LMFDB - Embedded newform 1184.2.y.a.529.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1184,2,Mod(529,1184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1184, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1184.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1184 = 2^{5} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1184.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.45428759932$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.25
Character	$\chi$	$=$	1184.529
Dual form			1184.2.y.a.1137.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03067 + 0.595057i) q^{3} +(-1.89805 + 3.28751i) q^{5} +(-0.213384 + 0.369592i) q^{7} +(-0.791813 - 1.37146i) q^{9} +5.01695i q^{11} +(-1.27662 + 2.21117i) q^{13} +(-3.91251 + 2.25889i) q^{15} +(-1.96229 + 1.13293i) q^{17} +(3.20006 - 5.54267i) q^{19} +(-0.439857 + 0.253952i) q^{21} -2.97488i q^{23} +(-4.70515 - 8.14956i) q^{25} -5.45504i q^{27} -8.86178 q^{29} -0.284019i q^{31} +(-2.98537 + 5.17082i) q^{33} +(-0.810025 - 1.40300i) q^{35} +(6.05179 + 0.613070i) q^{37} +(-2.63154 + 1.51932i) q^{39} +(-4.17825 + 7.23695i) q^{41} -7.89769 q^{43} +6.01159 q^{45} -2.01684 q^{47} +(3.40893 + 5.90445i) q^{49} -2.69663 q^{51} +(-5.23310 + 3.02133i) q^{53} +(-16.4933 - 9.52240i) q^{55} +(6.59642 - 3.80844i) q^{57} +(2.68998 + 4.65918i) q^{59} +(2.82477 - 4.89264i) q^{61} +0.675842 q^{63} +(-4.84616 - 8.39380i) q^{65} +(10.9562 + 6.32555i) q^{67} +(1.77022 - 3.06611i) q^{69} +(4.28852 - 7.42793i) q^{71} -4.78445 q^{73} -11.1993i q^{75} +(-1.85423 - 1.07054i) q^{77} +(-4.67103 - 2.69682i) q^{79} +(0.870623 - 1.50796i) q^{81} +(-10.4077 + 6.00888i) q^{83} -8.60140i q^{85} +(-9.13357 - 5.27327i) q^{87} +(-9.89138 + 5.71079i) q^{89} +(-0.544820 - 0.943656i) q^{91} +(0.169008 - 0.292730i) q^{93} +(12.1477 + 21.0405i) q^{95} +2.39634i q^{97} +(6.88056 - 3.97249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) $ 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1184\mathbb{Z}\right)^\times$.

$n$	$223$	$705$	$741$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	1.03067	+	0.595057i	0.595057	+	0.343557i	0.767095	−	0.641534i	$-0.221702\pi$
$3$	1.03067	+	0.595057i	0.595057	+	0.343557i	−0.172037	+	0.985090i	$0.555035\pi$
$4$		0			0
$5$	−1.89805	+	3.28751i	−0.848832	+	1.47022i	0.0334201	+	0.999441i	$0.489360\pi$
$5$	−1.89805	+	3.28751i	−0.848832	+	1.47022i	−0.882252	+	0.470778i	$0.843973\pi$
$6$		0			0
$7$	−0.213384	+	0.369592i	−0.0806516	+	0.139693i	−0.903530	−	0.428525i	$-0.859033\pi$
$7$	−0.213384	+	0.369592i	−0.0806516	+	0.139693i	0.822878	+	0.568218i	$0.192367\pi$
$8$		0			0
$9$	−0.791813	−	1.37146i	−0.263938	−	0.457154i
$10$		0			0
$11$			5.01695i			1.51267i	0.654186	+	0.756334i	$0.273012\pi$
$11$			5.01695i			1.51267i	−0.654186	+	0.756334i	$0.726988\pi$
$12$		0			0
$13$	−1.27662	+	2.21117i	−0.354070	+	0.613268i	−0.986958	−	0.160975i	$-0.948536\pi$
$13$	−1.27662	+	2.21117i	−0.354070	+	0.613268i	0.632888	+	0.774243i	$0.281869\pi$
$14$		0			0
$15$	−3.91251	+	2.25889i	−1.01021	+	0.583243i
$16$		0			0
$17$	−1.96229	+	1.13293i	−0.475925	+	0.274776i	−0.718717	−	0.695303i	$-0.755270\pi$
$17$	−1.96229	+	1.13293i	−0.475925	+	0.274776i	0.242792	+	0.970078i	$0.421937\pi$
$18$		0			0
$19$	3.20006	−	5.54267i	0.734145	−	1.27158i	−0.220953	−	0.975285i	$-0.570917\pi$
$19$	3.20006	−	5.54267i	0.734145	−	1.27158i	0.955097	−	0.296292i	$-0.0957501\pi$
$20$		0			0
$21$	−0.439857	+	0.253952i	−0.0959847	+	0.0554168i
$22$		0			0
$23$		−	2.97488i		−	0.620304i	−0.950687	−	0.310152i	$-0.899620\pi$
$23$		−	2.97488i		−	0.620304i	0.950687	−	0.310152i	$-0.100380\pi$
$24$		0			0
$25$	−4.70515	−	8.14956i	−0.941030	−	1.62991i
$26$		0			0
$27$		−	5.45504i		−	1.04982i
$28$		0			0
$29$	−8.86178			−1.64559			−0.822796	−	0.568337i	$-0.807587\pi$
$29$	−8.86178			−1.64559			−0.822796	+	0.568337i	$0.807587\pi$
$30$		0			0
$31$		−	0.284019i		−	0.0510113i	−0.999675	−	0.0255057i	$-0.991880\pi$
$31$		−	0.284019i		−	0.0510113i	0.999675	−	0.0255057i	$-0.00811958\pi$
$32$		0			0
$33$	−2.98537	+	5.17082i	−0.519687	+	0.900124i
$34$		0			0
$35$	−0.810025	−	1.40300i	−0.136919	−	0.237151i
$36$		0			0
$37$	6.05179	+	0.613070i	0.994908	+	0.100788i
$37$	6.05179	+	0.613070i	0.994908	+	0.100788i
$38$		0			0
$39$	−2.63154	+	1.51932i	−0.421384	+	0.243286i
$40$		0			0
$41$	−4.17825	+	7.23695i	−0.652534	+	1.13022i	0.329972	+	0.943991i	$0.392961\pi$
$41$	−4.17825	+	7.23695i	−0.652534	+	1.13022i	−0.982506	+	0.186231i	$0.940373\pi$
$42$		0			0
$43$	−7.89769			−1.20439			−0.602193	−	0.798350i	$-0.705706\pi$
$43$	−7.89769			−1.20439			−0.602193	+	0.798350i	$0.705706\pi$
$44$		0			0
$45$	6.01159			0.896155
$46$		0			0
$47$	−2.01684			−0.294186			−0.147093	−	0.989123i	$-0.546992\pi$
$47$	−2.01684			−0.294186			−0.147093	+	0.989123i	$0.546992\pi$
$48$		0			0
$49$	3.40893	+	5.90445i	0.486991	+	0.843493i
$50$		0			0
$51$	−2.69663			−0.377604
$52$		0			0
$53$	−5.23310	+	3.02133i	−0.718821	+	0.415012i	−0.814319	−	0.580418i	$-0.802889\pi$
$53$	−5.23310	+	3.02133i	−0.718821	+	0.415012i	0.0954974	+	0.995430i	$0.469556\pi$
$54$		0			0
$55$	−16.4933	−	9.52240i	−2.22395	−	1.28400i
$56$		0			0
$57$	6.59642	−	3.80844i	0.873717	−	0.504441i
$58$		0			0
$59$	2.68998	+	4.65918i	0.350205	+	0.606573i	0.986285	−	0.165050i	$-0.0527785\pi$
$59$	2.68998	+	4.65918i	0.350205	+	0.606573i	−0.636080	+	0.771623i	$0.719445\pi$
$60$		0			0
$61$	2.82477	−	4.89264i	0.361675	−	0.626439i	−0.626562	−	0.779372i	$-0.715538\pi$
$61$	2.82477	−	4.89264i	0.361675	−	0.626439i	0.988237	+	0.152933i	$0.0488718\pi$
$62$		0			0
$63$	0.675842			0.0851480
$64$		0			0
$65$	−4.84616	−	8.39380i	−0.601092	−	1.04112i
$66$		0			0
$67$	10.9562	+	6.32555i	1.33851	+	0.772790i	0.986587	−	0.163239i	$-0.0521942\pi$
$67$	10.9562	+	6.32555i	1.33851	+	0.772790i	0.351924	+	0.936029i	$0.385527\pi$
$68$		0			0
$69$	1.77022	−	3.06611i	0.213110	−	0.369117i
$70$		0			0
$71$	4.28852	−	7.42793i	0.508953	−	0.881533i	−0.490993	−	0.871163i	$-0.663366\pi$
$71$	4.28852	−	7.42793i	0.508953	−	0.881533i	0.999946	−	0.0103692i	$-0.00330067\pi$
$72$		0			0
$73$	−4.78445			−0.559978			−0.279989	−	0.960003i	$-0.590331\pi$
$73$	−4.78445			−0.559978			−0.279989	+	0.960003i	$0.590331\pi$
$74$		0			0
$75$		−	11.1993i		−	1.29319i
$76$		0			0
$77$	−1.85423	−	1.07054i	−0.211309	−	0.121999i
$78$		0			0
$79$	−4.67103	−	2.69682i	−0.525532	−	0.303416i	0.213663	−	0.976907i	$-0.431461\pi$
