LMFDB - Embedded newform 189.2.w.a.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (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			25.10
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.332947 + 0.121183i) q^{2} +(-1.35881 + 1.07408i) q^{3} +(-1.43592 + 1.20488i) q^{4} +(0.672463 + 0.244756i) q^{5} +(0.322250 - 0.522275i) q^{6} +(-2.22176 - 1.43659i) q^{7} +(0.686389 - 1.18886i) q^{8} +(0.692708 - 2.91893i) q^{9} +O(q^{10})$	\(q+(-0.332947 + 0.121183i) q^{2} +(-1.35881 + 1.07408i) q^{3} +(-1.43592 + 1.20488i) q^{4} +(0.672463 + 0.244756i) q^{5} +(0.322250 - 0.522275i) q^{6} +(-2.22176 - 1.43659i) q^{7} +(0.686389 - 1.18886i) q^{8} +(0.692708 - 2.91893i) q^{9} -0.253554 q^{10} +(-4.78127 + 1.74024i) q^{11} +(0.657001 - 3.17949i) q^{12} +(-0.350421 - 1.98733i) q^{13} +(0.913817 + 0.209071i) q^{14} +(-1.17663 + 0.389702i) q^{15} +(0.566532 - 3.21296i) q^{16} +0.150378 q^{17} +(0.123089 + 1.05579i) q^{18} -5.71705 q^{19} +(-1.26051 + 0.458786i) q^{20} +(4.56195 - 0.434288i) q^{21} +(1.38102 - 1.15882i) q^{22} +(1.48618 + 8.42853i) q^{23} +(0.344261 + 2.35267i) q^{24} +(-3.43792 - 2.88476i) q^{25} +(0.357502 + 0.619212i) q^{26} +(2.19391 + 4.71028i) q^{27} +(4.92119 - 0.614114i) q^{28} +(-0.930281 + 5.27589i) q^{29} +(0.344531 - 0.272338i) q^{30} +(3.54974 - 2.97858i) q^{31} +(0.677491 + 3.84224i) q^{32} +(4.62767 - 7.50012i) q^{33} +(-0.0500677 + 0.0182232i) q^{34} +(-1.14243 - 1.50985i) q^{35} +(2.52229 + 5.02598i) q^{36} +(-2.68940 + 4.65817i) q^{37} +(1.90347 - 0.692808i) q^{38} +(2.61071 + 2.32402i) q^{39} +(0.752552 - 0.631466i) q^{40} +(-0.573052 - 3.24994i) q^{41} +(-1.46626 + 0.697424i) q^{42} +(0.837375 + 0.702641i) q^{43} +(4.76875 - 8.25971i) q^{44} +(1.18025 - 1.79333i) q^{45} +(-1.51621 - 2.62615i) q^{46} +(-0.865979 - 0.726643i) q^{47} +(2.68117 + 4.97429i) q^{48} +(2.87239 + 6.38352i) q^{49} +(1.49423 + 0.543854i) q^{50} +(-0.204334 + 0.161517i) q^{51} +(2.89768 + 2.43144i) q^{52} +(-3.93191 + 6.81027i) q^{53} +(-1.30126 - 1.30241i) q^{54} -3.64116 q^{55} +(-3.23290 + 1.65529i) q^{56} +(7.76836 - 6.14056i) q^{57} +(-0.329612 - 1.86932i) q^{58} +(-1.52775 - 8.66431i) q^{59} +(1.22001 - 1.97728i) q^{60} +(-7.14771 - 5.99764i) q^{61} +(-0.820921 + 1.42188i) q^{62} +(-5.73235 + 5.49001i) q^{63} +(2.57135 + 4.45370i) q^{64} +(0.250768 - 1.42218i) q^{65} +(-0.631882 + 3.05793i) q^{66} +(-2.45427 - 0.893282i) q^{67} +(-0.215930 + 0.181187i) q^{68} +(-11.0723 - 9.85647i) q^{69} +(0.563336 + 0.364255i) q^{70} +(-0.174740 - 0.302658i) q^{71} +(-2.99473 - 2.82705i) q^{72} +(6.86264 + 11.8864i) q^{73} +(0.330936 - 1.87683i) q^{74} +(7.76993 + 0.227228i) q^{75} +(8.20923 - 6.88836i) q^{76} +(13.1228 + 3.00236i) q^{77} +(-1.15086 - 0.457403i) q^{78} +(-5.81489 + 2.11645i) q^{79} +(1.16736 - 2.02193i) q^{80} +(-8.04031 - 4.04393i) q^{81} +(0.584633 + 1.01261i) q^{82} +(-1.70577 + 9.67392i) q^{83} +(-6.02733 + 6.12021i) q^{84} +(0.101123 + 0.0368059i) q^{85} +(-0.363949 - 0.132467i) q^{86} +(-4.40265 - 8.16810i) q^{87} +(-1.21291 + 6.87875i) q^{88} +13.4648 q^{89} +(-0.175639 + 0.740108i) q^{90} +(-2.07644 + 4.91878i) q^{91} +(-12.2894 - 10.3120i) q^{92} +(-1.62417 + 7.86002i) q^{93} +(0.376382 + 0.136992i) q^{94} +(-3.84450 - 1.39928i) q^{95} +(-5.04745 - 4.49318i) q^{96} +(-12.7314 - 10.6829i) q^{97} +(-1.72993 - 1.77729i) q^{98} +(1.76762 + 15.1617i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.332947	+	0.121183i	−0.235429	+	0.0856891i	−0.457040	−	0.889446i	$-0.651091\pi$
$2$	−0.332947	+	0.121183i	−0.235429	+	0.0856891i	0.221612	+	0.975135i	$0.428868\pi$
$3$	−1.35881	+	1.07408i	−0.784507	+	0.620120i
$3$	−1.35881	+	1.07408i	−0.784507	+	0.620120i
$4$	−1.43592	+	1.20488i	−0.717960	+	0.602440i
$5$	0.672463	+	0.244756i	0.300734	+	0.109458i	0.487980	−	0.872855i	$-0.337734\pi$
$5$	0.672463	+	0.244756i	0.300734	+	0.109458i	−0.187246	+	0.982313i	$0.559956\pi$
$6$	0.322250	−	0.522275i	0.131558	−	0.213218i
$7$	−2.22176	−	1.43659i	−0.839745	−	0.542982i
$7$	−2.22176	−	1.43659i	−0.839745	−	0.542982i
$8$	0.686389	−	1.18886i	0.242675	−	0.420326i
$9$	0.692708	−	2.91893i	0.230903	−	0.972977i
$10$	−0.253554			−0.0801810
$11$	−4.78127	+	1.74024i	−1.44161	+	0.524702i	−0.940234	−	0.340528i	$-0.889394\pi$
$11$	−4.78127	+	1.74024i	−1.44161	+	0.524702i	−0.501374	+	0.865231i	$0.667172\pi$
$12$	0.657001	−	3.17949i	0.189660	−	0.917840i
$13$	−0.350421	−	1.98733i	−0.0971892	−	0.551187i	−0.994055	−	0.108884i	$-0.965272\pi$
$13$	−0.350421	−	1.98733i	−0.0971892	−	0.551187i	0.896865	−	0.442304i	$-0.145839\pi$
$14$	0.913817	+	0.209071i	0.244228	+	0.0558766i
$15$	−1.17663	+	0.389702i	−0.303806	+	0.100621i
$16$	0.566532	−	3.21296i	0.141633	−	0.803241i
$17$	0.150378			0.0364719			0.0182360	−	0.999834i	$-0.494195\pi$
$17$	0.150378			0.0364719			0.0182360	+	0.999834i	$0.494195\pi$
$18$	0.123089	+	1.05579i	0.0290124	+	0.248853i
$19$	−5.71705			−1.31158			−0.655791	−	0.754943i	$-0.727665\pi$
$19$	−5.71705			−1.31158			−0.655791	+	0.754943i	$0.727665\pi$
$20$	−1.26051	+	0.458786i	−0.281858	+	0.102588i
$21$	4.56195	−	0.434288i	0.995499	−	0.0947693i
$22$	1.38102	−	1.15882i	0.294435	−	0.247060i
$23$	1.48618	+	8.42853i	0.309889	+	1.75747i	0.599546	+	0.800340i	$0.295348\pi$
$23$	1.48618	+	8.42853i	0.309889	+	1.75747i	−0.289657	+	0.957131i	$0.593541\pi$
$24$	0.344261	+	2.35267i	0.0702719	+	0.480236i
$25$	−3.43792	−	2.88476i	−0.687584	−	0.576952i
$26$	0.357502	+	0.619212i	0.0701119	+	0.121437i
$27$	2.19391	+	4.71028i	0.422218	+	0.906495i
$28$	4.92119	−	0.614114i	0.930017	−	0.116057i
$29$	−0.930281	+	5.27589i	−0.172749	+	0.979707i	0.767961	+	0.640496i	$0.221271\pi$
$29$	−0.930281	+	5.27589i	−0.172749	+	0.979707i	−0.940710	+	0.339211i	$0.889840\pi$
$30$	0.344531	−	0.272338i	0.0629025	−	0.0497218i
$31$	3.54974	−	2.97858i	0.637552	−	0.534969i	−0.265714	−	0.964052i	$-0.585608\pi$
$31$	3.54974	−	2.97858i	0.637552	−	0.534969i	0.903265	+	0.429083i	$0.141163\pi$
$32$	0.677491	+	3.84224i	0.119765	+	0.679219i
$33$	4.62767	−	7.50012i	0.805573	−	1.30560i
$34$	−0.0500677	+	0.0182232i	−0.00858654	+	0.00312525i
$35$	−1.14243	−	1.50985i	−0.193106	−	0.255210i
$36$	2.52229	+	5.02598i	0.420381	+	0.837664i
$37$	−2.68940	+	4.65817i	−0.442134	+	0.765799i	−0.997848	−	0.0655752i	$-0.979112\pi$
$37$	−2.68940	+	4.65817i	−0.442134	+	0.765799i	0.555714	+	0.831374i	$0.312445\pi$
$38$	1.90347	−	0.692808i	0.308784	−	0.112388i
$39$	2.61071	+	2.32402i	0.418048	+	0.372141i
$40$	0.752552	−	0.631466i	0.118989	−	0.0998436i
$41$	−0.573052	−	3.24994i	−0.0894957	−	0.507556i	−0.996296	−	0.0859942i	$-0.972593\pi$
$41$	−0.573052	−	3.24994i	−0.0894957	−	0.507556i	0.906800	−	0.421561i	$-0.138518\pi$
$42$	−1.46626	+	0.697424i	−0.226249	+	0.107615i
$43$	0.837375	+	0.702641i	0.127699	+	0.107152i	0.704400	−	0.709803i	$-0.251216\pi$
$43$	0.837375	+	0.702641i	0.127699	+	0.107152i	−0.576702	+	0.816955i	$0.695661\pi$
$44$	4.76875	−	8.25971i	0.718916	−	1.24520i
$45$	1.18025	−	1.79333i	0.175941	−	0.267333i
$46$	−1.51621	−	2.62615i	−0.223553	−	0.387205i
$47$	−0.865979	−	0.726643i	−0.126316	−	0.105992i	0.577441	−	0.816432i	$-0.304051\pi$
$47$	−0.865979	−	0.726643i	−0.126316	−	0.105992i	−0.703757	+	0.710441i	$0.748496\pi$
$48$	2.68117	+	4.97429i	0.386993	+	0.717977i
$49$	2.87239	+	6.38352i	0.410342	+	0.911932i
$50$	1.49423	+	0.543854i	0.211316	+	0.0769126i
$51$	−0.204334	+	0.161517i	−0.0286125	+	0.0226170i
$52$	2.89768	+	2.43144i	0.401835	+	0.337180i
$53$	−3.93191	+	6.81027i	−0.540089	+	0.935462i	0.458809	+	0.888535i	$0.348276\pi$
$53$	−3.93191	+	6.81027i	−0.540089	+	0.935462i	−0.998898	+	0.0469274i	$0.985057\pi$
$54$	−1.30126	−	1.30241i	−0.177079	−	0.177236i
$55$	−3.64116			−0.490974
$56$	−3.23290	+	1.65529i	−0.432014	+	0.221198i
$57$	7.76836	−	6.14056i	1.02894	−	0.813338i
$58$	−0.329612	−	1.86932i	−0.0432802	−	0.245454i
$59$	−1.52775	−	8.66431i	−0.198896	−	1.12800i	−0.906760	−	0.421648i	$-0.861452\pi$
$59$	−1.52775	−	8.66431i	−0.198896	−	1.12800i	0.707863	−	0.706349i	$-0.249659\pi$
$60$	1.22001	−	1.97728i	0.157503	−	0.255266i
$61$	−7.14771	−	5.99764i	−0.915170	−	0.767919i	0.0579255	−	0.998321i	$-0.481551\pi$
$61$	−7.14771	−	5.99764i	−0.915170	−	0.767919i	−0.973096	+	0.230402i	$0.925996\pi$
$62$	−0.820921	+	1.42188i	−0.104257	+	0.180578i
$63$	−5.73235	+	5.49001i	−0.722208	+	0.691676i
$64$	2.57135	+	4.45370i	0.321418	+	0.556713i
$65$	0.250768	−	1.42218i	0.0311039	−	0.176399i
$66$	−0.631882	+	3.05793i	−0.0777793	+	0.376405i
$67$	−2.45427	−	0.893282i	−0.299837	−	0.109132i	0.187721	−	0.982222i	$-0.439890\pi$
$67$	−2.45427	−	0.893282i	−0.299837	−	0.109132i	−0.487558	+	0.873091i	$0.662112\pi$
$68$	−0.215930	+	0.181187i	−0.0261854	+	0.0219721i
$69$	−11.0723	−	9.85647i	−1.33295	−	1.18658i
$70$	0.563336	+	0.364255i	0.0673315	+	0.0435368i
$71$	−0.174740	−	0.302658i	−0.0207378	−	0.0359189i	0.855470	−	0.517852i	$-0.173268\pi$
$71$	−0.174740	−	0.302658i	−0.0207378	−	0.0359189i	−0.876208	+	0.481933i	$0.839935\pi$
$72$	−2.99473	−	2.82705i	−0.352933	−	0.333172i
$73$	6.86264	+	11.8864i	0.803211	+	1.39120i	0.917492	+	0.397755i	$0.130210\pi$
$73$	6.86264	+	11.8864i	0.803211	+	1.39120i	−0.114280	+	0.993449i	$0.536456\pi$
$74$	0.330936	−	1.87683i	0.0384705	−	0.218177i
$75$	7.76993	+	0.227228i	0.897194	+	0.0262380i
$76$	8.20923	−	6.88836i	0.941663	−	0.790149i
$77$	13.1228	+	3.00236i	1.49549	+	0.342151i
