LMFDB - Embedded newform 738.2.ba.c.503.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] 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("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,0,0,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$4$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			503.3
Character	$\chi$	$=$	738.503
Dual form			738.2.ba.c.179.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.156434 + 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(1.02120 + 0.520325i) q^{5} +(3.94156 - 0.946286i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.354169 + 1.09002i) q^{10} +(2.35154 - 2.75330i) q^{11} +(0.539975 + 0.881159i) q^{13} +(1.55123 + 3.74500i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-5.82843 + 0.458708i) q^{17} +(3.81951 - 6.23288i) q^{19} +(-1.13200 - 0.179292i) q^{20} +(3.08727 + 1.89188i) q^{22} +(-0.891840 - 0.647960i) q^{23} +(-2.16682 - 2.98238i) q^{25} +(-0.785839 + 0.671170i) q^{26} +(-3.45623 + 2.11798i) q^{28} +(5.68137 + 0.447134i) q^{29} +(9.29778 + 3.02103i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.36483 - 5.68492i) q^{34} +(4.51748 + 1.08455i) q^{35} +(1.87754 + 5.77846i) q^{37} +(6.75364 + 2.79745i) q^{38} -1.14611i q^{40} +(-3.92735 + 5.05727i) q^{41} +(-9.67201 + 1.53190i) q^{43} +(-1.38563 + 3.34521i) q^{44} +(0.500468 - 0.982224i) q^{46} +(-2.69563 + 11.2281i) q^{47} +(8.40342 - 4.28175i) q^{49} +(2.60669 - 2.60669i) q^{50} +(-0.785839 - 0.671170i) q^{52} +(-0.156540 + 1.98903i) q^{53} +(3.83400 - 1.58809i) q^{55} +(-2.63258 - 3.08235i) q^{56} +(0.447134 + 5.68137i) q^{58} +(-6.07134 + 8.35649i) q^{59} +(1.15060 - 7.26462i) q^{61} +(-1.52934 + 9.65590i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(0.0929308 + 1.18080i) q^{65} +(0.223375 + 0.261539i) q^{67} +(5.40142 - 2.23734i) q^{68} +(-0.364509 + 4.63153i) q^{70} +(2.82019 + 2.40867i) q^{71} +(7.82673 - 7.82673i) q^{73} +(-5.41361 + 2.75837i) q^{74} +(-1.70651 + 7.10811i) q^{76} +(6.66334 - 13.0775i) q^{77} +(-2.76569 + 6.67696i) q^{79} +(1.13200 - 0.179292i) q^{80} +(-5.60938 - 3.08786i) q^{82} -12.8601i q^{83} +(-6.19065 - 2.56425i) q^{85} +(-3.02607 - 9.31329i) q^{86} +(-3.52079 - 0.845267i) q^{88} +(-2.08562 - 8.68724i) q^{89} +(2.96217 + 2.96217i) q^{91} +(1.04842 + 0.340653i) q^{92} +(-11.5116 - 0.905980i) q^{94} +(7.14359 - 4.37760i) q^{95} +(-11.4307 + 9.76274i) q^{97} +(5.54362 + 7.63014i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{14} + 16 q^{16} - 16 q^{17} + 4 q^{19} - 4 q^{22} + 48 q^{23} + 40 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 40 q^{31} + 4 q^{34} - 52 q^{35} + 8 q^{37} + 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) $ 64 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^14 + 16 * q^16 - 16 * q^17 + 4 * q^19 - 4 * q^22 + 48 * q^23 + 40 * q^25 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 40 * q^31 + 4 * q^34 - 52 * q^35 + 8 * q^37 + 16 * q^38 + 12 * q^41 + 32 * q^43 - 4 * q^44 - 8 * q^47 + 48 * q^49 + 16 * q^50 - 20 * q^52 - 48 * q^53 - 36 * q^55 + 16 * q^56 - 20 * q^58 + 20 * q^59 + 24 * q^61 - 36 * q^62 + 60 * q^65 - 20 * q^67 + 12 * q^68 - 8 * q^70 - 8 * q^71 + 72 * q^73 - 12 * q^74 + 4 * q^76 - 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 - 32 * q^86 - 8 * q^88 + 84 * q^89 + 72 * q^91 + 12 * q^94 - 12 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$

Coefficient data

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

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

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

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$		0			0
$3$		0			0
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	1.02120	+	0.520325i	0.456693	+	0.232697i	0.667175	−	0.744901i	$-0.267503\pi$
$5$	1.02120	+	0.520325i	0.456693	+	0.232697i	−0.210482	+	0.977598i	$0.567503\pi$
$6$		0			0
$7$	3.94156	−	0.946286i	1.48977	−	0.357662i	0.594832	−	0.803850i	$-0.297219\pi$
$7$	3.94156	−	0.946286i	1.48977	−	0.357662i	0.894939	+	0.446188i	$0.147219\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$		0			0
$10$	−0.354169	+	1.09002i	−0.111998	+	0.344695i
$11$	2.35154	−	2.75330i	0.709017	−	0.830152i	−0.282617	−	0.959233i	$-0.591203\pi$
$11$	2.35154	−	2.75330i	0.709017	−	0.830152i	0.991634	+	0.129081i	$0.0412026\pi$
$12$		0			0
$13$	0.539975	+	0.881159i	0.149762	+	0.244389i	0.918720	−	0.394910i	$-0.129224\pi$
$13$	0.539975	+	0.881159i	0.149762	+	0.244389i	−0.768958	+	0.639300i	$0.779224\pi$
$14$	1.55123	+	3.74500i	0.414584	+	1.00089i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−5.82843	+	0.458708i	−1.41360	+	0.111253i	−0.762132	−	0.647421i	$-0.775847\pi$
$17$	−5.82843	+	0.458708i	−1.41360	+	0.111253i	−0.651470	+	0.758674i	$0.725847\pi$
$18$		0			0
$19$	3.81951	−	6.23288i	0.876256	−	1.42992i	−0.0264443	−	0.999650i	$-0.508418\pi$
$19$	3.81951	−	6.23288i	0.876256	−	1.42992i	0.902700	−	0.430270i	$-0.141582\pi$
$20$	−1.13200	−	0.179292i	−0.253124	−	0.0400909i
$21$		0			0
$22$	3.08727	+	1.89188i	0.658208	+	0.403350i
$23$	−0.891840	−	0.647960i	−0.185962	−	0.135109i	0.490910	−	0.871211i	$-0.336665\pi$
$23$	−0.891840	−	0.647960i	−0.185962	−	0.135109i	−0.676871	+	0.736102i	$0.736665\pi$
$24$		0			0
$25$	−2.16682	−	2.98238i	−0.433365	−	0.596475i
$26$	−0.785839	+	0.671170i	−0.154116	+	0.131627i
$27$		0			0
$28$	−3.45623	+	2.11798i	−0.653166	+	0.400261i
$29$	5.68137	+	0.447134i	1.05500	+	0.0830307i	0.594078	−	0.804408i	$-0.297517\pi$
$29$	5.68137	+	0.447134i	1.05500	+	0.0830307i	0.460927	+	0.887438i	$0.347517\pi$
$30$		0			0
$31$	9.29778	+	3.02103i	1.66993	+	0.542593i	0.982917	−	0.184051i	$-0.0589210\pi$
$31$	9.29778	+	3.02103i	1.66993	+	0.542593i	0.687014	+	0.726644i	$0.258921\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−1.36483	−	5.68492i	−0.234066	−	0.974955i
$35$	4.51748	+	1.08455i	0.763594	+	0.183323i
$36$		0			0
$37$	1.87754	+	5.77846i	0.308665	+	0.949973i	0.978284	+	0.207268i	$0.0664574\pi$
$37$	1.87754	+	5.77846i	0.308665	+	0.949973i	−0.669619	+	0.742705i	$0.733543\pi$
$38$	6.75364	+	2.79745i	1.09559	+	0.453806i
$39$		0			0
$40$		−	1.14611i		−	0.181217i
$41$	−3.92735	+	5.05727i	−0.613348	+	0.789812i
$41$	−3.92735	+	5.05727i	−0.613348	+	0.789812i
$42$		0			0
$43$	−9.67201	+	1.53190i	−1.47497	+	0.233612i	−0.841542	−	0.540191i	$-0.818352\pi$
$43$	−9.67201	+	1.53190i	−1.47497	+	0.233612i	−0.633426	+	0.773803i	$0.718352\pi$
$44$	−1.38563	+	3.34521i	−0.208892	+	0.504310i
$45$		0			0
$46$	0.500468	−	0.982224i	0.0737900	−	0.144821i
$47$	−2.69563	+	11.2281i	−0.393198	+	1.63779i	0.327724	+	0.944773i	$0.393718\pi$
$47$	−2.69563	+	11.2281i	−0.393198	+	1.63779i	−0.720923	+	0.693016i	$0.756282\pi$
$48$		0			0
$49$	8.40342	−	4.28175i	1.20049	−	0.611679i
$50$	2.60669	−	2.60669i	0.368642	−	0.368642i
$51$		0			0
$52$	−0.785839	−	0.671170i	−0.108976	−	0.0930746i
$53$	−0.156540	+	1.98903i	−0.0215024	+	0.273214i	0.976762	+	0.214326i	$0.0687555\pi$
$53$	−0.156540	+	1.98903i	−0.0215024	+	0.273214i	−0.998265	+	0.0588879i	$0.981245\pi$
$54$		0			0
$55$	3.83400	−	1.58809i	0.516976	−	0.214139i
$56$	−2.63258	−	3.08235i	−0.351793	−	0.411897i
$57$		0			0
$58$	0.447134	+	5.68137i	0.0587115	+	0.746001i
$59$	−6.07134	+	8.35649i	−0.790422	+	1.08792i	0.203634	+	0.979047i	$0.434725\pi$
$59$	−6.07134	+	8.35649i	−0.790422	+	1.08792i	−0.994055	+	0.108875i	$0.965275\pi$
$60$		0			0
$61$	1.15060	−	7.26462i	0.147320	−	0.930140i	−0.797683	−	0.603077i	$-0.793941\pi$
$61$	1.15060	−	7.26462i	0.147320	−	0.930140i	0.945003	−	0.327063i	$-0.106059\pi$
$62$	−1.52934	+	9.65590i	−0.194227	+	1.22630i
$63$		0			0
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	0.0929308	+	1.18080i	0.0115266	+	0.146460i
$66$		0			0
$67$	0.223375	+	0.261539i	0.0272897	+	0.0319521i	0.773883	−	0.633329i	$-0.218312\pi$
$67$	0.223375	+	0.261539i	0.0272897	+	0.0319521i	−0.746593	+	0.665281i	$0.768312\pi$
