LMFDB - Embedded newform 432.2.y.e.37.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.17
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38700 - 0.276075i) q^{2} +(1.84757 - 0.765835i) q^{4} +(0.0691269 - 0.0185225i) q^{5} +(1.28192 - 0.740118i) q^{7} +(2.35115 - 1.57228i) q^{8} +O(q^{10})$	\(q+(1.38700 - 0.276075i) q^{2} +(1.84757 - 0.765835i) q^{4} +(0.0691269 - 0.0185225i) q^{5} +(1.28192 - 0.740118i) q^{7} +(2.35115 - 1.57228i) q^{8} +(0.0907658 - 0.0447750i) q^{10} +(-0.587070 + 2.19098i) q^{11} +(0.104109 + 0.388539i) q^{13} +(1.57370 - 1.38045i) q^{14} +(2.82699 - 2.82986i) q^{16} +0.851000 q^{17} +(3.75230 - 3.75230i) q^{19} +(0.113531 - 0.0871613i) q^{20} +(-0.209396 + 3.20097i) q^{22} +(-7.44629 - 4.29912i) q^{23} +(-4.32569 + 2.49744i) q^{25} +(0.251665 + 0.510163i) q^{26} +(1.80163 - 2.34916i) q^{28} +(4.77230 + 1.27873i) q^{29} +(-4.50318 + 7.79974i) q^{31} +(3.13980 - 4.70549i) q^{32} +(1.18034 - 0.234940i) q^{34} +(0.0749065 - 0.0749065i) q^{35} +(4.13315 + 4.13315i) q^{37} +(4.16854 - 6.24038i) q^{38} +(0.133405 - 0.152236i) q^{40} +(2.05305 + 1.18533i) q^{41} +(-0.669562 + 2.49884i) q^{43} +(0.593275 + 4.49757i) q^{44} +(-11.5149 - 3.90716i) q^{46} +(-3.42005 - 5.92370i) q^{47} +(-2.40445 + 4.16463i) q^{49} +(-5.31027 + 4.65818i) q^{50} +(0.489904 + 0.638121i) q^{52} +(-3.95421 - 3.95421i) q^{53} +0.162329i q^{55} +(1.85032 - 3.75568i) q^{56} +(6.97222 + 0.456097i) q^{58} +(-13.7811 + 3.69264i) q^{59} +(-3.28936 - 0.881382i) q^{61} +(-4.09262 + 12.0615i) q^{62} +(3.05585 - 7.39336i) q^{64} +(0.0143934 + 0.0249301i) q^{65} +(-1.73506 - 6.47532i) q^{67} +(1.57228 - 0.651726i) q^{68} +(0.0832159 - 0.124576i) q^{70} +0.362864i q^{71} +15.8744i q^{73} +(6.87375 + 4.59164i) q^{74} +(4.05898 - 9.80627i) q^{76} +(0.869003 + 3.24316i) q^{77} +(-5.45338 - 9.44553i) q^{79} +(0.143005 - 0.247983i) q^{80} +(3.17483 + 1.07726i) q^{82} +(5.37105 + 1.43917i) q^{83} +(0.0588270 - 0.0157627i) q^{85} +(-0.238819 + 3.65075i) q^{86} +(2.06454 + 6.07436i) q^{88} +13.1832i q^{89} +(0.421024 + 0.421024i) q^{91} +(-17.0499 - 2.24027i) q^{92} +(-6.37901 - 7.27201i) q^{94} +(0.189883 - 0.328887i) q^{95} +(-0.627593 - 1.08702i) q^{97} +(-2.18523 + 6.44017i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.38700	−	0.276075i	0.980761	−	0.195215i
$2$	1.38700	−	0.276075i	0.980761	−	0.195215i
$3$		0			0
$3$		0			0
$4$	1.84757	−	0.765835i	0.923783	−	0.382917i
$5$	0.0691269	−	0.0185225i	0.0309145	−	0.00828352i	−0.243329	−	0.969944i	$-0.578239\pi$
$5$	0.0691269	−	0.0185225i	0.0309145	−	0.00828352i	0.274243	+	0.961660i	$0.411573\pi$
$6$		0			0
$7$	1.28192	−	0.740118i	0.484521	−	0.279738i	−0.237778	−	0.971320i	$-0.576419\pi$
$7$	1.28192	−	0.740118i	0.484521	−	0.279738i	0.722299	+	0.691581i	$0.243086\pi$
$8$	2.35115	−	1.57228i	0.831258	−	0.555886i
$9$		0			0
$10$	0.0907658	−	0.0447750i	0.0287027	−	0.0141591i
$11$	−0.587070	+	2.19098i	−0.177008	+	0.660604i	0.819192	+	0.573519i	$0.194422\pi$
$11$	−0.587070	+	2.19098i	−0.177008	+	0.660604i	−0.996201	+	0.0870855i	$0.972245\pi$
$12$		0			0
$13$	0.104109	+	0.388539i	0.0288745	+	0.107761i	0.978859	−	0.204535i	$-0.0655684\pi$
$13$	0.104109	+	0.388539i	0.0288745	+	0.107761i	−0.949985	+	0.312297i	$0.898902\pi$
$14$	1.57370	−	1.38045i	0.420590	−	0.368942i
$15$		0			0
$16$	2.82699	−	2.82986i	0.706748	−	0.707465i
$17$	0.851000			0.206398			0.103199	−	0.994661i	$-0.467092\pi$
$17$	0.851000			0.206398			0.103199	+	0.994661i	$0.467092\pi$
$18$		0			0
$19$	3.75230	−	3.75230i	0.860837	−	0.860837i	−0.130598	−	0.991435i	$-0.541690\pi$
$19$	3.75230	−	3.75230i	0.860837	−	0.860837i	0.991435	+	0.130598i	$0.0416898\pi$
$20$	0.113531	−	0.0871613i	0.0253864	−	0.0194899i
$21$		0			0
$22$	−0.209396	+	3.20097i	−0.0446433	+	0.682449i
$23$	−7.44629	−	4.29912i	−1.55266	−	0.896428i	−0.997924	−	0.0643999i	$-0.979487\pi$
$23$	−7.44629	−	4.29912i	−1.55266	−	0.896428i	−0.554734	−	0.832028i	$-0.687180\pi$
$24$		0			0
$25$	−4.32569	+	2.49744i	−0.865138	+	0.499488i
$26$	0.251665	+	0.510163i	0.0493556	+	0.100051i
$27$		0			0
$28$	1.80163	−	2.34916i	0.340475	−	0.443949i
$29$	4.77230	+	1.27873i	0.886193	+	0.237455i	0.673077	−	0.739572i	$-0.264972\pi$
$29$	4.77230	+	1.27873i	0.886193	+	0.237455i	0.213116	+	0.977027i	$0.431639\pi$
$30$		0			0
$31$	−4.50318	+	7.79974i	−0.808796	+	1.40088i	0.104902	+	0.994483i	$0.466547\pi$
$31$	−4.50318	+	7.79974i	−0.808796	+	1.40088i	−0.913698	+	0.406393i	$0.866786\pi$
$32$	3.13980	−	4.70549i	0.555044	−	0.831821i
$33$		0			0
$34$	1.18034	−	0.234940i	0.202427	−	0.0402919i
$35$	0.0749065	−	0.0749065i	0.0126615	−	0.0126615i
$36$		0			0
$37$	4.13315	+	4.13315i	0.679485	+	0.679485i	0.959884	−	0.280399i	$-0.0904666\pi$
$37$	4.13315	+	4.13315i	0.679485	+	0.679485i	−0.280399	+	0.959884i	$0.590467\pi$
$38$	4.16854	−	6.24038i	0.676227	−	1.01232i
$39$		0			0
$40$	0.133405	−	0.152236i	0.0210932	−	0.0240707i
$41$	2.05305	+	1.18533i	0.320633	+	0.185118i	0.651675	−	0.758499i	$-0.274067\pi$
$41$	2.05305	+	1.18533i	0.320633	+	0.185118i	−0.331042	+	0.943616i	$0.607400\pi$
$42$		0			0
$43$	−0.669562	+	2.49884i	−0.102107	+	0.381070i	−0.998001	−	0.0631989i	$-0.979870\pi$
$43$	−0.669562	+	2.49884i	−0.102107	+	0.381070i	0.895894	+	0.444269i	$0.146536\pi$
$44$	0.593275	+	4.49757i	0.0894396	+	0.678034i
$45$		0			0
$46$	−11.5149	−	3.90716i	−1.69778	−	0.576079i
$47$	−3.42005	−	5.92370i	−0.498865	−	0.864060i	0.501134	−	0.865370i	$-0.332916\pi$
$47$	−3.42005	−	5.92370i	−0.498865	−	0.864060i	−0.999999	+	0.00130966i	$0.999583\pi$
$48$		0			0
$49$	−2.40445	+	4.16463i	−0.343493	+	0.594947i
$50$	−5.31027	+	4.65818i	−0.750986	+	0.658766i
$51$		0			0
$52$	0.489904	+	0.638121i	0.0679375	+	0.0884914i
$53$	−3.95421	−	3.95421i	−0.543152	−	0.543152i	0.381300	−	0.924452i	$-0.375477\pi$
$53$	−3.95421	−	3.95421i	−0.543152	−	0.543152i	−0.924452	+	0.381300i	$0.875477\pi$
$54$		0			0
$55$			0.162329i			0.0218885i
$56$	1.85032	−	3.75568i	0.247260	−	0.501873i
$57$		0			0
$58$	6.97222	+	0.456097i	0.915498	+	0.0598884i
$59$	−13.7811	+	3.69264i	−1.79415	+	0.480741i	−0.993040	−	0.117777i	$-0.962423\pi$
$59$	−13.7811	+	3.69264i	−1.79415	+	0.480741i	−0.801109	+	0.598518i	$0.795756\pi$
$60$		0			0
$61$	−3.28936	−	0.881382i	−0.421160	−	0.112849i	0.0420139	−	0.999117i	$-0.486623\pi$
$61$	−3.28936	−	0.881382i	−0.421160	−	0.112849i	−0.463173	+	0.886268i	$0.653289\pi$
$62$	−4.09262	+	12.0615i	−0.519764	+	1.53181i
$63$		0			0
$64$	3.05585	−	7.39336i	0.381981	−	0.924170i
$65$	0.0143934	+	0.0249301i	0.00178528	+	0.00309220i
$66$		0			0
$67$	−1.73506	−	6.47532i	−0.211971	−	0.791086i	−0.987211	−	0.159419i	$-0.949038\pi$
$67$	−1.73506	−	6.47532i	−0.211971	−	0.791086i	0.775240	−	0.631667i	$-0.217629\pi$
$68$	1.57228	−	0.651726i	0.190667	−	0.0790333i
$69$		0			0
$70$	0.0832159	−	0.124576i	0.00994620	−	0.0148896i
$71$			0.362864i			0.0430640i	0.999768	+	0.0215320i	$0.00685439\pi$
$71$			0.362864i			0.0430640i	−0.999768	+	0.0215320i	$0.993146\pi$
$72$		0			0
$73$			15.8744i			1.85796i	0.370128	+	0.928981i	$0.379314\pi$
$73$			15.8744i			1.85796i	−0.370128	+	0.928981i	$0.620686\pi$
$74$	6.87375	+	4.59164i	0.799058	+	0.533767i
$75$		0			0
$76$	4.05898	−	9.80627i	0.465597	−	1.12486i
$77$	0.869003	+	3.24316i	0.0990321	+	0.369593i
$78$		0			0
$79$	−5.45338	−	9.44553i	−0.613553	−	1.06271i	−0.990637	−	0.136526i	$-0.956406\pi$
$79$	−5.45338	−	9.44553i	−0.613553	−	1.06271i	0.377083	−	0.926179i	$-0.376927\pi$
$80$	0.143005	−	0.247983i	0.0159885	−	0.0277253i
$81$		0			0
$82$	3.17483	+	1.07726i	0.350602	+	0.118964i
$83$	5.37105	+	1.43917i	0.589549	+	0.157969i	0.541247	−	0.840863i	$-0.317952\pi$