$78$	−1.15086	−	0.457403i	−0.130309	−	0.0517907i
$79$	−5.81489	+	2.11645i	−0.654226	+	0.238119i	−0.647742	−	0.761860i	$-0.724286\pi$
$79$	−5.81489	+	2.11645i	−0.654226	+	0.238119i	−0.00648464	+	0.999979i	$0.502064\pi$
$80$	1.16736	−	2.02193i	0.130515	−	0.226059i
$81$	−8.04031	−	4.04393i	−0.893368	−	0.449326i
$82$	0.584633	+	1.01261i	0.0645619	+	0.111824i
$83$	−1.70577	+	9.67392i	−0.187233	+	1.06185i	0.735820	+	0.677177i	$0.236797\pi$
$83$	−1.70577	+	9.67392i	−0.187233	+	1.06185i	−0.923053	+	0.384673i	$0.874314\pi$
$84$	−6.02733	+	6.12021i	−0.657636	+	0.667769i
$85$	0.101123	+	0.0368059i	0.0109684	+	0.00399216i
$86$	−0.363949	−	0.132467i	−0.0392457	−	0.0142843i
$87$	−4.40265	−	8.16810i	−0.472013	−	0.875712i
$88$	−1.21291	+	6.87875i	−0.129297	+	0.733277i
$89$	13.4648			1.42726			0.713630	−	0.700522i	$-0.247050\pi$
$89$	13.4648			1.42726			0.713630	+	0.700522i	$0.247050\pi$
$90$	−0.175639	+	0.740108i	−0.0185140	+	0.0780142i
$91$	−2.07644	+	4.91878i	−0.217671	+	0.515629i
$92$	−12.2894	−	10.3120i	−1.28126	−	1.07510i
$93$	−1.62417	+	7.86002i	−0.168419	+	0.815046i
$94$	0.376382	+	0.136992i	0.0388208	+	0.0141296i
$95$	−3.84450	−	1.39928i	−0.394438	−	0.143564i
$96$	−5.04745	−	4.49318i	−0.515154	−	0.458584i
$97$	−12.7314	−	10.6829i	−1.29267	−	1.08468i	−0.991362	−	0.131155i	$-0.958131\pi$
$97$	−12.7314	−	10.6829i	−1.29267	−	1.08468i	−0.301311	−	0.953526i	$-0.597424\pi$
$98$	−1.72993	−	1.77729i	−0.174749	−	0.179533i
$99$	1.76762	+	15.1617i	0.177652	+	1.52381i
$100$	8.41237			0.841237
$101$	2.80080	−	15.8842i	0.278691	−	1.58053i	−0.448299	−	0.893884i	$-0.647970\pi$
$101$	2.80080	−	15.8842i	0.278691	−	1.58053i	0.726989	−	0.686649i	$-0.240919\pi$
$102$	0.0484592	−	0.0785384i	0.00479818	−	0.00777646i
$103$	−1.89680	−	0.690380i	−0.186898	−	0.0680252i	0.246876	−	0.969047i	$-0.420596\pi$
$103$	−1.89680	−	0.690380i	−0.186898	−	0.0680252i	−0.433774	+	0.901022i	$0.642818\pi$
$104$	−2.60319	−	0.947483i	−0.255264	−	0.0929083i
$105$	3.17404	+	0.824524i	0.309754	+	0.0804654i
$106$	0.483830	−	2.74394i	0.0469937	−	0.266515i
$107$	−3.88151	−	6.72298i	−0.375240	−	0.649935i	0.615123	−	0.788431i	$-0.289106\pi$
$107$	−3.88151	−	6.72298i	−0.375240	−	0.649935i	−0.990363	+	0.138496i	$0.955773\pi$
$108$	−8.82560	−	4.12020i	−0.849244	−	0.396466i
$109$	0.400182	−	0.693136i	0.0383305	−	0.0663904i	−0.846224	−	0.532828i	$-0.821129\pi$
$109$	0.400182	−	0.693136i	0.0383305	−	0.0663904i	0.884554	+	0.466437i	$0.154463\pi$
$110$	1.21231	−	0.441246i	0.115590	−	0.0420712i
$111$	−1.34888	−	9.21818i	−0.128030	−	0.874951i
$112$	−5.87442	+	6.32454i	−0.555080	+	0.597613i
$113$	−5.75537	+	4.82933i	−0.541420	+	0.454305i	−0.872023	−	0.489465i	$-0.837192\pi$
$113$	−5.75537	+	4.82933i	−0.541420	+	0.454305i	0.330603	+	0.943770i	$0.392748\pi$
$114$	−1.84232	+	2.98587i	−0.172549	+	0.279653i
$115$	−1.06354	+	6.03163i	−0.0991755	+	0.562452i
$116$	−5.02100	−	8.69663i	−0.466188	−	0.807462i
$117$	−6.04363	−	0.353789i	−0.558734	−	0.0327078i
$118$	1.55862	+	2.69962i	0.143483	+	0.248520i
$119$	−0.334102	−	0.216032i	−0.0306271	−	0.0198036i
$120$	−0.344328	+	1.66634i	−0.0314327	+	0.152115i
$121$	11.4056	−	9.57048i	1.03688	−	0.870043i
$122$	3.10662	+	1.13072i	0.281260	+	0.102370i
$123$	4.26936	+	3.80054i	0.384955	+	0.342683i
$124$	−1.50830	+	8.55402i	−0.135450	+	0.768173i
$125$	−3.39486	−	5.88007i	−0.303646	−	0.525930i
$126$	1.24327	−	2.52254i	0.110759	−	0.224726i
$127$	6.72543	−	11.6488i	0.596785	−	1.03366i	−0.396507	−	0.918032i	$-0.629778\pi$
$127$	6.72543	−	11.6488i	0.596785	−	1.03366i	0.993292	−	0.115631i	$-0.0368889\pi$
$128$	−7.37330	−	6.18694i	−0.651714	−	0.546853i
$129$	−1.89252	−	0.0553459i	−0.166627	−	0.00487294i
$130$	0.0888507	+	0.503898i	0.00779272	+	0.0441947i
$131$	0.467421	+	2.65088i	0.0408388	+	0.231608i	0.998395	−	0.0566393i	$-0.0180385\pi$
$131$	0.467421	+	2.65088i	0.0408388	+	0.231608i	−0.957556	+	0.288248i	$0.906927\pi$
$132$	2.39178	+	16.3454i	0.208178	+	1.42268i
$133$	12.7019	+	8.21308i	1.10139	+	0.712165i
$134$	0.925393			0.0799417
$135$	0.322448	+	3.70446i	0.0277519	+	0.318829i
$136$	0.103217	−	0.178778i	0.00885083	−	0.0153301i
$137$	15.5520	+	13.0497i	1.32870	+	1.11491i	0.984380	+	0.176057i	$0.0563344\pi$
$137$	15.5520	+	13.0497i	1.32870	+	1.11491i	0.344318	+	0.938853i	$0.388110\pi$
$138$	4.88093	+	1.93990i	0.415493	+	0.165136i
$139$	5.28030	+	1.92187i	0.447869	+	0.163011i	0.556101	−	0.831115i	$-0.312297\pi$
$139$	5.28030	+	1.92187i	0.447869	+	0.163011i	−0.108232	+	0.994126i	$0.534519\pi$
$140$	3.45962	+	0.791524i	0.292392	+	0.0668960i
$141$	1.95717	+	0.0572365i	0.164823	+	0.00482018i
$142$	0.0948560	+	0.0795936i	0.00796014	+	0.00667935i
$143$	5.13390	+	8.89217i	0.429318	+	0.743601i
$144$	−8.98597	−	3.87931i	−0.748831	−	0.323276i
$145$	−1.91689	+	3.32014i	−0.159189	+	0.275723i
$146$	−3.72533	−	3.12592i	−0.308310	−	0.258703i
$147$	−10.7594	−	5.58879i	−0.887423	−	0.460956i
$148$	−1.75078	−	9.92917i	−0.143913	−	0.816172i
$149$	−1.93670	+	1.62508i	−0.158661	+	0.133132i	−0.718662	−	0.695360i	$-0.755245\pi$
$149$	−1.93670	+	1.62508i	−0.158661	+	0.133132i	0.560001	+	0.828492i	$0.310801\pi$
$150$	−2.61451	+	0.865926i	−0.213474	+	0.0707026i
$151$	11.7355	−	4.27138i	0.955022	−	0.347600i	0.182941	−	0.983124i	$-0.441438\pi$
$151$	11.7355	−	4.27138i	0.955022	−	0.347600i	0.772081	+	0.635524i	$0.219216\pi$
$152$	−3.92412	+	6.79677i	−0.318288	+	0.551291i
$153$	0.104168	−	0.438942i	0.00842146	−	0.0354863i
$154$	−4.73304	+	0.590635i	−0.381399	+	0.0475947i
$155$	3.11609	−	1.13417i	0.250291	−	0.0910983i
$156$	−6.54894	−	0.191521i	−0.524335	−	0.0153339i
$157$	−0.371726	−	2.10816i	−0.0296669	−	0.168250i	0.966375	−	0.257138i	$-0.0827796\pi$
$157$	−0.371726	−	2.10816i	−0.0296669	−	0.168250i	−0.996042	+	0.0888887i	$0.971668\pi$
$158$	1.67957	−	1.40933i	0.133620	−	0.112120i
$159$	−1.97206	−	13.4770i	−0.156395	−	1.06880i
$160$	−0.484826	+	2.74959i	−0.0383289	+	0.217374i
$161$	8.80646	−	20.8612i	0.694046	−	1.64409i
$162$	3.16705	+	0.372068i	0.248827	+	0.0292324i
$163$	1.46087	+	2.53031i	0.114425	+	0.198189i	0.917550	−	0.397621i	$-0.130164\pi$
$163$	1.46087	+	2.53031i	0.114425	+	0.198189i	−0.803125	+	0.595811i	$0.796831\pi$
$164$	4.73865	+	3.97620i	0.370026	+	0.310489i
$165$	4.94763	−	3.91090i	0.385173	−	0.304463i
$166$	−0.604380	−	3.42761i	−0.0469090	−	0.266034i
$167$	3.37327	−	2.83051i	0.261031	−	0.219031i	−0.502874	−	0.864360i	$-0.667724\pi$
$167$	3.37327	−	2.83051i	0.261031	−	0.219031i	0.763905	+	0.645329i	$0.223280\pi$
$168$	2.61497	−	5.72161i	0.201749	−	0.441432i
$169$	8.38930	−	3.05346i	0.645331	−	0.234881i
$170$	−0.0381289			−0.00292435
$171$	−3.96025	+	16.6877i	−0.302848	+	1.27614i
$172$	−2.04900			−0.156235
$173$	−1.50348	+	8.52665i	−0.114307	+	0.648269i	0.872783	+	0.488108i	$0.162313\pi$
$173$	−1.50348	+	8.52665i	−0.114307	+	0.648269i	−0.987091	+	0.160162i	$0.948798\pi$
$174$	2.45568	+	2.18602i	0.186165	+	0.165722i
$175$	3.49399	+	11.3481i	0.264121	+	0.857838i
$176$	2.88259	+	16.3480i	0.217283	+	1.23227i
$177$	11.3821	+	10.1322i	0.855529	+	0.761582i
$178$	−4.48304	+	1.63169i	−0.336018	+	0.122301i
$179$	−1.56390			−0.116891			−0.0584456	−	0.998291i	$-0.518614\pi$
$179$	−1.56390			−0.116891			−0.0584456	+	0.998291i	$0.518614\pi$
$180$	0.466004	+	3.99713i	0.0347339	+	0.297929i
$181$	−7.11167	+	12.3178i	−0.528606	+	0.915573i	0.470838	+	0.882220i	$0.343952\pi$
$181$	−7.11167	+	12.3178i	−0.528606	+	0.915573i	−0.999444	+	0.0333526i	$0.989382\pi$
$182$	0.0952741	−	1.88932i	0.00706219	−	0.140046i
$183$	16.1543	+	0.472424i	1.19416	+	0.0349226i
$184$	11.0404	+	4.01839i	0.813912	+	0.296240i
$185$	−2.94864	+	2.47420i	−0.216788	+	0.181907i
$186$	−0.411736	−	2.81379i	−0.0301899	−	0.206317i
$187$	−0.718996	+	0.261693i	−0.0525782	+	0.0191369i
$188$	2.11900			0.154544
$189$	1.89244	−	13.6169i	0.137655	−	0.990480i
$190$	1.44958			0.105164
$191$	−18.1815	+	6.61754i	−1.31557	+	0.478828i	−0.902036	−	0.431661i	$-0.857928\pi$
$191$	−18.1815	+	6.61754i	−1.31557	+	0.478828i	−0.413533	+	0.910489i	$0.635705\pi$
$192$	−8.27759	−	3.28989i	−0.597383	−	0.237427i
$193$	−2.15662	+	1.80962i	−0.155237	+	0.130259i	−0.717098	−	0.696972i	$-0.754530\pi$
$193$	−2.15662	+	1.80962i	−0.155237	+	0.130259i	0.561861	+	0.827232i	$0.310086\pi$
$194$	5.53344	+	2.01401i	0.397278	+	0.144597i
$195$	1.18678	+	2.20181i	0.0849874	+	0.157675i
$196$	−11.8159	−	5.70534i	−0.843994	−	0.407524i
$197$	−0.826620	+	1.43175i	−0.0588943	+	0.102008i	−0.893969	−	0.448128i	$-0.852091\pi$
$197$	−0.826620	+	1.43175i	−0.0588943	+	0.102008i	0.835075	+	0.550136i	$0.185424\pi$
$198$	−2.42586	−	4.83383i	−0.172398	−	0.343525i
$199$	5.95513			0.422148			0.211074	−	0.977470i	$-0.432304\pi$
$199$	5.95513			0.422148			0.211074	+	0.977470i	$0.432304\pi$
$200$	−5.78933	+	2.10714i	−0.409367	+	0.148997i
$201$	4.29434	−	1.42229i	0.302899	−	0.100320i
$202$	0.992366	+	5.62799i	0.0698226	+	0.395984i
$203$	9.64616	−	10.3853i	0.677028	−	0.728904i
$204$	0.0987982	−	0.478124i	0.00691725	−	0.0334754i
$205$	0.410088	−	2.32572i	0.0286418	−	0.162435i
$206$	0.715197			0.0498301
$207$	25.6318	+	1.50046i	1.78153	+	0.104289i
$208$	−6.58375			−0.456501
$209$	27.3348	−	9.94905i	1.89079	−	0.688190i
$210$	−1.15670	+	0.110116i	−0.0798201	+	0.00759870i
$211$	−8.68441	+	7.28708i	−0.597859	+	0.501664i	−0.890757	−	0.454480i	$-0.849825\pi$
