	0.599415	−	3.36817i	0.0313319	−	0.176057i
$367$	−20.9986	+	5.62655i	−1.09612	+	0.293704i	−0.761182	−	0.648538i	$-0.775381\pi$
$367$	−20.9986	+	5.62655i	−1.09612	+	0.293704i	−0.334934	+	0.942241i	$0.608714\pi$
$368$	5.62802	+	8.14728i	0.293381	+	0.424707i
$369$	7.76645	−	4.48396i	0.404305	−	0.233426i
$370$	−23.6203	−	19.2103i	−1.22796	−	0.998695i
$371$		0			0
$372$	3.05237	+	2.15177i	0.158258	+	0.111564i
$373$	−0.126511	+	0.472145i	−0.00655048	+	0.0244467i	−0.969124	−	0.246575i	$-0.920695\pi$
$373$	−0.126511	+	0.472145i	−0.00655048	+	0.0244467i	0.962573	+	0.271022i	$0.0873615\pi$
$374$	−1.14620	−	3.16478i	−0.0592686	−	0.163647i
$375$	1.96452	+	6.07903i	0.101447	+	0.313920i
$376$	35.4738	+	0.168959i	1.82942	+	0.00871339i
$377$	−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	$0.753484\pi$
$380$	5.85863	+	6.79023i	0.300541	+	0.348331i
$381$	−1.94004	+	3.36026i	−0.0993915	+	0.172151i
$382$	9.40562	−	20.0871i	0.481233	−	1.02774i
$383$	4.99551	+	1.33854i	0.255259	+	0.0683964i	0.384179	−	0.923259i	$-0.374484\pi$
$383$	4.99551	+	1.33854i	0.255259	+	0.0683964i	−0.128920	+	0.991655i	$0.541151\pi$
$384$	6.35370	+	1.19328i	0.324236	+	0.0608944i
$385$		0			0
$386$	7.06942	−	8.39789i	0.359824	−	0.427441i
$387$	3.24665	−	12.1167i	0.165037	−	0.615925i
$388$	1.32865	+	2.87307i	0.0674518	+	0.145858i
$389$	10.5873	+	6.11259i	0.536798	+	0.309921i	0.743780	−	0.668424i	$-0.233031\pi$
$389$	10.5873	+	6.11259i	0.536798	+	0.309921i	−0.206982	+	0.978345i	$0.566364\pi$
$390$	4.24438	−	3.07002i	0.214923	−	0.155456i
$391$		−	1.48782i		−	0.0752422i
$392$		0			0
$393$	−6.13820	−	6.13820i	−0.309631	−	0.309631i
$394$	−1.48223	+	8.32880i	−0.0746737	+	0.419599i
$395$	−7.50282	+	13.5186i	−0.377508	+	0.680192i
$396$	7.30538	−	19.8748i	0.367109	−	0.998746i
$397$	−16.8913	−	4.52602i	−0.847751	−	0.227154i	−0.191308	−	0.981530i	$-0.561273\pi$
$397$	−16.8913	−	4.52602i	−0.847751	−	0.227154i	−0.656443	+	0.754376i	$0.727940\pi$
$398$	−1.70494	−	19.8505i	−0.0854608	−	0.995013i
$399$		0			0
$400$	18.5987	−	7.35452i	0.929934	−	0.367726i
$401$	15.5612	+	26.9528i	0.777089	+	1.34596i	0.933613	+	0.358284i	$0.116638\pi$
$401$	15.5612	+	26.9528i	0.777089	+	1.34596i	−0.156524	+	0.987674i	$0.550029\pi$
$402$	−2.78398	−	1.30358i	−0.138852	−	0.0650165i
$403$	−2.45189	−	9.15057i	−0.122137	−	0.455823i
$404$	−22.8802	−	27.4440i	−1.13833	−	1.36539i
$405$	−13.7901	+	0.233399i	−0.685236	+	0.0115977i
$406$		0			0
$407$	−26.9604	−	26.9604i	−1.33638	−	1.33638i
$408$	−0.683566	−	0.690108i	−0.0338415	−	0.0341655i
$409$	−4.43457	−	2.56030i	−0.219275	−	0.126599i	0.386339	−	0.922357i	$-0.373739\pi$
$409$	−4.43457	−	2.56030i	−0.219275	−	0.126599i	−0.605615	+	0.795758i	$0.707073\pi$
$410$	9.68129	+	4.33497i	0.478125	+	0.214089i
$411$	−2.26530	+	1.30787i	−0.111739	+	0.0645126i
$412$	12.9255	−	18.3354i	0.636795	−	0.903319i
$413$		0			0
$414$	6.02770	−	7.16041i	0.296245	−	0.351915i
$415$	16.7752	+	4.19198i	0.823464	+	0.205776i
$416$	−10.4410	−	12.6456i	−0.511912	−	0.620002i
$417$	1.64453	+	6.13746i	0.0805329	+	0.300553i
$418$	6.42730	+	9.21023i	0.314370	+	0.450487i
$419$	−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	$0.132535\pi$
$422$	−13.9555	−	19.9981i	−0.679345	−	0.973491i
$423$	−8.67844	−	32.3884i	−0.421960	−	1.57478i
$424$	4.22210	+	7.39400i	0.205043	+	0.359084i
$425$	−2.92730	−	0.679088i	−0.141995	−	0.0329406i
$426$	2.52925	−	3.00454i	0.122543	−	0.145571i
$427$		0			0
$428$	−12.8538	−	9.06132i	−0.621314	−	0.437995i
$429$	5.68112	−	3.28000i	0.274287	−	0.158360i
$430$	13.8632	−	5.28794i	0.668545	−	0.255007i
$431$	21.0173	+	12.1344i	1.01237	+	0.584492i	0.911885	−	0.410447i	$-0.134627\pi$
$431$	21.0173	+	12.1344i	1.01237	+	0.584492i	0.100485	+	0.994939i	$0.467961\pi$
$432$	−1.04814	−	12.9252i	−0.0504287	−	0.621862i
$433$	−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
$436$	−0.621068	+	0.517787i	−0.0297438	+	0.0247975i
$437$	1.28488	+	4.79524i	0.0614641	+	0.229387i
$438$	7.15946	+	3.35236i	0.342092	+	0.160182i
$439$	7.62951	+	13.2147i	0.364137	+	0.630703i	0.988637	−	0.150321i	$-0.0480307\pi$
$439$	7.62951	+	13.2147i	0.364137	+	0.630703i	−0.624500	+	0.781024i	$0.714697\pi$
$440$	24.1122	−	6.77616i	1.14950	−	0.323041i
$441$		0			0
$442$	0.210852	+	2.45494i	0.0100292	+	0.116769i
$443$	−11.5487	−	3.09446i	−0.548695	−	0.147022i	−0.0261872	−	0.999657i	$-0.508337\pi$
