LMFDB - Embedded newform 980.2.s.f.619.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(19,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("980.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.6
Character	$\chi$	$=$	980.619
Dual form			980.2.s.f.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02517 + 0.974178i) q^{2} +(1.84964 + 1.06789i) q^{3} +(0.101955 - 1.99740i) q^{4} +(-1.92846 - 1.13183i) q^{5} +(-2.93651 + 0.707107i) q^{6} +(1.84130 + 2.14700i) q^{8} +(0.780776 + 1.35234i) q^{9} +O(q^{10})$	\(q+(-1.02517 + 0.974178i) q^{2} +(1.84964 + 1.06789i) q^{3} +(0.101955 - 1.99740i) q^{4} +(-1.92846 - 1.13183i) q^{5} +(-2.93651 + 0.707107i) q^{6} +(1.84130 + 2.14700i) q^{8} +(0.780776 + 1.35234i) q^{9} +(3.07961 - 0.718349i) q^{10} +(-2.01961 - 1.16602i) q^{11} +(2.32158 - 3.58559i) q^{12} +1.09190 q^{13} +(-2.35829 - 4.15286i) q^{15} +(-3.97921 - 0.407291i) q^{16} +(2.49037 - 4.31345i) q^{17} +(-2.11785 - 0.625771i) q^{18} +(-1.28751 - 2.23003i) q^{19} +(-2.45733 + 3.73652i) q^{20} +(3.20636 - 0.772087i) q^{22} +(-3.02045 - 5.23157i) q^{23} +(1.11298 + 5.93748i) q^{24} +(2.43794 + 4.36537i) q^{25} +(-1.11938 + 1.06370i) q^{26} -3.07221i q^{27} +0.561553 q^{29} +(6.46328 + 1.95999i) q^{30} +(-3.29801 + 5.71233i) q^{31} +(4.47615 - 3.45892i) q^{32} +(-2.49037 - 4.31345i) q^{33} +(1.64901 + 6.84809i) q^{34} +(2.78078 - 1.42164i) q^{36} +(4.76284 - 2.74983i) q^{37} +(3.49236 + 1.03190i) q^{38} +(2.01961 + 1.16602i) q^{39} +(-1.12085 - 6.22444i) q^{40} -8.48528i q^{41} -1.32431 q^{43} +(-2.53493 + 3.91509i) q^{44} +(0.0249209 - 3.49165i) q^{45} +(8.19296 + 2.42080i) q^{46} +(8.43723 - 4.87123i) q^{47} +(-6.92516 - 5.00270i) q^{48} +(-6.75195 - 2.10027i) q^{50} +(9.21257 - 5.31888i) q^{51} +(0.111324 - 2.18095i) q^{52} +(-7.43743 - 4.29400i) q^{53} +(2.99287 + 3.14954i) q^{54} +(2.57501 + 4.53448i) q^{55} -5.49966i q^{57} +(-0.575688 + 0.547052i) q^{58} +(7.16053 - 12.4024i) q^{59} +(-8.53535 + 4.28705i) q^{60} +(-0.536986 + 0.310029i) q^{61} +(-2.18379 - 9.06897i) q^{62} +(-1.21922 + 7.90655i) q^{64} +(-2.10568 - 1.23584i) q^{65} +(6.75512 + 1.99596i) q^{66} +(-2.35829 + 4.08469i) q^{67} +(-8.36177 - 5.41404i) q^{68} -12.9020i q^{69} +11.9473i q^{71} +(-1.46584 + 4.16640i) q^{72} +(4.98074 - 8.62689i) q^{73} +(-2.20391 + 7.45890i) q^{74} +(-0.152429 + 10.6778i) q^{75} +(-4.58552 + 2.34430i) q^{76} +(-3.20636 + 0.772087i) q^{78} +(-9.21257 + 5.31888i) q^{79} +(7.21278 + 5.28922i) q^{80} +(5.62311 - 9.73950i) q^{81} +(8.26617 + 8.69887i) q^{82} +3.86098i q^{83} +(-9.68466 + 5.49966i) q^{85} +(1.35764 - 1.29011i) q^{86} +(1.03867 + 0.599676i) q^{87} +(-1.21526 - 6.48311i) q^{88} +(2.44949 - 1.41421i) q^{89} +(3.37594 + 3.60382i) q^{90} +(-10.7575 + 5.49966i) q^{92} +(-12.2003 + 7.04383i) q^{93} +(-3.90416 + 13.2132i) q^{94} +(-0.0410947 + 5.75775i) q^{95} +(11.9730 - 1.61771i) q^{96} +14.9422 q^{97} -3.64162i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 8 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 8 * q^9	$ 32 q + 12 q^{4} - 8 q^{9} + 12 q^{16} - 8 q^{25} - 48 q^{29} + 4 q^{30} + 56 q^{36} - 32 q^{44} + 32 q^{46} - 24 q^{50} - 44 q^{60} - 72 q^{64} + 32 q^{65} - 88 q^{74} + 48 q^{81} - 112 q^{85} - 40 q^{86}+O(q^{100}) $ 32 * q + 12 * q^4 - 8 * q^9 + 12 * q^16 - 8 * q^25 - 48 * q^29 + 4 * q^30 + 56 * q^36 - 32 * q^44 + 32 * q^46 - 24 * q^50 - 44 * q^60 - 72 * q^64 + 32 * q^65 - 88 * q^74 + 48 * q^81 - 112 * q^85 - 40 * q^86

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.02517	+	0.974178i	−0.724906	+	0.688848i
$2$	−1.02517	+	0.974178i	−0.724906	+	0.688848i
$3$	1.84964	+	1.06789i	1.06789	+	0.616546i	0.927604	−	0.373565i	$-0.121865\pi$
$3$	1.84964	+	1.06789i	1.06789	+	0.616546i	0.140285	+	0.990111i	$0.455198\pi$
$4$	0.101955	−	1.99740i	0.0509776	−	0.998700i
$5$	−1.92846	−	1.13183i	−0.862435	−	0.506168i
$5$	−1.92846	−	1.13183i	−0.862435	−	0.506168i
$6$	−2.93651	+	0.707107i	−1.19883	+	0.288675i
$7$		0			0
$7$		0			0
$8$	1.84130	+	2.14700i	0.650998	+	0.759079i
$9$	0.780776	+	1.35234i	0.260259	+	0.450781i
$10$	3.07961	−	0.718349i	0.973857	−	0.227162i
$11$	−2.01961	−	1.16602i	−0.608936	−	0.351569i	0.163613	−	0.986525i	$-0.447685\pi$
$11$	−2.01961	−	1.16602i	−0.608936	−	0.351569i	−0.772549	+	0.634955i	$0.781019\pi$
$12$	2.32158	−	3.58559i	0.670183	−	1.03507i
$13$	1.09190			0.302837			0.151419	−	0.988470i	$-0.451616\pi$
$13$	1.09190			0.302837			0.151419	+	0.988470i	$0.451616\pi$
$14$		0			0
$15$	−2.35829	−	4.15286i	−0.608909	−	1.07226i
$16$	−3.97921	−	0.407291i	−0.994803	−	0.101823i
$17$	2.49037	−	4.31345i	0.604003	−	1.04616i	−0.388205	−	0.921573i	$-0.626905\pi$
$17$	2.49037	−	4.31345i	0.604003	−	1.04616i	0.992208	−	0.124591i	$-0.0397620\pi$
$18$	−2.11785	−	0.625771i	−0.499183	−	0.147496i
$19$	−1.28751	−	2.23003i	−0.295374	−	0.511603i	0.679698	−	0.733492i	$-0.262111\pi$
$19$	−1.28751	−	2.23003i	−0.295374	−	0.511603i	−0.975072	+	0.221889i	$0.928778\pi$
$20$	−2.45733	+	3.73652i	−0.549475	+	0.835510i
$21$		0			0
$22$	3.20636	−	0.772087i	0.683599	−	0.164609i
$23$	−3.02045	−	5.23157i	−0.629807	−	1.09086i	−0.987590	−	0.157053i	$-0.949801\pi$
$23$	−3.02045	−	5.23157i	−0.629807	−	1.09086i	0.357783	−	0.933805i	$-0.383533\pi$
$24$	1.11298	+	5.93748i	0.227186	+	1.21198i
$25$	2.43794	+	4.36537i	0.487588	+	0.873074i
$26$	−1.11938	+	1.06370i	−0.219529	+	0.208609i
$27$		−	3.07221i		−	0.591246i
$28$		0			0
$29$	0.561553			0.104278			0.0521389	−	0.998640i	$-0.483396\pi$
$29$	0.561553			0.104278			0.0521389	+	0.998640i	$0.483396\pi$
$30$	6.46328	+	1.95999i	1.18003	+	0.357844i
$31$	−3.29801	+	5.71233i	−0.592341	+	1.02596i	0.401576	+	0.915826i	$0.368463\pi$
$31$	−3.29801	+	5.71233i	−0.592341	+	1.02596i	−0.993916	+	0.110138i	$0.964871\pi$
$32$	4.47615	−	3.45892i	0.791279	−	0.611456i
$33$	−2.49037	−	4.31345i	−0.433518	−	0.750875i
$34$	1.64901	+	6.84809i	0.282802	+	1.17444i
$35$		0			0
$36$	2.78078	−	1.42164i	0.463463	−	0.236941i
$37$	4.76284	−	2.74983i	0.783006	−	0.452069i	−0.0544884	−	0.998514i	$-0.517353\pi$
$37$	4.76284	−	2.74983i	0.783006	−	0.452069i	0.837495	+	0.546446i	$0.184019\pi$
$38$	3.49236	+	1.03190i	0.566535	+	0.167396i
$39$	2.01961	+	1.16602i	0.323397	+	0.186713i
$40$	−1.12085	−	6.22444i	−0.177222	−	0.984171i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$		0			0
$43$	−1.32431			−0.201955			−0.100977	−	0.994889i	$-0.532197\pi$
$43$	−1.32431			−0.201955			−0.100977	+	0.994889i	$0.532197\pi$
$44$	−2.53493	+	3.91509i	−0.382154	+	0.590222i
$45$	0.0249209	−	3.49165i	0.00371498	−	0.520504i
$46$	8.19296	+	2.42080i	1.20799	+	0.356928i
$47$	8.43723	−	4.87123i	1.23070	−	0.710543i	0.263521	−	0.964654i	$-0.415116\pi$
$47$	8.43723	−	4.87123i	1.23070	−	0.710543i	0.967175	+	0.254111i	$0.0817829\pi$
$48$	−6.92516	−	5.00270i	−0.999561	−	0.722077i
$49$		0			0
$50$	−6.75195	−	2.10027i	−0.954870	−	0.297023i
$51$	9.21257	−	5.31888i	1.29002	−	0.744792i
$52$	0.111324	−	2.18095i	0.0154379	−	0.302444i
$53$	−7.43743	−	4.29400i	−1.02161	−	0.589826i	−0.107040	−	0.994255i	$-0.534137\pi$
$53$	−7.43743	−	4.29400i	−1.02161	−	0.589826i	−0.914570	+	0.404428i	$0.867471\pi$
$54$	2.99287	+	3.14954i	0.407279	+	0.428598i
$55$	2.57501	+	4.53448i	0.347214	+	0.611430i
$56$		0			0
$57$		−	5.49966i		−	0.728447i
$58$	−0.575688	+	0.547052i	−0.0755916	+	0.0718315i
$59$	7.16053	−	12.4024i	0.932222	−	1.61466i	0.152707	−	0.988272i	$-0.451201\pi$
$59$	7.16053	−	12.4024i	0.932222	−	1.61466i	0.779515	−	0.626384i	$-0.215466\pi$
$60$	−8.53535	+	4.28705i	−1.10191	+	0.553456i
$61$	−0.536986	+	0.310029i	−0.0687540	+	0.0396951i	−0.533983	−	0.845495i	$-0.679305\pi$
$61$	−0.536986	+	0.310029i	−0.0687540	+	0.0396951i	0.465229	+	0.885190i	$0.345972\pi$
$62$	−2.18379	−	9.06897i	−0.277342	−	1.15176i
$63$		0			0
$64$	−1.21922	+	7.90655i	−0.152403	+	0.988318i
$65$	−2.10568	−	1.23584i	−0.261177	−	0.153287i
$66$	6.75512	+	1.99596i	0.831498	+	0.245686i
$67$	−2.35829	+	4.08469i	−0.288112	+	0.499024i	−0.973359	−	0.229287i	$-0.926361\pi$
$67$	−2.35829	+	4.08469i	−0.288112	+	0.499024i	0.685247	+	0.728310i	$0.259694\pi$
$68$	−8.36177	−	5.41404i	−1.01401	−	0.656549i
$69$		−	12.9020i		−	1.55322i
$70$		0			0
$71$			11.9473i			1.41789i	0.705265	+	0.708943i	$0.250828\pi$
$71$			11.9473i			1.41789i	−0.705265	+	0.708943i	$0.749172\pi$
$72$	−1.46584	+	4.16640i	−0.172751	+	0.491015i
$73$	4.98074	−	8.62689i	0.582951	−	1.00970i	−0.412176	−	0.911104i	$-0.635231\pi$
$73$	4.98074	−	8.62689i	0.582951	−	1.00970i	0.995127	−	0.0985973i	$-0.0314356\pi$
$74$	−2.20391	+	7.45890i	−0.256199	+	0.867080i
$75$	−0.152429	+	10.6778i	−0.0176010	+	1.23297i
$76$	−4.58552	+	2.34430i	−0.525995	+	0.268910i
$77$		0			0
$78$	−3.20636	+	0.772087i	−0.363049	+	0.0874216i
