LMFDB - Embedded newform 841.2.e.k.651.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			651.2
Character	$\chi$	$=$	841.651
Dual form			841.2.e.k.270.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.179721 + 0.373194i) q^{2} +(0.323845 + 0.258258i) q^{3} +(1.14001 + 1.42952i) q^{4} +(-0.900969 - 0.433884i) q^{5} +(-0.154582 + 0.0744427i) q^{6} +(1.76350 - 2.21135i) q^{7} +(-1.54603 + 0.352871i) q^{8} +(-0.629384 - 2.75751i) q^{9} +O(q^{10})$	\(q+(-0.179721 + 0.373194i) q^{2} +(0.323845 + 0.258258i) q^{3} +(1.14001 + 1.42952i) q^{4} +(-0.900969 - 0.433884i) q^{5} +(-0.154582 + 0.0744427i) q^{6} +(1.76350 - 2.21135i) q^{7} +(-1.54603 + 0.352871i) q^{8} +(-0.629384 - 2.75751i) q^{9} +(0.323845 - 0.258258i) q^{10} +(2.35368 + 0.537213i) q^{11} +0.757359i q^{12} +(0.406863 - 1.78258i) q^{13} +(0.508326 + 1.05555i) q^{14} +(-0.179721 - 0.373194i) q^{15} +(-0.667563 + 2.92478i) q^{16} +4.82843i q^{17} +(1.14220 + 0.260699i) q^{18} +(4.69099 - 3.74094i) q^{19} +(-0.406863 - 1.78258i) q^{20} +(1.14220 - 0.260699i) q^{21} +(-0.623490 + 0.781831i) q^{22} +(6.89859 - 3.32218i) q^{23} +(-0.591805 - 0.284998i) q^{24} +(-2.49396 - 3.12733i) q^{25} +(0.592127 + 0.472206i) q^{26} +(1.04749 - 2.17513i) q^{27} +5.17157 q^{28} +0.171573 q^{30} +(1.76637 - 3.66791i) q^{31} +(-3.45117 - 2.75222i) q^{32} +(0.623490 + 0.781831i) q^{33} +(-1.80194 - 0.867767i) q^{34} +(-2.54832 + 1.22721i) q^{35} +(3.22442 - 4.04330i) q^{36} +(-3.89971 + 0.890084i) q^{37} +(0.553027 + 2.42297i) q^{38} +(0.592127 - 0.472206i) q^{39} +(1.54603 + 0.352871i) q^{40} +12.4853i q^{41} +(-0.107985 + 0.473114i) q^{42} +(2.78302 + 5.77901i) q^{43} +(1.91526 + 3.97707i) q^{44} +(-0.629384 + 2.75751i) q^{45} +3.17157i q^{46} +(-5.11120 - 1.16660i) q^{47} +(-0.971536 + 0.774774i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.61531 - 0.368685i) q^{50} +(-1.24698 + 1.56366i) q^{51} +(3.01207 - 1.45054i) q^{52} +(6.74401 + 3.24774i) q^{53} +(0.623490 + 0.781831i) q^{54} +(-1.88751 - 1.50524i) q^{55} +(-1.94609 + 4.04110i) q^{56} +2.48528 q^{57} +7.65685 q^{59} +(0.328606 - 0.682357i) q^{60} +(-0.647690 - 0.516516i) q^{61} +(1.05139 + 1.31840i) q^{62} +(-7.20775 - 3.47107i) q^{63} +(-3.75846 + 1.80998i) q^{64} +(-1.14001 + 1.42952i) q^{65} +(-0.403828 + 0.0921712i) q^{66} +(-1.25877 - 5.51503i) q^{67} +(-6.90234 + 5.50443i) q^{68} +(3.09205 + 0.705741i) q^{69} -1.17157i q^{70} +(-0.705741 + 3.09205i) q^{71} +(1.94609 + 4.04110i) q^{72} +(-1.73553 - 3.60388i) q^{73} +(0.368685 - 1.61531i) q^{74} -1.65685i q^{75} +(10.6955 + 2.44118i) q^{76} +(5.33868 - 4.25745i) q^{77} +(0.0698067 + 0.305843i) q^{78} +(-0.403828 + 0.0921712i) q^{79} +(1.87047 - 2.34549i) q^{80} +(-6.74401 + 3.24774i) q^{81} +(-4.65943 - 2.24386i) q^{82} +(-2.28001 - 2.85904i) q^{83} +(1.67479 + 1.33560i) q^{84} +(2.09498 - 4.35026i) q^{85} -2.65685 q^{86} -3.82843 q^{88} +(-1.94609 + 4.04110i) q^{89} +(-0.915973 - 0.730464i) q^{90} +(-3.22442 - 4.04330i) q^{91} +(12.6136 + 6.07437i) q^{92} +(1.51930 - 0.731654i) q^{93} +(1.35395 - 1.69780i) q^{94} +(-5.84957 + 1.33513i) q^{95} +(-0.406863 - 1.78258i) q^{96} +(9.76139 - 7.78445i) q^{97} +(0.403828 + 0.0921712i) q^{98} -6.82843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−0.179721	+	0.373194i	−0.127082	+	0.263888i	−0.954796	−	0.297262i	$-0.903927\pi$
$2$	−0.179721	+	0.373194i	−0.127082	+	0.263888i	0.827714	+	0.561150i	$0.189641\pi$
$3$	0.323845	+	0.258258i	0.186972	+	0.149105i	0.712503	−	0.701670i	$-0.247562\pi$
$3$	0.323845	+	0.258258i	0.186972	+	0.149105i	−0.525530	+	0.850775i	$0.676133\pi$
$4$	1.14001	+	1.42952i	0.570003	+	0.714761i
$5$	−0.900969	−	0.433884i	−0.402926	−	0.194039i	0.221435	−	0.975175i	$-0.428926\pi$
$5$	−0.900969	−	0.433884i	−0.402926	−	0.194039i	−0.624360	+	0.781136i	$0.714640\pi$
$6$	−0.154582	+	0.0744427i	−0.0631078	+	0.0303911i
$7$	1.76350	−	2.21135i	0.666539	−	0.835813i	−0.327499	−	0.944852i	$-0.606206\pi$
$7$	1.76350	−	2.21135i	0.666539	−	0.835813i	0.994038	+	0.109039i	$0.0347772\pi$
$8$	−1.54603	+	0.352871i	−0.546603	+	0.124759i
$9$	−0.629384	−	2.75751i	−0.209795	−	0.919171i
$10$	0.323845	−	0.258258i	0.102409	−	0.0816683i
$11$	2.35368	+	0.537213i	0.709662	+	0.161976i	0.562091	−	0.827076i	$-0.309997\pi$
$11$	2.35368	+	0.537213i	0.709662	+	0.161976i	0.147572	+	0.989051i	$0.452854\pi$
$12$			0.757359i			0.218631i
$13$	0.406863	−	1.78258i	0.112844	−	0.494400i	−0.886646	−	0.462449i	$-0.846971\pi$
$13$	0.406863	−	1.78258i	0.112844	−	0.494400i	0.999489	−	0.0319510i	$-0.0101720\pi$
$14$	0.508326	+	1.05555i	0.135856	+	0.282108i
$15$	−0.179721	−	0.373194i	−0.0464036	−	0.0963582i
$16$	−0.667563	+	2.92478i	−0.166891	+	0.731196i
$17$			4.82843i			1.17107i	0.810649	+	0.585533i	$0.199115\pi$
$17$			4.82843i			1.17107i	−0.810649	+	0.585533i	$0.800885\pi$
$18$	1.14220	+	0.260699i	0.269219	+	0.0614475i
$19$	4.69099	−	3.74094i	1.07619	−	0.858230i	0.0857663	−	0.996315i	$-0.472666\pi$
$19$	4.69099	−	3.74094i	1.07619	−	0.858230i	0.990420	+	0.138085i	$0.0440947\pi$
$20$	−0.406863	−	1.78258i	−0.0909774	−	0.398598i
$21$	1.14220	−	0.260699i	0.249248	−	0.0568893i
$22$	−0.623490	+	0.781831i	−0.132928	+	0.166687i
$23$	6.89859	−	3.32218i	1.43845	−	0.692723i	0.457906	−	0.889000i	$-0.348599\pi$
$23$	6.89859	−	3.32218i	1.43845	−	0.692723i	0.980548	+	0.196277i	$0.0628852\pi$
$24$	−0.591805	−	0.284998i	−0.120802	−	0.0581751i
$25$	−2.49396	−	3.12733i	−0.498792	−	0.625465i
$26$	0.592127	+	0.472206i	0.116126	+	0.0926072i
$27$	1.04749	−	2.17513i	0.201589	−	0.418604i
$28$	5.17157			0.977335
$29$		0			0
$29$		0			0
$30$	0.171573			0.0313248
$31$	1.76637	−	3.66791i	0.317249	−	0.658775i	−0.679975	−	0.733236i	$-0.738009\pi$
$31$	1.76637	−	3.66791i	0.317249	−	0.658775i	0.997224	+	0.0744605i	$0.0237235\pi$
$32$	−3.45117	−	2.75222i	−0.610087	−	0.486528i
$33$	0.623490	+	0.781831i	0.108536	+	0.136099i
$34$	−1.80194	−	0.867767i	−0.309030	−	0.148821i
$35$	−2.54832	+	1.22721i	−0.430746	+	0.207436i
$36$	3.22442	−	4.04330i	0.537404	−	0.673883i
$37$	−3.89971	+	0.890084i	−0.641109	+	0.146329i	−0.530703	−	0.847558i	$-0.678072\pi$
$37$	−3.89971	+	0.890084i	−0.641109	+	0.146329i	−0.110405	+	0.993887i	$0.535215\pi$
$38$	0.553027	+	2.42297i	0.0897128	+	0.393058i
$39$	0.592127	−	0.472206i	0.0948163	−	0.0756134i
$40$	1.54603	+	0.352871i	0.244448	+	0.0557938i
$41$			12.4853i			1.94987i	0.222483	+	0.974937i	$0.428584\pi$
$41$			12.4853i			1.94987i	−0.222483	+	0.974937i	$0.571416\pi$
$42$	−0.107985	+	0.473114i	−0.0166625	+	0.0730031i
$43$	2.78302	+	5.77901i	0.424407	+	0.881290i	0.998064	+	0.0621946i	$0.0198100\pi$
$43$	2.78302	+	5.77901i	0.424407	+	0.881290i	−0.573657	+	0.819096i	$0.694476\pi$
$44$	1.91526	+	3.97707i	0.288736	+	0.599566i
$45$	−0.629384	+	2.75751i	−0.0938231	+	0.411066i
$46$			3.17157i			0.467623i
$47$	−5.11120	−	1.16660i	−0.745545	−	0.170166i	−0.167160	−	0.985930i	$-0.553460\pi$
$47$	−5.11120	−	1.16660i	−0.745545	−	0.170166i	−0.578385	+	0.815764i	$0.696317\pi$
$48$	−0.971536	+	0.774774i	−0.140229	+	0.111829i
$49$	−0.222521	−	0.974928i	−0.0317887	−	0.139275i
$50$	1.61531	−	0.368685i	0.228440	−	0.0521399i
$51$	−1.24698	+	1.56366i	−0.174612	+	0.218957i
$52$	3.01207	−	1.45054i	0.417699	−	0.201153i
$53$	6.74401	+	3.24774i	0.926360	+	0.446112i	0.835338	−	0.549737i	$-0.185272\pi$
$53$	6.74401	+	3.24774i	0.926360	+	0.446112i	0.0910227	+	0.995849i	$0.470986\pi$
$54$	0.623490	+	0.781831i	0.0848462	+	0.106394i
$55$	−1.88751	−	1.50524i	−0.254512	−	0.202966i
$56$	−1.94609	+	4.04110i	−0.260057	+	0.540015i
$57$	2.48528			0.329184
$58$		0			0
$59$	7.65685			0.996838			0.498419	−	0.866936i	$-0.333914\pi$
$59$	7.65685			0.996838			0.498419	+	0.866936i	$0.333914\pi$
$60$	0.328606	−	0.682357i	0.0424228	−	0.0880919i
$61$	−0.647690	−	0.516516i	−0.0829283	−	0.0661331i	0.581148	−	0.813798i	$-0.302604\pi$
$61$	−0.647690	−	0.516516i	−0.0829283	−	0.0661331i	−0.664076	+	0.747665i	$0.731175\pi$
$62$	1.05139	+	1.31840i	0.133526	+	0.167436i
$63$	−7.20775	−	3.47107i	−0.908091	−	0.437314i
$64$	−3.75846	+	1.80998i	−0.469807	+	0.226247i
$65$	−1.14001	+	1.42952i	−0.141400	+	0.177310i
$66$	−0.403828	+	0.0921712i	−0.0497078	+	0.0113455i
$67$	−1.25877	−	5.51503i	−0.153783	−	0.673768i	−0.991765	−	0.128070i	$-0.959122\pi$
$67$	−1.25877	−	5.51503i	−0.153783	−	0.673768i	0.837982	−	0.545698i	$-0.183735\pi$
$68$	−6.90234	+	5.50443i	−0.837032	+	0.667511i
$69$	3.09205	+	0.705741i	0.372240	+	0.0849613i
$70$		−	1.17157i		−	0.140030i
$71$	−0.705741	+	3.09205i	−0.0837561	+	0.366959i	−0.999385	−	0.0350650i	$-0.988836\pi$
$71$	−0.705741	+	3.09205i	−0.0837561	+	0.366959i	0.915629	+	0.402024i	$0.131693\pi$
$72$	1.94609	+	4.04110i	0.229349	+	0.476248i
$73$	−1.73553	−	3.60388i	−0.203129	−	0.421802i	0.774373	−	0.632730i	$-0.218066\pi$
$73$	−1.73553	−	3.60388i	−0.203129	−	0.421802i	−0.977502	+	0.210928i	$0.932351\pi$
$74$	0.368685	−	1.61531i	0.0428587	−	0.187776i
$75$		−	1.65685i		−	0.191317i
$76$	10.6955	+	2.44118i	1.22686	+	0.280023i
$77$	5.33868	−	4.25745i	0.608399	−	0.485182i
$78$	0.0698067	+	0.305843i	0.00790405	+	0.0346299i
$79$	−0.403828	+	0.0921712i	−0.0454342	+	0.0103701i	−0.245178	−	0.969478i	$-0.578846\pi$
$79$	−0.403828	+	0.0921712i	−0.0454342	+	0.0103701i	0.199743	+	0.979848i	$0.435989\pi$
