LMFDB - Embedded newform 289.2.c.c.38.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,2,Mod(38,289)] 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("289.38"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.c (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.4
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.38
Dual form			289.2.c.c.251.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.41421i q^{2} +(0.765367 - 0.765367i) q^{3} -3.82843 q^{4} +(0.541196 - 0.541196i) q^{5} +(1.84776 + 1.84776i) q^{6} +(1.84776 + 1.84776i) q^{7} -4.41421i q^{8} +1.82843i q^{9} +(1.30656 + 1.30656i) q^{10} +(1.84776 + 1.84776i) q^{11} +(-2.93015 + 2.93015i) q^{12} -1.41421 q^{13} +(-4.46088 + 4.46088i) q^{14} -0.828427i q^{15} +3.00000 q^{16} -4.41421 q^{18} -0.828427i q^{19} +(-2.07193 + 2.07193i) q^{20} +2.82843 q^{21} +(-4.46088 + 4.46088i) q^{22} +(-3.37849 - 3.37849i) q^{23} +(-3.37849 - 3.37849i) q^{24} +4.41421i q^{25} -3.41421i q^{26} +(3.69552 + 3.69552i) q^{27} +(-7.07401 - 7.07401i) q^{28} +(-0.224171 + 0.224171i) q^{29} +2.00000 q^{30} +(5.54328 - 5.54328i) q^{31} -1.58579i q^{32} +2.82843 q^{33} +2.00000 q^{35} -7.00000i q^{36} +(6.53281 - 6.53281i) q^{37} +2.00000 q^{38} +(-1.08239 + 1.08239i) q^{39} +(-2.38896 - 2.38896i) q^{40} +(-0.858221 - 0.858221i) q^{41} +6.82843i q^{42} -0.828427i q^{43} +(-7.07401 - 7.07401i) q^{44} +(0.989538 + 0.989538i) q^{45} +(8.15640 - 8.15640i) q^{46} -5.17157 q^{47} +(2.29610 - 2.29610i) q^{48} -0.171573i q^{49} -10.6569 q^{50} +5.41421 q^{52} +1.41421i q^{53} +(-8.92177 + 8.92177i) q^{54} +2.00000 q^{55} +(8.15640 - 8.15640i) q^{56} +(-0.634051 - 0.634051i) q^{57} +(-0.541196 - 0.541196i) q^{58} -6.00000i q^{59} +3.17157i q^{60} +(-2.70598 - 2.70598i) q^{61} +(13.3827 + 13.3827i) q^{62} +(-3.37849 + 3.37849i) q^{63} +9.82843 q^{64} +(-0.765367 + 0.765367i) q^{65} +6.82843i q^{66} -1.17157 q^{67} -5.17157 q^{69} +4.82843i q^{70} +(-3.82683 + 3.82683i) q^{71} +8.07107 q^{72} +(9.14594 - 9.14594i) q^{73} +(15.7716 + 15.7716i) q^{74} +(3.37849 + 3.37849i) q^{75} +3.17157i q^{76} +6.82843i q^{77} +(-2.61313 - 2.61313i) q^{78} +(-3.37849 - 3.37849i) q^{79} +(1.62359 - 1.62359i) q^{80} +0.171573 q^{81} +(2.07193 - 2.07193i) q^{82} +11.6569i q^{83} -10.8284 q^{84} +2.00000 q^{86} +0.343146i q^{87} +(8.15640 - 8.15640i) q^{88} -6.58579 q^{89} +(-2.38896 + 2.38896i) q^{90} +(-2.61313 - 2.61313i) q^{91} +(12.9343 + 12.9343i) q^{92} -8.48528i q^{93} -12.4853i q^{94} +(-0.448342 - 0.448342i) q^{95} +(-1.21371 - 1.21371i) q^{96} +(7.29818 - 7.29818i) q^{97} +0.414214 q^{98} +(-3.37849 + 3.37849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 24 q^{16} - 24 q^{18} + 16 q^{30} + 16 q^{35} + 16 q^{38} - 64 q^{47} - 40 q^{50} + 32 q^{52} + 16 q^{55} + 56 q^{64} - 32 q^{67} - 64 q^{69} + 8 q^{72} + 24 q^{81} - 64 q^{84} + 16 q^{86}+ \cdots - 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 + 24 * q^16 - 24 * q^18 + 16 * q^30 + 16 * q^35 + 16 * q^38 - 64 * q^47 - 40 * q^50 + 32 * q^52 + 16 * q^55 + 56 * q^64 - 32 * q^67 - 64 * q^69 + 8 * q^72 + 24 * q^81 - 64 * q^84 + 16 * q^86 - 64 * q^89 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

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

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 $

$2$			2.41421i			1.70711i	0.521005	+	0.853553i	$0.325557\pi$
$2$			2.41421i			1.70711i	−0.521005	+	0.853553i	$0.674443\pi$
$3$	0.765367	−	0.765367i	0.441885	−	0.441885i	−0.450760	−	0.892645i	$-0.648847\pi$
$3$	0.765367	−	0.765367i	0.441885	−	0.441885i	0.892645	+	0.450760i	$0.148847\pi$
$4$	−3.82843			−1.91421
$5$	0.541196	−	0.541196i	0.242030	−	0.242030i	−0.575659	−	0.817690i	$-0.695255\pi$
$5$	0.541196	−	0.541196i	0.242030	−	0.242030i	0.817690	+	0.575659i	$0.195255\pi$
$6$	1.84776	+	1.84776i	0.754344	+	0.754344i
$7$	1.84776	+	1.84776i	0.698387	+	0.698387i	0.964063	−	0.265675i	$-0.0855949\pi$
$7$	1.84776	+	1.84776i	0.698387	+	0.698387i	−0.265675	+	0.964063i	$0.585595\pi$
$8$		−	4.41421i		−	1.56066i
$9$			1.82843i			0.609476i
$10$	1.30656	+	1.30656i	0.413171	+	0.413171i
$11$	1.84776	+	1.84776i	0.557120	+	0.557120i	0.928486	−	0.371366i	$-0.121111\pi$
$11$	1.84776	+	1.84776i	0.557120	+	0.557120i	−0.371366	+	0.928486i	$0.621111\pi$
$12$	−2.93015	+	2.93015i	−0.845862	+	0.845862i
$13$	−1.41421			−0.392232			−0.196116	−	0.980581i	$-0.562833\pi$
$13$	−1.41421			−0.392232			−0.196116	+	0.980581i	$0.562833\pi$
$14$	−4.46088	+	4.46088i	−1.19222	+	1.19222i
$15$		−	0.828427i		−	0.213899i
$16$	3.00000			0.750000
$17$		0			0
$17$		0			0
$18$	−4.41421			−1.04044
$19$		−	0.828427i		−	0.190054i	−0.995475	−	0.0950271i	$-0.969706\pi$
$19$		−	0.828427i		−	0.190054i	0.995475	−	0.0950271i	$-0.0302938\pi$
$20$	−2.07193	+	2.07193i	−0.463298	+	0.463298i
$21$	2.82843			0.617213
$22$	−4.46088	+	4.46088i	−0.951064	+	0.951064i
$23$	−3.37849	−	3.37849i	−0.704464	−	0.704464i	0.260901	−	0.965366i	$-0.415980\pi$
$23$	−3.37849	−	3.37849i	−0.704464	−	0.704464i	−0.965366	+	0.260901i	$0.915980\pi$
$24$	−3.37849	−	3.37849i	−0.689632	−	0.689632i
$25$			4.41421i			0.882843i
$26$		−	3.41421i		−	0.669582i
$27$	3.69552	+	3.69552i	0.711203	+	0.711203i
$28$	−7.07401	−	7.07401i	−1.33686	−	1.33686i
$29$	−0.224171	+	0.224171i	−0.0416275	+	0.0416275i	−0.727614	−	0.685987i	$-0.759371\pi$
$29$	−0.224171	+	0.224171i	−0.0416275	+	0.0416275i	0.685987	+	0.727614i	$0.259371\pi$
$30$	2.00000			0.365148
$31$	5.54328	−	5.54328i	0.995602	−	0.995602i	−0.00438840	−	0.999990i	$-0.501397\pi$
$31$	5.54328	−	5.54328i	0.995602	−	0.995602i	0.999990	+	0.00438840i	$0.00139687\pi$
$32$		−	1.58579i		−	0.280330i
$33$	2.82843			0.492366
$34$		0			0
$35$	2.00000			0.338062
$36$		−	7.00000i		−	1.16667i
$37$	6.53281	−	6.53281i	1.07399	−	1.07399i	0.0769535	−	0.997035i	$-0.475481\pi$
$37$	6.53281	−	6.53281i	1.07399	−	1.07399i	0.997035	−	0.0769535i	$-0.0245193\pi$
$38$	2.00000			0.324443
$39$	−1.08239	+	1.08239i	−0.173321	+	0.173321i
$40$	−2.38896	−	2.38896i	−0.377727	−	0.377727i
$41$	−0.858221	−	0.858221i	−0.134032	−	0.134032i	0.636908	−	0.770940i	$-0.280213\pi$
$41$	−0.858221	−	0.858221i	−0.134032	−	0.134032i	−0.770940	+	0.636908i	$0.780213\pi$
$42$			6.82843i			1.05365i
$43$		−	0.828427i		−	0.126334i	−0.998003	−	0.0631670i	$-0.979880\pi$
$43$		−	0.828427i		−	0.126334i	0.998003	−	0.0631670i	$-0.0201201\pi$
$44$	−7.07401	−	7.07401i	−1.06645	−	1.06645i
$45$	0.989538	+	0.989538i	0.147512	+	0.147512i
$46$	8.15640	−	8.15640i	1.20260	−	1.20260i
$47$	−5.17157			−0.754351			−0.377176	−	0.926142i	$-0.623105\pi$
$47$	−5.17157			−0.754351			−0.377176	+	0.926142i	$0.623105\pi$
$48$	2.29610	−	2.29610i	0.331414	−	0.331414i
$49$		−	0.171573i		−	0.0245104i
$50$	−10.6569			−1.50711
$51$		0			0
$52$	5.41421			0.750816
$53$			1.41421i			0.194257i	0.995272	+	0.0971286i	$0.0309658\pi$
$53$			1.41421i			0.194257i	−0.995272	+	0.0971286i	$0.969034\pi$
$54$	−8.92177	+	8.92177i	−1.21410	+	1.21410i
$55$	2.00000			0.269680
$56$	8.15640	−	8.15640i	1.08995	−	1.08995i
$57$	−0.634051	−	0.634051i	−0.0839821	−	0.0839821i
$58$	−0.541196	−	0.541196i	−0.0710625	−	0.0710625i
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$			3.17157i			0.409448i
$61$	−2.70598	−	2.70598i	−0.346465	−	0.346465i	0.512326	−	0.858791i	$-0.328784\pi$
$61$	−2.70598	−	2.70598i	−0.346465	−	0.346465i	−0.858791	+	0.512326i	$0.828784\pi$
$62$	13.3827	+	13.3827i	1.69960	+	1.69960i
$63$	−3.37849	+	3.37849i	−0.425650	+	0.425650i
$64$	9.82843			1.22855
$65$	−0.765367	+	0.765367i	−0.0949321	+	0.0949321i
$66$			6.82843i			0.840521i
$67$	−1.17157			−0.143130			−0.0715652	−	0.997436i	$-0.522799\pi$
$67$	−1.17157			−0.143130			−0.0715652	+	0.997436i	$0.522799\pi$
$68$		0			0
$69$	−5.17157			−0.622584
$70$			4.82843i			0.577107i
$71$	−3.82683	+	3.82683i	−0.454162	+	0.454162i	−0.896733	−	0.442572i	$-0.854066\pi$
$71$	−3.82683	+	3.82683i	−0.454162	+	0.454162i	0.442572	+	0.896733i	$0.354066\pi$
$72$	8.07107			0.951184
$73$	9.14594	−	9.14594i	1.07045	−	1.07045i	0.0731289	−	0.997322i	$-0.476702\pi$
