LMFDB - Embedded newform 960.2.cn.a.731.86

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			731.86
Character	$\chi$	$=$	960.731
Dual form			960.2.cn.a.851.86

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711347 + 1.22229i) q^{2} +(1.67348 - 0.446620i) q^{3} +(-0.987971 + 1.73894i) q^{4} +(0.980785 + 0.195090i) q^{5} +(1.73632 + 1.72777i) q^{6} +(2.69446 + 1.11608i) q^{7} +(-2.82827 + 0.0294054i) q^{8} +(2.60106 - 1.49482i) q^{9} +O(q^{10})$	\(q+(0.711347 + 1.22229i) q^{2} +(1.67348 - 0.446620i) q^{3} +(-0.987971 + 1.73894i) q^{4} +(0.980785 + 0.195090i) q^{5} +(1.73632 + 1.72777i) q^{6} +(2.69446 + 1.11608i) q^{7} +(-2.82827 + 0.0294054i) q^{8} +(2.60106 - 1.49482i) q^{9} +(0.459222 + 1.33758i) q^{10} +(4.93398 - 3.29678i) q^{11} +(-0.876703 + 3.35133i) q^{12} +(-0.992447 - 4.98937i) q^{13} +(0.552523 + 4.08732i) q^{14} +(1.72845 - 0.111559i) q^{15} +(-2.04783 - 3.43605i) q^{16} +(-3.61874 - 3.61874i) q^{17} +(3.67735 + 2.11591i) q^{18} +(1.36912 + 6.88305i) q^{19} +(-1.30824 + 1.51278i) q^{20} +(5.00758 + 0.664339i) q^{21} +(7.53938 + 3.68558i) q^{22} +(-0.0484528 + 0.0200698i) q^{23} +(-4.71992 + 1.31237i) q^{24} +(0.923880 + 0.382683i) q^{25} +(5.39246 - 4.76222i) q^{26} +(3.68520 - 3.66323i) q^{27} +(-4.60285 + 3.58285i) q^{28} +(-3.42952 + 5.13264i) q^{29} +(1.36589 + 2.03331i) q^{30} -7.39786 q^{31} +(2.74312 - 4.94725i) q^{32} +(6.78450 - 7.72070i) q^{33} +(1.84896 - 6.99731i) q^{34} +(2.42495 + 1.62030i) q^{35} +(0.0296266 + 5.99993i) q^{36} +(-6.78702 - 1.35002i) q^{37} +(-7.43914 + 6.56970i) q^{38} +(-3.88919 - 7.90635i) q^{39} +(-2.77967 - 0.522929i) q^{40} +(2.61970 + 6.32451i) q^{41} +(2.75012 + 6.59328i) q^{42} +(-10.4939 + 7.01179i) q^{43} +(0.858273 + 11.8370i) q^{44} +(2.84271 - 0.958654i) q^{45} +(-0.0589979 - 0.0449467i) q^{46} +(1.05283 - 1.05283i) q^{47} +(-4.96160 - 4.83555i) q^{48} +(1.06473 + 1.06473i) q^{49} +(0.189450 + 1.40147i) q^{50} +(-7.67208 - 4.43968i) q^{51} +(9.65672 + 3.20354i) q^{52} +(0.954072 + 1.42787i) q^{53} +(7.09898 + 1.89855i) q^{54} +(5.48234 - 2.27086i) q^{55} +(-7.65349 - 3.07735i) q^{56} +(5.36531 + 10.9072i) q^{57} +(-8.71313 - 0.540770i) q^{58} +(0.480276 - 2.41451i) q^{59} +(-1.51367 + 3.11590i) q^{60} +(-4.76601 + 7.13284i) q^{61} +(-5.26245 - 9.04231i) q^{62} +(8.67679 - 1.12473i) q^{63} +(7.99827 - 0.166333i) q^{64} -5.08711i q^{65} +(14.2630 + 2.80051i) q^{66} +(0.361832 + 0.241769i) q^{67} +(9.86798 - 2.71756i) q^{68} +(-0.0721212 + 0.0552264i) q^{69} +(-0.255491 + 4.11658i) q^{70} +(-0.152345 + 0.367794i) q^{71} +(-7.31256 + 4.30424i) q^{72} +(2.62190 + 6.32982i) q^{73} +(-3.17781 - 9.25601i) q^{74} +(1.71701 + 0.227789i) q^{75} +(-13.3219 - 4.41943i) q^{76} +(16.9739 - 3.37631i) q^{77} +(6.89727 - 10.3779i) q^{78} +(0.318893 - 0.318893i) q^{79} +(-1.33814 - 3.76953i) q^{80} +(4.53104 - 7.77623i) q^{81} +(-5.86685 + 7.70094i) q^{82} +(-0.150213 + 0.0298791i) q^{83} +(-6.10260 + 8.05154i) q^{84} +(-2.84322 - 4.25518i) q^{85} +(-16.0352 - 7.83872i) q^{86} +(-3.44689 + 10.1210i) q^{87} +(-13.8577 + 9.46928i) q^{88} +(-0.898989 + 2.17035i) q^{89} +(3.19390 + 2.79267i) q^{90} +(2.89443 - 14.5513i) q^{91} +(0.0129698 - 0.104085i) q^{92} +(-12.3802 + 3.30404i) q^{93} +(2.03579 + 0.537935i) q^{94} +7.01790i q^{95} +(2.38101 - 9.50425i) q^{96} +9.92918i q^{97} +(-0.544012 + 2.05879i) q^{98} +(7.90549 - 15.9505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	0.711347	+	1.22229i	0.502998	+	0.864287i
$2$	0.711347	+	1.22229i	0.502998	+	0.864287i
$3$	1.67348	−	0.446620i	0.966183	−	0.257856i
$3$	1.67348	−	0.446620i	0.966183	−	0.257856i
$4$	−0.987971	+	1.73894i	−0.493986	+	0.869470i
$5$	0.980785	+	0.195090i	0.438621	+	0.0872470i
$5$	0.980785	+	0.195090i	0.438621	+	0.0872470i
$6$	1.73632	+	1.72777i	0.708850	+	0.705359i
$7$	2.69446	+	1.11608i	1.01841	+	0.421839i	0.828516	−	0.559965i	$-0.189186\pi$
$7$	2.69446	+	1.11608i	1.01841	+	0.421839i	0.189894	+	0.981805i	$0.439186\pi$
$8$	−2.82827	+	0.0294054i	−0.999946	+	0.0103964i
$9$	2.60106	−	1.49482i	0.867020	−	0.498273i
$10$	0.459222	+	1.33758i	0.145219	+	0.422979i
$11$	4.93398	−	3.29678i	1.48765	−	0.994016i	0.495548	−	0.868580i	$-0.334967\pi$
$11$	4.93398	−	3.29678i	1.48765	−	0.994016i	0.992102	−	0.125435i	$-0.0400328\pi$
$12$	−0.876703	+	3.35133i	−0.253082	+	0.967445i
$13$	−0.992447	−	4.98937i	−0.275255	−	1.38380i	−0.832763	−	0.553630i	$-0.813242\pi$
$13$	−0.992447	−	4.98937i	−0.275255	−	1.38380i	0.557508	−	0.830172i	$-0.311758\pi$
$14$	0.552523	+	4.08732i	0.147668	+	1.09238i
$15$	1.72845	−	0.111559i	0.446285	−	0.0288044i
$16$	−2.04783	−	3.43605i	−0.511956	−	0.859011i
$17$	−3.61874	−	3.61874i	−0.877673	−	0.877673i	0.115621	−	0.993293i	$-0.463114\pi$
$17$	−3.61874	−	3.61874i	−0.877673	−	0.877673i	−0.993293	+	0.115621i	$0.963114\pi$
$18$	3.67735	+	2.11591i	0.866761	+	0.498724i
$19$	1.36912	+	6.88305i	0.314099	+	1.57908i	0.738914	+	0.673800i	$0.235339\pi$
$19$	1.36912	+	6.88305i	0.314099	+	1.57908i	−0.424815	+	0.905280i	$0.639661\pi$
$20$	−1.30824	+	1.51278i	−0.292531	+	0.338269i
$21$	5.00758	+	0.664339i	1.09274	+	0.144971i
$22$	7.53938	+	3.68558i	1.60740	+	0.785769i
$23$	−0.0484528	+	0.0200698i	−0.0101031	+	0.00418485i	−0.387729	−	0.921773i	$-0.626740\pi$
$23$	−0.0484528	+	0.0200698i	−0.0101031	+	0.00418485i	0.377626	+	0.925958i	$0.376740\pi$
$24$	−4.71992	+	1.31237i	−0.963450	+	0.267887i
$25$	0.923880	+	0.382683i	0.184776	+	0.0765367i
$26$	5.39246	−	4.76222i	1.05755	−	0.933949i
$27$	3.68520	−	3.66323i	0.709218	−	0.704989i
$28$	−4.60285	+	3.58285i	−0.869856	+	0.677095i
$29$	−3.42952	+	5.13264i	−0.636846	+	0.953107i	0.362928	+	0.931817i	$0.381777\pi$
$29$	−3.42952	+	5.13264i	−0.636846	+	0.953107i	−0.999773	+	0.0212895i	$0.993223\pi$
$30$	1.36589	+	2.03331i	0.249376	+	0.371230i
$31$	−7.39786			−1.32870			−0.664348	−	0.747424i	$-0.731291\pi$
$31$	−7.39786			−1.32870			−0.664348	+	0.747424i	$0.731291\pi$
$32$	2.74312	−	4.94725i	0.484920	−	0.874559i
$33$	6.78450	−	7.72070i	1.18103	−	1.34400i
$34$	1.84896	−	6.99731i	0.317094	−	1.20003i
$35$	2.42495	+	1.62030i	0.409891	+	0.273881i
$36$	0.0296266	+	5.99993i	0.00493776	+	0.999988i
$37$	−6.78702	−	1.35002i	−1.11578	−	0.221942i	−0.397435	−	0.917630i	$-0.630099\pi$
$37$	−6.78702	−	1.35002i	−1.11578	−	0.221942i	−0.718344	+	0.695688i	$0.755099\pi$
$38$	−7.43914	+	6.56970i	−1.20679	+	1.06575i
$39$	−3.88919	−	7.90635i	−0.622769	−	1.26603i
$40$	−2.77967	−	0.522929i	−0.439504	−	0.0826823i
$41$	2.61970	+	6.32451i	0.409128	+	0.987722i	0.985368	+	0.170442i	$0.0545194\pi$
$41$	2.61970	+	6.32451i	0.409128	+	0.987722i	−0.576240	+	0.817281i	$0.695481\pi$
$42$	2.75012	+	6.59328i	0.424352	+	1.01737i
$43$	−10.4939	+	7.01179i	−1.60030	+	1.06929i	−0.649107	+	0.760697i	$0.724857\pi$
$43$	−10.4939	+	7.01179i	−1.60030	+	1.06929i	−0.951195	+	0.308591i	$0.900143\pi$
$44$	0.858273	+	11.8370i	0.129389	+	1.78450i
$45$	2.84271	−	0.958654i	0.423766	−	0.142908i
$46$	−0.0589979	−	0.0449467i	−0.00869876	−	0.00662702i
$47$	1.05283	−	1.05283i	0.153571	−	0.153571i	−0.626140	−	0.779711i	$-0.715366\pi$
$47$	1.05283	−	1.05283i	0.153571	−	0.153571i	0.779711	+	0.626140i	$0.215366\pi$
$48$	−4.96160	−	4.83555i	−0.716145	−	0.697951i
$49$	1.06473	+	1.06473i	0.152104	+	0.152104i
$50$	0.189450	+	1.40147i	0.0267923	+	0.198197i
$51$	−7.67208	−	4.43968i	−1.07431	−	0.621679i
$52$	9.65672	+	3.20354i	1.33915	+	0.444252i
$53$	0.954072	+	1.42787i	0.131052	+	0.196133i	0.891192	−	0.453626i	$-0.149870\pi$
$53$	0.954072	+	1.42787i	0.131052	+	0.196133i	−0.760140	+	0.649759i	$0.774870\pi$
$54$	7.09898	+	1.89855i	0.966049	+	0.258360i
$55$	5.48234	−	2.27086i	0.739239	−	0.306203i
$56$	−7.65349	−	3.07735i	−1.02274	−	0.411229i
$57$	5.36531	+	10.9072i	0.710652	+	1.44469i
$58$	−8.71313	−	0.540770i	−1.14409	−	0.0710066i
$59$	0.480276	−	2.41451i	0.0625266	−	0.314343i	−0.936847	−	0.349740i	$-0.886270\pi$
$59$	0.480276	−	2.41451i	0.0625266	−	0.314343i	0.999373	+	0.0353978i	$0.0112698\pi$
$60$	−1.51367	+	3.11590i	−0.195414	+	0.402260i
$61$	−4.76601	+	7.13284i	−0.610225	+	0.913267i	−0.999971	−	0.00765598i	$-0.997563\pi$
$61$	−4.76601	+	7.13284i	−0.610225	+	0.913267i	0.389745	+	0.920923i	$0.372563\pi$
$62$	−5.26245	−	9.04231i	−0.668332	−	1.14838i
$63$	8.67679	−	1.12473i	1.09317	−	0.141703i
$64$	7.99827	−	0.166333i	0.999784	−	0.0207916i
$65$		−	5.08711i		−	0.630979i
$66$	14.2630	+	2.80051i	1.75566	+	0.344718i
$67$	0.361832	+	0.241769i	0.0442048	+	0.0295367i	0.577476	−	0.816407i	$-0.304038\pi$
$67$	0.361832	+	0.241769i	0.0442048	+	0.0295367i	−0.533271	+	0.845944i	$0.679038\pi$
$68$	9.86798	−	2.71756i	1.19667	−	0.329552i
$69$	−0.0721212	+	0.0552264i	−0.00868237	+	0.00664848i
$70$	−0.255491	+	4.11658i	−0.0305370	+	0.492025i
$71$	−0.152345	+	0.367794i	−0.0180800	+	0.0436491i	−0.932662	−	0.360752i	$-0.882520\pi$
$71$	−0.152345	+	0.367794i	−0.0180800	+	0.0436491i	0.914582	+	0.404401i	$0.132520\pi$
$72$	−7.31256	+	4.30424i	−0.861793	+	0.507260i
$73$	2.62190	+	6.32982i	0.306870	+	0.740849i	0.999803	+	0.0198475i	$0.00631807\pi$
$73$	2.62190	+	6.32982i	0.306870	+	0.740849i	−0.692933	+	0.721002i	$0.743682\pi$
$74$	−3.17781	−	9.25601i	−0.369413	−	1.07599i
$75$	1.71701	+	0.227789i	0.198263	+	0.0263028i
$76$	−13.3219	−	4.41943i	−1.52812	−	0.506944i
$77$	16.9739	−	3.37631i	1.93435	−	0.384767i
