LMFDB - Embedded newform 309.2.i.b.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,2,Mod(13,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("309.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	309.i (of order $17$, degree $16$, 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:	$2.46737742246$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			100.1
Character	$\chi$	$=$	309.100
Dual form			309.2.i.b.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.33806 + 1.44767i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(2.47932 - 4.97915i) q^{4} +(2.45619 - 0.951533i) q^{5} +(2.03225 + 1.85264i) q^{6} +(0.0680790 - 0.734689i) q^{7} +(0.903874 + 9.75436i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})$	\(q+(-2.33806 + 1.44767i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(2.47932 - 4.97915i) q^{4} +(2.45619 - 0.951533i) q^{5} +(2.03225 + 1.85264i) q^{6} +(0.0680790 - 0.734689i) q^{7} +(0.903874 + 9.75436i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-4.36522 + 5.78049i) q^{10} +(1.09088 - 0.675445i) q^{11} +(-5.46758 - 1.02207i) q^{12} +(0.520420 - 5.61622i) q^{13} +(0.904413 + 1.81631i) q^{14} +(-1.58738 - 2.10203i) q^{15} +(-9.53034 - 12.6202i) q^{16} +(-3.11275 + 2.83764i) q^{17} +(1.22576 - 2.46166i) q^{18} +(0.0307320 - 0.108012i) q^{19} +(1.35186 - 14.5889i) q^{20} +(-0.725274 + 0.135577i) q^{21} +(-1.57273 + 3.15847i) q^{22} +(-3.87985 - 2.40230i) q^{23} +(9.13464 - 3.53878i) q^{24} +(1.43240 - 1.30581i) q^{25} +(6.91365 + 13.8845i) q^{26} +(0.739009 + 0.673696i) q^{27} +(-3.48934 - 2.16051i) q^{28} +(9.59616 - 3.71757i) q^{29} +(6.75442 + 2.61668i) q^{30} +(0.645244 + 0.854441i) q^{31} +(22.2831 + 8.63253i) q^{32} +(-0.948194 - 0.864393i) q^{33} +(3.16983 - 11.1408i) q^{34} +(-0.531866 - 1.86931i) q^{35} +(0.513223 + 5.53856i) q^{36} +(-3.35481 - 0.627123i) q^{37} +(0.0845118 + 0.297028i) q^{38} +(-5.54425 + 1.03640i) q^{39} +(11.5017 + 23.0985i) q^{40} +(-1.47081 - 0.569795i) q^{41} +(1.49947 - 1.36694i) q^{42} +(9.13997 - 1.70856i) q^{43} +(-0.658497 - 7.10631i) q^{44} +(-1.58738 + 2.10203i) q^{45} +12.5491 q^{46} -13.4081 q^{47} +(-9.53034 + 12.6202i) q^{48} +(6.34568 + 1.18621i) q^{49} +(-1.45868 + 5.12671i) q^{50} +(3.58116 + 2.21736i) q^{51} +(-26.6738 - 16.5157i) q^{52} +(0.993383 - 3.49138i) q^{53} +(-2.70314 - 0.505304i) q^{54} +(2.03670 - 2.69703i) q^{55} +7.22796 q^{56} -0.112299 q^{57} +(-17.0546 + 22.5840i) q^{58} +(-1.16189 - 12.5388i) q^{59} +(-14.4019 + 2.69219i) q^{60} +(6.34896 - 5.78784i) q^{61} +(-2.74557 - 1.06364i) q^{62} +(0.328882 + 0.660484i) q^{63} +(-33.5061 + 6.26337i) q^{64} +(-4.06577 - 14.2897i) q^{65} +(3.46829 + 0.648336i) q^{66} +(-0.231156 - 2.49457i) q^{67} +(6.41156 + 22.5343i) q^{68} +(-1.24882 + 4.38916i) q^{69} +(3.94968 + 3.60061i) q^{70} +(-2.75630 - 1.06780i) q^{71} +(-5.90350 - 7.81749i) q^{72} +(12.8685 + 4.98529i) q^{73} +(8.75164 - 3.39040i) q^{74} +(-1.64796 - 1.02037i) q^{75} +(-0.461613 - 0.420815i) q^{76} +(-0.421976 - 0.847442i) q^{77} +(11.4624 - 10.4494i) q^{78} +(-8.45334 + 3.27484i) q^{79} +(-35.4168 - 21.9292i) q^{80} +(0.445738 - 0.895163i) q^{81} +(4.26372 - 0.797028i) q^{82} +(-1.43418 + 15.4773i) q^{83} +(-1.12313 + 3.94739i) q^{84} +(-4.94538 + 9.93167i) q^{85} +(-18.8964 + 17.2264i) q^{86} +(-6.20177 - 8.21247i) q^{87} +(7.57455 + 10.0303i) q^{88} +(2.71215 + 5.44673i) q^{89} +(0.668352 - 7.21267i) q^{90} +(-4.09075 - 0.764694i) q^{91} +(-21.5808 + 13.3623i) q^{92} +(0.645244 - 0.854441i) q^{93} +(31.3489 - 19.4104i) q^{94} +(-0.0272931 - 0.294540i) q^{95} +(2.20492 - 23.7949i) q^{96} +(7.57125 + 6.90211i) q^{97} +(-16.5538 + 6.41299i) q^{98} +(-0.571910 + 1.14855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) $ 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/309\mathbb{Z}\right)^\times$.

$n$	$104$	$211$
$\chi(n)$	$1$	$e\left(\frac{15}{17}\right)$

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 $

$2$	−2.33806	+	1.44767i	−1.65326	+	1.02366i	−0.703492	+	0.710703i	$0.748377\pi$
$2$	−2.33806	+	1.44767i	−1.65326	+	1.02366i	−0.949769	+	0.312953i	$0.898682\pi$
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$4$	2.47932	−	4.97915i	1.23966	−	2.48958i
$5$	2.45619	−	0.951533i	1.09844	−	0.425538i	0.257288	−	0.966335i	$-0.417171\pi$
$5$	2.45619	−	0.951533i	1.09844	−	0.425538i	0.841153	+	0.540797i	$0.181877\pi$
$6$	2.03225	+	1.85264i	0.829661	+	0.756336i
$7$	0.0680790	−	0.734689i	0.0257314	−	0.277686i	−0.973141	−	0.230210i	$-0.926059\pi$
$7$	0.0680790	−	0.734689i	0.0257314	−	0.277686i	0.998872	−	0.0474762i	$-0.0151178\pi$
$8$	0.903874	+	9.75436i	0.319568	+	3.44869i
$9$	−0.850217	+	0.526432i	−0.283406	+	0.175477i
$10$	−4.36522	+	5.78049i	−1.38040	+	1.82795i
$11$	1.09088	−	0.675445i	0.328913	−	0.203654i	−0.352034	−	0.935987i	$-0.614510\pi$
$11$	1.09088	−	0.675445i	0.328913	−	0.203654i	0.680947	+	0.732333i	$0.261569\pi$
$12$	−5.46758	−	1.02207i	−1.57835	−	0.295045i
$13$	0.520420	−	5.61622i	0.144338	−	1.55766i	−0.548242	−	0.836320i	$-0.684703\pi$
$13$	0.520420	−	5.61622i	0.144338	−	1.55766i	0.692580	−	0.721341i	$-0.256474\pi$
$14$	0.904413	+	1.81631i	0.241715	+	0.485428i
$15$	−1.58738	−	2.10203i	−0.409859	−	0.542741i
$16$	−9.53034	−	12.6202i	−2.38258	−	3.15505i
$17$	−3.11275	+	2.83764i	−0.754952	+	0.688230i	−0.956657	−	0.291217i	$-0.905940\pi$
$17$	−3.11275	+	2.83764i	−0.754952	+	0.688230i	0.201705	+	0.979446i	$0.435352\pi$
$18$	1.22576	−	2.46166i	0.288915	−	0.580220i
$19$	0.0307320	−	0.108012i	0.00705040	−	0.0247796i	−0.958221	−	0.286030i	$-0.907664\pi$
$19$	0.0307320	−	0.108012i	0.00705040	−	0.0247796i	0.965271	+	0.261250i	$0.0841349\pi$
$20$	1.35186	−	14.5889i	0.302285	−	3.26218i
$21$	−0.725274	+	0.135577i	−0.158268	+	0.0295854i
$22$	−1.57273	+	3.15847i	−0.335307	+	0.673387i
$23$	−3.87985	−	2.40230i	−0.809004	−	0.500914i	0.0585339	−	0.998285i	$-0.481357\pi$
$23$	−3.87985	−	2.40230i	−0.809004	−	0.500914i	−0.867538	+	0.497371i	$0.834299\pi$
$24$	9.13464	−	3.53878i	1.86460	−	0.722350i
$25$	1.43240	−	1.30581i	0.286481	−	0.261162i
$26$	6.91365	+	13.8845i	1.35588	+	2.72297i
$27$	0.739009	+	0.673696i	0.142222	+	0.129653i
$28$	−3.48934	−	2.16051i	−0.659423	−	0.408298i
$29$	9.59616	−	3.71757i	1.78196	−	0.690336i	0.784422	−	0.620227i	$-0.212960\pi$
$29$	9.59616	−	3.71757i	1.78196	−	0.690336i	0.997539	−	0.0701086i	$-0.0223346\pi$
$30$	6.75442	+	2.61668i	1.23318	+	0.477738i
$31$	0.645244	+	0.854441i	0.115889	+	0.153462i	0.852264	−	0.523111i	$-0.175229\pi$
$31$	0.645244	+	0.854441i	0.115889	+	0.153462i	−0.736375	+	0.676573i	$0.763464\pi$
$32$	22.2831	+	8.63253i	3.93914	+	1.52603i
$33$	−0.948194	−	0.864393i	−0.165059	−	0.150472i
$34$	3.16983	−	11.1408i	0.543622	−	1.91063i
$35$	−0.531866	−	1.86931i	−0.0899018	−	0.315972i
$36$	0.513223	+	5.53856i	0.0855372	+	0.923093i
$37$	−3.35481	−	0.627123i	−0.551528	−	0.103098i	−0.0993935	−	0.995048i	$-0.531690\pi$
$37$	−3.35481	−	0.627123i	−0.551528	−	0.103098i	−0.452135	+	0.891950i	$0.649337\pi$
$38$	0.0845118	+	0.297028i	0.0137096	+	0.0481843i
$39$	−5.54425	+	1.03640i	−0.887790	+	0.165957i
$40$	11.5017	+	23.0985i	1.81857	+	3.65219i
$41$	−1.47081	−	0.569795i	−0.229702	−	0.0889870i	0.243640	−	0.969866i	$-0.421658\pi$
$41$	−1.47081	−	0.569795i	−0.229702	−	0.0889870i	−0.473342	+	0.880879i	$0.656953\pi$
$42$	1.49947	−	1.36694i	0.231373	−	0.210924i
$43$	9.13997	−	1.70856i	1.39383	−	0.260553i	0.567332	−	0.823489i	$-0.307975\pi$
$43$	9.13997	−	1.70856i	1.39383	−	0.260553i	0.826500	+	0.562936i	$0.190328\pi$
$44$	−0.658497	−	7.10631i	−0.0992721	−	1.07132i
$45$	−1.58738	+	2.10203i	−0.236632	+	0.313352i
$46$	12.5491			1.85026
$47$	−13.4081			−1.95577			−0.977883	−	0.209151i	$-0.932930\pi$
$47$	−13.4081			−1.95577			−0.977883	+	0.209151i	$0.932930\pi$
$48$	−9.53034	+	12.6202i	−1.37559	+	1.82157i
$49$	6.34568	+	1.18621i	0.906525	+	0.169459i
$50$	−1.45868	+	5.12671i	−0.206288	+	0.725027i
$51$	3.58116	+	2.21736i	0.501463	+	0.310493i
$52$	−26.6738	−	16.5157i	−3.69898	−	2.29031i
$53$	0.993383	−	3.49138i	0.136452	−	0.479578i	−0.863230	−	0.504811i	$-0.831562\pi$
$53$	0.993383	−	3.49138i	0.136452	−	0.479578i	0.999682	+	0.0252330i	$0.00803277\pi$
$54$	−2.70314	−	0.505304i	−0.367850	−	0.0687632i
$55$	2.03670	−	2.69703i	0.274629	−	0.363667i
$56$	7.22796			0.965876
$57$	−0.112299			−0.0148743
$58$	−17.0546	+	22.5840i	−2.23938	+	2.96542i
$59$	−1.16189	−	12.5388i	−0.151265	−	1.63241i	−0.645978	−	0.763356i	$-0.723550\pi$
$59$	−1.16189	−	12.5388i	−0.151265	−	1.63241i	0.494713	−	0.869057i	$-0.335273\pi$
$60$	−14.4019	+	2.69219i	−1.85928	+	0.347560i
$61$	6.34896	−	5.78784i	0.812901	−	0.741057i	−0.156199	−	0.987726i	$-0.549924\pi$
$61$	6.34896	−	5.78784i	0.812901	−	0.741057i	0.969100	+	0.246668i	$0.0793358\pi$
$62$	−2.74557	−	1.06364i	−0.348687	−	0.135082i
$63$	0.328882	+	0.660484i	0.0414353	+	0.0832132i
$64$	−33.5061	+	6.26337i	−4.18826	+	0.782921i
$65$	−4.06577	−	14.2897i	−0.504297	−	1.77242i
$66$	3.46829	+	0.648336i	0.426917	+	0.0798047i
$67$	−0.231156	−	2.49457i	−0.0282401	−	0.304760i	−0.998126	−	0.0611983i	$-0.980508\pi$
$67$	−0.231156	−	2.49457i	−0.0282401	−	0.304760i	0.969885	−	0.243561i	$-0.0783157\pi$
$68$	6.41156	+	22.5343i	0.777515	+	2.73268i
$69$	−1.24882	+	4.38916i	−0.150341	+	0.528392i
$70$	3.94968	+	3.60061i	0.472078	+	0.430356i
