LMFDB - Embedded newform 648.2.v.b.35.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(35,648)] 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("648.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.28
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27615 + 0.609466i) q^{2} +(1.25710 + 1.55554i) q^{4} +(0.426624 + 0.155279i) q^{5} +(1.28150 + 0.225962i) q^{7} +(0.656202 + 2.75125i) q^{8} +(0.449799 + 0.458171i) q^{10} +(-0.00602720 - 0.0165596i) q^{11} +(1.43581 + 1.71113i) q^{13} +(1.49766 + 1.06939i) q^{14} +(-0.839384 + 3.91094i) q^{16} +(-1.27216 + 0.734483i) q^{17} +(0.677841 - 1.17406i) q^{19} +(0.294769 + 0.858831i) q^{20} +(0.00240091 - 0.0248058i) q^{22} +(-0.369486 - 2.09546i) q^{23} +(-3.67233 - 3.08145i) q^{25} +(0.789428 + 3.05873i) q^{26} +(1.25948 + 2.27747i) q^{28} +(5.56933 + 4.67322i) q^{29} +(8.87753 - 1.56535i) q^{31} +(-3.45476 + 4.47936i) q^{32} +(-2.07111 + 0.161969i) q^{34} +(0.511630 + 0.295390i) q^{35} +(-4.58718 + 2.64841i) q^{37} +(1.58057 - 1.08515i) q^{38} +(-0.147259 + 1.27565i) q^{40} +(-1.56527 - 1.86542i) q^{41} +(-10.1956 + 3.71089i) q^{43} +(0.0181822 - 0.0301926i) q^{44} +(0.805592 - 2.89930i) q^{46} +(0.791397 - 4.48824i) q^{47} +(-4.98668 - 1.81500i) q^{49} +(-2.80839 - 6.17054i) q^{50} +(-0.856765 + 4.38452i) q^{52} +10.4085 q^{53} -0.00800062i q^{55} +(0.219241 + 3.67400i) q^{56} +(4.25911 + 9.35804i) q^{58} +(3.75319 - 10.3118i) q^{59} +(-8.87057 - 1.56412i) q^{61} +(12.2831 + 3.41294i) q^{62} +(-7.13880 + 3.61076i) q^{64} +(0.346849 + 0.952961i) q^{65} +(3.70041 - 3.10502i) q^{67} +(-2.74175 - 1.05557i) q^{68} +(0.472885 + 0.688782i) q^{70} +(-5.03714 - 8.72458i) q^{71} +(-0.339460 + 0.587962i) q^{73} +(-7.46803 + 0.584031i) q^{74} +(2.67840 - 0.421502i) q^{76} +(-0.00398198 - 0.0225829i) q^{77} +(5.19665 - 6.19313i) q^{79} +(-0.965387 + 1.53816i) q^{80} +(-0.860607 - 3.33452i) q^{82} +(-1.29122 + 1.53881i) q^{83} +(-0.656785 + 0.115809i) q^{85} +(-15.2727 - 1.47822i) q^{86} +(0.0416046 - 0.0274488i) q^{88} +(0.103744 + 0.0598964i) q^{89} +(1.45333 + 2.51724i) q^{91} +(2.79508 - 3.20896i) q^{92} +(3.74536 - 5.24532i) q^{94} +(0.471489 - 0.395626i) q^{95} +(-10.4801 + 3.81446i) q^{97} +(-5.25755 - 5.35542i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.27615	+	0.609466i	0.902372	+	0.430957i
$2$	1.27615	+	0.609466i	0.902372	+	0.430957i
$3$		0			0
$3$		0			0
$4$	1.25710	+	1.55554i	0.628551	+	0.777768i
$5$	0.426624	+	0.155279i	0.190792	+	0.0694427i	0.435649	−	0.900116i	$-0.356519\pi$
$5$	0.426624	+	0.155279i	0.190792	+	0.0694427i	−0.244857	+	0.969559i	$0.578741\pi$
$6$		0			0
$7$	1.28150	+	0.225962i	0.484360	+	0.0854057i	0.410495	−	0.911863i	$-0.365356\pi$
$7$	1.28150	+	0.225962i	0.484360	+	0.0854057i	0.0738642	+	0.997268i	$0.476467\pi$
$8$	0.656202	+	2.75125i	0.232003	+	0.972715i
$9$		0			0
$10$	0.449799	+	0.458171i	0.142239	+	0.144887i
$11$	−0.00602720	−	0.0165596i	−0.00181727	−	0.00499290i	0.938781	−	0.344515i	$-0.111957\pi$
$11$	−0.00602720	−	0.0165596i	−0.00181727	−	0.00499290i	−0.940598	+	0.339522i	$0.889735\pi$
$12$		0			0
$13$	1.43581	+	1.71113i	0.398222	+	0.474582i	0.927477	−	0.373881i	$-0.121973\pi$
$13$	1.43581	+	1.71113i	0.398222	+	0.474582i	−0.529255	+	0.848463i	$0.677529\pi$
$14$	1.49766	+	1.06939i	0.400267	+	0.285806i
$15$		0			0
$16$	−0.839384	+	3.91094i	−0.209846	+	0.977734i
$17$	−1.27216	+	0.734483i	−0.308545	+	0.178138i	−0.646275	−	0.763105i	$-0.723674\pi$
$17$	−1.27216	+	0.734483i	−0.308545	+	0.178138i	0.337730	+	0.941243i	$0.390341\pi$
$18$		0			0
$19$	0.677841	−	1.17406i	0.155507	−	0.269347i	−0.777736	−	0.628591i	$-0.783632\pi$
$19$	0.677841	−	1.17406i	0.155507	−	0.269347i	0.933244	+	0.359244i	$0.116965\pi$
$20$	0.294769	+	0.858831i	0.0659124	+	0.192040i
$21$		0			0
$22$	0.00240091	−	0.0248058i	0.000511876	−	0.00528862i
$23$	−0.369486	−	2.09546i	−0.0770432	−	0.436933i	−0.998792	−	0.0491452i	$-0.984350\pi$
$23$	−0.369486	−	2.09546i	−0.0770432	−	0.436933i	0.921748	−	0.387788i	$-0.126761\pi$
$24$		0			0
$25$	−3.67233	−	3.08145i	−0.734465	−	0.616289i
$26$	0.789428	+	3.05873i	0.154820	+	0.599866i
$27$		0			0
$28$	1.25948	+	2.27747i	0.238019	+	0.430401i
$29$	5.56933	+	4.67322i	1.03420	+	0.867796i	0.991345	−	0.131286i	$-0.0419105\pi$
$29$	5.56933	+	4.67322i	1.03420	+	0.867796i	0.0428540	+	0.999081i	$0.486355\pi$
$30$		0			0
$31$	8.87753	−	1.56535i	1.59445	−	0.281145i	0.695279	−	0.718740i	$-0.255281\pi$
$31$	8.87753	−	1.56535i	1.59445	−	0.281145i	0.899172	+	0.437595i	$0.144170\pi$
$32$	−3.45476	+	4.47936i	−0.610721	+	0.791846i
$33$		0			0
$34$	−2.07111	+	0.161969i	−0.355192	+	0.0277775i
$35$	0.511630	+	0.295390i	0.0864813	+	0.0499300i
$36$		0			0
$37$	−4.58718	+	2.64841i	−0.754128	+	0.435396i	−0.827183	−	0.561932i	$-0.810058\pi$
$37$	−4.58718	+	2.64841i	−0.754128	+	0.435396i	0.0730557	+	0.997328i	$0.476725\pi$
$38$	1.58057	−	1.08515i	0.256403	−	0.176034i
$39$		0			0
$40$	−0.147259	+	1.27565i	−0.0232837	+	0.201697i
$41$	−1.56527	−	1.86542i	−0.244454	−	0.291329i	0.629841	−	0.776724i	$-0.283120\pi$
$41$	−1.56527	−	1.86542i	−0.244454	−	0.291329i	−0.874295	+	0.485395i	$0.838676\pi$
$42$		0			0
$43$	−10.1956	+	3.71089i	−1.55481	+	0.565906i	−0.969541	−	0.244930i	$-0.921235\pi$
$43$	−10.1956	+	3.71089i	−1.55481	+	0.565906i	−0.585273	+	0.810836i	$0.699013\pi$
$44$	0.0181822	−	0.0301926i	0.00274107	−	0.00455171i
$45$		0			0
$46$	0.805592	−	2.89930i	0.118778	−	0.427479i
$47$	0.791397	−	4.48824i	0.115437	−	0.654676i	−0.871096	−	0.491113i	$-0.836590\pi$
$47$	0.791397	−	4.48824i	0.115437	−	0.654676i	0.986533	−	0.163563i	$-0.0522988\pi$
$48$		0			0
$49$	−4.98668	−	1.81500i	−0.712382	−	0.259286i
$50$	−2.80839	−	6.17054i	−0.397166	−	0.872646i
$51$		0			0
$52$	−0.856765	+	4.38452i	−0.118812	+	0.608023i
$53$	10.4085			1.42972			0.714860	−	0.699267i	$-0.246490\pi$
$53$	10.4085			1.42972			0.714860	+	0.699267i	$0.246490\pi$
$54$		0			0
$55$		−	0.00800062i		−	0.00107880i
$56$	0.219241	+	3.67400i	0.0292973	+	0.490958i
$57$		0			0
$58$	4.25911	+	9.35804i	0.559249	+	1.22877i
$59$	3.75319	−	10.3118i	0.488624	−	1.34248i	−0.413302	−	0.910594i	$-0.635625\pi$
$59$	3.75319	−	10.3118i	0.488624	−	1.34248i	0.901926	−	0.431890i	$-0.142153\pi$
$60$		0			0
$61$	−8.87057	−	1.56412i	−1.13576	−	0.200265i	−0.426010	−	0.904718i	$-0.640081\pi$
$61$	−8.87057	−	1.56412i	−1.13576	−	0.200265i	−0.709750	+	0.704453i	$0.751192\pi$
$62$	12.2831	+	3.41294i	1.55995	+	0.433443i
$63$		0			0
$64$	−7.13880	+	3.61076i	−0.892350	+	0.451345i
$65$	0.346849	+	0.952961i	0.0430214	+	0.118200i
$66$		0			0
$67$	3.70041	−	3.10502i	0.452078	−	0.379338i	−0.388129	−	0.921605i	$-0.626878\pi$
$67$	3.70041	−	3.10502i	0.452078	−	0.379338i	0.840206	+	0.542267i	$0.182434\pi$
$68$	−2.74175	−	1.05557i	−0.332486	−	0.128007i
$69$		0			0
$70$	0.472885	+	0.688782i	0.0565206	+	0.0823252i
$71$	−5.03714	−	8.72458i	−0.597799	−	1.03542i	−0.993145	−	0.116886i	$-0.962709\pi$
$71$	−5.03714	−	8.72458i	−0.597799	−	1.03542i	0.395347	−	0.918532i	$-0.370624\pi$
$72$		0			0
$73$	−0.339460	+	0.587962i	−0.0397308	+	0.0688158i	−0.885207	−	0.465197i	$-0.845983\pi$
$73$	−0.339460	+	0.587962i	−0.0397308	+	0.0688158i	0.845476	+	0.534013i	$0.179317\pi$
$74$	−7.46803	+	0.584031i	−0.868141	+	0.0678922i
$75$		0			0
$76$	2.67840	−	0.421502i	0.307234	−	0.0483496i
$77$	−0.00398198	−	0.0225829i	−0.000453789	−	0.00257357i
$78$		0			0
$79$	5.19665	−	6.19313i	0.584669	−	0.696782i	−0.389903	−	0.920856i	$-0.627491\pi$
$79$	5.19665	−	6.19313i	0.584669	−	0.696782i	0.974572	+	0.224074i	$0.0719358\pi$
$80$	−0.965387	+	1.53816i	−0.107934	+	0.171972i
$81$		0			0
$82$	−0.860607	−	3.33452i	−0.0950382	−	0.368237i