$83$	5.37105	+	1.43917i	0.589549	+	0.157969i	0.0483022	+	0.998833i	$0.484619\pi$
$84$		0			0
$85$	0.0588270	−	0.0157627i	0.00638069	−	0.00170970i
$86$	−0.238819	+	3.65075i	−0.0257525	+	0.393671i
$87$		0			0
$88$	2.06454	+	6.07436i	0.220081	+	0.647529i
$89$			13.1832i			1.39741i	0.715408	+	0.698707i	$0.246241\pi$
$89$			13.1832i			1.39741i	−0.715408	+	0.698707i	$0.753759\pi$
$90$		0			0
$91$	0.421024	+	0.421024i	0.0441353	+	0.0441353i
$92$	−17.0499	−	2.24027i	−1.77758	−	0.233564i
$93$		0			0
$94$	−6.37901	−	7.27201i	−0.657945	−	0.750050i
$95$	0.189883	−	0.328887i	0.0194816	−	0.0337431i
$96$		0			0
$97$	−0.627593	−	1.08702i	−0.0637224	−	0.110370i	0.832404	−	0.554169i	$-0.186964\pi$
$97$	−0.627593	−	1.08702i	−0.0637224	−	0.110370i	−0.896127	+	0.443799i	$0.853631\pi$
$98$	−2.18523	+	6.44017i	−0.220742	+	0.650555i
$99$		0			0
$100$	−6.07937	+	7.92695i	−0.607937	+	0.792695i
$101$	1.43047	−	5.33858i	0.142337	−	0.531209i	−0.857522	−	0.514446i	$-0.827997\pi$
$101$	1.43047	−	5.33858i	0.142337	−	0.531209i	0.999860	−	0.0167625i	$-0.00533591\pi$
$102$		0			0
$103$	−9.59933	−	5.54217i	−0.945850	−	0.546087i	−0.0540605	−	0.998538i	$-0.517216\pi$
$103$	−9.59933	−	5.54217i	−0.945850	−	0.546087i	−0.891789	+	0.452451i	$0.850550\pi$
$104$	0.855668	+	0.749826i	0.0839052	+	0.0735265i
$105$		0			0
$106$	−6.57616	−	4.39285i	−0.638733	−	0.426671i
$107$	6.90288	+	6.90288i	0.667327	+	0.667327i	0.957096	−	0.289770i	$-0.0935787\pi$
$107$	6.90288	+	6.90288i	0.667327	+	0.667327i	−0.289770	+	0.957096i	$0.593579\pi$
$108$		0			0
$109$	9.39169	−	9.39169i	0.899560	−	0.899560i	−0.0958367	−	0.995397i	$-0.530553\pi$
$109$	9.39169	−	9.39169i	0.899560	−	0.899560i	0.995397	+	0.0958367i	$0.0305527\pi$
$110$	0.0448151	+	0.225152i	0.00427295	+	0.0214674i
$111$		0			0
$112$	1.52956	−	5.71997i	0.144529	−	0.540486i
$113$	5.81166	−	10.0661i	0.546715	−	0.946938i	−0.451782	−	0.892128i	$-0.649211\pi$
$113$	5.81166	−	10.0661i	0.546715	−	0.946938i	0.998497	−	0.0548097i	$-0.0174552\pi$
$114$		0			0
$115$	−0.594369	−	0.159261i	−0.0554252	−	0.0148511i
$116$	9.79642	−	1.29225i	0.909575	−	0.119982i
$117$		0			0
$118$	−18.0950	+	8.92633i	−1.66578	+	0.821736i
$119$	1.09092	−	0.629841i	0.100004	−	0.0577374i
$120$		0			0
$121$	5.07055	+	2.92749i	0.460959	+	0.266135i
$122$	−4.80569	−	0.314370i	−0.435087	−	0.0284617i
$123$		0			0
$124$	−2.34661	+	17.8592i	−0.210732	+	1.60381i
$125$	−0.505785	+	0.505785i	−0.0452388	+	0.0452388i
$126$		0			0
$127$	−10.1965			−0.904796			−0.452398	−	0.891816i	$-0.649431\pi$
$127$	−10.1965			−0.904796			−0.452398	+	0.891816i	$0.649431\pi$
$128$	2.19736	−	11.0983i	0.194221	−	0.980958i
$129$		0			0
$130$	0.0268463	+	0.0306046i	0.00235458	+	0.00268420i
$131$	1.82077	+	6.79522i	0.159082	+	0.593701i	0.998721	+	0.0505571i	$0.0160997\pi$
$131$	1.82077	+	6.79522i	0.159082	+	0.593701i	−0.839639	+	0.543144i	$0.817234\pi$
$132$		0			0
$133$	2.03301	−	7.58731i	0.176285	−	0.657903i
$134$	−4.19420	−	8.50229i	−0.362324	−	0.734486i
$135$		0			0
$136$	2.00083	−	1.33801i	0.171570	−	0.114734i
$137$	−12.5671	+	7.25564i	−1.07368	+	0.619891i	−0.929185	−	0.369614i	$-0.879490\pi$
$137$	−12.5671	+	7.25564i	−1.07368	+	0.619891i	−0.144497	+	0.989505i	$0.546157\pi$
$138$		0			0
$139$	5.09570	−	1.36539i	0.432212	−	0.115811i	−0.0361523	−	0.999346i	$-0.511510\pi$
$139$	5.09570	−	1.36539i	0.432212	−	0.115811i	0.468364	+	0.883535i	$0.344843\pi$
$140$	0.0810286	−	0.195761i	0.00684817	−	0.0165448i
$141$		0			0
$142$	0.100178	+	0.503294i	0.00840673	+	0.0422355i
$143$	−0.912398			−0.0762986
$144$		0			0
$145$	0.353579			0.0293632
$146$	4.38253	+	22.0179i	0.362701	+	1.82222i
$147$		0			0
$148$	10.8016	+	4.47095i	0.887883	+	0.367510i
$149$	19.3330	−	5.18027i	1.58382	−	0.424384i	0.643717	−	0.765264i	$-0.277391\pi$
$149$	19.3330	−	5.18027i	1.58382	−	0.424384i	0.940107	+	0.340879i	$0.110725\pi$
$150$		0			0
$151$	11.0910	−	6.40336i	0.902569	−	0.521098i	0.0245362	−	0.999699i	$-0.492189\pi$
$151$	11.0910	−	6.40336i	0.902569	−	0.521098i	0.878033	+	0.478601i	$0.158856\pi$
$152$	2.92256	−	14.7219i	0.237051	−	1.19411i
$153$		0			0
$154$	2.10067	+	4.25837i	0.169277	+	0.343149i
$155$	−0.166821	+	0.622583i	−0.0133993	+	0.0500070i
$156$		0			0
$157$	1.98067	+	7.39195i	0.158074	+	0.589942i	0.998822	+	0.0485153i	$0.0154490\pi$
$157$	1.98067	+	7.39195i	0.158074	+	0.589942i	−0.840748	+	0.541427i	$0.817884\pi$
$158$	−10.1715	−	11.5955i	−0.809204	−	0.922485i
$159$		0			0
$160$	0.129887	−	0.383433i	0.0102685	−	0.0303131i
$161$	−12.7274			−1.00306
$162$		0			0
$163$	10.3989	−	10.3989i	0.814504	−	0.814504i	−0.170802	−	0.985305i	$-0.554636\pi$
$163$	10.3989	−	10.3989i	0.814504	−	0.814504i	0.985305	+	0.170802i	$0.0546358\pi$
$164$	4.70092	+	0.617676i	0.367080	+	0.0482324i
$165$		0			0
$166$	7.84699	+	0.513321i	0.609045	+	0.0398414i
$167$	5.44443	+	3.14334i	0.421302	+	0.243239i	0.695634	−	0.718396i	$-0.255123\pi$
$167$	5.44443	+	3.14334i	0.421302	+	0.243239i	−0.274332	+	0.961635i	$0.588457\pi$
$168$		0			0
$169$	11.1182	−	6.41910i	0.855247	−	0.493777i
$170$	0.0772417	−	0.0381036i	0.00592417	−	0.00292241i
$171$		0			0
$172$	0.676639	+	5.12955i	0.0515933	+	0.391124i
$173$	11.3578	+	3.04333i	0.863521	+	0.231380i	0.663284	−	0.748368i	$-0.269162\pi$
$173$	11.3578	+	3.04333i	0.863521	+	0.231380i	0.200237	+	0.979748i	$0.435829\pi$
$174$		0			0
$175$	−3.69680	+	6.40305i	−0.279452	+	0.484025i
$176$	4.54051	+	7.85520i	0.342254	+	0.592108i
$177$		0			0
$178$	3.63955	+	18.2851i	0.272795	+	1.37053i
$179$	9.21801	−	9.21801i	0.688986	−	0.688986i	−0.273021	−	0.962008i	$-0.588023\pi$
$179$	9.21801	−	9.21801i	0.688986	−	0.688986i	0.962008	+	0.273021i	$0.0880230\pi$
$180$		0			0
$181$	−11.5919	−	11.5919i	−0.861621	−	0.861621i	0.129905	−	0.991526i	$-0.458533\pi$
$181$	−11.5919	−	11.5919i	−0.861621	−	0.861621i	−0.991526	+	0.129905i	$0.958533\pi$
$182$	0.700196	+	0.467728i	0.0519020	+	0.0346703i
$183$		0			0
$184$	−24.2668	+	1.59979i	−1.78897	+	0.117938i
$185$	0.362268	+	0.209155i	0.0266345	+	0.0153774i
$186$		0			0
$187$	−0.499597	+	1.86452i	−0.0365341	+	0.136347i
$188$	−10.8553	−	8.32523i	−0.791707	−	0.607179i
$189$		0			0
$190$	0.172571	−	0.508590i	0.0125196	−	0.0368970i
$191$	−11.1864	−	19.3755i	−0.809423	−	1.40196i	−0.913264	−	0.407368i	$-0.866447\pi$
$191$	−11.1864	−	19.3755i	−0.809423	−	1.40196i	0.103842	−	0.994594i	$-0.466887\pi$
$192$		0			0
$193$	7.17911	−	12.4346i	0.516764	−	0.895061i	−0.483047	−	0.875594i	$-0.660470\pi$
$193$	7.17911	−	12.4346i	0.516764	−	0.895061i	0.999811	−	0.0194663i	$-0.00619671\pi$
$194$	−1.17057	−	1.33444i	−0.0840423	−	0.0958074i
$195$		0			0
$196$	−1.25296	+	9.53584i	−0.0894971	+	0.681131i
$197$	−1.57538	−	1.57538i	−0.112241	−	0.112241i	0.648756	−	0.760997i	$-0.275290\pi$
$197$	−1.57538	−	1.57538i	−0.112241	−	0.112241i	−0.760997	+	0.648756i	$0.775290\pi$
$198$		0			0
$199$			1.72755i			0.122463i	0.998124	+	0.0612313i	$0.0195027\pi$
$199$			1.72755i			0.122463i	−0.998124	+	0.0612313i	$0.980497\pi$
$200$	−6.24368	+	12.6731i	−0.441495	+	0.896122i
$201$		0			0
$202$	0.510218	−	7.79956i	0.0358988	−	0.548775i
$203$	7.06413	−	1.89283i	0.495804	−	0.132850i
$204$		0			0
$205$	0.163877	+	0.0439106i	0.0114456	+	0.00306685i
$206$	−14.8444	−	5.03689i	−1.03426	−	0.350937i
$207$		0			0
$208$	1.39382	+	0.803784i	0.0966444	+	0.0557324i
$209$	6.01834	+	10.4241i	0.416297	+	0.721048i
$210$		0			0
$211$	3.19942	+	11.9404i	0.220257	+	0.822011i	0.984249	+	0.176785i	$0.0565698\pi$
$211$	3.19942	+	11.9404i	0.220257	+	0.822011i	−0.763992	+	0.645225i	$0.776764\pi$
$212$	−10.3339	−	4.27738i	−0.709737	−	0.293772i
$213$		0			0
$214$	11.4800	+	7.66862i	0.784760	+	0.524216i
$215$			0.185139i			0.0126264i
$216$		0			0
