LMFDB - Embedded newform 189.2.u.a.4.15

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			4.15
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.101938 + 0.578121i) q^{2} +(-0.121715 + 1.72777i) q^{3} +(1.55555 - 0.566175i) q^{4} +(-3.06658 + 1.11614i) q^{5} +(-1.01127 + 0.105760i) q^{6} +(-1.48906 + 2.18694i) q^{7} +(1.07293 + 1.85836i) q^{8} +(-2.97037 - 0.420592i) q^{9} +O(q^{10})$	\(q+(0.101938 + 0.578121i) q^{2} +(-0.121715 + 1.72777i) q^{3} +(1.55555 - 0.566175i) q^{4} +(-3.06658 + 1.11614i) q^{5} +(-1.01127 + 0.105760i) q^{6} +(-1.48906 + 2.18694i) q^{7} +(1.07293 + 1.85836i) q^{8} +(-2.97037 - 0.420592i) q^{9} +(-0.957867 - 1.65908i) q^{10} +(-0.0905002 - 0.0329394i) q^{11} +(0.788885 + 2.75655i) q^{12} +(5.41990 - 1.97268i) q^{13} +(-1.41611 - 0.637921i) q^{14} +(-1.55519 - 5.43419i) q^{15} +(1.57121 - 1.31840i) q^{16} +(1.82060 + 3.15337i) q^{17} +(-0.0596416 - 1.76011i) q^{18} +(-2.60995 + 4.52056i) q^{19} +(-4.13830 + 3.47244i) q^{20} +(-3.59729 - 2.83893i) q^{21} +(0.00981750 - 0.0556778i) q^{22} +(0.920962 - 5.22304i) q^{23} +(-3.34141 + 1.62758i) q^{24} +(4.32791 - 3.63155i) q^{25} +(1.69294 + 2.93226i) q^{26} +(1.08822 - 5.08092i) q^{27} +(-1.07811 + 4.24497i) q^{28} +(2.72930 + 0.993386i) q^{29} +(2.98309 - 1.45304i) q^{30} +(-1.19084 + 0.433429i) q^{31} +(4.21000 + 3.53261i) q^{32} +(0.0679269 - 0.152354i) q^{33} +(-1.63744 + 1.37398i) q^{34} +(2.12537 - 8.36843i) q^{35} +(-4.85870 + 1.02750i) q^{36} +6.83261 q^{37} +(-2.87948 - 1.04805i) q^{38} +(2.74865 + 9.60444i) q^{39} +(-5.36442 - 4.50128i) q^{40} +(1.79913 - 0.654829i) q^{41} +(1.27454 - 2.36906i) q^{42} +(-0.580627 - 3.29290i) q^{43} -0.159427 q^{44} +(9.57832 - 2.02558i) q^{45} +3.11343 q^{46} +(5.57827 + 2.03032i) q^{47} +(2.08665 + 2.87516i) q^{48} +(-2.56543 - 6.51296i) q^{49} +(2.54065 + 2.13186i) q^{50} +(-5.66989 + 2.76176i) q^{51} +(7.31406 - 6.13722i) q^{52} +(1.47412 - 2.55324i) q^{53} +(3.04832 + 0.111185i) q^{54} +0.314291 q^{55} +(-5.66178 - 0.420779i) q^{56} +(-7.49281 - 5.05961i) q^{57} +(-0.296076 + 1.67913i) q^{58} +(-6.58528 - 5.52571i) q^{59} +(-5.49588 - 7.57267i) q^{60} +(0.557272 + 0.202830i) q^{61} +(-0.371966 - 0.644265i) q^{62} +(5.34286 - 5.86974i) q^{63} +(0.437956 - 0.758562i) q^{64} +(-14.4188 + 12.0988i) q^{65} +(0.0950034 + 0.0237392i) q^{66} +(0.948490 - 5.37916i) q^{67} +(4.61740 + 3.87446i) q^{68} +(8.91211 + 2.22693i) q^{69} +(5.05462 + 0.375655i) q^{70} +(-6.46106 + 11.1909i) q^{71} +(-2.40538 - 5.97129i) q^{72} -12.5093 q^{73} +(0.696504 + 3.95007i) q^{74} +(5.74771 + 7.91965i) q^{75} +(-1.50048 + 8.50966i) q^{76} +(0.206796 - 0.148870i) q^{77} +(-5.27233 + 2.56811i) q^{78} +(2.23377 + 12.6684i) q^{79} +(-3.34672 + 5.79668i) q^{80} +(8.64621 + 2.49863i) q^{81} +(0.561970 + 0.973361i) q^{82} +(-1.05332 - 0.383377i) q^{83} +(-7.20310 - 2.37941i) q^{84} +(-9.10264 - 7.63802i) q^{85} +(1.84451 - 0.671345i) q^{86} +(-2.04854 + 4.59470i) q^{87} +(-0.0358867 - 0.203524i) q^{88} +(8.03254 - 13.9128i) q^{89} +(2.14743 + 5.33094i) q^{90} +(-3.75639 + 14.7904i) q^{91} +(-1.52455 - 8.64614i) q^{92} +(-0.603923 - 2.11025i) q^{93} +(-0.605133 + 3.43188i) q^{94} +(2.95801 - 16.7757i) q^{95} +(-6.61596 + 6.84394i) q^{96} +(-0.629031 - 3.56741i) q^{97} +(3.50376 - 2.14705i) q^{98} +(0.254965 + 0.135906i) 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 $

$2$	0.101938	+	0.578121i	0.0720812	+	0.408793i	0.999404	+	0.0345296i	$0.0109933\pi$
$2$	0.101938	+	0.578121i	0.0720812	+	0.408793i	−0.927322	+	0.374263i	$0.877896\pi$
$3$	−0.121715	+	1.72777i	−0.0702724	+	0.997528i
$3$	−0.121715	+	1.72777i	−0.0702724	+	0.997528i
$4$	1.55555	−	0.566175i	0.777777	−	0.283088i
$5$	−3.06658	+	1.11614i	−1.37142	+	0.499155i	−0.919565	−	0.392939i	$-0.871459\pi$
$5$	−3.06658	+	1.11614i	−1.37142	+	0.499155i	−0.451851	+	0.892093i	$0.649236\pi$
$6$	−1.01127	+	0.105760i	−0.412848	+	0.0431762i
$7$	−1.48906	+	2.18694i	−0.562810	+	0.826586i
$7$	−1.48906	+	2.18694i	−0.562810	+	0.826586i
$8$	1.07293	+	1.85836i	0.379337	+	0.657031i
$9$	−2.97037	−	0.420592i	−0.990124	−	0.140197i
$10$	−0.957867	−	1.65908i	−0.302904	−	0.524646i
$11$	−0.0905002	−	0.0329394i	−0.0272868	−	0.00993159i	0.328341	−	0.944559i	$-0.393511\pi$
$11$	−0.0905002	−	0.0329394i	−0.0272868	−	0.00993159i	−0.355628	+	0.934628i	$0.615733\pi$
$12$	0.788885	+	2.75655i	0.227732	+	0.795747i
$13$	5.41990	−	1.97268i	1.50321	−	0.547123i	0.546320	−	0.837576i	$-0.316028\pi$
$13$	5.41990	−	1.97268i	1.50321	−	0.547123i	0.956889	+	0.290453i	$0.0938060\pi$
$14$	−1.41611	−	0.637921i	−0.378471	−	0.170491i
$15$	−1.55519	−	5.43419i	−0.401548	−	1.40310i
$16$	1.57121	−	1.31840i	0.392803	−	0.329601i
$17$	1.82060	+	3.15337i	0.441561	+	0.764805i	0.997806	−	0.0662131i	$-0.0210917\pi$
$17$	1.82060	+	3.15337i	0.441561	+	0.764805i	−0.556245	+	0.831018i	$0.687758\pi$
$18$	−0.0596416	−	1.76011i	−0.0140577	−	0.414861i
$19$	−2.60995	+	4.52056i	−0.598763	+	1.03709i	0.394241	+	0.919007i	$0.371007\pi$
$19$	−2.60995	+	4.52056i	−0.598763	+	1.03709i	−0.993004	+	0.118081i	$0.962326\pi$
$20$	−4.13830	+	3.47244i	−0.925351	+	0.776462i
$21$	−3.59729	−	2.83893i	−0.784993	−	0.619505i
$22$	0.00981750	−	0.0556778i	0.00209310	−	0.0118705i
$23$	0.920962	−	5.22304i	0.192034	−	1.08908i	−0.724546	−	0.689227i	$-0.757950\pi$
$23$	0.920962	−	5.22304i	0.192034	−	1.08908i	0.916580	−	0.399852i	$-0.130938\pi$
$24$	−3.34141	+	1.62758i	−0.682063	+	0.332228i
$25$	4.32791	−	3.63155i	0.865582	−	0.726310i
$26$	1.69294	+	2.93226i	0.332013	+	0.575064i
$27$	1.08822	−	5.08092i	0.209429	−	0.977824i
$28$	−1.07811	+	4.24497i	−0.203744	+	0.802224i
$29$	2.72930	+	0.993386i	0.506819	+	0.184467i	0.582759	−	0.812645i	$-0.301973\pi$
$29$	2.72930	+	0.993386i	0.506819	+	0.184467i	−0.0759394	+	0.997112i	$0.524196\pi$
$30$	2.98309	−	1.45304i	0.544634	−	0.265287i
$31$	−1.19084	+	0.433429i	−0.213881	+	0.0778462i	−0.446738	−	0.894665i	$-0.647415\pi$
$31$	−1.19084	+	0.433429i	−0.213881	+	0.0778462i	0.232858	+	0.972511i	$0.425192\pi$
$32$	4.21000	+	3.53261i	0.744230	+	0.624483i
$33$	0.0679269	−	0.152354i	0.0118246	−	0.0265215i
$34$	−1.63744	+	1.37398i	−0.280819	+	0.235635i
$35$	2.12537	−	8.36843i	0.359253	−	1.41452i
$36$	−4.85870	+	1.02750i	−0.809783	+	0.171249i
$37$	6.83261			1.12327			0.561637	−	0.827384i	$-0.310172\pi$
$37$	6.83261			1.12327			0.561637	+	0.827384i	$0.310172\pi$
$38$	−2.87948	−	1.04805i	−0.467114	−	0.170015i
$39$	2.74865	+	9.60444i	0.440137	+	1.53794i
$40$	−5.36442	−	4.50128i	−0.848189	−	0.711715i
$41$	1.79913	−	0.654829i	0.280977	−	0.102267i	−0.197688	−	0.980265i	$-0.563343\pi$
$41$	1.79913	−	0.654829i	0.280977	−	0.102267i	0.478665	+	0.877998i	$0.341121\pi$
$42$	1.27454	−	2.36906i	0.196666	−	0.365554i
$43$	−0.580627	−	3.29290i	−0.0885448	−	0.502163i	−0.996535	−	0.0831717i	$-0.973495\pi$
$43$	−0.580627	−	3.29290i	−0.0885448	−	0.502163i	0.907990	−	0.418991i	$-0.137616\pi$
$44$	−0.159427			−0.0240346
$45$	9.57832	−	2.02558i	1.42785	−	0.301956i
$46$	3.11343			0.459050
$47$	5.57827	+	2.03032i	0.813674	+	0.296153i	0.715141	−	0.698981i	$-0.246363\pi$
$47$	5.57827	+	2.03032i	0.813674	+	0.296153i	0.0985334	+	0.995134i	$0.468585\pi$
$48$	2.08665	+	2.87516i	0.301183	+	0.414994i
$49$	−2.56543	−	6.51296i	−0.366490	−	0.930422i
$50$	2.54065	+	2.13186i	0.359303	+	0.301491i
$51$	−5.66989	+	2.76176i	−0.793944	+	0.386724i
$52$	7.31406	−	6.13722i	1.01428	−	0.851080i
$53$	1.47412	−	2.55324i	0.202485	−	0.350715i	−0.746843	−	0.665000i	$-0.768431\pi$
$53$	1.47412	−	2.55324i	0.202485	−	0.350715i	0.949329	+	0.314285i	$0.101765\pi$
$54$	3.04832	+	0.111185i	0.414823	+	0.0151304i
$55$	0.314291			0.0423790
$56$	−5.66178	−	0.420779i	−0.756587	−	0.0562289i
$57$	−7.49281	−	5.05961i	−0.992447	−	0.670161i
$58$	−0.296076	+	1.67913i	−0.0388767	+	0.220481i
$59$	−6.58528	−	5.52571i	−0.857331	−	0.719386i	0.104060	−	0.994571i	$-0.466816\pi$
$59$	−6.58528	−	5.52571i	−0.857331	−	0.719386i	−0.961391	+	0.275185i	$0.911261\pi$
$60$	−5.49588	−	7.57267i	−0.709516	−	0.977627i
$61$	0.557272	+	0.202830i	0.0713513	+	0.0259698i	0.377449	−	0.926030i	$-0.376801\pi$
$61$	0.557272	+	0.202830i	0.0713513	+	0.0259698i	−0.306098	+	0.952000i	$0.599023\pi$
$62$	−0.371966	−	0.644265i	−0.0472398	−	0.0818217i
$63$	5.34286	−	5.86974i	0.673137	−	0.739518i
$64$	0.437956	−	0.758562i	0.0547445	−	0.0948202i
$65$	−14.4188	+	12.0988i	−1.78843	+	1.50067i
$66$	0.0950034	+	0.0237392i	0.0116941	+	0.00292209i
$67$	0.948490	−	5.37916i	0.115877	−	0.657168i	−0.870436	−	0.492282i	$-0.836163\pi$
$67$	0.948490	−	5.37916i	0.115877	−	0.657168i	0.986312	−	0.164887i	$-0.0527259\pi$
$68$	4.61740	+	3.87446i	0.559942	+	0.469847i
$69$	8.91211	+	2.22693i	1.07289	+	0.268091i
$70$	5.05462	+	0.375655i	0.604142	+	0.0448994i
$71$	−6.46106	+	11.1909i	−0.766787	+	1.32811i	0.172509	+	0.985008i	$0.444813\pi$
$71$	−6.46106	+	11.1909i	−0.766787	+	1.32811i	−0.939296	+	0.343107i	$0.888521\pi$
$72$	−2.40538	−	5.97129i	−0.283477	−	0.703724i
$73$	−12.5093			−1.46410			−0.732050	−	0.681250i	$-0.761436\pi$
$73$	−12.5093			−1.46410			−0.732050	+	0.681250i	$0.761436\pi$
$74$	0.696504	+	3.95007i	0.0809670	+	0.459187i
$75$	5.74771	+	7.91965i	0.663688	+	0.914482i
$76$	−1.50048	+	8.50966i	−0.172117	+	0.976125i
$77$	0.206796	−	0.148870i	0.0235666	−	0.0169653i
$78$	−5.27233	+	2.56811i	−0.596974	+	0.290782i
