LMFDB - Embedded newform 288.2.w.a.35.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(35,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			35.8
Character	$\chi$	$=$	288.35
Dual form			288.2.w.a.107.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32473 - 0.495070i) q^{2} +(1.50981 - 1.31167i) q^{4} +(-0.0505677 + 0.0209458i) q^{5} +(1.44150 + 1.44150i) q^{7} +(1.35072 - 2.48506i) q^{8} +(-0.0566189 + 0.0527821i) q^{10} +(0.320987 - 0.132957i) q^{11} +(0.623666 - 1.50566i) q^{13} +(2.62325 + 1.19596i) q^{14} +(0.559063 - 3.96074i) q^{16} -5.65026 q^{17} +(4.13118 + 1.71119i) q^{19} +(-0.0488738 + 0.0979522i) q^{20} +(0.359398 - 0.335043i) q^{22} +(-3.03457 - 3.03457i) q^{23} +(-3.53342 + 3.53342i) q^{25} +(0.0807799 - 2.30335i) q^{26} +(4.06717 + 0.285627i) q^{28} +(-0.721807 + 1.74260i) q^{29} +5.26441i q^{31} +(-1.22024 - 5.52368i) q^{32} +(-7.48507 + 2.79728i) q^{34} +(-0.103087 - 0.0427001i) q^{35} +(-1.32038 - 3.18767i) q^{37} +(6.31986 + 0.221641i) q^{38} +(-0.0162513 + 0.153956i) q^{40} +(-6.90990 + 6.90990i) q^{41} +(3.40135 + 8.21159i) q^{43} +(0.310235 - 0.621769i) q^{44} +(-5.52231 - 2.51766i) q^{46} -3.23039i q^{47} -2.84413i q^{49} +(-2.93153 + 6.43010i) q^{50} +(-1.03331 - 3.09131i) q^{52} +(0.579972 + 1.40018i) q^{53} +(-0.0134467 + 0.0134467i) q^{55} +(5.52930 - 1.63516i) q^{56} +(-0.0934916 + 2.66581i) q^{58} +(4.21939 + 10.1865i) q^{59} +(-12.1464 - 5.03120i) q^{61} +(2.60625 + 6.97392i) q^{62} +(-4.35109 - 6.71327i) q^{64} +0.0892011i q^{65} +(3.34709 - 8.08060i) q^{67} +(-8.53083 + 7.41126i) q^{68} +(-0.157702 - 0.00553070i) q^{70} +(9.36679 - 9.36679i) q^{71} +(-1.72215 - 1.72215i) q^{73} +(-3.32726 - 3.56912i) q^{74} +(8.48182 - 2.83516i) q^{76} +(0.654363 + 0.271046i) q^{77} -15.1224 q^{79} +(0.0546904 + 0.211996i) q^{80} +(-5.73286 + 12.5746i) q^{82} +(-2.48612 + 6.00202i) q^{83} +(0.285721 - 0.118349i) q^{85} +(8.57118 + 9.19422i) q^{86} +(0.103158 - 0.977262i) q^{88} +(2.70367 + 2.70367i) q^{89} +(3.06943 - 1.27140i) q^{91} +(-8.56197 - 0.601286i) q^{92} +(-1.59927 - 4.27939i) q^{94} -0.244747 q^{95} +6.43802 q^{97} +(-1.40804 - 3.76770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52}+ \cdots - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	1.32473	−	0.495070i	0.936725	−	0.350067i
$2$	1.32473	−	0.495070i	0.936725	−	0.350067i
$3$		0			0
$3$		0			0
$4$	1.50981	−	1.31167i	0.754906	−	0.655833i
$5$	−0.0505677	+	0.0209458i	−0.0226146	+	0.00936726i	−0.393962	−	0.919127i	$-0.628896\pi$
$5$	−0.0505677	+	0.0209458i	−0.0226146	+	0.00936726i	0.371347	+	0.928494i	$0.378896\pi$
$6$		0			0
$7$	1.44150	+	1.44150i	0.544837	+	0.544837i	0.924943	−	0.380106i	$-0.124112\pi$
$7$	1.44150	+	1.44150i	0.544837	+	0.544837i	−0.380106	+	0.924943i	$0.624112\pi$
$8$	1.35072	−	2.48506i	0.477553	−	0.878603i
$9$		0			0
$10$	−0.0566189	+	0.0527821i	−0.0179045	+	0.0166912i
$11$	0.320987	−	0.132957i	0.0967813	−	0.0400881i	−0.333767	−	0.942655i	$-0.608320\pi$
$11$	0.320987	−	0.132957i	0.0967813	−	0.0400881i	0.430549	+	0.902567i	$0.358320\pi$
$12$		0			0
$13$	0.623666	−	1.50566i	0.172974	−	0.417595i	−0.813489	−	0.581580i	$-0.802435\pi$
$13$	0.623666	−	1.50566i	0.172974	−	0.417595i	0.986463	+	0.163985i	$0.0524347\pi$
$14$	2.62325	+	1.19596i	0.701092	+	0.319633i
$15$		0			0
$16$	0.559063	−	3.96074i	0.139766	−	0.990185i
$17$	−5.65026			−1.37039			−0.685195	−	0.728360i	$-0.740283\pi$
$17$	−5.65026			−1.37039			−0.685195	+	0.728360i	$0.740283\pi$
$18$		0			0
$19$	4.13118	+	1.71119i	0.947758	+	0.392574i	0.802388	−	0.596803i	$-0.203563\pi$
$19$	4.13118	+	1.71119i	0.947758	+	0.392574i	0.145370	+	0.989377i	$0.453563\pi$
$20$	−0.0488738	+	0.0979522i	−0.0109285	+	0.0219028i
$21$		0			0
$22$	0.359398	−	0.335043i	0.0766239	−	0.0714315i
$23$	−3.03457	−	3.03457i	−0.632752	−	0.632752i	0.316006	−	0.948757i	$-0.397658\pi$
$23$	−3.03457	−	3.03457i	−0.632752	−	0.632752i	−0.948757	+	0.316006i	$0.897658\pi$
$24$		0			0
$25$	−3.53342	+	3.53342i	−0.706683	+	0.706683i
$26$	0.0807799	−	2.30335i	0.0158422	−	0.451724i
$27$		0			0
$28$	4.06717	+	0.285627i	0.768623	+	0.0539785i
$29$	−0.721807	+	1.74260i	−0.134036	+	0.323592i	−0.976620	−	0.214973i	$-0.931034\pi$
$29$	−0.721807	+	1.74260i	−0.134036	+	0.323592i	0.842584	+	0.538565i	$0.181034\pi$
$30$		0			0
$31$			5.26441i			0.945516i	0.881192	+	0.472758i	$0.156742\pi$
$31$			5.26441i			0.945516i	−0.881192	+	0.472758i	$0.843258\pi$
$32$	−1.22024	−	5.52368i	−0.215709	−	0.976458i
$33$		0			0
$34$	−7.48507	+	2.79728i	−1.28368	+	0.479729i
$35$	−0.103087	−	0.0427001i	−0.0174249	−	0.00721763i
$36$		0			0
$37$	−1.32038	−	3.18767i	−0.217069	−	0.524050i	0.777409	−	0.628995i	$-0.216533\pi$
$37$	−1.32038	−	3.18767i	−0.217069	−	0.524050i	−0.994478	+	0.104945i	$0.966533\pi$
$38$	6.31986	+	0.221641i	1.02522	+	0.0359549i
$39$		0			0
$40$	−0.0162513	+	0.153956i	−0.00256956	+	0.0243426i
$41$	−6.90990	+	6.90990i	−1.07915	+	1.07915i	−0.0825597	+	0.996586i	$0.526310\pi$
$41$	−6.90990	+	6.90990i	−1.07915	+	1.07915i	−0.996586	+	0.0825597i	$0.973690\pi$
$42$		0			0
$43$	3.40135	+	8.21159i	0.518701	+	1.25226i	0.938701	+	0.344731i	$0.112030\pi$
$43$	3.40135	+	8.21159i	0.518701	+	1.25226i	−0.420000	+	0.907524i	$0.637970\pi$
$44$	0.310235	−	0.621769i	0.0467696	−	0.0937351i
$45$		0			0
$46$	−5.52231	−	2.51766i	−0.814219	−	0.371208i
$47$		−	3.23039i		−	0.471201i	−0.971850	−	0.235600i	$-0.924294\pi$
$47$		−	3.23039i		−	0.471201i	0.971850	−	0.235600i	$-0.0757057\pi$
$48$		0			0
$49$		−	2.84413i		−	0.406305i
$50$	−2.93153	+	6.43010i	−0.414581	+	0.909354i
$51$		0			0
$52$	−1.03331	−	3.09131i	−0.143294	−	0.428687i
$53$	0.579972	+	1.40018i	0.0796653	+	0.192329i	0.958694	−	0.284440i	$-0.0918077\pi$
$53$	0.579972	+	1.40018i	0.0796653	+	0.192329i	−0.879029	+	0.476769i	$0.841808\pi$
$54$		0			0