$80$	1.87047	−	2.34549i	0.209125	−	0.262234i
$81$	−6.74401	+	3.24774i	−0.749334	+	0.360860i
$82$	−4.65943	−	2.24386i	−0.514548	−	0.247793i
$83$	−2.28001	−	2.85904i	−0.250264	−	0.313821i	0.640792	−	0.767714i	$-0.278606\pi$
$83$	−2.28001	−	2.85904i	−0.250264	−	0.313821i	−0.891056	+	0.453894i	$0.850035\pi$
$84$	1.67479	+	1.33560i	0.182734	+	0.145726i
$85$	2.09498	−	4.35026i	0.227232	−	0.471852i
$86$	−2.65685			−0.286496
$87$		0			0
$88$	−3.82843			−0.408112
$89$	−1.94609	+	4.04110i	−0.206285	+	0.428356i	−0.978284	−	0.207268i	$-0.933543\pi$
$89$	−1.94609	+	4.04110i	−0.206285	+	0.428356i	0.771999	+	0.635624i	$0.219257\pi$
$90$	−0.915973	−	0.730464i	−0.0965520	−	0.0769976i
$91$	−3.22442	−	4.04330i	−0.338011	−	0.423853i
$92$	12.6136	+	6.07437i	1.31505	+	0.633297i
$93$	1.51930	−	0.731654i	0.157544	−	0.0758690i
$94$	1.35395	−	1.69780i	0.139650	−	0.175115i
$95$	−5.84957	+	1.33513i	−0.600153	+	0.136981i
$96$	−0.406863	−	1.78258i	−0.0415253	−	0.181934i
$97$	9.76139	−	7.78445i	0.991119	−	0.790391i	0.0133144	−	0.999911i	$-0.495762\pi$
$97$	9.76139	−	7.78445i	0.991119	−	0.790391i	0.977804	+	0.209521i	$0.0671904\pi$
$98$	0.403828	+	0.0921712i	0.0407928	+	0.00931070i
$99$		−	6.82843i		−	0.686283i
$100$	1.62745	−	7.13034i	0.162745	−	0.713034i
$101$	−5.92549	−	12.3044i	−0.589608	−	1.22433i	−0.955861	−	0.293818i	$-0.905074\pi$
$101$	−5.92549	−	12.3044i	−0.589608	−	1.22433i	0.366253	−	0.930515i	$-0.380640\pi$
$102$	−0.359441	−	0.746387i	−0.0355900	−	0.0739033i
$103$	−0.184342	+	0.807657i	−0.0181638	+	0.0795808i	−0.983197	−	0.182545i	$-0.941566\pi$
$103$	−0.184342	+	0.807657i	−0.0181638	+	0.0795808i	0.965034	+	0.262126i	$0.0844236\pi$
$104$			2.89949i			0.284319i
$105$	−1.14220	−	0.260699i	−0.111467	−	0.0254417i
$106$	−2.42407	+	1.93313i	−0.235447	+	0.187763i
$107$	2.04087	+	8.94162i	0.197298	+	0.864419i	0.972536	+	0.232751i	$0.0747726\pi$
$107$	2.04087	+	8.94162i	0.197298	+	0.864419i	−0.775238	+	0.631669i	$0.782370\pi$
$108$	4.30354	−	0.982255i	0.414108	−	0.0945175i
$109$	−0.837438	+	1.05011i	−0.0802120	+	0.100583i	−0.820318	−	0.571907i	$-0.806204\pi$
$109$	−0.837438	+	1.05011i	−0.0802120	+	0.100583i	0.740106	+	0.672490i	$0.234775\pi$
$110$	0.900969	−	0.433884i	0.0859040	−	0.0413692i
$111$	−1.49277	−	0.718882i	−0.141688	−	0.0682333i
$112$	5.29049	+	6.63406i	0.499904	+	0.626860i
$113$	7.28175	+	5.80700i	0.685009	+	0.546277i	0.902982	−	0.429678i	$-0.141373\pi$
$113$	7.28175	+	5.80700i	0.685009	+	0.546277i	−0.217973	+	0.975955i	$0.569944\pi$
$114$	−0.446656	+	0.927491i	−0.0418332	+	0.0868675i
$115$	−7.65685			−0.714005
$116$		0			0
$117$	−5.17157			−0.478112
$118$	−1.37609	+	2.85749i	−0.126680	+	0.263053i
$119$	10.6774	+	8.51491i	0.978792	+	0.780560i
$120$	0.409542	+	0.513549i	0.0373859	+	0.0468804i
$121$	−4.65943	−	2.24386i	−0.423584	−	0.203987i
$122$	0.309164	−	0.148885i	0.0279904	−	0.0134794i
$123$	−3.22442	+	4.04330i	−0.290736	+	0.364572i
$124$	7.25702	−	1.65637i	0.651700	−	0.148746i
$125$	2.00269	+	8.77435i	0.179126	+	0.784802i
$126$	2.59076	−	2.06606i	0.230803	−	0.184060i
$127$	−15.2643	−	3.48398i	−1.35449	−	0.309153i	−0.517176	−	0.855879i	$-0.673017\pi$
$127$	−15.2643	−	3.48398i	−1.35449	−	0.309153i	−0.837312	+	0.546726i	$0.815874\pi$
$128$		−	10.5563i		−	0.933058i
$129$	−0.591206	+	2.59024i	−0.0520528	+	0.228058i
$130$	−0.328606	−	0.682357i	−0.0288206	−	0.0598467i
$131$	0.569997	+	1.18361i	0.0498008	+	0.103413i	0.924384	−	0.381462i	$-0.124579\pi$
$131$	0.569997	+	1.18361i	0.0498008	+	0.103413i	−0.874584	+	0.484875i	$0.838865\pi$
$132$	−0.406863	+	1.78258i	−0.0354129	+	0.155154i
$133$		−	16.9706i		−	1.47153i
$134$	2.28440	+	0.521399i	0.197342	+	0.0450420i
$135$	−1.88751	+	1.50524i	−0.162451	+	0.129550i
$136$	−1.70381	−	7.46488i	−0.146101	−	0.640108i
$137$	−11.6991	+	2.67025i	−0.999525	+	0.228135i	−0.690823	−	0.723024i	$-0.742752\pi$
$137$	−11.6991	+	2.67025i	−0.999525	+	0.228135i	−0.308702	+	0.951159i	$0.599894\pi$
$138$	−0.819084	+	1.02710i	−0.0697250	+	0.0874324i
$139$	−12.6136	+	6.07437i	−1.06987	+	0.515222i	−0.884064	−	0.467365i	$-0.845203\pi$
$139$	−12.6136	+	6.07437i	−1.06987	+	0.515222i	−0.185804	+	0.982587i	$0.559489\pi$
$140$	−4.65943	−	2.24386i	−0.393793	−	0.189641i
$141$	−1.35395	−	1.69780i	−0.114023	−	0.142981i
$142$	−1.02710	−	0.819084i	−0.0861922	−	0.0687360i
$143$	1.91526	−	3.97707i	0.160162	−	0.332579i
$144$	8.48528			0.707107
$145$		0			0
$146$	1.65685			0.137122
$147$	0.179721	−	0.373194i	0.0148231	−	0.0307805i
$148$	−5.71809	−	4.56002i	−0.470024	−	0.374832i
$149$	1.35395	+	1.69780i	0.110920	+	0.139090i	0.834192	−	0.551474i	$-0.185934\pi$
$149$	1.35395	+	1.69780i	0.110920	+	0.139090i	−0.723272	+	0.690563i	$0.757363\pi$
$150$	0.618327	+	0.297771i	0.0504862	+	0.0243129i
$151$	12.7416	−	6.13604i	1.03690	−	0.499344i	0.163599	−	0.986527i	$-0.447690\pi$
$151$	12.7416	−	6.13604i	1.03690	−	0.499344i	0.873300	+	0.487183i	$0.161975\pi$
$152$	−5.93233	+	7.43891i	−0.481176	+	0.603375i
$153$	13.3144	−	3.03894i	1.07641	−	0.245683i
$154$	0.629384	+	2.75751i	0.0507172	+	0.222207i
$155$	−3.18289	+	2.53827i	−0.255656	+	0.203879i
$156$	1.35006	+	0.308142i	0.108091	+	0.0246711i
$157$		−	8.48528i		−	0.677199i	−0.940931	−	0.338600i	$-0.890047\pi$
$157$		−	8.48528i		−	0.677199i	0.940931	−	0.338600i	$-0.109953\pi$
$158$	0.0381786	−	0.167271i	0.00303732	−	0.0133074i
$159$	1.34526	+	2.79346i	0.106686	+	0.221536i
$160$	1.91526	+	3.97707i	0.151414	+	0.314415i
$161$	4.81910	−	21.1139i	0.379799	−	1.66401i
$162$		−	3.10051i		−	0.243599i
$163$	−17.6180	−	4.02119i	−1.37995	−	0.314964i	−0.532764	−	0.846264i	$-0.678847\pi$
$163$	−17.6180	−	4.02119i	−1.37995	−	0.314964i	−0.847184	+	0.531300i	$0.821704\pi$
$164$	−17.8480	+	14.2333i	−1.39369	+	1.11143i
$165$	−0.222521	−	0.974928i	−0.0173232	−	0.0758980i
$166$	1.47674	−	0.337057i	0.114617	−	0.0261607i
$167$	5.50443	−	6.90234i	0.425946	−	0.534119i	−0.521833	−	0.853048i	$-0.674752\pi$
$167$	5.50443	−	6.90234i	0.425946	−	0.534119i	0.947779	+	0.318928i	$0.103323\pi$
$168$	−1.67388	+	0.806097i	−0.129142	+	0.0621917i
$169$	8.70053	+	4.18995i	0.669271	+	0.322304i
$170$	1.24698	+	1.56366i	0.0956390	+	0.119927i
$171$	−13.2681	−	10.5810i	−1.01464	−	0.809147i
$172$	−5.08855	+	10.5665i	−0.387999	+	0.805688i
$173$	−23.6569			−1.79860			−0.899299	−	0.437335i	$-0.855922\pi$
$173$	−23.6569			−1.79860			−0.899299	+	0.437335i	$0.855922\pi$
$174$		0			0
$175$	−11.3137			−0.855236
$176$	−3.14246	+	6.52539i	−0.236872	+	0.491870i
$177$	2.47964	+	1.97744i	0.186381	+	0.148634i
$178$	−1.15836	−	1.45254i	−0.0868227	−	0.108872i
$179$	9.44691	+	4.54939i	0.706095	+	0.340038i	0.752233	−	0.658897i	$-0.228977\pi$
$179$	9.44691	+	4.54939i	0.706095	+	0.340038i	−0.0461374	+	0.998935i	$0.514691\pi$
$180$	−4.65943	+	2.24386i	−0.347293	+	0.167248i
$181$	−8.92445	+	11.1909i	−0.663349	+	0.831814i	−0.993703	−	0.112043i	$-0.964260\pi$
$181$	−8.92445	+	11.1909i	−0.663349	+	0.831814i	0.330354	+	0.943857i	$0.392832\pi$
$182$	2.08843	−	0.476670i	0.154805	−	0.0353331i
$183$	−0.0763571	−	0.334542i	−0.00564448	−	0.0247301i
$184$	−9.49310	+	7.57050i	−0.699841	+	0.558104i
$185$	3.89971	+	0.890084i	0.286713	+	0.0654403i
$186$			0.698485i			0.0512154i
$187$	−2.59389	+	11.3646i	−0.189684	+	0.831061i
$188$	−4.15912	−	8.63650i	−0.303335	−	0.629881i
$189$	−2.96274	−	6.15220i	−0.215508	−	0.447507i
$190$	0.553027	−	2.42297i	0.0401208	−	0.175781i
$191$		−	2.68629i		−	0.194373i	−0.995266	−	0.0971866i	$-0.969016\pi$
$191$		−	2.68629i		−	0.194373i	0.995266	−	0.0971866i	$-0.0309844\pi$
$192$	−1.68460	−	0.384499i	−0.121575	−	0.0277488i
$193$	−8.46601	+	6.75141i	−0.609396	+	0.485977i	−0.878890	−	0.477025i	$-0.841715\pi$
$193$	−8.46601	+	6.75141i	−0.609396	+	0.485977i	0.269493	+	0.963002i	$0.413144\pi$
$194$	1.15078	+	5.04191i	0.0826214	+	0.361988i
$195$	−0.738371	+	0.168528i	−0.0528758	+	0.0120686i
$196$	1.14001	−	1.42952i	0.0814290	−	0.102109i
$197$	−1.80194	+	0.867767i	−0.128383	+	0.0618259i	−0.496972	−	0.867766i	$-0.665555\pi$
$197$	−1.80194	+	0.867767i	−0.128383	+	0.0618259i	0.368590	+	0.929592i	$0.379841\pi$
$198$	2.54832	+	1.22721i	0.181102	+	0.0872139i
$199$	10.2784	+	12.8887i	0.728617	+	0.913657i	0.998791	−	0.0491548i	$-0.0156528\pi$
$199$	10.2784	+	12.8887i	0.728617	+	0.913657i	−0.270174	+	0.962811i	$0.587081\pi$
$200$	4.95927	+	3.95489i	0.350673	+	0.279653i
$201$	1.01665	−	2.11110i	0.0717092	−	0.148906i
$202$	5.65685			0.398015
$203$		0			0
$204$	−3.65685			−0.256031
$205$	5.41716	−	11.2488i	0.378351	−	0.785654i
$206$	−0.268282	−	0.213948i	−0.0186921	−	0.0149065i
$207$	−13.5028	−	16.9320i	−0.938511	−	1.17686i
$208$	4.94207	+	2.37997i	0.342671	+	0.165022i
$209$	13.0508	−	6.28493i	0.902742	−	0.434738i
$210$	0.302568	−	0.379408i	0.0208792	−	0.0261817i
$211$	16.9489	−	3.86848i	1.16681	−	0.266317i	0.405124	−	0.914262i	$-0.367229\pi$
$211$	16.9489	−	3.86848i	1.16681	−	0.266317i	0.761687	+	0.647945i	$0.224371\pi$
$212$	3.04549	+	13.3431i	0.209165	+	0.916411i
$213$	−1.02710	+	0.819084i	−0.0703756	+	0.0561227i
$214$	−3.70374	−	0.845355i	−0.253183	−	0.0577873i
$215$		−	6.41421i		−	0.437446i
$216$	−0.851905	+	3.73244i	−0.0579648	+	0.253960i
$217$	−4.99605	−	10.3744i	−0.339154	−	0.704260i
$218$	−0.241391	−	0.501253i	−0.0163491	−	0.0339492i
$219$	0.368685	−	1.61531i	0.0249134	−	0.109153i
