LMFDB - Embedded newform 289.2.c.d.251.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,2,Mod(38,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.38"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.4
Root			$-1.32893 + 1.32893i$ of defining polynomial
Character	$\chi$	$=$	289.251
Dual form			289.2.c.d.38.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.347296i q^{2} +(0.621819 + 0.621819i) q^{3} +1.87939 q^{4} +(1.65979 + 1.65979i) q^{5} +(0.215956 - 0.215956i) q^{6} +(1.32893 - 1.32893i) q^{7} -1.34730i q^{8} -2.22668i q^{9} +(0.576439 - 0.576439i) q^{10} +(-3.58091 + 3.58091i) q^{11} +(1.16864 + 1.16864i) q^{12} -4.71688 q^{13} +(-0.461531 - 0.461531i) q^{14} +2.06418i q^{15} +3.29086 q^{16} -0.773318 q^{18} -0.347296i q^{19} +(3.11938 + 3.11938i) q^{20} +1.65270 q^{21} +(1.24364 + 1.24364i) q^{22} +(-1.25393 + 1.25393i) q^{23} +(0.837775 - 0.837775i) q^{24} +0.509800i q^{25} +1.63816i q^{26} +(3.25005 - 3.25005i) q^{27} +(2.49756 - 2.49756i) q^{28} +(-1.57450 - 1.57450i) q^{29} +0.716881 q^{30} +(1.37431 + 1.37431i) q^{31} -3.83750i q^{32} -4.45336 q^{33} +4.41147 q^{35} -4.18479i q^{36} +(-4.36302 - 4.36302i) q^{37} -0.120615 q^{38} +(-2.93305 - 2.93305i) q^{39} +(2.23623 - 2.23623i) q^{40} +(-3.65592 + 3.65592i) q^{41} -0.573978i q^{42} -1.47565i q^{43} +(-6.72992 + 6.72992i) q^{44} +(3.69582 - 3.69582i) q^{45} +(0.435484 + 0.435484i) q^{46} +8.53209 q^{47} +(2.04632 + 2.04632i) q^{48} +3.46791i q^{49} +0.177052 q^{50} -8.86484 q^{52} +10.4534i q^{53} +(-1.12873 - 1.12873i) q^{54} -11.8871 q^{55} +(-1.79046 - 1.79046i) q^{56} +(0.215956 - 0.215956i) q^{57} +(-0.546819 + 0.546819i) q^{58} +5.00774i q^{59} +3.87939i q^{60} +(0.130668 - 0.130668i) q^{61} +(0.477292 - 0.477292i) q^{62} +(-2.95910 - 2.95910i) q^{63} +5.24897 q^{64} +(-7.82903 - 7.82903i) q^{65} +1.54664i q^{66} -2.44831 q^{67} -1.55943 q^{69} -1.53209i q^{70} +(-7.01540 - 7.01540i) q^{71} -3.00000 q^{72} +(-7.70865 - 7.70865i) q^{73} +(-1.51526 + 1.51526i) q^{74} +(-0.317004 + 0.317004i) q^{75} -0.652704i q^{76} +9.51754i q^{77} +(-1.01864 + 1.01864i) q^{78} +(3.13514 - 3.13514i) q^{79} +(5.46213 + 5.46213i) q^{80} -2.63816 q^{81} +(1.26969 + 1.26969i) q^{82} -13.5817i q^{83} +3.10607 q^{84} -0.512489 q^{86} -1.95811i q^{87} +(4.82455 + 4.82455i) q^{88} +6.32770 q^{89} +(-1.28355 - 1.28355i) q^{90} +(-6.26839 + 6.26839i) q^{91} +(-2.35661 + 2.35661i) q^{92} +1.70914i q^{93} -2.96316i q^{94} +(0.576439 - 0.576439i) q^{95} +(2.38623 - 2.38623i) q^{96} +(-6.55934 - 6.55934i) q^{97} +1.20439 q^{98} +(7.97356 + 7.97356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q - 24 * q^13 - 24 * q^16 - 36 * q^18 + 24 * q^21 - 24 * q^30 + 12 * q^35 - 24 * q^38 + 84 * q^47 + 84 * q^50 - 12 * q^52 - 24 * q^55 + 12 * q^64 - 36 * q^67 + 84 * q^69 - 36 * q^72 + 36 * q^81 - 12 * q^84 + 24 * q^86 + 60 * q^89 + 12 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	0.347296i		−	0.245576i	−0.992433	−	0.122788i	$-0.960817\pi$
$2$		−	0.347296i		−	0.245576i	0.992433	−	0.122788i	$-0.0391835\pi$
$3$	0.621819	+	0.621819i	0.359008	+	0.359008i	0.863447	−	0.504440i	$-0.168301\pi$
$3$	0.621819	+	0.621819i	0.359008	+	0.359008i	−0.504440	+	0.863447i	$0.668301\pi$
$4$	1.87939			0.939693
$5$	1.65979	+	1.65979i	0.742280	+	0.742280i	0.973016	−	0.230736i	$-0.0741134\pi$
$5$	1.65979	+	1.65979i	0.742280	+	0.742280i	−0.230736	+	0.973016i	$0.574113\pi$
$6$	0.215956	−	0.215956i	0.0881635	−	0.0881635i
$7$	1.32893	−	1.32893i	0.502287	−	0.502287i	−0.409861	−	0.912148i	$-0.634423\pi$
$7$	1.32893	−	1.32893i	0.502287	−	0.502287i	0.912148	+	0.409861i	$0.134423\pi$
$8$		−	1.34730i		−	0.476341i
$9$		−	2.22668i		−	0.742227i
$10$	0.576439	−	0.576439i	0.182286	−	0.182286i
$11$	−3.58091	+	3.58091i	−1.07969	+	1.07969i	−0.0831492	+	0.996537i	$0.526498\pi$
$11$	−3.58091	+	3.58091i	−1.07969	+	1.07969i	−0.996537	+	0.0831492i	$0.973502\pi$
$12$	1.16864	+	1.16864i	0.337357	+	0.337357i
$13$	−4.71688			−1.30823			−0.654114	−	0.756396i	$-0.726958\pi$
$13$	−4.71688			−1.30823			−0.654114	+	0.756396i	$0.726958\pi$
$14$	−0.461531	−	0.461531i	−0.123349	−	0.123349i
$15$			2.06418i			0.532968i
$16$	3.29086			0.822715
$17$		0			0
$17$		0			0
$18$	−0.773318			−0.182273
$19$		−	0.347296i		−	0.0796752i	−0.999206	−	0.0398376i	$-0.987316\pi$
$19$		−	0.347296i		−	0.0796752i	0.999206	−	0.0398376i	$-0.0126841\pi$
$20$	3.11938	+	3.11938i	0.697515	+	0.697515i
$21$	1.65270			0.360650
$22$	1.24364	+	1.24364i	0.265145	+	0.265145i
$23$	−1.25393	+	1.25393i	−0.261462	+	0.261462i	−0.825648	−	0.564186i	$-0.809190\pi$
$23$	−1.25393	+	1.25393i	−0.261462	+	0.261462i	0.564186	+	0.825648i	$0.309190\pi$
$24$	0.837775	−	0.837775i	0.171010	−	0.171010i
$25$			0.509800i			0.101960i
$26$			1.63816i			0.321269i
$27$	3.25005	−	3.25005i	0.625473	−	0.625473i
$28$	2.49756	−	2.49756i	0.471995	−	0.471995i
$29$	−1.57450	−	1.57450i	−0.292378	−	0.292378i	0.545641	−	0.838019i	$-0.316286\pi$
$29$	−1.57450	−	1.57450i	−0.292378	−	0.292378i	−0.838019	+	0.545641i	$0.816286\pi$
$30$	0.716881			0.130884
$31$	1.37431	+	1.37431i	0.246833	+	0.246833i	0.819669	−	0.572837i	$-0.194157\pi$
$31$	1.37431	+	1.37431i	0.246833	+	0.246833i	−0.572837	+	0.819669i	$0.694157\pi$
$32$		−	3.83750i		−	0.678380i
$33$	−4.45336			−0.775231
$34$		0			0
$35$	4.41147			0.745675
$36$		−	4.18479i		−	0.697465i
$37$	−4.36302	−	4.36302i	−0.717276	−	0.717276i	0.250770	−	0.968047i	$-0.419316\pi$
$37$	−4.36302	−	4.36302i	−0.717276	−	0.717276i	−0.968047	+	0.250770i	$0.919316\pi$
$38$	−0.120615			−0.0195663
$39$	−2.93305	−	2.93305i	−0.469664	−	0.469664i
$40$	2.23623	−	2.23623i	0.353579	−	0.353579i
$41$	−3.65592	+	3.65592i	−0.570958	+	0.570958i	−0.932396	−	0.361438i	$-0.882286\pi$
$41$	−3.65592	+	3.65592i	−0.570958	+	0.570958i	0.361438	+	0.932396i	$0.382286\pi$
$42$		−	0.573978i		−	0.0885667i
$43$		−	1.47565i		−	0.225035i	−0.993650	−	0.112517i	$-0.964109\pi$
$43$		−	1.47565i		−	0.225035i	0.993650	−	0.112517i	$-0.0358914\pi$
$44$	−6.72992	+	6.72992i	−1.01457	+	1.01457i
$45$	3.69582	−	3.69582i	0.550941	−	0.550941i
$46$	0.435484	+	0.435484i	0.0642086	+	0.0642086i
$47$	8.53209			1.24453			0.622267	−	0.782805i	$-0.286212\pi$
$47$	8.53209			1.24453			0.622267	+	0.782805i	$0.286212\pi$
$48$	2.04632	+	2.04632i	0.295361	+	0.295361i
$49$			3.46791i			0.495416i
$50$	0.177052			0.0250389
$51$		0			0
$52$	−8.86484			−1.22933
$53$			10.4534i			1.43588i	0.696105	+	0.717940i	$0.254915\pi$
$53$			10.4534i			1.43588i	−0.696105	+	0.717940i	$0.745085\pi$
$54$	−1.12873	−	1.12873i	−0.153601	−	0.153601i
$55$	−11.8871			−1.60286
$56$	−1.79046	−	1.79046i	−0.239260	−	0.239260i
$57$	0.215956	−	0.215956i	0.0286040	−	0.0286040i
$58$	−0.546819	+	0.546819i	−0.0718008	+	0.0718008i
$59$			5.00774i			0.651952i	0.945378	+	0.325976i	$0.105693\pi$
$59$			5.00774i			0.651952i	−0.945378	+	0.325976i	$0.894307\pi$
$60$			3.87939i			0.500826i
$61$	0.130668	−	0.130668i	0.0167303	−	0.0167303i	−0.698692	−	0.715422i	$-0.746234\pi$
$61$	0.130668	−	0.130668i	0.0167303	−	0.0167303i	0.715422	+	0.698692i	$0.246234\pi$
$62$	0.477292	−	0.477292i	0.0606161	−	0.0606161i
$63$	−2.95910	−	2.95910i	−0.372811	−	0.372811i
$64$	5.24897			0.656121
$65$	−7.82903	−	7.82903i	−0.971071	−	0.971071i
$66$			1.54664i			0.190378i
$67$	−2.44831			−0.299109			−0.149554	−	0.988754i	$-0.547784\pi$
$67$	−2.44831			−0.299109			−0.149554	+	0.988754i	$0.547784\pi$
$68$		0			0
$69$	−1.55943			−0.187733
$70$		−	1.53209i		−	0.183120i
$71$	−7.01540	−	7.01540i	−0.832575	−	0.832575i	0.155294	−	0.987868i	$-0.450368\pi$
$71$	−7.01540	−	7.01540i	−0.832575	−	0.832575i	−0.987868	+	0.155294i	$0.950368\pi$
$72$	−3.00000			−0.353553
$73$	−7.70865	−	7.70865i	−0.902229	−	0.902229i	0.0933997	−	0.995629i	$-0.470227\pi$
$73$	−7.70865	−	7.70865i	−0.902229	−	0.902229i	−0.995629	+	0.0933997i	$0.970227\pi$
$74$	−1.51526	+	1.51526i	−0.176146	+	0.176146i
