LMFDB - Embedded newform 738.2.ba.a.179.1

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 = [48,0,0,0,-4,0,4,0,0,0,-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:	$48$
Relative dimension:	$3$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			179.1
Character	$\chi$	$=$	738.179
Dual form			738.2.ba.a.503.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-2.39103 + 1.21829i) q^{5} +(2.33211 + 0.559890i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.829251 - 2.55217i) q^{10} +(2.62751 + 3.07642i) q^{11} +(0.335427 - 0.547368i) q^{13} +(-0.917819 + 2.21581i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-2.16833 - 0.170651i) q^{17} +(0.753114 + 1.22897i) q^{19} +(2.65047 - 0.419794i) q^{20} +(-3.44958 + 2.11390i) q^{22} +(-5.97763 + 4.34300i) q^{23} +(1.29386 - 1.78084i) q^{25} +(0.488156 + 0.416925i) q^{26} +(-2.04495 - 1.25315i) q^{28} +(-1.59275 + 0.125352i) q^{29} +(-4.31485 + 1.40198i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.507751 - 2.11493i) q^{34} +(-6.25825 + 1.50247i) q^{35} +(-1.00905 + 3.10554i) q^{37} +(-1.33165 + 0.551589i) q^{38} +2.68351i q^{40} +(-5.31184 - 3.57552i) q^{41} +(-3.14238 - 0.497704i) q^{43} +(-1.54825 - 3.73779i) q^{44} +(-3.35443 - 6.58343i) q^{46} +(2.13306 + 8.88484i) q^{47} +(-1.11179 - 0.566484i) q^{49} +(1.55651 + 1.55651i) q^{50} +(-0.488156 + 0.416925i) q^{52} +(0.138343 + 1.75782i) q^{53} +(-10.0304 - 4.15474i) q^{55} +(1.55762 - 1.82374i) q^{56} +(0.125352 - 1.59275i) q^{58} +(7.35405 + 10.1220i) q^{59} +(-0.621115 - 3.92156i) q^{61} +(-0.709728 - 4.48105i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(-0.135164 + 1.71742i) q^{65} +(0.129962 - 0.152166i) q^{67} +(2.00947 + 0.832348i) q^{68} +(-0.504969 - 6.41624i) q^{70} +(2.36149 - 2.01690i) q^{71} +(4.85557 + 4.85557i) q^{73} +(-2.90945 - 1.48244i) q^{74} +(-0.336481 - 1.40155i) q^{76} +(4.40519 + 8.64566i) q^{77} +(1.85049 + 4.46749i) q^{79} +(-2.65047 - 0.419794i) q^{80} +(4.36246 - 4.68711i) q^{82} -12.9508i q^{83} +(5.39243 - 2.23362i) q^{85} +(0.983152 - 3.02583i) q^{86} +(3.93398 - 0.944464i) q^{88} +(-0.348691 + 1.45240i) q^{89} +(1.08872 - 1.08872i) q^{91} +(7.02713 - 2.28325i) q^{92} +(-9.10914 + 0.716904i) q^{94} +(-3.29796 - 2.02099i) q^{95} +(13.8416 + 11.8218i) q^{97} +(0.733432 - 1.00948i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Character values

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

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{37}{40}\right)$

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
$5$	−2.39103	+	1.21829i	−1.06930	+	0.544836i	−0.897825	−	0.440353i	$-0.854853\pi$
$5$	−2.39103	+	1.21829i	−1.06930	+	0.544836i	−0.171475	+	0.985188i	$0.554853\pi$
$6$		0			0
$7$	2.33211	+	0.559890i	0.881455	+	0.211619i	0.648817	−	0.760945i	$-0.275264\pi$
$7$	2.33211	+	0.559890i	0.881455	+	0.211619i	0.232638	+	0.972563i	$0.425264\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$		0			0
$10$	−0.829251	−	2.55217i	−0.262232	−	0.807068i
$11$	2.62751	+	3.07642i	0.792224	+	0.927575i	0.998705	−	0.0508752i	$-0.0162011\pi$
$11$	2.62751	+	3.07642i	0.792224	+	0.927575i	−0.206481	+	0.978451i	$0.566201\pi$
$12$		0			0
$13$	0.335427	−	0.547368i	0.0930308	−	0.151812i	−0.802739	−	0.596330i	$-0.796625\pi$
$13$	0.335427	−	0.547368i	0.0930308	−	0.151812i	0.895770	+	0.444518i	$0.146625\pi$
$14$	−0.917819	+	2.21581i	−0.245297	+	0.592200i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−2.16833	−	0.170651i	−0.525896	−	0.0413889i	−0.187267	−	0.982309i	$-0.559963\pi$
$17$	−2.16833	−	0.170651i	−0.525896	−	0.0413889i	−0.338629	+	0.940920i	$0.609963\pi$
$18$		0			0
$19$	0.753114	+	1.22897i	0.172776	+	0.281945i	0.927294	−	0.374335i	$-0.122129\pi$
$19$	0.753114	+	1.22897i	0.172776	+	0.281945i	−0.754517	+	0.656280i	$0.772129\pi$
$20$	2.65047	−	0.419794i	0.592664	−	0.0938688i
$21$		0			0
$22$	−3.44958	+	2.11390i	−0.735452	+	0.450686i
$23$	−5.97763	+	4.34300i	−1.24642	+	0.905579i	−0.998009	−	0.0630749i	$-0.979909\pi$
$23$	−5.97763	+	4.34300i	−1.24642	+	0.905579i	−0.248414	+	0.968654i	$0.579909\pi$
$24$		0			0
$25$	1.29386	−	1.78084i	0.258772	−	0.356169i
$26$	0.488156	+	0.416925i	0.0957353	+	0.0817657i
$27$		0			0
$28$	−2.04495	−	1.25315i	−0.386460	−	0.236823i
$29$	−1.59275	+	0.125352i	−0.295766	+	0.0232773i	−0.225474	−	0.974249i	$-0.572393\pi$
$29$	−1.59275	+	0.125352i	−0.295766	+	0.0232773i	−0.0702917	+	0.997526i	$0.522393\pi$
$30$		0			0
$31$	−4.31485	+	1.40198i	−0.774970	+	0.251803i	−0.669691	−	0.742640i	$-0.733574\pi$
$31$	−4.31485	+	1.40198i	−0.774970	+	0.251803i	−0.105279	+	0.994443i	$0.533574\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	0.507751	−	2.11493i	0.0870785	−	0.362708i
$35$	−6.25825	+	1.50247i	−1.05784	+	0.253964i
$36$		0			0
$37$	−1.00905	+	3.10554i	−0.165887	+	0.510547i	−0.999101	−	0.0424041i	$-0.986498\pi$
$37$	−1.00905	+	3.10554i	−0.165887	+	0.510547i	0.833214	+	0.552951i	$0.186498\pi$
$38$	−1.33165	+	0.551589i	−0.216023	+	0.0894795i
$39$		0			0
$40$			2.68351i			0.424301i
$41$	−5.31184	−	3.57552i	−0.829570	−	0.558403i
$41$	−5.31184	−	3.57552i	−0.829570	−	0.558403i
$42$		0			0
$43$	−3.14238	−	0.497704i	−0.479208	−	0.0758991i	−0.0878424	−	0.996134i	$-0.527997\pi$
$43$	−3.14238	−	0.497704i	−0.479208	−	0.0758991i	−0.391366	+	0.920235i	$0.627997\pi$
$44$	−1.54825	−	3.73779i	−0.233407	−	0.563494i
$45$		0			0
$46$	−3.35443	−	6.58343i	−0.494583	−	0.970674i
$47$	2.13306	+	8.88484i	0.311139	+	1.29599i	0.880558	+	0.473939i	$0.157168\pi$
$47$	2.13306	+	8.88484i	0.311139	+	1.29599i	−0.569419	+	0.822048i	$0.692832\pi$
$48$		0			0
$49$	−1.11179	−	0.566484i	−0.158827	−	0.0809263i
$50$	1.55651	+	1.55651i	0.220124	+	0.220124i
$51$		0			0
$52$	−0.488156	+	0.416925i	−0.0676951	+	0.0578171i
$53$	0.138343	+	1.75782i	0.0190029	+	0.241455i	0.999082	+	0.0428459i	$0.0136425\pi$
$53$	0.138343	+	1.75782i	0.0190029	+	0.241455i	−0.980079	+	0.198609i	$0.936358\pi$
$54$		0			0
$55$	−10.0304	−	4.15474i	−1.35250	−	0.560225i
$56$	1.55762	−	1.82374i	0.208146	−	0.243708i
$57$		0			0
$58$	0.125352	−	1.59275i	0.0164595	−	0.209138i
$59$	7.35405	+	10.1220i	0.957415	+	1.31777i	0.948154	+	0.317812i	$0.102948\pi$
$59$	7.35405	+	10.1220i	0.957415	+	1.31777i	0.00926141	+	0.999957i	$0.497052\pi$
$60$		0			0
$61$	−0.621115	−	3.92156i	−0.0795256	−	0.502105i	−0.995012	−	0.0997558i	$-0.968194\pi$
$61$	−0.621115	−	3.92156i	−0.0795256	−	0.502105i	0.915486	−	0.402349i	$-0.131806\pi$
$62$	−0.709728	−	4.48105i	−0.0901356	−	0.569094i
$63$		0			0
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−0.135164	+	1.71742i	−0.0167650	+	0.213020i
$66$		0			0
$67$	0.129962	−	0.152166i	0.0158774	−	0.0185901i	−0.752410	−	0.658695i	$-0.771109\pi$
$67$	0.129962	−	0.152166i	0.0158774	−	0.0185901i	0.768288	+	0.640104i	$0.221109\pi$
$68$	2.00947	+	0.832348i	0.243684	+	0.100937i
$69$		0			0
$70$	−0.504969	−	6.41624i	−0.0603553	−	0.766887i
$71$	2.36149	−	2.01690i	0.280257	−	0.239362i	−0.498197	−	0.867064i	$-0.666004\pi$
$71$	2.36149	−	2.01690i	0.280257	−	0.239362i	0.778454	+	0.627702i	$0.216004\pi$
$72$		0			0
$73$	4.85557	+	4.85557i	0.568302	+	0.568302i	0.931652	−	0.363351i	$-0.118367\pi$
$73$	4.85557	+	4.85557i	0.568302	+	0.568302i	−0.363351	+	0.931652i	$0.618367\pi$
$74$	−2.90945	−	1.48244i	−0.338217	−	0.172330i
$75$		0			0
$76$	−0.336481	−	1.40155i	−0.0385970	−	0.160768i
$77$	4.40519	+	8.64566i	0.502018	+	0.985265i
$78$		0			0
$79$	1.85049	+	4.46749i	0.208197	+	0.502632i	0.993139	−	0.116937i	$-0.0373075\pi$
$79$	1.85049	+	4.46749i	0.208197	+	0.502632i	−0.784942	+	0.619569i	$0.787308\pi$
$80$	−2.65047	−	0.419794i	−0.296332	−	0.0469344i