$220$		−	4.41421i		−	0.297606i
$221$	8.60708	+	1.96451i	0.578975	+	0.132147i
$222$	0.536564	−	0.427896i	0.0360118	−	0.0287185i
$223$	1.96451	+	8.60708i	0.131553	+	0.576373i	0.997138	+	0.0756093i	$0.0240902\pi$
$223$	1.96451	+	8.60708i	0.131553	+	0.576373i	−0.865584	+	0.500763i	$0.833053\pi$
$224$	−12.1722	+	2.77824i	−0.813293	+	0.185629i
$225$	−7.05398	+	8.84541i	−0.470265	+	0.589694i
$226$	−3.47582	+	1.67386i	−0.231208	+	0.111344i
$227$	−18.1474	−	8.73935i	−1.20449	−	0.580051i	−0.279536	−	0.960135i	$-0.590181\pi$
$227$	−18.1474	−	8.73935i	−1.20449	−	0.580051i	−0.924952	+	0.380085i	$0.875895\pi$
$228$	2.83323	+	3.55276i	0.187636	+	0.235288i
$229$	−16.0160	−	12.7724i	−1.05837	−	0.844022i	−0.0702224	−	0.997531i	$-0.522371\pi$
$229$	−16.0160	−	12.7724i	−1.05837	−	0.844022i	−0.988147	+	0.153510i	$0.950942\pi$
$230$	1.37609	−	2.85749i	0.0907369	−	0.188417i
$231$	2.82843			0.186097
$232$		0			0
$233$	−4.31371			−0.282600			−0.141300	−	0.989967i	$-0.545128\pi$
$233$	−4.31371			−0.282600			−0.141300	+	0.989967i	$0.545128\pi$
$234$	0.929438	−	1.93000i	0.0607593	−	0.126168i
$235$	4.09886	+	3.26873i	0.267380	+	0.213229i
$236$	8.72886	+	10.9456i	0.568200	+	0.712501i
$237$	−0.154582	−	0.0744427i	−0.0100412	−	0.00483557i
$238$	−5.09665	+	2.45442i	−0.330367	+	0.159096i
$239$	−5.20187	+	6.52293i	−0.336481	+	0.421934i	−0.921071	−	0.389395i	$-0.872684\pi$
$239$	−5.20187	+	6.52293i	−0.336481	+	0.421934i	0.584590	+	0.811329i	$0.301255\pi$
$240$	1.21149	−	0.276514i	0.0782010	−	0.0178489i
$241$	0.959890	+	4.20555i	0.0618320	+	0.270904i	0.996389	−	0.0849110i	$-0.0270606\pi$
$241$	0.959890	+	4.20555i	0.0618320	+	0.270904i	−0.934557	+	0.355815i	$0.884203\pi$
$242$	1.67479	−	1.33560i	0.107660	−	0.0858556i
$243$	−10.0838	−	2.30157i	−0.646877	−	0.147646i
$244$		−	1.51472i		−	0.0969699i
$245$	−0.222521	+	0.974928i	−0.0142163	+	0.0622859i
$246$	−0.929438	−	1.93000i	−0.0592588	−	0.123052i
$247$	−4.75995	−	9.88414i	−0.302868	−	0.628912i
$248$	−1.43656	+	6.29398i	−0.0912217	+	0.399668i
$249$		−	1.51472i		−	0.0959914i
$250$	−3.63446	−	0.829541i	−0.229863	−	0.0524648i
$251$	4.63543	−	3.69663i	0.292585	−	0.233329i	−0.466185	−	0.884687i	$-0.654372\pi$
$251$	4.63543	−	3.69663i	0.292585	−	0.233329i	0.758770	+	0.651358i	$0.225800\pi$
$252$	−3.25491	−	14.2607i	−0.205040	−	0.898338i
$253$	18.0218	−	4.11336i	1.13302	−	0.258605i
$254$	4.04351	−	5.07040i	0.253712	−	0.318145i
$255$	1.80194	−	0.867767i	0.112842	−	0.0543417i
$256$	−3.57735	−	1.72276i	−0.223585	−	0.107673i
$257$	−14.8568	−	18.6298i	−0.926741	−	1.16210i	−0.986480	−	0.163882i	$-0.947598\pi$
$257$	−14.8568	−	18.6298i	−0.926741	−	1.16210i	0.0597394	−	0.998214i	$-0.480973\pi$
$258$	−0.860410	−	0.686154i	−0.0535668	−	0.0427181i
$259$	−4.90883	+	10.1933i	−0.305020	+	0.633381i
$260$	−3.34315			−0.207333
$261$		0			0
$262$	−0.544156			−0.0336181
$263$	−4.87800	+	10.1293i	−0.300790	+	0.624597i	−0.995507	−	0.0946858i	$-0.969815\pi$
$263$	−4.87800	+	10.1293i	−0.300790	+	0.624597i	0.694717	+	0.719283i	$0.255530\pi$
$264$	−1.23982	−	0.988722i	−0.0763055	−	0.0608516i
$265$	−4.66700	−	5.85223i	−0.286691	−	0.359500i
$266$	6.33330	+	3.04996i	0.388320	+	0.187005i
$267$	−1.67388	+	0.806097i	−0.102440	+	0.0493323i
$268$	6.44885	−	8.08660i	0.393926	−	0.493968i
$269$	−18.9680	+	4.32933i	−1.15650	+	0.263964i	−0.757405	−	0.652945i	$-0.773533\pi$
$269$	−18.9680	+	4.32933i	−1.15650	+	0.263964i	−0.399097	+	0.916909i	$0.630676\pi$
$270$	−0.222521	−	0.974928i	−0.0135422	−	0.0593322i
$271$	11.3806	−	9.07574i	0.691323	−	0.551312i	−0.213582	−	0.976925i	$-0.568513\pi$
$271$	11.3806	−	9.07574i	0.691323	−	0.551312i	0.904905	+	0.425613i	$0.139942\pi$
$272$	−14.1221	−	3.22328i	−0.856278	−	0.195440i
$273$		−	2.14214i		−	0.129648i
$274$	1.10605	−	4.84594i	0.0668192	−	0.292754i
$275$	−4.18995	−	8.70053i	−0.252664	−	0.524661i
$276$	2.51609	+	5.22471i	0.151451	+	0.314491i
$277$	−1.18241	+	5.18048i	−0.0710442	+	0.311265i	−0.997948	−	0.0640348i	$-0.979603\pi$
$277$	−1.18241	+	5.18048i	−0.0710442	+	0.311265i	0.926903	+	0.375300i	$0.122460\pi$
$278$		−	5.79899i		−	0.347800i
$279$	−11.2260	−	2.56227i	−0.672084	−	0.153399i
$280$	3.50673	−	2.79653i	0.209567	−	0.167124i
$281$	0.438491	+	1.92116i	0.0261582	+	0.114607i	0.986322	−	0.164833i	$-0.0527085\pi$
$281$	0.438491	+	1.92116i	0.0261582	+	0.114607i	−0.960163	+	0.279440i	$0.909851\pi$
$282$	0.876943	−	0.200156i	0.0522212	−	0.0119191i
$283$	−0.213948	+	0.268282i	−0.0127179	+	0.0159477i	−0.788150	−	0.615484i	$-0.788961\pi$
$283$	−0.213948	+	0.268282i	−0.0127179	+	0.0159477i	0.775432	+	0.631431i	$0.217532\pi$
$284$	−5.22471	+	2.51609i	−0.310029	+	0.149302i
$285$	−2.23916	−	1.07832i	−0.132636	−	0.0638744i
$286$	1.14001	+	1.42952i	0.0674099	+	0.0845294i
$287$	27.6094	+	22.0177i	1.62973	+	1.29967i
$288$	−5.41716	+	11.2488i	−0.319209	+	0.662845i
$289$	−6.31371			−0.371395
$290$		0			0
$291$	5.17157			0.303163
$292$	3.17330	−	6.58942i	0.185703	−	0.385617i
$293$	2.85904	+	2.28001i	0.167027	+	0.133200i	0.703436	−	0.710758i	$-0.251648\pi$
$293$	2.85904	+	2.28001i	0.167027	+	0.133200i	−0.536409	+	0.843958i	$0.680220\pi$
$294$	0.106974	+	0.134141i	0.00623885	+	0.00782327i
$295$	−6.89859	−	3.32218i	−0.401651	−	0.193425i
$296$	5.71498	−	2.75219i	0.332176	−	0.159968i
$297$	3.63396	−	4.55685i	0.210864	−	0.264415i
$298$	−0.876943	+	0.200156i	−0.0507999	+	0.0115948i
$299$	−3.11529	−	13.6490i	−0.180162	−	0.789342i
$300$	2.36851	−	1.88882i	0.136746	−	0.109051i
$301$	17.6873	+	4.03700i	1.01948	+	0.232689i
$302$			5.85786i			0.337082i
$303$	1.25877	−	5.51503i	0.0723144	−	0.316830i
$304$	7.80991	+	16.2174i	0.447929	+	0.930134i
$305$	0.359441	+	0.746387i	0.0205815	+	0.0427380i
$306$	−1.25877	+	5.51503i	−0.0719590	+	0.315273i
$307$			16.8995i			0.964505i	0.876032	+	0.482253i	$0.160181\pi$
$307$			16.8995i			0.964505i	−0.876032	+	0.482253i	$0.839819\pi$
$308$	12.1722	+	2.77824i	0.693578	+	0.158305i
$309$	−0.268282	+	0.213948i	−0.0152620	+	0.0121711i
$310$	−0.375235	−	1.64401i	−0.0213119	−	0.0933736i
$311$	−24.6790	+	5.63283i	−1.39942	+	0.319408i	−0.854662	−	0.519185i	$-0.826236\pi$
$311$	−24.6790	+	5.63283i	−1.39942	+	0.319408i	−0.544758	+	0.838593i	$0.683378\pi$
$312$	−0.748818	+	0.938988i	−0.0423934	+	0.0531597i
$313$	−3.75846	+	1.80998i	−0.212441	+	0.102306i	−0.537078	−	0.843533i	$-0.680472\pi$
$313$	−3.75846	+	1.80998i	−0.212441	+	0.102306i	0.324638	+	0.945838i	$0.394758\pi$
$314$	3.16665	+	1.52498i	0.178705	+	0.0860596i
$315$	4.98792	+	6.25465i	0.281037	+	0.352410i
$316$	−0.592127	−	0.472206i	−0.0333098	−	0.0265637i
$317$	8.44157	−	17.5291i	0.474126	−	0.984533i	−0.517535	−	0.855662i	$-0.673150\pi$
$317$	8.44157	−	17.5291i	0.474126	−	0.984533i	0.991661	−	0.128871i	$-0.0411353\pi$
$318$	−1.28427			−0.0720184
$319$		0			0
$320$	4.17157			0.233198
$321$	−1.64832	+	3.42277i	−0.0920002	+	0.191040i
$322$	7.01347	+	5.59305i	0.390845	+	0.311689i
$323$	18.0629	+	22.6501i	1.00504	+	1.26029i
$324$	−12.3309	−	5.93826i	−0.685051	−	0.329903i
$325$	−6.58942	+	3.17330i	−0.365515	+	0.176023i
$326$	4.66700	−	5.85223i	0.258481	−	0.324125i
$327$	−0.542400	+	0.123799i	−0.0299948	+	0.00684612i
$328$	−4.40569	−	19.3026i	−0.243264	−	1.06581i
$329$	−11.5933	+	9.24537i	−0.639161	+	0.509714i
$330$	0.403828	+	0.0921712i	0.0222300	+	0.00507386i
$331$			0.414214i			0.0227672i	0.999935	+	0.0113836i	$0.00362360\pi$
$331$			0.414214i			0.0227672i	−0.999935	+	0.0113836i	$0.996376\pi$
$332$	1.48784	−	6.51865i	0.0816558	−	0.357758i
$333$	4.90883	+	10.1933i	0.269002	+	0.558589i
$334$	1.58665	+	3.29471i	0.0868176	+	0.180279i
$335$	−1.25877	+	5.51503i	−0.0687739	+	0.301318i
$336$			3.51472i			0.191744i
$337$	17.3527	+	3.96065i	0.945264	+	0.215750i	0.667256	−	0.744829i	$-0.267469\pi$
$337$	17.3527	+	3.96065i	0.945264	+	0.215750i	0.278008	+	0.960579i	$0.410326\pi$
$338$	−3.12733	+	2.49396i	−0.170104	+	0.135653i
$339$	0.858456	+	3.76114i	0.0466249	+	0.204277i
$340$	8.60708	−	1.96451i	0.466784	−	0.106541i
$341$	6.12792	−	7.68417i	0.331846	−	0.416121i
$342$	6.33330	−	3.04996i	0.342466	−	0.164923i
$343$	15.2899	+	7.36325i	0.825580	+	0.397578i
$344$	−6.34187	−	7.95246i	−0.341931	−	0.428768i
$345$	−2.47964	−	1.97744i	−0.133499	−	0.106462i
$346$	4.25162	−	8.82858i	0.228569	−	0.474628i
$347$	14.4853			0.777611			0.388805	−	0.921320i	$-0.372888\pi$
$347$	14.4853			0.777611			0.388805	+	0.921320i	$0.372888\pi$
$348$		0			0
$349$	23.1421			1.23877			0.619385	−	0.785087i	$-0.287382\pi$
$349$	23.1421			1.23877			0.619385	+	0.785087i	$0.287382\pi$
$350$	2.03331	−	4.22220i	0.108685	−	0.225686i
$351$	−3.45117	−	2.75222i	−0.184210	−	0.146902i
$352$	−6.64444	−	8.33186i	−0.354150	−	0.444090i
$353$	−6.28026	−	3.02441i	−0.334265	−	0.160973i	0.259221	−	0.965818i	$-0.416534\pi$
$353$	−6.28026	−	3.02441i	−0.334265	−	0.160973i	−0.593485	+	0.804845i	$0.702249\pi$
$354$	−1.18361	+	0.569997i	−0.0629082	+	0.0302950i
$355$	1.97744	−	2.47964i	0.104952	−	0.131605i
$356$	−7.99539	+	1.82490i	−0.423755	+	0.0967193i
$357$	1.25877	+	5.51503i	0.0666211	+	0.291886i
$358$	−3.39561	+	2.70791i	−0.179463	+	0.143117i
$359$	17.6180	+	4.02119i	0.929842	+	0.212230i	0.660510	−	0.750817i	$-0.270340\pi$
$359$	17.6180	+	4.02119i	0.929842	+	0.212230i	0.269332	+	0.963047i	$0.413197\pi$
