LMFDB - Embedded newform 189.2.u.a.4.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.16
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.241593 + 1.37014i) q^{2} +(1.22928 + 1.22020i) q^{3} +(0.0604707 - 0.0220095i) q^{4} +(-1.40760 + 0.512324i) q^{5} +(-1.37486 + 1.97907i) q^{6} +(1.17416 - 2.37094i) q^{7} +(1.43604 + 2.48730i) q^{8} +(0.0222396 + 2.99992i) q^{9} +O(q^{10})$	\(q+(0.241593 + 1.37014i) q^{2} +(1.22928 + 1.22020i) q^{3} +(0.0604707 - 0.0220095i) q^{4} +(-1.40760 + 0.512324i) q^{5} +(-1.37486 + 1.97907i) q^{6} +(1.17416 - 2.37094i) q^{7} +(1.43604 + 2.48730i) q^{8} +(0.0222396 + 2.99992i) q^{9} +(-1.04202 - 1.80483i) q^{10} +(-1.11103 - 0.404380i) q^{11} +(0.101191 + 0.0467304i) q^{12} +(-2.36114 + 0.859386i) q^{13} +(3.53219 + 1.03596i) q^{14} +(-2.35546 - 1.08776i) q^{15} +(-2.96241 + 2.48576i) q^{16} +(-2.10228 - 3.64126i) q^{17} +(-4.10493 + 0.755229i) q^{18} +(4.18978 - 7.25691i) q^{19} +(-0.0738425 + 0.0619612i) q^{20} +(4.33638 - 1.48184i) q^{21} +(0.285642 - 1.61995i) q^{22} +(0.276391 - 1.56749i) q^{23} +(-1.26970 + 4.80983i) q^{24} +(-2.11136 + 1.77165i) q^{25} +(-1.74791 - 3.02747i) q^{26} +(-3.63315 + 3.71486i) q^{27} +(0.0188188 - 0.169215i) q^{28} +(2.66110 + 0.968563i) q^{29} +(0.921320 - 3.49011i) q^{30} +(-1.89719 + 0.690519i) q^{31} +(0.278752 + 0.233901i) q^{32} +(-0.872334 - 1.85276i) q^{33} +(4.48114 - 3.76012i) q^{34} +(-0.438052 + 3.93888i) q^{35} +(0.0673717 + 0.180918i) q^{36} +8.10687 q^{37} +(10.9552 + 3.98737i) q^{38} +(-3.95112 - 1.82464i) q^{39} +(-3.29567 - 2.76540i) q^{40} +(-4.86408 + 1.77038i) q^{41} +(3.07796 + 5.58344i) q^{42} +(-0.529220 - 3.00136i) q^{43} -0.0760847 q^{44} +(-1.56823 - 4.21129i) q^{45} +2.21446 q^{46} +(8.50342 + 3.09499i) q^{47} +(-6.67474 - 0.559042i) q^{48} +(-4.24271 - 5.56771i) q^{49} +(-2.93749 - 2.46485i) q^{50} +(1.85877 - 7.04131i) q^{51} +(-0.123865 + 0.103935i) q^{52} +(4.30504 - 7.45655i) q^{53} +(-5.96762 - 4.08044i) q^{54} +1.77105 q^{55} +(7.58337 - 0.484292i) q^{56} +(14.0053 - 3.80839i) q^{57} +(-0.684163 + 3.88008i) q^{58} +(-5.52413 - 4.63529i) q^{59} +(-0.166378 - 0.0139349i) q^{60} +(-5.98346 - 2.17780i) q^{61} +(-1.40445 - 2.43258i) q^{62} +(7.13874 + 3.46964i) q^{63} +(-4.12029 + 7.13655i) q^{64} +(2.88326 - 2.41934i) q^{65} +(2.32780 - 1.64283i) q^{66} +(-2.67531 + 15.1724i) q^{67} +(-0.207269 - 0.173919i) q^{68} +(2.25241 - 1.58963i) q^{69} +(-5.50264 + 0.351412i) q^{70} +(-2.99948 + 5.19525i) q^{71} +(-7.42975 + 4.36332i) q^{72} +0.905792 q^{73} +(1.95856 + 11.1075i) q^{74} +(-4.75721 - 0.398439i) q^{75} +(0.0936377 - 0.531046i) q^{76} +(-2.26328 + 2.15937i) q^{77} +(1.54545 - 5.85440i) q^{78} +(0.449343 + 2.54835i) q^{79} +(2.89637 - 5.01667i) q^{80} +(-8.99901 + 0.133434i) q^{81} +(-3.60079 - 6.23676i) q^{82} +(-13.1011 - 4.76840i) q^{83} +(0.229609 - 0.185049i) q^{84} +(4.82467 + 4.04838i) q^{85} +(3.98442 - 1.45021i) q^{86} +(2.08939 + 4.43770i) q^{87} +(-0.589665 - 3.34416i) q^{88} +(-7.38758 + 12.7957i) q^{89} +(5.39117 - 3.16611i) q^{90} +(-0.734800 + 6.60718i) q^{91} +(-0.0177862 - 0.100871i) q^{92} +(-3.17473 - 1.46610i) q^{93} +(-2.18621 + 12.3986i) q^{94} +(-2.17964 + 12.3613i) q^{95} +(0.0572583 + 0.627661i) q^{96} +(0.482171 + 2.73453i) q^{97} +(6.60353 - 7.15822i) q^{98} +(1.18840 - 3.34198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.241593	+	1.37014i	0.170832	+	0.968835i	0.942846	+	0.333229i	$0.108138\pi$
$2$	0.241593	+	1.37014i	0.170832	+	0.968835i	−0.772014	+	0.635605i	$0.780751\pi$
$3$	1.22928	+	1.22020i	0.709723	+	0.704481i
$3$	1.22928	+	1.22020i	0.709723	+	0.704481i
$4$	0.0604707	−	0.0220095i	0.0302354	−	0.0110048i
$5$	−1.40760	+	0.512324i	−0.629497	+	0.229118i	−0.637012	−	0.770854i	$-0.719830\pi$
$5$	−1.40760	+	0.512324i	−0.629497	+	0.229118i	0.00751528	+	0.999972i	$0.497608\pi$
$6$	−1.37486	+	1.97907i	−0.561282	+	0.807952i
$7$	1.17416	−	2.37094i	0.443790	−	0.896131i
$7$	1.17416	−	2.37094i	0.443790	−	0.896131i
$8$	1.43604	+	2.48730i	0.507717	+	0.879392i
$9$	0.0222396	+	2.99992i	0.00741321	+	0.999973i
$10$	−1.04202	−	1.80483i	−0.329516	−	0.570738i
$11$	−1.11103	−	0.404380i	−0.334987	−	0.121925i	0.169050	−	0.985608i	$-0.445930\pi$
$11$	−1.11103	−	0.404380i	−0.334987	−	0.121925i	−0.504037	+	0.863682i	$0.668152\pi$
$12$	0.101191	+	0.0467304i	0.0292114	+	0.0134899i
$13$	−2.36114	+	0.859386i	−0.654863	+	0.238351i	−0.648017	−	0.761626i	$-0.724401\pi$
$13$	−2.36114	+	0.859386i	−0.654863	+	0.238351i	−0.00684632	+	0.999977i	$0.502179\pi$
$14$	3.53219	+	1.03596i	0.944016	+	0.276871i
$15$	−2.35546	−	1.08776i	−0.608178	−	0.280858i
$16$	−2.96241	+	2.48576i	−0.740603	+	0.621440i
$17$	−2.10228	−	3.64126i	−0.509878	−	0.883135i	−0.999935	−	0.0114441i	$-0.996357\pi$
$17$	−2.10228	−	3.64126i	−0.509878	−	0.883135i	0.490056	−	0.871691i	$-0.336976\pi$
$18$	−4.10493	+	0.755229i	−0.967542	+	0.178009i
$19$	4.18978	−	7.25691i	0.961201	−	1.66485i	0.241709	−	0.970349i	$-0.422292\pi$
$19$	4.18978	−	7.25691i	0.961201	−	1.66485i	0.719492	−	0.694500i	$-0.244375\pi$
$20$	−0.0738425	+	0.0619612i	−0.0165117	+	0.0138549i
$21$	4.33638	−	1.48184i	0.946275	−	0.323363i
$22$	0.285642	−	1.61995i	0.0608990	−	0.345375i
$23$	0.276391	−	1.56749i	0.0576315	−	0.326845i	−0.942338	−	0.334663i	$-0.891378\pi$
$23$	0.276391	−	1.56749i	0.0576315	−	0.326845i	0.999969	+	0.00781827i	$0.00248866\pi$
$24$	−1.26970	+	4.80983i	−0.259176	+	0.981802i
$25$	−2.11136	+	1.77165i	−0.422273	+	0.354329i
$26$	−1.74791	−	3.02747i	−0.342794	−	0.593737i
$27$	−3.63315	+	3.71486i	−0.699200	+	0.714926i
$28$	0.0188188	−	0.169215i	0.00355642	−	0.0319787i
$29$	2.66110	+	0.968563i	0.494155	+	0.179858i	0.577063	−	0.816700i	$-0.304199\pi$
$29$	2.66110	+	0.968563i	0.494155	+	0.179858i	−0.0829085	+	0.996557i	$0.526421\pi$
$30$	0.921320	−	3.49011i	0.168209	−	0.637203i
$31$	−1.89719	+	0.690519i	−0.340745	+	0.124021i	−0.506724	−	0.862108i	$-0.669144\pi$
$31$	−1.89719	+	0.690519i	−0.340745	+	0.124021i	0.165979	+	0.986129i	$0.446921\pi$
$32$	0.278752	+	0.233901i	0.0492769	+	0.0413482i
$33$	−0.872334	−	1.85276i	−0.151854	−	0.322525i
$34$	4.48114	−	3.76012i	0.768508	−	0.644855i
$35$	−0.438052	+	3.93888i	−0.0740443	+	0.665792i
$36$	0.0673717	+	0.180918i	0.0112286	+	0.0301530i
$37$	8.10687			1.33276			0.666381	−	0.745611i	$-0.267842\pi$
$37$	8.10687			1.33276			0.666381	+	0.745611i	$0.267842\pi$
$38$	10.9552	+	3.98737i	1.77717	+	0.646836i
$39$	−3.95112	−	1.82464i	−0.632685	−	0.292176i
$40$	−3.29567	−	2.76540i	−0.521091	−	0.437248i
$41$	−4.86408	+	1.77038i	−0.759642	+	0.276487i	−0.692657	−	0.721267i	$-0.743560\pi$
$41$	−4.86408	+	1.77038i	−0.759642	+	0.276487i	−0.0669848	+	0.997754i	$0.521338\pi$
$42$	3.07796	+	5.58344i	0.474939	+	0.861543i
$43$	−0.529220	−	3.00136i	−0.0807054	−	0.457703i	−0.998201	−	0.0599569i	$-0.980904\pi$
$43$	−0.529220	−	3.00136i	−0.0807054	−	0.457703i	0.917496	−	0.397746i	$-0.130207\pi$
$44$	−0.0760847			−0.0114702
$45$	−1.56823	−	4.21129i	−0.233779	−	0.627781i
$46$	2.21446			0.326504
$47$	8.50342	+	3.09499i	1.24035	+	0.451451i	0.877130	−	0.480252i	$-0.159455\pi$
$47$	8.50342	+	3.09499i	1.24035	+	0.451451i	0.363221	+	0.931703i	$0.381677\pi$
$48$	−6.67474	−	0.559042i	−0.963416	−	0.0806907i
$49$	−4.24271	−	5.56771i	−0.606102	−	0.795387i
$50$	−2.93749	−	2.46485i	−0.415424	−	0.348582i
$51$	1.85877	−	7.04131i	0.260279	−	0.985980i
$52$	−0.123865	+	0.103935i	−0.0171770	+	0.0144132i
$53$	4.30504	−	7.45655i	0.591343	−	1.02424i	−0.402709	−	0.915328i	$-0.631931\pi$
$53$	4.30504	−	7.45655i	0.591343	−	1.02424i	0.994052	−	0.108908i	$-0.0347353\pi$
$54$	−5.96762	−	4.08044i	−0.812091	−	0.555277i
$55$	1.77105			0.238808
$56$	7.58337	−	0.484292i	1.01337	−	0.0647162i
$57$	14.0053	−	3.80839i	1.85504	−	0.504434i
$58$	−0.684163	+	3.88008i	−0.0898350	+	0.509479i
$59$	−5.52413	−	4.63529i	−0.719180	−	0.603464i	0.207978	−	0.978133i	$-0.433312\pi$
$59$	−5.52413	−	4.63529i	−0.719180	−	0.603464i	−0.927158	+	0.374670i	$0.877756\pi$
$60$	−0.166378	−	0.0139349i	−0.0214793	−	0.00179899i
$61$	−5.98346	−	2.17780i	−0.766103	−	0.278839i	−0.0707377	−	0.997495i	$-0.522535\pi$
$61$	−5.98346	−	2.17780i	−0.766103	−	0.278839i	−0.695366	+	0.718656i	$0.744758\pi$
$62$	−1.40445	−	2.43258i	−0.178366	−	0.308939i
$63$	7.13874	+	3.46964i	0.899396	+	0.437134i
$64$	−4.12029	+	7.13655i	−0.515036	+	0.892068i
$65$	2.88326	−	2.41934i	0.357624	−	0.300082i
$66$	2.32780	−	1.64283i	0.286532	−	0.202219i
$67$	−2.67531	+	15.1724i	−0.326841	+	1.85361i	0.169570	+	0.985518i	$0.445762\pi$
$67$	−2.67531	+	15.1724i	−0.326841	+	1.85361i	−0.496411	+	0.868088i	$0.665349\pi$
$68$	−0.207269	−	0.173919i	−0.0251351	−	0.0210908i
$69$	2.25241	−	1.58963i	0.271158	−	0.191369i
$70$	−5.50264	+	0.351412i	−0.657692	+	0.0420017i
$71$	−2.99948	+	5.19525i	−0.355973	+	0.616563i	−0.987284	−	0.158967i	$-0.949184\pi$
$71$	−2.99948	+	5.19525i	−0.355973	+	0.616563i	0.631311	+	0.775530i	$0.282517\pi$
$72$	−7.42975	+	4.36332i	−0.875604	+	0.514222i
$73$	0.905792			0.106015			0.0530075	−	0.998594i	$-0.483119\pi$
$73$	0.905792			0.106015			0.0530075	+	0.998594i	$0.483119\pi$
$74$	1.95856	+	11.1075i	0.227678	+	1.29123i
$75$	−4.75721	−	0.398439i	−0.549315	−	0.0460078i
$76$	0.0936377	−	0.531046i	0.0107410	−	0.0609151i
$77$	−2.26328	+	2.15937i	−0.257925	+	0.246083i
$78$	1.54545	−	5.85440i	0.174987	−	0.662880i
