LMFDB - Embedded newform 980.2.x.m.263.7

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			263.7
Character	$\chi$	$=$	980.263
Dual form			980.2.x.m.667.7

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599707 - 1.28076i) q^{2} +(-0.147892 - 0.551941i) q^{3} +(-1.28070 + 1.53616i) q^{4} +(-1.15064 - 1.91729i) q^{5} +(-0.618214 + 0.520418i) q^{6} +(2.73551 + 0.719030i) q^{8} +(2.31531 - 1.33674i) q^{9} +(-1.76555 + 2.62352i) q^{10} +(-3.42960 - 1.98008i) q^{11} +(1.03728 + 0.479687i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(-0.888062 + 0.918641i) q^{15} +(-0.719595 - 3.93474i) q^{16} +(0.155552 + 0.580528i) q^{17} +(-3.10056 - 2.16371i) q^{18} +(1.00269 + 1.73671i) q^{19} +(4.41891 + 0.687909i) q^{20} +(-0.479259 + 5.57997i) q^{22} +(2.39119 + 0.640717i) q^{23} +(-0.00769773 - 1.61618i) q^{24} +(-2.35203 + 4.41225i) q^{25} +(-1.39608 + 3.85472i) q^{26} +(-2.29237 - 2.29237i) q^{27} -7.25964i q^{29} +(1.70914 + 0.586482i) q^{30} +(-2.83005 - 1.63393i) q^{31} +(-4.60792 + 3.28132i) 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} +(1.62299 - 2.32572i) q^{38} +(-0.828248 + 1.43457i) q^{39} +(-1.76900 - 6.07212i) q^{40} +3.35439 q^{41} +(-3.31777 + 3.31777i) q^{43} +(7.43403 - 2.73253i) q^{44} +(-5.22703 - 2.90101i) q^{45} +(-0.613406 - 3.44679i) q^{46} +(-3.24611 + 12.1147i) q^{47} +(-2.06532 + 0.979091i) q^{48} +(7.06157 + 0.366343i) q^{50} +(0.297413 - 0.171711i) q^{51} +(5.77421 - 0.523658i) q^{52} +(2.90777 - 0.779134i) q^{53} +(-1.56123 + 4.31073i) q^{54} +(0.149853 + 8.85392i) q^{55} +(0.810271 - 0.810271i) q^{57} +(-9.29788 + 4.35366i) q^{58} +(-7.41735 + 12.8472i) q^{59} +(-0.273837 - 2.54072i) q^{60} +(2.11676 + 3.66633i) q^{61} +(-0.395476 + 4.60450i) q^{62} +(6.96599 + 3.93382i) q^{64} +(-1.57153 + 6.28888i) q^{65} +(3.15069 - 0.560711i) q^{66} +(-3.67445 + 0.984566i) q^{67} +(-1.09100 - 0.504532i) q^{68} -1.41455i q^{69} -4.86004i q^{71} +(7.29470 - 1.99190i) q^{72} +(-9.44944 + 2.53197i) q^{73} +(2.38565 + 13.4052i) q^{74} +(2.78315 + 0.645648i) q^{75} +(-3.95201 - 0.683915i) q^{76} +(2.33405 + 0.200469i) q^{78} +(3.45719 + 5.98803i) q^{79} +(-6.71606 + 5.90716i) q^{80} +(3.08400 - 5.34165i) q^{81} +(-2.01165 - 4.29618i) q^{82} +(5.46792 - 5.46792i) q^{83} +(0.934058 - 0.966221i) q^{85} +(6.23896 + 2.25958i) q^{86} +(-4.00690 + 1.07364i) q^{87} +(-7.95796 - 7.88251i) q^{88} +(3.35292 - 1.93581i) q^{89} +(-0.580822 + 8.43434i) q^{90} +(-4.04665 + 2.85269i) q^{92} +(-0.483291 + 1.80367i) q^{93} +(17.4627 - 3.10774i) q^{94} +(2.17604 - 3.92078i) q^{95} +(2.49257 + 2.05802i) 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

)

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

$2$	−0.599707	−	1.28076i	−0.424057	−	0.905636i
$2$	−0.599707	−	1.28076i	−0.424057	−	0.905636i
$3$	−0.147892	−	0.551941i	−0.0853856	−	0.318663i	0.910001	−	0.414605i	$-0.136080\pi$
$3$	−0.147892	−	0.551941i	−0.0853856	−	0.318663i	−0.995387	+	0.0959419i	$0.969414\pi$
$4$	−1.28070	+	1.53616i	−0.640352	+	0.768082i
$5$	−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
$8$	2.73551	+	0.719030i	0.967148	+	0.254216i
$9$	2.31531	−	1.33674i	0.771770	−	0.445581i
$10$	−1.76555	+	2.62352i	−0.558316	+	0.829629i
$11$	−3.42960	−	1.98008i	−1.03406	−	0.597017i	−0.115917	−	0.993259i	$-0.536981\pi$
$11$	−3.42960	−	1.98008i	−1.03406	−	0.597017i	−0.918146	+	0.396242i	$0.870314\pi$
$12$	1.03728	+	0.479687i	0.299436	+	0.138474i
$13$	−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
$16$	−0.719595	−	3.93474i	−0.179899	−	0.983685i
$17$	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	$0.893447\pi$
$18$	−3.10056	−	2.16371i	−0.730809	−	0.509990i
$19$	1.00269	+	1.73671i	0.230033	+	0.398428i	0.957817	−	0.287377i	$-0.0927834\pi$
$19$	1.00269	+	1.73671i	0.230033	+	0.398428i	−0.727785	+	0.685805i	$0.759450\pi$
$20$	4.41891	+	0.687909i	0.988099	+	0.153821i
$21$		0			0
$22$	−0.479259	+	5.57997i	−0.102178	+	1.18965i
$23$	2.39119	+	0.640717i	0.498597	+	0.133599i	0.499349	−	0.866401i	$-0.333573\pi$
$23$	2.39119	+	0.640717i	0.498597	+	0.133599i	−0.000751542		1.00000i	$0.500239\pi$
$24$	−0.00769773	−	1.61618i	−0.00157129	−	0.329901i
$25$	−2.35203	+	4.41225i	−0.470407	+	0.882450i
$26$	−1.39608	+	3.85472i	−0.273793	+	0.755972i
$27$	−2.29237	−	2.29237i	−0.441166	−	0.441166i
$28$		0			0
$29$		−	7.25964i		−	1.34808i	−0.738694	−	0.674041i	$-0.764557\pi$
$29$		−	7.25964i		−	1.34808i	0.738694	−	0.674041i	$-0.235443\pi$
$30$	1.70914	+	0.586482i	0.312044	+	0.107076i
$31$	−2.83005	−	1.63393i	−0.508292	−	0.293462i	0.223840	−	0.974626i	$-0.428141\pi$
$31$	−2.83005	−	1.63393i	−0.508292	−	0.293462i	−0.732131	+	0.681164i	$0.761474\pi$
$32$	−4.60792	+	3.28132i	−0.814573	+	0.580061i
$33$	−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	$0.873982\pi$
$38$	1.62299	−	2.32572i	0.263284	−	0.377282i
$39$	−0.828248	+	1.43457i	−0.132626	+	0.229715i
$40$	−1.76900	−	6.07212i	−0.279704	−	0.960086i
$41$	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	$-0.866461\pi$
$43$	−3.31777	+	3.31777i	−0.505955	+	0.505955i	0.407327	+	0.913282i	$0.366461\pi$
$44$	7.43403	−	2.73253i	1.12072	−	0.411944i
$45$	−5.22703	−	2.90101i	−0.779200	−	0.432457i
$46$	−0.613406	−	3.44679i	−0.0904417	−	0.508201i
$47$	−3.24611	+	12.1147i	−0.473494	+	1.76710i	0.153572	+	0.988137i	$0.450922\pi$
$47$	−3.24611	+	12.1147i	−0.473494	+	1.76710i	−0.627066	+	0.778966i	$0.715744\pi$
$48$	−2.06532	+	0.979091i	−0.298104	+	0.141320i
$49$		0			0
$50$	7.06157	+	0.366343i	0.998657	+	0.0518087i
$51$	0.297413	−	0.171711i	0.0416461	−	0.0240444i
$52$	5.77421	−	0.523658i	0.800739	−	0.0726183i
$53$	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	$0.350378\pi$
$54$	−1.56123	+	4.31073i	−0.212456	+	0.586615i
$55$	0.149853	+	8.85392i	0.0202062	+	1.19386i
$56$		0			0
$57$	0.810271	−	0.810271i	0.107323	−	0.107323i
$58$	−9.29788	+	4.35366i	−1.22087	+	0.571663i
$59$	−7.41735	+	12.8472i	−0.965657	+	1.67257i	−0.257818	+	0.966193i	$0.583004\pi$
$59$	−7.41735	+	12.8472i	−0.965657	+	1.67257i	−0.707839	+	0.706374i	$0.750330\pi$
$60$	−0.273837	−	2.54072i	−0.0353523	−	0.328005i
$61$	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	$0.745971\pi$
$62$	−0.395476	+	4.60450i	−0.0502255	+	0.584772i
$63$		0			0
$64$	6.96599	+	3.93382i	0.870749	+	0.491728i
$65$	−1.57153	+	6.28888i	−0.194925	+	0.780039i
$66$	3.15069	−	0.560711i	0.387824	−	0.0690188i
$67$	−3.67445	+	0.984566i	−0.448906	+	0.120284i	−0.476187	−	0.879344i	$-0.657982\pi$
$67$	−3.67445	+	0.984566i	−0.448906	+	0.120284i	0.0272817	+	0.999628i	$0.491315\pi$
$68$	−1.09100	−	0.504532i	−0.132303	−	0.0611834i
$69$		−	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	$-0.0931201\pi$
$72$	7.29470	−	1.99190i	0.859689	−	0.234747i
$73$	−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	$0.610691\pi$
$74$	2.38565	+	13.4052i	0.277326	+	1.55832i
$75$	2.78315	+	0.645648i	0.321370	+	0.0745530i
