LMFDB - Embedded newform 980.2.k.l.883.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("980.687");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			883.15
Character	$\chi$	$=$	980.883
Dual form			980.2.k.l.687.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26992 + 0.622342i) q^{2} +(2.09607 - 2.09607i) q^{3} +(1.22538 + 1.58065i) q^{4} +(2.14272 + 0.639344i) q^{5} +(3.96631 - 1.35737i) q^{6} +(0.572433 + 2.76990i) q^{8} -5.78704i q^{9} +O(q^{10})$	\(q+(1.26992 + 0.622342i) q^{2} +(2.09607 - 2.09607i) q^{3} +(1.22538 + 1.58065i) q^{4} +(2.14272 + 0.639344i) q^{5} +(3.96631 - 1.35737i) q^{6} +(0.572433 + 2.76990i) q^{8} -5.78704i q^{9} +(2.32318 + 2.14542i) q^{10} +0.214920i q^{11} +(5.88164 + 0.744658i) q^{12} +(-4.29923 - 4.29923i) q^{13} +(5.83140 - 3.15118i) q^{15} +(-0.996878 + 3.87379i) q^{16} +(-2.00932 + 2.00932i) q^{17} +(3.60152 - 7.34907i) q^{18} -0.877903 q^{19} +(1.61507 + 4.17032i) q^{20} +(-0.133754 + 0.272931i) q^{22} +(-0.0902398 + 0.0902398i) q^{23} +(7.00576 + 4.60604i) q^{24} +(4.18248 + 2.73987i) q^{25} +(-2.78408 - 8.13526i) q^{26} +(-5.84185 - 5.84185i) q^{27} -4.03098i q^{29} +(9.36651 - 0.372615i) q^{30} +8.60152i q^{31} +(-3.67677 + 4.29899i) q^{32} +(0.450489 + 0.450489i) q^{33} +(-3.80215 + 1.30119i) q^{34} +(9.14726 - 7.09134i) q^{36} +(-1.29227 + 1.29227i) q^{37} +(-1.11487 - 0.546356i) q^{38} -18.0230 q^{39} +(-0.544354 + 6.30109i) q^{40} -2.91481 q^{41} +(-2.06108 + 2.06108i) q^{43} +(-0.339713 + 0.263360i) q^{44} +(3.69991 - 12.4000i) q^{45} +(-0.170757 + 0.0584371i) q^{46} +(4.88813 + 4.88813i) q^{47} +(6.03021 + 10.2093i) q^{48} +(3.60627 + 6.08234i) q^{50} +8.42336i q^{51} +(1.52736 - 12.0638i) q^{52} +(-2.77420 - 2.77420i) q^{53} +(-3.78304 - 11.0543i) q^{54} +(-0.137408 + 0.460514i) q^{55} +(-1.84015 + 1.84015i) q^{57} +(2.50864 - 5.11901i) q^{58} -10.4920 q^{59} +(12.1266 + 5.35598i) q^{60} +8.32686 q^{61} +(-5.35309 + 10.9232i) q^{62} +(-7.34464 + 3.17116i) q^{64} +(-6.46335 - 11.9607i) q^{65} +(0.291726 + 0.852442i) q^{66} +(-0.555822 - 0.555822i) q^{67} +(-5.63820 - 0.713837i) q^{68} +0.378298i q^{69} +1.75036i q^{71} +(16.0295 - 3.31270i) q^{72} +(-4.18728 - 4.18728i) q^{73} +(-2.44532 + 0.836846i) q^{74} +(14.5097 - 3.02382i) q^{75} +(-1.07577 - 1.38765i) q^{76} +(-22.8877 - 11.2165i) q^{78} +12.4127 q^{79} +(-4.61271 + 7.66309i) q^{80} -7.12875 q^{81} +(-3.70157 - 1.81401i) q^{82} +(-5.30716 + 5.30716i) q^{83} +(-5.59005 + 3.02076i) q^{85} +(-3.90010 + 1.33471i) q^{86} +(-8.44922 - 8.44922i) q^{87} +(-0.595307 + 0.123028i) q^{88} -12.7409i q^{89} +(12.4156 - 13.4444i) q^{90} +(-0.253215 - 0.0320589i) q^{92} +(18.0294 + 18.0294i) q^{93} +(3.16544 + 9.24961i) q^{94} +(-1.88110 - 0.561282i) q^{95} +(1.30422 + 16.7178i) q^{96} +(2.58579 - 2.58579i) q^{97} +1.24375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 8 q^{6}+O(q^{10}) $ 36 * q + 8 * q^6	$ 36 q + 8 q^{6} + 16 q^{10} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} + 28 q^{18} - 20 q^{20} + 4 q^{22} - 20 q^{25} + 32 q^{26} - 4 q^{30} + 20 q^{37} + 36 q^{40} - 20 q^{45} + 16 q^{46} + 24 q^{48} + 40 q^{50} - 16 q^{52} - 44 q^{53} - 16 q^{57} - 4 q^{58} + 40 q^{60} + 64 q^{61} - 40 q^{62} + 4 q^{65} - 32 q^{66} - 80 q^{68} + 80 q^{72} - 52 q^{73} - 8 q^{76} - 76 q^{78} + 20 q^{80} - 36 q^{81} - 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} + 16 q^{90} - 56 q^{92} + 32 q^{93} - 120 q^{96} - 20 q^{97}+O(q^{100}) $ 36 * q + 8 * q^6 + 16 * q^10 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 + 28 * q^18 - 20 * q^20 + 4 * q^22 - 20 * q^25 + 32 * q^26 - 4 * q^30 + 20 * q^37 + 36 * q^40 - 20 * q^45 + 16 * q^46 + 24 * q^48 + 40 * q^50 - 16 * q^52 - 44 * q^53 - 16 * q^57 - 4 * q^58 + 40 * q^60 + 64 * q^61 - 40 * q^62 + 4 * q^65 - 32 * q^66 - 80 * q^68 + 80 * q^72 - 52 * q^73 - 8 * q^76 - 76 * q^78 + 20 * q^80 - 36 * q^81 - 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 + 16 * q^90 - 56 * q^92 + 32 * q^93 - 120 * q^96 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.26992	+	0.622342i	0.897967	+	0.440062i
$2$	1.26992	+	0.622342i	0.897967	+	0.440062i
$3$	2.09607	−	2.09607i	1.21017	−	1.21017i	0.239197	−	0.970971i	$-0.423116\pi$
$3$	2.09607	−	2.09607i	1.21017	−	1.21017i	0.970971	−	0.239197i	$-0.0768843\pi$
$4$	1.22538	+	1.58065i	0.612691	+	0.790323i
$5$	2.14272	+	0.639344i	0.958252	+	0.285923i
$5$	2.14272	+	0.639344i	0.958252	+	0.285923i
$6$	3.96631	−	1.35737i	1.61924	−	0.554143i
$7$		0			0
$7$		0			0
$8$	0.572433	+	2.76990i	0.202386	+	0.979306i
$9$		−	5.78704i		−	1.92901i
$10$	2.32318	+	2.14542i	0.734656	+	0.678440i
$11$			0.214920i			0.0648009i	0.999475	+	0.0324005i	$0.0103152\pi$
$11$			0.214920i			0.0648009i	−0.999475	+	0.0324005i	$0.989685\pi$
$12$	5.88164	+	0.744658i	1.69788	+	0.214964i
$13$	−4.29923	−	4.29923i	−1.19239	−	1.19239i	−0.976394	−	0.215999i	$-0.930699\pi$
$13$	−4.29923	−	4.29923i	−1.19239	−	1.19239i	−0.215999	−	0.976394i	$-0.569301\pi$
$14$		0			0
$15$	5.83140	−	3.15118i	1.50566	−	0.813631i
$16$	−0.996878	+	3.87379i	−0.249220	+	0.968447i
$17$	−2.00932	+	2.00932i	−0.487331	+	0.487331i	−0.907463	−	0.420132i	$-0.861984\pi$
$17$	−2.00932	+	2.00932i	−0.487331	+	0.487331i	0.420132	+	0.907463i	$0.361984\pi$
$18$	3.60152	−	7.34907i	0.848886	−	1.73219i
$19$	−0.877903			−0.201405			−0.100702	−	0.994917i	$-0.532109\pi$
$19$	−0.877903			−0.201405			−0.100702	+	0.994917i	$0.532109\pi$
$20$	1.61507	+	4.17032i	0.361141	+	0.932511i
$21$		0			0
$22$	−0.133754	+	0.272931i	−0.0285164	+	0.0581891i
$23$	−0.0902398	+	0.0902398i	−0.0188163	+	0.0188163i	−0.716452	−	0.697636i	$-0.754235\pi$
$23$	−0.0902398	+	0.0902398i	−0.0188163	+	0.0188163i	0.697636	+	0.716452i	$0.254235\pi$
$24$	7.00576	+	4.60604i	1.43005	+	0.940204i
$25$	4.18248	+	2.73987i	0.836496	+	0.547974i
$26$	−2.78408	−	8.13526i	−0.546003	−	1.59546i
$27$	−5.84185	−	5.84185i	−1.12426	−	1.12426i
$28$		0			0
$29$		−	4.03098i		−	0.748534i	−0.927321	−	0.374267i	$-0.877894\pi$
$29$		−	4.03098i		−	0.748534i	0.927321	−	0.374267i	$-0.122106\pi$
$30$	9.36651	−	0.372615i	1.71008	−	0.0680298i
$31$			8.60152i			1.54488i	0.635088	+	0.772440i	$0.280964\pi$
$31$			8.60152i			1.54488i	−0.635088	+	0.772440i	$0.719036\pi$
$32$	−3.67677	+	4.29899i	−0.649968	+	0.759962i
$33$	0.450489	+	0.450489i	0.0784200	+	0.0784200i
$34$	−3.80215	+	1.30119i	−0.652064	+	0.223152i
$35$		0			0
$36$	9.14726	−	7.09134i	1.52454	−	1.18189i
$37$	−1.29227	+	1.29227i	−0.212448	+	0.212448i	−0.805307	−	0.592858i	$-0.797999\pi$
$37$	−1.29227	+	1.29227i	−0.212448	+	0.212448i	0.592858	+	0.805307i	$0.297999\pi$
$38$	−1.11487	−	0.546356i	−0.180855	−	0.0886306i
$39$	−18.0230			−2.88599
$40$	−0.544354	+	6.30109i	−0.0860699	+	0.996289i
$41$	−2.91481			−0.455217			−0.227608	−	0.973753i	$-0.573091\pi$
$41$	−2.91481			−0.455217			−0.227608	+	0.973753i	$0.573091\pi$
$42$		0			0
$43$	−2.06108	+	2.06108i	−0.314312	+	0.314312i	−0.846578	−	0.532265i	$-0.821341\pi$
$43$	−2.06108	+	2.06108i	−0.314312	+	0.314312i	0.532265	+	0.846578i	$0.321341\pi$
$44$	−0.339713	+	0.263360i	−0.0512136	+	0.0397030i
$45$	3.69991	−	12.4000i	0.551550	−	1.84848i
$46$	−0.170757	+	0.0584371i	−0.0251768	+	0.00861609i
$47$	4.88813	+	4.88813i	0.713007	+	0.713007i	0.967163	−	0.254156i	$-0.0817977\pi$
$47$	4.88813	+	4.88813i	0.713007	+	0.713007i	−0.254156	+	0.967163i	$0.581798\pi$
$48$	6.03021	+	10.2093i	0.870386	+	1.47358i
$49$		0			0
$50$	3.60627	+	6.08234i	0.510004	+	0.860172i
$51$			8.42336i			1.17951i
$52$	1.52736	−	12.0638i	0.211807	−	1.67294i
$53$	−2.77420	−	2.77420i	−0.381066	−	0.381066i	0.490420	−	0.871486i	$-0.336843\pi$
$53$	−2.77420	−	2.77420i	−0.381066	−	0.381066i	−0.871486	+	0.490420i	$0.836843\pi$
$54$	−3.78304	−	11.0543i	−0.514807	−	1.50430i
$55$	−0.137408	+	0.460514i	−0.0185281	+	0.0620957i
$56$		0			0
$57$	−1.84015	+	1.84015i	−0.243734	+	0.243734i
$58$	2.50864	−	5.11901i	0.329401	−	0.672159i
$59$	−10.4920			−1.36594			−0.682972	−	0.730445i	$-0.739313\pi$
$59$	−10.4920			−1.36594			−0.682972	+	0.730445i	$0.739313\pi$
$60$	12.1266	+	5.35598i	1.56554	+	0.691454i
$61$	8.32686			1.06615			0.533073	−	0.846069i	$-0.321037\pi$
$61$	8.32686			1.06615			0.533073	+	0.846069i	$0.321037\pi$
$62$	−5.35309	+	10.9232i	−0.679843	+	1.38725i
$63$		0			0
$64$	−7.34464	+	3.17116i	−0.918080	+	0.396395i
$65$	−6.46335	−	11.9607i	−0.801680	−	1.48355i
$66$	0.291726	+	0.852442i	0.0359090	+	0.104928i
$67$	−0.555822	−	0.555822i	−0.0679045	−	0.0679045i	0.672339	−	0.740243i	$-0.265290\pi$
$67$	−0.555822	−	0.555822i	−0.0679045	−	0.0679045i	−0.740243	+	0.672339i	$0.765290\pi$