$79$	2.23377	+	12.6684i	0.251319	+	1.42530i	0.805347	+	0.592803i	$0.201979\pi$
$79$	2.23377	+	12.6684i	0.251319	+	1.42530i	−0.554028	+	0.832498i	$0.686910\pi$
$80$	−3.34672	+	5.79668i	−0.374174	+	0.648089i
$81$	8.64621	+	2.49863i	0.960689	+	0.277625i
$82$	0.561970	+	0.973361i	0.0620592	+	0.107490i
$83$	−1.05332	−	0.383377i	−0.115617	−	0.0420811i	0.283564	−	0.958953i	$-0.408483\pi$
$83$	−1.05332	−	0.383377i	−0.115617	−	0.0420811i	−0.399181	+	0.916872i	$0.630705\pi$
$84$	−7.20310	−	2.37941i	−0.785923	−	0.259615i
$85$	−9.10264	−	7.63802i	−0.987319	−	0.828459i
$86$	1.84451	−	0.671345i	0.198898	−	0.0723930i
$87$	−2.04854	+	4.59470i	−0.219626	+	0.492603i
$88$	−0.0358867	−	0.203524i	−0.00382554	−	0.0216957i
$89$	8.03254	−	13.9128i	0.851448	−	1.47475i	−0.0284540	−	0.999595i	$-0.509058\pi$
$89$	8.03254	−	13.9128i	0.851448	−	1.47475i	0.879902	−	0.475156i	$-0.157608\pi$
$90$	2.14743	+	5.33094i	0.226359	+	0.561930i
$91$	−3.75639	+	14.7904i	−0.393777	+	1.55046i
$92$	−1.52455	−	8.64614i	−0.158945	−	0.901422i
$93$	−0.603923	−	2.11025i	−0.0626239	−	0.218822i
$94$	−0.605133	+	3.43188i	−0.0624147	+	0.353971i
$95$	2.95801	−	16.7757i	0.303486	−	1.72115i
$96$	−6.61596	+	6.84394i	−0.675238	+	0.698506i
$97$	−0.629031	−	3.56741i	−0.0638684	−	0.362216i	−0.999946	−	0.0104214i	$-0.996683\pi$
$97$	−0.629031	−	3.56741i	−0.0638684	−	0.362216i	0.936077	−	0.351794i	$-0.114428\pi$
$98$	3.50376	−	2.14705i	0.353933	−	0.216884i
$99$	0.254965	+	0.135906i	0.0256250	+	0.0136590i
$100$	4.67621	−	8.09942i	0.467621	−	0.809942i
$101$	−2.08003	−	11.7964i	−0.206971	−	1.17379i	−0.894308	−	0.447451i	$-0.852332\pi$
$101$	−2.08003	−	11.7964i	−0.206971	−	1.17379i	0.687337	−	0.726338i	$-0.258779\pi$
$102$	−2.17461	−	2.99635i	−0.215319	−	0.296683i
$103$	−10.9845	+	3.99804i	−1.08234	+	0.393938i	−0.820777	−	0.571249i	$-0.806459\pi$
$103$	−10.9845	+	3.99804i	−1.08234	+	0.393938i	−0.261560	+	0.965187i	$0.584237\pi$
$104$	9.48112	+	7.95560i	0.929700	+	0.780111i
$105$	14.2000	+	4.69071i	1.38578	+	0.457766i
$106$	1.62635	+	0.591943i	0.157965	+	0.0574946i
$107$	6.42815	+	11.1339i	0.621433	+	1.07635i	0.989219	+	0.146443i	$0.0467826\pi$
$107$	6.42815	+	11.1339i	0.621433	+	1.07635i	−0.367786	+	0.929910i	$0.619884\pi$
$108$	−1.18390	−	8.51977i	−0.113921	−	0.819815i
$109$	−5.34505	+	9.25790i	−0.511963	+	0.886746i	0.487941	+	0.872877i	$0.337748\pi$
$109$	−5.34505	+	9.25790i	−0.511963	+	0.886746i	−0.999904	+	0.0138693i	$0.995585\pi$
$110$	0.0320383	+	0.181698i	0.00305473	+	0.0173242i
$111$	−0.831633	+	11.8052i	−0.0789351	+	1.12050i
$112$	0.543649	+	5.39932i	0.0513700	+	0.510188i
$113$	0.507156	−	2.87623i	0.0477093	−	0.270573i	−0.951616	−	0.307288i	$-0.900578\pi$
$113$	0.507156	−	2.87623i	0.0477093	−	0.270573i	0.999326	+	0.0367155i	$0.0116895\pi$
$114$	2.16126	−	4.84752i	0.202420	−	0.454012i
$115$	3.00546	+	17.0448i	0.280260	+	1.58943i
$116$	4.80801			0.446412
$117$	−16.9288	+	3.58003i	−1.56507	+	0.330974i
$118$	2.52323	−	4.37037i	0.232282	−	0.402325i
$119$	−9.60722	−	0.714000i	−0.880692	−	0.0654523i
$120$	8.43010	−	8.72060i	0.769560	−	0.796078i
$121$	−8.41938	−	7.06470i	−0.765399	−	0.642246i
$122$	−0.0604531	+	0.342846i	−0.00547316	+	0.0310399i
$123$	0.912412	+	3.18818i	0.0822694	+	0.287469i
$124$	−1.60701	+	1.34844i	−0.144314	+	0.121094i
$125$	−1.06009	+	1.83613i	−0.0948175	+	0.164229i
$126$	3.93806	+	2.49046i	0.350830	+	0.221868i
$127$	2.09216	+	3.62373i	0.185650	+	0.321554i	0.943795	−	0.330531i	$-0.107228\pi$
$127$	2.09216	+	3.62373i	0.185650	+	0.321554i	−0.758146	+	0.652085i	$0.773894\pi$
$128$	10.8118	+	3.93519i	0.955641	+	0.347825i
$129$	5.76004	−	0.602393i	0.507144	−	0.0530378i
$130$	−8.46437	−	7.10245i	−0.742374	−	0.622926i
$131$	2.46835	−	13.9987i	0.215661	−	1.22307i	−0.664096	−	0.747648i	$-0.731183\pi$
$131$	2.46835	−	13.9987i	0.215661	−	1.22307i	0.879756	−	0.475425i	$-0.157706\pi$
$132$	0.0194047	−	0.275454i	0.00168897	−	0.0239752i
$133$	−5.99984	−	12.4392i	−0.520253	−	1.07861i
$134$	3.20649			0.276998
$135$	2.33391	+	16.7957i	0.200871	+	1.44554i
$136$	−3.90674	+	6.76668i	−0.335000	+	0.580238i
$137$	−3.73856	+	3.13703i	−0.319407	+	0.268014i	−0.788367	−	0.615205i	$-0.789073\pi$
$137$	−3.73856	+	3.13703i	−0.319407	+	0.268014i	0.468960	+	0.883219i	$0.344629\pi$
$138$	−0.378952	+	5.37928i	−0.0322585	+	0.457915i
$139$	−6.80377	−	5.70904i	−0.577088	−	0.484235i	0.306901	−	0.951741i	$-0.400708\pi$
$139$	−6.80377	−	5.70904i	−0.577088	−	0.484235i	−0.883989	+	0.467507i	$0.845152\pi$
$140$	−1.43188	−	14.2209i	−0.121016	−	1.20188i
$141$	−4.18689	+	9.39084i	−0.352600	+	0.790851i
$142$	−7.12831	−	2.59449i	−0.598195	−	0.217725i
$143$	−0.555481			−0.0464516
$144$	−5.22159	+	3.25531i	−0.435132	+	0.271276i
$145$	−9.47839			−0.787137
$146$	−1.27517	−	7.23187i	−0.105534	−	0.598514i
$147$	11.5651	−	3.63974i	0.953876	−	0.300201i
$148$	10.6285	−	3.86845i	0.873656	−	0.317985i
$149$	−16.1062	−	13.5147i	−1.31947	−	1.10717i	−0.986417	−	0.164258i	$-0.947477\pi$
$149$	−16.1062	−	13.5147i	−1.31947	−	1.10717i	−0.333052	−	0.942909i	$-0.608078\pi$
$150$	−3.99260	+	4.13018i	−0.325994	+	0.337228i
$151$	10.2784	+	3.74103i	0.836445	+	0.304441i	0.724501	−	0.689274i	$-0.242070\pi$
$151$	10.2784	+	3.74103i	0.836445	+	0.304441i	0.111944	+	0.993715i	$0.464292\pi$
$152$	−11.2011			−0.908531
$153$	−4.08158	−	10.1324i	−0.329976	−	0.819157i
$154$	0.107145	+	0.104378i	0.00863401	+	0.00841099i
$155$	3.16803	−	2.65829i	0.254462	−	0.213519i
$156$	9.71347	+	13.3840i	0.777700	+	1.07158i
$157$	15.9298	+	13.3667i	1.27134	+	1.06678i	0.994377	+	0.105895i	$0.0337708\pi$
$157$	15.9298	+	13.3667i	1.27134	+	1.06678i	0.276958	+	0.960882i	$0.410674\pi$
$158$	−7.09613	+	2.58278i	−0.564538	+	0.205475i
$159$	4.23199	+	2.85770i	0.335619	+	0.226630i
$160$	−16.8532	−	6.13406i	−1.33236	−	0.484940i
$161$	10.0511	+	9.79148i	0.792139	+	0.771677i
$162$	−0.563129	+	5.25325i	−0.0442436	+	0.412735i
$163$	−2.63629	−	4.56618i	−0.206490	−	0.357651i	0.744117	−	0.668050i	$-0.232871\pi$
$163$	−2.63629	−	4.56618i	−0.206490	−	0.357651i	−0.950606	+	0.310399i	$0.899537\pi$
$164$	2.42789	−	2.03724i	0.189587	−	0.159082i
$165$	−0.0382540	+	0.543022i	−0.00297807	+	0.0422742i
$166$	0.114265	−	0.648026i	0.00886865	−	0.0502966i
$167$	−2.10338	+	11.9289i	−0.162764	+	0.923083i	0.788575	+	0.614938i	$0.210819\pi$
$167$	−2.10338	+	11.9289i	−0.162764	+	0.923083i	−0.951340	+	0.308144i	$0.900292\pi$
$168$	1.41613	−	9.73103i	0.109257	−	0.750766i
$169$	15.5252	−	13.0272i	1.19425	−	1.00209i
$170$	3.48779	−	6.04103i	0.267501	−	0.463326i
$171$	9.65382	−	12.3300i	0.738246	−	0.942900i
$172$	−2.76756	−	4.79355i	−0.211024	−	0.365504i
$173$	18.3911	−	15.4320i	1.39825	−	1.17327i	0.436385	−	0.899760i	$-0.356259\pi$
$173$	18.3911	−	15.4320i	1.39825	−	1.17327i	0.961868	−	0.273514i	$-0.0881859\pi$
$174$	−2.86511	−	0.715927i	−0.217204	−	0.0542743i
$175$	1.49748	+	14.8725i	0.113199	+	1.12425i
$176$	−0.185622	+	0.0675610i	−0.0139918	+	0.00509260i
$177$	10.3487	−	10.7053i	0.777854	−	0.804658i
$178$	8.86208	+	3.22553i	0.664241	+	0.241764i
$179$	−6.39598	−	11.0782i	−0.478058	−	0.828021i	0.521625	−	0.853175i	$-0.325326\pi$
$179$	−6.39598	−	11.0782i	−0.478058	−	0.828021i	−0.999684	+	0.0251534i	$0.991993\pi$
$180$	13.7528	−	8.57391i	1.02507	−	0.639061i
$181$	1.35421	+	2.34556i	0.100658	+	0.174344i	0.911956	−	0.410288i	$-0.134572\pi$
$181$	1.35421	+	2.34556i	0.100658	+	0.174344i	−0.811298	+	0.584633i	$0.801239\pi$
$182$	−8.93357	−	0.663936i	−0.662201	−	0.0492142i
$183$	−0.418272	+	0.938149i	−0.0309196	+	0.0693500i
$184$	10.6944	−	3.89245i	0.788404	−	0.286956i
$185$	−20.9527	+	7.62618i	−1.54048	+	0.560688i
$186$	1.15841	−	0.564255i	0.0849391	−	0.0413732i
$187$	−0.0608946	−	0.345350i	−0.00445305	−	0.0252545i
$188$	9.82681			0.716694
$189$	9.49125	+	9.94566i	0.690387	+	0.723440i
$190$	9.99993			0.725471
$191$	1.32139	+	7.49397i	0.0956123	+	0.542244i	0.994558	+	0.104184i	$0.0332232\pi$
$191$	1.32139	+	7.49397i	0.0956123	+	0.542244i	−0.898946	+	0.438060i	$0.855666\pi$
$192$	1.25731	+	0.849015i	0.0907388	+	0.0612724i
$193$	12.7550	−	4.64244i	0.918124	−	0.334170i	0.160632	−	0.987014i	$-0.448647\pi$
$193$	12.7550	−	4.64244i	0.918124	−	0.334170i	0.757492	+	0.652844i	$0.226424\pi$
$194$	1.99827	−	0.727312i	0.143468	−	0.0522179i
$195$	−19.1489	−	26.3849i	−1.37128	−	1.88946i
$196$	−7.67813	−	8.67877i	−0.548438	−	0.619912i
$197$	0.798142	+	1.38242i	0.0568653	+	0.0984936i	0.893057	−	0.449944i	$-0.148556\pi$
$197$	0.798142	+	1.38242i	0.0568653	+	0.0984936i	−0.836191	+	0.548438i	$0.815223\pi$
$198$	−0.0525792	+	0.161255i	−0.00373664	+	0.0114599i
$199$	−0.488401	−	0.845935i	−0.0346218	−	0.0599668i	0.848195	−	0.529684i	$-0.177689\pi$
$199$	−0.488401	−	0.845935i	−0.0346218	−	0.0599668i	−0.882817	+	0.469717i	$0.844356\pi$
$200$	11.3923	+	4.14645i	0.805555	+	0.293198i
$201$	9.17849	+	2.29350i	0.647401	+	0.161771i
$202$	6.60773	−	2.40502i	0.464918	−	0.169216i
$203$	−6.23656	+	4.48962i	−0.437721	+	0.315110i
$204$	−7.25618	+	7.50622i	−0.508034	+	0.525541i
$205$	−4.78629	+	4.01617i	−0.334289	+	0.280502i
$206$	−3.43109	−	5.94282i	−0.239055	−	0.414056i
$207$	−4.93237	+	15.1270i	−0.342823	+	1.05140i
$208$	5.91502	−	10.2451i	0.410133	−	0.710370i
$209$	0.385105	−	0.323141i	0.0266383	−	0.0223522i
$210$	−1.26427	+	8.68749i	−0.0872429	+	0.599494i