$360$		−	4.48528i		−	0.236395i
$361$	3.78286	−	16.5738i	0.199098	−	0.872304i
$362$	−2.57247	−	5.34178i	−0.135206	−	0.280758i
$363$	−0.929438	−	1.93000i	−0.0487828	−	0.101299i
$364$	2.10412	−	9.21877i	0.110286	−	0.483195i
$365$			4.00000i			0.209370i
$366$	0.138572	+	0.0316282i	0.00724327	+	0.00165323i
$367$	14.0730	−	11.2228i	0.734603	−	0.585826i	−0.183100	−	0.983094i	$-0.558613\pi$
$367$	14.0730	−	11.2228i	0.734603	−	0.585826i	0.917703	+	0.397268i	$0.130042\pi$
$368$	5.11143	+	22.3946i	0.266452	+	1.16740i
$369$	34.4283	−	7.85804i	1.79227	−	0.409073i
$370$	−1.03303	+	1.29538i	−0.0537048	+	0.0673436i
$371$	19.0749	−	9.18600i	0.990321	−	0.476913i
$372$	2.77792	+	1.33778i	0.144029	+	0.0693605i
$373$	−2.29837	−	2.88206i	−0.119005	−	0.149227i	0.718761	−	0.695258i	$-0.244710\pi$
$373$	−2.29837	−	2.88206i	−0.119005	−	0.149227i	−0.837765	+	0.546030i	$0.816138\pi$
$374$	−3.77502	−	3.01048i	−0.195201	−	0.155668i
$375$	−1.61748	+	3.35874i	−0.0835266	+	0.173445i
$376$	8.31371			0.428747
$377$		0			0
$378$	2.82843			0.145479
$379$	−11.7021	+	24.2996i	−0.601096	+	1.24819i	0.349261	+	0.937026i	$0.386433\pi$
$379$	−11.7021	+	24.2996i	−0.601096	+	1.24819i	−0.950357	+	0.311163i	$0.899282\pi$
$380$	−8.57713	−	6.84003i	−0.439998	−	0.350886i
$381$	−4.04351	−	5.07040i	−0.207155	−	0.259764i
$382$	1.00251	+	0.482782i	0.0512927	+	0.0247013i
$383$	−18.4566	+	8.88823i	−0.943088	+	0.454167i	−0.841258	−	0.540634i	$-0.818184\pi$
$383$	−18.4566	+	8.88823i	−0.943088	+	0.454167i	−0.101831	+	0.994802i	$0.532470\pi$
$384$	2.72626	−	3.41862i	0.139124	−	0.174456i
$385$	−6.65722	+	1.51947i	−0.339284	+	0.0774393i
$386$	−0.998069	−	4.37283i	−0.0508004	−	0.222571i
$387$	14.1841	−	11.3114i	0.721018	−	0.574993i
$388$	22.2561	+	5.07980i	1.12988	+	0.257888i
$389$			36.9706i			1.87448i	0.348682	+	0.937241i	$0.386629\pi$
$389$			36.9706i			1.87448i	−0.348682	+	0.937241i	$0.613371\pi$
$390$	0.0698067	−	0.305843i	0.00353480	−	0.0154870i
$391$	16.0409	+	33.3093i	0.811224	+	1.68453i
$392$	0.688047	+	1.42874i	0.0347516	+	0.0721625i
$393$	−0.121086	+	0.530513i	−0.00610798	+	0.0267608i
$394$		−	0.828427i		−	0.0417356i
$395$	0.403828	+	0.0921712i	0.0203188	+	0.00463764i
$396$	9.76139	−	7.78445i	0.490528	−	0.391183i
$397$	−6.82179	−	29.8882i	−0.342376	−	1.50005i	−0.794044	−	0.607861i	$-0.792028\pi$
$397$	−6.82179	−	29.8882i	−0.342376	−	1.50005i	0.451668	−	0.892186i	$-0.350829\pi$
$398$	−6.65722	+	1.51947i	−0.333696	+	0.0761640i
$399$	4.38278	−	5.49584i	0.219414	−	0.275136i
$400$	10.8116	−	5.20660i	0.540581	−	0.260330i
$401$	6.61595	+	3.18607i	0.330385	+	0.159105i	0.591721	−	0.806143i	$-0.298449\pi$
$401$	6.61595	+	3.18607i	0.330385	+	0.159105i	−0.261336	+	0.965248i	$0.584163\pi$
$402$	0.605136	+	0.758817i	0.0301814	+	0.0378463i
$403$	−5.81968	−	4.64104i	−0.289899	−	0.231187i
$404$	10.8343	−	22.4977i	0.539028	−	1.11930i
$405$	7.48528			0.371947
$406$		0			0
$407$	−9.65685			−0.478672
$408$	1.37609	−	2.85749i	0.0681268	−	0.141467i
$409$	−11.7045	−	9.33399i	−0.578748	−	0.461536i	0.289837	−	0.957076i	$-0.406399\pi$
$409$	−11.7045	−	9.33399i	−0.578748	−	0.461536i	−0.868585	+	0.495540i	$0.834970\pi$
$410$	3.22442	+	4.04330i	0.159243	+	0.199684i
$411$	−4.47832	−	2.15665i	−0.220899	−	0.106380i
$412$	−1.36471	+	0.657212i	−0.0672346	+	0.0323785i
$413$	13.5028	−	16.9320i	0.664431	−	0.833170i
$414$	8.74565	−	1.99614i	0.429825	−	0.0981048i
$415$	0.813727	+	3.56517i	0.0399443	+	0.175007i
$416$	−6.31021	+	5.03223i	−0.309384	+	0.246725i
$417$	−5.65360	−	1.29040i	−0.276858	−	0.0631910i
$418$			6.00000i			0.293470i
$419$	−5.89353	+	25.8212i	−0.287918	+	1.26145i	0.599459	+	0.800405i	$0.295382\pi$
$419$	−5.89353	+	25.8212i	−0.287918	+	1.26145i	−0.887377	+	0.461045i	$0.847475\pi$
$420$	−0.929438	−	1.93000i	−0.0453519	−	0.0941742i
$421$	10.8960	+	22.6258i	0.531038	+	1.10271i	0.978086	+	0.208202i	$0.0667611\pi$
$421$	10.8960	+	22.6258i	0.531038	+	1.10271i	−0.447048	+	0.894510i	$0.647525\pi$
$422$	−1.60238	+	7.02047i	−0.0780024	+	0.341751i
$423$			14.8284i			0.720983i
$424$	−11.5725	−	2.64134i	−0.562008	−	0.128275i
$425$	15.1001	−	12.0419i	0.732461	−	0.584118i
$426$	−0.121086	−	0.530513i	−0.00586664	−	0.0257034i
$427$	−2.28440	+	0.521399i	−0.110550	+	0.0252323i
$428$	−10.4556	+	13.1110i	−0.505393	+	0.633742i
$429$	1.64736	−	0.793325i	0.0795351	−	0.0383021i
$430$	2.39374	+	1.15277i	0.115437	+	0.0555913i
$431$	5.20187	+	6.52293i	0.250565	+	0.314199i	0.891168	−	0.453674i	$-0.149887\pi$
$431$	5.20187	+	6.52293i	0.250565	+	0.314199i	−0.640603	+	0.767872i	$0.721315\pi$
$432$	5.66252	+	4.51571i	0.272438	+	0.217262i
$433$	−6.34660	+	13.1788i	−0.304998	+	0.633335i	−0.995984	−	0.0895334i	$-0.971462\pi$
$433$	−6.34660	+	13.1788i	−0.304998	+	0.633335i	0.690986	+	0.722868i	$0.257177\pi$
$434$	4.76955			0.228946
$435$		0			0
$436$	−2.45584			−0.117614
$437$	19.9331	−	41.3915i	0.953530	−	1.98003i
$438$	0.536564	+	0.427896i	0.0256380	+	0.0204456i
$439$	7.26793	+	9.11370i	0.346879	+	0.434973i	0.924412	−	0.381394i	$-0.124556\pi$
$439$	7.26793	+	9.11370i	0.346879	+	0.434973i	−0.577533	+	0.816367i	$0.695985\pi$
$440$	3.44929	+	1.66109i	0.164439	+	0.0791895i
$441$	−2.54832	+	1.22721i	−0.121349	+	0.0584385i
$442$	−2.28001	+	2.85904i	−0.108449	+	0.135991i
$443$	−34.7629	+	7.93440i	−1.65163	+	0.376975i	−0.944088	−	0.329693i	$-0.893055\pi$
$443$	−34.7629	+	7.93440i	−1.65163	+	0.376975i	−0.707545	+	0.706668i	$0.750197\pi$
$444$	−0.674113	−	2.95348i	−0.0319920	−	0.140166i
$445$	3.50673	−	2.79653i	0.166235	−	0.132568i
$446$	−3.56517	−	0.813727i	−0.168816	−	0.0385311i
$447$			0.899495i			0.0425447i
$448$	−2.62552	+	11.5032i	−0.124044	+	0.543473i
$449$	−0.446656	−	0.927491i	−0.0210790	−	0.0437710i	0.890164	−	0.455641i	$-0.150590\pi$
$449$	−0.446656	−	0.927491i	−0.0210790	−	0.0437710i	−0.911243	+	0.411870i	$0.864876\pi$
$450$	−2.03331	−	4.22220i	−0.0958509	−	0.199037i
$451$	−6.70726	+	29.3864i	−0.315832	+	1.38375i
$452$			17.0294i			0.800997i
$453$	5.71100	+	1.30350i	0.268326	+	0.0612437i
$454$	6.52293	−	5.20187i	0.306136	−	0.244136i
$455$	1.15078	+	5.04191i	0.0539495	+	0.236368i
$456$	−3.84231	+	0.876983i	−0.179933	+	0.0410685i
$457$	−21.8038	+	27.3411i	−1.01994	+	1.27896i	−0.0601642	+	0.998188i	$0.519162\pi$
$457$	−21.8038	+	27.3411i	−1.01994	+	1.27896i	−0.959774	+	0.280774i	$0.909409\pi$
$458$	7.64497	−	3.68163i	0.357226	−	0.172031i
$459$	10.5025	+	5.05772i	0.490213	+	0.236074i
$460$	−8.72886	−	10.9456i	−0.406985	−	0.510343i
$461$	10.9456	+	8.72886i	0.509789	+	0.406543i	0.844318	−	0.535842i	$-0.180006\pi$
$461$	10.9456	+	8.72886i	0.509789	+	0.406543i	−0.334529	+	0.942385i	$0.608577\pi$
$462$	−0.508326	+	1.05555i	−0.0236495	+	0.0491087i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$		0			0
$465$	−1.68629			−0.0781999
$466$	0.775262	−	1.60985i	0.0359133	−	0.0745748i
$467$	−25.2964	−	20.1732i	−1.17058	−	0.933505i	−0.171911	−	0.985112i	$-0.554994\pi$
$467$	−25.2964	−	20.1732i	−1.17058	−	0.933505i	−0.998667	+	0.0516069i	$0.983566\pi$
$468$	−5.89562	−	7.39288i	−0.272525	−	0.341736i
$469$	−14.4155	−	6.94214i	−0.665646	−	0.320558i
$470$	−1.95652	+	0.942210i	−0.0902475	+	0.0434609i
$471$	2.19139	−	2.74792i	0.100974	−	0.126617i
$472$	−11.8377	+	2.70188i	−0.544875	+	0.124364i
$473$	3.44580	+	15.0970i	0.158438	+	0.694162i
$474$	0.0555631	−	0.0443101i	0.00255210	−	0.00203523i
$475$	−23.3983	−	5.34050i	−1.07359	−	0.245039i
$476$			24.9706i			1.14452i
$477$	4.71112	−	20.6408i	0.215707	−	0.945075i
$478$	−1.49943	−	3.11361i	−0.0685825	−	0.142413i
$479$	5.59688	+	11.6220i	0.255728	+	0.531025i	0.988822	−	0.149103i	$-0.0476386\pi$
$479$	5.59688	+	11.6220i	0.255728	+	0.531025i	−0.733094	+	0.680128i	$0.761924\pi$
$480$	−0.406863	+	1.78258i	−0.0185707	+	0.0813635i
$481$			7.31371i			0.333476i
$482$	−1.74200	−	0.397600i	−0.0793458	−	0.0181102i
$483$	7.01347	−	5.59305i	0.319124	−	0.254493i
$484$	−2.10412	−	9.21877i	−0.0956420	−	0.419035i
$485$	−12.1722	+	2.77824i	−0.552713	+	0.126153i
$486$	2.67120	−	3.34958i	0.121168	−	0.151940i
$487$	25.6644	−	12.3593i	1.16296	−	0.560053i	0.250060	−	0.968230i	$-0.419550\pi$
$487$	25.6644	−	12.3593i	1.16296	−	0.560053i	0.912903	+	0.408177i	$0.133835\pi$
$488$	1.18361	+	0.569997i	0.0535795	+	0.0258025i
$489$	−4.66700	−	5.85223i	−0.211049	−	0.264647i
$490$	−0.323845	−	0.258258i	−0.0146298	−	0.0116669i
$491$	−5.53521	+	11.4940i	−0.249801	+	0.518716i	−0.987732	−	0.156160i	$-0.950089\pi$
$491$	−5.53521	+	11.4940i	−0.249801	+	0.518716i	0.737931	+	0.674876i	$0.235803\pi$
$492$	−9.45584			−0.426302
$493$		0			0
$494$	4.54416			0.204451
$495$	−2.96274	+	6.15220i	−0.133165	+	0.276521i
$496$	9.54867	+	7.61481i	0.428748	+	0.341915i
$497$	5.59305	+	7.01347i	0.250883	+	0.314597i
$498$	0.565283	+	0.272226i	0.0253309	+	0.0121987i
$499$	−13.4880	+	6.49548i	−0.603806	+	0.290778i	−0.710703	−	0.703492i	$-0.751623\pi$
$499$	−13.4880	+	6.49548i	−0.603806	+	0.290778i	0.106897	+	0.994270i	$0.465909\pi$
$500$	−10.2601	+	12.8657i	−0.458843	+	0.575371i
$501$	3.56517	−	0.813727i	0.159280	−	0.0363546i
$502$	0.546477	+	2.39427i	0.0243905	+	0.106862i
$503$	−20.1149	+	16.0411i	−0.896879	+	0.715237i	−0.959173	−	0.282821i	$-0.908730\pi$
$503$	−20.1149	+	16.0411i	−0.896879	+	0.715237i	0.0622938	+	0.998058i	$0.480158\pi$
$504$	12.3682	+	2.82297i	0.550924	+	0.125745i
