LMFDB - Embedded newform 288.2.bc.a.13.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			13.16
Character	$\chi$	$=$	288.13
Dual form			288.2.bc.a.133.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.750744 + 1.19849i) q^{2} +(-0.667307 + 1.59834i) q^{3} +(-0.872768 - 1.79952i) q^{4} +(0.354821 - 2.69513i) q^{5} +(-1.41463 - 1.99971i) q^{6} +(0.937559 + 0.251218i) q^{7} +(2.81194 + 0.304973i) q^{8} +(-2.10940 - 2.13317i) q^{9} +O(q^{10})$	\(q+(-0.750744 + 1.19849i) q^{2} +(-0.667307 + 1.59834i) q^{3} +(-0.872768 - 1.79952i) q^{4} +(0.354821 - 2.69513i) q^{5} +(-1.41463 - 1.99971i) q^{6} +(0.937559 + 0.251218i) q^{7} +(2.81194 + 0.304973i) q^{8} +(-2.10940 - 2.13317i) q^{9} +(2.96372 + 2.44861i) q^{10} +(2.93602 - 3.82629i) q^{11} +(3.45866 - 0.194150i) q^{12} +(-0.0219633 + 0.0168530i) q^{13} +(-1.00495 + 0.935057i) q^{14} +(4.07098 + 2.36561i) q^{15} +(-2.47655 + 3.14113i) q^{16} -3.29855i q^{17} +(4.14021 - 0.926638i) q^{18} +(3.38569 + 1.40240i) q^{19} +(-5.15963 + 1.71372i) q^{20} +(-1.02717 + 1.33090i) q^{21} +(2.38159 + 6.39136i) q^{22} +(2.77999 - 0.744896i) q^{23} +(-2.36388 + 4.29093i) q^{24} +(-2.30823 - 0.618487i) q^{25} +(-0.00370942 - 0.0389751i) q^{26} +(4.81716 - 1.94807i) q^{27} +(-0.366199 - 1.90641i) q^{28} +(-4.92410 + 0.648270i) q^{29} +(-5.89142 + 3.10307i) q^{30} +(-5.47515 + 9.48323i) q^{31} +(-1.90536 - 5.32631i) q^{32} +(4.15650 + 7.24608i) q^{33} +(3.95329 + 2.47636i) q^{34} +(1.00973 - 2.43771i) q^{35} +(-1.99767 + 5.65768i) q^{36} +(3.32918 - 1.37899i) q^{37} +(-4.22255 + 3.00488i) q^{38} +(-0.0122806 - 0.0463510i) q^{39} +(1.81968 - 7.47034i) q^{40} +(3.77673 - 1.01197i) q^{41} +(-0.823932 - 2.23023i) q^{42} +(6.35198 - 8.27806i) q^{43} +(-9.44796 - 1.94396i) q^{44} +(-6.49765 + 4.92823i) q^{45} +(-1.19431 + 3.89102i) q^{46} +(3.46353 - 1.99967i) q^{47} +(-3.36798 - 6.05448i) q^{48} +(-5.24627 - 3.02894i) q^{49} +(2.47414 - 2.30206i) q^{50} +(5.27221 + 2.20114i) q^{51} +(0.0494962 + 0.0248146i) q^{52} +(-1.64575 - 3.97319i) q^{53} +(-1.28171 + 7.23583i) q^{54} +(-9.27061 - 9.27061i) q^{55} +(2.55974 + 0.992340i) q^{56} +(-4.50081 + 4.47566i) q^{57} +(2.91979 - 6.38818i) q^{58} +(1.31514 - 9.98946i) q^{59} +(0.703945 - 9.39043i) q^{60} +(11.5453 - 1.51997i) q^{61} +(-7.25515 - 13.6814i) q^{62} +(-1.44180 - 2.52990i) q^{63} +(7.81398 + 1.71513i) q^{64} +(0.0376281 + 0.0651738i) q^{65} +(-11.8048 - 0.458407i) q^{66} +(-0.285557 - 0.372146i) q^{67} +(-5.93581 + 2.87887i) q^{68} +(-0.664507 + 4.94045i) q^{69} +(2.16353 + 3.04025i) q^{70} +(-5.64222 + 5.64222i) q^{71} +(-5.28095 - 6.64166i) q^{72} +(0.935370 + 0.935370i) q^{73} +(-0.846650 + 5.02526i) q^{74} +(2.52885 - 3.27662i) q^{75} +(-0.431275 - 7.31659i) q^{76} +(3.71392 - 2.84979i) q^{77} +(0.0647709 + 0.0200794i) q^{78} +(-11.1410 + 6.43227i) q^{79} +(7.58703 + 7.78918i) q^{80} +(-0.100841 + 8.99944i) q^{81} +(-1.62252 + 5.28612i) q^{82} +(1.56915 + 11.9189i) q^{83} +(3.29147 + 0.686851i) q^{84} +(-8.89003 - 1.17040i) q^{85} +(5.15248 + 13.8275i) q^{86} +(2.24973 - 8.30299i) q^{87} +(9.42281 - 9.86389i) q^{88} +(-12.5247 + 12.5247i) q^{89} +(-1.02838 - 11.4872i) q^{90} +(-0.0248256 + 0.0102831i) q^{91} +(-3.76674 - 4.35253i) q^{92} +(-11.5039 - 15.0794i) q^{93} +(-0.203634 + 5.65226i) q^{94} +(4.98097 - 8.62729i) q^{95} +(9.78474 + 0.508861i) q^{96} +(-0.161572 - 0.279850i) q^{97} +(7.56876 - 4.01366i) q^{98} +(-14.3554 + 1.80816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.750744	+	1.19849i	−0.530856	+	0.847462i
$2$	−0.750744	+	1.19849i	−0.530856	+	0.847462i
$3$	−0.667307	+	1.59834i	−0.385270	+	0.922804i
$3$	−0.667307	+	1.59834i	−0.385270	+	0.922804i
$4$	−0.872768	−	1.79952i	−0.436384	−	0.899761i
$5$	0.354821	−	2.69513i	0.158681	−	1.20530i	−0.707918	−	0.706295i	$-0.750365\pi$
$5$	0.354821	−	2.69513i	0.158681	−	1.20530i	0.866599	−	0.499006i	$-0.166301\pi$
$6$	−1.41463	−	1.99971i	−0.577519	−	0.816378i
$7$	0.937559	+	0.251218i	0.354364	+	0.0949516i	0.431610	−	0.902061i	$-0.357946\pi$
$7$	0.937559	+	0.251218i	0.354364	+	0.0949516i	−0.0772454	+	0.997012i	$0.524613\pi$
$8$	2.81194	+	0.304973i	0.994170	+	0.107824i
$9$	−2.10940	−	2.13317i	−0.703134	−	0.711057i
$10$	2.96372	+	2.44861i	0.937210	+	0.774317i
$11$	2.93602	−	3.82629i	0.885243	−	1.15367i	−0.102053	−	0.994779i	$-0.532541\pi$
$11$	2.93602	−	3.82629i	0.885243	−	1.15367i	0.987296	−	0.158892i	$-0.0507921\pi$
$12$	3.45866	−	0.194150i	0.998428	−	0.0560462i
$13$	−0.0219633	+	0.0168530i	−0.00609151	+	0.00467418i	−0.611803	−	0.791010i	$-0.709555\pi$
$13$	−0.0219633	+	0.0168530i	−0.00609151	+	0.00467418i	0.605711	+	0.795685i	$0.292889\pi$
$14$	−1.00495	+	0.935057i	−0.268584	+	0.249905i
$15$	4.07098	+	2.36561i	1.05112	+	0.610798i
$16$	−2.47655	+	3.14113i	−0.619138	+	0.785282i
$17$		−	3.29855i		−	0.800015i	−0.916512	−	0.400008i	$-0.869007\pi$
$17$		−	3.29855i		−	0.800015i	0.916512	−	0.400008i	$-0.130993\pi$
$18$	4.14021	−	0.926638i	0.975857	−	0.218411i
$19$	3.38569	+	1.40240i	0.776730	+	0.321732i	0.735595	−	0.677421i	$-0.236903\pi$
$19$	3.38569	+	1.40240i	0.776730	+	0.321732i	0.0411350	+	0.999154i	$0.486903\pi$
$20$	−5.15963	+	1.71372i	−1.15373	+	0.383199i
$21$	−1.02717	+	1.33090i	−0.224148	+	0.290427i
$22$	2.38159	+	6.39136i	0.507756	+	1.36264i
$23$	2.77999	−	0.744896i	0.579668	−	0.155321i	0.0429409	−	0.999078i	$-0.486327\pi$
$23$	2.77999	−	0.744896i	0.579668	−	0.155321i	0.536727	+	0.843756i	$0.319661\pi$
$24$	−2.36388	+	4.29093i	−0.482524	+	0.875882i
$25$	−2.30823	−	0.618487i	−0.461645	−	0.123697i
$26$	−0.00370942	−	0.0389751i	−0.000727477	−	0.00764364i
$27$	4.81716	−	1.94807i	0.927063	−	0.374906i
$28$	−0.366199	−	1.90641i	−0.0692051	−	0.360278i
$29$	−4.92410	+	0.648270i	−0.914382	+	0.120381i	−0.573011	−	0.819548i	$-0.694225\pi$
$29$	−4.92410	+	0.648270i	−0.914382	+	0.120381i	−0.341371	+	0.939929i	$0.610891\pi$
$30$	−5.89142	+	3.10307i	−1.07562	+	0.566540i
$31$	−5.47515	+	9.48323i	−0.983366	+	1.70324i	−0.334380	+	0.942438i	$0.608527\pi$
$31$	−5.47515	+	9.48323i	−0.983366	+	1.70324i	−0.648985	+	0.760801i	$0.724806\pi$
$32$	−1.90536	−	5.32631i	−0.336824	−	0.941568i
$33$	4.15650	+	7.24608i	0.723554	+	1.26138i
$34$	3.95329	+	2.47636i	0.677983	+	0.424693i
$35$	1.00973	−	2.43771i	0.170676	−	0.412048i
$36$	−1.99767	+	5.65768i	−0.332945	+	0.942946i
$37$	3.32918	−	1.37899i	0.547314	−	0.226705i	−0.0918536	−	0.995773i	$-0.529279\pi$
$37$	3.32918	−	1.37899i	0.547314	−	0.226705i	0.639167	+	0.769068i	$0.279279\pi$
$38$	−4.22255	+	3.00488i	−0.684988	+	0.487456i
$39$	−0.0122806	−	0.0463510i	−0.00196648	−	0.00742209i
$40$	1.81968	−	7.47034i	0.287717	−	1.18116i
$41$	3.77673	−	1.01197i	0.589827	−	0.158044i	0.0484527	−	0.998825i	$-0.484571\pi$
$41$	3.77673	−	1.01197i	0.589827	−	0.158044i	0.541374	+	0.840782i	$0.317904\pi$
$42$	−0.823932	−	2.23023i	−0.127136	−	0.344131i
$43$	6.35198	−	8.27806i	0.968668	−	1.26239i	0.00370816	−	0.999993i	$-0.498820\pi$
$43$	6.35198	−	8.27806i	0.968668	−	1.26239i	0.964959	−	0.262399i	$-0.0845137\pi$
$44$	−9.44796	−	1.94396i	−1.42433	−	0.293063i
$45$	−6.49765	+	4.92823i	−0.968612	+	0.734657i
$46$	−1.19431	+	3.89102i	−0.176091	+	0.573700i
$47$	3.46353	−	1.99967i	0.505208	−	0.291682i	−0.225653	−	0.974208i	$-0.572452\pi$
$47$	3.46353	−	1.99967i	0.505208	−	0.291682i	0.730862	+	0.682525i	$0.239118\pi$
$48$	−3.36798	−	6.05448i	−0.486126	−	0.873889i
$49$	−5.24627	−	3.02894i	−0.749467	−	0.432705i
$50$	2.47414	−	2.30206i	0.349896	−	0.325561i
$51$	5.27221	+	2.20114i	0.738257	+	0.308222i
$52$	0.0494962	+	0.0248146i	0.00686388	+	0.00344116i
$53$	−1.64575	−	3.97319i	−0.226061	−	0.545759i	0.769630	−	0.638490i	$-0.220441\pi$
$53$	−1.64575	−	3.97319i	−0.226061	−	0.545759i	−0.995691	+	0.0927305i	$0.970441\pi$
$54$	−1.28171	+	7.23583i	−0.174418	+	0.984672i
$55$	−9.27061	−	9.27061i	−1.25005	−	1.25005i
$56$	2.55974	+	0.992340i	0.342060	+	0.132607i
$57$	−4.50081	+	4.47566i	−0.596146	+	0.592816i
$58$	2.91979	−	6.38818i	0.383387	−	0.838809i
$59$	1.31514	−	9.98946i	0.171216	−	1.30052i	−0.662808	−	0.748789i	$-0.730635\pi$
$59$	1.31514	−	9.98946i	0.171216	−	1.30052i	0.834024	−	0.551728i	$-0.186031\pi$
$60$	0.703945	−	9.39043i	0.0908789	−	1.21230i
$61$	11.5453	−	1.51997i	1.47823	−	0.194612i	0.652116	−	0.758120i	$-0.273882\pi$
$61$	11.5453	−	1.51997i	1.47823	−	0.194612i	0.826111	+	0.563507i	$0.190548\pi$
$62$	−7.25515	−	13.6814i	−0.921405	−	1.73754i
$63$	−1.44180	−	2.52990i	−0.181650	−	0.318737i
$64$	7.81398	+	1.71513i	0.976748	+	0.214391i
$65$	0.0376281	+	0.0651738i	0.00466719	+	0.00808381i
$66$	−11.8048	−	0.458407i	−1.45307	−	0.0564260i
$67$	−0.285557	−	0.372146i	−0.0348864	−	0.0454648i	0.775584	−	0.631244i	$-0.217455\pi$
$67$	−0.285557	−	0.372146i	−0.0348864	−	0.0454648i	−0.810471	+	0.585779i	$0.800789\pi$
$68$	−5.93581	+	2.87887i	−0.719822	+	0.349114i
$69$	−0.664507	+	4.94045i	−0.0799972	+	0.594760i
$70$	2.16353	+	3.04025i	0.258591	+	0.363380i
$71$	−5.64222	+	5.64222i	−0.669609	+	0.669609i	−0.957625	−	0.288017i	$-0.907004\pi$
$71$	−5.64222	+	5.64222i	−0.669609	+	0.669609i	0.288017	+	0.957625i	$0.407004\pi$
$72$	−5.28095	−	6.64166i	−0.622366	−	0.782727i
$73$	0.935370	+	0.935370i	0.109477	+	0.109477i	0.759723	−	0.650246i	$-0.225334\pi$
$73$	0.935370	+	0.935370i	0.109477	+	0.109477i	−0.650246	+	0.759723i	$0.725334\pi$
$74$	−0.846650	+	5.02526i	−0.0984210	+	0.584175i
$75$	2.52885	−	3.27662i	0.292006	−	0.378351i
$76$	−0.431275	−	7.31659i	−0.0494707	−	0.839270i