$211$	−8.68441	+	7.28708i	−0.597859	+	0.501664i	0.292897	+	0.956144i	$0.405381\pi$
$212$	−2.55965	−	14.5165i	−0.175797	−	0.996997i
$213$	0.562517	+	0.223570i	0.0385430	+	0.0153187i
$214$	2.10705	+	1.76802i	0.144035	+	0.120859i
$215$	0.391128	+	0.677453i	0.0266747	+	0.0462019i
$216$	7.10574	+	0.624838i	0.483485	+	0.0425148i
$217$	−12.1657	+	1.51815i	−0.825859	+	0.103059i
$218$	−0.0492433	+	0.279273i	−0.00333518	+	0.0189147i
$219$	−22.0920	−	8.78035i	−1.49284	−	0.593321i
$220$	5.22842	−	4.38717i	0.352500	−	0.295783i
$221$	−0.0526954	−	0.298850i	−0.00354468	−	0.0201029i
$222$	1.56619	+	2.90570i	0.105116	+	0.195018i
$223$	13.1147	−	4.77338i	0.878228	−	0.319649i	0.136734	−	0.990608i	$-0.456340\pi$
$223$	13.1147	−	4.77338i	0.878228	−	0.319649i	0.741494	+	0.670959i	$0.234117\pi$
$224$	4.01453	−	9.50980i	0.268232	−	0.635401i
$225$	−10.8019	+	8.03676i	−0.720126	+	0.535784i
$226$	1.33100	−	2.30536i	0.0885369	−	0.153350i
$227$	−0.536041	+	0.195103i	−0.0355783	+	0.0129494i	−0.359748	−	0.933050i	$-0.617137\pi$
$227$	−0.536041	+	0.195103i	−0.0355783	+	0.0129494i	0.324170	+	0.945999i	$0.394915\pi$
$228$	−3.75611	+	18.1773i	−0.248754	+	1.20382i
$229$	−9.04394	+	7.58877i	−0.597640	+	0.501480i	−0.890686	−	0.454619i	$-0.849776\pi$
$229$	−9.04394	+	7.58877i	−0.597640	+	0.501480i	0.293046	+	0.956098i	$0.405331\pi$
$230$	−0.376827	−	2.13709i	−0.0248472	−	0.140916i
$231$	−21.0562	+	10.0153i	−1.38539	+	0.658961i
$232$	5.63376	+	4.72728i	0.369874	+	0.310361i
$233$	−0.303597	+	0.525845i	−0.0198893	+	0.0344492i	−0.875799	−	0.482676i	$-0.839665\pi$
$233$	−0.303597	+	0.525845i	−0.0198893	+	0.0344492i	0.855909	+	0.517126i	$0.172998\pi$
$234$	2.05508	−	0.614591i	0.134345	−	0.0401770i
$235$	−0.404488	−	0.700594i	−0.0263859	−	0.0457017i
$236$	12.6332	+	10.6005i	0.822351	+	0.690034i
$237$	5.62808	−	9.12149i	0.365583	−	0.592505i
$238$	0.137417	+	0.0314396i	0.00890745	+	0.00203793i
$239$	−26.4949	−	9.64335i	−1.71381	−	0.623776i	−0.716536	−	0.697550i	$-0.754273\pi$
$239$	−26.4949	−	9.64335i	−1.71381	−	0.623776i	−0.997275	+	0.0737740i	$0.976496\pi$
$240$	0.585496	+	4.00126i	0.0377936	+	0.258280i
$241$	−15.7579	−	13.2225i	−1.01506	−	0.851733i	−0.0260580	−	0.999660i	$-0.508295\pi$
$241$	−15.7579	−	13.2225i	−1.01506	−	0.851733i	−0.988998	+	0.147927i	$0.952740\pi$
$242$	−2.63770	+	4.56863i	−0.169558	+	0.293682i
$243$	15.2687	−	3.14101i	0.979489	−	0.201496i
$244$	17.4900			1.11968
$245$	0.369169	+	4.99572i	0.0235853	+	0.319165i
$246$	−1.88203	−	0.748003i	−0.119994	−	0.0476910i
$247$	2.00337	+	11.3617i	0.127472	+	0.722927i
$248$	−1.10462	−	6.26461i	−0.0701434	−	0.397803i
$249$	−8.07274	−	14.9771i	−0.511589	−	0.949136i
$250$	1.84287	+	1.54635i	0.116553	+	0.0977999i
$251$	−11.6654	+	20.2050i	−0.736311	+	1.27533i	0.217834	+	0.975986i	$0.430101\pi$
$251$	−11.6654	+	20.2050i	−0.736311	+	1.27533i	−0.954146	+	0.299343i	$0.903233\pi$
$252$	1.61639	−	14.7900i	0.101823	−	0.931683i
$253$	−21.7735	−	37.7128i	−1.36889	−	2.37098i
$254$	−0.827578	+	4.69343i	−0.0519269	+	0.294492i
$255$	−0.176939	+	0.0586024i	−0.0110804	+	0.00366982i
$256$	−6.46043	−	2.35140i	−0.403777	−	0.146963i
$257$	−9.85324	+	8.26785i	−0.614628	+	0.515734i	−0.896110	−	0.443832i	$-0.853619\pi$
$257$	−9.85324	+	8.26785i	−0.614628	+	0.515734i	0.281482	+	0.959567i	$0.409174\pi$
$258$	0.636816	−	0.210914i	0.0396464	−	0.0131309i
$259$	12.6671	−	6.48574i	0.787094	−	0.403005i
$260$	1.35347	+	2.34428i	0.0839386	+	0.145386i
$261$	14.7555	+	6.37007i	0.913344	+	0.394298i
$262$	−0.476867	−	0.825958i	−0.0294609	−	0.0510278i
$263$	0.398867	−	2.26209i	0.0245952	−	0.139486i	−0.970037	−	0.242955i	$-0.921883\pi$
$263$	0.398867	−	2.26209i	0.0245952	−	0.139486i	0.994633	+	0.103469i	$0.0329943\pi$
$264$	−5.74021	−	10.6496i	−0.353286	−	0.655440i
$265$	−4.31092	+	3.61729i	−0.264818	+	0.222208i
$266$	−5.22433	−	1.19527i	−0.320325	−	0.0732867i
$267$	−18.2960	+	14.4622i	−1.11970	+	0.885073i
$268$	4.60044	−	1.67442i	0.281017	−	0.102282i
$269$	−13.5740	+	23.5109i	−0.827623	+	1.43349i	0.0722750	+	0.997385i	$0.476974\pi$
$269$	−13.5740	+	23.5109i	−0.827623	+	1.43349i	−0.899898	+	0.436100i	$0.856359\pi$
$270$	−0.556275	−	1.19431i	−0.0338538	−	0.0726836i
$271$	−6.12956	−	10.6167i	−0.372344	−	0.644919i	0.617581	−	0.786507i	$-0.288113\pi$
$271$	−6.12956	−	10.6167i	−0.372344	−	0.644919i	−0.989926	+	0.141588i	$0.954779\pi$
$272$	0.0851937	−	0.483157i	0.00516563	−	0.0292957i
$273$	−2.46168	−	8.91394i	−0.148987	−	0.539496i
$274$	−6.75939	−	2.46022i	−0.408350	−	0.148627i
$275$	21.4578	+	7.81001i	1.29396	+	0.470961i
$276$	27.7749	+	0.812263i	1.67185	+	0.0488925i
$277$	2.34696	−	13.3103i	0.141015	−	0.799736i	−0.829466	−	0.558557i	$-0.811355\pi$
$277$	2.34696	−	13.3103i	0.141015	−	0.799736i	0.970481	−	0.241178i	$-0.0775338\pi$
$278$	−1.99096			−0.119410
$279$	−6.23535	−	12.4247i	−0.373300	−	0.743849i
$280$	−2.57915	+	0.321851i	−0.154134	+	0.0192343i
$281$	−22.8526	−	19.1756i	−1.36327	−	1.14392i	−0.974957	−	0.222394i	$-0.928613\pi$
$281$	−22.8526	−	19.1756i	−1.36327	−	1.14392i	−0.388315	−	0.921527i	$-0.626943\pi$
$282$	−0.658569	+	0.218118i	−0.0392172	+	0.0129888i
$283$	−0.726887	−	0.264565i	−0.0432089	−	0.0157268i	0.320325	−	0.947308i	$-0.396208\pi$
$283$	−0.726887	−	0.264565i	−0.0432089	−	0.0157268i	−0.363534	+	0.931581i	$0.618430\pi$
$284$	0.615580	+	0.224053i	0.0365279	+	0.0132951i
$285$	6.72688	−	2.22794i	0.398466	−	0.131972i
$286$	−2.78689	−	2.33848i	−0.164792	−	0.138277i
$287$	−3.39567	+	8.04382i	−0.200440	+	0.474812i
$288$	11.6845	+	0.684003i	0.688518	+	0.0403053i
$289$	−16.9774			−0.998670
$290$	0.235877	−	1.33772i	0.0138512	−	0.0785539i
$291$	28.7737	+	0.841473i	1.68674	+	0.0493280i
$292$	−24.1760	−	8.79933i	−1.41479	−	0.514942i
$293$	3.09760	+	1.12743i	0.180964	+	0.0658654i	0.430913	−	0.902394i	$-0.358192\pi$
$293$	3.09760	+	1.12743i	0.180964	+	0.0658654i	−0.249949	+	0.968259i	$0.580414\pi$
$294$	4.25958	+	0.556913i	0.248424	+	0.0324798i
$295$	1.09329	−	6.20035i	0.0636538	−	0.360999i
$296$	3.69194	+	6.39463i	0.214590	+	0.371681i
$297$	−18.6867	−	18.7032i	−1.08431	−	1.08527i
$298$	0.447885	−	0.775760i	0.0259453	−	0.0449386i
$299$	16.2295	−	5.90706i	0.938578	−	0.341614i
$300$	−11.4308	+	9.03555i	−0.659957	+	0.521668i
$301$	−0.851032	−	2.76407i	−0.0490527	−	0.159318i
$302$	−3.38968	+	2.84428i	−0.195054	+	0.163670i
$303$	13.2551	+	24.5918i	0.761485	+	1.41276i
$304$	−3.23889	+	18.3687i	−0.185763	+	1.05352i
$305$	−3.33861	−	5.78263i	−0.191168	−	0.331113i
$306$	0.0185098	+	0.158768i	0.00105814	+	0.00907613i
$307$	0.162431	+	0.281338i	0.00927040	+	0.0160568i	0.870623	−	0.491950i	$-0.163716\pi$
$307$	0.162431	+	0.281338i	0.00927040	+	0.0160568i	−0.861353	+	0.508007i	$0.830382\pi$
$308$	−22.4608	+	11.5003i	−1.27983	+	0.655290i
$309$	3.31891	−	1.09923i	0.188806	−	0.0625327i
$310$	−0.900052	+	0.755233i	−0.0511195	+	0.0428944i
$311$	−11.4238	−	4.15792i	−0.647784	−	0.235774i	−0.00283086	−	0.999996i	$-0.500901\pi$
$311$	−11.4238	−	4.15792i	−0.647784	−	0.235774i	−0.644954	+	0.764222i	$0.723123\pi$
$312$	4.55490	−	1.50858i	0.257870	−	0.0854068i
$313$	−4.60076	+	26.0922i	−0.260050	+	1.47482i	0.522718	+	0.852506i	$0.324918\pi$
$313$	−4.60076	+	26.0922i	−0.260050	+	1.47482i	−0.782768	+	0.622313i	$0.786193\pi$
$314$	0.379238	+	0.656859i	0.0214016	+	0.0370687i
$315$	−5.19850	+	2.28880i	−0.292903	+	0.128959i
$316$	5.79966	−	10.0453i	0.326256	−	0.565092i
$317$	9.02799	+	7.57538i	0.507062	+	0.425476i	0.860094	−	0.510136i	$-0.170405\pi$
$317$	9.02799	+	7.57538i	0.507062	+	0.425476i	−0.353032	+	0.935611i	$0.614849\pi$
$318$	2.28977	+	4.24815i	0.128404	+	0.238224i
$319$	−4.73339	−	26.8444i	−0.265019	−	1.50300i
$320$	0.639062	+	3.62430i	0.0357247	+	0.202605i
$321$	12.4952	+	4.96617i	0.697416	+	0.277185i
$322$	−0.404069	+	8.01285i	−0.0225179	+	0.446539i
$323$	−0.859716			−0.0478359
$324$	16.4177	−	3.88085i	0.912095	−	0.215603i
$325$	−4.52826	+	7.84318i	−0.251183	+	0.435061i
$326$	−0.793023	−	0.665426i	−0.0439215	−	0.0368545i
$327$	0.200713	+	1.37167i	0.0110994	+	0.0758533i
$328$	−4.25706	−	1.54944i	−0.235057	−	0.0855537i
$329$	0.880103	+	2.85848i	0.0485216	+	0.157593i
$330$	−1.17337	+	1.90169i	−0.0645917	+	0.104684i
$331$	4.09341	+	3.43478i	0.224994	+	0.188793i	0.748316	−	0.663343i	$-0.230863\pi$
$331$	4.09341	+	3.43478i	0.224994	+	0.188793i	−0.523321	+	0.852135i	$0.675307\pi$
$332$	−9.20656	−	15.9462i	−0.505276	−	0.875163i
$333$	11.7339	+	11.0769i	0.643014	+	0.607011i
$334$	−0.780110	+	1.35119i	−0.0426857	+	0.0739339i
$335$	−1.43177	−	1.20140i	−0.0782260	−	0.0656394i
$336$	1.18914	−	14.9034i	0.0648730	−	0.813048i
$337$	3.67481	+	20.8409i	0.200180	+	1.13527i	0.904847	+	0.425737i	$0.139985\pi$
$337$	3.67481	+	20.8409i	0.200180	+	1.13527i	−0.704667	+	0.709538i	$0.748904\pi$
$338$	−2.42316	+	2.03328i	−0.131803	+	0.110596i
$339$	2.63335	−	12.7439i	0.143024	−	0.692151i
$340$	−0.189552	+	0.0689912i	−0.0102799	+	0.00374157i
$341$	−11.7888	+	20.4188i	−0.638400	+	1.10574i
$342$	−0.703706	−	6.03602i	−0.0380521	−	0.326391i
$343$	2.78878	−	18.3091i	0.150580	−	0.988598i
$344$	1.41011	−	0.513237i	0.0760279	−	0.0276719i
$345$	−5.03330	−	9.33813i	−0.270984	−	0.502748i
$346$	−0.532704	−	3.02112i	−0.0286384	−	0.162416i
$347$	−2.04113	+	1.71271i	−0.109573	+	0.0919430i	−0.695928	−	0.718111i	$-0.745007\pi$
$347$	−2.04113	+	1.71271i	−0.109573	+	0.0919430i	0.586355	+	0.810054i	$0.300562\pi$
