LMFDB - Embedded newform 288.2.bf.a.59.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (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			59.8
Character	$\chi$	$=$	288.59
Dual form			288.2.bf.a.83.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17466 - 0.787516i) q^{2} +(1.34151 + 1.09560i) q^{3} +(0.759636 + 1.85012i) q^{4} +(-2.18140 - 2.84285i) q^{5} +(-0.713010 - 2.34342i) q^{6} +(-4.36814 - 1.17044i) q^{7} +(0.564691 - 2.77148i) q^{8} +(0.599307 + 2.93953i) q^{9} +O(q^{10})$	\(q+(-1.17466 - 0.787516i) q^{2} +(1.34151 + 1.09560i) q^{3} +(0.759636 + 1.85012i) q^{4} +(-2.18140 - 2.84285i) q^{5} +(-0.713010 - 2.34342i) q^{6} +(-4.36814 - 1.17044i) q^{7} +(0.564691 - 2.77148i) q^{8} +(0.599307 + 2.93953i) q^{9} +(0.323599 + 5.05726i) q^{10} +(-3.64283 + 0.479588i) q^{11} +(-1.00794 + 3.31422i) q^{12} +(-0.415168 + 3.15351i) q^{13} +(4.20933 + 4.81485i) q^{14} +(0.188268 - 6.20367i) q^{15} +(-2.84591 + 2.81084i) q^{16} -0.548551 q^{17} +(1.61095 - 3.92490i) q^{18} +(-1.60531 - 3.87556i) q^{19} +(3.60256 - 6.19538i) q^{20} +(-4.57758 - 6.35591i) q^{21} +(4.65676 + 2.30544i) q^{22} +(-1.67586 - 6.25438i) q^{23} +(3.79399 - 3.09930i) q^{24} +(-2.02922 + 7.57315i) q^{25} +(2.97112 - 3.37734i) q^{26} +(-2.41658 + 4.60002i) q^{27} +(-1.15274 - 8.97071i) q^{28} +(0.938681 + 0.720275i) q^{29} +(-5.10664 + 7.13891i) q^{30} +(-0.160017 - 0.0923856i) q^{31} +(5.55654 - 1.06057i) q^{32} +(-5.41234 - 3.34773i) q^{33} +(0.644359 + 0.431993i) q^{34} +(6.20127 + 14.9712i) q^{35} +(-4.98323 + 3.34176i) q^{36} +(1.67841 + 0.695219i) q^{37} +(-1.16638 + 5.81666i) q^{38} +(-4.01195 + 3.77561i) q^{39} +(-9.11074 + 4.44037i) q^{40} +(5.14759 - 1.37929i) q^{41} +(0.371695 + 11.0709i) q^{42} +(-1.16689 - 8.86345i) q^{43} +(-3.65452 - 6.37538i) q^{44} +(7.04932 - 8.11602i) q^{45} +(-2.95687 + 8.66651i) q^{46} +(-3.46882 + 2.00272i) q^{47} +(-6.89738 + 0.652787i) q^{48} +(11.6486 + 6.72530i) q^{49} +(8.34762 - 7.29781i) q^{50} +(-0.735887 - 0.600994i) q^{51} +(-6.14976 + 1.62741i) q^{52} +(-7.86951 - 3.25966i) q^{53} +(6.46124 - 3.50034i) q^{54} +(9.30986 + 9.30986i) q^{55} +(-5.71051 + 11.4453i) q^{56} +(2.09253 - 6.95789i) q^{57} +(-0.535399 - 1.58530i) q^{58} +(-6.44770 + 4.94750i) q^{59} +(11.6206 - 4.36421i) q^{60} +(2.49837 - 3.25594i) q^{61} +(0.115209 + 0.234537i) q^{62} +(0.822684 - 13.5417i) q^{63} +(-7.36225 - 3.13007i) q^{64} +(9.87062 - 5.69880i) q^{65} +(3.72125 + 8.19474i) q^{66} +(-0.391739 + 2.97555i) q^{67} +(-0.416699 - 1.01489i) q^{68} +(4.60414 - 10.2264i) q^{69} +(4.50569 - 22.4696i) q^{70} +(5.84951 + 5.84951i) q^{71} +(8.48528 - 0.00104410i) q^{72} +(7.81569 - 7.81569i) q^{73} +(-1.42406 - 2.13842i) q^{74} +(-11.0194 + 7.93625i) q^{75} +(5.95081 - 5.91403i) q^{76} +(16.4737 + 2.16881i) q^{77} +(7.68602 - 1.27557i) q^{78} +(5.27449 + 9.13568i) q^{79} +(14.1989 + 1.95894i) q^{80} +(-8.28166 + 3.52336i) q^{81} +(-7.13286 - 2.43362i) q^{82} +(-9.01072 - 6.91417i) q^{83} +(8.28193 - 13.2973i) q^{84} +(1.19661 + 1.55945i) q^{85} +(-5.60941 + 11.3305i) q^{86} +(0.470116 + 1.99468i) q^{87} +(-0.727905 + 10.3669i) q^{88} +(-1.83525 + 1.83525i) q^{89} +(-14.6720 + 3.98208i) q^{90} +(5.50451 - 13.2891i) q^{91} +(10.2983 - 7.85159i) q^{92} +(-0.113446 - 0.299251i) q^{93} +(5.65184 + 0.379240i) q^{94} +(-7.51582 + 13.0178i) q^{95} +(8.61613 + 4.66500i) q^{96} +(-0.360120 - 0.623746i) q^{97} +(-8.38678 - 17.0734i) q^{98} +(-3.59294 - 10.4208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.17466	−	0.787516i	−0.830608	−	0.556858i
$2$	−1.17466	−	0.787516i	−0.830608	−	0.556858i
$3$	1.34151	+	1.09560i	0.774522	+	0.632547i
$3$	1.34151	+	1.09560i	0.774522	+	0.632547i
$4$	0.759636	+	1.85012i	0.379818	+	0.925061i
$5$	−2.18140	−	2.84285i	−0.975551	−	1.27136i	−0.962453	−	0.271448i	$-0.912497\pi$
$5$	−2.18140	−	2.84285i	−0.975551	−	1.27136i	−0.0130975	−	0.999914i	$-0.504169\pi$
$6$	−0.713010	−	2.34342i	−0.291085	−	0.956697i
$7$	−4.36814	−	1.17044i	−1.65100	−	0.442385i	−0.691110	−	0.722750i	$-0.742878\pi$
$7$	−4.36814	−	1.17044i	−1.65100	−	0.442385i	−0.959893	+	0.280365i	$0.909544\pi$
$8$	0.564691	−	2.77148i	0.199648	−	0.979868i
$9$	0.599307	+	2.93953i	0.199769	+	0.979843i
$10$	0.323599	+	5.05726i	0.102331	+	1.59925i
$11$	−3.64283	+	0.479588i	−1.09836	+	0.144601i	−0.657850	−	0.753149i	$-0.728534\pi$
$11$	−3.64283	+	0.479588i	−1.09836	+	0.144601i	−0.440505	+	0.897750i	$0.645201\pi$
$12$	−1.00794	+	3.31422i	−0.290967	+	0.956733i
$13$	−0.415168	+	3.15351i	−0.115147	+	0.874627i	0.832213	+	0.554456i	$0.187074\pi$
$13$	−0.415168	+	3.15351i	−0.115147	+	0.874627i	−0.947360	+	0.320171i	$0.896260\pi$
$14$	4.20933	+	4.81485i	1.12499	+	1.28682i
$15$	0.188268	−	6.20367i	0.0486106	−	1.60178i
$16$	−2.84591	+	2.81084i	−0.711477	+	0.702710i
$17$	−0.548551			−0.133043			−0.0665215	−	0.997785i	$-0.521190\pi$
$17$	−0.548551			−0.133043			−0.0665215	+	0.997785i	$0.521190\pi$
$18$	1.61095	−	3.92490i	0.379704	−	0.925108i
$19$	−1.60531	−	3.87556i	−0.368283	−	0.889114i	−0.994032	−	0.109089i	$-0.965207\pi$
$19$	−1.60531	−	3.87556i	−0.368283	−	0.889114i	0.625749	−	0.780025i	$-0.284793\pi$
$20$	3.60256	−	6.19538i	0.805557	−	1.38533i
$21$	−4.57758	−	6.35591i	−0.998909	−	1.38697i
$22$	4.65676	+	2.30544i	0.992825	+	0.491521i
$23$	−1.67586	−	6.25438i	−0.349440	−	1.30413i	−0.887339	−	0.461119i	$-0.847448\pi$
$23$	−1.67586	−	6.25438i	−0.349440	−	1.30413i	0.537898	−	0.843010i	$-0.319218\pi$
$24$	3.79399	−	3.09930i	0.774444	−	0.632642i
$25$	−2.02922	+	7.57315i	−0.405844	+	1.51463i
$26$	2.97112	−	3.37734i	0.582685	−	0.662351i
$27$	−2.41658	+	4.60002i	−0.465071	+	0.885273i
$28$	−1.15274	−	8.97071i	−0.217847	−	1.69530i
$29$	0.938681	+	0.720275i	0.174309	+	0.133752i	0.692231	−	0.721676i	$-0.256628\pi$
$29$	0.938681	+	0.720275i	0.174309	+	0.133752i	−0.517923	+	0.855428i	$0.673294\pi$
$30$	−5.10664	+	7.13891i	−0.932341	+	1.30338i
$31$	−0.160017	−	0.0923856i	−0.0287398	−	0.0165929i	0.485561	−	0.874203i	$-0.338615\pi$
$31$	−0.160017	−	0.0923856i	−0.0287398	−	0.0165929i	−0.514301	+	0.857610i	$0.671949\pi$
$32$	5.55654	−	1.06057i	0.982268	−	0.187484i
$33$	−5.41234	−	3.34773i	−0.942168	−	0.582764i
$34$	0.644359	+	0.431993i	0.110507	+	0.0740861i
$35$	6.20127	+	14.9712i	1.04821	+	2.53059i
$36$	−4.98323	+	3.34176i	−0.830539	+	0.556960i
$37$	1.67841	+	0.695219i	0.275929	+	0.114293i	0.516357	−	0.856374i	$-0.327288\pi$
$37$	1.67841	+	0.695219i	0.275929	+	0.114293i	−0.240428	+	0.970667i	$0.577288\pi$
$38$	−1.16638	+	5.81666i	−0.189212	+	0.943586i
$39$	−4.01195	+	3.77561i	−0.642426	+	0.604582i
$40$	−9.11074	+	4.44037i	−1.44053	+	0.702085i
$41$	5.14759	−	1.37929i	0.803918	−	0.215409i	0.166614	−	0.986022i	$-0.446716\pi$
$41$	5.14759	−	1.37929i	0.803918	−	0.215409i	0.637303	+	0.770613i	$0.280050\pi$
$42$	0.371695	+	11.0709i	0.0573538	+	1.70828i
$43$	−1.16689	−	8.86345i	−0.177950	−	1.35166i	−0.814381	−	0.580330i	$-0.802924\pi$
$43$	−1.16689	−	8.86345i	−0.177950	−	1.35166i	0.636432	−	0.771333i	$-0.280410\pi$
$44$	−3.65452	−	6.37538i	−0.550940	−	0.961124i
$45$	7.04932	−	8.11602i	1.05085	−	1.20987i
$46$	−2.95687	+	8.66651i	−0.435967	+	1.27781i
$47$	−3.46882	+	2.00272i	−0.505979	+	0.292127i	−0.731179	−	0.682185i	$-0.761030\pi$
$47$	−3.46882	+	2.00272i	−0.505979	+	0.292127i	0.225200	+	0.974312i	$0.427696\pi$
$48$	−6.89738	+	0.652787i	−0.995551	+	0.0942216i
$49$	11.6486	+	6.72530i	1.66408	+	0.960758i
$50$	8.34762	−	7.29781i	1.18053	−	1.03207i
$51$	−0.735887	−	0.600994i	−0.103045	−	0.0841560i
$52$	−6.14976	+	1.62741i	−0.852818	+	0.225681i
$53$	−7.86951	−	3.25966i	−1.08096	−	0.447748i	−0.230114	−	0.973164i	$-0.573910\pi$
$53$	−7.86951	−	3.25966i	−1.08096	−	0.447748i	−0.850846	+	0.525415i	$0.823910\pi$
$54$	6.46124	−	3.50034i	0.879263	−	0.476336i
$55$	9.30986	+	9.30986i	1.25534	+	1.25534i
$56$	−5.71051	+	11.4453i	−0.763099	+	1.52944i
$57$	2.09253	−	6.95789i	0.277163	−	0.921595i
$58$	−0.535399	−	1.58530i	−0.0703014	−	0.208161i
$59$	−6.44770	+	4.94750i	−0.839420	+	0.644109i	−0.936306	−	0.351186i	$-0.885778\pi$
$59$	−6.44770	+	4.94750i	−0.839420	+	0.644109i	0.0968860	+	0.995295i	$0.469112\pi$
$60$	11.6206	−	4.36421i	1.50021	−	0.563417i
$61$	2.49837	−	3.25594i	0.319884	−	0.416881i	−0.605540	−	0.795815i	$-0.707043\pi$
$61$	2.49837	−	3.25594i	0.319884	−	0.416881i	0.925424	+	0.378934i	$0.123709\pi$
$62$	0.115209	+	0.234537i	0.0146316	+	0.0297862i
$63$	0.822684	−	13.5417i	0.103648	−	1.70610i
$64$	−7.36225	−	3.13007i	−0.920281	−	0.391258i
$65$	9.87062	−	5.69880i	1.22430	−	0.706849i
$66$	3.72125	+	8.19474i	0.458054	+	1.00870i
$67$	−0.391739	+	2.97555i	−0.0478585	+	0.363521i	0.950712	+	0.310075i	$0.100354\pi$
$67$	−0.391739	+	2.97555i	−0.0478585	+	0.363521i	−0.998571	+	0.0534467i	$0.982979\pi$
$68$	−0.416699	−	1.01489i	−0.0505321	−	0.123073i
$69$	4.60414	−	10.2264i	0.554273	−	1.23111i
$70$	4.50569	−	22.4696i	0.538534	−	2.68563i
$71$	5.84951	+	5.84951i	0.694209	+	0.694209i	0.963155	−	0.268946i	$-0.0866754\pi$
$71$	5.84951	+	5.84951i	0.694209	+	0.694209i	−0.268946	+	0.963155i	$0.586675\pi$
$72$	8.48528	−	0.00104410i	1.00000	−	0.000123048i
$73$	7.81569	−	7.81569i	0.914758	−	0.914758i	−0.0818843	−	0.996642i	$-0.526094\pi$
$73$	7.81569	−	7.81569i	0.914758	−	0.914758i	0.996642	+	0.0818843i	$0.0260938\pi$
$74$	−1.42406	−	2.13842i	−0.165543	−	0.248586i
$75$	−11.0194	+	7.93625i	−1.27241	+	0.916400i
$76$	5.95081	−	5.91403i	0.682604	−	0.678386i