$77$	3.71392	−	2.84979i	0.423241	−	0.324764i
$78$	0.0647709	+	0.0200794i	0.00733386	+	0.00227355i
$79$	−11.1410	+	6.43227i	−1.25346	+	0.723687i	−0.971796	−	0.235825i	$-0.924221\pi$
$79$	−11.1410	+	6.43227i	−1.25346	+	0.723687i	−0.281668	+	0.959512i	$0.590888\pi$
$80$	7.58703	+	7.78918i	0.848256	+	0.870857i
$81$	−0.100841	+	8.99944i	−0.0112046	+	0.999937i
$82$	−1.62252	+	5.28612i	−0.179177	+	0.583754i
$83$	1.56915	+	11.9189i	0.172237	+	1.30827i	0.831149	+	0.556050i	$0.187684\pi$
$83$	1.56915	+	11.9189i	0.172237	+	1.30827i	−0.658912	+	0.752220i	$0.728983\pi$
$84$	3.29147	+	0.686851i	0.359129	+	0.0749416i
$85$	−8.89003	−	1.17040i	−0.964259	−	0.126947i
$86$	5.15248	+	13.8275i	0.555607	+	1.49106i
$87$	2.24973	−	8.30299i	0.241196	−	0.890174i
$88$	9.42281	−	9.86389i	1.00448	−	1.05149i
$89$	−12.5247	+	12.5247i	−1.32761	+	1.32761i	−0.420166	+	0.907447i	$0.638028\pi$
$89$	−12.5247	+	12.5247i	−1.32761	+	1.32761i	−0.907447	+	0.420166i	$0.861972\pi$
$90$	−1.02838	−	11.4872i	−0.108401	−	1.21086i
$91$	−0.0248256	+	0.0102831i	−0.00260243	+	0.00107796i
$92$	−3.76674	−	4.35253i	−0.392710	−	0.453782i
$93$	−11.5039	−	15.0794i	−1.19289	−	1.56366i
$94$	−0.203634	+	5.65226i	−0.0210033	+	0.582986i
$95$	4.98097	−	8.62729i	0.511036	−	0.885141i
$96$	9.78474	+	0.508861i	0.998650	+	0.0519354i
$97$	−0.161572	−	0.279850i	−0.0164051	−	0.0284145i	0.857706	−	0.514140i	$-0.171889\pi$
$97$	−0.161572	−	0.279850i	−0.0164051	−	0.0284145i	−0.874111	+	0.485725i	$0.838555\pi$
$98$	7.56876	−	4.01366i	0.764560	−	0.405441i
$99$	−14.3554	+	1.80816i	−1.44277	+	0.181727i
$100$	0.901564	+	4.69350i	0.0901564	+	0.469350i
$101$	−4.37204	−	3.35478i	−0.435034	−	0.333813i	0.367917	−	0.929859i	$-0.380071\pi$
$101$	−4.37204	−	3.35478i	−0.435034	−	0.333813i	−0.802951	+	0.596045i	$0.796738\pi$
$102$	−6.59614	+	4.66621i	−0.653115	+	0.462024i
$103$	1.93476	+	7.22063i	0.190638	+	0.711470i	0.993353	+	0.115108i	$0.0367213\pi$
$103$	1.93476	+	7.22063i	0.190638	+	0.711470i	−0.802715	+	0.596363i	$0.796612\pi$
$104$	−0.0668990	+	0.0406914i	−0.00655999	+	0.00399012i
$105$	3.22250	+	3.24060i	0.314484	+	0.316250i
$106$	5.99737	+	1.01043i	0.582516	+	0.0981415i
$107$	7.34138	+	17.7237i	0.709718	+	1.71341i	0.700704	+	0.713453i	$0.252870\pi$
$107$	7.34138	+	17.7237i	0.709718	+	1.71341i	0.00901484	+	0.999959i	$0.497130\pi$
$108$	−7.70985	−	6.96837i	−0.741881	−	0.670532i
$109$	−7.20083	−	2.98268i	−0.689715	−	0.285689i	0.0101666	−	0.999948i	$-0.496764\pi$
$109$	−7.20083	−	2.98268i	−0.689715	−	0.285689i	−0.699881	+	0.714259i	$0.746764\pi$
$110$	18.0706	−	4.15091i	1.72297	−	0.395773i
$111$	−0.0174834	+	6.24138i	−0.00165945	+	0.592406i
$112$	−3.11102	+	2.32284i	−0.293964	+	0.219488i
$113$	3.06448	+	1.76928i	0.288282	+	0.166440i	0.637167	−	0.770726i	$-0.280106\pi$
$113$	3.06448	+	1.76928i	0.288282	+	0.166440i	−0.348885	+	0.937166i	$0.613440\pi$
$114$	−1.98509	−	8.75426i	−0.185921	−	0.819911i
$115$	−1.02120	−	7.75675i	−0.0952270	−	0.723321i
$116$	5.46417	+	8.29523i	0.507335	+	0.770192i
$117$	0.0822797	+	0.0113016i	0.00760676	+	0.00104484i
$118$	10.9850	+	9.07571i	1.01125	+	0.835487i
$119$	0.828656	−	3.09258i	0.0759627	−	0.283497i
$120$	10.7259	+	7.89348i	0.979135	+	0.720573i
$121$	−3.17331	−	11.8429i	−0.288482	−	1.07663i
$122$	−6.84590	+	14.9781i	−0.619799	+	1.35605i
$123$	−0.902761	+	6.71181i	−0.0813992	+	0.605184i
$124$	21.8438	+	1.57598i	1.96163	+	0.141527i
$125$	2.71550	−	6.55580i	0.242882	−	0.586369i
$126$	4.11448	+	0.171318i	0.366547	+	0.0152623i
$127$	−8.95827			−0.794918			−0.397459	−	0.917620i	$-0.630108\pi$
$127$	−8.95827			−0.794918			−0.397459	+	0.917620i	$0.630108\pi$
$128$	−7.92187	+	8.07737i	−0.700201	+	0.713946i
$129$	8.99246	+	15.6766i	0.791742	+	1.38025i
$130$	−0.106359	−	0.00383181i	−0.00932833	−	0.000336072i
$131$	−0.373658	−	0.486961i	−0.0326467	−	0.0425460i	0.776745	−	0.629816i	$-0.216870\pi$
$131$	−0.373658	−	0.486961i	−0.0326467	−	0.0425460i	−0.809391	+	0.587270i	$0.800203\pi$
$132$	9.41180	−	13.8039i	0.819192	−	1.20147i
$133$	2.82198	+	2.16538i	0.244696	+	0.187762i
$134$	0.660394	−	0.0628524i	0.0570494	−	0.00542962i
$135$	−3.54108	−	13.6741i	−0.304768	−	1.17688i
$136$	1.00597	−	9.27531i	0.0862611	−	0.795351i
$137$	3.50427	−	13.0781i	0.299390	−	1.11734i	−0.638277	−	0.769807i	$-0.720353\pi$
$137$	3.50427	−	13.0781i	0.299390	−	1.11734i	0.937668	−	0.347533i	$-0.112981\pi$
$138$	−5.42222	−	4.50542i	−0.461570	−	0.383527i
$139$	−8.13681	−	1.07123i	−0.690155	−	0.0908607i	−0.222713	−	0.974884i	$-0.571491\pi$
$139$	−8.13681	−	1.07123i	−0.690155	−	0.0908607i	−0.467443	+	0.884023i	$0.654825\pi$
$140$	−5.26798	+	0.310520i	−0.445225	+	0.0262438i
$141$	0.884922	+	6.87031i	0.0745239	+	0.578585i
$142$	−2.52630	−	10.9980i	−0.212002	−	0.922934i
$143$			0.133519i			0.0111654i
$144$	11.9246	−	1.34299i	0.993718	−	0.111916i
$145$			13.5011i			1.12121i
$146$	−1.82326	+	0.418811i	−0.150894	+	0.0346610i
$147$	8.34215	−	6.36411i	0.688049	−	0.524903i
$148$	−5.38712	−	4.78739i	−0.442819	−	0.393521i
$149$	−6.27109	−	0.825605i	−0.513748	−	0.0676362i	−0.130805	−	0.991408i	$-0.541756\pi$
$149$	−6.27109	−	0.825605i	−0.513748	−	0.0676362i	−0.382943	+	0.923772i	$0.625089\pi$
$150$	2.02848	+	5.49070i	0.165625	+	0.448314i
$151$	0.674240	−	2.51630i	0.0548689	−	0.204773i	−0.933050	−	0.359748i	$-0.882863\pi$
$151$	0.674240	−	2.51630i	0.0548689	−	0.204773i	0.987919	+	0.154974i	$0.0495295\pi$
$152$	9.09265	+	4.97600i	0.737511	+	0.403607i
$153$	−7.03637	+	6.95797i	−0.568857	+	0.562518i
$154$	0.627252	+	6.59058i	0.0505454	+	0.531084i
$155$	23.6159	+	18.1211i	1.89687	+	1.45552i
$156$	−0.0726914	+	0.0625529i	−0.00581997	+	0.00500824i
$157$	6.10071	+	7.95060i	0.486890	+	0.634527i	0.970599	−	0.240702i	$-0.0773775\pi$
$157$	6.10071	+	7.95060i	0.486890	+	0.634527i	−0.483709	+	0.875229i	$0.660711\pi$
$158$	0.655023	−	18.1814i	0.0521108	−	1.44644i
$159$	7.44874	+	0.0208655i	0.590723	+	0.00165474i
$160$	−15.0312	+	3.24532i	−1.18832	+	0.256565i
$161$	2.79354			0.220161
$162$	−10.7100	−	6.87713i	−0.841461	−	0.540318i
$163$	−5.32263	+	12.8500i	−0.416900	+	1.00649i	0.566340	+	0.824172i	$0.308359\pi$
$163$	−5.32263	+	12.8500i	−0.416900	+	1.00649i	−0.983240	+	0.182315i	$0.941641\pi$
$164$	−5.11728	−	5.91309i	−0.399592	−	0.461735i
$165$	21.0040	−	8.63128i	1.63516	−	0.671944i
$166$	−15.4627	−	7.06742i	−1.20014	−	0.548538i
$167$	3.01121	+	11.2380i	0.233014	+	0.869621i	0.979034	+	0.203697i	$0.0652958\pi$
$167$	3.01121	+	11.2380i	0.233014	+	0.869621i	−0.746020	+	0.665924i	$0.768038\pi$
$168$	−3.29424	+	3.42915i	−0.254156	+	0.264565i
$169$	−3.36445	+	12.5563i	−0.258804	+	0.965869i
$170$	8.07685	−	9.77597i	0.619466	−	0.749783i
$171$	−4.15022	−	10.1805i	−0.317376	−	0.778520i
$172$	−20.4403	−	4.20569i	−1.55856	−	0.320681i
$173$	−2.10808	−	16.0125i	−0.160275	−	1.21741i	−0.862725	−	0.505673i	$-0.831244\pi$
$173$	−2.10808	−	16.0125i	−0.160275	−	1.21741i	0.702450	−	0.711733i	$-0.252089\pi$
$174$	8.26210	+	8.92970i	0.626348	+	0.676959i
$175$	−2.00872	−	1.15974i	−0.151845	−	0.0876678i
$176$	4.74768	+	18.6984i	0.357870	+	1.40945i
$177$	15.0890	+	8.76808i	1.13416	+	0.659049i
$178$	−5.60791	−	24.4136i	−0.420331	−	1.82987i
$179$	3.00771	+	1.24584i	0.224807	+	0.0931181i	0.492244	−	0.870457i	$-0.336177\pi$
$179$	3.00771	+	1.24584i	0.224807	+	0.0931181i	−0.267437	+	0.963575i	$0.586177\pi$
$180$	14.5394	+	7.39145i	1.08370	+	0.550926i
$181$	9.02933	+	21.7987i	0.671145	+	1.62029i	0.779668	+	0.626193i	$0.215388\pi$
$181$	9.02933	+	21.7987i	0.671145	+	1.62029i	−0.108523	+	0.994094i	$0.534612\pi$
$182$	0.00631346	−	0.0374733i	0.000467984	−	0.00277771i
$183$	−5.27484	+	19.4677i	−0.389927	+	1.43909i
$184$	8.04433	−	1.24678i	0.593036	−	0.0919137i
$185$	−2.53530	−	9.46188i	−0.186399	−	0.695651i
$186$	26.7090	−	2.46653i	1.95840	−	0.180855i
$187$	−12.6212	−	9.68460i	−0.922954	−	0.708208i
$188$	−6.62131	−	4.48745i	−0.482909	−	0.327281i
$189$	5.00576	−	0.616272i	0.364116	−	0.0448272i
$190$	6.60031	+	12.4465i	0.478837	+	0.902966i
$191$	10.1928	+	17.6544i	0.737525	+	1.27743i	0.953607	+	0.301056i	$0.0973390\pi$
$191$	10.1928	+	17.6544i	0.737525	+	1.27743i	−0.216082	+	0.976375i	$0.569328\pi$
$192$	−7.95569	+	11.3449i	−0.574153	+	0.818748i
$193$	11.6459	−	20.1714i	0.838293	−	1.45197i	−0.0530272	−	0.998593i	$-0.516887\pi$
$193$	11.6459	−	20.1714i	0.838293	−	1.45197i	0.891321	−	0.453374i	$-0.149780\pi$
$194$	0.456697	+	0.0164535i	0.0327890	+	0.00118129i
$195$	−0.129280	+	0.0166517i	−0.00925790	+	0.00119245i
$196$	−0.871857	+	12.0843i	−0.0622755	+	0.863167i
$197$	−21.2139	+	8.78709i	−1.51143	+	0.626054i	−0.975852	−	0.218433i	$-0.929905\pi$
$197$	−21.2139	+	8.78709i	−1.51143	+	0.626054i	−0.535576	+	0.844487i	$0.679905\pi$
$198$	8.61014	−	18.5623i	0.611896	−	1.31916i
$199$	1.30822	−	1.30822i	0.0927372	−	0.0927372i	−0.659216	−	0.751953i	$-0.729112\pi$
$199$	1.30822	−	1.30822i	0.0927372	−	0.0927372i	0.751953	+	0.659216i	$0.229112\pi$
$200$	−6.30196	−	2.44309i	−0.445616	−	0.172753i
$201$	0.785371	−	0.208083i	0.0553958	−	0.0146771i
$202$	7.30296	−	2.72127i	0.513835	−	0.191468i
$203$	−4.77949	−	0.629232i	−0.335454	−	0.0441634i
$204$	−0.640412	−	11.4085i	−0.0448378	−	0.798758i
$205$	−1.38734	−	10.5379i	−0.0968959	−	0.735997i
$206$	−10.1064	−	3.10205i	−0.704145	−	0.216130i
$207$	−7.45311	−	4.35891i	−0.518027	−	0.302965i
$208$	0.00145571	−	0.110727i	0.000100935	−	0.00767752i
$209$	15.3064	−	8.83717i	1.05877	−	0.611280i
$210$	−6.30311	+	1.42928i	−0.434956	+	0.0986295i