$75$	−0.317004	+	0.317004i	−0.0366044	+	0.0366044i
$76$		−	0.652704i		−	0.0748702i
$77$			9.51754i			1.08462i
$78$	−1.01864	+	1.01864i	−0.115338	+	0.115338i
$79$	3.13514	−	3.13514i	0.352731	−	0.352731i	−0.508394	−	0.861125i	$-0.669760\pi$
$79$	3.13514	−	3.13514i	0.352731	−	0.352731i	0.861125	+	0.508394i	$0.169760\pi$
$80$	5.46213	+	5.46213i	0.610685	+	0.610685i
$81$	−2.63816			−0.293128
$82$	1.26969	+	1.26969i	0.140213	+	0.140213i
$83$		−	13.5817i		−	1.49079i	−0.666625	−	0.745394i	$-0.732262\pi$
$83$		−	13.5817i		−	1.49079i	0.666625	−	0.745394i	$-0.267738\pi$
$84$	3.10607			0.338900
$85$		0			0
$86$	−0.512489			−0.0552631
$87$		−	1.95811i		−	0.209932i
$88$	4.82455	+	4.82455i	0.514299	+	0.514299i
$89$	6.32770			0.670734			0.335367	−	0.942087i	$-0.391140\pi$
$89$	6.32770			0.670734			0.335367	+	0.942087i	$0.391140\pi$
$90$	−1.28355	−	1.28355i	−0.135298	−	0.135298i
$91$	−6.26839	+	6.26839i	−0.657105	+	0.657105i
$92$	−2.35661	+	2.35661i	−0.245693	+	0.245693i
$93$			1.70914i			0.177230i
$94$		−	2.96316i		−	0.305627i
$95$	0.576439	−	0.576439i	0.0591414	−	0.0591414i
$96$	2.38623	−	2.38623i	0.243543	−	0.243543i
$97$	−6.55934	−	6.55934i	−0.666000	−	0.666000i	0.290787	−	0.956788i	$-0.406083\pi$
$97$	−6.55934	−	6.55934i	−0.666000	−	0.666000i	−0.956788	+	0.290787i	$0.906083\pi$
$98$	1.20439			0.121662
$99$	7.97356	+	7.97356i	0.801373	+	0.801373i
$100$			0.958111i			0.0958111i
$101$	−7.04963			−0.701464			−0.350732	−	0.936476i	$-0.614067\pi$
$101$	−7.04963			−0.701464			−0.350732	+	0.936476i	$0.614067\pi$
$102$		0			0
$103$	5.29860			0.522087			0.261043	−	0.965327i	$-0.415933\pi$
$103$	5.29860			0.522087			0.261043	+	0.965327i	$0.415933\pi$
$104$			6.35504i			0.623163i
$105$	2.74314	+	2.74314i	0.267703	+	0.267703i
$106$	3.63041			0.352617
$107$	11.0282	+	11.0282i	1.06614	+	1.06614i	0.997652	+	0.0684868i	$0.0218171\pi$
$107$	11.0282	+	11.0282i	1.06614	+	1.06614i	0.0684868	+	0.997652i	$0.478183\pi$
$108$	6.10810	−	6.10810i	0.587752	−	0.587752i
$109$	−1.32345	+	1.32345i	−0.126764	+	0.126764i	−0.767642	−	0.640879i	$-0.778570\pi$
$109$	−1.32345	+	1.32345i	−0.126764	+	0.126764i	0.640879	+	0.767642i	$0.278570\pi$
$110$			4.12836i			0.393623i
$111$		−	5.42602i		−	0.515015i
$112$	4.37331	−	4.37331i	0.413239	−	0.413239i
$113$	−8.56576	+	8.56576i	−0.805798	+	0.805798i	−0.983995	−	0.178196i	$-0.942974\pi$
$113$	−8.56576	+	8.56576i	−0.805798	+	0.805798i	0.178196	+	0.983995i	$0.442974\pi$
$114$	−0.0750006	−	0.0750006i	−0.00702445	−	0.00702445i
$115$	−4.16250			−0.388155
$116$	−2.95910	−	2.95910i	−0.274745	−	0.274745i
$117$			10.5030i			0.971002i
$118$	1.73917			0.160104
$119$		0			0
$120$	2.78106			0.253875
$121$		−	14.6459i		−	1.33145i
$122$	−0.0453805	−	0.0453805i	−0.00410856	−	0.00410856i
$123$	−4.54664			−0.409956
$124$	2.58285	+	2.58285i	0.231947	+	0.231947i
$125$	7.45279	−	7.45279i	0.666597	−	0.666597i
$126$	−1.02768	+	1.02768i	−0.0915533	+	0.0915533i
$127$		−	11.5398i		−	1.02399i	−0.858987	−	0.511997i	$-0.828906\pi$
$127$		−	11.5398i		−	1.02399i	0.858987	−	0.511997i	$-0.171094\pi$
$128$		−	9.49794i		−	0.839507i
$129$	0.917589	−	0.917589i	0.0807892	−	0.0807892i
$130$	−2.71899	+	2.71899i	−0.238471	+	0.238471i
$131$	13.6999	+	13.6999i	1.19697	+	1.19697i	0.975070	+	0.221900i	$0.0712257\pi$
$131$	13.6999	+	13.6999i	1.19697	+	1.19697i	0.221900	+	0.975070i	$0.428774\pi$
$132$	−8.36959			−0.728479
$133$	−0.461531	−	0.461531i	−0.0400198	−	0.0400198i
$134$			0.850289i			0.0734538i
$135$	10.7888			0.928552
$136$		0			0
$137$	−0.448311			−0.0383018			−0.0191509	−	0.999817i	$-0.506096\pi$
$137$	−0.448311			−0.0383018			−0.0191509	+	0.999817i	$0.506096\pi$
$138$			0.541584i			0.0461027i
$139$	8.25904	+	8.25904i	0.700523	+	0.700523i	0.964523	−	0.264000i	$-0.0850419\pi$
$139$	8.25904	+	8.25904i	0.700523	+	0.700523i	−0.264000	+	0.964523i	$0.585042\pi$
$140$	8.29086			0.700706
$141$	5.30542	+	5.30542i	0.446797	+	0.446797i
$142$	−2.43642	+	2.43642i	−0.204460	+	0.204460i
$143$	16.8907	−	16.8907i	1.41248	−	1.41248i
$144$		−	7.32770i		−	0.610641i
$145$		−	5.22668i		−	0.434052i
$146$	−2.67719	+	2.67719i	−0.221565	+	0.221565i
$147$	−2.15641	+	2.15641i	−0.177858	+	0.177858i
$148$	−8.19980	−	8.19980i	−0.674019	−	0.674019i
$149$	−8.46791			−0.693718			−0.346859	−	0.937917i	$-0.612752\pi$
$149$	−8.46791			−0.693718			−0.346859	+	0.937917i	$0.612752\pi$
$150$	0.110094	+	0.110094i	0.00898915	+	0.00898915i
$151$			13.7665i			1.12030i	0.828390	+	0.560151i	$0.189257\pi$
$151$			13.7665i			1.12030i	−0.828390	+	0.560151i	$0.810743\pi$
$152$	−0.467911			−0.0379526
$153$		0			0
$154$	3.30541			0.266357
$155$			4.56212i			0.366438i
$156$	−5.51233	−	5.51233i	−0.441339	−	0.441339i
$157$	17.9786			1.43485			0.717426	−	0.696635i	$-0.245320\pi$
$157$	17.9786			1.43485			0.717426	+	0.696635i	$0.245320\pi$
$158$	−1.08882	−	1.08882i	−0.0866222	−	0.0866222i
$159$	−6.50010	+	6.50010i	−0.515492	+	0.515492i
$160$	6.36943	−	6.36943i	0.503548	−	0.503548i
$161$			3.33275i			0.262657i
$162$			0.916222i			0.0719852i
$163$	5.11551	−	5.11551i	0.400678	−	0.400678i	−0.477794	−	0.878472i	$-0.658564\pi$
$163$	5.11551	−	5.11551i	0.400678	−	0.400678i	0.878472	+	0.477794i	$0.158564\pi$
$164$	−6.87087	+	6.87087i	−0.536525	+	0.536525i
$165$	−7.39164	−	7.39164i	−0.575439	−	0.575439i
$166$	−4.71688			−0.366101
$167$	−3.61053	−	3.61053i	−0.279392	−	0.279392i	0.553475	−	0.832866i	$-0.313302\pi$
$167$	−3.61053	−	3.61053i	−0.279392	−	0.279392i	−0.832866	+	0.553475i	$0.813302\pi$
$168$		−	2.22668i		−	0.171792i
$169$	9.24897			0.711459
$170$		0			0
$171$	−0.773318			−0.0591371
$172$		−	2.77332i		−	0.211464i
$173$	9.06909	+	9.06909i	0.689510	+	0.689510i	0.962124	−	0.272613i	$-0.0878879\pi$
$173$	9.06909	+	9.06909i	0.689510	+	0.689510i	−0.272613	+	0.962124i	$0.587888\pi$
$174$	−0.680045			−0.0515541
$175$	0.677487	+	0.677487i	0.0512132	+	0.0512132i
$176$	−11.7843	+	11.7843i	−0.888274	+	0.888274i
$177$	−3.11391	+	3.11391i	−0.234056	+	0.234056i
$178$		−	2.19759i		−	0.164716i
$179$			4.27126i			0.319249i	0.987178	+	0.159624i	$0.0510283\pi$
$179$			4.27126i			0.319249i	−0.987178	+	0.159624i	$0.948972\pi$
$180$	6.94587	−	6.94587i	0.517715	−	0.517715i
$181$	−0.327291	+	0.327291i	−0.0243273	+	0.0243273i	−0.719166	−	0.694838i	$-0.755476\pi$
$181$	−0.327291	+	0.327291i	−0.0243273	+	0.0243273i	0.694838	+	0.719166i	$0.255476\pi$
$182$	2.17699	+	2.17699i	0.161369	+	0.161369i
$183$	0.162504			0.0120126
$184$	1.68941	+	1.68941i	0.124545	+	0.124545i
$185$		−	14.4834i		−	1.06484i
$186$	0.593578			0.0435233
$187$		0			0
$188$	16.0351			1.16948
$189$		−	8.63816i		−	0.628333i
$190$	−0.200195	−	0.200195i	−0.0145237	−	0.0145237i
$191$	1.43107			0.103549			0.0517745	−	0.998659i	$-0.483512\pi$
$191$	1.43107			0.103549			0.0517745	+	0.998659i	$0.483512\pi$
$192$	3.26391	+	3.26391i	0.235552	+	0.235552i
$193$	17.4829	−	17.4829i	1.25845	−	1.25845i	0.306617	−	0.951833i	$-0.400803\pi$
$193$	17.4829	−	17.4829i	1.25845	−	1.25845i	0.951833	−	0.306617i	$-0.0991972\pi$
$194$	−2.27804	+	2.27804i	−0.163553	+	0.163553i
$195$		−	9.73648i		−	0.697244i
$196$			6.51754i			0.465539i
$197$	−8.31661	+	8.31661i	−0.592534	+	0.592534i	−0.938315	−	0.345781i	$-0.887614\pi$
$197$	−8.31661	+	8.31661i	−0.592534	+	0.592534i	0.345781	+	0.938315i	$0.387614\pi$
$198$	2.76919	−	2.76919i	0.196798	−	0.196798i
$199$	14.5100	+	14.5100i	1.02859	+	1.02859i	0.999579	+	0.0290069i	$0.00923449\pi$
$199$	14.5100	+	14.5100i	1.02859	+	1.02859i	0.0290069	+	0.999579i	$0.490766\pi$
$200$	0.686852			0.0485678
$201$	−1.52241	−	1.52241i	−0.107382	−	0.107382i
$202$			2.44831i			0.172263i
$203$	−4.18479			−0.293715
$204$		0			0
$205$	−12.1361			−0.847622
$206$		−	1.84018i		−	0.128212i
$207$	2.79209	+	2.79209i	0.194064	+	0.194064i
$208$	−15.5226			−1.07630
$209$	1.24364	+	1.24364i	0.0860243	+	0.0860243i
$210$	0.952682	−	0.952682i	0.0657413	−	0.0657413i
