LMFDB - Embedded newform 168.2.j.d.155.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(155,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("168.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + x^8 + 4x^6 + 4x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.3
Root			$1.19877 - 0.750295i$ of defining polynomial
Character	$\chi$	$=$	168.155
Dual form			168.2.j.d.155.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.750295 - 1.19877i) q^{2} +(1.67298 - 0.448478i) q^{3} +(-0.874114 + 1.79887i) q^{4} +0.896956 q^{5} +(-1.79285 - 1.66903i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(2.59774 - 1.50059i) q^{9} +O(q^{10})$	\(q+(-0.750295 - 1.19877i) q^{2} +(1.67298 - 0.448478i) q^{3} +(-0.874114 + 1.79887i) q^{4} +0.896956 q^{5} +(-1.79285 - 1.66903i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(2.59774 - 1.50059i) q^{9} +(-0.672982 - 1.07525i) q^{10} +(-0.655624 + 3.40149i) q^{12} -1.84951i q^{13} +(-1.19877 + 0.750295i) q^{14} +(1.50059 - 0.402265i) q^{15} +(-2.47185 - 3.14483i) q^{16} +4.12397i q^{17} +(-3.74794 - 1.98821i) q^{18} -0.654037 q^{19} +(-0.784042 + 1.61350i) q^{20} +(-0.448478 - 1.67298i) q^{21} -7.12515 q^{23} +(4.56953 - 1.76618i) q^{24} -4.19547 q^{25} +(-2.21714 + 1.38768i) q^{26} +(3.67298 - 3.67549i) q^{27} +(1.79887 + 0.874114i) q^{28} +7.79627 q^{29} +(-1.60811 - 1.49705i) q^{30} +(-1.91532 + 5.32274i) q^{32} +(4.94370 - 3.09419i) q^{34} -0.896956i q^{35} +(0.428647 + 5.98467i) q^{36} +10.6919i q^{37} +(0.490721 + 0.784042i) q^{38} +(-0.829463 - 3.09419i) q^{39} +(2.52249 - 0.270717i) q^{40} +10.1263i q^{41} +(-1.66903 + 1.79285i) q^{42} -1.19547 q^{43} +(2.33005 - 1.34596i) q^{45} +(5.34596 + 8.54143i) q^{46} -9.59019 q^{47} +(-5.54575 - 4.15267i) q^{48} -1.00000 q^{49} +(3.14784 + 5.02942i) q^{50} +(1.84951 + 6.89932i) q^{51} +(3.32702 + 1.61668i) q^{52} +8.24793 q^{53} +(-7.16190 - 1.64537i) q^{54} +(-0.301817 - 2.81228i) q^{56} +(-1.09419 + 0.293321i) q^{57} +(-5.84951 - 9.34596i) q^{58} -6.89932i q^{59} +(-0.588066 + 3.05099i) q^{60} -4.54143i q^{61} +(-1.50059 - 2.59774i) q^{63} +(7.81781 - 1.69759i) q^{64} -1.65893i q^{65} -5.49646 q^{67} +(-7.41847 - 3.60482i) q^{68} +(-11.9202 + 3.19547i) q^{69} +(-1.07525 + 0.672982i) q^{70} +4.12397 q^{71} +(6.85265 - 5.00412i) q^{72} -6.00000 q^{73} +(12.8172 - 8.02210i) q^{74} +(-7.01894 + 1.88158i) q^{75} +(0.571703 - 1.17653i) q^{76} +(-3.08689 + 3.31590i) q^{78} +13.3839i q^{79} +(-2.21714 - 2.82077i) q^{80} +(4.49646 - 7.79627i) q^{81} +(12.1392 - 7.59774i) q^{82} -13.3533i q^{83} +(3.40149 + 0.655624i) q^{84} +3.69901i q^{85} +(0.896956 + 1.43310i) q^{86} +(13.0430 - 3.49646i) q^{87} -13.7142i q^{89} +(-3.36173 - 1.78334i) q^{90} -1.84951 q^{91} +(6.22819 - 12.8172i) q^{92} +(7.19547 + 11.4965i) q^{94} -0.586642 q^{95} +(-0.817168 + 9.76382i) q^{96} -8.99291 q^{97} +(0.750295 + 1.19877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} - 10 q^{6} + 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 - 10 * q^6 + 4 * q^9	$ 12 q - 4 q^{4} - 10 q^{6} + 4 q^{9} + 12 q^{10} - 14 q^{12} + 4 q^{16} - 8 q^{18} - 48 q^{19} + 22 q^{24} + 4 q^{25} + 24 q^{27} + 8 q^{28} - 20 q^{30} - 8 q^{34} + 20 q^{36} - 4 q^{40} - 6 q^{42} + 40 q^{43} + 24 q^{46} - 26 q^{48} - 12 q^{49} + 8 q^{51} + 60 q^{52} + 18 q^{54} + 40 q^{57} - 56 q^{58} - 12 q^{60} + 20 q^{64} - 40 q^{67} - 20 q^{70} - 32 q^{72} - 72 q^{73} - 24 q^{75} - 12 q^{76} - 12 q^{78} + 28 q^{81} + 24 q^{82} + 6 q^{84} - 8 q^{90} - 8 q^{91} + 32 q^{94} + 18 q^{96} - 56 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 - 10 * q^6 + 4 * q^9 + 12 * q^10 - 14 * q^12 + 4 * q^16 - 8 * q^18 - 48 * q^19 + 22 * q^24 + 4 * q^25 + 24 * q^27 + 8 * q^28 - 20 * q^30 - 8 * q^34 + 20 * q^36 - 4 * q^40 - 6 * q^42 + 40 * q^43 + 24 * q^46 - 26 * q^48 - 12 * q^49 + 8 * q^51 + 60 * q^52 + 18 * q^54 + 40 * q^57 - 56 * q^58 - 12 * q^60 + 20 * q^64 - 40 * q^67 - 20 * q^70 - 32 * q^72 - 72 * q^73 - 24 * q^75 - 12 * q^76 - 12 * q^78 + 28 * q^81 + 24 * q^82 + 6 * q^84 - 8 * q^90 - 8 * q^91 + 32 * q^94 + 18 * q^96 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.750295	−	1.19877i	−0.530539	−	0.847661i
$2$	−0.750295	−	1.19877i	−0.530539	−	0.847661i
$3$	1.67298	−	0.448478i	0.965896	−	0.258929i
$3$	1.67298	−	0.448478i	0.965896	−	0.258929i
$4$	−0.874114	+	1.79887i	−0.437057	+	0.899434i
$5$	0.896956			0.401131			0.200565	−	0.979680i	$-0.435722\pi$
$5$	0.896956			0.401131			0.200565	+	0.979680i	$0.435722\pi$
$6$	−1.79285	−	1.66903i	−0.731929	−	0.681381i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.81228	−	0.301817i	0.994290	−	0.106709i
$9$	2.59774	−	1.50059i	0.865912	−	0.500197i
$10$	−0.672982	−	1.07525i	−0.212815	−	0.340023i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	−0.655624	+	3.40149i	−0.189262	+	0.981927i
$13$		−	1.84951i		−	0.512961i	−0.966549	−	0.256480i	$-0.917437\pi$
$13$		−	1.84951i		−	0.512961i	0.966549	−	0.256480i	$-0.0825629\pi$
$14$	−1.19877	+	0.750295i	−0.320386	+	0.200525i
$15$	1.50059	−	0.402265i	0.387451	−	0.103864i
$16$	−2.47185	−	3.14483i	−0.617962	−	0.786208i
$17$			4.12397i			1.00021i	0.865965	+	0.500104i	$0.166705\pi$
$17$			4.12397i			1.00021i	−0.865965	+	0.500104i	$0.833295\pi$
$18$	−3.74794	−	1.98821i	−0.883397	−	0.468625i
$19$	−0.654037			−0.150046			−0.0750232	−	0.997182i	$-0.523903\pi$
$19$	−0.654037			−0.150046			−0.0750232	+	0.997182i	$0.523903\pi$
$20$	−0.784042	+	1.61350i	−0.175317	+	0.360791i
$21$	−0.448478	−	1.67298i	−0.0978659	−	0.365075i
$22$		0			0
$23$	−7.12515			−1.48570			−0.742848	−	0.669460i	$-0.766525\pi$
$23$	−7.12515			−1.48570			−0.742848	+	0.669460i	$0.766525\pi$
$24$	4.56953	−	1.76618i	0.932752	−	0.360520i
$25$	−4.19547			−0.839094
$26$	−2.21714	+	1.38768i	−0.434817	+	0.272146i
$27$	3.67298	−	3.67549i	0.706866	−	0.707348i
$28$	1.79887	+	0.874114i	0.339954	+	0.165192i
$29$	7.79627			1.44773			0.723866	−	0.689941i	$-0.242363\pi$
$29$	7.79627			1.44773			0.723866	+	0.689941i	$0.242363\pi$
$30$	−1.60811	−	1.49705i	−0.293599	−	0.273323i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−1.91532	+	5.32274i	−0.338584	+	0.940936i
$33$		0			0
$34$	4.94370	−	3.09419i	0.847837	−	0.530649i
$35$		−	0.896956i		−	0.151613i
$36$	0.428647	+	5.98467i	0.0714411	+	0.997445i
$37$			10.6919i			1.75774i	0.477060	+	0.878871i	$0.341703\pi$
$37$			10.6919i			1.75774i	−0.477060	+	0.878871i	$0.658297\pi$
$38$	0.490721	+	0.784042i	0.0796054	+	0.127188i
$39$	−0.829463	−	3.09419i	−0.132820	−	0.495467i
$40$	2.52249	−	0.270717i	0.398840	−	0.0428041i
$41$			10.1263i			1.58147i	0.612161	+	0.790733i	$0.290301\pi$
$41$			10.1263i			1.58147i	−0.612161	+	0.790733i	$0.709699\pi$
$42$	−1.66903	+	1.79285i	−0.257538	+	0.276643i
$43$	−1.19547			−0.182308			−0.0911538	−	0.995837i	$-0.529055\pi$
$43$	−1.19547			−0.182308			−0.0911538	+	0.995837i	$0.529055\pi$
$44$		0			0
$45$	2.33005	−	1.34596i	0.347344	−	0.200644i
$46$	5.34596	+	8.54143i	0.788219	+	1.25937i
$47$	−9.59019			−1.39887			−0.699436	−	0.714695i	$-0.746565\pi$
$47$	−9.59019			−1.39887			−0.699436	+	0.714695i	$0.746565\pi$
$48$	−5.54575	−	4.15267i	−0.800459	−	0.599387i
$49$	−1.00000			−0.142857
$50$	3.14784	+	5.02942i	0.445172	+	0.711267i
$51$	1.84951	+	6.89932i	0.258983	+	0.966098i
$52$	3.32702	+	1.61668i	0.461374	+	0.224193i
$53$	8.24793			1.13294			0.566470	−	0.824082i	$-0.308309\pi$
$53$	8.24793			1.13294			0.566470	+	0.824082i	$0.308309\pi$
$54$	−7.16190	−	1.64537i	−0.974611	−	0.223907i
$55$		0			0
$56$	−0.301817	−	2.81228i	−0.0403320	−	0.375806i
$57$	−1.09419	+	0.293321i	−0.144929	+	0.0388513i
$58$	−5.84951	−	9.34596i	−0.768078	−	1.22719i
$59$		−	6.89932i		−	0.898215i	−0.893478	−	0.449107i	$-0.851742\pi$
$59$		−	6.89932i		−	0.898215i	0.893478	−	0.449107i	$-0.148258\pi$
$60$	−0.588066	+	3.05099i	−0.0759190	+	0.393881i
$61$		−	4.54143i		−	0.581471i	−0.956803	−	0.290735i	$-0.906100\pi$
$61$		−	4.54143i		−	0.581471i	0.956803	−	0.290735i	$-0.0939000\pi$
$62$		0			0