$211$	0.797672	−	4.52382i	0.0549140	−	0.311433i	−0.944962	−	0.327180i	$-0.893902\pi$
$211$	0.797672	−	4.52382i	0.0549140	−	0.311433i	0.999876	+	0.0157472i	$0.00501271\pi$
$212$	0.847483	−	4.80631i	0.0582053	−	0.330099i
$213$	−18.5489	−	12.5253i	−1.27095	−	0.858221i
$214$	−5.78146	+	4.85122i	−0.395212	+	0.331622i
$215$	5.45589	+	9.44988i	0.372089	+	0.644476i
$216$	10.6098	−	3.42914i	0.721905	−	0.233323i
$217$	0.825338	−	3.24969i	0.0560276	−	0.220603i
$218$	−5.89705	−	2.14635i	−0.399398	−	0.145369i
$219$	1.52257	−	21.6131i	0.102886	−	1.46048i
$220$	0.488897	−	0.177944i	0.0329614	−	0.0119970i
$221$	16.0881	+	13.4995i	1.08220	+	0.908074i
$222$	−6.90959	+	0.722614i	−0.463741	+	0.0484987i
$223$	11.6447	−	9.77106i	0.779787	−	0.654319i	−0.163408	−	0.986559i	$-0.552249\pi$
$223$	11.6447	−	9.77106i	0.779787	−	0.654319i	0.943195	+	0.332240i	$0.107804\pi$
$224$	−13.9945	+	3.94677i	−0.935049	+	0.263705i
$225$	−14.3829	+	8.96676i	−0.958860	+	0.597784i
$226$	1.71450			0.114047
$227$	20.5483	+	7.47896i	1.36384	+	0.496396i	0.917239	−	0.398338i	$-0.130413\pi$
$227$	20.5483	+	7.47896i	1.36384	+	0.496396i	0.446599	+	0.894734i	$0.352635\pi$
$228$	−14.5201	−	3.62824i	−0.961617	−	0.240286i
$229$	−0.228822	−	0.192005i	−0.0151210	−	0.0126880i	0.635196	−	0.772351i	$-0.280919\pi$
$229$	−0.228822	−	0.192005i	−0.0151210	−	0.0126880i	−0.650317	+	0.759663i	$0.725364\pi$
$230$	−9.54757	+	3.47503i	−0.629548	+	0.229137i
$231$	0.232043	+	0.375416i	0.0152673	+	0.0247006i
$232$	1.08227	+	6.13787i	0.0710547	+	0.402971i
$233$	−9.08213			−0.594990			−0.297495	−	0.954723i	$-0.596151\pi$
$233$	−9.08213			−0.594990			−0.297495	+	0.954723i	$0.596151\pi$
$234$	−3.79538	−	9.42195i	−0.248112	−	0.615932i
$235$	−19.3723			−1.26371
$236$	−13.3723	−	4.86711i	−0.870461	−	0.316822i
$237$	−22.1599	+	2.31751i	−1.43944	+	0.150538i
$238$	−0.566565	−	5.62691i	−0.0367249	−	0.364739i
$239$	9.43419	+	7.91623i	0.610247	+	0.512058i	0.894721	−	0.446626i	$-0.147374\pi$
$239$	9.43419	+	7.91623i	0.610247	+	0.512058i	−0.284474	+	0.958684i	$0.591819\pi$
$240$	−9.60798	−	6.48790i	−0.620193	−	0.418792i
$241$	−16.5906	+	13.9212i	−1.06869	+	0.896740i	−0.994933	−	0.100536i	$-0.967944\pi$
$241$	−16.5906	+	13.9212i	−1.06869	+	0.896740i	−0.0737601	+	0.997276i	$0.523500\pi$
$242$	3.22599	−	5.58758i	0.207375	−	0.359183i
$243$	−5.36943	+	14.6345i	−0.344449	+	0.938805i
$244$	0.981703			0.0628471
$245$	15.1365	+	17.1091i	0.967034	+	1.09306i
$246$	−1.75014	+	0.852482i	−0.111585	+	0.0543523i
$247$	−5.22802	+	29.6496i	−0.332651	+	1.88656i
$248$	−2.08315	−	1.74797i	−0.132280	−	0.110996i
$249$	0.790592	−	1.77323i	0.0501017	−	0.112374i
$250$	−1.16957	−	0.425689i	−0.0739701	−	0.0269229i
$251$	−11.0766	−	19.1853i	−0.699152	−	1.21097i	−0.968761	−	0.247997i	$-0.920228\pi$
$251$	−11.0766	−	19.1853i	−0.699152	−	1.21097i	0.269609	−	0.962970i	$-0.413105\pi$
$252$	4.98780	−	12.1557i	0.314202	−	0.765736i
$253$	−0.255391	+	0.442350i	−0.0160563	+	0.0278103i
$254$	−1.88168	+	1.57892i	−0.118067	+	0.0990703i
$255$	14.3047	−	14.7976i	0.895793	−	0.926661i
$256$	−0.868673	+	4.92649i	−0.0542921	+	0.307906i
$257$	13.1123	+	11.0025i	0.817920	+	0.686316i	0.952484	−	0.304588i	$-0.0985189\pi$
$257$	13.1123	+	11.0025i	0.817920	+	0.686316i	−0.134564	+	0.990905i	$0.542963\pi$
$258$	0.935425	+	3.26859i	0.0582370	+	0.203494i
$259$	−10.1741	+	14.9425i	−0.632190	+	0.928483i
$260$	−15.5791	+	26.9838i	−0.966176	+	1.67347i
$261$	−7.68924	−	4.09865i	−0.475952	−	0.253700i
$262$	8.34456			0.515528
$263$	1.76194	+	9.99245i	0.108646	+	0.616161i	0.989701	+	0.143148i	$0.0457225\pi$
$263$	1.76194	+	9.99245i	0.108646	+	0.616161i	−0.881055	+	0.473013i	$0.843166\pi$
$264$	0.356010	−	0.0372320i	0.0219109	−	0.00229147i
$265$	−1.67071	+	9.47505i	−0.102631	+	0.582048i
$266$	6.57972	−	4.73666i	0.403429	−	0.290423i
$267$	23.0604	+	15.5718i	1.41127	+	0.952977i
$268$	−1.57012	−	8.90457i	−0.0959101	−	0.543933i
$269$	7.74828	−	13.4204i	0.472421	−	0.818257i	−0.527081	−	0.849815i	$-0.676714\pi$
$269$	7.74828	−	13.4204i	0.472421	−	0.818257i	0.999502	+	0.0315578i	$0.0100468\pi$
$270$	−9.47201	+	3.06140i	−0.576448	+	0.186311i
$271$	−7.59076	−	13.1476i	−0.461106	−	0.798659i	0.537911	−	0.843002i	$-0.319214\pi$
$271$	−7.59076	−	13.1476i	−0.461106	−	0.798659i	−0.999016	+	0.0443433i	$0.985880\pi$
$272$	7.01796	+	2.55433i	0.425527	+	0.154879i
$273$	−25.0972	−	8.29040i	−1.51895	−	0.501758i
$274$	−2.19468	−	1.84156i	−0.132586	−	0.111253i
$275$	−0.511298	+	0.186097i	−0.0308324	+	0.0112221i
$276$	15.1241	−	1.58170i	0.910363	−	0.0952071i
$277$	−2.59581	−	14.7216i	−0.155967	−	0.884533i	−0.957896	−	0.287114i	$-0.907304\pi$
$277$	−2.59581	−	14.7216i	−0.155967	−	0.884533i	0.801929	−	0.597419i	$-0.203807\pi$
$278$	2.60695	−	4.51537i	0.156354	−	0.270814i
$279$	3.71953	−	0.786589i	0.222682	−	0.0470919i
$280$	17.8320	−	5.02901i	1.06566	−	0.300541i
$281$	2.25837	+	12.8079i	0.134723	+	0.764054i	0.975052	+	0.221977i	$0.0712509\pi$
$281$	2.25837	+	12.8079i	0.134723	+	0.764054i	−0.840329	+	0.542077i	$0.817638\pi$
$282$	−5.85584	−	1.46324i	−0.348710	−	0.0871348i
$283$	3.32897	−	18.8795i	0.197886	−	1.12227i	−0.710361	−	0.703837i	$-0.751468\pi$
$283$	3.32897	−	18.8795i	0.197886	−	1.12227i	0.908248	−	0.418433i	$-0.137420\pi$
$284$	−3.71453	+	21.0661i	−0.220417	+	1.25004i
$285$	28.6246	+	7.15263i	1.69557	+	0.423685i
$286$	−0.0566247	−	0.321135i	−0.00334829	−	0.0189891i
$287$	−1.24693	+	4.90967i	−0.0736039	+	0.289808i
$288$	−11.0195	−	12.2639i	−0.649329	−	0.722655i
$289$	1.87083	−	3.24036i	0.110049	−	0.190610i
$290$	−0.966211	−	5.47965i	−0.0567378	−	0.321776i
$291$	6.24023	−	0.652612i	0.365809	−	0.0382568i
$292$	−19.4589	+	7.08244i	−1.13874	+	0.414469i
$293$	−0.339856	−	0.285173i	−0.0198546	−	0.0166600i	0.632806	−	0.774310i	$-0.281903\pi$
$293$	−0.339856	−	0.285173i	−0.0198546	−	0.0166600i	−0.652661	+	0.757650i	$0.726347\pi$
$294$	3.28314	+	6.31501i	0.191476	+	0.368299i
$295$	26.3618	+	9.59490i	1.53484	+	0.558637i
$296$	7.33089	+	12.6975i	0.426099	+	0.738026i
$297$	−0.265847	+	0.423979i	−0.0154260	+	0.0246017i
$298$	6.17128	−	10.6890i	0.357493	−	0.619196i
$299$	−5.31187	−	30.1251i	−0.307193	−	1.74218i
$300$	13.4248	+	9.06523i	0.775079	+	0.523381i
$301$	8.06597	+	3.63351i	0.464915	+	0.209432i
$302$	−1.11501	+	6.32351i	−0.0641614	+	0.363877i
$303$	20.6347	−	2.15801i	1.18543	−	0.123974i
$304$	1.85914	+	10.5437i	0.106629	+	0.604723i
$305$	−1.93531			−0.110815
$306$	5.44169	−	3.39252i	0.311081	−	0.193938i
$307$	3.75570	−	6.50506i	0.214349	−	0.371263i	−0.738722	−	0.674010i	$-0.764570\pi$
$307$	3.75570	−	6.50506i	0.214349	−	0.371263i	0.953071	+	0.302747i	$0.0979037\pi$
$308$	0.237396	−	0.348658i	0.0135269	−	0.0198666i
$309$	−5.57070	−	19.4653i	−0.316906	−	1.10734i
$310$	1.85976	+	1.56052i	0.105627	+	0.0886316i
$311$	−3.98271	+	22.5871i	−0.225839	+	1.28080i	0.635236	+	0.772318i	$0.280903\pi$
$311$	−3.98271	+	22.5871i	−0.225839	+	1.28080i	−0.861075	+	0.508478i	$0.830208\pi$
$312$	−14.8994	+	15.4129i	−0.843514	+	0.872581i
$313$	0.147493	−	0.123762i	0.00833682	−	0.00699542i	−0.638610	−	0.769531i	$-0.720490\pi$
$313$	0.147493	−	0.123762i	0.00833682	−	0.00699542i	0.646947	+	0.762535i	$0.276046\pi$
$314$	−6.10370	+	10.5719i	−0.344452	+	0.596608i
$315$	−9.83282	+	23.9634i	−0.554017	+	1.35019i
$316$	10.6473	+	18.4416i	0.598955	+	1.03742i
$317$	−14.9829	−	5.45333i	−0.841523	−	0.306289i	−0.114944	−	0.993372i	$-0.536669\pi$
$317$	−14.9829	−	5.45333i	−0.841523	−	0.306289i	−0.726579	+	0.687083i	$0.758891\pi$
$318$	−1.22069	+	2.73791i	−0.0684531	+	0.153534i
$319$	−0.214281	−	0.179803i	−0.0119974	−	0.0100670i
$320$	−0.496362	+	2.81501i	−0.0277475	+	0.157364i
$321$	−20.0192	+	9.75120i	−1.11736	+	0.544259i
$322$	−4.63607	+	6.80888i	−0.258358	+	0.379444i
$323$	−19.0067			−1.05756
$324$	14.8643	−	1.00852i	0.825794	−	0.0560288i
$325$	16.2930	−	28.2202i	0.903770	−	1.56538i
$326$	2.37107	−	1.98956i	0.131321	−	0.110192i
$327$	−15.3449	−	10.3618i	−0.848577	−	0.573011i
$328$	3.14724	+	2.64085i	0.173777	+	0.145817i
$329$	−12.7465	+	9.17608i	−0.702740	+	0.505894i
$330$	−0.317832	+	0.0332393i	−0.0174961	+	0.00182976i
$331$	3.20535	+	1.16665i	0.176182	+	0.0641249i	0.428605	−	0.903492i	$-0.359005\pi$
$331$	3.20535	+	1.16665i	0.176182	+	0.0641249i	−0.252423	+	0.967617i	$0.581227\pi$
$332$	−1.85555			−0.101837
$333$	−20.2954	−	2.87374i	−1.11218	−	0.157480i
$334$	−7.11073			−0.389082
$335$	3.09529	+	17.5543i	0.169114	+	0.959092i
$336$	−9.39495	+	0.282119i	−0.512537	+	0.0153909i
$337$	−23.5993	+	8.58946i	−1.28554	+	0.467898i	−0.892260	−	0.451522i	$-0.850881\pi$
$337$	−23.5993	+	8.58946i	−1.28554	+	0.467898i	−0.393278	+	0.919420i	$0.628659\pi$
$338$	9.11393	+	7.64749i	0.495732	+	0.415969i
$339$	4.90773	+	1.22633i	0.266551	+	0.0666051i
$340$	−18.4841	−	6.72766i	−1.00244	−	0.364858i
$341$	0.122048			0.00660926
$342$	8.11233	+	4.32417i	0.438665	+	0.233824i
$343$	18.0635	+	4.08771i	0.975338	+	0.220716i
$344$	5.49644	−	4.61206i	0.296348	−	0.248666i
$345$	−29.8153	+	3.11812i	−1.60520	+	0.167874i
$346$	10.7963	+	9.05919i	0.580414	+	0.487025i
$347$	−14.2348	+	5.18104i	−0.764163	+	0.278133i	−0.694553	−	0.719442i	$-0.744398\pi$
$347$	−14.2348	+	5.18104i	−0.764163	+	0.278133i	−0.0696102	+	0.997574i	$0.522176\pi$
$348$	−0.585208	+	8.30713i	−0.0313704	+	0.445309i
$349$	13.1750	+	4.79529i	0.705239	+	0.256686i	0.669646	−	0.742680i	$-0.266446\pi$
