LMFDB - Embedded newform 980.2.x.l.263.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [72,0,0,0,0,16,0,0,0,-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			263.7
Character	$\chi$	$=$	980.263
Dual form			980.2.x.l.667.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.335576 - 1.37382i) q^{2} +(-0.346182 - 1.29197i) q^{3} +(-1.77478 + 0.922043i) q^{4} +(-1.92528 - 1.13723i) q^{5} +(-1.65877 + 0.909146i) q^{6} +(1.86230 + 2.12881i) q^{8} +(1.04873 - 0.605487i) q^{9} +(-0.916275 + 3.02662i) q^{10} +(4.33338 + 2.50188i) q^{11} +(1.80565 + 1.97376i) q^{12} +(3.27438 + 3.27438i) q^{13} +(-0.802768 + 2.88109i) q^{15} +(2.29967 - 3.27284i) q^{16} +(0.873420 + 3.25965i) q^{17} +(-1.18376 - 1.23759i) q^{18} +(0.214380 + 0.371316i) q^{19} +(4.46552 + 0.243138i) q^{20} +(1.98296 - 6.79287i) q^{22} +(3.47589 + 0.931361i) q^{23} +(2.10567 - 3.14299i) q^{24} +(2.41342 + 4.37898i) q^{25} +(3.39961 - 5.59722i) q^{26} +(-3.98268 - 3.98268i) q^{27} +7.51811i q^{29} +(4.22750 + 0.136036i) q^{30} +(-0.353285 - 0.203969i) q^{31} +(-5.26802 - 2.06105i) 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} +(0.438182 - 0.419124i) q^{38} +(3.09687 - 5.36393i) q^{39} +(-1.16449 - 6.21643i) q^{40} -5.67429 q^{41} +(4.01233 - 4.01233i) q^{43} +(-9.99763 - 0.444713i) q^{44} +(-2.70769 - 0.0269194i) q^{45} +(0.113101 - 5.08780i) q^{46} +(2.60987 - 9.74016i) q^{47} +(-5.02452 - 1.83811i) q^{48} +(5.20605 - 4.78508i) q^{50} +(3.90900 - 2.25686i) q^{51} +(-8.83042 - 2.79218i) q^{52} +(1.10820 - 0.296942i) q^{53} +(-4.13501 + 6.80799i) q^{54} +(-5.49776 - 9.74487i) q^{55} +(0.405515 - 0.405515i) q^{57} +(10.3285 - 2.52289i) q^{58} +(1.93762 - 3.35606i) q^{59} +(-1.23176 - 5.85349i) q^{60} +(6.11723 + 10.5954i) q^{61} +(-0.161663 + 0.553797i) q^{62} +(-1.06370 + 7.92897i) q^{64} +(-2.58038 - 10.0278i) q^{65} +(-9.46264 - 0.210354i) q^{66} +(11.3327 - 3.03658i) q^{67} +(-4.55566 - 4.97982i) q^{68} -4.81316i q^{69} +12.2700i q^{71} +(3.24202 + 1.10496i) q^{72} +(5.17303 - 1.38611i) q^{73} +(-0.141115 + 6.34796i) q^{74} +(4.82202 - 4.63398i) q^{75} +(-0.722846 - 0.461337i) q^{76} +(-8.40832 - 2.45454i) q^{78} +(-0.0987717 - 0.171078i) q^{79} +(-8.14949 + 3.68589i) q^{80} +(-1.95031 + 3.37804i) q^{81} +(1.90416 + 7.79547i) q^{82} +(-1.86715 + 1.86715i) q^{83} +(2.02539 - 7.26902i) q^{85} +(-6.85867 - 4.16579i) q^{86} +(9.71316 - 2.60263i) q^{87} +(2.74400 + 13.8842i) q^{88} +(-6.11311 + 3.52940i) q^{89} +(0.871651 + 3.72891i) q^{90} +(-7.02768 + 1.55196i) q^{92} +(-0.141221 + 0.527043i) q^{93} +(-14.2571 - 0.316934i) q^{94} +(0.00953113 - 0.958687i) q^{95} +(-0.839124 + 7.51962i) 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 $

$2$	−0.335576	−	1.37382i	−0.237288	−	0.971439i
$2$	−0.335576	−	1.37382i	−0.237288	−	0.971439i
$3$	−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	$-0.209517\pi$
$4$	−1.77478	+	0.922043i	−0.887389	+	0.461022i
$5$	−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
$8$	1.86230	+	2.12881i	0.658421	+	0.752650i
$9$	1.04873	−	0.605487i	0.349578	−	0.201829i
$10$	−0.916275	+	3.02662i	−0.289752	+	0.957102i
$11$	4.33338	+	2.50188i	1.30656	+	0.754345i	0.981521	−	0.191355i	$-0.0612881\pi$
$11$	4.33338	+	2.50188i	1.30656	+	0.754345i	0.325042	+	0.945699i	$0.394621\pi$
$12$	1.80565	+	1.97376i	0.521246	+	0.569776i
$13$	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
$16$	2.29967	−	3.27284i	0.574918	−	0.818211i
$17$	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	$0.782462\pi$
$18$	−1.18376	−	1.23759i	−0.279015	−	0.291702i
$19$	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	$0.817672\pi$
$20$	4.46552	+	0.243138i	0.998521	+	0.0543673i
$21$		0			0
$22$	1.98296	−	6.79287i	0.422768	−	1.44824i
$23$	3.47589	+	0.931361i	0.724773	+	0.194202i	0.602300	−	0.798270i	$-0.294251\pi$
$23$	3.47589	+	0.931361i	0.724773	+	0.194202i	0.122472	+	0.992472i	$0.460918\pi$
$24$	2.10567	−	3.14299i	0.429818	−	0.641560i
$25$	2.41342	+	4.37898i	0.482683	+	0.875795i
$26$	3.39961	−	5.59722i	0.666719	−	1.09771i
$27$	−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	$0.754056\pi$
$30$	4.22750	+	0.136036i	0.771832	+	0.0248367i
$31$	−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	$0.678330\pi$
$32$	−5.26802	−	2.06105i	−0.931263	−	0.364346i
$33$	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	$0.703653\pi$
$38$	0.438182	−	0.419124i	0.0710825	−	0.0679909i
$39$	3.09687	−	5.36393i	0.495895	−	0.858916i
$40$	−1.16449	−	6.21643i	−0.184122	−	0.982903i
$41$	−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	−0.331560	−	0.943434i	$-0.607575\pi$
$43$	4.01233	−	4.01233i	0.611875	−	0.611875i	0.943434	+	0.331560i	$0.107575\pi$
$44$	−9.99763	−	0.444713i	−1.50720	−	0.0670431i
$45$	−2.70769	−	0.0269194i	−0.403638	−	0.00401291i
$46$	0.113101	−	5.08780i	0.0166759	−	0.750155i
$47$	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	$-0.179688\pi$
$48$	−5.02452	−	1.83811i	−0.725227	−	0.265308i
$49$		0			0
$50$	5.20605	−	4.78508i	0.736247	−	0.676713i
$51$	3.90900	−	2.25686i	0.547370	−	0.316024i
$52$	−8.83042	−	2.79218i	−1.22456	−	0.387205i
$53$	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	$0.391559\pi$
$54$	−4.13501	+	6.80799i	−0.562704	+	0.926451i
$55$	−5.49776	−	9.74487i	−0.741318	−	1.31400i
$56$		0			0
$57$	0.405515	−	0.405515i	0.0537117	−	0.0537117i
$58$	10.3285	−	2.52289i	1.35620	−	0.331272i
$59$	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	$0.0854939\pi$
$60$	−1.23176	−	5.85349i	−0.159019	−	0.755682i
$61$	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	$0.546903\pi$
$62$	−0.161663	+	0.553797i	−0.0205313	+	0.0703323i
$63$		0			0
$64$	−1.06370	+	7.92897i	−0.132963	+	0.991121i
$65$	−2.58038	−	10.0278i	−0.320057	−	1.24380i
$66$	−9.46264	−	0.210354i	−1.16477	−	0.0258928i
$67$	11.3327	−	3.03658i	1.38451	−	0.370977i	0.511750	−	0.859134i	$-0.328997\pi$
$67$	11.3327	−	3.03658i	1.38451	−	0.370977i	0.872756	+	0.488157i	$0.162331\pi$
$68$	−4.55566	−	4.97982i	−0.552455	−	0.603892i
$69$		−	4.81316i		−	0.579436i
$70$		0			0
$71$			12.2700i			1.45618i	0.685482	+	0.728090i	$0.259592\pi$
$71$			12.2700i			1.45618i	−0.685482	+	0.728090i	$0.740408\pi$
$72$	3.24202	+	1.10496i	0.382076	+	0.130221i
$73$	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	$0.315196\pi$
$74$	−0.141115	+	6.34796i	−0.0164043	+	0.737935i
$75$	4.82202	−	4.63398i	0.556799	−	0.535086i
$76$	−0.722846	−	0.461337i	−0.0829161	−	0.0529189i
$77$		0			0
$78$	−8.40832	−	2.45454i	−0.952055	−	0.277922i
$79$	−0.0987717	−	0.171078i	−0.0111127	−	0.0192477i	0.860416	−	0.509593i	$-0.170204\pi$