$71$	−2.75630	−	1.06780i	−0.327113	−	0.126724i	0.192085	−	0.981378i	$-0.438475\pi$
$71$	−2.75630	−	1.06780i	−0.327113	−	0.126724i	−0.519198	+	0.854654i	$0.673769\pi$
$72$	−5.90350	−	7.81749i	−0.695734	−	0.921301i
$73$	12.8685	+	4.98529i	1.50615	+	0.583484i	0.966104	−	0.258153i	$-0.0831140\pi$
$73$	12.8685	+	4.98529i	1.50615	+	0.583484i	0.540043	+	0.841638i	$0.318408\pi$
$74$	8.75164	−	3.39040i	1.01736	−	0.394126i
$75$	−1.64796	−	1.02037i	−0.190290	−	0.117822i
$76$	−0.461613	−	0.420815i	−0.0529506	−	0.0482708i
$77$	−0.421976	−	0.847442i	−0.0480886	−	0.0965750i
$78$	11.4624	−	10.4494i	1.29787	−	1.18316i
$79$	−8.45334	+	3.27484i	−0.951075	+	0.368449i	−0.786274	−	0.617878i	$-0.787992\pi$
$79$	−8.45334	+	3.27484i	−0.951075	+	0.368449i	−0.164802	+	0.986327i	$0.552698\pi$
$80$	−35.4168	−	21.9292i	−3.95972	−	2.45176i
$81$	0.445738	−	0.895163i	0.0495265	−	0.0994626i
$82$	4.26372	−	0.797028i	0.470849	−	0.0880170i
$83$	−1.43418	+	15.4773i	−0.157422	+	1.69886i	0.440865	+	0.897573i	$0.354672\pi$
$83$	−1.43418	+	15.4773i	−0.157422	+	1.69886i	−0.598287	+	0.801282i	$0.704152\pi$
$84$	−1.12313	+	3.94739i	−0.122543	+	0.430695i
$85$	−4.94538	+	9.93167i	−0.536402	+	1.07724i
$86$	−18.8964	+	17.2264i	−2.03765	+	1.85757i
$87$	−6.20177	−	8.21247i	−0.664899	−	0.880469i
$88$	7.57455	+	10.0303i	0.807450	+	1.06924i
$89$	2.71215	+	5.44673i	0.287487	+	0.577352i	0.991083	−	0.133249i	$-0.0425409\pi$
$89$	2.71215	+	5.44673i	0.287487	+	0.577352i	−0.703596	+	0.710601i	$0.748423\pi$
$90$	0.668352	−	7.21267i	0.0704505	−	0.760282i
$91$	−4.09075	−	0.764694i	−0.428827	−	0.0801617i
$92$	−21.5808	+	13.3623i	−2.24996	+	1.39311i
$93$	0.645244	−	0.854441i	0.0669087	−	0.0886014i
$94$	31.3489	−	19.4104i	3.23339	−	2.00203i
$95$	−0.0272931	−	0.294540i	−0.00280022	−	0.0302191i
$96$	2.20492	−	23.7949i	0.225039	−	2.42856i
$97$	7.57125	+	6.90211i	0.768744	+	0.700803i	0.959772	−	0.280782i	$-0.0905937\pi$
$97$	7.57125	+	6.90211i	0.768744	+	0.700803i	−0.191027	+	0.981585i	$0.561182\pi$
$98$	−16.5538	+	6.41299i	−1.67219	+	0.647810i
$99$	−0.571910	+	1.14855i	−0.0574791	+	0.115434i
$100$	−2.95043	−	10.3697i	−0.295043	−	1.03697i
$101$	1.05559	−	0.653591i	0.105035	−	0.0650347i	−0.472910	−	0.881111i	$-0.656796\pi$
$101$	1.05559	−	0.653591i	0.105035	−	0.0650347i	0.577944	+	0.816076i	$0.303855\pi$
$102$	−11.5830			−1.14689
$103$	−9.51835	+	3.52151i	−0.937871	+	0.346984i
$103$	−9.51835	+	3.52151i	−0.937871	+	0.346984i
$104$	55.2531			5.41801
$105$	−1.65240	+	1.02312i	−0.161258	+	0.0998467i
$106$	2.73177	+	9.60116i	0.265333	+	0.932547i
$107$	−3.11962	+	6.26504i	−0.301585	+	0.605664i	−0.993176	−	0.116625i	$-0.962792\pi$
$107$	−3.11962	+	6.26504i	−0.301585	+	0.605664i	0.691591	+	0.722289i	$0.256910\pi$
$108$	5.18668	−	2.00933i	0.499088	−	0.193348i
$109$	−4.45860	−	4.06455i	−0.427056	−	0.389313i	0.431433	−	0.902145i	$-0.358008\pi$
$109$	−4.45860	−	4.06455i	−0.427056	−	0.389313i	−0.858489	+	0.512832i	$0.828596\pi$
$110$	−0.857537	+	9.25430i	−0.0817629	+	0.882362i
$111$	0.314905	+	3.39837i	0.0298895	+	0.322559i
$112$	−9.92075	+	6.14267i	−0.937422	+	0.580427i
$113$	7.23157	−	9.57614i	0.680289	−	0.900848i	−0.318604	−	0.947888i	$-0.603214\pi$
$113$	7.23157	−	9.57614i	0.680289	−	0.900848i	0.998893	+	0.0470401i	$0.0149789\pi$
$114$	0.262561	−	0.162571i	0.0245911	−	0.0152262i
$115$	−11.8155	−	2.20870i	−1.10180	−	0.205962i
$116$	5.28162	−	56.9978i	0.490387	−	5.29211i
$117$	2.51409	+	5.04898i	0.232428	+	0.466778i
$118$	20.8686	+	27.6345i	1.92111	+	2.54396i
$119$	1.87287	+	2.48008i	0.171686	+	0.227349i
$120$	19.0691	−	17.3838i	1.74077	−	1.58692i
$121$	−4.16933	+	8.37314i	−0.379030	+	0.761194i
$122$	−6.46540	+	22.7235i	−0.585350	+	2.05729i
$123$	−0.145537	+	1.57059i	−0.0131226	+	0.141616i
$124$	5.85416	−	1.09433i	0.525719	−	0.0982739i
$125$	−3.59477	+	7.21928i	−0.321526	+	0.645712i
$126$	−1.72511	−	1.06814i	−0.153685	−	0.0951577i
$127$	9.06762	−	3.51281i	0.804621	−	0.311712i	0.0764203	−	0.997076i	$-0.475651\pi$
$127$	9.06762	−	3.51281i	0.804621	−	0.311712i	0.728201	+	0.685364i	$0.240357\pi$
$128$	33.9521	−	30.9514i	3.00097	−	2.73575i
$129$	−4.14461	−	8.32349i	−0.364912	−	0.732843i
$130$	30.1928	+	27.5244i	2.64808	+	2.41405i
$131$	10.4138	+	6.44794i	0.909856	+	0.563359i	0.899661	−	0.436589i	$-0.143814\pi$
$131$	10.4138	+	6.44794i	0.909856	+	0.563359i	0.0101947	+	0.999948i	$0.496755\pi$
$132$	−6.65483	+	2.57809i	−0.579228	+	0.224394i
$133$	−0.0772629	−	0.0299318i	−0.00669954	−	0.00259542i
$134$	4.15176	+	5.49782i	0.358657	+	0.474939i
$135$	2.45619	+	0.951533i	0.211395	+	0.0818949i
$136$	−30.4929	−	27.7980i	−2.61475	−	2.38366i
$137$	−2.28650	+	8.03622i	−0.195349	+	0.686581i	0.800802	+	0.598929i	$0.204407\pi$
$137$	−2.28650	+	8.03622i	−0.195349	+	0.686581i	−0.996151	+	0.0876518i	$0.972064\pi$
$138$	−3.43421	−	12.0700i	−0.292340	−	1.02747i
$139$	0.819244	+	8.84105i	0.0694873	+	0.749888i	0.957188	+	0.289467i	$0.0934780\pi$
$139$	0.819244	+	8.84105i	0.0694873	+	0.749888i	−0.887701	+	0.460421i	$0.847698\pi$
$140$	−10.6263	−	1.98640i	−0.898084	−	0.167881i
$141$	3.66929	+	12.8962i	0.309010	+	1.08606i
$142$	7.99023	−	1.49363i	0.670525	−	0.125343i
$143$	−3.22573	−	6.47815i	−0.269749	−	0.541730i
$144$	14.7465	+	5.71284i	1.22888	+	0.476070i
$145$	20.0326	−	18.2621i	1.66362	−	1.51659i
$146$	−37.3045	+	6.97341i	−3.08734	+	0.577124i
$147$	−0.595647	−	6.42806i	−0.0491282	−	0.530177i
$148$	−11.4402	+	15.1493i	−0.940380	+	1.24526i
$149$	17.2578			1.41382			0.706908	−	0.707305i	$-0.250089\pi$
$149$	17.2578			1.41382			0.706908	+	0.707305i	$0.250089\pi$
$150$	5.33019			0.435208
$151$	−7.54757	+	9.99460i	−0.614213	+	0.813349i	−0.993727	−	0.111837i	$-0.964327\pi$
$151$	−7.54757	+	9.99460i	−0.614213	+	0.813349i	0.379514	+	0.925186i	$0.376091\pi$
$152$	1.08136	+	0.202142i	0.0877101	+	0.0163959i
$153$	1.15268	−	4.05126i	0.0931889	−	0.327525i
$154$	2.21342	+	1.37049i	0.178363	+	0.110437i
$155$	2.39787	+	1.48470i	0.192601	+	0.119254i
$156$	−8.58560	+	30.1752i	−0.687398	+	2.41595i
$157$	−4.76402	−	0.890550i	−0.380211	−	0.0710737i	−0.00982487	−	0.999952i	$-0.503127\pi$
$157$	−4.76402	−	0.890550i	−0.380211	−	0.0710737i	−0.370386	+	0.928878i	$0.620774\pi$
$158$	15.0236	−	19.8944i	1.19521	−	1.58272i
$159$	−3.62995			−0.287874
$160$	62.9457			4.97630
$161$	−2.02908	+	2.68694i	−0.159914	+	0.211760i
$162$	0.253734	+	2.73823i	0.0199353	+	0.215136i
$163$	2.64598	−	0.494619i	0.207249	−	0.0387416i	−0.0791010	−	0.996867i	$-0.525205\pi$
$163$	2.64598	−	0.494619i	0.207249	−	0.0387416i	0.286350	+	0.958125i	$0.407558\pi$
$164$	−6.48371	+	5.91068i	−0.506293	+	0.461547i
$165$	−3.15144	−	1.22088i	−0.245339	−	0.0950450i
$166$	−19.0528	−	38.2632i	−1.47878	−	2.96980i
$167$	1.32986	−	0.248594i	0.102908	−	0.0192368i	−0.132044	−	0.991244i	$-0.542154\pi$
$167$	1.32986	−	0.248594i	0.102908	−	0.0192368i	0.234951	+	0.972007i	$0.424507\pi$
$168$	−1.97802	−	6.95203i	−0.152608	−	0.536361i
$169$	−18.4925	−	3.45685i	−1.42250	−	0.265911i
$170$	−2.81513	−	30.3801i	−0.215911	−	2.33005i
$171$	0.0307320	+	0.108012i	0.00235013	+	0.00825986i
$172$	14.1538	−	49.7454i	1.07922	−	3.79305i
$173$	−2.27752	−	2.07623i	−0.173156	−	0.157853i	0.582478	−	0.812846i	$-0.302083\pi$
$173$	−2.27752	−	2.07623i	−0.173156	−	0.157853i	−0.755635	+	0.654993i	$0.772671\pi$
$174$	26.3891	+	10.2232i	2.00055	+	0.775017i
$175$	−0.861847	−	1.14127i	−0.0651495	−	0.0862719i
$176$	−18.9207	−	7.32993i	−1.42620	−	0.552514i
$177$	−11.7422	+	4.54894i	−0.882596	+	0.341919i
$178$	−14.2262	−	8.80851i	−1.06630	−	0.660225i
$179$	−3.27490	−	2.98547i	−0.244778	−	0.223144i	0.542004	−	0.840376i	$-0.317666\pi$
$179$	−3.27490	−	2.98547i	−0.244778	−	0.223144i	−0.786781	+	0.617232i	$0.788254\pi$
$180$	6.53069	+	13.1154i	0.486769	+	0.977564i
$181$	10.1986	−	9.29724i	0.758055	−	0.691058i	−0.199311	−	0.979936i	$-0.563870\pi$
$181$	10.1986	−	9.29724i	0.758055	−	0.691058i	0.957366	+	0.288878i	$0.0932822\pi$
$182$	10.6715	−	4.13414i	0.791021	−	0.306443i
$183$	−7.30437	−	4.52268i	−0.539955	−	0.334326i
$184$	19.9260	−	40.0168i	1.46896	−	2.95008i
$185$	−8.83679	+	1.65188i	−0.649693	+	0.121449i
$186$	−0.271675	+	2.93184i	−0.0199201	+	0.214973i
$187$	−1.47896	+	5.19802i	−0.108153	+	0.380117i
$188$	−33.2429	+	66.7608i	−2.42449	+	4.86903i
$189$	0.545268	−	0.497077i	0.0396624	−	0.0361571i
$190$	0.490209	+	0.649141i	0.0355635	+	0.0470937i
$191$	7.96935	+	10.5531i	0.576642	+	0.763597i	0.989079	−	0.147389i	$-0.0470870\pi$
$191$	7.96935	+	10.5531i	0.576642	+	0.763597i	−0.412437	+	0.910986i	$0.635322\pi$
$192$	15.1936	+	30.5129i	1.09651	+	2.20208i
$193$	−1.72752	+	18.6429i	−0.124350	+	1.34195i	0.673544	+	0.739147i	$0.264771\pi$
$193$	−1.72752	+	18.6429i	−0.124350	+	1.34195i	−0.797894	+	0.602798i	$0.794052\pi$
$194$	−27.6940	−	5.17691i	−1.98832	−	0.371681i
$195$	−12.6316	+	7.82113i	−0.904564	+	0.560082i
$196$	21.6393	−	28.6551i	1.54567	−	2.04679i
$197$	−7.57789	+	4.69203i	−0.539902	+	0.334293i	−0.769143	−	0.639076i	$-0.779317\pi$
$197$	−7.57789	+	4.69203i	−0.539902	+	0.334293i	0.229241	+	0.973370i	$0.426376\pi$
$198$	−0.325557	−	3.51332i	−0.0231363	−	0.249681i
$199$	−0.935478	+	10.0954i	−0.0663143	+	0.715645i	0.896063	+	0.443928i	$0.146415\pi$
$199$	−0.935478	+	10.0954i	−0.0663143	+	0.715645i	−0.962377	+	0.271718i	$0.912408\pi$
$200$	14.0320	+	12.7919i	0.992216	+	0.904524i