$68$	−5.63820	−	0.713837i	−0.683732	−	0.0865654i
$69$			0.378298i			0.0455418i
$70$		0			0
$71$			1.75036i			0.207729i	0.994591	+	0.103865i	$0.0331209\pi$
$71$			1.75036i			0.207729i	−0.994591	+	0.103865i	$0.966879\pi$
$72$	16.0295	−	3.31270i	1.88910	−	0.390405i
$73$	−4.18728	−	4.18728i	−0.490084	−	0.490084i	0.418249	−	0.908333i	$-0.362644\pi$
$73$	−4.18728	−	4.18728i	−0.490084	−	0.490084i	−0.908333	+	0.418249i	$0.862644\pi$
$74$	−2.44532	+	0.836846i	−0.284262	+	0.0972813i
$75$	14.5097	−	3.02382i	1.67544	−	0.349160i
$76$	−1.07577	−	1.38765i	−0.123399	−	0.159175i
$77$		0			0
$78$	−22.8877	−	11.2165i	−2.59153	−	1.27002i
$79$	12.4127			1.39654			0.698270	−	0.715834i	$-0.253953\pi$
$79$	12.4127			1.39654			0.698270	+	0.715834i	$0.253953\pi$
$80$	−4.61271	+	7.66309i	−0.515717	+	0.856759i
$81$	−7.12875			−0.792083
$82$	−3.70157	−	1.81401i	−0.408770	−	0.200324i
$83$	−5.30716	+	5.30716i	−0.582537	+	0.582537i	−0.935600	−	0.353063i	$-0.885140\pi$
$83$	−5.30716	+	5.30716i	−0.582537	+	0.582537i	0.353063	+	0.935600i	$0.385140\pi$
$84$		0			0
$85$	−5.59005	+	3.02076i	−0.606326	+	0.327647i
$86$	−3.90010	+	1.33471i	−0.420559	+	0.143925i
$87$	−8.44922	−	8.44922i	−0.905852	−	0.905852i
$88$	−0.595307	+	0.123028i	−0.0634599	+	0.0131148i
$89$		−	12.7409i		−	1.35053i	−0.737576	−	0.675264i	$-0.764029\pi$
$89$		−	12.7409i		−	1.35053i	0.737576	−	0.675264i	$-0.235971\pi$
$90$	12.4156	−	13.4444i	1.30872	−	1.41716i
$91$		0			0
$92$	−0.253215	−	0.0320589i	−0.0263995	−	0.00334237i
$93$	18.0294	+	18.0294i	1.86956	+	1.86956i
$94$	3.16544	+	9.24961i	0.326490	+	0.954024i
$95$	−1.88110	−	0.561282i	−0.192997	−	0.0575864i
$96$	1.30422	+	16.7178i	0.133111	+	1.70625i
$97$	2.58579	−	2.58579i	0.262547	−	0.262547i	−0.563541	−	0.826088i	$-0.690561\pi$
$97$	2.58579	−	2.58579i	0.262547	−	0.262547i	0.826088	+	0.563541i	$0.190561\pi$
$98$		0			0
$99$	1.24375			0.125002
$100$	0.794374	+	9.96840i	0.0794374	+	0.996840i
$101$	15.1945			1.51190			0.755952	−	0.654627i	$-0.227174\pi$
$101$	15.1945			1.51190			0.755952	+	0.654627i	$0.227174\pi$
$102$	−5.24221	+	10.6970i	−0.519056	+	1.05916i
$103$	1.08907	−	1.08907i	0.107309	−	0.107309i	−0.651414	−	0.758723i	$-0.725824\pi$
$103$	1.08907	−	1.08907i	0.107309	−	0.107309i	0.758723	+	0.651414i	$0.225824\pi$
$104$	9.44740	−	14.3694i	0.926394	−	1.40904i
$105$		0			0
$106$	−1.79651	−	5.24951i	−0.174492	−	0.509877i
$107$	−9.68529	−	9.68529i	−0.936312	−	0.936312i	0.0617779	−	0.998090i	$-0.480323\pi$
$107$	−9.68529	−	9.68529i	−0.936312	−	0.936312i	−0.998090	+	0.0617779i	$0.980323\pi$
$108$	2.07539	−	16.3924i	0.199705	−	1.57736i
$109$		−	12.0416i		−	1.15337i	−0.816966	−	0.576686i	$-0.804345\pi$
$109$		−	12.0416i		−	1.15337i	0.816966	−	0.576686i	$-0.195655\pi$
$110$	−0.461094	+	0.499300i	−0.0439636	+	0.0476064i
$111$			5.41740i			0.514197i
$112$		0			0
$113$	−3.14409	−	3.14409i	−0.295771	−	0.295771i	0.543584	−	0.839355i	$-0.317067\pi$
$113$	−3.14409	−	3.14409i	−0.295771	−	0.295771i	−0.839355	+	0.543584i	$0.817067\pi$
$114$	−3.48204	+	1.19164i	−0.326123	+	0.111607i
$115$	−0.251053	+	0.135664i	−0.0234108	+	0.0126507i
$116$	6.37154	−	4.93949i	0.591583	−	0.458620i
$117$	−24.8798	+	24.8798i	−2.30014	+	2.30014i
$118$	−13.3240	−	6.52961i	−1.22657	−	0.601100i
$119$		0			0
$120$	12.0665	+	14.3485i	1.10152	+	1.30984i
$121$	10.9538			0.995801
$122$	10.5744	+	5.18215i	0.957364	+	0.469170i
$123$	−6.10965	+	6.10965i	−0.550889	+	0.550889i
$124$	−13.5960	+	10.5402i	−1.22095	+	0.946534i
$125$	7.21015	+	8.54481i	0.644896	+	0.764271i
$126$		0			0
$127$	2.21268	+	2.21268i	0.196344	+	0.196344i	0.798431	−	0.602087i	$-0.205664\pi$
$127$	2.21268	+	2.21268i	0.196344	+	0.196344i	−0.602087	+	0.798431i	$0.705664\pi$
$128$	−11.3006	−	0.543764i	−0.998844	−	0.0480624i
$129$			8.64036i			0.760741i
$130$	−0.764266	−	19.2116i	−0.0670306	−	1.68497i
$131$		−	3.71791i		−	0.324835i	−0.986722	−	0.162418i	$-0.948071\pi$
$131$		−	3.71791i		−	0.324835i	0.986722	−	0.162418i	$-0.0519292\pi$
$132$	−0.160042	+	1.26408i	−0.0139299	+	0.110024i
$133$		0			0
$134$	−0.359937	−	1.05176i	−0.0310939	−	0.0908582i
$135$	−8.78248	−	16.2524i	−0.755875	−	1.39878i
$136$	−6.71580	−	4.41540i	−0.575875	−	0.378618i
$137$	1.84961	−	1.84961i	0.158023	−	0.158023i	−0.623667	−	0.781690i	$-0.714358\pi$
$137$	1.84961	−	1.84961i	0.158023	−	0.158023i	0.781690	+	0.623667i	$0.214358\pi$
$138$	−0.235431	+	0.480408i	−0.0200412	+	0.0408950i
$139$	−10.9071			−0.925130			−0.462565	−	0.886585i	$-0.653071\pi$
$139$	−10.9071			−0.925130			−0.462565	+	0.886585i	$0.653071\pi$
$140$		0			0
$141$	20.4918			1.72572
$142$	−1.08932	+	2.22281i	−0.0914137	+	0.186534i
$143$	0.923993	−	0.923993i	0.0772682	−	0.0772682i
$144$	22.4178	+	5.76898i	1.86815	+	0.480748i
$145$	2.57718	−	8.63725i	0.214023	−	0.717284i
$146$	−2.71158	−	7.92342i	−0.224412	−	0.655747i
$147$		0			0
$148$	−3.62615	−	0.459097i	−0.298068	−	0.0377376i
$149$		−	11.2422i		−	0.920997i	−0.887661	−	0.460498i	$-0.847671\pi$
$149$		−	11.2422i		−	0.920997i	0.887661	−	0.460498i	$-0.152329\pi$
$150$	20.3080	+	5.19002i	1.65814	+	0.423763i
$151$		−	9.08107i		−	0.739007i	−0.929229	−	0.369504i	$-0.879528\pi$
$151$		−	9.08107i		−	0.739007i	0.929229	−	0.369504i	$-0.120472\pi$
$152$	−0.502541	−	2.43170i	−0.0407615	−	0.197237i
$153$	11.6280	+	11.6280i	0.940069	+	0.940069i
$154$		0			0
$155$	−5.49933	+	18.4306i	−0.441717	+	1.48038i
$156$	−22.0851	−	28.4880i	−1.76822	−	2.28086i
$157$	−14.8107	+	14.8107i	−1.18202	+	1.18202i	−0.202799	+	0.979220i	$0.565004\pi$
$157$	−14.8107	+	14.8107i	−1.18202	+	1.18202i	−0.979220	+	0.202799i	$0.934996\pi$
$158$	15.7631	+	7.72495i	1.25405	+	0.614564i
$159$	−11.6299			−0.922307
$160$	−10.6268	+	6.86081i	−0.840124	+	0.542394i
$161$		0			0
$162$	−9.05292	−	4.43652i	−0.711265	−	0.348566i
$163$	−11.2444	+	11.2444i	−0.880727	+	0.880727i	−0.993608	−	0.112882i	$-0.963992\pi$
$163$	−11.2444	+	11.2444i	−0.880727	+	0.880727i	0.112882	+	0.993608i	$0.463992\pi$
$164$	−3.57176	−	4.60728i	−0.278907	−	0.359768i
$165$	0.677253	+	1.25329i	0.0527241	+	0.0975683i
$166$	−10.0425	+	3.43679i	−0.779452	+	0.266747i
$167$	12.0570	+	12.0570i	0.932995	+	0.932995i	0.997892	−	0.0648970i	$-0.0206719\pi$
$167$	12.0570	+	12.0570i	0.932995	+	0.932995i	−0.0648970	+	0.997892i	$0.520672\pi$
$168$		0			0
$169$			23.9668i			1.84360i
$170$	−8.97884	+	0.357193i	−0.688646	+	0.0273954i
$171$			5.08047i			0.388513i
$172$	−5.78345	−	0.732227i	−0.440984	−	0.0558318i
$173$	0.321011	+	0.321011i	0.0244060	+	0.0244060i	0.719204	−	0.694798i	$-0.244506\pi$
$173$	0.321011	+	0.321011i	0.0244060	+	0.0244060i	−0.694798	+	0.719204i	$0.744506\pi$
$174$	−5.47151	−	15.9881i	−0.414794	−	1.21206i
$175$		0			0
$176$	−0.832556	−	0.214249i	−0.0627563	−	0.0161497i
$177$	−21.9920	+	21.9920i	−1.65302	+	1.65302i
$178$	7.92917	−	16.1798i	0.594316	−	1.21273i
$179$	4.85521			0.362895			0.181448	−	0.983401i	$-0.441922\pi$
$179$	4.85521			0.362895			0.181448	+	0.983401i	$0.441922\pi$
$180$	24.1338	−	9.34649i	1.79883	−	0.696646i
$181$	−6.88269			−0.511586			−0.255793	−	0.966732i	$-0.582337\pi$
$181$	−6.88269			−0.511586			−0.255793	+	0.966732i	$0.582337\pi$
$182$		0			0
$183$	17.4537	−	17.4537i	1.29022	−	1.29022i
$184$	−0.301611	−	0.198299i	−0.0222351	−	0.0146188i
$185$	−3.59518	+	1.94277i	−0.264323	+	0.142835i
$186$	11.6754	+	34.1163i	0.856084	+	2.50153i
$187$	−0.431844	−	0.431844i	−0.0315795	−	0.0315795i
$188$	−1.73657	+	13.7162i	−0.126653	+	1.00036i
$189$		0			0
$190$	−2.03953	−	1.88347i	−0.147963	−	0.136641i
$191$			17.2429i			1.24765i	0.781563	+	0.623826i	$0.214423\pi$
$191$			17.2429i			1.24765i	−0.781563	+	0.623826i	$0.785577\pi$
$192$	−8.74792	+	22.0419i	−0.631327	+	1.59074i
$193$	−14.3334	−	14.3334i	−1.03174	−	1.03174i	−0.999480	−	0.0322597i	$-0.989730\pi$
$193$	−14.3334	−	14.3334i	−1.03174	−	1.03174i	−0.0322597	−	0.999480i	$-0.510270\pi$
$194$	4.89299	−	1.67450i	0.351296	−	0.120222i
$195$	−38.6182	−	11.5229i	−2.76551	−	0.825172i
$196$		0			0
$197$	−12.9394	+	12.9394i	−0.921891	+	0.921891i	−0.997163	−	0.0752724i	$-0.976017\pi$
$197$	−12.9394	+	12.9394i	−0.921891	+	0.921891i	0.0752724	+	0.997163i	$0.476017\pi$
$198$	1.57947	+	0.774040i	0.112248	+	0.0550086i
$199$	21.8858			1.55144			0.775720	−	0.631077i	$-0.217387\pi$
$199$	21.8858			1.55144			0.775720	+	0.631077i	$0.217387\pi$
$200$	−5.19496	+	13.1534i	−0.367339	+	0.930087i
$201$	−2.33009			−0.164352
$202$	19.2957	+	9.45614i	1.35764	+	0.665332i
$203$		0			0
$204$	−13.3143	+	10.3218i	−0.932190	+	0.722673i
$205$	−6.24561	−	1.86357i	−0.436213	−	0.130157i