$79$	−0.0987717	−	0.171078i	−0.0111127	−	0.0192477i	−0.871528	+	0.490345i	$0.836871\pi$
$80$	−8.14949	+	3.68589i	−0.911141	+	0.412095i
$81$	−1.95031	+	3.37804i	−0.216701	+	0.375337i
$82$	1.90416	+	7.79547i	0.210279	+	0.860866i
$83$	−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
$86$	−6.85867	−	4.16579i	−0.739590	−	0.449209i
$87$	9.71316	−	2.60263i	1.04136	−	0.279032i
$88$	2.74400	+	13.8842i	0.292512	+	1.48006i
$89$	−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	$0.455387\pi$
$90$	0.871651	+	3.72891i	0.0918801	+	0.393062i
$91$		0			0
$92$	−7.02768	+	1.55196i	−0.732687	+	0.161803i
$93$	−0.141221	+	0.527043i	−0.0146439	+	0.0546518i
$94$	−14.2571	−	0.316934i	−1.47050	−	0.0326892i
$95$	0.00953113	−	0.958687i	0.000977873	−	0.0983592i
$96$	−0.839124	+	7.51962i	−0.0856427	+	0.767468i
$97$	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
$100$	−8.32088	−	5.54643i	−0.832088	−	0.554643i
$101$	−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	$0.327246\pi$
$102$	−4.41230	−	4.61293i	−0.436883	−	0.456748i
$103$	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	−0.929909	−	0.367790i	$-0.880114\pi$
$107$	0.613518	−	2.28968i	0.0593110	−	0.221352i	0.989220	+	0.146439i	$0.0467811\pi$
$108$	10.7406	+	3.39617i	1.03351	+	0.326797i
$109$	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	$0.505707\pi$
$110$	−11.5428	+	10.8231i	−1.10056	+	1.03194i
$111$			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	$0.920450\pi$
$114$	−0.693186	−	0.421025i	−0.0649229	−	0.0394326i
$115$	−5.63289	−	5.74602i	−0.525270	−	0.535819i
$116$	−6.93202	−	13.3430i	−0.643622	−	1.23886i
$117$	5.41655	+	1.45136i	0.500760	+	0.134178i
$118$	−5.26084	−	1.53574i	−0.484300	−	0.141376i
$119$		0			0
$120$	−7.62830	+	3.65650i	−0.696366	+	0.333792i
$121$	7.01879	+	12.1569i	0.638072	+	1.10517i
$122$	12.5033	−	11.9595i	1.13200	−	1.08277i
$123$	1.96434	+	7.33101i	0.177118	+	0.661015i
$124$	0.815070	+	0.0362558i	0.0731954	+	0.00325587i
$125$	0.333400	−	11.1754i	0.0298202	−	0.999555i
$126$		0			0
$127$	−6.81065	−	6.81065i	−0.604347	−	0.604347i	0.337116	−	0.941463i	$-0.390549\pi$
$127$	−6.81065	−	6.81065i	−0.604347	−	0.604347i	−0.941463	+	0.337116i	$0.890549\pi$
$128$	11.2499	−	1.19943i	0.994364	−	0.106016i
$129$	−6.57280	−	3.79481i	−0.578703	−	0.334114i
$130$	−12.9105	+	6.91008i	−1.13233	+	0.606054i
$131$	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	$0.303087\pi$
$132$	2.88644	+	13.0706i	0.251233	+	1.13765i
$133$		0			0
$134$	−7.97469	−	14.5501i	−0.688909	−	1.25694i
$135$	3.13856	+	12.1970i	0.270124	+	1.04975i
$136$	−5.31262	+	7.92978i	−0.455553	+	0.679973i
$137$	−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	$-0.249378\pi$
$138$	−6.61243	+	1.61518i	−0.562887	+	0.137493i
$139$	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
$142$	16.8568	−	4.11751i	1.41459	−	0.345534i
$143$	5.99703	+	22.3812i	0.501497	+	1.87161i
$144$	0.430080	−	4.82476i	0.0358400	−	0.402064i
$145$	8.54982	−	14.4745i	0.710024	−	1.20204i
$146$	−3.64021	−	6.64168i	−0.301266	−	0.549669i
$147$		0			0
$148$	8.76832	−	1.93635i	0.720752	−	0.159167i
$149$	−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	$0.453465\pi$
$150$	−7.98442	−	5.06955i	−0.651925	−	0.413927i
$151$	0.549816	+	0.317436i	0.0447434	+	0.0258326i	0.522205	−	0.852820i	$-0.325110\pi$
$151$	0.549816	+	0.317436i	0.0447434	+	0.0258326i	−0.477461	+	0.878653i	$0.658443\pi$
$152$	−0.391225	+	1.14788i	−0.0317326	+	0.0931050i
$153$	2.88966	+	2.88966i	0.233615	+	0.233615i
$154$		0			0
$155$	0.448212	+	0.794463i	0.0360013	+	0.0638128i
$156$	−0.550474	+	12.3752i	−0.0440732	+	0.990811i
$157$	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	$0.805889\pi$
$158$	−0.201885	+	0.193104i	−0.0160611	+	0.0153625i
$159$	−0.767279	−	1.32897i	−0.0608492	−	0.105394i
$160$	7.79853	+	9.95906i	0.616528	+	0.787333i
$161$		0			0
$162$	5.29530	+	1.54579i	0.416038	+	0.121449i
$163$	−19.0319	−	5.09959i	−1.49069	−	0.399430i	−0.580723	−	0.814101i	$-0.697230\pi$
$163$	−19.0319	−	5.09959i	−1.49069	−	0.399430i	−0.909972	+	0.414671i	$0.863897\pi$
$164$	10.0706	−	5.23194i	0.786382	−	0.408546i
$165$	−10.6868	+	10.4764i	−0.831970	+	0.815590i
$166$	3.19170	+	1.93856i	0.247724	+	0.150461i
$167$	−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
$170$	−10.6660	−	0.343221i	−0.818046	−	0.0263238i
$171$	0.449654	+	0.259608i	0.0343859	+	0.0198527i
$172$	−3.42145	+	10.8205i	−0.260883	+	0.825058i
$173$	−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
$178$	6.90019	+	7.21394i	0.517191	+	0.540708i
$179$	11.8144	−	20.4632i	0.883050	−	1.52949i	0.0351179	−	0.999383i	$-0.488819\pi$
$179$	11.8144	−	20.4632i	0.883050	−	1.52949i	0.847932	−	0.530105i	$-0.177847\pi$
$180$	4.83036	−	2.44883i	0.360034	−	0.182525i
$181$	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
$184$	4.49044	+	9.13399i	0.331040	+	0.673367i
$185$	7.02806	+	7.16921i	0.516713	+	0.527091i
$186$	0.771454	+	0.0171494i	0.0565658	+	0.00125745i
$187$	−4.37038	+	16.3105i	−0.319594	+	1.19274i
$188$	4.34892	+	19.6930i	0.317177	+	1.43626i
$189$		0			0
$190$	−1.32026	+	0.308618i	−0.0957821	+	0.0223895i
$191$	−14.9539	+	8.63366i	−1.08203	+	0.624710i	−0.931443	−	0.363887i	$-0.881449\pi$
$191$	−14.9539	+	8.63366i	−1.08203	+	0.624710i	−0.150586	+	0.988597i	$0.548116\pi$
$192$	10.6122	−	1.37060i	0.765871	−	0.0989142i
$193$	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	$0.347754\pi$
$194$	−8.97347	−	5.45027i	−0.644258	−	0.391306i
$195$	−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	$0.156863\pi$
$198$	−2.03339	−	8.32457i	−0.144507	−	0.591601i
$199$	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	$-0.0831832\pi$
$200$	−4.82753	+	13.2927i	−0.341358	+	0.939933i
$201$	−7.84634	−	13.5903i	−0.553438	−	0.958583i
$202$	13.1888	+	3.85006i	0.927963	+	0.270889i
$203$		0			0
$204$	−4.85668	+	7.60970i	−0.340036	+	0.532786i
$205$	10.9246	+	6.45298i	0.763008	+	0.450695i
$206$	0.00389715	−	0.175311i	0.000271527	−	0.0122145i
$207$	4.20921	−	1.12785i	0.292560	−	0.0783913i
$208$	18.2465	−	3.18653i	1.26517	−	0.220946i
$209$			2.14541i			0.148401i
$210$		0			0
$211$			7.74837i			0.533420i	0.963777	+	0.266710i	$0.0859365\pi$
$211$			7.74837i			0.533420i	−0.963777	+	0.266710i	$0.914063\pi$
$212$	−1.69302	+	1.54882i	−0.116277	+	0.106373i
$213$	15.8524	−	4.24765i	1.08619	−	0.291044i
$214$	−3.35150	−	0.0745036i	−0.229104	−	0.00509296i
$215$	−12.2878	+	3.16192i	−0.838022	+	0.215641i
$216$	1.06146	−	15.8953i	0.0722230	−	1.08154i
$217$		0			0
$218$	4.00830	−	13.7309i	0.271476	−	0.929975i