$79$	−4.67103	−	2.69682i	−0.525532	−	0.303416i	−0.739195	+	0.673491i	$0.764794\pi$
$80$		0			0
$81$	0.870623	−	1.50796i	0.0967358	−	0.167551i
$82$		0			0
$83$	−10.4077	+	6.00888i	−1.14239	+	0.659560i	−0.947022	−	0.321170i	$-0.895924\pi$
$83$	−10.4077	+	6.00888i	−1.14239	+	0.659560i	−0.195370	+	0.980730i	$0.562591\pi$
$84$		0			0
$85$		−	8.60140i		−	0.932953i
$86$		0			0
$87$	−9.13357	−	5.27327i	−0.979221	−	0.565354i
$88$		0			0
$89$	−9.89138	+	5.71079i	−1.04848	+	0.605343i	−0.922225	−	0.386654i	$-0.873631\pi$
$89$	−9.89138	+	5.71079i	−1.04848	+	0.605343i	−0.126260	+	0.991997i	$0.540297\pi$
$90$		0			0
$91$	−0.544820	−	0.943656i	−0.0571127	−	0.0989221i
$92$		0			0
$93$	0.169008	−	0.292730i	0.0175253	−	0.0303547i
$94$		0			0
$95$	12.1477	+	21.0405i	1.24633	+	2.15871i
$96$		0			0
$97$			2.39634i			0.243311i	0.992572	+	0.121656i	$0.0388204\pi$
$97$			2.39634i			0.243311i	−0.992572	+	0.121656i	$0.961180\pi$
$98$		0			0
$99$	6.88056	−	3.97249i	0.691522	−	0.399250i
$100$		0			0
$101$		−	5.41079i		−	0.538394i	−0.963085	−	0.269197i	$-0.913242\pi$
$101$		−	5.41079i		−	0.538394i	0.963085	−	0.269197i	$-0.0867583\pi$
$102$		0			0
$103$		−	4.06263i		−	0.400303i	−0.979765	−	0.200152i	$-0.935857\pi$
$103$		−	4.06263i		−	0.400303i	0.979765	−	0.200152i	$-0.0641435\pi$
$104$		0			0
$105$		−	1.92805i		−	0.188158i
$106$		0			0
$107$	4.35758	+	2.51585i	0.421263	+	0.243217i	0.695618	−	0.718412i	$-0.255131\pi$
$107$	4.35758	+	2.51585i	0.421263	+	0.243217i	−0.274354	+	0.961629i	$0.588464\pi$
$108$		0			0
$109$	7.71267	+	13.3587i	0.738739	+	1.27953i	0.953063	+	0.302771i	$0.0979119\pi$
$109$	7.71267	+	13.3587i	0.738739	+	1.27953i	−0.214324	+	0.976763i	$0.568755\pi$
$110$		0			0
$111$	5.87258	+	4.23303i	0.557401	+	0.401782i
$112$		0			0
$113$	3.32630	−	1.92044i	0.312912	−	0.180660i	−0.335317	−	0.942105i	$-0.608843\pi$
$113$	3.32630	−	1.92044i	0.312912	−	0.180660i	0.648229	+	0.761446i	$0.275510\pi$
$114$		0			0
$115$	9.77993	+	5.64645i	0.911984	+	0.526534i
$116$		0			0
$117$	4.04338			0.373810
$118$		0			0
$119$		−	0.966996i		−	0.0886444i
$120$		0			0
$121$	−14.1698			−1.28816
$122$		0			0
$123$	−8.61280	+	4.97260i	−0.776590	+	0.448364i
$124$		0			0
$125$	16.7419			1.49744
$126$		0			0
$127$	5.14882	+	8.91801i	0.456884	+	0.791346i	0.998794	−	0.0490904i	$-0.0156323\pi$
$127$	5.14882	+	8.91801i	0.456884	+	0.791346i	−0.541911	+	0.840436i	$0.682299\pi$
$128$		0			0
$129$	−8.13991	−	4.69958i	−0.716679	−	0.413775i
$130$		0			0
$131$	4.30960	+	7.46445i	0.376532	+	0.652172i	0.990555	−	0.137116i	$-0.0437833\pi$
$131$	4.30960	+	7.46445i	0.376532	+	0.652172i	−0.614023	+	0.789288i	$0.710450\pi$
$132$		0			0
$133$	1.36569	+	2.36544i	0.118420	+	0.205109i
$134$		0			0
$135$	17.9335	+	10.3539i	1.54347	+	0.891123i
$136$		0			0
$137$	11.6222			0.992952			0.496476	−	0.868051i	$-0.334627\pi$
$137$	11.6222			0.992952			0.496476	+	0.868051i	$0.334627\pi$
$138$		0			0
$139$	−18.7411	+	10.8202i	−1.58960	+	0.917754i	−0.596223	+	0.802819i	$0.703333\pi$
$139$	−18.7411	+	10.8202i	−1.58960	+	0.917754i	−0.993373	+	0.114935i	$0.963334\pi$
$140$		0			0
$141$	−2.07869	−	1.20013i	−0.175057	−	0.101069i
$142$		0			0
$143$	−11.0933	−	6.40474i	−0.927671	−	0.535591i
$144$		0			0
$145$	16.8201	−	29.1332i	1.39683	−	2.41938i
$146$		0			0
$147$			8.11405i			0.669235i
$148$		0			0
$149$			19.9351i			1.63315i	0.577241	+	0.816574i	$0.304129\pi$
$149$			19.9351i			1.63315i	−0.577241	+	0.816574i	$0.695871\pi$
$150$		0			0
$151$	−0.659829	+	1.14286i	−0.0536961	+	0.0930044i	−0.891624	−	0.452776i	$-0.850434\pi$
$151$	−0.659829	+	1.14286i	−0.0536961	+	0.0930044i	0.837928	+	0.545781i	$0.183767\pi$
$152$		0			0
$153$	3.10754	+	1.79414i	0.251229	+	0.145047i
$154$		0			0
$155$	0.933715	+	0.539081i	0.0749978	+	0.0433000i
$156$		0			0
$157$	0.690561	−	0.398695i	0.0551128	−	0.0318194i	−0.472190	−	0.881497i	$-0.656537\pi$
$157$	0.690561	−	0.398695i	0.0551128	−	0.0318194i	0.527303	+	0.849677i	$0.323203\pi$
$158$		0			0
$159$	−7.19146			−0.570320
$160$		0			0
$161$	1.09949	+	0.634791i	0.0866520	+	0.0500285i
$162$		0			0
$163$	−0.587958	−	1.01837i	−0.0460524	−	0.0797651i	0.842080	−	0.539352i	$-0.181331\pi$
$163$	−0.587958	−	1.01837i	−0.0460524	−	0.0797651i	−0.888133	+	0.459587i	$0.847997\pi$
$164$		0			0
$165$	−11.3328	−	19.6289i	−0.882253	−	1.52811i
$166$		0			0
$167$	0.795728	+	0.459414i	0.0615753	+	0.0355505i	0.530472	−	0.847703i	$-0.322015\pi$
$167$	0.795728	+	0.459414i	0.0615753	+	0.0355505i	−0.468896	+	0.883253i	$0.655348\pi$
$168$		0			0
$169$	3.24049	+	5.61269i	0.249268	+	0.431745i
$170$		0			0
$171$	−10.1354			−0.775074
$172$		0			0
$173$	−15.3956	+	8.88863i	−1.17050	+	0.675790i	−0.953798	−	0.300448i	$-0.902864\pi$
$173$	−15.3956	+	8.88863i	−1.17050	+	0.675790i	−0.216704	+	0.976237i	$0.569531\pi$
$174$		0			0
$175$	4.01602			0.303582
$176$		0			0
$177$			6.40276i			0.481261i
$178$		0			0
$179$	8.33094			0.622684			0.311342	−	0.950298i	$-0.399222\pi$
$179$	8.33094			0.622684			0.311342	+	0.950298i	$0.399222\pi$
$180$		0			0
$181$	−2.29381	−	1.32433i	−0.170498	−	0.0984370i	0.412323	−	0.911038i	$-0.364718\pi$
$181$	−2.29381	−	1.32433i	−0.170498	−	0.0984370i	−0.582821	+	0.812601i	$0.698051\pi$
$182$		0			0
$183$	5.82281	−	3.36180i	0.430434	−	0.248511i
$184$		0			0
$185$	−13.5020	+	18.7317i	−0.992690	+	1.37718i
$186$		0			0
$187$	−5.68385	−	9.84472i	−0.415644	−	0.719917i
$188$		0			0
$189$	2.01614	+	1.16402i	0.146653	+	0.0846699i
$190$		0			0
$191$			4.08292i			0.295430i	0.989030	+	0.147715i	$0.0471918\pi$
$191$			4.08292i			0.295430i	−0.989030	+	0.147715i	$0.952808\pi$
$192$		0			0
$193$		−	24.2788i		−	1.74762i	−0.486264	−	0.873812i	$-0.661641\pi$
$193$		−	24.2788i		−	1.74762i	0.486264	−	0.873812i	$-0.338359\pi$
$194$		0			0
$195$		−	11.5350i		−	0.826037i
$196$		0			0
$197$	8.37198	−	4.83356i	0.596479	−	0.344377i	−0.171176	−	0.985240i	$-0.554757\pi$
$197$	8.37198	−	4.83356i	0.596479	−	0.344377i	0.767655	+	0.640863i	$0.221423\pi$
$198$		0			0
$199$			6.22007i			0.440929i	0.975395	+	0.220465i	$0.0707573\pi$
$199$			6.22007i			0.440929i	−0.975395	+	0.220465i	$0.929243\pi$
$200$		0			0
$201$	7.52814	+	13.0391i	0.530994	+	0.919708i
$202$		0			0
$203$	1.89096	−	3.27524i	0.132720	−	0.229877i
$204$		0			0
$205$	−15.8610	−	27.4721i	−1.10778	−	1.91874i
$206$		0			0
$207$	−4.07993	+	2.35555i	−0.283574	+	0.163722i