$68$	5.40142	−	2.23734i	0.655018	−	0.271318i
$69$		0			0
$70$	−0.364509	+	4.63153i	−0.0435672	+	0.553573i
$71$	2.82019	+	2.40867i	0.334694	+	0.285856i	0.800873	−	0.598835i	$-0.204369\pi$
$71$	2.82019	+	2.40867i	0.334694	+	0.285856i	−0.466178	+	0.884691i	$0.654369\pi$
$72$		0			0
$73$	7.82673	−	7.82673i	0.916050	−	0.916050i	−0.0806894	−	0.996739i	$-0.525712\pi$
$73$	7.82673	−	7.82673i	0.916050	−	0.916050i	0.996739	+	0.0806894i	$0.0257122\pi$
$74$	−5.41361	+	2.75837i	−0.629319	+	0.320654i
$75$		0			0
$76$	−1.70651	+	7.10811i	−0.195750	+	0.815356i
$77$	6.66334	−	13.0775i	0.759359	−	1.49033i
$78$		0			0
$79$	−2.76569	+	6.67696i	−0.311164	+	0.751217i	0.688498	+	0.725238i	$0.258270\pi$
$79$	−2.76569	+	6.67696i	−0.311164	+	0.751217i	−0.999662	+	0.0259788i	$0.991730\pi$
$80$	1.13200	−	0.179292i	0.126562	−	0.0200454i
$81$		0			0
$82$	−5.60938	−	3.08786i	−0.619452	−	0.340997i
$83$		−	12.8601i		−	1.41158i	−0.708420	−	0.705791i	$-0.750592\pi$
$83$		−	12.8601i		−	1.41158i	0.708420	−	0.705791i	$-0.249408\pi$
$84$		0			0
$85$	−6.19065	−	2.56425i	−0.671470	−	0.278132i
$86$	−3.02607	−	9.31329i	−0.326310	−	1.00428i
$87$		0			0
$88$	−3.52079	−	0.845267i	−0.375317	−	0.0901057i
$89$	−2.08562	−	8.68724i	−0.221075	−	0.920845i	−0.966992	−	0.254806i	$-0.917988\pi$
$89$	−2.08562	−	8.68724i	−0.221075	−	0.920845i	0.745917	−	0.666039i	$-0.232012\pi$
$90$		0			0
$91$	2.96217	+	2.96217i	0.310520	+	0.310520i
$92$	1.04842	+	0.340653i	0.109305	+	0.0355155i
$93$		0			0
$94$	−11.5116	−	0.905980i	−1.18733	−	0.0934447i
$95$	7.14359	−	4.37760i	0.732917	−	0.449132i
$96$		0			0
$97$	−11.4307	+	9.76274i	−1.16061	+	0.991256i	−0.160620	+	0.987016i	$0.551349\pi$
$97$	−11.4307	+	9.76274i	−1.16061	+	0.991256i	−0.999991	+	0.00423954i	$0.998651\pi$
$98$	5.54362	+	7.63014i	0.559991	+	0.770761i
$99$		0			0
$100$	2.98238	+	2.16682i	0.298238	+	0.216682i
$101$	−0.105344	−	0.0645549i	−0.0104821	−	0.00642345i	0.517248	−	0.855836i	$-0.326957\pi$
$101$	−0.105344	−	0.0645549i	−0.0104821	−	0.00642345i	−0.527730	+	0.849412i	$0.676957\pi$
$102$		0			0
$103$	−8.62748	−	1.36646i	−0.850090	−	0.134641i	−0.283837	−	0.958872i	$-0.591608\pi$
$103$	−8.62748	−	1.36646i	−0.850090	−	0.134641i	−0.566253	+	0.824231i	$0.691608\pi$
$104$	0.539975	−	0.881159i	0.0529489	−	0.0864047i
$105$		0			0
$106$	−1.98903	+	0.156540i	−0.193191	+	0.0152045i
$107$	−0.924438	+	0.671644i	−0.0893688	+	0.0649303i	−0.631572	−	0.775317i	$-0.717590\pi$
$107$	−0.924438	+	0.671644i	−0.0893688	+	0.0649303i	0.542204	+	0.840247i	$0.317590\pi$
$108$		0			0
$109$	4.19756	+	10.1338i	0.402053	+	0.970642i	0.987167	+	0.159691i	$0.0510498\pi$
$109$	4.19756	+	10.1338i	0.402053	+	0.970642i	−0.585114	+	0.810951i	$0.698950\pi$
$110$	2.16831	+	3.53836i	0.206740	+	0.337370i
$111$		0			0
$112$	2.63258	−	3.08235i	0.248755	−	0.291255i
$113$	1.41503	−	4.35501i	0.133115	−	0.409685i	−0.862177	−	0.506607i	$-0.830900\pi$
$113$	1.41503	−	4.35501i	0.133115	−	0.409685i	0.995292	+	0.0969215i	$0.0308996\pi$
$114$		0			0
$115$	−0.573594	−	1.12574i	−0.0534879	−	0.104976i
$116$	−5.54148	+	1.33039i	−0.514513	+	0.123524i
$117$		0			0
$118$	−9.20337	−	4.68935i	−0.847239	−	0.431690i
$119$	−22.5391	+	7.32339i	−2.06615	+	0.671334i
$120$		0			0
$121$	−0.330144	−	2.08445i	−0.0300131	−	0.189495i
$122$	7.35518			0.665907
$123$		0			0
$124$	−9.77627			−0.877935
$125$	−1.55740	−	9.83306i	−0.139298	−	0.879496i
$126$		0			0
$127$	−3.16855	+	1.02952i	−0.281163	+	0.0913556i	−0.446204	−	0.894931i	$-0.647224\pi$
$127$	−3.16855	+	1.02952i	−0.281163	+	0.0913556i	0.165041	+	0.986287i	$0.447224\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$		0			0
$130$	−1.15172	+	0.276504i	−0.101013	+	0.0242510i
$131$	−6.73569	−	13.2195i	−0.588500	−	1.15500i	−0.972769	−	0.231776i	$-0.925546\pi$
$131$	−6.73569	−	13.2195i	−0.588500	−	1.15500i	0.384269	−	0.923221i	$-0.374454\pi$
$132$		0			0
$133$	9.15677	−	28.1816i	0.793992	−	2.44366i
$134$	−0.223375	+	0.261539i	−0.0192967	+	0.0225935i
$135$		0			0
$136$	3.05476	+	4.98492i	0.261944	+	0.427454i
$137$	−4.94219	−	11.9315i	−0.422239	−	1.01938i	−0.981685	−	0.190509i	$-0.938986\pi$
$137$	−4.94219	−	11.9315i	−0.422239	−	1.01938i	0.559446	−	0.828867i	$-0.311014\pi$
$138$		0			0
$139$	−11.1387	+	8.09271i	−0.944769	+	0.686415i	−0.949564	−	0.313574i	$-0.898474\pi$
$139$	−11.1387	+	8.09271i	−0.944769	+	0.686415i	0.00479478	+	0.999989i	$0.498474\pi$
$140$	−4.63153	+	0.364509i	−0.391435	+	0.0308066i
$141$		0			0
$142$	−1.93784	+	3.16226i	−0.162620	+	0.265371i
$143$	3.69587	+	0.585368i	0.309064	+	0.0489510i
$144$		0			0
$145$	5.56914	+	3.41277i	0.462492	+	0.283415i
$146$	8.95474	+	6.50600i	0.741100	+	0.538441i
$147$		0			0
$148$	−3.57129	−	4.91545i	−0.293558	−	0.404048i
$149$	−2.35925	+	2.01499i	−0.193277	+	0.165074i	−0.740820	−	0.671703i	$-0.765563\pi$
$149$	−2.35925	+	2.01499i	−0.193277	+	0.165074i	0.547544	+	0.836777i	$0.315563\pi$
$150$		0			0
$151$	5.54239	−	3.39638i	0.451033	−	0.276394i	−0.278375	−	0.960473i	$-0.589796\pi$
$151$	5.54239	−	3.39638i	0.451033	−	0.276394i	0.729408	+	0.684079i	$0.239796\pi$
$152$	−7.28756	−	0.573543i	−0.591099	−	0.0465205i
$153$		0			0
$154$	13.9589	+	4.53553i	1.12484	+	0.365483i
$155$	7.92294	+	7.92294i	0.636385	+	0.636385i
$156$		0			0
$157$	−0.192522	−	0.801912i	−0.0153649	−	0.0639995i	0.964161	−	0.265319i	$-0.0854772\pi$
$157$	−0.192522	−	0.801912i	−0.0153649	−	0.0639995i	−0.979526	+	0.201319i	$0.935477\pi$
$158$	−7.02740	−	1.68713i	−0.559070	−	0.134221i
$159$		0			0
$160$	0.354169	+	1.09002i	0.0279995	+	0.0861736i
$161$	−4.12840	−	1.71004i	−0.325364	−	0.134770i
$162$		0			0
$163$			17.2108i			1.34805i	0.738707	+	0.674027i	$0.235437\pi$
$163$			17.2108i			1.34805i	−0.738707	+	0.674027i	$0.764563\pi$
$164$	2.17235	−	6.02336i	0.169632	−	0.470346i
$165$		0			0
$166$	12.7018	−	2.01177i	0.985850	−	0.156143i
$167$	4.86438	−	11.7437i	0.376417	−	0.908752i	−0.616214	−	0.787579i	$-0.711334\pi$
$167$	4.86438	−	11.7437i	0.376417	−	0.908752i	0.992631	−	0.121173i	$-0.0386656\pi$
$168$		0			0
$169$	5.41701	−	10.6315i	0.416693	−	0.817806i
$170$	1.56425	−	6.51557i	0.119972	−	0.499721i
$171$		0			0
$172$	8.72525	−	4.44574i	0.665294	−	0.338984i
$173$	−7.84430	+	7.84430i	−0.596391	+	0.596391i	−0.939350	−	0.342959i	$-0.888571\pi$
$173$	−7.84430	+	7.84430i	−0.596391	+	0.596391i	0.342959	+	0.939350i	$0.388571\pi$
$174$		0			0
$175$	−11.3629	−	9.70479i	−0.858951	−	0.733613i
$176$	0.284087	−	3.60967i	0.0214139	−	0.272089i
$177$		0			0
$178$	8.25402	−	3.41893i	0.618665	−	0.256259i
$179$	10.8319	+	12.6826i	0.809617	+	0.947939i	0.999426	−	0.0338817i	$-0.0107869\pi$
$179$	10.8319	+	12.6826i	0.809617	+	0.947939i	−0.189809	+	0.981821i	$0.560787\pi$
$180$		0			0
$181$	0.789838	+	10.0358i	0.0587082	+	0.745959i	0.953871	+	0.300218i	$0.0970595\pi$
$181$	0.789838	+	10.0358i	0.0587082	+	0.745959i	−0.895162	+	0.445740i	$0.852940\pi$
$182$	−2.46232	+	3.38909i	−0.182519	+	0.251216i
$183$		0			0
$184$	−0.172450	+	1.08880i	−0.0127131	+	0.0802676i
$185$	−1.08935	+	6.87787i	−0.0800904	+	0.505671i
$186$		0			0
$187$	−12.4428	+	17.1261i	−0.909911	+	1.25239i
$188$	−0.905980	−	11.5116i	−0.0660754	−	0.839567i
$189$		0			0
$190$	5.44121	+	6.37084i	0.394747	+	0.462189i
$191$	18.2427	−	7.55639i	1.32000	−	0.546761i	0.392213	−	0.919874i	$-0.371710\pi$
$191$	18.2427	−	7.55639i	1.32000	−	0.546761i	0.927786	+	0.373113i	$0.121710\pi$
$192$		0			0
$193$	1.33274	−	16.9341i	0.0959327	−	1.21894i	−0.740951	−	0.671559i	$-0.765625\pi$
$193$	1.33274	−	16.9341i	0.0959327	−	1.21894i	0.836883	−	0.547381i	$-0.184375\pi$
$194$	−11.4307	−	9.76274i	−0.820676	−	0.700924i
$195$		0			0
$196$	−6.66899	+	6.66899i	−0.476356	+	0.476356i
$197$	−14.6298	+	7.45426i	−1.04233	+	0.531094i	−0.889394	−	0.457142i	$-0.848873\pi$
$197$	−14.6298	+	7.45426i	−1.04233	+	0.531094i	−0.152937	+	0.988236i	$0.548873\pi$