$83$	−1.29122	+	1.53881i	−0.141729	+	0.168907i	−0.832240	−	0.554416i	$-0.812942\pi$
$83$	−1.29122	+	1.53881i	−0.141729	+	0.168907i	0.690510	+	0.723323i	$0.257386\pi$
$84$		0			0
$85$	−0.656785	+	0.115809i	−0.0712383	+	0.0125612i
$86$	−15.2727	−	1.47822i	−1.64690	−	0.159401i
$87$		0			0
$88$	0.0416046	−	0.0274488i	0.00443506	−	0.00292605i
$89$	0.103744	+	0.0598964i	0.0109968	+	0.00634901i	0.505488	−	0.862833i	$-0.331312\pi$
$89$	0.103744	+	0.0598964i	0.0109968	+	0.00634901i	−0.494492	+	0.869182i	$0.664646\pi$
$90$		0			0
$91$	1.45333	+	2.51724i	0.152351	+	0.263879i
$92$	2.79508	−	3.20896i	0.291407	−	0.334557i
$93$		0			0
$94$	3.74536	−	5.24532i	0.386305	−	0.541013i
$95$	0.471489	−	0.395626i	0.0483738	−	0.0405904i
$96$		0			0
$97$	−10.4801	+	3.81446i	−1.06410	+	0.387299i	−0.813966	−	0.580913i	$-0.802696\pi$
$97$	−10.4801	+	3.81446i	−1.06410	+	0.387299i	−0.250130	+	0.968212i	$0.580474\pi$
$98$	−5.25755	−	5.35542i	−0.531093	−	0.540979i
$99$		0			0
$100$	0.176811	−	9.58613i	0.0176811	−	0.958613i
$101$	−2.89743	+	16.4321i	−0.288305	+	1.63506i	0.404932	+	0.914347i	$0.367295\pi$
$101$	−2.89743	+	16.4321i	−0.288305	+	1.63506i	−0.693237	+	0.720710i	$0.743816\pi$
$102$		0			0
$103$	5.45676	−	14.9923i	0.537670	−	1.47724i	−0.312082	−	0.950055i	$-0.601026\pi$
$103$	5.45676	−	14.9923i	0.537670	−	1.47724i	0.849753	−	0.527182i	$-0.176751\pi$
$104$	−3.76557	+	5.07312i	−0.369245	+	0.497461i
$105$		0			0
$106$	13.2828	+	6.34364i	1.29014	+	0.616149i
$107$		−	6.73607i		−	0.651200i	−0.945508	−	0.325600i	$-0.894434\pi$
$107$		−	6.73607i		−	0.651200i	0.945508	−	0.325600i	$-0.105566\pi$
$108$		0			0
$109$		−	2.91699i		−	0.279397i	−0.990194	−	0.139699i	$-0.955387\pi$
$109$		−	2.91699i		−	0.279397i	0.990194	−	0.139699i	$-0.0446134\pi$
$110$	0.00487610	−	0.0102100i	0.000464918	−	0.000973482i
$111$		0			0
$112$	−1.95939	+	4.82218i	−0.185145	+	0.455653i
$113$	6.67148	−	18.3297i	0.627600	−	1.72432i	−0.0599724	−	0.998200i	$-0.519101\pi$
$113$	6.67148	−	18.3297i	0.627600	−	1.72432i	0.687572	−	0.726116i	$-0.258677\pi$
$114$		0			0
$115$	0.167748	−	0.951347i	0.0156426	−	0.0887136i
$116$	−0.268145	+	14.5380i	−0.0248967	+	1.34982i
$117$		0			0
$118$	11.0743	−	10.8719i	1.01947	−	1.00084i
$119$	−1.79623	+	0.653776i	−0.164661	+	0.0599315i
$120$		0			0
$121$	8.42625	−	7.07046i	0.766023	−	0.642769i
$122$	−10.3669	−	7.40236i	−0.938573	−	0.670178i
$123$		0			0
$124$	13.5949	+	11.8415i	1.22086	+	1.06340i
$125$	−2.22323	−	3.85075i	−0.198852	−	0.344422i
$126$		0			0
$127$	−14.9938	−	8.65666i	−1.33048	−	0.768154i	−0.345108	−	0.938563i	$-0.612158\pi$
$127$	−14.9938	−	8.65666i	−1.33048	−	0.768154i	−0.985373	+	0.170409i	$0.945491\pi$
$128$	−11.3108	+	0.257006i	−0.999742	+	0.0227164i
$129$		0			0
$130$	−0.138166	+	1.42751i	−0.0121180	+	0.125201i
$131$	3.03491	−	0.535137i	0.265162	−	0.0467552i	−0.0394865	−	0.999220i	$-0.512572\pi$
$131$	3.03491	−	0.535137i	0.265162	−	0.0467552i	0.304648	+	0.952465i	$0.401461\pi$
$132$		0			0
$133$	1.13394	−	1.35138i	0.0983252	−	0.117179i
$134$	6.61467	−	1.70718i	0.571421	−	0.147478i
$135$		0			0
$136$	−2.85554	−	3.01807i	−0.244861	−	0.258797i
$137$	−7.57425	+	9.02665i	−0.647112	+	0.771198i	−0.985476	−	0.169817i	$-0.945682\pi$
$137$	−7.57425	+	9.02665i	−0.647112	+	0.771198i	0.338363	+	0.941016i	$0.390127\pi$
$138$		0			0
$139$	−0.930383	−	5.27646i	−0.0789140	−	0.447544i	−0.998505	−	0.0546659i	$-0.982591\pi$
$139$	−0.930383	−	5.27646i	−0.0789140	−	0.447544i	0.919591	−	0.392878i	$-0.128520\pi$
$140$	0.183682	+	1.16719i	0.0155240	+	0.0986459i
$141$		0			0
$142$	−1.11080	−	14.2038i	−0.0932160	−	1.19196i
$143$	0.0196817	−	0.0340897i	0.00164587	−	0.00285073i
$144$		0			0
$145$	1.65036	+	2.85851i	0.137055	+	0.237386i
$146$	−0.791544	+	0.543437i	−0.0655086	+	0.0449752i
$147$		0			0
$148$	−9.88625	−	3.80620i	−0.812645	−	0.312868i
$149$	−10.9918	+	9.22325i	−0.900486	+	0.755598i	−0.970285	−	0.241963i	$-0.922209\pi$
$149$	−10.9918	+	9.22325i	−0.900486	+	0.755598i	0.0697991	+	0.997561i	$0.477764\pi$
$150$		0			0
$151$	4.06790	+	11.1765i	0.331041	+	0.909528i	0.987842	+	0.155464i	$0.0496872\pi$
$151$	4.06790	+	11.1765i	0.331041	+	0.909528i	−0.656800	+	0.754065i	$0.728091\pi$
$152$	3.67492	+	1.09450i	0.298076	+	0.0887753i
$153$		0			0
$154$	0.00868194	−	0.0312460i	0.000699610	−	0.00251788i
$155$	4.03044	+	0.710675i	0.323733	+	0.0570828i
$156$		0			0
$157$	−5.75062	+	15.7997i	−0.458950	+	1.26095i	0.467319	+	0.884089i	$0.345220\pi$
$157$	−5.75062	+	15.7997i	−0.458950	+	1.26095i	−0.926268	+	0.376865i	$0.877002\pi$
$158$	10.4062	−	4.73616i	0.827873	−	0.376789i
$159$		0			0
$160$	−2.16943	+	1.37455i	−0.171509	+	0.108668i
$161$		−	2.76881i		−	0.218213i
$162$		0			0
$163$	10.1776			0.797169			0.398585	−	0.917132i	$-0.369502\pi$
$163$	10.1776			0.797169			0.398585	+	0.917132i	$0.369502\pi$
$164$	0.934016	−	4.77985i	0.0729344	−	0.373244i
$165$		0			0
$166$	−2.58564	+	1.17680i	−0.200684	+	0.0913372i
$167$	15.0723	+	5.48587i	1.16633	+	0.424509i	0.851355	−	0.524591i	$-0.175782\pi$
$167$	15.0723	+	5.48587i	1.16633	+	0.424509i	0.314975	+	0.949100i	$0.398004\pi$
$168$		0			0
$169$	1.39101	−	7.88879i	0.107000	−	0.606830i
$170$	−0.908736	−	0.252499i	−0.0696968	−	0.0193658i
$171$		0			0
$172$	−18.5893	−	11.1946i	−1.41742	−	0.853584i
$173$	−12.7203	+	4.62982i	−0.967109	+	0.351999i	−0.776815	−	0.629729i	$-0.783166\pi$
$173$	−12.7203	+	4.62982i	−0.967109	+	0.351999i	−0.190293	+	0.981727i	$0.560944\pi$
$174$		0			0
$175$	−4.00978	−	4.77867i	−0.303111	−	0.361233i
$176$	0.0698226	−	0.00967213i	0.00526308	−	0.000729064i
$177$		0			0
$178$	0.0958874	+	0.139665i	0.00718706	+	0.0104683i
$179$	−9.84897	+	5.68630i	−0.736146	+	0.425014i	−0.820667	−	0.571407i	$-0.806398\pi$
$179$	−9.84897	+	5.68630i	−0.736146	+	0.425014i	0.0845201	+	0.996422i	$0.473064\pi$
$180$		0			0
$181$	12.8369	+	7.41138i	0.954159	+	0.550884i	0.894370	−	0.447327i	$-0.147624\pi$
$181$	12.8369	+	7.41138i	0.954159	+	0.550884i	0.0597883	+	0.998211i	$0.480957\pi$
$182$	0.320491	+	4.09813i	0.0237564	+	0.303774i
$183$		0			0
$184$	5.52268	−	2.39159i	0.407138	−	0.176311i
$185$	−2.36824	+	0.417585i	−0.174117	+	0.0307015i
$186$		0			0
$187$	0.0198303	+	0.0166396i	0.00145014	+	0.00121681i
$188$	7.97648	−	4.41113i	0.581745	−	0.321715i
$189$		0			0
$190$	0.842810	−	0.217521i	0.0611439	−	0.0157806i
$191$	−14.4389	−	12.1157i	−1.04476	−	0.876659i	−0.0522283	−	0.998635i	$-0.516632\pi$
$191$	−14.4389	−	12.1157i	−1.04476	−	0.876659i	−0.992533	+	0.121976i	$0.961077\pi$
$192$		0			0
$193$	−0.366460	−	2.07830i	−0.0263783	−	0.149599i	0.968774	−	0.247946i	$-0.0797556\pi$
$193$	−0.366460	−	2.07830i	−0.0263783	−	0.149599i	−0.995152	+	0.0983471i	$0.968644\pi$
$194$	−15.6990	−	1.51947i	−1.12712	−	0.109092i
$195$		0			0
$196$	−3.44547	−	10.0386i	−0.246105	−	0.717043i
$197$	5.72884	−	9.92264i	0.408163	−	0.706959i	−0.586521	−	0.809934i	$-0.699503\pi$
$197$	5.72884	−	9.92264i	0.408163	−	0.706959i	0.994684	+	0.102975i	$0.0328362\pi$
$198$		0			0
$199$	−4.92181	+	2.84161i	−0.348898	+	0.201436i	−0.664200	−	0.747555i	$-0.731228\pi$
$199$	−4.92181	+	2.84161i	−0.348898	+	0.201436i	0.315302	+	0.948991i	$0.397894\pi$
$200$	6.06805	−	12.1256i	0.429076	−	0.857406i
$201$		0			0
$202$	−13.7124	+	19.2039i	−0.964798	+	1.35118i
$203$	6.08110	+	7.24717i	0.426809	+	0.508652i
$204$		0			0
$205$	−0.378123	−	1.03889i	−0.0264093	−	0.0725589i
$206$	16.1009	−	15.8067i	1.12180	−	1.10130i
$207$		0			0
$208$	−7.89732	+	4.17906i	−0.547581	+	0.289766i
$209$	−0.0235273	−	0.00414851i	−0.00162742	−	0.000286958i
$210$		0			0
$211$	15.6412	+	5.69295i	1.07679	+	0.391919i	0.818711	−	0.574206i	$-0.194689\pi$
$211$	15.6412	+	5.69295i	1.07679	+	0.391919i	0.258077	+	0.966124i	$0.416911\pi$
