LMFDB - Embedded newform 342.2.x.b.281.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.1
Character	$\chi$	$=$	342.281
Dual form			342.2.x.b.185.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.62796 + 0.591401i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0346602 - 0.0952281i) q^{5} +(0.866942 - 1.49947i) q^{6} +(1.30506 + 2.26042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.30049 - 1.92555i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.62796 + 0.591401i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0346602 - 0.0952281i) q^{5} +(0.866942 - 1.49947i) q^{6} +(1.30506 + 2.26042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.30049 - 1.92555i) q^{9} +(0.0346602 + 0.0952281i) q^{10} -3.50077i q^{11} +(0.299725 + 1.70592i) q^{12} +(1.48386 + 4.07686i) q^{13} +(-2.45270 - 0.892710i) q^{14} +(-0.000107279 + 0.175525i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-2.30657 + 6.33725i) q^{17} +(-0.524556 + 2.95378i) q^{18} +(-4.07978 + 1.53473i) q^{19} +(-0.0877627 - 0.0506698i) q^{20} +(-3.46139 - 2.90806i) q^{21} +(2.25025 + 2.68175i) q^{22} +(-3.08818 - 0.544530i) q^{23} +(-1.32615 - 1.11415i) q^{24} +(3.82236 + 3.20734i) q^{25} +(-3.75725 - 2.16925i) q^{26} +(-2.60632 + 4.49523i) q^{27} +(2.45270 - 0.892710i) q^{28} +(0.579160 - 3.28458i) q^{29} +(-0.112743 - 0.134529i) q^{30} +9.69994i q^{31} +(0.939693 - 0.342020i) q^{32} +(2.07036 + 5.69910i) q^{33} +(-2.30657 - 6.33725i) q^{34} +(0.260489 - 0.0459313i) q^{35} +(-1.49682 - 2.59991i) q^{36} +3.15406i q^{37} +(2.13879 - 3.79810i) q^{38} +(-4.82671 - 5.75940i) q^{39} +(0.0998001 - 0.0175974i) q^{40} +(-6.18649 + 5.19108i) q^{41} +(4.52084 + 0.00276307i) q^{42} +(-1.56634 - 8.88314i) q^{43} +(-3.44759 - 0.607902i) q^{44} +(-0.103631 - 0.285811i) q^{45} +(2.71570 - 1.56791i) q^{46} +(-3.56978 - 0.629448i) q^{47} +(1.73205 + 0.00105860i) q^{48} +(0.0936613 - 0.162226i) q^{49} -4.98973 q^{50} +(0.00713918 - 11.6809i) q^{51} +(4.27259 - 0.753373i) q^{52} +(8.61956 + 7.23267i) q^{53} +(-0.892918 - 5.11886i) q^{54} +(-0.333372 - 0.121337i) q^{55} +(-1.30506 + 2.26042i) q^{56} +(5.73407 - 4.91126i) q^{57} +(1.66762 + 2.88841i) q^{58} +(0.963679 + 5.46529i) q^{59} +(0.172840 + 0.0305853i) q^{60} +(11.5303 - 4.19670i) q^{61} +(-6.23500 - 7.43058i) q^{62} +(7.35483 + 2.68712i) q^{63} +(-0.500000 + 0.866025i) q^{64} +0.439662 q^{65} +(-5.24930 - 3.03496i) q^{66} +(4.12214 - 4.91257i) q^{67} +(5.84044 + 3.37198i) q^{68} +(5.34946 - 0.939884i) q^{69} +(-0.170022 + 0.202625i) q^{70} +(1.27070 - 1.06625i) q^{71} +(2.81782 + 1.02951i) q^{72} +(0.643609 + 3.65009i) q^{73} +(-2.02739 - 2.41615i) q^{74} +(-8.11945 - 2.96086i) q^{75} +(0.802963 + 4.28430i) q^{76} +(7.91322 - 4.56870i) q^{77} +(7.39955 + 1.30940i) q^{78} +(-2.75149 + 7.55967i) q^{79} +(-0.0651399 + 0.0776307i) q^{80} +(1.58450 - 8.85942i) q^{81} +(1.40236 - 7.95320i) q^{82} +(5.57871 - 3.22087i) q^{83} +(-3.46494 + 2.90383i) q^{84} +(0.523538 + 0.439301i) q^{85} +(6.90986 + 5.79806i) q^{86} +(0.999657 + 5.68967i) q^{87} +(3.03176 - 1.75038i) q^{88} +(1.00556 - 5.70280i) q^{89} +(0.263102 + 0.152331i) q^{90} +(-7.27891 + 8.67467i) q^{91} +(-1.07251 + 2.94671i) q^{92} +(-5.73656 - 15.7911i) q^{93} +(3.13921 - 1.81242i) q^{94} +(0.00474295 + 0.441704i) q^{95} +(-1.32751 + 1.11253i) q^{96} +(-8.34594 - 9.94630i) q^{97} +(0.0325282 + 0.184477i) q^{98} +(-6.74092 - 8.05348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.62796	+	0.591401i	−0.939901	+	0.341446i
$3$	−1.62796	+	0.591401i	−0.939901	+	0.341446i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.0346602	−	0.0952281i	0.0155005	−	0.0425873i	−0.931701	−	0.363226i	$-0.881675\pi$
$5$	0.0346602	−	0.0952281i	0.0155005	−	0.0425873i	0.947202	+	0.320639i	$0.103898\pi$
$6$	0.866942	−	1.49947i	0.353928	−	0.612156i
$7$	1.30506	+	2.26042i	0.493265	+	0.854359i	0.999970	−	0.00776006i	$-0.00247013\pi$
$7$	1.30506	+	2.26042i	0.493265	+	0.854359i	−0.506705	+	0.862119i	$0.669137\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.30049	−	1.92555i	0.766830	−	0.641851i
$10$	0.0346602	+	0.0952281i	0.0109605	+	0.0301138i
$11$		−	3.50077i		−	1.05552i	−0.849393	−	0.527761i	$-0.823032\pi$
$11$		−	3.50077i		−	1.05552i	0.849393	−	0.527761i	$-0.176968\pi$
$12$	0.299725	+	1.70592i	0.0865231	+	0.492457i
$13$	1.48386	+	4.07686i	0.411548	+	1.13072i	0.956368	+	0.292165i	$0.0943756\pi$
$13$	1.48386	+	4.07686i	0.411548	+	1.13072i	−0.544820	+	0.838553i	$0.683402\pi$
$14$	−2.45270	−	0.892710i	−0.655512	−	0.238587i
$15$	−0.000107279		0.175525i	−2.76992e−5		0.0453205i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−2.30657	+	6.33725i	−0.559426	+	1.53701i	0.261049	+	0.965326i	$0.415932\pi$
$17$	−2.30657	+	6.33725i	−0.559426	+	1.53701i	−0.820474	+	0.571684i	$0.806290\pi$
$18$	−0.524556	+	2.95378i	−0.123639	+	0.696214i
$19$	−4.07978	+	1.53473i	−0.935966	+	0.352090i
$19$	−4.07978	+	1.53473i	−0.935966	+	0.352090i
$20$	−0.0877627	−	0.0506698i	−0.0196243	−	0.0113301i
$21$	−3.46139	−	2.90806i	−0.755337	−	0.634590i
$22$	2.25025	+	2.68175i	0.479755	+	0.571750i
$23$	−3.08818	−	0.544530i	−0.643930	−	0.113542i	−0.157859	−	0.987462i	$-0.550459\pi$
$23$	−3.08818	−	0.544530i	−0.643930	−	0.113542i	−0.486071	+	0.873919i	$0.661570\pi$
$24$	−1.32615	−	1.11415i	−0.270699	−	0.227425i
$25$	3.82236	+	3.20734i	0.764471	+	0.641467i
$26$	−3.75725	−	2.16925i	−0.736858	−	0.425425i
$27$	−2.60632	+	4.49523i	−0.501587	+	0.865107i
$28$	2.45270	−	0.892710i	0.463517	−	0.168706i
$29$	0.579160	−	3.28458i	0.107547	−	0.609931i	−0.882625	−	0.470078i	$-0.844226\pi$
$29$	0.579160	−	3.28458i	0.107547	−	0.609931i	0.990172	−	0.139853i	$-0.0446630\pi$
$30$	−0.112743	−	0.134529i	−0.0205840	−	0.0245616i
$31$			9.69994i			1.74216i	0.491141	+	0.871080i	$0.336580\pi$
$31$			9.69994i			1.74216i	−0.491141	+	0.871080i	$0.663420\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	2.07036	+	5.69910i	0.360403	+	0.992087i
$34$	−2.30657	−	6.33725i	−0.395574	−	1.08683i
$35$	0.260489	−	0.0459313i	0.0440307	−	0.00776380i
$36$	−1.49682	−	2.59991i	−0.249471	−	0.433318i
$37$			3.15406i			0.518524i	0.965807	+	0.259262i	$0.0834793\pi$
$37$			3.15406i			0.518524i	−0.965807	+	0.259262i	$0.916521\pi$
$38$	2.13879	−	3.79810i	0.346958	−	0.616133i
$39$	−4.82671	−	5.75940i	−0.772893	−	0.922242i
$40$	0.0998001	−	0.0175974i	0.0157798	−	0.00278240i
$41$	−6.18649	+	5.19108i	−0.966167	+	0.810711i	−0.981945	−	0.189165i	$-0.939422\pi$
$41$	−6.18649	+	5.19108i	−0.966167	+	0.810711i	0.0157780	+	0.999876i	$0.494978\pi$
$42$	4.52084	+	0.00276307i	0.697581	+	0.000426351i
$43$	−1.56634	−	8.88314i	−0.238864	−	1.35467i	−0.834321	−	0.551279i	$-0.814140\pi$
$43$	−1.56634	−	8.88314i	−0.238864	−	1.35467i	0.595457	−	0.803388i	$-0.296971\pi$
$44$	−3.44759	−	0.607902i	−0.519743	−	0.0916447i
$45$	−0.103631	−	0.285811i	−0.0154484	−	0.0426062i
$46$	2.71570	−	1.56791i	0.400408	−	0.231176i
$47$	−3.56978	−	0.629448i	−0.520705	−	0.0918144i	−0.0928827	−	0.995677i	$-0.529608\pi$
$47$	−3.56978	−	0.629448i	−0.520705	−	0.0918144i	−0.427823	+	0.903863i	$0.640719\pi$
$48$	1.73205	+	0.00105860i	0.250000	+	0.000152796i
$49$	0.0936613	−	0.162226i	0.0133802	−	0.0231752i
$50$	−4.98973			−0.705654
$51$	0.00713918	−	11.6809i	0.000999686	−	1.63565i
$52$	4.27259	−	0.753373i	0.592502	−	0.104474i
$53$	8.61956	+	7.23267i	1.18399	+	0.993484i	0.999944	+	0.0105654i	$0.00336314\pi$
$53$	8.61956	+	7.23267i	1.18399	+	0.993484i	0.184043	+	0.982918i	$0.441081\pi$
$54$	−0.892918	−	5.11886i	−0.121511	−	0.696588i
$55$	−0.333372	−	0.121337i	−0.0449518	−	0.0163611i
$56$	−1.30506	+	2.26042i	−0.174395	+	0.302062i
$57$	5.73407	−	4.91126i	0.759496	−	0.650512i
$58$	1.66762	+	2.88841i	0.218970	+	0.379267i
$59$	0.963679	+	5.46529i	0.125460	+	0.711521i	0.981033	+	0.193839i	$0.0620938\pi$
$59$	0.963679	+	5.46529i	0.125460	+	0.711521i	−0.855573	+	0.517682i	$0.826795\pi$
$60$	0.172840	+	0.0305853i	0.0223136	+	0.00394855i
$61$	11.5303	−	4.19670i	1.47631	−	0.537332i	0.526502	−	0.850174i	$-0.323503\pi$
$61$	11.5303	−	4.19670i	1.47631	−	0.537332i	0.949805	+	0.312842i	$0.101281\pi$
$62$	−6.23500	−	7.43058i	−0.791846	−	0.943685i
$63$	7.35483	+	2.68712i	0.926621	+	0.338546i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.439662			0.0545334
$66$	−5.24930	−	3.03496i	−0.646144	−	0.373578i
$67$	4.12214	−	4.91257i	0.503599	−	0.600166i	−0.453022	−	0.891499i	$-0.649654\pi$
$67$	4.12214	−	4.91257i	0.503599	−	0.600166i	0.956622	+	0.291333i	$0.0940987\pi$
$68$	5.84044	+	3.37198i	0.708258	+	0.408913i
$69$	5.34946	−	0.939884i	0.644000	−	0.113149i
$70$	−0.170022	+	0.202625i	−0.0203215	+	0.0242183i
$71$	1.27070	−	1.06625i	0.150805	−	0.126540i	−0.564264	−	0.825595i	$-0.690840\pi$
$71$	1.27070	−	1.06625i	0.150805	−	0.126540i	0.715069	+	0.699054i	$0.246395\pi$
$72$	2.81782	+	1.02951i	0.332083	+	0.121328i
$73$	0.643609	+	3.65009i	0.0753288	+	0.427211i	0.999028	+	0.0440910i	$0.0140392\pi$
$73$	0.643609	+	3.65009i	0.0753288	+	0.427211i	−0.923699	+	0.383120i	$0.874850\pi$
$74$	−2.02739	−	2.41615i	−0.235679	−	0.280872i
$75$	−8.11945	−	2.96086i	−0.937554	−	0.341891i
$76$	0.802963	+	4.28430i	0.0921061	+	0.491443i
$77$	7.91322	−	4.56870i	0.901795	−	0.520651i
$78$	7.39955	+	1.30940i	0.837834	+	0.148261i
$79$	−2.75149	+	7.55967i	−0.309567	+	0.850529i	0.683173	+	0.730256i	$0.260599\pi$