$78$	6.89727	−	10.3779i	0.780962	−	1.17506i
$79$	0.318893	−	0.318893i	0.0358783	−	0.0358783i	−0.688940	−	0.724818i	$-0.741924\pi$
$79$	0.318893	−	0.318893i	0.0358783	−	0.0358783i	0.724818	+	0.688940i	$0.241924\pi$
$80$	−1.33814	−	3.76953i	−0.149608	−	0.421447i
$81$	4.53104	−	7.77623i	0.503448	−	0.864025i
$82$	−5.86685	+	7.70094i	−0.647885	+	0.850427i
$83$	−0.150213	+	0.0298791i	−0.0164880	+	0.00327966i	−0.203327	−	0.979111i	$-0.565176\pi$
$83$	−0.150213	+	0.0298791i	−0.0164880	+	0.00327966i	0.186839	+	0.982390i	$0.440176\pi$
$84$	−6.10260	+	8.05154i	−0.665848	+	0.878495i
$85$	−2.84322	−	4.25518i	−0.308391	−	0.461540i
$86$	−16.0352	−	7.83872i	−1.72912	−	0.845271i
$87$	−3.44689	+	10.1210i	−0.369545	+	1.08509i
$88$	−13.8577	+	9.46928i	−1.47724	+	1.00943i
$89$	−0.898989	+	2.17035i	−0.0952927	+	0.230057i	−0.964337	−	0.264677i	$-0.914735\pi$
$89$	−0.898989	+	2.17035i	−0.0952927	+	0.230057i	0.869044	+	0.494734i	$0.164735\pi$
$90$	3.19390	+	2.79267i	0.336667	+	0.294373i
$91$	2.89443	−	14.5513i	0.303419	−	1.52539i
$92$	0.0129698	−	0.104085i	0.00135219	−	0.0108516i
$93$	−12.3802	+	3.30404i	−1.28376	+	0.342612i
$94$	2.03579	+	0.537935i	0.209976	+	0.0554837i
$95$			7.01790i			0.720021i
$96$	2.38101	−	9.50425i	0.243011	−	0.970024i
$97$			9.92918i			1.00816i	0.863658	+	0.504078i	$0.168167\pi$
$97$			9.92918i			1.00816i	−0.863658	+	0.504078i	$0.831833\pi$
$98$	−0.544012	+	2.05879i	−0.0549535	+	0.207969i
$99$	7.90549	−	15.9505i	0.794532	−	1.60309i
$100$	−1.57823	+	1.22849i	−0.157823	+	0.122849i
$101$	0.461131	−	2.31826i	0.0458842	−	0.230676i	−0.951038	−	0.309074i	$-0.899981\pi$
$101$	0.461131	−	2.31826i	0.0458842	−	0.230676i	0.996922	+	0.0783988i	$0.0249808\pi$
$102$	−0.0309492	−	12.5356i	−0.00306442	−	1.24121i
$103$	2.00382	−	4.83766i	0.197443	−	0.476669i	−0.793887	−	0.608065i	$-0.791946\pi$
$103$	2.00382	−	4.83766i	0.197443	−	0.476669i	0.991330	+	0.131396i	$0.0419460\pi$
$104$	2.95363	+	14.0821i	0.289627	+	1.38086i
$105$	4.78176	+	1.62851i	0.466652	+	0.158926i
$106$	−1.06659	+	2.18186i	−0.103596	+	0.211921i
$107$	−0.332123	−	0.497058i	−0.0321076	−	0.0480524i	0.815069	−	0.579364i	$-0.196699\pi$
$107$	−0.332123	−	0.497058i	−0.0321076	−	0.0480524i	−0.847176	+	0.531312i	$0.821699\pi$
$108$	2.72927	+	10.0275i	0.262624	+	0.964898i
$109$	−7.99770	+	1.59084i	−0.766041	+	0.152375i	−0.562619	−	0.826716i	$-0.690206\pi$
$109$	−7.99770	+	1.59084i	−0.766041	+	0.152375i	−0.203422	+	0.979091i	$0.565206\pi$
$110$	6.67549	+	5.08563i	0.636483	+	0.484895i
$111$	−11.9609	+	0.771986i	−1.13528	+	0.0732737i
$112$	−1.68288	−	11.5438i	−0.159017	−	1.09079i
$113$	12.4865	−	12.4865i	1.17463	−	1.17463i	0.193536	−	0.981093i	$-0.438004\pi$
$113$	12.4865	−	12.4865i	1.17463	−	1.17463i	0.981093	−	0.193536i	$-0.0619956\pi$
$114$	−9.51508	+	14.3167i	−0.891169	+	1.34088i
$115$	−0.0514372	+	0.0102315i	−0.00479655	+	0.000954093i
$116$	−5.53708	−	11.0346i	−0.514105	−	1.02454i
$117$	−10.0396	−	11.4941i	−0.928162	−	1.06263i
$118$	3.29287	−	1.13052i	0.303133	−	0.104073i
$119$	−5.71173	−	13.7893i	−0.523594	−	1.26407i
$120$	−4.88526	+	0.366345i	−0.445961	+	0.0334426i
$121$	9.26586	−	22.3698i	0.842351	−	2.03362i
$122$	−12.1087	−	0.751510i	−1.09627	−	0.0680385i
$123$	7.20866	+	9.41392i	0.649983	+	0.848825i
$124$	7.30888	−	12.8644i	0.656357	−	1.15526i
$125$	0.831470	+	0.555570i	0.0743689	+	0.0496917i
$126$	7.54695	+	9.80546i	0.672336	+	0.873540i
$127$			8.81913i			0.782571i	0.920269	+	0.391286i	$0.127970\pi$
$127$			8.81913i			0.782571i	−0.920269	+	0.391286i	$0.872030\pi$
$128$	5.89285	+	9.65786i	0.520859	+	0.853642i
$129$	−14.4297	+	16.4209i	−1.27046	+	1.44578i
$130$	6.21791	−	3.61870i	0.545347	−	0.317381i
$131$	6.12436	−	9.16575i	0.535088	−	0.800816i	−0.461164	−	0.887315i	$-0.652568\pi$
$131$	6.12436	−	9.16575i	0.535088	−	0.800816i	0.996252	+	0.0864992i	$0.0275680\pi$
$132$	6.72295	+	19.4257i	0.585158	+	1.69079i
$133$	−3.99300	+	20.0742i	−0.346237	+	1.74065i
$134$	−0.0381223	+	0.614244i	−0.00329327	+	0.0530626i
$135$	4.32905	−	2.87390i	0.372586	−	0.247346i
$136$	10.3412	+	10.1284i	0.886750	+	0.868501i
$137$	−3.29818	+	1.36615i	−0.281782	+	0.116718i	−0.519098	−	0.854714i	$-0.673732\pi$
$137$	−3.29818	+	1.36615i	−0.281782	+	0.116718i	0.237316	+	0.971432i	$0.423732\pi$
$138$	−0.118806	−	0.0488676i	−0.0101134	−	0.00415989i
$139$	0.844782	+	1.26431i	0.0716534	+	0.107237i	0.865566	−	0.500795i	$-0.166959\pi$
$139$	0.844782	+	1.26431i	0.0716534	+	0.107237i	−0.793912	+	0.608032i	$0.791959\pi$
$140$	−5.21338	+	2.61603i	−0.440611	+	0.221095i
$141$	1.29168	−	2.23211i	0.108779	−	0.187978i
$142$	−0.557919	+	0.0754194i	−0.0468196	+	0.00632905i
$143$	−21.3455	−	21.3455i	−1.78500	−	1.78500i
$144$	−10.4628	−	5.87624i	−0.871899	−	0.489686i
$145$	−4.36495	+	4.36495i	−0.362489	+	0.362489i
$146$	−5.87178	+	7.70741i	−0.485952	+	0.637870i
$147$	2.25733	+	1.30627i	0.186181	+	0.107739i
$148$	9.05298	−	10.4684i	0.744151	−	0.860500i
$149$	−9.51920	+	6.36053i	−0.779844	+	0.521075i	−0.880614	−	0.473835i	$-0.842869\pi$
$149$	−9.51920	+	6.36053i	−0.779844	+	0.521075i	0.100770	+	0.994910i	$0.467869\pi$
$150$	0.942963	+	2.26071i	0.0769926	+	0.184586i
$151$	1.17819	+	2.84441i	0.0958800	+	0.231475i	0.964541	−	0.263931i	$-0.0850192\pi$
$151$	1.17819	+	2.84441i	0.0958800	+	0.231475i	−0.868661	+	0.495406i	$0.835019\pi$
$152$	−4.07466	−	19.4269i	−0.330498	−	1.57573i
$153$	−14.8219	−	4.00320i	−1.19828	−	0.323640i
$154$	16.2011	+	18.3452i	1.30552	+	1.47830i
$155$	−7.25572	−	1.44325i	−0.582793	−	0.115925i
$156$	17.5911	+	1.04818i	1.40841	+	0.0839214i
$157$	−3.15007	−	2.10481i	−0.251403	−	0.167982i	0.423483	−	0.905904i	$-0.360807\pi$
$157$	−3.15007	−	2.10481i	−0.251403	−	0.167982i	−0.674886	+	0.737922i	$0.735807\pi$
$158$	0.616622	+	0.162935i	0.0490558	+	0.0129624i
$159$	2.23433	+	1.96340i	0.177194	+	0.155708i
$160$	3.65557	−	4.31704i	0.288998	−	0.341292i
$161$	−0.152954			−0.0120544
$162$	12.7279	+	0.00663124i	1.00000	+	0.000521000i
$163$	11.8076	−	17.6713i	0.924839	−	1.38412i	0.00155618	−	0.999999i	$-0.499505\pi$
$163$	11.8076	−	17.6713i	0.924839	−	1.38412i	0.923283	−	0.384121i	$-0.125495\pi$
$164$	−13.5861	−	1.69294i	−1.06090	−	0.132196i
$165$	8.16037	−	6.24876i	0.635284	−	0.486465i
$166$	−0.143374	−	0.162349i	−0.0111280	−	0.0126007i
$167$	−7.92310	−	3.28186i	−0.613108	−	0.253958i	0.0544486	−	0.998517i	$-0.482660\pi$
$167$	−7.92310	−	3.28186i	−0.613108	−	0.253958i	−0.667557	+	0.744559i	$0.732660\pi$
$168$	−14.1824	−	1.73168i	−1.09419	−	0.133602i
$169$	−11.8984	+	4.92848i	−0.915261	+	0.379113i
$170$	3.17854	−	6.50215i	0.243783	−	0.498692i
$171$	13.8501	+	15.8566i	1.05914	+	1.21259i
$172$	−1.82543	−	25.1757i	−0.139188	−	1.91963i
$173$	−1.15725	−	5.81787i	−0.0879838	−	0.442325i	−0.999516	−	0.0310967i	$-0.990100\pi$
$173$	−1.15725	−	5.81787i	−0.0879838	−	0.442325i	0.911533	−	0.411228i	$-0.134900\pi$
$174$	−14.8228	+	2.98649i	−1.12371	+	0.226405i
$175$	2.06225	+	2.06225i	0.155891	+	0.155891i
$176$	−21.4318	−	10.2021i	−1.61548	−	0.769015i
$177$	−0.274637	−	4.25513i	−0.0206430	−	0.319835i
$178$	−3.29229	+	0.445050i	−0.246767	+	0.0333579i
$179$	0.858399	+	4.31546i	0.0641597	+	0.322553i	0.999514	−	0.0311583i	$-0.00991961\pi$
$179$	0.858399	+	4.31546i	0.0641597	+	0.322553i	−0.935355	+	0.353711i	$0.884920\pi$
$180$	−1.14147	+	5.89042i	−0.0850802	+	0.439046i
$181$	−3.25967	+	2.17804i	−0.242289	+	0.161892i	−0.670786	−	0.741651i	$-0.734043\pi$
$181$	−3.25967	+	2.17804i	−0.242289	+	0.161892i	0.428497	+	0.903543i	$0.359043\pi$
$182$	19.8448	−	6.81319i	1.47100	−	0.505027i
$183$	−4.79015	+	14.0653i	−0.354098	+	1.03973i
$184$	0.136448	−	0.0581877i	0.0100591	−	0.00428966i
$185$	−6.39323	−	2.64816i	−0.470040	−	0.194697i
$186$	−12.8451	−	12.7818i	−0.941846	−	0.937207i
$187$	−29.7849	−	5.92459i	−2.17809	−	0.433249i
$188$	0.790645	+	2.87098i	0.0576637	+	0.209388i
$189$	14.0181	−	5.75744i	1.01967	−	0.418792i
$190$	−8.57789	+	4.99216i	−0.622305	+	0.362169i
$191$	−19.4273			−1.40571			−0.702855	−	0.711333i	$-0.748092\pi$
$191$	−19.4273			−1.40571			−0.702855	+	0.711333i	$0.748092\pi$
$192$	13.3106	−	3.85054i	0.960613	−	0.277889i
$193$	12.5311			0.902005			0.451002	−	0.892523i	$-0.351067\pi$
$193$	12.5311			0.902005			0.451002	+	0.892523i	$0.351067\pi$
$194$	−12.1363	+	7.06309i	−0.871336	+	0.507100i
$195$	−2.27201	−	8.51318i	−0.162702	−	0.609641i
$196$	−2.90342	+	0.799577i	−0.207387	+	0.0571126i
$197$	16.7075	+	3.32332i	1.19036	+	0.236777i	0.750242	−	0.661164i	$-0.229937\pi$
$197$	16.7075	+	3.32332i	1.19036	+	0.236777i	0.440117	+	0.897941i	$0.354937\pi$
$198$	25.1197	−	1.68357i	1.78518	−	0.119646i
$199$	6.43413	+	2.66510i	0.456103	+	0.188924i	0.598893	−	0.800829i	$-0.295607\pi$
$199$	6.43413	+	2.66510i	0.456103	+	0.188924i	−0.142790	+	0.989753i	$0.545607\pi$
$200$	−2.62424	−	1.05517i	−0.185562	−	0.0746116i
$201$	0.713497	+	0.242993i	0.0503262	+	0.0171394i
$202$	3.16161	−	1.08545i	0.222450	−	0.0763723i
$203$	−14.9691	+	10.0021i	−1.05063	+	0.702007i
$204$	15.3001	−	8.95501i	1.07122	−	0.626976i
$205$	1.33551	+	6.71406i	0.0932761	+	0.468930i
$206$	7.33843	−	0.992006i	0.511292	−	0.0691163i
$207$	−0.0960280	+	0.124631i	−0.00667441	+	0.00866245i
$208$	−15.1113	+	13.6274i	−1.04778	+	0.944893i
$209$	29.4471	+	29.4471i	2.03690	+	2.03690i
$210$	1.41099	+	7.00311i	0.0973675	+	0.483261i
