LMFDB - Embedded newform 195.2.s.b.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(38,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("195.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.s (of order $4$, degree $2$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.4
Character	$\chi$	$=$	195.77
Dual form			195.2.s.b.38.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25684 - 1.25684i) q^{2} +(1.36721 + 1.06336i) q^{3} +1.15927i q^{4} +(-0.261006 + 2.22078i) q^{5} +(-0.381882 - 3.05483i) q^{6} +(1.60133 - 1.60133i) q^{7} +(-1.05665 + 1.05665i) q^{8} +(0.738515 + 2.90768i) q^{9} +(3.11920 - 2.46312i) q^{10} +2.48179 q^{11} +(-1.23273 + 1.58497i) q^{12} +(0.624771 + 3.55101i) q^{13} -4.02523 q^{14} +(-2.71835 + 2.75873i) q^{15} +4.97463 q^{16} +(1.27410 - 1.27410i) q^{17} +(2.72628 - 4.58267i) q^{18} +1.93388 q^{19} +(-2.57450 - 0.302577i) q^{20} +(3.89216 - 0.486556i) q^{21} +(-3.11920 - 3.11920i) q^{22} +(-5.56883 - 5.56883i) q^{23} +(-2.56827 + 0.321058i) q^{24} +(-4.86375 - 1.15927i) q^{25} +(3.67780 - 5.24827i) q^{26} +(-2.08222 + 4.76071i) q^{27} +(1.85639 + 1.85639i) q^{28} +9.66063 q^{29} +(6.88379 - 0.0507495i) q^{30} -6.61976i q^{31} +(-4.13899 - 4.13899i) q^{32} +(3.39312 + 2.63904i) q^{33} -3.20267 q^{34} +(3.13826 + 3.97417i) q^{35} +(-3.37080 + 0.856142i) q^{36} +(-3.53521 + 3.53521i) q^{37} +(-2.43057 - 2.43057i) q^{38} +(-2.92182 + 5.51933i) q^{39} +(-2.07081 - 2.62239i) q^{40} -7.35052 q^{41} +(-5.50332 - 4.28028i) q^{42} +(-3.46312 + 3.46312i) q^{43} +2.87707i q^{44} +(-6.65008 + 0.881161i) q^{45} +13.9982i q^{46} +(-4.55353 - 4.55353i) q^{47} +(6.80136 + 5.28984i) q^{48} +1.87146i q^{49} +(4.65592 + 7.56996i) q^{50} +(3.09679 - 0.387128i) q^{51} +(-4.11659 + 0.724281i) q^{52} +(-3.97417 - 3.97417i) q^{53} +(8.60044 - 3.36643i) q^{54} +(-0.647761 + 5.51151i) q^{55} +3.38411i q^{56} +(2.64402 + 2.05642i) q^{57} +(-12.1418 - 12.1418i) q^{58} +2.79393i q^{59} +(-3.19812 - 3.15131i) q^{60} -2.54520 q^{61} +(-8.31996 + 8.31996i) q^{62} +(5.83877 + 3.47355i) q^{63} +0.454797i q^{64} +(-8.04909 + 0.460648i) q^{65} +(-0.947751 - 7.58144i) q^{66} +(1.34628 - 1.34628i) q^{67} +(1.47703 + 1.47703i) q^{68} +(-1.69206 - 13.5354i) q^{69} +(1.05061 - 8.93916i) q^{70} +6.58676 q^{71} +(-3.85277 - 2.29206i) q^{72} +(-2.82950 - 2.82950i) q^{73} +8.88637 q^{74} +(-5.41703 - 6.75691i) q^{75} +2.24190i q^{76} +(3.97417 - 3.97417i) q^{77} +(10.6091 - 3.26464i) q^{78} -6.48553i q^{79} +(-1.29841 + 11.0476i) q^{80} +(-7.90919 + 4.29473i) q^{81} +(9.23840 + 9.23840i) q^{82} +(3.17953 - 3.17953i) q^{83} +(0.564052 + 4.51208i) q^{84} +(2.49695 + 3.16204i) q^{85} +8.70515 q^{86} +(13.2081 + 10.2728i) q^{87} +(-2.62239 + 2.62239i) q^{88} -7.47217i q^{89} +(9.46554 + 7.25059i) q^{90} +(6.68682 + 4.68588i) q^{91} +(6.45580 - 6.45580i) q^{92} +(7.03922 - 9.05059i) q^{93} +11.4461i q^{94} +(-0.504754 + 4.29473i) q^{95} +(-1.25761 - 10.0601i) q^{96} +(9.27171 - 9.27171i) q^{97} +(2.35212 - 2.35212i) q^{98} +(1.83284 + 7.21624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 24 q^{10} - 24 q^{12} + 24 q^{16} + 24 q^{22} - 8 q^{25} - 16 q^{27} + 36 q^{30} - 8 q^{36} + 16 q^{40} + 12 q^{42} - 64 q^{43} - 20 q^{48} + 16 q^{51} - 72 q^{52} - 80 q^{55} + 8 q^{61}+ \cdots - 40 q^{91}+O(q^{100}) $ 32 * q - 4 * q^3 - 24 * q^10 - 24 * q^12 + 24 * q^16 + 24 * q^22 - 8 * q^25 - 16 * q^27 + 36 * q^30 - 8 * q^36 + 16 * q^40 + 12 * q^42 - 64 * q^43 - 20 * q^48 + 16 * q^51 - 72 * q^52 - 80 * q^55 + 8 * q^61 - 72 * q^66 + 44 * q^75 + 84 * q^78 + 112 * q^81 + 48 * q^82 + 20 * q^87 - 8 * q^88 + 44 * q^90 - 40 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.25684	−	1.25684i	−0.888717	−	0.888717i	0.105683	−	0.994400i	$-0.466297\pi$
$2$	−1.25684	−	1.25684i	−0.888717	−	0.888717i	−0.994400	+	0.105683i	$0.966297\pi$
$3$	1.36721	+	1.06336i	0.789358	+	0.613933i
$3$	1.36721	+	1.06336i	0.789358	+	0.613933i
$4$			1.15927i			0.579637i
$5$	−0.261006	+	2.22078i	−0.116725	+	0.993164i
$5$	−0.261006	+	2.22078i	−0.116725	+	0.993164i
$6$	−0.381882	−	3.05483i	−0.155903	−	1.24713i
$7$	1.60133	−	1.60133i	0.605247	−	0.605247i	−0.336453	−	0.941700i	$-0.609227\pi$
$7$	1.60133	−	1.60133i	0.605247	−	0.605247i	0.941700	+	0.336453i	$0.109227\pi$
$8$	−1.05665	+	1.05665i	−0.373584	+	0.373584i
$9$	0.738515	+	2.90768i	0.246172	+	0.969226i
$10$	3.11920	−	2.46312i	0.986378	−	0.778906i
$11$	2.48179			0.748287			0.374144	−	0.927371i	$-0.377937\pi$
$11$	2.48179			0.748287			0.374144	+	0.927371i	$0.377937\pi$
$12$	−1.23273	+	1.58497i	−0.355859	+	0.457541i
$13$	0.624771	+	3.55101i	0.173280	+	0.984873i
$13$	0.624771	+	3.55101i	0.173280	+	0.984873i
$14$	−4.02523			−1.07579
$15$	−2.71835	+	2.75873i	−0.701875	+	0.712300i
$16$	4.97463			1.24366
$17$	1.27410	−	1.27410i	0.309014	−	0.309014i	−0.535513	−	0.844527i	$-0.679882\pi$
$17$	1.27410	−	1.27410i	0.309014	−	0.309014i	0.844527	+	0.535513i	$0.179882\pi$
$18$	2.72628	−	4.58267i	0.642591	−	1.08015i
$19$	1.93388			0.443663			0.221831	−	0.975085i	$-0.428797\pi$
$19$	1.93388			0.443663			0.221831	+	0.975085i	$0.428797\pi$
$20$	−2.57450	−	0.302577i	−0.575675	−	0.0676583i
$21$	3.89216	−	0.486556i	0.849338	−	0.106175i
$22$	−3.11920	−	3.11920i	−0.665016	−	0.665016i
$23$	−5.56883	−	5.56883i	−1.16118	−	1.16118i	−0.984217	−	0.176964i	$-0.943372\pi$
$23$	−5.56883	−	5.56883i	−1.16118	−	1.16118i	−0.176964	−	0.984217i	$-0.556628\pi$
$24$	−2.56827	+	0.321058i	−0.524247	+	0.0655358i
$25$	−4.86375	−	1.15927i	−0.972750	−	0.231855i
$26$	3.67780	−	5.24827i	0.721276	−	1.02927i
$27$	−2.08222	+	4.76071i	−0.400723	+	0.916199i
$28$	1.85639	+	1.85639i	0.350824	+	0.350824i
$29$	9.66063			1.79393			0.896967	−	0.442098i	$-0.145766\pi$
$29$	9.66063			1.79393			0.896967	+	0.442098i	$0.145766\pi$
$30$	6.88379	−	0.0507495i	1.25680	−	0.00926554i
$31$		−	6.61976i		−	1.18894i	−0.804116	−	0.594472i	$-0.797361\pi$
$31$		−	6.61976i		−	1.18894i	0.804116	−	0.594472i	$-0.202639\pi$
$32$	−4.13899	−	4.13899i	−0.731677	−	0.731677i
$33$	3.39312	+	2.63904i	0.590667	+	0.459399i
$34$	−3.20267			−0.549253
$35$	3.13826	+	3.97417i	0.530462	+	0.671758i
$36$	−3.37080	+	0.856142i	−0.561800	+	0.142690i
$37$	−3.53521	+	3.53521i	−0.581186	+	0.581186i	−0.935229	−	0.354043i	$-0.884807\pi$
$37$	−3.53521	+	3.53521i	−0.581186	+	0.581186i	0.354043	+	0.935229i	$0.384807\pi$
$38$	−2.43057	−	2.43057i	−0.394291	−	0.394291i
$39$	−2.92182	+	5.51933i	−0.467866	+	0.883800i
$40$	−2.07081	−	2.62239i	−0.327423	−	0.414637i
$41$	−7.35052			−1.14796			−0.573979	−	0.818870i	$-0.694601\pi$
$41$	−7.35052			−1.14796			−0.573979	+	0.818870i	$0.694601\pi$
$42$	−5.50332	−	4.28028i	−0.849181	−	0.660462i
$43$	−3.46312	+	3.46312i	−0.528121	+	0.528121i	−0.920012	−	0.391891i	$-0.871821\pi$
$43$	−3.46312	+	3.46312i	−0.528121	+	0.528121i	0.391891	+	0.920012i	$0.371821\pi$
$44$			2.87707i			0.433735i
$45$	−6.65008	+	0.881161i	−0.991335	+	0.131356i
$46$			13.9982i			2.06392i
$47$	−4.55353	−	4.55353i	−0.664200	−	0.664200i	0.292167	−	0.956367i	$-0.405624\pi$
$47$	−4.55353	−	4.55353i	−0.664200	−	0.664200i	−0.956367	+	0.292167i	$0.905624\pi$
$48$	6.80136	+	5.28984i	0.981691	+	0.763523i
$49$			1.87146i			0.267351i
$50$	4.65592	+	7.56996i	0.658447	+	1.07055i
$51$	3.09679	−	0.387128i	0.433637	−	0.0542087i
$52$	−4.11659	+	0.724281i	−0.570869	+	0.100440i
$53$	−3.97417	−	3.97417i	−0.545894	−	0.545894i	0.379356	−	0.925251i	$-0.376145\pi$
$53$	−3.97417	−	3.97417i	−0.545894	−	0.545894i	−0.925251	+	0.379356i	$0.876145\pi$
$54$	8.60044	−	3.36643i	1.17037	−	0.458113i
$55$	−0.647761	+	5.51151i	−0.0873441	+	0.743172i
$56$			3.38411i			0.452221i
$57$	2.64402	+	2.05642i	0.350209	+	0.272379i
$58$	−12.1418	−	12.1418i	−1.59430	−	1.59430i
$59$			2.79393i			0.363739i	0.983323	+	0.181869i	$0.0582148\pi$
$59$			2.79393i			0.363739i	−0.983323	+	0.181869i	$0.941785\pi$
$60$	−3.19812	−	3.15131i	−0.412876	−	0.406833i
$61$	−2.54520			−0.325880			−0.162940	−	0.986636i	$-0.552098\pi$
$61$	−2.54520			−0.325880			−0.162940	+	0.986636i	$0.552098\pi$
$62$	−8.31996	+	8.31996i	−1.05664	+	1.05664i
$63$	5.83877	+	3.47355i	0.735616	+	0.437627i
$64$			0.454797i			0.0568496i
$65$	−8.04909	+	0.460648i	−0.998366	+	0.0571363i
$66$	−0.947751	−	7.58144i	−0.116660	−	0.933211i
$67$	1.34628	−	1.34628i	0.164475	−	0.164475i	−0.620071	−	0.784546i	$-0.712896\pi$
$67$	1.34628	−	1.34628i	0.164475	−	0.164475i	0.784546	+	0.620071i	$0.212896\pi$
$68$	1.47703	+	1.47703i	0.179116	+	0.179116i
$69$	−1.69206	−	13.5354i	−0.203700	−	1.62948i
$70$	1.05061	−	8.93916i	0.125572	−	1.06843i
$71$	6.58676			0.781704			0.390852	−	0.920453i	$-0.372180\pi$
$71$	6.58676			0.781704			0.390852	+	0.920453i	$0.372180\pi$
$72$	−3.85277	−	2.29206i	−0.454053	−	0.270121i
$73$	−2.82950	−	2.82950i	−0.331168	−	0.331168i	0.521862	−	0.853030i	$-0.325238\pi$