$79$	−9.21257	+	5.31888i	−1.03650	+	0.598421i	−0.918839	−	0.394634i	$-0.870872\pi$
$79$	−9.21257	+	5.31888i	−1.03650	+	0.598421i	−0.117657	+	0.993054i	$0.537538\pi$
$80$	7.21278	+	5.28922i	0.806413	+	0.591353i
$81$	5.62311	−	9.73950i	0.624790	−	1.08217i
$82$	8.26617	+	8.69887i	0.912846	+	0.960630i
$83$			3.86098i			0.423798i	0.977292	+	0.211899i	$0.0679648\pi$
$83$			3.86098i			0.423798i	−0.977292	+	0.211899i	$0.932035\pi$
$84$		0			0
$85$	−9.68466	+	5.49966i	−1.05045	+	0.596521i
$86$	1.35764	−	1.29011i	0.146398	−	0.139116i
$87$	1.03867	+	0.599676i	0.111357	+	0.0642921i
$88$	−1.21526	−	6.48311i	−0.129547	−	0.691102i
$89$	2.44949	−	1.41421i	0.259645	−	0.149906i	−0.364527	−	0.931193i	$-0.618769\pi$
$89$	2.44949	−	1.41421i	0.259645	−	0.149906i	0.624173	+	0.781286i	$0.285436\pi$
$90$	3.37594	+	3.60382i	0.355855	+	0.379876i
$91$		0			0
$92$	−10.7575	+	5.49966i	−1.12155	+	0.573379i
$93$	−12.2003	+	7.04383i	−1.26511	+	0.730411i
$94$	−3.90416	+	13.2132i	−0.402683	+	1.36284i
$95$	−0.0410947	+	5.75775i	−0.00421623	+	0.590733i
$96$	11.9730	−	1.61771i	1.22199	−	0.165107i
$97$	14.9422			1.51715			0.758576	−	0.651584i	$-0.225895\pi$
$97$	14.9422			1.51715			0.758576	+	0.651584i	$0.225895\pi$
$98$		0			0
$99$		−	3.64162i		−	0.365996i
$100$	8.96795	−	4.42446i	0.896795	−	0.442446i
$101$	−13.0860	−	7.55519i	−1.30210	−	0.751770i	−0.321339	−	0.946964i	$-0.604133\pi$
$101$	−13.0860	−	7.55519i	−1.30210	−	0.751770i	−0.980765	+	0.195194i	$0.937466\pi$
$102$	−4.26293	+	14.4274i	−0.422093	+	1.42853i
$103$	−4.73795	+	2.73546i	−0.466844	+	0.269532i	−0.714918	−	0.699209i	$-0.753536\pi$
$103$	−4.73795	+	2.73546i	−0.466844	+	0.269532i	0.248074	+	0.968741i	$0.420202\pi$
$104$	2.01051	+	2.34430i	0.197147	+	0.229878i
$105$		0			0
$106$	11.8078	−	2.84329i	1.14687	−	0.276165i
$107$	5.00691	+	8.67222i	0.484036	+	0.838375i	0.999832	−	0.0183365i	$-0.00583701\pi$
$107$	5.00691	+	8.67222i	0.484036	+	0.838375i	−0.515796	+	0.856712i	$0.672504\pi$
$108$	−6.13642	−	0.313227i	−0.590478	−	0.0301403i
$109$	−2.28078	+	3.95042i	−0.218459	+	0.378382i	−0.954337	−	0.298732i	$-0.903436\pi$
$109$	−2.28078	+	3.95042i	−0.218459	+	0.378382i	0.735878	+	0.677114i	$0.236770\pi$
$110$	−7.05722	−	2.14011i	−0.672880	−	0.204051i
$111$	11.7460			1.11489
$112$		0			0
$113$			5.49966i			0.517364i	0.965963	+	0.258682i	$0.0832882\pi$
$113$			5.49966i			0.517364i	−0.965963	+	0.258682i	$0.916712\pi$
$114$	5.35764	+	5.63809i	0.501789	+	0.528056i
$115$	−0.0964069	+	13.5075i	−0.00898999	+	1.25958i
$116$	0.0572532	−	1.12165i	0.00531583	−	0.104142i
$117$	0.852526	+	1.47662i	0.0788161	+	0.136513i
$118$	4.74137	+	19.6902i	0.436478	+	1.81263i
$119$		0			0
$120$	4.57385	−	12.7099i	0.417534	−	1.16025i
$121$	−2.78078	−	4.81645i	−0.252798	−	0.437859i
$122$	0.248480	−	0.840953i	0.0224963	−	0.0761363i
$123$	9.06134	−	15.6947i	0.817034	−	1.41514i
$124$	11.0736	+	7.16985i	0.994434	+	0.643872i
$125$	0.239369	−	11.1778i	0.0214098	−	0.999771i
$126$		0			0
$127$	5.29723			0.470053			0.235026	−	0.971989i	$-0.424482\pi$
$127$	5.29723			0.470053			0.235026	+	0.971989i	$0.424482\pi$
$128$	−6.45247	−	9.29331i	−0.570323	−	0.821420i
$129$	−2.44949	−	1.41421i	−0.215666	−	0.124515i
$130$	3.36261	−	0.784362i	0.294920	−	0.0687931i
$131$	1.28751	+	2.23003i	0.112490	+	0.194838i	0.916774	−	0.399407i	$-0.130784\pi$
$131$	1.28751	+	2.23003i	0.112490	+	0.194838i	−0.804284	+	0.594246i	$0.797451\pi$
$132$	−8.86958	+	4.53448i	−0.771998	+	0.394676i
$133$		0			0
$134$	−1.56155	−	6.48490i	−0.134898	−	0.560210i
$135$	−3.47720	+	5.92463i	−0.299270	+	0.509911i
$136$	13.8465	−	2.59553i	1.18733	−	0.222565i
$137$	2.67459	+	1.54417i	0.228505	+	0.131928i	0.609882	−	0.792492i	$-0.291217\pi$
$137$	2.67459	+	1.54417i	0.228505	+	0.131928i	−0.381377	+	0.924420i	$0.624550\pi$
$138$	12.5689	+	13.2268i	1.06993	+	1.12594i
$139$	−4.02102			−0.341058			−0.170529	−	0.985353i	$-0.554548\pi$
$139$	−4.02102			−0.341058			−0.170529	+	0.985353i	$0.554548\pi$
$140$		0			0
$141$	20.8078			1.75233
$142$	−11.6388	−	12.2481i	−0.976708	−	1.02783i
$143$	−2.20521	−	1.27318i	−0.184409	−	0.106468i
$144$	−2.55608	−	5.69927i	−0.213006	−	0.474939i
$145$	−1.08293	−	0.635580i	−0.0899328	−	0.0527821i
$146$	3.29801	+	13.6962i	0.272946	+	1.13350i
$147$		0			0
$148$	−5.00691	−	9.79366i	−0.411565	−	0.805034i
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$	−10.2458	−	11.0951i	−0.836568	−	0.905910i
$151$	4.28785	+	2.47559i	0.348940	+	0.201461i	0.664218	−	0.747539i	$-0.268764\pi$
$151$	4.28785	+	2.47559i	0.348940	+	0.201461i	−0.315278	+	0.948999i	$0.602098\pi$
$152$	2.41718	−	6.87042i	0.196059	−	0.557265i
$153$	7.77769			0.628789
$154$		0			0
$155$	12.8255	−	7.28323i	1.03017	−	0.585003i
$156$	2.53493	−	3.91509i	0.202956	−	0.313458i
$157$	−1.94442	+	3.36784i	−0.155182	+	0.268783i	−0.933125	−	0.359552i	$-0.882930\pi$
$157$	−1.94442	+	3.36784i	−0.155182	+	0.268783i	0.777943	+	0.628334i	$0.216263\pi$
$158$	4.26293	−	14.4274i	0.339141	−	1.14779i
$159$	−9.17104	−	15.8847i	−0.727311	−	1.25974i
$160$	−12.5470	+	1.60417i	−0.991926	+	0.126820i
$161$		0			0
$162$	3.72336	+	15.4626i	0.292535	+	1.21485i
$163$	5.75058	+	9.96029i	0.450420	+	0.780150i	0.998412	−	0.0563333i	$-0.0179410\pi$
$163$	5.75058	+	9.96029i	0.450420	+	0.780150i	−0.547992	+	0.836484i	$0.684608\pi$
$164$	−16.9485	−	0.865119i	−1.32346	−	0.0675544i
$165$	−0.0794878	+	11.1370i	−0.00618812	+	0.867013i
$166$	−3.76129	−	3.95817i	−0.291932	−	0.307214i
$167$		−	0.673500i		−	0.0521170i	−0.999660	−	0.0260585i	$-0.991704\pi$
$167$		−	0.673500i		−	0.0521170i	0.999660	−	0.0260585i	$-0.00829562\pi$
$168$		0			0
$169$	−11.8078			−0.908290
$170$	4.57080	−	15.0727i	0.350564	−	1.15602i
$171$	2.01051	−	3.48230i	0.153747	−	0.266298i
$172$	−0.135020	+	2.64517i	−0.0102952	+	0.201692i
$173$	5.52669	+	9.57250i	0.420186	+	0.727784i	0.995957	−	0.0898270i	$-0.0286314\pi$
$173$	5.52669	+	9.57250i	0.420186	+	0.727784i	−0.575771	+	0.817611i	$0.695298\pi$
$174$	−1.64901	+	0.397078i	−0.125011	+	0.0301024i
$175$		0			0
$176$	7.56155	+	5.46242i	0.569973	+	0.411746i
$177$	26.4888	−	15.2933i	1.99102	−	1.14952i
$178$	−1.13345	+	3.83605i	−0.0849559	+	0.287524i
$179$	−7.19296	−	4.15286i	−0.537627	−	0.310399i	0.206490	−	0.978449i	$-0.433796\pi$
$179$	−7.19296	−	4.15286i	−0.537627	−	0.310399i	−0.744117	+	0.668050i	$0.767129\pi$
$180$	−6.97168	−	0.405769i	−0.519638	−	0.0302442i
$181$			3.44849i			0.256324i	0.991753	+	0.128162i	$0.0409077\pi$
$181$			3.44849i			0.256324i	−0.991753	+	0.128162i	$0.959092\pi$
$182$		0			0
$183$	−1.32431			−0.0978956
$184$	5.67063	−	16.1178i	0.418044	−	1.18822i
$185$	−12.2973	−	0.0877692i	−0.904115	−	0.00645292i
$186$	5.64543	−	19.1064i	0.413943	−	1.40095i
$187$	−10.0592	+	5.80766i	−0.735599	+	0.424698i
$188$	−8.86958	−	17.3492i	−0.646881	−	1.26532i
$189$		0			0
$190$	−5.56695	−	5.94272i	−0.403869	−	0.431130i
$191$	−17.2910	+	9.98298i	−1.25113	+	0.722343i	−0.971335	−	0.237716i	$-0.923601\pi$
$191$	−17.2910	+	9.98298i	−1.25113	+	0.722343i	−0.279800	+	0.960058i	$0.590268\pi$
$192$	−10.6984	+	13.3223i	−0.772094	+	0.961452i
$193$	4.76284	+	2.74983i	0.342837	+	0.197937i	0.661526	−	0.749922i	$-0.269909\pi$
$193$	4.76284	+	2.74983i	0.342837	+	0.197937i	−0.318689	+	0.947859i	$0.603243\pi$
$194$	−15.3183	+	14.5564i	−1.09979	+	1.04509i
$195$	−2.57501	−	4.53448i	−0.184400	−	0.324721i
$196$		0			0
$197$		−	16.4990i		−	1.17550i	−0.809042	−	0.587751i	$-0.800013\pi$
$197$		−	16.4990i		−	1.17550i	0.809042	−	0.587751i	$-0.199987\pi$
$198$	3.54758	+	3.73328i	0.252116	+	0.265313i
$199$	9.17104	−	15.8847i	0.650118	−	1.12604i	−0.332976	−	0.942935i	$-0.608053\pi$
$199$	9.17104	−	15.8847i	0.650118	−	1.12604i	0.983094	−	0.183102i	$-0.0586138\pi$
$200$	−4.88348	+	13.2722i	−0.345314	+	0.938487i
$201$	−8.72399	+	5.03680i	−0.615343	+	0.355268i
$202$	20.7755	−	5.00270i	1.46176	−	0.351989i
$203$		0			0
$204$	−9.68466	−	18.9435i	−0.678062	−	1.32631i
$205$	−9.60387	+	16.3635i	−0.670763	+	1.14288i
$206$	2.19239	−	7.41992i	0.152751	−	0.516970i
$207$	4.71659	−	8.16937i	0.327826	−	0.567811i
$208$	−4.34488	−	0.444719i	−0.301263	−	0.0308357i
$209$			6.00505i			0.415378i
$210$		0			0
$211$			0.287088i			0.0197640i	0.999951	+	0.00988198i	$0.00314558\pi$
$211$			0.287088i			0.0197640i	−0.999951	+	0.00988198i	$0.996854\pi$
$212$	−9.33512	+	14.4177i	−0.641139	+	0.990213i
$213$	−12.7584	+	22.0982i	−0.874193	+	1.51415i
$214$	−13.5812	−	4.01290i	−0.928393	−	0.274316i
$215$	2.55388	+	1.49889i	0.174173	+	0.102223i
$216$	6.59603	−	5.65685i	0.448803	−	0.384900i
$217$		0			0
$218$	−1.51022	−	6.27174i	−0.102285	−	0.424776i
$219$	18.4251	−	10.6378i	1.24506	−	0.718833i
$220$	9.31971	−	4.68101i	0.628335	−	0.315594i
