LMFDB - Embedded newform 980.2.x.k.263.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			263.5
Character	$\chi$	$=$	980.263
Dual form			980.2.x.k.667.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977529 + 1.02198i) q^{2} +(-0.346182 - 1.29197i) q^{3} +(-0.0888759 - 1.99802i) q^{4} +(1.92528 + 1.13723i) q^{5} +(1.65877 + 0.909146i) q^{6} +(2.12881 + 1.86230i) q^{8} +(1.04873 - 0.605487i) q^{9} +(-3.04424 + 0.855919i) q^{10} +(-4.33338 - 2.50188i) q^{11} +(-2.55062 + 0.806505i) q^{12} +(-3.27438 - 3.27438i) q^{13} +(0.802768 - 2.88109i) q^{15} +(-3.98420 + 0.355152i) q^{16} +(-0.873420 - 3.25965i) q^{17} +(-0.406374 + 1.66366i) q^{18} +(0.214380 + 0.371316i) q^{19} +(2.10110 - 3.94783i) q^{20} +(6.79287 - 1.98296i) q^{22} +(-3.47589 - 0.931361i) q^{23} +(1.66907 - 3.39506i) q^{24} +(2.41342 + 4.37898i) q^{25} +(6.54714 - 0.145543i) q^{26} +(-3.98268 - 3.98268i) q^{27} +7.51811i q^{29} +(2.15968 + 3.63676i) q^{30} +(-0.353285 - 0.203969i) q^{31} +(3.53171 - 4.41894i) q^{32} +(-1.73221 + 6.46470i) q^{33} +(4.18508 + 2.29378i) q^{34} +(-1.30298 - 2.04158i) q^{36} +(-4.33681 - 1.16204i) q^{37} +(-0.589039 - 0.143881i) q^{38} +(-3.09687 + 5.36393i) q^{39} +(1.98071 + 6.00640i) q^{40} +5.67429 q^{41} +(-4.01233 + 4.01233i) q^{43} +(-4.61368 + 8.88056i) q^{44} +(2.70769 + 0.0269194i) q^{45} +(4.34961 - 2.64185i) q^{46} +(2.60987 - 9.74016i) q^{47} +(1.83811 + 5.02452i) q^{48} +(-6.83440 - 1.81412i) q^{50} +(-3.90900 + 2.25686i) q^{51} +(-6.25128 + 6.83330i) q^{52} +(1.10820 - 0.296942i) q^{53} +(7.96340 - 0.177026i) q^{54} +(-5.49776 - 9.74487i) q^{55} +(0.405515 - 0.405515i) q^{57} +(-7.68334 - 7.34916i) q^{58} +(1.93762 - 3.35606i) q^{59} +(-5.82784 - 1.34789i) q^{60} +(-6.11723 - 10.5954i) q^{61} +(0.553797 - 0.161663i) q^{62} +(1.06370 + 7.92897i) q^{64} +(-2.58038 - 10.0278i) q^{65} +(-4.91349 - 8.08971i) q^{66} +(-11.3327 + 3.03658i) q^{67} +(-6.43523 + 2.03482i) q^{68} +4.81316i q^{69} -12.2700i q^{71} +(3.36016 + 0.664085i) q^{72} +(-5.17303 + 1.38611i) q^{73} +(5.42693 - 3.29619i) q^{74} +(4.82202 - 4.63398i) q^{75} +(0.722846 - 0.461337i) q^{76} +(-2.45454 - 8.40832i) q^{78} +(0.0987717 + 0.171078i) q^{79} +(-8.07460 - 3.84719i) q^{80} +(-1.95031 + 3.37804i) q^{81} +(-5.54678 + 5.79900i) q^{82} +(-1.86715 + 1.86715i) q^{83} +(2.02539 - 7.26902i) q^{85} +(-0.178344 - 8.02268i) q^{86} +(9.71316 - 2.60263i) q^{87} +(-4.56572 - 13.3961i) q^{88} +(6.11311 - 3.52940i) q^{89} +(-2.67435 + 2.74088i) q^{90} +(-1.55196 + 7.02768i) q^{92} +(-0.141221 + 0.527043i) q^{93} +(7.40301 + 12.1885i) q^{94} +(-0.00953113 + 0.958687i) q^{95} +(-6.93175 - 3.03311i) q^{96} +(-5.24949 + 5.24949i) q^{97} -6.05942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48}+ \cdots + 40 q^{97}+O(q^{100}) $ 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−0.977529	+	1.02198i	−0.691217	+	0.722647i
$2$	−0.977529	+	1.02198i	−0.691217	+	0.722647i
$3$	−0.346182	−	1.29197i	−0.199868	−	0.745919i	−0.990953	−	0.134212i	$-0.957150\pi$
$3$	−0.346182	−	1.29197i	−0.199868	−	0.745919i	0.791084	−	0.611707i	$-0.209517\pi$
$4$	−0.0888759	−	1.99802i	−0.0444380	−	0.999012i
$5$	1.92528	+	1.13723i	0.861012	+	0.508585i
$5$	1.92528	+	1.13723i	0.861012	+	0.508585i
$6$	1.65877	+	0.909146i	0.677188	+	0.371157i
$7$		0			0
$7$		0			0
$8$	2.12881	+	1.86230i	0.752650	+	0.658421i
$9$	1.04873	−	0.605487i	0.349578	−	0.201829i
$10$	−3.04424	+	0.855919i	−0.962673	+	0.270665i
$11$	−4.33338	−	2.50188i	−1.30656	−	0.754345i	−0.325042	−	0.945699i	$-0.605379\pi$
$11$	−4.33338	−	2.50188i	−1.30656	−	0.754345i	−0.981521	+	0.191355i	$0.938712\pi$
$12$	−2.55062	+	0.806505i	−0.736300	+	0.232818i
$13$	−3.27438	−	3.27438i	−0.908150	−	0.908150i	0.0879732	−	0.996123i	$-0.471961\pi$
$13$	−3.27438	−	3.27438i	−0.908150	−	0.908150i	−0.996123	+	0.0879732i	$0.971961\pi$
$14$		0			0
$15$	0.802768	−	2.88109i	0.207274	−	0.743895i
$16$	−3.98420	+	0.355152i	−0.996051	+	0.0887881i
$17$	−0.873420	−	3.25965i	−0.211835	−	0.790581i	−0.987257	−	0.159136i	$-0.949129\pi$
$17$	−0.873420	−	3.25965i	−0.211835	−	0.790581i	0.775421	−	0.631444i	$-0.217538\pi$
$18$	−0.406374	+	1.66366i	−0.0957832	+	0.392129i
$19$	0.214380	+	0.371316i	0.0491820	+	0.0851858i	0.889568	−	0.456802i	$-0.151005\pi$
$19$	0.214380	+	0.371316i	0.0491820	+	0.0851858i	−0.840386	+	0.541988i	$0.817672\pi$
$20$	2.10110	−	3.94783i	0.469821	−	0.882762i
$21$		0			0
$22$	6.79287	−	1.98296i	1.44824	−	0.422768i
$23$	−3.47589	−	0.931361i	−0.724773	−	0.194202i	−0.122472	−	0.992472i	$-0.539082\pi$
$23$	−3.47589	−	0.931361i	−0.724773	−	0.194202i	−0.602300	+	0.798270i	$0.705749\pi$
$24$	1.66907	−	3.39506i	0.340698	−	0.693013i
$25$	2.41342	+	4.37898i	0.482683	+	0.875795i
$26$	6.54714	−	0.145543i	1.28400	−	0.0285433i
$27$	−3.98268	−	3.98268i	−0.766468	−	0.766468i
$28$		0			0
$29$			7.51811i			1.39608i	0.716060	+	0.698039i	$0.245944\pi$
$29$			7.51811i			1.39608i	−0.716060	+	0.698039i	$0.754056\pi$
$30$	2.15968	+	3.63676i	0.394302	+	0.663979i
$31$	−0.353285	−	0.203969i	−0.0634518	−	0.0366339i	0.467938	−	0.883761i	$-0.344997\pi$
$31$	−0.353285	−	0.203969i	−0.0634518	−	0.0366339i	−0.531390	+	0.847127i	$0.678330\pi$
$32$	3.53171	−	4.41894i	0.624325	−	0.781165i
$33$	−1.73221	+	6.46470i	−0.301539	+	1.12536i
$34$	4.18508	+	2.29378i	0.717735	+	0.393381i
$35$		0			0
$36$	−1.30298	−	2.04158i	−0.217164	−	0.340264i
$37$	−4.33681	−	1.16204i	−0.712967	−	0.191039i	−0.115935	−	0.993257i	$-0.536987\pi$
$37$	−4.33681	−	1.16204i	−0.712967	−	0.191039i	−0.597031	+	0.802218i	$0.703653\pi$
$38$	−0.589039	−	0.143881i	−0.0955547	−	0.0233406i
$39$	−3.09687	+	5.36393i	−0.495895	+	0.858916i
$40$	1.98071	+	6.00640i	0.313177	+	0.949695i
$41$	5.67429			0.886176			0.443088	−	0.896478i	$-0.353883\pi$
$41$	5.67429			0.886176			0.443088	+	0.896478i	$0.353883\pi$
$42$		0			0
$43$	−4.01233	+	4.01233i	−0.611875	+	0.611875i	−0.943434	−	0.331560i	$-0.892425\pi$
$43$	−4.01233	+	4.01233i	−0.611875	+	0.611875i	0.331560	+	0.943434i	$0.392425\pi$
$44$	−4.61368	+	8.88056i	−0.695538	+	1.33879i
$45$	2.70769	+	0.0269194i	0.403638	+	0.00401291i
$46$	4.34961	−	2.64185i	0.641315	−	0.389519i
$47$	2.60987	−	9.74016i	0.380689	−	1.42075i	−0.464164	−	0.885749i	$-0.653645\pi$
$47$	2.60987	−	9.74016i	0.380689	−	1.42075i	0.844852	−	0.535000i	$-0.179688\pi$
$48$	1.83811	+	5.02452i	0.265308	+	0.725227i
$49$		0			0
$50$	−6.83440	−	1.81412i	−0.966530	−	0.256555i
$51$	−3.90900	+	2.25686i	−0.547370	+	0.316024i
$52$	−6.25128	+	6.83330i	−0.866896	+	0.947609i
$53$	1.10820	−	0.296942i	0.152223	−	0.0407881i	−0.181903	−	0.983317i	$-0.558226\pi$
$53$	1.10820	−	0.296942i	0.152223	−	0.0407881i	0.334126	+	0.942528i	$0.391559\pi$
$54$	7.96340	−	0.177026i	1.08368	−	0.0240902i
$55$	−5.49776	−	9.74487i	−0.741318	−	1.31400i
$56$		0			0
$57$	0.405515	−	0.405515i	0.0537117	−	0.0537117i
$58$	−7.68334	−	7.34916i	−1.00887	−	0.964992i
$59$	1.93762	−	3.35606i	0.252257	−	0.436921i	−0.711890	−	0.702291i	$-0.752161\pi$
$59$	1.93762	−	3.35606i	0.252257	−	0.436921i	0.964147	+	0.265370i	$0.0854939\pi$
$60$	−5.82784	−	1.34789i	−0.752371	−	0.174012i
$61$	−6.11723	−	10.5954i	−0.783231	−	1.35660i	−0.930050	−	0.367433i	$-0.880237\pi$
$61$	−6.11723	−	10.5954i	−0.783231	−	1.35660i	0.146819	−	0.989163i	$-0.453097\pi$
$62$	0.553797	−	0.161663i	0.0703323	−	0.0205313i
$63$		0			0
$64$	1.06370	+	7.92897i	0.132963	+	0.991121i
$65$	−2.58038	−	10.0278i	−0.320057	−	1.24380i
$66$	−4.91349	−	8.08971i	−0.604809	−	0.995774i
$67$	−11.3327	+	3.03658i	−1.38451	+	0.370977i	−0.872756	−	0.488157i	$-0.837669\pi$
$67$	−11.3327	+	3.03658i	−1.38451	+	0.370977i	−0.511750	+	0.859134i	$0.671003\pi$
$68$	−6.43523	+	2.03482i	−0.780386	+	0.246758i
$69$			4.81316i			0.579436i
$70$		0			0
$71$		−	12.2700i		−	1.45618i	−0.685482	−	0.728090i	$-0.740408\pi$
$71$		−	12.2700i		−	1.45618i	0.685482	−	0.728090i	$-0.259592\pi$
$72$	3.36016	+	0.664085i	0.395998	+	0.0782631i
$73$	−5.17303	+	1.38611i	−0.605457	+	0.162232i	−0.548508	−	0.836145i	$-0.684804\pi$
$73$	−5.17303	+	1.38611i	−0.605457	+	0.162232i	−0.0569493	+	0.998377i	$0.518137\pi$
$74$	5.42693	−	3.29619i	0.630868	−	0.383174i
$75$	4.82202	−	4.63398i	0.556799	−	0.535086i
$76$	0.722846	−	0.461337i	0.0829161	−	0.0529189i
$77$		0			0
$78$	−2.45454	−	8.40832i	−0.277922	−	0.952055i
$79$	0.0987717	+	0.171078i	0.0111127	+	0.0192477i	0.871528	−	0.490345i	$-0.163129\pi$
$79$	0.0987717	+	0.171078i	0.0111127	+	0.0192477i	−0.860416	+	0.509593i	$0.829796\pi$
$80$	−8.07460	−	3.84719i	−0.902768	−	0.430129i
$81$	−1.95031	+	3.37804i	−0.216701	+	0.375337i
$82$	−5.54678	+	5.79900i	−0.612540	+	0.640392i
$83$	−1.86715	+	1.86715i	−0.204946	+	0.204946i	−0.802115	−	0.597169i	$-0.796292\pi$