$79$	0.449343	+	2.54835i	0.0505551	+	0.286712i	0.999595	−	0.0284425i	$-0.00905474\pi$
$79$	0.449343	+	2.54835i	0.0505551	+	0.286712i	−0.949040	+	0.315155i	$0.897944\pi$
$80$	2.89637	−	5.01667i	0.323824	−	0.560880i
$81$	−8.99901	+	0.133434i	−0.999890	+	0.0148260i
$82$	−3.60079	−	6.23676i	−0.397641	−	0.688735i
$83$	−13.1011	−	4.76840i	−1.43803	−	0.523400i	−0.498808	−	0.866713i	$-0.666229\pi$
$83$	−13.1011	−	4.76840i	−1.43803	−	0.523400i	−0.939221	+	0.343313i	$0.888451\pi$
$84$	0.229609	−	0.185049i	0.0250524	−	0.0201906i
$85$	4.82467	+	4.04838i	0.523309	+	0.439108i
$86$	3.98442	−	1.45021i	0.429651	−	0.156380i
$87$	2.08939	+	4.43770i	0.224007	+	0.475771i
$88$	−0.589665	−	3.34416i	−0.0628585	−	0.356488i
$89$	−7.38758	+	12.7957i	−0.783082	+	1.35634i	0.147056	+	0.989128i	$0.453020\pi$
$89$	−7.38758	+	12.7957i	−0.783082	+	1.35634i	−0.930138	+	0.367210i	$0.880313\pi$
$90$	5.39117	−	3.16611i	0.568280	−	0.333738i
$91$	−0.734800	+	6.60718i	−0.0770280	+	0.692621i
$92$	−0.0177862	−	0.100871i	−0.00185434	−	0.0105165i
$93$	−3.17473	−	1.46610i	−0.329205	−	0.152028i
$94$	−2.18621	+	12.3986i	−0.225490	+	1.27882i
$95$	−2.17964	+	12.3613i	−0.223626	+	1.26825i
$96$	0.0572583	+	0.627661i	0.00584390	+	0.0640604i
$97$	0.482171	+	2.73453i	0.0489570	+	0.277649i	0.999452	−	0.0330897i	$-0.0105347\pi$
$97$	0.482171	+	2.73453i	0.0489570	+	0.277649i	−0.950495	+	0.310739i	$0.899424\pi$
$98$	6.60353	−	7.15822i	0.667057	−	0.723090i
$99$	1.18840	−	3.34198i	0.119439	−	0.335881i
$100$	−0.0886827	+	0.153603i	−0.00886827	+	0.0153603i
$101$	−0.751421	−	4.26152i	−0.0747692	−	0.424037i	−0.999099	−	0.0424424i	$-0.986486\pi$
$101$	−0.751421	−	4.26152i	−0.0747692	−	0.424037i	0.924330	−	0.381595i	$-0.124625\pi$
$102$	10.0966	+	0.845642i	0.999716	+	0.0837311i
$103$	5.44529	−	1.98192i	0.536541	−	0.195285i	−0.0595157	−	0.998227i	$-0.518956\pi$
$103$	5.44529	−	1.98192i	0.536541	−	0.195285i	0.596056	+	0.802943i	$0.296733\pi$
$104$	−5.52825	−	4.63875i	−0.542089	−	0.454867i
$105$	−5.34470	+	4.30746i	−0.521589	+	0.420365i
$106$	11.2566	+	4.09706i	1.09334	+	0.397941i
$107$	−6.82838	−	11.8271i	−0.660125	−	1.14337i	−0.980583	−	0.196106i	$-0.937170\pi$
$107$	−6.82838	−	11.8271i	−0.660125	−	1.14337i	0.320458	−	0.947263i	$-0.396163\pi$
$108$	−0.137937	+	0.304605i	−0.0132730	+	0.0293106i
$109$	0.0243962	−	0.0422554i	0.00233673	−	0.00404733i	−0.864855	−	0.502022i	$-0.832590\pi$
$109$	0.0243962	−	0.0422554i	0.00233673	−	0.00404733i	0.867191	+	0.497975i	$0.165923\pi$
$110$	0.427873	+	2.42659i	0.0407961	+	0.231366i
$111$	9.96559	+	9.89198i	0.945892	+	0.938905i
$112$	2.41525	+	9.94237i	0.228220	+	0.939466i
$113$	−0.0236776	+	0.134282i	−0.00222740	+	0.0126322i	−0.985901	−	0.167328i	$-0.946486\pi$
$113$	−0.0236776	+	0.134282i	−0.00222740	+	0.0126322i	0.983674	+	0.179961i	$0.0575971\pi$
$114$	8.60159	+	18.2691i	0.805613	+	1.71105i
$115$	0.414016	+	2.34800i	0.0386072	+	0.218952i
$116$	0.182237			0.0169202
$117$	−2.63060	−	7.06412i	−0.243199	−	0.653079i
$118$	5.01641	−	8.68868i	0.461798	−	0.799857i
$119$	−11.1016	+	0.708975i	−1.01768	+	0.0649916i
$120$	−0.676962	−	7.42080i	−0.0617979	−	0.677423i
$121$	−7.35563	−	6.17211i	−0.668694	−	0.561101i
$122$	1.53833	−	8.72431i	0.139274	−	0.789862i
$123$	−8.13951	−	3.75885i	−0.733915	−	0.338924i
$124$	−0.0995262	+	0.0835124i	−0.00893772	+	0.00749964i
$125$	5.80913	−	10.0617i	0.519585	−	0.899947i
$126$	−3.02923	+	10.6193i	−0.269865	+	0.946043i
$127$	11.0674	+	19.1693i	0.982072	+	1.70100i	0.654288	+	0.756245i	$0.272968\pi$
$127$	11.0674	+	19.1693i	0.982072	+	1.70100i	0.327783	+	0.944753i	$0.393698\pi$
$128$	−10.0896	−	3.67232i	−0.891804	−	0.324590i
$129$	3.01169	−	4.33525i	0.265164	−	0.381698i
$130$	4.01141	+	3.36597i	0.351824	+	0.295215i
$131$	−3.61711	+	20.5137i	−0.316029	+	1.79229i	0.250364	+	0.968152i	$0.419450\pi$
$131$	−3.61711	+	20.5137i	−0.316029	+	1.79229i	−0.566392	+	0.824136i	$0.691661\pi$
$132$	−0.0935292	−	0.0928384i	−0.00814067	−	0.00808054i
$133$	−12.2862	−	18.4545i	−1.06535	−	1.60020i
$134$	−21.4347			−1.85167
$135$	3.21080	−	7.09039i	0.276342	−	0.610243i
$136$	6.03793	−	10.4580i	0.517748	−	0.896766i
$137$	−3.17727	+	2.66604i	−0.271452	+	0.227775i	−0.768344	−	0.640037i	$-0.778919\pi$
$137$	−3.17727	+	2.66604i	−0.271452	+	0.227775i	0.496892	+	0.867812i	$0.334475\pi$
$138$	2.72218	+	2.70207i	0.231727	+	0.230016i
$139$	7.09184	+	5.95076i	0.601522	+	0.504737i	0.891935	−	0.452165i	$-0.149348\pi$
$139$	7.09184	+	5.95076i	0.601522	+	0.504737i	−0.290412	+	0.956902i	$0.593792\pi$
$140$	0.0602036	+	0.247828i	0.00508814	+	0.0209453i
$141$	6.67655	+	14.1804i	0.562267	+	1.19421i
$142$	−7.84287	−	2.85457i	−0.658159	−	0.239550i
$143$	2.97081			0.248432
$144$	−7.52296	−	8.83171i	−0.626913	−	0.735976i
$145$	−4.24198			−0.352278
$146$	0.218833	+	1.24106i	0.0181107	+	0.102711i
$147$	1.57824	−	12.0212i	0.130171	−	0.991492i
$148$	0.490229	−	0.178429i	0.0402966	−	0.0146667i
$149$	−3.48562	−	2.92478i	−0.285553	−	0.239607i	0.488748	−	0.872425i	$-0.337454\pi$
$149$	−3.48562	−	2.92478i	−0.285553	−	0.239607i	−0.774301	+	0.632818i	$0.781898\pi$
$150$	−0.603388	−	6.61429i	−0.0492665	−	0.540055i
$151$	12.3342	+	4.48927i	1.00374	+	0.365332i	0.791026	−	0.611782i	$-0.209547\pi$
$151$	12.3342	+	4.48927i	1.00374	+	0.365332i	0.212715	+	0.977114i	$0.431769\pi$
$152$	24.0668			1.95207
$153$	10.8767	−	6.38765i	0.879331	−	0.516411i
$154$	−3.50543	−	2.57932i	−0.282475	−	0.207848i
$155$	2.31671	−	1.94395i	0.186082	−	0.156142i
$156$	−0.279086	−	0.0233748i	−0.0223448	−	0.00187149i
$157$	−2.61344	−	2.19294i	−0.208575	−	0.175015i	0.532516	−	0.846420i	$-0.321247\pi$
$157$	−2.61344	−	2.19294i	−0.208575	−	0.175015i	−0.741091	+	0.671405i	$0.765691\pi$
$158$	−3.38304	+	1.23133i	−0.269140	+	0.0979590i
$159$	14.3905	−	3.91316i	1.14124	−	0.310334i
$160$	−0.512204	−	0.186427i	−0.0404933	−	0.0147383i
$161$	−3.39190	−	2.49579i	−0.267319	−	0.196696i
$162$	−2.35692	−	12.2977i	−0.185177	−	0.966195i
$163$	3.87804	+	6.71697i	0.303752	+	0.526113i	0.976983	−	0.213319i	$-0.0684273\pi$
$163$	3.87804	+	6.71697i	0.303752	+	0.526113i	−0.673231	+	0.739432i	$0.735094\pi$
$164$	−0.255169	+	0.214113i	−0.0199254	+	0.0167194i
$165$	2.17711	+	2.16103i	0.169488	+	0.168236i
$166$	3.36825	−	19.1023i	0.261427	−	1.48263i
$167$	−0.160402	+	0.909682i	−0.0124122	+	0.0703933i	−0.990385	−	0.138341i	$-0.955823\pi$
$167$	−0.160402	+	0.909682i	−0.0124122	+	0.0703933i	0.977972	+	0.208734i	$0.0669343\pi$
$168$	9.91298	+	8.65787i	0.764803	+	0.667969i
$169$	−5.12212	+	4.29797i	−0.394009	+	0.330613i
$170$	−4.38124	+	7.58853i	−0.336026	+	0.582014i
$171$	21.8633	+	12.4076i	1.67193	+	0.948833i
$172$	−0.0980609	−	0.169846i	−0.00747707	−	0.0129507i
$173$	12.2389	−	10.2697i	0.930509	−	0.780790i	−0.0453998	−	0.998969i	$-0.514456\pi$
$173$	12.2389	−	10.2697i	0.930509	−	0.780790i	0.975909	+	0.218179i	$0.0700117\pi$
$174$	−5.57549	+	3.93488i	−0.422677	+	0.298302i
$175$	1.72139	+	7.08611i	0.130125	+	0.535659i
$176$	4.29651	−	1.56380i	0.323861	−	0.117876i
$177$	−1.13471	−	12.4386i	−0.0852899	−	0.934941i
$178$	−19.3166	−	7.03068i	−1.44784	−	0.526972i
$179$	−1.95353	−	3.38361i	−0.146014	−	0.252903i	0.783737	−	0.621093i	$-0.213311\pi$
$179$	−1.95353	−	3.38361i	−0.146014	−	0.252903i	−0.929751	+	0.368190i	$0.879978\pi$
$180$	−0.187521	−	0.220143i	−0.0139770	−	0.0164085i
$181$	3.48391	+	6.03431i	0.258957	+	0.448527i	0.965963	−	0.258681i	$-0.0832879\pi$
$181$	3.48391	+	6.03431i	0.258957	+	0.448527i	−0.707006	+	0.707208i	$0.749955\pi$
$182$	−9.23028	+	0.589468i	−0.684194	+	0.0436942i
$183$	−4.69798	−	9.97811i	−0.347284	−	0.737603i
$184$	4.29573	−	1.56352i	0.316685	−	0.115264i
$185$	−11.4112	+	4.15335i	−0.838970	+	0.305360i
$186$	1.24177	−	4.70403i	0.0910511	−	0.344916i
$187$	0.863235	+	4.89565i	0.0631260	+	0.358005i
$188$	0.582327			0.0424706
$189$	4.54183	+	12.9758i	0.330370	+	0.943852i
$190$	−17.4633			−1.26692
$191$	−3.45160	−	19.5750i	−0.249749	−	1.41640i	−0.809200	−	0.587533i	$-0.800099\pi$
$191$	−3.45160	−	19.5750i	−0.249749	−	1.41640i	0.559451	−	0.828863i	$-0.311012\pi$
$192$	−13.7730	+	3.74523i	−0.993978	+	0.270288i
$193$	3.54038	−	1.28859i	0.254842	−	0.0927550i	−0.211440	−	0.977391i	$-0.567815\pi$
$193$	3.54038	−	1.28859i	0.254842	−	0.0927550i	0.466282	+	0.884636i	$0.345593\pi$
$194$	−3.63019	+	1.32128i	−0.260633	+	0.0948625i
$195$	6.49639	+	0.544104i	0.465216	+	0.0389641i
$196$	−0.379103	−	0.243303i	−0.0270788	−	0.0173788i
$197$	−8.94755	−	15.4976i	−0.637487	−	1.10416i	−0.985982	−	0.166849i	$-0.946641\pi$
$197$	−8.94755	−	15.4976i	−0.637487	−	1.10416i	0.348496	−	0.937310i	$-0.386693\pi$
$198$	4.86608	+	0.820874i	0.345817	+	0.0583370i
$199$	0.815532	+	1.41254i	0.0578115	+	0.100132i	0.893483	−	0.449098i	$-0.148254\pi$
$199$	0.815532	+	1.41254i	0.0578115	+	0.100132i	−0.835671	+	0.549230i	$0.814921\pi$
$200$	−7.43861	−	2.70743i	−0.525989	−	0.191445i
$201$	−21.8020	+	15.3867i	−1.53780	+	1.08529i
$202$	5.65734	−	2.05910i	0.398049	−	0.144878i
$203$	5.42096	−	5.17207i	0.380477	−	0.363008i
$204$	−0.0425750	−	0.466704i	−0.00298085	−	0.0326758i
$205$	5.93967	−	4.98397i	0.414844	−	0.348096i
$206$	4.03106	+	6.98199i	0.280857	+	0.486458i
$207$	4.70849	+	0.794290i	0.327263	+	0.0552070i
$208$	4.85846	−	8.41509i	0.336873	−	0.583482i
$209$	−7.58950	+	6.36835i	−0.524977	+	0.440508i
$210$	−7.19306	−	6.28233i	−0.496368	−	0.433522i
