LMFDB - Embedded newform 578.2.c.g.327.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(251,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.251"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.c (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.6
Root			$1.08335 - 1.08335i$ of defining polynomial
Character	$\chi$	$=$	578.327
Dual form			578.2.c.g.251.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(2.28161 - 2.28161i) q^{3} -1.00000 q^{4} +(-0.837775 + 0.837775i) q^{5} +(-2.28161 - 2.28161i) q^{6} +(-0.792394 - 0.792394i) q^{7} +1.00000i q^{8} -7.41147i q^{9} +(0.837775 + 0.837775i) q^{10} +(-2.41228 - 2.41228i) q^{11} +(-2.28161 + 2.28161i) q^{12} -0.347296 q^{13} +(-0.792394 + 0.792394i) q^{14} +3.82295i q^{15} +1.00000 q^{16} -7.41147 q^{18} +0.347296i q^{19} +(0.837775 - 0.837775i) q^{20} -3.61587 q^{21} +(-2.41228 + 2.41228i) q^{22} +(-0.290956 - 0.290956i) q^{23} +(2.28161 + 2.28161i) q^{24} +3.59627i q^{25} +0.347296i q^{26} +(-10.0653 - 10.0653i) q^{27} +(0.792394 + 0.792394i) q^{28} +(6.20915 - 6.20915i) q^{29} +3.82295 q^{30} +(6.16377 - 6.16377i) q^{31} -1.00000i q^{32} -11.0077 q^{33} +1.32770 q^{35} +7.41147i q^{36} +(-0.336337 + 0.336337i) q^{37} +0.347296 q^{38} +(-0.792394 + 0.792394i) q^{39} +(-0.837775 - 0.837775i) q^{40} +(-1.86546 - 1.86546i) q^{41} +3.61587i q^{42} +9.33275i q^{43} +(2.41228 + 2.41228i) q^{44} +(6.20915 + 6.20915i) q^{45} +(-0.290956 + 0.290956i) q^{46} +7.86484 q^{47} +(2.28161 - 2.28161i) q^{48} -5.74422i q^{49} +3.59627 q^{50} +0.347296 q^{52} +8.41921i q^{53} +(-10.0653 + 10.0653i) q^{54} +4.04189 q^{55} +(0.792394 - 0.792394i) q^{56} +(0.792394 + 0.792394i) q^{57} +(-6.20915 - 6.20915i) q^{58} +6.41147i q^{59} -3.82295i q^{60} +(4.03216 + 4.03216i) q^{61} +(-6.16377 - 6.16377i) q^{62} +(-5.87281 + 5.87281i) q^{63} -1.00000 q^{64} +(0.290956 - 0.290956i) q^{65} +11.0077i q^{66} +7.31315 q^{67} -1.32770 q^{69} -1.32770i q^{70} +(5.37137 - 5.37137i) q^{71} +7.41147 q^{72} +(-6.39358 + 6.39358i) q^{73} +(0.336337 + 0.336337i) q^{74} +(8.20527 + 8.20527i) q^{75} -0.347296i q^{76} +3.82295i q^{77} +(0.792394 + 0.792394i) q^{78} +(9.38777 + 9.38777i) q^{79} +(-0.837775 + 0.837775i) q^{80} -23.6955 q^{81} +(-1.86546 + 1.86546i) q^{82} -7.73917i q^{83} +3.61587 q^{84} +9.33275 q^{86} -28.3337i q^{87} +(2.41228 - 2.41228i) q^{88} -7.18479 q^{89} +(6.20915 - 6.20915i) q^{90} +(0.275196 + 0.275196i) q^{91} +(0.290956 + 0.290956i) q^{92} -28.1266i q^{93} -7.86484i q^{94} +(-0.290956 - 0.290956i) q^{95} +(-2.28161 - 2.28161i) q^{96} +(-0.156715 + 0.156715i) q^{97} -5.74422 q^{98} +(-17.8785 + 17.8785i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 12 q^{16} - 48 q^{18} - 36 q^{30} - 36 q^{33} - 12 q^{50} + 36 q^{55} - 12 q^{64} + 48 q^{72} - 12 q^{81} + 36 q^{86} - 72 q^{89} + 48 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 + 12 * q^16 - 48 * q^18 - 36 * q^30 - 36 * q^33 - 12 * q^50 + 36 * q^55 - 12 * q^64 + 48 * q^72 - 12 * q^81 + 36 * q^86 - 72 * q^89 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	2.28161	−	2.28161i	1.31729	−	1.31729i	0.401372	−	0.915915i	$-0.368533\pi$
$3$	2.28161	−	2.28161i	1.31729	−	1.31729i	0.915915	−	0.401372i	$-0.131467\pi$
$4$	−1.00000			−0.500000
$5$	−0.837775	+	0.837775i	−0.374664	+	0.374664i	−0.869173	−	0.494508i	$-0.835348\pi$
$5$	−0.837775	+	0.837775i	−0.374664	+	0.374664i	0.494508	+	0.869173i	$0.335348\pi$
$6$	−2.28161	−	2.28161i	−0.931463	−	0.931463i
$7$	−0.792394	−	0.792394i	−0.299497	−	0.299497i	0.541320	−	0.840817i	$-0.317925\pi$
$7$	−0.792394	−	0.792394i	−0.299497	−	0.299497i	−0.840817	+	0.541320i	$0.817925\pi$
$8$			1.00000i			0.353553i
$9$		−	7.41147i		−	2.47049i
$10$	0.837775	+	0.837775i	0.264928	+	0.264928i
$11$	−2.41228	−	2.41228i	−0.727329	−	0.727329i	0.242758	−	0.970087i	$-0.421948\pi$
$11$	−2.41228	−	2.41228i	−0.727329	−	0.727329i	−0.970087	+	0.242758i	$0.921948\pi$
$12$	−2.28161	+	2.28161i	−0.658644	+	0.658644i
$13$	−0.347296			−0.0963227			−0.0481613	−	0.998840i	$-0.515336\pi$
$13$	−0.347296			−0.0963227			−0.0481613	+	0.998840i	$0.515336\pi$
$14$	−0.792394	+	0.792394i	−0.211776	+	0.211776i
$15$			3.82295i			0.987081i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−7.41147			−1.74690
$19$			0.347296i			0.0796752i	0.999206	+	0.0398376i	$0.0126841\pi$
$19$			0.347296i			0.0796752i	−0.999206	+	0.0398376i	$0.987316\pi$
$20$	0.837775	−	0.837775i	0.187332	−	0.187332i
$21$	−3.61587			−0.789047
$22$	−2.41228	+	2.41228i	−0.514299	+	0.514299i
$23$	−0.290956	−	0.290956i	−0.0606686	−	0.0606686i	0.676122	−	0.736790i	$-0.263659\pi$
$23$	−0.290956	−	0.290956i	−0.0606686	−	0.0606686i	−0.736790	+	0.676122i	$0.763659\pi$
$24$	2.28161	+	2.28161i	0.465731	+	0.465731i
$25$			3.59627i			0.719253i
$26$			0.347296i			0.0681104i
$27$	−10.0653	−	10.0653i	−1.93706	−	1.93706i
$28$	0.792394	+	0.792394i	0.149748	+	0.149748i
$29$	6.20915	−	6.20915i	1.15301	−	1.15301i	0.167063	−	0.985946i	$-0.446572\pi$
$29$	6.20915	−	6.20915i	1.15301	−	1.15301i	0.985946	−	0.167063i	$-0.0534285\pi$
$30$	3.82295			0.697972
$31$	6.16377	−	6.16377i	1.10705	−	1.10705i	0.113508	−	0.993537i	$-0.463791\pi$
$31$	6.16377	−	6.16377i	1.10705	−	1.10705i	0.993537	−	0.113508i	$-0.0362087\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−11.0077			−1.91620
$34$		0			0
$35$	1.32770			0.224422
$36$			7.41147i			1.23525i
$37$	−0.336337	+	0.336337i	−0.0552934	+	0.0552934i	−0.734213	−	0.678919i	$-0.762449\pi$
$37$	−0.336337	+	0.336337i	−0.0552934	+	0.0552934i	0.678919	+	0.734213i	$0.262449\pi$
$38$	0.347296			0.0563389
$39$	−0.792394	+	0.792394i	−0.126885	+	0.126885i
$40$	−0.837775	−	0.837775i	−0.132464	−	0.132464i
$41$	−1.86546	−	1.86546i	−0.291336	−	0.291336i	0.546272	−	0.837608i	$-0.316046\pi$
$41$	−1.86546	−	1.86546i	−0.291336	−	0.291336i	−0.837608	+	0.546272i	$0.816046\pi$
$42$			3.61587i			0.557940i
$43$			9.33275i			1.42323i	0.702569	+	0.711615i	$0.252036\pi$
$43$			9.33275i			1.42323i	−0.702569	+	0.711615i	$0.747964\pi$
$44$	2.41228	+	2.41228i	0.363664	+	0.363664i
$45$	6.20915	+	6.20915i	0.925605	+	0.925605i
$46$	−0.290956	+	0.290956i	−0.0428991	+	0.0428991i
$47$	7.86484			1.14720			0.573602	−	0.819134i	$-0.305546\pi$
$47$	7.86484			1.14720			0.573602	+	0.819134i	$0.305546\pi$
$48$	2.28161	−	2.28161i	0.329322	−	0.329322i
$49$		−	5.74422i		−	0.820603i
$50$	3.59627			0.508589
$51$		0			0
$52$	0.347296			0.0481613
$53$			8.41921i			1.15647i	0.815871	+	0.578234i	$0.196258\pi$
$53$			8.41921i			1.15647i	−0.815871	+	0.578234i	$0.803742\pi$
$54$	−10.0653	+	10.0653i	−1.36971	+	1.36971i
$55$	4.04189			0.545008
$56$	0.792394	−	0.792394i	0.105888	−	0.105888i
$57$	0.792394	+	0.792394i	0.104955	+	0.104955i
$58$	−6.20915	−	6.20915i	−0.815301	−	0.815301i
$59$			6.41147i			0.834703i	0.908745	+	0.417351i	$0.137042\pi$
$59$			6.41147i			0.834703i	−0.908745	+	0.417351i	$0.862958\pi$
$60$		−	3.82295i		−	0.493540i
$61$	4.03216	+	4.03216i	0.516265	+	0.516265i	0.916439	−	0.400174i	$-0.131050\pi$
$61$	4.03216	+	4.03216i	0.516265	+	0.516265i	−0.400174	+	0.916439i	$0.631050\pi$
$62$	−6.16377	−	6.16377i	−0.782799	−	0.782799i
$63$	−5.87281	+	5.87281i	−0.739904	+	0.739904i
$64$	−1.00000			−0.125000
$65$	0.290956	−	0.290956i	0.0360887	−	0.0360887i
$66$			11.0077i			1.35496i
$67$	7.31315			0.893443			0.446722	−	0.894673i	$-0.352591\pi$
$67$	7.31315			0.893443			0.446722	+	0.894673i	$0.352591\pi$
$68$		0			0
$69$	−1.32770			−0.159836
$70$		−	1.32770i		−	0.158690i
$71$	5.37137	−	5.37137i	0.637465	−	0.637465i	−0.312465	−	0.949929i	$-0.601155\pi$
$71$	5.37137	−	5.37137i	0.637465	−	0.637465i	0.949929	+	0.312465i	$0.101155\pi$
$72$	7.41147			0.873451
$73$	−6.39358	+	6.39358i	−0.748312	+	0.748312i	−0.974162	−	0.225850i	$-0.927484\pi$
$73$	−6.39358	+	6.39358i	−0.748312	+	0.748312i	0.225850	+	0.974162i	$0.427484\pi$
$74$	0.336337	+	0.336337i	0.0390983	+	0.0390983i