$83$	−1.86715	+	1.86715i	−0.204946	+	0.204946i	0.597169	+	0.802115i	$0.296292\pi$
$84$		0			0
$85$	2.02539	−	7.26902i	0.219684	−	0.788436i
$86$	−0.178344	−	8.02268i	−0.0192313	−	0.865108i
$87$	9.71316	−	2.60263i	1.04136	−	0.279032i
$88$	−4.56572	−	13.3961i	−0.486708	−	1.42803i
$89$	6.11311	−	3.52940i	0.647988	−	0.374116i	−0.139697	−	0.990194i	$-0.544613\pi$
$89$	6.11311	−	3.52940i	0.647988	−	0.374116i	0.787685	+	0.616078i	$0.211279\pi$
$90$	−2.67435	+	2.74088i	−0.281901	+	0.288914i
$91$		0			0
$92$	−1.55196	+	7.02768i	−0.161803	+	0.732687i
$93$	−0.141221	+	0.527043i	−0.0146439	+	0.0546518i
$94$	7.40301	+	12.1885i	0.763562	+	1.25715i
$95$	−0.00953113	+	0.958687i	−0.000977873	+	0.0983592i
$96$	−6.93175	−	3.03311i	−0.707468	−	0.309565i
$97$	−5.24949	+	5.24949i	−0.533005	+	0.533005i	−0.921465	−	0.388460i	$-0.873007\pi$
$97$	−5.24949	+	5.24949i	−0.533005	+	0.533005i	0.388460	+	0.921465i	$0.373007\pi$
$98$		0			0
$99$	−6.05942			−0.608994
$100$	8.53480	−	5.21125i	0.853480	−	0.521125i
$101$	4.85758	−	8.41357i	0.483347	−	0.837181i	−0.516470	−	0.856305i	$-0.672754\pi$
$101$	4.85758	−	8.41357i	0.483347	−	0.837181i	0.999817	+	0.0191239i	$0.00608769\pi$
$102$	1.51470	−	6.20106i	0.149977	−	0.613997i
$103$	0.119769	+	0.0320920i	0.0118012	+	0.00316212i	0.264715	−	0.964327i	$-0.414722\pi$
$103$	0.119769	+	0.0320920i	0.0118012	+	0.00316212i	−0.252914	+	0.967489i	$0.581389\pi$
$104$	−0.872681	−	13.0684i	−0.0855734	−	1.28146i
$105$		0			0
$106$	−0.779831	+	1.42283i	−0.0757439	+	0.138197i
$107$	−0.613518	+	2.28968i	−0.0593110	+	0.221352i	−0.989220	−	0.146439i	$-0.953219\pi$
$107$	−0.613518	+	2.28968i	−0.0593110	+	0.221352i	0.929909	+	0.367790i	$0.119886\pi$
$108$	−7.60354	+	8.31146i	−0.731651	+	0.799771i
$109$	8.75938	+	5.05723i	0.838996	+	0.484395i	0.856923	−	0.515445i	$-0.172373\pi$
$109$	8.75938	+	5.05723i	0.838996	+	0.484395i	−0.0179266	+	0.999839i	$0.505707\pi$
$110$	15.3333	+	3.90730i	1.46197	+	0.372546i
$111$			6.00530i			0.569998i
$112$		0			0
$113$	−7.67087	−	7.67087i	−0.721614	−	0.721614i	0.247320	−	0.968934i	$-0.420450\pi$
$113$	−7.67087	−	7.67087i	−0.721614	−	0.721614i	−0.968934	+	0.247320i	$0.920450\pi$
$114$	0.0180247	+	0.810829i	0.00168817	+	0.0759411i
$115$	−5.63289	−	5.74602i	−0.525270	−	0.535819i
$116$	15.0214	−	0.668179i	1.39470	−	0.0620388i
$117$	−5.41655	−	1.45136i	−0.500760	−	0.134178i
$118$	1.53574	+	5.26084i	0.141376	+	0.484300i
$119$		0			0
$120$	7.07439	−	4.63832i	0.645801	−	0.423419i
$121$	7.01879	+	12.1569i	0.638072	+	1.10517i
$122$	16.8080	+	4.10559i	1.52172	+	0.371703i
$123$	−1.96434	−	7.33101i	−0.177118	−	0.661015i
$124$	−0.376136	+	0.723999i	−0.0337780	+	0.0650170i
$125$	−0.333400	+	11.1754i	−0.0298202	+	0.999555i
$126$		0			0
$127$	6.81065	+	6.81065i	0.604347	+	0.604347i	0.941463	−	0.337116i	$-0.109451\pi$
$127$	6.81065	+	6.81065i	0.604347	+	0.604347i	−0.337116	+	0.941463i	$0.609451\pi$
$128$	−9.14303	−	6.66371i	−0.808137	−	0.588995i
$129$	6.57280	+	3.79481i	0.578703	+	0.334114i
$130$	12.7706	+	7.16540i	1.12006	+	0.628447i
$131$	1.88090	−	1.08594i	0.164335	−	0.0948786i	−0.415577	−	0.909558i	$-0.636420\pi$
$131$	1.88090	−	1.08594i	0.164335	−	0.0948786i	0.579912	+	0.814679i	$0.303087\pi$
$132$	13.0706	+	2.88644i	1.13765	+	0.251233i
$133$		0			0
$134$	7.97469	−	14.5501i	0.688909	−	1.25694i
$135$	−3.13856	−	12.1970i	−0.270124	−	1.04975i
$136$	4.21108	−	8.56575i	0.361097	−	0.734507i
$137$	−3.01914	−	11.2676i	−0.257943	−	0.962655i	−0.966430	−	0.256931i	$-0.917289\pi$
$137$	−3.01914	−	11.2676i	−0.257943	−	0.962655i	0.708487	−	0.705724i	$-0.249378\pi$
$138$	−4.91894	−	4.70500i	−0.418728	−	0.400516i
$139$	15.0008			1.27235			0.636175	−	0.771545i	$-0.280516\pi$
$139$	15.0008			1.27235			0.636175	+	0.771545i	$0.280516\pi$
$140$		0			0
$141$	−13.4875			−1.13585
$142$	12.5397	+	11.9943i	1.05230	+	1.00654i
$143$	5.99703	+	22.3812i	0.501497	+	1.87161i
$144$	−3.96333	+	2.78484i	−0.330277	+	0.232070i
$145$	−8.54982	+	14.4745i	−0.710024	+	1.20204i
$146$	3.64021	−	6.64168i	0.301266	−	0.549669i
$147$		0			0
$148$	−1.93635	+	8.76832i	−0.159167	+	0.720752i
$149$	−7.79115	+	4.49822i	−0.638276	+	0.368509i	−0.783950	−	0.620824i	$-0.786798\pi$
$149$	−7.79115	+	4.49822i	−0.638276	+	0.368509i	0.145674	+	0.989333i	$0.453465\pi$
$150$	0.0221620	+	9.45784i	0.00180952	+	0.772230i
$151$	−0.549816	−	0.317436i	−0.0447434	−	0.0258326i	0.477461	−	0.878653i	$-0.341557\pi$
$151$	−0.549816	−	0.317436i	−0.0447434	−	0.0258326i	−0.522205	+	0.852820i	$0.674890\pi$
$152$	−0.235127	+	1.18970i	−0.0190713	+	0.0964976i
$153$	−2.88966	−	2.88966i	−0.233615	−	0.233615i
$154$		0			0
$155$	−0.448212	−	0.794463i	−0.0360013	−	0.0638128i
$156$	10.9925	+	5.71089i	0.880104	+	0.457237i
$157$	−2.21196	−	8.25515i	−0.176534	−	0.658832i	−0.996285	−	0.0861134i	$-0.972555\pi$
$157$	−2.21196	−	8.25515i	−0.176534	−	0.658832i	0.819752	−	0.572719i	$-0.194111\pi$
$158$	−0.271389	−	0.0662908i	−0.0215906	−	0.00527381i
$159$	−0.767279	−	1.32897i	−0.0608492	−	0.105394i
$160$	11.8249	−	4.49132i	0.934840	−	0.355070i
$161$		0			0
$162$	−1.54579	−	5.29530i	−0.121449	−	0.416038i
$163$	19.0319	+	5.09959i	1.49069	+	0.399430i	0.909972	−	0.414671i	$-0.136103\pi$
$163$	19.0319	+	5.09959i	1.49069	+	0.399430i	0.580723	+	0.814101i	$0.302770\pi$
$164$	−0.504308	−	11.3374i	−0.0393798	−	0.885300i
$165$	−10.6868	+	10.4764i	−0.831970	+	0.815590i
$166$	−0.0829927	−	3.73337i	−0.00644149	−	0.289766i
$167$	−8.56192	−	8.56192i	−0.662541	−	0.662541i	0.293437	−	0.955978i	$-0.405201\pi$
$167$	−8.56192	−	8.56192i	−0.662541	−	0.662541i	−0.955978	+	0.293437i	$0.905201\pi$
$168$		0			0
$169$			8.44313i			0.649471i
$170$	5.44890	+	9.17558i	0.417911	+	0.703735i
$171$	0.449654	+	0.259608i	0.0343859	+	0.0198527i
$172$	8.37333	+	7.66013i	0.638461	+	0.584080i
$173$	4.79365	−	17.8901i	0.364454	−	1.36016i	−0.503705	−	0.863876i	$-0.668030\pi$
$173$	4.79365	−	17.8901i	0.364454	−	1.36016i	0.868159	−	0.496286i	$-0.165303\pi$
$174$	−6.83506	+	12.4708i	−0.518165	+	0.945407i
$175$		0			0
$176$	18.1536	+	8.42898i	1.36838	+	0.635358i
$177$	−5.00669	−	1.34154i	−0.376326	−	0.100836i
$178$	−2.36877	+	9.69755i	−0.177546	+	0.726862i
$179$	−11.8144	+	20.4632i	−0.883050	+	1.52949i	−0.0351179	+	0.999383i	$0.511181\pi$
$179$	−11.8144	+	20.4632i	−0.883050	+	1.52949i	−0.847932	+	0.530105i	$0.822153\pi$
$180$	−0.186862	−	5.41241i	−0.0139279	−	0.403418i
$181$	−0.943069			−0.0700978			−0.0350489	−	0.999386i	$-0.511159\pi$
$181$	−0.943069			−0.0700978			−0.0350489	+	0.999386i	$0.511159\pi$
$182$		0			0
$183$	−11.5712	+	11.5712i	−0.855368	+	0.855368i
$184$	−5.66505	−	8.45583i	−0.417633	−	0.623372i
$185$	−7.02806	−	7.16921i	−0.516713	−	0.527091i
$186$	−0.400579	−	0.659524i	−0.0293719	−	0.0483587i
$187$	−4.37038	+	16.3105i	−0.319594	+	1.19274i
$188$	−19.6930	−	4.34892i	−1.43626	−	0.317177i
$189$		0			0
$190$	−0.970440	−	0.946885i	−0.0704031	−	0.0686942i
$191$	14.9539	−	8.63366i	1.08203	−	0.624710i	0.150586	−	0.988597i	$-0.451884\pi$
$191$	14.9539	−	8.63366i	1.08203	−	0.624710i	0.931443	+	0.363887i	$0.118551\pi$
$192$	9.87575	−	4.11914i	0.712721	−	0.297273i
$193$	5.76504	−	1.54474i	0.414977	−	0.111193i	−0.0452888	−	0.998974i	$-0.514421\pi$
$193$	5.76504	−	1.54474i	0.414977	−	0.111193i	0.460266	+	0.887781i	$0.347754\pi$
$194$	−0.233334	−	10.4964i	−0.0167524	−	0.753597i
$195$	−12.0624	+	6.80522i	−0.863804	+	0.487332i
$196$		0			0
$197$	5.72538	−	5.72538i	0.407917	−	0.407917i	−0.473095	−	0.881012i	$-0.656863\pi$
$197$	5.72538	−	5.72538i	0.407917	−	0.407917i	0.881012	+	0.473095i	$0.156863\pi$
$198$	5.92325	−	6.19259i	0.420947	−	0.440088i
$199$	9.97026	−	17.2690i	0.706773	−	1.22417i	−0.259275	−	0.965804i	$-0.583483\pi$
$199$	9.97026	−	17.2690i	0.706773	−	1.22417i	0.966048	−	0.258363i	$-0.0831832\pi$
$200$	−3.01724	+	13.8165i	−0.213351	+	0.976976i
$201$	7.84634	+	13.5903i	0.553438	+	0.958583i
$202$	3.85006	+	13.1888i	0.270889	+	0.927963i
$203$		0			0
$204$	4.85668	+	7.60970i	0.340036	+	0.532786i
$205$	10.9246	+	6.45298i	0.763008	+	0.450695i
$206$	−0.149875	+	0.0910303i	−0.0104423	+	0.00634238i
$207$	−4.20921	+	1.12785i	−0.292560	+	0.0783913i
$208$	14.2087	+	11.8829i	0.985196	+	0.823930i
$209$		−	2.14541i		−	0.148401i
$210$		0			0
$211$		−	7.74837i		−	0.533420i	−0.963777	−	0.266710i	$-0.914063\pi$
$211$		−	7.74837i		−	0.533420i	0.963777	−	0.266710i	$-0.0859365\pi$
$212$	−0.691789	−	2.18782i	−0.0475123	−	0.150260i
$213$	−15.8524	+	4.24765i	−1.08619	+	0.291044i
$214$	−1.74027	−	2.86523i	−0.118962	−	0.195863i
$215$	−12.2878	+	3.16192i	−0.838022	+	0.215641i
$216$	−1.06146	−	15.8953i	−0.0722230	−	1.08154i
$217$		0			0
$218$	−13.7309	+	4.00830i	−0.929975	+	0.271476i
$219$	3.58162	+	6.20355i	0.242023	+	0.419197i