$201$	−2.33608	+	0.905002i	−0.164774	+	0.0638339i
$202$	−1.52184	+	3.05627i	−0.107077	+	0.215039i
$203$	−2.07796	−	7.30328i	−0.145844	−	0.512590i
$204$	19.9194	−	12.3336i	1.39464	−	0.863524i
$205$	−4.15477			−0.290181
$206$	17.1565	−	22.0129i	1.19535	−	1.53371i
$207$	4.56336			0.317175
$208$	−75.8377	+	46.9567i	−5.25840	+	3.25586i
$209$	−0.0394310	−	0.138586i	−0.00272750	−	0.00958618i
$210$	2.38228	−	4.78426i	0.164393	−	0.330145i
$211$	−2.61989	+	1.01495i	−0.180361	+	0.0698722i	−0.449729	−	0.893165i	$-0.648479\pi$
$211$	−2.61989	+	1.01495i	−0.180361	+	0.0698722i	0.269368	+	0.963037i	$0.413185\pi$
$212$	−14.9212	−	13.6025i	−1.02479	−	0.934222i
$213$	−0.272737	+	2.94330i	−0.0186876	+	0.201672i
$214$	−1.77583	−	19.1642i	−0.121393	−	1.31004i
$215$	20.8238	−	12.8935i	1.42017	−	0.879331i
$216$	−5.90350	+	7.81749i	−0.401682	+	0.531913i
$217$	0.671676	−	0.415884i	0.0455963	−	0.0282321i
$218$	16.3086	+	3.04861i	1.10456	+	0.206478i
$219$	1.27334	−	13.7416i	0.0860446	−	0.928569i
$220$	−8.37928	−	16.8279i	−0.564931	−	1.13453i
$221$	14.3169	+	18.9586i	0.963059	+	1.27530i
$222$	−5.65597	−	7.48972i	−0.379604	−	0.502677i
$223$	1.85172	−	1.68806i	0.124000	−	0.113041i	−0.609320	−	0.792924i	$-0.708558\pi$
$223$	1.85172	−	1.68806i	0.124000	−	0.113041i	0.733321	+	0.679883i	$0.237969\pi$
$224$	7.85924	−	15.7835i	0.525118	−	1.05458i
$225$	−0.530435	+	1.86429i	−0.0353623	+	0.124286i
$226$	−3.04479	+	32.8585i	−0.202537	+	2.18572i
$227$	26.4627	−	4.94673i	1.75639	−	0.328326i	0.795645	−	0.605763i	$-0.207132\pi$
$227$	26.4627	−	4.94673i	1.75639	−	0.328326i	0.960744	+	0.277437i	$0.0894850\pi$
$228$	−0.278425	+	0.559152i	−0.0184391	+	0.0370308i
$229$	7.50481	+	4.64678i	0.495932	+	0.307068i	0.751511	−	0.659720i	$-0.229325\pi$
$229$	7.50481	+	4.64678i	0.495932	+	0.307068i	−0.255580	+	0.966788i	$0.582266\pi$
$230$	30.8229	−	11.9408i	2.03240	−	0.787356i
$231$	−0.699612	+	0.637781i	−0.0460311	+	0.0419629i
$232$	44.9362	+	90.2441i	2.95021	+	5.92482i
$233$	−10.1300	−	9.23470i	−0.663637	−	0.604986i	0.270148	−	0.962819i	$-0.412927\pi$
$233$	−10.1300	−	9.23470i	−0.663637	−	0.604986i	−0.933785	+	0.357833i	$0.883516\pi$
$234$	−13.1873	−	8.16526i	−0.862084	−	0.533780i
$235$	−32.9327	+	12.7582i	−2.14829	+	0.832254i
$236$	−65.3133	−	25.3025i	−4.25153	−	1.64705i
$237$	5.46319	+	7.23444i	0.354873	+	0.469927i
$238$	−7.96924	−	3.08730i	−0.516569	−	0.200120i
$239$	1.82070	+	1.65979i	0.117771	+	0.107363i	0.730439	−	0.682978i	$-0.239315\pi$
$239$	1.82070	+	1.65979i	0.117771	+	0.107363i	−0.612668	+	0.790340i	$0.709904\pi$
$240$	−11.3998	+	40.0660i	−0.735852	+	2.58625i
$241$	2.41028	+	8.47126i	0.155260	+	0.545682i	0.999946	+	0.0104195i	$0.00331669\pi$
$241$	2.41028	+	8.47126i	0.155260	+	0.545682i	−0.844686	+	0.535262i	$0.820213\pi$
$242$	−2.37337	−	25.6127i	−0.152566	−	1.64645i
$243$	−0.982973	−	0.183750i	−0.0630578	−	0.0117875i
$244$	−13.0774	−	45.9624i	−0.837197	−	2.94244i
$245$	16.7149	−	3.12456i	1.06788	−	0.199621i
$246$	−1.93342	−	3.88284i	−0.123271	−	0.247561i
$247$	−0.590625	−	0.228809i	−0.0375805	−	0.0145588i
$248$	−7.75130	+	7.06625i	−0.492208	+	0.448707i
$249$	15.2790	−	2.85613i	0.968264	−	0.181000i
$250$	−2.04631	−	22.0832i	−0.129420	−	1.39666i
$251$	−2.19335	+	2.90446i	−0.138443	+	0.183328i	−0.861957	−	0.506982i	$-0.830761\pi$
$251$	−2.19335	+	2.90446i	−0.138443	+	0.183328i	0.723514	+	0.690310i	$0.242526\pi$
$252$	4.10406			0.258531
$253$	−5.85507			−0.368105
$254$	−16.1153	+	21.3401i	−1.01116	+	1.33900i
$255$	10.9059	+	2.03867i	0.682954	+	0.127666i
$256$	−15.9184	+	55.9474i	−0.994900	+	3.49671i
$257$	16.4607	+	10.1920i	1.02679	+	0.635761i	0.933017	−	0.359832i	$-0.117166\pi$
$257$	16.4607	+	10.1920i	1.02679	+	0.635761i	0.0937728	+	0.995594i	$0.470107\pi$
$258$	21.7400	+	13.4608i	1.35347	+	0.838035i
$259$	−0.689133	+	2.42205i	−0.0428207	+	0.150499i
$260$	−81.2310	−	15.1847i	−5.03773	−	0.941716i
$261$	−6.20177	+	8.21247i	−0.383880	+	0.508339i
$262$	−33.6825			−2.08091
$263$	0.602658			0.0371615			0.0185807	−	0.999827i	$-0.494085\pi$
$263$	0.602658			0.0371615			0.0185807	+	0.999827i	$0.494085\pi$
$264$	7.57455	−	10.0303i	0.466181	−	0.617324i
$265$	−0.882225	−	9.52073i	−0.0541947	−	0.584854i
$266$	0.223977	−	0.0418685i	0.0137329	−	0.00256712i
$267$	4.49659	−	4.09918i	0.275187	−	0.250866i
$268$	−12.9939	−	5.03388i	−0.793731	−	0.307493i
$269$	2.55167	+	5.12445i	0.155578	+	0.312443i	0.959215	−	0.282677i	$-0.0912223\pi$
$269$	2.55167	+	5.12445i	0.155578	+	0.312443i	−0.803637	+	0.595120i	$0.797105\pi$
$270$	−7.12023	+	1.33100i	−0.433323	+	0.0810022i
$271$	2.06915	+	7.27231i	0.125692	+	0.441762i	0.998966	−	0.0454682i	$-0.0144780\pi$
$271$	2.06915	+	7.27231i	0.125692	+	0.441762i	−0.873274	+	0.487230i	$0.838007\pi$
$272$	65.4772	+	12.2398i	3.97014	+	0.742147i
$273$	0.383985	+	4.14386i	0.0232398	+	0.250798i
$274$	−6.28779	−	22.0993i	−0.379860	−	1.33507i
$275$	0.680581	−	2.39199i	0.0410406	−	0.144243i
$276$	18.7580	+	17.1002i	1.12910	+	1.02931i
$277$	10.2140	+	3.95693i	0.613701	+	0.237749i	0.647973	−	0.761663i	$-0.275617\pi$
$277$	10.2140	+	3.95693i	0.613701	+	0.237749i	−0.0342716	+	0.999413i	$0.510911\pi$
$278$	−14.7143	−	19.4849i	−0.882508	−	1.16863i
$279$	−0.998402	−	0.386783i	−0.0597728	−	0.0231561i
$280$	17.7532	−	6.87764i	1.06096	−	0.411017i
$281$	−10.2705	−	6.35921i	−0.612686	−	0.379359i	0.184730	−	0.982789i	$-0.440859\pi$
$281$	−10.2705	−	6.35921i	−0.612686	−	0.379359i	−0.797416	+	0.603430i	$0.793800\pi$
$282$	−27.2485	−	24.8403i	−1.62262	−	1.47922i
$283$	−1.22964	−	2.46945i	−0.0730945	−	0.146794i	0.855602	−	0.517634i	$-0.173187\pi$
$283$	−1.22964	−	2.46945i	−0.0730945	−	0.146794i	−0.928696	+	0.370841i	$0.879070\pi$
$284$	−12.1505	+	11.0766i	−0.720999	+	0.657278i
$285$	−0.275827	+	0.106856i	−0.0163386	+	0.00632959i
$286$	16.9202	+	10.4765i	1.00051	+	0.619490i
$287$	−0.518753	+	1.04180i	−0.0306210	+	0.0614954i
$288$	−23.4899	+	4.39103i	−1.38416	+	0.258744i
$289$	0.0684082	−	0.738242i	0.00402401	−	0.0434260i
$290$	−20.4000	+	71.6985i	−1.19793	+	4.21028i
$291$	4.56665	−	9.17108i	0.267702	−	0.537618i
$292$	56.7278	−	51.7142i	3.31974	−	3.02634i
$293$	−6.43100	−	8.51602i	−0.375703	−	0.497511i	0.570404	−	0.821364i	$-0.306787\pi$
$293$	−6.43100	−	8.51602i	−0.375703	−	0.497511i	−0.946108	+	0.323853i	$0.895022\pi$
$294$	10.6984	+	14.1669i	0.623941	+	0.826231i
$295$	−14.7849	−	29.6921i	−0.860810	−	1.72874i
$296$	3.08486	−	33.2909i	0.179304	−	1.93499i
$297$	1.26122	+	0.235762i	0.0731831	+	0.0136803i
$298$	−40.3499	+	24.9836i	−2.33741	+	1.44726i
$299$	−15.5110	+	20.5399i	−0.897024	+	1.18785i
$300$	−9.16641	+	5.67560i	−0.529223	+	0.327681i
$301$	−0.633018	−	6.83136i	−0.0364866	−	0.393753i
$302$	3.17784	−	34.2944i	0.182864	−	1.97342i
$303$	−0.917515	−	0.836425i	−0.0527099	−	0.0480514i
$304$	−1.65602	+	0.641544i	−0.0949791	+	0.0367951i
$305$	10.0869	−	20.2573i	0.577576	−	1.15993i
$306$	3.16983	+	11.1408i	0.181207	+	0.636878i
$307$	13.3217	−	8.24846i	0.760311	−	0.470764i	−0.0907227	−	0.995876i	$-0.528918\pi$
$307$	13.3217	−	8.24846i	0.760311	−	0.470764i	0.851033	+	0.525112i	$0.175977\pi$
$308$	−5.26576			−0.300045
$309$	5.99190	+	8.19129i	0.340867	+	0.465986i
$310$	−7.75572			−0.440495
$311$	0.842421	−	0.521605i	0.0477693	−	0.0295775i	−0.502340	−	0.864670i	$-0.667527\pi$
$311$	0.842421	−	0.521605i	0.0477693	−	0.0295775i	0.550109	+	0.835093i	$0.314586\pi$
$312$	−15.1207	−	53.1438i	−0.856042	−	3.00868i
$313$	5.74560	−	11.5387i	0.324761	−	0.652207i	−0.671271	−	0.741212i	$-0.734251\pi$
$313$	5.74560	−	11.5387i	0.324761	−	0.652207i	0.996031	+	0.0890052i	$0.0283688\pi$
$314$	12.4278	−	4.81456i	0.701342	−	0.271701i
$315$	1.43627	+	1.30933i	0.0809246	+	0.0737725i
$316$	−4.65263	+	50.2099i	−0.261731	+	2.82453i
$317$	−2.41306	−	26.0411i	−0.135531	−	1.46261i	−0.743545	−	0.668685i	$-0.766857\pi$
$317$	−2.41306	−	26.0411i	−0.135531	−	1.46261i	0.608014	−	0.793926i	$-0.291966\pi$
$318$	8.48706	−	5.25496i	0.475931	−	0.294684i
$319$	7.95725	−	10.5371i	0.445521	−	0.589965i
$320$	−76.3374	+	47.2661i	−4.26739	+	2.64226i
$321$	6.87960	+	1.28602i	0.383982	+	0.0717786i
$322$	0.854327	−	9.21966i	0.0476098	−	0.513792i
$323$	0.210838	+	0.423420i	0.0117313	+	0.0235597i
$324$	−3.35203	−	4.43880i	−0.186224	−	0.246600i
$325$	−6.58827	−	8.72428i	−0.365451	−	0.483936i
$326$	−5.47043	+	4.98695i	−0.302979	+	0.276202i
$327$	−2.68923	+	5.40071i	−0.148715	+	0.298660i
$328$	4.22856	−	14.8618i	0.233483	−	0.820608i
$329$	−0.912807	+	9.85076i	−0.0503247	+	0.543090i
$330$	9.13569	−	1.70776i	0.502903	−	0.0940089i
$331$	−0.779155	+	1.56475i	−0.0428262	+	0.0860066i	−0.915543	−	0.402220i	$-0.868239\pi$
$331$	−0.779155	+	1.56475i	−0.0428262	+	0.0860066i	0.872717	+	0.488227i	$0.162356\pi$
$332$	73.5081	+	45.5143i	4.03428	+	2.49792i
$333$	3.18246	−	1.23289i	0.174398	−	0.0675620i
$334$	−2.74942	+	2.50643i	−0.150441	+	0.137146i
$335$	−2.94142	−	5.90717i	−0.160707	−	0.322743i
$336$	8.62311	+	7.86101i	0.470429	+	0.428853i
$337$	−6.32864	−	3.91853i	−0.344743	−	0.213456i	0.343128	−	0.939289i	$-0.388513\pi$
$337$	−6.32864	−	3.91853i	−0.344743	−	0.213456i	−0.687871	+	0.725833i	$0.741455\pi$
$338$	48.2410	−	18.6887i	2.62396	−	1.01653i
$339$	−11.1896	−	4.33487i	−0.607735	−	0.235438i
$340$	37.1901	+	49.2476i	2.01692	+	2.67083i
$341$	1.28101	+	0.496267i	0.0693707	+	0.0268743i
$342$	−0.228218	−	0.208049i	−0.0123406	−	0.0112500i