$206$	2.06081	−	0.705257i	0.143583	−	0.0491376i
$207$	0.522222	+	0.522222i	0.0362969	+	0.0362969i
$208$	20.9401	−	12.3685i	1.45194	−	0.857602i
$209$		−	0.188679i		−	0.0130512i
$210$		0			0
$211$		−	3.39701i		−	0.233860i	−0.993140	−	0.116930i	$-0.962695\pi$
$211$		−	3.39701i		−	0.233860i	0.993140	−	0.116930i	$-0.0373053\pi$
$212$	0.985571	−	7.78448i	0.0676893	−	0.534640i
$213$	3.66888	+	3.66888i	0.251387	+	0.251387i
$214$	−6.27196	−	18.3271i	−0.428742	−	1.25281i
$215$	−5.73406	+	3.09858i	−0.391059	+	0.211321i
$216$	12.8372	−	19.5254i	0.873464	−	1.32853i
$217$		0			0
$218$	7.49397	−	15.2918i	0.507555	−	1.03569i
$219$	−17.5537			−1.18617
$220$	−0.896286	+	0.347112i	−0.0604276	+	0.0234023i
$221$	17.2771			1.16218
$222$	−3.37147	+	6.87965i	−0.226278	+	0.461732i
$223$	19.7618	−	19.7618i	1.32335	−	1.32335i	0.412300	−	0.911048i	$-0.364725\pi$
$223$	19.7618	−	19.7618i	1.32335	−	1.32335i	0.911048	−	0.412300i	$-0.135275\pi$
$224$		0			0
$225$	15.8557	−	24.2042i	1.05705	−	1.61361i
$226$	−2.03604	−	5.94944i	−0.135435	−	0.395751i
$227$	−14.7580	−	14.7580i	−0.979521	−	0.979521i	0.0202733	−	0.999794i	$-0.493546\pi$
$227$	−14.7580	−	14.7580i	−0.979521	−	0.979521i	−0.999794	+	0.0202733i	$0.993546\pi$
$228$	−5.16351	−	0.653738i	−0.341962	−	0.0432948i
$229$			3.25813i			0.215303i	0.994189	+	0.107652i	$0.0343331\pi$
$229$			3.25813i			0.215303i	−0.994189	+	0.107652i	$0.965667\pi$
$230$	−0.403246	+	0.0160417i	−0.0265892	+	0.00105776i
$231$		0			0
$232$	11.1654	−	2.30746i	0.733043	−	0.151492i
$233$	4.88513	+	4.88513i	0.320035	+	0.320035i	0.848781	−	0.528745i	$-0.177337\pi$
$233$	4.88513	+	4.88513i	0.320035	+	0.320035i	−0.528745	+	0.848781i	$0.677337\pi$
$234$	−47.0791	+	16.1116i	−3.07766	+	1.05325i
$235$	7.34868	+	13.5991i	0.479375	+	0.887106i
$236$	−12.8567	−	16.5841i	−0.836901	−	1.07954i
$237$	26.0180	−	26.0180i	1.69005	−	1.69005i
$238$		0			0
$239$	10.2770			0.664761			0.332380	−	0.943145i	$-0.392148\pi$
$239$	10.2770			0.664761			0.332380	+	0.943145i	$0.392148\pi$
$240$	6.39381	+	25.7310i	0.412718	+	1.66093i
$241$	−4.78849			−0.308454			−0.154227	−	0.988035i	$-0.549289\pi$
$241$	−4.78849			−0.308454			−0.154227	+	0.988035i	$0.549289\pi$
$242$	13.9104	+	6.81701i	0.894197	+	0.438214i
$243$	2.58317	−	2.58317i	0.165710	−	0.165710i
$244$	10.2036	+	13.1618i	0.653218	+	0.842599i
$245$		0			0
$246$	−11.5611	+	3.95647i	−0.737106	+	0.252255i
$247$	3.77431	+	3.77431i	0.240154	+	0.240154i
$248$	−23.8253	+	4.92380i	−1.51291	+	0.312661i
$249$			22.2484i			1.40994i
$250$	3.83851	+	15.3384i	0.242769	+	0.970084i
$251$			26.2656i			1.65787i	0.559347	+	0.828934i	$0.311052\pi$
$251$			26.2656i			1.65787i	−0.559347	+	0.828934i	$0.688948\pi$
$252$		0			0
$253$	−0.0193944	−	0.0193944i	−0.00121931	−	0.00121931i
$254$	1.43288	+	4.18697i	0.0899069	+	0.262714i
$255$	−5.38542	+	18.0489i	−0.337248	+	1.13026i
$256$	−14.0125	−	7.72339i	−0.875779	−	0.482712i
$257$	16.3898	−	16.3898i	1.02237	−	1.02237i	0.0226254	−	0.999744i	$-0.492798\pi$
$257$	16.3898	−	16.3898i	1.02237	−	1.02237i	0.999744	−	0.0226254i	$-0.00720250\pi$
$258$	−5.37725	+	10.9725i	−0.334773	+	0.683121i
$259$		0			0
$260$	10.9856	−	24.8727i	0.681298	−	1.54254i
$261$	−23.3274			−1.44393
$262$	2.31381	−	4.72144i	0.142948	−	0.291691i
$263$	−4.21519	+	4.21519i	−0.259920	+	0.259920i	−0.825021	−	0.565102i	$-0.808837\pi$
$263$	−4.21519	+	4.21519i	−0.259920	+	0.259920i	0.565102	+	0.825021i	$0.308837\pi$
$264$	−0.989932	+	1.50568i	−0.0609261	+	0.0926683i
$265$	−4.17066	−	7.71800i	−0.256202	−	0.474113i
$266$		0			0
$267$	−26.7058	−	26.7058i	−1.63437	−	1.63437i
$268$	0.197463	−	1.55965i	0.0120620	−	0.0952710i
$269$			0.0668035i			0.00407308i	0.999998	+	0.00203654i	$0.000648251\pi$
$269$			0.0668035i			0.00407308i	−0.999998	+	0.00203654i	$0.999352\pi$
$270$	−1.03849	−	26.1049i	−0.0632007	−	1.58869i
$271$			2.78031i			0.168892i	0.996428	+	0.0844459i	$0.0269120\pi$
$271$			2.78031i			0.168892i	−0.996428	+	0.0844459i	$0.973088\pi$
$272$	−5.78063	−	9.78672i	−0.350502	−	0.593407i
$273$		0			0
$274$	3.49994	−	1.19776i	0.211439	−	0.0723596i
$275$	−0.588854	+	0.898900i	−0.0355092	+	0.0542057i
$276$	−0.597955	+	0.463560i	−0.0359927	+	0.0279030i
$277$	4.05025	−	4.05025i	0.243356	−	0.243356i	−0.574881	−	0.818237i	$-0.694952\pi$
$277$	4.05025	−	4.05025i	0.243356	−	0.243356i	0.818237	+	0.574881i	$0.194952\pi$
$278$	−13.8511	−	6.78796i	−0.830737	−	0.407115i
$279$	49.7774			2.98010
$280$		0			0
$281$	−22.9229			−1.36746			−0.683732	−	0.729734i	$-0.739644\pi$
$281$	−22.9229			−1.36746			−0.683732	+	0.729734i	$0.739644\pi$
$282$	26.0228	+	12.7529i	1.54964	+	0.759422i
$283$	−0.402053	+	0.402053i	−0.0238995	+	0.0238995i	−0.718956	−	0.695056i	$-0.755380\pi$
$283$	−0.402053	+	0.402053i	−0.0238995	+	0.0238995i	0.695056	+	0.718956i	$0.255380\pi$
$284$	−2.76669	+	2.14486i	−0.164173	+	0.127274i
$285$	−5.11941	+	2.76643i	−0.303248	+	0.163869i
$286$	1.74843	−	0.598356i	0.103387	−	0.0353815i
$287$		0			0
$288$	24.8785	+	21.2776i	1.46598	+	1.25380i
$289$			8.92528i			0.525016i
$290$	8.64813	−	9.36470i	0.507835	−	0.549914i
$291$		−	10.8400i		−	0.635453i
$292$	1.48759	−	11.7496i	0.0870544	−	0.687594i
$293$	1.43269	+	1.43269i	0.0836989	+	0.0836989i	0.747717	−	0.664018i	$-0.231150\pi$
$293$	1.43269	+	1.43269i	0.0836989	+	0.0836989i	−0.664018	+	0.747717i	$0.731150\pi$
$294$		0			0
$295$	−22.4814	−	6.70801i	−1.30892	−	0.390555i
$296$	−4.31920	−	2.83972i	−0.251049	−	0.165056i
$297$	1.25553	−	1.25553i	0.0728534	−	0.0728534i
$298$	6.99649	−	14.2767i	0.405296	−	0.827025i
$299$	0.775924			0.0448728
$300$	22.5596	+	19.2294i	1.30248	+	1.11021i
$301$		0			0
$302$	5.65153	−	11.5322i	0.325209	−	0.663604i
$303$	31.8487	−	31.8487i	1.82966	−	1.82966i
$304$	0.875163	−	3.40081i	0.0501940	−	0.195050i
$305$	17.8421	+	5.32373i	1.02164	+	0.304836i
$306$	7.53003	+	22.0032i	0.430463	+	1.25784i
$307$	−1.51038	−	1.51038i	−0.0862017	−	0.0862017i	0.662691	−	0.748893i	$-0.269414\pi$
$307$	−1.51038	−	1.51038i	−0.0862017	−	0.0862017i	−0.748893	+	0.662691i	$0.769414\pi$
$308$		0			0
$309$		−	4.56555i		−	0.259725i
$310$	−18.4539	+	19.9829i	−1.04811	+	1.13495i
$311$		−	12.7459i		−	0.722753i	−0.932420	−	0.361376i	$-0.882307\pi$
$311$		−	12.7459i		−	0.722753i	0.932420	−	0.361376i	$-0.117693\pi$
$312$	−10.3170	−	49.9219i	−0.584083	−	2.82627i
$313$	14.3977	+	14.3977i	0.813804	+	0.813804i	0.985202	−	0.171398i	$-0.0548283\pi$
$313$	14.3977	+	14.3977i	0.813804	+	0.813804i	−0.171398	+	0.985202i	$0.554828\pi$
$314$	−28.0256	+	9.59103i	−1.58158	+	0.541253i
$315$		0			0
$316$	15.2103	+	19.6201i	0.855648	+	1.10372i
$317$	6.99137	−	6.99137i	0.392674	−	0.392674i	−0.482965	−	0.875640i	$-0.660440\pi$
$317$	6.99137	−	6.99137i	0.392674	−	0.392674i	0.875640	+	0.482965i	$0.160440\pi$
$318$	−14.7690	−	7.23774i	−0.828202	−	0.405872i
$319$	0.866339			0.0485057
$320$	−17.7650	+	2.09915i	−0.993091	+	0.117346i
$321$	−40.6021			−2.26619
$322$		0			0
$323$	1.76399	−	1.76399i	0.0981509	−	0.0981509i
$324$	−8.73544	−	11.2680i	−0.485302	−	0.626001i
$325$	−6.20212	−	29.7608i	−0.344032	−	1.65083i
$326$	−21.2773	+	7.28158i	−1.17844	+	0.403290i
$327$	−25.2400	−	25.2400i	−1.39578	−	1.39578i
$328$	−1.66853	−	8.07372i	−0.0921294	−	0.445797i
$329$		0			0
$330$	0.0800825	+	2.01306i	0.00440840	+	0.110815i
$331$		−	29.3504i		−	1.61324i	−0.591069	−	0.806621i	$-0.701294\pi$
$331$		−	29.3504i		−	1.61324i	0.591069	−	0.806621i	$-0.298706\pi$
$332$	−14.8920	−	1.88544i	−0.817307	−	0.103477i
$333$	7.47844	+	7.47844i	0.409816	+	0.409816i
$334$	7.80779	+	22.8149i	0.427224	+	1.24837i
$335$	−0.835609	−	1.54633i	−0.0456542	−	0.0844852i
$336$		0			0
$337$	21.9434	−	21.9434i	1.19533	−	1.19533i	0.219784	−	0.975549i	$-0.429465\pi$
$337$	21.9434	−	21.9434i	1.19533	−	1.19533i	0.975549	−	0.219784i	$-0.0705353\pi$
$338$	−14.9155	+	30.4359i	−0.811298	+	1.65549i
$339$	−13.1805			−0.715866
$340$	−11.6247	−	5.13430i	−0.630437	−	0.278447i
$341$	−1.84864			−0.100110
$342$	−3.16179	+	6.45177i	−0.170970	+	0.348872i
$343$		0			0
$344$	−6.88881	−	4.52915i	−0.371420	−	0.244195i
$345$	−0.241863	+	0.810587i	−0.0130215	+	0.0436405i
$346$	0.207879	+	0.607435i	0.0111756	+	0.0326559i
$347$	5.74445	+	5.74445i	0.308378	+	0.308378i	0.844280	−	0.535902i	$-0.180028\pi$
$347$	5.74445	+	5.74445i	0.308378	+	0.308378i	−0.535902	+	0.844280i	$0.680028\pi$
$348$	3.00170	−	23.7087i	0.160908	−	1.27092i
$349$		−	8.46417i		−	0.453076i	−0.974002	−	0.226538i	$-0.927259\pi$
$349$		−	8.46417i		−	0.453076i	0.974002	−	0.226538i	$-0.0727408\pi$
$350$		0			0
$351$			50.2309i			2.68113i
