LMFDB - Embedded newform 490.2.g.c.293.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(97,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("490.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.8
Root			$0.144868 - 1.25092i$ of defining polynomial
Character	$\chi$	$=$	490.293
Dual form			490.2.g.c.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.42962 - 1.42962i) q^{3} -1.00000i q^{4} +(0.204875 - 2.22666i) q^{5} -2.02179i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.08763i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.42962 - 1.42962i) q^{3} -1.00000i q^{4} +(0.204875 - 2.22666i) q^{5} -2.02179i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.08763i q^{9} +(-1.42962 - 1.71936i) q^{10} -4.03997 q^{11} +(-1.42962 - 1.42962i) q^{12} +(0.204875 - 0.204875i) q^{13} +(-2.89039 - 3.47617i) q^{15} -1.00000 q^{16} +(1.44231 + 1.44231i) q^{17} +(-0.769067 - 0.769067i) q^{18} +6.20333 q^{19} +(-2.22666 - 0.204875i) q^{20} +(-2.85669 + 2.85669i) q^{22} +(3.20895 + 3.20895i) q^{23} -2.02179 q^{24} +(-4.91605 - 0.912375i) q^{25} -0.289737i q^{26} +(2.73397 + 2.73397i) q^{27} +7.15869i q^{29} +(-4.50184 - 0.414214i) q^{30} -7.31256i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.77563 + 5.77563i) q^{33} +2.03974 q^{34} -1.08763 q^{36} +(3.27091 - 3.27091i) q^{37} +(4.38642 - 4.38642i) q^{38} -0.585786i q^{39} +(-1.71936 + 1.42962i) q^{40} -2.58745i q^{41} +(-4.97801 - 4.97801i) q^{43} +4.03997i q^{44} +(-2.42177 - 0.222827i) q^{45} +4.53813 q^{46} +(-0.222827 - 0.222827i) q^{47} +(-1.42962 + 1.42962i) q^{48} +(-4.12132 + 2.83103i) q^{50} +4.12392 q^{51} +(-0.204875 - 0.204875i) q^{52} +(5.85669 + 5.85669i) q^{53} +3.86642 q^{54} +(-0.827689 + 8.99566i) q^{55} +(8.86840 - 8.86840i) q^{57} +(5.06196 + 5.06196i) q^{58} -0.855404 q^{59} +(-3.47617 + 2.89039i) q^{60} -6.92077i q^{61} +(-5.17076 - 5.17076i) q^{62} +1.00000i q^{64} +(-0.414214 - 0.498161i) q^{65} +8.16797i q^{66} +(-2.23353 + 2.23353i) q^{67} +(1.44231 - 1.44231i) q^{68} +9.17514 q^{69} +7.12240 q^{71} +(-0.769067 + 0.769067i) q^{72} +(-8.15002 + 8.15002i) q^{73} -4.62576i q^{74} +(-8.33243 + 5.72374i) q^{75} -6.20333i q^{76} +(-0.414214 - 0.414214i) q^{78} -5.07627i q^{79} +(-0.204875 + 2.22666i) q^{80} +11.0799 q^{81} +(-1.82961 - 1.82961i) q^{82} +(-3.85372 + 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} -7.03997 q^{86} +(10.2342 + 10.2342i) q^{87} +(2.85669 + 2.85669i) q^{88} +3.07230 q^{89} +(-1.87002 + 1.55489i) q^{90} +(3.20895 - 3.20895i) q^{92} +(-10.4542 - 10.4542i) q^{93} -0.315125 q^{94} +(1.27091 - 13.8127i) q^{95} +2.02179i q^{96} +(-6.63103 - 6.63103i) q^{97} +4.39398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) $ 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.42962	−	1.42962i	0.825391	−	0.825391i	−0.161484	−	0.986875i	$-0.551628\pi$
$3$	1.42962	−	1.42962i	0.825391	−	0.825391i	0.986875	+	0.161484i	$0.0516280\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.204875	−	2.22666i	0.0916228	−	0.995794i
$5$	0.204875	−	2.22666i	0.0916228	−	0.995794i
$6$		−	2.02179i		−	0.825391i
$7$		0			0
$7$		0			0
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.08763i		−	0.362542i
$10$	−1.42962	−	1.71936i	−0.452085	−	0.543708i
$11$	−4.03997			−1.21810			−0.609049	−	0.793133i	$-0.708449\pi$
$11$	−4.03997			−1.21810			−0.609049	+	0.793133i	$0.708449\pi$
$12$	−1.42962	−	1.42962i	−0.412696	−	0.412696i
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	−0.678125	−	0.734947i	$-0.737207\pi$
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	0.734947	+	0.678125i	$0.237207\pi$
$14$		0			0
$15$	−2.89039	−	3.47617i	−0.746295	−	0.897544i
$16$	−1.00000			−0.250000
$17$	1.44231	+	1.44231i	0.349813	+	0.349813i	0.860040	−	0.510227i	$-0.170439\pi$
$17$	1.44231	+	1.44231i	0.349813	+	0.349813i	−0.510227	+	0.860040i	$0.670439\pi$
$18$	−0.769067	−	0.769067i	−0.181271	−	0.181271i
$19$	6.20333			1.42314			0.711571	−	0.702615i	$-0.247984\pi$
$19$	6.20333			1.42314			0.711571	+	0.702615i	$0.247984\pi$
$20$	−2.22666	−	0.204875i	−0.497897	−	0.0458114i
$21$		0			0
$22$	−2.85669	+	2.85669i	−0.609049	+	0.609049i
$23$	3.20895	+	3.20895i	0.669111	+	0.669111i	0.957510	−	0.288399i	$-0.0931229\pi$
$23$	3.20895	+	3.20895i	0.669111	+	0.669111i	−0.288399	+	0.957510i	$0.593123\pi$
$24$	−2.02179			−0.412696
$25$	−4.91605	−	0.912375i	−0.983211	−	0.182475i
$26$		−	0.289737i		−	0.0568221i
$27$	2.73397	+	2.73397i	0.526152	+	0.526152i
$28$		0			0
$29$			7.15869i			1.32934i	0.747139	+	0.664668i	$0.231427\pi$
$29$			7.15869i			1.32934i	−0.747139	+	0.664668i	$0.768573\pi$
$30$	−4.50184	−	0.414214i	−0.821920	−	0.0756247i
$31$		−	7.31256i		−	1.31338i	−0.754163	−	0.656688i	$-0.771957\pi$
$31$		−	7.31256i		−	1.31338i	0.754163	−	0.656688i	$-0.228043\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−5.77563	+	5.77563i	−1.00541	+	1.00541i
$34$	2.03974			0.349813
$35$		0			0
$36$	−1.08763			−0.181271
$37$	3.27091	−	3.27091i	0.537734	−	0.537734i	−0.385129	−	0.922863i	$-0.625843\pi$
$37$	3.27091	−	3.27091i	0.537734	−	0.537734i	0.922863	+	0.385129i	$0.125843\pi$
$38$	4.38642	−	4.38642i	0.711571	−	0.711571i
$39$		−	0.585786i		−	0.0938009i
$40$	−1.71936	+	1.42962i	−0.271854	+	0.226043i
$41$		−	2.58745i		−	0.404093i	−0.979376	−	0.202046i	$-0.935241\pi$
$41$		−	2.58745i		−	0.404093i	0.979376	−	0.202046i	$-0.0647591\pi$
$42$		0			0
$43$	−4.97801	−	4.97801i	−0.759140	−	0.759140i	0.217026	−	0.976166i	$-0.430364\pi$
$43$	−4.97801	−	4.97801i	−0.759140	−	0.759140i	−0.976166	+	0.217026i	$0.930364\pi$
$44$			4.03997i			0.609049i
$45$	−2.42177	−	0.222827i	−0.361017	−	0.0332171i
$46$	4.53813			0.669111
$47$	−0.222827	−	0.222827i	−0.0325027	−	0.0325027i	0.690669	−	0.723171i	$-0.257316\pi$
$47$	−0.222827	−	0.222827i	−0.0325027	−	0.0325027i	−0.723171	+	0.690669i	$0.757316\pi$
$48$	−1.42962	+	1.42962i	−0.206348	+	0.206348i
$49$		0			0
$50$	−4.12132	+	2.83103i	−0.582843	+	0.400368i
$51$	4.12392			0.577464
$52$	−0.204875	−	0.204875i	−0.0284110	−	0.0284110i
$53$	5.85669	+	5.85669i	0.804479	+	0.804479i	0.983792	−	0.179313i	$-0.0573876\pi$
$53$	5.85669	+	5.85669i	0.804479	+	0.804479i	−0.179313	+	0.983792i	$0.557388\pi$
$54$	3.86642			0.526152
$55$	−0.827689	+	8.99566i	−0.111606	+	1.21297i
$56$		0			0
$57$	8.86840	−	8.86840i	1.17465	−	1.17465i
$58$	5.06196	+	5.06196i	0.664668	+	0.664668i
$59$	−0.855404			−0.111364			−0.0556821	−	0.998449i	$-0.517733\pi$
$59$	−0.855404			−0.111364			−0.0556821	+	0.998449i	$0.517733\pi$
$60$	−3.47617	+	2.89039i	−0.448772	+	0.373147i
$61$		−	6.92077i		−	0.886113i	−0.896494	−	0.443057i	$-0.853894\pi$
$61$		−	6.92077i		−	0.886113i	0.896494	−	0.443057i	$-0.146106\pi$
$62$	−5.17076	−	5.17076i	−0.656688	−	0.656688i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.414214	−	0.498161i	−0.0513769	−	0.0617893i
$66$			8.16797i			1.00541i
$67$	−2.23353	+	2.23353i	−0.272870	+	0.272870i	−0.830254	−	0.557385i	$-0.811805\pi$
$67$	−2.23353	+	2.23353i	−0.272870	+	0.272870i	0.557385	+	0.830254i	$0.311805\pi$
$68$	1.44231	−	1.44231i	0.174906	−	0.174906i
$69$	9.17514			1.10456
$70$		0			0
$71$	7.12240			0.845273			0.422637	−	0.906299i	$-0.361105\pi$
$71$	7.12240			0.845273			0.422637	+	0.906299i	$0.361105\pi$
$72$	−0.769067	+	0.769067i	−0.0906355	+	0.0906355i
$73$	−8.15002	+	8.15002i	−0.953887	+	0.953887i	−0.998983	−	0.0450954i	$-0.985641\pi$
$73$	−8.15002	+	8.15002i	−0.953887	+	0.953887i	0.0450954	+	0.998983i	$0.485641\pi$
$74$		−	4.62576i		−	0.537734i
$75$	−8.33243	+	5.72374i	−0.962147	+	0.660920i
$76$		−	6.20333i		−	0.711571i
$77$		0			0
$78$	−0.414214	−	0.414214i	−0.0469005	−	0.0469005i
$79$		−	5.07627i		−	0.571125i	−0.958360	−	0.285562i	$-0.907820\pi$
$79$		−	5.07627i		−	0.571125i	0.958360	−	0.285562i	$-0.0921804\pi$