$76$	−3.95201	−	0.683915i	−0.453327	−	0.0784504i
$77$		0			0
$78$	2.33405	+	0.200469i	0.264279	+	0.0226987i
$79$	3.45719	+	5.98803i	0.388965	+	0.673706i	0.992311	−	0.123773i	$-0.0394995\pi$
$79$	3.45719	+	5.98803i	0.388965	+	0.673706i	−0.603346	+	0.797480i	$0.706166\pi$
$80$	−6.71606	+	5.90716i	−0.750878	+	0.660441i
$81$	3.08400	−	5.34165i	0.342667	−	0.593517i
$82$	−2.01165	−	4.29618i	−0.222150	−	0.474433i
$83$	5.46792	−	5.46792i	0.600182	−	0.600182i	−0.340179	−	0.940361i	$-0.610488\pi$
$83$	5.46792	−	5.46792i	0.600182	−	0.600182i	0.940361	+	0.340179i	$0.110488\pi$
$84$		0			0
$85$	0.934058	−	0.966221i	0.101313	−	0.104801i
$86$	6.23896	+	2.25958i	0.672764	+	0.243657i
$87$	−4.00690	+	1.07364i	−0.429584	+	0.115107i
$88$	−7.95796	−	7.88251i	−0.848321	−	0.840278i
$89$	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	$0.267550\pi$
$90$	−0.580822	+	8.43434i	−0.0612240	+	0.889057i
$91$		0			0
$92$	−4.04665	+	2.85269i	−0.421893	+	0.297413i
$93$	−0.483291	+	1.80367i	−0.0501149	+	0.187031i
$94$	17.4627	−	3.10774i	1.80114	−	0.320539i
$95$	2.17604	−	3.92078i	0.223257	−	0.402264i
$96$	2.49257	+	2.05802i	0.254397	+	0.210046i
$97$	−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
$100$	−3.76567	−	9.26389i	−0.376567	−	0.926389i
$101$	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	$-0.181816\pi$
$102$	−0.398282	−	0.277938i	−0.0394357	−	0.0275200i
$103$	−10.8345	−	2.90309i	−1.06755	−	0.286050i	−0.318066	−	0.948069i	$-0.603033\pi$
$103$	−10.8345	−	2.90309i	−1.06755	−	0.286050i	−0.749487	+	0.662019i	$0.769700\pi$
$104$	−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	$0.207440\pi$
$107$	−2.03518	+	7.59541i	−0.196749	+	0.734276i	−0.991807	+	0.127743i	$0.959227\pi$
$108$	6.45729	−	0.585606i	0.621353	−	0.0563500i
$109$	−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	$0.672830\pi$
$110$	11.2499	−	5.50168i	1.07264	−	0.524565i
$111$			5.50146i			0.522175i
$112$		0			0
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	0.518834	−	0.854875i	$-0.326366\pi$
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	−0.854875	+	0.518834i	$0.826366\pi$
$114$	−1.52369	−	0.551839i	−0.142707	−	0.0516845i
$115$	−1.52297	−	5.32185i	−0.142017	−	0.496265i
$116$	11.1520	+	9.29746i	1.03544	+	0.863247i
$117$	−7.48624	−	2.00593i	−0.692103	−	0.185448i
$118$	20.9025	+	1.79530i	1.92423	+	0.165270i
$119$		0			0
$120$	−3.08983	+	1.87440i	−0.282062	+	0.171109i
$121$	2.34144	+	4.05549i	0.212858	+	0.368681i
$122$	3.42627	−	4.90979i	0.310200	−	0.444511i
$123$	−0.496088	−	1.85143i	−0.0447308	−	0.166937i
$124$	6.13444	−	2.25484i	0.550889	−	0.202490i
$125$	11.1659	−	0.567387i	0.998711	−	0.0507486i
$126$		0			0
$127$	−4.80151	−	4.80151i	−0.426065	−	0.426065i	0.461221	−	0.887286i	$-0.347412\pi$
$127$	−4.80151	−	4.80151i	−0.426065	−	0.426065i	−0.887286	+	0.461221i	$0.847412\pi$
$128$	0.860741	−	11.2809i	0.0760795	−	0.997102i
$129$	2.32188	+	1.34054i	0.204431	+	0.118028i
$130$	8.99701	−	1.75872i	0.789090	−	0.154250i
$131$	13.1564	−	7.59586i	1.14948	−	0.663653i	0.200720	−	0.979649i	$-0.435672\pi$
$131$	13.1564	−	7.59586i	1.14948	−	0.663653i	0.948761	+	0.315996i	$0.102339\pi$
$132$	−2.60763	−	3.69903i	−0.226965	−	0.321959i
$133$		0			0
$134$	3.46459	+	4.11565i	0.299295	+	0.355538i
$135$	−1.75744	+	7.03284i	−0.151257	+	0.605291i
$136$	0.00809642	+	1.69989i	0.000694263	+	0.145764i
$137$	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	$0.854018\pi$
$138$	−1.81171	+	0.848317i	−0.154223	+	0.0722135i
$139$	−11.1198			−0.943167			−0.471583	−	0.881821i	$-0.656317\pi$
$139$	−11.1198			−0.943167			−0.471583	+	0.881821i	$0.656317\pi$
$140$		0			0
$141$	7.16665			0.603541
$142$	−6.22456	+	2.91460i	−0.522353	+	0.244588i
$143$	2.97133	+	11.0891i	0.248475	+	0.927321i
$144$	−6.92583	−	8.14823i	−0.577152	−	0.679019i
$145$	−13.9189	+	8.35327i	−1.15590	+	0.693701i
$146$	8.90975	+	10.5841i	0.737376	+	0.875942i
$147$		0			0
$148$	15.7382	−	11.0946i	1.29367	−	0.911973i
$149$	−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	$0.397631\pi$
$150$	−0.842152	−	3.95175i	−0.0687614	−	0.322659i
$151$	12.7632	+	7.36881i	1.03865	+	0.599666i	0.919451	−	0.393205i	$-0.128634\pi$
$151$	12.7632	+	7.36881i	1.03865	+	0.599666i	0.119200	+	0.992870i	$0.461967\pi$
$152$	1.49412	+	5.47174i	0.121189	+	0.443817i
$153$	1.13617	+	1.13617i	0.0918538	+	0.0918538i
$154$		0			0
$155$	0.123656	+	7.30611i	0.00993233	+	0.586841i
$156$	−1.14299	−	3.10958i	−0.0915124	−	0.248966i
$157$	−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	$-0.229631\pi$
$158$	5.59595	−	8.01890i	0.445190	−	0.637950i
$159$	−0.860073	−	1.48969i	−0.0682082	−	0.118140i
$160$	11.5933	+	5.05911i	0.916534	+	0.399958i
$161$		0			0
$162$	−8.69088	−	0.746452i	−0.682820	−	0.0586468i
$163$	−17.7367	−	4.75254i	−1.38925	−	0.372248i	−0.514776	−	0.857324i	$-0.672125\pi$
$163$	−17.7367	−	4.75254i	−1.38925	−	0.372248i	−0.874472	+	0.485077i	$0.838792\pi$
$164$	−4.29598	+	5.15289i	−0.335460	+	0.402373i
$165$	4.86468	−	1.39214i	0.378715	−	0.108378i
$166$	−10.2822	−	3.72396i	−0.798057	−	0.289035i
$167$	−13.1233	−	13.1233i	−1.01551	−	1.01551i	−0.999878	−	0.0156336i	$-0.995023\pi$
$167$	−13.1233	−	13.1233i	−1.01551	−	1.01551i	−0.0156336	−	0.999878i	$-0.504977\pi$
$168$		0			0
$169$		−	4.59606i		−	0.353543i
$170$	−1.79766	−	0.616858i	−0.137874	−	0.0473108i
$171$	4.64307	+	2.68068i	0.355064	+	0.204996i
$172$	−0.847554	−	9.34571i	−0.0646254	−	0.712604i
$173$	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
$178$	−4.49008	−	3.13338i	−0.336546	−	0.234856i
$179$	−2.56434	+	4.44157i	−0.191668	+	0.331979i	−0.945803	−	0.324741i	$-0.894723\pi$
$179$	−2.56434	+	4.44157i	−0.191668	+	0.331979i	0.754135	+	0.656719i	$0.228056\pi$
$180$	11.1507	−	4.31423i	0.831125	−	0.321564i
$181$	−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
$184$	6.08042	+	3.47202i	0.448254	+	0.255961i
$185$	5.92309	+	20.6977i	0.435474	+	1.52172i
$186$	2.59990	−	0.462690i	0.190634	−	0.0339260i
$187$	0.616011	−	2.29899i	0.0450472	−	0.168118i
$188$	−14.4528	−	20.5018i	−1.05408	−	1.49525i
$189$		0			0
$190$	−6.32658	−	0.435673i	−0.458978	−	0.0316070i
$191$	13.5825	−	7.84185i	0.982794	−	0.567416i	0.0796814	−	0.996820i	$-0.474610\pi$
$191$	13.5825	−	7.84185i	0.982794	−	0.567416i	0.903112	+	0.429404i	$0.141276\pi$
$192$	1.14102	−	4.42660i	0.0823463	−	0.319462i
$193$	−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	$0.506791\pi$
$194$	2.10451	+	0.762199i	0.151095	+	0.0547227i
$195$	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	$0.181645\pi$
$198$	6.34936	+	13.5600i	0.451230	+	0.963667i
$199$	7.04403	−	12.2006i	0.499338	−	0.864879i	−0.500661	−	0.865643i	$-0.666910\pi$
$199$	7.04403	−	12.2006i	0.499338	−	0.864879i	1.00000		0.000763945i	$0.000243171\pi$
$200$	−9.60655	+	10.3785i	−0.679285	+	0.733874i
$201$	1.08685	+	1.88247i	0.0766601	+	0.132779i