$343$	2.71694	−	9.54904i	0.146701	−	0.515600i
$344$	24.9273	+	87.6103i	1.34399	+	4.72363i
$345$	1.10908	+	11.9689i	0.0597109	+	0.644383i
$346$	8.33067	+	1.55727i	0.447860	+	0.0837195i
$347$	−0.388532	−	1.36555i	−0.0208575	−	0.0733065i	0.950698	−	0.310117i	$-0.100368\pi$
$347$	−0.388532	−	1.36555i	−0.0208575	−	0.0733065i	−0.971556	+	0.236811i	$0.923898\pi$
$348$	−56.2673	+	10.5182i	−3.01625	+	0.563834i
$349$	9.86710	+	19.8158i	0.528174	+	1.06072i	0.985223	+	0.171275i	$0.0547886\pi$
$349$	9.86710	+	19.8158i	0.528174	+	1.06072i	−0.457049	+	0.889441i	$0.651094\pi$
$350$	3.66724	+	1.42069i	0.196022	+	0.0759393i
$351$	4.16822	−	3.79984i	0.222483	−	0.202820i
$352$	30.1390	−	5.63396i	1.60642	−	0.300291i
$353$	1.66895	+	18.0109i	0.0888294	+	0.958622i	0.917196	+	0.398436i	$0.130447\pi$
$353$	1.66895	+	18.0109i	0.0888294	+	0.958622i	−0.828367	+	0.560186i	$0.810730\pi$
$354$	20.8686	−	27.6345i	1.10915	−	1.46876i
$355$	−7.78605			−0.413240
$356$	33.8444			1.79375
$357$	1.87287	−	2.48008i	0.0991230	−	0.131260i
$358$	11.9789	+	2.23924i	0.633104	+	0.118348i
$359$	−7.34132	+	25.8021i	−0.387460	+	1.36178i	0.485605	+	0.874178i	$0.338599\pi$
$359$	−7.34132	+	25.8021i	−0.387460	+	1.36178i	−0.873065	+	0.487603i	$0.837871\pi$
$360$	−21.9387	−	13.5839i	−1.15627	−	0.715933i
$361$	16.1434	+	9.99557i	0.849653	+	0.526083i
$362$	−10.3856	+	36.5017i	−0.545857	+	1.91849i
$363$	9.19449	+	1.71875i	0.482585	+	0.0902109i
$364$	−13.9498	+	18.4726i	−0.731169	+	0.968225i
$365$	36.3512			1.90271
$366$	23.6254			1.23492
$367$	1.93844	−	2.56691i	0.101186	−	0.133992i	−0.744607	−	0.667503i	$-0.767363\pi$
$367$	1.93844	−	2.56691i	0.101186	−	0.133992i	0.845793	+	0.533511i	$0.179128\pi$
$368$	6.65873	+	71.8592i	0.347110	+	3.74592i
$369$	1.55047	−	0.289832i	0.0807141	−	0.0150881i
$370$	18.2696	−	16.6549i	0.949791	−	0.865849i
$371$	−2.49745	−	0.967518i	−0.129661	−	0.0502310i
$372$	−2.65462	−	5.33120i	−0.137636	−	0.276410i
$373$	−14.6978	+	2.74750i	−0.761026	+	0.142260i	−0.549937	−	0.835206i	$-0.685348\pi$
$373$	−14.6978	+	2.74750i	−0.761026	+	0.142260i	−0.211089	+	0.977467i	$0.567701\pi$
$374$	−4.06709	−	14.2944i	−0.210304	−	0.739143i
$375$	7.92745	+	1.48190i	0.409372	+	0.0765248i
$376$	−12.1192	−	130.787i	−0.625000	−	6.74483i
$377$	−15.8847	−	55.8289i	−0.818103	−	2.87533i
$378$	−0.555268	+	1.95157i	−0.0285599	+	0.100378i
$379$	−9.66150	−	8.80762i	−0.496278	−	0.452417i	0.386444	−	0.922313i	$-0.373703\pi$
$379$	−9.66150	−	8.80762i	−0.496278	−	0.452417i	−0.882722	+	0.469896i	$0.844291\pi$
$380$	−1.53423	−	0.594363i	−0.0787042	−	0.0304902i
$381$	−5.86019	−	7.76014i	−0.300226	−	0.397564i
$382$	−33.9103	−	13.1369i	−1.73500	−	0.672142i
$383$	26.9435	−	10.4380i	1.37675	−	0.533356i	0.444698	−	0.895681i	$-0.353311\pi$
$383$	26.9435	−	10.4380i	1.37675	−	0.533356i	0.932052	+	0.362325i	$0.118017\pi$
$384$	−39.0613	−	24.1857i	−1.99334	−	1.23422i
$385$	−1.84282	−	1.67995i	−0.0939189	−	0.0856184i
$386$	−22.9497	−	46.0892i	−1.16811	−	2.34588i
$387$	−6.87152	+	6.26422i	−0.349299	+	0.318428i
$388$	53.1383	−	20.5859i	2.69769	−	1.04509i
$389$	−28.6537	−	17.7416i	−1.45280	−	0.899537i	−0.999968	−	0.00794208i	$-0.997472\pi$
$389$	−28.6537	−	17.7416i	−1.45280	−	0.899537i	−0.452834	−	0.891595i	$-0.649587\pi$
$390$	18.2110	−	36.5726i	0.922149	−	1.85192i
$391$	18.8938	−	3.53187i	0.955503	−	0.178614i
$392$	−5.83505	+	62.9702i	−0.294714	+	3.18048i
$393$	3.35193	−	11.7808i	0.169082	−	0.594263i
$394$	10.9251	−	21.9405i	0.550398	−	1.10535i
$395$	−17.6469	+	16.0873i	−0.887911	+	0.809438i
$396$	4.30086	+	5.69525i	0.216126	+	0.286197i
$397$	1.68026	+	2.22503i	0.0843299	+	0.111671i	0.838226	−	0.545322i	$-0.183593\pi$
$397$	1.68026	+	2.22503i	0.0843299	+	0.111671i	−0.753897	+	0.656993i	$0.771828\pi$
$398$	−12.4276	−	24.9580i	−0.622940	−	1.25103i
$399$	−0.00764518	+	0.0825046i	−0.000382738	+	0.00413040i
$400$	−30.1309	−	5.63244i	−1.50654	−	0.281622i
$401$	−12.5114	+	7.74674i	−0.624791	+	0.386854i	−0.802004	−	0.597318i	$-0.796233\pi$
$401$	−12.5114	+	7.74674i	−0.624791	+	0.386854i	0.177214	+	0.984172i	$0.443292\pi$
$402$	4.15176	−	5.49782i	0.207071	−	0.274206i
$403$	5.13453	−	3.17917i	0.255769	−	0.158366i
$404$	−0.637191	−	6.87638i	−0.0317014	−	0.342113i
$405$	0.243040	−	2.62282i	0.0120768	−	0.130329i
$406$	15.4311	+	14.0673i	0.765835	+	0.698150i
$407$	−4.08329	+	1.58188i	−0.202401	+	0.0784106i
$408$	−18.3920	+	36.9361i	−0.910540	+	1.82861i
$409$	−4.99026	−	17.5390i	−0.246753	−	0.867245i	−0.981910	−	0.189349i	$-0.939362\pi$
$409$	−4.99026	−	17.5390i	−0.246753	−	0.867245i	0.735157	−	0.677897i	$-0.237108\pi$
$410$	9.71411	−	6.01472i	0.479746	−	0.297046i
$411$	8.35518			0.412131
$412$	−6.06494	+	56.1243i	−0.298798	+	2.76505i
$413$	−9.29122			−0.457191
$414$	−10.6694	+	6.60623i	−0.524374	+	0.324678i
$415$	11.2045	+	39.3799i	0.550009	+	1.93308i
$416$	60.0788	−	120.655i	2.94561	−	5.91558i
$417$	8.27935	−	3.20744i	0.405441	−	0.157069i
$418$	0.292818	+	0.266939i	0.0143222	+	0.0130564i
$419$	1.28901	−	13.9106i	0.0629723	−	0.679579i	−0.904478	−	0.426520i	$-0.859740\pi$
$419$	1.28901	−	13.9106i	0.0629723	−	0.679579i	0.967451	−	0.253060i	$-0.0814369\pi$
$420$	0.997453	+	10.7642i	0.0486707	+	0.525240i
$421$	−28.6333	+	17.7290i	−1.39550	+	0.864057i	−0.998553	−	0.0537836i	$-0.982872\pi$
$421$	−28.6333	+	17.7290i	−1.39550	+	0.864057i	−0.396948	+	0.917841i	$0.629931\pi$
$422$	4.65616	−	6.16576i	0.226658	−	0.300144i
$423$	11.3998	−	7.05844i	0.554276	−	0.343193i
$424$	34.9541	+	6.53405i	1.69752	+	0.317321i
$425$	−0.753291	+	8.12931i	−0.0365400	+	0.394329i
$426$	−3.62324	−	7.27646i	−0.175547	−	0.352545i
$427$	−3.82004	−	5.05854i	−0.184864	−	0.244800i
$428$	23.4600	+	31.0661i	1.13398	+	1.50164i
$429$	−5.34808	+	4.87542i	−0.258208	+	0.235388i
$430$	−30.0217	+	60.2918i	−1.44778	+	2.90753i
$431$	−5.32626	+	18.7199i	−0.256557	+	0.901704i	0.721334	+	0.692587i	$0.243529\pi$
$431$	−5.32626	+	18.7199i	−0.256557	+	0.901704i	−0.977891	+	0.209116i	$0.932941\pi$
$432$	1.45917	−	15.7470i	0.0702045	−	0.757627i
$433$	8.58852	−	1.60547i	0.412738	−	0.0771541i	0.0267146	−	0.999643i	$-0.491495\pi$
$433$	8.58852	−	1.60547i	0.412738	−	0.0771541i	0.386023	+	0.922489i	$0.373848\pi$
$434$	−0.968359	+	1.94473i	−0.0464827	+	0.0933499i
$435$	−23.0471	−	14.2702i	−1.10503	−	0.684203i
$436$	−31.2923	+	12.1227i	−1.49863	+	0.580572i
$437$	−0.378712	+	0.345242i	−0.0181162	+	0.0165151i
$438$	16.9161	+	33.9720i	0.808281	+	1.62325i
$439$	−10.4840	−	9.55744i	−0.500375	−	0.456152i	0.383727	−	0.923447i	$-0.374640\pi$
$439$	−10.4840	−	9.55744i	−0.500375	−	0.456152i	−0.884102	+	0.467295i	$0.845229\pi$
$440$	28.1487	+	17.4289i	1.34194	+	0.830892i
$441$	−6.01966	+	2.33203i	−0.286651	+	0.111049i
$442$	−60.9197	−	23.6004i	−2.89765	−	1.12256i
$443$	−7.25942	−	9.61302i	−0.344905	−	0.456729i	0.592192	−	0.805797i	$-0.298263\pi$
$443$	−7.25942	−	9.61302i	−0.344905	−	0.456729i	−0.937097	+	0.349068i	$0.886498\pi$
$444$	17.7017	+	6.85769i	0.840088	+	0.325452i
$445$	11.8443	+	10.7975i	0.561473	+	0.511850i
$446$	−1.88568	+	6.62747i	−0.0892895	+	0.313820i
$447$	−4.72283	−	16.5990i	−0.223382	−	0.785107i
$448$	2.32057	+	25.0430i	0.109637	+	1.18317i
$449$	29.0305	+	5.42674i	1.37003	+	0.256103i	0.816799	−	0.576923i	$-0.195747\pi$
$449$	29.0305	+	5.42674i	1.37003	+	0.256103i	0.553234	+	0.833026i	$0.313394\pi$
$450$	−1.45868	−	5.12671i	−0.0687626	−	0.241676i
$451$	−1.98934	+	0.371873i	−0.0936746	+	0.0175108i
$452$	−29.7517	−	59.7494i	−1.39940	−	2.81038i
$453$	11.6786	+	4.52430i	0.548706	+	0.212570i
$454$	−54.7102	+	49.8749i	−2.56768	+	2.34075i
$455$	−10.7753	+	2.01425i	−0.505153	+	0.0944295i
$456$	−0.101504	−	1.09540i	−0.00475336	−	0.0512969i
$457$	−12.7134	+	16.8352i	−0.594706	+	0.787518i	−0.991461	−	0.130407i	$-0.958372\pi$
$457$	−12.7134	+	16.8352i	−0.594706	+	0.787518i	0.396755	+	0.917925i	$0.370136\pi$
$458$	−24.2737			−1.13424
$459$	−4.21205			−0.196602
$460$	−40.2919	+	53.3551i	−1.87862	+	2.48770i
$461$	16.1680	+	3.02232i	0.753019	+	0.140764i	0.546246	−	0.837625i	$-0.316057\pi$
$461$	16.1680	+	3.02232i	0.753019	+	0.140764i	0.206774	+	0.978389i	$0.433704\pi$
$462$	0.712443	−	2.50398i	0.0331459	−	0.116496i
$463$	−25.3881	−	15.7196i	−1.17988	−	0.730554i	−0.210860	−	0.977516i	$-0.567626\pi$
$463$	−25.3881	−	15.7196i	−1.17988	−	0.730554i	−0.969025	+	0.246963i	$0.920568\pi$
$464$	−138.371	−	85.6758i	−6.42372	−	3.97740i
$465$	0.771812	−	2.71264i	0.0357919	−	0.125796i
$466$	37.0533	+	6.92647i	1.71646	+	0.320863i
$467$	−22.3016	+	29.5321i	−1.03200	+	1.36658i	−0.103756	+	0.994603i	$0.533086\pi$
$467$	−22.3016	+	29.5321i	−1.03200	+	1.36658i	−0.928240	+	0.371981i	$0.878679\pi$
$468$	31.3729			1.45021
$469$	−1.84847			−0.0853543
$470$	58.5292	−	77.5052i	2.69975	−	3.57505i
$471$	0.447183	+	4.82587i	0.0206051	+	0.222364i
$472$	121.258	−	22.6670i	5.58134	−	1.04333i
$473$	8.81659	−	8.03738i	0.405387	−	0.369559i
$474$	−23.2464	−	9.00569i	−1.06774	−	0.413645i
$475$	−0.0970221	−	0.194847i	−0.00445168	−	0.00894018i
$476$	16.9922	−	3.17639i	0.778836	−	0.145590i
$477$	0.993383	+	3.49138i	0.0454839	+	0.159859i
$478$	−6.65973	−	1.24492i	−0.304609	−	0.0569413i
$479$	−2.81808	−	30.4120i	−0.128762	−	1.38956i	−0.777661	−	0.628684i	$-0.783594\pi$
$479$	−2.81808	−	30.4120i	−0.128762	−	1.38956i	0.648899	−	0.760874i	$-0.275230\pi$
$480$	−17.2259	−	60.5428i	−0.786252	−	2.76339i