$219$	−3.58162	−	6.20355i	−0.242023	−	0.419197i
$220$	18.7425	+	12.2258i	1.26362	+	0.824263i
$221$	−7.81342	+	13.5332i	−0.525587	+	0.910344i
$222$	8.25021	−	2.01523i	0.553718	−	0.135254i
$223$	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
$226$	−7.96425	+	13.1126i	−0.529774	+	0.872235i
$227$	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	$0.343126\pi$
$228$	−0.345796	+	1.09360i	−0.0229009	+	0.0724255i
$229$	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	$0.279975\pi$
$230$	−6.00375	+	9.66682i	−0.395875	+	0.637411i
$231$		0			0
$232$	−16.0047	+	14.0009i	−1.05076	+	0.919207i
$233$	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	$0.0470537\pi$
$234$	0.176248	−	7.92842i	0.0115217	−	0.518297i
$235$	−16.1015	+	15.7845i	−1.05035	+	1.02967i
$236$	−0.344415	+	7.74282i	−0.0224195	+	0.504015i
$237$	−0.186834	+	0.186834i	−0.0121362	+	0.0121362i
$238$		0			0
$239$	−11.2814			−0.729734			−0.364867	−	0.931060i	$-0.618886\pi$
$239$	−11.2814			−0.729734			−0.364867	+	0.931060i	$0.618886\pi$
$240$	7.58326	+	9.25290i	0.489497	+	0.597272i
$241$	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	$-0.151402\pi$
$242$	14.3461	−	13.7221i	0.922201	−	0.882092i
$243$	−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
$248$	−0.223709	−	1.13193i	−0.0142055	−	0.0718775i
$249$	3.05867	+	1.76592i	0.193835	+	0.111911i
$250$	−15.4649	+	3.29215i	−0.978083	+	0.208214i
$251$			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
$254$	−7.07114	+	11.6421i	−0.443683	+	0.730491i
$255$	−10.0925	−	0.100338i	−0.632017	−	0.00628342i
$256$	−5.42302	−	15.0529i	−0.338939	−	0.940809i
$257$	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	$0.528075\pi$
$258$	−3.00772	+	10.3033i	−0.187253	+	0.641456i
$259$		0			0
$260$	13.8257	+	15.4179i	0.857433	+	0.956180i
$261$	4.55212	+	7.88449i	0.281769	+	0.488038i
$262$	−2.12307	−	2.21960i	−0.131163	−	0.137128i
$263$	−3.78833	−	14.1383i	−0.233599	−	0.871802i	−0.978776	−	0.204935i	$-0.934302\pi$
$263$	−3.78833	−	14.1383i	−0.233599	−	0.871802i	0.745177	−	0.666867i	$-0.232365\pi$
$264$	16.9880	−	8.35163i	1.04554	−	0.514007i
$265$	−2.47129	−	0.688584i	−0.151810	−	0.0422994i
$266$		0			0
$267$	6.67613	+	6.67613i	0.408572	+	0.408572i
$268$	−17.3131	+	15.8385i	−1.05757	+	0.967489i
$269$	−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	$0.871146\pi$
$270$	15.7033	−	8.40485i	0.955673	−	0.511503i
$271$	−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	$0.470061\pi$
$272$	12.6769	+	4.63755i	0.768650	+	0.281193i
$273$		0			0
$274$	−14.4665	+	7.92889i	−0.873954	+	0.479002i
$275$	−0.497417	+	25.0138i	−0.0299954	+	1.50839i
$276$	4.43794	+	8.54229i	0.267133	+	0.514185i
$277$	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	$0.848650\pi$
$278$	−5.03390	−	20.6084i	−0.301913	−	1.23601i
$279$	−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	$0.341960\pi$
$282$	4.52607	+	18.5294i	0.269524	+	1.10341i
$283$	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	$0.695274\pi$
$284$	−11.3135	−	21.7765i	−0.671330	−	1.29220i
$285$	−1.24189	+	0.319566i	−0.0735634	+	0.0189295i
$286$	28.7354	−	15.7495i	1.69916	−	0.931285i
$287$		0			0
$288$	−6.77270	+	1.02822i	−0.399085	+	0.0605885i
$289$	4.85999	−	2.80592i	0.285882	−	0.165054i
$290$	−22.7545	−	6.88865i	−1.33619	−	0.404516i
$291$	−8.59946	−	4.96490i	−0.504109	−	0.291048i
$292$	−7.90292	+	7.22979i	−0.462484	+	0.423092i
$293$	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
$296$	−5.60264	−	11.3963i	−0.325647	−	0.662398i
$297$	−7.29429	−	27.2227i	−0.423258	−	1.57962i
$298$	8.79428	+	9.19416i	0.509439	+	0.532604i
$299$	8.33175	+	14.4310i	0.481837	+	0.834567i
$300$	−4.28528	+	12.6704i	−0.247411	+	0.731526i
$301$		0			0
$302$	0.251596	−	0.861873i	0.0144777	−	0.0495952i
$303$	12.5517	+	3.36321i	0.721075	+	0.193211i
$304$	1.70826	+	0.152275i	0.0979756	+	0.00873356i
$305$	0.271967	−	27.3557i	0.0155728	−	1.56639i
$306$	3.00018	−	4.93958i	0.171509	−	0.282377i
$307$	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
$310$	0.941042	−	0.882367i	0.0534476	−	0.0501151i
$311$	−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	$0.823948\pi$
$312$	17.1861	−	3.39657i	0.972971	−	0.192293i
$313$	−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	$0.638367\pi$
$318$	−1.56828	+	1.50007i	−0.0879450	+	0.0841200i
$319$	−18.8094	+	32.5788i	−1.05312	+	1.82406i
$320$	11.0650	−	14.0558i	0.618552	−	0.785744i
$321$	−3.17059			−0.176965
$322$		0			0
$323$	−1.02312	+	1.02312i	−0.0569278	+	0.0569278i
$324$	0.346671	−	7.79354i	0.0192595	−	0.432974i
$325$	−6.43599	+	22.2409i	−0.357005	+	1.23370i
$326$	−0.619277	+	27.8578i	−0.0342986	+	1.54290i
$327$	3.50144	−	13.0676i	0.193630	−	0.722638i
$328$	−10.5672	−	12.0795i	−0.583477	−	0.666980i
$329$		0			0
$330$	17.9790	+	11.1662i	0.989712	+	0.614678i
$331$	26.9329	−	15.5497i	1.48036	−	0.854689i	0.480612	−	0.876933i	$-0.340415\pi$
$331$	26.9329	−	15.5497i	1.48036	−	0.854689i	0.999753	+	0.0222445i	$0.00708123\pi$
$332$	1.59218	−	5.03536i	0.0873823	−	0.276352i
$333$	−5.25176	+	1.40720i	−0.287795	+	0.0771143i
$334$	−8.88939	+	14.6357i	−0.486406	+	0.800832i
$335$	−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	$0.368342\pi$
$338$	11.5994	−	2.83331i	0.630922	−	0.154112i
$339$	−7.25500	+	12.5660i	−0.394038	+	0.682493i
$340$	3.10773	+	14.7684i	0.168540	+	0.800929i
$341$	−1.02061	−	1.76775i	−0.0552692	−	0.0957290i
$342$	0.205762	−	0.704863i	0.0111264	−	0.0381147i
$343$		0			0
$344$	16.0137	+	1.06936i	0.863399	+	0.0576559i
$345$	−5.47367	+	9.26669i	−0.294693	+	0.498902i
$346$	26.1865	+	0.582125i	1.40780	+	0.0312952i
$347$	−30.6251	+	8.20598i	−1.64404	+	0.440520i	−0.957936	−	0.286980i	$-0.907349\pi$
$347$	−30.6251	+	8.20598i	−1.64404	+	0.440520i	−0.686107	+	0.727500i	$0.740682\pi$
$348$	−14.8390	+	13.5751i	−0.795452	+	0.727699i
$349$			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
$352$	−17.6718	−	22.1113i	−0.941912	−	1.17854i
$353$	−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	$0.431339\pi$
$354$	−0.162912	+	7.32849i	−0.00865868	+	0.389505i
$355$	13.9538	−	23.6232i	0.740591	−	1.25379i
$356$	7.59514	−	11.9005i	0.402542	−	0.630723i
$357$		0			0
$358$	−32.0774	−	9.36396i	−1.69534	−	0.494901i
$359$	−15.4616	−	26.7802i	−0.816031	−	1.41341i	−0.908585	−	0.417699i	$-0.862837\pi$
$359$	−15.4616	−	26.7802i	−0.816031	−	1.41341i	0.0925546	−	0.995708i	$-0.470497\pi$
$360$	−4.98521	−	5.81429i	−0.262744	−	0.306440i
$361$	9.40808	−	16.2953i	0.495162	−	0.857646i
$362$	−0.316471	−	1.29561i	−0.0166334	−	0.0680957i