$505$			13.6569i			0.607722i
$506$	−1.70381	+	7.46488i	−0.0757436	+	0.331854i
$507$	1.73553	+	3.60388i	0.0770778	+	0.160054i
$508$	−12.4210	−	25.7924i	−0.551091	−	1.14435i
$509$	6.11605	−	26.7962i	0.271089	−	1.18772i	−0.637640	−	0.770334i	$-0.720089\pi$
$509$	6.11605	−	26.7962i	0.271089	−	1.18772i	0.908730	−	0.417385i	$-0.137053\pi$
$510$			0.828427i			0.0366834i
$511$	−11.0301	−	2.51754i	−0.487941	−	0.111369i
$512$	17.7924	−	14.1890i	0.786321	−	0.627070i
$513$	−3.22328	−	14.1221i	−0.142311	−	0.623506i
$514$	9.62259	−	2.19629i	0.424434	−	0.0968744i
$515$	0.516516	−	0.647690i	0.0227604	−	0.0285406i
$516$	−4.37678	+	2.10775i	−0.192677	+	0.0927884i
$517$	−11.4034	−	5.49160i	−0.501522	−	0.241520i
$518$	−2.92185	−	3.66389i	−0.128379	−	0.160982i
$519$	−7.66116	−	6.10957i	−0.336288	−	0.268180i
$520$	1.25804	−	2.61235i	0.0551689	−	0.114559i
$521$	0.857864			0.0375837			0.0187919	−	0.999823i	$-0.494018\pi$
$521$	0.857864			0.0375837			0.0187919	+	0.999823i	$0.494018\pi$
$522$		0			0
$523$	27.3137			1.19435			0.597173	−	0.802113i	$-0.296291\pi$
$523$	27.3137			1.19435			0.597173	+	0.802113i	$0.296291\pi$
$524$	−1.04220	+	2.16415i	−0.0455286	+	0.0945411i
$525$	−3.66389	−	2.92185i	−0.159905	−	0.127520i
$526$	−2.90350	−	3.64088i	−0.126599	−	0.158750i
$527$	17.7102	+	8.52879i	0.771469	+	0.371520i
$528$	−2.70291	+	1.30165i	−0.117629	+	0.0566471i
$529$	22.2133	−	27.8546i	0.965797	−	1.21107i
$530$	3.02277	−	0.689927i	0.131301	−	0.0299685i
$531$	−4.81910	−	21.1139i	−0.209131	−	0.916264i
$532$	24.2598	−	19.3465i	1.05180	−	0.838779i
$533$	22.2561	+	5.07980i	0.964017	+	0.220031i
$534$		−	0.769553i		−	0.0333018i
$535$	2.04087	−	8.94162i	0.0882344	−	0.386580i
$536$	3.89218	+	8.08220i	0.168117	+	0.349098i
$537$	1.88442	+	3.91304i	0.0813187	+	0.168860i
$538$	1.79327	−	7.85682i	0.0773133	−	0.338732i
$539$		−	2.41421i		−	0.103988i
$540$	−4.30354	−	0.982255i	−0.185195	−	0.0422695i
$541$	−16.9320	+	13.5028i	−0.727964	+	0.580532i	−0.915784	−	0.401672i	$-0.868429\pi$
$541$	−16.9320	+	13.5028i	−0.727964	+	0.580532i	0.187820	+	0.982204i	$0.439858\pi$
$542$	1.34168	+	5.87827i	0.0576299	+	0.252493i
$543$	−5.78028	+	1.31931i	−0.248056	+	0.0566171i
$544$	13.2889	−	16.6637i	0.569756	−	0.714451i
$545$	1.21013	−	0.582769i	0.0518364	−	0.0249631i
$546$	0.799431	+	0.384986i	0.0342125	+	0.0164759i
$547$	−2.36863	−	2.97017i	−0.101275	−	0.126995i	0.728611	−	0.684928i	$-0.240166\pi$
$547$	−2.36863	−	2.97017i	−0.101275	−	0.126995i	−0.829886	+	0.557932i	$0.811595\pi$
$548$	−17.1543	−	13.6801i	−0.732794	−	0.584384i
$549$	−1.01665	+	2.11110i	−0.0433897	+	0.0900996i
$550$	4.00000			0.170561
$551$		0			0
$552$	−5.02944			−0.214067
$553$	−0.508326	+	1.05555i	−0.0216162	+	0.0448866i
$554$	−1.72082	−	1.37231i	−0.0731106	−	0.0583038i
$555$	1.03303	+	1.29538i	0.0438498	+	0.0549859i
$556$	−23.0630	−	11.1065i	−0.978088	−	0.471023i
$557$	4.78749	−	2.30553i	0.202852	−	0.0976885i	−0.329700	−	0.944086i	$-0.606947\pi$
$557$	4.78749	−	2.30553i	0.202852	−	0.0976885i	0.532552	+	0.846397i	$0.321233\pi$
$558$	2.97377	−	3.72899i	0.125890	−	0.157861i
$559$	11.4339	−	2.60971i	0.483602	−	0.110379i
$560$	−1.88815	−	8.27254i	−0.0797890	−	0.349579i
$561$	−3.77502	+	3.01048i	−0.159381	+	0.127102i
$562$	−0.795769	−	0.181629i	−0.0335675	−	0.00766156i
$563$		−	9.24264i		−	0.389531i	−0.980850	−	0.194765i	$-0.937605\pi$
$563$		−	9.24264i		−	0.389531i	0.980850	−	0.194765i	$-0.0623946\pi$
$564$	0.883533	−	3.87101i	0.0372035	−	0.162999i
$565$	−4.04107	−	8.39136i	−0.170009	−	0.353027i
$566$	−0.0616703	−	0.128060i	−0.00259220	−	0.00538275i
$567$	−4.71112	+	20.6408i	−0.197848	+	0.866830i
$568$		−	5.02944i		−	0.211030i
$569$	27.6325	+	6.30694i	1.15842	+	0.264401i	0.758201	−	0.652021i	$-0.226078\pi$
$569$	27.6325	+	6.30694i	1.15842	+	0.264401i	0.400214	+	0.916422i	$0.368936\pi$
$570$	0.804846	−	0.641844i	0.0337113	−	0.0268839i
$571$	6.81524	+	29.8595i	0.285209	+	1.24958i	0.891016	+	0.453971i	$0.149993\pi$
$571$	6.81524	+	29.8595i	0.285209	+	1.24958i	−0.605808	+	0.795611i	$0.707150\pi$
$572$	7.86871	−	1.79598i	0.329007	−	0.0750938i
$573$	0.693756	−	0.869943i	0.0289821	−	0.0363424i
$574$	−13.1788	+	6.34660i	−0.550074	+	0.264902i
$575$	−27.5943	−	13.2887i	−1.15076	−	0.554179i
$576$	7.35655	+	9.22482i	0.306523	+	0.384368i
$577$	7.66116	+	6.10957i	0.318938	+	0.254345i	0.769852	−	0.638223i	$-0.220330\pi$
$577$	7.66116	+	6.10957i	0.318938	+	0.254345i	−0.450913	+	0.892568i	$0.648902\pi$
$578$	1.13470	−	2.35624i	0.0471974	−	0.0980065i
$579$	−4.48528			−0.186402
$580$		0			0
$581$	−10.3431			−0.429106
$582$	−0.929438	+	1.93000i	−0.0385264	+	0.0800010i
$583$	14.1285	+	11.2671i	0.585144	+	0.466637i
$584$	3.95489	+	4.95927i	0.163654	+	0.205216i
$585$	4.65943	+	2.24386i	0.192644	+	0.0927723i
$586$	−1.36471	+	0.657212i	−0.0563758	+	0.0271492i
$587$	−2.28001	+	2.85904i	−0.0941061	+	0.118005i	−0.826655	−	0.562709i	$-0.809759\pi$
$587$	−2.28001	+	2.85904i	−0.0941061	+	0.118005i	0.732549	+	0.680714i	$0.238331\pi$
$588$	0.738371	−	0.168528i	0.0304499	−	0.00694999i
$589$	−5.43539	−	23.8140i	−0.223961	−	0.981238i
$590$	2.47964	−	1.97744i	0.102085	−	0.0814101i
$591$	−0.807657	−	0.184342i	−0.0332226	−	0.00758283i
$592$		−	12.0000i		−	0.493197i
$593$	−0.559578	+	2.45167i	−0.0229791	+	0.100678i	−0.985117	−	0.171885i	$-0.945014\pi$
$593$	−0.559578	+	2.45167i	−0.0229791	+	0.100678i	0.962138	+	0.272563i	$0.0878714\pi$
$594$	1.04749	+	2.17513i	0.0429790	+	0.0892467i
$595$	−5.92549	−	12.3044i	−0.242921	−	0.504431i
$596$	−0.883533	+	3.87101i	−0.0361909	+	0.158563i
$597$			6.82843i			0.279469i
$598$	5.65360	+	1.29040i	0.231193	+	0.0527682i
$599$	−34.2990	+	27.3525i	−1.40142	+	1.11759i	−0.424150	+	0.905592i	$0.639427\pi$
$599$	−34.2990	+	27.3525i	−1.40142	+	1.11759i	−0.977269	+	0.212002i	$0.932002\pi$
$600$	0.584655	+	2.56154i	0.0238685	+	0.104575i
$601$	22.2561	−	5.07980i	0.907844	−	0.207209i	0.256992	−	0.966414i	$-0.417269\pi$
$601$	22.2561	−	5.07980i	0.907844	−	0.207209i	0.650853	+	0.759204i	$0.274412\pi$
$602$	−4.68535	+	5.87524i	−0.190961	+	0.239457i
$603$	−14.4155	+	6.94214i	−0.587045	+	0.282706i
$604$	23.2971	+	11.2193i	0.947947	+	0.456507i
$605$	3.22442	+	4.04330i	0.131091	+	0.164383i
$606$	1.83195	+	1.46093i	0.0744177	+	0.0593461i
$607$	7.69186	−	15.9723i	0.312203	−	0.648296i	−0.684537	−	0.728978i	$-0.739996\pi$
$607$	7.69186	−	15.9723i	0.312203	−	0.648296i	0.996740	+	0.0806822i	$0.0257099\pi$
$608$	−26.4853			−1.07412
$609$		0			0
$610$	−0.343146			−0.0138936
$611$	−4.15912	+	8.63650i	−0.168260	+	0.349395i
$612$	19.5228	+	15.5689i	0.789161	+	0.629335i
$613$	5.61141	+	7.03648i	0.226643	+	0.284201i	0.882131	−	0.471005i	$-0.156108\pi$
$613$	5.61141	+	7.03648i	0.226643	+	0.284201i	−0.655488	+	0.755205i	$0.727537\pi$
$614$	−6.30678	−	3.03719i	−0.254521	−	0.122571i
$615$	4.65943	−	2.24386i	0.187886	−	0.0904812i
$616$	−6.75141	+	8.46601i	−0.272022	+	0.341105i
$617$	22.7292	−	5.18779i	0.915043	−	0.208852i	0.261025	−	0.965332i	$-0.415939\pi$
$617$	22.7292	−	5.18779i	0.915043	−	0.208852i	0.654017	+	0.756480i	$0.273082\pi$
$618$	−0.0316282	−	0.138572i	−0.00127227	−	0.00557418i
$619$	−28.4698	+	22.7039i	−1.14430	+	0.912546i	−0.997065	−	0.0765556i	$-0.975608\pi$
$619$	−28.4698	+	22.7039i	−1.14430	+	0.912546i	−0.147232	+	0.989102i	$0.547036\pi$
$620$	−7.25702	−	1.65637i	−0.291449	−	0.0665213i
$621$		−	18.4853i		−	0.741789i
$622$	2.33319	−	10.2224i	0.0935526	−	0.409881i
$623$	5.50438	+	11.4300i	0.220528	+	0.457931i
$624$	0.985818	+	2.04707i	0.0394643	+	0.0819484i
$625$	−2.44773	+	10.7242i	−0.0979092	+	0.428968i
$626$		−	1.72792i		−	0.0690617i
$627$	5.84957	+	1.33513i	0.233609	+	0.0533198i
$628$	12.1299	−	9.67327i	0.484036	−	0.386005i
$629$	−4.29770	−	18.8295i	−0.171361	−	0.750780i
$630$	−3.23063	+	0.737370i	−0.128711	+	0.0293775i
$631$	19.4352	−	24.3709i	0.773701	−	0.970191i	−0.226291	−	0.974060i	$-0.572660\pi$
$631$	19.4352	−	24.3709i	0.773701	−	0.970191i	0.999993	+	0.00386883i	$0.00123149\pi$
$632$	0.591805	−	0.284998i	0.0235407	−	0.0113366i
$633$	6.48789	+	3.12440i	0.257870	+	0.124184i
$634$	5.02463	+	6.30068i	0.199553	+	0.250232i
$635$	12.2410	+	9.76189i	0.485770	+	0.387389i
$636$	−2.45971	+	5.10764i	−0.0975337	+	0.202531i
$637$	−1.82843			−0.0724449
$638$		0			0
$639$	8.97056			0.354870
$640$	−4.58023	+	9.51094i	−0.181049	+	0.375953i
$641$	17.0431	+	13.5914i	0.673163	+	0.536830i	0.899336	−	0.437257i	$-0.144050\pi$
$641$	17.0431	+	13.5914i	0.673163	+	0.536830i	−0.226173	+	0.974087i	$0.572621\pi$
$642$	−0.981119	−	1.23028i	−0.0387217	−	0.0485555i
$643$	13.9783	+	6.73158i	0.551249	+	0.265468i	0.688707	−	0.725040i	$-0.258179\pi$
$643$	13.9783	+	6.73158i	0.551249	+	0.265468i	−0.137457	+	0.990508i	$0.543893\pi$
$644$	35.6765	−	17.1809i	1.40585	−	0.677023i
$645$	1.65652	−	2.07721i	0.0652255	−	0.0817902i
$646$	−11.6991	+	2.67025i	−0.460296	+	0.105060i
$647$	6.30694	+	27.6325i	0.247952	+	1.08635i	0.933573	+	0.358388i	$0.116674\pi$
$647$	6.30694	+	27.6325i	0.247952	+	1.08635i	−0.685621	+	0.727959i	$0.740469\pi$
$648$	9.28038	−	7.40086i	0.364568	−	0.290733i
$649$	18.0218	+	4.11336i	0.707418	+	0.161464i
$650$		−	3.02944i		−	0.118824i
$651$	1.06133	−	4.64997i	0.0415966	−	0.182247i
$652$	−14.3362	−	29.7695i	−0.561450	−	1.16586i