$80$	−0.204875	+	2.22666i	−0.0229057	+	0.248948i
$81$	11.0799			1.23111
$82$	−1.82961	−	1.82961i	−0.202046	−	0.202046i
$83$	−3.85372	+	3.85372i	−0.423001	+	0.423001i	−0.886236	−	0.463235i	$-0.846689\pi$
$83$	−3.85372	+	3.85372i	−0.423001	+	0.423001i	0.463235	+	0.886236i	$0.346689\pi$
$84$		0			0
$85$	3.50704	−	2.91605i	0.380392	−	0.316290i
$86$	−7.03997			−0.759140
$87$	10.2342	+	10.2342i	1.09722	+	1.09722i
$88$	2.85669	+	2.85669i	0.304524	+	0.304524i
$89$	3.07230			0.325664			0.162832	−	0.986654i	$-0.447937\pi$
$89$	3.07230			0.325664			0.162832	+	0.986654i	$0.447937\pi$
$90$	−1.87002	+	1.55489i	−0.197117	+	0.163900i
$91$		0			0
$92$	3.20895	−	3.20895i	0.334556	−	0.334556i
$93$	−10.4542	−	10.4542i	−1.08405	−	1.08405i
$94$	−0.315125			−0.0325027
$95$	1.27091	−	13.8127i	0.130392	−	1.41716i
$96$			2.02179i			0.206348i
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$		0			0
$99$			4.39398i			0.441611i
$100$	−0.912375	+	4.91605i	−0.0912375	+	0.491605i
$101$			9.88844i			0.983936i	0.870613	+	0.491968i	$0.163722\pi$
$101$			9.88844i			0.983936i	−0.870613	+	0.491968i	$0.836278\pi$
$102$	2.91605	−	2.91605i	0.288732	−	0.288732i
$103$	−3.02785	+	3.02785i	−0.298343	+	0.298343i	−0.840365	−	0.542022i	$-0.817659\pi$
$103$	−3.02785	+	3.02785i	−0.298343	+	0.298343i	0.542022	+	0.840365i	$0.317659\pi$
$104$	−0.289737			−0.0284110
$105$		0			0
$106$	8.28261			0.804479
$107$	−10.5161	+	10.5161i	−1.01663	+	1.01663i	−0.0167751	+	0.999859i	$0.505340\pi$
$107$	−10.5161	+	10.5161i	−1.01663	+	1.01663i	−0.999859	+	0.0167751i	$0.994660\pi$
$108$	2.73397	−	2.73397i	0.263076	−	0.263076i
$109$			13.2313i			1.26733i	0.773609	+	0.633664i	$0.218450\pi$
$109$			13.2313i			1.26733i	−0.773609	+	0.633664i	$0.781550\pi$
$110$	5.77563	+	6.94616i	0.550684	+	0.662290i
$111$		−	9.35230i		−	0.887681i
$112$		0			0
$113$	9.75336	+	9.75336i	0.917519	+	0.917519i	0.996848	−	0.0793296i	$-0.0252780\pi$
$113$	9.75336	+	9.75336i	0.917519	+	0.917519i	−0.0793296	+	0.996848i	$0.525278\pi$
$114$		−	12.5418i		−	1.17465i
$115$	7.80267	−	6.48781i	0.727603	−	0.604991i
$116$	7.15869			0.664668
$117$	−0.222827	−	0.222827i	−0.0206004	−	0.0206004i
$118$	−0.604862	+	0.604862i	−0.0556821	+	0.0556821i
$119$		0			0
$120$	−0.414214	+	4.50184i	−0.0378124	+	0.410960i
$121$	5.32139			0.483762
$122$	−4.89372	−	4.89372i	−0.443057	−	0.443057i
$123$	−3.69908	−	3.69908i	−0.333535	−	0.333535i
$124$	−7.31256			−0.656688
$125$	−3.03873	+	10.7595i	−0.271792	+	0.962356i
$126$		0			0
$127$	−2.19984	+	2.19984i	−0.195204	+	0.195204i	−0.797940	−	0.602736i	$-0.794077\pi$
$127$	−2.19984	+	2.19984i	−0.195204	+	0.195204i	0.602736	+	0.797940i	$0.294077\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−14.2333			−1.25317
$130$	−0.645146	−	0.0593598i	−0.0565831	−	0.00520620i
$131$		−	7.29876i		−	0.637695i	−0.947806	−	0.318848i	$-0.896704\pi$
$131$		−	7.29876i		−	0.637695i	0.947806	−	0.318848i	$-0.103296\pi$
$132$	5.77563	+	5.77563i	0.502704	+	0.502704i
$133$		0			0
$134$			3.15869i			0.272870i
$135$	6.64775	−	5.52750i	0.572147	−	0.475732i
$136$		−	2.03974i		−	0.174906i
$137$	5.07627	−	5.07627i	0.433695	−	0.433695i	−0.456188	−	0.889883i	$-0.650786\pi$
$137$	5.07627	−	5.07627i	0.433695	−	0.433695i	0.889883	+	0.456188i	$0.150786\pi$
$138$	6.48781	−	6.48781i	0.552279	−	0.552279i
$139$	12.4172			1.05321			0.526605	−	0.850110i	$-0.323465\pi$
$139$	12.4172			1.05321			0.526605	+	0.850110i	$0.323465\pi$
$140$		0			0
$141$	−0.637116			−0.0536549
$142$	5.03630	−	5.03630i	0.422637	−	0.422637i
$143$	−0.827689	+	0.827689i	−0.0692148	+	0.0692148i
$144$			1.08763i			0.0906355i
$145$	15.9400	+	1.46664i	1.32374	+	0.121798i
$146$			11.5259i			0.953887i
$147$		0			0
$148$	−3.27091	−	3.27091i	−0.268867	−	0.268867i
$149$			23.9483i			1.96193i	0.194197	+	0.980963i	$0.437790\pi$
$149$			23.9483i			1.96193i	−0.194197	+	0.980963i	$0.562210\pi$
$150$	−1.84463	+	9.93921i	−0.150613	+	0.811533i
$151$	−3.54334			−0.288353			−0.144176	−	0.989552i	$-0.546053\pi$
$151$	−3.54334			−0.288353			−0.144176	+	0.989552i	$0.546053\pi$
$152$	−4.38642	−	4.38642i	−0.355785	−	0.355785i
$153$	1.56870	−	1.56870i	0.126822	−	0.126822i
$154$		0			0
$155$	−16.2826	−	1.49816i	−1.30785	−	0.120335i
$156$	−0.585786			−0.0469005
$157$	4.32927	+	4.32927i	0.345513	+	0.345513i	0.858435	−	0.512922i	$-0.171437\pi$
$157$	4.32927	+	4.32927i	0.345513	+	0.345513i	−0.512922	+	0.858435i	$0.671437\pi$
$158$	−3.58946	−	3.58946i	−0.285562	−	0.285562i
$159$	16.7457			1.32802
$160$	1.42962	+	1.71936i	0.113021	+	0.135927i
$161$		0			0
$162$	7.83471	−	7.83471i	0.615553	−	0.615553i
$163$	−11.7082	−	11.7082i	−0.917056	−	0.917056i	0.0797585	−	0.996814i	$-0.474585\pi$
$163$	−11.7082	−	11.7082i	−0.917056	−	0.917056i	−0.996814	+	0.0797585i	$0.974585\pi$
$164$	−2.58745			−0.202046
$165$	11.6771	+	14.0437i	0.909060	+	1.09330i
$166$			5.44998i			0.423001i
$167$	−10.2873	−	10.2873i	−0.796056	−	0.796056i	0.186415	−	0.982471i	$-0.440313\pi$
$167$	−10.2873	−	10.2873i	−0.796056	−	0.796056i	−0.982471	+	0.186415i	$0.940313\pi$
$168$		0			0
$169$			12.9161i			0.993543i
$170$	0.417892	−	4.54181i	0.0320508	−	0.348341i
$171$		−	6.74690i		−	0.515948i
$172$	−4.97801	+	4.97801i	−0.379570	+	0.379570i
$173$	−5.49565	+	5.49565i	−0.417827	+	0.417827i	−0.884454	−	0.466627i	$-0.845469\pi$
$173$	−5.49565	+	5.49565i	−0.417827	+	0.417827i	0.466627	+	0.884454i	$0.345469\pi$
$174$	14.4734			1.09722
$175$		0			0
$176$	4.03997			0.304524
$177$	−1.22290	+	1.22290i	−0.0919190	+	0.0919190i
$178$	2.17245	−	2.17245i	0.162832	−	0.162832i
$179$		−	3.86472i		−	0.288863i	−0.989515	−	0.144431i	$-0.953865\pi$
$179$		−	3.86472i		−	0.288863i	0.989515	−	0.144431i	$-0.0461353\pi$
$180$	−0.222827	+	2.42177i	−0.0166086	+	0.180508i
$181$			6.99107i			0.519642i	0.965657	+	0.259821i	$0.0836636\pi$
$181$			6.99107i			0.519642i	−0.965657	+	0.259821i	$0.916336\pi$
$182$		0			0
$183$	−9.89407	−	9.89407i	−0.731390	−	0.731390i
$184$		−	4.53813i		−	0.334556i
$185$	−6.61308	−	7.95333i	−0.486203	−	0.584741i
$186$	−14.7845			−1.08405
$187$	−5.82691	−	5.82691i	−0.426106	−	0.426106i
$188$	−0.222827	+	0.222827i	−0.0162513	+	0.0162513i
$189$		0			0
$190$	−8.86840	−	10.6657i	−0.643381	−	0.773774i
$191$	4.47442			0.323758			0.161879	−	0.986811i	$-0.448245\pi$
$191$	4.47442			0.323758			0.161879	+	0.986811i	$0.448245\pi$
$192$	1.42962	+	1.42962i	0.103174	+	0.103174i
$193$	−14.1950	−	14.1950i	−1.02178	−	1.02178i	−0.999758	−	0.0220201i	$-0.992990\pi$
$193$	−14.1950	−	14.1950i	−1.02178	−	1.02178i	−0.0220201	−	0.999758i	$-0.507010\pi$
$194$	−9.37769			−0.673279
$195$	−1.30435	−	0.120013i	−0.0934064	−	0.00859431i
$196$		0			0
$197$	−7.84901	+	7.84901i	−0.559219	+	0.559219i	−0.929085	−	0.369866i	$-0.879404\pi$
$197$	−7.84901	+	7.84901i	−0.559219	+	0.559219i	0.369866	+	0.929085i	$0.379404\pi$
$198$	3.10701	+	3.10701i	0.220806	+	0.220806i
$199$	10.8021			0.765737			0.382869	−	0.923803i	$-0.374936\pi$
$199$	10.8021			0.765737			0.382869	+	0.923803i	$0.374936\pi$
$200$	2.83103	+	4.12132i	0.200184	+	0.291421i
$201$			6.38621i			0.450448i
$202$	6.99218	+	6.99218i	0.491968	+	0.491968i
$203$		0			0
$204$		−	4.12392i		−	0.288732i
$205$	−5.76139	−	0.530105i	−0.402393	−	0.0370241i
$206$			4.28203i			0.298343i
$207$	3.49013	−	3.49013i	0.242581	−	0.242581i
$208$	−0.204875	+	0.204875i	−0.0142055	+	0.0142055i
$209$	−25.0613			−1.73353
$210$		0			0
$211$	7.56555			0.520834			0.260417	−	0.965496i	$-0.416140\pi$
$211$	7.56555			0.520834			0.260417	+	0.965496i	$0.416140\pi$
$212$	5.85669	−	5.85669i	0.402239	−	0.402239i
$213$	10.1823	−	10.1823i	0.697681	−	0.697681i
$214$			14.8721i			1.01663i
$215$	−12.1042	+	10.0645i	−0.825501	+	0.686392i
$216$		−	3.86642i		−	0.263076i
$217$		0			0
$218$	9.35593	+	9.35593i	0.633664	+	0.633664i