$221$	2.71922	−	4.70983i	0.182915	−	0.316818i
$222$	−12.0417	+	11.4427i	−0.808187	+	0.767986i
$223$			0.147647i			0.00988718i	0.999988	+	0.00494359i	$0.00157360\pi$
$223$			0.147647i			0.00988718i	−0.999988	+	0.00494359i	$0.998426\pi$
$224$		0			0
$225$	−4.00000	+	6.70531i	−0.266667	+	0.447021i
$226$	−5.35764	−	5.63809i	−0.356385	−	0.375040i
$227$	−8.79279	−	5.07652i	−0.583598	−	0.336941i	0.178964	−	0.983856i	$-0.442725\pi$
$227$	−8.79279	−	5.07652i	−0.583598	−	0.336941i	−0.762562	+	0.646915i	$0.776059\pi$
$228$	−10.9850	−	0.560719i	−0.727500	−	0.0371345i
$229$	−8.18700	+	4.72677i	−0.541012	+	0.312354i	−0.745489	−	0.666518i	$-0.767784\pi$
$229$	−8.18700	+	4.72677i	−0.541012	+	0.312354i	0.204477	+	0.978871i	$0.434451\pi$
$230$	−13.0599	−	13.9414i	−0.861143	−	0.919271i
$231$		0			0
$232$	1.03399	+	1.20565i	0.0678846	+	0.0791551i
$233$	−9.52568	+	5.49966i	−0.624048	+	0.360294i	−0.778443	−	0.627715i	$-0.783990\pi$
$233$	−9.52568	+	5.49966i	−0.624048	+	0.360294i	0.154395	+	0.988009i	$0.450657\pi$
$234$	−2.31248	−	0.683276i	−0.151171	−	0.0446672i
$235$	−21.7843	−	0.155480i	−1.42105	−	0.0101424i
$236$	−24.0425	−	15.5669i	−1.56503	−	1.01332i
$237$	−22.7199			−1.47582
$238$		0			0
$239$			2.33205i			0.150848i	0.997152	+	0.0754238i	$0.0240310\pi$
$239$			2.33205i			0.150848i	−0.997152	+	0.0754238i	$0.975969\pi$
$240$	7.69273	+	17.4856i	0.496564	+	1.12869i
$241$	13.9245	+	8.03932i	0.896957	+	0.517858i	0.876212	−	0.481927i	$-0.160063\pi$
$241$	13.9245	+	8.03932i	0.896957	+	0.517858i	0.0207451	+	0.999785i	$0.493396\pi$
$242$	7.54285	+	2.22871i	0.484873	+	0.143267i
$243$	12.8196	−	7.40140i	0.822378	−	0.474800i
$244$	0.564503	+	1.10418i	0.0361386	+	0.0706882i
$245$		0			0
$246$	6.00000	+	24.9171i	0.382546	+	1.58866i
$247$	−1.40582	−	2.43495i	−0.0894503	−	0.154932i
$248$	−18.3370	+	3.43727i	−1.16440	+	0.218267i
$249$	−4.12311	+	7.14143i	−0.261291	+	0.452570i
$250$	10.6437	+	11.6923i	0.673170	+	0.739488i
$251$	−9.17104			−0.578871			−0.289435	−	0.957198i	$-0.593468\pi$
$251$	−9.17104			−0.578871			−0.289435	+	0.957198i	$0.593468\pi$
$252$		0			0
$253$			14.0877i			0.885683i
$254$	−5.43057	+	5.16044i	−0.340744	+	0.323795i
$255$	−23.7861	−	0.169768i	−1.48955	−	0.0106313i
$256$	15.6682	+	3.24139i	0.979264	+	0.202587i
$257$	3.27569	+	5.67366i	0.204332	+	0.353913i	0.949920	−	0.312494i	$-0.101165\pi$
$257$	3.27569	+	5.67366i	0.204332	+	0.353913i	−0.745588	+	0.666407i	$0.767831\pi$
$258$	3.88884	−	0.936426i	0.242109	−	0.0582994i
$259$		0			0
$260$	−2.68314	+	4.07988i	−0.166402	+	0.253024i
$261$	0.438447	+	0.759413i	0.0271392	+	0.0470065i
$262$	−3.49236	−	1.03190i	−0.215758	−	0.0637510i
$263$	−11.7915	+	20.4234i	−0.727093	+	1.25936i	0.231013	+	0.972951i	$0.425796\pi$
$263$	−11.7915	+	20.4234i	−0.727093	+	1.25936i	−0.958107	+	0.286412i	$0.907537\pi$
$264$	4.67545	−	13.2892i	0.287754	−	0.817892i
$265$	9.48274	+	16.6987i	0.582520	+	1.02579i
$266$		0			0
$267$	6.04090			0.369697
$268$	7.91831	+	5.12691i	0.483688	+	0.313176i
$269$	−0.838532	−	0.484127i	−0.0511262	−	0.0295177i	0.474219	−	0.880407i	$-0.342730\pi$
$269$	−0.838532	−	0.484127i	−0.0511262	−	0.0295177i	−0.525345	+	0.850889i	$0.676064\pi$
$270$	−2.20692	−	9.46118i	−0.134309	−	0.575789i
$271$	3.29801	+	5.71233i	0.200340	+	0.346999i	0.948638	−	0.316364i	$-0.102462\pi$
$271$	3.29801	+	5.71233i	0.200340	+	0.346999i	−0.748298	+	0.663363i	$0.769129\pi$
$272$	−11.6665	+	16.1498i	−0.707387	+	0.979226i
$273$		0			0
$274$	−4.24621	+	1.02248i	−0.256523	+	0.0617703i
$275$	0.166436	−	11.6591i	0.0100365	−	0.703067i
$276$	−25.7705	−	1.31543i	−1.55120	−	0.0791795i
$277$	−16.9631	−	9.79366i	−1.01921	−	0.588444i	−0.105338	−	0.994436i	$-0.533593\pi$
$277$	−16.9631	−	9.79366i	−1.01921	−	0.588444i	−0.913876	+	0.405993i	$0.866926\pi$
$278$	4.12223	−	3.91718i	0.247235	−	0.234937i
$279$	−10.3000			−0.616648
$280$		0			0
$281$	17.0540			1.01735			0.508677	−	0.860957i	$-0.330135\pi$
$281$	17.0540			1.01735			0.508677	+	0.860957i	$0.330135\pi$
$282$	−21.3315	+	20.2705i	−1.27027	+	1.20709i
$283$	−6.45972	−	3.72952i	−0.383991	−	0.221697i	0.295563	−	0.955323i	$-0.404493\pi$
$283$	−6.45972	−	3.72952i	−0.383991	−	0.221697i	−0.679553	+	0.733626i	$0.737826\pi$
$284$	23.8636	+	1.21809i	1.41604	+	0.0722805i
$285$	−6.22466	+	10.6059i	−0.368717	+	0.628238i
$286$	3.50102	−	0.843038i	0.207019	−	0.0498499i
$287$		0			0
$288$	8.17252	+	3.35265i	0.481570	+	0.197557i
$289$	−3.90388	−	6.76172i	−0.229640	−	0.397748i
$290$	1.72936	−	0.403391i	0.101552	−	0.0236879i
$291$	27.6377	+	15.9566i	1.62015	+	0.935395i
$292$	−16.7235	−	10.8281i	−0.978671	−	0.633666i
$293$	−14.4635			−0.844965			−0.422483	−	0.906371i	$-0.638841\pi$
$293$	−14.4635			−0.844965			−0.422483	+	0.906371i	$0.638841\pi$
$294$		0			0
$295$	−27.8462	+	15.8131i	−1.62127	+	0.920674i
$296$	14.6737	+	5.16256i	0.852892	+	0.300068i
$297$	−3.58227	+	6.20467i	−0.207864	+	0.360031i
$298$	−2.71250	−	0.801472i	−0.157131	−	0.0464280i
$299$	−3.29801	−	5.71233i	−0.190729	−	0.330352i
$300$	21.3123	+	1.39312i	1.23047	+	0.0804318i
$301$		0			0
$302$	−6.80745	+	1.63922i	−0.391725	+	0.0943266i
$303$	−16.1362	−	27.9488i	−0.927002	−	1.60561i
$304$	4.21499	+	9.39813i	0.241746	+	0.539020i
$305$	1.38646	+	0.00989553i	0.0793883	+	0.000566616i
$306$	−7.97347	+	7.57685i	−0.455813	+	0.433140i
$307$			13.8987i			0.793243i	0.917982	+	0.396622i	$0.129818\pi$
$307$			13.8987i			0.793243i	−0.917982	+	0.396622i	$0.870182\pi$
$308$		0			0
$309$	−11.6847			−0.664717
$310$	−6.05314	+	19.9608i	−0.343795	+	1.13370i
$311$	0.723002	−	1.25228i	0.0409977	−	0.0710101i	−0.844798	−	0.535085i	$-0.820280\pi$
$311$	0.723002	−	1.25228i	0.0409977	−	0.0710101i	0.885796	+	0.464075i	$0.153613\pi$
$312$	1.21526	+	6.48311i	0.0688006	+	0.367034i
$313$	−3.58227	−	6.20467i	−0.202482	−	0.350708i	0.746846	−	0.664997i	$-0.231567\pi$
$313$	−3.58227	−	6.20467i	−0.202482	−	0.350708i	−0.949327	+	0.314289i	$0.898234\pi$
$314$	−1.28751	−	5.34683i	−0.0726581	−	0.301739i
$315$		0			0
$316$	9.68466	+	18.9435i	0.544805	+	1.06565i
$317$	21.1396	−	12.2050i	1.18732	−	0.685499i	0.229623	−	0.973280i	$-0.426251\pi$
$317$	21.1396	−	12.2050i	1.18732	−	0.685499i	0.957696	+	0.287781i	$0.0929174\pi$
$318$	24.8764	+	7.35033i	1.39500	+	0.412186i
$319$	−1.13412	−	0.654784i	−0.0634985	−	0.0366609i
$320$	11.3001	−	13.8675i	0.631693	−	0.775219i
$321$			21.3873i			1.19372i
$322$		0			0
$323$	−12.8255			−0.713628
$324$	−18.8804	−	12.2246i	−1.04891	−	0.679143i
$325$	2.66197	+	4.76653i	0.147660	+	0.264399i
$326$	−15.5984	−	4.60893i	−0.863917	−	0.255265i
$327$	−8.43723	+	4.87123i	−0.466580	+	0.269380i
$328$	18.2179	−	15.6240i	1.00592	−	0.862689i
$329$		0			0
$330$	−10.7679	−	11.4948i	−0.592754	−	0.632766i
$331$	7.19296	−	4.15286i	0.395361	−	0.228262i	−0.289120	−	0.957293i	$-0.593363\pi$
$331$	7.19296	−	4.15286i	0.395361	−	0.228262i	0.684480	+	0.729031i	$0.260029\pi$
$332$	7.71193	+	0.393648i	0.423247	+	0.0216042i
$333$	7.43743	+	4.29400i	0.407569	+	0.235310i
$334$	0.656109	+	0.690453i	0.0359007	+	0.0377799i
$335$	9.17104	−	5.20798i	0.501067	−	0.284543i
$336$		0			0
$337$		−	30.5866i		−	1.66616i	−0.553153	−	0.833080i	$-0.686575\pi$
$337$		−	30.5866i		−	1.66616i	0.553153	−	0.833080i	$-0.313425\pi$
$338$	12.1050	−	11.5029i	0.658425	−	0.625673i
$339$	−5.87302	+	10.1724i	−0.318979	+	0.552488i
$340$	9.99761	+	19.9049i	0.542196	+	1.07949i
$341$	13.3214	−	7.69113i	0.721395	−	0.416498i
$342$	1.33126	+	5.52855i	0.0719866	+	0.298950i
$343$		0			0
$344$	−2.43845	−	2.84329i	−0.131472	−	0.153300i
$345$	−14.6028	+	24.8811i	−0.786191	+	1.33955i
$346$	−14.9911	−	4.42949i	−0.805928	−	0.238131i
$347$	0.662153	−	1.14688i	0.0355463	−	0.0615679i	−0.847705	−	0.530468i	$-0.822016\pi$
$347$	0.662153	−	1.14688i	0.0355463	−	0.0615679i	0.883251	+	0.468900i	$0.155350\pi$
$348$	1.30369	−	2.01350i	0.0698852	−	0.107935i
$349$			18.8307i			1.00799i	0.863708	+	0.503993i	$0.168136\pi$
$349$			18.8307i			1.00799i	−0.863708	+	0.503993i	$0.831864\pi$
$350$		0			0
$351$		−	3.35453i		−	0.179051i
$352$	−13.0733	+	1.76637i	−0.696807	+	0.0941480i
$353$	8.08427	−	14.0024i	0.430282	−	0.745270i	−0.566615	−	0.823982i	$-0.691747\pi$
$353$	8.08427	−	14.0024i	0.430282	−	0.745270i	0.996897	+	0.0787120i	$0.0250808\pi$
$354$	−12.2572	+	41.4831i	−0.651461	+	2.20480i
$355$	13.5223	−	23.0400i	0.717689	−	1.22284i
$356$	−2.57501	−	5.03680i	−0.136475	−	0.266950i
$357$		0			0
$358$	11.4196	−	2.74983i	0.603547	−	0.145333i
$359$	8.96394	−	5.17534i	0.473099	−	0.273144i	−0.244437	−	0.969665i	$-0.578603\pi$
$359$	8.96394	−	5.17534i	0.473099	−	0.273144i	0.717536	+	0.696521i	$0.245270\pi$
$360$	7.54246	−	6.37567i	0.397523	−	0.336027i
$361$	6.18466	−	10.7121i	0.325508	−	0.563797i