$79$	−2.75149	+	7.55967i	−0.309567	+	0.850529i	−0.992741	+	0.120273i	$0.961623\pi$
$80$	−0.0651399	+	0.0776307i	−0.00728286	+	0.00867937i
$81$	1.58450	−	8.85942i	0.176055	−	0.984380i
$82$	1.40236	−	7.95320i	0.154865	−	0.878284i
$83$	5.57871	−	3.22087i	0.612343	−	0.353536i	−0.161539	−	0.986866i	$-0.551646\pi$
$83$	5.57871	−	3.22087i	0.612343	−	0.353536i	0.773882	+	0.633330i	$0.218312\pi$
$84$	−3.46494	+	2.90383i	−0.378056	+	0.316833i
$85$	0.523538	+	0.439301i	0.0567857	+	0.0476489i
$86$	6.90986	+	5.79806i	0.745109	+	0.625221i
$87$	0.999657	+	5.68967i	0.107174	+	0.609996i
$88$	3.03176	−	1.75038i	0.323186	−	0.186592i
$89$	1.00556	−	5.70280i	0.106589	−	0.604496i	−0.883985	−	0.467516i	$-0.845149\pi$
$89$	1.00556	−	5.70280i	0.106589	−	0.604496i	0.990574	−	0.136980i	$-0.0437397\pi$
$90$	0.263102	+	0.152331i	0.0277334	+	0.0160571i
$91$	−7.27891	+	8.67467i	−0.763037	+	0.909352i
$92$	−1.07251	+	2.94671i	−0.111817	+	0.307216i
$93$	−5.73656	−	15.7911i	−0.594853	−	1.63746i
$94$	3.13921	−	1.81242i	0.323785	−	0.186937i
$95$	0.00474295	+	0.441704i	0.000486617	+	0.0453179i
$96$	−1.32751	+	1.11253i	−0.135488	+	0.113547i
$97$	−8.34594	−	9.94630i	−0.847402	−	1.00989i	−0.999767	−	0.0215700i	$-0.993134\pi$
$97$	−8.34594	−	9.94630i	−0.847402	−	1.00989i	0.152365	−	0.988324i	$-0.451311\pi$
$98$	0.0325282	+	0.184477i	0.00328585	+	0.0186350i
$99$	−6.74092	−	8.05348i	−0.677487	−	0.809405i
$100$	3.82236	−	3.20734i	0.382236	−	0.320734i
$101$	3.92157	−	4.67355i	0.390211	−	0.465036i	−0.534798	−	0.844980i	$-0.679612\pi$
$101$	3.92157	−	4.67355i	0.390211	−	0.465036i	0.925009	+	0.379944i	$0.124057\pi$
$102$	7.50286	+	8.95266i	0.742894	+	0.886446i
$103$	5.19092	+	2.99698i	0.511476	+	0.295301i	0.733440	−	0.679754i	$-0.237913\pi$
$103$	5.19092	+	2.99698i	0.511476	+	0.295301i	−0.221964	+	0.975055i	$0.571247\pi$
$104$	−2.78874	+	3.32349i	−0.273458	+	0.325895i
$105$	−0.396902	+	0.228828i	−0.0387336	+	0.0223313i
$106$	−11.2520			−1.09289
$107$	−6.90458	+	11.9591i	−0.667491	+	1.15613i	0.311112	+	0.950373i	$0.399298\pi$
$107$	−6.90458	+	11.9591i	−0.667491	+	1.15613i	−0.978603	+	0.205755i	$0.934035\pi$
$108$	3.97435	+	3.34732i	0.382432	+	0.322096i
$109$	1.25233	+	1.49247i	0.119951	+	0.142952i	0.822678	−	0.568507i	$-0.192479\pi$
$109$	1.25233	+	1.49247i	0.119951	+	0.142952i	−0.702727	+	0.711460i	$0.748034\pi$
$110$	0.333372	−	0.121337i	0.0317857	−	0.0115691i
$111$	−1.86531	−	5.13467i	−0.177048	−	0.487362i
$112$	−0.453241	−	2.57046i	−0.0428272	−	0.242885i
$113$	−8.34491	−	14.4538i	−0.785024	−	1.35970i	−0.928985	−	0.370117i	$-0.879317\pi$
$113$	−8.34491	−	14.4538i	−0.785024	−	1.35970i	0.143961	−	0.989583i	$-0.454016\pi$
$114$	−1.23566	+	7.44803i	−0.115730	+	0.697572i
$115$	−0.158892	+	0.275208i	−0.0148167	+	0.0256633i
$116$	−3.13411	−	1.14072i	−0.290995	−	0.105913i
$117$	11.2638	+	6.52153i	1.04134	+	0.602916i
$118$	−4.25124	−	3.56722i	−0.391359	−	0.328389i
$119$	−17.3351	+	3.05664i	−1.58910	+	0.280202i
$120$	−0.152063	+	0.0876698i	−0.0138814	+	0.00800312i
$121$	−1.25539			−0.114126
$122$	−6.13516	+	10.6264i	−0.555451	+	0.962070i
$123$	7.00133	−	12.1096i	0.631288	−	1.09188i
$124$	9.55257	+	1.68438i	0.857846	+	0.151261i
$125$	0.876726	−	0.506178i	0.0784167	−	0.0452739i
$126$	−7.36137	+	2.66913i	−0.655803	+	0.237785i
$127$	−1.54256	−	0.271995i	−0.136880	−	0.0241356i	0.104788	−	0.994495i	$-0.466583\pi$
$127$	−1.54256	−	0.271995i	−0.136880	−	0.0241356i	−0.241668	+	0.970359i	$0.577695\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	7.80343	+	13.5350i	0.687054	+	1.19169i
$130$	−0.336801	+	0.282610i	−0.0295394	+	0.0247865i
$131$	8.68898	−	1.53210i	0.759160	−	0.133860i	0.219349	−	0.975647i	$-0.429607\pi$
$131$	8.68898	−	1.53210i	0.759160	−	0.133860i	0.539811	+	0.841786i	$0.318496\pi$
$132$	5.97204	−	1.04927i	0.519799	−	0.0913270i
$133$	−8.79347	−	7.21913i	−0.762490	−	0.625978i
$134$			6.41291i			0.553991i
$135$	0.337737	+	0.404001i	0.0290677	+	0.0347709i
$136$	−6.64151	+	1.17108i	−0.569504	+	0.100419i
$137$	5.34515	+	14.6857i	0.456667	+	1.25468i	0.927951	+	0.372702i	$0.121569\pi$
$137$	5.34515	+	14.6857i	0.456667	+	1.25468i	−0.471284	+	0.881982i	$0.656209\pi$
$138$	−3.49378	+	4.15856i	−0.297410	+	0.354000i
$139$	−10.5711	+	3.84758i	−0.896632	+	0.326347i	−0.748902	−	0.662681i	$-0.769419\pi$
$139$	−10.5711	+	3.84758i	−0.896632	+	0.326347i	−0.147730	+	0.989028i	$0.547197\pi$
$140$		−	0.264508i		−	0.0223550i
$141$	6.18370	−	1.08646i	0.520762	−	0.0914962i
$142$	−0.288045	+	1.63358i	−0.0241722	+	0.137087i
$143$	14.2721	−	5.19464i	1.19350	−	0.434397i
$144$	−2.82033	+	1.02261i	−0.235027	+	0.0852178i
$145$	−0.292710	−	0.168996i	−0.0243083	−	0.0140344i
$146$	−2.83927	−	2.38243i	−0.234979	−	0.197171i
$147$	−0.0565358	+	0.319489i	−0.00466300	+	0.0263510i
$148$	3.10614	+	0.547697i	0.255323	+	0.0450204i
$149$	10.7197	+	12.7753i	0.878194	+	1.04659i	0.998548	+	0.0538601i	$0.0171525\pi$
$149$	10.7197	+	12.7753i	0.878194	+	1.04659i	−0.120354	+	0.992731i	$0.538403\pi$
$150$	8.12307	−	2.95093i	0.663246	−	0.240943i
$151$	−1.93693	−	1.11828i	−0.157625	−	0.0910047i	0.419113	−	0.907934i	$-0.362341\pi$
$151$	−1.93693	−	1.11828i	−0.157625	−	0.0910047i	−0.576738	+	0.816929i	$0.695674\pi$
$152$	−3.36900	−	2.76583i	−0.273262	−	0.224339i
$153$	6.89647	+	19.0202i	0.557546	+	1.53769i
$154$	−3.12517	+	8.58634i	−0.251834	+	0.691907i
$155$	0.923707	+	0.336202i	0.0741939	+	0.0270044i
$156$	−6.51005	+	3.75328i	−0.521221	+	0.300503i
$157$	−17.2230	−	6.26867i	−1.37455	−	0.500295i	−0.454027	−	0.890988i	$-0.650013\pi$
$157$	−17.2230	−	6.26867i	−1.37455	−	0.500295i	−0.920521	+	0.390693i	$0.872235\pi$
$158$	−2.75149	−	7.55967i	−0.218897	−	0.601415i
$159$	−18.3097	−	6.67686i	−1.45205	−	0.529509i
$160$		−	0.101340i		−	0.00801160i
$161$	−2.79938	−	7.69124i	−0.220622	−	0.606154i
$162$	4.48093	+	7.80521i	0.352055	+	0.613235i
$163$	−9.63769	−	16.6930i	−0.754882	−	1.30749i	−0.945433	−	0.325817i	$-0.894361\pi$
$163$	−9.63769	−	16.6930i	−0.754882	−	1.30749i	0.190551	−	0.981677i	$-0.438973\pi$
$164$	4.03794	+	6.99392i	0.315310	+	0.546134i
$165$	0.614474		0.000375557i	0.0478367		2.92371e-5i
$166$	−2.20320	+	6.05326i	−0.171002	+	0.469824i
$167$	3.22350	−	18.2814i	0.249442	−	1.41465i	−0.560505	−	0.828151i	$-0.689393\pi$
$167$	3.22350	−	18.2814i	0.249442	−	1.41465i	0.809947	−	0.586504i	$-0.199496\pi$
$168$	0.787757	−	4.45168i	0.0607768	−	0.343455i
$169$	−4.46038	+	3.74270i	−0.343106	+	0.287900i
$170$	−0.683431			−0.0524168
$171$	−6.43030	+	11.3865i	−0.491737	+	0.870744i
$172$	−9.02018			−0.687782
$173$	3.11111	−	2.61053i	0.236534	−	0.198475i	−0.516814	−	0.856098i	$-0.672882\pi$
$173$	3.11111	−	2.61053i	0.236534	−	0.198475i	0.753348	+	0.657622i	$0.228438\pi$
$174$	−4.42303	−	3.71597i	−0.335309	−	0.281707i
$175$	−2.26155	+	12.8259i	−0.170957	+	0.969546i
$176$	−1.19733	+	3.28965i	−0.0902524	+	0.247967i
$177$	−4.80101	−	8.32734i	−0.360866	−	0.625921i
$178$	2.89539	+	5.01496i	0.217019	+	0.375887i
$179$	−5.18047	−	8.97284i	−0.387207	−	0.670662i	0.604866	−	0.796327i	$-0.293227\pi$
$179$	−5.18047	−	8.97284i	−0.387207	−	0.670662i	−0.992073	+	0.125666i	$0.959893\pi$
$180$	−0.299465	+	0.0524263i	−0.0223208	+	0.00390763i
$181$	−5.65507	−	15.5372i	−0.420338	−	1.15487i	−0.951513	−	0.307608i	$-0.900472\pi$
$181$	−5.65507	−	15.5372i	−0.420338	−	1.15487i	0.531175	−	0.847262i	$-0.321751\pi$
$182$		−	11.3240i		−	0.839389i
$183$	−16.2889	+	13.6511i	−1.20411	+	1.00912i
$184$	−1.07251	−	2.94671i	−0.0790668	−	0.217234i
$185$	0.300355	+	0.109320i	0.0220825	+	0.00803739i
$186$	14.5448	+	8.40928i	1.06647	+	0.616599i
$187$	22.1853	+	8.07477i	1.62235	+	0.590486i
$188$	−1.23977	+	3.40624i	−0.0904196	+	0.248426i
$189$	−13.5625	−	0.0248676i	−0.986527	−	0.00180885i
$190$	−0.287555	−	0.335316i	−0.0208614	−	0.0243264i
$191$	9.99155	+	5.76862i	0.722963	+	0.417403i	0.815842	−	0.578274i	$-0.196274\pi$
$191$	9.99155	+	5.76862i	0.722963	+	0.417403i	−0.0928792	+	0.995677i	$0.529607\pi$
$192$	0.301810	−	1.70555i	0.0217813	−	0.123088i
$193$	10.2833	+	12.2551i	0.740206	+	0.882143i	0.996426	−	0.0844758i	$-0.0269216\pi$
$193$	10.2833	+	12.2551i	0.740206	+	0.882143i	−0.256220	+	0.966619i	$0.582477\pi$
$194$	12.7867	+	2.25464i	0.918033	+	0.161874i
$195$	−0.715752	+	0.260017i	−0.0512560	+	0.0186202i
$196$	−0.143497	−	0.120409i	−0.0102498	−	0.00860062i
$197$	3.83461	+	2.21391i	0.273205	+	0.157735i	0.630343	−	0.776317i	$-0.282914\pi$
$197$	3.83461	+	2.21391i	0.273205	+	0.157735i	−0.357138	+	0.934051i	$0.616248\pi$
$198$	10.3405	+	1.83635i	0.734869	+	0.130504i
$199$	−5.64363	+	2.05411i	−0.400066	+	0.145612i	−0.534214	−	0.845349i	$-0.679392\pi$
$199$	−5.64363	+	2.05411i	−0.400066	+	0.145612i	0.134148	+	0.990961i	$0.457170\pi$
$200$	−0.866458	+	4.91393i	−0.0612678	+	0.347467i
$201$	−3.80536	+	10.4353i	−0.268410	+	0.736049i
$202$			6.10089i			0.429257i
$203$	8.18037	−	2.97741i	0.574149	−	0.208973i
$204$	−11.5022	−	2.03539i	−0.805314	−	0.142506i
$205$	0.279912	+	0.769052i	0.0195499	+	0.0537129i
$206$	−5.90289	+	1.04084i	−0.411274	+	0.0725187i
$207$	−8.15285	+	4.69377i	−0.566662	+	0.326240i
$208$		−	4.33850i		−	0.300821i
$209$	5.37272	+	14.2824i	0.371639	+	0.987933i
$210$	0.156956	−	0.430416i	0.0108310	−	0.0297015i
$211$	24.2274	−	4.27194i	1.66788	−	0.294092i	0.741576	−	0.670868i	$-0.234078\pi$