$55$	−0.0134467	+	0.0134467i	−0.00181315	+	0.00181315i
$56$	5.52930	−	1.63516i	0.738884	−	0.218507i
$57$		0			0
$58$	−0.0934916	+	2.66581i	−0.0122760	+	0.350038i
$59$	4.21939	+	10.1865i	0.549317	+	1.32617i	0.917988	+	0.396609i	$0.129813\pi$
$59$	4.21939	+	10.1865i	0.549317	+	1.32617i	−0.368671	+	0.929560i	$0.620187\pi$
$60$		0			0
$61$	−12.1464	−	5.03120i	−1.55519	−	0.644180i	−0.570942	−	0.820990i	$-0.693422\pi$
$61$	−12.1464	−	5.03120i	−1.55519	−	0.644180i	−0.984245	+	0.176811i	$0.943422\pi$
$62$	2.60625	+	6.97392i	0.330994	+	0.885688i
$63$		0			0
$64$	−4.35109	−	6.71327i	−0.543886	−	0.839159i
$65$			0.0892011i			0.0110640i
$66$		0			0
$67$	3.34709	−	8.08060i	0.408913	−	0.987203i	−0.576512	−	0.817089i	$-0.695586\pi$
$67$	3.34709	−	8.08060i	0.408913	−	0.987203i	0.985424	−	0.170114i	$-0.0544135\pi$
$68$	−8.53083	+	7.41126i	−1.03452	+	0.898747i
$69$		0			0
$70$	−0.157702	−	0.00553070i	−0.0188490	−	0.000661045i
$71$	9.36679	−	9.36679i	1.11163	−	1.11163i	0.118704	−	0.992930i	$-0.462126\pi$
$71$	9.36679	−	9.36679i	1.11163	−	1.11163i	0.992930	−	0.118704i	$-0.0378741\pi$
$72$		0			0
$73$	−1.72215	−	1.72215i	−0.201562	−	0.201562i	0.599107	−	0.800669i	$-0.295522\pi$
$73$	−1.72215	−	1.72215i	−0.201562	−	0.201562i	−0.800669	+	0.599107i	$0.795522\pi$
$74$	−3.32726	−	3.56912i	−0.386786	−	0.414902i
$75$		0			0
$76$	8.48182	−	2.83516i	0.972932	−	0.325215i
$77$	0.654363	+	0.271046i	0.0745716	+	0.0308886i
$78$		0			0
$79$	−15.1224			−1.70140			−0.850702	−	0.525648i	$-0.823823\pi$
$79$	−15.1224			−1.70140			−0.850702	+	0.525648i	$0.823823\pi$
$80$	0.0546904	+	0.211996i	0.00611458	+	0.0237018i
$81$		0			0
$82$	−5.73286	+	12.5746i	−0.633089	+	1.38864i
$83$	−2.48612	+	6.00202i	−0.272887	+	0.658807i	−0.999604	−	0.0281294i	$-0.991045\pi$
$83$	−2.48612	+	6.00202i	−0.272887	+	0.658807i	0.726717	+	0.686936i	$0.241045\pi$
$84$		0			0
$85$	0.285721	−	0.118349i	0.0309908	−	0.0128368i
$86$	8.57118	+	9.19422i	0.924254	+	0.991438i
$87$		0			0
$88$	0.103158	−	0.977262i	0.0109967	−	0.104177i
$89$	2.70367	+	2.70367i	0.286588	+	0.286588i	0.835730	−	0.549141i	$-0.185045\pi$
$89$	2.70367	+	2.70367i	0.286588	+	0.286588i	−0.549141	+	0.835730i	$0.685045\pi$
$90$		0			0
$91$	3.06943	−	1.27140i	0.321764	−	0.133279i
$92$	−8.56197	−	0.601286i	−0.892647	−	0.0626884i
$93$		0			0
$94$	−1.59927	−	4.27939i	−0.164952	−	0.441385i
$95$	−0.244747			−0.0251105
$96$		0			0
$97$	6.43802			0.653682			0.326841	−	0.945079i	$-0.394016\pi$
$97$	6.43802			0.653682			0.326841	+	0.945079i	$0.394016\pi$
$98$	−1.40804	−	3.76770i	−0.142234	−	0.380596i
$99$		0			0
$100$	−0.700130	+	9.96945i	−0.0700130	+	0.996945i
$101$	17.7633	−	7.35780i	1.76751	−	0.732128i	0.772206	−	0.635372i	$-0.219153\pi$
$101$	17.7633	−	7.35780i	1.76751	−	0.732128i	0.995308	−	0.0967565i	$-0.0308468\pi$
$102$		0			0
$103$	6.97813	+	6.97813i	0.687575	+	0.687575i	0.961695	−	0.274120i	$-0.0883866\pi$
$103$	6.97813	+	6.97813i	0.687575	+	0.687575i	−0.274120	+	0.961695i	$0.588387\pi$
$104$	−2.89927	−	3.58358i	−0.284296	−	0.351399i
$105$		0			0
$106$	1.46149	+	1.56773i	0.141952	+	0.152271i
$107$	13.1509	−	5.44730i	1.27135	−	0.526611i	0.357976	−	0.933731i	$-0.383467\pi$
$107$	13.1509	−	5.44730i	1.27135	−	0.526611i	0.913375	+	0.407120i	$0.133467\pi$
$108$		0			0
$109$	6.94514	−	16.7671i	0.665224	−	1.60599i	−0.124280	−	0.992247i	$-0.539662\pi$
$109$	6.94514	−	16.7671i	0.665224	−	1.60599i	0.789504	−	0.613745i	$-0.210338\pi$
$110$	−0.0111562	+	0.0244703i	−0.00106370	+	0.00233315i
$111$		0			0
$112$	6.51531	−	4.90353i	0.615639	−	0.463340i
$113$	−11.5862			−1.08994			−0.544969	−	0.838456i	$-0.683458\pi$
$113$	−11.5862			−1.08994			−0.544969	+	0.838456i	$0.683458\pi$
$114$		0			0
$115$	0.217013	+	0.0898897i	0.0202366	+	0.00838226i
$116$	1.19591	+	3.57776i	0.111038	+	0.332187i
$117$		0			0
$118$	10.6326	+	11.4055i	0.978807	+	1.04996i
$119$	−8.14488	−	8.14488i	−0.746640	−	0.746640i
$120$		0			0
$121$	−7.69282	+	7.69282i	−0.699347	+	0.699347i
$122$	−18.5815	−	0.651663i	−1.68229	−	0.0589988i
$123$		0			0
$124$	6.90515	+	7.94827i	0.620101	+	0.713776i
$125$	0.209396	−	0.505526i	0.0187289	−	0.0452156i
$126$		0			0
$127$		−	11.5409i		−	1.02409i	−0.858958	−	0.512045i	$-0.828888\pi$
$127$		−	11.5409i		−	1.02409i	0.858958	−	0.512045i	$-0.171112\pi$
$128$	−9.08755	−	6.73917i	−0.803233	−	0.595664i
$129$		0			0
$130$	0.0441608	+	0.118167i	0.00387315	+	0.0103640i
$131$	1.46501	+	0.606825i	0.127998	+	0.0530186i	0.445763	−	0.895151i	$-0.352932\pi$
$131$	1.46501	+	0.606825i	0.127998	+	0.0530186i	−0.317765	+	0.948169i	$0.602932\pi$
$132$		0			0
$133$	3.48843	+	8.42181i	0.302485	+	0.730263i
$134$	0.433530	−	12.3616i	0.0374513	−	1.06788i
$135$		0			0
$136$	−7.63195	+	14.0413i	−0.654434	+	1.20403i
$137$	2.76283	−	2.76283i	0.236044	−	0.236044i	−0.579166	−	0.815210i	$-0.696622\pi$
$137$	2.76283	−	2.76283i	0.236044	−	0.236044i	0.815210	+	0.579166i	$0.196622\pi$
$138$		0			0
$139$	2.52007	+	6.08399i	0.213750	+	0.516037i	0.993994	−	0.109438i	$-0.0349052\pi$
$139$	2.52007	+	6.08399i	0.213750	+	0.516037i	−0.780244	+	0.625475i	$0.784905\pi$
$140$	−0.211650	+	0.0707468i	−0.0178877	+	0.00597919i
$141$		0			0
$142$	7.77124	−	17.0457i	0.652148	−	1.43044i
$143$		−	0.566219i		−	0.0473496i
$144$		0			0
$145$		−	0.103238i		−	0.00857345i
$146$	−3.13396	−	1.42879i	−0.259368	−	0.118248i
$147$		0			0
$148$	−6.17468	−	3.08089i	−0.507556	−	0.253248i
$149$	−2.06361	−	4.98199i	−0.169057	−	0.408140i	0.816531	−	0.577301i	$-0.195894\pi$
$149$	−2.06361	−	4.98199i	−0.169057	−	0.408140i	−0.985588	+	0.169161i	$0.945894\pi$
$150$		0			0
$151$	0.971232	−	0.971232i	0.0790378	−	0.0790378i	−0.666483	−	0.745520i	$-0.732201\pi$
$151$	0.971232	−	0.971232i	0.0790378	−	0.0790378i	0.745520	+	0.666483i	$0.232201\pi$
$152$	9.83251	−	7.95490i	0.797522	−	0.645228i
$153$		0			0