$211$	−3.35851	−	16.8844i	−0.231209	−	1.16237i	−0.905646	−	0.424035i	$-0.860613\pi$
$211$	−3.35851	−	16.8844i	−0.231209	−	1.16237i	0.674437	−	0.738333i	$-0.264387\pi$
$212$	−3.42558	+	0.248380i	−0.235270	+	0.0170588i
$213$	−0.0906822	+	0.683535i	−0.00621344	+	0.0468350i
$214$	0.371292	−	0.759531i	0.0253810	−	0.0519205i
$215$	−11.6602	+	4.82980i	−0.795218	+	0.329390i
$216$	−10.3150	+	10.4690i	−0.701850	+	0.712325i
$217$	−19.9332	−	8.25662i	−1.35316	−	0.560496i
$218$	−7.63361	−	8.64385i	−0.517013	−	0.585435i
$219$	7.21471	+	9.42182i	0.487525	+	0.636668i
$220$	−1.46751	+	11.7770i	−0.0989392	+	0.794006i
$221$	−14.4638	+	21.6466i	−0.972941	+	1.45611i
$222$	−9.45192	−	14.0705i	−0.634371	−	0.944348i
$223$	19.5353			1.30818			0.654089	−	0.756417i	$-0.273052\pi$
$223$	19.5353			1.30818			0.654089	+	0.756417i	$0.273052\pi$
$224$	12.9128	−	10.2686i	0.862770	−	0.686101i
$225$	2.97511	−	0.385649i	0.198341	−	0.0257099i
$226$	24.1443	+	6.37984i	1.60605	+	0.424381i
$227$	4.31941	+	2.88613i	0.286689	+	0.191559i	0.690596	−	0.723240i	$-0.257348\pi$
$227$	4.31941	+	2.88613i	0.286689	+	0.191559i	−0.403907	+	0.914800i	$0.632348\pi$
$228$	−24.2677	−	1.44601i	−1.60717	−	0.0957643i
$229$	16.8824	+	3.35812i	1.11562	+	0.221911i	0.718275	−	0.695759i	$-0.244932\pi$
$229$	16.8824	+	3.35812i	1.11562	+	0.221911i	0.397345	+	0.917669i	$0.369932\pi$
$230$	−0.0490956	−	0.0555929i	−0.00323727	−	0.00366569i
$231$	26.8975	−	13.2311i	1.76972	−	0.870540i
$232$	9.54869	−	14.6174i	0.626902	−	0.959676i
$233$	−8.84034	−	21.3425i	−0.579150	−	1.39819i	−0.893577	−	0.448910i	$-0.851812\pi$
$233$	−8.84034	−	21.3425i	−0.579150	−	1.39819i	0.314427	−	0.949282i	$-0.398188\pi$
$234$	6.90747	−	20.4476i	0.451555	−	1.33670i
$235$	1.23800	−	0.827206i	0.0807583	−	0.0539609i
$236$	3.72419	+	3.22064i	0.242424	+	0.209646i
$237$	0.391236	−	0.676084i	0.0254135	−	0.0439164i
$238$	12.7915	−	16.7904i	0.829151	−	1.08836i
$239$	−5.05628	+	5.05628i	−0.327064	+	0.327064i	−0.851469	−	0.524405i	$-0.824288\pi$
$239$	−5.05628	+	5.05628i	−0.327064	+	0.327064i	0.524405	+	0.851469i	$0.324288\pi$
$240$	−3.92290	−	5.71059i	−0.253222	−	0.368617i
$241$	19.7234	+	19.7234i	1.27049	+	1.27049i	0.945830	+	0.324663i	$0.105251\pi$
$241$	19.7234	+	19.7234i	1.27049	+	1.27049i	0.324663	+	0.945830i	$0.394749\pi$
$242$	33.9335	−	4.58712i	2.18133	−	0.294872i
$243$	4.10957	−	15.0370i	0.263629	−	0.964624i
$244$	−7.69490	−	15.3349i	−0.492616	−	0.981713i
$245$	0.836551	+	1.25199i	0.0534453	+	0.0799865i
$246$	−6.37865	+	15.5076i	−0.406688	+	0.988729i
$247$	32.9833	−	13.6621i	2.09868	−	0.869300i
$248$	20.9232	−	0.217537i	1.32862	−	0.0138136i
$249$	−0.238033	+	0.117090i	−0.0150847	+	0.00742028i
$250$	−0.0876030	+	1.41150i	−0.00554050	+	0.0892710i
$251$	6.07642	−	30.5482i	0.383540	−	1.92819i	0.0115941	−	0.999933i	$-0.496309\pi$
$251$	6.07642	−	30.5482i	0.383540	−	1.92819i	0.371946	−	0.928254i	$-0.378691\pi$
$252$	−6.61658	+	16.1996i	−0.416805	+	1.02048i
$253$	−0.172899	+	0.258762i	−0.0108701	+	0.0162682i
$254$	−10.7795	+	6.27346i	−0.676367	+	0.393632i
$255$	−6.65852	−	5.85112i	−0.416973	−	0.366411i
$256$	−7.61282	+	14.0728i	−0.475801	+	0.879553i
$257$			11.4997i			0.717332i	0.933466	+	0.358666i	$0.116768\pi$
$257$			11.4997i			0.717332i	−0.933466	+	0.358666i	$0.883232\pi$
$258$	−30.3355	−	5.95629i	−1.88861	−	0.370822i
$259$	−16.7806	−	11.2124i	−1.04270	−	0.696707i
$260$	8.84619	+	5.02592i	0.548617	+	0.311694i
$261$	−1.24803	+	18.4768i	−0.0772509	+	1.14369i
$262$	15.5597	+	0.965696i	0.961283	+	0.0596609i
$263$	8.33112	−	20.1131i	0.513719	−	1.24023i	−0.427985	−	0.903786i	$-0.640777\pi$
$263$	8.33112	−	20.1131i	0.513719	−	1.24023i	0.941704	−	0.336442i	$-0.109223\pi$
$264$	−18.9614	+	22.0358i	−1.16699	+	1.35621i
$265$	0.657176	+	1.58656i	0.0403700	+	0.0974618i
$266$	−27.3768	+	9.39910i	−1.67858	+	0.576296i
$267$	−0.535116	+	4.03354i	−0.0327486	+	0.246849i
$268$	−0.777901	+	0.390344i	−0.0475179	+	0.0238441i
$269$	−7.66204	+	1.52408i	−0.467163	+	0.0929245i	−0.423058	−	0.906102i	$-0.639043\pi$
$269$	−7.66204	+	1.52408i	−0.467163	+	0.0929245i	−0.0441046	+	0.999027i	$0.514043\pi$
$270$	6.59219	+	3.24701i	0.401188	+	0.197607i
$271$	−6.18314	+	6.18314i	−0.375599	+	0.375599i	−0.869512	−	0.493912i	$-0.835566\pi$
$271$	−6.18314	+	6.18314i	−0.375599	+	0.375599i	0.493912	+	0.869512i	$0.335566\pi$
$272$	−5.02360	+	19.8447i	−0.304601	+	1.20326i
$273$	−1.65513	−	25.6440i	−0.100173	−	1.55205i
$274$	−4.01597	−	3.05951i	−0.242614	−	0.184832i
$275$	5.82002	−	1.15767i	0.350961	−	0.0698104i
$276$	−0.0247818	−	0.179977i	−0.00149169	−	0.0108333i
$277$	12.8024	+	19.1601i	0.769220	+	1.15122i	0.984623	+	0.174694i	$0.0558937\pi$
$277$	12.8024	+	19.1601i	0.769220	+	1.15122i	−0.215402	+	0.976525i	$0.569106\pi$
$278$	−0.944411	+	1.93193i	−0.0566420	+	0.115869i
$279$	−19.2423	+	11.0585i	−1.15201	+	0.662053i
$280$	−6.90607	−	4.51134i	−0.412717	−	0.269604i
$281$	−6.70772	+	16.1939i	−0.400149	+	0.966045i	0.587480	+	0.809238i	$0.300120\pi$
$281$	−6.70772	+	16.1939i	−0.400149	+	0.966045i	−0.987629	+	0.156807i	$0.949880\pi$
$282$	3.64711	−	0.00900433i	0.217182	−	0.000536200i
$283$	4.10022	−	20.6132i	0.243733	−	1.22533i	−0.644021	−	0.765008i	$-0.722735\pi$
$283$	4.10022	−	20.6132i	0.243733	−	1.22533i	0.887754	−	0.460319i	$-0.152265\pi$
$284$	−0.489058	−	0.628288i	−0.0290203	−	0.0372821i
$285$	3.13433	+	11.7443i	0.185662	+	0.695672i
$286$	10.9063	−	41.2745i	0.644903	−	2.44061i
$287$			19.9649i			1.17849i
$288$	−0.260222	−	16.9686i	−0.0153337	−	0.999882i
$289$			9.19052i			0.540619i
$290$	−8.44021	−	2.23023i	−0.495626	−	0.130963i
$291$	4.43457	+	16.6163i	0.259959	+	0.974063i
$292$	−13.5975	−	1.69436i	−0.795736	−	0.0991547i
$293$	4.66445	−	23.4498i	0.272500	−	1.36995i	−0.565711	−	0.824604i	$-0.691398\pi$
$293$	4.66445	−	23.4498i	0.272500	−	1.36995i	0.838211	−	0.545346i	$-0.183602\pi$
$294$	0.00910605	+	3.68831i	0.000531076	+	0.215107i
$295$	0.942095	−	2.27442i	0.0548509	−	0.132422i
$296$	19.2352	+	3.61866i	1.11803	+	0.210330i
$297$	6.10584	−	30.2236i	0.354297	−	1.75375i
$298$	−14.5458	−	7.11066i	−0.842618	−	0.411909i
$299$	0.148223	+	0.221831i	0.00857193	+	0.0128288i
$300$	−2.09247	+	2.76072i	−0.120809	+	0.159390i
$301$	−36.1011	+	7.18095i	−2.08083	+	0.413903i
$302$	−2.63858	+	3.46345i	−0.151833	+	0.199299i
$303$	−0.263690	−	4.08551i	−0.0151486	−	0.234706i
$304$	20.8467	−	18.7997i	1.19564	−	1.07823i
$305$	−6.06598	+	6.06598i	−0.347337	+	0.347337i
$306$	−5.65046	−	20.9643i	−0.323015	−	1.19845i
$307$	−7.07567	+	1.40744i	−0.403830	+	0.0803267i	−0.392826	−	0.919613i	$-0.628503\pi$
$307$	−7.07567	+	1.40744i	−0.403830	+	0.0803267i	−0.0110035	+	0.999939i	$0.503503\pi$
$308$	−10.8985	+	32.8523i	−0.620999	+	1.87193i
$309$	1.19276	−	8.99067i	0.0678538	−	0.511461i
$310$	−3.39726	−	9.89522i	−0.192952	−	0.562011i
$311$	0.819405	+	1.97822i	0.0464642	+	0.112175i	0.945408	−	0.325890i	$-0.105664\pi$
$311$	0.819405	+	1.97822i	0.0464642	+	0.112175i	−0.898943	+	0.438065i	$0.855664\pi$
$312$	11.2322	+	22.2470i	0.635897	+	1.25949i
$313$	0.487103	−	1.17597i	0.0275327	−	0.0664698i	−0.909515	−	0.415671i	$-0.863547\pi$
$313$	0.487103	−	1.17597i	0.0275327	−	0.0664698i	0.937048	+	0.349201i	$0.113547\pi$
$314$	0.331889	−	5.34754i	0.0187296	−	0.301779i
$315$	8.72950	+	0.589639i	0.491851	+	0.0332224i
$316$	0.239479	+	0.869593i	0.0134717	+	0.0489184i
$317$	−8.75910	−	5.85265i	−0.491960	−	0.328717i	0.284722	−	0.958610i	$-0.408099\pi$
$317$	−8.75910	−	5.85265i	−0.491960	−	0.328717i	−0.776682	+	0.629893i	$0.783099\pi$
$318$	−0.810453	+	4.12766i	−0.0454480	+	0.231468i
$319$			36.6307i			2.05092i
$320$	7.87704	+	1.39725i	0.440340	+	0.0781086i
$321$	−0.777798	−	0.683483i	−0.0434124	−	0.0381483i
$322$	−0.108803	−	0.186953i	−0.00606336	−	0.0104185i
$323$	19.9535	−	29.8624i	1.11024	−	1.66159i
$324$	9.04586	+	15.5619i	0.502548	+	0.864549i
$325$	0.992447	−	4.98937i	0.0550510	−	0.276760i
$326$	29.9986	+	1.86183i	1.66147	+	0.103117i
$327$	−12.6735	+	6.23417i	−0.700845	+	0.344751i
$328$	−7.59520	−	17.8104i	−0.419375	−	0.983415i
$329$	4.01186	−	1.66177i	0.221181	−	0.0916163i
$330$	13.4426	+	5.52928i	0.739992	+	0.304377i
$331$	1.47965	+	2.21445i	0.0813289	+	0.121717i	0.869904	−	0.493221i	$-0.164181\pi$
$331$	1.47965	+	2.21445i	0.0813289	+	0.121717i	−0.788575	+	0.614939i	$0.789181\pi$
$332$	0.0964477	−	0.290731i	0.00529325	−	0.0159559i
$333$	−19.6715	+	6.63387i	−1.07799	+	0.363534i
$334$	−1.62470	−	12.0188i	−0.0888999	−	0.657642i
$335$	0.307713	+	0.307713i	0.0168122	+	0.0168122i
$336$	−7.97196	−	18.5667i	−0.434906	−	1.01290i
$337$	7.16607	−	7.16607i	0.390361	−	0.390361i	−0.484455	−	0.874816i	$-0.660982\pi$
$337$	7.16607	−	7.16607i	0.390361	−	0.390361i	0.874816	+	0.484455i	$0.160982\pi$
$338$	−14.4879	−	11.0374i	−0.788038	−	0.600355i
$339$	15.3191	−	26.4726i	0.832022	−	1.43779i
$340$	10.2085	−	0.740196i	0.553636	−	0.0401428i
$341$	−36.5009	+	24.3891i	−1.97663	+	1.32074i
$342$	−9.52915	+	28.2084i	−0.515278	+	1.52533i
$343$	−6.13203	−	14.8040i	−0.331099	−	0.799343i
$344$	29.4734	−	20.1398i	1.58910	−	1.08587i
$345$	−0.0815095	+	0.0400951i	−0.00438833	+	0.00215865i
$346$	6.28791	−	5.55301i	0.338040	−	0.298532i
$347$	−1.70885	−	0.339911i	−0.0917359	−	0.0182474i	0.149009	−	0.988836i	$-0.452392\pi$
$347$	−1.70885	−	0.339911i	−0.0917359	−	0.0182474i	−0.240745	+	0.970588i	$0.577392\pi$