$81$		0			0
$82$	4.36246	−	4.68711i	0.481753	−	0.517604i
$83$		−	12.9508i		−	1.42154i	−0.703426	−	0.710768i	$-0.748347\pi$
$83$		−	12.9508i		−	1.42154i	0.703426	−	0.710768i	$-0.251653\pi$
$84$		0			0
$85$	5.39243	−	2.23362i	0.584891	−	0.242270i
$86$	0.983152	−	3.02583i	0.106016	−	0.326284i
$87$		0			0
$88$	3.93398	−	0.944464i	0.419363	−	0.100680i
$89$	−0.348691	+	1.45240i	−0.0369612	+	0.153954i	−0.987799	−	0.155736i	$-0.950225\pi$
$89$	−0.348691	+	1.45240i	−0.0369612	+	0.153954i	0.950838	+	0.309690i	$0.100225\pi$
$90$		0			0
$91$	1.08872	−	1.08872i	0.114129	−	0.114129i
$92$	7.02713	−	2.28325i	0.732629	−	0.238046i
$93$		0			0
$94$	−9.10914	+	0.716904i	−0.939536	+	0.0739431i
$95$	−3.29796	−	2.02099i	−0.338363	−	0.207349i
$96$		0			0
$97$	13.8416	+	11.8218i	1.40540	+	1.20033i	0.950868	+	0.309598i	$0.100194\pi$
$97$	13.8416	+	11.8218i	1.40540	+	1.20033i	0.454534	+	0.890729i	$0.349806\pi$
$98$	0.733432	−	1.00948i	0.0740878	−	0.101973i
$99$		0			0
$100$	−1.78084	+	1.29386i	−0.178084	+	0.129386i
$101$	5.41258	−	3.31683i	0.538572	−	0.330037i	−0.226470	−	0.974018i	$-0.572718\pi$
$101$	5.41258	−	3.31683i	0.538572	−	0.330037i	0.765041	+	0.643981i	$0.222718\pi$
$102$		0			0
$103$	11.3049	−	1.79052i	1.11390	−	0.176425i	0.427761	−	0.903892i	$-0.359303\pi$
$103$	11.3049	−	1.79052i	1.11390	−	0.176425i	0.686143	+	0.727467i	$0.259303\pi$
$104$	−0.335427	−	0.547368i	−0.0328914	−	0.0536738i
$105$		0			0
$106$	−1.75782	−	0.138343i	−0.170735	−	0.0134371i
$107$	−3.18783	−	2.31609i	−0.308179	−	0.223905i	0.422936	−	0.906160i	$-0.361000\pi$
$107$	−3.18783	−	2.31609i	−0.308179	−	0.223905i	−0.731115	+	0.682255i	$0.761000\pi$
$108$		0			0
$109$	−7.80848	+	18.8513i	−0.747917	+	1.80563i	−0.177800	+	0.984067i	$0.556898\pi$
$109$	−7.80848	+	18.8513i	−0.747917	+	1.80563i	−0.570117	+	0.821564i	$0.693102\pi$
$110$	5.67269	−	9.25699i	0.540870	−	0.882619i
$111$		0			0
$112$	1.55762	+	1.82374i	0.147181	+	0.172327i
$113$	−5.20333	−	16.0142i	−0.489488	−	1.50649i	−0.825373	−	0.564587i	$-0.809035\pi$
$113$	−5.20333	−	16.0142i	−0.489488	−	1.50649i	0.335885	−	0.941903i	$-0.390965\pi$
$114$		0			0
$115$	9.00165	−	17.6667i	0.839408	−	1.64743i
$116$	1.55353	+	0.372969i	0.144241	+	0.0346293i
$117$		0			0
$118$	−11.1478	+	5.68008i	−1.02624	+	0.522894i
$119$	−4.96123	−	1.61200i	−0.454795	−	0.147772i
$120$		0			0
$121$	−0.839767	+	5.30208i	−0.0763425	+	0.482007i
$122$	3.97045			0.359467
$123$		0			0
$124$	4.53690			0.407426
$125$	1.17490	−	7.41803i	0.105086	−	0.663489i
$126$		0			0
$127$	−13.5980	−	4.41826i	−1.20663	−	0.392058i	−0.364433	−	0.931229i	$-0.618737\pi$
$127$	−13.5980	−	4.41826i	−1.20663	−	0.392058i	−0.842196	+	0.539172i	$0.818737\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$		0			0
$130$	−1.67513	−	0.402163i	−0.146919	−	0.0352721i
$131$	8.05987	−	15.8184i	0.704194	−	1.38206i	−0.210372	−	0.977621i	$-0.567468\pi$
$131$	8.05987	−	15.8184i	0.704194	−	1.38206i	0.914566	−	0.404437i	$-0.132532\pi$
$132$		0			0
$133$	1.06826	+	3.28775i	0.0926296	+	0.285084i
$134$	0.129962	+	0.152166i	0.0112270	+	0.0131452i
$135$		0			0
$136$	−1.13645	+	1.85452i	−0.0974498	+	0.159024i
$137$	−5.61717	+	13.5611i	−0.479908	+	1.15860i	0.479744	+	0.877408i	$0.340729\pi$
$137$	−5.61717	+	13.5611i	−0.479908	+	1.15860i	−0.959652	+	0.281191i	$0.909271\pi$
$138$		0			0
$139$	−4.05689	−	2.94750i	−0.344101	−	0.250004i	0.402289	−	0.915513i	$-0.368215\pi$
$139$	−4.05689	−	2.94750i	−0.344101	−	0.250004i	−0.746390	+	0.665509i	$0.768215\pi$
$140$	6.41624	+	0.504969i	0.542271	+	0.0426776i
$141$		0			0
$142$	1.62265	+	2.64793i	0.136170	+	0.222209i
$143$	2.56527	−	0.406299i	0.214519	−	0.0339764i
$144$		0			0
$145$	3.65559	−	2.24015i	0.303580	−	0.186034i
$146$	−5.55537	+	4.03621i	−0.459766	+	0.334039i
$147$		0			0
$148$	1.91933	−	2.64173i	0.157768	−	0.217149i
$149$	8.58164	+	7.32941i	0.703035	+	0.600449i	0.927407	−	0.374055i	$-0.122033\pi$
$149$	8.58164	+	7.32941i	0.703035	+	0.600449i	−0.224371	+	0.974504i	$0.572033\pi$
$150$		0			0
$151$	5.51617	+	3.38031i	0.448899	+	0.275086i	0.728520	−	0.685025i	$-0.240209\pi$
$151$	5.51617	+	3.38031i	0.448899	+	0.275086i	−0.279620	+	0.960111i	$0.590209\pi$
$152$	1.43693	−	0.113089i	0.116550	−	0.00917270i
$153$		0			0
$154$	−9.22835	+	2.99847i	−0.743641	+	0.241624i
$155$	8.60891	−	8.60891i	0.691485	−	0.691485i
$156$		0			0
$157$	2.63827	−	10.9892i	0.210557	−	0.877033i	−0.762596	−	0.646875i	$-0.776076\pi$
$157$	2.63827	−	10.9892i	0.210557	−	0.877033i	0.973153	−	0.230158i	$-0.0739243\pi$
$158$	−4.70197	+	1.12884i	−0.374068	+	0.0898059i
$159$		0			0
$160$	0.829251	−	2.55217i	0.0655581	−	0.201767i
$161$	−16.3721	+	6.78155i	−1.29030	+	0.534461i
$162$		0			0
$163$			16.8538i			1.32009i	0.751225	+	0.660047i	$0.229464\pi$
$163$			16.8538i			1.32009i	−0.751225	+	0.660047i	$0.770536\pi$
$164$	3.94696	+	5.04197i	0.308206	+	0.393712i
$165$		0			0
$166$	12.7914	+	2.02595i	0.992803	+	0.157245i
$167$	2.65318	+	6.40534i	0.205309	+	0.495660i	0.992673	−	0.120828i	$-0.0385550\pi$
$167$	2.65318	+	6.40534i	0.205309	+	0.495660i	−0.787364	+	0.616488i	$0.788555\pi$
$168$		0			0
$169$	5.71478	+	11.2159i	0.439598	+	0.862760i
$170$	1.36256	+	5.67545i	0.104503	+	0.435287i
$171$		0			0
$172$	2.83478	+	1.44439i	0.216150	+	0.110134i
$173$	−4.63314	−	4.63314i	−0.352251	−	0.352251i	0.508695	−	0.860947i	$-0.330128\pi$
$173$	−4.63314	−	4.63314i	−0.352251	−	0.352251i	−0.860947	+	0.508695i	$0.830128\pi$
$174$		0			0
$175$	4.01450	−	3.42870i	0.303467	−	0.259186i
$176$	0.317427	+	4.03329i	0.0239269	+	0.304021i
$177$		0			0
$178$	−1.37997	−	0.571604i	−0.103433	−	0.0428435i
$179$	13.5747	−	15.8940i	1.01462	−	1.18797i	0.0325500	−	0.999470i	$-0.489637\pi$
$179$	13.5747	−	15.8940i	1.01462	−	1.18797i	0.982073	−	0.188501i	$-0.0603628\pi$
$180$		0			0
$181$	−0.981979	+	12.4772i	−0.0729899	+	0.927425i	0.846010	+	0.533167i	$0.178998\pi$
$181$	−0.981979	+	12.4772i	−0.0729899	+	0.927425i	−0.919000	+	0.394258i	$0.871002\pi$
$182$	0.905002	+	1.24563i	0.0670832	+	0.0923321i
$183$		0			0
$184$	1.15586	+	7.29779i	0.0852109	+	0.538000i
$185$	−1.37078	−	8.65474i	−0.100781	−	0.636309i
$186$		0			0
$187$	−5.17231	−	7.11907i	−0.378236	−	0.520598i
$188$	0.716904	−	9.10914i	0.0522856	−	0.664352i
$189$		0			0
$190$	2.51202	−	2.94120i	0.182241	−	0.213377i
$191$	4.39403	+	1.82007i	0.317941	+	0.131696i	0.535946	−	0.844252i	$-0.319955\pi$
$191$	4.39403	+	1.82007i	0.317941	+	0.131696i	−0.218005	+	0.975948i	$0.569955\pi$
$192$		0			0
$193$	0.685447	+	8.70943i	0.0493396	+	0.626919i	0.971025	+	0.238980i	$0.0768129\pi$
$193$	0.685447	+	8.70943i	0.0493396	+	0.626919i	−0.921685	+	0.387939i	$0.873187\pi$
$194$	−13.8416	+	11.8218i	−0.993769	+	0.848759i
$195$		0			0
$196$	0.882320	+	0.882320i	0.0630228	+	0.0630228i
$197$	6.49234	+	3.30801i	0.462560	+	0.235686i	0.669710	−	0.742623i	$-0.266419\pi$
$197$	6.49234	+	3.30801i	0.462560	+	0.235686i	−0.207149	+	0.978309i	$0.566419\pi$
$198$		0			0
$199$	−2.01747	−	8.40336i	−0.143015	−	0.595698i	−0.997136	−	0.0756253i	$-0.975905\pi$
$199$	−2.01747	−	8.40336i	−0.143015	−	0.595698i	0.854122	−	0.520073i	$-0.174095\pi$
$200$	−0.999344	−	1.96132i	−0.0706643	−	0.138686i
$201$		0			0
$202$	2.42928	+	5.86481i	0.170924	+	0.412646i
$203$	−3.78464	−	0.599428i	−0.265630	−	0.0420716i
$204$		0			0
$205$	17.0568	+	2.07782i	1.19130	+	0.145121i
$206$			11.4458i			0.797467i
$207$		0			0
$208$	0.593101	−	0.245671i	0.0411242	−	0.0170342i
$209$	−1.80201	+	5.54603i	−0.124648	+	0.383627i
$210$		0			0
$211$	20.1662	−	4.84149i	1.38830	−	0.333302i	0.530675	−	0.847575i	$-0.321938\pi$