$75$	8.20527	+	8.20527i	0.947463	+	0.947463i
$76$		−	0.347296i		−	0.0398376i
$77$			3.82295i			0.435665i
$78$	0.792394	+	0.792394i	0.0897210	+	0.0897210i
$79$	9.38777	+	9.38777i	1.05621	+	1.05621i	0.998323	+	0.0578833i	$0.0184351\pi$
$79$	9.38777	+	9.38777i	1.05621	+	1.05621i	0.0578833	+	0.998323i	$0.481565\pi$
$80$	−0.837775	+	0.837775i	−0.0936661	+	0.0936661i
$81$	−23.6955			−2.63284
$82$	−1.86546	+	1.86546i	−0.206005	+	0.206005i
$83$		−	7.73917i		−	0.849484i	−0.905314	−	0.424742i	$-0.860365\pi$
$83$		−	7.73917i		−	0.849484i	0.905314	−	0.424742i	$-0.139635\pi$
$84$	3.61587			0.394523
$85$		0			0
$86$	9.33275			1.00638
$87$		−	28.3337i		−	3.03769i
$88$	2.41228	−	2.41228i	0.257150	−	0.257150i
$89$	−7.18479			−0.761586			−0.380793	−	0.924660i	$-0.624349\pi$
$89$	−7.18479			−0.761586			−0.380793	+	0.924660i	$0.624349\pi$
$90$	6.20915	−	6.20915i	0.654502	−	0.654502i
$91$	0.275196	+	0.275196i	0.0288483	+	0.0288483i
$92$	0.290956	+	0.290956i	0.0303343	+	0.0303343i
$93$		−	28.1266i		−	2.91659i
$94$		−	7.86484i		−	0.811196i
$95$	−0.290956	−	0.290956i	−0.0298515	−	0.0298515i
$96$	−2.28161	−	2.28161i	−0.232866	−	0.232866i
$97$	−0.156715	+	0.156715i	−0.0159120	+	0.0159120i	−0.715018	−	0.699106i	$-0.753582\pi$
$97$	−0.156715	+	0.156715i	−0.0159120	+	0.0159120i	0.699106	+	0.715018i	$0.253582\pi$
$98$	−5.74422			−0.580254
$99$	−17.8785	+	17.8785i	−1.79686	+	1.79686i
$100$		−	3.59627i		−	0.359627i
$101$	−4.86484			−0.484069			−0.242035	−	0.970268i	$-0.577815\pi$
$101$	−4.86484			−0.484069			−0.242035	+	0.970268i	$0.577815\pi$
$102$		0			0
$103$	12.3969			1.22151			0.610753	−	0.791821i	$-0.290867\pi$
$103$	12.3969			1.22151			0.610753	+	0.791821i	$0.290867\pi$
$104$		−	0.347296i		−	0.0340552i
$105$	3.02928	−	3.02928i	0.295628	−	0.295628i
$106$	8.41921			0.817746
$107$	6.26291	−	6.26291i	0.605459	−	0.605459i	−0.336297	−	0.941756i	$-0.609175\pi$
$107$	6.26291	−	6.26291i	0.605459	−	0.605459i	0.941756	+	0.336297i	$0.109175\pi$
$108$	10.0653	+	10.0653i	0.968530	+	0.968530i
$109$	−8.39518	−	8.39518i	−0.804112	−	0.804112i	0.179623	−	0.983736i	$-0.442512\pi$
$109$	−8.39518	−	8.39518i	−0.804112	−	0.804112i	−0.983736	+	0.179623i	$0.942512\pi$
$110$		−	4.04189i		−	0.385379i
$111$			1.53478i			0.145675i
$112$	−0.792394	−	0.792394i	−0.0748742	−	0.0748742i
$113$	−7.68260	−	7.68260i	−0.722718	−	0.722718i	0.246440	−	0.969158i	$-0.420739\pi$
$113$	−7.68260	−	7.68260i	−0.722718	−	0.722718i	−0.969158	+	0.246440i	$0.920739\pi$
$114$	0.792394	−	0.792394i	0.0742145	−	0.0742145i
$115$	0.487511			0.0454607
$116$	−6.20915	+	6.20915i	−0.576505	+	0.576505i
$117$			2.57398i			0.237964i
$118$	6.41147			0.590224
$119$		0			0
$120$	−3.82295			−0.348986
$121$			0.638156i			0.0580142i
$122$	4.03216	−	4.03216i	0.365054	−	0.365054i
$123$	−8.51249			−0.767545
$124$	−6.16377	+	6.16377i	−0.553523	+	0.553523i
$125$	−7.20174	−	7.20174i	−0.644143	−	0.644143i
$126$	5.87281	+	5.87281i	0.523191	+	0.523191i
$127$			6.55169i			0.581368i	0.956819	+	0.290684i	$0.0938829\pi$
$127$			6.55169i			0.581368i	−0.956819	+	0.290684i	$0.906117\pi$
$128$			1.00000i			0.0883883i
$129$	21.2937	+	21.2937i	1.87480	+	1.87480i
$130$	−0.290956	−	0.290956i	−0.0255185	−	0.0255185i
$131$	−0.0350936	+	0.0350936i	−0.00306614	+	0.00306614i	−0.708638	−	0.705572i	$-0.750690\pi$
$131$	−0.0350936	+	0.0350936i	−0.00306614	+	0.00306614i	0.705572	+	0.708638i	$0.250690\pi$
$132$	11.0077			0.958101
$133$	0.275196	−	0.275196i	0.0238625	−	0.0238625i
$134$		−	7.31315i		−	0.631760i
$135$	16.8648			1.45149
$136$		0			0
$137$	−8.13341			−0.694884			−0.347442	−	0.937701i	$-0.612950\pi$
$137$	−8.13341			−0.694884			−0.347442	+	0.937701i	$0.612950\pi$
$138$			1.32770i			0.113021i
$139$	−10.8770	+	10.8770i	−0.922574	+	0.922574i	−0.997211	−	0.0746370i	$-0.976220\pi$
$139$	−10.8770	+	10.8770i	−0.922574	+	0.922574i	0.0746370	+	0.997211i	$0.476220\pi$
$140$	−1.32770			−0.112211
$141$	17.9445	−	17.9445i	1.51120	−	1.51120i
$142$	−5.37137	−	5.37137i	−0.450755	−	0.450755i
$143$	0.837775	+	0.837775i	0.0700583	+	0.0700583i
$144$		−	7.41147i		−	0.617623i
$145$			10.4037i			0.863983i
$146$	6.39358	+	6.39358i	0.529137	+	0.529137i
$147$	−13.1061	−	13.1061i	−1.08097	−	1.08097i
$148$	0.336337	−	0.336337i	0.0276467	−	0.0276467i
$149$	16.1088			1.31968			0.659840	−	0.751406i	$-0.270624\pi$
$149$	16.1088			1.31968			0.659840	+	0.751406i	$0.270624\pi$
$150$	8.20527	−	8.20527i	0.669958	−	0.669958i
$151$		−	2.70233i		−	0.219913i	−0.993936	−	0.109956i	$-0.964929\pi$
$151$		−	2.70233i		−	0.219913i	0.993936	−	0.109956i	$-0.0350711\pi$
$152$	−0.347296			−0.0281695
$153$		0			0
$154$	3.82295			0.308062
$155$			10.3277i			0.829541i
$156$	0.792394	−	0.792394i	0.0634423	−	0.0634423i
$157$	23.5594			1.88025			0.940124	−	0.340834i	$-0.110709\pi$
$157$	23.5594			1.88025			0.940124	+	0.340834i	$0.110709\pi$
$158$	9.38777	−	9.38777i	0.746851	−	0.746851i
$159$	19.2094	+	19.2094i	1.52340	+	1.52340i
$160$	0.837775	+	0.837775i	0.0662319	+	0.0662319i
$161$			0.461104i			0.0363401i
$162$			23.6955i			1.86170i
$163$	−1.32535	−	1.32535i	−0.103810	−	0.103810i	0.653294	−	0.757104i	$-0.273386\pi$
$163$	−1.32535	−	1.32535i	−0.103810	−	0.103810i	−0.757104	+	0.653294i	$0.773386\pi$
$164$	1.86546	+	1.86546i	0.145668	+	0.145668i
$165$	9.22201	−	9.22201i	0.717932	−	0.717932i
$166$	−7.73917			−0.600676
$167$	6.26291	−	6.26291i	0.484639	−	0.484639i	−0.421971	−	0.906609i	$-0.638661\pi$
$167$	6.26291	−	6.26291i	0.484639	−	0.484639i	0.906609	+	0.421971i	$0.138661\pi$
$168$		−	3.61587i		−	0.278970i
$169$	−12.8794			−0.990722
$170$		0			0
$171$	2.57398			0.196837
$172$		−	9.33275i		−	0.711615i
$173$	−4.53360	+	4.53360i	−0.344683	+	0.344683i	−0.858125	−	0.513442i	$-0.828370\pi$
$173$	−4.53360	+	4.53360i	−0.344683	+	0.344683i	0.513442	+	0.858125i	$0.328370\pi$
$174$	−28.3337			−2.14797
$175$	2.84966	−	2.84966i	0.215414	−	0.215414i
$176$	−2.41228	−	2.41228i	−0.181832	−	0.181832i
$177$	14.6285	+	14.6285i	1.09954	+	1.09954i
$178$			7.18479i			0.538523i
$179$			1.26083i			0.0942388i	0.998889	+	0.0471194i	$0.0150041\pi$
$179$			1.26083i			0.0942388i	−0.998889	+	0.0471194i	$0.984996\pi$
$180$	−6.20915	−	6.20915i	−0.462802	−	0.462802i
$181$	10.8335	+	10.8335i	0.805248	+	0.805248i	0.983910	−	0.178662i	$-0.0571770\pi$
$181$	10.8335	+	10.8335i	0.805248	+	0.805248i	−0.178662	+	0.983910i	$0.557177\pi$
$182$	0.275196	−	0.275196i	0.0203989	−	0.0203989i
$183$	18.3996			1.36014
$184$	0.290956	−	0.290956i	0.0214496	−	0.0214496i
$185$		−	0.563549i		−	0.0414329i
$186$	−28.1266			−2.06234
$187$		0			0
$188$	−7.86484			−0.573602
$189$			15.9513i			1.16029i
$190$	−0.290956	+	0.290956i	−0.0211082	+	0.0211082i
$191$	−10.3601			−0.749630			−0.374815	−	0.927100i	$-0.622294\pi$
$191$	−10.3601			−0.749630			−0.374815	+	0.927100i	$0.622294\pi$
$192$	−2.28161	+	2.28161i	−0.164661	+	0.164661i
$193$	10.7862	+	10.7862i	0.776409	+	0.776409i	0.979218	−	0.202809i	$-0.0650071\pi$
$193$	10.7862	+	10.7862i	0.776409	+	0.776409i	−0.202809	+	0.979218i	$0.565007\pi$
$194$	0.156715	+	0.156715i	0.0112515	+	0.0112515i
$195$		−	1.32770i		−	0.0950783i
$196$			5.74422i			0.410302i
$197$	−15.0205	−	15.0205i	−1.07016	−	1.07016i	−0.997345	−	0.0728196i	$-0.976800\pi$
$197$	−15.0205	−	15.0205i	−1.07016	−	1.07016i	−0.0728196	−	0.997345i	$-0.523200\pi$
$198$	17.8785	+	17.8785i	1.27057	+	1.27057i
$199$	−9.25163	+	9.25163i	−0.655831	+	0.655831i	−0.954391	−	0.298560i	$-0.903494\pi$
$199$	−9.25163	+	9.25163i	−0.655831	+	0.655831i	0.298560	+	0.954391i	$0.403494\pi$
$200$	−3.59627			−0.254294
$201$	16.6857	−	16.6857i	1.17692	−	1.17692i
$202$			4.86484i			0.342289i
$203$	−9.84018			−0.690646
$204$		0			0
$205$	3.12567			0.218306
$206$		−	12.3969i		−	0.863735i
$207$	−2.15641	+	2.15641i	−0.149881	+	0.149881i
$208$	−0.347296			−0.0240807
$209$	0.837775	−	0.837775i	0.0579501	−	0.0579501i