$77$	16.4737	+	2.16881i	1.87736	+	0.247159i
$78$	7.68602	−	1.27557i	0.870271	−	0.144430i
$79$	5.27449	+	9.13568i	0.593426	+	1.02784i	0.993767	+	0.111478i	$0.0355585\pi$
$79$	5.27449	+	9.13568i	0.593426	+	1.02784i	−0.400341	+	0.916366i	$0.631108\pi$
$80$	14.1989	+	1.95894i	1.58748	+	0.219016i
$81$	−8.28166	+	3.52336i	−0.920185	+	0.391485i
$82$	−7.13286	−	2.43362i	−0.787693	−	0.268748i
$83$	−9.01072	−	6.91417i	−0.989055	−	0.758929i	−0.0185052	−	0.999829i	$-0.505891\pi$
$83$	−9.01072	−	6.91417i	−0.989055	−	0.758929i	−0.970550	+	0.240900i	$0.922557\pi$
$84$	8.28193	−	13.2973i	0.903632	−	1.45085i
$85$	1.19661	+	1.55945i	0.129790	+	0.169146i
$86$	−5.60941	+	11.3305i	−0.604878	+	1.22179i
$87$	0.470116	+	1.99468i	0.0504017	+	0.213852i
$88$	−0.727905	+	10.3669i	−0.0775949	+	1.10511i
$89$	−1.83525	+	1.83525i	−0.194536	+	0.194536i	−0.797653	−	0.603117i	$-0.793925\pi$
$89$	−1.83525	+	1.83525i	−0.194536	+	0.194536i	0.603117	+	0.797653i	$0.293925\pi$
$90$	−14.6720	+	3.98208i	−1.54657	+	0.419748i
$91$	5.50451	−	13.2891i	0.577029	−	1.39307i
$92$	10.2983	−	7.85159i	1.07368	−	0.818585i
$93$	−0.113446	−	0.299251i	−0.0117638	−	0.0310309i
$94$	5.65184	+	0.379240i	0.582943	+	0.0391156i
$95$	−7.51582	+	13.0178i	−0.771107	+	1.33560i
$96$	8.61613	+	4.66500i	0.879380	+	0.476120i
$97$	−0.360120	−	0.623746i	−0.0365646	−	0.0633318i	0.847164	−	0.531332i	$-0.178308\pi$
$97$	−0.360120	−	0.623746i	−0.0365646	−	0.0633318i	−0.883729	+	0.468000i	$0.844975\pi$
$98$	−8.38678	−	17.0734i	−0.847193	−	1.72467i
$99$	−3.59294	−	10.4208i	−0.361104	−	1.04733i
$100$	−15.5527	+	1.99853i	−1.55527	+	0.199853i
$101$	−8.24210	+	1.08509i	−0.820120	+	0.107971i	−0.528899	−	0.848685i	$-0.677395\pi$
$101$	−8.24210	+	1.08509i	−0.820120	+	0.107971i	−0.291221	+	0.956656i	$0.594062\pi$
$102$	0.391122	+	1.28548i	0.0387268	+	0.127282i
$103$	0.0222082	+	0.0828821i	0.00218824	+	0.00816661i	0.967011	−	0.254733i	$-0.0819877\pi$
$103$	0.0222082	+	0.0828821i	0.00218824	+	0.00816661i	−0.964823	+	0.262900i	$0.915321\pi$
$104$	8.50547	+	2.93139i	0.834030	+	0.287447i
$105$	−8.08340	+	26.8781i	−0.788859	+	2.62304i
$106$	6.67694	+	10.0263i	0.648522	+	0.973845i
$107$	3.87704	−	9.35999i	0.374807	−	0.904865i	−0.618114	−	0.786089i	$-0.712103\pi$
$107$	3.87704	−	9.35999i	0.374807	−	0.904865i	0.992921	−	0.118776i	$-0.0378970\pi$
$108$	−10.3463	−	0.976634i	−0.995574	−	0.0939766i
$109$	−4.70621	+	1.94937i	−0.450773	+	0.186716i	−0.596507	−	0.802608i	$-0.703445\pi$
$109$	−4.70621	+	1.94937i	−0.450773	+	0.186716i	0.145735	+	0.989324i	$0.453445\pi$
$110$	−3.60422	−	18.2676i	−0.343649	−	1.74174i
$111$	1.48992	+	2.77151i	0.141417	+	0.263060i
$112$	15.7213	−	8.94718i	1.48552	−	0.845429i
$113$	−0.260086	+	0.450482i	−0.0244668	+	0.0423778i	−0.878000	−	0.478661i	$-0.841122\pi$
$113$	−0.260086	+	0.450482i	−0.0244668	+	0.0423778i	0.853533	+	0.521039i	$0.174455\pi$
$114$	−7.93746	+	6.52522i	−0.743411	+	0.611143i
$115$	−14.1246	+	18.4075i	−1.31712	+	1.71651i
$116$	−0.619542	+	2.28382i	−0.0575231	+	0.212048i
$117$	−9.51865	+	0.669525i	−0.880000	+	0.0618976i
$118$	11.4701	−	0.733937i	1.05591	−	0.0675643i
$119$	2.39615	+	0.642046i	0.219654	+	0.0588562i
$120$	−17.0870	−	4.02494i	−1.55983	−	0.367425i
$121$	2.41504	−	0.647108i	0.219549	−	0.0588280i
$122$	−5.49884	+	1.85710i	−0.497841	+	0.168134i
$123$	8.41670	+	3.78938i	0.758909	+	0.341677i
$124$	0.0493704	−	0.366230i	0.00443359	−	0.0328884i
$125$	9.40303	−	3.89486i	0.841033	−	0.348367i
$126$	−11.6307	+	15.2590i	−1.03615	+	1.35938i
$127$			4.56666i			0.405226i	0.979259	+	0.202613i	$0.0649433\pi$
$127$			4.56666i			0.405226i	−0.979259	+	0.202613i	$0.935057\pi$
$128$	6.18313	+	9.47464i	0.546517	+	0.837448i
$129$	8.14542	−	13.1689i	0.717164	−	1.15945i
$130$	−16.0825	−	1.07914i	−1.41053	−	0.0946466i
$131$	−7.75064	−	1.02039i	−0.677177	−	0.0891520i	−0.215910	−	0.976413i	$-0.569272\pi$
$131$	−7.75064	−	1.02039i	−0.677177	−	0.0891520i	−0.461267	+	0.887261i	$0.652605\pi$
$132$	2.08230	−	12.5565i	0.181241	−	1.09291i
$133$	2.47611	+	18.8079i	0.214706	+	1.63085i
$134$	2.80345	−	3.18675i	0.242181	−	0.275293i
$135$	18.3487	−	3.16448i	1.57920	−	0.272355i
$136$	−0.309762	+	1.52030i	−0.0265618	+	0.130365i
$137$	−0.494554	+	1.84570i	−0.0422526	+	0.157689i	−0.983829	−	0.179111i	$-0.942678\pi$
$137$	−0.494554	+	1.84570i	−0.0422526	+	0.157689i	0.941576	+	0.336800i	$0.109345\pi$
$138$	−13.4617	+	8.38667i	−1.14594	+	0.713921i
$139$	3.62898	−	2.78461i	0.307806	−	0.236188i	−0.443294	−	0.896376i	$-0.646190\pi$
$139$	3.62898	−	2.78461i	0.307806	−	0.236188i	0.751100	+	0.660189i	$0.229524\pi$
$140$	−22.9878	+	22.8457i	−1.94283	+	1.93082i
$141$	−6.84765	−	1.11377i	−0.576676	−	0.0937965i
$142$	−2.26458	−	11.4777i	−0.190039	−	0.963191i
$143$		−	11.6868i		−	0.977302i
$144$	−9.96811	−	6.68107i	−0.830676	−	0.556756i
$145$		−	4.23974i		−	0.352091i
$146$	−15.3357	+	3.02577i	−1.26919	+	0.250414i
$147$	8.25843	+	21.7843i	0.681143	+	1.79674i
$148$	−0.0112626	+	3.63337i	−0.000925781	+	0.298662i
$149$	−14.3195	+	10.9878i	−1.17310	+	0.900153i	−0.996456	−	0.0841209i	$-0.973192\pi$
$149$	−14.3195	+	10.9878i	−1.17310	+	0.900153i	−0.176647	+	0.984274i	$0.556525\pi$
$150$	19.1939	−	0.644417i	1.56718	−	0.0526164i
$151$	5.69935	−	21.2703i	0.463807	−	1.73095i	−0.197009	−	0.980402i	$-0.563123\pi$
$151$	5.69935	−	21.2703i	0.463807	−	1.73095i	0.660816	−	0.750548i	$-0.270210\pi$
$152$	−11.6475	+	2.26059i	−0.944741	+	0.183358i
$153$	−0.328750	−	1.61248i	−0.0265779	−	0.130361i
$154$	−17.6430	−	15.5210i	−1.42171	−	1.25071i
$155$	0.0864210	+	0.656433i	0.00694150	+	0.0527260i
$156$	−10.0330	−	4.55451i	−0.803280	−	0.364653i
$157$	−13.0597	−	1.71935i	−1.04228	−	0.137219i	−0.410100	−	0.912041i	$-0.634506\pi$
$157$	−13.0597	−	1.71935i	−1.04228	−	0.137219i	−0.632180	+	0.774822i	$0.717839\pi$
$158$	0.998788	−	14.8850i	0.0794593	−	1.18419i
$159$	−6.98575	−	12.9947i	−0.554006	−	1.03055i
$160$	−15.1361	−	13.4829i	−1.19661	−	1.06592i
$161$			29.2815i			2.30771i
$162$	12.5028	+	2.38321i	0.982314	+	0.187242i
$163$	−7.22192	+	2.99142i	−0.565664	+	0.234306i	−0.647142	−	0.762369i	$-0.724036\pi$
$163$	−7.22192	+	2.99142i	−0.565664	+	0.234306i	0.0814780	+	0.996675i	$0.474036\pi$
$164$	6.46215	+	8.47591i	0.504609	+	0.661857i
$165$	2.28937	+	22.6892i	0.178228	+	1.76635i
$166$	5.13948	+	15.2179i	0.398901	+	1.18114i
$167$	−9.42043	+	2.52420i	−0.728974	+	0.195328i	−0.604172	−	0.796854i	$-0.706496\pi$
$167$	−9.42043	+	2.52420i	−0.728974	+	0.195328i	−0.124802	+	0.992182i	$0.539830\pi$
$168$	−20.2002	+	9.09755i	−1.55848	+	0.701892i
$169$	2.78476	+	0.746175i	0.214212	+	0.0573981i
$170$	−0.177511	−	2.77416i	−0.0136144	−	0.212769i
$171$	10.4302	−	7.04150i	0.797620	−	0.538477i
$172$	15.5120	−	8.89189i	1.18278	−	0.678000i
$173$	3.15239	−	4.10828i	0.239672	−	0.312347i	−0.657994	−	0.753023i	$-0.728595\pi$
$173$	3.15239	−	4.10828i	0.239672	−	0.312347i	0.897666	+	0.440677i	$0.145261\pi$
$174$	1.01862	−	2.71329i	0.0772213	−	0.205694i
$175$	17.7278	−	30.7055i	1.34010	−	2.32112i
$176$	9.01912	−	11.6043i	0.679842	−	0.874705i
$177$	−14.0702	−	0.427000i	−1.05758	−	0.0320953i
$178$	3.60107	−	0.710497i	0.269912	−	0.0532540i
$179$	−1.62007	+	0.671055i	−0.121090	+	0.0501570i	−0.442406	−	0.896815i	$-0.645875\pi$
$179$	−1.62007	+	0.671055i	−0.121090	+	0.0501570i	0.321316	+	0.946972i	$0.395875\pi$
$180$	20.3706	+	6.87689i	1.51833	+	0.512573i
$181$	7.39266	−	17.8475i	0.549492	−	1.32659i	−0.368366	−	0.929681i	$-0.620083\pi$
$181$	7.39266	−	17.8475i	0.549492	−	1.32659i	0.917858	−	0.396910i	$-0.129917\pi$
$182$	−16.9313	+	11.2752i	−1.25503	+	0.835773i
$183$	6.91882	−	1.63066i	0.511454	−	0.120542i
$184$	−18.2803	+	1.11281i	−1.34764	+	0.0820378i
$185$	−1.68487	−	6.28802i	−0.123874	−	0.462304i
$186$	−0.102405	+	0.440858i	−0.00750869	+	0.0323253i
$187$	1.99828	−	0.263078i	0.146129	−	0.0192382i
$188$	−6.34032	−	4.89640i	−0.462415	−	0.357106i
$189$	15.9400	−	17.2651i	1.15947	−	1.25585i
$190$	19.0802	−	9.37259i	1.38423	−	0.679959i
$191$	7.17360	+	12.4250i	0.519064	+	0.899045i	0.999755	+	0.0221545i	$0.00705258\pi$
$191$	7.17360	+	12.4250i	0.519064	+	0.899045i	−0.480691	+	0.876890i	$0.659614\pi$
$192$	−6.44723	−	12.2651i	−0.465289	−	0.885159i
$193$	9.64687	−	16.7089i	0.694397	−	1.20273i	−0.275987	−	0.961162i	$-0.589005\pi$
$193$	9.64687	−	16.7089i	0.694397	−	1.20273i	0.970384	−	0.241569i	$-0.0776621\pi$
$194$	−0.0681930	+	1.01629i	−0.00489597	+	0.0729652i
$195$	19.4852	+	3.16927i	1.39536	+	0.226956i
$196$	−3.59397	+	26.6601i	−0.256712	+	1.90429i
$197$	4.38481	−	10.5859i	0.312405	−	0.754211i	−0.687210	−	0.726459i	$-0.741165\pi$
$197$	4.38481	−	10.5859i	0.312405	−	0.754211i	0.999615	−	0.0277529i	$-0.00883514\pi$
$198$	−3.98608	+	15.0703i	−0.283278	+	1.07100i
$199$	−5.46573	+	5.46573i	−0.387455	+	0.387455i	−0.873779	−	0.486324i	$-0.838338\pi$
$199$	−5.46573	+	5.46573i	−0.387455	+	0.387455i	0.486324	+	0.873779i	$0.338338\pi$
$200$	19.8430	+	9.90044i	1.40311	+	0.700067i
$201$	−3.78554	+	3.56255i	−0.267012	+	0.251283i
$202$	10.5362	+	5.21618i	0.741322	+	0.367009i
$203$	−3.25725	−	4.24494i	−0.228614	−	0.297936i
$204$	0.552906	−	1.81802i	0.0387112	−	0.127287i
$205$	−15.1501	−	11.6250i	−1.05813	−	0.811928i
$206$	0.0391840	−	0.114847i	0.00273008	−	0.00800179i
$207$	17.3806	−	8.67452i	1.20803	−	0.602921i
$208$	−7.68248	−	10.1416i	−0.532684	−	0.703192i
$209$	7.70654	+	13.3481i	0.533073	+	0.923309i