$211$	2.81112	−	15.9427i	0.193526	−	1.09754i	−0.720977	−	0.692959i	$-0.756307\pi$
$211$	2.81112	−	15.9427i	0.193526	−	1.09754i	0.914503	−	0.404580i	$-0.132582\pi$
$212$	0.0962137	−	0.545655i	0.00660798	−	0.0374757i
$213$	−10.0264	+	2.72644i	−0.686999	+	0.186813i
$214$	14.5551	−	12.2132i	0.994966	−	0.834875i
$215$	2.28260	+	3.95357i	0.155672	+	0.269632i
$216$	−14.4573	−	3.70203i	−0.983696	−	0.251891i
$217$	−0.590414	+	5.30889i	−0.0400799	+	0.360391i
$218$	0.0637897	+	0.0232176i	0.00432039	+	0.00157249i
$219$	1.11347	+	1.10524i	0.0752412	+	0.0746855i
$220$	0.107097	−	0.0389800i	0.00722046	−	0.00262803i
$221$	8.09303	+	6.79086i	0.544396	+	0.456803i
$222$	−11.1458	+	16.0441i	−0.748056	+	1.07681i
$223$	−1.84110	+	1.54487i	−0.123289	+	0.103452i	−0.702348	−	0.711834i	$-0.747865\pi$
$223$	−1.84110	+	1.54487i	−0.123289	+	0.103452i	0.579058	+	0.815286i	$0.303420\pi$
$224$	0.881863	−	0.386268i	0.0589219	−	0.0258086i
$225$	−5.36175	−	6.29452i	−0.357450	−	0.419635i
$226$	−0.189706			−0.0126190
$227$	16.0531	+	5.84287i	1.06548	+	0.387805i	0.814486	−	0.580183i	$-0.197019\pi$
$227$	16.0531	+	5.84287i	1.06548	+	0.387805i	0.250998	+	0.967987i	$0.419241\pi$
$228$	0.763087	−	0.538546i	0.0505367	−	0.0356661i
$229$	−3.48723	−	2.92613i	−0.230443	−	0.193364i	0.520254	−	0.854012i	$-0.325837\pi$
$229$	−3.48723	−	2.92613i	−0.230443	−	0.193364i	−0.750696	+	0.660647i	$0.770282\pi$
$230$	−3.11706	+	1.13452i	−0.205533	+	0.0748080i
$231$	−5.41705	−	0.107185i	−0.356416	−	0.00705228i
$232$	1.41235	+	8.00985i	0.0927255	+	0.525872i
$233$	20.0330			1.31241			0.656203	−	0.754584i	$-0.272161\pi$
$233$	20.0330			1.31241			0.656203	+	0.754584i	$0.272161\pi$
$234$	9.04330	−	5.31093i	0.591179	−	0.347186i
$235$	−13.5550			−0.884233
$236$	−0.436069	−	0.158716i	−0.0283857	−	0.0103315i
$237$	−2.55713	+	3.68092i	−0.166103	+	0.239101i
$238$	−3.65346	−	15.0395i	−0.236819	−	0.974864i
$239$	12.5959	+	10.5692i	0.814758	+	0.683663i	0.951738	−	0.306911i	$-0.0992953\pi$
$239$	12.5959	+	10.5692i	0.814758	+	0.683663i	−0.136980	+	0.990574i	$0.543740\pi$
$240$	9.68176	−	2.63272i	0.624955	−	0.169942i
$241$	−13.7434	+	11.5321i	−0.885292	+	0.742848i	−0.967260	−	0.253787i	$-0.918324\pi$
$241$	−13.7434	+	11.5321i	−0.885292	+	0.742848i	0.0819685	+	0.996635i	$0.473879\pi$
$242$	6.67958	−	11.5694i	0.429380	−	0.743708i
$243$	−11.2251	−	10.8165i	−0.720090	−	0.693881i
$244$	−0.409757			−0.0262320
$245$	8.82451	+	5.66346i	0.563777	+	0.361825i
$246$	3.18370	−	12.0604i	0.202985	−	0.768942i
$247$	−3.65618	+	20.7352i	−0.232637	+	1.31935i
$248$	−4.44196	−	3.72725i	−0.282065	−	0.236681i
$249$	−10.2864	−	21.8476i	−0.651877	−	1.38453i
$250$	15.1894	+	5.52849i	0.960662	+	0.349652i
$251$	14.3169	+	24.7975i	0.903672	+	1.56521i	0.822690	+	0.568490i	$0.192472\pi$
$251$	14.3169	+	24.7975i	0.903672	+	1.56521i	0.0809817	+	0.996716i	$0.474194\pi$
$252$	0.508050	+	0.0526916i	0.0320041	+	0.00331926i
$253$	−0.940940	+	1.62976i	−0.0591564	+	0.102462i
$254$	−23.5908	+	19.7950i	−1.48022	+	1.24205i
$255$	0.991033	+	10.8636i	0.0620609	+	0.680307i
$256$	−0.267908	+	1.51938i	−0.0167443	+	0.0949615i
$257$	5.25101	+	4.40612i	0.327549	+	0.274846i	0.791700	−	0.610910i	$-0.209196\pi$
$257$	5.25101	+	4.40612i	0.327549	+	0.274846i	−0.464151	+	0.885756i	$0.653641\pi$
$258$	6.66750	+	3.07907i	0.415100	+	0.191695i
$259$	9.51874	−	19.2209i	0.591466	−	1.19433i
$260$	0.121104	−	0.209759i	0.00751056	−	0.0130087i
$261$	−2.84643	+	8.00463i	−0.176189	+	0.495474i
$262$	−28.9805			−1.79042
$263$	−2.76530	−	15.6828i	−0.170516	−	0.967043i	−0.943193	−	0.332244i	$-0.892194\pi$
$263$	−2.76530	−	15.6828i	−0.170516	−	0.967043i	0.772678	−	0.634799i	$-0.218917\pi$
$264$	3.35567	−	4.83040i	0.206527	−	0.297290i
$265$	−2.23960	+	12.7014i	−0.137578	+	0.780241i
$266$	22.3169	−	21.2923i	1.36834	−	1.30552i
$267$	−24.6946	+	6.71511i	−1.51129	+	0.410958i
$268$	0.172160	+	0.976370i	0.0105164	+	0.0596413i
$269$	6.07914	−	10.5294i	0.370652	−	0.641988i	−0.619014	−	0.785380i	$-0.712468\pi$
$269$	6.07914	−	10.5294i	0.370652	−	0.641988i	0.989666	+	0.143392i	$0.0458009\pi$
$270$	10.4905	+	2.68626i	0.638433	+	0.163481i
$271$	13.6112	+	23.5753i	0.826822	+	1.43210i	0.900519	+	0.434817i	$0.143187\pi$
$271$	13.6112	+	23.5753i	0.826822	+	1.43210i	−0.0736971	+	0.997281i	$0.523480\pi$
$272$	15.2791	+	5.56114i	0.926433	+	0.337194i
$273$	−8.96534	+	7.22545i	−0.542607	+	0.437304i
$274$	−4.42045	−	3.70920i	−0.267049	−	0.224081i
$275$	3.06220	−	1.11455i	0.184657	−	0.0672098i
$276$	0.101218	−	0.145701i	0.00609260	−	0.00877014i
$277$	−0.937620	−	5.31751i	−0.0563361	−	0.319498i	0.943597	−	0.331097i	$-0.107419\pi$
$277$	−0.937620	−	5.31751i	−0.0563361	−	0.319498i	−0.999933	+	0.0115993i	$0.996308\pi$
$278$	−6.44004	+	11.1545i	−0.386248	+	0.669001i
$279$	−2.11369	−	5.67604i	−0.126544	−	0.339816i
$280$	−10.4262	+	4.56683i	−0.623086	+	0.272920i
$281$	−0.0216404	−	0.122729i	−0.00129096	−	0.00732137i	0.984155	−	0.177308i	$-0.0567388\pi$
$281$	−0.0216404	−	0.122729i	−0.00129096	−	0.00732137i	−0.985446	+	0.169986i	$0.945628\pi$
$282$	−17.8162	+	12.5737i	−1.06094	+	0.748753i
$283$	4.54984	−	25.8034i	0.270460	−	1.53385i	−0.482564	−	0.875861i	$-0.660294\pi$
$283$	4.54984	−	25.8034i	0.270460	−	1.53385i	0.753024	−	0.657994i	$-0.228595\pi$
$284$	−0.0670357	+	0.380178i	−0.00397783	+	0.0225594i
$285$	−17.7626	+	12.5359i	−1.05217	+	0.742563i
$286$	0.717725	+	4.07042i	0.0424400	+	0.240689i
$287$	−1.51373	+	13.6112i	−0.0893525	+	0.803441i
$288$	−0.695483	+	0.841435i	−0.0409818	+	0.0495820i
$289$	−0.339174	+	0.587466i	−0.0199514	+	0.0345568i
$290$	−1.02483	−	5.81211i	−0.0601802	−	0.341299i
$291$	−2.74394	+	3.94983i	−0.160853	+	0.231543i
$292$	0.0547739	−	0.0199361i	0.00320540	−	0.00116667i
$293$	12.4678	+	10.4618i	0.728378	+	0.611182i	0.929689	−	0.368345i	$-0.120076\pi$
$293$	12.4678	+	10.4618i	0.728378	+	0.611182i	−0.201311	+	0.979527i	$0.564520\pi$
$294$	16.8520	−	0.741826i	0.982829	−	0.0432642i
$295$	10.1505	+	3.69449i	0.590986	+	0.215101i
$296$	11.6418	+	20.1642i	0.676666	+	1.17202i
$297$	5.53874	−	2.65813i	0.321390	−	0.154241i
$298$	3.16526	−	5.48238i	0.183358	−	0.317586i
$299$	0.694482	+	3.93860i	0.0401629	+	0.227775i
$300$	−0.296441	+	0.0806101i	−0.0171150	+	0.00465402i
$301$	−7.73743	−	2.26932i	−0.445978	−	0.130801i
$302$	−3.17108	+	17.9841i	−0.182475	+	1.03487i
$303$	4.27619	−	6.15547i	0.245661	−	0.353622i
$304$	5.62708	+	31.9127i	0.322735	+	1.83032i
$305$	9.53804			0.546147
$306$	11.3797	+	13.3594i	0.650534	+	0.763707i
$307$	1.64814	−	2.85466i	0.0940643	−	0.162924i	−0.815153	−	0.579245i	$-0.803347\pi$
$307$	1.64814	−	2.85466i	0.0940643	−	0.162924i	0.909218	+	0.416321i	$0.136681\pi$
$308$	−0.0893354	+	0.180392i	−0.00509036	+	0.0102788i
$309$	9.11211	+	4.20800i	0.518370	+	0.239385i
$310$	3.22318	+	2.70457i	0.183064	+	0.153609i
$311$	−0.534692	+	3.03239i	−0.0303196	+	0.171951i	−0.996207	−	0.0870097i	$-0.972269\pi$
$311$	−0.534692	+	3.03239i	−0.0303196	+	0.171951i	0.965888	+	0.258961i	$0.0833800\pi$
$312$	−1.13555	−	12.4479i	−0.0642881	−	0.704721i
$313$	6.02411	−	5.05483i	0.340503	−	0.285716i	−0.456460	−	0.889744i	$-0.650883\pi$
$313$	6.02411	−	5.05483i	0.340503	−	0.285716i	0.796963	+	0.604028i	$0.206438\pi$
$314$	2.37324	−	4.11057i	0.133930	−	0.231973i
$315$	−11.8261	−	1.22652i	−0.666323	−	0.0691066i
$316$	0.0832602	+	0.144211i	0.00468375	+	0.00811250i
$317$	25.7274	+	9.36401i	1.44500	+	0.525935i	0.941189	−	0.337881i	$-0.109710\pi$
$317$	25.7274	+	9.36401i	1.44500	+	0.525935i	0.503806	+	0.863817i	$0.331932\pi$
$318$	8.83822	+	18.7717i	0.495623	+	1.05266i
$319$	−2.56489	−	2.15219i	−0.143606	−	0.120500i
$320$	2.14349	−	12.1563i	0.119825	−	0.679559i
$321$	6.03743	−	22.8707i	0.336976	−	1.27652i
$322$	2.60012	−	5.25034i	0.144899	−	0.292590i
$323$	−35.2324			−1.96038
$324$	−0.541240	+	0.206133i	−0.0300689	+	0.0114518i
$325$	3.46271	−	5.99759i	0.192077	−	0.332686i
$326$	−8.26627	+	6.93623i	−0.457826	+	0.384162i
$327$	0.0815496	−	0.0221754i	0.00450970	−	0.00122630i
$328$	−11.3885	−	9.55608i	−0.628824	−	0.527646i
$329$	17.3224	−	16.5271i	0.955014	−	0.911168i
$330$	−2.43494	+	3.50503i	−0.134039	+	0.192946i
$331$	−10.9089	−	3.97050i	−0.599606	−	0.218239i	0.0243434	−	0.999704i	$-0.492251\pi$
$331$	−10.9089	−	3.97050i	−0.599606	−	0.218239i	−0.623949	+	0.781465i	$0.714473\pi$
$332$	−0.897181			−0.0492392
$333$	0.180294	+	24.3200i	0.00988004	+	1.33273i
$334$	−1.28514			−0.0703199
$335$	−4.00744	−	22.7273i	−0.218950	−	1.24172i
$336$	−9.16265	+	15.1690i	−0.499863	+	0.827537i
$337$	14.9687	−	5.44815i	0.815395	−	0.296780i	0.0995447	−	0.995033i	$-0.468261\pi$
$337$	14.9687	−	5.44815i	0.815395	−	0.296780i	0.715851	+	0.698253i	$0.246039\pi$
$338$	−7.12629	−	5.97966i	−0.387619	−	0.325251i
$339$	−0.192957	+	0.136179i	−0.0104800	+	0.00739621i
$340$	0.380854	+	0.138620i	0.0206547	+	0.00751771i
$341$	2.38705			0.129266
$342$	−11.7181	+	32.9534i	−0.633644	+	1.78191i
$343$	−18.1823	+	3.52185i	−0.981753	+	0.190162i
$344$	6.70529	−	5.62640i	0.361525	−	0.303355i
$345$	−2.35608	+	3.39152i	−0.126847	+	0.182593i
$346$	17.0277	+	14.2880i	0.915417	+	0.768126i
$347$	22.0682	−	8.03219i	1.18469	−	0.431190i	0.326831	−	0.945083i	$-0.394019\pi$
$347$	22.0682	−	8.03219i	1.18469	−	0.431190i	0.857855	+	0.513892i	$0.171797\pi$
$348$	0.224019	+	0.222364i	0.0120087	+	0.0119200i
$349$	−16.1149	−	5.86535i	−0.862612	−	0.313965i	−0.127440	−	0.991846i	$-0.540676\pi$