$154$	1.00104	+	0.0351070i	0.0806661	+	0.00282901i
$155$	−0.110268	−	0.266209i	−0.00885690	−	0.0213824i
$156$		0			0
$157$	−10.5849	−	4.38441i	−0.844767	−	0.349914i	−0.0820357	−	0.996629i	$-0.526142\pi$
$157$	−10.5849	−	4.38441i	−0.844767	−	0.349914i	−0.762731	+	0.646715i	$0.776142\pi$
$158$	−20.0331	+	7.48665i	−1.59375	+	0.595606i
$159$		0			0
$160$	0.177403	+	0.253761i	0.0140249	+	0.0200616i
$161$		−	8.74869i		−	0.689493i
$162$		0			0
$163$	7.42825	−	17.9334i	0.581826	−	1.40465i	−0.309331	−	0.950955i	$-0.600105\pi$
$163$	7.42825	−	17.9334i	0.581826	−	1.40465i	0.891156	−	0.453697i	$-0.149895\pi$
$164$	−1.36917	+	19.4961i	−0.106914	+	1.52239i
$165$		0			0
$166$	−0.322013	+	9.18185i	−0.0249930	+	0.712649i
$167$	6.24060	−	6.24060i	0.482912	−	0.482912i	−0.423148	−	0.906060i	$-0.639075\pi$
$167$	6.24060	−	6.24060i	0.482912	−	0.482912i	0.906060	+	0.423148i	$0.139075\pi$
$168$		0			0
$169$	7.31433	+	7.31433i	0.562641	+	0.562641i
$170$	0.319911	−	0.298233i	0.0245361	−	0.0228734i
$171$		0			0
$172$	15.9063	+	7.93651i	1.21284	+	0.605153i
$173$	9.66545	+	4.00356i	0.734850	+	0.304385i	0.718544	−	0.695482i	$-0.244809\pi$
$173$	9.66545	+	4.00356i	0.734850	+	0.304385i	0.0163069	+	0.999867i	$0.494809\pi$
$174$		0			0
$175$	−10.1869			−0.770055
$176$	−0.347157	−	1.34568i	−0.0261679	−	0.101434i
$177$		0			0
$178$	4.92013	+	2.24312i	0.368779	+	0.168129i
$179$	−3.15817	+	7.62449i	−0.236053	+	0.569881i	−0.996868	−	0.0790873i	$-0.974799\pi$
$179$	−3.15817	+	7.62449i	−0.236053	+	0.569881i	0.760815	+	0.648969i	$0.224799\pi$
$180$		0			0
$181$	10.2651	−	4.25196i	0.763002	−	0.316046i	0.0329681	−	0.999456i	$-0.489504\pi$
$181$	10.2651	−	4.25196i	0.763002	−	0.316046i	0.730034	+	0.683410i	$0.239504\pi$
$182$	3.43673	−	3.20385i	0.254748	−	0.237485i
$183$		0			0
$184$	−11.6400	+	3.44223i	−0.858110	+	0.253765i
$185$	0.133537	+	0.133537i	0.00981782	+	0.00981782i
$186$		0			0
$187$	−1.81366	+	0.751244i	−0.132628	+	0.0549364i
$188$	−4.23719	−	4.87728i	−0.309029	−	0.355712i
$189$		0			0
$190$	−0.324223	+	0.121167i	−0.0235216	+	0.00879036i
$191$	−6.11953			−0.442794			−0.221397	−	0.975184i	$-0.571062\pi$
$191$	−6.11953			−0.442794			−0.221397	+	0.975184i	$0.571062\pi$
$192$		0			0
$193$	14.6513			1.05462			0.527310	−	0.849673i	$-0.323201\pi$
$193$	14.6513			1.05462			0.527310	+	0.849673i	$0.323201\pi$
$194$	8.52863	−	3.18727i	0.612320	−	0.228833i
$195$		0			0
$196$	−3.73055	−	4.29410i	−0.266468	−	0.306722i
$197$	20.1664	−	8.35319i	1.43680	−	0.595140i	0.477776	−	0.878482i	$-0.341443\pi$
$197$	20.1664	−	8.35319i	1.43680	−	0.595140i	0.959019	+	0.283341i	$0.0914429\pi$
$198$		0			0
$199$	−1.34312	−	1.34312i	−0.0952113	−	0.0952113i	0.657897	−	0.753108i	$-0.271446\pi$
$199$	−1.34312	−	1.34312i	−0.0952113	−	0.0952113i	−0.753108	+	0.657897i	$0.771446\pi$
$200$	4.00809	+	13.5534i	0.283415	+	0.958373i
$201$		0			0
$202$	19.8889	−	18.5412i	1.39938	−	1.30455i
$203$	−3.55245	+	1.47147i	−0.249333	+	0.103277i
$204$		0			0
$205$	0.204684	−	0.494152i	0.0142958	−	0.0345131i
$206$	12.6988	+	5.78946i	0.884766	+	0.403371i
$207$		0			0
$208$	−5.61486	−	3.31194i	−0.389321	−	0.229641i
$209$	1.55357			0.107463
$210$		0			0
$211$	−14.6312	−	6.06043i	−1.00725	−	0.417217i	−0.182800	−	0.983150i	$-0.558516\pi$
$211$	−14.6312	−	6.06043i	−1.00725	−	0.417217i	−0.824451	+	0.565933i	$0.808516\pi$
$212$	2.71221	+	1.35327i	0.186275	+	0.0929431i
$213$		0			0
$214$	14.7246	−	13.7268i	1.00656	−	0.938347i
$215$	−0.343997	−	0.343997i	−0.0234604	−	0.0234604i
$216$		0			0
$217$	−7.58867	+	7.58867i	−0.515153	+	0.515153i
$218$	0.899565	−	25.6501i	0.0609262	−	1.73725i
$219$		0			0
$220$	−0.00266440	+	0.0379395i	−0.000179634	+	0.00255788i
$221$	−3.52387	+	8.50739i	−0.237041	+	0.572269i
$222$		0			0
$223$		−	0.0733906i		−	0.00491460i	−0.999997	−	0.00245730i	$-0.999218\pi$
$223$		−	0.0733906i		−	0.00491460i	0.999997	−	0.00245730i	$-0.000782183\pi$
$224$	6.20343	−	9.72138i	0.414484	−	0.649537i
$225$		0			0
$226$	−15.3486	+	5.73597i	−1.02097	+	0.381551i
$227$	−14.3718	−	5.95299i	−0.953888	−	0.395114i	−0.149198	−	0.988807i	$-0.547669\pi$
$227$	−14.3718	−	5.95299i	−0.953888	−	0.395114i	−0.804691	+	0.593694i	$0.797669\pi$
$228$		0			0
$229$	10.0229	+	24.1975i	0.662333	+	1.59901i	0.794138	+	0.607737i	$0.207923\pi$
$229$	10.0229	+	24.1975i	0.662333	+	1.59901i	−0.131806	+	0.991276i	$0.542077\pi$
$230$	0.331985	+	0.0116429i	0.0218904	+	0.000767710i
$231$		0			0
$232$	3.35550	+	4.14750i	0.220299	+	0.272297i
$233$	−4.88581	+	4.88581i	−0.320080	+	0.320080i	−0.848798	−	0.528718i	$-0.822673\pi$
$233$	−4.88581	+	4.88581i	−0.320080	+	0.320080i	0.528718	+	0.848798i	$0.322673\pi$
$234$		0			0
$235$	0.0676632	+	0.163353i	0.00441386	+	0.0106560i
$236$	19.7318	+	9.84527i	1.28443	+	0.640872i
$237$		0			0
$238$	−14.8220	−	6.75747i	−0.960770	−	0.438022i
$239$			24.3341i			1.57404i	0.616928	+	0.787020i	$0.288377\pi$
$239$			24.3341i			1.57404i	−0.616928	+	0.787020i	$0.711623\pi$
$240$		0			0
$241$			3.20992i			0.206769i	0.994641	+	0.103384i	$0.0329672\pi$
$241$			3.20992i			0.206769i	−0.994641	+	0.103384i	$0.967033\pi$
$242$	−6.38242	+	13.9994i	−0.410277	+	0.899914i
$243$		0			0
$244$	−24.9380	+	8.33585i	−1.59649	+	0.533648i
$245$	0.0595727	+	0.143821i	0.00380596	+	0.00918841i
$246$		0			0
$247$	5.15295	−	5.15295i	0.327875	−	0.327875i
$248$	13.0824	+	7.11077i	0.830733	+	0.451534i
$249$		0			0
$250$	0.0271218	−	0.773350i	0.00171533	−	0.0489109i
$251$	8.63734	+	20.8524i	0.545184	+	1.31619i	0.921024	+	0.389506i	$0.127354\pi$
$251$	8.63734	+	20.8524i	0.545184	+	1.31619i	−0.375840	+	0.926685i	$0.622646\pi$
$252$		0			0
$253$	−1.37753	−	0.570590i	−0.0866043	−	0.0358727i
$254$	−5.71356	−	15.2886i	−0.358501	−	0.959291i
$255$		0			0
$256$	−15.3749	−	4.42861i	−0.960931	−	0.276788i
$257$		−	11.4338i		−	0.713221i	−0.934253	−	0.356611i	$-0.883932\pi$
