LMFDB - Embedded newform 980.2.x.l.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.l.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	$0.0428502\pi$
$3$	0.346182	+	1.29197i	0.199868	+	0.745919i	−0.791084	+	0.611707i	$0.790483\pi$
$4$	−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	0.996123	−	0.0879732i	$-0.0280390\pi$
$13$	3.27438	+	3.27438i	0.908150	+	0.908150i	−0.0879732	+	0.996123i	$0.528039\pi$
$14$		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	$0.0508710\pi$
$17$	0.873420	+	3.25965i	0.211835	+	0.790581i	−0.775421	+	0.631444i	$0.782462\pi$
$18$	−0.406374	+	1.66366i	−0.0957832	+	0.392129i
$19$	−0.214380	−	0.371316i	−0.0491820	−	0.0851858i	0.840386	−	0.541988i	$-0.182328\pi$
$19$	−0.214380	−	0.371316i	−0.0491820	−	0.0851858i	−0.889568	+	0.456802i	$0.848995\pi$
$20$	−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	0.531390	−	0.847127i	$-0.321670\pi$
$31$	0.353285	+	0.203969i	0.0634518	+	0.0366339i	−0.467938	+	0.883761i	$0.655003\pi$
$32$	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	$-0.646117\pi$
$41$	−5.67429			−0.886176			−0.443088	+	0.896478i	$0.646117\pi$
$42$		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	$0.346355\pi$
$47$	−2.60987	+	9.74016i	−0.380689	+	1.42075i	−0.844852	+	0.535000i	$0.820312\pi$
$48$	−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	−0.964147	−	0.265370i	$-0.914506\pi$
$59$	−1.93762	+	3.35606i	−0.252257	+	0.436921i	0.711890	+	0.702291i	$0.247839\pi$
$60$	−5.82784	−	1.34789i	−0.752371	−	0.174012i
$61$	6.11723	+	10.5954i	0.783231	+	1.35660i	0.930050	+	0.367433i	$0.119763\pi$
$61$	6.11723	+	10.5954i	0.783231	+	1.35660i	−0.146819	+	0.989163i	$0.546903\pi$
$62$	−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	0.0569493	−	0.998377i	$-0.481863\pi$
$73$	5.17303	−	1.38611i	0.605457	−	0.162232i	0.548508	+	0.836145i	$0.315196\pi$
$74$	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	−0.597169	−	0.802115i	$-0.703708\pi$
$83$	1.86715	−	1.86715i	0.204946	−	0.204946i	0.802115	+	0.597169i	$0.203708\pi$
$84$		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	−0.787685	−	0.616078i	$-0.788721\pi$
$89$	−6.11311	+	3.52940i	−0.647988	+	0.374116i	0.139697	+	0.990194i	$0.455387\pi$
$90$	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	−0.388460	−	0.921465i	$-0.626993\pi$
$97$	5.24949	−	5.24949i	0.533005	−	0.533005i	0.921465	+	0.388460i	$0.126993\pi$
$98$		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	−0.999817	−	0.0191239i	$-0.993912\pi$
$101$	−4.85758	+	8.41357i	−0.483347	+	0.837181i	0.516470	+	0.856305i	$0.327246\pi$
$102$	1.51470	−	6.20106i	0.149977	−	0.613997i
$103$	−0.119769	−	0.0320920i	−0.0118012	−	0.00316212i	0.252914	−	0.967489i	$-0.418611\pi$
$103$	−0.119769	−	0.0320920i	−0.0118012	−	0.00316212i	−0.264715	+	0.964327i	$0.585278\pi$
$104$	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	−0.579912	−	0.814679i	$-0.696913\pi$
$131$	−1.88090	+	1.08594i	−0.164335	+	0.0948786i	0.415577	+	0.909558i	$0.363580\pi$
$132$	−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	$-0.719484\pi$
$139$	−15.0008			−1.27235			−0.636175	+	0.771545i	$0.719484\pi$
$140$		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	$0.0274447\pi$
$157$	2.21196	+	8.25515i	0.176534	+	0.658832i	−0.819752	+	0.572719i	$0.805889\pi$
$158$	−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	0.955978	−	0.293437i	$-0.0947992\pi$