$211$	24.2274	−	4.27194i	1.66788	−	0.294092i	0.926304	+	0.376776i	$0.122967\pi$
$212$	8.61956	−	7.23267i	0.591994	−	0.496742i
$213$	−1.43807	+	2.48730i	−0.0985350	+	0.170427i
$214$	−2.39794	−	13.5994i	−0.163920	−	0.929634i
$215$	−0.900215	−	0.158732i	−0.0613941	−	0.0108254i
$216$	−5.19614	−	0.00952743i	−0.353553	−	0.000648259i
$217$	−21.9260	+	12.6590i	−1.48843	+	0.859346i
$218$	−1.91868	−	0.338315i	−0.129949	−	0.0229136i
$219$	−3.20644	−	5.56156i	−0.216671	−	0.375815i
$220$	−0.177383	+	0.307237i	−0.0119592	+	0.0207139i
$221$	−29.2587			−1.96815
$222$	4.72942	+	2.73439i	0.317418	+	0.183520i
$223$	11.3498	−	2.00128i	0.760042	−	0.134016i	0.219822	−	0.975540i	$-0.429452\pi$
$223$	11.3498	−	2.00128i	0.760042	−	0.134016i	0.540220	+	0.841524i	$0.318341\pi$
$224$	1.99946	+	1.67775i	0.133595	+	0.112099i
$225$	14.9692	+	0.0182979i	0.997945	+	0.00121986i
$226$	15.6833	+	5.70826i	1.04324	+	0.379708i
$227$	1.00948	−	1.74847i	0.0670016	−	0.116050i	−0.830579	−	0.556902i	$-0.811990\pi$
$227$	1.00948	−	1.74847i	0.0670016	−	0.116050i	0.897580	+	0.440851i	$0.145323\pi$
$228$	−3.84093	−	6.49979i	−0.254372	−	0.430459i
$229$	−9.74982	−	16.8872i	−0.644286	−	1.11594i	−0.984466	−	0.175576i	$-0.943821\pi$
$229$	−9.74982	−	16.8872i	−0.644286	−	1.11594i	0.340180	−	0.940360i	$-0.389512\pi$
$230$	−0.0551825	−	0.312955i	−0.00363862	−	0.0206357i
$231$	−10.1804	+	12.1175i	−0.669824	+	0.797275i
$232$	3.13411	−	1.14072i	0.205764	−	0.0748921i
$233$	12.0057	+	14.3079i	0.786521	+	0.937339i	0.999208	−	0.0397813i	$-0.0126661\pi$
$233$	12.0057	+	14.3079i	0.786521	+	0.937339i	−0.212688	+	0.977120i	$0.568222\pi$
$234$	−12.8205	+	2.24445i	−0.838104	+	0.146724i
$235$	−0.183670	+	0.318126i	−0.0119813	+	0.0207523i
$236$	5.54960			0.361248
$237$	0.00851629	−	13.9341i	0.000553192	−	0.905114i
$238$	11.3147	−	13.4843i	0.733421	−	0.874057i
$239$	−3.46875	−	2.00268i	−0.224375	−	0.129543i	0.383600	−	0.923499i	$-0.374684\pi$
$239$	−3.46875	−	2.00268i	−0.224375	−	0.129543i	−0.607974	+	0.793957i	$0.708018\pi$
$240$	0.0601340	−	0.164903i	0.00388164	−	0.0106445i
$241$	7.44457	−	8.87209i	0.479547	−	0.571502i	−0.470980	−	0.882144i	$-0.656100\pi$
$241$	7.44457	−	8.87209i	0.479547	−	0.571502i	0.950527	+	0.310642i	$0.100544\pi$
$242$	0.961684	−	0.806948i	0.0618194	−	0.0518726i
$243$	2.65998	+	15.3598i	0.170638	+	0.985334i
$244$	−2.13072	−	12.0839i	−0.136405	−	0.773593i
$245$	−0.0122022	−	0.0145420i	−0.000779568	−	0.000929053i
$246$	2.42054	+	13.7768i	0.154328	+	0.878378i
$247$	−12.3107	−	14.3554i	−0.783309	−	0.913411i
$248$	−8.40039	+	4.84997i	−0.533425	+	0.307973i
$249$	−7.17707	+	8.54269i	−0.454829	+	0.541371i
$250$	−0.346246	+	0.951303i	−0.0218985	+	0.0601657i
$251$	8.76057	−	10.4404i	0.552962	−	0.658994i	−0.415079	−	0.909785i	$-0.636246\pi$
$251$	8.76057	−	10.4404i	0.552962	−	0.658994i	0.968041	+	0.250791i	$0.0806906\pi$
$252$	3.92345	−	6.77648i	0.247154	−	0.426878i
$253$	−1.90627	+	10.8110i	−0.119846	+	0.679683i
$254$	1.35650	−	0.783178i	0.0851146	−	0.0491410i
$255$	−1.11210	−	0.405542i	−0.0696425	−	0.0253960i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	11.1431	+	9.35021i	0.695090	+	0.583250i	0.920372	−	0.391044i	$-0.127886\pi$
$257$	11.1431	+	9.35021i	0.695090	+	0.583250i	−0.225282	+	0.974294i	$0.572330\pi$
$258$	−14.6779	−	5.35249i	−0.913808	−	0.333232i
$259$	−7.12950	+	4.11622i	−0.443006	+	0.255770i
$260$	0.0763466	−	0.432983i	0.00473481	−	0.0268525i
$261$	−4.99228	−	8.67134i	−0.309014	−	0.536742i
$262$	−5.67133	+	6.75883i	−0.350376	+	0.417562i
$263$	1.42575	−	3.91721i	0.0879154	−	0.241546i	−0.887941	−	0.459956i	$-0.847865\pi$
$263$	1.42575	−	3.91721i	0.0879154	−	0.241546i	0.975857	+	0.218411i	$0.0700872\pi$
$264$	−3.90039	+	4.64254i	−0.240052	+	0.285728i
$265$	0.987509	−	0.570139i	0.0606622	−	0.0350233i
$266$	11.3766	−	0.122160i	0.697541	−	0.00749009i
$267$	1.73564	+	9.87861i	0.106219	+	0.604561i
$268$	−4.12214	−	4.91257i	−0.251800	−	0.300083i
$269$	2.64136	+	14.9799i	0.161047	+	0.913340i	0.953048	+	0.302821i	$0.0979283\pi$
$269$	2.64136	+	14.9799i	0.161047	+	0.913340i	−0.792001	+	0.610520i	$0.790961\pi$
$270$	−0.518408	−	0.0923897i	−0.0315493	−	0.00562266i
$271$	12.9922	−	10.9017i	0.789217	−	0.662232i	−0.156334	−	0.987704i	$-0.549968\pi$
$271$	12.9922	−	10.9017i	0.789217	−	0.662232i	0.945552	+	0.325472i	$0.105523\pi$
$272$	4.33494	−	5.16617i	0.262844	−	0.313245i
$273$	6.71954	−	18.4267i	0.406685	−	1.11524i
$274$	−13.5344	−	7.81409i	−0.817643	−	0.472067i
$275$	11.2281	−	13.3812i	0.677083	−	0.806916i
$276$	0.00331959	−	5.43140i	0.000199816	−	0.326932i
$277$	16.9329			1.01740			0.508701	−	0.860943i	$-0.330126\pi$
$277$	16.9329			1.01740			0.508701	+	0.860943i	$0.330126\pi$
$278$	5.62478	−	9.74241i	0.337352	−	0.584311i
$279$	18.6777	+	22.3146i	1.11821	+	1.33594i
$280$	0.170022	+	0.202625i	0.0101608	+	0.0121091i
$281$	−9.06973	+	3.30111i	−0.541055	+	0.196928i	−0.598068	−	0.801446i	$-0.704065\pi$
$281$	−9.06973	+	3.30111i	−0.541055	+	0.196928i	0.0570129	+	0.998373i	$0.481842\pi$
$282$	−4.03863	+	4.80708i	−0.240497	+	0.286257i
$283$	3.19263	+	18.1063i	0.189782	+	1.07631i	0.919655	+	0.392726i	$0.128468\pi$
$283$	3.19263	+	18.1063i	0.189782	+	1.07631i	−0.729873	+	0.683583i	$0.760421\pi$
$284$	−0.829393	−	1.43655i	−0.0492154	−	0.0852436i
$285$	−0.268946	−	0.716270i	−0.0159310	−	0.0424282i
$286$	−7.59405	+	13.1533i	−0.449046	+	0.777770i
$287$	−19.8077	−	7.20943i	−1.16921	−	0.425559i
$288$	1.50317	−	2.59624i	0.0885754	−	0.152985i
$289$	−21.8177	−	18.3073i	−1.28340	−	1.07690i
$290$	0.332858	−	0.0586919i	0.0195461	−	0.00344650i
$291$	19.4691	+	11.2564i	1.14130	+	0.659859i
$292$	3.70640			0.216901
$293$	7.44591	−	12.8967i	0.434995	−	0.753433i	−0.562300	−	0.826933i	$-0.690083\pi$
$293$	7.44591	−	12.8967i	0.434995	−	0.753433i	0.997295	+	0.0734998i	$0.0234168\pi$
$294$	−0.162054	−	0.281083i	−0.00945120	−	0.0163931i
$295$	0.553851	+	0.0976589i	0.0322464	+	0.00568592i
$296$	−2.73150	+	1.57703i	−0.158765	+	0.0916630i
$297$	15.7368	+	9.12414i	0.913139	+	0.529436i
$298$	−16.4236	−	2.89592i	−0.951392	−	0.167756i
$299$	−2.36244	−	13.3981i	−0.136624	−	0.774832i
$300$	−4.32581	+	7.48195i	−0.249751	+	0.431971i
$301$	18.0355	−	15.1336i	1.03955	−	0.872285i
$302$	2.20259	−	0.388376i	0.126745	−	0.0223485i
$303$	−3.62021	+	9.92756i	−0.207976	+	0.570324i
$304$	4.35865	−	0.0468025i	0.249986	−	0.00268431i
$305$		−	1.24347i		−	0.0712009i
$306$	−17.5089	−	10.1374i	−1.00092	−	0.579514i
$307$	6.20149	−	1.09349i	0.353938	−	0.0624088i	0.00614742	−	0.999981i	$-0.498043\pi$
$307$	6.20149	−	1.09349i	0.353938	−	0.0624088i	0.347790	+	0.937572i	$0.386932\pi$
$308$	−3.12517	−	8.58634i	−0.178073	−	0.489252i
$309$	−10.2230	−	1.80904i	−0.581567	−	0.102912i
$310$	−0.923707	+	0.336202i	−0.0524630	+	0.0190950i
$311$		−	5.79304i		−	0.328493i	−0.986419	−	0.164247i	$-0.947481\pi$
$311$		−	5.79304i		−	0.328493i	0.986419	−	0.164247i	$-0.0525193\pi$
$312$	2.57443	−	7.05976i	0.145748	−	0.399680i
$313$	1.83311	−	10.3961i	0.103613	−	0.587620i	−0.888152	−	0.459550i	$-0.848011\pi$
$313$	1.83311	−	10.3961i	0.103613	−	0.587620i	0.991765	−	0.128070i	$-0.0408782\pi$
$314$	17.2230	−	6.26867i	0.971952	−	0.353762i
$315$	0.510810	−	0.607250i	0.0287809	−	0.0342147i
$316$	6.96703	+	4.02242i	0.391926	+	0.226279i
$317$	−16.7744	−	14.0754i	−0.942145	−	0.790553i	0.0358124	−	0.999359i	$-0.488598\pi$
$317$	−16.7744	−	14.0754i	−0.942145	−	0.790553i	−0.977957	+	0.208805i	$0.933043\pi$
$318$	18.3178	−	6.65447i	1.02721	−	0.373164i
$319$	−11.4986	−	2.02750i	−0.643795	−	0.113518i
$320$	0.0651399	+	0.0776307i	0.00364143	+	0.00433969i
$321$	4.16774	−	23.5523i	0.232621	−	1.31456i
$322$	7.08828	+	4.09242i	0.395015	+	0.228062i
$323$	−0.315634	−	29.3946i	−0.0175624	−	1.63556i
$324$	−8.44968	−	3.09885i	−0.469427	−	0.172158i
$325$	−7.40404	+	20.3424i	−0.410702	+	1.12840i
$326$	18.1129	+	6.59257i	1.00318	+	0.365129i
$327$	−2.92138	−	1.68904i	−0.161553	−	0.0934043i
$328$	−7.58885	−	2.76212i	−0.419024	−	0.152512i
$329$	−3.23594	−	8.89067i	−0.178403	−	0.490158i
$330$	−0.470956	+	0.394689i	−0.0259253	+	0.0217269i
$331$		−	4.28312i		−	0.235422i	−0.993048	−	0.117711i	$-0.962444\pi$
$331$		−	4.28312i		−	0.235422i	0.993048	−	0.117711i	$-0.0375556\pi$
$332$	−2.20320	−	6.05326i	−0.120917	−	0.332216i
$333$	6.07330	+	7.25588i	0.332815	+	0.397620i
$334$	9.28169	+	16.0764i	0.507872	+	0.879660i
$335$	−0.324941	−	0.562814i	−0.0177534	−	0.0307498i
$336$	2.25803	+	3.91655i	0.123186	+	0.213665i
$337$	−1.77498	+	4.87670i	−0.0966891	+	0.265651i	−0.978602	−	0.205761i	$-0.934033\pi$
$337$	−1.77498	+	4.87670i	−0.0966891	+	0.265651i	0.881913	+	0.471412i	$0.156255\pi$
$338$	1.01109	−	5.73416i	0.0549958	−	0.311897i
$339$	22.1332	+	18.5950i	1.20211	+	1.00994i
$340$	0.523538	−	0.439301i	0.0283929	−	0.0238244i
$341$	33.9572			1.83889
$342$	−2.39318	−	12.8558i	−0.129408	−	0.695164i
$343$	18.7597			1.01293
$344$	6.90986	−	5.79806i	0.372555	−	0.312610i
$345$	0.0959101	−	0.541996i	0.00516363	−	0.0291801i
$346$	−0.705232	+	3.99957i	−0.0379135	+	0.215018i
$347$	−3.16959	+	8.70838i	−0.170153	+	0.467490i	−0.995233	−	0.0975248i	$-0.968907\pi$
$347$	−3.16959	+	8.70838i	−0.170153	+	0.467490i	0.825081	+	0.565015i	$0.191130\pi$
$348$	5.77682	+	0.00353071i	0.309670	+	0.000189266i
$349$	−11.1240	−	19.2673i	−0.595453	−	1.03135i	−0.993483	−	0.113982i	$-0.963639\pi$