$217$			13.3316i			0.905005i
$218$	10.4335	−	15.6191i	0.706646	−	1.05786i
$219$		0			0
$220$	0.124318	+	0.299914i	0.00838149	+	0.0202202i
$221$	0.0885965	+	0.330647i	0.00595964	+	0.0222417i
$222$		0			0
$223$	−7.22081	−	12.5068i	−0.483541	−	0.837518i	0.516280	−	0.856420i	$-0.327316\pi$
$223$	−7.22081	−	12.5068i	−0.483541	−	0.837518i	−0.999821	+	0.0189019i	$0.993983\pi$
$224$	0.542360	−	8.35590i	0.0362380	−	0.558302i
$225$		0			0
$226$	5.28180	−	15.5662i	0.351340	−	1.03545i
$227$	1.61577	+	0.432945i	0.107243	+	0.0287356i	0.312041	−	0.950069i	$-0.398987\pi$
$227$	1.61577	+	0.432945i	0.107243	+	0.0287356i	−0.204799	+	0.978804i	$0.565654\pi$
$228$		0			0
$229$	−19.6207	+	5.25735i	−1.29657	+	0.347416i	−0.840153	−	0.542349i	$-0.817535\pi$
$229$	−19.6207	+	5.25735i	−1.29657	+	0.347416i	−0.456420	+	0.889765i	$0.650868\pi$
$230$	−0.868361	−	0.0568049i	−0.0572580	−	0.00374561i
$231$		0			0
$232$	13.2309	−	4.49690i	0.868653	−	0.295236i
$233$		−	23.5814i		−	1.54487i	−0.635094	−	0.772435i	$-0.719039\pi$
$233$		−	23.5814i		−	1.54487i	0.635094	−	0.772435i	$-0.280961\pi$
$234$		0			0
$235$	−0.346139	−	0.346139i	−0.0225796	−	0.0225796i
$236$	−22.6336	+	17.3765i	−1.47332	+	1.13111i
$237$		0			0
$238$	1.33922	−	1.17477i	0.0868089	−	0.0761488i
$239$	−4.28400	+	7.42011i	−0.277109	+	0.479967i	−0.970665	−	0.240436i	$-0.922710\pi$
$239$	−4.28400	+	7.42011i	−0.277109	+	0.479967i	0.693556	+	0.720403i	$0.256043\pi$
$240$		0			0
$241$	3.69013	+	6.39149i	0.237702	+	0.411712i	0.960055	−	0.279813i	$-0.0902725\pi$
$241$	3.69013	+	6.39149i	0.237702	+	0.411712i	−0.722352	+	0.691525i	$0.756939\pi$
$242$	7.84109	+	2.66058i	0.504044	+	0.171029i
$243$		0			0
$244$	−6.75230	+	0.890698i	−0.432272	+	0.0570211i
$245$	−0.0890729	+	0.332424i	−0.00569066	+	0.0212378i
$246$		0			0
$247$	1.84856	+	1.06727i	0.117621	+	0.0679086i
$248$	1.67573	+	25.4187i	0.106409	+	1.61409i
$249$		0			0
$250$	−0.561892	+	0.841161i	−0.0355372	+	0.0531997i
$251$	8.74661	+	8.74661i	0.552081	+	0.552081i	0.927041	−	0.374960i	$-0.122343\pi$
$251$	8.74661	+	8.74661i	0.552081	+	0.552081i	−0.374960	+	0.927041i	$0.622343\pi$
$252$		0			0
$253$	13.7908	−	13.7908i	0.867017	−	0.867017i
$254$	−14.1426	+	2.81501i	−0.887388	+	0.176629i
$255$		0			0
$256$	−0.0162117	−	16.0000i	−0.00101323	−	0.999999i
$257$	−2.21071	+	3.82905i	−0.137900	+	0.238850i	−0.926702	−	0.375798i	$-0.877369\pi$
$257$	−2.21071	+	3.82905i	−0.137900	+	0.238850i	0.788802	+	0.614648i	$0.210702\pi$
$258$		0			0
$259$	8.35739	+	2.23936i	0.519303	+	0.139147i
$260$	0.0456852	+	0.0350371i	0.00283327	+	0.00217291i
$261$		0			0
$262$	4.40141	+	8.92234i	0.271920	+	0.551224i
$263$	9.48601	−	5.47675i	0.584932	−	0.337711i	−0.178159	−	0.984002i	$-0.557014\pi$
$263$	9.48601	−	5.47675i	0.584932	−	0.337711i	0.763091	+	0.646291i	$0.223681\pi$
$264$		0			0
$265$	−0.346584	−	0.200100i	−0.0212905	−	0.0122921i
$266$	0.725133	−	11.0849i	0.0444607	−	0.679659i
$267$		0			0
$268$	−8.16465	−	10.6348i	−0.498736	−	0.649624i
$269$	10.6376	−	10.6376i	0.648586	−	0.648586i	−0.304065	−	0.952651i	$-0.598344\pi$
$269$	10.6376	−	10.6376i	0.648586	−	0.648586i	0.952651	+	0.304065i	$0.0983441\pi$
$270$		0			0
$271$	19.1209			1.16151			0.580757	−	0.814077i	$-0.302757\pi$
$271$	19.1209			1.16151			0.580757	+	0.814077i	$0.302757\pi$
$272$	2.40577	−	2.40821i	0.145871	−	0.146019i
$273$		0			0
$274$	−15.4276	+	13.5331i	−0.932014	+	0.817563i
$275$	−2.93235	−	10.9437i	−0.176827	−	0.659928i
$276$		0			0
$277$	2.70176	−	10.0831i	0.162333	−	0.605835i	−0.836032	−	0.548680i	$-0.815130\pi$
$277$	2.70176	−	10.0831i	0.162333	−	0.605835i	0.998365	−	0.0571550i	$-0.0182029\pi$
$278$	6.69082	−	3.30060i	0.401289	−	0.197957i
$279$		0			0
$280$	0.0583425	−	0.293891i	0.00348663	−	0.0175633i
$281$	−12.1779	+	7.03092i	−0.726473	+	0.419429i	−0.817130	−	0.576453i	$-0.804436\pi$
$281$	−12.1779	+	7.03092i	−0.726473	+	0.419429i	0.0906576	+	0.995882i	$0.471103\pi$
$282$		0			0
$283$	24.6641	−	6.60872i	1.46613	−	0.392848i	0.564526	−	0.825415i	$-0.309059\pi$
$283$	24.6641	−	6.60872i	1.46613	−	0.392848i	0.901601	+	0.432568i	$0.142392\pi$
$284$	0.277894	+	0.670415i	0.0164900	+	0.0397818i
$285$		0			0
$286$	−1.26550	+	0.251890i	−0.0748306	+	0.0148946i
$287$	3.50914			0.207138
$288$		0			0
$289$	−16.2758			−0.957400
$290$	0.490416	−	0.0976145i	0.0287982	−	0.00573212i
$291$		0			0
$292$	12.1572	+	29.3290i	0.711446	+	1.71635i
$293$	13.2569	−	3.55218i	0.774476	−	0.207520i	0.150128	−	0.988667i	$-0.452031\pi$
$293$	13.2569	−	3.55218i	0.774476	−	0.207520i	0.624348	+	0.781146i	$0.285365\pi$
$294$		0			0
$295$	−0.884250	+	0.510522i	−0.0514830	+	0.0297237i
$296$	16.2161	+	3.21919i	0.942544	+	0.187111i
$297$		0			0
$298$	25.3849	−	12.5224i	1.47051	−	0.725405i
$299$	0.895150	−	3.34075i	0.0517679	−	0.193200i
$300$		0			0
$301$	0.991111	+	3.69888i	0.0571267	+	0.213200i
$302$	13.6154	−	11.9434i	0.783478	−	0.687267i
$303$		0			0
$304$	−0.0107535	−	21.2262i	−0.000616757	−	1.21741i
$305$	−0.243709			−0.0139547
$306$		0			0
$307$	−14.1122	+	14.1122i	−0.805426	+	0.805426i	−0.983938	−	0.178512i	$-0.942872\pi$
$307$	−14.1122	+	14.1122i	−0.805426	+	0.805426i	0.178512	+	0.983938i	$0.442872\pi$
$308$	4.08927	+	5.32644i	0.233008	+	0.303502i
$309$		0			0
$310$	−0.0595013	+	0.909580i	−0.00337945	+	0.0516607i
$311$	11.2914	+	6.51907i	0.640274	+	0.369662i	0.784720	−	0.619850i	$-0.212807\pi$
$311$	11.2914	+	6.51907i	0.640274	+	0.369662i	−0.144446	+	0.989513i	$0.546140\pi$
$312$		0			0
$313$	−6.50512	+	3.75573i	−0.367691	+	0.212287i	−0.672449	−	0.740143i	$-0.734758\pi$
$313$	−6.50512	+	3.75573i	−0.367691	+	0.212287i	0.304758	+	0.952430i	$0.401424\pi$
$314$	4.78793	+	9.70586i	0.270199	+	0.547733i
$315$		0			0
$316$	−17.3092	−	13.2748i	−0.973718	−	0.746768i
$317$	−1.45660	−	0.390294i	−0.0818107	−	0.0219211i	0.217682	−	0.976020i	$-0.430151\pi$
$317$	−1.45660	−	0.390294i	−0.0818107	−	0.0219211i	−0.299492	+	0.954099i	$0.596817\pi$
$318$		0			0
$319$	−5.60335	+	9.70528i	−0.313727	+	0.543391i
$320$	0.0742980	−	0.567682i	0.00415338	−	0.0317344i
$321$		0			0
$322$	−17.6530	+	3.51372i	−0.983763	+	0.195812i
$323$	3.19321	−	3.19321i	0.177675	−	0.177675i
$324$		0			0
$325$	−1.42069	−	1.42069i	−0.0788059	−	0.0788059i
$326$	11.5524	−	17.2942i	0.639830	−	0.957836i
$327$		0			0
$328$	6.69072	−	0.441086i	0.369433	−	0.0243549i
$329$	−8.76847	−	5.06248i	−0.483422	−	0.279104i
$330$		0			0
$331$	−5.29948	+	19.7779i	−0.291286	+	1.08709i	0.652837	+	0.757499i	$0.273579\pi$
$331$	−5.29948	+	19.7779i	−0.291286	+	1.08709i	−0.944122	+	0.329595i	$0.893088\pi$
$332$	11.0255	−	1.45438i	0.605105	−	0.0798195i
$333$		0			0
$334$	8.41924	+	2.85676i	0.460680	+	0.156315i
$335$	−0.239878	−	0.415481i	−0.0131059	−	0.0227002i
$336$		0			0
$337$	4.81432	−	8.33864i	0.262253	−	0.454235i	−0.704588	−	0.709617i	$-0.748868\pi$
$337$	4.81432	−	8.33864i	0.262253	−	0.454235i	0.966840	+	0.255382i	$0.0822013\pi$
$338$	13.6489	−	11.9728i	0.742400	−	0.651233i
$339$		0			0
$340$	0.0966152	−	0.0741743i	0.00523969	−	0.00402267i
$341$	−14.4454	−	14.4454i	−0.782261	−	0.782261i
$342$		0			0
$343$			17.4800i			0.943829i
$344$	2.35464	+	6.92790i	0.126954	+	0.373527i
$345$		0			0
$346$	16.5936	+	1.08549i	0.892076	+	0.0583563i
$347$	−8.72145	+	2.33691i	−0.468192	+	0.125452i	−0.485199	−	0.874404i	$-0.661253\pi$
$347$	−8.72145	+	2.33691i	−0.468192	+	0.125452i	0.0170070	+	0.999855i	$0.494586\pi$
$348$		0			0
$349$	−26.4971	−	7.09989i	−1.41836	−	0.380048i	−0.533458	−	0.845826i	$-0.679108\pi$
$349$	−26.4971	−	7.09989i	−1.41836	−	0.380048i	−0.884902	+	0.465778i	$0.845775\pi$
$350$	−3.35976	+	9.90165i	−0.179587	+	0.529266i
$351$		0			0
$352$	8.46634	+	9.64168i	0.451257	+	0.513903i