$653$	0.806097	+	1.67388i	0.0315450	+	0.0655039i	0.916146	−	0.400845i	$-0.131283\pi$
$653$	0.806097	+	1.67388i	0.0315450	+	0.0655039i	−0.884601	+	0.466349i	$0.845569\pi$
$654$	0.0512794	−	0.224670i	0.00200518	−	0.00878528i
$655$		−	1.31371i		−	0.0513308i
$656$	−36.5167	−	8.33471i	−1.42574	−	0.325416i
$657$	−8.84541	+	7.05398i	−0.345092	+	0.275202i
$658$	−1.36675	−	5.98814i	−0.0532816	−	0.233442i
$659$	−11.2953	+	2.57808i	−0.440003	+	0.100428i	−0.436783	−	0.899567i	$-0.643882\pi$
$659$	−11.2953	+	2.57808i	−0.440003	+	0.100428i	−0.00322003	+	0.999995i	$0.501025\pi$
$660$	1.14001	−	1.42952i	0.0443747	−	0.0556441i
$661$	−9.62802	+	4.63661i	−0.374486	+	0.180343i	−0.611654	−	0.791126i	$-0.709495\pi$
$661$	−9.62802	+	4.63661i	−0.374486	+	0.180343i	0.237167	+	0.971469i	$0.423781\pi$
$662$	−0.154582	−	0.0744427i	−0.00600799	−	0.00289330i
$663$	2.28001	+	2.85904i	0.0885483	+	0.111036i
$664$	4.53383	+	3.61561i	0.175947	+	0.140313i
$665$	−7.36325	+	15.2899i	−0.285535	+	0.592919i
$666$	−4.68629			−0.181590
$667$		0			0
$668$	16.1421			0.624558
$669$	−1.58665	+	3.29471i	−0.0613434	+	0.127381i
$670$	−1.83195	−	1.46093i	−0.0707742	−	0.0564406i
$671$	−1.24698	−	1.56366i	−0.0481391	−	0.0603645i
$672$	−4.65943	−	2.24386i	−0.179741	−	0.0865588i
$673$	21.2876	−	10.2516i	0.820575	−	0.395168i	0.0240033	−	0.999712i	$-0.492359\pi$
$673$	21.2876	−	10.2516i	0.820575	−	0.395168i	0.796572	+	0.604544i	$0.206644\pi$
$674$	−4.59673	+	5.76412i	−0.177059	+	0.222026i
$675$	−9.41474	+	2.14885i	−0.362373	+	0.0827094i
$676$	3.92902	+	17.2142i	0.151116	+	0.662083i
$677$	17.2003	−	13.7168i	0.661061	−	0.527179i	−0.234501	−	0.972116i	$-0.575346\pi$
$677$	17.2003	−	13.7168i	0.661061	−	0.527179i	0.895562	+	0.444937i	$0.146774\pi$
$678$	−1.55792	−	0.355584i	−0.0598314	−	0.0136561i
$679$		−	35.3137i		−	1.35522i
$680$	−1.70381	+	7.46488i	−0.0653381	+	0.286265i
$681$	−3.61996	−	7.51691i	−0.138717	−	0.288049i
$682$	1.76637	+	3.66791i	0.0676378	+	0.140451i
$683$	2.88622	−	12.6454i	0.110438	−	0.483861i	−0.889214	−	0.457491i	$-0.848748\pi$
$683$	2.88622	−	12.6454i	0.110438	−	0.483861i	0.999652	−	0.0263700i	$-0.00839480\pi$
$684$		−	31.0294i		−	1.18644i
$685$	11.6991	+	2.67025i	0.447001	+	0.102025i
$686$	−5.49584	+	4.38278i	−0.209832	+	0.167335i
$687$	−1.88815	−	8.27254i	−0.0720375	−	0.315617i
$688$	−18.7602	+	4.28189i	−0.715225	+	0.163246i
$689$	8.53326	−	10.7004i	0.325091	−	0.407652i
$690$	1.18361	−	0.569997i	0.0450593	−	0.0216994i
$691$	−43.2465	−	20.8264i	−1.64517	−	0.792274i	−0.999591	−	0.0285844i	$-0.990900\pi$
$691$	−43.2465	−	20.8264i	−1.64517	−	0.792274i	−0.645583	−	0.763690i	$-0.723386\pi$
$692$	−26.9689	−	33.8180i	−1.02521	−	1.28557i
$693$	−15.1001	−	12.0419i	−0.573604	−	0.457434i
$694$	−2.60330	+	5.40581i	−0.0988200	+	0.205202i
$695$	14.0000			0.531050
$696$		0			0
$697$	−60.2843			−2.28343
$698$	−4.15912	+	8.63650i	−0.157425	+	0.326896i
$699$	−1.39697	−	1.11405i	−0.0528384	−	0.0421372i
$700$	−12.8977	−	16.1732i	−0.487487	−	0.611289i
$701$	19.9229	+	9.59434i	0.752476	+	0.362373i	0.770480	−	0.637465i	$-0.220017\pi$
$701$	19.9229	+	9.59434i	0.752476	+	0.362373i	−0.0180038	+	0.999838i	$0.505731\pi$
$702$	1.64736	−	0.793325i	0.0621754	−	0.0299421i
$703$	−14.9638	+	18.7640i	−0.564369	+	0.707696i
$704$	−9.81857	+	2.24102i	−0.370051	+	0.0844617i
$705$	0.483220	+	2.11713i	0.0181991	+	0.0797356i
$706$	2.25738	−	1.80020i	0.0849577	−	0.0677515i
$707$	−37.6589	−	8.59541i	−1.41631	−	0.323264i
$708$			5.79899i			0.217939i
$709$	0.190893	−	0.836356i	0.00716913	−	0.0314100i	−0.971217	−	0.238197i	$-0.923444\pi$
$709$	0.190893	−	0.836356i	0.00716913	−	0.0314100i	0.978386	+	0.206787i	$0.0663007\pi$
$710$	0.569997	+	1.18361i	0.0213916	+	0.0444201i
$711$	0.508326	+	1.05555i	0.0190637	+	0.0395862i
$712$	1.58272	−	6.93437i	0.0593151	−	0.259876i
$713$		−	31.1716i		−	1.16738i
$714$	−2.28440	−	0.521399i	−0.0854915	−	0.0195129i
$715$	−3.45117	+	2.75222i	−0.129066	+	0.102927i
$716$	4.26608	+	18.6909i	0.159431	+	0.698512i
$717$	−3.36920	+	0.768998i	−0.125825	+	0.0287187i
$718$	−4.66700	+	5.85223i	−0.174171	+	0.218403i
$719$	−7.33581	+	3.53274i	−0.273580	+	0.131749i	−0.565644	−	0.824650i	$-0.691372\pi$
$719$	−7.33581	+	3.53274i	−0.273580	+	0.131749i	0.292064	+	0.956399i	$0.405658\pi$
$720$	−7.64497	−	3.68163i	−0.284911	−	0.137206i
$721$	1.46093	+	1.83195i	0.0544078	+	0.0682252i
$722$	5.50537	+	4.39038i	0.204889	+	0.163393i
$723$	−0.775262	+	1.60985i	−0.0288323	+	0.0598709i
$724$	−26.1716			−0.972659
$725$		0			0
$726$	0.887302			0.0329309
$727$	9.24767	−	19.2030i	0.342977	−	0.712199i	−0.656121	−	0.754656i	$-0.727804\pi$
$727$	9.24767	−	19.2030i	0.342977	−	0.712199i	0.999098	+	0.0424562i	$0.0135183\pi$
$728$	6.41181	+	5.11325i	0.237637	+	0.189510i
$729$	11.3298	+	14.2071i	0.419622	+	0.526189i
$730$	−1.49277	−	0.718882i	−0.0552500	−	0.0266070i
$731$	−27.9035	+	13.4376i	−1.03205	+	0.497008i
$732$	0.391188	−	0.490534i	0.0144587	−	0.0181307i
$733$	48.0199	−	10.9602i	1.77366	−	0.404825i	0.794391	−	0.607407i	$-0.207790\pi$
$733$	48.0199	−	10.9602i	1.77366	−	0.404825i	0.979265	+	0.202582i	$0.0649332\pi$
$734$	1.65908	+	7.26891i	0.0612378	+	0.268300i
$735$	−0.323845	+	0.258258i	−0.0119452	+	0.00952599i
$736$	−32.9516	−	7.52098i	−1.21461	−	0.277227i
$737$		−	13.6569i		−	0.503057i
$738$	−3.25491	+	14.2607i	−0.119815	+	0.524943i
$739$	−4.36967	−	9.07372i	−0.160741	−	0.333782i	0.805006	−	0.593266i	$-0.202162\pi$
$739$	−4.36967	−	9.07372i	−0.160741	−	0.333782i	−0.965747	+	0.259484i	$0.916448\pi$
$740$	3.17330	+	6.58942i	0.116653	+	0.242232i
$741$	1.01117	−	4.43022i	0.0371463	−	0.162748i
$742$			8.76955i			0.321940i
$743$	−12.0337	−	2.74661i	−0.441473	−	0.100763i	−0.00399403	−	0.999992i	$-0.501271\pi$
$743$	−12.0337	−	2.74661i	−0.441473	−	0.100763i	−0.437479	+	0.899229i	$0.644128\pi$
$744$	−2.09069	+	1.66727i	−0.0766486	+	0.0611252i
$745$	−0.483220	−	2.11713i	−0.0177038	−	0.0775655i
$746$	1.48863	−	0.339770i	0.0545026	−	0.0124399i
$747$	−6.44885	+	8.08660i	−0.235951	+	0.295873i
$748$	−19.2030	+	9.24767i	−0.702131	+	0.338128i
$749$	23.3721	+	11.2554i	0.854000	+	0.411265i
$750$	−0.962765	−	1.20727i	−0.0351552	−	0.0440833i
$751$	2.10023	+	1.67488i	0.0766384	+	0.0611171i	0.661060	−	0.750333i	$-0.270107\pi$
$751$	2.10023	+	1.67488i	0.0766384	+	0.0611171i	−0.584421	+	0.811450i	$0.698678\pi$
$752$	6.82409	−	14.1704i	0.248849	−	0.516740i
$753$	2.45584			0.0894959
$754$		0			0
$755$	−14.1421			−0.514685
$756$	5.41716	−	11.2488i	0.197020	−	0.409117i
$757$	−33.2163	−	26.4891i	−1.20727	−	0.962764i	−0.207388	−	0.978259i	$-0.566496\pi$
$757$	−33.2163	−	26.4891i	−1.20727	−	0.962764i	−0.999880	+	0.0154946i	$0.995068\pi$
$758$	−6.96536	−	8.73429i	−0.252993	−	0.317244i
$759$	6.89859	+	3.32218i	0.250403	+	0.120588i
$760$	8.57247	−	4.12828i	0.310956	−	0.149749i
$761$	−20.9480	+	26.2680i	−0.759364	+	0.952213i	−0.999830	−	0.0184449i	$-0.994128\pi$
$761$	−20.9480	+	26.2680i	−0.759364	+	0.952213i	0.240466	+	0.970658i	$0.422700\pi$
$762$	2.61894	−	0.597756i	0.0948742	−	0.0216544i
$763$	0.845355	+	3.70374i	0.0306039	+	0.134084i
$764$	3.84011	−	3.06239i	0.138930	−	0.110793i
$765$	−13.3144	−	3.03894i	−0.481385	−	0.109873i
$766$		−	8.48528i		−	0.306586i
$767$	3.11529	−	13.6490i	0.112487	−	0.492836i
$768$	−0.713592	−	1.48179i	−0.0257495	−	0.0534694i
$769$	−5.68939	−	11.8141i	−0.205165	−	0.426029i	0.772843	−	0.634597i	$-0.218834\pi$
$769$	−5.68939	−	11.8141i	−0.205165	−	0.426029i	−0.978008	+	0.208568i	$0.933120\pi$
$770$	0.629384	−	2.75751i	0.0226814	−	0.0993739i
$771$		−	9.87006i		−	0.355461i
$772$	−19.3026	−	4.40569i	−0.694715	−	0.158564i
$773$	−28.5253	+	22.7482i	−1.02599	+	0.818196i	−0.983501	−	0.180901i	$-0.942099\pi$
$773$	−28.5253	+	22.7482i	−1.02599	+	0.818196i	−0.0424840	+	0.999097i	$0.513527\pi$
$774$	1.67218	+	7.32631i	0.0601053	+	0.263339i
$775$	−15.8760	+	3.62359i	−0.570282	+	0.130163i
$776$	−12.3445	+	15.4795i	−0.443141	+	0.555681i
$777$	−4.22220	+	2.03331i	−0.151471	+	0.0729444i
$778$	−13.7972	−	6.64437i	−0.494653	−	0.238212i
$779$	46.7067	+	58.5683i	1.67344	+	2.09843i
$780$	−1.08266	−	0.863394i	−0.0387655	−	0.0309145i
$781$	−3.32218	+	6.89859i	−0.118877	+	0.246851i
$782$	−15.3137			−0.547617
$783$		0			0
$784$	3.00000			0.107143
$785$	−3.68163	+	7.64497i	−0.131403	+	0.272861i
$786$	−0.176222	−	0.140533i	−0.00628564	−	0.00501263i
$787$	−26.2385	−	32.9020i	−0.935301	−	1.17283i	−0.984736	−	0.174053i	$-0.944314\pi$
$787$	−26.2385	−	32.9020i	−0.935301	−	1.17283i	0.0494353	−	0.998777i	$-0.484258\pi$
$788$	−3.29471	−	1.58665i	−0.117369	−	0.0565221i
$789$	−4.19568	+	2.02053i	−0.149370	+	0.0719329i
$790$	−0.106974	+	0.134141i	−0.00380596	+	0.00477253i
$791$	25.6827	−	5.86190i	0.913171	−	0.208425i
$792$	2.40955	+	10.5569i	0.0856197	+	0.375124i
$793$	−1.18425	+	0.944412i	−0.0420541	+	0.0335370i
$794$	12.3801	+	2.82568i	0.439354	+	0.100280i
$795$		−	3.10051i		−	0.109964i
$796$	−6.70726	+	29.3864i	−0.237732	+	1.04157i
$797$	−24.1847	−	50.2201i	−0.856667	−	1.77889i	−0.571981	−	0.820267i	$-0.693825\pi$
$797$	−24.1847	−	50.2201i	−0.856667	−	1.77889i	−0.284686	−	0.958621i	$-0.591889\pi$
$798$	1.26333	+	2.62334i	0.0447215	+	0.0928652i
$799$	5.63283	−	24.6790i	0.199275	−	0.873082i
$800$			17.6569i			0.624264i
$801$	12.3682	+	2.82297i	0.437010	+	0.0997446i