$481$	−5.26798	+	18.5150i	−0.240199	+	0.844212i
$482$	−17.8990	−	16.3171i	−0.815276	−	0.743222i
$483$	3.13965	+	1.21631i	0.142859	+	0.0553438i
$484$	31.3540	+	41.5194i	1.42518	+	1.88725i
$485$	25.1640	+	9.74859i	1.14264	+	0.442661i
$486$	2.56426	−	0.993401i	0.116317	−	0.0450616i
$487$	−5.90337	−	3.65521i	−0.267507	−	0.165633i	0.386124	−	0.922447i	$-0.373814\pi$
$487$	−5.90337	−	3.65521i	−0.267507	−	0.165633i	−0.653631	+	0.756814i	$0.726755\pi$
$488$	62.1954	+	56.6986i	2.81545	+	2.56662i
$489$	−1.19984	−	2.40961i	−0.0542589	−	0.108966i
$490$	−34.5572	+	31.5030i	−1.56113	+	1.42316i
$491$	−8.15280	+	3.15841i	−0.367931	+	0.142537i	−0.538107	−	0.842877i	$-0.680860\pi$
$491$	−8.15280	+	3.15841i	−0.367931	+	0.142537i	0.170176	+	0.985414i	$0.445566\pi$
$492$	7.45940	+	4.61867i	0.336296	+	0.208226i
$493$	−19.3213	+	38.8023i	−0.870186	+	1.74757i
$494$	1.71216	−	0.320058i	0.0770336	−	0.0144001i
$495$	−0.311836	+	3.36525i	−0.0140160	+	0.151257i
$496$	4.63383	−	16.2862i	0.208065	−	0.731273i
$497$	−0.972146	+	1.95233i	−0.0436067	+	0.0875741i
$498$	−31.5884	+	28.7967i	−1.41551	+	1.29041i
$499$	−9.18196	−	12.1589i	−0.411041	−	0.544306i	0.544656	−	0.838660i	$-0.316660\pi$
$499$	−9.18196	−	12.1589i	−0.411041	−	0.544306i	−0.955697	+	0.294354i	$0.904896\pi$
$500$	27.0333	+	35.7979i	1.20897	+	1.60093i
$501$	−0.603038	−	1.21106i	−0.0269417	−	0.0541063i
$502$	0.923490	−	9.96604i	0.0412174	−	0.444806i
$503$	15.3835	+	2.87568i	0.685918	+	0.128220i	0.515162	−	0.857093i	$-0.327732\pi$
$503$	15.3835	+	2.87568i	0.685918	+	0.128220i	0.170756	+	0.985313i	$0.445379\pi$
$504$	−6.14533	+	3.80503i	−0.273735	+	0.169489i
$505$	1.97080	−	2.60977i	0.0876996	−	0.116133i
$506$	13.6895	−	8.47620i	0.608574	−	0.376813i
$507$	1.73583	+	18.7326i	0.0770908	+	0.831942i
$508$	4.99072	−	53.8585i	0.221428	−	2.38958i
$509$	−0.986253	−	0.899089i	−0.0437149	−	0.0398514i	0.651543	−	0.758611i	$-0.274122\pi$
$509$	−0.986253	−	0.899089i	−0.0437149	−	0.0398514i	−0.695258	+	0.718760i	$0.744710\pi$
$510$	−28.4500	+	11.0216i	−1.25979	+	0.488044i
$511$	4.53872	−	9.11497i	0.200781	−	0.403223i
$512$	−18.6293	−	65.4753i	−0.823307	−	2.89362i
$513$	0.0954783	−	0.0591176i	0.00421547	−	0.00261011i
$514$	−53.2408			−2.34835
$515$	−20.0280	+	17.7065i	−0.882541	+	0.780242i
$516$	−51.7198			−2.27684
$517$	−14.6266	+	9.05641i	−0.643277	+	0.398300i
$518$	−1.89509	−	6.66055i	−0.0832655	−	0.292648i
$519$	−1.37370	+	2.75876i	−0.0602987	+	0.121096i
$520$	135.712	−	52.5751i	5.95136	−	2.30557i
$521$	−6.71832	−	6.12456i	−0.294335	−	0.268322i	0.513034	−	0.858368i	$-0.328521\pi$
$521$	−6.71832	−	6.12456i	−0.294335	−	0.268322i	−0.807370	+	0.590046i	$0.799110\pi$
$522$	2.61120	−	28.1794i	0.114289	−	1.23338i
$523$	−1.47637	−	15.9326i	−0.0645573	−	0.696684i	−0.965094	−	0.261904i	$-0.915650\pi$
$523$	−1.47637	−	15.9326i	−0.0645573	−	0.696684i	0.900537	−	0.434780i	$-0.143174\pi$
$524$	57.9244	−	35.8653i	2.53044	−	1.56678i
$525$	−0.861847	+	1.14127i	−0.0376141	+	0.0498091i
$526$	−1.40905	+	0.872449i	−0.0614376	+	0.0380406i
$527$	−4.43308	−	0.828686i	−0.193108	−	0.0360981i
$528$	−1.87221	+	20.2044i	−0.0814775	+	0.879282i
$529$	−0.969817	−	1.94766i	−0.0421660	−	0.0846807i
$530$	15.8456	+	20.9829i	0.688287	+	0.911439i
$531$	7.58869	+	10.0490i	0.329321	+	0.436091i
$532$	−0.340595	+	0.310493i	−0.0147667	+	0.0134616i
$533$	−3.96553	+	7.96387i	−0.171766	+	0.344953i
$534$	−4.57906	+	16.0937i	−0.198155	+	0.696443i
$535$	−1.70098	+	18.3565i	−0.0735399	+	0.793622i
$536$	24.1240	−	4.50955i	1.04200	−	0.194783i
$537$	−1.97528	+	3.96690i	−0.0852396	+	0.171184i
$538$	−13.3845	−	8.28731i	−0.577045	−	0.357291i
$539$	7.72360	−	2.99214i	0.332679	−	0.128881i
$540$	10.8275	−	9.87059i	0.465942	−	0.424762i
$541$	9.37881	+	18.8352i	0.403227	+	0.809788i	0.999973	+	0.00735841i	$0.00234228\pi$
$541$	9.37881	+	18.8352i	0.403227	+	0.809788i	−0.596746	+	0.802430i	$0.703540\pi$
$542$	−15.3657	−	14.0077i	−0.660014	−	0.601682i
$543$	−11.7333	−	7.26495i	−0.503524	−	0.311769i
$544$	−93.8578	+	36.3607i	−4.02412	+	1.55895i
$545$	−14.8187	−	5.74080i	−0.634764	−	0.245909i
$546$	−6.89671	−	9.13272i	−0.295152	−	0.390844i
$547$	−21.8139	−	8.45074i	−0.932693	−	0.361327i	−0.153527	−	0.988144i	$-0.549063\pi$
$547$	−21.8139	−	8.45074i	−0.932693	−	0.361327i	−0.779166	+	0.626817i	$0.784357\pi$
$548$	34.3446	+	31.3093i	1.46713	+	1.33747i
$549$	−2.35109	+	8.26322i	−0.100342	+	0.352666i
$550$	1.87157	+	6.57789i	0.0798040	+	0.280482i
$551$	−0.106632	−	1.15075i	−0.00454269	−	0.0490234i
$552$	−43.9422	−	8.21422i	−1.87030	−	0.349620i
$553$	1.83050	+	6.43353i	0.0778406	+	0.273581i
$554$	−29.6094	+	5.53495i	−1.25798	+	0.235158i
$555$	4.00712	+	8.04739i	0.170093	+	0.341593i
$556$	46.0521	+	17.8407i	1.95304	+	0.756613i
$557$	6.20423	−	5.65591i	0.262882	−	0.239648i	−0.531513	−	0.847050i	$-0.678376\pi$
$557$	6.20423	−	5.65591i	0.262882	−	0.239648i	0.794395	+	0.607402i	$0.207788\pi$
$558$	2.89426	−	0.541031i	0.122524	−	0.0229037i
$559$	−4.83902	−	52.2213i	−0.204669	−	2.20873i
$560$	−18.5223	+	24.5275i	−0.782709	+	1.03647i
$561$	5.40433			0.228171
$562$	33.2191			1.40126
$563$	−8.32138	+	11.0193i	−0.350704	+	0.464408i	−0.938840	−	0.344355i	$-0.888098\pi$
$563$	−8.32138	+	11.0193i	−0.350704	+	0.464408i	0.588135	+	0.808763i	$0.299862\pi$
$564$	73.3096	+	13.7039i	3.08689	+	0.577040i
$565$	8.65008	−	30.4019i	0.363912	−	1.27902i
$566$	6.44992	+	3.99362i	0.271110	+	0.167864i
$567$	−0.627321	−	0.388421i	−0.0263450	−	0.0163121i
$568$	7.92433	−	27.8511i	0.332497	−	1.16861i
$569$	−3.17311	−	0.593157i	−0.133024	−	0.0248664i	0.116817	−	0.993154i	$-0.462731\pi$
$569$	−3.17311	−	0.593157i	−0.133024	−	0.0248664i	−0.249840	+	0.968287i	$0.580378\pi$
$570$	0.490209	−	0.649141i	0.0205326	−	0.0271895i
$571$	41.4711			1.73551			0.867755	−	0.496993i	$-0.165562\pi$
$571$	41.4711			1.73551			0.867755	+	0.496993i	$0.165562\pi$
$572$	−40.2533			−1.68308
$573$	7.96935	−	10.5531i	0.332924	−	0.440863i
$574$	−0.295298	−	3.18677i	−0.0123255	−	0.133013i
$575$	−8.69445	+	1.62528i	−0.362584	+	0.0677787i
$576$	25.1902	−	22.9639i	1.04959	−	0.956829i
$577$	38.6336	+	14.9667i	1.60834	+	0.623073i	0.987036	−	0.160498i	$-0.0513101\pi$
$577$	38.6336	+	14.9667i	1.60834	+	0.623073i	0.621302	+	0.783572i	$0.286604\pi$
$578$	0.908787	+	1.82509i	0.0378006	+	0.0759138i
$579$	18.4040	−	3.44030i	0.764843	−	0.142974i
$580$	−41.2626	−	145.023i	−1.71334	−	6.02175i
$581$	11.2734	+	2.10736i	0.467698	+	0.0874280i
$582$	2.59955	+	28.0536i	0.107755	+	1.16286i
$583$	−1.27457	−	4.47966i	−0.0527874	−	0.185528i
$584$	−36.9968	+	130.030i	−1.53094	+	5.38069i
$585$	10.9793	+	10.0090i	0.453940	+	0.413821i
$586$	27.3645	+	10.6011i	1.13042	+	0.437925i
$587$	−2.67404	−	3.54101i	−0.110370	−	0.146153i	0.739479	−	0.673179i	$-0.235072\pi$
$587$	−2.67404	−	3.54101i	−0.110370	−	0.146153i	−0.849849	+	0.527026i	$0.823307\pi$
$588$	−33.4831	−	12.9714i	−1.38082	−	0.534932i
$589$	0.112119	−	0.0434352i	0.00461979	−	0.00178972i
$590$	77.5523	+	48.0184i	3.19278	+	1.97688i
$591$	6.58670	+	6.00457i	0.270941	+	0.246995i
$592$	24.0581	+	48.3151i	0.988781	+	1.98574i
$593$	−11.4264	+	10.4165i	−0.469226	+	0.427756i	−0.873457	−	0.486901i	$-0.838127\pi$
$593$	−11.4264	+	10.4165i	−0.469226	+	0.427756i	0.404232	+	0.914657i	$0.367539\pi$
$594$	−3.29011	+	1.27459i	−0.134995	+	0.0522972i
$595$	6.96001	+	4.30946i	0.285333	+	0.176671i
$596$	42.7878	−	85.9294i	1.75265	−	3.51980i
$597$	9.96604	−	1.86298i	0.407883	−	0.0762465i
$598$	6.53078	−	70.4783i	0.267063	−	2.88207i
$599$	6.25011	−	21.9669i	0.255372	−	0.897541i	−0.723027	−	0.690819i	$-0.757250\pi$
$599$	6.25011	−	21.9669i	0.255372	−	0.897541i	0.978400	−	0.206722i	$-0.0662795\pi$
$600$	8.46353	−	16.9971i	0.345522	−	0.693902i
$601$	−31.5219	+	28.7360i	−1.28580	+	1.17217i	−0.310678	+	0.950515i	$0.600556\pi$
$601$	−31.5219	+	28.7360i	−1.28580	+	1.17217i	−0.975126	+	0.221651i	$0.928856\pi$
$602$	11.3696	+	15.0557i	0.463389	+	0.613626i
$603$	1.50975	+	1.99923i	0.0614819	+	0.0814151i
$604$	31.0518	+	62.3604i	1.26348	+	2.53741i
$605$	−2.27334	+	24.5333i	−0.0924244	+	0.997419i
$606$	3.35607	+	0.627359i	0.136331	+	0.0254847i
$607$	9.71922	−	6.01789i	0.394491	−	0.244258i	−0.314824	−	0.949150i	$-0.601946\pi$
$607$	9.71922	−	6.01789i	0.394491	−	0.244258i	0.709315	+	0.704892i	$0.249004\pi$
$608$	1.61722	−	2.14155i	0.0655869	−	0.0868511i
$609$	−6.45582	+	3.99728i	−0.261603	+	0.161978i
$610$	5.74193	+	61.9653i	0.232484	+	2.50890i
$611$	−6.97782	+	75.3027i	−0.282292	+	3.04642i
$612$	−17.3140	−	15.7838i	−0.699876	−	0.638022i
$613$	14.9336	−	5.78531i	0.603162	−	0.233666i	−0.0402456	−	0.999190i	$-0.512814\pi$
$613$	14.9336	−	5.78531i	0.603162	−	0.233666i	0.643408	+	0.765523i	$0.277520\pi$
$614$	−19.2060	+	38.5708i	−0.775091	+	1.55659i
$615$	1.13701	+	3.99616i	0.0458485	+	0.161141i
$616$	7.88484	−	4.88209i	0.317689	−	0.196705i
$617$	20.9348			0.842804			0.421402	−	0.906874i	$-0.361538\pi$
$617$	20.9348			0.842804			0.421402	+	0.906874i	$0.361538\pi$
$618$	−25.8677	−	10.4775i	−1.04055	−	0.421466i
$619$	−16.6256			−0.668241			−0.334120	−	0.942530i	$-0.608439\pi$
$619$	−16.6256			−0.668241			−0.334120	+	0.942530i	$0.608439\pi$
$620$	13.3376	−	8.25831i	0.535652	−	0.331662i
$621$	−1.24882	−	4.38916i	−0.0501135	−	0.176131i
$622$	−1.21452	+	2.43909i	−0.0486980	+	0.0977987i