$211$	−15.3568	+	15.3568i	−1.05721	+	1.05721i	−0.0589455	+	0.998261i	$0.518774\pi$
$211$	−15.3568	+	15.3568i	−1.05721	+	1.05721i	−0.998261	+	0.0589455i	$0.981226\pi$
$212$			19.6459i			1.34929i
$213$		−	8.72462i		−	0.597801i
$214$	3.83006	−	3.83006i	0.261818	−	0.261818i
$215$	2.44927	−	2.44927i	0.167039	−	0.167039i
$216$	−4.37878	−	4.37878i	−0.297938	−	0.297938i
$217$	3.65270			0.247962
$218$	0.459630	+	0.459630i	0.0311301	+	0.0311301i
$219$		−	9.58677i		−	0.647814i
$220$	−22.3405			−1.50620
$221$		0			0
$222$	−1.88444			−0.126475
$223$			19.9513i			1.33604i	0.744144	+	0.668019i	$0.232858\pi$
$223$			19.9513i			1.33604i	−0.744144	+	0.668019i	$0.767142\pi$
$224$	−5.09975	−	5.09975i	−0.340741	−	0.340741i
$225$	1.13516			0.0756775
$226$	2.97486	+	2.97486i	0.197884	+	0.197884i
$227$	−2.98514	+	2.98514i	−0.198131	+	0.198131i	−0.799198	−	0.601067i	$-0.794742\pi$
$227$	−2.98514	+	2.98514i	−0.198131	+	0.198131i	0.601067	+	0.799198i	$0.294742\pi$
$228$	0.405864	−	0.405864i	0.0268790	−	0.0268790i
$229$			14.5057i			0.958562i	0.877661	+	0.479281i	$0.159103\pi$
$229$			14.5057i			0.958562i	−0.877661	+	0.479281i	$0.840897\pi$
$230$			1.44562i			0.0953215i
$231$	−5.91819	+	5.91819i	−0.389388	+	0.389388i
$232$	−2.12132	+	2.12132i	−0.139272	+	0.139272i
$233$	−3.62563	−	3.62563i	−0.237523	−	0.237523i	0.578301	−	0.815824i	$-0.303716\pi$
$233$	−3.62563	−	3.62563i	−0.237523	−	0.237523i	−0.815824	+	0.578301i	$0.803716\pi$
$234$	3.64765			0.238454
$235$	14.1615	+	14.1615i	0.923792	+	0.923792i
$236$			9.41147i			0.612635i
$237$	3.89899			0.253266
$238$		0			0
$239$	−15.8503			−1.02527			−0.512635	−	0.858607i	$-0.671331\pi$
$239$	−15.8503			−1.02527			−0.512635	+	0.858607i	$0.671331\pi$
$240$			6.79292i			0.438481i
$241$	−12.8103	−	12.8103i	−0.825184	−	0.825184i	0.161662	−	0.986846i	$-0.448314\pi$
$241$	−12.8103	−	12.8103i	−0.825184	−	0.825184i	−0.986846	+	0.161662i	$0.948314\pi$
$242$	−5.08647			−0.326970
$243$	−11.3906	−	11.3906i	−0.730708	−	0.730708i
$244$	0.245576	−	0.245576i	0.0157214	−	0.0157214i
$245$	−5.75600	+	5.75600i	−0.367737	+	0.367737i
$246$			1.57903i			0.100675i
$247$			1.63816i			0.104233i
$248$	1.85160	−	1.85160i	0.117577	−	0.117577i
$249$	8.44537	−	8.44537i	0.535204	−	0.535204i
$250$	−2.58833	−	2.58833i	−0.163700	−	0.163700i
$251$	29.6810			1.87345			0.936723	−	0.350070i	$-0.113842\pi$
$251$	29.6810			1.87345			0.936723	+	0.350070i	$0.113842\pi$
$252$	−5.56128	−	5.56128i	−0.350328	−	0.350328i
$253$		−	8.98040i		−	0.564593i
$254$	−4.00774			−0.251468
$255$		0			0
$256$	7.19934			0.449959
$257$		−	7.39693i		−	0.461408i	−0.973024	−	0.230704i	$-0.925897\pi$
$257$		−	7.39693i		−	0.461408i	0.973024	−	0.230704i	$-0.0741028\pi$
$258$	−0.318675	−	0.318675i	−0.0198399	−	0.0198399i
$259$	−11.5963			−0.720557
$260$	−14.7138	−	14.7138i	−0.912509	−	0.912509i
$261$	−3.50591	+	3.50591i	−0.217011	+	0.217011i
$262$	4.75794	−	4.75794i	0.293946	−	0.293946i
$263$		−	23.1908i		−	1.43000i	−0.699122	−	0.715002i	$-0.746426\pi$
$263$		−	23.1908i		−	1.43000i	0.699122	−	0.715002i	$-0.253574\pi$
$264$			6.00000i			0.369274i
$265$	−17.3504	+	17.3504i	−1.06583	+	1.06583i
$266$	−0.160288	+	0.160288i	−0.00982789	+	0.00982789i
$267$	3.93468	+	3.93468i	0.240799	+	0.240799i
$268$	−4.60132			−0.281070
$269$	−11.2478	−	11.2478i	−0.685788	−	0.685788i	0.275510	−	0.961298i	$-0.411153\pi$
$269$	−11.2478	−	11.2478i	−0.685788	−	0.685788i	−0.961298	+	0.275510i	$0.911153\pi$
$270$		−	3.74691i		−	0.228030i
$271$	17.0000			1.03268			0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000			1.03268			0.516338	+	0.856385i	$0.327295\pi$
$272$		0			0
$273$	−7.79561			−0.471812
$274$			0.155697i			0.00940598i
$275$	−1.82555	−	1.82555i	−0.110085	−	0.110085i
$276$	−2.93077			−0.176412
$277$	−11.8834	−	11.8834i	−0.714006	−	0.714006i	0.253365	−	0.967371i	$-0.418463\pi$
$277$	−11.8834	−	11.8834i	−0.714006	−	0.714006i	−0.967371	+	0.253365i	$0.918463\pi$
$278$	2.86833	−	2.86833i	0.172031	−	0.172031i
$279$	3.06014	−	3.06014i	0.183206	−	0.183206i
$280$		−	5.94356i		−	0.355196i
$281$			28.3209i			1.68948i	0.535175	+	0.844741i	$0.320246\pi$
$281$			28.3209i			1.68948i	−0.535175	+	0.844741i	$0.679754\pi$
$282$	1.84255	−	1.84255i	0.109722	−	0.109722i
$283$	22.7932	−	22.7932i	1.35491	−	1.35491i	0.474844	−	0.880070i	$-0.342505\pi$
$283$	22.7932	−	22.7932i	1.35491	−	1.35491i	0.880070	−	0.474844i	$-0.157495\pi$
$284$	−13.1846	−	13.1846i	−0.782364	−	0.782364i
$285$	0.716881			0.0424644
$286$	−5.86610	−	5.86610i	−0.346869	−	0.346869i
$287$			9.71688i			0.573569i
$288$	−8.54488			−0.503512
$289$		0			0
$290$	−1.81521			−0.106593
$291$		−	8.15745i		−	0.478198i
$292$	−14.4875	−	14.4875i	−0.847818	−	0.847818i
$293$	−13.9709			−0.816189			−0.408094	−	0.912940i	$-0.633807\pi$
$293$	−13.9709			−0.816189			−0.408094	+	0.912940i	$0.633807\pi$
$294$	0.748915	+	0.748915i	0.0436776	+	0.0436776i
$295$	−8.31179	+	8.31179i	−0.483931	+	0.483931i
$296$	−5.87828	+	5.87828i	−0.341668	+	0.341668i
$297$			23.2763i			1.35063i
$298$			2.94087i			0.170360i
$299$	5.91462	−	5.91462i	0.342051	−	0.342051i
$300$	−0.595772	+	0.595772i	−0.0343969	+	0.0343969i
$301$	−1.96103	−	1.96103i	−0.113032	−	0.113032i
$302$	4.78106			0.275119
$303$	−4.38360	−	4.38360i	−0.251831	−	0.251831i
$304$		−	1.14290i		−	0.0655500i
$305$	0.433763			0.0248372
$306$		0			0
$307$	9.04963			0.516490			0.258245	−	0.966080i	$-0.416856\pi$
$307$	9.04963			0.516490			0.258245	+	0.966080i	$0.416856\pi$
$308$			17.8871i			1.01921i
$309$	3.29477	+	3.29477i	0.187433	+	0.187433i
$310$	1.58441			0.0899883
$311$	1.65979	+	1.65979i	0.0941180	+	0.0941180i	0.752598	−	0.658480i	$-0.228800\pi$
$311$	1.65979	+	1.65979i	0.0941180	+	0.0941180i	−0.658480	+	0.752598i	$0.728800\pi$
$312$	−3.95168	+	3.95168i	−0.223720	+	0.223720i
$313$	10.6974	−	10.6974i	0.604651	−	0.604651i	−0.336892	−	0.941543i	$-0.609376\pi$
$313$	10.6974	−	10.6974i	0.604651	−	0.604651i	0.941543	+	0.336892i	$0.109376\pi$
$314$		−	6.24392i		−	0.352365i
$315$		−	9.82295i		−	0.553460i
$316$	5.89214	−	5.89214i	0.331459	−	0.331459i
$317$	7.30993	−	7.30993i	0.410567	−	0.410567i	−0.471369	−	0.881936i	$-0.656240\pi$
$317$	7.30993	−	7.30993i	0.410567	−	0.410567i	0.881936	+	0.471369i	$0.156240\pi$
$318$	2.25746	+	2.25746i	0.126592	+	0.126592i
$319$	11.2763			0.631352
$320$	8.71218	+	8.71218i	0.487026	+	0.487026i
$321$			13.7151i			0.765504i
$322$	1.15745			0.0645022
$323$		0			0
$324$	−4.95811			−0.275451
$325$		−	2.40467i		−	0.133387i
$326$	−1.77660	−	1.77660i	−0.0983966	−	0.0983966i
$327$	−1.64590			−0.0910183
$328$	4.92560	+	4.92560i	0.271971	+	0.271971i
$329$	11.3385	−	11.3385i	0.625113	−	0.625113i
$330$	−2.56709	+	2.56709i	−0.141314	+	0.141314i
$331$			18.2567i			1.00348i	0.865019	+	0.501740i	$0.167307\pi$
$331$			18.2567i			1.00348i	−0.865019	+	0.501740i	$0.832693\pi$
$332$		−	25.5253i		−	1.40088i
$333$	−9.71506	+	9.71506i	−0.532382	+	0.532382i
$334$	−1.25393	+	1.25393i	−0.0686117	+	0.0686117i
$335$	−4.06368	−	4.06368i	−0.222023	−	0.222023i
$336$	5.43882			0.296712
$337$	11.6639	+	11.6639i	0.635373	+	0.635373i	0.949411	−	0.314037i	$-0.101682\pi$
$337$	11.6639	+	11.6639i	0.635373	+	0.635373i	−0.314037	+	0.949411i	$0.601682\pi$
$338$		−	3.21213i		−	0.174717i
$339$	−10.6527			−0.578575
$340$		0			0
$341$	−9.84255			−0.533004
$342$			0.268571i			0.0145226i
$343$	13.9111	+	13.9111i	0.751128	+	0.751128i
$344$	−1.98814			−0.107193
$345$	−2.58833	−	2.58833i	−0.139351	−	0.139351i
$346$	3.14966	−	3.14966i	0.169327	−	0.169327i
$347$	−14.5468	+	14.5468i	−0.780911	+	0.780911i	−0.979985	−	0.199074i	$-0.936207\pi$
$347$	−14.5468	+	14.5468i	−0.780911	+	0.780911i	0.199074	+	0.979985i	$0.436207\pi$
$348$		−	3.68004i		−	0.197271i
$349$			6.42427i			0.343883i	0.985107	+	0.171942i	$0.0550040\pi$
$349$			6.42427i			0.343883i	−0.985107	+	0.171942i	$0.944996\pi$
$350$	0.235289	−	0.235289i	0.0125767	−	0.0125767i