$802$	−2.37804	+	1.89643i	−0.0839716	+	0.0669651i
$803$	−2.14885	−	9.41474i	−0.0758313	−	0.332239i
$804$	4.17686	−	0.953340i	0.147306	−	0.0336217i
$805$	−13.5028	+	16.9320i	−0.475912	+	0.596775i
$806$	2.77792	−	1.33778i	0.0978481	−	0.0471212i
$807$	−7.26080	−	3.49661i	−0.255592	−	0.123087i
$808$	13.5028	+	16.9320i	0.475028	+	0.595666i
$809$	−15.8589	−	12.6470i	−0.557569	−	0.444646i	0.303721	−	0.952761i	$-0.401771\pi$
$809$	−15.8589	−	12.6470i	−0.557569	−	0.444646i	−0.861289	+	0.508115i	$0.830342\pi$
$810$	−1.34526	+	2.79346i	−0.0472676	+	0.0981521i
$811$	−5.17157			−0.181598			−0.0907992	−	0.995869i	$-0.528942\pi$
$811$	−5.17157			−0.181598			−0.0907992	+	0.995869i	$0.528942\pi$
$812$		0			0
$813$	6.02944			0.211462
$814$	1.73553	−	3.60388i	0.0608305	−	0.126316i
$815$	14.1285	+	11.2671i	0.494901	+	0.394670i
$816$	−3.74094	−	4.69099i	−0.130959	−	0.164217i
$817$	34.6740	+	16.6981i	1.21309	+	0.584194i
$818$	5.58692	−	2.69052i	0.195342	−	0.0940717i
$819$	−9.12005	+	11.4362i	−0.318680	+	0.399612i
$820$	22.2561	−	5.07980i	0.777216	−	0.177394i
$821$	3.44580	+	15.0970i	0.120259	+	0.526890i	0.998789	+	0.0492022i	$0.0156679\pi$
$821$	3.44580	+	15.0970i	0.120259	+	0.526890i	−0.878530	+	0.477688i	$0.841475\pi$
$822$	1.60969	−	1.28369i	0.0561445	−	0.0447737i
$823$	2.22700	+	0.508298i	0.0776283	+	0.0177182i	0.261159	−	0.965296i	$-0.415895\pi$
$823$	2.22700	+	0.508298i	0.0776283	+	0.0177182i	−0.183530	+	0.983014i	$0.558753\pi$
$824$		−	1.31371i		−	0.0457652i
$825$	0.890084	−	3.89971i	0.0309887	−	0.135771i
$826$	3.89218	+	8.08220i	0.135426	+	0.281216i
$827$	−5.68410	−	11.8031i	−0.197655	−	0.410436i	0.778458	−	0.627696i	$-0.216002\pi$
$827$	−5.68410	−	11.8031i	−0.197655	−	0.410436i	−0.976114	+	0.217261i	$0.930288\pi$
$828$	8.81138	−	38.6052i	0.306217	−	1.34162i
$829$		−	9.79899i		−	0.340333i	−0.985415	−	0.170166i	$-0.945569\pi$
$829$		−	9.79899i		−	0.340333i	0.985415	−	0.170166i	$-0.0544306\pi$
$830$	−1.47674	−	0.337057i	−0.0512584	−	0.0116994i
$831$	−1.72082	+	1.37231i	−0.0596946	+	0.0476048i
$832$	1.69726	+	7.43618i	0.0588419	+	0.257803i
$833$	4.70737	−	1.07443i	0.163101	−	0.0372267i
$834$	1.49764	−	1.87798i	0.0518589	−	0.0650290i
$835$	−7.95414	+	3.83051i	−0.275264	+	0.132560i
$836$	23.8624	+	11.4915i	0.825299	+	0.397443i
$837$	−6.12792	−	7.68417i	−0.211812	−	0.265604i
$838$	−8.57713	−	6.84003i	−0.296292	−	0.236285i
$839$	−9.57628	+	19.8853i	−0.330610	+	0.686518i	−0.998322	−	0.0579009i	$-0.981559\pi$
$839$	−9.57628	+	19.8853i	−0.330610	+	0.686518i	0.667713	+	0.744419i	$0.267274\pi$
$840$	1.85786			0.0641024
$841$		0			0
$842$	−10.4020			−0.358477
$843$	−0.354151	+	0.735401i	−0.0121976	+	0.0253286i
$844$	24.8519	+	19.8187i	0.855438	+	0.682189i
$845$	−6.02095	−	7.55003i	−0.207127	−	0.259729i
$846$	−5.53387	−	2.66497i	−0.190258	−	0.0916237i
$847$	−13.1788	+	6.34660i	−0.452831	+	0.218072i
$848$	−14.0010	+	17.5567i	−0.480796	+	0.602899i
$849$	−0.138572	+	0.0316282i	−0.00475578	+	0.00108548i
$850$	1.78017	+	7.79942i	0.0610592	+	0.267518i
$851$	−23.9455	+	19.0959i	−0.820840	+	0.654598i
$852$	−2.34180	−	0.534500i	−0.0802286	−	0.0183117i
$853$			10.9706i			0.375625i	0.982205	+	0.187812i	$0.0601397\pi$
$853$			10.9706i			0.375625i	−0.982205	+	0.187812i	$0.939860\pi$
$854$	0.215971	−	0.946229i	0.00739036	−	0.0323793i
$855$	7.36325	+	15.2899i	0.251818	+	0.522905i
$856$	−6.31047	−	13.1038i	−0.215688	−	0.447880i
$857$	2.63207	−	11.5319i	0.0899099	−	0.393921i	−0.909870	−	0.414893i	$-0.863819\pi$
$857$	2.63207	−	11.5319i	0.0899099	−	0.393921i	0.999780	+	0.0209721i	$0.00667612\pi$
$858$			0.757359i			0.0258558i
$859$	5.58431	+	1.27458i	0.190534	+	0.0434882i	0.316723	−	0.948518i	$-0.397417\pi$
$859$	5.58431	+	1.27458i	0.190534	+	0.0434882i	−0.126189	+	0.992006i	$0.540275\pi$
$860$	9.16926	−	7.31224i	0.312669	−	0.249345i
$861$	3.25491	+	14.2607i	0.110927	+	0.486003i
$862$	−3.36920	+	0.768998i	−0.114755	+	0.0261922i
$863$	28.1273	−	35.2705i	0.957465	−	1.20062i	−0.0221536	−	0.999755i	$-0.507052\pi$
$863$	28.1273	−	35.2705i	0.957465	−	1.20062i	0.979618	−	0.200868i	$-0.0643763\pi$
$864$	−9.60149	+	4.62384i	−0.326649	+	0.157306i
$865$	21.3141	+	10.2643i	0.724701	+	0.348997i
$866$	−3.77765	−	4.73702i	−0.128370	−	0.160970i
$867$	−2.04466	−	1.63057i	−0.0694404	−	0.0553769i
$868$	9.13491	−	18.9688i	0.310059	−	0.643844i
$869$	−1.00000			−0.0339227
$870$		0			0
$871$	−10.3431			−0.350464
$872$	0.924147	−	1.91901i	0.0312956	−	0.0649859i
$873$	−27.6094	−	22.0177i	−0.934436	−	0.745187i
$874$	11.8647	+	14.8778i	0.401328	+	0.503250i
$875$	22.9349	+	11.0449i	0.775342	+	0.373385i
$876$	2.72943	−	1.31442i	0.0922188	−	0.0444103i
$877$	−5.52279	+	6.92536i	−0.186491	+	0.233853i	−0.866284	−	0.499551i	$-0.833498\pi$
$877$	−5.52279	+	6.92536i	−0.186491	+	0.233853i	0.679793	+	0.733404i	$0.262070\pi$
$878$	−4.70737	+	1.07443i	−0.158866	+	0.0362601i
$879$	0.337057	+	1.47674i	0.0113686	+	0.0498093i
$880$	5.66252	−	4.51571i	0.190884	−	0.152225i
$881$	13.6490	+	3.11529i	0.459846	+	0.104957i	0.446167	−	0.894950i	$-0.352789\pi$
$881$	13.6490	+	3.11529i	0.459846	+	0.104957i	0.0136788	+	0.999906i	$0.495646\pi$
$882$		−	1.17157i		−	0.0394489i
$883$	−10.3308	+	45.2624i	−0.347661	+	1.52320i	0.434815	+	0.900520i	$0.356814\pi$
$883$	−10.3308	+	45.2624i	−0.347661	+	1.52320i	−0.782476	+	0.622681i	$0.786043\pi$
$884$	7.00381	+	14.5436i	0.235564	+	0.489153i
$885$	−1.37609	−	2.85749i	−0.0462569	−	0.0960534i
$886$	3.28653	−	14.3992i	0.110413	−	0.483752i
$887$		−	36.8995i		−	1.23896i	−0.785011	−	0.619482i	$-0.787343\pi$
$887$		−	36.8995i		−	1.23896i	0.785011	−	0.619482i	$-0.212657\pi$
$888$	2.56154	+	0.584655i	0.0859597	+	0.0196197i
$889$	−34.6228	+	27.6108i	−1.16121	+	0.926036i
$890$	0.413414	+	1.81128i	0.0138577	+	0.0607144i
$891$	−17.6180	+	4.02119i	−0.590225	+	0.134715i
$892$	−10.0645	+	12.6204i	−0.336983	+	0.422563i
$893$	−28.3407	+	13.6482i	−0.948387	+	0.456719i
$894$	−0.335686	−	0.161658i	−0.0112270	−	0.00540664i
$895$	−6.53747	−	8.19772i	−0.218523	−	0.274020i
$896$	−23.3438	−	18.6161i	−0.779862	−	0.621919i
$897$	2.51609	−	5.22471i	0.0840097	−	0.174448i
$898$	0.426407			0.0142294
$899$		0			0
$900$	−20.6863			−0.689543
$901$	−15.6815	+	32.5629i	−0.522426	+	1.08483i
$902$	−9.76139	−	7.78445i	−0.325019	−	0.259194i
$903$	4.68535	+	5.87524i	0.155919	+	0.195516i
$904$	−13.3069	−	6.40827i	−0.442581	−	0.213136i
$905$	12.8962	−	6.21049i	0.428684	−	0.206444i
$906$	−1.51284	+	1.89704i	−0.0502607	+	0.0630250i
$907$	−33.4247	+	7.62897i	−1.10985	+	0.253316i	−0.737882	−	0.674930i	$-0.764174\pi$
$907$	−33.4247	+	7.62897i	−1.10985	+	0.253316i	−0.371967	+	0.928246i	$0.621317\pi$
$908$	−8.19510	−	35.9051i	−0.271964	−	1.19155i
$909$	−30.2001	+	24.0838i	−1.00168	+	0.798809i
$910$	−2.08843	−	0.476670i	−0.0692307	−	0.0158015i
$911$		−	46.5563i		−	1.54248i	−0.636544	−	0.771240i	$-0.719637\pi$
$911$		−	46.5563i		−	1.54248i	0.636544	−	0.771240i	$-0.280363\pi$
$912$	−1.65908	+	7.26891i	−0.0549377	+	0.240698i
$913$	−3.83051	−	7.95414i	−0.126771	−	0.263244i
$914$	−6.28493	−	13.0508i	−0.207887	−	0.431682i
$915$	−0.0763571	+	0.334542i	−0.00252429	+	0.0110596i
$916$		−	37.4558i		−	1.23758i
$917$	3.62257	+	0.826827i	0.119628	+	0.0273042i
$918$	−3.77502	+	3.01048i	−0.124594	+	0.0993605i
$919$	4.48205	+	19.6371i	0.147849	+	0.647769i	0.993481	+	0.114002i	$0.0363670\pi$
$919$	4.48205	+	19.6371i	0.147849	+	0.647769i	−0.845631	+	0.533767i	$0.820776\pi$
$920$	11.8377	−	2.70188i	0.390278	−	0.0890783i
$921$	−4.36443	+	5.47282i	−0.143813	+	0.180336i
$922$	−5.22471	+	2.51609i	−0.172067	+	0.0828629i
$923$	5.22471	+	2.51609i	0.171973	+	0.0828180i
$924$	3.22442	+	4.04330i	0.106076	+	0.133015i
$925$	12.5093	+	9.97584i	0.411303	+	0.328003i
$926$	−4.67273	+	9.70303i	−0.153556	+	0.318861i
$927$	2.34315			0.0769590
$928$		0			0
$929$	41.3137			1.35546			0.677729	−	0.735311i	$-0.262964\pi$
$929$	41.3137			1.35546			0.677729	+	0.735311i	$0.262964\pi$
$930$	0.303061	−	0.629313i	0.00993777	−	0.0206360i
$931$	−4.69099	−	3.74094i	−0.153741	−	0.122604i
$932$	−4.91765	−	6.16654i	−0.161083	−	0.201992i
$933$	−9.44691	−	4.54939i	−0.309278	−	0.148940i
$934$	12.0748	−	5.81492i	0.395100	−	0.190270i
$935$	7.26793	−	9.11370i	0.237687	−	0.298050i
$936$	7.99539	−	1.82490i	0.261338	−	0.0596486i
$937$	6.37020	+	27.9097i	0.208105	+	0.911769i	0.965826	+	0.259190i	$0.0834557\pi$
$937$	6.37020	+	27.9097i	0.208105	+	0.911769i	−0.757721	+	0.652579i	$0.773687\pi$
$938$	5.18152	−	4.13213i	0.169183	−	0.134919i
$939$	−1.68460	−	0.384499i	−0.0549748	−	0.0125476i
$940$			9.58579i			0.312654i
$941$	5.02852	−	22.0314i	0.163925	−	0.718203i	−0.824421	−	0.565978i	$-0.808499\pi$
$941$	5.02852	−	22.0314i	0.163925	−	0.718203i	0.988346	−	0.152226i	$-0.0486440\pi$
$942$	0.631667	+	1.31167i	0.0205808	+	0.0427365i
$943$	41.4784	+	86.1308i	1.35072	+	2.80480i
$944$	−5.11143	+	22.3946i	−0.166363	+	0.728884i
$945$			6.82843i			0.222129i
$946$	−6.25340	−	1.42730i	−0.203315	−	0.0464054i
$947$	30.7923	−	24.5560i	1.00061	−	0.797963i	0.0211898	−	0.999775i	$-0.493255\pi$
$947$	30.7923	−	24.5560i	1.00061	−	0.797963i	0.979424	+	0.201812i	$0.0646832\pi$
$948$	−0.0698067	−	0.305843i	−0.00226722	−	0.00993332i
$949$	−7.13034	+	1.62745i	−0.231461	+	0.0528294i