$210$	30.6622	−	25.2068i	2.11589	−	1.73943i
$211$	−19.3264	−	2.54437i	−1.33048	−	0.175162i	−0.568461	−	0.822711i	$-0.692461\pi$
$211$	−19.3264	−	2.54437i	−1.33048	−	0.175162i	−0.762024	+	0.647549i	$0.775794\pi$
$212$	0.0528067	−	17.0357i	0.00362678	−	1.17002i
$213$	1.43844	+	14.2559i	0.0985605	+	0.976800i
$214$	−11.9253	+	7.94154i	−0.815199	+	0.542873i
$215$	−22.6520	+	22.6520i	−1.54485	+	1.54485i
$216$	11.3842	+	9.29510i	0.774600	+	0.632452i
$217$	0.590843	+	0.590843i	0.0401091	+	0.0401091i
$218$	7.06334	+	1.41637i	0.478390	+	0.0959286i
$219$	19.0477	−	1.92194i	1.28713	−	0.129873i
$220$	−10.1523	+	24.2965i	−0.684467	+	1.63807i
$221$	0.227741	−	1.72986i	0.0153195	−	0.116363i
$222$	0.432470	−	4.42891i	0.0290255	−	0.297249i
$223$	2.82654	−	1.63191i	0.189279	−	0.109281i	−0.402366	−	0.915479i	$-0.631812\pi$
$223$	2.82654	−	1.63191i	0.189279	−	0.109281i	0.591645	+	0.806198i	$0.298479\pi$
$224$	−25.5131	−	1.87088i	−1.70467	−	0.125004i
$225$	−23.4776	−	1.42631i	−1.56518	−	0.0950871i
$226$	0.660274	−	0.324340i	0.0439207	−	0.0215748i
$227$	−11.4259	+	14.8905i	−0.758363	+	0.988318i	0.241477	+	0.970407i	$0.422368\pi$
$227$	−11.4259	+	14.8905i	−0.758363	+	0.988318i	−0.999840	+	0.0179111i	$0.994298\pi$
$228$	14.4625	−	1.41402i	0.957803	−	0.0936455i
$229$	−19.9938	+	15.3418i	−1.32123	+	1.01382i	−0.323518	+	0.946222i	$0.604866\pi$
$229$	−19.9938	+	15.3418i	−1.32123	+	1.01382i	−0.997713	+	0.0675940i	$0.978468\pi$
$230$	31.0877	−	10.4992i	2.04986	−	0.692294i
$231$	19.7236	+	20.9582i	1.29772	+	1.37895i
$232$	2.52630	−	2.19481i	0.165860	−	0.144096i
$233$	4.53387	+	4.53387i	0.297024	+	0.297024i	0.839847	−	0.542823i	$-0.182645\pi$
$233$	4.53387	+	4.53387i	0.297024	+	0.297024i	−0.542823	+	0.839847i	$0.682645\pi$
$234$	11.7084	+	6.70963i	0.765403	+	0.438623i
$235$	13.2603	+	5.49260i	0.865007	+	0.358298i
$236$	−14.0514	−	8.17075i	−0.914667	−	0.531870i
$237$	−2.93329	+	18.0344i	−0.190538	+	1.17146i
$238$	−2.30903	−	2.64119i	−0.149672	−	0.171203i
$239$	−8.65398	−	4.99638i	−0.559780	−	0.323189i	0.193277	−	0.981144i	$-0.438088\pi$
$239$	−8.65398	−	4.99638i	−0.559780	−	0.323189i	−0.753057	+	0.657955i	$0.771422\pi$
$240$	16.9017	+	18.1843i	1.09100	+	1.17379i
$241$	7.59062	−	4.38245i	0.488955	−	0.282298i	−0.235186	−	0.971950i	$-0.575570\pi$
$241$	7.59062	−	4.38245i	0.488955	−	0.282298i	0.724141	+	0.689652i	$0.242237\pi$
$242$	−3.34645	−	1.14175i	−0.215118	−	0.0733948i
$243$	−14.9702	−	4.34678i	−0.960336	−	0.278846i
$244$	7.92174	+	2.14897i	0.507138	+	0.137573i
$245$	−6.29111	−	47.7857i	−0.401924	−	3.05292i
$246$	−6.90254	−	11.0795i	−0.440090	−	0.706404i
$247$	12.8881	−	3.45335i	0.820050	−	0.219732i
$248$	−0.346405	+	0.391314i	−0.0219967	+	0.0248485i
$249$	−4.51280	−	19.1476i	−0.285987	−	1.21343i
$250$	−14.1126	−	2.82992i	−0.892559	−	0.178980i
$251$	19.0187	+	7.87782i	1.20045	+	0.497244i	0.891145	−	0.453719i	$-0.149903\pi$
$251$	19.0187	+	7.87782i	1.20045	+	0.497244i	0.309307	+	0.950962i	$0.399903\pi$
$252$	25.6788	−	8.76472i	1.61761	−	0.552125i
$253$	9.10439	+	21.9799i	0.572388	+	1.38187i
$254$	3.59632	−	5.36426i	0.225653	−	0.336584i
$255$	−0.103275	+	3.40302i	−0.00646731	+	0.213106i
$256$	0.198379	−	15.9988i	0.0123987	−	0.999923i
$257$	−13.7450	−	7.93568i	−0.857390	−	0.495014i	0.00574760	−	0.999983i	$-0.498170\pi$
$257$	−13.7450	−	7.93568i	−0.857390	−	0.495014i	−0.863137	+	0.504969i	$0.831504\pi$
$258$	−19.9388	+	9.05425i	−1.24133	+	0.563693i
$259$	−6.51781	−	5.00129i	−0.404997	−	0.310765i
$260$	18.0416	+	13.9328i	1.11889	+	0.864078i
$261$	−1.55471	+	3.19095i	−0.0962343	+	0.197515i
$262$	8.30077	+	7.30237i	0.512823	+	0.451142i
$263$	7.00558	−	26.1452i	0.431983	−	1.61218i	−0.316202	−	0.948692i	$-0.602408\pi$
$263$	7.00558	−	26.1452i	0.431983	−	1.61218i	0.748185	−	0.663490i	$-0.230925\pi$
$264$	−12.3345	+	13.1098i	−0.759134	+	0.806851i
$265$	7.89980	+	29.4825i	0.485281	+	1.81109i
$266$	11.9030	−	24.0428i	0.729817	−	1.47416i
$267$	−4.47270	+	0.451302i	−0.273725	+	0.0276193i
$268$	−5.80271	+	1.53557i	−0.354457	+	0.0937998i
$269$	−7.59306	−	18.3313i	−0.462957	−	1.11768i	−0.967177	−	0.254102i	$-0.918220\pi$
$269$	−7.59306	−	18.3313i	−0.462957	−	1.11768i	0.504220	−	0.863575i	$-0.331780\pi$
$270$	−24.0455	−	10.7327i	−1.46336	−	0.653172i
$271$	−24.2269			−1.47168			−0.735840	−	0.677156i	$-0.763212\pi$
$271$	−24.2269			−1.47168			−0.735840	+	0.677156i	$0.763212\pi$
$272$	1.56112	−	1.54189i	0.0946571	−	0.0934906i
$273$	21.9439	−	11.7967i	1.32811	−	0.713967i
$274$	2.03445	−	1.77859i	0.122906	−	0.107449i
$275$	3.76012	−	28.5609i	0.226744	−	1.72229i
$276$	22.4176	+	0.749885i	1.34938	+	0.0451378i
$277$	4.68801	−	0.617189i	0.281675	−	0.0370833i	0.0116352	−	0.999932i	$-0.496296\pi$
$277$	4.68801	−	0.617189i	0.281675	−	0.0370833i	0.270040	+	0.962849i	$0.412963\pi$
$278$	−6.45573	+	0.413083i	−0.387189	+	0.0247751i
$279$	0.175671	−	0.525740i	0.0105171	−	0.0314753i
$280$	44.9942	−	8.73262i	2.68892	−	0.521874i
$281$	8.00579	+	2.14514i	0.477585	+	0.127969i	0.489578	−	0.871959i	$-0.337151\pi$
$281$	8.00579	+	2.14514i	0.477585	+	0.127969i	−0.0119927	+	0.999928i	$0.503817\pi$
$282$	7.16652	+	6.70093i	0.426760	+	0.399035i
$283$	−15.2166	−	19.8307i	−0.904534	−	1.17881i	−0.983313	−	0.181920i	$-0.941769\pi$
$283$	−15.2166	−	19.8307i	−0.904534	−	1.17881i	0.0787792	−	0.996892i	$-0.474898\pi$
$284$	−6.37881	+	15.2658i	−0.378513	+	0.905859i
$285$	−24.3449	+	9.22915i	−1.44207	+	0.546688i
$286$	−9.20357	+	13.7280i	−0.544218	+	0.811754i
$287$	−24.0998			−1.42256
$288$	6.44765	+	15.6980i	0.379932	+	0.925015i
$289$	−16.6991			−0.982300
$290$	−3.33886	+	4.98024i	−0.196065	+	0.292450i
$291$	0.200273	−	1.23131i	0.0117402	−	0.0721807i
$292$	20.3971	+	8.52291i	1.19365	+	0.498766i
$293$	−4.09079	−	5.33122i	−0.238986	−	0.311453i	0.658426	−	0.752645i	$-0.271222\pi$
$293$	−4.09079	−	5.33122i	−0.238986	−	0.311453i	−0.897413	+	0.441192i	$0.854556\pi$
$294$	7.45467	−	32.0927i	0.434765	−	1.87168i
$295$	28.1300	+	7.53741i	1.63779	+	0.438845i
$296$	2.87457	−	4.25910i	0.167081	−	0.247555i
$297$	6.59708	−	17.9160i	0.382802	−	1.03959i
$298$	25.4736	−	1.62998i	1.47565	−	0.0944223i
$299$	20.4190	−	2.68822i	1.18086	−	0.155463i
$300$	−23.0538	−	14.3586i	−1.33101	−	0.828992i
$301$	−5.27697	+	40.0826i	−0.304160	+	2.31032i
$302$	−23.4455	+	20.4969i	−1.34913	+	1.17947i
$303$	−12.2457	−	7.57441i	−0.703498	−	0.435138i
$304$	15.4621	+	6.51722i	0.886814	+	0.373788i
$305$	−14.7061			−0.842069
$306$	−0.883686	+	2.15301i	−0.0505170	+	0.123079i
$307$	−5.23742	−	12.6443i	−0.298916	−	0.721646i	−0.999964	−	0.00853194i	$-0.997284\pi$
$307$	−5.23742	−	12.6443i	−0.298916	−	0.721646i	0.701048	−	0.713114i	$-0.252716\pi$
$308$	8.50148	+	32.1260i	0.484417	+	1.83055i
$309$	−0.0610133	+	0.135519i	−0.00347093	+	0.00770939i
$310$	0.415437	−	0.839141i	0.0235952	−	0.0476600i
$311$	6.03849	+	22.5359i	0.342411	+	1.27790i	0.895607	+	0.444845i	$0.146741\pi$
$311$	6.03849	+	22.5359i	0.342411	+	1.27790i	−0.553196	+	0.833051i	$0.686592\pi$
$312$	8.19854	+	13.2511i	0.464151	+	0.750197i
$313$	−8.08791	+	30.1845i	−0.457156	+	1.70613i	0.224517	+	0.974470i	$0.427920\pi$
$313$	−8.08791	+	30.1845i	−0.457156	+	1.70613i	−0.681672	+	0.731657i	$0.738747\pi$
$314$	13.9867	+	12.3044i	0.789314	+	0.694377i
$315$	−40.2918	+	27.2011i	−2.27018	+	1.53261i
$316$	−12.8954	+	16.6982i	−0.725425	+	0.939349i
$317$	12.5842	+	9.65622i	0.706801	+	0.542347i	0.898428	−	0.439120i	$-0.144710\pi$
$317$	12.5842	+	9.65622i	0.706801	+	0.542347i	−0.191627	+	0.981468i	$0.561376\pi$
$318$	−2.02771	+	20.7657i	−0.113708	+	1.16448i
$319$	−3.76489	−	2.17366i	−0.210794	−	0.121702i
$320$	7.16167	+	27.7577i	0.400350	+	1.55170i
$321$	15.4559	−	8.30885i	0.862666	−	0.463755i
$322$	23.0597	−	34.3957i	1.28507	−	1.91680i
$323$	0.880593	+	2.12594i	0.0489975	+	0.118290i
$324$	−12.8097	−	12.6456i	−0.711650	−	0.702534i
$325$	−23.0396	−	9.54330i	−1.27800	−	0.529367i
$326$	10.8391	+	2.17349i	0.600320	+	0.120379i
$327$	−8.44917	−	2.54103i	−0.467240	−	0.140519i
$328$	−0.915888	−	15.0453i	−0.0505714	−	0.830739i
$329$	17.4964	−	4.68813i	0.964605	−	0.258465i
$330$	15.1789	−	28.4549i	0.835571	−	1.56639i
$331$	0.682595	+	5.18482i	0.0375188	+	0.284984i	0.999911	+	0.0133207i	$0.00424023\pi$
$331$	0.682595	+	5.18482i	0.0375188	+	0.284984i	−0.962392	+	0.271663i	$0.912426\pi$
$332$	5.94720	−	21.9232i	0.326395	−	1.20319i
$333$	−1.03774	+	5.35038i	−0.0568676	+	0.293199i
$334$	13.0536	+	4.45368i	0.714262	+	0.243694i
$335$	9.31359	−	5.37720i	0.508856	−	0.293788i
$336$	30.8928	+	5.22151i	1.68534	+	0.284857i
$337$	−21.4590	−	12.3894i	−1.16895	−	0.674892i	−0.215515	−	0.976500i	$-0.569143\pi$
$337$	−21.4590	−	12.3894i	−1.16895	−	0.674892i	−0.953432	+	0.301609i	$0.902476\pi$
$338$	−2.68351	−	3.06954i	−0.145964	−	0.166961i
$339$	−0.842458	+	0.319376i	−0.0457560	+	0.0173461i
$340$	−1.97619	+	3.39848i	−0.107174	+	0.184309i
$341$	0.627220	+	0.259803i	0.0339659	+	0.0140691i
$342$	−17.7972	+	0.0573572i	−0.962365	+	0.00310152i
$343$	−20.6271	−	20.6271i	−1.11376	−	1.11376i
$344$	−25.2238	−	1.77108i	−1.35998	−	0.0954902i
$345$	−39.1156	+	9.21895i	−2.10591	+	0.496332i
$346$	−6.93832	+	2.34326i	−0.373006	+	0.125974i
$347$	15.0586	−	11.5549i	0.808390	−	0.620299i	−0.119635	−	0.992818i	$-0.538172\pi$
$347$	15.0586	−	11.5549i	0.808390	−	0.620299i	0.928025	+	0.372519i	$0.121506\pi$
$348$	−3.33329	+	2.38500i	−0.178683	+	0.127850i