$349$	13.1750	+	4.79529i	0.705239	+	0.256686i	0.0355929	+	0.999366i	$0.488668\pi$
$350$	−8.44543	+	2.38180i	−0.451427	+	0.127313i
$351$	−4.12497	−	29.6848i	−0.220175	−	1.58446i
$352$	−0.264644	−	0.458377i	−0.0141056	−	0.0244316i
$353$	−20.1070	+	16.8717i	−1.07019	+	0.897992i	−0.995069	−	0.0991824i	$-0.968377\pi$
$353$	−20.1070	+	16.8717i	−1.07019	+	0.897992i	−0.0751164	+	0.997175i	$0.523933\pi$
$354$	7.24387	+	4.89151i	0.385007	+	0.259981i
$355$	7.32273	−	41.5292i	0.388650	−	2.20414i
$356$	4.61798	−	26.1899i	0.244753	−	1.38806i
$357$	2.40297	−	16.5121i	0.127179	−	0.873916i
$358$	5.75252	−	4.82694i	0.304030	−	0.255112i
$359$	10.1476	−	17.5761i	0.535567	−	0.927630i	−0.463568	−	0.886061i	$-0.653431\pi$
$359$	10.1476	−	17.5761i	0.535567	−	0.927630i	0.999136	−	0.0415688i	$-0.0132356\pi$
$360$	14.0411	+	15.6267i	0.740031	+	0.823599i
$361$	−4.12364	−	7.14236i	−0.217034	−	0.375913i
$362$	−1.21797	+	1.02200i	−0.0640152	+	0.0537151i
$363$	13.2309	−	13.6869i	0.694444	−	0.718374i
$364$	2.53071	+	25.1341i	0.132645	+	1.31738i
$365$	38.3607	−	13.9622i	2.00789	−	0.730813i
$366$	−0.585001	−	0.146179i	−0.0305785	−	0.00764088i
$367$	−18.8888	−	6.87495i	−0.985986	−	0.358870i	−0.201821	−	0.979422i	$-0.564686\pi$
$367$	−18.8888	−	6.87495i	−0.985986	−	0.358870i	−0.784165	+	0.620553i	$0.786908\pi$
$368$	−5.43904	−	9.42069i	−0.283530	−	0.491088i
$369$	−5.61949	+	1.18839i	−0.292539	+	0.0618649i
$370$	−6.54474	−	11.3358i	−0.340245	−	0.589321i
$371$	3.38875	+	7.02572i	0.175935	+	0.364757i
$372$	−2.13420	−	2.94068i	−0.110653	−	0.152467i
$373$	30.6252	−	11.1467i	1.58571	−	0.577152i	0.609275	−	0.792959i	$-0.291460\pi$
$373$	30.6252	−	11.1467i	1.58571	−	0.577152i	0.976436	+	0.215807i	$0.0692382\pi$
$374$	0.193447	−	0.0704088i	0.0100029	−	0.00364075i
$375$	−3.04338	−	2.05508i	−0.157160	−	0.106124i
$376$	2.21199	+	12.5448i	0.114075	+	0.646951i
$377$	16.7522			0.862781
$378$	−4.78227	+	6.50093i	−0.245973	+	0.334372i
$379$	−13.7037			−0.703914			−0.351957	−	0.936016i	$-0.614484\pi$
$379$	−13.7037			−0.703914			−0.351957	+	0.936016i	$0.614484\pi$
$380$	−4.89665	−	27.7703i	−0.251193	−	1.42459i
$381$	−6.51562	+	3.17371i	−0.333806	+	0.162594i
$382$	−4.19772	+	1.52784i	−0.214774	+	0.0781713i
$383$	−8.31613	+	3.02683i	−0.424935	+	0.154664i	−0.545630	−	0.838026i	$-0.683710\pi$
$383$	−8.31613	+	3.02683i	−0.424935	+	0.154664i	0.120696	+	0.992690i	$0.461487\pi$
$384$	−8.11507	+	18.2014i	−0.414120	+	0.928836i
$385$	−0.467997	+	0.687336i	−0.0238513	+	0.0350299i
$386$	3.98411	+	6.90068i	0.202786	+	0.351235i
$387$	0.339711	+	10.0253i	0.0172685	+	0.509617i
$388$	−2.99827	−	5.19316i	−0.152214	−	0.263643i
$389$	−13.9400	−	5.07373i	−0.706784	−	0.257248i	−0.0364792	−	0.999334i	$-0.511614\pi$
$389$	−13.9400	−	5.07373i	−0.706784	−	0.257248i	−0.670304	+	0.742086i	$0.733836\pi$
$390$	13.3016	−	13.7600i	0.673555	−	0.696765i
$391$	18.1469	−	6.60493i	0.917728	−	0.334026i
$392$	9.35093	−	11.7554i	0.472293	−	0.593738i
$393$	23.8861	+	5.96859i	1.20489	+	0.301076i
$394$	−0.717846	+	0.602344i	−0.0361646	+	0.0303457i
$395$	−20.9897	−	36.3553i	−1.05611	−	1.82923i
$396$	0.473558	+	0.0670538i	0.0237972	+	0.00336958i
$397$	2.74774	−	4.75923i	0.137905	−	0.238859i	−0.788798	−	0.614652i	$-0.789296\pi$
$397$	2.74774	−	4.75923i	0.137905	−	0.238859i	0.926704	+	0.375793i	$0.122630\pi$
$398$	0.439266	−	0.368588i	0.0220184	−	0.0184756i
$399$	22.2223	−	8.85231i	1.11251	−	0.443170i
$400$	2.01222	−	11.4119i	0.100611	−	0.570593i
$401$	−1.51394	+	8.58600i	−0.0756027	+	0.428764i	0.923389	+	0.383866i	$0.125408\pi$
$401$	−1.51394	+	8.58600i	−0.0756027	+	0.428764i	−0.998992	+	0.0448984i	$0.985704\pi$
$402$	−0.390279	+	5.54007i	−0.0194653	+	0.276314i
$403$	−5.59920	+	4.69829i	−0.278916	+	0.234038i
$404$	−9.91445	−	17.1723i	−0.493262	−	0.854355i
$405$	−29.3031	+	1.98817i	−1.45608	+	0.0987929i
$406$	−3.23129	−	3.14782i	−0.160366	−	0.156224i
$407$	−0.618352	−	0.225062i	−0.0306506	−	0.0111559i
$408$	−11.2157	−	7.57356i	−0.555262	−	0.374947i
$409$	8.60119	−	3.13058i	0.425301	−	0.154797i	−0.120497	−	0.992714i	$-0.538449\pi$
$409$	8.60119	−	3.13058i	0.425301	−	0.154797i	0.545798	+	0.837917i	$0.316227\pi$
$410$	−2.80974	−	2.35765i	−0.138763	−	0.116436i
$411$	−4.96502	−	6.84120i	−0.244906	−	0.337451i
$412$	−14.8234	+	12.4383i	−0.730297	+	0.612792i
$413$	21.8903	−	6.17354i	1.07715	−	0.303780i
$414$	−9.24803	−	1.30948i	−0.454516	−	0.0643575i
$415$	3.65799			0.179564
$416$	29.7865	+	10.8414i	1.46040	+	0.531543i
$417$	10.6920	−	11.0605i	0.523591	−	0.541633i
$418$	0.226072	+	0.189697i	0.0110575	+	0.00927837i
$419$	−22.0176	+	8.01376i	−1.07563	+	0.391498i	−0.818280	−	0.574820i	$-0.805072\pi$
$419$	−22.0176	+	8.01376i	−1.07563	+	0.391498i	−0.257352	+	0.966318i	$0.582850\pi$
$420$	24.7447	−	0.743053i	1.20742	−	0.0362573i
$421$	−7.02955	−	39.8665i	−0.342599	−	1.94298i	−0.332721	−	0.943025i	$-0.607967\pi$
$421$	−7.02955	−	39.8665i	−0.342599	−	1.94298i	−0.00987782	−	0.999951i	$-0.503144\pi$
$422$	2.69663			0.131270
$423$	−15.7156	−	8.37699i	−0.764118	−	0.407303i
$424$	6.32647			0.307241
$425$	19.3310	+	7.03592i	0.937693	+	0.341292i
$426$	5.35031	−	12.0003i	0.259223	−	0.581416i
$427$	−1.27339	+	0.916695i	−0.0616235	+	0.0443620i
$428$	16.3031	+	13.6799i	0.788038	+	0.661243i
$429$	0.0676105	−	0.959742i	0.00326427	−	0.0463368i
$430$	−4.90701	+	4.11747i	−0.236637	+	0.198562i
$431$	−8.08832	+	14.0094i	−0.389601	+	0.674808i	−0.992396	−	0.123088i	$-0.960720\pi$
$431$	−8.08832	+	14.0094i	−0.389601	+	0.674808i	0.602795	+	0.797896i	$0.294054\pi$
$432$	−4.98887	−	9.41792i	−0.240027	−	0.453120i
$433$	3.63457			0.174666			0.0873332	−	0.996179i	$-0.472166\pi$
$433$	3.63457			0.174666			0.0873332	+	0.996179i	$0.472166\pi$
$434$	1.96285	+	0.145877i	0.0942197	+	0.00700233i
$435$	1.15367	−	16.3765i	0.0553140	−	0.785192i
$436$	−3.07292	+	17.4274i	−0.147166	+	0.834621i
$437$	21.2074	+	17.7951i	1.01449	+	0.851256i
$438$	12.6502	−	1.32298i	0.604451	−	0.0632143i
$439$	−2.31491	−	0.842557i	−0.110484	−	0.0402130i	0.286186	−	0.958174i	$-0.407612\pi$
$439$	−2.31491	−	0.842557i	−0.110484	−	0.0402130i	−0.396671	+	0.917961i	$0.629835\pi$
$440$	0.337211	+	0.584067i	0.0160759	+	0.0278443i
$441$	4.88097	+	20.4249i	0.232427	+	0.972614i
$442$	−6.16435	+	10.6770i	−0.293208	+	0.507851i
$443$	2.87842	−	2.41528i	0.136758	−	0.114754i	−0.571843	−	0.820363i	$-0.693771\pi$
$443$	2.87842	−	2.41528i	0.136758	−	0.114754i	0.708601	+	0.705610i	$0.249327\pi$
$444$	5.39014	+	18.8344i	0.255805	+	0.893842i
$445$	−9.10378	+	51.6301i	−0.431560	+	2.44750i
$446$	6.83589	+	5.73599i	0.323689	+	0.271607i
$447$	25.3106	−	26.1828i	1.19715	−	1.23840i
$448$	1.00679	+	2.08732i	0.0475663	+	0.0986168i
$449$	−0.189743	+	0.328645i	−0.00895453	+	0.0155097i	−0.870468	−	0.492225i	$-0.836184\pi$
$449$	−0.189743	+	0.328645i	−0.00895453	+	0.0155097i	0.861513	+	0.507735i	$0.169517\pi$
$450$	−6.65004	−	7.40100i	−0.313486	−	0.348886i
$451$	−0.184391			−0.00868264
$452$	−0.839539	−	4.76126i	−0.0394886	−	0.223951i
$453$	−7.71468	+	17.3034i	−0.362467	+	0.812983i
$454$	−2.22909	+	12.6418i	−0.104616	+	0.593308i
$455$	−4.98898	−	49.5487i	−0.233887	−	2.32288i
$456$	1.36335	−	19.3530i	0.0638446	−	0.906285i
$457$	−3.56540	−	20.2204i	−0.166782	−	0.945869i	−0.947208	−	0.320620i	$-0.896109\pi$
$457$	−3.56540	−	20.2204i	−0.166782	−	0.945869i	0.780426	−	0.625249i	$-0.215002\pi$
$458$	0.0876762	−	0.151860i	0.00409684	−	0.00709593i
$459$	18.0033	−	5.81875i	0.840320	−	0.271596i
$460$	14.3255	+	24.8125i	0.667929	+	1.15689i
$461$	9.70572	+	3.53259i	0.452041	+	0.164529i	0.558000	−	0.829841i	$-0.311569\pi$
$461$	9.70572	+	3.53259i	0.452041	+	0.164529i	−0.105959	+	0.994370i	$0.533791\pi$
$462$	−0.193382	+	0.172418i	−0.00899693	+	0.00802161i
$463$	−16.6071	−	13.9350i	−0.771797	−	0.647615i	0.169371	−	0.985552i	$-0.445826\pi$
$463$	−16.6071	−	13.9350i	−0.771797	−	0.647615i	−0.941169	+	0.337938i	$0.890271\pi$
$464$	5.59800	−	2.03750i	0.259880	−	0.0945887i
$465$	4.20732	+	5.79718i	0.195110	+	0.268838i
$466$	−0.925817	−	5.25057i	−0.0428876	−	0.243228i
$467$	−6.01844	+	10.4243i	−0.278500	+	0.482377i	−0.971012	−	0.239030i	$-0.923171\pi$
$467$	−6.01844	+	10.4243i	−0.278500	+	0.482377i	0.692512	+	0.721406i	$0.256504\pi$
$468$	−24.3067	+	15.1536i	−1.12358	+	0.700475i
$469$	10.3515	+	10.0842i	0.477990	+	0.465643i
$470$	−1.97478	−	11.1995i	−0.0910899	−	0.516597i
$471$	−25.0334	+	25.8961i	−1.15348	+	1.19323i
$472$	3.20325	−	18.1665i	0.147442	−	0.836182i
$473$	−0.0559192	+	0.317134i	−0.00257117	+	0.0145818i
$474$	−3.59874	−	12.5748i	−0.165296	−	0.577581i
$475$	5.12102	+	29.0427i	0.234968	+	1.33257i
$476$	−15.3488	+	4.32870i	−0.703511	+	0.198406i
$477$	−5.45254	+	6.96408i	−0.249655	+	0.318863i
$478$	−3.61483	+	6.26107i	−0.165338	+	0.286374i
$479$	−1.76841	−	10.0292i	−0.0808007	−	0.458244i	−0.998184	−	0.0602388i	$-0.980814\pi$
$479$	−1.76841	−	10.0292i	−0.0808007	−	0.458244i	0.917383	−	0.398005i	$-0.130297\pi$
$480$	12.6495	−	28.3718i	0.577370	−	1.29499i
$481$	37.0321	−	13.4786i	1.68852	−	0.614570i
$482$	−9.73932	−	8.17226i	−0.443614	−	0.372236i
$483$	−18.1408	+	16.1742i	−0.825435	+	0.735953i
$484$	−17.0967	−	6.22267i	−0.777121	−	0.282849i
$485$	5.91072	+	10.2377i	0.268392	+	0.464868i
$486$	−9.00787	−	1.61236i	−0.408605	−	0.0731380i