$210$	−3.02928	−	3.02928i	−0.209040	−	0.209040i
$211$	−7.03663	−	7.03663i	−0.484422	−	0.484422i	0.422119	−	0.906541i	$-0.361287\pi$
$211$	−7.03663	−	7.03663i	−0.484422	−	0.484422i	−0.906541	+	0.422119i	$0.861287\pi$
$212$		−	8.41921i		−	0.578234i
$213$		−	24.5107i		−	1.67945i
$214$	−6.26291	−	6.26291i	−0.428124	−	0.428124i
$215$	−7.81874	−	7.81874i	−0.533234	−	0.533234i
$216$	10.0653	−	10.0653i	0.684854	−	0.684854i
$217$	−9.76827			−0.663113
$218$	−8.39518	+	8.39518i	−0.568593	+	0.568593i
$219$			29.1753i			1.97148i
$220$	−4.04189			−0.272504
$221$		0			0
$222$	1.53478			0.103008
$223$			19.7638i			1.32348i	0.749732	+	0.661742i	$0.230182\pi$
$223$			19.7638i			1.32348i	−0.749732	+	0.661742i	$0.769818\pi$
$224$	−0.792394	+	0.792394i	−0.0529441	+	0.0529441i
$225$	26.6536			1.77691
$226$	−7.68260	+	7.68260i	−0.511039	+	0.511039i
$227$	2.51332	+	2.51332i	0.166815	+	0.166815i	0.785578	−	0.618763i	$-0.212366\pi$
$227$	2.51332	+	2.51332i	0.166815	+	0.166815i	−0.618763	+	0.785578i	$0.712366\pi$
$228$	−0.792394	−	0.792394i	−0.0524776	−	0.0524776i
$229$			2.04189i			0.134932i	0.997722	+	0.0674659i	$0.0214914\pi$
$229$			2.04189i			0.134932i	−0.997722	+	0.0674659i	$0.978509\pi$
$230$		−	0.487511i		−	0.0321456i
$231$	8.72247	+	8.72247i	0.573896	+	0.573896i
$232$	6.20915	+	6.20915i	0.407650	+	0.407650i
$233$	2.76919	−	2.76919i	0.181415	−	0.181415i	−0.610557	−	0.791972i	$-0.709054\pi$
$233$	2.76919	−	2.76919i	0.181415	−	0.181415i	0.791972	+	0.610557i	$0.209054\pi$
$234$	2.57398			0.168266
$235$	−6.58896	+	6.58896i	−0.429817	+	0.429817i
$236$		−	6.41147i		−	0.417351i
$237$	42.8384			2.78266
$238$		0			0
$239$	−21.5544			−1.39424			−0.697118	−	0.716956i	$-0.745535\pi$
$239$	−21.5544			−1.39424			−0.697118	+	0.716956i	$0.745535\pi$
$240$			3.82295i			0.246770i
$241$	−17.8138	+	17.8138i	−1.14749	+	1.14749i	−0.160443	+	0.987045i	$0.551292\pi$
$241$	−17.8138	+	17.8138i	−1.14749	+	1.14749i	−0.987045	+	0.160443i	$0.948708\pi$
$242$	0.638156			0.0410222
$243$	−23.8681	+	23.8681i	−1.53114	+	1.53114i
$244$	−4.03216	−	4.03216i	−0.258133	−	0.258133i
$245$	4.81237	+	4.81237i	0.307451	+	0.307451i
$246$			8.51249i			0.542736i
$247$		−	0.120615i		−	0.00767453i
$248$	6.16377	+	6.16377i	0.391400	+	0.391400i
$249$	−17.6578	−	17.6578i	−1.11901	−	1.11901i
$250$	−7.20174	+	7.20174i	−0.455478	+	0.455478i
$251$	−3.07604			−0.194158			−0.0970789	−	0.995277i	$-0.530950\pi$
$251$	−3.07604			−0.194158			−0.0970789	+	0.995277i	$0.530950\pi$
$252$	5.87281	−	5.87281i	0.369952	−	0.369952i
$253$			1.40373i			0.0882520i
$254$	6.55169			0.411090
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	24.9394i		−	1.55568i	−0.628462	−	0.777840i	$-0.716315\pi$
$257$		−	24.9394i		−	1.55568i	0.628462	−	0.777840i	$-0.283685\pi$
$258$	21.2937	−	21.2937i	1.32569	−	1.32569i
$259$	0.533023			0.0331204
$260$	−0.290956	+	0.290956i	−0.0180443	+	0.0180443i
$261$	−46.0189	−	46.0189i	−2.84850	−	2.84850i
$262$	0.0350936	+	0.0350936i	0.00216809	+	0.00216809i
$263$			15.2422i			0.939872i	0.882700	+	0.469936i	$0.155723\pi$
$263$			15.2422i			0.939872i	−0.882700	+	0.469936i	$0.844277\pi$
$264$		−	11.0077i		−	0.677480i
$265$	−7.05341	−	7.05341i	−0.433287	−	0.433287i
$266$	−0.275196	−	0.275196i	−0.0168733	−	0.0168733i
$267$	−16.3929	+	16.3929i	−1.00323	+	1.00323i
$268$	−7.31315			−0.446722
$269$	−2.66814	+	2.66814i	−0.162679	+	0.162679i	−0.783753	−	0.621073i	$-0.786697\pi$
$269$	−2.66814	+	2.66814i	−0.162679	+	0.162679i	0.621073	+	0.783753i	$0.286697\pi$
$270$		−	16.8648i		−	1.02636i
$271$	4.72462			0.287000			0.143500	−	0.989650i	$-0.454164\pi$
$271$	4.72462			0.287000			0.143500	+	0.989650i	$0.454164\pi$
$272$		0			0
$273$	1.25578			0.0760031
$274$			8.13341i			0.491357i
$275$	8.67519	−	8.67519i	0.523134	−	0.523134i
$276$	1.32770			0.0799179
$277$	−12.8889	+	12.8889i	−0.774417	+	0.774417i	−0.978875	−	0.204458i	$-0.934457\pi$
$277$	−12.8889	+	12.8889i	−0.774417	+	0.774417i	0.204458	+	0.978875i	$0.434457\pi$
$278$	10.8770	+	10.8770i	0.652358	+	0.652358i
$279$	−45.6826	−	45.6826i	−2.73495	−	2.73495i
$280$			1.32770i			0.0793450i
$281$		−	25.3773i		−	1.51388i	−0.653482	−	0.756942i	$-0.726692\pi$
$281$		−	25.3773i		−	1.51388i	0.653482	−	0.756942i	$-0.273308\pi$
$282$	−17.9445	−	17.9445i	−1.06858	−	1.06858i
$283$	9.22391	+	9.22391i	0.548304	+	0.548304i	0.925950	−	0.377646i	$-0.123266\pi$
$283$	9.22391	+	9.22391i	0.548304	+	0.548304i	−0.377646	+	0.925950i	$0.623266\pi$
$284$	−5.37137	+	5.37137i	−0.318732	+	0.318732i
$285$	−1.32770			−0.0786459
$286$	0.837775	−	0.837775i	0.0495387	−	0.0495387i
$287$			2.95636i			0.174508i
$288$	−7.41147			−0.436725
$289$		0			0
$290$	10.4037			0.610928
$291$			0.715127i			0.0419215i
$292$	6.39358	−	6.39358i	0.374156	−	0.374156i
$293$	−3.80571			−0.222332			−0.111166	−	0.993802i	$-0.535459\pi$
$293$	−3.80571			−0.222332			−0.111166	+	0.993802i	$0.535459\pi$
$294$	−13.1061	+	13.1061i	−0.764361	+	0.764361i
$295$	−5.37137	−	5.37137i	−0.312733	−	0.312733i
$296$	−0.336337	−	0.336337i	−0.0195492	−	0.0195492i
$297$			48.5604i			2.81776i
$298$		−	16.1088i		−	0.933155i
$299$	0.101048	+	0.101048i	0.00584376	+	0.00584376i
$300$	−8.20527	−	8.20527i	−0.473732	−	0.473732i
$301$	7.39522	−	7.39522i	0.426253	−	0.426253i
$302$	−2.70233			−0.155502
$303$	−11.0997	+	11.0997i	−0.637658	+	0.637658i
$304$			0.347296i			0.0199188i
$305$	−6.75608			−0.386852
$306$		0			0
$307$	13.1070			0.748056			0.374028	−	0.927417i	$-0.377976\pi$
$307$	13.1070			0.748056			0.374028	+	0.927417i	$0.377976\pi$
$308$		−	3.82295i		−	0.217833i
$309$	28.2849	−	28.2849i	1.60907	−	1.60907i
$310$	10.3277			0.586574
$311$	−7.30278	+	7.30278i	−0.414103	+	0.414103i	−0.883165	−	0.469062i	$-0.844592\pi$
$311$	−7.30278	+	7.30278i	−0.414103	+	0.414103i	0.469062	+	0.883165i	$0.344592\pi$
$312$	−0.792394	−	0.792394i	−0.0448605	−	0.0448605i
$313$	15.3568	+	15.3568i	0.868018	+	0.868018i	0.992253	−	0.124234i	$-0.0396475\pi$
$313$	15.3568	+	15.3568i	0.868018	+	0.868018i	−0.124234	+	0.992253i	$0.539647\pi$
$314$		−	23.5594i		−	1.32954i
$315$		−	9.84018i		−	0.554432i
$316$	−9.38777	−	9.38777i	−0.528103	−	0.528103i
$317$	7.90760	+	7.90760i	0.444135	+	0.444135i	0.893399	−	0.449264i	$-0.148314\pi$
$317$	7.90760	+	7.90760i	0.444135	+	0.444135i	−0.449264	+	0.893399i	$0.648314\pi$
$318$	19.2094	−	19.2094i	1.07721	−	1.07721i
$319$	−29.9564			−1.67723
$320$	0.837775	−	0.837775i	0.0468330	−	0.0468330i
$321$		−	28.5790i		−	1.59513i
$322$	0.461104			0.0256963
$323$		0			0
$324$	23.6955			1.31642
$325$		−	1.24897i		−	0.0692804i
$326$	−1.32535	+	1.32535i	−0.0734045	+	0.0734045i
$327$	−38.3090			−2.11849
$328$	1.86546	−	1.86546i	0.103003	−	0.103003i
$329$	−6.23205	−	6.23205i	−0.343584	−	0.343584i
$330$	−9.22201	−	9.22201i	−0.507655	−	0.507655i
$331$		−	18.0847i		−	0.994026i	−0.867743	−	0.497013i	$-0.834430\pi$
$331$		−	18.0847i		−	0.994026i	0.867743	−	0.497013i	$-0.165570\pi$
$332$			7.73917i			0.424742i
$333$	2.49275	+	2.49275i	0.136602	+	0.136602i
$334$	−6.26291	−	6.26291i	−0.342691	−	0.342691i
$335$	−6.12677	+	6.12677i	−0.334741	+	0.334741i
$336$	−3.61587			−0.197262
$337$	−1.18797	+	1.18797i	−0.0647129	+	0.0647129i	−0.738723	−	0.674010i	$-0.764571\pi$
$337$	−1.18797	+	1.18797i	−0.0647129	+	0.0647129i	0.674010	+	0.738723i	$0.264571\pi$
$338$			12.8794i			0.700546i
$339$	−35.0574			−1.90406
$340$		0			0
$341$	−29.7374			−1.61037
$342$		−	2.57398i		−	0.139185i
$343$	−10.0984	+	10.0984i	−0.545265	+	0.545265i
$344$	−9.33275			−0.503188
$345$	1.11231	−	1.11231i	0.0598848	−	0.0598848i
$346$	4.53360	+	4.53360i	0.243728	+	0.243728i
$347$	15.8933	+	15.8933i	0.853200	+	0.853200i	0.990526	−	0.137326i	$-0.0438509\pi$
$347$	15.8933	+	15.8933i	0.853200	+	0.853200i	−0.137326	+	0.990526i	$0.543851\pi$
$348$			28.3337i			1.51884i
$349$			21.1070i			1.12983i	0.825148	+	0.564916i	$0.191091\pi$
$349$			21.1070i			1.12983i	−0.825148	+	0.564916i	$0.808909\pi$