$212$	13.0846	+	16.1908i	0.898653	+	1.11199i
$213$		0			0
$214$	4.10540	−	8.59621i	0.280640	−	0.587625i
$215$	−4.92591			−0.335945
$216$		0			0
$217$	11.7302			0.796300
$218$	1.77781	−	3.72251i	0.120408	−	0.252120i
$219$		0			0
$220$	0.0124453	−	0.0100576i	0.000839059	−	0.000678083i
$221$	−3.08338	−	1.12226i	−0.207410	−	0.0754912i
$222$		0			0
$223$	2.73564	+	0.482367i	0.183192	+	0.0323017i	0.264491	−	0.964388i	$-0.414796\pi$
$223$	2.73564	+	0.482367i	0.183192	+	0.0323017i	−0.0812995	+	0.996690i	$0.525907\pi$
$224$	−5.43942	+	4.95963i	−0.363437	+	0.331379i
$225$		0			0
$226$	19.6851	−	19.3254i	1.30944	−	1.28551i
$227$	8.45693	+	23.2352i	0.561306	+	1.54218i	0.817724	+	0.575611i	$0.195236\pi$
$227$	8.45693	+	23.2352i	0.561306	+	1.54218i	−0.256418	+	0.966566i	$0.582542\pi$
$228$		0			0
$229$	10.0744	+	12.0062i	0.665736	+	0.793393i	0.988197	−	0.153190i	$-0.0489546\pi$
$229$	10.0744	+	12.0062i	0.665736	+	0.793393i	−0.322461	+	0.946583i	$0.604510\pi$
$230$	0.793885	−	1.11182i	0.0523472	−	0.0733114i
$231$		0			0
$232$	−9.20261	+	18.3892i	−0.604181	+	1.20731i
$233$	−17.5198	+	10.1151i	−1.14776	+	0.662659i	−0.948340	−	0.317255i	$-0.897239\pi$
$233$	−17.5198	+	10.1151i	−1.14776	+	0.662659i	−0.199419	+	0.979914i	$0.563906\pi$
$234$		0			0
$235$	1.03456	−	1.79190i	0.0674870	−	0.116891i
$236$	20.7585	−	7.12478i	1.35127	−	0.463784i
$237$		0			0
$238$	−2.69071	−	0.260429i	−0.174413	−	0.0168811i
$239$	1.48780	+	8.43773i	0.0962378	+	0.545791i	0.994361	+	0.106048i	$0.0338196\pi$
$239$	1.48780	+	8.43773i	0.0962378	+	0.545791i	−0.898123	+	0.439744i	$0.855069\pi$
$240$		0			0
$241$	11.0727	+	9.29110i	0.713255	+	0.598492i	0.925510	−	0.378722i	$-0.123636\pi$
$241$	11.0727	+	9.29110i	0.713255	+	0.598492i	−0.212255	+	0.977214i	$0.568081\pi$
$242$	15.0623	−	3.88744i	0.968244	−	0.249894i
$243$		0			0
$244$	−8.71818	−	15.7648i	−0.558124	−	1.00924i
$245$	−1.84561	−	1.54865i	−0.117912	−	0.0989395i
$246$		0			0
$247$	2.98221	−	0.525844i	0.189754	−	0.0334587i
$248$	10.1321	+	23.3972i	0.643391	+	1.48572i
$249$		0			0
$250$	−0.490270	−	6.26911i	−0.0310074	−	0.396493i
$251$	−12.7128	−	7.33976i	−0.802427	−	0.463281i	0.0418921	−	0.999122i	$-0.486661\pi$
$251$	−12.7128	−	7.33976i	−0.802427	−	0.463281i	−0.844319	+	0.535841i	$0.819995\pi$
$252$		0			0
$253$	−0.0324730	+	0.0187483i	−0.00204156	+	0.00117869i
$254$	−13.8583	−	20.1854i	−0.869548	−	1.26654i
$255$		0			0
$256$	−14.5909	−	6.56556i	−0.911929	−	0.410348i
$257$	14.4703	+	17.2450i	0.902633	+	1.07572i	0.996782	+	0.0801575i	$0.0255423\pi$
$257$	14.4703	+	17.2450i	0.902633	+	1.07572i	−0.0941497	+	0.995558i	$0.530013\pi$
$258$		0			0
$259$	−6.47689	+	2.35739i	−0.402454	+	0.146481i
$260$	−1.04634	+	1.73751i	−0.0648912	+	0.107756i
$261$		0			0
$262$	4.19914	+	1.16676i	0.259424	+	0.0720828i
$263$	3.07511	−	17.4398i	0.189620	−	1.07539i	−0.730255	−	0.683175i	$-0.760599\pi$
$263$	3.07511	−	17.4398i	0.189620	−	1.07539i	0.919875	−	0.392212i	$-0.128290\pi$
$264$		0			0
$265$	4.44053	+	1.61622i	0.272780	+	0.0992836i
$266$	2.27070	−	1.03346i	0.139225	−	0.0633655i
$267$		0			0
$268$	9.48177	+	1.85280i	0.579191	+	0.113178i
$269$	10.2475			0.624803			0.312402	−	0.949950i	$-0.398867\pi$
$269$	10.2475			0.624803			0.312402	+	0.949950i	$0.398867\pi$
$270$		0			0
$271$			18.7315i			1.13786i	0.822386	+	0.568929i	$0.192642\pi$
$271$			18.7315i			1.13786i	−0.822386	+	0.568929i	$0.807358\pi$
$272$	−1.80468	−	5.59186i	−0.109425	−	0.339056i
$273$		0			0
$274$	−15.1673	+	6.90308i	−0.916290	+	0.417030i
$275$	−0.0288937	+	0.0793847i	−0.00174235	+	0.00478708i
$276$		0			0
$277$	−21.4560	−	3.78327i	−1.28917	−	0.227315i	−0.513299	−	0.858210i	$-0.671577\pi$
$277$	−21.4560	−	3.78327i	−1.28917	−	0.227315i	−0.775868	+	0.630895i	$0.782688\pi$
$278$	2.02852	−	7.30058i	0.121662	−	0.437860i
$279$		0			0
$280$	−0.476959	+	1.60146i	−0.0285038	+	0.0957055i
$281$	3.95262	+	10.8597i	0.235793	+	0.647837i	0.999996	+	0.00286067i	$0.000910580\pi$
$281$	3.95262	+	10.8597i	0.235793	+	0.647837i	−0.764203	+	0.644976i	$0.776867\pi$
$282$		0			0
$283$	−3.28791	+	2.75888i	−0.195446	+	0.163998i	−0.735259	−	0.677786i	$-0.762939\pi$
$283$	−3.28791	+	2.75888i	−0.195446	+	0.163998i	0.539813	+	0.841785i	$0.318495\pi$
$284$	7.23920	−	18.8032i	0.429567	−	1.11576i
$285$		0			0
$286$	0.0458933	−	0.0315082i	0.00271373	−	0.00186312i
$287$	−1.58437	−	2.74421i	−0.0935226	−	0.161986i
$288$		0			0
$289$	−7.42107	+	12.8537i	−0.436533	+	0.756098i
$290$	0.363940	+	4.65372i	0.0213713	+	0.273276i
$291$		0			0
$292$	−1.34133	+	0.211087i	−0.0784956	+	0.0123529i
$293$	−2.18285	−	12.3796i	−0.127523	−	0.723221i	−0.979777	−	0.200092i	$-0.935876\pi$
$293$	−2.18285	−	12.3796i	−0.127523	−	0.723221i	0.852254	−	0.523129i	$-0.175235\pi$
$294$		0			0
$295$	3.20241	−	3.81648i	0.186451	−	0.222204i
$296$	−10.2966	−	10.8826i	−0.598476	−	0.632538i
$297$		0			0
$298$	−19.6485	+	5.07107i	−1.13820	+	0.293759i
$299$	3.05509	−	3.64092i	0.176681	−	0.210560i
$300$		0			0
$301$	−13.9041	+	2.45167i	−0.801421	+	0.141312i
$302$	−1.62043	+	16.7421i	−0.0932455	+	0.963398i
$303$		0			0
$304$	4.02269	+	3.63648i	0.230717	+	0.208566i
$305$	−3.54153	−	2.04470i	−0.202787	−	0.117079i
$306$		0			0
$307$	7.46768	+	12.9344i	0.426203	+	0.738205i	0.996532	−	0.0832113i	$-0.0265176\pi$
$307$	7.46768	+	12.9344i	0.426203	+	0.738205i	−0.570329	+	0.821416i	$0.693184\pi$
$308$	0.0301228	−	0.0345832i	0.00171641	−	0.00197056i
$309$		0			0
$310$	4.71030	+	3.36334i	0.267527	+	0.191025i
$311$	0.935160	−	0.784692i	0.0530280	−	0.0444958i	−0.615888	−	0.787833i	$-0.711203\pi$
$311$	0.935160	−	0.784692i	0.0530280	−	0.0444958i	0.668916	+	0.743338i	$0.266758\pi$
$312$		0			0
$313$	−3.74180	+	1.36190i	−0.211499	+	0.0769794i	−0.445597	−	0.895234i	$-0.647009\pi$
$313$	−3.74180	+	1.36190i	−0.211499	+	0.0769794i	0.234098	+	0.972213i	$0.424786\pi$
$314$	−16.9680	+	16.6579i	−0.957561	+	0.940062i
$315$		0			0
$316$	16.1664	+	0.298179i	0.909429	+	0.0167739i
$317$	−1.28552	+	7.29053i	−0.0722018	+	0.409477i	0.927190	+	0.374593i	$0.122217\pi$
$317$	−1.28552	+	7.29053i	−0.0722018	+	0.409477i	−0.999391	+	0.0348844i	$0.988894\pi$
$318$		0			0
$319$	0.0438192	−	0.120392i	0.00245340	−	0.00674067i
$320$	−3.60626	+	0.431935i	−0.201596	+	0.0241459i
$321$		0			0
$322$	1.68750	−	3.53341i	0.0940404	−	0.196909i
$323$			1.99145i			0.110807i
$324$		0			0
$325$		−	10.7082i		−	0.593984i
$326$	12.9881	+	6.20288i	0.719343	+	0.343546i
$327$		0			0
$328$	4.10510	−	5.53055i	0.226666	−	0.305373i
$329$	2.02834	−	5.57283i	0.111826	−	0.307240i
$330$		0			0
$331$	0.520452	−	2.95163i	0.0286066	−	0.162236i	−0.967158	−	0.254176i	$-0.918196\pi$
$331$	0.520452	−	2.95163i	0.0286066	−	0.162236i	0.995765	+	0.0919400i	$0.0293068\pi$
$332$	−4.01687	−	0.0740888i	−0.220454	−	0.00406615i
$333$		0			0
$334$	15.8910	+	16.1868i	0.869518	+	0.885704i
$335$	2.06083	−	0.750081i	0.112595	−	0.0409813i
$336$		0			0
$337$	−10.0788	+	8.45709i	−0.549025	+	0.460687i	−0.874611	−	0.484826i	$-0.838883\pi$
$337$	−10.0788	+	8.45709i	−0.549025	+	0.460687i	0.325586	+	0.945513i	$0.394439\pi$
$338$	6.58307	−	9.21948i	0.358072	−	0.501474i
$339$		0			0
$340$	−1.00579	−	0.876069i	−0.0545467	−	0.0475115i
$341$	−0.0794281	−	0.137574i	−0.00430127	−	0.00745003i
$342$		0			0
$343$	−13.8688	−	8.00714i	−0.748844	−	0.432345i
$344$	−16.9000	−	25.6156i	−0.911186	−	1.38110i
$345$		0			0
$346$	−19.0547	−	1.84427i	−1.02439	−	0.0991487i
$347$	−28.8369	+	5.08472i	−1.54804	+	0.272962i	−0.881385	−	0.472400i	$-0.843388\pi$
$347$	−28.8369	+	5.08472i	−1.54804	+	0.272962i	−0.666660	+	0.745362i	$0.732277\pi$
$348$		0			0
$349$	13.4766	−	16.0608i	0.721385	−	0.859713i	−0.273380	−	0.961906i	$-0.588141\pi$