$257$		−	11.4338i		−	0.713221i	0.934253	−	0.356611i	$-0.116068\pi$
$258$		0			0
$259$	2.69171	−	6.49837i	0.167255	−	0.403789i
$260$	0.117002	+	0.134677i	0.00725616	+	0.00835230i
$261$		0			0
$262$	2.24116	+	0.0785986i	0.138459	+	0.00485584i
$263$	−10.2028	+	10.2028i	−0.629129	+	0.629129i	−0.947849	−	0.318720i	$-0.896747\pi$
$263$	−10.2028	+	10.2028i	−0.629129	+	0.629129i	0.318720	+	0.947849i	$0.396747\pi$
$264$		0			0
$265$	−0.0586557	−	0.0586557i	−0.00360319	−	0.00360319i
$266$	8.79060	+	9.42959i	0.538986	+	0.578165i
$267$		0			0
$268$	−5.54557	−	16.5905i	−0.338750	−	1.01342i
$269$	−24.4000	−	10.1068i	−1.48770	−	0.616223i	−0.516881	−	0.856057i	$-0.672907\pi$
$269$	−24.4000	−	10.1068i	−1.48770	−	0.616223i	−0.970814	+	0.239834i	$0.922907\pi$
$270$		0			0
$271$	−23.0385			−1.39949			−0.699746	−	0.714392i	$-0.746703\pi$
$271$	−23.0385			−1.39949			−0.699746	+	0.714392i	$0.746703\pi$
$272$	−3.15885	+	22.3792i	−0.191534	+	1.35694i
$273$		0			0
$274$	2.29221	−	5.02779i	0.138477	−	0.303740i
$275$	−0.664388	+	1.60397i	−0.0400641	+	0.0967233i
$276$		0			0
$277$	0.872254	−	0.361300i	0.0524087	−	0.0217084i	−0.356325	−	0.934362i	$-0.615970\pi$
$277$	0.872254	−	0.361300i	0.0524087	−	0.0217084i	0.408734	+	0.912654i	$0.365970\pi$
$278$	6.35041	+	6.81202i	0.380872	+	0.408558i
$279$		0			0
$280$	−0.245355	+	0.198502i	−0.0146627	+	0.0118628i
$281$	15.0398	+	15.0398i	0.897197	+	0.897197i	0.995187	−	0.0979901i	$-0.0312413\pi$
$281$	15.0398	+	15.0398i	0.897197	+	0.897197i	−0.0979901	+	0.995187i	$0.531241\pi$
$282$		0			0
$283$	−25.3592	+	10.5041i	−1.50745	+	0.624405i	−0.975029	−	0.222077i	$-0.928716\pi$
$283$	−25.3592	+	10.5041i	−1.50745	+	0.624405i	−0.532417	+	0.846482i	$0.678716\pi$
$284$	1.85599	−	26.4282i	0.110133	−	1.56823i
$285$		0			0
$286$	−0.280318	−	0.750087i	−0.0165755	−	0.0443536i
$287$	−19.9213			−1.17592
$288$		0			0
$289$	14.9255			0.877970
$290$	−0.0511100	−	0.136762i	−0.00300128	−	0.00803096i
$291$		0			0
$292$	−4.85899	−	0.341235i	−0.284351	−	0.0199693i
$293$	−17.2872	+	7.16058i	−1.00993	+	0.418326i	−0.825428	−	0.564507i	$-0.809066\pi$
$293$	−17.2872	+	7.16058i	−1.00993	+	0.418326i	−0.184499	+	0.982833i	$0.559066\pi$
$294$		0			0
$295$	−0.426729	−	0.426729i	−0.0248451	−	0.0248451i
$296$	−9.70503	−	1.02444i	−0.564093	−	0.0595446i
$297$		0			0
$298$	−5.20015	−	5.57815i	−0.301237	−	0.323134i
$299$	−6.46159	+	2.67648i	−0.373684	+	0.154785i
$300$		0			0
$301$	−6.93397	+	16.7401i	−0.399668	+	0.964883i
$302$	0.805792	−	1.76745i	0.0463681	−	0.101705i
$303$		0			0
$304$	9.08718	−	15.4059i	0.521185	−	0.883587i
$305$	0.719598			0.0412041
$306$		0			0
$307$	0.389197	+	0.161211i	0.0222126	+	0.00920078i	0.393762	−	0.919212i	$-0.371173\pi$
$307$	0.389197	+	0.161211i	0.0222126	+	0.00920078i	−0.371549	+	0.928413i	$0.621173\pi$
$308$	1.34349	−	0.449077i	0.0765522	−	0.0255886i
$309$		0			0
$310$	−0.277867	−	0.298065i	−0.0157818	−	0.0169290i
$311$	−3.59481	−	3.59481i	−0.203843	−	0.203843i	0.597801	−	0.801644i	$-0.296041\pi$
$311$	−3.59481	−	3.59481i	−0.203843	−	0.203843i	−0.801644	+	0.597801i	$0.796041\pi$
$312$		0			0
$313$	−16.1765	+	16.1765i	−0.914351	+	0.914351i	−0.996611	−	0.0822596i	$-0.973786\pi$
$313$	−16.1765	+	16.1765i	−0.914351	+	0.914351i	0.0822596	+	0.996611i	$0.473786\pi$
$314$	−16.1927	−	0.567888i	−0.913808	−	0.0320478i
$315$		0			0
$316$	−22.8320	+	19.8356i	−1.28440	+	1.11584i
$317$	1.85103	−	4.46879i	0.103964	−	0.250992i	−0.863334	−	0.504632i	$-0.831628\pi$
$317$	1.85103	−	4.46879i	0.103964	−	0.250992i	0.967299	+	0.253640i	$0.0816280\pi$
$318$		0			0
$319$			0.655321i			0.0366909i
$320$	0.360640	+	0.248338i	0.0201604	+	0.0138825i
$321$		0			0
$322$	−4.33121	−	11.5896i	−0.241369	−	0.645865i
$323$	−23.3423	−	9.66869i	−1.29880	−	0.537980i
$324$		0			0
$325$	3.11646	+	7.52380i	0.172870	+	0.417345i
$326$	0.962139	−	27.4344i	0.0532880	−	1.51945i
$327$		0			0
$328$	7.83818	+	26.5049i	0.432791	+	1.46349i
$329$	4.65662	−	4.65662i	0.256728	−	0.256728i
$330$		0			0
$331$	6.31236	+	15.2394i	0.346959	+	0.837632i	0.996976	+	0.0777129i	$0.0247617\pi$
$331$	6.31236	+	15.2394i	0.346959	+	0.837632i	−0.650017	+	0.759920i	$0.725238\pi$
$332$	4.11908	+	12.3229i	0.226064	+	0.676305i
$333$		0			0
$334$	5.17757	−	11.3566i	0.283304	−	0.621407i
$335$			0.478725i			0.0261556i
$336$		0			0
$337$		−	13.9550i		−	0.760179i	−0.924950	−	0.380089i	$-0.875893\pi$
$337$		−	13.9550i		−	0.760179i	0.924950	−	0.380089i	$-0.124107\pi$
$338$	13.3106	+	6.06840i	0.724001	+	0.330077i
$339$		0			0
$340$	0.276150	−	0.553456i	0.0149763	−	0.0300154i
$341$	0.699942	+	1.68981i	0.0379040	+	0.0915083i
$342$		0			0
$343$	14.1904	−	14.1904i	0.766207	−	0.766207i
$344$	25.0006	+	2.63902i	1.34794	+	0.142286i
$345$		0			0
$346$	14.7861	+	0.518558i	0.794908	+	0.0278779i
$347$	−6.72778	−	16.2423i	−0.361166	−	0.871932i	−0.995130	−	0.0985697i	$-0.968573\pi$
$347$	−6.72778	−	16.2423i	−0.361166	−	0.871932i	0.633964	−	0.773363i	$-0.281427\pi$
$348$		0			0
$349$	18.1387	+	7.51328i	0.970940	+	0.402177i	0.811062	−	0.584960i	$-0.198890\pi$
$349$	18.1387	+	7.51328i	0.970940	+	0.402177i	0.159878	+	0.987137i	$0.448890\pi$
$350$	−13.4948	+	5.04321i	−0.721329	+	0.269571i
$351$		0			0
$352$	−1.12609	−	1.61079i	−0.0600210	−	0.0858555i
$353$			1.36137i			0.0724586i	0.999344	+	0.0362293i	$0.0115347\pi$
$353$			1.36137i			0.0724586i	−0.999344	+	0.0362293i	$0.988465\pi$
$354$		0			0
$355$	−0.277462	+	0.669853i	−0.0147262	+	0.0355521i
$356$	7.62834	+	0.535720i	0.404301	+	0.0283931i
$357$		0			0
$358$	−0.409060	+	11.6639i	−0.0216195	+	0.616456i
$359$	1.43099	−	1.43099i	0.0755246	−	0.0755246i	−0.668335	−	0.743860i	$-0.732993\pi$
$359$	1.43099	−	1.43099i	0.0755246	−	0.0755246i	0.743860	+	0.668335i	$0.232993\pi$
$360$		0			0
$361$	0.703464	+	0.703464i	0.0370244	+	0.0370244i