$208$		0			0
$209$	27.8073	+	16.0546i	1.92347	+	1.11052i
$210$		0			0
$211$		−	8.16336i		−	0.561989i	−0.959709	−	0.280995i	$-0.909336\pi$
$211$		−	8.16336i		−	0.561989i	0.959709	−	0.280995i	$-0.0906643\pi$
$212$		0			0
$213$	8.84008	−	5.10382i	0.605713	−	0.349708i
$214$		0			0
$215$	14.9902	−	25.9637i	1.02232	−	1.77071i
$216$		0			0
$217$	0.104971	+	0.0606051i	0.00712591	+	0.00411414i
$218$		0			0
$219$	−4.93119	−	2.84703i	−0.333219	−	0.192384i
$220$		0			0
$221$		−	5.78527i		−	0.389160i
$222$		0			0
$223$	7.08841			0.474675			0.237337	−	0.971427i	$-0.423725\pi$
$223$	7.08841			0.474675			0.237337	+	0.971427i	$0.423725\pi$
$224$		0			0
$225$	−7.45120	+	12.9059i	−0.496747	+	0.860391i
$226$		0			0
$227$	6.23792	−	10.8044i	0.414025	−	0.717113i	−0.581300	−	0.813689i	$-0.697456\pi$
$227$	6.23792	−	10.8044i	0.414025	−	0.717113i	0.995326	+	0.0965761i	$0.0307891\pi$
$228$		0			0
$229$	−4.55067	−	2.62733i	−0.300716	−	0.173619i	0.342048	−	0.939682i	$-0.388879\pi$
$229$	−4.55067	−	2.62733i	−0.300716	−	0.173619i	−0.642765	+	0.766064i	$0.722213\pi$
$230$		0			0
$231$	−1.27406	−	2.20674i	−0.0838272	−	0.145193i
$232$		0			0
$233$	12.4536			0.815861			0.407931	−	0.913013i	$-0.366251\pi$
$233$	12.4536			0.815861			0.407931	+	0.913013i	$0.366251\pi$
$234$		0			0
$235$	3.82805	−	6.63037i	0.249714	−	0.432518i
$236$		0			0
$237$	−3.20953	−	5.55907i	−0.208481	−	0.361100i
$238$		0			0
$239$	22.7951	−	13.1608i	1.47449	−	0.851298i	0.474905	−	0.880037i	$-0.342482\pi$
$239$	22.7951	−	13.1608i	1.47449	−	0.851298i	0.999587	+	0.0287388i	$0.00914910\pi$
$240$		0			0
$241$	12.3723	+	7.14314i	0.796968	+	0.460130i	0.842410	−	0.538837i	$-0.181136\pi$
$241$	12.3723	+	7.14314i	0.796968	+	0.460130i	−0.0454417	+	0.998967i	$0.514470\pi$
$242$		0			0
$243$	−12.3780	+	7.14642i	−0.794047	+	0.458443i
$244$		0			0
$245$	−25.8812			−1.65349
$246$		0			0
$247$	8.17052	+	14.1518i	0.519878	+	0.900455i
$248$		0			0
$249$	−14.3025			−0.906385
$250$		0			0
$251$	−7.93287			−0.500718			−0.250359	−	0.968153i	$-0.580549\pi$
$251$	−7.93287			−0.500718			−0.250359	+	0.968153i	$0.580549\pi$
$252$		0			0
$253$	14.9248			0.938315
$254$		0			0
$255$	5.11833	−	8.86520i	0.320522	−	0.555160i
$256$		0			0
$257$	0.633271	−	0.365619i	0.0395024	−	0.0228067i	−0.480119	−	0.877204i	$-0.659406\pi$
$257$	0.633271	−	0.365619i	0.0395024	−	0.0228067i	0.519621	+	0.854397i	$0.326073\pi$
$258$		0			0
$259$	−1.51794	+	2.10587i	−0.0943203	+	0.130853i
$260$		0			0
$261$	7.01688	+	12.1536i	0.434334	+	0.752288i
$262$		0			0
$263$	−13.9848	+	24.2223i	−0.862338	+	1.49361i	0.00732770	+	0.999973i	$0.497667\pi$
$263$	−13.9848	+	24.2223i	−0.862338	+	1.49361i	−0.869666	+	0.493641i	$0.835666\pi$
$264$		0			0
$265$		−	22.9385i		−	1.40910i
$266$		0			0
$267$	−13.5930			−0.831878
$268$		0			0
$269$		−	7.77440i		−	0.474014i	−0.971508	−	0.237007i	$-0.923834\pi$
$269$		−	7.77440i		−	0.474014i	0.971508	−	0.237007i	$-0.0761664\pi$
$270$		0			0
$271$	9.35939	+	16.2109i	0.568543	+	0.984745i	0.996710	+	0.0810455i	$0.0258259\pi$
$271$	9.35939	+	16.2109i	0.568543	+	0.984745i	−0.428168	+	0.903699i	$0.640841\pi$
$272$		0			0
$273$		−	1.29680i		−	0.0784857i
$274$		0			0
$275$	40.8860	−	23.6055i	2.46552	−	1.42347i
$276$		0			0
$277$	−14.9708	+	25.9301i	−0.899507	+	1.55799i	−0.0713808	+	0.997449i	$0.522741\pi$
$277$	−14.9708	+	25.9301i	−0.899507	+	1.55799i	−0.828126	+	0.560542i	$0.810593\pi$
$278$		0			0
$279$	−0.389521	+	0.224890i	−0.0233200	+	0.0134638i
$280$		0			0
$281$	−8.39994	+	4.84971i	−0.501099	+	0.289309i	−0.729167	−	0.684336i	$-0.760092\pi$
$281$	−8.39994	+	4.84971i	−0.501099	+	0.289309i	0.228069	+	0.973645i	$0.426759\pi$
$282$		0			0
$283$	8.71005	−	15.0862i	0.517758	−	0.896784i	−0.482029	−	0.876155i	$-0.660100\pi$
$283$	8.71005	−	15.0862i	0.517758	−	0.896784i	0.999787	−	0.0206286i	$-0.00656675\pi$
$284$		0			0
$285$			28.9144i			1.71274i
$286$		0			0
$287$	−1.78315	−	3.08850i	−0.105256	−	0.182308i
$288$		0			0
$289$	−5.93295	+	10.2762i	−0.348997	+	0.604480i
$290$		0			0
$291$	−1.42596	+	2.46983i	−0.0835912	+	0.144784i
$292$		0			0
$293$	9.21758	+	5.32177i	0.538497	+	0.310901i	0.744470	−	0.667656i	$-0.232702\pi$
$293$	9.21758	+	5.32177i	0.538497	+	0.310901i	−0.205973	+	0.978558i	$0.566036\pi$
$294$		0			0
$295$	−20.4228			−1.18906
$296$		0			0
$297$	27.3677			1.58803
$298$		0			0
$299$	6.57795	+	3.79778i	0.380413	+	0.219631i
$300$		0			0
$301$	1.68524	−	2.91892i	0.0971357	−	0.168244i
$302$		0			0
$303$	3.21973	−	5.57674i	0.184969	−	0.320375i
$304$		0			0
$305$	10.7231	+	18.5729i	0.614002	+	1.06348i
$306$		0			0
$307$			19.6128i			1.11936i	0.828709	+	0.559680i	$0.189076\pi$
$307$			19.6128i			1.11936i	−0.828709	+	0.559680i	$0.810924\pi$
$308$		0			0
$309$	2.41750	−	4.18723i	0.137527	−	0.238203i
$310$		0			0
$311$	11.5797	−	6.68556i	0.656626	−	0.379103i	−0.134364	−	0.990932i	$-0.542899\pi$
$311$	11.5797	−	6.68556i	0.656626	−	0.379103i	0.790990	+	0.611829i	$0.209566\pi$
$312$		0			0
$313$	16.2902	−	9.40513i	0.920774	−	0.531609i	0.0368924	−	0.999319i	$-0.488254\pi$
$313$	16.2902	−	9.40513i	0.920774	−	0.531609i	0.883882	+	0.467710i	$0.154921\pi$
$314$		0			0
$315$	−1.28278	+	2.22184i	−0.0722763	+	0.125186i
$316$		0			0
$317$	1.03008	−	0.594719i	0.0578552	−	0.0334027i	−0.470793	−	0.882244i	$-0.656032\pi$
$317$	1.03008	−	0.594719i	0.0578552	−	0.0334027i	0.528649	+	0.848841i	$0.322699\pi$
$318$		0			0
$319$		−	44.4591i		−	2.48923i
$320$		0			0
$321$	2.99415	+	5.18602i	0.167117	+	0.289456i
$322$		0			0
$323$			14.5018i			0.806900i
$324$		0			0
$325$	24.0267			1.33276
$326$		0			0
$327$			18.3579i			1.01519i
$328$		0			0
$329$	0.430361	−	0.745406i	0.0237265	−	0.0410956i
$330$		0			0
$331$	−6.03836	−	10.4587i	−0.331898	−	0.574865i	0.650986	−	0.759090i	$-0.274356\pi$
$331$	−6.03836	−	10.4587i	−0.331898	−	0.574865i	−0.982884	+	0.184225i	$0.941022\pi$
$332$		0			0
$333$	−3.95109	−	8.78523i	−0.216518	−	0.481428i
$334$		0			0
$335$	−41.5907	+	24.0124i	−2.27234	+	1.31194i
$336$		0			0
$337$	5.72219	−	9.91113i	0.311708	−	0.539894i	−0.667024	−	0.745036i	$-0.732432\pi$
$337$	5.72219	−	9.91113i	0.311708	−	0.539894i	0.978732	+	0.205142i	$0.0657657\pi$
$338$		0			0
$339$	4.57109			0.248268
$340$		0			0
$341$	1.42491			0.0771632
$342$		0			0
$343$	−5.89703			−0.318410
$344$		0			0
$345$	6.71992	+	11.6392i	0.361788	+	0.626636i
$346$		0			0
$347$	−12.4825			−0.670094			−0.335047	−	0.942201i	$-0.608752\pi$