$73$	−2.82950	−	2.82950i	−0.331168	−	0.331168i	−0.853030	+	0.521862i	$0.825238\pi$
$74$	8.88637			1.03302
$75$	−5.41703	−	6.75691i	−0.625505	−	0.780220i
$76$			2.24190i			0.257163i
$77$	3.97417	−	3.97417i	0.452899	−	0.452899i
$78$	10.6091	−	3.26464i	1.20125	−	0.369647i
$79$		−	6.48553i		−	0.729679i	−0.931070	−	0.364840i	$-0.881124\pi$
$79$		−	6.48553i		−	0.729679i	0.931070	−	0.364840i	$-0.118876\pi$
$80$	−1.29841	+	11.0476i	−0.145166	+	1.23516i
$81$	−7.90919	+	4.29473i	−0.878799	+	0.477192i
$82$	9.23840	+	9.23840i	1.02021	+	1.02021i
$83$	3.17953	−	3.17953i	0.348999	−	0.348999i	−0.510738	−	0.859736i	$-0.670628\pi$
$83$	3.17953	−	3.17953i	0.348999	−	0.348999i	0.859736	+	0.510738i	$0.170628\pi$
$84$	0.564052	+	4.51208i	0.0615431	+	0.492308i
$85$	2.49695	+	3.16204i	0.270832	+	0.342972i
$86$	8.70515			0.938700
$87$	13.2081	+	10.2728i	1.41606	+	1.10136i
$88$	−2.62239	+	2.62239i	−0.279548	+	0.279548i
$89$		−	7.47217i		−	0.792049i	−0.918240	−	0.396024i	$-0.870390\pi$
$89$		−	7.47217i		−	0.792049i	0.918240	−	0.396024i	$-0.129610\pi$
$90$	9.46554	+	7.25059i	0.997755	+	0.764279i
$91$	6.68682	+	4.68588i	0.700969	+	0.491214i
$92$	6.45580	−	6.45580i	0.673064	−	0.673064i
$93$	7.03922	−	9.05059i	0.729933	−	0.938503i
$94$			11.4461i			1.18057i
$95$	−0.504754	+	4.29473i	−0.0517867	+	0.440630i
$96$	−1.25761	−	10.0601i	−0.128354	−	1.02676i
$97$	9.27171	−	9.27171i	0.941399	−	0.941399i	−0.0569765	−	0.998376i	$-0.518146\pi$
$97$	9.27171	−	9.27171i	0.941399	−	0.941399i	0.998376	+	0.0569765i	$0.0181460\pi$
$98$	2.35212	−	2.35212i	0.237600	−	0.237600i
$99$	1.83284	+	7.21624i	0.184207	+	0.725260i
$100$	1.34392	−	5.63842i	0.134392	−	0.563842i
$101$		−	10.3634i		−	1.03120i	−0.856830	−	0.515599i	$-0.827570\pi$
$101$		−	10.3634i		−	1.03120i	0.856830	−	0.515599i	$-0.172430\pi$
$102$	−4.37871	−	3.40560i	−0.433557	−	0.337205i
$103$	7.07081	−	7.07081i	0.696707	−	0.696707i	−0.266992	−	0.963699i	$-0.586030\pi$
$103$	7.07081	−	7.07081i	0.696707	−	0.696707i	0.963699	+	0.266992i	$0.0860296\pi$
$104$	−4.41236	−	3.09202i	−0.432667	−	0.303198i
$105$	0.0646598	+	8.77063i	0.00631015	+	0.855926i
$106$			9.98977i			0.970292i
$107$	−2.61477	+	2.61477i	−0.252779	+	0.252779i	−0.822109	−	0.569330i	$-0.807203\pi$
$107$	−2.61477	+	2.61477i	−0.252779	+	0.252779i	0.569330	+	0.822109i	$0.307203\pi$
$108$	−5.51897	−	2.41386i	−0.531063	−	0.232274i
$109$	−15.7300			−1.50666			−0.753331	−	0.657642i	$-0.771554\pi$
$109$	−15.7300			−1.50666			−0.753331	+	0.657642i	$0.771554\pi$
$110$	7.74120	−	6.11294i	0.738094	−	0.582846i
$111$	−8.59259	+	1.07415i	−0.815573	+	0.101954i
$112$	7.96605	−	7.96605i	0.752721	−	0.752721i
$113$	4.86114	+	4.86114i	0.457298	+	0.457298i	0.897768	−	0.440470i	$-0.145188\pi$
$113$	4.86114	+	4.86114i	0.457298	+	0.457298i	−0.440470	+	0.897768i	$0.645188\pi$
$114$	−0.738515	−	5.90768i	−0.0691683	−	0.553305i
$115$	13.8207	−	10.9137i	1.28878	−	1.01770i
$116$			11.1993i			1.03983i
$117$	−9.86379	+	4.43911i	−0.911908	+	0.410396i
$118$	3.51151	−	3.51151i	0.323261	−	0.323261i
$119$		−	4.08052i		−	0.374060i
$120$	−0.0426664	−	5.78738i	−0.00389489	−	0.528313i
$121$	−4.84073			−0.440066
$122$	3.19890	+	3.19890i	0.289615	+	0.289615i
$123$	−10.0497	−	7.81628i	−0.906150	−	0.704770i
$124$	7.67412			0.689156
$125$	3.84396	−	10.4988i	0.343815	−	0.939038i
$126$	−2.97269	−	11.7041i	−0.264828	−	1.04268i
$127$	6.90382	+	6.90382i	0.612615	+	0.612615i	0.943627	−	0.331011i	$-0.107390\pi$
$127$	6.90382	+	6.90382i	0.612615	+	0.612615i	−0.331011	+	0.943627i	$0.607390\pi$
$128$	−7.70637	+	7.70637i	−0.681153	+	0.681153i
$129$	−8.41736	+	1.05225i	−0.741107	+	0.0926453i
$130$	10.6953	+	9.53743i	0.938044	+	0.836488i
$131$			15.9988i			1.39782i	0.715209	+	0.698911i	$0.246332\pi$
$131$			15.9988i			1.39782i	−0.715209	+	0.698911i	$0.753668\pi$
$132$	−3.05938	+	3.93356i	−0.266284	+	0.342372i
$133$	3.09679	−	3.09679i	0.268526	−	0.268526i
$134$	−3.38411			−0.292343
$135$	−10.0290	−	5.86672i	−0.863162	−	0.504927i
$136$			2.69256i			0.230886i
$137$	6.47173	+	6.47173i	0.552917	+	0.552917i	0.927282	−	0.374364i	$-0.122139\pi$
$137$	6.47173	+	6.47173i	0.552917	+	0.552917i	−0.374364	+	0.927282i	$0.622139\pi$
$138$	−14.8852	+	19.1385i	−1.26711	+	1.62917i
$139$		−	11.9913i		−	1.01709i	−0.861036	−	0.508543i	$-0.830184\pi$
$139$		−	11.9913i		−	1.01709i	0.861036	−	0.508543i	$-0.169816\pi$
$140$	−4.60716	+	3.63810i	−0.389376	+	0.307476i
$141$	−1.38356	−	11.0677i	−0.116517	−	0.932066i
$142$	−8.27848	−	8.27848i	−0.694714	−	0.694714i
$143$	1.55055	+	8.81285i	0.129664	+	0.736968i
$144$	3.67384	+	14.4646i	0.306153	+	1.20539i
$145$	−2.52148	+	21.4542i	−0.209397	+	1.78167i
$146$			7.11243i			0.588629i
$147$	−1.99004	+	2.55867i	−0.164136	+	0.211036i
$148$	−4.09828	−	4.09828i	−0.336877	−	0.336877i
$149$			3.57788i			0.293111i	0.989202	+	0.146556i	$0.0468187\pi$
$149$			3.57788i			0.293111i	−0.989202	+	0.146556i	$0.953181\pi$
$150$	−1.68401	+	15.3006i	−0.137498	+	1.24929i
$151$		−	1.93388i		−	0.157377i	−0.996899	−	0.0786885i	$-0.974927\pi$
$151$		−	1.93388i		−	0.157377i	0.996899	−	0.0786885i	$-0.0250732\pi$
$152$	−2.04344	+	2.04344i	−0.165745	+	0.165745i
$153$	4.64561	+	2.76373i	0.375575	+	0.223434i
$154$	−9.98977			−0.804998
$155$	14.7011	+	1.72780i	1.18082	+	0.138780i
$156$	−6.39841	−	3.38719i	−0.512283	−	0.271192i
$157$	−9.89449	−	9.89449i	−0.789666	−	0.789666i	0.191773	−	0.981439i	$-0.438576\pi$
$157$	−9.89449	−	9.89449i	−0.789666	−	0.789666i	−0.981439	+	0.191773i	$0.938576\pi$
$158$	−8.15125	+	8.15125i	−0.648479	+	0.648479i
$159$	−1.20753	−	9.65951i	−0.0957633	−	0.766049i
$160$	10.2721	−	8.11149i	0.812080	−	0.641270i
$161$	−17.8351			−1.40560
$162$	15.3383	+	4.54279i	1.20509	+	0.356915i
$163$	3.08455	+	3.08455i	0.241600	+	0.241600i	0.817512	−	0.575912i	$-0.195353\pi$
$163$	3.08455	+	3.08455i	0.241600	+	0.241600i	−0.575912	+	0.817512i	$0.695353\pi$
$164$		−	8.52127i		−	0.665400i
$165$	−6.74637	+	6.84658i	−0.525204	+	0.533005i
$166$	−7.99229			−0.620322
$167$	0.544208	+	0.544208i	0.0421121	+	0.0421121i	0.727849	−	0.685737i	$-0.240520\pi$
$167$	0.544208	+	0.544208i	0.0421121	+	0.0421121i	−0.685737	+	0.727849i	$0.740520\pi$
$168$	−3.59854	+	4.62679i	−0.277634	+	0.356964i
$169$	−12.2193	+	4.43714i	−0.939948	+	0.341318i
$170$	0.835915	−	7.11243i	0.0641117	−	0.545498i
$171$	1.42820	+	5.62310i	0.109217	+	0.430010i
$172$	−4.01470	−	4.01470i	−0.306118	−	0.306118i
$173$	−1.92582	−	1.92582i	−0.146417	−	0.146417i	0.630098	−	0.776515i	$-0.283015\pi$
$173$	−1.92582	−	1.92582i	−0.146417	−	0.146417i	−0.776515	+	0.630098i	$0.783015\pi$
$174$	−3.68922	−	29.5116i	−0.279679	−	2.23727i
$175$	−9.64488	+	5.93211i	−0.729084	+	0.448425i
$176$	12.3460			0.930614
$177$	−2.97096	+	3.81988i	−0.223311	+	0.287120i
$178$	−9.39129	+	9.39129i	−0.703907	+	0.703907i
$179$	18.3117			1.36868			0.684342	−	0.729161i	$-0.260090\pi$
$179$	18.3117			1.36868			0.684342	+	0.729161i	$0.260090\pi$
$180$	−1.02151	−	7.70927i	−0.0761386	−	0.574615i
$181$	−2.27148			−0.168838			−0.0844189	−	0.996430i	$-0.526903\pi$
$181$	−2.27148			−0.168838			−0.0844189	+	0.996430i	$0.526903\pi$
$182$	−2.51485	−	14.2936i	−0.186413	−	1.05951i
$183$	−3.47982	−	2.70648i	−0.257236	−	0.200069i
$184$	11.7687			0.867597
$185$	−6.92823	−	8.77366i	−0.509374	−	0.645052i
$186$	−20.2223	+	2.52797i	−1.48277	+	0.185360i
$187$	3.16204	−	3.16204i	0.231232	−	0.231232i
$188$	5.27879	−	5.27879i	0.384995	−	0.384995i
$189$	4.28917	+	10.9578i	0.311991	+	0.797064i
$190$	6.03216	−	4.76338i	0.437619	−	0.345572i
$191$		−	16.8964i		−	1.22258i	−0.791407	−	0.611289i	$-0.790651\pi$
$191$		−	16.8964i		−	1.22258i	0.791407	−	0.611289i	$-0.209349\pi$
$192$	−0.483614	+	0.621802i	−0.0349019	+	0.0448747i
$193$	14.4083	+	14.4083i	1.03713	+	1.03713i	0.999284	+	0.0378452i	$0.0120494\pi$
$193$	14.4083	+	14.4083i	1.03713	+	1.03713i	0.0378452	+	0.999284i	$0.487951\pi$
$194$	−23.3060			−1.67328
$195$	−11.4946	−	7.92931i	−0.823146	−	0.567829i
$196$	−2.16954			−0.154967
$197$	17.1945	+	17.1945i	1.22506	+	1.22506i	0.965810	+	0.259249i	$0.0834752\pi$
$197$	17.1945	+	17.1945i	1.22506	+	1.22506i	0.259249	+	0.965810i	$0.416525\pi$
$198$	6.76606	−	11.3732i	0.480843	−	0.808259i
$199$			18.0401i			1.27883i	0.768861	+	0.639416i	$0.220824\pi$
$199$			18.0401i			1.27883i	−0.768861	+	0.639416i	$0.779176\pi$
$200$	6.36426	−	3.91435i	0.450021	−	0.276787i
$201$	3.27224	−	0.409060i	0.230806	−	0.0288529i
$202$	−13.0251	+	13.0251i	−0.916443	+	0.916443i
$203$	15.4699	−	15.4699i	1.08577	−	1.08577i
$204$	0.448787	+	3.59003i	0.0314214	+	0.251352i
$205$	1.91853	−	16.3239i	0.133996	−	1.14011i
$206$	−17.7737			−1.23835
$207$	12.0797	−	20.3050i	0.839597	−	1.41130i
$208$	3.10801	+	17.6650i	0.215502	+	1.22484i
$209$	4.79948			0.331987