$352$	−0.923941	−	0.790213i	−0.0492462	−	0.0421185i
$353$	−14.7063	−	14.7063i	−0.782739	−	0.782739i	0.197553	−	0.980292i	$-0.436700\pi$
$353$	−14.7063	−	14.7063i	−0.782739	−	0.782739i	−0.980292	+	0.197553i	$0.936700\pi$
$354$	−41.6146	+	14.2415i	−2.21179	+	0.756928i
$355$	−1.11908	+	3.75052i	−0.0593946	+	0.199057i
$356$	20.1388	−	15.6124i	1.06735	−	0.827457i
$357$		0			0
$358$	6.16571	+	3.02160i	0.325868	+	0.159696i
$359$	23.5648			1.24370			0.621851	−	0.783135i	$-0.286381\pi$
$359$	23.5648			1.24370			0.621851	+	0.783135i	$0.286381\pi$
$360$	36.4647	+	3.15020i	1.92186	+	0.166030i
$361$	−18.2293			−0.959436
$362$	−8.74045	−	4.28338i	−0.459388	−	0.225130i
$363$	22.9600	−	22.9600i	1.20509	−	1.20509i
$364$		0			0
$365$	−6.29504	−	11.6493i	−0.329498	−	0.609751i
$366$	33.0269	−	11.3026i	1.72635	−	0.590797i
$367$	3.77172	+	3.77172i	0.196882	+	0.196882i	0.798662	−	0.601780i	$-0.205542\pi$
$367$	3.77172	+	3.77172i	0.196882	+	0.196882i	−0.601780	+	0.798662i	$0.705542\pi$
$368$	−0.259612	−	0.439528i	−0.0135332	−	0.0229120i
$369$			16.8681i			0.878120i
$370$	−5.77466	+	0.229725i	−0.300210	+	0.0119428i
$371$		0			0
$372$	−6.40519	+	50.5911i	−0.332094	+	2.62302i
$373$	−22.7964	−	22.7964i	−1.18035	−	1.18035i	−0.979653	−	0.200699i	$-0.935679\pi$
$373$	−22.7964	−	22.7964i	−1.18035	−	1.18035i	−0.200699	−	0.979653i	$-0.564321\pi$
$374$	−0.279652	−	0.817160i	−0.0144604	−	0.0422543i
$375$	33.0235	+	2.79753i	1.70533	+	0.144464i
$376$	−10.7415	+	16.3377i	−0.553950	+	0.842554i
$377$	−17.3301	+	17.3301i	−0.892546	+	0.892546i
$378$		0			0
$379$	3.18566			0.163637			0.0818183	−	0.996647i	$-0.473927\pi$
$379$	3.18566			0.163637			0.0818183	+	0.996647i	$0.473927\pi$
$380$	−1.41788	−	3.66114i	−0.0727355	−	0.187812i
$381$	9.27589			0.475218
$382$	−10.7310	+	21.8971i	−0.549044	+	1.12035i
$383$	−19.9331	+	19.9331i	−1.01853	+	1.01853i	−0.0187081	+	0.999825i	$0.505955\pi$
$383$	−19.9331	+	19.9331i	−1.01853	+	1.01853i	−0.999825	+	0.0187081i	$0.994045\pi$
$384$	−24.8267	+	22.5472i	−1.26693	+	1.15061i
$385$		0			0
$386$	−9.28195	−	27.1225i	−0.472439	−	1.38050i
$387$	11.9276	+	11.9276i	0.606313	+	0.606313i
$388$	7.25580	+	0.918636i	0.368357	+	0.0466367i
$389$			16.3461i			0.828781i	0.910099	+	0.414391i	$0.136005\pi$
$389$			16.3461i			0.828781i	−0.910099	+	0.414391i	$0.863995\pi$
$390$	−41.8708	−	38.6669i	−2.12021	−	1.95797i
$391$		−	0.362641i		−	0.0183395i
$392$		0			0
$393$	−7.79301	−	7.79301i	−0.393105	−	0.393105i
$394$	−24.4846	+	8.37921i	−1.23352	+	0.422139i
$395$	26.5970	+	7.93600i	1.33824	+	0.399304i
$396$	1.52407	+	1.96593i	0.0765876	+	0.0987919i
$397$	10.7408	−	10.7408i	0.539067	−	0.539067i	−0.384188	−	0.923255i	$-0.625519\pi$
$397$	10.7408	−	10.7408i	0.539067	−	0.539067i	0.923255	+	0.384188i	$0.125519\pi$
$398$	27.7931	+	13.6204i	1.39314	+	0.682730i
$399$		0			0
$400$	−14.7831	+	13.4707i	−0.739154	+	0.673536i
$401$	23.7605			1.18654			0.593271	−	0.805003i	$-0.297836\pi$
$401$	23.7605			1.18654			0.593271	+	0.805003i	$0.297836\pi$
$402$	−2.95902	−	1.45011i	−0.147583	−	0.0723250i
$403$	36.9800	−	36.9800i	1.84210	−	1.84210i
$404$	18.6190	+	24.0170i	0.926330	+	1.19489i
$405$	−15.2749	−	4.55772i	−0.759015	−	0.226475i
$406$		0			0
$407$	−0.277736	−	0.277736i	−0.0137669	−	0.0137669i
$408$	−23.3318	+	4.82181i	−1.15510	+	0.238715i
$409$			22.5684i			1.11593i	0.829863	+	0.557967i	$0.188418\pi$
$409$			22.5684i			1.11593i	−0.829863	+	0.557967i	$0.811582\pi$
$410$	−6.77164	−	6.25348i	−0.334428	−	0.308837i
$411$		−	7.75384i		−	0.382469i
$412$	3.05596	+	0.386907i	0.150557	+	0.0190615i
$413$		0			0
$414$	0.338178	+	0.988179i	0.0166206	+	0.0485663i
$415$	−14.7649	+	7.97865i	−0.724778	+	0.391657i
$416$	34.2897	−	2.67507i	1.68119	−	0.131156i
$417$	−22.8621	+	22.8621i	−1.11956	+	1.11956i
$418$	0.117423	−	0.239607i	0.00574335	−	0.0117196i
$419$	12.4351			0.607495			0.303748	−	0.952753i	$-0.401762\pi$
$419$	12.4351			0.607495			0.303748	+	0.952753i	$0.401762\pi$
$420$		0			0
$421$	−31.2799			−1.52449			−0.762244	−	0.647289i	$-0.775902\pi$
$421$	−31.2799			−1.52449			−0.762244	+	0.647289i	$0.775902\pi$
$422$	2.11410	−	4.31392i	0.102913	−	0.209998i
$423$	28.2878	−	28.2878i	1.37540	−	1.37540i
$424$	6.09620	−	9.27229i	0.296058	−	0.450302i
$425$	−13.9092	+	2.89866i	−0.674695	+	0.140606i
$426$	2.37588	+	6.94246i	0.115112	+	0.336364i
$427$		0			0
$428$	3.44083	−	27.1772i	0.166319	−	1.31366i
$429$		−	3.87351i		−	0.187015i
$430$	−9.21015	+	0.366394i	−0.444153	+	0.0176691i
$431$			19.1288i			0.921402i	0.887556	+	0.460701i	$0.152402\pi$
$431$			19.1288i			0.921402i	−0.887556	+	0.460701i	$0.847598\pi$
$432$	28.4537	−	16.8065i	1.36898	−	0.808602i
$433$	−4.87478	−	4.87478i	−0.234267	−	0.234267i	0.580204	−	0.814471i	$-0.302973\pi$
$433$	−4.87478	−	4.87478i	−0.234267	−	0.234267i	−0.814471	+	0.580204i	$0.802973\pi$
$434$		0			0
$435$	−12.7023	−	23.5063i	−0.609030	−	1.12704i
$436$	19.0334	−	14.7555i	0.911536	−	0.706661i
$437$	0.0792218	−	0.0792218i	0.00378969	−	0.00378969i
$438$	−22.2917	−	10.9244i	−1.06514	−	0.521987i
$439$	32.7840			1.56470			0.782349	−	0.622841i	$-0.214022\pi$
$439$	32.7840			1.56470			0.782349	+	0.622841i	$0.214022\pi$
$440$	−1.35423	−	0.116993i	−0.0645605	−	0.00557741i
$441$		0			0
$442$	21.9404	+	10.7522i	1.04360	+	0.511431i
$443$	−8.51358	+	8.51358i	−0.404493	+	0.404493i	−0.879813	−	0.475320i	$-0.842332\pi$
$443$	−8.51358	+	8.51358i	−0.404493	+	0.404493i	0.475320	+	0.879813i	$0.342332\pi$
$444$	−8.56299	+	6.63838i	−0.406381	+	0.315044i
$445$	8.14580	−	27.3001i	0.386148	−	1.29415i
$446$	37.3945	−	12.7973i	1.77068	−	0.605968i
$447$	−23.5645	−	23.5645i	−1.11456	−	1.11456i
$448$		0			0
$449$			5.52889i			0.260925i	0.991453	+	0.130462i	$0.0416462\pi$
$449$			5.52889i			0.260925i	−0.991453	+	0.130462i	$0.958354\pi$
$450$	35.1988	−	20.8696i	1.65929	−	0.983804i
$451$		−	0.626452i		−	0.0294985i
$452$	1.11698	−	8.82241i	0.0525383	−	0.414971i
$453$	−19.0346	−	19.0346i	−0.894323	−	0.894323i
$454$	−9.55691	−	27.9259i	−0.448528	−	1.31063i
$455$		0			0
$456$	−6.15038	−	4.04366i	−0.288018	−	0.189362i
$457$	19.0996	−	19.0996i	0.893440	−	0.893440i	−0.101405	−	0.994845i	$-0.532334\pi$
$457$	19.0996	−	19.0996i	0.893440	−	0.893440i	0.994845	+	0.101405i	$0.0323338\pi$
$458$	−2.02767	+	4.13755i	−0.0947467	+	0.193335i
$459$	23.4763			1.09578
$460$	−0.522072	−	0.230585i	−0.0243417	−	0.0107511i
$461$	8.24886			0.384188			0.192094	−	0.981377i	$-0.438472\pi$
$461$	8.24886			0.384188			0.192094	+	0.981377i	$0.438472\pi$
$462$		0			0
$463$	15.4884	−	15.4884i	0.719806	−	0.719806i	−0.248759	−	0.968565i	$-0.580023\pi$
$463$	15.4884	−	15.4884i	0.719806	−	0.719806i	0.968565	+	0.248759i	$0.0800227\pi$
$464$	15.6152	+	4.01839i	0.724915	+	0.186549i
$465$	27.1050	+	50.1590i	1.25696	+	2.32607i
$466$	3.16349	+	9.24392i	0.146546	+	0.428217i
$467$	27.7817	+	27.7817i	1.28558	+	1.28558i	0.937442	+	0.348141i	$0.113187\pi$
$467$	27.7817	+	27.7817i	1.28558	+	1.28558i	0.348141	+	0.937442i	$0.386813\pi$
$468$	−69.8135	−	8.83889i	−3.22713	−	0.408578i
$469$		0			0
$470$	0.868953	+	21.8431i	0.0400818	+	1.00755i
$471$			62.0885i			2.86089i
$472$	−6.00597	−	29.0618i	−0.276447	−	1.33768i
$473$	−0.442969	−	0.442969i	−0.0203677	−	0.0203677i
$474$	49.2328	−	16.8486i	2.26134	−	0.773883i
$475$	−3.67181	−	2.40534i	−0.168474	−	0.110365i
$476$		0			0
$477$	−16.0544	+	16.0544i	−0.735082	+	0.735082i
$478$	13.0509	+	6.39578i	0.596934	+	0.292536i
$479$	3.86716			0.176695			0.0883475	−	0.996090i	$-0.471841\pi$
$479$	3.86716			0.176695			0.0883475	+	0.996090i	$0.471841\pi$
$480$	−7.89384	+	36.6553i	−0.360303	+	1.67308i
$481$	11.1116			0.506644
$482$	−6.08099	−	2.98008i	−0.276982	−	0.135739i
$483$		0			0
$484$	13.4226	+	17.3141i	0.610118	+	0.787004i
$485$	7.19383	−	3.88741i	0.326655	−	0.176518i
$486$	4.88803	−	1.67280i	0.221725	−	0.0758797i
$487$	−0.314754	−	0.314754i	−0.0142629	−	0.0142629i	0.699939	−	0.714202i	$-0.253210\pi$
$487$	−0.314754	−	0.314754i	−0.0142629	−	0.0142629i	−0.714202	+	0.699939i	$0.753210\pi$
$488$	4.76657	+	23.0645i	0.215773	+	1.04408i
$489$			47.1380i			2.13165i
$490$		0			0
$491$			40.4240i			1.82431i	0.409844	+	0.912156i	$0.365583\pi$
$491$			40.4240i			1.82431i	−0.409844	+	0.912156i	$0.634417\pi$
$492$	−17.1439	−	2.17054i	−0.772905	−	0.0978553i
$493$	8.09952	+	8.09952i	0.364784	+	0.364784i
$494$	2.44415	+	7.14198i	0.109968	+	0.321333i
$495$	2.66501	+	0.795187i	0.119783	+	0.0357410i
$496$	−33.3205	−	8.57467i	−1.49613	−	0.385014i
$497$		0			0
$498$	−13.8461	+	28.2536i	−0.620459	+	1.26608i
$499$	31.7874			1.42300			0.711501	−	0.702686i	$-0.248016\pi$