$348$	−14.1945	−	15.9932i	−0.760904	−	0.857327i
$349$	−8.09664	−	5.41000i	−0.433403	−	0.289591i	0.319668	−	0.947530i	$-0.396429\pi$
$349$	−8.09664	−	5.41000i	−0.433403	−	0.289591i	−0.753071	+	0.657939i	$0.771429\pi$
$350$	−1.05369	+	3.98764i	−0.0563219	+	0.213148i
$351$	−21.9346	−	14.7513i	−1.17078	−	0.787364i
$352$	−2.77550	−	33.4531i	−0.147935	−	1.78306i
$353$	28.0876			1.49495			0.747475	−	0.664290i	$-0.231266\pi$
$353$	28.0876			1.49495			0.747475	+	0.664290i	$0.231266\pi$
$354$	5.00563	−	3.36256i	0.266046	−	0.178718i
$355$	−0.221171	+	0.331005i	−0.0117385	+	0.0175679i
$356$	−2.88594	−	3.70753i	−0.152954	−	0.196499i
$357$	−15.7171	−	20.5252i	−0.831835	−	1.08631i
$358$	−4.66411	+	4.11900i	−0.246506	+	0.217696i
$359$	18.6359	+	7.71924i	0.983565	+	0.407406i	0.815745	−	0.578412i	$-0.196327\pi$
$359$	18.6359	+	7.71924i	0.983565	+	0.407406i	0.167820	+	0.985818i	$0.446327\pi$
$360$	−8.01177	+	2.79493i	−0.422257	+	0.147306i
$361$	−27.9482	+	11.5765i	−1.47096	+	0.609290i
$362$	−4.98095	−	2.43491i	−0.261793	−	0.127976i
$363$	5.51543	−	41.5737i	0.289485	−	2.18205i
$364$	22.4442	+	19.4095i	1.17640	+	1.01733i
$365$	1.33663	+	6.71970i	0.0699625	+	0.351725i
$366$	−20.5992	+	4.15034i	−1.07674	+	0.216942i
$367$	−2.37265	−	2.37265i	−0.123851	−	0.123851i	0.642464	−	0.766316i	$-0.277912\pi$
$367$	−2.37265	−	2.37265i	−0.123851	−	0.123851i	−0.766316	+	0.642464i	$0.777912\pi$
$368$	0.168184	+	0.125387i	0.00876719	+	0.00653623i
$369$	16.2680	+	12.5345i	0.846877	+	0.652518i
$370$	−1.31099	−	9.69812i	−0.0681551	−	0.504181i
$371$	0.977089	+	4.91216i	0.0507279	+	0.255027i
$372$	6.48573	−	24.7927i	0.336269	−	1.28544i
$373$	−16.5047	+	11.0281i	−0.854580	+	0.571012i	−0.903887	−	0.427771i	$-0.859299\pi$
$373$	−16.5047	+	11.0281i	−0.854580	+	0.571012i	0.0493067	+	0.998784i	$0.484299\pi$
$374$	−13.9459	−	40.6202i	−0.721124	−	2.10042i
$375$	1.63958	+	0.558384i	0.0846673	+	0.0288348i
$376$	−2.94674	+	3.00866i	−0.151967	+	0.155160i
$377$	29.0122	+	12.0173i	1.49421	+	0.618920i
$378$	17.0090	+	13.0386i	0.874848	+	0.670633i
$379$	24.6522	+	4.90362i	1.26630	+	0.251882i	0.782142	−	0.623100i	$-0.214127\pi$
$379$	24.6522	+	4.90362i	1.26630	+	0.251882i	0.484155	+	0.874982i	$0.339127\pi$
$380$	−12.2037	−	6.93348i	−0.626037	−	0.355680i
$381$	3.93880	+	14.7586i	0.201791	+	0.756108i
$382$	−13.8196	−	23.7457i	−0.707070	−	1.21494i
$383$	0.486693			0.0248689			0.0124344	−	0.999923i	$-0.496042\pi$
$383$	0.486693			0.0248689			0.0124344	+	0.999923i	$0.496042\pi$
$384$	14.1750	+	13.5304i	0.723363	+	0.690468i
$385$	17.3064			0.882016
$386$	8.91392	+	15.3165i	0.453707	+	0.779591i
$387$	−16.8139	+	33.9245i	−0.854697	+	1.72448i
$388$	−17.2662	−	9.80974i	−0.876561	−	0.498014i
$389$	−32.3010	−	6.42508i	−1.63773	−	0.325764i	−0.711488	−	0.702698i	$-0.751978\pi$
$389$	−32.3010	−	6.42508i	−1.63773	−	0.325764i	−0.926240	+	0.376934i	$0.876978\pi$
$390$	8.78936	−	8.83287i	0.445066	−	0.447270i
$391$	0.247965	+	0.102711i	0.0125402	+	0.00519430i
$392$	−3.04265	−	2.98003i	−0.153677	−	0.150514i
$393$	6.15538	−	18.0740i	0.310498	−	0.911711i
$394$	7.82275	+	22.7854i	0.394105	+	1.14791i
$395$	0.374978	−	0.250553i	0.0188672	−	0.0126067i
$396$	19.9266	+	29.5058i	1.00135	+	1.48272i
$397$	−0.604285	−	3.03795i	−0.0303282	−	0.152470i	0.962654	−	0.270735i	$-0.0872668\pi$
$397$	−0.604285	−	3.03795i	−0.0303282	−	0.152470i	−0.992982	+	0.118265i	$0.962267\pi$
$398$	1.31938	+	9.76016i	0.0661343	+	0.489233i
$399$	2.28333	+	35.3770i	0.114309	+	1.77107i
$400$	−0.577027	−	3.95816i	−0.0288513	−	0.197908i
$401$	17.5618	+	17.5618i	0.876993	+	0.876993i	0.993222	−	0.116229i	$-0.0370807\pi$
$401$	17.5618	+	17.5618i	0.876993	+	0.876993i	−0.116229	+	0.993222i	$0.537081\pi$
$402$	0.210537	+	1.04495i	0.0105006	+	0.0521174i
$403$	7.34199	+	36.9107i	0.365730	+	1.83865i
$404$	3.57573	+	3.09225i	0.177899	+	0.153845i
$405$	5.96104	−	6.74285i	0.296206	−	0.335055i
$406$	−22.8736	−	11.1817i	−1.13520	−	0.554936i
$407$	−37.9377	+	15.7143i	−1.88050	+	0.778929i
$408$	21.8293	+	12.3310i	1.08071	+	0.610477i
$409$	33.6787	+	13.9502i	1.66531	+	0.689793i	0.998464	−	0.0554061i	$-0.0176453\pi$
$409$	33.6787	+	13.9502i	1.66531	+	0.689793i	0.666843	+	0.745199i	$0.267645\pi$
$410$	−7.25650	+	6.40840i	−0.358373	+	0.316489i
$411$	−4.90928	+	3.75925i	−0.242157	+	0.185430i
$412$	6.43268	+	8.26400i	0.316916	+	0.407138i
$413$	3.98888	−	5.96977i	0.196280	−	0.293753i
$414$	−0.220644	−	0.0287179i	−0.0108441	−	0.00141141i
$415$	−0.153155			−0.00751811
$416$	−27.4060	−	8.77654i	−1.34369	−	0.430305i
$417$	1.97839	+	1.73849i	0.0968821	+	0.0851343i
$418$	−15.0457	+	56.9399i	−0.735910	+	2.78502i
$419$	−31.4002	−	20.9809i	−1.53400	−	1.02499i	−0.981498	−	0.191474i	$-0.938673\pi$
$419$	−31.4002	−	20.9809i	−1.53400	−	1.02499i	−0.552502	−	0.833512i	$-0.686327\pi$
$420$	−7.55611	+	6.70628i	−0.368701	+	0.327233i
$421$	8.12211	+	1.61559i	0.395847	+	0.0787389i	0.389000	−	0.921238i	$-0.372821\pi$
$421$	8.12211	+	1.61559i	0.395847	+	0.0787389i	0.00684703	+	0.999977i	$0.497821\pi$
$422$	18.2485	−	16.1157i	0.888322	−	0.784500i
$423$	1.16469	−	4.31228i	0.0566291	−	0.209670i
$424$	−2.74036	−	4.01035i	−0.133084	−	0.194760i
$425$	−1.95845	−	4.72811i	−0.0949986	−	0.229347i
$426$	−0.899982	+	0.375391i	−0.0436043	+	0.0181877i
$427$	−20.8027	+	13.8999i	−1.00671	+	0.672663i
$428$	1.19248	−	0.0864640i	0.0576408	−	0.00417939i
$429$	−45.2547	−	26.1880i	−2.18492	−	1.26437i
$430$	−14.1978	−	10.8164i	−0.684681	−	0.521614i
$431$	19.6095	−	19.6095i	0.944555	−	0.944555i	−0.0539867	−	0.998542i	$-0.517193\pi$
$431$	19.6095	−	19.6095i	0.944555	−	0.944555i	0.998542	+	0.0539867i	$0.0171929\pi$
$432$	−20.1337	−	5.16086i	−0.968683	−	0.248302i
$433$	12.7025	+	12.7025i	0.610441	+	0.610441i	0.943061	−	0.332620i	$-0.107933\pi$
$433$	12.7025	+	12.7025i	0.610441	+	0.610441i	−0.332620	+	0.943061i	$0.607933\pi$
$434$	−4.08749	−	30.2375i	−0.196206	−	1.45145i
$435$	−5.35517	+	9.25412i	−0.256761	+	0.443701i
$436$	5.13512	−	15.4792i	0.245928	−	0.741321i
$437$	−0.204480	−	0.306025i	−0.00978158	−	0.0146392i
$438$	−6.38401	+	15.5206i	−0.305040	+	0.741605i
$439$	37.9138	−	15.7044i	1.80953	−	0.749530i	0.827317	−	0.561736i	$-0.189866\pi$
$439$	37.9138	−	15.7044i	1.80953	−	0.749530i	0.982208	−	0.187794i	$-0.0601338\pi$
$440$	−15.4388	+	6.58383i	−0.736015	+	0.313872i
$441$	4.36099	+	1.17785i	0.207666	+	0.0560879i
$442$	−36.7471	−	2.28067i	−1.74788	−	0.108480i
$443$	1.13526	−	5.70735i	0.0539380	−	0.271165i	−0.944400	−	0.328800i	$-0.893356\pi$
$443$	1.13526	−	5.70735i	0.0539380	−	0.271165i	0.998338	+	0.0576350i	$0.0183560\pi$
$444$	10.4746	−	21.5619i	0.497101	−	1.02328i
$445$	−1.30513	+	1.95327i	−0.0618691	+	0.0925937i
$446$	13.8964	+	23.8777i	0.658011	+	1.13064i
$447$	−13.0894	+	14.8957i	−0.619110	+	0.704541i
$448$	21.7367	+	8.47855i	1.02696	+	0.400574i
$449$		−	13.9354i		−	0.657654i	−0.944390	−	0.328827i	$-0.893347\pi$
$449$		−	13.9354i		−	0.657654i	0.944390	−	0.328827i	$-0.106653\pi$
$450$	2.58771	+	3.36211i	0.121986	+	0.158491i
$451$	33.7760	+	22.5684i	1.59045	+	1.06271i
$452$	9.37696	+	34.0495i	0.441055	+	1.60155i
$453$	3.24205	+	4.23385i	0.152325	+	0.198924i
$454$	−0.455089	+	7.33260i	−0.0213584	+	0.344136i
$455$	5.67763	−	13.7070i	0.266172	−	0.642595i
$456$	−15.4953	−	30.6907i	−0.725634	−	1.43722i
$457$	−10.6769	−	25.7762i	−0.499442	−	1.20576i	−0.949785	−	0.312905i	$-0.898698\pi$
$457$	−10.6769	−	25.7762i	−0.499442	−	1.20576i	0.450342	−	0.892856i	$-0.351302\pi$
$458$	7.90466	+	23.0239i	0.369360	+	1.07584i
$459$	−26.5921	−	0.0795076i	−1.24121	−	0.00371110i
$460$	0.0330265	−	0.0995547i	0.00153987	−	0.00464176i
$461$	27.7466	−	5.51914i	1.29229	−	0.257052i	0.499374	−	0.866386i	$-0.333563\pi$
$461$	27.7466	−	5.51914i	1.29229	−	0.257052i	0.792913	+	0.609334i	$0.208563\pi$
$462$	35.3056	+	23.4646i	1.64257	+	1.09167i
$463$	−26.4389	+	26.4389i	−1.22872	+	1.22872i	−0.264272	+	0.964448i	$0.585132\pi$
$463$	−26.4389	+	26.4389i	−1.22872	+	1.22872i	−0.964448	+	0.264272i	$0.914868\pi$
$464$	24.6590	+	1.27323i	1.14477	+	0.0591084i
$465$	−12.7869	+	0.825298i	−0.592977	+	0.0382723i
$466$	19.7981	−	25.9873i	0.917128	−	1.20384i
$467$	5.20920	−	1.03617i	0.241053	−	0.0479484i	−0.0730851	−	0.997326i	$-0.523284\pi$
$467$	5.20920	−	1.03617i	0.241053	−	0.0479484i	0.314138	+	0.949377i	$0.398284\pi$
$468$	29.9064	−	6.10243i	1.38243	−	0.282085i
$469$	0.705109	+	1.05527i	0.0325589	+	0.0487278i
$470$	1.89173	+	0.924762i	0.0872590	+	0.0426561i
$471$	−6.21163	−	2.11547i	−0.286217	−	0.0974757i
$472$	−1.28735	+	6.84302i	−0.0592552	+	0.314976i
$473$	−28.6603	+	69.1920i	−1.31780	+	3.18145i
$474$	1.10467	−	0.00272732i	0.0507394	−	0.000125270i
$475$	−1.36912	+	6.88305i	−0.0628197	+	0.315816i
$476$	29.6219	+	3.69111i	1.35772	+	0.169182i
$477$	4.61601	+	2.28781i	0.211352	+	0.104752i
$478$	−9.77699	−	2.58346i	−0.447189	−	0.118165i
$479$			30.0492i			1.37298i	0.727139	+	0.686491i	$0.240850\pi$
$479$			30.0492i			1.37298i	−0.727139	+	0.686491i	$0.759150\pi$
$480$	4.18945	−	8.85712i	0.191221	−	0.404270i
$481$			35.2027i			1.60511i
$482$	−10.0775	+	38.1378i	−0.459015	+	1.73713i
$483$	−0.255965	+	0.0683122i	−0.0116468	+	0.00310831i
$484$	29.7453	+	38.2135i	1.35206	+	1.73698i
$485$	−1.93709	+	9.73839i	−0.0879586	+	0.442198i
$486$	21.3029	−	5.67345i	0.966318	−	0.257353i
