LMFDB - Embedded newform 648.2.v.b.179.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("648.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.16
Character	$\chi$	$=$	648.179
Dual form			648.2.v.b.467.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0739917 - 1.41228i) q^{2} +(-1.98905 - 0.208993i) q^{4} +(0.586059 - 3.32370i) q^{5} +(-1.89356 - 2.25666i) q^{7} +(-0.442330 + 2.79363i) q^{8} +O(q^{10})$	\(q+(0.0739917 - 1.41228i) q^{2} +(-1.98905 - 0.208993i) q^{4} +(0.586059 - 3.32370i) q^{5} +(-1.89356 - 2.25666i) q^{7} +(-0.442330 + 2.79363i) q^{8} +(-4.65063 - 1.07360i) q^{10} +(-3.51297 + 0.619431i) q^{11} +(-0.204490 - 0.561832i) q^{13} +(-3.32714 + 2.50726i) q^{14} +(3.91264 + 0.831397i) q^{16} +(1.97627 + 1.14100i) q^{17} +(2.72623 + 4.72197i) q^{19} +(-1.86033 + 6.48853i) q^{20} +(0.614878 + 5.00711i) q^{22} +(-6.69233 - 5.61553i) q^{23} +(-6.00508 - 2.18567i) q^{25} +(-0.808593 + 0.247226i) q^{26} +(3.29477 + 4.88435i) q^{28} +(4.86478 + 1.77064i) q^{29} +(-0.468156 + 0.557926i) q^{31} +(1.46367 - 5.46422i) q^{32} +(1.75764 - 2.70662i) q^{34} +(-8.61021 + 4.97111i) q^{35} +(-0.422340 - 0.243838i) q^{37} +(6.87044 - 3.50080i) q^{38} +(9.02596 + 3.10740i) q^{40} +(-0.645850 - 1.77446i) q^{41} +(-1.01523 - 5.75766i) q^{43} +(7.11693 - 0.497893i) q^{44} +(-8.42586 + 9.03591i) q^{46} +(-3.87524 + 3.25171i) q^{47} +(-0.291398 + 1.65260i) q^{49} +(-3.53110 + 8.31912i) q^{50} +(0.289322 + 1.16025i) q^{52} -13.0806 q^{53} +12.0391i q^{55} +(7.14184 - 4.29172i) q^{56} +(2.86058 - 6.73941i) q^{58} +(-7.04866 - 1.24287i) q^{59} +(5.74555 + 6.84728i) q^{61} +(0.753306 + 0.702447i) q^{62} +(-7.60869 - 2.47141i) q^{64} +(-1.98721 + 0.350398i) q^{65} +(2.79254 - 1.01640i) q^{67} +(-3.69245 - 2.68254i) q^{68} +(6.38350 + 12.5278i) q^{70} +(1.67775 - 2.90596i) q^{71} +(-5.59255 - 9.68658i) q^{73} +(-0.375616 + 0.578418i) q^{74} +(-4.43575 - 9.96200i) q^{76} +(8.04987 + 6.75464i) q^{77} +(5.79167 - 15.9125i) q^{79} +(5.05636 - 12.5172i) q^{80} +(-2.55381 + 0.780824i) q^{82} +(-2.75916 + 7.58072i) q^{83} +(4.95057 - 5.89986i) q^{85} +(-8.20653 + 1.00777i) q^{86} +(-0.176569 - 10.0879i) q^{88} +(13.3509 - 7.70815i) q^{89} +(-0.880649 + 1.52533i) q^{91} +(12.1378 + 12.5682i) q^{92} +(4.30558 + 5.71351i) q^{94} +(17.2922 - 6.29383i) q^{95} +(-1.67485 - 9.49852i) q^{97} +(2.31237 + 0.533814i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	0.0739917	−	1.41228i	0.0523200	−	0.998630i
$2$	0.0739917	−	1.41228i	0.0523200	−	0.998630i
$3$		0			0
$3$		0			0
$4$	−1.98905	−	0.208993i	−0.994525	−	0.104497i
$5$	0.586059	−	3.32370i	0.262093	−	1.48641i	−0.515092	−	0.857135i	$-0.672242\pi$
$5$	0.586059	−	3.32370i	0.262093	−	1.48641i	0.777186	−	0.629271i	$-0.216646\pi$
$6$		0			0
$7$	−1.89356	−	2.25666i	−0.715700	−	0.852937i	0.278506	−	0.960435i	$-0.410161\pi$
$7$	−1.89356	−	2.25666i	−0.715700	−	0.852937i	−0.994205	+	0.107497i	$0.965716\pi$
$8$	−0.442330	+	2.79363i	−0.156387	+	0.987696i
$9$		0			0
$10$	−4.65063	−	1.07360i	−1.47066	−	0.339503i
$11$	−3.51297	+	0.619431i	−1.05920	+	0.186765i	−0.676001	−	0.736901i	$-0.736289\pi$
$11$	−3.51297	+	0.619431i	−1.05920	+	0.186765i	−0.383198	+	0.923666i	$0.625177\pi$
$12$		0			0
$13$	−0.204490	−	0.561832i	−0.0567153	−	0.155824i	0.908099	−	0.418755i	$-0.137533\pi$
$13$	−0.204490	−	0.561832i	−0.0567153	−	0.155824i	−0.964815	+	0.262930i	$0.915311\pi$
$14$	−3.32714	+	2.50726i	−0.889215	+	0.670094i
$15$		0			0
$16$	3.91264	+	0.831397i	0.978161	+	0.207849i
$17$	1.97627	+	1.14100i	0.479317	+	0.276734i	0.720132	−	0.693837i	$-0.244081\pi$
$17$	1.97627	+	1.14100i	0.479317	+	0.276734i	−0.240815	+	0.970571i	$0.577415\pi$
$18$		0			0
$19$	2.72623	+	4.72197i	0.625440	+	1.08329i	0.988456	+	0.151511i	$0.0484139\pi$
$19$	2.72623	+	4.72197i	0.625440	+	1.08329i	−0.363016	+	0.931783i	$0.618253\pi$
$20$	−1.86033	+	6.48853i	−0.415983	+	1.45088i
$21$		0			0
$22$	0.614878	+	5.00711i	0.131092	+	1.06752i
$23$	−6.69233	−	5.61553i	−1.39545	−	1.17092i	−0.963078	−	0.269222i	$-0.913234\pi$
$23$	−6.69233	−	5.61553i	−1.39545	−	1.17092i	−0.432368	−	0.901697i	$-0.642322\pi$
$24$		0			0
$25$	−6.00508	−	2.18567i	−1.20102	−	0.437134i
$26$	−0.808593	+	0.247226i	−0.158578	+	0.0484849i
$27$		0			0
$28$	3.29477	+	4.88435i	0.622652	+	0.923056i
$29$	4.86478	+	1.77064i	0.903368	+	0.328799i	0.751601	−	0.659618i	$-0.229282\pi$
$29$	4.86478	+	1.77064i	0.903368	+	0.328799i	0.151766	+	0.988416i	$0.451504\pi$
$30$		0			0
$31$	−0.468156	+	0.557926i	−0.0840832	+	0.100206i	−0.806446	−	0.591308i	$-0.798612\pi$
$31$	−0.468156	+	0.557926i	−0.0840832	+	0.100206i	0.722363	+	0.691515i	$0.243056\pi$
$32$	1.46367	−	5.46422i	0.258742	−	0.965947i
$33$		0			0
$34$	1.75764	−	2.70662i	0.301433	−	0.464182i
$35$	−8.61021	+	4.97111i	−1.45539	+	0.840271i
$36$		0			0
$37$	−0.422340	−	0.243838i	−0.0694322	−	0.0400867i	0.464882	−	0.885373i	$-0.346097\pi$
$37$	−0.422340	−	0.243838i	−0.0694322	−	0.0400867i	−0.534314	+	0.845286i	$0.679430\pi$
$38$	6.87044	−	3.50080i	1.11453	−	0.567905i
$39$		0			0
$40$	9.02596	+	3.10740i	1.42713	+	0.491323i
$41$	−0.645850	−	1.77446i	−0.100865	−	0.277124i	0.878988	−	0.476843i	$-0.158219\pi$
$41$	−0.645850	−	1.77446i	−0.100865	−	0.277124i	−0.979853	+	0.199720i	$0.935997\pi$
$42$		0			0
$43$	−1.01523	−	5.75766i	−0.154821	−	0.878035i	−0.958949	−	0.283578i	$-0.908478\pi$
$43$	−1.01523	−	5.75766i	−0.154821	−	0.878035i	0.804128	−	0.594456i	$-0.202633\pi$
$44$	7.11693	−	0.497893i	1.07292	−	0.0750601i
$45$		0			0
$46$	−8.42586	+	9.03591i	−1.24232	+	1.33227i
$47$	−3.87524	+	3.25171i	−0.565262	+	0.474311i	−0.880070	−	0.474844i	$-0.842504\pi$
$47$	−3.87524	+	3.25171i	−0.565262	+	0.474311i	0.314808	+	0.949155i	$0.398060\pi$
$48$		0			0
$49$	−0.291398	+	1.65260i	−0.0416284	+	0.236086i
$50$	−3.53110	+	8.31912i	−0.499373	+	1.17650i
$51$		0			0
$52$	0.289322	+	1.16025i	0.0401217	+	0.160898i
$53$	−13.0806			−1.79676			−0.898380	−	0.439220i	$-0.855255\pi$
$53$	−13.0806			−1.79676			−0.898380	+	0.439220i	$0.855255\pi$
$54$		0			0
$55$			12.0391i			1.62335i
$56$	7.14184	−	4.29172i	0.954369	−	0.573505i
$57$		0			0
$58$	2.86058	−	6.73941i	0.375613	−	0.884927i
$59$	−7.04866	−	1.24287i	−0.917658	−	0.161808i	−0.305179	−	0.952295i	$-0.598716\pi$
$59$	−7.04866	−	1.24287i	−0.917658	−	0.161808i	−0.612479	+	0.790487i	$0.709827\pi$
$60$		0			0
$61$	5.74555	+	6.84728i	0.735642	+	0.876705i	0.996050	−	0.0887943i	$-0.0283014\pi$
$61$	5.74555	+	6.84728i	0.735642	+	0.876705i	−0.260408	+	0.965499i	$0.583857\pi$
$62$	0.753306	+	0.702447i	0.0956700	+	0.0892109i
$63$		0			0
$64$	−7.60869	−	2.47141i	−0.951086	−	0.308926i
$65$	−1.98721	+	0.350398i	−0.246483	+	0.0434615i
$66$		0			0
$67$	2.79254	−	1.01640i	0.341163	−	0.124173i	−0.165756	−	0.986167i	$-0.553006\pi$
$67$	2.79254	−	1.01640i	0.341163	−	0.124173i	0.506919	+	0.861994i	$0.330784\pi$
$68$	−3.69245	−	2.68254i	−0.447775	−	0.325306i
$69$		0			0
$70$	6.38350	+	12.5278i	0.762974	+	1.49736i
$71$	1.67775	−	2.90596i	0.199113	−	0.344873i	−0.749128	−	0.662425i	$-0.769527\pi$
$71$	1.67775	−	2.90596i	0.199113	−	0.344873i	0.948241	+	0.317552i	$0.102861\pi$
$72$		0			0
$73$	−5.59255	−	9.68658i	−0.654558	−	1.13373i	−0.982004	−	0.188858i	$-0.939521\pi$
$73$	−5.59255	−	9.68658i	−0.654558	−	1.13373i	0.327446	−	0.944870i	$-0.393812\pi$
$74$	−0.375616	+	0.578418i	−0.0436645	+	0.0672398i
$75$		0			0
$76$	−4.43575	−	9.96200i	−0.508815	−	1.14272i
$77$	8.04987	+	6.75464i	0.917368	+	0.769763i
$78$		0			0
$79$	5.79167	−	15.9125i	0.651614	−	1.79030i	0.0399179	−	0.999203i	$-0.487290\pi$
$79$	5.79167	−	15.9125i	0.651614	−	1.79030i	0.611696	−	0.791093i	$-0.290487\pi$
$80$	5.05636	−	12.5172i	0.565318	−	1.39947i