$220$	−18.9819	+	11.8508i	−1.27976	+	0.798977i
$221$	−7.81342	+	13.5332i	−0.525587	+	0.910344i
$222$	−6.13728	−	5.87035i	−0.411907	−	0.393992i
$223$	11.1091	−	11.1091i	0.743923	−	0.743923i	−0.229407	−	0.973331i	$-0.573679\pi$
$223$	11.1091	−	11.1091i	0.743923	−	0.743923i	0.973331	+	0.229407i	$0.0736787\pi$
$224$		0			0
$225$	5.18244	+	3.13109i	0.345496	+	0.208739i
$226$	15.3379	−	0.340962i	1.02026	−	0.0226804i
$227$	6.66488	−	1.78585i	0.442364	−	0.118531i	−0.0307604	−	0.999527i	$-0.509793\pi$
$227$	6.66488	−	1.78585i	0.442364	−	0.118531i	0.473124	+	0.880996i	$0.343126\pi$
$228$	−0.846269	−	0.774188i	−0.0560455	−	0.0512718i
$229$	−4.37314	+	2.52483i	−0.288985	+	0.166846i	−0.637484	−	0.770463i	$-0.720025\pi$
$229$	−4.37314	+	2.52483i	−0.288985	+	0.166846i	0.348499	+	0.937309i	$0.386692\pi$
$230$	11.3786	−	0.139791i	0.750283	−	0.00921752i
$231$		0			0
$232$	−14.0009	+	16.0047i	−0.919207	+	1.05076i
$233$	0.898620	−	3.35370i	0.0588706	−	0.219708i	−0.930223	−	0.366994i	$-0.880387\pi$
$233$	0.898620	−	3.35370i	0.0588706	−	0.219708i	0.989094	+	0.147286i	$0.0470537\pi$
$234$	6.77809	−	4.11684i	0.443097	−	0.269127i
$235$	16.1015	−	15.7845i	1.05035	−	1.02967i
$236$	−6.87769	−	3.57314i	−0.447699	−	0.232592i
$237$	0.186834	−	0.186834i	0.0121362	−	0.0121362i
$238$		0			0
$239$	11.2814			0.729734			0.364867	−	0.931060i	$-0.381114\pi$
$239$	11.2814			0.729734			0.364867	+	0.931060i	$0.381114\pi$
$240$	−2.17516	+	11.7640i	−0.140406	+	0.759360i
$241$	−13.0568	+	22.6150i	−0.841062	+	1.45676i	0.0479359	+	0.998850i	$0.484736\pi$
$241$	−13.0568	+	22.6150i	−0.841062	+	1.45676i	−0.888998	+	0.457912i	$0.848598\pi$
$242$	−19.2851	−	4.71067i	−1.23970	−	0.302813i
$243$	−11.2819	−	3.02297i	−0.723732	−	0.193923i
$244$	−20.6261	+	13.1641i	−1.32045	+	0.842742i
$245$		0			0
$246$	9.41232	+	5.15876i	0.600108	+	0.328911i
$247$	0.513870	−	1.91779i	0.0326968	−	0.122026i
$248$	−0.372227	−	1.09213i	−0.0236364	−	0.0693505i
$249$	3.05867	+	1.76592i	0.193835	+	0.111911i
$250$	−11.0951	−	11.2650i	−0.701714	−	0.712459i
$251$			26.0311i			1.64307i	0.570157	+	0.821536i	$0.306882\pi$
$251$			26.0311i			1.64307i	−0.570157	+	0.821536i	$0.693118\pi$
$252$		0			0
$253$	12.7322	+	12.7322i	0.800466	+	0.800466i
$254$	−13.6179	+	0.302726i	−0.854465	+	0.0189947i
$255$	−10.0925	−	0.100338i	−0.632017	−	0.00628342i
$256$	15.7477	−	2.83000i	0.984233	−	0.176875i
$257$	−5.34936	−	1.43336i	−0.333684	−	0.0894104i	0.0880868	−	0.996113i	$-0.471925\pi$
$257$	−5.34936	−	1.43336i	−0.333684	−	0.0894104i	−0.421771	+	0.906702i	$0.638591\pi$
$258$	−10.3033	+	3.00772i	−0.641456	+	0.187253i
$259$		0			0
$260$	−19.8065	+	6.04689i	−1.22835	+	0.375012i
$261$	4.55212	+	7.88449i	0.281769	+	0.488038i
$262$	−0.728827	+	2.98377i	−0.0450271	+	0.184338i
$263$	3.78833	+	14.1383i	0.233599	+	0.871802i	0.978776	+	0.204935i	$0.0656984\pi$
$263$	3.78833	+	14.1383i	0.233599	+	0.871802i	−0.745177	+	0.666867i	$0.767635\pi$
$264$	−15.7267	+	10.5363i	−0.967914	+	0.648462i
$265$	2.47129	+	0.688584i	0.151810	+	0.0422994i
$266$		0			0
$267$	−6.67613	−	6.67613i	−0.408572	−	0.408572i
$268$	7.07436	+	22.3731i	0.432136	+	1.36665i
$269$	17.0194	+	9.82616i	1.03769	+	0.599112i	0.919179	−	0.393841i	$-0.128854\pi$
$269$	17.0194	+	9.82616i	1.03769	+	0.599112i	0.118513	+	0.992953i	$0.462187\pi$
$270$	15.5331	+	8.71539i	0.945315	+	0.530402i
$271$	−11.8744	+	6.85570i	−0.721320	+	0.416454i	−0.815238	−	0.579126i	$-0.803394\pi$
$271$	−11.8744	+	6.85570i	−0.721320	+	0.416454i	0.0939185	+	0.995580i	$0.470061\pi$
$272$	4.63755	+	12.6769i	0.281193	+	0.768650i
$273$		0			0
$274$	14.4665	+	7.92889i	0.873954	+	0.479002i
$275$	0.497417	−	25.0138i	0.0299954	−	1.50839i
$276$	9.61681	−	0.427774i	0.578864	−	0.0257490i
$277$	1.82693	+	6.81819i	0.109770	+	0.409666i	0.998843	−	0.0481000i	$-0.0153166\pi$
$277$	1.82693	+	6.81819i	0.109770	+	0.409666i	−0.889073	+	0.457765i	$0.848650\pi$
$278$	−14.6637	+	15.3305i	−0.879470	+	0.919460i
$279$	−0.494002			−0.0295751
$280$		0			0
$281$	15.9701			0.952697			0.476348	−	0.879257i	$-0.341960\pi$
$281$	15.9701			0.952697			0.476348	+	0.879257i	$0.341960\pi$
$282$	13.1844	−	13.7839i	0.785119	−	0.820819i
$283$	5.58000	+	20.8249i	0.331697	+	1.23791i	0.907406	+	0.420255i	$0.138059\pi$
$283$	5.58000	+	20.8249i	0.331697	+	1.23791i	−0.575710	+	0.817654i	$0.695274\pi$
$284$	−24.5157	+	1.09051i	−1.45474	+	0.0647096i
$285$	1.24189	−	0.319566i	0.0735634	−	0.0189295i
$286$	−28.7354	−	15.7495i	−1.69916	−	0.931285i
$287$		0			0
$288$	1.02822	−	6.77270i	0.0605885	−	0.399085i
$289$	4.85999	−	2.80592i	0.285882	−	0.165054i
$290$	−6.43489	−	22.8869i	−0.377870	−	1.34397i
$291$	8.59946	+	4.96490i	0.504109	+	0.291048i
$292$	3.22924	+	10.2126i	0.188977	+	0.597650i
$293$	−19.8931	−	19.8931i	−1.16217	−	1.16217i	−0.984000	−	0.178170i	$-0.942982\pi$
$293$	−19.8931	−	19.8931i	−1.16217	−	1.16217i	−0.178170	−	0.984000i	$-0.557018\pi$
$294$		0			0
$295$	7.54707	−	4.25783i	0.439408	−	0.247901i
$296$	−7.06819	−	10.5502i	−0.410830	−	0.613218i
$297$	7.29429	+	27.2227i	0.423258	+	1.57962i
$298$	3.01899	−	12.3595i	0.174885	−	0.715968i
$299$	8.33175	+	14.4310i	0.481837	+	0.834567i
$300$	−9.68737	−	9.22266i	−0.559300	−	0.532471i
$301$		0			0
$302$	0.861873	−	0.251596i	0.0495952	−	0.0144777i
$303$	−12.5517	−	3.36321i	−0.721075	−	0.193211i
$304$	−0.986005	−	1.40326i	−0.0565513	−	0.0804826i
$305$	0.271967	−	27.3557i	0.0155728	−	1.56639i
$306$	5.77789	−	0.128442i	0.330300	−	0.00734256i
$307$	14.1084	+	14.1084i	0.805207	+	0.805207i	0.983904	−	0.178697i	$-0.0571882\pi$
$307$	14.1084	+	14.1084i	0.805207	+	0.805207i	−0.178697	+	0.983904i	$0.557188\pi$
$308$		0			0
$309$		−	0.165847i		−	0.00943473i
$310$	1.25006	+	0.318548i	0.0709989	+	0.0180923i
$311$	−14.4861	−	8.36354i	−0.821430	−	0.474253i	0.0294794	−	0.999565i	$-0.490615\pi$
$311$	−14.4861	−	8.36354i	−0.821430	−	0.474253i	−0.850909	+	0.525313i	$0.823948\pi$
$312$	−16.5819	+	5.65153i	−0.938764	+	0.319955i
$313$	2.09639	−	7.82385i	0.118495	−	0.442230i	−0.881029	−	0.473062i	$-0.843149\pi$
$313$	2.09639	−	7.82385i	0.118495	−	0.442230i	0.999525	+	0.0308314i	$0.00981550\pi$
$314$	10.5988	+	5.80907i	0.598127	+	0.327825i
$315$		0			0
$316$	0.333039	−	0.212553i	0.0187349	−	0.0119570i
$317$	−5.91723	−	1.58552i	−0.332345	−	0.0890516i	0.0887878	−	0.996051i	$-0.471701\pi$
$317$	−5.91723	−	1.58552i	−0.332345	−	0.0890516i	−0.421133	+	0.906999i	$0.638367\pi$
$318$	2.10821	+	0.514961i	0.118223	+	0.0288776i
$319$	18.8094	−	32.5788i	1.05312	−	1.82406i
$320$	−6.96913	+	16.4752i	−0.389586	+	0.920990i
$321$	3.17059			0.176965
$322$		0			0
$323$	1.02312	−	1.02312i	0.0569278	−	0.0569278i
$324$	6.92274	+	3.59654i	0.384596	+	0.199808i
$325$	6.43599	−	22.2409i	0.357005	−	1.23370i
$326$	−23.8159	+	14.4652i	−1.31904	+	0.801153i
$327$	3.50144	−	13.0676i	0.193630	−	0.722638i
$328$	12.0795	+	10.5672i	0.666980	+	0.583477i
$329$		0			0
$330$	−0.259992	−	21.1627i	−0.0143121	−	1.16497i
$331$	−26.9329	+	15.5497i	−1.48036	+	0.854689i	−0.999753	−	0.0222445i	$-0.992919\pi$
$331$	−26.9329	+	15.5497i	−1.48036	+	0.854689i	−0.480612	+	0.876933i	$0.659585\pi$
$332$	3.89655	+	3.56466i	0.213851	+	0.195636i
$333$	−5.25176	+	1.40720i	−0.287795	+	0.0771143i
$334$	17.1196	−	0.380568i	0.936743	−	0.0208238i
$335$	−25.2719	−	7.04159i	−1.38075	−	0.384723i
$336$		0			0
$337$	−9.43123	+	9.43123i	−0.513752	+	0.513752i	−0.915674	−	0.401922i	$-0.868342\pi$
$337$	−9.43123	+	9.43123i	−0.513752	+	0.513752i	0.401922	+	0.915674i	$0.368342\pi$
$338$	−8.62869	−	8.25340i	−0.469339	−	0.448926i
$339$	−7.25500	+	12.5660i	−0.394038	+	0.682493i
$340$	−14.7037	−	3.40074i	−0.797419	−	0.184431i
$341$	1.02061	+	1.76775i	0.0552692	+	0.0957290i
$342$	−0.704863	+	0.205762i	−0.0381147	+	0.0111264i
$343$		0			0
$344$	−16.0137	+	1.06936i	−0.863399	+	0.0576559i
$345$	−5.47367	+	9.26669i	−0.294693	+	0.498902i
$346$	13.5974	+	22.3871i	0.731000	+	1.20354i
$347$	30.6251	−	8.20598i	1.64404	−	0.440520i	0.686107	−	0.727500i	$-0.259318\pi$
$347$	30.6251	−	8.20598i	1.64404	−	0.440520i	0.957936	+	0.286980i	$0.0926514\pi$
$348$	−6.06339	−	19.1758i	−0.325032	−	1.02793i
$349$		−	13.8389i		−	0.740778i	−0.928877	−	0.370389i	$-0.879224\pi$
$349$		−	13.8389i		−	0.740778i	0.928877	−	0.370389i	$-0.120776\pi$
$350$		0			0
$351$			26.0816i			1.39214i
$352$	−26.3599	+	10.3130i	−1.40499	+	0.549686i
$353$	1.67242	−	0.448123i	0.0890139	−	0.0238512i	−0.214037	−	0.976826i	$-0.568661\pi$
$353$	1.67242	−	0.448123i	0.0890139	−	0.0238512i	0.303051	+	0.952974i	$0.401995\pi$
$354$	6.26521	−	3.80533i	0.332992	−	0.202251i
$355$	13.9538	−	23.6232i	0.740591	−	1.25379i
$356$	−7.59514	−	11.9005i	−0.402542	−	0.630723i
$357$		0			0
$358$	−9.36396	−	32.0774i	−0.494901	−	1.69534i