$487$	−10.1529	+	24.5112i	−0.460071	+	1.11071i	0.508296	+	0.861182i	$0.330276\pi$
$487$	−10.1529	+	24.5112i	−0.460071	+	1.11071i	−0.968368	+	0.249528i	$0.919724\pi$
$488$	13.2698	−	20.3138i	0.600698	−	0.919561i
$489$	11.8674	−	34.8460i	0.536660	−	1.57579i
$490$	−0.935209	+	1.91310i	−0.0422484	+	0.0864251i
$491$	−4.83592	−	7.23747i	−0.218242	−	0.326622i	0.706153	−	0.708060i	$-0.250429\pi$
$491$	−4.83592	−	7.23747i	−0.218242	−	0.326622i	−0.924395	+	0.381437i	$0.875429\pi$
$492$	−23.4922	+	3.23475i	−1.05911	+	0.145834i
$493$	30.9842	−	6.16314i	1.39546	−	0.277574i
$494$	40.1616	+	30.5965i	1.80696	+	1.37660i
$495$	10.8654	−	14.1017i	0.488363	−	0.633827i
$496$	15.1495	+	25.4194i	0.680234	+	1.14136i
$497$	−0.820975	+	0.820975i	−0.0368258	+	0.0368258i
$498$	−0.312442	−	0.207653i	−0.0140008	−	0.00930515i
$499$	−37.1775	+	7.39506i	−1.66429	+	0.331049i	−0.935403	−	0.353582i	$-0.884963\pi$
$499$	−37.1775	+	7.39506i	−1.66429	+	0.331049i	−0.728890	+	0.684631i	$0.759963\pi$
$500$	−1.78757	+	0.896989i	−0.0799426	+	0.0401145i
$501$	−14.7249	−	1.95350i	−0.657859	−	0.0872759i
$502$	41.6611	−	14.3033i	1.85943	−	0.638386i
$503$	5.28340	+	12.7553i	0.235575	+	0.568729i	0.996816	−	0.0797408i	$-0.0254093\pi$
$503$	5.28340	+	12.7553i	0.235575	+	0.568729i	−0.761240	+	0.648470i	$0.775409\pi$
$504$	−24.5073	+	3.43619i	−1.09164	+	0.153060i
$505$	0.904541	−	2.18375i	0.0402515	−	0.0971758i
$506$	−0.439273	−	0.0272630i	−0.0195281	−	0.00121199i
$507$	−17.7105	+	13.5618i	−0.786553	+	0.602299i
$508$	−15.3359	−	8.71305i	−0.680423	−	0.386579i
$509$	24.4046	+	16.3066i	1.08172	+	0.722779i	0.962824	−	0.270128i	$-0.0870662\pi$
$509$	24.4046	+	16.3066i	1.08172	+	0.722779i	0.118891	+	0.992907i	$0.462066\pi$
$510$	2.41523	−	12.3008i	0.106948	−	0.544689i
$511$			19.9817i			0.883938i
$512$	−22.6164	+	0.705628i	−0.999514	+	0.0311846i
$513$	30.2597	+	20.3500i	1.33600	+	0.898476i
$514$	−14.0559	+	8.18028i	−0.619981	+	0.360817i
$515$	2.90910	−	4.35378i	0.128190	−	0.191850i
$516$	−14.2988	−	41.3157i	−0.629469	−	1.81882i
$517$	1.72370	−	8.66561i	0.0758081	−	0.381113i
$518$	1.76799	−	28.4867i	0.0776811	−	1.25163i
$519$	−4.53501	−	9.21923i	−0.199065	−	0.404679i
$520$	0.149589	+	14.3878i	0.00655989	+	0.630945i
$521$	−11.9108	+	4.93363i	−0.521823	+	0.216146i	−0.628018	−	0.778199i	$-0.716133\pi$
$521$	−11.9108	+	4.93363i	−0.521823	+	0.216146i	0.106194	+	0.994345i	$0.466133\pi$
$522$	−23.4717	+	11.6180i	−1.02733	+	0.508505i
$523$	0.579406	+	0.867142i	0.0253356	+	0.0379175i	0.843921	−	0.536467i	$-0.180241\pi$
$523$	0.579406	+	0.867142i	0.0253356	+	0.0379175i	−0.818586	+	0.574385i	$0.805241\pi$
$524$	9.88801	+	19.7054i	0.431960	+	0.860834i
$525$	4.37217	+	2.53009i	0.190817	+	0.110422i
$526$	30.5103	−	4.12437i	1.33031	−	0.179831i
$527$	26.7709	+	26.7709i	1.16616	+	1.16616i
$528$	−40.4221	−	7.50119i	−1.75915	−	0.326447i
$529$	−16.2615	+	16.2615i	−0.707022	+	0.707022i
$530$	−1.47176	+	1.93186i	−0.0639290	+	0.0839144i
$531$	−2.36003	−	6.99822i	−0.102416	−	0.303697i
$532$	−30.9628	−	26.7763i	−1.34241	−	1.16090i
$533$	28.9554	−	19.3474i	1.25420	−	0.838027i
$534$	−5.31080	+	2.21518i	−0.229821	+	0.0958604i
$535$	−0.228771	−	0.552301i	−0.00989062	−	0.0238781i
$536$	−1.03047	−	0.673148i	−0.0445095	−	0.0290756i
$537$	3.36388	+	6.83846i	0.145162	+	0.295101i
$538$	−7.31323	−	8.28107i	−0.315296	−	0.357022i
$539$	8.76351	+	1.74317i	0.377471	+	0.0750836i
$540$	0.720554	+	10.3673i	0.0310077	+	0.446137i
$541$	8.49539	+	5.67644i	0.365245	+	0.244049i	0.724627	−	0.689142i	$-0.242012\pi$
$541$	8.49539	+	5.67644i	0.365245	+	0.244049i	−0.359381	+	0.933191i	$0.617012\pi$
$542$	−11.9559	−	3.15922i	−0.513551	−	0.135700i
$543$	−4.48223	+	5.10074i	−0.192351	+	0.218894i
$544$	−27.8294	+	7.97618i	−1.19318	+	0.341976i
$545$	−8.15439			−0.349295
$546$	30.1670	−	20.2648i	1.29103	−	0.867254i
$547$	−7.38176	+	11.0476i	−0.315621	+	0.472361i	−0.955031	−	0.296505i	$-0.904179\pi$
$547$	−7.38176	+	11.0476i	−0.315621	+	0.472361i	0.639410	+	0.768866i	$0.279179\pi$
$548$	0.882851	−	7.08505i	0.0377135	−	0.302658i
$549$	−1.73439	+	25.6773i	−0.0740218	+	1.09588i
$550$	5.55507	+	6.29023i	0.236869	+	0.268216i
$551$	−40.0236	−	16.5783i	−1.70506	−	0.706261i
$552$	0.202355	−	0.158316i	0.00861278	−	0.00673839i
$553$	1.21515	−	0.503334i	0.0516736	−	0.0214039i
$554$	−14.3122	+	29.2777i	−0.608068	+	1.24389i
$555$	−11.8817	−	1.57630i	−0.504348	−	0.0669101i
$556$	−3.03317	+	0.219928i	−0.128635	+	0.00932702i
$557$	−6.70520	−	33.7093i	−0.284108	−	1.42831i	−0.814306	−	0.580435i	$-0.802882\pi$
$557$	−6.70520	−	33.7093i	−0.284108	−	1.42831i	0.530198	−	0.847874i	$-0.322118\pi$
$558$	−27.2046	−	15.6532i	−1.15166	−	0.662653i
$559$	45.3990	+	45.3990i	1.92017	+	1.92017i
$560$	0.601548	−	11.6503i	0.0254200	−	0.492316i
$561$	−52.4905	+	3.38787i	−2.21615	+	0.143036i
$562$	−24.5651	+	3.32070i	−1.03621	+	0.140075i
$563$	−6.00465	−	30.1874i	−0.253066	−	1.27225i	−0.873049	−	0.487633i	$-0.837860\pi$
$563$	−6.00465	−	30.1874i	−0.253066	−	1.27225i	0.619983	−	0.784615i	$-0.287140\pi$
$564$	2.60537	+	4.45141i	0.109706	+	0.187438i
$565$	14.6825	−	9.81056i	0.617699	−	0.412733i
$566$	28.1119	−	9.65149i	1.18163	−	0.405682i
$567$	20.8876	−	15.8957i	0.877197	−	0.667558i
$568$	0.420059	−	1.04470i	0.0176253	−	0.0438347i
$569$	−7.20877	−	2.98597i	−0.302207	−	0.125178i	0.226427	−	0.974028i	$-0.427296\pi$
$569$	−7.20877	−	2.98597i	−0.302207	−	0.125178i	−0.528634	+	0.848850i	$0.677296\pi$
$570$	−12.1253	+	12.1853i	−0.507873	+	0.510387i
$571$	−19.8189	−	3.94222i	−0.829394	−	0.164977i	−0.237904	−	0.971289i	$-0.576460\pi$
$571$	−19.8189	−	3.94222i	−0.829394	−	0.164977i	−0.591490	+	0.806312i	$0.701460\pi$
$572$	58.2074	−	16.0298i	2.43377	−	0.670241i
$573$	−32.5112	+	8.67662i	−1.35817	+	0.362471i
$574$	−24.4029	+	14.2020i	−1.01856	+	0.592780i
$575$	−0.0524450			−0.00218711
$576$	20.5554	−	12.3886i	0.856473	−	0.516192i
$577$	−30.6119			−1.27439			−0.637195	−	0.770703i	$-0.719905\pi$
$577$	−30.6119			−1.27439			−0.637195	+	0.770703i	$0.719905\pi$
$578$	−11.2334	+	6.53764i	−0.467250	+	0.271930i
$579$	20.9704	−	5.59662i	0.871502	−	0.232588i
$580$	−3.27794	−	11.9028i	−0.136109	−	0.494238i
$581$	−0.438089	−	0.0871414i	−0.0181750	−	0.00361523i
$582$	−17.1553	+	17.2402i	−0.711111	+	0.714631i
$583$	9.41474	+	3.89971i	0.389919	+	0.161510i
$584$	−7.60157	−	17.8254i	−0.314555	−	0.737619i
$585$	−7.60431	−	13.2319i	−0.314400	−	0.547071i
$586$	31.9804	−	10.9796i	1.32110	−	0.453564i
$587$	−15.0001	+	10.0227i	−0.619118	+	0.413682i	−0.825190	−	0.564855i	$-0.808932\pi$
$587$	−15.0001	+	10.0227i	−0.619118	+	0.413682i	0.206072	+	0.978537i	$0.433932\pi$
$588$	−4.50170	+	2.63480i	−0.185647	+	0.108657i
$589$	−10.1286	−	50.9199i	−0.417341	−	2.09812i
$590$	3.45015	−	0.466390i	0.142040	−	0.0192010i
$591$	29.4439	−	1.90038i	1.21116	−	0.0781713i
$592$	9.25989	+	26.0851i	0.380579	+	1.07209i
$593$	7.54651	+	7.54651i	0.309898	+	0.309898i	0.844870	−	0.534972i	$-0.179678\pi$
$593$	7.54651	+	7.54651i	0.309898	+	0.309898i	−0.534972	+	0.844870i	$0.679678\pi$
$594$	41.2853	−	14.0364i	1.69396	−	0.575919i
$595$	−2.91182	−	14.6387i	−0.119373	−	0.600128i
$596$	−1.65588	−	22.8373i	−0.0678275	−	0.935454i
$597$	11.9577	+	1.58638i	0.489395	+	0.0649263i
$598$	−0.165703	+	0.338969i	−0.00677611	+	0.0138615i
$599$	1.70964	−	0.708157i	0.0698541	−	0.0289345i	−0.347483	−	0.937686i	$-0.612964\pi$
$599$	1.70964	−	0.708157i	0.0698541	−	0.0289345i	0.417337	+	0.908752i	$0.362964\pi$
$600$	−4.86286	−	0.593761i	−0.198526	−	0.0242402i
$601$	15.0867	+	6.24913i	0.615401	+	0.254907i	0.668536	−	0.743680i	$-0.266921\pi$
$601$	15.0867	+	6.24913i	0.615401	+	0.254907i	−0.0531350	+	0.998587i	$0.516921\pi$
$602$	−34.4576	−	39.0177i	−1.40439	−	1.59024i
$603$	1.30255	+	0.0879813i	0.0530438	+	0.00358288i
$604$	−6.11028	−	0.761388i	−0.248624	−	0.0309804i
$605$	13.4519	−	20.1323i	0.546899	−	0.818493i
$606$	4.80609	−	3.22852i	0.195234	−	0.131150i
$607$	−13.7340			−0.557447			−0.278724	−	0.960371i	$-0.589911\pi$
$607$	−13.7340			−0.557447			−0.278724	+	0.960371i	$0.589911\pi$
$608$	37.8079	+	12.1076i	1.53331	+	0.491029i
$609$	−20.5834	+	23.4238i	−0.834082	+	0.949178i
$610$	−11.7294	−	3.09935i	−0.474909	−	0.125489i
$611$	−6.29785	−	4.20809i	−0.254784	−	0.170241i
$612$	21.6049	−	21.8194i	0.873328	−	0.881996i
$613$	0.256655	+	0.0510518i	0.0103662	+	0.00206196i	0.200271	−	0.979741i	$-0.435818\pi$
$613$	0.256655	+	0.0510518i	0.0103662	+	0.00206196i	−0.189905	+	0.981803i	$0.560818\pi$
$614$	−6.75355	−	7.64732i	−0.272551	−	0.308621i
$615$	5.23358	+	10.6394i	0.211038	+	0.429021i
$616$	−47.9075	+	10.0483i	−1.93025	+	0.404856i
$617$	7.43091	+	17.9398i	0.299157	+	0.722229i	0.999961	+	0.00887483i	$0.00282498\pi$
$617$	7.43091	+	17.9398i	0.299157	+	0.722229i	−0.700803	+	0.713354i	$0.747175\pi$
$618$	11.8376	−	4.93759i	0.476180	−	0.198619i
$619$	16.2366	−	10.8490i	0.652606	−	0.436057i	−0.184698	−	0.982795i	$-0.559131\pi$
$619$	16.2366	−	10.8490i	0.652606	−	0.436057i	0.837304	+	0.546738i	$0.184131\pi$
$620$	9.67817	−	11.1914i	0.388685	−	0.449456i
$621$	−0.105038	+	0.251455i	−0.00421504	+	0.0100906i
$622$	−1.83507	+	2.40875i	−0.0735796	+	0.0965820i
$623$	−4.84458	+	4.84458i	−0.194094	+	0.194094i
$624$	−19.2022	+	29.5543i	−0.768703	+	1.18312i
$625$	0.707107	+	0.707107i	0.0282843	+	0.0282843i
$626$	1.78387	−	0.241143i	0.0712979	−	0.00963803i