$349$	−11.1240	−	19.2673i	−0.595453	−	1.03135i	0.398030	−	0.917372i	$-0.369694\pi$
$350$	−6.51187	−	11.2789i	−0.348074	−	0.602882i
$351$	−22.1938	−	3.95534i	−1.18462	−	0.211121i
$352$	−1.19733	−	3.28965i	−0.0638181	−	0.175339i
$353$			29.9660i			1.59493i	0.603366	+	0.797464i	$0.293826\pi$
$353$			29.9660i			1.59493i	−0.603366	+	0.797464i	$0.706174\pi$
$354$	9.03050	+	3.29308i	0.479966	+	0.175025i
$355$	−0.0574938	−	0.157963i	−0.00305146	−	0.00838381i
$356$	−5.44155	−	1.98056i	−0.288402	−	0.104970i
$357$	26.4130	−	15.2281i	1.39793	−	0.805954i
$358$	9.73611	+	3.54365i	0.514569	+	0.187288i
$359$	−2.13134	+	5.85582i	−0.112488	+	0.309058i	−0.983144	−	0.182835i	$-0.941473\pi$
$359$	−2.13134	+	5.85582i	−0.112488	+	0.309058i	0.870656	+	0.491893i	$0.163695\pi$
$360$	0.195704	−	0.232653i	0.0103145	−	0.0122619i
$361$	14.2892	−	12.5227i	0.752065	−	0.659089i
$362$	14.3191	+	8.26716i	0.752597	+	0.434512i
$363$	2.04372	−	0.742439i	0.107267	−	0.0389679i
$364$	7.27891	+	8.67467i	0.381519	+	0.454676i
$365$	0.369899	+	0.0652231i	0.0193614	+	0.00341393i
$366$	3.70330	−	20.9277i	0.193575	−	1.09391i
$367$	16.3918	+	13.7544i	0.855646	+	0.717972i	0.961026	−	0.276460i	$-0.0891612\pi$
$367$	16.3918	+	13.7544i	0.855646	+	0.717972i	−0.105379	+	0.994432i	$0.533606\pi$
$368$	2.71570	+	1.56791i	0.141566	+	0.0817330i
$369$	−4.23625	+	23.8544i	−0.220530	+	1.24181i
$370$	−0.300355	+	0.109320i	−0.0156147	+	0.00568329i
$371$	−5.09988	+	28.9229i	−0.264773	+	1.50160i
$372$	−16.5473	+	2.90731i	−0.857939	+	0.150737i
$373$		−	8.09931i		−	0.419366i	−0.977769	−	0.209683i	$-0.932757\pi$
$373$		−	8.09931i		−	0.419366i	0.977769	−	0.209683i	$-0.0672433\pi$
$374$	−22.1853	+	8.07477i	−1.14717	+	0.417537i
$375$	−1.12792	+	1.34253i	−0.0582454	+	0.0693281i
$376$	−1.23977	−	3.40624i	−0.0639363	−	0.175663i
$377$	14.2502	−	2.51269i	0.733920	−	0.129410i
$378$	10.4055	−	8.69876i	0.535200	−	0.447416i
$379$			3.85212i			0.197870i	0.995094	+	0.0989351i	$0.0315436\pi$
$379$			3.85212i			0.197870i	−0.995094	+	0.0989351i	$0.968456\pi$
$380$	0.435817	+	0.0720302i	0.0223569	+	0.00369507i
$381$	2.67208	−	0.469476i	0.136895	−	0.0240520i
$382$	−11.3620	+	2.00342i	−0.581329	+	0.102504i
$383$	−17.3797	+	14.5833i	−0.888061	+	0.745172i	−0.967820	−	0.251642i	$-0.919029\pi$
$383$	−17.3797	+	14.5833i	−0.888061	+	0.745172i	0.0797591	+	0.996814i	$0.474585\pi$
$384$	0.865108	+	1.50053i	0.0441474	+	0.0765736i
$385$	−0.160795	−	0.911913i	−0.00819486	−	0.0464754i
$386$	−15.7549	−	2.77801i	−0.801902	−	0.141397i
$387$	−20.7083	−	17.4195i	−1.05266	−	0.885483i
$388$	−11.2445	+	6.49199i	−0.570851	+	0.329581i
$389$	−21.8011	−	3.84413i	−1.10536	−	0.194905i	−0.408956	−	0.912554i	$-0.634107\pi$
$389$	−21.8011	−	3.84413i	−1.10536	−	0.194905i	−0.696405	+	0.717649i	$0.745218\pi$
$390$	0.381162	−	0.659261i	0.0193009	−	0.0333830i
$391$	10.5739	−	18.3146i	0.534747	−	0.926209i
$392$	0.187323			0.00946122
$393$	−13.2392	+	7.63287i	−0.667829	+	0.385027i
$394$	−4.36056	+	0.768884i	−0.219682	+	0.0387358i
$395$	0.624526	+	0.524039i	0.0314233	+	0.0263673i
$396$	−9.10168	+	5.24003i	−0.457377	+	0.263322i
$397$	0.845454	+	0.307720i	0.0424321	+	0.0154440i	0.363149	−	0.931731i	$-0.381702\pi$
$397$	0.845454	+	0.307720i	0.0424321	+	0.0154440i	−0.320717	+	0.947175i	$0.603924\pi$
$398$	3.00291	−	5.20120i	0.150522	−	0.260712i
$399$	18.5848	+	6.55196i	0.930403	+	0.328008i
$400$	−2.49487	−	4.32123i	−0.124743	−	0.216062i
$401$	−3.10720	−	17.6218i	−0.155166	−	0.879991i	−0.958634	−	0.284642i	$-0.908125\pi$
$401$	−3.10720	−	17.6218i	−0.155166	−	0.879991i	0.803468	−	0.595348i	$-0.202986\pi$
$402$	−3.79260	−	10.4399i	−0.189158	−	0.520697i
$403$	−39.5453	+	14.3933i	−1.96989	+	0.716982i
$404$	−3.92157	−	4.67355i	−0.195106	−	0.232518i
$405$	−0.788747	−	0.457958i	−0.0391932	−	0.0227561i
$406$	−4.35268	+	7.53907i	−0.216020	+	0.374158i
$407$	11.0416			0.547313
$408$	10.1195	−	5.83426i	0.500990	−	0.288839i
$409$	−5.52883	+	6.58901i	−0.273383	+	0.325805i	−0.885215	−	0.465183i	$-0.845989\pi$
$409$	−5.52883	+	6.58901i	−0.273383	+	0.325805i	0.611831	+	0.790988i	$0.290433\pi$
$410$	−0.708762	−	0.409204i	−0.0350033	−	0.0202091i
$411$	−17.3868	−	20.7465i	−0.857629	−	1.02335i
$412$	3.85284	−	4.59164i	0.189816	−	0.226214i
$413$	−11.0962	+	9.31083i	−0.546009	+	0.458156i
$414$	3.22835	−	8.83619i	0.158665	−	0.434275i
$415$	−0.113358	−	0.642886i	−0.00556453	−	0.0315580i
$416$	2.78874	+	3.32349i	0.136729	+	0.162947i
$417$	14.9339	−	12.5155i	0.731316	−	0.612885i
$418$	−13.2963	−	7.48742i	−0.650342	−	0.366222i
$419$	0.466275	−	0.269204i	0.0227790	−	0.0131515i	−0.488567	−	0.872526i	$-0.662480\pi$
$419$	0.466275	−	0.269204i	0.0227790	−	0.0131515i	0.511346	+	0.859375i	$0.329147\pi$
$420$	0.156430	+	0.430607i	0.00763301	+	0.0210115i
$421$	−7.76088	+	21.3228i	−0.378242	+	1.03921i	0.593843	+	0.804581i	$0.297610\pi$
$421$	−7.76088	+	21.3228i	−0.378242	+	1.03921i	−0.972085	+	0.234630i	$0.924612\pi$
$422$	−15.8133	+	18.8455i	−0.769779	+	0.917387i
$423$	−9.42427	+	5.42575i	−0.458224	+	0.263809i
$424$	−1.95390	+	11.0811i	−0.0948896	+	0.538145i
$425$	−29.1422	+	16.8253i	−1.41361	+	0.816146i
$426$	−0.497179	−	2.82976i	−0.0240884	−	0.137102i
$427$	24.5340	+	20.5865i	1.18728	+	0.996250i
$428$	10.5784	+	8.87636i	0.511328	+	0.429055i
$429$	−20.1623	+	16.8972i	−0.973446	+	0.815805i
$430$	0.791636	−	0.457051i	0.0381761	−	0.0220410i
$431$	5.34135	−	30.2923i	0.257284	−	1.45913i	−0.532858	−	0.846204i	$-0.678882\pi$
$431$	5.34135	−	30.2923i	0.257284	−	1.45913i	0.790142	−	0.612924i	$-0.210007\pi$
$432$	3.98660	−	3.33272i	0.191805	−	0.160345i
$433$	3.38501	−	4.03410i	0.162673	−	0.193866i	−0.678550	−	0.734554i	$-0.737391\pi$
$433$	3.38501	−	4.03410i	0.162673	−	0.193866i	0.841224	+	0.540688i	$0.181836\pi$
$434$	8.65924	−	23.7911i	0.415657	−	1.14201i
$435$	0.576465	+	0.102010i	0.0276394	+	0.00489099i
$436$	1.68726	−	0.974138i	0.0808049	−	0.0466528i
$437$	13.4348	−	2.51795i	0.642674	−	0.120450i
$438$	6.03117	+	2.19934i	0.288181	+	0.105089i
$439$	−17.3919	−	20.7269i	−0.830071	−	0.989240i	−0.999993	−	0.00378278i	$-0.998796\pi$
$439$	−17.3919	−	20.7269i	−0.830071	−	0.989240i	0.169922	−	0.985458i	$-0.445649\pi$
$440$	−0.0616046	−	0.349377i	−0.00293688	−	0.0166559i
$441$	−0.0969081	−	0.553549i	−0.00461467	−	0.0263595i
$442$	22.4135	−	18.8071i	1.06610	−	0.894564i
$443$	−2.37439	+	2.82969i	−0.112811	+	0.134442i	−0.819495	−	0.573087i	$-0.805746\pi$
$443$	−2.37439	+	2.82969i	−0.112811	+	0.134442i	0.706684	+	0.707529i	$0.250190\pi$
$444$	−5.38057	+	0.945350i	−0.255351	+	0.0448643i
$445$	−0.508215	−	0.293418i	−0.0240917	−	0.0139093i
$446$	−7.40809	+	8.82862i	−0.350783	+	0.418047i
$447$	−25.0066	−	14.4579i	−1.18277	−	0.683837i
$448$	−2.61011			−0.123316
$449$	−19.1661	+	33.1966i	−0.904502	+	1.56664i	−0.0829177	+	0.996556i	$0.526424\pi$
$449$	−19.1661	+	33.1966i	−0.904502	+	1.56664i	−0.821584	+	0.570087i	$0.806909\pi$
$450$	−11.4788	+	9.60799i	−0.541117	+	0.452925i
$451$	18.1728	+	21.6575i	0.855723	+	1.01981i
$452$	−15.6833	+	5.70826i	−0.737681	+	0.268494i
$453$	3.81459	+	0.675019i	0.179225	+	0.0317151i
$454$	0.350589	+	1.98829i	0.0164540	+	0.0933150i
$455$	0.573784	+	0.993823i	0.0268994	+	0.0465911i
$456$	7.12031	+	2.51022i	0.333439	+	0.117552i
$457$	−6.92136	+	11.9881i	−0.323768	+	0.560782i	−0.981262	−	0.192677i	$-0.938283\pi$
$457$	−6.92136	+	11.9881i	−0.323768	+	0.560782i	0.657495	+	0.753459i	$0.271616\pi$
$458$	18.3237	+	6.66927i	0.856209	+	0.311634i
$459$	−22.4757	−	26.8855i	−1.04908	−	1.25491i
$460$	0.243436	+	0.204267i	0.0113503	+	0.00952400i
$461$	−17.0482	+	3.00605i	−0.794012	+	0.140006i	−0.555919	−	0.831237i	$-0.687633\pi$
$461$	−17.0482	+	3.00605i	−0.794012	+	0.140006i	−0.238093	+	0.971242i	$0.576522\pi$
$462$	0.00967288	−	15.8264i	0.000450023	−	0.736312i
$463$	24.0394			1.11721			0.558603	−	0.829435i	$-0.311337\pi$
$463$	24.0394			1.11721			0.558603	+	0.829435i	$0.311337\pi$
$464$	−1.66762	+	2.88841i	−0.0774175	+	0.134091i
$465$	−1.70259	−	0.00104059i	−0.0789555	−	4.82564e-5i
$466$	−18.3938	−	3.24333i	−0.852078	−	0.150244i
$467$	−11.4337	+	6.60127i	−0.529090	+	0.305470i	−0.740646	−	0.671896i	$-0.765480\pi$
$467$	−11.4337	+	6.60127i	−0.529090	+	0.305470i	0.211556	+	0.977366i	$0.432147\pi$
$468$	8.37839	−	9.96023i	0.387291	−	0.460412i
$469$	16.4841	+	2.90659i	0.761165	+	0.134214i
$470$	−0.0637880	−	0.361760i	−0.00294232	−	0.0166867i
$471$	31.7457	+	0.0194025i	1.46276	+	0.000894019i
$472$	−4.25124	+	3.56722i	−0.195679	+	0.164194i
$473$	−31.0978	+	5.48339i	−1.42988	+	0.252126i
$474$	8.95011	+	10.6796i	0.411092	+	0.490529i
$475$	−20.5168	−	7.21897i	−0.941373	−	0.331229i
$476$			17.6025i			0.806809i
$477$	33.7561	+	0.0412624i	1.54558	+	0.00188928i
$478$	3.94451	−	0.695524i	0.180418	−	0.0318125i
$479$	−0.471950	−	1.29667i	−0.0215640	−	0.0592465i	0.928444	−	0.371473i	$-0.121147\pi$
$479$	−0.471950	−	1.29667i	−0.0215640	−	0.0592465i	−0.950008	+	0.312227i	$0.898925\pi$
$480$	0.0599324	+	0.164977i	0.00273553	+	0.00753012i
$481$	−12.8587	+	4.68017i	−0.586304	+	0.213397i
$482$			11.5817i			0.527532i
$483$	9.10588	+	10.8654i	0.414332	+	0.494395i
$484$	−0.217996	+	1.23632i	−0.00990891	+	0.0561962i
$485$	−1.23644	+	0.450027i	−0.0561438	+	0.0204347i
$486$	−11.9108	−	10.0565i	−0.540284	−	0.456173i
$487$	22.4046	+	12.9353i	1.01525	+	0.586154i	0.912724	−	0.408576i	$-0.133975\pi$