$348$	16.1634	+	6.42408i	0.866451	+	0.344367i
$349$	0.406133	−	2.30330i	0.0217398	−	0.123293i	−0.972007	−	0.234954i	$-0.924506\pi$
$349$	0.406133	−	2.30330i	0.0217398	−	0.123293i	0.993746	+	0.111661i	$0.0356172\pi$
$350$	−2.53851	−	3.35491i	−0.135689	−	0.179328i
$351$	8.59212	−	6.01061i	0.458613	−	0.320822i
$352$	−9.92570	−	17.1918i	−0.529042	−	0.916327i
$353$	20.2826	+	17.0191i	1.07954	+	0.905838i	0.995882	−	0.0906571i	$-0.0288967\pi$
$353$	20.2826	+	17.0191i	1.07954	+	0.905838i	0.0836533	+	0.996495i	$0.473341\pi$
$354$	−5.01747	−	1.99417i	−0.266676	−	0.105989i
$355$	−0.0434285	−	0.246295i	−0.00230494	−	0.0130720i
$356$	−19.3343	+	16.2234i	−1.02472	+	0.859839i
$357$	0.686015	−	0.0653071i	0.0363078	−	0.00345642i
$358$	0.520695	−	0.189517i	0.0275196	−	0.0100163i
$359$	−12.6188			−0.665993			−0.332996	−	0.942928i	$-0.608060\pi$
$359$	−12.6188			−0.665993			−0.332996	+	0.942928i	$0.608060\pi$
$360$	−1.32191	−	2.63407i	−0.0696706	−	0.138828i
$361$	13.6847			0.720245
$362$	0.875106	−	4.96297i	0.0459945	−	0.260848i
$363$	−5.21862	+	25.2550i	−0.273906	+	1.32554i
$364$	−2.94494	−	9.56485i	−0.154357	−	0.501334i
$365$	1.70559	+	9.67287i	0.0892745	+	0.506301i
$366$	−5.43577	+	1.80033i	−0.284132	+	0.0941046i
$367$	−12.5033	+	4.55083i	−0.652668	+	0.237552i	−0.647067	−	0.762433i	$-0.724005\pi$
$367$	−12.5033	+	4.55083i	−0.652668	+	0.237552i	−0.00560008	+	0.999984i	$0.501783\pi$
$368$	27.9225			1.45556
$369$	−9.88331	−	0.578560i	−0.514505	−	0.0301186i
$370$	0.681909	−	1.18110i	0.0354507	−	0.0614025i
$371$	18.5193	−	9.48219i	0.961476	−	0.492291i
$372$	−7.13820	−	13.2433i	−0.370098	−	0.686633i
$373$	−10.0006	−	3.63990i	−0.517809	−	0.188467i	0.0698778	−	0.997556i	$-0.477739\pi$
$373$	−10.0006	−	3.63990i	−0.517809	−	0.188467i	−0.587687	+	0.809088i	$0.699961\pi$
$374$	0.207675	−	0.174260i	0.0107386	−	0.00901076i
$375$	10.9286	+	4.34353i	0.564351	+	0.224299i
$376$	−1.45828	+	0.530769i	−0.0752048	+	0.0273723i
$377$	10.8109			0.556792
$378$	1.02004	+	4.76302i	0.0524654	+	0.244983i
$379$	9.30276			0.477851			0.238925	−	0.971038i	$-0.423205\pi$
$379$	9.30276			0.477851			0.238925	+	0.971038i	$0.423205\pi$
$380$	7.20637	−	2.62290i	0.369679	−	0.134552i
$381$	3.37316	+	23.0521i	0.172812	+	1.18099i
$382$	5.25155	−	4.40657i	0.268693	−	0.225460i
$383$	−11.0428	−	4.01926i	−0.564263	−	0.205375i	0.0441096	−	0.999027i	$-0.485955\pi$
$383$	−11.0428	−	4.01926i	−0.564263	−	0.205375i	−0.608372	+	0.793652i	$0.708177\pi$
$384$	16.6641	+	0.487335i	0.850389	+	0.0248692i
$385$	8.08977	+	5.23088i	0.412293	+	0.266590i
$386$	0.498745	−	0.863851i	0.0253854	−	0.0439689i
$387$	2.63102	−	1.95751i	0.133742	−	0.0995061i
$388$	31.1528			1.58154
$389$	13.3171	−	4.84704i	0.675206	−	0.245755i	0.0184180	−	0.999830i	$-0.494137\pi$
$389$	13.3171	−	4.84704i	0.675206	−	0.245755i	0.656788	+	0.754076i	$0.271915\pi$
$390$	−0.661957	−	0.589266i	−0.0335195	−	0.0298387i
$391$	0.223488	+	1.26746i	0.0113023	+	0.0640983i
$392$	9.56070	+	0.966706i	0.482888	+	0.0488260i
$393$	−3.48239	−	3.09998i	−0.175663	−	0.156373i
$394$	0.101717	−	0.576868i	0.00512445	−	0.0290622i
$395$	−4.42831			−0.222812
$396$	−20.8062	−	19.6412i	−1.04555	−	0.987008i
$397$	30.5582			1.53367			0.766837	−	0.641842i	$-0.221829\pi$
$397$	30.5582			1.53367			0.766837	+	0.641842i	$0.221829\pi$
$398$	−1.98274	+	0.721659i	−0.0993859	+	0.0361735i
$399$	−26.0809	+	2.48284i	−1.30568	+	0.124298i
$400$	−11.2163	+	9.41161i	−0.560816	+	0.470580i
$401$	−6.52419	−	37.0005i	−0.325803	−	1.84772i	−0.503974	−	0.863719i	$-0.668129\pi$
$401$	−6.52419	−	37.0005i	−0.325803	−	1.84772i	0.178171	−	0.983999i	$-0.442982\pi$
$402$	−1.25743	+	0.993945i	−0.0627149	+	0.0495735i
$403$	−7.16334	−	6.01076i	−0.356831	−	0.299417i
$404$	15.1168	+	26.1830i	0.752088	+	1.30265i
$405$	−4.41703	−	4.68731i	−0.219484	−	0.232914i
$406$	−1.95314	+	4.62670i	−0.0969328	+	0.229619i
$407$	4.75240	−	26.9522i	0.235568	−	1.33597i
$408$	0.0517691	+	0.353788i	0.00256295	+	0.0175151i
$409$	9.32825	−	7.82733i	0.461252	−	0.387037i	−0.382339	−	0.924022i	$-0.624881\pi$
$409$	9.32825	−	7.82733i	0.461252	−	0.387037i	0.843592	+	0.536985i	$0.180437\pi$
$410$	0.145300	+	0.824037i	0.00717585	+	0.0406963i
$411$	−35.1486	−	1.02790i	−1.73375	−	0.0507027i
$412$	3.55549	−	1.29409i	0.175166	−	0.0637553i
$413$	−9.05281	+	21.4447i	−0.445460	+	1.05523i
$414$	−8.71585	+	2.60656i	−0.428361	+	0.128105i
$415$	−3.51482	+	6.08785i	−0.172536	+	0.298841i
$416$	7.39842	−	2.69280i	0.362737	−	0.132026i
$417$	−9.23914	+	3.06001i	−0.452443	+	0.149849i
$418$	−7.89537	+	6.62501i	−0.386175	+	0.324040i
$419$	−4.74992	−	26.9381i	−0.232049	−	1.31601i	−0.848741	−	0.528809i	$-0.822639\pi$
$419$	−4.74992	−	26.9381i	−0.232049	−	1.31601i	0.616692	−	0.787204i	$-0.288472\pi$
$420$	−5.55112	+	2.64038i	−0.270867	+	0.128837i
$421$	16.1084	+	13.5166i	0.785075	+	0.658757i	0.944521	−	0.328450i	$-0.106526\pi$
$421$	16.1084	+	13.5166i	0.785075	+	0.658757i	−0.159446	+	0.987207i	$0.550971\pi$
$422$	2.00838	−	3.47861i	0.0977663	−	0.169336i
$423$	−2.72089	+	2.02438i	−0.132294	+	0.0984288i
$424$	5.39764	+	9.34899i	0.262133	+	0.454027i
$425$	−0.516986	−	0.433803i	−0.0250775	−	0.0210425i
$426$	−0.214381	−	0.00626946i	−0.0103868	−	0.000303757i
$427$	7.26428	+	23.5936i	0.351543	+	1.14178i
$428$	13.6739	+	4.97691i	0.660955	+	0.240568i
$429$	−16.5269	−	6.56853i	−0.797925	−	0.317131i
$430$	−0.212320	−	0.178158i	−0.0102390	−	0.00859153i
$431$	−2.96128	+	5.12909i	−0.142640	+	0.247060i	−0.928490	−	0.371358i	$-0.878892\pi$
$431$	−2.96128	+	5.12909i	−0.142640	+	0.247060i	0.785850	+	0.618417i	$0.212226\pi$
$432$	16.3769	−	4.38041i	0.787933	−	0.210753i
$433$	−24.0751			−1.15698			−0.578488	−	0.815691i	$-0.696357\pi$
$433$	−24.0751			−1.15698			−0.578488	+	0.815691i	$0.696357\pi$
$434$	3.86654	−	1.97973i	0.185600	−	0.0950301i
$435$	−0.961421	−	6.57032i	−0.0460966	−	0.315023i
$436$	0.260516	+	1.47746i	0.0124765	+	0.0707575i
$437$	−8.49655	−	48.1863i	−0.406445	−	2.30507i
$438$	8.41948	+	0.246224i	0.402298	+	0.0117650i
$439$	13.4427	+	11.2797i	0.641584	+	0.538353i	0.904504	−	0.426465i	$-0.140241\pi$
$439$	13.4427	+	11.2797i	0.641584	+	0.538353i	−0.262920	+	0.964818i	$0.584686\pi$
$440$	−2.49925	+	4.32884i	−0.119147	+	0.206369i
$441$	20.6228	−	3.96240i	0.982038	−	0.188686i
$442$	0.0537603	+	0.0931155i	0.00255712	+	0.00442905i
$443$	−3.52462	+	19.9891i	−0.167460	+	0.949711i	0.779032	+	0.626984i	$0.215711\pi$
$443$	−3.52462	+	19.9891i	−0.167460	+	0.949711i	−0.946492	+	0.322727i	$0.895400\pi$
$444$	13.0437	+	11.6113i	0.619026	+	0.551050i
$445$	9.05454	+	3.29558i	0.429226	+	0.156226i
$446$	−3.78806	+	3.17856i	−0.179370	+	0.150509i
$447$	0.886130	−	4.28834i	0.0419125	−	0.202832i
$448$	0.685262	−	13.5890i	0.0323756	−	0.642021i
$449$	17.5137	+	30.3347i	0.826525	+	1.43158i	0.900748	+	0.434341i	$0.143019\pi$
$449$	17.5137	+	30.3347i	0.826525	+	1.43158i	−0.0742237	+	0.997242i	$0.523648\pi$
$450$	2.62254	−	3.98481i	0.123628	−	0.187846i
$451$	8.39560	+	14.5416i	0.395333	+	0.684738i
$452$	2.44549	−	13.8691i	0.115026	−	0.652346i
$453$	−11.3585	+	18.4088i	−0.533668	+	0.864923i
$454$	0.154830	−	0.129918i	0.00726653	−	0.00609734i
$455$	−2.60024	+	2.79947i	−0.121901	+	0.131241i
$456$	−1.96816	−	13.4503i	−0.0921674	−	0.629869i
$457$	18.4173	−	6.70333i	0.861523	−	0.313569i	0.126793	−	0.991929i	$-0.459531\pi$
$457$	18.4173	−	6.70333i	0.861523	−	0.313569i	0.734729	+	0.678361i	$0.237309\pi$
$458$	2.09152	−	3.62262i	0.0977305	−	0.169274i
$459$	0.329914	+	0.708321i	0.0153991	+	0.0330616i
$460$	−5.74023	−	9.94237i	−0.267640	−	0.463565i
$461$	−4.07687	+	23.1211i	−0.189879	+	1.07686i	0.729647	+	0.683825i	$0.239685\pi$
$461$	−4.07687	+	23.1211i	−0.189879	+	1.07686i	−0.919525	+	0.393031i	$0.871426\pi$
$462$	5.79690	−	5.88622i	0.269696	−	0.273852i
$463$	−16.7390	−	6.09249i	−0.777927	−	0.283142i	−0.0776189	−	0.996983i	$-0.524732\pi$
$463$	−16.7390	−	6.09249i	−0.777927	−	0.283142i	−0.700308	+	0.713841i	$0.746954\pi$
$464$	16.4242	+	5.97792i	0.762474	+	0.277518i
$465$	−3.01598	+	4.88804i	−0.139863	+	0.226677i
$466$	0.0373582	−	0.211869i	0.00173059	−	0.00981464i
$467$	23.0193			1.06520			0.532602	−	0.846366i	$-0.321214\pi$
$467$	23.0193			1.06520			0.532602	+	0.846366i	$0.321214\pi$
$468$	9.10445	−	6.77384i	0.420853	−	0.313121i
$469$	4.16951	+	5.51045i	0.192530	+	0.254449i
$470$	0.219573	+	0.184244i	0.0101281	+	0.00849852i
$471$	2.76944	+	2.46532i	0.127609	+	0.113596i
$472$	−11.3493	−	4.13080i	−0.522393	−	0.190136i
$473$	−5.22648	−	1.90228i	−0.240314	−	0.0874672i
$474$	−0.768483	+	3.71900i	−0.0352976	+	0.170819i
$475$	19.6548	+	16.4923i	0.901823	+	0.756719i
$476$	0.740036	−	0.0923489i	0.0339195	−	0.00423281i
$477$	17.1550	+	16.1945i	0.785475	+	0.741495i
$478$	9.98999			0.456931
$479$	2.00153	−	11.3513i	0.0914524	−	0.518652i	−0.904324	−	0.426846i	$-0.859625\pi$
$479$	2.00153	−	11.3513i	0.0914524	−	0.518652i	0.995777	−	0.0918065i	$-0.0292641\pi$
$480$	−2.29449	−	4.25690i	−0.104729	−	0.194300i
$481$	10.1998	+	3.71241i	0.465069	+	0.169271i
$482$	6.84888	+	2.49279i	0.311958	+	0.113543i
$483$	10.4403	+	37.8051i	0.475049	+	1.72019i
$484$	−4.84633	+	27.4849i	−0.220288	+	1.24931i
$485$	−5.94666	−	10.2999i	−0.270024	−	0.467695i
$486$	−4.70304	+	2.89609i	−0.213334	+	0.131370i
$487$	−3.30029	+	5.71627i	−0.149550	+	0.259029i	−0.931061	−	0.364863i	$-0.881116\pi$
$487$	−3.30029	+	5.71627i	−0.149550	+	0.259029i	0.781511	+	0.623891i	$0.214449\pi$