$347$	−12.4825			−0.670094			−0.335047	+	0.942201i	$0.608752\pi$
$348$		0			0
$349$	−27.1204	+	15.6580i	−1.45172	+	0.838152i	−0.998579	−	0.0532860i	$-0.983031\pi$
$349$	−27.1204	+	15.6580i	−1.45172	+	0.838152i	−0.453143	+	0.891438i	$0.649697\pi$
$350$		0			0
$351$	12.0620	+	6.96401i	0.643823	+	0.371711i
$352$		0			0
$353$	4.49580	−	2.59565i	0.239287	−	0.138153i	−0.375562	−	0.926797i	$-0.622550\pi$
$353$	4.49580	−	2.59565i	0.239287	−	0.138153i	0.614849	+	0.788645i	$0.289217\pi$
$354$		0			0
$355$	16.2796	+	28.1971i	0.864031	+	1.49655i
$356$		0			0
$357$	0.575418	−	0.996653i	0.0304543	−	0.0527485i
$358$		0			0
$359$	23.7552			1.25375			0.626876	−	0.779119i	$-0.284333\pi$
$359$	23.7552			1.25375			0.626876	+	0.779119i	$0.284333\pi$
$360$		0			0
$361$	−10.9808	−	19.0193i	−0.577938	−	1.00102i
$362$		0			0
$363$	−14.6044	−	8.43185i	−0.766532	−	0.442557i
$364$		0			0
$365$	9.08111	−	15.7289i	0.475327	−	0.823291i
$366$		0			0
$367$	17.5385	−	30.3775i	0.915501	−	1.58569i	0.109334	−	0.994005i	$-0.465128\pi$
$367$	17.5385	−	30.3775i	0.915501	−	1.58569i	0.806167	−	0.591688i	$-0.201538\pi$
$368$		0			0
$369$	13.2336			0.688913
$370$		0			0
$371$		−	2.57882i		−	0.133885i
$372$		0			0
$373$	24.4329	+	14.1063i	1.26509	+	0.730398i	0.974054	−	0.226316i	$-0.0726681\pi$
$373$	24.4329	+	14.1063i	1.26509	+	0.730398i	0.291032	+	0.956713i	$0.406001\pi$
$374$		0			0
$375$	17.2554	+	9.96239i	0.891063	+	0.514456i
$376$		0			0
$377$	11.3131	−	19.5949i	0.582655	−	1.00919i
$378$		0			0
$379$	6.51732	−	3.76278i	0.334772	−	0.193281i	−0.323186	−	0.946336i	$-0.604754\pi$
$379$	6.51732	−	3.76278i	0.334772	−	0.193281i	0.657958	+	0.753055i	$0.271420\pi$
$380$		0			0
$381$			12.2554i			0.627861i
$382$		0			0
$383$	−11.7019	−	6.75608i	−0.597938	−	0.345220i	0.170292	−	0.985394i	$-0.445529\pi$
$383$	−11.7019	−	6.75608i	−0.597938	−	0.345220i	−0.768230	+	0.640174i	$0.778862\pi$
$384$		0			0
$385$	7.03881	−	4.06386i	0.358731	−	0.207113i
$386$		0			0
$387$	6.25350	+	10.8314i	0.317883	+	0.550590i
$388$		0			0
$389$	12.1713	−	21.0813i	0.617110	−	1.06887i	−0.372901	−	0.927871i	$-0.621637\pi$
$389$	12.1713	−	21.0813i	0.617110	−	1.06887i	0.990010	−	0.140994i	$-0.0450298\pi$
$390$		0			0
$391$	3.37032	+	5.83757i	0.170444	+	0.295219i
$392$		0			0
$393$			10.2578i			0.517440i
$394$		0			0
$395$	17.7317	−	10.2374i	0.892177	−	0.515099i
$396$		0			0
$397$			37.9459i			1.90445i	0.305395	+	0.952226i	$0.401211\pi$
$397$			37.9459i			1.90445i	−0.305395	+	0.952226i	$0.598789\pi$
$398$		0			0
$399$			3.25064i			0.162736i
$400$		0			0
$401$			12.9699i			0.647685i	0.946111	+	0.323843i	$0.104975\pi$
$401$			12.9699i			0.647685i	−0.946111	+	0.323843i	$0.895025\pi$
$402$		0			0
$403$	0.628014	+	0.362584i	0.0312836	+	0.0180616i
$404$		0			0
$405$	3.30496	+	5.72436i	0.164225	+	0.284446i
$406$		0			0
$407$	−3.07574	+	30.3615i	−0.152459	+	1.50497i
$408$		0			0
$409$	−28.6468	+	16.5392i	−1.41649	+	0.817811i	−0.995989	−	0.0894801i	$-0.971479\pi$
$409$	−28.6468	+	16.5392i	−1.41649	+	0.817811i	−0.420502	+	0.907292i	$0.638146\pi$
$410$		0			0
$411$	11.9786	+	6.91588i	0.590863	+	0.341135i
$412$		0			0
$413$	−2.29599			−0.112978
$414$		0			0
$415$		−	45.6205i		−	2.23942i
$416$		0			0
$417$	−25.7545			−1.26120
$418$		0			0
$419$	26.9463	−	15.5574i	1.31641	−	0.760031i	0.333263	−	0.942834i	$-0.391850\pi$
$419$	26.9463	−	15.5574i	1.31641	−	0.760031i	0.983150	+	0.182803i	$0.0585170\pi$
$420$		0			0
$421$	−22.9118			−1.11665			−0.558327	−	0.829621i	$-0.688556\pi$
$421$	−22.9118			−1.11665			−0.558327	+	0.829621i	$0.688556\pi$
$422$		0			0
$423$	1.59696	+	2.76601i	0.0776467	+	0.134488i
$424$		0			0
$425$	18.4657	+	10.6612i	0.895720	+	0.517144i
$426$		0			0
$427$	1.20552	+	2.08803i	0.0583393	+	0.101047i
$428$		0			0
$429$	−7.62237	−	13.2023i	−0.368012	−	0.637415i
$430$		0			0
$431$	−9.41345	−	5.43486i	−0.453430	−	0.261788i	0.255848	−	0.966717i	$-0.417645\pi$
$431$	−9.41345	−	5.43486i	−0.453430	−	0.261788i	−0.709278	+	0.704929i	$0.750979\pi$
$432$		0			0
$433$	−33.2508			−1.59793			−0.798966	−	0.601376i	$-0.794619\pi$
$433$	−33.2508			−1.59793			−0.798966	+	0.601376i	$0.794619\pi$
$434$		0			0
$435$	34.6719	−	20.0178i	1.66239	−	0.959780i
$436$		0			0
$437$	−16.4888	−	9.51979i	−0.788764	−	0.455393i
$438$		0			0
$439$	11.2077	+	6.47079i	0.534916	+	0.308834i	0.743016	−	0.669274i	$-0.233395\pi$
$439$	11.2077	+	6.47079i	0.534916	+	0.308834i	−0.208100	+	0.978108i	$0.566728\pi$
$440$		0			0
$441$	5.39848	−	9.35044i	0.257070	−	0.445259i
$442$		0			0
$443$			1.77080i			0.0841332i	0.999115	+	0.0420666i	$0.0133942\pi$
$443$			1.77080i			0.0841332i	−0.999115	+	0.0420666i	$0.986606\pi$
$444$		0			0
$445$		−	43.3574i		−	2.05534i
$446$		0			0
$447$	−11.8625	+	20.5465i	−0.561079	+	0.971817i
$448$		0			0
$449$	−14.8682	−	8.58415i	−0.701673	−	0.405111i	0.106297	−	0.994334i	$-0.466101\pi$
$449$	−14.8682	−	8.58415i	−0.701673	−	0.405111i	−0.807970	+	0.589223i	$0.799434\pi$
$450$		0			0
$451$	−36.3074	−	20.9621i	−1.70965	−	0.987067i
$452$		0			0
$453$	−1.36013	+	0.785272i	−0.0639045	+	0.0368953i
$454$		0			0
$455$	4.13637			0.193916
$456$		0			0
$457$	−18.3049	−	10.5684i	−0.856268	−	0.494367i	0.00649254	−	0.999979i	$-0.497933\pi$
$457$	−18.3049	−	10.5684i	−0.856268	−	0.494367i	−0.862761	+	0.505612i	$0.831267\pi$
$458$		0			0
$459$	6.18017	+	10.7044i	0.288466	+	0.499637i
$460$		0			0
$461$	2.42205	+	4.19511i	0.112806	+	0.195386i	0.916901	−	0.399116i	$-0.130683\pi$
$461$	2.42205	+	4.19511i	0.112806	+	0.195386i	−0.804095	+	0.594501i	$0.797350\pi$
$462$		0			0
$463$	−29.1589	−	16.8349i	−1.35513	−	0.782383i	−0.366165	−	0.930550i	$-0.619330\pi$
$463$	−29.1589	−	16.8349i	−1.35513	−	0.782383i	−0.988962	+	0.148166i	$0.952663\pi$
$464$		0			0
$465$	0.641568	+	1.11123i	0.0297520	+	0.0515320i
$466$		0			0
$467$	−3.33438			−0.154297			−0.0771484	−	0.997020i	$-0.524582\pi$
$467$	−3.33438			−0.154297			−0.0771484	+	0.997020i	$0.524582\pi$
$468$		0			0
$469$	−4.67575	+	2.69955i	−0.215906	+	0.124653i
$470$		0			0
$471$	0.948987			0.0437270
$472$		0			0
$473$		−	39.6223i		−	1.82184i
$474$		0			0
$475$	−60.2271			−2.76341
$476$		0			0
$477$	8.28727	+	4.78466i	0.379448	+	0.219075i
$478$		0			0
$479$	−1.41671	+	0.817941i	−0.0647314	+	0.0373727i	−0.532016	−	0.846734i	$-0.678566\pi$
$479$	−1.41671	+	0.817941i	−0.0647314	+	0.0373727i	0.467285	+	0.884107i	$0.345232\pi$