$350$	−2.84966	−	2.84966i	−0.152321	−	0.152321i
$351$	3.49563	+	3.49563i	0.186583	+	0.186583i
$352$	−2.41228	+	2.41228i	−0.128575	+	0.128575i
$353$	−3.86659			−0.205798			−0.102899	−	0.994692i	$-0.532812\pi$
$353$	−3.86659			−0.205798			−0.102899	+	0.994692i	$0.532812\pi$
$354$	14.6285	−	14.6285i	0.777495	−	0.777495i
$355$			9.00000i			0.477670i
$356$	7.18479			0.380793
$357$		0			0
$358$	1.26083			0.0666369
$359$			36.4347i			1.92295i	0.274893	+	0.961475i	$0.411358\pi$
$359$			36.4347i			1.92295i	−0.274893	+	0.961475i	$0.588642\pi$
$360$	−6.20915	+	6.20915i	−0.327251	+	0.327251i
$361$	18.8794			0.993652
$362$	10.8335	−	10.8335i	0.569396	−	0.569396i
$363$	1.45602	+	1.45602i	0.0764213	+	0.0764213i
$364$	−0.275196	−	0.275196i	−0.0144242	−	0.0144242i
$365$		−	10.7128i		−	0.560732i
$366$		−	18.3996i		−	0.961763i
$367$	−9.72768	−	9.72768i	−0.507781	−	0.507781i	0.406064	−	0.913845i	$-0.366901\pi$
$367$	−9.72768	−	9.72768i	−0.507781	−	0.507781i	−0.913845	+	0.406064i	$0.866901\pi$
$368$	−0.290956	−	0.290956i	−0.0151671	−	0.0151671i
$369$	−13.8258	+	13.8258i	−0.719742	+	0.719742i
$370$	−0.563549			−0.0292975
$371$	6.67134	−	6.67134i	0.346359	−	0.346359i
$372$			28.1266i			1.45830i
$373$	22.7638			1.17867			0.589333	−	0.807890i	$-0.299391\pi$
$373$	22.7638			1.17867			0.589333	+	0.807890i	$0.299391\pi$
$374$		0			0
$375$	−32.8631			−1.69704
$376$			7.86484i			0.405598i
$377$	−2.15641	+	2.15641i	−0.111061	+	0.111061i
$378$	15.9513			0.820447
$379$	−6.30639	+	6.30639i	−0.323938	+	0.323938i	−0.850276	−	0.526338i	$-0.823565\pi$
$379$	−6.30639	+	6.30639i	−0.323938	+	0.323938i	0.526338	+	0.850276i	$0.323565\pi$
$380$	0.290956	+	0.290956i	0.0149257	+	0.0149257i
$381$	14.9484	+	14.9484i	0.765829	+	0.765829i
$382$			10.3601i			0.530068i
$383$		−	19.4097i		−	0.991790i	−0.868382	−	0.495895i	$-0.834840\pi$
$383$		−	19.4097i		−	0.991790i	0.868382	−	0.495895i	$-0.165160\pi$
$384$	2.28161	+	2.28161i	0.116433	+	0.116433i
$385$	−3.20277	−	3.20277i	−0.163228	−	0.163228i
$386$	10.7862	−	10.7862i	0.549004	−	0.549004i
$387$	69.1694			3.51608
$388$	0.156715	−	0.156715i	0.00795602	−	0.00795602i
$389$			35.6614i			1.80810i	0.427423	+	0.904052i	$0.359422\pi$
$389$			35.6614i			1.80810i	−0.427423	+	0.904052i	$0.640578\pi$
$390$	−1.32770			−0.0672305
$391$		0			0
$392$	5.74422			0.290127
$393$			0.160140i			0.00807798i
$394$	−15.0205	+	15.0205i	−0.756721	+	0.756721i
$395$	−15.7297			−0.791446
$396$	17.8785	−	17.8785i	0.898430	−	0.898430i
$397$	5.26485	+	5.26485i	0.264235	+	0.264235i	0.826772	−	0.562537i	$-0.190175\pi$
$397$	5.26485	+	5.26485i	0.264235	+	0.264235i	−0.562537	+	0.826772i	$0.690175\pi$
$398$	9.25163	+	9.25163i	0.463742	+	0.463742i
$399$		−	1.25578i		−	0.0628675i
$400$			3.59627i			0.179813i
$401$	−1.67555	−	1.67555i	−0.0836730	−	0.0836730i	0.664032	−	0.747705i	$-0.268844\pi$
$401$	−1.67555	−	1.67555i	−0.0836730	−	0.0836730i	−0.747705	+	0.664032i	$0.768844\pi$
$402$	−16.6857	−	16.6857i	−0.832209	−	0.832209i
$403$	−2.14065	+	2.14065i	−0.106634	+	0.106634i
$404$	4.86484			0.242035
$405$	19.8515	−	19.8515i	0.986430	−	0.986430i
$406$			9.84018i			0.488360i
$407$	1.62267			0.0804330
$408$		0			0
$409$	−28.8357			−1.42584			−0.712918	−	0.701248i	$-0.752627\pi$
$409$	−28.8357			−1.42584			−0.712918	+	0.701248i	$0.752627\pi$
$410$		−	3.12567i		−	0.154366i
$411$	−18.5573	+	18.5573i	−0.915362	+	0.915362i
$412$	−12.3969			−0.610753
$413$	5.08042	−	5.08042i	0.249991	−	0.249991i
$414$	2.15641	+	2.15641i	0.105982	+	0.105982i
$415$	6.48368	+	6.48368i	0.318271	+	0.318271i
$416$			0.347296i			0.0170276i
$417$			49.6340i			2.43059i
$418$	−0.837775	−	0.837775i	−0.0409769	−	0.0409769i
$419$	21.6941	+	21.6941i	1.05982	+	1.05982i	0.998093	+	0.0617318i	$0.0196623\pi$
$419$	21.6941	+	21.6941i	1.05982	+	1.05982i	0.0617318	+	0.998093i	$0.480338\pi$
$420$	−3.02928	+	3.02928i	−0.147814	+	0.147814i
$421$	6.20708			0.302515			0.151257	−	0.988494i	$-0.451668\pi$
$421$	6.20708			0.302515			0.151257	+	0.988494i	$0.451668\pi$
$422$	−7.03663	+	7.03663i	−0.342538	+	0.342538i
$423$		−	58.2900i		−	2.83416i
$424$	−8.41921			−0.408873
$425$		0			0
$426$	−24.5107			−1.18755
$427$		−	6.39012i		−	0.309240i
$428$	−6.26291	+	6.26291i	−0.302729	+	0.302729i
$429$	3.82295			0.184574
$430$	−7.81874	+	7.81874i	−0.377053	+	0.377053i
$431$	6.17405	+	6.17405i	0.297394	+	0.297394i	0.839992	−	0.542599i	$-0.182559\pi$
$431$	6.17405	+	6.17405i	0.297394	+	0.297394i	−0.542599	+	0.839992i	$0.682559\pi$
$432$	−10.0653	−	10.0653i	−0.484265	−	0.484265i
$433$		−	20.9855i		−	1.00850i	−0.863559	−	0.504248i	$-0.831770\pi$
$433$		−	20.9855i		−	1.00850i	0.863559	−	0.504248i	$-0.168230\pi$
$434$			9.76827i			0.468892i
$435$	23.7372	+	23.7372i	1.13811	+	1.13811i
$436$	8.39518	+	8.39518i	0.402056	+	0.402056i
$437$	0.101048	−	0.101048i	0.00483378	−	0.00483378i
$438$	29.1753			1.39405
$439$	−5.98648	+	5.98648i	−0.285719	+	0.285719i	−0.835385	−	0.549666i	$-0.814755\pi$
$439$	−5.98648	+	5.98648i	−0.285719	+	0.285719i	0.549666	+	0.835385i	$0.314755\pi$
$440$			4.04189i			0.192690i
$441$	−42.5732			−2.02729
$442$		0			0
$443$	23.9564			1.13820			0.569100	−	0.822268i	$-0.307292\pi$
$443$	23.9564			1.13820			0.569100	+	0.822268i	$0.307292\pi$
$444$		−	1.53478i		−	0.0728373i
$445$	6.01924	−	6.01924i	0.285339	−	0.285339i
$446$	19.7638			0.935844
$447$	36.7539	−	36.7539i	1.73840	−	1.73840i
$448$	0.792394	+	0.792394i	0.0374371	+	0.0374371i
$449$	−4.33150	−	4.33150i	−0.204416	−	0.204416i	0.597473	−	0.801889i	$-0.296172\pi$
$449$	−4.33150	−	4.33150i	−0.204416	−	0.204416i	−0.801889	+	0.597473i	$0.796172\pi$
$450$		−	26.6536i		−	1.25646i
$451$			9.00000i			0.423793i
$452$	7.68260	+	7.68260i	0.361359	+	0.361359i
$453$	−6.16567	−	6.16567i	−0.289688	−	0.289688i
$454$	2.51332	−	2.51332i	0.117956	−	0.117956i
$455$	−0.461104			−0.0216169
$456$	−0.792394	+	0.792394i	−0.0371073	+	0.0371073i
$457$			1.01691i			0.0475691i	0.999717	+	0.0237846i	$0.00757158\pi$
$457$			1.01691i			0.0475691i	−0.999717	+	0.0237846i	$0.992428\pi$
$458$	2.04189			0.0954112
$459$		0			0
$460$	−0.487511			−0.0227303
$461$		−	23.0838i		−	1.07512i	−0.843226	−	0.537559i	$-0.819346\pi$
$461$		−	23.0838i		−	1.07512i	0.843226	−	0.537559i	$-0.180654\pi$
$462$	8.72247	−	8.72247i	0.405806	−	0.405806i
$463$	−19.3628			−0.899865			−0.449932	−	0.893063i	$-0.648552\pi$
$463$	−19.3628			−0.899865			−0.449932	+	0.893063i	$0.648552\pi$
$464$	6.20915	−	6.20915i	0.288252	−	0.288252i
$465$	23.5638	+	23.5638i	1.09274	+	1.09274i
$466$	−2.76919	−	2.76919i	−0.128280	−	0.128280i
$467$			10.6895i			0.494653i	0.968932	+	0.247326i	$0.0795520\pi$
$467$			10.6895i			0.494653i	−0.968932	+	0.247326i	$0.920448\pi$
$468$		−	2.57398i		−	0.118982i
$469$	−5.79490	−	5.79490i	−0.267583	−	0.267583i
$470$	6.58896	+	6.58896i	0.303926	+	0.303926i
$471$	53.7534	−	53.7534i	2.47683	−	2.47683i
$472$	−6.41147			−0.295112
$473$	22.5132	−	22.5132i	1.03516	−	1.03516i
$474$		−	42.8384i		−	1.96763i
$475$	−1.24897			−0.0573067
$476$		0			0
$477$	62.3988			2.85704
$478$			21.5544i			0.985874i
$479$	13.4460	−	13.4460i	0.614362	−	0.614362i	−0.329717	−	0.944080i	$-0.606953\pi$
$479$	13.4460	−	13.4460i	0.614362	−	0.614362i	0.944080	+	0.329717i	$0.106953\pi$
$480$	3.82295			0.174493
$481$	0.116809	−	0.116809i	0.00532601	−	0.00532601i
$482$	17.8138	+	17.8138i	0.811397	+	0.811397i
$483$	1.05206	+	1.05206i	0.0478703	+	0.0478703i
$484$		−	0.638156i		−	0.0290071i
$485$		−	0.262585i		−	0.0119234i
$486$	23.8681	+	23.8681i	1.08268	+	1.08268i
$487$	−2.21398	−	2.21398i	−0.100325	−	0.100325i	0.655163	−	0.755488i	$-0.272600\pi$
$487$	−2.21398	−	2.21398i	−0.100325	−	0.100325i	−0.755488	+	0.655163i	$0.772600\pi$
$488$	−4.03216	+	4.03216i	−0.182527	+	0.182527i
$489$	−6.04788			−0.273494
$490$	4.81237	−	4.81237i	0.217400	−	0.217400i
$491$			33.3851i			1.50665i	0.657650	+	0.753323i	$0.271551\pi$