$211$	5.21219	−	3.99946i	0.358822	−	0.275334i	−0.413580	−	0.910468i	$-0.635722\pi$
$211$	5.21219	−	3.99946i	0.358822	−	0.275334i	0.772402	+	0.635134i	$0.219055\pi$
$212$	−5.71348	+	6.42923i	−0.392403	+	0.441561i
$213$	−5.25311	−	12.7833i	−0.359937	−	0.875898i
$214$	−26.7532	−	4.50734i	−1.82881	−	0.308115i
$215$	−20.0567	−	20.0567i	−1.36785	−	1.36785i
$216$	14.1397	−	4.00874i	0.962082	−	0.272760i
$217$	−7.51564	+	7.51564i	−0.510195	+	0.510195i
$218$	8.98070	−	6.39091i	0.608250	−	0.432847i
$219$	−2.11922	+	0.870864i	−0.143204	+	0.0588475i
$220$	−8.59157	+	24.7738i	−0.579243	+	1.67025i
$221$	0.0555905	+	0.0724469i	0.00373942	+	0.00487330i
$222$	−7.46712	−	4.70663i	−0.501160	−	0.315888i
$223$	12.4983	+	21.6476i	0.836946	+	1.44963i	0.892436	+	0.451174i	$0.148995\pi$
$223$	12.4983	+	21.6476i	0.836946	+	1.44963i	−0.0554901	+	0.998459i	$0.517672\pi$
$224$	−0.448324	−	5.47239i	−0.0299549	−	0.365640i
$225$	3.54964	+	6.22848i	0.236642	+	0.415232i
$226$	−4.42110	+	2.34448i	−0.294087	+	0.155952i
$227$	−15.6291	+	2.05761i	−1.03734	+	0.136568i	−0.629909	−	0.776669i	$-0.716908\pi$
$227$	−15.6291	+	2.05761i	−1.03734	+	0.136568i	−0.407429	+	0.913237i	$0.633575\pi$
$228$	11.9822	+	4.19308i	0.793541	+	0.277694i
$229$	1.29501	−	9.83660i	0.0855769	−	0.650021i	−0.893871	−	0.448324i	$-0.852021\pi$
$229$	1.29501	−	9.83660i	0.0855769	−	0.650021i	0.979448	−	0.201697i	$-0.0646456\pi$
$230$	10.0631	+	4.59944i	0.663539	+	0.303278i
$231$	2.07662	+	7.83782i	0.136632	+	0.515690i
$232$	−14.0440	+	0.321176i	−0.922031	+	0.0210862i
$233$	5.11506	+	5.11506i	0.335099	+	0.335099i	0.854519	−	0.519420i	$-0.173852\pi$
$233$	5.11506	+	5.11506i	0.335099	+	0.335099i	−0.519420	+	0.854519i	$0.673852\pi$
$234$	−0.0753159	+	0.0901270i	−0.00492355	+	0.00589179i
$235$	−4.16045	−	10.0442i	−0.271398	−	0.655212i
$236$	−19.1241	+	6.35186i	−1.24487	+	0.413471i
$237$	−2.84650	−	22.0995i	−0.184900	−	1.43552i
$238$	3.08433	+	3.31488i	0.199927	+	0.214871i
$239$	−14.3834	−	8.30423i	−0.930382	−	0.537156i	−0.0434496	−	0.999056i	$-0.513835\pi$
$239$	−14.3834	−	8.30423i	−0.930382	−	0.537156i	−0.886932	+	0.461899i	$0.847168\pi$
$240$	−17.5127	+	6.92891i	−1.13044	+	0.447259i
$241$	17.5753	−	10.1471i	1.13213	−	0.653634i	0.187658	−	0.982234i	$-0.439910\pi$
$241$	17.5753	−	10.1471i	1.13213	−	0.653634i	0.944469	+	0.328601i	$0.106577\pi$
$242$	16.5760	+	5.08783i	1.06555	+	0.327058i
$243$	−14.3169	−	6.16657i	−0.918429	−	0.395585i
$244$	−12.8116	−	19.4495i	−0.820179	−	1.24512i
$245$	−10.0249	+	13.0647i	−0.640466	+	0.834672i
$246$	−7.36632	−	6.12080i	−0.469659	−	0.390248i
$247$	−0.0979954	+	0.0262578i	−0.00623530	+	0.00167074i
$248$	−18.2879	+	24.9965i	−1.16128	+	1.58728i
$249$	−20.0976	−	5.44552i	−1.27363	−	0.345096i
$250$	5.81843	+	8.17624i	0.367990	+	0.517111i
$251$	13.6810	−	5.66685i	0.863536	−	0.357688i	0.0934468	−	0.995624i	$-0.470211\pi$
$251$	13.6810	−	5.66685i	0.863536	−	0.357688i	0.770090	+	0.637936i	$0.220211\pi$
$252$	−3.29424	+	4.80256i	−0.207518	+	0.302533i
$253$	5.31191	−	12.8241i	0.333957	−	0.806243i
$254$	6.72537	−	10.7364i	0.421987	−	0.673663i
$255$	7.80307	−	13.4283i	0.488647	−	0.840913i
$256$	−3.73338	−	15.5583i	−0.233336	−	0.972396i
$257$	0.217962	−	0.377521i	0.0135961	−	0.0235491i	−0.859147	−	0.511728i	$-0.829005\pi$
$257$	0.217962	−	0.377521i	0.0135961	−	0.0235491i	0.872743	+	0.488179i	$0.162339\pi$
$258$	−25.5394	−	0.991749i	−1.59001	−	0.0617436i
$259$	3.46773	−	0.456535i	0.215474	−	0.0283677i
$260$	0.0844410	−	0.124594i	0.00523681	−	0.00772700i
$261$	11.7698	+	9.13648i	0.728531	+	0.565534i
$262$	0.864140	−	0.0822437i	0.0533868	−	0.00508104i
$263$	−10.6548	−	2.85494i	−0.657002	−	0.176043i	−0.0851096	−	0.996372i	$-0.527124\pi$
$263$	−10.6548	−	2.85494i	−0.657002	−	0.176043i	−0.571893	+	0.820328i	$0.693791\pi$
$264$	9.47797	+	21.6431i	0.583329	+	1.33204i
$265$	−11.2922	+	3.02574i	−0.693676	+	0.185870i
$266$	−4.71377	+	1.75647i	−0.289020	+	0.107696i
$267$	−11.6609	−	28.3765i	−0.713637	−	1.73662i
$268$	−0.420459	+	0.838664i	−0.0256836	+	0.0512295i
$269$	−6.92885	−	2.87002i	−0.422460	−	0.174988i	0.161317	−	0.986903i	$-0.448426\pi$
$269$	−6.92885	−	2.87002i	−0.422460	−	0.174988i	−0.583777	+	0.811914i	$0.698426\pi$
$270$	19.0468	+	6.02180i	1.15915	+	0.366475i
$271$			1.31948i			0.0801525i	0.999197	+	0.0400763i	$0.0127601\pi$
$271$			1.31948i			0.0801525i	−0.999197	+	0.0400763i	$0.987240\pi$
$272$	10.3612	+	8.16903i	0.628238	+	0.495320i
$273$	0.000130374	−	0.0465419i	7.89058e−6	−	0.00281684i
$274$	13.0432	+	14.0182i	0.787970	+	0.846869i
$275$	−9.14350	+	7.01606i	−0.551374	+	0.423084i
$276$	9.47041	−	3.11607i	0.570051	−	0.187566i
$277$	−0.104331	+	0.135967i	−0.00626864	+	0.00816945i	−0.796477	−	0.604669i	$-0.793306\pi$
$277$	−0.104331	+	0.135967i	−0.00626864	+	0.00816945i	0.790209	+	0.612838i	$0.209972\pi$
$278$	7.39252	−	8.94768i	0.443374	−	0.536646i
$279$	31.7787	−	8.32453i	1.90254	−	0.498377i
$280$	3.58274	−	6.54675i	0.214110	−	0.391243i
$281$	25.5371	+	6.84266i	1.52342	+	0.408199i	0.920865	−	0.389881i	$-0.127484\pi$
$281$	25.5371	+	6.84266i	1.52342	+	0.408199i	0.602553	+	0.798079i	$0.294150\pi$
$282$	−8.89837	−	4.09727i	−0.529890	−	0.243989i
$283$	0.157617	−	1.19722i	0.00936935	−	0.0711673i	−0.986121	−	0.166026i	$-0.946907\pi$
$283$	0.157617	−	1.19722i	0.00936935	−	0.0711673i	0.995491	+	0.0948585i	$0.0302398\pi$
$284$	15.0776	+	5.22895i	0.894694	+	0.310281i
$285$	10.4655	+	13.7183i	0.619925	+	0.812604i
$286$	−0.160021	−	0.100238i	−0.00946224	−	0.00592721i
$287$	3.79514			0.224020
$288$	−7.34276	+	15.2998i	−0.432676	+	0.901549i
$289$	6.11958			0.359975
$290$	−16.1810	−	10.1359i	−0.950181	−	0.595200i
$291$	0.555115	−	0.0715009i	0.0325414	−	0.00419146i
$292$	0.866857	−	2.49958i	0.0507290	−	0.146277i
$293$	−2.73728	+	20.7917i	−0.159914	+	1.21466i	0.703696	+	0.710502i	$0.251532\pi$
$293$	−2.73728	+	20.7917i	−0.159914	+	1.21466i	−0.863609	+	0.504162i	$0.831801\pi$
$294$	1.36452	+	14.7758i	0.0795805	+	0.861744i
$295$	−26.4563	−	7.08895i	−1.54035	−	0.412734i
$296$	9.78200	−	2.86233i	0.568567	−	0.166369i
$297$	6.68938	−	24.1514i	0.388157	−	1.40141i
$298$	5.69747	−	6.89604i	0.330045	−	0.399477i
$299$	−0.0485039	+	0.0632115i	−0.00280505	+	0.00365562i
$300$	−8.10344	−	1.69099i	−0.467852	−	0.0976295i
$301$	8.03496	−	6.16544i	0.463127	−	0.355370i
$302$	2.50958	+	2.69717i	0.144410	+	0.155204i
$303$	8.27959	−	4.74935i	0.475650	−	0.272843i
$304$	−12.7899	+	7.16177i	−0.733554	+	0.410756i
$305$		−	31.6555i		−	1.81259i
$306$	−3.05656	−	13.6567i	−0.174732	−	0.780701i
$307$	−2.35166	−	0.974088i	−0.134216	−	0.0555941i	0.314564	−	0.949236i	$-0.398142\pi$
$307$	−2.35166	−	0.974088i	−0.134216	−	0.0555941i	−0.448781	+	0.893642i	$0.648142\pi$
$308$	−8.36966	−	4.19608i	−0.476906	−	0.239094i
$309$	−12.8321	−	1.72596i	−0.729994	−	0.0981867i
$310$	−39.4475	+	14.6992i	−2.24047	+	0.834856i
$311$	−7.24717	+	1.94187i	−0.410949	+	0.110114i	−0.458370	−	0.888761i	$-0.651567\pi$
$311$	−7.24717	+	1.94187i	−0.410949	+	0.110114i	0.0474207	+	0.998875i	$0.484900\pi$
$312$	−0.0203966	−	0.134081i	−0.00115473	−	0.00759086i
$313$	13.7213	+	3.67661i	0.775574	+	0.207814i	0.624833	−	0.780759i	$-0.285167\pi$
$313$	13.7213	+	3.67661i	0.775574	+	0.207814i	0.150742	+	0.988573i	$0.451834\pi$
$314$	−14.1088	+	1.34279i	−0.796206	+	0.0757781i
$315$	−7.32999	+	2.98818i	−0.412998	+	0.168365i
$316$	21.2985	+	14.4346i	1.19814	+	0.812011i
$317$	−1.34200	+	0.176677i	−0.0753740	+	0.00992317i	−0.168119	−	0.985767i	$-0.553769\pi$
$317$	−1.34200	+	0.176677i	−0.0753740	+	0.00992317i	0.0927449	+	0.995690i	$0.470436\pi$
$318$	−5.61710	+	8.91159i	−0.314991	+	0.499737i
$319$	−11.9768	+	20.7444i	−0.670570	+	1.16146i
$320$	7.39508	−	20.4512i	0.413397	−	1.14326i
$321$	−33.2275	−	0.0930772i	−1.85458	−	0.00519506i
$322$	−2.09723	+	3.34803i	−0.116874	+	0.186578i
$323$	4.62588	−	11.1679i	0.257391	−	0.621396i
$324$	16.2827	−	7.67295i	0.904594	−	0.426275i
$325$	0.0611195	−	0.0253165i	0.00339030	−	0.00140431i
$326$	−11.4047	−	16.0262i	−0.631645	−	0.887607i
$327$	9.57252	−	9.51904i	0.529361	−	0.526404i
$328$	10.9286	−	1.69380i	0.603429	−	0.0935245i
$329$	3.74962	−	1.00471i	0.206723	−	0.0553914i
$330$	−5.42408	+	31.6530i	−0.298586	+	1.74244i
$331$	−14.0762	+	18.3444i	−0.773697	+	1.00830i	0.225722	+	0.974192i	$0.427526\pi$
$331$	−14.0762	+	18.3444i	−0.773697	+	1.00830i	−0.999418	+	0.0341091i	$0.989141\pi$
$332$	20.0788	−	13.2262i	1.10197	−	0.725880i
$333$	−9.96420	−	4.19286i	−0.546035	−	0.229767i
$334$	−15.7293	−	4.82793i	−0.860668	−	0.264173i
$335$	−1.10430	+	0.637571i	−0.0603346	+	0.0348342i
$336$	−1.63669	−	6.52253i	−0.0892886	−	0.355833i
$337$	−0.221559	−	0.127917i	−0.0120691	−	0.00696810i	0.493953	−	0.869488i	$-0.335551\pi$
$337$	−0.221559	−	0.127917i	−0.0120691	−	0.00696810i	−0.506022	+	0.862520i	$0.668885\pi$
$338$	−12.5228	−	13.4588i	−0.681150	−	0.732064i
$339$	−4.87286	+	3.71743i	−0.264657	+	0.201903i
$340$	5.65279	+	17.0193i	0.306565	+	0.923000i
$341$	20.2105	+	48.7925i	1.09446	+	2.64226i
$342$	15.3170	+	2.66892i	0.828247	+	0.144318i
$343$	−8.96215	−	8.96215i	−0.483911	−	0.483911i
$344$	20.3860	−	21.3402i	1.09914	−	1.15059i
$345$	13.0794	+	3.54391i	0.704171	+	0.190798i
$346$	20.7735	+	9.49474i	1.11679	+	0.510441i
$347$	−2.36313	+	17.9498i	−0.126860	+	0.963594i	0.803077	+	0.595875i	$0.203195\pi$
$347$	−2.36313	+	17.9498i	−0.126860	+	0.963594i	−0.929937	+	0.367719i	$0.880139\pi$
$348$	−16.9049	+	3.19815i	−0.906198	+	0.171439i