$202$	−25.1727	−	2.16206i	−1.77114	−	0.152122i
$203$		0			0
$204$	−0.117121	+	0.676785i	−0.00820011	+	0.0473845i
$205$	−3.85971	−	6.43135i	−0.269574	−	0.449185i
$206$	2.77934	+	15.6174i	0.193646	+	1.08812i
$207$	6.39282	−	1.71295i	0.444332	−	0.119058i
$208$	−6.59063	+	9.54078i	−0.456978	+	0.661534i
$209$		−	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	$-0.202273\pi$
$212$	−2.52711	+	5.46465i	−0.173563	+	0.375314i
$213$	−2.68246	+	0.718762i	−0.183799	+	0.0492488i
$214$	10.9484	−	1.94843i	0.748419	−	0.133192i
$215$	10.1787	+	2.54357i	0.694182	+	0.173470i
$216$	−4.62250	−	7.91907i	−0.314522	−	0.538824i
$217$		0			0
$218$	−0.0489282	+	0.569667i	−0.00331383	+	0.0385827i
$219$	2.79500	+	4.84108i	0.188868	+	0.327130i
$220$	−13.7930	−	11.1091i	−0.929923	−	0.748972i
$221$	0.871146	−	1.50887i	0.0585996	−	0.101498i
$222$	7.04606	−	3.29926i	0.472900	−	0.221432i
$223$	11.5356	−	11.5356i	0.772484	−	0.772484i	−0.206056	−	0.978540i	$-0.566063\pi$
$223$	11.5356	−	11.5356i	0.772484	−	0.772484i	0.978540	+	0.206056i	$0.0660630\pi$
$224$		0			0
$225$	0.452361	+	13.3598i	0.0301574	+	0.890653i
$226$	−2.43284	+	6.71735i	−0.161830	+	0.446831i
$227$	11.6773	−	3.12892i	0.775049	−	0.207674i	0.150448	−	0.988618i	$-0.451928\pi$
$227$	11.6773	−	3.12892i	0.775049	−	0.207674i	0.624601	+	0.780944i	$0.285262\pi$
$228$	0.206991	+	2.28242i	0.0137083	+	0.151157i
$229$	−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	$0.356427\pi$
$230$	−5.90269	+	5.14211i	−0.389212	+	0.339060i
$231$		0			0
$232$	5.21990	−	19.8588i	0.342703	−	1.30379i
$233$	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	$0.0715790\pi$
$234$	1.92042	+	10.7911i	0.125542	+	0.705434i
$235$	26.9625	−	7.71591i	1.75884	−	0.503330i
$236$	−10.2360	−	27.8478i	−0.666308	−	1.81274i
$237$	2.79375	−	2.79375i	0.181474	−	0.181474i
$238$		0			0
$239$	−19.8536			−1.28422			−0.642111	−	0.766612i	$-0.721941\pi$
$239$	−19.8536			−1.28422			−0.642111	+	0.766612i	$0.721941\pi$
$240$	4.25366	+	2.83325i	0.274572	+	0.182885i
$241$	−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	$0.256588\pi$
$242$	3.78994	−	5.43093i	0.243627	−	0.349113i
$243$	−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
$248$	−6.56677	−	6.50451i	−0.416990	−	0.413037i
$249$	−3.82663	−	2.20931i	−0.242503	−	0.140009i
$250$	−7.42297	−	13.9606i	−0.469470	−	0.882948i
$251$			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
$254$	−3.27009	+	9.02909i	−0.205184	+	0.566535i
$255$	−0.671437	−	0.372649i	−0.0420470	−	0.0233362i
$256$	−14.9644	+	5.66284i	−0.935273	+	0.353927i
$257$	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	$0.396084\pi$
$258$	0.324464	−	3.77771i	0.0202003	−	0.235190i
$259$		0			0
$260$	−7.64807	−	10.4683i	−0.474313	−	0.649218i
$261$	−9.70429	−	16.8083i	−0.600680	−	1.04041i
$262$	−17.6185	−	12.2949i	−1.08847	−	0.759584i
$263$	−4.97016	−	18.5489i	−0.306473	−	1.14377i	−0.931670	−	0.363306i	$-0.881648\pi$
$263$	−4.97016	−	18.5489i	−0.306473	−	1.14377i	0.625197	−	0.780467i	$-0.285019\pi$
$264$	−3.17376	+	5.55809i	−0.195332	+	0.342077i
$265$	−4.83964	−	4.67854i	−0.297297	−	0.287401i
$266$		0			0
$267$	−1.56432	−	1.56432i	−0.0957350	−	0.0957350i
$268$	3.19343	−	6.90549i	0.195070	−	0.421820i
$269$	−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	$0.810769\pi$
$270$	10.0613	−	1.96678i	0.612314	−	0.119694i
$271$	17.9057	−	10.3379i	1.08770	−	0.627981i	0.154733	−	0.987956i	$-0.450548\pi$
$271$	17.9057	−	10.3379i	1.08770	−	0.627981i	0.932962	+	0.359975i	$0.117215\pi$
$272$	2.17229	−	1.02980i	0.131715	−	0.0624409i
$273$		0			0
$274$	4.95263	−	4.16917i	0.299199	−	0.251869i
$275$	16.8031	−	10.4750i	1.01327	−	0.631668i
$276$	2.17298	+	1.81162i	0.130798	+	0.109047i
$277$	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	$0.869893\pi$
$278$	6.66860	+	14.2418i	0.399956	+	0.854166i
$279$	−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	$0.593547\pi$
$282$	−4.29789	−	9.17878i	−0.255935	−	0.546588i
$283$	−0.366980	−	1.36959i	−0.0218147	−	0.0814136i	0.954160	−	0.299296i	$-0.0967518\pi$
$283$	−0.366980	−	1.36959i	−0.0218147	−	0.0814136i	−0.975975	+	0.217882i	$0.930085\pi$
$284$	7.46581	+	6.22427i	0.443015	+	0.369343i
$285$	−2.48586	−	0.621194i	−0.147250	−	0.0367963i
$286$	12.4206	−	10.4558i	0.734447	−	0.618264i
$287$		0			0
$288$	−6.28248	+	13.7569i	−0.370199	+	0.810632i
$289$	14.4096	−	8.31940i	0.847624	−	0.489376i
$290$	19.0458	+	12.8173i	1.11841	+	0.752655i
$291$	0.783214	+	0.452189i	0.0459128	+	0.0265078i
$292$	8.21242	−	17.7586i	0.480596	−	1.03924i
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	0.860880	−	0.508809i	$-0.169914\pi$
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	−0.508809	+	0.860880i	$0.669914\pi$
$294$		0			0
$295$	33.1667	−	0.561349i	1.93104	−	0.0326830i
$296$	−23.6479	−	13.5033i	−1.37450	−	0.784866i
$297$	3.32283	+	12.4010i	0.192810	+	0.719578i
$298$	5.68028	+	3.96395i	0.329050	+	0.229625i
$299$	−3.58824	−	6.21502i	−0.207513	−	0.359424i
$300$	−4.55621	+	3.44849i	−0.263053	+	0.199099i
$301$		0			0
$302$	1.78355	−	20.7657i	0.102632	−	1.19493i
$303$	−9.86060	−	2.64214i	−0.566477	−	0.151787i
$304$	6.11196	−	5.19504i	0.350545	−	0.297956i
$305$	4.59380	−	8.27709i	0.263040	−	0.473945i
$306$	0.773794	−	2.13653i	0.0442349	−	0.122137i
$307$	11.0030	+	11.0030i	0.627975	+	0.627975i	0.947558	−	0.319583i	$-0.103543\pi$
$307$	11.0030	+	11.0030i	0.627975	+	0.627975i	−0.319583	+	0.947558i	$0.603543\pi$
$308$		0			0
$309$			6.40934i			0.364615i
$310$	9.28323	−	4.53989i	0.527252	−	0.257849i
$311$	−21.9956	−	12.6992i	−1.24726	−	0.720104i	−0.276695	−	0.960958i	$-0.589239\pi$
$311$	−21.9956	−	12.6992i	−1.24726	−	0.720104i	−0.970561	+	0.240854i	$0.922572\pi$
$312$	−3.29718	+	3.32873i	−0.186666	+	0.188452i
$313$	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	$0.585249\pi$
$318$	−1.39215	+	1.99493i	−0.0780677	+	0.111870i
$319$	−14.3747	+	24.8977i	−0.804828	+	1.39400i
$320$	−0.473083	−	17.8823i	−0.0264462	−	0.999650i
$321$	4.49321			0.250786
$322$		0			0
$323$	−0.852238	+	0.852238i	−0.0474198	+	0.0474198i
$324$	4.25595	+	11.5786i	0.236442	+	0.643256i
$325$	13.8659	−	4.22317i	0.769142	−	0.234259i
$326$	4.54996	+	25.5667i	0.251999	+	1.41601i
$327$	−0.0597926	+	0.223149i	−0.00330654	+	0.0123402i
$328$	9.17595	+	2.41191i	0.506657	+	0.133175i
$329$		0			0
$330$	−4.70038	−	5.39563i	−0.258747	−	0.297020i
$331$	−1.84066	+	1.06270i	−0.101172	+	0.0584115i	−0.549732	−	0.835341i	$-0.685270\pi$
$331$	−1.84066	+	1.06270i	−0.101172	+	0.0584115i	0.448560	+	0.893753i	$0.351937\pi$
$332$	1.39683	+	15.4024i	0.0766610	+	0.845316i
$333$	−24.8628	+	6.66198i	−1.36248	+	0.365074i
$334$	−8.93770	+	24.6780i	−0.489049	+	1.35032i
$335$	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	$0.917414\pi$
$338$	−5.88646	+	2.75629i	−0.320181	+	0.149922i
$339$	−1.44333	+	2.49992i	−0.0783909	+	0.135777i
$340$	0.288021	+	2.67231i	0.0156201	+	0.144926i