$491$			33.3851i			1.50665i	−0.657650	+	0.753323i	$0.728449\pi$
$492$	8.51249			0.383773
$493$		0			0
$494$	−0.120615			−0.00542671
$495$		−	29.9564i		−	1.34644i
$496$	6.16377	−	6.16377i	0.276761	−	0.276761i
$497$	−8.51249			−0.381837
$498$	−17.6578	+	17.6578i	−0.791263	+	0.791263i
$499$	−2.77947	−	2.77947i	−0.124426	−	0.124426i	0.642151	−	0.766578i	$-0.278042\pi$
$499$	−2.77947	−	2.77947i	−0.124426	−	0.124426i	−0.766578	+	0.642151i	$0.778042\pi$
$500$	7.20174	+	7.20174i	0.322071	+	0.322071i
$501$		−	28.5790i		−	1.27682i
$502$			3.07604i			0.137290i
$503$	−3.16768	−	3.16768i	−0.141240	−	0.141240i	0.632952	−	0.774191i	$-0.281843\pi$
$503$	−3.16768	−	3.16768i	−0.141240	−	0.141240i	−0.774191	+	0.632952i	$0.781843\pi$
$504$	−5.87281	−	5.87281i	−0.261596	−	0.261596i
$505$	4.07564	−	4.07564i	0.181364	−	0.181364i
$506$	1.40373			0.0624036
$507$	−29.3857	+	29.3857i	−1.30507	+	1.30507i
$508$		−	6.55169i		−	0.290684i
$509$	−2.58853			−0.114734			−0.0573672	−	0.998353i	$-0.518271\pi$
$509$	−2.58853			−0.114734			−0.0573672	+	0.998353i	$0.518271\pi$
$510$		0			0
$511$	10.1325			0.448234
$512$		−	1.00000i		−	0.0441942i
$513$	3.49563	−	3.49563i	0.154336	−	0.154336i
$514$	−24.9394			−1.10003
$515$	−10.3858	+	10.3858i	−0.457654	+	0.457654i
$516$	−21.2937	−	21.2937i	−0.937402	−	0.937402i
$517$	−18.9722	−	18.9722i	−0.834395	−	0.834395i
$518$		−	0.533023i		−	0.0234197i
$519$			20.6878i			0.908093i
$520$	0.290956	+	0.290956i	0.0127593	+	0.0127593i
$521$	−27.1543	−	27.1543i	−1.18965	−	1.18965i	−0.977164	−	0.212488i	$-0.931843\pi$
$521$	−27.1543	−	27.1543i	−1.18965	−	1.18965i	−0.212488	−	0.977164i	$-0.568157\pi$
$522$	−46.0189	+	46.0189i	−2.01419	+	2.01419i
$523$	−31.6614			−1.38446			−0.692228	−	0.721679i	$-0.743371\pi$
$523$	−31.6614			−1.38446			−0.692228	+	0.721679i	$0.743371\pi$
$524$	0.0350936	−	0.0350936i	0.00153307	−	0.00153307i
$525$		−	13.0036i		−	0.567525i
$526$	15.2422			0.664590
$527$		0			0
$528$	−11.0077			−0.479050
$529$		−	22.8307i		−	0.992639i
$530$	−7.05341	+	7.05341i	−0.306380	+	0.306380i
$531$	47.5185			2.06213
$532$	−0.275196	+	0.275196i	−0.0119312	+	0.0119312i
$533$	0.647867	+	0.647867i	0.0280622	+	0.0280622i
$534$	16.3929	+	16.3929i	0.709389	+	0.709389i
$535$			10.4938i			0.453687i
$536$			7.31315i			0.315880i
$537$	2.87672	+	2.87672i	0.124140	+	0.124140i
$538$	2.66814	+	2.66814i	0.115032	+	0.115032i
$539$	−13.8567	+	13.8567i	−0.596848	+	0.596848i
$540$	−16.8648			−0.725747
$541$	−26.8272	+	26.8272i	−1.15339	+	1.15339i	−0.167525	+	0.985868i	$0.553578\pi$
$541$	−26.8272	+	26.8272i	−1.15339	+	1.15339i	−0.985868	+	0.167525i	$0.946422\pi$
$542$		−	4.72462i		−	0.202940i
$543$	49.4356			2.12149
$544$		0			0
$545$	14.0665			0.602544
$546$		−	1.25578i		−	0.0537423i
$547$	1.05249	−	1.05249i	0.0450012	−	0.0450012i	−0.684248	−	0.729249i	$-0.739869\pi$
$547$	1.05249	−	1.05249i	0.0450012	−	0.0450012i	0.729249	+	0.684248i	$0.239869\pi$
$548$	8.13341			0.347442
$549$	29.8842	−	29.8842i	1.27543	−	1.27543i
$550$	−8.67519	−	8.67519i	−0.369911	−	0.369911i
$551$	2.15641	+	2.15641i	0.0918663	+	0.0918663i
$552$		−	1.32770i		−	0.0565105i
$553$		−	14.8776i		−	0.632661i
$554$	12.8889	+	12.8889i	0.547596	+	0.547596i
$555$	−1.28580	−	1.28580i	−0.0545791	−	0.0545791i
$556$	10.8770	−	10.8770i	0.461287	−	0.461287i
$557$	−23.3259			−0.988352			−0.494176	−	0.869362i	$-0.664530\pi$
$557$	−23.3259			−0.988352			−0.494176	+	0.869362i	$0.664530\pi$
$558$	−45.6826	+	45.6826i	−1.93390	+	1.93390i
$559$		−	3.24123i		−	0.137089i
$560$	1.32770			0.0561054
$561$		0			0
$562$	−25.3773			−1.07048
$563$		−	4.37733i		−	0.184482i	−0.995737	−	0.0922411i	$-0.970597\pi$
$563$		−	4.37733i		−	0.184482i	0.995737	−	0.0922411i	$-0.0294031\pi$
$564$	−17.9445	+	17.9445i	−0.755599	+	0.755599i
$565$	12.8726			0.541553
$566$	9.22391	−	9.22391i	0.387710	−	0.387710i
$567$	18.7762	+	18.7762i	0.788526	+	0.788526i
$568$	5.37137	+	5.37137i	0.225378	+	0.225378i
$569$		−	4.69553i		−	0.196847i	−0.995145	−	0.0984234i	$-0.968620\pi$
$569$		−	4.69553i		−	0.196847i	0.995145	−	0.0984234i	$-0.0313799\pi$
$570$			1.32770i			0.0556111i
$571$	9.52325	+	9.52325i	0.398536	+	0.398536i	0.877716	−	0.479181i	$-0.159066\pi$
$571$	9.52325	+	9.52325i	0.398536	+	0.398536i	−0.479181	+	0.877716i	$0.659066\pi$
$572$	−0.837775	−	0.837775i	−0.0350291	−	0.0350291i
$573$	−23.6377	+	23.6377i	−0.987478	+	0.987478i
$574$	2.95636			0.123396
$575$	1.04636	−	1.04636i	0.0436361	−	0.0436361i
$576$			7.41147i			0.308811i
$577$	22.8066			0.949453			0.474727	−	0.880133i	$-0.342547\pi$
$577$	22.8066			0.949453			0.474727	+	0.880133i	$0.342547\pi$
$578$		0			0
$579$	49.2199			2.04551
$580$		−	10.4037i		−	0.431992i
$581$	−6.13247	+	6.13247i	−0.254418	+	0.254418i
$582$	0.715127			0.0296430
$583$	20.3095	−	20.3095i	0.841132	−	0.841132i
$584$	−6.39358	−	6.39358i	−0.264568	−	0.264568i
$585$	−2.15641	−	2.15641i	−0.0891567	−	0.0891567i
$586$			3.80571i			0.157213i
$587$		−	38.5945i		−	1.59297i	−0.604661	−	0.796483i	$-0.706691\pi$
$587$		−	38.5945i		−	1.59297i	0.604661	−	0.796483i	$-0.293309\pi$
$588$	13.1061	+	13.1061i	0.540485	+	0.540485i
$589$	2.14065	+	2.14065i	0.0882041	+	0.0882041i
$590$	−5.37137	+	5.37137i	−0.221136	+	0.221136i
$591$	−68.5417			−2.81943
$592$	−0.336337	+	0.336337i	−0.0138234	+	0.0138234i
$593$			2.30272i			0.0945613i	0.998882	+	0.0472807i	$0.0150555\pi$
$593$			2.30272i			0.0945613i	−0.998882	+	0.0472807i	$0.984944\pi$
$594$	48.5604			1.99246
$595$		0			0
$596$	−16.1088			−0.659840
$597$			42.2172i			1.72783i
$598$	0.101048	−	0.101048i	0.00413216	−	0.00413216i
$599$	29.1830			1.19239			0.596193	−	0.802841i	$-0.296679\pi$
$599$	29.1830			1.19239			0.596193	+	0.802841i	$0.296679\pi$
$600$	−8.20527	+	8.20527i	−0.334979	+	0.334979i
$601$	9.92978	+	9.92978i	0.405044	+	0.405044i	0.880006	−	0.474962i	$-0.157538\pi$
$601$	9.92978	+	9.92978i	0.405044	+	0.405044i	−0.474962	+	0.880006i	$0.657538\pi$
$602$	−7.39522	−	7.39522i	−0.301407	−	0.301407i
$603$		−	54.2012i		−	2.20724i
$604$			2.70233i			0.109956i
$605$	−0.534631	−	0.534631i	−0.0217358	−	0.0217358i
$606$	11.0997	+	11.0997i	0.450893	+	0.450893i
$607$	−7.25740	+	7.25740i	−0.294569	+	0.294569i	−0.838882	−	0.544313i	$-0.816790\pi$
$607$	−7.25740	+	7.25740i	−0.294569	+	0.294569i	0.544313	+	0.838882i	$0.316790\pi$
$608$	0.347296			0.0140847
$609$	−22.4514	+	22.4514i	−0.909779	+	0.909779i
$610$			6.75608i			0.273546i
$611$	−2.73143			−0.110502
$612$		0			0
$613$	2.66725			0.107729			0.0538646	−	0.998548i	$-0.482846\pi$
$613$	2.66725			0.107729			0.0538646	+	0.998548i	$0.482846\pi$
$614$		−	13.1070i		−	0.528955i
$615$	7.13155	−	7.13155i	0.287572	−	0.287572i
$616$	−3.82295			−0.154031
$617$	−27.9692	+	27.9692i	−1.12600	+	1.12600i	−0.135175	+	0.990822i	$0.543160\pi$
$617$	−27.9692	+	27.9692i	−1.12600	+	1.12600i	−0.990822	+	0.135175i	$0.956840\pi$
$618$	−28.2849	−	28.2849i	−1.13779	−	1.13779i
$619$	15.8286	+	15.8286i	0.636206	+	0.636206i	0.949618	−	0.313411i	$-0.101472\pi$
$619$	15.8286	+	15.8286i	0.636206	+	0.636206i	−0.313411	+	0.949618i	$0.601472\pi$
$620$		−	10.3277i		−	0.414770i
$621$			5.85710i			0.235037i
$622$	7.30278	+	7.30278i	0.292815	+	0.292815i
$623$	5.69319	+	5.69319i	0.228093	+	0.228093i
$624$	−0.792394	+	0.792394i	−0.0317212	+	0.0317212i
$625$	−5.91447			−0.236579
$626$	15.3568	−	15.3568i	0.613782	−	0.613782i
$627$		−	3.82295i		−	0.152674i
$628$	−23.5594			−0.940124
$629$		0			0
$630$	−9.84018			−0.392042
$631$		−	13.9727i		−	0.556243i	−0.960546	−	0.278121i	$-0.910288\pi$
$631$		−	13.9727i		−	0.556243i	0.960546	−	0.278121i	$-0.0897117\pi$
$632$	−9.38777	+	9.38777i	−0.373425	+	0.373425i
$633$	−32.1097			−1.27625
$634$	7.90760	−	7.90760i	0.314051	−	0.314051i
$635$	−5.48884	−	5.48884i	−0.217818	−	0.217818i
$636$	−19.2094	−	19.2094i	−0.761700	−	0.761700i
$637$			1.99495i			0.0790427i
$638$			29.9564i			1.18598i