$73$	9.14594	−	9.14594i	1.07045	−	1.07045i	0.997322	−	0.0731289i	$-0.0232984\pi$
$74$	15.7716	+	15.7716i	1.83341	+	1.83341i
$75$	3.37849	+	3.37849i	0.390115	+	0.390115i
$76$			3.17157i			0.363804i
$77$			6.82843i			0.778171i
$78$	−2.61313	−	2.61313i	−0.295878	−	0.295878i
$79$	−3.37849	−	3.37849i	−0.380110	−	0.380110i	0.491032	−	0.871142i	$-0.336620\pi$
$79$	−3.37849	−	3.37849i	−0.380110	−	0.380110i	−0.871142	+	0.491032i	$0.836620\pi$
$80$	1.62359	−	1.62359i	0.181523	−	0.181523i
$81$	0.171573			0.0190637
$82$	2.07193	−	2.07193i	0.228806	−	0.228806i
$83$			11.6569i			1.27951i	0.768581	+	0.639753i	$0.220963\pi$
$83$			11.6569i			1.27951i	−0.768581	+	0.639753i	$0.779037\pi$
$84$	−10.8284			−1.18148
$85$		0			0
$86$	2.00000			0.215666
$87$			0.343146i			0.0367891i
$88$	8.15640	−	8.15640i	0.869475	−	0.869475i
$89$	−6.58579			−0.698092			−0.349046	−	0.937106i	$-0.613494\pi$
$89$	−6.58579			−0.698092			−0.349046	+	0.937106i	$0.613494\pi$
$90$	−2.38896	+	2.38896i	−0.251818	+	0.251818i
$91$	−2.61313	−	2.61313i	−0.273930	−	0.273930i
$92$	12.9343	+	12.9343i	1.34850	+	1.34850i
$93$		−	8.48528i		−	0.879883i
$94$		−	12.4853i		−	1.28776i
$95$	−0.448342	−	0.448342i	−0.0459989	−	0.0459989i
$96$	−1.21371	−	1.21371i	−0.123874	−	0.123874i
$97$	7.29818	−	7.29818i	0.741018	−	0.741018i	−0.231756	−	0.972774i	$-0.574447\pi$
$97$	7.29818	−	7.29818i	0.741018	−	0.741018i	0.972774	+	0.231756i	$0.0744471\pi$
$98$	0.414214			0.0418419
$99$	−3.37849	+	3.37849i	−0.339551	+	0.339551i
$100$		−	16.8995i		−	1.68995i
$101$	10.5858			1.05333			0.526663	−	0.850074i	$-0.323443\pi$
$101$	10.5858			1.05333			0.526663	+	0.850074i	$0.323443\pi$
$102$		0			0
$103$	12.4853			1.23021			0.615106	−	0.788445i	$-0.289113\pi$
$103$	12.4853			1.23021			0.615106	+	0.788445i	$0.289113\pi$
$104$			6.24264i			0.612141i
$105$	1.53073	−	1.53073i	0.149384	−	0.149384i
$106$	−3.41421			−0.331618
$107$	−0.317025	+	0.317025i	−0.0306480	+	0.0306480i	−0.722265	−	0.691617i	$-0.756899\pi$
$107$	−0.317025	+	0.317025i	−0.0306480	+	0.0306480i	0.691617	+	0.722265i	$0.256899\pi$
$108$	−14.1480	−	14.1480i	−1.36139	−	1.36139i
$109$	−10.9937	−	10.9937i	−1.05301	−	1.05301i	−0.998514	−	0.0544912i	$-0.982646\pi$
$109$	−10.9937	−	10.9937i	−1.05301	−	1.05301i	−0.0544912	−	0.998514i	$-0.517354\pi$
$110$			4.82843i			0.460372i
$111$		−	10.0000i		−	0.949158i
$112$	5.54328	+	5.54328i	0.523790	+	0.523790i
$113$	−9.33165	−	9.33165i	−0.877848	−	0.877848i	0.115464	−	0.993312i	$-0.463165\pi$
$113$	−9.33165	−	9.33165i	−0.877848	−	0.877848i	−0.993312	+	0.115464i	$0.963165\pi$
$114$	1.53073	−	1.53073i	0.143366	−	0.143366i
$115$	−3.65685			−0.341003
$116$	0.858221	−	0.858221i	0.0796839	−	0.0796839i
$117$		−	2.58579i		−	0.239056i
$118$	14.4853			1.33348
$119$		0			0
$120$	−3.65685			−0.333824
$121$		−	4.17157i		−	0.379234i
$122$	6.53281	−	6.53281i	0.591453	−	0.591453i
$123$	−1.31371			−0.118453
$124$	−21.2220	+	21.2220i	−1.90579	+	1.90579i
$125$	5.09494	+	5.09494i	0.455705	+	0.455705i
$126$	−8.15640	−	8.15640i	−0.726630	−	0.726630i
$127$			5.31371i			0.471515i	0.971812	+	0.235758i	$0.0757572\pi$
$127$			5.31371i			0.471515i	−0.971812	+	0.235758i	$0.924243\pi$
$128$			20.5563i			1.81694i
$129$	−0.634051	−	0.634051i	−0.0558250	−	0.0558250i
$130$	−1.84776	−	1.84776i	−0.162059	−	0.162059i
$131$	−10.7695	+	10.7695i	−0.940938	+	0.940938i	−0.998351	−	0.0574124i	$-0.981715\pi$
$131$	−10.7695	+	10.7695i	−0.940938	+	0.940938i	0.0574124	+	0.998351i	$0.481715\pi$
$132$	−10.8284			−0.942494
$133$	1.53073	−	1.53073i	0.132731	−	0.132731i
$134$		−	2.82843i		−	0.244339i
$135$	4.00000			0.344265
$136$		0			0
$137$	−16.7279			−1.42916			−0.714581	−	0.699552i	$-0.753383\pi$
$137$	−16.7279			−1.42916			−0.714581	+	0.699552i	$0.753383\pi$
$138$		−	12.4853i		−	1.06282i
$139$	−15.0991	+	15.0991i	−1.28069	+	1.28069i	−0.340413	+	0.940276i	$0.610567\pi$
$139$	−15.0991	+	15.0991i	−1.28069	+	1.28069i	−0.940276	+	0.340413i	$0.889433\pi$
$140$	−7.65685			−0.647122
$141$	−3.95815	+	3.95815i	−0.333336	+	0.333336i
$142$	−9.23880	−	9.23880i	−0.775302	−	0.775302i
$143$	−2.61313	−	2.61313i	−0.218521	−	0.218521i
$144$			5.48528i			0.457107i
$145$			0.242641i			0.0201502i
$146$	22.0803	+	22.0803i	1.82737	+	1.82737i
$147$	−0.131316	−	0.131316i	−0.0108308	−	0.0108308i
$148$	−25.0104	+	25.0104i	−2.05584	+	2.05584i
$149$	16.9706			1.39028			0.695141	−	0.718873i	$-0.255342\pi$
$149$	16.9706			1.39028			0.695141	+	0.718873i	$0.255342\pi$
$150$	−8.15640	+	8.15640i	−0.665968	+	0.665968i
$151$			7.17157i			0.583614i	0.956477	+	0.291807i	$0.0942566\pi$
$151$			7.17157i			0.583614i	−0.956477	+	0.291807i	$0.905743\pi$
$152$	−3.65685			−0.296610
$153$		0			0
$154$	−16.4853			−1.32842
$155$		−	6.00000i		−	0.481932i
$156$	4.14386	−	4.14386i	0.331774	−	0.331774i
$157$	9.65685			0.770701			0.385350	−	0.922770i	$-0.374081\pi$
$157$	9.65685			0.770701			0.385350	+	0.922770i	$0.374081\pi$
$158$	8.15640	−	8.15640i	0.648889	−	0.648889i
$159$	1.08239	+	1.08239i	0.0858393	+	0.0858393i
$160$	−0.858221	−	0.858221i	−0.0678484	−	0.0678484i
$161$		−	12.4853i		−	0.983978i
$162$			0.414214i			0.0325437i
$163$	−5.99162	−	5.99162i	−0.469300	−	0.469300i	0.432388	−	0.901688i	$-0.357671\pi$
$163$	−5.99162	−	5.99162i	−0.469300	−	0.469300i	−0.901688	+	0.432388i	$0.857671\pi$
$164$	3.28564	+	3.28564i	0.256565	+	0.256565i
$165$	1.53073	−	1.53073i	0.119167	−	0.119167i
$166$	−28.1421			−2.18425
$167$	−1.39942	+	1.39942i	−0.108290	+	0.108290i	−0.759176	−	0.650886i	$-0.774398\pi$
$167$	−1.39942	+	1.39942i	−0.108290	+	0.108290i	0.650886	+	0.759176i	$0.274398\pi$
$168$		−	12.4853i		−	0.963260i
$169$	−11.0000			−0.846154
$170$		0			0
$171$	1.51472			0.115833
$172$			3.17157i			0.241830i
$173$	2.07193	−	2.07193i	0.157526	−	0.157526i	−0.623944	−	0.781469i	$-0.714470\pi$
$173$	2.07193	−	2.07193i	0.157526	−	0.157526i	0.781469	+	0.623944i	$0.214470\pi$
$174$	−0.828427			−0.0628029
$175$	−8.15640	+	8.15640i	−0.616566	+	0.616566i
$176$	5.54328	+	5.54328i	0.417840	+	0.417840i
$177$	−4.59220	−	4.59220i	−0.345171	−	0.345171i
$178$		−	15.8995i		−	1.19172i
$179$		−	6.00000i		−	0.448461i	−0.974536	−	0.224231i	$-0.928013\pi$
$179$		−	6.00000i		−	0.448461i	0.974536	−	0.224231i	$-0.0719869\pi$
$180$	−3.78837	−	3.78837i	−0.282369	−	0.282369i
$181$	8.24926	+	8.24926i	0.613162	+	0.613162i	0.943769	−	0.330606i	$-0.107253\pi$
$181$	8.24926	+	8.24926i	0.613162	+	0.613162i	−0.330606	+	0.943769i	$0.607253\pi$
$182$	6.30864	−	6.30864i	0.467628	−	0.467628i
$183$	−4.14214			−0.306195
$184$	−14.9134	+	14.9134i	−1.09943	+	1.09943i
$185$		−	7.07107i		−	0.519875i
$186$	20.4853			1.50205
$187$		0			0
$188$	19.7990			1.44399
$189$			13.6569i			0.993390i
$190$	1.08239	−	1.08239i	0.0785250	−	0.0785250i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$	7.52235	−	7.52235i	0.542879	−	0.542879i
$193$	1.62359	+	1.62359i	0.116868	+	0.116868i	0.763122	−	0.646254i	$-0.223665\pi$
$193$	1.62359	+	1.62359i	0.116868	+	0.116868i	−0.646254	+	0.763122i	$0.723665\pi$
$194$	17.6194	+	17.6194i	1.26500	+	1.26500i
$195$			1.17157i			0.0838981i
$196$			0.656854i			0.0469182i
$197$	−3.28564	−	3.28564i	−0.234092	−	0.234092i	0.580306	−	0.814398i	$-0.302933\pi$
$197$	−3.28564	−	3.28564i	−0.234092	−	0.234092i	−0.814398	+	0.580306i	$0.802933\pi$
$198$	−8.15640	−	8.15640i	−0.579650	−	0.579650i
$199$	8.15640	−	8.15640i	0.578192	−	0.578192i	−0.356213	−	0.934405i	$-0.615932\pi$
$199$	8.15640	−	8.15640i	0.578192	−	0.578192i	0.934405	+	0.356213i	$0.115932\pi$
$200$	19.4853			1.37782
$201$	−0.896683	+	0.896683i	−0.0632471	+	0.0632471i
$202$			25.5563i			1.79814i
$203$	−0.828427			−0.0581442
$204$		0			0
$205$	−0.928932			−0.0648794
$206$			30.1421i			2.10010i
$207$	6.17733	−	6.17733i	0.429354	−	0.429354i
$208$	−4.24264			−0.294174
$209$	1.53073	−	1.53073i	0.105883	−	0.105883i
$210$	3.69552	+	3.69552i	0.255015	+	0.255015i
$211$	15.0991	+	15.0991i	1.03946	+	1.03946i	0.999189	+	0.0402762i	$0.0128238\pi$
$211$	15.0991	+	15.0991i	1.03946	+	1.03946i	0.0402762	+	0.999189i	$0.487176\pi$
$212$		−	5.41421i		−	0.371850i