$362$	11.4935	−	10.7147i	0.604086	−	0.563150i
$363$		0			0
$364$	2.96661	−	5.94565i	0.155493	−	0.311637i
$365$	0.123157	+	0.0510132i	0.00644632	+	0.00267015i
$366$		0			0
$367$	4.44867			0.232219			0.116109	−	0.993236i	$-0.462958\pi$
$367$	4.44867			0.232219			0.116109	+	0.993236i	$0.462958\pi$
$368$	−13.7157	+	10.3226i	−0.714978	+	0.538104i
$369$		0			0
$370$	0.243010	+	0.110790i	0.0126335	+	0.00575970i
$371$	−1.18233	+	2.85439i	−0.0613834	+	0.148193i
$372$		0			0
$373$	−15.1942	+	6.29364i	−0.786726	+	0.325873i	−0.739626	−	0.673018i	$-0.764998\pi$
$373$	−15.1942	+	6.29364i	−0.786726	+	0.325873i	−0.0470995	+	0.998890i	$0.514998\pi$
$374$	−2.03069	+	1.89308i	−0.105005	+	0.0978890i
$375$		0			0
$376$	−8.02773	−	4.36337i	−0.413998	−	0.225023i
$377$	2.17359	+	2.17359i	0.111946	+	0.111946i
$378$		0			0
$379$	7.31677	−	3.03071i	0.375837	−	0.155677i	−0.186765	−	0.982405i	$-0.559800\pi$
$379$	7.31677	−	3.03071i	0.375837	−	0.155677i	0.562602	+	0.826728i	$0.309800\pi$
$380$	−0.369522	+	0.321026i	−0.0189561	+	0.0164683i
$381$		0			0
$382$	−8.10671	+	3.02959i	−0.414776	+	0.155007i
$383$	37.8805			1.93560			0.967801	−	0.251716i	$-0.0809948\pi$
$383$	37.8805			1.93560			0.967801	+	0.251716i	$0.0809948\pi$
$384$		0			0
$385$	−0.0387669			−0.00197575
$386$	19.4089	−	7.25340i	0.987889	−	0.369188i
$387$		0			0
$388$	9.72020	−	8.44453i	0.493468	−	0.428706i
$389$	−11.3365	+	4.69571i	−0.574781	+	0.238082i	−0.651088	−	0.759002i	$-0.725687\pi$
$389$	−11.3365	+	4.69571i	−0.574781	+	0.238082i	0.0763069	+	0.997084i	$0.475687\pi$
$390$		0			0
$391$	17.1461	+	17.1461i	0.867117	+	0.867117i
$392$	−7.06785	−	3.84164i	−0.356980	−	0.194032i
$393$		0			0
$394$	22.5796	−	21.0495i	1.13754	−	1.06046i
$395$	0.764706	−	0.316752i	0.0384765	−	0.0159375i
$396$		0			0
$397$	2.58068	−	6.23031i	0.129520	−	0.312690i	−0.845794	−	0.533509i	$-0.820873\pi$
$397$	2.58068	−	6.23031i	0.129520	−	0.312690i	0.975315	+	0.220819i	$0.0708730\pi$
$398$	−2.44421	−	1.11433i	−0.122517	−	0.0558564i
$399$		0			0
$400$	12.0195	+	15.9703i	0.600977	+	0.798517i
$401$	−0.816119			−0.0407550			−0.0203775	−	0.999792i	$-0.506487\pi$
$401$	−0.816119			−0.0407550			−0.0203775	+	0.999792i	$0.506487\pi$
$402$		0			0
$403$	7.92642	+	3.28323i	0.394843	+	0.163549i
$404$	17.1683	−	34.4084i	0.854153	−	1.71188i
$405$		0			0
$406$	−3.97755	+	3.70801i	−0.197402	+	0.184025i
$407$	−0.847648	−	0.847648i	−0.0420164	−	0.0420164i
$408$		0			0
$409$	17.3208	−	17.3208i	0.856460	−	0.856460i	−0.134459	−	0.990919i	$-0.542930\pi$
$409$	17.3208	−	17.3208i	0.856460	−	0.856460i	0.990919	+	0.134459i	$0.0429297\pi$
$410$	0.0265116	−	0.755950i	0.00130932	−	0.0373337i
$411$		0			0
$412$	19.6886	+	1.38268i	0.969989	+	0.0681200i
$413$	−8.60162	+	20.7661i	−0.423258	+	1.02183i
$414$		0			0
$415$		−	0.355582i		−	0.0174548i
$416$	−9.07781	−	1.60767i	−0.445076	−	0.0788223i
$417$		0			0
$418$	2.05806	−	0.769127i	0.100663	−	0.0376192i
$419$	11.8029	+	4.88890i	0.576607	+	0.238839i	0.651877	−	0.758325i	$-0.273982\pi$
$419$	11.8029	+	4.88890i	0.576607	+	0.238839i	−0.0752697	+	0.997163i	$0.523982\pi$
$420$		0			0
$421$	0.806753	+	1.94767i	0.0393187	+	0.0949238i	0.942319	−	0.334716i	$-0.108640\pi$
$421$	0.806753	+	1.94767i	0.0393187	+	0.0949238i	−0.903000	+	0.429640i	$0.858640\pi$
$422$	−22.3827	−	0.784973i	−1.08957	−	0.0382119i
$423$		0			0
$424$	4.26291	+	0.449985i	0.207025	+	0.0218532i
$425$	19.9647	−	19.9647i	0.968432	−	0.968432i
$426$		0			0
$427$	−10.2566	−	24.7616i	−0.496351	−	1.19830i
$428$	12.7104	−	25.4741i	0.614381	−	1.23134i
$429$		0			0
$430$	−0.626005	−	0.285400i	−0.0301887	−	0.0137632i
$431$			33.1877i			1.59860i	0.600934	+	0.799299i	$0.294795\pi$
$431$			33.1877i			1.59860i	−0.600934	+	0.799299i	$0.705205\pi$
$432$		0			0
$433$		−	14.0761i		−	0.676453i	−0.941065	−	0.338227i	$-0.890173\pi$
$433$		−	14.0761i		−	0.676453i	0.941065	−	0.338227i	$-0.109827\pi$
$434$	−6.29601	+	13.8099i	−0.302218	+	0.662894i
$435$		0			0
$436$	−11.5069	−	34.4248i	−0.551082	−	1.64865i
$437$	−7.34363	−	17.7291i	−0.351293	−	0.848098i
$438$		0			0
$439$	1.50704	−	1.50704i	0.0719273	−	0.0719273i	−0.670228	−	0.742155i	$-0.733804\pi$
$439$	1.50704	−	1.50704i	0.0719273	−	0.0719273i	0.742155	+	0.670228i	$0.233804\pi$
$440$	0.0152531	+	0.0515787i	0.000727164	+	0.00245892i
$441$		0			0
$442$	−0.456428	+	13.0145i	−0.0217100	+	0.619039i
$443$	−10.4760	−	25.2913i	−0.497731	−	1.20163i	−0.950703	−	0.310103i	$-0.899636\pi$
$443$	−10.4760	−	25.2913i	−0.497731	−	1.20163i	0.452972	−	0.891525i	$-0.350364\pi$
$444$		0			0
$445$	−0.193349	−	0.0800878i	−0.00916562	−	0.00379652i
$446$	−0.0363335	−	0.0972226i	−0.00172044	−	0.00460362i
$447$		0			0
$448$	3.40510	−	15.9493i	0.160876	−	0.753535i
$449$		−	13.5428i		−	0.639126i	−0.947565	−	0.319563i	$-0.896464\pi$
$449$		−	13.5428i		−	0.639126i	0.947565	−	0.319563i	$-0.103536\pi$
$450$		0			0
$451$	−1.29927	+	3.13671i	−0.0611802	+	0.147702i
$452$	−17.4930	+	15.1972i	−0.822800	+	0.714817i
$453$		0			0
$454$	−21.9859	−	0.771057i	−1.03185	−	0.0361875i
$455$	−0.128584	+	0.128584i	−0.00602810	+	0.00602810i
$456$		0			0
$457$	−14.4316	−	14.4316i	−0.675084	−	0.675084i	0.283800	−	0.958884i	$-0.408405\pi$
$457$	−14.4316	−	14.4316i	−0.675084	−	0.675084i	−0.958884	+	0.283800i	$0.908405\pi$
$458$	25.2571	+	27.0930i	1.18019	+	1.26597i
$459$		0			0
$460$	0.445554	−	0.148932i	0.0207741	−	0.00694399i
$461$	9.33454	+	3.86649i	0.434753	+	0.180080i	0.589316	−	0.807902i	$-0.299397\pi$
$461$	9.33454	+	3.86649i	0.434753	+	0.180080i	−0.154564	+	0.987983i	$0.549397\pi$
$462$		0			0
$463$	33.3750			1.55107			0.775534	−	0.631306i	$-0.217481\pi$
$463$	33.3750			1.55107			0.775534	+	0.631306i	$0.217481\pi$
$464$	6.49843	+	3.83311i	0.301682	+	0.177948i
$465$		0			0
$466$	−4.05355	+	8.89118i	−0.187777	+	0.411876i