$63$	−1.50059	−	2.59774i	−0.189057	−	0.327284i
$64$	7.81781	−	1.69759i	0.977227	−	0.212199i
$65$		−	1.65893i		−	0.205764i
$66$		0			0
$67$	−5.49646			−0.671499			−0.335750	−	0.941951i	$-0.608990\pi$
$67$	−5.49646			−0.671499			−0.335750	+	0.941951i	$0.608990\pi$
$68$	−7.41847	−	3.60482i	−0.899621	−	0.437148i
$69$	−11.9202	+	3.19547i	−1.43503	+	0.384689i
$70$	−1.07525	+	0.672982i	−0.128517	+	0.0804367i
$71$	4.12397			0.489425			0.244712	−	0.969596i	$-0.421306\pi$
$71$	4.12397			0.489425			0.244712	+	0.969596i	$0.421306\pi$
$72$	6.85265	−	5.00412i	0.807592	−	0.589741i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	12.8172	−	8.02210i	1.48997	−	0.932550i
$75$	−7.01894	+	1.88158i	−0.810478	+	0.217266i
$76$	0.571703	−	1.17653i	0.0655788	−	0.134957i
$77$		0			0
$78$	−3.08689	+	3.31590i	−0.349522	+	0.375451i
$79$			13.3839i			1.50580i	0.658134	+	0.752901i	$0.271346\pi$
$79$			13.3839i			1.50580i	−0.658134	+	0.752901i	$0.728654\pi$
$80$	−2.21714	−	2.82077i	−0.247884	−	0.315372i
$81$	4.49646	−	7.79627i	0.499606	−	0.866253i
$82$	12.1392	−	7.59774i	1.34055	−	0.839029i
$83$		−	13.3533i		−	1.46572i	−0.680380	−	0.732860i	$-0.738185\pi$
$83$		−	13.3533i		−	1.46572i	0.680380	−	0.732860i	$-0.261815\pi$
$84$	3.40149	+	0.655624i	0.371133	+	0.0715345i
$85$			3.69901i			0.401214i
$86$	0.896956	+	1.43310i	0.0967212	+	0.154535i
$87$	13.0430	−	3.49646i	1.39836	−	0.374859i
$88$		0			0
$89$		−	13.7142i		−	1.45370i	−0.686798	−	0.726849i	$-0.740984\pi$
$89$		−	13.7142i		−	1.45370i	0.686798	−	0.726849i	$-0.259016\pi$
$90$	−3.36173	−	1.78334i	−0.354358	−	0.187980i
$91$	−1.84951			−0.193881
$92$	6.22819	−	12.8172i	0.649334	−	1.33628i
$93$		0			0
$94$	7.19547	+	11.4965i	0.742156	+	1.18577i
$95$	−0.586642			−0.0601882
$96$	−0.817168	+	9.76382i	−0.0834019	+	0.996516i
$97$	−8.99291			−0.913092			−0.456546	−	0.889700i	$-0.650914\pi$
$97$	−8.99291			−0.913092			−0.456546	+	0.889700i	$0.650914\pi$
$98$	0.750295	+	1.19877i	0.0757913	+	0.121094i
$99$		0			0
$100$	3.66732	−	7.54710i	0.366732	−	0.754710i
$101$	−7.35097			−0.731449			−0.365725	−	0.930723i	$-0.619179\pi$
$101$	−7.35097			−0.731449			−0.365725	+	0.930723i	$0.619179\pi$
$102$	6.88304	−	7.39366i	0.681523	−	0.732082i
$103$		−	13.3839i		−	1.31875i	−0.751814	−	0.659375i	$-0.770821\pi$
$103$		−	13.3839i		−	1.31875i	0.751814	−	0.659375i	$-0.229179\pi$
$104$	−0.558213	−	5.20133i	−0.0547373	−	0.510032i
$105$	−0.402265	−	1.50059i	−0.0392570	−	0.146443i
$106$	−6.18838	−	9.88740i	−0.601069	−	0.960349i
$107$			1.79391i			0.173424i	0.996233	+	0.0867120i	$0.0276360\pi$
$107$			1.79391i			0.173424i	−0.996233	+	0.0867120i	$0.972364\pi$
$108$	3.40111	+	9.82000i	0.327272	+	0.944930i
$109$		−	5.30807i		−	0.508421i	−0.967149	−	0.254211i	$-0.918184\pi$
$109$		−	5.30807i		−	0.508421i	0.967149	−	0.254211i	$-0.0818156\pi$
$110$		0			0
$111$	4.79509	+	17.8874i	0.455130	+	1.69780i
$112$	−3.14483	+	2.47185i	−0.297159	+	0.233568i
$113$			3.00118i			0.282327i	0.989986	+	0.141164i	$0.0450844\pi$
$113$			3.00118i			0.282327i	−0.989986	+	0.141164i	$0.954916\pi$
$114$	1.17259	+	1.09161i	0.109823	+	0.102239i
$115$	−6.39094			−0.595958
$116$	−6.81483	+	14.0245i	−0.632741	+	1.30214i
$117$	−2.77535	−	4.80453i	−0.256581	−	0.444179i
$118$	−8.27072	+	5.17653i	−0.761381	+	0.476538i
$119$	4.12397			0.378043
$120$	4.09867	−	1.58418i	0.374155	−	0.144616i
$121$	11.0000			1.00000
$122$	−5.44415	+	3.40742i	−0.492890	+	0.308493i
$123$	4.54143	+	16.9412i	0.409487	+	1.52753i
$124$		0			0
$125$	−8.24793			−0.737717
$126$	−1.98821	+	3.74794i	−0.177124	+	0.333893i
$127$			14.1884i			1.25902i	0.776994	+	0.629508i	$0.216743\pi$
$127$			14.1884i			1.25902i	−0.776994	+	0.629508i	$0.783257\pi$
$128$	−7.90069	−	8.09809i	−0.698329	−	0.715777i
$129$	−2.00000	+	0.536142i	−0.176090	+	0.0472047i
$130$	−1.98868	+	1.24468i	−0.174418	+	0.109166i
$131$			16.9412i			1.48016i	0.672521	+	0.740078i	$0.265211\pi$
$131$			16.9412i			1.48016i	−0.672521	+	0.740078i	$0.734789\pi$
$132$		0			0
$133$			0.654037i			0.0567122i
$134$	4.12397	+	6.58900i	0.356256	+	0.569203i
$135$	3.29450	−	3.29675i	0.283546	−	0.283739i
$136$	1.24468	+	11.5977i	0.106731	+	0.994498i
$137$		−	11.8358i		−	1.01120i	−0.862769	−	0.505598i	$-0.831272\pi$
$137$		−	11.8358i		−	1.01120i	0.862769	−	0.505598i	$-0.168728\pi$
$138$	12.7743	+	11.8921i	1.08742	+	1.01232i
$139$	11.0450			0.936823			0.468411	−	0.883510i	$-0.344827\pi$
$139$	11.0450			0.936823			0.468411	+	0.883510i	$0.344827\pi$
$140$	1.61350	+	0.784042i	0.136366	+	0.0662636i
$141$	−16.0442	+	4.30099i	−1.35117	+	0.362208i
$142$	−3.09419	−	4.94370i	−0.259659	−	0.414866i
$143$		0			0
$144$	−11.1403	−	4.46020i	−0.928359	−	0.371684i
$145$	6.99291			0.580730
$146$	4.50177	+	7.19264i	0.372569	+	0.595267i
$147$	−1.67298	+	0.448478i	−0.137985	+	0.0369898i
$148$	−19.2334	−	9.34596i	−1.58097	−	0.768233i
$149$	−4.66011			−0.381771			−0.190885	−	0.981612i	$-0.561136\pi$
$149$	−4.66011			−0.381771			−0.190885	+	0.981612i	$0.561136\pi$
$150$	7.52186	+	7.00239i	0.614158	+	0.571742i
$151$		−	12.5793i		−	1.02369i	−0.859078	−	0.511845i	$-0.828962\pi$
$151$		−	12.5793i		−	1.02369i	0.859078	−	0.511845i	$-0.171038\pi$
$152$	−1.83933	+	0.197400i	−0.149190	+	0.0160112i
$153$	6.18838	+	10.7130i	0.500301	+	0.866092i
$154$		0			0
$155$		0			0
$156$	6.29109	+	1.21258i	0.503690	+	0.0970843i
$157$		−	19.5343i		−	1.55901i	−0.626396	−	0.779505i	$-0.715471\pi$
$157$		−	19.5343i		−	1.55901i	0.626396	−	0.779505i	$-0.284529\pi$
$158$	16.0442	−	10.0418i	1.27641	−	0.798886i
$159$	13.7986	−	3.69901i	1.09430	−	0.293351i
$160$	−1.71796	+	4.77426i	−0.135817	+	0.377438i
$161$			7.12515i			0.561540i
$162$	−12.7196	+	0.459276i	−0.999349	+	0.0360841i
$163$	9.19547			0.720245			0.360122	−	0.932905i	$-0.382735\pi$
$163$	9.19547			0.720245			0.360122	+	0.932905i	$0.382735\pi$
$164$	−18.2159	−	8.85156i	−1.42242	−	0.691191i
$165$		0			0
$166$	−16.0076	+	10.0189i	−1.24243	+	0.777621i
$167$	11.8358			0.915878			0.457939	−	0.888984i	$-0.348588\pi$
$167$	11.8358			0.915878			0.457939	+	0.888984i	$0.348588\pi$
$168$	−1.76618	−	4.56953i	−0.136264	−	0.352547i
$169$	9.57932			0.736871
$170$	4.43428	−	2.77535i	0.340094	−	0.212860i
$171$	−1.69901	+	0.981441i	−0.129927	+	0.0750527i
$172$	1.04498	−	2.15049i	0.0796788	−	0.163974i
$173$	19.3557			1.47159			0.735793	−	0.677206i	$-0.236810\pi$
$173$	19.3557			1.47159			0.735793	+	0.677206i	$0.236810\pi$
$174$	−13.9776	−	13.0123i	−1.05964	−	0.986456i
$175$			4.19547i			0.317148i
$176$		0			0
$177$	−3.09419	−	11.5424i	−0.232574	−	0.867582i
$178$	−16.4402	+	10.2897i	−1.23224	+	0.771243i
$179$			14.7019i			1.09888i	0.835535	+	0.549438i	$0.185158\pi$
$179$			14.7019i			1.09888i	−0.835535	+	0.549438i	$0.814842\pi$
$180$	0.384477	+	5.36798i	0.0286572	+	0.400106i
$181$		−	4.54143i		−	0.337562i	−0.985654	−	0.168781i	$-0.946017\pi$
$181$		−	4.54143i		−	0.337562i	0.985654	−	0.168781i	$-0.0539831\pi$
$182$	1.38768	+	2.21714i	0.102861	+	0.164345i
$183$	−2.03673	−	7.59774i	−0.150560	−	0.561641i
$184$	−20.0379	+	2.15049i	−1.47721	+	0.158536i
$185$			9.59019i			0.705084i
$186$		0			0
$187$		0			0
$188$	8.38292	−	17.2515i	0.611387	−	1.25819i
$189$	−3.67549	−	3.67298i	−0.267352	−	0.267170i
$190$	0.440155	+	0.703251i	0.0319322	+	0.0510192i
$191$	−1.70943			−0.123690			−0.0618449	−	0.998086i	$-0.519698\pi$
$191$	−1.70943			−0.123690			−0.0618449	+	0.998086i	$0.519698\pi$
$192$	12.3177	−	6.34615i	0.888955	−	0.457994i
$193$	16.1884			1.16527			0.582633	−	0.812736i	$-0.302023\pi$
$193$	16.1884			1.16527			0.582633	+	0.812736i	$0.302023\pi$
$194$	6.74734	+	10.7805i	0.484431	+	0.773992i
$195$	−0.743992	−	2.77535i	−0.0532783	−	0.198747i
$196$	0.874114	−	1.79887i	0.0624367	−	0.128491i
$197$	−9.59019			−0.683272			−0.341636	−	0.939832i	$-0.610981\pi$
$197$	−9.59019			−0.683272			−0.341636	+	0.939832i	$0.610981\pi$
$198$		0			0
$199$		−	14.3909i		−	1.02015i	−0.860131	−	0.510073i	$-0.829618\pi$
$199$		−	14.3909i		−	1.02015i	0.860131	−	0.510073i	$-0.170382\pi$