$210$	10.9420	−	11.1045i	0.755068	−	0.766284i
$211$	21.6248			1.48871			0.744356	−	0.667783i	$-0.232756\pi$
$211$	21.6248			1.48871			0.744356	+	0.667783i	$0.232756\pi$
$212$	4.60716	−	4.60716i	0.316421	−	0.316421i
$213$	9.00547	+	7.00412i	0.617045	+	0.479914i
$214$	6.57267			0.449298
$215$	−6.78694	−	8.59473i	−0.462865	−	0.586156i
$216$	−2.83024	−	7.23061i	−0.192574	−	0.491981i
$217$	−10.6005	−	10.6005i	−0.719606	−	0.719606i
$218$	19.7700	+	19.7700i	1.33900	+	1.33900i
$219$	−0.859726	−	6.87730i	−0.0580949	−	0.464725i
$220$	−6.38936	−	0.750933i	−0.430770	−	0.0506279i
$221$	5.32036	+	3.72832i	0.357886	+	0.250794i
$222$	12.1495	+	9.44945i	0.815422	+	0.634205i
$223$	−16.9827	−	16.9827i	−1.13725	−	1.13725i	−0.988942	−	0.148304i	$-0.952619\pi$
$223$	−16.9827	−	16.9827i	−1.13725	−	1.13725i	−0.148304	−	0.988942i	$-0.547381\pi$
$224$	−13.2558			−0.885691
$225$	−0.221157	−	14.9984i	−0.0147438	−	0.999891i
$226$		−	12.2193i		−	0.812817i
$227$	6.28938	+	6.28938i	0.417441	+	0.417441i	0.884321	−	0.466880i	$-0.154622\pi$
$227$	6.28938	+	6.28938i	0.417441	+	0.417441i	−0.466880	+	0.884321i	$0.654622\pi$
$228$	−2.38395	+	3.06514i	−0.157881	+	0.202994i
$229$	−12.0643			−0.797233			−0.398617	−	0.917118i	$-0.630510\pi$
$229$	−12.0643			−0.797233			−0.398617	+	0.917118i	$0.630510\pi$
$230$	−31.0870	−	3.65361i	−2.04982	−	0.240912i
$231$	9.65951	−	1.20753i	0.635549	−	0.0794496i
$232$	−10.2079	+	10.2079i	−0.670184	+	0.670184i
$233$	−8.29631	−	8.29631i	−0.543510	−	0.543510i	0.381046	−	0.924556i	$-0.375564\pi$
$233$	−8.29631	−	8.29631i	−0.543510	−	0.543510i	−0.924556	+	0.381046i	$0.875564\pi$
$234$	17.9764	+	6.81793i	1.17515	+	0.445702i
$235$	11.3009	−	8.92390i	0.737189	−	0.582131i
$236$	−3.23893			−0.210837
$237$	6.89648	−	8.86707i	0.447974	−	0.575978i
$238$	−5.12854	+	5.12854i	−0.332434	+	0.332434i
$239$			29.0823i			1.88118i	0.339550	+	0.940588i	$0.389725\pi$
$239$			29.0823i			1.88118i	−0.339550	+	0.940588i	$0.610275\pi$
$240$	−13.5228	+	13.7237i	−0.872892	+	0.885858i
$241$			4.33077i			0.278970i	0.990224	+	0.139485i	$0.0445446\pi$
$241$			4.33077i			0.278970i	−0.990224	+	0.139485i	$0.955455\pi$
$242$	6.08400	+	6.08400i	0.391094	+	0.391094i
$243$	−15.3804	−	2.53856i	−0.986651	−	0.162849i
$244$		−	2.95059i		−	0.188892i
$245$	−4.15611	−	0.488462i	−0.265524	−	0.0312067i
$246$	2.80704	+	22.4546i	0.178970	+	1.43165i
$247$	1.20823	+	6.86723i	0.0768781	+	0.436951i
$248$	6.99480	+	6.99480i	0.444170	+	0.444170i
$249$	7.72807	−	0.966081i	0.489747	−	0.0612229i
$250$	−18.0265	+	8.36399i	−1.14009	+	0.528985i
$251$			6.63509i			0.418803i	0.977830	+	0.209401i	$0.0671515\pi$
$251$			6.63509i			0.418803i	−0.977830	+	0.209401i	$0.932848\pi$
$252$	−4.02680	+	6.76874i	−0.253665	+	0.426391i
$253$	−13.8207	−	13.8207i	−0.868897	−	0.868897i
$254$		−	17.3540i		−	1.08888i
$255$	0.0514465	+	6.97834i	0.00322171	+	0.437001i
$256$	20.2809			1.26756
$257$	9.21184	−	9.21184i	0.574619	−	0.574619i	−0.358797	−	0.933416i	$-0.616813\pi$
$257$	9.21184	−	9.21184i	0.574619	−	0.574619i	0.933416	+	0.358797i	$0.116813\pi$
$258$	11.9017	+	9.25674i	0.740970	+	0.576299i
$259$			11.3221i			0.703522i
$260$	−0.534017	−	9.33110i	−0.0331183	−	0.578690i
$261$	7.13452	+	28.0900i	0.441616	+	1.73873i
$262$	20.1079	−	20.1079i	1.24227	−	1.24227i
$263$	−8.70709	−	8.70709i	−0.536902	−	0.536902i	0.385716	−	0.922618i	$-0.373955\pi$
$263$	−8.70709	−	8.70709i	−0.536902	−	0.536902i	−0.922618	+	0.385716i	$0.873955\pi$
$264$	−6.37391	+	0.796799i	−0.392287	+	0.0490396i
$265$	9.86305	−	7.78849i	0.605883	−	0.478443i
$266$	−7.78431			−0.477287
$267$	7.94564	−	10.2160i	0.486265	−	0.625210i
$268$	1.56071	+	1.56071i	0.0953356	+	0.0953356i
$269$	−19.9624			−1.21713			−0.608564	−	0.793505i	$-0.708254\pi$
$269$	−19.9624			−1.21713			−0.608564	+	0.793505i	$0.708254\pi$
$270$	5.23135	+	19.9784i	0.318370	+	1.21584i
$271$		−	15.4343i		−	0.937569i	−0.883313	−	0.468784i	$-0.844692\pi$
$271$		−	15.4343i		−	0.937569i	0.883313	−	0.468784i	$-0.155308\pi$
$272$	6.33817	−	6.33817i	0.384308	−	0.384308i
$273$	4.15947	+	13.5171i	0.251743	+	0.818092i
$274$		−	16.2678i		−	0.982774i
$275$	−12.0708	−	2.87707i	−0.727897	−	0.173494i
$276$	15.6913	−	1.96156i	0.944504	−	0.118072i
$277$	8.39129	+	8.39129i	0.504184	+	0.504184i	0.912735	−	0.408551i	$-0.133966\pi$
$277$	8.39129	+	8.39129i	0.504184	+	0.504184i	−0.408551	+	0.912735i	$0.633966\pi$
$278$	−15.0711	+	15.0711i	−0.903903	+	0.903903i
$279$	19.2481	−	4.88880i	1.15236	−	0.292685i
$280$	−7.51538	−	0.883273i	−0.449130	−	0.0527857i
$281$	−20.3080			−1.21148			−0.605738	−	0.795664i	$-0.707122\pi$
$281$	−20.3080			−1.21148			−0.605738	+	0.795664i	$0.707122\pi$
$282$	−12.1713	+	15.6492i	−0.724793	+	0.931894i
$283$	−13.2101	+	13.2101i	−0.785258	+	0.785258i	−0.980713	−	0.195455i	$-0.937382\pi$
$283$	−13.2101	+	13.2101i	−0.785258	+	0.785258i	0.195455	+	0.980713i	$0.437382\pi$
$284$			7.63586i			0.453105i
$285$	−5.25696	+	5.33505i	−0.311396	+	0.316021i
$286$	9.12752	−	13.0251i	0.539722	−	0.770190i
$287$	−11.7706	+	11.7706i	−0.694799	+	0.694799i
$288$	8.97814	−	15.0916i	0.529042	−	0.889278i
$289$			13.7533i			0.809020i
$290$	30.1334	−	23.7953i	1.76950	−	1.39731i
$291$	22.5355	−	2.81715i	1.32106	−	0.165145i
$292$	3.28016	−	3.28016i	0.191957	−	0.191957i
$293$	−9.32896	+	9.32896i	−0.545004	+	0.545004i	−0.924992	−	0.379988i	$-0.875928\pi$
$293$	−9.32896	+	9.32896i	−0.545004	+	0.545004i	0.379988	+	0.924992i	$0.375928\pi$
$294$	5.71699	−	0.714678i	0.333422	−	0.0416808i
$295$	−6.20471	−	0.729232i	−0.361252	−	0.0424575i
$296$		−	7.47100i		−	0.434243i
$297$	−5.16762	+	11.8151i	−0.299856	+	0.685580i
$298$	4.49681	−	4.49681i	0.260493	−	0.260493i
$299$	16.2957	−	23.2542i	0.942405	−	1.34483i
$300$	7.83311	−	6.27982i	0.452245	−	0.362566i
$301$			11.0912i			0.639287i
$302$	−2.43057	+	2.43057i	−0.139864	+	0.139864i
$303$	11.0201	−	14.1689i	0.633086	−	0.813984i
$304$	9.62035			0.551765
$305$	0.664313	−	5.65234i	0.0380384	−	0.323652i
$306$	−2.36522	−	9.31233i	−0.135211	−	0.532350i
$307$	−16.2646	+	16.2646i	−0.928272	+	0.928272i	−0.997594	−	0.0693223i	$-0.977916\pi$
$307$	−16.2646	+	16.2646i	−0.928272	+	0.928272i	0.0693223	+	0.997594i	$0.477916\pi$
$308$	4.60716	+	4.60716i	0.262517	+	0.262517i
$309$	17.1861	−	2.14842i	0.977683	−	0.122220i
$310$	−16.3053	−	20.6484i	−0.926077	−	1.17275i
$311$			4.98446i			0.282643i	0.989964	+	0.141321i	$0.0451351\pi$
$311$			4.98446i			0.282643i	−0.989964	+	0.141321i	$0.954865\pi$
$312$	−2.74467	−	8.91938i	−0.155386	−	0.504960i
$313$	−14.2484	+	14.2484i	−0.805365	+	0.805365i	−0.983928	−	0.178564i	$-0.942855\pi$
$313$	−14.2484	+	14.2484i	−0.805365	+	0.805365i	0.178564	+	0.983928i	$0.442855\pi$
$314$			24.8715i			1.40358i
$315$	−9.23796	+	12.0600i	−0.520500	+	0.679506i
$316$	7.51851			0.422949
$317$	−14.3178	−	14.3178i	−0.804168	−	0.804168i	0.179576	−	0.983744i	$-0.442527\pi$
$317$	−14.3178	−	14.3178i	−0.804168	−	0.804168i	−0.983744	+	0.179576i	$0.942527\pi$
$318$	−10.6228	+	13.6581i	−0.595695	+	0.765908i
$319$	23.9756			1.34238
$320$	−1.01000	−	0.118705i	−0.0564610	−	0.00663579i
$321$	−6.35538	+	0.794482i	−0.354723	+	0.0443437i
$322$	22.4158	+	22.4158i	1.24918	+	1.24918i
$323$	2.46396	−	2.46396i	0.137098	−	0.137098i
$324$	−4.97877	−	9.16892i	−0.276598	−	0.509385i
$325$	1.07786	−	17.9955i	0.0597889	−	0.998211i
$326$		−	7.75354i		−	0.429429i
$327$	−21.5062	−	16.7267i	−1.18930	−	0.924990i
$328$	7.76696	−	7.76696i	0.428859	−	0.428859i
$329$	−14.5834			−0.804011
$330$	17.0841	−	0.125949i	0.940449	−	0.00693329i
$331$			15.6364i			0.859455i	0.902959	+	0.429728i	$0.141390\pi$
$331$			15.6364i			0.859455i	−0.902959	+	0.429728i	$0.858610\pi$
$332$	3.68595	+	3.68595i	0.202293	+	0.202293i
$333$	−12.8901	−	7.66846i	−0.706372	−	0.420229i
$334$		−	1.36796i		−	0.0748514i
$335$	2.63841	+	3.34119i	0.144152	+	0.182549i
$336$	19.3620	−	2.42044i	1.05629	−	0.132046i
$337$	12.4230	+	12.4230i	0.676726	+	0.676726i	0.959258	−	0.282532i	$-0.0911742\pi$
$337$	12.4230	+	12.4230i	0.676726	+	0.676726i	−0.282532	+	0.959258i	$0.591174\pi$
$338$	20.9344	+	9.78093i	1.13868	+	0.532013i
$339$	1.47703	+	11.8154i	0.0802213	+	0.641722i
$340$	−3.66568	+	2.89465i	−0.198799	+	0.156984i
$341$		−	16.4289i		−	0.889672i
$342$	5.27231	−	8.86234i	0.285094	−	0.479220i
$343$	14.2062	+	14.2062i	0.767061	+	0.767061i
$344$		−	7.31864i		−	0.394595i
$345$	30.5009	−	0.224862i	1.64211	−	0.0121062i
$346$			4.84087i			0.260247i
$347$	−6.65873	+	6.65873i	−0.357459	+	0.357459i	−0.862876	−	0.505416i	$-0.831339\pi$
$347$	−6.65873	+	6.65873i	−0.357459	+	0.357459i	0.505416	+	0.862876i	$0.331339\pi$
$348$	−11.9089	+	15.3118i	−0.638387	+	0.820798i
$349$	−3.35766			−0.179731			−0.0898657	−	0.995954i	$-0.528644\pi$
$349$	−3.35766			−0.179731			−0.0898657	+	0.995954i	$0.528644\pi$