$341$	6.47062	+	11.2074i	0.350404	+	0.606917i
$342$	0.648831	−	7.55429i	0.0350848	−	0.408489i
$343$		0			0
$344$	−11.4613	+	6.69020i	−0.617955	+	0.360711i
$345$	−2.71211	+	1.62765i	−0.146015	+	0.0876296i
$346$	−10.7977	+	1.92160i	−0.580487	+	0.103306i
$347$	−17.6420	+	4.72717i	−0.947074	+	0.253768i	−0.699120	−	0.715004i	$-0.746425\pi$
$347$	−17.6420	+	4.72717i	−0.947074	+	0.253768i	−0.247954	+	0.968772i	$0.579758\pi$
$348$	3.48236	−	7.53027i	0.186674	−	0.403665i
$349$			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
$352$	22.3006	−	2.12956i	1.18863	−	0.113506i
$353$	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	$0.267516\pi$
$354$	−2.10042	−	11.8025i	−0.111636	−	0.627293i
$355$	−9.31813	+	5.59218i	−0.494555	+	0.296802i
$356$	−1.32038	+	7.62983i	−0.0699799	+	0.404380i
$357$		0			0
$358$	7.22645	+	0.620673i	0.381930	+	0.0328036i
$359$	−4.43990	−	7.69014i	−0.234329	−	0.405870i	0.724748	−	0.689014i	$-0.241956\pi$
$359$	−4.43990	−	7.69014i	−0.234329	−	0.405870i	−0.959078	+	0.283144i	$0.908623\pi$
$360$	−12.2127	−	11.6941i	−0.643664	−	0.616335i
$361$	7.48923	−	12.9717i	0.394170	−	0.682723i
$362$	10.8723	+	23.2195i	0.571436	+	1.22039i
$363$	1.89211	−	1.89211i	0.0993101	−	0.0993101i
$364$		0			0
$365$	15.7275	+	15.2040i	0.823214	+	0.795812i
$366$	−3.21663	−	1.16498i	−0.168136	−	0.0608944i
$367$	20.9986	−	5.62655i	1.09612	−	0.293704i	0.334934	−	0.942241i	$-0.391286\pi$
$367$	20.9986	−	5.62655i	1.09612	−	0.293704i	0.761182	+	0.648538i	$0.224619\pi$
$368$	0.800369	−	9.86977i	0.0417221	−	0.514497i
$369$	7.76645	−	4.48396i	0.404305	−	0.233426i
$370$	22.9567	−	19.9986i	1.19346	−	1.03968i
$371$		0			0
$372$	−2.15177	−	3.05237i	−0.111564	−	0.158258i
$373$	−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	$0.0873615\pi$
$374$	−3.31388	+	0.589753i	−0.171357	+	0.0304954i
$375$	−1.96452	−	6.07903i	−0.101447	−	0.313920i
$376$	−17.5906	+	30.8057i	−0.907164	+	1.58868i
$377$	−14.8813	+	14.8813i	−0.766427	+	0.766427i
$378$		0			0
$379$	27.8315			1.42961			0.714805	−	0.699324i	$-0.246516\pi$
$379$	27.8315			1.42961			0.714805	+	0.699324i	$0.246516\pi$
$380$	3.23610	+	8.36412i	0.166008	+	0.429070i
$381$	−1.94004	+	3.36026i	−0.0993915	+	0.172151i
$382$	−18.1890	−	12.6931i	−0.930633	−	0.649437i
$383$	−4.99551	−	1.33854i	−0.255259	−	0.0683964i	0.128920	−	0.991655i	$-0.458849\pi$
$383$	−4.99551	−	1.33854i	−0.255259	−	0.0683964i	−0.384179	+	0.923259i	$0.625516\pi$
$384$	−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
$388$	−0.285895	−	3.15248i	−0.0145141	−	0.160043i
$389$	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	$0.566364\pi$
$390$	−2.30130	−	4.70572i	−0.116531	−	0.238283i
$391$			1.48782i			0.0752422i
$392$		0			0
$393$	−6.13820	−	6.13820i	−0.309631	−	0.309631i
$394$	−7.95407	−	2.88075i	−0.400720	−	0.145130i
$395$	7.50282	−	13.5186i	0.377508	−	0.680192i
$396$	13.5594	−	16.2640i	0.681385	−	0.817299i
$397$	−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	$0.727940\pi$
$398$	−19.8505	−	1.70494i	−0.995013	−	0.0854608i
$399$		0			0
$400$	19.0536	+	6.07962i	0.952678	+	0.303981i
$401$	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	$0.550029\pi$
$402$	1.75921	−	2.52092i	0.0877414	−	0.125732i
$403$	2.45189	+	9.15057i	0.122137	+	0.455823i
$404$	12.3271	+	33.5368i	0.613298	+	1.66852i
$405$	−13.7901	+	0.233399i	−0.685236	+	0.0115977i
$406$		0			0
$407$	26.9604	+	26.9604i	1.33638	+	1.33638i
$408$	0.937040	−	0.255869i	0.0463904	−	0.0126674i
$409$	−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	$0.707073\pi$
$410$	−5.92234	+	8.80030i	−0.292484	+	0.434616i
$411$	2.26530	−	1.30787i	0.111739	−	0.0645126i
$412$	18.3354	−	12.9255i	0.903319	−	0.636795i
$413$		0			0
$414$	−6.02770	−	7.16041i	−0.296245	−	0.351915i
$415$	−16.7752	−	4.19198i	−0.823464	−	0.205776i
$416$	16.1719	+	2.71936i	0.792894	+	0.133328i
$417$	1.64453	+	6.13746i	0.0805329	+	0.300553i
$418$	−10.1713	+	4.76264i	−0.497496	+	0.232948i
$419$	14.0529			0.686531			0.343266	−	0.939238i	$-0.388467\pi$
$419$	14.0529			0.686531			0.343266	+	0.939238i	$0.388467\pi$
$420$		0			0
$421$	37.5305			1.82913			0.914563	−	0.404443i	$-0.132535\pi$
$421$	37.5305			1.82913			0.914563	+	0.404443i	$0.132535\pi$
$422$	−22.0849	+	10.3411i	−1.07508	+	0.503395i
$423$	8.67844	+	32.3884i	0.421960	+	1.57478i
$424$	8.51444	−	0.0405536i	0.413498	−	0.00196946i
$425$	−2.92730	−	0.679088i	−0.141995	−	0.0329406i
$426$	2.52925	+	3.00454i	0.122543	+	0.145571i
$427$		0			0
$428$	−9.06132	−	12.8538i	−0.437995	−	0.621314i
$429$	5.68112	−	3.28000i	0.274287	−	0.158360i
$430$	−2.84654	−	14.5619i	−0.137272	−	0.702237i
$431$	−21.0173	−	12.1344i	−1.01237	−	0.584492i	−0.100485	−	0.994939i	$-0.532039\pi$
$431$	−21.0173	−	12.1344i	−1.01237	−	0.584492i	−0.911885	+	0.410447i	$0.865373\pi$
$432$	−7.37030	+	10.6694i	−0.354604	+	0.513334i
$433$	−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
$436$	0.758950	−	0.278968i	0.0363471	−	0.0133601i
$437$	1.28488	+	4.79524i	0.0614641	+	0.229387i
$438$	4.52409	−	6.48296i	0.216169	−	0.309768i
$439$	−7.62951	−	13.2147i	−0.364137	−	0.630703i	0.624500	−	0.781024i	$-0.285303\pi$
$439$	−7.62951	−	13.2147i	−0.364137	−	0.630703i	−0.988637	+	0.150321i	$0.951969\pi$
$440$	−5.95631	+	24.3277i	−0.283956	+	1.15978i
$441$		0			0
$442$	−2.45494	−	0.210852i	−0.116769	−	0.0100292i
$443$	11.5487	+	3.09446i	0.548695	+	0.147022i	0.522507	−	0.852635i	$-0.324997\pi$
$443$	11.5487	+	3.09446i	0.548695	+	0.147022i	0.0261872	+	0.999657i	$0.491663\pi$
$444$	−8.45113	−	7.04574i	−0.401073	−	0.334376i
$445$	−7.56953	−	4.20111i	−0.358830	−	0.199152i
$446$	−21.6924	−	7.85641i	−1.02717	−	0.372012i
$447$	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	$0.895105\pi$
$450$	16.8394	−	8.59132i	0.793818	−	0.404999i
$451$	−11.5042	−	6.64196i	−0.541712	−	0.312758i
$452$	10.0623	−	0.912543i	0.473292	−	0.0429224i
$453$	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	$0.477533\pi$
$458$	2.54432	+	1.77554i	0.118888	+	0.0829653i
$459$	0.974202	−	1.68737i	0.0454718	−	0.0787595i
$460$	10.1257	+	4.47619i	0.472113	+	0.208704i
$461$	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	$-0.707638\pi$
$463$	4.03783	−	4.03783i	0.187654	−	0.187654i	0.794681	+	0.607027i	$0.207638\pi$
$464$	−28.5648	+	5.22400i	−1.32609	+	0.242518i
$465$	4.01425	−	1.14877i	0.186157	−	0.0532728i
$466$	−1.56929	+	0.279277i	−0.0726958	+	0.0129373i
$467$	−3.17857	+	11.8626i	−0.147087	+	0.548935i	0.852567	+	0.522618i	$0.175045\pi$
$467$	−3.17857	+	11.8626i	−0.147087	+	0.548935i	−0.999654	+	0.0263172i	$0.991622\pi$
$468$	12.6691	−	8.93108i	0.585629	−	0.412839i
$469$		0			0
$470$	−26.0518	−	29.9052i	−1.20168	−	1.37943i
$471$	−5.50108	+	3.17605i	−0.253477	+	0.146345i
$472$	−29.5278	+	29.8104i	−1.35913	+	1.37213i
$473$	17.9481	−	4.80917i	0.825253	−	0.221126i
$474$	−5.25356	−	1.90270i	−0.241304	−	0.0873939i