$488$	−12.0365	+	4.38091i	−0.544865	+	0.198315i
$489$	−4.70280	−	1.86910i	−0.212668	−	0.0845238i
$490$	−0.728308	−	1.61857i	−0.0329016	−	0.0731196i
$491$	−11.7863	+	9.88984i	−0.531906	+	0.446322i	−0.868759	−	0.495235i	$-0.835082\pi$
$491$	−11.7863	+	9.88984i	−0.531906	+	0.446322i	0.336853	+	0.941557i	$0.390638\pi$
$492$	−10.7097	−	0.313199i	−0.482829	−	0.0141201i
$493$	−0.139893	+	0.793375i	−0.00630048	+	0.0357318i
$494$	−2.04386	−	3.54006i	−0.0919575	−	0.159275i
$495$	−2.52226	+	10.6283i	−0.113367	+	0.477707i
$496$	−7.55904	−	13.0926i	−0.339411	−	0.587877i
$497$	−0.0465681	+	0.923463i	−0.00208886	+	0.0414230i
$498$	4.50276	+	4.00831i	0.201774	+	0.179616i
$499$	−21.7134	+	18.2197i	−0.972025	+	0.815626i	−0.982867	−	0.184316i	$-0.940993\pi$
$499$	−21.7134	+	18.2197i	−0.972025	+	0.815626i	0.0108423	+	0.999941i	$0.496549\pi$
$500$	11.9595	+	4.35291i	0.534847	+	0.194668i
$501$	−1.54343	+	7.46927i	−0.0689553	+	0.333702i
$502$	1.43545	−	8.14083i	0.0640672	−	0.363343i
$503$	−16.1381	−	27.9520i	−0.719563	−	1.24632i	−0.961173	−	0.275946i	$-0.911009\pi$
$503$	−16.1381	−	27.9520i	−0.719563	−	1.24632i	0.241610	−	0.970373i	$-0.422324\pi$
$504$	2.59223	+	10.5832i	0.115467	+	0.471415i
$505$	5.77119	−	9.99599i	0.256814	−	0.444816i
$506$	11.8196	+	9.91779i	0.525443	+	0.440899i
$507$	−8.11978	+	13.1598i	−0.360612	+	0.584448i
$508$	4.37821	+	24.8301i	0.194252	+	1.10166i
$509$	−5.29686	−	30.0400i	−0.234779	−	1.33150i	−0.843079	−	0.537790i	$-0.819259\pi$
$509$	−5.29686	−	30.0400i	−0.234779	−	1.33150i	0.608300	−	0.793708i	$-0.291852\pi$
$510$	0.0518098	−	0.0409535i	0.00229418	−	0.00181345i
$511$	1.82889	−	36.2676i	0.0809054	−	1.60438i
$512$	21.6863			0.958406
$513$	−12.5427	−	26.9289i	−0.553773	−	1.18894i
$514$	2.27868	−	3.94680i	0.100508	−	0.174086i
$515$	−1.10656	−	0.928510i	−0.0487607	−	0.0409151i
$516$	2.78420	−	2.20079i	0.122567	−	0.0968844i
$517$	5.40502	+	1.96727i	0.237712	+	0.0865203i
$518$	−3.43150	+	3.69444i	−0.150772	+	0.162324i
$519$	−7.11536	−	13.2009i	−0.312330	−	0.579456i
$520$	−1.51864	−	1.27429i	−0.0665970	−	0.0558815i
$521$	9.39223	+	16.2678i	0.411481	+	0.712706i	0.995052	−	0.0993562i	$-0.0316783\pi$
$521$	9.39223	+	16.2678i	0.411481	+	0.712706i	−0.583571	+	0.812062i	$0.698345\pi$
$522$	−5.68475	−	0.332780i	−0.248815	−	0.0145654i
$523$	14.3995	−	24.9407i	0.629648	−	1.09058i	−0.357974	−	0.933732i	$-0.616532\pi$
$523$	14.3995	−	24.9407i	0.629648	−	1.09058i	0.987622	−	0.156851i	$-0.0501343\pi$
$524$	−3.86517	−	3.24326i	−0.168851	−	0.141683i
$525$	−16.9364	−	11.6671i	−0.739167	−	0.509193i
$526$	0.141324	+	0.801490i	0.00616204	+	0.0349466i
$527$	0.533801	−	0.447912i	0.0232527	−	0.0195114i
$528$	−21.4759	−	19.1176i	−0.934617	−	0.831986i
$529$	−47.2185	+	17.1861i	−2.05298	+	0.747223i
$530$	0.996954	−	1.72677i	0.0433049	−	0.0750063i
$531$	−26.3488	−	1.54244i	−1.14344	−	0.0669360i
$532$	−28.1347	+	3.51092i	−1.21979	+	0.152218i
$533$	−6.25791	+	2.27769i	−0.271060	+	0.0986578i
$534$	4.33902	−	7.03230i	0.187768	−	0.304317i
$535$	−0.964681	−	5.47098i	−0.0417068	−	0.236531i
$536$	−2.74657	+	2.30465i	−0.118634	+	0.0995457i
$537$	2.12504	−	1.67975i	0.0917020	−	0.0724866i
$538$	1.67031	−	9.47282i	0.0720123	−	0.408402i
$539$	−24.8426	−	25.5227i	−1.07004	−	1.09934i
$540$	−4.92645	−	4.93080i	−0.212000	−	0.212188i
$541$	10.6884	+	18.5129i	0.459531	+	0.795931i	0.998936	−	0.0461153i	$-0.0146842\pi$
$541$	10.6884	+	18.5129i	0.459531	+	0.795931i	−0.539405	+	0.842046i	$0.681351\pi$
$542$	3.32738	+	2.79200i	0.142923	+	0.119927i
$543$	−3.56688	−	24.3760i	−0.153070	−	1.04607i
$544$	0.101879	+	0.577787i	0.00436805	+	0.0247724i
$545$	0.438757	−	0.368161i	0.0187943	−	0.0157703i
$546$	1.89982	+	2.66955i	0.0813049	+	0.114246i
$547$	41.0437	−	14.9387i	1.75490	−	0.638733i	0.755047	−	0.655671i	$-0.227614\pi$
$547$	41.0437	−	14.9387i	1.75490	−	0.638733i	0.999857	+	0.0169386i	$0.00539198\pi$
$548$	−38.0548			−1.62562
$549$	−22.4580	+	16.7090i	−0.958482	+	0.713125i
$550$	−8.09075			−0.344991
$551$	5.31846	−	30.1625i	0.226574	−	1.28497i
$552$	−19.3179	+	6.39809i	−0.822224	+	0.272321i
$553$	15.9597	+	3.65141i	0.678677	+	0.155274i
$554$	0.831561	+	4.71602i	0.0353296	+	0.200364i
$555$	1.34914	−	6.52903i	0.0572677	−	0.277142i
$556$	−9.89771	+	3.60247i	−0.419757	+	0.152779i
$557$	−24.6269			−1.04348			−0.521738	−	0.853106i	$-0.674716\pi$
$557$	−24.6269			−1.04348			−0.521738	+	0.853106i	$0.674716\pi$
$558$	3.58170	+	3.38116i	0.151625	+	0.143136i
$559$	1.10295	−	1.91036i	0.0466498	−	0.0807998i
$560$	−5.49830	+	2.81521i	−0.232346	+	0.118965i
$561$	0.695897	−	1.12785i	0.0293808	−	0.0476178i
$562$	9.93245	+	3.61512i	0.418975	+	0.152494i
$563$	−23.1514	+	19.4263i	−0.975715	+	0.818722i	−0.983437	−	0.181248i	$-0.941986\pi$
$563$	−23.1514	+	19.4263i	−0.975715	+	0.818722i	0.00772229	+	0.999970i	$0.497542\pi$
$564$	−2.87930	+	2.27597i	−0.121241	+	0.0958356i
$565$	−5.05228	+	1.83888i	−0.212551	+	0.0773623i
$566$	0.274075			0.0115202
$567$	12.0541	+	20.5353i	0.506225	+	0.862401i
$568$	−0.479758			−0.0201302
$569$	14.8959	−	5.42165i	0.624467	−	0.227287i	−0.0103543	−	0.999946i	$-0.503296\pi$
$569$	14.8959	−	5.42165i	0.624467	−	0.227287i	0.634821	+	0.772659i	$0.281074\pi$
$570$	−1.96970	+	1.55697i	−0.0825018	+	0.0652142i
$571$	2.54430	−	2.13492i	0.106476	−	0.0893438i	−0.587996	−	0.808864i	$-0.700083\pi$
$571$	2.54430	−	2.13492i	0.106476	−	0.0893438i	0.694471	+	0.719520i	$0.255638\pi$
$572$	−18.0859	−	6.58272i	−0.756208	−	0.275237i
$573$	17.5974	−	28.5203i	0.735143	−	1.19145i
$574$	0.155804	−	3.08966i	0.00650315	−	0.128960i
$575$	19.2049	−	33.2639i	0.800901	−	1.38720i
$576$	14.7812	−	4.42046i	0.615885	−	0.184186i
$577$	−19.9248			−0.829482			−0.414741	−	0.909939i	$-0.636128\pi$
$577$	−19.9248			−0.829482			−0.414741	+	0.909939i	$0.636128\pi$
$578$	5.65257	−	2.05737i	0.235116	−	0.0855751i
$579$	0.986754	−	4.77530i	0.0410081	−	0.198455i
$580$	−1.24788	−	7.07708i	−0.0518154	−	0.293860i
$581$	17.6873	−	19.0426i	0.733793	−	0.790019i
$582$	−9.68208	+	3.20671i	−0.401335	+	0.132922i
$583$	6.94803	−	39.4042i	0.287758	−	1.63196i
$584$	18.8418			0.779678
$585$	−3.97752	−	1.71713i	−0.164450	−	0.0709945i
$586$	−1.16796			−0.0482480
$587$	−23.6476	+	8.60703i	−0.976041	+	0.355250i	−0.780300	−	0.625405i	$-0.784934\pi$
$587$	−23.6476	+	8.60703i	−0.976041	+	0.355250i	−0.195742	+	0.980656i	$0.562711\pi$
$588$	22.1835	−	4.93877i	0.914833	−	0.203671i
$589$	−20.2940	+	17.0287i	−0.836201	+	0.701656i
$590$	0.387368	+	2.19688i	0.0159477	+	0.0904439i
$591$	−0.414594	−	2.83332i	−0.0170541	−	0.116547i
$592$	13.4429	+	11.2799i	0.552500	+	0.463602i
$593$	−19.8891	−	34.4490i	−0.816749	−	1.41465i	−0.908066	−	0.418828i	$-0.862441\pi$
$593$	−19.8891	−	34.4490i	−0.816749	−	1.41465i	0.0913170	−	0.995822i	$-0.470892\pi$
$594$	8.48818	+	3.96267i	0.348274	+	0.162590i
$595$	−0.171796	−	0.227047i	−0.00704295	−	0.00930801i
$596$	0.822914	−	4.66698i	0.0337079	−	0.191167i
$597$	−8.09187	+	6.39628i	−0.331178	+	0.261783i
$598$	−4.68773	+	3.93348i	−0.191696	+	0.160852i
$599$	1.09126	+	6.18886i	0.0445878	+	0.252870i	0.998952	−	0.0457760i	$-0.0145761\pi$
$599$	1.09126	+	6.18886i	0.0445878	+	0.252870i	−0.954364	+	0.298646i	$0.903465\pi$
$600$	5.60333	−	9.08139i	0.228755	−	0.370746i
$601$	−38.8099	+	14.1257i	−1.58309	+	0.576198i	−0.975873	−	0.218338i	$-0.929936\pi$
$601$	−38.8099	+	14.1257i	−1.58309	+	0.576198i	−0.607217	+	0.794536i	$0.707714\pi$
$602$	0.618305	+	0.817156i	0.0252002	+	0.0333048i
$603$	−4.30752	+	6.54507i	−0.175416	+	0.266536i
$604$	−11.7048	+	20.2732i	−0.476260	+	0.824907i
$605$	10.0123	−	3.64418i	0.407058	−	0.148157i
$606$	−7.39334	−	6.58146i	−0.300334	−	0.267354i
$607$	32.4883	−	27.2609i	1.31866	−	1.10649i	0.332070	−	0.943255i	$-0.392253\pi$
$607$	32.4883	−	27.2609i	1.31866	−	1.10649i	0.986588	−	0.163231i	$-0.0521916\pi$
$608$	−3.87325	−	21.9663i	−0.157081	−	0.890851i
$609$	−1.95264	+	24.4723i	−0.0791252	+	0.991669i
$610$	1.81233	+	1.52073i	0.0733792	+	0.0615725i
$611$	−1.14063	+	1.97562i	−0.0461448	+	0.0799251i
$612$	0.379296	+	0.755795i	0.0153321	+	0.0305512i
$613$	1.38233	+	2.39427i	0.0558319	+	0.0967037i	0.892591	−	0.450868i	$-0.148886\pi$
$613$	1.38233	+	2.39427i	0.0558319	+	0.0967037i	−0.836759	+	0.547572i	$0.815552\pi$
$614$	−0.0881740	−	0.0739868i	−0.00355841	−	0.00298586i
$615$	1.94078	+	3.60067i	0.0782598	+	0.145193i
$616$	12.5768	−	13.5404i	0.506732	−	0.545560i
$617$	0.602814	+	0.219406i	0.0242684	+	0.00883297i	0.354126	−	0.935198i	$-0.384778\pi$
$617$	0.602814	+	0.219406i	0.0242684	+	0.00883297i	−0.329857	+	0.944031i	$0.607001\pi$
$618$	−0.971814	+	0.768178i	−0.0390921	+	0.0309007i
$619$	21.4610	+	18.0079i	0.862590	+	0.723799i	0.962524	−	0.271195i	$-0.0874189\pi$
$619$	21.4610	+	18.0079i	0.862590	+	0.723799i	−0.0999347	+	0.994994i	$0.531863\pi$
$620$	−3.10793	+	5.38309i	−0.124817	+	0.216190i
$621$	−36.4402	+	25.4917i	−1.46230	+	1.02295i
$622$	4.30739			0.172710
$623$	−29.9154	−	19.3434i	−1.19853	−	0.774976i
$624$	8.94605	−	7.07147i	0.358128	−	0.283086i
$625$	3.05284	+	17.3135i	0.122113	+	0.692540i
$626$	−1.63012	−	9.24485i	−0.0651525	−	0.369498i
$627$	−26.4566	+	42.8785i	−1.05657	+	1.71240i
$628$	3.07385	+	2.57927i	0.122660	+	0.102924i
$629$	−0.404425	+	0.700484i	−0.0161255	+	0.0279301i
$630$	1.45346	−	1.39202i	0.0579073	−	0.0554593i