$443$	−11.5487	−	3.09446i	−0.548695	−	0.147022i	−0.522507	+	0.852635i	$0.675003\pi$
$444$	−10.3274	−	3.79603i	−0.490115	−	0.180152i
$445$	−7.56953	−	4.20111i	−0.358830	−	0.199152i
$446$	4.04235	−	22.7144i	0.191411	−	1.07556i
$447$	−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	$0.895105\pi$
$450$	−11.3370	−	15.1278i	−0.534429	−	0.713132i
$451$	11.5042	+	6.64196i	0.541712	+	0.312758i
$452$	−9.17049	+	4.24087i	−0.431344	+	0.199474i
$453$	2.17958	−	8.13430i	0.102406	−	0.382183i
$454$	11.0104	−	13.0794i	0.516741	−	0.613847i
$455$		0			0
$456$	2.79911	+	1.63389i	0.131080	+	0.0765140i
$457$	13.4754	+	3.61073i	0.630354	+	0.168903i	0.559830	−	0.828607i	$-0.310866\pi$
$457$	13.4754	+	3.61073i	0.630354	+	0.168903i	0.0705235	+	0.997510i	$0.477533\pi$
$458$	1.31567	−	2.80982i	0.0614774	−	0.131294i
$459$	−0.974202	+	1.68737i	−0.0454718	+	0.0787595i
$460$	11.0411	+	0.813184i	0.514792	+	0.0379149i
$461$	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	$0.292362\pi$
$464$	−18.8065	+	22.1259i	−0.873071	+	1.02717i
$465$	4.01425	−	1.14877i	0.186157	−	0.0532728i
$466$	0.542782	+	1.49868i	0.0251439	+	0.0694250i
$467$	3.17857	−	11.8626i	0.147087	−	0.548935i	−0.852567	−	0.522618i	$-0.824955\pi$
$467$	3.17857	−	11.8626i	0.147087	−	0.548935i	0.999654	−	0.0263172i	$-0.00837800\pi$
$468$	−8.93108	+	12.6691i	−0.412839	+	0.585629i
$469$		0			0
$470$	25.0249	−	30.7697i	1.15431	−	1.41930i
$471$	5.50108	−	3.17605i	0.253477	−	0.146345i
$472$	40.4770	+	11.0527i	1.86310	+	0.508740i
$473$	17.9481	−	4.80917i	0.825253	−	0.221126i
$474$	−0.978994	+	5.50107i	−0.0449667	+	0.252672i
$475$	10.0211	−	0.339315i	0.459802	−	0.0155688i
$476$		0			0
$477$	5.69088	−	5.69088i	0.260568	−	0.260568i
$478$	−23.0250	+	16.0679i	−1.05314	+	0.734928i
$479$	−12.0422	+	20.8577i	−0.550223	+	0.953014i	0.448035	+	0.894016i	$0.352124\pi$
$479$	−12.0422	+	20.8577i	−0.550223	+	0.953014i	−0.998258	+	0.0589981i	$0.981209\pi$
$480$	5.49488	−	4.69553i	0.250806	−	0.214321i
$481$	13.9553	+	24.1713i	0.636308	+	1.10212i
$482$	−1.04741	−	12.1950i	−0.0477084	−	0.555465i
$483$		0			0
$484$	9.22859	−	1.59705i	0.419481	−	0.0725932i
$485$	3.43346	+	0.857991i	0.155905	+	0.0389594i
$486$	−17.6186	+	6.38100i	−0.799198	+	0.289448i
$487$	3.31498	−	0.888247i	0.150216	−	0.0402503i	−0.182927	−	0.983126i	$-0.558557\pi$
$487$	3.31498	−	0.888247i	0.150216	−	0.0402503i	0.333144	+	0.942876i	$0.391891\pi$
$488$	−8.50726	+	8.42661i	−0.385106	+	0.381455i
$489$			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	$0.974520\pi$
$492$	3.81781	+	0.346234i	0.172120	+	0.0156094i
$493$	4.21443	−	1.12925i	0.189808	−	0.0508590i
$494$	−2.79966	−	7.73016i	−0.125963	−	0.347796i
$495$	−12.1824	−	20.2993i	−0.547558	−	0.912383i
$496$	−4.39260	−	12.3113i	−0.197234	−	0.552792i
$497$		0			0
$498$	6.22594	−	0.534740i	0.278991	−	0.0239623i
$499$	15.1647	+	26.2660i	0.678864	+	1.17583i	0.975323	+	0.220781i	$0.0708606\pi$
$499$	15.1647	+	26.2660i	0.678864	+	1.17583i	−0.296460	+	0.955045i	$0.595806\pi$
$500$	6.63944	−	21.3522i	0.296925	−	0.954901i
$501$	−5.30246	+	9.18412i	−0.236896	+	0.410316i
$502$	1.25949	+	1.80482i	0.0562136	+	0.0805532i
$503$	−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
$506$	13.6498	+	2.42919i	0.606809	+	0.107990i
$507$	2.53676	−	0.679722i	0.112661	−	0.0301875i
$508$	12.3265	−	5.70035i	0.546899	−	0.252912i
$509$	8.23953	−	4.75709i	0.365211	−	0.210854i	−0.306153	−	0.951982i	$-0.599042\pi$
$509$	8.23953	−	4.75709i	0.365211	−	0.210854i	0.671364	+	0.741128i	$0.265709\pi$
$510$	−1.08029	+	0.111230i	−0.0478359	+	0.00492537i
$511$		0			0
$512$	−15.7698	−	16.2270i	−0.696931	−	0.717138i
$513$	1.68264	−	6.27970i	0.0742904	−	0.277256i
$514$	−23.6578	+	8.56822i	−1.04350	+	0.377928i
$515$	−6.90056	−	24.1133i	−0.304075	−	1.06256i
$516$	4.11858	−	3.43367i	0.181310	−	0.151159i
$517$	35.1209	−	35.1209i	1.54461	−	1.54461i
$518$		0			0
$519$	4.43134			0.194514
$520$	−18.3332	+	0.222954i	−0.803966	+	0.00977717i
$521$	−2.30406	+	3.99075i	−0.100943	+	0.174838i	−0.912073	−	0.410027i	$-0.865519\pi$
$521$	−2.30406	+	3.99075i	−0.100943	+	0.174838i	0.811131	+	0.584865i	$0.198853\pi$
$522$	24.8578	+	11.6395i	1.08800	+	0.509445i
$523$	33.1997	+	8.89583i	1.45172	+	0.388987i	0.896622	−	0.442797i	$-0.146014\pi$
$523$	33.1997	+	8.89583i	1.45172	+	0.388987i	0.555099	+	0.831784i	$0.312680\pi$
$524$	5.18099	+	29.9384i	0.226333	+	1.30787i
$525$		0			0