$211$	20.1662	−	4.84149i	1.38830	−	0.333302i	0.857626	+	0.514273i	$0.171938\pi$
$212$	0.411624	−	1.71454i	0.0282704	−	0.117755i
$213$		0			0
$214$	2.78626	−	2.78626i	0.190465	−	0.190465i
$215$	8.11986	−	2.63830i	0.553770	−	0.179931i
$216$		0			0
$217$	−10.8477	+	0.853730i	−0.736387	+	0.0579549i
$218$	−17.3977	−	10.6613i	−1.17832	−	0.722077i
$219$		0			0
$220$	8.25561	+	7.05096i	0.556593	+	0.475376i
$221$	−0.820725	+	1.12963i	−0.0552079	+	0.0759872i
$222$		0			0
$223$	1.76713	−	1.28390i	0.118336	−	0.0859761i	−0.527043	−	0.849838i	$-0.676699\pi$
$223$	1.76713	−	1.28390i	0.118336	−	0.0859761i	0.645379	+	0.763862i	$0.276699\pi$
$224$	−2.04495	+	1.25315i	−0.136634	+	0.0837295i
$225$		0			0
$226$	16.6310	−	2.63410i	1.10628	−	0.175218i
$227$	−0.953494	−	1.55596i	−0.0632856	−	0.103273i	0.819432	−	0.573176i	$-0.194289\pi$
$227$	−0.953494	−	1.55596i	−0.0632856	−	0.103273i	−0.882718	+	0.469903i	$0.844289\pi$
$228$		0			0
$229$	27.3585	+	2.15316i	1.80790	+	0.142285i	0.937035	−	0.349235i	$-0.113558\pi$
$229$	27.3585	+	2.15316i	1.80790	+	0.142285i	0.870867	+	0.491520i	$0.163558\pi$
$230$	16.0411	+	11.6545i	1.05772	+	0.768476i
$231$		0			0
$232$	−0.611402	+	1.47606i	−0.0401405	+	0.0969078i
$233$	3.23450	−	5.27823i	0.211899	−	0.345788i	−0.728977	−	0.684538i	$-0.760004\pi$
$233$	3.23450	−	5.27823i	0.211899	−	0.345788i	0.940876	+	0.338750i	$0.110004\pi$
$234$		0			0
$235$	−15.9245	−	18.6452i	−1.03880	−	1.21628i
$236$	−3.86625	−	11.8991i	−0.251671	−	0.774565i
$237$		0			0
$238$	2.36826	−	4.64797i	0.153512	−	0.301283i
$239$	7.78832	+	1.86981i	0.503785	+	0.120948i	0.477369	−	0.878703i	$-0.341591\pi$
$239$	7.78832	+	1.86981i	0.503785	+	0.120948i	0.0264158	+	0.999651i	$0.491591\pi$
$240$		0			0
$241$	14.6771	−	7.47834i	0.945433	−	0.481722i	0.0878874	−	0.996130i	$-0.471988\pi$
$241$	14.6771	−	7.47834i	0.945433	−	0.481722i	0.857545	+	0.514408i	$0.171988\pi$
$242$	−5.10544	−	1.65886i	−0.328190	−	0.106635i
$243$		0			0
$244$	−0.621115	+	3.92156i	−0.0397628	+	0.251052i
$245$	3.34846			0.213925
$246$		0			0
$247$	0.925314			0.0588763
$248$	−0.709728	+	4.48105i	−0.0450678	+	0.284547i
$249$		0			0
$250$	7.14291	+	2.32087i	0.451757	+	0.146785i
$251$	23.6070	−	12.0284i	1.49006	−	0.759223i	0.496027	−	0.868307i	$-0.334792\pi$
$251$	23.6070	−	12.0284i	1.49006	−	0.759223i	0.994033	+	0.109084i	$0.0347918\pi$
$252$		0			0
$253$	−29.0672	−	6.97842i	−1.82744	−	0.438729i
$254$	6.49107	−	12.7394i	0.407286	−	0.799343i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	14.1052	+	16.5151i	0.879859	+	1.03018i	0.999303	+	0.0373414i	$0.0118889\pi$
$257$	14.1052	+	16.5151i	0.879859	+	1.03018i	−0.119444	+	0.992841i	$0.538111\pi$
$258$		0			0
$259$	−4.09197	+	6.67749i	−0.254263	+	0.414919i
$260$	0.659260	−	1.59159i	0.0408856	−	0.0987065i
$261$		0			0
$262$	14.3628	+	10.4352i	0.887336	+	0.644687i
$263$	−7.30680	−	0.575058i	−0.450557	−	0.0354596i	−0.148849	−	0.988860i	$-0.547557\pi$
$263$	−7.30680	−	0.575058i	−0.450557	−	0.0354596i	−0.301708	+	0.953400i	$0.597557\pi$
$264$		0			0
$265$	−2.47232	−	4.03445i	−0.151873	−	0.247835i
$266$	−3.41439	+	0.540786i	−0.209350	+	0.0331577i
$267$		0			0
$268$	−0.170624	+	0.104558i	−0.0104225	+	0.00638691i
$269$	−13.7566	+	9.99472i	−0.838752	+	0.609389i	−0.922022	−	0.387138i	$-0.873464\pi$
$269$	−13.7566	+	9.99472i	−0.838752	+	0.609389i	0.0832699	+	0.996527i	$0.473464\pi$
$270$		0			0
$271$	−13.0240	+	17.9260i	−0.791151	+	1.08893i	0.202812	+	0.979218i	$0.434992\pi$
$271$	−13.0240	+	17.9260i	−0.791151	+	1.08893i	−0.993964	+	0.109709i	$0.965008\pi$
$272$	−1.65391	−	1.41257i	−0.100283	−	0.0856496i
$273$		0			0
$274$	−12.5154	−	7.66943i	−0.756082	−	0.463327i
$275$	8.87825	−	0.698733i	0.535379	−	0.0421352i
$276$		0			0
$277$	−11.8409	+	3.84733i	−0.711448	+	0.231164i	−0.642312	−	0.766444i	$-0.722025\pi$
$277$	−11.8409	+	3.84733i	−0.711448	+	0.231164i	−0.0691368	+	0.997607i	$0.522025\pi$
$278$	3.54585	−	3.54585i	0.212666	−	0.212666i
$279$		0			0
$280$	−1.50247	+	6.25825i	−0.0897899	+	0.374002i
$281$	−31.0222	+	7.44777i	−1.85063	+	0.444297i	−0.997056	−	0.0766781i	$-0.975569\pi$
$281$	−31.0222	+	7.44777i	−1.85063	+	0.444297i	−0.853572	+	0.520975i	$0.825569\pi$
$282$		0			0
$283$	6.39636	−	19.6860i	0.380224	−	1.17021i	−0.559662	−	0.828721i	$-0.689069\pi$
$283$	6.39636	−	19.6860i	0.380224	−	1.17021i	0.939886	−	0.341488i	$-0.110931\pi$
$284$	−2.86917	+	1.18845i	−0.170254	+	0.0705215i
$285$		0			0
$286$			2.59725i			0.153579i
$287$	−10.3859	−	11.3126i	−0.613060	−	0.667759i
$288$		0			0
$289$	−12.1182	−	1.91933i	−0.712835	−	0.112902i
$290$	1.64071	+	3.96102i	0.0963456	+	0.232599i
$291$		0			0
$292$	−3.11747	−	6.11838i	−0.182436	−	0.358051i
$293$	−4.57360	−	19.0504i	−0.267193	−	1.11294i	−0.930996	−	0.365030i	$-0.881059\pi$
$293$	−4.57360	−	19.0504i	−0.267193	−	1.11294i	0.663803	−	0.747907i	$-0.268941\pi$
$294$		0			0
$295$	−29.9152	−	15.2426i	−1.74173	−	0.887457i
$296$	2.30895	+	2.30895i	0.134205	+	0.134205i
$297$		0			0
$298$	−8.58164	+	7.32941i	−0.497121	+	0.424582i
$299$	0.372159	+	4.72873i	0.0215225	+	0.273469i
$300$		0			0
$301$	−7.04971	−	2.92008i	−0.406338	−	0.168311i
$302$	−4.20161	+	4.91946i	−0.241776	+	0.283083i
$303$		0			0
$304$	−0.113089	+	1.43693i	−0.00648608	+	0.0824134i
$305$	6.26270	+	8.61987i	0.358601	+	0.493572i
$306$		0			0
$307$	−1.57217	−	9.92632i	−0.0897288	−	0.566525i	−0.991062	−	0.133399i	$-0.957411\pi$
$307$	−1.57217	−	9.92632i	−0.0897288	−	0.566525i	0.901334	−	0.433126i	$-0.142589\pi$
$308$	−1.51792	−	9.58379i	−0.0864917	−	0.546087i
$309$		0			0
$310$	7.15619	+	9.84966i	0.406445	+	0.559423i
$311$	−0.556511	+	7.07115i	−0.0315569	+	0.400968i	0.960772	+	0.277340i	$0.0894529\pi$
$311$	−0.556511	+	7.07115i	−0.0315569	+	0.400968i	−0.992329	+	0.123628i	$0.960547\pi$
$312$		0			0
$313$	−11.2409	+	13.1614i	−0.635371	+	0.743924i	−0.980906	−	0.194482i	$-0.937697\pi$
$313$	−11.2409	+	13.1614i	−0.635371	+	0.743924i	0.345535	+	0.938406i	$0.387697\pi$
$314$	10.4412	+	4.32488i	0.589230	+	0.244067i
$315$		0			0
$316$	−0.379395	−	4.82067i	−0.0213426	−	0.271184i
$317$	−5.13167	+	4.38286i	−0.288223	+	0.246166i	−0.781790	−	0.623542i	$-0.785693\pi$
$317$	−5.13167	+	4.38286i	−0.288223	+	0.246166i	0.493566	+	0.869708i	$0.335693\pi$
$318$		0			0
$319$	−4.57059	−	4.57059i	−0.255904	−	0.255904i
$320$	2.39103	+	1.21829i	0.133663	+	0.0681045i
$321$		0			0
$322$	−4.13689	−	17.2314i	−0.230540	−	0.960268i
$323$	−1.42327	−	2.79333i	−0.0791929	−	0.155425i
$324$		0			0
$325$	−0.540781	−	1.30556i	−0.0299971	−	0.0724194i
$326$	−16.6463	−	2.63652i	−0.921955	−	0.146023i
$327$		0			0
$328$	−5.59734	+	3.10963i	−0.309061	+	0.171701i
$329$			21.9147i			1.20820i
$330$		0			0
$331$	6.47343	−	2.68138i	0.355812	−	0.147382i	−0.197615	−	0.980280i	$-0.563320\pi$
$331$	6.47343	−	2.68138i	0.355812	−	0.147382i	0.553427	+	0.832898i	$0.313320\pi$
$332$	−4.00202	+	12.3170i	−0.219640	+	0.675981i
$333$		0			0
$334$	−6.74152	+	1.61850i	−0.368880	+	0.0885602i
$335$	−0.125361	+	0.522166i	−0.00684920	+	0.0285290i
$336$		0			0
$337$	−20.2903	+	20.2903i	−1.10528	+	1.10528i	−0.111520	+	0.993762i	$0.535572\pi$
$337$	−20.2903	+	20.2903i	−1.10528	+	1.10528i	−0.993762	+	0.111520i	$0.964428\pi$
$338$	−11.9718	+	3.88987i	−0.651179	+	0.211581i
$339$		0			0
$340$	−5.81873	+	0.457944i	−0.315565	+	0.0248355i
$341$	−15.6504	−	9.59058i	−0.847517	−	0.519359i
$342$		0			0
$343$	−15.0418	−	12.8469i	−0.812182	−	0.693669i
$344$	−1.87007	+	2.57393i	−0.100827	+	0.138777i
$345$		0			0
$346$	5.30088	−	3.85132i	0.284977	−	0.207048i
$347$	20.1613	−	12.3549i	1.08232	−	0.663243i	0.137386	−	0.990518i	$-0.456130\pi$