$349$	9.59981	−	12.5107i	0.513866	−	0.669683i	−0.462296	−	0.886726i	$-0.652974\pi$
$349$	9.59981	−	12.5107i	0.513866	−	0.669683i	0.976162	+	0.217042i	$0.0696410\pi$
$350$	−45.0052	+	22.1075i	−2.40563	+	1.18169i
$351$	−13.5029	−	9.53049i	−0.720732	−	0.508700i
$352$	−19.7329	+	6.52833i	−1.05177	+	0.347961i
$353$	14.2883	−	8.24933i	0.760487	−	0.439068i	−0.0689834	−	0.997618i	$-0.521976\pi$
$353$	14.2883	−	8.24933i	0.760487	−	0.439068i	0.829471	+	0.558550i	$0.188642\pi$
$354$	16.1913	+	11.5821i	0.860560	+	0.615580i
$355$	3.86919	−	29.3894i	0.205355	−	1.55983i
$356$	−4.78955	−	2.00131i	−0.253845	−	0.106069i
$357$	2.51103	+	3.48654i	0.132898	+	0.184527i
$358$	2.43149	+	0.487573i	0.128508	+	0.0257690i
$359$	13.1558	+	13.1558i	0.694335	+	0.694335i	0.963183	−	0.268848i	$-0.0866428\pi$
$359$	13.1558	+	13.1558i	0.694335	+	0.694335i	−0.268848	+	0.963183i	$0.586643\pi$
$360$	−18.5127	−	24.1201i	−0.975707	−	1.27124i
$361$	0.992098	−	0.992098i	0.0522157	−	0.0522157i
$362$	−22.7390	+	15.1428i	−1.19514	+	0.795887i
$363$	3.94878	+	1.77782i	0.207257	+	0.0933115i
$364$	28.7678	+	0.0891735i	1.50784	+	0.00467396i
$365$	−39.2680	−	5.16973i	−2.05538	−	0.270596i
$366$	−9.41140	−	3.53322i	−0.491942	−	0.184684i
$367$	4.84907	+	8.39884i	0.253119	+	0.438416i	0.964383	−	0.264510i	$-0.0852101\pi$
$367$	4.84907	+	8.39884i	0.253119	+	0.438416i	−0.711264	+	0.702925i	$0.751877\pi$
$368$	22.3494	+	13.0888i	1.16504	+	0.682302i
$369$	7.13945	+	14.3049i	0.371665	+	0.744681i
$370$	−2.97277	+	8.71312i	−0.154547	+	0.452974i
$371$	30.5599	+	23.4494i	1.58659	+	1.21743i
$372$	0.467473	−	0.437211i	0.0242374	−	0.0226683i
$373$	23.3575	+	30.4400i	1.20940	+	1.57612i	0.696174	+	0.717873i	$0.254884\pi$
$373$	23.3575	+	30.4400i	1.20940	+	1.57612i	0.513229	+	0.858252i	$0.328449\pi$
$374$	−2.55447	−	1.26465i	−0.132088	−	0.0653935i
$375$	16.8815	+	5.07699i	0.871757	+	0.262175i
$376$	3.59170	+	10.7447i	0.185228	+	0.554115i
$377$	−2.66111	+	2.66111i	−0.137054	+	0.137054i
$378$	−32.3206	+	7.72750i	−1.66239	+	0.397460i
$379$	−7.58988	+	18.3236i	−0.389866	+	0.941220i	0.600101	+	0.799924i	$0.295127\pi$
$379$	−7.58988	+	18.3236i	−0.389866	+	0.941220i	−0.989967	+	0.141296i	$0.954873\pi$
$380$	−29.7938	−	4.01642i	−1.52839	−	0.206038i
$381$	−5.00325	+	6.12623i	−0.256324	+	0.313856i
$382$	1.35841	−	20.2445i	0.0695022	−	1.03580i
$383$	14.7727	−	25.5871i	0.754850	−	1.30744i	−0.190599	−	0.981668i	$-0.561043\pi$
$383$	14.7727	−	25.5871i	0.754850	−	1.30744i	0.945449	−	0.325770i	$-0.105624\pi$
$384$	−2.08570	+	19.4846i	−0.106436	+	0.994320i
$385$	−29.7702	−	51.5635i	−1.51723	−	2.62792i
$386$	−24.4903	+	12.0301i	−1.24652	+	0.612317i
$387$	25.3550	−	8.74205i	1.28887	−	0.444383i
$388$	0.880446	−	1.14008i	0.0446979	−	0.0578790i
$389$	18.9667	−	2.49701i	0.961649	−	0.126603i	0.366675	−	0.930349i	$-0.380496\pi$
$389$	18.9667	−	2.49701i	0.961649	−	0.126603i	0.594973	+	0.803746i	$0.297163\pi$
$390$	−20.3925	−	19.0677i	−1.03262	−	0.965530i
$391$	0.919292	+	3.43084i	0.0464906	+	0.173505i
$392$	25.2169	−	28.4861i	1.27365	−	1.43877i
$393$	−9.27963	−	9.86050i	−0.468096	−	0.497396i
$394$	−13.4872	+	8.98164i	−0.679475	+	0.452489i
$395$	14.4656	−	34.9231i	0.727845	−	1.75717i
$396$	16.5504	−	14.5634i	0.831690	−	0.731837i
$397$	12.1717	−	5.04169i	0.610881	−	0.253035i	−0.0557244	−	0.998446i	$-0.517747\pi$
$397$	12.1717	−	5.04169i	0.610881	−	0.253035i	0.666605	+	0.745411i	$0.267747\pi$
$398$	10.7247	−	2.11600i	0.537581	−	0.106066i
$399$	−17.2843	+	27.9439i	−0.865296	+	1.39894i
$400$	−15.5119	−	27.2563i	−0.775597	−	1.36282i
$401$	4.86455	−	8.42564i	0.242924	−	0.420757i	−0.718622	−	0.695401i	$-0.755227\pi$
$401$	4.86455	−	8.42564i	0.242924	−	0.420757i	0.961546	+	0.274644i	$0.0885601\pi$
$402$	7.25228	−	1.20359i	0.361711	−	0.0600295i
$403$	0.357773	−	0.466258i	0.0178219	−	0.0232260i
$404$	−8.26855	−	14.4246i	−0.411376	−	0.717652i
$405$	28.0820	+	15.8577i	1.39541	+	0.787975i
$406$	0.483197	+	7.55148i	0.0239807	+	0.374774i
$407$	−6.44758	−	1.72762i	−0.319595	−	0.0856351i
$408$	−2.08119	+	1.70012i	−0.103034	+	0.0841686i
$409$	9.64097	−	2.58329i	0.476715	−	0.127735i	−0.0124575	−	0.999922i	$-0.503965\pi$
$409$	9.64097	−	2.58329i	0.476715	−	0.127735i	0.489173	+	0.872187i	$0.337299\pi$
$410$	8.64119	+	25.5863i	0.426758	+	1.26362i
$411$	−2.68560	+	1.93419i	−0.132471	+	0.0954067i
$412$	−0.136472	+	0.104048i	−0.00672349	+	0.00512608i
$413$	33.9552	−	14.0647i	1.67083	−	0.692080i
$414$	−27.2475	−	3.49791i	−1.33914	−	0.171913i
$415$			40.6987i			1.99782i
$416$	1.03762	+	17.9629i	0.0508736	+	0.880706i
$417$	7.91914	+	0.240329i	0.387802	+	0.0117690i
$418$	1.45933	−	21.7485i	0.0713780	−	1.06375i
$419$	28.5651	+	3.76066i	1.39549	+	0.183720i	0.790477	−	0.612492i	$-0.209833\pi$
$419$	28.5651	+	3.76066i	1.39549	+	0.183720i	0.605018	+	0.796212i	$0.293166\pi$
$420$	−55.8683	+	5.46231i	−2.72609	+	0.266533i
$421$	−2.62414	−	19.9323i	−0.127893	−	0.971441i	−0.928260	−	0.371931i	$-0.878696\pi$
$421$	−2.62414	−	19.9323i	−0.127893	−	0.971441i	0.800368	−	0.599509i	$-0.204638\pi$
$422$	20.6981	+	18.2086i	1.00757	+	0.886382i
$423$	−7.96595	−	8.99644i	−0.387318	−	0.437422i
$424$	−13.4779	+	19.9695i	−0.654546	+	0.969806i
$425$	1.11313	−	4.15426i	0.0539947	−	0.201511i
$426$	9.53710	−	17.8786i	0.462074	−	0.866221i
$427$	−14.7241	+	11.2982i	−0.712551	+	0.546759i
$428$	20.2623	+	0.0628083i	0.979414	+	0.00303595i
$429$	12.8041	−	15.6780i	0.618189	−	0.756942i
$430$	44.4472	−	8.76950i	2.14343	−	0.422903i
$431$			3.21501i			0.154862i	0.996998	+	0.0774308i	$0.0246717\pi$
$431$			3.21501i			0.154862i	−0.996998	+	0.0774308i	$0.975328\pi$
$432$	−6.05254	−	19.8838i	−0.291203	−	0.956661i
$433$		−	16.4770i		−	0.791833i	−0.918287	−	0.395917i	$-0.870427\pi$
$433$		−	16.4770i		−	0.791833i	0.918287	−	0.395917i	$-0.129573\pi$
$434$	−0.228739	−	1.15934i	−0.0109798	−	0.0556499i
$435$	4.64507	−	5.68766i	0.222714	−	0.272702i
$436$	−7.18158	−	7.22624i	−0.343935	−	0.346074i
$437$	−21.5489	+	16.5351i	−1.03083	+	0.790980i
$438$	−23.8881	−	12.7428i	−1.14142	−	0.608874i
$439$	5.38636	−	20.1022i	0.257077	−	0.959424i	−0.709847	−	0.704356i	$-0.751236\pi$
$439$	5.38636	−	20.1022i	0.257077	−	0.959424i	0.966923	−	0.255067i	$-0.0820976\pi$
$440$	31.0593	−	20.5449i	1.48070	−	0.979442i
$441$	−12.7882	+	38.2718i	−0.608960	+	1.82247i
$442$	−1.62981	+	1.85264i	−0.0775222	+	0.0881212i
$443$	−2.25818	−	17.1526i	−0.107289	−	0.814945i	−0.957486	−	0.288479i	$-0.906850\pi$
$443$	−2.25818	−	17.1526i	−0.107289	−	0.814945i	0.850197	−	0.526465i	$-0.176483\pi$
$444$	−3.99585	+	4.86187i	−0.189634	+	0.230734i
$445$	9.22073	+	1.21393i	0.437105	+	0.0575459i
$446$	−4.60537	−	0.309021i	−0.218071	−	0.0146326i
$447$	−31.2481	−	0.948313i	−1.47798	−	0.0448537i
$448$	28.4958	+	22.2896i	1.34630	+	1.05309i
$449$			33.6970i			1.59026i	0.606440	+	0.795129i	$0.292597\pi$
$449$			33.6970i			1.59026i	−0.606440	+	0.795129i	$0.707403\pi$
$450$	26.4549	+	20.1644i	1.24710	+	0.950561i
$451$	−18.0903	+	7.49325i	−0.851839	+	0.352843i
$452$	−1.03102	−	0.138989i	−0.0484950	−	0.00653748i
$453$	30.9495	−	22.2901i	1.45414	−	1.04728i
$454$	25.1480	−	8.49316i	1.18025	−	0.398604i
$455$	−49.7864	+	13.3402i	−2.33402	+	0.625399i
$456$	−18.1020	−	9.72848i	−0.847706	−	0.455578i
$457$	−25.2453	−	6.76446i	−1.18093	−	0.316428i	−0.385632	−	0.922653i	$-0.626017\pi$
$457$	−25.2453	−	6.76446i	−1.18093	−	0.316428i	−0.795294	+	0.606224i	$0.792683\pi$
$458$	35.5678	−	2.27588i	1.66198	−	0.106345i
$459$	1.32562	−	2.52334i	0.0618745	−	0.117779i
$460$	−44.7857	−	12.1492i	−2.08814	−	0.566459i
$461$	−10.6804	+	13.9190i	−0.497436	+	0.648271i	−0.972835	−	0.231499i	$-0.925637\pi$
$461$	−10.6804	+	13.9190i	−0.497436	+	0.648271i	0.475399	+	0.879770i	$0.342304\pi$
$462$	−6.66351	−	40.1513i	−0.310015	−	1.86801i
$463$	−10.6746	+	18.4889i	−0.496091	+	0.859254i	−0.999990	−	0.00450820i	$-0.998565\pi$
$463$	−10.6746	+	18.4889i	−0.496091	+	0.859254i	0.503899	+	0.863763i	$0.331898\pi$
$464$	−4.69598	+	0.588644i	−0.218005	+	0.0273271i
$465$	−0.603255	+	0.975296i	−0.0279753	+	0.0452283i
$466$	−1.75524	−	8.89624i	−0.0813101	−	0.412110i
$467$	16.4864	−	6.82888i	0.762898	−	0.316003i	0.0329063	−	0.999458i	$-0.489524\pi$
$467$	16.4864	−	6.82888i	0.762898	−	0.316003i	0.729992	+	0.683456i	$0.239524\pi$
$468$	−8.46941	−	17.1021i	−0.391499	−	0.790544i
$469$	5.19387	−	12.5391i	0.239831	−	0.579003i
$470$	−11.2508	−	16.8946i	−0.518960	−	0.779291i
$471$	−15.6361	−	16.6148i	−0.720471	−	0.765569i
$472$	10.0709	+	20.6635i	0.463553	+	0.951116i
$473$	8.50161	+	31.7284i	0.390904	+	1.45887i
$474$	17.6480	−	18.8742i	0.810598	−	0.866919i
$475$	32.6077	−	4.29289i	1.49614	−	0.196971i
$476$	0.632336	+	4.92089i	0.0289831	+	0.225549i
$477$	4.86561	−	25.0862i	0.222781	−	1.14862i
$478$	6.23073	+	12.6842i	0.284987	+	0.580161i
$479$	−6.41448	−	11.1102i	−0.293085	−	0.507638i	0.681453	−	0.731862i	$-0.261349\pi$
$479$	−6.41448	−	11.1102i	−0.293085	−	0.507638i	−0.974538	+	0.224224i	$0.928015\pi$
$480$	−5.53330	−	34.6706i	−0.252559	−	1.58249i
$481$	−2.88920	+	5.00425i	−0.131736	+	0.228174i
$482$	−12.3676	−	0.829869i	−0.563330	−	0.0377995i
$483$	−32.0809	+	39.2815i	−1.45973	+	1.78737i
$484$	3.03178	+	3.97656i	0.137808	+	0.180753i
$485$	−0.987653	+	2.38440i	−0.0448470	+	0.108270i
$486$	14.1616	+	16.8952i	0.642384	+	0.766383i
$487$	−11.8024	+	11.8024i	−0.534818	+	0.534818i	−0.922002	−	0.387185i	$-0.873448\pi$