$349$	−16.1149	−	5.86535i	−0.862612	−	0.313965i	−0.735171	+	0.677881i	$0.762898\pi$
$350$	−9.29308	+	4.07050i	−0.496736	+	0.217577i
$351$	5.38589	−	11.8936i	0.287478	−	0.634834i
$352$	−0.215116	−	0.372591i	−0.0114657	−	0.0198592i
$353$	−5.04422	+	4.23260i	−0.268477	+	0.225279i	−0.767080	−	0.641552i	$-0.778291\pi$
$353$	−5.04422	+	4.23260i	−0.268477	+	0.225279i	0.498603	+	0.866830i	$0.333847\pi$
$354$	16.7684	−	4.55978i	0.891233	−	0.242349i
$355$	1.56041	−	8.84954i	0.0828181	−	0.469685i
$356$	−0.165106	+	0.936361i	−0.00875059	+	0.0496270i
$357$	−14.5120	−	12.6746i	−0.768058	−	0.670812i
$358$	4.16406	−	3.49406i	0.220078	−	0.184667i
$359$	−15.0217	+	26.0183i	−0.792813	+	1.37319i	0.131405	+	0.991329i	$0.458051\pi$
$359$	−15.0217	+	26.0183i	−0.792813	+	1.37319i	−0.924218	+	0.381864i	$0.875282\pi$
$360$	8.22267	−	9.94824i	0.433373	−	0.524318i
$361$	−25.6085	−	44.3552i	−1.34782	−	2.33448i
$362$	−7.42616	+	6.23129i	−0.390310	+	0.327509i
$363$	−1.51092	−	16.5626i	−0.0793026	−	0.869308i
$364$	0.100987	+	0.415714i	0.00529317	+	0.0217893i
$365$	−1.27499	+	0.464059i	−0.0667361	+	0.0242900i
$366$	12.5364	−	8.84752i	0.655289	−	0.462467i
$367$	−10.3248	−	3.75791i	−0.538949	−	0.196162i	0.0581805	−	0.998306i	$-0.481470\pi$
$367$	−10.3248	−	3.75791i	−0.538949	−	0.196162i	−0.597130	+	0.802145i	$0.703692\pi$
$368$	3.07762	+	5.33060i	0.160432	+	0.277877i
$369$	−5.41917	−	14.5525i	−0.282111	−	0.757572i
$370$	−8.44753	−	14.6315i	−0.439166	−	0.760658i
$371$	−12.6242	−	18.9621i	−0.655418	−	0.984466i
$372$	−0.224247	−	0.0187818i	−0.0116267	−	0.000973789i
$373$	−20.2756	+	7.37970i	−1.04983	+	0.382106i	−0.808598	−	0.588362i	$-0.799773\pi$
$373$	−20.2756	+	7.37970i	−1.04983	+	0.382106i	−0.241230	+	0.970468i	$0.577551\pi$
$374$	−6.49917	+	2.36551i	−0.336064	+	0.122317i
$375$	19.4183	−	5.28034i	1.00276	−	0.272676i
$376$	4.51310	+	25.5951i	0.232745	+	1.31996i
$377$	−7.11562			−0.366473
$378$	−16.6814	+	9.35780i	−0.857999	+	0.481313i
$379$	−15.1400			−0.777690			−0.388845	−	0.921303i	$-0.627126\pi$
$379$	−15.1400			−0.777690			−0.388845	+	0.921303i	$0.627126\pi$
$380$	0.140263	+	0.795472i	0.00719535	+	0.0408069i
$381$	−9.78541	+	37.0687i	−0.501322	+	1.89909i
$382$	25.9866	−	9.45834i	1.32959	−	0.483931i
$383$	−15.4247	+	5.61413i	−0.788165	+	0.286869i	−0.704573	−	0.709631i	$-0.748861\pi$
$383$	−15.4247	+	5.61413i	−0.788165	+	0.286869i	−0.0835919	+	0.996500i	$0.526639\pi$
$384$	−7.92197	−	16.8256i	−0.404266	−	0.858628i
$385$	2.07949	−	4.19906i	0.105981	−	0.214004i
$386$	2.62088	+	4.53950i	0.133399	+	0.231054i
$387$	8.99206	−	1.65437i	0.457092	−	0.0840962i
$388$	0.0893429	+	0.154746i	0.00453570	+	0.00785606i
$389$	−16.6939	−	6.07609i	−0.846415	−	0.308070i	−0.117837	−	0.993033i	$-0.537596\pi$
$389$	−16.6939	−	6.07609i	−0.846415	−	0.308070i	−0.728578	+	0.684963i	$0.759818\pi$
$390$	0.823981	+	9.03241i	0.0417239	+	0.457374i
$391$	−6.28869	+	2.28890i	−0.318033	+	0.115755i
$392$	7.75584	−	18.5483i	0.391729	−	0.936833i
$393$	−29.4771	+	20.8034i	−1.48693	+	1.04939i
$394$	19.0722	−	16.0035i	0.960845	−	0.806245i
$395$	−1.93808	−	3.35685i	−0.0975153	−	0.168901i
$396$	−0.00169210	−	0.228248i	−8.50310e−5	−	0.0114699i
$397$	17.9394	−	31.0719i	0.900351	−	1.55945i	0.0733119	−	0.997309i	$-0.476643\pi$
$397$	17.9394	−	31.0719i	0.900351	−	1.55945i	0.827039	−	0.562144i	$-0.190024\pi$
$398$	−1.73835	+	1.45865i	−0.0871358	+	0.0731156i
$399$	7.41490	−	37.6773i	0.371209	−	1.88622i
$400$	1.85085	−	10.4967i	0.0925425	−	0.524835i
$401$	6.89398	−	39.0977i	0.344269	−	1.95245i	0.0423895	−	0.999101i	$-0.486503\pi$
$401$	6.89398	−	39.0977i	0.344269	−	1.95245i	0.301880	−	0.953346i	$-0.402386\pi$
$402$	−26.3491	−	26.1545i	−1.31417	−	1.30447i
$403$	3.88611	−	3.26083i	0.193581	−	0.162434i
$404$	−0.139233	−	0.241159i	−0.00692711	−	0.0119981i
$405$	12.5986	−	4.79823i	0.626031	−	0.238426i
$406$	8.39612	+	6.17793i	0.416693	+	0.306606i
$407$	−9.00694	−	3.27826i	−0.446458	−	0.162497i
$408$	20.1831	−	5.48830i	0.999212	−	0.271712i
$409$	27.5620	−	10.0318i	1.36285	−	0.496039i	0.445919	−	0.895073i	$-0.352877\pi$
$409$	27.5620	−	10.0318i	1.36285	−	0.496039i	0.916936	+	0.399035i	$0.130655\pi$
$410$	8.26371	+	6.93408i	0.408116	+	0.342450i
$411$	−7.15883	−	0.599587i	−0.353119	−	0.0295754i
$412$	0.285660	−	0.239697i	0.0140734	−	0.0118090i
$413$	−17.4762	+	7.65481i	−0.859947	+	0.376669i
$414$	0.0492487	+	6.64319i	0.00242044	+	0.326495i
$415$	20.8840			1.02516
$416$	−0.859184	−	0.312718i	−0.0421250	−	0.0153322i
$417$	1.45673	+	15.9686i	0.0713364	+	0.781984i
$418$	−10.5591	−	8.86013i	−0.516462	−	0.433363i
$419$	1.85671	−	0.675787i	0.0907062	−	0.0330143i	−0.296268	−	0.955105i	$-0.595742\pi$
$419$	1.85671	−	0.675787i	0.0907062	−	0.0330143i	0.386975	+	0.922090i	$0.373520\pi$
$420$	−0.228392	+	0.378110i	−0.0111444	+	0.0184499i
$421$	1.75257	+	9.93930i	0.0854148	+	0.484412i	0.997266	+	0.0738913i	$0.0235418\pi$
$421$	1.75257	+	9.93930i	0.0854148	+	0.484412i	−0.911851	+	0.410520i	$0.865347\pi$
$422$	22.5228			1.09639
$423$	−9.09561	+	25.5784i	−0.442244	+	1.24366i
$424$	24.7289			1.20094
$425$	10.8897	+	3.96353i	0.528228	+	0.192259i
$426$	−6.15792	−	13.0789i	−0.298352	−	0.633675i
$427$	−12.1890	+	11.6293i	−0.589865	+	0.562783i
$428$	−0.673226	−	0.564904i	−0.0325416	−	0.0273057i
$429$	3.65194	+	3.62497i	0.176318	+	0.175015i
$430$	−4.86549	+	4.08263i	−0.234635	+	0.196882i
$431$	−4.32476	+	7.49071i	−0.208317	+	0.360815i	−0.951184	−	0.308623i	$-0.900132\pi$
$431$	−4.32476	+	7.49071i	−0.208317	+	0.360815i	0.742868	+	0.669438i	$0.233465\pi$
$432$	1.52864	−	20.0361i	0.0735465	−	0.963987i
$433$	−1.05611			−0.0507535			−0.0253768	−	0.999678i	$-0.508079\pi$
$433$	−1.05611			−0.0507535			−0.0253768	+	0.999678i	$0.508079\pi$
$434$	−7.41656	+	0.473639i	−0.356006	+	0.0227354i
$435$	−5.21457	−	5.17605i	−0.250019	−	0.248173i
$436$	0.000545232	−	0.00309216i	2.61119e−5	−	0.000148088i
$437$	−10.2171	−	8.57319i	−0.488752	−	0.410111i
$438$	−1.24533	+	1.79263i	−0.0595043	+	0.0856550i
$439$	13.2198	+	4.81162i	0.630948	+	0.229646i	0.637644	−	0.770331i	$-0.279909\pi$
$439$	13.2198	+	4.81162i	0.630948	+	0.229646i	−0.00669596	+	0.999978i	$0.502131\pi$
$440$	2.54330	+	4.40513i	0.121247	+	0.210006i
$441$	16.6083	−	12.8516i	0.790872	−	0.611981i
$442$	−7.34921	+	12.7292i	−0.349566	+	0.605467i
$443$	−13.0670	+	10.9645i	−0.620832	+	0.520940i	−0.898065	−	0.439863i	$-0.855027\pi$
$443$	−13.0670	+	10.9645i	−0.620832	+	0.520940i	0.277233	+	0.960803i	$0.410583\pi$
$444$	0.820345	+	0.378837i	0.0389318	+	0.0179788i
$445$	3.84322	−	21.7960i	0.182186	−	1.03323i
$446$	−2.56148	−	2.14934i	−0.121290	−	0.101774i
$447$	−0.715979	−	7.84850i	−0.0338646	−	0.371221i
$448$	12.0825	+	18.1484i	0.570843	+	0.857430i
$449$	−4.77255	+	8.26630i	−0.225231	+	0.390111i	−0.956389	−	0.292097i	$-0.905647\pi$
$449$	−4.77255	+	8.26630i	−0.225231	+	0.390111i	0.731158	+	0.682208i	$0.238980\pi$
$450$	7.32901	−	8.86705i	0.345493	−	0.417997i
$451$	6.12003			0.288181
$452$	0.00152369	+	0.00864128i	7.16684e−5	+	0.000406452i
$453$	9.68431	+	20.5687i	0.455009	+	0.966401i
$454$	−4.12722	+	23.4066i	−0.193700	+	1.09853i
$455$	−2.35071	−	9.67672i	−0.110203	−	0.453651i
$456$	29.5847	+	29.3662i	1.38543	+	1.37520i
$457$	0.305035	+	1.72994i	0.0142689	+	0.0809232i	0.991111	−	0.133040i	$-0.0424739\pi$
$457$	0.305035	+	1.72994i	0.0142689	+	0.0809232i	−0.976842	+	0.213963i	$0.931363\pi$
$458$	3.16672	−	5.48492i	0.147971	−	0.256294i
$459$	21.1647	+	5.41955i	0.987883	+	0.252963i
$460$	0.0767143	+	0.132873i	0.00357682	+	0.00619524i
$461$	29.5905	+	10.7700i	1.37816	+	0.501611i	0.921621	−	0.388090i	$-0.126865\pi$
$461$	29.5905	+	10.7700i	1.37816	+	0.501611i	0.456543	+	0.889701i	$0.349087\pi$
$462$	−1.16186	−	7.44801i	−0.0540546	−	0.346513i
$463$	−26.1835	−	21.9706i	−1.21685	−	1.02106i	−0.998983	−	0.0450813i	$-0.985645\pi$
$463$	−26.1835	−	21.9706i	−1.21685	−	1.02106i	−0.217868	−	0.975978i	$-0.569910\pi$
$464$	−10.2909	+	3.74558i	−0.477743	+	0.173884i
$465$	5.21987	+	0.437189i	0.242066	+	0.0202742i
$466$	4.83983	+	27.4480i	0.224201	+	1.27151i
$467$	11.5411	−	19.9898i	0.534059	−	0.925017i	−0.465150	−	0.885232i	$-0.653999\pi$
$467$	11.5411	−	19.9898i	0.534059	−	0.925017i	0.999208	−	0.0397847i	$-0.0126672\pi$
$468$	−0.314552	−	0.369275i	−0.0145402	−	0.0170697i
$469$	32.8317	+	24.1578i	1.51603	+	1.11550i
$470$	−3.27480	−	18.5723i	−0.151055	−	0.856676i
$471$	−0.536825	−	5.88463i	−0.0247356	−	0.271150i
$472$	3.59647	−	20.3966i	0.165541	−	0.938830i
$473$	−0.625712	+	3.54859i	−0.0287703	+	0.163164i
$474$	−5.66115	−	2.61434i	−0.260025	−	0.120080i
$475$	4.01052	+	22.7448i	0.184015	+	1.04360i
$476$	−0.655718	+	0.287214i	−0.0300548	+	0.0131644i
$477$	22.4648	+	12.7489i	1.02859	+	0.583734i
$478$	−11.4382	+	19.8115i	−0.523170	+	0.906157i
$479$	0.733041	+	4.15728i	0.0334935	+	0.189951i	0.996964	−	0.0778632i	$-0.0248097\pi$
$479$	0.733041	+	4.15728i	0.0334935	+	0.189951i	−0.963471	+	0.267814i	$0.913699\pi$
$480$	−0.402162	−	0.854159i	−0.0183561	−	0.0389869i
$481$	−19.1415	+	6.96693i	−0.872777	+	0.317665i
$482$	−19.1209	−	16.0443i	−0.870933	−	0.730799i
$483$	−1.12423	−	7.20680i	−0.0511544	−	0.327921i
$484$	−0.580646	−	0.211338i	−0.0263930	−	0.00960627i
$485$	−2.07967	−	3.60209i	−0.0944328	−	0.163562i
$486$	12.1083	−	17.9931i	0.549242	−	0.816185i