$349$	17.3935	−	2.28990i	0.931052	−	0.122575i	0.350283	−	0.936644i	$-0.386085\pi$
$349$	17.3935	−	2.28990i	0.931052	−	0.122575i	0.580769	+	0.814068i	$0.302752\pi$
$350$	2.89797	−	1.53677i	0.154903	−	0.0821440i
$351$	−0.0729697	+	0.123970i	−0.00389484	+	0.00661701i
$352$	−25.9742	−	8.34767i	−1.38443	−	0.444932i
$353$	13.8308	+	23.9557i	0.736141	+	1.27503i	0.954221	+	0.299103i	$0.0966873\pi$
$353$	13.8308	+	23.9557i	0.736141	+	1.27503i	−0.218080	+	0.975931i	$0.569979\pi$
$354$	−21.8364	+	11.5015i	−1.16059	+	0.611296i
$355$	13.2046	+	17.2085i	0.700826	+	0.913334i
$356$	33.4696	+	11.6073i	1.77388	+	0.615185i
$357$	4.39004	+	3.38818i	0.232346	+	0.179321i
$358$	−3.75115	+	2.66942i	−0.198254	+	0.141083i
$359$	−11.2641	+	11.2641i	−0.594496	+	0.594496i	−0.938843	−	0.344347i	$-0.888100\pi$
$359$	−11.2641	+	11.2641i	−0.594496	+	0.594496i	0.344347	+	0.938843i	$0.388100\pi$
$360$	−19.7740	+	11.8763i	−1.04218	+	0.625934i
$361$	−3.93886	−	3.93886i	−0.207309	−	0.207309i
$362$	−32.9043	−	5.54368i	−1.72941	−	0.291369i
$363$	21.0467	+	2.83084i	1.10466	+	0.148581i
$364$	0.0401717	+	0.0356995i	0.00210557	+	0.00187116i
$365$	2.85284	−	2.18906i	0.149324	−	0.114581i
$366$	−19.3718	−	20.9371i	−1.01258	−	1.09440i
$367$	18.6369	−	10.7600i	0.972840	−	0.561669i	0.0727390	−	0.997351i	$-0.476826\pi$
$367$	18.6369	−	10.7600i	0.972840	−	0.561669i	0.900101	+	0.435682i	$0.143493\pi$
$368$	−4.54497	+	10.5771i	−0.236923	+	0.551368i
$369$	−10.1254	−	5.92176i	−0.527105	−	0.308275i
$370$	13.2434	+	4.06491i	0.688489	+	0.211324i
$371$	−0.544849	−	4.13854i	−0.0282872	−	0.214862i
$372$	−17.0955	+	33.8623i	−0.886360	+	1.75568i
$373$	13.2844	+	1.74893i	0.687842	+	0.0905561i	0.466342	−	0.884604i	$-0.345572\pi$
$373$	13.2844	+	1.74893i	0.687842	+	0.0905561i	0.221499	+	0.975160i	$0.428905\pi$
$374$	21.0822	−	7.85578i	1.09013	−	0.406213i
$375$	8.66635	+	8.71504i	0.447528	+	0.450043i
$376$	10.3491	−	4.56667i	0.533713	−	0.235508i
$377$	0.0972239	−	0.0972239i	0.00500729	−	0.00500729i
$378$	−3.01945	+	6.46203i	−0.155304	+	0.332371i
$379$	27.8635	−	11.5414i	1.43125	−	0.592843i	0.473590	−	0.880746i	$-0.342958\pi$
$379$	27.8635	−	11.5414i	1.43125	−	0.592843i	0.957660	+	0.287903i	$0.0929579\pi$
$380$	−19.8722	−	1.43373i	−1.01942	−	0.0735490i
$381$	5.97792	−	14.3184i	0.306258	−	0.733554i
$382$	−28.8109	−	1.03797i	−1.47409	−	0.0531072i
$383$	8.46829	−	14.6675i	0.432709	−	0.749474i	−0.564396	−	0.825504i	$-0.690891\pi$
$383$	8.46829	−	14.6675i	0.432709	−	0.749474i	0.997106	+	0.0760296i	$0.0242244\pi$
$384$	−7.62410	−	18.0520i	−0.389066	−	0.921210i
$385$	−6.36280	−	11.0207i	−0.324278	−	0.561667i
$386$	15.4321	+	29.1011i	0.785474	+	1.48121i
$387$	−31.0574	+	3.91190i	−1.57874	+	0.198853i
$388$	−0.362582	+	0.534996i	−0.0184073	+	0.0271603i
$389$	−20.1319	−	15.4478i	−1.02073	−	0.783232i	−0.0442878	−	0.999019i	$-0.514102\pi$
$389$	−20.1319	−	15.4478i	−1.02073	−	0.783232i	−0.976441	+	0.215786i	$0.930769\pi$
$390$	0.0770989	−	0.167442i	0.00390405	−	0.00847874i
$391$	−2.45707	−	9.16993i	−0.124260	−	0.463743i
$392$	−13.8284	−	10.1172i	−0.698442	−	0.510993i
$393$	1.02768	−	0.272282i	0.0518394	−	0.0137348i
$394$	5.39495	−	32.0215i	0.271793	−	1.61322i
$395$	13.3828	+	32.3089i	0.673360	+	1.62564i
$396$	15.7827	+	24.2547i	0.793113	+	1.21884i
$397$	22.9801	+	9.51866i	1.15334	+	0.477728i	0.875651	−	0.482944i	$-0.160433\pi$
$397$	22.9801	+	9.51866i	1.15334	+	0.477728i	0.277686	+	0.960672i	$0.410433\pi$
$398$	0.585754	+	2.55003i	0.0293612	+	0.127821i
$399$	−5.34414	+	3.06551i	−0.267542	+	0.153468i
$400$	7.65919	−	5.71872i	0.382959	−	0.285936i
$401$	−18.9312	−	10.9299i	−0.945377	−	0.545814i	−0.0537352	−	0.998555i	$-0.517113\pi$
$401$	−18.9312	−	10.9299i	−0.945377	−	0.545814i	−0.891642	+	0.452742i	$0.850446\pi$
$402$	−0.340226	+	1.09748i	−0.0169689	+	0.0547373i
$403$	−0.0395689	−	0.300555i	−0.00197107	−	0.0149717i
$404$	−2.22123	+	10.7955i	−0.110510	+	0.537097i
$405$	24.2189	+	3.46497i	1.20345	+	0.172176i
$406$	4.34230	−	5.25579i	0.215505	−	0.260840i
$407$	4.49810	−	16.7872i	0.222963	−	0.832108i
$408$	14.1538	+	7.79736i	0.700720	+	0.386027i
$409$	−5.85579	−	21.8541i	−0.289550	−	1.08062i	−0.945450	−	0.325767i	$-0.894377\pi$
$409$	−5.85579	−	21.8541i	−0.289550	−	1.08062i	0.655900	−	0.754848i	$-0.272289\pi$
$410$	13.6711	+	6.24853i	0.675168	+	0.308593i
$411$	18.5649	+	14.3282i	0.915740	+	0.706756i
$412$	11.3051	−	9.78358i	0.556961	−	0.482003i
$413$	3.74255	−	9.03533i	0.184159	−	0.444599i
$414$	10.8195	−	5.66007i	0.531749	−	0.278177i
$415$	32.6798			1.60419
$416$	0.131612	+	0.0848721i	0.00645283	+	0.00416120i
$417$	7.14195	−	12.2906i	0.349743	−	0.601872i
$418$	−0.899922	+	24.9791i	−0.0440166	+	1.22177i
$419$	−10.9615	−	14.2853i	−0.535502	−	0.697880i	0.444745	−	0.895657i	$-0.353294\pi$
$419$	−10.9615	−	14.2853i	−0.535502	−	0.697880i	−0.980247	+	0.197777i	$0.936628\pi$
$420$	3.01904	−	8.62725i	0.147314	−	0.420966i
$421$	−5.18506	−	3.97864i	−0.252704	−	0.193907i	0.474639	−	0.880181i	$-0.342579\pi$
$421$	−5.18506	−	3.97864i	−0.252704	−	0.193907i	−0.727343	+	0.686274i	$0.759245\pi$
$422$	0.880297	+	9.24934i	0.0428522	+	0.450251i
$423$	−11.5716	−	3.17020i	−0.562632	−	0.154140i
$424$	−3.41602	−	11.6743i	−0.165897	−	0.566952i
$425$	−2.04011	+	7.61379i	−0.0989598	+	0.369323i
$426$	19.2644	+	3.30117i	0.933365	+	0.159942i
$427$	11.2063	+	1.47533i	0.542309	+	0.0713964i
$428$	25.4868	−	28.6796i	1.23195	−	1.38628i
$429$	−0.213409	−	0.0890979i	−0.0103035	−	0.00430169i
$430$	39.0952	−	8.98035i	1.88534	−	0.433071i
$431$		−	12.5320i		−	0.603643i	−0.953364	−	0.301822i	$-0.902405\pi$
$431$		−	12.5320i		−	0.603643i	0.953364	−	0.301822i	$-0.0975947\pi$
$432$	−5.81081	+	19.9558i	−0.279573	+	0.960125i
$433$		−	11.7403i		−	0.564202i	−0.959385	−	0.282101i	$-0.908969\pi$
$433$		−	11.7403i		−	0.564202i	0.959385	−	0.282101i	$-0.0910314\pi$
$434$	−3.36512	−	14.6498i	−0.161531	−	0.703211i
$435$	−21.5794	−	9.00940i	−1.03465	−	0.431967i
$436$	0.917256	+	15.5612i	0.0439286	+	0.745248i
$437$	10.4568	+	1.37667i	0.500217	+	0.0658549i
$438$	0.547269	−	3.19367i	0.0261495	−	0.152599i
$439$	−7.24806	+	27.0501i	−0.345931	+	1.29103i	0.545590	+	0.838052i	$0.316306\pi$
$439$	−7.24806	+	27.0501i	−0.345931	+	1.29103i	−0.891521	+	0.452979i	$0.850361\pi$
$440$	−23.2411	−	28.8957i	−1.10798	−	1.37755i
$441$	4.60526	+	17.5804i	0.219298	+	0.837164i
$442$	−0.128561	+	0.0122357i	−0.00611503	+	0.000581993i
$443$	−12.8316	−	9.84601i	−0.609646	−	0.467798i	0.257210	−	0.966355i	$-0.417197\pi$
$443$	−12.8316	−	9.84601i	−0.609646	−	0.467798i	−0.866857	+	0.498557i	$0.833863\pi$
$444$	11.2468	−	5.41582i	0.533747	−	0.257023i
$445$	29.3117	+	38.1997i	1.38951	+	1.81084i
$446$	−35.3275	−	1.27275i	−1.67281	−	0.0602663i
$447$	5.50435	−	9.47243i	0.260347	−	0.448030i
$448$	6.89520	+	3.57105i	0.325768	+	0.168716i
$449$	−35.0163			−1.65252			−0.826262	−	0.563286i	$-0.809537\pi$
$449$	−35.0163			−1.65252			−0.826262	+	0.563286i	$0.809537\pi$
$450$	−10.1297	−	0.421777i	−0.477516	−	0.0198828i
$451$	7.21645	−	17.4221i	0.339809	−	0.820373i
$452$	0.509273	−	7.05876i	0.0239542	−	0.332016i
$453$	3.57198	+	2.75681i	0.167826	+	0.129526i
$454$	9.26740	−	20.2761i	0.434941	−	0.951603i
$455$	0.0189057	+	0.0705571i	0.000886314	+	0.00330777i
$456$	−14.0209	+	11.2127i	−0.656591	+	0.525081i
$457$	−5.18483	+	19.3501i	−0.242536	+	0.905158i	0.732069	+	0.681230i	$0.238555\pi$
$457$	−5.18483	+	19.3501i	−0.242536	+	0.905158i	−0.974606	+	0.223928i	$0.928112\pi$
$458$	10.8169	+	8.93683i	0.505439	+	0.417591i
$459$	−6.42580	−	15.8896i	−0.299931	−	0.741665i
$460$	−13.0672	+	8.60751i	−0.609260	+	0.401327i
$461$	4.66786	+	35.4559i	0.217404	+	1.65135i	0.657543	+	0.753417i	$0.271596\pi$
$461$	4.66786	+	35.4559i	0.217404	+	1.65135i	−0.440139	+	0.897930i	$0.645071\pi$
$462$	−10.9526	−	3.39537i	−0.509560	−	0.157967i
$463$	9.76811	+	5.63962i	0.453963	+	0.262095i	0.709502	−	0.704703i	$-0.248920\pi$
$463$	9.76811	+	5.63962i	0.453963	+	0.262095i	−0.255540	+	0.966799i	$0.582253\pi$
$464$	10.1585	−	17.0727i	0.471596	−	0.792580i
$465$	−44.7228	+	25.6540i	−2.07397	+	1.18967i
$466$	−9.97047	+	2.29026i	−0.461873	+	0.106094i
$467$	8.71923	+	3.61163i	0.403478	+	0.167126i	0.575188	−	0.818022i	$-0.304929\pi$
$467$	8.71923	+	3.61163i	0.403478	+	0.167126i	−0.171710	+	0.985148i	$0.554929\pi$
$468$	−0.0514736	−	0.157928i	−0.00237937	−	0.00730021i
$469$	−0.174237	−	0.420646i	−0.00804553	−	0.0194236i
$470$	15.1613	+	2.55436i	0.699341	+	0.117824i
$471$	−16.7788	+	4.44554i	−0.773128	+	0.204840i
$472$	6.74460	−	27.6887i	0.310446	−	1.27447i
$473$	−13.0248	−	48.6091i	−0.598879	−	2.23505i
$474$	28.6231	+	13.1795i	1.31470	+	0.605356i
$475$	−6.94757	−	5.33105i	−0.318776	−	0.244606i
$476$	−6.28840	+	1.20793i	−0.288228	+	0.0553652i
$477$	−5.00394	+	11.8917i	−0.229115	+	0.544484i
$478$	20.7508	−	11.0040i	0.949118	−	0.503311i
$479$	−2.02686	−	3.51062i	−0.0926096	−	0.160405i	0.815999	−	0.578054i	$-0.196188\pi$
$479$	−2.02686	−	3.51062i	−0.0926096	−	0.160405i	−0.908608	+	0.417649i	$0.862854\pi$
$480$	4.84328	−	26.1906i	0.221065	−	1.19543i
$481$	−0.0498795	+	0.0863938i	−0.00227431	+	0.00393922i
$482$	−1.03332	+	28.6818i	−0.0470664	+	1.30642i
$483$	−1.86415	+	4.46503i	−0.0848216	+	0.203166i
$484$	−18.5421	+	16.0466i	−0.842821	+	0.729389i
$485$	−0.811564	+	0.336161i	−0.0368512	+	0.0152643i
$486$	18.1389	−	12.5292i	0.822797	−	0.568335i
$487$	12.3011	−	12.3011i	0.557416	−	0.557416i	−0.371155	−	0.928571i	$-0.621038\pi$