$627$	62.4308	+	36.1274i	2.49325	+	1.44279i
$628$	6.77232	−	3.39829i	0.270245	−	0.135607i
$629$	19.6751	+	29.4458i	0.784496	+	1.17408i
$630$	5.48899	+	11.0894i	0.218687	+	0.441812i
$631$	−38.0092	+	15.7439i	−1.51312	+	0.626757i	−0.976200	−	0.216874i	$-0.930414\pi$
$631$	−38.0092	+	15.7439i	−1.51312	+	0.626757i	−0.536925	+	0.843630i	$0.680414\pi$
$632$	−0.892539	+	0.911294i	−0.0355033	+	0.0362493i
$633$	−13.1613	−	26.7556i	−0.523114	−	1.06344i
$634$	0.922852	−	14.8694i	0.0366511	−	0.590539i
$635$	−1.72053	+	8.64968i	−0.0682771	+	0.343252i
$636$	−5.62170	+	1.94559i	−0.222915	+	0.0771477i
$637$	4.25563	−	6.36900i	0.168614	−	0.252349i
$638$	−44.7732	+	26.0571i	−1.77259	+	1.03161i
$639$	0.153526	+	1.18438i	0.00607338	+	0.0468534i
$640$	3.89547	+	10.6219i	0.153982	+	0.419869i
$641$			12.0556i			0.476169i	0.971244	+	0.238085i	$0.0765195\pi$
$641$			12.0556i			0.476169i	−0.971244	+	0.238085i	$0.923480\pi$
$642$	0.282128	−	1.43689i	0.0111347	−	0.0567093i
$643$	15.3018	+	10.2244i	0.603445	+	0.403209i	0.819423	−	0.573189i	$-0.194294\pi$
$643$	15.3018	+	10.2244i	0.603445	+	0.403209i	−0.215978	+	0.976398i	$0.569294\pi$
$644$	0.151114	−	0.265977i	0.00595472	−	0.0104810i
$645$	−17.3560	+	13.2902i	−0.683391	+	0.523303i
$646$	50.6943	+	3.14628i	1.99454	+	0.123789i
$647$	11.3290	−	27.3505i	0.445387	−	1.07526i	−0.528643	−	0.848844i	$-0.677299\pi$
$647$	11.3290	−	27.3505i	0.445387	−	1.07526i	0.974031	−	0.226416i	$-0.0727009\pi$
$648$	−12.5863	+	22.1265i	−0.494439	+	0.869213i
$649$	−5.59043	−	13.4965i	−0.219444	−	0.529784i
$650$	6.80441	−	2.33612i	0.266891	−	0.0916300i
$651$	−37.0454	−	4.91469i	−1.45193	−	0.192622i
$652$	19.0637	+	37.9913i	0.746593	+	1.48785i
$653$	−35.6704	+	7.09529i	−1.39589	+	0.277660i	−0.835009	−	0.550236i	$-0.814538\pi$
$653$	−35.6704	+	7.09529i	−1.39589	+	0.277660i	−0.560882	+	0.827896i	$0.689538\pi$
$654$	−16.6352	−	11.0560i	−0.650487	−	0.432323i
$655$	7.79483	−	7.79483i	0.304569	−	0.304569i
$656$	16.3666	−	21.9529i	0.639009	−	0.857116i
$657$	16.2816	+	12.5450i	0.635207	+	0.489427i
$658$	4.88499	+	3.72156i	0.190437	+	0.145081i
$659$	−13.9565	+	2.77613i	−0.543669	+	0.108143i	−0.459282	−	0.888291i	$-0.651893\pi$
$659$	−13.9565	+	2.77613i	−0.543669	+	0.108143i	−0.0843871	+	0.996433i	$0.526893\pi$
$660$	2.80401	+	20.3640i	0.109146	+	0.792667i
$661$	−16.6474	−	24.9145i	−0.647508	−	0.969064i	−0.999454	−	0.0330434i	$-0.989480\pi$
$661$	−16.6474	−	24.9145i	−0.647508	−	0.969064i	0.351946	−	0.936020i	$-0.385520\pi$
$662$	−1.65415	+	3.38380i	−0.0642904	+	0.131515i
$663$	−14.5371	+	42.6850i	−0.564572	+	1.65775i
$664$	0.423964	−	0.0889235i	0.0164530	−	0.00345090i
$665$	−7.83255	+	18.9094i	−0.303733	+	0.733277i
$666$	−22.1017	−	19.3252i	−0.856425	−	0.748837i
$667$	0.0631588	−	0.317521i	0.00244552	−	0.0122944i
$668$	13.5348	−	10.5354i	0.523675	−	0.407628i
$669$	32.6919	−	8.72485i	1.26394	−	0.337322i
$670$	−0.157223	+	0.595004i	−0.00607405	+	0.0229870i
$671$			50.9058i			1.96519i
$672$	17.0231	−	22.9514i	0.656679	−	0.885370i
$673$			7.17836i			0.276705i	0.990383	+	0.138353i	$0.0441807\pi$
$673$			7.17836i			0.276705i	−0.990383	+	0.138353i	$0.955819\pi$
$674$	13.8565	+	3.66143i	0.533734	+	0.141033i
$675$	4.80654	−	1.97412i	0.185004	−	0.0759839i
$676$	3.18494	−	25.5598i	0.122498	−	0.983069i
$677$	9.41449	−	47.3299i	0.361828	−	1.81903i	−0.186126	−	0.982526i	$-0.559593\pi$
$677$	9.41449	−	47.3299i	0.361828	−	1.81903i	0.547954	−	0.836508i	$-0.315407\pi$
$678$	43.2543	−	0.106790i	1.66117	−	0.00410126i
$679$	−11.0818	+	26.7538i	−0.425279	+	1.02672i
$680$	8.16654	+	11.9512i	0.313173	+	0.458308i
$681$	8.51744	+	2.90075i	0.326389	+	0.111157i
$682$	−55.7753	−	27.2654i	−2.13575	−	1.04405i
$683$	5.27236	+	7.89065i	0.201741	+	0.301927i	0.918521	−	0.395373i	$-0.129385\pi$
$683$	5.27236	+	7.89065i	0.201741	+	0.301927i	−0.716779	+	0.697300i	$0.754385\pi$
$684$	−41.2572	+	8.41856i	−1.57751	+	0.321892i
$685$	−3.50132	+	0.696457i	−0.133779	+	0.0266102i
$686$	13.7328	−	18.0259i	0.524320	−	0.688232i
$687$	29.7521	−	1.92028i	1.13511	−	0.0732633i
$688$	45.5825	+	21.6985i	1.73782	+	0.827249i
$689$	6.17730	−	6.17730i	0.235336	−	0.235336i
$690$	−0.106989	−	0.0711065i	−0.00407301	−	0.00270698i
$691$	−42.3731	+	8.42853i	−1.61195	+	0.320637i	−0.917142	−	0.398560i	$-0.869510\pi$
$691$	−42.3731	+	8.42853i	−1.61195	+	0.320637i	−0.694807	+	0.719197i	$0.744510\pi$
$692$	11.2603	+	3.73551i	0.428051	+	0.142003i
$693$	39.1031	−	34.1549i	1.48540	−	1.29744i
$694$	−0.800116	−	2.33050i	−0.0303720	−	0.0884646i
$695$	0.581896	+	1.40482i	0.0220726	+	0.0532879i
$696$	9.45113	−	28.7265i	0.358244	−	1.08887i
$697$	13.4067	−	32.3667i	0.507816	−	1.22598i
$698$	0.853055	−	13.7448i	0.0322886	−	0.520249i
$699$	−24.3261	−	31.7679i	−0.920097	−	1.20157i
$700$	−5.62357	+	1.54869i	−0.212551	+	0.0585348i
$701$	−0.548009	−	0.366168i	−0.0206980	−	0.0138300i	0.545178	−	0.838320i	$-0.316462\pi$
$701$	−0.548009	−	0.366168i	−0.0206980	−	0.0138300i	−0.565876	+	0.824490i	$0.691462\pi$
$702$	2.42719	−	37.3036i	0.0916084	−	1.40793i
$703$		−	48.5637i		−	1.83162i
$704$	38.9149	−	27.1892i	1.46666	−	1.02473i
$705$	1.70232	−	1.93723i	0.0641131	−	0.0729602i
$706$	19.9800	+	34.3310i	0.751957	+	1.29207i
$707$	3.82987	−	5.73180i	0.144037	−	0.215567i
$708$	7.67076	+	3.72637i	0.288285	+	0.140046i
$709$	9.17055	−	46.1035i	0.344407	−	1.73145i	−0.288729	−	0.957411i	$-0.593232\pi$
$709$	9.17055	−	46.1035i	0.344407	−	1.73145i	0.633136	−	0.774041i	$-0.281768\pi$
$710$	−0.561913	−	0.0348745i	−0.0210882	−	0.00130882i
$711$	0.352773	−	1.30615i	0.0132300	−	0.0489843i
$712$	2.47877	−	6.16479i	0.0928958	−	0.231035i
$713$	0.358447	−	0.148474i	0.0134240	−	0.00556039i
$714$	13.9074	−	33.8113i	0.520471	−	1.26536i
$715$	−16.7711	−	25.0997i	−0.627203	−	0.938676i
$716$	−8.35240	−	2.77085i	−0.312144	−	0.103551i
$717$	−6.20334	+	10.7198i	−0.231668	+	0.400339i
$718$	3.82146	+	28.2695i	0.142616	+	1.05501i
$719$	12.9261	+	12.9261i	0.482064	+	0.482064i	0.905790	−	0.423726i	$-0.139278\pi$
$719$	12.9261	+	12.9261i	0.482064	+	0.482064i	−0.423726	+	0.905790i	$0.639278\pi$
$720$	−9.11535	−	7.80451i	−0.339709	−	0.290857i
$721$	10.7985	−	10.7985i	0.402155	−	0.402155i
$722$	−34.0307	−	25.9258i	−1.26649	−	0.964857i
$723$	41.8155	+	24.1978i	1.55513	+	0.899925i
$724$	−0.567024	−	7.82021i	−0.0210733	−	0.290636i
$725$	−5.13264	+	3.42952i	−0.190621	+	0.127369i
$726$	54.7383	−	22.8319i	2.03153	−	0.847369i
$727$	−9.82583	−	23.7216i	−0.364420	−	0.879787i	−0.994643	−	0.103373i	$-0.967036\pi$
$727$	−9.82583	−	23.7216i	−0.364420	−	0.879787i	0.630223	−	0.776414i	$-0.282964\pi$
$728$	−7.75836	+	41.2402i	−0.287544	+	1.52846i
$729$	0.161453	−	26.9995i	0.00597974	−	0.999982i
$730$	−7.26259	+	6.41379i	−0.268801	+	0.237385i
$731$	63.3484	+	12.6008i	2.34303	+	0.466057i
$732$	−19.7261	−	22.2258i	−0.729098	−	0.821491i
$733$	5.43120	+	3.62901i	0.200606	+	0.134041i	0.651816	−	0.758377i	$-0.274007\pi$
$733$	5.43120	+	3.62901i	0.200606	+	0.134041i	−0.451210	+	0.892418i	$0.649007\pi$
$734$	1.21228	−	4.58783i	0.0447461	−	0.169340i
$735$	1.95911	+	1.72155i	0.0722629	+	0.0635004i
$736$	−0.0336214	+	0.294762i	−0.00123930	+	0.0108651i
$737$	2.58233			0.0951213
$738$	−3.74853	+	28.8005i	−0.137985	+	1.06016i
$739$	−5.37399	+	8.04274i	−0.197685	+	0.295857i	−0.917047	−	0.398778i	$-0.869434\pi$
$739$	−5.37399	+	8.04274i	−0.197685	+	0.295857i	0.719362	+	0.694635i	$0.244434\pi$
$740$	10.9213	−	8.50113i	0.401476	−	0.312508i
$741$	49.0950	−	37.5943i	1.80355	−	1.38106i
$742$	−5.30902	+	4.68853i	−0.194900	+	0.172121i
$743$	16.9994	+	7.04139i	0.623648	+	0.258324i	0.672052	−	0.740504i	$-0.265413\pi$
$743$	16.9994	+	7.04139i	0.623648	+	0.258324i	−0.0484032	+	0.998828i	$0.515413\pi$
$744$	34.9174	−	9.70876i	1.28013	−	0.355940i
$745$	−10.5772	+	4.38121i	−0.387518	+	0.160515i
$746$	−25.2200	−	12.3287i	−0.923371	−	0.451385i
$747$	−0.346048	+	0.302258i	−0.0126612	+	0.0110590i
$748$	39.7292	−	45.9409i	1.45264	−	1.67977i
$749$	−0.340136	−	1.70998i	−0.0124283	−	0.0624813i
$750$	0.483802	+	2.40124i	0.0176659	+	0.0876808i
$751$	−29.5611	−	29.5611i	−1.07870	−	1.07870i	−0.996626	−	0.0820728i	$-0.973846\pi$
$751$	−29.5611	−	29.5611i	−1.07870	−	1.07870i	−0.0820728	−	0.996626i	$-0.526154\pi$
$752$	−5.77360	−	1.46156i	−0.210542	−	0.0532977i
$753$	−3.47469	−	53.8357i	−0.126625	−	1.96188i
$754$	5.94922	+	44.0097i	0.216658	+	1.60274i
$755$	0.600638	+	3.01961i	0.0218594	+	0.109895i
$756$	−3.83763	+	30.0648i	−0.139573	+	1.09345i
$757$	16.2097	−	10.8310i	0.589152	−	0.393659i	−0.224959	−	0.974368i	$-0.572225\pi$
$757$	16.2097	−	10.8310i	0.589152	−	0.393659i	0.814111	+	0.580710i	$0.197225\pi$
$758$	11.5426	+	33.6202i	0.419247	+	1.22114i
$759$	−0.173775	+	0.510253i	−0.00630763	+	0.0185210i
$760$	−0.206364	−	19.8485i	−0.00748561	−	0.719982i
$761$	−14.8234	−	6.14007i	−0.537349	−	0.222577i	0.0974694	−	0.995239i	$-0.468925\pi$
$761$	−14.8234	−	6.14007i	−0.537349	−	0.222577i	−0.634819	+	0.772661i	$0.718925\pi$
$762$	−15.2374	+	15.3129i	−0.551994	+	0.554726i
$763$	−23.3250	−	4.63963i	−0.844421	−	0.167966i
$764$	19.1936	−	33.7829i	0.694401	−	1.22222i
$765$	−13.7561	−	6.81789i	−0.497354	−	0.246501i
$766$	0.346208	+	0.594879i	0.0125090	+	0.0214938i
$767$	−12.5235			−0.452198
$768$	−6.45467	+	26.9506i	−0.232913	+	0.972498i
$769$	−0.331567			−0.0119566			−0.00597830	−	0.999982i	$-0.501903\pi$