$487$	−6.00383	+	10.3989i	−0.272060	+	0.471221i	−0.969389	−	0.245530i	$-0.921038\pi$
$487$	−6.00383	+	10.3989i	−0.272060	+	0.471221i	0.697330	+	0.716751i	$0.254371\pi$
$488$	−3.17566	−	18.0100i	−0.143755	−	0.815276i
$489$	−3.42884	+	12.9890i	−0.155057	+	0.587382i
$490$	−5.62779	+	13.4590i	−0.254238	+	0.608018i
$491$	2.09395	−	11.8754i	0.0944985	−	0.535927i	−0.900401	−	0.435060i	$-0.856727\pi$
$491$	2.09395	−	11.8754i	0.0944985	−	0.535927i	0.994900	−	0.100867i	$-0.0321618\pi$
$492$	−0.574933	−	0.0481534i	−0.0259200	−	0.00217092i
$493$	−2.06760	−	11.7260i	−0.0931201	−	0.528111i
$494$	−29.2935			−1.31798
$495$	0.0393875	+	5.31301i	0.00177034	+	0.238802i
$496$	3.90378	−	6.76155i	0.175285	−	0.303603i
$497$	8.79577	+	13.2116i	0.394544	+	0.592623i
$498$	27.4491	−	19.3721i	1.23002	−	0.868083i
$499$	−24.6105	−	20.6507i	−1.10172	−	0.924451i	−0.104178	−	0.994559i	$-0.533221\pi$
$499$	−24.6105	−	20.6507i	−1.10172	−	0.924451i	−0.997539	+	0.0701078i	$0.977666\pi$
$500$	0.129829	−	0.736296i	0.00580612	−	0.0329282i
$501$	−1.30717	+	0.922529i	−0.0584000	+	0.0412156i
$502$	−30.5172	+	25.6070i	−1.36205	+	1.14290i
$503$	−1.09621	+	1.89869i	−0.0488776	+	0.0846585i	−0.889429	−	0.457073i	$-0.848898\pi$
$503$	−1.09621	+	1.89869i	−0.0488776	+	0.0846585i	0.840552	+	0.541732i	$0.182231\pi$
$504$	1.62149	+	22.7387i	0.0722267	+	1.01286i
$505$	3.24098	+	5.61354i	0.144222	+	0.249799i
$506$	−2.46032	−	0.895482i	−0.109374	−	0.0398090i
$507$	−11.5409	−	0.966604i	−0.512548	−	0.0429284i
$508$	1.09116	+	0.915592i	0.0484124	+	0.0406228i
$509$	−1.10374	+	6.25962i	−0.0489224	+	0.277453i	−0.999449	−	0.0331902i	$-0.989433\pi$
$509$	−1.10374	+	6.25962i	−0.0489224	+	0.277453i	0.950527	+	0.310643i	$0.100544\pi$
$510$	−14.6453	+	3.98242i	−0.648503	+	0.176345i
$511$	1.06354	−	2.14758i	0.0470483	−	0.0950033i
$512$	−23.6208			−1.04390
$513$	11.7363	+	41.9299i	0.518172	+	1.85125i
$514$	−4.76839	+	8.25909i	−0.210325	+	0.364293i
$515$	−6.64940	+	5.57951i	−0.293008	+	0.245863i
$516$	0.0867022	−	0.328442i	0.00381685	−	0.0144588i
$517$	−8.19596	−	6.87723i	−0.360458	−	0.302460i
$518$	28.6350	+	8.39837i	1.25815	+	0.369003i
$519$	27.5761	+	2.30963i	1.21045	+	0.101381i
$520$	10.1581	+	3.69724i	0.445462	+	0.162135i
$521$	−3.47193			−0.152108			−0.0760541	−	0.997104i	$-0.524232\pi$
$521$	−3.47193			−0.152108			−0.0760541	+	0.997104i	$0.524232\pi$
$522$	−11.6551	−	1.96614i	−0.510131	−	0.0860556i
$523$	−20.1799			−0.882406			−0.441203	−	0.897407i	$-0.645448\pi$
$523$	−20.1799			−0.882406			−0.441203	+	0.897407i	$0.645448\pi$
$524$	0.232767	+	1.32009i	0.0101685	+	0.0576683i
$525$	−6.53038	+	10.8112i	−0.285009	+	0.471840i
$526$	20.8195	−	7.57769i	0.907775	−	0.330403i
$527$	6.50278	+	5.45648i	0.283265	+	0.237688i
$528$	7.18974	+	3.32024i	0.312893	+	0.144495i
$529$	19.2323	+	6.99998i	0.836187	+	0.304347i
$530$	−17.9438			−0.779427
$531$	13.7826	−	16.6750i	0.598116	−	0.723634i
$532$	−1.14913	−	0.845540i	−0.0498212	−	0.0366588i
$533$	9.96336	−	8.36025i	0.431561	−	0.362123i
$534$	−15.1667	−	32.2127i	−0.656326	−	1.39398i
$535$	15.6709	+	13.1495i	0.677513	+	0.568501i
$536$	−41.5802	+	15.1339i	−1.79599	+	0.653687i
$537$	1.72725	−	6.54309i	0.0745362	−	0.282355i
$538$	15.8954	+	5.78545i	0.685299	+	0.249429i
$539$	2.46229	+	7.90154i	0.106058	+	0.340343i
$540$	0.0381035	−	0.499429i	0.00163971	−	0.0214920i
$541$	−6.85818	−	11.8787i	−0.294856	−	0.510706i	0.680095	−	0.733124i	$-0.261938\pi$
$541$	−6.85818	−	11.8787i	−0.294856	−	0.510706i	−0.974951	+	0.222418i	$0.928605\pi$
$542$	−29.0131	+	24.3449i	−1.24622	+	1.04570i
$543$	−3.08036	+	11.6689i	−0.132191	+	0.500760i
$544$	0.265678	−	1.50673i	0.0113908	−	0.0646006i
$545$	−0.0126916	+	0.0719774i	−0.000543647	+	0.00308317i
$546$	−12.0658	−	10.5381i	−0.516370	−	0.450991i
$547$	33.7869	−	28.3506i	1.44463	−	1.21218i	0.508238	−	0.861217i	$-0.330297\pi$
$547$	33.7869	−	28.3506i	1.44463	−	1.21218i	0.936387	−	0.350968i	$-0.114147\pi$
$548$	−0.133453	+	0.231148i	−0.00570084	+	0.00987414i
$549$	6.40015	−	17.9983i	0.273152	−	0.768149i
$550$	2.26689	+	3.92637i	0.0966606	+	0.167421i
$551$	18.1782	−	15.2533i	0.774418	−	0.649814i
$552$	7.18843	+	3.31964i	0.305960	+	0.141293i
$553$	6.56959	+	1.92680i	0.279367	+	0.0819359i
$554$	7.05920	−	2.56934i	0.299917	−	0.109161i
$555$	−19.0954	−	8.81833i	−0.810556	−	0.374317i
$556$	0.559822	+	0.203759i	0.0237418	+	0.00864129i
$557$	2.53989	+	4.39922i	0.107619	+	0.186401i	0.914805	−	0.403896i	$-0.132344\pi$
$557$	2.53989	+	4.39922i	0.107619	+	0.186401i	−0.807186	+	0.590297i	$0.799011\pi$
$558$	7.26632	−	4.26734i	0.307608	−	0.180651i
$559$	3.82889	+	6.63183i	0.161945	+	0.280497i
$560$	−8.49342	−	12.7575i	−0.358912	−	0.539102i
$561$	−4.91250	+	7.07142i	−0.207406	+	0.298556i
$562$	0.162927	−	0.0593006i	0.00687266	−	0.00250144i
$563$	14.8345	−	5.39933i	0.625201	−	0.227554i	−0.00994033	−	0.999951i	$-0.503164\pi$
$563$	14.8345	−	5.39933i	0.625201	−	0.227554i	0.635141	+	0.772396i	$0.280942\pi$
$564$	0.715841	+	0.710554i	0.0301424	+	0.0299197i
$565$	−0.0354675	−	0.201146i	−0.00149213	−	0.00846228i
$566$	36.4535			1.53225
$567$	−10.2499	+	21.4928i	−0.430455	+	0.902612i
$568$	−17.2295			−0.722934
$569$	−5.08899	−	28.8611i	−0.213342	−	1.20992i	−0.883761	−	0.467938i	$-0.844997\pi$
$569$	−5.08899	−	28.8611i	−0.213342	−	1.20992i	0.670420	−	0.741982i	$-0.266114\pi$
$570$	−21.4673	−	21.3087i	−0.899165	−	0.892524i
$571$	−26.6981	+	9.71730i	−1.11728	+	0.406656i	−0.833658	−	0.552280i	$-0.813758\pi$
$571$	−26.6981	+	9.71730i	−1.11728	+	0.406656i	−0.283620	+	0.958937i	$0.591536\pi$
$572$	0.179647	−	0.0653862i	0.00751142	−	0.00273393i
$573$	19.6424	−	28.2747i	0.820572	−	1.18119i
$574$	−19.0149	+	1.21433i	−0.793666	+	0.0506854i
$575$	2.19348	+	3.79921i	0.0914743	+	0.158438i
$576$	−21.5007	−	12.2018i	−0.895862	−	0.508409i
$577$	3.35621	+	5.81313i	0.139721	+	0.242004i	0.927391	−	0.374094i	$-0.122046\pi$
$577$	3.35621	+	5.81313i	0.139721	+	0.242004i	−0.787670	+	0.616097i	$0.788713\pi$
$578$	−0.886852	−	0.322788i	−0.0368882	−	0.0134262i
$579$	5.92444	+	2.73592i	0.246211	+	0.113701i
$580$	−0.256516	+	0.0933641i	−0.0106512	+	0.00387673i
$581$	−26.6883	+	25.4630i	−1.10722	+	1.05638i
$582$	−6.07473	−	2.80533i	−0.251806	−	0.116285i
$583$	−7.79829	+	6.54354i	−0.322972	+	0.271006i
$584$	1.30075	+	2.25297i	0.0538256	+	0.0932287i
$585$	7.32195	+	8.59573i	0.302725	+	0.355390i
$586$	−11.3219	+	19.6101i	−0.467704	+	0.810088i
$587$	−29.4619	+	24.7214i	−1.21602	+	1.02036i	−0.216998	+	0.976172i	$0.569626\pi$
$587$	−29.4619	+	24.7214i	−1.21602	+	1.02036i	−0.999023	+	0.0441907i	$0.985929\pi$
$588$	−0.169144	−	0.761667i	−0.00697538	−	0.0314106i
$589$	−2.93775	+	16.6608i	−0.121048	+	0.686497i
$590$	−2.60967	+	14.8002i	−0.107439	+	0.609314i
$591$	7.91113	−	29.9686i	0.325420	−	1.23274i
$592$	−24.0159	+	20.1517i	−0.987048	+	0.828232i
$593$	−5.11127	−	8.85299i	−0.209895	−	0.363549i	0.741786	−	0.670636i	$-0.233979\pi$
$593$	−5.11127	−	8.85299i	−0.209895	−	0.363549i	−0.951681	+	0.307088i	$0.900646\pi$
$594$	4.98013	+	6.94666i	0.204337	+	0.285025i
$595$	15.2634	−	6.68557i	0.625738	−	0.274082i
$596$	−0.275151	−	0.100147i	−0.0112706	−	0.00410217i
$597$	−0.721066	+	2.73151i	−0.0295113	+	0.111793i
$598$	−5.22865	+	1.90307i	−0.213815	+	0.0778224i
$599$	−13.7117	−	11.5055i	−0.560247	−	0.470103i	0.318146	−	0.948042i	$-0.396940\pi$
$599$	−13.7117	−	11.5055i	−0.560247	−	0.470103i	−0.878393	+	0.477939i	$0.841384\pi$
$600$	−5.84051	−	12.4048i	−0.238438	−	0.506422i
$601$	−24.1774	+	20.2873i	−0.986217	+	0.827534i	−0.985016	−	0.172465i	$-0.944827\pi$
$601$	−24.1774	+	20.2873i	−0.986217	+	0.827534i	−0.00120136	+	0.999999i	$0.500382\pi$
$602$	1.23997	−	11.1496i	0.0505375	−	0.454424i
$603$	−45.5755	−	7.68827i	−1.85598	−	0.313091i
$604$	0.844664			0.0343689
$605$	13.5159	+	4.91939i	0.549499	+	0.200001i
$606$	9.46694	+	4.37186i	0.384568	+	0.177595i
$607$	28.8780	+	24.2315i	1.17212	+	0.983527i	0.999999	−	0.00154846i	$-0.000492889\pi$
$607$	28.8780	+	24.2315i	1.17212	+	0.983527i	0.172123	+	0.985075i	$0.444937\pi$
$608$	2.86531	−	1.04289i	0.116203	−	0.0422946i
$609$	12.9748	+	0.256728i	0.525765	+	0.0104031i
$610$	2.30432	+	13.0684i	0.0932992	+	0.529126i
$611$	−22.7376			−0.919864
$612$	0.517134	−	0.625658i	0.0209039	−	0.0252907i
$613$	−43.5292			−1.75813			−0.879063	−	0.476705i	$-0.841831\pi$
$613$	−43.5292			−1.75813			−0.879063	+	0.476705i	$0.841831\pi$
$614$	4.30946	+	1.56852i	0.173916	+	0.0633001i
$615$	13.3829	+	1.12088i	0.539651	+	0.0451984i
$616$	−8.62115	−	2.52850i	−0.347356	−	0.101876i
$617$	32.1635	+	26.9884i	1.29486	+	1.08651i	0.991010	+	0.133791i	$0.0427152\pi$
$617$	32.1635	+	26.9884i	1.29486	+	1.08651i	0.303846	+	0.952721i	$0.401729\pi$
$618$	−3.56412	+	13.5015i	−0.143370	+	0.543109i
$619$	−7.64938	+	6.41859i	−0.307455	+	0.257985i	−0.783439	−	0.621469i	$-0.786536\pi$
$619$	−7.64938	+	6.41859i	−0.307455	+	0.257985i	0.475984	+	0.879454i	$0.342092\pi$
$620$	0.0973075	−	0.168542i	0.00390796	−	0.00676879i
$621$	4.81885	+	6.72169i	0.193374	+	0.269732i
$622$	−4.28397			−0.171772
$623$	21.6636	+	32.5396i	0.867933	+	1.30367i
$624$	16.2405	−	4.41620i	0.650138	−	0.176789i
$625$	−0.629033	+	3.56742i	−0.0251613	+	0.142697i
$626$	8.38120	+	7.03267i	0.334980	+	0.281082i
$627$	−17.1002	−	1.43223i	−0.682917	−	0.0571976i
$628$	−0.206302	−	0.0750878i	−0.00823235	−	0.00299633i
$629$	−17.0429	−	29.5192i	−0.679546	−	1.17701i