$487$	12.3011	−	12.3011i	0.557416	−	0.557416i	0.928571	+	0.371155i	$0.121038\pi$
$488$	32.9283	−	0.753047i	1.49059	−	0.0340888i
$489$	−16.9868	−	17.0823i	−0.768171	−	0.772486i
$490$	−8.13180	−	21.8230i	−0.367357	−	0.985861i
$491$	−9.34607	−	1.23043i	−0.421782	−	0.0555287i	−0.0833520	−	0.996520i	$-0.526563\pi$
$491$	−9.34607	−	1.23043i	−0.421782	−	0.0555287i	−0.338430	+	0.940991i	$0.609896\pi$
$492$	12.8660	−	4.23332i	0.580042	−	0.190853i
$493$	2.13835	+	16.2424i	0.0963064	+	0.731520i
$494$	0.0420997	−	0.137160i	0.00189415	−	0.00617110i
$495$	−0.220352	+	39.3313i	−0.00990409	+	1.76781i
$496$	−16.2286	−	40.6839i	−0.728684	−	1.82676i
$497$	−6.70735	+	3.87249i	−0.300866	+	0.173705i
$498$	21.6146	−	19.9986i	0.968572	−	0.896160i
$499$	22.4072	−	17.1936i	1.00308	−	0.769692i	0.0298594	−	0.999554i	$-0.490494\pi$
$499$	22.4072	−	17.1936i	1.00308	−	0.769692i	0.973223	+	0.229862i	$0.0738274\pi$
$500$	−14.1673	+	0.835091i	−0.633581	+	0.0373464i
$501$	−19.9715	−	2.68624i	−0.892263	−	0.120012i
$502$	−3.47924	+	20.6509i	−0.155286	+	0.921695i
$503$	−9.24415	−	9.24415i	−0.412176	−	0.412176i	0.470320	−	0.882496i	$-0.344139\pi$
$503$	−9.24415	−	9.24415i	−0.412176	−	0.412176i	−0.882496	+	0.470320i	$0.844139\pi$
$504$	−3.28270	−	7.55362i	−0.146223	−	0.336465i
$505$	−10.5929	+	10.5929i	−0.471377	+	0.471377i
$506$	11.3817	+	15.9939i	0.505977	+	0.711014i
$507$	−17.8242	−	13.7564i	−0.791598	−	0.610945i
$508$	7.81849	+	16.1206i	0.346890	+	0.715236i
$509$	−9.53601	−	12.4276i	−0.422676	−	0.550842i	0.532673	−	0.846321i	$-0.321188\pi$
$509$	−9.53601	−	12.4276i	−0.422676	−	0.550842i	−0.955349	+	0.295479i	$0.904521\pi$
$510$	10.2356	+	19.4331i	0.453241	+	0.860514i
$511$	0.641983	+	1.11195i	0.0283997	+	0.0491897i
$512$	21.4494	+	7.20590i	0.947937	+	0.318459i
$513$	19.0414	+	0.160020i	0.840697	+	0.00706506i
$514$	0.288823	+	0.544647i	0.0127394	+	0.0240234i
$515$	20.1471	−	2.65241i	0.887786	−	0.116879i
$516$	20.3621	−	29.8642i	0.896393	−	1.31470i
$517$	2.51767	−	19.1236i	0.110727	−	0.841053i
$518$	−2.05622	+	4.49879i	−0.0903452	+	0.197665i
$519$	27.0002	+	7.31580i	1.18518	+	0.321128i
$520$	0.0859316	+	0.194740i	0.00376835	+	0.00853992i
$521$	10.8201	+	10.8201i	0.474037	+	0.474037i	0.903218	−	0.429182i	$-0.141198\pi$
$521$	10.8201	+	10.8201i	0.474037	+	0.474037i	−0.429182	+	0.903218i	$0.641198\pi$
$522$	−19.7861	+	7.24683i	−0.866013	+	0.317185i
$523$	0.0452919	+	0.109344i	0.00198048	+	0.00478130i	0.924867	−	0.380292i	$-0.124176\pi$
$523$	0.0452919	+	0.109344i	0.00198048	+	0.00478130i	−0.922886	+	0.385073i	$0.874176\pi$
$524$	−0.550179	+	1.09741i	−0.0240347	+	0.0479406i
$525$	3.19409	−	2.43673i	0.139402	−	0.106348i
$526$	11.4206	−	10.6264i	0.497964	−	0.463331i
$527$	31.2809	+	18.0600i	1.36262	+	0.786708i
$528$	−33.0547	−	4.88917i	−1.43852	−	0.212774i
$529$	−12.7451	+	7.35840i	−0.554136	+	0.319930i
$530$	4.85124	−	15.8052i	0.210724	−	0.686534i
$531$	−24.0834	+	18.2664i	−1.04513	+	0.792693i
$532$	1.43371	−	6.96808i	0.0621594	−	0.302104i
$533$	−0.0658946	+	0.0858755i	−0.00285421	+	0.00371968i
$534$	42.7634	+	7.32797i	1.85055	+	0.317112i
$535$	50.3726	−	13.4973i	2.17780	−	0.583539i
$536$	−0.689475	−	1.13354i	−0.0297808	−	0.0489614i
$537$	−3.99834	+	3.97600i	−0.172541	+	0.171577i
$538$	8.64149	−	6.14952i	0.372561	−	0.265125i
$539$	−26.9927	+	11.1808i	−1.16266	+	0.481589i
$540$	−21.5163	+	18.3066i	−0.925915	+	0.787789i
$541$	−11.7600	+	28.3912i	−0.505602	+	1.22063i	0.440789	+	0.897611i	$0.354699\pi$
$541$	−11.7600	+	28.3912i	−0.505602	+	1.22063i	−0.946392	+	0.323022i	$0.895301\pi$
$542$	−1.58138	−	0.990589i	−0.0679262	−	0.0425494i
$543$	−40.8672	−	0.114478i	−1.75378	−	0.00491271i
$544$	−17.5691	+	6.28493i	−0.753269	+	0.269464i
$545$	−10.5937	+	18.3489i	−0.453786	+	0.785981i
$546$	0.0556822	+	0.0350973i	0.00238298	+	0.00150203i
$547$	−2.15904	+	0.284243i	−0.0923138	+	0.0121533i	−0.176542	−	0.984293i	$-0.556491\pi$
$547$	−2.15904	+	0.284243i	−0.0923138	+	0.0121533i	0.0842278	+	0.996447i	$0.473158\pi$
$548$	−26.5928	+	5.10816i	−1.13599	+	0.218210i
$549$	−27.5961	−	21.4219i	−1.17777	−	0.914265i
$550$	−1.54426	−	16.2257i	−0.0658476	−	0.691865i
$551$	−17.5806	−	4.71070i	−0.748958	−	0.200683i
$552$	−3.37526	+	13.6896i	−0.143660	+	0.582667i
$553$	−12.0613	+	3.23181i	−0.512898	+	0.137431i
$554$	−0.0846293	−	0.227116i	−0.00359555	−	0.00964923i
$555$	16.8152	+	2.26169i	0.713764	+	0.0960036i
$556$	5.17384	+	15.5773i	0.219420	+	0.660625i
$557$	−9.49325	−	3.93223i	−0.402242	−	0.166614i	0.172385	−	0.985030i	$-0.444853\pi$
$557$	−9.49325	−	3.93223i	−0.402242	−	0.166614i	−0.574627	+	0.818416i	$0.694853\pi$
$558$	−13.8807	+	44.3361i	−0.587619	+	1.87690i
$559$			0.288863i			0.0122176i
$560$	5.15651	+	9.20882i	0.217902	+	0.389144i
$561$	23.9015	−	13.7104i	1.00912	−	0.578855i
$562$	−27.3727	+	25.4690i	−1.15465	+	1.07434i
$563$	−16.6002	+	12.7378i	−0.699614	+	0.536833i	−0.896198	−	0.443654i	$-0.853682\pi$
$563$	−16.6002	+	12.7378i	−0.699614	+	0.536833i	0.196584	+	0.980487i	$0.437015\pi$
$564$	11.5909	−	7.58862i	0.488067	−	0.319539i
$565$	5.85578	−	7.63140i	0.246354	−	0.321055i
$566$	1.31653	+	1.08771i	0.0553378	+	0.0457197i
$567$	−2.35537	+	8.41217i	−0.0989161	+	0.353278i
$568$	−17.5863	+	14.1448i	−0.737905	+	0.593505i
$569$	37.1625	+	9.95767i	1.55793	+	0.417447i	0.932009	−	0.362436i	$-0.118055\pi$
$569$	37.1625	+	9.95767i	1.55793	+	0.417447i	0.625925	+	0.779883i	$0.284721\pi$
$570$	−24.2983	+	2.24390i	−1.01774	+	0.0939867i
$571$	−1.13501	+	8.62127i	−0.0474988	+	0.360789i	0.951146	+	0.308742i	$0.0999079\pi$
$571$	−1.13501	+	8.62127i	−0.0474988	+	0.360789i	−0.998645	+	0.0520470i	$0.983425\pi$
$572$	0.240270	−	0.116531i	0.0100462	−	0.00487240i
$573$	−35.0196	+	4.51066i	−1.46296	+	0.188435i
$574$	−2.84918	+	4.54844i	−0.118922	+	0.189848i
$575$	−6.87755			−0.286814
$576$	−12.8242	−	20.2865i	−0.534340	−	0.845269i
$577$	27.4595			1.14315			0.571576	−	0.820549i	$-0.306332\pi$
$577$	27.4595			1.14315			0.571576	+	0.820549i	$0.306332\pi$
$578$	−4.59423	+	7.33427i	−0.191095	+	0.305065i
$579$	24.4693	+	32.0747i	1.01691	+	1.33298i
$580$	24.2956	−	11.7833i	1.00882	−	0.489277i
$581$	−1.52307	+	11.5689i	−0.0631877	+	0.479958i
$582$	−0.331056	+	0.718980i	−0.0137227	+	0.0298027i
$583$	−20.0345	−	5.36823i	−0.829745	−	0.222330i
$584$	2.34494	+	2.91547i	0.0970343	+	0.120643i
$585$	0.0596540	−	0.217745i	0.00246639	−	0.00900264i
$586$	−22.8637	−	18.8898i	−0.944490	−	0.780332i
$587$	7.67650	−	10.0042i	0.316843	−	0.412918i	−0.607597	−	0.794246i	$-0.707866\pi$
$587$	7.67650	−	10.0042i	0.316843	−	0.412918i	0.924440	+	0.381328i	$0.124533\pi$
$588$	−18.7331	−	9.45749i	−0.772541	−	0.390020i
$589$	−31.8364	+	24.4289i	−1.31180	+	1.00658i
$590$	28.3580	−	26.3857i	1.16748	−	1.08628i
$591$	0.111406	−	39.7708i	0.00458265	−	1.63595i
$592$	−3.91330	+	13.8725i	−0.160836	+	0.570157i
$593$			4.33633i			0.178072i	0.996028	+	0.0890358i	$0.0283786\pi$
$593$			4.33633i			0.178072i	−0.996028	+	0.0890358i	$0.971621\pi$
$594$	23.9233	+	26.1487i	0.981584	+	1.07289i
$595$	−8.04091	−	3.33065i	−0.329645	−	0.136543i
$596$	3.98752	+	12.0055i	0.163335	+	0.491766i
$597$	1.21800	+	2.96397i	0.0498494	+	0.121307i
$598$	−0.0393445	−	0.105587i	−0.00160892	−	0.00431778i
$599$	10.0831	−	2.70175i	0.411982	−	0.110390i	−0.0468740	−	0.998901i	$-0.514926\pi$
$599$	10.0831	−	2.70175i	0.411982	−	0.110390i	0.458856	+	0.888510i	$0.348259\pi$
$600$	8.11025	−	8.44241i	0.331099	−	0.344660i
$601$	−18.3519	−	4.91736i	−0.748588	−	0.200583i	−0.135696	−	0.990751i	$-0.543327\pi$
$601$	−18.3519	−	4.91736i	−0.748588	−	0.200583i	−0.612892	+	0.790167i	$0.709994\pi$
$602$	1.35704	+	14.2585i	0.0553088	+	0.581133i
$603$	−0.191495	+	1.39415i	−0.00779828	+	0.0567741i
$604$	−5.11659	+	0.982835i	−0.208191	+	0.0399910i
$605$	−33.0443	+	4.35036i	−1.34344	+	0.176867i
$606$	−0.523790	+	13.4886i	−0.0212775	+	0.547936i
$607$	−15.9239	+	27.5811i	−0.646332	+	1.11948i	0.337660	+	0.941268i	$0.390365\pi$
$607$	−15.9239	+	27.5811i	−0.646332	+	1.11948i	−0.983992	+	0.178212i	$0.942969\pi$
$608$	1.01864	−	20.7053i	0.0413114	−	0.839711i
$609$	4.19512	−	7.21937i	0.169995	−	0.292544i
$610$	37.9389	+	23.7652i	1.53610	+	0.962224i
$611$	−0.0423700	+	0.102290i	−0.00171411	+	0.00413822i
$612$	18.6621	+	6.58940i	0.754372	+	0.266361i
$613$	−31.4939	+	13.0452i	−1.27203	+	0.526890i	−0.913579	−	0.406661i	$-0.866693\pi$
$613$	−31.4939	+	13.0452i	−1.27203	+	0.526890i	−0.358446	+	0.933551i	$0.616693\pi$
$614$	2.93293	−	2.08715i	0.118363	−	0.0842306i
$615$	17.7689	+	4.81456i	0.716512	+	0.194142i
$616$	11.3124	−	6.88080i	0.455791	−	0.277235i
$617$	4.12801	−	1.10610i	0.166187	−	0.0445297i	−0.174766	−	0.984610i	$-0.555917\pi$
$617$	4.12801	−	1.10610i	0.166187	−	0.0445297i	0.340953	+	0.940080i	$0.389250\pi$
$618$	11.7022	−	14.0835i	0.470731	−	0.566520i
$619$	−10.6552	+	13.8861i	−0.428267	+	0.558128i	−0.956786	−	0.290793i	$-0.906081\pi$
$619$	−10.6552	+	13.8861i	−0.428267	+	0.558128i	0.528519	+	0.848921i	$0.322748\pi$
$620$	11.9981	−	58.3128i	0.481857	−	2.34190i
$621$	11.9405	−	9.00389i	0.479157	−	0.361314i
$622$	3.11345	−	10.1435i	0.124838	−	0.406718i
$623$	−14.8891	+	8.59620i	−0.596517	+	0.344400i
$624$	0.176008	+	0.0762155i	0.00704596	+	0.00305106i
$625$	−27.0527	−	15.6189i	−1.08211	−	0.624756i
$626$	−14.7076	+	13.6847i	−0.587833	+	0.546950i
$627$	3.91074	+	30.3620i	0.156180	+	1.21254i
$628$	8.98277	−	17.9174i	0.358452	−	0.714982i
$629$	−4.54867	−	10.9815i	−0.181367	−	0.437859i
$630$	1.92163	−	11.0283i	0.0765596	−	0.439378i