$631$	2.12621	+	3.68270i	0.0846429	+	0.146606i	0.905239	−	0.424903i	$-0.139692\pi$
$631$	2.12621	+	3.68270i	0.0846429	+	0.146606i	−0.820596	+	0.571509i	$0.806358\pi$
$632$	−1.47512	+	8.36580i	−0.0586770	+	0.332774i
$633$	3.97352	−	19.2295i	0.157933	−	0.764303i
$634$	−3.92384	−	1.42816i	−0.155836	−	0.0567196i
$635$	7.37371	−	6.18728i	0.292617	−	0.245535i
$636$	19.0699	+	16.9758i	0.756172	+	0.673135i
$637$	11.6796	−	7.94532i	0.462765	−	0.314805i
$638$	4.82904	+	8.36414i	0.191183	+	0.331139i
$639$	−1.00448	+	0.300400i	−0.0397367	+	0.0118836i
$640$	−3.44398	−	5.96515i	−0.136135	−	0.235793i
$641$	−0.121849	+	0.691040i	−0.00481275	+	0.0272944i	−0.987120	−	0.159984i	$-0.948856\pi$
$641$	−0.121849	+	0.691040i	−0.00481275	+	0.0272944i	0.982307	+	0.187279i	$0.0599668\pi$
$642$	−4.76206	−	0.139264i	−0.187944	−	0.00549632i
$643$	11.1146	−	9.32627i	0.438318	−	0.367792i	−0.396762	−	0.917922i	$-0.629866\pi$
$643$	11.1146	−	9.32627i	0.438318	−	0.367792i	0.835079	+	0.550129i	$0.185422\pi$
$644$	12.4898	+	40.5657i	0.492169	+	1.59851i
$645$	−1.25910	−	0.500425i	−0.0495772	−	0.0197042i
$646$	0.286240	−	0.104183i	0.0112619	−	0.00409901i
$647$	3.74943	−	6.49420i	0.147405	−	0.255313i	−0.782862	−	0.622195i	$-0.786241\pi$
$647$	3.74943	−	6.49420i	0.147405	−	0.255313i	0.930268	+	0.366881i	$0.119575\pi$
$648$	−10.3265	+	6.78310i	−0.405661	+	0.266465i
$649$	22.3826	+	38.7678i	0.878594	+	1.52177i
$650$	0.557212	−	3.16011i	0.0218557	−	0.123950i
$651$	14.9002	−	15.1298i	0.583983	−	0.592982i
$652$	−5.14642	−	1.87314i	−0.201549	−	0.0733580i
$653$	22.9164	+	8.34090i	0.896790	+	0.326405i	0.748966	−	0.662609i	$-0.230551\pi$
$653$	22.9164	+	8.34090i	0.896790	+	0.326405i	0.147824	+	0.989014i	$0.452773\pi$
$654$	−0.233049	−	0.432368i	−0.00911293	−	0.0169069i
$655$	−0.334496	+	1.89702i	−0.0130698	+	0.0741227i
$656$	−10.7666			−0.420365
$657$	39.4495	−	11.7977i	1.53907	−	0.460274i
$658$	−0.639426	−	0.845070i	−0.0249274	−	0.0329442i
$659$	0.249541	+	0.209389i	0.00972072	+	0.00815665i	0.647635	−	0.761951i	$-0.275758\pi$
$659$	0.249541	+	0.209389i	0.00972072	+	0.00815665i	−0.637914	+	0.770107i	$0.720203\pi$
$660$	−2.39225	+	11.5770i	−0.0931181	+	0.450636i
$661$	6.53818	+	2.37970i	0.254306	+	0.0925597i	0.466027	−	0.884770i	$-0.345685\pi$
$661$	6.53818	+	2.37970i	0.254306	+	0.0925597i	−0.211722	+	0.977330i	$0.567907\pi$
$662$	−1.77912	−	0.647548i	−0.0691476	−	0.0251677i
$663$	0.392592	+	0.349481i	0.0152470	+	0.0135727i
$664$	10.3301	+	8.66800i	0.400886	+	0.336384i
$665$	6.53134	+	8.63186i	0.253274	+	0.334729i
$666$	−5.24910	−	2.26608i	−0.203398	−	0.0878086i
$667$	−45.8505			−1.77534
$668$	−1.43332	+	8.12877i	−0.0554569	+	0.314512i
$669$	−12.6934	+	20.5724i	−0.490755	+	0.795373i
$670$	0.622292	+	0.226496i	0.0240412	+	0.00875030i
$671$	44.6125	+	16.2376i	1.72225	+	0.626846i
$672$	4.75932	+	17.2339i	0.183595	+	0.664812i
$673$	−5.49346	+	31.1549i	−0.211757	+	1.20093i	0.674689	+	0.738102i	$0.264278\pi$
$673$	−5.49346	+	31.1549i	−0.211757	+	1.20093i	−0.886446	+	0.462832i	$0.846833\pi$
$674$	−3.74907	−	6.49358i	−0.144409	−	0.250123i
$675$	6.04555	−	22.5225i	0.232693	−	0.866891i
$676$	−8.36732	+	14.4926i	−0.321820	+	0.557409i
$677$	−12.8853	+	4.68987i	−0.495223	+	0.180246i	−0.577544	−	0.816360i	$-0.695989\pi$
$677$	−12.8853	+	4.68987i	−0.495223	+	0.180246i	0.0823214	+	0.996606i	$0.473767\pi$
$678$	0.667568	+	4.56214i	0.0256378	+	0.175208i
$679$	12.9390	+	42.0245i	0.496553	+	1.61275i
$680$	0.113167	−	0.0949584i	0.00433975	−	0.00364149i
$681$	0.518820	−	0.840858i	0.0198812	−	0.0322217i
$682$	1.45064	−	8.22698i	0.0555478	−	0.315027i
$683$	14.6873	+	25.4392i	0.561994	+	0.973402i	0.997322	+	0.0731304i	$0.0232989\pi$
$683$	14.6873	+	25.4392i	0.561994	+	0.973402i	−0.435328	+	0.900272i	$0.643368\pi$
$684$	−14.4201	−	28.7338i	−0.551364	−	1.09866i
$685$	7.26415	+	12.5819i	0.277549	+	0.480729i
$686$	1.29023	+	6.43390i	0.0492612	+	0.245648i
$687$	4.13803	−	20.0256i	0.157876	−	0.764023i
$688$	2.73196	−	2.29239i	0.104155	−	0.0873964i
$689$	14.9121	+	5.42756i	0.568106	+	0.206774i
$690$	2.80744	+	2.49915i	0.106877	+	0.0951411i
$691$	2.65548	−	15.0600i	0.101019	−	0.572908i	−0.891717	−	0.452594i	$-0.850499\pi$
$691$	2.65548	−	15.0600i	0.101019	−	0.572908i	0.992736	−	0.120314i	$-0.0383901\pi$
$692$	−8.11472	−	14.0551i	−0.308475	−	0.534295i
$693$	17.8540	−	36.2249i	0.678217	−	1.37607i
$694$	0.472036	−	0.817590i	0.0179182	−	0.0310353i
$695$	3.08041	+	2.58477i	0.116847	+	0.0980461i
$696$	−12.7327	−	0.372361i	−0.482630	−	0.0141143i
$697$	−0.0861742	−	0.488718i	−0.00326408	−	0.0185115i
$698$	0.143899	+	0.816092i	0.00544666	+	0.0308895i
$699$	−0.152270	−	1.04061i	−0.00575938	−	0.0393594i
$700$	−18.6902	−	12.0852i	−0.706424	−	0.456776i
$701$	32.3125			1.22043			0.610213	−	0.792237i	$-0.291084\pi$
$701$	32.3125			1.22043			0.610213	+	0.792237i	$0.291084\pi$
$702$	−2.13234	+	3.04243i	−0.0804798	+	0.114829i
$703$	15.3754	−	26.6310i	0.579895	−	1.00441i
$704$	−20.0448	−	16.8196i	−0.755468	−	0.633913i
$705$	1.30211	+	0.517519i	0.0490405	+	0.0194909i
$706$	−8.81546	−	3.20857i	−0.331774	−	0.120756i
$707$	−29.0418	+	31.2671i	−1.09223	+	1.17592i
$708$	−28.5518	−	0.834985i	−1.07304	−	0.0313806i
$709$	−25.3147	−	21.2416i	−0.950714	−	0.797744i	0.0287034	−	0.999588i	$-0.490862\pi$
$709$	−25.3147	−	21.2416i	−0.950714	−	0.797744i	−0.979418	+	0.201844i	$0.935307\pi$
$710$	0.0443061	+	0.0767404i	0.00166278	+	0.00288001i
$711$	2.14974	+	18.4393i	0.0806216	+	0.691529i
$712$	9.24206	−	16.0077i	0.346361	−	0.599914i
$713$	30.3806	+	25.4924i	1.13776	+	0.954697i
$714$	−0.220492	+	0.104877i	−0.00825172	+	0.00392492i
$715$	1.27594	+	7.23621i	0.0477174	+	0.270619i
$716$	2.24563	−	1.88431i	0.0839233	−	0.0704200i
$717$	46.3591	−	15.3542i	1.73131	−	0.573411i
$718$	4.20138	−	1.52918i	0.156794	−	0.0570683i
$719$	14.5924	−	25.2747i	0.544204	−	0.942589i	−0.454453	−	0.890771i	$-0.650165\pi$
$719$	14.5924	−	25.2747i	0.544204	−	0.942589i	0.998657	−	0.0518177i	$-0.0165015\pi$
$720$	−5.09324	−	4.80807i	−0.189814	−	0.179186i
$721$	3.22244	+	4.25880i	0.120010	+	0.158606i
$722$	−4.55626	+	1.65834i	−0.169567	+	0.0617172i
$723$	35.6139	+	1.04151i	1.32450	+	0.0387342i
$724$	−4.62965	−	26.2560i	−0.172060	−	0.975798i
$725$	18.4179	−	15.4544i	0.684023	−	0.573964i
$726$	−1.32295	−	9.04097i	−0.0490991	−	0.335542i
$727$	−1.89093	+	10.7240i	−0.0701309	+	0.397732i	0.929454	+	0.368937i	$0.120278\pi$
$727$	−1.89093	+	10.7240i	−0.0701309	+	0.397732i	−0.999585	+	0.0287951i	$0.990833\pi$
$728$	4.42250	+	5.84480i	0.163909	+	0.216623i
$729$	−17.3735	+	20.6678i	−0.643465	+	0.765476i
$730$	−1.74005	−	3.01386i	−0.0644023	−	0.111548i
$731$	0.125922	+	0.105661i	0.00465741	+	0.00390803i
$732$	−23.7655	+	18.7856i	−0.878398	+	0.694336i
$733$	−7.44629	−	42.2300i	−0.275035	−	1.55980i	−0.738851	−	0.673869i	$-0.764631\pi$
$733$	−7.44629	−	42.2300i	−0.275035	−	1.55980i	0.463816	−	0.885932i	$-0.346480\pi$
$734$	3.61145	−	3.03037i	0.133301	−	0.111853i
$735$	−5.86742	−	6.39169i	−0.216423	−	0.235761i
$736$	−31.3776	+	11.4205i	−1.15659	+	0.420966i
$737$	13.2891			0.489510
$738$	3.36073	−	1.00506i	0.123710	−	0.0369966i
$739$	26.7432			0.983763			0.491882	−	0.870662i	$-0.336309\pi$
$739$	26.7432			0.983763			0.491882	+	0.870662i	$0.336309\pi$
$740$	1.25289	−	7.10551i	0.0460573	−	0.261204i
$741$	−14.9255	−	13.2866i	−0.548304	−	0.488094i
$742$	−5.01688	+	5.40129i	−0.184175	+	0.198287i
$743$	6.35951	+	36.0666i	0.233308	+	1.32315i	0.846148	+	0.532948i	$0.178916\pi$
$743$	6.35951	+	36.0666i	0.233308	+	1.32315i	−0.612840	+	0.790207i	$0.709973\pi$
$744$	8.22965	+	7.32594i	0.301714	+	0.268582i
$745$	−1.70011	+	0.618788i	−0.0622871	+	0.0226706i
$746$	3.77075			0.138057
$747$	27.0559	+	11.6802i	0.989924	+	0.427357i
$748$	0.717112	−	1.24208i	0.0262202	−	0.0454148i
$749$	−1.03442	+	20.5130i	−0.0377970	+	0.749528i
$750$	−4.16501	−	0.121804i	−0.152085	−	0.00444764i
$751$	28.8365	+	10.4956i	1.05226	+	0.382990i	0.809514	−	0.587100i	$-0.199731\pi$
$751$	28.8365	+	10.4956i	1.05226	+	0.382990i	0.242743	+	0.970091i	$0.421953\pi$
$752$	−2.82528	+	2.37069i	−0.103027	+	0.0864503i
$753$	−5.85081	−	39.9842i	−0.213215	−	1.45711i
$754$	−3.59947	+	1.31010i	−0.131085	+	0.0477110i
$755$	8.93714			0.325256
$756$	13.6893	+	21.8329i	0.497874	+	0.794054i
$757$	−13.3564			−0.485447			−0.242723	−	0.970096i	$-0.578041\pi$
$757$	−13.3564			−0.485447			−0.242723	+	0.970096i	$0.578041\pi$
$758$	−3.09732	+	1.12733i	−0.112500	+	0.0409466i
$759$	70.0925	+	27.8579i	2.54420	+	1.01118i
$760$	−4.30238	+	3.61012i	−0.156064	+	0.130953i
$761$	10.9272	+	3.97718i	0.396111	+	0.144173i	0.532393	−	0.846497i	$-0.321293\pi$
$761$	10.9272	+	3.97718i	0.396111	+	0.144173i	−0.136282	+	0.990670i	$0.543515\pi$
$762$	−3.91660	−	7.26635i	−0.141883	−	0.263232i
$763$	−1.88486	+	0.965079i	−0.0682366	+	0.0349382i
$764$	18.1339	−	31.4088i	0.656061	−	1.13633i
$765$	0.177483	−	0.269676i	0.00641690	−	0.00975016i
$766$	4.16374			0.150442
$767$	−16.6835	+	6.07231i	−0.602407	+	0.219258i
$768$	11.3041	−	3.74391i	0.407900	−	0.135097i
$769$	−4.77224	−	27.0647i	−0.172091	−	0.975979i	−0.941448	−	0.337159i	$-0.890534\pi$
$769$	−4.77224	−	27.0647i	−0.172091	−	0.975979i	0.769356	−	0.638820i	$-0.220577\pi$
$770$	−3.32736	−	0.761262i	−0.119910	−	0.0274340i
$771$	4.50832	−	21.8176i	0.162363	−	0.785740i
$772$	0.916360	−	5.19693i	0.0329805	−	0.187042i