$350$	19.5777	+	4.66634i	1.04647	+	0.249427i
$351$	−18.2062	−	4.41961i	−0.971777	−	0.235901i
$352$	−10.2721	−	10.2721i	−0.547504	−	0.547504i
$353$	−10.8383	+	10.8383i	−0.576864	+	0.576864i	−0.934038	−	0.357174i	$-0.883740\pi$
$353$	−10.8383	+	10.8383i	−0.576864	+	0.576864i	0.357174	+	0.934038i	$0.383740\pi$
$354$	8.53498	−	1.06695i	0.453629	−	0.0567079i
$355$	−1.71918	+	14.6278i	−0.0912447	+	0.776361i
$356$	8.66230			0.459101
$357$	4.33907	−	5.57891i	0.229648	−	0.295267i
$358$	−23.0149	−	23.0149i	−1.21637	−	1.21637i
$359$			3.08162i			0.162642i	0.996688	+	0.0813208i	$0.0259138\pi$
$359$			3.08162i			0.162642i	−0.996688	+	0.0813208i	$0.974086\pi$
$360$	6.09575	−	7.95792i	0.321274	−	0.419419i
$361$	−15.2601			−0.803163
$362$	2.85488	+	2.85488i	0.150049	+	0.150049i
$363$	−6.61828	−	5.14745i	−0.347370	−	0.270171i
$364$	−5.43222	+	7.75186i	−0.284726	+	0.406308i
$365$	7.02221	−	5.54518i	0.367559	−	0.290248i
$366$	0.971968	+	7.77516i	0.0508056	+	0.406414i
$367$	−20.0354	−	20.0354i	−1.04584	−	1.04584i	−0.998898	−	0.0469411i	$-0.985053\pi$
$367$	−20.0354	−	20.0354i	−1.04584	−	1.04584i	−0.0469411	−	0.998898i	$-0.514947\pi$
$368$	−27.7029	−	27.7029i	−1.44411	−	1.44411i
$369$	−5.42847	−	21.3730i	−0.282595	−	1.11263i
$370$	−2.31939	+	19.7347i	−0.120580	+	1.02596i
$371$	−12.7280			−0.660802
$372$	10.4921	+	8.16038i	0.543991	+	0.423096i
$373$	25.3623	−	25.3623i	1.31321	−	1.31321i	0.394171	−	0.919037i	$-0.371032\pi$
$373$	25.3623	−	25.3623i	1.31321	−	1.31321i	0.919037	−	0.394171i	$-0.128968\pi$
$374$	−7.94834			−0.410999
$375$	16.4195	−	10.2665i	0.847899	−	0.530157i
$376$	9.62301			0.496269
$377$	6.03568	+	34.3050i	0.310853	+	1.76680i
$378$	8.38140	−	19.1630i	0.431092	−	0.985636i
$379$	−17.3539			−0.891410			−0.445705	−	0.895180i	$-0.647047\pi$
$379$	−17.3539			−0.891410			−0.445705	+	0.895180i	$0.647047\pi$
$380$	−4.97877	−	0.585149i	−0.255406	−	0.0300175i
$381$	2.09769	+	16.7802i	0.107468	+	0.859678i
$382$	−21.2360	+	21.2360i	−1.08653	+	1.08653i
$383$	16.1283	−	16.1283i	0.824118	−	0.824118i	−0.162577	−	0.986696i	$-0.551981\pi$
$383$	16.1283	−	16.1283i	0.824118	−	0.824118i	0.986696	+	0.162577i	$0.0519807\pi$
$384$	−18.7309	+	2.34154i	−0.955857	+	0.119491i
$385$	7.78849	+	9.86305i	0.396938	+	0.502668i
$386$		−	36.2176i		−	1.84343i
$387$	−12.6272	−	7.51207i	−0.641877	−	0.381860i
$388$	10.7484	+	10.7484i	0.545670	+	0.545670i
$389$	−6.50195			−0.329662			−0.164831	−	0.986322i	$-0.552708\pi$
$389$	−6.50195			−0.329662			−0.164831	+	0.986322i	$0.552708\pi$
$390$	4.48101	+	24.4127i	0.226905	+	1.23618i
$391$	−14.1905			−0.717643
$392$	−1.97749	−	1.97749i	−0.0998782	−	0.0998782i
$393$	−17.0125	+	21.8737i	−0.858169	+	1.10338i
$394$		−	43.2214i		−	2.17746i
$395$	14.4030	+	1.69276i	0.724691	+	0.0851721i
$396$	−8.36561	+	2.12476i	−0.420388	+	0.106773i
$397$	26.0994	−	26.0994i	1.30989	−	1.30989i	0.388402	−	0.921490i	$-0.373027\pi$
$397$	26.0994	−	26.0994i	1.30989	−	1.30989i	0.921490	−	0.388402i	$-0.126973\pi$
$398$	22.6735	−	22.6735i	1.13652	−	1.13652i
$399$	7.52697	−	0.940942i	0.376820	−	0.0471060i
$400$	−24.1954	−	5.76696i	−1.20977	−	0.288348i
$401$	17.6000			0.878901			0.439450	−	0.898267i	$-0.355173\pi$
$401$	17.6000			0.878901			0.439450	+	0.898267i	$0.355173\pi$
$402$	−4.62679	−	3.59854i	−0.230763	−	0.179479i
$403$	23.5068	−	4.13584i	1.17096	−	0.206021i
$404$	12.0140			0.597720
$405$	−7.47332	−	18.6855i	−0.371352	−	0.928492i
$406$	−38.8862			−1.92989
$407$	−8.77366	+	8.77366i	−0.434894	+	0.434894i
$408$	−2.86318	+	3.68130i	−0.141748	+	0.182251i
$409$	34.0937			1.68583			0.842913	−	0.538049i	$-0.180839\pi$
$409$	34.0937			1.68583			0.842913	+	0.538049i	$0.180839\pi$
$410$	−22.9278	+	18.1052i	−1.13232	+	0.894153i
$411$	1.96640	+	15.7300i	0.0969953	+	0.775904i
$412$	8.19701	+	8.19701i	0.403837	+	0.403837i
$413$	4.47402	+	4.47402i	0.220152	+	0.220152i
$414$	−40.7023	+	10.3379i	−2.00041	+	0.508080i
$415$	6.23117	+	7.89092i	0.305876	+	0.387350i
$416$	12.1117	−	17.2835i	0.593823	−	0.847393i
$417$	12.7511	−	16.3946i	0.624423	−	0.802845i
$418$	−6.03216	−	6.03216i	−0.295043	−	0.295043i
$419$	−14.9518			−0.730444			−0.365222	−	0.930920i	$-0.619007\pi$
$419$	−14.9518			−0.730444			−0.365222	+	0.930920i	$0.619007\pi$
$420$	−10.1676	+	0.0749585i	−0.496126	+	0.00365760i
$421$			26.9421i			1.31308i	0.754293	+	0.656538i	$0.227980\pi$
$421$			26.9421i			1.31308i	−0.754293	+	0.656538i	$0.772020\pi$
$422$	−27.1788	−	27.1788i	−1.32304	−	1.32304i
$423$	9.87734	−	16.6030i	0.480253	−	0.807267i
$424$	8.39865			0.407875
$425$	−7.67393	+	4.71987i	−0.372240	+	0.228947i
$426$	−2.51537	−	20.1214i	−0.121870	−	0.974886i
$427$	−4.07572	+	4.07572i	−0.197238	+	0.197238i
$428$	−3.03123	−	3.03123i	−0.146520	−	0.146520i
$429$	−7.25134	+	13.6978i	−0.350098	+	0.661336i
$430$	−2.27209	+	19.3322i	−0.109570	+	0.932283i
$431$	14.0679			0.677627			0.338814	−	0.940854i	$-0.389974\pi$
$431$	14.0679			0.677627			0.338814	+	0.940854i	$0.389974\pi$
$432$	−10.3583	+	23.6828i	−0.498362	+	1.13944i
$433$	−14.6474	+	14.6474i	−0.703907	+	0.703907i	−0.965247	−	0.261340i	$-0.915836\pi$
$433$	−14.6474	+	14.6474i	−0.703907	+	0.703907i	0.261340	+	0.965247i	$0.415836\pi$
$434$			26.6461i			1.27905i
$435$	−26.2610	+	26.6510i	−1.25912	+	1.27782i
$436$		−	18.2354i		−	0.873317i
$437$	−10.7695	−	10.7695i	−0.515173	−	0.515173i
$438$	−7.56310	+	9.72417i	−0.361379	+	0.464639i
$439$		−	0.499524i		−	0.0238410i	−0.999929	−	0.0119205i	$-0.996206\pi$
$439$		−	0.499524i		−	0.0238410i	0.999929	−	0.0119205i	$-0.00379450\pi$
$440$	−5.13931	−	6.50822i	−0.245007	−	0.310267i
$441$	−5.44160	+	1.38210i	−0.259124	+	0.0658144i
$442$	−2.00093	−	11.3727i	−0.0951748	−	0.540944i
$443$	−3.46942	−	3.46942i	−0.164837	−	0.164837i	0.619869	−	0.784706i	$-0.287186\pi$
$443$	−3.46942	−	3.46942i	−0.164837	−	0.164837i	−0.784706	+	0.619869i	$0.787186\pi$
$444$	−1.24524	−	9.96117i	−0.0590965	−	0.472736i
$445$	16.5941	+	1.95028i	0.786634	+	0.0924521i
$446$			42.6889i			2.02138i
$447$	−3.80459	+	4.89171i	−0.179951	+	0.231370i
$448$	0.728281	+	0.728281i	0.0344081	+	0.0344081i
$449$		−	14.7638i		−	0.696745i	−0.937356	−	0.348372i	$-0.886734\pi$
$449$		−	14.7638i		−	0.696745i	0.937356	−	0.348372i	$-0.113266\pi$
$450$	−18.5725	+	19.1285i	−0.875518	+	0.901724i
$451$	−18.2424			−0.859003
$452$	−5.63540	+	5.63540i	−0.265067	+	0.265067i
$453$	2.05642	−	2.64402i	0.0966190	−	0.124227i
$454$		−	15.8094i		−	0.741974i
$455$	−12.1516	+	13.6269i	−0.569677	+	0.638840i
$456$	−4.96674	+	0.620889i	−0.232589	+	0.0290758i
$457$	−5.40394	+	5.40394i	−0.252786	+	0.252786i	−0.822112	−	0.569326i	$-0.807204\pi$
$457$	−5.40394	+	5.40394i	−0.252786	+	0.252786i	0.569326	+	0.822112i	$0.307204\pi$
$458$	15.1629	+	15.1629i	0.708515	+	0.708515i
$459$	3.41267	+	8.71857i	0.159290	+	0.406948i
$460$	12.6519	+	16.0219i	0.589899	+	0.747026i
$461$	−14.9553			−0.696538			−0.348269	−	0.937395i	$-0.613230\pi$
$461$	−14.9553			−0.696538			−0.348269	+	0.937395i	$0.613230\pi$
$462$	−13.6581	−	10.6228i	−0.635432	−	0.494215i
$463$	13.0006	+	13.0006i	0.604188	+	0.604188i	0.941421	−	0.337233i	$-0.109491\pi$
$463$	13.0006	+	13.0006i	0.604188	+	0.604188i	−0.337233	+	0.941421i	$0.609491\pi$
$464$	48.0581			2.23104
$465$	18.2621	+	17.9948i	0.846886	+	0.834490i
$466$			20.8542i			0.966053i
$467$	−0.156785	+	0.156785i	−0.00725515	+	0.00725515i	−0.710725	−	0.703470i	$-0.751633\pi$
$467$	−0.156785	+	0.156785i	−0.00725515	+	0.00725515i	0.703470	+	0.710725i	$0.251633\pi$
$468$	−5.14614	−	11.4348i	−0.237881	−	0.528576i
$469$		−	4.31170i		−	0.199096i
$470$	−25.4192	−	2.98749i	−1.17250	−	0.137803i
$471$	−3.00638	−	24.0493i	−0.138527	−	1.10813i
$472$	−2.95222	−	2.95222i	−0.135887	−	0.135887i
$473$	−8.59473	+	8.59473i	−0.395186	+	0.395186i
$474$	−19.8122	+	2.47671i	−0.910004	+	0.113759i
$475$	−9.40592	−	2.24190i	−0.431573	−	0.102865i
$476$	4.73044			0.216819
$477$	8.62063	−	14.4906i	0.394711	−	0.663479i
$478$	36.5517	−	36.5517i	1.67183	−	1.67183i
$479$			26.4947i			1.21057i	0.796008	+	0.605286i	$0.206941\pi$
$479$			26.4947i			1.21057i	−0.796008	+	0.605286i	$0.793059\pi$
$480$	22.6696	−	0.167127i	1.03472	−	0.00762827i
$481$	−14.7623	−	10.3449i	−0.673102	−	0.471686i
$482$	5.44307	−	5.44307i	0.247925	−	0.247925i
$483$	−24.3843	−	18.9652i	−1.10952	−	0.862947i
$484$		−	5.61173i		−	0.255079i
$485$	18.1705	+	23.0104i	0.825079	+	1.04485i
$486$	16.1401	+	22.5212i	0.732128	+	1.02158i
$487$	4.60192	−	4.60192i	0.208533	−	0.208533i	−0.595111	−	0.803644i	$-0.702892\pi$
$487$	4.60192	−	4.60192i	0.208533	−	0.208533i	0.803644	+	0.595111i	$0.202892\pi$
$488$	2.68940	−	2.68940i	0.121743	−	0.121743i
$489$	0.937222	+	7.49722i	0.0423827	+	0.339036i
$490$	4.60963	+	5.83746i	0.208242	+	0.263710i
$491$		−	2.85195i		−	0.128707i	−0.997927	−	0.0643533i	$-0.979502\pi$