$631$	23.4841	+	23.4841i	0.934889	+	0.934889i	0.998006	−	0.0631174i	$-0.0201043\pi$
$631$	23.4841	+	23.4841i	0.934889	+	0.934889i	−0.0631174	+	0.998006i	$0.520104\pi$
$632$	−33.2895	+	14.6894i	−1.32419	+	0.584314i
$633$	2.91437	+	10.9997i	0.115836	+	0.437201i
$634$	0.795748	−	1.74101i	0.0316032	−	0.0691444i
$635$	−3.17859	+	24.1438i	−0.126138	+	0.958116i
$636$	−6.46347	−	13.4224i	−0.256293	−	0.532231i
$637$	0.166272	−	0.0218901i	0.00658793	−	0.000867318i
$638$	−15.8705	−	29.9278i	−0.628318	−	1.18485i
$639$	23.9375	+	0.134109i	0.946955	+	0.00530528i
$640$	18.9588	+	24.2165i	0.749411	+	0.957242i
$641$	−20.1075	−	34.8272i	−0.794197	−	1.37559i	−0.923348	−	0.383965i	$-0.874558\pi$
$641$	−20.1075	−	34.8272i	−0.794197	−	1.37559i	0.129150	−	0.991625i	$-0.458775\pi$
$642$	25.0569	−	39.7530i	0.988915	−	1.56893i
$643$	17.3566	+	22.6195i	0.684477	+	0.892028i	0.998349	−	0.0574375i	$-0.0182930\pi$
$643$	17.3566	+	22.6195i	0.684477	+	0.892028i	−0.313872	+	0.949465i	$0.601626\pi$
$644$	−2.43811	−	5.02703i	−0.0960749	−	0.198093i
$645$	45.4414	−	18.6735i	1.78925	−	0.735268i
$646$	9.91174	+	13.9283i	0.389972	+	0.548001i
$647$	21.4624	−	21.4624i	0.843774	−	0.843774i	−0.145573	−	0.989347i	$-0.546503\pi$
$647$	21.4624	−	21.4624i	0.843774	−	0.843774i	0.989347	+	0.145573i	$0.0465026\pi$
$648$	−3.02815	+	25.2751i	−0.118957	+	0.992899i
$649$	−34.3613	−	34.3613i	−1.34880	−	1.34880i
$650$	−0.0155434	+	0.0922575i	−0.000609663	+	0.00361864i
$651$	−6.99733	−	17.0278i	−0.274247	−	0.667372i
$652$	27.7692	−	1.63685i	1.08753	−	0.0641041i
$653$	12.5369	−	9.61989i	0.490606	−	0.376455i	−0.333628	−	0.942705i	$-0.608273\pi$
$653$	12.5369	−	9.61989i	0.490606	−	0.376455i	0.824234	+	0.566250i	$0.191606\pi$
$654$	4.22199	+	18.6189i	0.165093	+	0.728059i
$655$	−1.44501	+	0.834275i	−0.0564611	+	0.0325978i
$656$	−6.17454	+	14.3694i	−0.241075	+	0.561031i
$657$	0.0222327	−	3.96838i	0.000867381	−	0.154821i
$658$	−1.61087	+	5.24817i	−0.0627982	+	0.204595i
$659$	−0.865492	−	6.57407i	−0.0337148	−	0.256089i	0.966284	−	0.257478i	$-0.0828914\pi$
$659$	−0.865492	−	6.57407i	−0.0337148	−	0.256089i	−0.999999	+	0.00138843i	$0.999558\pi$
$660$	−33.8638	−	30.2640i	−1.31814	−	1.17802i
$661$	−47.7962	−	6.29248i	−1.85906	−	0.244749i	−0.884123	−	0.467253i	$-0.845244\pi$
$661$	−47.7962	−	6.29248i	−1.85906	−	0.244749i	−0.974932	+	0.222504i	$0.928577\pi$
$662$	−11.4181	−	30.6422i	−0.443775	−	1.19094i
$663$	−0.152891	+	0.0405083i	−0.00593779	+	0.00157321i
$664$	0.777414	+	33.9938i	0.0301695	+	1.31921i
$665$	6.83728	−	6.83728i	0.265138	−	0.265138i
$666$	12.5057	−	8.79426i	0.484585	−	0.340771i
$667$	−13.2060	+	5.47012i	−0.511340	+	0.211804i
$668$	17.5949	−	15.2269i	0.680767	−	0.589146i
$669$	−42.9405	+	5.53090i	−1.66018	+	0.213837i
$670$	0.0649262	−	1.80215i	0.00250832	−	0.0696233i
$671$	28.0814	−	48.6384i	1.08407	−	1.87767i
$672$	9.04594	+	2.93519i	0.348955	+	0.113227i
$673$	1.41006	+	2.44229i	0.0543537	+	0.0941434i	0.891922	−	0.452189i	$-0.149357\pi$
$673$	1.41006	+	2.44229i	0.0543537	+	0.0941434i	−0.837568	+	0.546333i	$0.816023\pi$
$674$	0.319642	−	0.169504i	0.0123122	−	0.00652905i
$675$	−12.3239	+	1.51723i	−0.474349	+	0.0583983i
$676$	25.5317	−	4.90434i	0.981989	−	0.188628i
$677$	16.9590	+	13.0131i	0.651789	+	0.500135i	0.880923	−	0.473260i	$-0.156923\pi$
$677$	16.9590	+	13.0131i	0.651789	+	0.500135i	−0.229134	+	0.973395i	$0.573589\pi$
$678$	−0.797050	−	8.63092i	−0.0306105	−	0.331469i
$679$	−0.0811795	−	0.302966i	−0.00311538	−	0.0116268i
$680$	−24.6413	−	6.00230i	−0.944950	−	0.230178i
$681$	7.14063	−	26.3537i	0.273629	−	1.00988i
$682$	−73.6503	−	12.4085i	−2.82022	−	0.475146i
$683$	−4.05765	−	9.79602i	−0.155262	−	0.374834i	0.827039	−	0.562144i	$-0.190023\pi$
$683$	−4.05765	−	9.79602i	−0.155262	−	0.374834i	−0.982301	+	0.187309i	$0.940023\pi$
$684$	−14.6978	+	16.3536i	−0.561984	+	0.625296i
$685$	−34.0039	−	14.0849i	−1.29922	−	0.538156i
$686$	17.4694	−	4.01279i	0.666983	−	0.153209i
$687$	14.8581	+	8.63391i	0.566872	+	0.329404i
$688$	10.2714	+	40.4534i	0.391595	+	1.54227i
$689$	0.103106	+	0.0595284i	0.00392803	+	0.00226785i
$690$	−14.0666	+	13.0150i	−0.535507	+	0.495472i
$691$	−6.41683	−	48.7407i	−0.244108	−	1.85418i	−0.473429	−	0.880832i	$-0.656984\pi$
$691$	−6.41683	−	48.7407i	−0.244108	−	1.85418i	0.229321	−	0.973351i	$-0.426349\pi$
$692$	−26.9749	+	17.7687i	−1.02543	+	0.675465i
$693$	−13.9133	−	1.91107i	−0.528521	−	0.0725957i
$694$	−19.7386	−	16.3079i	−0.749265	−	0.619038i
$695$	−5.77423	+	21.5497i	−0.219029	+	0.817427i
$696$	8.85828	−	22.6614i	0.335772	−	0.858978i
$697$	−3.33804	−	12.4577i	−0.126437	−	0.471871i
$698$	−10.3136	+	22.5651i	−0.390377	+	0.854101i
$699$	−11.5889	+	4.76231i	−0.438334	+	0.180127i
$700$	−0.333822	+	4.62692i	−0.0126173	+	0.174881i
$701$	11.8123	−	28.5175i	0.446146	−	1.07709i	−0.527608	−	0.849488i	$-0.676911\pi$
$701$	11.8123	−	28.5175i	0.446146	−	1.07709i	0.973754	−	0.227603i	$-0.0730889\pi$
$702$	−0.0937950	−	0.180523i	−0.00354007	−	0.00681340i
$703$	13.2055			0.498053
$704$	29.5046	−	24.8629i	1.11200	−	0.937057i
$705$	18.8304	+	0.0527479i	0.709194	+	0.00198660i
$706$	−39.0941	−	1.40845i	−1.47133	−	0.0530075i
$707$	−3.25626	−	4.24364i	−0.122464	−	0.159599i
$708$	2.60916	−	34.8055i	0.0980582	−	1.30807i
$709$	2.61601	+	2.00733i	0.0982463	+	0.0753870i	0.656717	−	0.754138i	$-0.271945\pi$
$709$	2.61601	+	2.00733i	0.0982463	+	0.0753870i	−0.558470	+	0.829525i	$0.688611\pi$
$710$	−30.5375	+	2.90638i	−1.14605	+	0.109075i
$711$	37.2221	+	10.1975i	1.39594	+	0.382435i
$712$	−39.0383	+	31.3989i	−1.46302	+	1.17672i
$713$	−8.15683	+	30.4417i	−0.305476	+	1.14005i
$714$	−7.35651	+	2.71778i	−0.275310	+	0.101710i
$715$	0.359851	+	0.0473752i	0.0134576	+	0.00177173i
$716$	−0.383128	−	6.49977i	−0.0143182	−	0.242908i
$717$	22.8711	−	17.4481i	0.854138	−	0.651610i
$718$	−5.04348	−	21.9564i	−0.188221	−	0.819405i
$719$		−	4.64530i		−	0.173241i	−0.996241	−	0.0866203i	$-0.972393\pi$
$719$		−	4.64530i		−	0.173241i	0.996241	−	0.0866203i	$-0.0276067\pi$
$720$	0.611554	−	32.6150i	0.0227913	−	1.21549i
$721$			7.25582i			0.270221i
$722$	7.67778	−	1.76362i	0.285737	−	0.0656352i
$723$	4.49044	+	34.8627i	0.167001	+	1.29656i
$724$	31.3468	−	35.2737i	1.16499	−	1.31094i
$725$	11.7669	+	1.54914i	0.437011	+	0.0575335i
$726$	−19.1934	+	23.0990i	−0.712333	+	0.857285i
$727$	1.40742	−	5.25258i	0.0521985	−	0.194807i	−0.934903	−	0.354903i	$-0.884514\pi$
$727$	1.40742	−	5.25258i	0.0521985	−	0.194807i	0.987101	+	0.160096i	$0.0511804\pi$
$728$	−0.0729442	+	0.0213443i	−0.00270349	+	0.000791073i
$729$	19.4101	−	18.7683i	0.718891	−	0.695123i
$730$	0.481821	+	5.06253i	0.0178330	+	0.187373i
$731$	−27.3056	−	20.9523i	−1.00993	−	0.774949i
$732$	39.6362	−	7.49857i	1.46500	−	0.277155i
$733$	4.07078	+	5.30514i	0.150358	+	0.195950i	0.862459	−	0.506127i	$-0.168923\pi$
$733$	4.07078	+	5.30514i	0.150358	+	0.195950i	−0.712102	+	0.702076i	$0.752256\pi$
$734$	−1.09573	+	30.4142i	−0.0404443	+	1.12261i
$735$	−14.1922	−	24.7414i	−0.523486	−	0.912598i
$736$	−9.26443	−	13.3878i	−0.341492	−	0.493480i
$737$	−2.26234			−0.0833344
$738$	14.6987	−	7.68945i	0.541068	−	0.283052i
$739$	−1.37536	+	3.32042i	−0.0505936	+	0.122144i	−0.947156	−	0.320775i	$-0.896057\pi$
$739$	−1.37536	+	3.32042i	−0.0505936	+	0.122144i	0.896562	+	0.442918i	$0.146057\pi$
$740$	−14.8141	+	12.8204i	−0.544578	+	0.471286i
$741$	0.0234241	−	0.174152i	0.000860504	−	0.00639764i
$742$	5.36905	+	2.45399i	0.197104	+	0.0900886i
$743$	2.02693	+	7.56460i	0.0743608	+	0.277518i	0.993088	−	0.117375i	$-0.0374481\pi$
$743$	2.02693	+	7.56460i	0.0743608	+	0.277518i	−0.918727	+	0.394894i	$0.870781\pi$
$744$	−27.7493	−	45.9107i	−1.01734	−	1.68317i
$745$	−4.45023	+	16.6085i	−0.163044	+	0.608488i
$746$	−12.0693	+	14.6083i	−0.441888	+	0.534848i
$747$	22.1151	−	28.4890i	0.809149	−	1.04236i
$748$	−6.41225	+	31.1645i	−0.234455	+	1.13949i
$749$	2.43047	+	18.4613i	0.0888076	+	0.674561i
$750$	−16.9511	+	3.84379i	−0.618967	+	0.140356i
$751$	−37.0327	−	21.3809i	−1.35134	−	0.780198i	−0.362906	−	0.931826i	$-0.618215\pi$
$751$	−37.0327	−	21.3809i	−1.35134	−	0.780198i	−0.988438	+	0.151628i	$0.951549\pi$
$752$	−2.29639	+	15.8317i	−0.0837409	+	0.577323i
$753$	−0.0718467	+	25.6484i	−0.00261824	+	0.934681i
$754$	0.0435319	+	0.189512i	0.00158534	+	0.00690163i
$755$	−6.54253	−	2.71000i	−0.238107	−	0.0986271i
$756$	−5.47786	−	8.47011i	−0.199228	−	0.308055i
$757$	−5.38622	−	13.0035i	−0.195765	−	0.472620i	0.795264	−	0.606263i	$-0.207332\pi$
$757$	−5.38622	−	13.0035i	−0.195765	−	0.472620i	−0.991029	+	0.133644i	$0.957332\pi$
$758$	−7.08601	+	42.0588i	−0.257375	+	1.52764i
$759$	16.9526	+	17.0478i	0.615341	+	0.618798i
$760$	16.6373	−	22.7403i	0.603497	−	0.824878i
$761$	8.17391	+	30.5054i	0.296304	+	1.10582i	0.940176	+	0.340688i	$0.110660\pi$
$761$	8.17391	+	30.5054i	0.296304	+	1.10582i	−0.643872	+	0.765133i	$0.722673\pi$
$762$	12.6726	+	17.9139i	0.459080	+	0.648953i
$763$	−6.00190	−	4.60542i	−0.217284	−	0.166728i
$764$	22.8736	−	33.7504i	0.827538	−	1.22105i
$765$	16.2560	+	21.4328i	0.587737	+	0.774904i
$766$	11.2214	+	21.1607i	0.405445	+	0.764568i
$767$	0.139468	+	0.241565i	0.00503589	+	0.00872241i
$768$	27.3589	+	4.41497i	0.987228	+	0.159311i
$769$	−16.7281	+	28.9740i	−0.603232	+	1.04483i	0.389097	+	0.921197i	$0.372787\pi$
$769$	−16.7281	+	28.9740i	−0.603232	+	1.04483i	−0.992328	+	0.123631i	$0.960546\pi$
$770$	17.9851	+	0.647948i	0.648136	+	0.0233504i
$771$	0.457961	+	0.600300i	0.0164931	+	0.0216193i