$198$		0			0
$199$	−4.15650	+	17.3131i	−0.294646	+	1.22729i	0.606960	+	0.794733i	$0.292389\pi$
$199$	−4.15650	+	17.3131i	−0.294646	+	1.22729i	−0.901606	+	0.432558i	$0.857611\pi$
$200$	−1.67360	+	3.28463i	−0.118341	+	0.232258i
$201$		0			0
$202$	0.0472807	−	0.114146i	0.00332666	−	0.00803126i
$203$	22.8166	−	3.61380i	1.60141	−	0.253639i
$204$		0			0
$205$	−6.64201	+	3.12096i	−0.463898	+	0.217977i
$206$		−	8.73502i		−	0.608598i
$207$		0			0
$208$	0.954781	+	0.395483i	0.0662021	+	0.0274218i
$209$	−8.17925	−	25.1732i	−0.565771	−	1.74126i
$210$		0			0
$211$	−17.3634	−	4.16858i	−1.19535	−	0.286977i	−0.413532	−	0.910490i	$-0.635705\pi$
$211$	−17.3634	−	4.16858i	−1.19535	−	0.286977i	−0.781813	+	0.623512i	$0.785705\pi$
$212$	−0.465765	−	1.94005i	−0.0319889	−	0.133243i
$213$		0			0
$214$	−0.807989	−	0.807989i	−0.0552330	−	0.0552330i
$215$	−10.6741	−	3.46823i	−0.727968	−	0.236531i
$216$		0			0
$217$	39.5066	+	3.10923i	2.68188	+	0.211068i
$218$	−9.35239	+	5.73115i	−0.633424	+	0.388163i
$219$		0			0
$220$	−3.15560	+	2.69514i	−0.212751	+	0.181706i
$221$	−3.55140	−	4.88808i	−0.238893	−	0.328808i
$222$		0			0
$223$	−20.4316	−	14.8444i	−1.36820	−	0.994058i	−0.997875	−	0.0651564i	$-0.979245\pi$
$223$	−20.4316	−	14.8444i	−1.36820	−	0.994058i	−0.370328	−	0.928901i	$-0.620755\pi$
$224$	3.45623	+	2.11798i	0.230929	+	0.141514i
$225$		0			0
$226$	4.52276	+	0.716334i	0.300849	+	0.0476498i
$227$	−0.150402	+	0.245434i	−0.00998254	+	0.0162900i	−0.857593	−	0.514330i	$-0.828041\pi$
$227$	−0.150402	+	0.245434i	−0.00998254	+	0.0162900i	0.847610	+	0.530620i	$0.178041\pi$
$228$		0			0
$229$	−3.80872	+	0.299753i	−0.251687	+	0.0198082i	−0.203675	−	0.979039i	$-0.565289\pi$
$229$	−3.80872	+	0.299753i	−0.251687	+	0.0198082i	−0.0480121	+	0.998847i	$0.515289\pi$
$230$	1.02215	−	0.742636i	0.0673987	−	0.0489680i
$231$		0			0
$232$	−2.18089	−	5.26514i	−0.143182	−	0.345673i
$233$	−11.3962	−	18.5969i	−0.746589	−	1.21832i	−0.969883	−	0.243572i	$-0.921681\pi$
$233$	−11.3962	−	18.5969i	−0.746589	−	1.21832i	0.223293	−	0.974751i	$-0.428319\pi$
$234$		0			0
$235$	−8.59504	+	10.0635i	−0.560679	+	0.656470i
$236$	3.19189	−	9.82364i	0.207775	−	0.639465i
$237$		0			0
$238$	−10.7591	−	21.1159i	−0.697410	−	1.36874i
$239$	4.77537	−	1.14647i	0.308893	−	0.0741587i	−0.0760352	−	0.997105i	$-0.524226\pi$
$239$	4.77537	−	1.14647i	0.308893	−	0.0741587i	0.384928	+	0.922946i	$0.374226\pi$
$240$		0			0
$241$	−6.53500	−	3.32975i	−0.420956	−	0.214488i	0.230664	−	0.973034i	$-0.425910\pi$
$241$	−6.53500	−	3.32975i	−0.420956	−	0.214488i	−0.651620	+	0.758546i	$0.725910\pi$
$242$	2.00714	−	0.652160i	0.129024	−	0.0419224i
$243$		0			0
$244$	1.15060	+	7.26462i	0.0736598	+	0.465070i
$245$	10.8094			0.690590
$246$		0			0
$247$	7.55459			0.480687
$248$	−1.52934	−	9.65590i	−0.0971135	−	0.613151i
$249$		0			0
$250$	9.46837	−	3.07646i	0.598832	−	0.194572i
$251$	14.5763	+	7.42699i	0.920047	+	0.468787i	0.848825	−	0.528673i	$-0.177310\pi$
$251$	14.5763	+	7.42699i	0.920047	+	0.468787i	0.0712212	+	0.997461i	$0.477310\pi$
$252$		0			0
$253$	−3.88123	+	0.931801i	−0.244011	+	0.0585818i
$254$	−1.51252	−	2.96849i	−0.0949040	−	0.186260i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.73991	+	9.06228i	−0.482803	+	0.565289i	−0.947326	−	0.320272i	$-0.896226\pi$
$257$	−7.73991	+	9.06228i	−0.482803	+	0.565289i	0.464523	+	0.885561i	$0.346226\pi$
$258$		0			0
$259$	12.8685	+	20.9995i	0.799610	+	1.30484i
$260$	−0.453269	−	1.09429i	−0.0281106	−	0.0678649i
$261$		0			0
$262$	12.0031	−	8.72076i	0.741554	−	0.538770i
$263$	7.93495	−	0.624494i	0.489290	−	0.0385080i	0.168585	−	0.985687i	$-0.446080\pi$
$263$	7.93495	−	0.624494i	0.489290	−	0.0385080i	0.320705	+	0.947179i	$0.396080\pi$
$264$		0			0
$265$	−1.19480	+	1.94973i	−0.0733959	+	0.119771i
$266$	29.2671	+	4.63545i	1.79448	+	0.284218i
$267$		0			0
$268$	−0.293263	−	0.179712i	−0.0179139	−	0.0109776i
$269$	11.1099	+	8.07183i	0.677384	+	0.492148i	0.872489	−	0.488634i	$-0.162505\pi$
$269$	11.1099	+	8.07183i	0.677384	+	0.492148i	−0.195105	+	0.980782i	$0.562505\pi$
$270$		0			0
$271$	−4.54279	−	6.25261i	−0.275955	−	0.379819i	0.648434	−	0.761271i	$-0.275424\pi$
$271$	−4.54279	−	6.25261i	−0.275955	−	0.379819i	−0.924389	+	0.381452i	$0.875424\pi$
$272$	−4.44568	+	3.79697i	−0.269559	+	0.230225i
$273$		0			0
$274$	11.0115	−	6.74784i	0.665227	−	0.407652i
$275$	−13.3068	−	1.04727i	−0.802428	−	0.0631525i
$276$		0			0
$277$	6.23588	+	2.02616i	0.374678	+	0.121740i	0.490301	−	0.871553i	$-0.336887\pi$
$277$	6.23588	+	2.02616i	0.374678	+	0.121740i	−0.115624	+	0.993293i	$0.536887\pi$
$278$	−9.73555	−	9.73555i	−0.583899	−	0.583899i
$279$		0			0
$280$	−1.08455	−	4.51748i	−0.0648144	−	0.269971i
$281$	−14.0867	−	3.38192i	−0.840342	−	0.201748i	−0.209645	−	0.977778i	$-0.567231\pi$
$281$	−14.0867	−	3.38192i	−0.840342	−	0.201748i	−0.630697	+	0.776029i	$0.717231\pi$
$282$		0			0
$283$	0.279578	+	0.860452i	0.0166192	+	0.0511486i	0.959022	−	0.283331i	$-0.0914395\pi$
$283$	0.279578	+	0.860452i	0.0166192	+	0.0511486i	−0.942403	+	0.334480i	$0.891439\pi$
$284$	−3.42647	−	1.41929i	−0.203324	−	0.0842195i
$285$		0			0
$286$			3.74194i			0.221266i
$287$	−10.6943	+	23.6499i	−0.631263	+	1.39601i
$288$		0			0
$289$	16.9695	−	2.68771i	0.998207	−	0.158100i
$290$	−2.49955	+	6.03445i	−0.146779	+	0.354355i
$291$		0			0
$292$	−5.02507	+	9.86226i	−0.294070	+	0.577145i
$293$	−5.75810	+	23.9842i	−0.336392	+	1.40117i	0.506106	+	0.862472i	$0.331085\pi$
$293$	−5.75810	+	23.9842i	−0.336392	+	1.40117i	−0.842497	+	0.538701i	$0.818915\pi$
$294$		0			0
$295$	−10.5481	+	5.37454i	−0.614135	+	0.312918i
$296$	4.29626	−	4.29626i	0.249715	−	0.249715i
$297$		0			0
$298$	−2.35925	−	2.01499i	−0.136667	−	0.116725i
$299$	0.0893843	−	1.13573i	0.00516923	−	0.0656812i
$300$		0			0
$301$	−36.6732	+	15.1906i	−2.11381	+	0.875569i
$302$	4.22159	+	4.94284i	0.242925	+	0.284429i
$303$		0			0
$304$	−0.573543	−	7.28756i	−0.0328950	−	0.417970i
$305$	4.95496	−	6.81992i	0.283720	−	0.390507i
$306$		0			0
$307$	2.08906	−	13.1898i	0.119229	−	0.752782i	−0.853544	−	0.521021i	$-0.825551\pi$
$307$	2.08906	−	13.1898i	0.119229	−	0.752782i	0.972773	−	0.231761i	$-0.0744487\pi$
$308$	−2.29603	+	14.4966i	−0.130829	+	0.826019i
$309$		0			0
$310$	−6.58597	+	9.06481i	−0.374058	+	0.514847i
$311$	0.921123	+	11.7040i	0.0522321	+	0.663672i	0.966185	+	0.257851i	$0.0830143\pi$
$311$	0.921123	+	11.7040i	0.0522321	+	0.663672i	−0.913953	+	0.405821i	$0.866986\pi$
$312$		0			0
$313$	1.03877	+	1.21624i	0.0587145	+	0.0687458i	0.788986	−	0.614411i	$-0.210606\pi$
$313$	1.03877	+	1.21624i	0.0587145	+	0.0687458i	−0.730271	+	0.683157i	$0.760606\pi$
$314$	0.761922	−	0.315598i	0.0429977	−	0.0178102i
$315$		0			0
$316$	0.567031	−	7.20481i	0.0318980	−	0.405302i
$317$	2.54153	+	2.17067i	0.142746	+	0.121917i	0.717954	−	0.696090i	$-0.245079\pi$
$317$	2.54153	+	2.17067i	0.142746	+	0.121917i	−0.575208	+	0.818007i	$0.695079\pi$
$318$		0			0
$319$	14.5911	−	14.5911i	0.816944	−	0.816944i
$320$	−1.02120	+	0.520325i	−0.0570866	+	0.0290871i
$321$		0			0
$322$	1.04316	−	4.34508i	0.0581331	−	0.242142i
$323$	−19.4027	+	38.0799i	−1.07960	+	2.11882i
$324$		0			0
$325$	1.45792	−	3.51972i	0.0808707	−	0.195239i
$326$	−16.9989	+	2.69236i	−0.941482	+	0.149116i
$327$		0			0
$328$	6.28904	+	1.20334i	0.347254	+	0.0664434i
$329$			46.8072i			2.58056i
$330$		0			0
$331$	−24.9722	−	10.3438i	−1.37260	−	0.568549i	−0.430106	−	0.902778i	$-0.641524\pi$
$331$	−24.9722	−	10.3438i	−1.37260	−	0.568549i	−0.942492	+	0.334230i	$0.891524\pi$
$332$	3.97400	+	12.2307i	0.218101	+	0.671247i
$333$		0			0
$334$	12.3600	+	2.96738i	0.676311	+	0.162368i
$335$	0.0920247	+	0.383310i	0.00502785	+	0.0209425i
$336$		0			0
$337$	7.01392	+	7.01392i	0.382073	+	0.382073i	0.871848	−	0.489776i	$-0.162921\pi$
$337$	7.01392	+	7.01392i	0.382073	+	0.382073i	−0.489776	+	0.871848i	$0.662921\pi$