$491$		−	2.85195i		−	0.128707i	0.997927	−	0.0643533i	$-0.0204985\pi$
$492$	9.06121	−	11.6504i	0.408511	−	0.525238i
$493$	12.3086	−	12.3086i	0.554351	−	0.554351i
$494$	7.11243	−	10.1495i	0.320003	−	0.456649i
$495$	−16.5041	+	2.18685i	−0.741804	+	0.0982918i
$496$		−	32.9309i		−	1.47864i
$497$	10.5476	−	10.5476i	0.473124	−	0.473124i
$498$	−10.9271	−	8.49871i	−0.489656	−	0.380836i
$499$	−16.5848			−0.742440			−0.371220	−	0.928545i	$-0.621060\pi$
$499$	−16.5848			−0.742440			−0.371220	+	0.928545i	$0.621060\pi$
$500$	12.1709	+	4.45621i	0.544301	+	0.199288i
$501$	0.165354	+	1.32274i	0.00738749	+	0.0590955i
$502$	8.33922	−	8.33922i	0.372197	−	0.372197i
$503$	25.3184	+	25.3184i	1.12889	+	1.12889i	0.990357	+	0.138536i	$0.0442398\pi$
$503$	25.3184	+	25.3184i	1.12889	+	1.12889i	0.138536	+	0.990357i	$0.455760\pi$
$504$	−9.83991	+	2.49922i	−0.438305	+	0.111324i
$505$	23.0149	+	2.70491i	1.02415	+	0.120367i
$506$			34.7406i			1.54441i
$507$	−21.4246	−	6.92710i	−0.951502	−	0.307643i
$508$	−8.00343	+	8.00343i	−0.355095	+	0.355095i
$509$			4.71947i			0.209187i	0.994515	+	0.104593i	$0.0333541\pi$
$509$			4.71947i			0.209187i	−0.994515	+	0.104593i	$0.966646\pi$
$510$	8.70597	−	8.83529i	0.385507	−	0.391233i
$511$	−9.06194			−0.400877
$512$	−10.0770	−	10.0770i	−0.445345	−	0.445345i
$513$	−4.02676	+	9.20665i	−0.177786	+	0.406484i
$514$	−23.1555			−1.02135
$515$	13.8572	+	17.5482i	0.610621	+	0.773268i
$516$	−1.21984	−	9.75803i	−0.0537007	−	0.429573i
$517$	−11.3009	−	11.3009i	−0.497013	−	0.497013i
$518$	14.2300	−	14.2300i	0.625232	−	0.625232i
$519$	−0.585149	−	4.68084i	−0.0256852	−	0.205466i
$520$	8.01836	−	8.99185i	0.351628	−	0.394319i
$521$		−	3.26079i		−	0.142858i	−0.997446	−	0.0714290i	$-0.977244\pi$
$521$		−	3.26079i		−	0.142858i	0.997446	−	0.0714290i	$-0.0227559\pi$
$522$	26.3376	−	44.2715i	1.15277	−	1.93771i
$523$	3.50662	−	3.50662i	0.153334	−	0.153334i	−0.626271	−	0.779605i	$-0.715420\pi$
$523$	3.50662	−	3.50662i	0.153334	−	0.153334i	0.779605	+	0.626271i	$0.215420\pi$
$524$	−18.5470			−0.810229
$525$	−19.4945	−	2.14559i	−0.850811	−	0.0936412i
$526$			21.8868i			0.954308i
$527$	−8.43423	−	8.43423i	−0.367401	−	0.367401i
$528$	16.8795	+	13.1283i	0.734587	+	0.571335i
$529$			39.0237i			1.69668i
$530$	−22.1851	−	2.60739i	−0.963659	−	0.113258i
$531$	−8.12385	+	2.06336i	−0.352545	+	0.0895422i
$532$	3.59003	+	3.59003i	0.155647	+	0.155647i
$533$	−4.59240	−	26.1018i	−0.198919	−	1.13059i
$534$	−22.8262	+	2.85349i	−0.987787	+	0.123483i
$535$	−5.12436	−	6.48930i	−0.221545	−	0.280557i
$536$			2.84511i			0.122890i
$537$	25.0360	+	19.4720i	1.08038	+	0.840281i
$538$	25.0894	+	25.0894i	1.08168	+	1.08168i
$539$			4.64457i			0.200056i
$540$	6.80114	−	11.6264i	0.292675	−	0.500321i
$541$		−	37.7594i		−	1.62340i	−0.584072	−	0.811702i	$-0.698541\pi$
$541$		−	37.7594i		−	1.62340i	0.584072	−	0.811702i	$-0.301459\pi$
$542$	−19.3984	+	19.3984i	−0.833234	+	0.833234i
$543$	−3.10558	−	2.41541i	−0.133273	−	0.103655i
$544$	−10.5470			−0.452197
$545$	4.10562	−	34.9329i	0.175866	−	1.49636i
$546$	11.7610	−	22.2165i	0.503324	−	0.950781i
$547$	16.3924	+	16.3924i	0.700888	+	0.700888i	0.964601	−	0.263714i	$-0.0849474\pi$
$547$	16.3924	+	16.3924i	0.700888	+	0.700888i	−0.263714	+	0.964601i	$0.584947\pi$
$548$	−7.50251	+	7.50251i	−0.320491	+	0.320491i
$549$	−1.87967	−	7.40063i	−0.0802224	−	0.315851i
$550$	11.5550	+	18.7870i	0.492707	+	0.801082i
$551$	18.6825			0.795901
$552$	16.0902	+	12.5144i	0.684844	+	0.532647i
$553$	−10.3855	−	10.3855i	−0.441636	−	0.441636i
$554$		−	21.0930i		−	0.896154i
$555$	−0.142747	−	19.3626i	−0.00605929	−	0.821898i
$556$	13.9012			0.589541
$557$	9.89147	+	9.89147i	0.419115	+	0.419115i	0.884899	−	0.465784i	$-0.154227\pi$
$557$	9.89147	+	9.89147i	0.419115	+	0.419115i	−0.465784	+	0.884899i	$0.654227\pi$
$558$	−30.3362	−	18.0473i	−1.28423	−	0.764005i
$559$	−14.4612	−	10.1339i	−0.611644	−	0.428619i
$560$	15.6117	+	19.7700i	0.659714	+	0.835437i
$561$	7.68558	−	0.960769i	0.324485	−	0.0405637i
$562$	25.5239	+	25.5239i	1.07666	+	1.07666i
$563$	−1.00460	−	1.00460i	−0.0423388	−	0.0423388i	0.685620	−	0.727959i	$-0.259531\pi$
$563$	−1.00460	−	1.00460i	−0.0423388	−	0.0423388i	−0.727959	+	0.685620i	$0.759531\pi$
$564$	12.8305	−	1.60393i	0.540260	−	0.0675376i
$565$	−12.0643	+	9.52676i	−0.507550	+	0.400794i
$566$	33.2058			1.39574
$567$	−5.78796	+	19.5426i	−0.243071	+	0.820710i
$568$	−6.95993	+	6.95993i	−0.292032	+	0.292032i
$569$	−5.08203			−0.213050			−0.106525	−	0.994310i	$-0.533972\pi$
$569$	−5.08203			−0.213050			−0.106525	+	0.994310i	$0.533972\pi$
$570$	13.3124	−	0.0981434i	0.557596	−	0.00411077i
$571$	−19.2348			−0.804953			−0.402476	−	0.915430i	$-0.631850\pi$
$571$	−19.2348			−0.804953			−0.402476	+	0.915430i	$0.631850\pi$
$572$	−10.2165	+	1.79751i	−0.427174	+	0.0751578i
$573$	17.9670	−	23.1009i	0.750582	−	0.965052i
$574$	29.5875			1.23496
$575$	20.6296	+	33.5412i	0.860314	+	1.39876i
$576$	−1.32240	+	0.335874i	−0.0551001	+	0.0139948i
$577$	9.22836	−	9.22836i	0.384182	−	0.384182i	−0.488424	−	0.872606i	$-0.662428\pi$
$577$	9.22836	−	9.22836i	0.384182	−	0.384182i	0.872606	+	0.488424i	$0.162428\pi$
$578$	17.2857	−	17.2857i	0.718990	−	0.718990i
$579$	4.37786	+	35.0203i	0.181938	+	1.45539i
$580$	−24.8713	−	2.92309i	−1.03272	−	0.121375i
$581$		−	10.1830i		−	0.422461i
$582$	−31.8642	−	24.7828i	−1.32081	−	1.02728i
$583$	−9.86305	−	9.86305i	−0.408486	−	0.408486i
$584$	5.97960			0.247438
$585$	−7.28379	−	23.0640i	−0.301148	−	0.953578i
$586$	23.4500			0.968709
$587$	−1.06387	−	1.06387i	−0.0439105	−	0.0439105i	0.684811	−	0.728721i	$-0.259885\pi$
$587$	−1.06387	−	1.06387i	−0.0439105	−	0.0439105i	−0.728721	+	0.684811i	$0.759885\pi$
$588$	−2.96621	−	2.30701i	−0.122324	−	0.0951393i
$589$		−	12.8018i		−	0.527490i
$590$	6.88178	+	8.71483i	0.283319	+	0.358784i
$591$	5.22446	+	41.7925i	0.214906	+	1.71912i
$592$	−17.5864	+	17.5864i	−0.722796	+	0.722796i
$593$	2.68739	−	2.68739i	0.110358	−	0.110358i	−0.649772	−	0.760129i	$-0.725135\pi$
$593$	2.68739	−	2.68739i	0.110358	−	0.110358i	0.760129	+	0.649772i	$0.225135\pi$
$594$	21.3445	−	8.35477i	0.875774	−	0.342800i
$595$	9.06194	+	1.06504i	0.371503	+	0.0436623i
$596$	−4.14774			−0.169898
$597$	−19.1832	+	24.6646i	−0.785117	+	1.00946i
$598$	−49.7078	+	8.74568i	−2.03270	+	0.357637i
$599$	−25.8330			−1.05551			−0.527754	−	0.849397i	$-0.676966\pi$
$599$	−25.8330			−1.05551			−0.527754	+	0.849397i	$0.676966\pi$
$600$	12.8636	+	1.41579i	0.525156	+	0.0577992i
$601$	26.5776			1.08412			0.542062	−	0.840338i	$-0.317644\pi$
$601$	26.5776			1.08412			0.542062	+	0.840338i	$0.317644\pi$
$602$	13.9398	−	13.9398i	0.568146	−	0.568146i
$603$	4.90881	+	2.92031i	0.199902	+	0.118924i
$604$	2.24190			0.0912216
$605$	1.26346	−	10.7502i	0.0513668	−	0.437058i
$606$	−31.6584	+	3.95760i	−1.28604	+	0.160767i
$607$	6.01113	+	6.01113i	0.243984	+	0.243984i	0.818496	−	0.574512i	$-0.194808\pi$
$607$	6.01113	+	6.01113i	0.243984	+	0.243984i	−0.574512	+	0.818496i	$0.694808\pi$
$608$	−8.00431	−	8.00431i	−0.324618	−	0.324618i
$609$	37.6007	−	4.70044i	1.52366	−	0.190471i
$610$	−7.93900	+	6.26914i	−0.321441	+	0.253830i
$611$	13.3247	−	19.0145i	0.539060	−	0.769245i
$612$	−3.20392	+	5.38554i	−0.129511	+	0.217698i
$613$	−3.14970	−	3.14970i	−0.127215	−	0.127215i	0.640632	−	0.767848i	$-0.278672\pi$
$613$	−3.14970	−	3.14970i	−0.127215	−	0.127215i	−0.767848	+	0.640632i	$0.778672\pi$
$614$	40.8840			1.64994
$615$	19.9813	−	20.2781i	0.805723	−	0.817692i
$616$			8.39865i			0.338391i
$617$	−2.15262	−	2.15262i	−0.0866613	−	0.0866613i	0.662447	−	0.749109i	$-0.269518\pi$
$617$	−2.15262	−	2.15262i	−0.0866613	−	0.0866613i	−0.749109	+	0.662447i	$0.769518\pi$
$618$	−24.3003	−	18.8999i	−0.977503	−	0.760265i
$619$	12.1579			0.488668			0.244334	−	0.969691i	$-0.421431\pi$
$619$	12.1579			0.488668			0.244334	+	0.969691i	$0.421431\pi$
$620$	−2.00299	+	17.0426i	−0.0804420	+	0.684446i
$621$	38.1071	−	14.9161i	1.52918	−	0.598562i
$622$	6.26465	−	6.26465i	0.251190	−	0.251190i
$623$	−11.9654	−	11.9654i	−0.479385	−	0.479385i
$624$	−14.5350	+	27.4566i	−0.581865	+	1.09914i
$625$	22.3122	+	11.2768i	0.892487	+	0.451074i
$626$	35.8157			1.43148
$627$	6.56189	+	5.10360i	0.262057	+	0.203818i
$628$	11.4704	−	11.4704i	0.457720	−	0.457720i
$629$			9.00843i			0.359190i
$630$	26.7681	−	3.54687i	1.06647	−	0.141311i
$631$		−	24.6040i		−	0.979470i	−0.871871	−	0.489735i	$-0.837093\pi$
$631$		−	24.6040i		−	0.979470i	0.871871	−	0.489735i	$-0.162907\pi$
$632$	6.85297	+	6.85297i	0.272596	+	0.272596i
$633$	29.5656	+	22.9950i	1.17513	+	0.913970i
$634$			35.9903i			1.42936i
$635$	−17.1338	+	13.5300i	−0.679935	+	0.536920i
$636$	11.1980	−	1.39986i	0.444030	−	0.0555080i
$637$	−6.64557	+	1.16923i	−0.263307	+	0.0463268i