$772$	−46.4630	−	3.35220i	−1.67224	−	0.120648i
$773$	30.8912	−	12.7956i	1.11108	−	0.460224i	0.249770	−	0.968305i	$-0.419645\pi$
$773$	30.8912	−	12.7956i	1.11108	−	0.460224i	0.861309	+	0.508081i	$0.169645\pi$
$774$	18.6278	−	40.1589i	0.669561	−	1.44348i
$775$	18.5031	−	18.5031i	0.664652	−	0.664652i
$776$	−0.368983	−	0.836197i	−0.0132457	−	0.0300177i
$777$	−1.58434	+	5.84727i	−0.0568379	+	0.209770i
$778$	33.6279	−	12.5306i	1.20562	−	0.449245i
$779$	14.2060	+	1.87026i	0.508984	+	0.0670090i
$780$	0.142796	+	0.218108i	0.00511292	+	0.00780953i
$781$	5.02313	+	38.1545i	0.179742	+	1.36527i
$782$	12.8347	+	3.93948i	0.458969	+	0.140875i
$783$	−22.4573	+	12.7153i	−0.802558	+	0.454408i
$784$	22.5069	−	8.97789i	0.803819	−	0.320639i
$785$	23.5926	−	13.6212i	0.842056	−	0.486161i
$786$	−0.445193	+	1.43607i	−0.0158795	+	0.0512231i
$787$	31.5873	−	24.2378i	1.12596	−	0.863983i	0.134061	−	0.990973i	$-0.457198\pi$
$787$	31.5873	−	24.2378i	1.12596	−	0.863983i	0.991904	+	0.126990i	$0.0405316\pi$
$788$	34.3274	+	30.5058i	1.22286	+	1.08672i
$789$	11.6732	−	15.1249i	0.415577	−	0.538460i
$790$	−48.7690	−	8.21653i	−1.73512	−	0.292331i
$791$	2.42865	+	2.42865i	0.0863530	+	0.0863530i
$792$	−40.9179	+	0.706432i	−1.45395	+	0.0251020i
$793$	−0.227957	+	0.227957i	−0.00809498	+	0.00809498i
$794$	−28.6602	+	20.3954i	−1.01711	+	0.723805i
$795$	2.69920	−	20.0679i	0.0957309	−	0.711737i
$796$	−3.49594	−	1.21240i	−0.123910	−	0.0429723i
$797$	−6.15692	−	8.02385i	−0.218089	−	0.284219i	0.671477	−	0.741025i	$-0.265660\pi$
$797$	−6.15692	−	8.02385i	−0.218089	−	0.284219i	−0.889566	+	0.456806i	$0.848993\pi$
$798$	0.338085	−	8.70633i	0.0119681	−	0.308201i
$799$	−6.59602	−	11.4246i	−0.233350	−	0.404174i
$800$	1.10375	+	13.4728i	0.0390235	+	0.476334i
$801$	53.1369	+	0.297698i	1.87750	+	0.0105186i
$802$	27.3119	−	14.4833i	0.964415	−	0.511423i
$803$	6.32526	−	0.832737i	0.223214	−	0.0293866i
$804$	−1.05990	−	1.23168i	−0.0373797	−	0.0434381i
$805$	0.991206	−	7.52896i	0.0349354	−	0.265361i
$806$	0.389920	+	0.178217i	0.0137343	+	0.00627743i
$807$	9.21096	−	9.15950i	0.324241	−	0.322430i
$808$	−11.2708	−	10.7668i	−0.396505	−	0.378775i
$809$	12.5983	+	12.5983i	0.442933	+	0.442933i	0.892996	−	0.450064i	$-0.148599\pi$
$809$	12.5983	+	12.5983i	0.442933	+	0.442933i	−0.450064	+	0.892996i	$0.648599\pi$
$810$	−22.3349	+	26.4249i	−0.784770	+	0.928475i
$811$	−4.16856	−	10.0638i	−0.146378	−	0.353388i	0.833637	−	0.552313i	$-0.186255\pi$
$811$	−4.16856	−	10.0638i	−0.146378	−	0.353388i	−0.980015	+	0.198926i	$0.936255\pi$
$812$	3.03907	+	9.14997i	0.106650	+	0.321101i
$813$	−2.10898	−	0.880496i	−0.0739650	−	0.0308803i
$814$	16.7424	+	17.9938i	0.586819	+	0.630682i
$815$	32.7438	+	18.9046i	1.14697	+	0.662201i
$816$	−19.9710	+	11.1094i	−0.699124	+	0.388909i
$817$	33.1150	−	19.1189i	1.15855	−	0.668887i
$818$	30.5882	+	9.38870i	1.06949	+	0.328268i
$819$	0.0743029	+	0.0312661i	0.00259635	+	0.00109253i
$820$	−17.7523	+	11.6937i	−0.619937	+	0.408361i
$821$	17.9378	−	23.3769i	0.626032	−	0.815861i	−0.367427	−	0.930052i	$-0.619761\pi$
$821$	17.9378	−	23.3769i	0.626032	−	0.815861i	0.993459	+	0.114192i	$0.0364278\pi$
$822$	−31.1097	+	11.4931i	−1.08507	+	0.400869i
$823$	0.129807	−	0.0347816i	0.00452478	−	0.00121241i	−0.256556	−	0.966529i	$-0.582588\pi$
$823$	0.129807	−	0.0347816i	0.00452478	−	0.00121241i	0.261081	+	0.965317i	$0.415921\pi$
$824$	3.23833	+	20.8940i	0.112813	+	0.727878i
$825$	−5.11254	−	19.2963i	−0.177996	−	0.671812i
$826$	8.01907	+	11.2686i	0.279019	+	0.392086i
$827$	−25.3300	+	10.4920i	−0.880810	+	0.364843i	−0.776811	−	0.629734i	$-0.783164\pi$
$827$	−25.3300	+	10.4920i	−0.880810	+	0.364843i	−0.103999	+	0.994577i	$0.533164\pi$
$828$	−1.33911	+	17.2163i	−0.0465374	+	0.598309i
$829$	−3.99208	+	9.63774i	−0.138651	+	0.334733i	−0.977919	−	0.208985i	$-0.932984\pi$
$829$	−3.99208	+	9.63774i	−0.138651	+	0.334733i	0.839268	+	0.543718i	$0.182984\pi$
$830$	−24.5342	+	39.1665i	−0.851593	+	1.35949i
$831$	−0.147701	−	0.257488i	−0.00512368	−	0.00893216i
$832$	−0.200526	+	0.0940192i	−0.00695198	+	0.00325953i
$833$	−9.99109	+	17.3051i	−0.346171	+	0.599585i
$834$	9.36839	+	17.7866i	0.324401	+	0.615901i
$835$	31.3563	−	4.12814i	1.08513	−	0.142860i
$836$	−29.2616	−	19.8314i	−1.01203	−	0.685885i
$837$	−7.90067	+	56.3482i	−0.273087	+	1.94768i
$838$	25.3500	−	2.41266i	0.875702	−	0.0833441i
$839$	29.8051	+	7.98626i	1.02899	+	0.275716i	0.733543	−	0.679643i	$-0.237865\pi$
$839$	29.8051	+	7.98626i	1.02899	+	0.275716i	0.295445	+	0.955360i	$0.404532\pi$
$840$	8.07316	+	10.0951i	0.278551	+	0.348316i
$841$	−4.18538	+	1.12147i	−0.144323	+	0.0386713i
$842$	8.66102	−	3.22732i	0.298478	−	0.111221i
$843$	−27.9780	+	36.2510i	−0.963614	+	1.24855i
$844$	−11.7461	−	5.88886i	−0.404319	−	0.202703i
$845$	32.6471	+	13.5229i	1.12310	+	0.465201i
$846$	12.4868	−	11.4885i	0.429305	−	0.394983i
$847$		−	11.9006i		−	0.408911i
$848$	16.5561	+	4.67030i	0.568538	+	0.160379i
$849$	1.80839	+	1.05084i	0.0620637	+	0.0360647i
$850$	−7.59347	−	8.16106i	−0.260454	−	0.279922i
$851$	8.22788	−	6.31347i	0.282048	−	0.216423i
$852$	−18.4191	+	20.6099i	−0.631027	+	0.706085i
$853$	29.8772	−	38.9368i	1.02298	−	1.33317i	0.0812860	−	0.996691i	$-0.474097\pi$
$853$	29.8772	−	38.9368i	1.02298	−	1.33317i	0.941691	−	0.336479i	$-0.109236\pi$
$854$	−10.1812	+	12.3230i	−0.348394	+	0.421685i
$855$	−28.9103	+	7.57316i	−0.988713	+	0.258997i
$856$	15.2383	+	52.0768i	0.520833	+	1.77995i
$857$	−10.3053	−	2.76129i	−0.352021	−	0.0943238i	0.0784753	−	0.996916i	$-0.474995\pi$
$857$	−10.3053	−	2.76129i	−0.352021	−	0.0943238i	−0.430496	+	0.902592i	$0.641661\pi$
$858$	0.266998	−	0.188879i	0.00911517	−	0.00644822i
$859$	−0.375755	+	2.85414i	−0.0128206	+	0.0973821i	−0.996659	−	0.0816777i	$-0.973972\pi$
$859$	−0.375755	+	2.85414i	−0.0128206	+	0.0973821i	0.983838	+	0.179060i	$0.0573055\pi$
$860$	−18.5876	+	53.5972i	−0.633831	+	1.82765i
$861$	−2.53252	+	6.06593i	−0.0863081	+	0.206726i
$862$	15.0195	+	9.40829i	0.511565	+	0.320448i
$863$	−25.8243			−0.879069			−0.439535	−	0.898226i	$-0.644857\pi$
$863$	−25.8243			−0.879069			−0.439535	+	0.898226i	$0.644857\pi$
$864$	−19.5545	−	21.9459i	−0.665256	−	0.746615i
$865$	−43.9038			−1.49277
$866$	14.0706	+	8.81395i	0.478140	+	0.299510i
$867$	−4.08364	+	9.78119i	−0.138688	+	0.332187i
$868$	20.0840	+	6.96514i	0.681694	+	0.236412i
$869$	−8.09848	+	61.5141i	−0.274722	+	2.08672i
$870$	26.9983	−	19.0990i	0.915328	−	0.647518i
$871$	0.0125435	+	0.00336103i	0.000425022	+	0.000113884i
$872$	−19.3387	−	10.5832i	−0.654889	−	0.358392i
$873$	−0.256149	+	0.934977i	−0.00866933	+	0.0316442i
$874$	−9.50031	+	11.4989i	−0.321353	+	0.388956i
$875$	4.19288	−	5.46427i	0.141745	−	0.184726i
$876$	3.41673	+	3.05352i	0.115441	+	0.103169i
$877$	21.4045	−	16.4242i	0.722778	−	0.554607i	−0.180546	−	0.983567i	$-0.557786\pi$
$877$	21.4045	−	16.4242i	0.722778	−	0.554607i	0.903324	+	0.428959i	$0.141120\pi$
$878$	−26.9779	−	28.9944i	−0.910461	−	0.978515i
$879$	−31.4057	−	18.2496i	−1.05929	−	0.615542i
$880$	52.0793	−	6.16103i	1.75559	−	0.207688i
$881$			33.9088i			1.14242i	0.820805	+	0.571208i	$0.193525\pi$
$881$			33.9088i			1.14242i	−0.820805	+	0.571208i	$0.806475\pi$
$882$	−24.5274	−	7.67904i	−0.825880	−	0.258567i
$883$	−10.7549	−	4.45481i	−0.361930	−	0.149916i	0.194306	−	0.980941i	$-0.437755\pi$
$883$	−10.7549	−	4.45481i	−0.361930	−	0.149916i	−0.556235	+	0.831025i	$0.687755\pi$
$884$	0.0818521	−	0.163266i	0.00275299	−	0.00549121i
$885$	28.9851	−	37.5558i	0.974322	−	1.26242i
$886$	21.4336	−	7.98671i	0.720075	−	0.268319i
$887$	−13.1593	+	3.52603i	−0.441847	+	0.118392i	−0.472882	−	0.881126i	$-0.656786\pi$
$887$	−13.1593	+	3.52603i	−0.441847	+	0.118392i	0.0310353	+	0.999518i	$0.490120\pi$
$888$	−1.95262	+	17.5450i	−0.0655255	+	0.588773i
$889$	−8.39891	−	2.25048i	−0.281690	−	0.0754787i
$890$	−67.7876	+	6.45162i	−2.27225	+	0.216259i
$891$	34.1384	+	26.8083i	1.14368	+	0.898113i
$892$	28.0473	−	41.3843i	0.939093	−	1.38565i
$893$	14.5308	−	1.91301i	0.486254	−	0.0640166i
$894$	7.22028	+	13.7083i	0.241482	+	0.458474i
$895$	4.42489	−	7.66414i	0.147908	−	0.256184i
$896$	−9.45641	+	5.58290i	−0.315916	+	0.186512i
$897$	−0.0686667	−	0.119707i	−0.00229271	−	0.00399691i
$898$	26.2883	−	41.9668i	0.877252	−	1.40045i
$899$	20.8125	−	50.2457i	0.694135	−	1.67579i
$900$	8.11027	−	11.8237i	0.270342	−	0.394122i
$901$	−13.1057	+	5.42858i	−0.436616	+	0.180852i
$902$	15.4625	+	21.7284i	0.514845	+	0.723475i
$903$	4.49270	+	16.9569i	0.149508	+	0.564289i
$904$	8.07753	+	5.90968i	0.268655	+	0.196553i
$905$	61.9543	−	16.6006i	2.05943	−	0.551823i
$906$	−5.98566	+	2.21134i	−0.198860	+	0.0734667i
$907$	−17.2616	+	22.4958i	−0.573163	+	0.746960i	−0.986526	−	0.163606i	$-0.947687\pi$
$907$	−17.2616	+	22.4958i	−0.573163	+	0.746960i	0.413363	+	0.910566i	$0.364354\pi$
$908$	17.3433	+	26.3290i	0.575556	+	0.873760i
$909$	2.06606	+	16.4029i	0.0685269	+	0.544050i
$910$	−0.0987555	−	0.0303119i	−0.00327371	−	0.00100483i
$911$	−0.313403	+	0.180943i	−0.0103835	+	0.00599491i	−0.505183	−	0.863012i	$-0.668575\pi$
$911$	−0.313403	+	0.180943i	−0.0103835	+	0.00599491i	0.494799	+	0.869007i	$0.335242\pi$
$912$	−2.91215	−	25.2218i	−0.0964308	−	0.835178i
$913$	50.2123	+	28.9901i	1.66178	+	0.959431i
$914$	−19.2984	−	20.7409i	−0.638335	−	0.686049i
$915$	50.5964	+	21.1239i	1.67266	+	0.698336i
$916$	−18.8314	+	6.25467i	−0.622208	+	0.206660i
$917$	−0.227993	−	0.550424i	−0.00752900	−	0.0181766i