$487$	−11.8024	+	11.8024i	−0.534818	+	0.534818i	0.387185	+	0.922002i	$0.373448\pi$
$488$	−7.61298	−	8.76280i	−0.344624	−	0.396673i
$489$	−12.9657	−	3.89934i	−0.586329	−	0.176334i
$490$	−30.2421	+	61.0862i	−1.36620	+	2.75959i
$491$	15.1412	+	19.7324i	0.683314	+	0.890512i	0.998282	−	0.0585900i	$-0.0186605\pi$
$491$	15.1412	+	19.7324i	0.683314	+	0.890512i	−0.314968	+	0.949102i	$0.601994\pi$
$492$	−0.617183	+	18.4505i	−0.0278248	+	0.831812i
$493$	−0.514914	−	0.395108i	−0.0231906	−	0.0177947i
$494$	−17.8587	−	6.09308i	−0.803499	−	0.274141i
$495$	−21.7871	+	32.9461i	−0.979259	+	1.48082i
$496$	0.715073	−	0.186860i	0.0321077	−	0.00839025i
$497$	−18.7050	−	32.3980i	−0.839033	−	1.45325i
$498$	−9.77807	+	26.0458i	−0.438166	+	1.16714i
$499$	34.3399	+	4.52093i	1.53727	+	0.202385i	0.851078	−	0.525040i	$-0.175950\pi$
$499$	34.3399	+	4.52093i	1.53727	+	0.202385i	0.686188	+	0.727425i	$0.259283\pi$
$500$	14.3489	+	14.4381i	0.641700	+	0.645691i
$501$	−15.4031	−	6.93481i	−0.688161	−	0.309825i
$502$	−16.1366	−	24.2313i	−0.720210	−	1.08150i
$503$	−18.4325	+	18.4325i	−0.821864	+	0.821864i	−0.986375	−	0.164511i	$-0.947395\pi$
$503$	−18.4325	+	18.4325i	−0.821864	+	0.821864i	0.164511	+	0.986375i	$0.447395\pi$
$504$	−37.0661	−	9.92696i	−1.65106	−	0.442182i
$505$	21.0641	+	21.0641i	0.937338	+	0.937338i
$506$	6.61503	−	32.9887i	0.294074	−	1.46653i
$507$	2.91828	+	4.05200i	0.129605	+	0.179955i
$508$	−8.44889	+	3.46900i	−0.374859	+	0.153912i
$509$	3.68944	−	28.0241i	0.163531	−	1.24214i	−0.691042	−	0.722814i	$-0.742848\pi$
$509$	3.68944	−	28.0241i	0.163531	−	1.24214i	0.854574	−	0.519330i	$-0.173818\pi$
$510$	2.80125	−	3.91605i	0.124041	−	0.173406i
$511$	−43.2879	+	24.9923i	−1.91494	+	1.10559i
$512$	−12.8323	+	18.6368i	−0.567114	+	0.823639i
$513$	21.7070	+	1.98115i	0.958387	+	0.0874699i
$514$	9.89618	+	20.1461i	0.436502	+	0.888607i
$515$	0.187177	−	0.243933i	0.00824799	−	0.0107490i
$516$	30.5516	+	5.06648i	1.34496	+	0.223039i
$517$	11.6758	−	8.95918i	0.513503	−	0.394024i
$518$	3.71759	+	11.0077i	0.163342	+	0.483650i
$519$	8.73002	−	2.05753i	0.383205	−	0.0903156i
$520$	−10.2203	−	30.5743i	−0.448189	−	1.34077i
$521$	−11.9747	−	11.9747i	−0.524623	−	0.524623i	0.394341	−	0.918964i	$-0.370973\pi$
$521$	−11.9747	−	11.9747i	−0.524623	−	0.524623i	−0.918964	+	0.394341i	$0.870973\pi$
$522$	4.33918	−	2.52391i	0.189921	−	0.110468i
$523$	4.32899	+	1.79313i	0.189294	+	0.0784079i	0.475317	−	0.879815i	$-0.342333\pi$
$523$	4.32899	+	1.79313i	0.189294	+	0.0784079i	−0.286023	+	0.958223i	$0.592333\pi$
$524$	−3.99981	−	15.1148i	−0.174733	−	0.660292i
$525$	57.4232	−	21.7691i	2.50615	−	0.950083i
$526$	−28.8189	+	25.1946i	−1.25656	+	1.09854i
$527$	0.0877771	+	0.0506782i	0.00382363	+	0.00220758i
$528$	24.8129	−	5.68589i	1.07984	−	0.247447i
$529$	−16.3902	+	9.46288i	−0.712617	+	0.411429i
$530$	13.9384	−	40.8530i	0.605444	−	1.77454i
$531$	−18.4075	−	15.9881i	−0.798816	−	0.693826i
$532$	−32.9160	+	18.8683i	−1.42709	+	0.818043i
$533$	2.21250	+	16.8056i	0.0958340	+	0.727932i
$534$	5.60930	+	2.99220i	0.242738	+	0.129485i
$535$	−35.0664	+	9.39602i	−1.51605	+	0.406225i
$536$	8.02548	+	2.76596i	0.346648	+	0.119471i
$537$	−2.90855	−	0.874726i	−0.125513	−	0.0377472i
$538$	−5.51694	+	27.5126i	−0.237852	+	1.18615i
$539$	−45.6592	−	18.9126i	−1.96668	−	0.814625i
$540$	19.7930	+	31.5435i	0.851755	+	1.35741i
$541$	11.7299	+	28.3184i	0.504306	+	1.21750i	0.947117	+	0.320888i	$0.103981\pi$
$541$	11.7299	+	28.3184i	0.504306	+	1.21750i	−0.442811	+	0.896615i	$0.646019\pi$
$542$	28.4583	+	19.0791i	1.22239	+	0.819517i
$543$	29.4711	−	15.8432i	1.26472	−	0.679895i
$544$	−3.04805	+	0.581776i	−0.130684	+	0.0249435i
$545$	15.8079	+	9.12669i	0.677136	+	0.390944i
$546$	−35.0666	−	3.42415i	−1.50071	−	0.146540i
$547$	−12.4519	−	9.55467i	−0.532404	−	0.408528i	0.307267	−	0.951623i	$-0.400586\pi$
$547$	−12.4519	−	9.55467i	−0.532404	−	0.408528i	−0.839671	+	0.543095i	$0.817252\pi$
$548$	−3.79045	+	0.487074i	−0.161920	+	0.0208068i
$549$	11.0682	+	5.39273i	0.472380	+	0.230156i
$550$	−26.9090	+	30.5881i	−1.14741	+	1.30428i
$551$	1.28460	−	4.79418i	0.0547256	−	0.204239i
$552$	−25.7424	−	18.5351i	−1.09567	−	0.788904i
$553$	−12.3470	−	46.0794i	−0.525046	−	1.95950i
$554$	−5.99285	−	2.96690i	−0.254612	−	0.126052i
$555$	4.62890	−	10.2814i	0.196486	−	0.436421i
$556$	7.90857	+	4.59876i	0.335398	+	0.195031i
$557$	16.5582	+	39.9749i	0.701592	+	1.69379i	0.720011	+	0.693962i	$0.244137\pi$
$557$	16.5582	+	39.9749i	0.701592	+	1.69379i	−0.0184193	+	0.999830i	$0.505863\pi$
$558$	−0.620382	+	0.479221i	−0.0262629	+	0.0202870i
$559$	28.4354			1.20269
$560$	−59.7298	−	25.1758i	−2.52404	−	1.06387i
$561$	2.96894	+	1.83640i	0.125349	+	0.0775328i
$562$	−7.71472	−	8.82450i	−0.325426	−	0.372239i
$563$	−1.57180	+	11.9390i	−0.0662434	+	0.503168i	0.925872	+	0.377838i	$0.123332\pi$
$563$	−1.57180	+	11.9390i	−0.0662434	+	0.503168i	−0.992115	+	0.125330i	$0.960001\pi$
$564$	−3.14110	−	13.5150i	−0.132264	−	0.569086i
$565$	1.84800	−	0.243294i	0.0777461	−	0.0102355i
$566$	2.25731	+	35.2776i	0.0948818	+	1.48283i
$567$	40.2994	−	5.69736i	1.69241	−	0.239266i
$568$	19.5150	−	12.9087i	0.818830	−	0.541635i
$569$	0.325744	+	0.0872828i	0.0136559	+	0.00365908i	0.265641	−	0.964072i	$-0.414417\pi$
$569$	0.325744	+	0.0872828i	0.0136559	+	0.00365908i	−0.251985	+	0.967731i	$0.581083\pi$
$570$	35.8650	+	8.33092i	1.50222	+	0.348944i
$571$	6.71492	+	8.75105i	0.281010	+	0.366220i	0.912438	−	0.409215i	$-0.134197\pi$
$571$	6.71492	+	8.75105i	0.281010	+	0.366220i	−0.631428	+	0.775435i	$0.717531\pi$
$572$	21.6221	−	8.87773i	0.904064	−	0.371197i
$573$	−3.98945	+	24.5278i	−0.166662	+	1.02466i
$574$	28.3090	+	18.9790i	1.18159	+	0.792167i
$575$	50.7660			2.11709
$576$	4.78867	−	23.5174i	0.199528	−	0.979892i
$577$	32.2236			1.34149			0.670743	−	0.741690i	$-0.265975\pi$
$577$	32.2236			1.34149			0.670743	+	0.741690i	$0.265975\pi$
$578$	19.6157	+	13.1508i	0.815905	+	0.547002i
$579$	31.2477	−	11.8460i	1.29861	−	0.492303i
$580$	7.84404	−	3.22066i	0.325706	−	0.133731i
$581$	31.2675	+	40.7486i	1.29719	+	1.69054i
$582$	−1.20493	+	1.28865i	−0.0499459	+	0.0534162i
$583$	30.2306	+	8.10027i	1.25202	+	0.335479i
$584$	−17.2476	−	26.0745i	−0.713711	−	1.07897i
$585$	22.6673	+	25.5996i	0.937179	+	1.05841i
$586$	0.606848	+	9.48391i	0.0250687	+	0.391777i
$587$	−28.5847	+	3.76324i	−1.17982	+	0.155326i	−0.694815	−	0.719188i	$-0.744514\pi$
$587$	−28.5847	+	3.76324i	−1.17982	+	0.155326i	−0.485000	+	0.874514i	$0.661181\pi$
$588$	−34.0302	+	31.8272i	−1.40338	+	1.31253i
$589$	−0.101170	+	0.768461i	−0.00416863	+	0.0316639i
$590$	−27.1073	−	31.0067i	−1.11599	−	1.27653i
$591$	17.4802	−	9.39705i	0.719038	−	0.386543i
$592$	−6.73074	+	2.73920i	−0.276632	+	0.112581i
$593$	−11.1599			−0.458281			−0.229140	−	0.973393i	$-0.573591\pi$
$593$	−11.1599			−0.458281			−0.229140	+	0.973393i	$0.573591\pi$
$594$	−21.8585	+	15.8499i	−0.896865	+	0.650329i
$595$	−3.40171	−	8.21245i	−0.139456	−	0.336678i
$596$	−31.2064	−	18.1462i	−1.27826	−	0.743298i
$597$	−13.3206	+	1.34407i	−0.545176	+	0.0550091i
$598$	−26.1023	−	12.9226i	−1.06740	−	0.528444i
$599$	−6.22375	−	23.2273i	−0.254295	−	0.949044i	−0.968481	−	0.249087i	$-0.919869\pi$
$599$	−6.22375	−	23.2273i	−0.254295	−	0.949044i	0.714186	−	0.699956i	$-0.246797\pi$
$600$	15.7726	+	35.0216i	0.643915	+	1.42975i
$601$	10.8265	−	40.4050i	0.441622	−	1.64815i	−0.283083	−	0.959095i	$-0.591357\pi$
$601$	10.8265	−	40.4050i	0.441622	−	1.64815i	0.724705	−	0.689059i	$-0.241976\pi$
$602$	37.7643	−	42.9276i	1.53916	−	1.74960i
$603$	−8.98149	+	0.631742i	−0.365754	+	0.0257265i
$604$	43.6820	−	5.61315i	1.77740	−	0.228396i
$605$	−7.10780	−	5.45401i	−0.288973	−	0.221737i
$606$	8.41953	+	18.5410i	0.342020	+	0.753178i
$607$	25.8246	+	14.9098i	1.04819	+	0.605172i	0.922142	−	0.386853i	$-0.126438\pi$
$607$	25.8246	+	14.9098i	1.04819	+	0.605172i	0.126046	+	0.992024i	$0.459771\pi$
$608$	−13.0303	−	19.8322i	−0.528447	−	0.804301i
$609$	0.281121	−	9.26329i	0.0113916	−	0.375368i
$610$	17.2746	+	11.5813i	0.699429	+	0.468913i
$611$	−4.87547	−	11.7704i	−0.197240	−	0.476180i
$612$	2.73356	−	1.83313i	0.110497	−	0.0740997i
$613$	−25.4017	−	10.5217i	−1.02597	−	0.424969i	−0.194711	−	0.980861i	$-0.562377\pi$
$613$	−25.4017	−	10.5217i	−1.02597	−	0.424969i	−0.831255	+	0.555892i	$0.812377\pi$
$614$	−3.80539	+	18.9772i	−0.153573	+	0.765858i
$615$	−7.58754	−	32.1936i	−0.305959	−	1.29817i
$616$	15.3134	−	44.4320i	0.616994	−	1.79022i
$617$	−0.296777	+	0.0795213i	−0.0119478	+	0.00320141i	−0.264788	−	0.964307i	$-0.585302\pi$
$617$	−0.296777	+	0.0795213i	−0.0119478	+	0.00320141i	0.252840	+	0.967508i	$0.418635\pi$
$618$	0.178393	−	0.111139i	0.00717601	−	0.00447066i
$619$	2.25511	+	17.1293i	0.0906405	+	0.688483i	0.975084	+	0.221836i	$0.0712049\pi$
$619$	2.25511	+	17.1293i	0.0906405	+	0.688483i	−0.884444	+	0.466647i	$0.845462\pi$
$620$	−1.14883	+	0.658539i	−0.0461382	+	0.0264476i
$621$	32.8201	+	7.40524i	1.31702	+	0.297162i
$622$	10.6543	−	31.2274i	0.427198	−	1.25210i
$623$	10.1647	−	5.86857i	0.407239	−	0.235119i
$624$	0.805000	−	22.0220i	0.0322258	−	0.881585i
$625$	2.36524	+	1.36557i	0.0946097	+	0.0546230i
$626$	33.2713	−	29.0870i	1.32979	−	1.16255i
$627$	−4.28583	+	26.3500i	−0.171160	+	1.05232i
$628$	−6.73963	−	25.4682i	−0.268941	−	1.01629i
$629$	−0.920692	−	0.381363i	−0.0367104	−	0.0152059i
$630$	68.7503	−	0.221570i	2.73908	−	0.00882755i