$338$	11.3480	+	3.68719i	0.617249	+	0.200557i
$339$		0			0
$340$	6.68005	+	0.525732i	0.362277	+	0.0285118i
$341$	30.1820	−	18.4955i	1.63444	−	1.00159i
$342$		0			0
$343$	7.49436	−	6.40079i	0.404657	−	0.345610i
$344$	5.75593	+	7.92236i	0.310339	+	0.427145i
$345$		0			0
$346$	−8.97484	−	6.52060i	−0.482490	−	0.350550i
$347$	22.4676	+	13.7682i	1.20612	+	0.739114i	0.972430	−	0.233197i	$-0.0749185\pi$
$347$	22.4676	+	13.7682i	1.20612	+	0.739114i	0.233694	+	0.972310i	$0.424919\pi$
$348$		0			0
$349$	19.2100	+	3.04257i	1.02829	+	0.162865i	0.647713	−	0.761885i	$-0.275726\pi$
$349$	19.2100	+	3.04257i	1.02829	+	0.162865i	0.380576	+	0.924750i	$0.375726\pi$
$350$	7.80777	−	12.7411i	0.417343	−	0.681042i
$351$		0			0
$352$	3.60967	−	0.284087i	0.192396	−	0.0151419i
$353$	25.1588	−	18.2789i	1.33907	−	0.972889i	0.339588	−	0.940574i	$-0.389712\pi$
$353$	25.1588	−	18.2789i	1.33907	−	0.972889i	0.999478	−	0.0323144i	$-0.0102878\pi$
$354$		0			0
$355$	1.62667	+	3.92713i	0.0863348	+	0.208431i
$356$	4.66805	+	7.61756i	0.247406	+	0.403730i
$357$		0			0
$358$	−10.8319	+	12.6826i	−0.572485	+	0.670294i
$359$	−1.26525	+	3.89405i	−0.0667775	+	0.205520i	−0.978877	−	0.204448i	$-0.934460\pi$
$359$	−1.26525	+	3.89405i	−0.0667775	+	0.205520i	0.912100	+	0.409968i	$0.134460\pi$
$360$		0			0
$361$	−15.6343	−	30.6840i	−0.822856	−	1.61495i
$362$	−9.78873	+	2.35007i	−0.514484	+	0.123517i
$363$		0			0
$364$	−3.73255	−	1.90183i	−0.195639	−	0.0996831i
$365$	12.0651	−	3.92018i	0.631515	−	0.205192i
$366$		0			0
$367$	3.06408	+	19.3458i	0.159944	+	1.00984i	0.928843	+	0.370474i	$0.120805\pi$
$367$	3.06408	+	19.3458i	0.159944	+	1.00984i	−0.768899	+	0.639370i	$0.779195\pi$
$368$	−1.10238			−0.0574653
$369$		0			0
$370$	−6.96360			−0.362020
$371$	1.26518	+	7.98800i	0.0656846	+	0.414717i
$372$		0			0
$373$	−3.65279	+	1.18686i	−0.189134	+	0.0614535i	−0.402053	−	0.915616i	$-0.631703\pi$
$373$	−3.65279	+	1.18686i	−0.189134	+	0.0614535i	0.212918	+	0.977070i	$0.431703\pi$
$374$	−18.8618	−	9.61054i	−0.975318	−	0.496949i
$375$		0			0
$376$	11.2281	−	2.69563i	0.579046	−	0.139017i
$377$	2.67380	+	5.24763i	0.137708	+	0.270267i
$378$		0			0
$379$	−9.08124	+	27.9492i	−0.466472	+	1.43565i	0.390650	+	0.920539i	$0.372250\pi$
$379$	−9.08124	+	27.9492i	−0.466472	+	1.43565i	−0.857122	+	0.515114i	$0.827750\pi$
$380$	−5.44121	+	6.37084i	−0.279128	+	0.326817i
$381$		0			0
$382$	10.3172	+	16.8361i	0.527872	+	0.861408i
$383$	−5.76464	−	13.9171i	−0.294559	−	0.711129i	−0.999997	−	0.00235734i	$-0.999250\pi$
$383$	−5.76464	−	13.9171i	−0.294559	−	0.711129i	0.705438	−	0.708772i	$-0.250750\pi$
$384$		0			0
$385$	13.6092	−	9.88763i	0.693587	−	0.503920i
$386$	16.9341	−	1.33274i	0.861921	−	0.0678347i
$387$		0			0
$388$	7.85439	−	12.8172i	0.398746	−	0.650694i
$389$	−26.1126	−	4.13584i	−1.32396	−	0.209695i	−0.545884	−	0.837861i	$-0.683806\pi$
$389$	−26.1126	−	4.13584i	−1.32396	−	0.209695i	−0.778080	+	0.628166i	$0.783806\pi$
$390$		0			0
$391$	5.49526	+	3.36750i	0.277907	+	0.170302i
$392$	−7.63014	−	5.54362i	−0.385380	−	0.279995i
$393$		0			0
$394$	−9.65109	−	13.2836i	−0.486215	−	0.669217i
$395$	−6.29850	+	5.37943i	−0.316912	+	0.270668i
$396$		0			0
$397$	6.57589	−	4.02971i	0.330034	−	0.202245i	−0.347602	−	0.937642i	$-0.613004\pi$
$397$	6.57589	−	4.02971i	0.330034	−	0.202245i	0.677637	+	0.735397i	$0.263004\pi$
$398$	−17.7501	−	1.39697i	−0.889734	−	0.0700236i
$399$		0			0
$400$	−3.50599	−	1.13917i	−0.175300	−	0.0569583i
$401$	−5.54304	−	5.54304i	−0.276806	−	0.276806i	0.555027	−	0.831833i	$-0.312708\pi$
$401$	−5.54304	−	5.54304i	−0.276806	−	0.276806i	−0.831833	+	0.555027i	$0.812708\pi$
$402$		0			0
$403$	2.35856	+	9.82410i	0.117488	+	0.489373i
$404$	0.120137	+	0.0288423i	0.00597703	+	0.00143496i
$405$		0			0
$406$	7.13861	+	21.9704i	0.354283	+	1.09037i
$407$	20.3250	+	8.41887i	1.00747	+	0.417308i
$408$		0			0
$409$			4.08678i			0.202078i	0.994882	+	0.101039i	$0.0322167\pi$
$409$			4.08678i			0.202078i	−0.994882	+	0.101039i	$0.967783\pi$
$410$	−4.12158	−	6.07201i	−0.203550	−	0.299875i
$411$		0			0
$412$	8.62748	−	1.36646i	0.425045	−	0.0673206i
$413$	−16.0230	+	38.6828i	−0.788438	+	1.90346i
$414$		0			0
$415$	6.69145	−	13.1327i	0.328470	−	0.644659i
$416$	−0.241253	+	1.00489i	−0.0118284	+	0.0492689i
$417$		0			0
$418$	23.5837	−	12.0165i	1.15352	−	0.587746i
$419$	9.69760	−	9.69760i	0.473759	−	0.473759i	−0.429370	−	0.903129i	$-0.641264\pi$
$419$	9.69760	−	9.69760i	0.473759	−	0.473759i	0.903129	+	0.429370i	$0.141264\pi$
$420$		0			0
$421$	5.18184	+	4.42571i	0.252548	+	0.215696i	0.766705	−	0.642000i	$-0.221895\pi$
$421$	5.18184	+	4.42571i	0.252548	+	0.215696i	−0.514157	+	0.857696i	$0.671895\pi$
$422$	1.40103	−	17.8017i	0.0682009	−	0.866575i
$423$		0			0
$424$	1.84330	−	0.763521i	0.0895187	−	0.0370799i
$425$	13.9972	+	16.3886i	0.678965	+	0.794966i
$426$		0			0
$427$	−2.33923	−	29.7228i	−0.113203	−	1.43839i
$428$	0.671644	−	0.924438i	0.0324651	−	0.0446844i
$429$		0			0
$430$	1.75573	−	11.0852i	0.0846688	−	0.534578i
$431$	−1.00234	+	6.32853i	−0.0482811	+	0.304835i	−0.999998	−	0.00214331i	$-0.999318\pi$
$431$	−1.00234	+	6.32853i	−0.0482811	+	0.304835i	0.951717	+	0.306978i	$0.0993178\pi$
$432$		0			0
$433$	−10.6940	+	14.7191i	−0.513923	+	0.707354i	−0.984575	−	0.174965i	$-0.944019\pi$
$433$	−10.6940	+	14.7191i	−0.513923	+	0.707354i	0.470652	+	0.882319i	$0.344019\pi$
$434$	3.10923	+	39.5066i	0.149248	+	1.89638i
$435$		0			0
$436$	−7.12363	−	8.34070i	−0.341160	−	0.399447i
$437$	−7.44505	+	3.08384i	−0.356145	+	0.147520i
$438$		0			0
$439$	−0.504774	+	6.41377i	−0.0240916	+	0.306112i	0.973052	+	0.230585i	$0.0740640\pi$
$439$	−0.504774	+	6.41377i	−0.0240916	+	0.306112i	−0.997144	+	0.0755273i	$0.975936\pi$
$440$	−3.15560	−	2.69514i	−0.150437	−	0.128486i
$441$		0			0
$442$	4.27234	−	4.27234i	0.203215	−	0.203215i
$443$	23.4040	−	11.9250i	1.11196	−	0.566572i	0.201217	−	0.979547i	$-0.435510\pi$
$443$	23.4040	−	11.9250i	1.11196	−	0.566572i	0.910742	+	0.412975i	$0.135510\pi$
$444$		0			0
$445$	2.39036	−	9.95657i	0.113314	−	0.471987i
$446$	11.4655	−	22.5023i	0.542906	−	1.06551i
$447$		0			0
$448$	−1.55123	+	3.74500i	−0.0732888	+	0.176935i
$449$	20.8093	−	3.29587i	0.982052	−	0.155542i	0.355293	−	0.934755i	$-0.384381\pi$
$449$	20.8093	−	3.29587i	0.982052	−	0.155542i	0.626759	+	0.779213i	$0.284381\pi$
$450$		0			0
$451$	4.68886	+	22.7056i	0.220790	+	1.06916i
$452$			4.57913i			0.215384i
$453$		0			0
$454$	−0.265940	−	0.110156i	−0.0124812	−	0.00516988i
$455$	1.48366	+	4.56625i	0.0695553	+	0.214069i
$456$		0			0
$457$	−33.1569	−	7.96026i	−1.55101	−	0.372365i	−0.634678	−	0.772777i	$-0.718867\pi$
$457$	−33.1569	−	7.96026i	−1.55101	−	0.372365i	−0.916336	+	0.400411i	$0.868867\pi$
$458$	−0.891877	−	3.71494i	−0.0416747	−	0.173588i
$459$		0			0
$460$	0.893393	+	0.893393i	0.0416547	+	0.0416547i
$461$	−15.9609	−	5.18603i	−0.743376	−	0.241537i	−0.0872472	−	0.996187i	$-0.527807\pi$
$461$	−15.9609	−	5.18603i	−0.743376	−	0.241537i	−0.656128	+	0.754649i	$0.727807\pi$
$462$		0			0
$463$	0.284906	+	0.0224226i	0.0132407	+	0.00104207i	0.0850777	−	0.996374i	$-0.472886\pi$
$463$	0.284906	+	0.0224226i	0.0132407	+	0.00104207i	−0.0718370	+	0.997416i	$0.522886\pi$
$464$	4.85915	−	2.97769i	0.225580	−	0.138236i
$465$		0			0
$466$	16.5852	−	14.1651i	0.768294	−	0.656185i
$467$	−2.27480	−	3.13100i	−0.105265	−	0.144885i	0.753134	−	0.657867i	$-0.228541\pi$
$467$	−2.27480	−	3.13100i	−0.105265	−	0.144885i	−0.858400	+	0.512981i	$0.828541\pi$
$468$		0			0
$469$	1.12794	+	0.819496i	0.0520834	+	0.0378408i
$470$	−11.2842	−	6.91494i	−0.520499	−	0.318962i
$471$		0			0
$472$	10.2020	+	1.61584i	0.469586	+	0.0743751i
$473$	−18.5264	+	30.2323i	−0.851844	+	1.39008i
$474$		0			0
$475$	−26.8650	+	2.11432i	−1.23265	+	0.0970117i
$476$	19.1729	−	13.9299i	0.878787	−	0.638476i
$477$		0			0
$478$	1.87938	+	4.53723i	0.0859610	+	0.207528i