$200$	−11.7988	+	1.26627i	−0.834303	+	0.0895385i
$201$	−9.19547	+	2.46504i	−0.648598	+	0.173870i
$202$	5.51540	+	8.81215i	0.388062	+	0.620021i
$203$		−	7.79627i		−	0.547191i
$204$	−14.0276	−	2.70377i	−0.982131	−	0.189302i
$205$			9.08287i			0.634375i
$206$	−16.0442	+	10.0418i	−1.11785	+	0.699648i
$207$	−18.5092	+	10.6919i	−1.28648	+	0.743140i
$208$	−5.81639	+	4.57170i	−0.403294	+	0.316991i
$209$		0			0
$210$	−1.49705	+	1.60811i	−0.103306	+	0.110970i
$211$	15.8874			1.09373			0.546867	−	0.837220i	$-0.315820\pi$
$211$	15.8874			1.09373			0.546867	+	0.837220i	$0.315820\pi$
$212$	−7.20963	+	14.8369i	−0.495160	+	1.01900i
$213$	6.89932	−	1.84951i	0.472733	−	0.126726i
$214$	2.15049	−	1.34596i	0.147005	−	0.0920082i
$215$	−1.07228			−0.0731292
$216$	9.22012	−	11.4451i	0.627350	−	0.778738i
$217$		0			0
$218$	−6.36318	+	3.98262i	−0.430969	+	0.269737i
$219$	−10.0379	+	2.69087i	−0.678298	+	0.181832i
$220$		0			0
$221$	7.62730			0.513068
$222$	17.8452	−	19.1691i	1.19769	−	1.28654i
$223$		−	9.00709i		−	0.603159i	−0.953441	−	0.301580i	$-0.902486\pi$
$223$		−	9.00709i		−	0.603159i	0.953441	−	0.301580i	$-0.0975139\pi$
$224$	5.32274	+	1.91532i	0.355640	+	0.127973i
$225$	−10.8987	+	6.29568i	−0.726581	+	0.419712i
$226$	3.59774	−	2.25177i	0.239318	−	0.149786i
$227$		−	22.9435i		−	1.52282i	−0.648274	−	0.761408i	$-0.724509\pi$
$227$		−	22.9435i		−	1.52282i	0.648274	−	0.761408i	$-0.275491\pi$
$228$	0.428802	−	2.22470i	0.0283981	−	0.147334i
$229$			10.9324i			0.722432i	0.932482	+	0.361216i	$0.117638\pi$
$229$			10.9324i			0.722432i	−0.932482	+	0.361216i	$0.882362\pi$
$230$	4.79509	+	7.66129i	0.316179	+	0.505170i
$231$		0			0
$232$	21.9253	−	2.35305i	1.43947	−	0.154485i
$233$			8.24793i			0.540340i	0.962813	+	0.270170i	$0.0870799\pi$
$233$			8.24793i			0.540340i	−0.962813	+	0.270170i	$0.912920\pi$
$234$	−3.67721	+	6.93183i	−0.240387	+	0.453148i
$235$	−8.60197			−0.561131
$236$	12.4110	+	6.03079i	0.807885	+	0.392571i
$237$	6.00236	+	22.3909i	0.389895	+	1.45445i
$238$	−3.09419	−	4.94370i	−0.200567	−	0.320452i
$239$	−4.87958			−0.315634			−0.157817	−	0.987468i	$-0.550446\pi$
$239$	−4.87958			−0.315634			−0.157817	+	0.987468i	$0.550446\pi$
$240$	−4.97429	−	3.72477i	−0.321089	−	0.240433i
$241$	−4.99291			−0.321622			−0.160811	−	0.986985i	$-0.551411\pi$
$241$	−4.99291			−0.321622			−0.160811	+	0.986985i	$0.551411\pi$
$242$	−8.25325	−	13.1865i	−0.530539	−	0.847661i
$243$	4.02603	−	15.0596i	0.258270	−	0.966073i
$244$	8.16944	+	3.96973i	0.522995	+	0.254136i
$245$	−0.896956			−0.0573044
$246$	16.9012	−	18.1550i	1.07758	−	1.15752i
$247$			1.20965i			0.0769679i
$248$		0			0
$249$	−5.98868	−	22.3399i	−0.379517	−	1.41573i
$250$	6.18838	+	9.88740i	0.391388	+	0.625334i
$251$			11.1078i			0.701116i	0.936541	+	0.350558i	$0.114008\pi$
$251$			11.1078i			0.701116i	−0.936541	+	0.350558i	$0.885992\pi$
$252$	5.98467	−	0.428647i	0.376999	−	0.0270022i
$253$		0			0
$254$	17.0087	−	10.6455i	1.06722	−	0.667957i
$255$	1.65893	+	6.18838i	0.103886	+	0.387532i
$256$	−3.77992	+	15.5471i	−0.236245	+	0.971693i
$257$		−	11.4686i		−	0.715390i	−0.933838	−	0.357695i	$-0.883563\pi$
$257$		−	11.4686i		−	0.715390i	0.933838	−	0.357695i	$-0.116437\pi$
$258$	2.14330	+	1.99528i	0.133436	+	0.124221i
$259$	10.6919			0.664364
$260$	2.98419	+	1.45009i	0.185071	+	0.0899308i
$261$	20.2527	−	11.6990i	1.25361	−	0.724151i
$262$	20.3086	−	12.7109i	1.25467	−	0.785280i
$263$	−12.3719			−0.762884			−0.381442	−	0.924393i	$-0.624572\pi$
$263$	−12.3719			−0.762884			−0.381442	+	0.924393i	$0.624572\pi$
$264$		0			0
$265$	7.39803			0.454457
$266$	0.784042	−	0.490721i	0.0480727	−	0.0300880i
$267$	−6.15049	−	22.9435i	−0.376404	−	1.40412i
$268$	4.80453	−	9.88740i	0.293483	−	0.603969i
$269$	−24.7374			−1.50827			−0.754134	−	0.656721i	$-0.771943\pi$
$269$	−24.7374			−1.50827			−0.754134	+	0.656721i	$0.771943\pi$
$270$	−6.42390	−	1.47583i	−0.390946	−	0.0898159i
$271$			20.7819i			1.26241i	0.775616	+	0.631205i	$0.217439\pi$
$271$			20.7819i			1.26241i	−0.775616	+	0.631205i	$0.782561\pi$
$272$	12.9692	−	10.1938i	0.786372	−	0.618091i
$273$	−3.09419	+	0.829463i	−0.187269	+	0.0502014i
$274$	−14.1884	+	8.88031i	−0.857152	+	0.536479i
$275$		0			0
$276$	4.67142	−	24.2361i	0.281186	−	1.45884i
$277$			1.60906i			0.0966790i	0.998831	+	0.0483395i	$0.0153929\pi$
$277$			1.60906i			0.0966790i	−0.998831	+	0.0483395i	$0.984607\pi$
$278$	−8.28699	−	13.2404i	−0.497021	−	0.794108i
$279$		0			0
$280$	−0.270717	−	2.52249i	−0.0161784	−	0.150748i
$281$			4.66011i			0.277999i	0.990292	+	0.138999i	$0.0443886\pi$
$281$			4.66011i			0.277999i	−0.990292	+	0.138999i	$0.955611\pi$
$282$	17.1938	+	16.0064i	1.02388	+	0.953164i
$283$	13.7369			0.816574			0.408287	−	0.912854i	$-0.366126\pi$
$283$	13.7369			0.816574			0.408287	+	0.912854i	$0.366126\pi$
$284$	−3.60482	+	7.41847i	−0.213906	+	0.440205i
$285$	−0.981441	+	0.263096i	−0.0581356	+	0.0155845i
$286$		0			0
$287$	10.1263			0.597738
$288$	3.01175	+	16.7012i	0.177469	+	0.984126i
$289$	−0.00708757			−0.000416916
$290$	−5.24675	−	8.38292i	−0.308100	−	0.492262i
$291$	−15.0450	+	4.03312i	−0.881952	+	0.236426i
$292$	5.24468	−	10.7932i	0.306922	−	0.631625i
$293$	19.3557			1.13077			0.565386	−	0.824826i	$-0.308727\pi$
$293$	19.3557			1.13077			0.565386	+	0.824826i	$0.308727\pi$
$294$	1.79285	+	1.66903i	0.104561	+	0.0973401i
$295$		−	6.18838i		−	0.360302i
$296$	3.22701	+	30.0687i	0.187566	+	1.74771i
$297$		0			0
$298$	3.49646	+	5.58641i	0.202544	+	0.323612i
$299$			13.1780i			0.762104i
$300$	2.75065	−	14.2709i	0.158809	−	0.823929i
$301$			1.19547i			0.0689058i
$302$	−15.0798	+	9.43821i	−0.867742	+	0.543108i
$303$	−12.2980	+	3.29675i	−0.706504	+	0.189393i
$304$	1.61668	+	2.05683i	0.0927230	+	0.117968i
$305$		−	4.07347i		−	0.233246i
$306$	8.19931	−	15.4564i	0.468723	−	0.883581i
$307$	−30.8198			−1.75898			−0.879489	−	0.475920i	$-0.842115\pi$
$307$	−30.8198			−1.75898			−0.879489	+	0.475920i	$0.842115\pi$
$308$		0			0
$309$	−6.00236	−	22.3909i	−0.341462	−	1.27378i
$310$		0			0
$311$	−6.00236			−0.340363			−0.170181	−	0.985413i	$-0.554435\pi$
$311$	−6.00236			−0.340363			−0.170181	+	0.985413i	$0.554435\pi$
$312$	−3.26656	−	8.45138i	−0.184933	−	0.478465i
$313$	−13.7748			−0.778597			−0.389299	−	0.921112i	$-0.627283\pi$
$313$	−13.7748			−0.778597			−0.389299	+	0.921112i	$0.627283\pi$
$314$	−23.4172	+	14.6565i	−1.32151	+	0.827116i
$315$	−1.34596	−	2.33005i	−0.0758364	−	0.131284i
$316$	−24.0758	−	11.6990i	−1.35437	−	0.658121i
$317$	−3.75679			−0.211003			−0.105501	−	0.994419i	$-0.533645\pi$
$317$	−3.75679			−0.211003			−0.105501	+	0.994419i	$0.533645\pi$
$318$	−14.7873	−	13.7661i	−0.829232	−	0.771963i
$319$		0			0
$320$	7.01223	−	1.52266i	0.391996	−	0.0851194i
$321$	0.804530	+	3.00118i	0.0449045	+	0.167510i
$322$	8.54143	−	5.34596i	0.475995	−	0.297919i
$323$		−	2.69722i		−	0.150078i
$324$	10.0940	+	14.9034i	0.560780	+	0.827965i
$325$			7.75955i			0.430423i
$326$	−6.89932	−	11.0233i	−0.382118	−	0.610523i
$327$	−2.38055	−	8.88031i	−0.131645	−	0.491082i
$328$	3.05630	+	28.4780i	0.168756	+	1.57244i
$329$			9.59019i			0.528724i
$330$		0			0
$331$	−6.20256			−0.340923			−0.170462	−	0.985364i	$-0.554526\pi$
$331$	−6.20256			−0.340923			−0.170462	+	0.985364i	$0.554526\pi$
$332$	24.0209	+	11.6723i	1.31832	+	0.640603i
$333$	16.0442	+	27.7748i	0.879217	+	1.52205i
$334$	−8.88031	−	14.1884i	−0.485909	−	0.776354i
$335$	−4.93008			−0.269359
$336$	−4.15267	+	5.54575i	−0.226547	+	0.302545i
$337$	−14.5793			−0.794186			−0.397093	−	0.917778i	$-0.629981\pi$
$337$	−14.5793			−0.794186			−0.397093	+	0.917778i	$0.629981\pi$
$338$	−7.18732	−	11.4834i	−0.390939	−	0.624617i
$339$	1.34596	+	5.02092i	0.0731027	+	0.272699i
$340$	−6.65404	−	3.23336i	−0.360866	−	0.175354i
$341$		0			0
$342$	2.45129	+	1.30036i	0.132550	+	0.0703155i
$343$			1.00000i			0.0539949i
$344$	−3.36199	+	0.360814i	−0.181267	+	0.0194538i
$345$	−10.6919	+	2.86620i	−0.575634	+	0.154311i
$346$	−14.5225	−	23.2031i	−0.780734	−	1.24741i