$623$	4.18629	−	1.62178i	0.167720	−	0.0649752i
$624$	65.9181	+	60.0923i	2.63884	+	2.40562i
$625$	−2.85427	+	30.8025i	−0.114171	+	1.23210i
$626$	3.27066	+	35.2960i	0.130722	+	1.41071i
$627$	−0.122504	+	0.0758516i	−0.00489236	+	0.00302922i
$628$	−16.2457	+	21.5128i	−0.648276	+	0.858456i
$629$	12.2222	−	7.56769i	0.487332	−	0.301744i
$630$	−5.25357	−	0.982062i	−0.209307	−	0.0391263i
$631$	3.60116	−	38.8628i	0.143360	−	1.54710i	−0.555301	−	0.831649i	$-0.687397\pi$
$631$	3.60116	−	38.8628i	0.143360	−	1.54710i	0.698661	−	0.715453i	$-0.253779\pi$
$632$	−39.5848	−	79.4969i	−1.57460	−	3.16222i
$633$	1.69317	+	2.24213i	0.0672976	+	0.0891165i
$634$	43.3407	+	57.3923i	1.72128	+	2.27934i
$635$	18.9292	−	17.2563i	0.751184	−	0.684794i
$636$	−8.99983	+	18.0741i	−0.356866	+	0.716684i
$637$	9.96445	−	35.0214i	0.394806	−	1.38760i
$638$	−3.35034	+	36.1559i	−0.132641	+	1.43143i
$639$	2.90558	−	0.543147i	0.114943	−	0.0214866i
$640$	53.9415	−	108.329i	2.13222	−	4.28208i
$641$	−9.97157	−	6.17413i	−0.393853	−	0.243864i	0.315190	−	0.949029i	$-0.397932\pi$
$641$	−9.97157	−	6.17413i	−0.393853	−	0.243864i	−0.709043	+	0.705165i	$0.750873\pi$
$642$	−17.9467	+	6.95258i	−0.708298	+	0.274396i
$643$	1.09640	−	0.999504i	0.0432379	−	0.0394166i	−0.651788	−	0.758401i	$-0.725981\pi$
$643$	1.09640	−	0.999504i	0.0432379	−	0.0394166i	0.695026	+	0.718984i	$0.255393\pi$
$644$	8.34792	+	16.7649i	0.328954	+	0.660629i
$645$	−18.1000	−	16.5003i	−0.712687	−	0.649700i
$646$	−1.10592	−	0.684759i	−0.0435120	−	0.0269415i
$647$	19.2427	−	7.45468i	0.756510	−	0.293074i	0.0480696	−	0.998844i	$-0.484693\pi$
$647$	19.2427	−	7.45468i	0.756510	−	0.293074i	0.708441	+	0.705770i	$0.249399\pi$
$648$	9.13464	+	3.53878i	0.358842	+	0.139016i
$649$	−9.73675	−	12.8935i	−0.382201	−	0.506116i
$650$	28.0336	+	10.8603i	1.09957	+	0.425976i
$651$	−0.583821	−	0.532223i	−0.0228817	−	0.0208595i
$652$	4.09746	−	14.4011i	0.160469	−	0.563989i
$653$	−8.32864	−	29.2721i	−0.325925	−	1.14551i	−0.935660	−	0.352902i	$-0.885195\pi$
$653$	−8.32864	−	29.2721i	−0.325925	−	1.14551i	0.609735	−	0.792605i	$-0.291276\pi$
$654$	−1.53083	−	16.5203i	−0.0598603	−	0.645996i
$655$	31.7136	+	5.92830i	1.23915	+	0.231638i
$656$	6.82639	+	23.9923i	0.266526	+	0.936741i
$657$	−13.5655	+	2.53582i	−0.529239	+	0.0989319i
$658$	−12.1264	−	24.3531i	−0.472737	−	0.949385i
$659$	−24.8167	−	9.61403i	−0.966721	−	0.374510i	−0.174441	−	0.984668i	$-0.555812\pi$
$659$	−24.8167	−	9.61403i	−0.966721	−	0.374510i	−0.792280	+	0.610158i	$0.791106\pi$
$660$	−13.8924	+	12.6646i	−0.540760	+	0.492968i
$661$	−10.1241	+	1.89252i	−0.393782	+	0.0736105i	−0.376917	−	0.926247i	$-0.623016\pi$
$661$	−10.1241	+	1.89252i	−0.393782	+	0.0736105i	−0.0168651	+	0.999858i	$0.505369\pi$
$662$	−0.443530	−	4.78645i	−0.0172383	−	0.186031i
$663$	14.3169	−	18.9586i	0.556022	−	0.736293i
$664$	−152.268			−5.90913
$665$	−0.218253			−0.00846350
$666$	−5.65597	+	7.48972i	−0.219165	+	0.290221i
$667$	−46.1623	−	8.62924i	−1.78741	−	0.334125i
$668$	2.05937	−	7.23793i	0.0796794	−	0.280044i
$669$	−2.13037	−	1.31907i	−0.0823648	−	0.0509981i
$670$	15.4289	+	9.55314i	0.596069	+	0.369070i
$671$	3.01659	−	10.6022i	0.116454	−	0.409294i
$672$	−17.3317	−	3.23986i	−0.668587	−	0.124980i
$673$	−9.28441	+	12.2945i	−0.357888	+	0.473920i	−0.940968	−	0.338494i	$-0.890082\pi$
$673$	−9.28441	+	12.2945i	−0.357888	+	0.473920i	0.583081	+	0.812414i	$0.301847\pi$
$674$	20.4695			0.788455
$675$	1.93828			0.0746044
$676$	−63.0610	+	83.5063i	−2.42542	+	3.21178i
$677$	0.0194577	+	0.209982i	0.000747821	+	0.00807027i	0.996100	−	0.0882325i	$-0.0281218\pi$
$677$	0.0194577	+	0.209982i	0.000747821	+	0.00807027i	−0.995352	+	0.0963027i	$0.969298\pi$
$678$	32.4374	−	6.06361i	1.24575	−	0.232871i
$679$	5.58635	−	5.09263i	0.214384	−	0.195437i
$680$	−101.347	−	39.2621i	−3.88648	−	1.50563i
$681$	−11.9997	−	24.0987i	−0.459831	−	0.923466i
$682$	−3.71352	+	0.694177i	−0.142198	+	0.0265814i
$683$	10.0862	+	35.4491i	0.385936	+	1.35642i	0.874978	+	0.484163i	$0.160876\pi$
$683$	10.0862	+	35.4491i	0.385936	+	1.35642i	−0.489042	+	0.872260i	$0.662653\pi$
$684$	0.614002	+	0.114777i	0.0234769	+	0.00438860i
$685$	2.03065	+	21.9142i	0.0775870	+	0.837297i
$686$	7.47147	+	26.2595i	0.285262	+	1.00259i
$687$	2.41560	−	8.48997i	0.0921611	−	0.323913i
$688$	−108.669	−	99.0652i	−4.14298	−	3.77683i
$689$	−19.0914	−	7.39605i	−0.727324	−	0.281767i
$690$	−19.9201	−	26.3785i	−0.758345	−	1.00421i
$691$	33.0532	+	12.8049i	1.25740	+	0.487121i	0.895486	−	0.445090i	$-0.146828\pi$
$691$	33.0532	+	12.8049i	1.25740	+	0.487121i	0.361917	+	0.932210i	$0.382122\pi$
$692$	−15.9846	+	6.19245i	−0.607642	+	0.235402i
$693$	0.804892	+	0.498368i	0.0305753	+	0.0189314i
$694$	2.88527	+	2.63028i	0.109524	+	0.0998439i
$695$	10.4248	+	20.9357i	0.395434	+	0.794138i
$696$	74.5017	−	67.9173i	2.82398	−	2.57440i
$697$	6.19513	−	2.40001i	0.234657	−	0.0909068i
$698$	−51.7566	−	32.0464i	−1.95902	−	1.21297i
$699$	−6.10997	+	12.2705i	−0.231100	+	0.464112i
$700$	−7.81936	+	1.46169i	−0.295544	+	0.0552468i
$701$	2.86082	−	30.8732i	0.108052	−	1.16606i	−0.753167	−	0.657829i	$-0.771475\pi$
$701$	2.86082	−	30.8732i	0.108052	−	1.16606i	0.861219	−	0.508234i	$-0.169702\pi$
$702$	−4.24467	+	14.9185i	−0.160205	+	0.563061i
$703$	−0.170837	+	0.343087i	−0.00644323	+	0.0129398i
$704$	−32.3206	+	29.4641i	−1.21813	+	1.11047i
$705$	21.2836	+	28.1841i	0.801588	+	1.06147i
$706$	−29.9759	−	39.6945i	−1.12816	−	1.49392i
$707$	−0.408323	−	0.820023i	−0.0153566	−	0.0308401i
$708$	−6.46277	+	69.7444i	−0.242886	+	2.62115i
$709$	−22.9824	−	4.29615i	−0.863121	−	0.161345i	−0.266467	−	0.963844i	$-0.585856\pi$
$709$	−22.9824	−	4.29615i	−0.863121	−	0.161345i	−0.596654	+	0.802499i	$0.703504\pi$
$710$	18.2043	−	11.2716i	0.683194	−	0.423016i
$711$	5.46319	−	7.23444i	0.204886	−	0.271313i
$712$	−50.6779	+	31.3784i	−1.89923	+	1.17596i
$713$	−0.450824	−	4.86517i	−0.0168835	−	0.182202i
$714$	−0.788558	+	8.50990i	−0.0295110	+	0.318475i
$715$	−14.0872	−	12.8422i	−0.526831	−	0.480270i
$716$	−22.9846	+	8.90430i	−0.858977	+	0.332769i
$717$	1.09817	−	2.20542i	0.0410118	−	0.0823628i
$718$	−20.1883	−	70.9547i	−0.753422	−	2.64801i
$719$	1.32270	−	0.818982i	0.0493284	−	0.0305429i	−0.501546	−	0.865131i	$-0.667235\pi$
$719$	1.32270	−	0.818982i	0.0493284	−	0.0305429i	0.550875	+	0.834588i	$0.314294\pi$
$720$	41.6562			1.55244
$721$	1.93921	+	7.23277i	0.0722201	+	0.269362i
$722$	−52.2146			−1.94323
$723$	7.48827	−	4.63654i	0.278492	−	0.172435i
$724$	−21.0068	−	73.8312i	−0.780711	−	2.74392i
$725$	8.89114	−	17.8558i	0.330209	−	0.663148i
$726$	−23.9855	+	9.29202i	−0.890184	+	0.344859i
$727$	7.72542	+	7.04265i	0.286520	+	0.261197i	0.804176	−	0.594391i	$-0.202607\pi$
$727$	7.72542	+	7.04265i	0.286520	+	0.261197i	−0.517656	+	0.855589i	$0.673195\pi$
$728$	3.76157	−	40.5938i	0.139413	−	1.50451i
$729$	0.0922684	+	0.995734i	0.00341735	+	0.0368790i
$730$	−84.9914	+	52.6244i	−3.14567	+	1.94772i
$731$	−23.6021	+	31.2543i	−0.872957	+	1.15598i
$732$	−40.6290	+	25.1564i	−1.50169	+	0.929808i
$733$	−26.2716	−	4.91101i	−0.970363	−	0.181392i	−0.325375	−	0.945585i	$-0.605491\pi$
$733$	−26.2716	−	4.91101i	−0.970363	−	0.181392i	−0.644988	+	0.764193i	$0.723138\pi$
$734$	−0.816166	+	8.80783i	−0.0301252	+	0.325103i
$735$	−7.57953	−	15.2217i	−0.279575	−	0.561463i
$736$	−65.7172	−	87.0236i	−2.42237	−	3.20773i
$737$	−1.93711	−	2.56514i	−0.0713542	−	0.0944882i
$738$	−3.20551	+	2.92221i	−0.117996	+	0.107568i
$739$	−18.1383	+	36.4265i	−0.667227	+	1.33997i	0.260050	+	0.965595i	$0.416261\pi$
$739$	−18.1383	+	36.4265i	−0.667227	+	1.33997i	−0.927277	+	0.374377i	$0.877857\pi$
$740$	−13.6843	+	48.0953i	−0.503044	+	1.76802i
$741$	−0.0584425	+	0.630695i	−0.00214694	+	0.0231691i
$742$	7.23985	−	1.35336i	0.265783	−	0.0496835i
$743$	10.1745	−	20.4331i	0.373265	−	0.749617i	−0.626286	−	0.779594i	$-0.715426\pi$
$743$	10.1745	−	20.4331i	0.373265	−	0.749617i	0.999551	+	0.0299765i	$0.00954326\pi$
$744$	8.91774	+	5.52163i	0.326940	+	0.202433i
$745$	42.3885	−	16.4214i	1.55299	−	0.601633i
$746$	30.3870	−	27.7014i	1.11255	−	1.01422i
$747$	−6.92839	−	13.9141i	−0.253496	−	0.509089i
$748$	22.2149	+	20.2516i	0.812258	+	0.740471i
$749$	4.39047	+	2.71847i	0.160424	+	0.0993306i
$750$	−20.6802	+	8.01154i	−0.755133	+	0.292540i
$751$	25.2912	+	9.79786i	0.922889	+	0.357529i	0.775353	−	0.631528i	$-0.217572\pi$
$751$	25.2912	+	9.79786i	0.922889	+	0.357529i	0.147536	+	0.989057i	$0.452866\pi$
$752$	127.783	+	169.213i	4.65978	+	6.17055i
$753$	3.39382	+	1.31477i	0.123678	+	0.0479130i
$754$	117.961	+	107.536i	4.29589	+	3.91622i
$755$	−9.02807	+	31.7304i	−0.328565	+	1.15479i
$756$	−1.12313	−	3.94739i	−0.0408478	−	0.143565i
$757$	−2.97663	−	32.1230i	−0.108188	−	1.16753i	−0.860757	−	0.509017i	$-0.830009\pi$
$757$	−2.97663	−	32.1230i	−0.108188	−	1.16753i	0.752569	−	0.658514i	$-0.228814\pi$
$758$	35.3397	+	6.60614i	1.28360	+	0.239946i
$759$	1.60232	+	5.63156i	0.0581604	+	0.204413i
$760$	2.84838	−	0.532454i	0.103321	−	0.0193141i
$761$	−17.3520	−	34.8475i	−0.629010	−	1.26322i	−0.948843	−	0.315749i	$-0.897744\pi$
$761$	−17.3520	−	34.8475i	−0.629010	−	1.26322i	0.319833	−	0.947474i	$-0.396373\pi$
$762$	24.9356	+	9.66010i	0.903322	+	0.349949i
$763$	−3.28972	+	2.99897i	−0.119096	+	0.108570i
$764$	72.3042	−	13.5160i	2.61587	−	0.488992i
$765$	−1.02370	−	11.0475i	−0.0370119	−	0.399423i