$479$	−7.47500	−	12.1981i	−0.341541	−	0.557345i	0.635044	−	0.772476i	$-0.280982\pi$
$479$	−7.47500	−	12.1981i	−0.341541	−	0.557345i	−0.976585	+	0.215131i	$0.930982\pi$
$480$		0			0
$481$	−4.07792	+	4.77463i	−0.185937	+	0.217704i
$482$	2.26646	−	6.97543i	0.103234	−	0.317722i
$483$		0			0
$484$	0.958116	+	1.88041i	0.0435507	+	0.0854732i
$485$	−16.7528	+	4.02199i	−0.760704	+	0.182629i
$486$		0			0
$487$	10.1121	+	5.15238i	0.458223	+	0.233476i	0.667837	−	0.744308i	$-0.267220\pi$
$487$	10.1121	+	5.15238i	0.458223	+	0.233476i	−0.209613	+	0.977784i	$0.567220\pi$
$488$	−6.99519	+	2.27288i	−0.316657	+	0.102888i
$489$		0			0
$490$	1.69097	+	10.6764i	0.0763902	+	0.482309i
$491$	22.4129			1.01148			0.505741	−	0.862686i	$-0.331219\pi$
$491$	22.4129			1.01148			0.505741	+	0.862686i	$0.331219\pi$
$492$		0			0
$493$	−33.3186			−1.50059
$494$	1.18180	+	7.46158i	0.0531716	+	0.335713i
$495$		0			0
$496$	9.29778	−	3.02103i	0.417483	−	0.135648i
$497$	13.3952	+	6.82521i	0.600858	+	0.306152i
$498$		0			0
$499$	19.5606	−	4.69608i	0.875651	−	0.210225i	0.229384	−	0.973336i	$-0.426329\pi$
$499$	19.5606	−	4.69608i	0.875651	−	0.210225i	0.646268	+	0.763111i	$0.276329\pi$
$500$	4.51976	+	8.87054i	0.202130	+	0.396702i
$501$		0			0
$502$	−5.05531	+	15.5587i	−0.225630	+	0.694417i
$503$	−15.2872	+	17.8990i	−0.681622	+	0.798077i	−0.988102	−	0.153800i	$-0.950849\pi$
$503$	−15.2872	+	17.8990i	−0.681622	+	0.798077i	0.306480	+	0.951877i	$0.400849\pi$
$504$		0			0
$505$	−0.0739873	−	0.120736i	−0.00329239	−	0.00537270i
$506$	−1.52749	−	3.68768i	−0.0679051	−	0.163937i
$507$		0			0
$508$	2.69533	−	1.95827i	0.119586	−	0.0868843i
$509$	27.3387	−	2.15161i	1.21177	−	0.0953682i	0.543578	−	0.839359i	$-0.317069\pi$
$509$	27.3387	−	2.15161i	1.21177	−	0.0953682i	0.668190	+	0.743990i	$0.267069\pi$
$510$		0			0
$511$	23.4432	−	38.2559i	1.03707	−	1.69234i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$		0			0
$514$	−10.1615	−	6.22697i	−0.448204	−	0.274660i
$515$	−8.09934	−	5.88451i	−0.356900	−	0.259303i
$516$		0			0
$517$	24.5755	+	33.8253i	1.08083	+	1.48763i
$518$	−18.7279	+	15.9951i	−0.822855	+	0.702785i
$519$		0			0
$520$	1.00991	−	0.618873i	0.0442874	−	0.0271394i
$521$	15.1086	+	1.18907i	0.661920	+	0.0520942i	0.404969	−	0.914330i	$-0.367282\pi$
$521$	15.1086	+	1.18907i	0.661920	+	0.0520942i	0.256951	+	0.966425i	$0.417282\pi$
$522$		0			0
$523$	38.9231	+	12.6469i	1.70199	+	0.553010i	0.988968	−	0.148132i	$-0.0473260\pi$
$523$	38.9231	+	12.6469i	1.70199	+	0.553010i	0.713022	+	0.701142i	$0.247326\pi$
$524$	10.4911	+	10.4911i	0.458305	+	0.458305i
$525$		0			0
$526$	1.85811	+	7.73957i	0.0810172	+	0.337461i
$527$	−55.5773	−	13.3429i	−2.42098	−	0.581227i
$528$		0			0
$529$	−6.73186	−	20.7185i	−0.292690	−	0.900806i
$530$	−2.11264	−	0.875083i	−0.0917671	−	0.0380112i
$531$		0			0
$532$			29.6319i			1.28471i
$533$	−6.57692	−	0.729819i	−0.284878	−	0.0316120i
$534$		0			0
$535$	−1.29351	+	0.204871i	−0.0559231	+	0.00885735i
$536$	0.131623	−	0.317765i	0.00568523	−	0.0137254i
$537$		0			0
$538$	−6.23448	+	12.2358i	−0.268787	+	0.527525i
$539$	7.97203	−	33.2059i	0.343380	−	1.43028i
$540$		0			0
$541$	24.3483	−	12.4061i	1.04681	−	0.533378i	0.156005	−	0.987756i	$-0.450138\pi$
$541$	24.3483	−	12.4061i	1.04681	−	0.533378i	0.890809	+	0.454378i	$0.150138\pi$
$542$	5.46499	−	5.46499i	0.234741	−	0.234741i
$543$		0			0
$544$	−4.44568	−	3.79697i	−0.190607	−	0.162794i
$545$	−0.986344	+	12.5327i	−0.0422503	+	0.536841i
$546$		0			0
$547$	16.3718	−	6.78142i	0.700008	−	0.289953i	−0.00415508	−	0.999991i	$-0.501323\pi$
$547$	16.3718	−	6.78142i	0.700008	−	0.289953i	0.704163	+	0.710039i	$0.251323\pi$
$548$	8.38733	+	9.82031i	0.358289	+	0.419503i
$549$		0			0
$550$	−1.04727	−	13.3068i	−0.0446555	−	0.567403i
$551$	24.4870	−	33.7035i	1.04318	−	1.43582i
$552$		0			0
$553$	−4.58282	+	28.9348i	−0.194881	+	1.23043i
$554$	−1.02571	+	6.47607i	−0.0435782	+	0.275142i
$555$		0			0
$556$	8.09271	−	11.1387i	0.343207	−	0.472385i
$557$	−1.28081	−	16.2742i	−0.0542696	−	0.689561i	−0.962533	−	0.271163i	$-0.912592\pi$
$557$	−1.28081	−	16.2742i	−0.0542696	−	0.689561i	0.908264	−	0.418398i	$-0.137408\pi$
$558$		0			0
$559$	−6.57249	−	7.69539i	−0.277987	−	0.325480i
$560$	4.29220	−	1.77789i	0.181379	−	0.0751295i
$561$		0			0
$562$	1.13663	−	14.4423i	0.0479460	−	0.609212i
$563$	−0.129985	−	0.111017i	−0.00547820	−	0.00467882i	0.646705	−	0.762740i	$-0.276147\pi$
$563$	−0.129985	−	0.111017i	−0.00547820	−	0.00467882i	−0.652183	+	0.758062i	$0.726147\pi$
$564$		0			0
$565$	3.71105	−	3.71105i	0.156125	−	0.156125i
$566$	−0.806123	+	0.410740i	−0.0338839	+	0.0172647i
$567$		0			0
$568$	0.865800	−	3.60631i	0.0363281	−	0.151318i
$569$	16.3958	−	32.1786i	0.687348	−	1.34900i	−0.238516	−	0.971139i	$-0.576661\pi$
$569$	16.3958	−	32.1786i	0.687348	−	1.34900i	0.925864	−	0.377857i	$-0.123339\pi$
$570$		0			0
$571$	−15.7371	+	37.9927i	−0.658576	+	1.58994i	0.141428	+	0.989949i	$0.454831\pi$
$571$	−15.7371	+	37.9927i	−0.658576	+	1.58994i	−0.800004	+	0.599994i	$0.795169\pi$
$572$	−3.69587	+	0.585368i	−0.154532	+	0.0244755i
$573$		0			0
$574$	−25.0317	−	6.86294i	−1.04480	−	0.286453i
$575$			4.06382i			0.169473i
$576$		0			0
$577$	−23.2459	−	9.62876i	−0.967739	−	0.400851i	−0.157869	−	0.987460i	$-0.550462\pi$
$577$	−23.2459	−	9.62876i	−0.967739	−	0.400851i	−0.809870	+	0.586609i	$0.800462\pi$
$578$	5.30923	+	16.3401i	0.220835	+	0.679660i
$579$		0			0
$580$	−6.35117	−	1.52478i	−0.263718	−	0.0633131i
$581$	−12.1693	−	50.6890i	−0.504870	−	2.10293i
$582$		0			0
$583$	5.10828	+	5.10828i	0.211563	+	0.211563i
$584$	−10.5269	−	3.42041i	−0.435608	−	0.141537i
$585$		0			0
$586$	−24.5897	−	1.93525i	−1.01579	−	0.0799444i
$587$	−21.2399	+	13.0158i	−0.876664	+	0.537220i	−0.886499	−	0.462731i	$-0.846869\pi$
$587$	−21.2399	+	13.0158i	−0.876664	+	0.537220i	0.00983478	+	0.999952i	$0.496869\pi$
$588$		0			0
$589$	54.3427	−	46.4131i	2.23915	−	1.91242i
$590$	−6.95846	−	9.57749i	−0.286475	−	0.394299i
$591$		0			0
$592$	4.91545	+	3.57129i	0.202024	+	0.146779i
$593$	−17.4100	−	10.6688i	−0.714942	−	0.438117i	0.116890	−	0.993145i	$-0.462708\pi$
$593$	−17.4100	−	10.6688i	−0.714942	−	0.438117i	−0.831832	+	0.555028i	$0.812708\pi$
$594$		0			0
$595$	−26.8273	−	4.24903i	−1.09981	−	0.174193i
$596$	1.62111	−	2.64541i	0.0664033	−	0.108360i
$597$		0			0
$598$	1.13573	−	0.0893843i	0.0464437	−	0.00365519i
$599$	−6.22315	+	4.52138i	−0.254271	+	0.184739i	−0.707618	−	0.706596i	$-0.750230\pi$
$599$	−6.22315	+	4.52138i	−0.254271	+	0.184739i	0.453346	+	0.891334i	$0.350230\pi$
$600$		0			0
$601$	−5.38186	−	12.9930i	−0.219530	−	0.529994i	0.775294	−	0.631600i	$-0.217602\pi$
$601$	−5.38186	−	12.9930i	−0.219530	−	0.529994i	−0.994825	+	0.101607i	$0.967602\pi$
$602$	−20.7405	−	33.8454i	−0.845319	−	1.37944i
$603$		0			0
$604$	−4.22159	+	4.94284i	−0.171774	+	0.201121i
$605$	0.747450	−	2.30041i	0.0303882	−	0.0935251i
$606$		0			0
$607$	−11.7522	−	23.0650i	−0.477008	−	0.936180i	−0.996649	−	0.0817959i	$-0.973934\pi$
$607$	−11.7522	−	23.0650i	−0.477008	−	0.936180i	0.519641	−	0.854384i	$-0.326066\pi$
$608$	7.10811	−	1.70651i	0.288272	−	0.0692080i
$609$		0			0
$610$	7.51108	+	3.82709i	0.304115	+	0.154954i
$611$	−11.3493	+	3.68762i	−0.459145	+	0.149185i
$612$		0			0
$613$	−1.34719	−	8.50582i	−0.0544125	−	0.343547i	−0.999843	−	0.0177229i	$-0.994358\pi$
$613$	−1.34719	−	8.50582i	−0.0544125	−	0.343547i	0.945430	−	0.325824i	$-0.105642\pi$
$614$	13.3542			0.538933
$615$		0			0
$616$	−14.6773			−0.591364
$617$	4.52096	+	28.5442i	0.182007	+	1.14915i	0.894367	+	0.447334i	$0.147626\pi$
$617$	4.52096	+	28.5442i	0.182007	+	1.14915i	−0.712360	+	0.701814i	$0.752374\pi$
$618$		0			0
$619$	−4.45505	+	1.44753i	−0.179064	+	0.0581813i	−0.397176	−	0.917742i	$-0.630010\pi$
$619$	−4.45505	+	1.44753i	−0.179064	+	0.0581813i	0.218113	+	0.975924i	$0.430010\pi$