$467$	13.5324	−	32.6702i	0.626207	−	1.51180i	−0.218095	−	0.975928i	$-0.569984\pi$
$467$	13.5324	−	32.6702i	0.626207	−	1.51180i	0.844301	−	0.535869i	$-0.180016\pi$
$468$		0			0
$469$	16.4731	−	6.82337i	0.760656	−	0.315074i
$470$	0.170507	+	0.182901i	0.00786489	+	0.00843659i
$471$		0			0
$472$	31.0133	+	3.27371i	1.42750	+	0.150685i
$473$	2.18358	+	2.18358i	0.100401	+	0.100401i
$474$		0			0
$475$	−20.6435	+	8.55083i	−0.947190	+	0.392339i
$476$	−22.9806	−	1.61387i	−1.05331	−	0.0739716i
$477$		0			0
$478$	12.0471	+	32.2360i	0.551020	+	1.47444i
$479$	−16.4726			−0.752653			−0.376326	−	0.926487i	$-0.622813\pi$
$479$	−16.4726			−0.752653			−0.376326	+	0.926487i	$0.622813\pi$
$480$		0			0
$481$	−5.62303			−0.256388
$482$	1.58913	+	4.25227i	0.0723830	+	0.193685i
$483$		0			0
$484$	−1.52430	+	21.7051i	−0.0692862	+	0.986596i
$485$	−0.325556	+	0.134850i	−0.0147827	+	0.00612321i
$486$		0			0
$487$	−3.20291	−	3.20291i	−0.145138	−	0.145138i	0.630804	−	0.775942i	$-0.282725\pi$
$487$	−3.20291	−	3.20291i	−0.145138	−	0.145138i	−0.775942	+	0.630804i	$0.782725\pi$
$488$	−28.9093	+	23.3888i	−1.30866	+	1.05876i
$489$		0			0
$490$	0.150119	+	0.161032i	0.00678170	+	0.00727466i
$491$	36.4450	−	15.0960i	1.64474	−	0.681274i	0.647977	−	0.761660i	$-0.275615\pi$
$491$	36.4450	−	15.0960i	1.64474	−	0.681274i	0.996764	+	0.0803853i	$0.0256151\pi$
$492$		0			0
$493$	4.07840	−	9.84613i	0.183682	−	0.443447i
$494$	4.27519	−	9.37733i	0.192350	−	0.421906i
$495$		0			0
$496$	20.8510	+	2.94314i	0.936236	+	0.132151i
$497$	27.0045			1.21132
$498$		0			0
$499$	−17.7901	−	7.36890i	−0.796395	−	0.329877i	−0.0528833	−	0.998601i	$-0.516841\pi$
$499$	−17.7901	−	7.36890i	−0.796395	−	0.329877i	−0.743511	+	0.668723i	$0.766841\pi$
$500$	−0.346933	−	1.03791i	−0.0155153	−	0.0464166i
$501$		0			0
$502$	21.7655	+	23.3477i	0.971443	+	1.04206i
$503$	24.4309	+	24.4309i	1.08932	+	1.08932i	0.995598	+	0.0937240i	$0.0298771\pi$
$503$	24.4309	+	24.4309i	1.08932	+	1.08932i	0.0937240	+	0.995598i	$0.470123\pi$
$504$		0			0
$505$	−0.744134	+	0.744134i	−0.0331135	+	0.0331135i
$506$	−2.10733	−	0.0739053i	−0.0936823	−	0.00328549i
$507$		0			0
$508$	−15.1378	−	17.4246i	−0.671633	−	0.773092i
$509$	−0.742577	+	1.79274i	−0.0329141	+	0.0794618i	−0.939482	−	0.342599i	$-0.888693\pi$
$509$	−0.742577	+	1.79274i	−0.0329141	+	0.0794618i	0.906568	+	0.422060i	$0.138693\pi$
$510$		0			0
$511$		−	4.96496i		−	0.219637i
$512$	−22.5600	+	1.74495i	−0.997022	+	0.0771165i
$513$		0			0
$514$	−5.66053	−	15.1467i	−0.249675	−	0.668092i
$515$	−0.499031	−	0.206705i	−0.0219899	−	0.00910852i
$516$		0			0
$517$	−0.429504	−	1.03691i	−0.0188896	−	0.0456034i
$518$	0.348642	−	9.94116i	0.0153185	−	0.436789i
$519$		0			0
$520$	0.221670	+	0.120486i	0.00972089	+	0.00528366i
$521$	−9.94706	+	9.94706i	−0.435788	+	0.435788i	−0.890592	−	0.454803i	$-0.849710\pi$
$521$	−9.94706	+	9.94706i	−0.435788	+	0.435788i	0.454803	+	0.890592i	$0.349710\pi$
$522$		0			0
$523$	12.9517	+	31.2681i	0.566338	+	1.36726i	0.904621	+	0.426216i	$0.140154\pi$
$523$	12.9517	+	31.2681i	0.566338	+	1.36726i	−0.338284	+	0.941044i	$0.609846\pi$
$524$	3.00783	−	1.00541i	0.131398	−	0.0439214i
$525$		0			0
$526$	−8.46481	+	18.5670i	−0.369083	+	0.809558i
$527$		−	29.7453i		−	1.29573i
$528$		0			0
$529$		−	4.58277i		−	0.199251i
$530$	−0.106742	−	0.0486642i	−0.00463656	−	0.00211384i
$531$		0			0
$532$	16.3135	+	8.13969i	0.707278	+	0.352900i
$533$	6.09451	+	14.7134i	0.263983	+	0.637310i
$534$		0			0
$535$	−0.550915	+	0.550915i	−0.0238181	+	0.0238181i
$536$	−15.5598	−	19.2324i	−0.672081	−	0.830714i
$537$		0			0
$538$	−37.3270	−	1.30908i	−1.60928	−	0.0564384i
$539$	−0.378148	−	0.912930i	−0.0162880	−	0.0393227i
$540$		0			0
$541$	−24.6347	−	10.2040i	−1.05913	−	0.438705i	−0.215986	−	0.976396i	$-0.569296\pi$
$541$	−24.6347	−	10.2040i	−1.05913	−	0.438705i	−0.843142	+	0.537692i	$0.819296\pi$
$542$	−30.5198	+	11.4057i	−1.31094	+	0.489916i
$543$		0			0
$544$	6.89465	+	31.2102i	0.295606	+	1.33813i
$545$			0.993343i			0.0425502i
$546$		0			0
$547$	−5.59032	+	13.4962i	−0.239025	+	0.577057i	−0.997182	−	0.0750145i	$-0.976100\pi$
$547$	−5.59032	+	13.4962i	−0.239025	+	0.577057i	0.758158	+	0.652071i	$0.226100\pi$
$548$	0.547442	−	7.79526i	0.0233856	−	0.332997i
$549$		0			0
$550$	−0.0860544	+	2.45375i	−0.00366937	+	0.104628i
$551$	−5.96383	+	5.96383i	−0.254068	+	0.254068i
$552$		0			0
$553$	−21.7990	−	21.7990i	−0.926989	−	0.926989i
$554$	0.976632	−	0.910451i	0.0414931	−	0.0386813i
$555$		0			0
$556$	11.7850	+	5.88018i	0.499795	+	0.249375i
$557$	−32.9643	−	13.6543i	−1.39674	−	0.578549i	−0.447838	−	0.894115i	$-0.647806\pi$
$557$	−32.9643	−	13.6543i	−1.39674	−	0.578549i	−0.948904	+	0.315565i	$0.897806\pi$
$558$		0			0
$559$	14.4852			0.612658
$560$	−0.226756	+	0.384429i	−0.00958219	+	0.0162451i
$561$		0			0
$562$	27.3693	+	12.4779i	1.15451	+	0.526347i
$563$	11.6660	−	28.1642i	0.491663	−	1.18698i	−0.462211	−	0.886770i	$-0.652944\pi$
$563$	11.6660	−	28.1642i	0.491663	−	1.18698i	0.953873	−	0.300209i	$-0.0970564\pi$
$564$		0			0
$565$	0.585887	−	0.242683i	0.0246485	−	0.0102097i
$566$	−28.3937	+	26.4697i	−1.19348	+	1.11260i
$567$		0			0
$568$	−10.6251	−	35.9290i	−0.445820	−	1.50755i
$569$	−2.70810	−	2.70810i	−0.113529	−	0.113529i	0.648060	−	0.761589i	$-0.275581\pi$
$569$	−2.70810	−	2.70810i	−0.113529	−	0.113529i	−0.761589	+	0.648060i	$0.775581\pi$
$570$		0			0
$571$	13.3976	−	5.54948i	0.560673	−	0.232238i	−0.0843044	−	0.996440i	$-0.526867\pi$
$571$	13.3976	−	5.54948i	0.560673	−	0.232238i	0.644977	+	0.764202i	$0.276867\pi$
$572$	−0.742691	−	0.854884i	−0.0310534	−	0.0357445i
$573$		0			0
$574$	−26.3903	+	9.86244i	−1.10151	+	0.411650i
$575$	21.4448			0.894310
$576$		0			0
$577$	−31.1960			−1.29871			−0.649354	−	0.760486i	$-0.724961\pi$
$577$	−31.1960			−1.29871			−0.649354	+	0.760486i	$0.724961\pi$