$639$	−39.8098	−	39.8098i	−1.57485	−	1.57485i
$640$	−0.837775	−	0.837775i	−0.0331160	−	0.0331160i
$641$	17.3855	−	17.3855i	0.686685	−	0.686685i	−0.274813	−	0.961498i	$-0.588616\pi$
$641$	17.3855	−	17.3855i	0.686685	−	0.686685i	0.961498	+	0.274813i	$0.0886159\pi$
$642$	−28.5790			−1.12792
$643$	21.0008	−	21.0008i	0.828192	−	0.828192i	−0.159075	−	0.987267i	$-0.550851\pi$
$643$	21.0008	−	21.0008i	0.828192	−	0.828192i	0.987267	+	0.159075i	$0.0508512\pi$
$644$		−	0.461104i		−	0.0181700i
$645$	−35.6786			−1.40484
$646$		0			0
$647$	16.3946			0.644537			0.322268	−	0.946648i	$-0.395555\pi$
$647$	16.3946			0.644537			0.322268	+	0.946648i	$0.395555\pi$
$648$		−	23.6955i		−	0.930848i
$649$	15.4662	−	15.4662i	0.607103	−	0.607103i
$650$	−1.24897			−0.0489886
$651$	−22.2874	+	22.2874i	−0.873510	+	0.873510i
$652$	1.32535	+	1.32535i	0.0519048	+	0.0519048i
$653$	−25.3361	−	25.3361i	−0.991479	−	0.991479i	0.00848489	−	0.999964i	$-0.497299\pi$
$653$	−25.3361	−	25.3361i	−0.991479	−	0.991479i	−0.999964	+	0.00848489i	$0.997299\pi$
$654$			38.3090i			1.49800i
$655$		−	0.0588011i		−	0.00229755i
$656$	−1.86546	−	1.86546i	−0.0728339	−	0.0728339i
$657$	47.3859	+	47.3859i	1.84870	+	1.84870i
$658$	−6.23205	+	6.23205i	−0.242951	+	0.242951i
$659$	28.5354			1.11158			0.555790	−	0.831322i	$-0.312416\pi$
$659$	28.5354			1.11158			0.555790	+	0.831322i	$0.312416\pi$
$660$	−9.22201	+	9.22201i	−0.358966	+	0.358966i
$661$		−	45.1462i		−	1.75598i	−0.478676	−	0.877992i	$-0.658883\pi$
$661$		−	45.1462i		−	1.75598i	0.478676	−	0.877992i	$-0.341117\pi$
$662$	−18.0847			−0.702882
$663$		0			0
$664$	7.73917			0.300338
$665$			0.461104i			0.0178808i
$666$	2.49275	−	2.49275i	0.0965921	−	0.0965921i
$667$	−3.61318			−0.139903
$668$	−6.26291	+	6.26291i	−0.242319	+	0.242319i
$669$	45.0933	+	45.0933i	1.74341	+	1.74341i
$670$	6.12677	+	6.12677i	0.236698	+	0.236698i
$671$		−	19.4534i		−	0.750989i
$672$			3.61587i			0.139485i
$673$	3.47315	+	3.47315i	0.133880	+	0.133880i	0.770871	−	0.636991i	$-0.219821\pi$
$673$	3.47315	+	3.47315i	0.133880	+	0.133880i	−0.636991	+	0.770871i	$0.719821\pi$
$674$	1.18797	+	1.18797i	0.0457589	+	0.0457589i
$675$	36.1973	−	36.1973i	1.39324	−	1.39324i
$676$	12.8794			0.495361
$677$	−13.2855	+	13.2855i	−0.510602	+	0.510602i	−0.914711	−	0.404109i	$-0.867582\pi$
$677$	−13.2855	+	13.2855i	−0.510602	+	0.510602i	0.404109	+	0.914711i	$0.367582\pi$
$678$			35.0574i			1.34637i
$679$	0.248361			0.00953122
$680$		0			0
$681$	11.4688			0.439487
$682$			29.7374i			1.13870i
$683$	18.0806	−	18.0806i	0.691836	−	0.691836i	−0.270800	−	0.962636i	$-0.587288\pi$
$683$	18.0806	−	18.0806i	0.691836	−	0.691836i	0.962636	+	0.270800i	$0.0872882\pi$
$684$	−2.57398			−0.0984185
$685$	6.81396	−	6.81396i	0.260348	−	0.260348i
$686$	10.0984	+	10.0984i	0.385561	+	0.385561i
$687$	4.65879	+	4.65879i	0.177744	+	0.177744i
$688$			9.33275i			0.355808i
$689$		−	2.92396i		−	0.111394i
$690$	−1.11231	−	1.11231i	−0.0423449	−	0.0423449i
$691$	−29.4220	−	29.4220i	−1.11927	−	1.11927i	−0.991849	−	0.127418i	$-0.959331\pi$
$691$	−29.4220	−	29.4220i	−1.11927	−	1.11927i	−0.127418	−	0.991849i	$-0.540669\pi$
$692$	4.53360	−	4.53360i	0.172341	−	0.172341i
$693$	28.3337			1.07631
$694$	15.8933	−	15.8933i	0.603303	−	0.603303i
$695$		−	18.2249i		−	0.691311i
$696$	28.3337			1.07399
$697$		0			0
$698$	21.1070			0.798912
$699$		−	12.6364i		−	0.477953i
$700$	−2.84966	+	2.84966i	−0.107707	+	0.107707i
$701$	0.746911			0.0282104			0.0141052	−	0.999901i	$-0.495510\pi$
$701$	0.746911			0.0282104			0.0141052	+	0.999901i	$0.495510\pi$
$702$	3.49563	−	3.49563i	0.131934	−	0.131934i
$703$	−0.116809	−	0.116809i	−0.00440552	−	0.00440552i
$704$	2.41228	+	2.41228i	0.0909161	+	0.0909161i
$705$			30.0669i			1.13238i
$706$			3.86659i			0.145521i
$707$	3.85487	+	3.85487i	0.144977	+	0.144977i
$708$	−14.6285	−	14.6285i	−0.549772	−	0.549772i
$709$	14.9419	−	14.9419i	0.561155	−	0.561155i	−0.368480	−	0.929635i	$-0.620122\pi$
$709$	14.9419	−	14.9419i	0.561155	−	0.561155i	0.929635	+	0.368480i	$0.120122\pi$
$710$	9.00000			0.337764
$711$	69.5772	−	69.5772i	2.60935	−	2.60935i
$712$		−	7.18479i		−	0.269261i
$713$	−3.58677			−0.134326
$714$		0			0
$715$	−1.40373			−0.0524967
$716$		−	1.26083i		−	0.0471194i
$717$	−49.1786	+	49.1786i	−1.83661	+	1.83661i
$718$	36.4347			1.35973
$719$	−2.44737	+	2.44737i	−0.0912715	+	0.0912715i	−0.751268	−	0.659997i	$-0.770558\pi$
$719$	−2.44737	+	2.44737i	−0.0912715	+	0.0912715i	0.659997	+	0.751268i	$0.270558\pi$
$720$	6.20915	+	6.20915i	0.231401	+	0.231401i
$721$	−9.82325	−	9.82325i	−0.365837	−	0.365837i
$722$		−	18.8794i		−	0.702618i
$723$			81.2883i			3.02314i
$724$	−10.8335	−	10.8335i	−0.402624	−	0.402624i
$725$	22.3297	+	22.3297i	0.829306	+	0.829306i
$726$	1.45602	−	1.45602i	0.0540380	−	0.0540380i
$727$	36.3327			1.34751			0.673754	−	0.738956i	$-0.264681\pi$
$727$	36.3327			1.34751			0.673754	+	0.738956i	$0.264681\pi$
$728$	−0.275196	+	0.275196i	−0.0101994	+	0.0101994i
$729$			37.8289i			1.40107i
$730$	−10.7128			−0.396497
$731$		0			0
$732$	−18.3996			−0.680069
$733$			6.90167i			0.254919i	0.991844	+	0.127460i	$0.0406823\pi$
$733$			6.90167i			0.254919i	−0.991844	+	0.127460i	$0.959318\pi$
$734$	−9.72768	+	9.72768i	−0.359055	+	0.359055i
$735$	21.9599			0.810002
$736$	−0.290956	+	0.290956i	−0.0107248	+	0.0107248i
$737$	−17.6413	−	17.6413i	−0.649827	−	0.649827i
$738$	13.8258	+	13.8258i	0.508934	+	0.508934i
$739$			36.3651i			1.33771i	0.743391	+	0.668857i	$0.233216\pi$
$739$			36.3651i			1.33771i	−0.743391	+	0.668857i	$0.766784\pi$
$740$			0.563549i			0.0207165i
$741$	−0.275196	−	0.275196i	−0.0101096	−	0.0101096i
$742$	−6.67134	−	6.67134i	−0.244913	−	0.244913i
$743$	−34.1639	+	34.1639i	−1.25335	+	1.25335i	−0.299143	+	0.954208i	$0.596701\pi$
$743$	−34.1639	+	34.1639i	−1.25335	+	1.25335i	−0.954208	+	0.299143i	$0.903299\pi$
$744$	28.1266			1.03117
$745$	−13.4955	+	13.4955i	−0.494437	+	0.494437i
$746$		−	22.7638i		−	0.833443i
$747$	−57.3587			−2.09864
$748$		0			0
$749$	−9.92539			−0.362666
$750$			32.8631i			1.19999i
$751$	7.73827	−	7.73827i	0.282373	−	0.282373i	−0.551681	−	0.834055i	$-0.686014\pi$
$751$	7.73827	−	7.73827i	0.282373	−	0.282373i	0.834055	+	0.551681i	$0.186014\pi$
$752$	7.86484			0.286801
$753$	−7.01831	+	7.01831i	−0.255762	+	0.255762i
$754$	2.15641	+	2.15641i	0.0785320	+	0.0785320i
$755$	2.26395	+	2.26395i	0.0823935	+	0.0823935i
$756$		−	15.9513i		−	0.580143i
$757$		−	20.0601i		−	0.729095i	−0.931185	−	0.364548i	$-0.881224\pi$
$757$		−	20.0601i		−	0.729095i	0.931185	−	0.364548i	$-0.118776\pi$
$758$	6.30639	+	6.30639i	0.229058	+	0.229058i
$759$	3.20277	+	3.20277i	0.116253	+	0.116253i
$760$	0.290956	−	0.290956i	0.0105541	−	0.0105541i
$761$	36.4671			1.32193			0.660965	−	0.750416i	$-0.270147\pi$
$761$	36.4671			1.32193			0.660965	+	0.750416i	$0.270147\pi$
$762$	14.9484	−	14.9484i	0.541523	−	0.541523i
$763$			13.3046i			0.481658i
$764$	10.3601			0.374815
$765$		0			0
$766$	−19.4097			−0.701302
$767$		−	2.22668i		−	0.0804008i
$768$	2.28161	−	2.28161i	0.0823305	−	0.0823305i
$769$	−45.8120			−1.65202			−0.826012	−	0.563653i	$-0.809396\pi$
$769$	−45.8120			−1.65202			−0.826012	+	0.563653i	$0.809396\pi$
$770$	−3.20277	+	3.20277i	−0.115420	+	0.115420i
$771$	−56.9020	−	56.9020i	−2.04928	−	2.04928i
$772$	−10.7862	−	10.7862i	−0.388205	−	0.388205i
$773$			42.1549i			1.51621i	0.652135	+	0.758103i	$0.273873\pi$
$773$			42.1549i			1.51621i	−0.652135	+	0.758103i	$0.726127\pi$
$774$		−	69.1694i		−	2.48624i
$775$	22.1665	+	22.1665i	0.796246	+	0.796246i
$776$	−0.156715	−	0.156715i	−0.00562576	−	0.00562576i
$777$	1.21615	−	1.21615i	0.0436291	−	0.0436291i
$778$	35.6614			1.27852
$779$	0.647867	−	0.647867i	0.0232122	−	0.0232122i
$780$			1.32770i			0.0475391i
$781$	−25.9145			−0.927293
$782$		0			0
$783$	−124.993			−4.46690
$784$		−	5.74422i		−	0.205151i
$785$	−19.7375	+	19.7375i	−0.704461	+	0.704461i