$81$		0			0
$82$	−2.55381	+	0.780824i	−0.282022	+	0.0862276i
$83$	−2.75916	+	7.58072i	−0.302857	+	0.832092i	0.691144	+	0.722717i	$0.257107\pi$
$83$	−2.75916	+	7.58072i	−0.302857	+	0.832092i	−0.994001	+	0.109375i	$0.965115\pi$
$84$		0			0
$85$	4.95057	−	5.89986i	0.536965	−	0.639929i
$86$	−8.20653	+	1.00777i	−0.884933	+	0.108670i
$87$		0			0
$88$	−0.176569	−	10.0879i	−0.0188223	−	1.07537i
$89$	13.3509	−	7.70815i	1.41519	−	0.817063i	0.419323	−	0.907837i	$-0.362268\pi$
$89$	13.3509	−	7.70815i	1.41519	−	0.817063i	0.995871	+	0.0907747i	$0.0289343\pi$
$90$		0			0
$91$	−0.880649	+	1.52533i	−0.0923171	+	0.159898i
$92$	12.1378	+	12.5682i	1.26545	+	1.31033i
$93$		0			0
$94$	4.30558	+	5.71351i	0.444087	+	0.589303i
$95$	17.2922	−	6.29383i	1.77414	−	0.645733i
$96$		0			0
$97$	−1.67485	−	9.49852i	−0.170055	−	0.964429i	−0.943698	−	0.330807i	$-0.892679\pi$
$97$	−1.67485	−	9.49852i	−0.170055	−	0.964429i	0.773643	−	0.633621i	$-0.218432\pi$
$98$	2.31237	+	0.533814i	0.233585	+	0.0539234i
$99$		0			0
$100$	11.4876	+	5.60243i	1.14876	+	0.560243i
$101$	1.58712	−	1.33175i	0.157924	−	0.132514i	−0.560402	−	0.828221i	$-0.689353\pi$
$101$	1.58712	−	1.33175i	0.157924	−	0.132514i	0.718326	+	0.695707i	$0.244909\pi$
$102$		0			0
$103$	−5.47205	−	0.964870i	−0.539177	−	0.0950715i	−0.102573	−	0.994725i	$-0.532708\pi$
$103$	−5.47205	−	0.964870i	−0.539177	−	0.0950715i	−0.436604	+	0.899654i	$0.643819\pi$
$104$	1.66000	−	0.322754i	0.162776	−	0.0316486i
$105$		0			0
$106$	−0.967856	+	18.4734i	−0.0940064	+	1.79430i
$107$			11.8518i			1.14576i	0.819640	+	0.572879i	$0.194174\pi$
$107$			11.8518i			1.14576i	−0.819640	+	0.572879i	$0.805826\pi$
$108$		0			0
$109$		−	5.60849i		−	0.537196i	−0.963252	−	0.268598i	$-0.913440\pi$
$109$		−	5.60849i		−	0.537196i	0.963252	−	0.268598i	$-0.0865603\pi$
$110$	17.0025	+	0.890792i	1.62113	+	0.0849337i
$111$		0			0
$112$	−5.53266	−	10.4038i	−0.522787	−	0.983068i
$113$	−1.25678	−	0.221604i	−0.118228	−	0.0208467i	0.114221	−	0.993455i	$-0.463563\pi$
$113$	−1.25678	−	0.221604i	−0.118228	−	0.0208467i	−0.232449	+	0.972609i	$0.574674\pi$
$114$		0			0
$115$	−22.5865	+	18.9523i	−2.10620	+	1.76731i
$116$	−9.30625	−	4.53859i	−0.864063	−	0.421398i
$117$		0			0
$118$	−2.27682	+	9.86270i	−0.209598	+	0.907935i
$119$	−1.16734	−	6.62034i	−0.107010	−	0.606886i
$120$		0			0
$121$	1.62062	−	0.589859i	0.147329	−	0.0536235i
$122$	10.0954	−	7.60767i	0.913993	−	0.688766i
$123$		0			0
$124$	1.04779	−	1.01190i	0.0940941	−	0.0908715i
$125$	−2.34641	+	4.06411i	−0.209870	+	0.363505i
$126$		0			0
$127$	5.76339	−	3.32750i	0.511419	−	0.295268i	−0.221998	−	0.975047i	$-0.571258\pi$
$127$	5.76339	−	3.32750i	0.511419	−	0.295268i	0.733417	+	0.679779i	$0.237925\pi$
$128$	−4.05329	+	10.5627i	−0.358264	+	0.933621i
$129$		0			0
$130$	0.347822	+	2.83241i	0.0305060	+	0.248419i
$131$	10.6613	−	12.7057i	0.931486	−	1.11010i	−0.0622173	−	0.998063i	$-0.519817\pi$
$131$	10.6613	−	12.7057i	0.931486	−	1.11010i	0.993704	−	0.112040i	$-0.0357384\pi$
$132$		0			0
$133$	5.49359	−	15.0935i	0.476355	−	1.30877i
$134$	−1.22882	−	4.01904i	−0.106153	−	0.347193i
$135$		0			0
$136$	−4.06170	+	5.01627i	−0.348288	+	0.430142i
$137$	6.41579	−	17.6272i	0.548138	−	1.50600i	−0.288085	−	0.957605i	$-0.593018\pi$
$137$	6.41579	−	17.6272i	0.548138	−	1.50600i	0.836222	−	0.548391i	$-0.184759\pi$
$138$		0			0
$139$	−0.589031	−	0.494256i	−0.0499610	−	0.0419223i	0.617465	−	0.786598i	$-0.288160\pi$
$139$	−0.589031	−	0.494256i	−0.0499610	−	0.0419223i	−0.667426	+	0.744676i	$0.732604\pi$
$140$	18.1651	−	8.08831i	1.53523	−	0.683587i
$141$		0			0
$142$	−3.97987	−	2.58447i	−0.333984	−	0.216884i
$143$	1.06638	+	1.84703i	0.0891754	+	0.154456i
$144$		0			0
$145$	8.73612	−	15.1314i	0.725495	−	1.25659i
$146$	−14.0939	+	7.18150i	−1.16642	+	0.594345i
$147$		0			0
$148$	0.789094	+	0.573272i	0.0648631	+	0.0471227i
$149$	−2.83808	+	1.03298i	−0.232504	+	0.0846246i	−0.455645	−	0.890162i	$-0.650591\pi$
$149$	−2.83808	+	1.03298i	−0.232504	+	0.0846246i	0.223141	+	0.974786i	$0.428369\pi$
$150$		0			0
$151$	−2.11341	+	0.372652i	−0.171987	+	0.0303260i	−0.258978	−	0.965883i	$-0.583386\pi$
$151$	−2.11341	+	0.372652i	−0.171987	+	0.0303260i	0.0869913	+	0.996209i	$0.472275\pi$
$152$	−14.3973	+	5.52740i	−1.16778	+	0.448331i
$153$		0			0
$154$	10.1350	−	10.8689i	0.816705	−	0.875837i
$155$	1.58001	+	1.88299i	0.126910	+	0.151245i
$156$		0			0
$157$	−7.69184	−	1.35628i	−0.613876	−	0.108243i	−0.141939	−	0.989875i	$-0.545334\pi$
$157$	−7.69184	−	1.35628i	−0.613876	−	0.108243i	−0.471936	+	0.881633i	$0.656445\pi$
$158$	−22.0443	−	9.35684i	−1.75375	−	0.744390i
$159$		0			0
$160$	−17.3037	−	8.06714i	−1.36797	−	0.637764i
$161$			25.7357i			2.02825i
$162$		0			0
$163$	12.9106			1.01124			0.505620	−	0.862756i	$-0.331264\pi$
$163$	12.9106			1.01124			0.505620	+	0.862756i	$0.331264\pi$
$164$	0.913779	+	3.66447i	0.0713541	+	0.286147i
$165$		0			0
$166$	10.5019	+	4.45760i	0.815107	+	0.345977i
$167$	−2.62966	+	14.9135i	−0.203489	+	1.15404i	0.696310	+	0.717741i	$0.254824\pi$
$167$	−2.62966	+	14.9135i	−0.203489	+	1.15404i	−0.899800	+	0.436304i	$0.856287\pi$
$168$		0			0
$169$	9.68474	−	8.12646i	0.744980	−	0.625112i
$170$	−7.96593	−	7.42811i	−0.610959	−	0.569710i
$171$		0			0
$172$	0.816033	+	11.6645i	0.0622219	+	0.889406i
$173$	−3.13725	−	17.7922i	−0.238521	−	1.35272i	−0.835071	−	0.550142i	$-0.814574\pi$
$173$	−3.13725	−	17.7922i	−0.238521	−	1.35272i	0.596551	−	0.802576i	$-0.296538\pi$
$174$		0			0
$175$	6.43868	+	17.6901i	0.486719	+	1.33725i
$176$	−14.2600	−	0.497057i	−1.07489	−	0.0374671i
$177$		0			0
$178$	−9.89819	−	19.4255i	−0.741901	−	1.45600i
$179$	−5.86858	−	3.38823i	−0.438638	−	0.253248i	0.264381	−	0.964418i	$-0.414832\pi$
$179$	−5.86858	−	3.38823i	−0.438638	−	0.253248i	−0.703020	+	0.711170i	$0.748166\pi$
$180$		0			0
$181$	−8.33722	+	4.81350i	−0.619701	+	0.357784i	−0.776753	−	0.629806i	$-0.783134\pi$
$181$	−8.33722	+	4.81350i	−0.619701	+	0.357784i	0.157052	+	0.987590i	$0.449801\pi$
$182$	2.08903	+	1.35658i	0.154849	+	0.100557i
$183$		0			0
$184$	18.6479	−	16.2119i	1.37474	−	1.19516i
$185$	−1.05796	+	1.26083i	−0.0777828	+	0.0926980i
$186$		0			0
$187$	−7.64936	−	2.78414i	−0.559377	−	0.203596i
$188$	8.38763	−	5.65792i	0.611731	−	0.412646i
$189$		0			0
$190$	−7.60916	−	24.8870i	−0.552026	−	1.80549i
$191$	0.938669	+	0.341648i	0.0679197	+	0.0247208i	0.375757	−	0.926718i	$-0.377383\pi$
$191$	0.938669	+	0.341648i	0.0679197	+	0.0247208i	−0.307837	+	0.951439i	$0.599605\pi$
$192$		0			0
$193$	−0.369507	−	0.310054i	−0.0265977	−	0.0223181i	0.629392	−	0.777088i	$-0.283304\pi$
$193$	−0.369507	−	0.310054i	−0.0265977	−	0.0223181i	−0.655990	+	0.754770i	$0.727748\pi$
$194$	−13.5385	+	1.66253i	−0.972005	+	0.119363i
$195$		0			0
$196$	0.924989	−	3.22621i	0.0660707	−	0.230444i
$197$	6.10771	+	10.5789i	0.435157	+	0.753713i	0.997308	−	0.0733207i	$-0.0233597\pi$
$197$	6.10771	+	10.5789i	0.435157	+	0.753713i	−0.562152	+	0.827034i	$0.690026\pi$
$198$		0			0
$199$	−11.7431	−	6.77986i	−0.832444	−	0.480612i	0.0222449	−	0.999753i	$-0.492919\pi$
$199$	−11.7431	−	6.77986i	−0.832444	−	0.480612i	−0.854689	+	0.519141i	$0.826252\pi$
$200$	8.76217	−	15.8092i	0.619579	−	1.11788i
$201$		0			0
$202$	−1.76336	−	2.33999i	−0.124070	−	0.164641i
$203$	−5.21605	−	14.3310i	−0.366095	−	1.00584i
$204$		0			0
$205$	−6.27628	+	1.10668i	−0.438355	+	0.0772937i
$206$	−1.76755	+	7.65665i	−0.123151	+	0.533464i
$207$		0			0
$208$	−0.332992	−	2.36826i	−0.0230888	−	0.164209i
$209$	−12.5021	−	14.8994i	−0.864788	−	1.03061i
$210$		0			0
$211$	−2.37424	+	13.4650i	−0.163449	+	0.926968i	0.787199	+	0.616699i	$0.211530\pi$