$766$	−47.8850	+	63.4099i	−1.73015	+	2.29109i
$767$	−71.0254			−2.56458
$768$	58.1679			2.09895
$769$	−29.2270	+	38.7028i	−1.05395	+	1.39566i	−0.139850	+	0.990173i	$0.544662\pi$
$769$	−29.2270	+	38.7028i	−1.05395	+	1.39566i	−0.914102	+	0.405485i	$0.867103\pi$
$770$	6.74065	+	1.26005i	0.242916	+	0.0454089i
$771$	5.29827	−	18.6215i	0.190813	−	0.670637i
$772$	88.5428	+	54.8234i	3.18672	+	1.97314i
$773$	−18.2072	−	11.2734i	−0.654866	−	0.405476i	0.158394	−	0.987376i	$-0.449368\pi$
$773$	−18.2072	−	11.2734i	−0.654866	−	0.405476i	−0.813260	+	0.581900i	$0.802309\pi$
$774$	6.99755	−	24.5938i	0.251522	−	0.884007i
$775$	2.03999	+	0.381340i	0.0732785	+	0.0136981i
$776$	−60.4822	+	80.0914i	−2.17118	+	2.87511i
$777$	2.51818			0.0903393
$778$	92.6783			3.32268
$779$	−0.106745	+	0.141354i	−0.00382455	+	0.00506453i
$780$	7.62488	+	82.2856i	0.273014	+	2.94630i
$781$	−3.72804	+	0.696891i	−0.133400	+	0.0249367i
$782$	−39.0620	+	35.6098i	−1.39686	+	1.27340i
$783$	9.59616	+	3.71757i	0.342939	+	0.132855i
$784$	−45.5062	−	91.3888i	−1.62522	−	3.26388i
$785$	−12.5487	+	2.34576i	−0.447883	+	0.0837239i
$786$	9.21766	+	32.3967i	0.328783	+	1.15555i
$787$	41.6878	+	7.79280i	1.48601	+	0.277783i	0.863308	−	0.504677i	$-0.168388\pi$
$787$	41.6878	+	7.79280i	1.48601	+	0.277783i	0.622700	+	0.782460i	$0.286036\pi$
$788$	4.57430	+	49.3646i	0.162953	+	1.75854i
$789$	−0.164925	−	0.579652i	−0.00587149	−	0.0206362i
$790$	17.9705	−	63.1599i	0.639363	−	2.24713i
$791$	−6.54317	−	5.96489i	−0.232648	−	0.212087i
$792$	−11.7203	−	4.54047i	−0.416463	−	0.161339i
$793$	−29.2017	−	38.6693i	−1.03698	−	1.37319i
$794$	−7.14966	−	2.76979i	−0.253732	−	0.0982963i
$795$	−8.91585	+	3.45402i	−0.316213	+	0.122501i
$796$	47.9473	+	29.6877i	1.69945	+	1.05225i
$797$	18.8253	+	17.1616i	0.666828	+	0.607894i	0.934648	−	0.355575i	$-0.115715\pi$
$797$	18.8253	+	17.1616i	0.666828	+	0.607894i	−0.267820	+	0.963469i	$0.586303\pi$
$798$	−0.101564	−	0.203969i	−0.00359534	−	0.00722042i
$799$	41.7359	−	38.0473i	1.47651	−	1.34602i
$800$	43.1909	−	16.7322i	1.52703	−	0.591574i
$801$	−5.17325	−	3.20314i	−0.182788	−	0.113177i
$802$	18.0378	−	36.2248i	0.636937	−	1.27914i
$803$	17.4053	−	3.25362i	0.614220	−	0.114818i
$804$	−1.28575	+	13.8755i	−0.0453450	+	0.489351i
$805$	−2.42710	+	8.53036i	−0.0855439	+	0.300656i
$806$	−7.40248	+	14.8662i	−0.260741	+	0.523639i
$807$	4.23052	−	3.85663i	0.148922	−	0.135760i
$808$	7.32947	+	9.70579i	0.257850	+	0.341449i
$809$	−28.1441	−	37.2688i	−0.989494	−	1.31030i	−0.950388	−	0.311066i	$-0.899314\pi$
$809$	−28.1441	−	37.2688i	−0.989494	−	1.31030i	−0.0391055	−	0.999235i	$-0.512451\pi$
$810$	3.22873	+	6.48417i	0.113446	+	0.227831i
$811$	1.62391	−	17.5247i	0.0570230	−	0.615377i	−0.918491	−	0.395441i	$-0.870592\pi$
$811$	1.62391	−	17.5247i	0.0570230	−	0.615377i	0.975514	−	0.219936i	$-0.0705847\pi$
$812$	−41.5161	−	7.76071i	−1.45693	−	0.272347i
$813$	6.42845	−	3.98033i	0.225455	−	0.139596i
$814$	7.25696	−	9.60977i	0.254356	−	0.336822i
$815$	6.02838	−	3.73262i	0.211165	−	0.130748i
$816$	−6.14612	−	66.3272i	−0.215157	−	2.32192i
$817$	0.0963453	−	1.03973i	0.00337070	−	0.0363756i
$818$	37.0581	+	33.7829i	1.29571	+	1.18119i
$819$	3.88059	−	1.50335i	0.135599	−	0.0525312i
$820$	−10.3010	+	20.6872i	−0.359727	+	0.722429i
$821$	4.81871	+	16.9360i	0.168174	+	0.591071i	0.999383	+	0.0351113i	$0.0111786\pi$
$821$	4.81871	+	16.9360i	0.168174	+	0.591071i	−0.831209	+	0.555960i	$0.812351\pi$
$822$	−19.5349	+	12.0955i	−0.681359	+	0.421880i
$823$	−15.2179			−0.530461			−0.265231	−	0.964185i	$-0.585448\pi$
$823$	−15.2179			−0.530461			−0.265231	+	0.964185i	$0.585448\pi$
$824$	−42.9534	−	89.6624i	−1.49635	−	3.12354i
$825$	−2.48693			−0.0865838
$826$	21.7235	−	13.4506i	0.755856	−	0.468006i
$827$	−2.42357	−	8.51797i	−0.0842758	−	0.296199i	0.908217	−	0.418499i	$-0.137444\pi$
$827$	−2.42357	−	8.51797i	−0.0842758	−	0.296199i	−0.992493	+	0.122300i	$0.960973\pi$
$828$	11.3140	−	22.7217i	0.393190	−	0.789633i
$829$	−23.2569	+	9.00979i	−0.807747	+	0.312923i	−0.729474	−	0.684009i	$-0.760235\pi$
$829$	−23.2569	+	9.00979i	−0.807747	+	0.312923i	−0.0782736	+	0.996932i	$0.524941\pi$
$830$	−83.2059	−	75.8522i	−2.88812	−	2.63287i
$831$	1.01068	−	10.9070i	0.0350601	−	0.378359i
$832$	17.7393	+	191.437i	0.614998	+	6.63689i
$833$	−23.1185	+	14.3144i	−0.801010	+	0.495964i
$834$	−14.7143	+	19.4849i	−0.509516	+	0.674708i
$835$	3.02984	−	1.87600i	0.104852	−	0.0649217i
$836$	−0.787802	−	0.147266i	−0.0272467	−	0.00509329i
$837$	−0.0987922	+	1.06614i	−0.00341476	+	0.0368511i
$838$	17.1242	+	34.3900i	0.591546	+	1.18798i
$839$	14.5353	+	19.2479i	0.501815	+	0.664510i	0.976468	−	0.215663i	$-0.0691912\pi$
$839$	14.5353	+	19.2479i	0.501815	+	0.664510i	−0.474653	+	0.880173i	$0.657426\pi$
$840$	−11.4735	−	15.1934i	−0.395873	−	0.524221i
$841$	56.8346	−	51.8116i	1.95982	−	1.78661i
$842$	41.2808	−	82.9030i	1.42263	−	2.85702i
$843$	−3.30580	+	11.6187i	−0.113858	+	0.400169i
$844$	−1.44196	+	15.5612i	−0.0496344	+	0.535640i
$845$	−48.7103	+	9.10554i	−1.67569	+	0.313240i
$846$	−16.4351	+	33.0061i	−0.565051	+	1.13477i
$847$	5.86781	+	3.63319i	0.201620	+	0.124838i
$848$	−53.5292	+	20.7373i	−1.83820	+	0.712123i
$849$	−2.03867	+	1.85850i	−0.0699671	+	0.0637834i
$850$	−10.0073	−	20.0974i	−0.343247	−	0.689334i
$851$	11.5096	+	10.4924i	0.394545	+	0.359675i
$852$	13.9789	+	8.65539i	0.478911	+	0.296529i
$853$	9.95371	−	3.85609i	0.340808	−	0.132030i	−0.184754	−	0.982785i	$-0.559149\pi$
$853$	9.95371	−	3.85609i	0.340808	−	0.132030i	0.525563	+	0.850755i	$0.323855\pi$
$854$	16.2546	+	6.29706i	0.556220	+	0.215481i
$855$	0.178260	+	0.236055i	0.00609637	+	0.00807290i
$856$	−63.9312	−	24.7671i	−2.18512	−	0.846521i
$857$	−28.6289	−	26.0987i	−0.977945	−	0.891515i	0.0161673	−	0.999869i	$-0.494854\pi$
$857$	−28.6289	−	26.0987i	−0.977945	−	0.891515i	−0.994112	+	0.108355i	$0.965442\pi$
$858$	5.44617	−	19.1413i	0.185929	−	0.653473i
$859$	12.8444	+	45.1435i	0.438246	+	1.54028i	0.795314	+	0.606198i	$0.207306\pi$
$859$	12.8444	+	45.1435i	0.438246	+	1.54028i	−0.357067	+	0.934079i	$0.616223\pi$
$860$	−12.5700	−	135.652i	−0.428633	−	4.62569i
$861$	1.14399	+	0.213849i	0.0389871	+	0.00728795i
$862$	−14.6470	−	51.4789i	−0.498879	−	1.75338i
$863$	45.7826	−	8.55826i	1.55846	−	0.291327i	0.667220	−	0.744860i	$-0.267484\pi$
$863$	45.7826	−	8.55826i	1.55846	−	0.291327i	0.891239	+	0.453534i	$0.149837\pi$
$864$	10.6517	+	21.3916i	0.362379	+	0.727756i
$865$	−7.56961	−	2.93248i	−0.257374	−	0.0997074i
$866$	−17.7563	+	16.1870i	−0.603384	+	0.550057i
$867$	−0.728781	+	0.136233i	−0.0247507	+	0.00462671i
$868$	−0.405449	−	4.37549i	−0.0137618	−	0.148514i
$869$	−7.00962	+	9.28223i	−0.237785	+	0.314878i
$870$	74.5442			2.52729
$871$	−14.1303			−0.478788
$872$	35.6171	−	47.1646i	1.20615	−	1.59719i
$873$	−10.0707	−	1.88254i	−0.340842	−	0.0637143i
$874$	0.385658	−	1.35545i	0.0130451	−	0.0458486i
$875$	5.05920	+	3.13252i	0.171032	+	0.105899i
$876$	−65.2643	−	40.4100i	−2.20508	−	1.36533i
$877$	15.3258	−	53.8647i	0.517516	−	1.81888i	−0.0543341	−	0.998523i	$-0.517304\pi$
$877$	15.3258	−	53.8647i	0.517516	−	1.81888i	0.571850	−	0.820358i	$-0.306226\pi$
$878$	38.3483	+	7.16854i	1.29419	+	0.241927i
$879$	−6.43100	+	8.51602i	−0.216912	+	0.287238i
$880$	−53.4475			−1.80172
$881$	−7.36630			−0.248177			−0.124089	−	0.992271i	$-0.539601\pi$
$881$	−7.36630			−0.248177			−0.124089	+	0.992271i	$0.539601\pi$
$882$	10.6984	−	14.1669i	0.360232	−	0.477025i
$883$	0.376858	+	4.06695i	0.0126823	+	0.136864i	0.999721	−	0.0236183i	$-0.00751864\pi$
$883$	0.376858	+	4.06695i	0.0126823	+	0.136864i	−0.987039	+	0.160482i	$0.948695\pi$
$884$	129.894	−	24.2814i	4.36882	−	0.816673i
$885$	−24.5125	+	22.3461i	−0.823979	+	0.751157i
$886$	30.8895	+	11.9666i	1.03775	+	0.402027i
$887$	12.4994	+	25.1021i	0.419688	+	0.842847i	0.999603	+	0.0281702i	$0.00896804\pi$
$887$	12.4994	+	25.1021i	0.419688	+	0.842847i	−0.579915	+	0.814677i	$0.696914\pi$
$888$	−32.8643	+	6.14339i	−1.10285	+	0.206159i
$889$	−1.96351	−	6.90103i	−0.0658541	−	0.231453i
$890$	−43.3239	−	8.09864i	−1.45222	−	0.271467i
$891$	−0.118386	−	1.27759i	−0.00396608	−	0.0428008i
$892$	−3.81412	−	13.4052i	−0.127706	−	0.448841i
$893$	−0.412056	+	1.44823i	−0.0137889	+	0.0484631i
$894$	35.0721	+	31.9725i	1.17299	+	1.06932i
$895$	−10.8845	−	4.21670i	−0.363830	−	0.140949i
$896$	−20.4283	−	27.0514i	−0.682460	−	0.903724i
$897$	24.0006	+	9.29787i	0.801356	+	0.310447i
$898$	−75.7312	+	29.3384i	−2.52718	+	0.979036i
$899$	9.36830	+	5.80061i	0.312450	+	0.193461i
$900$	7.96744	+	7.26329i	0.265581	+	0.242110i
$901$	6.81514	+	13.6866i	0.227045	+	0.455968i
$902$	4.11287	−	3.74937i	0.136943	−	0.124840i
$903$	−6.39734	+	2.47834i	−0.212890	+	0.0824741i
$904$	99.9456	+	61.8837i	3.32414	+	2.05822i
$905$	16.2030	−	32.5401i	0.538607	−	1.08167i
$906$	−33.8549	+	6.32857i	−1.12475	+	0.210253i
$907$	1.53164	−	16.5291i	0.0508574	−	0.548838i	−0.931745	−	0.363114i	$-0.881713\pi$
$907$	1.53164	−	16.5291i	0.0508574	−	0.548838i	0.982602	−	0.185724i	$-0.0594631\pi$
$908$	40.9790	−	144.026i	1.35994	−	4.77968i
$909$	−0.553405	+	1.11139i	−0.0183553	+	0.0368624i
$910$	22.2773	−	20.3085i	0.738487	−	0.673220i
$911$	16.7937	+	22.2385i	0.556400	+	0.736793i	0.986095	−	0.166181i	$-0.0531436\pi$
$911$	16.7937	+	22.2385i	0.556400	+	0.736793i	−0.429695	+	0.902974i	$0.641379\pi$