$363$	13.2766	−	13.2766i	0.696839	−	0.696839i
$364$		0			0
$365$	−11.5359	−	3.21428i	−0.603815	−	0.168243i
$366$	−19.7798	−	12.0138i	−1.03391	−	0.627969i
$367$	−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	$0.521656\pi$
$368$	11.0416	−	9.23421i	0.575583	−	0.481367i
$369$	−5.95082	+	3.43571i	−0.309788	+	0.178856i
$370$	7.49077	−	12.0611i	0.389427	−	0.627028i
$371$		0			0
$372$	−0.235321	−	1.06560i	−0.0122008	−	0.0552486i
$373$	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	$-0.113864\pi$
$374$	23.8743	+	0.530725i	1.23451	+	0.0274431i
$375$	−14.5536	+	3.43797i	−0.751547	+	0.177536i
$376$	25.5954	−	12.5831i	1.31998	−	0.648926i
$377$	−24.6171	+	24.6171i	−1.26785	+	1.26785i
$378$		0			0
$379$	−6.09622			−0.313142			−0.156571	−	0.987667i	$-0.550044\pi$
$379$	−6.09622			−0.313142			−0.156571	+	0.987667i	$0.550044\pi$
$380$	0.867035	+	1.71024i	0.0444780	+	0.0877337i
$381$	−6.44142	+	11.1569i	−0.330004	+	0.571584i
$382$	16.8793	+	17.6468i	0.863620	+	0.902890i
$383$	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
$388$	−4.47642	+	14.1569i	−0.227256	+	0.718710i
$389$	−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	$0.846279\pi$
$390$	13.3970	+	14.2879i	0.678384	+	0.723495i
$391$			12.1436i			0.614130i
$392$		0			0
$393$	−2.05413	−	2.05413i	−0.103617	−	0.103617i
$394$	−9.78696	−	5.94436i	−0.493060	−	0.299473i
$395$	−0.00439130	+	0.441698i	−0.000220950	+	0.0222243i
$396$	−10.7541	+	5.58705i	−0.540415	+	0.280760i
$397$	−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	$0.625024\pi$
$398$	−27.0703	−	7.90231i	−1.35691	−	0.396107i
$399$		0			0
$400$	19.8818	+	2.17148i	0.994088	+	0.108574i
$401$	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	$0.740047\pi$
$402$	−16.0376	+	15.3400i	−0.799881	+	0.765091i
$403$	−0.488916	−	1.82466i	−0.0243546	−	0.0908928i
$404$	0.863443	−	19.4111i	0.0429579	−	0.965739i
$405$	7.59650	−	4.28572i	0.377473	−	0.212959i
$406$		0			0
$407$	−15.8857	−	15.8857i	−0.787427	−	0.787427i
$408$	12.0842	+	4.11859i	0.598255	+	0.203901i
$409$	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	$0.631437\pi$
$410$	5.19921	−	17.1739i	0.256771	−	0.848160i
$411$	−13.5122	+	7.80127i	−0.666508	+	0.384808i
$412$	−0.242153	+	0.0534760i	−0.0119300	+	0.00263457i
$413$		0			0
$414$	−2.96198	−	5.40423i	−0.145573	−	0.265603i
$415$	5.71816	−	1.47141i	0.280694	−	0.0722286i
$416$	−10.5008	−	23.9982i	−0.514846	−	1.17661i
$417$	−5.19300	−	19.3805i	−0.254302	−	0.949069i
$418$	2.94741	−	0.719946i	0.144162	−	0.0352137i
$419$	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	$0.592528\pi$
$422$	10.6449	−	2.60016i	0.518185	−	0.126574i
$423$	−3.16048	−	11.7951i	−0.153668	−	0.573497i
$424$	2.69593	+	1.80616i	0.130926	+	0.0877150i
$425$	−12.1660	+	11.6916i	−0.590137	+	0.567124i
$426$	−11.1552	−	20.3530i	−0.540472	−	0.986108i
$427$		0			0
$428$	1.02233	+	4.62937i	0.0494160	+	0.223769i
$429$	26.8398	−	15.4960i	1.29584	−	0.748152i
$430$	8.46741	+	15.8202i	0.408335	+	0.762918i
$431$	14.4038	+	8.31606i	0.693809	+	0.400571i	0.805037	−	0.593224i	$-0.202145\pi$
$431$	14.4038	+	8.31606i	0.693809	+	0.400571i	−0.111229	+	0.993795i	$0.535479\pi$
$432$	−22.1936	+	3.87584i	−1.06779	+	0.186476i
$433$	−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
$436$	−20.2089	−	0.898932i	−0.967832	−	0.0430510i
$437$	0.399330	+	1.49032i	0.0191025	+	0.0712916i
$438$	−7.32067	+	7.00227i	−0.349795	+	0.334581i
$439$	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	$0.625796\pi$
$440$	10.5066	−	29.8516i	0.500880	−	1.42312i
$441$		0			0
$442$	21.2143	+	6.19282i	1.00906	+	0.294563i
$443$	−1.73983	−	0.466187i	−0.0826619	−	0.0221492i	0.217251	−	0.976116i	$-0.430291\pi$
$443$	−1.73983	−	0.466187i	−0.0826619	−	0.0221492i	−0.299913	+	0.953967i	$0.596958\pi$
$444$	−5.53715	−	10.6581i	−0.262781	−	0.505810i
$445$	15.7832	+	0.156914i	0.748195	+	0.00743845i
$446$	−18.9900	−	11.5340i	−0.899201	−	0.546152i
$447$	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	$-0.223626\pi$
$450$	2.56246	−	8.17048i	0.120795	−	0.385160i
$451$	−24.5889	−	14.1964i	−1.15784	−	0.668482i
$452$	20.6870	+	6.54121i	0.973032	+	0.307673i
$453$	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	$0.611853\pi$
$458$	−4.93620	−	5.16065i	−0.230653	−	0.241141i
$459$	9.50359	−	16.4607i	0.443590	−	0.768320i
$460$	15.2952	+	5.00413i	0.713143	+	0.233319i
$461$	−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	−0.423801	−	0.905755i	$-0.639304\pi$
$463$	10.3704	−	10.3704i	0.481955	−	0.481955i	0.905755	+	0.423801i	$0.139304\pi$
$464$	24.6056	+	17.2892i	1.14229	+	0.802630i
$465$	0.871259	−	0.854106i	0.0404037	−	0.0396082i
$466$	−4.90894	−	0.109125i	−0.227402	−	0.00505514i
$467$	−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	$0.121227\pi$
$468$	−10.9514	+	2.41845i	−0.506228	+	0.111793i
$469$		0			0
$470$	27.0884	+	16.8238i	1.24950	+	0.776022i
$471$	9.89965	−	5.71557i	0.456152	−	0.263359i
$472$	10.7528	−	2.12514i	0.494940	−	0.0978174i
$473$	27.4253	−	7.34859i	1.26102	−	0.337889i
$474$	0.319374	+	0.193980i	0.0146693	+	0.00890978i
$475$	−1.10860	+	1.83490i	−0.0508660	+	0.0841911i
$476$		0			0
$477$	0.982415	−	0.982415i	0.0449817	−	0.0449817i
$478$	3.78577	+	15.4987i	0.173157	+	0.708893i
$479$	−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	$0.197428\pi$
$480$	10.1671	−	13.5231i	0.464062	−	0.617243i
$481$	−10.3954	−	18.0053i	−0.473988	−	0.820972i
$482$	−35.4506	−	10.3487i	−1.61473	−	0.471369i
$483$		0			0
$484$	−23.6660	−	15.1042i	−1.07573	−	0.686553i
$485$	−16.0766	+	4.13687i	−0.730002	+	0.187845i
$486$	−0.367099	+	16.5137i	−0.0166520	+	0.749077i
$487$	−22.6422	+	6.06695i	−1.02601	+	0.274920i	−0.732306	−	0.680975i	$-0.761556\pi$
$487$	−22.6422	+	6.06695i	−1.02601	+	0.274920i	−0.293708	+	0.955895i	$0.594889\pi$
$488$	−11.1634	+	32.7542i	−0.505346	+	1.48271i
$489$			26.3540i			1.19177i
$490$		0			0
$491$			43.0124i			1.94112i	0.240851	+	0.970562i	$0.422573\pi$
$491$			43.0124i			1.94112i	−0.240851	+	0.970562i	$0.577427\pi$
$492$	−10.2458	−	11.1997i	−0.461915	−	0.504922i
$493$	−24.5064	+	6.56647i	−1.10371	+	0.295739i
$494$	2.80715	+	0.0624028i	0.126300	+	0.00280763i
$495$	−11.6661	−	6.89095i	−0.524351	−	0.309725i
$496$	−1.48000	+	0.687184i	−0.0664538	+	0.0308555i
$497$		0			0
$498$	1.39965	−	4.79467i	0.0627199	−	0.214854i
$499$	−0.280975	−	0.486663i	−0.0125782	−	0.0217860i	0.859668	−	0.510853i	$-0.170671\pi$
$499$	−0.280975	−	0.486663i	−0.0125782	−	0.0217860i	−0.872246	+	0.489067i	$0.837337\pi$
$500$	9.71246	+	20.1412i	0.434355	+	0.900742i
$501$	−8.09775	+	14.0257i	−0.361781	+	0.626623i