$347$			8.41690i			0.451843i	0.974146	+	0.225921i	$0.0725393\pi$
$347$			8.41690i			0.451843i	−0.974146	+	0.225921i	$0.927461\pi$
$348$	−5.11143	+	26.5190i	−0.274001	+	1.42157i
$349$		−	25.9253i		−	1.38775i	−0.720096	−	0.693874i	$-0.755902\pi$
$349$		−	25.9253i		−	1.38775i	0.720096	−	0.693874i	$-0.244098\pi$
$350$	5.02942	−	3.14784i	0.268834	−	0.168259i
$351$	−6.79784	−	6.79321i	−0.362842	−	0.362594i
$352$		0			0
$353$			13.7142i			0.729931i	0.931021	+	0.364965i	$0.118919\pi$
$353$			13.7142i			0.729931i	−0.931021	+	0.364965i	$0.881081\pi$
$354$	−11.5152	+	12.3695i	−0.612026	+	0.657430i
$355$	3.69901			0.196323
$356$	24.6699	+	11.9877i	1.30750	+	0.635348i
$357$	6.89932	−	1.84951i	0.365151	−	0.0978863i
$358$	17.6243	−	11.0308i	0.931473	−	0.582996i
$359$	26.3055			1.38835			0.694176	−	0.719805i	$-0.255769\pi$
$359$	26.3055			1.38835			0.694176	+	0.719805i	$0.255769\pi$
$360$	6.14652	−	4.48847i	0.323950	−	0.236563i
$361$	−18.5722			−0.977486
$362$	−5.44415	+	3.40742i	−0.286138	+	0.179090i
$363$	18.4028	−	4.93326i	0.965896	−	0.258929i
$364$	1.61668	−	3.32702i	0.0847371	−	0.174383i
$365$	−5.38173			−0.281693
$366$	−7.57981	+	8.14212i	−0.396203	+	0.425596i
$367$			19.7748i			1.03224i	0.856518	+	0.516118i	$0.172623\pi$
$367$			19.7748i			1.03224i	−0.856518	+	0.516118i	$0.827377\pi$
$368$	17.6123	+	22.4074i	0.918104	+	1.16807i
$369$	15.1955	+	26.3055i	0.791045	+	1.36941i
$370$	11.4965	−	7.19547i	0.597672	−	0.374075i
$371$		−	8.24793i		−	0.428211i
$372$		0			0
$373$		−	3.77479i		−	0.195451i	−0.995213	−	0.0977257i	$-0.968843\pi$
$373$		−	3.77479i		−	0.195451i	0.995213	−	0.0977257i	$-0.0311568\pi$
$374$		0			0
$375$	−13.7986	+	3.69901i	−0.712558	+	0.191016i
$376$	−26.9703	+	2.89448i	−1.39089	+	0.149272i
$377$		−	14.4193i		−	0.742630i
$378$	−1.64537	+	7.16190i	−0.0846288	+	0.368368i
$379$	−8.59350			−0.441418			−0.220709	−	0.975340i	$-0.570837\pi$
$379$	−8.59350			−0.441418			−0.220709	+	0.975340i	$0.570837\pi$
$380$	0.512792	−	1.05529i	0.0263057	−	0.0541353i
$381$	6.36318	+	23.7369i	0.325995	+	1.21608i
$382$	1.28257	+	2.04921i	0.0656222	+	0.104847i
$383$	−17.8381			−0.911485			−0.455743	−	0.890112i	$-0.650626\pi$
$383$	−17.8381			−0.911485			−0.455743	+	0.890112i	$0.650626\pi$
$384$	−16.8495	−	10.0047i	−0.859849	−	0.510549i
$385$		0			0
$386$	−12.1461	−	19.4062i	−0.618219	−	0.987749i
$387$	−3.10552	+	1.79391i	−0.157862	+	0.0911896i
$388$	7.86083	−	16.1771i	0.399073	−	0.821266i
$389$	7.79627			0.395287			0.197643	−	0.980274i	$-0.436671\pi$
$389$	7.79627			0.395287			0.197643	+	0.980274i	$0.436671\pi$
$390$	−2.76880	+	2.97421i	−0.140204	+	0.150605i
$391$		−	29.3839i		−	1.48601i
$392$	−2.81228	+	0.301817i	−0.142041	+	0.0152441i
$393$	7.59774	+	28.3422i	0.383255	+	1.42968i
$394$	7.19547	+	11.4965i	0.362503	+	0.579183i
$395$			12.0047i			0.604023i
$396$		0			0
$397$			22.2263i			1.11550i	0.830007	+	0.557752i	$0.188336\pi$
$397$			22.2263i			1.11550i	−0.830007	+	0.557752i	$0.811664\pi$
$398$	−17.2515	+	10.7975i	−0.864738	+	0.541227i
$399$	0.293321	+	1.09419i	0.0146844	+	0.0547781i
$400$	10.3706	+	13.1940i	0.518529	+	0.659702i
$401$			5.24675i			0.262010i	0.991382	+	0.131005i	$0.0418204\pi$
$401$			5.24675i			0.262010i	−0.991382	+	0.131005i	$0.958180\pi$
$402$	9.85434	+	9.17378i	0.491490	+	0.457546i
$403$		0			0
$404$	6.42559	−	13.2234i	0.319685	−	0.657890i
$405$	4.03312	−	6.99291i	0.200407	−	0.347481i
$406$	−9.34596	+	5.84951i	−0.463832	+	0.290306i
$407$		0			0
$408$	7.28366	+	18.8446i	0.360595	+	0.932946i
$409$	28.1657			1.39271			0.696353	−	0.717699i	$-0.254805\pi$
$409$	28.1657			1.39271			0.696353	+	0.717699i	$0.254805\pi$
$410$	10.8883	−	6.81483i	0.537735	−	0.336561i
$411$	−5.30807	−	19.8010i	−0.261828	−	0.976711i
$412$	24.0758	+	11.6990i	1.18613	+	0.576369i
$413$	−6.89932			−0.339493
$414$	26.7046	+	14.1663i	1.31246	+	0.696235i
$415$		−	11.9774i		−	0.587945i
$416$	9.84444	+	3.54240i	0.482663	+	0.173681i
$417$	18.4780	−	4.95343i	0.904874	−	0.242570i
$418$		0			0
$419$		−	2.23921i		−	0.109393i	−0.998503	−	0.0546963i	$-0.982581\pi$
$419$		−	2.23921i		−	0.109393i	0.998503	−	0.0546963i	$-0.0174191\pi$
$420$	3.05099	+	0.588066i	0.148873	+	0.0286947i
$421$			6.99291i			0.340814i	0.985374	+	0.170407i	$0.0545082\pi$
$421$			6.99291i			0.340814i	−0.985374	+	0.170407i	$0.945492\pi$
$422$	−11.9202	−	19.0454i	−0.580268	−	0.927115i
$423$	−24.9128	+	14.3909i	−1.21130	+	0.699711i
$424$	23.1955	−	2.48937i	1.12647	−	0.120894i
$425$		−	17.3020i		−	0.839269i
$426$	−7.39366	−	6.88304i	−0.358224	−	0.333484i
$427$	−4.54143			−0.219775
$428$	−3.22701	−	1.56808i	−0.155983	−	0.0757962i
$429$		0			0
$430$	0.804530	+	1.28543i	0.0387979	+	0.0619887i
$431$	9.80966			0.472515			0.236257	−	0.971691i	$-0.424079\pi$
$431$	9.80966			0.472515			0.236257	+	0.971691i	$0.424079\pi$
$432$	−20.6378	−	2.46566i	−0.992939	−	0.118629i
$433$	−23.3839			−1.12376			−0.561878	−	0.827220i	$-0.689921\pi$
$433$	−23.3839			−1.12376			−0.561878	+	0.827220i	$0.689921\pi$
$434$		0			0
$435$	11.6990	−	3.13617i	0.560925	−	0.150368i
$436$	9.54852	+	4.63986i	0.457291	+	0.222209i
$437$	4.66011			0.222923
$438$	10.7571	+	10.0142i	0.513995	+	0.478497i
$439$			20.3768i			0.972530i	0.873811	+	0.486265i	$0.161641\pi$
$439$			20.3768i			0.972530i	−0.873811	+	0.486265i	$0.838359\pi$
$440$		0			0
$441$	−2.59774	+	1.50059i	−0.123702	+	0.0714567i
$442$	−5.72273	−	9.14341i	−0.272202	−	0.434907i
$443$		−	36.5668i		−	1.73734i	−0.495389	−	0.868671i	$-0.664974\pi$
$443$		−	36.5668i		−	1.73734i	0.495389	−	0.868671i	$-0.335026\pi$
$444$	−36.3685	−	7.00989i	−1.72597	−	0.332675i
$445$		−	12.3010i		−	0.583123i
$446$	−10.7975	+	6.75798i	−0.511274	+	0.319999i
$447$	−7.79627	+	2.08995i	−0.368751	+	0.0988515i
$448$	−1.69759	−	7.81781i	−0.0802035	−	0.369357i
$449$		−	19.1804i		−	0.905178i	−0.891719	−	0.452589i	$-0.850501\pi$
$449$		−	19.1804i		−	0.905178i	0.891719	−	0.452589i	$-0.149499\pi$
$450$	15.7244	+	8.34147i	0.741253	+	0.393221i
$451$		0			0
$452$	−5.39873	−	2.62337i	−0.253935	−	0.123393i
$453$	−5.64155	−	21.0450i	−0.265063	−	0.988779i
$454$	−27.5041	+	17.2144i	−1.29083	+	0.807913i
$455$	−1.65893			−0.0777717
$456$	−2.98864	+	1.15515i	−0.139956	+	0.0540947i
$457$	−20.5935			−0.963323			−0.481662	−	0.876357i	$-0.659967\pi$
$457$	−20.5935			−0.963323			−0.481662	+	0.876357i	$0.659967\pi$
$458$	13.1054	−	8.20251i	0.612377	−	0.383278i
$459$	15.1576	+	15.1472i	0.707495	+	0.707013i
$460$	5.58641	−	11.4965i	0.260468	−	0.536025i
$461$	−2.69087			−0.125326			−0.0626631	−	0.998035i	$-0.519959\pi$
$461$	−2.69087			−0.125326			−0.0626631	+	0.998035i	$0.519959\pi$
$462$		0			0
$463$			4.78188i			0.222233i	0.993807	+	0.111116i	$0.0354427\pi$
$463$			4.78188i			0.222233i	−0.993807	+	0.111116i	$0.964557\pi$
$464$	−19.2712	−	24.5180i	−0.894644	−	1.13822i
$465$		0			0
$466$	9.88740	−	6.18838i	0.458025	−	0.286671i
$467$			23.8341i			1.10291i	0.834204	+	0.551456i	$0.185927\pi$
$467$			23.8341i			1.10291i	−0.834204	+	0.551456i	$0.814073\pi$
$468$	11.0687	−	0.792785i	0.511650	−	0.0366465i
$469$			5.49646i			0.253803i
$470$	6.45402	+	10.3118i	0.297702	+	0.475648i
$471$	−8.76072	−	32.6806i	−0.403673	−	1.50584i
$472$	−2.08233	−	19.4028i	−0.0958472	−	0.893086i
$473$		0			0
$474$	22.3381	−	23.9953i	1.02602	−	1.10214i
$475$	2.74399			0.125903
$476$	−3.60482	+	7.41847i	−0.165226	+	0.340025i
$477$	21.4259	−	12.3768i	0.981026	−	0.566693i
$478$	3.66112	+	5.84951i	0.167456	+	0.267550i
$479$	15.5925			0.712442			0.356221	−	0.934402i	$-0.384065\pi$
$479$	15.5925			0.712442			0.356221	+	0.934402i	$0.384065\pi$
$480$	−0.732964	+	8.75772i	−0.0334551	+	0.399733i
$481$	19.7748			0.901653
$482$	3.74616	+	5.98537i	0.170633	+	0.272626i
$483$	3.19547	+	11.9202i	0.145399	+	0.542390i
$484$	−9.61525	+	19.7875i	−0.437057	+	0.899434i
$485$	−8.06624			−0.366269
$486$	−21.0737	+	6.47283i	−0.955924	+	0.293614i
$487$		−	16.2026i		−	0.734208i	−0.930180	−	0.367104i	$-0.880349\pi$