$213$			5.85786i			0.401374i
$214$	−0.765367	−	0.765367i	−0.0523194	−	0.0523194i
$215$	−0.448342	−	0.448342i	−0.0305766	−	0.0305766i
$216$	16.3128	−	16.3128i	1.10995	−	1.10995i
$217$	20.4853			1.39063
$218$	26.5411	−	26.5411i	1.79759	−	1.79759i
$219$		−	14.0000i		−	0.946032i
$220$	−7.65685			−0.516225
$221$		0			0
$222$	24.1421			1.62031
$223$		−	4.82843i		−	0.323335i	−0.986845	−	0.161668i	$-0.948313\pi$
$223$		−	4.82843i		−	0.323335i	0.986845	−	0.161668i	$-0.0516873\pi$
$224$	2.93015	−	2.93015i	0.195779	−	0.195779i
$225$	−8.07107			−0.538071
$226$	22.5286	−	22.5286i	1.49858	−	1.49858i
$227$	12.3003	+	12.3003i	0.816397	+	0.816397i	0.985584	−	0.169187i	$-0.0541141\pi$
$227$	12.3003	+	12.3003i	0.816397	+	0.816397i	−0.169187	+	0.985584i	$0.554114\pi$
$228$	2.42742	+	2.42742i	0.160760	+	0.160760i
$229$			17.1716i			1.13473i	0.823467	+	0.567365i	$0.192037\pi$
$229$			17.1716i			1.13473i	−0.823467	+	0.567365i	$0.807963\pi$
$230$		−	8.82843i		−	0.582129i
$231$	5.22625	+	5.22625i	0.343862	+	0.343862i
$232$	0.989538	+	0.989538i	0.0649663	+	0.0649663i
$233$	6.21579	−	6.21579i	0.407210	−	0.407210i	−0.473555	−	0.880764i	$-0.657029\pi$
$233$	6.21579	−	6.21579i	0.407210	−	0.407210i	0.880764	+	0.473555i	$0.157029\pi$
$234$	6.24264			0.408094
$235$	−2.79884	+	2.79884i	−0.182576	+	0.182576i
$236$			22.9706i			1.49526i
$237$	−5.17157			−0.335930
$238$		0			0
$239$	14.8284			0.959171			0.479586	−	0.877495i	$-0.340787\pi$
$239$	14.8284			0.959171			0.479586	+	0.877495i	$0.340787\pi$
$240$		−	2.48528i		−	0.160424i
$241$	−2.52027	+	2.52027i	−0.162345	+	0.162345i	−0.783605	−	0.621260i	$-0.786621\pi$
$241$	−2.52027	+	2.52027i	−0.162345	+	0.162345i	0.621260	+	0.783605i	$0.286621\pi$
$242$	10.0711			0.647393
$243$	−10.9552	+	10.9552i	−0.702779	+	0.702779i
$244$	10.3596	+	10.3596i	0.663209	+	0.663209i
$245$	−0.0928546	−	0.0928546i	−0.00593226	−	0.00593226i
$246$		−	3.17157i		−	0.202212i
$247$			1.17157i			0.0745454i
$248$	−24.4692	−	24.4692i	−1.55380	−	1.55380i
$249$	8.92177	+	8.92177i	0.565394	+	0.565394i
$250$	−12.3003	+	12.3003i	−0.777937	+	0.777937i
$251$	−20.4853			−1.29302			−0.646510	−	0.762906i	$-0.723772\pi$
$251$	−20.4853			−1.29302			−0.646510	+	0.762906i	$0.723772\pi$
$252$	12.9343	−	12.9343i	0.814785	−	0.814785i
$253$		−	12.4853i		−	0.784943i
$254$	−12.8284			−0.804927
$255$		0			0
$256$	−29.9706			−1.87316
$257$			6.14214i			0.383136i	0.981479	+	0.191568i	$0.0613572\pi$
$257$			6.14214i			0.383136i	−0.981479	+	0.191568i	$0.938643\pi$
$258$	1.53073	−	1.53073i	0.0952993	−	0.0952993i
$259$	24.1421			1.50012
$260$	2.93015	−	2.93015i	0.181720	−	0.181720i
$261$	−0.409880	−	0.409880i	−0.0253709	−	0.0253709i
$262$	−25.9999	−	25.9999i	−1.60628	−	1.60628i
$263$			10.4853i			0.646550i	0.946305	+	0.323275i	$0.104784\pi$
$263$			10.4853i			0.646550i	−0.946305	+	0.323275i	$0.895216\pi$
$264$		−	12.4853i		−	0.768416i
$265$	0.765367	+	0.765367i	0.0470161	+	0.0470161i
$266$	3.69552	+	3.69552i	0.226587	+	0.226587i
$267$	−5.04054	+	5.04054i	−0.308476	+	0.308476i
$268$	4.48528			0.273982
$269$	−18.7018	+	18.7018i	−1.14027	+	1.14027i	−0.151865	+	0.988401i	$0.548528\pi$
$269$	−18.7018	+	18.7018i	−1.14027	+	1.14027i	−0.988401	+	0.151865i	$0.951472\pi$
$270$			9.65685i			0.587697i
$271$	−22.1421			−1.34504			−0.672519	−	0.740079i	$-0.734788\pi$
$271$	−22.1421			−1.34504			−0.672519	+	0.740079i	$0.734788\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$		−	40.3848i		−	2.43973i
$275$	−8.15640	+	8.15640i	−0.491850	+	0.491850i
$276$	19.7990			1.19176
$277$	14.1096	−	14.1096i	0.847761	−	0.847761i	−0.142092	−	0.989853i	$-0.545383\pi$
$277$	14.1096	−	14.1096i	0.847761	−	0.847761i	0.989853	+	0.142092i	$0.0453829\pi$
$278$	−36.4524	−	36.4524i	−2.18627	−	2.18627i
$279$	10.1355	+	10.1355i	0.606795	+	0.606795i
$280$		−	8.82843i		−	0.527599i
$281$		−	1.89949i		−	0.113314i	−0.998394	−	0.0566572i	$-0.981956\pi$
$281$		−	1.89949i		−	0.113314i	0.998394	−	0.0566572i	$-0.0180442\pi$
$282$	−9.55582	−	9.55582i	−0.569041	−	0.569041i
$283$	13.1969	+	13.1969i	0.784477	+	0.784477i	0.980583	−	0.196106i	$-0.0628296\pi$
$283$	13.1969	+	13.1969i	0.784477	+	0.784477i	−0.196106	+	0.980583i	$0.562830\pi$
$284$	14.6508	−	14.6508i	0.869362	−	0.869362i
$285$	−0.686292			−0.0406524
$286$	6.30864	−	6.30864i	0.373038	−	0.373038i
$287$		−	3.17157i		−	0.187212i
$288$	2.89949			0.170854
$289$		0			0
$290$	−0.585786			−0.0343986
$291$		−	11.1716i		−	0.654889i
$292$	−35.0146	+	35.0146i	−2.04907	+	2.04907i
$293$	12.3431			0.721094			0.360547	−	0.932741i	$-0.382590\pi$
$293$	12.3431			0.721094			0.360547	+	0.932741i	$0.382590\pi$
$294$	0.317025	−	0.317025i	0.0184893	−	0.0184893i
$295$	−3.24718	−	3.24718i	−0.189058	−	0.189058i
$296$	−28.8372	−	28.8372i	−1.67613	−	1.67613i
$297$			13.6569i			0.792451i
$298$			40.9706i			2.37336i
$299$	4.77791	+	4.77791i	0.276314	+	0.276314i
$300$	−12.9343	−	12.9343i	−0.746763	−	0.746763i
$301$	1.53073	−	1.53073i	0.0882300	−	0.0882300i
$302$	−17.3137			−0.996292
$303$	8.10201	−	8.10201i	0.465448	−	0.465448i
$304$		−	2.48528i		−	0.142541i
$305$	−2.92893			−0.167710
$306$		0			0
$307$	−26.1421			−1.49201			−0.746005	−	0.665940i	$-0.768031\pi$
$307$	−26.1421			−1.49201			−0.746005	+	0.665940i	$0.768031\pi$
$308$		−	26.1421i		−	1.48959i
$309$	9.55582	−	9.55582i	0.543612	−	0.543612i
$310$	14.4853			0.822709
$311$	−18.1606	+	18.1606i	−1.02979	+	1.02979i	−0.0302488	+	0.999542i	$0.509630\pi$
$311$	−18.1606	+	18.1606i	−1.02979	+	1.02979i	−0.999542	+	0.0302488i	$0.990370\pi$
$312$	4.77791	+	4.77791i	0.270496	+	0.270496i
$313$	6.98116	+	6.98116i	0.394598	+	0.394598i	0.876323	−	0.481724i	$-0.159989\pi$
$313$	6.98116	+	6.98116i	0.394598	+	0.394598i	−0.481724	+	0.876323i	$0.659989\pi$
$314$			23.3137i			1.31567i
$315$			3.65685i			0.206040i
$316$	12.9343	+	12.9343i	0.727612	+	0.727612i
$317$	−13.6068	−	13.6068i	−0.764235	−	0.764235i	0.212850	−	0.977085i	$-0.431726\pi$
$317$	−13.6068	−	13.6068i	−0.764235	−	0.764235i	−0.977085	+	0.212850i	$0.931726\pi$
$318$	−2.61313	+	2.61313i	−0.146537	+	0.146537i
$319$	−0.828427			−0.0463830
$320$	5.31911	−	5.31911i	0.297347	−	0.297347i
$321$			0.485281i			0.0270858i
$322$	30.1421			1.67976
$323$		0			0
$324$	−0.656854			−0.0364919
$325$		−	6.24264i		−	0.346279i
$326$	14.4650	−	14.4650i	0.801145	−	0.801145i
$327$	−16.8284			−0.930614
$328$	−3.78837	+	3.78837i	−0.209178	+	0.209178i
$329$	−9.55582	−	9.55582i	−0.526829	−	0.526829i
$330$	3.69552	+	3.69552i	0.203432	+	0.203432i
$331$			21.7990i			1.19818i	0.800681	+	0.599090i	$0.204471\pi$
$331$			21.7990i			1.19818i	−0.800681	+	0.599090i	$0.795529\pi$
$332$		−	44.6274i		−	2.44925i
$333$	11.9448	+	11.9448i	0.654570	+	0.654570i
$334$	−3.37849	−	3.37849i	−0.184863	−	0.184863i
$335$	−0.634051	+	0.634051i	−0.0346419	+	0.0346419i
$336$	8.48528			0.462910
$337$	3.97408	−	3.97408i	0.216482	−	0.216482i	−0.590532	−	0.807014i	$-0.701082\pi$
$337$	3.97408	−	3.97408i	0.216482	−	0.216482i	0.807014	+	0.590532i	$0.201082\pi$
$338$		−	26.5563i		−	1.44447i
$339$	−14.2843			−0.775815
$340$		0			0
$341$	20.4853			1.10934
$342$			3.65685i			0.197740i
$343$	13.2513	−	13.2513i	0.715505	−	0.715505i
$344$	−3.65685			−0.197164
$345$	−2.79884	+	2.79884i	−0.150684	+	0.150684i
$346$	5.00208	+	5.00208i	0.268914	+	0.268914i
$347$	−11.8519	−	11.8519i	−0.636244	−	0.636244i	0.313383	−	0.949627i	$-0.398538\pi$
$347$	−11.8519	−	11.8519i	−0.636244	−	0.636244i	−0.949627	+	0.313383i	$0.898538\pi$
$348$		−	1.31371i		−	0.0704222i
$349$			4.24264i			0.227103i	0.993532	+	0.113552i	$0.0362227\pi$
$349$			4.24264i			0.227103i	−0.993532	+	0.113552i	$0.963777\pi$
$350$	−19.6913	−	19.6913i	−1.05254	−	1.05254i
$351$	−5.22625	−	5.22625i	−0.278957	−	0.278957i
$352$	2.93015	−	2.93015i	0.156178	−	0.156178i
$353$	14.0000			0.745145			0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000			0.745145			0.372572	+	0.928003i	$0.378476\pi$
$354$	11.0866	−	11.0866i	0.589244	−	0.589244i
$355$			4.14214i			0.219842i
$356$	25.2132			1.33630
$357$		0			0
$358$	14.4853			0.765571