$359$	15.4616	+	26.7802i	0.816031	+	1.41341i	0.908585	+	0.417699i	$0.137163\pi$
$359$	15.4616	+	26.7802i	0.816031	+	1.41341i	−0.0925546	+	0.995708i	$0.529503\pi$
$360$	5.71403	+	5.09982i	0.301156	+	0.268784i
$361$	9.40808	−	16.2953i	0.495162	−	0.857646i
$362$	0.921877	−	0.963795i	0.0484528	−	0.0506559i
$363$	13.2766	−	13.2766i	0.696839	−	0.696839i
$364$		0			0
$365$	−11.5359	−	3.21428i	−0.603815	−	0.168243i
$366$	−0.514327	−	23.1367i	−0.0268843	−	1.20937i
$367$	−11.9867	+	3.21183i	−0.625700	+	0.167656i	−0.557718	−	0.830031i	$-0.688323\pi$
$367$	−11.9867	+	3.21183i	−0.625700	+	0.167656i	−0.0679826	+	0.997687i	$0.521656\pi$
$368$	14.1794	+	2.47626i	0.739153	+	0.129084i
$369$	5.95082	−	3.43571i	0.309788	−	0.178856i
$370$	14.1969	−	0.174414i	0.738062	−	0.00906737i
$371$		0			0
$372$	1.06560	+	0.235321i	0.0552486	+	0.0122008i
$373$	5.80479	−	21.6638i	0.300561	−	1.12171i	−0.636139	−	0.771574i	$-0.719470\pi$
$373$	5.80479	−	21.6638i	0.300561	−	1.12171i	0.936700	−	0.350133i	$-0.113864\pi$
$374$	−12.3968	−	20.4104i	−0.641022	−	1.05540i
$375$	14.5536	−	3.43797i	0.751547	−	0.177536i
$376$	23.6950	−	15.8747i	1.22198	−	0.818673i
$377$	24.6171	−	24.6171i	1.26785	−	1.26785i
$378$		0			0
$379$	6.09622			0.313142			0.156571	−	0.987667i	$-0.449956\pi$
$379$	6.09622			0.313142			0.156571	+	0.987667i	$0.449956\pi$
$380$	1.91633	−	0.0661608i	0.0983055	−	0.00339398i
$381$	6.44142	−	11.1569i	0.330004	−	0.571584i
$382$	−5.79450	+	23.7222i	−0.296472	+	1.21374i
$383$	26.6446	+	7.13940i	1.36148	+	0.364806i	0.864358	−	0.502877i	$-0.167725\pi$
$383$	26.6446	+	7.13940i	1.36148	+	0.364806i	0.497118	+	0.867683i	$0.334392\pi$
$384$	−5.44416	+	14.1194i	−0.277821	+	0.720526i
$385$		0			0
$386$	−4.05681	+	7.40177i	−0.206486	+	0.376740i
$387$	−1.77845	+	6.63728i	−0.0904039	+	0.337392i
$388$	10.9552	+	10.0221i	0.556164	+	0.508793i
$389$	−18.2694	−	10.5478i	−0.926296	−	0.534797i	−0.0406576	−	0.999173i	$-0.512945\pi$
$389$	−18.2694	−	10.5478i	−0.926296	−	0.534797i	−0.885638	+	0.464376i	$0.846279\pi$
$390$	4.83652	−	18.9798i	0.244907	−	0.961078i
$391$			12.1436i			0.614130i
$392$		0			0
$393$	−2.05413	−	2.05413i	−0.103617	−	0.103617i
$394$	0.254487	+	11.4479i	0.0128209	+	0.576739i
$395$	−0.00439130	+	0.441698i	−0.000220950	+	0.0222243i
$396$	0.538536	+	12.1069i	0.0270625	+	0.608393i
$397$	5.02710	+	1.34701i	0.252303	+	0.0676043i	0.382754	−	0.923850i	$-0.374976\pi$
$397$	5.02710	+	1.34701i	0.252303	+	0.0676043i	−0.130451	+	0.991455i	$0.541642\pi$
$398$	7.90231	+	27.0703i	0.396107	+	1.35691i
$399$		0			0
$400$	−11.1707	−	16.5896i	−0.558537	−	0.829480i
$401$	5.78504	+	10.0200i	0.288891	+	0.500374i	0.973545	−	0.228494i	$-0.0733801\pi$
$401$	5.78504	+	10.0200i	0.288891	+	0.500374i	−0.684654	+	0.728868i	$0.740047\pi$
$402$	−21.5590	−	5.26608i	−1.07526	−	0.262648i
$403$	0.488916	+	1.82466i	0.0243546	+	0.0908928i
$404$	−17.2422	−	8.95779i	−0.857833	−	0.445667i
$405$	−7.59650	+	4.28572i	−0.377473	+	0.212959i
$406$		0			0
$407$	15.8857	+	15.8857i	0.787427	+	0.787427i
$408$	−12.5245	−	2.47528i	−0.620055	−	0.122545i
$409$	−3.86895	−	2.23374i	−0.191307	−	0.110451i	0.401287	−	0.915952i	$-0.368563\pi$
$409$	−3.86895	−	2.23374i	−0.191307	−	0.110451i	−0.592594	+	0.805501i	$0.701896\pi$
$410$	−17.2739	+	4.85674i	−0.853098	+	0.239857i
$411$	−13.5122	+	7.80127i	−0.666508	+	0.384808i
$412$	0.0534760	−	0.242153i	0.00263457	−	0.0119300i
$413$		0			0
$414$	2.96198	−	5.40423i	0.145573	−	0.265603i
$415$	−5.71816	+	1.47141i	−0.280694	+	0.0722286i
$416$	−26.0334	+	2.90511i	−1.27639	+	0.142434i
$417$	−5.19300	−	19.3805i	−0.254302	−	0.949069i
$418$	2.19256	+	2.09720i	0.107241	+	0.102577i
$419$	25.3590			1.23887			0.619433	−	0.785049i	$-0.287362\pi$
$419$	25.3590			1.23887			0.619433	+	0.785049i	$0.287362\pi$
$420$		0			0
$421$	−11.7614			−0.573218			−0.286609	−	0.958048i	$-0.592528\pi$
$421$	−11.7614			−0.573218			−0.286609	+	0.958048i	$0.592528\pi$
$422$	7.91866	+	7.57425i	0.385474	+	0.368709i
$423$	−3.16048	−	11.7951i	−0.153668	−	0.573497i
$424$	2.91215	+	1.43167i	0.141427	+	0.0695279i
$425$	12.1660	−	11.6916i	0.590137	−	0.567124i
$426$	11.1552	−	20.3530i	0.540472	−	0.986108i
$427$		0			0
$428$	4.62937	+	1.02233i	0.223769	+	0.0494160i
$429$	26.8398	−	15.4960i	1.29584	−	0.748152i
$430$	8.78027	−	15.6487i	0.423422	−	0.754649i
$431$	−14.4038	−	8.31606i	−0.693809	−	0.400571i	0.111229	−	0.993795i	$-0.464521\pi$
$431$	−14.4038	−	8.31606i	−0.693809	−	0.400571i	−0.805037	+	0.593224i	$0.797855\pi$
$432$	17.2823	+	14.4534i	0.831494	+	0.695388i
$433$	25.8715	+	25.8715i	1.24330	+	1.24330i	0.958623	+	0.284680i	$0.0918874\pi$
$433$	25.8715	+	25.8715i	1.24330	+	1.24330i	0.284680	+	0.958623i	$0.408113\pi$
$434$		0			0
$435$	21.6604	+	6.03530i	1.03853	+	0.289370i
$436$	9.32597	−	17.9509i	0.446633	−	0.859693i
$437$	−0.399330	−	1.49032i	−0.0191025	−	0.0712916i
$438$	−9.84102	−	2.40381i	−0.470222	−	0.114858i
$439$	12.7134	+	22.0202i	0.606775	+	1.05097i	0.991768	+	0.128046i	$0.0408706\pi$
$439$	12.7134	+	22.0202i	0.606775	+	1.05097i	−0.384993	+	0.922920i	$0.625796\pi$
$440$	6.44412	−	30.9835i	0.307211	−	1.47708i
$441$		0			0
$442$	−6.19282	−	21.2143i	−0.294563	−	1.00906i
$443$	1.73983	+	0.466187i	0.0826619	+	0.0221492i	0.299913	−	0.953967i	$-0.403042\pi$
$443$	1.73983	+	0.466187i	0.0826619	+	0.0221492i	−0.217251	+	0.976116i	$0.569709\pi$
$444$	11.9987	−	0.533726i	0.569435	−	0.0253295i
$445$	15.7832	+	0.156914i	0.748195	+	0.00743845i
$446$	0.493790	+	22.2128i	0.0233816	+	1.05181i
$447$	8.50872	+	8.50872i	0.402449	+	0.402449i
$448$		0			0
$449$		−	27.3838i		−	1.29232i	−0.763202	−	0.646160i	$-0.776374\pi$
$449$		−	27.3838i		−	1.29232i	0.763202	−	0.646160i	$-0.223626\pi$
$450$	−8.26589	+	2.23561i	−0.389658	+	0.105388i
$451$	−24.5889	−	14.1964i	−1.15784	−	0.668482i
$452$	−14.6448	+	16.0083i	−0.688834	+	0.752969i
$453$	−0.219781	+	0.820236i	−0.0103262	+	0.0385380i
$454$	−4.69001	+	8.55708i	−0.220113	+	0.401604i
$455$		0			0
$456$	1.61845	−	0.108077i	0.0757911	−	0.00506117i
$457$	−3.69520	−	0.990127i	−0.172854	−	0.0463162i	0.171354	−	0.985210i	$-0.445186\pi$
$457$	−3.69520	−	0.990127i	−0.172854	−	0.0463162i	−0.344208	+	0.938893i	$0.611853\pi$
$458$	1.69455	−	6.93735i	0.0791810	−	0.324161i
$459$	−9.50359	+	16.4607i	−0.443590	+	0.768320i
$460$	−10.9801	+	11.7653i	−0.511948	+	0.548561i
$461$	24.8145			1.15573			0.577864	−	0.816133i	$-0.303886\pi$
$461$	24.8145			1.15573			0.577864	+	0.816133i	$0.303886\pi$
$462$		0			0
$463$	−10.3704	+	10.3704i	−0.481955	+	0.481955i	−0.905755	−	0.423801i	$-0.860696\pi$
$463$	−10.3704	+	10.3704i	−0.481955	+	0.481955i	0.423801	+	0.905755i	$0.360696\pi$
$464$	−2.67007	−	29.9537i	−0.123955	−	1.39056i
$465$	−0.871259	+	0.854106i	−0.0404037	+	0.0396082i
$466$	2.54897	+	4.19670i	0.118079	+	0.194409i
$467$	−1.32853	+	4.95815i	−0.0614772	+	0.229436i	−0.989828	−	0.142269i	$-0.954560\pi$
$467$	−1.32853	+	4.95815i	−0.0614772	+	0.229436i	0.928351	+	0.371705i	$0.121227\pi$
$468$	−2.41845	+	10.9514i	−0.111793	+	0.506228i
$469$		0			0
$470$	0.391722	+	31.8852i	0.0180688	+	1.47076i
$471$	−9.89965	+	5.71557i	−0.456152	+	0.263359i
$472$	10.3748	−	3.53600i	0.477539	−	0.162758i
$473$	27.4253	−	7.34859i	1.26102	−	0.337889i
$474$	0.00830457	+	0.373576i	0.000381441	+	0.0171589i
$475$	−1.10860	+	1.83490i	−0.0508660	+	0.0841911i
$476$		0			0
$477$	0.982415	−	0.982415i	0.0449817	−	0.0449817i
$478$	−11.0279	+	11.5294i	−0.504405	+	0.527341i
$479$	−2.11175	+	3.65765i	−0.0964882	+	0.167122i	−0.910229	−	0.414106i	$-0.864094\pi$
$479$	−2.11175	+	3.65765i	−0.0964882	+	0.167122i	0.813741	+	0.581228i	$0.197428\pi$
$480$	−9.89622	−	13.7226i	−0.451698	−	0.626347i
$481$	10.3954	+	18.0053i	0.473988	+	0.820972i
$482$	−10.3487	−	35.4506i	−0.471369	−	1.61473i
$483$		0			0
$484$	23.6660	−	15.1042i	1.07573	−	0.686553i
$485$	−16.0766	+	4.13687i	−0.730002	+	0.187845i
$486$	14.1177	−	8.57477i	0.640394	−	0.388960i
$487$	22.6422	−	6.06695i	1.02601	−	0.274920i	0.293708	−	0.955895i	$-0.405111\pi$
$487$	22.6422	−	6.06695i	1.02601	−	0.274920i	0.732306	+	0.680975i	$0.238444\pi$
$488$	6.70924	−	33.9477i	0.303713	−	1.53674i
$489$		−	26.3540i		−	1.19177i
$490$		0			0
$491$		−	43.0124i		−	1.94112i	−0.240851	−	0.970562i	$-0.577427\pi$
$491$		−	43.0124i		−	1.94112i	0.240851	−	0.970562i	$-0.422573\pi$
$492$	−14.4730	+	4.57635i	−0.652491	+	0.206318i
$493$	24.5064	−	6.56647i	1.10371	−	0.295739i
$494$	1.45762	+	2.39986i	0.0655812	+	0.107975i
$495$	−11.6661	−	6.89095i	−0.524351	−	0.309725i
$496$	1.48000	+	0.687184i	0.0664538	+	0.0308555i
$497$		0			0
$498$	−4.79467	+	1.39965i	−0.214854	+	0.0627199i
$499$	0.280975	+	0.486663i	0.0125782	+	0.0217860i	0.872246	−	0.489067i	$-0.162663\pi$