$219$			23.3028i			1.57466i
$220$	8.99566	+	0.827689i	0.606487	+	0.0558028i
$221$	0.590988			0.0397541
$222$	−6.61308	−	6.61308i	−0.443841	−	0.443841i
$223$	9.35230	−	9.35230i	0.626277	−	0.626277i	−0.320853	−	0.947129i	$-0.603969\pi$
$223$	9.35230	−	9.35230i	0.626277	−	0.626277i	0.947129	+	0.320853i	$0.103969\pi$
$224$		0			0
$225$	−0.992322	+	5.34682i	−0.0661548	+	0.356455i
$226$	13.7933			0.917519
$227$	−11.4508	−	11.4508i	−0.760014	−	0.760014i	0.216311	−	0.976325i	$-0.430598\pi$
$227$	−11.4508	−	11.4508i	−0.760014	−	0.760014i	−0.976325	+	0.216311i	$0.930598\pi$
$228$	−8.86840	−	8.86840i	−0.587324	−	0.587324i
$229$	−11.7764			−0.778207			−0.389103	−	0.921194i	$-0.627215\pi$
$229$	−11.7764			−0.778207			−0.389103	+	0.921194i	$0.627215\pi$
$230$	0.929750	−	10.1049i	0.0613059	−	0.666297i
$231$		0			0
$232$	5.06196	−	5.06196i	0.332334	−	0.332334i
$233$	−4.04765	−	4.04765i	−0.265170	−	0.265170i	0.561980	−	0.827151i	$-0.310040\pi$
$233$	−4.04765	−	4.04765i	−0.265170	−	0.265170i	−0.827151	+	0.561980i	$0.810040\pi$
$234$	−0.315125			−0.0206004
$235$	−0.541813	+	0.450509i	−0.0353440	+	0.0293880i
$236$			0.855404i			0.0556821i
$237$	−7.25713	−	7.25713i	−0.471402	−	0.471402i
$238$		0			0
$239$		−	8.33794i		−	0.539337i	−0.962953	−	0.269668i	$-0.913086\pi$
$239$		−	8.33794i		−	0.539337i	0.962953	−	0.269668i	$-0.0869141\pi$
$240$	2.89039	+	3.47617i	0.186574	+	0.224386i
$241$		−	2.96438i		−	0.190953i	−0.995432	−	0.0954763i	$-0.969563\pi$
$241$		−	2.96438i		−	0.190953i	0.995432	−	0.0954763i	$-0.0304374\pi$
$242$	3.76279	−	3.76279i	0.241881	−	0.241881i
$243$	7.63821	−	7.63821i	0.489991	−	0.489991i
$244$	−6.92077			−0.443057
$245$		0			0
$246$	−5.23128			−0.333535
$247$	1.27091	−	1.27091i	0.0808658	−	0.0808658i
$248$	−5.17076	+	5.17076i	−0.328344	+	0.328344i
$249$			11.0187i			0.698283i
$250$	5.45939	+	9.75680i	0.345282	+	0.617074i
$251$		−	16.1800i		−	1.02127i	−0.859796	−	0.510637i	$-0.829410\pi$
$251$		−	16.1800i		−	1.02127i	0.859796	−	0.510637i	$-0.170590\pi$
$252$		0			0
$253$	−12.9641	−	12.9641i	−0.815043	−	0.815043i
$254$			3.11104i			0.195204i
$255$	0.844888	−	9.18258i	0.0529089	−	0.575036i
$256$	1.00000			0.0625000
$257$	−4.11867	−	4.11867i	−0.256916	−	0.256916i	0.566883	−	0.823799i	$-0.308149\pi$
$257$	−4.11867	−	4.11867i	−0.256916	−	0.256916i	−0.823799	+	0.566883i	$0.808149\pi$
$258$	−10.0645	+	10.0645i	−0.626587	+	0.626587i
$259$		0			0
$260$	−0.498161	+	0.414214i	−0.0308946	+	0.0256884i
$261$	7.78598			0.481940
$262$	−5.16100	−	5.16100i	−0.318848	−	0.318848i
$263$	1.22833	+	1.22833i	0.0757422	+	0.0757422i	0.743963	−	0.668221i	$-0.232944\pi$
$263$	1.22833	+	1.22833i	0.0757422	+	0.0757422i	−0.668221	+	0.743963i	$0.732944\pi$
$264$	8.16797			0.502704
$265$	14.2408	−	11.8410i	0.874803	−	0.727386i
$266$		0			0
$267$	4.39223	−	4.39223i	0.268800	−	0.268800i
$268$	2.23353	+	2.23353i	0.136435	+	0.136435i
$269$	3.78337			0.230676			0.115338	−	0.993326i	$-0.463205\pi$
$269$	3.78337			0.230676			0.115338	+	0.993326i	$0.463205\pi$
$270$	0.792131	−	8.60920i	0.0482076	−	0.523939i
$271$		−	21.2498i		−	1.29083i	−0.763831	−	0.645416i	$-0.776684\pi$
$271$		−	21.2498i		−	1.29083i	0.763831	−	0.645416i	$-0.223316\pi$
$272$	−1.44231	−	1.44231i	−0.0874531	−	0.0874531i
$273$		0			0
$274$		−	7.17893i		−	0.433695i
$275$	19.8607	+	3.68597i	1.19765	+	0.222272i
$276$		−	9.17514i		−	0.552279i
$277$	−3.45787	+	3.45787i	−0.207763	+	0.207763i	−0.803316	−	0.595553i	$-0.796933\pi$
$277$	−3.45787	+	3.45787i	−0.207763	+	0.207763i	0.595553	+	0.803316i	$0.296933\pi$
$278$	8.78027	−	8.78027i	0.526605	−	0.526605i
$279$	−7.95333			−0.476153
$280$		0			0
$281$	−29.4776			−1.75849			−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−29.4776			−1.75849			−0.879243	+	0.476373i	$0.841951\pi$
$282$	−0.450509	+	0.450509i	−0.0268274	+	0.0268274i
$283$	−7.97872	+	7.97872i	−0.474286	+	0.474286i	−0.903298	−	0.429013i	$-0.858862\pi$
$283$	−7.97872	+	7.97872i	−0.474286	+	0.474286i	0.429013	+	0.903298i	$0.358862\pi$
$284$		−	7.12240i		−	0.422637i
$285$	−17.9300	−	21.5638i	−1.06208	−	1.27733i
$286$			1.17053i			0.0692148i
$287$		0			0
$288$	0.769067	+	0.769067i	0.0453177	+	0.0453177i
$289$		−	12.8395i		−	0.755262i
$290$	12.3083	−	10.2342i	0.722771	−	0.600973i
$291$	−18.9597			−1.11144
$292$	8.15002	+	8.15002i	0.476944	+	0.476944i
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	−0.886105	−	0.463485i	$-0.846599\pi$
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	0.463485	+	0.886105i	$0.346599\pi$
$294$		0			0
$295$	−0.175251	+	1.90470i	−0.0102035	+	0.110896i
$296$	−4.62576			−0.268867
$297$	−11.0452	−	11.0452i	−0.640905	−	0.640905i
$298$	16.9340	+	16.9340i	0.980963	+	0.980963i
$299$	1.31486			0.0760406
$300$	5.72374	+	8.33243i	0.330460	+	0.481073i
$301$		0			0
$302$	−2.50552	+	2.50552i	−0.144176	+	0.144176i
$303$	14.1367	+	14.1367i	0.812133	+	0.812133i
$304$	−6.20333			−0.355785
$305$	−15.4102	−	1.41789i	−0.882386	−	0.0811882i
$306$		−	2.21847i		−	0.126822i
$307$	−1.07859	−	1.07859i	−0.0615584	−	0.0615584i	0.675657	−	0.737216i	$-0.263860\pi$
$307$	−1.07859	−	1.07859i	−0.0615584	−	0.0615584i	−0.737216	+	0.675657i	$0.763860\pi$
$308$		0			0
$309$			8.65735i			0.492500i
$310$	−12.5729	+	10.4542i	−0.714093	+	0.593758i
$311$			9.62824i			0.545967i	0.962019	+	0.272984i	$0.0880105\pi$
$311$			9.62824i			0.545967i	−0.962019	+	0.272984i	$0.911990\pi$
$312$	−0.414214	+	0.414214i	−0.0234502	+	0.0234502i
$313$	−2.14023	+	2.14023i	−0.120973	+	0.120973i	−0.765001	−	0.644029i	$-0.777262\pi$
$313$	−2.14023	+	2.14023i	−0.120973	+	0.120973i	0.644029	+	0.765001i	$0.277262\pi$
$314$	6.12251			0.345513
$315$		0			0
$316$	−5.07627			−0.285562
$317$	1.37792	−	1.37792i	0.0773916	−	0.0773916i	−0.667351	−	0.744743i	$-0.732572\pi$
$317$	1.37792	−	1.37792i	0.0773916	−	0.0773916i	0.744743	+	0.667351i	$0.232572\pi$
$318$	11.8410	−	11.8410i	0.664010	−	0.664010i
$319$		−	28.9209i		−	1.61926i
$320$	2.22666	+	0.204875i	0.124474	+	0.0114529i
$321$			30.0682i			1.67824i
$322$		0			0
$323$	8.94715	+	8.94715i	0.497833	+	0.497833i
$324$		−	11.0799i		−	0.615553i
$325$	−1.19410	+	0.820253i	−0.0662367	+	0.0454995i
$326$	−16.5579			−0.917056
$327$	18.9157	+	18.9157i	1.04604	+	1.04604i
$328$	−1.82961	+	1.82961i	−0.101023	+	0.101023i
$329$		0			0
$330$	18.1873	+	1.67341i	1.00118	+	0.0921183i
$331$	−28.8935			−1.58813			−0.794066	−	0.607832i	$-0.792039\pi$
$331$	−28.8935			−1.58813			−0.794066	+	0.607832i	$0.792039\pi$
$332$	3.85372	+	3.85372i	0.211500	+	0.211500i
$333$	−3.55752	−	3.55752i	−0.194951	−	0.194951i
$334$	−14.5485			−0.796056
$335$	4.51573	+	5.43092i	0.246721	+	0.296723i
$336$		0			0
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	−0.729173	−	0.684329i	$-0.760095\pi$
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	0.684329	+	0.729173i	$0.260095\pi$
$338$	9.13303	+	9.13303i	0.496771	+	0.496771i
$339$	27.8872			1.51462
$340$	−2.91605	−	3.50704i	−0.158145	−	0.190196i
$341$			29.5426i			1.59982i
$342$	−4.77078	−	4.77078i	−0.257974	−	0.257974i
$343$		0			0
$344$			7.03997i			0.379570i
$345$	1.87976	−	20.4300i	0.101203	−	1.09991i
$346$			7.77203i			0.417827i
$347$	−11.8116	+	11.8116i	−0.634082	+	0.634082i	−0.949089	−	0.315007i	$-0.897993\pi$
$347$	−11.8116	+	11.8116i	−0.634082	+	0.634082i	0.315007	+	0.949089i	$0.397993\pi$
$348$	10.2342	−	10.2342i	0.548611	−	0.548611i
$349$	36.7146			1.96529			0.982644	−	0.185503i	$-0.0593916\pi$
$349$	36.7146			1.96529			0.982644	+	0.185503i	$0.0593916\pi$
$350$		0			0
$351$	1.12024			0.0597942
$352$	2.85669	−	2.85669i	0.152262	−	0.152262i
$353$	−10.0910	+	10.0910i	−0.537089	+	0.537089i	−0.922673	−	0.385584i	$-0.874000\pi$
$353$	−10.0910	+	10.0910i	−0.537089	+	0.537089i	0.385584	+	0.922673i	$0.374000\pi$