$773$	−52.2223			−1.87830			−0.939152	−	0.343502i	$-0.888387\pi$
$773$	−52.2223			−1.87830			−0.939152	+	0.343502i	$0.888387\pi$
$774$	−0.638772	+	0.970582i	−0.0229602	+	0.0348868i
$775$	−20.7962			−0.747022
$776$	−21.4391	+	7.80319i	−0.769619	+	0.280118i
$777$	−10.2459	+	22.4183i	−0.367570	+	0.804253i
$778$	−3.84652	+	3.22761i	−0.137904	+	0.115716i
$779$	3.27617	+	18.5801i	0.117381	+	0.665700i
$780$	−4.35704	−	1.73169i	−0.156007	−	0.0620043i
$781$	1.36218	+	1.14300i	0.0487425	+	0.0408999i
$782$	−0.228004	−	0.394915i	−0.00815341	−	0.0141221i
$783$	−26.8919	+	7.19291i	−0.961037	+	0.257054i
$784$	22.1373	−	5.61242i	0.790619	−	0.200444i
$785$	0.266014	−	1.50864i	0.00949446	−	0.0538457i
$786$	1.53511	+	0.610124i	0.0547557	+	0.0217624i
$787$	15.9120	−	13.3518i	0.567202	−	0.475939i	−0.313514	−	0.949583i	$-0.601506\pi$
$787$	15.9120	−	13.3518i	0.567202	−	0.475939i	0.880716	+	0.473645i	$0.157062\pi$
$788$	−0.538124	−	3.05186i	−0.0191699	−	0.108718i
$789$	1.88768	+	3.50215i	0.0672031	+	0.124680i
$790$	1.47439	−	0.536635i	0.0524565	−	0.0190926i
$791$	19.7248	−	2.46145i	0.701334	−	0.0875193i
$792$	19.2384	+	8.30536i	0.683607	+	0.295118i
$793$	−9.41461	+	16.3066i	−0.334323	+	0.579064i
$794$	−10.1743	+	3.70313i	−0.361071	+	0.131419i
$795$	1.97245	−	9.54547i	0.0699555	−	0.338543i
$796$	−8.55110	+	7.17522i	−0.303086	+	0.254319i
$797$	3.46521	+	19.6522i	0.122744	+	0.696115i	0.982622	+	0.185616i	$0.0594281\pi$
$797$	3.46521	+	19.6522i	0.122744	+	0.696115i	−0.859878	+	0.510499i	$0.829461\pi$
$798$	8.38267	−	3.98721i	0.296743	−	0.141146i
$799$	−0.130224	−	0.109271i	−0.00460699	−	0.00386572i
$800$	8.75478	−	15.1637i	0.309528	−	0.536119i
$801$	9.32714	−	39.3027i	0.329558	−	1.38869i
$802$	6.65603	+	11.5286i	0.235033	+	0.407089i
$803$	−53.4974	−	44.8897i	−1.88788	−	1.58412i
$804$	−4.45264	+	7.21645i	−0.157033	+	0.254505i
$805$	11.0279	−	11.8729i	0.388683	−	0.418466i
$806$	3.11341	+	1.13319i	0.109665	+	0.0399149i
$807$	−6.80810	−	46.5263i	−0.239657	−	1.63780i
$808$	−16.9616	−	14.2325i	−0.596707	−	0.500697i
$809$	−5.97695	+	10.3524i	−0.210139	+	0.363971i	−0.951758	−	0.306851i	$-0.900725\pi$
$809$	−5.97695	+	10.3524i	−0.210139	+	0.363971i	0.741619	+	0.670821i	$0.234058\pi$
$810$	2.03866	+	1.02536i	0.0716311	+	0.0360274i
$811$	21.4437			0.752989			0.376494	−	0.926419i	$-0.377129\pi$
$811$	21.4437			0.752989			0.376494	+	0.926419i	$0.377129\pi$
$812$	−1.33809	+	26.5349i	−0.0469579	+	0.931193i
$813$	19.7321	+	7.84242i	0.692034	+	0.275046i
$814$	1.68384	+	9.54955i	0.0590187	+	0.334712i
$815$	0.363074	+	2.05910i	0.0127179	+	0.0721270i
$816$	0.403188	+	0.748022i	0.0141144	+	0.0261860i
$817$	−4.78732	−	4.01703i	−0.167487	−	0.140538i
$818$	−2.15727	+	3.73651i	−0.0754273	+	0.130644i
$819$	12.9192	+	9.46828i	0.451434	+	0.330848i
$820$	2.21336	+	3.83366i	0.0772940	+	0.133877i
$821$	−1.11017	+	6.29611i	−0.0387453	+	0.219736i	−0.998033	−	0.0626963i	$-0.980030\pi$
$821$	−1.11017	+	6.29611i	−0.0387453	+	0.219736i	0.959287	+	0.282432i	$0.0911412\pi$
$822$	11.8272	−	3.91716i	0.412520	−	0.136627i
$823$	−31.2689	−	11.3809i	−1.08997	−	0.396715i	−0.266357	−	0.963874i	$-0.585820\pi$
$823$	−31.2689	−	11.3809i	−1.08997	−	0.396715i	−0.823608	+	0.567160i	$0.808042\pi$
$824$	−2.12271	+	1.78117i	−0.0739482	+	0.0620499i
$825$	−37.5456	+	12.4351i	−1.30717	+	0.432935i
$826$	0.415373	−	8.23700i	0.0144527	−	0.286602i
$827$	−6.75037	−	11.6920i	−0.234733	−	0.406570i	0.724462	−	0.689315i	$-0.242088\pi$
$827$	−6.75037	−	11.6920i	−0.234733	−	0.406570i	−0.959195	+	0.282745i	$0.908755\pi$
$828$	−38.6131	+	28.7287i	−1.34190	+	0.998391i
$829$	−4.08010	−	7.06694i	−0.141708	−	0.245445i	0.786432	−	0.617677i	$-0.211926\pi$
$829$	−4.08010	−	7.06694i	−0.141708	−	0.245445i	−0.928140	+	0.372232i	$0.878593\pi$
$830$	0.432506	−	2.45287i	0.0150125	−	0.0851402i
$831$	11.1072	+	20.6069i	0.385305	+	0.714844i
$832$	7.94994	−	6.67079i	0.275615	−	0.231268i
$833$	0.431943	+	0.959939i	0.0149659	+	0.0332599i
$834$	2.70532	−	2.13844i	0.0936777	−	0.0740483i
$835$	2.96118	−	1.07778i	0.102476	−	0.0372982i
$836$	−27.2632	+	47.2212i	−0.942916	+	1.63318i
$837$	21.8178	+	10.1855i	0.754132	+	0.352064i
$838$	4.84590	+	8.39335i	0.167399	+	0.289944i
$839$	4.98580	−	28.2759i	0.172129	−	0.976192i	−0.769277	−	0.638916i	$-0.779383\pi$
$839$	4.98580	−	28.2759i	0.172129	−	0.976192i	0.941406	−	0.337276i	$-0.109506\pi$
$840$	3.15887	−	3.20754i	0.108991	−	0.110671i
$841$	0.281540	+	0.102472i	0.00970827	+	0.00353352i
$842$	−7.00121	−	2.54823i	−0.241278	−	0.0878179i
$843$	51.6484	+	1.51043i	1.77886	+	0.0520220i
$844$	3.69006	−	20.9273i	0.127017	−	0.720349i
$845$	6.38884			0.219783
$846$	0.660592	−	1.00374i	0.0227116	−	0.0345092i
$847$	−39.0895	+	4.87796i	−1.34313	+	0.167609i
$848$	19.6536	+	16.4913i	0.674907	+	0.566314i
$849$	1.27186	−	0.421241i	0.0436502	−	0.0144570i
$850$	0.224698	+	0.0817835i	0.00770709	+	0.00280515i
$851$	−43.2585	−	15.7448i	−1.48288	−	0.539725i
$852$	−1.07710	+	0.356737i	−0.0369010	+	0.0122216i
$853$	−9.98426	−	8.37779i	−0.341855	−	0.286850i	0.455655	−	0.890157i	$-0.349405\pi$
$853$	−9.98426	−	8.37779i	−0.341855	−	0.286850i	−0.797509	+	0.603306i	$0.793850\pi$
$854$	−5.27776	−	6.97512i	−0.180601	−	0.238684i
$855$	−6.74753	+	10.2525i	−0.230761	+	0.350630i
$856$	−10.6569			−0.364246
$857$	−8.39151	+	47.5906i	−0.286648	+	1.62566i	0.412688	+	0.910872i	$0.364590\pi$
$857$	−8.39151	+	47.5906i	−0.286648	+	1.62566i	−0.699337	+	0.714792i	$0.746521\pi$
$858$	6.29856	+	0.184198i	0.215029	+	0.00628843i
$859$	15.5345	+	5.65409i	0.530030	+	0.192915i	0.593152	−	0.805091i	$-0.297883\pi$
$859$	15.5345	+	5.65409i	0.530030	+	0.192915i	−0.0631217	+	0.998006i	$0.520106\pi$
$860$	−1.37788	−	0.501507i	−0.0469852	−	0.0171012i
$861$	−4.02565	−	14.5772i	−0.137194	−	0.496790i
$862$	0.364392	−	2.06657i	0.0124112	−	0.0703876i
$863$	1.27036	+	2.20033i	0.0432436	+	0.0749001i	0.886837	−	0.462082i	$-0.152898\pi$
$863$	1.27036	+	2.20033i	0.0432436	+	0.0749001i	−0.843593	+	0.536982i	$0.819564\pi$
$864$	−16.6117	+	11.6207i	−0.565142	+	0.395344i
$865$	−3.09799	+	5.36587i	−0.105335	+	0.182445i
$866$	8.01573	−	2.91749i	0.272385	−	0.0991402i
$867$	23.0690	−	18.2351i	0.783464	−	0.619295i
$868$	15.6397	−	16.8381i	0.530847	−	0.571523i
$869$	24.1195	−	20.2386i	0.818196	−	0.686548i
$870$	1.11631	+	2.07106i	0.0378465	+	0.0702155i
$871$	−0.915223	+	5.19049i	−0.0310111	+	0.175873i
$872$	−0.549361	−	0.951522i	−0.0186037	−	0.0322226i
$873$	−40.0017	+	29.7618i	−1.35385	+	1.00728i
$874$	8.66825	+	15.0139i	0.293208	+	0.507851i
$875$	−0.904729	+	17.9411i	−0.0305854	+	0.606520i
$876$	42.3016	−	14.0103i	1.42924	−	0.473364i
$877$	21.5212	−	18.0584i	0.726719	−	0.609789i	−0.202516	−	0.979279i	$-0.564912\pi$
$877$	21.5212	−	18.0584i	0.726719	−	0.609789i	0.929235	+	0.369490i	$0.120467\pi$
$878$	−5.84261	−	2.12654i	−0.197178	−	0.0717671i
$879$	−5.41999	+	1.79510i	−0.182812	+	0.0605473i
$880$	−2.06284	+	11.6989i	−0.0695382	+	0.394371i
$881$	0.380064	+	0.658290i	0.0128047	+	0.0221784i	0.872357	−	0.488870i	$-0.162591\pi$
$881$	0.380064	+	0.658290i	0.0128047	+	0.0221784i	−0.859552	+	0.511048i	$0.829257\pi$
$882$	−6.38612	+	3.81839i	−0.215032	+	0.128572i
$883$	5.35116	−	9.26848i	0.180081	−	0.311909i	−0.761827	−	0.647780i	$-0.775697\pi$
$883$	5.35116	−	9.26848i	0.180081	−	0.311909i	0.941908	+	0.335871i	$0.109031\pi$
$884$	0.435746	+	0.365634i	0.0146557	+	0.0122976i
$885$	5.17410	+	9.59936i	0.173926	+	0.322679i
$886$	−1.24882	−	7.08243i	−0.0419550	−	0.237939i
$887$	7.32459	+	41.5398i	0.245936	+	1.39477i	0.818310	+	0.574777i	$0.194911\pi$
$887$	7.32459	+	41.5398i	0.245936	+	1.39477i	−0.572374	+	0.819992i	$0.693978\pi$
$888$	−11.8850	−	4.72363i	−0.398834	−	0.158515i
$889$	−31.6768	+	16.2190i	−1.06241	+	0.543969i
$890$	−3.41405			−0.114439
$891$	45.4803	+	5.34307i	1.52365	+	0.178999i
$892$	−13.0804	+	22.6559i	−0.437964	+	0.758575i
$893$	4.95085	+	4.15425i	0.165674	+	0.139017i
$894$	0.224639	+	1.53517i	0.00751304	+	0.0513438i
$895$	−1.05166	−	0.382774i	−0.0351532	−	0.0127947i
$896$	7.49356	+	24.3383i	0.250342	+	0.813086i
$897$	−15.7081	+	25.4584i	−0.524479	+	0.850030i
$898$	−9.50718	−	7.97747i	−0.317259	−	0.266212i
$899$	12.4124	+	21.4989i	0.413977	+	0.717029i
$900$	5.82732	−	24.5551i	0.194244	−	0.818504i
$901$	−0.591271	+	1.02411i	−0.0196981	+	0.0341181i
$902$	−4.55748	−	3.82418i	−0.151747	−	0.127331i
$903$	4.12521	+	2.84175i	0.137278	+	0.0945676i
$904$	1.79098	+	10.1571i	0.0595670	+	0.337821i
$905$	−7.79718	+	6.54261i	−0.259187	+	0.217484i
$906$	1.55094	−	7.50562i	0.0515265	−	0.249357i
$907$	−6.01269	+	2.18844i	−0.199648	+	0.0726660i	−0.439909	−	0.898042i	$-0.644989\pi$
$907$	−6.01269	+	2.18844i	−0.199648	+	0.0726660i	0.240261	+	0.970708i	$0.422767\pi$
$908$	0.534637	−	0.926018i	0.0177425	−	0.0307310i
$909$	−44.4246	−	19.1784i	−1.47347	−	0.636109i
$910$	0.526492	−	1.24718i	0.0174530	−	0.0413436i
$911$	−6.52231	+	2.37393i	−0.216094	+	0.0786517i	−0.447799	−	0.894134i	$-0.647792\pi$
$911$	−6.52231	+	2.37393i	−0.216094	+	0.0786517i	0.231705	+	0.972786i	$0.425570\pi$
$912$	−15.3284	−	28.4383i	−0.507573	−	0.941686i
$913$	−8.67919	−	49.2221i	−0.287239	−	1.62901i
$914$	−5.31964	+	4.46370i	−0.175958	+	0.147646i
$915$	10.7475	+	4.27155i	0.355302	+	0.141213i
$916$	3.84282	−	21.7937i	0.126970	−	0.720085i
$917$	2.76974	−	6.56110i	0.0914649	−	0.216667i
$918$	−0.195680	−	0.195853i	−0.00645841	−	0.00646412i