$502$	35.7622	−	8.73542i	1.59614	−	0.389881i
$503$	−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
$506$	13.2192	−	21.7644i	0.587663	−	0.967545i
$507$	10.9083	−	2.92286i	0.484453	−	0.129809i
$508$	18.3671	+	5.80768i	0.814908	+	0.257674i
$509$	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	$0.199284\pi$
$510$	3.24895	+	13.8990i	0.143866	+	0.615457i
$511$		0			0
$512$	−18.8602	+	12.5017i	−0.833512	+	0.552501i
$513$	0.625029	−	2.33264i	0.0275957	−	0.102989i
$514$	0.174062	−	7.83008i	0.00767756	−	0.345370i
$515$	−0.194093	−	0.197991i	−0.00855276	−	0.00872453i
$516$	15.1642	+	0.674534i	0.667569	+	0.0296947i
$517$	35.6783	−	35.6783i	1.56913	−	1.56913i
$518$		0			0
$519$	24.7730			1.08741
$520$	16.5420	−	24.1679i	0.725413	−	1.05983i
$521$	−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	$0.264484\pi$
$522$	9.30432	−	8.89964i	0.407239	−	0.389527i
$523$	−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
$528$	−17.1744	−	20.5359i	−0.747421	−	0.893712i
$529$	−8.70422	−	5.02539i	−0.378444	−	0.218495i
$530$	−0.116687	+	3.62619i	−0.00506855	+	0.157512i
$531$		−	4.69281i		−	0.203651i
$532$		0			0
$533$	−18.5798	−	18.5798i	−0.804780	−	0.804780i
$534$	6.93147	−	11.4122i	0.299954	−	0.493853i
$535$	−3.78509	+	3.71057i	−0.163644	+	0.160422i
$536$	27.5691	+	18.4701i	1.19080	+	0.797789i
$537$	−30.5277	−	8.17987i	−1.31737	−	0.352988i
$538$	−7.78810	+	26.6791i	−0.335769	+	1.15022i
$539$		0			0
$540$	−16.8164	−	18.7531i	−0.723664	−	0.807005i
$541$	−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	$-0.334162\pi$
$542$	13.4033	+	14.0127i	0.575720	+	0.601899i
$543$	−0.326474	−	1.21842i	−0.0140103	−	0.0522872i
$544$	2.11712	−	18.9721i	0.0907706	−	0.813421i
$545$	−11.1130	−	19.6980i	−0.476030	−	0.843770i
$546$		0			0
$547$	−5.99240	−	5.99240i	−0.256216	−	0.256216i	0.567297	−	0.823513i	$-0.307989\pi$
$547$	−5.99240	−	5.99240i	−0.256216	−	0.256216i	−0.823513	+	0.567297i	$0.807989\pi$
$548$	15.7475	+	17.2137i	0.672700	+	0.735332i
$549$	12.8307	+	7.40781i	0.547601	+	0.316158i
$550$	34.5315	−	7.71068i	1.47243	−	0.328784i
$551$	−2.79160	+	1.61173i	−0.118926	+	0.0686619i
$552$	10.2463	−	8.96353i	0.436113	−	0.381513i
$553$		0			0
$554$	8.75392	−	4.79790i	0.371918	−	0.203843i
$555$	6.82941	−	11.5619i	0.289892	−	0.490775i
$556$	−26.6231	+	13.8314i	−1.12907	+	0.586581i
$557$	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	$0.751773\pi$
$558$	0.165775	+	0.678671i	0.00701782	+	0.0287304i
$559$	26.2758			1.11135
$560$		0			0
$561$	22.5856			0.953564
$562$	−5.35918	−	21.9401i	−0.226063	−	0.925487i
$563$	−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	$0.979462\pi$
$564$	23.9373	−	12.4360i	1.00794	−	0.523652i
$565$	6.04503	+	23.4921i	0.254316	+	0.988321i
$566$	26.7371	−	14.6542i	1.12385	−	0.615964i
$567$		0			0
$568$	−26.1205	+	22.8504i	−1.09599	+	0.958780i
$569$	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	$0.313269\pi$
$570$	0.855777	+	1.59890i	0.0358446	+	0.0669707i
$571$	15.8499	+	9.15092i	0.663296	+	0.382954i	0.793532	−	0.608529i	$-0.208240\pi$
$571$	15.8499	+	9.15092i	0.663296	+	0.382954i	−0.130236	+	0.991483i	$0.541573\pi$
$572$	−31.2799	−	34.1922i	−1.30788	−	1.42965i
$573$	16.3312	+	16.3312i	0.682246	+	0.682246i
$574$		0			0
$575$	4.31035	+	17.4686i	0.179754	+	0.728491i
$576$	3.68535	+	8.95944i	0.153556	+	0.373310i
$577$	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	$0.909675\pi$
$578$	−5.48572	−	5.73516i	−0.228176	−	0.238551i
$579$	−3.99151	−	6.91350i	−0.165881	−	0.287315i
$580$	−1.82794	+	33.5723i	−0.0759010	+	1.39401i
$581$		0			0
$582$	−3.93512	+	13.4802i	−0.163116	+	0.558774i
$583$	5.54517	+	1.48582i	0.229658	+	0.0615366i
$584$	12.5845	+	8.43107i	0.520750	+	0.348880i
$585$	−8.77785	−	8.95414i	−0.362919	−	0.370208i
$586$	20.6540	−	34.0053i	0.853209	−	1.40475i
$587$	−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
$590$	8.38212	+	8.93951i	0.345086	+	0.368034i
$591$	−9.37905	−	5.41499i	−0.385802	−	0.222743i
$592$	−13.7764	+	11.5214i	−0.566207	+	0.473525i
$593$	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
$598$	17.0297	−	16.2890i	0.696397	−	0.666108i
$599$	0.992946	−	1.71983i	0.0405707	−	0.0702705i	−0.845027	−	0.534724i	$-0.820416\pi$
$599$	0.992946	−	1.71983i	0.0405707	−	0.0702705i	0.885598	+	0.464453i	$0.153749\pi$
$600$	18.8449	+	1.63534i	0.769341	+	0.0667624i
$601$	−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
$604$	−1.26849	−	0.0564249i	−0.0516142	−	0.00229590i
$605$	0.312049	−	31.3874i	0.0126866	−	1.27608i
$606$	0.408417	−	18.3724i	0.0165908	−	0.746327i
$607$	−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	$0.132363\pi$
$608$	−0.364053	−	2.39795i	−0.0147643	−	0.0972497i
$609$		0			0
$610$	−37.6732	+	8.80629i	−1.52534	+	0.356556i
$611$	40.4387	−	23.3473i	1.63597	−	0.944530i
$612$	−7.79290	−	2.46411i	−0.315009	−	0.0996058i
$613$	−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	$0.557343\pi$
$614$	14.6480	−	24.1168i	0.591144	−	0.973276i
$615$	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	$0.221414\pi$
$618$	−0.227845	+	0.0556544i	−0.00916527	+	0.00223875i
$619$	−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	$0.760562\pi$
$620$	−1.52801	−	0.996724i	−0.0613662	−	0.0400294i
$621$	−10.1340	−	17.5527i	−0.406665	−	0.704365i
$622$	−6.62884	+	22.7079i	−0.265792	+	0.910504i
$623$		0			0
$624$	−10.4335	−	22.4708i	−0.417675	−	0.899553i
$625$	−13.3509	+	21.1366i	−0.534034	+	0.845463i
$626$	11.4521	+	0.254579i	0.457717	+	0.0101750i
$627$	2.77180	−	0.742701i	0.110695	−	0.0296606i
$628$	−11.5373	−	12.6115i	−0.460390	−	0.503255i
$629$		−	15.1514i		−	0.604126i
$630$		0			0
$631$			22.2381i			0.885285i	0.896698	+	0.442643i	$0.145959\pi$
$631$			22.2381i			0.885285i	−0.896698	+	0.442643i	$0.854041\pi$
$632$	0.180250	−	0.528864i	0.00716997	−	0.0210371i
$633$	10.0107	−	2.68235i	0.397888	−	0.106614i
$634$	−0.192540	+	8.66129i	−0.00764675	+	0.343984i
$635$	5.36714	+	20.8577i	0.212988	+	0.827712i
$636$	2.58712	+	1.65116i	0.102586	+	0.0654726i
$637$		0			0
$638$	51.0695	+	14.9081i	2.02186	+	0.590217i
$639$	7.42932	+	12.8680i	0.293899	+	0.509048i
$640$	−23.0233	−	10.4845i	−0.910078	−	0.414438i
$641$	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	$0.0137355\pi$
$642$	1.06397	+	4.35582i	0.0419916	+	0.171911i
$643$	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
$646$	1.74891	+	1.06225i	0.0688101	+	0.0417936i
$647$	−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	$0.473043\pi$
$648$	−10.8233	+	2.13906i	−0.425178	+	0.0840301i
$649$	16.7929	−	9.69538i	0.659179	−	0.380577i