$347$	20.1613	−	12.3549i	1.08232	−	0.663243i	0.944929	+	0.327274i	$0.106130\pi$
$348$		0			0
$349$	14.6675	−	2.32311i	0.785134	−	0.124353i	0.249020	−	0.968498i	$-0.419892\pi$
$349$	14.6675	−	2.32311i	0.785134	−	0.124353i	0.536114	+	0.844145i	$0.319892\pi$
$350$	2.75848	+	4.50144i	0.147447	+	0.240612i
$351$		0			0
$352$	−4.03329	−	0.317427i	−0.214975	−	0.0169189i
$353$	10.0897	+	7.33058i	0.537019	+	0.390167i	0.822977	−	0.568075i	$-0.192312\pi$
$353$	10.0897	+	7.33058i	0.537019	+	0.390167i	−0.285958	+	0.958242i	$0.592312\pi$
$354$		0			0
$355$	−3.18922	+	7.69945i	−0.169266	+	0.408645i
$356$	0.780442	−	1.27356i	0.0413633	−	0.0674988i
$357$		0			0
$358$	13.5747	+	15.8940i	0.717447	+	0.840022i
$359$	−2.51900	−	7.75268i	−0.132948	−	0.409171i	0.862317	−	0.506368i	$-0.169012\pi$
$359$	−2.51900	−	7.75268i	−0.132948	−	0.409171i	−0.995265	+	0.0971972i	$0.969012\pi$
$360$		0			0
$361$	7.68263	−	15.0780i	0.404349	−	0.793580i
$362$	−12.1700	−	2.92176i	−0.639641	−	0.153564i
$363$		0			0
$364$	−1.37187	+	0.699001i	−0.0719053	+	0.0366376i
$365$	−17.5253	−	5.69432i	−0.917316	−	0.298054i
$366$		0			0
$367$	−2.70932	+	17.1060i	−0.141426	+	0.892926i	0.810309	+	0.586003i	$0.199299\pi$
$367$	−2.70932	+	17.1060i	−0.141426	+	0.892926i	−0.951734	+	0.306923i	$0.900701\pi$
$368$	−7.38876			−0.385166
$369$		0			0
$370$	8.76262			0.455547
$371$	−0.661554	+	4.17689i	−0.0343462	+	0.216853i
$372$		0			0
$373$	−19.0287	−	6.18281i	−0.985271	−	0.320134i	−0.228306	−	0.973589i	$-0.573319\pi$
$373$	−19.0287	−	6.18281i	−0.985271	−	0.320134i	−0.756965	+	0.653455i	$0.773319\pi$
$374$	7.84055	−	3.99496i	0.405425	−	0.206574i
$375$		0			0
$376$	8.88484	+	2.13306i	0.458201	+	0.110004i
$377$	−0.465637	+	0.913864i	−0.0239815	+	0.0470664i
$378$		0			0
$379$	−10.7150	−	32.9773i	−0.550391	−	1.69393i	−0.707815	−	0.706398i	$-0.750319\pi$
$379$	−10.7150	−	32.9773i	−0.550391	−	1.69393i	0.157424	−	0.987531i	$-0.449681\pi$
$380$	2.51202	+	2.94120i	0.128864	+	0.150880i
$381$		0			0
$382$	−2.48504	+	4.05521i	−0.127146	+	0.207483i
$383$	−9.24400	+	22.3170i	−0.472346	+	1.14034i	0.490777	+	0.871285i	$0.336713\pi$
$383$	−9.24400	+	22.3170i	−0.472346	+	1.14034i	−0.963123	+	0.269060i	$0.913287\pi$
$384$		0			0
$385$	−21.0658	−	15.3052i	−1.07361	−	0.780027i
$386$	−8.70943	−	0.685447i	−0.443299	−	0.0348884i
$387$		0			0
$388$	−9.51100	−	15.5205i	−0.482848	−	0.787936i
$389$	9.18313	−	1.45446i	0.465603	−	0.0737443i	0.0807746	−	0.996732i	$-0.474261\pi$
$389$	9.18313	−	1.45446i	0.465603	−	0.0737443i	0.384828	+	0.922988i	$0.374261\pi$
$390$		0			0
$391$	13.7026	−	8.39696i	0.692970	−	0.424653i
$392$	−1.00948	+	0.733432i	−0.0509866	+	0.0370439i
$393$		0			0
$394$	−4.28291	+	5.89493i	−0.215770	+	0.296982i
$395$	−9.86728	−	8.42745i	−0.496477	−	0.424031i
$396$		0			0
$397$	−23.1422	−	14.1815i	−1.16147	−	0.711751i	−0.198169	−	0.980168i	$-0.563500\pi$
$397$	−23.1422	−	14.1815i	−1.16147	−	0.711751i	−0.963303	+	0.268417i	$0.913500\pi$
$398$	8.61550	−	0.678055i	0.431856	−	0.0339878i
$399$		0			0
$400$	2.09351	−	0.680222i	0.104675	−	0.0340111i
$401$	11.6877	−	11.6877i	0.583657	−	0.583657i	−0.352250	−	0.935906i	$-0.614583\pi$
$401$	11.6877	−	11.6877i	0.583657	−	0.583657i	0.935906	+	0.352250i	$0.114583\pi$
$402$		0			0
$403$	−0.679921	+	2.83207i	−0.0338693	+	0.141076i
$404$	−6.17263	+	1.48192i	−0.307100	+	0.0737281i
$405$		0			0
$406$	1.18410	−	3.64428i	0.0587657	−	0.180862i
$407$	−12.2052	+	5.05557i	−0.604990	+	0.250595i
$408$		0			0
$409$		−	2.09539i		−	0.103611i	−0.998657	−	0.0518053i	$-0.983502\pi$
$409$		−	2.09539i		−	0.103611i	0.998657	−	0.0518053i	$-0.0164975\pi$
$410$	−4.72051	+	16.5217i	−0.233129	+	0.815950i
$411$		0			0
$412$	−11.3049	−	1.79052i	−0.556952	−	0.0882125i
$413$	11.4832	+	27.7230i	0.565054	+	1.36416i
$414$		0			0
$415$	15.7778	+	30.9658i	0.774504	+	1.52005i
$416$	0.149864	+	0.624230i	0.00734771	+	0.0306054i
$417$		0			0
$418$	−5.19585	−	2.64742i	−0.254137	−	0.129489i
$419$	0.166341	+	0.166341i	0.00812629	+	0.00812629i	0.711158	−	0.703032i	$-0.248171\pi$
$419$	0.166341	+	0.166341i	0.00812629	+	0.00812629i	−0.703032	+	0.711158i	$0.748171\pi$
$420$		0			0
$421$	24.0076	−	20.5044i	1.17006	−	0.999324i	0.170154	−	0.985417i	$-0.445573\pi$
$421$	24.0076	−	20.5044i	1.17006	−	0.999324i	0.999903	−	0.0139063i	$-0.00442666\pi$
$422$	1.62718	+	20.6753i	0.0792101	+	1.00646i
$423$		0			0
$424$	1.62904	+	0.674769i	0.0791130	+	0.0327697i
$425$	−3.10941	+	3.64065i	−0.150828	+	0.176597i
$426$		0			0
$427$	0.747137	−	9.49327i	0.0361565	−	0.459412i
$428$	2.31609	+	3.18783i	0.111953	+	0.154089i
$429$		0			0
$430$	1.33559	+	8.43261i	0.0644081	+	0.406657i
$431$	−3.32985	−	21.0238i	−0.160393	−	1.01268i	−0.928222	−	0.372027i	$-0.878663\pi$
$431$	−3.32985	−	21.0238i	−0.160393	−	1.01268i	0.767829	−	0.640655i	$-0.221337\pi$
$432$		0			0
$433$	12.3234	+	16.9617i	0.592225	+	0.815128i	0.994969	−	0.100185i	$-0.0319433\pi$
$433$	12.3234	+	16.9617i	0.592225	+	0.815128i	−0.402744	+	0.915313i	$0.631943\pi$
$434$	0.853730	−	10.8477i	0.0409803	−	0.520705i
$435$		0			0
$436$	13.2517	−	15.5157i	0.634641	−	0.743069i
$437$	−9.83926	−	4.07556i	−0.470676	−	0.194960i
$438$		0			0
$439$	−0.704291	−	8.94886i	−0.0336140	−	0.427106i	−0.990583	−	0.136915i	$-0.956281\pi$
$439$	−0.704291	−	8.94886i	−0.0336140	−	0.427106i	0.956969	−	0.290191i	$-0.0937187\pi$
$440$	−8.25561	+	7.05096i	−0.393571	+	0.336141i
$441$		0			0
$442$	−0.987333	−	0.987333i	−0.0469627	−	0.0469627i
$443$	31.7493	+	16.1771i	1.50846	+	0.768597i	0.995935	−	0.0900779i	$-0.0287116\pi$
$443$	31.7493	+	16.1771i	1.50846	+	0.768597i	0.512521	+	0.858675i	$0.328712\pi$
$444$		0			0
$445$	−0.935717	−	3.89754i	−0.0443572	−	0.184761i
$446$	0.991650	+	1.94622i	0.0469560	+	0.0921563i
$447$		0			0
$448$	−0.917819	−	2.21581i	−0.0433629	−	0.104687i
$449$	22.2616	+	3.52589i	1.05059	+	0.166397i	0.657771	−	0.753218i	$-0.271500\pi$
$449$	22.2616	+	3.52589i	1.05059	+	0.166397i	0.392820	+	0.919615i	$0.371500\pi$
$450$		0			0
$451$	−2.95710	−	25.7362i	−0.139244	−	1.21187i
$452$			16.8383i			0.792009i
$453$		0			0
$454$	1.68596	−	0.698349i	0.0791262	−	0.0327751i
$455$	−1.27678	+	3.92953i	−0.0598565	+	0.184219i
$456$		0			0
$457$	11.5524	−	2.77348i	0.540398	−	0.129738i	0.0459472	−	0.998944i	$-0.485369\pi$
$457$	11.5524	−	2.77348i	0.540398	−	0.129738i	0.494450	+	0.869206i	$0.335369\pi$
$458$	−6.40647	+	26.6849i	−0.299355	+	1.24690i
$459$		0			0
$460$	−14.0204	+	14.0204i	−0.653704	+	0.653704i
$461$	17.7549	−	5.76890i	0.826926	−	0.268685i	0.135176	−	0.990822i	$-0.456840\pi$
$461$	17.7549	−	5.76890i	0.826926	−	0.268685i	0.691750	+	0.722137i	$0.256840\pi$
$462$		0			0
$463$	−12.6408	+	0.994856i	−0.587470	+	0.0462349i	−0.368711	−	0.929544i	$-0.620201\pi$
$463$	−12.6408	+	0.994856i	−0.587470	+	0.0462349i	−0.218759	+	0.975779i	$0.570201\pi$
$464$	−1.36224	−	0.834781i	−0.0632403	−	0.0387537i
$465$		0			0
$466$	4.70726	+	4.02038i	0.218059	+	0.186240i
$467$	12.3675	−	17.0224i	0.572298	−	0.787701i	−0.420527	−	0.907280i	$-0.638155\pi$
$467$	12.3675	−	17.0224i	0.572298	−	0.787701i	0.992825	+	0.119579i	$0.0381546\pi$
$468$		0			0
$469$	0.388283	−	0.282104i	0.0179292	−	0.0130264i
$470$	20.9068	−	12.8117i	0.964359	−	0.590960i
$471$		0			0
$472$	12.3574	−	1.95722i	0.568796	−	0.0900884i
$473$	−6.72548	−	10.9750i	−0.309238	−	0.504631i
$474$		0			0
$475$	3.16303	+	0.248936i	0.145130	+	0.0114219i
$476$	4.22027	+	3.06621i	0.193436	+	0.140539i
$477$		0			0
$478$	−3.06515	+	7.39993i	−0.140197	+	0.338465i
$479$	−20.2124	+	32.9836i	−0.923526	+	1.50706i	−0.0627773	+	0.998028i	$0.519996\pi$
$479$	−20.2124	+	32.9836i	−0.923526	+	1.50706i	−0.860749	+	0.509030i	$0.830004\pi$