$211$	−2.37424	+	13.4650i	−0.163449	+	0.926968i	−0.950649	+	0.310269i	$0.899581\pi$
$212$	26.0180	+	2.73376i	1.78692	+	0.187755i
$213$		0			0
$214$	16.7380	+	0.876936i	1.14419	+	0.0599461i
$215$	−19.7317			−1.34569
$216$		0			0
$217$	2.14553			0.145648
$218$	−7.92074	−	0.414982i	−0.536460	−	0.0281061i
$219$		0			0
$220$	2.51609	−	23.9464i	0.169635	−	1.61446i
$221$	0.236923	−	1.34366i	0.0159372	−	0.0903842i
$222$		0			0
$223$	−3.52036	−	4.19541i	−0.235741	−	0.280945i	0.635184	−	0.772361i	$-0.280924\pi$
$223$	−3.52036	−	4.19541i	−0.235741	−	0.280945i	−0.870925	+	0.491415i	$0.836480\pi$
$224$	−15.1024	+	7.04385i	−1.00907	+	0.470637i
$225$		0			0
$226$	−0.405957	+	1.75852i	−0.0270039	+	0.116975i
$227$	−10.8215	+	1.90812i	−0.718247	+	0.126646i	−0.520814	−	0.853670i	$-0.674372\pi$
$227$	−10.8215	+	1.90812i	−0.718247	+	0.126646i	−0.197433	+	0.980316i	$0.563261\pi$
$228$		0			0
$229$	9.00757	+	24.7481i	0.595237	+	1.63540i	0.760640	+	0.649174i	$0.224885\pi$
$229$	9.00757	+	24.7481i	0.595237	+	1.63540i	−0.165403	+	0.986226i	$0.552892\pi$
$230$	25.0947	+	33.3006i	1.65469	+	2.19578i
$231$		0			0
$232$	−7.09833	+	12.8072i	−0.466028	+	0.840832i
$233$	8.32478	+	4.80631i	0.545374	+	0.314872i	0.747254	−	0.664538i	$-0.231372\pi$
$233$	8.32478	+	4.80631i	0.545374	+	0.314872i	−0.201880	+	0.979410i	$0.564705\pi$
$234$		0			0
$235$	8.53661	+	14.7858i	0.556867	+	0.964522i
$236$	13.7604	+	3.94525i	0.895725	+	0.256814i
$237$		0			0
$238$	−9.43613	+	1.15876i	−0.611653	+	0.0751115i
$239$	11.0157	+	9.24328i	0.712547	+	0.597898i	0.925313	−	0.379205i	$-0.123803\pi$
$239$	11.0157	+	9.24328i	0.712547	+	0.597898i	−0.212765	+	0.977103i	$0.568247\pi$
$240$		0			0
$241$	12.6743	+	4.61308i	0.816426	+	0.297155i	0.716276	−	0.697818i	$-0.245845\pi$
$241$	12.6743	+	4.61308i	0.816426	+	0.297155i	0.100150	+	0.994972i	$0.468068\pi$
$242$	−0.713131	−	2.33241i	−0.0458418	−	0.149933i
$243$		0			0
$244$	−9.99715	−	14.8204i	−0.640002	−	0.948777i
$245$	5.32199	+	1.93704i	0.340009	+	0.123753i
$246$		0			0
$247$	2.09547	−	2.49728i	0.133331	−	0.158898i
$248$	−1.35156	−	1.55464i	−0.0858240	−	0.0987196i
$249$		0			0
$250$	5.56603	+	3.61449i	0.352027	+	0.228601i
$251$	12.4670	−	7.19782i	0.786910	−	0.454323i	−0.0519636	−	0.998649i	$-0.516548\pi$
$251$	12.4670	−	7.19782i	0.786910	−	0.454323i	0.838874	+	0.544326i	$0.183215\pi$
$252$		0			0
$253$	26.9884	+	15.5817i	1.69674	+	0.979615i
$254$	−4.27290	−	8.38571i	−0.268106	−	0.526167i
$255$		0			0
$256$	14.6176	+	6.50592i	0.913597	+	0.406620i
$257$	−1.76587	−	4.85170i	−0.110152	−	0.302641i	0.872353	−	0.488877i	$-0.162593\pi$
$257$	−1.76587	−	4.85170i	−0.110152	−	0.302641i	−0.982505	+	0.186236i	$0.940371\pi$
$258$		0			0
$259$	0.249467	+	1.41480i	0.0155011	+	0.0879113i
$260$	4.02588	−	0.281647i	0.249675	−	0.0174670i
$261$		0			0
$262$	−17.1551	−	15.9969i	−1.05985	−	0.988291i
$263$	0.180828	−	0.151733i	0.0111503	−	0.00935624i	−0.637195	−	0.770702i	$-0.719906\pi$
$263$	0.180828	−	0.151733i	0.0111503	−	0.00935624i	0.648346	+	0.761346i	$0.275461\pi$
$264$		0			0
$265$	−7.66600	+	43.4761i	−0.470919	+	2.67071i
$266$	−20.9097	−	8.87527i	−1.28206	−	0.544177i
$267$		0			0
$268$	−5.76692	+	1.43805i	−0.352271	+	0.0878430i
$269$	18.1431			1.10620			0.553102	−	0.833114i	$-0.313444\pi$
$269$	18.1431			1.10620			0.553102	+	0.833114i	$0.313444\pi$
$270$		0			0
$271$		−	7.29313i		−	0.443026i	−0.975157	−	0.221513i	$-0.928900\pi$
$271$		−	7.29313i		−	0.443026i	0.975157	−	0.221513i	$-0.0710995\pi$
$272$	6.78383	+	6.10740i	0.411330	+	0.370316i
$273$		0			0
$274$	−24.4198	−	10.3651i	−1.47525	−	0.626181i
$275$	22.4495	+	3.95846i	1.35376	+	0.238704i
$276$		0			0
$277$	−8.65619	−	10.3160i	−0.520100	−	0.619831i	0.440505	−	0.897750i	$-0.354800\pi$
$277$	−8.65619	−	10.3160i	−0.520100	−	0.619831i	−0.960604	+	0.277920i	$0.910355\pi$
$278$	−0.741610	+	0.795305i	−0.0444788	+	0.0476992i
$279$		0			0
$280$	−10.0789	−	26.2526i	−0.602327	−	1.56889i
$281$	−8.48774	+	1.49662i	−0.506336	+	0.0892807i	−0.420980	−	0.907070i	$-0.638314\pi$
$281$	−8.48774	+	1.49662i	−0.506336	+	0.0892807i	−0.0853558	+	0.996351i	$0.527203\pi$
$282$		0			0
$283$	25.0099	−	9.10286i	1.48668	−	0.541109i	0.534110	−	0.845415i	$-0.320647\pi$
$283$	25.0099	−	9.10286i	1.48668	−	0.541109i	0.952574	+	0.304306i	$0.0984246\pi$
$284$	−3.94446	+	5.42945i	−0.234061	+	0.322179i
$285$		0			0
$286$	2.68742	−	1.36936i	0.158910	−	0.0809721i
$287$	−2.78139	+	4.81751i	−0.164180	+	0.284369i
$288$		0			0
$289$	−5.89623	−	10.2126i	−0.346837	−	0.600739i
$290$	−20.7233	−	13.4574i	−1.21692	−	0.790247i
$291$		0			0
$292$	9.09943	+	20.4359i	0.532504	+	1.19592i
$293$	5.26423	+	4.41721i	0.307540	+	0.258056i	0.783474	−	0.621424i	$-0.213446\pi$
$293$	5.26423	+	4.41721i	0.307540	+	0.258056i	−0.475935	+	0.879481i	$0.657890\pi$
$294$		0			0
$295$	−8.26186	+	22.6993i	−0.481024	+	1.32160i
$296$	0.868005	−	1.07200i	0.0504518	−	0.0623088i
$297$		0			0
$298$	1.24885	+	4.08458i	0.0723441	+	0.236613i
$299$	−1.78647	+	4.90828i	−0.103314	+	0.283853i
$300$		0			0
$301$	−11.0707	+	13.1935i	−0.638103	+	0.760462i
$302$	0.369912	+	3.01230i	0.0212861	+	0.173338i
$303$		0			0
$304$	6.74094	+	20.7420i	0.386619	+	1.18963i
$305$	26.1256	−	15.0836i	1.49595	−	0.863685i
$306$		0			0
$307$	2.12558	−	3.68162i	0.121314	−	0.210121i	−0.798972	−	0.601368i	$-0.794623\pi$
$307$	2.12558	−	3.68162i	0.121314	−	0.210121i	0.920286	+	0.391247i	$0.127956\pi$
$308$	−14.5999	−	15.1177i	−0.831908	−	0.861411i
$309$		0			0
$310$	2.77621	−	2.09209i	0.157678	−	0.118823i
$311$	−1.79911	+	0.654823i	−0.102018	+	0.0371316i	−0.392525	−	0.919741i	$-0.628398\pi$
$311$	−1.79911	+	0.654823i	−0.102018	+	0.0371316i	0.290507	+	0.956873i	$0.406176\pi$
$312$		0			0
$313$	3.78761	+	21.4806i	0.214088	+	1.21415i	0.882482	+	0.470347i	$0.155871\pi$
$313$	3.78761	+	21.4806i	0.214088	+	1.21415i	−0.668393	+	0.743808i	$0.733018\pi$
$314$	−2.48457	+	10.7627i	−0.140213	+	0.607372i
$315$		0			0
$316$	−14.8455	+	30.4403i	−0.835127	+	1.71240i
$317$	0.457251	−	0.383679i	0.0256818	−	0.0215496i	−0.629856	−	0.776712i	$-0.716886\pi$
$317$	0.457251	−	0.383679i	0.0256818	−	0.0215496i	0.655538	+	0.755162i	$0.272442\pi$
$318$		0			0
$319$	−18.1866	−	3.20679i	−1.01825	−	0.179546i
$320$	−12.6734	+	23.8406i	−0.708463	+	1.33273i
$321$		0			0
$322$	36.3459	+	1.90422i	2.02548	+	0.106118i
$323$			12.4425i			0.692322i
$324$		0			0
$325$			3.82080i			0.211940i
$326$	0.955280	−	18.2334i	0.0529081	−	1.00986i
$327$		0			0
$328$	5.24285	−	1.01937i	0.289488	−	0.0562852i
$329$	14.6760	+	2.58778i	0.809115	+	0.142669i
$330$		0			0
$331$	−3.25579	+	2.73193i	−0.178954	+	0.150161i	−0.727865	−	0.685721i	$-0.759487\pi$
$331$	−3.25579	+	2.73193i	−0.178954	+	0.150161i	0.548911	+	0.835881i	$0.315043\pi$
$332$	7.07242	−	14.5018i	0.388150	−	0.795889i
$333$		0			0
$334$	20.8675	+	4.81728i	1.14182	+	0.263590i
$335$	−1.74163	−	9.87725i	−0.0951552	−	0.539652i
$336$		0			0
$337$	4.55155	−	1.65663i	0.247939	−	0.0902424i	−0.215061	−	0.976601i	$-0.568995\pi$
$337$	4.55155	−	1.65663i	0.247939	−	0.0902424i	0.463000	+	0.886358i	$0.346773\pi$
$338$	−10.7602	−	14.2788i	−0.585279	−	0.776665i
$339$		0			0
$340$	−11.0800	+	10.7005i	−0.600895	+	0.580315i
$341$	1.29902	−	2.24997i	0.0703458	−	0.121842i
$342$		0			0
$343$	−13.5772	+	7.83879i	−0.733099	+	0.423255i
$344$	16.5338	−	0.289392i	0.891443	−	0.0156030i
$345$		0			0
$346$	−25.3597	+	3.11419i	−1.36334	+	0.167420i
$347$	13.5458	−	16.1432i	0.727176	−	0.866615i	−0.268131	−	0.963382i	$-0.586406\pi$
$347$	13.5458	−	16.1432i	0.727176	−	0.866615i	0.995307	+	0.0967678i	$0.0308504\pi$
$348$		0			0
$349$	−6.80166	+	18.6874i	−0.364084	+	1.00031i	0.613486	+	0.789705i	$0.289767\pi$