$167$	8.56192	+	8.56192i	0.662541	+	0.662541i	−0.293437	+	0.955978i	$0.594799\pi$
$168$		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	$0.331970\pi$
$173$	−4.79365	+	17.8901i	−0.364454	+	1.36016i	−0.868159	+	0.496286i	$0.834697\pi$
$174$	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	$-0.488841\pi$
$181$	0.943069			0.0700978			0.0350489	+	0.999386i	$0.488841\pi$
$182$		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	$0.416517\pi$
$199$	−9.97026	+	17.2690i	−0.706773	+	1.22417i	−0.966048	+	0.258363i	$0.916817\pi$
$200$	−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	−0.973331	−	0.229407i	$-0.926321\pi$
$223$	−11.1091	+	11.1091i	−0.743923	+	0.743923i	0.229407	+	0.973331i	$0.426321\pi$
$224$		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	−0.473124	−	0.880996i	$-0.656874\pi$
$227$	−6.66488	+	1.78585i	−0.442364	+	0.118531i	0.0307604	+	0.999527i	$0.490207\pi$
$228$	−0.846269	−	0.774188i	−0.0560455	−	0.0512718i
$229$	4.37314	−	2.52483i	0.288985	−	0.166846i	−0.348499	−	0.937309i	$-0.613308\pi$
$229$	4.37314	−	2.52483i	0.288985	−	0.166846i	0.637484	+	0.770463i	$0.279975\pi$
$230$	−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	$-0.515264\pi$
$241$	13.0568	−	22.6150i	0.841062	−	1.45676i	0.888998	−	0.457912i	$-0.151402\pi$
$242$	−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	$-0.693118\pi$
$251$		−	26.0311i		−	1.64307i	0.570157	−	0.821536i	$-0.306882\pi$
$252$		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	0.421771	−	0.906702i	$-0.361409\pi$
$257$	5.34936	+	1.43336i	0.333684	+	0.0894104i	−0.0880868	+	0.996113i	$0.528075\pi$
$258$	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	−0.118513	−	0.992953i	$-0.537813\pi$
$269$	−17.0194	−	9.82616i	−1.03769	−	0.599112i	−0.919179	+	0.393841i	$0.871146\pi$
$270$	15.5331	+	8.71539i	0.945315	+	0.530402i
$271$	11.8744	−	6.85570i	0.721320	−	0.416454i	−0.0939185	−	0.995580i	$-0.529939\pi$
$271$	11.8744	−	6.85570i	0.721320	−	0.416454i	0.815238	+	0.579126i	$0.196606\pi$
$272$	−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	$-0.861941\pi$
$283$	−5.58000	−	20.8249i	−0.331697	−	1.23791i	0.575710	−	0.817654i	$-0.304726\pi$
$284$	−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	$0.0570177\pi$
$293$	19.8931	+	19.8931i	1.16217	+	1.16217i	0.178170	+	0.984000i	$0.442982\pi$
$294$		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	0.178697	−	0.983904i	$-0.442812\pi$
$307$	−14.1084	−	14.1084i	−0.805207	−	0.805207i	−0.983904	+	0.178697i	$0.942812\pi$
$308$		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	0.850909	−	0.525313i	$-0.176052\pi$
$311$	14.4861	+	8.36354i	0.821430	+	0.474253i	−0.0294794	+	0.999565i	$0.509385\pi$
$312$	−16.5819	+	5.65153i	−0.938764	+	0.319955i
$313$	−2.09639	+	7.82385i	−0.118495	+	0.442230i	−0.999525	−	0.0308314i	$-0.990185\pi$
$313$	−2.09639	+	7.82385i	−0.118495	+	0.442230i	0.881029	+	0.473062i	$0.156851\pi$
$314$	−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	$0.120776\pi$
$349$			13.8389i			0.740778i	−0.928877	+	0.370389i	$0.879224\pi$
$350$		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	−0.303051	−	0.952974i	$-0.598005\pi$
$353$	−1.67242	+	0.448123i	−0.0890139	+	0.0238512i	0.214037	+	0.976826i	$0.431339\pi$
$354$	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	0.0679826	−	0.997687i	$-0.478344\pi$
$367$	11.9867	−	3.21183i	0.625700	−	0.167656i	0.557718	+	0.830031i	$0.311677\pi$