$487$	22.4046	+	12.9353i	1.01525	+	0.586154i	0.102524	+	0.994730i	$0.467308\pi$
$488$	9.39961	+	7.88721i	0.425500	+	0.357037i
$489$	25.5620	+	21.4757i	1.15595	+	0.971164i
$490$	0.0186948	+	0.00329640i	0.000844546	+	0.000148916i
$491$	11.9987	+	14.2995i	0.541495	+	0.645328i	0.965522	−	0.260321i	$-0.0838284\pi$
$491$	11.9987	+	14.2995i	0.541495	+	0.645328i	−0.424027	+	0.905649i	$0.639384\pi$
$492$	−10.7098	−	8.99776i	−0.482836	−	0.405651i
$493$	19.4793	+	11.2464i	0.877305	+	0.506512i
$494$	18.6580	+	3.08372i	0.839462	+	0.138743i
$495$	−1.00056	+	0.362789i	−0.0449718	+	0.0163062i
$496$	3.31757	−	9.11496i	0.148963	−	0.409274i
$497$	4.06851	+	1.48081i	0.182497	+	0.0664236i
$498$	0.00681925	−	11.1574i	0.000305578	−	0.499976i
$499$	5.65472	+	2.05815i	0.253140	+	0.0921354i	0.465473	−	0.885062i	$-0.345884\pi$
$499$	5.65472	+	2.05815i	0.253140	+	0.0921354i	−0.212333	+	0.977197i	$0.568106\pi$
$500$	−0.346246	−	0.951303i	−0.0154846	−	0.0425436i
$501$	5.56391	+	31.6677i	0.248577	+	1.41481i
$502$			13.6290i			0.608293i
$503$	11.8481	+	32.5523i	0.528279	+	1.45144i	0.861095	+	0.508444i	$0.169779\pi$
$503$	11.8481	+	32.5523i	0.528279	+	1.45144i	−0.332816	+	0.942992i	$0.607999\pi$
$504$	1.35030	+	7.71303i	0.0601470	+	0.343566i
$505$	−0.309131	−	0.535430i	−0.0137561	−	0.0238263i
$506$	−5.48890	−	9.50705i	−0.244011	−	0.422640i
$507$	5.04787	−	8.73084i	0.224184	−	0.387750i
$508$	−0.535725	+	1.47189i	−0.0237690	+	0.0653047i
$509$	1.00897	−	5.72214i	0.0447217	−	0.253629i	−0.954248	−	0.299017i	$-0.903341\pi$
$509$	1.00897	−	5.72214i	0.0447217	−	0.253629i	0.998969	+	0.0453877i	$0.0144523\pi$
$510$	1.11260	−	0.404182i	0.0492666	−	0.0178975i
$511$	−7.41080	+	6.21840i	−0.327834	+	0.275086i
$512$	−1.00000			−0.0441942
$513$	3.73429	−	22.3395i	0.164873	−	0.986315i
$514$	−14.5463			−0.641612
$515$	0.465315	−	0.390446i	0.0205042	−	0.0172051i
$516$	14.6845	−	5.33455i	0.646448	−	0.234840i
$517$	−2.20355	+	12.4970i	−0.0969121	+	0.549616i
$518$	2.81566	−	7.73597i	0.123713	−	0.339899i
$519$	−3.52089	+	6.08975i	−0.154550	+	0.267310i
$520$	0.219831	+	0.380759i	0.00964024	+	0.0166974i
$521$	9.26152	+	16.0414i	0.405755	+	0.702788i	0.994409	−	0.105597i	$-0.0336754\pi$
$521$	9.26152	+	16.0414i	0.405755	+	0.702788i	−0.588654	+	0.808385i	$0.700342\pi$
$522$	9.39813	+	3.43366i	0.411345	+	0.150287i
$523$	−11.5780	−	31.8102i	−0.506269	−	1.39096i	−0.885058	−	0.465480i	$-0.845882\pi$
$523$	−11.5780	−	31.8102i	−0.506269	−	1.39096i	0.378789	−	0.925483i	$-0.376340\pi$
$524$		−	8.82302i		−	0.385436i
$525$	−3.90354	−	22.2175i	−0.170365	−	0.969650i
$526$	1.42575	+	3.91721i	0.0621656	+	0.170799i
$527$	−61.4709	−	22.3736i	−2.67772	−	0.974609i
$528$	0.00370593	−	6.06351i	0.000161280	−	0.263880i
$529$	−12.3726	−	4.50325i	−0.537938	−	0.195793i
$530$	−0.389998	+	1.07151i	−0.0169404	+	0.0465434i
$531$	12.7406	+	10.7172i	0.552897	+	0.465088i
$532$	−8.63642	+	7.40629i	−0.374436	+	0.321103i
$533$	−30.3432	−	17.5186i	−1.31431	−	0.758816i
$534$	−7.67943	−	6.45181i	−0.332321	−	0.279197i
$535$	0.899527	+	1.07201i	0.0388900	+	0.0463472i
$536$	6.31548	+	1.11359i	0.272787	+	0.0480998i
$537$	13.7401	+	11.5437i	0.592931	+	0.498146i
$538$	−11.6523	−	9.77743i	−0.502366	−	0.421535i
$539$	−0.567916	−	0.327887i	−0.0244619	−	0.0141231i
$540$	0.456510	−	0.262452i	0.0196451	−	0.0112941i
$541$	16.1080	−	5.86282i	0.692535	−	0.252062i	0.0283150	−	0.999599i	$-0.490986\pi$
$541$	16.1080	−	5.86282i	0.692535	−	0.252062i	0.664220	+	0.747537i	$0.268764\pi$
$542$	−2.94508	+	16.7024i	−0.126502	+	0.717429i
$543$	18.3949	+	21.9494i	0.789402	+	0.941941i
$544$			6.74396i			0.289145i
$545$	0.185531	−	0.0675277i	0.00794726	−	0.00289257i
$546$	6.69701	+	18.4349i	0.286606	+	0.788943i
$547$	4.23859	+	11.6454i	0.181229	+	0.497923i	0.996727	−	0.0808366i	$-0.0257592\pi$
$547$	4.23859	+	11.6454i	0.181229	+	0.497923i	−0.815498	+	0.578760i	$0.803537\pi$
$548$	15.3908	−	2.71381i	0.657461	−	0.115928i
$549$	18.4444	−	31.8567i	0.787189	−	1.35961i
$550$			17.4679i			0.744834i
$551$	2.67808	+	14.2892i	0.114090	+	0.608741i
$552$	3.48870	+	4.16283i	0.148489	+	0.177182i
$553$	−20.6789	+	3.64625i	−0.879356	+	0.155054i
$554$	−12.9714	+	10.8843i	−0.551102	+	0.462429i
$555$	−0.553617		0.000338363i	−0.0234998		1.43627e-5i
$556$	1.95347	+	11.0787i	0.0828454	+	0.469840i
$557$	9.84548	+	1.73602i	0.417167	+	0.0735577i	0.378292	−	0.925686i	$-0.376512\pi$
$557$	9.84548	+	1.73602i	0.417167	+	0.0735577i	0.0388747	+	0.999244i	$0.487623\pi$
$558$	−28.6515	−	5.08816i	−1.21292	−	0.215399i
$559$	33.8911	−	19.5670i	1.43344	−	0.827598i
$560$	−0.260489	−	0.0459313i	−0.0110077	−	0.00194095i
$561$	−40.8921	−	0.0249926i	−1.72647	−	0.00105519i
$562$	4.82590	−	8.35871i	0.203568	−	0.352591i
$563$	18.0567			0.761001			0.380500	−	0.924781i	$-0.375752\pi$
$563$	18.0567			0.761001			0.380500	+	0.924781i	$0.375752\pi$
$564$	0.00383728	−	6.27842i	0.000161578	−	0.264369i
$565$	−1.66565	+	0.293698i	−0.0700743	+	0.0123560i
$566$	−14.0842	−	11.8181i	−0.592004	−	0.496750i
$567$	22.0939	−	7.98040i	0.927856	−	0.335145i
$568$	1.55875	+	0.567338i	0.0654036	+	0.0238050i
$569$	13.1135	−	22.7133i	0.549748	−	0.952192i	−0.448543	−	0.893761i	$-0.648057\pi$
$569$	13.1135	−	22.7133i	0.549748	−	0.952192i	0.998291	−	0.0584309i	$-0.0186097\pi$
$570$	0.666434	+	0.375820i	0.0279138	+	0.0157414i
$571$	17.6245	+	30.5266i	0.737564	+	1.27750i	0.953589	+	0.301110i	$0.0973572\pi$
$571$	17.6245	+	30.5266i	0.737564	+	1.27750i	−0.216026	+	0.976388i	$0.569309\pi$
$572$	−2.63739	−	14.9574i	−0.110275	−	0.625399i
$573$	−19.6774	−	3.48206i	−0.822035	−	0.145465i
$574$	19.8077	−	7.20943i	0.826759	−	0.300916i
$575$	−10.0576	−	11.9862i	−0.419433	−	0.499860i
$576$	0.517333	+	2.95506i	0.0215555	+	0.123127i
$577$	4.26155	−	7.38122i	0.177411	−	0.307284i	−0.763582	−	0.645710i	$-0.776561\pi$
$577$	4.26155	−	7.38122i	0.177411	−	0.307284i	0.940993	+	0.338426i	$0.109895\pi$
$578$	28.4810			1.18465
$579$	−23.9884	−	13.8693i	−0.996924	−	0.576387i
$580$	−0.217258	+	0.258918i	−0.00902113	+	0.0107510i
$581$	14.5611	+	8.40683i	0.604094	+	0.348774i
$582$	−22.1496	+	3.89162i	−0.918132	+	0.161313i
$583$	25.3199	−	30.1751i	1.04864	−	1.24972i
$584$	−2.83927	+	2.38243i	−0.117490	+	0.0985855i
$585$	1.01144	−	0.846593i	0.0418178	−	0.0350023i
$586$	2.58594	+	14.6656i	0.106824	+	0.605830i
$587$	−7.65658	−	9.12475i	−0.316021	−	0.376619i	0.584528	−	0.811373i	$-0.301280\pi$
$587$	−7.65658	−	9.12475i	−0.316021	−	0.376619i	−0.900549	+	0.434755i	$0.856835\pi$
$588$	0.304818	+	0.111156i	0.0125705	+	0.00458398i
$589$	−14.8867	−	39.5736i	−0.613397	−	1.63060i
$590$	−0.487048	+	0.281198i	−0.0200515	+	0.0115767i
$591$	−7.55190	−	1.33636i	−0.310644	−	0.0549706i
$592$	1.07875	−	2.96385i	0.0443364	−	0.121813i
$593$	−27.9905	+	33.3578i	−1.14943	+	1.36984i	−0.231632	+	0.972803i	$0.574407\pi$
$593$	−27.9905	+	33.3578i	−1.14943	+	1.36984i	−0.917802	+	0.397039i	$0.870038\pi$
$594$	−17.9199	+	3.12590i	−0.735264	+	0.128257i
$595$	−0.309759	+	1.75673i	−0.0126989	+	0.0720189i
$596$	14.4426	−	8.33847i	0.591594	−	0.341557i
$597$	7.97278	−	6.68166i	0.326304	−	0.273462i
$598$	10.4219	+	8.74498i	0.426182	+	0.357609i
$599$	26.2159	+	21.9977i	1.07115	+	0.898803i	0.995156	−	0.0983054i	$-0.0313422\pi$
$599$	26.2159	+	21.9977i	1.07115	+	0.898803i	0.0759951	+	0.997108i	$0.475787\pi$
$600$	−1.49555	−	8.51208i	−0.0610554	−	0.347504i
$601$	−2.64878	+	1.52928i	−0.108046	+	0.0623804i	−0.553049	−	0.833149i	$-0.686536\pi$
$601$	−2.64878	+	1.52928i	−0.108046	+	0.0623804i	0.445003	+	0.895529i	$0.353203\pi$
$602$	−4.08832	+	23.1860i	−0.166627	+	0.944990i
$603$	0.0235168	−	19.2387i	0.000957680	−	0.783461i
$604$	−1.43764	+	1.71331i	−0.0584967	+	0.0697136i
$605$	−0.0435120	+	0.119548i	−0.00176902	+	0.00486033i
$606$	−3.60807	−	9.93198i	−0.146568	−	0.403459i
$607$	−22.8514	+	13.1933i	−0.927509	+	0.535498i	−0.886023	−	0.463642i	$-0.846543\pi$
$607$	−22.8514	+	13.1933i	−0.927509	+	0.535498i	−0.0414861	+	0.999139i	$0.513209\pi$
$608$	−3.30883	+	2.83754i	−0.134191	+	0.115077i
$609$	−11.5564	+	9.68498i	−0.468291	+	0.392455i
$610$	0.799287	+	0.952553i	0.0323622	+	0.0385677i
$611$	−2.73086	−	15.4875i	−0.110479	−	0.626557i
$612$	19.9288	−	3.48887i	0.805574	−	0.141029i
$613$	13.0354	−	10.9380i	0.526495	−	0.441781i	−0.340394	−	0.940283i	$-0.610561\pi$
$613$	13.0354	−	10.9380i	0.526495	−	0.441781i	0.866889	+	0.498501i	$0.166116\pi$
$614$	−4.04774	+	4.82390i	−0.163353	+	0.194677i
$615$	−0.910503	−	1.08644i	−0.0367150	−	0.0438096i
$616$	7.91322	+	4.56870i	0.318833	+	0.184078i
$617$	−29.7602	+	35.4669i	−1.19810	+	1.42784i	−0.321308	+	0.946975i	$0.604122\pi$
$617$	−29.7602	+	35.4669i	−1.19810	+	1.42784i	−0.876794	+	0.480867i	$0.840322\pi$
$618$	8.99411	−	5.18542i	0.361796	−	0.208588i
$619$	−32.8492			−1.32032			−0.660161	−	0.751124i	$-0.729512\pi$
$619$	−32.8492			−1.32032			−0.660161	+	0.751124i	$0.729512\pi$
$620$	0.491494	−	0.851293i	0.0197389	−	0.0341887i
$621$	10.4966	−	12.4629i	0.421213	−	0.500118i
$622$	3.72370	+	4.43773i	0.149307	+	0.177937i
$623$	14.2031	−	5.16949i	0.569033	−	0.207111i
$624$	2.56580	+	7.06290i	0.102714	+	0.282742i
$625$	4.31447	+	24.4686i	0.172579	+	0.978744i
$626$	5.27822	+	9.14214i	0.210960	+	0.365393i
$627$	−17.1932	−	20.0737i	−0.686629	−	0.801665i
$628$	−9.16419	+	15.8728i	−0.365691	+	0.633395i