$480$		0			0
$481$	1.36141	+	1.59400i	0.0620748	+	0.0726803i
$482$	5.09027	+	15.6662i	0.231855	+	0.713577i
$483$		0			0
$484$	2.43710	−	4.78308i	0.110777	−	0.217413i
$485$	−47.4981	−	11.4033i	−2.15678	−	0.517796i
$486$		0			0
$487$	−6.77515	+	3.45211i	−0.307012	+	0.156430i	−0.600708	−	0.799469i	$-0.705115\pi$
$487$	−6.77515	+	3.45211i	−0.307012	+	0.156430i	0.293696	+	0.955899i	$0.405115\pi$
$488$	−3.77612	−	1.22694i	−0.170937	−	0.0555408i
$489$		0			0
$490$	−0.523814	+	3.30723i	−0.0236635	+	0.149406i
$491$	−36.0652			−1.62760			−0.813799	−	0.581146i	$-0.802604\pi$
$491$	−36.0652			−1.62760			−0.813799	+	0.581146i	$0.802604\pi$
$492$		0			0
$493$	3.47498			0.156505
$494$	−0.144751	+	0.913922i	−0.00651265	+	0.0411193i
$495$		0			0
$496$	−4.31485	−	1.40198i	−0.193743	−	0.0629508i
$497$	6.63650	−	3.38147i	0.297688	−	0.151679i
$498$		0			0
$499$	−7.16050	−	1.71908i	−0.320548	−	0.0769567i	0.0699784	−	0.997549i	$-0.477707\pi$
$499$	−7.16050	−	1.71908i	−0.320548	−	0.0769567i	−0.390526	+	0.920592i	$0.627707\pi$
$500$	−3.40970	+	6.69191i	−0.152486	+	0.299271i
$501$		0			0
$502$	8.18732	+	25.1980i	0.365418	+	1.12464i
$503$	1.94640	+	2.27894i	0.0867858	+	0.101613i	0.802100	−	0.597190i	$-0.203716\pi$
$503$	1.94640	+	2.27894i	0.0867858	+	0.101613i	−0.715314	+	0.698803i	$0.753716\pi$
$504$		0			0
$505$	−8.90076	+	14.5247i	−0.396079	+	0.646342i
$506$	11.4396	−	27.6177i	0.508553	−	1.22776i
$507$		0			0
$508$	11.5672	+	8.40404i	0.513210	+	0.372869i
$509$	11.5306	+	0.907481i	0.511087	+	0.0402234i	0.331381	−	0.943497i	$-0.392485\pi$
$509$	11.5306	+	0.907481i	0.511087	+	0.0402234i	0.179706	+	0.983720i	$0.442485\pi$
$510$		0			0
$511$	8.60514	+	14.0423i	0.380669	+	0.621196i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$		0			0
$514$	−18.5183	+	11.3480i	−0.816807	+	0.500540i
$515$	−24.8489	+	18.0538i	−1.09497	+	0.795546i
$516$		0			0
$517$	−21.7289	+	29.9072i	−0.955634	+	1.31532i
$518$	−5.95516	−	5.08618i	−0.261655	−	0.223474i
$519$		0			0
$520$	1.46887	+	0.900124i	0.0644141	+	0.0394730i
$521$	3.16521	−	0.249108i	0.138671	−	0.0109136i	−0.00893383	−	0.999960i	$-0.502844\pi$
$521$	3.16521	−	0.249108i	0.138671	−	0.0109136i	0.147604	+	0.989046i	$0.452844\pi$
$522$		0			0
$523$	8.79408	−	2.85737i	0.384538	−	0.124944i	−0.110367	−	0.993891i	$-0.535203\pi$
$523$	8.79408	−	2.85737i	0.384538	−	0.124944i	0.494905	+	0.868947i	$0.335203\pi$
$524$	−12.5535	+	12.5535i	−0.548404	+	0.548404i
$525$		0			0
$526$	1.71101	−	7.12689i	0.0746037	−	0.310747i
$527$	9.59526	−	2.30362i	0.417976	−	0.100347i
$528$		0			0
$529$	9.76302	−	30.0475i	0.424479	−	1.30641i
$530$	4.37154	−	1.81075i	0.189888	−	0.0786540i
$531$		0			0
$532$		−	3.45695i		−	0.149878i
$533$	−3.73886	+	1.70820i	−0.161948	+	0.0739904i
$534$		0			0
$535$	10.4439	+	1.65414i	0.451527	+	0.0715149i
$536$	−0.0765796	−	0.184879i	−0.00330773	−	0.00798558i
$537$		0			0
$538$	−7.71967	−	15.1507i	−0.332819	−	0.653193i
$539$	−1.17849	−	4.90877i	−0.0507612	−	0.211436i
$540$		0			0
$541$	32.8239	+	16.7246i	1.41121	+	0.719046i	0.982823	−	0.184550i	$-0.0590828\pi$
$541$	32.8239	+	16.7246i	1.41121	+	0.719046i	0.428385	+	0.903596i	$0.359083\pi$
$542$	−15.6679	−	15.6679i	−0.672994	−	0.672994i
$543$		0			0
$544$	1.65391	−	1.41257i	0.0709106	−	0.0605634i
$545$	−4.29609	−	54.5871i	−0.184024	−	2.33825i
$546$		0			0
$547$	−16.3989	−	6.79263i	−0.701164	−	0.290432i	0.00347853	−	0.999994i	$-0.498893\pi$
$547$	−16.3989	−	6.79263i	−0.701164	−	0.290432i	−0.704643	+	0.709562i	$0.748893\pi$
$548$	9.53285	−	11.1615i	0.407223	−	0.476797i
$549$		0			0
$550$	−0.698733	+	8.87825i	−0.0297941	+	0.378570i
$551$	−1.35357	−	1.86303i	−0.0576642	−	0.0793679i
$552$		0			0
$553$	1.81425	+	11.4547i	0.0771499	+	0.487105i
$554$	−1.94764	−	12.2969i	−0.0827474	−	0.522447i
$555$		0			0
$556$	2.94750	+	4.05689i	0.125002	+	0.172050i
$557$	−3.53529	+	44.9201i	−0.149795	+	1.90332i	0.222059	+	0.975033i	$0.428722\pi$
$557$	−3.53529	+	44.9201i	−0.149795	+	1.90332i	−0.371854	+	0.928291i	$0.621278\pi$
$558$		0			0
$559$	−1.32647	+	1.55309i	−0.0561035	+	0.0656888i
$560$	−5.94616	−	2.46298i	−0.251271	−	0.104080i
$561$		0			0
$562$	−2.50313	−	31.8053i	−0.105588	−	1.34163i
$563$	−11.3275	+	9.67457i	−0.477396	+	0.407734i	−0.855318	−	0.518103i	$-0.826638\pi$
$563$	−11.3275	+	9.67457i	−0.477396	+	0.407734i	0.377923	+	0.925837i	$0.376638\pi$
$564$		0			0
$565$	31.9513	+	31.9513i	1.34420	+	1.34420i
$566$	18.4430	+	9.39717i	0.775216	+	0.394993i
$567$		0			0
$568$	−0.724980	−	3.01976i	−0.0304195	−	0.126706i
$569$	16.7277	+	32.8299i	0.701261	+	1.37630i	0.916617	+	0.399766i	$0.130909\pi$
$569$	16.7277	+	32.8299i	0.701261	+	1.37630i	−0.215357	+	0.976535i	$0.569091\pi$
$570$		0			0
$571$	5.95598	+	14.3790i	0.249250	+	0.601743i	0.998141	−	0.0609505i	$-0.0194132\pi$
$571$	5.95598	+	14.3790i	0.249250	+	0.601743i	−0.748891	+	0.662694i	$0.769413\pi$
$572$	−2.56527	−	0.406299i	−0.107259	−	0.0169882i
$573$		0			0
$574$	12.7980	−	8.48835i	0.534178	−	0.354297i
$575$			16.2645i			0.678275i
$576$		0			0
$577$	15.5676	−	6.44829i	0.648086	−	0.268446i	−0.0343297	−	0.999411i	$-0.510930\pi$
$577$	15.5676	−	6.44829i	0.648086	−	0.268446i	0.682415	+	0.730965i	$0.260930\pi$
$578$	3.79140	−	11.6687i	0.157702	−	0.485356i
$579$		0			0
$580$	−4.16891	+	1.00087i	−0.173105	+	0.0415587i
$581$	7.25103	−	30.2027i	0.300824	−	1.25302i
$582$		0			0
$583$	−5.04429	+	5.04429i	−0.208913	+	0.208913i
$584$	6.53073	−	2.12196i	0.270244	−	0.0878075i
$585$		0			0
$586$	19.5313	−	1.53715i	0.806832	−	0.0634991i
$587$	26.2550	+	16.0891i	1.08366	+	0.664068i	0.945263	−	0.326309i	$-0.105805\pi$
$587$	26.2550	+	16.0891i	1.08366	+	0.664068i	0.138397	+	0.990377i	$0.455805\pi$
$588$		0			0
$589$	−4.97257	−	4.24697i	−0.204891	−	0.174994i
$590$	19.7347	−	27.1625i	0.812464	−	1.11826i
$591$		0			0
$592$	−2.64173	+	1.91933i	−0.108574	+	0.0788838i
$593$	21.2999	−	13.0526i	0.874682	−	0.536006i	−0.0111892	−	0.999937i	$-0.503562\pi$
$593$	21.2999	−	13.0526i	0.874682	−	0.536006i	0.885871	+	0.463932i	$0.153562\pi$
$594$		0			0
$595$	13.8263	−	2.18987i	0.566824	−	0.0897761i
$596$	−5.89671	−	9.62256i	−0.241539	−	0.394155i
$597$		0			0
$598$	−4.72873	−	0.372159i	−0.193372	−	0.0152187i
$599$	−26.8508	−	19.5083i	−1.09709	−	0.797086i	−0.116511	−	0.993189i	$-0.537171\pi$
$599$	−26.8508	−	19.5083i	−1.09709	−	0.797086i	−0.980583	+	0.196104i	$0.937171\pi$
$600$		0			0
$601$	17.9947	−	43.4432i	0.734021	−	1.77208i	0.105316	−	0.994439i	$-0.466414\pi$
$601$	17.9947	−	43.4432i	0.734021	−	1.77208i	0.628704	−	0.777644i	$-0.283586\pi$
$602$	3.98695	−	6.50611i	0.162496	−	0.265169i
$603$		0			0
$604$	−4.20161	−	4.91946i	−0.170961	−	0.200170i
$605$	−4.45156	−	13.7005i	−0.180982	−	0.557005i
$606$		0			0
$607$	−1.84422	+	3.61948i	−0.0748544	+	0.146910i	−0.925401	−	0.378990i	$-0.876271\pi$
$607$	−1.84422	+	3.61948i	−0.0748544	+	0.146910i	0.850546	+	0.525900i	$0.176271\pi$
$608$	−1.40155	−	0.336481i	−0.0568402	−	0.0136461i
$609$		0			0
$610$	−9.49345	+	4.83715i	−0.384379	+	0.195851i
$611$	5.57876	+	1.81265i	0.225692	+	0.0733319i
$612$		0			0
$613$	−4.72778	+	29.8500i	−0.190953	+	1.20563i	0.686919	+	0.726734i	$0.258963\pi$
$613$	−4.72778	+	29.8500i	−0.190953	+	1.20563i	−0.877872	+	0.478896i	$0.841037\pi$
$614$	10.0501			0.405587
$615$		0			0
$616$	9.70326			0.390955
$617$	3.33985	−	21.0870i	0.134457	−	0.848931i	−0.824599	−	0.565717i	$-0.808599\pi$
$617$	3.33985	−	21.0870i	0.134457	−	0.848931i	0.959057	−	0.283214i	$-0.0914006\pi$
$618$		0			0
$619$	−10.5946	−	3.44239i	−0.425832	−	0.138361i	0.0882577	−	0.996098i	$-0.471870\pi$
$619$	−10.5946	−	3.44239i	−0.425832	−	0.138361i	−0.514090	+	0.857737i	$0.671870\pi$