$578$	19.7722	−	7.38916i	0.822416	−	0.307348i
$579$		0			0
$580$	−0.135414	−	0.155870i	−0.00562275	−	0.00647214i
$581$	−12.2357	+	5.06818i	−0.507622	+	0.210264i
$582$		0			0
$583$	0.372327	+	0.372327i	0.0154202	+	0.0154202i
$584$	−6.60578	+	1.95350i	−0.273349	+	0.0808363i
$585$		0			0
$586$	−19.3558	+	18.0442i	−0.799582	+	0.745398i
$587$	−20.0976	+	8.32471i	−0.829518	+	0.343598i	−0.756712	−	0.653749i	$-0.773195\pi$
$587$	−20.0976	+	8.32471i	−0.829518	+	0.343598i	−0.0728061	+	0.997346i	$0.523195\pi$
$588$		0			0
$589$	−9.00842	+	21.7482i	−0.371185	+	0.896121i
$590$	−0.776561	−	0.354040i	−0.0319705	−	0.0145756i
$591$		0			0
$592$	−13.3637	+	3.44756i	−0.549245	+	0.141694i
$593$	13.4216			0.551158			0.275579	−	0.961278i	$-0.411130\pi$
$593$	13.4216			0.551158			0.275579	+	0.961278i	$0.411130\pi$
$594$		0			0
$595$	0.582469	+	0.241267i	0.0238789	+	0.00989097i
$596$	−9.65037	−	4.81510i	−0.395294	−	0.197234i
$597$		0			0
$598$	−7.23481	+	6.74455i	−0.295853	+	0.275805i
$599$	18.3224	+	18.3224i	0.748635	+	0.748635i	0.974223	−	0.225588i	$-0.0724304\pi$
$599$	18.3224	+	18.3224i	0.748635	+	0.748635i	−0.225588	+	0.974223i	$0.572430\pi$
$600$		0			0
$601$	7.64445	−	7.64445i	0.311824	−	0.311824i	−0.533792	−	0.845616i	$-0.679234\pi$
$601$	7.64445	−	7.64445i	0.311824	−	0.311824i	0.845616	+	0.533792i	$0.179234\pi$
$602$	−0.898118	+	25.6089i	−0.0366046	+	1.04374i
$603$		0			0
$604$	0.192445	−	2.74031i	0.00783049	−	0.111502i
$605$	0.227876	−	0.550141i	0.00926447	−	0.0223664i
$606$		0			0
$607$			13.1965i			0.535628i	0.963471	+	0.267814i	$0.0863013\pi$
$607$			13.1965i			0.535628i	−0.963471	+	0.267814i	$0.913699\pi$
$608$	4.41106	−	24.9074i	0.178892	−	1.01013i
$609$		0			0
$610$	0.953273	−	0.356251i	0.0385969	−	0.0144242i
$611$	−4.86387	−	2.01468i	−0.196771	−	0.0815053i
$612$		0			0
$613$	−7.87596	−	19.0142i	−0.318107	−	0.767978i	−0.999354	−	0.0359251i	$-0.988562\pi$
$613$	−7.87596	−	19.0142i	−0.318107	−	0.767978i	0.681247	−	0.732053i	$-0.261438\pi$
$614$	0.595391	+	0.0208807i	0.0240280	+	0.000842677i
$615$		0			0
$616$	1.55743	−	1.26003i	0.0627507	−	0.0507679i
$617$	2.36409	−	2.36409i	0.0951748	−	0.0951748i	−0.657916	−	0.753091i	$-0.728562\pi$
$617$	2.36409	−	2.36409i	0.0951748	−	0.0951748i	0.753091	+	0.657916i	$0.228562\pi$
$618$		0			0
$619$	−9.55563	−	23.0693i	−0.384073	−	0.927235i	−0.991169	−	0.132606i	$-0.957665\pi$
$619$	−9.55563	−	23.0693i	−0.384073	−	0.927235i	0.607095	−	0.794629i	$-0.292335\pi$
$620$	−0.515661	−	0.257292i	−0.0207094	−	0.0103331i
$621$		0			0
$622$	−6.54183	−	2.98247i	−0.262304	−	0.119586i
$623$			7.79470i			0.312288i
$624$		0			0
$625$		−	24.9551i		−	0.998203i
$626$	−13.4210	+	29.4380i	−0.536411	+	1.17658i
$627$		0			0
$628$	−21.7321	+	7.26423i	−0.867205	+	0.289874i
$629$	7.46048	+	18.0112i	0.297469	+	0.718153i
$630$		0			0
$631$	−1.69280	+	1.69280i	−0.0673892	+	0.0673892i	−0.739998	−	0.672609i	$-0.765174\pi$
$631$	−1.69280	+	1.69280i	−0.0673892	+	0.0673892i	0.672609	+	0.739998i	$0.265174\pi$
$632$	−20.4262	+	37.5802i	−0.812511	+	1.49486i
$633$		0			0
$634$	0.239754	−	6.83632i	0.00952183	−	0.271505i
$635$	0.241734	+	0.583598i	0.00959292	+	0.0231594i
$636$		0			0
$637$	−4.28230	−	1.77379i	−0.169671	−	0.0702800i
$638$	0.324429	+	0.868122i	0.0128443	+	0.0343693i
$639$		0			0
$640$	0.600694	+	0.150438i	0.0237445	+	0.00594660i
$641$			39.0060i			1.54065i	0.637654	+	0.770323i	$0.279905\pi$
$641$			39.0060i			1.54065i	−0.637654	+	0.770323i	$0.720095\pi$
$642$		0			0
$643$	−8.76787	+	21.1675i	−0.345771	+	0.834765i	0.651339	+	0.758787i	$0.274208\pi$
$643$	−8.76787	+	21.1675i	−0.345771	+	0.834765i	−0.997110	+	0.0759778i	$0.975792\pi$
$644$	−11.4754	−	13.2089i	−0.452193	−	0.520503i
$645$		0			0
$646$	−35.7089	−	1.25233i	−1.40495	−	0.0492723i
$647$	17.6444	−	17.6444i	0.693674	−	0.693674i	−0.269364	−	0.963038i	$-0.586814\pi$
$647$	17.6444	−	17.6444i	0.693674	−	0.693674i	0.963038	+	0.269364i	$0.0868136\pi$
$648$		0			0
$649$	2.70874	+	2.70874i	0.106327	+	0.106327i
$650$	7.85327	+	8.42413i	0.308031	+	0.330421i
$651$		0			0
$652$	−12.3074	−	36.8194i	−0.481993	−	1.44196i
$653$	−3.16105	−	1.30935i	−0.123701	−	0.0512387i	0.319974	−	0.947426i	$-0.396326\pi$
$653$	−3.16105	−	1.30935i	−0.123701	−	0.0512387i	−0.443676	+	0.896187i	$0.646326\pi$
$654$		0			0
$655$	−0.0867924			−0.00339126
$656$	23.5053	+	31.2314i	0.917726	+	1.21938i
$657$		0			0
$658$	3.86341	−	8.47411i	0.150611	−	0.330355i
$659$	−9.00896	+	21.7495i	−0.350939	+	0.847242i	0.645565	+	0.763705i	$0.276622\pi$
$659$	−9.00896	+	21.7495i	−0.350939	+	0.847242i	−0.996505	+	0.0835372i	$0.973378\pi$
$660$		0			0
$661$	−27.2013	+	11.2672i	−1.05801	+	0.438242i	−0.842744	−	0.538314i	$-0.819061\pi$
$661$	−27.2013	+	11.2672i	−1.05801	+	0.438242i	−0.215265	+	0.976556i	$0.569061\pi$
$662$	15.9067	+	17.0630i	0.618232	+	0.663172i
$663$		0			0
$664$	11.5573	+	14.2852i	0.448512	+	0.554375i
$665$	−0.352804	−	0.352804i	−0.0136811	−	0.0136811i
$666$		0			0
$667$	7.47840	−	3.09766i	0.289565	−	0.119942i
$668$	1.23655	−	17.6077i	0.0478434	−	0.681263i
$669$		0			0
$670$	0.237002	+	0.634181i	0.00915620	+	0.0245006i
$671$	−4.56777			−0.176337
$672$		0			0
$673$	−40.2867			−1.55294			−0.776469	−	0.630155i	$-0.782991\pi$
$673$	−40.2867			−1.55294			−0.776469	+	0.630155i	$0.782991\pi$
$674$	−6.90871	−	18.4866i	−0.266114	−	0.712078i
$675$		0			0
$676$	20.6372	+	1.44930i	0.793739	+	0.0557424i
$677$	−20.8698	+	8.64457i	−0.802093	+	0.332238i	−0.745794	−	0.666176i	$-0.767930\pi$
$677$	−20.8698	+	8.64457i	−0.802093	+	0.332238i	−0.0562986	+	0.998414i	$0.517930\pi$
$678$		0			0
$679$	9.28043	+	9.28043i	0.356150	+	0.356150i
$680$	0.0918242	−	0.869892i	0.00352130	−	0.0333589i
$681$		0			0
$682$	1.76381	+	1.89202i	0.0675396	+	0.0724491i
$683$	13.3957	−	5.54867i	0.512572	−	0.212314i	−0.111379	−	0.993778i	$-0.535527\pi$