$620$	−9.98348	−	5.08684i	−0.400946	−	0.204292i
$621$		0			0
$622$	−11.4158	+	2.74069i	−0.457731	+	0.109892i
$623$	−16.4412	−	32.2677i	−0.658703	−	1.29278i
$624$		0			0
$625$	−2.16986	+	6.67813i	−0.0867943	+	0.267125i
$626$	−1.03877	+	1.21624i	−0.0415174	+	0.0486106i
$627$		0			0
$628$	0.430904	+	0.703171i	0.0171949	+	0.0280596i
$629$	−13.5937	−	32.8181i	−0.542017	−	1.30854i
$630$		0			0
$631$	22.4927	−	16.3419i	0.895421	−	0.650562i	−0.0418647	−	0.999123i	$-0.513330\pi$
$631$	22.4927	−	16.3419i	0.895421	−	0.650562i	0.937286	+	0.348562i	$0.113330\pi$
$632$	7.20481	−	0.567031i	0.286592	−	0.0225553i
$633$		0			0
$634$	−1.74636	+	2.84980i	−0.0693569	+	0.113180i
$635$	−3.77140	−	0.597331i	−0.149663	−	0.0237044i
$636$		0			0
$637$	8.31054	+	5.09270i	0.329276	+	0.201780i
$638$	16.6940	+	12.1289i	0.660922	+	0.480188i
$639$		0			0
$640$	−0.673669	−	0.927226i	−0.0266291	−	0.0366518i
$641$	31.8036	−	27.1628i	1.25617	−	1.07287i	0.261993	−	0.965070i	$-0.415620\pi$
$641$	31.8036	−	27.1628i	1.25617	−	1.07287i	0.994173	−	0.107797i	$-0.0343797\pi$
$642$		0			0
$643$	−17.1495	+	10.5092i	−0.676310	+	0.414444i	−0.817805	−	0.575495i	$-0.804809\pi$
$643$	−17.1495	+	10.5092i	−0.676310	+	0.414444i	0.141494	+	0.989939i	$0.454809\pi$
$644$	4.45477	+	0.350598i	0.175543	+	0.0138155i
$645$		0			0
$646$	−40.6464	−	13.2068i	−1.59921	−	0.519615i
$647$	20.2146	+	20.2146i	0.794718	+	0.794718i	0.982257	−	0.187539i	$-0.0600512\pi$
$647$	20.2146	+	20.2146i	0.794718	+	0.794718i	−0.187539	+	0.982257i	$0.560051\pi$
$648$		0			0
$649$	8.73092	+	36.3669i	0.342719	+	1.42753i
$650$	3.70446	+	0.889362i	0.145301	+	0.0348836i
$651$		0			0
$652$	−5.31843	−	16.3684i	−0.208286	−	0.641038i
$653$	−41.8308	−	17.3269i	−1.63696	−	0.678053i	−0.640978	−	0.767559i	$-0.721471\pi$
$653$	−41.8308	−	17.3269i	−1.63696	−	0.678053i	−0.995986	+	0.0895066i	$0.971471\pi$
$654$		0			0
$655$		−	17.0045i		−	0.664420i
$656$	−0.204703	+	6.39985i	−0.00799232	+	0.249872i
$657$		0			0
$658$	−46.2309	+	7.32225i	−1.80227	+	0.285451i
$659$	−6.88701	+	16.6267i	−0.268280	+	0.647685i	−0.999403	−	0.0345612i	$-0.988997\pi$
$659$	−6.88701	+	16.6267i	−0.268280	+	0.647685i	0.731123	+	0.682246i	$0.238997\pi$
$660$		0			0
$661$	−3.84280	+	7.54191i	−0.149467	+	0.293346i	−0.953585	−	0.301124i	$-0.902638\pi$
$661$	−3.84280	+	7.54191i	−0.149467	+	0.293346i	0.804118	+	0.594470i	$0.202638\pi$
$662$	6.30997	−	26.2829i	0.245244	−	1.02151i
$663$		0			0
$664$	−11.4585	+	5.83837i	−0.444674	+	0.226573i
$665$	24.0145	−	24.0145i	0.931241	−	0.931241i
$666$		0			0
$667$	−4.77715	−	4.08007i	−0.184972	−	0.157981i
$668$	−0.997313	+	12.6721i	−0.0385872	+	0.490297i
$669$		0			0
$670$	−0.364195	+	0.150855i	−0.0140701	+	0.00582802i
$671$	−17.2960	−	20.2510i	−0.667705	−	0.781783i
$672$		0			0
$673$	3.02444	+	38.4292i	0.116584	+	1.48134i	0.725566	+	0.688153i	$0.241578\pi$
$673$	3.02444	+	38.4292i	0.116584	+	1.48134i	−0.608982	+	0.793184i	$0.708422\pi$
$674$	−5.83035	+	8.02479i	−0.224577	+	0.309103i
$675$		0			0
$676$	−1.86657	+	11.7851i	−0.0717913	+	0.453272i
$677$	−4.37692	+	27.6348i	−0.168219	+	1.06209i	0.748668	+	0.662945i	$0.230694\pi$
$677$	−4.37692	+	27.6348i	−0.168219	+	1.06209i	−0.916887	+	0.399147i	$0.869306\pi$
$678$		0			0
$679$	−35.8165	+	49.2971i	−1.37451	+	1.89185i
$680$	0.525732	+	6.68005i	0.0201609	+	0.256168i
$681$		0			0
$682$	22.9893	+	26.9170i	0.880306	+	1.03071i
$683$	−6.95480	+	2.88077i	−0.266118	+	0.110230i	−0.511753	−	0.859133i	$-0.671004\pi$
$683$	−6.95480	+	2.88077i	−0.266118	+	0.110230i	0.245635	+	0.969362i	$0.421004\pi$
$684$		0			0
$685$	1.16132	−	14.7559i	0.0443716	−	0.563795i
$686$	7.49436	+	6.40079i	0.286136	+	0.244383i
$687$		0			0
$688$	−6.92440	+	6.92440i	−0.263990	+	0.263990i
$689$	−1.83718	+	0.936088i	−0.0699908	+	0.0356621i
$690$		0			0
$691$	3.01251	−	12.5480i	0.114601	−	0.477349i	−0.885322	−	0.464978i	$-0.846062\pi$
$691$	3.01251	−	12.5480i	0.114601	−	0.477349i	0.999923	−	0.0123706i	$-0.00393778\pi$
$692$	5.03635	−	9.88439i	0.191453	−	0.375748i
$693$		0			0
$694$	−10.0839	+	24.3448i	−0.382781	+	0.924116i
$695$	−15.5856	+	2.46852i	−0.591195	+	0.0936362i
$696$		0			0
$697$	20.5705	−	31.2774i	0.779162	−	1.18472i
$698$			19.4495i			0.736174i
$699$		0			0
$700$	13.8057	+	5.71849i	0.521805	+	0.216139i
$701$	−11.8059	−	36.3347i	−0.445901	−	1.37234i	−0.881493	−	0.472198i	$-0.843461\pi$
$701$	−11.8059	−	36.3347i	−0.445901	−	1.37234i	0.435592	−	0.900144i	$-0.356539\pi$
$702$		0			0
$703$	43.1877	+	10.3685i	1.62886	+	0.391054i
$704$	0.845267	+	3.52079i	0.0318572	+	0.132695i
$705$		0			0
$706$	21.9896	+	21.9896i	0.827588	+	0.827588i
$707$	−0.476308	−	0.154762i	−0.0179134	−	0.00582041i
$708$		0			0
$709$	−11.5326	−	0.907637i	−0.433117	−	0.0340870i	−0.139973	−	0.990155i	$-0.544702\pi$
$709$	−11.5326	−	0.907637i	−0.433117	−	0.0340870i	−0.293144	+	0.956068i	$0.594702\pi$
$710$	−3.62432	+	2.22098i	−0.136018	+	0.0833520i
$711$		0			0
$712$	−6.79353	+	5.80222i	−0.254598	+	0.217448i
$713$	−6.33463	−	8.71887i	−0.237234	−	0.326524i
$714$		0			0
$715$	3.46963	+	2.52083i	0.129757	+	0.0942737i
$716$	−14.2209	−	8.71458i	−0.531460	−	0.325679i
$717$		0			0
$718$	−4.04404	−	0.640513i	−0.150922	−	0.0239037i
$719$	−13.2432	+	21.6110i	−0.493889	+	0.805954i	−0.998347	−	0.0574827i	$-0.981693\pi$
$719$	−13.2432	+	21.6110i	−0.493889	+	0.805954i	0.504457	+	0.863437i	$0.331693\pi$
$720$		0			0
$721$	−35.2988	+	2.77808i	−1.31460	+	0.103461i
$722$	27.8605	−	20.2418i	1.03686	−	0.753322i
$723$		0			0
$724$	−3.85243	−	9.30059i	−0.143174	−	0.345654i
$725$	−10.9770	−	17.9129i	−0.407676	−	0.665267i
$726$		0			0
$727$	−11.3480	+	13.2868i	−0.420874	+	0.492780i	−0.929818	−	0.368020i	$-0.880036\pi$
$727$	−11.3480	+	13.2868i	−0.420874	+	0.492780i	0.508944	+	0.860800i	$0.330036\pi$
$728$	1.29452	−	3.98411i	0.0479780	−	0.147661i
$729$		0			0
$730$	5.75931	+	11.3033i	0.213162	+	0.418353i
$731$	55.6700	−	13.3652i	2.05903	−	0.494329i
$732$		0			0
$733$	−1.86276	−	0.949125i	−0.0688027	−	0.0350567i	0.419251	−	0.907871i	$-0.362293\pi$
$733$	−1.86276	−	0.949125i	−0.0688027	−	0.0350567i	−0.488053	+	0.872814i	$0.662293\pi$
$734$	−18.6283	+	6.05271i	−0.687584	+	0.223410i
$735$		0			0
$736$	−0.172450	−	1.08880i	−0.00635657	−	0.0401338i
$737$	1.24537			0.0458739
$738$		0			0
$739$	−16.8125			−0.618457			−0.309228	−	0.950988i	$-0.600071\pi$
$739$	−16.8125			−0.618457			−0.309228	+	0.950988i	$0.600071\pi$
$740$	−1.08935	−	6.87787i	−0.0400452	−	0.252835i
$741$		0			0
$742$	−7.69174	+	2.49920i	−0.282373	+	0.0917485i
$743$	32.8476	+	16.7367i	1.20506	+	0.614010i	0.936979	−	0.349385i	$-0.113609\pi$
$743$	32.8476	+	16.7367i	1.20506	+	0.614010i	0.268084	+	0.963395i	$0.413609\pi$
$744$		0			0
$745$	−3.45770	+	0.830120i	−0.126680	+	0.0304132i
$746$	−1.74368	−	3.42216i	−0.0638405	−	0.125294i
$747$		0			0
$748$	6.54159	−	20.1330i	0.239184	−	0.736134i
$749$	−3.00817	+	3.52211i	−0.109916	+	0.128695i
$750$		0			0
$751$	−16.0999	−	26.2727i	−0.587495	−	0.958705i	−0.998883	−	0.0472446i	$-0.984956\pi$
$751$	−16.0999	−	26.2727i	−0.587495	−	0.958705i	0.411388	−	0.911460i	$-0.365044\pi$
$752$	4.41891	+	10.6682i	0.161141	+	0.389029i
$753$		0			0
$754$	−4.76475	+	3.46179i	−0.173522	+	0.126071i
$755$	7.42709	−	0.584524i	0.270299	−	0.0212730i
$756$		0			0
$757$	22.3211	−	36.4248i	0.811275	−	1.32388i	−0.131792	−	0.991277i	$-0.542073\pi$
$757$	22.3211	−	36.4248i	0.811275	−	1.32388i	0.943067	−	0.332603i	$-0.107927\pi$
$758$	−29.0257	−	4.59722i	−1.05426	−	0.166978i
$759$		0			0
$760$	−7.14359	−	4.37760i	−0.259125	−	0.158792i
$761$	1.71802	+	1.24822i	0.0622782	+	0.0452478i	0.618489	−	0.785794i	$-0.287745\pi$
$761$	1.71802	+	1.24822i	0.0622782	+	0.0452478i	−0.556211	+	0.831041i	$0.687745\pi$
$762$		0			0
$763$	26.1344	+	35.9709i	0.946129	+	1.30224i
$764$	−15.0148	+	12.8239i	−0.543218	+	0.463952i
$765$		0			0
$766$	12.8439	−	7.87078i	0.464070	−	0.284383i