$353$	2.21080	+	3.82922i	0.117669	+	0.203809i	0.918844	−	0.394622i	$-0.129124\pi$
$353$	2.21080	+	3.82922i	0.117669	+	0.203809i	−0.801174	+	0.598431i	$0.795791\pi$
$354$		0			0
$355$	0.00672115	+	0.0250837i	0.000356722	+	0.00133130i
$356$	10.0961	+	24.3568i	0.535094	+	1.29091i
$357$		0			0
$358$	10.2406	−	15.3303i	0.541231	−	0.810231i
$359$			21.7288i			1.14680i	0.819275	+	0.573400i	$0.194376\pi$
$359$			21.7288i			1.14680i	−0.819275	+	0.573400i	$0.805624\pi$
$360$		0			0
$361$		−	9.15954i		−	0.482081i
$362$	−19.2783	−	12.8778i	−1.01325	−	0.676843i
$363$		0			0
$364$	1.10030	+	0.455434i	0.0576716	+	0.0238712i
$365$	0.294034	+	1.09735i	0.0153905	+	0.0574380i
$366$		0			0
$367$	1.28705	+	2.22924i	0.0671835	+	0.116365i	0.897660	−	0.440688i	$-0.145265\pi$
$367$	1.28705	+	2.22924i	0.0671835	+	0.116365i	−0.830477	+	0.557053i	$0.811932\pi$
$368$	−33.2165	+	8.91837i	−1.73153	+	0.464902i
$369$		0			0
$370$	0.560210	+	0.190087i	0.0291239	+	0.00988213i
$371$	−7.99556	−	2.14241i	−0.415109	−	0.111228i
$372$		0			0
$373$	1.42780	−	0.382578i	0.0739287	−	0.0198091i	−0.221665	−	0.975123i	$-0.571149\pi$
$373$	1.42780	−	0.382578i	0.0739287	−	0.0198091i	0.295594	+	0.955314i	$0.404483\pi$
$374$	−0.178196	+	2.72403i	−0.00921428	+	0.140856i
$375$		0			0
$376$	−17.3548	−	8.55024i	−0.895005	−	0.440945i
$377$			1.98735i			0.102354i
$378$		0			0
$379$	4.66662	+	4.66662i	0.239708	+	0.239708i	0.816729	−	0.577021i	$-0.195785\pi$
$379$	4.66662	+	4.66662i	0.239708	+	0.239708i	−0.577021	+	0.816729i	$0.695785\pi$
$380$	0.0989481	−	0.753060i	0.00507593	−	0.0386311i
$381$		0			0
$382$	−20.8647	−	23.7856i	−1.06753	−	1.21698i
$383$	1.48376	−	2.56995i	0.0758165	−	0.131318i	−0.825625	−	0.564220i	$-0.809177\pi$
$383$	1.48376	−	2.56995i	0.0758165	−	0.131318i	0.901441	+	0.432902i	$0.142510\pi$
$384$		0			0
$385$	0.120143	+	0.208094i	0.00612305	+	0.0106054i
$386$	6.52458	−	19.2288i	0.332092	−	0.978720i
$387$		0			0
$388$	−1.99200	−	1.52771i	−0.101128	−	0.0775579i
$389$	−7.85632	+	29.3202i	−0.398331	+	1.48659i	0.417700	+	0.908585i	$0.362836\pi$
$389$	−7.85632	+	29.3202i	−0.398331	+	1.48659i	−0.816031	+	0.578008i	$0.803830\pi$
$390$		0			0
$391$	−6.33679	−	3.65855i	−0.320465	−	0.185021i
$392$	0.894746	+	13.5722i	0.0451915	+	0.685498i
$393$		0			0
$394$	−2.61997	−	1.75013i	−0.131992	−	0.0881703i
$395$	−0.551930	−	0.551930i	−0.0277706	−	0.0277706i
$396$		0			0
$397$	11.6823	−	11.6823i	0.586319	−	0.586319i	−0.350314	−	0.936632i	$-0.613925\pi$
$397$	11.6823	−	11.6823i	0.586319	−	0.586319i	0.936632	+	0.350314i	$0.113925\pi$
$398$	0.476933	+	2.39612i	0.0239065	+	0.120107i
$399$		0			0
$400$	−5.16130	+	19.3013i	−0.258065	+	0.965067i
$401$	−0.390756	+	0.676809i	−0.0195134	+	0.0337982i	−0.875617	−	0.483006i	$-0.839545\pi$
$401$	−0.390756	+	0.676809i	−0.0195134	+	0.0337982i	0.856104	+	0.516804i	$0.172878\pi$
$402$		0			0
$403$	−3.49932	−	0.937641i	−0.174314	−	0.0467072i
$404$	−1.44559	−	10.9589i	−0.0719207	−	0.545225i
$405$		0			0
$406$	9.27541	−	4.57559i	0.460331	−	0.227083i
$407$	−11.4821	+	6.62918i	−0.569145	+	0.328596i
$408$		0			0
$409$	−26.9864	−	15.5806i	−1.33439	−	0.770412i	−0.348423	−	0.937338i	$-0.613283\pi$
$409$	−26.9864	−	15.5806i	−1.33439	−	0.770412i	−0.985969	+	0.166926i	$0.946616\pi$
$410$	0.239420	+	0.0156620i	0.0118241	+	0.000773490i
$411$		0			0
$412$	−21.9798	−	2.88803i	−1.08287	−	0.142283i
$413$	−14.9333	+	14.9333i	−0.734822	+	0.734822i
$414$		0			0
$415$	0.397941			0.0195342
$416$	2.15515	+	0.730052i	0.105665	+	0.0357937i
$417$		0			0
$418$	11.2253	+	12.7967i	0.549047	+	0.625908i
$419$	5.93759	+	22.1594i	0.290070	+	1.08256i	0.945054	+	0.326914i	$0.106009\pi$
$419$	5.93759	+	22.1594i	0.290070	+	1.08256i	−0.654984	+	0.755643i	$0.727325\pi$
$420$		0			0
$421$	−6.71096	+	25.0456i	−0.327072	+	1.22065i	0.585140	+	0.810932i	$0.301039\pi$
$421$	−6.71096	+	25.0456i	−0.327072	+	1.22065i	−0.912212	+	0.409718i	$0.865627\pi$
$422$	7.73405	+	15.6781i	0.376488	+	0.763198i
$423$		0			0
$424$	−15.5141	−	3.07981i	−0.753430	−	0.149569i
$425$	−3.68116	+	2.12532i	−0.178563	+	0.103093i
$426$		0			0
$427$	−4.86903	+	1.30465i	−0.235629	+	0.0631366i
$428$	18.0400	+	7.46706i	0.871996	+	0.360934i
$429$		0			0
$430$	0.0511123	+	0.256789i	0.00246485	+	0.0123835i
$431$	−8.53959			−0.411338			−0.205669	−	0.978622i	$-0.565937\pi$
$431$	−8.53959			−0.411338			−0.205669	+	0.978622i	$0.565937\pi$
$432$		0			0
$433$	−9.28283			−0.446104			−0.223052	−	0.974807i	$-0.571602\pi$
$433$	−9.28283			−0.446104			−0.223052	+	0.974807i	$0.571602\pi$
$434$	3.68051	+	18.4909i	0.176670	+	0.887593i
$435$		0			0
$436$	10.1593	−	24.5442i	0.486541	−	1.17546i
$437$	−44.0723	+	11.8091i	−2.10826	+	0.564908i
$438$		0			0
$439$	−12.0947	+	6.98286i	−0.577247	+	0.333274i	−0.760038	−	0.649878i	$-0.774820\pi$
$439$	−12.0947	+	6.98286i	−0.577247	+	0.333274i	0.182792	+	0.983152i	$0.441487\pi$
$440$	0.255228	+	0.381662i	0.0121675	+	0.0181950i
$441$		0			0
$442$	0.214167	+	0.434149i	0.0101869	+	0.0206504i
$443$	3.19925	−	11.9398i	0.152001	−	0.567276i	−0.847343	−	0.531047i	$-0.821799\pi$
$443$	3.19925	−	11.9398i	0.152001	−	0.567276i	0.999344	−	0.0362287i	$-0.0115345\pi$
$444$		0			0
$445$	0.244185	+	0.911312i	0.0115755	+	0.0432004i
$446$	−13.4681	−	15.3535i	−0.637734	−	0.727010i
$447$		0			0
$448$	−1.55460	−	11.7394i	−0.0734479	−	0.554635i
$449$	−15.5226			−0.732554			−0.366277	−	0.930506i	$-0.619368\pi$
$449$	−15.5226			−0.732554			−0.366277	+	0.930506i	$0.619368\pi$
$450$		0			0
$451$	−3.80232	+	3.80232i	−0.179044	+	0.179044i
$452$	3.02846	−	23.0485i	0.142447	−	1.08411i
$453$		0			0
$454$	2.36061	+	0.154422i	0.110789	+	0.00724739i
$455$	0.0369025	+	0.0213057i	0.00173002	+	0.000998825i
$456$		0			0
$457$	23.3712	−	13.4934i	1.09326	−	0.631194i	0.158817	−	0.987308i	$-0.449232\pi$
$457$	23.3712	−	13.4934i	1.09326	−	0.631194i	0.934442	+	0.356114i	$0.115899\pi$
$458$	−25.7626	+	12.7088i	−1.20381	+	0.593842i
$459$		0			0
$460$	−1.22010	+	0.160944i	−0.0568876	+	0.00750406i
$461$	−22.8014	−	6.10962i	−1.06197	−	0.284554i	−0.314779	−	0.949165i	$-0.601930\pi$
$461$	−22.8014	−	6.10962i	−1.06197	−	0.284554i	−0.747189	+	0.664611i	$0.768597\pi$
$462$		0			0
$463$	11.7055	−	20.2745i	0.544001	−	0.942238i	−0.454668	−	0.890661i	$-0.650242\pi$
$463$	11.7055	−	20.2745i	0.544001	−	0.942238i	0.998669	−	0.0515769i	$-0.0164247\pi$
$464$	17.1099	−	9.88996i	0.794306	−	0.459130i
$465$		0			0
$466$	−6.51024	−	32.7075i	−0.301581	−	1.51515i
$467$	−17.4581	+	17.4581i	−0.807865	+	0.807865i	−0.984310	−	0.176446i	$-0.943540\pi$
$467$	−17.4581	+	17.4581i	−0.807865	+	0.807865i	0.176446	+	0.984310i	$0.443540\pi$
$468$		0			0
$469$	−7.01671	−	7.01671i	−0.324001	−	0.324001i
$470$	−0.575657	−	0.384536i	−0.0265531	−	0.0177373i
$471$		0			0
$472$	−26.5957	+	30.3498i	−1.22416	+	1.39696i
$473$	−5.08182	−	2.93399i	−0.233662	−	0.134905i
$474$		0			0
$475$	−6.86016	+	25.6024i	−0.314766	+	1.17472i
$476$	1.53318	−	1.99913i	0.0702734	−	0.0916301i
$477$		0			0
$478$	−3.89343	+	11.4744i	−0.178081	+	0.524828i
$479$	9.62715	+	16.6747i	0.439876	+	0.761887i	0.997679	−	0.0680859i	$-0.0216892\pi$
$479$	9.62715	+	16.6747i	0.439876	+	0.761887i	−0.557804	+	0.829973i	$0.688356\pi$
$480$		0			0
$481$	−1.17559	+	2.03618i	−0.0536023	+	0.0928420i
$482$	6.88276	+	7.84628i	0.313501	+	0.357388i
$483$		0			0
$484$	11.6101	+	1.52551i	0.527734	+	0.0693415i
$485$	−0.0635180	−	0.0635180i	−0.00288420	−	0.00288420i
$486$		0			0
$487$			15.8010i			0.716012i	0.933719	+	0.358006i	$0.116543\pi$
$487$			15.8010i			0.716012i	−0.933719	+	0.358006i	$0.883457\pi$
$488$	−9.11958	+	3.09954i	−0.412824	+	0.140310i
$489$		0			0
$490$	−0.0317704	+	0.485665i	−0.00143524	+	0.0219401i