$349$	13.4766	−	16.0608i	0.721385	−	0.859713i	0.994765	+	0.102193i	$0.0325859\pi$
$350$	−2.20463	−	8.54210i	−0.117843	−	0.456595i
$351$		0			0
$352$	0.0949988	+	0.0302114i	0.00506345	+	0.00161028i
$353$	−2.02760	+	2.41640i	−0.107918	+	0.128612i	−0.817300	−	0.576213i	$-0.804530\pi$
$353$	−2.02760	+	2.41640i	−0.107918	+	0.128612i	0.709381	+	0.704825i	$0.248974\pi$
$354$		0			0
$355$	−0.794226	−	4.50428i	−0.0421532	−	0.239062i
$356$	0.0372454	+	0.236673i	0.00197400	+	0.0125436i
$357$		0			0
$358$	−16.0343	+	1.25395i	−0.847441	+	0.0662734i
$359$	−15.2950	+	26.4917i	−0.807240	+	1.39818i	0.107529	+	0.994202i	$0.465706\pi$
$359$	−15.2950	+	26.4917i	−0.807240	+	1.39818i	−0.914768	+	0.403979i	$0.867627\pi$
$360$		0			0
$361$	8.58106	+	14.8628i	0.451635	+	0.782255i
$362$	11.8648	+	17.2817i	0.623599	+	0.908304i
$363$		0			0
$364$	−2.08868	+	5.42514i	−0.109476	+	0.284355i
$365$	−0.236120	+	0.198128i	−0.0123591	+	0.0103705i
$366$		0			0
$367$	7.65245	+	21.0249i	0.399455	+	1.09749i	0.962551	+	0.271101i	$0.0873878\pi$
$367$	7.65245	+	21.0249i	0.399455	+	1.09749i	−0.563096	+	0.826391i	$0.690390\pi$
$368$	8.50535	+	0.313859i	0.443372	+	0.0163610i
$369$		0			0
$370$	−3.27673	−	0.910464i	−0.170349	−	0.0473327i
$371$	13.3385	+	2.35193i	0.692499	+	0.122106i
$372$		0			0
$373$	−3.91132	+	10.7463i	−0.202521	+	0.556421i	−0.998824	−	0.0484764i	$-0.984563\pi$
$373$	−3.91132	+	10.7463i	−0.202521	+	0.556421i	0.796304	+	0.604897i	$0.206786\pi$
$374$	0.0151651	+	0.0333205i	0.000784170	+	0.00172296i
$375$		0			0
$376$	12.8676	−	0.767856i	0.663595	−	0.0395992i
$377$			16.2397i			0.836387i
$378$		0			0
$379$	−21.7004			−1.11468			−0.557338	−	0.830286i	$-0.688177\pi$
$379$	−21.7004			−1.11468			−0.557338	+	0.830286i	$0.688177\pi$
$380$	1.20812	+	0.236075i	0.0619753	+	0.0121104i
$381$		0			0
$382$	−11.0421	−	24.2614i	−0.564961	−	1.24132i
$383$	31.1726	+	11.3459i	1.59285	+	0.579749i	0.977946	−	0.208856i	$-0.0669740\pi$
$383$	31.1726	+	11.3459i	1.59285	+	0.579749i	0.614900	+	0.788605i	$0.289196\pi$
$384$		0			0
$385$	0.00180784	−	0.0102528i	9.21359e−5	−	0.000522529i
$386$	0.798994	−	2.87556i	0.0406677	−	0.146362i
$387$		0			0
$388$	−19.1081	−	11.5071i	−0.970068	−	0.584182i
$389$	6.54404	−	2.38183i	0.331796	−	0.120764i	−0.170750	−	0.985314i	$-0.554619\pi$
$389$	6.54404	−	2.38183i	0.331796	−	0.120764i	0.502546	+	0.864551i	$0.332397\pi$
$390$		0			0
$391$	2.00913	+	2.39438i	0.101606	+	0.121089i
$392$	1.72126	−	14.9106i	0.0869369	−	0.753100i
$393$		0			0
$394$	13.3584	−	9.17122i	0.672984	−	0.462039i
$395$	3.17868	−	1.83521i	0.159937	−	0.0923395i
$396$		0			0
$397$	31.8597	+	18.3942i	1.59899	+	0.923178i	0.991682	+	0.128712i	$0.0410841\pi$
$397$	31.8597	+	18.3942i	1.59899	+	0.923178i	0.607308	+	0.794466i	$0.292249\pi$
$398$	−8.01281	+	0.626635i	−0.401646	+	0.0314104i
$399$		0			0
$400$	15.1338	−	11.7757i	0.756692	−	0.588786i
$401$	−3.00611	+	0.530059i	−0.150118	+	0.0264699i	−0.248202	−	0.968708i	$-0.579840\pi$
$401$	−3.00611	+	0.530059i	−0.150118	+	0.0264699i	0.0980840	+	0.995178i	$0.468729\pi$
$402$		0			0
$403$	15.4250	+	12.9431i	0.768372	+	0.644740i
$404$	−29.2031	+	16.1498i	−1.45291	+	0.803483i
$405$		0			0
$406$	3.34347	+	12.9547i	0.165934	+	0.642930i
$407$	0.0715044	+	0.0599993i	0.00354434	+	0.00297406i
$408$		0			0
$409$	−4.18256	−	23.7205i	−0.206814	−	1.17290i	−0.894559	−	0.446949i	$-0.852511\pi$
$409$	−4.18256	−	23.7205i	−0.206814	−	1.17290i	0.687745	−	0.725952i	$-0.258601\pi$
$410$	0.150624	−	1.55622i	0.00743879	−	0.0768564i
$411$		0			0
$412$	30.1808	−	10.3587i	1.48690	−	0.510337i
$413$	7.13978	−	12.3665i	0.351326	−	0.608514i
$414$		0			0
$415$	−0.789809	+	0.455997i	−0.0387702	+	0.0223840i
$416$	−12.6251	+	0.519953i	−0.618998	+	0.0254928i
$417$		0			0
$418$	−0.0274960	−	0.0196332i	−0.00134487	−	0.000960292i
$419$	19.0854	+	22.7451i	0.932383	+	1.11117i	0.993590	+	0.113046i	$0.0360607\pi$
$419$	19.0854	+	22.7451i	0.932383	+	1.11117i	−0.0612068	+	0.998125i	$0.519495\pi$
$420$		0			0
$421$	−9.82045	−	26.9815i	−0.478619	−	1.31500i	−0.910666	−	0.413144i	$-0.864430\pi$
$421$	−9.82045	−	26.9815i	−0.478619	−	1.31500i	0.432046	−	0.901851i	$-0.357792\pi$
$422$	16.4909	+	16.7978i	0.802763	+	0.817706i
$423$		0			0
$424$	6.83010	+	28.6365i	0.331699	+	1.39071i
$425$	6.93506	+	1.22284i	0.336400	+	0.0593164i
$426$		0			0
$427$	−11.0142	−	4.00883i	−0.533013	−	0.194001i
$428$	10.4782	−	8.46793i	0.506483	−	0.409313i
$429$		0			0
$430$	−6.28619	−	3.00218i	−0.303147	−	0.144778i
$431$	−26.5585			−1.27928			−0.639639	−	0.768675i	$-0.720916\pi$
$431$	−26.5585			−1.27928			−0.639639	+	0.768675i	$0.720916\pi$
$432$		0			0
$433$	−1.55270			−0.0746180			−0.0373090	−	0.999304i	$-0.511879\pi$
$433$	−1.55270			−0.0746180			−0.0373090	+	0.999304i	$0.511879\pi$
$434$	14.9695	+	7.14917i	0.718559	+	0.343171i
$435$		0			0
$436$	4.53749	−	3.66696i	0.217306	−	0.175616i
$437$	−2.71064	−	0.986591i	−0.129667	−	0.0471951i
$438$		0			0
$439$	−1.13120	−	0.199460i	−0.0539891	−	0.00951973i	0.146588	−	0.989198i	$-0.453171\pi$
$439$	−1.13120	−	0.199460i	−0.0539891	−	0.00951973i	−0.200577	+	0.979678i	$0.564282\pi$
$440$	0.0220117	−	0.00525002i	0.00104937	−	0.000250285i
$441$		0			0
$442$	−3.25087	−	3.31138i	−0.154628	−	0.157506i
$443$	−5.79518	−	15.9221i	−0.275337	−	0.756483i	−0.997875	−	0.0651518i	$-0.979247\pi$
$443$	−5.79518	−	15.9221i	−0.275337	−	0.756483i	0.722538	−	0.691331i	$-0.242975\pi$
$444$		0			0
$445$	0.0349590	+	0.0416625i	0.00165721	+	0.00197499i
$446$	3.19709	+	2.28285i	0.151387	+	0.108096i
$447$		0			0
$448$	−9.96423	+	3.01407i	−0.470766	+	0.142401i
$449$	26.5725	−	15.3416i	1.25403	−	0.724017i	0.282126	−	0.959377i	$-0.408961\pi$
$449$	26.5725	−	15.3416i	1.25403	−	0.724017i	0.971908	+	0.235361i	$0.0756272\pi$
$450$		0			0
$451$	−0.0214563	+	0.0371634i	−0.00101034	+	0.00174996i
$452$	36.8993	−	12.6646i	1.73560	−	0.595694i
$453$		0			0
$454$	−3.36879	+	34.8058i	−0.158105	+	1.63352i
$455$	0.229153	+	1.29959i	0.0107428	+	0.0609257i
$456$		0			0
$457$	5.48725	+	4.60435i	0.256683	+	0.215382i	0.762044	−	0.647526i	$-0.224196\pi$
$457$	5.48725	+	4.60435i	0.256683	+	0.215382i	−0.505361	+	0.862908i	$0.668641\pi$
$458$	5.53905	+	21.4617i	0.258823	+	1.00284i
$459$		0			0
$460$	1.69073	−	0.935003i	0.0788308	−	0.0435948i
$461$	6.34887	+	5.32733i	0.295696	+	0.248119i	0.778550	−	0.627582i	$-0.215955\pi$
$461$	6.34887	+	5.32733i	0.295696	+	0.248119i	−0.482854	+	0.875701i	$0.660400\pi$
$462$		0			0
$463$	−0.381159	+	0.0672086i	−0.0177140	+	0.00312345i	−0.182498	−	0.983206i	$-0.558418\pi$
$463$	−0.381159	+	0.0672086i	−0.0177140	+	0.00312345i	0.164784	+	0.986330i	$0.447307\pi$
$464$	−22.9515	+	17.8587i	−1.06550	+	0.829068i
$465$		0			0
$466$	−28.5226	+	2.23059i	−1.32128	+	0.103330i
$467$	5.76908	+	3.33078i	0.266961	+	0.154130i	0.627506	−	0.778612i	$-0.284076\pi$
$467$	5.76908	+	3.33078i	0.266961	+	0.154130i	−0.360545	+	0.932742i	$0.617409\pi$
$468$		0			0
$469$	5.44368	−	3.14291i	0.251366	−	0.145126i
$470$	2.41235	−	1.65621i	0.111273	−	0.0763951i
$471$		0			0
$472$	30.8333	+	3.55935i	1.41922	+	0.163832i
$473$	0.122902	+	0.146469i	0.00565103	+	0.00673463i
$474$		0			0
$475$	−6.10704	+	2.22278i	−0.280210	+	0.101988i
$476$	−3.27502	−	1.97224i	−0.150110	−	0.0903977i
$477$		0			0
$478$	−3.24386	+	11.6745i	−0.148371	+	0.533981i
$479$	−0.196814	+	1.11619i	−0.00899268	+	0.0510000i	−0.988974	−	0.148090i	$-0.952687\pi$
$479$	−0.196814	+	1.11619i	−0.00899268	+	0.0510000i	0.979981	+	0.199090i	$0.0637986\pi$
$480$		0			0
$481$	−11.1181	−	4.04665i	−0.506941	−	0.184511i
$482$	8.46779	+	18.6052i	0.385697	+	0.847446i
$483$		0			0
$484$	21.5910	+	4.21904i	0.981410	+	0.191774i
$485$	−5.06338			−0.229916
$486$		0			0