$480$		0			0
$481$	−9.08143	+	12.5989i	−0.414078	+	0.574459i
$482$		0			0
$483$	0.755474	+	1.30852i	0.0343753	+	0.0595397i
$484$		0			0
$485$	−7.87799	−	4.54836i	−0.357721	−	0.206530i
$486$		0			0
$487$			5.27573i			0.239066i	0.992830	+	0.119533i	$0.0381397\pi$
$487$			5.27573i			0.239066i	−0.992830	+	0.119533i	$0.961860\pi$
$488$		0			0
$489$		−	1.39947i		−	0.0632864i
$490$		0			0
$491$		−	22.0882i		−	0.996828i	−0.866939	−	0.498414i	$-0.833916\pi$
$491$		−	22.0882i		−	0.996828i	0.866939	−	0.498414i	$-0.166084\pi$
$492$		0			0
$493$	17.3894	−	10.0398i	0.783179	−	0.452168i
$494$		0			0
$495$			30.1599i			1.35559i
$496$		0			0
$497$	1.83020	+	3.17000i	0.0820958	+	0.142194i
$498$		0			0
$499$	−9.83969	+	17.0428i	−0.440485	+	0.762943i	−0.997725	−	0.0674087i	$-0.978527\pi$
$499$	−9.83969	+	17.0428i	−0.440485	+	0.762943i	0.557240	+	0.830351i	$0.311860\pi$
$500$		0			0
$501$	0.546755	+	0.947008i	0.0244272	+	0.0423092i
$502$		0			0
$503$	31.4456	−	18.1551i	1.40209	−	0.809498i	0.407484	−	0.913212i	$-0.366406\pi$
$503$	31.4456	−	18.1551i	1.40209	−	0.809498i	0.994607	+	0.103714i	$0.0330728\pi$
$504$		0			0
$505$	17.7880	+	10.2699i	0.791557	+	0.457006i
$506$		0			0
$507$			7.71311i			0.342551i
$508$		0			0
$509$	5.13131	−	2.96256i	0.227441	−	0.131313i	−0.381950	−	0.924183i	$-0.624747\pi$
$509$	5.13131	−	2.96256i	0.227441	−	0.131313i	0.609391	+	0.792870i	$0.291414\pi$
$510$		0			0
$511$	1.02093	−	1.76830i	0.0451631	−	0.0782248i
$512$		0			0
$513$	−30.2355	−	17.4565i	−1.33493	−	0.770722i
$514$		0			0
$515$	13.3559	+	7.71106i	0.588533	+	0.339790i
$516$		0			0
$517$		−	10.1184i		−	0.445005i
$518$		0			0
$519$	−21.1570			−0.928688
$520$		0			0
$521$	−11.1420	+	19.2986i	−0.488141	+	0.845486i	−0.999907	−	0.0136393i	$-0.995658\pi$
$521$	−11.1420	+	19.2986i	−0.488141	+	0.845486i	0.511766	+	0.859125i	$0.328992\pi$
$522$		0			0
$523$	−12.7748	+	22.1267i	−0.558604	+	0.967531i	0.439009	+	0.898483i	$0.355330\pi$
$523$	−12.7748	+	22.1267i	−0.558604	+	0.967531i	−0.997613	+	0.0690486i	$0.978004\pi$
$524$		0			0
$525$	4.13919	+	2.38976i	0.180649	+	0.104298i
$526$		0			0
$527$	0.321773	+	0.557328i	0.0140167	+	0.0242776i
$528$		0			0
$529$	14.1501			0.615222
$530$		0			0
$531$	4.25992	−	7.37840i	0.184865	−	0.320195i
$532$		0			0
$533$	−10.6681	−	18.4776i	−0.462086	−	0.800356i
$534$		0			0
$535$	−16.5418	+	9.55040i	−0.715163	+	0.412900i
$536$		0			0
$537$	8.58645	+	4.95739i	0.370533	+	0.213927i
$538$		0			0
$539$	−29.6223	+	17.1025i	−1.27592	+	0.736655i
$540$		0			0
$541$	−1.59945			−0.0687659			−0.0343829	−	0.999409i	$-0.510947\pi$
$541$	−1.59945			−0.0687659			−0.0343829	+	0.999409i	$0.510947\pi$
$542$		0			0
$543$	−1.57611	−	2.72990i	−0.0676374	−	0.117151i
$544$		0			0
$545$	−58.5559			−2.50826
$546$		0			0
$547$	20.8576			0.891806			0.445903	−	0.895081i	$-0.352883\pi$
$547$	20.8576			0.891806			0.445903	+	0.895081i	$0.352883\pi$
$548$		0			0
$549$	−8.94676			−0.381839
$550$		0			0
$551$	−28.3583	+	49.1180i	−1.20810	+	2.09250i
$552$		0			0
$553$	1.99345	−	1.15092i	0.0847701	−	0.0489420i
$554$		0			0
$555$	−25.0626	+	11.2717i	−1.06385	+	0.478456i
$556$		0			0
$557$	13.7514	+	23.8181i	0.582665	+	1.00921i	0.995162	+	0.0982469i	$0.0313235\pi$
$557$	13.7514	+	23.8181i	0.582665	+	1.00921i	−0.412497	+	0.910959i	$0.635343\pi$
$558$		0			0
$559$	10.0823	−	17.4631i	0.426438	−	0.738611i
$560$		0			0
$561$		−	13.5289i		−	0.571189i
$562$		0			0
$563$	−19.3088			−0.813771			−0.406885	−	0.913479i	$-0.633385\pi$
$563$	−19.3088			−0.813771			−0.406885	+	0.913479i	$0.633385\pi$
$564$		0			0
$565$			14.5803i			0.613399i
$566$		0			0
$567$	0.371554	+	0.643550i	0.0156038	+	0.0270266i
$568$		0			0
$569$		−	19.8789i		−	0.833366i	−0.909052	−	0.416683i	$-0.863193\pi$
$569$		−	19.8789i		−	0.833366i	0.909052	−	0.416683i	$-0.136807\pi$
$570$		0			0
$571$	−20.4611	+	11.8132i	−0.856270	+	0.494368i	−0.862761	−	0.505611i	$-0.831267\pi$
$571$	−20.4611	+	11.8132i	−0.856270	+	0.494368i	0.00649165	+	0.999979i	$0.497934\pi$
$572$		0			0
$573$	−2.42957	+	4.20815i	−0.101497	+	0.175798i
$574$		0			0
$575$	−24.2439	+	13.9972i	−1.01104	+	0.583725i
$576$		0			0
$577$	13.9615	−	8.06069i	0.581226	−	0.335571i	−0.180395	−	0.983594i	$-0.557737\pi$
$577$	13.9615	−	8.06069i	0.581226	−	0.335571i	0.761620	+	0.648023i	$0.224404\pi$
$578$		0			0
$579$	14.4473	−	25.0234i	0.600408	−	1.03994i
$580$		0			0
$581$		−	5.12880i		−	0.212778i
$582$		0			0
$583$	−15.1579	−	26.2542i	−0.627775	−	1.08734i
$584$		0			0
$585$	−7.67451	+	13.2926i	−0.317302	+	0.549583i
$586$		0			0
$587$	−17.1134	+	29.6413i	−0.706345	+	1.22343i	0.259858	+	0.965647i	$0.416324\pi$
$587$	−17.1134	+	29.6413i	−0.706345	+	1.22343i	−0.966204	+	0.257779i	$0.917009\pi$
$588$		0			0
$589$	−1.57422	−	0.908879i	−0.0648648	−	0.0374497i
$590$		0			0
$591$	11.5050			0.473252
$592$		0			0
$593$	13.2117			0.542539			0.271269	−	0.962503i	$-0.412557\pi$
$593$	13.2117			0.542539			0.271269	+	0.962503i	$0.412557\pi$
$594$		0			0
$595$	3.17901	+	1.83540i	0.130327	+	0.0752441i
$596$		0			0
$597$	−3.70130	+	6.41084i	−0.151484	+	0.262378i
$598$		0			0
$599$	−4.55540	+	7.89019i	−0.186129	+	0.322384i	−0.943956	−	0.330070i	$-0.892927\pi$
$599$	−4.55540	+	7.89019i	−0.186129	+	0.322384i	0.757828	+	0.652455i	$0.226261\pi$
$600$		0			0
$601$	8.08129	+	13.9972i	0.329643	+	0.570958i	0.982441	−	0.186574i	$-0.0597384\pi$
$601$	8.08129	+	13.9972i	0.329643	+	0.570958i	−0.652798	+	0.757532i	$0.726405\pi$
$602$		0			0
$603$		−	20.0346i		−	0.815874i
$604$		0			0
$605$	26.8949	−	46.5834i	1.09343	−	1.89388i
$606$		0			0
$607$	4.02567	−	2.32422i	0.163397	−	0.0943374i	−0.416072	−	0.909332i	$-0.636593\pi$
$607$	4.02567	−	2.32422i	0.163397	−	0.0943374i	0.579469	+	0.814995i	$0.303260\pi$
$608$		0			0
$609$	3.89792	−	2.25046i	0.157952	−	0.0911934i
$610$		0			0
$611$	2.57473	−	4.45956i	0.104162	−	0.180415i
$612$		0			0
$613$	23.5335	−	13.5871i	0.950508	−	0.548776i	0.0572692	−	0.998359i	$-0.481761\pi$
$613$	23.5335	−	13.5871i	0.950508	−	0.548776i	0.893239	+	0.449583i	$0.148427\pi$
$614$		0			0
$615$		−	37.7529i		−	1.52234i
$616$		0			0
$617$	−3.69054	−	6.39220i	−0.148575	−	0.257340i	0.782126	−	0.623121i	$-0.214135\pi$
$617$	−3.69054	−	6.39220i	−0.148575	−	0.257340i	−0.930701	+	0.365780i	$0.880802\pi$
$618$		0			0
$619$		−	23.3239i		−	0.937465i	−0.883340	−	0.468732i	$-0.844711\pi$