$487$	−2.52733	+	4.37746i	−0.114524	+	0.198362i	−0.917589	−	0.397529i	$-0.869868\pi$
$487$	−2.52733	+	4.37746i	−0.114524	+	0.198362i	0.803065	+	0.595891i	$0.203201\pi$
$488$	0.220979	+	1.25324i	0.0100033	+	0.0567313i
$489$	8.21018	−	3.99912i	0.371277	−	0.180846i
$490$	−8.34814	+	10.4948i	−0.377131	+	0.474106i
$491$	−4.49122	+	25.4710i	−0.202686	+	1.14949i	0.698354	+	0.715753i	$0.253916\pi$
$491$	−4.49122	+	25.4710i	−0.202686	+	1.14949i	−0.901040	+	0.433736i	$0.857195\pi$
$492$	3.22437	+	4.44280i	0.145366	+	0.200297i
$493$	1.83646	+	10.4151i	0.0827099	+	0.469071i
$494$	−17.6740			−0.795189
$495$	−0.933561	−	0.132188i	−0.0419604	−	0.00594142i
$496$	−1.29962	+	2.25101i	−0.0583548	+	0.101073i
$497$	−14.8529	−	30.7938i	−0.666246	−	1.38129i
$498$	1.10573	+	0.276297i	0.0495490	+	0.0123812i
$499$	11.1820	+	9.38282i	0.500576	+	0.420033i	0.857798	−	0.513986i	$-0.171832\pi$
$499$	11.1820	+	9.38282i	0.500576	+	0.420033i	−0.357223	+	0.934019i	$0.616276\pi$
$500$	−0.609456	+	3.45640i	−0.0272557	+	0.154575i
$501$	−20.3543	−	5.08608i	−0.909363	−	0.227229i
$502$	9.96229	−	8.35936i	0.444639	−	0.373096i
$503$	7.08301	−	12.2681i	0.315816	−	0.547009i	−0.663795	−	0.747915i	$-0.731055\pi$
$503$	7.08301	−	12.2681i	0.315816	−	0.547009i	0.979611	+	0.200906i	$0.0643884\pi$
$504$	16.6406	+	3.63117i	0.741232	+	0.161745i
$505$	19.5451	+	33.8531i	0.869746	+	1.50644i
$506$	−0.281766	−	0.102554i	−0.0125260	−	0.00455910i
$507$	20.6184	+	28.4097i	0.915694	+	1.26172i
$508$	5.30614	+	4.45238i	0.235422	+	0.197542i
$509$	−6.86956	+	38.9592i	−0.304488	+	1.72684i	0.321418	+	0.946938i	$0.395841\pi$
$509$	−6.86956	+	38.9592i	−0.304488	+	1.72684i	−0.625906	+	0.779899i	$0.715270\pi$
$510$	10.0130	+	6.76138i	0.443382	+	0.299399i
$511$	18.6270	−	27.3571i	0.824011	−	1.21021i
$512$	20.0748			0.887189
$513$	20.1284	+	18.1803i	0.888691	+	0.802681i
$514$	−5.02413	+	8.70204i	−0.221605	+	0.383831i
$515$	29.2225	−	24.5206i	1.28770	−	1.08051i
$516$	8.61899	−	4.19825i	0.379430	−	0.184818i
$517$	−0.437957	−	0.367489i	−0.0192613	−	0.0161622i
$518$	−9.67571	−	4.35866i	−0.425126	−	0.191509i
$519$	24.4245	+	33.6540i	1.07211	+	1.47725i
$520$	−37.9542	−	13.8142i	−1.66440	−	0.605793i
$521$	−28.3116			−1.24035			−0.620177	−	0.784462i	$-0.712939\pi$
$521$	−28.3116			−1.24035			−0.620177	+	0.784462i	$0.712939\pi$
$522$	1.58568	−	4.86311i	0.0694035	−	0.212853i
$523$	−44.4149			−1.94213			−0.971064	−	0.238819i	$-0.923240\pi$
$523$	−44.4149			−1.94213			−0.971064	+	0.238819i	$0.923240\pi$
$524$	−4.08607	−	23.1732i	−0.178501	−	1.01233i
$525$	−25.8785	+	0.777100i	−1.12943	+	0.0339154i
$526$	−5.59723	+	2.03723i	−0.244051	+	0.0888273i
$527$	−3.53480	−	2.96605i	−0.153978	−	0.129203i
$528$	−0.0941367	−	0.328936i	−0.00409677	−	0.0143151i
$529$	−4.81902	−	1.75398i	−0.209523	−	0.0762600i
$530$	−5.64803			−0.245335
$531$	17.2367	+	19.1831i	0.748008	+	0.832476i
$532$	−16.3758	−	15.9528i	−0.709982	−	0.691643i
$533$	8.45932	−	7.09821i	0.366414	−	0.307458i
$534$	−6.65163	+	14.9190i	−0.287844	+	0.645610i
$535$	−32.1395	−	26.9682i	−1.38951	−	1.16594i
$536$	11.0141	−	4.00880i	0.475736	−	0.173154i
$537$	19.9190	−	9.70240i	0.859569	−	0.418689i
$538$	8.54847	+	3.11139i	0.368551	+	0.134141i
$539$	0.0176389	+	0.673927i	0.000759762	+	0.0290281i
$540$	13.1398	+	24.8052i	0.565447	+	1.06744i
$541$	−1.22108	−	2.11497i	−0.0524983	−	0.0909298i	0.838582	−	0.544775i	$-0.183385\pi$
$541$	−1.22108	−	2.11497i	−0.0524983	−	0.0909298i	−0.891080	+	0.453846i	$0.850052\pi$
$542$	6.82710	−	5.72861i	0.293249	−	0.246065i
$543$	−4.21742	+	2.05427i	−0.180987	+	0.0881573i
$544$	−3.47491	+	19.7072i	−0.148985	+	0.844938i
$545$	6.05788	−	34.3559i	0.259491	−	1.47165i
$546$	2.23448	−	15.3543i	0.0956269	−	0.657105i
$547$	−20.8943	+	17.5324i	−0.893375	+	0.749630i	−0.968884	−	0.247515i	$-0.920386\pi$
$547$	−20.8943	+	17.5324i	−0.893375	+	0.749630i	0.0755094	+	0.997145i	$0.475942\pi$
$548$	−4.03943	+	6.99649i	−0.172556	+	0.298875i
$549$	−1.56999	−	0.836865i	−0.0670057	−	0.0357165i
$550$	−0.159707	−	0.276621i	−0.00680995	−	0.0117952i
$551$	−11.6140	+	9.74530i	−0.494773	+	0.415164i
$552$	5.42359	+	18.9513i	0.230843	+	0.806620i
$553$	−31.0312	−	13.9788i	−1.31958	−	0.594437i
$554$	8.24623	−	3.00138i	0.350349	−	0.127516i
$555$	−10.6260	−	37.1297i	−0.451049	−	1.57607i
$556$	−13.8159	−	5.02859i	−0.585926	−	0.213260i
$557$	6.71021	+	11.6224i	0.284321	+	0.492458i	0.972444	−	0.233136i	$-0.0748987\pi$
$557$	6.71021	+	11.6224i	0.284321	+	0.492458i	−0.688124	+	0.725593i	$0.741565\pi$
$558$	0.833905	+	2.07015i	0.0353020	+	0.0876365i
$559$	−9.64279	−	16.7018i	−0.407846	−	0.706411i
$560$	−7.69356	−	15.9507i	−0.325112	−	0.674038i
$561$	0.604097	−	0.0631773i	0.0255050	−	0.00266735i
$562$	−7.17428	+	2.61123i	−0.302629	+	0.110148i
$563$	−10.0960	+	3.67466i	−0.425498	+	0.154868i	−0.545888	−	0.837858i	$-0.683808\pi$
$563$	−10.0960	+	3.67466i	−0.425498	+	0.154868i	0.120390	+	0.992727i	$0.461585\pi$
$564$	−1.19607	+	16.9785i	−0.0503638	+	0.714922i
$565$	1.65505	+	9.38624i	0.0696284	+	0.394882i
$566$	11.2540			0.473040
$567$	−18.3390	+	15.1882i	−0.770167	+	0.637842i
$568$	−27.7290			−1.16348
$569$	1.32694	+	7.52545i	0.0556282	+	0.315483i	0.999907	−	0.0136646i	$-0.00434970\pi$
$569$	1.32694	+	7.52545i	0.0556282	+	0.315483i	−0.944278	+	0.329148i	$0.893239\pi$
$570$	−1.21714	+	17.2776i	−0.0509806	+	0.723678i
$571$	23.1959	−	8.44260i	0.970717	−	0.353312i	0.192492	−	0.981298i	$-0.438343\pi$
$571$	23.1959	−	8.44260i	0.970717	−	0.353312i	0.778224	+	0.627986i	$0.216121\pi$
$572$	−0.864080	+	0.314499i	−0.0361290	+	0.0131499i
$573$	−13.1087	+	1.37092i	−0.547623	+	0.0572712i
$574$	−2.96549	−	0.220393i	−0.123777	−	0.00919901i
$575$	−14.9819	−	25.9494i	−0.624787	−	1.08216i
$576$	−1.61994	+	2.06901i	−0.0674973	+	0.0862087i
$577$	3.47770	+	6.02355i	0.144778	+	0.250764i	0.929290	−	0.369350i	$-0.120420\pi$
$577$	3.47770	+	6.02355i	0.144778	+	0.250764i	−0.784512	+	0.620114i	$0.787086\pi$
$578$	2.06403	+	0.751246i	0.0858523	+	0.0312477i
$579$	6.46858	+	22.6027i	0.268825	+	0.939338i
$580$	−14.7441	+	5.36643i	−0.612217	+	0.222829i
$581$	2.40687	−	1.73268i	0.0998539	−	0.0718836i
$582$	1.01341	+	3.54108i	0.0420070	+	0.146782i
$583$	−0.217510	+	0.182512i	−0.00900834	+	0.00755889i
$584$	−13.4215	−	23.2468i	−0.555388	−	0.961959i
$585$	47.9177	−	29.8734i	1.98115	−	1.23511i
$586$	0.130220	−	0.225548i	0.00537935	−	0.00931730i
$587$	−23.5728	+	19.7799i	−0.972953	+	0.816405i	−0.983011	−	0.183545i	$-0.941243\pi$
$587$	−23.5728	+	19.7799i	−0.972953	+	0.816405i	0.0100583	+	0.999949i	$0.496798\pi$
$588$	15.9295	−	12.2097i	0.656920	−	0.503519i
$589$	1.14868	−	6.51448i	0.0473305	−	0.268424i
$590$	−2.85974	+	16.2184i	−0.117734	+	0.667700i
$591$	−2.48565	+	1.21074i	−0.102246	+	0.0498033i
$592$	10.7355	−	9.00813i	0.441225	−	0.370232i
$593$	0.193094	+	0.334449i	0.00792943	+	0.0137342i	0.869963	−	0.493117i	$-0.164143\pi$
$593$	0.193094	+	0.334449i	0.00792943	+	0.0137342i	−0.862033	+	0.506851i	$0.830809\pi$
$594$	−0.272211	−	0.110472i	−0.0111689	−	0.00453272i
$595$	30.2582	−	8.53350i	1.24047	−	0.349839i
$596$	−32.7057	−	11.9039i	−1.33968	−	0.487603i
$597$	1.52103	−	0.740881i	0.0622515	−	0.0303222i
$598$	16.8745	−	6.14180i	0.690048	−	0.251157i
$599$	−8.77714	−	7.36490i	−0.358624	−	0.300922i	0.445618	−	0.895223i	$-0.352984\pi$
$599$	−8.77714	−	7.36490i	−0.358624	−	0.300922i	−0.804242	+	0.594302i	$0.797428\pi$
$600$	−8.55072	+	19.1785i	−0.349082	+	0.782960i
$601$	−15.5980	+	13.0882i	−0.636254	+	0.533881i	−0.902865	−	0.429924i	$-0.858541\pi$
$601$	−15.5980	+	13.0882i	−0.636254	+	0.533881i	0.266611	+	0.963804i	$0.414096\pi$
$602$	−1.27838	+	5.03350i	−0.0521028	+	0.205150i
$603$	−5.07980	+	15.5792i	−0.206865	+	0.634432i
$604$	18.1067			0.736751
$605$	33.7039	+	12.2672i	1.37026	+	0.498734i
$606$	3.35105	+	11.7094i	0.136127	+	0.475660i
$607$	12.2197	+	10.2536i	0.495984	+	0.416180i	0.856165	−	0.516703i	$-0.172841\pi$
$607$	12.2197	+	10.2536i	0.495984	+	0.416180i	−0.360181	+	0.932882i	$0.617285\pi$
$608$	−26.9573	+	9.81164i	−1.09326	+	0.397914i
$609$	−6.99795	−	11.3218i	−0.283571	−	0.458782i
$610$	−0.197282	−	1.11884i	−0.00798770	−	0.0453005i
$611$	34.2388			1.38515
$612$	−12.0858	−	13.4506i	−0.488541	−	0.543709i
$613$	7.96647			0.321763			0.160881	−	0.986974i	$-0.448566\pi$
$613$	7.96647			0.321763			0.160881	+	0.986974i	$0.448566\pi$
$614$	4.14356	+	1.50813i	0.167220	+	0.0608632i
$615$	−6.35645	−	8.75843i	−0.256317	−	0.353174i
$616$	0.498532	+	0.224576i	0.0200864	+	0.00904843i
$617$	−26.1777	−	21.9657i	−1.05387	−	0.884306i	−0.0603792	−	0.998176i	$-0.519231\pi$
$617$	−26.1777	−	21.9657i	−1.05387	−	0.884306i	−0.993496	+	0.113869i	$0.963675\pi$
$618$	10.6854	−	5.20480i	0.429831	−	0.209368i
$619$	−26.7530	+	22.4484i	−1.07529	+	0.902279i	−0.995522	−	0.0945346i	$-0.969864\pi$
$619$	−26.7530	+	22.4484i	−1.07529	+	0.902279i	−0.0797721	+	0.996813i	$0.525419\pi$
$620$	3.42298	−	5.92877i	0.137470	−	0.238105i
$621$	−25.5356	−	10.3632i	−1.02471	−	0.415860i
$622$	−13.4641			−0.539859
$623$	18.4655	+	38.2836i	0.739805	+	1.53380i
$624$	16.9812	+	11.4668i	0.679793	+	0.459038i
$625$	−3.70382	+	21.0054i	−0.148153	+	0.840217i
$626$	0.0865844	+	0.0726530i	0.00346061	+	0.00290380i
$627$	0.511441	+	0.704704i	0.0204250	+	0.0281432i
$628$	32.3475	+	11.7735i	1.29081	+	0.469815i
$629$	12.4395	+	21.5458i	0.495994	+	0.859086i