$487$		−	16.2026i		−	0.734208i	0.930180	−	0.367104i	$-0.119651\pi$
$488$	−1.37068	−	12.7718i	−0.0620479	−	0.578151i
$489$	15.3839	−	4.12397i	0.695682	−	0.186492i
$490$	0.672982	+	1.07525i	0.0304022	+	0.0485747i
$491$		−	6.62299i		−	0.298891i	−0.988770	−	0.149446i	$-0.952251\pi$
$491$		−	6.62299i		−	0.298891i	0.988770	−	0.149446i	$-0.0477489\pi$
$492$	−34.4446	−	6.63907i	−1.55288	−	0.299312i
$493$			32.1516i			1.44803i
$494$	1.45009	−	0.907591i	0.0652427	−	0.0408345i
$495$		0			0
$496$		0			0
$497$		−	4.12397i		−	0.184985i
$498$	−22.2872	+	23.9406i	−0.998712	+	1.07280i
$499$	21.2713			0.952232			0.476116	−	0.879383i	$-0.342044\pi$
$499$	21.2713			0.952232			0.476116	+	0.879383i	$0.342044\pi$
$500$	7.20963	−	14.8369i	0.322425	−	0.663528i
$501$	19.8010	−	5.30807i	0.884643	−	0.237147i
$502$	13.3157	−	8.33411i	0.594309	−	0.371969i
$503$	−1.07228			−0.0478108			−0.0239054	−	0.999714i	$-0.507610\pi$
$503$	−1.07228			−0.0478108			−0.0239054	+	0.999714i	$0.507610\pi$
$504$	−5.00412	−	6.85265i	−0.222901	−	0.305241i
$505$	−6.59350			−0.293407
$506$		0			0
$507$	16.0260	−	4.29611i	0.711741	−	0.190797i
$508$	−25.5230	−	12.4023i	−1.13240	−	0.550262i
$509$	1.78755			0.0792320			0.0396160	−	0.999215i	$-0.487387\pi$
$509$	1.78755			0.0792320			0.0396160	+	0.999215i	$0.487387\pi$
$510$	6.17378	−	6.63179i	0.273380	−	0.293661i
$511$			6.00000i			0.265424i
$512$	21.4735	−	7.13364i	0.949004	−	0.315265i
$513$	−2.40226	+	2.40390i	−0.106063	+	0.106135i
$514$	−13.7482	+	8.60482i	−0.606408	+	0.379542i
$515$		−	12.0047i		−	0.528991i
$516$	0.783780	−	4.06638i	0.0345040	−	0.179013i
$517$		0			0
$518$	−8.02210	−	12.8172i	−0.352471	−	0.563155i
$519$	32.3817	−	8.68060i	1.42140	−	0.381036i
$520$	−0.500693	−	4.66536i	−0.0219568	−	0.204590i
$521$		−	8.95304i		−	0.392240i	−0.980580	−	0.196120i	$-0.937166\pi$
$521$		−	8.95304i		−	0.392240i	0.980580	−	0.196120i	$-0.0628342\pi$
$522$	−29.2199	−	15.5006i	−1.27892	−	0.678444i
$523$	1.25601			0.0549214			0.0274607	−	0.999623i	$-0.491258\pi$
$523$	1.25601			0.0549214			0.0274607	+	0.999623i	$0.491258\pi$
$524$	−30.4749	−	14.8085i	−1.33130	−	0.646913i
$525$	1.88158	+	7.01894i	0.0821187	+	0.306332i
$526$	9.28257	+	14.8311i	0.404739	+	0.646666i
$527$		0			0
$528$		0			0
$529$	27.7677			1.20729
$530$	−5.55071	−	8.86856i	−0.241107	−	0.385226i
$531$	−10.3531	−	17.9226i	−0.449284	−	0.777775i
$532$	−1.17653	−	0.571703i	−0.0510088	−	0.0247865i
$533$	18.7287			0.811231
$534$	−22.8894	+	24.5875i	−0.990521	+	1.06400i
$535$			1.60906i			0.0695657i
$536$	−15.4576	+	1.65893i	−0.667665	+	0.0716547i
$537$	6.59350	+	24.5961i	0.284530	+	1.06140i
$538$	18.5604	+	29.6546i	0.800195	+	1.27850i
$539$		0			0
$540$	3.05065	+	8.80811i	0.131279	+	0.379041i
$541$		−	44.3768i		−	1.90791i	−0.299956	−	0.953953i	$-0.596972\pi$
$541$		−	44.3768i		−	1.90791i	0.299956	−	0.953953i	$-0.403028\pi$
$542$	24.9128	−	15.5925i	1.07009	−	0.669757i
$543$	−2.03673	−	7.59774i	−0.0874046	−	0.326050i
$544$	−21.9508	−	7.89872i	−0.941132	−	0.338655i
$545$		−	4.76111i		−	0.203943i
$546$	3.31590	+	3.08689i	0.141907	+	0.132107i
$547$	−6.80453			−0.290941			−0.145470	−	0.989363i	$-0.546470\pi$
$547$	−6.80453			−0.290941			−0.145470	+	0.989363i	$0.546470\pi$
$548$	21.2910	+	10.3458i	0.909504	+	0.441951i
$549$	−6.81483	−	11.7974i	−0.290850	−	0.503503i
$550$		0			0
$551$	−5.09905			−0.217227
$552$	−32.5586	+	12.5843i	−1.38578	+	0.535623i
$553$	13.3839			0.569139
$554$	1.92890	−	1.20727i	0.0819510	−	0.0512920i
$555$	4.30099	+	16.0442i	0.182567	+	0.681039i
$556$	−9.65457	+	19.8685i	−0.409445	+	0.842610i
$557$	−46.6087			−1.97487			−0.987436	−	0.158017i	$-0.949490\pi$
$557$	−46.6087			−1.97487			−0.987436	+	0.158017i	$0.949490\pi$
$558$		0			0
$559$			2.21103i			0.0935166i
$560$	−2.82077	+	2.21714i	−0.119199	+	0.0936912i
$561$		0			0
$562$	5.58641	−	3.49646i	0.235649	−	0.147489i
$563$			6.89932i			0.290772i	0.989375	+	0.145386i	$0.0464423\pi$
$563$			6.89932i			0.290772i	−0.989375	+	0.145386i	$0.953558\pi$
$564$	6.28756	−	32.6210i	0.264754	−	1.37359i
$565$			2.69193i			0.113250i
$566$	−10.3067	−	16.4674i	−0.433224	−	0.692178i
$567$	−7.79627	−	4.49646i	−0.327413	−	0.188833i
$568$	11.5977	−	1.24468i	0.486630	−	0.0522258i
$569$			6.75798i			0.283309i	0.989916	+	0.141655i	$0.0452422\pi$
$569$			6.75798i			0.283309i	−0.989916	+	0.141655i	$0.954758\pi$
$570$	1.05176	+	0.979126i	0.0440535	+	0.0410111i
$571$	17.1955			0.719608			0.359804	−	0.933028i	$-0.382844\pi$
$571$	17.1955			0.719608			0.359804	+	0.933028i	$0.382844\pi$
$572$		0			0
$573$	−2.85984	+	0.766640i	−0.119471	+	0.0320268i
$574$	−7.59774	−	12.1392i	−0.317123	−	0.506679i
$575$	29.8933			1.24664
$576$	17.7612	−	16.1412i	0.740051	−	0.672551i
$577$	−27.1586			−1.13063			−0.565315	−	0.824875i	$-0.691245\pi$
$577$	−27.1586			−1.13063			−0.565315	+	0.824875i	$0.691245\pi$
$578$	0.00531777	+	0.00849639i	0.000221190	+	0.000353403i
$579$	27.0829	−	7.26013i	1.12553	−	0.301721i
$580$	−6.11260	+	12.5793i	−0.253812	+	0.522328i
$581$	−13.3533			−0.553990
$582$	16.1230	+	15.0095i	0.668319	+	0.622163i
$583$		0			0
$584$	−16.8737	+	1.81090i	−0.698237	+	0.0749358i
$585$	−2.48937	−	4.30945i	−0.102923	−	0.178174i
$586$	−14.5225	−	23.2031i	−0.599918	−	0.958511i
$587$			26.5313i			1.09507i	0.836784	+	0.547533i	$0.184433\pi$
$587$			26.5313i			1.09507i	−0.836784	+	0.547533i	$0.815567\pi$
$588$	0.655624	−	3.40149i	0.0270375	−	0.140275i
$589$		0			0
$590$	−7.41847	+	4.64311i	−0.305413	+	0.191154i
$591$	−16.0442	+	4.30099i	−0.659970	+	0.176919i
$592$	33.6243	−	26.4288i	1.38195	−	1.08622i
$593$		−	27.9644i		−	1.14836i	−0.818728	−	0.574181i	$-0.805321\pi$
$593$		−	27.9644i		−	1.14836i	0.818728	−	0.574181i	$-0.194679\pi$
$594$		0			0
$595$	3.69901			0.151645
$596$	4.07347	−	8.38292i	0.166856	−	0.343378i
$597$	−6.45402	−	24.0758i	−0.264145	−	0.985356i
$598$	15.7974	−	9.88740i	0.646005	−	0.404326i
$599$	35.0391			1.43166			0.715829	−	0.698275i	$-0.246049\pi$
$599$	35.0391			1.43166			0.715829	+	0.698275i	$0.246049\pi$
$600$	−19.1713	+	7.40995i	−0.782666	+	0.302510i
$601$	6.37677			0.260114			0.130057	−	0.991507i	$-0.458484\pi$
$601$	6.37677			0.260114			0.130057	+	0.991507i	$0.458484\pi$
$602$	1.43310	−	0.896956i	0.0584087	−	0.0365572i
$603$	−14.2783	+	8.24793i	−0.581459	+	0.335882i
$604$	22.6285	+	10.9958i	0.920742	+	0.447411i
$605$	9.86651			0.401131
$606$	13.1792	+	12.2690i	0.535369	+	0.498395i
$607$			8.60197i			0.349143i	0.984644	+	0.174572i	$0.0558541\pi$
$607$			8.60197i			0.349143i	−0.984644	+	0.174572i	$0.944146\pi$
$608$	1.25269	−	3.48127i	0.0508033	−	0.141184i
$609$	−3.49646	−	13.0430i	−0.141684	−	0.528530i
$610$	−4.88316	+	3.05630i	−0.197713	+	0.123746i
$611$			17.7371i			0.717567i
$612$	−24.6806	+	1.76772i	−0.997653	+	0.0714560i
$613$			19.2939i			0.779273i	0.920969	+	0.389637i	$0.127399\pi$
$613$			19.2939i			0.779273i	−0.920969	+	0.389637i	$0.872601\pi$
$614$	23.1239	+	36.9459i	0.933206	+	1.49102i
$615$	4.07347	+	15.1955i	0.164258	+	0.612741i
$616$		0			0
$617$		−	10.0758i		−	0.405638i	−0.979216	−	0.202819i	$-0.934990\pi$
$617$		−	10.0758i		−	0.405638i	0.979216	−	0.202819i	$-0.0650102\pi$
$618$	−22.3381	+	23.9953i	−0.898571	+	0.965232i
$619$	−16.7298			−0.672428			−0.336214	−	0.941786i	$-0.609147\pi$
$619$	−16.7298			−0.672428			−0.336214	+	0.941786i	$0.609147\pi$
$620$		0			0
$621$	−26.1705	+	26.1884i	−1.05019	+	1.05090i
$622$	4.50354	+	7.19547i	0.180576	+	0.288512i
$623$	−13.7142			−0.549446
$624$	−7.68040	+	10.2569i	−0.307462	+	0.410604i
$625$	13.5793			0.543173
$626$	10.3352	+	16.5129i	0.413076	+	0.659986i
$627$		0			0
$628$	35.1397	+	17.0752i	1.40223	+	0.681377i
$629$	−44.0931			−1.75811
$630$	−1.78334	+	3.36173i	−0.0710498	+	0.133935i
$631$			20.7819i			0.827314i	0.910433	+	0.413657i	$0.135749\pi$
$631$			20.7819i			0.827314i	−0.910433	+	0.413657i	$0.864251\pi$
$632$	4.03948	+	37.6391i	0.160682	+	1.49720i
$633$	26.5793	−	7.12515i	1.05643	−	0.283199i
$634$	2.81870	+	4.50354i	0.111945	+	0.178859i
$635$			12.7264i			0.505030i