$619$		−	23.3239i		−	0.937465i	0.883340	−	0.468732i	$-0.155289\pi$
$620$		0			0
$621$	−16.2281			−0.651210
$622$		0			0
$623$		−	4.87437i		−	0.195287i
$624$		0			0
$625$	−8.25113	+	14.2914i	−0.330045	+	0.571655i
$626$		0			0
$627$	19.1068	+	33.0939i	0.763051	+	1.32164i
$628$		0			0
$629$	−12.5699	+	5.65322i	−0.501196	+	0.225409i
$630$		0			0
$631$	−29.8300	+	17.2224i	−1.18751	+	0.685611i	−0.957741	−	0.287633i	$-0.907132\pi$
$631$	−29.8300	+	17.2224i	−1.18751	+	0.685611i	−0.229773	+	0.973244i	$0.573798\pi$
$632$		0			0
$633$	4.85767	−	8.41373i	0.193075	−	0.334416i
$634$		0			0
$635$	−39.0907			−1.55127
$636$		0			0
$637$	−17.4076			−0.689716
$638$		0			0
$639$	−13.5828			−0.537328
$640$		0			0
$641$	0.434949	+	0.753353i	0.0171794	+	0.0297557i	0.874487	−	0.485048i	$-0.161198\pi$
$641$	0.434949	+	0.753353i	0.0171794	+	0.0297557i	−0.857308	+	0.514804i	$0.827865\pi$
$642$		0			0
$643$	22.5045			0.887492			0.443746	−	0.896153i	$-0.353649\pi$
$643$	22.5045			0.887492			0.443746	+	0.896153i	$0.353649\pi$
$644$		0			0
$645$	30.8998	−	17.8400i	1.21668	−	0.702450i
$646$		0			0
$647$	−9.57728	−	5.52945i	−0.376522	−	0.217385i	0.299782	−	0.954008i	$-0.403086\pi$
$647$	−9.57728	−	5.52945i	−0.376522	−	0.217385i	−0.676304	+	0.736623i	$0.736419\pi$
$648$		0			0
$649$	−23.3749	+	13.4955i	−0.917544	+	0.529744i
$650$		0			0
$651$	0.0721271	+	0.124928i	0.00282688	+	0.00489630i
$652$		0			0
$653$	−16.3051	+	28.2413i	−0.638068	+	1.10517i	0.347788	+	0.937573i	$0.386933\pi$
$653$	−16.3051	+	28.2413i	−0.638068	+	1.10517i	−0.985856	+	0.167593i	$0.946401\pi$
$654$		0			0
$655$	−32.7193			−1.27845
$656$		0			0
$657$	3.78840	+	6.56169i	0.147799	+	0.255996i
$658$		0			0
$659$	35.2571	+	20.3557i	1.37342	+	0.792945i	0.991357	−	0.131191i	$-0.0418800\pi$
$659$	35.2571	+	20.3557i	1.37342	+	0.792945i	0.382064	+	0.924136i	$0.375213\pi$
$660$		0			0
$661$	4.03995	−	6.99740i	0.157136	−	0.272167i	−0.776699	−	0.629872i	$-0.783107\pi$
$661$	4.03995	−	6.99740i	0.157136	−	0.272167i	0.933835	+	0.357705i	$0.116441\pi$
$662$		0			0
$663$	3.44257	−	5.96270i	0.133698	−	0.231572i
$664$		0			0
$665$	−10.3685			−0.402074
$666$		0			0
$667$			26.3627i			1.02077i
$668$		0			0
$669$	7.30580	+	4.21801i	0.282459	+	0.163078i
$670$		0			0
$671$	24.5462	+	14.1717i	0.947594	+	0.547094i
$672$		0			0
$673$	−0.0151282	+	0.0262027i	−0.000583148	+	0.00101004i	−0.866317	−	0.499495i	$-0.833519\pi$
$673$	−0.0151282	+	0.0262027i	−0.000583148	+	0.00101004i	0.865734	+	0.500505i	$0.166852\pi$
$674$		0			0
$675$	−44.4562	+	25.6668i	−1.71112	+	0.987915i
$676$		0			0
$677$		−	19.8875i		−	0.764340i	−0.924092	−	0.382170i	$-0.875177\pi$
$677$		−	19.8875i		−	0.764340i	0.924092	−	0.382170i	$-0.124823\pi$
$678$		0			0
$679$	−0.885668	−	0.511340i	−0.0339888	−	0.0196234i
$680$		0			0
$681$	12.8585	−	7.42384i	0.492738	−	0.284482i
$682$		0			0
$683$	−15.3476	−	26.5829i	−0.587261	−	1.01717i	−0.994589	−	0.103884i	$-0.966873\pi$
$683$	−15.3476	−	26.5829i	−0.587261	−	1.01717i	0.407329	−	0.913282i	$-0.366460\pi$
$684$		0			0
$685$	−22.0595	+	38.2081i	−0.842849	+	1.45986i
$686$		0			0
$687$	−3.12682	−	5.41581i	−0.119296	−	0.206626i
$688$		0			0
$689$		−	15.4283i		−	0.587773i
$690$		0			0
$691$	−21.0711	+	12.1654i	−0.801584	+	0.462795i	−0.844025	−	0.536304i	$-0.819820\pi$
$691$	−21.0711	+	12.1654i	−0.801584	+	0.462795i	0.0424409	+	0.999099i	$0.486487\pi$
$692$		0			0
$693$			3.39066i			0.128801i
$694$		0			0
$695$		−	82.1486i		−	3.11607i
$696$		0			0
$697$		−	18.9347i		−	0.717201i
$698$		0			0
$699$	12.8355	+	7.41060i	0.485484	+	0.280294i
$700$		0			0
$701$	−12.9329	−	22.4005i	−0.488469	−	0.846054i	0.511443	−	0.859317i	$-0.329111\pi$
$701$	−12.9329	−	22.4005i	−0.488469	−	0.846054i	−0.999912	+	0.0132638i	$0.995778\pi$
$702$		0			0
$703$	22.7642	−	31.5812i	0.858566	−	1.19111i
$704$		0			0
$705$	7.89090	−	4.55581i	0.297188	−	0.171582i
$706$		0			0
$707$	1.99979	+	1.15458i	0.0752097	+	0.0434223i
$708$		0			0
$709$	−41.3033			−1.55118			−0.775589	−	0.631238i	$-0.782547\pi$
$709$	−41.3033			−1.55118			−0.775589	+	0.631238i	$0.782547\pi$
$710$		0			0
$711$			8.54152i			0.320332i
$712$		0			0
$713$	−0.844921			−0.0316425
$714$		0			0
$715$	42.1113	−	24.3130i	1.57487	−	0.909253i
$716$		0			0
$717$	31.3256			1.16988
$718$		0			0
$719$	26.1816	+	45.3478i	0.976407	+	1.69119i	0.675210	+	0.737625i	$0.264053\pi$
$719$	26.1816	+	45.3478i	0.976407	+	1.69119i	0.301197	+	0.953562i	$0.402614\pi$
$720$		0			0
$721$	1.50152	+	0.866901i	0.0559194	+	0.0322851i
$722$		0			0
$723$	8.50115	+	14.7244i	0.316161	+	0.547607i
$724$		0			0
$725$	41.6960	+	72.2196i	1.54855	+	2.68217i
$726$		0			0
$727$	1.52964	+	0.883136i	0.0567311	+	0.0327537i	0.528097	−	0.849184i	$-0.322906\pi$
$727$	1.52964	+	0.883136i	0.0567311	+	0.0327537i	−0.471366	+	0.881938i	$0.656239\pi$
$728$		0			0
$729$	−22.2339			−0.823476
$730$		0			0
$731$	15.4976	−	8.94752i	0.573198	−	0.330936i
$732$		0			0
$733$	38.1733	+	22.0394i	1.40996	+	0.814043i	0.995384	−	0.0959706i	$-0.0305955\pi$
$733$	38.1733	+	22.0394i	1.40996	+	0.814043i	0.414579	+	0.910013i	$0.363929\pi$
$734$		0			0
$735$	−26.6750	−	15.4008i	−0.983923	−	0.568068i
$736$		0			0
$737$	−31.7350	+	54.9666i	−1.16897	+	2.02472i
$738$		0			0
$739$			21.1088i			0.776498i	0.921554	+	0.388249i	$0.126920\pi$
$739$			21.1088i			0.776498i	−0.921554	+	0.388249i	$0.873080\pi$
$740$		0			0
$741$			19.4477i			0.714430i
$742$		0			0
$743$	−5.22651	+	9.05258i	−0.191742	+	0.332107i	−0.945828	−	0.324669i	$-0.894747\pi$
$743$	−5.22651	+	9.05258i	−0.191742	+	0.332107i	0.754086	+	0.656776i	$0.228080\pi$
$744$		0			0
$745$	−65.5369	−	37.8377i	−2.40109	−	1.38627i
$746$		0			0
$747$	16.4819	+	9.51582i	0.603041	+	0.348166i
$748$		0			0
$749$	−1.85968	+	1.07369i	−0.0679511	+	0.0392316i
$750$		0			0
$751$	31.6105			1.15348			0.576742	−	0.816927i	$-0.304324\pi$
$751$	31.6105			1.15348			0.576742	+	0.816927i	$0.304324\pi$
$752$		0			0
$753$	−8.17617	−	4.72051i	−0.297956	−	0.172025i
$754$		0			0
$755$	−2.50477	−	4.33839i	−0.0911579	−	0.157890i
$756$		0			0
$757$	−7.68179	−	13.3052i	−0.279199	−	0.483587i	0.691987	−	0.721910i	$-0.256736\pi$
$757$	−7.68179	−	13.3052i	−0.279199	−	0.483587i	−0.971186	+	0.238323i	$0.923402\pi$
$758$		0			0
$759$	15.3825	+	8.88112i	0.558351	+	0.322364i
$760$		0			0
$761$	6.77803	+	11.7399i	0.245703	+	0.425571i	0.962329	−	0.271887i	$-0.0876478\pi$