$351$	−15.3301	+	15.3301i	−0.818261	+	0.818261i
$352$	13.7417	+	13.7417i	0.732437	+	0.732437i
$353$	−27.1685			−1.44603			−0.723016	−	0.690831i	$-0.757245\pi$
$353$	−27.1685			−1.44603			−0.723016	+	0.690831i	$0.757245\pi$
$354$	1.08145	+	1.08145i	0.0574784	+	0.0574784i
$355$		−	23.2882i		−	1.23601i
$356$	11.8922			0.630284
$357$		0			0
$358$	1.48339			0.0783997
$359$		−	16.8949i		−	0.891677i	−0.895113	−	0.445838i	$-0.852906\pi$
$359$		−	16.8949i		−	0.891677i	0.895113	−	0.445838i	$-0.147094\pi$
$360$	−4.97937	−	4.97937i	−0.262436	−	0.262436i
$361$	18.8794			0.993652
$362$	0.113667	+	0.113667i	0.00597419	+	0.00597419i
$363$	9.10710	−	9.10710i	0.477999	−	0.477999i
$364$	−11.7807	+	11.7807i	−0.617477	+	0.617477i
$365$		−	25.5895i		−	1.33941i
$366$		−	0.0564370i		−	0.00295001i
$367$	1.05183	−	1.05183i	0.0549051	−	0.0549051i	−0.679121	−	0.734026i	$-0.737639\pi$
$367$	1.05183	−	1.05183i	0.0549051	−	0.0549051i	0.734026	+	0.679121i	$0.237639\pi$
$368$	−4.12649	+	4.12649i	−0.215108	+	0.215108i
$369$	8.14056	+	8.14056i	0.423781	+	0.423781i
$370$	−5.03003			−0.261499
$371$	13.8917	+	13.8917i	0.721224	+	0.721224i
$372$			3.21213i			0.166541i
$373$	−24.0496			−1.24524			−0.622621	−	0.782523i	$-0.713932\pi$
$373$	−24.0496			−1.24524			−0.622621	+	0.782523i	$0.713932\pi$
$374$		0			0
$375$	9.26857			0.478627
$376$		−	11.4953i		−	0.592822i
$377$	7.42674	+	7.42674i	0.382496	+	0.382496i
$378$	−3.00000			−0.154303
$379$	14.2818	+	14.2818i	0.733609	+	0.733609i	0.971333	−	0.237724i	$-0.0764012\pi$
$379$	14.2818	+	14.2818i	0.733609	+	0.733609i	−0.237724	+	0.971333i	$0.576401\pi$
$380$	1.08335	−	1.08335i	0.0555747	−	0.0555747i
$381$	7.17569	−	7.17569i	0.367622	−	0.367622i
$382$		−	0.497007i		−	0.0254291i
$383$		−	8.52528i		−	0.435622i	−0.975991	−	0.217811i	$-0.930108\pi$
$383$		−	8.52528i		−	0.435622i	0.975991	−	0.217811i	$-0.0698916\pi$
$384$	5.90600	−	5.90600i	0.301389	−	0.301389i
$385$	−15.7971	+	15.7971i	−0.805095	+	0.805095i
$386$	−6.07176	−	6.07176i	−0.309045	−	0.309045i
$387$	−3.28581			−0.167027
$388$	−12.3275	−	12.3275i	−0.625836	−	0.625836i
$389$			12.9162i			0.654878i	0.944872	+	0.327439i	$0.106186\pi$
$389$			12.9162i			0.654878i	−0.944872	+	0.327439i	$0.893814\pi$
$390$	−3.38144			−0.171226
$391$		0			0
$392$	4.67230			0.235987
$393$			17.0378i			0.859442i
$394$	2.88833	+	2.88833i	0.145512	+	0.145512i
$395$	10.4074			0.523651
$396$	14.9854	+	14.9854i	0.753044	+	0.753044i
$397$	−17.1296	+	17.1296i	−0.859710	+	0.859710i	−0.991304	−	0.131593i	$-0.957991\pi$
$397$	−17.1296	+	17.1296i	−0.859710	+	0.859710i	0.131593	+	0.991304i	$0.457991\pi$
$398$	5.03927	−	5.03927i	0.252596	−	0.252596i
$399$		−	0.573978i		−	0.0287348i
$400$			1.67768i			0.0838840i
$401$	18.0575	−	18.0575i	0.901748	−	0.901748i	−0.0938395	−	0.995587i	$-0.529914\pi$
$401$	18.0575	−	18.0575i	0.901748	−	0.901748i	0.995587	+	0.0938395i	$0.0299141\pi$
$402$	−0.528726	+	0.528726i	−0.0263705	+	0.0263705i
$403$	−6.48244	−	6.48244i	−0.322913	−	0.322913i
$404$	−13.2490			−0.659161
$405$	−4.37878	−	4.37878i	−0.217583	−	0.217583i
$406$			1.45336i			0.0721292i
$407$	31.2472			1.54887
$408$		0			0
$409$	10.3523			0.511891			0.255945	−	0.966691i	$-0.417613\pi$
$409$	10.3523			0.511891			0.255945	+	0.966691i	$0.417613\pi$
$410$			4.21482i			0.208155i
$411$	−0.278768	−	0.278768i	−0.0137506	−	0.0137506i
$412$	9.95811			0.490601
$413$	6.65492	+	6.65492i	0.327467	+	0.327467i
$414$	0.969684	−	0.969684i	0.0476574	−	0.0476574i
$415$	22.5428	−	22.5428i	1.10658	−	1.10658i
$416$			18.1010i			0.887475i
$417$			10.2713i			0.502986i
$418$	0.431911	−	0.431911i	0.0211255	−	0.0211255i
$419$	−0.928536	+	0.928536i	−0.0453619	+	0.0453619i	−0.729424	−	0.684062i	$-0.760212\pi$
$419$	−0.928536	+	0.928536i	−0.0453619	+	0.0453619i	0.684062	+	0.729424i	$0.260212\pi$
$420$	5.15542	+	5.15542i	0.251559	+	0.251559i
$421$	−8.01548			−0.390651			−0.195325	−	0.980739i	$-0.562576\pi$
$421$	−8.01548			−0.390651			−0.195325	+	0.980739i	$0.562576\pi$
$422$	5.33337	+	5.33337i	0.259624	+	0.259624i
$423$		−	18.9982i		−	0.923726i
$424$	14.0838			0.683969
$425$		0			0
$426$	−3.03003			−0.146805
$427$		−	0.347296i		−	0.0168068i
$428$	20.7263	+	20.7263i	1.00184	+	1.00184i
$429$	21.0060			1.01418
$430$	−0.850623	−	0.850623i	−0.0410207	−	0.0410207i
$431$	−10.4136	+	10.4136i	−0.501603	+	0.501603i	−0.911936	−	0.410333i	$-0.865413\pi$
$431$	−10.4136	+	10.4136i	−0.501603	+	0.501603i	0.410333	+	0.911936i	$0.365413\pi$
$432$	10.6955	−	10.6955i	0.514586	−	0.514586i
$433$		−	8.24123i		−	0.396048i	−0.980197	−	0.198024i	$-0.936548\pi$
$433$		−	8.24123i		−	0.396048i	0.980197	−	0.198024i	$-0.0634524\pi$
$434$		−	1.26857i		−	0.0608933i
$435$	3.25005	−	3.25005i	0.155828	−	0.155828i
$436$	−2.48728	+	2.48728i	−0.119119	+	0.119119i
$437$	0.435484	+	0.435484i	0.0208320	+	0.0208320i
$438$	−3.32945			−0.159087
$439$	−28.2534	−	28.2534i	−1.34846	−	1.34846i	−0.887334	−	0.461128i	$-0.847445\pi$
$439$	−28.2534	−	28.2534i	−1.34846	−	1.34846i	−0.461128	−	0.887334i	$-0.652555\pi$
$440$			16.0155i			0.763508i
$441$	7.72193			0.367711
$442$		0			0
$443$	13.9463			0.662606			0.331303	−	0.943524i	$-0.392512\pi$
$443$	13.9463			0.662606			0.331303	+	0.943524i	$0.392512\pi$
$444$		−	10.1976i		−	0.483956i
$445$	10.5026	+	10.5026i	0.497873	+	0.497873i
$446$	6.92902			0.328098
$447$	−5.26551	−	5.26551i	−0.249050	−	0.249050i
$448$	6.97549	−	6.97549i	0.329561	−	0.329561i
$449$	7.23493	−	7.23493i	0.341437	−	0.341437i	−0.515470	−	0.856908i	$-0.672383\pi$
$449$	7.23493	−	7.23493i	0.341437	−	0.341437i	0.856908	+	0.515470i	$0.172383\pi$
$450$		−	0.394238i		−	0.0185846i
$451$		−	26.1830i		−	1.23291i
$452$	−16.0984	+	16.0984i	−0.757203	+	0.757203i
$453$	−8.56028	+	8.56028i	−0.402197	+	0.402197i
$454$	1.03673	+	1.03673i	0.0486561	+	0.0486561i
$455$	−20.8084			−0.975513
$456$	−0.290956	−	0.290956i	−0.0136253	−	0.0136253i
$457$			11.7706i			0.550607i	0.961357	+	0.275303i	$0.0887783\pi$
$457$			11.7706i			0.550607i	−0.961357	+	0.275303i	$0.911222\pi$
$458$	5.03777			0.235400
$459$		0			0
$460$	−7.82295			−0.364747
$461$		−	19.5003i		−	0.908220i	−0.890946	−	0.454110i	$-0.849957\pi$
$461$		−	19.5003i		−	0.908220i	0.890946	−	0.454110i	$-0.150043\pi$
$462$	2.05537	+	2.05537i	0.0956243	+	0.0956243i
$463$	1.43107			0.0665077			0.0332538	−	0.999447i	$-0.489413\pi$
$463$	1.43107			0.0665077			0.0332538	+	0.999447i	$0.489413\pi$
$464$	−5.18146	−	5.18146i	−0.240543	−	0.240543i
$465$	−2.83681	+	2.83681i	−0.131554	+	0.131554i
$466$	−1.25917	+	1.25917i	−0.0583299	+	0.0583299i
$467$		−	10.6895i		−	0.494653i	−0.968932	−	0.247326i	$-0.920448\pi$
$467$		−	10.6895i		−	0.494653i	0.968932	−	0.247326i	$-0.0795520\pi$
$468$			19.7392i			0.912443i
$469$	−3.25362	+	3.25362i	−0.150238	+	0.150238i
$470$	4.91823	−	4.91823i	0.226861	−	0.226861i
$471$	11.1795	+	11.1795i	0.515123	+	0.515123i
$472$	6.74691			0.310552
$473$	5.28418	+	5.28418i	0.242967	+	0.242967i
$474$		−	1.35410i		−	0.0621960i
$475$	0.177052			0.00812369
$476$		0			0
$477$	23.2763			1.06575
$478$			5.50475i			0.251781i
$479$	−27.4835	−	27.4835i	−1.25575	−	1.25575i	−0.953101	−	0.302651i	$-0.902128\pi$
$479$	−27.4835	−	27.4835i	−1.25575	−	1.25575i	−0.302651	−	0.953101i	$-0.597872\pi$
$480$	7.92127			0.361555
$481$	20.5799	+	20.5799i	0.938361	+	0.938361i
$482$	−4.44897	+	4.44897i	−0.202645	+	0.202645i
$483$	−2.07237	+	2.07237i	−0.0942960	+	0.0942960i
$484$		−	27.5253i		−	1.25115i
$485$		−	21.7743i		−	0.988718i
$486$	−3.95592	+	3.95592i	−0.179444	+	0.179444i
$487$	−26.1727	+	26.1727i	−1.18600	+	1.18600i	−0.207832	+	0.978165i	$0.566641\pi$
$487$	−26.1727	+	26.1727i	−1.18600	+	1.18600i	−0.978165	+	0.207832i	$0.933359\pi$
$488$	−0.176049	−	0.176049i	−0.00796935	−	0.00796935i
$489$	6.36184			0.287693
$490$	1.99904	+	1.99904i	0.0903073	+	0.0903073i
$491$			25.4175i			1.14707i	0.819180	+	0.573537i	$0.194429\pi$