$354$			1.72945i			0.0919190i
$355$	1.45920	−	15.8592i	0.0774463	−	0.841718i
$356$		−	3.07230i		−	0.162832i
$357$		0			0
$358$	−2.73277	−	2.73277i	−0.144431	−	0.144431i
$359$		−	27.0888i		−	1.42969i	−0.699281	−	0.714847i	$-0.746496\pi$
$359$		−	27.0888i		−	1.42969i	0.699281	−	0.714847i	$-0.253504\pi$
$360$	1.55489	+	1.87002i	0.0819499	+	0.0985585i
$361$	19.4813			1.02533
$362$	4.94343	+	4.94343i	0.259821	+	0.259821i
$363$	7.60756	−	7.60756i	0.399293	−	0.399293i
$364$		0			0
$365$	16.4776	+	19.8171i	0.862477	+	1.03727i
$366$	−13.9923			−0.731390
$367$	−16.0312	−	16.0312i	−0.836821	−	0.836821i	0.151618	−	0.988439i	$-0.451552\pi$
$367$	−16.0312	−	16.0312i	−0.836821	−	0.836821i	−0.988439	+	0.151618i	$0.951552\pi$
$368$	−3.20895	−	3.20895i	−0.167278	−	0.167278i
$369$	−2.81418			−0.146500
$370$	−10.3000	−	0.947702i	−0.535472	−	0.0492687i
$371$		0			0
$372$	−10.4542	+	10.4542i	−0.542024	+	0.542024i
$373$	−9.07627	−	9.07627i	−0.469951	−	0.469951i	0.431947	−	0.901899i	$-0.357827\pi$
$373$	−9.07627	−	9.07627i	−0.469951	−	0.469951i	−0.901899	+	0.431947i	$0.857827\pi$
$374$	−8.24050			−0.426106
$375$	11.0377	+	19.7262i	0.569986	+	1.01866i
$376$			0.315125i			0.0162513i
$377$	1.46664	+	1.46664i	0.0755356	+	0.0755356i
$378$		0			0
$379$		−	14.4739i		−	0.743476i	−0.928338	−	0.371738i	$-0.878762\pi$
$379$		−	14.4739i		−	0.743476i	0.928338	−	0.371738i	$-0.121238\pi$
$380$	−13.8127	−	1.27091i	−0.708578	−	0.0651961i
$381$			6.28987i			0.322240i
$382$	3.16389	−	3.16389i	0.161879	−	0.161879i
$383$	−1.23855	+	1.23855i	−0.0632870	+	0.0632870i	−0.738042	−	0.674755i	$-0.764249\pi$
$383$	−1.23855	+	1.23855i	−0.0632870	+	0.0632870i	0.674755	+	0.738042i	$0.264249\pi$
$384$	2.02179			0.103174
$385$		0			0
$386$	−20.0747			−1.02178
$387$	−5.41421	+	5.41421i	−0.275220	+	0.275220i
$388$	−6.63103	+	6.63103i	−0.336640	+	0.336640i
$389$			2.78230i			0.141068i	0.997509	+	0.0705341i	$0.0224704\pi$
$389$			2.78230i			0.141068i	−0.997509	+	0.0705341i	$0.977530\pi$
$390$	−1.00718	+	0.837452i	−0.0510003	+	0.0424060i
$391$			9.25661i			0.468127i
$392$		0			0
$393$	−10.4344	−	10.4344i	−0.526348	−	0.526348i
$394$			11.1002i			0.559219i
$395$	−11.3031	−	1.04000i	−0.568723	−	0.0523281i
$396$	4.39398			0.220806
$397$	28.0495	+	28.0495i	1.40776	+	1.40776i	0.771342	+	0.636421i	$0.219586\pi$
$397$	28.0495	+	28.0495i	1.40776	+	1.40776i	0.636421	+	0.771342i	$0.280414\pi$
$398$	7.63821	−	7.63821i	0.382869	−	0.382869i
$399$		0			0
$400$	4.91605	+	0.912375i	0.245803	+	0.0456187i
$401$	−19.9706			−0.997282			−0.498641	−	0.866809i	$-0.666167\pi$
$401$	−19.9706			−0.997282			−0.498641	+	0.866809i	$0.666167\pi$
$402$	4.51573	+	4.51573i	0.225224	+	0.225224i
$403$	−1.49816	−	1.49816i	−0.0746287	−	0.0746287i
$404$	9.88844			0.491968
$405$	2.27000	−	24.6713i	0.112797	−	1.22593i
$406$		0			0
$407$	−13.2144	+	13.2144i	−0.655012	+	0.655012i
$408$	−2.91605	−	2.91605i	−0.144366	−	0.144366i
$409$	15.3056			0.756813			0.378407	−	0.925639i	$-0.376472\pi$
$409$	15.3056			0.756813			0.378407	+	0.925639i	$0.376472\pi$
$410$	−4.44876	+	3.69908i	−0.219708	+	0.182684i
$411$		−	14.5143i		−	0.715936i
$412$	3.02785	+	3.02785i	0.149172	+	0.149172i
$413$		0			0
$414$		−	4.93579i		−	0.242581i
$415$	7.79141	+	9.37047i	0.382465	+	0.459978i
$416$			0.289737i			0.0142055i
$417$	17.7518	−	17.7518i	0.869311	−	0.869311i
$418$	−17.7210	+	17.7210i	−0.866763	+	0.866763i
$419$	−27.7027			−1.35337			−0.676684	−	0.736274i	$-0.736584\pi$
$419$	−27.7027			−1.35337			−0.676684	+	0.736274i	$0.736584\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$	5.34965	−	5.34965i	0.260417	−	0.260417i
$423$	−0.242352	+	0.242352i	−0.0117836	+	0.0117836i
$424$		−	8.28261i		−	0.402239i
$425$	−5.77456	−	8.40642i	−0.280107	−	0.407771i
$426$		−	14.4000i		−	0.697681i
$427$		0			0
$428$	10.5161	+	10.5161i	0.508317	+	0.508317i
$429$			2.36656i			0.114259i
$430$	−1.44231	+	15.6756i	−0.0695546	+	0.755947i
$431$	23.9173			1.15205			0.576027	−	0.817431i	$-0.304602\pi$
$431$	23.9173			1.15205			0.576027	+	0.817431i	$0.304602\pi$
$432$	−2.73397	−	2.73397i	−0.131538	−	0.131538i
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	−0.949772	−	0.312943i	$-0.898685\pi$
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	0.312943	+	0.949772i	$0.398685\pi$
$434$		0			0
$435$	24.8849	−	20.6914i	1.19314	−	0.992077i
$436$	13.2313			0.633664
$437$	19.9061	+	19.9061i	0.952240	+	0.952240i
$438$	16.4776	+	16.4776i	0.787330	+	0.787330i
$439$	14.1077			0.673322			0.336661	−	0.941626i	$-0.390702\pi$
$439$	14.1077			0.673322			0.336661	+	0.941626i	$0.390702\pi$
$440$	6.94616	−	5.77563i	0.331145	−	0.275342i
$441$		0			0
$442$	0.417892	−	0.417892i	0.0198771	−	0.0198771i
$443$	14.8941	+	14.8941i	0.707638	+	0.707638i	0.966038	−	0.258400i	$-0.0831951\pi$
$443$	14.8941	+	14.8941i	0.707638	+	0.707638i	−0.258400	+	0.966038i	$0.583195\pi$
$444$	−9.35230			−0.443841
$445$	0.629438	−	6.84098i	0.0298382	−	0.324294i
$446$		−	13.2262i		−	0.626277i
$447$	34.2370	+	34.2370i	1.61936	+	1.61936i
$448$		0			0
$449$		−	31.3247i		−	1.47831i	−0.673538	−	0.739153i	$-0.735226\pi$
$449$		−	31.3247i		−	1.47831i	0.673538	−	0.739153i	$-0.264774\pi$
$450$	3.07910	+	4.48245i	0.145150	+	0.211305i
$451$			10.4532i			0.492224i
$452$	9.75336	−	9.75336i	0.458759	−	0.458759i
$453$	−5.06562	+	5.06562i	−0.238004	+	0.238004i
$454$	−16.1938			−0.760014
$455$		0			0
$456$	−12.5418			−0.587324
$457$	−2.02342	+	2.02342i	−0.0946514	+	0.0946514i	−0.752847	−	0.658196i	$-0.771320\pi$
$457$	−2.02342	+	2.02342i	−0.0946514	+	0.0946514i	0.658196	+	0.752847i	$0.271320\pi$
$458$	−8.32718	+	8.32718i	−0.389103	+	0.389103i
$459$			7.88648i			0.368109i
$460$	−6.48781	−	7.80267i	−0.302496	−	0.363801i
$461$			3.02674i			0.140969i	0.997513	+	0.0704846i	$0.0224546\pi$
$461$			3.02674i			0.140969i	−0.997513	+	0.0704846i	$0.977545\pi$
$462$		0			0
$463$	19.2889	+	19.2889i	0.896431	+	0.896431i	0.995118	−	0.0986876i	$-0.0314644\pi$
$463$	19.2889	+	19.2889i	0.896431	+	0.896431i	−0.0986876	+	0.995118i	$0.531464\pi$
$464$		−	7.15869i		−	0.332334i
$465$	−25.4197	+	21.1361i	−1.17881	+	0.980165i
$466$	−5.72424			−0.265170
$467$	−17.7688	−	17.7688i	−0.822244	−	0.822244i	0.164185	−	0.986430i	$-0.447500\pi$
$467$	−17.7688	−	17.7688i	−0.822244	−	0.822244i	−0.986430	+	0.164185i	$0.947500\pi$
$468$	−0.222827	+	0.222827i	−0.0103002	+	0.0103002i
$469$		0			0
$470$	−0.0645612	+	0.701677i	−0.00297799	+	0.0323660i
$471$	12.3784			0.570367
$472$	0.604862	+	0.604862i	0.0278410	+	0.0278410i
$473$	20.1110	+	20.1110i	0.924707	+	0.924707i
$474$	−10.2631			−0.471402
$475$	−30.4959	−	5.65976i	−1.39925	−	0.259688i
$476$		0			0
$477$	6.36989	−	6.36989i	0.291657	−	0.291657i
$478$	−5.89582	−	5.89582i	−0.269668	−	0.269668i
$479$	8.28692			0.378639			0.189319	−	0.981916i	$-0.439372\pi$
$479$	8.28692			0.378639			0.189319	+	0.981916i	$0.439372\pi$
$480$	4.50184	+	0.414214i	0.205480	+	0.0189062i
$481$		−	1.34025i		−	0.0611103i
$482$	−2.09613	−	2.09613i	−0.0954763	−	0.0954763i
$483$		0			0
$484$		−	5.32139i		−	0.241881i
$485$	−16.1236	+	13.4065i	−0.732135	+	0.608759i
$486$		−	10.8021i		−	0.489991i
$487$	7.55069	−	7.55069i	0.342155	−	0.342155i	−0.515022	−	0.857177i	$-0.672216\pi$
$487$	7.55069	−	7.55069i	0.342155	−	0.342155i	0.857177	+	0.515022i	$0.172216\pi$
$488$	−4.89372	+	4.89372i	−0.221528	+	0.221528i
$489$	−33.4765			−1.51386
$490$		0			0
$491$	25.7259			1.16100			0.580498	−	0.814262i	$-0.302858\pi$
$491$	25.7259			1.16100			0.580498	+	0.814262i	$0.302858\pi$
$492$	−3.69908	+	3.69908i	−0.166767	+	0.166767i
$493$	−10.3251	+	10.3251i	−0.465018	+	0.465018i
$494$		−	1.79733i		−	0.0808658i
$495$	9.78391	+	0.900216i	0.439754	+	0.0404617i
$496$			7.31256i			0.328344i
$497$		0			0
$498$	7.79141	+	7.79141i	0.349141	+	0.349141i