$786$	0.160140			0.00571200
$787$	15.7080	−	15.7080i	0.559931	−	0.559931i	−0.369357	−	0.929288i	$-0.620422\pi$
$787$	15.7080	−	15.7080i	0.559931	−	0.559931i	0.929288	+	0.369357i	$0.120422\pi$
$788$	15.0205	+	15.0205i	0.535082	+	0.535082i
$789$	34.7766	+	34.7766i	1.23808	+	1.23808i
$790$			15.7297i			0.559637i
$791$			12.1753i			0.432904i
$792$	−17.8785	−	17.8785i	−0.635286	−	0.635286i
$793$	−1.40035	−	1.40035i	−0.0497280	−	0.0497280i
$794$	5.26485	−	5.26485i	0.186843	−	0.186843i
$795$	−32.1862			−1.14153
$796$	9.25163	−	9.25163i	0.327915	−	0.327915i
$797$			5.68180i			0.201260i	0.994924	+	0.100630i	$0.0320858\pi$
$797$			5.68180i			0.201260i	−0.994924	+	0.100630i	$0.967914\pi$
$798$	−1.25578			−0.0444540
$799$		0			0
$800$	3.59627			0.127147
$801$			53.2499i			1.88149i
$802$	−1.67555	+	1.67555i	−0.0591657	+	0.0591657i
$803$	30.8462			1.08854
$804$	−16.6857	+	16.6857i	−0.588461	+	0.588461i
$805$	−0.386301	−	0.386301i	−0.0136153	−	0.0136153i
$806$	2.14065	+	2.14065i	0.0754013	+	0.0754013i
$807$			12.1753i			0.428591i
$808$		−	4.86484i		−	0.171144i
$809$	−12.6311	−	12.6311i	−0.444086	−	0.444086i	0.449297	−	0.893383i	$-0.351675\pi$
$809$	−12.6311	−	12.6311i	−0.444086	−	0.444086i	−0.893383	+	0.449297i	$0.851675\pi$
$810$	−19.8515	−	19.8515i	−0.697511	−	0.697511i
$811$	−1.76631	+	1.76631i	−0.0620236	+	0.0620236i	−0.737438	−	0.675415i	$-0.763965\pi$
$811$	−1.76631	+	1.76631i	−0.0620236	+	0.0620236i	0.675415	+	0.737438i	$0.263965\pi$
$812$	9.84018			0.345323
$813$	10.7797	−	10.7797i	0.378062	−	0.378062i
$814$		−	1.62267i		−	0.0568747i
$815$	2.22070			0.0777876
$816$		0			0
$817$	−3.24123			−0.113396
$818$			28.8357i			1.00822i
$819$	2.03961	−	2.03961i	0.0712696	−	0.0712696i
$820$	−3.12567			−0.109153
$821$	−18.1817	+	18.1817i	−0.634545	+	0.634545i	−0.949204	−	0.314660i	$-0.898110\pi$
$821$	−18.1817	+	18.1817i	−0.634545	+	0.634545i	0.314660	+	0.949204i	$0.398110\pi$
$822$	18.5573	+	18.5573i	0.647259	+	0.647259i
$823$	−9.42601	−	9.42601i	−0.328570	−	0.328570i	0.523473	−	0.852042i	$-0.324636\pi$
$823$	−9.42601	−	9.42601i	−0.328570	−	0.328570i	−0.852042	+	0.523473i	$0.824636\pi$
$824$			12.3969i			0.431867i
$825$		−	39.5868i		−	1.37823i
$826$	−5.08042	−	5.08042i	−0.176770	−	0.176770i
$827$	−7.98004	−	7.98004i	−0.277493	−	0.277493i	0.554614	−	0.832108i	$-0.312866\pi$
$827$	−7.98004	−	7.98004i	−0.277493	−	0.277493i	−0.832108	+	0.554614i	$0.812866\pi$
$828$	2.15641	−	2.15641i	0.0749406	−	0.0749406i
$829$	25.9786			0.902276			0.451138	−	0.892454i	$-0.351018\pi$
$829$	25.9786			0.902276			0.451138	+	0.892454i	$0.351018\pi$
$830$	6.48368	−	6.48368i	0.225052	−	0.225052i
$831$			58.8147i			2.04026i
$832$	0.347296			0.0120403
$833$		0			0
$834$	49.6340			1.71869
$835$			10.4938i			0.363154i
$836$	−0.837775	+	0.837775i	−0.0289750	+	0.0289750i
$837$	−124.080			−4.28882
$838$	21.6941	−	21.6941i	0.749409	−	0.749409i
$839$	−14.8306	−	14.8306i	−0.512008	−	0.512008i	0.403133	−	0.915141i	$-0.367921\pi$
$839$	−14.8306	−	14.8306i	−0.512008	−	0.512008i	−0.915141	+	0.403133i	$0.867921\pi$
$840$	3.02928	+	3.02928i	0.104520	+	0.104520i
$841$		−	48.1070i		−	1.65886i
$842$		−	6.20708i		−	0.213910i
$843$	−57.9011	−	57.9011i	−1.99422	−	1.99422i
$844$	7.03663	+	7.03663i	0.242211	+	0.242211i
$845$	10.7900	−	10.7900i	0.371188	−	0.371188i
$846$	−58.2900			−2.00405
$847$	0.505671	−	0.505671i	0.0173751	−	0.0173751i
$848$			8.41921i			0.289117i
$849$	42.0907			1.44455
$850$		0			0
$851$	0.195718			0.00670914
$852$			24.5107i			0.839724i
$853$	36.0377	−	36.0377i	1.23391	−	1.23391i	0.271458	−	0.962450i	$-0.412494\pi$
$853$	36.0377	−	36.0377i	1.23391	−	1.23391i	0.962450	−	0.271458i	$-0.0875057\pi$
$854$	−6.39012			−0.218665
$855$	−2.15641	+	2.15641i	−0.0737478	+	0.0737478i
$856$	6.26291	+	6.26291i	0.214062	+	0.214062i
$857$	−27.5814	−	27.5814i	−0.942163	−	0.942163i	0.0562539	−	0.998416i	$-0.482084\pi$
$857$	−27.5814	−	27.5814i	−0.942163	−	0.942163i	−0.998416	+	0.0562539i	$0.982084\pi$
$858$		−	3.82295i		−	0.130513i
$859$			12.6742i			0.432437i	0.976345	+	0.216219i	$0.0693724\pi$
$859$			12.6742i			0.432437i	−0.976345	+	0.216219i	$0.930628\pi$
$860$	7.81874	+	7.81874i	0.266617	+	0.266617i
$861$	6.74525	+	6.74525i	0.229877	+	0.229877i
$862$	6.17405	−	6.17405i	0.210289	−	0.210289i
$863$	−31.9905			−1.08897			−0.544485	−	0.838771i	$-0.683275\pi$
$863$	−31.9905			−1.08897			−0.544485	+	0.838771i	$0.683275\pi$
$864$	−10.0653	+	10.0653i	−0.342427	+	0.342427i
$865$		−	7.59627i		−	0.258281i
$866$	−20.9855			−0.713115
$867$		0			0
$868$	9.76827			0.331557
$869$		−	45.2918i		−	1.53642i
$870$	23.7372	−	23.7372i	0.804768	−	0.804768i
$871$	−2.53983			−0.0860588
$872$	8.39518	−	8.39518i	0.284297	−	0.284297i
$873$	1.16149	+	1.16149i	0.0393106	+	0.0393106i
$874$	−0.101048	−	0.101048i	−0.00341800	−	0.00341800i
$875$			11.4132i			0.385838i
$876$		−	29.1753i		−	0.985742i
$877$	20.2383	+	20.2383i	0.683398	+	0.683398i	0.960764	−	0.277366i	$-0.0894615\pi$
$877$	20.2383	+	20.2383i	0.683398	+	0.683398i	−0.277366	+	0.960764i	$0.589462\pi$
$878$	5.98648	+	5.98648i	0.202034	+	0.202034i
$879$	−8.68314	+	8.68314i	−0.292875	+	0.292875i
$880$	4.04189			0.136252
$881$	−12.9113	+	12.9113i	−0.434994	+	0.434994i	−0.890323	−	0.455329i	$-0.849522\pi$
$881$	−12.9113	+	12.9113i	−0.434994	+	0.434994i	0.455329	+	0.890323i	$0.349522\pi$
$882$			42.5732i			1.43351i
$883$	−18.4688			−0.621526			−0.310763	−	0.950487i	$-0.600585\pi$
$883$	−18.4688			−0.621526			−0.310763	+	0.950487i	$0.600585\pi$
$884$		0			0
$885$	−24.5107			−0.823919
$886$		−	23.9564i		−	0.804830i
$887$	30.7491	−	30.7491i	1.03245	−	1.03245i	0.0329974	−	0.999455i	$-0.489495\pi$
$887$	30.7491	−	30.7491i	1.03245	−	1.03245i	0.999455	−	0.0329974i	$-0.0105053\pi$
$888$	−1.53478			−0.0515038
$889$	5.19152	−	5.19152i	0.174118	−	0.174118i
$890$	−6.01924	−	6.01924i	−0.201765	−	0.201765i
$891$	57.1602	+	57.1602i	1.91494	+	1.91494i
$892$		−	19.7638i		−	0.661742i
$893$			2.73143i			0.0914038i
$894$	−36.7539	−	36.7539i	−1.22923	−	1.22923i
$895$	−1.05629	−	1.05629i	−0.0353079	−	0.0353079i
$896$	0.792394	−	0.792394i	0.0264720	−	0.0264720i
$897$	0.461104			0.0153958
$898$	−4.33150	+	4.33150i	−0.144544	+	0.144544i
$899$		−	76.5435i		−	2.55287i
$900$	−26.6536			−0.888455
$901$		0			0
$902$	9.00000			0.299667
$903$		−	33.7460i		−	1.12300i
$904$	7.68260	−	7.68260i	0.255519	−	0.255519i
$905$	−18.1521			−0.603395
$906$	−6.16567	+	6.16567i	−0.204841	+	0.204841i
$907$	−18.6671	−	18.6671i	−0.619831	−	0.619831i	0.325657	−	0.945488i	$-0.394415\pi$
$907$	−18.6671	−	18.6671i	−0.619831	−	0.619831i	−0.945488	+	0.325657i	$0.894415\pi$
$908$	−2.51332	−	2.51332i	−0.0834076	−	0.0834076i
$909$			36.0556i			1.19589i
$910$			0.461104i			0.0152854i
$911$	1.88188	+	1.88188i	0.0623494	+	0.0623494i	0.737594	−	0.675245i	$-0.235962\pi$
$911$	1.88188	+	1.88188i	0.0623494	+	0.0623494i	−0.675245	+	0.737594i	$0.735962\pi$
$912$	0.792394	+	0.792394i	0.0262388	+	0.0262388i
$913$	−18.6690	+	18.6690i	−0.617854	+	0.617854i
$914$	1.01691			0.0336365
$915$	−15.4147	+	15.4147i	−0.509595	+	0.509595i
$916$		−	2.04189i		−	0.0674659i
$917$	0.0556159			0.00183660
$918$		0			0
$919$	15.1088			0.498392			0.249196	−	0.968453i	$-0.419834\pi$
$919$	15.1088			0.498392			0.249196	+	0.968453i	$0.419834\pi$
$920$			0.487511i			0.0160728i
$921$	29.9050	−	29.9050i	0.985405	−	0.985405i
$922$	−23.0838			−0.760224
$923$	−1.86546	+	1.86546i	−0.0614023	+	0.0614023i
$924$	−8.72247	−	8.72247i	−0.286948	−	0.286948i
$925$	−1.20956	−	1.20956i	−0.0397700	−	0.0397700i
$926$			19.3628i			0.636300i
$927$		−	91.8795i		−	3.01772i
$928$	−6.20915	−	6.20915i	−0.203825	−	0.203825i
$929$	3.49373	+	3.49373i	0.114625	+	0.114625i	0.762093	−	0.647468i	$-0.224172\pi$
$929$	3.49373	+	3.49373i	0.114625	+	0.114625i	−0.647468	+	0.762093i	$0.724172\pi$
$930$	23.5638	−	23.5638i	0.772686	−	0.772686i
$931$	1.99495			0.0653818