$359$			28.8284i			1.52151i	0.649041	+	0.760753i	$0.275170\pi$
$359$			28.8284i			1.52151i	−0.649041	+	0.760753i	$0.724830\pi$
$360$	4.36803	−	4.36803i	0.230215	−	0.230215i
$361$	18.3137			0.963879
$362$	−19.9155	+	19.9155i	−1.04673	+	1.04673i
$363$	−3.19278	−	3.19278i	−0.167578	−	0.167578i
$364$	10.0042	+	10.0042i	0.524361	+	0.524361i
$365$		−	9.89949i		−	0.518163i
$366$		−	10.0000i		−	0.522708i
$367$	−3.11586	−	3.11586i	−0.162647	−	0.162647i	0.621091	−	0.783738i	$-0.286690\pi$
$367$	−3.11586	−	3.11586i	−0.162647	−	0.162647i	−0.783738	+	0.621091i	$0.786690\pi$
$368$	−10.1355	−	10.1355i	−0.528348	−	0.528348i
$369$	1.56920	−	1.56920i	0.0816890	−	0.0816890i
$370$	17.0711			0.887483
$371$	−2.61313	+	2.61313i	−0.135667	+	0.135667i
$372$			32.4853i			1.68428i
$373$	−11.5563			−0.598365			−0.299183	−	0.954196i	$-0.596714\pi$
$373$	−11.5563			−0.598365			−0.299183	+	0.954196i	$0.596714\pi$
$374$		0			0
$375$	7.79899			0.402738
$376$			22.8284i			1.17729i
$377$	0.317025	−	0.317025i	0.0163276	−	0.0163276i
$378$	−32.9706			−1.69582
$379$	1.84776	−	1.84776i	0.0949130	−	0.0949130i	−0.658056	−	0.752969i	$-0.728621\pi$
$379$	1.84776	−	1.84776i	0.0949130	−	0.0949130i	0.752969	+	0.658056i	$0.228621\pi$
$380$	1.71644	+	1.71644i	0.0880517	+	0.0880517i
$381$	4.06694	+	4.06694i	0.208355	+	0.208355i
$382$		−	48.2843i		−	2.47044i
$383$		−	22.4853i		−	1.14894i	−0.818524	−	0.574472i	$-0.805207\pi$
$383$		−	22.4853i		−	1.14894i	0.818524	−	0.574472i	$-0.194793\pi$
$384$	15.7331	+	15.7331i	0.802879	+	0.802879i
$385$	3.69552	+	3.69552i	0.188341	+	0.188341i
$386$	−3.91969	+	3.91969i	−0.199507	+	0.199507i
$387$	1.51472			0.0769975
$388$	−27.9406	+	27.9406i	−1.41847	+	1.41847i
$389$		−	12.1421i		−	0.615631i	−0.951446	−	0.307815i	$-0.900402\pi$
$389$		−	12.1421i		−	0.615631i	0.951446	−	0.307815i	$-0.0995979\pi$
$390$	−2.82843			−0.143223
$391$		0			0
$392$	−0.757359			−0.0382524
$393$			16.4853i			0.831572i
$394$	7.93223	−	7.93223i	0.399620	−	0.399620i
$395$	−3.65685			−0.183996
$396$	12.9343	−	12.9343i	0.649974	−	0.649974i
$397$	12.5788	+	12.5788i	0.631313	+	0.631313i	0.948397	−	0.317084i	$-0.102704\pi$
$397$	12.5788	+	12.5788i	0.631313	+	0.631313i	−0.317084	+	0.948397i	$0.602704\pi$
$398$	19.6913	+	19.6913i	0.987036	+	0.987036i
$399$		−	2.34315i		−	0.117304i
$400$			13.2426i			0.662132i
$401$	−0.409880	−	0.409880i	−0.0204684	−	0.0204684i	0.696799	−	0.717267i	$-0.254607\pi$
$401$	−0.409880	−	0.409880i	−0.0204684	−	0.0204684i	−0.717267	+	0.696799i	$0.754607\pi$
$402$	−2.16478	−	2.16478i	−0.107970	−	0.107970i
$403$	−7.83938	+	7.83938i	−0.390507	+	0.390507i
$404$	−40.5269			−2.01629
$405$	0.0928546	−	0.0928546i	0.00461398	−	0.00461398i
$406$		−	2.00000i		−	0.0992583i
$407$	24.1421			1.19668
$408$		0			0
$409$	−3.31371			−0.163852			−0.0819262	−	0.996638i	$-0.526107\pi$
$409$	−3.31371			−0.163852			−0.0819262	+	0.996638i	$0.526107\pi$
$410$		−	2.24264i		−	0.110756i
$411$	−12.8030	+	12.8030i	−0.631525	+	0.631525i
$412$	−47.7990			−2.35489
$413$	11.0866	−	11.0866i	0.545534	−	0.545534i
$414$	14.9134	+	14.9134i	0.732953	+	0.732953i
$415$	6.30864	+	6.30864i	0.309679	+	0.309679i
$416$			2.24264i			0.109955i
$417$			23.1127i			1.13183i
$418$	3.69552	+	3.69552i	0.180754	+	0.180754i
$419$	9.42450	+	9.42450i	0.460417	+	0.460417i	0.898792	−	0.438375i	$-0.144446\pi$
$419$	9.42450	+	9.42450i	0.460417	+	0.460417i	−0.438375	+	0.898792i	$0.644446\pi$
$420$	−5.86030	+	5.86030i	−0.285953	+	0.285953i
$421$	−14.5858			−0.710868			−0.355434	−	0.934701i	$-0.615667\pi$
$421$	−14.5858			−0.710868			−0.355434	+	0.934701i	$0.615667\pi$
$422$	−36.4524	+	36.4524i	−1.77448	+	1.77448i
$423$		−	9.45584i		−	0.459759i
$424$	6.24264			0.303169
$425$		0			0
$426$	−14.1421			−0.685189
$427$		−	10.0000i		−	0.483934i
$428$	1.21371	−	1.21371i	0.0586668	−	0.0586668i
$429$	−4.00000			−0.193122
$430$	1.08239	−	1.08239i	0.0521976	−	0.0521976i
$431$	5.17186	+	5.17186i	0.249120	+	0.249120i	0.820609	−	0.571490i	$-0.193634\pi$
$431$	5.17186	+	5.17186i	0.249120	+	0.249120i	−0.571490	+	0.820609i	$0.693634\pi$
$432$	11.0866	+	11.0866i	0.533402	+	0.533402i
$433$		−	20.8284i		−	1.00095i	−0.865751	−	0.500475i	$-0.833159\pi$
$433$		−	20.8284i		−	1.00095i	0.865751	−	0.500475i	$-0.166841\pi$
$434$			49.4558i			2.37396i
$435$	0.185709	+	0.185709i	0.00890407	+	0.00890407i
$436$	42.0886	+	42.0886i	2.01568	+	2.01568i
$437$	−2.79884	+	2.79884i	−0.133886	+	0.133886i
$438$	33.7990			1.61498
$439$	7.52235	−	7.52235i	0.359022	−	0.359022i	−0.504430	−	0.863452i	$-0.668297\pi$
$439$	7.52235	−	7.52235i	0.359022	−	0.359022i	0.863452	+	0.504430i	$0.168297\pi$
$440$		−	8.82843i		−	0.420879i
$441$	0.313708			0.0149385
$442$		0			0
$443$	−23.7990			−1.13072			−0.565362	−	0.824843i	$-0.691264\pi$
$443$	−23.7990			−1.13072			−0.565362	+	0.824843i	$0.691264\pi$
$444$			38.2843i			1.81689i
$445$	−3.56420	+	3.56420i	−0.168959	+	0.168959i
$446$	11.6569			0.551968
$447$	12.9887	−	12.9887i	0.614345	−	0.614345i
$448$	18.1606	+	18.1606i	0.858006	+	0.858006i
$449$	−8.56628	−	8.56628i	−0.404268	−	0.404268i	0.475466	−	0.879734i	$-0.342279\pi$
$449$	−8.56628	−	8.56628i	−0.404268	−	0.404268i	−0.879734	+	0.475466i	$0.842279\pi$
$450$		−	19.4853i		−	0.918545i
$451$		−	3.17157i		−	0.149344i
$452$	35.7255	+	35.7255i	1.68039	+	1.68039i
$453$	5.48888	+	5.48888i	0.257890	+	0.257890i
$454$	−29.6955	+	29.6955i	−1.39368	+	1.39368i
$455$	−2.82843			−0.132599
$456$	−2.79884	+	2.79884i	−0.131067	+	0.131067i
$457$			13.1716i			0.616140i	0.951364	+	0.308070i	$0.0996831\pi$
$457$			13.1716i			0.616140i	−0.951364	+	0.308070i	$0.900317\pi$
$458$	−41.4558			−1.93710
$459$		0			0
$460$	14.0000			0.652753
$461$		−	24.0416i		−	1.11973i	−0.828584	−	0.559865i	$-0.810853\pi$
$461$		−	24.0416i		−	1.11973i	0.828584	−	0.559865i	$-0.189147\pi$
$462$	−12.6173	+	12.6173i	−0.587009	+	0.587009i
$463$	−14.6274			−0.679794			−0.339897	−	0.940463i	$-0.610392\pi$
$463$	−14.6274			−0.679794			−0.339897	+	0.940463i	$0.610392\pi$
$464$	−0.672512	+	0.672512i	−0.0312206	+	0.0312206i
$465$	−4.59220	−	4.59220i	−0.212958	−	0.212958i
$466$	15.0062	+	15.0062i	0.695151	+	0.695151i
$467$		−	32.6274i		−	1.50982i	−0.655830	−	0.754908i	$-0.727681\pi$
$467$		−	32.6274i		−	1.50982i	0.655830	−	0.754908i	$-0.272319\pi$
$468$			9.89949i			0.457604i
$469$	−2.16478	−	2.16478i	−0.0999605	−	0.0999605i
$470$	−6.75699	−	6.75699i	−0.311677	−	0.311677i
$471$	7.39104	−	7.39104i	0.340561	−	0.340561i
$472$	−26.4853			−1.21908
$473$	1.53073	−	1.53073i	0.0703832	−	0.0703832i
$474$		−	12.4853i		−	0.573468i
$475$	3.65685			0.167788
$476$		0			0
$477$	−2.58579			−0.118395
$478$			35.7990i			1.63741i
$479$	3.64113	−	3.64113i	0.166367	−	0.166367i	−0.619013	−	0.785381i	$-0.712467\pi$
$479$	3.64113	−	3.64113i	0.166367	−	0.166367i	0.785381	+	0.619013i	$0.212467\pi$
$480$	−1.31371			−0.0599623
$481$	−9.23880	+	9.23880i	−0.421253	+	0.421253i
$482$	−6.08447	−	6.08447i	−0.277140	−	0.277140i
$483$	−9.55582	−	9.55582i	−0.434805	−	0.434805i
$484$			15.9706i			0.725935i
$485$		−	7.89949i		−	0.358698i
$486$	−26.4483	−	26.4483i	−1.19972	−	1.19972i
$487$	−18.6089	−	18.6089i	−0.843250	−	0.843250i	0.146030	−	0.989280i	$-0.453350\pi$
$487$	−18.6089	−	18.6089i	−0.843250	−	0.843250i	−0.989280	+	0.146030i	$0.953350\pi$
$488$	−11.9448	+	11.9448i	−0.540715	+	0.540715i
$489$	−9.17157			−0.414753
$490$	0.224171	−	0.224171i	0.0101270	−	0.0101270i
$491$			37.1127i			1.67487i	0.546535	+	0.837436i	$0.315947\pi$
$491$			37.1127i			1.67487i	−0.546535	+	0.837436i	$0.684053\pi$
$492$	5.02944			0.226745
$493$		0			0
$494$	−2.82843			−0.127257
$495$			3.65685i			0.164363i
$496$	16.6298	−	16.6298i	0.746701	−	0.746701i
$497$	−14.1421			−0.634361
$498$	−21.5391	+	21.5391i	−0.965188	+	0.965188i
$499$	−15.1760	−	15.1760i	−0.679372	−	0.679372i	0.280486	−	0.959858i	$-0.409504\pi$
$499$	−15.1760	−	15.1760i	−0.679372	−	0.679372i	−0.959858	+	0.280486i	$0.909504\pi$
$500$	−19.5056	−	19.5056i	−0.872316	−	0.872316i
$501$			2.14214i			0.0957036i
$502$		−	49.4558i		−	2.20732i