$638$	−30.1334	−	30.1334i	−1.19299	−	1.19299i
$639$	4.86442	+	19.1522i	0.192434	+	0.757648i
$640$	−15.1028	−	19.1256i	−0.596989	−	0.756005i
$641$		−	4.97308i		−	0.196425i	−0.995165	−	0.0982124i	$-0.968688\pi$
$641$		−	4.97308i		−	0.196425i	0.995165	−	0.0982124i	$-0.0313124\pi$
$642$	8.98621	+	6.98914i	0.354657	+	0.275839i
$643$	19.7877	+	19.7877i	0.780349	+	0.780349i	0.979890	−	0.199540i	$-0.0639448\pi$
$643$	19.7877	+	19.7877i	0.780349	+	0.780349i	−0.199540	+	0.979890i	$0.563945\pi$
$644$		−	20.6758i		−	0.814740i
$645$	−0.139836	−	18.9678i	−0.00550605	−	0.746855i
$646$	−6.19358			−0.243683
$647$	−27.8871	+	27.8871i	−1.09635	+	1.09635i	−0.101520	+	0.994833i	$0.532371\pi$
$647$	−27.8871	+	27.8871i	−1.09635	+	1.09635i	−0.994833	+	0.101520i	$0.967629\pi$
$648$	3.81924	−	12.8953i	0.150034	−	0.506576i
$649$			6.93395i			0.272181i
$650$	−23.9721	+	21.2627i	−0.940263	+	0.833992i
$651$	−3.22089	−	25.7652i	−0.126236	−	1.00982i
$652$	−3.57584	+	3.57584i	−0.140041	+	0.140041i
$653$	14.6549	+	14.6549i	0.573491	+	0.573491i	0.933102	−	0.359611i	$-0.117091\pi$
$653$	14.6549	+	14.6549i	0.573491	+	0.573491i	−0.359611	+	0.933102i	$0.617091\pi$
$654$	6.00701	+	48.0525i	0.234893	+	1.87900i
$655$	−35.5299	−	4.17578i	−1.38827	−	0.163161i
$656$	−36.5661			−1.42767
$657$	6.13764	−	10.3169i	0.239452	−	0.402500i
$658$	18.3290	+	18.3290i	0.714538	+	0.714538i
$659$	27.9107			1.08725			0.543624	−	0.839329i	$-0.317052\pi$
$659$	27.9107			1.08725			0.543624	+	0.839329i	$0.317052\pi$
$660$	−7.93706	−	7.82089i	−0.308950	−	0.304428i
$661$		−	33.0735i		−	1.28641i	−0.765693	−	0.643206i	$-0.777604\pi$
$661$		−	33.0735i		−	1.28641i	0.765693	−	0.643206i	$-0.222396\pi$
$662$	19.6524	−	19.6524i	0.763813	−	0.763813i
$663$	3.30948	+	10.7549i	0.128529	+	0.417684i
$664$			6.71933i			0.260760i
$665$	6.06902	+	7.68558i	0.235346	+	0.298034i
$666$	6.56272	+	25.8387i	0.254300	+	1.00123i
$667$	−53.7984	−	53.7984i	−2.08308	−	2.08308i
$668$	−0.630886	+	0.630886i	−0.0244097	+	0.0244097i
$669$	−5.16010	−	41.2777i	−0.199501	−	1.59589i
$670$	0.883273	−	7.51538i	0.0341238	−	0.290344i
$671$	−6.31666			−0.243852
$672$	−18.1234	−	14.0957i	−0.699127	−	0.543755i
$673$	6.43667	−	6.43667i	0.248115	−	0.248115i	−0.572082	−	0.820197i	$-0.693864\pi$
$673$	6.43667	−	6.43667i	0.248115	−	0.248115i	0.820197	+	0.572082i	$0.193864\pi$
$674$		−	31.2275i		−	1.20284i
$675$	15.6464	−	20.7411i	0.602228	−	0.798324i
$676$	−5.14386	−	14.1655i	−0.197841	−	0.544829i
$677$	3.03614	−	3.03614i	0.116688	−	0.116688i	−0.646351	−	0.763040i	$-0.723706\pi$
$677$	3.03614	−	3.03614i	0.116688	−	0.116688i	0.763040	+	0.646351i	$0.223706\pi$
$678$	12.9936	−	16.7064i	0.499016	−	0.641604i
$679$		−	29.6942i		−	1.13956i
$680$	−5.97960	−	0.702775i	−0.229307	−	0.0269502i
$681$	1.91099	+	15.2868i	0.0732294	+	0.585791i
$682$	−20.6484	+	20.6484i	−0.790667	+	0.790667i
$683$	−6.75351	+	6.75351i	−0.258416	+	0.258416i	−0.824410	−	0.565994i	$-0.808493\pi$
$683$	−6.75351	+	6.75351i	−0.258416	+	0.258416i	0.565994	+	0.824410i	$0.308493\pi$
$684$	−6.51872	+	1.65568i	−0.249250	+	0.0633064i
$685$	−16.0615	+	12.6831i	−0.613677	+	0.484598i
$686$		−	35.7097i		−	1.36340i
$687$	−16.4944	−	12.8288i	−0.629302	−	0.489448i
$688$	−17.2277	+	17.2277i	−0.656801	+	0.656801i
$689$	11.6294	−	16.5953i	0.443044	−	0.632229i
$690$	−38.6173	−	38.0520i	−1.47013	−	1.44862i
$691$		−	20.7041i		−	0.787620i	−0.919192	−	0.393810i	$-0.871157\pi$
$691$		−	20.7041i		−	0.787620i	0.919192	−	0.393810i	$-0.128843\pi$
$692$	2.23255	−	2.23255i	0.0848688	−	0.0848688i
$693$	14.4906	+	8.62063i	0.550452	+	0.327471i
$694$	16.7379			0.635361
$695$	26.6300	+	3.12979i	1.01013	+	0.118720i
$696$	−24.8111	+	3.10163i	−0.940464	+	0.117567i
$697$	−9.36529	+	9.36529i	−0.354736	+	0.354736i
$698$	4.22003	+	4.22003i	0.159730	+	0.159730i
$699$	−2.52079	−	20.1648i	−0.0953449	−	0.762702i
$700$	−6.87694	−	11.1811i	−0.259924	−	0.422604i
$701$			52.1479i			1.96960i	0.173691	+	0.984800i	$0.444431\pi$
$701$			52.1479i			1.96960i	−0.173691	+	0.984800i	$0.555569\pi$
$702$	17.3275	+	28.4370i	0.653985	+	1.07328i
$703$	−6.83669	+	6.83669i	−0.257850	+	0.257850i
$704$			1.12871i			0.0425398i
$705$	24.9400	−	0.183866i	0.939295	−	0.00692478i
$706$	27.2439			1.02534
$707$	−16.5953	−	16.5953i	−0.624129	−	0.624129i
$708$	−4.42829	−	3.44416i	−0.166425	−	0.129440i
$709$	−4.45911			−0.167465			−0.0837327	−	0.996488i	$-0.526684\pi$
$709$	−4.45911			−0.167465			−0.0837327	+	0.996488i	$0.526684\pi$
$710$	20.5454	−	16.2240i	0.771056	−	0.608875i
$711$	18.8578	−	4.78966i	0.707224	−	0.179626i
$712$	7.89550	+	7.89550i	0.295896	+	0.295896i
$713$	−36.8643	+	36.8643i	−1.38058	+	1.38058i
$714$	−12.4653	+	1.55828i	−0.466502	+	0.0583171i
$715$	−19.9761	+	1.14323i	−0.747065	+	0.0427544i
$716$			21.2283i			0.793340i
$717$	−30.9250	+	39.7615i	−1.15492	+	1.48492i
$718$	3.87309	−	3.87309i	0.144542	−	0.144542i
$719$	6.74702			0.251621			0.125811	−	0.992054i	$-0.459847\pi$
$719$	6.74702			0.251621			0.125811	+	0.992054i	$0.459847\pi$
$720$	−33.0817	+	4.38345i	−1.23288	+	0.163362i
$721$		−	22.6454i		−	0.843360i
$722$	19.1795	+	19.1795i	0.713785	+	0.713785i
$723$	−4.60519	+	5.92107i	−0.171269	+	0.220207i
$724$		−	2.63327i		−	0.0978646i
$725$	−46.9869	−	11.1993i	−1.74505	−	0.415932i
$726$	1.84859	+	14.7876i	0.0686075	+	0.548819i
$727$	9.42881	+	9.42881i	0.349695	+	0.349695i	0.859996	−	0.510301i	$-0.170466\pi$
$727$	9.42881	+	9.42881i	0.349695	+	0.349695i	−0.510301	+	0.859996i	$0.670466\pi$
$728$	−12.0170	+	2.11430i	−0.445380	+	0.0783611i
$729$	−18.3288	−	19.8257i	−0.678843	−	0.734284i
$730$	−15.7952	−	1.85639i	−0.584605	−	0.0687079i
$731$			8.82471i			0.326394i
$732$	3.13755	−	4.03407i	0.115967	−	0.149103i
$733$	20.5774	+	20.5774i	0.760042	+	0.760042i	0.976330	−	0.216288i	$-0.0693950\pi$
$733$	20.5774	+	20.5774i	0.760042	+	0.760042i	−0.216288	+	0.976330i	$0.569395\pi$
$734$			50.3624i			1.85891i
$735$	−5.16285	−	5.08728i	−0.190435	−	0.187647i
$736$			46.0986i			1.69922i
$737$	3.34119	−	3.34119i	0.123074	−	0.123074i
$738$	−20.0396	+	33.6850i	−0.737668	+	1.23996i
$739$	11.6627			0.429020			0.214510	−	0.976722i	$-0.431185\pi$
$739$	11.6627			0.429020			0.214510	+	0.976722i	$0.431185\pi$
$740$	10.1711	−	8.03172i	0.373896	−	0.295252i
$741$	−5.65045	+	10.6737i	−0.207575	+	0.392109i
$742$	15.9970	+	15.9970i	0.587267	+	0.587267i
$743$	−8.16248	+	8.16248i	−0.299452	+	0.299452i	−0.840799	−	0.541347i	$-0.817915\pi$
$743$	−8.16248	+	8.16248i	−0.299452	+	0.299452i	0.541347	+	0.840799i	$0.317915\pi$
$744$	2.12533	+	17.0014i	0.0779184	+	0.623300i
$745$	−7.94569	−	0.933847i	−0.291108	−	0.0342135i
$746$	−63.7524			−2.33414
$747$	11.5932	+	6.89692i	0.424172	+	0.252345i
$748$	3.66568	+	3.66568i	0.134030	+	0.134030i
$749$			8.37423i			0.305988i
$750$	−33.5399	−	7.73337i	−1.22470	−	0.282383i
$751$	−36.7121			−1.33964			−0.669822	−	0.742522i	$-0.733630\pi$
$751$	−36.7121			−1.33964			−0.669822	+	0.742522i	$0.733630\pi$
$752$	−22.6521	−	22.6521i	−0.826038	−	0.826038i
$753$	−7.05551	+	9.07154i	−0.257117	+	0.330585i
$754$	35.5299	−	50.7016i	1.29392	−	1.84644i
$755$	4.29473	+	0.504754i	0.156301	+	0.0183699i
$756$	−12.7031	+	4.97232i	−0.462008	+	0.180842i
$757$	5.75644	+	5.75644i	0.209221	+	0.209221i	0.803937	−	0.594715i	$-0.202735\pi$
$757$	5.75644	+	5.75644i	0.209221	+	0.209221i	−0.594715	+	0.803937i	$0.702735\pi$
$758$	21.8110	+	21.8110i	0.792212	+	0.792212i
$759$	−4.19933	−	33.5921i	−0.152426	−	1.21932i
$760$	−4.00469	−	5.07140i	−0.145266	−	0.183959i
$761$	23.9994			0.869978			0.434989	−	0.900436i	$-0.356752\pi$
$761$	23.9994			0.869978			0.434989	+	0.900436i	$0.356752\pi$
$762$	18.4536	−	23.7265i	0.668502	−	0.859519i
$763$	−25.1890	+	25.1890i	−0.911903	+	0.911903i
$764$	19.5875			0.708652
$765$	−7.35017	+	9.59555i	−0.265746	+	0.346928i
$766$	−40.5413			−1.46482
$767$	−9.92127	+	1.74557i	−0.358236	+	0.0630288i
$768$	27.7282	+	21.5660i	1.00055	+	0.778194i
$769$	−14.2146			−0.512592			−0.256296	−	0.966598i	$-0.582502\pi$
$769$	−14.2146			−0.512592			−0.256296	+	0.966598i	$0.582502\pi$
$770$	2.60739	−	22.1851i	0.0939637	−	0.799496i
$771$	22.3900	−	2.79896i	0.806358	−	0.100802i
$772$	−16.7031	+	16.7031i	−0.601158	+	0.601158i
$773$	−14.3909	+	14.3909i	−0.517605	+	0.517605i	−0.916846	−	0.399241i	$-0.869274\pi$
$773$	−14.3909	+	14.3909i	−0.517605	+	0.517605i	0.399241	+	0.916846i	$0.369274\pi$
$774$	6.42888	+	25.3118i	0.231081	+	0.909813i
$775$	−7.67412	+	32.1969i	−0.275663	+	1.15655i
$776$			19.5940i			0.703383i
$777$	−12.0395	+	15.4797i	−0.431916	+	0.555331i
$778$	8.17188	+	8.17188i	0.292976	+	0.292976i
$779$	−14.2150			−0.509307
$780$	9.19224	−	13.3254i	0.329135	−	0.477126i
$781$	16.3469			0.584940
$782$	17.8351	+	17.8351i	0.637782	+	0.637782i
$783$	−20.1155	+	45.9915i	−0.718870	+	1.64360i