$475$	−10.0211	+	0.339315i	−0.459802	+	0.0155688i
$476$		0			0
$477$	5.69088	−	5.69088i	0.260568	−	0.260568i
$478$	11.9063	+	25.4277i	0.544583	+	1.16304i
$479$	12.0422	−	20.8577i	0.550223	−	0.953014i	−0.448035	−	0.894016i	$-0.647876\pi$
$479$	12.0422	−	20.8577i	0.550223	−	0.953014i	0.998258	−	0.0589981i	$-0.0187906\pi$
$480$	1.07777	−	7.14704i	0.0491931	−	0.326216i
$481$	13.9553	+	24.1713i	0.636308	+	1.10212i
$482$	12.1950	+	1.04741i	0.555465	+	0.0477084i
$483$		0			0
$484$	−9.22859	−	1.59705i	−0.419481	−	0.0725932i
$485$	3.43346	+	0.857991i	0.155905	+	0.0389594i
$486$	3.28321	+	18.4487i	0.148929	+	0.836850i
$487$	−3.31498	+	0.888247i	−0.150216	+	0.0402503i	−0.333144	−	0.942876i	$-0.608109\pi$
$487$	−3.31498	+	0.888247i	−0.150216	+	0.0402503i	0.182927	+	0.983126i	$0.441443\pi$
$488$	3.15420	+	11.5513i	0.142784	+	0.522902i
$489$			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	$-0.0254801\pi$
$492$	3.47943	+	1.60906i	0.156865	+	0.0725419i
$493$	4.21443	−	1.12925i	0.189808	−	0.0508590i
$494$	−8.09435	+	1.44051i	−0.364182	+	0.0648114i
$495$	12.1824	+	20.2993i	0.547558	+	0.912383i
$496$	−4.39260	+	12.3113i	−0.197234	+	0.552792i
$497$		0			0
$498$	−0.534740	+	6.22594i	−0.0239623	+	0.278991i
$499$	−15.1647	−	26.2660i	−0.678864	−	1.17583i	−0.975323	−	0.220781i	$-0.929139\pi$
$499$	−15.1647	−	26.2660i	−0.678864	−	1.17583i	0.296460	−	0.955045i	$-0.404194\pi$
$500$	−13.4287	+	17.8794i	−0.600548	+	0.799589i
$501$	−5.30246	+	9.18412i	−0.236896	+	0.410316i
$502$	1.99316	−	0.933280i	0.0889590	−	0.0416543i
$503$	6.85172	−	6.85172i	0.305503	−	0.305503i	−0.537659	−	0.843162i	$-0.680691\pi$
$503$	6.85172	−	6.85172i	0.305503	−	0.305503i	0.843162	+	0.537659i	$0.180691\pi$
$504$		0			0
$505$	−39.9423	+	0.676027i	−1.77741	+	0.0300828i
$506$	−4.72118	+	13.0357i	−0.209882	+	0.579507i
$507$	−2.53676	+	0.679722i	−0.112661	+	0.0301875i
$508$	13.5252	−	1.22659i	0.600084	−	0.0544211i
$509$	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	$0.265709\pi$
$510$	−0.0746093	+	1.08343i	−0.00330376	+	0.0479751i
$511$		0			0
$512$	16.2270	+	15.7698i	0.717138	+	0.696931i
$513$	1.68264	−	6.27970i	0.0742904	−	0.277256i
$514$	−4.40860	−	24.7723i	−0.194455	−	1.09266i
$515$	6.90056	+	24.1133i	0.304075	+	1.06256i
$516$	−5.03294	+	1.84996i	−0.221563	+	0.0814399i
$517$	35.1209	−	35.1209i	1.54461	−	1.54461i
$518$		0			0
$519$	−4.43134			−0.194514
$520$	−8.82083	+	16.0733i	−0.386819	+	0.704860i
$521$	−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	$0.198853\pi$
$522$	−15.7077	+	22.5089i	−0.687509	+	0.985190i
$523$	−33.1997	−	8.89583i	−1.45172	−	0.388987i	−0.555099	−	0.831784i	$-0.687320\pi$
$523$	−33.1997	−	8.89583i	−1.45172	−	0.388987i	−0.896622	+	0.442797i	$0.853986\pi$
$524$	−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
$528$	9.02191	+	0.731614i	0.392628	+	0.0318394i
$529$	−14.6113	−	8.43585i	−0.635275	−	0.366776i
$530$	−3.08974	+	9.00418i	−0.134210	+	0.391117i
$531$			39.6604i			1.72112i
$532$		0			0
$533$	−6.87606	−	6.87606i	−0.297835	−	0.297835i
$534$	−1.06539	+	2.94166i	−0.0461040	+	0.127298i
$535$	16.9044	−	4.83757i	0.730841	−	0.209146i
$536$	−10.7594	+	0.0512463i	−0.464736	+	0.00221350i
$537$	2.83073	+	0.758493i	0.122155	+	0.0327314i
$538$	−1.73639	+	20.2166i	−0.0748610	+	0.871601i
$539$		0			0
$540$	−8.55283	−	11.7067i	−0.368055	−	0.503777i
$541$	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	$0.724677\pi$
$542$	−23.9785	−	16.7333i	−1.02997	−	0.718756i
$543$	2.68120	+	10.0064i	0.115061	+	0.429414i
$544$	−2.62167	−	2.16461i	−0.112403	−	0.0928070i
$545$	0.0152987	+	0.903909i	0.000655326	+	0.0387192i
$546$		0			0
$547$	6.09970	+	6.09970i	0.260804	+	0.260804i	0.825381	−	0.564577i	$-0.190961\pi$
$547$	6.09970	+	6.09970i	0.260804	+	0.260804i	−0.564577	+	0.825381i	$0.690961\pi$
$548$	−8.30984	−	3.84287i	−0.354979	−	0.164159i
$549$	9.80190	+	5.65913i	0.418335	+	0.241526i
$550$	−23.4930	−	15.2389i	−1.00174	−	0.649788i
$551$	12.6079	−	7.27916i	0.537114	−	0.310103i
$552$	1.01711	−	3.86952i	0.0432909	−	0.164698i
$553$		0			0
$554$	5.27285	−	4.43873i	0.224022	−	0.188584i
$555$	10.5479	−	6.33022i	0.447734	−	0.268703i
$556$	14.2411	−	17.0818i	0.603959	−	0.724429i
$557$	−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	$-0.172447\pi$
$558$	5.23939	+	11.1895i	0.221801	+	0.473689i
$559$	13.6020			0.575303
$560$		0			0
$561$	−1.36001			−0.0574196
$562$	5.82413	+	12.4383i	0.245676	+	0.524678i
$563$	−5.39902	−	20.1494i	−0.227542	−	0.849197i	−0.981370	−	0.192126i	$-0.938462\pi$
$563$	−5.39902	−	20.1494i	−0.227542	−	0.849197i	0.753829	−	0.657071i	$-0.228205\pi$
$564$	−9.17836	+	11.0091i	−0.386479	+	0.463569i
$565$	−2.73860	+	10.9592i	−0.115214	+	0.461056i
$566$	−1.53404	+	1.29137i	−0.0644804	+	0.0542801i
$567$		0			0
$568$	3.49451	−	13.2947i	0.146627	−	0.557832i
$569$	−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	$0.386959\pi$
$570$	0.695185	+	3.55633i	0.0291181	+	0.148958i
$571$	−28.4622	−	16.4326i	−1.19110	−	0.687684i	−0.232547	−	0.972585i	$-0.574706\pi$
$571$	−28.4622	−	16.4326i	−1.19110	−	0.687684i	−0.958557	+	0.284901i	$0.908039\pi$
$572$	−20.8401	−	9.63747i	−0.871369	−	0.402963i
$573$	−6.33698	−	6.33698i	−0.264731	−	0.264731i
$574$		0			0
$575$	−8.45116	+	9.04353i	−0.352438	+	0.377141i
$576$	21.3869	−	0.203733i	0.891123	−	0.00848889i
$577$	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	$0.617697\pi$
$578$	−19.2967	−	13.4661i	−0.802637	−	0.560116i
$579$	2.21768	+	3.84114i	0.0921638	+	0.159632i
$580$	4.99397	−	32.0797i	0.207363	−	1.33204i
$581$		0			0
$582$	0.109448	−	1.27429i	0.00453675	−	0.0528211i
$583$	−11.5152	−	3.08550i	−0.476912	−	0.127788i
$584$	−27.6696	+	0.131788i	−1.14498	+	0.00545343i
$585$	4.76804	+	16.6614i	0.197134	+	0.688865i
$586$	4.10437	−	11.3326i	0.169550	−	0.468146i
$587$	−6.10922	−	6.10922i	−0.252155	−	0.252155i	0.569699	−	0.821854i	$-0.307060\pi$
$587$	−6.10922	−	6.10922i	−0.252155	−	0.252155i	−0.821854	+	0.569699i	$0.807060\pi$
$588$		0			0
$589$		−	6.55329i		−	0.270023i
$590$	−20.6092	−	42.1420i	−0.848468	−	1.73496i
$591$	−2.96018	−	1.70906i	−0.121765	−	0.0703013i
$592$	−3.11278	+	38.3853i	−0.127935	+	1.57763i
$593$	−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
$598$	−5.80807	+	8.32287i	−0.237509	+	0.340347i
$599$	5.01596	−	8.68789i	0.204946	−	0.354978i	−0.745169	−	0.666875i	$-0.767631\pi$
$599$	5.01596	−	8.68789i	0.204946	−	0.354978i	0.950116	+	0.311898i	$0.100965\pi$
$600$	7.14908	+	3.76734i	0.291860	+	0.153801i
$601$	−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
$604$	−27.6655	+	10.1690i	−1.12569	+	0.413772i
$605$	5.08141	−	9.15566i	0.206589	−	0.372230i
$606$	2.52952	+	14.2136i	0.102755	+	0.577388i
$607$	−6.47873	+	24.1790i	−0.262964	+	0.981394i	0.700521	+	0.713632i	$0.252951\pi$
$607$	−6.47873	+	24.1790i	−0.262964	+	0.981394i	−0.963485	+	0.267762i	$0.913716\pi$
$608$	−10.3190	−	4.71247i	−0.418491	−	0.191116i