$630$	−14.8561	−	3.24177i	−0.591881	−	0.129155i
$631$	−7.65980	+	13.2672i	−0.304932	+	0.528157i	−0.977246	−	0.212108i	$-0.931967\pi$
$631$	−7.65980	+	13.2672i	−0.304932	+	0.528157i	0.672314	+	0.740266i	$0.265300\pi$
$632$	−21.1457	+	17.7434i	−0.841132	+	0.705794i
$633$	7.71904	+	1.92881i	0.306804	+	0.0766634i
$634$	1.62535	−	9.21782i	0.0645509	−	0.366087i
$635$	−10.4604	−	8.77732i	−0.415108	−	0.348317i
$636$	8.20105	+	2.04926i	0.325193	+	0.0812583i
$637$	−26.7523	−	30.2388i	−1.05997	−	1.19810i
$638$	0.0821045	−	0.142209i	0.00325055	−	0.00563011i
$639$	23.8986	−	30.5236i	0.945412	−	1.20750i
$640$	−37.5476			−1.48420
$641$	3.41750	+	19.3816i	0.134983	+	0.765528i	0.974871	+	0.222769i	$0.0715095\pi$
$641$	3.41750	+	19.3816i	0.134983	+	0.765528i	−0.839888	+	0.542760i	$0.817379\pi$
$642$	−7.67809	−	10.5795i	−0.303030	−	0.417539i
$643$	−1.40911	+	7.99147i	−0.0555700	+	0.315153i	−0.999904	−	0.0138344i	$-0.995596\pi$
$643$	−1.40911	+	7.99147i	−0.0555700	+	0.315153i	0.944334	+	0.328987i	$0.106707\pi$
$644$	21.1787	+	9.54049i	0.834559	+	0.375948i
$645$	−16.9913	+	8.27632i	−0.669031	+	0.325880i
$646$	−1.93751	−	10.9882i	−0.0762302	−	0.432323i
$647$	9.47724	−	16.4151i	0.372589	−	0.645343i	−0.617374	−	0.786670i	$-0.711804\pi$
$647$	9.47724	−	16.4151i	0.372589	−	0.645343i	0.989963	+	0.141327i	$0.0451369\pi$
$648$	4.63339	+	18.7486i	0.182017	+	0.736516i
$649$	0.413956	+	0.716993i	0.0162492	+	0.0281444i
$650$	17.9756	+	6.54257i	0.705060	+	0.256621i
$651$	5.51426	+	1.82153i	0.216121	+	0.0713914i
$652$	−6.68614	−	5.61034i	−0.261850	−	0.219718i
$653$	−11.8795	+	4.32379i	−0.464881	+	0.169203i	−0.563832	−	0.825889i	$-0.690673\pi$
$653$	−11.8795	+	4.32379i	−0.464881	+	0.169203i	0.0989511	+	0.995092i	$0.468451\pi$
$654$	4.42616	−	9.92749i	0.173076	−	0.388196i
$655$	8.05518	+	45.6832i	0.314742	+	1.78499i
$656$	1.96348	−	3.40085i	0.0766611	−	0.132781i
$657$	37.1572	+	5.26130i	1.44964	+	0.205263i
$658$	−6.60424	−	6.43365i	−0.257460	−	0.250810i
$659$	−3.99230	−	22.6415i	−0.155518	−	0.881987i	−0.958311	−	0.285728i	$-0.907765\pi$
$659$	−3.99230	−	22.6415i	−0.155518	−	0.881987i	0.802793	−	0.596258i	$-0.203347\pi$
$660$	0.247940	+	0.866359i	0.00965103	+	0.0337230i
$661$	4.37526	−	24.8133i	0.170178	−	0.965127i	−0.773386	−	0.633936i	$-0.781438\pi$
$661$	4.37526	−	24.8133i	0.170178	−	0.965127i	0.943564	−	0.331191i	$-0.107450\pi$
$662$	−0.347717	+	1.97200i	−0.0135144	+	0.0766441i
$663$	−25.2822	+	26.1534i	−0.981878	+	1.01571i
$664$	−0.417681	−	2.36879i	−0.0162092	−	0.0919267i
$665$	32.2829	+	31.4490i	1.25188	+	1.21954i
$666$	−0.407508	−	12.0261i	−0.0157906	−	0.466003i
$667$	7.70208	−	13.3404i	0.298226	−	0.516542i
$668$	3.48190	+	19.7469i	0.134719	+	0.764029i
$669$	15.4648	+	21.3086i	0.597904	+	0.823839i
$670$	−9.83295	+	3.57890i	−0.379880	+	0.138265i
$671$	−0.0437521	−	0.0367124i	−0.00168903	−	0.00141726i
$672$	−5.11576	−	24.6597i	−0.197345	−	0.951269i
$673$	15.1371	+	5.50946i	0.583493	+	0.212374i	0.616865	−	0.787069i	$-0.288402\pi$
$673$	15.1371	+	5.50946i	0.583493	+	0.212374i	−0.0333723	+	0.999443i	$0.510625\pi$
$674$	−7.37142	−	12.7677i	−0.283936	−	0.491792i
$675$	−13.7419	−	25.9417i	−0.528925	−	0.998498i
$676$	16.7747	−	29.0546i	0.645179	−	1.11748i
$677$	0.849819	+	4.81956i	0.0326612	+	0.185231i	0.996774	−	0.0802631i	$-0.0255761\pi$
$677$	0.849819	+	4.81956i	0.0326612	+	0.185231i	−0.964113	+	0.265494i	$0.914465\pi$
$678$	−0.208681	+	2.96227i	−0.00801436	+	0.113765i
$679$	8.73839	+	3.93642i	0.335348	+	0.151066i
$680$	4.42775	−	25.1110i	0.169797	−	0.962965i
$681$	−15.4230	+	34.5924i	−0.591009	+	1.32558i
$682$	0.0124413	+	0.0705584i	0.000476404	+	0.00270182i
$683$	29.0638			1.11209			0.556047	−	0.831151i	$-0.312317\pi$
$683$	29.0638			1.11209			0.556047	+	0.831151i	$0.312317\pi$
$684$	8.03608	−	24.6457i	0.307267	−	0.942354i
$685$	7.96323	−	13.7927i	0.304259	−	0.526993i
$686$	−0.521829	+	10.8596i	−0.0199235	+	0.414621i
$687$	0.359591	−	0.371982i	0.0137193	−	0.0141920i
$688$	−5.25366	−	4.40834i	−0.200294	−	0.168066i
$689$	2.95282	−	16.7463i	0.112493	−	0.637982i
$690$	−4.84197	−	16.9190i	−0.184331	−	0.644094i
$691$	−2.46249	+	2.06627i	−0.0936774	+	0.0786047i	−0.688424	−	0.725309i	$-0.741697\pi$
$691$	−2.46249	+	2.06627i	−0.0936774	+	0.0786047i	0.594746	+	0.803913i	$0.297253\pi$
$692$	19.8712	−	34.4179i	0.755389	−	1.30837i
$693$	−0.676875	+	0.355222i	−0.0257124	+	0.0134938i
$694$	−4.44633	−	7.70127i	−0.168780	−	0.292336i
$695$	27.2364	+	9.91324i	1.03314	+	0.376031i
$696$	−10.7366	+	1.12284i	−0.406968	+	0.0425613i
$697$	5.34041	+	4.48114i	0.202283	+	0.169735i
$698$	−1.42922	+	8.10553i	−0.0540969	+	0.306799i
$699$	1.10543	−	15.6918i	0.0418114	−	0.593520i
$700$	10.7498	+	22.2871i	0.406306	+	0.842372i
$701$	−19.4165			−0.733351			−0.366675	−	0.930349i	$-0.619504\pi$
$701$	−19.4165			−0.733351			−0.366675	+	0.930349i	$0.619504\pi$
$702$	16.7409	−	5.41075i	0.631845	−	0.204216i
$703$	−17.8327	+	30.8872i	−0.672575	+	1.16493i
$704$	−0.0646216	+	0.0542240i	−0.00243552	+	0.00204364i
$705$	2.35791	−	33.4709i	0.0888040	−	1.26059i
$706$	−11.8036	−	9.90437i	−0.444233	−	0.372756i
$707$	28.8954	+	13.0167i	1.08672	+	0.489542i
$708$	10.0369	−	22.5118i	0.377208	−	0.846045i
$709$	16.3562	+	5.95319i	0.614272	+	0.223577i	0.630371	−	0.776294i	$-0.282903\pi$
$709$	16.3562	+	5.95319i	0.614272	+	0.223577i	−0.0160996	+	0.999870i	$0.505125\pi$
$710$	24.7554			0.929053
$711$	−1.30693	−	38.5692i	−0.0490136	−	1.44646i
$712$	34.4733			1.29194
$713$	1.16710	+	6.61896i	0.0437083	+	0.247882i
$714$	9.79097	−	0.294011i	0.366418	−	0.0110031i
$715$	1.70343	−	0.619996i	0.0637045	−	0.0231865i
$716$	−16.2215	−	13.6114i	−0.606225	−	0.508683i
$717$	−14.8257	+	15.3366i	−0.553676	+	0.572755i
$718$	11.1955	+	4.07484i	0.417813	+	0.152072i
$719$	−24.3736			−0.908980			−0.454490	−	0.890752i	$-0.650179\pi$
$719$	−24.3736			−0.908980			−0.454490	+	0.890752i	$0.650179\pi$
$720$	12.3790	−	15.8107i	0.461339	−	0.589230i
$721$	7.61308	−	29.9758i	0.283526	−	1.11636i
$722$	3.70879	−	3.11204i	0.138027	−	0.115818i
$723$	−22.0332	−	30.3591i	−0.819424	−	1.12907i
$724$	3.43455	+	2.88193i	0.127644	+	0.107106i
$725$	15.4197	−	5.61232i	0.572674	−	0.208436i
$726$	9.26140	+	6.25386i	0.343723	+	0.232103i
$727$	14.0755	+	5.12306i	0.522031	+	0.190004i	0.589577	−	0.807712i	$-0.299295\pi$
$727$	14.0755	+	5.12306i	0.522031	+	0.190004i	−0.0675456	+	0.997716i	$0.521517\pi$
$728$	−31.5163	+	8.88831i	−1.16807	+	0.329423i
$729$	−24.6315	−	11.0584i	−0.912279	−	0.409569i
$730$	11.9822	+	20.7538i	0.443482	+	0.768134i
$731$	9.32666	−	7.82599i	0.344959	−	0.289455i
$732$	−0.119488	+	1.69616i	−0.00441641	+	0.0626917i
$733$	−1.73526	+	9.84113i	−0.0640932	+	0.363490i	0.935845	+	0.352411i	$0.114638\pi$
$733$	−1.73526	+	9.84113i	−0.0640932	+	0.363490i	−0.999939	+	0.0110797i	$0.996473\pi$
$734$	2.04906	−	11.6208i	0.0756323	−	0.428932i
$735$	−31.4029	+	24.0699i	−1.15831	+	0.887832i
$736$	22.3282	−	18.7356i	0.823029	−	0.690603i
$737$	−0.263025	+	0.455572i	−0.00968863	+	0.0167812i
$738$	−1.25987	−	3.12760i	−0.0463765	−	0.115129i
$739$	−8.47592	−	14.6807i	−0.311792	−	0.540039i	0.666958	−	0.745095i	$-0.267596\pi$
$739$	−8.47592	−	14.6807i	−0.311792	−	0.540039i	−0.978750	+	0.205056i	$0.934263\pi$
$740$	−28.2754	+	23.7258i	−1.03942	+	0.872179i
$741$	−50.5913	−	12.6416i	−1.85852	−	0.464401i
$742$	−3.71627	+	2.67530i	−0.136429	+	0.0982133i
$743$	4.70157	−	1.71123i	0.172484	−	0.0627790i	−0.254335	−	0.967116i	$-0.581857\pi$
$743$	4.70157	−	1.71123i	0.172484	−	0.0627790i	0.426819	+	0.904337i	$0.359634\pi$
$744$	3.27364	−	3.38645i	0.120018	−	0.124153i
$745$	64.4752	+	23.4671i	2.36219	+	0.859766i
$746$	9.56599	+	16.5688i	0.350236	+	0.606626i
$747$	2.96750	+	1.58179i	0.108575	+	0.0578746i
$748$	−0.290253	−	0.502734i	−0.0106127	−	0.0183818i
$749$	−33.9210	−	2.52098i	−1.23945	−	0.0921147i
$750$	0.877846	−	1.96893i	0.0320544	−	0.0718953i
$751$	−46.4009	+	16.8886i	−1.69319	+	0.616272i	−0.995022	−	0.0996584i	$-0.968225\pi$
$751$	−46.4009	+	16.8886i	−1.69319	+	0.616272i	−0.698172	+	0.715930i	$0.746003\pi$
$752$	11.4414	−	4.16434i	0.417226	−	0.151858i
$753$	34.4960	−	16.8027i	1.25710	−	0.612326i
$754$	1.70769	+	9.68478i	0.0621904	+	0.352699i
$755$	−35.6951			−1.29908
$756$	20.3951	+	10.0973i	0.741764	+	0.367235i
$757$	25.2822			0.918897			0.459449	−	0.888204i	$-0.348047\pi$
$757$	25.2822			0.918897			0.459449	+	0.888204i	$0.348047\pi$
$758$	−1.39694	−	7.92242i	−0.0507390	−	0.287755i
$759$	−0.733193	−	0.495097i	−0.0266132	−	0.0179709i
$760$	34.3491	−	12.5021i	1.24597	−	0.453498i
$761$	−5.31141	+	1.93320i	−0.192538	+	0.0700783i	−0.436490	−	0.899709i	$-0.643779\pi$
$761$	−5.31141	+	1.93320i	−0.192538	+	0.0700783i	0.243951	+	0.969787i	$0.421556\pi$
$762$	−2.49898	−	3.44329i	−0.0905285	−	0.124737i
$763$	−12.2874	−	25.4748i	−0.444834	−	0.922251i
$764$	6.29839	+	10.9091i	0.227868	+	0.394678i
$765$	23.8257	+	26.5162i	0.861421	+	0.958697i
$766$	−2.59760	−	4.49918i	−0.0938552	−	0.162562i
$767$	−46.5920	−	16.9581i	−1.68234	−	0.612322i
$768$	−8.40610	−	2.10049i	−0.303329	−	0.0757951i
$769$	4.79031	−	1.74353i	0.172743	−	0.0628733i	−0.254201	−	0.967151i	$-0.581812\pi$
$769$	4.79031	−	1.74353i	0.172743	−	0.0628733i	0.426944	+	0.904278i	$0.359590\pi$
$770$	−0.445070	−	0.200493i	−0.0160392	−	0.00722526i