$368$	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	−0.497118	−	0.867683i	$-0.665608\pi$
$383$	−26.6446	−	7.13940i	−1.36148	−	0.364806i	−0.864358	+	0.502877i	$0.832275\pi$
$384$	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	0.130451	−	0.991455i	$-0.458358\pi$
$397$	−5.02710	−	1.34701i	−0.252303	−	0.0676043i	−0.382754	+	0.923850i	$0.625024\pi$
$398$	−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	0.592594	−	0.805501i	$-0.298104\pi$
$409$	3.86895	+	2.23374i	0.191307	+	0.110451i	−0.401287	+	0.915952i	$0.631437\pi$
$410$	−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	$-0.712638\pi$
$419$	−25.3590			−1.23887			−0.619433	+	0.785049i	$0.712638\pi$
$420$		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	$-0.908113\pi$
$433$	−25.8715	−	25.8715i	−1.24330	−	1.24330i	−0.284680	−	0.958623i	$-0.591887\pi$
$434$		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	$-0.959129\pi$
$439$	−12.7134	−	22.0202i	−0.606775	−	1.05097i	0.384993	−	0.922920i	$-0.374204\pi$
$440$	−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	$-0.696114\pi$
$461$	−24.8145			−1.15573			−0.577864	+	0.816133i	$0.696114\pi$
$462$		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	−0.928351	−	0.371705i	$-0.878773\pi$
$467$	1.32853	−	4.95815i	0.0614772	−	0.229436i	0.989828	+	0.142269i	$0.0454399\pi$
$468$	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	−0.813741	−	0.581228i	$-0.802572\pi$
$479$	2.11175	−	3.65765i	0.0964882	−	0.167122i	0.910229	+	0.414106i	$0.135906\pi$
$480$	−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	−0.466425	−	0.884561i	$-0.654458\pi$
$503$	9.37781	−	9.37781i	0.418136	−	0.418136i	0.884561	+	0.466425i	$0.154458\pi$
$504$		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	−0.102290	−	0.994755i	$-0.532617\pi$
$509$	15.9743	−	9.22275i	0.708047	−	0.408791i	0.810338	+	0.585963i	$0.199284\pi$
$510$	−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	−0.976699	−	0.214614i	$-0.931150\pi$
$521$	−6.90441	+	11.9588i	−0.302488	+	0.523924i	0.674211	+	0.738539i	$0.264484\pi$
$522$	−12.5076	−	3.05516i	−0.547443	−	0.133721i
$523$	12.2607	+	3.28525i	0.536124	+	0.143654i	0.516715	−	0.856158i	$-0.327155\pi$
$523$	12.2607	+	3.28525i	0.536124	+	0.143654i	0.0194092	+	0.999812i	$0.493821\pi$
$524$	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	0.997919	−	0.0644770i	$-0.0205379\pi$
$563$	2.40734	+	8.98432i	0.101457	+	0.378644i	−0.896462	+	0.443121i	$0.853871\pi$
$564$	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	0.971378	−	0.237541i	$-0.0763414\pi$
$577$	0.273102	+	1.01923i	0.0113694	+	0.0424312i	−0.960008	+	0.279972i	$0.909675\pi$
$578$	−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	$0.0812219\pi$
$587$	29.5589	+	29.5589i	1.22003	+	1.22003i	0.252406	+	0.967621i	$0.418778\pi$
$588$		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	−0.946949	−	0.321385i	$-0.895852\pi$
$593$	0.823702	−	3.07410i	0.0338254	−	0.126238i	0.980774	+	0.195147i	$0.0625183\pi$
$594$	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	$-0.708329\pi$
$601$	−29.8474			−1.21750			−0.608750	+	0.793362i	$0.708329\pi$
$602$		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	−0.914781	−	0.403950i	$-0.867637\pi$
$607$	1.95663	−	7.30226i	0.0794173	−	0.296389i	0.994199	+	0.107560i	$0.0343038\pi$
$608$	−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	$-0.427229\pi$