$630$	−1.17658	−	16.4997i	−0.0468762	−	0.657362i
$631$	7.43447	−	12.8769i	0.295962	−	0.512621i	−0.679246	−	0.733910i	$-0.737693\pi$
$631$	7.43447	−	12.8769i	0.295962	−	0.512621i	0.975208	+	0.221290i	$0.0710266\pi$
$632$	−5.69323	+	4.77719i	−0.226465	+	0.190026i
$633$	22.9089	−	16.1678i	0.910545	−	0.642614i
$634$	−6.61445	+	37.5124i	−0.262693	+	1.48981i
$635$	−25.3993	−	21.3126i	−1.00794	−	0.845763i
$636$	0.784080	−	0.553361i	0.0310908	−	0.0219422i
$637$	14.8025	+	9.50004i	0.586495	+	0.376405i
$638$	2.32915	−	4.03421i	0.0922119	−	0.159716i
$639$	−15.6520	−	8.88266i	−0.619185	−	0.351392i
$640$	16.0835			0.635758
$641$	5.34482	+	30.3120i	0.211108	+	1.19725i	0.887535	+	0.460741i	$0.152416\pi$
$641$	5.34482	+	30.3120i	0.211108	+	1.19725i	−0.676427	+	0.736510i	$0.736473\pi$
$642$	32.7947	+	2.74672i	1.29430	+	0.108404i
$643$	−3.77799	+	21.4260i	−0.148989	+	0.844960i	0.815088	+	0.579338i	$0.196689\pi$
$643$	−3.77799	+	21.4260i	−0.148989	+	0.844960i	−0.964077	+	0.265623i	$0.914422\pi$
$644$	−0.260042	−	0.0762679i	−0.0102471	−	0.00300538i
$645$	−2.01820	+	7.64525i	−0.0794664	+	0.301032i
$646$	−8.51188	−	48.2733i	−0.334895	−	1.89929i
$647$	7.94373	−	13.7589i	0.312300	−	0.540920i	−0.666560	−	0.745452i	$-0.732234\pi$
$647$	7.94373	−	13.7589i	0.312300	−	0.540920i	0.978860	+	0.204532i	$0.0655671\pi$
$648$	−13.2548	−	22.1916i	−0.520699	−	0.871768i
$649$	4.26302	+	7.38378i	0.167338	+	0.289839i
$650$	9.05409	+	3.29542i	0.355131	+	0.129257i
$651$	−7.20367	+	5.80567i	−0.282334	+	0.227542i
$652$	0.382345	+	0.320826i	0.0149738	+	0.0125645i
$653$	30.4461	−	11.0815i	1.19145	−	0.433652i	0.331216	−	0.943555i	$-0.392541\pi$
$653$	30.4461	−	11.0815i	1.19145	−	0.433652i	0.860232	+	0.509903i	$0.170319\pi$
$654$	0.0500852	+	0.106377i	0.00195849	+	0.00415966i
$655$	−5.41820	−	30.7281i	−0.211707	−	1.20065i
$656$	10.0087	−	17.3355i	0.390773	−	0.676839i
$657$	0.0201445	+	2.71730i	0.000785911	+	0.106012i
$658$	26.8294	+	19.7413i	1.04592	+	0.769594i
$659$	0.0439021	+	0.248981i	0.00171018	+	0.00969892i	0.985651	−	0.168797i	$-0.0539881\pi$
$659$	0.0439021	+	0.248981i	0.00171018	+	0.00969892i	−0.983941	+	0.178496i	$0.942877\pi$
$660$	0.179215	+	0.0827619i	0.00697593	+	0.00322150i
$661$	−2.33884	+	13.2642i	−0.0909704	+	0.515919i	0.904938	+	0.425544i	$0.139917\pi$
$661$	−2.33884	+	13.2642i	−0.0909704	+	0.515919i	−0.995908	+	0.0903741i	$0.971194\pi$
$662$	2.80464	−	15.9059i	0.109005	−	0.618201i
$663$	1.66239	+	18.2229i	0.0645617	+	0.707720i
$664$	−6.95325	−	39.4338i	−0.269838	−	1.53033i
$665$	26.7488	+	19.6819i	1.03727	+	0.763233i
$666$	−33.2782	+	6.12255i	−1.28950	+	0.237244i
$667$	2.25372	−	3.90356i	0.0872644	−	0.151146i
$668$	0.0103221	+	0.0585395i	0.000399374	+	0.00226496i
$669$	−4.14827	−	0.347437i	−0.160381	−	0.0134327i
$670$	30.1714	−	10.9815i	1.16562	−	0.424252i
$671$	5.76711	+	4.83918i	0.222637	+	0.186815i
$672$	1.55538	+	0.601216i	0.0599999	+	0.0231924i
$673$	3.17733	+	1.15645i	0.122477	+	0.0445780i	0.402532	−	0.915406i	$-0.368130\pi$
$673$	3.17733	+	1.15645i	0.122477	+	0.0445780i	−0.280055	+	0.959984i	$0.590353\pi$
$674$	11.0810	+	19.1929i	0.426826	+	0.739284i
$675$	1.08949	−	14.2801i	0.0419343	−	0.549641i
$676$	−0.215142	+	0.372637i	−0.00827470	+	0.0143322i
$677$	−4.50614	−	25.5556i	−0.173185	−	0.982180i	−0.940218	−	0.340573i	$-0.889379\pi$
$677$	−4.50614	−	25.5556i	−0.173185	−	0.982180i	0.767033	−	0.641607i	$-0.221732\pi$
$678$	−0.233201	−	0.231478i	−0.00895602	−	0.00888987i
$679$	7.04954	+	2.06756i	0.270537	+	0.0793458i
$680$	−3.14109	+	17.8140i	−0.120455	+	0.683137i
$681$	12.6043	+	26.7705i	0.482998	+	1.02585i
$682$	0.576694	+	3.27060i	0.0220828	+	0.125238i
$683$	40.9371			1.56641			0.783207	−	0.621761i	$-0.213583\pi$
$683$	40.9371			1.56641			0.783207	+	0.621761i	$0.213583\pi$
$684$	1.59518	+	0.269095i	0.0609931	+	0.0102891i
$685$	3.10644	−	5.38051i	0.118691	−	0.205579i
$686$	−9.21814	−	24.0614i	−0.351950	−	0.918670i
$687$	−0.716310	−	7.85213i	−0.0273289	−	0.299578i
$688$	9.02842	+	7.57575i	0.344205	+	0.288823i
$689$	−3.75677	+	21.3057i	−0.143121	+	0.811682i
$690$	−5.21607	−	2.40880i	−0.198572	−	0.0917013i
$691$	13.9178	−	11.6785i	0.529460	−	0.444270i	−0.338455	−	0.940983i	$-0.609904\pi$
$691$	13.9178	−	11.6785i	0.529460	−	0.444270i	0.867915	+	0.496713i	$0.165460\pi$
$692$	0.514066	−	0.890389i	0.0195419	−	0.0338475i
$693$	−6.52826	−	6.74163i	−0.247988	−	0.256093i
$694$	16.3367	+	28.2961i	0.620134	+	1.07410i
$695$	−13.0312	−	4.74296i	−0.494301	−	0.179911i
$696$	−8.03742	+	11.5697i	−0.304658	+	0.438547i
$697$	16.6721	+	13.9895i	0.631500	+	0.529892i
$698$	4.14310	−	23.4967i	0.156819	−	0.889364i
$699$	24.6261	+	24.4442i	0.931445	+	0.924566i
$700$	0.260056	+	0.390615i	0.00982919	+	0.0147639i
$701$	34.1406			1.28947			0.644736	−	0.764405i	$-0.276967\pi$
$701$	34.1406			1.28947			0.644736	+	0.764405i	$0.276967\pi$
$702$	17.5971	+	4.50601i	0.664159	+	0.170068i
$703$	33.9660	−	58.8309i	1.28105	−	2.21885i
$704$	7.46362	−	6.26272i	0.281296	−	0.236035i
$705$	−16.6629	−	16.5398i	−0.627561	−	0.622925i
$706$	−7.01790	−	5.88872i	−0.264122	−	0.221625i
$707$	−10.9861	−	3.22212i	−0.413175	−	0.121180i
$708$	−0.342384	−	0.727196i	−0.0128676	−	0.0273297i
$709$	−4.62717	−	1.68415i	−0.173777	−	0.0632496i	0.253666	−	0.967292i	$-0.418363\pi$
$709$	−4.62717	−	1.68415i	−0.173777	−	0.0632496i	−0.427443	+	0.904042i	$0.640586\pi$
$710$	12.5021			0.469195
$711$	−7.63486	+	1.40467i	−0.286329	+	0.0526792i
$712$	−42.4355			−1.59034
$713$	0.558018	+	3.16468i	0.0208979	+	0.118518i
$714$	13.8600	−	22.9456i	0.518698	−	0.858718i
$715$	−4.18171	+	1.52202i	−0.156387	+	0.0569202i
$716$	−0.192603	−	0.161613i	−0.00719792	−	0.00603977i
$717$	2.58731	+	28.3618i	0.0966248	+	1.05919i
$718$	−39.2778	−	14.2960i	−1.46583	−	0.533520i
$719$	−32.3183			−1.20527			−0.602635	−	0.798017i	$-0.705883\pi$
$719$	−32.3183			−1.20527			−0.602635	+	0.798017i	$0.705883\pi$
$720$	15.1140	+	8.57731i	0.563266	+	0.319658i
$721$	1.69460	−	15.2376i	0.0631103	−	0.567476i
$722$	54.5860	−	45.8031i	2.03148	−	1.70461i
$723$	−30.9659	−	2.59354i	−1.15163	−	0.0964549i
$724$	0.343487	+	0.288220i	0.0127656	+	0.0107116i
$725$	−7.33451	+	2.66954i	−0.272397	+	0.0991444i
$726$	22.3280	−	6.07155i	0.828669	−	0.225337i
$727$	−7.03337	−	2.55994i	−0.260853	−	0.0949428i	0.208283	−	0.978069i	$-0.433212\pi$
$727$	−7.03337	−	2.55994i	−0.260853	−	0.0949428i	−0.469136	+	0.883126i	$0.655435\pi$
$728$	−17.4892	+	7.66052i	−0.648194	+	0.283918i
$729$	−0.600426	−	26.9933i	−0.0222380	−	0.999753i
$730$	−0.943854	−	1.63480i	−0.0349336	−	0.0605068i
$731$	−9.81615	+	8.23673i	−0.363063	+	0.304646i
$732$	−0.503704	−	0.499984i	−0.0186174	−	0.0184799i
$733$	−0.160809	+	0.911991i	−0.00593960	+	0.0336852i	−0.987634	−	0.156780i	$-0.949889\pi$
$733$	−0.160809	+	0.911991i	−0.00593960	+	0.0336852i	0.981694	+	0.190465i	$0.0609997\pi$
$734$	2.65448	−	15.0543i	0.0979785	−	0.555663i
$735$	3.93722	+	17.7296i	0.145227	+	0.653966i
$736$	0.443682	−	0.372293i	0.0163543	−	0.0137229i
$737$	9.10776	−	15.7751i	0.335489	−	0.581083i
$738$	18.6297	−	10.9408i	0.685768	−	0.402736i
$739$	6.25043	+	10.8261i	0.229926	+	0.398243i	0.957786	−	0.287482i	$-0.0928183\pi$
$739$	6.25043	+	10.8261i	0.229926	+	0.398243i	−0.727860	+	0.685726i	$0.759485\pi$
$740$	−0.598632	+	0.502312i	−0.0220061	+	0.0184653i
$741$	−29.7955	+	21.0281i	−1.09457	+	0.772486i
$742$	22.9309	−	21.8781i	0.841818	−	0.803169i
$743$	17.4978	−	6.36868i	0.641932	−	0.233644i	−0.000484263	−	1.00000i	$-0.500154\pi$
$743$	17.4978	−	6.36868i	0.641932	−	0.233644i	0.642417	+	0.766356i	$0.277932\pi$
$744$	−0.912421	−	10.0019i	−0.0334510	−	0.366687i
$745$	6.40478	+	2.33115i	0.234653	+	0.0854067i
$746$	−15.0096	−	25.9975i	−0.549542	−	0.951834i
$747$	14.0134	−	39.4082i	0.512725	−	1.44187i
$748$	0.159952	+	0.277044i	0.00584841	+	0.0101297i
$749$	−36.0589	+	2.30281i	−1.31756	+	0.0841428i
$750$	11.9261	+	25.3301i	0.435480	+	0.924924i
$751$	0.207541	−	0.0755387i	0.00757328	−	0.00275645i	−0.338231	−	0.941063i	$-0.609828\pi$
$751$	0.207541	−	0.0755387i	0.00757328	−	0.00275645i	0.345804	+	0.938307i	$0.387606\pi$
$752$	−32.8840	+	11.9688i	−1.19916	+	0.436458i
$753$	−12.6585	+	47.9524i	−0.461301	+	1.74748i
$754$	−1.71908	−	9.74939i	−0.0626052	−	0.355052i
$755$	−19.6615			−0.715556
$756$	0.560240	+	0.684694i	0.0203757	+	0.0249021i
$757$	−47.1721			−1.71450			−0.857250	−	0.514900i	$-0.827829\pi$
$757$	−47.1721			−1.71450			−0.857250	+	0.514900i	$0.827829\pi$
$758$	−3.65771	−	20.7439i	−0.132854	−	0.753453i
$759$	−3.14530	+	0.855288i	−0.114167	+	0.0310450i
$760$	−33.8764	+	12.3300i	−1.22882	+	0.447256i
$761$	−12.6984	+	4.62185i	−0.460318	+	0.167542i	−0.561761	−	0.827299i	$-0.689876\pi$
$761$	−12.6984	+	4.62185i	−0.460318	+	0.167542i	0.101443	+	0.994841i	$0.467654\pi$
$762$	−53.1534	−	4.45185i	−1.92554	−	0.161274i
$763$	−0.0715401	−	0.107456i	−0.00258993	−	0.00389018i
$764$	−0.639557	−	1.10775i	−0.0231384	−	0.0400768i
$765$	−12.0375	+	14.5637i	−0.435217	+	0.526550i
$766$	−11.4186	−	19.7776i	−0.412572	−	0.714595i
$767$	17.0268	+	6.19724i	0.614801	+	0.223769i
$768$	−2.18328	+	1.54084i	−0.0787824	+	0.0556003i
$769$	22.2329	−	8.09212i	0.801739	−	0.291809i	0.0915322	−	0.995802i	$-0.470824\pi$
$769$	22.2329	−	8.09212i	0.801739	−	0.291809i	0.710207	+	0.703993i	$0.248601\pi$
$770$	6.25568	+	1.83473i	0.225439	+	0.0661192i