$620$	−10.8479	+	5.52726i	−0.435661	+	0.221980i
$621$		0			0
$622$	−6.89703	−	1.65583i	−0.276546	−	0.0663928i
$623$	−1.62637	+	3.19193i	−0.0651592	+	0.127882i
$624$		0			0
$625$	9.62920	+	29.6356i	0.385168	+	1.18543i
$626$	−11.2409	−	13.1614i	−0.449275	−	0.526034i
$627$		0			0
$628$	−5.90499	+	9.63607i	−0.235635	+	0.384521i
$629$	2.71791	−	6.56162i	0.108370	−	0.261629i
$630$		0			0
$631$	5.50490	+	3.99955i	0.219147	+	0.159219i	0.691943	−	0.721953i	$-0.256755\pi$
$631$	5.50490	+	3.99955i	0.219147	+	0.159219i	−0.472796	+	0.881172i	$0.656755\pi$
$632$	4.82067	+	0.379395i	0.191756	+	0.0150915i
$633$		0			0
$634$	−3.52613	−	5.75412i	−0.140041	−	0.228525i
$635$	37.8960	−	6.00213i	1.50386	−	0.238187i
$636$		0			0
$637$	−0.682999	+	0.418542i	−0.0270614	+	0.0165833i
$638$	5.22932	−	3.79932i	0.207031	−	0.150417i
$639$		0			0
$640$	−1.57733	+	2.17101i	−0.0623494	+	0.0858166i
$641$	−19.0349	−	16.2573i	−0.751832	−	0.642126i	0.188620	−	0.982050i	$-0.439598\pi$
$641$	−19.0349	−	16.2573i	−0.751832	−	0.642126i	−0.940453	+	0.339924i	$0.889598\pi$
$642$		0			0
$643$	−15.4866	−	9.49019i	−0.610731	−	0.374257i	0.182474	−	0.983211i	$-0.441589\pi$
$643$	−15.4866	−	9.49019i	−0.610731	−	0.374257i	−0.793205	+	0.608954i	$0.791589\pi$
$644$	17.6664	−	1.39038i	0.696154	−	0.0547885i
$645$		0			0
$646$	2.98159	−	0.968776i	0.117309	−	0.0381160i
$647$	0.0218838	−	0.0218838i	0.000860341	−	0.000860341i	−0.706676	−	0.707537i	$-0.749806\pi$
$647$	0.0218838	−	0.0218838i	0.000860341	−	0.000860341i	0.707537	+	0.706676i	$0.249806\pi$
$648$		0			0
$649$	−11.8166	+	49.2197i	−0.463843	+	1.93204i
$650$	1.37408	−	0.329888i	0.0538960	−	0.0129393i
$651$		0			0
$652$	5.20812	−	16.0289i	0.203966	−	0.627742i
$653$	−10.7278	+	4.44362i	−0.419813	+	0.173892i	−0.582582	−	0.812772i	$-0.697957\pi$
$653$	−10.7278	+	4.44362i	−0.419813	+	0.173892i	0.162769	+	0.986664i	$0.447957\pi$
$654$		0			0
$655$			47.6414i			1.86150i
$656$	−2.19573	−	6.01488i	−0.0857287	−	0.234842i
$657$		0			0
$658$	−21.6449	−	3.42821i	−0.843806	−	0.133646i
$659$	9.55878	+	23.0769i	0.372357	+	0.898949i	0.993350	+	0.115133i	$0.0367295\pi$
$659$	9.55878	+	23.0769i	0.372357	+	0.898949i	−0.620993	+	0.783816i	$0.713270\pi$
$660$		0			0
$661$	10.2255	+	20.0687i	0.397726	+	0.780581i	0.999841	−	0.0178285i	$-0.00567529\pi$
$661$	10.2255	+	20.0687i	0.397726	+	0.780581i	−0.602115	+	0.798409i	$0.705675\pi$
$662$	1.63570	+	6.81319i	0.0635734	+	0.264802i
$663$		0			0
$664$	−11.5393	−	5.87955i	−0.447810	−	0.228171i
$665$	−6.55967	−	6.55967i	−0.254373	−	0.254373i
$666$		0			0
$667$	8.97645	−	7.66661i	0.347570	−	0.296852i
$668$	−0.543964	−	6.91171i	−0.0210466	−	0.267422i
$669$		0			0
$670$	−0.496127	−	0.205502i	−0.0191670	−	0.00793925i
$671$	10.4324	−	12.2148i	0.402738	−	0.471546i
$672$		0			0
$673$	1.84802	−	23.4814i	0.0712361	−	0.905141i	−0.852652	−	0.522479i	$-0.825007\pi$
$673$	1.84802	−	23.4814i	0.0712361	−	0.905141i	0.923888	−	0.382662i	$-0.124993\pi$
$674$	−16.8664	−	23.2146i	−0.649669	−	0.894192i
$675$		0			0
$676$	−1.96918	−	12.4329i	−0.0757376	−	0.478188i
$677$	3.15427	+	19.9153i	0.121229	+	0.765407i	0.971145	+	0.238489i	$0.0766522\pi$
$677$	3.15427	+	19.9153i	0.121229	+	0.765407i	−0.849917	+	0.526917i	$0.823348\pi$
$678$		0			0
$679$	25.6612	+	35.3196i	0.984787	+	1.35544i
$680$	0.457944	−	5.81873i	0.0175614	−	0.223138i
$681$		0			0
$682$	11.9208	−	13.9574i	0.456470	−	0.534457i
$683$	7.80506	+	3.23296i	0.298652	+	0.123706i	0.526978	−	0.849879i	$-0.323325\pi$
$683$	7.80506	+	3.23296i	0.298652	+	0.123706i	−0.228326	+	0.973585i	$0.573325\pi$
$684$		0			0
$685$	−3.09048	−	39.2682i	−0.118081	−	1.50036i
$686$	15.0418	−	12.8469i	0.574299	−	0.490498i
$687$		0			0
$688$	−2.24969	−	2.24969i	−0.0857688	−	0.0857688i
$689$	1.00858	+	0.513896i	0.0384238	+	0.0195779i
$690$		0			0
$691$	−5.18167	−	21.5832i	−0.197120	−	0.821064i	−0.980017	−	0.198913i	$-0.936259\pi$
$691$	−5.18167	−	21.5832i	−0.197120	−	0.821064i	0.782897	−	0.622151i	$-0.213741\pi$
$692$	2.97466	+	5.83810i	0.113080	+	0.221931i
$693$		0			0
$694$	9.04883	+	21.8458i	0.343489	+	0.829255i
$695$	13.2910	+	2.10510i	0.504158	+	0.0798508i
$696$		0			0
$697$	10.9076	+	8.65937i	0.413156	+	0.327997i
$698$			14.8503i			0.562094i
$699$		0			0
$700$	−4.87754	+	2.02034i	−0.184354	+	0.0763618i
$701$	−8.83838	+	27.2017i	−0.333821	+	1.02740i	0.633479	+	0.773760i	$0.281626\pi$
$701$	−8.83838	+	27.2017i	−0.333821	+	1.02740i	−0.967300	+	0.253635i	$0.918374\pi$
$702$		0			0
$703$	−4.57654	+	1.09873i	−0.172607	+	0.0414394i
$704$	0.944464	−	3.93398i	0.0355958	−	0.148267i
$705$		0			0
$706$	−8.81870	+	8.81870i	−0.331896	+	0.331896i
$707$	14.4798	−	4.70477i	0.544568	−	0.176941i
$708$		0			0
$709$	35.4088	−	2.78673i	1.32981	−	0.104658i	0.606444	−	0.795127i	$-0.292596\pi$
$709$	35.4088	−	2.78673i	1.32981	−	0.104658i	0.723362	+	0.690469i	$0.242596\pi$
$710$	−7.10576	−	4.35441i	−0.266674	−	0.163418i
$711$		0			0
$712$	1.13580	+	0.970062i	0.0425658	+	0.0363546i
$713$	19.7038	−	27.1200i	0.737913	−	1.01565i
$714$		0			0
$715$	−5.63865	+	4.09672i	−0.210873	+	0.153209i
$716$	−17.8218	+	10.9212i	−0.666034	+	0.408146i
$717$		0			0
$718$	8.05129	−	1.27520i	0.300471	−	0.0475900i
$719$	2.23174	+	3.64186i	0.0832297	+	0.135819i	0.891546	−	0.452929i	$-0.149621\pi$
$719$	2.23174	+	3.64186i	0.0832297	+	0.135819i	−0.808317	+	0.588748i	$0.799621\pi$
$720$		0			0
$721$	27.3667	+	2.15381i	1.01919	+	0.0802120i
$722$	13.6906	+	9.94677i	0.509510	+	0.370180i
$723$		0			0
$724$	4.78959	−	11.5631i	0.178004	−	0.429739i
$725$	−1.83756	+	2.99862i	−0.0682451	+	0.111366i
$726$		0			0
$727$	29.0710	+	34.0378i	1.07819	+	1.26239i	0.963131	+	0.269034i	$0.0867044\pi$
$727$	29.0710	+	34.0378i	1.07819	+	1.26239i	0.115055	+	0.993359i	$0.463296\pi$
$728$	−0.475788	−	1.46432i	−0.0176339	−	0.0542715i
$729$		0			0
$730$	8.36577	−	16.4188i	0.309631	−	0.607685i
$731$	6.72876	+	1.61543i	0.248872	+	0.0597490i
$732$		0			0
$733$	−1.88820	+	0.962085i	−0.0697422	+	0.0355354i	−0.488514	−	0.872556i	$-0.662461\pi$
$733$	−1.88820	+	0.962085i	−0.0697422	+	0.0355354i	0.418772	+	0.908092i	$0.362461\pi$
$734$	−16.4716	−	5.35194i	−0.607977	−	0.197544i
$735$		0			0
$736$	1.15586	−	7.29779i	0.0426055	−	0.269000i
$737$	0.809605			0.0298222
$738$		0			0
$739$	32.3300			1.18928			0.594640	−	0.803992i	$-0.297295\pi$
$739$	32.3300			1.18928			0.594640	+	0.803992i	$0.297295\pi$
$740$	−1.37078	+	8.65474i	−0.0503907	+	0.318154i
$741$		0			0
$742$	−4.02197	−	1.30682i	−0.147651	−	0.0479748i
$743$	−18.3539	+	9.35177i	−0.673339	+	0.343083i	−0.757004	−	0.653411i	$-0.773337\pi$
$743$	−18.3539	+	9.35177i	−0.673339	+	0.343083i	0.0836648	+	0.996494i	$0.473337\pi$
$744$		0			0
$745$	−29.4483	−	7.06991i	−1.07890	−	0.259021i
$746$	9.08344	−	17.8273i	0.332569	−	0.652702i
$747$		0			0
$748$	2.71924	+	8.36897i	0.0994253	+	0.306000i
$749$	−6.13761	−	7.18621i	−0.224263	−	0.262579i
$750$		0			0
$751$	23.0098	−	37.5486i	0.839639	−	1.37017i	−0.0877792	−	0.996140i	$-0.527977\pi$
$751$	23.0098	−	37.5486i	0.839639	−	1.37017i	0.927418	−	0.374026i	$-0.122023\pi$
$752$	−3.49669	+	8.44177i	−0.127511	+	0.307840i
$753$		0			0
$754$	−0.829771	−	0.602864i	−0.0302185	−	0.0219550i
$755$	−17.3075	−	1.36213i	−0.629885	−	0.0495730i
$756$		0			0
$757$	−14.0860	−	22.9862i	−0.511963	−	0.835448i	0.487323	−	0.873222i	$-0.337973\pi$
$757$	−14.0860	−	22.9862i	−0.511963	−	0.835448i	−0.999286	+	0.0377740i	$0.987973\pi$
$758$	34.2475	−	5.42427i	1.24392	−	0.197018i
$759$		0			0
$760$	−3.29796	+	2.02099i	−0.119630	+	0.0733091i
$761$	−5.08791	+	3.69658i	−0.184436	+	0.134001i	−0.676172	−	0.736743i	$-0.736363\pi$