$491$	10.9388	−	2.93103i	0.493659	−	0.132276i	−0.00339642	−	0.999994i	$-0.501081\pi$
$491$	10.9388	−	2.93103i	0.493659	−	0.132276i	0.497056	+	0.867719i	$0.334414\pi$
$492$		0			0
$493$	4.06122	+	1.08820i	0.182908	+	0.0490101i
$494$	2.85861	+	0.969964i	0.128615	+	0.0436407i
$495$		0			0
$496$	9.34171	+	34.7932i	0.419455	+	1.56226i
$497$	0.268562	+	0.465164i	0.0120467	+	0.0208654i
$498$		0			0
$499$	−1.04051	−	3.88323i	−0.0465796	−	0.173837i	0.938717	−	0.344688i	$-0.112015\pi$
$499$	−1.04051	−	3.88323i	−0.0465796	−	0.173837i	−0.985297	+	0.170850i	$0.945349\pi$
$500$	−0.547123	+	1.32182i	−0.0244681	+	0.0591135i
$501$		0			0
$502$	14.5463	+	9.71687i	0.649234	+	0.433685i
$503$		−	24.1846i		−	1.07834i	−0.842198	−	0.539169i	$-0.818739\pi$
$503$		−	24.1846i		−	1.07834i	0.842198	−	0.539169i	$-0.181261\pi$
$504$		0			0
$505$		−	0.395536i		−	0.0176011i
$506$	15.3206	−	22.9351i	0.681082	−	1.01959i
$507$		0			0
$508$	−18.8388	+	7.80886i	−0.835835	+	0.346462i
$509$	−3.36446	−	12.5563i	−0.149127	−	0.556550i	−0.999537	−	0.0304290i	$-0.990313\pi$
$509$	−3.36446	−	12.5563i	−0.149127	−	0.556550i	0.850410	−	0.526121i	$-0.176354\pi$
$510$		0			0
$511$	11.7490	+	20.3498i	0.519743	+	0.900222i
$512$	−4.43968	−	22.1876i	−0.196208	−	0.980562i
$513$		0			0
$514$	−2.00915	+	5.92124i	−0.0886199	+	0.261175i
$515$	−0.766227	−	0.205310i	−0.0337640	−	0.00904703i
$516$		0			0
$517$	14.9865	−	4.01562i	0.659105	−	0.176607i
$518$	12.2100	+	0.798731i	0.536475	+	0.0350942i
$519$		0			0
$520$	0.0730384	+	0.0359841i	0.00320295	+	0.00157801i
$521$		−	3.39592i		−	0.148778i	−0.997229	−	0.0743889i	$-0.976299\pi$
$521$		−	3.39592i		−	0.148778i	0.997229	−	0.0743889i	$-0.0237006\pi$
$522$		0			0
$523$	−21.4956	−	21.4956i	−0.939938	−	0.939938i	0.0583574	−	0.998296i	$-0.481414\pi$
$523$	−21.4956	−	21.4956i	−0.939938	−	0.939938i	−0.998296	+	0.0583574i	$0.981414\pi$
$524$	8.56802	+	11.1602i	0.374296	+	0.487536i
$525$		0			0
$526$	11.6451	−	10.2151i	0.507753	−	0.445401i
$527$	−3.83221	+	6.63758i	−0.166934	+	0.289138i
$528$		0			0
$529$	25.4648	+	44.1063i	1.10716	+	1.91767i
$530$	−0.535956	−	0.181857i	−0.0232805	−	0.00789936i
$531$		0			0
$532$	−2.05450	−	15.5750i	−0.0890739	−	0.675262i
$533$	−0.246806	+	0.921094i	−0.0106904	+	0.0398970i
$534$		0			0
$535$	0.605034	+	0.349316i	0.0261579	+	0.0151023i
$536$	−14.2604	−	12.4965i	−0.615956	−	0.539765i
$537$		0			0
$538$	11.8176	−	17.6912i	0.509494	−	0.762721i
$539$	−7.71302	−	7.71302i	−0.332223	−	0.332223i
$540$		0			0
$541$	−14.7438	+	14.7438i	−0.633886	+	0.633886i	−0.949041	−	0.315154i	$-0.897944\pi$
$541$	−14.7438	+	14.7438i	−0.633886	+	0.633886i	0.315154	+	0.949041i	$0.397944\pi$
$542$	26.5208	−	5.27881i	1.13917	−	0.226744i
$543$		0			0
$544$	2.67197	−	4.00437i	0.114560	−	0.171686i
$545$	0.475261	−	0.823176i	0.0203579	−	0.0352610i
$546$		0			0
$547$	−30.6555	−	8.21413i	−1.31074	−	0.351211i	−0.465236	−	0.885186i	$-0.654031\pi$
$547$	−30.6555	−	8.21413i	−1.31074	−	0.351211i	−0.845500	+	0.533976i	$0.820697\pi$
$548$	−17.6620	+	23.0296i	−0.754482	+	0.983776i
$549$		0			0
$550$	−7.08845	−	14.3694i	−0.302252	−	0.612712i
$551$	22.7053	−	13.1089i	0.967278	−	0.558458i
$552$		0			0
$553$	−13.9816	−	8.07229i	−0.594559	−	0.343269i
$554$	0.963661	−	14.7312i	0.0409420	−	0.625869i
$555$		0			0
$556$	8.36898	−	6.42512i	0.354924	−	0.272486i
$557$	16.6150	−	16.6150i	0.704002	−	0.704002i	−0.261265	−	0.965267i	$-0.584140\pi$
$557$	16.6150	−	16.6150i	0.704002	−	0.704002i	0.965267	+	0.261265i	$0.0841398\pi$
$558$		0			0
$559$	−1.04060			−0.0440129
$560$	−0.000214671	−	0.423735i	−9.07149e−6	−	0.0179061i
$561$		0			0
$562$	−14.9497	+	13.1139i	−0.630617	+	0.553178i
$563$	0.625738	+	2.33528i	0.0263717	+	0.0984205i	0.977857	−	0.209273i	$-0.0671096\pi$
$563$	0.625738	+	2.33528i	0.0263717	+	0.0984205i	−0.951486	+	0.307693i	$0.900443\pi$
$564$		0			0
$565$	0.215293	−	0.803484i	0.00905745	−	0.0338028i
$566$	32.3847	−	15.9755i	1.36123	−	0.671499i
$567$		0			0
$568$	0.570525	+	0.853149i	0.0239387	+	0.0357974i
$569$	8.83926	−	5.10335i	0.370561	−	0.213943i	−0.303143	−	0.952945i	$-0.598036\pi$
$569$	8.83926	−	5.10335i	0.370561	−	0.213943i	0.673703	+	0.739002i	$0.264703\pi$
$570$		0			0
$571$	20.9394	−	5.61069i	0.876285	−	0.234800i	0.207481	−	0.978239i	$-0.433473\pi$
$571$	20.9394	−	5.61069i	0.876285	−	0.234800i	0.668804	+	0.743439i	$0.266807\pi$
$572$	−1.68572	+	0.698746i	−0.0704833	+	0.0292161i
$573$		0			0
$574$	4.86719	−	0.968786i	0.203153	−	0.0404363i
$575$	42.9471			1.79102
$576$		0			0
$577$	−17.0725			−0.710737			−0.355369	−	0.934726i	$-0.615645\pi$
$577$	−17.0725			−0.710737			−0.355369	+	0.934726i	$0.615645\pi$
$578$	−22.5746	+	4.49334i	−0.938980	+	0.186898i
$579$		0			0
$580$	0.653261	−	0.270783i	0.0271252	−	0.0112437i
$581$	7.95043	−	2.13031i	0.329839	−	0.0883802i
$582$		0			0
$583$	10.9850	−	6.34217i	0.454951	−	0.262666i
$584$	24.9591	+	37.3232i	1.03282	+	1.54445i
$585$		0			0
$586$	17.4067	−	8.58678i	0.719065	−	0.354717i
$587$	3.63287	−	13.5581i	0.149945	−	0.559602i	−0.849541	−	0.527523i	$-0.823121\pi$
$587$	3.63287	−	13.5581i	0.149945	−	0.559602i	0.999485	−	0.0320783i	$-0.0102126\pi$
$588$		0			0
$589$	12.3697	+	46.1643i	0.509684	+	1.90217i
$590$	−1.08552	+	0.952216i	−0.0446900	+	0.0392021i
$591$		0			0
$592$	23.3806	−	0.0118450i	0.960937	−	0.000486825i
$593$	27.5850			1.13278			0.566390	−	0.824137i	$-0.308340\pi$
$593$	27.5850			1.13278			0.566390	+	0.824137i	$0.308340\pi$
$594$		0			0
$595$	0.0637455	−	0.0637455i	0.00261331	−	0.00261331i
$596$	31.7518	−	24.3768i	1.30061	−	0.998513i
$597$		0			0
$598$	0.319281	−	4.88076i	0.0130564	−	0.199589i
$599$	−34.8788	−	20.1373i	−1.42511	−	0.822788i	−0.428380	−	0.903598i	$-0.640916\pi$
$599$	−34.8788	−	20.1373i	−1.42511	−	0.822788i	−0.996729	+	0.0808109i	$0.974249\pi$
$600$		0			0
$601$	5.90297	−	3.40808i	0.240787	−	0.139018i	−0.374751	−	0.927125i	$-0.622272\pi$
$601$	5.90297	−	3.40808i	0.240787	−	0.139018i	0.615538	+	0.788107i	$0.288939\pi$
$602$	2.39584	+	4.85674i	0.0976473	+	0.197946i
$603$		0			0
$604$	15.5873	−	20.3245i	0.634240	−	0.826991i
$605$	0.404736	+	0.108449i	0.0164549	+	0.00440907i
$606$		0			0
$607$	−1.09235	+	1.89200i	−0.0443370	+	0.0767939i	−0.887342	−	0.461111i	$-0.847451\pi$
$607$	−1.09235	+	1.89200i	−0.0443370	+	0.0767939i	0.843005	+	0.537905i	$0.180784\pi$
$608$	−5.87495	−	29.4379i	−0.238261	−	1.19386i
$609$		0			0
$610$	−0.338025	+	0.0672819i	−0.0136862	+	0.00272417i
$611$	1.94553	−	1.94553i	0.0787077	−	0.0787077i
$612$		0			0
$613$	15.3068	+	15.3068i	0.618236	+	0.618236i	0.945079	−	0.326843i	$-0.105985\pi$
$613$	15.3068	+	15.3068i	0.618236	+	0.618236i	−0.326843	+	0.945079i	$0.605985\pi$
$614$	−15.6777	+	23.4697i	−0.632699	+	0.947161i
$615$		0			0
$616$	7.14233	+	6.25886i	0.287773	+	0.252177i
$617$	10.1056	+	5.83447i	0.406836	+	0.234887i	0.689429	−	0.724353i	$-0.257861\pi$
$617$	10.1056	+	5.83447i	0.406836	+	0.234887i	−0.282593	+	0.959240i	$0.591195\pi$
$618$		0			0
$619$	−1.13744	+	4.24500i	−0.0457178	+	0.170621i	−0.985010	−	0.172497i	$-0.944816\pi$
$619$	−1.13744	+	4.24500i	−0.0457178	+	0.170621i	0.939292	+	0.343118i	$0.111483\pi$
$620$	0.168584	+	1.27802i	0.00677049	+	0.0513265i
$621$		0			0
$622$	17.4609	+	5.92472i	0.700119	+	0.237560i
$623$	9.75711	+	16.8998i	0.390910	+	0.677076i
$624$		0			0
$625$	12.4616	−	21.5841i	0.498464	−	0.863365i
$626$	−7.98577	+	7.00512i	−0.319175	+	0.279981i
$627$		0			0
$628$	9.32043	+	12.1402i	0.371926	+	0.484449i
$629$	3.51731	+	3.51731i	0.140244	+	0.140244i
$630$		0			0
$631$			31.5374i			1.25548i	0.778422	+	0.627742i	$0.216021\pi$
$631$			31.5374i			1.25548i	−0.778422	+	0.627742i	$0.783979\pi$