$503$	−15.0991	−	15.0991i	−0.673235	−	0.673235i	0.285225	−	0.958461i	$-0.407932\pi$
$503$	−15.0991	−	15.0991i	−0.673235	−	0.673235i	−0.958461	+	0.285225i	$0.907932\pi$
$504$	14.9134	+	14.9134i	0.664295	+	0.664295i
$505$	5.72899	−	5.72899i	0.254937	−	0.254937i
$506$	30.1421			1.33998
$507$	−8.41904	+	8.41904i	−0.373902	+	0.373902i
$508$		−	20.3431i		−	0.902581i
$509$	36.9706			1.63869			0.819346	−	0.573300i	$-0.194337\pi$
$509$	36.9706			1.63869			0.819346	+	0.573300i	$0.194337\pi$
$510$		0			0
$511$	33.7990			1.49518
$512$		−	31.2426i		−	1.38074i
$513$	3.06147	−	3.06147i	0.135167	−	0.135167i
$514$	−14.8284			−0.654054
$515$	6.75699	−	6.75699i	0.297748	−	0.297748i
$516$	2.42742	+	2.42742i	0.106861	+	0.106861i
$517$	−9.55582	−	9.55582i	−0.420265	−	0.420265i
$518$			58.2843i			2.56086i
$519$		−	3.17157i		−	0.139217i
$520$	3.37849	+	3.37849i	0.148157	+	0.148157i
$521$	−13.1585	−	13.1585i	−0.576484	−	0.576484i	0.357449	−	0.933933i	$-0.383647\pi$
$521$	−13.1585	−	13.1585i	−0.576484	−	0.576484i	−0.933933	+	0.357449i	$0.883647\pi$
$522$	0.989538	−	0.989538i	0.0433109	−	0.0433109i
$523$	−1.17157			−0.0512293			−0.0256147	−	0.999672i	$-0.508154\pi$
$523$	−1.17157			−0.0512293			−0.0256147	+	0.999672i	$0.508154\pi$
$524$	41.2304	−	41.2304i	1.80116	−	1.80116i
$525$			12.4853i			0.544902i
$526$	−25.3137			−1.10373
$527$		0			0
$528$	8.48528			0.369274
$529$		−	0.171573i		−	0.00745969i
$530$	−1.84776	+	1.84776i	−0.0802615	+	0.0802615i
$531$	10.9706			0.476082
$532$	−5.86030	+	5.86030i	−0.254076	+	0.254076i
$533$	1.21371	+	1.21371i	0.0525715	+	0.0525715i
$534$	−12.1689	−	12.1689i	−0.526602	−	0.526602i
$535$			0.343146i			0.0148355i
$536$			5.17157i			0.223378i
$537$	−4.59220	−	4.59220i	−0.198168	−	0.198168i
$538$	−45.1500	−	45.1500i	−1.94656	−	1.94656i
$539$	0.317025	−	0.317025i	0.0136552	−	0.0136552i
$540$	−15.3137			−0.658997
$541$	13.0272	−	13.0272i	0.560082	−	0.560082i	−0.369249	−	0.929331i	$-0.620385\pi$
$541$	13.0272	−	13.0272i	0.560082	−	0.560082i	0.929331	+	0.369249i	$0.120385\pi$
$542$		−	53.4558i		−	2.29613i
$543$	12.6274			0.541894
$544$		0			0
$545$	−11.8995			−0.509718
$546$		−	9.65685i		−	0.413275i
$547$	5.72899	−	5.72899i	0.244954	−	0.244954i	−0.573942	−	0.818896i	$-0.694587\pi$
$547$	5.72899	−	5.72899i	0.244954	−	0.244954i	0.818896	+	0.573942i	$0.194587\pi$
$548$	64.0416			2.73572
$549$	4.94769	−	4.94769i	0.211162	−	0.211162i
$550$	−19.6913	−	19.6913i	−0.839640	−	0.839640i
$551$	0.185709	+	0.185709i	0.00791148	+	0.00791148i
$552$			22.8284i			0.971642i
$553$		−	12.4853i		−	0.530928i
$554$	34.0635	+	34.0635i	1.44722	+	1.44722i
$555$	−5.41196	−	5.41196i	−0.229725	−	0.229725i
$556$	57.8058	−	57.8058i	2.45151	−	2.45151i
$557$	19.7574			0.837146			0.418573	−	0.908183i	$-0.362530\pi$
$557$	19.7574			0.837146			0.418573	+	0.908183i	$0.362530\pi$
$558$	−24.4692	+	24.4692i	−1.03586	+	1.03586i
$559$			1.17157i			0.0495523i
$560$	6.00000			0.253546
$561$		0			0
$562$	4.58579			0.193440
$563$		−	34.7696i		−	1.46536i	−0.680572	−	0.732681i	$-0.738269\pi$
$563$		−	34.7696i		−	1.46536i	0.680572	−	0.732681i	$-0.261731\pi$
$564$	15.1535	−	15.1535i	0.638077	−	0.638077i
$565$	−10.1005			−0.424931
$566$	−31.8602	+	31.8602i	−1.33919	+	1.33919i
$567$	0.317025	+	0.317025i	0.0133138	+	0.0133138i
$568$	16.8925	+	16.8925i	0.708792	+	0.708792i
$569$		−	12.0416i		−	0.504811i	−0.967621	−	0.252406i	$-0.918778\pi$
$569$		−	12.0416i		−	0.504811i	0.967621	−	0.252406i	$-0.0812218\pi$
$570$		−	1.65685i		−	0.0693980i
$571$	−3.00707	−	3.00707i	−0.125842	−	0.125842i	0.641381	−	0.767223i	$-0.278362\pi$
$571$	−3.00707	−	3.00707i	−0.125842	−	0.125842i	−0.767223	+	0.641381i	$0.778362\pi$
$572$	10.0042	+	10.0042i	0.418295	+	0.418295i
$573$	−15.3073	+	15.3073i	−0.639473	+	0.639473i
$574$	7.65685			0.319591
$575$	14.9134	−	14.9134i	0.621931	−	0.621931i
$576$			17.9706i			0.748773i
$577$	27.0711			1.12698			0.563492	−	0.826122i	$-0.309458\pi$
$577$	27.0711			1.12698			0.563492	+	0.826122i	$0.309458\pi$
$578$		0			0
$579$	2.48528			0.103285
$580$		−	0.928932i		−	0.0385718i
$581$	−21.5391	+	21.5391i	−0.893591	+	0.893591i
$582$	26.9706			1.11797
$583$	−2.61313	+	2.61313i	−0.108225	+	0.108225i
$584$	−40.3721	−	40.3721i	−1.67061	−	1.67061i
$585$	−1.39942	−	1.39942i	−0.0578588	−	0.0578588i
$586$			29.7990i			1.23098i
$587$			45.3137i			1.87030i	0.354256	+	0.935148i	$0.384734\pi$
$587$			45.3137i			1.87030i	−0.354256	+	0.935148i	$0.615266\pi$
$588$	0.502734	+	0.502734i	0.0207324	+	0.0207324i
$589$	−4.59220	−	4.59220i	−0.189218	−	0.189218i
$590$	7.83938	−	7.83938i	0.322742	−	0.322742i
$591$	−5.02944			−0.206883
$592$	19.5984	−	19.5984i	0.805491	−	0.805491i
$593$			12.9289i			0.530928i	0.964121	+	0.265464i	$0.0855251\pi$
$593$			12.9289i			0.530928i	−0.964121	+	0.265464i	$0.914475\pi$
$594$	−32.9706			−1.35280
$595$		0			0
$596$	−64.9706			−2.66130
$597$		−	12.4853i		−	0.510989i
$598$	−11.5349	+	11.5349i	−0.471697	+	0.471697i
$599$	10.6274			0.434224			0.217112	−	0.976147i	$-0.430336\pi$
$599$	10.6274			0.434224			0.217112	+	0.976147i	$0.430336\pi$
$600$	14.9134	−	14.9134i	0.608837	−	0.608837i
$601$	−5.95316	−	5.95316i	−0.242834	−	0.242834i	0.575187	−	0.818022i	$-0.304929\pi$
$601$	−5.95316	−	5.95316i	−0.242834	−	0.242834i	−0.818022	+	0.575187i	$0.804929\pi$
$602$	3.69552	+	3.69552i	0.150618	+	0.150618i
$603$		−	2.14214i		−	0.0872345i
$604$		−	27.4558i		−	1.11716i
$605$	−2.25764	−	2.25764i	−0.0917861	−	0.0917861i
$606$	19.5600	+	19.5600i	0.794570	+	0.794570i
$607$	11.5893	−	11.5893i	0.470395	−	0.470395i	−0.431648	−	0.902042i	$-0.642068\pi$
$607$	11.5893	−	11.5893i	0.470395	−	0.470395i	0.902042	+	0.431648i	$0.142068\pi$
$608$	−1.31371			−0.0532779
$609$	−0.634051	+	0.634051i	−0.0256930	+	0.0256930i
$610$		−	7.07107i		−	0.286299i
$611$	7.31371			0.295881
$612$		0			0
$613$	5.31371			0.214619			0.107309	−	0.994226i	$-0.465776\pi$
$613$	5.31371			0.214619			0.107309	+	0.994226i	$0.465776\pi$
$614$		−	63.1127i		−	2.54702i
$615$	−0.710974	+	0.710974i	−0.0286692	+	0.0286692i
$616$	30.1421			1.21446
$617$	2.07193	−	2.07193i	0.0834128	−	0.0834128i	−0.664169	−	0.747582i	$-0.731215\pi$
$617$	2.07193	−	2.07193i	0.0834128	−	0.0834128i	0.747582	+	0.664169i	$0.231215\pi$
$618$	23.0698	+	23.0698i	0.928003	+	0.928003i
$619$	−20.1396	−	20.1396i	−0.809480	−	0.809480i	0.175075	−	0.984555i	$-0.443983\pi$
$619$	−20.1396	−	20.1396i	−0.809480	−	0.809480i	−0.984555	+	0.175075i	$0.943983\pi$
$620$			22.9706i			0.922520i
$621$		−	24.9706i		−	1.00203i
$622$	−43.8435	−	43.8435i	−1.75796	−	1.75796i
$623$	−12.1689	−	12.1689i	−0.487539	−	0.487539i
$624$	−3.24718	+	3.24718i	−0.129991	+	0.129991i
$625$	−16.5563			−0.662254
$626$	−16.8540	+	16.8540i	−0.673621	+	0.673621i
$627$		−	2.34315i		−	0.0935762i
$628$	−36.9706			−1.47529
$629$		0			0
$630$	−8.82843			−0.351733
$631$			29.3137i			1.16696i	0.812127	+	0.583480i	$0.198309\pi$
$631$			29.3137i			1.16696i	−0.812127	+	0.583480i	$0.801691\pi$
$632$	−14.9134	+	14.9134i	−0.593223	+	0.593223i
$633$	23.1127			0.918647
$634$	32.8498	−	32.8498i	1.30463	−	1.30463i
$635$	2.87576	+	2.87576i	0.114121	+	0.114121i
$636$	−4.14386	−	4.14386i	−0.164315	−	0.164315i
$637$			0.242641i			0.00961377i
$638$		−	2.00000i		−	0.0791808i
$639$	−6.99709	−	6.99709i	−0.276801	−	0.276801i
$640$	11.1250	+	11.1250i	0.439755	+	0.439755i
$641$	−29.2856	+	29.2856i	−1.15671	+	1.15671i	−0.171532	+	0.985178i	$0.554872\pi$
$641$	−29.2856	+	29.2856i	−1.15671	+	1.15671i	−0.985178	+	0.171532i	$0.945128\pi$
$642$	−1.17157			−0.0462383
$643$	−20.4023	+	20.4023i	−0.804587	+	0.804587i	−0.983809	−	0.179222i	$-0.942642\pi$
$643$	−20.4023	+	20.4023i	−0.804587	+	0.804587i	0.179222	+	0.983809i	$0.442642\pi$
$644$			47.7990i			1.88354i
$645$	−0.686292			−0.0270227
$646$		0			0
$647$	−2.82843			−0.111197			−0.0555985	−	0.998453i	$-0.517707\pi$
$647$	−2.82843			−0.111197			−0.0555985	+	0.998453i	$0.517707\pi$
$648$		−	0.757359i		−	0.0297519i
$649$	11.0866	−	11.0866i	0.435185	−	0.435185i
$650$	15.0711			0.591136
$651$	15.6788	−	15.6788i	0.614499	−	0.614499i
$652$	22.9385	+	22.9385i	0.898340	+	0.898340i