$950$	6.19819	−	7.77228i	0.201096	−	0.252166i
$951$	7.26080	−	3.49661i	0.235447	−	0.113385i
$952$	−19.5122	−	9.39656i	−0.632392	−	0.304544i
$953$	6.00260	+	7.52702i	0.194443	+	0.243824i	0.869490	−	0.493951i	$-0.164448\pi$
$953$	6.00260	+	7.52702i	0.194443	+	0.243824i	−0.675046	+	0.737775i	$0.735876\pi$
$954$	6.85631	+	5.46773i	0.221981	+	0.177024i
$955$	−1.16554	+	2.42027i	−0.0377159	+	0.0783179i
$956$	−15.2548			−0.493377
$957$		0			0
$958$	−5.34315			−0.172629
$959$	−14.7265	+	30.5799i	−0.475544	+	0.987476i
$960$	1.35094	+	1.07734i	0.0436015	+	0.0347711i
$961$	8.99472	+	11.2790i	0.290152	+	0.363839i
$962$	−2.72943	−	1.31442i	−0.0880003	−	0.0423787i
$963$	23.3721	−	11.2554i	0.753157	−	0.362701i
$964$	−4.91765	+	6.16654i	−0.158387	+	0.198611i
$965$	10.5569	−	2.40955i	0.339840	−	0.0775662i
$966$	0.826827	+	3.62257i	0.0266027	+	0.116554i
$967$	20.9197	−	16.6829i	0.672734	−	0.536487i	−0.226470	−	0.974018i	$-0.572718\pi$
$967$	20.9197	−	16.6829i	0.672734	−	0.536487i	0.899203	+	0.437531i	$0.144147\pi$
$968$	7.99539	+	1.82490i	0.256982	+	0.0586544i
$969$			12.0000i			0.385496i
$970$	1.15078	−	5.04191i	0.0369494	−	0.161886i
$971$	−1.88442	−	3.91304i	−0.0604739	−	0.125575i	0.868541	−	0.495617i	$-0.165058\pi$
$971$	−1.88442	−	3.91304i	−0.0604739	−	0.125575i	−0.929015	+	0.370041i	$0.879344\pi$
$972$	−8.20547	−	17.0388i	−0.263191	−	0.546521i
$973$	−8.81138	+	38.6052i	−0.282480	+	1.23763i
$974$			11.7990i			0.378064i
$975$	−2.95348	−	0.674113i	−0.0945872	−	0.0215889i
$976$	1.94307	−	1.54955i	0.0621962	−	0.0495998i
$977$	−9.30770	−	40.7797i	−0.297780	−	1.30466i	−0.873425	−	0.486959i	$-0.838106\pi$
$977$	−9.30770	−	40.7797i	−0.297780	−	1.30466i	0.575645	−	0.817700i	$-0.304751\pi$
$978$	3.02277	−	0.689927i	0.0966575	−	0.0220614i
$979$	−6.75141	+	8.46601i	−0.215776	+	0.270575i
$980$	−1.64736	+	0.793325i	−0.0526229	+	0.0253418i
$981$	3.42277	+	1.64832i	0.109281	+	0.0526268i
$982$	−3.29469	−	4.13141i	−0.105138	−	0.131839i
$983$	24.9170	+	19.8707i	0.794729	+	0.633775i	0.934321	−	0.356434i	$-0.116007\pi$
$983$	24.9170	+	19.8707i	0.794729	+	0.633775i	−0.139591	+	0.990209i	$0.544579\pi$
$984$	3.55828	−	7.38885i	0.113434	−	0.235548i
$985$	2.00000			0.0637253
$986$		0			0
$987$	−6.14214			−0.195506
$988$	8.70322	−	18.0724i	0.276886	−	0.574960i
$989$	38.3979	+	30.6213i	1.22098	+	0.973700i
$990$	−1.76350	−	2.21135i	−0.0560476	−	0.0702814i
$991$	−6.46136	−	3.11163i	−0.205252	−	0.0988441i	0.328434	−	0.944527i	$-0.393479\pi$
$991$	−6.46136	−	3.11163i	−0.205252	−	0.0988441i	−0.533686	+	0.845683i	$0.679193\pi$
$992$	−16.1909	+	7.79713i	−0.514062	+	0.247559i
$993$	−0.106974	+	0.134141i	−0.00339472	+	0.00425684i
$994$	−3.62257	+	0.826827i	−0.114901	+	0.0262254i
$995$	−3.66832	−	16.0720i	−0.116294	−	0.509515i
$996$	2.16532	−	1.72679i	0.0686109	−	0.0547154i
$997$	−27.5751	−	6.29384i	−0.873313	−	0.199328i	−0.237703	−	0.971338i	$-0.576394\pi$
$997$	−27.5751	−	6.29384i	−0.873313	−	0.199328i	−0.635610	+	0.772010i	$0.719252\pi$
$998$		−	6.20101i		−	0.196290i
$999$	−2.14885	+	9.41474i	−0.0679867	+	0.297869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.k.651.2		24
29.2	odd	28		841.2.d.f.574.1		12
29.3	odd	28		841.2.a.d.1.1		2
29.4	even	14	inner	841.2.e.k.63.2		24
29.5	even	14	inner	841.2.e.k.267.3		24
29.6	even	14	inner	841.2.e.k.236.2		24
29.7	even	7		841.2.b.a.840.2		4
29.8	odd	28		841.2.d.j.571.1		12
29.9	even	14	inner	841.2.e.k.270.2		24
29.10	odd	28		841.2.d.j.778.2		12
29.11	odd	28		841.2.d.f.645.2		12
29.12	odd	4		841.2.d.j.190.1		12
29.13	even	14	inner	841.2.e.k.196.3		24
29.14	odd	28		841.2.d.f.605.2		12
29.15	odd	28		841.2.d.j.605.1		12
29.16	even	7	inner	841.2.e.k.196.2		24
29.17	odd	4		841.2.d.f.190.2		12
29.18	odd	28		841.2.d.j.645.1		12
29.19	odd	28		841.2.d.f.778.1		12
29.20	even	7	inner	841.2.e.k.270.3		24
29.21	odd	28		841.2.d.f.571.2		12
29.22	even	14		841.2.b.a.840.3		4
29.23	even	7	inner	841.2.e.k.236.3		24
29.24	even	7	inner	841.2.e.k.267.2		24
29.25	even	7	inner	841.2.e.k.63.3		24
29.26	odd	28		29.2.a.a.1.2	✓	2
29.27	odd	28		841.2.d.j.574.2		12
29.28	even	2	inner	841.2.e.k.651.3		24
87.26	even	28		261.2.a.d.1.1		2
87.32	even	28		7569.2.a.c.1.2		2
116.55	even	28		464.2.a.h.1.2		2
145.84	odd	28		725.2.a.b.1.1		2
145.113	even	28		725.2.b.b.349.2		4
145.142	even	28		725.2.b.b.349.3		4
203.55	even	28		1421.2.a.j.1.2		2
232.171	even	28		1856.2.a.w.1.1		2
232.229	odd	28		1856.2.a.r.1.2		2
319.142	even	28		3509.2.a.j.1.1		2
348.287	odd	28		4176.2.a.bq.1.1		2
377.142	odd	28		4901.2.a.g.1.1		2
435.374	even	28		6525.2.a.o.1.2		2
493.84	odd	28		8381.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.2	✓	2	29.26	odd	28
261.2.a.d.1.1		2	87.26	even	28
464.2.a.h.1.2		2	116.55	even	28
725.2.a.b.1.1		2	145.84	odd	28
725.2.b.b.349.2		4	145.113	even	28
725.2.b.b.349.3		4	145.142	even	28
841.2.a.d.1.1		2	29.3	odd	28
841.2.b.a.840.2		4	29.7	even	7
841.2.b.a.840.3		4	29.22	even	14
841.2.d.f.190.2		12	29.17	odd	4
841.2.d.f.571.2		12	29.21	odd	28
841.2.d.f.574.1		12	29.2	odd	28
841.2.d.f.605.2		12	29.14	odd	28
841.2.d.f.645.2		12	29.11	odd	28
841.2.d.f.778.1		12	29.19	odd	28
841.2.d.j.190.1		12	29.12	odd	4
841.2.d.j.571.1		12	29.8	odd	28
841.2.d.j.574.2		12	29.27	odd	28
841.2.d.j.605.1		12	29.15	odd	28
841.2.d.j.645.1		12	29.18	odd	28
841.2.d.j.778.2		12	29.10	odd	28
841.2.e.k.63.2		24	29.4	even	14	inner
841.2.e.k.63.3		24	29.25	even	7	inner
841.2.e.k.196.2		24	29.16	even	7	inner
841.2.e.k.196.3		24	29.13	even	14	inner
841.2.e.k.236.2		24	29.6	even	14	inner
841.2.e.k.236.3		24	29.23	even	7	inner
841.2.e.k.267.2		24	29.24	even	7	inner
841.2.e.k.267.3		24	29.5	even	14	inner
841.2.e.k.270.2		24	29.9	even	14	inner
841.2.e.k.270.3		24	29.20	even	7	inner
841.2.e.k.651.2		24	1.1	even	1	trivial
841.2.e.k.651.3		24	29.28	even	2	inner
1421.2.a.j.1.2		2	203.55	even	28
1856.2.a.r.1.2		2	232.229	odd	28
1856.2.a.w.1.1		2	232.171	even	28
3509.2.a.j.1.1		2	319.142	even	28
4176.2.a.bq.1.1		2	348.287	odd	28
4901.2.a.g.1.1		2	377.142	odd	28
6525.2.a.o.1.2		2	435.374	even	28
7569.2.a.c.1.2		2	87.32	even	28
8381.2.a.e.1.2		2	493.84	odd	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.179721 + 0.373194i) q^{2} +(0.323845 + 0.258258i) q^{3} +(1.14001 + 1.42952i) q^{4} +(-0.900969 - 0.433884i) q^{5} +(-0.154582 + 0.0744427i) q^{6} +(1.76350 - 2.21135i) q^{7} +(-1.54603 + 0.352871i) q^{8} +(-0.629384 - 2.75751i) q^{9} +O(q^{10})\)	\(q+(-0.179721 + 0.373194i) q^{2} +(0.323845 + 0.258258i) q^{3} +(1.14001 + 1.42952i) q^{4} +(-0.900969 - 0.433884i) q^{5} +(-0.154582 + 0.0744427i) q^{6} +(1.76350 - 2.21135i) q^{7} +(-1.54603 + 0.352871i) q^{8} +(-0.629384 - 2.75751i) q^{9} +(0.323845 - 0.258258i) q^{10} +(2.35368 + 0.537213i) q^{11} +0.757359i q^{12} +(0.406863 - 1.78258i) q^{13} +(0.508326 + 1.05555i) q^{14} +(-0.179721 - 0.373194i) q^{15} +(-0.667563 + 2.92478i) q^{16} +4.82843i q^{17} +(1.14220 + 0.260699i) q^{18} +(4.69099 - 3.74094i) q^{19} +(-0.406863 - 1.78258i) q^{20} +(1.14220 - 0.260699i) q^{21} +(-0.623490 + 0.781831i) q^{22} +(6.89859 - 3.32218i) q^{23} +(-0.591805 - 0.284998i) q^{24} +(-2.49396 - 3.12733i) q^{25} +(0.592127 + 0.472206i) q^{26} +(1.04749 - 2.17513i) q^{27} +5.17157 q^{28} +0.171573 q^{30} +(1.76637 - 3.66791i) q^{31} +(-3.45117 - 2.75222i) q^{32} +(0.623490 + 0.781831i) q^{33} +(-1.80194 - 0.867767i) q^{34} +(-2.54832 + 1.22721i) q^{35} +(3.22442 - 4.04330i) q^{36} +(-3.89971 + 0.890084i) q^{37} +(0.553027 + 2.42297i) q^{38} +(0.592127 - 0.472206i) q^{39} +(1.54603 + 0.352871i) q^{40} +12.4853i q^{41} +(-0.107985 + 0.473114i) q^{42} +(2.78302 + 5.77901i) q^{43} +(1.91526 + 3.97707i) q^{44} +(-0.629384 + 2.75751i) q^{45} +3.17157i q^{46} +(-5.11120 - 1.16660i) q^{47} +(-0.971536 + 0.774774i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.61531 - 0.368685i) q^{50} +(-1.24698 + 1.56366i) q^{51} +(3.01207 - 1.45054i) q^{52} +(6.74401 + 3.24774i) q^{53} +(0.623490 + 0.781831i) q^{54} +(-1.88751 - 1.50524i) q^{55} +(-1.94609 + 4.04110i) q^{56} +2.48528 q^{57} +7.65685 q^{59} +(0.328606 - 0.682357i) q^{60} +(-0.647690 - 0.516516i) q^{61} +(1.05139 + 1.31840i) q^{62} +(-7.20775 - 3.47107i) q^{63} +(-3.75846 + 1.80998i) q^{64} +(-1.14001 + 1.42952i) q^{65} +(-0.403828 + 0.0921712i) q^{66} +(-1.25877 - 5.51503i) q^{67} +(-6.90234 + 5.50443i) q^{68} +(3.09205 + 0.705741i) q^{69} -1.17157i q^{70} +(-0.705741 + 3.09205i) q^{71} +(1.94609 + 4.04110i) q^{72} +(-1.73553 - 3.60388i) q^{73} +(0.368685 - 1.61531i) q^{74} -1.65685i q^{75} +(10.6955 + 2.44118i) q^{76} +(5.33868 - 4.25745i) q^{77} +(0.0698067 + 0.305843i) q^{78} +(-0.403828 + 0.0921712i) q^{79} +(1.87047 - 2.34549i) q^{80} +(-6.74401 + 3.24774i) q^{81} +(-4.65943 - 2.24386i) q^{82} +(-2.28001 - 2.85904i) q^{83} +(1.67479 + 1.33560i) q^{84} +(2.09498 - 4.35026i) q^{85} -2.65685 q^{86} -3.82843 q^{88} +(-1.94609 + 4.04110i) q^{89} +(-0.915973 - 0.730464i) q^{90} +(-3.22442 - 4.04330i) q^{91} +(12.6136 + 6.07437i) q^{92} +(1.51930 - 0.731654i) q^{93} +(1.35395 - 1.69780i) q^{94} +(-5.84957 + 1.33513i) q^{95} +(-0.406863 - 1.78258i) q^{96} +(9.76139 - 7.78445i) q^{97} +(0.403828 + 0.0921712i) q^{98} -6.82843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

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