$619$	23.8051	−	41.2316i	0.956808	−	1.65724i	0.730176	−	0.683259i	$-0.239438\pi$
$620$	−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	−0.957127	−	0.289668i	$-0.906455\pi$
$643$	−16.9251	+	16.9251i	−0.667460	+	0.667460i	0.289668	+	0.957127i	$0.406455\pi$
$644$		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	−0.0845859	−	0.996416i	$-0.526957\pi$
$647$	8.65768	−	2.31982i	0.340369	−	0.0912015i	0.424955	+	0.905215i	$0.360290\pi$
$648$	−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	$-0.634801\pi$
$661$	15.0159	−	26.0082i	0.584049	−	1.01160i	0.994993	−	0.0999425i	$-0.0318659\pi$
$662$	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	0.442748	−	0.896646i	$-0.354004\pi$
$677$	9.83150	+	2.63434i	0.377855	+	0.101246i	−0.0648924	+	0.997892i	$0.520670\pi$
$678$	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	−0.454101	−	0.890950i	$-0.650040\pi$
$691$	2.37720	−	1.37248i	0.0904331	−	0.0522116i	0.544535	+	0.838738i	$0.316706\pi$
$692$	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	0.983279	−	0.182107i	$-0.0582918\pi$
$719$	8.95406	+	15.5089i	0.333930	+	0.578384i	−0.649349	+	0.760491i	$0.724958\pi$
$720$	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	0.856876	−	0.515522i	$-0.172402\pi$
$727$	9.20391	+	9.20391i	0.341354	+	0.341354i	−0.515522	+	0.856876i	$0.672402\pi$
$728$		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	$-0.805106\pi$
$733$	4.81185	−	17.9581i	0.177730	−	0.663297i	0.996071	−	0.0885635i	$-0.0282276\pi$
$734$	−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	0.902907	−	0.429836i	$-0.141429\pi$
$761$	2.18495	+	3.78445i	0.0792044	+	0.137186i	−0.823702	+	0.567022i	$0.808095\pi$
$762$	−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	$0.0520218\pi$
$769$			9.02388i			0.325409i	−0.986675	+	0.162705i	$0.947978\pi$
$770$		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	−0.807911	−	0.589305i	$-0.799402\pi$
$773$	−33.7229	+	9.03604i	−1.21293	+	0.325004i	−0.405019	+	0.914308i	$0.632735\pi$
$774$	−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	−0.191627	−	0.981468i	$-0.561376\pi$
$787$	3.73542	−	1.00090i	0.133154	−	0.0356784i	0.324780	+	0.945789i	$0.394710\pi$
$788$	−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	$-0.414819\pi$
$797$	34.6913	−	34.6913i	1.22883	−	1.22883i	0.964408	−	0.264420i	$-0.0851806\pi$
$798$		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	$0.0507401\pi$
$811$			9.04068i			0.317461i	−0.987322	+	0.158731i	$0.949260\pi$
$812$		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	0.828438	−	0.560081i	$-0.189230\pi$
$829$	21.8135	+	12.5940i	0.757613	+	0.437408i	−0.0708254	+	0.997489i	$0.522563\pi$
$830$	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	$-0.501514\pi$
$839$	−0.275469			−0.00951026			−0.00475513	+	0.999989i	$0.501514\pi$
$840$		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	0.967538	−	0.252725i	$-0.0813269\pi$
$853$	20.8769	+	20.8769i	0.714813	+	0.714813i	−0.252725	+	0.967538i	$0.581327\pi$
$854$		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	$-0.946692\pi$
$857$	−6.30707	−	23.5383i	−0.215445	−	0.804053i	0.770564	−	0.637363i	$-0.219975\pi$
$858$	−10.4001	+	42.5774i	−0.355055	+	1.45357i
$859$	28.1658	+	48.7846i	0.961004	+	1.66451i	0.719988	+	0.693987i	$0.244147\pi$
$859$	28.1658	+	48.7846i	0.961004	+	1.66451i	0.241017	+	0.970521i	$0.422519\pi$