$932$	−2.76919	+	2.76919i	−0.0907077	+	0.0907077i
$933$			33.3242i			1.09098i
$934$	10.6895			0.349772
$935$		0			0
$936$	−2.57398			−0.0841331
$937$			3.41416i			0.111536i	0.998444	+	0.0557679i	$0.0177607\pi$
$937$			3.41416i			0.111536i	−0.998444	+	0.0557679i	$0.982239\pi$
$938$	−5.79490	+	5.79490i	−0.189210	+	0.189210i
$939$	70.0765			2.28686
$940$	6.58896	−	6.58896i	0.214908	−	0.214908i
$941$	−19.9834	−	19.9834i	−0.651441	−	0.651441i	0.301899	−	0.953340i	$-0.402379\pi$
$941$	−19.9834	−	19.9834i	−0.651441	−	0.651441i	−0.953340	+	0.301899i	$0.902379\pi$
$942$	−53.7534	−	53.7534i	−1.75138	−	1.75138i
$943$			1.08553i			0.0353498i
$944$			6.41147i			0.208676i
$945$	−13.3636	−	13.3636i	−0.434718	−	0.434718i
$946$	−22.5132	−	22.5132i	−0.731966	−	0.731966i
$947$	4.30211	−	4.30211i	0.139800	−	0.139800i	−0.633743	−	0.773543i	$-0.718483\pi$
$947$	4.30211	−	4.30211i	0.139800	−	0.139800i	0.773543	+	0.633743i	$0.218483\pi$
$948$	−42.8384			−1.39133
$949$	2.22047	−	2.22047i	0.0720794	−	0.0720794i
$950$			1.24897i			0.0405219i
$951$	36.0841			1.17011
$952$		0			0
$953$	26.7110			0.865254			0.432627	−	0.901573i	$-0.357587\pi$
$953$	26.7110			0.865254			0.432627	+	0.901573i	$0.357587\pi$
$954$		−	62.3988i		−	2.02024i
$955$	8.67942	−	8.67942i	0.280860	−	0.280860i
$956$	21.5544			0.697118
$957$	−68.3487	+	68.3487i	−2.20940	+	2.20940i
$958$	−13.4460	−	13.4460i	−0.434420	−	0.434420i
$959$	6.44487	+	6.44487i	0.208116	+	0.208116i
$960$		−	3.82295i		−	0.123385i
$961$		−	44.9840i		−	1.45110i
$962$	−0.116809	−	0.116809i	−0.00376606	−	0.00376606i
$963$	−46.4174	−	46.4174i	−1.49578	−	1.49578i
$964$	17.8138	−	17.8138i	0.573744	−	0.573744i
$965$	−18.0729			−0.581786
$966$	1.05206	−	1.05206i	0.0338494	−	0.0338494i
$967$		−	27.1070i		−	0.871702i	−0.900019	−	0.435851i	$-0.856447\pi$
$967$		−	27.1070i		−	0.871702i	0.900019	−	0.435851i	$-0.143553\pi$
$968$	−0.638156			−0.0205111
$969$		0			0
$970$	−0.262585			−0.00843108
$971$			50.0725i			1.60690i	0.595370	+	0.803452i	$0.297006\pi$
$971$			50.0725i			1.60690i	−0.595370	+	0.803452i	$0.702994\pi$
$972$	23.8681	−	23.8681i	0.765571	−	0.765571i
$973$	17.2377			0.552616
$974$	−2.21398	+	2.21398i	−0.0709406	+	0.0709406i
$975$	−2.84966	−	2.84966i	−0.0912622	−	0.0912622i
$976$	4.03216	+	4.03216i	0.129066	+	0.129066i
$977$		−	2.25309i		−	0.0720827i	−0.999350	−	0.0360414i	$-0.988525\pi$
$977$		−	2.25309i		−	0.0720827i	0.999350	−	0.0360414i	$-0.0114748\pi$
$978$			6.04788i			0.193390i
$979$	17.3317	+	17.3317i	0.553924	+	0.553924i
$980$	−4.81237	−	4.81237i	−0.153725	−	0.153725i
$981$	−62.2207	+	62.2207i	−1.98655	+	1.98655i
$982$	33.3851			1.06536
$983$	24.5399	−	24.5399i	0.782702	−	0.782702i	−0.197584	−	0.980286i	$-0.563309\pi$
$983$	24.5399	−	24.5399i	0.782702	−	0.782702i	0.980286	+	0.197584i	$0.0633095\pi$
$984$		−	8.51249i		−	0.271368i
$985$	25.1676			0.801905
$986$		0			0
$987$	−28.4382			−0.905198
$988$			0.120615i			0.00383727i
$989$	2.71542	−	2.71542i	0.0863453	−	0.0863453i
$990$	−29.9564			−0.952075
$991$	10.8328	−	10.8328i	0.344117	−	0.344117i	−0.513796	−	0.857912i	$-0.671761\pi$
$991$	10.8328	−	10.8328i	0.344117	−	0.344117i	0.857912	+	0.513796i	$0.171761\pi$
$992$	−6.16377	−	6.16377i	−0.195700	−	0.195700i
$993$	−41.2622	−	41.2622i	−1.30942	−	1.30942i
$994$			8.51249i			0.270000i
$995$		−	15.5016i		−	0.491433i
$996$	17.6578	+	17.6578i	0.559507	+	0.559507i
$997$	−37.1992	−	37.1992i	−1.17811	−	1.17811i	−0.980225	−	0.197886i	$-0.936592\pi$
$997$	−37.1992	−	37.1992i	−1.17811	−	1.17811i	−0.197886	−	0.980225i	$-0.563408\pi$
$998$	−2.77947	+	2.77947i	−0.0879827	+	0.0879827i
$999$	6.77063			0.214213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.c.g.327.6		12
17.2	even	8		578.2.b.f.577.1		6
17.3	odd	16		578.2.d.h.155.6		24
17.4	even	4	inner	578.2.c.g.251.1		12
17.5	odd	16		578.2.d.h.423.6		24
17.6	odd	16		578.2.d.h.399.6		24
17.7	odd	16		578.2.d.h.179.1		24
17.8	even	8		578.2.a.e.1.1	✓	3
17.9	even	8		578.2.a.f.1.3	yes	3
17.10	odd	16		578.2.d.h.179.6		24
17.11	odd	16		578.2.d.h.399.1		24
17.12	odd	16		578.2.d.h.423.1		24
17.13	even	4	inner	578.2.c.g.251.6		12
17.14	odd	16		578.2.d.h.155.1		24
17.15	even	8		578.2.b.f.577.6		6
17.16	even	2	inner	578.2.c.g.327.1		12
51.8	odd	8		5202.2.a.bn.1.2		3
51.26	odd	8		5202.2.a.bo.1.2		3
68.43	odd	8		4624.2.a.ba.1.1		3
68.59	odd	8		4624.2.a.bj.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
578.2.a.e.1.1	✓	3	17.8	even	8
578.2.a.f.1.3	yes	3	17.9	even	8
578.2.b.f.577.1		6	17.2	even	8
578.2.b.f.577.6		6	17.15	even	8
578.2.c.g.251.1		12	17.4	even	4	inner
578.2.c.g.251.6		12	17.13	even	4	inner
578.2.c.g.327.1		12	17.16	even	2	inner
578.2.c.g.327.6		12	1.1	even	1	trivial
578.2.d.h.155.1		24	17.14	odd	16
578.2.d.h.155.6		24	17.3	odd	16
578.2.d.h.179.1		24	17.7	odd	16
578.2.d.h.179.6		24	17.10	odd	16
578.2.d.h.399.1		24	17.11	odd	16
578.2.d.h.399.6		24	17.6	odd	16
578.2.d.h.423.1		24	17.12	odd	16
578.2.d.h.423.6		24	17.5	odd	16
4624.2.a.ba.1.1		3	68.43	odd	8
4624.2.a.bj.1.3		3	68.59	odd	8
5202.2.a.bn.1.2		3	51.8	odd	8
5202.2.a.bo.1.2		3	51.26	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.c (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(2.28161 - 2.28161i) q^{3} -1.00000 q^{4} +(-0.837775 + 0.837775i) q^{5} +(-2.28161 - 2.28161i) q^{6} +(-0.792394 - 0.792394i) q^{7} +1.00000i q^{8} -7.41147i q^{9} +(0.837775 + 0.837775i) q^{10} +(-2.41228 - 2.41228i) q^{11} +(-2.28161 + 2.28161i) q^{12} -0.347296 q^{13} +(-0.792394 + 0.792394i) q^{14} +3.82295i q^{15} +1.00000 q^{16} -7.41147 q^{18} +0.347296i q^{19} +(0.837775 - 0.837775i) q^{20} -3.61587 q^{21} +(-2.41228 + 2.41228i) q^{22} +(-0.290956 - 0.290956i) q^{23} +(2.28161 + 2.28161i) q^{24} +3.59627i q^{25} +0.347296i q^{26} +(-10.0653 - 10.0653i) q^{27} +(0.792394 + 0.792394i) q^{28} +(6.20915 - 6.20915i) q^{29} +3.82295 q^{30} +(6.16377 - 6.16377i) q^{31} -1.00000i q^{32} -11.0077 q^{33} +1.32770 q^{35} +7.41147i q^{36} +(-0.336337 + 0.336337i) q^{37} +0.347296 q^{38} +(-0.792394 + 0.792394i) q^{39} +(-0.837775 - 0.837775i) q^{40} +(-1.86546 - 1.86546i) q^{41} +3.61587i q^{42} +9.33275i q^{43} +(2.41228 + 2.41228i) q^{44} +(6.20915 + 6.20915i) q^{45} +(-0.290956 + 0.290956i) q^{46} +7.86484 q^{47} +(2.28161 - 2.28161i) q^{48} -5.74422i q^{49} +3.59627 q^{50} +0.347296 q^{52} +8.41921i q^{53} +(-10.0653 + 10.0653i) q^{54} +4.04189 q^{55} +(0.792394 - 0.792394i) q^{56} +(0.792394 + 0.792394i) q^{57} +(-6.20915 - 6.20915i) q^{58} +6.41147i q^{59} -3.82295i q^{60} +(4.03216 + 4.03216i) q^{61} +(-6.16377 - 6.16377i) q^{62} +(-5.87281 + 5.87281i) q^{63} -1.00000 q^{64} +(0.290956 - 0.290956i) q^{65} +11.0077i q^{66} +7.31315 q^{67} -1.32770 q^{69} -1.32770i q^{70} +(5.37137 - 5.37137i) q^{71} +7.41147 q^{72} +(-6.39358 + 6.39358i) q^{73} +(0.336337 + 0.336337i) q^{74} +(8.20527 + 8.20527i) q^{75} -0.347296i q^{76} +3.82295i q^{77} +(0.792394 + 0.792394i) q^{78} +(9.38777 + 9.38777i) q^{79} +(-0.837775 + 0.837775i) q^{80} -23.6955 q^{81} +(-1.86546 + 1.86546i) q^{82} -7.73917i q^{83} +3.61587 q^{84} +9.33275 q^{86} -28.3337i q^{87} +(2.41228 - 2.41228i) q^{88} -7.18479 q^{89} +(6.20915 - 6.20915i) q^{90} +(0.275196 + 0.275196i) q^{91} +(0.290956 + 0.290956i) q^{92} -28.1266i q^{93} -7.86484i q^{94} +(-0.290956 - 0.290956i) q^{95} +(-2.28161 - 2.28161i) q^{96} +(-0.156715 + 0.156715i) q^{97} -5.74422 q^{98} +(-17.8785 + 17.8785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 12 q^{16} - 48 q^{18} - 36 q^{30} - 36 q^{33} - 12 q^{50} + 36 q^{55} - 12 q^{64} + 48 q^{72} - 12 q^{81} + 36 q^{86} - 72 q^{89} + 48 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 + 12 * q^16 - 48 * q^18 - 36 * q^30 - 36 * q^33 - 12 * q^50 + 36 * q^55 - 12 * q^64 + 48 * q^72 - 12 * q^81 + 36 * q^86 - 72 * q^89 + 48 * q^98

Introduction

L-functions

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