$650$	32.7148	+	1.37841i	1.28318	+	0.0540658i
$651$		0			0
$652$	38.4795	−	8.49762i	1.50697	−	0.332792i
$653$	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	$-0.0483068\pi$
$654$	−19.1275	−	0.425204i	−0.747945	−	0.0166268i
$655$	−4.85621	−	0.0482798i	−0.189748	−	0.00188645i
$656$	−13.0490	+	18.5711i	−0.509478	+	0.725079i
$657$	4.58586	−	4.58586i	0.178911	−	0.178911i
$658$		0			0
$659$	−6.31956			−0.246175			−0.123088	−	0.992396i	$-0.539280\pi$
$659$	−6.31956			−0.246175			−0.123088	+	0.992396i	$0.539280\pi$
$660$	9.30704	−	28.4471i	0.362276	−	1.10730i
$661$	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	$-0.0318659\pi$
$662$	−30.4006	−	31.7829i	−1.18155	−	1.23528i
$663$	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
$668$	23.0900	+	7.30104i	0.893378	+	0.282486i
$669$	−18.1985	−	10.5069i	−0.703593	−	0.406220i
$670$	−1.19326	+	37.0821i	−0.0460997	+	1.43260i
$671$			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	$0.451388\pi$
$674$	16.1217	+	9.79194i	0.620986	+	0.377172i
$675$	7.82821	−	27.0519i	0.301308	−	1.04123i
$676$	−7.78493	−	14.9847i	−0.299420	−	0.576334i
$677$	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	$0.520670\pi$
$678$	19.6981	+	5.75023i	0.756501	+	0.220836i
$679$		0			0
$680$	19.2463	−	9.22539i	0.738061	−	0.353777i
$681$	−4.61453	−	7.99259i	−0.176829	−	0.306277i
$682$	−2.08608	+	1.99535i	−0.0798802	+	0.0764060i
$683$	−0.862105	−	3.21742i	−0.0329875	−	0.123111i	0.947469	−	0.319849i	$-0.103632\pi$
$683$	−0.862105	−	3.21742i	−0.0329875	−	0.123111i	−0.980456	+	0.196737i	$0.936965\pi$
$684$	−1.03741	−	0.0461458i	−0.0396662	−	0.00176443i
$685$	−7.00114	+	25.1267i	−0.267500	+	0.960043i
$686$		0			0
$687$	−4.77591	−	4.77591i	−0.182212	−	0.182212i
$688$	−3.90469	−	22.3588i	−0.148865	−	0.852420i
$689$	4.60097	+	2.65637i	0.175283	+	0.101200i
$690$	14.5676	+	4.41018i	0.554580	+	0.167893i
$691$	−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	$0.349960\pi$
$692$	−7.98782	−	36.1710i	−0.303652	−	1.37501i
$693$		0			0
$694$	21.5506	+	39.3198i	0.818050	+	1.49256i
$695$	−28.8807	−	17.0593i	−1.09551	−	0.647098i
$696$	23.6293	+	15.8306i	0.895667	+	0.600059i
$697$	−4.95604	−	18.4962i	−0.187723	−	0.700593i
$698$	19.0122	−	4.64399i	0.719621	−	0.175778i
$699$	−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	$0.828346\pi$
$702$	−35.8316	+	8.75237i	−1.35237	+	0.330337i
$703$	−0.498237	−	1.85945i	−0.0187914	−	0.0701303i
$704$	−24.4467	+	31.6980i	−0.921371	+	1.19466i
$705$	25.9672	+	15.3384i	0.977981	+	0.577676i
$706$	1.17687	+	2.14723i	0.0442919	+	0.0808120i
$707$		0			0
$708$	10.1227	−	2.23545i	0.380435	−	0.0840135i
$709$	−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	$0.632987\pi$
$710$	−37.1366	−	11.2427i	−1.39371	−	0.421930i
$711$	−0.207170	−	0.119610i	−0.00776950	−	0.00448572i
$712$	−18.8979	−	6.44087i	−0.708227	−	0.241382i
$713$	−1.03801	−	1.03801i	−0.0388737	−	0.0388737i
$714$		0			0
$715$	13.9066	−	49.9102i	0.520079	−	1.86653i
$716$	−2.10003	+	47.2109i	−0.0784819	+	1.76436i
$717$	3.90543	+	14.5752i	0.145851	+	0.544323i
$718$	−31.6028	+	30.2283i	−1.17940	+	1.12811i
$719$	−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	$0.941708\pi$
$720$	−6.31489	+	8.79993i	−0.235342	+	0.327954i
$721$		0			0
$722$	−25.5439	−	7.45674i	−0.950647	−	0.277511i
$723$	−33.7379	−	9.04005i	−1.25473	−	0.336203i
$724$	−1.67374	+	0.869550i	−0.0622040	+	0.0323166i
$725$	−32.9216	+	18.1443i	−1.22268	+	0.673863i
$726$	−22.6949	−	13.7843i	−0.842288	−	0.511585i
$727$	−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
$730$	−0.544688	+	16.9269i	−0.0201598	+	0.626491i
$731$	16.5832	+	9.57434i	0.613353	+	0.354120i
$732$	−9.86716	+	31.2055i	−0.364701	+	1.15339i
$733$	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
$738$	6.71701	+	7.02244i	0.247257	+	0.258499i
$739$	−3.53772	+	6.12751i	−0.130137	+	0.225404i	−0.923729	−	0.383046i	$-0.874875\pi$
$739$	−3.53772	+	6.12751i	−0.130137	+	0.225404i	0.793592	+	0.608450i	$0.208208\pi$
$740$	−19.0836	−	6.24357i	−0.701526	−	0.229518i
$741$	2.65562			0.0975566
$742$		0			0
$743$	−34.5013	+	34.5013i	−1.26573	+	1.26573i	−0.317456	+	0.948273i	$0.602828\pi$
$743$	−34.5013	+	34.5013i	−1.26573	+	1.26573i	−0.948273	+	0.317456i	$0.897172\pi$
$744$	−1.38497	+	0.680878i	−0.0507755	+	0.0249622i
$745$	20.1157	+	0.199987i	0.736981	+	0.00732696i
$746$	−31.7101	−	0.704915i	−1.16099	−	0.0258088i
$747$	−0.827608	+	3.08868i	−0.0302806	+	0.113009i
$748$	−7.28252	−	32.9772i	−0.266275	−	1.20576i
$749$		0			0
$750$	9.60701	+	18.8404i	0.350799	+	0.687955i
$751$	−7.29278	+	4.21049i	−0.266117	+	0.153643i	−0.627122	−	0.778921i	$-0.715767\pi$
$751$	−7.29278	+	4.21049i	−0.266117	+	0.153643i	0.361004	+	0.932564i	$0.382434\pi$
$752$	−25.8762	−	30.9409i	−0.943608	−	1.12830i
$753$	33.6314	−	9.01152i	1.22560	−	0.328398i
$754$	42.0805	+	25.5587i	1.53248	+	0.930792i
$755$	−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	$0.246008\pi$
$758$	2.04574	+	8.37512i	0.0743047	+	0.304198i
$759$	12.0419	−	20.8573i	0.437095	−	0.757070i
$760$	2.05862	−	1.76507i	0.0746739	−	0.0640258i
$761$	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	$0.808095\pi$
$762$	17.4892	+	5.10540i	0.633565	+	0.184949i
$763$		0			0
$764$	18.5793	−	29.1110i	0.672176	−	1.05320i
$765$	−2.27720	−	8.84962i	−0.0823323	−	0.319959i
$766$	0.866986	−	39.0008i	0.0313255	−	1.40916i
$767$	17.3335	−	4.64450i	0.625877	−	0.167703i
$768$	−17.5706	+	12.2174i	−0.634024	+	0.440858i
$769$			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
$772$	−8.80735	+	8.05719i	−0.316984	+	0.289985i
$773$	−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	$0.632735\pi$
$774$	−9.71525	−	0.215970i	−0.349208	−	0.00776287i
$775$	0.0405526	−	2.03929i	0.00145669	−	0.0732533i
$776$	20.9513	+	1.39908i	0.752108	+	0.0502242i
$777$		0			0
$778$	−8.36010	+	28.6385i	−0.299724	+	1.02674i
$779$	−1.21645	−	2.10696i	−0.0435839	−	0.0754896i
$780$	15.1333	−	23.1998i	0.541859	−	0.830685i
$781$	−30.6980	+	53.1705i	−1.09846	+	1.90259i
$782$	16.6832	−	4.07511i	0.596590	−	0.145726i
$783$	29.9422	−	29.9422i	1.07005	−	1.07005i
$784$		0			0
$785$	5.12936	−	18.4090i	0.183075	−	0.657045i
$786$	−2.13269	+	3.51132i	−0.0760706	+	0.125245i
$787$	−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	$0.438624\pi$
$788$	−4.88223	+	15.4403i	−0.173922	+	0.550039i
$789$	−16.9547	+	9.78882i	−0.603605	+	0.348491i
$790$	0.608289	−	0.142190i	0.0216420	−	0.00505891i
$791$		0			0
$792$	11.2844	+	12.8994i	0.400975	+	0.458359i
$793$	−14.6631	+	54.7234i	−0.520701	+	1.94328i