$362$	−3.35944	−	3.53529i	−0.176568	−	0.185811i
$363$		−	11.8782i		−	0.623446i
$364$		0			0
$365$	−19.3693	+	10.9993i	−1.01384	+	0.575730i
$366$	1.35764	−	1.29011i	0.0709651	−	0.0674351i
$367$	20.2462	+	11.6891i	1.05684	+	0.610168i	0.924557	−	0.381043i	$-0.124435\pi$
$367$	20.2462	+	11.6891i	1.05684	+	0.610168i	0.132286	+	0.991212i	$0.457768\pi$
$368$	9.88823	+	22.0477i	0.515460	+	1.14932i
$369$	11.4750	−	6.62511i	0.597366	−	0.344889i
$370$	12.6923	−	11.8898i	0.659843	−	0.618120i
$371$		0			0
$372$	12.8255	+	25.0870i	0.664969	+	1.30070i
$373$	10.1120	−	5.83817i	0.523580	−	0.302289i	−0.214818	−	0.976654i	$-0.568916\pi$
$373$	10.1120	−	5.83817i	0.523580	−	0.302289i	0.738398	+	0.674365i	$0.235582\pi$
$374$	4.65468	−	15.7533i	0.240688	−	0.814582i
$375$	12.3794	−	20.4192i	0.639268	−	1.05444i
$376$	25.9940	+	9.14532i	1.34054	+	0.471634i
$377$	0.613157			0.0315792
$378$		0			0
$379$		−	24.9171i		−	1.27991i	−0.768414	−	0.639954i	$-0.778954\pi$
$379$		−	24.9171i		−	1.27991i	0.768414	−	0.639954i	$-0.221046\pi$
$380$	11.4963	+	0.669116i	0.589750	+	0.0343249i
$381$	9.79796	+	5.65685i	0.501965	+	0.289809i
$382$	8.00108	−	27.0788i	0.409371	−	1.38547i
$383$	−16.1633	+	9.33190i	−0.825907	+	0.476838i	−0.852449	−	0.522810i	$-0.824884\pi$
$383$	−16.1633	+	9.33190i	−0.825907	+	0.476838i	0.0265422	+	0.999648i	$0.491550\pi$
$384$	−2.01051	−	24.0798i	−0.102598	−	1.22882i
$385$		0			0
$386$	−7.56155	+	1.82081i	−0.384873	+	0.0926767i
$387$	−1.03399	−	1.79092i	−0.0525605	−	0.0910375i
$388$	1.52344	−	29.8456i	0.0773408	−	1.51518i
$389$	5.96543	−	10.3324i	0.302460	−	0.523875i	−0.674233	−	0.738519i	$-0.735526\pi$
$389$	5.96543	−	10.3324i	0.302460	−	0.523875i	0.976692	+	0.214643i	$0.0688589\pi$
$390$	7.05722	+	2.14011i	0.357356	+	0.108369i
$391$	−30.0881			−1.52162
$392$		0			0
$393$			5.49966i			0.277421i
$394$	16.0729	+	16.9143i	0.809742	+	0.852129i
$395$	23.7861	+	0.169768i	1.19681	+	0.00854197i
$396$	−7.27376	−	0.371282i	−0.365520	−	0.0186576i
$397$	−10.5074	−	18.1994i	−0.527353	−	0.913402i	−0.999492	−	0.0318775i	$-0.989851\pi$
$397$	−10.5074	−	18.1994i	−0.527353	−	0.913402i	0.472139	−	0.881524i	$-0.343482\pi$
$398$	6.07263	+	25.2188i	0.304394	+	1.26410i
$399$		0			0
$400$	−7.92309	−	18.3637i	−0.396155	−	0.918184i
$401$	−6.71922	−	11.6380i	−0.335542	−	0.581176i	0.648047	−	0.761601i	$-0.275586\pi$
$401$	−6.71922	−	11.6380i	−0.335542	−	0.581176i	−0.983589	+	0.180425i	$0.942253\pi$
$402$	4.03685	−	13.6623i	0.201340	−	0.681413i
$403$	−3.60109	+	6.23726i	−0.179383	+	0.310700i
$404$	−16.4249	+	25.3676i	−0.817171	+	1.26209i
$405$	−21.8674	+	12.4179i	−1.08660	+	0.617050i
$406$		0			0
$407$	−12.8255			−0.635734
$408$	28.3827	+	9.98574i	1.40516	+	0.494368i
$409$	26.1720	+	15.1104i	1.29412	+	0.747161i	0.979382	−	0.202018i	$-0.0647499\pi$
$409$	26.1720	+	15.1104i	1.29412	+	0.747161i	0.314738	+	0.949178i	$0.398083\pi$
$410$	−6.09539	−	26.1313i	−0.301030	−	1.29053i
$411$	3.29801	+	5.71233i	0.162679	+	0.281768i
$412$	4.98074	+	9.74247i	0.245383	+	0.479977i
$413$		0			0
$414$	3.12311	+	12.9698i	0.153492	+	0.637431i
$415$	4.36996	−	7.44577i	0.214513	−	0.365498i
$416$	4.88749	−	3.77677i	0.239629	−	0.185172i
$417$	−7.43743	−	4.29400i	−0.364212	−	0.210278i
$418$	−5.84999	−	6.15621i	−0.286132	−	0.301110i
$419$	22.3631			1.09251			0.546254	−	0.837619i	$-0.316053\pi$
$419$	22.3631			1.09251			0.546254	+	0.837619i	$0.316053\pi$
$420$		0			0
$421$	12.5616			0.612213			0.306106	−	0.951997i	$-0.400974\pi$
$421$	12.5616			0.612213			0.306106	+	0.951997i	$0.400974\pi$
$422$	−0.279675	−	0.294315i	−0.0136144	−	0.0143270i
$423$	13.1752	+	7.60669i	0.640599	+	0.369850i
$424$	−4.47532	−	23.8747i	−0.217341	−	1.15946i
$425$	24.9012	+	0.355471i	1.20788	+	0.0172429i
$426$	−8.44804	−	35.0835i	−0.409309	−	1.69980i
$427$		0			0
$428$	17.8324	−	9.11662i	0.861960	−	0.440668i
$429$	−2.71922	−	4.70983i	−0.131285	−	0.227393i
$430$	−4.07834	+	0.951314i	−0.196675	+	0.0458765i
$431$	−10.0981	−	5.83012i	−0.486407	−	0.280827i	0.236676	−	0.971589i	$-0.423942\pi$
$431$	−10.0981	−	5.83012i	−0.486407	−	0.280827i	−0.723083	+	0.690762i	$0.757275\pi$
$432$	−1.25128	+	12.2250i	−0.0602023	+	0.588173i
$433$	9.00400			0.432705			0.216352	−	0.976315i	$-0.430584\pi$
$433$	9.00400			0.432705			0.216352	+	0.976315i	$0.430584\pi$
$434$		0			0
$435$	−1.32431	−	2.33205i	−0.0634957	−	0.111813i
$436$	7.65803	+	4.95839i	0.366753	+	0.237464i
$437$	−7.77769	+	13.4713i	−0.372057	+	0.644422i
$438$	−8.52587	+	28.8549i	−0.407382	+	1.37874i
$439$	15.7671	+	27.3094i	0.752521	+	1.30340i	0.946597	+	0.322418i	$0.104496\pi$
$439$	15.7671	+	27.3094i	0.752521	+	1.30340i	−0.194076	+	0.980986i	$0.562171\pi$
$440$	−4.99417	+	13.8779i	−0.238088	+	0.661603i
$441$		0			0
$442$	1.80054	+	7.47740i	0.0856431	+	0.355663i
$443$	8.77102	+	15.1919i	0.416724	+	0.721787i	0.995608	−	0.0936230i	$-0.0298448\pi$
$443$	8.77102	+	15.1919i	0.416724	+	0.721787i	−0.578884	+	0.815410i	$0.696512\pi$
$444$	1.19757	−	23.4616i	0.0568342	−	1.11344i
$445$	−6.32439	−	0.0451390i	−0.299805	−	0.00213979i
$446$	−0.143835	−	0.151364i	−0.00681076	−	0.00716728i
$447$			4.27156i			0.202038i
$448$		0			0
$449$	6.31534			0.298039			0.149020	−	0.988834i	$-0.452388\pi$
$449$	6.31534			0.298039			0.149020	+	0.988834i	$0.452388\pi$
$450$	−2.43148	−	10.7708i	−0.114621	−	0.507741i
$451$	−9.89404	+	17.1370i	−0.465892	+	0.806949i
$452$	10.9850	+	0.560719i	0.516691	+	0.0263740i
$453$	5.28732	+	9.15790i	0.248420	+	0.430276i
$454$	13.9596	−	3.36144i	0.655155	−	0.157760i
$455$		0			0
$456$	11.8078	−	10.1265i	0.552949	−	0.474218i
$457$	8.93935	−	5.16114i	0.418165	−	0.241428i	−0.276127	−	0.961121i	$-0.589051\pi$
$457$	8.93935	−	5.16114i	0.418165	−	0.241428i	0.694292	+	0.719693i	$0.255718\pi$
$458$	3.78837	−	12.8213i	0.177019	−	0.599102i
$459$	−13.2518	−	7.65093i	−0.618541	−	0.357115i
$460$	26.9701	+	1.56972i	1.25749	+	0.0731888i
$461$		−	21.1154i		−	0.983444i	−0.870752	−	0.491722i	$-0.836368\pi$
$461$		−	21.1154i		−	0.983444i	0.870752	−	0.491722i	$-0.163632\pi$
$462$		0			0
$463$	24.3266			1.13055			0.565277	−	0.824901i	$-0.308769\pi$
$463$	24.3266			1.13055			0.565277	+	0.824901i	$0.308769\pi$
$464$	−2.23454	−	0.228715i	−0.103736	−	0.0106178i
$465$	31.5002	+	0.224825i	1.46078	+	0.0104260i
$466$	4.40782	−	14.9178i	0.204188	−	0.691054i
$467$	−20.0903	+	11.5991i	−0.929668	+	0.536744i	−0.886707	−	0.462333i	$-0.847013\pi$
$467$	−20.0903	+	11.5991i	−0.929668	+	0.536744i	−0.0429615	+	0.999077i	$0.513679\pi$
$468$	3.03632	−	1.55229i	0.140354	−	0.0717545i
$469$		0			0
$470$	22.4841	−	21.0624i	1.03711	−	0.971534i
$471$	−7.19296	+	4.15286i	−0.331434	+	0.191353i
$472$	39.8127	−	7.46289i	1.83253	−	0.343507i
$473$	2.67459	+	1.54417i	0.122978	+	0.0710012i
$474$	23.2918	−	22.1332i	1.06983	−	1.01661i
$475$	6.59603	−	11.0571i	0.302646	−	0.507335i
$476$		0			0
$477$		−	13.4106i		−	0.614030i
$478$	−2.27183	−	2.39075i	−0.103911	−	0.109350i
$479$	−15.0441	+	26.0571i	−0.687381	+	1.19058i	0.285301	+	0.958438i	$0.407906\pi$
$479$	−15.0441	+	26.0571i	−0.687381	+	1.19058i	−0.972682	+	0.232141i	$0.925427\pi$
$480$	−24.9205	−	10.4317i	−1.13746	−	0.476138i
$481$	5.20053	−	3.00252i	0.237124	−	0.136903i
$482$	−22.1067	+	5.32326i	−1.00693	+	0.242468i
$483$		0			0
$484$	−9.90388	+	5.06326i	−0.450176	+	0.230148i
$485$	−28.8155	−	16.9120i	−1.30844	−	0.767934i
$486$	−5.93202	+	20.0763i	−0.269082	+	0.910679i
$487$	0.580639	−	1.00570i	0.0263112	−	0.0455724i	−0.852570	−	0.522613i	$-0.824957\pi$
$487$	0.580639	−	1.00570i	0.0263112	−	0.0455724i	0.878881	+	0.477041i	$0.158291\pi$
$488$	−1.65439	−	0.582053i	−0.0748905	−	0.0263483i
$489$			24.5639i			1.11082i
$490$		0			0
$491$		−	14.2794i		−	0.644419i	−0.946668	−	0.322210i	$-0.895574\pi$
$491$		−	14.2794i		−	0.644419i	0.946668	−	0.322210i	$-0.104426\pi$
$492$	−30.4248	−	19.6993i	−1.37165	−	0.888112i
$493$	1.39847	−	2.42223i	0.0629841	−	0.109092i
$494$	3.81329	+	1.12673i	0.171568	+	0.0506938i
$495$	−4.12168	+	7.02272i	−0.185256	+	0.315648i
$496$	15.4501	−	21.3873i	0.693729	−	0.960318i
$497$		0			0
$498$	−2.73013	−	11.3378i	−0.122340	−	0.508060i
$499$	−22.2157	+	12.8263i	−0.994513	+	0.574182i	−0.906620	−	0.421948i	$-0.861347\pi$
$499$	−22.2157	+	12.8263i	−0.994513	+	0.574182i	−0.0878928	+	0.996130i	$0.528013\pi$
$500$	−22.3021	−	1.61775i	−0.997379	−	0.0723479i
$501$	0.719224	−	1.24573i	0.0321325	−	0.0556552i
$502$	9.40189	−	8.93422i	0.419627	−	0.398754i
$503$		−	18.8114i		−	0.838761i	−0.907811	−	0.419380i	$-0.862247\pi$
$503$		−	18.8114i		−	0.838761i	0.907811	−	0.419380i	$-0.137753\pi$
$504$		0			0
$505$	16.6847	+	29.3810i	0.742458	+	1.30744i
$506$	−13.7239	−	14.4423i	−0.610101	−	0.642037i
$507$	−21.8401	−	12.6094i	−0.969953	−	0.560003i