$609$		0			0
$610$	−13.3559	−	0.919741i	−0.540765	−	0.0372392i
$611$	31.4876	−	18.1794i	1.27385	−	0.735458i
$612$	−3.20044	+	0.290245i	−0.129370	+	0.0117325i
$613$	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	$0.356067\pi$
$614$	7.49366	−	20.6908i	0.302420	−	0.835013i
$615$	−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	$0.407606\pi$
$618$	8.20884	−	3.84372i	0.330208	−	0.154617i
$619$	−14.8926	+	25.7947i	−0.598582	+	1.03677i	0.394448	+	0.918918i	$0.370936\pi$
$619$	−14.8926	+	25.7947i	−0.598582	+	1.03677i	−0.993031	+	0.117857i	$0.962398\pi$
$620$	−11.3817	−	9.16700i	−0.457102	−	0.368156i
$621$	−4.01273	−	6.95024i	−0.161025	−	0.278904i
$622$	−3.07371	+	35.7869i	−0.123244	+	1.43492i
$623$		0			0
$624$	6.24065	+	2.22663i	0.249826	+	0.0891367i
$625$	−13.9359	−	20.7555i	−0.557435	−	0.830221i
$626$	−36.1262	+	6.42919i	−1.44390	+	0.256962i
$627$	−4.38331	+	1.17450i	−0.175052	+	0.0469051i
$628$	20.1797	+	9.33206i	0.805258	+	0.372390i
$629$		−	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	$-0.0592556\pi$
$632$	5.15160	+	18.8661i	0.204920	+	0.750454i
$633$	−9.51742	+	2.55019i	−0.378284	+	0.101361i
$634$	0.0531042	+	0.298398i	0.00210904	+	0.0118509i
$635$	−3.68108	+	14.7307i	−0.146079	+	0.584571i
$636$	3.38991	+	0.586639i	0.134418	+	0.0232618i
$637$		0			0
$638$	40.5086	+	3.47925i	1.60375	+	0.137745i
$639$	−6.49663	−	11.2525i	−0.257003	−	0.445142i
$640$	−22.6192	+	11.3300i	−0.894104	+	0.447859i
$641$	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	$0.149412\pi$
$642$	−2.69461	−	5.75473i	−0.106348	−	0.227121i
$643$	−4.45513	+	4.45513i	−0.175693	+	0.175693i	−0.789475	−	0.613782i	$-0.789647\pi$
$643$	−4.45513	+	4.45513i	−0.175693	+	0.175693i	0.613782	+	0.789475i	$0.289647\pi$
$644$		0			0
$645$	−0.101453	−	5.99422i	−0.00399470	−	0.236022i
$646$	1.60261	+	0.580421i	0.0630537	+	0.0228364i
$647$	−20.8568	+	5.58856i	−0.819964	+	0.219709i	−0.644331	−	0.764747i	$-0.722864\pi$
$647$	−20.8568	+	5.58856i	−0.819964	+	0.219709i	−0.175633	+	0.984456i	$0.556197\pi$
$648$	12.2771	−	12.3946i	0.482291	−	0.486907i
$649$	50.8771	−	29.3739i	1.99710	−	1.15303i
$650$	−13.7244	−	15.2263i	−0.538313	−	0.597223i
$651$		0			0
$652$	30.0162	−	21.1599i	1.17552	−	0.828686i
$653$	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	$-0.109916\pi$
$654$	0.321659	−	0.0572438i	0.0125779	−	0.00223841i
$655$	−29.7018	−	16.4846i	−1.16055	−	0.644106i
$656$	−2.41380	−	13.1987i	−0.0942431	−	0.515321i
$657$	−18.4938	+	18.4938i	−0.721511	+	0.721511i
$658$		0			0
$659$	−8.28576			−0.322768			−0.161384	−	0.986892i	$-0.551596\pi$
$659$	−8.28576			−0.322768			−0.161384	+	0.986892i	$0.551596\pi$
$660$	−4.09167	+	9.25586i	−0.159268	+	0.360284i
$661$	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	$0.0330490\pi$
$662$	2.46493	+	1.72013i	0.0958021	+	0.0668549i
$663$	−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
$668$	36.9666	−	3.35247i	1.43028	−	0.129711i
$669$	−8.07303	−	4.66096i	−0.312121	−	0.180203i
$670$	3.90440	−	11.3783i	0.150840	−	0.439581i
$671$		−	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	$0.459104\pi$
$674$	42.2218	+	15.2916i	1.62632	+	0.589011i
$675$	15.5062	−	4.72277i	0.596835	−	0.181779i
$676$	7.06030	+	5.88620i	0.271550	+	0.226392i
$677$	−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	$0.854512\pi$
$678$	4.06738	+	0.349344i	0.156207	+	0.0134165i
$679$		0			0
$680$	3.24986	−	1.97149i	0.124627	−	0.0756031i
$681$	−3.45396	−	5.98243i	−0.132356	−	0.229247i
$682$	10.4736	−	15.0085i	0.401055	−	0.574705i
$683$	3.07415	+	11.4729i	0.117629	+	0.438998i	0.999470	−	0.0325489i	$-0.0103625\pi$
$683$	3.07415	+	11.4729i	0.117629	+	0.438998i	−0.881841	+	0.471547i	$0.843696\pi$
$684$	−10.0644	+	3.69936i	−0.384820	+	0.141448i
$685$	7.11444	−	7.35942i	0.271829	−	0.281189i
$686$		0			0
$687$	0.886428	+	0.886428i	0.0338193	+	0.0338193i
$688$	15.4420	+	10.6671i	0.588721	+	0.406680i
$689$	−7.55767	−	4.36343i	−0.287924	−	0.166233i
$690$	3.71110	+	2.49746i	0.141279	+	0.0950768i
$691$	−6.84816	+	3.95379i	−0.260516	+	0.150409i	−0.624570	−	0.780969i	$-0.714726\pi$
$691$	−6.84816	+	3.95379i	−0.260516	+	0.150409i	0.364054	+	0.931378i	$0.381392\pi$
$692$	8.93656	+	12.6769i	0.339717	+	0.481902i
$693$		0			0
$694$	16.6344	+	19.7603i	0.631434	+	0.750092i
$695$	12.7949	+	21.3199i	0.485338	+	0.808709i
$696$	−11.7329	+	0.0558828i	−0.444733	+	0.00211823i
$697$	0.521782	+	1.94732i	0.0197639	+	0.0737599i
$698$	27.6737	−	12.9580i	1.04747	−	0.490467i
$699$	−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	$0.314099\pi$
$702$	12.0367	−	5.63611i	0.454298	−	0.212721i
$703$	−4.99713	−	18.6496i	−0.188470	−	0.703381i
$704$	−16.1013	−	27.2847i	−0.606840	−	1.02833i
$705$	−8.24627	−	13.7406i	−0.310572	−	0.517500i
$706$	−15.4556	−	18.3600i	−0.581678	−	0.690986i
$707$		0			0
$708$	−13.8565	+	9.76814i	−0.520759	+	0.367109i
$709$	−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	$0.504430\pi$
$710$	12.7504	+	8.58064i	0.478514	+	0.322026i
$711$	16.0089	+	9.24277i	0.600382	+	0.346631i
$712$	10.5638	−	2.88457i	0.395897	−	0.108104i
$713$	−5.72029	−	5.72029i	−0.214227	−	0.214227i
$714$		0			0
$715$	17.8422	−	18.4566i	0.667261	−	0.690237i
$716$	−3.53882	−	9.62759i	−0.132252	−	0.359800i
$717$	2.93619	+	10.9580i	0.109654	+	0.409234i
$718$	−7.18660	+	10.2983i	−0.268202	+	0.384329i
$719$	−17.9745	−	31.1327i	−0.670335	−	1.16105i	−0.977809	−	0.209498i	$-0.932817\pi$
$719$	−17.9745	−	31.1327i	−0.670335	−	1.16105i	0.307474	−	0.951557i	$-0.400516\pi$
$720$	−7.65338	+	22.6546i	−0.285225	+	0.844286i
$721$		0			0
$722$	−21.1050	−	1.81269i	−0.785448	−	0.0674615i
$723$	4.77699	+	1.27999i	0.177658	+	0.0476033i
$724$	23.2184	−	27.8497i	0.862905	−	1.03503i
$725$	32.0314	+	17.0749i	1.18961	+	0.634147i
$726$	−3.55806	−	1.28863i	−0.132052	−	0.0478257i
$727$	5.64012	+	5.64012i	0.209180	+	0.209180i	0.803919	−	0.594739i	$-0.202744\pi$
$727$	5.64012	+	5.64012i	0.209180	+	0.209180i	−0.594739	+	0.803919i	$0.702744\pi$
$728$		0			0
$729$		−	10.9327i		−	0.404916i
$730$	10.0408	−	29.2611i	0.371626	−	1.08300i
$731$	−2.44214	−	1.40997i	−0.0903260	−	0.0521497i
$732$	0.436975	+	4.81839i	0.0161511	+	0.178093i
$733$	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
$738$	−10.4005	−	7.25791i	−0.382847	−	0.267168i
$739$	11.4543	−	19.8395i	0.421355	−	0.729808i	−0.574717	−	0.818352i	$-0.694888\pi$
$739$	11.4543	−	19.8395i	0.421355	−	0.729808i	0.996072	+	0.0885439i	$0.0282214\pi$
$740$	−39.3807	−	17.4087i	−1.44766	−	0.639958i
$741$	−3.32190			−0.122033
$742$		0			0
$743$	−21.3493	+	21.3493i	−0.783229	+	0.783229i	−0.980374	−	0.197145i	$-0.936833\pi$
$743$	−21.3493	+	21.3493i	−0.783229	+	0.783229i	0.197145	+	0.980374i	$0.436833\pi$
$744$	−2.61893	+	4.58644i	−0.0960148	+	0.168147i
$745$	9.57601	+	5.31470i	0.350838	+	0.194716i
$746$	0.680575	−	0.121118i	0.0249176	−	0.00443445i