$349$	−6.80166	+	18.6874i	−0.364084	+	1.00031i	−0.977571	+	0.210608i	$0.932456\pi$
$350$	25.4598	−	7.78428i	1.36088	−	0.416087i
$351$		0			0
$352$	−1.75710	+	20.1023i	−0.0936538	+	1.07145i
$353$	−7.96814	+	21.8923i	−0.424101	+	1.16521i	0.525238	+	0.850955i	$0.323976\pi$
$353$	−7.96814	+	21.8923i	−0.424101	+	1.16521i	−0.949339	+	0.314253i	$0.898246\pi$
$354$		0			0
$355$	−8.67527	−	7.27942i	−0.460436	−	0.386351i
$356$	−28.1666	+	12.5417i	−1.49283	+	0.664706i
$357$		0			0
$358$	−5.21934	+	8.03736i	−0.275851	+	0.424788i
$359$	−5.84236	−	10.1193i	−0.308348	−	0.534075i	0.669653	−	0.742674i	$-0.266443\pi$
$359$	−5.84236	−	10.1193i	−0.308348	−	0.534075i	−0.978001	+	0.208599i	$0.933110\pi$
$360$		0			0
$361$	−5.36466	+	9.29186i	−0.282351	+	0.489045i
$362$	6.18111	+	12.1306i	0.324872	+	0.637571i
$363$		0			0
$364$	2.07044	−	2.84991i	0.108520	−	0.149376i
$365$	−35.4729	+	12.9111i	−1.85674	+	0.675797i
$366$		0			0
$367$	3.28119	−	0.578562i	0.171277	−	0.0302007i	−0.0873521	−	0.996178i	$-0.527841\pi$
$367$	3.28119	−	0.578562i	0.171277	−	0.0302007i	0.258629	+	0.965977i	$0.416729\pi$
$368$	−21.5160	−	27.5355i	−1.12160	−	1.43539i
$369$		0			0
$370$	1.70236	+	1.58742i	0.0885014	+	0.0825262i
$371$	24.7689	+	29.5185i	1.28594	+	1.53252i
$372$		0			0
$373$	−34.7339	−	6.12453i	−1.79845	−	0.317116i	−0.828425	−	0.560101i	$-0.810762\pi$
$373$	−34.7339	−	6.12453i	−1.79845	−	0.317116i	−0.970030	+	0.242985i	$0.921874\pi$
$374$	−4.49796	+	10.5970i	−0.232584	+	0.547958i
$375$		0			0
$376$	−7.36993	−	12.2643i	−0.380075	−	0.632483i
$377$		−	3.09527i		−	0.159414i
$378$		0			0
$379$	15.7785			0.810486			0.405243	−	0.914209i	$-0.367187\pi$
$379$	15.7785			0.810486			0.405243	+	0.914209i	$0.367187\pi$
$380$	−35.7103	+	8.90480i	−1.83190	+	0.456807i
$381$		0			0
$382$	0.551955	−	1.30038i	0.0282405	−	0.0665333i
$383$	−1.89462	+	10.7449i	−0.0968106	+	0.549040i	0.897367	+	0.441285i	$0.145477\pi$
$383$	−1.89462	+	10.7449i	−0.0968106	+	0.549040i	−0.994177	+	0.107755i	$0.965634\pi$
$384$		0			0
$385$	27.1681	−	22.7968i	1.38462	−	1.16183i
$386$	−0.465222	+	0.498905i	−0.0236792	+	0.0253936i
$387$		0			0
$388$	1.34622	+	19.2431i	0.0683442	+	0.976919i
$389$	4.60469	+	26.1145i	0.233467	+	1.32406i	0.845818	+	0.533471i	$0.179113\pi$
$389$	4.60469	+	26.1145i	0.233467	+	1.32406i	−0.612352	+	0.790586i	$0.709776\pi$
$390$		0			0
$391$	−6.81854	−	18.7338i	−0.344828	−	0.947408i
$392$	−4.48786	−	1.54505i	−0.226671	−	0.0780370i
$393$		0			0
$394$	15.3922	−	7.84303i	0.775449	−	0.395126i
$395$	−49.4942	−	28.5755i	−2.49032	−	1.43779i
$396$		0			0
$397$	21.7835	−	12.5767i	1.09328	−	0.631208i	0.158835	−	0.987305i	$-0.449226\pi$
$397$	21.7835	−	12.5767i	1.09328	−	0.631208i	0.934449	+	0.356098i	$0.115893\pi$
$398$	−10.4439	+	16.0828i	−0.523507	+	0.806158i
$399$		0			0
$400$	−21.6786	−	13.5444i	−1.08393	−	0.677218i
$401$	−13.8988	+	16.5639i	−0.694071	+	0.827162i	−0.991842	−	0.127475i	$-0.959313\pi$
$401$	−13.8988	+	16.5639i	−0.694071	+	0.827162i	0.297770	+	0.954638i	$0.403757\pi$
$402$		0			0
$403$	0.409194	+	0.148934i	0.0203834	+	0.00741895i
$404$	−3.43518	+	2.31722i	−0.170907	+	0.115286i
$405$		0			0
$406$	−20.6252	+	6.30613i	−1.02361	+	0.312968i
$407$	1.63471	+	0.594984i	0.0810293	+	0.0294923i
$408$		0			0
$409$	11.4354	+	9.59540i	0.565442	+	0.474462i	0.880130	−	0.474733i	$-0.157455\pi$
$409$	11.4354	+	9.59540i	0.565442	+	0.474462i	−0.314688	+	0.949195i	$0.601900\pi$
$410$	1.09854	+	8.94573i	0.0542532	+	0.441798i
$411$		0			0
$412$	10.6825	+	3.06280i	0.526290	+	0.150893i
$413$	10.5424	+	18.2599i	0.518755	+	0.898510i
$414$		0			0
$415$	23.5791	+	13.6134i	1.15745	+	0.668254i
$416$	−3.36928	+	0.295045i	−0.165192	+	0.0144658i
$417$		0			0
$418$	−21.9671	+	16.5540i	−1.07445	+	0.809681i
$419$	5.14629	+	14.1393i	0.251413	+	0.690751i	0.999627	+	0.0272945i	$0.00868919\pi$
$419$	5.14629	+	14.1393i	0.251413	+	0.690751i	−0.748214	+	0.663457i	$0.769089\pi$
$420$		0			0
$421$	5.74293	−	1.01263i	0.279893	−	0.0493527i	−0.0319393	−	0.999490i	$-0.510168\pi$
$421$	5.74293	−	1.01263i	0.279893	−	0.0493527i	0.311832	+	0.950137i	$0.399057\pi$
$422$	18.8406	+	4.34938i	0.917147	+	0.211725i
$423$		0			0
$424$	5.78594	−	36.5423i	0.280990	−	1.77465i
$425$	−9.37384	−	11.1713i	−0.454698	−	0.541888i
$426$		0			0
$427$	4.57243	−	25.9315i	0.221275	−	1.25491i
$428$	2.47695	−	23.5739i	0.119728	−	1.13949i
$429$		0			0
$430$	−1.45998	+	27.8667i	−0.0704067	+	1.34385i
$431$	−2.52134			−0.121449			−0.0607244	−	0.998155i	$-0.519341\pi$
$431$	−2.52134			−0.121449			−0.0607244	+	0.998155i	$0.519341\pi$
$432$		0			0
$433$	−32.6249			−1.56785			−0.783927	−	0.620854i	$-0.786786\pi$
$433$	−32.6249			−1.56785			−0.783927	+	0.620854i	$0.786786\pi$
$434$	0.158751	−	3.03008i	0.00762031	−	0.145449i
$435$		0			0
$436$	−1.17214	+	11.1556i	−0.0561352	+	0.534255i
$437$	8.27153	−	46.9102i	0.395681	−	2.24402i
$438$		0			0
$439$	6.25287	+	7.45188i	0.298433	+	0.355659i	0.894335	−	0.447399i	$-0.147650\pi$
$439$	6.25287	+	7.45188i	0.298433	+	0.355659i	−0.595901	+	0.803058i	$0.703205\pi$
$440$	−33.6327	−	5.32524i	−1.60338	−	0.253871i
$441$		0			0
$442$	−1.88009	−	0.434020i	−0.0894266	−	0.0206442i
$443$	17.6810	−	3.11764i	0.840050	−	0.148123i	0.262963	−	0.964806i	$-0.415300\pi$
$443$	17.6810	−	3.11764i	0.840050	−	0.148123i	0.577087	+	0.816683i	$0.304189\pi$
$444$		0			0
$445$	−17.7952	−	48.8919i	−0.843574	−	2.31770i
$446$	−6.18555	+	4.66130i	−0.292894	+	0.220719i
$447$		0			0
$448$	8.83041	+	21.8500i	0.417197	+	1.03232i
$449$	5.44960	+	3.14633i	0.257182	+	0.148484i	0.623049	−	0.782183i	$-0.285894\pi$
$449$	5.44960	+	3.14633i	0.257182	+	0.148484i	−0.365866	+	0.930667i	$0.619227\pi$
$450$		0			0
$451$	3.36801	+	5.83356i	0.158593	+	0.274691i
$452$	2.45348	+	0.703439i	0.115402	+	0.0330870i
$453$		0			0
$454$	1.89409	+	15.4241i	0.0888942	+	0.723890i
$455$	4.55363	+	3.82095i	0.213477	+	0.179129i
$456$		0			0
$457$	−26.0970	−	9.49851i	−1.22076	−	0.444322i	−0.350339	−	0.936623i	$-0.613934\pi$
$457$	−26.0970	−	9.49851i	−1.22076	−	0.444322i	−0.870425	+	0.492301i	$0.836156\pi$
$458$	35.6176	−	10.8900i	1.66430	−	0.508858i
$459$		0			0
$460$	48.8865	−	32.9766i	2.27934	−	1.53754i
$461$	−31.8699	−	11.5997i	−1.48433	−	0.540251i	−0.532379	−	0.846506i	$-0.678702\pi$
$461$	−31.8699	−	11.5997i	−1.48433	−	0.540251i	−0.951950	+	0.306255i	$0.900924\pi$
$462$		0			0
$463$	24.5141	−	29.2148i	1.13927	−	1.35773i	0.214712	−	0.976677i	$-0.431119\pi$
$463$	24.5141	−	29.2148i	1.13927	−	1.35773i	0.924555	−	0.381049i	$-0.124437\pi$
$464$	17.5621	+	10.9724i	0.815298	+	0.509382i
$465$		0			0
$466$	7.40381	−	11.4013i	0.342975	−	0.528153i
$467$	13.7803	−	7.95604i	0.637674	−	0.368161i	−0.146044	−	0.989278i	$-0.546654\pi$
$467$	13.7803	−	7.95604i	0.637674	−	0.368161i	0.783718	+	0.621117i	$0.213321\pi$
$468$		0			0
$469$	−7.58152	−	4.37719i	−0.350082	−	0.202120i
$470$	21.5133	−	10.9620i	0.992336	−	0.505641i
$471$		0			0
$472$	6.58994	−	19.1416i	0.303327	−	0.881062i
$473$	7.13294	+	19.5976i	0.327973	+	0.901099i
$474$		0			0
$475$	−6.05057	−	34.3145i	−0.277619	−	1.57446i
$476$	0.938300	+	13.4122i	0.0430069	+	0.614745i
$477$		0			0
$478$	13.8691	−	14.8733i	0.634360	−	0.680289i
$479$	9.67464	−	8.11798i	0.442045	−	0.370920i	−0.394429	−	0.918927i	$-0.629058\pi$
$479$	9.67464	−	8.11798i	0.442045	−	0.370920i	0.836474	+	0.548006i	$0.184613\pi$
$480$		0			0
$481$	−0.0506316	+	0.287146i	−0.00230860	+	0.0130927i
$482$	7.45274	−	17.5583i	0.339463	−	0.799761i
$483$		0			0
$484$	−3.34678	+	0.834560i	−0.152126	+	0.0379345i
$485$	−32.5518			−1.47810
$486$		0			0
$487$			0.979490i			0.0443849i	0.999754	+	0.0221925i	$0.00706466\pi$