$784$			9.30982i			0.332494i
$785$	24.5560	−	19.3910i	0.876442	−	0.692094i
$786$	48.8736	−	6.10966i	1.74326	−	0.217924i
$787$	16.3053	−	16.3053i	0.581220	−	0.581220i	−0.354019	−	0.935238i	$-0.615185\pi$
$787$	16.3053	−	16.3053i	0.581220	−	0.581220i	0.935238	+	0.354019i	$0.115185\pi$
$788$	−19.9332	+	19.9332i	−0.710090	+	0.710090i
$789$	−2.64560	−	21.1632i	−0.0941858	−	0.753430i
$790$	−15.9746	−	20.2297i	−0.568352	−	0.719740i
$791$	15.5686			0.553557
$792$	−9.56175	−	5.68840i	−0.339762	−	0.202128i
$793$	−1.59017	−	9.03804i	−0.0564686	−	0.320950i
$794$	−65.6054			−2.32825
$795$	21.7668	−	0.160472i	0.771990	−	0.00569136i
$796$	−20.9135			−0.741258
$797$	32.3953	−	32.3953i	1.14750	−	1.14750i	0.160459	−	0.987042i	$-0.448703\pi$
$797$	32.3953	−	32.3953i	1.14750	−	1.14750i	0.987042	−	0.160459i	$-0.0512975\pi$
$798$	−10.6428	−	8.27756i	−0.376750	−	0.293022i
$799$	−11.6033			−0.410495
$800$	15.3328	+	24.9292i	0.542096	+	0.881382i
$801$	21.7267	−	5.51831i	0.767674	−	0.194980i
$802$	−22.1203	−	22.1203i	−0.781094	−	0.781094i
$803$	−7.02221	−	7.02221i	−0.247809	−	0.247809i
$804$	0.474213	+	3.79342i	0.0167242	+	0.133784i
$805$	4.65507	−	39.6079i	0.164070	−	1.39600i
$806$	−34.7423	−	24.3462i	−1.22375	−	0.857557i
$807$	−27.2927	−	21.2273i	−0.960749	−	0.747235i
$808$	10.9505	+	10.9505i	0.385238	+	0.385238i
$809$	−9.15265			−0.321790			−0.160895	−	0.986972i	$-0.551438\pi$
$809$	−9.15265			−0.321790			−0.160895	+	0.986972i	$0.551438\pi$
$810$	−14.0919	+	32.8774i	−0.495140	+	1.15519i
$811$			5.06477i			0.177848i	0.996038	+	0.0889240i	$0.0283428\pi$
$811$			5.06477i			0.177848i	−0.996038	+	0.0889240i	$0.971657\pi$
$812$	17.9338	+	17.9338i	0.629355	+	0.629355i
$813$	16.4123	−	21.1019i	0.575605	−	0.740077i
$814$	22.0541			0.772996
$815$	−7.65520	+	6.04503i	−0.268150	+	0.211748i
$816$	15.4054	−	1.92582i	0.539296	−	0.0674171i
$817$	−6.69726	+	6.69726i	−0.234307	+	0.234307i
$818$	−42.8502	−	42.8502i	−1.49822	−	1.49822i
$819$	−8.68672	+	22.9037i	−0.303539	+	0.800320i
$820$	18.9239	+	2.22410i	0.660851	+	0.0776690i
$821$	−25.6728			−0.895986			−0.447993	−	0.894037i	$-0.647861\pi$
$821$	−25.6728			−0.895986			−0.447993	+	0.894037i	$0.647861\pi$
$822$	17.2986	−	22.2415i	0.603358	−	0.775761i
$823$	18.2052	−	18.2052i	0.634593	−	0.634593i	−0.314624	−	0.949216i	$-0.601878\pi$
$823$	18.2052	−	18.2052i	0.634593	−	0.634593i	0.949216	+	0.314624i	$0.101878\pi$
$824$			14.9428i			0.520557i
$825$	−13.4439	−	16.7692i	−0.468057	−	0.583829i
$826$		−	11.2462i		−	0.391306i
$827$	−37.3547	−	37.3547i	−1.29895	−	1.29895i	−0.929086	−	0.369865i	$-0.879404\pi$
$827$	−37.3547	−	37.3547i	−1.29895	−	1.29895i	−0.369865	−	0.929086i	$-0.620596\pi$
$828$	23.5391	+	14.0037i	0.818040	+	0.486662i
$829$			13.2807i			0.461257i	0.973042	+	0.230628i	$0.0740782\pi$
$829$			13.2807i			0.461257i	−0.973042	+	0.230628i	$0.925922\pi$
$830$	2.08603	−	17.7491i	0.0724073	−	0.616082i
$831$	2.54965	+	20.3956i	0.0884463	+	0.707517i
$832$	−1.61499	+	0.284144i	−0.0559896	+	0.00985092i
$833$	2.38443	+	2.38443i	0.0826154	+	0.0826154i
$834$	−36.6313	+	4.57926i	−1.26844	+	0.158567i
$835$	−1.35061	+	1.06653i	−0.0467397	+	0.0369086i
$836$			5.56392i			0.192432i
$837$	31.5148	+	13.7838i	1.08931	+	0.476437i
$838$	18.7920	+	18.7920i	0.649159	+	0.649159i
$839$		−	41.5203i		−	1.43344i	−0.697362	−	0.716719i	$-0.745643\pi$
$839$		−	41.5203i		−	1.43344i	0.697362	−	0.716719i	$-0.254357\pi$
$840$	−9.33585	−	9.19920i	−0.322117	−	0.317403i
$841$	64.3277			2.21820
$842$	33.8618	−	33.8618i	1.16695	−	1.16695i
$843$	−27.7653	−	21.5948i	−0.956288	−	0.743765i
$844$			25.0691i			0.862913i
$845$	−6.66460	−	28.2946i	−0.229269	−	0.973363i
$846$	−33.2815	+	8.45310i	−1.14424	+	0.290623i
$847$	−7.75162	+	7.75162i	−0.266349	+	0.266349i
$848$	−19.7700	−	19.7700i	−0.678906	−	0.678906i
$849$	−32.1080	+	4.01381i	−1.10195	+	0.137753i
$850$	15.5770	+	3.71277i	0.534286	+	0.127347i
$851$	39.3740			1.34972
$852$	−8.11970	+	10.4398i	−0.278176	+	0.357662i
$853$	−28.1269	−	28.1269i	−0.963046	−	0.963046i	0.0362950	−	0.999341i	$-0.488444\pi$
$853$	−28.1269	−	28.1269i	−0.963046	−	0.963046i	−0.999341	+	0.0362950i	$0.988444\pi$
$854$	10.2450			0.350578
$855$	−12.8605	+	1.70406i	−0.439819	+	0.0582776i
$856$		−	5.52581i		−	0.188868i
$857$	−1.93395	+	1.93395i	−0.0660625	+	0.0660625i	−0.739366	−	0.673304i	$-0.764875\pi$
$857$	−1.93395	+	1.93395i	−0.0660625	+	0.0660625i	0.673304	+	0.739366i	$0.264875\pi$
$858$	26.3296	−	8.10214i	0.898879	−	0.276603i
$859$		−	17.6240i		−	0.601324i	−0.953731	−	0.300662i	$-0.902792\pi$
$859$		−	17.6240i		−	0.601324i	0.953731	−	0.300662i	$-0.0972076\pi$
$860$	9.96365	−	7.86793i	0.339758	−	0.268294i
$861$	−28.6094	+	3.57644i	−0.975005	+	0.121885i
$862$	−17.6810	−	17.6810i	−0.602219	−	0.602219i
$863$	18.9188	−	18.9188i	0.644003	−	0.644003i	−0.307534	−	0.951537i	$-0.599504\pi$
$863$	18.9188	−	18.9188i	0.644003	−	0.644003i	0.951537	+	0.307534i	$0.0995038\pi$
$864$	28.3228	−	11.0863i	0.963561	−	0.377162i
$865$	4.77947	−	3.77417i	0.162507	−	0.128326i
$866$	36.8187			1.25115
$867$	−14.6248	+	18.8037i	−0.496684	+	0.638606i
$868$	12.2888	−	12.2888i	0.417110	−	0.417110i
$869$		−	16.0957i		−	0.546010i
$870$	66.5017	−	0.490272i	2.25462	−	0.0166218i
$871$	5.62178	+	3.93954i	0.190487	+	0.133486i
$872$	16.6212	−	16.6212i	0.562864	−	0.562864i
$873$	33.8064	+	20.1118i	1.14417	+	0.680683i
$874$			27.0709i			0.915686i
$875$	−10.6565	−	22.9675i	−0.360257	−	0.776443i
$876$	7.97267	−	0.996659i	0.269372	−	0.0336740i
$877$	−7.67412	+	7.67412i	−0.259137	+	0.259137i	−0.824703	−	0.565566i	$-0.808658\pi$
$877$	−7.67412	+	7.67412i	−0.259137	+	0.259137i	0.565566	+	0.824703i	$0.308658\pi$
$878$	−0.627820	+	0.627820i	−0.0211879	+	0.0211879i
$879$	−22.6747	+	2.83455i	−0.764799	+	0.0956070i
$880$	−3.22237	+	27.4177i	−0.108626	+	0.924252i
$881$			22.3843i			0.754145i	0.926184	+	0.377073i	$0.123069\pi$
$881$			22.3843i			0.754145i	−0.926184	+	0.377073i	$0.876931\pi$
$882$	8.57628	+	5.10213i	0.288778	+	0.171798i
$883$	25.3525	−	25.3525i	0.853181	−	0.853181i	−0.137342	−	0.990524i	$-0.543856\pi$
$883$	25.3525	−	25.3525i	0.853181	−	0.853181i	0.990524	+	0.137342i	$0.0438561\pi$
$884$	−4.32214	+	6.16775i	−0.145369	+	0.207444i
$885$	−7.70769	−	7.59488i	−0.259091	−	0.255299i
$886$			8.72098i			0.292987i
$887$	16.1083	−	16.1083i	0.540864	−	0.540864i	−0.382919	−	0.923782i	$-0.625081\pi$
$887$	16.1083	−	16.1083i	0.540864	−	0.540864i	0.923782	+	0.382919i	$0.125081\pi$
$888$	7.94439	−	10.2144i	0.266596	−	0.342773i
$889$	22.1107			0.741568
$890$	−18.4048	−	23.3072i	−0.616932	−	0.781259i
$891$	−19.6289	+	10.6586i	−0.657594	+	0.357077i
$892$	19.6876	−	19.6876i	0.659190	−	0.659190i
$893$	−8.80598	−	8.80598i	−0.294681	−	0.294681i
$894$	10.9298	−	1.36633i	0.365548	−	0.0456969i
$895$	−4.77947	+	40.6664i	−0.159760	+	1.35933i
$896$			24.6809i			0.824533i
$897$	47.0073	−	14.4651i	1.56953	−	0.482974i
$898$	−18.5556	+	18.5556i	−0.619209	+	0.619209i
$899$		−	63.9511i		−	2.13289i
$900$	17.3872	−	0.256382i	0.579574	−	0.00854607i
$901$	−10.1270			−0.337379
$902$	22.9278	+	22.9278i	0.763411	+	0.763411i
$903$	−11.7940	+	15.1640i	−0.392480	+	0.504626i
$904$	−10.2731			−0.341678
$905$	0.592869	−	5.04446i	0.0197076	−	0.167684i
$906$	−5.90768	+	0.738515i	−0.196269	+	0.0245355i
$907$	7.78524	+	7.78524i	0.258505	+	0.258505i	0.824446	−	0.565941i	$-0.191487\pi$
$907$	7.78524	+	7.78524i	0.258505	+	0.258505i	−0.565941	+	0.824446i	$0.691487\pi$
$908$	−7.29112	+	7.29112i	−0.241964	+	0.241964i
$909$	30.1334	−	7.65353i	0.999463	−	0.253852i
$910$	32.3994	−	1.85421i	1.07403	−	0.0614665i
$911$		−	13.2800i		−	0.439986i	−0.975501	−	0.219993i	$-0.929397\pi$
$911$		−	13.2800i		−	0.439986i	0.975501	−	0.219993i	$-0.0706034\pi$
$912$	13.1530	+	10.2299i	0.435540	+	0.338747i
$913$	7.89092	−	7.89092i	0.261151	−	0.261151i
$914$	13.5837			0.449310
$915$	6.91875	−	7.02152i	0.228727	−	0.232124i
$916$		−	13.9859i		−	0.462106i
$917$	25.6194	+	25.6194i	0.846028	+	0.846028i
$918$	6.66865	−	15.2470i	0.220098	−	0.503225i
$919$			17.0532i			0.562534i	0.959630	+	0.281267i	$0.0907546\pi$
$919$			17.0532i			0.562534i	−0.959630	+	0.281267i	$0.909245\pi$
$920$	−3.07169	+	26.1356i	−0.101271	+	0.861666i
$921$	−39.5324	+	4.94192i	−1.30264	+	0.162842i
$922$	18.7964	+	18.7964i	0.619026	+	0.619026i
$923$	4.11522	+	23.3896i	0.135454	+	0.769879i
$924$	1.39986	+	11.1980i	0.0460519	+	0.368388i
$925$	21.2927	−	13.0961i	0.700099	−	0.430598i
$926$		−	32.6792i		−	1.07390i
$927$	25.7815	+	15.3377i	0.846777	+	0.503757i
$928$	−39.9852	−	39.9852i	−1.31258	−	1.31258i
$929$			17.0211i			0.558445i	0.960226	+	0.279223i	$0.0900768\pi$
$929$			17.0211i			0.558445i	−0.960226	+	0.279223i	$0.909923\pi$
$930$	−0.335949	−	45.5690i	−0.0110162	−	1.49427i