$499$	0.280975	+	0.486663i	0.0125782	+	0.0217860i	−0.859668	+	0.510853i	$0.829329\pi$
$500$	22.3583	−	0.327080i	0.999893	−	0.0146275i
$501$	−8.09775	+	14.0257i	−0.361781	+	0.626623i
$502$	−26.6032	−	25.4462i	−1.18736	−	1.13572i
$503$	−9.37781	+	9.37781i	−0.418136	+	0.418136i	−0.884561	−	0.466425i	$-0.845542\pi$
$503$	−9.37781	+	9.37781i	−0.418136	+	0.418136i	0.466425	+	0.884561i	$0.345542\pi$
$504$		0			0
$505$	18.9204	−	10.6743i	0.841945	−	0.475000i
$506$	−25.4581	+	0.565932i	−1.13175	+	0.0251588i
$507$	10.9083	−	2.92286i	0.484453	−	0.129809i
$508$	13.0025	−	14.2131i	0.576894	−	0.630606i
$509$	−15.9743	+	9.22275i	−0.708047	+	0.408791i	−0.810338	−	0.585963i	$-0.800716\pi$
$509$	−15.9743	+	9.22275i	−0.708047	+	0.408791i	0.102290	+	0.994755i	$0.467383\pi$
$510$	9.96825	−	10.2162i	0.441402	−	0.452382i
$511$		0			0
$512$	−12.5017	+	18.8602i	−0.552501	+	0.833512i
$513$	0.625029	−	2.33264i	0.0275957	−	0.102989i
$514$	6.69402	−	4.06578i	0.295260	−	0.179334i
$515$	0.194093	+	0.197991i	0.00855276	+	0.00872453i
$516$	6.99796	−	13.4699i	0.308068	−	0.592979i
$517$	−35.6783	+	35.6783i	−1.56913	+	1.56913i
$518$		0			0
$519$	−24.7730			−1.08741
$520$	13.1816	−	26.1528i	0.578053	−	1.14688i
$521$	6.90441	−	11.9588i	0.302488	−	0.523924i	−0.674211	−	0.738539i	$-0.735516\pi$
$521$	6.90441	−	11.9588i	0.302488	−	0.523924i	0.976699	+	0.214614i	$0.0688495\pi$
$522$	−12.5076	−	3.05516i	−0.547443	−	0.133721i
$523$	−12.2607	−	3.28525i	−0.536124	−	0.143654i	−0.0194092	−	0.999812i	$-0.506179\pi$
$523$	−12.2607	−	3.28525i	−0.536124	−	0.143654i	−0.516715	+	0.856158i	$0.672845\pi$
$524$	−2.33689	−	3.66156i	−0.102088	−	0.159956i
$525$		0			0
$526$	−18.1522	−	9.94896i	−0.791473	−	0.433795i
$527$	−0.356301	+	1.32973i	−0.0155207	+	0.0579241i
$528$	4.60552	−	26.3719i	0.200430	−	1.14769i
$529$	−8.70422	−	5.02539i	−0.378444	−	0.218495i
$530$	−3.11948	+	1.85249i	−0.135501	+	0.0804672i
$531$		−	4.69281i		−	0.203651i
$532$		0			0
$533$	−18.5798	−	18.5798i	−0.804780	−	0.804780i
$534$	13.3490	−	0.296747i	0.577666	−	0.0128415i
$535$	−3.78509	+	3.71057i	−0.163644	+	0.160422i
$536$	−29.7802	−	14.6405i	−1.28631	−	0.632372i
$537$	30.5277	+	8.17987i	1.31737	+	0.352988i
$538$	−26.6791	+	7.78810i	−1.15022	+	0.335769i
$539$		0			0
$540$	−24.0910	+	7.35494i	−1.03671	+	0.316506i
$541$	−11.6821	−	20.2340i	−0.502254	−	0.869929i	−0.999997	−	0.00260457i	$-0.999171\pi$
$541$	−11.6821	−	20.2340i	−0.502254	−	0.869929i	0.497743	−	0.867325i	$-0.334162\pi$
$542$	4.60121	−	18.8370i	0.197639	−	0.809120i
$543$	0.326474	+	1.21842i	0.0140103	+	0.0522872i
$544$	−17.4888	−	7.65256i	−0.749828	−	0.328101i
$545$	11.1130	+	19.6980i	0.476030	+	0.843770i
$546$		0			0
$547$	5.99240	+	5.99240i	0.256216	+	0.256216i	0.823513	−	0.567297i	$-0.192011\pi$
$547$	5.99240	+	5.99240i	0.256216	+	0.256216i	−0.567297	+	0.823513i	$0.692011\pi$
$548$	−22.2446	+	7.03373i	−0.950241	+	0.300466i
$549$	−12.8307	−	7.40781i	−0.547601	−	0.316158i
$550$	25.0773	+	24.9601i	1.06930	+	1.06430i
$551$	−2.79160	+	1.61173i	−0.118926	+	0.0686619i
$552$	−8.96353	+	10.2463i	−0.381513	+	0.436113i
$553$		0			0
$554$	−8.75392	−	4.79790i	−0.371918	−	0.203843i
$555$	−6.82941	+	11.5619i	−0.289892	+	0.490775i
$556$	−1.33321	−	29.9719i	−0.0565406	−	1.27109i
$557$	6.04931	+	22.5763i	0.256317	+	0.956589i	0.967353	+	0.253433i	$0.0815598\pi$
$557$	6.04931	+	22.5763i	0.256317	+	0.956589i	−0.711036	+	0.703156i	$0.751773\pi$
$558$	0.482901	−	0.504859i	0.0204428	−	0.0213724i
$559$	26.2758			1.11135
$560$		0			0
$561$	22.5856			0.953564
$562$	−15.6112	+	16.3211i	−0.658520	+	0.688464i
$563$	−2.40734	−	8.98432i	−0.101457	−	0.378644i	0.896462	−	0.443121i	$-0.146129\pi$
$563$	−2.40734	−	8.98432i	−0.101457	−	0.378644i	−0.997919	+	0.0644770i	$0.979462\pi$
$564$	1.19871	+	26.9483i	0.0504749	+	1.13473i
$565$	−6.04503	−	23.4921i	−0.254316	−	0.988321i
$566$	−26.7371	−	14.6542i	−1.12385	−	0.615964i
$567$		0			0
$568$	22.8504	−	26.1205i	0.958780	−	1.09599i
$569$	2.60258	−	1.50260i	0.109106	−	0.0629922i	−0.444454	−	0.895802i	$-0.646602\pi$
$569$	2.60258	−	1.50260i	0.109106	−	0.0629922i	0.553560	+	0.832809i	$0.313269\pi$
$570$	−0.887397	+	1.58157i	−0.0371690	+	0.0662448i
$571$	−15.8499	−	9.15092i	−0.663296	−	0.382954i	0.130236	−	0.991483i	$-0.458427\pi$
$571$	−15.8499	−	9.15092i	−0.663296	−	0.382954i	−0.793532	+	0.608529i	$0.791760\pi$
$572$	44.1853	−	13.9714i	1.84748	−	0.584172i
$573$	−16.3312	−	16.3312i	−0.682246	−	0.682246i
$574$		0			0
$575$	−4.31035	−	17.4686i	−0.179754	−	0.728491i
$576$	5.91643	+	7.67132i	0.246518	+	0.319638i
$577$	−0.273102	−	1.01923i	−0.0113694	−	0.0424312i	0.960008	−	0.279972i	$-0.0903253\pi$
$577$	−0.273102	−	1.01923i	−0.0113694	−	0.0424312i	−0.971378	+	0.237541i	$0.923659\pi$
$578$	−1.88319	+	7.70966i	−0.0783306	+	0.320680i
$579$	−3.99151	−	6.91350i	−0.165881	−	0.287315i
$580$	29.6802	+	15.7963i	1.23240	+	0.655906i
$581$		0			0
$582$	−13.4802	+	3.93512i	−0.558774	+	0.163116i
$583$	−5.54517	−	1.48582i	−0.229658	−	0.0615366i
$584$	−13.5938	−	6.68295i	−0.562514	−	0.276542i
$585$	−8.77785	−	8.95414i	−0.362919	−	0.370208i
$586$	39.7765	−	0.884229i	1.64315	−	0.0365272i
$587$	−29.5589	−	29.5589i	−1.22003	−	1.22003i	−0.967621	−	0.252406i	$-0.918778\pi$
$587$	−29.5589	−	29.5589i	−1.22003	−	1.22003i	−0.252406	−	0.967621i	$-0.581222\pi$
$588$		0			0
$589$		−	0.174907i		−	0.00720692i
$590$	−3.02607	+	11.8751i	−0.124581	+	0.488890i
$591$	−9.37905	−	5.41499i	−0.385802	−	0.222743i
$592$	17.6914	+	3.08959i	0.727113	+	0.126981i
$593$	−0.823702	+	3.07410i	−0.0338254	+	0.126238i	−0.980774	−	0.195147i	$-0.937482\pi$
$593$	−0.823702	+	3.07410i	−0.0338254	+	0.126238i	0.946949	+	0.321385i	$0.104148\pi$
$594$	−34.9513	−	19.1563i	−1.43407	−	0.785994i
$595$		0			0
$596$	9.68000	+	15.1671i	0.396508	+	0.621269i
$597$	−25.7625	−	6.90305i	−1.05439	−	0.282523i
$598$	−22.8927	−	5.59187i	−0.936152	−	0.228668i
$599$	−0.992946	+	1.71983i	−0.0405707	+	0.0702705i	−0.885598	−	0.464453i	$-0.846251\pi$
$599$	−0.992946	+	1.71983i	−0.0405707	+	0.0702705i	0.845027	+	0.534724i	$0.179584\pi$
$600$	18.8950	−	0.884855i	0.771386	−	0.0361240i
$601$	29.8474			1.21750			0.608750	−	0.793362i	$-0.291671\pi$
$601$	29.8474			1.21750			0.608750	+	0.793362i	$0.291671\pi$
$602$		0			0
$603$	−10.0464	+	10.0464i	−0.409119	+	0.409119i
$604$	−0.585380	+	1.12676i	−0.0238188	+	0.0458471i
$605$	−0.312049	+	31.3874i	−0.0126866	+	1.27608i
$606$	15.7067	−	9.53989i	0.638043	−	0.387532i
$607$	−1.95663	+	7.30226i	−0.0794173	+	0.296389i	−0.994199	−	0.107560i	$-0.965696\pi$
$607$	−1.95663	+	7.30226i	−0.0794173	+	0.296389i	0.914781	+	0.403950i	$0.132363\pi$
$608$	2.39795	+	0.364053i	0.0972497	+	0.0147643i
$609$		0			0
$610$	27.6911	+	27.0190i	1.12118	+	1.09397i
$611$	−40.4387	+	23.3473i	−1.63597	+	0.944530i
$612$	−5.51679	+	6.03043i	−0.223003	+	0.243766i
$613$	−20.4572	+	5.48148i	−0.826257	+	0.221395i	−0.647080	−	0.762422i	$-0.724010\pi$
$613$	−20.4572	+	5.48148i	−0.826257	+	0.221395i	−0.179177	+	0.983817i	$0.557343\pi$
$614$	−28.2098	+	0.627102i	−1.13845	+	0.0253078i
$615$	4.55514	−	16.3482i	0.183681	−	0.659222i
$616$		0			0
$617$	3.15050	−	3.15050i	0.126835	−	0.126835i	−0.640840	−	0.767675i	$-0.721414\pi$
$617$	3.15050	−	3.15050i	0.126835	−	0.126835i	0.767675	+	0.640840i	$0.221414\pi$
$618$	0.169492	+	0.162121i	0.00681798	+	0.00652145i
$619$	−23.8051	+	41.2316i	−0.956808	+	1.65724i	−0.226631	+	0.973981i	$0.572771\pi$
$619$	−23.8051	+	41.2316i	−0.956808	+	1.65724i	−0.730176	+	0.683259i	$0.760562\pi$
$620$	−1.54752	+	0.966148i	−0.0621500	+	0.0388014i
$621$	10.1340	+	17.5527i	0.406665	+	0.704365i
$622$	22.7079	−	6.62884i	0.910504	−	0.265792i
$623$		0			0
$624$	10.4335	−	22.4708i	0.417675	−	0.899553i
$625$	−13.3509	+	21.1366i	−0.534034	+	0.845463i
$626$	5.94651	+	9.79050i	0.237670	+	0.391307i
$627$	−2.77180	+	0.742701i	−0.110695	+	0.0296606i
$628$	−16.2974	+	5.15323i	−0.650337	+	0.205636i
$629$			15.1514i			0.604126i
$630$		0			0
$631$		−	22.2381i		−	0.885285i	−0.896698	−	0.442643i	$-0.854041\pi$
$631$		−	22.2381i		−	0.885285i	0.896698	−	0.442643i	$-0.145959\pi$
$632$	−0.108331	+	0.548134i	−0.00430916	+	0.0218036i
$633$	−10.0107	+	2.68235i	−0.397888	+	0.106614i
$634$	7.40463	−	4.49739i	0.294075	−	0.178614i
$635$	5.36714	+	20.8577i	0.212988	+	0.827712i
$636$	−2.58712	+	1.65116i	−0.102586	+	0.0654726i
$637$		0			0
$638$	14.9081	+	51.0695i	0.590217	+	2.02186i
$639$	−7.42932	−	12.8680i	−0.293899	−	0.509048i
$640$	−10.0247	−	23.2272i	−0.396262	−	0.918137i
$641$	11.7014	−	20.2673i	0.462176	−	0.800512i	−0.536893	−	0.843650i	$-0.680402\pi$
$641$	11.7014	−	20.2673i	0.462176	−	0.800512i	0.999069	+	0.0431381i	$0.0137355\pi$
$642$	−3.09934	+	3.24027i	−0.122321	+	0.127883i