$771$	1.07861	+	11.8236i	0.0388451	+	0.425816i
$772$	0.185728	−	0.155844i	0.00668450	−	0.00560896i
$773$	−16.2739	−	28.1872i	−0.585331	−	1.01382i	−0.994834	−	0.101514i	$-0.967631\pi$
$773$	−16.2739	−	28.1872i	−0.585331	−	1.01382i	0.409503	−	0.912309i	$-0.365702\pi$
$774$	4.43913	+	11.9207i	0.159561	+	0.428480i
$775$	2.78230	−	4.81908i	0.0999430	−	0.173106i
$776$	−6.10916	+	5.12619i	−0.219306	+	0.184020i
$777$	35.1545	−	12.0131i	1.26116	−	0.430967i
$778$	4.29196	−	24.3409i	0.153874	−	0.872664i
$779$	−7.53193	+	42.7157i	−0.269860	+	1.53045i
$780$	0.404817	−	0.110080i	0.0144948	−	0.00394151i
$781$	5.43336	−	4.55913i	0.194421	−	0.163138i
$782$	−4.65541	−	8.06341i	−0.166477	−	0.288347i
$783$	−13.2663	+	6.36670i	−0.474098	+	0.227527i
$784$	26.4087	+	5.94749i	0.943166	+	0.212411i
$785$	4.80217	+	1.74785i	0.171397	+	0.0623833i
$786$	−35.6250	−	35.3619i	−1.27070	−	1.26132i
$787$	−3.03147	+	1.10336i	−0.108060	+	0.0393307i	−0.395484	−	0.918473i	$-0.629423\pi$
$787$	−3.03147	+	1.10336i	−0.108060	+	0.0393307i	0.287424	+	0.957803i	$0.407201\pi$
$788$	−0.882161	−	0.740221i	−0.0314257	−	0.0263693i
$789$	15.7368	−	22.6527i	0.560244	−	0.806457i
$790$	4.13112	−	3.46643i	0.146979	−	0.123330i
$791$	0.290574	+	0.213807i	0.0103316	+	0.00760209i
$792$	10.0191	−	1.84332i	0.356012	−	0.0654995i
$793$	15.9994			0.568154
$794$	46.9068	+	17.0727i	1.66466	+	0.605887i
$795$	−18.2513	+	12.8808i	−0.647307	+	0.456834i
$796$	0.0804052	+	0.0674680i	0.00284989	+	0.00239134i
$797$	4.72969	−	1.72147i	0.167534	−	0.0609775i	−0.256891	−	0.966440i	$-0.582698\pi$
$797$	4.72969	−	1.72147i	0.167534	−	0.0609775i	0.424426	+	0.905463i	$0.360476\pi$
$798$	53.4145	+	1.05689i	1.89085	+	0.0374137i
$799$	−6.60692	−	37.4697i	−0.233736	−	1.32558i
$800$	−1.00294			−0.0354591
$801$	−38.5503	−	21.8776i	−1.36211	−	0.773006i
$802$	55.2349			1.95041
$803$	−1.00636	−	0.366284i	−0.0355136	−	0.0129259i
$804$	−0.979730	+	1.41030i	−0.0345524	+	0.0497374i
$805$	6.05309	+	1.77531i	0.213343	+	0.0625716i
$806$	5.40664	+	4.53671i	0.190441	+	0.159799i
$807$	20.3209	−	5.52577i	0.715329	−	0.194516i
$808$	9.52059	−	7.98873i	0.334933	−	0.281042i
$809$	−4.67728	+	8.10129i	−0.164445	+	0.284826i	−0.936458	−	0.350780i	$-0.885916\pi$
$809$	−4.67728	+	8.10129i	−0.164445	+	0.284826i	0.772013	+	0.635606i	$0.219250\pi$
$810$	9.61798	+	16.1027i	0.337941	+	0.565790i
$811$	6.50486			0.228416			0.114208	−	0.993457i	$-0.463567\pi$
$811$	6.50486			0.228416			0.114208	+	0.993457i	$0.463567\pi$
$812$	0.213974	−	0.432072i	0.00750902	−	0.0151628i
$813$	−12.0346	+	45.5889i	−0.422071	+	1.59887i
$814$	2.31566	−	13.1328i	0.0811639	−	0.460303i
$815$	−8.89999	−	7.46798i	−0.311753	−	0.261592i
$816$	11.9966	+	25.4797i	0.419964	+	0.891968i
$817$	−23.9979	−	8.73452i	−0.839580	−	0.305582i
$818$	20.4037	+	35.3402i	0.713398	+	1.23564i
$819$	−19.8373	−	2.05740i	−0.693173	−	0.0718913i
$820$	0.249481	−	0.432114i	0.00871226	−	0.0150901i
$821$	−5.83840	+	4.89900i	−0.203761	+	0.170976i	−0.738958	−	0.673751i	$-0.764682\pi$
$821$	−5.83840	+	4.89900i	−0.203761	+	0.170976i	0.535197	+	0.844727i	$0.320237\pi$
$822$	−0.908003	−	9.95345i	−0.0316702	−	0.347167i
$823$	1.87586	−	10.6385i	0.0653883	−	0.370836i	−0.934501	−	0.355960i	$-0.884154\pi$
$823$	1.87586	−	10.6385i	0.0653883	−	0.370836i	0.999889	−	0.0148752i	$-0.00473510\pi$
$824$	12.7493	+	10.6979i	0.444143	+	0.372680i
$825$	5.12426	+	2.36640i	0.178404	+	0.0823873i
$826$	−14.7103	−	22.0955i	−0.511836	−	0.768800i
$827$	7.38485	−	12.7909i	0.256796	−	0.444784i	−0.708586	−	0.705625i	$-0.750666\pi$
$827$	7.38485	−	12.7909i	0.256796	−	0.444784i	0.965382	+	0.260841i	$0.0839997\pi$
$828$	0.302208	−	0.0556005i	0.0105025	−	0.00193225i
$829$	−36.6482			−1.27284			−0.636422	−	0.771341i	$-0.719586\pi$
$829$	−36.6482			−1.27284			−0.636422	+	0.771341i	$0.719586\pi$
$830$	5.04542	+	28.6140i	0.175129	+	0.993206i
$831$	5.33581	−	7.68077i	0.185097	−	0.266443i
$832$	3.59554	−	20.3913i	0.124653	−	0.706942i
$833$	−11.3541	+	27.1537i	−0.393396	+	0.940820i
$834$	−21.5272	+	5.85381i	−0.745427	+	0.202701i
$835$	−0.240271	−	1.36264i	−0.00831492	−	0.0471563i
$836$	−0.318778	+	0.552140i	−0.0110252	+	0.0190962i
$837$	4.32758	−	9.55655i	0.149583	−	0.330323i
$838$	1.37449	+	2.38068i	0.0474809	+	0.0822394i
$839$	−22.2115	−	8.08433i	−0.766827	−	0.279102i	−0.0711584	−	0.997465i	$-0.522670\pi$
$839$	−22.2115	−	8.08433i	−0.766827	−	0.279102i	−0.695669	+	0.718363i	$0.744892\pi$
$840$	−18.3891	−	7.10815i	−0.634485	−	0.245254i
$841$	−16.0719	−	13.4859i	−0.554204	−	0.465033i
$842$	−13.1948	+	4.80252i	−0.454723	+	0.165506i
$843$	0.123151	−	0.177273i	0.00424155	−	0.00610560i
$844$	−0.180900	−	1.02594i	−0.00622685	−	0.0353142i
$845$	5.00794	−	8.67400i	0.172278	−	0.298395i
$846$	−37.2434	−	6.28270i	−1.28045	−	0.216004i
$847$	−23.2704	+	10.1927i	−0.799579	+	0.350227i
$848$	5.78188	+	32.7907i	0.198551	+	1.12604i
$849$	37.0783	−	26.1678i	1.27252	−	0.898078i
$850$	−2.79971	+	15.8780i	−0.0960294	+	0.544610i
$851$	2.24067	−	12.7075i	0.0768091	−	0.435606i
$852$	−0.546297	+	0.385547i	−0.0187158	+	0.0132086i
$853$	−3.92214	−	22.2436i	−0.134292	−	0.761605i	−0.975350	−	0.220662i	$-0.929178\pi$
$853$	−3.92214	−	22.2436i	−0.134292	−	0.761605i	0.841059	−	0.540944i	$-0.181933\pi$
$854$	−18.8786	−	13.8910i	−0.646011	−	0.475340i
$855$	−37.1315	−	6.26382i	−1.26987	−	0.214218i
$856$	19.6117	−	33.9684i	0.670313	−	1.16102i
$857$	3.87860	+	21.9966i	0.132490	+	0.751390i	0.976575	+	0.215179i	$0.0690336\pi$
$857$	3.87860	+	21.9966i	0.132490	+	0.751390i	−0.844084	+	0.536211i	$0.819855\pi$
$858$	−4.08443	+	5.87944i	−0.139440	+	0.200721i
$859$	11.1839	−	4.07061i	0.381590	−	0.138887i	−0.144101	−	0.989563i	$-0.546029\pi$
$859$	11.1839	−	4.07061i	0.381590	−	0.138887i	0.525691	+	0.850676i	$0.323807\pi$
$860$	0.225047	+	0.188837i	0.00767403	+	0.00643928i
$861$	−18.4691	+	14.8848i	−0.629424	+	0.507273i
$862$	−11.3081	−	4.11583i	−0.385157	−	0.140186i
$863$	14.7919	+	25.6203i	0.503521	+	0.872124i	0.999992	+	0.00407023i	$0.00129560\pi$
$863$	14.7919	+	25.6203i	0.503521	+	0.872124i	−0.496471	+	0.868053i	$0.665371\pi$
$864$	−1.88166	+	0.185729i	−0.0640153	+	0.00631863i
$865$	−11.9661	+	20.7259i	−0.406860	+	0.704701i
$866$	−0.255149	−	1.44702i	−0.00867031	−	0.0491718i
$867$	−1.13376	+	0.308299i	−0.0385046	+	0.0104704i
$868$	0.0811435	+	0.334027i	0.00275419	+	0.0113376i
$869$	0.531272	−	3.01299i	0.0180222	−	0.102209i
$870$	5.83211	−	8.39518i	0.197727	−	0.284623i
$871$	−6.72218	−	38.1234i	−0.227772	−	1.29176i
$872$	0.140136			0.00474559
$873$	−8.19263	+	1.50729i	−0.277278	+	0.0510139i
$874$	9.27808	−	16.0701i	0.313836	−	0.543580i
$875$	−17.0349	−	25.5871i	−0.575884	−	0.865003i
$876$	0.0916582	+	0.0423280i	0.00309684	+	0.00143013i
$877$	28.7678	+	24.1391i	0.971420	+	0.815118i	0.982773	−	0.184817i	$-0.0591693\pi$
$877$	28.7678	+	24.1391i	0.971420	+	0.815118i	−0.0113527	+	0.999936i	$0.503614\pi$
$878$	−3.39878	+	19.2755i	−0.114703	+	0.650515i
$879$	2.56101	+	28.0736i	0.0863807	+	0.946899i
$880$	−5.24658	+	4.40241i	−0.176862	+	0.148405i
$881$	−1.68286	+	2.91480i	−0.0566970	+	0.0982022i	−0.892981	−	0.450095i	$-0.851390\pi$
$881$	−1.68286	+	2.91480i	−0.0566970	+	0.0982022i	0.836284	+	0.548297i	$0.184724\pi$
$882$	21.6209	+	19.6509i	0.728015	+	0.661679i
$883$	14.9614	+	25.9139i	0.503491	+	0.872071i	0.999992	+	0.00403531i	$0.00128448\pi$
$883$	14.9614	+	25.9139i	0.503491	+	0.872071i	−0.496501	+	0.868036i	$0.665382\pi$
$884$	0.638856	+	0.232524i	0.0214870	+	0.00782064i
$885$	7.96979	+	16.9272i	0.267902	+	0.569001i
$886$	−18.1798	−	15.2547i	−0.610763	−	0.512491i
$887$	−4.84584	+	27.4821i	−0.162707	+	0.922760i	0.788689	+	0.614792i	$0.210760\pi$
$887$	−4.84584	+	27.4821i	−0.162707	+	0.922760i	−0.951397	+	0.307968i	$0.900351\pi$
$888$	−10.2933	+	38.9927i	−0.345420	+	1.30851i
$889$	58.4440	−	3.73237i	1.96015	−	0.125180i
$890$	30.7920			1.03215
$891$	10.0521	+	3.49077i	0.336758	+	0.116945i
$892$	−0.0773309	+	0.133941i	−0.00258923	+	0.00448468i
$893$	58.0875	−	48.7412i	1.94382	−	1.63106i
$894$	10.5806	−	2.87713i	0.353867	−	0.0962256i
$895$	4.48329	+	3.76193i	0.149860	+	0.125747i
$896$	−20.5536	+	19.6100i	−0.686649	+	0.655124i
$897$	−3.95216	+	5.68903i	−0.131959	+	0.189951i
$898$	−12.4790	−	4.54198i	−0.416429	−	0.151568i
$899$	−5.71742			−0.190687
$900$	−0.462768	−	0.262625i	−0.0154256	−	0.00875415i
$901$	−36.2016			−1.20605
$902$	1.47855	+	8.38529i	0.0492304	+	0.279200i
$903$	−6.74242	−	12.2308i	−0.224374	−	0.407016i
$904$	−0.368002	+	0.133942i	−0.0122396	+	0.00445484i
$905$	−7.99547	−	6.70899i	−0.265778	−	0.223015i
$906$	−25.8423	+	18.2381i	−0.858553	+	0.605920i
$907$	−23.1027	−	8.40869i	−0.767112	−	0.279206i	−0.0713243	−	0.997453i	$-0.522723\pi$
$907$	−23.1027	−	8.40869i	−0.767112	−	0.279206i	−0.695788	+	0.718247i	$0.744945\pi$
$908$	1.09934			0.0364830
$909$	12.7675	−	2.34898i	0.423471	−	0.0779106i
$910$	12.6905	−	5.55863i	0.420687	−	0.184267i
$911$	22.6425	−	18.9993i	0.750178	−	0.629474i	−0.185372	−	0.982668i	$-0.559349\pi$
$911$	22.6425	−	18.9993i	0.750178	−	0.629474i	0.935550	+	0.353194i	$0.114905\pi$
$912$	−32.0226	+	46.0957i	−1.06037	+	1.52638i
$913$	12.6274	+	10.5956i	0.417905	+	0.350664i
$914$	−2.29656	+	0.835881i	−0.0759636	+	0.0276485i
$915$	11.7249	+	11.6383i	0.387613	+	0.384750i
$916$	−0.275278	−	0.100193i	−0.00909545	−	0.00331047i