$632$	−27.6728	−	13.6336i	−1.10076	−	0.542317i
$633$		0			0
$634$	−2.12806	−	0.139210i	−0.0845160	−	0.00552872i
$635$	−0.704855	+	0.188865i	−0.0279713	+	0.00749489i
$636$		0			0
$637$	−1.86844	−	0.500648i	−0.0740304	−	0.0198364i
$638$	−5.09248	+	15.0082i	−0.201613	+	0.594181i
$639$		0			0
$640$	−0.0536713	−	0.807890i	−0.00212154	−	0.0319347i
$641$	−9.38996	−	16.2639i	−0.370881	−	0.642385i	0.618820	−	0.785533i	$-0.287611\pi$
$641$	−9.38996	−	16.2639i	−0.370881	−	0.642385i	−0.989701	+	0.143148i	$0.954278\pi$
$642$		0			0
$643$	−6.94427	−	25.9164i	−0.273855	−	1.02204i	−0.956605	−	0.291389i	$-0.905883\pi$
$643$	−6.94427	−	25.9164i	−0.273855	−	1.02204i	0.682749	−	0.730653i	$-0.260784\pi$
$644$	−23.5147	+	9.74710i	−0.926610	+	0.384090i
$645$		0			0
$646$	3.54743	−	5.31056i	0.139572	−	0.208941i
$647$			16.5176i			0.649373i	0.945822	+	0.324686i	$0.105259\pi$
$647$			16.5176i			0.649373i	−0.945822	+	0.324686i	$0.894741\pi$
$648$		0			0
$649$		−	32.3620i		−	1.27032i
$650$	−2.36273	−	1.57829i	−0.0926738	−	0.0619057i
$651$		0			0
$652$	11.2488	−	27.1765i	0.440537	−	1.06431i
$653$	−10.8252	−	40.4003i	−0.423624	−	1.58099i	−0.766909	−	0.641756i	$-0.778206\pi$
$653$	−10.8252	−	40.4003i	−0.423624	−	1.58099i	0.343285	−	0.939231i	$-0.388460\pi$
$654$		0			0
$655$	0.251729	+	0.436008i	0.00983587	+	0.0170362i
$656$	9.15829	−	2.45893i	0.357571	−	0.0960050i
$657$		0			0
$658$	−13.5595	−	4.60093i	−0.528606	−	0.179363i
$659$	11.3797	+	3.04918i	0.443290	+	0.118779i	0.473558	−	0.880763i	$-0.342969\pi$
$659$	11.3797	+	3.04918i	0.443290	+	0.118779i	−0.0302682	+	0.999542i	$0.509636\pi$
$660$		0			0
$661$	39.1808	−	10.4985i	1.52396	−	0.408343i	0.602913	−	0.797807i	$-0.294006\pi$
$661$	39.1808	−	10.4985i	1.52396	−	0.408343i	0.921042	+	0.389464i	$0.127340\pi$
$662$	−1.89021	+	28.8951i	−0.0734652	+	1.12304i
$663$		0			0
$664$	14.8909	−	5.06111i	0.577881	−	0.196409i
$665$		−	0.562144i		−	0.0217990i
$666$		0			0
$667$	−30.0385	−	30.0385i	−1.16309	−	1.16309i
$668$	12.4662	+	1.63800i	0.482332	+	0.0633759i
$669$		0			0
$670$	−0.447416	−	0.510050i	−0.0172852	−	0.0197050i
$671$	3.86217	−	6.68948i	0.149098	−	0.258245i
$672$		0			0
$673$	−6.73175	−	11.6597i	−0.259490	−	0.449450i	0.706615	−	0.707598i	$-0.250221\pi$
$673$	−6.73175	−	11.6597i	−0.259490	−	0.449450i	−0.966105	+	0.258148i	$0.916888\pi$
$674$	4.37539	−	12.8949i	0.168534	−	0.496691i
$675$		0			0
$676$	15.6256	−	20.3744i	0.600986	−	0.783631i
$677$	−2.56756	+	9.58227i	−0.0986794	+	0.368277i	−0.997552	−	0.0699343i	$-0.977721\pi$
$677$	−2.56756	+	9.58227i	−0.0986794	+	0.368277i	0.898872	+	0.438211i	$0.144388\pi$
$678$		0			0
$679$	−1.60905	−	0.928986i	−0.0617497	−	0.0356512i
$680$	0.113528	−	0.129553i	0.00435360	−	0.00496814i
$681$		0			0
$682$	−24.0238	−	16.0478i	−0.919919	−	0.614502i
$683$	−4.48800	−	4.48800i	−0.171728	−	0.171728i	0.616010	−	0.787738i	$-0.288748\pi$
$683$	−4.48800	−	4.48800i	−0.171728	−	0.171728i	−0.787738	+	0.616010i	$0.788748\pi$
$684$		0			0
$685$	−0.734335	+	0.734335i	−0.0280575	+	0.0280575i
$686$	4.82578	+	24.2448i	0.184249	+	0.925671i
$687$		0			0
$688$	5.17852	+	8.95898i	0.197429	+	0.341558i
$689$	1.12470	−	1.94803i	0.0428475	−	0.0742140i
$690$		0			0
$691$	35.9149	+	9.62336i	1.36627	+	0.366090i	0.866114	−	0.499847i	$-0.166610\pi$
$691$	35.9149	+	9.62336i	1.36627	+	0.366090i	0.500153	+	0.865937i	$0.333277\pi$
$692$	23.3150	−	3.07549i	0.886305	−	0.116913i
$693$		0			0
$694$	−11.4515	+	5.64908i	−0.434694	+	0.214436i
$695$	0.326960	−	0.188770i	0.0124023	−	0.00716047i
$696$		0			0
$697$	1.74715	+	1.00872i	0.0661780	+	0.0382079i
$698$	−38.7118	−	2.53238i	−1.46526	−	0.0958520i
$699$		0			0
$700$	−1.92640	+	14.6612i	−0.0728112	+	0.554141i
$701$	−36.9558	+	36.9558i	−1.39580	+	1.39580i	−0.584175	+	0.811628i	$0.698582\pi$
$701$	−36.9558	+	36.9558i	−1.39580	+	1.39580i	−0.811628	+	0.584175i	$0.801418\pi$
$702$		0			0
$703$	31.0176			1.16985
$704$	14.4047	+	11.0357i	0.542897	+	0.415924i
$705$		0			0
$706$	4.12354	+	4.70080i	0.155192	+	0.176917i
$707$	−2.11743	−	7.90237i	−0.0796343	−	0.297199i
$708$		0			0
$709$	−1.53529	+	5.72979i	−0.0576591	+	0.215187i	−0.988744	−	0.149615i	$-0.952197\pi$
$709$	−1.53529	+	5.72979i	−0.0576591	+	0.215187i	0.931085	+	0.364802i	$0.118863\pi$
$710$	0.0162472	+	0.0329356i	0.000609748	+	0.00123605i
$711$		0			0
$712$	20.7277	+	30.9957i	0.776803	+	1.16161i
$713$	67.0640	−	38.7194i	2.51157	−	1.45005i
$714$		0			0
$715$	−0.0630713	+	0.0168999i	−0.00235873	+	0.000632021i
$716$	9.97140	−	24.0903i	0.372649	−	0.900299i
$717$		0			0
$718$	5.99877	+	30.1379i	0.223872	+	1.12474i
$719$	−9.58462			−0.357446			−0.178723	−	0.983899i	$-0.557197\pi$
$719$	−9.58462			−0.357446			−0.178723	+	0.983899i	$0.557197\pi$
$720$		0			0
$721$	−16.4075			−0.611046
$722$	−2.52872	−	12.7043i	−0.0941093	−	0.472806i
$723$		0			0
$724$	−30.2943	−	12.5393i	−1.12588	−	0.466021i
$725$	−23.8370	+	6.38711i	−0.885285	+	0.237211i
$726$		0			0
$727$	34.4374	−	19.8824i	1.27721	−	0.737399i	0.300877	−	0.953663i	$-0.402721\pi$
$727$	34.4374	−	19.8824i	1.27721	−	0.737399i	0.976335	+	0.216264i	$0.0693872\pi$
$728$	1.65186	+	0.327923i	0.0612220	+	0.0121536i
$729$		0			0
$730$	0.710778	+	1.44086i	0.0263071	+	0.0533284i
$731$	−0.569798	+	2.12651i	−0.0210747	+	0.0786520i
$732$		0			0
$733$	−9.37557	−	34.9901i	−0.346295	−	1.29239i	−0.891092	−	0.453822i	$-0.850060\pi$
$733$	−9.37557	−	34.9901i	−0.346295	−	1.29239i	0.544798	−	0.838567i	$-0.316606\pi$
$734$	2.40058	+	2.73664i	0.0886071	+	0.101011i
$735$		0			0
$736$	−43.6093	+	21.5401i	−1.60746	+	0.793978i
$737$	15.2059			0.560115
$738$		0			0
$739$	−7.78860	+	7.78860i	−0.286508	+	0.286508i	−0.835698	−	0.549190i	$-0.814936\pi$
$739$	−7.78860	+	7.78860i	−0.286508	+	0.286508i	0.549190	+	0.835698i	$0.314936\pi$
$740$	0.829492	+	0.108991i	0.0304927	+	0.00400659i
$741$		0			0
$742$	−11.6814	−	0.764150i	−0.428836	−	0.0280528i
$743$	3.75539	+	2.16817i	0.137772	+	0.0795426i	0.567302	−	0.823510i	$-0.307987\pi$
$743$	3.75539	+	2.16817i	0.137772	+	0.0795426i	−0.429530	+	0.903053i	$0.641321\pi$
$744$		0			0
$745$	1.24048	−	0.716193i	0.0454477	−	0.0262393i
$746$	1.87475	−	0.924818i	0.0686393	−	0.0338600i
$747$		0			0
$748$	0.504878	+	3.82743i	0.0184602	+	0.139945i
$749$	13.9579	+	3.74001i	0.510011	+	0.136657i
$750$		0			0
$751$	−6.74026	+	11.6745i	−0.245956	+	0.426008i	−0.962400	−	0.271637i	$-0.912435\pi$
$751$	−6.74026	+	11.6745i	−0.245956	+	0.426008i	0.716444	+	0.697644i	$0.245768\pi$
$752$	−26.4317	−	7.06800i	−0.963865	−	0.257743i
$753$		0			0
$754$	0.548657	+	2.75646i	0.0199809	+	0.100384i
$755$	0.648077	−	0.648077i	0.0235859	−	0.0235859i
$756$		0			0
$757$	25.9901	+	25.9901i	0.944625	+	0.944625i	0.998545	−	0.0539205i	$-0.0171718\pi$
$757$	25.9901	+	25.9901i	0.944625	+	0.944625i	−0.0539205	+	0.998545i	$0.517172\pi$
$758$	7.76096	+	5.18428i	0.281891	+	0.188302i
$759$		0			0
$760$	−0.0706594	−	1.07181i	−0.00256309	−	0.0388788i
$761$	29.3955	+	16.9715i	1.06558	+	0.615216i	0.926972	−	0.375131i	$-0.122402\pi$
$761$	29.3955	+	16.9715i	1.06558	+	0.615216i	0.138613	+	0.990347i	$0.455736\pi$
$762$		0			0
$763$	5.08845	−	18.9904i	0.184214	−	0.687498i
$764$	−35.5061	−	27.2305i	−1.28457	−	0.985165i
$765$		0			0
$766$	1.34848	−	3.97416i	0.0487227	−	0.143592i
$767$	−2.86947	−	4.97006i	−0.103610	−	0.179459i
$768$		0			0
$769$	2.38011	−	4.12248i	0.0858291	−	0.148660i	−0.819915	−	0.572485i	$-0.805979\pi$
$769$	2.38011	−	4.12248i	0.0858291	−	0.148660i	0.905744	+	0.423825i	$0.139313\pi$
$770$	0.224088	+	0.255459i	0.00807559	+	0.00920609i
$771$		0			0
$772$	3.74103	−	28.4717i	0.134643	−	1.02472i
$773$	38.1267	+	38.1267i	1.37132	+	1.37132i	0.858486	+	0.512837i	$0.171405\pi$