$487$			41.9634i			1.90154i	0.309896	+	0.950771i	$0.399706\pi$
$487$			41.9634i			1.90154i	−0.309896	+	0.950771i	$0.600294\pi$
$488$	−1.51760	−	25.4316i	−0.0686983	−	1.15123i
$489$		0			0
$490$	−1.41142	−	3.10114i	−0.0637614	−	0.140095i
$491$	7.04382	−	19.3527i	0.317883	−	0.873377i	−0.673119	−	0.739534i	$-0.735046\pi$
$491$	7.04382	−	19.3527i	0.317883	−	0.873377i	0.991003	−	0.133843i	$-0.0427317\pi$
$492$		0			0
$493$	−10.5175	−	1.85452i	−0.473684	−	0.0835233i
$494$	4.12622	+	1.14650i	0.185648	+	0.0515835i
$495$		0			0
$496$	−1.32968	+	36.0334i	−0.0597045	+	1.61795i
$497$	−4.48365	−	12.3187i	−0.201119	−	0.552570i
$498$		0			0
$499$	7.68110	−	6.44521i	0.343853	−	0.288527i	−0.454463	−	0.890766i	$-0.650169\pi$
$499$	7.68110	−	6.44521i	0.343853	−	0.288527i	0.798316	+	0.602239i	$0.205724\pi$
$500$	3.19515	−	8.29911i	0.142891	−	0.371147i
$501$		0			0
$502$	−11.7501	−	17.1146i	−0.524433	−	0.763864i
$503$	12.3849	+	21.4513i	0.552216	+	0.956466i	0.998114	+	0.0613824i	$0.0195509\pi$
$503$	12.3849	+	21.4513i	0.552216	+	0.956466i	−0.445898	+	0.895084i	$0.647116\pi$
$504$		0			0
$505$	−3.78767	+	6.56044i	−0.168549	+	0.291936i
$506$	−0.0528667	+	0.00413440i	−0.00235021	+	0.000183796i
$507$		0			0
$508$	−5.38297	−	34.2057i	−0.238831	−	1.51763i
$509$	−5.29018	−	30.0021i	−0.234483	−	1.32982i	−0.843700	−	0.536816i	$-0.819627\pi$
$509$	−5.29018	−	30.0021i	−0.234483	−	1.32982i	0.609217	−	0.793004i	$-0.291484\pi$
$510$		0			0
$511$	−0.567874	+	0.676766i	−0.0251213	+	0.0299383i
$512$	−14.6186	−	17.2713i	−0.646057	−	0.763289i
$513$		0			0
$514$	7.95597	+	30.8264i	0.350923	+	1.35969i
$515$	4.65597	−	5.54877i	0.205167	−	0.244508i
$516$		0			0
$517$	−0.0790932	+	0.0139463i	−0.00347852	+	0.000613356i
$518$	−9.70221	−	0.939060i	−0.426291	−	0.0412599i
$519$		0			0
$520$	−2.39423	+	1.57961i	−0.104994	+	0.0692703i
$521$	2.67309	+	1.54331i	0.117110	+	0.0676136i	0.557411	−	0.830237i	$-0.311795\pi$
$521$	2.67309	+	1.54331i	0.117110	+	0.0676136i	−0.440301	+	0.897850i	$0.645128\pi$
$522$		0			0
$523$	−6.24198	−	10.8114i	−0.272943	−	0.472750i	0.696671	−	0.717390i	$-0.254664\pi$
$523$	−6.24198	−	10.8114i	−0.272943	−	0.472750i	−0.969614	+	0.244640i	$0.921330\pi$
$524$	4.64762	+	4.04820i	0.203032	+	0.176846i
$525$		0			0
$526$	14.5533	−	20.3816i	0.634553	−	0.888681i
$527$	−10.1439	+	8.51177i	−0.441877	+	0.370779i
$528$		0			0
$529$	17.3585	−	6.31798i	0.754717	−	0.274695i
$530$	4.68174	+	4.76889i	0.203362	+	0.207147i
$531$		0			0
$532$	3.52760	+	0.0650645i	0.152941	+	0.00282091i
$533$	0.944542	−	5.35676i	0.0409126	−	0.232027i
$534$		0			0
$535$	1.04597	−	2.87377i	0.0452211	−	0.124244i
$536$	10.9709	+	8.14326i	0.473871	+	0.351735i
$537$		0			0
$538$	13.0774	+	6.24552i	0.563805	+	0.269264i
$539$			0.0935167i			0.00402805i
$540$		0			0
$541$		−	35.0866i		−	1.50849i	−0.656592	−	0.754246i	$-0.728003\pi$
$541$		−	35.0866i		−	1.50849i	0.656592	−	0.754246i	$-0.271997\pi$
$542$	−11.4162	+	23.9042i	−0.490368	+	1.02677i
$543$		0			0
$544$	1.10500	−	8.23593i	0.0473767	−	0.353113i
$545$	0.452947	−	1.24446i	0.0194021	−	0.0533069i
$546$		0			0
$547$	−0.423952	+	2.40435i	−0.0181269	+	0.102803i	−0.992529	−	0.122010i	$-0.961066\pi$
$547$	−0.423952	+	2.40435i	−0.0181269	+	0.102803i	0.974402	+	0.224813i	$0.0721771\pi$
$548$	−23.5629	−	0.434604i	−1.00656	−	0.0185654i
$549$		0			0
$550$	−0.0852548	+	0.0836968i	−0.00363528	+	0.00356884i
$551$	9.26174	−	3.37100i	0.394563	−	0.143609i
$552$		0			0
$553$	8.05890	−	6.76222i	0.342699	−	0.287559i
$554$	−25.0752	−	17.9047i	−1.06535	−	0.760699i
$555$		0			0
$556$	7.03814	−	8.08030i	0.298484	−	0.342681i
$557$	3.41195	+	5.90968i	0.144569	+	0.250401i	0.929212	−	0.369547i	$-0.120487\pi$
$557$	3.41195	+	5.90968i	0.144569	+	0.250401i	−0.784643	+	0.619948i	$0.787154\pi$
$558$		0			0
$559$	−20.9888	−	12.1179i	−0.887730	−	0.512531i
$560$	−1.58471	+	1.75301i	−0.0669660	+	0.0740781i
$561$		0			0
$562$	−1.57451	+	16.2676i	−0.0664167	+	0.686207i
$563$	−20.6520	+	3.64150i	−0.870377	+	0.153471i	−0.590962	−	0.806699i	$-0.701252\pi$
$563$	−20.6520	+	3.64150i	−0.870377	+	0.153471i	−0.279415	+	0.960170i	$0.590141\pi$
$564$		0			0
$565$	5.69243	−	6.78397i	0.239482	−	0.285404i
$566$	−5.87730	+	1.51687i	−0.247041	+	0.0637589i
$567$		0			0
$568$	20.6982	−	19.5835i	0.868476	−	0.821707i
$569$	20.8313	−	24.8258i	0.873295	−	1.04075i	−0.125521	−	0.992091i	$-0.540060\pi$
$569$	20.8313	−	24.8258i	0.873295	−	1.04075i	0.998815	−	0.0486610i	$-0.0154954\pi$
$570$		0			0
$571$	−0.396543	−	2.24891i	−0.0165948	−	0.0941139i	0.975385	−	0.220507i	$-0.0707711\pi$
$571$	−0.396543	−	2.24891i	−0.0165948	−	0.0941139i	−0.991980	+	0.126393i	$0.959660\pi$
$572$	0.0777697	−	0.0122387i	0.00325172	−	0.000511725i
$573$		0			0
$574$	−0.349388	−	4.46764i	−0.0145832	−	0.186476i
$575$	−5.10017	+	8.83376i	−0.212692	+	0.368393i
$576$		0			0
$577$	−10.7395	−	18.6014i	−0.447092	−	0.774387i	0.551103	−	0.834437i	$-0.314207\pi$
$577$	−10.7395	−	18.6014i	−0.447092	−	0.774387i	−0.998195	+	0.0600507i	$0.980874\pi$
$578$	−17.3042	+	11.8803i	−0.719762	+	0.494155i
$579$		0			0
$580$	−2.37184	+	6.16064i	−0.0984853	+	0.255806i
$581$	−2.00240	+	1.68021i	−0.0830736	+	0.0697070i
$582$		0			0
$583$	−0.0627342	−	0.172361i	−0.00259818	−	0.00713845i
$584$	−1.84039	−	0.548119i	−0.0761558	−	0.0226813i
$585$		0			0
$586$	4.75928	−	17.1285i	0.196604	−	0.707572i
$587$	−18.6609	−	3.29041i	−0.770216	−	0.135810i	−0.225287	−	0.974292i	$-0.572332\pi$
$587$	−18.6609	−	3.29041i	−0.770216	−	0.135810i	−0.544928	+	0.838483i	$0.683443\pi$
$588$		0			0
$589$	4.17975	−	11.4838i	0.172224	−	0.473180i
$590$	6.41276	−	2.91863i	0.264009	−	0.120158i
$591$		0			0
$592$	−6.50736	−	20.1632i	−0.267451	−	0.828703i
$593$		−	23.6650i		−	0.971804i	−0.874013	−	0.485902i	$-0.838491\pi$
$593$		−	23.6650i		−	0.971804i	0.874013	−	0.485902i	$-0.161509\pi$
$594$		0			0
$595$	−0.867835			−0.0355778
$596$	−28.1650	−	5.50363i	−1.15368	−	0.225437i
$597$		0			0
$598$	6.11776	−	2.78437i	0.250174	−	0.113861i
$599$	8.37844	+	3.04950i	0.342334	+	0.124599i	0.507465	−	0.861672i	$-0.330583\pi$
$599$	8.37844	+	3.04950i	0.342334	+	0.124599i	−0.165131	+	0.986272i	$0.552805\pi$
$600$		0			0
$601$	4.44934	−	25.2334i	0.181492	−	1.02929i	−0.748888	−	0.662697i	$-0.769412\pi$
$601$	4.44934	−	25.2334i	0.181492	−	1.02929i	0.930380	−	0.366597i	$-0.119477\pi$
$602$	−19.2379	−	5.34540i	−0.784080	−	0.217862i
$603$		0			0
$604$	−12.2716	+	20.3777i	−0.499326	+	0.829159i
$605$	4.69274	−	1.70802i	0.190787	−	0.0694407i
$606$		0			0
$607$	−8.91382	−	10.6231i	−0.361801	−	0.431177i	0.554182	−	0.832396i	$-0.313031\pi$
$607$	−8.91382	−	10.6231i	−0.361801	−	0.431177i	−0.915982	+	0.401218i	$0.868587\pi$
$608$	2.91723	+	7.09237i	0.118309	+	0.287634i
$609$		0			0
$610$	−3.27334	−	4.76778i	−0.132533	−	0.193042i
$611$	8.81625	−	5.09007i	0.356667	−	0.205922i
$612$		0			0
$613$	17.7329	+	10.2381i	0.716224	+	0.413512i	0.813361	−	0.581759i	$-0.197635\pi$
$613$	17.7329	+	10.2381i	0.716224	+	0.413512i	−0.0971374	+	0.995271i	$0.530969\pi$
$614$	1.64678	+	21.0575i	0.0664587	+	0.849811i
$615$		0			0
$616$	0.0595184	−	0.0257744i	0.00239807	−	0.00103848i
$617$	−45.9610	+	8.10416i	−1.85032	+	0.326261i	−0.984675	−	0.174399i	$-0.944202\pi$
$617$	−45.9610	+	8.10416i	−1.85032	+	0.326261i	−0.865644	+	0.500660i	$0.833091\pi$
$618$		0			0
$619$	−20.3900	−	17.1092i	−0.819542	−	0.687678i	0.133323	−	0.991073i	$-0.457435\pi$
$619$	−20.3900	−	17.1092i	−0.819542	−	0.687678i	−0.952865	+	0.303395i	$0.901880\pi$
$620$	3.96119	+	7.16288i	0.159085	+	0.287668i
$621$		0			0
$622$	1.67164	−	0.431435i	0.0670268	−	0.0172990i
$623$	0.119413	+	0.100199i	0.00478417	+	0.00401439i
$624$		0			0
$625$	3.81170	+	21.6172i	0.152468	+	0.864688i