$487$			0.979490i			0.0443849i	−0.999754	+	0.0221925i	$0.992935\pi$
$488$	−21.6702	+	13.0222i	−0.980962	+	0.589486i
$489$		0			0
$490$	3.12943	−	7.37279i	0.141373	−	0.333069i
$491$	2.99103	+	0.527400i	0.134983	+	0.0238012i	0.240732	−	0.970592i	$-0.422613\pi$
$491$	2.99103	+	0.527400i	0.134983	+	0.0238012i	−0.105748	+	0.994393i	$0.533724\pi$
$492$		0			0
$493$	7.59385	+	9.04999i	0.342010	+	0.407591i
$494$	−3.37180	−	3.14415i	−0.151705	−	0.141462i
$495$		0			0
$496$	−2.29558	+	1.79374i	−0.103075	+	0.0805414i
$497$	−9.73469	+	1.71649i	−0.436660	+	0.0769950i
$498$		0			0
$499$	−11.5067	+	4.18808i	−0.515109	+	0.187484i	−0.586477	−	0.809966i	$-0.699486\pi$
$499$	−11.5067	+	4.18808i	−0.515109	+	0.187484i	0.0713684	+	0.997450i	$0.477263\pi$
$500$	5.51651	−	7.59333i	0.246706	−	0.339584i
$501$		0			0
$502$	−9.24287	−	18.1394i	−0.412529	−	0.809602i
$503$	18.8493	−	32.6480i	0.840450	−	1.45570i	−0.0490653	−	0.998796i	$-0.515624\pi$
$503$	18.8493	−	32.6480i	0.840450	−	1.45570i	0.889515	−	0.456906i	$-0.151042\pi$
$504$		0			0
$505$	−3.49620	−	6.05559i	−0.155579	−	0.269470i
$506$	24.0026	−	36.9621i	1.06705	−	1.64317i
$507$		0			0
$508$	−12.1591	+	5.41405i	−0.539473	+	0.240210i
$509$	−5.48541	−	4.60281i	−0.243137	−	0.204016i	0.513074	−	0.858345i	$-0.328507\pi$
$509$	−5.48541	−	4.60281i	−0.243137	−	0.204016i	−0.756210	+	0.654329i	$0.772951\pi$
$510$		0			0
$511$	−11.2695	+	30.9626i	−0.498532	+	1.36971i
$512$	10.2697	−	20.1627i	0.453862	−	0.891072i
$513$		0			0
$514$	−6.98260	+	2.13492i	−0.307989	+	0.0941672i
$515$	−6.41388	+	17.6220i	−0.282630	+	0.776518i
$516$		0			0
$517$	11.5994	−	13.8236i	0.510140	−	0.607961i
$518$	2.01655	−	0.247633i	0.0886020	−	0.0108804i
$519$		0			0
$520$	−0.0998810	−	5.70650i	−0.00438007	−	0.250247i
$521$	−11.2996	+	6.52385i	−0.495046	+	0.285815i	−0.726665	−	0.686992i	$-0.758931\pi$
$521$	−11.2996	+	6.52385i	−0.495046	+	0.285815i	0.231619	+	0.972806i	$0.425598\pi$
$522$		0			0
$523$	9.72356	−	16.8417i	0.425181	−	0.736436i	−0.571256	−	0.820772i	$-0.693544\pi$
$523$	9.72356	−	16.8417i	0.425181	−	0.736436i	0.996437	+	0.0843361i	$0.0268769\pi$
$524$	−23.8614	+	23.0441i	−1.04239	+	1.00669i
$525$		0			0
$526$	−0.200909	−	0.266606i	−0.00876004	−	0.0116246i
$527$	−1.56180	+	0.568448i	−0.0680330	+	0.0247620i
$528$		0			0
$529$	9.25917	+	52.5113i	0.402572	+	2.28310i
$530$	60.8330	+	14.0434i	2.64242	+	0.610006i
$531$		0			0
$532$	−14.0815	+	28.8736i	−0.610509	+	1.25183i
$533$	−0.864878	+	0.725718i	−0.0374620	+	0.0314344i
$534$		0			0
$535$	39.3919	+	6.94586i	1.70306	+	0.300296i
$536$	1.60422	+	8.25090i	0.0692918	+	0.356384i
$537$		0			0
$538$	1.34244	−	25.6231i	0.0578766	−	1.10469i
$539$		−	5.98604i		−	0.257837i
$540$		0			0
$541$		−	8.91838i		−	0.383431i	−0.981451	−	0.191716i	$-0.938595\pi$
$541$		−	8.91838i		−	0.383431i	0.981451	−	0.191716i	$-0.0614051\pi$
$542$	−10.2999	−	0.539631i	−0.442419	−	0.0231791i
$543$		0			0
$544$	9.12729	−	9.12875i	0.391329	−	0.391392i
$545$	−18.6410	−	3.28691i	−0.798491	−	0.140796i
$546$		0			0
$547$	−10.8502	+	9.10444i	−0.463923	+	0.389278i	−0.844572	−	0.535442i	$-0.820145\pi$
$547$	−10.8502	+	9.10444i	−0.463923	+	0.389278i	0.380649	+	0.924720i	$0.375701\pi$
$548$	−16.4453	+	33.7206i	−0.702508	+	1.44047i
$549$		0			0
$550$	7.25152	−	31.4121i	0.309206	−	1.33941i
$551$	4.90163	+	27.7985i	0.208816	+	1.18426i
$552$		0			0
$553$	−46.8760	+	17.0615i	−1.99337	+	0.725527i
$554$	−15.2096	+	11.4616i	−0.646194	+	0.486958i
$555$		0			0
$556$	1.06832	+	1.10620i	0.0453067	+	0.0469135i
$557$	14.2671	−	24.7114i	0.604517	−	1.04705i	−0.387611	−	0.921823i	$-0.626700\pi$
$557$	14.2671	−	24.7114i	0.604517	−	1.04705i	0.992128	−	0.125231i	$-0.0399671\pi$
$558$		0			0
$559$	−3.02723	+	1.74777i	−0.128038	+	0.0739229i
$560$	−37.8217	+	12.2917i	−1.59826	+	0.519418i
$561$		0			0
$562$	1.48562	+	12.0978i	0.0626669	+	0.510314i
$563$	−3.67507	+	4.37978i	−0.154886	+	0.184586i	−0.837907	−	0.545813i	$-0.816221\pi$
$563$	−3.67507	+	4.37978i	−0.154886	+	0.184586i	0.683022	+	0.730398i	$0.260666\pi$
$564$		0			0
$565$	−1.47309	+	4.04728i	−0.0619734	+	0.170271i
$566$	−11.0052	−	35.9944i	−0.462584	−	1.51296i
$567$		0			0
$568$	7.37603	+	5.97241i	0.309491	+	0.250597i
$569$	11.0377	−	30.3258i	0.462723	−	1.27132i	−0.460706	−	0.887553i	$-0.652404\pi$
$569$	11.0377	−	30.3258i	0.462723	−	1.27132i	0.923429	−	0.383769i	$-0.125374\pi$
$570$		0			0
$571$	−3.60436	−	3.02442i	−0.150838	−	0.126568i	0.564246	−	0.825607i	$-0.309167\pi$
$571$	−3.60436	−	3.02442i	−0.150838	−	0.126568i	−0.715084	+	0.699039i	$0.753611\pi$
$572$	−1.73507	−	3.89670i	−0.0725470	−	0.162929i
$573$		0			0
$574$	6.59786	+	4.28455i	0.275389	+	0.178834i
$575$	27.9143	+	48.3489i	1.16411	+	2.01629i
$576$		0			0
$577$	−5.60346	+	9.70547i	−0.233275	+	0.404044i	−0.958770	−	0.284183i	$-0.908278\pi$
$577$	−5.60346	+	9.70547i	−0.233275	+	0.404044i	0.725495	+	0.688227i	$0.241611\pi$
$578$	−14.8592	+	7.57146i	−0.618063	+	0.314931i
$579$		0			0
$580$	−20.5389	+	28.2713i	−0.852833	+	1.17390i
$581$	22.3318	−	8.12809i	0.926477	−	0.337210i
$582$		0			0
$583$	45.9517	−	8.10253i	1.90313	−	0.335573i
$584$	29.5344	−	11.3388i	1.22214	−	0.469204i
$585$		0			0
$586$	6.62784	−	7.10771i	0.273793	−	0.293617i
$587$	−24.7159	−	29.4553i	−1.02013	−	1.21575i	−0.976235	−	0.216713i	$-0.930466\pi$
$587$	−24.7159	−	29.4553i	−1.02013	−	1.21575i	−0.0438990	−	0.999036i	$-0.513978\pi$
$588$		0			0
$589$	−3.91081	−	0.689581i	−0.161142	−	0.0284137i
$590$	31.4464	+	13.3476i	1.29463	+	0.549512i
$591$		0			0
$592$	−1.44974	−	1.30518i	−0.0595839	−	0.0536427i
$593$		−	13.0127i		−	0.534370i	−0.963645	−	0.267185i	$-0.913907\pi$
$593$		−	13.0127i		−	0.534370i	0.963645	−	0.267185i	$-0.0860934\pi$
$594$		0			0
$595$	−22.6882			−0.930125
$596$	5.86096	−	1.46150i	0.240074	−	0.0598654i
$597$		0			0
$598$	6.79967	+	2.88616i	0.278059	+	0.118024i
$599$	−1.26632	+	7.18164i	−0.0517403	+	0.293434i	−0.999688	−	0.0249933i	$-0.992044\pi$
$599$	−1.26632	+	7.18164i	−0.0517403	+	0.293434i	0.947947	+	0.318427i	$0.103155\pi$
$600$		0			0
$601$	24.0699	−	20.1971i	0.981833	−	0.823856i	−0.00253165	−	0.999997i	$-0.500806\pi$
$601$	24.0699	−	20.1971i	0.981833	−	0.823856i	0.984365	+	0.176141i	$0.0563614\pi$
$602$	17.8138	+	16.6111i	0.726035	+	0.677017i
$603$		0			0
$604$	4.28157	−	0.299534i	0.174214	−	0.0121879i
$605$	−1.01074	−	5.73217i	−0.0410923	−	0.233046i
$606$		0			0
$607$	9.22172	+	25.3365i	0.374298	+	1.02838i	0.973681	+	0.227913i	$0.0731903\pi$
$607$	9.22172	+	25.3365i	0.374298	+	1.02838i	−0.599383	+	0.800462i	$0.704588\pi$
$608$	29.7922	−	7.98534i	1.20823	−	0.323848i
$609$		0			0
$610$	−19.3691	−	38.0126i	−0.784234	−	1.53908i
$611$	2.61936	+	1.51229i	0.105968	+	0.0611807i
$612$		0			0
$613$	3.01282	−	1.73945i	0.121687	−	0.0702559i	−0.437921	−	0.899013i	$-0.644285\pi$
$613$	3.01282	−	1.73945i	0.121687	−	0.0702559i	0.559608	+	0.828758i	$0.310952\pi$
$614$	−5.04219	−	3.27432i	−0.203486	−	0.132141i
$615$		0			0
$616$	−22.4306	+	19.5005i	−0.903756	+	0.785699i
$617$	−23.1805	+	27.6254i	−0.933210	+	1.11216i	0.0602731	+	0.998182i	$0.480803\pi$
$617$	−23.1805	+	27.6254i	−0.933210	+	1.11216i	−0.993484	+	0.113975i	$0.963642\pi$
$618$		0			0
$619$	20.9325	+	7.61881i	0.841349	+	0.306226i	0.726508	−	0.687158i	$-0.241142\pi$
$619$	20.9325	+	7.61881i	0.841349	+	0.306226i	0.114841	+	0.993384i	$0.463364\pi$
$620$	−2.74920	−	4.07557i	−0.110410	−	0.163679i
$621$		0			0
$622$	0.791672	+	2.58929i	0.0317432	+	0.103821i
$623$	−42.6755	−	15.5326i	−1.70976	−	0.622301i
$624$		0			0
$625$	−12.3442	−	10.3580i	−0.493768	−	0.414320i
$626$	30.6168	−	3.75977i	1.22369	−	0.150270i
$627$		0			0