$794$	−0.163576	+	7.35836i	−0.00580510	+	0.261138i
$795$	−0.0341126	+	3.43121i	−0.00120985	+	0.121692i
$796$	−1.77223	+	39.8417i	−0.0628151	+	1.41215i
$797$	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
$800$	−3.68862	−	28.0427i	−0.130412	−	0.991460i
$801$	−4.27402	+	7.40281i	−0.151015	+	0.261566i
$802$	11.8244	−	11.3101i	0.417533	−	0.399373i
$803$	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
$808$	−26.9572	+	5.32768i	−0.948350	+	0.187427i
$809$	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	$0.443264\pi$
$810$	−8.43702	−	8.99806i	−0.296447	−	0.316160i
$811$		−	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
$814$	−16.4933	+	27.1551i	−0.578090	+	0.951784i
$815$	30.8424	+	31.4618i	1.08036	+	1.10206i
$816$	1.60306	−	17.9836i	0.0561184	−	0.629552i
$817$	2.35001	+	0.629682i	0.0822163	+	0.0220298i
$818$	1.77044	−	6.06484i	0.0619019	−	0.212052i
$819$		0			0
$820$	−25.3387	−	1.37964i	−0.884865	−	0.0481790i
$821$	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	$0.830163\pi$
$822$	15.2519	+	15.9454i	0.531972	+	0.556161i
$823$	1.69940	+	6.34226i	0.0592375	+	0.221077i	0.989199	−	0.146580i	$-0.0468266\pi$
$823$	1.69940	+	6.34226i	0.0592375	+	0.221077i	−0.929961	+	0.367657i	$0.880160\pi$
$824$	0.154727	+	0.314731i	0.00539019	+	0.0109642i
$825$	32.4893	−	8.01669i	1.13113	−	0.279105i
$826$		0			0
$827$	−6.28320	−	6.28320i	−0.218488	−	0.218488i	0.589373	−	0.807861i	$-0.299375\pi$
$827$	−6.28320	−	6.28320i	−0.218488	−	0.218488i	−0.807861	+	0.589373i	$0.799375\pi$
$828$	−6.43048	+	5.88276i	−0.223475	+	0.204440i
$829$	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	$0.522563\pi$
$830$	−3.94033	−	7.36197i	−0.136771	−	0.255538i
$831$	8.17644	−	4.72067i	0.283638	−	0.163758i
$832$	−29.4454	+	22.4795i	−1.02084	+	0.779336i
$833$		0			0
$834$	−24.8828	+	13.6379i	−0.861621	+	0.472242i
$835$	6.74723	+	26.2210i	0.233498	+	0.907414i
$836$	−1.97816	−	3.80762i	−0.0684160	−	0.131689i
$837$	0.594677	+	2.21936i	0.0205550	+	0.0767125i
$838$	−8.50986	−	34.8387i	−0.293968	−	1.20348i
$839$	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
$842$	3.94686	+	16.1581i	0.136018	+	0.556846i
$843$	−5.52857	−	20.6329i	−0.190414	−	0.710635i
$844$	−7.14433	−	13.7516i	−0.245918	−	0.473351i
$845$	9.60178	−	16.2554i	0.330311	−	0.559203i
$846$	−15.1438	+	8.30009i	−0.520654	+	0.285363i
$847$		0			0
$848$	1.57666	−	4.30984i	0.0541426	−	0.148001i
$849$	24.9734	−	14.4184i	0.857084	−	0.494838i
$850$	20.1448	+	12.7905i	0.690960	+	0.438711i
$851$	−13.9920	−	8.07827i	−0.479638	−	0.276919i
$852$	−24.2181	+	22.1553i	−0.829697	+	0.759027i
$853$	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
$856$	6.01686	−	2.95800i	0.205652	−	0.101102i
$857$	−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	$-0.219975\pi$
$858$	−30.2955	−	31.6731i	−1.03427	−	1.08130i
$859$	−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	$-0.577481\pi$
$860$	18.8927	−	16.9416i	0.644236	−	0.577704i
$861$		0			0
$862$	6.59121	−	22.5790i	0.224498	−	0.769044i
$863$	−14.3793	−	3.85293i	−0.489479	−	0.131155i	0.00563418	−	0.999984i	$-0.498207\pi$
$863$	−14.3793	−	3.85293i	−0.489479	−	0.131155i	−0.495113	+	0.868829i	$0.664873\pi$
$864$	12.7723	+	29.1894i	0.434524	+	0.993043i
$865$	29.5743	−	28.9921i	1.00556	−	0.985760i
$866$	−26.8610	+	44.2246i	−0.912772	+	1.50281i
$867$	−5.30760	−	5.30760i	−0.180255	−	0.180255i
$868$		0			0
$869$		−	0.988459i		−	0.0335312i
$870$	−1.02274	+	31.7828i	−0.0346740	+	1.07754i
$871$	47.0504	+	27.1646i	1.59424	+	0.920436i
$872$	5.54666	+	28.0652i	0.187834	+	0.950406i
$873$	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	$0.292397\pi$
$878$	25.9855	−	24.8553i	0.876969	−	0.838827i
$879$	18.8147	−	32.5880i	0.634603	−	1.09917i
$880$	−44.5365	−	4.41668i	−1.50132	−	0.148886i
$881$	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	−0.439224	−	0.898377i	$-0.644747\pi$
$883$	13.6439	−	13.6439i	0.459153	−	0.459153i	0.898377	+	0.439224i	$0.144747\pi$
$884$	1.38885	−	31.2228i	0.0467121	−	1.05014i
$885$	8.11365	+	8.27660i	0.272737	+	0.278215i
$886$	−0.0566122	+	2.54666i	−0.00190192	+	0.0855568i
$887$	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	$-0.103077\pi$
$888$	−12.7842	+	11.1836i	−0.429009	+	0.375299i
$889$		0			0
$890$	−5.08089	−	21.7360i	−0.170312	−	0.728591i
$891$	−16.9029	+	9.75888i	−0.566268	+	0.326935i
$892$	−9.47315	+	29.9594i	−0.317185	+	1.00311i
$893$	4.17618	−	1.11901i	0.139751	−	0.0374461i
$894$	8.83415	−	14.5448i	0.295458	−	0.486451i
$895$	−46.0174	+	25.9616i	−1.53819	+	0.867801i
$896$		0			0
$897$	15.7601	−	15.7601i	0.526215	−	0.526215i
$898$	−37.6204	+	9.18933i	−1.25541	+	0.306652i
$899$	1.53346	−	2.65603i	0.0511438	−	0.0885836i
$900$	−12.0847	−	0.778550i	−0.402823	−	0.0259517i
$901$	1.93585	+	3.35299i	0.0644926	+	0.111704i
$902$	−11.2519	+	38.5447i	−0.374647	+	1.28340i
$903$		0			0
$904$	2.04442	−	30.6153i	0.0679965	−	1.01825i
$905$	−1.81567	−	1.07249i	−0.0603550	−	0.0356507i
$906$	−1.20061	−	0.0266895i	−0.0398877	−	0.000886701i
$907$	13.8355	−	3.70721i	0.459400	−	0.123096i	−0.0216943	−	0.999765i	$-0.506906\pi$
$907$	13.8355	−	3.70721i	0.459400	−	0.123096i	0.481095	+	0.876669i	$0.340239\pi$
$908$	−10.1821	+	9.31480i	−0.337903	+	0.309122i
$909$			11.7648i			0.390214i
$910$		0			0
$911$		−	1.96705i		−	0.0651712i	−0.999469	−	0.0325856i	$-0.989626\pi$
$911$		−	1.96705i		−	0.0651712i	0.999469	−	0.0325856i	$-0.0103742\pi$
$912$	−0.394636	−	2.25974i	−0.0130677	−	0.0748274i
$913$	−12.7624	+	3.41969i	−0.422375	+	0.113175i
$914$	−0.120238	+	5.40882i	−0.00397711	+	0.178908i
$915$	−35.4369	+	9.11870i	−1.17151	+	0.301455i
$916$	−5.43335	+	8.51325i	−0.179523	+	0.281286i
$917$		0			0
$918$	−25.8033	−	7.53244i	−0.851635	−	0.248607i
$919$	−4.25783	−	7.37478i	−0.140453	−	0.243271i	0.787214	−	0.616679i	$-0.211523\pi$
$919$	−4.25783	−	7.37478i	−0.140453	−	0.243271i	−0.927667	+	0.373408i	$0.878189\pi$
$920$	1.74209	−	22.6922i	0.0574351	−	0.748138i
$921$	13.3435	−	23.1116i	0.439684	−	0.761555i
$922$	8.32716	+	34.0908i	0.274240	+	1.12272i
$923$	−40.1766	+	40.1766i	−1.32243	+	1.32243i
$924$		0			0
$925$	−5.37795	−	21.7953i	−0.176826	−	0.716624i
$926$	−17.7272	−	10.7671i	−0.582552	−	0.353828i
$927$	0.145037	−	0.0388626i	0.00476364	−	0.00127641i
$928$	15.4952	−	39.6055i	0.508656	−	1.30012i
$929$	−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	$0.531369\pi$
$930$	−1.46576	−	0.910338i	−0.0480643	−	0.0298512i
$931$		0			0
$932$	1.49740	+	6.78063i	0.0490490	+	0.222107i
$933$	−5.79062	+	21.6109i	−0.189576	+	0.707508i
$934$	7.25745	+	0.161333i	0.237471	+	0.00527897i