$499$	31.7874			1.42300			0.711501	+	0.702686i	$0.248016\pi$
$500$	−4.67112	+	21.8673i	−0.208899	+	0.977937i
$501$	50.5445			2.25816
$502$	−16.3461	+	33.3551i	−0.729564	+	1.48871i
$503$	−6.28613	+	6.28613i	−0.280285	+	0.280285i	−0.833222	−	0.552938i	$-0.813507\pi$
$503$	−6.28613	+	6.28613i	−0.280285	+	0.280285i	0.552938	+	0.833222i	$0.313507\pi$
$504$		0			0
$505$	32.5574	+	9.71448i	1.44879	+	0.432289i
$506$	−0.0125593	−	0.0366992i	−0.000558330	−	0.00163148i
$507$	50.2362	+	50.2362i	2.23107	+	2.23107i
$508$	−0.786085	+	6.20885i	−0.0348769	+	0.275473i
$509$		−	3.09416i		−	0.137146i	−0.997646	−	0.0685730i	$-0.978155\pi$
$509$		−	3.09416i		−	0.137146i	0.997646	−	0.0685730i	$-0.0218446\pi$
$510$	−18.0716	+	19.5690i	−0.800224	+	0.866531i
$511$		0			0
$512$	−12.9881	−	18.5286i	−0.573998	−	0.818857i
$513$	5.12858	+	5.12858i	0.226432	+	0.226432i
$514$	31.0138	−	10.6137i	1.36796	−	0.468149i
$515$	3.02986	−	1.63728i	0.133512	−	0.0721472i
$516$	−13.6573	+	10.5877i	−0.601231	+	0.466099i
$517$	−1.05056	+	1.05056i	−0.0462035	+	0.0462035i
$518$		0			0
$519$	1.34572			0.0590707
$520$	29.4301	−	24.7495i	1.29060	−	1.08534i
$521$	−5.11386			−0.224042			−0.112021	−	0.993706i	$-0.535732\pi$
$521$	−5.11386			−0.224042			−0.112021	+	0.993706i	$0.535732\pi$
$522$	−29.6239	−	14.5176i	−1.29660	−	0.635420i
$523$	−17.9247	+	17.9247i	−0.783791	+	0.783791i	−0.980468	−	0.196677i	$-0.936985\pi$
$523$	−17.9247	+	17.9247i	−0.783791	+	0.783791i	0.196677	+	0.980468i	$0.436985\pi$
$524$	5.87669	−	4.55586i	0.256725	−	0.199024i
$525$		0			0
$526$	−7.97623	+	2.72966i	−0.347780	+	0.119019i
$527$	−17.2832	−	17.2832i	−0.752868	−	0.752868i
$528$	−2.19418	+	1.29602i	−0.0954895	+	0.0564018i
$529$			22.9837i			0.999292i
$530$	−0.493164	−	12.3968i	−0.0214217	−	0.538482i
$531$			60.7177i			2.63493i
$532$		0			0
$533$	12.5314	+	12.5314i	0.542797	+	0.542797i
$534$	−17.2940	−	50.5343i	−0.748386	−	2.18683i
$535$	−14.5606	−	26.9451i	−0.629510	−	1.16494i
$536$	1.22140	−	1.85774i	0.0527564	−	0.0802422i
$537$	10.1769	−	10.1769i	0.439164	−	0.439164i
$538$	−0.0415746	+	0.0848349i	−0.00179241	+	0.00365749i
$539$		0			0
$540$	14.9274	−	33.7974i	0.642371	−	1.45441i
$541$	1.00395			0.0431633			0.0215817	−	0.999767i	$-0.493130\pi$
$541$	1.00395			0.0431633			0.0215817	+	0.999767i	$0.493130\pi$
$542$	−1.73030	+	3.53077i	−0.0743229	+	0.151659i
$543$	−14.4266	+	14.4266i	−0.619105	+	0.619105i
$544$	−1.25024	−	16.0259i	−0.0536036	−	0.687103i
$545$	7.69870	−	25.8017i	0.329776	−	1.10522i
$546$		0			0
$547$	11.1953	+	11.1953i	0.478676	+	0.478676i	0.904708	−	0.426032i	$-0.140089\pi$
$547$	11.1953	+	11.1953i	0.478676	+	0.478676i	−0.426032	+	0.904708i	$0.640089\pi$
$548$	5.19006	+	0.657099i	0.221708	+	0.0280699i
$549$		−	48.1879i		−	2.05661i
$550$	−1.30722	+	0.775061i	−0.0557400	+	0.0330487i
$551$			3.53881i			0.150758i
$552$	−1.04785	+	0.216550i	−0.0445993	+	0.00921700i
$553$		0			0
$554$	7.66412	−	2.62285i	0.325617	−	0.111434i
$555$	−3.46358	+	11.6080i	−0.147021	+	0.492730i
$556$	−13.3654	−	17.2403i	−0.566819	−	0.731151i
$557$	−7.46496	+	7.46496i	−0.316301	+	0.316301i	−0.847344	−	0.531044i	$-0.821800\pi$
$557$	−7.46496	+	7.46496i	−0.316301	+	0.316301i	0.531044	+	0.847344i	$0.321800\pi$
$558$	63.2132	+	30.9785i	2.67603	+	1.31143i
$559$	17.7221			0.749567
$560$		0			0
$561$	−1.81035			−0.0764331
$562$	−29.1101	−	14.2658i	−1.22794	−	0.601769i
$563$	5.26839	−	5.26839i	0.222036	−	0.222036i	−0.587319	−	0.809355i	$-0.699817\pi$
$563$	5.26839	−	5.26839i	0.222036	−	0.222036i	0.809355	+	0.587319i	$0.199817\pi$
$564$	25.1102	+	32.3902i	1.05733	+	1.36387i
$565$	−4.72675	−	8.74706i	−0.198856	−	0.367992i
$566$	−0.760788	+	0.260360i	−0.0319783	+	0.0109437i
$567$		0			0
$568$	−4.84831	+	1.00196i	−0.203430	+	0.0420414i
$569$			27.2916i			1.14413i	0.820210	+	0.572063i	$0.193857\pi$
$569$			27.2916i			1.14413i	−0.820210	+	0.572063i	$0.806143\pi$
$570$	−8.22290	+	0.327120i	−0.344419	+	0.0137015i
$571$		−	6.44056i		−	0.269529i	−0.990878	−	0.134765i	$-0.956972\pi$
$571$		−	6.44056i		−	0.269529i	0.990878	−	0.134765i	$-0.0430278\pi$
$572$	2.59275	+	0.328261i	0.108408	+	0.0137253i
$573$	36.1424	+	36.1424i	1.50987	+	1.50987i
$574$		0			0
$575$	−0.624671	+	0.130181i	−0.0260506	+	0.00542892i
$576$	18.3516	+	42.5038i	0.764652	+	1.77099i
$577$	10.4727	−	10.4727i	0.435984	−	0.435984i	−0.454674	−	0.890658i	$-0.650244\pi$
$577$	10.4727	−	10.4727i	0.435984	−	0.435984i	0.890658	+	0.454674i	$0.150244\pi$
$578$	−5.55457	+	11.3344i	−0.231040	+	0.471448i
$579$	−60.0876			−2.49716
$580$	16.8105	−	6.51032i	0.698016	−	0.270326i
$581$		0			0
$582$	6.74619	−	13.7659i	0.279639	−	0.570616i
$583$	0.596232	−	0.596232i	0.0246934	−	0.0246934i
$584$	9.20139	−	13.9953i	0.380756	−	0.579128i
$585$	−69.2173	+	37.4037i	−2.86178	+	1.54645i
$586$	0.927778	+	2.71103i	0.0383262	+	0.111992i
$587$	−15.0807	−	15.0807i	−0.622447	−	0.622447i	0.323710	−	0.946156i	$-0.395070\pi$
$587$	−15.0807	−	15.0807i	−0.622447	−	0.622447i	−0.946156	+	0.323710i	$0.895070\pi$
$588$		0			0
$589$		−	7.55131i		−	0.311146i
$590$	−24.3749	−	22.5097i	−1.00350	−	0.926711i
$591$			54.2436i			2.23129i
$592$	−3.71775	−	6.29423i	−0.152799	−	0.258691i
$593$	−25.3176	−	25.3176i	−1.03967	−	1.03967i	−0.999180	−	0.0404897i	$-0.987108\pi$
$593$	−25.3176	−	25.3176i	−1.03967	−	1.03967i	−0.0404897	−	0.999180i	$-0.512892\pi$
$594$	2.37579	−	0.813053i	0.0974800	−	0.0333600i
$595$		0			0
$596$	17.7699	−	13.7760i	0.727884	−	0.564286i
$597$	45.8741	−	45.8741i	1.87750	−	1.87750i
$598$	0.985359	+	0.482890i	0.0402943	+	0.0197468i
$599$	−22.3540			−0.913359			−0.456680	−	0.889631i	$-0.650961\pi$
$599$	−22.3540			−0.913359			−0.456680	+	0.889631i	$0.650961\pi$
$600$	16.6815	+	38.4595i	0.681020	+	1.57010i
$601$	43.6119			1.77897			0.889483	−	0.456969i	$-0.151065\pi$
$601$	43.6119			1.77897			0.889483	+	0.456969i	$0.151065\pi$
$602$		0			0
$603$	−3.21657	+	3.21657i	−0.130989	+	0.130989i
$604$	14.3540	−	11.1278i	0.584054	−	0.452783i
$605$	23.4709	+	7.00325i	0.954229	+	0.284723i
$606$	60.2660	−	20.6244i	2.44814	−	0.837811i
$607$	−16.8823	−	16.8823i	−0.685232	−	0.685232i	0.275943	−	0.961174i	$-0.411010\pi$
$607$	−16.8823	−	16.8823i	−0.685232	−	0.685232i	−0.961174	+	0.275943i	$0.911010\pi$
$608$	3.22785	−	3.77410i	0.130907	−	0.153060i
$609$		0			0
$610$	19.3448	+	17.8646i	0.783250	+	0.723316i
$611$		−	42.0304i		−	1.70037i
$612$	−4.13101	+	32.6285i	−0.166986	+	1.31893i
$613$	−20.8003	−	20.8003i	−0.840115	−	0.840115i	0.148759	−	0.988874i	$-0.452472\pi$
$613$	−20.8003	−	20.8003i	−0.840115	−	0.840115i	−0.988874	+	0.148759i	$0.952472\pi$
$614$	−0.978084	−	2.85802i	−0.0394722	−	0.115340i
$615$	−16.9974	+	9.18509i	−0.685403	+	0.370379i
$616$		0			0
$617$	12.8248	−	12.8248i	0.516307	−	0.516307i	−0.400145	−	0.916452i	$-0.631040\pi$
$617$	12.8248	−	12.8248i	0.516307	−	0.516307i	0.916452	+	0.400145i	$0.131040\pi$
$618$	2.84133	−	5.79787i	0.114295	−	0.233224i
$619$	−14.7614			−0.593309			−0.296655	−	0.954985i	$-0.595871\pi$
$619$	−14.7614			−0.593309			−0.296655	+	0.954985i	$0.595871\pi$
$620$	−35.8711	+	13.8921i	−1.44062	+	0.557919i
$621$	1.05433			0.0423090
$622$	7.93229	−	16.1862i	0.318056	−	0.649008i
$623$		0			0
$624$	17.9667	−	69.8173i	0.719245	−	2.79493i
$625$	9.98625	+	22.9189i	0.399450	+	0.916755i
$626$	9.32359	+	27.2441i	0.372645	+	1.08889i
$627$	−0.395486	−	0.395486i	−0.0157942	−	0.0157942i
$628$	−41.5591	−	5.26168i	−1.65839	−	0.209964i
$629$		−	5.19318i		−	0.207066i
$630$		0			0
$631$		−	31.4840i		−	1.25336i	−0.779278	−	0.626678i	$-0.784414\pi$
$631$		−	31.4840i		−	1.25336i	0.779278	−	0.626678i	$-0.215586\pi$
$632$	7.10545	+	34.3819i	0.282640	+	1.36764i
$633$	−7.12038	−	7.12038i	−0.283010	−	0.283010i
$634$	13.2295	−	4.52744i	0.525410	−	0.179808i
$635$	3.32649	+	6.15582i	0.132008	+	0.244286i
$636$	−14.2510	−	18.3827i	−0.565089	−	0.728920i
$637$		0			0
$638$	1.10018	+	0.539159i	0.0435565	+	0.0213455i
$639$	10.1294			0.400713
$640$	−23.8664	−	8.39013i	−0.943403	−	0.331649i
$641$	−22.8470			−0.902403			−0.451201	−	0.892422i	$-0.649004\pi$
$641$	−22.8470			−0.902403			−0.451201	+	0.892422i	$0.649004\pi$
$642$	−51.5614	−	25.2684i	−2.03496	−	0.997264i
$643$	13.3643	−	13.3643i	0.527038	−	0.527038i	−0.392650	−	0.919688i	$-0.628442\pi$
$643$	13.3643	−	13.3643i	0.527038	−	0.527038i	0.919688	+	0.392650i	$0.128442\pi$
$644$		0			0
$645$	−5.52416	+	18.5138i	−0.217514	+	0.728982i
$646$	3.33792	−	1.14232i	0.131329	−	0.0449438i
$647$	−16.5557	−	16.5557i	−0.650872	−	0.650872i	0.302331	−	0.953203i	$-0.402235\pi$