$628$	15.0160	+	4.30525i	0.599204	+	0.171798i
$629$	−0.556439	−	0.963781i	−0.0221867	−	0.0384285i
$630$		0			0
$631$	−8.28573	−	4.78377i	−0.329850	−	0.190439i	0.325925	−	0.945396i	$-0.394324\pi$
$631$	−8.28573	−	4.78377i	−0.329850	−	0.190439i	−0.655774	+	0.754957i	$0.727658\pi$
$632$	41.8917	+	23.2183i	1.66636	+	0.923576i
$633$		0			0
$634$	−0.508028	−	0.674154i	−0.0201764	−	0.0267741i
$635$	−7.68193	−	21.1059i	−0.304848	−	0.837563i
$636$		0			0
$637$	0.988073	−	0.174224i	0.0391489	−	0.00690300i
$638$	−5.87453	+	25.4472i	−0.232575	+	1.00747i
$639$		0			0
$640$	32.7319	+	19.6623i	1.29384	+	0.777221i
$641$	−1.06709	−	1.27171i	−0.0421477	−	0.0502297i	0.744559	−	0.667557i	$-0.232660\pi$
$641$	−1.06709	−	1.27171i	−0.0421477	−	0.0502297i	−0.786706	+	0.617327i	$0.788215\pi$
$642$		0			0
$643$	5.71286	−	32.3993i	0.225293	−	1.27770i	−0.636830	−	0.771004i	$-0.719755\pi$
$643$	5.71286	−	32.3993i	0.225293	−	1.27770i	0.862124	−	0.506698i	$-0.169134\pi$
$644$	5.37858	−	51.1895i	0.211946	−	2.01715i
$645$		0			0
$646$	17.5723	+	0.920644i	0.691373	+	0.0362223i
$647$	25.6189			1.00718			0.503592	−	0.863942i	$-0.332012\pi$
$647$	25.6189			1.00718			0.503592	+	0.863942i	$0.332012\pi$
$648$		0			0
$649$	25.5316			1.00220
$650$	5.39602	+	0.282707i	0.211649	+	0.0110887i
$651$		0			0
$652$	−25.6799	−	2.69824i	−1.00570	−	0.105671i
$653$	−7.68220	+	43.5679i	−0.300628	+	1.70495i	0.342775	+	0.939417i	$0.388633\pi$
$653$	−7.68220	+	43.5679i	−0.300628	+	1.70495i	−0.643403	+	0.765528i	$0.722478\pi$
$654$		0			0
$655$	−35.9818	−	42.8815i	−1.40593	−	1.67552i
$656$	−1.05170	−	7.47978i	−0.0410621	−	0.292036i
$657$		0			0
$658$	4.74056	−	20.5351i	0.184806	−	0.800542i
$659$	28.0225	−	4.94113i	1.09160	−	0.192479i	0.401262	−	0.915963i	$-0.368572\pi$
$659$	28.0225	−	4.94113i	1.09160	−	0.192479i	0.690341	+	0.723484i	$0.257461\pi$
$660$		0			0
$661$	10.5767	+	29.0592i	0.411385	+	1.13027i	0.956455	+	0.291881i	$0.0942811\pi$
$661$	10.5767	+	29.0592i	0.411385	+	1.13027i	−0.545069	+	0.838391i	$0.683497\pi$
$662$	3.61734	+	4.80022i	0.140592	+	0.186566i
$663$		0			0
$664$	−19.9572	−	11.0612i	−0.774491	−	0.429259i
$665$	−46.9468	−	27.1048i	−1.82052	−	1.05108i
$666$		0			0
$667$	−22.6137	−	39.1680i	−0.875604	−	1.51659i
$668$	8.34736	−	29.1142i	0.322969	−	1.12646i
$669$		0			0
$670$	−14.0783	+	1.72882i	−0.543891	+	0.0667903i
$671$	−24.4253	−	20.4953i	−0.942930	−	0.791212i
$672$		0			0
$673$	−5.42191	−	1.97341i	−0.208999	−	0.0760695i	0.235399	−	0.971899i	$-0.424360\pi$
$673$	−5.42191	−	1.97341i	−0.208999	−	0.0760695i	−0.444398	+	0.895829i	$0.646583\pi$
$674$	−2.00284	−	6.55063i	−0.0771466	−	0.252321i
$675$		0			0
$676$	−20.9618	+	14.1399i	−0.806223	+	0.543842i
$677$	38.0136	+	13.8358i	1.46098	+	0.531754i	0.945635	−	0.325229i	$-0.105441\pi$
$677$	38.0136	+	13.8358i	1.46098	+	0.531754i	0.515346	+	0.856982i	$0.327664\pi$
$678$		0			0
$679$	−18.2635	+	21.7656i	−0.700889	+	0.835287i
$680$	14.2922	+	16.4397i	0.548081	+	0.630434i
$681$		0			0
$682$	−3.08146	−	2.00105i	−0.117995	−	0.0766242i
$683$	6.34298	−	3.66212i	0.242707	−	0.140127i	−0.373713	−	0.927544i	$-0.621916\pi$
$683$	6.34298	−	3.66212i	0.242707	−	0.140127i	0.616420	+	0.787417i	$0.288582\pi$
$684$		0			0
$685$	−54.8277	−	31.6548i	−2.09486	−	1.20947i
$686$	10.0659	+	19.7548i	0.384320	+	0.754240i
$687$		0			0
$688$	0.814663	−	23.3717i	0.0310587	−	0.891039i
$689$	2.67485	+	7.34910i	0.101904	+	0.279978i
$690$		0			0
$691$	−4.43476	−	25.1508i	−0.168706	−	0.956781i	−0.945160	−	0.326607i	$-0.894095\pi$
$691$	−4.43476	−	25.1508i	−0.168706	−	0.956781i	0.776454	−	0.630174i	$-0.217016\pi$
$692$	2.52169	+	36.0453i	0.0958603	+	1.37024i
$693$		0			0
$694$	−21.7965	−	20.3249i	−0.827382	−	0.771521i
$695$	−1.98797	+	1.66810i	−0.0754079	+	0.0632748i
$696$		0			0
$697$	0.748285	−	4.24373i	0.0283433	−	0.160743i
$698$	25.8885	+	10.9885i	0.979894	+	0.415922i
$699$		0			0
$700$	−9.10975	−	36.5322i	−0.344316	−	1.38079i
$701$	19.0555			0.719715			0.359857	−	0.933007i	$-0.382825\pi$
$701$	19.0555			0.719715			0.359857	+	0.933007i	$0.382825\pi$
$702$		0			0
$703$		−	2.65903i		−	0.100287i
$704$	28.2599	+	3.96891i	1.06509	+	0.149584i
$705$		0			0
$706$	30.3284	+	12.8731i	1.14142	+	0.484484i
$707$	−6.01061	−	1.05983i	−0.226052	−	0.0398591i
$708$		0			0
$709$	20.4893	+	24.4183i	0.769494	+	0.917047i	0.998408	−	0.0563997i	$-0.0179621\pi$
$709$	20.4893	+	24.4183i	0.769494	+	0.917047i	−0.228915	+	0.973447i	$0.573518\pi$
$710$	−10.9225	+	11.7133i	−0.409912	+	0.439591i
$711$		0			0
$712$	15.6282	+	40.7070i	0.585691	+	1.52556i
$713$	6.26610	−	1.10488i	0.234667	−	0.0413782i
$714$		0			0
$715$	6.76394	−	2.46187i	0.252957	−	0.0920689i
$716$	10.9648	+	7.96585i	0.409773	+	0.297698i
$717$		0			0
$718$	−14.7235	+	7.50229i	−0.549476	+	0.279983i
$719$	16.9767	−	29.4045i	0.633124	−	1.09660i	−0.353785	−	0.935327i	$-0.615106\pi$
$719$	16.9767	−	29.4045i	0.633124	−	1.09660i	0.986909	−	0.161277i	$-0.0515611\pi$
$720$		0			0
$721$	8.18429	+	14.1756i	0.304799	+	0.527927i
$722$	12.7257	+	8.26390i	0.473603	+	0.307551i
$723$		0			0
$724$	17.5891	−	7.83187i	0.653695	−	0.291069i
$725$	−25.3434	−	21.2656i	−0.941230	−	0.789786i
$726$		0			0
$727$	17.7280	−	48.7074i	0.657497	−	1.80646i	0.0695178	−	0.997581i	$-0.477854\pi$
$727$	17.7280	−	48.7074i	0.657497	−	1.80646i	0.587979	−	0.808876i	$-0.299924\pi$
$728$	−3.87166	−	3.13490i	−0.143493	−	0.116187i
$729$		0			0
$730$	15.6093	+	51.0528i	0.577727	+	1.88955i
$731$	4.56313	−	12.5371i	0.168773	−	0.463701i
$732$		0			0
$733$	2.97953	−	3.55086i	0.110051	−	0.131154i	−0.708207	−	0.706005i	$-0.750496\pi$
$733$	2.97953	−	3.55086i	0.110051	−	0.131154i	0.818258	+	0.574851i	$0.194940\pi$
$734$	−0.574309	−	4.67675i	−0.0211981	−	0.172622i
$735$		0			0
$736$	−40.4798	+	28.3491i	−1.49211	+	1.04496i
$737$	−9.18051	+	5.30037i	−0.338168	+	0.195242i
$738$		0			0
$739$	−25.0295	+	43.3524i	−0.920726	+	1.59474i	−0.122430	+	0.992477i	$0.539069\pi$
$739$	−25.0295	+	43.3524i	−0.920726	+	1.59474i	−0.798295	+	0.602266i	$0.794264\pi$
$740$	2.36784	−	2.28674i	0.0870436	−	0.0840624i
$741$		0			0
$742$	43.5210	−	32.7965i	1.59770	−	1.20400i
$743$	−11.2170	+	4.08266i	−0.411512	+	0.149778i	−0.539477	−	0.842000i	$-0.681378\pi$
$743$	−11.2170	+	4.08266i	−0.411512	+	0.149778i	0.127964	+	0.991779i	$0.459156\pi$
$744$		0			0
$745$	1.77002	+	10.0383i	0.0648487	+	0.367775i
$746$	−11.2195	+	48.6008i	−0.410777	+	1.77940i
$747$		0			0
$748$	14.6331	+	7.13646i	0.535039	+	0.260935i
$749$	26.7455	−	22.4422i	0.977260	−	0.820019i
$750$		0			0
$751$	−19.4858	−	3.43587i	−0.711046	−	0.125377i	−0.193585	−	0.981083i	$-0.562012\pi$
$751$	−19.4858	−	3.43587i	−0.711046	−	0.125377i	−0.517461	+	0.855707i	$0.673123\pi$
$752$	−17.8659	+	9.50093i	−0.651502	+	0.346463i
$753$		0			0
$754$	−4.37137	−	0.229024i	−0.159196	−	0.00834056i
$755$			7.24276i			0.263591i
$756$		0			0
$757$			16.3318i			0.593590i	0.954941	+	0.296795i	$0.0959178\pi$
$757$			16.3318i			0.593590i	−0.954941	+	0.296795i	$0.904082\pi$
$758$	1.16748	−	22.2836i	0.0424046	−	0.809376i
$759$		0			0
$760$	9.93378	+	51.0918i	0.360336	+	1.85329i
$761$	−40.2204	−	7.09194i	−1.45799	−	0.257082i	−0.612242	−	0.790670i	$-0.709732\pi$
$761$	−40.2204	−	7.09194i	−1.45799	−	0.257082i	−0.845745	+	0.533588i	$0.820843\pi$
$762$		0			0
$763$	−12.6565	+	10.6200i	−0.458195	+	0.384471i
$764$	−1.79566	−	0.875730i	−0.0649647	−	0.0316828i
$765$		0			0
$766$	15.0346	+	3.47076i	0.543223	+	0.125404i
$767$	0.743098	+	4.21432i	0.0268317	+	0.152170i
$768$		0			0
$769$	23.2382	−	8.45800i	0.837989	−	0.305003i	0.112856	−	0.993611i	$-0.464000\pi$
$769$	23.2382	−	8.45800i	0.837989	−	0.305003i	0.725134	+	0.688608i	$0.241778\pi$