$935$	26.9630	−	26.4321i	0.881784	−	0.864423i
$936$	6.99754	+	14.2337i	0.228722	+	0.465243i
$937$	−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
$940$	14.0226	−	42.8604i	0.457368	−	1.39795i
$941$	−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	$0.237797\pi$
$942$	−11.1743	−	11.6824i	−0.364077	−	0.380632i
$943$	−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	$0.285639\pi$
$947$	−9.45619	+	35.2910i	−0.307285	+	1.14680i	−0.930960	+	0.365120i	$0.881028\pi$
$948$	0.159320	−	0.503858i	0.00517446	−	0.0163645i
$949$	21.4771	+	12.3998i	0.697177	+	0.402515i
$950$	2.89285	+	0.907268i	0.0938565	+	0.0294357i
$951$			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	$0.716079\pi$
$954$	−1.67934	−	1.01999i	−0.0543706	−	0.0330234i
$955$	38.6090	+	0.383845i	1.24936	+	0.0124209i
$956$	20.0220	−	10.4020i	0.647558	−	0.336423i
$957$	48.6023	+	13.0229i	1.57109	+	0.420972i
$958$	5.73362	+	1.67375i	0.185245	+	0.0540763i
$959$		0			0
$960$	−21.9902	−	9.42975i	−0.709730	−	0.304344i
$961$	−15.4168	−	26.7027i	−0.497316	−	0.861376i
$962$	−21.2477	+	20.3236i	−0.685053	+	0.655258i
$963$	−0.742954	−	2.77274i	−0.0239414	−	0.0893504i
$964$	−2.32087	+	52.1756i	−0.0747501	+	1.68046i
$965$	−12.8561	−	3.58212i	−0.413851	−	0.115313i
$966$		0			0
$967$	24.8629	+	24.8629i	0.799538	+	0.799538i	0.983023	−	0.183485i	$-0.0587378\pi$
$967$	24.8629	+	24.8629i	0.799538	+	0.799538i	−0.183485	+	0.983023i	$0.558738\pi$
$968$	−12.8087	+	37.5815i	−0.411688	+	1.20791i
$969$	1.67602	+	0.967651i	0.0538415	+	0.0310854i
$970$	11.0782	+	20.6982i	0.355701	+	0.664579i
$971$	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	$0.118966\pi$
$972$	22.8101	−	5.03727i	0.731634	−	0.161571i
$973$		0			0
$974$	15.9331	+	29.0704i	0.510529	+	0.931476i
$975$	30.9625	+	0.615711i	0.991595	+	0.0197185i
$976$	48.7446	+	4.34510i	1.56028	+	0.139083i
$977$	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	$0.590808\pi$
$978$	36.2058	−	8.84378i	1.15773	−	0.282793i
$979$	−35.3206			−1.12885
$980$		0			0
$981$	12.2483			0.391060
$982$	59.0915	−	14.4339i	1.88568	−	0.460605i
$983$	−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	$-0.302904\pi$
$984$	−11.9482	+	17.8342i	−0.380894	+	0.568534i
$985$	−17.5341	+	4.51190i	−0.558681	+	0.143761i
$986$	17.2449	+	31.4639i	0.549190	+	1.00201i
$987$		0			0
$988$	−0.856280	−	3.87746i	−0.0272419	−	0.123359i
$989$	17.6833	−	10.2095i	0.562298	−	0.324643i
$990$	−5.55209	+	18.3396i	−0.176457	+	0.582870i
$991$	20.3753	+	11.7637i	0.647242	+	0.373685i	0.787399	−	0.616444i	$-0.211427\pi$
$991$	20.3753	+	11.7637i	0.647242	+	0.373685i	−0.140157	+	0.990129i	$0.544761\pi$
$992$	1.44072	+	1.80265i	0.0457429	+	0.0572342i
$993$	−29.4134	−	29.4134i	−0.933406	−	0.933406i
$994$		0			0
$995$	−38.8344	+	21.9092i	−1.23113	+	0.694568i
$996$	−7.05672	−	0.313896i	−0.223601	−	0.00994618i
$997$	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	$0.738283\pi$
$998$	−0.574301	+	0.549323i	−0.0181792	+	0.0173885i
$999$	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.263.7		72
4.3	odd	2	inner	980.2.x.l.263.5		72
5.2	odd	4	inner	980.2.x.l.67.17		72
7.2	even	3	inner	980.2.x.l.863.5		72
7.3	odd	6		140.2.k.a.43.18	yes	36
7.4	even	3		980.2.k.l.883.18		36
7.5	odd	6		980.2.x.k.863.5		72
7.6	odd	2		980.2.x.k.263.7		72
20.7	even	4	inner	980.2.x.l.67.5		72
28.3	even	6		140.2.k.a.43.8	✓	36
28.11	odd	6		980.2.k.l.883.8		36
28.19	even	6		980.2.x.k.863.17		72
28.23	odd	6	inner	980.2.x.l.863.17		72
28.27	even	2		980.2.x.k.263.5		72
35.2	odd	12	inner	980.2.x.l.667.5		72
35.3	even	12		700.2.k.b.407.11		36
35.12	even	12		980.2.x.k.667.5		72
35.17	even	12		140.2.k.a.127.8	yes	36
35.24	odd	6		700.2.k.b.43.1		36
35.27	even	4		980.2.x.k.67.17		72
35.32	odd	12		980.2.k.l.687.8		36
140.3	odd	12		700.2.k.b.407.1		36
140.27	odd	4		980.2.x.k.67.5		72
140.47	odd	12		980.2.x.k.667.7		72
140.59	even	6		700.2.k.b.43.11		36
140.67	even	12		980.2.k.l.687.18		36
140.87	odd	12		140.2.k.a.127.18	yes	36
140.107	even	12	inner	980.2.x.l.667.7		72

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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+(-0.335576 - 1.37382i) q^{2} +(-0.346182 - 1.29197i) q^{3} +(-1.77478 + 0.922043i) q^{4} +(-1.92528 - 1.13723i) q^{5} +(-1.65877 + 0.909146i) q^{6} +(1.86230 + 2.12881i) q^{8} +(1.04873 - 0.605487i) q^{9} +(-0.916275 + 3.02662i) q^{10} +(4.33338 + 2.50188i) q^{11} +(1.80565 + 1.97376i) q^{12} +(3.27438 + 3.27438i) q^{13} +(-0.802768 + 2.88109i) q^{15} +(2.29967 - 3.27284i) q^{16} +(0.873420 + 3.25965i) q^{17} +(-1.18376 - 1.23759i) q^{18} +(0.214380 + 0.371316i) q^{19} +(4.46552 + 0.243138i) q^{20} +(1.98296 - 6.79287i) q^{22} +(3.47589 + 0.931361i) q^{23} +(2.10567 - 3.14299i) q^{24} +(2.41342 + 4.37898i) q^{25} +(3.39961 - 5.59722i) q^{26} +(-3.98268 - 3.98268i) q^{27} +7.51811i q^{29} +(4.22750 + 0.136036i) q^{30} +(-0.353285 - 0.203969i) q^{31} +(-5.26802 - 2.06105i) 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} +(0.438182 - 0.419124i) q^{38} +(3.09687 - 5.36393i) q^{39} +(-1.16449 - 6.21643i) q^{40} -5.67429 q^{41} +(4.01233 - 4.01233i) q^{43} +(-9.99763 - 0.444713i) q^{44} +(-2.70769 - 0.0269194i) q^{45} +(0.113101 - 5.08780i) q^{46} +(2.60987 - 9.74016i) q^{47} +(-5.02452 - 1.83811i) q^{48} +(5.20605 - 4.78508i) q^{50} +(3.90900 - 2.25686i) q^{51} +(-8.83042 - 2.79218i) q^{52} +(1.10820 - 0.296942i) q^{53} +(-4.13501 + 6.80799i) q^{54} +(-5.49776 - 9.74487i) q^{55} +(0.405515 - 0.405515i) q^{57} +(10.3285 - 2.52289i) q^{58} +(1.93762 - 3.35606i) q^{59} +(-1.23176 - 5.85349i) q^{60} +(6.11723 + 10.5954i) q^{61} +(-0.161663 + 0.553797i) q^{62} +(-1.06370 + 7.92897i) q^{64} +(-2.58038 - 10.0278i) q^{65} +(-9.46264 - 0.210354i) q^{66} +(11.3327 - 3.03658i) q^{67} +(-4.55566 - 4.97982i) q^{68} -4.81316i q^{69} +12.2700i q^{71} +(3.24202 + 1.10496i) q^{72} +(5.17303 - 1.38611i) q^{73} +(-0.141115 + 6.34796i) q^{74} +(4.82202 - 4.63398i) q^{75} +(-0.722846 - 0.461337i) q^{76} +(-8.40832 - 2.45454i) q^{78} +(-0.0987717 - 0.171078i) q^{79} +(-8.14949 + 3.68589i) q^{80} +(-1.95031 + 3.37804i) q^{81} +(1.90416 + 7.79547i) q^{82} +(-1.86715 + 1.86715i) q^{83} +(2.02539 - 7.26902i) q^{85} +(-6.85867 - 4.16579i) q^{86} +(9.71316 - 2.60263i) q^{87} +(2.74400 + 13.8842i) q^{88} +(-6.11311 + 3.52940i) q^{89} +(0.871651 + 3.72891i) q^{90} +(-7.02768 + 1.55196i) q^{92} +(-0.141221 + 0.527043i) q^{93} +(-14.2571 - 0.316934i) q^{94} +(0.00953113 - 0.958687i) q^{95} +(-0.839124 + 7.51962i) 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