$526$	−20.7761	−	17.4895i	−0.905880	−	0.762578i
$527$	−0.508322	+	1.89708i	−0.0221429	+	0.0826383i
$528$	7.44740	−	5.14455i	0.324106	−	0.223888i
$529$	−14.6113	−	8.43585i	−0.635275	−	0.366776i
$530$	9.39917	+	1.50909i	0.408274	+	0.0655507i
$531$		−	39.6604i		−	1.72112i
$532$		0			0
$533$	−6.87606	−	6.87606i	−0.297835	−	0.297835i
$534$	−3.08025	−	0.548175i	−0.133295	−	0.0237218i
$535$	−16.9044	+	4.83757i	−0.730841	+	0.209146i
$536$	5.33533	+	9.34355i	0.230451	+	0.403580i
$537$	2.83073	+	0.758493i	0.122155	+	0.0327314i
$538$	20.2166	−	1.73639i	0.871601	−	0.0748610i
$539$		0			0
$540$	−11.9894	−	8.15177i	−0.515943	−	0.350796i
$541$	7.78637	+	13.4864i	0.334762	+	0.579825i	0.983439	−	0.181239i	$-0.0580107\pi$
$541$	7.78637	+	13.4864i	0.334762	+	0.579825i	−0.648677	+	0.761064i	$0.724677\pi$
$542$	12.3994	−	26.4807i	0.532599	−	1.13744i
$543$	−2.68120	−	10.0064i	−0.115061	−	0.429414i
$544$	0.563774	+	3.35274i	0.0241716	+	0.143748i
$545$	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	$0.809039\pi$
$548$	9.11797	+	0.826900i	0.389500	+	0.0353234i
$549$	9.80190	+	5.65913i	0.418335	+	0.241526i
$550$	11.0097	−	25.7474i	0.469454	−	1.09787i
$551$	−12.6079	+	7.27916i	−0.537114	+	0.310103i
$552$	3.86952	−	1.01711i	0.164698	−	0.0432909i
$553$		0			0
$554$	−5.27285	−	4.43873i	−0.224022	−	0.188584i
$555$	−10.5479	+	6.33022i	−0.447734	+	0.268703i
$556$	7.67269	−	20.8741i	0.325395	−	0.885258i
$557$	−3.37568	−	12.5982i	−0.143032	−	0.533804i	−0.999835	−	0.0181595i	$-0.994219\pi$
$557$	−3.37568	−	12.5982i	−0.143032	−	0.533804i	0.856803	−	0.515644i	$-0.172447\pi$
$558$	−10.1322	+	7.07068i	−0.428930	+	0.299326i
$559$	−13.6020			−0.575303
$560$		0			0
$561$	−1.36001			−0.0574196
$562$	11.2630	−	7.85981i	0.475100	−	0.331546i
$563$	5.39902	+	20.1494i	0.227542	+	0.849197i	0.981370	+	0.192126i	$0.0615383\pi$
$563$	5.39902	+	20.1494i	0.227542	+	0.849197i	−0.753829	+	0.657071i	$0.771795\pi$
$564$	4.94502	−	13.4533i	0.208223	−	0.566485i
$565$	−2.73860	+	10.9592i	−0.115214	+	0.461056i
$566$	−1.53404	−	1.29137i	−0.0644804	−	0.0542801i
$567$		0			0
$568$	−13.2947	+	3.49451i	−0.557832	+	0.146627i
$569$	−6.92763	+	3.99967i	−0.290422	+	0.167675i	−0.638132	−	0.769927i	$-0.720293\pi$
$569$	−6.92763	+	3.99967i	−0.290422	+	0.167675i	0.347710	+	0.937602i	$0.386959\pi$
$570$	3.38570	−	1.29143i	0.141811	−	0.0540921i
$571$	28.4622	+	16.4326i	1.19110	+	0.687684i	0.958557	−	0.284901i	$-0.0919607\pi$
$571$	28.4622	+	16.4326i	1.19110	+	0.687684i	0.232547	+	0.972585i	$0.425294\pi$
$572$	−22.8668	−	2.07377i	−0.956109	−	0.0867087i
$573$	−6.33698	−	6.33698i	−0.264731	−	0.264731i
$574$		0			0
$575$	8.45116	−	9.04353i	0.352438	−	0.377141i
$576$	−10.8699	+	18.4198i	−0.452913	+	0.767490i
$577$	10.0357	+	37.4537i	0.417791	+	1.55922i	0.779178	+	0.626802i	$0.215637\pi$
$577$	10.0357	+	37.4537i	0.417791	+	1.55922i	−0.361387	+	0.932416i	$0.617697\pi$
$578$	−9.97839	+	21.3103i	−0.415046	+	0.886393i
$579$	−2.21768	−	3.84114i	−0.0921638	−	0.159632i
$580$	6.07671	+	31.8924i	0.252321	+	1.32426i
$581$		0			0
$582$	1.27429	−	0.109448i	0.0528211	−	0.00453675i
$583$	11.5152	+	3.08550i	0.476912	+	0.127788i
$584$	−13.7207	−	24.0285i	−0.567765	−	0.994304i
$585$	4.76804	+	16.6614i	0.197134	+	0.688865i
$586$	−11.8665	−	2.11182i	−0.490201	−	0.0872383i
$587$	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
$590$	38.0105	−	27.4934i	1.56487	−	1.13189i
$591$	2.96018	+	1.70906i	0.121765	+	0.0703013i
$592$	21.8884	+	31.6863i	0.899608	+	1.30230i
$593$	−11.1027	+	41.4359i	−0.455934	+	1.70157i	0.229392	+	0.973334i	$0.426326\pi$
$593$	−11.1027	+	41.4359i	−0.455934	+	1.70157i	−0.685327	+	0.728236i	$0.740341\pi$
$594$	−13.8900	−	11.6927i	−0.569913	−	0.479757i
$595$		0			0
$596$	1.67038	+	9.65229i	0.0684212	+	0.395373i
$597$	−7.77578	−	2.08351i	−0.318242	−	0.0852726i
$598$	−9.19137	−	4.30378i	−0.375863	−	0.175995i
$599$	−5.01596	+	8.68789i	−0.204946	+	0.354978i	−0.950116	−	0.311898i	$-0.899035\pi$
$599$	−5.01596	+	8.68789i	−0.204946	+	0.354978i	0.745169	+	0.666875i	$0.232369\pi$
$600$	−0.234994	−	8.07756i	−0.00959361	−	0.329765i
$601$	−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
$604$	−22.6394	+	18.8745i	−0.921184	+	0.767994i
$605$	5.08141	−	9.15566i	0.206589	−	0.372230i
$606$	−13.5741	+	4.91618i	−0.551410	+	0.199706i
$607$	6.47873	−	24.1790i	0.262964	−	0.981394i	−0.700521	−	0.713632i	$-0.747049\pi$