$636$	−5.40754	+	28.0553i	−0.214423	+	1.11246i
$637$			1.84951i			0.0732801i
$638$		0			0
$639$	10.7130	−	6.18838i	0.423799	−	0.244809i
$640$	−7.08657	−	7.26363i	−0.280121	−	0.287120i
$641$			37.6051i			1.48531i	0.669672	+	0.742657i	$0.266435\pi$
$641$			37.6051i			1.48531i	−0.669672	+	0.742657i	$0.733565\pi$
$642$	2.99410	−	3.21622i	0.118168	−	0.126934i
$643$	−25.7369			−1.01496			−0.507482	−	0.861662i	$-0.669424\pi$
$643$	−25.7369			−1.01496			−0.507482	+	0.861662i	$0.669424\pi$
$644$	−12.8172	−	6.22819i	−0.505068	−	0.245425i
$645$	−1.79391	+	0.480896i	−0.0706352	+	0.0189352i
$646$	−3.23336	+	2.02371i	−0.127215	+	0.0796220i
$647$	41.8476			1.64520			0.822599	−	0.568622i	$-0.192523\pi$
$647$	41.8476			1.64520			0.822599	+	0.568622i	$0.192523\pi$
$648$	10.2922	−	23.2824i	0.404317	−	0.914619i
$649$		0			0
$650$	9.30194	−	5.82196i	0.364852	−	0.228356i
$651$		0			0
$652$	−8.03789	+	16.5414i	−0.314788	+	0.647813i
$653$	−10.0418			−0.392968			−0.196484	−	0.980507i	$-0.562952\pi$
$653$	−10.0418			−0.392968			−0.196484	+	0.980507i	$0.562952\pi$
$654$	−8.85936	+	9.51660i	−0.346428	+	0.372128i
$655$			15.1955i			0.593736i
$656$	31.8456	−	25.0308i	1.24336	−	0.977287i
$657$	−15.5864	+	9.00354i	−0.608084	+	0.351262i
$658$	11.4965	−	7.19547i	0.448179	−	0.280509i
$659$			48.5843i			1.89257i	0.323327	+	0.946287i	$0.395199\pi$
$659$			48.5843i			1.89257i	−0.323327	+	0.946287i	$0.604801\pi$
$660$		0			0
$661$			0.164668i			0.00640485i	0.999995	+	0.00320242i	$0.00101936\pi$
$661$			0.164668i			0.00640485i	−0.999995	+	0.00320242i	$0.998981\pi$
$662$	4.65375	+	7.43546i	0.180873	+	0.288987i
$663$	12.7603	−	3.42068i	0.495570	−	0.132848i
$664$	−4.03027	−	37.5533i	−0.156405	−	1.45735i
$665$			0.586642i			0.0227490i
$666$	21.2578	−	40.0727i	0.823723	−	1.55278i
$667$	−55.5496			−2.15089
$668$	−10.3458	+	21.2910i	−0.400291	+	0.823772i
$669$	−4.03948	−	15.0687i	−0.156175	−	0.582589i
$670$	3.69901	+	5.91005i	0.142905	+	0.228325i
$671$		0			0
$672$	9.76382	+	0.817168i	0.376648	+	0.0315230i
$673$	7.00709			0.270103			0.135052	−	0.990839i	$-0.456880\pi$
$673$	7.00709			0.270103			0.135052	+	0.990839i	$0.456880\pi$
$674$	10.9388	+	17.4773i	0.421347	+	0.673200i
$675$	−15.4099	+	15.4204i	−0.593127	+	0.593531i
$676$	−8.37342	+	17.2319i	−0.322055	+	0.662767i
$677$	−6.27869			−0.241310			−0.120655	−	0.992695i	$-0.538499\pi$
$677$	−6.27869			−0.241310			−0.120655	+	0.992695i	$0.538499\pi$
$678$	5.00908	−	5.38068i	0.192372	−	0.206644i
$679$			8.99291i			0.345116i
$680$	1.11643	+	10.4027i	0.0428130	+	0.398924i
$681$	−10.2897	−	38.3841i	−0.394301	−	1.47088i
$682$		0			0
$683$		−	30.2945i		−	1.15919i	−0.814906	−	0.579593i	$-0.803211\pi$
$683$		−	30.2945i		−	1.15919i	0.814906	−	0.579593i	$-0.196789\pi$
$684$	−0.280351	−	3.91419i	−0.0107195	−	0.149663i
$685$		−	10.6161i		−	0.405622i
$686$	1.19877	−	0.750295i	0.0457694	−	0.0286464i
$687$	4.90293	+	18.2897i	0.187058	+	0.697794i
$688$	2.95502	+	3.75955i	0.112659	+	0.143332i
$689$		−	15.2546i		−	0.581154i
$690$	11.4580	+	10.6667i	0.436199	+	0.406074i
$691$	−15.6469			−0.595238			−0.297619	−	0.954685i	$-0.596193\pi$
$691$	−15.6469			−0.595238			−0.297619	+	0.954685i	$0.596193\pi$
$692$	−16.9191	+	34.8183i	−0.643167	+	1.32359i
$693$		0			0
$694$	10.0900	−	6.31516i	0.383009	−	0.239720i
$695$	9.90686			0.375788
$696$	35.6253	−	13.7696i	1.35037	−	0.521936i
$697$	−41.7606			−1.58180
$698$	−31.0785	+	19.4516i	−1.17634	+	0.736255i
$699$	3.69901	+	13.7986i	0.139910	+	0.521912i
$700$	−7.54710	−	3.66732i	−0.285253	−	0.138612i
$701$	6.45402			0.243765			0.121882	−	0.992545i	$-0.461107\pi$
$701$	6.45402			0.243765			0.121882	+	0.992545i	$0.461107\pi$
$702$	−3.04313	+	13.2460i	−0.114855	+	0.499937i
$703$		−	6.99291i		−	0.263743i
$704$		0			0
$705$	−14.3909	+	3.85779i	−0.541994	+	0.145293i
$706$	16.4402	−	10.2897i	0.618733	−	0.387257i
$707$			7.35097i			0.276462i
$708$	23.4680	+	4.52336i	0.881981	+	0.169998i
$709$			18.0900i			0.679383i	0.940537	+	0.339691i	$0.110323\pi$
$709$			18.0900i			0.679383i	−0.940537	+	0.339691i	$0.889677\pi$
$710$	−2.77535	−	4.43428i	−0.104157	−	0.166416i
$711$	20.0837	+	34.7677i	0.753197	+	1.30389i
$712$	−4.13917	−	38.5680i	−0.155122	−	1.44540i
$713$		0			0
$714$	−7.39366	−	6.88304i	−0.276701	−	0.257591i
$715$		0			0
$716$	−26.4469	−	12.8512i	−0.988366	−	0.480271i
$717$	−8.16344	+	2.18838i	−0.304869	+	0.0817267i
$718$	−19.7369	−	31.5343i	−0.736575	−	1.17685i
$719$	5.83339			0.217549			0.108774	−	0.994066i	$-0.465307\pi$
$719$	5.83339			0.217549			0.108774	+	0.994066i	$0.465307\pi$
$720$	−9.99237	−	4.00061i	−0.372394	−	0.149094i
$721$	−13.3839			−0.498441
$722$	13.9347	+	22.2639i	0.518594	+	0.828576i
$723$	−8.35305	+	2.23921i	−0.310653	+	0.0832771i
$724$	8.16944	+	3.96973i	0.303615	+	0.147534i
$725$	−32.7090			−1.21478
$726$	−19.7214	−	18.3594i	−0.731929	−	0.681381i
$727$			4.22521i			0.156704i	0.996926	+	0.0783521i	$0.0249658\pi$
$727$			4.22521i			0.156704i	−0.996926	+	0.0783521i	$0.975034\pi$
$728$	−5.20133	+	0.558213i	−0.192774	+	0.0206888i
$729$	−0.0184116	−	27.0000i	−0.000681912	−	1.00000i
$730$	4.03789	+	6.45148i	0.149449	+	0.238780i
$731$		−	4.93008i		−	0.182346i
$732$	15.4477	+	2.97747i	0.570962	+	0.110051i
$733$		−	43.6101i		−	1.61078i	−0.592747	−	0.805388i	$-0.701957\pi$
$733$		−	43.6101i		−	1.61078i	0.592747	−	0.805388i	$-0.298043\pi$
$734$	23.7055	−	14.8369i	0.874986	−	0.547641i
$735$	−1.50059	+	0.402265i	−0.0553501	+	0.0148378i
$736$	13.6469	−	37.9253i	0.503033	−	1.39794i
$737$		0			0
$738$	20.1333	−	37.9528i	0.741115	−	1.39706i
$739$	−5.97735			−0.219880			−0.109940	−	0.993938i	$-0.535066\pi$
$739$	−5.97735			−0.219880			−0.109940	+	0.993938i	$0.535066\pi$
$740$	−17.2515	−	8.38292i	−0.634177	−	0.308162i
$741$	0.542499	+	2.02371i	0.0199292	+	0.0743430i
$742$	−9.88740	+	6.18838i	−0.362978	+	0.227183i
$743$	−49.9770			−1.83348			−0.916740	−	0.399485i	$-0.869189\pi$
$743$	−49.9770			−1.83348			−0.916740	+	0.399485i	$0.869189\pi$
$744$		0			0
$745$	−4.17991			−0.153140
$746$	−4.52512	+	2.83221i	−0.165676	+	0.103695i
$747$	−20.0379	−	34.6884i	−0.733148	−	1.26918i
$748$		0			0
$749$	1.79391			0.0655481
$750$	14.7873	+	13.7661i	0.539957	+	0.502666i
$751$		−	31.7974i		−	1.16031i	−0.814508	−	0.580153i	$-0.802993\pi$
$751$		−	31.7974i		−	1.16031i	0.814508	−	0.580153i	$-0.197007\pi$
$752$	23.7055	+	30.1595i	0.864450	+	1.09980i
$753$	4.98159	+	18.5831i	0.181539	+	0.677206i
$754$	−17.2854	+	10.8187i	−0.629498	+	0.393994i
$755$		−	11.2831i		−	0.410634i
$756$	9.82000	−	3.40111i	0.357150	−	0.123697i
$757$			34.0900i			1.23902i	0.784989	+	0.619510i	$0.212669\pi$
$757$			34.0900i			1.23902i	−0.784989	+	0.619510i	$0.787331\pi$
$758$	6.44766	+	10.3017i	0.234190	+	0.374173i
$759$		0			0
$760$	−1.64980	+	0.177059i	−0.0598445	+	0.00642260i
$761$		−	0.806113i		−	0.0292216i	−0.999893	−	0.0146108i	$-0.995349\pi$
$761$		−	0.806113i		−	0.0292216i	0.999893	−	0.0146108i	$-0.00465092\pi$
$762$	23.6809	−	25.4377i	0.857869	−	0.921510i
$763$	−5.30807			−0.192165
$764$	1.49423	−	3.07503i	0.0540595	−	0.111251i
$765$	5.55071	+	9.60906i	0.200686	+	0.347416i
$766$	13.3839	+	21.3839i	0.483578	+	0.772630i
$767$	−12.7603			−0.460749
$768$	0.648787	+	27.7052i	0.0234111	+	0.999726i
$769$	−17.7748			−0.640975			−0.320488	−	0.947253i	$-0.603847\pi$
$769$	−17.7748			−0.640975			−0.320488	+	0.947253i	$0.603847\pi$
$770$		0			0
$771$	−5.14341	−	19.1867i	−0.185235	−	0.690993i
$772$	−14.1505	+	29.1208i	−0.509287	+	1.04808i
$773$	17.3928			0.625576			0.312788	−	0.949823i	$-0.398737\pi$
$773$	17.3928			0.625576			0.312788	+	0.949823i	$0.398737\pi$
$774$	4.48055	+	2.37685i	0.161050	+	0.0854339i
$775$		0			0
$776$	−25.2906	+	2.71422i	−0.907878	+	0.0974347i
$777$	17.8874	−	4.79509i	0.641707	−	0.172023i
$778$	−5.84951	−	9.34596i	−0.209715	−	0.335069i
$779$		−	6.62299i		−	0.237293i
$780$	5.64283	+	1.08763i	0.202046	+	0.0389435i
$781$		0			0
$782$	−35.2246	+	22.0466i	−1.25963	+	0.788384i