$631$	0.464983	+	0.464983i	0.0185107	+	0.0185107i	0.716302	−	0.697791i	$-0.245834\pi$
$631$	0.464983	+	0.464983i	0.0185107	+	0.0185107i	−0.697791	+	0.716302i	$0.745834\pi$
$632$	28.2979	−	9.45932i	1.12563	−	0.376272i
$633$	−23.1390	−	24.5874i	−0.919692	−	0.977260i
$634$	−7.17772	−	21.2530i	−0.285064	−	0.844066i
$635$	12.9823	−	9.96171i	0.515189	−	0.395318i
$636$	18.7352	−	22.7958i	0.742900	−	0.903910i
$637$	−26.0444	+	33.9418i	−1.03192	+	1.34482i
$638$	2.71066	+	5.51822i	0.107316	+	0.218469i
$639$	−13.6891	+	20.7004i	−0.541534	+	0.818897i
$640$	13.4471	−	38.2457i	0.531545	−	1.51179i
$641$	−24.4921	+	14.1405i	−0.967379	+	0.558517i	−0.898436	−	0.439104i	$-0.855296\pi$
$641$	−24.4921	+	14.1405i	−0.967379	+	0.558517i	−0.0689430	+	0.997621i	$0.521963\pi$
$642$	−24.6988	−	2.41176i	−0.974782	−	0.0951844i
$643$	0.931085	−	7.07229i	0.0367184	−	0.278904i	−0.963229	−	0.268681i	$-0.913412\pi$
$643$	0.931085	−	7.07229i	0.0367184	−	0.278904i	0.999948	−	0.0102234i	$-0.00325425\pi$
$644$	−54.1744	+	22.2433i	−2.13477	+	0.876508i
$645$	−55.2056	+	5.57032i	−2.17372	+	0.219331i
$646$	0.639818	−	3.19073i	0.0251733	−	0.125538i
$647$	−6.76117	−	6.76117i	−0.265809	−	0.265809i	0.561600	−	0.827409i	$-0.310186\pi$
$647$	−6.76117	−	6.76117i	−0.265809	−	0.265809i	−0.827409	+	0.561600i	$0.810186\pi$
$648$	5.08836	+	24.9421i	0.199890	+	0.979818i
$649$	21.1151	−	21.1151i	0.828842	−	0.828842i
$650$	19.5481	+	29.3541i	0.766738	+	1.15136i
$651$	0.145293	+	1.43995i	0.00569450	+	0.0564362i
$652$	−11.0205	−	11.0890i	−0.431596	−	0.434280i
$653$	−4.80307	−	0.632336i	−0.187959	−	0.0247452i	0.0359591	−	0.999353i	$-0.488551\pi$
$653$	−4.80307	−	0.632336i	−0.187959	−	0.0247452i	−0.223918	+	0.974608i	$0.571885\pi$
$654$	7.92377	+	9.63869i	0.309844	+	0.376903i
$655$	14.0064	+	24.2598i	0.547276	+	0.947909i
$656$	−10.7726	+	18.3944i	−0.420599	+	0.718179i
$657$	27.6585	+	18.2905i	1.07906	+	0.713579i
$658$	−24.2442	−	8.27172i	−0.945137	−	0.322465i
$659$	19.9076	+	15.2757i	0.775491	+	0.595055i	0.918846	−	0.394616i	$-0.129122\pi$
$659$	19.9076	+	15.2757i	0.775491	+	0.595055i	−0.143355	+	0.989671i	$0.545789\pi$
$660$	−40.2387	+	21.4712i	−1.56629	+	0.835763i
$661$	−24.1237	−	31.4386i	−0.938303	−	1.22282i	−0.974708	−	0.223484i	$-0.928257\pi$
$661$	−24.1237	−	31.4386i	−0.938303	−	1.22282i	0.0364042	−	0.999337i	$-0.488410\pi$
$662$	3.28132	−	6.62794i	0.127532	−	0.257602i
$663$	2.20076	−	2.07112i	0.0854703	−	0.0804355i
$664$	−24.2508	+	21.0687i	−0.941113	+	0.817624i
$665$	48.0667	−	48.0667i	1.86395	−	1.86395i
$666$	5.43249	−	5.46762i	0.210505	−	0.211866i
$667$	2.93178	−	7.07795i	0.113519	−	0.274059i
$668$	−11.8262	−	15.5115i	−0.457568	−	0.600157i
$669$	5.57976	+	0.907550i	0.215726	+	0.0350879i
$670$	−15.1749	−	1.01824i	−0.586258	−	0.0393380i
$671$	−7.53964	+	13.0590i	−0.291065	+	0.504139i
$672$	−32.1764	−	30.4621i	−1.24123	−	1.17510i
$673$	14.6744	+	25.4169i	0.565658	+	0.979748i	0.996988	+	0.0775538i	$0.0247110\pi$
$673$	14.6744	+	25.4169i	0.565658	+	0.979748i	−0.431331	+	0.902194i	$0.641956\pi$
$674$	15.4501	+	31.4526i	0.595117	+	1.21151i
$675$	−29.9328	−	27.6356i	−1.15212	−	1.06369i
$676$	0.734890	+	5.71897i	0.0282650	+	0.219960i
$677$	−11.3752	+	1.49757i	−0.437184	+	0.0575564i	−0.345906	−	0.938269i	$-0.612429\pi$
$677$	−11.3752	+	1.49757i	−0.437184	+	0.0575564i	−0.0912780	+	0.995825i	$0.529095\pi$
$678$	1.24111	+	0.288292i	0.0476646	+	0.0110718i
$679$	0.842997	+	3.14611i	0.0323513	+	0.120737i
$680$	4.99770	−	2.43577i	0.191653	−	0.0934075i
$681$	−31.6421	+	7.45755i	−1.21253	+	0.285774i
$682$	−0.532169	−	0.799126i	−0.0203778	−	0.0306001i
$683$	8.71675	−	21.0441i	0.333537	−	0.805230i	−0.664769	−	0.747049i	$-0.731470\pi$
$683$	8.71675	−	21.0441i	0.333537	−	0.805230i	0.998306	−	0.0581811i	$-0.0185301\pi$
$684$	20.9508	+	13.9483i	0.801075	+	0.533325i
$685$	6.32587	−	2.62026i	0.241699	−	0.100115i
$686$	7.98559	+	40.4740i	0.304891	+	1.54530i
$687$	−43.6305	−	1.32409i	−1.66461	−	0.0505174i
$688$	28.2346	+	21.9446i	1.07643	+	0.836630i
$689$	13.5465	−	23.4633i	0.516082	−	0.893880i
$690$	53.2075	+	19.9751i	2.02557	+	0.760438i
$691$	27.0714	−	35.2802i	1.02985	−	1.34212i	0.0917370	−	0.995783i	$-0.470758\pi$
$691$	27.0714	−	35.2802i	1.02985	−	1.34212i	0.938110	−	0.346339i	$-0.112575\pi$
$692$	9.99549	+	2.71152i	0.379972	+	0.103077i
$693$	3.49755	+	49.7248i	0.132861	+	1.88889i
$694$	−26.7884	+	1.71411i	−1.01687	+	0.0650667i
$695$	−15.8325	−	4.24230i	−0.600560	−	0.160920i
$696$	5.79369	−	0.176540i	0.219609	−	0.00669173i
$697$	−2.82371	+	0.756611i	−0.106956	+	0.0286587i
$698$	−21.1289	+	7.13578i	−0.799739	+	0.270093i
$699$	1.11492	+	11.0496i	0.0421701	+	0.417933i
$700$	70.2757	+	9.47368i	2.65617	+	0.358071i
$701$	6.28674	−	2.60405i	0.237447	−	0.0983538i	−0.260787	−	0.965396i	$-0.583982\pi$
$701$	6.28674	−	2.60405i	0.237447	−	0.0983538i	0.498234	+	0.867043i	$0.333982\pi$
$702$	8.35587	+	21.8288i	0.315372	+	0.823876i
$703$		−	7.62081i		−	0.287424i
$704$	28.3206	+	7.87146i	1.06737	+	0.296667i
$705$	11.7712	+	21.8964i	0.443327	+	0.824667i
$706$	−23.2803	−	1.56211i	−0.876165	−	0.0587908i
$707$	37.2727	+	4.90705i	1.40178	+	0.184548i
$708$	−9.89820	−	26.3559i	−0.371997	−	0.990515i
$709$	4.06425	+	30.8711i	0.152636	+	1.15939i	0.880631	+	0.473804i	$0.157119\pi$
$709$	4.06425	+	30.8711i	0.152636	+	1.15939i	−0.727994	+	0.685583i	$0.759547\pi$
$710$	−27.6896	+	31.4754i	−1.03917	+	1.18125i
$711$	−23.6936	+	20.9796i	−0.888578	+	0.786796i
$712$	4.05001	+	6.12270i	0.151780	+	0.229458i
$713$	−0.309650	+	1.15563i	−0.0115965	+	0.0432786i
$714$	−0.203894	−	6.07297i	−0.00763053	−	0.227275i
$715$	−33.2239	+	25.4936i	−1.24250	+	0.953407i
$716$	−2.47220	−	2.48757i	−0.0923903	−	0.0929649i
$717$	−6.13537	−	16.1840i	−0.229130	−	0.604404i
$718$	−5.09313	−	25.8139i	−0.190074	−	0.963366i
$719$		−	11.3802i		−	0.424408i	−0.977225	−	0.212204i	$-0.931936\pi$
$719$		−	11.3802i		−	0.424408i	0.977225	−	0.212204i	$-0.0680642\pi$
$720$	2.75111	+	42.9119i	0.102528	+	1.59923i
$721$		−	0.388034i		−	0.0144511i
$722$	−1.94667	+	0.384081i	−0.0724475	+	0.0142940i
$723$	14.9843	+	2.43720i	0.557273	+	0.0906406i
$724$	38.6357	+	0.119762i	1.43588	+	0.00445091i
$725$	−7.35955	+	5.64718i	−0.273327	+	0.209731i
$726$	−3.23840	−	5.19806i	−0.120188	−	0.192918i
$727$	4.15788	−	15.5174i	0.154207	−	0.575509i	−0.844965	−	0.534822i	$-0.820379\pi$
$727$	4.15788	−	15.5174i	0.154207	−	0.575509i	0.999172	−	0.0406873i	$-0.0129547\pi$
$728$	−33.7221	−	22.7599i	−1.24982	−	0.843537i
$729$	−15.3203	−	22.2326i	−0.567418	−	0.823430i
$730$	42.0552	+	36.9968i	1.55653	+	1.36931i
$731$	0.640101	+	4.86205i	0.0236750	+	0.179829i
$732$	8.27270	+	11.5620i	0.305768	+	0.427342i
$733$	−38.4290	−	5.05928i	−1.41941	−	0.186869i	−0.618561	−	0.785737i	$-0.712284\pi$
$733$	−38.4290	−	5.05928i	−1.41941	−	0.186869i	−0.800848	+	0.598868i	$0.795617\pi$
$734$	0.918230	−	13.6845i	0.0338925	−	0.505103i
$735$	43.9146	−	70.9977i	1.61981	−	2.61879i
$736$	−15.9452	−	32.9754i	−0.587747	−	1.21549i
$737$		−	11.0273i		−	0.406196i
$738$	2.87891	−	22.4257i	0.105974	−	0.825503i
$739$	−32.9185	+	13.6353i	−1.21093	+	0.501582i	−0.894514	−	0.447040i	$-0.852478\pi$
$739$	−32.9185	+	13.6353i	−1.21093	+	0.501582i	−0.316412	+	0.948622i	$0.602478\pi$
$740$	10.3537	−	7.89381i	0.380610	−	0.290182i
$741$	21.0730	+	9.48752i	0.774137	+	0.348533i
$742$	−17.4306	−	51.6115i	−0.639897	−	1.89472i
$743$	−4.21059	+	1.12822i	−0.154472	+	0.0413905i	−0.335226	−	0.942138i	$-0.608813\pi$
$743$	−4.21059	+	1.12822i	−0.154472	+	0.0413905i	0.180755	+	0.983528i	$0.442146\pi$
$744$	−0.893431	+	0.145430i	−0.0327548	+	0.00533171i
$745$	62.4732	+	16.7397i	2.28884	+	0.613293i
$746$	−3.46496	−	54.1510i	−0.126861	−	1.98261i
$747$	14.9242	−	30.6310i	0.546048	−	1.12073i
$748$	2.00469	+	3.49722i	0.0732987	+	0.127871i
$749$	−27.8908	+	36.3479i	−1.01911	+	1.32812i
$750$	−15.8318	−	19.2582i	−0.578094	−	0.703209i
$751$	−14.4737	+	25.0691i	−0.528151	+	0.914784i	0.471310	+	0.881967i	$0.343781\pi$
$751$	−14.4737	+	25.0691i	−0.528151	+	0.914784i	−0.999461	+	0.0328169i	$0.989552\pi$
$752$	4.24260	−	15.4498i	0.154712	−	0.563398i
$753$	16.8829	+	31.4052i	0.615247	+	1.14447i
$754$	5.22155	−	1.03022i	0.190158	−	0.0375184i
$755$	−72.9008	+	30.1965i	−2.65313	+	1.09896i
$756$	44.0511	+	16.3758i	1.60212	+	0.595583i
$757$	−6.47525	+	15.6326i	−0.235347	+	0.568178i	−0.996791	−	0.0800533i	$-0.974491\pi$
$757$	−6.47525	+	15.6326i	−0.235347	+	0.568178i	0.761444	+	0.648231i	$0.224491\pi$
$758$	23.3456	−	15.5468i	0.847952	−	0.564684i
$759$	−11.8676	+	39.4611i	−0.430768	+	1.43235i
$760$	31.8345	+	28.1810i	1.15476	+	1.02223i
$761$	−9.06452	−	33.8293i	−0.328589	−	1.22631i	−0.910655	−	0.413168i	$-0.864422\pi$
$761$	−9.06452	−	33.8293i	−0.328589	−	1.22631i	0.582066	−	0.813142i	$-0.302245\pi$
$762$	10.7016	−	3.25607i	0.387678	−	0.117955i
$763$	22.8390	−	3.00681i	0.826828	−	0.108854i
$764$	−17.5385	+	22.7106i	−0.634522	+	0.821639i
$765$	−3.86691	+	4.45205i	−0.139808	+	0.160964i
$766$	−37.5031	+	18.4223i	−1.35504	+	0.665624i
$767$	−12.9251	−	22.3870i	−0.466699	−	0.808346i
$768$	17.7944	−	21.2452i	0.642101	−	0.766620i
$769$	7.48877	−	12.9709i	0.270052	−	0.467743i	−0.698823	−	0.715295i	$-0.746293\pi$
$769$	7.48877	−	12.9709i	0.270052	−	0.467743i	0.968875	+	0.247551i	$0.0796258\pi$
$770$	−5.63734	+	84.0139i	−0.203156	+	3.02765i
$771$	−9.74472	−	25.7049i	−0.350948	−	0.925739i
$772$	38.2416	+	5.15524i	1.37634	+	0.185541i