$773$	38.1267	+	38.1267i	1.37132	+	1.37132i	0.512837	+	0.858486i	$0.328595\pi$
$774$		0			0
$775$		−	44.9857i		−	1.61593i
$776$	−3.18468	−	1.56900i	−0.114323	−	0.0563240i
$777$		0			0
$778$	−2.80218	+	42.8362i	−0.100463	+	1.53575i
$779$	12.1514	−	3.25596i	0.435369	−	0.116657i
$780$		0			0
$781$	−0.795027	−	0.213027i	−0.0284483	−	0.00762270i
$782$	−9.79919	−	3.32499i	−0.350418	−	0.118902i
$783$		0			0
$784$	4.98795	+	18.5776i	0.178141	+	0.663487i
$785$	0.273835	+	0.474296i	0.00977359	+	0.0169284i
$786$		0			0
$787$	6.10176	+	22.7721i	0.217504	+	0.811736i	0.985270	+	0.171006i	$0.0547017\pi$
$787$	6.10176	+	22.7721i	0.217504	+	0.811736i	−0.767766	+	0.640730i	$0.778632\pi$
$788$	−4.11709	−	1.70413i	−0.146665	−	0.0607072i
$789$		0			0
$790$	−0.917904	−	0.613156i	−0.0326576	−	0.0218151i
$791$		−	17.2053i		−	0.611749i
$792$		0			0
$793$		−	1.36980i		−	0.0486432i
$794$	12.9782	−	19.4286i	0.460580	−	0.689496i
$795$		0			0
$796$	1.32302	+	3.19176i	0.0468931	+	0.113129i
$797$	11.8678	+	44.2911i	0.420378	+	1.56887i	0.773814	+	0.633413i	$0.218346\pi$
$797$	11.8678	+	44.2911i	0.420378	+	1.56887i	−0.353436	+	0.935459i	$0.614987\pi$
$798$		0			0
$799$	−2.91046	−	5.04107i	−0.102965	−	0.178340i
$800$	−1.83013	+	28.1960i	−0.0647049	+	0.996878i
$801$		0			0
$802$	−0.355130	+	1.04662i	−0.0125401	+	0.0369573i
$803$	−34.7805	−	9.31941i	−1.22738	−	0.328875i
$804$		0			0
$805$	−0.879807	+	0.235744i	−0.0310091	+	0.00830887i
$806$	−5.11244	−	0.334437i	−0.180078	−	0.0117800i
$807$		0			0
$808$	−5.03051	−	14.8009i	−0.176973	−	0.520695i
$809$			8.89301i			0.312662i	0.987705	+	0.156331i	$0.0499666\pi$
$809$			8.89301i			0.312662i	−0.987705	+	0.156331i	$0.950033\pi$
$810$		0			0
$811$	−31.7492	−	31.7492i	−1.11487	−	1.11487i	−0.992483	−	0.122384i	$-0.960946\pi$
$811$	−31.7492	−	31.7492i	−1.11487	−	1.11487i	−0.122384	−	0.992483i	$-0.539054\pi$
$812$	11.6018	−	8.90707i	0.407145	−	0.312577i
$813$		0			0
$814$	−14.0955	+	12.3646i	−0.494048	+	0.433380i
$815$	0.526230	−	0.911457i	0.0184330	−	0.0319269i
$816$		0			0
$817$	6.86401	+	11.8888i	0.240141	+	0.415937i
$818$	−41.7317	−	14.1601i	−1.45911	−	0.495097i
$819$		0			0
$820$	0.336401	−	0.0443747i	0.0117476	−	0.00154963i
$821$	12.5747	−	46.9294i	0.438860	−	1.63785i	−0.292797	−	0.956175i	$-0.594586\pi$
$821$	12.5747	−	46.9294i	0.438860	−	1.63785i	0.731657	−	0.681673i	$-0.238747\pi$
$822$		0			0
$823$	−9.69600	−	5.59799i	−0.337981	−	0.195134i	0.321398	−	0.946944i	$-0.395847\pi$
$823$	−9.69600	−	5.59799i	−0.337981	−	0.195134i	−0.659379	+	0.751811i	$0.729181\pi$
$824$	−31.2834	+	2.06236i	−1.08981	+	0.0718456i
$825$		0			0
$826$	−16.5899	+	24.8353i	−0.577236	+	0.864132i
$827$	−11.9898	−	11.9898i	−0.416927	−	0.416927i	0.467216	−	0.884143i	$-0.345257\pi$
$827$	−11.9898	−	11.9898i	−0.416927	−	0.416927i	−0.884143	+	0.467216i	$0.845257\pi$
$828$		0			0
$829$	−34.3253	+	34.3253i	−1.19217	+	1.19217i	−0.215708	+	0.976458i	$0.569206\pi$
$829$	−34.3253	+	34.3253i	−1.19217	+	1.19217i	−0.976458	+	0.215708i	$0.930794\pi$
$830$	0.551946	−	0.109862i	0.0191583	−	0.00381335i
$831$		0			0
$832$	3.19075	+	0.417603i	0.110619	+	0.0144778i
$833$	−2.04619	+	3.54410i	−0.0708962	+	0.122796i
$834$		0			0
$835$	0.434579	+	0.116445i	0.0150392	+	0.00402975i
$836$	19.1024	+	14.6501i	0.660670	+	0.506684i
$837$		0			0
$838$	14.3531	+	29.0959i	0.495820	+	1.00510i
$839$	−43.4830	+	25.1049i	−1.50120	+	0.866719i	−0.501202	+	0.865331i	$0.667109\pi$
$839$	−43.4830	+	25.1049i	−1.50120	+	0.866719i	−0.999999	+	0.00138814i	$0.999558\pi$
$840$		0			0
$841$	−3.97509	−	2.29502i	−0.137072	−	0.0791386i
$842$	−2.39366	+	36.5911i	−0.0824908	+	1.26101i
$843$		0			0
$844$	15.0555	+	19.6104i	0.518232	+	0.675019i
$845$	0.649670	−	0.649670i	0.0223493	−	0.0223493i
$846$		0			0
$847$	8.66674			0.297793
$848$	−22.3684	+	0.0113321i	−0.768133	+	0.000389148i
$849$		0			0
$850$	−4.51904	+	3.96411i	−0.155002	+	0.135968i
$851$	−13.0077	−	48.5455i	−0.445899	−	1.66412i
$852$		0			0
$853$	6.97320	−	26.0243i	0.238758	−	0.891056i	−0.737661	−	0.675171i	$-0.764070\pi$
$853$	6.97320	−	26.0243i	0.238758	−	0.891056i	0.976419	−	0.215885i	$-0.0692635\pi$
$854$	−6.39319	+	3.15378i	−0.218770	+	0.107920i
$855$		0			0
$856$	27.0830	+	5.37645i	0.925679	+	0.183763i
$857$	12.5955	−	7.27203i	0.430255	−	0.248408i	−0.269200	−	0.963084i	$-0.586759\pi$
$857$	12.5955	−	7.27203i	0.430255	−	0.248408i	0.699455	+	0.714676i	$0.253426\pi$
$858$		0			0
$859$	4.49231	−	1.20371i	0.153276	−	0.0410701i	−0.181365	−	0.983416i	$-0.558052\pi$
$859$	4.49231	−	1.20371i	0.153276	−	0.0410701i	0.334641	+	0.942346i	$0.391385\pi$
$860$	0.141786	+	0.342057i	0.00483486	+	0.0116640i
$861$		0			0
$862$	−11.8445	+	2.35757i	−0.403424	+	0.0802991i
$863$	−6.06219			−0.206359			−0.103180	−	0.994663i	$-0.532902\pi$
$863$	−6.06219			−0.206359			−0.103180	+	0.994663i	$0.532902\pi$
$864$		0			0
$865$	0.841503			0.0286120
$866$	−12.8753	+	2.56276i	−0.437521	+	0.0870860i
$867$		0			0
$868$	10.2098	+	24.6309i	0.346542	+	0.836028i
$869$	23.8965	−	6.40303i	0.810632	−	0.217208i
$870$		0			0
$871$	2.33528	−	1.34827i	0.0791278	−	0.0456845i
$872$	7.31491	−	36.8477i	0.247714	−	1.24782i
$873$		0			0
$874$	−57.8683	+	28.5466i	−1.95742	+	0.965603i
$875$	−0.274036	+	1.02272i	−0.00926412	+	0.0345742i
$876$		0			0
$877$	5.44913	+	20.3364i	0.184004	+	0.686713i	0.994842	+	0.101441i	$0.0323454\pi$
$877$	5.44913	+	20.3364i	0.184004	+	0.686713i	−0.810837	+	0.585271i	$0.800988\pi$
$878$	−14.8476	+	13.0243i	−0.501081	+	0.439548i
$879$		0			0
$880$	0.459370	+	0.458904i	0.0154853	+	0.0154697i
$881$	−3.07747			−0.103682			−0.0518412	−	0.998655i	$-0.516509\pi$
$881$	−3.07747			−0.103682			−0.0518412	+	0.998655i	$0.516509\pi$
$882$		0			0
$883$	−2.89268	+	2.89268i	−0.0973465	+	0.0973465i	−0.754103	−	0.656756i	$-0.771928\pi$
$883$	−2.89268	+	2.89268i	−0.0973465	+	0.0973465i	0.656756	+	0.754103i	$0.271928\pi$
$884$	0.416908	+	0.543041i	0.0140221	+	0.0182644i
$885$		0			0
$886$	1.14111	−	17.4438i	0.0383362	−	0.586034i
$887$	43.0227	+	24.8392i	1.44456	+	0.834017i	0.998149	−	0.0608108i	$-0.0193686\pi$
$887$	43.0227	+	24.8392i	1.44456	+	0.834017i	0.446411	+	0.894828i	$0.352702\pi$
$888$		0			0
$889$	−13.0712	+	7.54664i	−0.438393	+	0.253106i
$890$	0.590277	+	1.19658i	0.0197861	+	0.0401095i
$891$		0			0
$892$	−22.9191	−	17.5772i	−0.767387	−	0.588528i
$893$	−35.0606	−	9.39445i	−1.17326	−	0.314373i
$894$		0			0
$895$	0.466472	−	0.807953i	0.0155924	−	0.0270069i
$896$	−5.39719	−	15.8534i	−0.180308	−	0.529626i
$897$		0			0
$898$	−21.5299	+	4.28539i	−0.718461	+	0.143005i
$899$	−31.4643	+	31.4643i	−1.04939	+	1.04939i
$900$		0			0
$901$	−3.36503	−	3.36503i	−0.112105	−	0.112105i
$902$	−4.22411	+	6.32356i	−0.140647	+	0.210551i
$903$		0			0
$904$	−2.16264	−	32.8045i	−0.0719283	−	1.09106i
$905$	−1.01603	−	0.586603i	−0.0337738	−	0.0194993i
$906$		0			0
$907$	3.27515	−	12.2230i	0.108750	−	0.405859i	−0.889994	−	0.455973i	$-0.849292\pi$
$907$	3.27515	−	12.2230i	0.108750	−	0.405859i	0.998744	+	0.0501131i	$0.0159582\pi$
$908$	3.31681	−	0.437521i	0.110072	−	0.0145196i
$909$		0			0
$910$	0.0570659	+	0.0193632i	0.00189172	+	0.000641884i
$911$	26.6903	+	46.2289i	0.884289	+	1.53163i	0.846526	+	0.532347i	$0.178690\pi$
$911$	26.6903	+	46.2289i	0.884289	+	1.53163i	0.0377625	+	0.999287i	$0.487977\pi$
$912$		0			0
$913$	−6.30637	+	10.9230i	−0.208710	+	0.361497i
$914$	28.6908	−	25.1676i	0.949008	−	0.832470i
$915$		0			0
$916$	−32.2243	+	24.7395i	−1.06472	+	0.817417i
$917$	7.36336	+	7.36336i	0.243160	+	0.243160i
$918$		0			0
$919$		−	38.5309i		−	1.27102i	−0.772094	−	0.635509i	$-0.780790\pi$
$919$		−	38.5309i		−	1.27102i	0.772094	−	0.635509i	$-0.219210\pi$