$860$	−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	$-0.451860\pi$
$881$	8.94374			0.301322			0.150661	+	0.988585i	$0.451860\pi$
$882$		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	$0.269743\pi$
$887$	−8.52105	+	31.8010i	−0.286109	+	1.06777i	−0.948025	+	0.318195i	$0.896923\pi$
$888$	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	−0.911018	−	0.412367i	$-0.864702\pi$
$929$	−30.7662	+	17.7629i	−1.00941	+	0.582781i	−0.0983891	+	0.995148i	$0.531369\pi$
$930$	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	−0.979411	−	0.201876i	$-0.935296\pi$
$937$	−23.8007	+	23.8007i	−0.777536	+	0.777536i	0.201876	+	0.979411i	$0.435296\pi$
$938$		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	−0.955297	−	0.295649i	$-0.904464\pi$
$941$	−6.79801	+	11.7745i	−0.221609	+	0.383838i	0.733688	+	0.679487i	$0.237797\pi$
$942$	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	−0.930967	−	0.365104i	$-0.881034\pi$
$971$	−33.6619	+	19.4347i	−1.08026	+	0.623689i	−0.149294	+	0.988793i	$0.547700\pi$
$972$	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	$0.136237\pi$
$983$	10.3281	+	38.5452i	0.329417	+	1.22940i	−0.580380	+	0.814346i	$0.697096\pi$
$984$	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	$0.0950499\pi$
$997$	8.68766	+	32.4228i	0.275141	+	1.02684i	−0.680606	+	0.732650i	$0.738283\pi$
$998$	−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.l.263.5		72
4.3	odd	2	inner	980.2.x.l.263.7		72
5.2	odd	4	inner	980.2.x.l.67.5		72
7.2	even	3	inner	980.2.x.l.863.17		72
7.3	odd	6		140.2.k.a.43.8	✓	36
7.4	even	3		980.2.k.l.883.8		36
7.5	odd	6		980.2.x.k.863.17		72
7.6	odd	2		980.2.x.k.263.5		72
20.7	even	4	inner	980.2.x.l.67.17		72
28.3	even	6		140.2.k.a.43.18	yes	36
28.11	odd	6		980.2.k.l.883.18		36
28.19	even	6		980.2.x.k.863.5		72
28.23	odd	6	inner	980.2.x.l.863.5		72
28.27	even	2		980.2.x.k.263.7		72
35.2	odd	12	inner	980.2.x.l.667.7		72
35.3	even	12		700.2.k.b.407.1		36
35.12	even	12		980.2.x.k.667.7		72
35.17	even	12		140.2.k.a.127.18	yes	36
35.24	odd	6		700.2.k.b.43.11		36
35.27	even	4		980.2.x.k.67.5		72
35.32	odd	12		980.2.k.l.687.18		36
140.3	odd	12		700.2.k.b.407.11		36
140.27	odd	4		980.2.x.k.67.17		72
140.47	odd	12		980.2.x.k.667.5		72
140.59	even	6		700.2.k.b.43.1		36
140.67	even	12		980.2.k.l.687.8		36
140.87	odd	12		140.2.k.a.127.8	yes	36
140.107	even	12	inner	980.2.x.l.667.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.8	✓	36	7.3	odd	6
140.2.k.a.43.18	yes	36	28.3	even	6
140.2.k.a.127.8	yes	36	140.87	odd	12
140.2.k.a.127.18	yes	36	35.17	even	12
700.2.k.b.43.1		36	140.59	even	6
700.2.k.b.43.11		36	35.24	odd	6
700.2.k.b.407.1		36	35.3	even	12
700.2.k.b.407.11		36	140.3	odd	12
980.2.k.l.687.8		36	140.67	even	12
980.2.k.l.687.18		36	35.32	odd	12
980.2.k.l.883.8		36	7.4	even	3
980.2.k.l.883.18		36	28.11	odd	6
980.2.x.k.67.5		72	35.27	even	4
980.2.x.k.67.17		72	140.27	odd	4
980.2.x.k.263.5		72	7.6	odd	2
980.2.x.k.263.7		72	28.27	even	2
980.2.x.k.667.5		72	140.47	odd	12
980.2.x.k.667.7		72	35.12	even	12
980.2.x.k.863.5		72	28.19	even	6
980.2.x.k.863.17		72	7.5	odd	6
980.2.x.l.67.5		72	5.2	odd	4	inner
980.2.x.l.67.17		72	20.7	even	4	inner
980.2.x.l.263.5		72	1.1	even	1	trivial
980.2.x.l.263.7		72	4.3	odd	2	inner
980.2.x.l.667.5		72	140.107	even	12	inner
980.2.x.l.667.7		72	35.2	odd	12	inner
980.2.x.l.863.5		72	28.23	odd	6	inner
980.2.x.l.863.17		72	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more