$761$	6.77803	+	11.7399i	0.245703	+	0.425571i	−0.716626	+	0.697458i	$0.754314\pi$
$762$		0			0
$763$	−6.58304			−0.238322
$764$		0			0
$765$	−11.7965	+	6.81070i	−0.426503	+	0.246241i
$766$		0			0
$767$	−13.7363			−0.495989
$768$		0			0
$769$			0.216663i			0.00781308i	0.999992	+	0.00390654i	$0.00124349\pi$
$769$			0.216663i			0.00781308i	−0.999992	+	0.00390654i	$0.998757\pi$
$770$		0			0
$771$	0.870258			0.0313416
$772$		0			0
$773$	10.0040	+	5.77582i	0.359819	+	0.207742i	0.669002	−	0.743261i	$-0.266722\pi$
$773$	10.0040	+	5.77582i	0.359819	+	0.207742i	−0.309182	+	0.951003i	$0.600055\pi$
$774$		0			0
$775$	−2.31463	+	1.33635i	−0.0831440	+	0.0480032i
$776$		0			0
$777$	−2.81761	+	1.26720i	−0.101081	+	0.0454605i
$778$		0			0
$779$	26.7414	+	46.3174i	0.958108	+	1.65949i
$780$		0			0
$781$	37.2656	+	21.5153i	1.33347	+	0.769877i
$782$		0			0
$783$			48.3414i			1.72758i
$784$		0			0
$785$			3.02697i			0.108037i
$786$		0			0
$787$		−	39.2723i		−	1.39991i	−0.714189	−	0.699953i	$-0.753204\pi$
$787$		−	39.2723i		−	1.39991i	0.714189	−	0.699953i	$-0.246796\pi$
$788$		0			0
$789$	−28.8274	+	16.6435i	−1.02628	+	0.592524i
$790$		0			0
$791$			1.63917i			0.0582820i
$792$		0			0
$793$	7.21231	+	12.4921i	0.256117	+	0.443607i
$794$		0			0
$795$	13.6497	−	23.6420i	0.484105	−	0.838495i
$796$		0			0
$797$	−19.4526	−	33.6930i	−0.689048	−	1.19347i	−0.972146	−	0.234375i	$-0.924696\pi$
$797$	−19.4526	−	33.6930i	−0.689048	−	1.19347i	0.283098	−	0.959091i	$-0.408638\pi$
$798$		0			0
$799$	3.95762	−	2.28493i	0.140010	−	0.0808350i
$800$		0			0
$801$	15.6643	+	9.04376i	0.553469	+	0.319546i
$802$		0			0
$803$		−	24.0034i		−	0.847061i
$804$		0			0
$805$	−4.17376	+	2.40972i	−0.147106	+	0.0849316i
$806$		0			0
$807$	4.62622	−	8.01284i	0.162851	−	0.282065i
$808$		0			0
$809$	41.3750	+	23.8879i	1.45467	+	0.839853i	0.998741	−	0.0501646i	$-0.0159746\pi$
$809$	41.3750	+	23.8879i	1.45467	+	0.839853i	0.455927	+	0.890017i	$0.349308\pi$
$810$		0			0
$811$	−33.0646	−	19.0899i	−1.16106	−	0.670336i	−0.209500	−	0.977809i	$-0.567184\pi$
$811$	−33.0646	−	19.0899i	−1.16106	−	0.670336i	−0.951557	+	0.307472i	$0.900517\pi$
$812$		0			0
$813$			22.2775i			0.781306i
$814$		0			0
$815$	4.46388			0.156363
$816$		0			0
$817$	−25.2731	+	43.7743i	−0.884194	+	1.53147i
$818$		0			0
$819$	−0.862792	+	1.49440i	−0.0301484	+	0.0522186i
$820$		0			0
$821$	−20.4469	−	11.8050i	−0.713601	−	0.411997i	0.0987922	−	0.995108i	$-0.468502\pi$
$821$	−20.4469	−	11.8050i	−0.713601	−	0.411997i	−0.812393	+	0.583111i	$0.801835\pi$
$822$		0			0
$823$	−23.5696	−	40.8237i	−0.821584	−	1.42303i	−0.904502	−	0.426469i	$-0.859757\pi$
$823$	−23.5696	−	40.8237i	−0.821584	−	1.42303i	0.0829178	−	0.996556i	$-0.473576\pi$
$824$		0			0
$825$	56.1865			1.95616
$826$		0			0
$827$	18.2448	−	31.6008i	0.634432	−	1.09887i	−0.352203	−	0.935924i	$-0.614567\pi$
$827$	18.2448	−	31.6008i	0.634432	−	1.09887i	0.986635	−	0.162945i	$-0.0520993\pi$
$828$		0			0
$829$	0.443993	+	0.769018i	0.0154205	+	0.0267091i	0.873633	−	0.486586i	$-0.161758\pi$
$829$	0.443993	+	0.769018i	0.0154205	+	0.0267091i	−0.858212	+	0.513295i	$0.828425\pi$
$830$		0			0
$831$	−30.8598	+	17.8169i	−1.07052	+	0.618063i
$832$		0			0
$833$	−13.3786	−	7.72416i	−0.463542	−	0.267626i
$834$		0			0
$835$	−3.02066	+	1.74398i	−0.104534	+	0.0603528i
$836$		0			0
$837$	−1.54934			−0.0535529
$838$		0			0
$839$	−0.939799	−	1.62778i	−0.0324455	−	0.0561972i	0.849347	−	0.527835i	$-0.176996\pi$
$839$	−0.939799	−	1.62778i	−0.0324455	−	0.0561972i	−0.881792	+	0.471638i	$0.843663\pi$
$840$		0			0
$841$	49.5312			1.70797
$842$		0			0
$843$	−11.5434			−0.397577
$844$		0			0
$845$	−24.6024			−0.846347
$846$		0			0
$847$	3.02361	−	5.23705i	0.103893	−	0.179947i
$848$		0			0
$849$	17.9544	−	10.3660i	0.616192	−	0.355759i
$850$		0			0
$851$	1.82381	−	18.0033i	0.0625193	−	0.617146i
$852$		0			0
$853$	−10.7629	−	18.6419i	−0.368516	−	0.638288i	0.620818	−	0.783955i	$-0.286801\pi$
$853$	−10.7629	−	18.6419i	−0.368516	−	0.638288i	−0.989334	+	0.145667i	$0.953467\pi$
$854$		0			0
$855$	19.2375	−	33.3203i	0.657908	−	1.13953i
$856$		0			0
$857$			5.86496i			0.200343i	0.994970	+	0.100172i	$0.0319392\pi$
$857$			5.86496i			0.200343i	−0.994970	+	0.100172i	$0.968061\pi$
$858$		0			0
$859$	34.0633			1.16223			0.581113	−	0.813823i	$-0.302618\pi$
$859$	34.0633			1.16223			0.581113	+	0.813823i	$0.302618\pi$
$860$		0			0
$861$		−	4.24430i		−	0.144645i
$862$		0			0
$863$	1.29900	+	2.24993i	0.0442184	+	0.0765886i	0.887288	−	0.461217i	$-0.152587\pi$
$863$	1.29900	+	2.24993i	0.0442184	+	0.0765886i	−0.843069	+	0.537805i	$0.819254\pi$
$864$		0			0
$865$		−	67.4841i		−	2.29453i
$866$		0			0
$867$	−12.2298	+	7.06089i	−0.415346	+	0.239800i
$868$		0			0
$869$	13.5298	−	23.4344i	0.458968	−	0.794956i
$870$		0			0
$871$	−27.9737	+	16.1506i	−0.947854	+	0.547244i
$872$		0			0
$873$	3.28648	−	1.89745i	0.111231	−	0.0642191i
$874$		0			0
$875$	−3.57246	+	6.18767i	−0.120771	+	0.209182i
$876$		0			0
$877$		−	20.1301i		−	0.679747i	−0.940471	−	0.339873i	$-0.889616\pi$
$877$		−	20.1301i		−	0.679747i	0.940471	−	0.339873i	$-0.110384\pi$
$878$		0			0
$879$	6.33352	+	10.9700i	0.213624	+	0.370008i
$880$		0			0
$881$	7.56128	−	13.0965i	0.254746	−	0.441233i	−0.710080	−	0.704121i	$-0.751341\pi$
$881$	7.56128	−	13.0965i	0.254746	−	0.441233i	0.964827	+	0.262887i	$0.0846748\pi$
$882$		0			0
$883$	17.6714	−	30.6078i	0.594691	−	1.03003i	−0.398900	−	0.916995i	$-0.630608\pi$
$883$	17.6714	−	30.6078i	0.594691	−	1.03003i	0.993590	−	0.113040i	$-0.0360588\pi$
$884$		0			0
$885$	−21.0492	−	12.1527i	−0.707560	−	0.408510i
$886$		0			0
$887$	−25.2875			−0.849070			−0.424535	−	0.905412i	$-0.639562\pi$
$887$	−25.2875			−0.849070			−0.424535	+	0.905412i	$0.639562\pi$
$888$		0			0
$889$	−4.39470			−0.147394
$890$		0			0
$891$	7.56538	+	4.36787i	0.253450	+	0.146329i
$892$		0			0
$893$	−6.45400	+	11.1787i	−0.215975	+	0.374080i
$894$		0			0
$895$	−15.8125	+	27.3881i	−0.528554	+	0.915482i
$896$		0			0
$897$	4.51980	+	7.82852i	0.150912	+	0.261387i
$898$		0			0
$899$			2.51691i			0.0839438i
$900$		0			0
$901$	6.84590	−	11.8575i	0.228070	−	0.395029i
$902$		0			0
$903$	3.47385	−	2.00563i	0.115603	−	0.0667432i
$904$		0			0
$905$	8.70753	−	5.02729i	0.289448	−	0.167113i
$906$		0			0
$907$	28.1116	−	48.6907i	0.933430	−	1.61675i	0.156020	−	0.987754i	$-0.450134\pi$
$907$	28.1116	−	48.6907i	0.933430	−	1.61675i	0.777410	−	0.628994i	$-0.216533\pi$