$931$			3.61918i			0.118614i
$932$	9.61770	−	9.61770i	0.315038	−	0.315038i
$933$	−5.30030	+	6.81480i	−0.173524	+	0.223106i
$934$	0.394106			0.0128955
$935$	6.19690	+	7.84753i	0.202660	+	0.256642i
$936$	5.73201	−	15.1132i	0.187357	−	0.493991i
$937$	10.5008	+	10.5008i	0.343048	+	0.343048i	0.857512	−	0.514464i	$-0.172009\pi$
$937$	10.5008	+	10.5008i	0.343048	+	0.343048i	−0.514464	+	0.857512i	$0.672009\pi$
$938$	−5.41909	+	5.41909i	−0.176940	+	0.176940i
$939$	−34.6316	+	4.32928i	−1.13016	+	0.141281i
$940$	10.3452	+	13.1008i	0.337425	+	0.427302i
$941$	−49.0451			−1.59882			−0.799412	−	0.600783i	$-0.794856\pi$
$941$	−49.0451			−1.59882			−0.799412	+	0.600783i	$0.794856\pi$
$942$	−26.4474	+	34.0045i	−0.861704	+	1.10793i
$943$	40.9338	+	40.9338i	1.33299	+	1.33299i
$944$			13.8988i			0.452367i
$945$	−25.4544	+	6.66525i	−0.828032	+	0.216821i
$946$	21.6043			0.702417
$947$	10.6955	+	10.6955i	0.347558	+	0.347558i	0.859199	−	0.511641i	$-0.170962\pi$
$947$	10.6955	+	10.6955i	0.347558	+	0.347558i	−0.511641	+	0.859199i	$0.670962\pi$
$948$	10.2794	+	7.99491i	0.333858	+	0.259663i
$949$	8.27978	−	11.8154i	0.268773	−	0.383543i
$950$	9.00400	+	14.6394i	0.292128	+	0.474965i
$951$	−4.35038	−	34.8004i	−0.141071	−	1.12848i
$952$	4.31170	+	4.31170i	0.139743	+	0.139743i
$953$	−15.7057	−	15.7057i	−0.508756	−	0.508756i	0.405388	−	0.914145i	$-0.367136\pi$
$953$	−15.7057	−	15.7057i	−0.508756	−	0.508756i	−0.914145	+	0.405388i	$0.867136\pi$
$954$	−29.0470	+	7.37759i	−0.940432	+	0.238858i
$955$	37.5232	+	4.41005i	1.21422	+	0.142706i
$956$	−33.7143			−1.09040
$957$	32.7797	+	25.4948i	1.05962	+	0.824130i
$958$	33.2995	−	33.2995i	1.07586	−	1.07586i
$959$	20.7268			0.669303
$960$	−1.25466	−	1.23630i	−0.0404940	−	0.0399013i
$961$	−12.8213			−0.413589
$962$	5.55195	+	31.5556i	0.179002	+	1.01739i
$963$	−9.53395	−	5.67186i	−0.307227	−	0.182773i
$964$	−5.02055			−0.161701
$965$	−35.7582	+	28.2370i	−1.15110	+	0.908980i
$966$	6.81091	+	54.4832i	0.219138	+	1.75297i
$967$	31.6460	−	31.6460i	1.01767	−	1.01767i	0.0178258	−	0.999841i	$-0.494326\pi$
$967$	31.6460	−	31.6460i	1.01767	−	1.01767i	0.999841	−	0.0178258i	$-0.00567443\pi$
$968$	5.11497	−	5.11497i	0.164402	−	0.164402i
$969$	5.98882	−	0.748659i	0.192389	−	0.0240504i
$970$	6.08301	−	51.7576i	0.195314	−	1.66184i
$971$		−	35.7161i		−	1.14618i	−0.819491	−	0.573092i	$-0.805744\pi$
$971$		−	35.7161i		−	1.14618i	0.819491	−	0.573092i	$-0.194256\pi$
$972$	2.94288	−	17.8301i	0.0943931	−	0.571900i
$973$	−19.2020	−	19.2020i	−0.615589	−	0.615589i
$974$	−11.5677			−0.370653
$975$	20.6094	−	23.4574i	0.660030	−	0.751239i
$976$	−12.6614			−0.405283
$977$	3.00427	+	3.00427i	0.0961151	+	0.0961151i	0.753529	−	0.657414i	$-0.228350\pi$
$977$	3.00427	+	3.00427i	0.0961151	+	0.0961151i	−0.657414	+	0.753529i	$0.728350\pi$
$978$	8.24484	−	10.6007i	0.263641	−	0.338973i
$979$		−	18.5443i		−	0.592680i
$980$	0.566261	−	4.81807i	0.0180886	−	0.153908i
$981$	−11.6168	−	45.7378i	−0.370897	−	1.46030i
$982$	−3.58443	+	3.58443i	−0.114384	+	0.114384i
$983$	−41.1733	+	41.1733i	−1.31322	+	1.31322i	−0.394198	+	0.919025i	$0.628978\pi$
$983$	−41.1733	+	41.1733i	−1.31322	+	1.31322i	−0.919025	+	0.394198i	$0.871022\pi$
$984$	18.8782	−	2.35995i	0.601814	−	0.0752324i
$985$	−42.6732	+	33.6975i	−1.35968	+	1.07369i
$986$	−30.9398			−0.985323
$987$	−19.9386	−	15.5075i	−0.634652	−	0.493609i
$988$	−7.96100	+	1.40067i	−0.253273	+	0.0445614i
$989$	38.5710			1.22649
$990$	23.4915	+	17.9944i	0.746607	+	0.571900i
$991$	−30.2659			−0.961429			−0.480715	−	0.876877i	$-0.659623\pi$
$991$	−30.2659			−0.961429			−0.480715	+	0.876877i	$0.659623\pi$
$992$	−27.3991	+	27.3991i	−0.869923	+	0.869923i
$993$	−16.6272	+	21.3782i	−0.527648	+	0.678418i
$994$	−26.5132			−0.840948
$995$	−40.0632	−	4.70858i	−1.27009	−	0.149272i
$996$	1.11995	+	8.95895i	0.0354871	+	0.283875i
$997$	15.8921	+	15.8921i	0.503309	+	0.503309i	0.912465	−	0.409155i	$-0.134177\pi$
$997$	15.8921	+	15.8921i	0.503309	+	0.503309i	−0.409155	+	0.912465i	$0.634177\pi$
$998$	20.8444	+	20.8444i	0.659819	+	0.659819i
$999$	−9.46906	−	24.1912i	−0.299588	−	0.765376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.s.b.77.4	yes	32
3.2	odd	2	inner	195.2.s.b.77.13	yes	32
5.2	odd	4		975.2.s.e.818.14		32
5.3	odd	4	inner	195.2.s.b.38.3	✓	32
5.4	even	2		975.2.s.e.857.13		32
13.12	even	2	inner	195.2.s.b.77.14	yes	32
15.2	even	4		975.2.s.e.818.3		32
15.8	even	4	inner	195.2.s.b.38.14	yes	32
15.14	odd	2		975.2.s.e.857.4		32
39.38	odd	2	inner	195.2.s.b.77.3	yes	32
65.12	odd	4		975.2.s.e.818.4		32
65.38	odd	4	inner	195.2.s.b.38.13	yes	32
65.64	even	2		975.2.s.e.857.3		32
195.38	even	4	inner	195.2.s.b.38.4	yes	32
195.77	even	4		975.2.s.e.818.13		32
195.194	odd	2		975.2.s.e.857.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.s.b.38.3	✓	32	5.3	odd	4	inner
195.2.s.b.38.4	yes	32	195.38	even	4	inner
195.2.s.b.38.13	yes	32	65.38	odd	4	inner
195.2.s.b.38.14	yes	32	15.8	even	4	inner
195.2.s.b.77.3	yes	32	39.38	odd	2	inner
195.2.s.b.77.4	yes	32	1.1	even	1	trivial
195.2.s.b.77.13	yes	32	3.2	odd	2	inner
195.2.s.b.77.14	yes	32	13.12	even	2	inner
975.2.s.e.818.3		32	15.2	even	4
975.2.s.e.818.4		32	65.12	odd	4
975.2.s.e.818.13		32	195.77	even	4
975.2.s.e.818.14		32	5.2	odd	4
975.2.s.e.857.3		32	65.64	even	2
975.2.s.e.857.4		32	15.14	odd	2
975.2.s.e.857.13		32	5.4	even	2
975.2.s.e.857.14		32	195.194	odd	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25684 - 1.25684i) q^{2} +(1.36721 + 1.06336i) q^{3} +1.15927i q^{4} +(-0.261006 + 2.22078i) q^{5} +(-0.381882 - 3.05483i) q^{6} +(1.60133 - 1.60133i) q^{7} +(-1.05665 + 1.05665i) q^{8} +(0.738515 + 2.90768i) q^{9} +(3.11920 - 2.46312i) q^{10} +2.48179 q^{11} +(-1.23273 + 1.58497i) q^{12} +(0.624771 + 3.55101i) q^{13} -4.02523 q^{14} +(-2.71835 + 2.75873i) q^{15} +4.97463 q^{16} +(1.27410 - 1.27410i) q^{17} +(2.72628 - 4.58267i) q^{18} +1.93388 q^{19} +(-2.57450 - 0.302577i) q^{20} +(3.89216 - 0.486556i) q^{21} +(-3.11920 - 3.11920i) q^{22} +(-5.56883 - 5.56883i) q^{23} +(-2.56827 + 0.321058i) q^{24} +(-4.86375 - 1.15927i) q^{25} +(3.67780 - 5.24827i) q^{26} +(-2.08222 + 4.76071i) q^{27} +(1.85639 + 1.85639i) q^{28} +9.66063 q^{29} +(6.88379 - 0.0507495i) q^{30} -6.61976i q^{31} +(-4.13899 - 4.13899i) q^{32} +(3.39312 + 2.63904i) q^{33} -3.20267 q^{34} +(3.13826 + 3.97417i) q^{35} +(-3.37080 + 0.856142i) q^{36} +(-3.53521 + 3.53521i) q^{37} +(-2.43057 - 2.43057i) q^{38} +(-2.92182 + 5.51933i) q^{39} +(-2.07081 - 2.62239i) q^{40} -7.35052 q^{41} +(-5.50332 - 4.28028i) q^{42} +(-3.46312 + 3.46312i) q^{43} +2.87707i q^{44} +(-6.65008 + 0.881161i) q^{45} +13.9982i q^{46} +(-4.55353 - 4.55353i) q^{47} +(6.80136 + 5.28984i) q^{48} +1.87146i q^{49} +(4.65592 + 7.56996i) q^{50} +(3.09679 - 0.387128i) q^{51} +(-4.11659 + 0.724281i) q^{52} +(-3.97417 - 3.97417i) q^{53} +(8.60044 - 3.36643i) q^{54} +(-0.647761 + 5.51151i) q^{55} +3.38411i q^{56} +(2.64402 + 2.05642i) q^{57} +(-12.1418 - 12.1418i) q^{58} +2.79393i q^{59} +(-3.19812 - 3.15131i) q^{60} -2.54520 q^{61} +(-8.31996 + 8.31996i) q^{62} +(5.83877 + 3.47355i) q^{63} +0.454797i q^{64} +(-8.04909 + 0.460648i) q^{65} +(-0.947751 - 7.58144i) q^{66} +(1.34628 - 1.34628i) q^{67} +(1.47703 + 1.47703i) q^{68} +(-1.69206 - 13.5354i) q^{69} +(1.05061 - 8.93916i) q^{70} +6.58676 q^{71} +(-3.85277 - 2.29206i) q^{72} +(-2.82950 - 2.82950i) q^{73} +8.88637 q^{74} +(-5.41703 - 6.75691i) q^{75} +2.24190i q^{76} +(3.97417 - 3.97417i) q^{77} +(10.6091 - 3.26464i) q^{78} -6.48553i q^{79} +(-1.29841 + 11.0476i) q^{80} +(-7.90919 + 4.29473i) q^{81} +(9.23840 + 9.23840i) q^{82} +(3.17953 - 3.17953i) q^{83} +(0.564052 + 4.51208i) q^{84} +(2.49695 + 3.16204i) q^{85} +8.70515 q^{86} +(13.2081 + 10.2728i) q^{87} +(-2.62239 + 2.62239i) q^{88} -7.47217i q^{89} +(9.46554 + 7.25059i) q^{90} +(6.68682 + 4.68588i) q^{91} +(6.45580 - 6.45580i) q^{92} +(7.03922 - 9.05059i) q^{93} +11.4461i q^{94} +(-0.504754 + 4.29473i) q^{95} +(-1.25761 - 10.0601i) q^{96} +(9.27171 - 9.27171i) q^{97} +(2.35212 - 2.35212i) q^{98} +(1.83284 + 7.21624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 24 q^{10} - 24 q^{12} + 24 q^{16} + 24 q^{22} - 8 q^{25} - 16 q^{27} + 36 q^{30} - 8 q^{36} + 16 q^{40} + 12 q^{42} - 64 q^{43} - 20 q^{48} + 16 q^{51} - 72 q^{52} - 80 q^{55} + 8 q^{61}+ \cdots - 40 q^{91}+O(q^{100}) \) 32 * q - 4 * q^3 - 24 * q^10 - 24 * q^12 + 24 * q^16 + 24 * q^22 - 8 * q^25 - 16 * q^27 + 36 * q^30 - 8 * q^36 + 16 * q^40 + 12 * q^42 - 64 * q^43 - 20 * q^48 + 16 * q^51 - 72 * q^52 - 80 * q^55 + 8 * q^61 - 72 * q^66 + 44 * q^75 + 84 * q^78 + 112 * q^81 + 48 * q^82 + 20 * q^87 - 8 * q^88 + 44 * q^90 - 40 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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