$643$	16.9251	−	16.9251i	0.667460	−	0.667460i	−0.289668	−	0.957127i	$-0.593545\pi$
$643$	16.9251	−	16.9251i	0.667460	−	0.667460i	0.957127	+	0.289668i	$0.0935447\pi$
$644$		0			0
$645$	8.33892	+	14.7809i	0.328345	+	0.581996i
$646$	0.0454765	+	2.04573i	0.00178925	+	0.0804881i
$647$	−8.65768	+	2.31982i	−0.340369	+	0.0912015i	−0.424955	−	0.905215i	$-0.639710\pi$
$647$	−8.65768	+	2.31982i	−0.340369	+	0.0912015i	0.0845859	+	0.996416i	$0.473043\pi$
$648$	−10.4428	+	3.55916i	−0.410230	+	0.139817i
$649$	−16.7929	+	9.69538i	−0.659179	+	0.380577i
$650$	16.4383	+	28.3185i	0.644763	+	1.11074i
$651$		0			0
$652$	8.49762	−	38.4795i	0.332792	−	1.50697i
$653$	5.31582	−	19.8389i	0.208024	−	0.776356i	−0.780483	−	0.625178i	$-0.785027\pi$
$653$	5.31582	−	19.8389i	0.208024	−	0.776356i	0.988506	−	0.151178i	$-0.0483068\pi$
$654$	9.93200	+	16.3523i	0.388372	+	0.639426i
$655$	4.85621	+	0.0482798i	0.189748	+	0.00188645i
$656$	−22.6075	+	2.01524i	−0.882676	+	0.0786819i
$657$	−4.58586	+	4.58586i	−0.178911	+	0.178911i
$658$		0			0
$659$	6.31956			0.246175			0.123088	−	0.992396i	$-0.460720\pi$
$659$	6.31956			0.246175			0.123088	+	0.992396i	$0.460720\pi$
$660$	21.8820	+	20.4215i	0.851755	+	0.794905i
$661$	−15.0159	+	26.0082i	−0.584049	+	1.01160i	0.410944	+	0.911661i	$0.365199\pi$
$661$	−15.0159	+	26.0082i	−0.584049	+	1.01160i	−0.994993	+	0.0999425i	$0.968134\pi$
$662$	10.4362	−	42.7251i	0.405615	−	1.66056i
$663$	20.1894	+	5.40973i	0.784091	+	0.210097i
$664$	−7.45200	+	0.497628i	−0.289193	+	0.0193117i
$665$		0			0
$666$	3.69561	−	6.74276i	0.143202	−	0.261277i
$667$	7.00207	−	26.1321i	0.271121	−	1.01184i
$668$	−16.3460	+	17.8679i	−0.632445	+	0.691329i
$669$	−18.1985	−	10.5069i	−0.703593	−	0.406220i
$670$	31.9003	−	18.9439i	1.23242	−	0.731868i
$671$			61.2183i			2.36331i
$672$		0			0
$673$	29.5868	+	29.5868i	1.14049	+	1.14049i	0.988361	+	0.152127i	$0.0486122\pi$
$673$	29.5868	+	29.5868i	1.14049	+	1.14049i	0.152127	+	0.988361i	$0.451388\pi$
$674$	−0.419208	−	18.8578i	−0.0161473	−	0.726375i
$675$	7.82821	−	27.0519i	0.301308	−	1.04123i
$676$	16.8696	−	0.750391i	0.648830	−	0.0288612i
$677$	−9.83150	−	2.63434i	−0.377855	−	0.101246i	0.0648924	−	0.997892i	$-0.479330\pi$
$677$	−9.83150	−	2.63434i	−0.377855	−	0.101246i	−0.442748	+	0.896646i	$0.645996\pi$
$678$	−5.75023	−	19.6981i	−0.220836	−	0.756501i
$679$		0			0
$680$	17.8488	−	11.7025i	0.684468	−	0.448771i
$681$	−4.61453	−	7.99259i	−0.176829	−	0.306277i
$682$	−2.80428	−	0.684985i	−0.107381	−	0.0262294i
$683$	0.862105	+	3.21742i	0.0329875	+	0.123111i	0.980456	−	0.196737i	$-0.0630346\pi$
$683$	0.862105	+	3.21742i	0.0329875	+	0.123111i	−0.947469	+	0.319849i	$0.896368\pi$
$684$	0.478740	−	0.921493i	0.0183051	−	0.0352342i
$685$	7.00114	−	25.1267i	0.267500	−	0.960043i
$686$		0			0
$687$	4.77591	+	4.77591i	0.182212	+	0.182212i
$688$	14.5609	−	17.4109i	0.555131	−	0.663785i
$689$	−4.60097	−	2.65637i	−0.175283	−	0.101200i
$690$	−4.11968	−	14.6524i	−0.156833	−	0.557808i
$691$	−2.37720	+	1.37248i	−0.0904331	+	0.0522116i	−0.544535	−	0.838738i	$-0.683294\pi$
$691$	−2.37720	+	1.37248i	−0.0904331	+	0.0522116i	0.454101	+	0.890950i	$0.349960\pi$
$692$	−36.1710	−	7.98782i	−1.37501	−	0.303652i
$693$		0			0
$694$	−21.5506	+	39.3198i	−0.818050	+	1.49256i
$695$	28.8807	+	17.0593i	1.09551	+	0.647098i
$696$	25.5244	+	12.5483i	0.967500	+	0.475641i
$697$	−4.95604	−	18.4962i	−0.187723	−	0.700593i
$698$	14.1430	+	13.5279i	0.535321	+	0.512038i
$699$	−4.64396			−0.175651
$700$		0			0
$701$	−45.4380			−1.71617			−0.858085	−	0.513508i	$-0.828346\pi$
$701$	−45.4380			−1.71617			−0.858085	+	0.513508i	$0.828346\pi$
$702$	−26.6549	−	25.4956i	−1.00602	−	0.962268i
$703$	−0.498237	−	1.85945i	−0.0187914	−	0.0701303i
$704$	15.2279	−	37.0205i	0.573922	−	1.39526i
$705$	−25.9672	−	15.3384i	−0.977981	−	0.577676i
$706$	−1.17687	+	2.14723i	−0.0442919	+	0.0808120i
$707$		0			0
$708$	−2.23545	+	10.1227i	−0.0840135	+	0.380435i
$709$	−37.2819	+	21.5247i	−1.40015	+	0.808377i	−0.994408	−	0.105610i	$-0.966321\pi$
$709$	−37.2819	+	21.5247i	−1.40015	+	0.808377i	−0.405743	+	0.913987i	$0.632987\pi$
$710$	10.5021	+	37.3528i	0.394137	+	1.40183i
$711$	0.207170	+	0.119610i	0.00776950	+	0.00448572i
$712$	19.5865	+	3.87097i	0.734034	+	0.145071i
$713$	1.03801	+	1.03801i	0.0388737	+	0.0388737i
$714$		0			0
$715$	−13.9066	+	49.9102i	−0.520079	+	1.86653i
$716$	41.9359	+	21.7868i	1.56722	+	0.814211i
$717$	−3.90543	−	14.5752i	−0.145851	−	0.544323i
$718$	−42.4829	−	10.3771i	−1.58545	−	0.387269i
$719$	−8.95406	−	15.5089i	−0.333930	−	0.578384i	0.649349	−	0.760491i	$-0.275042\pi$
$719$	−8.95406	−	15.5089i	−0.333930	−	0.578384i	−0.983279	+	0.182107i	$0.941708\pi$
$720$	−10.7975	+	0.854389i	−0.402400	+	0.0318412i
$721$		0			0
$722$	7.45674	+	25.5439i	0.277511	+	0.950647i
$723$	33.7379	+	9.04005i	1.25473	+	0.336203i
$724$	0.0838161	+	1.88427i	0.00311500	+	0.0700285i
$725$	−32.9216	+	18.1443i	−1.22268	+	0.673863i
$726$	0.590129	+	26.5466i	0.0219017	+	0.985235i
$727$	−9.20391	−	9.20391i	−0.341354	−	0.341354i	0.515522	−	0.856876i	$-0.327598\pi$
$727$	−9.20391	−	9.20391i	−0.341354	−	0.341354i	−0.856876	+	0.515522i	$0.827598\pi$
$728$		0			0
$729$			27.3242i			1.01201i
$730$	14.5616	−	8.64734i	0.538947	−	0.320053i
$731$	16.5832	+	9.57434i	0.613353	+	0.354120i
$732$	24.1479	+	22.0911i	0.892533	+	0.816512i
$733$	−4.81185	+	17.9581i	−0.177730	+	0.663297i	0.818341	+	0.574734i	$0.194894\pi$
$733$	−4.81185	+	17.9581i	−0.177730	+	0.663297i	−0.996071	+	0.0885635i	$0.971772\pi$
$734$	8.43492	−	15.3898i	0.311339	−	0.568047i
$735$		0			0
$736$	−16.3915	+	12.0704i	−0.604197	+	0.444922i
$737$	56.7059	+	15.1943i	2.08879	+	0.559690i
$738$	−2.30588	+	9.44011i	−0.0848807	+	0.347495i
$739$	3.53772	−	6.12751i	0.130137	−	0.225404i	−0.793592	−	0.608450i	$-0.791792\pi$
$739$	3.53772	−	6.12751i	0.130137	−	0.225404i	0.923729	+	0.383046i	$0.125125\pi$
$740$	−13.6996	+	14.6794i	−0.503608	+	0.539626i
$741$	−2.65562			−0.0975566
$742$		0			0
$743$	34.5013	−	34.5013i	1.26573	−	1.26573i	0.317456	−	0.948273i	$-0.397172\pi$
$743$	34.5013	−	34.5013i	1.26573	−	1.26573i	0.948273	−	0.317456i	$-0.102828\pi$
$744$	−1.28214	+	0.858982i	−0.0470057	+	0.0314918i
$745$	−20.1157	−	0.199987i	−0.736981	−	0.00732696i
$746$	16.4655	+	27.1093i	0.602846	+	0.992542i
$747$	−0.827608	+	3.08868i	−0.0302806	+	0.113009i
$748$	32.9772	+	7.28252i	1.20576	+	0.266275i
$749$		0			0
$750$	−10.7131	+	18.2342i	−0.391186	+	0.665819i
$751$	7.29278	−	4.21049i	0.266117	−	0.153643i	−0.361004	−	0.932564i	$-0.617566\pi$
$751$	7.29278	−	4.21049i	0.266117	−	0.153643i	0.627122	+	0.778921i	$0.284233\pi$
$752$	−6.93900	+	39.7337i	−0.253039	+	1.44894i
$753$	33.6314	−	9.01152i	1.22560	−	0.328398i
$754$	1.09421	+	49.2221i	0.0398486	+	1.79256i
$755$	−0.697552	−	1.23642i	−0.0253865	−	0.0449980i
$756$		0			0
$757$	0.487957	−	0.487957i	0.0177351	−	0.0177351i	−0.698184	−	0.715919i	$-0.746008\pi$
$757$	0.487957	−	0.487957i	0.0177351	−	0.0177351i	0.715919	+	0.698184i	$0.246008\pi$
$758$	−5.95923	+	6.23020i	−0.216449	+	0.226291i
$759$	12.0419	−	20.8573i	0.437095	−	0.757070i
$760$	−1.80565	+	2.02312i	−0.0654978	+	0.0733862i
$761$	−2.18495	−	3.78445i	−0.0792044	−	0.137186i	0.823702	−	0.567022i	$-0.191905\pi$
$761$	−2.18495	−	3.78445i	−0.0792044	−	0.137186i	−0.902907	+	0.429836i	$0.858571\pi$
$762$	5.10540	+	17.4892i	0.184949	+	0.633565i
$763$		0			0
$764$	−18.5793	−	29.1110i	−0.672176	−	1.05320i
$765$	−2.27720	−	8.84962i	−0.0823323	−	0.319959i
$766$	−33.3422	+	20.2512i	−1.20470	+	0.731706i
$767$	−17.3335	+	4.64450i	−0.625877	+	0.167703i
$768$	−9.10785	−	19.3659i	−0.328651	−	0.698806i
$769$		−	9.02388i		−	0.325409i	−0.986675	−	0.162705i	$-0.947978\pi$
$769$		−	9.02388i		−	0.325409i	0.986675	−	0.162705i	$-0.0520218\pi$
$770$		0			0
$771$			7.40742i			0.266772i
$772$	−3.59880	−	11.3814i	−0.129524	−	0.409626i
$773$	33.7229	−	9.03604i	1.21293	−	0.325004i	0.405019	−	0.914308i	$-0.367265\pi$
$773$	33.7229	−	9.03604i	1.21293	−	0.325004i	0.807911	+	0.589305i	$0.200598\pi$
$774$	−5.04466	−	8.30567i	−0.181327	−	0.298541i
$775$	0.0405526	−	2.03929i	0.00145669	−	0.0732533i
$776$	−20.9513	+	1.39908i	−0.752108	+	0.0502242i
$777$		0			0
$778$	28.6385	−	8.36010i	1.02674	−	0.299724i
$779$	1.21645	+	2.10696i	0.0435839	+	0.0754896i
$780$	14.6691	+	23.4961i	0.525236	+	0.841294i
$781$	−30.6980	+	53.1705i	−1.09846	+	1.90259i
$782$	−12.4105	−	11.8708i	−0.443800	−	0.424497i
$783$	29.9422	−	29.9422i	1.07005	−	1.07005i
$784$		0			0
$785$	5.12936	−	18.4090i	0.183075	−	0.657045i
$786$	4.10724	−	0.0913038i	0.146500	−	0.00325670i
$787$	−3.73542	+	1.00090i	−0.133154	+	0.0356784i	−0.324780	−	0.945789i	$-0.605290\pi$