$767$	−10.6418	−	0.837525i	−0.384252	−	0.0302413i
$768$		0			0
$769$	−9.87630	−	3.20900i	−0.356148	−	0.115720i	0.125478	−	0.992096i	$-0.459954\pi$
$769$	−9.87630	−	3.20900i	−0.356148	−	0.115720i	−0.481626	+	0.876377i	$0.659954\pi$
$770$	11.8948	+	11.8948i	0.428660	+	0.428660i
$771$		0			0
$772$	3.96540	+	16.5171i	0.142718	+	0.594463i
$773$	33.4580	+	8.03256i	1.20340	+	0.288911i	0.785084	−	0.619390i	$-0.212620\pi$
$773$	33.4580	+	8.03256i	1.20340	+	0.288911i	0.418317	+	0.908301i	$0.362620\pi$
$774$		0			0
$775$	−11.1368	−	34.2755i	−0.400046	−	1.23121i
$776$	13.8881	+	5.75264i	0.498553	+	0.206508i
$777$		0			0
$778$		−	26.4381i		−	0.947853i
$779$	16.5208	+	43.7950i	0.591918	+	1.56912i
$780$		0			0
$781$	13.2636	−	2.10074i	0.474608	−	0.0751705i
$782$	−2.46639	+	5.95439i	−0.0881979	+	0.212929i
$783$		0			0
$784$	4.28175	−	8.40342i	0.152920	−	0.300122i
$785$	0.220652	−	0.919083i	0.00787542	−	0.0328035i
$786$		0			0
$787$	−14.4610	+	7.36826i	−0.515480	+	0.262650i	−0.692322	−	0.721589i	$-0.743412\pi$
$787$	−14.4610	+	7.36826i	−0.515480	+	0.262650i	0.176842	+	0.984239i	$0.443412\pi$
$788$	11.6103	−	11.6103i	0.413599	−	0.413599i
$789$		0			0
$790$	−6.29850	−	5.37943i	−0.224091	−	0.191391i
$791$	1.45634	−	18.5046i	0.0517816	−	0.657947i
$792$		0			0
$793$	7.02258	−	2.90885i	0.249379	−	0.103296i
$794$	5.00879	+	5.86454i	0.177755	+	0.208125i
$795$		0			0
$796$	−1.39697	−	17.7501i	−0.0495142	−	0.629137i
$797$	−15.4487	+	21.2633i	−0.547222	+	0.753186i	−0.989632	−	0.143627i	$-0.954123\pi$
$797$	−15.4487	+	21.2633i	−0.547222	+	0.753186i	0.442410	+	0.896813i	$0.354123\pi$
$798$		0			0
$799$	10.5609	−	66.6788i	0.373617	−	2.35893i
$800$	0.576683	−	3.64104i	0.0203888	−	0.128730i
$801$		0			0
$802$	4.60767	−	6.34192i	0.162703	−	0.223941i
$803$	−3.14447	−	39.9543i	−0.110966	−	1.40996i
$804$		0			0
$805$	−3.32613	−	3.89440i	−0.117231	−	0.137259i
$806$	−9.33419	+	3.86635i	−0.328783	+	0.136186i
$807$		0			0
$808$	−0.00969365	+	0.123170i	−0.000341022	+	0.00433309i
$809$	−30.6091	−	26.1426i	−1.07616	−	0.919126i	−0.0791842	−	0.996860i	$-0.525232\pi$
$809$	−30.6091	−	26.1426i	−1.07616	−	0.919126i	−0.996974	+	0.0777339i	$0.975232\pi$
$810$		0			0
$811$	−39.5075	+	39.5075i	−1.38729	+	1.38729i	−0.556340	+	0.830955i	$0.687795\pi$
$811$	−39.5075	+	39.5075i	−1.38729	+	1.38729i	−0.830955	+	0.556340i	$0.812205\pi$
$812$	−20.5832	+	10.4876i	−0.722327	+	0.368044i
$813$		0			0
$814$	−5.13570	+	21.3917i	−0.180006	+	0.749780i
$815$	−8.95521	+	17.5756i	−0.313687	+	0.615646i
$816$		0			0
$817$	−27.3943	+	66.1356i	−0.958404	+	2.31379i
$818$	−4.03646	+	0.639312i	−0.141132	+	0.0223530i
$819$		0			0
$820$	5.35250	−	5.02071i	0.186917	−	0.175331i
$821$		−	24.9218i		−	0.869778i	−0.900484	−	0.434889i	$-0.856788\pi$
$821$		−	24.9218i		−	0.869778i	0.900484	−	0.434889i	$-0.143212\pi$
$822$		0			0
$823$	40.8105	+	16.9043i	1.42257	+	0.589246i	0.955504	−	0.294979i	$-0.0953126\pi$
$823$	40.8105	+	16.9043i	1.42257	+	0.589246i	0.467062	+	0.884225i	$0.345313\pi$
$824$	2.69927	+	8.30750i	0.0940335	+	0.289405i
$825$		0			0
$826$	−40.7131	−	9.77436i	−1.41659	−	0.340093i
$827$	6.68016	+	27.8249i	0.232292	+	0.967565i	0.959625	+	0.281281i	$0.0907593\pi$
$827$	6.68016	+	27.8249i	0.232292	+	0.967565i	−0.727334	+	0.686284i	$0.759241\pi$
$828$		0			0
$829$	25.2878	+	25.2878i	0.878280	+	0.878280i	0.993357	−	0.115076i	$-0.0367112\pi$
$829$	25.2878	+	25.2878i	0.878280	+	0.878280i	−0.115076	+	0.993357i	$0.536711\pi$
$830$	14.0178	+	4.55466i	0.486565	+	0.158094i
$831$		0			0
$832$	−1.03026	−	0.0810833i	−0.0357179	−	0.00281106i
$833$	−47.0147	+	28.8106i	−1.62896	+	0.998229i
$834$		0			0
$835$	11.0780	−	9.46152i	0.383370	−	0.327429i
$836$	15.5579	+	21.4136i	0.538080	+	0.740604i
$837$		0			0
$838$	11.0952	+	8.06117i	0.383279	+	0.278468i
$839$	−41.7031	−	25.5557i	−1.43975	−	0.882281i	−0.439876	−	0.898058i	$-0.644978\pi$
$839$	−41.7031	−	25.5557i	−1.43975	−	0.882281i	−0.999876	+	0.0157774i	$0.994978\pi$
$840$		0			0
$841$	3.43512	+	0.544069i	0.118452	+	0.0187610i
$842$	−3.56060	+	5.81038i	−0.122707	+	0.200239i
$843$		0			0
$844$	17.8017	−	1.40103i	0.612761	−	0.0482253i
$845$	11.0637	−	8.03821i	0.380601	−	0.276523i
$846$		0			0
$847$	−3.27377	−	7.90358i	−0.112488	−	0.271570i
$848$	1.04248	+	1.70117i	0.0357988	+	0.0584183i
$849$		0			0
$850$	−13.9972	+	16.3886i	−0.480101	+	0.562126i
$851$	2.06975	−	6.37003i	0.0709501	−	0.218362i
$852$		0			0
$853$	−23.6622	−	46.4396i	−0.810177	−	1.59006i	−0.807355	−	0.590066i	$-0.799102\pi$
$853$	−23.6622	−	46.4396i	−0.810177	−	1.59006i	−0.00282162	−	0.999996i	$-0.500898\pi$
$854$	28.9909	−	6.96010i	0.992048	−	0.238170i
$855$		0			0
$856$	1.01813	+	0.518761i	0.0347988	+	0.0177309i
$857$	−29.7842	+	9.67747i	−1.01741	+	0.330576i	−0.769801	−	0.638284i	$-0.779645\pi$
$857$	−29.7842	+	9.67747i	−1.01741	+	0.330576i	−0.247608	+	0.968860i	$0.579645\pi$
$858$		0			0
$859$	2.59112	+	16.3597i	0.0884079	+	0.558186i	0.991640	+	0.129034i	$0.0411875\pi$
$859$	2.59112	+	16.3597i	0.0884079	+	0.558186i	−0.903232	+	0.429152i	$0.858812\pi$
$860$	11.2234			0.382715
$861$		0			0
$862$	−6.40742			−0.218237
$863$	−6.43147	−	40.6067i	−0.218930	−	1.38227i	−0.815058	−	0.579379i	$-0.803295\pi$
$863$	−6.43147	−	40.6067i	−0.218930	−	1.38227i	0.596128	−	0.802889i	$-0.296705\pi$
$864$		0			0
$865$	−12.0921	+	3.92898i	−0.411145	+	0.133589i
$866$	−16.2108	−	8.25981i	−0.550865	−	0.280680i
$867$		0			0
$868$	−38.5338	+	9.25114i	−1.30792	+	0.314004i
$869$	11.8801	+	23.3159i	0.403004	+	0.790939i
$870$		0			0
$871$	−0.109840	+	0.338054i	−0.00372180	+	0.0114545i
$872$	7.12363	−	8.34070i	0.241237	−	0.282452i
$873$		0			0
$874$	−4.21054	−	6.87097i	−0.142423	−	0.232414i
$875$	−15.4435	−	37.2839i	−0.522085	−	1.26043i
$876$		0			0
$877$	−24.8667	+	18.0667i	−0.839688	+	0.610069i	−0.922283	−	0.386514i	$-0.873679\pi$
$877$	−24.8667	+	18.0667i	−0.839688	+	0.610069i	0.0825957	+	0.996583i	$0.473679\pi$
$878$	−6.41377	+	0.504774i	−0.216454	+	0.0170353i
$879$		0			0
$880$	2.16831	−	3.53836i	0.0730938	−	0.119278i
$881$	30.6211	+	4.84990i	1.03165	+	0.163397i	0.649231	−	0.760592i	$-0.275091\pi$
$881$	30.6211	+	4.84990i	1.03165	+	0.163397i	0.382419	+	0.923989i	$0.375091\pi$
$882$		0			0
$883$	−13.4552	−	8.24534i	−0.452802	−	0.277478i	0.277341	−	0.960772i	$-0.410547\pi$
$883$	−13.4552	−	8.24534i	−0.452802	−	0.277478i	−0.730143	+	0.683294i	$0.760547\pi$
$884$	4.88808	+	3.55140i	0.164404	+	0.119447i
$885$		0			0
$886$	15.4393	+	21.2504i	0.518695	+	0.713922i
$887$	−22.5931	+	19.2963i	−0.758601	+	0.647906i	−0.942183	−	0.335098i	$-0.891231\pi$
$887$	−22.5931	+	19.2963i	−0.758601	+	0.647906i	0.183582	+	0.983004i	$0.441231\pi$
$888$		0			0
$889$	−11.5148	+	7.05629i	−0.386195	+	0.236660i
$890$	10.2079	+	0.803381i	0.342170	+	0.0269294i
$891$		0			0
$892$	24.0188	+	7.80419i	0.804209	+	0.261303i
$893$	59.6875	+	59.6875i	1.99736	+	1.99736i
$894$		0			0
$895$	4.46247	+	18.5875i	0.149164	+	0.621312i
$896$	−3.94156	−	0.946286i	−0.131678	−	0.0316132i
$897$		0			0
$898$	6.51059	+	20.0375i	0.217261	+	0.668661i
$899$	51.4734	+	21.3210i	1.71673	+	0.711094i
$900$		0			0
$901$		−	11.6647i		−	0.388608i
$902$	−21.6925	+	8.18307i	−0.722282	+	0.272466i
$903$		0			0
$904$	−4.52276	+	0.716334i	−0.150425	+	0.0238249i
$905$	−4.41533	+	10.6595i	−0.146770	+	0.354335i
$906$		0			0
$907$	−2.44671	+	4.80194i	−0.0812417	+	0.159446i	−0.928054	−	0.372447i	$-0.878519\pi$
$907$	−2.44671	+	4.80194i	−0.0812417	+	0.159446i	0.846812	+	0.531892i	$0.178519\pi$
$908$	0.0671977	−	0.279898i	0.00223003	−	0.00928875i
$909$		0			0
$910$	−4.27794	+	2.17972i	−0.141812	+	0.0722569i
$911$	37.6715	−	37.6715i	1.24811	−	1.24811i	0.291560	−	0.956553i	$-0.405826\pi$
$911$	37.6715	−	37.6715i	1.24811	−	1.24811i	0.956553	−	0.291560i	$-0.0941743\pi$
$912$		0			0
$913$	−35.4078	−	30.2411i	−1.17183	−	1.00084i