$920$	−1.64786	+	0.560070i	−0.0543282	+	0.0184650i
$921$		0			0
$922$	−33.3124	−	2.17917i	−1.09709	−	0.0717672i
$923$	−0.140987	+	0.0377773i	−0.00464064	+	0.00124345i
$924$		0			0
$925$	−28.2010	−	7.55643i	−0.927243	−	0.248454i
$926$	10.6383	−	31.3525i	0.349597	−	1.03031i
$927$		0			0
$928$	21.0011	−	18.4410i	0.689396	−	0.605357i
$929$	−5.92500	−	10.2624i	−0.194393	−	0.336699i	0.752308	−	0.658811i	$-0.228940\pi$
$929$	−5.92500	−	10.2624i	−0.194393	−	0.336699i	−0.946701	+	0.322113i	$0.895607\pi$
$930$		0			0
$931$	6.60473	+	24.6492i	0.216461	+	0.807844i
$932$	−18.0595	−	43.5682i	−0.591558	−	1.42712i
$933$		0			0
$934$	−19.3947	+	29.0342i	−0.634615	+	0.950029i
$935$			0.138142i			0.00451774i
$936$		0			0
$937$		−	0.288917i		−	0.00943850i	−0.999989	−	0.00471925i	$-0.998498\pi$
$937$		−	0.288917i		−	0.00943850i	0.999989	−	0.00471925i	$-0.00150219\pi$
$938$	−11.6693	−	7.79507i	−0.381018	−	0.254518i
$939$		0			0
$940$	−0.904600	−	0.374429i	−0.0295048	−	0.0122125i
$941$	8.87473	+	33.1209i	0.289308	+	1.07971i	0.945634	+	0.325234i	$0.105443\pi$
$941$	8.87473	+	33.1209i	0.289308	+	1.07971i	−0.656326	+	0.754478i	$0.727890\pi$
$942$		0			0
$943$	−10.1917	−	17.6526i	−0.331889	−	0.574849i
$944$	−28.5095	+	49.4377i	−0.927905	+	1.60906i
$945$		0			0
$946$	−7.85851	−	2.66650i	−0.255502	−	0.0866953i
$947$	−22.3187	−	5.98027i	−0.725259	−	0.194333i	−0.122742	−	0.992439i	$-0.539169\pi$
$947$	−22.3187	−	5.98027i	−0.725259	−	0.194333i	−0.602517	+	0.798106i	$0.705835\pi$
$948$		0			0
$949$	−6.16783	+	1.65267i	−0.200216	+	0.0536478i
$950$	−2.44687	+	37.4046i	−0.0793870	+	1.21357i
$951$		0			0
$952$	1.57462	−	3.19608i	0.0510338	−	0.103586i
$953$			31.0900i			1.00710i	0.863965	+	0.503552i	$0.167974\pi$
$953$			31.0900i			1.00710i	−0.863965	+	0.503552i	$0.832026\pi$
$954$		0			0
$955$	−1.13217	−	1.13217i	−0.0366361	−	0.0366361i
$956$	−2.23239	+	16.9900i	−0.0722008	+	0.549495i
$957$		0			0
$958$	17.9564	+	20.4701i	0.580144	+	0.661359i
$959$	−10.7401	+	18.6023i	−0.346815	+	0.600701i
$960$		0			0
$961$	−25.0573	−	43.4006i	−0.808302	−	1.40002i
$962$	−1.06841	+	3.14875i	−0.0344470	+	0.101520i
$963$		0			0
$964$	11.7126	+	8.98266i	0.377237	+	0.289312i
$965$	0.265950	−	0.992539i	0.00856124	−	0.0319510i
$966$		0			0
$967$	−24.9481	−	14.4038i	−0.802277	−	0.463195i	0.0419899	−	0.999118i	$-0.486630\pi$
$967$	−24.9481	−	14.4038i	−0.802277	−	0.463195i	−0.844267	+	0.535923i	$0.819964\pi$
$968$	16.5245	−	1.08938i	0.531117	−	0.0350139i
$969$		0			0
$970$	−0.105635	−	0.0705640i	−0.00339175	−	0.00226567i
$971$	−11.6466	−	11.6466i	−0.373757	−	0.373757i	0.495087	−	0.868844i	$-0.335136\pi$
$971$	−11.6466	−	11.6466i	−0.373757	−	0.373757i	−0.868844	+	0.495087i	$0.835136\pi$
$972$		0			0
$973$	5.52175	−	5.52175i	0.177019	−	0.177019i
$974$	4.36227	+	21.9161i	0.139776	+	0.702237i
$975$		0			0
$976$	−11.7932	+	6.81677i	−0.377491	+	0.218200i
$977$	12.0661	−	20.8990i	0.386028	−	0.668619i	−0.605884	−	0.795553i	$-0.707180\pi$
$977$	12.0661	−	20.8990i	0.386028	−	0.668619i	0.991911	+	0.126934i	$0.0405136\pi$
$978$		0			0
$979$	−28.8840	−	7.73945i	−0.923137	−	0.247354i
$980$	0.0900143	+	0.682391i	0.00287540	+	0.0217982i
$981$		0			0
$982$	14.3629	−	7.08527i	0.458339	−	0.226100i
$983$	−18.5016	+	10.6819i	−0.590109	+	0.340700i	−0.765141	−	0.643863i	$-0.777331\pi$
$983$	−18.5016	+	10.6819i	−0.590109	+	0.340700i	0.175031	+	0.984563i	$0.443997\pi$
$984$		0			0
$985$	−0.138081	−	0.0797210i	−0.00439962	−	0.00254012i
$986$	5.93336	+	0.388138i	0.188957	+	0.0123608i
$987$		0			0
$988$	4.23269	+	0.556153i	0.134660	+	0.0176936i
$989$	15.7286	−	15.7286i	0.500139	−	0.500139i
$990$		0			0
$991$	28.0624			0.891433			0.445717	−	0.895174i	$-0.352949\pi$
$991$	28.0624			0.891433			0.445717	+	0.895174i	$0.352949\pi$
$992$	22.5625	+	45.6793i	0.716361	+	1.45032i
$993$		0			0
$994$	0.500917	+	0.571041i	0.0158881	+	0.0181123i
$995$	0.0319985	+	0.119420i	0.00101442	+	0.00378587i
$996$		0			0
$997$	−15.0100	+	56.0181i	−0.475372	+	1.77411i	0.144603	+	0.989490i	$0.453810\pi$
$997$	−15.0100	+	56.0181i	−0.475372	+	1.77411i	−0.619975	+	0.784622i	$0.712857\pi$
$998$	−2.51525	−	5.09880i	−0.0796190	−	0.161400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.17		72
3.2	odd	2		144.2.x.e.85.2	yes	72
4.3	odd	2		1728.2.bc.e.1009.10		72
9.2	odd	6		144.2.x.e.133.12	yes	72
9.7	even	3	inner	432.2.y.e.181.7		72
12.11	even	2		576.2.bb.e.49.7		72
16.3	odd	4		1728.2.bc.e.145.9		72
16.13	even	4	inner	432.2.y.e.253.7		72
36.7	odd	6		1728.2.bc.e.1585.9		72
36.11	even	6		576.2.bb.e.241.4		72
48.29	odd	4		144.2.x.e.13.12	✓	72
48.35	even	4		576.2.bb.e.337.4		72
144.29	odd	12		144.2.x.e.61.2	yes	72
144.61	even	12	inner	432.2.y.e.397.17		72
144.83	even	12		576.2.bb.e.529.7		72
144.115	odd	12		1728.2.bc.e.721.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.12	✓	72	48.29	odd	4
144.2.x.e.61.2	yes	72	144.29	odd	12
144.2.x.e.85.2	yes	72	3.2	odd	2
144.2.x.e.133.12	yes	72	9.2	odd	6
432.2.y.e.37.17		72	1.1	even	1	trivial
432.2.y.e.181.7		72	9.7	even	3	inner
432.2.y.e.253.7		72	16.13	even	4	inner
432.2.y.e.397.17		72	144.61	even	12	inner
576.2.bb.e.49.7		72	12.11	even	2
576.2.bb.e.241.4		72	36.11	even	6
576.2.bb.e.337.4		72	48.35	even	4
576.2.bb.e.529.7		72	144.83	even	12
1728.2.bc.e.145.9		72	16.3	odd	4
1728.2.bc.e.721.10		72	144.115	odd	12
1728.2.bc.e.1009.10		72	4.3	odd	2
1728.2.bc.e.1585.9		72	36.7	odd	6

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38700 - 0.276075i) q^{2} +(1.84757 - 0.765835i) q^{4} +(0.0691269 - 0.0185225i) q^{5} +(1.28192 - 0.740118i) q^{7} +(2.35115 - 1.57228i) q^{8} +O(q^{10})\)	\(q+(1.38700 - 0.276075i) q^{2} +(1.84757 - 0.765835i) q^{4} +(0.0691269 - 0.0185225i) q^{5} +(1.28192 - 0.740118i) q^{7} +(2.35115 - 1.57228i) q^{8} +(0.0907658 - 0.0447750i) q^{10} +(-0.587070 + 2.19098i) q^{11} +(0.104109 + 0.388539i) q^{13} +(1.57370 - 1.38045i) q^{14} +(2.82699 - 2.82986i) q^{16} +0.851000 q^{17} +(3.75230 - 3.75230i) q^{19} +(0.113531 - 0.0871613i) q^{20} +(-0.209396 + 3.20097i) q^{22} +(-7.44629 - 4.29912i) q^{23} +(-4.32569 + 2.49744i) q^{25} +(0.251665 + 0.510163i) q^{26} +(1.80163 - 2.34916i) q^{28} +(4.77230 + 1.27873i) q^{29} +(-4.50318 + 7.79974i) q^{31} +(3.13980 - 4.70549i) q^{32} +(1.18034 - 0.234940i) q^{34} +(0.0749065 - 0.0749065i) q^{35} +(4.13315 + 4.13315i) q^{37} +(4.16854 - 6.24038i) q^{38} +(0.133405 - 0.152236i) q^{40} +(2.05305 + 1.18533i) q^{41} +(-0.669562 + 2.49884i) q^{43} +(0.593275 + 4.49757i) q^{44} +(-11.5149 - 3.90716i) q^{46} +(-3.42005 - 5.92370i) q^{47} +(-2.40445 + 4.16463i) q^{49} +(-5.31027 + 4.65818i) q^{50} +(0.489904 + 0.638121i) q^{52} +(-3.95421 - 3.95421i) q^{53} +0.162329i q^{55} +(1.85032 - 3.75568i) q^{56} +(6.97222 + 0.456097i) q^{58} +(-13.7811 + 3.69264i) q^{59} +(-3.28936 - 0.881382i) q^{61} +(-4.09262 + 12.0615i) q^{62} +(3.05585 - 7.39336i) q^{64} +(0.0143934 + 0.0249301i) q^{65} +(-1.73506 - 6.47532i) q^{67} +(1.57228 - 0.651726i) q^{68} +(0.0832159 - 0.124576i) q^{70} +0.362864i q^{71} +15.8744i q^{73} +(6.87375 + 4.59164i) q^{74} +(4.05898 - 9.80627i) q^{76} +(0.869003 + 3.24316i) q^{77} +(-5.45338 - 9.44553i) q^{79} +(0.143005 - 0.247983i) q^{80} +(3.17483 + 1.07726i) q^{82} +(5.37105 + 1.43917i) q^{83} +(0.0588270 - 0.0157627i) q^{85} +(-0.238819 + 3.65075i) q^{86} +(2.06454 + 6.07436i) q^{88} +13.1832i q^{89} +(0.421024 + 0.421024i) q^{91} +(-17.0499 - 2.24027i) q^{92} +(-6.37901 - 7.27201i) q^{94} +(0.189883 - 0.328887i) q^{95} +(-0.627593 - 1.08702i) q^{97} +(-2.18523 + 6.44017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

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