$626$	−5.60513	−	0.542510i	−0.224026	−	0.0216831i
$627$		0			0
$628$	−31.8061	+	10.9166i	−1.26920	+	0.435618i
$629$	3.89042	−	6.73841i	0.155121	−	0.268678i
$630$		0			0
$631$	24.6191	−	14.2138i	0.980071	−	0.565844i	0.0777793	−	0.996971i	$-0.475217\pi$
$631$	24.6191	−	14.2138i	0.980071	−	0.565844i	0.902292	+	0.431126i	$0.141884\pi$
$632$	20.4489	+	10.2334i	0.813415	+	0.407062i
$633$		0			0
$634$	−6.08384	+	8.52031i	−0.241620	+	0.338385i
$635$	−5.05252	−	6.02135i	−0.200503	−	0.238950i
$636$		0			0
$637$	−4.05421	−	11.1389i	−0.160634	−	0.441337i
$638$	0.129295	−	0.126932i	0.00511882	−	0.00502528i
$639$		0			0
$640$	−4.86537	−	1.64668i	−0.192321	−	0.0650907i
$641$	−19.2764	−	3.39896i	−0.761373	−	0.134251i	−0.220537	−	0.975379i	$-0.570781\pi$
$641$	−19.2764	−	3.39896i	−0.761373	−	0.134251i	−0.540836	+	0.841128i	$0.681892\pi$
$642$		0			0
$643$	−10.2317	−	3.72402i	−0.403497	−	0.146861i	0.132296	−	0.991210i	$-0.457765\pi$
$643$	−10.2317	−	3.72402i	−0.403497	−	0.146861i	−0.535793	+	0.844349i	$0.679987\pi$
$644$	4.30698	−	3.48068i	0.169719	−	0.137158i
$645$		0			0
$646$	−1.21372	+	2.54138i	−0.0477532	+	0.0999894i
$647$	−19.0202			−0.747763			−0.373881	−	0.927477i	$-0.621973\pi$
$647$	−19.0202			−0.747763			−0.373881	+	0.927477i	$0.621973\pi$
$648$		0			0
$649$	−0.193381			−0.00759085
$650$	6.52628	−	13.6652i	0.255982	−	0.535995i
$651$		0			0
$652$	12.7943	+	15.8316i	0.501062	+	0.620013i
$653$	−11.7763	−	4.28623i	−0.460843	−	0.167733i	0.101157	−	0.994871i	$-0.467746\pi$
$653$	−11.7763	−	4.28623i	−0.460843	−	0.167733i	−0.562000	+	0.827137i	$0.689968\pi$
$654$		0			0
$655$	1.37786	+	0.242955i	0.0538376	+	0.00949302i
$656$	8.60939	−	4.55587i	0.336140	−	0.177877i
$657$		0			0
$658$	5.98491	−	5.87554i	0.233316	−	0.229052i
$659$	−9.65592	−	26.5294i	−0.376141	−	1.03344i	−0.972942	−	0.231050i	$-0.925784\pi$
$659$	−9.65592	−	26.5294i	−0.376141	−	1.03344i	0.596801	−	0.802389i	$-0.296438\pi$
$660$		0			0
$661$	−10.6735	−	12.7202i	−0.415150	−	0.494757i	0.517427	−	0.855727i	$-0.326890\pi$
$661$	−10.6735	−	12.7202i	−0.415150	−	0.494757i	−0.932577	+	0.360971i	$0.882445\pi$
$662$	2.46309	−	3.44952i	0.0957307	−	0.134069i
$663$		0			0
$664$	−5.08096	−	2.54269i	−0.197180	−	0.0986756i
$665$	0.693608	−	0.400455i	0.0268970	−	0.0155290i
$666$		0			0
$667$	7.73476	−	13.3970i	0.299491	−	0.518734i
$668$	10.4140	+	30.3418i	0.402929	+	1.17396i
$669$		0			0
$670$	3.08707	+	0.298792i	0.119264	+	0.0115433i
$671$	0.0275635	+	0.156320i	0.00106408	+	0.00603468i
$672$		0			0
$673$	4.64214	+	3.89522i	0.178941	+	0.150150i	0.727859	−	0.685727i	$-0.240516\pi$
$673$	4.64214	+	3.89522i	0.178941	+	0.150150i	−0.548918	+	0.835876i	$0.684960\pi$
$674$	−18.0163	+	4.64982i	−0.693962	+	0.179105i
$675$		0			0
$676$	14.0199	−	7.75326i	0.539228	−	0.298202i
$677$	−5.34485	−	4.48486i	−0.205419	−	0.172367i	0.534274	−	0.845311i	$-0.320585\pi$
$677$	−5.34485	−	4.48486i	−0.205419	−	0.172367i	−0.739693	+	0.672944i	$0.765029\pi$
$678$		0			0
$679$	−14.2922	+	2.52009i	−0.548483	+	0.0967123i
$680$	−0.749603	−	1.73099i	−0.0287460	−	0.0663804i
$681$		0			0
$682$	−0.0175156	−	0.223973i	−0.000670707	−	0.00857636i
$683$	−25.8624	−	14.9317i	−0.989597	−	0.571344i	−0.0844432	−	0.996428i	$-0.526911\pi$
$683$	−25.8624	−	14.9317i	−0.989597	−	0.571344i	−0.905154	+	0.425084i	$0.860244\pi$
$684$		0			0
$685$	−4.63301	+	2.67487i	−0.177018	+	0.102201i
$686$	−12.8185	−	18.6708i	−0.489413	−	0.712856i
$687$		0			0
$688$	−5.95505	−	42.9892i	−0.227034	−	1.63895i
$689$	14.9446	+	17.8103i	0.569346	+	0.678520i
$690$		0			0
$691$	31.1175	−	11.3259i	1.18377	−	0.430856i	0.326236	−	0.945288i	$-0.394220\pi$
$691$	31.1175	−	11.3259i	1.18377	−	0.430856i	0.857531	+	0.514432i	$0.171997\pi$
$692$	−23.1926	−	13.9668i	−0.881651	−	0.530937i
$693$		0			0
$694$	−39.8991	−	11.0862i	−1.51455	−	0.420828i
$695$	0.422398	−	2.39554i	0.0160225	−	0.0908679i
$696$		0			0
$697$	3.36139	+	1.22345i	0.127322	+	0.0463414i
$698$	26.9866	−	12.2824i	1.02146	−	0.464895i
$699$		0			0
$700$	2.39268	−	12.2446i	0.0904350	−	0.462803i
$701$	−9.68894			−0.365946			−0.182973	−	0.983118i	$-0.558572\pi$
$701$	−9.68894			−0.365946			−0.182973	+	0.983118i	$0.558572\pi$
$702$		0			0
$703$			7.18080i			0.270829i
$704$	0.102820	+	0.0964528i	0.00387516	+	0.00363520i
$705$		0			0
$706$	−4.06024	+	1.84793i	−0.152809	+	0.0695478i
$707$	−7.42607	+	20.4030i	−0.279286	+	0.767333i
$708$		0			0
$709$	24.6853	+	4.35269i	0.927077	+	0.163469i	0.616748	−	0.787161i	$-0.288450\pi$
$709$	24.6853	+	4.35269i	0.927077	+	0.163469i	0.310329	+	0.950629i	$0.399561\pi$
$710$	1.73166	−	6.23218i	0.0649879	−	0.233890i
$711$		0			0
$712$	−0.0967135	+	0.324729i	−0.00362449	+	0.0121697i
$713$	−6.56025	−	18.0241i	−0.245683	−	0.675009i
$714$		0			0
$715$	0.0136901	−	0.0114874i	0.000511981	−	0.000429603i
$716$	−21.2264	−	8.17215i	−0.793268	−	0.305408i
$717$		0			0
$718$	−35.6645	+	24.4856i	−1.33099	+	0.913793i
$719$	16.4482	+	28.4892i	0.613415	+	1.06247i	0.990660	+	0.136353i	$0.0435381\pi$
$719$	16.4482	+	28.4892i	0.613415	+	1.06247i	−0.377245	+	0.926113i	$0.623129\pi$
$720$		0			0
$721$	10.3805	−	17.9796i	0.386590	−	0.669594i
$722$	1.89231	+	24.1970i	0.0704244	+	0.900520i
$723$		0			0
$724$	4.60862	+	29.2851i	0.171278	+	1.08837i
$725$	−6.05210	−	34.3232i	−0.224769	−	1.27473i
$726$		0			0
$727$	−20.0843	+	23.9355i	−0.744884	+	0.887719i	−0.996792	−	0.0800327i	$-0.974498\pi$
$727$	−20.0843	+	23.9355i	−0.744884	+	0.887719i	0.251908	+	0.967751i	$0.418942\pi$
$728$	−5.97190	+	5.65031i	−0.221333	+	0.209414i
$729$		0			0
$730$	−0.422076	+	0.108934i	−0.0156217	+	0.00403182i
$731$	10.2449	−	12.2094i	0.378920	−	0.451579i
$732$		0			0
$733$	16.2456	−	2.86454i	0.600046	−	0.105804i	0.134630	−	0.990896i	$-0.457016\pi$
$733$	16.2456	−	2.86454i	0.600046	−	0.105804i	0.465417	+	0.885092i	$0.345904\pi$
$734$	−3.04832	+	31.4948i	−0.112516	+	1.16249i
$735$		0			0
$736$	10.6628	+	5.58425i	0.393036	+	0.205838i
$737$	−0.0737209	−	0.0425628i	−0.00271554	−	0.00156782i
$738$		0			0
$739$	−11.5876	−	20.0704i	−0.426258	−	0.738301i	0.570279	−	0.821451i	$-0.306835\pi$
$739$	−11.5876	−	20.0704i	−0.426258	−	0.738301i	−0.996537	+	0.0831501i	$0.973502\pi$
$740$	−3.62670	−	3.15894i	−0.133320	−	0.116125i
$741$		0			0
$742$	15.5884	+	11.1308i	0.572269	+	0.408623i
$743$	2.55778	−	2.14623i	0.0938358	−	0.0787376i	−0.594663	−	0.803975i	$-0.702714\pi$
$743$	2.55778	−	2.14623i	0.0938358	−	0.0787376i	0.688499	+	0.725238i	$0.258270\pi$
$744$		0			0
$745$	−6.12156	+	2.22807i	−0.224277	+	0.0816300i
$746$	−11.5409	+	11.3300i	−0.422542	+	0.414821i
$747$		0			0
$748$	−0.000954765		0.0517644i	−3.49097e−5		0.00189270i
$749$	1.52210	−	8.63224i	0.0556162	−	0.315415i
$750$		0			0
$751$	−0.701648	+	1.92776i	−0.0256035	+	0.0703450i	−0.951836	−	0.306608i	$-0.900806\pi$
$751$	−0.701648	+	1.92776i	−0.0256035	+	0.0703450i	0.926232	+	0.376953i	$0.123028\pi$
$752$	16.8889	+	6.86246i	0.615876	+	0.250248i
$753$		0			0
$754$	−9.89754	+	20.7243i	−0.360447	+	0.754733i
$755$			5.39982i			0.196519i
$756$		0			0
$757$		−	41.6394i		−	1.51341i	−0.653756	−	0.756705i	$-0.726808\pi$
$757$		−	41.6394i		−	1.51341i	0.653756	−	0.756705i	$-0.273192\pi$
$758$	−27.6929	−	13.2257i	−1.00585	−	0.480377i
$759$		0			0
$760$	1.39786	+	1.03758i	0.0507057	+	0.0376368i
$761$	14.1101	−	38.7671i	0.511490	−	1.40531i	−0.368195	−	0.929749i	$-0.620024\pi$
$761$	14.1101	−	38.7671i	0.511490	−	1.40531i	0.879684	−	0.475558i	$-0.157754\pi$
$762$		0			0
$763$	0.659130	−	3.73811i	0.0238621	−	0.135329i
$764$	0.695186	−	37.6909i	0.0251509	−	1.36361i
$765$		0			0
$766$	32.8659	+	33.4777i	1.18749	+	1.20960i
$767$	23.0337	−	8.38359i	0.831700	−	0.302714i
$768$		0			0