$491$			25.4175i			1.14707i	−0.819180	+	0.573537i	$0.805571\pi$
$492$	−8.54488			−0.385233
$493$		0			0
$494$	0.568926			0.0255972
$495$			26.4688i			1.18969i
$496$	4.52265	+	4.52265i	0.203073	+	0.203073i
$497$	−18.6459			−0.836383
$498$	−2.93305	−	2.93305i	−0.131433	−	0.131433i
$499$	15.4318	−	15.4318i	0.690823	−	0.690823i	−0.271590	−	0.962413i	$-0.587549\pi$
$499$	15.4318	−	15.4318i	0.690823	−	0.690823i	0.962413	+	0.271590i	$0.0875495\pi$
$500$	14.0067	−	14.0067i	0.626397	−	0.626397i
$501$		−	4.49020i		−	0.200607i
$502$		−	10.3081i		−	0.460073i
$503$	23.6436	−	23.6436i	1.05421	−	1.05421i	0.0557712	−	0.998444i	$-0.482238\pi$
$503$	23.6436	−	23.6436i	1.05421	−	1.05421i	0.998444	−	0.0557712i	$-0.0177617\pi$
$504$	−3.98678	+	3.98678i	−0.177585	+	0.177585i
$505$	−11.7009	−	11.7009i	−0.520683	−	0.520683i
$506$	−3.11886			−0.138650
$507$	5.75119	+	5.75119i	0.255419	+	0.255419i
$508$		−	21.6878i		−	0.962240i
$509$	−19.1530			−0.848942			−0.424471	−	0.905441i	$-0.639540\pi$
$509$	−19.1530			−0.848942			−0.424471	+	0.905441i	$0.639540\pi$
$510$		0			0
$511$	−20.4884			−0.906355
$512$		−	21.4962i		−	0.950006i
$513$	−1.12873	−	1.12873i	−0.0498347	−	0.0498347i
$514$	−2.56893			−0.113310
$515$	8.79456	+	8.79456i	0.387535	+	0.387535i
$516$	1.72450	−	1.72450i	0.0759170	−	0.0759170i
$517$	−30.5527	+	30.5527i	−1.34371	+	1.34371i
$518$			4.02734i			0.176951i
$519$			11.2787i			0.495079i
$520$	−10.5480	+	10.5480i	−0.462561	+	0.462561i
$521$	25.1256	−	25.1256i	1.10077	−	1.10077i	0.106457	−	0.994317i	$-0.466049\pi$
$521$	25.1256	−	25.1256i	1.10077	−	1.10077i	0.994317	−	0.106457i	$-0.0339507\pi$
$522$	1.21759	+	1.21759i	0.0532925	+	0.0532925i
$523$	11.8307			0.517320			0.258660	−	0.965968i	$-0.416719\pi$
$523$	11.8307			0.517320			0.258660	+	0.965968i	$0.416719\pi$
$524$	25.7475	+	25.7475i	1.12478	+	1.12478i
$525$			0.842549i			0.0367718i
$526$	−8.05407			−0.351174
$527$		0			0
$528$	−14.6554			−0.637794
$529$			19.8553i			0.863276i
$530$	6.02572	+	6.02572i	0.261741	+	0.261741i
$531$	11.1506			0.483897
$532$	−0.867395	−	0.867395i	−0.0376063	−	0.0376063i
$533$	17.2445	−	17.2445i	0.746943	−	0.746943i
$534$	1.36650	−	1.36650i	0.0591343	−	0.0591343i
$535$			36.6091i			1.58275i
$536$			3.29860i			0.142478i
$537$	−2.65595	+	2.65595i	−0.114613	+	0.114613i
$538$	−3.90630	+	3.90630i	−0.168413	+	0.168413i
$539$	−12.4183	−	12.4183i	−0.534894	−	0.534894i
$540$	20.2763			0.872554
$541$	−3.93045	−	3.93045i	−0.168983	−	0.168983i	0.617549	−	0.786532i	$-0.288126\pi$
$541$	−3.93045	−	3.93045i	−0.168983	−	0.168983i	−0.786532	+	0.617549i	$0.788126\pi$
$542$		−	5.90404i		−	0.253600i
$543$	−0.407031			−0.0174674
$544$		0			0
$545$	−4.39330			−0.188188
$546$			2.70739i			0.115865i
$547$	−3.55297	−	3.55297i	−0.151914	−	0.151914i	0.627058	−	0.778972i	$-0.284259\pi$
$547$	−3.55297	−	3.55297i	−0.151914	−	0.151914i	−0.778972	+	0.627058i	$0.784259\pi$
$548$	−0.842549			−0.0359919
$549$	−0.290956	−	0.290956i	−0.0124177	−	0.0124177i
$550$	−0.634007	+	0.634007i	−0.0270342	+	0.0270342i
$551$	−0.546819	+	0.546819i	−0.0232953	+	0.0232953i
$552$			2.10101i			0.0894251i
$553$		−	8.33275i		−	0.354345i
$554$	−4.12707	+	4.12707i	−0.175343	+	0.175343i
$555$	9.00605	−	9.00605i	0.382286	−	0.382286i
$556$	15.5219	+	15.5219i	0.658276	+	0.658276i
$557$	−3.86659			−0.163833			−0.0819164	−	0.996639i	$-0.526104\pi$
$557$	−3.86659			−0.163833			−0.0819164	+	0.996639i	$0.526104\pi$
$558$	−1.06278	−	1.06278i	−0.0449909	−	0.0449909i
$559$			6.96048i			0.294397i
$560$	14.5175			0.613478
$561$		0			0
$562$	9.83574			0.414896
$563$		−	28.8411i		−	1.21551i	−0.794125	−	0.607754i	$-0.792071\pi$
$563$		−	28.8411i		−	1.21551i	0.794125	−	0.607754i	$-0.207929\pi$
$564$	9.97092	+	9.97092i	0.419852	+	0.419852i
$565$	−28.4347			−1.19626
$566$	−7.91599	−	7.91599i	−0.332734	−	0.332734i
$567$	−3.50591	+	3.50591i	−0.147235	+	0.147235i
$568$	−9.45182	+	9.45182i	−0.396590	+	0.396590i
$569$			2.16157i			0.0906177i	0.998973	+	0.0453089i	$0.0144272\pi$
$569$			2.16157i			0.0906177i	−0.998973	+	0.0453089i	$0.985573\pi$
$570$		−	0.248970i		−	0.0104282i
$571$	−4.04412	+	4.04412i	−0.169241	+	0.169241i	−0.786646	−	0.617405i	$-0.788184\pi$
$571$	−4.04412	+	4.04412i	−0.169241	+	0.169241i	0.617405	+	0.786646i	$0.288184\pi$
$572$	31.7442	−	31.7442i	1.32729	−	1.32729i
$573$	0.889870	+	0.889870i	0.0371748	+	0.0371748i
$574$	3.37464			0.140855
$575$	−0.639251	−	0.639251i	−0.0266586	−	0.0266586i
$576$		−	11.6878i		−	0.486991i
$577$	−10.8007			−0.449637			−0.224819	−	0.974401i	$-0.572179\pi$
$577$	−10.8007			−0.449637			−0.224819	+	0.974401i	$0.572179\pi$
$578$		0			0
$579$	21.7425			0.903586
$580$		−	9.82295i		−	0.407876i
$581$	−18.0491	−	18.0491i	−0.748803	−	0.748803i
$582$	−2.83305			−0.117434
$583$	−37.4326	−	37.4326i	−1.55030	−	1.55030i
$584$	−10.3858	+	10.3858i	−0.429769	+	0.429769i
$585$	−17.4328	+	17.4328i	−0.720756	+	0.720756i
$586$			4.85204i			0.200436i
$587$			20.8188i			0.859285i	0.902999	+	0.429643i	$0.141360\pi$
$587$			20.8188i			0.859285i	−0.902999	+	0.429643i	$0.858640\pi$
$588$	−4.05273	+	4.05273i	−0.167132	+	0.167132i
$589$	0.477292	−	0.477292i	0.0196665	−	0.0196665i
$590$	2.88666	+	2.88666i	0.118842	+	0.118842i
$591$	−10.3429			−0.425448
$592$	−14.3581	−	14.3581i	−0.590114	−	0.590114i
$593$		−	20.6313i		−	0.847228i	−0.905843	−	0.423614i	$-0.860761\pi$
$593$		−	20.6313i		−	0.847228i	0.905843	−	0.423614i	$-0.139239\pi$
$594$	8.08378			0.331681
$595$		0			0
$596$	−15.9145			−0.651882
$597$			18.0452i			0.738540i
$598$	−2.05413	−	2.05413i	−0.0839994	−	0.0839994i
$599$	−31.8212			−1.30018			−0.650089	−	0.759858i	$-0.725269\pi$
$599$	−31.8212			−1.30018			−0.650089	+	0.759858i	$0.725269\pi$
$600$	0.427098	+	0.427098i	0.0174362	+	0.0174362i
$601$	−34.0242	+	34.0242i	−1.38787	+	1.38787i	−0.558102	+	0.829772i	$0.688470\pi$
$601$	−34.0242	+	34.0242i	−1.38787	+	1.38787i	−0.829772	+	0.558102i	$0.811530\pi$
$602$	−0.681059	+	0.681059i	−0.0277579	+	0.0277579i
$603$			5.45161i			0.222007i
$604$			25.8726i			1.05274i
$605$	24.3091	−	24.3091i	0.988305	−	0.988305i
$606$	−1.52241	+	1.52241i	−0.0618435	+	0.0618435i
$607$	−10.9429	−	10.9429i	−0.444160	−	0.444160i	0.449247	−	0.893407i	$-0.351692\pi$
$607$	−10.9429	−	10.9429i	−0.444160	−	0.444160i	−0.893407	+	0.449247i	$0.851692\pi$
$608$	−1.33275			−0.0540501
$609$	−2.60218	−	2.60218i	−0.105446	−	0.105446i
$610$		−	0.150644i		−	0.00609941i
$611$	−40.2449			−1.62813
$612$		0			0
$613$	−5.04963			−0.203953			−0.101976	−	0.994787i	$-0.532517\pi$
$613$	−5.04963			−0.203953			−0.101976	+	0.994787i	$0.532517\pi$
$614$		−	3.14290i		−	0.126837i
$615$	−7.54646	−	7.54646i	−0.304303	−	0.304303i
$616$	12.8229			0.516651
$617$	−19.5207	−	19.5207i	−0.785872	−	0.785872i	0.194943	−	0.980815i	$-0.437548\pi$
$617$	−19.5207	−	19.5207i	−0.785872	−	0.785872i	−0.980815	+	0.194943i	$0.937548\pi$
$618$	1.14426	−	1.14426i	0.0460290	−	0.0460290i
$619$	10.4886	−	10.4886i	0.421571	−	0.421571i	−0.464174	−	0.885744i	$-0.653649\pi$
$619$	10.4886	−	10.4886i	0.421571	−	0.421571i	0.885744	+	0.464174i	$0.153649\pi$
$620$			8.57398i			0.344339i
$621$			8.15064i			0.327074i
$622$	0.576439	−	0.576439i	0.0231131	−	0.0231131i
$623$	8.40904	−	8.40904i	0.336901	−	0.336901i
$624$	−9.65225	−	9.65225i	−0.386399	−	0.386399i
$625$	27.2891			1.09156
$626$	−3.71516	−	3.71516i	−0.148487	−	0.148487i
$627$			1.54664i			0.0617667i
$628$	33.7888			1.34832
$629$		0			0
$630$	−3.41147			−0.135916
$631$			34.0506i			1.35553i	0.735278	+	0.677766i	$0.237052\pi$
$631$			34.0506i			1.35553i	−0.735278	+	0.677766i	$0.762948\pi$
$632$	−4.22397	−	4.22397i	−0.168020	−	0.168020i
$633$	−19.0983			−0.759090
$634$	−2.53871	−	2.53871i	−0.100825	−	0.100825i
$635$	19.1537	−	19.1537i	0.760091	−	0.760091i
$636$	−12.2162	+	12.2162i	−0.484404	+	0.484404i
$637$		−	16.3577i		−	0.648117i
$638$		−	3.91622i		−	0.155045i
$639$	−15.6211	+	15.6211i	−0.617960	+	0.617960i