$629$	−19.9881	−	7.27506i	−0.796976	−	0.290076i
$630$	−0.000969979		0.793523i	−3.86449e−5		0.0316147i
$631$	1.50615	+	1.26381i	0.0599589	+	0.0503115i	0.672275	−	0.740302i	$-0.265317\pi$
$631$	1.50615	+	1.26381i	0.0599589	+	0.0503115i	−0.612316	+	0.790613i	$0.709762\pi$
$632$	−7.92261	+	1.39697i	−0.315145	+	0.0555685i
$633$	−36.9147	+	21.2826i	−1.46723	+	0.845909i
$634$	21.8974			0.869658
$635$	−0.0793670	+	0.137468i	−0.00314958	+	0.00545524i
$636$	−9.75486	+	16.8721i	−0.386805	+	0.669022i
$637$	0.800353	+	0.141124i	0.0317111	+	0.00559153i
$638$	10.1117	−	5.83797i	0.400324	−	0.231127i
$639$	0.870125	−	4.89969i	0.0344216	−	0.193829i
$640$	−0.0998001	−	0.0175974i	−0.00394494	−	0.000695600i
$641$	−5.00360	−	28.3768i	−0.197630	−	1.12082i	−0.908623	−	0.417617i	$-0.862865\pi$
$641$	−5.00360	−	28.3768i	−0.197630	−	1.12082i	0.710993	−	0.703199i	$-0.248246\pi$
$642$	11.9464	+	20.7210i	0.471488	+	0.817795i
$643$	−21.4435	+	17.9933i	−0.845651	+	0.709585i	−0.958827	−	0.283990i	$-0.908342\pi$
$643$	−21.4435	+	17.9933i	−0.845651	+	0.709585i	0.113177	+	0.993575i	$0.463897\pi$
$644$	−8.06050	+	1.42128i	−0.317628	+	0.0560064i
$645$	1.55939	−	0.273979i	0.0614007	−	0.0107879i
$646$	19.1362	+	22.3147i	0.752906	+	0.877958i
$647$		−	42.3012i		−	1.66303i	−0.555501	−	0.831516i	$-0.687474\pi$
$647$		−	42.3012i		−	1.66303i	0.555501	−	0.831516i	$-0.312526\pi$
$648$	8.46473	−	3.05750i	0.332526	−	0.120110i
$649$	19.1327	−	3.37362i	0.751025	−	0.132426i
$650$	−7.40404	−	20.3424i	−0.290410	−	0.797896i
$651$	28.2080	−	33.5753i	1.10556	−	1.31592i
$652$	−18.1129	+	6.59257i	−0.709357	+	0.258185i
$653$		−	24.6508i		−	0.964659i	−0.875990	−	0.482329i	$-0.839791\pi$
$653$		−	24.6508i		−	0.964659i	0.875990	−	0.482329i	$-0.160209\pi$
$654$	3.32360	−	0.583947i	0.129963	−	0.0228341i
$655$	0.155263	−	0.880538i	0.00606662	−	0.0344055i
$656$	7.58885	−	2.76212i	0.296295	−	0.107843i
$657$	8.50905	+	7.15769i	0.331970	+	0.279248i
$658$	8.19368	+	4.73063i	0.319423	+	0.184419i
$659$	30.8532	+	25.8889i	1.20187	+	1.00849i	0.999575	+	0.0291637i	$0.00928440\pi$
$659$	30.8532	+	25.8889i	1.20187	+	1.00849i	0.202295	+	0.979325i	$0.435160\pi$
$660$	0.107072	−	0.605074i	0.00416778	−	0.0235525i
$661$	−34.7964	−	6.13555i	−1.35343	−	0.238645i	−0.550555	−	0.834799i	$-0.685584\pi$
$661$	−34.7964	−	6.13555i	−1.35343	−	0.238645i	−0.802870	+	0.596154i	$0.796695\pi$
$662$	2.75314	+	3.28106i	0.107004	+	0.127522i
$663$	47.6319	−	17.3036i	1.84987	−	0.672018i
$664$	5.57871	+	3.22087i	0.216496	+	0.124994i
$665$	−0.992247	+	0.587169i	−0.0384777	+	0.0227694i
$666$	−9.31641	−	1.65448i	−0.361004	−	0.0641098i
$667$	−3.57710	+	9.82801i	−0.138506	+	0.380542i
$668$	−17.4439	−	6.34905i	−0.674924	−	0.245652i
$669$	−17.2935	+	9.97032i	−0.668606	+	0.385475i
$670$	0.610689	+	0.222273i	0.0235930	+	0.00858715i
$671$	−14.6917	−	40.3650i	−0.567165	−	1.55827i
$672$	−4.24726	−	1.54882i	−0.163842	−	0.0597469i
$673$		−	15.4074i		−	0.593910i	−0.954891	−	0.296955i	$-0.904029\pi$
$673$		−	15.4074i		−	0.593910i	0.954891	−	0.296955i	$-0.0959712\pi$
$674$	−1.77498	−	4.87670i	−0.0683695	−	0.187844i
$675$	−24.3800	+	8.82301i	−0.938387	+	0.339598i
$676$	2.91131	+	5.04253i	0.111973	+	0.193944i
$677$	−5.96794	−	10.3368i	−0.229366	−	0.397274i	0.728254	−	0.685307i	$-0.240332\pi$
$677$	−5.96794	−	10.3368i	−0.229366	−	0.397274i	−0.957620	+	0.288033i	$0.906999\pi$
$678$	−28.9076	−	0.0176679i	−1.11019	−	0.000678532i
$679$	11.5909	−	31.8458i	0.444819	−	1.22213i
$680$	−0.118677	+	0.673048i	−0.00455104	+	0.0258102i
$681$	−0.609342	+	3.44344i	−0.0233501	+	0.131953i
$682$	−26.0128	+	21.8273i	−0.996080	+	0.835810i
$683$	−28.8040			−1.10215			−0.551076	−	0.834455i	$-0.685783\pi$
$683$	−28.8040			−1.10215			−0.551076	+	0.834455i	$0.685783\pi$
$684$	10.0969	+	8.30984i	0.386063	+	0.317735i
$685$	1.58376			0.0605122
$686$	−14.3708	+	12.0585i	−0.548679	+	0.460396i
$687$	25.8594	+	21.7256i	0.986597	+	0.828882i
$688$	−1.56634	+	8.88314i	−0.0597161	+	0.338667i
$689$	−16.6964	+	45.8730i	−0.636082	+	1.74762i
$690$	0.274917	+	0.476843i	0.0104659	+	0.0181531i
$691$	14.7985	+	25.6318i	0.562962	+	0.975079i	0.997236	+	0.0742980i	$0.0236716\pi$
$691$	14.7985	+	25.6318i	0.562962	+	0.975079i	−0.434274	+	0.900781i	$0.642995\pi$
$692$	−2.03063	−	3.51716i	−0.0771931	−	0.133702i
$693$	9.40700	−	25.7476i	0.357342	−	0.978069i
$694$	−3.16959	−	8.70838i	−0.120316	−	0.330566i
$695$			1.14003i			0.0432437i
$696$	−4.42757	+	3.71056i	−0.167827	+	0.140649i
$697$	−18.6276	−	51.1789i	−0.705571	−	1.93854i
$698$	20.9062	+	7.60925i	0.791313	+	0.288014i
$699$	−28.0065	−	16.1924i	−1.05930	−	0.612452i
$700$	12.2383	+	4.45438i	0.462565	+	0.168360i
$701$	−0.0620944	+	0.170603i	−0.00234527	+	0.00644358i	−0.940860	−	0.338796i	$-0.889980\pi$
$701$	−0.0620944	+	0.170603i	−0.00234527	+	0.00644358i	0.938514	+	0.345240i	$0.112202\pi$
$702$	19.5439	−	11.2359i	0.737637	−	0.424073i
$703$	−4.84061	−	12.8679i	−0.182567	−	0.485321i
$704$	3.03176	+	1.75038i	0.114264	+	0.0659701i
$705$	0.110867	−	0.626519i	0.00417550	−	0.0235961i
$706$	−19.2618	−	22.9553i	−0.724926	−	0.863933i
$707$	15.6821	+	2.76517i	0.589785	+	0.103995i
$708$	−9.03452	+	3.28204i	−0.339538	+	0.123347i
$709$	16.1787	+	13.5755i	0.607604	+	0.509840i	0.893880	−	0.448307i	$-0.147973\pi$
$709$	16.1787	+	13.5755i	0.607604	+	0.509840i	−0.286276	+	0.958147i	$0.592417\pi$
$710$	0.145580	+	0.0840504i	0.00546350	+	0.00315435i
$711$	8.22676	+	22.6891i	0.308527	+	0.850907i
$712$	5.44155	−	1.98056i	0.203931	−	0.0742247i
$713$	5.28191	−	29.9552i	0.197809	−	1.12183i
$714$	−10.4452	+	28.6433i	−0.390900	+	1.07195i
$715$		−	1.53916i		−	0.0575612i
$716$	−9.73611	+	3.54365i	−0.363855	+	0.132433i
$717$	6.83136	+	1.20886i	0.255122	+	0.0451456i
$718$	−2.13134	−	5.85582i	−0.0795411	−	0.218537i
$719$	−6.95818	+	1.22691i	−0.259496	+	0.0457562i	−0.301883	−	0.953345i	$-0.597615\pi$
$719$	−6.95818	+	1.22691i	−0.259496	+	0.0457562i	0.0423864	+	0.999101i	$0.486504\pi$
$720$	−0.000371624		0.304019i	−1.38496e−5		0.0113301i
$721$			15.6449i			0.582646i
$722$	−2.89676	+	18.7779i	−0.107806	+	0.698840i
$723$	−6.87247	+	18.8461i	−0.255590	+	0.700894i
$724$	−16.2831	+	2.87115i	−0.605158	+	0.106706i
$725$	12.7485	−	10.6973i	0.473468	−	0.397286i
$726$	−1.08835	+	1.88242i	−0.0403924	+	0.0698631i
$727$	6.30576	+	35.7617i	0.233868	+	1.32633i	0.844985	+	0.534789i	$0.179609\pi$
$727$	6.30576	+	35.7617i	0.233868	+	1.32633i	−0.611118	+	0.791540i	$0.709280\pi$
$728$	−11.1519	−	1.96639i	−0.413318	−	0.0728792i
$729$	−13.4142	−	23.4320i	−0.496821	−	0.867853i
$730$	−0.325284	+	0.187803i	−0.0120393	+	0.00695088i
$731$	59.9076	+	10.5633i	2.21576	+	0.390699i
$732$	10.6152	+	18.4120i	0.392347	+	0.680526i
$733$	21.9876	−	38.0837i	0.812132	−	1.40665i	−0.0992364	−	0.995064i	$-0.531640\pi$
$733$	21.9876	−	38.0837i	0.812132	−	1.40665i	0.911369	−	0.411591i	$-0.135027\pi$
$734$	−21.3980			−0.789815
$735$	0.0284648	+	0.0164573i	0.00104994	+	0.000607038i
$736$	−3.08818	+	0.544530i	−0.113832	+	0.0200716i
$737$	−17.1978	−	14.4307i	−0.633489	−	0.531560i
$738$	−12.0882	−	20.9966i	−0.444972	−	0.772894i
$739$	41.7072	+	15.1802i	1.53422	+	0.558412i	0.964651	−	0.263529i	$-0.0848866\pi$
$739$	41.7072	+	15.1802i	1.53422	+	0.558412i	0.569573	+	0.821941i	$0.307109\pi$
$740$	0.159816	−	0.276809i	0.00587494	−	0.0101757i
$741$	28.5310	+	16.0894i	1.04811	+	0.591059i
$742$	−14.6845	−	25.4344i	−0.539086	−	0.933724i
$743$	8.84302	+	50.1513i	0.324419	+	1.83987i	0.513726	+	0.857954i	$0.328265\pi$
$743$	8.84302	+	50.1513i	0.324419	+	1.83987i	−0.189307	+	0.981918i	$0.560624\pi$
$744$	10.8072	−	12.8635i	0.396211	−	0.471600i
$745$	1.58811	−	0.578026i	0.0581840	−	0.0211772i
$746$	5.20614	+	6.20443i	0.190610	+	0.227160i
$747$	6.63181	−	18.1517i	0.242645	−	0.664135i
$748$	11.8045	−	20.4460i	0.431616	−	0.747581i
$749$	−36.0434			−1.31700
$750$	0.00107168	−	1.75345i	3.91323e−5	−	0.0640270i
$751$	31.0235	−	36.9724i	1.13207	−	1.34914i	0.203021	−	0.979174i	$-0.434924\pi$
$751$	31.0235	−	36.9724i	1.13207	−	1.34914i	0.929044	−	0.369969i	$-0.120632\pi$
$752$	3.13921	+	1.81242i	0.114475	+	0.0660923i
$753$	−8.08734	+	22.1776i	−0.294719	+	0.808196i
$754$	−9.30113	+	11.0847i	−0.338727	+	0.403679i
$755$	−0.173626	+	0.145690i	−0.00631891	+	0.00530220i
$756$	−2.37959	+	13.3521i	−0.0865450	+	0.485613i
$757$	−6.82028	−	38.6797i	−0.247887	−	1.40584i	−0.813691	−	0.581298i	$-0.802545\pi$
$757$	−6.82028	−	38.6797i	−0.247887	−	1.40584i	0.565804	−	0.824540i	$-0.308566\pi$
$758$	−2.47610	−	2.95090i	−0.0899359	−	0.107181i
$759$	−3.29032	−	18.7272i	−0.119431	−	0.679756i
$760$	−0.380155	+	0.224959i	−0.0137897	+	0.00816014i
$761$	42.6846	−	24.6439i	1.54731	−	0.893342i	0.548969	−	0.835843i	$-0.315021\pi$
$761$	42.6846	−	24.6439i	1.54731	−	0.893342i	0.998346	−	0.0574994i	$-0.0183127\pi$
$762$	−1.74516	+	2.07722i	−0.0632204	+	0.0752497i
$763$	−1.73925	+	4.77854i	−0.0629650	+	0.172995i
$764$	7.41600	−	8.83804i	0.268301	−	0.319749i
$765$	2.05029	+	0.00250622i	0.0741284	+	9.06124e-5i
$766$	3.93966	−	22.3429i	0.142346	−	0.807282i
$767$	−20.8513	+	12.0385i	−0.752896	+	0.434685i
$768$	−1.62723	−	0.593391i	−0.0587177	−	0.0214122i
$769$	6.05347	+	5.07947i	0.218294	+	0.183170i	0.745376	−	0.666644i	$-0.232270\pi$
$769$	6.05347	+	5.07947i	0.218294	+	0.183170i	−0.527083	+	0.849814i	$0.676714\pi$