$773$	0.942718	−	2.27592i	0.0339072	−	0.0818593i	−0.906019	−	0.423237i	$-0.860894\pi$
$773$	0.942718	−	2.27592i	0.0339072	−	0.0818593i	0.939926	+	0.341378i	$0.110894\pi$
$774$	−36.6680	−	9.69860i	−1.31800	−	0.348609i
$775$	1.02436	−	1.02436i	0.0367961	−	0.0367961i
$776$	−1.93206	+	0.645842i	−0.0693568	+	0.0231844i
$777$	−3.26429	−	13.8502i	−0.117106	−	0.496874i
$778$	−24.2458	−	12.0034i	−0.869253	−	0.430344i
$779$	−13.6090	−	17.7356i	−0.487593	−	0.635443i
$780$	8.93810	+	38.4574i	0.320035	+	1.37700i
$781$	−24.1141	−	18.5034i	−0.862871	−	0.662105i
$782$	1.62199	−	4.75402i	0.0580024	−	0.170003i
$783$	−5.58168	+	2.57735i	−0.199473	+	0.0921068i
$784$	−52.0545	+	13.6026i	−1.85909	+	0.485809i
$785$	23.6006	+	40.8774i	0.842342	+	1.45898i
$786$	3.13508	+	18.8906i	0.111825	+	0.673804i
$787$	−48.6332	−	6.40269i	−1.73359	−	0.228231i	−0.803432	−	0.595396i	$-0.796995\pi$
$787$	−48.6332	−	6.40269i	−1.73359	−	0.228231i	−0.930156	+	0.367165i	$0.880328\pi$
$788$	22.9160	+	0.0710342i	0.816349	+	0.00253049i
$789$	38.0428	−	27.3987i	1.35436	−	0.975421i
$790$	−44.4947	+	29.6308i	−1.58305	+	1.05422i
$791$	1.66335	−	1.66335i	0.0591421	−	0.0591421i
$792$	−30.9100	+	4.07324i	−1.09834	+	0.144736i
$793$	9.23041	+	9.23041i	0.327781	+	0.327781i
$794$	−18.2680	−	3.66317i	−0.648307	−	0.130001i
$795$	−21.7034	+	48.2061i	−0.769741	+	1.70970i
$796$	−14.2642	−	5.96031i	−0.505582	−	0.211257i
$797$	−3.87042	+	29.3987i	−0.137097	+	1.04136i	0.775167	+	0.631756i	$0.217665\pi$
$797$	−3.87042	+	29.3987i	−0.137097	+	1.04136i	−0.912265	+	0.409601i	$0.865668\pi$
$798$	42.3093	−	19.2128i	1.49773	−	0.680125i
$799$	1.90282	−	1.09859i	0.0673170	−	0.0388655i
$800$	−3.24359	+	44.2327i	−0.114678	+	1.56386i
$801$	−6.49463	−	4.29488i	−0.229477	−	0.151752i
$802$	−12.3495	+	6.06632i	−0.436076	+	0.214209i
$803$	−24.7229	+	32.2196i	−0.872454	+	1.13700i
$804$	−9.46678	−	4.29748i	−0.333868	−	0.151561i
$805$	83.2430	−	63.8746i	2.93393	−	2.25128i
$806$	−0.787446	+	0.265942i	−0.0277366	+	0.00936739i
$807$	9.89762	−	32.9106i	0.348413	−	1.15851i
$808$	−1.64692	+	23.4556i	−0.0579386	+	0.825165i
$809$	−17.1736	−	17.1736i	−0.603790	−	0.603790i	0.337526	−	0.941316i	$-0.390410\pi$
$809$	−17.1736	−	17.1736i	−0.603790	−	0.603790i	−0.941316	+	0.337526i	$0.890410\pi$
$810$	−20.4985	−	40.7424i	−0.720244	−	1.43154i
$811$	7.57232	+	3.13656i	0.265900	+	0.110139i	0.511650	−	0.859194i	$-0.329034\pi$
$811$	7.57232	+	3.13656i	0.265900	+	0.110139i	−0.245750	+	0.969333i	$0.579034\pi$
$812$	5.37933	−	9.25093i	0.188777	−	0.324644i
$813$	−32.5007	−	26.5431i	−1.13985	−	0.930906i
$814$	6.21316	+	7.10694i	0.217771	+	0.249098i
$815$	24.2580	+	14.0054i	0.849721	+	0.490587i
$816$	3.78356	−	0.358086i	0.132451	−	0.0125355i
$817$	−32.4776	+	18.7509i	−1.13625	+	0.656012i
$818$	−13.3592	−	4.55794i	−0.467094	−	0.159365i
$819$	42.3625	+	8.21644i	1.48026	+	0.287106i
$820$	9.99924	−	36.8603i	0.349189	−	1.28722i
$821$	−4.08720	−	31.0454i	−0.142644	−	1.08349i	−0.901668	−	0.432429i	$-0.857657\pi$
$821$	−4.08720	−	31.0454i	−0.142644	−	1.08349i	0.759024	−	0.651063i	$-0.225677\pi$
$822$	4.67787	−	0.157055i	0.163159	−	0.00547791i
$823$	−1.21632	+	0.325912i	−0.0423983	+	0.0113606i	−0.279956	−	0.960013i	$-0.590320\pi$
$823$	−1.21632	+	0.325912i	−0.0423983	+	0.0113606i	0.237558	+	0.971373i	$0.423653\pi$
$824$	0.242247	−	0.0147469i	0.00843908	−	0.000513731i
$825$	36.3357	−	34.1952i	1.26505	−	1.19052i
$826$	−50.9620	−	10.2191i	−1.77319	−	0.355568i
$827$	−21.3377	−	8.83835i	−0.741983	−	0.307339i	−0.0205172	−	0.999790i	$-0.506531\pi$
$827$	−21.3377	−	8.83835i	−0.741983	−	0.307339i	−0.721466	+	0.692450i	$0.756531\pi$
$828$	29.2518	+	25.5667i	1.01657	+	0.888505i
$829$	−14.4612	−	34.9125i	−0.502259	−	1.21256i	−0.948250	−	0.317524i	$-0.897149\pi$
$829$	−14.4612	−	34.9125i	−0.502259	−	1.21256i	0.445991	−	0.895037i	$-0.352851\pi$
$830$	32.0509	−	47.8070i	1.11250	−	1.65940i
$831$	6.96522	+	4.30824i	0.241621	+	0.149451i
$832$	12.9273	−	21.9174i	0.448172	−	0.759850i
$833$	−6.38983	−	3.68917i	−0.221394	−	0.127822i
$834$	−9.11301	−	6.51876i	−0.315558	−	0.225726i
$835$	27.7256	+	21.2746i	0.959484	+	0.736238i
$836$	−18.8415	+	24.3978i	−0.651647	+	0.843814i
$837$	0.811668	−	0.512821i	0.0280553	−	0.0177257i
$838$	−30.5926	−	26.9129i	−1.05680	−	0.929692i
$839$	−1.06322	+	3.96800i	−0.0367065	+	0.136991i	−0.981847	−	0.189672i	$-0.939257\pi$
$839$	−1.06322	+	3.96800i	−0.0367065	+	0.136991i	0.945141	+	0.326663i	$0.105924\pi$
$840$	69.9277	+	37.5809i	2.41274	+	1.29666i
$841$	−7.14343	−	26.6596i	−0.246325	−	0.919298i
$842$	−12.6146	+	25.4802i	−0.434726	+	0.878104i
$843$	8.38963	+	11.6489i	0.288954	+	0.401210i
$844$	−9.97363	−	37.6890i	−0.343306	−	1.29731i
$845$	−3.95341	−	9.54437i	−0.136001	−	0.328336i
$846$	2.27240	+	16.8410i	0.0781269	+	0.579007i
$847$	−11.3066			−0.388501
$848$	31.5583	−	12.8432i	1.08372	−	0.441039i
$849$	1.31329	−	43.2745i	0.0450720	−	1.48518i
$850$	−4.57909	+	4.00322i	−0.157062	+	0.137309i
$851$	1.53540	−	11.6625i	0.0526327	−	0.399785i
$852$	−25.2825	+	13.4906i	−0.866165	+	0.462180i
$853$	4.89172	−	0.644007i	0.167489	−	0.0220504i	−0.0463151	−	0.998927i	$-0.514748\pi$
$853$	4.89172	−	0.644007i	0.167489	−	0.0220504i	0.213804	+	0.976876i	$0.431414\pi$
$854$	26.1933	−	1.67604i	0.896318	−	0.0573527i
$855$	−42.7704	−	14.2913i	−1.46272	−	0.488753i
$856$	−23.7517	−	16.0306i	−0.811818	−	0.547916i
$857$	5.17007	+	1.38532i	0.176606	+	0.0473215i	0.346038	−	0.938220i	$-0.387527\pi$
$857$	5.17007	+	1.38532i	0.176606	+	0.0473215i	−0.169432	+	0.985542i	$0.554193\pi$
$858$	−27.3871	+	8.33282i	−0.934982	+	0.284478i
$859$	0.647462	+	0.843789i	0.0220911	+	0.0287897i	0.804268	−	0.594266i	$-0.202558\pi$
$859$	0.647462	+	0.843789i	0.0220911	+	0.0287897i	−0.782177	+	0.623056i	$0.785891\pi$
$860$	−59.1163	−	24.7017i	−2.01585	−	0.842322i
$861$	−32.3301	−	26.4038i	−1.10181	−	0.899839i
$862$	2.53187	−	3.77653i	0.0862360	−	0.128629i
$863$	35.7552			1.21712			0.608560	−	0.793508i	$-0.291748\pi$
$863$	35.7552			1.21712			0.608560	+	0.793508i	$0.291748\pi$
$864$	−8.54920	+	28.1231i	−0.290850	+	0.956769i
$865$	−18.5559			−0.630918
$866$	−12.9759	+	19.3548i	−0.440939	+	0.657702i
$867$	−22.4020	−	18.2956i	−0.760813	−	0.621350i
$868$	−0.644307	+	1.54196i	−0.0218692	+	0.0523375i
$869$	−23.5954	−	30.7502i	−0.800421	−	1.04313i
$870$	−9.93549	+	3.02298i	−0.336845	+	0.102488i
$871$	−9.22080	−	2.47070i	−0.312435	−	0.0837166i
$872$	2.74511	+	14.1440i	0.0929610	+	0.478975i
$873$	1.61770	−	1.43240i	0.0547507	−	0.0484793i
$874$	38.3343	−	2.45290i	1.29668	−	0.0829705i
$875$	−45.6325	+	6.00763i	−1.54266	+	0.203095i
$876$	18.0252	+	33.7807i	0.609014	+	1.14134i
$877$	3.25664	−	24.7367i	0.109969	−	0.835297i	−0.844200	−	0.536029i	$-0.819924\pi$
$877$	3.25664	−	24.7367i	0.109969	−	0.835297i	0.954169	−	0.299269i	$-0.0967428\pi$
$878$	−22.1579	+	19.3713i	−0.747793	+	0.653749i
$879$	0.353060	−	11.6338i	0.0119084	−	0.392397i
$880$	−52.6635	−	0.326492i	−1.77529	−	0.0110061i
$881$	−35.4424			−1.19408			−0.597042	−	0.802210i	$-0.703657\pi$
$881$	−35.4424			−1.19408			−0.597042	+	0.802210i	$0.703657\pi$
$882$	45.1614	−	34.8854i	1.52066	−	1.17465i
$883$	21.6672	+	52.3093i	0.729160	+	1.76035i	0.645377	+	0.763864i	$0.276700\pi$
$883$	21.6672	+	52.3093i	0.729160	+	1.76035i	0.0837828	+	0.996484i	$0.473300\pi$
$884$	3.37345	−	0.892716i	0.113462	−	0.0300253i
$885$	29.4787	+	40.9309i	0.990916	+	1.37588i
$886$	−10.8554	+	21.9268i	−0.364693	+	0.736644i
$887$	15.1787	+	56.6476i	0.509650	+	1.90204i	0.423865	+	0.905725i	$0.360673\pi$
$887$	15.1787	+	56.6476i	0.509650	+	1.90204i	0.0857847	+	0.996314i	$0.472660\pi$
$888$	8.52255	−	2.56424i	0.285998	−	0.0860502i
$889$	5.34501	−	19.9478i	0.179266	−	0.669029i
$890$	−9.87520	−	8.68743i	−0.331017	−	0.291203i
$891$	28.4789	−	16.8068i	0.954081	−	0.563049i
$892$	5.16637	+	3.98980i	0.172983	+	0.133588i
$893$	13.3302	+	10.2286i	0.446078	+	0.342287i
$894$	35.9589	+	25.7223i	1.20265	+	0.860283i
$895$	5.44173	+	3.14178i	0.181897	+	0.105018i
$896$	−15.9193	−	48.6236i	−0.531827	−	1.62440i
$897$	30.3376	+	18.7649i	1.01294	+	0.626541i
$898$	26.5369	−	39.5824i	0.885548	−	1.32088i
$899$	−0.0836614	−	0.201977i	−0.00279027	−	0.00673630i
$900$	−15.1956	−	44.5200i	−0.506520	−	1.48400i
$901$	4.31683	+	1.78809i	0.143814	+	0.0595698i
$902$	27.1509	+	5.44442i	0.904028	+	0.181279i
$903$	−50.9937	+	47.9898i	−1.69697	+	1.59700i
$904$	1.10164	+	0.975207i	0.0366399	+	0.0324349i
$905$	−66.8640	+	17.9162i	−2.22264	+	0.595553i
$906$	−53.9089	+	1.80994i	−1.79100	+	0.0601311i
$907$	2.17405	+	16.5136i	0.0721882	+	0.548324i	0.988878	+	0.148726i	$0.0475171\pi$
$907$	2.17405	+	16.5136i	0.0721882	+	0.548324i	−0.916690	+	0.399599i	$0.869150\pi$
$908$	−36.2288	−	9.82794i	−1.20229	−	0.326151i
$909$	−8.12921	−	23.5776i	−0.269629	−	0.782019i
$910$	68.9875	+	23.5374i	2.28691	+	0.780258i
$911$	24.2343	−	13.9917i	0.802919	−	0.463566i	−0.0415716	−	0.999136i	$-0.513236\pi$
$911$	24.2343	−	13.9917i	0.802919	−	0.463566i	0.844491	+	0.535570i	$0.179903\pi$
$912$	13.6023	+	25.6833i	0.450418	+	0.850458i
$913$	36.1405	+	20.8657i	1.19608	+	0.690555i
$914$	24.3274	+	27.8270i	0.804680	+	0.920436i
$915$	−19.7284	−	16.1121i	−0.652201	−	0.532648i
$916$	−43.5723	−	25.3369i	−1.43967	−	0.837154i
$917$	32.6616	+	13.5289i	1.07858	+	0.446763i
$918$	−3.54432	+	1.92011i	−0.116980	+	0.0633732i
$919$	29.6812	+	29.6812i	0.979092	+	0.979092i	0.999786	−	0.0206940i	$-0.00658758\pi$