$508$	0.540080	−	10.5807i	0.0239622	−	0.469442i
$509$	24.2595	−	14.0062i	1.07528	−	0.620814i	0.145662	−	0.989334i	$-0.453469\pi$
$509$	24.2595	−	14.0062i	1.07528	−	0.620814i	0.929620	+	0.368520i	$0.120136\pi$
$510$	24.5503	−	22.9979i	1.08710	−	1.01836i
$511$		0			0
$512$	−19.2203	+	11.9407i	−0.849426	+	0.527707i
$513$	−6.85110	+	3.95548i	−0.302483	+	0.174639i
$514$	−8.88529	−	2.62537i	−0.391913	−	0.115800i
$515$	12.2330	+	0.0873105i	0.539051	+	0.00384736i
$516$	−3.07449	+	4.74842i	−0.135347	+	0.209038i
$517$	−22.7199			−0.999220
$518$		0			0
$519$			23.6076i			1.03626i
$520$	−1.22385	−	6.79644i	−0.0536693	−	0.298044i
$521$	2.44949	+	1.41421i	0.107314	+	0.0619578i	0.552696	−	0.833383i	$-0.313599\pi$
$521$	2.44949	+	1.41421i	0.107314	+	0.0619578i	−0.445382	+	0.895340i	$0.646932\pi$
$522$	−1.18929	−	0.351403i	−0.0520537	−	0.0153805i
$523$	18.1408	−	10.4736i	0.793243	−	0.457979i	−0.0478601	−	0.998854i	$-0.515240\pi$
$523$	18.1408	−	10.4736i	0.793243	−	0.457979i	0.841103	+	0.540875i	$0.181907\pi$
$524$	4.58552	−	2.34430i	0.200319	−	0.102411i
$525$		0			0
$526$	−7.80776	−	32.4245i	−0.340435	−	1.41378i
$527$	16.4265	+	28.4516i	0.715552	+	1.23937i
$528$	8.15288	+	18.1784i	0.354808	+	0.791114i
$529$	−6.74621	+	11.6848i	−0.293314	+	0.508034i
$530$	−25.9889	−	7.88116i	−1.12889	−	0.342336i
$531$	22.3631			0.970476
$532$		0			0
$533$		−	9.26504i		−	0.401313i
$534$	−6.19296	+	5.88491i	−0.267995	+	0.254665i
$535$	0.159811	−	22.3910i	0.00690923	−	0.968048i
$536$	−13.1122	+	2.45788i	−0.566359	+	0.106164i
$537$	−8.86958	−	15.3626i	−0.382751	−	0.662944i
$538$	1.33126	−	0.320566i	0.0573949	−	0.0138206i
$539$		0			0
$540$	11.4793	+	7.54941i	0.493992	+	0.324875i
$541$	9.71922	+	16.8342i	0.417862	+	0.723758i	0.995724	−	0.0923761i	$-0.0294462\pi$
$541$	9.71922	+	16.8342i	0.417862	+	0.723758i	−0.577862	+	0.816134i	$0.696113\pi$
$542$	−8.94585	−	2.64327i	−0.384257	−	0.113538i
$543$	−3.68260	+	6.37845i	−0.158036	+	0.273726i
$544$	−3.77258	−	27.9216i	−0.161748	−	1.19713i
$545$	8.86958	−	5.03680i	0.379931	−	0.215753i
$546$		0			0
$547$	33.4337			1.42952			0.714762	−	0.699368i	$-0.246535\pi$
$547$	33.4337			1.42952			0.714762	+	0.699368i	$0.246535\pi$
$548$	3.35702	−	5.18478i	0.143405	−	0.221483i
$549$	−0.838532	−	0.484127i	−0.0357877	−	0.0206620i
$550$	11.1874	+	12.1147i	0.477031	+	0.516571i
$551$	−0.723002	−	1.25228i	−0.0308009	−	0.0533488i
$552$	27.7006	−	23.7565i	1.17902	−	1.01114i
$553$		0			0
$554$	26.9309	−	6.48490i	1.14418	−	0.275517i
$555$	−22.6518	−	13.2945i	−0.961516	−	0.564320i
$556$	−0.409964	+	8.03158i	−0.0173863	+	0.340615i
$557$	7.43743	+	4.29400i	0.315134	+	0.181943i	0.649222	−	0.760599i	$-0.275095\pi$
$557$	7.43743	+	4.29400i	0.315134	+	0.181943i	−0.334088	+	0.942542i	$0.608428\pi$
$558$	10.5593	−	10.0341i	0.447012	−	0.424776i
$559$	−1.44600			−0.0611595
$560$		0			0
$561$	−24.8078			−1.04738
$562$	−17.4833	+	16.6136i	−0.737487	+	0.700803i
$563$	−5.87645	−	3.39277i	−0.247663	−	0.142988i	0.371031	−	0.928621i	$-0.379004\pi$
$563$	−5.87645	−	3.39277i	−0.247663	−	0.142988i	−0.618694	+	0.785632i	$0.712338\pi$
$564$	2.12146	−	41.5614i	0.0893296	−	1.75005i
$565$	6.22466	−	10.6059i	0.261873	−	0.446193i
$566$	10.2555	−	2.46952i	0.431073	−	0.103801i
$567$		0			0
$568$	−25.6509	+	21.9986i	−1.07629	+	0.923042i
$569$	21.9309	+	37.9854i	0.919390	+	1.59243i	0.800344	+	0.599541i	$0.204650\pi$
$569$	21.9309	+	37.9854i	0.919390	+	1.59243i	0.119046	+	0.992889i	$0.462016\pi$
$570$	−3.95067	−	16.9368i	−0.165475	−	0.709403i
$571$	−13.5004	−	7.79447i	−0.564975	−	0.326188i	0.190165	−	0.981752i	$-0.439098\pi$
$571$	−13.5004	−	7.79447i	−0.564975	−	0.326188i	−0.755140	+	0.655564i	$0.772431\pi$
$572$	−2.76787	+	4.27487i	−0.115731	+	0.178741i
$573$	−42.6429			−1.78143
$574$		0			0
$575$	15.4741	−	25.9396i	0.645313	−	1.08176i
$576$	−11.6443	+	4.52444i	−0.485180	+	0.188518i
$577$	18.0457	−	31.2561i	0.751254	−	1.30121i	−0.195961	−	0.980612i	$-0.562783\pi$
$577$	18.0457	−	31.2561i	0.751254	−	1.30121i	0.947215	−	0.320599i	$-0.103884\pi$
$578$	10.5893	+	3.12885i	0.440456	+	0.130143i
$579$	5.87302	+	10.1724i	0.244075	+	0.422750i
$580$	−1.37992	+	2.09825i	−0.0572980	+	0.0871251i
$581$		0			0
$582$	−43.8780	+	10.5657i	−1.81880	+	0.437964i
$583$	10.0138	+	17.3444i	0.414730	+	0.718333i
$584$	27.6930	−	5.19105i	1.14594	−	0.214807i
$585$	0.0272110	−	3.81252i	0.00112504	−	0.157628i
$586$	14.8276	−	14.0900i	0.612521	−	0.582053i
$587$		−	2.80928i		−	0.115951i	−0.998318	−	0.0579757i	$-0.981535\pi$
$587$		−	2.80928i		−	0.115951i	0.998318	−	0.0579757i	$-0.0184646\pi$
$588$		0			0
$589$	16.9848			0.699848
$590$	13.1424	−	43.3383i	0.541063	−	1.78421i
$591$	17.6191	−	30.5171i	0.724752	−	1.25531i
$592$	−20.0723	+	9.00228i	−0.824968	+	0.369992i
$593$	−3.10353	−	5.37547i	−0.127447	−	0.220744i	0.795240	−	0.606295i	$-0.207345\pi$
$593$	−3.10353	−	5.37547i	−0.127447	−	0.220744i	−0.922687	+	0.385551i	$0.874011\pi$
$594$	−2.37201	−	9.85061i	−0.0973247	−	0.404176i
$595$		0			0
$596$	3.56155	−	1.82081i	0.145887	−	0.0745832i
$597$	33.9262	−	19.5873i	1.38851	−	0.801655i
$598$	8.94585	+	2.64327i	0.365823	+	0.108091i
$599$	15.5200	+	8.96050i	0.634131	+	0.366116i	0.782350	−	0.622839i	$-0.214021\pi$
$599$	15.5200	+	8.96050i	0.634131	+	0.366116i	−0.148219	+	0.988955i	$0.547354\pi$
$600$	−23.2059	+	19.3338i	−0.947378	+	0.789299i
$601$			42.2309i			1.72263i	0.508068	+	0.861317i	$0.330360\pi$
$601$			42.2309i			1.72263i	−0.508068	+	0.861317i	$0.669640\pi$
$602$		0			0
$603$	−7.36520			−0.299934
$604$	5.38192	−	8.31215i	0.218987	−	0.338217i
$605$	−0.0887570	+	12.4357i	−0.00360849	+	0.505583i
$606$	43.7695	+	12.9327i	1.77801	+	0.525357i
$607$	38.9423	−	22.4833i	1.58062	−	0.912570i	0.585848	−	0.810421i	$-0.300761\pi$
$607$	38.9423	−	22.4833i	1.58062	−	0.912570i	0.994769	−	0.102149i	$-0.0325719\pi$
$608$	−13.4765	−	5.52855i	−0.546546	−	0.224212i
$609$		0			0
$610$	−1.43100	+	1.34051i	−0.0579393	+	0.0542757i
$611$	9.21257	−	5.31888i	0.372701	−	0.215179i
$612$	0.792976	−	15.5351i	0.0320542	−	0.627971i
$613$	41.3637	+	23.8813i	1.67066	+	0.964557i	0.967268	+	0.253757i	$0.0816664\pi$
$613$	41.3637	+	23.8813i	1.67066	+	0.964557i	0.703394	+	0.710800i	$0.251667\pi$
$614$	−13.5399	−	14.2486i	−0.546424	−	0.575027i
$615$	−35.2381	+	20.0108i	−1.42094	+	0.806913i
$616$		0			0
$617$			14.7647i			0.594404i	0.954815	+	0.297202i	$0.0960535\pi$
$617$			14.7647i			0.594404i	−0.954815	+	0.297202i	$0.903946\pi$
$618$	11.9788	−	11.3829i	0.481857	−	0.457889i
$619$	−13.0336	+	22.5748i	−0.523863	+	0.907357i	0.475751	+	0.879580i	$0.342176\pi$
$619$	−13.0336	+	22.5748i	−0.523863	+	0.907357i	−0.999614	+	0.0277772i	$0.991157\pi$
$620$	−13.2399	−	26.3601i	−0.531727	−	1.05865i
$621$	−16.0725	+	9.27944i	−0.644965	+	0.372371i
$622$	0.478739	+	1.98813i	0.0191957	+	0.0797168i
$623$		0			0
$624$	−7.56155	−	5.46242i	−0.302704	−	0.218672i
$625$	−13.1129	+	21.2850i	−0.524517	+	0.851400i
$626$	9.71689	+	2.87109i	0.388365	+	0.114752i
$627$	−6.41273	+	11.1072i	−0.256100	+	0.443578i
$628$	6.52867	+	4.22716i	0.260522	+	0.168682i
$629$		−	27.3924i		−	1.09220i
$630$		0			0
$631$			33.9582i			1.35186i	0.736968	+	0.675928i	$0.236257\pi$
$631$			33.9582i			1.35186i	−0.736968	+	0.675928i	$0.763743\pi$
$632$	−28.3827	−	9.98574i	−1.12901	−	0.397211i
$633$	−0.306579	+	0.531010i	−0.0121854	+	0.0211057i
$634$	−9.78194	+	33.1059i	−0.388490	+	1.31480i
$635$	−10.2155	−	5.99554i	−0.405390	−	0.237926i
$636$	−32.6631	+	16.6987i	−1.29518	+	0.662147i
$637$		0			0
$638$	1.80054	−	0.433567i	0.0712842	−	0.0171651i
$639$	−16.1569	+	9.32819i	−0.639157	+	0.369018i
$640$	1.92493	+	25.2249i	0.0760896	+	0.997101i
$641$	−19.9309	+	34.5213i	−0.787222	+	1.36351i	0.140441	+	0.990089i	$0.455148\pi$
$641$	−19.9309	+	34.5213i	−0.787222	+	1.36351i	−0.927663	+	0.373419i	$0.878185\pi$
$642$	−20.8350	−	21.9257i	−0.822293	−	0.865337i
$643$			36.8341i			1.45260i	0.687380	+	0.726298i	$0.258761\pi$
$643$			36.8341i			1.45260i	−0.687380	+	0.726298i	$0.741239\pi$
$644$		0			0
$645$	3.12311	+	5.49966i	0.122972	+	0.216549i
$646$	13.1483	−	12.4943i	0.517313	−	0.491581i
$647$	31.6716	+	18.2856i	1.24514	+	0.718881i	0.970136	−	0.242563i	$-0.0779881\pi$
$647$	31.6716	+	18.2856i	1.24514	+	0.718881i	0.275002	+	0.961444i	$0.411321\pi$
$648$	31.2646	−	5.86055i	1.22819	−	0.230224i
$649$	−28.9230	+	16.6987i	−1.13533	+	0.655481i
$650$	−7.37243	−	2.29328i	−0.289170	−	0.0899497i
$651$		0			0
$652$	20.4810	−	10.4707i	0.802097	−	0.410064i
$653$	−14.2885	+	8.24948i	−0.559153	+	0.322827i	−0.752806	−	0.658243i	$-0.771300\pi$
$653$	−14.2885	+	8.24948i	−0.559153	+	0.322827i	0.193652	+	0.981070i	$0.437967\pi$
$654$	3.90416	−	13.2132i	0.152665	−	0.516677i
$655$	0.0410947	−	5.75775i	0.00160570	−	0.224974i