$770$	0.709342	+	0.595209i	0.0255629	+	0.0214498i
$771$	−23.6703	−	8.63167i	−0.852465	−	0.310862i
$772$	13.8546	−	7.99896i	0.498638	−	0.287889i
$773$	−1.29841	+	7.36367i	−0.0467007	+	0.264853i	−0.999214	−	0.0396446i	$-0.987377\pi$
$773$	−1.29841	+	7.36367i	−0.0467007	+	0.264853i	0.952513	+	0.304498i	$0.0984885\pi$
$774$	27.0605	+	0.0330780i	0.972670	+	0.00118896i
$775$	−31.1110	+	37.0766i	−1.11754	+	1.33183i
$776$	4.44078	−	12.2009i	0.159415	−	0.437989i
$777$	9.17219	−	10.9174i	0.329050	−	0.391661i
$778$	19.1716	−	11.0687i	0.687335	−	0.396833i
$779$	17.2726	−	30.6730i	0.618857	−	1.09898i
$780$	0.131778	+	0.750029i	0.00471840	+	0.0268554i
$781$	−3.73268	−	4.44844i	−0.133566	−	0.159178i
$782$	3.67229	+	20.8266i	0.131321	+	0.744757i
$783$	13.2555	+	11.1641i	0.473711	+	0.398973i
$784$	−0.143497	+	0.120409i	−0.00512491	+	0.00430031i
$785$	−1.19391	+	1.42284i	−0.0426124	+	0.0507835i
$786$	5.23550	−	14.3571i	0.186744	−	0.512101i
$787$	−3.95810	−	2.28521i	−0.141091	−	0.0814589i	0.427793	−	0.903877i	$-0.359291\pi$
$787$	−3.95810	−	2.28521i	−0.141091	−	0.0814589i	−0.568884	+	0.822418i	$0.692625\pi$
$788$	2.84615	−	3.39191i	0.101390	−	0.120832i
$789$	−0.00441291	+	7.22024i	−0.000157104	+	0.257048i
$790$	−0.815261			−0.0290057
$791$	21.7812	−	37.7261i	0.774449	−	1.34138i
$792$	3.60406	−	9.86454i	0.128065	−	0.350521i
$793$	34.2187	+	40.7802i	1.21514	+	1.44815i
$794$	−0.845454	+	0.307720i	−0.0300040	+	0.0109206i
$795$	−1.27044	+	1.51218i	−0.0450579	+	0.0536313i
$796$	1.04290	+	5.91458i	0.0369646	+	0.209637i
$797$	−21.6931	−	37.5736i	−0.768410	−	1.33092i	−0.938425	−	0.345483i	$-0.887715\pi$
$797$	−21.6931	−	37.5736i	−0.768410	−	1.33092i	0.170015	−	0.985441i	$-0.445618\pi$
$798$	−18.4483	+	6.92698i	−0.653063	+	0.245212i
$799$	12.2229	−	21.1707i	0.432416	−	0.748966i
$800$	4.68881	+	1.70659i	0.165775	+	0.0603370i
$801$	−8.66777	−	15.0555i	−0.306261	−	0.531960i
$802$	13.7073	+	11.5018i	0.484022	+	0.406143i
$803$	12.7781	−	2.25313i	0.450930	−	0.0795111i
$804$	9.61597	+	5.55962i	0.339129	+	0.196073i
$805$	−0.829449			−0.0292342
$806$	21.0416	−	36.4451i	0.741159	−	1.28373i
$807$	−13.1592	−	22.8245i	−0.463224	−	0.803461i
$808$	6.00820	+	1.05941i	0.211368	+	0.0372698i
$809$	35.2135	−	20.3305i	1.23804	−	0.714783i	0.269347	−	0.963043i	$-0.413192\pi$
$809$	35.2135	−	20.3305i	1.23804	−	0.714783i	0.968693	+	0.248261i	$0.0798589\pi$
$810$	0.898585	−	0.156181i	0.0315731	−	0.00548763i
$811$	0.291977	+	0.0514834i	0.0102527	+	0.00180783i	0.178772	−	0.983890i	$-0.442787\pi$
$811$	0.291977	+	0.0514834i	0.0102527	+	0.00180783i	−0.168519	+	0.985698i	$0.553899\pi$
$812$	−1.51167	−	8.57311i	−0.0530493	−	0.300857i
$813$	−14.7034	+	25.4311i	−0.515670	+	0.891908i
$814$	−8.45838	+	7.09743i	−0.296466	+	0.248765i
$815$	−1.92368	+	0.339197i	−0.0673837	+	0.0118816i
$816$	−4.00181	+	10.9740i	−0.140091	+	0.384167i
$817$	20.0235	+	33.8374i	0.700534	+	1.18382i
$818$		−	8.60134i		−	0.300739i
$819$	−0.0415263	+	33.9719i	−0.00145104	+	1.18707i
$820$	0.805974	−	0.142115i	0.0281458	−	0.00496287i
$821$	−9.70546	−	26.6655i	−0.338723	−	0.930633i	−0.985758	−	0.168173i	$-0.946213\pi$
$821$	−9.70546	−	26.6655i	−0.338723	−	0.930633i	0.647035	−	0.762461i	$-0.276009\pi$
$822$	26.6547	+	4.71674i	0.929689	+	0.164515i
$823$	−28.4074	+	10.3394i	−0.990219	+	0.360410i	−0.785805	−	0.618474i	$-0.787751\pi$
$823$	−28.4074	+	10.3394i	−0.990219	+	0.360410i	−0.204414	+	0.978885i	$0.565529\pi$
$824$			5.99396i			0.208809i
$825$	−10.3653	+	28.4243i	−0.360873	+	0.989608i
$826$	2.51531	−	14.2650i	0.0875188	−	0.496344i
$827$	−17.3684	+	6.32160i	−0.603960	+	0.219823i	−0.625858	−	0.779937i	$-0.715251\pi$
$827$	−17.3684	+	6.32160i	−0.603960	+	0.219823i	0.0218984	+	0.999760i	$0.493029\pi$
$828$	3.20673	+	8.84405i	0.111442	+	0.307352i
$829$	−37.9948	−	21.9363i	−1.31961	−	0.761879i	−0.335947	−	0.941881i	$-0.609056\pi$
$829$	−37.9948	−	21.9363i	−1.31961	−	0.761879i	−0.983666	+	0.180002i	$0.942390\pi$
$830$	0.500077	+	0.419614i	0.0173579	+	0.0145650i
$831$	−27.5661	+	10.0142i	−0.956258	+	0.347388i
$832$	−4.27259	−	0.753373i	−0.148125	−	0.0261185i
$833$	0.812031	+	0.967741i	0.0281352	+	0.0335303i
$834$	−3.39523	+	19.1867i	−0.117567	+	0.664382i
$835$	−1.62917	−	0.940604i	−0.0563799	−	0.0325509i
$836$	14.9984	−	2.81099i	0.518729	−	0.0972200i
$837$	−43.6034	−	25.2812i	−1.50716	−	0.873845i
$838$	−0.184146	+	0.505938i	−0.00636123	+	0.0174773i
$839$	7.44769	+	2.71074i	0.257123	+	0.0935851i	0.467366	−	0.884064i	$-0.345203\pi$
$839$	7.44769	+	2.71074i	0.257123	+	0.0935851i	−0.210243	+	0.977649i	$0.567425\pi$
$840$	−0.396621	−	0.229313i	−0.0136847	−	0.00791205i
$841$	16.7981	+	6.11399i	0.579243	+	0.210827i
$842$	−7.76088	−	21.3228i	−0.267457	−	0.734833i
$843$	12.8129	−	10.7379i	0.441298	−	0.369834i
$844$		−	24.6011i		−	0.846805i
$845$	0.201813	+	0.554477i	0.00694258	+	0.0190746i
$846$	3.73180	−	10.2142i	0.128302	−	0.351170i
$847$	−1.63835	−	2.83771i	−0.0562944	−	0.0975048i
$848$	−5.62602	−	9.74455i	−0.193198	−	0.334629i
$849$	−15.9056	−	27.5882i	−0.545878	−	0.946824i
$850$	11.5092	−	31.6212i	0.394761	−	1.08460i
$851$	1.71748	−	9.74031i	0.0588744	−	0.333893i
$852$	2.19979	+	1.84814i	0.0753637	+	0.0633162i
$853$	−7.52845	+	6.31712i	−0.257769	+	0.216294i	−0.762509	−	0.646977i	$-0.776033\pi$
$853$	−7.52845	+	6.31712i	−0.257769	+	0.216294i	0.504740	+	0.863271i	$0.331588\pi$
$854$	−32.0269			−1.09594
$855$	0.861435	+	1.00700i	0.0294605	+	0.0344387i
$856$	−13.8092			−0.471987
$857$	20.7759	−	17.4330i	0.709690	−	0.595501i	−0.214822	−	0.976653i	$-0.568917\pi$
$857$	20.7759	−	17.4330i	0.709690	−	0.595501i	0.924512	+	0.381152i	$0.124473\pi$
$858$	4.58392	−	25.9041i	0.156492	−	0.884352i
$859$	0.742058	−	4.20842i	0.0253187	−	0.143589i	−0.969528	−	0.244981i	$-0.921218\pi$
$859$	0.742058	−	4.20842i	0.0253187	−	0.143589i	0.994847	+	0.101391i	$0.0323294\pi$
$860$	−0.312641	+	0.858975i	−0.0106610	+	0.0292908i
$861$	36.5098	+	0.0223143i	1.24425	+	0.000760468i
$862$	15.3798	+	26.6386i	0.523838	+	0.907314i
$863$	9.44892	+	16.3660i	0.321645	+	0.557106i	0.980828	−	0.194877i	$-0.0624309\pi$
$863$	9.44892	+	16.3660i	0.321645	+	0.557106i	−0.659183	+	0.751983i	$0.729098\pi$
$864$	−0.911684	+	5.11555i	−0.0310161	+	0.174034i
$865$	−0.140764	−	0.386747i	−0.00478613	−	0.0131498i
$866$			5.26614i			0.178951i
$867$	46.3453	+	16.9004i	1.57397	+	0.573967i
$868$	8.65924	+	23.7911i	0.293914	+	0.807521i
$869$	26.4647	+	9.63235i	0.897752	+	0.326755i
$870$	−0.507168	+	0.292401i	−0.0171946	+	0.00991331i
$871$	26.1445	+	9.51583i	0.885874	+	0.322432i
$872$	−0.666350	+	1.83078i	−0.0225654	+	0.0619981i
$873$	−38.3519	−	6.81082i	−1.29801	−	0.230511i
$874$	−8.67316	+	10.5646i	−0.293374	+	0.357353i
$875$	2.28835	+	1.32118i	0.0773604	+	0.0446640i
$876$	−6.03386	+	2.19197i	−0.203865	+	0.0740598i
$877$	3.99257	+	4.75816i	0.134819	+	0.160672i	0.829230	−	0.558907i	$-0.188779\pi$
$877$	3.99257	+	4.75816i	0.134819	+	0.160672i	−0.694411	+	0.719579i	$0.744335\pi$
$878$	26.6460	+	4.69840i	0.899258	+	0.158563i
$879$	−4.49450	+	25.3988i	−0.151596	+	0.856680i
$880$	0.271767	+	0.228040i	0.00916127	+	0.00768722i
$881$	33.7969	+	19.5127i	1.13865	+	0.657399i	0.946095	−	0.323888i	$-0.104990\pi$
$881$	33.7969	+	19.5127i	1.13865	+	0.657399i	0.192552	+	0.981287i	$0.438323\pi$
$882$	0.430050	+	0.361752i	0.0144806	+	0.0121808i
$883$	0.491528	−	0.178902i	0.0165412	−	0.00602052i	−0.333736	−	0.942666i	$-0.608309\pi$
$883$	0.491528	−	0.178902i	0.0165412	−	0.00602052i	0.350278	+	0.936646i	$0.386087\pi$
$884$	−5.08072	+	28.8142i	−0.170883	+	0.969126i
$885$	−0.959401	+	0.168564i	−0.0322499	+	0.00566621i
$886$		−	3.69389i		−	0.124099i
$887$	−3.43464	+	1.25011i	−0.115324	+	0.0419745i	−0.399038	−	0.916935i	$-0.630656\pi$
$887$	−3.43464	+	1.25011i	−0.115324	+	0.0419745i	0.283714	+	0.958909i	$0.408434\pi$
$888$	3.51410	−	4.18275i	0.117925	−	0.140364i
$889$	−1.39830	−	3.84180i	−0.0468976	−	0.128850i
$890$	0.577920	−	0.101903i	0.0193719	−	0.00341579i
$891$	−31.0148	−	5.54696i	−1.03903	−	0.185830i
$892$		−	11.5249i		−	0.385883i
$893$	15.5299	−	2.91062i	0.519690	−	0.0974001i
$894$	28.4495	−	4.99849i	0.951494	−	0.167175i
$895$	−1.03402	+	0.182326i	−0.0345636	+	0.00609449i
$896$	1.99946	−	1.67775i	0.0667973	−	0.0560496i
$897$	11.7696	+	20.4144i	0.392976	+	0.681616i
$898$	−6.65630	−	37.7498i	−0.222124	−	1.25973i
$899$	31.8602	+	5.61781i	1.06260	+	0.187365i
$900$	2.61739	−	14.7386i	0.0872464	−	0.491286i
$901$	−65.7169	+	37.9417i	−2.18935	+	1.26402i
$902$	−27.8423	−	4.90935i	−0.927048	−	0.163464i
$903$	−20.4110	+	35.3030i	−0.679235	+	1.17481i
$904$	8.34491	−	14.4538i	0.277548	−	0.480727i
$905$	−1.67558			−0.0556982
$906$	−3.35604	+	1.93487i	−0.111497	+	0.0642819i
$907$	−35.3948	+	6.24105i	−1.17526	+	0.207231i	−0.726979	−	0.686660i	$-0.759076\pi$
$907$	−35.3948	+	6.24105i	−1.17526	+	0.207231i	−0.448285	+	0.893891i	$0.647965\pi$
$908$	−1.54661	−	1.29776i	−0.0513262	−	0.0430678i
$909$	0.0223726	−	18.3026i	0.000742053	−	0.607061i
$910$	−1.07836	−	0.392491i	−0.0357473	−	0.0130110i
$911$	11.3924	−	19.7323i	0.377448	−	0.653759i	−0.613242	−	0.789895i	$-0.710135\pi$
$911$	11.3924	−	19.7323i	0.377448	−	0.653759i	0.990690	+	0.136136i	$0.0434684\pi$
$912$	−7.06801	+	2.65390i	−0.234045	+	0.0878795i
$913$	−11.2755	−	19.5298i	−0.373165	−	0.646341i
$914$	−2.40376	−	13.6324i	−0.0795094	−	0.450920i