$761$	−5.08791	+	3.69658i	−0.184436	+	0.134001i	0.491736	+	0.870744i	$0.336363\pi$
$762$		0			0
$763$	−28.7649	+	39.5915i	−1.04136	+	1.43331i
$764$	−3.61654	−	3.08882i	−0.130842	−	0.111750i
$765$		0			0
$766$	−20.5962	−	12.6213i	−0.744169	−	0.456027i
$767$	8.00719	−	0.630180i	0.289123	−	0.0227545i
$768$		0			0
$769$	−15.9465	+	5.18135i	−0.575047	+	0.186844i	−0.582081	−	0.813131i	$-0.697761\pi$
$769$	−15.9465	+	5.18135i	−0.575047	+	0.186844i	0.00703341	+	0.999975i	$0.497761\pi$
$770$	18.4122	−	18.4122i	0.663530	−	0.663530i
$771$		0			0
$772$	2.03946	−	8.49498i	0.0734019	−	0.305741i
$773$	30.0859	−	7.22299i	1.08211	−	0.259793i	0.347089	−	0.937832i	$-0.387170\pi$
$773$	30.0859	−	7.22299i	1.08211	−	0.259793i	0.735026	+	0.678039i	$0.237170\pi$
$774$		0			0
$775$	−3.08610	+	9.49804i	−0.110856	+	0.341180i
$776$	16.8173	−	6.96595i	0.603706	−	0.250063i
$777$		0			0
$778$			9.29760i			0.333335i
$779$	0.393793	−	9.22087i	0.0141091	−	0.330372i
$780$		0			0
$781$	12.4097	+	1.96550i	0.444054	+	0.0703312i
$782$	6.15002	+	14.8475i	0.219924	+	0.530944i
$783$		0			0
$784$	−0.566484	−	1.11179i	−0.0202316	−	0.0397067i
$785$	7.07984	+	29.4896i	0.252690	+	1.05253i
$786$		0			0
$787$	−37.8371	−	19.2789i	−1.34875	−	0.687220i	−0.377658	−	0.925945i	$-0.623271\pi$
$787$	−37.8371	−	19.2789i	−1.34875	−	0.687220i	−0.971087	+	0.238725i	$0.923271\pi$
$788$	−5.15235	−	5.15235i	−0.183545	−	0.183545i
$789$		0			0
$790$	9.86728	−	8.42745i	0.351062	−	0.299835i
$791$	−3.16855	−	40.2602i	−0.112661	−	1.43149i
$792$		0			0
$793$	−2.35488	−	0.975422i	−0.0836241	−	0.0346382i
$794$	17.6272	−	20.6388i	0.625565	−	0.732442i
$795$		0			0
$796$	−0.678055	+	8.61550i	−0.0240330	+	0.305368i
$797$	−7.76681	−	10.6901i	−0.275114	−	0.378662i	0.648994	−	0.760794i	$-0.275190\pi$
$797$	−7.76681	−	10.6901i	−0.275114	−	0.378662i	−0.924108	+	0.382131i	$0.875190\pi$
$798$		0			0
$799$	−3.10896	−	19.6292i	−0.109987	−	0.694432i
$800$	0.344350	+	2.17414i	0.0121746	+	0.0768675i
$801$		0			0
$802$	9.71546	+	13.3722i	0.343065	+	0.472188i
$803$	−2.17971	+	27.6959i	−0.0769203	+	0.977366i
$804$		0			0
$805$	30.8843	−	36.1608i	1.08853	−	1.27450i
$806$	−2.69084	−	1.11458i	−0.0947809	−	0.0392595i
$807$		0			0
$808$	−0.498060	−	6.32845i	−0.0175217	−	0.222634i
$809$	−30.8888	+	26.3815i	−1.08599	+	0.927524i	−0.997647	−	0.0685655i	$-0.978158\pi$
$809$	−30.8888	+	26.3815i	−1.08599	+	0.927524i	−0.0883450	+	0.996090i	$0.528158\pi$
$810$		0			0
$811$	−9.64302	−	9.64302i	−0.338612	−	0.338612i	0.517233	−	0.855845i	$-0.326962\pi$
$811$	−9.64302	−	9.64302i	−0.338612	−	0.338612i	−0.855845	+	0.517233i	$0.826962\pi$
$812$	3.41417	+	1.73961i	0.119814	+	0.0610483i
$813$		0			0
$814$	−3.08401	−	12.8458i	−0.108094	−	0.450246i
$815$	−20.5328	−	40.2980i	−0.719234	−	1.41158i
$816$		0			0
$817$	−1.75491	−	4.23672i	−0.0613964	−	0.148224i
$818$	2.06960	+	0.327792i	0.0723618	+	0.0114610i
$819$		0			0
$820$	−15.5799	−	7.24696i	−0.544073	−	0.253075i
$821$		−	16.7984i		−	0.586267i	−0.956072	−	0.293133i	$-0.905302\pi$
$821$		−	16.7984i		−	0.586267i	0.956072	−	0.293133i	$-0.0946980\pi$
$822$		0			0
$823$	38.5837	−	15.9819i	1.34494	−	0.557094i	0.410063	−	0.912057i	$-0.365507\pi$
$823$	38.5837	−	15.9819i	1.34494	−	0.557094i	0.934880	+	0.354964i	$0.115507\pi$
$824$	3.53695	−	10.8856i	0.123215	−	0.379218i
$825$		0			0
$826$	−29.1781	+	7.00504i	−1.01523	+	0.243736i
$827$	−4.13080	+	17.2060i	−0.143642	+	0.598312i	0.853387	+	0.521279i	$0.174545\pi$
$827$	−4.13080	+	17.2060i	−0.143642	+	0.598312i	−0.997029	+	0.0770332i	$0.975455\pi$
$828$		0			0
$829$	−23.4482	+	23.4482i	−0.814391	+	0.814391i	−0.985289	−	0.170898i	$-0.945333\pi$
$829$	−23.4482	+	23.4482i	−0.814391	+	0.814391i	0.170898	+	0.985289i	$0.445333\pi$
$830$	−33.0527	+	10.7395i	−1.14728	+	0.372773i
$831$		0			0
$832$	−0.639989	+	0.0503682i	−0.0221876	+	0.00174620i
$833$	2.31405	+	1.41805i	0.0801770	+	0.0491325i
$834$		0			0
$835$	−14.1474	−	12.0830i	−0.489590	−	0.418149i
$836$	3.42763	−	4.71773i	0.118547	−	0.163166i
$837$		0			0
$838$	−0.190315	+	0.138272i	−0.00657431	+	0.00477651i
$839$	33.4212	−	20.4805i	1.15383	−	0.707066i	0.192181	−	0.981359i	$-0.438444\pi$
$839$	33.4212	−	20.4805i	1.15383	−	0.707066i	0.961646	+	0.274293i	$0.0884438\pi$
$840$		0			0
$841$	−26.1218	+	4.13729i	−0.900753	+	0.142665i
$842$	16.4964	+	26.9196i	0.568502	+	0.927711i
$843$		0			0
$844$	−20.6753	−	1.62718i	−0.711675	−	0.0560100i
$845$	−27.3284	−	19.8552i	−0.940125	−	0.683041i
$846$		0			0
$847$	−4.92701	+	11.8949i	−0.169294	+	0.408712i
$848$	−0.921299	+	1.50342i	−0.0316375	+	0.0516277i
$849$		0			0
$850$	−3.10941	−	3.64065i	−0.106652	−	0.124873i
$851$	−7.45563	−	22.9461i	−0.255576	−	0.786581i
$852$		0			0
$853$	−13.1643	+	25.8364i	−0.450736	+	0.884620i	0.548101	+	0.836412i	$0.315351\pi$
$853$	−13.1643	+	25.8364i	−0.450736	+	0.884620i	−0.998837	+	0.0482078i	$0.984649\pi$
$854$	9.25952	+	2.22301i	0.316854	+	0.0760699i
$855$		0			0
$856$	−3.51090	+	1.78889i	−0.120000	+	0.0611431i
$857$	24.0974	+	7.82971i	0.823151	+	0.267458i	0.690158	−	0.723659i	$-0.257541\pi$
$857$	24.0974	+	7.82971i	0.823151	+	0.267458i	0.132993	+	0.991117i	$0.457541\pi$
$858$		0			0
$859$	−1.86434	+	11.7710i	−0.0636105	+	0.401621i	0.935254	+	0.353978i	$0.115171\pi$
$859$	−1.86434	+	11.7710i	−0.0636105	+	0.401621i	−0.998864	+	0.0476433i	$0.984829\pi$
$860$	−8.53772			−0.291134
$861$		0			0
$862$	21.2859			0.725000
$863$	−1.93190	+	12.1975i	−0.0657625	+	0.415208i	0.932742	+	0.360544i	$0.117409\pi$
$863$	−1.93190	+	12.1975i	−0.0657625	+	0.415208i	−0.998505	+	0.0546642i	$0.982591\pi$
$864$		0			0
$865$	16.7225	+	5.43346i	0.568581	+	0.184743i
$866$	−18.6807	+	9.51829i	−0.634796	+	0.323445i
$867$		0			0
$868$	10.5806	+	2.54017i	0.359128	+	0.0862189i
$869$	−8.88168	+	17.4313i	−0.301290	+	0.591315i
$870$		0			0
$871$	−0.0396980	−	0.122178i	−0.00134512	−	0.00413984i
$872$	13.2517	+	15.5157i	0.448759	+	0.525429i
$873$		0			0
$874$	5.56458	−	9.08057i	0.188225	−	0.307155i
$875$	6.89328	−	16.6419i	0.233035	−	0.562597i
$876$		0			0
$877$	−5.42894	−	3.94435i	−0.183322	−	0.133191i	0.492339	−	0.870403i	$-0.336142\pi$
$877$	−5.42894	−	3.94435i	−0.183322	−	0.133191i	−0.675662	+	0.737212i	$0.736142\pi$
$878$	8.94886	+	0.704291i	0.302009	+	0.0237687i
$879$		0			0
$880$	−5.67269	−	9.25699i	−0.191226	−	0.312053i
$881$	37.3995	−	5.92350i	1.26002	−	0.199568i	0.509533	−	0.860451i	$-0.329818\pi$
$881$	37.3995	−	5.92350i	1.26002	−	0.199568i	0.750488	+	0.660884i	$0.229818\pi$
$882$		0			0
$883$	30.1820	−	18.4955i	1.01570	−	0.622424i	0.0881478	−	0.996107i	$-0.471905\pi$
$883$	30.1820	−	18.4955i	1.01570	−	0.622424i	0.927556	+	0.373683i	$0.121905\pi$
$884$	1.12963	−	0.820725i	0.0379936	−	0.0276040i
$885$		0			0
$886$	−20.9446	+	28.8278i	−0.703648	+	0.968488i
$887$	−35.4592	−	30.2850i	−1.19060	−	1.01687i	−0.999376	−	0.0353251i	$-0.988753\pi$
$887$	−35.4592	−	30.2850i	−1.19060	−	1.01687i	−0.191227	−	0.981546i	$-0.561247\pi$
$888$		0			0
$889$	−29.2383	−	17.9173i	−0.980622	−	0.600926i
$890$	3.99593	−	0.314487i	0.133944	−	0.0105416i
$891$		0			0
$892$	−2.07739	+	0.674985i	−0.0695561	+	0.0226002i
$893$	−9.31276	+	9.31276i	−0.311640	+	0.311640i
$894$		0			0
$895$	−13.0941	+	54.5409i	−0.437688	+	1.82310i
$896$	2.33211	−	0.559890i	0.0779103	−	0.0187046i
$897$		0			0
$898$	−6.96497	+	21.4360i	−0.232424	+	0.715327i
$899$	6.69673	−	2.77387i	0.223348	−	0.0925139i
$900$		0			0
$901$		−	3.83514i		−	0.127767i
$902$	25.8819	+	1.10533i	0.861773	+	0.0368035i
$903$		0			0
$904$	−16.6310	−	2.63410i	−0.553140	−	0.0876088i
$905$	−12.8529	−	31.0297i	−0.427246	−	1.03146i