$912$	1.07024	+	1.41723i	0.0354393	+	0.0469293i
$913$	8.88955	+	17.8526i	0.294201	+	0.590835i
$914$	5.35286	−	57.7665i	0.177057	−	1.91075i
$915$	−22.2444	−	4.15820i	−0.735377	−	0.137466i
$916$	41.7439	−	25.8467i	1.37926	−	0.854000i
$917$	5.44619	−	7.21192i	0.179849	−	0.238159i
$918$	9.84805	−	6.09766i	0.325034	−	0.201253i
$919$	−3.04447	−	32.8551i	−0.100428	−	1.08379i	−0.885580	−	0.464486i	$-0.846239\pi$
$919$	−3.04447	−	32.8551i	−0.100428	−	1.08379i	0.785153	−	0.619302i	$-0.212584\pi$
$920$	10.8647	−	117.249i	0.358199	−	3.86559i
$921$	−11.5792	−	10.5559i	−0.381549	−	0.347828i
$922$	−42.1772	+	16.3395i	−1.38903	+	0.538113i
$923$	−7.43143	+	14.9243i	−0.244608	+	0.491240i
$924$	1.44104	+	5.06474i	0.0474069	+	0.166618i
$925$	−5.62436	+	3.48245i	−0.184928	+	0.114502i
$926$	82.1158			2.69849
$927$	6.23883	−	8.00481i	0.204910	−	0.262913i
$928$	245.925			8.07287
$929$	3.75098	−	2.32251i	0.123066	−	0.0761990i	−0.463519	−	0.886087i	$-0.653413\pi$
$929$	3.75098	−	2.32251i	0.123066	−	0.0761990i	0.586585	+	0.809888i	$0.300472\pi$
$930$	2.12245	+	7.45965i	0.0695980	+	0.244612i
$931$	0.323140	−	0.648953i	0.0105905	−	0.0212686i
$932$	−71.0965	+	27.5429i	−2.32884	+	0.902199i
$933$	−0.732233	−	0.667518i	−0.0239722	−	0.0218536i
$934$	9.38992	−	101.333i	0.307247	−	3.31573i
$935$	1.31347	+	14.1746i	0.0429551	+	0.463559i
$936$	−46.9771	+	29.0870i	−1.53549	+	0.950738i
$937$	13.6066	−	18.0180i	0.444508	−	0.588623i	−0.519509	−	0.854465i	$-0.673885\pi$
$937$	13.6066	−	18.0180i	0.444508	−	0.588623i	0.964017	+	0.265842i	$0.0856499\pi$
$938$	4.32184	−	2.67597i	0.141113	−	0.0873734i
$939$	−12.6706	−	2.36855i	−0.413489	−	0.0772945i
$940$	−18.1258	+	195.609i	−0.591199	+	6.38006i
$941$	−2.12296	−	4.26348i	−0.0692066	−	0.138986i	0.857859	−	0.513886i	$-0.171795\pi$
$941$	−2.12296	−	4.26348i	−0.0692066	−	0.138986i	−0.927065	+	0.374900i	$0.877677\pi$
$942$	−8.03180	−	10.6358i	−0.261690	−	0.346534i
$943$	4.33770	+	5.74404i	0.141255	+	0.187052i
$944$	−147.169	+	134.162i	−4.78994	+	4.36661i
$945$	0.866296	−	1.73976i	0.0281806	−	0.0565943i
$946$	−8.97829	+	31.5554i	−0.291909	+	1.02595i
$947$	2.42477	−	26.1674i	0.0787944	−	0.850327i	−0.861004	−	0.508598i	$-0.830164\pi$
$947$	2.42477	−	26.1674i	0.0787944	−	0.850327i	0.939799	−	0.341729i	$-0.111012\pi$
$948$	49.5664	−	9.26557i	1.60984	−	0.300932i
$949$	34.6955	−	69.6781i	1.12627	−	2.26185i
$950$	0.508917	+	0.315108i	0.0165115	+	0.0102235i
$951$	−24.3866	+	9.44742i	−0.790789	+	0.306353i
$952$	−22.4988	+	20.5104i	−0.729190	+	0.664745i
$953$	−25.8737	−	51.9613i	−0.838130	−	1.68319i	−0.724078	−	0.689718i	$-0.757735\pi$
$953$	−25.8737	−	51.9613i	−0.838130	−	1.68319i	−0.114052	−	0.993475i	$-0.536383\pi$
$954$	−7.37695	−	6.72498i	−0.238838	−	0.217729i
$955$	29.6159	+	18.3374i	0.958346	+	0.593383i
$956$	12.7784	−	4.95039i	0.413284	−	0.160107i
$957$	−12.3125	−	4.76987i	−0.398005	−	0.154188i
$958$	50.6153	+	67.0255i	1.63531	+	2.16550i
$959$	5.74846	+	2.22697i	0.185628	+	0.0719125i
$960$	66.3525	+	60.4883i	2.14152	+	1.95225i
$961$	8.16982	−	28.7140i	0.263543	−	0.926256i
$962$	−14.4867	−	50.9156i	−0.467071	−	1.64158i
$963$	−0.645764	−	6.96891i	−0.0208095	−	0.224570i
$964$	48.1556	+	9.00184i	1.55099	+	0.289930i
$965$	13.4962	+	47.4343i	0.434458	+	1.52696i
$966$	−9.10150	+	1.70137i	−0.292836	+	0.0547405i
$967$	18.6242	+	37.4024i	0.598914	+	1.20278i	0.962515	+	0.271227i	$0.0874293\pi$
$967$	18.6242	+	37.4024i	0.598914	+	1.20278i	−0.363602	+	0.931555i	$0.618453\pi$
$968$	−85.4431	−	33.1008i	−2.74625	−	1.06390i
$969$	0.349557	−	0.318664i	0.0112294	−	0.0102369i
$970$	−72.9478	+	13.6363i	−2.34221	+	0.437835i
$971$	−3.54870	−	38.2965i	−0.113883	−	1.22899i	−0.840446	−	0.541895i	$-0.817707\pi$
$971$	−3.54870	−	38.2965i	−0.113883	−	1.22899i	0.726563	−	0.687099i	$-0.241116\pi$
$972$	−3.35203	+	4.43880i	−0.107516	+	0.142375i
$973$	6.55120			0.210022
$974$	19.0940			0.611811
$975$	−6.58827	+	8.72428i	−0.210993	+	0.279400i
$976$	−133.552	−	24.9651i	−4.27488	−	0.799114i
$977$	−7.98104	+	28.0504i	−0.255336	+	0.897413i	0.723079	+	0.690765i	$0.242726\pi$
$977$	−7.98104	+	28.0504i	−0.255336	+	0.897413i	−0.978415	+	0.206648i	$0.933744\pi$
$978$	6.29363	+	3.89685i	0.201248	+	0.124608i
$979$	6.63759	+	4.10982i	0.212138	+	0.131351i
$980$	25.8840	−	90.9729i	0.826835	−	2.90602i
$981$	5.93048	+	1.10860i	0.189346	+	0.0353949i
$982$	14.4894	−	19.1871i	0.462376	−	0.612285i
$983$	30.5450			0.974234			0.487117	−	0.873337i	$-0.338049\pi$
$983$	30.5450			0.974234			0.487117	+	0.873337i	$0.338049\pi$
$984$	−15.4517			−0.492582
$985$	−14.1481	+	18.7351i	−0.450796	+	0.596951i
$986$	−10.9985	−	118.693i	−0.350265	−	3.77996i
$987$	9.72451	−	1.81783i	0.309535	−	0.0578621i
$988$	−2.60363	+	2.37352i	−0.0828324	+	0.0755117i
$989$	−39.5662	−	15.3280i	−1.25813	−	0.487402i
$990$	−4.14267	−	8.31960i	−0.131663	−	0.264414i
$991$	30.3660	−	5.67638i	0.964607	−	0.180316i	0.322193	−	0.946674i	$-0.395580\pi$
$991$	30.3660	−	5.67638i	0.964607	−	0.180316i	0.642414	+	0.766358i	$0.277933\pi$
$992$	7.00206	+	24.6097i	0.222316	+	0.781359i
$993$	1.71825	+	0.321196i	0.0545269	+	0.0101928i
$994$	−0.553389	−	5.97202i	−0.0175524	−	0.189421i
$995$	7.30841	+	25.6864i	0.231692	+	0.814313i
$996$	23.6604	−	83.1576i	0.749707	−	2.63495i
$997$	38.1082	+	34.7402i	1.20690	+	1.10023i	0.992342	+	0.123522i	$0.0394189\pi$
$997$	38.1082	+	34.7402i	1.20690	+	1.10023i	0.214557	+	0.976712i	$0.431169\pi$
$998$	39.0700	+	15.1358i	1.23674	+	0.479116i
$999$	−2.05675	−	2.72357i	−0.0650726	−	0.0861701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.2.i.b.100.1	yes	160
3.2	odd	2		927.2.u.c.100.10		160
103.34	even	17	inner	309.2.i.b.34.1	✓	160
309.137	odd	34		927.2.u.c.343.10		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.i.b.34.1	✓	160	103.34	even	17	inner
309.2.i.b.100.1	yes	160	1.1	even	1	trivial
927.2.u.c.100.10		160	3.2	odd	2
927.2.u.c.343.10		160	309.137	odd	34

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.33806 + 1.44767i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(2.47932 - 4.97915i) q^{4} +(2.45619 - 0.951533i) q^{5} +(2.03225 + 1.85264i) q^{6} +(0.0680790 - 0.734689i) q^{7} +(0.903874 + 9.75436i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})\)	\(q+(-2.33806 + 1.44767i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(2.47932 - 4.97915i) q^{4} +(2.45619 - 0.951533i) q^{5} +(2.03225 + 1.85264i) q^{6} +(0.0680790 - 0.734689i) q^{7} +(0.903874 + 9.75436i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-4.36522 + 5.78049i) q^{10} +(1.09088 - 0.675445i) q^{11} +(-5.46758 - 1.02207i) q^{12} +(0.520420 - 5.61622i) q^{13} +(0.904413 + 1.81631i) q^{14} +(-1.58738 - 2.10203i) q^{15} +(-9.53034 - 12.6202i) q^{16} +(-3.11275 + 2.83764i) q^{17} +(1.22576 - 2.46166i) q^{18} +(0.0307320 - 0.108012i) q^{19} +(1.35186 - 14.5889i) q^{20} +(-0.725274 + 0.135577i) q^{21} +(-1.57273 + 3.15847i) q^{22} +(-3.87985 - 2.40230i) q^{23} +(9.13464 - 3.53878i) q^{24} +(1.43240 - 1.30581i) q^{25} +(6.91365 + 13.8845i) q^{26} +(0.739009 + 0.673696i) q^{27} +(-3.48934 - 2.16051i) q^{28} +(9.59616 - 3.71757i) q^{29} +(6.75442 + 2.61668i) q^{30} +(0.645244 + 0.854441i) q^{31} +(22.2831 + 8.63253i) q^{32} +(-0.948194 - 0.864393i) q^{33} +(3.16983 - 11.1408i) q^{34} +(-0.531866 - 1.86931i) q^{35} +(0.513223 + 5.53856i) q^{36} +(-3.35481 - 0.627123i) q^{37} +(0.0845118 + 0.297028i) q^{38} +(-5.54425 + 1.03640i) q^{39} +(11.5017 + 23.0985i) q^{40} +(-1.47081 - 0.569795i) q^{41} +(1.49947 - 1.36694i) q^{42} +(9.13997 - 1.70856i) q^{43} +(-0.658497 - 7.10631i) q^{44} +(-1.58738 + 2.10203i) q^{45} +12.5491 q^{46} -13.4081 q^{47} +(-9.53034 + 12.6202i) q^{48} +(6.34568 + 1.18621i) q^{49} +(-1.45868 + 5.12671i) q^{50} +(3.58116 + 2.21736i) q^{51} +(-26.6738 - 16.5157i) q^{52} +(0.993383 - 3.49138i) q^{53} +(-2.70314 - 0.505304i) q^{54} +(2.03670 - 2.69703i) q^{55} +7.22796 q^{56} -0.112299 q^{57} +(-17.0546 + 22.5840i) q^{58} +(-1.16189 - 12.5388i) q^{59} +(-14.4019 + 2.69219i) q^{60} +(6.34896 - 5.78784i) q^{61} +(-2.74557 - 1.06364i) q^{62} +(0.328882 + 0.660484i) q^{63} +(-33.5061 + 6.26337i) q^{64} +(-4.06577 - 14.2897i) q^{65} +(3.46829 + 0.648336i) q^{66} +(-0.231156 - 2.49457i) q^{67} +(6.41156 + 22.5343i) q^{68} +(-1.24882 + 4.38916i) q^{69} +(3.94968 + 3.60061i) q^{70} +(-2.75630 - 1.06780i) q^{71} +(-5.90350 - 7.81749i) q^{72} +(12.8685 + 4.98529i) q^{73} +(8.75164 - 3.39040i) q^{74} +(-1.64796 - 1.02037i) q^{75} +(-0.461613 - 0.420815i) q^{76} +(-0.421976 - 0.847442i) q^{77} +(11.4624 - 10.4494i) q^{78} +(-8.45334 + 3.27484i) q^{79} +(-35.4168 - 21.9292i) q^{80} +(0.445738 - 0.895163i) q^{81} +(4.26372 - 0.797028i) q^{82} +(-1.43418 + 15.4773i) q^{83} +(-1.12313 + 3.94739i) q^{84} +(-4.94538 + 9.93167i) q^{85} +(-18.8964 + 17.2264i) q^{86} +(-6.20177 - 8.21247i) q^{87} +(7.57455 + 10.0303i) q^{88} +(2.71215 + 5.44673i) q^{89} +(0.668352 - 7.21267i) q^{90} +(-4.09075 - 0.764694i) q^{91} +(-21.5808 + 13.3623i) q^{92} +(0.645244 - 0.854441i) q^{93} +(31.3489 - 19.4104i) q^{94} +(-0.0272931 - 0.294540i) q^{95} +(2.20492 - 23.7949i) q^{96} +(7.57125 + 6.90211i) q^{97} +(-16.5538 + 6.41299i) q^{98} +(-0.571910 + 1.14855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Introduction

L-functions

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