$747$	5.35071	−	19.9691i	0.195772	−	0.730632i
$748$	2.74269	+	3.89061i	0.100283	+	0.142255i
$749$		0			0
$750$	−6.60765	+	6.16171i	−0.241277	+	0.224994i
$751$	−31.7774	+	18.3467i	−1.15958	+	0.669481i	−0.951202	−	0.308568i	$-0.900150\pi$
$751$	−31.7774	+	18.3467i	−1.15958	+	0.669481i	−0.208373	+	0.978049i	$0.566817\pi$
$752$	50.0039	+	4.05497i	1.82345	+	0.147869i
$753$	0.858946	−	0.230154i	0.0313017	−	0.00838728i
$754$	27.9839	+	10.1350i	1.01911	+	0.369095i
$755$	−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	$0.0457363\pi$
$758$	−16.6907	−	35.6456i	−0.606235	−	1.29471i
$759$	−2.80093	+	4.85135i	−0.101667	+	0.176093i
$760$	8.77174	−	9.16069i	0.318184	−	0.332293i
$761$	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	$0.789234\pi$
$762$	5.46715	+	0.469568i	0.198054	+	0.0170107i
$763$		0			0
$764$	−5.34878	+	30.9080i	−0.193512	+	1.11821i
$765$	0.871044	−	3.48570i	0.0314927	−	0.126026i
$766$	1.28149	+	7.20080i	0.0463020	+	0.260175i
$767$	41.5398	−	11.1305i	1.49991	−	0.401901i
$768$	5.33867	+	7.42196i	0.192643	+	0.267817i
$769$			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
$772$	6.51613	−	14.0905i	0.234521	−	0.507129i
$773$	−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	$0.572857\pi$
$774$	17.4656	−	3.10826i	0.627788	−	0.111724i
$775$	13.8657	−	8.64382i	0.498070	−	0.310495i
$776$	−3.86612	+	2.25673i	−0.138786	+	0.0810117i
$777$		0			0
$778$	1.47949	−	17.2256i	0.0530423	−	0.617568i
$779$	3.36341	+	5.82559i	0.120507	+	0.208724i
$780$	−4.64681	+	5.76947i	−0.166382	+	0.206580i
$781$	−9.62327	+	16.6680i	−0.344348	+	0.596428i
$782$	1.90554	−	0.892254i	0.0681420	−	0.0319070i
$783$	−16.6418	+	16.6418i	−0.594728	+	0.594728i
$784$		0			0
$785$	−17.2768	+	17.8717i	−0.616635	+	0.637868i
$786$	−4.18045	+	11.5427i	−0.149112	+	0.411714i
$787$	10.7705	−	2.88594i	0.383926	−	0.102873i	−0.0616935	−	0.998095i	$-0.519650\pi$
$787$	10.7705	−	2.88594i	0.383926	−	0.102873i	0.445619	+	0.895222i	$0.352983\pi$
$788$	1.08055	+	11.9149i	0.0384930	+	0.424450i
$789$	−9.50285	+	5.48647i	−0.338310	+	0.195324i
$790$	−21.8135	−	1.50217i	−0.776091	−	0.0534447i
$791$		0			0
$792$	−28.9620	−	7.61269i	−1.02912	−	0.270505i
$793$	3.17643	−	11.8546i	0.112798	−	0.420969i
$794$	4.33309	+	24.3480i	0.153775	+	0.864080i
$795$	−1.86654	+	3.36312i	−0.0661992	+	0.119277i
$796$	9.72083	+	26.4462i	0.344546	+	0.937360i
$797$	−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
$800$	−3.64001	−	28.0491i	−0.128694	−	0.991684i
$801$	5.17536	−	8.96399i	0.182863	−	0.316727i
$802$	25.1880	−	36.0940i	0.889418	−	1.27452i
$803$	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
$808$	35.5600	−	35.9004i	1.25100	−	1.26297i
$809$	−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	$0.861244\pi$
$810$	8.56895	+	17.5219i	0.301082	+	0.615656i
$811$		−	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
$814$	18.3615	−	50.6982i	0.643572	−	1.77697i
$815$	11.2966	+	39.4750i	0.395704	+	1.38275i
$816$	−0.889656	−	1.04668i	−0.0311442	−	0.0366411i
$817$	−9.08868	−	2.43530i	−0.317973	−	0.0852005i
$818$	−0.619695	+	7.21506i	−0.0216671	+	0.252269i
$819$		0			0
$820$	14.8228	+	2.30751i	0.517633	+	0.0805819i
$821$	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	$0.768576\pi$
$822$	−3.03359	−	2.11697i	−0.105809	−	0.0738380i
$823$	8.69051	+	32.4334i	0.302932	+	1.13056i	0.934711	+	0.355409i	$0.115659\pi$
$823$	8.69051	+	32.4334i	0.302932	+	1.13056i	−0.631779	+	0.775149i	$0.717675\pi$
$824$	−27.5504	−	15.7317i	−0.959763	−	0.548041i
$825$	−8.26665	−	7.72517i	−0.287808	−	0.268956i
$826$		0			0
$827$	−4.77258	−	4.77258i	−0.165959	−	0.165959i	0.619242	−	0.785200i	$-0.287440\pi$
$827$	−4.77258	−	4.77258i	−0.165959	−	0.165959i	−0.785200	+	0.619242i	$0.787440\pi$
$828$	−5.55594	+	12.0142i	−0.193082	+	0.417522i
$829$	−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	$0.866354\pi$
$830$	4.69129	+	23.9990i	0.162837	+	0.833019i
$831$	2.41177	−	1.39244i	0.0836634	−	0.0483031i
$832$	−6.21555	−	22.3432i	−0.215485	−	0.774611i
$833$		0			0
$834$	6.87439	−	5.78693i	0.238041	−	0.200385i
$835$	−10.0610	+	40.2615i	−0.348174	+	1.39331i
$836$	12.1996	+	10.1709i	0.421933	+	0.351767i
$837$	2.74194	+	10.2331i	0.0947755	+	0.353707i
$838$	−8.42764	−	17.9985i	−0.291128	−	0.621747i
$839$	3.12360			0.107839			0.0539193	−	0.998545i	$-0.482829\pi$
$839$	3.12360			0.107839			0.0539193	+	0.998545i	$0.482829\pi$
$840$		0			0
$841$	−23.7024			−0.817325
$842$	−22.5073	−	48.0677i	−0.775653	−	1.65652i
$843$	1.43627	+	5.36025i	0.0494679	+	0.184617i
$844$	26.4889	+	22.0839i	0.911785	+	0.760158i
$845$	−8.81201	+	5.28843i	−0.303142	+	0.181928i
$846$	36.2773	−	30.5386i	1.24724	−	1.04994i
$847$		0			0
$848$	−5.15811	−	10.8807i	−0.177130	−	0.373643i
$849$	−0.701659	+	0.405103i	−0.0240809	+	0.0139031i
$850$	0.885770	+	4.15643i	0.0303817	+	0.142564i
$851$	−20.6409	−	11.9171i	−0.707562	−	0.408511i
$852$	2.33130	−	5.04121i	0.0798689	−	0.172709i
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	0.760202	−	0.649686i	$-0.225100\pi$
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	−0.649686	+	0.760202i	$0.725100\pi$
$854$		0			0
$855$	−0.202875	−	11.9866i	−0.00693817	−	0.409934i
$856$	−11.0286	+	19.3139i	−0.376949	+	0.660137i
$857$	−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	$-0.312087\pi$
$858$	−7.60790	−	5.30913i	−0.259729	−	0.181251i
$859$	6.97976	+	12.0893i	0.238146	+	0.412482i	0.960182	−	0.279374i	$-0.0901269\pi$
$859$	6.97976	+	12.0893i	0.238146	+	0.412482i	−0.722036	+	0.691855i	$0.756794\pi$
$860$	−16.9432	+	12.3786i	−0.577760	+	0.422107i
$861$		0			0
$862$	−2.93700	+	34.1953i	−0.100035	+	1.16470i
$863$	39.9587	+	10.7069i	1.36021	+	0.364467i	0.863893	−	0.503675i	$-0.168019\pi$
$863$	39.9587	+	10.7069i	1.36021	+	0.364467i	0.496316	+	0.868142i	$0.334686\pi$
$864$	18.0850	+	3.04106i	0.615266	+	0.103459i
$865$	−16.6717	+	4.77096i	−0.566853	+	0.162218i
$866$	−0.0172735	+	0.0476940i	−0.000586977	+	0.00162071i
$867$	−6.72289	−	6.72289i	−0.228321	−	0.228321i
$868$		0			0
$869$		−	27.3821i		−	0.928873i
$870$	4.25765	−	12.4077i	0.144348	−	0.420661i
$871$	9.55038	+	5.51391i	0.323602	+	0.186832i
$872$	−0.812439	−	0.804736i	−0.0275126	−	0.0272518i
$873$	−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	$0.781756\pi$
$878$	−12.3494	+	17.6965i	−0.416773	+	0.597229i
$879$	2.43499	−	4.21753i	0.0821303	−	0.142254i
$880$	34.7301	−	6.96087i	1.17075	−	0.234651i
$881$	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	$-0.892484\pi$
$883$	−18.1891	+	18.1891i	−0.612111	+	0.612111i	0.331385	+	0.943496i	$0.392484\pi$
$884$	1.20219	+	3.27064i	0.0404340	+	0.110003i
$885$	−5.21492	−	18.2230i	−0.175298	−	0.612560i
$886$	−2.96255	−	16.6469i	−0.0995289	−	0.559263i
$887$	5.23085	−	19.5218i	0.175635	−	0.655477i	−0.820808	−	0.571204i	$-0.806476\pi$
$887$	5.23085	−	19.5218i	0.175635	−	0.655477i	0.996443	−	0.0842733i	$-0.0268569\pi$