$647$	−16.5557	−	16.5557i	−0.650872	−	0.650872i	−0.953203	+	0.302331i	$0.902235\pi$
$648$	−4.08073	−	19.7459i	−0.160306	−	0.775692i
$649$		−	2.25495i		−	0.0885144i
$650$	10.6452	−	41.6536i	0.417539	−	1.63379i
$651$		0			0
$652$	−31.5520	−	3.99471i	−1.23567	−	0.156445i
$653$	15.6135	+	15.6135i	0.611004	+	0.611004i	0.943208	−	0.332204i	$-0.107792\pi$
$653$	15.6135	+	15.6135i	0.611004	+	0.611004i	−0.332204	+	0.943208i	$0.607792\pi$
$654$	−16.3448	−	47.7606i	−0.639133	−	1.86759i
$655$	2.37702	−	7.96643i	0.0928780	−	0.311274i
$656$	2.90571	−	11.2914i	0.113449	−	0.440853i
$657$	−24.2320	+	24.2320i	−0.945379	+	0.945379i
$658$		0			0
$659$	−23.8406			−0.928696			−0.464348	−	0.885653i	$-0.653711\pi$
$659$	−23.8406			−0.928696			−0.464348	+	0.885653i	$0.653711\pi$
$660$	−1.15111	+	2.60625i	−0.0448069	+	0.101448i
$661$	−22.0247			−0.856662			−0.428331	−	0.903622i	$-0.640898\pi$
$661$	−22.0247			−0.856662			−0.428331	+	0.903622i	$0.640898\pi$
$662$	18.2660	−	37.2725i	0.709926	−	1.44864i
$663$	36.2140	−	36.2140i	1.40643	−	1.40643i
$664$	−17.7383	−	11.6623i	−0.688379	−	0.452585i
$665$		0			0
$666$	4.84286	+	14.1512i	0.187657	+	0.548346i
$667$	0.363755	+	0.363755i	0.0140846	+	0.0140846i
$668$	−4.28339	+	33.8321i	−0.165729	+	1.30900i
$669$		−	82.8444i		−	3.20295i
$670$	−0.0988075	−	2.48375i	−0.00381727	−	0.0959556i
$671$			1.78961i			0.0690872i
$672$		0			0
$673$	15.2135	+	15.2135i	0.586437	+	0.586437i	0.936665	−	0.350227i	$-0.113896\pi$
$673$	15.2135	+	15.2135i	0.586437	+	0.586437i	−0.350227	+	0.936665i	$0.613896\pi$
$674$	41.5226	−	14.2100i	1.59939	−	0.547349i
$675$	−8.42751	−	40.4393i	−0.324375	−	1.55651i
$676$	−37.8830	+	29.3685i	−1.45704	+	1.12956i
$677$	8.40158	−	8.40158i	0.322899	−	0.322899i	−0.526979	−	0.849878i	$-0.676675\pi$
$677$	8.40158	−	8.40158i	0.322899	−	0.322899i	0.849878	+	0.526979i	$0.176675\pi$
$678$	−16.7381	−	8.20277i	−0.642825	−	0.315026i
$679$		0			0
$680$	−11.5671	−	13.7547i	−0.443578	−	0.527467i
$681$	−61.8676			−2.37077
$682$	−2.34762	−	1.15049i	−0.0898952	−	0.0440544i
$683$	−25.3664	+	25.3664i	−0.970617	+	0.970617i	−0.999580	−	0.0289635i	$-0.990779\pi$
$683$	−25.3664	+	25.3664i	−0.970617	+	0.970617i	0.0289635	+	0.999580i	$0.490779\pi$
$684$	−8.03041	+	6.22551i	−0.307051	+	0.238038i
$685$	5.14573	−	2.78066i	0.196608	−	0.106243i
$686$		0			0
$687$	6.82927	+	6.82927i	0.260553	+	0.260553i
$688$	−5.92955	−	10.0388i	−0.226062	−	0.382727i
$689$			23.8539i			0.908760i
$690$	−0.811608	+	0.878857i	−0.0308974	+	0.0334575i
$691$		−	43.8205i		−	1.66701i	−0.552512	−	0.833505i	$-0.686331\pi$
$691$		−	43.8205i		−	1.66701i	0.552512	−	0.833505i	$-0.313669\pi$
$692$	−0.114043	+	0.900764i	−0.00433527	+	0.0342419i
$693$		0			0
$694$	3.71997	+	10.8700i	0.141208	+	0.412619i
$695$	−23.3709	−	6.97341i	−0.886508	−	0.264516i
$696$	18.5668	−	28.2401i	0.703775	−	1.07044i
$697$	5.85678	−	5.85678i	0.221841	−	0.221841i
$698$	5.26760	−	10.7488i	0.199382	−	0.406848i
$699$	20.4792			0.774593
$700$		0			0
$701$	38.4455			1.45207			0.726033	−	0.687660i	$-0.241362\pi$
$701$	38.4455			1.45207			0.726033	+	0.687660i	$0.241362\pi$
$702$	−31.2608	+	63.7891i	−1.17986	+	2.40757i
$703$	1.13449	−	1.13449i	0.0427882	−	0.0427882i
$704$	−0.681547	−	1.57851i	−0.0256868	−	0.0594925i
$705$	43.9080	+	13.1013i	1.65367	+	0.493423i
$706$	−9.52347	−	27.8282i	−0.358420	−	1.04733i
$707$		0			0
$708$	−61.7102	−	7.81296i	−2.31921	−	0.293629i
$709$			39.0425i			1.46627i	0.680082	+	0.733137i	$0.261944\pi$
$709$			39.0425i			1.46627i	−0.680082	+	0.733137i	$0.738056\pi$
$710$	−3.75524	+	4.06640i	−0.140932	+	0.152609i
$711$		−	71.8330i		−	2.69395i
$712$	35.2909	−	7.29329i	1.32258	−	0.273328i
$713$	−0.776200	−	0.776200i	−0.0290689	−	0.0290689i
$714$		0			0
$715$	2.57061	−	1.38911i	0.0961352	−	0.0519496i
$716$	5.94948	+	7.67436i	0.222343	+	0.286804i
$717$	21.5412	−	21.5412i	0.804473	−	0.804473i
$718$	29.9254	+	14.6654i	1.11680	+	0.547306i
$719$	4.65847			0.173732			0.0868659	−	0.996220i	$-0.472315\pi$
$719$	4.65847			0.173732			0.0868659	+	0.996220i	$0.472315\pi$
$720$	44.3466	+	26.6940i	1.65270	+	0.994825i
$721$		0			0
$722$	−23.1497	−	11.3448i	−0.861542	−	0.422211i
$723$	−10.0370	+	10.0370i	−0.373281	+	0.373281i
$724$	−8.43392	−	10.8791i	−0.313444	−	0.404318i
$725$	11.0443	−	16.8595i	0.410177	−	0.626145i
$726$	43.4462	−	14.8683i	1.61244	−	0.551816i
$727$	−8.55868	−	8.55868i	−0.317424	−	0.317424i	0.530353	−	0.847777i	$-0.322059\pi$
$727$	−8.55868	−	8.55868i	−0.317424	−	0.317424i	−0.847777	+	0.530353i	$0.822059\pi$
$728$		0			0
$729$		−	32.2153i		−	1.19316i
$730$	−0.744364	−	18.7113i	−0.0275502	−	0.692535i
$731$		−	8.28274i		−	0.306348i
$732$	48.9756	+	6.20066i	1.81019	+	0.229183i
$733$	0.785057	+	0.785057i	0.0289967	+	0.0289967i	0.721456	−	0.692460i	$-0.243473\pi$
$733$	0.785057	+	0.785057i	0.0289967	+	0.0289967i	−0.692460	+	0.721456i	$0.743473\pi$
$734$	2.44248	+	7.13708i	0.0901535	+	0.263434i
$735$		0			0
$736$	−0.0561491	−	0.719731i	−0.00206968	−	0.0265297i
$737$	0.119458	−	0.119458i	0.00440028	−	0.00440028i
$738$	−10.4977	+	21.4211i	−0.386427	+	0.788523i
$739$	4.86588			0.178994			0.0894972	−	0.995987i	$-0.471474\pi$
$739$	4.86588			0.178994			0.0894972	+	0.995987i	$0.471474\pi$
$740$	−7.47630	−	3.30208i	−0.274834	−	0.121387i
$741$	15.8225			0.581253
$742$		0			0
$743$	−24.8474	+	24.8474i	−0.911564	+	0.911564i	−0.996395	−	0.0848314i	$-0.972965\pi$
$743$	−24.8474	+	24.8474i	−0.911564	+	0.911564i	0.0848314	+	0.996395i	$0.472965\pi$
$744$	−39.6190	+	60.2603i	−1.45250	+	2.20925i
$745$	7.18763	−	24.0889i	0.263334	−	0.882547i
$746$	−14.7624	−	43.1367i	−0.540490	−	1.57935i
$747$	30.7128	+	30.7128i	1.12372	+	1.12372i
$748$	0.153418	−	1.21176i	0.00560952	−	0.0443065i
$749$		0			0
$750$	40.1962	+	24.1046i	1.46776	+	0.880174i
$751$			20.0268i			0.730789i	0.930853	+	0.365394i	$0.119066\pi$
$751$			20.0268i			0.730789i	−0.930853	+	0.365394i	$0.880934\pi$
$752$	−23.8084	+	14.0627i	−0.868205	+	0.512814i
$753$	55.0545	+	55.0545i	2.00630	+	2.00630i
$754$	−32.7931	+	11.2226i	−1.19425	+	0.408702i
$755$	5.80593	−	19.4582i	0.211299	−	0.708156i
$756$		0			0
$757$	10.7543	−	10.7543i	0.390871	−	0.390871i	−0.484127	−	0.874998i	$-0.660863\pi$
$757$	10.7543	−	10.7543i	0.390871	−	0.390871i	0.874998	+	0.484127i	$0.160863\pi$
$758$	4.04553	+	1.98257i	0.146940	+	0.0720102i
$759$	−0.0813040			−0.00295115
$760$	0.477890	−	5.53174i	0.0173349	−	0.200657i
$761$	−20.6034			−0.746874			−0.373437	−	0.927655i	$-0.621821\pi$
$761$	−20.6034			−0.746874			−0.373437	+	0.927655i	$0.621821\pi$
$762$	11.7796	+	5.77277i	0.426730	+	0.209125i
$763$		0			0
$764$	−27.2549	+	21.1291i	−0.986048	+	0.764426i
$765$	17.4813	+	32.3499i	0.632036	+	1.16961i
$766$	−37.7186	+	12.9082i	−1.36283	+	0.466392i
$767$	45.1076	+	45.1076i	1.62874	+	1.62874i
$768$	−45.5599	+	13.1824i	−1.64400	+	0.475678i
$769$			9.33534i			0.336641i	0.985732	+	0.168320i	$0.0538343\pi$
$769$			9.33534i			0.336641i	−0.985732	+	0.168320i	$0.946166\pi$
$770$		0			0
$771$		−	68.7086i		−	2.47448i
$772$	5.09212	−	40.2199i	0.183269	−	1.44754i
$773$	10.3739	+	10.3739i	0.373125	+	0.373125i	0.868614	−	0.495489i	$-0.165011\pi$
$773$	10.3739	+	10.3739i	0.373125	+	0.373125i	−0.495489	+	0.868614i	$0.665011\pi$
$774$	7.72401	+	22.5701i	0.277634	+	0.811264i
$775$	−23.5670	+	35.9757i	−0.846553	+	1.29228i
$776$	8.64256	+	5.68218i	0.310250	+	0.203978i
$777$		0			0
$778$	−10.1729	+	20.7582i	−0.364715	+	0.744218i
$779$	2.55892			0.0916829
$780$	−29.1084	−	75.1617i	−1.04225	−	2.69122i
$781$	−0.376187			−0.0134610
$782$	0.225687	−	0.460524i	0.00807053	−	0.0164683i
$783$	−23.5484	+	23.5484i	−0.841550	+	0.841550i
$784$		0			0
$785$	−41.2042	+	22.2660i	−1.47064	+	0.794706i
$786$	−5.04657	−	14.7464i	−0.180005	−	0.525986i
$787$	−20.1167	−	20.1167i	−0.717081	−	0.717081i	0.250925	−	0.968007i	$-0.419265\pi$
$787$	−20.1167	−	20.1167i	−0.717081	−	0.717081i	−0.968007	+	0.250925i	$0.919265\pi$
$788$	−36.3082	−	4.59688i	−1.29342	−	0.163757i
$789$			17.6707i			0.629093i
$790$	28.8371	+	26.6305i	1.02598	+	0.947469i
$791$		0			0
$792$	0.711966	+	3.44507i	0.0252986	+	0.122415i
$793$	−35.7991	−	35.7991i	−1.27126	−	1.27126i
$794$	20.3244	−	6.95551i	0.721287	−	0.246842i
$795$	−24.9195	−	7.43548i	−0.883803	−	0.263709i
$796$	26.8184	+	34.5936i	0.950553	+	1.22614i
$797$	4.43257	−	4.43257i	0.157010	−	0.157010i	−0.624231	−	0.781240i	$-0.714587\pi$
$797$	4.43257	−	4.43257i	0.157010	−	0.157010i	0.781240	+	0.624231i	$0.214587\pi$
$798$		0			0
$799$	−19.6436			−0.694941
$800$	−27.1567	+	7.90657i	−0.960134	+	0.279540i
$801$	−73.7319			−2.60519