$499$		−	14.5988i		−	0.653532i	−0.945105	−	0.326766i	$-0.894041\pi$
$499$		−	14.5988i		−	0.653532i	0.945105	−	0.326766i	$-0.105959\pi$
$500$	10.7595	+	3.03873i	0.481178	+	0.135896i
$501$	−29.4139			−1.31412
$502$	−11.4410	−	11.4410i	−0.510637	−	0.510637i
$503$	13.9891	−	13.9891i	0.623744	−	0.623744i	−0.322743	−	0.946487i	$-0.604605\pi$
$503$	13.9891	−	13.9891i	0.623744	−	0.623744i	0.946487	+	0.322743i	$0.104605\pi$
$504$		0			0
$505$	22.0182	+	2.02589i	0.979798	+	0.0901510i
$506$	−18.3339			−0.815043
$507$	18.4650	+	18.4650i	0.820061	+	0.820061i
$508$	2.19984	+	2.19984i	0.0976020	+	0.0976020i
$509$	−2.85767			−0.126664			−0.0633319	−	0.997993i	$-0.520173\pi$
$509$	−2.85767			−0.126664			−0.0633319	+	0.997993i	$0.520173\pi$
$510$	−5.89564	−	7.09049i	−0.261063	−	0.313972i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	16.9597	+	16.9597i	0.748789	+	0.748789i
$514$	−5.82469			−0.256916
$515$	6.12167	+	7.36233i	0.269753	+	0.324423i
$516$			14.2333i			0.626587i
$517$	0.900216	+	0.900216i	0.0395914	+	0.0395914i
$518$		0			0
$519$			15.7134i			0.689741i
$520$	−0.0593598	+	0.645146i	−0.00260310	+	0.0282915i
$521$		−	28.6269i		−	1.25417i	−0.778951	−	0.627084i	$-0.784248\pi$
$521$		−	28.6269i		−	1.25417i	0.778951	−	0.627084i	$-0.215752\pi$
$522$	5.50552	−	5.50552i	0.240970	−	0.240970i
$523$	−22.3326	+	22.3326i	−0.976535	+	0.976535i	−0.999731	−	0.0231958i	$-0.992616\pi$
$523$	−22.3326	+	22.3326i	−0.976535	+	0.976535i	0.0231958	+	0.999731i	$0.492616\pi$
$524$	−7.29876			−0.318848
$525$		0			0
$526$	1.73712			0.0757422
$527$	10.5470	−	10.5470i	0.459435	−	0.459435i
$528$	5.77563	−	5.77563i	0.251352	−	0.251352i
$529$		−	2.40533i		−	0.104580i
$530$	1.69690	−	18.4426i	0.0737086	−	0.801095i
$531$			0.930359i			0.0403742i
$532$		0			0
$533$	−0.530105	−	0.530105i	−0.0229614	−	0.0229614i
$534$		−	6.21155i		−	0.268800i
$535$	21.2614	+	25.5704i	0.919211	+	1.10551i
$536$	3.15869			0.136435
$537$	−5.52508	−	5.52508i	−0.238425	−	0.238425i
$538$	2.67525	−	2.67525i	0.115338	−	0.115338i
$539$		0			0
$540$	−5.52750	−	6.64775i	−0.237866	−	0.286073i
$541$	36.9989			1.59071			0.795353	−	0.606147i	$-0.207286\pi$
$541$	36.9989			1.59071			0.795353	+	0.606147i	$0.207286\pi$
$542$	−15.0259	−	15.0259i	−0.645416	−	0.645416i
$543$	9.99457	+	9.99457i	0.428908	+	0.428908i
$544$	−2.03974			−0.0874531
$545$	29.4616	+	2.71076i	1.26200	+	0.116116i
$546$		0			0
$547$	−20.0765	+	20.0765i	−0.858409	+	0.858409i	−0.991151	−	0.132742i	$-0.957622\pi$
$547$	−20.0765	+	20.0765i	−0.858409	+	0.858409i	0.132742	+	0.991151i	$0.457622\pi$
$548$	−5.07627	−	5.07627i	−0.216847	−	0.216847i
$549$	−7.52720			−0.321253
$550$	16.6500	−	11.4373i	0.709959	−	0.487687i
$551$			44.4077i			1.89183i
$552$	−6.48781	−	6.48781i	−0.276139	−	0.276139i
$553$		0			0
$554$			4.89016i			0.207763i
$555$	−20.8244	−	1.91605i	−0.883948	−	0.0813319i
$556$		−	12.4172i		−	0.526605i
$557$	−18.1818	+	18.1818i	−0.770386	+	0.770386i	−0.978174	−	0.207788i	$-0.933374\pi$
$557$	−18.1818	+	18.1818i	−0.770386	+	0.770386i	0.207788	+	0.978174i	$0.433374\pi$
$558$	−5.62385	+	5.62385i	−0.238077	+	0.238077i
$559$	−2.03974			−0.0862718
$560$		0			0
$561$	−16.6605			−0.703408
$562$	−20.8438	+	20.8438i	−0.879243	+	0.879243i
$563$	3.79500	−	3.79500i	0.159940	−	0.159940i	−0.622600	−	0.782540i	$-0.713924\pi$
$563$	3.79500	−	3.79500i	0.159940	−	0.159940i	0.782540	+	0.622600i	$0.213924\pi$
$564$			0.637116i			0.0268274i
$565$	23.7157	−	19.7192i	0.997725	−	0.829594i
$566$			11.2836i			0.474286i
$567$		0			0
$568$	−5.03630	−	5.03630i	−0.211318	−	0.211318i
$569$			25.5003i			1.06903i	0.845159	+	0.534514i	$0.179505\pi$
$569$			25.5003i			1.06903i	−0.845159	+	0.534514i	$0.820495\pi$
$570$	−27.9264	−	2.56950i	−1.16971	−	0.107625i
$571$	15.9047			0.665591			0.332795	−	0.942999i	$-0.392008\pi$
$571$	15.9047			0.665591			0.332795	+	0.942999i	$0.392008\pi$
$572$	0.827689	+	0.827689i	0.0346074	+	0.0346074i
$573$	6.39672	−	6.39672i	0.267227	−	0.267227i
$574$		0			0
$575$	−12.8476	−	18.7031i	−0.535781	−	0.779973i
$576$	1.08763			0.0453177
$577$	16.2985	+	16.2985i	0.678514	+	0.678514i	0.959664	−	0.281150i	$-0.0907159\pi$
$577$	16.2985	+	16.2985i	0.678514	+	0.678514i	−0.281150	+	0.959664i	$0.590716\pi$
$578$	−9.07887	−	9.07887i	−0.377631	−	0.377631i
$579$	−40.5869			−1.68673
$580$	1.46664	−	15.9400i	0.0608988	−	0.661872i
$581$		0			0
$582$	−13.4065	+	13.4065i	−0.555719	+	0.555719i
$583$	−23.6609	−	23.6609i	−0.979934	−	0.979934i
$584$	11.5259			0.476944
$585$	−0.541813	+	0.450509i	−0.0224012	+	0.0186263i
$586$			10.2305i			0.422619i
$587$	28.2277	+	28.2277i	1.16508	+	1.16508i	0.983348	+	0.181734i	$0.0581711\pi$
$587$	28.2277	+	28.2277i	1.16508	+	1.16508i	0.181734	+	0.983348i	$0.441829\pi$
$588$		0			0
$589$		−	45.3622i		−	1.86912i
$590$	1.22290	+	1.47074i	0.0503461	+	0.0605496i
$591$			22.4422i			0.923149i
$592$	−3.27091	+	3.27091i	−0.134433	+	0.134433i
$593$	25.0523	−	25.0523i	1.02877	−	1.02877i	0.0292000	−	0.999574i	$-0.490704\pi$
$593$	25.0523	−	25.0523i	1.02877	−	1.02877i	0.999574	−	0.0292000i	$-0.00929596\pi$
$594$	−15.6202			−0.640905
$595$		0			0
$596$	23.9483			0.980963
$597$	15.4428	−	15.4428i	0.632033	−	0.632033i
$598$	0.929750	−	0.929750i	0.0380203	−	0.0380203i
$599$		−	16.7823i		−	0.685706i	−0.939389	−	0.342853i	$-0.888607\pi$
$599$		−	16.7823i		−	0.685706i	0.939389	−	0.342853i	$-0.111393\pi$
$600$	9.93921	+	1.84463i	0.405767	+	0.0753066i
$601$			1.73528i			0.0707833i	0.999374	+	0.0353917i	$0.0112679\pi$
$601$			1.73528i			0.0707833i	−0.999374	+	0.0353917i	$0.988732\pi$
$602$		0			0
$603$	2.42925	+	2.42925i	0.0989266	+	0.0989266i
$604$			3.54334i			0.144176i
$605$	1.09022	−	11.8489i	0.0443237	−	0.481728i
$606$	19.9923			0.812133
$607$	27.8860	+	27.8860i	1.13186	+	1.13186i	0.989868	+	0.141989i	$0.0453496\pi$
$607$	27.8860	+	27.8860i	1.13186	+	1.13186i	0.141989	+	0.989868i	$0.454650\pi$
$608$	−4.38642	+	4.38642i	−0.177893	+	0.177893i
$609$		0			0
$610$	−11.8993	+	9.89407i	−0.481787	+	0.400599i
$611$	−0.0913034			−0.00369374
$612$	−1.56870	−	1.56870i	−0.0634108	−	0.0634108i
$613$	0.241791	+	0.241791i	0.00976586	+	0.00976586i	0.711973	−	0.702207i	$-0.247802\pi$
$613$	0.241791	+	0.241791i	0.00976586	+	0.00976586i	−0.702207	+	0.711973i	$0.747802\pi$
$614$	−1.52536			−0.0615584
$615$	−8.99444	+	7.47875i	−0.362691	+	0.301572i
$616$		0			0
$617$	11.1876	−	11.1876i	0.450397	−	0.450397i	−0.445089	−	0.895486i	$-0.646828\pi$
$617$	11.1876	−	11.1876i	0.450397	−	0.450397i	0.895486	+	0.445089i	$0.146828\pi$
$618$	6.12167	+	6.12167i	0.246250	+	0.246250i
$619$	−36.5364			−1.46852			−0.734260	−	0.678868i	$-0.762471\pi$
$619$	−36.5364			−1.46852			−0.734260	+	0.678868i	$0.762471\pi$
$620$	−1.49816	+	16.2826i	−0.0601676	+	0.653926i
$621$			17.5463i			0.704109i
$622$	6.80819	+	6.80819i	0.272984	+	0.272984i
$623$		0			0
$624$			0.585786i			0.0234502i
$625$	23.3351	+	8.97056i	0.933406	+	0.358823i
$626$			3.02674i			0.120973i
$627$	−35.8281	+	35.8281i	−1.43084	+	1.43084i
$628$	4.32927	−	4.32927i	0.172757	−	0.172757i
$629$	9.43535			0.376212
$630$		0			0
$631$	−35.8189			−1.42593			−0.712964	−	0.701201i	$-0.752648\pi$
$631$	−35.8189			−1.42593			−0.712964	+	0.701201i	$0.752648\pi$
$632$	−3.58946	+	3.58946i	−0.142781	+	0.142781i
$633$	10.8159	−	10.8159i	0.429892	−	0.429892i
$634$		−	1.94867i		−	0.0773916i
$635$	4.44761	+	5.34899i	0.176498	+	0.212268i
$636$		−	16.7457i		−	0.664010i
$637$		0			0
$638$	−20.4502	−	20.4502i	−0.809631	−	0.809631i
$639$		−	7.74650i		−	0.306447i
$640$	1.71936	−	1.42962i	0.0679635	−	0.0565107i
$641$	−14.3315			−0.566059			−0.283029	−	0.959111i	$-0.591339\pi$
$641$	−14.3315			−0.566059			−0.283029	+	0.959111i	$0.591339\pi$
$642$	21.2614	+	21.2614i	0.839121	+	0.839121i