$918$	23.8677	+	4.22777i	0.787753	+	0.139537i
$919$	−29.0153	−	29.0153i	−0.957127	−	0.957127i	0.0419914	−	0.999118i	$-0.486630\pi$
$919$	−29.0153	−	29.0153i	−0.957127	−	0.957127i	−0.999118	+	0.0419914i	$0.986630\pi$
$920$	−0.505936	−	22.1229i	−0.0166802	−	0.729371i
$921$	3.12620	−	3.10874i	0.103012	−	0.102436i
$922$	−45.9980	−	21.0239i	−1.51486	−	0.692386i
$923$	0.0288332	−	0.219010i	0.000949057	−	0.00720880i
$924$	12.2919	−	10.5775i	0.404374	−	0.347975i
$925$	−8.53738	+	1.12397i	−0.280707	+	0.0369558i
$926$	−14.0924	+	7.47310i	−0.463105	+	0.245581i
$927$	11.3217	−	19.3584i	0.371852	−	0.635813i
$928$	12.8351	+	24.9921i	0.421332	+	0.820405i
$929$	20.8908	+	36.1839i	0.685404	+	1.18715i	0.973310	+	0.229496i	$0.0737078\pi$
$929$	20.8908	+	36.1839i	0.685404	+	1.18715i	−0.287905	+	0.957659i	$0.592959\pi$
$930$	2.82929	−	72.8595i	0.0927761	−	2.38916i
$931$	−13.5145	−	17.6124i	−0.442919	−	0.577223i
$932$	4.74040	−	13.6689i	0.155277	−	0.447741i
$933$	1.73231	−	12.8793i	0.0567132	−	0.421649i
$934$	−10.8744	+	7.73853i	−0.355822	+	0.253212i
$935$	−30.5796	+	30.5796i	−1.00006	+	1.00006i
$936$	0.227919	+	0.0568726i	0.00744976	+	0.00185894i
$937$	5.57046	+	5.57046i	0.181979	+	0.181979i	0.792218	−	0.610239i	$-0.208926\pi$
$937$	5.57046	+	5.57046i	0.181979	+	0.181979i	−0.610239	+	0.792218i	$0.708926\pi$
$938$	0.634949	+	0.106975i	0.0207318	+	0.00349287i
$939$	−15.0328	+	19.4779i	−0.490577	+	0.635638i
$940$	−14.4437	+	16.2531i	−0.471101	+	0.530117i
$941$	−2.45144	+	1.88106i	−0.0799148	+	0.0613208i	−0.647946	−	0.761686i	$-0.724372\pi$
$941$	−2.45144	+	1.88106i	−0.0799148	+	0.0613208i	0.568031	+	0.823007i	$0.307705\pi$
$942$	7.26866	−	23.4468i	0.236826	−	0.763937i
$943$	9.74546	−	5.62655i	0.317356	−	0.183226i
$944$	28.1212	+	28.8704i	0.915266	+	0.939653i
$945$	0.115215	−	13.7099i	0.00374795	−	0.445982i
$946$	68.0358	+	20.8829i	2.21204	+	0.678961i
$947$	−6.91329	−	52.5117i	−0.224652	−	1.70640i	−0.617313	−	0.786717i	$-0.711779\pi$
$947$	−6.91329	−	52.5117i	−0.224652	−	1.70640i	0.392662	−	0.919683i	$-0.371554\pi$
$948$	−37.2842	+	24.4101i	−1.21093	+	0.792802i
$949$	−0.0363076	−	0.00477998i	−0.00117859	−	0.000155165i
$950$	11.6051	−	4.32435i	0.376518	−	0.140300i
$951$	0.613132	−	2.26287i	0.0198822	−	0.0733785i
$952$	3.27328	−	8.44344i	0.106088	−	0.273653i
$953$	5.79722	−	5.79722i	0.187790	−	0.187790i	−0.606950	−	0.794740i	$-0.707607\pi$
$953$	5.79722	−	5.79722i	0.187790	−	0.187790i	0.794740	+	0.606950i	$0.207607\pi$
$954$	−10.4954	−	14.9248i	−0.339803	−	0.483209i
$955$	51.1977	−	21.2068i	1.65672	−	0.686236i
$956$	−2.39031	+	33.1308i	−0.0773082	+	1.07153i
$957$	−25.1644	−	32.9858i	−0.813451	−	1.06628i
$958$	5.72911	+	0.206403i	0.185099	+	0.00666857i
$959$	6.57093	−	11.3812i	0.212186	−	0.367518i
$960$	27.7532	+	25.4671i	0.895731	+	0.821947i
$961$	−44.4545	−	76.9974i	−1.43402	−	2.48379i
$962$	−0.0660956	−	0.124640i	−0.00213101	−	0.00401855i
$963$	22.3217	−	53.0468i	0.719306	−	1.70941i
$964$	−33.5992	−	22.7711i	−1.08216	−	0.733408i
$965$	−50.2323	−	38.5446i	−1.61704	−	1.24080i
$966$	−3.95181	−	5.58626i	−0.127147	−	0.179735i
$967$	−1.64075	−	6.12337i	−0.0527630	−	0.196914i	0.934513	−	0.355928i	$-0.115835\pi$
$967$	−1.64075	−	6.12337i	−0.0527630	−	0.196914i	−0.987276	+	0.159014i	$0.949169\pi$
$968$	−5.31136	−	34.2694i	−0.170713	−	1.10146i
$969$	14.7632	+	14.8461i	0.474262	+	0.476926i
$970$	0.206390	−	1.22502i	0.00662679	−	0.0393331i
$971$	10.6843	+	25.7941i	0.342875	+	0.827772i	0.997423	+	0.0717519i	$0.0228590\pi$
$971$	10.6843	+	25.7941i	0.342875	+	0.827772i	−0.654548	+	0.756020i	$0.727141\pi$
$972$	1.39846	+	31.1455i	0.0448557	+	0.998993i
$973$	−7.35963	−	3.04846i	−0.235939	−	0.0977291i
$974$	5.50780	+	23.9778i	0.176481	+	0.768297i
$975$	−0.000320974		0.114584i	−1.02794e−5		0.00366962i
$976$	−23.8182	+	40.0296i	−0.762401	+	1.28132i
$977$	−8.62193	−	4.97787i	−0.275840	−	0.159256i	0.355699	−	0.934601i	$-0.384243\pi$
$977$	−8.62193	−	4.97787i	−0.275840	−	0.159256i	−0.631539	+	0.775344i	$0.717576\pi$
$978$	33.2257	−	7.53418i	1.06244	−	0.240917i
$979$	11.1504	+	84.6958i	0.356369	+	2.70689i
$980$	32.2596	+	6.63755i	1.03049	+	0.212029i
$981$	8.82688	+	21.6523i	0.281821	+	0.691305i
$982$	8.49117	−	10.2775i	0.270964	−	0.327967i
$983$	1.78398	−	6.65792i	0.0569002	−	0.212355i	−0.931622	−	0.363428i	$-0.881606\pi$
$983$	1.78398	−	6.65792i	0.0569002	−	0.212355i	0.988523	+	0.151073i	$0.0482730\pi$
$984$	−4.58543	+	18.5979i	−0.146178	+	0.592879i
$985$	16.1552	+	60.2922i	0.514749	+	1.92107i
$986$	−21.0717	−	9.63106i	−0.671060	−	0.306715i
$987$	−0.896281	+	6.66363i	−0.0285289	+	0.212106i
$988$	0.132779	+	0.153428i	0.00422425	+	0.00488119i
$989$	11.4921	−	27.7445i	0.365429	−	0.882223i
$990$	−46.9728	−	29.7918i	−1.49289	−	0.946845i
$991$	−47.2772			−1.50181			−0.750905	−	0.660411i	$-0.770382\pi$
$991$	−47.2772			−1.50181			−0.750905	+	0.660411i	$0.770382\pi$
$992$	60.9428	+	11.0933i	1.93494	+	0.352214i
$993$	−19.9276	−	34.7399i	−0.632382	−	1.10244i
$994$	0.394350	−	10.9460i	0.0125080	−	0.347184i
$995$	−3.06164	−	3.99001i	−0.0970606	−	0.126492i
$996$	7.74121	+	40.9187i	0.245290	+	1.29656i
$997$	17.6226	+	13.5223i	0.558112	+	0.428255i	0.848916	−	0.528528i	$-0.177256\pi$
$997$	17.6226	+	13.5223i	0.558112	+	0.428255i	−0.290804	+	0.956783i	$0.593923\pi$
$998$	3.78439	+	39.7628i	0.119793	+	1.25867i
$999$	13.3508	−	13.1283i	0.422401	−	0.415361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.13.16	✓	368
3.2	odd	2		864.2.bk.a.685.31		368
9.2	odd	6		864.2.bk.a.397.1		368
9.7	even	3	inner	288.2.bc.a.205.46	yes	368
32.5	even	8	inner	288.2.bc.a.229.46	yes	368
96.5	odd	8		864.2.bk.a.37.1		368
288.101	odd	24		864.2.bk.a.613.31		368
288.133	even	24	inner	288.2.bc.a.133.16	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.16	✓	368	1.1	even	1	trivial
288.2.bc.a.133.16	yes	368	288.133	even	24	inner
288.2.bc.a.205.46	yes	368	9.7	even	3	inner
288.2.bc.a.229.46	yes	368	32.5	even	8	inner
864.2.bk.a.37.1		368	96.5	odd	8
864.2.bk.a.397.1		368	9.2	odd	6
864.2.bk.a.613.31		368	288.101	odd	24
864.2.bk.a.685.31		368	3.2	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.750744 + 1.19849i) q^{2} +(-0.667307 + 1.59834i) q^{3} +(-0.872768 - 1.79952i) q^{4} +(0.354821 - 2.69513i) q^{5} +(-1.41463 - 1.99971i) q^{6} +(0.937559 + 0.251218i) q^{7} +(2.81194 + 0.304973i) q^{8} +(-2.10940 - 2.13317i) q^{9} +O(q^{10})\)	\(q+(-0.750744 + 1.19849i) q^{2} +(-0.667307 + 1.59834i) q^{3} +(-0.872768 - 1.79952i) q^{4} +(0.354821 - 2.69513i) q^{5} +(-1.41463 - 1.99971i) q^{6} +(0.937559 + 0.251218i) q^{7} +(2.81194 + 0.304973i) q^{8} +(-2.10940 - 2.13317i) q^{9} +(2.96372 + 2.44861i) q^{10} +(2.93602 - 3.82629i) q^{11} +(3.45866 - 0.194150i) q^{12} +(-0.0219633 + 0.0168530i) q^{13} +(-1.00495 + 0.935057i) q^{14} +(4.07098 + 2.36561i) q^{15} +(-2.47655 + 3.14113i) q^{16} -3.29855i q^{17} +(4.14021 - 0.926638i) q^{18} +(3.38569 + 1.40240i) q^{19} +(-5.15963 + 1.71372i) q^{20} +(-1.02717 + 1.33090i) q^{21} +(2.38159 + 6.39136i) q^{22} +(2.77999 - 0.744896i) q^{23} +(-2.36388 + 4.29093i) q^{24} +(-2.30823 - 0.618487i) q^{25} +(-0.00370942 - 0.0389751i) q^{26} +(4.81716 - 1.94807i) q^{27} +(-0.366199 - 1.90641i) q^{28} +(-4.92410 + 0.648270i) q^{29} +(-5.89142 + 3.10307i) q^{30} +(-5.47515 + 9.48323i) q^{31} +(-1.90536 - 5.32631i) q^{32} +(4.15650 + 7.24608i) q^{33} +(3.95329 + 2.47636i) q^{34} +(1.00973 - 2.43771i) q^{35} +(-1.99767 + 5.65768i) q^{36} +(3.32918 - 1.37899i) q^{37} +(-4.22255 + 3.00488i) q^{38} +(-0.0122806 - 0.0463510i) q^{39} +(1.81968 - 7.47034i) q^{40} +(3.77673 - 1.01197i) q^{41} +(-0.823932 - 2.23023i) q^{42} +(6.35198 - 8.27806i) q^{43} +(-9.44796 - 1.94396i) q^{44} +(-6.49765 + 4.92823i) q^{45} +(-1.19431 + 3.89102i) q^{46} +(3.46353 - 1.99967i) q^{47} +(-3.36798 - 6.05448i) q^{48} +(-5.24627 - 3.02894i) q^{49} +(2.47414 - 2.30206i) q^{50} +(5.27221 + 2.20114i) q^{51} +(0.0494962 + 0.0248146i) q^{52} +(-1.64575 - 3.97319i) q^{53} +(-1.28171 + 7.23583i) q^{54} +(-9.27061 - 9.27061i) q^{55} +(2.55974 + 0.992340i) q^{56} +(-4.50081 + 4.47566i) q^{57} +(2.91979 - 6.38818i) q^{58} +(1.31514 - 9.98946i) q^{59} +(0.703945 - 9.39043i) q^{60} +(11.5453 - 1.51997i) q^{61} +(-7.25515 - 13.6814i) q^{62} +(-1.44180 - 2.52990i) q^{63} +(7.81398 + 1.71513i) q^{64} +(0.0376281 + 0.0651738i) q^{65} +(-11.8048 - 0.458407i) q^{66} +(-0.285557 - 0.372146i) q^{67} +(-5.93581 + 2.87887i) q^{68} +(-0.664507 + 4.94045i) q^{69} +(2.16353 + 3.04025i) q^{70} +(-5.64222 + 5.64222i) q^{71} +(-5.28095 - 6.64166i) q^{72} +(0.935370 + 0.935370i) q^{73} +(-0.846650 + 5.02526i) q^{74} +(2.52885 - 3.27662i) q^{75} +(-0.431275 - 7.31659i) q^{76} +(3.71392 - 2.84979i) q^{77} +(0.0647709 + 0.0200794i) q^{78} +(-11.1410 + 6.43227i) q^{79} +(7.58703 + 7.78918i) q^{80} +(-0.100841 + 8.99944i) q^{81} +(-1.62252 + 5.28612i) q^{82} +(1.56915 + 11.9189i) q^{83} +(3.29147 + 0.686851i) q^{84} +(-8.89003 - 1.17040i) q^{85} +(5.15248 + 13.8275i) q^{86} +(2.24973 - 8.30299i) q^{87} +(9.42281 - 9.86389i) q^{88} +(-12.5247 + 12.5247i) q^{89} +(-1.02838 - 11.4872i) q^{90} +(-0.0248256 + 0.0102831i) q^{91} +(-3.76674 - 4.35253i) q^{92} +(-11.5039 - 15.0794i) q^{93} +(-0.203634 + 5.65226i) q^{94} +(4.98097 - 8.62729i) q^{95} +(9.78474 + 0.508861i) q^{96} +(-0.161572 - 0.279850i) q^{97} +(7.56876 - 4.01366i) q^{98} +(-14.3554 + 1.80816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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