$908$		0			0
$909$	−7.42069	+	4.28434i	−0.246129	+	0.142103i
$910$		0			0
$911$		−	4.64280i		−	0.153823i	−0.997038	−	0.0769115i	$-0.975494\pi$
$911$		−	4.64280i		−	0.153823i	0.997038	−	0.0769115i	$-0.0245059\pi$
$912$		0			0
$913$	−30.1463	−	52.2148i	−0.997695	−	1.72806i
$914$		0			0
$915$			25.5234i			0.843777i
$916$		0			0
$917$	−3.67840			−0.121472
$918$		0			0
$919$			35.6030i			1.17444i	0.809429	+	0.587218i	$0.199777\pi$
$919$			35.6030i			1.17444i	−0.809429	+	0.587218i	$0.800223\pi$
$920$		0			0
$921$	−11.6707	+	20.2143i	−0.384564	+	0.666084i
$922$		0			0
$923$	10.9496	+	18.9653i	0.360410	+	0.624249i
$924$		0			0
$925$	−23.4783	−	52.2040i	−0.771962	−	1.71646i
$926$		0			0
$927$	−5.57174	+	3.21685i	−0.183000	+	0.105655i
$928$		0			0
$929$	−8.97349	+	15.5425i	−0.294411	+	0.509934i	−0.974848	−	0.222872i	$-0.928457\pi$
$929$	−8.97349	+	15.5425i	−0.294411	+	0.509934i	0.680437	+	0.732807i	$0.261790\pi$
$930$		0			0
$931$	43.6352			1.43009
$932$		0			0
$933$	15.9132			0.520973
$934$		0			0
$935$	43.1528			1.41125
$936$		0			0
$937$	−9.51155	−	16.4745i	−0.310729	−	0.538198i	0.667792	−	0.744348i	$-0.267240\pi$
$937$	−9.51155	−	16.4745i	−0.310729	−	0.538198i	−0.978520	+	0.206150i	$0.933906\pi$
$938$		0			0
$939$	22.3864			0.730551
$940$		0			0
$941$	−28.6171	+	16.5221i	−0.932892	+	0.538605i	−0.887725	−	0.460374i	$-0.847715\pi$
$941$	−28.6171	+	16.5221i	−0.932892	+	0.538605i	−0.0451668	+	0.998979i	$0.514382\pi$
$942$		0			0
$943$	21.5290	+	12.4298i	0.701081	+	0.404769i
$944$		0			0
$945$	−7.65345	+	4.41872i	−0.248967	+	0.143741i
$946$		0			0
$947$	−22.2200	−	38.4861i	−0.722052	−	1.25063i	−0.960176	−	0.279396i	$-0.909866\pi$
$947$	−22.2200	−	38.4861i	−0.722052	−	1.25063i	0.238124	−	0.971235i	$-0.423468\pi$
$948$		0			0
$949$	6.10793	−	10.5792i	0.198272	−	0.343417i
$950$		0			0
$951$	1.41557			0.0459029
$952$		0			0
$953$	−12.2359	−	21.1931i	−0.396359	−	0.686513i	0.596915	−	0.802305i	$-0.296393\pi$
$953$	−12.2359	−	21.1931i	−0.396359	−	0.686513i	−0.993274	+	0.115791i	$0.963060\pi$
$954$		0			0
$955$	−13.4227	−	7.74957i	−0.434347	−	0.250770i
$956$		0			0
$957$	26.4557	−	45.8227i	0.855193	−	1.48124i
$958$		0			0
$959$	−2.47999	+	4.29547i	−0.0800831	+	0.138708i
$960$		0			0
$961$	30.9193			0.997398
$962$		0			0
$963$		−	7.96834i		−	0.256776i
$964$		0			0
$965$	79.8167	+	46.0822i	2.56939	+	1.48344i
$966$		0			0
$967$	31.3620	+	18.1068i	1.00853	+	0.582277i	0.910762	−	0.412932i	$-0.135495\pi$
$967$	31.3620	+	18.1068i	1.00853	+	0.582277i	0.0977711	+	0.995209i	$0.468829\pi$
$968$		0			0
$969$	−8.62939	+	14.9465i	−0.277216	+	0.480152i
$970$		0			0
$971$	−28.9581	+	16.7190i	−0.929311	+	0.536538i	−0.886594	−	0.462549i	$-0.846935\pi$
$971$	−28.9581	+	16.7190i	−0.929311	+	0.536538i	−0.0427176	+	0.999087i	$0.513602\pi$
$972$		0			0
$973$		−	9.23540i		−	0.296073i
$974$		0			0
$975$	24.7636	+	14.2973i	0.793071	+	0.457880i
$976$		0			0
$977$	23.0664	−	13.3174i	0.737958	−	0.426060i	−0.0833682	−	0.996519i	$-0.526568\pi$
$977$	23.0664	−	13.3174i	0.737958	−	0.426060i	0.821327	+	0.570458i	$0.193234\pi$
$978$		0			0
$979$	−28.6508	−	49.6246i	−0.915683	−	1.58601i
$980$		0			0
$981$	12.2140	−	21.1552i	0.389962	−	0.675435i
$982$		0			0
$983$	−12.1934	−	21.1195i	−0.388908	−	0.673608i	0.603395	−	0.797442i	$-0.293814\pi$
$983$	−12.1934	−	21.1195i	−0.388908	−	0.673608i	−0.992303	+	0.123834i	$0.960481\pi$
$984$		0			0
$985$			36.6973i			1.16927i
$986$		0			0
$987$	0.887119	−	0.512179i	0.0282373	−	0.0163028i
$988$		0			0
$989$			23.4946i			0.747086i
$990$		0			0
$991$		−	16.0860i		−	0.510988i	−0.966811	−	0.255494i	$-0.917762\pi$
$991$		−	16.0860i		−	0.510988i	0.966811	−	0.255494i	$-0.0822382\pi$
$992$		0			0
$993$		−	14.3727i		−	0.456103i
$994$		0			0
$995$	−20.4485	−	11.8060i	−0.648263	−	0.374275i
$996$		0			0
$997$	10.6753	+	18.4902i	0.338091	+	0.585590i	0.984074	−	0.177762i	$-0.0568856\pi$
$997$	10.6753	+	18.4902i	0.338091	+	0.585590i	−0.645983	+	0.763352i	$0.723552\pi$
$998$		0			0
$999$	3.34432	−	33.0128i	0.105810	−	1.04448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1184.2.y.a.529.25		72
4.3	odd	2		296.2.q.a.85.24	yes	72
8.3	odd	2		296.2.q.a.85.12	✓	72
8.5	even	2	inner	1184.2.y.a.529.12		72
37.27	even	6	inner	1184.2.y.a.1137.12		72
148.27	odd	6		296.2.q.a.101.12	yes	72
296.27	odd	6		296.2.q.a.101.24	yes	72
296.101	even	6	inner	1184.2.y.a.1137.25		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.12	✓	72	8.3	odd	2
296.2.q.a.85.24	yes	72	4.3	odd	2
296.2.q.a.101.12	yes	72	148.27	odd	6
296.2.q.a.101.24	yes	72	296.27	odd	6
1184.2.y.a.529.12		72	8.5	even	2	inner
1184.2.y.a.529.25		72	1.1	even	1	trivial
1184.2.y.a.1137.12		72	37.27	even	6	inner
1184.2.y.a.1137.25		72	296.101	even	6	inner

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:	\( N \)	\(=\)	\( 1184 = 2^{5} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1184.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03067 + 0.595057i) q^{3} +(-1.89805 + 3.28751i) q^{5} +(-0.213384 + 0.369592i) q^{7} +(-0.791813 - 1.37146i) q^{9} +5.01695i q^{11} +(-1.27662 + 2.21117i) q^{13} +(-3.91251 + 2.25889i) q^{15} +(-1.96229 + 1.13293i) q^{17} +(3.20006 - 5.54267i) q^{19} +(-0.439857 + 0.253952i) q^{21} -2.97488i q^{23} +(-4.70515 - 8.14956i) q^{25} -5.45504i q^{27} -8.86178 q^{29} -0.284019i q^{31} +(-2.98537 + 5.17082i) q^{33} +(-0.810025 - 1.40300i) q^{35} +(6.05179 + 0.613070i) q^{37} +(-2.63154 + 1.51932i) q^{39} +(-4.17825 + 7.23695i) q^{41} -7.89769 q^{43} +6.01159 q^{45} -2.01684 q^{47} +(3.40893 + 5.90445i) q^{49} -2.69663 q^{51} +(-5.23310 + 3.02133i) q^{53} +(-16.4933 - 9.52240i) q^{55} +(6.59642 - 3.80844i) q^{57} +(2.68998 + 4.65918i) q^{59} +(2.82477 - 4.89264i) q^{61} +0.675842 q^{63} +(-4.84616 - 8.39380i) q^{65} +(10.9562 + 6.32555i) q^{67} +(1.77022 - 3.06611i) q^{69} +(4.28852 - 7.42793i) q^{71} -4.78445 q^{73} -11.1993i q^{75} +(-1.85423 - 1.07054i) q^{77} +(-4.67103 - 2.69682i) q^{79} +(0.870623 - 1.50796i) q^{81} +(-10.4077 + 6.00888i) q^{83} -8.60140i q^{85} +(-9.13357 - 5.27327i) q^{87} +(-9.89138 + 5.71079i) q^{89} +(-0.544820 - 0.943656i) q^{91} +(0.169008 - 0.292730i) q^{93} +(12.1477 + 21.0405i) q^{95} +2.39634i q^{97} +(6.88056 - 3.97249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) \) 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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