$802$	30.1739	+	14.7871i	1.06548	+	0.522152i
$803$	0.899932	−	0.899932i	0.0317579	−	0.0317579i
$804$	−2.85525	−	3.68304i	−0.100697	−	0.129891i
$805$		0			0
$806$	69.9757	−	23.9473i	2.46479	−	0.843509i
$807$	0.140025	+	0.140025i	0.00492911	+	0.00492911i
$808$	8.69781	+	42.0870i	0.305988	+	1.48062i
$809$		−	2.61396i		−	0.0919020i	−0.998944	−	0.0459510i	$-0.985368\pi$
$809$		−	2.61396i		−	0.0919020i	0.998944	−	0.0459510i	$-0.0146318\pi$
$810$	−16.5614	−	15.2941i	−0.581908	−	0.537381i
$811$		−	20.5143i		−	0.720354i	−0.932884	−	0.360177i	$-0.882716\pi$
$811$		−	20.5143i		−	0.720354i	0.932884	−	0.360177i	$-0.117284\pi$
$812$		0			0
$813$	5.82774	+	5.82774i	0.204388	+	0.204388i
$814$	−0.179855	−	0.525548i	−0.00630392	−	0.0184205i
$815$	−31.2825	+	16.9045i	−1.09578	+	0.592138i
$816$	−32.6303	−	8.39706i	−1.14229	−	0.293956i
$817$	1.80943	−	1.80943i	0.0633040	−	0.0633040i
$818$	−14.0452	+	28.6600i	−0.491080	+	1.00207i
$819$		0			0
$820$	−4.70763	−	12.1557i	−0.164397	−	0.424495i
$821$	−7.11902			−0.248456			−0.124228	−	0.992254i	$-0.539645\pi$
$821$	−7.11902			−0.248456			−0.124228	+	0.992254i	$0.539645\pi$
$822$	4.82554	−	9.84674i	0.168310	−	0.343444i
$823$	−15.9450	+	15.9450i	−0.555807	+	0.555807i	−0.928111	−	0.372304i	$-0.878568\pi$
$823$	−15.9450	+	15.9450i	−0.555807	+	0.555807i	0.372304	+	0.928111i	$0.378568\pi$
$824$	3.64003	+	2.39319i	0.126807	+	0.0833708i
$825$	0.649880	+	3.11844i	0.0226259	+	0.108570i
$826$		0			0
$827$	27.0197	+	27.0197i	0.939566	+	0.939566i	0.998275	−	0.0587089i	$-0.0186984\pi$
$827$	27.0197	+	27.0197i	0.939566	+	0.939566i	−0.0587089	+	0.998275i	$0.518698\pi$
$828$	−0.185526	+	1.46537i	−0.00644748	+	0.0509251i
$829$			22.0054i			0.764278i	0.924105	+	0.382139i	$0.124812\pi$
$829$			22.0054i			0.764278i	−0.924105	+	0.382139i	$0.875188\pi$
$830$	−23.7156	+	0.943444i	−0.823181	+	0.0327474i
$831$		−	16.9792i		−	0.589003i
$832$	45.2099	+	17.9428i	1.56737	+	0.622054i
$833$		0			0
$834$	−43.2611	+	14.8050i	−1.49801	+	0.512654i
$835$	18.1261	+	33.5432i	0.627280	+	1.16081i
$836$	0.298235	−	0.231204i	0.0103147	−	0.00799637i
$837$	50.2488	−	50.2488i	1.73685	−	1.73685i
$838$	15.7916	+	7.73889i	0.545511	+	0.267335i
$839$	−47.2741			−1.63208			−0.816041	−	0.577994i	$-0.803836\pi$
$839$	−47.2741			−1.63208			−0.816041	+	0.577994i	$0.803836\pi$
$840$		0			0
$841$	12.7512			0.439697
$842$	−39.7229	−	19.4668i	−1.36894	−	0.670869i
$843$	−48.0480	+	48.0480i	−1.65486	+	1.65486i
$844$	5.36947	−	4.16263i	0.184825	−	0.143284i
$845$	−15.3230	+	51.3541i	−0.527128	+	1.76663i
$846$	53.5279	−	18.3185i	1.84033	−	0.629804i
$847$		0			0
$848$	13.5122	−	7.98113i	0.464011	−	0.274073i
$849$			1.68546i			0.0578449i
$850$	−19.4675	−	4.97521i	−0.667730	−	0.170648i
$851$		−	0.233229i		−	0.00799499i
$852$	−1.30342	+	10.2950i	−0.0446543	+	0.352700i
$853$	−11.2255	−	11.2255i	−0.384355	−	0.384355i	0.488313	−	0.872668i	$-0.337612\pi$
$853$	−11.2255	−	11.2255i	−0.384355	−	0.384355i	−0.872668	+	0.488313i	$0.837612\pi$
$854$		0			0
$855$	−3.24817	+	10.8860i	−0.111085	+	0.372294i
$856$	21.2831	−	32.3714i	0.727440	−	1.10643i
$857$	−3.34445	+	3.34445i	−0.114244	+	0.114244i	−0.761918	−	0.647674i	$-0.775742\pi$
$857$	−3.34445	+	3.34445i	−0.114244	+	0.114244i	0.647674	+	0.761918i	$0.275742\pi$
$858$	2.41065	−	4.91904i	0.0822982	−	0.167933i
$859$	5.60701			0.191309			0.0956543	−	0.995415i	$-0.469506\pi$
$859$	5.60701			0.191309			0.0956543	+	0.995415i	$0.469506\pi$
$860$	−11.9242	−	5.26657i	−0.406610	−	0.179589i
$861$		0			0
$862$	−11.9046	+	24.2920i	−0.405474	+	0.827389i
$863$	35.2995	−	35.2995i	1.20161	−	1.20161i	0.227931	−	0.973677i	$-0.426804\pi$
$863$	35.2995	−	35.2995i	1.20161	−	1.20161i	0.973677	−	0.227931i	$-0.0731959\pi$
$864$	46.5932	−	3.63492i	1.58513	−	0.123662i
$865$	0.482599	+	0.893071i	0.0164088	+	0.0303653i
$866$	−3.15679	−	9.22435i	−0.107272	−	0.313456i
$867$	18.7080	+	18.7080i	0.635358	+	0.635358i
$868$		0			0
$869$			2.66775i			0.0904971i
$870$	−1.50200	−	37.7562i	−0.0509226	−	1.28006i
$871$			4.77922i			0.161938i
$872$	33.3539	−	6.89299i	1.12950	−	0.233426i
$873$	−14.9641	−	14.9641i	−0.506458	−	0.506458i
$874$	0.149908	−	0.0513022i	0.00507072	−	0.00173532i
$875$		0			0
$876$	−21.5100	−	27.7461i	−0.726754	−	0.937455i
$877$	19.6457	−	19.6457i	0.663389	−	0.663389i	−0.292789	−	0.956177i	$-0.594583\pi$
$877$	19.6457	−	19.6457i	0.663389	−	0.663389i	0.956177	+	0.292789i	$0.0945832\pi$
$878$	41.6330	+	20.4029i	1.40505	+	0.688564i
$879$	6.00606			0.202579
$880$	−1.64695	−	0.991366i	−0.0555188	−	0.0334189i
$881$	3.05077			0.102783			0.0513915	−	0.998679i	$-0.483634\pi$
$881$	3.05077			0.102783			0.0513915	+	0.998679i	$0.483634\pi$
$882$		0			0
$883$	15.9128	−	15.9128i	0.535509	−	0.535509i	−0.386697	−	0.922207i	$-0.626384\pi$
$883$	15.9128	−	15.9128i	0.535509	−	0.535509i	0.922207	+	0.386697i	$0.126384\pi$
$884$	21.1710	+	27.3089i	0.712058	+	0.918498i
$885$	−61.1832	+	33.0622i	−2.05665	+	1.11137i
$886$	−16.1099	+	5.51319i	−0.541223	+	0.185219i
$887$	27.6148	+	27.6148i	0.927215	+	0.927215i	0.997525	−	0.0703102i	$-0.0223989\pi$
$887$	27.6148	+	27.6148i	0.927215	+	0.927215i	−0.0703102	+	0.997525i	$0.522399\pi$
$888$	−15.0056	+	3.10110i	−0.503556	+	0.104066i
$889$		0			0
$890$	27.3345	−	29.5994i	0.916253	−	0.992174i
$891$		−	1.53211i		−	0.0513277i
$892$	55.4522	+	7.02064i	1.85668	+	0.235068i
$893$	−4.29131	−	4.29131i	−0.143603	−	0.143603i
$894$	−15.2598	−	44.5901i	−0.510364	−	1.49132i
$895$	10.4033	+	3.10415i	0.347745	+	0.103760i
$896$		0			0
$897$	1.62639	−	1.62639i	0.0543037	−	0.0543037i
$898$	−3.44086	+	7.02124i	−0.114823	+	0.234302i
$899$	34.6725			1.15639
$900$	57.6876	−	4.59708i	1.92292	−	0.153236i
$901$	11.1485			0.371411
$902$	0.389867	−	0.795543i	0.0129812	−	0.0264887i
$903$		0			0
$904$	6.90903	−	10.5086i	0.229791	−	0.349511i
$905$	−14.7477	−	4.40041i	−0.490229	−	0.146274i
$906$	−12.3263	−	36.0184i	−0.409516	−	1.19663i
$907$	−34.9739	−	34.9739i	−1.16129	−	1.16129i	−0.984193	−	0.177098i	$-0.943329\pi$
$907$	−34.9739	−	34.9739i	−1.16129	−	1.16129i	−0.177098	−	0.984193i	$-0.556671\pi$
$908$	5.24297	−	41.4113i	0.173994	−	1.37428i
$909$		−	87.9310i		−	2.91649i
$910$		0			0
$911$			29.9032i			0.990736i	0.868683	+	0.495368i	$0.164967\pi$
$911$			29.9032i			0.990736i	−0.868683	+	0.495368i	$0.835033\pi$
$912$	−5.29395	−	8.96276i	−0.175300	−	0.296786i
$913$	−1.14062	−	1.14062i	−0.0377489	−	0.0377489i
$914$	36.1413	−	12.3684i	1.19545	−	0.409111i
$915$	48.5573	−	26.2394i	1.60525	−	0.867449i
$916$	−5.14994	+	3.99245i	−0.170159	+	0.131914i
$917$		0			0
$918$	29.8129	+	14.6103i	0.983973	+	0.482210i
$919$	−46.1221			−1.52143			−0.760714	−	0.649087i	$-0.775151\pi$
$919$	−46.1221			−1.52143			−0.760714	+	0.649087i	$0.775151\pi$
$920$	−0.519486	−	0.617731i	−0.0171270	−	0.0203660i
$921$	−6.33172			−0.208637
$922$	10.4754	+	5.13361i	0.344988	+	0.169066i
$923$	7.52519	−	7.52519i	0.247695	−	0.247695i
$924$		0			0
$925$	−8.94556	+	1.86425i	−0.294128	+	0.0612961i
$926$	29.3080	−	10.0299i	0.963122	−	0.329603i
$927$	−6.30250	−	6.30250i	−0.207001	−	0.207001i
$928$	17.3291	+	14.8210i	0.568857	+	0.486523i
$929$			36.7649i			1.20622i	0.797659	+	0.603108i	$0.206071\pi$
$929$			36.7649i			1.20622i	−0.797659	+	0.603108i	$0.793929\pi$
$930$	3.20505	+	80.5663i	0.105098	+	2.64187i
$931$		0			0
$932$	−1.73551	+	13.7078i	−0.0568484	+	0.449014i
$933$	−26.7163	−	26.7163i	−0.874652	−	0.874652i
$934$	17.9908	+	52.5701i	0.588675	+	1.72015i
$935$	−0.649222	−	1.20142i	−0.0212318	−	0.0392905i
$936$	−83.1566	−	54.6725i	−2.71806	−	1.78703i
$937$	−25.1593	+	25.1593i	−0.821917	+	0.821917i	−0.986383	−	0.164465i	$-0.947410\pi$
$937$	−25.1593	+	25.1593i	−0.821917	+	0.821917i	0.164465	+	0.986383i	$0.447410\pi$
$938$		0			0
$939$	60.3571			1.96968
$940$	−12.4904	+	28.2797i	−0.407391	+	0.922383i
$941$	25.6403			0.835851			0.417926	−	0.908481i	$-0.362757\pi$
$941$	25.6403			0.835851			0.417926	+	0.908481i	$0.362757\pi$
$942$	−38.6402	+	78.8472i	−1.25897	+	2.56898i
$943$	0.263032	−	0.263032i	0.00856550	−	0.00856550i
$944$	10.4593	−	40.6438i	0.340420	−	1.32284i
$945$		0			0
$946$	−0.286856	−	0.838211i	−0.00932649	−	0.0272526i
$947$	−2.04606	−	2.04606i	−0.0664879	−	0.0664879i	0.673081	−	0.739569i	$-0.264971\pi$
$947$	−2.04606	−	2.04606i	−0.0664879	−	0.0664879i	−0.739569	+	0.673081i	$0.764971\pi$
$948$	73.0071	+	9.24323i	2.37116	+	0.300206i
$949$			36.0042i			1.16874i
$950$	−3.16596	−	5.33970i	−0.102717	−	0.173243i
$951$		−	29.3088i		−	0.950404i
$952$		0			0
$953$	−29.4048	−	29.4048i	−0.952513	−	0.952513i	0.0464091	−	0.998923i	$-0.485222\pi$