$771$	−20.6057	+	21.3158i	−0.742097	+	0.767669i
$772$	17.2126	−	14.4431i	0.619496	−	0.519819i
$773$	21.8698	+	37.8796i	0.786603	+	1.36244i	0.928037	+	0.372488i	$0.121495\pi$
$773$	21.8698	+	37.8796i	0.786603	+	1.36244i	−0.141435	+	0.989948i	$0.545171\pi$
$774$	−5.76123	+	1.21836i	−0.207083	+	0.0437931i
$775$	−3.57982	+	6.20043i	−0.128591	+	0.222726i
$776$	5.95465	−	4.99654i	0.213759	−	0.179365i
$777$	−24.5789	−	19.3973i	−0.881762	−	0.695874i
$778$	1.51221	−	8.57618i	0.0542154	−	0.307471i
$779$	−1.73543	+	9.84214i	−0.0621784	+	0.352631i
$780$	−44.7256	−	30.2015i	−1.60143	−	1.08139i
$781$	0.953348	−	0.799954i	0.0341135	−	0.0286246i
$782$	5.66831	+	9.81780i	0.202698	+	0.351084i
$783$	8.01741	−	12.7864i	0.286519	−	0.456947i
$784$	−12.6175	−	6.85096i	−0.450626	−	0.244677i
$785$	−63.7691	−	23.2101i	−2.27602	−	0.828402i
$786$	−1.01566	+	14.4175i	−0.0362274	+	0.514254i
$787$	5.44226	−	1.98082i	0.193996	−	0.0706086i	−0.243195	−	0.969977i	$-0.578196\pi$
$787$	5.44226	−	1.98082i	0.193996	−	0.0706086i	0.437191	+	0.899369i	$0.355973\pi$
$788$	2.02425	+	1.69854i	0.0721108	+	0.0605081i
$789$	−17.4791	+	1.82799i	−0.622273	+	0.0650781i
$790$	18.8781	−	15.8406i	0.671652	−	0.563583i
$791$	5.53496	+	5.39198i	0.196800	+	0.191717i
$792$	0.0209965	+	0.619635i	0.000746077	+	0.0220178i
$793$	3.42048			0.121465
$794$	3.03151	+	1.10338i	0.107584	+	0.0391575i
$795$	−16.1673	−	4.03985i	−0.573397	−	0.143279i
$796$	−1.23868	−	1.03938i	−0.0439039	−	0.0368397i
$797$	15.0146	−	5.46488i	0.531846	−	0.193576i	−0.0621164	−	0.998069i	$-0.519785\pi$
$797$	15.0146	−	5.46488i	0.531846	−	0.193576i	0.593962	+	0.804493i	$0.297563\pi$
$798$	7.38300	+	11.9448i	0.261355	+	0.422840i
$799$	3.75343	+	21.2868i	0.132787	+	0.753072i
$800$	31.0494			1.09776
$801$	−29.7112	+	37.9477i	−1.04979	+	1.34081i
$802$	−5.11807			−0.180725
$803$	1.13209	+	0.412048i	0.0399507	+	0.0145409i
$804$	15.5762	−	1.62898i	0.549329	−	0.0574496i
$805$	−41.7512	−	18.8079i	−1.47154	−	0.662891i
$806$	−3.28695	−	2.75808i	−0.115778	−	0.0971491i
$807$	22.2443	+	15.0207i	0.783036	+	0.528754i
$808$	19.6904	−	16.5222i	0.692704	−	0.581248i
$809$	12.2565	−	21.2288i	0.430914	−	0.746365i	−0.566038	−	0.824379i	$-0.691525\pi$
$809$	12.2565	−	21.2288i	0.430914	−	0.746365i	0.996952	+	0.0780141i	$0.0248579\pi$
$810$	−4.13651	−	16.7381i	−0.145342	−	0.588115i
$811$	−13.5257			−0.474951			−0.237475	−	0.971394i	$-0.576320\pi$
$811$	−13.5257			−0.474951			−0.237475	+	0.971394i	$0.576320\pi$
$812$	−7.15939	+	10.5148i	−0.251245	+	0.368998i
$813$	23.6399	−	11.5148i	0.829087	−	0.403842i
$814$	0.0670791	−	0.380425i	0.00235112	−	0.0133339i
$815$	13.1809	+	11.0601i	0.461707	+	0.387418i
$816$	−5.26749	+	11.8145i	−0.184399	+	0.413591i
$817$	16.4012	+	5.96954i	0.573804	+	0.208848i
$818$	2.68664	+	4.65340i	0.0939362	+	0.162702i
$819$	17.3786	−	42.3532i	0.607258	−	1.47994i
$820$	−5.17147	+	8.95724i	−0.180595	+	0.312801i
$821$	−25.2681	+	21.2024i	−0.881862	+	0.739970i	−0.966561	−	0.256437i	$-0.917452\pi$
$821$	−25.2681	+	21.2024i	−0.881862	+	0.739970i	0.0846992	+	0.996407i	$0.473007\pi$
$822$	3.44891	−	3.56776i	0.120295	−	0.124440i
$823$	8.05299	−	45.6708i	0.280710	−	1.59198i	−0.439510	−	0.898238i	$-0.644848\pi$
$823$	8.05299	−	45.6708i	0.280710	−	1.59198i	0.720220	−	0.693746i	$-0.244041\pi$
$824$	−19.2154	−	16.1236i	−0.669400	−	0.561693i
$825$	−0.259300	−	0.906055i	−0.00902767	−	0.0315448i
$826$	5.80051	+	12.0259i	0.201825	+	0.418434i
$827$	4.00088	−	6.92973i	0.139124	−	0.240970i	−0.788041	−	0.615623i	$-0.788905\pi$
$827$	4.00088	−	6.92973i	0.139124	−	0.240970i	0.927165	+	0.374652i	$0.122238\pi$
$828$	0.891976	+	26.3235i	0.0309983	+	0.914803i
$829$	−2.28106			−0.0792244			−0.0396122	−	0.999215i	$-0.512612\pi$
$829$	−2.28106			−0.0792244			−0.0396122	+	0.999215i	$0.512612\pi$
$830$	0.372889	+	2.11476i	0.0129432	+	0.0734044i
$831$	25.7514	−	2.69312i	0.893307	−	0.0934233i
$832$	0.877275	−	4.97527i	0.0304140	−	0.172487i
$833$	15.8672	−	19.9472i	0.549765	−	0.691131i
$834$	7.48421	+	5.05380i	0.259157	+	0.174999i
$835$	−6.86414	−	38.9285i	−0.237543	−	1.34718i
$836$	0.416097	−	0.720701i	0.0143910	−	0.0249260i
$837$	0.906322	+	6.52222i	0.0313271	+	0.225441i
$838$	−6.87736	−	11.9119i	−0.237574	−	0.411491i
$839$	38.9227	+	14.1667i	1.34376	+	0.489088i	0.910995	−	0.412418i	$-0.135316\pi$
$839$	38.9227	+	14.1667i	1.34376	+	0.489088i	0.432765	+	0.901507i	$0.357538\pi$
$840$	6.51855	+	31.4216i	0.224911	+	1.08415i
$841$	−15.7530	−	13.2183i	−0.543207	−	0.455805i
$842$	22.3311	−	8.12785i	0.769580	−	0.280104i
$843$	−22.4039	+	2.34303i	−0.771632	+	0.0806984i
$844$	−1.32046	−	7.48867i	−0.0454519	−	0.257771i
$845$	−33.0691	+	57.2774i	−1.13761	+	1.97040i
$846$	3.24089	−	9.93944i	0.111424	−	0.341725i
$847$	27.9870	−	7.89297i	0.961645	−	0.271206i
$848$	−1.05006	−	5.95516i	−0.0360591	−	0.204501i
$849$	32.2142	+	8.04961i	1.10559	+	0.276262i
$850$	−2.09704	+	11.8929i	−0.0719278	+	0.407923i
$851$	6.29258	−	35.6870i	0.215707	−	1.22333i
$852$	−35.9453	−	8.98191i	−1.23146	−	0.307715i
$853$	−1.19101	−	6.75457i	−0.0407795	−	0.231272i	0.957605	−	0.288083i	$-0.0930179\pi$
$853$	−1.19101	−	6.75457i	−0.0407795	−	0.231272i	−0.998385	+	0.0568109i	$0.981907\pi$
$854$	−0.659767	−	0.642725i	−0.0225768	−	0.0219936i
$855$	−15.8421	+	48.5860i	−0.541790	+	1.66161i
$856$	−13.7939	+	23.8917i	−0.471465	+	0.816601i
$857$	1.63620	+	9.27938i	0.0558917	+	0.316977i	0.999917	−	0.0128960i	$-0.00410503\pi$
$857$	1.63620	+	9.27938i	0.0558917	+	0.316977i	−0.944025	+	0.329873i	$0.892994\pi$
$858$	0.561739	−	0.0587474i	0.0191774	−	0.00200560i
$859$	24.9608	−	9.08500i	0.851652	−	0.309976i	0.120938	−	0.992660i	$-0.461410\pi$
$859$	24.9608	−	9.08500i	0.851652	−	0.309976i	0.730714	+	0.682684i	$0.239187\pi$
$860$	13.8372	+	11.6108i	0.471845	+	0.395925i
$861$	−8.33100	−	2.75199i	−0.283920	−	0.0937875i
$862$	−8.92362	−	3.24793i	−0.303940	−	0.110625i
$863$	−20.6034	−	35.6861i	−0.701347	−	1.21477i	−0.967994	−	0.250974i	$-0.919249\pi$
$863$	−20.6034	−	35.6861i	−0.701347	−	1.21477i	0.266647	−	0.963794i	$-0.414084\pi$
$864$	22.5303	−	17.5464i	0.766498	−	0.596941i
$865$	−39.1736	+	67.8506i	−1.33194	+	2.30699i
$866$	0.370502	+	2.10122i	0.0125902	+	0.0714024i
$867$	5.37089	+	3.62676i	0.182405	+	0.123171i
$868$	−0.556037	−	5.52235i	−0.0188731	−	0.187441i
$869$	0.215131	−	1.22007i	0.00729781	−	0.0413879i
$870$	9.58518	−	1.00243i	0.324968	−	0.0339856i
$871$	−5.47064	−	31.0255i	−0.185366	−	1.05126i
$872$	−22.9394			−0.776826
$873$	0.368031	+	10.8611i	0.0124560	+	0.367593i
$874$	−8.12588	+	14.0744i	−0.274862	+	0.476075i
$875$	−2.43698	−	5.05246i	−0.0823849	−	0.170804i
$876$	−9.86839	−	34.4824i	−0.333422	−	1.16505i
$877$	−27.9982	−	23.4933i	−0.945433	−	0.793313i	0.0330892	−	0.999452i	$-0.489465\pi$
$877$	−27.9982	−	23.4933i	−0.945433	−	0.793313i	−0.978523	+	0.206140i	$0.933910\pi$
$878$	0.251122	−	1.42418i	0.00847496	−	0.0480639i
$879$	0.534079	−	0.552483i	0.0180140	−	0.0186348i
$880$	0.493818	−	0.414362i	0.0166466	−	0.0139681i
$881$	−12.6271	+	21.8708i	−0.425418	+	0.736846i	−0.996459	−	0.0840757i	$-0.973206\pi$
$881$	−12.6271	+	21.8708i	−0.425418	+	0.736846i	0.571041	+	0.820921i	$0.306540\pi$
$882$	−11.3105	+	4.90387i	−0.380844	+	0.165122i
$883$	9.34378	+	16.1839i	0.314443	+	0.544631i	0.979319	−	0.202322i	$-0.0648489\pi$
$883$	9.34378	+	16.1839i	0.314443	+	0.544631i	−0.664876	+	0.746954i	$0.731516\pi$
$884$	32.6689	+	11.8905i	1.09878	+	0.399921i
$885$	−19.7864	+	44.3792i	−0.665113	+	1.49179i
$886$	1.68975	+	1.41787i	0.0567681	+	0.0476341i
$887$	2.23485	−	12.6745i	0.0750389	−	0.425567i	−0.924026	−	0.382330i	$-0.875122\pi$
$887$	2.23485	−	12.6745i	0.0750389	−	0.425567i	0.999065	−	0.0432371i	$-0.0137671\pi$
$888$	−22.8306	+	11.1206i	−0.766144	+	0.373183i
$889$	−11.0402	−	0.820502i	−0.370278	−	0.0275187i
$890$	−30.7764			−1.03163
$891$	−0.700180	−	0.510927i	−0.0234569	−	0.0171167i
$892$	12.5818	−	21.7923i	0.421270	−	0.729662i
$893$	−23.7372	+	19.9179i	−0.794334	+	0.666526i
$894$	17.7169	+	11.9636i	0.592543	+	0.400121i
$895$	31.9786	+	26.8333i	1.06893	+	0.896937i
$896$	−24.7055	+	17.7852i	−0.825352	+	0.594160i
$897$	52.6957	−	5.51099i	1.75946	−	0.184007i
$898$	−0.209338	−	0.0761929i	−0.00698571	−	0.00254259i
$899$	−3.68072			−0.122759
$900$	−17.2966	+	22.0915i	−0.576554	+	0.736384i
$901$	10.7351			0.357638
$902$	−0.0187965	−	0.106600i	−0.000625855	−	0.00354940i
$903$	−7.25963	+	13.4939i	−0.241585	+	0.449048i
$904$	5.88922	−	2.14350i	0.195872	−	0.0712917i
$905$	−6.77078	−	5.68136i	−0.225068	−	0.188855i
$906$	−10.7899	−	2.69614i	−0.358469	−	0.0895733i
$907$	41.8226	+	15.2222i	1.38869	+	0.505444i	0.924802	−	0.380448i	$-0.124230\pi$
$907$	41.8226	+	15.2222i	1.38869	+	0.505444i	0.463893	+	0.885891i	$0.346452\pi$
$908$	36.1984			1.20128
$909$	1.21698	+	35.9146i	0.0403646	+	1.19121i
$910$	28.1366	−	7.93514i	0.932718	−	0.263047i
$911$	38.0299	−	31.9108i	1.25999	−	1.05725i	0.264302	−	0.964440i	$-0.414859\pi$
$911$	38.0299	−	31.9108i	1.25999	−	1.05725i	0.995684	−	0.0928131i	$-0.0295859\pi$
$912$	−18.4434	+	1.92884i	−0.610722	+	0.0638701i
$913$	0.0826974	+	0.0693913i	0.00273688	+	0.00229652i
$914$	11.3264	−	4.12246i	0.374643	−	0.136359i
$915$	0.235556	−	3.34376i	0.00778725	−	0.110541i
$916$	−0.464654	−	0.169120i	−0.0153526	−	0.00558789i
$917$	26.9388	+	26.2430i	0.889599	+	0.866620i