$653$	−6.71852	−	6.71852i	−0.262916	−	0.262916i	0.563322	−	0.826238i	$-0.309523\pi$
$653$	−6.71852	−	6.71852i	−0.262916	−	0.262916i	−0.826238	+	0.563322i	$0.809523\pi$
$654$		−	40.6274i		−	1.58866i
$655$			11.6569i			0.455471i
$656$	−2.57466	−	2.57466i	−0.100524	−	0.100524i
$657$	16.7227	+	16.7227i	0.652414	+	0.652414i
$658$	23.0698	−	23.0698i	0.899354	−	0.899354i
$659$	8.48528			0.330540			0.165270	−	0.986248i	$-0.447151\pi$
$659$	8.48528			0.330540			0.165270	+	0.986248i	$0.447151\pi$
$660$	−5.86030	+	5.86030i	−0.228112	+	0.228112i
$661$			1.21320i			0.0471881i	0.999722	+	0.0235941i	$0.00751092\pi$
$661$			1.21320i			0.0471881i	−0.999722	+	0.0235941i	$0.992489\pi$
$662$	−52.6274			−2.04542
$663$		0			0
$664$	51.4558			1.99687
$665$		−	1.65685i		−	0.0642501i
$666$	−28.8372	+	28.8372i	−1.11742	+	1.11742i
$667$	1.51472			0.0586501
$668$	5.35757	−	5.35757i	0.207291	−	0.207291i
$669$	−3.69552	−	3.69552i	−0.142877	−	0.142877i
$670$	−1.53073	−	1.53073i	−0.0591374	−	0.0591374i
$671$		−	10.0000i		−	0.386046i
$672$		−	4.48528i		−	0.173023i
$673$	3.15432	+	3.15432i	0.121590	+	0.121590i	0.765284	−	0.643693i	$-0.222599\pi$
$673$	3.15432	+	3.15432i	0.121590	+	0.121590i	−0.643693	+	0.765284i	$0.722599\pi$
$674$	9.59428	+	9.59428i	0.369558	+	0.369558i
$675$	−16.3128	+	16.3128i	−0.627880	+	0.627880i
$676$	42.1127			1.61972
$677$	26.9351	−	26.9351i	1.03520	−	1.03520i	0.0358421	−	0.999357i	$-0.488589\pi$
$677$	26.9351	−	26.9351i	1.03520	−	1.03520i	0.999357	−	0.0358421i	$-0.0114113\pi$
$678$		−	34.4853i		−	1.32440i
$679$	26.9706			1.03504
$680$		0			0
$681$	18.8284			0.721507
$682$			49.4558i			1.89376i
$683$	−16.8155	+	16.8155i	−0.643429	+	0.643429i	−0.951397	−	0.307968i	$-0.900351\pi$
$683$	−16.8155	+	16.8155i	−0.643429	+	0.643429i	0.307968	+	0.951397i	$0.400351\pi$
$684$	−5.79899			−0.221730
$685$	−9.05309	+	9.05309i	−0.345901	+	0.345901i
$686$	31.9916	+	31.9916i	1.22144	+	1.22144i
$687$	13.1426	+	13.1426i	0.501420	+	0.501420i
$688$		−	2.48528i		−	0.0947505i
$689$		−	2.00000i		−	0.0761939i
$690$	−6.75699	−	6.75699i	−0.257234	−	0.257234i
$691$	14.0936	+	14.0936i	0.536147	+	0.536147i	0.922395	−	0.386248i	$-0.126229\pi$
$691$	14.0936	+	14.0936i	0.536147	+	0.536147i	−0.386248	+	0.922395i	$0.626229\pi$
$692$	−7.93223	+	7.93223i	−0.301538	+	0.301538i
$693$	−12.4853			−0.474277
$694$	28.6131	−	28.6131i	1.08614	−	1.08614i
$695$			16.3431i			0.619931i
$696$	1.51472			0.0574153
$697$		0			0
$698$	−10.2426			−0.387690
$699$		−	9.51472i		−	0.359880i
$700$	31.2262	−	31.2262i	1.18024	−	1.18024i
$701$	−37.6985			−1.42385			−0.711926	−	0.702254i	$-0.752177\pi$
$701$	−37.6985			−1.42385			−0.711926	+	0.702254i	$0.752177\pi$
$702$	12.6173	−	12.6173i	0.476209	−	0.476209i
$703$	−5.41196	−	5.41196i	−0.204116	−	0.204116i
$704$	18.1606	+	18.1606i	0.684452	+	0.684452i
$705$			4.28427i			0.161355i
$706$			33.7990i			1.27204i
$707$	19.5600	+	19.5600i	0.735629	+	0.735629i
$708$	17.5809	+	17.5809i	0.660731	+	0.660731i
$709$	17.1710	−	17.1710i	0.644871	−	0.644871i	−0.306878	−	0.951749i	$-0.599284\pi$
$709$	17.1710	−	17.1710i	0.644871	−	0.644871i	0.951749	+	0.306878i	$0.0992842\pi$
$710$	−10.0000			−0.375293
$711$	6.17733	−	6.17733i	0.231668	−	0.231668i
$712$			29.0711i			1.08948i
$713$	−37.4558			−1.40273
$714$		0			0
$715$	−2.82843			−0.105777
$716$			22.9706i			0.858450i
$717$	11.3492	−	11.3492i	0.423843	−	0.423843i
$718$	−69.5980			−2.59737
$719$	24.0209	−	24.0209i	0.895827	−	0.895827i	−0.0992367	−	0.995064i	$-0.531640\pi$
$719$	24.0209	−	24.0209i	0.895827	−	0.895827i	0.995064	+	0.0992367i	$0.0316401\pi$
$720$	2.96861	+	2.96861i	0.110634	+	0.110634i
$721$	23.0698	+	23.0698i	0.859164	+	0.859164i
$722$			44.2132i			1.64545i
$723$			3.85786i			0.143476i
$724$	−31.5817	−	31.5817i	−1.17372	−	1.17372i
$725$	−0.989538	−	0.989538i	−0.0367505	−	0.0367505i
$726$	7.70806	−	7.70806i	0.286073	−	0.286073i
$727$	43.1127			1.59896			0.799481	−	0.600692i	$-0.205108\pi$
$727$	43.1127			1.59896			0.799481	+	0.600692i	$0.205108\pi$
$728$	−11.5349	+	11.5349i	−0.427512	+	0.427512i
$729$			17.2843i			0.640158i
$730$	23.8995			0.884560
$731$		0			0
$732$	15.8579			0.586124
$733$			36.0416i			1.33123i	0.746296	+	0.665614i	$0.231830\pi$
$733$			36.0416i			1.33123i	−0.746296	+	0.665614i	$0.768170\pi$
$734$	7.52235	−	7.52235i	0.277655	−	0.277655i
$735$	−0.142136			−0.00524275
$736$	−5.35757	+	5.35757i	−0.197483	+	0.197483i
$737$	−2.16478	−	2.16478i	−0.0797409	−	0.0797409i
$738$	3.78837	+	3.78837i	0.139452	+	0.139452i
$739$		−	22.2843i		−	0.819740i	−0.912144	−	0.409870i	$-0.865574\pi$
$739$		−	22.2843i		−	0.819740i	0.912144	−	0.409870i	$-0.134426\pi$
$740$			27.0711i			0.995152i
$741$	0.896683	+	0.896683i	0.0329405	+	0.0329405i
$742$	−6.30864	−	6.30864i	−0.231598	−	0.231598i
$743$	36.0810	−	36.0810i	1.32368	−	1.32368i	0.412915	−	0.910770i	$-0.364511\pi$
$743$	36.0810	−	36.0810i	1.32368	−	1.32368i	0.910770	−	0.412915i	$-0.135489\pi$
$744$	−37.4558			−1.37320
$745$	9.18440	−	9.18440i	0.336490	−	0.336490i
$746$		−	27.8995i		−	1.02147i
$747$	−21.3137			−0.779828
$748$		0			0
$749$	−1.17157			−0.0428083
$750$			18.8284i			0.687517i
$751$	33.6536	−	33.6536i	1.22804	−	1.22804i	0.263333	−	0.964705i	$-0.415178\pi$
$751$	33.6536	−	33.6536i	1.22804	−	1.22804i	0.964705	−	0.263333i	$-0.0848217\pi$
$752$	−15.5147			−0.565764
$753$	−15.6788	+	15.6788i	−0.571366	+	0.571366i
$754$	0.765367	+	0.765367i	0.0278730	+	0.0278730i
$755$	3.88123	+	3.88123i	0.141252	+	0.141252i
$756$		−	52.2843i		−	1.90156i
$757$		−	2.54416i		−	0.0924689i	−0.998931	−	0.0462345i	$-0.985278\pi$
$757$		−	2.54416i		−	0.0924689i	0.998931	−	0.0462345i	$-0.0147221\pi$
$758$	4.46088	+	4.46088i	0.162027	+	0.162027i
$759$	−9.55582	−	9.55582i	−0.346854	−	0.346854i
$760$	−1.97908	+	1.97908i	−0.0717886	+	0.0717886i
$761$	−37.6985			−1.36657			−0.683285	−	0.730152i	$-0.739449\pi$
$761$	−37.6985			−1.36657			−0.683285	+	0.730152i	$0.739449\pi$
$762$	−9.81845	+	9.81845i	−0.355685	+	0.355685i
$763$		−	40.6274i		−	1.47081i
$764$	76.5685			2.77015
$765$		0			0
$766$	54.2843			1.96137
$767$			8.48528i			0.306386i
$768$	−22.9385	+	22.9385i	−0.827721	+	0.827721i
$769$	−12.7279			−0.458981			−0.229490	−	0.973311i	$-0.573706\pi$
$769$	−12.7279			−0.458981			−0.229490	+	0.973311i	$0.573706\pi$
$770$	−8.92177	+	8.92177i	−0.321518	+	0.321518i
$771$	4.70099	+	4.70099i	0.169302	+	0.169302i
$772$	−6.21579	−	6.21579i	−0.223711	−	0.223711i
$773$			0.828427i			0.0297965i	0.999889	+	0.0148982i	$0.00474243\pi$
$773$			0.828427i			0.0297965i	−0.999889	+	0.0148982i	$0.995258\pi$
$774$			3.65685i			0.131443i
$775$	24.4692	+	24.4692i	0.878960	+	0.878960i
$776$	−32.2157	−	32.2157i	−1.15648	−	1.15648i
$777$	18.4776	−	18.4776i	0.662880	−	0.662880i
$778$	29.3137			1.05095
$779$	−0.710974	+	0.710974i	−0.0254733	+	0.0254733i
$780$		−	4.48528i		−	0.160599i
$781$	−14.1421			−0.506045
$782$		0			0
$783$	−1.65685			−0.0592111
$784$		−	0.514719i		−	0.0183828i
$785$	5.22625	−	5.22625i	0.186533	−	0.186533i
$786$	−39.7990			−1.41958
$787$	14.5420	−	14.5420i	0.518365	−	0.518365i	−0.398711	−	0.917077i	$-0.630542\pi$
$787$	14.5420	−	14.5420i	0.518365	−	0.518365i	0.917077	+	0.398711i	$0.130542\pi$
$788$	12.5788	+	12.5788i	0.448102	+	0.448102i
$789$	8.02509	+	8.02509i	0.285701	+	0.285701i
$790$		−	8.82843i		−	0.314101i
$791$		−	34.4853i		−	1.22616i
$792$	14.9134	+	14.9134i	0.529924	+	0.529924i
$793$	3.82683	+	3.82683i	0.135895	+	0.135895i
$794$	−30.3680	+	30.3680i	−1.07772	+	1.07772i
$795$	1.17157			0.0415514
$796$	−31.2262	+	31.2262i	−1.10678	+	1.10678i
$797$		−	25.2132i		−	0.893097i	−0.894759	−	0.446549i	$-0.852653\pi$
$797$		−	25.2132i		−	0.893097i	0.894759	−	0.446549i	$-0.147347\pi$
$798$	5.65685			0.200250
$799$		0			0
$800$	7.00000			0.247487
$801$		−	12.0416i		−	0.425470i
$802$	0.989538	−	0.989538i	0.0349418	−	0.0349418i
$803$	33.7990			1.19274
$804$	3.43289	−	3.43289i	0.121069	−	0.121069i
$805$	−6.75699	−	6.75699i	−0.238152	−	0.238152i
$806$	−18.9259	−	18.9259i	−0.666638	−	0.666638i
$807$			28.6274i			1.00773i