$953$	−29.4048	−	29.4048i	−0.952513	−	0.952513i	−0.998923	+	0.0464091i	$0.985222\pi$
$954$	−30.3791	+	10.3965i	−0.983561	+	0.336598i
$955$	−11.0241	+	36.9467i	−0.356733	+	1.19557i
$956$	12.5932	+	16.2442i	0.407293	+	0.525376i
$957$	1.81591	−	1.81591i	0.0587000	−	0.0587000i
$958$	4.91097	+	2.40669i	0.158666	+	0.0777567i
$959$		0			0
$960$	−32.8367	+	41.6366i	−1.05980	+	1.34382i
$961$	−42.9862			−1.38665
$962$	14.1108	+	6.91519i	0.454950	+	0.222955i
$963$	−56.0492	+	56.0492i	−1.80616	+	1.80616i
$964$	−5.86774	−	7.56891i	−0.188987	−	0.243778i
$965$	−21.5484	−	39.8763i	−0.693668	−	1.28367i
$966$		0			0
$967$	−33.9934	−	33.9934i	−1.09315	−	1.09315i	−0.995190	−	0.0979625i	$-0.968767\pi$
$967$	−33.9934	−	33.9934i	−1.09315	−	1.09315i	−0.0979625	−	0.995190i	$-0.531233\pi$
$968$	6.27032	+	30.3409i	0.201536	+	0.975194i
$969$		−	7.39489i		−	0.237558i
$970$	11.5549	−	0.459671i	0.371004	−	0.0147591i
$971$		−	13.5798i		−	0.435796i	−0.975972	−	0.217898i	$-0.930080\pi$
$971$		−	13.5798i		−	0.435796i	0.975972	−	0.217898i	$-0.0699200\pi$
$972$	7.24844	+	0.917705i	0.232494	+	0.0294354i
$973$		0			0
$974$	−0.203827	−	0.595596i	−0.00653104	−	0.0190841i
$975$	−75.3809	−	49.3807i	−2.41412	−	1.58145i
$976$	−8.30087	+	32.2565i	−0.265704	+	1.03251i
$977$	−29.3429	+	29.3429i	−0.938764	+	0.938764i	−0.998230	−	0.0594666i	$-0.981060\pi$
$977$	−29.3429	+	29.3429i	−0.938764	+	0.938764i	0.0594666	+	0.998230i	$0.481060\pi$
$978$	−29.3359	+	59.8614i	−0.938060	+	1.91416i
$979$	2.73827			0.0875155
$980$		0			0
$981$	−69.6851			−2.22487
$982$	−25.1576	+	51.3352i	−0.802810	+	1.63817i
$983$	1.45861	−	1.45861i	0.0465225	−	0.0465225i	−0.683463	−	0.729985i	$-0.739527\pi$
$983$	1.45861	−	1.45861i	0.0465225	−	0.0465225i	0.729985	+	0.683463i	$0.239527\pi$
$984$	−20.4205	−	13.4257i	−0.650981	−	0.427997i
$985$	−35.9981	+	19.4527i	−1.14699	+	0.619814i
$986$	5.24505	+	15.3264i	0.167037	+	0.488092i
$987$		0			0
$988$	−1.34087	+	10.5908i	−0.0426589	+	0.336939i
$989$		−	0.371983i		−	0.0118284i
$990$	2.88947	+	2.66837i	0.0918334	+	0.0848064i
$991$			29.9628i			0.951798i	0.879500	+	0.475899i	$0.157877\pi$
$991$			29.9628i			0.951798i	−0.879500	+	0.475899i	$0.842123\pi$
$992$	−36.9779	−	31.6258i	−1.17405	−	1.00412i
$993$	−61.5205	−	61.5205i	−1.95229	−	1.95229i
$994$		0			0
$995$	46.8950	+	13.9925i	1.48667	+	0.443593i
$996$	−35.1668	+	27.2628i	−1.11430	+	0.863855i
$997$	41.4242	−	41.4242i	1.31192	−	1.31192i	0.391919	−	0.920000i	$-0.371811\pi$
$997$	41.4242	−	41.4242i	1.31192	−	1.31192i	0.920000	−	0.391919i	$-0.128189\pi$
$998$	40.3674	+	19.7826i	1.27781	+	0.626209i
$999$	15.0985			0.477696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.l.883.15		36
4.3	odd	2	inner	980.2.k.l.883.7		36
5.2	odd	4	inner	980.2.k.l.687.7		36
7.2	even	3		980.2.x.l.263.10		72
7.3	odd	6		980.2.x.k.863.4		72
7.4	even	3		980.2.x.l.863.4		72
7.5	odd	6		980.2.x.k.263.10		72
7.6	odd	2		140.2.k.a.43.15	yes	36
20.7	even	4	inner	980.2.k.l.687.15		36
28.3	even	6		980.2.x.k.863.18		72
28.11	odd	6		980.2.x.l.863.18		72
28.19	even	6		980.2.x.k.263.6		72
28.23	odd	6		980.2.x.l.263.6		72
28.27	even	2		140.2.k.a.43.7	✓	36
35.2	odd	12		980.2.x.l.67.18		72
35.12	even	12		980.2.x.k.67.18		72
35.13	even	4		700.2.k.b.407.12		36
35.17	even	12		980.2.x.k.667.6		72
35.27	even	4		140.2.k.a.127.7	yes	36
35.32	odd	12		980.2.x.l.667.6		72
35.34	odd	2		700.2.k.b.43.4		36
140.27	odd	4		140.2.k.a.127.15	yes	36
140.47	odd	12		980.2.x.k.67.4		72
140.67	even	12		980.2.x.l.667.10		72
140.83	odd	4		700.2.k.b.407.4		36
140.87	odd	12		980.2.x.k.667.10		72
140.107	even	12		980.2.x.l.67.4		72
140.139	even	2		700.2.k.b.43.12		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.7	✓	36	28.27	even	2
140.2.k.a.43.15	yes	36	7.6	odd	2
140.2.k.a.127.7	yes	36	35.27	even	4
140.2.k.a.127.15	yes	36	140.27	odd	4
700.2.k.b.43.4		36	35.34	odd	2
700.2.k.b.43.12		36	140.139	even	2
700.2.k.b.407.4		36	140.83	odd	4
700.2.k.b.407.12		36	35.13	even	4
980.2.k.l.687.7		36	5.2	odd	4	inner
980.2.k.l.687.15		36	20.7	even	4	inner
980.2.k.l.883.7		36	4.3	odd	2	inner
980.2.k.l.883.15		36	1.1	even	1	trivial
980.2.x.k.67.4		72	140.47	odd	12
980.2.x.k.67.18		72	35.12	even	12
980.2.x.k.263.6		72	28.19	even	6
980.2.x.k.263.10		72	7.5	odd	6
980.2.x.k.667.6		72	35.17	even	12
980.2.x.k.667.10		72	140.87	odd	12
980.2.x.k.863.4		72	7.3	odd	6
980.2.x.k.863.18		72	28.3	even	6
980.2.x.l.67.4		72	140.107	even	12
980.2.x.l.67.18		72	35.2	odd	12
980.2.x.l.263.6		72	28.23	odd	6
980.2.x.l.263.10		72	7.2	even	3
980.2.x.l.667.6		72	35.32	odd	12
980.2.x.l.667.10		72	140.67	even	12
980.2.x.l.863.4		72	7.4	even	3
980.2.x.l.863.18		72	28.11	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26992 + 0.622342i) q^{2} +(2.09607 - 2.09607i) q^{3} +(1.22538 + 1.58065i) q^{4} +(2.14272 + 0.639344i) q^{5} +(3.96631 - 1.35737i) q^{6} +(0.572433 + 2.76990i) q^{8} -5.78704i q^{9} +O(q^{10})\)	\(q+(1.26992 + 0.622342i) q^{2} +(2.09607 - 2.09607i) q^{3} +(1.22538 + 1.58065i) q^{4} +(2.14272 + 0.639344i) q^{5} +(3.96631 - 1.35737i) q^{6} +(0.572433 + 2.76990i) q^{8} -5.78704i q^{9} +(2.32318 + 2.14542i) q^{10} +0.214920i q^{11} +(5.88164 + 0.744658i) q^{12} +(-4.29923 - 4.29923i) q^{13} +(5.83140 - 3.15118i) q^{15} +(-0.996878 + 3.87379i) q^{16} +(-2.00932 + 2.00932i) q^{17} +(3.60152 - 7.34907i) q^{18} -0.877903 q^{19} +(1.61507 + 4.17032i) q^{20} +(-0.133754 + 0.272931i) q^{22} +(-0.0902398 + 0.0902398i) q^{23} +(7.00576 + 4.60604i) q^{24} +(4.18248 + 2.73987i) q^{25} +(-2.78408 - 8.13526i) q^{26} +(-5.84185 - 5.84185i) q^{27} -4.03098i q^{29} +(9.36651 - 0.372615i) q^{30} +8.60152i q^{31} +(-3.67677 + 4.29899i) q^{32} +(0.450489 + 0.450489i) q^{33} +(-3.80215 + 1.30119i) q^{34} +(9.14726 - 7.09134i) q^{36} +(-1.29227 + 1.29227i) q^{37} +(-1.11487 - 0.546356i) q^{38} -18.0230 q^{39} +(-0.544354 + 6.30109i) q^{40} -2.91481 q^{41} +(-2.06108 + 2.06108i) q^{43} +(-0.339713 + 0.263360i) q^{44} +(3.69991 - 12.4000i) q^{45} +(-0.170757 + 0.0584371i) q^{46} +(4.88813 + 4.88813i) q^{47} +(6.03021 + 10.2093i) q^{48} +(3.60627 + 6.08234i) q^{50} +8.42336i q^{51} +(1.52736 - 12.0638i) q^{52} +(-2.77420 - 2.77420i) q^{53} +(-3.78304 - 11.0543i) q^{54} +(-0.137408 + 0.460514i) q^{55} +(-1.84015 + 1.84015i) q^{57} +(2.50864 - 5.11901i) q^{58} -10.4920 q^{59} +(12.1266 + 5.35598i) q^{60} +8.32686 q^{61} +(-5.35309 + 10.9232i) q^{62} +(-7.34464 + 3.17116i) q^{64} +(-6.46335 - 11.9607i) q^{65} +(0.291726 + 0.852442i) q^{66} +(-0.555822 - 0.555822i) q^{67} +(-5.63820 - 0.713837i) q^{68} +0.378298i q^{69} +1.75036i q^{71} +(16.0295 - 3.31270i) q^{72} +(-4.18728 - 4.18728i) q^{73} +(-2.44532 + 0.836846i) q^{74} +(14.5097 - 3.02382i) q^{75} +(-1.07577 - 1.38765i) q^{76} +(-22.8877 - 11.2165i) q^{78} +12.4127 q^{79} +(-4.61271 + 7.66309i) q^{80} -7.12875 q^{81} +(-3.70157 - 1.81401i) q^{82} +(-5.30716 + 5.30716i) q^{83} +(-5.59005 + 3.02076i) q^{85} +(-3.90010 + 1.33471i) q^{86} +(-8.44922 - 8.44922i) q^{87} +(-0.595307 + 0.123028i) q^{88} -12.7409i q^{89} +(12.4156 - 13.4444i) q^{90} +(-0.253215 - 0.0320589i) q^{92} +(18.0294 + 18.0294i) q^{93} +(3.16544 + 9.24961i) q^{94} +(-1.88110 - 0.561282i) q^{95} +(1.30422 + 16.7178i) q^{96} +(2.58579 - 2.58579i) q^{97} +1.24375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 8 q^{6}+O(q^{10}) \) 36 * q + 8 * q^6	\( 36 q + 8 q^{6} + 16 q^{10} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} + 28 q^{18} - 20 q^{20} + 4 q^{22} - 20 q^{25} + 32 q^{26} - 4 q^{30} + 20 q^{37} + 36 q^{40} - 20 q^{45} + 16 q^{46} + 24 q^{48} + 40 q^{50} - 16 q^{52} - 44 q^{53} - 16 q^{57} - 4 q^{58} + 40 q^{60} + 64 q^{61} - 40 q^{62} + 4 q^{65} - 32 q^{66} - 80 q^{68} + 80 q^{72} - 52 q^{73} - 8 q^{76} - 76 q^{78} + 20 q^{80} - 36 q^{81} - 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} + 16 q^{90} - 56 q^{92} + 32 q^{93} - 120 q^{96} - 20 q^{97}+O(q^{100}) \) 36 * q + 8 * q^6 + 16 * q^10 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 + 28 * q^18 - 20 * q^20 + 4 * q^22 - 20 * q^25 + 32 * q^26 - 4 * q^30 + 20 * q^37 + 36 * q^40 - 20 * q^45 + 16 * q^46 + 24 * q^48 + 40 * q^50 - 16 * q^52 - 44 * q^53 - 16 * q^57 - 4 * q^58 + 40 * q^60 + 64 * q^61 - 40 * q^62 + 4 * q^65 - 32 * q^66 - 80 * q^68 + 80 * q^72 - 52 * q^73 - 8 * q^76 - 76 * q^78 + 20 * q^80 - 36 * q^81 - 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 + 16 * q^90 - 56 * q^92 + 32 * q^93 - 120 * q^96 - 20 * q^97

Introduction

L-functions

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