$656$	−3.45598	+	33.7647i	−0.134933	+	1.31829i
$657$	15.5554			0.606873
$658$		0			0
$659$			42.8381i			1.66874i	0.551207	+	0.834368i	$0.314167\pi$
$659$			42.8381i			1.66874i	−0.551207	+	0.834368i	$0.685833\pi$
$660$	22.2369	+	1.29424i	0.865571	+	0.0503783i
$661$	1.30941	+	0.755989i	0.0509302	+	0.0294046i	0.525249	−	0.850949i	$-0.323972\pi$
$661$	1.30941	+	0.755989i	0.0509302	+	0.0294046i	−0.474319	+	0.880353i	$0.657306\pi$
$662$	−3.32840	+	11.2646i	−0.129362	+	0.437812i
$663$	10.0592	−	5.80766i	0.390666	−	0.225551i
$664$	−8.28954	+	7.10923i	−0.321696	+	0.275892i
$665$		0			0
$666$	−11.8078	+	2.84329i	−0.457542	+	0.110175i
$667$	−1.69614	−	2.93780i	−0.0656748	−	0.113752i
$668$	−1.34525	−	0.0686668i	−0.0520492	−	0.00265680i
$669$	−0.157671	+	0.273094i	−0.00609590	+	0.0105584i
$670$	−4.32839	+	14.2733i	−0.167220	+	0.551426i
$671$	1.44600			0.0558224
$672$		0			0
$673$		−	14.0877i		−	0.543039i	−0.962433	−	0.271520i	$-0.912474\pi$
$673$		−	14.0877i		−	0.543039i	0.962433	−	0.271520i	$-0.0875262\pi$
$674$	29.7968	+	31.3566i	1.14773	+	1.20781i
$675$	13.4113	−	7.48985i	0.516202	−	0.288284i
$676$	−1.20386	+	23.5848i	−0.0463024	+	0.907109i
$677$	23.2659	+	40.2976i	0.894179	+	1.54876i	0.834817	+	0.550528i	$0.185573\pi$
$677$	23.2659	+	40.2976i	0.894179	+	1.54876i	0.0593624	+	0.998236i	$0.481093\pi$
$678$	−3.88884	−	16.1498i	−0.149350	−	0.620230i
$679$		0			0
$680$	−29.6401	−	10.6664i	−1.13665	−	0.409040i
$681$	−10.8423	−	18.7795i	−0.415479	−	0.719631i
$682$	−6.16422	+	20.8622i	−0.236040	+	0.798853i
$683$	10.0953	−	17.4856i	0.386287	−	0.669069i	−0.605660	−	0.795724i	$-0.707091\pi$
$683$	10.0953	−	17.4856i	0.386287	−	0.669069i	0.991947	+	0.126655i	$0.0404241\pi$
$684$	−6.75057	−	4.37083i	−0.258114	−	0.167123i
$685$	−3.41011	−	6.00505i	−0.130293	−	0.229441i
$686$		0			0
$687$	−20.1907			−0.770322
$688$	5.26970	+	0.539378i	0.200905	+	0.0205636i
$689$	−8.12090	−	4.68860i	−0.309381	−	0.178621i
$690$	−9.26815	−	39.7331i	−0.352833	−	1.51261i
$691$	−18.9066	−	32.7472i	−0.719240	−	1.24576i	−0.961301	−	0.275500i	$-0.911157\pi$
$691$	−18.9066	−	32.7472i	−0.719240	−	1.24576i	0.242061	−	0.970261i	$-0.422177\pi$
$692$	19.6836	−	10.0630i	0.748258	−	0.382539i
$693$		0			0
$694$	0.438447	+	1.82081i	0.0166432	+	0.0691169i
$695$	7.75438	+	4.55109i	0.294140	+	0.172633i
$696$	0.624998	+	3.33421i	0.0236905	+	0.126383i
$697$	−36.6008	−	21.1315i	−1.38635	−	0.800412i
$698$	−18.3445	−	19.3047i	−0.694349	−	0.730695i
$699$	−23.4921			−0.888553
$700$		0			0
$701$	−30.6695			−1.15837			−0.579186	−	0.815196i	$-0.696629\pi$
$701$	−30.6695			−1.15837			−0.579186	+	0.815196i	$0.696629\pi$
$702$	3.26791	+	3.43897i	0.123339	+	0.129795i
$703$	−12.2644	−	7.08084i	−0.462559	−	0.267059i
$704$	11.6816	−	14.5465i	0.440266	−	0.548243i
$705$	−40.1270	−	23.5508i	−1.51127	−	0.886974i
$706$	5.35302	+	22.2303i	0.201464	+	0.836650i
$707$		0			0
$708$	−27.8462	−	54.4679i	−1.04652	−	2.04703i
$709$	−15.4039	−	26.6803i	−0.578505	−	1.00200i	−0.995651	−	0.0931605i	$-0.970303\pi$
$709$	−15.4039	−	26.6803i	−0.578505	−	1.00200i	0.417146	−	0.908839i	$-0.363030\pi$
$710$	8.58235	+	36.7931i	0.322090	+	1.38082i
$711$	−14.3859	−	8.30571i	−0.539514	−	0.311489i
$712$	7.54656	+	2.65506i	0.282819	+	0.0995027i
$713$	39.8459			1.49224
$714$		0			0
$715$	2.81164	+	4.95118i	0.105150	+	0.185164i
$716$	−9.02827	+	13.9438i	−0.337402	+	0.521104i
$717$	−2.49037	+	4.31345i	−0.0930046	+	0.161089i
$718$	−4.14789	+	14.0381i	−0.154798	+	0.523897i
$719$	13.5981	+	23.5525i	0.507122	+	0.878361i	0.999966	+	0.00824342i	$0.00262399\pi$
$719$	13.5981	+	23.5525i	0.507122	+	0.878361i	−0.492844	+	0.870118i	$0.664043\pi$
$720$	−1.52128	+	13.8839i	−0.0566948	+	0.517421i
$721$		0			0
$722$	4.09519	+	17.0067i	0.152407	+	0.632926i
$723$	17.1702	+	29.7397i	0.638567	+	1.10603i
$724$	6.88800	+	0.351591i	0.255991	+	0.0130668i
$725$	1.36903	+	2.45139i	0.0508445	+	0.0910422i
$726$	11.5715	+	12.1772i	0.429460	+	0.451940i
$727$		−	32.8255i		−	1.21743i	−0.793389	−	0.608715i	$-0.791685\pi$
$727$		−	32.8255i		−	1.21743i	0.793389	−	0.608715i	$-0.208315\pi$
$728$		0			0
$729$	−2.12311			−0.0786335
$730$	9.14160	−	30.1453i	0.338346	−	1.11573i
$731$	−3.29801	+	5.71233i	−0.121981	+	0.211278i
$732$	−0.135020	+	2.64517i	−0.00499048	+	0.0977683i
$733$	−12.2125	−	21.1526i	−0.451078	−	0.781290i	0.547375	−	0.836887i	$-0.315627\pi$
$733$	−12.2125	−	21.1526i	−0.451078	−	0.781290i	−0.998453	+	0.0555970i	$0.982294\pi$
$734$	−32.1431	+	7.74001i	−1.18642	+	0.285689i
$735$		0			0
$736$	−31.6155	−	12.9698i	−1.16536	−	0.478073i
$737$	9.52568	−	5.49966i	0.350883	−	0.202582i
$738$	−5.30984	+	17.9706i	−0.195458	+	0.661506i
$739$	42.9091	+	24.7736i	1.57844	+	0.911311i	0.995078	+	0.0990973i	$0.0315955\pi$
$739$	42.9091	+	24.7736i	1.57844	+	0.911311i	0.583360	+	0.812214i	$0.301738\pi$
$740$	−1.42908	+	24.5537i	−0.0525341	+	0.902610i
$741$		−	6.00505i		−	0.220601i
$742$		0			0
$743$	9.43318			0.346070			0.173035	−	0.984916i	$-0.444643\pi$
$743$	9.43318			0.346070			0.173035	+	0.984916i	$0.444643\pi$
$744$	−37.5875	−	13.2242i	−1.37802	−	0.484822i
$745$	0.0319181	−	4.47202i	0.00116939	−	0.163842i
$746$	−4.67913	+	15.8360i	−0.171315	+	0.579798i
$747$	−5.22138	+	3.01457i	−0.191040	+	0.110297i
$748$	10.5746	+	20.6843i	0.386647	+	0.756293i
$749$		0			0
$750$	7.20097	+	32.9929i	0.262942	+	1.20473i
$751$	32.5624	−	18.7999i	1.18822	−	0.686019i	0.230318	−	0.973115i	$-0.426023\pi$
$751$	32.5624	−	18.7999i	1.18822	−	0.686019i	0.957902	+	0.287096i	$0.0926900\pi$
$752$	−35.5575	+	15.9473i	−1.29665	+	0.581537i
$753$	−16.9631	−	9.79366i	−0.618170	−	0.356901i
$754$	−0.628591	+	0.597324i	−0.0228919	+	0.0217533i
$755$	−5.46702	−	9.62719i	−0.198965	−	0.350369i
$756$		0			0
$757$		−	25.7640i		−	0.936409i	−0.883620	−	0.468204i	$-0.844901\pi$
$757$		−	25.7640i		−	0.936409i	0.883620	−	0.468204i	$-0.155099\pi$
$758$	24.2737	+	25.5443i	0.881661	+	0.927813i
$759$	−15.0441	+	26.0571i	−0.546065	+	0.945812i
$760$	−12.4376	+	10.5135i	−0.451158	+	0.381366i
$761$	37.3454	−	21.5614i	1.35377	−	0.781600i	0.364996	−	0.931009i	$-0.381070\pi$
$761$	37.3454	−	21.5614i	1.35377	−	0.781600i	0.988775	+	0.149409i	$0.0477372\pi$
$762$	−15.5554	+	3.74571i	−0.563512	+	0.135693i
$763$		0			0
$764$	18.1771	+	35.5549i	0.657624	+	1.28633i
$765$	−14.9990	−	8.80299i	−0.542289	−	0.318273i
$766$	7.47926	−	25.3127i	0.270236	−	0.914587i
$767$	7.81855	−	13.5421i	0.282312	−	0.488978i
$768$	25.5191	+	22.7273i	0.920842	+	0.820102i
$769$			14.4903i			0.522535i	0.965266	+	0.261267i	$0.0841404\pi$
$769$			14.4903i			0.522535i	−0.965266	+	0.261267i	$0.915860\pi$
$770$		0			0
$771$			13.9923i			0.503920i
$772$	5.97810	−	9.23294i	0.215157	−	0.332301i
$773$	−7.84490	+	13.5878i	−0.282161	+	0.488718i	−0.971917	−	0.235325i	$-0.924385\pi$
$773$	−7.84490	+	13.5878i	−0.282161	+	0.488718i	0.689756	+	0.724042i	$0.257718\pi$
$774$	2.80469	+	0.828712i	0.100812	+	0.0297874i
$775$	−32.9768	−	0.470753i	−1.18456	−	0.0169099i
$776$	27.5131	+	32.0810i	0.987663	+	1.15164i
$777$		0			0
$778$	3.95003	+	16.4039i	0.141616	+	0.588109i
$779$	−18.9224	+	10.9248i	−0.677965	+	0.391423i
$780$	−9.31971	+	4.68101i	−0.333699	+	0.167607i
$781$	13.9309	−	24.1290i	0.498486	−	0.863403i
$782$	30.8455	−	29.3112i	1.10303	−	1.04817i
$783$		−	1.72521i		−	0.0616538i
$784$		0			0
$785$	7.56155	−	4.29400i	0.269883	−	0.153259i
$786$	−5.35764	−	5.63809i	−0.191101	−	0.201104i
$787$	−28.4557	−	16.4289i	−1.01434	−	0.585628i	−0.101878	−	0.994797i	$-0.532485\pi$
$787$	−28.4557	−	16.4289i	−1.01434	−	0.585628i	−0.912459	+	0.409169i	$0.865819\pi$
$788$	−32.9550	−	1.68216i	−1.17397	−	0.0599243i
$789$	−43.6199	+	25.1840i	−1.55291	+	0.896573i
$790$	−24.5503	+	22.9979i	−0.873460	+	0.818228i
$791$		0			0
$792$	7.81855	−	6.70531i	0.277820	−	0.238263i
$793$	−0.586333	+	0.338519i	−0.0208213	+	0.0120212i
$794$	28.5014	+	8.42141i	1.01148	+	0.298865i
$795$	−0.292722	+	41.0131i	−0.0103818	+	1.45458i
$796$	−30.7931	−	19.9378i	−1.09143	−	0.706675i
$797$	2.04937			0.0725925			0.0362963	−	0.999341i	$-0.488444\pi$
$797$	2.04937			0.0725925			0.0362963	+	0.999341i	$0.488444\pi$
$798$		0			0
$799$		−	48.5247i		−	1.71668i
$800$	26.0120	+	11.1074i	0.919664	+	0.392707i
$801$	3.82501	+	2.20837i	0.135150	+	0.0780289i
$802$	18.2259	+	5.38527i	0.643578	+	0.190161i
$803$	−20.1183	+	11.6153i	−0.709960	+	0.409896i
$804$	9.17104	+	17.9388i	0.323438	+	0.632653i
$805$		0			0
$806$	−2.38447	−	9.90237i	−0.0839894	−	0.348796i
$807$	−1.03399	−	1.79092i	−0.0363981	−	0.0630433i
$808$	−7.87422	−	42.0070i	−0.277014	−	1.47780i
$809$	13.5270	−	23.4294i	0.475584	−	0.823735i	−0.524025	−	0.851703i	$-0.675570\pi$
$809$	13.5270	−	23.4294i	0.475584	−	0.823735i	0.999609	+	0.0279678i	$0.00890360\pi$