$769$	−33.4132	+	28.0370i	−1.20491	+	1.01104i	−0.205437	+	0.978670i	$0.565861\pi$
$769$	−33.4132	+	28.0370i	−1.20491	+	1.01104i	−0.999476	+	0.0323712i	$0.989694\pi$
$770$	0.00855577	−	0.0119822i	0.000308329	−	0.000431809i
$771$		0			0
$772$	2.77219	−	3.18267i	0.0997732	−	0.114547i
$773$	−3.52468	−	6.10492i	−0.126774	−	0.219579i	0.795651	−	0.605755i	$-0.207129\pi$
$773$	−3.52468	−	6.10492i	−0.126774	−	0.219579i	−0.922425	+	0.386176i	$0.873796\pi$
$774$		0			0
$775$	−37.4247	−	21.6072i	−1.34434	−	0.776153i
$776$	−17.3716	−	26.3305i	−0.623605	−	0.945208i
$777$		0			0
$778$	9.80280	+	0.948795i	0.351447	+	0.0340160i
$779$	−3.25111	+	0.573258i	−0.116483	+	0.0205391i
$780$		0			0
$781$	−0.114116	+	0.135998i	−0.00408338	+	0.00486638i
$782$	1.10465	+	4.28008i	0.0395020	+	0.153055i
$783$		0			0
$784$	11.2841	−	17.9791i	0.403004	−	0.642111i
$785$	−4.90671	+	5.84759i	−0.175128	+	0.208709i
$786$		0			0
$787$	8.03739	+	45.5823i	0.286502	+	1.62483i	0.699871	+	0.714270i	$0.253241\pi$
$787$	8.03739	+	45.5823i	0.286502	+	1.62483i	−0.413369	+	0.910564i	$0.635648\pi$
$788$	22.6368	−	3.56237i	0.806402	−	0.126904i
$789$		0			0
$790$	5.17496	−	0.404704i	0.184117	−	0.0143987i
$791$	12.6913	−	21.9820i	0.451250	−	0.781589i
$792$		0			0
$793$	−10.0600	−	17.4245i	−0.357242	−	0.618762i
$794$	29.4470	+	42.8911i	1.04503	+	1.52215i
$795$		0			0
$796$	−10.6074	−	4.08386i	−0.375971	−	0.144748i
$797$	−10.7323	+	9.00550i	−0.380159	+	0.318991i	−0.812765	−	0.582592i	$-0.802039\pi$
$797$	−10.7323	+	9.00550i	−0.380159	+	0.318991i	0.432606	+	0.901583i	$0.357594\pi$
$798$		0			0
$799$	2.28975	+	6.29103i	0.0810054	+	0.222561i
$800$	26.4899	−	5.80399i	0.936559	−	0.205202i
$801$		0			0
$802$	−4.15930	−	1.15569i	−0.146870	−	0.0408088i
$803$	0.0117824	+	0.00207756i	0.000415792	+	7.33153e-5i
$804$		0			0
$805$	0.429937	−	1.18124i	0.0151533	−	0.0416333i
$806$	11.7962	+	25.9182i	0.415502	+	0.912931i
$807$		0			0
$808$	−47.1102	+	2.81124i	−1.65733	+	0.0988991i
$809$			25.2574i			0.888002i	0.896026	+	0.444001i	$0.146441\pi$
$809$			25.2574i			0.888002i	−0.896026	+	0.444001i	$0.853559\pi$
$810$		0			0
$811$	−36.9593			−1.29782			−0.648908	−	0.760867i	$-0.724774\pi$
$811$	−36.9593			−1.29782			−0.648908	+	0.760867i	$0.724774\pi$
$812$	−3.62867	+	18.5698i	−0.127341	+	0.651672i
$813$		0			0
$814$	0.0546826	+	0.120147i	0.00191662	+	0.00421116i
$815$	4.34200	+	1.58036i	0.152094	+	0.0553576i
$816$		0			0
$817$	−2.55420	+	14.4856i	−0.0893602	+	0.506787i
$818$	9.11925	−	32.8199i	0.318847	−	1.14752i
$819$		0			0
$820$	1.14068	−	1.89417i	0.0398344	−	0.0661473i
$821$	−5.42437	+	1.97431i	−0.189312	+	0.0689038i	−0.434936	−	0.900461i	$-0.643229\pi$
$821$	−5.42437	+	1.97431i	−0.189312	+	0.0689038i	0.245625	+	0.969365i	$0.421007\pi$
$822$		0			0
$823$	−12.2571	−	14.6074i	−0.427254	−	0.509182i	0.508874	−	0.860841i	$-0.330062\pi$
$823$	−12.2571	−	14.6074i	−0.427254	−	0.509182i	−0.936128	+	0.351659i	$0.885618\pi$
$824$	44.8284	+	5.17493i	1.56167	+	0.180277i
$825$		0			0
$826$	16.6483	−	11.4300i	0.579270	−	0.397700i
$827$	23.7503	−	13.7122i	0.825878	−	0.476821i	−0.0265613	−	0.999647i	$-0.508456\pi$
$827$	23.7503	−	13.7122i	0.825878	−	0.476821i	0.852439	+	0.522826i	$0.175122\pi$
$828$		0			0
$829$	23.8710	+	13.7819i	0.829073	+	0.478666i	0.853535	−	0.521035i	$-0.174454\pi$
$829$	23.8710	+	13.7819i	0.829073	+	0.478666i	−0.0244622	+	0.999701i	$0.507787\pi$
$830$	−1.28583	+	0.100557i	−0.0446317	+	0.00349038i
$831$		0			0
$832$	−16.4284	−	7.03105i	−0.569553	−	0.243758i
$833$	7.67695	−	1.35365i	0.265991	−	0.0469013i
$834$		0			0
$835$	5.57837	+	4.68081i	0.193048	+	0.161986i
$836$	−0.0231231	−	0.0418127i	−0.000799731	−	0.00144612i
$837$		0			0
$838$	10.4934	+	40.6580i	0.362489	+	1.40451i
$839$	22.7744	+	19.1100i	0.786259	+	0.659750i	0.944816	−	0.327600i	$-0.106240\pi$
$839$	22.7744	+	19.1100i	0.786259	+	0.659750i	−0.158558	+	0.987350i	$0.550684\pi$
$840$		0			0
$841$	4.14263	+	23.4940i	0.142849	+	0.810138i
$842$	3.91194	−	40.4175i	0.134814	−	1.39288i
$843$		0			0
$844$	10.8071	+	31.4871i	0.371995	+	1.08383i
$845$	1.81840	−	3.14956i	0.0625548	−	0.108348i
$846$		0			0
$847$	12.3959	−	7.15675i	0.425927	−	0.245909i
$848$	−8.73675	+	40.7071i	−0.300021	+	1.39789i
$849$		0			0
$850$	8.10488	+	5.78721i	0.277995	+	0.198500i
$851$	7.24453	+	8.63370i	0.248339	+	0.295959i
$852$		0			0
$853$	14.9845	+	41.1697i	0.513061	+	1.40962i	0.878031	+	0.478604i	$0.158857\pi$
$853$	14.9845	+	41.1697i	0.513061	+	1.40962i	−0.364970	+	0.931019i	$0.618921\pi$
$854$	−11.6124	−	11.8286i	−0.397370	−	0.404767i
$855$		0			0
$856$	18.5326	−	4.42022i	0.633432	−	0.151080i
$857$	12.6966	+	2.23875i	0.433708	+	0.0764744i	0.386240	−	0.922398i	$-0.373774\pi$
$857$	12.6966	+	2.23875i	0.433708	+	0.0764744i	0.0474680	+	0.998873i	$0.484885\pi$
$858$		0			0
$859$	−26.7551	−	9.73806i	−0.912872	−	0.332258i	−0.157473	−	0.987523i	$-0.550335\pi$
$859$	−26.7551	−	9.73806i	−0.912872	−	0.332258i	−0.755399	+	0.655265i	$0.772557\pi$
$860$	−6.19238	−	7.66244i	−0.211158	−	0.261287i
$861$		0			0
$862$	−33.8926	−	16.1865i	−1.15439	−	0.551315i
$863$	46.6170			1.58686			0.793431	−	0.608660i	$-0.208293\pi$
$863$	46.6170			1.58686			0.793431	+	0.608660i	$0.208293\pi$
$864$		0			0
$865$	−6.14571			−0.208961
$866$	−1.98147	−	0.946317i	−0.0673332	−	0.0321572i
$867$		0			0
$868$	14.7461	+	18.2468i	0.500515	+	0.619336i
$869$	−0.133877	−	0.0487272i	−0.00454146	−	0.00165296i
$870$		0			0
$871$	10.6262	+	1.87368i	0.360054	+	0.0634873i
$872$	8.02539	−	1.91414i	0.271774	−	0.0648209i
$873$		0			0
$874$	−2.85788	−	2.91108i	−0.0966692	−	0.0984686i
$875$	−1.97894	−	5.43708i	−0.0669003	−	0.183807i
$876$		0			0
$877$	3.98303	+	4.74679i	0.134497	+	0.160288i	0.829089	−	0.559116i	$-0.188859\pi$
$877$	3.98303	+	4.74679i	0.134497	+	0.160288i	−0.694592	+	0.719404i	$0.744415\pi$
$878$	−1.32201	−	0.943966i	−0.0446156	−	0.0318573i
$879$		0			0
$880$	0.0312899	+	0.00671560i	0.00105478	+	0.000226383i
$881$	21.9173	−	12.6539i	0.738412	−	0.426322i	−0.0830799	−	0.996543i	$-0.526476\pi$
$881$	21.9173	−	12.6539i	0.738412	−	0.426322i	0.821492	+	0.570221i	$0.193142\pi$
$882$		0			0
$883$	15.7424	−	27.2667i	0.529775	−	0.917597i	−0.469622	−	0.882868i	$-0.655610\pi$
$883$	15.7424	−	27.2667i	0.529775	−	0.917597i	0.999397	−	0.0347290i	$-0.0110568\pi$
$884$	−2.13041	−	6.20710i	−0.0716535	−	0.208767i
$885$		0			0
$886$	2.30849	−	23.8509i	0.0775552	−	0.801288i
$887$	0.0310073	+	0.175851i	0.00104112	+	0.00590451i	0.985324	−	0.170695i	$-0.0546013\pi$
$887$	0.0310073	+	0.175851i	0.00104112	+	0.00590451i	−0.984283	+	0.176600i	$0.943490\pi$
$888$		0			0
$889$	−17.2584	−	14.4815i	−0.578827	−	0.485694i
$890$	0.0192209	+	0.0744737i	0.000644287	+	0.00249636i
$891$		0			0
$892$	2.68864	+	4.86177i	0.0900223	+	0.162784i
$893$	−4.73299	−	3.97145i	−0.158384	−	0.132900i
$894$		0			0
$895$	−5.08477	+	0.896582i	−0.169965	+	0.0299694i
$896$	−14.5528	−	2.22646i	−0.486175	−	0.0743807i
$897$		0			0
$898$	43.2606	−	3.38316i	1.44363	−	0.112898i
$899$	56.7571	+	32.7687i	1.89296	+	1.09290i
$900$		0			0
$901$	−13.2413	+	7.64488i	−0.441132	+	0.254688i
$902$	−0.0500313	+	0.0343491i	−0.00166586	+	0.00114370i
$903$		0			0
$904$	54.8076	+	6.32691i	1.82287	+	0.210430i
$905$	4.32570	+	5.15517i	0.143791	+	0.171364i
$906$		0			0
$907$	−18.2575	+	6.64519i	−0.606231	+	0.220650i	−0.626853	−	0.779137i	$-0.715657\pi$
$907$	−18.2575	+	6.64519i	−0.606231	+	0.220650i	0.0206225	+	0.999787i	$0.493435\pi$
$908$	−25.5120	+	42.3641i	−0.846646	+	1.40590i
$909$		0			0
$910$	−0.499623	+	1.79813i	−0.0165623	+	0.0596074i
$911$	−0.423720	+	2.40304i	−0.0140385	+	0.0796161i	−0.991022	−	0.133698i	$-0.957315\pi$
$911$	−0.423720	+	2.40304i	−0.0140385	+	0.0796161i	0.976984	+	0.213314i	$0.0684258\pi$