$808$		−	46.7279i		−	1.64388i
$809$	−24.9560	−	24.9560i	−0.877407	−	0.877407i	0.115859	−	0.993266i	$-0.463038\pi$
$809$	−24.9560	−	24.9560i	−0.877407	−	0.877407i	−0.993266	+	0.115859i	$0.963038\pi$
$810$	0.224171	+	0.224171i	0.00787656	+	0.00787656i
$811$	−38.9886	+	38.9886i	−1.36908	+	1.36908i	−0.507317	+	0.861759i	$0.669363\pi$
$811$	−38.9886	+	38.9886i	−1.36908	+	1.36908i	−0.861759	+	0.507317i	$0.830637\pi$
$812$	3.17157			0.111300
$813$	−16.9469	+	16.9469i	−0.594352	+	0.594352i
$814$			58.2843i			2.04286i
$815$	−6.48528			−0.227169
$816$		0			0
$817$	−0.686292			−0.0240103
$818$		−	8.00000i		−	0.279713i
$819$	4.77791	−	4.77791i	0.166954	−	0.166954i
$820$	3.55635			0.124193
$821$	−27.1752	+	27.1752i	−0.948421	+	0.948421i	−0.998734	−	0.0503128i	$-0.983978\pi$
$821$	−27.1752	+	27.1752i	−0.948421	+	0.948421i	0.0503128	+	0.998734i	$0.483978\pi$
$822$	−30.9092	−	30.9092i	−1.07808	−	1.07808i
$823$	−6.88830	−	6.88830i	−0.240111	−	0.240111i	0.576785	−	0.816896i	$-0.304307\pi$
$823$	−6.88830	−	6.88830i	−0.240111	−	0.240111i	−0.816896	+	0.576785i	$0.804307\pi$
$824$		−	55.1127i		−	1.91994i
$825$			12.4853i			0.434682i
$826$	26.7653	+	26.7653i	0.931284	+	0.931284i
$827$	33.1283	+	33.1283i	1.15199	+	1.15199i	0.986154	+	0.165831i	$0.0530307\pi$
$827$	33.1283	+	33.1283i	1.15199	+	1.15199i	0.165831	+	0.986154i	$0.446969\pi$
$828$	−23.6494	+	23.6494i	−0.821875	+	0.821875i
$829$	−53.9411			−1.87345			−0.936726	−	0.350062i	$-0.886160\pi$
$829$	−53.9411			−1.87345			−0.936726	+	0.350062i	$0.886160\pi$
$830$	−15.2304	+	15.2304i	−0.528655	+	0.528655i
$831$		−	21.5980i		−	0.749226i
$832$	−13.8995			−0.481878
$833$		0			0
$834$	−55.7990			−1.93216
$835$			1.51472i			0.0524190i
$836$	−5.86030	+	5.86030i	−0.202683	+	0.202683i
$837$	40.9706			1.41615
$838$	−22.7528	+	22.7528i	−0.785981	+	0.785981i
$839$	−11.8519	−	11.8519i	−0.409174	−	0.409174i	0.472277	−	0.881450i	$-0.343432\pi$
$839$	−11.8519	−	11.8519i	−0.409174	−	0.409174i	−0.881450	+	0.472277i	$0.843432\pi$
$840$	−6.75699	−	6.75699i	−0.233138	−	0.233138i
$841$			28.8995i			0.996534i
$842$		−	35.2132i		−	1.21353i
$843$	−1.45381	−	1.45381i	−0.0500719	−	0.0500719i
$844$	−57.8058	−	57.8058i	−1.98976	−	1.98976i
$845$	−5.95316	+	5.95316i	−0.204795	+	0.204795i
$846$	22.8284			0.784857
$847$	7.70806	−	7.70806i	0.264852	−	0.264852i
$848$			4.24264i			0.145693i
$849$	20.2010			0.693297
$850$		0			0
$851$	−44.1421			−1.51317
$852$		−	22.4264i		−	0.768316i
$853$	−13.5524	+	13.5524i	−0.464026	+	0.464026i	−0.899973	−	0.435946i	$-0.856414\pi$
$853$	−13.5524	+	13.5524i	−0.464026	+	0.464026i	0.435946	+	0.899973i	$0.356414\pi$
$854$	24.1421			0.826127
$855$	0.819760	−	0.819760i	0.0280352	−	0.0280352i
$856$	1.39942	+	1.39942i	0.0478311	+	0.0478311i
$857$	6.53281	+	6.53281i	0.223157	+	0.223157i	0.809826	−	0.586670i	$-0.199561\pi$
$857$	6.53281	+	6.53281i	0.223157	+	0.223157i	−0.586670	+	0.809826i	$0.699561\pi$
$858$		−	9.65685i		−	0.329680i
$859$			34.9706i			1.19318i	0.802546	+	0.596590i	$0.203478\pi$
$859$			34.9706i			1.19318i	−0.802546	+	0.596590i	$0.796522\pi$
$860$	1.71644	+	1.71644i	0.0585302	+	0.0585302i
$861$	−2.42742	−	2.42742i	−0.0827261	−	0.0827261i
$862$	−12.4860	+	12.4860i	−0.425274	+	0.425274i
$863$	10.6274			0.361761			0.180881	−	0.983505i	$-0.442105\pi$
$863$	10.6274			0.361761			0.180881	+	0.983505i	$0.442105\pi$
$864$	5.86030	−	5.86030i	0.199372	−	0.199372i
$865$		−	2.24264i		−	0.0762521i
$866$	50.2843			1.70873
$867$		0			0
$868$	−78.4264			−2.66197
$869$		−	12.4853i		−	0.423534i
$870$	−0.448342	+	0.448342i	−0.0152002	+	0.0152002i
$871$	1.65685			0.0561404
$872$	−48.5285	+	48.5285i	−1.64338	+	1.64338i
$873$	13.3442	+	13.3442i	0.451633	+	0.451633i
$874$	−6.75699	−	6.75699i	−0.228558	−	0.228558i
$875$			18.8284i			0.636517i
$876$			53.5980i			1.81091i
$877$	35.5173	+	35.5173i	1.19933	+	1.19933i	0.974366	+	0.224968i	$0.0722277\pi$
$877$	35.5173	+	35.5173i	1.19933	+	1.19933i	0.224968	+	0.974366i	$0.427772\pi$
$878$	18.1606	+	18.1606i	0.612889	+	0.612889i
$879$	9.44703	−	9.44703i	0.318641	−	0.318641i
$880$	6.00000			0.202260
$881$	−23.7967	+	23.7967i	−0.801731	+	0.801731i	−0.983366	−	0.181635i	$-0.941861\pi$
$881$	−23.7967	+	23.7967i	−0.801731	+	0.801731i	0.181635	+	0.983366i	$0.441861\pi$
$882$			0.757359i			0.0255016i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$	−4.97056			−0.167084
$886$		−	57.4558i		−	1.93027i
$887$	31.1493	−	31.1493i	1.04589	−	1.04589i	0.0469951	−	0.998895i	$-0.485035\pi$
$887$	31.1493	−	31.1493i	1.04589	−	1.04589i	0.998895	−	0.0469951i	$-0.0149645\pi$
$888$	−44.1421			−1.48131
$889$	−9.81845	+	9.81845i	−0.329300	+	0.329300i
$890$	−8.60474	−	8.60474i	−0.288432	−	0.288432i
$891$	0.317025	+	0.317025i	0.0106207	+	0.0106207i
$892$			18.4853i			0.618933i
$893$			4.28427i			0.143368i
$894$	31.3575	+	31.3575i	1.04875	+	1.04875i
$895$	−3.24718	−	3.24718i	−0.108541	−	0.108541i
$896$	−37.9832	+	37.9832i	−1.26893	+	1.26893i
$897$	7.31371			0.244198
$898$	20.6808	−	20.6808i	0.690128	−	0.690128i
$899$			2.48528i			0.0828888i
$900$	30.8995			1.02998
$901$		0			0
$902$	7.65685			0.254945
$903$		−	2.34315i		−	0.0779750i
$904$	−41.1919	+	41.1919i	−1.37002	+	1.37002i
$905$	8.92893			0.296808
$906$	−13.2513	+	13.2513i	−0.440246	+	0.440246i
$907$	9.50143	+	9.50143i	0.315490	+	0.315490i	0.847032	−	0.531542i	$-0.178387\pi$
$907$	9.50143	+	9.50143i	0.315490	+	0.315490i	−0.531542	+	0.847032i	$0.678387\pi$
$908$	−47.0907	−	47.0907i	−1.56276	−	1.56276i
$909$			19.3553i			0.641976i
$910$		−	6.82843i		−	0.226360i
$911$	4.01254	+	4.01254i	0.132941	+	0.132941i	0.770446	−	0.637505i	$-0.220033\pi$
$911$	4.01254	+	4.01254i	0.132941	+	0.132941i	−0.637505	+	0.770446i	$0.720033\pi$
$912$	−1.90215	−	1.90215i	−0.0629865	−	0.0629865i
$913$	−21.5391	+	21.5391i	−0.712839	+	0.712839i
$914$	−31.7990			−1.05182
$915$	−2.24171	+	2.24171i	−0.0741086	+	0.0741086i
$916$		−	65.7401i		−	2.17211i
$917$	−39.7990			−1.31428
$918$		0			0
$919$	19.3137			0.637100			0.318550	−	0.947906i	$-0.396804\pi$
$919$	19.3137			0.637100			0.318550	+	0.947906i	$0.396804\pi$
$920$			16.1421i			0.532190i
$921$	−20.0083	+	20.0083i	−0.659297	+	0.659297i
$922$	58.0416			1.91150
$923$	5.41196	−	5.41196i	0.178137	−	0.178137i
$924$	−20.0083	−	20.0083i	−0.658226	−	0.658226i
$925$	28.8372	+	28.8372i	0.948163	+	0.948163i
$926$		−	35.3137i		−	1.16048i
$927$			22.8284i			0.749784i
$928$	0.355487	+	0.355487i	0.0116694	+	0.0116694i
$929$	−12.2618	−	12.2618i	−0.402297	−	0.402297i	0.476745	−	0.879042i	$-0.341817\pi$
$929$	−12.2618	−	12.2618i	−0.402297	−	0.402297i	−0.879042	+	0.476745i	$0.841817\pi$
$930$	11.0866	−	11.0866i	0.363542	−	0.363542i
$931$	−0.142136			−0.00465831
$932$	−23.7967	+	23.7967i	−0.779487	+	0.779487i
$933$			27.7990i			0.910098i
$934$	78.7696			2.57742
$935$		0			0
$936$	−11.4142			−0.373085
$937$		−	27.5563i		−	0.900227i	−0.892971	−	0.450113i	$-0.851384\pi$
$937$		−	27.5563i		−	0.900227i	0.892971	−	0.450113i	$-0.148616\pi$
$938$	5.22625	−	5.22625i	0.170643	−	0.170643i
$939$	10.6863			0.348734
$940$	10.7151	−	10.7151i	0.349489	−	0.349489i
$941$	−28.2032	−	28.2032i	−0.919398	−	0.919398i	0.0775878	−	0.996986i	$-0.475278\pi$
$941$	−28.2032	−	28.2032i	−0.919398	−	0.919398i	−0.996986	+	0.0775878i	$0.975278\pi$
$942$	17.8435	+	17.8435i	0.581374	+	0.581374i
$943$			5.79899i			0.188841i
$944$		−	18.0000i		−	0.585850i
$945$	7.39104	+	7.39104i	0.240430	+	0.240430i
$946$	3.69552	+	3.69552i	0.120152	+	0.120152i
$947$	21.6704	−	21.6704i	0.704193	−	0.704193i	−0.261115	−	0.965308i	$-0.584090\pi$
$947$	21.6704	−	21.6704i	0.704193	−	0.704193i	0.965308	+	0.261115i	$0.0840902\pi$
$948$	19.7990			0.643041
$949$	−12.9343	+	12.9343i	−0.419866	+	0.419866i
$950$			8.82843i			0.286432i
$951$	−20.8284			−0.675408
$952$		0			0
$953$	49.6985			1.60989			0.804946	−	0.593348i	$-0.202194\pi$
$953$	49.6985			1.60989			0.804946	+	0.593348i	$0.202194\pi$
$954$		−	6.24264i		−	0.202113i
$955$	−10.8239	+	10.8239i	−0.350254	+	0.350254i
$956$	−56.7696			−1.83606
$957$	−0.634051	+	0.634051i	−0.0204959	+	0.0204959i