$787$	−3.73542	+	1.00090i	−0.133154	+	0.0356784i	0.191627	+	0.981468i	$0.438624\pi$
$788$	−11.9483	−	10.9306i	−0.425641	−	0.389387i
$789$	16.9547	−	9.78882i	0.603605	−	0.348491i
$790$	−0.447113	−	0.436261i	−0.0159076	−	0.0155215i
$791$		0			0
$792$	−12.8994	−	11.2844i	−0.458359	−	0.400975i
$793$	−14.6631	+	54.7234i	−0.520701	+	1.94328i
$794$	−6.29074	+	3.82084i	−0.223250	+	0.135597i
$795$	0.0341126	−	3.43121i	0.00120985	−	0.121692i
$796$	−35.3900	−	18.3860i	−1.25437	−	0.651675i
$797$	−34.6913	+	34.6913i	−1.22883	+	1.22883i	−0.264420	+	0.964408i	$0.585181\pi$
$797$	−34.6913	+	34.6913i	−1.22883	+	1.22883i	−0.964408	+	0.264420i	$0.914819\pi$
$798$		0			0
$799$	−34.0290			−1.20386
$800$	27.8739	+	4.80056i	0.985491	+	0.169725i
$801$	4.27402	−	7.40281i	0.151015	−	0.261566i
$802$	−15.8952	−	3.88264i	−0.561280	−	0.137101i
$803$	25.8846	+	6.93575i	0.913447	+	0.244757i
$804$	26.4563	−	16.8850i	0.933042	−	0.595489i
$805$		0			0
$806$	−2.34269	−	1.28400i	−0.0825177	−	0.0452268i
$807$	6.80328	−	25.3902i	0.239487	−	0.893777i
$808$	26.0094	−	8.86468i	0.915009	−	0.311858i
$809$	31.8064	+	18.3634i	1.11825	+	0.645624i	0.940955	−	0.338533i	$-0.109931\pi$
$809$	31.8064	+	18.3634i	1.11825	+	0.645624i	0.177299	+	0.984157i	$0.443264\pi$
$810$	3.04589	−	11.9529i	0.107022	−	0.419981i
$811$		−	9.04068i		−	0.317461i	−0.987322	−	0.158731i	$-0.949260\pi$
$811$		−	9.04068i		−	0.317461i	0.987322	−	0.158731i	$-0.0507401\pi$
$812$		0			0
$813$	12.9681	+	12.9681i	0.454810	+	0.454810i
$814$	−31.7636	+	0.706104i	−1.11331	+	0.0247489i
$815$	30.8424	+	31.4618i	1.08036	+	1.10206i
$816$	14.7727	−	10.3801i	0.517149	−	0.363376i
$817$	−2.35001	−	0.629682i	−0.0822163	−	0.0220298i
$818$	6.06484	−	1.77044i	0.212052	−	0.0619019i
$819$		0			0
$820$	11.9223	−	22.4011i	0.416344	−	0.782282i
$821$	0.285380	+	0.494293i	0.00995984	+	0.0172510i	0.870962	−	0.491350i	$-0.163496\pi$
$821$	0.285380	+	0.494293i	0.00995984	+	0.0172510i	−0.861003	+	0.508601i	$0.830163\pi$
$822$	5.23584	−	21.4351i	0.182621	−	0.747636i
$823$	−1.69940	−	6.34226i	−0.0592375	−	0.221077i	0.929961	−	0.367657i	$-0.119840\pi$
$823$	−1.69940	−	6.34226i	−0.0592375	−	0.221077i	−0.989199	+	0.146580i	$0.953173\pi$
$824$	0.195201	+	0.291363i	0.00680015	+	0.0101501i
$825$	−32.4893	+	8.01669i	−1.13113	+	0.279105i
$826$		0			0
$827$	6.28320	+	6.28320i	0.218488	+	0.218488i	0.807861	−	0.589373i	$-0.200625\pi$
$827$	6.28320	+	6.28320i	0.218488	+	0.218488i	−0.589373	+	0.807861i	$0.700625\pi$
$828$	2.62758	+	8.30986i	0.0913146	+	0.288788i
$829$	−21.8135	−	12.5940i	−0.757613	−	0.437408i	0.0708254	−	0.997489i	$-0.477437\pi$
$829$	−21.8135	−	12.5940i	−0.757613	−	0.437408i	−0.828438	+	0.560081i	$0.810770\pi$
$830$	4.08592	−	7.28218i	0.141824	−	0.252768i
$831$	8.17644	−	4.72067i	0.283638	−	0.163758i
$832$	22.4795	−	29.4454i	0.779336	−	1.02084i
$833$		0			0
$834$	24.8828	+	13.6379i	0.861621	+	0.472242i
$835$	−6.74723	−	26.2210i	−0.233498	−	0.907414i
$836$	−4.28657	+	0.190675i	−0.148254	+	0.00659463i
$837$	0.594677	+	2.21936i	0.0205550	+	0.0767125i
$838$	−24.7891	+	25.9163i	−0.856326	+	0.895264i
$839$	0.275469			0.00951026			0.00475513	−	0.999989i	$-0.498486\pi$
$839$	0.275469			0.00951026			0.00475513	+	0.999989i	$0.498486\pi$
$840$		0			0
$841$	−27.5219			−0.949032
$842$	11.4971	−	12.0199i	0.396218	−	0.414234i
$843$	−5.52857	−	20.6329i	−0.190414	−	0.710635i
$844$	−15.4814	+	0.688643i	−0.532893	+	0.0237041i
$845$	−9.60178	+	16.2554i	−0.330311	+	0.559203i
$846$	15.1438	+	8.30009i	0.520654	+	0.285363i
$847$		0			0
$848$	−4.30984	+	1.57666i	−0.148001	+	0.0541426i
$849$	24.9734	−	14.4184i	0.857084	−	0.494838i
$850$	0.0559150	+	23.8622i	0.00191787	+	0.818467i
$851$	13.9920	+	8.07827i	0.479638	+	0.276919i
$852$	9.89581	+	31.2961i	0.339025	+	1.07219i
$853$	−20.8769	−	20.8769i	−0.714813	−	0.714813i	0.252725	−	0.967538i	$-0.418673\pi$
$853$	−20.8769	−	20.8769i	−0.714813	−	0.714813i	−0.967538	+	0.252725i	$0.918673\pi$
$854$		0			0
$855$	0.570477	+	1.01118i	0.0195099	+	0.0345816i
$856$	−5.57013	+	3.73175i	−0.190383	+	0.127549i
$857$	6.30707	+	23.5383i	0.215445	+	0.804053i	0.986009	+	0.166690i	$0.0533079\pi$
$857$	6.30707	+	23.5383i	0.215445	+	0.804053i	−0.770564	+	0.637363i	$0.780025\pi$
$858$	−10.4001	+	42.5774i	−0.355055	+	1.45357i
$859$	−28.1658	−	48.7846i	−0.961004	−	1.66451i	−0.719988	−	0.693987i	$-0.755853\pi$
$859$	−28.1658	−	48.7846i	−0.961004	−	1.66451i	−0.241017	−	0.970521i	$-0.577481\pi$
$860$	7.40969	+	24.2703i	0.252668	+	0.827611i
$861$		0			0
$862$	22.5790	−	6.59121i	0.769044	−	0.224498i
$863$	14.3793	+	3.85293i	0.489479	+	0.131155i	0.495113	−	0.868829i	$-0.335127\pi$
$863$	14.3793	+	3.85293i	0.489479	+	0.131155i	−0.00563418	+	0.999984i	$0.501793\pi$
$864$	−31.6649	+	3.53353i	−1.07726	+	0.120213i
$865$	29.5743	−	28.9921i	1.00556	−	0.985760i
$866$	−51.7301	+	1.14996i	−1.75786	+	0.0390772i
$867$	−5.30760	−	5.30760i	−0.180255	−	0.180255i
$868$		0			0
$869$		−	0.988459i		−	0.0335312i
$870$	−27.3416	+	16.2367i	−0.926966	+	0.550477i
$871$	47.0504	+	27.1646i	1.59424	+	0.920436i
$872$	9.22903	+	27.0785i	0.312534	+	0.916993i
$873$	−2.32682	+	8.68382i	−0.0787510	+	0.293903i
$874$	1.91343	+	1.04872i	0.0647227	+	0.0354736i
$875$		0			0
$876$	12.0765	−	7.70751i	0.408028	−	0.260413i
$877$	45.3079	+	12.1402i	1.52994	+	0.409946i	0.922999	−	0.384803i	$-0.125730\pi$
$877$	45.3079	+	12.1402i	1.52994	+	0.409946i	0.606939	+	0.794748i	$0.292397\pi$
$878$	−34.9318	−	8.53259i	−1.17889	−	0.287961i
$879$	−18.8147	+	32.5880i	−0.634603	+	1.09917i
$880$	25.3651	+	36.8730i	0.855058	+	1.24299i
$881$	−8.94374			−0.301322			−0.150661	−	0.988585i	$-0.548140\pi$
$881$	−8.94374			−0.301322			−0.150661	+	0.988585i	$0.548140\pi$
$882$		0			0
$883$	−13.6439	+	13.6439i	−0.459153	+	0.459153i	−0.898377	−	0.439224i	$-0.855253\pi$
$883$	−13.6439	+	13.6439i	−0.459153	+	0.459153i	0.439224	+	0.898377i	$0.355253\pi$
$884$	27.7342	+	14.4086i	0.932801	+	0.484614i
$885$	−8.11365	−	8.27660i	−0.272737	−	0.278215i
$886$	−2.17717	+	1.32236i	−0.0731434	+	0.0444255i
$887$	8.52105	−	31.8010i	0.286109	−	1.06777i	−0.661917	−	0.749578i	$-0.730257\pi$
$887$	8.52105	−	31.8010i	0.286109	−	1.06777i	0.948025	−	0.318195i	$-0.103077\pi$
$888$	−11.1836	+	12.7842i	−0.375299	+	0.429009i
$889$		0			0
$890$	−15.5889	+	15.9767i	−0.522541	+	0.535540i
$891$	16.9029	−	9.75888i	0.566268	−	0.326935i
$892$	−23.1837	−	21.2090i	−0.776247	−	0.710130i
$893$	4.17618	−	1.11901i	0.139751	−	0.0374461i
$894$	−17.0132	+	0.378203i	−0.569008	+	0.0126490i
$895$	−46.0174	+	25.9616i	−1.53819	+	0.867801i
$896$		0			0
$897$	15.7601	−	15.7601i	0.526215	−	0.526215i
$898$	27.9856	+	26.7684i	0.933891	+	0.893273i
$899$	1.53346	−	2.65603i	0.0511438	−	0.0885836i
$900$	5.79540	−	10.6329i	0.193180	−	0.354431i
$901$	−1.93585	−	3.35299i	−0.0644926	−	0.111704i
$902$	38.5447	−	11.2519i	1.28340	−	0.374647i
$903$		0			0
$904$	−2.04442	−	30.6153i	−0.0679965	−	1.01825i
$905$	−1.81567	−	1.07249i	−0.0603550	−	0.0356507i
$906$	−0.623420	−	1.02642i	−0.0207117	−	0.0341004i
$907$	−13.8355	+	3.70721i	−0.459400	+	0.123096i	−0.481095	−	0.876669i	$-0.659761\pi$
$907$	−13.8355	+	3.70721i	−0.459400	+	0.123096i	0.0216943	+	0.999765i	$0.493094\pi$
$908$	−4.16052	−	13.1579i	−0.138072	−	0.436659i
$909$		−	11.7648i		−	0.390214i
$910$		0			0
$911$			1.96705i			0.0651712i	0.999469	+	0.0325856i	$0.0103742\pi$
$911$			1.96705i			0.0651712i	−0.999469	+	0.0325856i	$0.989626\pi$
$912$	−1.47163	+	1.75967i	−0.0487307	+	0.0582686i
$913$	12.7624	−	3.41969i	0.422375	−	0.113175i
$914$	4.62406	−	2.80854i	0.152950	−	0.0928982i
$915$	−35.4369	+	9.11870i	−1.17151	+	0.301455i
$916$	5.43335	+	8.51325i	0.179523	+	0.281286i
$917$		0			0
$918$	−7.53244	−	25.8033i	−0.248607	−	0.851635i
$919$	4.25783	+	7.37478i	0.140453	+	0.243271i	0.927667	−	0.373408i	$-0.121811\pi$
$919$	4.25783	+	7.37478i	0.140453	+	0.243271i	−0.787214	+	0.616679i	$0.788477\pi$
$920$	−1.29059	−	22.7223i	−0.0425495	−	0.749133i
$921$	13.3435	−	23.1116i	0.439684	−	0.761555i
$922$	−24.2569	+	25.3599i	−0.798859	+	0.835184i
$923$	−40.1766	+	40.1766i	−1.32243	+	1.32243i
$924$		0			0
$925$	−5.37795	−	21.7953i	−0.176826	−	0.716624i
$926$	−0.460954	−	20.7357i	−0.0151479	−	0.681418i
$927$	0.145037	−	0.0388626i	0.00476364	−	0.00127641i
$928$	33.2220	+	26.5518i	1.09057	+	0.871605i
$929$	30.7662	−	17.7629i	1.00941	−	0.582781i	0.0983891	−	0.995148i	$-0.468631\pi$
$929$	30.7662	−	17.7629i	1.00941	−	0.582781i	0.911018	+	0.412367i	$0.135298\pi$
$930$	−0.0211962	−	1.72532i	−0.000695051	−	0.0565755i
$931$		0			0
$932$	−6.78063	−	1.49740i	−0.222107	−	0.0490490i
$933$	−5.79062	+	21.6109i	−0.189576	+	0.707508i
$934$	−3.76844	−	6.20447i	−0.123307	−	0.203016i
$935$	−26.9630	+	26.4321i	−0.881784	+	0.864423i