$607$	6.47873	−	24.1790i	0.262964	−	0.981394i	0.963485	−	0.267762i	$-0.0862842\pi$
$608$	−4.71247	−	10.3190i	−0.191116	−	0.418491i
$609$		0			0
$610$	1.37118	+	13.3171i	0.0555177	+	0.539196i
$611$	−31.4876	+	18.1794i	−1.27385	+	0.735458i
$612$	2.91678	−	1.34886i	0.117904	−	0.0545244i
$613$	9.05103	−	2.42522i	0.365568	−	0.0979535i	−0.0713590	−	0.997451i	$-0.522734\pi$
$613$	9.05103	−	2.42522i	0.365568	−	0.0979535i	0.436927	+	0.899497i	$0.356067\pi$
$614$	21.6656	+	3.85571i	0.874353	+	0.155604i
$615$	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	$0.407606\pi$
$618$	−5.18720	−	7.43318i	−0.208660	−	0.299006i
$619$	14.8926	−	25.7947i	0.598582	−	1.03677i	−0.394448	−	0.918918i	$-0.629064\pi$
$619$	14.8926	−	25.7947i	0.598582	−	1.03677i	0.993031	−	0.117857i	$-0.0376023\pi$
$620$	−13.8004	−	4.80912i	−0.554236	−	0.193139i
$621$	−4.01273	−	6.95024i	−0.161025	−	0.278904i
$622$	−35.7869	+	3.07371i	−1.43492	+	0.123244i
$623$		0			0
$624$	−6.24065	+	2.22663i	−0.249826	+	0.0891367i
$625$	−13.9359	−	20.7555i	−0.557435	−	0.830221i
$626$	12.4953	+	34.5008i	0.499412	+	1.37893i
$627$	4.38331	−	1.17450i	0.175052	−	0.0469051i
$628$	−22.1422	−	2.00805i	−0.883569	−	0.0801301i
$629$		−	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	$0.940744\pi$
$632$	13.8945	−	13.7627i	0.552693	−	0.547453i
$633$	−9.51742	+	2.55019i	−0.378284	+	0.101361i
$634$	0.284972	−	0.103209i	0.0113177	−	0.00409896i
$635$	3.68108	−	14.7307i	0.146079	−	0.584571i
$636$	3.38991	−	0.586639i	0.134418	−	0.0232618i
$637$		0			0
$638$	3.47925	+	40.5086i	0.137745	+	1.60375i
$639$	6.49663	+	11.2525i	0.257003	+	0.445142i
$640$	−25.1887	+	2.35127i	−0.995672	+	0.0929422i
$641$	1.37174	−	2.37592i	0.0541805	−	0.0938434i	−0.837663	−	0.546187i	$-0.816079\pi$
$641$	1.37174	−	2.37592i	0.0541805	−	0.0938434i	0.891844	+	0.452344i	$0.149412\pi$
$642$	−5.21096	+	3.63644i	−0.205660	+	0.143519i
$643$	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
$646$	−0.298644	+	1.67811i	−0.0117500	+	0.0660243i
$647$	20.8568	−	5.58856i	0.819964	−	0.219709i	0.175633	−	0.984456i	$-0.443803\pi$
$647$	20.8568	−	5.58856i	0.819964	−	0.219709i	0.644331	+	0.764747i	$0.277136\pi$
$648$	16.8296	+	4.59551i	0.661130	+	0.180528i
$649$	50.8771	−	29.3739i	1.99710	−	1.15303i
$650$	−12.6630	+	16.1197i	−0.496683	+	0.632268i
$651$		0			0
$652$	21.1599	−	30.0162i	0.828686	−	1.17552i
$653$	7.54635	−	28.1634i	0.295311	−	1.10212i	−0.645658	−	0.763627i	$-0.723417\pi$
$653$	7.54635	−	28.1634i	0.295311	−	1.10212i	0.940970	−	0.338491i	$-0.109916\pi$
$654$	0.111255	+	0.307187i	0.00435041	+	0.0120119i
$655$	29.7018	+	16.4846i	1.16055	+	0.644106i
$656$	−10.2235	−	8.68974i	−0.399159	−	0.339277i
$657$	−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	$0.448404\pi$
$660$	0.743328	−	10.0926i	0.0289340	−	0.392853i
$661$	10.4781	−	18.1487i	0.407553	−	0.705902i	−0.587062	−	0.809542i	$-0.699716\pi$
$661$	10.4781	−	18.1487i	0.407553	−	0.705902i	0.994615	+	0.103640i	$0.0330490\pi$
$662$	−1.27462	+	2.72214i	−0.0495396	+	0.105799i
$663$	0.961643	+	0.257671i	0.0373471	+	0.0100071i
$664$	−18.8891	−	11.0259i	−0.733040	−	0.427889i
$665$		0			0
$666$	23.4428	−	27.8482i	0.908391	−	1.07909i
$667$	−4.65138	+	17.3592i	−0.180102	+	0.672150i
$668$	33.6902	−	15.5800i	1.30351	−	0.602807i
$669$	−8.07303	−	4.66096i	−0.312121	−	0.180203i
$670$	11.8774	+	1.90699i	0.458865	+	0.0736733i
$671$			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	$0.459104\pi$
$674$	7.86798	−	44.2110i	0.303063	−	1.70294i
$675$	−15.5062	+	4.72277i	−0.596835	+	0.181779i
$676$	−8.62775	−	3.17130i	−0.331836	−	0.121973i
$677$	−37.8274	−	10.1358i	−1.45383	−	0.389551i	−0.556473	−	0.830866i	$-0.687846\pi$
$677$	−37.8274	−	10.1358i	−1.45383	−	0.389551i	−0.897353	+	0.441314i	$0.854512\pi$
$678$	0.349344	+	4.06738i	0.0134165	+	0.156207i
$679$		0			0
$680$	3.31472	+	1.86038i	0.127114	+	0.0713424i
$681$	−3.45396	−	5.98243i	−0.132356	−	0.229247i
$682$	−16.5747	−	7.76095i	−0.634676	−	0.297182i
$683$	−3.07415	−	11.4729i	−0.117629	−	0.438998i	0.881841	−	0.471547i	$-0.156304\pi$
$683$	−3.07415	−	11.4729i	−0.117629	−	0.438998i	−0.999470	+	0.0325489i	$0.989638\pi$
$684$	−8.23591	+	6.86631i	−0.314908	+	0.262540i
$685$	7.11444	−	7.35942i	0.271829	−	0.281189i
$686$		0			0
$687$	−0.886428	−	0.886428i	−0.0338193	−	0.0338193i
$688$	−18.7067	+	1.51698i	−0.713187	+	0.0578345i
$689$	−7.55767	−	4.36343i	−0.287924	−	0.166233i