$917$	44.3896	+	32.6622i	1.46587	+	1.07860i
$918$	−2.31231	+	30.3079i	−0.0763177	+	1.00031i
$919$	14.5940	+	25.2776i	0.481412	+	0.833831i	0.999772	−	0.0213317i	$-0.00679061\pi$
$919$	14.5940	+	25.2776i	0.481412	+	0.833831i	−0.518360	+	0.855162i	$0.673457\pi$
$920$	−5.24563	+	4.40161i	−0.172943	+	0.145117i
$921$	5.50927	−	1.49811i	0.181536	−	0.0493645i
$922$	−7.60763	+	43.1450i	−0.250544	+	1.42090i
$923$	2.61748	−	14.8445i	0.0861553	−	0.488611i
$924$	−0.329932	+	0.112745i	−0.0108540	+	0.00370905i
$925$	−17.1166	+	14.3625i	−0.562789	+	0.472236i
$926$	23.7770	−	41.1830i	0.781361	−	1.35336i
$927$	6.06671	+	16.2914i	0.199257	+	0.535078i
$928$	0.515240	+	0.892423i	0.0169136	+	0.0292952i
$929$	−27.7275	+	23.2661i	−0.909708	+	0.763336i	−0.972063	−	0.234718i	$-0.924583\pi$
$929$	−27.7275	+	23.2661i	−0.909708	+	0.763336i	0.0623551	+	0.998054i	$0.480139\pi$
$930$	0.662071	+	7.25757i	0.0217102	+	0.237985i
$931$	−58.1804	+	7.46150i	−1.90679	+	0.244541i
$932$	1.21141	−	0.440918i	0.0396811	−	0.0144427i
$933$	−4.35739	+	3.07521i	−0.142655	+	0.100678i
$934$	30.1770	+	10.9835i	0.987423	+	0.359392i
$935$	−3.72325	−	6.44885i	−0.121763	−	0.210900i
$936$	13.7929	−	16.6875i	0.450836	−	0.545446i
$937$	−4.59371	−	7.95654i	−0.150070	−	0.259929i	0.781183	−	0.624302i	$-0.214617\pi$
$937$	−4.59371	−	7.95654i	−0.150070	−	0.259929i	−0.931253	+	0.364373i	$0.881283\pi$
$938$	−25.1676	+	50.8203i	−0.821753	+	1.65934i
$939$	13.5732	+	1.13682i	0.442944	+	0.0370987i
$940$	−0.819683	+	0.298340i	−0.0267351	+	0.00973079i
$941$	−25.3681	+	9.23323i	−0.826976	+	0.300995i	−0.720617	−	0.693333i	$-0.756141\pi$
$941$	−25.3681	+	9.23323i	−0.826976	+	0.300995i	−0.106359	+	0.994328i	$0.533919\pi$
$942$	7.93307	−	2.15721i	0.258474	−	0.0702856i
$943$	1.43067	+	8.11373i	0.0465890	+	0.264219i
$944$	27.8870			0.907644
$945$	−13.0409	−	15.9378i	−0.424220	−	0.518458i
$946$	−5.01323			−0.162994
$947$	7.04005	+	39.9261i	0.228771	+	1.29742i	0.855343	+	0.518061i	$0.173346\pi$
$947$	7.04005	+	39.9261i	0.228771	+	1.29742i	−0.626572	+	0.779363i	$0.715543\pi$
$948$	−0.0736159	+	0.278869i	−0.00239093	+	0.00905724i
$949$	−2.13871	+	0.778425i	−0.0694253	+	0.0252687i
$950$	−30.1946	+	10.9899i	−0.979643	+	0.356561i
$951$	20.2002	+	42.9035i	0.655035	+	1.39124i
$952$	−17.7058	−	26.5949i	−0.573848	−	0.861945i
$953$	−4.29093	−	7.43211i	−0.138997	−	0.240750i	0.788120	−	0.615521i	$-0.211054\pi$
$953$	−4.29093	−	7.43211i	−0.138997	−	0.240750i	−0.927117	+	0.374772i	$0.877721\pi$
$954$	−12.0405	+	33.8599i	−0.389825	+	1.09626i
$955$	14.8872	+	25.7854i	0.481739	+	0.834396i
$956$	0.994303	+	0.361897i	0.0321581	+	0.0117046i
$957$	−0.526852	−	5.77531i	−0.0170307	−	0.186689i
$958$	−5.51896	+	2.00874i	−0.178309	+	0.0648993i
$959$	2.59042	+	10.6635i	0.0836490	+	0.344341i
$960$	17.4680	−	12.3280i	0.563778	−	0.397884i
$961$	−20.6249	+	17.3063i	−0.665319	+	0.558269i
$962$	−14.1701	−	24.5434i	−0.456863	−	0.791310i
$963$	35.3285	−	20.7476i	1.13844	−	0.668582i
$964$	−0.577259	+	0.999841i	−0.0185922	+	0.0322027i
$965$	−4.32326	+	3.62764i	−0.139171	+	0.116778i
$966$	9.60271	−	3.28146i	0.308962	−	0.105579i
$967$	6.00307	−	34.0451i	0.193046	−	1.09482i	−0.722128	−	0.691759i	$-0.756836\pi$
$967$	6.00307	−	34.0451i	0.193046	−	1.09482i	0.915174	−	0.403058i	$-0.132053\pi$
$968$	4.78887	−	27.1590i	0.153920	−	0.872925i
$969$	−43.3103	−	42.9904i	−1.39133	−	1.38105i
$970$	4.43293	−	3.71967i	0.142333	−	0.119431i
$971$	−18.6050	−	32.2249i	−0.597064	−	1.03414i	−0.993252	−	0.115975i	$-0.963001\pi$
$971$	−18.6050	−	32.2249i	−0.597064	−	1.03414i	0.396188	−	0.918169i	$-0.370333\pi$
$972$	−0.916856	−	0.407025i	−0.0294082	−	0.0130553i
$973$	22.4358	−	9.82720i	0.719260	−	0.315046i
$974$	−15.6985	−	5.71378i	−0.503012	−	0.183081i
$975$	11.5749	−	3.14750i	0.370692	−	0.100801i
$976$	23.1390	−	8.42189i	0.740660	−	0.269578i
$977$	−6.23270	−	5.22985i	−0.199402	−	0.167318i	0.537619	−	0.843188i	$-0.319324\pi$
$977$	−6.23270	−	5.22985i	−0.199402	−	0.167318i	−0.737021	+	0.675870i	$0.763768\pi$
$978$	−18.6251	−	1.55994i	−0.595565	−	0.0498814i
$979$	13.3821	−	11.2289i	0.427694	−	0.358878i
$980$	0.658275	+	0.148250i	0.0210278	+	0.00473567i
$981$	0.127305	+	0.0722468i	0.00406455	+	0.00230666i
$982$	16.7768			0.535368
$983$	49.8706	+	18.1514i	1.59062	+	0.578940i	0.977479	−	0.211030i	$-0.0676819\pi$
$983$	49.8706	+	18.1514i	1.59062	+	0.578940i	0.613145	+	0.789970i	$0.289904\pi$
$984$	−2.33930	−	25.6432i	−0.0745743	−	0.817477i
$985$	20.5344	+	17.2304i	0.654279	+	0.549005i
$986$	15.5667	−	5.66581i	0.495744	−	0.180436i
$987$	41.4603	+	0.820361i	1.31970	+	0.0261124i
$988$	0.235281	+	1.33435i	0.00748529	+	0.0424512i
$989$	−4.85088			−0.154249
$990$	−7.27004	+	1.33755i	−0.231057	+	0.0425101i
$991$	26.0463			0.827387			0.413693	−	0.910416i	$-0.364239\pi$
$991$	26.0463			0.827387			0.413693	+	0.910416i	$0.364239\pi$
$992$	−0.690357	−	0.251269i	−0.0219189	−	0.00797781i
$993$	−8.56522	−	18.1918i	−0.271809	−	0.577300i
$994$	−15.9768	+	15.2433i	−0.506753	+	0.483487i
$995$	−1.87162	−	1.57048i	−0.0593344	−	0.0497874i
$996$	−1.10288	−	1.09474i	−0.0349462	−	0.0346881i
$997$	−27.0566	+	22.7032i	−0.856892	+	0.719018i	−0.961296	−	0.275517i	$-0.911151\pi$
$997$	−27.0566	+	22.7032i	−0.856892	+	0.719018i	0.104404	+	0.994535i	$0.466707\pi$
$998$	22.3486	−	38.7089i	0.707432	−	1.22531i
$999$	−29.4535	+	30.1159i	−0.931868	+	0.952826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.16	✓	132
3.2	odd	2		567.2.u.a.550.7		132
7.2	even	3		189.2.w.a.58.16	yes	132
21.2	odd	6		567.2.w.a.226.7		132
27.7	even	9		189.2.w.a.88.16	yes	132
27.20	odd	18		567.2.w.a.424.7		132
189.128	odd	18		567.2.u.a.100.7		132
189.142	even	9	inner	189.2.u.a.142.16	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.16	✓	132	1.1	even	1	trivial
189.2.u.a.142.16	yes	132	189.142	even	9	inner
189.2.w.a.58.16	yes	132	7.2	even	3
189.2.w.a.88.16	yes	132	27.7	even	9
567.2.u.a.100.7		132	189.128	odd	18
567.2.u.a.550.7		132	3.2	odd	2
567.2.w.a.226.7		132	21.2	odd	6
567.2.w.a.424.7		132	27.20	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.241593 + 1.37014i) q^{2} +(1.22928 + 1.22020i) q^{3} +(0.0604707 - 0.0220095i) q^{4} +(-1.40760 + 0.512324i) q^{5} +(-1.37486 + 1.97907i) q^{6} +(1.17416 - 2.37094i) q^{7} +(1.43604 + 2.48730i) q^{8} +(0.0222396 + 2.99992i) q^{9} +O(q^{10})\)	\(q+(0.241593 + 1.37014i) q^{2} +(1.22928 + 1.22020i) q^{3} +(0.0604707 - 0.0220095i) q^{4} +(-1.40760 + 0.512324i) q^{5} +(-1.37486 + 1.97907i) q^{6} +(1.17416 - 2.37094i) q^{7} +(1.43604 + 2.48730i) q^{8} +(0.0222396 + 2.99992i) q^{9} +(-1.04202 - 1.80483i) q^{10} +(-1.11103 - 0.404380i) q^{11} +(0.101191 + 0.0467304i) q^{12} +(-2.36114 + 0.859386i) q^{13} +(3.53219 + 1.03596i) q^{14} +(-2.35546 - 1.08776i) q^{15} +(-2.96241 + 2.48576i) q^{16} +(-2.10228 - 3.64126i) q^{17} +(-4.10493 + 0.755229i) q^{18} +(4.18978 - 7.25691i) q^{19} +(-0.0738425 + 0.0619612i) q^{20} +(4.33638 - 1.48184i) q^{21} +(0.285642 - 1.61995i) q^{22} +(0.276391 - 1.56749i) q^{23} +(-1.26970 + 4.80983i) q^{24} +(-2.11136 + 1.77165i) q^{25} +(-1.74791 - 3.02747i) q^{26} +(-3.63315 + 3.71486i) q^{27} +(0.0188188 - 0.169215i) q^{28} +(2.66110 + 0.968563i) q^{29} +(0.921320 - 3.49011i) q^{30} +(-1.89719 + 0.690519i) q^{31} +(0.278752 + 0.233901i) q^{32} +(-0.872334 - 1.85276i) q^{33} +(4.48114 - 3.76012i) q^{34} +(-0.438052 + 3.93888i) q^{35} +(0.0673717 + 0.180918i) q^{36} +8.10687 q^{37} +(10.9552 + 3.98737i) q^{38} +(-3.95112 - 1.82464i) q^{39} +(-3.29567 - 2.76540i) q^{40} +(-4.86408 + 1.77038i) q^{41} +(3.07796 + 5.58344i) q^{42} +(-0.529220 - 3.00136i) q^{43} -0.0760847 q^{44} +(-1.56823 - 4.21129i) q^{45} +2.21446 q^{46} +(8.50342 + 3.09499i) q^{47} +(-6.67474 - 0.559042i) q^{48} +(-4.24271 - 5.56771i) q^{49} +(-2.93749 - 2.46485i) q^{50} +(1.85877 - 7.04131i) q^{51} +(-0.123865 + 0.103935i) q^{52} +(4.30504 - 7.45655i) q^{53} +(-5.96762 - 4.08044i) q^{54} +1.77105 q^{55} +(7.58337 - 0.484292i) q^{56} +(14.0053 - 3.80839i) q^{57} +(-0.684163 + 3.88008i) q^{58} +(-5.52413 - 4.63529i) q^{59} +(-0.166378 - 0.0139349i) q^{60} +(-5.98346 - 2.17780i) q^{61} +(-1.40445 - 2.43258i) q^{62} +(7.13874 + 3.46964i) q^{63} +(-4.12029 + 7.13655i) q^{64} +(2.88326 - 2.41934i) q^{65} +(2.32780 - 1.64283i) q^{66} +(-2.67531 + 15.1724i) q^{67} +(-0.207269 - 0.173919i) q^{68} +(2.25241 - 1.58963i) q^{69} +(-5.50264 + 0.351412i) q^{70} +(-2.99948 + 5.19525i) q^{71} +(-7.42975 + 4.36332i) q^{72} +0.905792 q^{73} +(1.95856 + 11.1075i) q^{74} +(-4.75721 - 0.398439i) q^{75} +(0.0936377 - 0.531046i) q^{76} +(-2.26328 + 2.15937i) q^{77} +(1.54545 - 5.85440i) q^{78} +(0.449343 + 2.54835i) q^{79} +(2.89637 - 5.01667i) q^{80} +(-8.99901 + 0.133434i) q^{81} +(-3.60079 - 6.23676i) q^{82} +(-13.1011 - 4.76840i) q^{83} +(0.229609 - 0.185049i) q^{84} +(4.82467 + 4.04838i) q^{85} +(3.98442 - 1.45021i) q^{86} +(2.08939 + 4.43770i) q^{87} +(-0.589665 - 3.34416i) q^{88} +(-7.38758 + 12.7957i) q^{89} +(5.39117 - 3.16611i) q^{90} +(-0.734800 + 6.60718i) q^{91} +(-0.0177862 - 0.100871i) q^{92} +(-3.17473 - 1.46610i) q^{93} +(-2.18621 + 12.3986i) q^{94} +(-2.17964 + 12.3613i) q^{95} +(0.0572583 + 0.627661i) q^{96} +(0.482171 + 2.73453i) q^{97} +(6.60353 - 7.15822i) q^{98} +(1.18840 - 3.34198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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