$640$	15.7646	−	15.7646i	0.623150	−	0.623150i
$641$	−10.6230	−	10.6230i	−0.419584	−	0.419584i	0.465476	−	0.885060i	$-0.345883\pi$
$641$	−10.6230	−	10.6230i	−0.419584	−	0.419584i	−0.885060	+	0.465476i	$0.845883\pi$
$642$	4.76321			0.187989
$643$	12.5851	+	12.5851i	0.496307	+	0.496307i	0.910286	−	0.413980i	$-0.135862\pi$
$643$	12.5851	+	12.5851i	0.496307	+	0.496307i	−0.413980	+	0.910286i	$0.635862\pi$
$644$			6.26352i			0.246817i
$645$	3.04601			0.119936
$646$		0			0
$647$	−46.4971			−1.82799			−0.913995	−	0.405725i	$-0.867019\pi$
$647$	−46.4971			−1.82799			−0.913995	+	0.405725i	$0.867019\pi$
$648$			3.55438i			0.139629i
$649$	−17.9323	−	17.9323i	−0.703904	−	0.703904i
$650$	−0.835132			−0.0327566
$651$	2.27132	+	2.27132i	0.0890201	+	0.0890201i
$652$	9.61401	−	9.61401i	0.376514	−	0.376514i
$653$	21.5882	−	21.5882i	0.844812	−	0.844812i	−0.144668	−	0.989480i	$-0.546212\pi$
$653$	21.5882	−	21.5882i	0.844812	−	0.844812i	0.989480	+	0.144668i	$0.0462115\pi$
$654$			0.571614i			0.0223519i
$655$			45.4780i			1.77697i
$656$	−12.0311	+	12.0311i	−0.469736	+	0.469736i
$657$	−17.1647	+	17.1647i	−0.669659	+	0.669659i
$658$	−3.93782	−	3.93782i	−0.153512	−	0.153512i
$659$	9.83481			0.383110			0.191555	−	0.981482i	$-0.438647\pi$
$659$	9.83481			0.383110			0.191555	+	0.981482i	$0.438647\pi$
$660$	−13.8917	−	13.8917i	−0.540736	−	0.540736i
$661$		−	12.4361i		−	0.483709i	−0.970312	−	0.241855i	$-0.922244\pi$
$661$		−	12.4361i		−	0.483709i	0.970312	−	0.241855i	$-0.0777557\pi$
$662$	6.34049			0.246430
$663$		0			0
$664$	−18.2986			−0.710123
$665$		−	1.53209i		−	0.0594119i
$666$	3.37401	+	3.37401i	0.130740	+	0.130740i
$667$	3.94862			0.152891
$668$	−6.78559	−	6.78559i	−0.262542	−	0.262542i
$669$	−12.4061	+	12.4061i	−0.479648	+	0.479648i
$670$	−1.41130	+	1.41130i	−0.0545233	+	0.0545233i
$671$			0.935822i			0.0361270i
$672$		−	6.34224i		−	0.244657i
$673$	−8.91785	+	8.91785i	−0.343758	+	0.343758i	−0.857778	−	0.514020i	$-0.828156\pi$
$673$	−8.91785	+	8.91785i	−0.343758	+	0.343758i	0.514020	+	0.857778i	$0.328156\pi$
$674$	4.05083	−	4.05083i	0.156032	−	0.156032i
$675$	1.65688	+	1.65688i	0.0637732	+	0.0637732i
$676$	17.3824			0.668553
$677$	3.21663	+	3.21663i	0.123625	+	0.123625i	0.766212	−	0.642587i	$-0.222139\pi$
$677$	3.21663	+	3.21663i	0.123625	+	0.123625i	−0.642587	+	0.766212i	$0.722139\pi$
$678$			3.69965i			0.142084i
$679$	−17.4338			−0.669046
$680$		0			0
$681$	−3.71244			−0.142261
$682$			3.41828i			0.130893i
$683$	−3.44186	−	3.44186i	−0.131699	−	0.131699i	0.638184	−	0.769884i	$-0.279686\pi$
$683$	−3.44186	−	3.44186i	−0.131699	−	0.131699i	−0.769884	+	0.638184i	$0.779686\pi$
$684$	−1.45336			−0.0555707
$685$	−0.744101	−	0.744101i	−0.0284307	−	0.0284307i
$686$	4.83127	−	4.83127i	0.184459	−	0.184459i
$687$	−9.01991	+	9.01991i	−0.344131	+	0.344131i
$688$		−	4.85616i		−	0.185139i
$689$		−	49.3073i		−	1.87846i
$690$	−0.898916	+	0.898916i	−0.0342211	+	0.0342211i
$691$	−3.90083	+	3.90083i	−0.148395	+	0.148395i	−0.777401	−	0.629006i	$-0.783462\pi$
$691$	−3.90083	+	3.90083i	−0.148395	+	0.148395i	0.629006	+	0.777401i	$0.283462\pi$
$692$	17.0443	+	17.0443i	0.647928	+	0.647928i
$693$	21.1925			0.805038
$694$	5.05204	+	5.05204i	0.191773	+	0.191773i
$695$			27.4165i			1.03997i
$696$	−2.63816			−0.0999990
$697$		0			0
$698$	2.23112			0.0844493
$699$		−	4.50898i		−	0.170545i
$700$	1.27326	+	1.27326i	0.0481247	+	0.0481247i
$701$	−22.3233			−0.843138			−0.421569	−	0.906796i	$-0.638520\pi$
$701$	−22.3233			−0.843138			−0.421569	+	0.906796i	$0.638520\pi$
$702$	5.32409	+	5.32409i	0.200945	+	0.200945i
$703$	−1.51526	+	1.51526i	−0.0571492	+	0.0571492i
$704$	−18.7961	+	18.7961i	−0.708405	+	0.708405i
$705$			17.6117i			0.663297i
$706$			9.43552i			0.355110i
$707$	−9.36844	+	9.36844i	−0.352336	+	0.352336i
$708$	−5.85224	+	5.85224i	−0.219940	+	0.219940i
$709$	24.5908	+	24.5908i	0.923526	+	0.923526i	0.997277	−	0.0737506i	$-0.0234969\pi$
$709$	24.5908	+	24.5908i	0.923526	+	0.923526i	−0.0737506	+	0.997277i	$0.523497\pi$
$710$	−8.08790			−0.303533
$711$	−6.98097	−	6.98097i	−0.261807	−	0.261807i
$712$		−	8.52528i		−	0.319498i
$713$	−3.44656			−0.129075
$714$		0			0
$715$	56.0702			2.09691
$716$			8.02734i			0.299996i
$717$	−9.85602	−	9.85602i	−0.368080	−	0.368080i
$718$	−5.86753			−0.218974
$719$	−3.00514	−	3.00514i	−0.112073	−	0.112073i	0.648847	−	0.760919i	$-0.275252\pi$
$719$	−3.00514	−	3.00514i	−0.112073	−	0.112073i	−0.760919	+	0.648847i	$0.775252\pi$
$720$	12.1624	−	12.1624i	0.453267	−	0.453267i
$721$	7.04145	−	7.04145i	0.262237	−	0.262237i
$722$		−	6.55674i		−	0.244017i
$723$		−	15.9314i		−	0.592494i
$724$	−0.615105	+	0.615105i	−0.0228602	+	0.0228602i
$725$	0.802681	−	0.802681i	0.0298108	−	0.0298108i
$726$	−3.16286	−	3.16286i	−0.117385	−	0.117385i
$727$	−29.1644			−1.08165			−0.540823	−	0.841136i	$-0.681887\pi$
$727$	−29.1644			−1.08165			−0.540823	+	0.841136i	$0.681887\pi$
$728$	8.44537	+	8.44537i	0.313006	+	0.313006i
$729$		−	6.25133i		−	0.231531i
$730$	−8.88713			−0.328927
$731$		0			0
$732$	0.305407			0.0112882
$733$			0.502993i			0.0185785i	0.999957	+	0.00928924i	$0.00295690\pi$
$733$			0.502993i			0.0185785i	−0.999957	+	0.00928924i	$0.997043\pi$
$734$	−0.365297	−	0.365297i	−0.0134833	−	0.0134833i
$735$	−7.15839			−0.264041
$736$	4.81193	+	4.81193i	0.177370	+	0.177370i
$737$	8.76719	−	8.76719i	0.322944	−	0.322944i
$738$	2.82719	−	2.82719i	0.104070	−	0.104070i
$739$			14.9581i			0.550243i	0.961409	+	0.275122i	$0.0887181\pi$
$739$			14.9581i			0.550243i	−0.961409	+	0.275122i	$0.911282\pi$
$740$		−	27.2199i		−	1.00062i
$741$	−1.01864	+	1.01864i	−0.0374206	+	0.0374206i
$742$	4.82455	−	4.82455i	0.177115	−	0.177115i
$743$	−16.5290	−	16.5290i	−0.606391	−	0.606391i	0.335610	−	0.942001i	$-0.391058\pi$
$743$	−16.5290	−	16.5290i	−0.606391	−	0.606391i	−0.942001	+	0.335610i	$0.891058\pi$
$744$	2.30272			0.0844218
$745$	−14.0549	−	14.0549i	−0.514933	−	0.514933i
$746$			8.35235i			0.305801i
$747$	−30.2422			−1.10650
$748$		0			0
$749$	29.3114			1.07102
$750$		−	3.21894i		−	0.117539i
$751$	12.0414	+	12.0414i	0.439397	+	0.439397i	0.891809	−	0.452412i	$-0.149436\pi$
$751$	12.0414	+	12.0414i	0.439397	+	0.439397i	−0.452412	+	0.891809i	$0.649436\pi$
$752$	28.0779			1.02390
$753$	18.4562	+	18.4562i	0.672581	+	0.672581i
$754$	2.57928	−	2.57928i	0.0939318	−	0.0939318i
$755$	−22.8495	+	22.8495i	−0.831579	+	0.831579i
$756$		−	16.2344i		−	0.590440i
$757$			16.3746i			0.595146i	0.954699	+	0.297573i	$0.0961772\pi$
$757$			16.3746i			0.595146i	−0.954699	+	0.297573i	$0.903823\pi$
$758$	4.96003	−	4.96003i	0.180157	−	0.180157i
$759$	5.58419	−	5.58419i	0.202693	−	0.202693i
$760$	−0.776634	−	0.776634i	−0.0281715	−	0.0281715i
$761$	18.8803			0.684411			0.342206	−	0.939625i	$-0.388826\pi$
$761$	18.8803			0.684411			0.342206	+	0.939625i	$0.388826\pi$
$762$	−2.49209	−	2.49209i	−0.0902789	−	0.0902789i
$763$			3.51754i			0.127344i
$764$	2.68954			0.0973042
$765$		0			0
$766$	−2.96080			−0.106978
$767$		−	23.6209i		−	0.852902i
$768$	4.47669	+	4.47669i	0.161539	+	0.161539i
$769$	27.4766			0.990831			0.495416	−	0.868656i	$-0.335016\pi$
$769$	27.4766			0.990831			0.495416	+	0.868656i	$0.335016\pi$
$770$	5.48628	+	5.48628i	0.197712	+	0.197712i
$771$	4.59955	−	4.59955i	0.165649	−	0.165649i
$772$	32.8572	−	32.8572i	1.18256	−	1.18256i
$773$			9.90436i			0.356235i	0.984009	+	0.178118i	$0.0570007\pi$
$773$			9.90436i			0.356235i	−0.984009	+	0.178118i	$0.942999\pi$
$774$			1.14115i			0.0410177i
$775$	−0.700622	+	0.700622i	−0.0251671	+	0.0251671i
$776$	−8.83738	+	8.83738i	−0.317243	+	0.317243i
$777$	−7.21078	−	7.21078i	−0.258685	−	0.258685i
$778$	4.48576			0.160822
$779$	1.26969	+	1.26969i	0.0454912	+	0.0454912i
$780$		−	18.2986i		−	0.655195i
$781$	50.2431			1.79784
$782$		0			0
$783$	−10.2344			−0.365748
$784$			11.4124i			0.407586i
$785$	29.8408	+	29.8408i	1.06506	+	1.06506i