$783$	28.6356	−	28.6551i	1.02335	−	1.02405i
$784$	2.47185	+	3.14483i	0.0882803	+	0.112315i
$785$		−	17.5214i		−	0.625367i
$786$	28.2754	−	30.3730i	1.00855	−	1.08337i
$787$	19.0450			0.678880			0.339440	−	0.940628i	$-0.389762\pi$
$787$	19.0450			0.678880			0.339440	+	0.940628i	$0.389762\pi$
$788$	8.38292	−	17.2515i	0.298629	−	0.614558i
$789$	−20.6980	+	5.54852i	−0.736867	+	0.197533i
$790$	14.3909	−	9.00709i	0.512007	−	0.320458i
$791$	3.00118			0.106710
$792$		0			0
$793$	−8.39941			−0.298272
$794$	26.6443	−	16.6763i	0.945569	−	0.591819i
$795$	12.3768	−	3.31785i	0.438959	−	0.117672i
$796$	25.8874	+	12.5793i	0.917554	+	0.445862i
$797$	41.2333			1.46056			0.730279	−	0.683149i	$-0.239390\pi$
$797$	41.2333			1.46056			0.730279	+	0.683149i	$0.239390\pi$
$798$	1.09161	−	1.17259i	0.0386426	−	0.0415093i
$799$		−	39.5496i		−	1.39916i
$800$	8.03568	−	22.3314i	0.284104	−	0.789534i
$801$	−20.5793	−	35.6257i	−0.727135	−	1.25877i
$802$	6.28966	−	3.93661i	0.222096	−	0.139007i
$803$		0			0
$804$	3.60361	−	18.6962i	0.127090	−	0.659363i
$805$			6.39094i			0.225251i
$806$		0			0
$807$	−41.3853	+	11.0942i	−1.45683	+	0.390534i
$808$	−20.6730	+	2.21865i	−0.727273	+	0.0780519i
$809$			37.5041i			1.31857i	0.751891	+	0.659287i	$0.229142\pi$
$809$			37.5041i			1.31857i	−0.751891	+	0.659287i	$0.770858\pi$
$810$	−11.4089	+	0.411950i	−0.400870	+	0.0144745i
$811$	52.9097			1.85791			0.928956	−	0.370190i	$-0.120708\pi$
$811$	52.9097			1.85791			0.928956	+	0.370190i	$0.120708\pi$
$812$	14.0245	+	6.81483i	0.492162	+	0.239154i
$813$	9.32021	+	34.7677i	0.326874	+	1.21936i
$814$		0			0
$815$	8.24793			0.288912
$816$	17.1255	−	22.8705i	0.599512	−	0.800626i
$817$	0.781882			0.0273546
$818$	−21.1326	−	33.7643i	−0.738885	−	1.18054i
$819$	−4.80453	+	2.77535i	−0.167884	+	0.0969787i
$820$	−16.3389	−	7.93946i	−0.570578	−	0.277258i
$821$	31.0161			1.08247			0.541235	−	0.840871i	$-0.317957\pi$
$821$	31.0161			1.08247			0.541235	+	0.840871i	$0.317957\pi$
$822$	−19.7543	+	21.2198i	−0.689010	+	0.740124i
$823$			42.1657i			1.46981i	0.678173	+	0.734903i	$0.262772\pi$
$823$			42.1657i			1.46981i	−0.678173	+	0.734903i	$0.737228\pi$
$824$	−4.03948	−	37.6391i	−0.140722	−	1.31122i
$825$		0			0
$826$	5.17653	+	8.27072i	0.180114	+	0.287775i
$827$			26.7067i			0.928682i	0.885656	+	0.464341i	$0.153709\pi$
$827$			26.7067i			0.928682i	−0.885656	+	0.464341i	$0.846291\pi$
$828$	−3.05417	−	42.6416i	−0.106140	−	1.48190i
$829$		−	49.3233i		−	1.71307i	−0.516089	−	0.856535i	$-0.672613\pi$
$829$		−	49.3233i		−	1.71307i	0.516089	−	0.856535i	$-0.327387\pi$
$830$	−14.3581	+	8.98655i	−0.498378	+	0.311928i
$831$	0.721627	+	2.69193i	0.0250330	+	0.0933819i
$832$	−3.13970	−	14.4591i	−0.108850	−	0.501279i
$833$		−	4.12397i		−	0.142887i
$834$	−19.8020	−	18.4344i	−0.685688	−	0.638333i
$835$	10.6161			0.367387
$836$		0			0
$837$		0			0
$838$	−2.68431	+	1.68007i	−0.0927278	+	0.0580370i
$839$	−46.3387			−1.59979			−0.799895	−	0.600140i	$-0.795111\pi$
$839$	−46.3387			−1.59979			−0.799895	+	0.600140i	$0.795111\pi$
$840$	−1.58418	−	4.09867i	−0.0546596	−	0.141417i
$841$	31.7819			1.09593
$842$	8.38292	−	5.24675i	0.288894	−	0.180815i
$843$	2.08995	+	7.79627i	0.0719819	+	0.268518i
$844$	−13.8874	+	28.5793i	−0.478024	+	0.983741i
$845$	8.59223			0.295582
$846$	35.9434	+	19.0673i	1.23576	+	0.655547i
$847$		−	11.0000i		−	0.377964i
$848$	−20.3876	−	25.9383i	−0.700114	−	0.890726i
$849$	22.9816	−	6.16070i	0.788726	−	0.211435i
$850$	−20.7411	+	12.9816i	−0.711415	+	0.445265i
$851$		−	76.1815i		−	2.61147i
$852$	−2.70377	+	14.0276i	−0.0926297	+	0.480579i
$853$		−	1.84951i		−	0.0633259i	−0.999499	−	0.0316630i	$-0.989920\pi$
$853$		−	1.84951i		−	0.0633259i	0.999499	−	0.0316630i	$-0.0100803\pi$
$854$	3.40742	+	5.44415i	0.116599	+	0.186295i
$855$	−1.52394	+	0.880309i	−0.0521177	+	0.0301059i
$856$	0.541434	+	5.04498i	0.0185058	+	0.172434i
$857$			55.5617i			1.89795i	0.315348	+	0.948976i	$0.397879\pi$
$857$			55.5617i			1.89795i	−0.315348	+	0.948976i	$0.602121\pi$
$858$		0			0
$859$	21.9621			0.749338			0.374669	−	0.927159i	$-0.377756\pi$
$859$	21.9621			0.749338			0.374669	+	0.927159i	$0.377756\pi$
$860$	0.937299	−	1.92890i	0.0319616	−	0.0657748i
$861$	16.9412	−	4.54143i	0.577353	−	0.154772i
$862$	−7.36014	−	11.7596i	−0.250687	−	0.400532i
$863$	23.0344			0.784099			0.392049	−	0.919944i	$-0.371766\pi$
$863$	23.0344			0.784099			0.392049	+	0.919944i	$0.371766\pi$
$864$	12.5287	+	26.5901i	0.426235	+	0.904612i
$865$	17.3612			0.590299
$866$	17.5448	+	28.0319i	0.596196	+	0.952564i
$867$	−0.0118574	+	0.00317862i	−0.000402698	+	0.000107952i
$868$		0			0
$869$		0			0
$870$	−12.5373	−	11.6714i	−0.425053	−	0.395698i
$871$			10.1657i			0.344453i
$872$	−1.60207	−	14.9278i	−0.0542529	−	0.505518i
$873$	−23.3612	+	13.4947i	−0.790657	+	0.456726i
$874$	−3.49646	−	5.58641i	−0.118269	−	0.188963i
$875$			8.24793i			0.278831i
$876$	3.93375	−	20.4090i	0.132909	−	0.689555i
$877$			24.6778i			0.833308i	0.909065	+	0.416654i	$0.136797\pi$
$877$			24.6778i			0.833308i	−0.909065	+	0.416654i	$0.863203\pi$
$878$	24.4271	−	15.2886i	0.824375	−	0.515965i
$879$	32.3817	−	8.68060i	1.09221	−	0.292789i
$880$		0			0
$881$		−	16.3987i		−	0.552485i	−0.961088	−	0.276242i	$-0.910911\pi$
$881$		−	16.3987i		−	0.552485i	0.961088	−	0.276242i	$-0.0890893\pi$
$882$	3.74794	+	1.98821i	0.126200	+	0.0669465i
$883$	18.2783			0.615115			0.307558	−	0.951529i	$-0.400488\pi$
$883$	18.2783			0.615115			0.307558	+	0.951529i	$0.400488\pi$
$884$	−6.66713	+	13.7205i	−0.224240	+	0.461471i
$885$	−2.77535	−	10.3531i	−0.0932925	−	0.348014i
$886$	−43.8353	+	27.4359i	−1.47268	+	0.921728i
$887$	−28.6696			−0.962629			−0.481315	−	0.876548i	$-0.659841\pi$
$887$	−28.6696			−0.962629			−0.481315	+	0.876548i	$0.659841\pi$
$888$	18.8839	+	48.8571i	0.633701	+	1.63954i
$889$	14.1884			0.475863
$890$	−14.7461	+	9.22937i	−0.494290	+	0.309369i
$891$		0			0
$892$	16.2026	+	7.87322i	0.542502	+	0.263615i
$893$	6.27233			0.209896
$894$	8.35489	+	7.77788i	0.279429	+	0.260131i
$895$			13.1870i			0.440793i
$896$	−8.09809	+	7.90069i	−0.270538	+	0.263944i
$897$	5.91005	+	22.0466i	0.197331	+	0.736113i
$898$	−22.9929	+	14.3909i	−0.767283	+	0.480232i
$899$		0			0
$900$	−1.79838	−	25.1085i	−0.0599458	−	0.836950i
$901$			34.0142i			1.13318i
$902$		0			0
$903$	0.536142	+	2.00000i	0.0178417	+	0.0665558i
$904$	0.905809	+	8.44015i	0.0301267	+	0.280715i
$905$		−	4.07347i		−	0.135407i
$906$	−20.9953	+	22.5529i	−0.697523	+	0.749269i
$907$	5.87322			0.195017			0.0975086	−	0.995235i	$-0.468913\pi$
$907$	5.87322			0.195017			0.0975086	+	0.995235i	$0.468913\pi$
$908$	41.2724	+	20.0553i	1.36967	+	0.665557i
$909$	−19.0959	+	11.0308i	−0.633371	+	0.365869i
$910$	1.24468	+	1.98868i	0.0412609	+	0.0659240i
$911$	−40.4548			−1.34033			−0.670164	−	0.742213i	$-0.733776\pi$
$911$	−40.4548			−1.34033			−0.670164	+	0.742213i	$0.733776\pi$
$912$	3.62712	+	2.71600i	0.120106	+	0.0899358i
$913$		0			0
$914$	15.4512	+	24.6869i	0.511080	+	0.816571i
$915$	−1.82686	−	6.81483i	−0.0603941	−	0.225291i
$916$	−19.6659	−	9.55614i	−0.649779	−	0.315744i
$917$	16.9412			0.559446
$918$	6.78545	−	29.5354i	0.223953	−	0.974814i
$919$			27.3697i			0.902842i	0.892311	+	0.451421i	$0.149083\pi$
$919$			27.3697i			0.902842i	−0.892311	+	0.451421i	$0.850917\pi$
$920$	−17.9731	+	1.92890i	−0.592556	+	0.0635939i
$921$	−51.5609	+	13.8220i	−1.69899	+	0.455450i
$922$	2.01894	+	3.22574i	0.0664904	+	0.106234i
$923$		−	7.62730i		−	0.251056i
$924$		0			0
$925$		−	44.8577i		−	1.47491i
$926$	5.73239	−	3.58782i	0.188378	−	0.117903i
$927$	−20.0837	−	34.7677i	−0.659635	−	1.14192i
$928$	−14.9324	+	41.4975i	−0.490179	+	1.36222i
$929$			23.3043i			0.764590i	0.924040	+	0.382295i	$0.124866\pi$
$929$			23.3043i			0.764590i	−0.924040	+	0.382295i	$0.875134\pi$
$930$		0			0
$931$	0.654037			0.0214352
$932$	−14.8369	−	7.20963i	−0.486000	−	0.236159i
$933$	−10.0418	+	2.69193i	−0.328755	+	0.0881297i
$934$	28.5717	−	17.8826i	0.934895	−	0.585137i
$935$		0			0