$919$	−26.6246	−	46.1152i	−0.878265	−	1.52120i	−0.853243	−	0.521513i	$-0.825368\pi$
$919$	−26.6246	−	46.1152i	−0.878265	−	1.52120i	−0.0250224	−	0.999687i	$-0.507966\pi$
$920$	6.44076	+	5.40444i	0.212346	+	0.178179i
$921$	−0.522891	−	0.207821i	−0.0172298	−	0.00684792i
$922$	−1.44449	−	8.19213i	−0.0475719	−	0.269793i
$923$	−0.540251	+	0.453324i	−0.0177826	+	0.0149213i
$924$	18.1677	−	39.7514i	0.597673	−	1.30773i
$925$	22.6836	−	8.25617i	0.745833	−	0.271461i
$926$	6.31150			0.207409
$927$	−3.32910	+	5.05841i	−0.109342	+	0.166140i
$928$	−20.9015			−0.686125
$929$	2.41534	−	13.6981i	0.0792448	−	0.449420i	−0.919206	−	0.393777i	$-0.871168\pi$
$929$	2.41534	−	13.6981i	0.0792448	−	0.449420i	0.998451	−	0.0556425i	$-0.0177207\pi$
$930$	0.411816	−	1.99294i	0.0135040	−	0.0653512i
$931$	−16.4216	−	36.4949i	−0.538197	−	1.19607i
$932$	−0.197639	−	1.12087i	−0.00647389	−	0.0367153i
$933$	19.9887	−	6.62026i	0.654400	−	0.216737i
$934$	−7.66419	+	2.78954i	−0.250780	+	0.0912765i
$935$	−0.547549			−0.0179068
$936$	−4.56889	+	6.94220i	−0.149339	+	0.226913i
$937$	−8.38816	+	14.5287i	−0.274029	+	0.474633i	−0.969890	−	0.243544i	$-0.921690\pi$
$937$	−8.38816	+	14.5287i	−0.274029	+	0.474633i	0.695860	+	0.718177i	$0.255023\pi$
$938$	−2.05600	−	1.32941i	−0.0671306	−	0.0434069i
$939$	−21.7736	−	40.3958i	−0.710553	−	1.31827i
$940$	1.42495	+	0.518638i	0.0464766	+	0.0169161i
$941$	−40.7461	+	34.1900i	−1.32828	+	1.11456i	−0.343810	+	0.939039i	$0.611718\pi$
$941$	−40.7461	+	34.1900i	−1.32828	+	1.11456i	−0.984475	+	0.175524i	$0.943838\pi$
$942$	−1.22083	−	0.485212i	−0.0397767	−	0.0158091i
$943$	26.5406	−	9.65998i	0.864280	−	0.314572i
$944$	−28.7036			−0.934223
$945$	4.60541	−	8.69364i	0.149814	−	0.282804i
$946$	1.97066			0.0640718
$947$	−43.3686	+	15.7849i	−1.40929	+	0.512940i	−0.930922	−	0.365219i	$-0.880994\pi$
$947$	−43.3686	+	15.7849i	−1.40929	+	0.512940i	−0.478369	+	0.878159i	$0.658772\pi$
$948$	2.90884	+	19.8789i	0.0944747	+	0.645637i
$949$	21.2175	−	17.8036i	0.688750	−	0.577930i
$950$	−8.54257	−	3.10924i	−0.277158	−	0.100877i
$951$	−20.4038	−	0.596701i	−0.661640	−	0.0193493i
$952$	−0.486155	+	0.248919i	−0.0157564	+	0.00806752i
$953$	−12.2632	+	21.2404i	−0.397243	+	0.688045i	−0.993385	−	0.114834i	$-0.963366\pi$
$953$	−12.2632	+	21.2404i	−0.397243	+	0.688045i	0.596142	+	0.802879i	$0.296700\pi$
$954$	−7.67421	−	3.31301i	−0.248462	−	0.107263i
$955$	−13.8461			−0.448049
$956$	49.6636	−	18.0761i	1.60624	−	0.584622i
$957$	35.2647	+	31.3923i	1.13995	+	1.01477i
$958$	0.709172	+	4.02192i	0.0229123	+	0.129942i
$959$	−15.8057	−	51.3352i	−0.510391	−	1.65770i
$960$	−4.76115	−	4.23832i	−0.153665	−	0.136791i
$961$	−1.65442	+	9.38267i	−0.0533683	+	0.302667i
$962$	−3.84586			−0.123995
$963$	−22.3127	+	6.67281i	−0.719016	+	0.215028i
$964$	38.5586			1.24189
$965$	−1.89316	+	0.689054i	−0.0609430	+	0.0221814i
$966$	−8.05738	−	11.3219i	−0.259242	−	0.364277i
$967$	−7.51127	+	6.30270i	−0.241546	+	0.202681i	−0.755522	−	0.655123i	$-0.772617\pi$
$967$	−7.51127	+	6.30270i	−0.241546	+	0.202681i	0.513976	+	0.857805i	$0.328172\pi$
$968$	−3.54925	−	20.1288i	−0.114077	−	0.646964i
$969$	1.16819	−	0.923403i	0.0375276	−	0.0296640i
$970$	3.22809	+	2.70869i	0.103648	+	0.0869708i
$971$	−3.71712	−	6.43824i	−0.119288	−	0.206613i	0.800198	−	0.599736i	$-0.204728\pi$
$971$	−3.71712	−	6.43824i	−0.119288	−	0.206613i	−0.919486	+	0.393123i	$0.871395\pi$
$972$	−18.1401	+	22.9072i	−0.581845	+	0.734750i
$973$	−8.97058	−	11.8556i	−0.287584	−	0.380072i
$974$	0.406108	−	2.30315i	0.0130125	−	0.0737977i
$975$	−2.27117	−	15.5211i	−0.0727355	−	0.497072i
$976$	−23.3196	+	19.5675i	−0.746442	+	0.626339i
$977$	1.23326	+	6.99419i	0.0394556	+	0.223764i	0.998160	−	0.0606420i	$-0.0193148\pi$
$977$	1.23326	+	6.99419i	0.0394556	+	0.223764i	−0.958704	+	0.284406i	$0.908204\pi$
$978$	1.79228	+	0.0524145i	0.0573109	+	0.00167603i
$979$	−64.3787	+	23.4319i	−2.05755	+	0.748887i
$980$	−6.54934	−	6.72865i	−0.209211	−	0.214939i
$981$	−1.74601	−	1.64825i	−0.0557457	−	0.0526244i
$982$	2.72572	−	4.72108i	0.0869811	−	0.150656i
$983$	52.0919	−	18.9599i	1.66148	−	0.604727i	0.670881	−	0.741565i	$-0.265916\pi$
$983$	52.0919	−	18.9599i	1.66148	−	0.604727i	0.990594	+	0.136837i	$0.0436937\pi$
$984$	7.44875	−	2.46703i	0.237457	−	0.0786460i
$985$	−0.906301	+	0.760477i	−0.0288771	+	0.0242308i
$986$	−0.0495663	−	0.281104i	−0.00157851	−	0.00895218i
$987$	−4.26613	−	2.93883i	−0.135792	−	0.0935438i
$988$	−16.5662	−	13.9007i	−0.527040	−	0.442239i
$989$	−4.67775	+	8.10209i	−0.148744	+	0.257632i
$990$	−0.448187	−	3.84431i	−0.0142443	−	0.122180i
$991$	−8.56188	−	14.8296i	−0.271977	−	0.471078i	0.697391	−	0.716691i	$-0.254344\pi$
$991$	−8.56188	−	14.8296i	−0.271977	−	0.471078i	−0.969368	+	0.245613i	$0.921011\pi$
$992$	13.8494	+	11.6210i	0.439718	+	0.368967i
$993$	−9.25138	−	0.270552i	−0.293584	−	0.00858571i
$994$	−0.0964030	−	0.313107i	−0.00305772	−	0.00993116i
$995$	4.00461	+	1.45756i	0.126955	+	0.0462077i
$996$	29.6375	+	11.7793i	0.939099	+	0.373240i
$997$	−46.2166	−	38.7804i	−1.46370	−	1.22819i	−0.921757	−	0.387769i	$-0.873246\pi$
$997$	−46.2166	−	38.7804i	−1.46370	−	1.22819i	−0.541939	−	0.840418i	$-0.682310\pi$
$998$	5.02149	−	8.69748i	0.158952	−	0.275314i
$999$	−27.8416	−	2.44823i	−0.880869	−	0.0774585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.10	yes	132
3.2	odd	2		567.2.w.a.235.13		132
7.2	even	3		189.2.u.a.79.13	yes	132
21.2	odd	6		567.2.u.a.478.10		132
27.13	even	9		189.2.u.a.67.13	✓	132
27.14	odd	18		567.2.u.a.172.10		132
189.121	even	9	inner	189.2.w.a.121.10	yes	132
189.149	odd	18		567.2.w.a.415.13		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.13	✓	132	27.13	even	9
189.2.u.a.79.13	yes	132	7.2	even	3
189.2.w.a.25.10	yes	132	1.1	even	1	trivial
189.2.w.a.121.10	yes	132	189.121	even	9	inner
567.2.u.a.172.10		132	27.14	odd	18
567.2.u.a.478.10		132	21.2	odd	6
567.2.w.a.235.13		132	3.2	odd	2
567.2.w.a.415.13		132	189.149	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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.332947 + 0.121183i) q^{2} +(-1.35881 + 1.07408i) q^{3} +(-1.43592 + 1.20488i) q^{4} +(0.672463 + 0.244756i) q^{5} +(0.322250 - 0.522275i) q^{6} +(-2.22176 - 1.43659i) q^{7} +(0.686389 - 1.18886i) q^{8} +(0.692708 - 2.91893i) q^{9} +O(q^{10})\)	\(q+(-0.332947 + 0.121183i) q^{2} +(-1.35881 + 1.07408i) q^{3} +(-1.43592 + 1.20488i) q^{4} +(0.672463 + 0.244756i) q^{5} +(0.322250 - 0.522275i) q^{6} +(-2.22176 - 1.43659i) q^{7} +(0.686389 - 1.18886i) q^{8} +(0.692708 - 2.91893i) q^{9} -0.253554 q^{10} +(-4.78127 + 1.74024i) q^{11} +(0.657001 - 3.17949i) q^{12} +(-0.350421 - 1.98733i) q^{13} +(0.913817 + 0.209071i) q^{14} +(-1.17663 + 0.389702i) q^{15} +(0.566532 - 3.21296i) q^{16} +0.150378 q^{17} +(0.123089 + 1.05579i) q^{18} -5.71705 q^{19} +(-1.26051 + 0.458786i) q^{20} +(4.56195 - 0.434288i) q^{21} +(1.38102 - 1.15882i) q^{22} +(1.48618 + 8.42853i) q^{23} +(0.344261 + 2.35267i) q^{24} +(-3.43792 - 2.88476i) q^{25} +(0.357502 + 0.619212i) q^{26} +(2.19391 + 4.71028i) q^{27} +(4.92119 - 0.614114i) q^{28} +(-0.930281 + 5.27589i) q^{29} +(0.344531 - 0.272338i) q^{30} +(3.54974 - 2.97858i) q^{31} +(0.677491 + 3.84224i) q^{32} +(4.62767 - 7.50012i) q^{33} +(-0.0500677 + 0.0182232i) q^{34} +(-1.14243 - 1.50985i) q^{35} +(2.52229 + 5.02598i) q^{36} +(-2.68940 + 4.65817i) q^{37} +(1.90347 - 0.692808i) q^{38} +(2.61071 + 2.32402i) q^{39} +(0.752552 - 0.631466i) q^{40} +(-0.573052 - 3.24994i) q^{41} +(-1.46626 + 0.697424i) q^{42} +(0.837375 + 0.702641i) q^{43} +(4.76875 - 8.25971i) q^{44} +(1.18025 - 1.79333i) q^{45} +(-1.51621 - 2.62615i) q^{46} +(-0.865979 - 0.726643i) q^{47} +(2.68117 + 4.97429i) q^{48} +(2.87239 + 6.38352i) q^{49} +(1.49423 + 0.543854i) q^{50} +(-0.204334 + 0.161517i) q^{51} +(2.89768 + 2.43144i) q^{52} +(-3.93191 + 6.81027i) q^{53} +(-1.30126 - 1.30241i) q^{54} -3.64116 q^{55} +(-3.23290 + 1.65529i) q^{56} +(7.76836 - 6.14056i) q^{57} +(-0.329612 - 1.86932i) q^{58} +(-1.52775 - 8.66431i) q^{59} +(1.22001 - 1.97728i) q^{60} +(-7.14771 - 5.99764i) q^{61} +(-0.820921 + 1.42188i) q^{62} +(-5.73235 + 5.49001i) q^{63} +(2.57135 + 4.45370i) q^{64} +(0.250768 - 1.42218i) q^{65} +(-0.631882 + 3.05793i) q^{66} +(-2.45427 - 0.893282i) q^{67} +(-0.215930 + 0.181187i) q^{68} +(-11.0723 - 9.85647i) q^{69} +(0.563336 + 0.364255i) q^{70} +(-0.174740 - 0.302658i) q^{71} +(-2.99473 - 2.82705i) q^{72} +(6.86264 + 11.8864i) q^{73} +(0.330936 - 1.87683i) q^{74} +(7.76993 + 0.227228i) q^{75} +(8.20923 - 6.88836i) q^{76} +(13.1228 + 3.00236i) q^{77} +(-1.15086 - 0.457403i) q^{78} +(-5.81489 + 2.11645i) q^{79} +(1.16736 - 2.02193i) q^{80} +(-8.04031 - 4.04393i) q^{81} +(0.584633 + 1.01261i) q^{82} +(-1.70577 + 9.67392i) q^{83} +(-6.02733 + 6.12021i) q^{84} +(0.101123 + 0.0368059i) q^{85} +(-0.363949 - 0.132467i) q^{86} +(-4.40265 - 8.16810i) q^{87} +(-1.21291 + 6.87875i) q^{88} +13.4648 q^{89} +(-0.175639 + 0.740108i) q^{90} +(-2.07644 + 4.91878i) q^{91} +(-12.2894 - 10.3120i) q^{92} +(-1.62417 + 7.86002i) q^{93} +(0.376382 + 0.136992i) q^{94} +(-3.84450 - 1.39928i) q^{95} +(-5.04745 - 4.49318i) q^{96} +(-12.7314 - 10.6829i) q^{97} +(-1.72993 - 1.77729i) q^{98} +(1.76762 + 15.1617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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