$643$	7.65201	−	7.65201i	0.301766	−	0.301766i	−0.539939	−	0.841704i	$-0.681553\pi$
$643$	7.65201	−	7.65201i	0.301766	−	0.301766i	0.841704	+	0.539939i	$0.181553\pi$
$644$		0			0
$645$	−2.91605	+	31.6928i	−0.114819	+	1.24790i
$646$	12.6532			0.497833
$647$	−22.8742	−	22.8742i	−0.899278	−	0.899278i	0.0960943	−	0.995372i	$-0.469365\pi$
$647$	−22.8742	−	22.8742i	−0.899278	−	0.899278i	−0.995372	+	0.0960943i	$0.969365\pi$
$648$	−7.83471	−	7.83471i	−0.307776	−	0.307776i
$649$	3.45581			0.135652
$650$	−0.264349	+	1.42436i	−0.0103686	+	0.0558681i
$651$		0			0
$652$	−11.7082	+	11.7082i	−0.458528	+	0.458528i
$653$	−0.362210	−	0.362210i	−0.0141744	−	0.0141744i	0.699984	−	0.714158i	$-0.253190\pi$
$653$	−0.362210	−	0.362210i	−0.0141744	−	0.0141744i	−0.714158	+	0.699984i	$0.753190\pi$
$654$	26.7508			1.04604
$655$	−16.2519	−	1.49533i	−0.635013	−	0.0584275i
$656$			2.58745i			0.101023i
$657$	8.86417	+	8.86417i	0.345824	+	0.345824i
$658$		0			0
$659$		−	19.5542i		−	0.761723i	−0.924632	−	0.380862i	$-0.875627\pi$
$659$		−	19.5542i		−	0.761723i	0.924632	−	0.380862i	$-0.124373\pi$
$660$	14.0437	−	11.6771i	0.546648	−	0.454530i
$661$		−	39.2972i		−	1.52848i	−0.644930	−	0.764242i	$-0.723113\pi$
$661$		−	39.2972i		−	1.52848i	0.644930	−	0.764242i	$-0.276887\pi$
$662$	−20.4308	+	20.4308i	−0.794066	+	0.794066i
$663$	0.844888	−	0.844888i	0.0328127	−	0.0328127i
$664$	5.44998			0.211500
$665$		0			0
$666$	−5.03109			−0.194951
$667$	−22.9719	+	22.9719i	−0.889474	+	0.889474i
$668$	−10.2873	+	10.2873i	−0.398028	+	0.398028i
$669$		−	26.7405i		−	1.03385i
$670$	7.03334	+	0.647137i	0.271722	+	0.0250011i
$671$			27.9597i			1.07937i
$672$		0			0
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	0.967037	−	0.254636i	$-0.0819556\pi$
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	−0.254636	+	0.967037i	$0.581956\pi$
$674$			1.16422i			0.0448440i
$675$	−10.9459	−	15.9347i	−0.421309	−	0.613328i
$676$	12.9161			0.496771
$677$	−29.1321	−	29.1321i	−1.11964	−	1.11964i	−0.991795	−	0.127842i	$-0.959195\pi$
$677$	−29.1321	−	29.1321i	−1.11964	−	1.11964i	−0.127842	−	0.991795i	$-0.540805\pi$
$678$	19.7192	−	19.7192i	0.757312	−	0.757312i
$679$		0			0
$680$	−4.54181	−	0.417892i	−0.174171	−	0.0160254i
$681$	−32.7405			−1.25462
$682$	20.8898	+	20.8898i	0.799910	+	0.799910i
$683$	−6.45442	−	6.45442i	−0.246971	−	0.246971i	0.572755	−	0.819726i	$-0.305875\pi$
$683$	−6.45442	−	6.45442i	−0.246971	−	0.246971i	−0.819726	+	0.572755i	$0.805875\pi$
$684$	−6.74690			−0.257974
$685$	−10.2631	−	12.3431i	−0.392134	−	0.471607i
$686$		0			0
$687$	−16.8358	+	16.8358i	−0.642325	+	0.642325i
$688$	4.97801	+	4.97801i	0.189785	+	0.189785i
$689$	2.39978			0.0914243
$690$	−13.1170	−	15.7753i	−0.499354	−	0.600557i
$691$		−	48.4941i		−	1.84480i	−0.386234	−	0.922401i	$-0.626224\pi$
$691$		−	48.4941i		−	1.84480i	0.386234	−	0.922401i	$-0.373776\pi$
$692$	5.49565	+	5.49565i	0.208913	+	0.208913i
$693$		0			0
$694$			16.7042i			0.634082i
$695$	2.54397	−	27.6489i	0.0964982	−	1.04878i
$696$		−	14.4734i		−	0.548611i
$697$	3.73192	−	3.73192i	0.141357	−	0.141357i
$698$	25.9611	−	25.9611i	0.982644	−	0.982644i
$699$	−11.5732			−0.437739
$700$		0			0
$701$	−30.8898			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$701$	−30.8898			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$702$	0.792131	−	0.792131i	0.0298971	−	0.0298971i
$703$	20.2905	−	20.2905i	0.765271	−	0.765271i
$704$		−	4.03997i		−	0.152262i
$705$	−0.130529	+	1.41864i	−0.00491601	+	0.0534292i
$706$			14.2708i			0.537089i
$707$		0			0
$708$	1.22290	+	1.22290i	0.0459595	+	0.0459595i
$709$		−	14.7055i		−	0.552278i	−0.961118	−	0.276139i	$-0.910945\pi$
$709$		−	14.7055i		−	0.552278i	0.961118	−	0.276139i	$-0.0890550\pi$
$710$	−10.1823	−	12.2459i	−0.382136	−	0.459582i
$711$	−5.52108			−0.207057
$712$	−2.17245	−	2.17245i	−0.0814159	−	0.0814159i
$713$	23.4656	−	23.4656i	0.878795	−	0.878795i
$714$		0			0
$715$	1.67341	+	2.01256i	0.0625821	+	0.0752654i
$716$	−3.86472			−0.144431
$717$	−11.9201	−	11.9201i	−0.445164	−	0.445164i
$718$	−19.1547	−	19.1547i	−0.714847	−	0.714847i
$719$	−23.4720			−0.875358			−0.437679	−	0.899131i	$-0.644199\pi$
$719$	−23.4720			−0.875358			−0.437679	+	0.899131i	$0.644199\pi$
$720$	2.42177	+	0.222827i	0.0902542	+	0.00830428i
$721$		0			0
$722$	13.7753	−	13.7753i	0.512665	−	0.512665i
$723$	−4.23794	−	4.23794i	−0.157611	−	0.157611i
$724$	6.99107			0.259821
$725$	6.53141	−	35.1925i	0.242570	−	1.30702i
$726$		−	10.7587i		−	0.399293i
$727$	−14.1380	−	14.1380i	−0.524349	−	0.524349i	0.394533	−	0.918882i	$-0.370907\pi$
$727$	−14.1380	−	14.1380i	−0.524349	−	0.524349i	−0.918882	+	0.394533i	$0.870907\pi$
$728$		0			0
$729$			11.4004i			0.422236i
$730$	25.6642	+	2.36136i	0.949875	+	0.0873979i
$731$		−	14.3597i		−	0.531113i
$732$	−9.89407	+	9.89407i	−0.365695	+	0.365695i
$733$	19.6123	−	19.6123i	0.724395	−	0.724395i	−0.245102	−	0.969497i	$-0.578821\pi$
$733$	19.6123	−	19.6123i	0.724395	−	0.724395i	0.969497	+	0.245102i	$0.0788214\pi$
$734$	−22.6715			−0.836821
$735$		0			0
$736$	−4.53813			−0.167278
$737$	9.02342	−	9.02342i	0.332382	−	0.332382i
$738$	−1.98993	+	1.98993i	−0.0732502	+	0.0732502i
$739$			13.5620i			0.498888i	0.968389	+	0.249444i	$0.0802479\pi$
$739$			13.5620i			0.498888i	−0.968389	+	0.249444i	$0.919752\pi$
$740$	−7.95333	+	6.61308i	−0.292370	+	0.243102i
$741$		−	3.63383i		−	0.133492i
$742$		0			0
$743$	13.5961	+	13.5961i	0.498791	+	0.498791i	0.911062	−	0.412270i	$-0.135264\pi$
$743$	13.5961	+	13.5961i	0.498791	+	0.498791i	−0.412270	+	0.911062i	$0.635264\pi$
$744$			14.7845i			0.542024i
$745$	53.3249	+	4.90642i	1.95367	+	0.179757i
$746$	−12.8358			−0.469951
$747$	4.19141	+	4.19141i	0.153355	+	0.153355i
$748$	−5.82691	+	5.82691i	−0.213053	+	0.213053i
$749$		0			0
$750$	21.7534	+	6.14366i	0.794320	+	0.224335i
$751$	43.6619			1.59324			0.796622	−	0.604478i	$-0.206618\pi$
$751$	43.6619			1.59324			0.796622	+	0.604478i	$0.206618\pi$
$752$	0.222827	+	0.222827i	0.00812567	+	0.00812567i
$753$	−23.1313	−	23.1313i	−0.842951	−	0.842951i
$754$	2.07414			0.0755356
$755$	−0.725941	+	7.88981i	−0.0264197	+	0.287140i
$756$		0			0
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	−0.549056	−	0.835785i	$-0.685013\pi$
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	0.835785	+	0.549056i	$0.185013\pi$
$758$	−10.2346	−	10.2346i	−0.371738	−	0.371738i
$759$	−37.0673			−1.34546
$760$	−10.6657	+	8.86840i	−0.386887	+	0.321691i
$761$		−	1.97365i		−	0.0715447i	−0.999360	−	0.0357724i	$-0.988611\pi$
$761$		−	1.97365i		−	0.0715447i	0.999360	−	0.0357724i	$-0.0113891\pi$
$762$	4.44761	+	4.44761i	0.161120	+	0.161120i
$763$		0			0
$764$		−	4.47442i		−	0.161879i
$765$	−3.17157	−	3.81435i	−0.114668	−	0.137908i
$766$			1.75158i			0.0632870i
$767$	−0.175251	+	0.175251i	−0.00632794	+	0.00632794i
$768$	1.42962	−	1.42962i	0.0515870	−	0.0515870i
$769$	−17.4914			−0.630756			−0.315378	−	0.948966i	$-0.602131\pi$
$769$	−17.4914			−0.630756			−0.315378	+	0.948966i	$0.602131\pi$
$770$		0			0
$771$	−11.7763			−0.424112
$772$	−14.1950	+	14.1950i	−0.510889	+	0.510889i
$773$	31.6197	−	31.6197i	1.13728	−	1.13728i	0.148345	−	0.988936i	$-0.452605\pi$
$773$	31.6197	−	31.6197i	1.13728	−	1.13728i	0.988936	−	0.148345i	$-0.0473947\pi$
$774$			7.65685i			0.275220i
$775$	−6.67180	+	35.9490i	−0.239658	+	1.29132i
$776$			9.37769i			0.336640i
$777$		0			0
$778$	1.96738	+	1.96738i	0.0705341	+	0.0705341i
$779$		−	16.0508i		−	0.575081i
$780$	−0.120013	+	1.30435i	−0.00429715	+	0.0467032i
$781$	−28.7743			−1.02963
$782$	6.54541	+	6.54541i	0.234064	+	0.234064i
$783$	−19.5716	+	19.5716i	−0.699433	+	0.699433i
$784$		0			0
$785$	10.5268	−	8.75286i	0.375717	−	0.312403i
$786$	−14.7565			−0.526348
$787$	−18.3483	−	18.3483i	−0.654047	−	0.654047i	0.299918	−	0.953965i	$-0.403041\pi$