$936$	−9.25515	−	12.6740i	−0.302514	−	0.414263i
$937$	46.7535			1.52737			0.763686	−	0.645588i	$-0.223388\pi$
$937$	46.7535			1.52737			0.763686	+	0.645588i	$0.223388\pi$
$938$	6.58900	−	4.12397i	0.215139	−	0.134652i
$939$	−23.0450	+	6.17769i	−0.752044	+	0.201601i
$940$	7.51910	−	15.4738i	0.245246	−	0.504700i
$941$	51.4441			1.67703			0.838515	−	0.544879i	$-0.183424\pi$
$941$	51.4441			1.67703			0.838515	+	0.544879i	$0.183424\pi$
$942$	−32.6035	+	35.0222i	−1.06228	+	1.14109i
$943$		−	72.1516i		−	2.34958i
$944$	−21.6972	+	17.0541i	−0.706183	+	0.555063i
$945$	−3.29675	−	3.29450i	−0.107243	−	0.107170i
$946$		0			0
$947$		−	16.4959i		−	0.536043i	−0.963413	−	0.268022i	$-0.913630\pi$
$947$		−	16.4959i		−	0.536043i	0.963413	−	0.268022i	$-0.0863699\pi$
$948$	−45.5251	−	8.77478i	−1.47859	−	0.284992i
$949$			11.0970i			0.360225i
$950$	−2.05880	−	3.28942i	−0.0667964	−	0.106723i
$951$	−6.28505	+	1.68484i	−0.203807	+	0.0546346i
$952$	11.5977	−	1.24468i	0.375885	−	0.0403405i
$953$		−	21.3249i		−	0.690783i	−0.938459	−	0.345391i	$-0.887746\pi$
$953$		−	21.3249i		−	0.690783i	0.938459	−	0.345391i	$-0.112254\pi$
$954$	−30.9127	−	16.3986i	−1.00084	−	0.530925i
$955$	−1.53328			−0.0496158
$956$	4.26531	−	8.77771i	0.137950	−	0.283892i
$957$		0			0
$958$	−11.6990	−	18.6919i	−0.377978	−	0.603909i
$959$	−11.8358			−0.382196
$960$	11.0485	−	5.69222i	0.356587	−	0.183715i
$961$	31.0000			1.00000
$962$	−14.8369	−	23.7055i	−0.478362	−	0.764296i
$963$	2.69193	+	4.66011i	0.0867461	+	0.150170i
$964$	4.36437	−	8.98159i	0.140567	−	0.289277i
$965$	14.5203			0.467424
$966$	11.8921	−	12.7743i	0.382623	−	0.411008i
$967$		−	16.2026i		−	0.521039i	−0.965469	−	0.260520i	$-0.916106\pi$
$967$		−	16.2026i		−	0.521039i	0.965469	−	0.260520i	$-0.0838939\pi$
$968$	30.9351	−	3.31999i	0.994290	−	0.106709i
$969$	−1.20965	−	4.51241i	−0.0388594	−	0.144959i
$970$	6.05207	+	9.66960i	0.194320	+	0.310472i
$971$			0.175328i			0.00562655i	0.999996	+	0.00281328i	$0.000895495\pi$
$971$			0.175328i			0.00562655i	−0.999996	+	0.00281328i	$0.999105\pi$
$972$	23.5710	+	20.4061i	0.756040	+	0.654526i
$973$		−	11.0450i		−	0.354086i
$974$	−19.4232	+	12.1567i	−0.622359	+	0.389526i
$975$	3.47999	+	12.9816i	0.111449	+	0.415744i
$976$	−14.2820	+	11.2257i	−0.457157	+	0.359327i
$977$			46.6087i			1.49114i	0.666425	+	0.745572i	$0.267824\pi$
$977$			46.6087i			1.49114i	−0.666425	+	0.745572i	$0.732176\pi$
$978$	−16.4861	−	15.3476i	−0.527168	−	0.490761i
$979$		0			0
$980$	0.784042	−	1.61350i	0.0250453	−	0.0515415i
$981$	−7.96524	−	13.7890i	−0.254311	−	0.440248i
$982$	−7.93946	+	4.96920i	−0.253358	+	0.158573i
$983$	−40.4373			−1.28975			−0.644875	−	0.764288i	$-0.723091\pi$
$983$	−40.4373			−1.28975			−0.644875	+	0.764288i	$0.723091\pi$
$984$	17.8849	+	46.2726i	0.570150	+	1.47512i
$985$	−8.60197			−0.274082
$986$	38.5424	−	24.1232i	1.22744	−	0.768238i
$987$	4.30099	+	16.0442i	0.136902	+	0.510693i
$988$	−2.17599	−	1.05737i	−0.0692275	−	0.0336394i
$989$	8.51790			0.270853
$990$		0			0
$991$		−	16.6020i		−	0.527379i	−0.964608	−	0.263690i	$-0.915061\pi$
$991$		−	16.6020i		−	0.527379i	0.964608	−	0.263690i	$-0.0849394\pi$
$992$		0			0
$993$	−10.3768	+	2.78171i	−0.329297	+	0.0882749i
$994$	−4.94370	+	3.09419i	−0.156805	+	0.0981418i
$995$		−	12.9080i		−	0.409212i
$996$	45.4213	+	8.75477i	1.43923	+	0.277406i
$997$			31.3091i			0.991570i	0.868445	+	0.495785i	$0.165120\pi$
$997$			31.3091i			0.991570i	−0.868445	+	0.495785i	$0.834880\pi$
$998$	−15.9597	−	25.4994i	−0.505196	−	0.807170i
$999$	39.2980	+	39.2713i	1.24333	+	1.24249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.j.d.155.3	✓	12
3.2	odd	2	inner	168.2.j.d.155.10	yes	12
4.3	odd	2		672.2.j.d.239.4		12
8.3	odd	2	inner	168.2.j.d.155.9	yes	12
8.5	even	2		672.2.j.d.239.3		12
12.11	even	2		672.2.j.d.239.1		12
24.5	odd	2		672.2.j.d.239.2		12
24.11	even	2	inner	168.2.j.d.155.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.j.d.155.3	✓	12	1.1	even	1	trivial
168.2.j.d.155.4	yes	12	24.11	even	2	inner
168.2.j.d.155.9	yes	12	8.3	odd	2	inner
168.2.j.d.155.10	yes	12	3.2	odd	2	inner
672.2.j.d.239.1		12	12.11	even	2
672.2.j.d.239.2		12	24.5	odd	2
672.2.j.d.239.3		12	8.5	even	2
672.2.j.d.239.4		12	4.3	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.750295 - 1.19877i) q^{2} +(1.67298 - 0.448478i) q^{3} +(-0.874114 + 1.79887i) q^{4} +0.896956 q^{5} +(-1.79285 - 1.66903i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(2.59774 - 1.50059i) q^{9} +O(q^{10})\)	\(q+(-0.750295 - 1.19877i) q^{2} +(1.67298 - 0.448478i) q^{3} +(-0.874114 + 1.79887i) q^{4} +0.896956 q^{5} +(-1.79285 - 1.66903i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(2.59774 - 1.50059i) q^{9} +(-0.672982 - 1.07525i) q^{10} +(-0.655624 + 3.40149i) q^{12} -1.84951i q^{13} +(-1.19877 + 0.750295i) q^{14} +(1.50059 - 0.402265i) q^{15} +(-2.47185 - 3.14483i) q^{16} +4.12397i q^{17} +(-3.74794 - 1.98821i) q^{18} -0.654037 q^{19} +(-0.784042 + 1.61350i) q^{20} +(-0.448478 - 1.67298i) q^{21} -7.12515 q^{23} +(4.56953 - 1.76618i) q^{24} -4.19547 q^{25} +(-2.21714 + 1.38768i) q^{26} +(3.67298 - 3.67549i) q^{27} +(1.79887 + 0.874114i) q^{28} +7.79627 q^{29} +(-1.60811 - 1.49705i) q^{30} +(-1.91532 + 5.32274i) q^{32} +(4.94370 - 3.09419i) q^{34} -0.896956i q^{35} +(0.428647 + 5.98467i) q^{36} +10.6919i q^{37} +(0.490721 + 0.784042i) q^{38} +(-0.829463 - 3.09419i) q^{39} +(2.52249 - 0.270717i) q^{40} +10.1263i q^{41} +(-1.66903 + 1.79285i) q^{42} -1.19547 q^{43} +(2.33005 - 1.34596i) q^{45} +(5.34596 + 8.54143i) q^{46} -9.59019 q^{47} +(-5.54575 - 4.15267i) q^{48} -1.00000 q^{49} +(3.14784 + 5.02942i) q^{50} +(1.84951 + 6.89932i) q^{51} +(3.32702 + 1.61668i) q^{52} +8.24793 q^{53} +(-7.16190 - 1.64537i) q^{54} +(-0.301817 - 2.81228i) q^{56} +(-1.09419 + 0.293321i) q^{57} +(-5.84951 - 9.34596i) q^{58} -6.89932i q^{59} +(-0.588066 + 3.05099i) q^{60} -4.54143i q^{61} +(-1.50059 - 2.59774i) q^{63} +(7.81781 - 1.69759i) q^{64} -1.65893i q^{65} -5.49646 q^{67} +(-7.41847 - 3.60482i) q^{68} +(-11.9202 + 3.19547i) q^{69} +(-1.07525 + 0.672982i) q^{70} +4.12397 q^{71} +(6.85265 - 5.00412i) q^{72} -6.00000 q^{73} +(12.8172 - 8.02210i) q^{74} +(-7.01894 + 1.88158i) q^{75} +(0.571703 - 1.17653i) q^{76} +(-3.08689 + 3.31590i) q^{78} +13.3839i q^{79} +(-2.21714 - 2.82077i) q^{80} +(4.49646 - 7.79627i) q^{81} +(12.1392 - 7.59774i) q^{82} -13.3533i q^{83} +(3.40149 + 0.655624i) q^{84} +3.69901i q^{85} +(0.896956 + 1.43310i) q^{86} +(13.0430 - 3.49646i) q^{87} -13.7142i q^{89} +(-3.36173 - 1.78334i) q^{90} -1.84951 q^{91} +(6.22819 - 12.8172i) q^{92} +(7.19547 + 11.4965i) q^{94} -0.586642 q^{95} +(-0.817168 + 9.76382i) q^{96} -8.99291 q^{97} +(0.750295 + 1.19877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 10 q^{6} + 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 - 10 * q^6 + 4 * q^9	\( 12 q - 4 q^{4} - 10 q^{6} + 4 q^{9} + 12 q^{10} - 14 q^{12} + 4 q^{16} - 8 q^{18} - 48 q^{19} + 22 q^{24} + 4 q^{25} + 24 q^{27} + 8 q^{28} - 20 q^{30} - 8 q^{34} + 20 q^{36} - 4 q^{40} - 6 q^{42} + 40 q^{43} + 24 q^{46} - 26 q^{48} - 12 q^{49} + 8 q^{51} + 60 q^{52} + 18 q^{54} + 40 q^{57} - 56 q^{58} - 12 q^{60} + 20 q^{64} - 40 q^{67} - 20 q^{70} - 32 q^{72} - 72 q^{73} - 24 q^{75} - 12 q^{76} - 12 q^{78} + 28 q^{81} + 24 q^{82} + 6 q^{84} - 8 q^{90} - 8 q^{91} + 32 q^{94} + 18 q^{96} - 56 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 - 10 * q^6 + 4 * q^9 + 12 * q^10 - 14 * q^12 + 4 * q^16 - 8 * q^18 - 48 * q^19 + 22 * q^24 + 4 * q^25 + 24 * q^27 + 8 * q^28 - 20 * q^30 - 8 * q^34 + 20 * q^36 - 4 * q^40 - 6 * q^42 + 40 * q^43 + 24 * q^46 - 26 * q^48 - 12 * q^49 + 8 * q^51 + 60 * q^52 + 18 * q^54 + 40 * q^57 - 56 * q^58 - 12 * q^60 + 20 * q^64 - 40 * q^67 - 20 * q^70 - 32 * q^72 - 72 * q^73 - 24 * q^75 - 12 * q^76 - 12 * q^78 + 28 * q^81 + 24 * q^82 + 6 * q^84 - 8 * q^90 - 8 * q^91 + 32 * q^94 + 18 * q^96 - 56 * q^97

Introduction

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