$690$	1.82807	−	4.08262i	0.0695933	−	0.155423i
$691$	6.84816	−	3.95379i	0.260516	−	0.150409i	−0.364054	−	0.931378i	$-0.618608\pi$
$691$	6.84816	−	3.95379i	0.260516	−	0.150409i	0.624570	+	0.780969i	$0.285274\pi$
$692$	−12.6769	−	8.93656i	−0.481902	−	0.339717i
$693$		0			0
$694$	−16.6344	+	19.7603i	−0.631434	+	0.750092i
$695$	−12.7949	−	21.3199i	−0.485338	−	0.808709i
$696$	5.81804	+	10.1889i	0.220532	+	0.386210i
$697$	0.521782	+	1.94732i	0.0197639	+	0.0737599i
$698$	−17.4871	−	25.0588i	−0.661898	−	0.948490i
$699$	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	$0.314099\pi$
$702$	7.60607	+	10.8994i	0.287073	+	0.411371i
$703$	4.99713	+	18.6496i	0.188470	+	0.703381i
$704$	−31.6799	−	0.301784i	−1.19398	−	0.0113739i
$705$	−8.24627	−	13.7406i	−0.310572	−	0.517500i
$706$	−15.4556	+	18.3600i	−0.581678	+	0.690986i
$707$		0			0
$708$	9.76814	−	13.8565i	0.367109	−	0.520759i
$709$	−23.6133	+	13.6331i	−0.886816	+	0.512003i	−0.872900	−	0.487900i	$-0.837763\pi$
$709$	−23.6133	+	13.6331i	−0.886816	+	0.512003i	−0.0139163	+	0.999903i	$0.504430\pi$
$710$	−6.28077	+	14.0268i	−0.235713	+	0.526417i
$711$	−16.0089	−	9.24277i	−0.600382	−	0.346631i
$712$	7.70627	+	7.78003i	0.288805	+	0.291569i
$713$	−5.72029	−	5.72029i	−0.214227	−	0.214227i
$714$		0			0
$715$	−17.8422	+	18.4566i	−0.667261	+	0.690237i
$716$	−6.56833	−	7.87850i	−0.245470	−	0.294433i
$717$	2.93619	+	10.9580i	0.109654	+	0.409234i
$718$	−11.3729	−	5.32528i	−0.424434	−	0.198738i
$719$	17.9745	+	31.1327i	0.670335	+	1.16105i	0.977809	+	0.209498i	$0.0671831\pi$
$719$	17.9745	+	31.1327i	0.670335	+	1.16105i	−0.307474	+	0.951557i	$0.599484\pi$
$720$	8.41564	+	22.3826i	0.313632	+	0.834150i
$721$		0			0
$722$	1.81269	+	21.1050i	0.0674615	+	0.785448i
$723$	−4.77699	−	1.27999i	−0.177658	−	0.0476033i
$724$	−12.5094	+	34.0326i	−0.464907	+	1.26481i
$725$	32.0314	+	17.0749i	1.18961	+	0.634147i
$726$	0.663039	−	3.72568i	0.0246077	−	0.138273i
$727$	−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
$730$	−30.5447	−	4.90413i	−1.13051	−	0.181510i
$731$	2.44214	+	1.40997i	0.0903260	+	0.0521497i
$732$	2.03076	+	4.39133i	0.0750591	+	0.162308i
$733$	4.16444	−	15.5419i	0.153817	−	0.574053i	−0.845387	−	0.534155i	$-0.820630\pi$
$733$	4.16444	−	15.5419i	0.153817	−	0.574053i	0.999204	−	0.0398983i	$-0.0127034\pi$
$734$	19.7993	−	23.5199i	0.730804	−	0.868136i
$735$		0			0
$736$	−13.1208	−	4.89388i	−0.483640	−	0.180391i
$737$	14.5514	+	3.89904i	0.536008	+	0.143623i
$738$	−5.37812	+	11.4858i	−0.197971	+	0.422797i
$739$	−11.4543	+	19.8395i	−0.421355	+	0.729808i	−0.996072	−	0.0885439i	$-0.971779\pi$
$739$	−11.4543	+	19.8395i	−0.421355	+	0.729808i	0.574717	+	0.818352i	$0.305112\pi$
$740$	42.9407	+	3.16262i	1.57853	+	0.116260i
$741$	−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	$0.0631669\pi$
$744$	−5.28144	−	0.0251551i	−0.193627	−	0.000922230i
$745$	9.57601	+	5.31470i	0.350838	+	0.194716i
$746$	−0.235396	−	0.649954i	−0.00861846	−	0.0237965i
$747$	−5.35071	+	19.9691i	−0.195772	+	0.730632i
$748$	3.89061	+	2.74269i	0.142255	+	0.100283i
$749$		0			0
$750$	−7.19821	−	5.46018i	−0.262841	−	0.199378i
$751$	31.7774	−	18.3467i	1.15958	−	0.669481i	0.208373	−	0.978049i	$-0.433183\pi$
$751$	31.7774	−	18.3467i	1.15958	−	0.669481i	0.951202	+	0.308568i	$0.0998498\pi$
$752$	−41.2772	+	28.5137i	−1.50522	+	1.03979i
$753$	0.858946	−	0.230154i	0.0313017	−	0.00838728i
$754$	5.21476	−	29.3023i	0.189910	−	1.06713i
$755$	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	$0.0457363\pi$
$758$	32.2774	−	22.5246i	1.17237	−	0.818130i
$759$	2.80093	−	4.85135i	0.101667	−	0.176093i
$760$	−12.2900	−	3.13341i	−0.445804	−	0.113661i
$761$	3.80960	+	6.59842i	0.138098	+	0.239192i	0.926777	−	0.375613i	$-0.122568\pi$
$761$	3.80960	+	6.59842i	0.138098	+	0.239192i	−0.788679	+	0.614806i	$0.789234\pi$
$762$	−0.469568	−	5.46715i	−0.0170107	−	0.198054i
$763$		0			0
$764$	5.34878	+	30.9080i	0.193512	+	1.11821i
$765$	0.871044	−	3.48570i	0.0314927	−	0.126026i
$766$	−6.87682	+	2.49060i	−0.248470	+	0.0899890i
$767$	−41.5398	+	11.1305i	−1.49991	+	0.401901i
$768$	−8.33440	+	3.75827i	−0.300742	+	0.135615i
$769$			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
$772$	−1.40213	+	15.4608i	−0.0504637	+	0.556447i
$773$	−25.3103	+	6.78186i	−0.910347	+	0.243927i	−0.683454	−	0.729993i	$-0.739523\pi$
$773$	−25.3103	+	6.78186i	−0.910347	+	0.243927i	−0.226892	+	0.973920i	$0.572857\pi$