$888$	−3.95571	+	15.0493i	−0.132745	+	0.505020i
$889$		0			0
$890$	−0.841118	+	12.2142i	−0.0281943	+	0.409421i
$891$	−21.1538	+	12.2132i	−0.708679	+	0.409156i
$892$	2.94689	+	32.4944i	0.0986690	+	1.08799i
$893$	−24.2944	+	6.50968i	−0.812983	+	0.217838i
$894$	1.34780	−	3.72142i	0.0450771	−	0.124463i
$895$	11.4664	−	0.194071i	0.383281	−	0.00648706i
$896$		0			0
$897$	−2.89965	+	2.89965i	−0.0968165	+	0.0968165i
$898$	17.5646	−	8.22450i	0.586139	−	0.274455i
$899$	−11.8617	+	20.5451i	−0.395611	+	0.685219i
$900$	−21.1022	−	16.4150i	−0.703405	−	0.547168i
$901$	0.904619	+	1.56685i	0.0301372	+	0.0521992i
$902$	−1.60762	+	18.7174i	−0.0535279	+	0.623221i
$903$		0			0
$904$	−7.20319	−	12.3402i	−0.239574	−	0.410428i
$905$	20.8605	+	34.7594i	0.693426	+	1.15544i
$906$	−11.7252	+	2.08667i	−0.389544	+	0.0693250i
$907$	40.8315	−	10.9408i	1.35579	−	0.363282i	0.493520	−	0.869734i	$-0.335710\pi$
$907$	40.8315	−	10.9408i	1.35579	−	0.363282i	0.862268	+	0.506452i	$0.169043\pi$
$908$	−10.1486	+	21.9454i	−0.336794	+	0.728285i
$909$		−	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	$-0.287696\pi$
$912$	−3.77127	−	2.60514i	−0.124879	−	0.0862647i
$913$	−29.5797	+	7.92585i	−0.978945	+	0.262307i
$914$	−3.45682	−	19.4242i	−0.114341	−	0.642495i
$915$	−5.24786	−	1.31139i	−0.173489	−	0.0433533i
$916$	0.748196	−	4.32346i	0.0247211	−	0.142851i
$917$		0			0
$918$	−2.74535	−	0.235796i	−0.0906101	−	0.00778242i
$919$	15.8502	+	27.4533i	0.522849	+	0.905601i	0.999646	+	0.0265881i	$0.00846425\pi$
$919$	15.8502	+	27.4533i	0.522849	+	0.905601i	−0.476797	+	0.879013i	$0.658202\pi$
$920$	−0.339510	−	15.6530i	−0.0111933	−	0.516065i
$921$	4.44575	−	7.70027i	0.146493	−	0.253733i
$922$	−16.5872	−	35.4244i	−0.546270	−	1.16664i
$923$	−9.96245	+	9.96245i	−0.327918	+	0.327918i
$924$		0			0
$925$	32.8681	−	35.1720i	1.08070	−	1.15645i
$926$	−7.59302	−	2.74999i	−0.249522	−	0.0903703i
$927$	−28.9659	+	7.76138i	−0.951364	+	0.254917i
$928$	23.8212	+	33.4519i	0.781970	+	1.09811i
$929$	−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	$0.583065\pi$
$930$	−3.87867	−	4.45238i	−0.127187	−	0.145999i
$931$		0			0
$932$	1.29880	+	1.84240i	0.0425436	+	0.0603498i
$933$	−3.75622	+	14.0184i	−0.122973	+	0.458941i
$934$	17.0994	−	3.04308i	0.559509	−	0.0995726i
$935$	−5.11664	+	1.46424i	−0.167332	+	0.0478858i
$936$	−19.0363	−	10.8701i	−0.622222	−	0.355299i
$937$	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
$940$	−22.6781	+	51.3006i	−0.739677	+	1.67324i
$941$	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	$0.0143342\pi$
$942$	7.36681	+	5.14088i	0.240023	+	0.167499i
$943$	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	$0.215408\pi$
$947$	−6.42148	+	23.9653i	−0.208670	+	0.778767i	−0.988299	+	0.152526i	$0.951259\pi$
$948$	0.713689	+	7.86962i	0.0231796	+	0.255593i
$949$	24.5603	+	14.1799i	0.797263	+	0.460300i
$950$	6.44433	+	12.6312i	0.209082	+	0.409811i
$951$			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	$0.896846\pi$
$954$	−10.7015	−	3.87581i	−0.346475	−	0.125484i
$955$	−30.6637	−	17.0184i	−0.992255	−	0.550704i
$956$	25.4266	−	30.4983i	0.822354	−	0.986387i
$957$	15.8680	+	4.25181i	0.512938	+	0.137441i
$958$	−33.9356	−	2.91470i	−1.09641	−	0.0941696i
$959$		0			0
$960$	−9.80001	+	2.90576i	−0.316294	+	0.0937832i
$961$	−10.1606	−	17.5986i	−0.327760	−	0.567697i
$962$	22.5886	−	32.3692i	0.728287	−	1.04362i
$963$	5.44104	+	20.3062i	0.175335	+	0.654359i
$964$	−5.97191	−	16.2470i	−0.192342	−	0.523280i
$965$	12.4789	+	12.0636i	0.401711	+	0.388339i
$966$		0			0
$967$	−34.9483	−	34.9483i	−1.12386	−	1.12386i	−0.991155	−	0.132706i	$-0.957633\pi$
$967$	−34.9483	−	34.9483i	−1.12386	−	1.12386i	−0.132706	−	0.991155i	$-0.542367\pi$
$968$	3.48900	+	12.7774i	0.112141	+	0.410681i
$969$	0.596424	+	0.344346i	0.0191599	+	0.0110620i
$970$	−0.960188	−	4.91199i	−0.0308298	−	0.157715i
$971$	42.2275	−	24.3801i	1.35515	−	0.782393i	0.366180	−	0.930544i	$-0.380665\pi$
$971$	42.2275	−	24.3801i	1.35515	−	0.782393i	0.988965	+	0.148150i	$0.0473320\pi$
$972$	21.6594	−	15.2688i	0.694726	−	0.489747i
$973$		0			0
$974$	3.12565	+	3.71302i	0.100152	+	0.118973i
$975$	−4.38160	−	7.02859i	−0.140324	−	0.225095i
$976$	12.9029	−	10.9672i	0.413010	−	0.351050i
$977$	−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	$-0.333977\pi$
$978$	13.4384	−	6.29242i	0.429712	−	0.201209i
$979$	−15.3322			−0.490020
$980$		0			0
$981$	−1.08089			−0.0345101
$982$	−4.53864	+	2.12518i	−0.144834	+	0.0678173i
$983$	−1.61969	−	6.04477i	−0.0516601	−	0.192798i	0.935273	−	0.353926i	$-0.115154\pi$
$983$	−1.61969	−	6.04477i	−0.0516601	−	0.192798i	−0.986934	+	0.161128i	$0.948487\pi$
$984$	−0.0258212	−	5.42129i	−0.000823149	−	0.172824i
$985$	−12.9769	−	3.24280i	−0.413477	−	0.103324i
$986$	−3.97373	−	4.72046i	−0.126549	−	0.150330i
$987$		0			0
$988$	6.69918	+	9.50305i	0.213129	+	0.302332i
$989$	−10.0592	+	5.80766i	−0.319863	+	0.184673i
$990$	18.6927	−	27.7763i	0.594092	−	0.882790i
$991$	23.9504	+	13.8278i	0.760809	+	0.439253i	0.829586	−	0.558379i	$-0.188576\pi$
$991$	23.9504	+	13.8278i	0.760809	+	0.439253i	−0.0687769	+	0.997632i	$0.521910\pi$
$992$	18.4021	−	1.75728i	0.584267	−	0.0557936i
$993$	0.858769	+	0.858769i	0.0272522	+	0.0272522i
$994$		0			0
$995$	−31.4974	+	0.533095i	−0.998534	+	0.0169003i
$996$	8.29463	−	3.04886i	0.262826	−	0.0966069i
$997$	−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	$0.962092\pi$
$998$	−24.5461	+	35.1742i	−0.776994	+	1.11342i
$999$	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.263.7		72
4.3	odd	2	inner	980.2.x.m.263.3		72
5.2	odd	4	inner	980.2.x.m.67.17		72
7.2	even	3	inner	980.2.x.m.863.6		72
7.3	odd	6		980.2.k.k.883.17		36
7.4	even	3		980.2.k.j.883.17		36
7.5	odd	6		140.2.w.b.23.6	✓	72
7.6	odd	2		140.2.w.b.123.7	yes	72
20.7	even	4	inner	980.2.x.m.67.6		72
28.3	even	6		980.2.k.k.883.9		36
28.11	odd	6		980.2.k.j.883.9		36
28.19	even	6		140.2.w.b.23.17	yes	72
28.23	odd	6	inner	980.2.x.m.863.17		72
28.27	even	2		140.2.w.b.123.3	yes	72
35.2	odd	12	inner	980.2.x.m.667.3		72
35.12	even	12		140.2.w.b.107.3	yes	72
35.13	even	4		700.2.be.e.207.2		72
35.17	even	12		980.2.k.k.687.9		36
35.19	odd	6		700.2.be.e.443.13		72
35.27	even	4		140.2.w.b.67.17	yes	72
35.32	odd	12		980.2.k.j.687.9		36
35.33	even	12		700.2.be.e.107.16		72
35.34	odd	2		700.2.be.e.543.12		72
140.19	even	6		700.2.be.e.443.2		72
140.27	odd	4		140.2.w.b.67.6	yes	72
140.47	odd	12		140.2.w.b.107.7	yes	72
140.67	even	12		980.2.k.j.687.17		36
140.83	odd	4		700.2.be.e.207.13		72
140.87	odd	12		980.2.k.k.687.17		36
140.103	odd	12		700.2.be.e.107.12		72
140.107	even	12	inner	980.2.x.m.667.7		72
140.139	even	2		700.2.be.e.543.16		72

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

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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.263.7

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