$958$	8.79045	+	8.79045i	0.284007	+	0.284007i
$959$	−30.9092	−	30.9092i	−0.998109	−	0.998109i
$960$		−	8.14214i		−	0.262786i
$961$		−	30.4558i		−	0.982447i
$962$	−22.3044	−	22.3044i	−0.719124	−	0.719124i
$963$	−0.579658	−	0.579658i	−0.0186792	−	0.0186792i
$964$	9.64868	−	9.64868i	0.310763	−	0.310763i
$965$	1.75736			0.0565714
$966$	23.0698	−	23.0698i	0.742258	−	0.742258i
$967$		−	43.6569i		−	1.40391i	−0.712221	−	0.701955i	$-0.752311\pi$
$967$		−	43.6569i		−	1.40391i	0.712221	−	0.701955i	$-0.247689\pi$
$968$	−18.4142			−0.591855
$969$		0			0
$970$	19.0711			0.612335
$971$			51.7401i			1.66042i	0.557451	+	0.830210i	$0.311779\pi$
$971$			51.7401i			1.66042i	−0.557451	+	0.830210i	$0.688221\pi$
$972$	41.9413	−	41.9413i	1.34527	−	1.34527i
$973$	−55.7990			−1.78883
$974$	44.9259	−	44.9259i	1.43952	−	1.43952i
$975$	−4.77791	−	4.77791i	−0.153016	−	0.153016i
$976$	−8.11794	−	8.11794i	−0.259849	−	0.259849i
$977$			38.3848i			1.22804i	0.789291	+	0.614019i	$0.210448\pi$
$977$			38.3848i			1.22804i	−0.789291	+	0.614019i	$0.789552\pi$
$978$		−	22.1421i		−	0.708027i
$979$	−12.1689	−	12.1689i	−0.388921	−	0.388921i
$980$	0.355487	+	0.355487i	0.0113556	+	0.0113556i
$981$	20.1012	−	20.1012i	0.641781	−	0.641781i
$982$	−89.5980			−2.85919
$983$	−6.88830	+	6.88830i	−0.219703	+	0.219703i	−0.808373	−	0.588670i	$-0.799652\pi$
$983$	−6.88830	+	6.88830i	−0.219703	+	0.219703i	0.588670	+	0.808373i	$0.299652\pi$
$984$			5.79899i			0.184865i
$985$	−3.55635			−0.113315
$986$		0			0
$987$	−14.6274			−0.465596
$988$		−	4.48528i		−	0.142696i
$989$	−2.79884	+	2.79884i	−0.0889978	+	0.0889978i
$990$	−8.82843			−0.280586
$991$	−28.8757	+	28.8757i	−0.917267	+	0.917267i	−0.996830	−	0.0795630i	$-0.974648\pi$
$991$	−28.8757	+	28.8757i	−0.917267	+	0.917267i	0.0795630	+	0.996830i	$0.474648\pi$
$992$	−8.79045	−	8.79045i	−0.279097	−	0.279097i
$993$	16.6842	+	16.6842i	0.529458	+	0.529458i
$994$		−	34.1421i		−	1.08292i
$995$		−	8.82843i		−	0.279880i
$996$	−34.1563	−	34.1563i	−1.08229	−	1.08229i
$997$	5.31911	+	5.31911i	0.168458	+	0.168458i	0.786301	−	0.617843i	$-0.211993\pi$
$997$	5.31911	+	5.31911i	0.168458	+	0.168458i	−0.617843	+	0.786301i	$0.711993\pi$
$998$	36.6382	−	36.6382i	1.15976	−	1.15976i
$999$	48.2843			1.52765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.c.38.4		8
17.2	even	8		289.2.b.b.288.1		4
17.3	odd	16		289.2.d.c.155.1		4
17.4	even	4	inner	289.2.c.c.251.1		8
17.5	odd	16		17.2.d.a.15.1	yes	4
17.6	odd	16		17.2.d.a.8.1	✓	4
17.7	odd	16		289.2.d.b.179.1		4
17.8	even	8		289.2.a.f.1.3		4
17.9	even	8		289.2.a.f.1.4		4
17.10	odd	16		289.2.d.c.179.1		4
17.11	odd	16		289.2.d.a.110.1		4
17.12	odd	16		289.2.d.a.134.1		4
17.13	even	4	inner	289.2.c.c.251.2		8
17.14	odd	16		289.2.d.b.155.1		4
17.15	even	8		289.2.b.b.288.2		4
17.16	even	2	inner	289.2.c.c.38.3		8
51.5	even	16		153.2.l.c.100.1		4
51.8	odd	8		2601.2.a.bb.1.1		4
51.23	even	16		153.2.l.c.127.1		4
51.26	odd	8		2601.2.a.bb.1.2		4
68.23	even	16		272.2.v.d.161.1		4
68.39	even	16		272.2.v.d.49.1		4
68.43	odd	8		4624.2.a.bp.1.2		4
68.59	odd	8		4624.2.a.bp.1.3		4
85.9	even	8		7225.2.a.u.1.1		4
85.22	even	16		425.2.n.b.49.1		4
85.23	even	16		425.2.n.b.399.1		4
85.39	odd	16		425.2.m.a.151.1		4
85.57	even	16		425.2.n.a.399.1		4
85.59	even	8		7225.2.a.u.1.2		4
85.73	even	16		425.2.n.a.49.1		4
85.74	odd	16		425.2.m.a.76.1		4
119.5	even	48		833.2.v.a.508.1		8
119.6	even	16		833.2.l.a.246.1		4
119.23	odd	48		833.2.v.b.263.1		8
119.39	odd	48		833.2.v.b.814.1		8
119.40	even	48		833.2.v.a.263.1		8
119.73	even	48		833.2.v.a.814.1		8
119.74	odd	48		833.2.v.b.569.1		8
119.90	even	16		833.2.l.a.491.1		4
119.107	odd	48		833.2.v.b.508.1		8
119.108	even	48		833.2.v.a.569.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	17.6	odd	16
17.2.d.a.15.1	yes	4	17.5	odd	16
153.2.l.c.100.1		4	51.5	even	16
153.2.l.c.127.1		4	51.23	even	16
272.2.v.d.49.1		4	68.39	even	16
272.2.v.d.161.1		4	68.23	even	16
289.2.a.f.1.3		4	17.8	even	8
289.2.a.f.1.4		4	17.9	even	8
289.2.b.b.288.1		4	17.2	even	8
289.2.b.b.288.2		4	17.15	even	8
289.2.c.c.38.3		8	17.16	even	2	inner
289.2.c.c.38.4		8	1.1	even	1	trivial
289.2.c.c.251.1		8	17.4	even	4	inner
289.2.c.c.251.2		8	17.13	even	4	inner
289.2.d.a.110.1		4	17.11	odd	16
289.2.d.a.134.1		4	17.12	odd	16
289.2.d.b.155.1		4	17.14	odd	16
289.2.d.b.179.1		4	17.7	odd	16
289.2.d.c.155.1		4	17.3	odd	16
289.2.d.c.179.1		4	17.10	odd	16
425.2.m.a.76.1		4	85.74	odd	16
425.2.m.a.151.1		4	85.39	odd	16
425.2.n.a.49.1		4	85.73	even	16
425.2.n.a.399.1		4	85.57	even	16
425.2.n.b.49.1		4	85.22	even	16
425.2.n.b.399.1		4	85.23	even	16
833.2.l.a.246.1		4	119.6	even	16
833.2.l.a.491.1		4	119.90	even	16
833.2.v.a.263.1		8	119.40	even	48
833.2.v.a.508.1		8	119.5	even	48
833.2.v.a.569.1		8	119.108	even	48
833.2.v.a.814.1		8	119.73	even	48
833.2.v.b.263.1		8	119.23	odd	48
833.2.v.b.508.1		8	119.107	odd	48
833.2.v.b.569.1		8	119.74	odd	48
833.2.v.b.814.1		8	119.39	odd	48
2601.2.a.bb.1.1		4	51.8	odd	8
2601.2.a.bb.1.2		4	51.26	odd	8
4624.2.a.bp.1.2		4	68.43	odd	8
4624.2.a.bp.1.3		4	68.59	odd	8
7225.2.a.u.1.1		4	85.9	even	8
7225.2.a.u.1.2		4	85.59	even	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.c (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.41421i q^{2} +(0.765367 - 0.765367i) q^{3} -3.82843 q^{4} +(0.541196 - 0.541196i) q^{5} +(1.84776 + 1.84776i) q^{6} +(1.84776 + 1.84776i) q^{7} -4.41421i q^{8} +1.82843i q^{9} +(1.30656 + 1.30656i) q^{10} +(1.84776 + 1.84776i) q^{11} +(-2.93015 + 2.93015i) q^{12} -1.41421 q^{13} +(-4.46088 + 4.46088i) q^{14} -0.828427i q^{15} +3.00000 q^{16} -4.41421 q^{18} -0.828427i q^{19} +(-2.07193 + 2.07193i) q^{20} +2.82843 q^{21} +(-4.46088 + 4.46088i) q^{22} +(-3.37849 - 3.37849i) q^{23} +(-3.37849 - 3.37849i) q^{24} +4.41421i q^{25} -3.41421i q^{26} +(3.69552 + 3.69552i) q^{27} +(-7.07401 - 7.07401i) q^{28} +(-0.224171 + 0.224171i) q^{29} +2.00000 q^{30} +(5.54328 - 5.54328i) q^{31} -1.58579i q^{32} +2.82843 q^{33} +2.00000 q^{35} -7.00000i q^{36} +(6.53281 - 6.53281i) q^{37} +2.00000 q^{38} +(-1.08239 + 1.08239i) q^{39} +(-2.38896 - 2.38896i) q^{40} +(-0.858221 - 0.858221i) q^{41} +6.82843i q^{42} -0.828427i q^{43} +(-7.07401 - 7.07401i) q^{44} +(0.989538 + 0.989538i) q^{45} +(8.15640 - 8.15640i) q^{46} -5.17157 q^{47} +(2.29610 - 2.29610i) q^{48} -0.171573i q^{49} -10.6569 q^{50} +5.41421 q^{52} +1.41421i q^{53} +(-8.92177 + 8.92177i) q^{54} +2.00000 q^{55} +(8.15640 - 8.15640i) q^{56} +(-0.634051 - 0.634051i) q^{57} +(-0.541196 - 0.541196i) q^{58} -6.00000i q^{59} +3.17157i q^{60} +(-2.70598 - 2.70598i) q^{61} +(13.3827 + 13.3827i) q^{62} +(-3.37849 + 3.37849i) q^{63} +9.82843 q^{64} +(-0.765367 + 0.765367i) q^{65} +6.82843i q^{66} -1.17157 q^{67} -5.17157 q^{69} +4.82843i q^{70} +(-3.82683 + 3.82683i) q^{71} +8.07107 q^{72} +(9.14594 - 9.14594i) q^{73} +(15.7716 + 15.7716i) q^{74} +(3.37849 + 3.37849i) q^{75} +3.17157i q^{76} +6.82843i q^{77} +(-2.61313 - 2.61313i) q^{78} +(-3.37849 - 3.37849i) q^{79} +(1.62359 - 1.62359i) q^{80} +0.171573 q^{81} +(2.07193 - 2.07193i) q^{82} +11.6569i q^{83} -10.8284 q^{84} +2.00000 q^{86} +0.343146i q^{87} +(8.15640 - 8.15640i) q^{88} -6.58579 q^{89} +(-2.38896 + 2.38896i) q^{90} +(-2.61313 - 2.61313i) q^{91} +(12.9343 + 12.9343i) q^{92} -8.48528i q^{93} -12.4853i q^{94} +(-0.448342 - 0.448342i) q^{95} +(-1.21371 - 1.21371i) q^{96} +(7.29818 - 7.29818i) q^{97} +0.414214 q^{98} +(-3.37849 + 3.37849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 24 q^{16} - 24 q^{18} + 16 q^{30} + 16 q^{35} + 16 q^{38} - 64 q^{47} - 40 q^{50} + 32 q^{52} + 16 q^{55} + 56 q^{64} - 32 q^{67} - 64 q^{69} + 8 q^{72} + 24 q^{81} - 64 q^{84} + 16 q^{86}+ \cdots - 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 + 24 * q^16 - 24 * q^18 + 16 * q^30 + 16 * q^35 + 16 * q^38 - 64 * q^47 - 40 * q^50 + 32 * q^52 + 16 * q^55 + 56 * q^64 - 32 * q^67 - 64 * q^69 + 8 * q^72 + 24 * q^81 - 64 * q^84 + 16 * q^86 - 64 * q^89 - 8 * q^98

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