$774$	6.04097	+	16.6798i	0.217138	+	0.599543i
$775$	−13.8657	+	8.64382i	−0.498070	+	0.310495i
$776$	−3.86612	−	2.25673i	−0.138786	−	0.0810117i
$777$		0			0
$778$	−17.2256	+	1.47949i	−0.617568	+	0.0530423i
$779$	−3.36341	−	5.82559i	−0.120507	−	0.208724i
$780$	−2.43777	+	6.99549i	−0.0872861	+	0.250479i
$781$	−9.62327	+	16.6680i	−0.344348	+	0.596428i
$782$	1.20412	+	1.72549i	0.0430592	+	0.0617032i
$783$	16.6418	−	16.6418i	0.594728	−	0.594728i
$784$		0			0
$785$	−17.2768	+	17.8717i	−0.616635	+	0.637868i
$786$	12.0865	+	2.15096i	0.431111	+	0.0767224i
$787$	−10.7705	+	2.88594i	−0.383926	+	0.102873i	−0.445619	−	0.895222i	$-0.647017\pi$
$787$	−10.7705	+	2.88594i	−0.383926	+	0.102873i	0.0616935	+	0.998095i	$0.480350\pi$
$788$	−5.02166	−	10.8589i	−0.178889	−	0.386831i
$789$	−9.50285	+	5.48647i	−0.338310	+	0.195324i
$790$	−2.23949	−	21.7502i	−0.0796773	−	0.773838i
$791$		0			0
$792$	7.61269	+	28.9620i	0.270505	+	1.02912i
$793$	3.17643	−	11.8546i	0.112798	−	0.420969i
$794$	23.2526	−	8.42146i	0.825203	−	0.298866i
$795$	1.86654	−	3.36312i	0.0661992	−	0.119277i
$796$	18.0426	+	21.6416i	0.639504	+	0.767065i
$797$	−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
$800$	−15.6175	+	23.5816i	−0.552163	+	0.833736i
$801$	5.17536	−	8.96399i	0.182863	−	0.316727i
$802$	−39.8604	−	18.6643i	−1.40752	−	0.659060i
$803$	−37.4213	−	10.0270i	−1.32057	−	0.353846i
$804$	4.28371	−	0.741317i	0.151075	−	0.0261442i
$805$		0			0
$806$	10.2493	+	8.62795i	0.361016	+	0.303906i
$807$	2.12195	−	7.91923i	0.0746962	−	0.278770i
$808$	48.7461	+	13.3106i	1.71488	+	0.468267i
$809$	−28.2738	−	16.3239i	−0.994055	−	0.573918i	−0.0875707	−	0.996158i	$-0.527910\pi$
$809$	−28.2738	−	16.3239i	−0.994055	−	0.573918i	−0.906484	+	0.422241i	$0.861244\pi$
$810$	15.8041	−	11.4313i	0.555299	−	0.401654i
$811$			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
$814$	53.0867	+	9.44755i	1.86069	+	0.331136i
$815$	−11.2966	−	39.4750i	−0.395704	−	1.38275i
$816$	1.35128	+	0.247125i	0.0473042	+	0.00865110i
$817$	−9.08868	−	2.43530i	−0.317973	−	0.0852005i
$818$	7.21506	−	0.619695i	0.252269	−	0.0216671i
$819$		0			0
$820$	−14.7362	+	2.80780i	−0.514610	+	0.0980527i
$821$	5.78912	+	10.0271i	0.202042	+	0.349947i	0.949186	−	0.314715i	$-0.101909\pi$
$821$	5.78912	+	10.0271i	0.202042	+	0.349947i	−0.747144	+	0.664662i	$0.768576\pi$
$822$	1.56868	−	3.35015i	0.0547140	−	0.116850i
$823$	−8.69051	−	32.4334i	−0.302932	−	1.13056i	−0.934711	−	0.355409i	$-0.884341\pi$
$823$	−8.69051	−	32.4334i	−0.302932	−	1.13056i	0.631779	−	0.775149i	$-0.282325\pi$
$824$	−0.151105	+	31.7252i	−0.00526398	+	1.10520i
$825$	−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	$0.712560\pi$
$828$	−1.19552	+	13.1826i	−0.0415470	+	0.458126i
$829$	−29.2731	−	16.9008i	−1.01670	−	0.586989i	−0.103550	−	0.994624i	$-0.533020\pi$
$829$	−29.2731	−	16.9008i	−1.01670	−	0.586989i	−0.913145	+	0.407635i	$0.866354\pi$
$830$	−22.8476	+	8.71491i	−0.793052	+	0.302499i
$831$	−2.41177	+	1.39244i	−0.0836634	+	0.0483031i
$832$	22.3432	+	6.21555i	0.774611	+	0.215485i
$833$		0			0
$834$	−6.87439	−	5.78693i	−0.238041	−	0.200385i
$835$	10.0610	−	40.2615i	0.348174	−	1.39331i
$836$	−14.9080	−	5.47975i	−0.515605	−	0.189521i
$837$	2.74194	+	10.2331i	0.0947755	+	0.353707i
$838$	16.2978	−	11.3733i	0.562998	−	0.392885i
$839$	−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
$842$	−43.5258	+	30.3742i	−1.50000	+	1.04676i
$843$	−1.43627	−	5.36025i	−0.0494679	−	0.184617i
$844$	32.3696	+	11.8981i	1.11421	+	0.409550i
$845$	−8.81201	+	5.28843i	−0.303142	+	0.181928i
$846$	36.2773	+	30.5386i	1.24724	+	1.04994i
$847$		0			0
$848$	−10.8807	−	5.15811i	−0.373643	−	0.177130i
$849$	−0.701659	+	0.405103i	−0.0240809	+	0.0139031i
$850$	3.94451	−	1.58155i	0.135296	−	0.0542468i
$851$	20.6409	+	11.9171i	0.707562	+	0.408511i
$852$	−0.501644	+	5.53147i	−0.0171860	+	0.189505i
$853$	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
$856$	22.2406	+	0.105930i	0.760170	+	0.00362063i
$857$	−9.97671	−	37.2336i	−0.340798	−	1.27187i	−0.897445	−	0.441126i	$-0.854579\pi$
$857$	−9.97671	−	37.2336i	−0.340798	−	1.27187i	0.556647	−	0.830749i	$-0.312087\pi$
$858$	−3.93407	+	8.40179i	−0.134307	+	0.286832i
$859$	−6.97976	−	12.0893i	−0.238146	−	0.412482i	0.722036	−	0.691855i	$-0.243206\pi$
$859$	−6.97976	−	12.0893i	−0.238146	−	0.412482i	−0.960182	+	0.279374i	$0.909873\pi$