$918$	5.19916	+	9.81491i	0.171598	+	0.323940i
$919$	−6.48805	−	11.2376i	−0.214021	−	0.370695i	0.738948	−	0.673762i	$-0.235323\pi$
$919$	−6.48805	−	11.2376i	−0.214021	−	0.370695i	−0.952969	+	0.303067i	$0.901989\pi$
$920$	−28.4508	+	23.8730i	−0.937995	+	0.787071i
$921$	10.7821	+	7.28074i	0.355282	+	0.239908i
$922$	−1.05288	+	5.97118i	−0.0346748	+	0.196650i
$923$	−12.9422	+	73.3991i	−0.425999	+	2.41596i
$924$	0.573506	+	0.452603i	0.0188670	+	0.0148895i
$925$	29.5709	−	24.8130i	0.972287	−	0.815845i
$926$	6.36322	−	11.0214i	0.209108	−	0.362186i
$927$	34.3096	−	7.25565i	1.12688	−	0.238307i
$928$	7.98113	+	13.8237i	0.261993	+	0.453786i
$929$	14.9852	−	12.5740i	0.491647	−	0.412541i	−0.362969	−	0.931801i	$-0.618237\pi$
$929$	14.9852	−	12.5740i	0.491647	−	0.412541i	0.854616	+	0.519260i	$0.173793\pi$
$930$	−2.92258	+	3.02329i	−0.0958352	+	0.0991376i
$931$	36.1378	+	5.40130i	1.18437	+	0.177020i
$932$	−14.1277	+	5.14208i	−0.462770	+	0.168434i
$933$	−38.5405	−	9.63040i	−1.26176	−	0.315285i
$934$	−6.63998	−	2.41676i	−0.217267	−	0.0790787i
$935$	0.572199	+	0.991077i	0.0187129	+	0.0324117i
$936$	−24.8164	−	27.6188i	−0.811148	−	0.902747i
$937$	20.7355	+	35.9149i	0.677399	+	1.17329i	0.975761	+	0.218837i	$0.0702262\pi$
$937$	20.7355	+	35.9149i	0.677399	+	1.17329i	−0.298362	+	0.954453i	$0.596440\pi$
$938$	−4.77464	+	7.01240i	−0.155898	+	0.228963i
$939$	0.195879	+	0.269898i	0.00639228	+	0.00880780i
$940$	−30.1347	+	10.9681i	−0.982885	+	0.357741i
$941$	−9.67269	+	3.52057i	−0.315321	+	0.114767i	−0.494832	−	0.868989i	$-0.664771\pi$
$941$	−9.67269	+	3.52057i	−0.315321	+	0.114767i	0.179512	+	0.983756i	$0.442548\pi$
$942$	−17.5229	−	11.8325i	−0.570927	−	0.385525i
$943$	−1.76327	−	9.99999i	−0.0574199	−	0.325644i
$944$	−17.6320			−0.573872
$945$	−40.2065	−	19.9056i	−1.30792	−	0.647528i
$946$	−0.189042			−0.00614628
$947$	−8.00288	−	45.3866i	−0.260059	−	1.47487i	−0.782745	−	0.622342i	$-0.786181\pi$
$947$	−8.00288	−	45.3866i	−0.260059	−	1.47487i	0.522687	−	0.852525i	$-0.324930\pi$
$948$	−33.1587	+	16.1514i	−1.07695	+	0.524572i
$949$	−67.7990	+	24.6768i	−2.20085	+	0.801044i
$950$	−16.2682	+	5.92113i	−0.527809	+	0.192107i
$951$	11.2457	−	25.2232i	0.364668	−	0.817919i
$952$	−8.98097	−	18.6198i	−0.291075	−	0.603470i
$953$	17.9366	+	31.0670i	0.581022	+	1.00636i	0.995359	+	0.0962364i	$0.0306805\pi$
$953$	17.9366	+	31.0670i	0.581022	+	1.00636i	−0.414336	+	0.910124i	$0.635986\pi$
$954$	−4.58190	−	2.44232i	−0.148344	−	0.0790731i
$955$	−12.4165	−	21.5060i	−0.401788	−	0.695917i
$956$	19.1574	+	6.97271i	0.619593	+	0.225513i
$957$	0.336740	−	0.348343i	0.0108852	−	0.0112603i
$958$	5.61779	−	2.04471i	0.181503	−	0.0660615i
$959$	−1.29357	−	12.8472i	−0.0417714	−	0.414859i
$960$	−4.80327	−	1.20023i	−0.155025	−	0.0387372i
$961$	−22.5171	+	18.8941i	−0.726360	+	0.609488i
$962$	11.5672	+	20.0350i	0.372942	+	0.645955i
$963$	−14.4112	−	35.7754i	−0.464394	−	1.15285i
$964$	−17.9257	+	31.0483i	−0.577349	+	0.999997i
$965$	−33.9326	+	28.4728i	−1.09233	+	0.916572i
$966$	−11.1999	−	8.83880i	−0.360351	−	0.284384i
$967$	−6.85579	+	38.8811i	−0.220467	+	1.25033i	0.650696	+	0.759338i	$0.274477\pi$
$967$	−6.85579	+	38.8811i	−0.220467	+	1.25033i	−0.871163	+	0.490993i	$0.836634\pi$
$968$	4.09540	−	23.2262i	0.131631	−	0.746518i
$969$	2.31340	−	32.8392i	0.0743172	−	1.05495i
$970$	−5.31608	+	4.46072i	−0.170689	+	0.143225i
$971$	−1.49349	−	2.58681i	−0.0479285	−	0.0830145i	0.841066	−	0.540933i	$-0.181929\pi$
$971$	−1.49349	−	2.58681i	−0.0479285	−	0.0830145i	−0.888994	+	0.457918i	$0.848595\pi$
$972$	−0.0667253	+	25.8048i	−0.00214022	+	0.827690i
$973$	22.6165	−	6.37837i	0.725053	−	0.204481i
$974$	−2.78833	−	1.01487i	−0.0893440	−	0.0325185i
$975$	46.7749	+	31.5853i	1.49800	+	1.01154i
$976$	1.14300	−	0.416019i	0.0365866	−	0.0133165i
$977$	−37.2399	−	31.2480i	−1.19141	−	0.999711i	−0.999834	−	0.0182330i	$-0.994196\pi$
$977$	−37.2399	−	31.2480i	−1.19141	−	0.999711i	−0.191575	−	0.981478i	$-0.561360\pi$
$978$	3.14891	+	4.33881i	0.100691	+	0.138740i
$979$	−1.18522	+	0.994521i	−0.0378799	+	0.0317850i
$980$	33.2324	+	18.0442i	1.06157	+	0.576402i
$981$	19.7706	−	25.2513i	0.631226	−	0.806212i
$982$	−15.1831			−0.484513
$983$	20.7683	+	7.55903i	0.662405	+	0.241096i	0.651274	−	0.758842i	$-0.274235\pi$
$983$	20.7683	+	7.55903i	0.662405	+	0.241096i	0.0111306	+	0.999938i	$0.496457\pi$
$984$	−4.94585	+	5.11628i	−0.157668	+	0.163101i
$985$	−3.99055	−	3.34847i	−0.127150	−	0.106691i
$986$	−5.83396	+	2.12339i	−0.185791	+	0.0676225i
$987$	−14.3027	−	23.1400i	−0.455260	−	0.736553i
$988$	8.65438	+	49.0815i	0.275333	+	1.56149i
$989$	−17.7337			−0.563898
$990$	−0.0187448	−	0.553186i	−0.000595750	−	0.0175814i
$991$	3.89220			0.123640			0.0618199	−	0.998087i	$-0.480310\pi$
$991$	3.89220			0.123640			0.0618199	+	0.998087i	$0.480310\pi$
$992$	−6.54456	−	2.38203i	−0.207790	−	0.0756294i
$993$	−2.40584	+	5.39610i	−0.0763471	+	0.171240i
$994$	16.2885	−	11.7259i	0.516639	−	0.371922i
$995$	2.44191	+	2.04900i	0.0774136	+	0.0649577i
$996$	0.225849	−	3.20597i	0.00715630	−	0.101585i
$997$	15.4476	−	12.9621i	0.489230	−	0.410513i	−0.364520	−	0.931195i	$-0.618767\pi$
$997$	15.4476	−	12.9621i	0.489230	−	0.410513i	0.853750	+	0.520683i	$0.174323\pi$
$998$	−4.28453	+	7.42102i	−0.135624	+	0.234908i
$999$	7.43542	−	34.7160i	0.235246	−	1.09836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.15	✓	132
3.2	odd	2		567.2.u.a.550.8		132
7.2	even	3		189.2.w.a.58.15	yes	132
21.2	odd	6		567.2.w.a.226.8		132
27.7	even	9		189.2.w.a.88.15	yes	132
27.20	odd	18		567.2.w.a.424.8		132
189.128	odd	18		567.2.u.a.100.8		132
189.142	even	9	inner	189.2.u.a.142.15	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.15	✓	132	1.1	even	1	trivial
189.2.u.a.142.15	yes	132	189.142	even	9	inner
189.2.w.a.58.15	yes	132	7.2	even	3
189.2.w.a.88.15	yes	132	27.7	even	9
567.2.u.a.100.8		132	189.128	odd	18
567.2.u.a.550.8		132	3.2	odd	2
567.2.w.a.226.8		132	21.2	odd	6
567.2.w.a.424.8		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)

\(f(q)\)	\(=\)	\(q+(0.101938 + 0.578121i) q^{2} +(-0.121715 + 1.72777i) q^{3} +(1.55555 - 0.566175i) q^{4} +(-3.06658 + 1.11614i) q^{5} +(-1.01127 + 0.105760i) q^{6} +(-1.48906 + 2.18694i) q^{7} +(1.07293 + 1.85836i) q^{8} +(-2.97037 - 0.420592i) q^{9} +O(q^{10})\)	\(q+(0.101938 + 0.578121i) q^{2} +(-0.121715 + 1.72777i) q^{3} +(1.55555 - 0.566175i) q^{4} +(-3.06658 + 1.11614i) q^{5} +(-1.01127 + 0.105760i) q^{6} +(-1.48906 + 2.18694i) q^{7} +(1.07293 + 1.85836i) q^{8} +(-2.97037 - 0.420592i) q^{9} +(-0.957867 - 1.65908i) q^{10} +(-0.0905002 - 0.0329394i) q^{11} +(0.788885 + 2.75655i) q^{12} +(5.41990 - 1.97268i) q^{13} +(-1.41611 - 0.637921i) q^{14} +(-1.55519 - 5.43419i) q^{15} +(1.57121 - 1.31840i) q^{16} +(1.82060 + 3.15337i) q^{17} +(-0.0596416 - 1.76011i) q^{18} +(-2.60995 + 4.52056i) q^{19} +(-4.13830 + 3.47244i) q^{20} +(-3.59729 - 2.83893i) q^{21} +(0.00981750 - 0.0556778i) q^{22} +(0.920962 - 5.22304i) q^{23} +(-3.34141 + 1.62758i) q^{24} +(4.32791 - 3.63155i) q^{25} +(1.69294 + 2.93226i) q^{26} +(1.08822 - 5.08092i) q^{27} +(-1.07811 + 4.24497i) q^{28} +(2.72930 + 0.993386i) q^{29} +(2.98309 - 1.45304i) q^{30} +(-1.19084 + 0.433429i) q^{31} +(4.21000 + 3.53261i) q^{32} +(0.0679269 - 0.152354i) q^{33} +(-1.63744 + 1.37398i) q^{34} +(2.12537 - 8.36843i) q^{35} +(-4.85870 + 1.02750i) q^{36} +6.83261 q^{37} +(-2.87948 - 1.04805i) q^{38} +(2.74865 + 9.60444i) q^{39} +(-5.36442 - 4.50128i) q^{40} +(1.79913 - 0.654829i) q^{41} +(1.27454 - 2.36906i) q^{42} +(-0.580627 - 3.29290i) q^{43} -0.159427 q^{44} +(9.57832 - 2.02558i) q^{45} +3.11343 q^{46} +(5.57827 + 2.03032i) q^{47} +(2.08665 + 2.87516i) q^{48} +(-2.56543 - 6.51296i) q^{49} +(2.54065 + 2.13186i) q^{50} +(-5.66989 + 2.76176i) q^{51} +(7.31406 - 6.13722i) q^{52} +(1.47412 - 2.55324i) q^{53} +(3.04832 + 0.111185i) q^{54} +0.314291 q^{55} +(-5.66178 - 0.420779i) q^{56} +(-7.49281 - 5.05961i) q^{57} +(-0.296076 + 1.67913i) q^{58} +(-6.58528 - 5.52571i) q^{59} +(-5.49588 - 7.57267i) q^{60} +(0.557272 + 0.202830i) q^{61} +(-0.371966 - 0.644265i) q^{62} +(5.34286 - 5.86974i) q^{63} +(0.437956 - 0.758562i) q^{64} +(-14.4188 + 12.0988i) q^{65} +(0.0950034 + 0.0237392i) q^{66} +(0.948490 - 5.37916i) q^{67} +(4.61740 + 3.87446i) q^{68} +(8.91211 + 2.22693i) q^{69} +(5.05462 + 0.375655i) q^{70} +(-6.46106 + 11.1909i) q^{71} +(-2.40538 - 5.97129i) q^{72} -12.5093 q^{73} +(0.696504 + 3.95007i) q^{74} +(5.74771 + 7.91965i) q^{75} +(-1.50048 + 8.50966i) q^{76} +(0.206796 - 0.148870i) q^{77} +(-5.27233 + 2.56811i) q^{78} +(2.23377 + 12.6684i) q^{79} +(-3.34672 + 5.79668i) q^{80} +(8.64621 + 2.49863i) q^{81} +(0.561970 + 0.973361i) q^{82} +(-1.05332 - 0.383377i) q^{83} +(-7.20310 - 2.37941i) q^{84} +(-9.10264 - 7.63802i) q^{85} +(1.84451 - 0.671345i) q^{86} +(-2.04854 + 4.59470i) q^{87} +(-0.0358867 - 0.203524i) q^{88} +(8.03254 - 13.9128i) q^{89} +(2.14743 + 5.33094i) q^{90} +(-3.75639 + 14.7904i) q^{91} +(-1.52455 - 8.64614i) q^{92} +(-0.603923 - 2.11025i) q^{93} +(-0.605133 + 3.43188i) q^{94} +(2.95801 - 16.7757i) q^{95} +(-6.61596 + 6.84394i) q^{96} +(-0.629031 - 3.56741i) q^{97} +(3.50376 - 2.14705i) q^{98} +(0.254965 + 0.135906i) 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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