$810$	10.3206	−	34.0332i	0.362629	−	1.19580i
$811$	9.17104			0.322039			0.161019	−	0.986951i	$-0.448522\pi$
$811$	9.17104			0.322039			0.161019	+	0.986951i	$0.448522\pi$
$812$		0			0
$813$			14.0877i			0.494076i
$814$	13.1483	−	12.4943i	0.460848	−	0.437924i
$815$	0.183547	−	25.7167i	0.00642938	−	0.900817i
$816$	−38.8251	+	17.4127i	−1.35915	+	0.609568i
$817$	1.70505	+	2.95324i	0.0596522	+	0.103321i
$818$	−41.5510	+	10.0054i	−1.45280	+	0.349830i
$819$		0			0
$820$	31.7054	+	20.8511i	1.10720	+	0.728152i
$821$	17.9654	+	31.1170i	0.626998	+	1.08599i	0.988151	+	0.153486i	$0.0490499\pi$
$821$	17.9654	+	31.1170i	0.626998	+	1.08599i	−0.361153	+	0.932507i	$0.617617\pi$
$822$	−8.94585	−	2.64327i	−0.312022	−	0.0921945i
$823$	−11.4196	+	19.7794i	−0.398064	+	0.689466i	−0.993487	−	0.113946i	$-0.963651\pi$
$823$	−11.4196	+	19.7794i	−0.398064	+	0.689466i	0.595423	+	0.803412i	$0.296984\pi$
$824$	−14.5970	−	5.13558i	−0.508511	−	0.178906i
$825$	12.7584	−	21.3873i	0.444191	−	0.744610i
$826$		0			0
$827$	4.71659			0.164012			0.0820059	−	0.996632i	$-0.473867\pi$
$827$	4.71659			0.164012			0.0820059	+	0.996632i	$0.473867\pi$
$828$	−15.8366	−	10.2538i	−0.550361	−	0.356345i
$829$	−37.5809	−	21.6973i	−1.30524	−	0.753579i	−0.323940	−	0.946077i	$-0.605008\pi$
$829$	−37.5809	−	21.6973i	−1.30524	−	0.753579i	−0.981297	+	0.192498i	$0.938341\pi$
$830$	2.77353	+	11.8903i	0.0962708	+	0.412719i
$831$	−20.9171	−	36.2295i	−0.725606	−	1.25679i
$832$	−1.33126	+	8.63312i	−0.0461533	+	0.299300i
$833$		0			0
$834$	11.8078	−	2.84329i	0.408869	−	0.0984550i
$835$	−0.762285	+	1.29882i	−0.0263800	+	0.0449475i
$836$	11.9945	+	0.612246i	0.414838	+	0.0211750i
$837$	17.5494	+	10.1322i	0.606598	+	0.350219i
$838$	−22.9260	+	21.7856i	−0.791966	+	0.752572i
$839$	32.3461			1.11671			0.558356	−	0.829601i	$-0.311432\pi$
$839$	32.3461			1.11671			0.558356	+	0.829601i	$0.311432\pi$
$840$		0			0
$841$	−28.6847			−0.989126
$842$	−12.8778	+	12.2372i	−0.443797	+	0.421721i
$843$	31.5437	+	18.2118i	1.08642	+	0.627246i
$844$	0.573430	+	0.0292701i	0.0197383	+	0.00100752i
$845$	22.7708	+	13.3643i	0.783341	+	0.459747i
$846$	−20.9171	+	5.03680i	−0.719144	+	0.173169i
$847$		0			0
$848$	27.8462	+	20.1159i	0.956242	+	0.690784i
$849$	−7.96543	−	13.7965i	−0.273373	−	0.473496i
$850$	−25.8743	+	23.8937i	−0.887480	+	0.819548i
$851$	−28.7718	−	16.6114i	−0.986286	−	0.569432i
$852$	42.8382	+	27.7367i	1.46761	+	0.950244i
$853$	−2.93137			−0.100368			−0.0501840	−	0.998740i	$-0.515981\pi$
$853$	−2.93137			−0.100368			−0.0501840	+	0.998740i	$0.515981\pi$
$854$		0			0
$855$	−7.81855	+	4.43994i	−0.267389	+	0.151843i
$856$	−9.40004	+	26.7180i	−0.321287	+	0.913202i
$857$	−2.79695	+	4.84446i	−0.0955419	+	0.165483i	−0.909835	−	0.414971i	$-0.863792\pi$
$857$	−2.79695	+	4.84446i	−0.0955419	+	0.165483i	0.814293	+	0.580454i	$0.197125\pi$
$858$	7.37589	+	2.17938i	0.251809	+	0.0744029i
$859$	4.58552	+	7.94235i	0.156456	+	0.270990i	0.933588	−	0.358348i	$-0.116660\pi$
$859$	4.58552	+	7.94235i	0.156456	+	0.270990i	−0.777132	+	0.629337i	$0.783326\pi$
$860$	3.25425	−	4.94829i	0.110969	−	0.168735i
$861$		0			0
$862$	16.0318	−	3.86043i	0.546046	−	0.131487i
$863$	−15.3926	−	26.6607i	−0.523969	−	0.907541i	−0.999611	−	0.0279016i	$-0.991118\pi$
$863$	−15.3926	−	26.6607i	−0.523969	−	0.907541i	0.475642	−	0.879639i	$-0.342216\pi$
$864$	−10.6265	−	13.7516i	−0.361521	−	0.467841i
$865$	0.176401	−	24.7155i	0.00599782	−	0.840351i
$866$	−9.23065	+	8.77150i	−0.313670	+	0.298068i
$867$		−	16.6757i		−	0.566335i
$868$		0			0
$869$	24.8078			0.841546
$870$	3.62947	+	1.10064i	0.123051	+	0.0373152i
$871$	−2.57501	+	4.46005i	−0.0872509	+	0.151123i
$872$	−12.6812	+	2.37708i	−0.429438	+	0.0804982i
$873$	11.6665	+	20.2070i	0.394852	+	0.683904i
$874$	−5.15002	−	21.3873i	−0.174202	−	0.723436i
$875$		0			0
$876$	−19.3693	−	37.8869i	−0.654429	−	1.28008i
$877$	−4.76284	+	2.74983i	−0.160830	+	0.0928551i	−0.578255	−	0.815856i	$-0.696266\pi$
$877$	−4.76284	+	2.74983i	−0.160830	+	0.0928551i	0.417425	+	0.908711i	$0.362933\pi$
$878$	−42.7681	−	12.6369i	−1.44335	−	0.426474i
$879$	−26.7522	−	15.4454i	−0.902330	−	0.520960i
$880$	−8.39966	−	19.0924i	−0.283152	−	0.643606i
$881$		−	30.7645i		−	1.03648i	−0.855234	−	0.518241i	$-0.826587\pi$
$881$		−	30.7645i		−	1.03648i	0.855234	−	0.518241i	$-0.173413\pi$
$882$		0			0
$883$	−48.4902			−1.63183			−0.815913	−	0.578175i	$-0.803765\pi$
$883$	−48.4902			−1.63183			−0.815913	+	0.578175i	$0.803765\pi$
$884$	−9.13018	−	5.91157i	−0.307081	−	0.198828i
$885$	−68.3920	−	0.488133i	−2.29897	−	0.0164084i
$886$	−23.7914	−	7.02973i	−0.799287	−	0.236168i
$887$	27.5169	−	15.8869i	0.923927	−	0.533429i	0.0390409	−	0.999238i	$-0.487570\pi$
$887$	27.5169	−	15.8869i	0.923927	−	0.533429i	0.884886	+	0.465808i	$0.154236\pi$
$888$	21.6280	+	25.2188i	0.725788	+	0.846287i
$889$		0			0
$890$	6.52757	−	6.11481i	0.218804	−	0.204969i
$891$	−22.7130	+	13.1134i	−0.760914	+	0.439314i
$892$	0.294910	+	0.0150534i	0.00987432	+	0.000504025i
$893$	−21.7260	−	12.5435i	−0.727031	−	0.419752i
$894$	−4.16126	−	4.37908i	−0.139173	−	0.146458i
$895$	9.17104	+	16.1498i	0.306554	+	0.539829i
$896$		0			0
$897$		−	14.0877i		−	0.470373i
$898$	−6.47431	+	6.15227i	−0.216051	+	0.205304i
$899$	−1.85201	+	3.20777i	−0.0617680	+	0.106985i
$900$	12.9854	+	8.67324i	0.432845	+	0.289108i
$901$	−37.0439	+	21.3873i	−1.23411	+	0.712514i
$902$	−6.55137	−	27.2069i	−0.218137	−	0.905891i
$903$		0			0
$904$	−11.8078	+	10.1265i	−0.392720	+	0.336803i
$905$	3.90309	−	6.65028i	0.129743	−	0.221063i
$906$	−14.3418	−	4.23764i	−0.476476	−	0.140786i
$907$	26.8937	−	46.5813i	0.892991	−	1.54671i	0.0567196	−	0.998390i	$-0.481936\pi$
$907$	26.8937	−	46.5813i	0.892991	−	1.54671i	0.836271	−	0.548316i	$-0.184731\pi$
$908$	−11.0363	+	17.0451i	−0.366253	+	0.565663i
$909$		−	23.5957i		−	0.782619i
$910$		0			0
$911$		−	56.0950i		−	1.85851i	−0.369438	−	0.929255i	$-0.620450\pi$
$911$		−	56.0950i		−	1.85851i	0.369438	−	0.929255i	$-0.379550\pi$
$912$	−2.23996	+	21.8843i	−0.0741724	+	0.724661i
$913$	4.50200	−	7.79769i	0.148994	−	0.258066i
$914$	−4.13651	+	13.9996i	−0.136823	+	0.463065i
$915$	2.55388	+	1.49889i	0.0844286	+	0.0495516i
$916$	8.60654	+	16.8346i	0.284368	+	0.556232i
$917$		0			0
$918$	21.0387	−	5.06609i	0.694382	−	0.167206i
$919$	33.9452	−	19.5983i	1.11975	−	0.646487i	0.178411	−	0.983956i	$-0.442904\pi$
$919$	33.9452	−	19.5983i	1.11975	−	0.646487i	0.941337	+	0.337469i	$0.109571\pi$
$920$	−29.1781	+	24.6644i	−0.961975	+	0.813161i
$921$	−14.8423	+	25.7077i	−0.489071	+	0.847096i
$922$	20.5702	+	21.6470i	0.677443	+	0.712905i
$923$			13.0452i			0.429389i
$924$		0			0
$925$	23.6155	+	14.0877i	0.776474	+	0.463199i
$926$	−24.9390	+	23.6984i	−0.819545	+	0.778779i
$927$	−7.39856	−	4.27156i	−0.243000	−	0.140296i
$928$	2.51359	−	1.94236i	0.0825128	−	0.0637612i
$929$	25.0980	−	14.4903i	0.823438	−	0.475412i	−0.0281624	−	0.999603i	$-0.508966\pi$
$929$	25.0980	−	14.4903i	0.823438	−	0.475412i	0.851601	+	0.524191i	$0.175632\pi$
$930$	−32.5121	+	30.4563i	−1.06611	+	0.998700i
$931$		0			0
$932$	10.0138	+	19.5873i	0.328013	+	0.641604i
$933$	2.67459	−	1.54417i	0.0875620	−	0.0505540i
$934$	9.29639	−	31.4626i	0.304187	−	1.02949i
$935$	25.9720	+	0.185369i	0.849375	+	0.00606223i
$936$	−1.60054	+	4.54927i	−0.0523154	+	0.148698i
$937$	49.4631			1.61589			0.807944	−	0.589259i	$-0.200580\pi$
$937$	49.4631			1.61589			0.807944	+	0.589259i	$0.200580\pi$
$938$		0			0
$939$		−	15.3019i		−	0.499357i
$940$	−2.53158	+	43.4960i	−0.0825709	+	1.41868i
$941$	−7.58391	−	4.37857i	−0.247228	−	0.142737i	0.371266	−	0.928527i	$-0.378924\pi$
$941$	−7.58391	−	4.37857i	−0.247228	−	0.142737i	−0.618494	+	0.785789i	$0.712257\pi$
$942$	3.32840	−	11.2646i	0.108445	−	0.367021i
$943$	−44.3913	+	25.6294i	−1.44558	+	0.834606i
$944$	−33.5446	+	46.4354i	−1.09179	+	1.51134i
$945$		0			0
$946$	−4.24621	+	1.02248i	−0.138056	+	0.0332437i
$947$	−26.3131	−	45.5756i	−0.855060	−	1.48101i	−0.876589	−	0.481239i	$-0.840187\pi$
$947$	−26.3131	−	45.5756i	−0.855060	−	1.48101i	0.0215294	−	0.999768i	$-0.493146\pi$
$948$	−2.31641	+	45.3807i	−0.0752336	+	1.47390i
$949$	5.43845	−	9.41967i	0.176539	−	0.305775i
$950$	4.00952	+	17.7611i	0.130086	+	0.576247i
$951$	52.1342			1.69057
$952$		0			0
$953$			31.2637i			1.01273i	0.862319	+	0.506365i	$0.169011\pi$
$953$			31.2637i			1.01273i	−0.862319	+	0.506365i	$0.830989\pi$
$954$	13.0643	+	13.7482i	0.422973	+	0.445114i
$955$	44.6441	+	0.318637i	1.44465	+	0.0103109i
$956$	4.65803	+	0.237764i	0.150652	+	0.00768985i
$957$	−1.39847	−	2.42223i	−0.0452062	−	0.0782995i
$958$	−9.96148	−	41.3686i	−0.321841	−	1.33656i
$959$		0			0
$960$	35.7100	−	13.5827i	1.15254	−	0.438380i