$912$		0			0
$913$	0.0332645	+	0.0121073i	0.00110089	+	0.000400693i
$914$	4.19634	+	9.22011i	0.138803	+	0.304974i
$915$		0			0
$916$	−6.01153	+	30.7641i	−0.198626	+	1.01648i
$917$	4.01015			0.132427
$918$		0			0
$919$			2.20402i			0.0727038i	0.999339	+	0.0363519i	$0.0115737\pi$
$919$			2.20402i			0.0727038i	−0.999339	+	0.0363519i	$0.988426\pi$
$920$	2.72748	−	0.162758i	0.0899222	−	0.00536599i
$921$		0			0
$922$	4.85526	+	10.6679i	0.159900	+	0.351328i
$923$	7.69653	−	21.1460i	0.253334	−	0.696030i
$924$		0			0
$925$	25.0065	+	4.40933i	0.822210	+	0.144978i
$926$	−0.527376	−	0.146535i	−0.0173307	−	0.00481545i
$927$		0			0
$928$	−40.1737	+	8.80214i	−1.31877	+	0.288944i
$929$	−3.30889	−	9.09111i	−0.108561	−	0.298270i	0.873502	−	0.486820i	$-0.161843\pi$
$929$	−3.30889	−	9.09111i	−0.108561	−	0.298270i	−0.982063	+	0.188551i	$0.939621\pi$
$930$		0			0
$931$	−5.51109	+	4.62435i	−0.180619	+	0.151557i
$932$	−37.7585	−	14.5370i	−1.23682	−	0.476175i
$933$		0			0
$934$	5.33220	+	7.76662i	0.174475	+	0.254131i
$935$	0.00587632	+	0.0101781i	0.000192176	+	0.000332859i
$936$		0			0
$937$	−22.2202	+	38.4864i	−0.725901	+	1.25730i	0.232701	+	0.972548i	$0.425243\pi$
$937$	−22.2202	+	38.4864i	−0.725901	+	1.25730i	−0.958602	+	0.284749i	$0.908090\pi$
$938$	8.86243	−	0.693079i	0.289369	−	0.0226298i
$939$		0			0
$940$	4.08792	−	0.643318i	0.133333	−	0.0209827i
$941$	7.38960	+	41.9085i	0.240894	+	1.36618i	0.829838	+	0.558004i	$0.188433\pi$
$941$	7.38960	+	41.9085i	0.240894	+	1.36618i	−0.588944	+	0.808174i	$0.700456\pi$
$942$		0			0
$943$	−3.33056	+	3.96920i	−0.108458	+	0.129255i
$944$	37.1785	+	23.3341i	1.21006	+	0.759460i
$945$		0			0
$946$	0.0675731	+	0.261820i	0.00219699	+	0.00851250i
$947$	−30.3650	+	36.1877i	−0.986731	+	1.17594i	−0.00233119	+	0.999997i	$0.500742\pi$
$947$	−30.3650	+	36.1877i	−0.986731	+	1.17594i	−0.984400	+	0.175943i	$0.943702\pi$
$948$		0			0
$949$	−1.49348	+	0.263341i	−0.0484804	+	0.00854841i
$950$	−9.14819	−	0.885437i	−0.296807	−	0.0287274i
$951$		0			0
$952$	−2.97740	−	4.51289i	−0.0964980	−	0.146264i
$953$	23.8540	+	13.7721i	0.772707	+	0.446123i	0.833840	−	0.552007i	$-0.186138\pi$
$953$	23.8540	+	13.7721i	0.772707	+	0.446123i	−0.0611321	+	0.998130i	$0.519471\pi$
$954$		0			0
$955$	−4.27868	−	7.41089i	−0.138455	−	0.239811i
$956$	−11.2549	+	12.9214i	−0.364009	+	0.417909i
$957$		0			0
$958$	−0.931443	+	1.30447i	−0.0300936	+	0.0421455i
$959$	−11.7461	+	9.85611i	−0.379300	+	0.318270i
$960$		0			0
$961$	47.2298	−	17.1902i	1.52354	−	0.554524i
$962$	−11.7220	−	11.9402i	−0.377933	−	0.384968i
$963$		0			0
$964$	−0.533115	+	28.9039i	−0.0171705	+	0.930930i
$965$	0.166374	−	0.943555i	0.00535578	−	0.0303741i
$966$		0			0
$967$	0.543982	−	1.49458i	0.0174933	−	0.0480624i	−0.930639	−	0.365939i	$-0.880748\pi$
$967$	0.543982	−	1.49458i	0.0174933	−	0.0480624i	0.948132	+	0.317877i	$0.102970\pi$
$968$	24.9820	+	18.5431i	0.802951	+	0.595998i
$969$		0			0
$970$	−6.46162	−	3.08596i	−0.207470	−	0.0990842i
$971$		−	9.93969i		−	0.318980i	−0.987200	−	0.159490i	$-0.949015\pi$
$971$		−	9.93969i		−	0.318980i	0.987200	−	0.159490i	$-0.0509849\pi$
$972$		0			0
$973$		−	6.97199i		−	0.223512i
$974$	−25.5752	+	53.5514i	−0.819483	+	1.71590i
$975$		0			0
$976$	13.5630	−	33.3794i	0.434141	−	1.06845i
$977$	−13.5121	+	37.1242i	−0.432290	+	1.18771i	0.512113	+	0.858918i	$0.328863\pi$
$977$	−13.5121	+	37.1242i	−0.432290	+	1.18771i	−0.944403	+	0.328789i	$0.893359\pi$
$978$		0			0
$979$	0.000366577	−	0.00207896i	1.17158e−5	−	6.64438e-5i
$980$	0.0888600	−	4.81772i	0.00283853	−	0.153896i
$981$		0			0
$982$	20.7838	−	20.4040i	0.663237	−	0.651117i
$983$	−30.2880	+	11.0239i	−0.966036	+	0.351608i	−0.776396	−	0.630245i	$-0.782954\pi$
$983$	−30.2880	+	11.0239i	−0.966036	+	0.351608i	−0.189640	+	0.981854i	$0.560732\pi$
$984$		0			0
$985$	3.98484	−	3.34368i	0.126967	−	0.106538i
$986$	−12.2916	−	8.77669i	−0.391444	−	0.279507i
$987$		0			0
$988$	4.56692	+	3.97790i	0.145293	+	0.126554i
$989$	11.5432	+	19.9933i	0.367051	+	0.635751i
$990$		0			0
$991$	−2.66599	−	1.53921i	−0.0846881	−	0.0488947i	0.457058	−	0.889437i	$-0.348903\pi$
$991$	−2.66599	−	1.53921i	−0.0846881	−	0.0488947i	−0.541746	+	0.840542i	$0.682237\pi$
$992$	−23.6580	+	45.1735i	−0.751142	+	1.43426i
$993$		0			0
$994$	1.78604	−	18.4531i	0.0566499	−	0.585297i
$995$	−2.54100	+	0.448048i	−0.0805553	+	0.0142041i
$996$		0			0
$997$	−27.9424	+	33.3004i	−0.884944	+	1.05464i	0.113190	+	0.993573i	$0.463893\pi$
$997$	−27.9424	+	33.3004i	−0.884944	+	1.05464i	−0.998134	+	0.0610619i	$0.980551\pi$
$998$	13.7303	−	3.54367i	0.434626	−	0.112173i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.28		192
3.2	odd	2		216.2.v.b.11.5	✓	192
8.3	odd	2	inner	648.2.v.b.35.11		192
12.11	even	2		864.2.bh.b.335.1		192
24.5	odd	2		864.2.bh.b.335.2		192
24.11	even	2		216.2.v.b.11.22	yes	192
27.5	odd	18	inner	648.2.v.b.611.11		192
27.22	even	9		216.2.v.b.59.22	yes	192
108.103	odd	18		864.2.bh.b.815.2		192
216.59	even	18	inner	648.2.v.b.611.28		192
216.157	even	18		864.2.bh.b.815.1		192
216.211	odd	18		216.2.v.b.59.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.5	✓	192	3.2	odd	2
216.2.v.b.11.22	yes	192	24.11	even	2
216.2.v.b.59.5	yes	192	216.211	odd	18
216.2.v.b.59.22	yes	192	27.22	even	9
648.2.v.b.35.11		192	8.3	odd	2	inner
648.2.v.b.35.28		192	1.1	even	1	trivial
648.2.v.b.611.11		192	27.5	odd	18	inner
648.2.v.b.611.28		192	216.59	even	18	inner
864.2.bh.b.335.1		192	12.11	even	2
864.2.bh.b.335.2		192	24.5	odd	2
864.2.bh.b.815.1		192	216.157	even	18
864.2.bh.b.815.2		192	108.103	odd	18

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.27615 + 0.609466i) q^{2} +(1.25710 + 1.55554i) q^{4} +(0.426624 + 0.155279i) q^{5} +(1.28150 + 0.225962i) q^{7} +(0.656202 + 2.75125i) q^{8} +(0.449799 + 0.458171i) q^{10} +(-0.00602720 - 0.0165596i) q^{11} +(1.43581 + 1.71113i) q^{13} +(1.49766 + 1.06939i) q^{14} +(-0.839384 + 3.91094i) q^{16} +(-1.27216 + 0.734483i) q^{17} +(0.677841 - 1.17406i) q^{19} +(0.294769 + 0.858831i) q^{20} +(0.00240091 - 0.0248058i) q^{22} +(-0.369486 - 2.09546i) q^{23} +(-3.67233 - 3.08145i) q^{25} +(0.789428 + 3.05873i) q^{26} +(1.25948 + 2.27747i) q^{28} +(5.56933 + 4.67322i) q^{29} +(8.87753 - 1.56535i) q^{31} +(-3.45476 + 4.47936i) q^{32} +(-2.07111 + 0.161969i) q^{34} +(0.511630 + 0.295390i) q^{35} +(-4.58718 + 2.64841i) q^{37} +(1.58057 - 1.08515i) q^{38} +(-0.147259 + 1.27565i) q^{40} +(-1.56527 - 1.86542i) q^{41} +(-10.1956 + 3.71089i) q^{43} +(0.0181822 - 0.0301926i) q^{44} +(0.805592 - 2.89930i) q^{46} +(0.791397 - 4.48824i) q^{47} +(-4.98668 - 1.81500i) q^{49} +(-2.80839 - 6.17054i) q^{50} +(-0.856765 + 4.38452i) q^{52} +10.4085 q^{53} -0.00800062i q^{55} +(0.219241 + 3.67400i) q^{56} +(4.25911 + 9.35804i) q^{58} +(3.75319 - 10.3118i) q^{59} +(-8.87057 - 1.56412i) q^{61} +(12.2831 + 3.41294i) q^{62} +(-7.13880 + 3.61076i) q^{64} +(0.346849 + 0.952961i) q^{65} +(3.70041 - 3.10502i) q^{67} +(-2.74175 - 1.05557i) q^{68} +(0.472885 + 0.688782i) q^{70} +(-5.03714 - 8.72458i) q^{71} +(-0.339460 + 0.587962i) q^{73} +(-7.46803 + 0.584031i) q^{74} +(2.67840 - 0.421502i) q^{76} +(-0.00398198 - 0.0225829i) q^{77} +(5.19665 - 6.19313i) q^{79} +(-0.965387 + 1.53816i) q^{80} +(-0.860607 - 3.33452i) q^{82} +(-1.29122 + 1.53881i) q^{83} +(-0.656785 + 0.115809i) q^{85} +(-15.2727 - 1.47822i) q^{86} +(0.0416046 - 0.0274488i) q^{88} +(0.103744 + 0.0598964i) q^{89} +(1.45333 + 2.51724i) q^{91} +(2.79508 - 3.20896i) q^{92} +(3.74536 - 5.24532i) q^{94} +(0.471489 - 0.395626i) q^{95} +(-10.4801 + 3.81446i) q^{97} +(-5.25755 - 5.35542i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more