$914$	2.67538	−	33.9939i	0.0884937	−	1.12442i
$915$		0			0
$916$	3.52968	−	1.46204i	0.116624	−	0.0483072i
$917$	−39.0586	−	45.7318i	−1.28983	−	1.51020i
$918$		0			0
$919$	−0.0910825	−	1.15731i	−0.00300453	−	0.0381762i	0.995232	−	0.0975328i	$-0.0310951\pi$
$919$	−0.0910825	−	1.15731i	−0.00300453	−	0.0381762i	−0.998237	+	0.0593566i	$0.981095\pi$
$920$	−0.742636	+	1.02215i	−0.0244840	+	0.0336993i
$921$		0			0
$922$	2.62534	−	16.5757i	0.0864608	−	0.545892i
$923$	−0.599588	+	3.78565i	−0.0197357	+	0.124606i
$924$		0			0
$925$	13.1653	−	18.1204i	0.432871	−	0.595796i
$926$	0.0224226	+	0.284906i	0.000736851	+	0.00936258i
$927$		0			0
$928$	3.70117	+	4.33351i	0.121497	+	0.142254i
$929$	−54.6108	+	22.6205i	−1.79172	+	0.742155i	−0.802331	+	0.596880i	$0.796407\pi$
$929$	−54.6108	+	22.6205i	−1.79172	+	0.742155i	−0.989391	+	0.145276i	$0.953593\pi$
$930$		0			0
$931$	5.40930	−	68.7317i	0.177283	−	2.25259i
$932$	16.5852	+	14.1651i	0.543266	+	0.463993i
$933$		0			0
$934$	2.73659	−	2.73659i	0.0895440	−	0.0895440i
$935$	−21.6177	+	11.0148i	−0.706975	+	0.360222i
$936$		0			0
$937$	−0.0173212	+	0.0721482i	−0.000565860	+	0.00235698i	−0.972652	−	0.232267i	$-0.925386\pi$
$937$	−0.0173212	+	0.0721482i	−0.000565860	+	0.00235698i	0.972086	+	0.234624i	$0.0753858\pi$
$938$	−0.632958	+	1.24225i	−0.0206668	+	0.0405609i
$939$		0			0
$940$	5.06458	−	12.2270i	0.165188	−	0.398800i
$941$	35.7442	−	5.66133i	1.16523	−	0.184554i	0.456294	−	0.889829i	$-0.349177\pi$
$941$	35.7442	−	5.66133i	1.16523	−	0.184554i	0.708934	+	0.705275i	$0.249177\pi$
$942$		0			0
$943$	6.77947	−	1.96551i	0.220770	−	0.0640059i
$944$			10.3292i			0.336186i
$945$		0			0
$946$	−32.7583	−	13.5689i	−1.06506	−	0.441164i
$947$	4.38478	+	13.4950i	0.142486	+	0.438527i	0.996679	−	0.0814289i	$-0.0259484\pi$
$947$	4.38478	+	13.4950i	0.142486	+	0.438527i	−0.854193	+	0.519956i	$0.825948\pi$
$948$		0			0
$949$	11.1228	+	2.67036i	0.361062	+	0.0866834i
$950$	−6.29090	−	26.2035i	−0.204104	−	0.850154i
$951$		0			0
$952$	16.7577	+	16.7577i	0.543120	+	0.543120i
$953$	22.7649	+	7.39676i	0.737427	+	0.239605i	0.653563	−	0.756872i	$-0.273274\pi$
$953$	22.7649	+	7.39676i	0.737427	+	0.239605i	0.0838647	+	0.996477i	$0.473274\pi$
$954$		0			0
$955$	22.5612	+	1.77560i	0.730063	+	0.0574572i
$956$	−4.18737	+	2.56602i	−0.135429	+	0.0829912i
$957$		0			0
$958$	10.8786	−	9.29117i	0.351470	−	0.300184i
$959$	−30.7705	−	42.3520i	−0.993633	−	1.36762i
$960$		0			0
$961$	52.2426	+	37.9565i	1.68524	+	1.22440i
$962$	−5.35377	−	3.28080i	−0.172613	−	0.105777i
$963$		0			0
$964$	7.24410	+	1.14735i	0.233317	+	0.0369538i
$965$	10.1722	−	16.5995i	0.327455	−	0.534358i
$966$		0			0
$967$	−29.5128	+	2.32271i	−0.949068	+	0.0746932i	−0.543534	−	0.839387i	$-0.682914\pi$
$967$	−29.5128	+	2.32271i	−0.949068	+	0.0746932i	−0.405533	+	0.914080i	$0.632914\pi$
$968$	−1.70738	+	1.24048i	−0.0548771	+	0.0398706i
$969$		0			0
$970$	−6.59318	−	15.9173i	−0.211694	−	0.511075i
$971$	−7.68386	−	12.5389i	−0.246587	−	0.402393i	0.705269	−	0.708940i	$-0.250826\pi$
$971$	−7.68386	−	12.5389i	−0.246587	−	0.402393i	−0.951856	+	0.306547i	$0.900826\pi$
$972$		0			0
$973$	−36.2457	+	42.4383i	−1.16198	+	1.36051i
$974$	−3.50706	+	10.7936i	−0.112373	+	0.345850i
$975$		0			0
$976$	−3.33918	−	6.55351i	−0.106885	−	0.209773i
$977$	30.0895	−	7.22384i	0.962647	−	0.231111i	0.278485	−	0.960441i	$-0.410168\pi$
$977$	30.0895	−	7.22384i	0.962647	−	0.231111i	0.684163	+	0.729330i	$0.260168\pi$
$978$		0			0
$979$	−28.8230	−	14.6861i	−0.921188	−	0.469369i
$980$	−10.2804	+	3.34030i	−0.328395	+	0.106702i
$981$		0			0
$982$	3.50615	+	22.1370i	0.111886	+	0.706419i
$983$	−10.4847			−0.334409			−0.167205	−	0.985922i	$-0.553474\pi$
$983$	−10.4847			−0.334409			−0.167205	+	0.985922i	$0.553474\pi$
$984$		0			0
$985$	−18.8185			−0.599608
$986$	−5.21218	−	32.9084i	−0.165990	−	1.04802i
$987$		0			0
$988$	−7.18485	+	2.33450i	−0.228580	+	0.0742703i
$989$	9.61850	+	4.90087i	0.305851	+	0.155839i
$990$		0			0
$991$	6.46056	−	1.55104i	0.205226	−	0.0492705i	−0.129529	−	0.991576i	$-0.541346\pi$
$991$	6.46056	−	1.55104i	0.205226	−	0.0492705i	0.334755	+	0.942305i	$0.391346\pi$
$992$	4.43833	+	8.71072i	0.140917	+	0.276566i
$993$		0			0
$994$	−4.64570	+	14.2980i	−0.147353	+	0.453505i
$995$	−13.2530	+	15.5173i	−0.420149	+	0.491932i
$996$		0			0
$997$	−18.4529	−	30.1124i	−0.584410	−	0.953670i	−0.999045	−	0.0436826i	$-0.986091\pi$
$997$	−18.4529	−	30.1124i	−0.584410	−	0.953670i	0.414636	−	0.909987i	$-0.363909\pi$
$998$	7.69821	+	18.5851i	0.243683	+	0.588302i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.c.503.3	yes	64
3.2	odd	2		738.2.ba.d.503.2	yes	64
41.15	odd	40		738.2.ba.d.179.2	yes	64
123.56	even	40	inner	738.2.ba.c.179.3	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.c.179.3	✓	64	123.56	even	40	inner
738.2.ba.c.503.3	yes	64	1.1	even	1	trivial
738.2.ba.d.179.2	yes	64	41.15	odd	40
738.2.ba.d.503.2	yes	64	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(1.02120 + 0.520325i) q^{5} +(3.94156 - 0.946286i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.354169 + 1.09002i) q^{10} +(2.35154 - 2.75330i) q^{11} +(0.539975 + 0.881159i) q^{13} +(1.55123 + 3.74500i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-5.82843 + 0.458708i) q^{17} +(3.81951 - 6.23288i) q^{19} +(-1.13200 - 0.179292i) q^{20} +(3.08727 + 1.89188i) q^{22} +(-0.891840 - 0.647960i) q^{23} +(-2.16682 - 2.98238i) q^{25} +(-0.785839 + 0.671170i) q^{26} +(-3.45623 + 2.11798i) q^{28} +(5.68137 + 0.447134i) q^{29} +(9.29778 + 3.02103i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.36483 - 5.68492i) q^{34} +(4.51748 + 1.08455i) q^{35} +(1.87754 + 5.77846i) q^{37} +(6.75364 + 2.79745i) q^{38} -1.14611i q^{40} +(-3.92735 + 5.05727i) q^{41} +(-9.67201 + 1.53190i) q^{43} +(-1.38563 + 3.34521i) q^{44} +(0.500468 - 0.982224i) q^{46} +(-2.69563 + 11.2281i) q^{47} +(8.40342 - 4.28175i) q^{49} +(2.60669 - 2.60669i) q^{50} +(-0.785839 - 0.671170i) q^{52} +(-0.156540 + 1.98903i) q^{53} +(3.83400 - 1.58809i) q^{55} +(-2.63258 - 3.08235i) q^{56} +(0.447134 + 5.68137i) q^{58} +(-6.07134 + 8.35649i) q^{59} +(1.15060 - 7.26462i) q^{61} +(-1.52934 + 9.65590i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(0.0929308 + 1.18080i) q^{65} +(0.223375 + 0.261539i) q^{67} +(5.40142 - 2.23734i) q^{68} +(-0.364509 + 4.63153i) q^{70} +(2.82019 + 2.40867i) q^{71} +(7.82673 - 7.82673i) q^{73} +(-5.41361 + 2.75837i) q^{74} +(-1.70651 + 7.10811i) q^{76} +(6.66334 - 13.0775i) q^{77} +(-2.76569 + 6.67696i) q^{79} +(1.13200 - 0.179292i) q^{80} +(-5.60938 - 3.08786i) q^{82} -12.8601i q^{83} +(-6.19065 - 2.56425i) q^{85} +(-3.02607 - 9.31329i) q^{86} +(-3.52079 - 0.845267i) q^{88} +(-2.08562 - 8.68724i) q^{89} +(2.96217 + 2.96217i) q^{91} +(1.04842 + 0.340653i) q^{92} +(-11.5116 - 0.905980i) q^{94} +(7.14359 - 4.37760i) q^{95} +(-11.4307 + 9.76274i) q^{97} +(5.54362 + 7.63014i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{14} + 16 q^{16} - 16 q^{17} + 4 q^{19} - 4 q^{22} + 48 q^{23} + 40 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 40 q^{31} + 4 q^{34} - 52 q^{35} + 8 q^{37} + 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) \) 64 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^14 + 16 * q^16 - 16 * q^17 + 4 * q^19 - 4 * q^22 + 48 * q^23 + 40 * q^25 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 40 * q^31 + 4 * q^34 - 52 * q^35 + 8 * q^37 + 16 * q^38 + 12 * q^41 + 32 * q^43 - 4 * q^44 - 8 * q^47 + 48 * q^49 + 16 * q^50 - 20 * q^52 - 48 * q^53 - 36 * q^55 + 16 * q^56 - 20 * q^58 + 20 * q^59 + 24 * q^61 - 36 * q^62 + 60 * q^65 - 20 * q^67 + 12 * q^68 - 8 * q^70 - 8 * q^71 + 72 * q^73 - 12 * q^74 + 4 * q^76 - 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 - 32 * q^86 - 8 * q^88 + 84 * q^89 + 72 * q^91 + 12 * q^94 - 12 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more