$786$	5.91716			0.211058
$787$	35.9524	+	35.9524i	1.28157	+	1.28157i	0.939777	+	0.341789i	$0.111033\pi$
$787$	35.9524	+	35.9524i	1.28157	+	1.28157i	0.341789	+	0.939777i	$0.388967\pi$
$788$	−15.6301	+	15.6301i	−0.556800	+	0.556800i
$789$	14.4205	−	14.4205i	0.513382	−	0.513382i
$790$		−	3.61444i		−	0.128596i
$791$			22.7665i			0.809484i
$792$	10.7427	−	10.7427i	0.381727	−	0.381727i
$793$	−0.616346	+	0.616346i	−0.0218871	+	0.0218871i
$794$	5.94905	+	5.94905i	0.211124	+	0.211124i
$795$	−21.5776			−0.765279
$796$	27.2699	+	27.2699i	0.966555	+	0.966555i
$797$		−	5.38650i		−	0.190800i	−0.995439	−	0.0953998i	$-0.969587\pi$
$797$		−	5.38650i		−	0.190800i	0.995439	−	0.0953998i	$-0.0304129\pi$
$798$	−0.199340			−0.00705658
$799$		0			0
$800$	1.95636			0.0691676
$801$		−	14.0898i		−	0.497837i
$802$	−6.27130	−	6.27130i	−0.221447	−	0.221447i
$803$	55.2080			1.94825
$804$	−2.86119	−	2.86119i	−0.100906	−	0.100906i
$805$	−5.53166	+	5.53166i	−0.194965	+	0.194965i
$806$	−2.25133	+	2.25133i	−0.0792997	+	0.0792997i
$807$		−	13.9881i		−	0.492406i
$808$			9.49794i			0.334136i
$809$	34.4233	−	34.4233i	1.21026	−	1.21026i	0.239318	−	0.970941i	$-0.423076\pi$
$809$	34.4233	−	34.4233i	1.21026	−	1.21026i	0.970941	−	0.239318i	$-0.0769238\pi$
$810$	−1.52074	+	1.52074i	−0.0534332	+	0.0534332i
$811$	−11.2629	−	11.2629i	−0.395492	−	0.395492i	0.481147	−	0.876640i	$-0.340220\pi$
$811$	−11.2629	−	11.2629i	−0.395492	−	0.395492i	−0.876640	+	0.481147i	$0.840220\pi$
$812$	−7.86484			−0.276002
$813$	10.5709	+	10.5709i	0.370739	+	0.370739i
$814$		−	10.8520i		−	0.380364i
$815$	16.9813			0.594830
$816$		0			0
$817$	−0.512489			−0.0179297
$818$		−	3.59533i		−	0.125708i
$819$	13.9577	+	13.9577i	0.487722	+	0.487722i
$820$	−22.8084			−0.796504
$821$	−12.0922	−	12.0922i	−0.422022	−	0.422022i	0.463877	−	0.885899i	$-0.346458\pi$
$821$	−12.0922	−	12.0922i	−0.422022	−	0.422022i	−0.885899	+	0.463877i	$0.846458\pi$
$822$	−0.0968152	+	0.0968152i	−0.00337682	+	0.00337682i
$823$	−3.97583	+	3.97583i	−0.138589	+	0.138589i	−0.772998	−	0.634409i	$-0.781244\pi$
$823$	−3.97583	+	3.97583i	−0.138589	+	0.138589i	0.634409	+	0.772998i	$0.281244\pi$
$824$		−	7.13878i		−	0.248691i
$825$		−	2.27033i		−	0.0790426i
$826$	2.31123	−	2.31123i	0.0804179	−	0.0804179i
$827$	−12.6294	+	12.6294i	−0.439168	+	0.439168i	−0.891732	−	0.452564i	$-0.850510\pi$
$827$	−12.6294	+	12.6294i	−0.439168	+	0.439168i	0.452564	+	0.891732i	$0.350510\pi$
$828$	5.24742	+	5.24742i	0.182360	+	0.182360i
$829$	−35.8161			−1.24395			−0.621973	−	0.783039i	$-0.713669\pi$
$829$	−35.8161			−1.24395			−0.621973	+	0.783039i	$0.713669\pi$
$830$	−7.82903	−	7.82903i	−0.271750	−	0.271750i
$831$		−	14.7787i		−	0.512667i
$832$	−24.7588			−0.858356
$833$		0			0
$834$	3.56717			0.123521
$835$		−	11.9855i		−	0.414774i
$836$	2.33728	+	2.33728i	0.0808364	+	0.0808364i
$837$	8.93313			0.308774
$838$	0.322477	+	0.322477i	0.0111398	+	0.0111398i
$839$	−25.2956	+	25.2956i	−0.873300	+	0.873300i	−0.992830	−	0.119531i	$-0.961861\pi$
$839$	−25.2956	+	25.2956i	−0.873300	+	0.873300i	0.119531	+	0.992830i	$0.461861\pi$
$840$	3.69582	−	3.69582i	0.127518	−	0.127518i
$841$		−	24.0419i		−	0.829031i
$842$			2.78375i			0.0959343i
$843$	−17.6105	+	17.6105i	−0.606537	+	0.606537i
$844$	−28.8614	+	28.8614i	−0.993449	+	0.993449i
$845$	15.3513	+	15.3513i	0.528102	+	0.528102i
$846$	−6.59802			−0.226845
$847$	−19.4633	−	19.4633i	−0.668767	−	0.668767i
$848$			34.4005i			1.18132i
$849$	28.3465			0.972849
$850$		0			0
$851$	10.9418			0.375080
$852$		−	16.3969i		−	0.561749i
$853$	−7.82546	−	7.82546i	−0.267939	−	0.267939i	0.560331	−	0.828269i	$-0.310674\pi$
$853$	−7.82546	−	7.82546i	−0.267939	−	0.267939i	−0.828269	+	0.560331i	$0.810674\pi$
$854$	−0.120615			−0.00412735
$855$	−1.28355	−	1.28355i	−0.0438963	−	0.0438963i
$856$	14.8583	−	14.8583i	0.507846	−	0.507846i
$857$	19.1446	−	19.1446i	0.653968	−	0.653968i	−0.299978	−	0.953946i	$-0.596979\pi$
$857$	19.1446	−	19.1446i	0.653968	−	0.653968i	0.953946	+	0.299978i	$0.0969793\pi$
$858$		−	7.29530i		−	0.249058i
$859$		−	51.7279i		−	1.76493i	−0.470374	−	0.882467i	$-0.655881\pi$
$859$		−	51.7279i		−	1.76493i	0.470374	−	0.882467i	$-0.344119\pi$
$860$	4.60312	−	4.60312i	0.156965	−	0.156965i
$861$	−6.04214	+	6.04214i	−0.205916	+	0.205916i
$862$	3.61659	+	3.61659i	0.123181	+	0.123181i
$863$	−45.4712			−1.54786			−0.773929	−	0.633272i	$-0.781711\pi$
$863$	−45.4712			−1.54786			−0.773929	+	0.633272i	$0.781711\pi$
$864$	−12.4721	−	12.4721i	−0.424308	−	0.424308i
$865$			30.1056i			1.02362i
$866$	−2.86215			−0.0972598
$867$		0			0
$868$	6.86484			0.233008
$869$			22.4534i			0.761678i
$870$	−1.12873	−	1.12873i	−0.0382676	−	0.0382676i
$871$	11.5484			0.391302
$872$	1.78308	+	1.78308i	0.0603828	+	0.0603828i
$873$	−14.6056	+	14.6056i	−0.494324	+	0.494324i
$874$	0.151242	−	0.151242i	0.00511583	−	0.00511583i
$875$		−	19.8084i		−	0.669646i
$876$		−	18.0172i		−	0.608746i
$877$	26.5048	−	26.5048i	0.895002	−	0.895002i	−0.0999866	−	0.994989i	$-0.531880\pi$
$877$	26.5048	−	26.5048i	0.895002	−	0.895002i	0.994989	+	0.0999866i	$0.0318800\pi$
$878$	−9.81231	+	9.81231i	−0.331149	+	0.331149i
$879$	−8.68738	−	8.68738i	−0.293018	−	0.293018i
$880$	−39.1189			−1.31870
$881$	12.8664	+	12.8664i	0.433480	+	0.433480i	0.889810	−	0.456330i	$-0.150837\pi$
$881$	12.8664	+	12.8664i	0.433480	+	0.433480i	−0.456330	+	0.889810i	$0.650837\pi$
$882$		−	2.68180i		−	0.0903009i
$883$	0.397860			0.0133891			0.00669453	−	0.999978i	$-0.497869\pi$
$883$	0.397860			0.0133891			0.00669453	+	0.999978i	$0.497869\pi$
$884$		0			0
$885$	−10.3369			−0.347470
$886$		−	4.84348i		−	0.162720i
$887$	16.8174	+	16.8174i	0.564674	+	0.564674i	0.930631	−	0.365958i	$-0.119259\pi$
$887$	16.8174	+	16.8174i	0.564674	+	0.564674i	−0.365958	+	0.930631i	$0.619259\pi$
$888$	−7.31046			−0.245323
$889$	−15.3356	−	15.3356i	−0.514339	−	0.514339i
$890$	3.64753	−	3.64753i	0.122265	−	0.122265i
$891$	9.44701	−	9.44701i	0.316487	−	0.316487i
$892$			37.4962i			1.25547i
$893$		−	2.96316i		−	0.0991585i
$894$	−1.82869	+	1.82869i	−0.0611606	+	0.0611606i
$895$	−7.08939	+	7.08939i	−0.236972	+	0.236972i
$896$	−12.6221	−	12.6221i	−0.421673	−	0.421673i
$897$	7.35565			0.245598
$898$	−2.51266	−	2.51266i	−0.0838487	−	0.0838487i
$899$		−	4.32770i		−	0.144337i
$900$	2.13341			0.0711136
$901$		0			0
$902$	−9.09327			−0.302773
$903$		−	2.43882i		−	0.0811587i
$904$	11.5406	+	11.5406i	0.383835	+	0.383835i
$905$	−1.08647			−0.0361154
$906$	2.97295	+	2.97295i	0.0987698	+	0.0987698i
$907$	26.5315	−	26.5315i	0.880963	−	0.880963i	−0.112670	−	0.993633i	$-0.535940\pi$
$907$	26.5315	−	26.5315i	0.880963	−	0.880963i	0.993633	+	0.112670i	$0.0359401\pi$
$908$	−5.61023	+	5.61023i	−0.186182	+	0.186182i
$909$			15.6973i			0.520646i
$910$			7.22668i			0.239562i
$911$	−10.4403	+	10.4403i	−0.345901	+	0.345901i	−0.858580	−	0.512679i	$-0.828653\pi$
$911$	−10.4403	+	10.4403i	−0.345901	+	0.345901i	0.512679	+	0.858580i	$0.328653\pi$
$912$	0.710679	−	0.710679i	0.0235329	−	0.0235329i
$913$	48.6350	+	48.6350i	1.60958	+	1.60958i
$914$	4.08790			0.135216
$915$	0.269722	+	0.269722i	0.00891674	+	0.00891674i
$916$			27.2618i			0.900754i
$917$	36.4124			1.20244
$918$		0			0
$919$	−48.5476			−1.60144			−0.800718	−	0.599041i	$-0.795549\pi$
$919$	−48.5476			−1.60144			−0.800718	+	0.599041i	$0.795549\pi$
$920$			5.60813i			0.184894i
$921$	5.62723	+	5.62723i	0.185424	+	0.185424i
$922$	−6.77238			−0.223037
$923$	33.0908	+	33.0908i	1.08920	+	1.08920i
$924$	−11.1226	+	11.1226i	−0.365905	+	0.365905i
$925$	2.22427	−	2.22427i	0.0731335	−	0.0731335i
$926$		−	0.497007i		−	0.0163327i
$927$		−	11.7983i		−	0.387507i
$928$	−6.04214	+	6.04214i	−0.198343	+	0.198343i
$929$	−7.96451	+	7.96451i	−0.261307	+	0.261307i	−0.825585	−	0.564278i	$-0.809155\pi$
$929$	−7.96451	+	7.96451i	−0.261307	+	0.261307i	0.564278	+	0.825585i	$0.309155\pi$
$930$	0.985215	+	0.985215i	0.0323065	+	0.0323065i