$769$	−0.331567			−0.0119566			−0.00597830	+	0.999982i	$0.501903\pi$
$770$	12.3109	+	21.1534i	0.443653	+	0.762316i
$771$	5.13600	+	19.2445i	0.184969	+	0.693074i
$772$	−12.3803	+	21.7907i	−0.445577	+	0.784266i
$773$	−6.94996	−	1.38243i	−0.249973	−	0.0497226i	0.0685135	−	0.997650i	$-0.478174\pi$
$773$	−6.94996	−	1.38243i	−0.249973	−	0.0497226i	−0.318486	+	0.947928i	$0.603174\pi$
$774$	−53.4260	+	3.58073i	−1.92036	+	0.128707i
$775$	−6.83474	−	2.83104i	−0.245511	−	0.101694i
$776$	−0.291971	−	28.0824i	−0.0104812	−	1.00810i
$777$	−33.0897	−	11.2692i	−1.18709	−	0.404281i
$778$	−15.1240	−	44.0516i	−0.542220	−	1.57933i
$779$	−39.9452	+	26.6905i	−1.43119	+	0.956288i
$780$	17.0486	+	4.45989i	0.610437	+	0.159690i
$781$	0.460867	+	2.31693i	0.0164911	+	0.0829064i
$782$	0.0508476	+	0.376148i	0.00181830	+	0.0134510i
$783$	6.16357	+	31.4779i	0.220268	+	1.12493i
$784$	1.47807	−	5.83883i	0.0527884	−	0.208529i
$785$	−2.67892	−	2.67892i	−0.0956146	−	0.0956146i
$786$	26.4702	−	5.33322i	0.944160	−	0.190230i
$787$	4.88767	+	24.5720i	0.174227	+	0.875896i	0.964690	+	0.263387i	$0.0848396\pi$
$787$	4.88767	+	24.5720i	0.174227	+	0.875896i	−0.790464	+	0.612509i	$0.790160\pi$
$788$	−22.2856	+	25.7699i	−0.793890	+	0.918016i
$789$	4.95904	−	37.3797i	0.176546	−	1.33075i
$790$	0.572987	+	0.280101i	0.0203860	+	0.00996556i
$791$	47.5802	−	19.7084i	1.69176	−	0.700749i
$792$	−21.8899	+	45.3449i	−0.777822	+	1.61126i
$793$	40.3184	+	16.7004i	1.43175	+	0.593049i
$794$	3.28339	−	2.89964i	0.116523	−	0.102904i
$795$	1.80836	+	2.36157i	0.0641360	+	0.0837563i
$796$	−10.9912	+	8.55552i	−0.389572	+	0.303242i
$797$	−30.1755	+	45.1608i	−1.06887	+	1.59968i	−0.307280	+	0.951619i	$0.599419\pi$
$797$	−30.1755	+	45.1608i	−1.06887	+	1.59968i	−0.761590	+	0.648059i	$0.775581\pi$
$798$	−41.6166	+	27.9562i	−1.47321	+	0.989639i
$799$	−7.61985			−0.269571
$800$	4.42754	−	3.52092i	0.156537	−	0.124483i
$801$	0.905956	+	6.98904i	0.0320104	+	0.246946i
$802$	−8.97302	+	33.9581i	−0.316848	+	1.19910i
$803$	33.8044	+	22.5874i	1.19293	+	0.797091i
$804$	−1.12746	+	1.00066i	−0.0397626	+	0.0352905i
$805$	−0.150015	−	0.0298398i	−0.00528733	−	0.00105171i
$806$	−39.8927	+	35.2303i	−1.40516	+	1.24093i
$807$	−12.1416	+	5.97253i	−0.427404	+	0.210243i
$808$	−1.23604	+	6.57024i	−0.0434836	+	0.231140i
$809$	11.7326	+	28.3250i	0.412497	+	0.995855i	0.984465	+	0.175579i	$0.0561798\pi$
$809$	11.7326	+	28.3250i	0.412497	+	0.995855i	−0.571969	+	0.820275i	$0.693820\pi$
$810$	12.4821	+	2.48960i	0.438575	+	0.0874756i
$811$	−15.4035	+	10.2923i	−0.540889	+	0.361410i	−0.795805	−	0.605553i	$-0.792952\pi$
$811$	−15.4035	+	10.2923i	−0.540889	+	0.361410i	0.254916	+	0.966963i	$0.417952\pi$
$812$	−2.60390	−	35.9122i	−0.0913791	−	1.26027i
$813$	−7.58584	+	13.1089i	−0.266047	+	0.459748i
$814$	−46.1943	−	35.1924i	−1.61911	−	1.23349i
$815$	15.0282	−	15.0282i	0.526414	−	0.526414i
$816$	0.456148	+	35.4533i	0.0159684	+	1.24111i
$817$	−62.6299	−	62.6299i	−2.19114	−	2.19114i
$818$	6.90613	+	51.0885i	0.241467	+	1.78627i
$819$	−14.2230	−	42.1755i	−0.496990	−	1.47373i
$820$	−12.9948	−	4.31093i	−0.453798	−	0.150544i
$821$	−19.6441	−	29.3995i	−0.685584	−	1.02605i	−0.997122	−	0.0758149i	$-0.975844\pi$
$821$	−19.6441	−	29.3995i	−0.685584	−	1.02605i	0.311538	−	0.950234i	$-0.399156\pi$
$822$	−8.08708	−	3.32641i	−0.282069	−	0.116022i
$823$	22.3593	−	9.26154i	0.779397	−	0.322837i	0.0427252	−	0.999087i	$-0.486396\pi$
$823$	22.3593	−	9.26154i	0.779397	−	0.322837i	0.736672	+	0.676250i	$0.236396\pi$
$824$	−5.52511	+	13.7412i	−0.192476	+	0.478696i
$825$	9.22264	−	4.53668i	0.321091	−	0.157947i
$826$	10.1343	+	0.628971i	0.352616	+	0.0218847i
$827$	−4.96975	+	24.9846i	−0.172815	+	0.868800i	0.792931	+	0.609311i	$0.208554\pi$
$827$	−4.96975	+	24.9846i	−0.172815	+	0.868800i	−0.965746	+	0.259489i	$0.916446\pi$
$828$	−0.121853	−	0.290119i	−0.00423468	−	0.0100823i
$829$	3.55170	−	5.31550i	0.123356	−	0.184615i	−0.764652	−	0.644443i	$-0.777089\pi$
$829$	3.55170	−	5.31550i	0.123356	−	0.184615i	0.888008	+	0.459828i	$0.152089\pi$
$830$	−0.108947	−	0.187200i	−0.00378159	−	0.00649780i
$831$	29.9818	+	26.3462i	1.04006	+	0.913941i
$832$	−8.76775	−	39.7412i	−0.303967	−	1.37778i
$833$		−	7.70593i		−	0.266995i
$834$	−0.717615	+	3.65483i	−0.0248490	+	0.126556i
$835$	−7.13061	−	4.76452i	−0.246765	−	0.164883i
$836$	−80.2997	+	22.1139i	−2.77722	+	0.764824i
$837$	−27.2626	+	27.1001i	−0.942335	+	0.936716i
$838$	3.30830	−	53.3048i	0.114283	−	1.84138i
$839$	−1.06615	+	2.57391i	−0.0368076	+	0.0888613i	−0.941214	−	0.337810i	$-0.890314\pi$
$839$	−1.06615	+	2.57391i	−0.0368076	+	0.0888613i	0.904407	+	0.426671i	$0.140314\pi$
$840$	−13.5720	−	4.46525i	−0.468279	−	0.154066i
$841$	−3.48455	−	8.41244i	−0.120157	−	0.290084i
$842$	3.80292	+	11.0768i	0.131057	+	0.381731i
$843$	−3.99272	+	30.0959i	−0.137516	+	1.03656i
$844$	32.6790	+	10.8410i	1.12486	+	0.373163i
$845$	−12.6313	+	2.51251i	−0.434529	+	0.0864331i
$846$	6.09934	−	1.64394i	0.209700	−	0.0565199i
$847$	49.9330	−	49.9330i	1.71572	−	1.71572i
$848$	2.95245	−	6.20226i	0.101388	−	0.212987i
$849$	−2.34464	−	36.3270i	−0.0804678	−	1.24674i
$850$	4.38597	−	5.75711i	0.150438	−	0.197467i
$851$	0.355945	−	0.0708018i	0.0122016	−	0.00242706i
$852$	−1.09904	−	0.833004i	−0.0376523	−	0.0285382i
$853$	−16.5283	−	24.7363i	−0.565917	−	0.846955i	0.432589	−	0.901591i	$-0.357600\pi$
$853$	−16.5283	−	24.7363i	−0.565917	−	0.846955i	−0.998506	+	0.0546361i	$0.982600\pi$
$854$	−31.7876	−	15.5392i	−1.08775	−	0.531740i
$855$	10.4905	+	18.2540i	0.358767	+	0.624273i
$856$	0.953952	+	1.39605i	0.0326054	+	0.0477160i
$857$	11.7222	−	28.2998i	0.400422	−	0.966704i	−0.587142	−	0.809484i	$-0.699747\pi$
$857$	11.7222	−	28.2998i	0.400422	−	0.966704i	0.987564	−	0.157220i	$-0.0502531\pi$
$858$	−0.182557	−	73.9429i	−0.00623240	−	2.52437i
$859$	1.77710	−	8.93407i	0.0606338	−	0.304827i	−0.938554	−	0.345134i	$-0.887834\pi$
$859$	1.77710	−	8.93407i	0.0606338	−	0.304827i	0.999187	+	0.0403070i	$0.0128336\pi$
$860$	3.12118	−	25.0481i	0.106431	−	0.854132i
$861$	8.91674	+	33.4109i	0.303882	+	1.13864i
$862$	37.9175	+	10.0193i	1.29148	+	0.341258i
$863$		−	35.2042i		−	1.19837i	−0.800612	−	0.599183i	$-0.795492\pi$
$863$		−	35.2042i		−	1.19837i	0.800612	−	0.599183i	$-0.204508\pi$
$864$	−8.01398	−	28.2803i	−0.272641	−	0.962116i
$865$		−	5.93185i		−	0.201689i
$866$	−6.49019	+	24.5619i	−0.220546	+	0.834647i
$867$	4.10467	+	15.3801i	0.139402	+	0.522337i
$868$	34.0512	−	26.5054i	1.15577	−	0.899653i
$869$	0.522091	−	2.62473i	0.0177107	−	0.0890378i
$870$	−15.1206	+	0.0373311i	−0.512636	+	0.00126564i
$871$	0.847173	−	2.04526i	0.0287053	−	0.0693008i
$872$	22.5729	−	4.73451i	0.764415	−	0.160331i
$873$	14.8423	+	25.8264i	0.502336	+	0.874091i
$874$	0.228595	−	0.467623i	0.00773233	−	0.0158176i
$875$	1.62030	+	2.42495i	0.0547761	+	0.0819783i
$876$	−23.5119	+	3.23746i	−0.794394	+	0.109384i
$877$	−31.6900	+	6.30353i	−1.07010	+	0.212855i	−0.698551	−	0.715560i	$-0.746172\pi$
$877$	−31.6900	+	6.30353i	−1.07010	+	0.212855i	−0.371544	+	0.928415i	$0.621172\pi$
$878$	46.1651	+	35.1702i	1.55800	+	1.18694i
$879$	−2.66728	−	41.3259i	−0.0899652	−	1.39389i
$880$	−19.0297	−	14.1872i	−0.641490	−	0.478252i
$881$	18.6816	−	18.6816i	0.629399	−	0.629399i	−0.318518	−	0.947917i	$-0.603185\pi$
$881$	18.6816	−	18.6816i	0.629399	−	0.629399i	0.947917	+	0.318518i	$0.103185\pi$
$882$	1.66251	+	6.16824i	0.0559797	+	0.207696i
$883$	9.85289	−	1.95986i	0.331576	−	0.0659546i	−0.0264949	−	0.999649i	$-0.508435\pi$
$883$	9.85289	−	1.95986i	0.331576	−	0.0659546i	0.358071	+	0.933694i	$0.383435\pi$
$884$	−23.3523	−	46.5379i	−0.785424	−	1.56524i
$885$	0.560775	−	4.22695i	0.0188502	−	0.142087i
$886$	7.78359	−	2.67229i	0.261495	−	0.0897774i
$887$	−10.7389	−	25.9261i	−0.360578	−	0.870513i	−0.995216	−	0.0977031i	$-0.968850\pi$
$887$	−10.7389	−	25.9261i	−0.360578	−	0.870513i	0.634637	−	0.772810i	$-0.281150\pi$
$888$	33.8059	−	2.53510i	1.13445	−	0.0850725i
$889$	−9.84287	+	23.7628i	−0.330119	+	0.796979i
$890$	−3.31585	−	0.205794i	−0.111148	−	0.00689824i
$891$	−3.28047	−	53.3055i	−0.109900	−	1.78580i
$892$	−19.3003	+	33.9707i	−0.646221	+	1.13742i
$893$	8.68816	+	5.80524i	0.290738	+	0.194265i
$894$	−27.5179	−	5.40306i	−0.920337	−	0.180706i
$895$			4.40001i			0.147076i
$896$	5.09909	+	32.5996i	0.170349	+	1.08908i
$897$	0.347121	+	0.305030i	0.0115900	+	0.0101846i
$898$	17.0331	−	9.91293i	0.568402	−	0.330799i
$899$	25.3711	−	37.9706i	0.846174	−	1.26639i
$900$	−2.26870	+	5.55455i	−0.0756234	+	0.185152i
$901$	1.71455	−	8.61962i	0.0571199	−	0.287161i
$902$	−3.55861	+	57.3380i	−0.118489	+	1.90915i
$903$	−57.2072	+	28.1406i	−1.90374	+	0.936462i
$904$	−34.9480	+	35.6824i	−1.16235	+	1.18678i
$905$	−3.62195	+	1.50026i	−0.120398	+	0.0498703i
$906$	−2.86876	+	6.97446i	−0.0953082	+	0.231711i
$907$	8.42868	+	12.6144i	0.279870	+	0.418854i	0.944597	−	0.328231i	$-0.106452\pi$
$907$	8.42868	+	12.6144i	0.279870	+	0.418854i	−0.664728	+	0.747086i	$0.731452\pi$
$908$	−9.28626	+	4.65977i	−0.308176	+	0.154640i
$909$	−2.26595	−	6.71925i	−0.0751568	−	0.222863i
$910$	20.7927	−	2.81075i	0.689271	−	0.0931754i
$911$	36.1108	+	36.1108i	1.19640	+	1.19640i	0.975236	+	0.221169i	$0.0709871\pi$
$911$	36.1108	+	36.1108i	1.19640	+	1.19640i	0.221169	+	0.975236i	$0.429013\pi$
$912$	26.4903	−	40.7714i	0.877181	−	1.35008i