$961$	−6.25379	−	10.8319i	−0.201735	−	0.349415i
$962$	−2.40644	+	8.14434i	−0.0775867	+	0.262584i
$963$	−7.81855	+	13.5421i	−0.251949	+	0.436389i
$964$	17.4774	−	26.9932i	0.562910	−	0.869391i
$965$	−6.07263	−	10.6937i	−0.195485	−	0.344241i
$966$		0			0
$967$	16.2177			0.521527			0.260764	−	0.965403i	$-0.416026\pi$
$967$	16.2177			0.521527			0.260764	+	0.965403i	$0.416026\pi$
$968$	5.22067	−	14.8389i	0.167799	−	0.476939i
$969$	−23.7225	−	13.6962i	−0.762076	−	0.439985i
$970$	46.0161	−	10.7337i	1.47749	−	0.344639i
$971$	18.1836	+	31.4949i	0.583539	+	1.01072i	0.995056	+	0.0993168i	$0.0316657\pi$
$971$	18.1836	+	31.4949i	0.583539	+	1.01072i	−0.411517	+	0.911402i	$0.635001\pi$
$972$	−13.4765	−	26.3605i	−0.432260	−	0.845513i
$973$		0			0
$974$	0.384472	+	1.59666i	0.0123193	+	0.0511602i
$975$	−0.166436	+	11.6591i	−0.00533023	+	0.373388i
$976$	2.26305	−	1.01496i	0.0724385	−	0.0324881i
$977$	12.2003	+	7.04383i	0.390321	+	0.225352i	0.682299	−	0.731073i	$-0.260980\pi$
$977$	12.2003	+	7.04383i	0.390321	+	0.225352i	−0.291978	+	0.956425i	$0.594313\pi$
$978$	−23.9296	−	25.1822i	−0.765185	−	0.805239i
$979$	−6.59603			−0.210810
$980$		0			0
$981$	−7.12311			−0.227423
$982$	13.9107	+	14.6388i	0.443907	+	0.467143i
$983$	−38.7426	−	22.3680i	−1.23570	−	0.713430i	−0.267485	−	0.963562i	$-0.586193\pi$
$983$	−38.7426	−	22.3680i	−1.23570	−	0.713430i	−0.968212	+	0.250132i	$0.919526\pi$
$984$	50.3812	−	9.44397i	1.60609	−	0.301063i
$985$	−18.6740	+	31.8176i	−0.595002	+	1.01379i
$986$	0.926004	+	3.84556i	0.0294900	+	0.122468i
$987$		0			0
$988$	−5.00691	+	2.55973i	−0.159291	+	0.0814359i
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$	−2.61595	−	11.2147i	−0.0831404	−	0.356428i
$991$	−0.497251	−	0.287088i	−0.0157957	−	0.00911966i	0.492081	−	0.870549i	$-0.336236\pi$
$991$	−0.497251	−	0.287088i	−0.0157957	−	0.00911966i	−0.507877	+	0.861430i	$0.669570\pi$
$992$	4.99606	+	36.9768i	0.158625	+	1.17401i
$993$	17.7392			0.562935
$994$		0			0
$995$	−35.6647	+	20.2530i	−1.13065	+	0.642065i
$996$	13.8439	+	8.96360i	0.438661	+	0.284022i
$997$	−23.8790	+	41.3597i	−0.756256	+	1.30987i	0.188492	+	0.982075i	$0.439640\pi$
$997$	−23.8790	+	41.3597i	−0.756256	+	1.30987i	−0.944748	+	0.327799i	$0.893693\pi$
$998$	10.2799	−	34.7912i	0.325404	−	1.10130i
$999$	−8.44804	−	14.6324i	−0.267284	−	0.462950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.f.619.6		32
4.3	odd	2	inner	980.2.s.f.619.1		32
5.4	even	2	inner	980.2.s.f.619.11		32
7.2	even	3	inner	980.2.s.f.19.15		32
7.3	odd	6		140.2.c.b.139.6	yes	16
7.4	even	3		140.2.c.b.139.5	✓	16
7.5	odd	6	inner	980.2.s.f.19.16		32
7.6	odd	2	inner	980.2.s.f.619.5		32
20.19	odd	2	inner	980.2.s.f.619.16		32
28.3	even	6		140.2.c.b.139.9	yes	16
28.11	odd	6		140.2.c.b.139.10	yes	16
28.19	even	6	inner	980.2.s.f.19.11		32
28.23	odd	6	inner	980.2.s.f.19.12		32
28.27	even	2	inner	980.2.s.f.619.2		32
35.3	even	12		700.2.g.l.251.3		16
35.4	even	6		140.2.c.b.139.12	yes	16
35.9	even	6	inner	980.2.s.f.19.2		32
35.17	even	12		700.2.g.l.251.14		16
35.18	odd	12		700.2.g.l.251.4		16
35.19	odd	6	inner	980.2.s.f.19.1		32
35.24	odd	6		140.2.c.b.139.11	yes	16
35.32	odd	12		700.2.g.l.251.13		16
35.34	odd	2	inner	980.2.s.f.619.12		32
56.3	even	6		2240.2.e.f.2239.15		16
56.11	odd	6		2240.2.e.f.2239.2		16
56.45	odd	6		2240.2.e.f.2239.3		16
56.53	even	6		2240.2.e.f.2239.14		16
140.3	odd	12		700.2.g.l.251.2		16
140.19	even	6	inner	980.2.s.f.19.6		32
140.39	odd	6		140.2.c.b.139.7	yes	16
140.59	even	6		140.2.c.b.139.8	yes	16
140.67	even	12		700.2.g.l.251.16		16
140.79	odd	6	inner	980.2.s.f.19.5		32
140.87	odd	12		700.2.g.l.251.15		16
140.123	even	12		700.2.g.l.251.1		16
140.139	even	2	inner	980.2.s.f.619.15		32
280.59	even	6		2240.2.e.f.2239.1		16
280.109	even	6		2240.2.e.f.2239.4		16
280.179	odd	6		2240.2.e.f.2239.16		16
280.269	odd	6		2240.2.e.f.2239.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.5	✓	16	7.4	even	3
140.2.c.b.139.6	yes	16	7.3	odd	6
140.2.c.b.139.7	yes	16	140.39	odd	6
140.2.c.b.139.8	yes	16	140.59	even	6
140.2.c.b.139.9	yes	16	28.3	even	6
140.2.c.b.139.10	yes	16	28.11	odd	6
140.2.c.b.139.11	yes	16	35.24	odd	6
140.2.c.b.139.12	yes	16	35.4	even	6
700.2.g.l.251.1		16	140.123	even	12
700.2.g.l.251.2		16	140.3	odd	12
700.2.g.l.251.3		16	35.3	even	12
700.2.g.l.251.4		16	35.18	odd	12
700.2.g.l.251.13		16	35.32	odd	12
700.2.g.l.251.14		16	35.17	even	12
700.2.g.l.251.15		16	140.87	odd	12
700.2.g.l.251.16		16	140.67	even	12
980.2.s.f.19.1		32	35.19	odd	6	inner
980.2.s.f.19.2		32	35.9	even	6	inner
980.2.s.f.19.5		32	140.79	odd	6	inner
980.2.s.f.19.6		32	140.19	even	6	inner
980.2.s.f.19.11		32	28.19	even	6	inner
980.2.s.f.19.12		32	28.23	odd	6	inner
980.2.s.f.19.15		32	7.2	even	3	inner
980.2.s.f.19.16		32	7.5	odd	6	inner
980.2.s.f.619.1		32	4.3	odd	2	inner
980.2.s.f.619.2		32	28.27	even	2	inner
980.2.s.f.619.5		32	7.6	odd	2	inner
980.2.s.f.619.6		32	1.1	even	1	trivial
980.2.s.f.619.11		32	5.4	even	2	inner
980.2.s.f.619.12		32	35.34	odd	2	inner
980.2.s.f.619.15		32	140.139	even	2	inner
980.2.s.f.619.16		32	20.19	odd	2	inner
2240.2.e.f.2239.1		16	280.59	even	6
2240.2.e.f.2239.2		16	56.11	odd	6
2240.2.e.f.2239.3		16	56.45	odd	6
2240.2.e.f.2239.4		16	280.109	even	6
2240.2.e.f.2239.13		16	280.269	odd	6
2240.2.e.f.2239.14		16	56.53	even	6
2240.2.e.f.2239.15		16	56.3	even	6
2240.2.e.f.2239.16		16	280.179	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02517 + 0.974178i) q^{2} +(1.84964 + 1.06789i) q^{3} +(0.101955 - 1.99740i) q^{4} +(-1.92846 - 1.13183i) q^{5} +(-2.93651 + 0.707107i) q^{6} +(1.84130 + 2.14700i) q^{8} +(0.780776 + 1.35234i) q^{9} +O(q^{10})\)	\(q+(-1.02517 + 0.974178i) q^{2} +(1.84964 + 1.06789i) q^{3} +(0.101955 - 1.99740i) q^{4} +(-1.92846 - 1.13183i) q^{5} +(-2.93651 + 0.707107i) q^{6} +(1.84130 + 2.14700i) q^{8} +(0.780776 + 1.35234i) q^{9} +(3.07961 - 0.718349i) q^{10} +(-2.01961 - 1.16602i) q^{11} +(2.32158 - 3.58559i) q^{12} +1.09190 q^{13} +(-2.35829 - 4.15286i) q^{15} +(-3.97921 - 0.407291i) q^{16} +(2.49037 - 4.31345i) q^{17} +(-2.11785 - 0.625771i) q^{18} +(-1.28751 - 2.23003i) q^{19} +(-2.45733 + 3.73652i) q^{20} +(3.20636 - 0.772087i) q^{22} +(-3.02045 - 5.23157i) q^{23} +(1.11298 + 5.93748i) q^{24} +(2.43794 + 4.36537i) q^{25} +(-1.11938 + 1.06370i) q^{26} -3.07221i q^{27} +0.561553 q^{29} +(6.46328 + 1.95999i) q^{30} +(-3.29801 + 5.71233i) q^{31} +(4.47615 - 3.45892i) q^{32} +(-2.49037 - 4.31345i) q^{33} +(1.64901 + 6.84809i) q^{34} +(2.78078 - 1.42164i) q^{36} +(4.76284 - 2.74983i) q^{37} +(3.49236 + 1.03190i) q^{38} +(2.01961 + 1.16602i) q^{39} +(-1.12085 - 6.22444i) q^{40} -8.48528i q^{41} -1.32431 q^{43} +(-2.53493 + 3.91509i) q^{44} +(0.0249209 - 3.49165i) q^{45} +(8.19296 + 2.42080i) q^{46} +(8.43723 - 4.87123i) q^{47} +(-6.92516 - 5.00270i) q^{48} +(-6.75195 - 2.10027i) q^{50} +(9.21257 - 5.31888i) q^{51} +(0.111324 - 2.18095i) q^{52} +(-7.43743 - 4.29400i) q^{53} +(2.99287 + 3.14954i) q^{54} +(2.57501 + 4.53448i) q^{55} -5.49966i q^{57} +(-0.575688 + 0.547052i) q^{58} +(7.16053 - 12.4024i) q^{59} +(-8.53535 + 4.28705i) q^{60} +(-0.536986 + 0.310029i) q^{61} +(-2.18379 - 9.06897i) q^{62} +(-1.21922 + 7.90655i) q^{64} +(-2.10568 - 1.23584i) q^{65} +(6.75512 + 1.99596i) q^{66} +(-2.35829 + 4.08469i) q^{67} +(-8.36177 - 5.41404i) q^{68} -12.9020i q^{69} +11.9473i q^{71} +(-1.46584 + 4.16640i) q^{72} +(4.98074 - 8.62689i) q^{73} +(-2.20391 + 7.45890i) q^{74} +(-0.152429 + 10.6778i) q^{75} +(-4.58552 + 2.34430i) q^{76} +(-3.20636 + 0.772087i) q^{78} +(-9.21257 + 5.31888i) q^{79} +(7.21278 + 5.28922i) q^{80} +(5.62311 - 9.73950i) q^{81} +(8.26617 + 8.69887i) q^{82} +3.86098i q^{83} +(-9.68466 + 5.49966i) q^{85} +(1.35764 - 1.29011i) q^{86} +(1.03867 + 0.599676i) q^{87} +(-1.21526 - 6.48311i) q^{88} +(2.44949 - 1.41421i) q^{89} +(3.37594 + 3.60382i) q^{90} +(-10.7575 + 5.49966i) q^{92} +(-12.2003 + 7.04383i) q^{93} +(-3.90416 + 13.2132i) q^{94} +(-0.0410947 + 5.75775i) q^{95} +(11.9730 - 1.61771i) q^{96} +14.9422 q^{97} -3.64162i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 8 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 8 * q^9	\( 32 q + 12 q^{4} - 8 q^{9} + 12 q^{16} - 8 q^{25} - 48 q^{29} + 4 q^{30} + 56 q^{36} - 32 q^{44} + 32 q^{46} - 24 q^{50} - 44 q^{60} - 72 q^{64} + 32 q^{65} - 88 q^{74} + 48 q^{81} - 112 q^{85} - 40 q^{86}+O(q^{100}) \) 32 * q + 12 * q^4 - 8 * q^9 + 12 * q^16 - 8 * q^25 - 48 * q^29 + 4 * q^30 + 56 * q^36 - 32 * q^44 + 32 * q^46 - 24 * q^50 - 44 * q^60 - 72 * q^64 + 32 * q^65 - 88 * q^74 + 48 * q^81 - 112 * q^85 - 40 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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