$860$	−11.7981	+	17.3524i	−0.402313	+	0.591713i
$861$		0			0
$862$	−34.1953	+	2.93700i	−1.16470	+	0.100035i
$863$	−39.9587	−	10.7069i	−1.36021	−	0.364467i	−0.496316	−	0.868142i	$-0.665314\pi$
$863$	−39.9587	−	10.7069i	−1.36021	−	0.364467i	−0.863893	+	0.503675i	$0.831981\pi$
$864$	11.6762	+	14.1416i	0.397231	+	0.481106i
$865$	−16.6717	+	4.77096i	−0.566853	+	0.162218i
$866$	0.0499409	+	0.00888771i	0.00169706	+	0.000302017i
$867$	6.72289	+	6.72289i	0.228321	+	0.228321i
$868$		0			0
$869$		−	27.3821i		−	0.928873i
$870$	12.9520	+	2.07952i	0.439115	+	0.0705024i
$871$	−9.55038	−	5.51391i	−0.323602	−	0.186832i
$872$	0.301224	−	1.10314i	0.0102007	−	0.0373571i
$873$	−1.09515	+	4.08717i	−0.0370653	+	0.138330i
$874$	−5.37101	−	4.52136i	−0.181677	−	0.152937i
$875$		0			0
$876$	−11.0163	+	1.90642i	−0.372205	+	0.0644118i
$877$	−33.3976	−	8.94885i	−1.12776	−	0.302181i	−0.353737	−	0.935345i	$-0.615089\pi$
$877$	−33.3976	−	8.94885i	−1.12776	−	0.302181i	−0.774018	+	0.633164i	$0.781756\pi$
$878$	−19.5432	−	9.15094i	−0.659550	−	0.308829i
$879$	−2.43499	+	4.21753i	−0.0821303	+	0.142254i
$880$	−22.4799	+	27.3731i	−0.757796	+	0.922746i
$881$	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	$0.107516\pi$
$884$	−2.23136	−	2.67645i	−0.0750488	−	0.0900186i
$885$	−5.21492	−	18.2230i	−0.175298	−	0.612560i
$886$	15.8979	−	5.75780i	0.534101	−	0.193437i
$887$	−5.23085	+	19.5218i	−0.175635	+	0.655477i	0.820808	+	0.571204i	$0.193524\pi$
$887$	−5.23085	+	19.5218i	−0.175635	+	0.655477i	−0.996443	+	0.0842733i	$0.973143\pi$
$888$	15.0493	−	3.95571i	0.505020	−	0.132745i
$889$		0			0
$890$	12.1787	−	1.25397i	0.408233	−	0.0420332i
$891$	21.1538	−	12.2132i	0.708679	−	0.409156i
$892$	13.6951	+	29.6144i	0.458546	+	0.991563i
$893$	−24.2944	+	6.50968i	−0.812983	+	0.217838i
$894$	3.89674	+	0.693481i	0.130326	+	0.0231935i
$895$	−11.4664	+	0.194071i	−0.383281	+	0.00648706i
$896$		0			0
$897$	−2.89965	+	2.89965i	−0.0968165	+	0.0968165i
$898$	−11.0992	−	15.9049i	−0.370384	−	0.530755i
$899$	11.8617	−	20.5451i	0.395611	−	0.685219i
$900$	25.3912	+	8.36914i	0.846372	+	0.278971i
$901$	0.904619	+	1.56685i	0.0301372	+	0.0521992i
$902$	−18.7174	+	1.60762i	−0.623221	+	0.0535279i
$903$		0			0
$904$	7.20319	−	12.3402i	0.239574	−	0.410428i
$905$	20.8605	+	34.7594i	0.693426	+	1.15544i
$906$	4.05550	+	11.1977i	0.134735	+	0.372018i
$907$	−40.8315	+	10.9408i	−1.35579	+	0.363282i	−0.862268	−	0.506452i	$-0.830957\pi$
$907$	−40.8315	+	10.9408i	−1.35579	+	0.363282i	−0.493520	+	0.869734i	$0.664290\pi$
$908$	−2.18376	+	24.0796i	−0.0724706	+	0.799110i
$909$		−	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	$0.712304\pi$
$912$	−4.56859	+	0.370480i	−0.151281	+	0.0122678i
$913$	−29.5797	+	7.92585i	−0.978945	+	0.262307i
$914$	−18.5503	+	6.71841i	−0.613588	+	0.222225i
$915$	5.24786	+	1.31139i	0.173489	+	0.0433533i
$916$	0.748196	+	4.32346i	0.0247211	+	0.142851i
$917$		0			0
$918$	−0.235796	−	2.74535i	−0.00778242	−	0.0906101i
$919$	−15.8502	−	27.4533i	−0.522849	−	0.905601i	−0.999646	−	0.0265881i	$-0.991536\pi$
$919$	−15.8502	−	27.4533i	−0.522849	−	0.905601i	0.476797	−	0.879013i	$-0.341798\pi$
$920$	−13.4629	+	7.99265i	−0.443859	+	0.263510i
$921$	4.44575	−	7.70027i	0.146493	−	0.253733i
$922$	−32.0771	+	22.3848i	−1.05640	+	0.737205i
$923$	9.96245	−	9.96245i	0.327918	−	0.327918i
$924$		0			0
$925$	32.8681	−	35.1720i	1.08070	−	1.15645i
$926$	1.41495	−	7.95074i	0.0464981	−	0.261278i
$927$	28.9659	−	7.76138i	0.951364	−	0.254917i
$928$	3.90384	−	40.8808i	0.128150	−	1.34198i
$929$	−37.2981	+	21.5341i	−1.22371	+	0.706509i	−0.965707	−	0.259635i	$-0.916398\pi$
$929$	−37.2981	+	21.5341i	−1.22371	+	0.706509i	−0.258003	+	0.966144i	$0.583065\pi$
$930$	−3.72578	+	4.58109i	−0.122173	+	0.150220i
$931$		0			0
$932$	−1.84240	−	1.29880i	−0.0603498	−	0.0425436i
$933$	−3.75622	+	14.0184i	−0.122973	+	0.458941i
$934$	5.91430	+	16.3300i	0.193522	+	0.534335i
$935$	5.11664	−	1.46424i	0.167332	−	0.0478858i
$936$	0.104408	−	21.9210i	0.00341268	−	0.716509i
$937$	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
$940$	−4.11989	+	55.9381i	−0.134376	+	1.82450i
$941$	14.1264	−	24.4676i	0.460507	−	0.797622i	−0.538479	−	0.842639i	$-0.681001\pi$
$941$	14.1264	−	24.4676i	0.460507	−	0.797622i	0.998986	+	0.0450169i	$0.0143342\pi$
$942$	−3.80940	+	8.13554i	−0.124117	+	0.265070i
$943$	−8.02098	−	2.14922i	−0.261199	−	0.0699881i
$944$	−55.8880	+	19.9406i	−1.81900	+	0.649010i