$787$	−18.3483	−	18.3483i	−0.654047	−	0.654047i	−0.953965	+	0.299918i	$0.903041\pi$
$788$	7.84901	+	7.84901i	0.279610	+	0.279610i
$789$	3.51210			0.125034
$790$	−8.72792	+	7.25713i	−0.310525	+	0.258197i
$791$		0			0
$792$	3.10701	−	3.10701i	0.110403	−	0.110403i
$793$	−1.41789	−	1.41789i	−0.0503508	−	0.0503508i
$794$	39.6680			1.40776
$795$	3.43077	−	37.2870i	0.121677	−	1.32243i
$796$		−	10.8021i		−	0.382869i
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.911698	−	0.410861i	$-0.865228\pi$
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.410861	−	0.911698i	$-0.634772\pi$
$798$		0			0
$799$		−	0.642773i		−	0.0227397i
$800$	4.12132	−	2.83103i	0.145711	−	0.100092i
$801$		−	3.34152i		−	0.118067i
$802$	−14.1213	+	14.1213i	−0.498641	+	0.498641i
$803$	32.9259	−	32.9259i	1.16193	−	1.16193i
$804$	6.38621			0.225224
$805$		0			0
$806$	−2.11872			−0.0746287
$807$	5.40878	−	5.40878i	0.190398	−	0.190398i
$808$	6.99218	−	6.99218i	0.245984	−	0.245984i
$809$			16.0505i			0.564306i	0.959369	+	0.282153i	$0.0910486\pi$
$809$			16.0505i			0.564306i	−0.959369	+	0.282153i	$0.908951\pi$
$810$	−15.8401	−	19.0504i	−0.556565	−	0.669362i
$811$		−	35.4040i		−	1.24320i	−0.783334	−	0.621602i	$-0.786482\pi$
$811$		−	35.4040i		−	1.24320i	0.783334	−	0.621602i	$-0.213518\pi$
$812$		0			0
$813$	−30.3791	−	30.3791i	−1.06544	−	1.06544i
$814$			18.6879i			0.655012i
$815$	−28.4689	+	23.6715i	−0.997222	+	0.829175i
$816$	−4.12392			−0.144366
$817$	−30.8802	−	30.8802i	−1.08036	−	1.08036i
$818$	10.8227	−	10.8227i	0.378407	−	0.378407i
$819$		0			0
$820$	−0.530105	+	5.76139i	−0.0185121	+	0.201196i
$821$	26.8462			0.936938			0.468469	−	0.883480i	$-0.344806\pi$
$821$	26.8462			0.936938			0.468469	+	0.883480i	$0.344806\pi$
$822$	−10.2631	−	10.2631i	−0.357968	−	0.357968i
$823$	19.7862	+	19.7862i	0.689704	+	0.689704i	0.962166	−	0.272463i	$-0.0878381\pi$
$823$	19.7862	+	19.7862i	0.689704	+	0.689704i	−0.272463	+	0.962166i	$0.587838\pi$
$824$	4.28203			0.149172
$825$	33.6628	−	23.1237i	1.17199	−	0.805066i
$826$		0			0
$827$	16.8901	−	16.8901i	0.587325	−	0.587325i	−0.349581	−	0.936906i	$-0.613676\pi$
$827$	16.8901	−	16.8901i	0.587325	−	0.587325i	0.936906	+	0.349581i	$0.113676\pi$
$828$	−3.49013	−	3.49013i	−0.121290	−	0.121290i
$829$	−14.1682			−0.492083			−0.246042	−	0.969259i	$-0.579130\pi$
$829$	−14.1682			−0.492083			−0.246042	+	0.969259i	$0.579130\pi$
$830$	12.1353	+	1.11657i	0.421222	+	0.0387565i
$831$			9.88686i			0.342972i
$832$	0.204875	+	0.204875i	0.00710276	+	0.00710276i
$833$		0			0
$834$		−	25.1049i		−	0.869311i
$835$	−25.0140	+	20.7988i	−0.865645	+	0.719771i
$836$			25.0613i			0.866763i
$837$	19.9923	−	19.9923i	0.691036	−	0.691036i
$838$	−19.5888	+	19.5888i	−0.676684	+	0.676684i
$839$	18.1874			0.627900			0.313950	−	0.949439i	$-0.398348\pi$
$839$	18.1874			0.627900			0.313950	+	0.949439i	$0.398348\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$	23.3458	−	23.3458i	0.804549	−	0.804549i
$843$	−42.1418	+	42.1418i	−1.45144	+	1.45144i
$844$		−	7.56555i		−	0.260417i
$845$	28.7597	+	2.64618i	0.989363	+	0.0910312i
$846$			0.342738i			0.0117836i
$847$		0			0
$848$	−5.85669	−	5.85669i	−0.201120	−	0.201120i
$849$			22.8131i			0.782943i
$850$	−10.0275	−	1.86101i	−0.343939	−	0.0638320i
$851$	20.9923			0.719608
$852$	−10.1823	−	10.1823i	−0.348841	−	0.348841i
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	−0.939933	−	0.341359i	$-0.889113\pi$
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	0.341359	+	0.939933i	$0.389113\pi$
$854$		0			0
$855$	−15.0231	−	1.38227i	−0.513778	−	0.0472726i
$856$	14.8721			0.508317
$857$	18.4941	+	18.4941i	0.631747	+	0.631747i	0.948506	−	0.316759i	$-0.102595\pi$
$857$	18.4941	+	18.4941i	0.631747	+	0.631747i	−0.316759	+	0.948506i	$0.602595\pi$
$858$	1.67341	+	1.67341i	0.0571293	+	0.0571293i
$859$	−48.8251			−1.66589			−0.832946	−	0.553354i	$-0.813348\pi$
$859$	−48.8251			−1.66589			−0.832946	+	0.553354i	$0.813348\pi$
$860$	10.0645	+	12.1042i	0.343196	+	0.412751i
$861$		0			0
$862$	16.9121	−	16.9121i	0.576027	−	0.576027i
$863$	10.8532	+	10.8532i	0.369449	+	0.369449i	0.867276	−	0.497827i	$-0.165869\pi$
$863$	10.8532	+	10.8532i	0.369449	+	0.369449i	−0.497827	+	0.867276i	$0.665869\pi$
$864$	−3.86642			−0.131538
$865$	11.1110	+	13.3629i	0.377787	+	0.454352i
$866$			18.7405i			0.636829i
$867$	−18.3555	−	18.3555i	−0.623387	−	0.623387i
$868$		0			0
$869$			20.5080i			0.695686i
$870$	2.96523	−	32.2273i	0.100531	−	1.09261i
$871$			0.915190i			0.0310100i
$872$	9.35593	−	9.35593i	0.316832	−	0.316832i
$873$	−7.21208	+	7.21208i	−0.244092	+	0.244092i
$874$	28.1515			0.952240
$875$		0			0
$876$	23.3028			0.787330
$877$	−27.9035	+	27.9035i	−0.942235	+	0.942235i	−0.998420	−	0.0561853i	$-0.982106\pi$
$877$	−27.9035	+	27.9035i	−0.942235	+	0.942235i	0.0561853	+	0.998420i	$0.482106\pi$
$878$	9.97563	−	9.97563i	0.336661	−	0.336661i
$879$			20.6839i			0.697652i
$880$	0.827689	−	8.99566i	0.0279014	−	0.303244i
$881$		−	52.5926i		−	1.77189i	−0.463791	−	0.885945i	$-0.653511\pi$
$881$		−	52.5926i		−	1.77189i	0.463791	−	0.885945i	$-0.346489\pi$
$882$		0			0
$883$	13.0940	+	13.0940i	0.440649	+	0.440649i	0.892230	−	0.451581i	$-0.149140\pi$
$883$	13.0940	+	13.0940i	0.440649	+	0.440649i	−0.451581	+	0.892230i	$0.649140\pi$
$884$		−	0.590988i		−	0.0198771i
$885$	2.47245	+	2.97353i	0.0831105	+	0.0999542i
$886$	21.0634			0.707638
$887$	26.1335	+	26.1335i	0.877477	+	0.877477i	0.993273	−	0.115796i	$-0.0369419\pi$
$887$	26.1335	+	26.1335i	0.877477	+	0.877477i	−0.115796	+	0.993273i	$0.536942\pi$
$888$	−6.61308	+	6.61308i	−0.221920	+	0.221920i
$889$		0			0
$890$	−4.39223	−	5.28239i	−0.147228	−	0.177066i
$891$	−44.7627			−1.49961
$892$	−9.35230	−	9.35230i	−0.313138	−	0.313138i
$893$	−1.38227	−	1.38227i	−0.0462559	−	0.0462559i
$894$	48.4185			1.61936
$895$	−8.60543	−	0.791785i	−0.287648	−	0.0264664i
$896$		0			0
$897$	1.87976	−	1.87976i	0.0627633	−	0.0627633i
$898$	−22.1499	−	22.1499i	−0.739153	−	0.739153i
$899$	52.3484			1.74592
$900$	5.34682	+	0.992322i	0.178227	+	0.0330774i
$901$			16.8944i			0.562833i
$902$	7.39156	+	7.39156i	0.246112	+	0.246112i
$903$		0			0
$904$		−	13.7933i		−	0.458759i
$905$	15.5668	+	1.43229i	0.517456	+	0.0476111i
$906$			7.16387i			0.238004i
$907$	−11.7173	+	11.7173i	−0.389066	+	0.389066i	−0.874354	−	0.485288i	$-0.838715\pi$
$907$	−11.7173	+	11.7173i	−0.389066	+	0.389066i	0.485288	+	0.874354i	$0.338715\pi$
$908$	−11.4508	+	11.4508i	−0.380007	+	0.380007i
$909$	10.7549			0.356718
$910$		0			0
$911$	−1.46770			−0.0486270			−0.0243135	−	0.999704i	$-0.507740\pi$
$911$	−1.46770			−0.0486270			−0.0243135	+	0.999704i	$0.507740\pi$
$912$	−8.86840	+	8.86840i	−0.293662	+	0.293662i
$913$	15.5689	−	15.5689i	0.515256	−	0.515256i
$914$			2.86154i			0.0946514i
$915$	−24.0578	+	20.0037i	−0.795326	+	0.661302i
$916$			11.7764i			0.389103i
$917$		0			0
$918$	5.57658	+	5.57658i	0.184055	+	0.184055i
$919$			27.8886i			0.919961i	0.887929	+	0.459981i	$0.152144\pi$
$919$			27.8886i			0.919961i	−0.887929	+	0.459981i	$0.847856\pi$
$920$	−10.1049	−	0.929750i	−0.333149	−	0.0306529i
$921$	−3.08395			−0.101620
$922$	2.14023	+	2.14023i	0.0704846	+	0.0704846i
$923$	1.45920	−	1.45920i	0.0480302	−	0.0480302i
$924$		0			0
$925$	−19.0642	+	13.0957i	−0.626828	+	0.430582i
$926$	27.2786			0.896431
$927$	3.29317	+	3.29317i	0.108162	+	0.108162i
$928$	−5.06196	−	5.06196i	−0.166167	−	0.166167i
$929$	33.2936			1.09233			0.546164	−	0.837678i	$-0.316087\pi$
$929$	33.2936			1.09233			0.546164	+	0.837678i	$0.316087\pi$
$930$	−3.02896	+	32.9200i	−0.0993236	+	1.07949i
$931$		0			0
$932$	−4.04765	+	4.04765i	−0.132585	+	0.132585i
$933$	13.7647	+	13.7647i	0.450637	+	0.450637i
$934$	−25.1289			−0.822244
$935$	−14.1684	+	11.7808i	−0.463355	+	0.385273i