$936$	−8.82796	−	13.1769i	−0.288551	−	0.430700i
$937$	23.8007	−	23.8007i	0.777536	−	0.777536i	−0.201876	−	0.979411i	$-0.564704\pi$
$937$	23.8007	−	23.8007i	0.777536	−	0.777536i	0.979411	+	0.201876i	$0.0647037\pi$
$938$		0			0
$939$	−10.8339			−0.353551
$940$	−32.9689	−	30.7684i	−1.07533	−	1.00355i
$941$	6.79801	−	11.7745i	0.221609	−	0.383838i	−0.733688	−	0.679487i	$-0.762203\pi$
$941$	6.79801	−	11.7745i	0.221609	−	0.383838i	0.955297	+	0.295649i	$0.0955359\pi$
$942$	3.83601	−	15.7044i	0.124984	−	0.511676i
$943$	−19.7232	−	5.28482i	−0.642276	−	0.172097i
$944$	−6.52796	+	14.0594i	−0.212467	+	0.457593i
$945$		0			0
$946$	−19.2989	+	35.2115i	−0.627463	+	1.14483i
$947$	9.45619	−	35.2910i	0.307285	−	1.14680i	−0.623675	−	0.781683i	$-0.714361\pi$
$947$	9.45619	−	35.2910i	0.307285	−	1.14680i	0.930960	−	0.365120i	$-0.118972\pi$
$948$	−0.389904	−	0.356694i	−0.0126635	−	0.0115849i
$949$	21.4771	+	12.3998i	0.697177	+	0.402515i
$950$	−0.791544	−	2.92663i	−0.0256811	−	0.0949525i
$951$			8.19376i			0.265701i
$952$		0			0
$953$	4.64369	+	4.64369i	0.150424	+	0.150424i	0.778307	−	0.627883i	$-0.216079\pi$
$953$	4.64369	+	4.64369i	0.150424	+	0.150424i	−0.627883	+	0.778307i	$0.716079\pi$
$954$	0.0436673	+	1.96434i	0.00141378	+	0.0635980i
$955$	38.6090	+	0.383845i	1.24936	+	0.0124209i
$956$	−1.00265	−	22.5406i	−0.0324279	−	0.729014i
$957$	−48.6023	−	13.0229i	−1.57109	−	0.420972i
$958$	−1.67375	−	5.73362i	−0.0540763	−	0.185245i
$959$		0			0
$960$	23.6980	+	3.30050i	0.764850	+	0.106523i
$961$	−15.4168	−	26.7027i	−0.497316	−	0.861376i
$962$	−28.5628	−	6.97688i	−0.920902	−	0.224943i
$963$	0.742954	+	2.77274i	0.0239414	+	0.0893504i
$964$	46.3458	+	24.0779i	1.49270	+	0.775496i
$965$	12.8561	+	3.58212i	0.413851	+	0.115313i
$966$		0			0
$967$	−24.8629	−	24.8629i	−0.799538	−	0.799538i	0.183485	−	0.983023i	$-0.441262\pi$
$967$	−24.8629	−	24.8629i	−0.799538	−	0.799538i	−0.983023	+	0.183485i	$0.941262\pi$
$968$	−7.69805	+	38.9509i	−0.247425	+	1.25193i
$969$	−1.67602	−	0.967651i	−0.0538415	−	0.0310854i
$970$	11.4876	−	20.4739i	0.368844	−	0.657376i
$971$	33.6619	−	19.4347i	1.08026	−	0.623689i	0.149294	−	0.988793i	$-0.452300\pi$
$971$	33.6619	−	19.4347i	1.08026	−	0.623689i	0.930967	+	0.365104i	$0.118966\pi$
$972$	−5.03727	+	22.8101i	−0.161571	+	0.731634i
$973$		0			0
$974$	−15.9331	+	29.0704i	−0.510529	+	0.931476i
$975$	−30.9625	−	0.615711i	−0.991595	−	0.0197185i
$976$	28.1353	+	40.0415i	0.900588	+	1.28170i
$977$	13.8183	+	51.5706i	0.442087	+	1.64989i	0.723515	+	0.690309i	$0.242525\pi$
$977$	13.8183	+	51.5706i	0.442087	+	1.64989i	−0.281428	+	0.959582i	$0.590808\pi$
$978$	26.9332	+	25.7618i	0.861230	+	0.823772i
$979$	−35.3206			−1.12885
$980$		0			0
$981$	12.2483			0.391060
$982$	43.9577	+	42.0459i	1.40275	+	1.34174i
$983$	−10.3281	−	38.5452i	−0.329417	−	1.22940i	−0.909797	−	0.415054i	$-0.863763\pi$
$983$	−10.3281	−	38.5452i	−0.329417	−	1.22940i	0.580380	−	0.814346i	$-0.302904\pi$
$984$	9.47080	−	19.2645i	0.301918	−	0.614131i
$985$	17.5341	−	4.51190i	0.558681	−	0.143761i
$986$	−17.2449	+	31.4639i	−0.549190	+	1.00201i
$987$		0			0
$988$	−3.87746	−	0.856280i	−0.123359	−	0.0272419i
$989$	17.6833	−	10.2095i	0.562298	−	0.324643i
$990$	18.4463	−	5.18637i	0.586263	−	0.164834i
$991$	−20.3753	−	11.7637i	−0.647242	−	0.373685i	0.140157	−	0.990129i	$-0.455239\pi$
$991$	−20.3753	−	11.7637i	−0.647242	−	0.373685i	−0.787399	+	0.616444i	$0.788573\pi$
$992$	−2.14903	+	0.840782i	−0.0682316	+	0.0266949i
$993$	29.4134	+	29.4134i	0.933406	+	0.933406i
$994$		0			0
$995$	38.8344	−	21.9092i	1.23113	−	0.694568i
$996$	3.25652	−	6.26825i	0.103187	−	0.198617i
$997$	−8.68766	−	32.4228i	−0.275141	−	1.02684i	−0.955747	−	0.294190i	$-0.904950\pi$
$997$	−8.68766	−	32.4228i	−0.275141	−	1.02684i	0.680606	−	0.732650i	$-0.261717\pi$
$998$	−0.772020	−	0.188577i	−0.0244379	−	0.00596930i
$999$	12.6441	+	21.9002i	0.400041	+	0.692891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.k.263.5		72
4.3	odd	2	inner	980.2.x.k.263.7		72
5.2	odd	4	inner	980.2.x.k.67.5		72
7.2	even	3	inner	980.2.x.k.863.17		72
7.3	odd	6		980.2.k.l.883.8		36
7.4	even	3		140.2.k.a.43.8	✓	36
7.5	odd	6		980.2.x.l.863.17		72
7.6	odd	2		980.2.x.l.263.5		72
20.7	even	4	inner	980.2.x.k.67.17		72
28.3	even	6		980.2.k.l.883.18		36
28.11	odd	6		140.2.k.a.43.18	yes	36
28.19	even	6		980.2.x.l.863.5		72
28.23	odd	6	inner	980.2.x.k.863.5		72
28.27	even	2		980.2.x.l.263.7		72
35.2	odd	12	inner	980.2.x.k.667.7		72
35.4	even	6		700.2.k.b.43.11		36
35.12	even	12		980.2.x.l.667.7		72
35.17	even	12		980.2.k.l.687.18		36
35.18	odd	12		700.2.k.b.407.1		36
35.27	even	4		980.2.x.l.67.5		72
35.32	odd	12		140.2.k.a.127.18	yes	36
140.27	odd	4		980.2.x.l.67.17		72
140.39	odd	6		700.2.k.b.43.1		36
140.47	odd	12		980.2.x.l.667.5		72
140.67	even	12		140.2.k.a.127.8	yes	36
140.87	odd	12		980.2.k.l.687.8		36
140.107	even	12	inner	980.2.x.k.667.5		72
140.123	even	12		700.2.k.b.407.11		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.8	✓	36	7.4	even	3
140.2.k.a.43.18	yes	36	28.11	odd	6
140.2.k.a.127.8	yes	36	140.67	even	12
140.2.k.a.127.18	yes	36	35.32	odd	12
700.2.k.b.43.1		36	140.39	odd	6
700.2.k.b.43.11		36	35.4	even	6
700.2.k.b.407.1		36	35.18	odd	12
700.2.k.b.407.11		36	140.123	even	12
980.2.k.l.687.8		36	140.87	odd	12
980.2.k.l.687.18		36	35.17	even	12
980.2.k.l.883.8		36	7.3	odd	6
980.2.k.l.883.18		36	28.3	even	6
980.2.x.k.67.5		72	5.2	odd	4	inner
980.2.x.k.67.17		72	20.7	even	4	inner
980.2.x.k.263.5		72	1.1	even	1	trivial
980.2.x.k.263.7		72	4.3	odd	2	inner
980.2.x.k.667.5		72	140.107	even	12	inner
980.2.x.k.667.7		72	35.2	odd	12	inner
980.2.x.k.863.5		72	28.23	odd	6	inner
980.2.x.k.863.17		72	7.2	even	3	inner
980.2.x.l.67.5		72	35.27	even	4
980.2.x.l.67.17		72	140.27	odd	4
980.2.x.l.263.5		72	7.6	odd	2
980.2.x.l.263.7		72	28.27	even	2
980.2.x.l.667.5		72	140.47	odd	12
980.2.x.l.667.7		72	35.12	even	12
980.2.x.l.863.5		72	28.19	even	6
980.2.x.l.863.17		72	7.5	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.977529 + 1.02198i) q^{2} +(-0.346182 - 1.29197i) q^{3} +(-0.0888759 - 1.99802i) q^{4} +(1.92528 + 1.13723i) q^{5} +(1.65877 + 0.909146i) q^{6} +(2.12881 + 1.86230i) q^{8} +(1.04873 - 0.605487i) q^{9} +(-3.04424 + 0.855919i) q^{10} +(-4.33338 - 2.50188i) q^{11} +(-2.55062 + 0.806505i) q^{12} +(-3.27438 - 3.27438i) q^{13} +(0.802768 - 2.88109i) q^{15} +(-3.98420 + 0.355152i) q^{16} +(-0.873420 - 3.25965i) q^{17} +(-0.406374 + 1.66366i) q^{18} +(0.214380 + 0.371316i) q^{19} +(2.10110 - 3.94783i) q^{20} +(6.79287 - 1.98296i) q^{22} +(-3.47589 - 0.931361i) q^{23} +(1.66907 - 3.39506i) q^{24} +(2.41342 + 4.37898i) q^{25} +(6.54714 - 0.145543i) q^{26} +(-3.98268 - 3.98268i) q^{27} +7.51811i q^{29} +(2.15968 + 3.63676i) q^{30} +(-0.353285 - 0.203969i) q^{31} +(3.53171 - 4.41894i) q^{32} +(-1.73221 + 6.46470i) q^{33} +(4.18508 + 2.29378i) q^{34} +(-1.30298 - 2.04158i) q^{36} +(-4.33681 - 1.16204i) q^{37} +(-0.589039 - 0.143881i) q^{38} +(-3.09687 + 5.36393i) q^{39} +(1.98071 + 6.00640i) q^{40} +5.67429 q^{41} +(-4.01233 + 4.01233i) q^{43} +(-4.61368 + 8.88056i) q^{44} +(2.70769 + 0.0269194i) q^{45} +(4.34961 - 2.64185i) q^{46} +(2.60987 - 9.74016i) q^{47} +(1.83811 + 5.02452i) q^{48} +(-6.83440 - 1.81412i) q^{50} +(-3.90900 + 2.25686i) q^{51} +(-6.25128 + 6.83330i) q^{52} +(1.10820 - 0.296942i) q^{53} +(7.96340 - 0.177026i) q^{54} +(-5.49776 - 9.74487i) q^{55} +(0.405515 - 0.405515i) q^{57} +(-7.68334 - 7.34916i) q^{58} +(1.93762 - 3.35606i) q^{59} +(-5.82784 - 1.34789i) q^{60} +(-6.11723 - 10.5954i) q^{61} +(0.553797 - 0.161663i) q^{62} +(1.06370 + 7.92897i) q^{64} +(-2.58038 - 10.0278i) q^{65} +(-4.91349 - 8.08971i) q^{66} +(-11.3327 + 3.03658i) q^{67} +(-6.43523 + 2.03482i) q^{68} +4.81316i q^{69} -12.2700i q^{71} +(3.36016 + 0.664085i) q^{72} +(-5.17303 + 1.38611i) q^{73} +(5.42693 - 3.29619i) q^{74} +(4.82202 - 4.63398i) q^{75} +(0.722846 - 0.461337i) q^{76} +(-2.45454 - 8.40832i) q^{78} +(0.0987717 + 0.171078i) q^{79} +(-8.07460 - 3.84719i) q^{80} +(-1.95031 + 3.37804i) q^{81} +(-5.54678 + 5.79900i) q^{82} +(-1.86715 + 1.86715i) q^{83} +(2.02539 - 7.26902i) q^{85} +(-0.178344 - 8.02268i) q^{86} +(9.71316 - 2.60263i) q^{87} +(-4.56572 - 13.3961i) q^{88} +(6.11311 - 3.52940i) q^{89} +(-2.67435 + 2.74088i) q^{90} +(-1.55196 + 7.02768i) q^{92} +(-0.141221 + 0.527043i) q^{93} +(7.40301 + 12.1885i) q^{94} +(-0.00953113 + 0.958687i) q^{95} +(-6.93175 - 3.03311i) q^{96} +(-5.24949 + 5.24949i) q^{97} -6.05942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48}+ \cdots + 40 q^{97}+O(q^{100}) \) 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

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