$913$	−0.642641	+	0.642641i	−0.0212683	+	0.0212683i
$914$	23.9110	−	31.3860i	0.790905	−	1.03816i
$915$	−7.44210	+	12.8605i	−0.246028	+	0.425154i
$916$	−22.5189	+	26.0398i	−0.744045	+	0.860378i
$917$	26.7316	−	17.8615i	0.882754	−	0.589838i
$918$	−18.8190	−	32.5597i	−0.621119	−	1.07463i
$919$	1.30174	+	3.14268i	0.0429405	+	0.103668i	0.943895	−	0.330247i	$-0.107132\pi$
$919$	1.30174	+	3.14268i	0.0429405	+	0.103668i	−0.900954	+	0.433914i	$0.857132\pi$
$920$	0.145178	−	0.0304500i	0.00478637	−	0.00100391i
$921$	−11.2124	+	5.51545i	−0.369461	+	0.181740i
$922$	26.4834	+	29.9883i	0.872185	+	0.987612i
$923$	1.98625	+	0.395090i	0.0653783	+	0.0130045i
$924$	−3.56591	+	59.8450i	−0.117310	+	1.96876i
$925$	−5.75375	−	3.84454i	−0.189182	−	0.126408i
$926$	−51.1232	−	13.5087i	−1.68001	−	0.443923i
$927$	−2.01935	−	15.5784i	−0.0663243	−	0.511662i
$928$	15.9849	+	31.0461i	0.524729	+	1.01914i
$929$	7.38819			0.242399			0.121199	−	0.992628i	$-0.461326\pi$
$929$	7.38819			0.242399			0.121199	+	0.992628i	$0.461326\pi$
$930$	−10.1047	−	15.0422i	−0.331345	−	0.493252i
$931$	−5.87083	+	8.78631i	−0.192409	+	0.287960i
$932$	45.8473	+	5.71292i	1.50178	+	0.187133i
$933$	2.25477	+	2.94454i	0.0738178	+	0.0964000i
$934$	4.97205	+	5.63006i	0.162690	+	0.184221i
$935$	−28.0568	−	11.6215i	−0.917555	−	0.380064i
$936$	28.7328	+	32.2133i	0.939160	+	1.05292i
$937$	34.8670	−	14.4424i	1.13906	−	0.471813i	0.268206	−	0.963362i	$-0.413569\pi$
$937$	34.8670	−	14.4424i	1.13906	−	0.471813i	0.870850	+	0.491549i	$0.163569\pi$
$938$	−0.788266	+	1.61251i	−0.0257378	+	0.0526503i
$939$	0.289944	−	2.18551i	0.00946197	−	0.0713215i
$940$	0.215352	+	2.97006i	0.00702401	+	0.0968728i
$941$	4.40591	+	22.1500i	0.143629	+	0.722070i	0.983732	+	0.179643i	$0.0574943\pi$
$941$	4.40591	+	22.1500i	0.143629	+	0.722070i	−0.840103	+	0.542427i	$0.817506\pi$
$942$	−1.83291	−	9.09722i	−0.0597195	−	0.296404i
$943$	−0.253863	−	0.253863i	−0.00826693	−	0.00826693i
$944$	−9.27989	+	3.29425i	−0.302035	+	0.107219i
$945$	14.8720	−	2.91202i	0.483785	−	0.0947280i
$946$	−104.960	+	14.1884i	−3.41254	+	0.461306i
$947$	−6.28068	−	31.5751i	−0.204095	−	1.02605i	−0.937956	−	0.346754i	$-0.887284\pi$
$947$	−6.28068	−	31.5751i	−0.204095	−	1.02605i	0.733862	−	0.679299i	$-0.237716\pi$
$948$	0.789140	+	1.34829i	0.0256301	+	0.0437904i
$949$	28.9797	−	19.3636i	0.940721	−	0.628569i
$950$	−9.38699	+	3.22277i	−0.304554	+	0.104561i
$951$	−17.2721	−	5.88229i	−0.560086	−	0.190746i
$952$	16.5598	+	38.8321i	0.536707	+	1.25856i
$953$	−29.9589	−	12.4094i	−0.970463	−	0.401979i	−0.159578	−	0.987185i	$-0.551013\pi$
$953$	−29.9589	−	12.4094i	−0.970463	−	0.401979i	−0.810884	+	0.585206i	$0.801013\pi$
$954$	0.487219	+	7.26951i	0.0157743	+	0.235359i
$955$	−19.0540	−	3.79008i	−0.616573	−	0.122644i
$956$	−3.79711	−	13.7880i	−0.122807	−	0.445937i
$957$	16.3600	+	61.3006i	0.528844	+	1.98157i
$958$	−36.7287	+	21.3754i	−1.18665	+	0.690607i
$959$	−10.4115			−0.336206
$960$	13.8061	−	1.17978i	0.445590	−	0.0380772i
$961$	23.7284			0.765432
$962$	−43.0278	+	25.0414i	−1.38727	+	0.807366i
$963$	−1.60688	−	0.796414i	−0.0517811	−	0.0256641i
$964$	−53.7838	+	14.8116i	−1.73226	+	0.477050i
$965$	12.2903	+	2.44469i	0.395638	+	0.0786973i
$966$	−0.265577	−	0.264269i	−0.00854480	−	0.00850271i
$967$	49.0518	+	20.3179i	1.57740	+	0.653381i	0.987999	−	0.154460i	$-0.0493637\pi$
$967$	49.0518	+	20.3179i	1.57740	+	0.653381i	0.589401	+	0.807840i	$0.299364\pi$
$968$	−25.5486	+	63.5403i	−0.821163	+	2.04226i
$969$	20.0545	−	58.8858i	0.644243	−	1.89168i
$970$	−13.2811	+	4.55970i	−0.426429	+	0.146403i
$971$	−5.26189	+	3.51588i	−0.168862	+	0.112830i	−0.637130	−	0.770757i	$-0.719878\pi$
$971$	−5.26189	+	3.51588i	−0.168862	+	0.112830i	0.468267	+	0.883587i	$0.344878\pi$
$972$	22.0883	+	22.0024i	0.708483	+	0.705728i
$973$	0.865162	+	4.34946i	0.0277358	+	0.139437i
$974$	−37.1820	+	5.02625i	−1.19139	+	0.161052i
$975$	−0.567513	−	8.79284i	−0.0181750	−	0.281596i
$976$	34.2687	+	1.76942i	1.09692	+	0.0566377i
$977$	−35.9804	−	35.9804i	−1.15112	−	1.15112i	−0.986329	−	0.164786i	$-0.947307\pi$
$977$	−35.9804	−	35.9804i	−1.15112	−	1.15112i	−0.164786	−	0.986329i	$-0.552693\pi$
$978$	51.0336	−	10.2823i	1.63187	−	0.328790i
$979$	2.71958	+	13.6722i	0.0869180	+	0.436967i
$980$	−3.00362	+	0.217785i	−0.0959470	+	0.00695688i
$981$	−18.4245	+	16.0930i	−0.588249	+	0.513810i
$982$	5.40624	−	11.0592i	0.172520	−	0.352914i
$983$	12.1350	−	5.02647i	0.387045	−	0.160319i	−0.180671	−	0.983544i	$-0.557827\pi$
$983$	12.1350	−	5.02647i	0.387045	−	0.160319i	0.567717	+	0.823224i	$0.307827\pi$
$984$	−20.6649	−	26.4132i	−0.658773	−	0.842021i
$985$	15.7381	+	6.51893i	0.501457	+	0.207710i
$986$	29.5736	+	33.4874i	0.941816	+	1.06646i
$987$	5.97159	−	4.57271i	0.190078	−	0.145551i
$988$	−8.82892	+	70.8537i	−0.280885	+	2.25416i
$989$	0.367733	−	0.550351i	0.0116932	−	0.0175002i
$990$	24.9654	+	3.24938i	0.793454	+	0.103272i
$991$	3.54351			0.112563			0.0562816	−	0.998415i	$-0.482076\pi$
$991$	3.54351			0.112563			0.0562816	+	0.998415i	$0.482076\pi$
$992$	−20.2932	+	36.5991i	−0.644311	+	1.16202i
$993$	3.46518	+	3.04500i	0.109964	+	0.0966300i
$994$	−1.58747	−	0.419469i	−0.0503514	−	0.0133048i
$995$	5.79056	+	3.86913i	0.183573	+	0.122660i
$996$	0.0315570	−	0.529607i	0.000999923	−	0.0167812i
$997$	−43.2012	−	8.59325i	−1.36820	−	0.272151i	−0.544299	−	0.838891i	$-0.683204\pi$
$997$	−43.2012	−	8.59325i	−1.36820	−	0.272151i	−0.823897	+	0.566740i	$0.808204\pi$
$998$	−35.4850	−	40.1811i	−1.12326	−	1.27191i
$999$	−29.9570	+	19.8873i	−0.947797	+	0.629207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.731.86	yes	1024
3.2	odd	2	inner	960.2.cn.a.731.43	✓	1024
64.19	odd	16	inner	960.2.cn.a.851.43	yes	1024
192.83	even	16	inner	960.2.cn.a.851.86	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.731.43	✓	1024	3.2	odd	2	inner
960.2.cn.a.731.86	yes	1024	1.1	even	1	trivial
960.2.cn.a.851.43	yes	1024	64.19	odd	16	inner
960.2.cn.a.851.86	yes	1024	192.83	even	16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.711347 + 1.22229i) q^{2} +(1.67348 - 0.446620i) q^{3} +(-0.987971 + 1.73894i) q^{4} +(0.980785 + 0.195090i) q^{5} +(1.73632 + 1.72777i) q^{6} +(2.69446 + 1.11608i) q^{7} +(-2.82827 + 0.0294054i) q^{8} +(2.60106 - 1.49482i) q^{9} +O(q^{10})\)	\(q+(0.711347 + 1.22229i) q^{2} +(1.67348 - 0.446620i) q^{3} +(-0.987971 + 1.73894i) q^{4} +(0.980785 + 0.195090i) q^{5} +(1.73632 + 1.72777i) q^{6} +(2.69446 + 1.11608i) q^{7} +(-2.82827 + 0.0294054i) q^{8} +(2.60106 - 1.49482i) q^{9} +(0.459222 + 1.33758i) q^{10} +(4.93398 - 3.29678i) q^{11} +(-0.876703 + 3.35133i) q^{12} +(-0.992447 - 4.98937i) q^{13} +(0.552523 + 4.08732i) q^{14} +(1.72845 - 0.111559i) q^{15} +(-2.04783 - 3.43605i) q^{16} +(-3.61874 - 3.61874i) q^{17} +(3.67735 + 2.11591i) q^{18} +(1.36912 + 6.88305i) q^{19} +(-1.30824 + 1.51278i) q^{20} +(5.00758 + 0.664339i) q^{21} +(7.53938 + 3.68558i) q^{22} +(-0.0484528 + 0.0200698i) q^{23} +(-4.71992 + 1.31237i) q^{24} +(0.923880 + 0.382683i) q^{25} +(5.39246 - 4.76222i) q^{26} +(3.68520 - 3.66323i) q^{27} +(-4.60285 + 3.58285i) q^{28} +(-3.42952 + 5.13264i) q^{29} +(1.36589 + 2.03331i) q^{30} -7.39786 q^{31} +(2.74312 - 4.94725i) q^{32} +(6.78450 - 7.72070i) q^{33} +(1.84896 - 6.99731i) q^{34} +(2.42495 + 1.62030i) q^{35} +(0.0296266 + 5.99993i) q^{36} +(-6.78702 - 1.35002i) q^{37} +(-7.43914 + 6.56970i) q^{38} +(-3.88919 - 7.90635i) q^{39} +(-2.77967 - 0.522929i) q^{40} +(2.61970 + 6.32451i) q^{41} +(2.75012 + 6.59328i) q^{42} +(-10.4939 + 7.01179i) q^{43} +(0.858273 + 11.8370i) q^{44} +(2.84271 - 0.958654i) q^{45} +(-0.0589979 - 0.0449467i) q^{46} +(1.05283 - 1.05283i) q^{47} +(-4.96160 - 4.83555i) q^{48} +(1.06473 + 1.06473i) q^{49} +(0.189450 + 1.40147i) q^{50} +(-7.67208 - 4.43968i) q^{51} +(9.65672 + 3.20354i) q^{52} +(0.954072 + 1.42787i) q^{53} +(7.09898 + 1.89855i) q^{54} +(5.48234 - 2.27086i) q^{55} +(-7.65349 - 3.07735i) q^{56} +(5.36531 + 10.9072i) q^{57} +(-8.71313 - 0.540770i) q^{58} +(0.480276 - 2.41451i) q^{59} +(-1.51367 + 3.11590i) q^{60} +(-4.76601 + 7.13284i) q^{61} +(-5.26245 - 9.04231i) q^{62} +(8.67679 - 1.12473i) q^{63} +(7.99827 - 0.166333i) q^{64} -5.08711i q^{65} +(14.2630 + 2.80051i) q^{66} +(0.361832 + 0.241769i) q^{67} +(9.86798 - 2.71756i) q^{68} +(-0.0721212 + 0.0552264i) q^{69} +(-0.255491 + 4.11658i) q^{70} +(-0.152345 + 0.367794i) q^{71} +(-7.31256 + 4.30424i) q^{72} +(2.62190 + 6.32982i) q^{73} +(-3.17781 - 9.25601i) q^{74} +(1.71701 + 0.227789i) q^{75} +(-13.3219 - 4.41943i) q^{76} +(16.9739 - 3.37631i) q^{77} +(6.89727 - 10.3779i) q^{78} +(0.318893 - 0.318893i) q^{79} +(-1.33814 - 3.76953i) q^{80} +(4.53104 - 7.77623i) q^{81} +(-5.86685 + 7.70094i) q^{82} +(-0.150213 + 0.0298791i) q^{83} +(-6.10260 + 8.05154i) q^{84} +(-2.84322 - 4.25518i) q^{85} +(-16.0352 - 7.83872i) q^{86} +(-3.44689 + 10.1210i) q^{87} +(-13.8577 + 9.46928i) q^{88} +(-0.898989 + 2.17035i) q^{89} +(3.19390 + 2.79267i) q^{90} +(2.89443 - 14.5513i) q^{91} +(0.0129698 - 0.104085i) q^{92} +(-12.3802 + 3.30404i) q^{93} +(2.03579 + 0.537935i) q^{94} +7.01790i q^{95} +(2.38101 - 9.50425i) q^{96} +9.92918i q^{97} +(-0.544012 + 2.05879i) q^{98} +(7.90549 - 15.9505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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