$936$			0.315125i			0.0103002i
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	0.988654	−	0.150212i	$-0.0479957\pi$
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	−0.150212	+	0.988654i	$0.547996\pi$
$938$		0			0
$939$			6.11942i			0.199700i
$940$	0.450509	+	0.541813i	0.0146940	+	0.0176720i
$941$			24.3333i			0.793242i	0.917983	+	0.396621i	$0.129817\pi$
$941$			24.3333i			0.793242i	−0.917983	+	0.396621i	$0.870183\pi$
$942$	8.75286	−	8.75286i	0.285184	−	0.285184i
$943$	8.30300	−	8.30300i	0.270383	−	0.270383i
$944$	0.855404			0.0278410
$945$		0			0
$946$	28.4413			0.924707
$947$	−1.52032	+	1.52032i	−0.0494039	+	0.0494039i	−0.731377	−	0.681973i	$-0.761122\pi$
$947$	−1.52032	+	1.52032i	−0.0494039	+	0.0494039i	0.681973	+	0.731377i	$0.261122\pi$
$948$	−7.25713	+	7.25713i	−0.235701	+	0.235701i
$949$			3.33947i			0.108404i
$950$	−25.5659	+	17.5618i	−0.829467	+	0.569780i
$951$		−	3.93980i		−	0.127757i
$952$		0			0
$953$	−13.1863	−	13.1863i	−0.427146	−	0.427146i	0.460509	−	0.887655i	$-0.347667\pi$
$953$	−13.1863	−	13.1863i	−0.427146	−	0.427146i	−0.887655	+	0.460509i	$0.847667\pi$
$954$		−	9.00838i		−	0.291657i
$955$	0.916697	−	9.96303i	0.0296636	−	0.322396i
$956$	−8.33794			−0.269668
$957$	−41.3459	−	41.3459i	−1.33652	−	1.33652i
$958$	5.85973	−	5.85973i	0.189319	−	0.189319i
$959$		0			0
$960$	3.47617	−	2.89039i	0.112193	−	0.0932869i
$961$	−22.4736			−0.724955
$962$	−0.947702	−	0.947702i	−0.0305551	−	0.0305551i
$963$	11.4376	+	11.4376i	0.368572	+	0.368572i
$964$	−2.96438			−0.0954763
$965$	−34.5156	+	28.6993i	−1.11110	+	0.923862i
$966$		0			0
$967$	−27.7931	+	27.7931i	−0.893766	+	0.893766i	−0.994875	−	0.101109i	$-0.967761\pi$
$967$	−27.7931	+	27.7931i	−0.893766	+	0.893766i	0.101109	+	0.994875i	$0.467761\pi$
$968$	−3.76279	−	3.76279i	−0.120941	−	0.120941i
$969$	25.5820			0.821813
$970$	−1.92125	+	20.8810i	−0.0616877	+	0.670447i
$971$			13.9752i			0.448486i	0.974533	+	0.224243i	$0.0719909\pi$
$971$			13.9752i			0.448486i	−0.974533	+	0.224243i	$0.928009\pi$
$972$	−7.63821	−	7.63821i	−0.244996	−	0.244996i
$973$		0			0
$974$		−	10.6783i		−	0.342155i
$975$	−0.534457	+	2.87976i	−0.0171163	+	0.0922260i
$976$			6.92077i			0.221528i
$977$	5.90367	−	5.90367i	0.188875	−	0.188875i	−0.606335	−	0.795210i	$-0.707361\pi$
$977$	5.90367	−	5.90367i	0.188875	−	0.188875i	0.795210	+	0.606335i	$0.207361\pi$
$978$	−23.6715	+	23.6715i	−0.756930	+	0.756930i
$979$	−12.4120			−0.396690
$980$		0			0
$981$	14.3907			0.459459
$982$	18.1910	−	18.1910i	0.580498	−	0.580498i
$983$	−17.2224	+	17.2224i	−0.549309	+	0.549309i	−0.926241	−	0.376932i	$-0.876979\pi$
$983$	−17.2224	+	17.2224i	−0.549309	+	0.549309i	0.376932	+	0.926241i	$0.376979\pi$
$984$			5.23128i			0.166767i
$985$	15.8690	+	19.0852i	0.505630	+	0.608104i
$986$			14.6019i			0.465018i
$987$		0			0
$988$	−1.27091	−	1.27091i	−0.0404329	−	0.0404329i
$989$		−	31.9483i		−	1.01590i
$990$	7.55482	−	6.28172i	0.240108	−	0.199646i
$991$	17.4400			0.554001			0.277000	−	0.960870i	$-0.410660\pi$
$991$	17.4400			0.554001			0.277000	+	0.960870i	$0.410660\pi$
$992$	5.17076	+	5.17076i	0.164172	+	0.164172i
$993$	−41.3067	+	41.3067i	−1.31083	+	1.31083i
$994$		0			0
$995$	2.21307	−	24.0525i	0.0701590	−	0.762516i
$996$	11.0187			0.349141
$997$	−18.5048	−	18.5048i	−0.586054	−	0.586054i	0.350506	−	0.936560i	$-0.386010\pi$
$997$	−18.5048	−	18.5048i	−0.586054	−	0.586054i	−0.936560	+	0.350506i	$0.886010\pi$
$998$	−10.3229	−	10.3229i	−0.326766	−	0.326766i
$999$	17.8851			0.565860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.g.c.293.8		16
5.2	odd	4	inner	490.2.g.c.97.5		16
7.2	even	3		70.2.k.a.3.2	✓	16
7.3	odd	6		70.2.k.a.33.4	yes	16
7.4	even	3		490.2.l.c.313.3		16
7.5	odd	6		490.2.l.c.423.1		16
7.6	odd	2	inner	490.2.g.c.293.5		16
21.2	odd	6		630.2.bv.c.73.4		16
21.17	even	6		630.2.bv.c.523.2		16
28.3	even	6		560.2.ci.c.33.1		16
28.23	odd	6		560.2.ci.c.353.1		16
35.2	odd	12		70.2.k.a.17.4	yes	16
35.3	even	12		350.2.o.c.257.3		16
35.9	even	6		350.2.o.c.143.3		16
35.12	even	12		490.2.l.c.227.3		16
35.17	even	12		70.2.k.a.47.2	yes	16
35.23	odd	12		350.2.o.c.157.1		16
35.24	odd	6		350.2.o.c.243.1		16
35.27	even	4	inner	490.2.g.c.97.8		16
35.32	odd	12		490.2.l.c.117.1		16
105.2	even	12		630.2.bv.c.577.2		16
105.17	odd	12		630.2.bv.c.397.4		16
140.87	odd	12		560.2.ci.c.257.1		16
140.107	even	12		560.2.ci.c.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	7.2	even	3
70.2.k.a.17.4	yes	16	35.2	odd	12
70.2.k.a.33.4	yes	16	7.3	odd	6
70.2.k.a.47.2	yes	16	35.17	even	12
350.2.o.c.143.3		16	35.9	even	6
350.2.o.c.157.1		16	35.23	odd	12
350.2.o.c.243.1		16	35.24	odd	6
350.2.o.c.257.3		16	35.3	even	12
490.2.g.c.97.5		16	5.2	odd	4	inner
490.2.g.c.97.8		16	35.27	even	4	inner
490.2.g.c.293.5		16	7.6	odd	2	inner
490.2.g.c.293.8		16	1.1	even	1	trivial
490.2.l.c.117.1		16	35.32	odd	12
490.2.l.c.227.3		16	35.12	even	12
490.2.l.c.313.3		16	7.4	even	3
490.2.l.c.423.1		16	7.5	odd	6
560.2.ci.c.17.1		16	140.107	even	12
560.2.ci.c.33.1		16	28.3	even	6
560.2.ci.c.257.1		16	140.87	odd	12
560.2.ci.c.353.1		16	28.23	odd	6
630.2.bv.c.73.4		16	21.2	odd	6
630.2.bv.c.397.4		16	105.17	odd	12
630.2.bv.c.523.2		16	21.17	even	6
630.2.bv.c.577.2		16	105.2	even	12

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.42962 - 1.42962i) q^{3} -1.00000i q^{4} +(0.204875 - 2.22666i) q^{5} -2.02179i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.08763i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.42962 - 1.42962i) q^{3} -1.00000i q^{4} +(0.204875 - 2.22666i) q^{5} -2.02179i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.08763i q^{9} +(-1.42962 - 1.71936i) q^{10} -4.03997 q^{11} +(-1.42962 - 1.42962i) q^{12} +(0.204875 - 0.204875i) q^{13} +(-2.89039 - 3.47617i) q^{15} -1.00000 q^{16} +(1.44231 + 1.44231i) q^{17} +(-0.769067 - 0.769067i) q^{18} +6.20333 q^{19} +(-2.22666 - 0.204875i) q^{20} +(-2.85669 + 2.85669i) q^{22} +(3.20895 + 3.20895i) q^{23} -2.02179 q^{24} +(-4.91605 - 0.912375i) q^{25} -0.289737i q^{26} +(2.73397 + 2.73397i) q^{27} +7.15869i q^{29} +(-4.50184 - 0.414214i) q^{30} -7.31256i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.77563 + 5.77563i) q^{33} +2.03974 q^{34} -1.08763 q^{36} +(3.27091 - 3.27091i) q^{37} +(4.38642 - 4.38642i) q^{38} -0.585786i q^{39} +(-1.71936 + 1.42962i) q^{40} -2.58745i q^{41} +(-4.97801 - 4.97801i) q^{43} +4.03997i q^{44} +(-2.42177 - 0.222827i) q^{45} +4.53813 q^{46} +(-0.222827 - 0.222827i) q^{47} +(-1.42962 + 1.42962i) q^{48} +(-4.12132 + 2.83103i) q^{50} +4.12392 q^{51} +(-0.204875 - 0.204875i) q^{52} +(5.85669 + 5.85669i) q^{53} +3.86642 q^{54} +(-0.827689 + 8.99566i) q^{55} +(8.86840 - 8.86840i) q^{57} +(5.06196 + 5.06196i) q^{58} -0.855404 q^{59} +(-3.47617 + 2.89039i) q^{60} -6.92077i q^{61} +(-5.17076 - 5.17076i) q^{62} +1.00000i q^{64} +(-0.414214 - 0.498161i) q^{65} +8.16797i q^{66} +(-2.23353 + 2.23353i) q^{67} +(1.44231 - 1.44231i) q^{68} +9.17514 q^{69} +7.12240 q^{71} +(-0.769067 + 0.769067i) q^{72} +(-8.15002 + 8.15002i) q^{73} -4.62576i q^{74} +(-8.33243 + 5.72374i) q^{75} -6.20333i q^{76} +(-0.414214 - 0.414214i) q^{78} -5.07627i q^{79} +(-0.204875 + 2.22666i) q^{80} +11.0799 q^{81} +(-1.82961 - 1.82961i) q^{82} +(-3.85372 + 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} -7.03997 q^{86} +(10.2342 + 10.2342i) q^{87} +(2.85669 + 2.85669i) q^{88} +3.07230 q^{89} +(-1.87002 + 1.55489i) q^{90} +(3.20895 - 3.20895i) q^{92} +(-10.4542 - 10.4542i) q^{93} -0.315125 q^{94} +(1.27091 - 13.8127i) q^{95} +2.02179i q^{96} +(-6.63103 - 6.63103i) q^{97} +4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) \) 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

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