$770$	−30.1851	−	40.0557i	−1.08780	−	1.44351i
$771$		0			0
$772$	0.670170	+	0.693937i	0.0241199	+	0.0249753i
$773$	9.22148	−	15.9721i	0.331674	−	0.574475i	−0.651167	−	0.758935i	$-0.725720\pi$
$773$	9.22148	−	15.9721i	0.331674	−	0.574475i	0.982840	+	0.184459i	$0.0590534\pi$
$774$		0			0
$775$	4.03076	−	2.32716i	0.144789	−	0.0835940i
$776$	27.2761	−	0.477415i	0.979156	−	0.0171382i
$777$		0			0
$778$	37.2216	−	4.57084i	1.33446	−	0.163872i
$779$	6.61820	−	7.88727i	0.237122	−	0.282591i
$780$		0			0
$781$	−4.09386	+	11.2478i	−0.146490	+	0.402477i
$782$	−26.9618	+	8.24352i	−0.964152	+	0.294788i
$783$		0			0
$784$	−2.51411	+	6.22378i	−0.0897895	+	0.222278i
$785$	−9.01574	+	24.7705i	−0.321786	+	0.884099i
$786$		0			0
$787$	−25.2598	−	21.1955i	−0.900415	−	0.755538i	0.0698563	−	0.997557i	$-0.477746\pi$
$787$	−25.2598	−	21.1955i	−0.900415	−	0.755538i	−0.970272	+	0.242019i	$0.922190\pi$
$788$	−9.93764	−	22.3184i	−0.354014	−	0.795059i
$789$		0			0
$790$	−44.0186	+	67.7851i	−1.56611	+	2.41169i
$791$	1.87970	+	3.25574i	0.0668345	+	0.115761i
$792$		0			0
$793$	2.67211	−	4.62823i	0.0948895	−	0.164353i
$794$	−16.1500	−	31.6949i	−0.573142	−	1.12481i
$795$		0			0
$796$	21.9406	+	15.9397i	0.777664	+	0.564968i
$797$	24.1141	−	8.77682i	0.854166	−	0.310891i	0.122428	−	0.992477i	$-0.460932\pi$
$797$	24.1141	−	8.77682i	0.854166	−	0.310891i	0.731738	+	0.681586i	$0.238710\pi$
$798$		0			0
$799$	−11.3687	+	2.00462i	−0.402197	+	0.0709182i
$800$	−20.7324	+	29.6140i	−0.733002	+	1.04701i
$801$		0			0
$802$	22.3644	+	20.8545i	0.789715	+	0.736398i
$803$	25.6466	+	30.5644i	0.905049	+	1.07860i
$804$		0			0
$805$	85.5378	+	15.0826i	3.01481	+	0.531592i
$806$	0.240613	−	0.566875i	0.00847525	−	0.0199673i
$807$		0			0
$808$	3.01838	+	5.02288i	0.106186	+	0.176704i
$809$			35.5723i			1.25066i	0.780362	+	0.625328i	$0.215035\pi$
$809$			35.5723i			1.25066i	−0.780362	+	0.625328i	$0.784965\pi$
$810$		0			0
$811$	5.98290			0.210088			0.105044	−	0.994468i	$-0.466502\pi$
$811$	5.98290			0.210088			0.105044	+	0.994468i	$0.466502\pi$
$812$	7.37990	+	29.5952i	0.258984	+	1.03859i
$813$		0			0
$814$	0.961237	−	2.26463i	0.0336913	−	0.0793753i
$815$	7.56640	−	42.9112i	0.265039	−	1.50311i
$816$		0			0
$817$	24.4197	−	20.4906i	0.854338	−	0.716875i
$818$	14.3975	−	15.4399i	0.503396	−	0.539843i
$819$		0			0
$820$	12.7151	−	0.889537i	0.444032	−	0.0310640i
$821$	−1.31505	−	7.45804i	−0.0458957	−	0.260287i	0.953223	−	0.302269i	$-0.0977440\pi$
$821$	−1.31505	−	7.45804i	−0.0458957	−	0.260287i	−0.999118	+	0.0419816i	$0.986633\pi$
$822$		0			0
$823$	−8.60702	−	23.6476i	−0.300022	−	0.824303i	−0.994495	−	0.104784i	$-0.966585\pi$
$823$	−8.60702	−	23.6476i	−0.300022	−	0.824303i	0.694473	−	0.719519i	$-0.255637\pi$
$824$	5.11593	−	14.8601i	0.178222	−	0.517675i
$825$		0			0
$826$	26.5681	−	13.5376i	0.924421	−	0.471035i
$827$	−2.17911	−	1.25811i	−0.0757749	−	0.0437487i	0.461634	−	0.887071i	$-0.347263\pi$
$827$	−2.17911	−	1.25811i	−0.0757749	−	0.0437487i	−0.537409	+	0.843322i	$0.680597\pi$
$828$		0			0
$829$	23.0116	−	13.2858i	0.799227	−	0.461434i	−0.0439737	−	0.999033i	$-0.514002\pi$
$829$	23.0116	−	13.2858i	0.799227	−	0.461434i	0.843201	+	0.537599i	$0.180668\pi$
$830$	20.9705	−	32.2929i	0.727897	−	1.12090i
$831$		0			0
$832$	0.167387	+	4.78018i	0.00580308	+	0.165723i
$833$	−2.46151	+	2.93351i	−0.0852862	+	0.101640i
$834$		0			0
$835$	48.0271	+	17.4804i	1.66205	+	0.604935i
$836$	21.7534	+	32.2485i	0.752357	+	1.11534i
$837$		0			0
$838$	20.3494	−	6.22180i	0.702959	−	0.214929i
$839$	20.0868	+	7.31100i	0.693473	+	0.252404i	0.664622	−	0.747180i	$-0.268593\pi$
$839$	20.0868	+	7.31100i	0.693473	+	0.252404i	0.0288517	+	0.999584i	$0.490815\pi$
$840$		0			0
$841$	−1.68433	−	1.41332i	−0.0580803	−	0.0487351i
$842$	−1.00519	−	8.18553i	−0.0346411	−	0.282092i
$843$		0			0
$844$	7.53658	−	26.2863i	0.259420	−	0.904813i
$845$	−21.3341	−	36.9518i	−0.733916	−	1.27118i
$846$		0			0
$847$	−4.39987	−	2.54026i	−0.151181	−	0.0872845i
$848$	−51.1797	−	10.8752i	−1.75752	−	0.373455i
$849$		0			0
$850$	−16.4706	+	12.4119i	−0.564935	+	0.425723i
$851$	1.45716	+	4.00350i	0.0499507	+	0.137238i
$852$		0			0
$853$	−10.2340	+	1.80454i	−0.350407	+	0.0617861i	−0.346081	−	0.938205i	$-0.612488\pi$
$853$	−10.2340	+	1.80454i	−0.350407	+	0.0617861i	−0.00432523	+	0.999991i	$0.501377\pi$
$854$	−36.2842	−	8.37625i	−1.24162	−	0.286629i
$855$		0			0
$856$	−33.1095	−	5.24241i	−1.13166	−	0.179182i
$857$	18.8893	+	22.5114i	0.645245	+	0.768973i	0.985189	−	0.171472i	$-0.0548525\pi$
$857$	18.8893	+	22.5114i	0.645245	+	0.768973i	−0.339944	+	0.940446i	$0.610408\pi$
$858$		0			0
$859$	2.76131	−	15.6602i	0.0942148	−	0.534319i	−0.900770	−	0.434296i	$-0.856997\pi$
$859$	2.76131	−	15.6602i	0.0942148	−	0.534319i	0.994985	−	0.100023i	$-0.0318916\pi$
$860$	39.2474	+	4.12380i	1.33833	+	0.140621i
$861$		0			0
$862$	−0.186558	+	3.56083i	−0.00635420	+	0.121283i
$863$	−25.8291			−0.879233			−0.439617	−	0.898185i	$-0.644886\pi$
$863$	−25.8291			−0.879233			−0.439617	+	0.898185i	$0.644886\pi$
$864$		0			0
$865$	−60.9747			−2.07320
$866$	−2.41397	+	46.0754i	−0.0820301	+	1.56571i
$867$		0			0
$868$	−4.26757	−	0.448402i	−0.144851	−	0.0152198i
$869$	−10.4893	+	59.4876i	−0.355824	+	2.01798i
$870$		0			0
$871$	−1.14209	−	1.36109i	−0.0386984	−	0.0461189i
$872$	15.6680	+	2.48080i	0.530586	+	0.0840106i
$873$		0			0
$874$	−65.6381	−	15.1527i	−2.22024	−	0.512546i
$875$	13.6144	−	2.40058i	0.460250	−	0.0811546i
$876$		0			0
$877$	4.98502	+	13.6962i	0.168332	+	0.462489i	0.994961	−	0.100258i	$-0.0319668\pi$
$877$	4.98502	+	13.6962i	0.168332	+	0.462489i	−0.826629	+	0.562747i	$0.809745\pi$
$878$	10.9868	−	8.27941i	0.370786	−	0.279416i
$879$		0			0
$880$	−10.0093	+	47.1047i	−0.337412	+	1.58790i
$881$	10.8614	+	6.27081i	0.365929	+	0.211269i	0.671678	−	0.740843i	$-0.265574\pi$
$881$	10.8614	+	6.27081i	0.365929	+	0.211269i	−0.305750	+	0.952112i	$0.598907\pi$
$882$		0			0
$883$	14.5195	+	25.1485i	0.488620	+	0.846315i	0.999914	−	0.0130911i	$-0.00416714\pi$
$883$	14.5195	+	25.1485i	0.488620	+	0.846315i	−0.511294	+	0.859406i	$0.670834\pi$
$884$	−0.752067	+	2.62309i	−0.0252948	+	0.0882240i
$885$		0			0
$886$	−3.09472	−	25.2011i	−0.103969	−	0.846649i
$887$	16.1110	+	13.5188i	0.540955	+	0.453915i	0.871864	−	0.489747i	$-0.162911\pi$
$887$	16.1110	+	13.5188i	0.540955	+	0.453915i	−0.330909	+	0.943663i	$0.607355\pi$
$888$		0			0
$889$	−18.4224	−	6.70520i	−0.617867	−	0.224885i
$890$	−70.3656	+	21.5142i	−2.35866	+	0.721156i
$891$		0			0
$892$	6.12537	+	9.08061i	0.205093	+	0.304041i
$893$	−25.9193	−	9.43384i	−0.867355	−	0.315692i
$894$		0			0
$895$	−14.7008	+	17.5197i	−0.491394	+	0.585620i
$896$	31.5116	−	10.8543i	1.05273	−	0.362615i
$897$		0			0
$898$	4.84671	−	7.46354i	0.161737	−	0.249061i
$899$	−3.26536	+	1.88526i	−0.108906	+	0.0628768i
$900$		0			0
$901$	−25.8509	−	14.9250i	−0.861217	−	0.497224i
$902$	8.48780	−	4.32492i	0.282613	−	0.144004i
$903$		0			0
$904$	1.17499	−	3.41294i	0.0390795	−	0.113513i
$905$	11.1125	+	30.5315i	0.369393	+	1.01490i
$906$		0			0
$907$	−1.09570	−	6.21403i	−0.0363822	−	0.206333i	0.961198	−	0.275859i	$-0.0889624\pi$
$907$	−1.09570	−	6.21403i	−0.0363822	−	0.206333i	−0.997580	+	0.0695260i	$0.977851\pi$
$908$	21.9233	−	1.53373i	0.727549	−	0.0508986i
$909$		0			0
$910$	5.73317	−	6.14827i	0.190053	−	0.203813i
$911$	−30.4836	+	25.5788i	−1.00997	+	0.847463i	−0.988334	−	0.152303i	$-0.951331\pi$
$911$	−30.4836	+	25.5788i	−1.00997	+	0.847463i	−0.0216332	+	0.999766i	$0.506887\pi$
$912$		0			0
$913$	4.99710	−	28.3399i	0.165380	−	0.937915i
$914$	−15.3455	+	36.1533i	−0.507584	+	1.19585i
$915$		0			0
$916$	−12.7443	−	51.1077i	−0.421084	−	1.68865i