$919$	29.6812	+	29.6812i	0.979092	+	0.979092i	−0.0206940	+	0.999786i	$0.506588\pi$
$920$	43.0401	+	49.5406i	1.41899	+	1.63330i
$921$	6.82703	−	22.7006i	0.224958	−	0.748009i
$922$	23.5072	−	7.93901i	0.774169	−	0.261458i
$923$	−20.8750	+	16.0180i	−0.687110	+	0.527238i
$924$	−23.7925	+	52.4116i	−0.782715	+	1.72421i
$925$	−8.67086	+	11.3001i	−0.285096	+	0.371545i
$926$	27.0993	−	13.3117i	0.890540	−	0.437451i
$927$	−0.230325	+	0.114953i	−0.00756486	+	0.00377557i
$928$	5.97973	+	3.00671i	0.196294	+	0.0987000i
$929$	−46.9099	+	27.0834i	−1.53906	+	0.888579i	−0.540169	+	0.841556i	$0.681640\pi$
$929$	−46.9099	+	27.0834i	−1.53906	+	0.888579i	−0.998894	+	0.0470223i	$0.985027\pi$
$930$	1.47668	−	0.670564i	0.0484222	−	0.0219887i
$931$	7.36476	−	55.9409i	0.241370	−	1.83339i
$932$	−4.94413	+	11.8323i	−0.161950	+	0.387580i
$933$	−16.5897	+	36.8480i	−0.543124	+	1.20635i
$934$	−24.7437	−	4.96170i	−0.809638	−	0.162352i
$935$	−5.10693	−	5.10693i	−0.167015	−	0.167015i
$936$	−3.51952	+	26.7589i	−0.115039	+	0.874641i
$937$	−6.99087	+	6.99087i	−0.228382	+	0.228382i	−0.812016	−	0.583635i	$-0.801630\pi$
$937$	−6.99087	+	6.99087i	−0.228382	+	0.228382i	0.583635	+	0.812016i	$0.301630\pi$
$938$	−15.9758	+	10.6389i	−0.521628	+	0.347372i
$939$	−43.9202	+	31.6317i	−1.43328	+	1.03226i
$940$	−0.0889806	+	28.7056i	−0.00290223	+	0.936273i
$941$	51.8718	+	6.82906i	1.69097	+	0.222621i	0.913656	−	0.406488i	$-0.133247\pi$
$941$	51.8718	+	6.82906i	1.69097	+	0.222621i	0.777317	+	0.629109i	$0.216580\pi$
$942$	5.28256	+	31.8303i	0.172115	+	1.03709i
$943$	−17.2532	−	29.8835i	−0.561842	−	0.973139i
$944$	4.44296	−	32.2036i	0.144606	−	1.04814i
$945$	−83.8535	−	7.65314i	−2.72776	−	0.248957i
$946$	15.0002	−	43.9652i	0.487698	−	1.42943i
$947$	−10.6489	−	8.17121i	−0.346044	−	0.265529i	0.421086	−	0.907021i	$-0.361649\pi$
$947$	−10.6489	−	8.17121i	−0.346044	−	0.265529i	−0.767130	+	0.641492i	$0.778316\pi$
$948$	−35.5940	+	8.27260i	−1.15604	+	0.268681i
$949$	21.4021	+	27.8917i	0.694740	+	0.905403i
$950$	−41.6836	−	20.6364i	−1.35239	−	0.669535i
$951$	6.30251	+	26.7413i	0.204373	+	0.867145i
$952$	3.13250	−	6.27833i	0.101525	−	0.203482i
$953$	−38.1452	+	38.1452i	−1.23564	+	1.23564i	−0.273880	+	0.961764i	$0.588307\pi$
$953$	−38.1452	+	38.1452i	−1.23564	+	1.23564i	−0.961764	+	0.273880i	$0.911693\pi$
$954$	−25.4712	+	25.6359i	−0.824661	+	0.829993i
$955$	19.6741	−	47.4975i	0.636639	−	1.53698i
$956$	2.67004	−	19.8064i	0.0863553	−	0.640584i
$957$	−2.66918	−	7.04082i	−0.0862823	−	0.227598i
$958$	−1.21466	+	18.1022i	−0.0392438	+	0.584855i
$959$	4.32056	−	7.48343i	0.139518	−	0.241653i
$960$	−20.8040	+	45.0836i	−0.671445	+	1.45507i
$961$	−15.4829	−	26.8172i	−0.499449	−	0.865072i
$962$	7.33475	−	3.60298i	0.236482	−	0.116165i
$963$	29.8375	+	5.78715i	0.961500	+	0.186488i
$964$	13.8742	+	10.7145i	0.446857	+	0.345091i
$965$	−68.5445	+	9.02406i	−2.20653	+	0.290495i
$966$	68.6189	−	20.8780i	2.20778	−	0.671739i
$967$	−4.34170	−	16.2034i	−0.139620	−	0.521067i	−0.999936	−	0.0113072i	$-0.996401\pi$
$967$	−4.34170	−	16.2034i	−0.139620	−	0.521067i	0.860316	−	0.509760i	$-0.170266\pi$
$968$	−0.429698	−	7.05867i	−0.0138110	−	0.226874i
$969$	−1.14786	+	3.81675i	−0.0368746	+	0.122612i
$970$	3.03791	−	2.02306i	0.0975414	−	0.0649566i
$971$	−6.55231	+	15.8187i	−0.210274	+	0.507645i	−0.993465	−	0.114135i	$-0.963590\pi$
$971$	−6.55231	+	15.8187i	−0.210274	+	0.507645i	0.783192	+	0.621780i	$0.213590\pi$
$972$	−3.32978	−	30.9986i	−0.106803	−	0.994280i
$973$	−19.1111	+	7.91608i	−0.612674	+	0.253778i
$974$	23.1583	−	4.56918i	0.742041	−	0.146406i
$975$	−20.4522	−	38.0447i	−0.654994	−	1.21840i
$976$	2.04179	+	16.2886i	0.0653561	+	0.521386i
$977$	−19.4339	+	33.6605i	−0.621746	+	1.07690i	0.367414	+	0.930057i	$0.380243\pi$
$977$	−19.4339	+	33.6605i	−0.621746	+	1.07690i	−0.989160	+	0.146839i	$0.953090\pi$
$978$	12.1594	+	14.7911i	0.388816	+	0.472966i
$979$	5.80533	−	7.56565i	0.185539	−	0.241799i
$980$	83.6305	−	47.9391i	2.67148	−	1.53136i
$981$	−8.55070	−	12.6658i	−0.273003	−	0.404386i
$982$	−2.24613	−	35.1028i	−0.0716767	−	1.12018i
$983$	0.301417	+	0.0807644i	0.00961370	+	0.00257598i	0.263623	−	0.964626i	$-0.415083\pi$
$983$	0.301417	+	0.0807644i	0.00961370	+	0.00257598i	−0.254009	+	0.967202i	$0.581749\pi$
$984$	15.2550	−	21.1869i	0.486313	−	0.675415i
$985$	−39.6591	+	10.6266i	−1.26364	+	0.338592i
$986$	0.293694	+	0.869619i	0.00935311	+	0.0276943i
$987$	28.6079	+	12.8799i	0.910599	+	0.409971i
$988$	16.1794	+	21.2213i	0.514735	+	0.675138i
$989$	−53.4798	+	22.1521i	−1.70056	+	0.704395i
$990$	51.5380	−	21.5426i	1.63799	−	0.684669i
$991$		−	52.8061i		−	1.67744i	−0.544563	−	0.838720i	$-0.683304\pi$
$991$		−	52.8061i		−	1.67744i	0.544563	−	0.838720i	$-0.316696\pi$
$992$	−0.987120	−	0.343636i	−0.0313411	−	0.0109105i
$993$	−4.76480	+	7.70335i	−0.151206	+	0.244458i
$994$	−3.54202	+	52.7870i	−0.112346	+	1.67430i
$995$	27.4612	+	3.61533i	0.870578	+	0.114614i
$996$	31.9973	−	22.8944i	1.01387	−	0.725438i
$997$	−5.16472	−	39.2299i	−0.163568	−	1.24242i	−0.854480	−	0.519485i	$-0.826124\pi$
$997$	−5.16472	−	39.2299i	−0.163568	−	1.24242i	0.690912	−	0.722939i	$-0.257209\pi$
$998$	−36.7773	−	32.3538i	−1.16416	−	1.02414i
$999$	−7.25403	+	6.04065i	−0.229507	+	0.191118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.59.8	✓	368
3.2	odd	2		864.2.bn.a.827.39		368
9.2	odd	6	inner	288.2.bf.a.155.24	yes	368
9.7	even	3		864.2.bn.a.251.23		368
32.19	odd	8	inner	288.2.bf.a.275.24	yes	368
96.83	even	8		864.2.bn.a.179.23		368
288.83	even	24	inner	288.2.bf.a.83.8	yes	368
288.115	odd	24		864.2.bn.a.467.39		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.8	✓	368	1.1	even	1	trivial
288.2.bf.a.83.8	yes	368	288.83	even	24	inner
288.2.bf.a.155.24	yes	368	9.2	odd	6	inner
288.2.bf.a.275.24	yes	368	32.19	odd	8	inner
864.2.bn.a.179.23		368	96.83	even	8
864.2.bn.a.251.23		368	9.7	even	3
864.2.bn.a.467.39		368	288.115	odd	24
864.2.bn.a.827.39		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.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17466 - 0.787516i) q^{2} +(1.34151 + 1.09560i) q^{3} +(0.759636 + 1.85012i) q^{4} +(-2.18140 - 2.84285i) q^{5} +(-0.713010 - 2.34342i) q^{6} +(-4.36814 - 1.17044i) q^{7} +(0.564691 - 2.77148i) q^{8} +(0.599307 + 2.93953i) q^{9} +O(q^{10})\)	\(q+(-1.17466 - 0.787516i) q^{2} +(1.34151 + 1.09560i) q^{3} +(0.759636 + 1.85012i) q^{4} +(-2.18140 - 2.84285i) q^{5} +(-0.713010 - 2.34342i) q^{6} +(-4.36814 - 1.17044i) q^{7} +(0.564691 - 2.77148i) q^{8} +(0.599307 + 2.93953i) q^{9} +(0.323599 + 5.05726i) q^{10} +(-3.64283 + 0.479588i) q^{11} +(-1.00794 + 3.31422i) q^{12} +(-0.415168 + 3.15351i) q^{13} +(4.20933 + 4.81485i) q^{14} +(0.188268 - 6.20367i) q^{15} +(-2.84591 + 2.81084i) q^{16} -0.548551 q^{17} +(1.61095 - 3.92490i) q^{18} +(-1.60531 - 3.87556i) q^{19} +(3.60256 - 6.19538i) q^{20} +(-4.57758 - 6.35591i) q^{21} +(4.65676 + 2.30544i) q^{22} +(-1.67586 - 6.25438i) q^{23} +(3.79399 - 3.09930i) q^{24} +(-2.02922 + 7.57315i) q^{25} +(2.97112 - 3.37734i) q^{26} +(-2.41658 + 4.60002i) q^{27} +(-1.15274 - 8.97071i) q^{28} +(0.938681 + 0.720275i) q^{29} +(-5.10664 + 7.13891i) q^{30} +(-0.160017 - 0.0923856i) q^{31} +(5.55654 - 1.06057i) q^{32} +(-5.41234 - 3.34773i) q^{33} +(0.644359 + 0.431993i) q^{34} +(6.20127 + 14.9712i) q^{35} +(-4.98323 + 3.34176i) q^{36} +(1.67841 + 0.695219i) q^{37} +(-1.16638 + 5.81666i) q^{38} +(-4.01195 + 3.77561i) q^{39} +(-9.11074 + 4.44037i) q^{40} +(5.14759 - 1.37929i) q^{41} +(0.371695 + 11.0709i) q^{42} +(-1.16689 - 8.86345i) q^{43} +(-3.65452 - 6.37538i) q^{44} +(7.04932 - 8.11602i) q^{45} +(-2.95687 + 8.66651i) q^{46} +(-3.46882 + 2.00272i) q^{47} +(-6.89738 + 0.652787i) q^{48} +(11.6486 + 6.72530i) q^{49} +(8.34762 - 7.29781i) q^{50} +(-0.735887 - 0.600994i) q^{51} +(-6.14976 + 1.62741i) q^{52} +(-7.86951 - 3.25966i) q^{53} +(6.46124 - 3.50034i) q^{54} +(9.30986 + 9.30986i) q^{55} +(-5.71051 + 11.4453i) q^{56} +(2.09253 - 6.95789i) q^{57} +(-0.535399 - 1.58530i) q^{58} +(-6.44770 + 4.94750i) q^{59} +(11.6206 - 4.36421i) q^{60} +(2.49837 - 3.25594i) q^{61} +(0.115209 + 0.234537i) q^{62} +(0.822684 - 13.5417i) q^{63} +(-7.36225 - 3.13007i) q^{64} +(9.87062 - 5.69880i) q^{65} +(3.72125 + 8.19474i) q^{66} +(-0.391739 + 2.97555i) q^{67} +(-0.416699 - 1.01489i) q^{68} +(4.60414 - 10.2264i) q^{69} +(4.50569 - 22.4696i) q^{70} +(5.84951 + 5.84951i) q^{71} +(8.48528 - 0.00104410i) q^{72} +(7.81569 - 7.81569i) q^{73} +(-1.42406 - 2.13842i) q^{74} +(-11.0194 + 7.93625i) q^{75} +(5.95081 - 5.91403i) q^{76} +(16.4737 + 2.16881i) q^{77} +(7.68602 - 1.27557i) q^{78} +(5.27449 + 9.13568i) q^{79} +(14.1989 + 1.95894i) q^{80} +(-8.28166 + 3.52336i) q^{81} +(-7.13286 - 2.43362i) q^{82} +(-9.01072 - 6.91417i) q^{83} +(8.28193 - 13.2973i) q^{84} +(1.19661 + 1.55945i) q^{85} +(-5.60941 + 11.3305i) q^{86} +(0.470116 + 1.99468i) q^{87} +(-0.727905 + 10.3669i) q^{88} +(-1.83525 + 1.83525i) q^{89} +(-14.6720 + 3.98208i) q^{90} +(5.50451 - 13.2891i) q^{91} +(10.2983 - 7.85159i) q^{92} +(-0.113446 - 0.299251i) q^{93} +(5.65184 + 0.379240i) q^{94} +(-7.51582 + 13.0178i) q^{95} +(8.61613 + 4.66500i) q^{96} +(-0.360120 - 0.623746i) q^{97} +(-8.38678 - 17.0734i) q^{98} +(-3.59294 - 10.4208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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