$931$	1.20439			0.0394724
$932$	−6.81396	−	6.81396i	−0.223199	−	0.223199i
$933$			2.06418i			0.0675781i
$934$	−3.71244			−0.121475
$935$		0			0
$936$	14.1506			0.462528
$937$		−	2.39775i		−	0.0783310i	−0.999233	−	0.0391655i	$-0.987530\pi$
$937$		−	2.39775i		−	0.0783310i	0.999233	−	0.0391655i	$-0.0124700\pi$
$938$	1.12997	+	1.12997i	0.0368949	+	0.0368949i
$939$	13.3037			0.434148
$940$	26.6149	+	26.6149i	0.868081	+	0.868081i
$941$	24.3101	−	24.3101i	0.792487	−	0.792487i	−0.189411	−	0.981898i	$-0.560658\pi$
$941$	24.3101	−	24.3101i	0.792487	−	0.792487i	0.981898	+	0.189411i	$0.0606578\pi$
$942$	3.88259	−	3.88259i	0.126502	−	0.126502i
$943$		−	9.16849i		−	0.298567i
$944$			16.4798i			0.536371i
$945$	14.3375	−	14.3375i	0.466399	−	0.466399i
$946$	1.83518	−	1.83518i	0.0596668	−	0.0596668i
$947$	−14.5165	−	14.5165i	−0.471722	−	0.471722i	0.430749	−	0.902472i	$-0.358249\pi$
$947$	−14.5165	−	14.5165i	−0.471722	−	0.471722i	−0.902472	+	0.430749i	$0.858249\pi$
$948$	7.32770			0.237993
$949$	36.3608	+	36.3608i	1.18032	+	1.18032i
$950$		−	0.0614894i		−	0.00199498i
$951$	9.09091			0.294793
$952$		0			0
$953$	16.5517			0.536162			0.268081	−	0.963396i	$-0.413611\pi$
$953$	16.5517			0.536162			0.268081	+	0.963396i	$0.413611\pi$
$954$		−	8.08378i		−	0.261722i
$955$	2.37528	+	2.37528i	0.0768623	+	0.0768623i
$956$	−29.7888			−0.963439
$957$	7.01183	+	7.01183i	0.226660	+	0.226660i
$958$	−9.54492	+	9.54492i	−0.308382	+	0.308382i
$959$	−0.595772	+	0.595772i	−0.0192385	+	0.0192385i
$960$			10.8348i			0.349692i
$961$		−	27.2226i		−	0.878147i
$962$	7.14731	−	7.14731i	0.230438	−	0.230438i
$963$	24.5563	−	24.5563i	0.791317	−	0.791317i
$964$	−24.0755	−	24.0755i	−0.775419	−	0.775419i
$965$	58.0360			1.86825
$966$	0.719726	+	0.719726i	0.0231568	+	0.0231568i
$967$		−	3.92665i		−	0.126273i	−0.998005	−	0.0631363i	$-0.979890\pi$
$967$		−	3.92665i		−	0.126273i	0.998005	−	0.0631363i	$-0.0201103\pi$
$968$	−19.7324			−0.634222
$969$		0			0
$970$	−7.56212			−0.242805
$971$			4.25402i			0.136518i	0.997668	+	0.0682590i	$0.0217444\pi$
$971$			4.25402i			0.136518i	−0.997668	+	0.0682590i	$0.978256\pi$
$972$	−21.4073	−	21.4073i	−0.686641	−	0.686641i
$973$	21.9513			0.703726
$974$	9.08967	+	9.08967i	0.291252	+	0.291252i
$975$	1.49527	−	1.49527i	0.0478869	−	0.0478869i
$976$	0.430010	−	0.430010i	0.0137643	−	0.0137643i
$977$		−	48.5431i		−	1.55303i	−0.630097	−	0.776516i	$-0.716985\pi$
$977$		−	48.5431i		−	1.55303i	0.630097	−	0.776516i	$-0.283015\pi$
$978$		−	2.20945i		−	0.0706503i
$979$	−22.6589	+	22.6589i	−0.724183	+	0.724183i
$980$	−10.8177	+	10.8177i	−0.345560	+	0.345560i
$981$	2.94691	+	2.94691i	0.0940875	+	0.0940875i
$982$	8.82739			0.281693
$983$	−24.7910	−	24.7910i	−0.790709	−	0.790709i	0.190900	−	0.981609i	$-0.438859\pi$
$983$	−24.7910	−	24.7910i	−0.790709	−	0.790709i	−0.981609	+	0.190900i	$0.938859\pi$
$984$			6.12567i			0.195279i
$985$	−27.6076			−0.879652
$986$		0			0
$987$	14.1010			0.448840
$988$			3.07873i			0.0979473i
$989$	1.85036	+	1.85036i	0.0588379	+	0.0588379i
$990$	9.19253			0.292158
$991$	−37.6177	−	37.6177i	−1.19497	−	1.19497i	−0.975655	−	0.219310i	$-0.929619\pi$
$991$	−37.6177	−	37.6177i	−1.19497	−	1.19497i	−0.219310	−	0.975655i	$-0.570381\pi$
$992$	5.27390	−	5.27390i	0.167446	−	0.167446i
$993$	−11.3524	+	11.3524i	−0.360257	+	0.360257i
$994$			6.47565i			0.205395i
$995$			48.1671i			1.52700i
$996$	15.8721	−	15.8721i	0.502927	−	0.502927i
$997$	15.9660	−	15.9660i	0.505649	−	0.505649i	−0.407539	−	0.913188i	$-0.633613\pi$
$997$	15.9660	−	15.9660i	0.505649	−	0.505649i	0.913188	+	0.407539i	$0.133613\pi$
$998$	−5.35941	−	5.35941i	−0.169649	−	0.169649i
$999$	−28.3601			−0.897274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.d.251.4		12
17.2	even	8		289.2.a.d.1.2	✓	3
17.3	odd	16		289.2.d.f.134.4		24
17.4	even	4	inner	289.2.c.d.38.4		12
17.5	odd	16		289.2.d.f.155.3		24
17.6	odd	16		289.2.d.f.179.4		24
17.7	odd	16		289.2.d.f.110.4		24
17.8	even	8		289.2.b.d.288.3		6
17.9	even	8		289.2.b.d.288.4		6
17.10	odd	16		289.2.d.f.110.3		24
17.11	odd	16		289.2.d.f.179.3		24
17.12	odd	16		289.2.d.f.155.4		24
17.13	even	4	inner	289.2.c.d.38.3		12
17.14	odd	16		289.2.d.f.134.3		24
17.15	even	8		289.2.a.e.1.2	yes	3
17.16	even	2	inner	289.2.c.d.251.3		12
51.2	odd	8		2601.2.a.x.1.2		3
51.32	odd	8		2601.2.a.w.1.2		3
68.15	odd	8		4624.2.a.bd.1.3		3
68.19	odd	8		4624.2.a.bg.1.1		3
85.19	even	8		7225.2.a.t.1.2		3
85.49	even	8		7225.2.a.s.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.2	✓	3	17.2	even	8
289.2.a.e.1.2	yes	3	17.15	even	8
289.2.b.d.288.3		6	17.8	even	8
289.2.b.d.288.4		6	17.9	even	8
289.2.c.d.38.3		12	17.13	even	4	inner
289.2.c.d.38.4		12	17.4	even	4	inner
289.2.c.d.251.3		12	17.16	even	2	inner
289.2.c.d.251.4		12	1.1	even	1	trivial
289.2.d.f.110.3		24	17.10	odd	16
289.2.d.f.110.4		24	17.7	odd	16
289.2.d.f.134.3		24	17.14	odd	16
289.2.d.f.134.4		24	17.3	odd	16
289.2.d.f.155.3		24	17.5	odd	16
289.2.d.f.155.4		24	17.12	odd	16
289.2.d.f.179.3		24	17.11	odd	16
289.2.d.f.179.4		24	17.6	odd	16
2601.2.a.w.1.2		3	51.32	odd	8
2601.2.a.x.1.2		3	51.2	odd	8
4624.2.a.bd.1.3		3	68.15	odd	8
4624.2.a.bg.1.1		3	68.19	odd	8
7225.2.a.s.1.2		3	85.49	even	8
7225.2.a.t.1.2		3	85.19	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.347296i q^{2} +(0.621819 + 0.621819i) q^{3} +1.87939 q^{4} +(1.65979 + 1.65979i) q^{5} +(0.215956 - 0.215956i) q^{6} +(1.32893 - 1.32893i) q^{7} -1.34730i q^{8} -2.22668i q^{9} +(0.576439 - 0.576439i) q^{10} +(-3.58091 + 3.58091i) q^{11} +(1.16864 + 1.16864i) q^{12} -4.71688 q^{13} +(-0.461531 - 0.461531i) q^{14} +2.06418i q^{15} +3.29086 q^{16} -0.773318 q^{18} -0.347296i q^{19} +(3.11938 + 3.11938i) q^{20} +1.65270 q^{21} +(1.24364 + 1.24364i) q^{22} +(-1.25393 + 1.25393i) q^{23} +(0.837775 - 0.837775i) q^{24} +0.509800i q^{25} +1.63816i q^{26} +(3.25005 - 3.25005i) q^{27} +(2.49756 - 2.49756i) q^{28} +(-1.57450 - 1.57450i) q^{29} +0.716881 q^{30} +(1.37431 + 1.37431i) q^{31} -3.83750i q^{32} -4.45336 q^{33} +4.41147 q^{35} -4.18479i q^{36} +(-4.36302 - 4.36302i) q^{37} -0.120615 q^{38} +(-2.93305 - 2.93305i) q^{39} +(2.23623 - 2.23623i) q^{40} +(-3.65592 + 3.65592i) q^{41} -0.573978i q^{42} -1.47565i q^{43} +(-6.72992 + 6.72992i) q^{44} +(3.69582 - 3.69582i) q^{45} +(0.435484 + 0.435484i) q^{46} +8.53209 q^{47} +(2.04632 + 2.04632i) q^{48} +3.46791i q^{49} +0.177052 q^{50} -8.86484 q^{52} +10.4534i q^{53} +(-1.12873 - 1.12873i) q^{54} -11.8871 q^{55} +(-1.79046 - 1.79046i) q^{56} +(0.215956 - 0.215956i) q^{57} +(-0.546819 + 0.546819i) q^{58} +5.00774i q^{59} +3.87939i q^{60} +(0.130668 - 0.130668i) q^{61} +(0.477292 - 0.477292i) q^{62} +(-2.95910 - 2.95910i) q^{63} +5.24897 q^{64} +(-7.82903 - 7.82903i) q^{65} +1.54664i q^{66} -2.44831 q^{67} -1.55943 q^{69} -1.53209i q^{70} +(-7.01540 - 7.01540i) q^{71} -3.00000 q^{72} +(-7.70865 - 7.70865i) q^{73} +(-1.51526 + 1.51526i) q^{74} +(-0.317004 + 0.317004i) q^{75} -0.652704i q^{76} +9.51754i q^{77} +(-1.01864 + 1.01864i) q^{78} +(3.13514 - 3.13514i) q^{79} +(5.46213 + 5.46213i) q^{80} -2.63816 q^{81} +(1.26969 + 1.26969i) q^{82} -13.5817i q^{83} +3.10607 q^{84} -0.512489 q^{86} -1.95811i q^{87} +(4.82455 + 4.82455i) q^{88} +6.32770 q^{89} +(-1.28355 - 1.28355i) q^{90} +(-6.26839 + 6.26839i) q^{91} +(-2.35661 + 2.35661i) q^{92} +1.70914i q^{93} -2.96316i q^{94} +(0.576439 - 0.576439i) q^{95} +(2.38623 - 2.38623i) q^{96} +(-6.55934 - 6.55934i) q^{97} +1.20439 q^{98} +(7.97356 + 7.97356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q - 24 * q^13 - 24 * q^16 - 36 * q^18 + 24 * q^21 - 24 * q^30 + 12 * q^35 - 24 * q^38 + 84 * q^47 + 84 * q^50 - 12 * q^52 - 24 * q^55 + 12 * q^64 - 36 * q^67 + 84 * q^69 - 36 * q^72 + 36 * q^81 - 12 * q^84 + 24 * q^86 + 60 * q^89 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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