$917$	−48.8604			−1.61351
$918$		0			0
$919$		−	43.2414i		−	1.42640i	−0.700960	−	0.713201i	$-0.747245\pi$
$919$		−	43.2414i		−	1.42640i	0.700960	−	0.713201i	$-0.252755\pi$
$920$	−42.9549	−	71.4813i	−1.41618	−	2.35667i
$921$		0			0
$922$	−18.7401	+	44.1508i	−0.617172	+	1.45403i
$923$	−1.97574	−	0.348377i	−0.0650324	−	0.0114670i
$924$		0			0
$925$	2.00323	+	2.38736i	0.0658659	+	0.0784960i
$926$	−39.4455	−	36.7824i	−1.29626	−	1.20874i
$927$		0			0
$928$	16.7956	−	23.9906i	0.551341	−	0.787531i
$929$	4.34064	−	0.765372i	0.142412	−	0.0251111i	−0.101988	−	0.994786i	$-0.532520\pi$
$929$	4.34064	−	0.765372i	0.142412	−	0.0251111i	0.244400	+	0.969675i	$0.421409\pi$
$930$		0			0
$931$	−8.59796	+	3.12940i	−0.281787	+	0.102562i
$932$	−15.5539	−	11.2998i	−0.509485	−	0.370138i
$933$		0			0
$934$	−10.2165	−	20.0502i	−0.334294	−	0.656063i
$935$	−13.7366	+	23.7925i	−0.449236	+	0.778099i
$936$		0			0
$937$	0.581707	+	1.00755i	0.0190035	+	0.0329151i	0.875371	−	0.483452i	$-0.160617\pi$
$937$	0.581707	+	1.00755i	0.0190035	+	0.0329151i	−0.856367	+	0.516367i	$0.827284\pi$
$938$	−6.74278	+	10.3833i	−0.220160	+	0.339028i
$939$		0			0
$940$	−13.8896	−	31.1939i	−0.453029	−	1.01743i
$941$	−24.6581	−	20.6906i	−0.803833	−	0.674496i	0.145295	−	0.989388i	$-0.453587\pi$
$941$	−24.6581	−	20.6906i	−0.803833	−	0.674496i	−0.949127	+	0.314893i	$0.898031\pi$
$942$		0			0
$943$	−5.64228	+	15.5021i	−0.183738	+	0.504816i
$944$	−26.5456	−	10.7231i	−0.863985	−	0.349008i
$945$		0			0
$946$	28.2050	−	8.62363i	0.917024	−	0.280378i
$947$	9.21146	−	25.3083i	0.299332	−	0.822408i	−0.695280	−	0.718739i	$-0.744719\pi$
$947$	9.21146	−	25.3083i	0.299332	−	0.822408i	0.994612	−	0.103669i	$-0.0330583\pi$
$948$		0			0
$949$	−4.29861	+	5.12288i	−0.139539	+	0.166296i
$950$	−48.9092	+	6.00609i	−1.58682	+	0.194863i
$951$		0			0
$952$	19.0111	−	0.332752i	0.616153	−	0.0107845i
$953$	24.2787	−	14.0173i	0.786465	−	0.454066i	−0.0522513	−	0.998634i	$-0.516640\pi$
$953$	24.2787	−	14.0173i	0.786465	−	0.454066i	0.838717	+	0.544568i	$0.183306\pi$
$954$		0			0
$955$	1.68565	−	2.91963i	0.0545464	−	0.0944771i
$956$	−19.9790	−	20.6876i	−0.646168	−	0.669084i
$957$		0			0
$958$	−10.7490	−	14.2639i	−0.347284	−	0.460846i
$959$	−51.9274	+	18.9000i	−1.67682	+	0.610313i
$960$		0			0
$961$	5.29098	+	30.0066i	0.170677	+	0.967956i
$962$	0.401784	+	0.0927523i	0.0129540	+	0.00299045i
$963$		0			0
$964$	−24.2458	−	11.8245i	−0.780905	−	0.380842i
$965$	−1.24708	+	1.04642i	−0.0401449	+	0.0336856i
$966$		0			0
$967$	46.5149	+	8.20184i	1.49582	+	0.263753i	0.860880	−	0.508809i	$-0.169914\pi$
$967$	46.5149	+	8.20184i	1.49582	+	0.263753i	0.634940	+	0.772562i	$0.281025\pi$
$968$	0.930995	+	4.78833i	0.0299233	+	0.153903i
$969$		0			0
$970$	−2.40856	+	45.9722i	−0.0773343	+	1.47608i
$971$		−	3.24802i		−	0.104234i	−0.998641	−	0.0521170i	$-0.983403\pi$
$971$		−	3.24802i		−	0.104234i	0.998641	−	0.0521170i	$-0.0165969\pi$
$972$		0			0
$973$			2.26515i			0.0726173i
$974$	1.38331	+	0.0724741i	0.0443241	+	0.00232222i
$975$		0			0
$976$	16.7875	+	31.5678i	0.537354	+	1.01046i
$977$	−25.4482	−	4.48720i	−0.814160	−	0.143558i	−0.248962	−	0.968513i	$-0.580089\pi$
$977$	−25.4482	−	4.48720i	−0.814160	−	0.143558i	−0.565198	+	0.824955i	$0.691200\pi$
$978$		0			0
$979$	−42.1267	+	35.3485i	−1.34637	+	1.12974i
$980$	−10.1809	−	4.96514i	−0.325216	−	0.158606i
$981$		0			0
$982$	0.966146	−	4.18514i	0.0308310	−	0.133553i
$983$	5.64306	+	32.0034i	0.179986	+	1.02075i	0.932230	+	0.361866i	$0.117860\pi$
$983$	5.64306	+	32.0034i	0.179986	+	1.02075i	−0.752244	+	0.658884i	$0.771029\pi$
$984$		0			0
$985$	38.7405	−	14.1004i	1.23438	−	0.449276i
$986$	13.3430	−	10.0550i	0.424927	−	0.320216i
$987$		0			0
$988$	−4.68990	+	4.52927i	−0.149206	+	0.144095i
$989$	−25.5381	+	44.2332i	−0.812063	+	1.40653i
$990$		0			0
$991$	−4.42071	+	2.55230i	−0.140429	+	0.0810765i	−0.568568	−	0.822636i	$-0.692502\pi$
$991$	−4.42071	+	2.55230i	−0.140429	+	0.0810765i	0.428140	+	0.903713i	$0.359169\pi$
$992$	2.36341	+	3.37472i	0.0750382	+	0.107148i
$993$		0			0
$994$	1.70387	+	13.8751i	0.0540435	+	0.440091i
$995$	−29.4164	+	35.0571i	−0.932562	+	1.11138i
$996$		0			0
$997$	11.4461	−	31.4478i	0.362501	−	0.995963i	−0.615641	−	0.788026i	$-0.711103\pi$
$997$	11.4461	−	31.4478i	0.362501	−	0.995963i	0.978142	−	0.207937i	$-0.0666748\pi$
$998$	5.06333	+	16.5605i	0.160277	+	0.524212i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.179.16		192
3.2	odd	2		216.2.v.b.131.17	yes	192
8.3	odd	2	inner	648.2.v.b.179.23		192
12.11	even	2		864.2.bh.b.239.9		192
24.5	odd	2		864.2.bh.b.239.10		192
24.11	even	2		216.2.v.b.131.10	✓	192
27.7	even	9		216.2.v.b.155.10	yes	192
27.20	odd	18	inner	648.2.v.b.467.23		192
108.7	odd	18		864.2.bh.b.47.10		192
216.61	even	18		864.2.bh.b.47.9		192
216.115	odd	18		216.2.v.b.155.17	yes	192
216.155	even	18	inner	648.2.v.b.467.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.10	✓	192	24.11	even	2
216.2.v.b.131.17	yes	192	3.2	odd	2
216.2.v.b.155.10	yes	192	27.7	even	9
216.2.v.b.155.17	yes	192	216.115	odd	18
648.2.v.b.179.16		192	1.1	even	1	trivial
648.2.v.b.179.23		192	8.3	odd	2	inner
648.2.v.b.467.16		192	216.155	even	18	inner
648.2.v.b.467.23		192	27.20	odd	18	inner
864.2.bh.b.47.9		192	216.61	even	18
864.2.bh.b.47.10		192	108.7	odd	18
864.2.bh.b.239.9		192	12.11	even	2
864.2.bh.b.239.10		192	24.5	odd	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0739917 - 1.41228i) q^{2} +(-1.98905 - 0.208993i) q^{4} +(0.586059 - 3.32370i) q^{5} +(-1.89356 - 2.25666i) q^{7} +(-0.442330 + 2.79363i) q^{8} +O(q^{10})\)	\(q+(0.0739917 - 1.41228i) q^{2} +(-1.98905 - 0.208993i) q^{4} +(0.586059 - 3.32370i) q^{5} +(-1.89356 - 2.25666i) q^{7} +(-0.442330 + 2.79363i) q^{8} +(-4.65063 - 1.07360i) q^{10} +(-3.51297 + 0.619431i) q^{11} +(-0.204490 - 0.561832i) q^{13} +(-3.32714 + 2.50726i) q^{14} +(3.91264 + 0.831397i) q^{16} +(1.97627 + 1.14100i) q^{17} +(2.72623 + 4.72197i) q^{19} +(-1.86033 + 6.48853i) q^{20} +(0.614878 + 5.00711i) q^{22} +(-6.69233 - 5.61553i) q^{23} +(-6.00508 - 2.18567i) q^{25} +(-0.808593 + 0.247226i) q^{26} +(3.29477 + 4.88435i) q^{28} +(4.86478 + 1.77064i) q^{29} +(-0.468156 + 0.557926i) q^{31} +(1.46367 - 5.46422i) q^{32} +(1.75764 - 2.70662i) q^{34} +(-8.61021 + 4.97111i) q^{35} +(-0.422340 - 0.243838i) q^{37} +(6.87044 - 3.50080i) q^{38} +(9.02596 + 3.10740i) q^{40} +(-0.645850 - 1.77446i) q^{41} +(-1.01523 - 5.75766i) q^{43} +(7.11693 - 0.497893i) q^{44} +(-8.42586 + 9.03591i) q^{46} +(-3.87524 + 3.25171i) q^{47} +(-0.291398 + 1.65260i) q^{49} +(-3.53110 + 8.31912i) q^{50} +(0.289322 + 1.16025i) q^{52} -13.0806 q^{53} +12.0391i q^{55} +(7.14184 - 4.29172i) q^{56} +(2.86058 - 6.73941i) q^{58} +(-7.04866 - 1.24287i) q^{59} +(5.74555 + 6.84728i) q^{61} +(0.753306 + 0.702447i) q^{62} +(-7.60869 - 2.47141i) q^{64} +(-1.98721 + 0.350398i) q^{65} +(2.79254 - 1.01640i) q^{67} +(-3.69245 - 2.68254i) q^{68} +(6.38350 + 12.5278i) q^{70} +(1.67775 - 2.90596i) q^{71} +(-5.59255 - 9.68658i) q^{73} +(-0.375616 + 0.578418i) q^{74} +(-4.43575 - 9.96200i) q^{76} +(8.04987 + 6.75464i) q^{77} +(5.79167 - 15.9125i) q^{79} +(5.05636 - 12.5172i) q^{80} +(-2.55381 + 0.780824i) q^{82} +(-2.75916 + 7.58072i) q^{83} +(4.95057 - 5.89986i) q^{85} +(-8.20653 + 1.00777i) q^{86} +(-0.176569 - 10.0879i) q^{88} +(13.3509 - 7.70815i) q^{89} +(-0.880649 + 1.52533i) q^{91} +(12.1378 + 12.5682i) q^{92} +(4.30558 + 5.71351i) q^{94} +(17.2922 - 6.29383i) q^{95} +(-1.67485 - 9.49852i) q^{97} +(2.31237 + 0.533814i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

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