$945$		0			0
$946$	−16.9230	+	20.1031i	−0.550213	+	0.653609i
$947$	6.42148	−	23.9653i	0.208670	−	0.778767i	−0.779629	−	0.626241i	$-0.784592\pi$
$947$	6.42148	−	23.9653i	0.208670	−	0.778767i	0.988299	−	0.152526i	$-0.0487408\pi$
$948$	−3.31674	−	7.17214i	−0.107723	−	0.232940i
$949$	24.5603	+	14.1799i	0.797263	+	0.460300i
$950$	−11.3473	+	8.50382i	−0.368156	+	0.275900i
$951$		−	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	$0.896846\pi$
$954$	−1.99422	+	11.2057i	−0.0645651	+	0.362798i
$955$	30.6637	+	17.0184i	0.992255	+	0.550704i
$956$	13.6991	−	37.2692i	0.443059	−	1.20537i
$957$	15.8680	+	4.25181i	0.512938	+	0.137441i
$958$	−2.91470	−	33.9356i	−0.0941696	−	1.09641i
$959$		0			0
$960$	−2.57246	+	9.89272i	−0.0830259	+	0.319286i
$961$	−10.1606	−	17.5986i	−0.327760	−	0.567697i
$962$	−35.7469	−	16.7382i	−1.15253	−	0.539661i
$963$	−5.44104	−	20.3062i	−0.175335	−	0.654359i
$964$	11.0843	+	13.2953i	0.357003	+	0.428213i
$965$	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	$0.457633\pi$
$968$	−9.41026	+	9.32104i	−0.302457	+	0.299590i
$969$	0.596424	+	0.344346i	0.0191599	+	0.0110620i
$970$	−4.67632	+	1.78372i	−0.150148	+	0.0572718i
$971$	−42.2275	+	24.3801i	−1.35515	+	0.782393i	−0.988965	−	0.148150i	$-0.952668\pi$
$971$	−42.2275	+	24.3801i	−1.35515	+	0.782393i	−0.366180	+	0.930544i	$0.619335\pi$
$972$	15.2688	−	21.6594i	0.489747	−	0.694726i
$973$		0			0
$974$	−3.12565	+	3.71302i	−0.100152	+	0.118973i
$975$	4.38160	+	7.02859i	0.140324	+	0.225095i
$976$	3.04642	−	16.6578i	0.0975134	−	0.533203i
$977$	−11.4640	−	42.7841i	−0.366765	−	1.36879i	−0.865012	−	0.501750i	$-0.832690\pi$
$977$	−11.4640	−	42.7841i	−0.366765	−	1.36879i	0.498248	−	0.867035i	$-0.333977\pi$
$978$	−8.49178	−	12.1686i	−0.271537	−	0.389109i
$979$	15.3322			0.490020
$980$		0			0
$981$	−1.08089			−0.0345101
$982$	−2.86799	−	4.10978i	−0.0915212	−	0.131148i
$983$	1.61969	+	6.04477i	0.0516601	+	0.192798i	0.986934	−	0.161128i	$-0.0515131\pi$
$983$	1.61969	+	6.04477i	0.0516601	+	0.192798i	−0.935273	+	0.353926i	$0.884846\pi$
$984$	−4.70789	+	2.68828i	−0.150082	+	0.0856993i
$985$	−12.9769	−	3.24280i	−0.413477	−	0.103324i
$986$	−3.97373	+	4.72046i	−0.126549	+	0.150330i
$987$		0			0
$988$	9.50305	+	6.69918i	0.302332	+	0.213129i
$989$	−10.0592	+	5.80766i	−0.319863	+	0.184673i
$990$	30.5570	+	13.6825i	0.971165	+	0.434857i
$991$	−23.9504	−	13.8278i	−0.760809	−	0.439253i	0.0687769	−	0.997632i	$-0.478090\pi$
$991$	−23.9504	−	13.8278i	−0.760809	−	0.439253i	−0.829586	+	0.558379i	$0.811424\pi$
$992$	15.0580	+	10.7229i	0.478093	+	0.340452i
$993$	0.858769	+	0.858769i	0.0272522	+	0.0272522i
$994$		0			0
$995$	31.4974	−	0.533095i	0.998534	−	0.0169003i
$996$	−6.78771	+	5.65893i	−0.215077	+	0.179310i
$997$	−2.32458	−	8.67546i	−0.0736203	−	0.274755i	0.919297	−	0.393565i	$-0.128758\pi$
$997$	−2.32458	−	8.67546i	−0.0736203	−	0.274755i	−0.992917	+	0.118811i	$0.962092\pi$
$998$	−38.8447	−	18.1887i	−1.22961	−	0.575753i
$999$	−15.6062	−	27.0308i	−0.493759	−	0.855216i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.6	✓	72	28.19	even	6
140.2.w.b.23.17	yes	72	7.5	odd	6
140.2.w.b.67.6	yes	72	35.27	even	4
140.2.w.b.67.17	yes	72	140.27	odd	4
140.2.w.b.107.3	yes	72	140.47	odd	12
140.2.w.b.107.7	yes	72	35.12	even	12
140.2.w.b.123.3	yes	72	7.6	odd	2
140.2.w.b.123.7	yes	72	28.27	even	2
700.2.be.e.107.12		72	35.33	even	12
700.2.be.e.107.16		72	140.103	odd	12
700.2.be.e.207.2		72	140.83	odd	4
700.2.be.e.207.13		72	35.13	even	4
700.2.be.e.443.2		72	35.19	odd	6
700.2.be.e.443.13		72	140.19	even	6
700.2.be.e.543.12		72	140.139	even	2
700.2.be.e.543.16		72	35.34	odd	2
980.2.k.j.687.9		36	140.67	even	12
980.2.k.j.687.17		36	35.32	odd	12
980.2.k.j.883.9		36	7.4	even	3
980.2.k.j.883.17		36	28.11	odd	6
980.2.k.k.687.9		36	140.87	odd	12
980.2.k.k.687.17		36	35.17	even	12
980.2.k.k.883.9		36	7.3	odd	6
980.2.k.k.883.17		36	28.3	even	6
980.2.x.m.67.6		72	5.2	odd	4	inner
980.2.x.m.67.17		72	20.7	even	4	inner
980.2.x.m.263.3		72	1.1	even	1	trivial
980.2.x.m.263.7		72	4.3	odd	2	inner
980.2.x.m.667.3		72	140.107	even	12	inner
980.2.x.m.667.7		72	35.2	odd	12	inner
980.2.x.m.863.6		72	28.23	odd	6	inner
980.2.x.m.863.17		72	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	980.2.x.m.263.3

Level	$980$
Weight	$2$
Character	980.263
Analytic conductor	$7.825$
Analytic rank	$0$
Dimension	$72$
Inner twists	$8$