$915$	0.735390	+	2.02432i	0.0243112	+	0.0669218i
$916$	−18.3237	+	6.66927i	−0.605431	+	0.220359i
$917$	14.8028	+	17.6413i	0.488832	+	0.582567i
$918$	34.4991	+	6.14836i	1.13864	+	0.202926i
$919$	9.96133	−	17.2535i	0.328594	−	0.569141i	−0.653639	−	0.756806i	$-0.726759\pi$
$919$	9.96133	−	17.2535i	0.328594	−	0.569141i	0.982233	+	0.187665i	$0.0600919\pi$
$920$	−0.317783			−0.0104770
$921$	−9.44907	+	5.44773i	−0.311357	+	0.179509i
$922$	11.1274	−	13.2611i	0.366461	−	0.436731i
$923$	6.23248	+	3.59832i	0.205145	+	0.118440i
$924$	10.1656	+	12.1300i	0.334424	+	0.399047i
$925$	−10.1161	+	12.0559i	−0.332616	+	0.396397i
$926$	−18.4153	+	15.4522i	−0.605163	+	0.507792i
$927$	17.7125	−	3.10087i	0.581754	−	0.101846i
$928$	−0.579160	−	3.28458i	−0.0190119	−	0.107822i
$929$	21.9769	+	26.1910i	0.721037	+	0.859299i	0.994731	−	0.102518i	$-0.0326900\pi$
$929$	21.9769	+	26.1910i	0.721037	+	0.859299i	−0.273694	+	0.961817i	$0.588246\pi$
$930$	1.30493	−	1.09360i	0.0427902	−	0.0358607i
$931$	−0.133145	+	0.805592i	−0.00436366	+	0.0264022i
$932$	16.1753	−	9.33879i	0.529838	−	0.305902i
$933$	3.42601	+	9.43083i	0.112163	+	0.308751i
$934$	4.51553	−	12.4063i	0.147753	−	0.405947i
$935$	1.53789	−	1.83279i	0.0502944	−	0.0599386i
$936$	−0.0159098	+	13.0155i	−0.000520027	+	0.425425i
$937$	−4.69098	+	26.6039i	−0.153248	+	0.869111i	0.807123	+	0.590384i	$0.201024\pi$
$937$	−4.69098	+	26.6039i	−0.153248	+	0.869111i	−0.960370	+	0.278727i	$0.910087\pi$
$938$	−14.4959	+	8.36920i	−0.473307	+	0.273264i
$939$	3.16403	+	18.0084i	0.103254	+	0.587683i
$940$	0.281399	+	0.236122i	0.00917823	+	0.00770145i
$941$	26.8617	+	22.5396i	0.875665	+	0.734770i	0.965283	−	0.261206i	$-0.0841202\pi$
$941$	26.8617	+	22.5396i	0.875665	+	0.734770i	−0.0896182	+	0.995976i	$0.528565\pi$
$942$	−24.3311	+	20.3909i	−0.792749	+	0.664370i
$943$	21.9317	−	12.6623i	0.714195	−	0.412340i
$944$	0.963679	−	5.46529i	0.0313651	−	0.177880i
$945$	−0.472447	+	1.29067i	−0.0153687	+	0.0419855i
$946$	20.2977	−	24.1898i	0.659934	−	0.786479i
$947$	−1.19027	+	3.27023i	−0.0386785	+	0.106268i	−0.957528	−	0.288339i	$-0.906897\pi$
$947$	−1.19027	+	3.27023i	−0.0386785	+	0.106268i	0.918850	+	0.394607i	$0.129119\pi$
$948$	−13.7209	−	2.42801i	−0.445634	−	0.0788581i
$949$	−13.9259	+	8.04011i	−0.452053	+	0.260993i
$950$	20.3570	−	7.65787i	0.660469	−	0.248454i
$951$	35.6322	+	12.9937i	1.15545	+	0.421351i
$952$	−11.3147	−	13.4843i	−0.366710	−	0.437028i
$953$	−5.72797	−	32.4849i	−0.185547	−	1.05229i	−0.925250	−	0.379357i	$-0.876145\pi$
$953$	−5.72797	−	32.4849i	−0.185547	−	1.05229i	0.739703	−	0.672933i	$-0.234966\pi$
$954$	−25.8852	+	21.6664i	−0.838064	+	0.701475i
$955$	0.895644	−	0.751535i	0.0289824	−	0.0243191i
$956$	−2.57460	+	3.06829i	−0.0832685	+	0.0992355i
$957$	19.9182	−	3.49957i	0.643865	−	0.113125i
$958$	1.19502	+	0.689945i	0.0386093	+	0.0222911i
$959$	−26.2201	+	31.2479i	−0.846692	+	1.00905i
$960$	−0.151956	−	0.0878556i	−0.00490435	−	0.00283553i
$961$	−63.0888			−2.03512
$962$	6.84195	−	11.8506i	0.220593	−	0.382079i
$963$	7.14393	+	40.8069i	0.230210	+	1.31498i
$964$	−7.44457	−	8.87209i	−0.239773	−	0.285751i
$965$	1.52345	−	0.554491i	0.0490417	−	0.0178497i
$966$	−13.9597	−	2.47027i	−0.449145	−	0.0794795i
$967$	−4.83055	−	27.3954i	−0.155340	−	0.880976i	−0.958474	−	0.285179i	$-0.907947\pi$
$967$	−4.83055	−	27.3954i	−0.155340	−	0.880976i	0.803134	−	0.595798i	$-0.203164\pi$
$968$	−0.627694	−	1.08720i	−0.0201749	−	0.0349439i
$969$	17.8978	+	47.6664i	0.574961	+	1.53127i
$970$	0.657896	−	1.13951i	0.0211238	−	0.0365874i
$971$	−13.9621	−	5.08178i	−0.448064	−	0.163082i	0.108126	−	0.994137i	$-0.465515\pi$
$971$	−13.9621	−	5.08178i	−0.448064	−	0.163082i	−0.556190	+	0.831055i	$0.687737\pi$
$972$	15.5884	+	0.0476371i	0.499998	+	0.00152796i
$973$	−22.4931	−	18.8739i	−0.721094	−	0.605070i
$974$	−25.4776	+	4.49238i	−0.816353	+	0.143945i
$975$	0.0229166	−	37.4954i	0.000733919	−	1.20081i
$976$	−12.2703			−0.392763
$977$	2.39571	−	4.14950i	0.0766457	−	0.132754i	−0.825155	−	0.564906i	$-0.808912\pi$
$977$	2.39571	−	4.14950i	0.0766457	−	0.132754i	0.901801	+	0.432152i	$0.142246\pi$
$978$	−33.3859	−	0.0204050i	−1.06756	−	0.000652480i
$979$	−19.9642	−	3.52023i	−0.638059	−	0.112507i
$980$	−0.0164399	+	0.00949161i	−0.000525155	+	0.000303198i
$981$	5.75479	+	1.02198i	0.183736	+	0.0326293i
$982$	−18.3831	−	3.24144i	−0.586628	−	0.103438i
$983$	−9.93692	−	56.3551i	−0.316938	−	1.79745i	−0.561138	−	0.827722i	$-0.689636\pi$
$983$	−9.93692	−	56.3551i	−0.316938	−	1.79745i	0.244199	−	0.969725i	$-0.421475\pi$
$984$	13.9878	+	0.00854916i	0.445916	+	0.000272537i
$985$	0.343735	−	0.288428i	0.0109523	−	0.00919009i
$986$	−22.1511	+	3.90583i	−0.705434	+	0.124387i
$987$	10.5259	+	12.5599i	0.335044	+	0.399786i
$988$	−16.2750	+	9.63085i	−0.517777	+	0.306398i
$989$			28.2857i			0.899432i
$990$	0.533276	−	0.921060i	0.0169486	−	0.0292732i
$991$	9.01034	−	1.58877i	0.286223	−	0.0504688i	−0.0286934	−	0.999588i	$-0.509135\pi$
$991$	9.01034	−	1.58877i	0.286223	−	0.0504688i	0.314916	+	0.949119i	$0.398024\pi$
$992$	3.31757	+	9.11496i	0.105333	+	0.289400i
$993$	2.53305	+	6.97274i	0.0803838	+	0.221273i
$994$	−4.06851	+	1.48081i	−0.129045	+	0.0469686i
$995$			0.608628i			0.0192948i
$996$	7.16663	+	8.55146i	0.227083	+	0.270963i
$997$	−1.65185	+	9.36811i	−0.0523146	+	0.296691i	−0.999728	−	0.0233213i	$-0.992576\pi$
$997$	−1.65185	+	9.36811i	−0.0523146	+	0.296691i	0.947413	+	0.320012i	$0.103687\pi$
$998$	−5.65472	+	2.05815i	−0.178997	+	0.0651496i
$999$	−14.1782	−	8.22050i	−0.448579	−	0.260085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.b.281.1	yes	48
9.5	odd	6		342.2.bf.b.167.1	yes	48
19.14	odd	18		342.2.bf.b.299.1	yes	48
171.14	even	18	inner	342.2.x.b.185.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.b.185.1	✓	48	171.14	even	18	inner
342.2.x.b.281.1	yes	48	1.1	even	1	trivial
342.2.bf.b.167.1	yes	48	9.5	odd	6
342.2.bf.b.299.1	yes	48	19.14	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.62796 + 0.591401i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0346602 - 0.0952281i) q^{5} +(0.866942 - 1.49947i) q^{6} +(1.30506 + 2.26042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.30049 - 1.92555i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.62796 + 0.591401i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.0346602 - 0.0952281i) q^{5} +(0.866942 - 1.49947i) q^{6} +(1.30506 + 2.26042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.30049 - 1.92555i) q^{9} +(0.0346602 + 0.0952281i) q^{10} -3.50077i q^{11} +(0.299725 + 1.70592i) q^{12} +(1.48386 + 4.07686i) q^{13} +(-2.45270 - 0.892710i) q^{14} +(-0.000107279 + 0.175525i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-2.30657 + 6.33725i) q^{17} +(-0.524556 + 2.95378i) q^{18} +(-4.07978 + 1.53473i) q^{19} +(-0.0877627 - 0.0506698i) q^{20} +(-3.46139 - 2.90806i) q^{21} +(2.25025 + 2.68175i) q^{22} +(-3.08818 - 0.544530i) q^{23} +(-1.32615 - 1.11415i) q^{24} +(3.82236 + 3.20734i) q^{25} +(-3.75725 - 2.16925i) q^{26} +(-2.60632 + 4.49523i) q^{27} +(2.45270 - 0.892710i) q^{28} +(0.579160 - 3.28458i) q^{29} +(-0.112743 - 0.134529i) q^{30} +9.69994i q^{31} +(0.939693 - 0.342020i) q^{32} +(2.07036 + 5.69910i) q^{33} +(-2.30657 - 6.33725i) q^{34} +(0.260489 - 0.0459313i) q^{35} +(-1.49682 - 2.59991i) q^{36} +3.15406i q^{37} +(2.13879 - 3.79810i) q^{38} +(-4.82671 - 5.75940i) q^{39} +(0.0998001 - 0.0175974i) q^{40} +(-6.18649 + 5.19108i) q^{41} +(4.52084 + 0.00276307i) q^{42} +(-1.56634 - 8.88314i) q^{43} +(-3.44759 - 0.607902i) q^{44} +(-0.103631 - 0.285811i) q^{45} +(2.71570 - 1.56791i) q^{46} +(-3.56978 - 0.629448i) q^{47} +(1.73205 + 0.00105860i) q^{48} +(0.0936613 - 0.162226i) q^{49} -4.98973 q^{50} +(0.00713918 - 11.6809i) q^{51} +(4.27259 - 0.753373i) q^{52} +(8.61956 + 7.23267i) q^{53} +(-0.892918 - 5.11886i) q^{54} +(-0.333372 - 0.121337i) q^{55} +(-1.30506 + 2.26042i) q^{56} +(5.73407 - 4.91126i) q^{57} +(1.66762 + 2.88841i) q^{58} +(0.963679 + 5.46529i) q^{59} +(0.172840 + 0.0305853i) q^{60} +(11.5303 - 4.19670i) q^{61} +(-6.23500 - 7.43058i) q^{62} +(7.35483 + 2.68712i) q^{63} +(-0.500000 + 0.866025i) q^{64} +0.439662 q^{65} +(-5.24930 - 3.03496i) q^{66} +(4.12214 - 4.91257i) q^{67} +(5.84044 + 3.37198i) q^{68} +(5.34946 - 0.939884i) q^{69} +(-0.170022 + 0.202625i) q^{70} +(1.27070 - 1.06625i) q^{71} +(2.81782 + 1.02951i) q^{72} +(0.643609 + 3.65009i) q^{73} +(-2.02739 - 2.41615i) q^{74} +(-8.11945 - 2.96086i) q^{75} +(0.802963 + 4.28430i) q^{76} +(7.91322 - 4.56870i) q^{77} +(7.39955 + 1.30940i) q^{78} +(-2.75149 + 7.55967i) q^{79} +(-0.0651399 + 0.0776307i) q^{80} +(1.58450 - 8.85942i) q^{81} +(1.40236 - 7.95320i) q^{82} +(5.57871 - 3.22087i) q^{83} +(-3.46494 + 2.90383i) q^{84} +(0.523538 + 0.439301i) q^{85} +(6.90986 + 5.79806i) q^{86} +(0.999657 + 5.68967i) q^{87} +(3.03176 - 1.75038i) q^{88} +(1.00556 - 5.70280i) q^{89} +(0.263102 + 0.152331i) q^{90} +(-7.27891 + 8.67467i) q^{91} +(-1.07251 + 2.94671i) q^{92} +(-5.73656 - 15.7911i) q^{93} +(3.13921 - 1.81242i) q^{94} +(0.00474295 + 0.441704i) q^{95} +(-1.32751 + 1.11253i) q^{96} +(-8.34594 - 9.94630i) q^{97} +(0.0325282 + 0.184477i) q^{98} +(-6.74092 - 8.05348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Introduction

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