$906$		0			0
$907$	13.2797	+	26.0629i	0.440946	+	0.865406i	0.999357	+	0.0358414i	$0.0114111\pi$
$907$	13.2797	+	26.0629i	0.440946	+	0.865406i	−0.558411	+	0.829564i	$0.688589\pi$
$908$	0.426008	+	1.77445i	0.0141376	+	0.0588873i
$909$		0			0
$910$	−3.68142	−	1.87578i	−0.122038	−	0.0621814i
$911$	−16.5129	−	16.5129i	−0.547097	−	0.547097i	0.378503	−	0.925600i	$-0.376439\pi$
$911$	−16.5129	−	16.5129i	−0.547097	−	0.547097i	−0.925600	+	0.378503i	$0.876439\pi$
$912$		0			0
$913$	39.8422	−	34.0284i	1.31858	−	1.12618i
$914$	0.932145	+	11.8440i	0.0308326	+	0.391765i
$915$		0			0
$916$	−25.3541	−	10.5020i	−0.837724	−	0.346997i
$917$	27.6530	−	32.3776i	0.913184	−	1.06920i
$918$		0			0
$919$	−3.36291	+	42.7298i	−0.110932	+	1.40953i	0.649625	+	0.760255i	$0.274926\pi$
$919$	−3.36291	+	42.7298i	−0.110932	+	1.40953i	−0.760557	+	0.649271i	$0.775074\pi$
$920$	−11.6545	−	16.0411i	−0.384238	−	0.528858i
$921$		0			0
$922$	2.92041	+	18.4387i	0.0961785	+	0.607247i
$923$	−0.311879	−	1.96913i	−0.0102656	−	0.0648147i
$924$		0			0
$925$	4.22490	+	5.81508i	0.138914	+	0.191199i
$926$	0.994856	−	12.6408i	0.0326930	−	0.415404i
$927$		0			0
$928$	1.03760	−	1.21488i	0.0340610	−	0.0398804i
$929$	7.25279	+	3.00420i	0.237956	+	0.0985647i	0.498475	−	0.866904i	$-0.333894\pi$
$929$	7.25279	+	3.00420i	0.237956	+	0.0985647i	−0.260519	+	0.965469i	$0.583894\pi$
$930$		0			0
$931$	−0.141111	−	1.79298i	−0.00462472	−	0.0587626i
$932$	−4.70726	+	4.02038i	−0.154191	+	0.131692i
$933$		0			0
$934$	14.8781	+	14.8781i	0.486826	+	0.486826i
$935$	21.0402	+	10.7205i	0.688088	+	0.350599i
$936$		0			0
$937$	0.102860	+	0.428443i	0.00336029	+	0.0139966i	0.974025	−	0.226441i	$-0.0727091\pi$
$937$	0.102860	+	0.428443i	0.00336029	+	0.0139966i	−0.970665	+	0.240438i	$0.922709\pi$
$938$	0.217890	+	0.427633i	0.00711436	+	0.0139627i
$939$		0			0
$940$	9.38343	+	22.6536i	0.306054	+	0.738879i
$941$	0.499973	+	0.0791879i	0.0162987	+	0.00258145i	0.164578	−	0.986364i	$-0.447374\pi$
$941$	0.499973	+	0.0791879i	0.0162987	+	0.00258145i	−0.148280	+	0.988945i	$0.547374\pi$
$942$		0			0
$943$	47.2807	−	1.69617i	1.53967	−	0.0552348i
$944$			12.5114i			0.407213i
$945$		0			0
$946$	11.8920	−	4.92582i	0.386641	−	0.160152i
$947$	−11.3618	+	34.9681i	−0.369210	+	1.13631i	0.578092	+	0.815971i	$0.303797\pi$
$947$	−11.3618	+	34.9681i	−0.369210	+	1.13631i	−0.947302	+	0.320341i	$0.896203\pi$
$948$		0			0
$949$	4.28648	−	1.02909i	0.139145	−	0.0334057i
$950$	−0.740677	+	3.08514i	−0.0240307	+	0.100095i
$951$		0			0
$952$	−3.68865	+	3.68865i	−0.119550	+	0.119550i
$953$	−56.0825	+	18.2223i	−1.81669	+	0.590278i	−0.816779	+	0.576950i	$0.804243\pi$
$953$	−56.0825	+	18.2223i	−1.81669	+	0.590278i	−0.999911	+	0.0133281i	$0.995757\pi$
$954$		0			0
$955$	−12.7236	+	1.00137i	−0.411727	+	0.0324036i
$956$	−6.82933	−	4.18502i	−0.220876	−	0.135353i
$957$		0			0
$958$	−29.4156	−	25.1233i	−0.950374	−	0.811696i
$959$	−20.6926	+	28.4809i	−0.668198	+	0.919695i
$960$		0			0
$961$	−8.42712	+	6.12266i	−0.271843	+	0.197505i
$962$	−1.78735	+	1.09529i	−0.0576264	+	0.0353135i
$963$		0			0
$964$	−16.2697	+	2.57686i	−0.524010	+	0.0829951i
$965$	−12.2495	−	19.9894i	−0.394327	−	0.643482i
$966$		0			0
$967$	−25.9232	−	2.04020i	−0.833633	−	0.0656083i	−0.345544	−	0.938402i	$-0.612306\pi$
$967$	−25.9232	−	2.04020i	−0.833633	−	0.0656083i	−0.488089	+	0.872794i	$0.662306\pi$
$968$	4.34294	+	3.15533i	0.139587	+	0.101416i
$969$		0			0
$970$	18.6932	−	45.1295i	0.600203	−	1.44902i
$971$	−1.02865	+	1.67861i	−0.0330110	+	0.0538691i	−0.868720	−	0.495303i	$-0.835057\pi$
$971$	−1.02865	+	1.67861i	−0.0330110	+	0.0538691i	0.835709	+	0.549172i	$0.185057\pi$
$972$		0			0
$973$	−7.81083	−	9.14531i	−0.250404	−	0.293185i
$974$	−2.34974	−	7.23177i	−0.0752907	−	0.231721i
$975$		0			0
$976$	1.80255	−	3.53769i	0.0576981	−	0.113239i
$977$	−17.2603	−	4.14382i	−0.552205	−	0.132573i	−0.0522656	−	0.998633i	$-0.516644\pi$
$977$	−17.2603	−	4.14382i	−0.552205	−	0.132573i	−0.499939	+	0.866061i	$0.666644\pi$
$978$		0			0
$979$	−5.38439	+	2.74348i	−0.172086	+	0.0876821i
$980$	−3.18457	−	1.03473i	−0.101727	−	0.0330532i
$981$		0			0
$982$	5.64183	−	35.6211i	0.180038	−	1.13672i
$983$	−34.5126			−1.10078			−0.550390	−	0.834907i	$-0.685521\pi$
$983$	−34.5126			−1.10078			−0.550390	+	0.834907i	$0.685521\pi$
$984$		0			0
$985$	−19.5535			−0.623026
$986$	−0.543607	+	3.43220i	−0.0173120	+	0.109304i
$987$		0			0
$988$	−0.880026	−	0.285938i	−0.0279973	−	0.00909689i
$989$	20.9455	−	10.6723i	0.666028	−	0.339358i
$990$		0			0
$991$	23.2340	+	5.57800i	0.738054	+	0.177191i	0.585007	−	0.811028i	$-0.301092\pi$
$991$	23.2340	+	5.57800i	0.738054	+	0.177191i	0.153046	+	0.988219i	$0.451092\pi$
$992$	2.05971	−	4.04241i	0.0653959	−	0.128347i
$993$		0			0
$994$	2.30166	+	7.08377i	0.0730041	+	0.224684i
$995$	15.0615	+	17.6348i	0.477483	+	0.559061i
$996$		0			0
$997$	−25.5769	+	41.7378i	−0.810030	+	1.32185i	0.133663	+	0.991027i	$0.457326\pi$
$997$	−25.5769	+	41.7378i	−0.810030	+	1.32185i	−0.943693	+	0.330822i	$0.892674\pi$
$998$	2.81807	−	6.80342i	0.0892044	−	0.215358i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.a.179.1	✓	48
3.2	odd	2		738.2.ba.b.179.3	yes	48
41.11	odd	40		738.2.ba.b.503.3	yes	48
123.11	even	40	inner	738.2.ba.a.503.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.179.1	✓	48	1.1	even	1	trivial
738.2.ba.a.503.1	yes	48	123.11	even	40	inner
738.2.ba.b.179.3	yes	48	3.2	odd	2
738.2.ba.b.503.3	yes	48	41.11	odd	40

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)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-2.39103 + 1.21829i) q^{5} +(2.33211 + 0.559890i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.829251 - 2.55217i) q^{10} +(2.62751 + 3.07642i) q^{11} +(0.335427 - 0.547368i) q^{13} +(-0.917819 + 2.21581i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-2.16833 - 0.170651i) q^{17} +(0.753114 + 1.22897i) q^{19} +(2.65047 - 0.419794i) q^{20} +(-3.44958 + 2.11390i) q^{22} +(-5.97763 + 4.34300i) q^{23} +(1.29386 - 1.78084i) q^{25} +(0.488156 + 0.416925i) q^{26} +(-2.04495 - 1.25315i) q^{28} +(-1.59275 + 0.125352i) q^{29} +(-4.31485 + 1.40198i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.507751 - 2.11493i) q^{34} +(-6.25825 + 1.50247i) q^{35} +(-1.00905 + 3.10554i) q^{37} +(-1.33165 + 0.551589i) q^{38} +2.68351i q^{40} +(-5.31184 - 3.57552i) q^{41} +(-3.14238 - 0.497704i) q^{43} +(-1.54825 - 3.73779i) q^{44} +(-3.35443 - 6.58343i) q^{46} +(2.13306 + 8.88484i) q^{47} +(-1.11179 - 0.566484i) q^{49} +(1.55651 + 1.55651i) q^{50} +(-0.488156 + 0.416925i) q^{52} +(0.138343 + 1.75782i) q^{53} +(-10.0304 - 4.15474i) q^{55} +(1.55762 - 1.82374i) q^{56} +(0.125352 - 1.59275i) q^{58} +(7.35405 + 10.1220i) q^{59} +(-0.621115 - 3.92156i) q^{61} +(-0.709728 - 4.48105i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(-0.135164 + 1.71742i) q^{65} +(0.129962 - 0.152166i) q^{67} +(2.00947 + 0.832348i) q^{68} +(-0.504969 - 6.41624i) q^{70} +(2.36149 - 2.01690i) q^{71} +(4.85557 + 4.85557i) q^{73} +(-2.90945 - 1.48244i) q^{74} +(-0.336481 - 1.40155i) q^{76} +(4.40519 + 8.64566i) q^{77} +(1.85049 + 4.46749i) q^{79} +(-2.65047 - 0.419794i) q^{80} +(4.36246 - 4.68711i) q^{82} -12.9508i q^{83} +(5.39243 - 2.23362i) q^{85} +(0.983152 - 3.02583i) q^{86} +(3.93398 - 0.944464i) q^{88} +(-0.348691 + 1.45240i) q^{89} +(1.08872 - 1.08872i) q^{91} +(7.02713 - 2.28325i) q^{92} +(-9.10914 + 0.716904i) q^{94} +(-3.29796 - 2.02099i) q^{95} +(13.8416 + 11.8218i) q^{97} +(0.733432 - 1.00948i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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