$683$	13.3957	−	5.54867i	0.512572	−	0.212314i	0.623950	+	0.781464i	$0.285527\pi$
$684$		0			0
$685$	−0.0818402	+	0.197580i	−0.00312695	+	0.00754913i
$686$	11.7732	−	25.8236i	0.449501	−	0.985949i
$687$		0			0
$688$	34.4255	−	8.88107i	1.31246	−	0.338587i
$689$	2.46990			0.0940957
$690$		0			0
$691$	4.05430	+	1.67935i	0.154233	+	0.0638854i	0.458464	−	0.888713i	$-0.348400\pi$
$691$	4.05430	+	1.67935i	0.154233	+	0.0638854i	−0.304232	+	0.952598i	$0.598400\pi$
$692$	19.8443	−	6.63322i	0.754369	−	0.252157i
$693$		0			0
$694$	−16.9536	−	18.1859i	−0.643548	−	0.690328i
$695$	−0.254868	−	0.254868i	−0.00966771	−	0.00966771i
$696$		0			0
$697$	39.0428	−	39.0428i	1.47885	−	1.47885i
$698$	27.7484	+	0.973153i	1.05029	+	0.0368344i
$699$		0			0
$700$	−15.3802	+	13.3618i	−0.581319	+	0.505027i
$701$	−8.00533	+	19.3266i	−0.302357	+	0.729954i	0.697553	+	0.716533i	$0.254272\pi$
$701$	−8.00533	+	19.3266i	−0.302357	+	0.729954i	−0.999910	+	0.0134211i	$0.995728\pi$
$702$		0			0
$703$		−	15.4283i		−	0.581888i
$704$	−2.28922	−	1.57637i	−0.0862783	−	0.0594115i
$705$		0			0
$706$	0.673975	+	1.80345i	0.0253654	+	0.0678738i
$707$	36.2122	+	14.9996i	1.36190	+	0.564117i
$708$		0			0
$709$	−7.37340	−	17.8010i	−0.276914	−	0.668529i	0.722833	−	0.691022i	$-0.242839\pi$
$709$	−7.37340	−	17.8010i	−0.276914	−	0.668529i	−0.999747	+	0.0224936i	$0.992839\pi$
$710$	−0.0359381	+	1.02474i	−0.00134873	+	0.0384577i
$711$		0			0
$712$	10.3707	−	3.06688i	0.388658	−	0.114936i
$713$	15.9752	−	15.9752i	0.598277	−	0.598277i
$714$		0			0
$715$	0.0118599	+	0.0286324i	0.000443536	+	0.00107079i
$716$	5.23255	+	15.6540i	0.195550	+	0.585018i
$717$		0			0
$718$	1.18723	−	2.60411i	0.0443071	−	0.0971845i
$719$		−	14.6223i		−	0.545320i	−0.962110	−	0.272660i	$-0.912097\pi$
$719$		−	14.6223i		−	0.545320i	0.962110	−	0.272660i	$-0.0879035\pi$
$720$		0			0
$721$			20.1180i			0.749233i
$722$	1.28016	+	0.583635i	0.0476427	+	0.0217206i
$723$		0			0
$724$	9.92128	−	19.8841i	0.368722	−	0.738987i
$725$	−3.60687	−	8.70776i	−0.133956	−	0.323398i
$726$		0			0
$727$	−20.9235	+	20.9235i	−0.776011	+	0.776011i	−0.979150	−	0.203139i	$-0.934886\pi$
$727$	−20.9235	+	20.9235i	−0.776011	+	0.776011i	0.203139	+	0.979150i	$0.434886\pi$
$728$	0.986446	−	9.34505i	0.0365601	−	0.346351i
$729$		0			0
$730$	0.188404	+	0.00660745i	0.00697316	+	0.000244553i
$731$	−19.2185	−	46.3976i	−0.710823	−	1.71608i
$732$		0			0
$733$	23.8873	+	9.89446i	0.882299	+	0.365460i	0.777388	−	0.629021i	$-0.216544\pi$
$733$	23.8873	+	9.89446i	0.882299	+	0.365460i	0.104911	+	0.994482i	$0.466544\pi$
$734$	5.89328	−	2.20240i	0.217525	−	0.0812922i
$735$		0			0
$736$	−13.0591	+	20.4649i	−0.481365	+	0.754345i
$737$		−	3.03879i		−	0.111935i
$738$		0			0
$739$	−12.2087	+	29.4745i	−0.449106	+	1.08424i	0.523552	+	0.851994i	$0.324607\pi$
$739$	−12.2087	+	29.4745i	−0.449106	+	1.08424i	−0.972658	+	0.232243i	$0.925393\pi$
$740$	0.376771	+	0.0264597i	0.0138504	+	0.000972679i
$741$		0			0
$742$	−0.153140	+	4.36663i	−0.00562195	+	0.160304i
$743$	−6.80000	+	6.80000i	−0.249468	+	0.249468i	−0.820752	−	0.571284i	$-0.806445\pi$
$743$	−6.80000	+	6.80000i	−0.249468	+	0.249468i	0.571284	+	0.820752i	$0.306445\pi$
$744$		0			0
$745$	0.208704	+	0.208704i	0.00764632	+	0.00764632i
$746$	−17.0124	+	15.8596i	−0.622868	+	0.580660i
$747$		0			0
$748$	−1.75291	+	3.51316i	−0.0640927	+	0.128454i
$749$	26.8095	+	11.1048i	0.979596	+	0.405762i
$750$		0			0
$751$	44.9473			1.64015			0.820074	−	0.572257i	$-0.193932\pi$
$751$	44.9473			1.64015			0.820074	+	0.572257i	$0.193932\pi$
$752$	−12.7947	−	1.80599i	−0.466576	−	0.0658577i
$753$		0			0
$754$	3.95550	+	1.80334i	0.144051	+	0.0656738i
$755$	−0.0287697	+	0.0694563i	−0.00104704	+	0.00252777i
$756$		0			0
$757$	−1.70690	+	0.707023i	−0.0620385	+	0.0256972i	−0.413487	−	0.910510i	$-0.635689\pi$
$757$	−1.70690	+	0.707023i	−0.0620385	+	0.0256972i	0.351448	+	0.936207i	$0.385689\pi$
$758$	8.19233	−	7.63718i	0.297559	−	0.277395i
$759$		0			0
$760$	−0.330586	+	0.608212i	−0.0119916	+	0.0220622i
$761$	−12.7724	−	12.7724i	−0.463001	−	0.463001i	0.436637	−	0.899638i	$-0.356169\pi$
$761$	−12.7724	−	12.7724i	−0.463001	−	0.463001i	−0.899638	+	0.436637i	$0.856169\pi$
$762$		0			0
$763$	34.1812	−	14.1583i	1.23744	−	0.512566i
$764$	−9.23934	+	8.02678i	−0.334267	+	0.290399i
$765$		0			0
$766$	50.1814	−	18.7535i	1.81313	−	0.677591i
$767$	17.9689			0.648820
$768$		0			0
$769$	19.1995			0.692350			0.346175	−	0.938170i	$-0.387480\pi$
$769$	19.1995			0.692350			0.346175	+	0.938170i	$0.387480\pi$
$770$	−0.0513556	+	0.0191923i	−0.00185073	+	0.000691644i
$771$		0			0
$772$	22.1206	−	19.2176i	0.796139	−	0.691655i
$773$	−23.1310	+	9.58115i	−0.831962	+	0.344610i	−0.757679	−	0.652627i	$-0.773667\pi$
$773$	−23.1310	+	9.58115i	−0.831962	+	0.344610i	−0.0742831	+	0.997237i	$0.523667\pi$
$774$		0			0
$775$	−18.6014	−	18.6014i	−0.668180	−	0.668180i
$776$	8.69599	−	15.9989i	0.312168	−	0.574327i
$777$		0			0
$778$	−12.6930	+	11.8329i	−0.455067	+	0.424229i
$779$	−40.3703	+	16.7219i	−1.44641	+	0.599124i
$780$		0			0
$781$	1.76124	−	4.25200i	0.0630221	−	0.152149i
$782$	31.2025	+	14.2254i	1.11580	+	0.508700i
$783$		0			0
$784$	−11.2649	−	1.59005i	−0.402317	−	0.0567875i
$785$	0.627089			0.0223818
$786$		0			0
$787$	4.05121	+	1.67807i	0.144410	+	0.0598166i	0.453718	−	0.891145i	$-0.350097\pi$
$787$	4.05121	+	1.67807i	0.144410	+	0.0598166i	−0.309308	+	0.950962i	$0.600097\pi$
$788$	19.4908	−	39.0633i	0.694333	−	1.39157i
$789$		0			0
$790$	0.856214	−	0.798193i	0.0304627	−	0.0283984i
$791$	−16.7015	−	16.7015i	−0.593839	−	0.593839i
$792$		0			0
$793$	−15.1506	+	15.1506i	−0.538013	+	0.538013i
$794$	0.334260	−	9.53108i	0.0118625	−	0.338245i
$795$		0			0
$796$	−3.78958	−	0.266133i	−0.134318	−	0.00943284i
$797$	14.5713	−	35.1783i	0.516144	−	1.24608i	−0.424111	−	0.905610i	$-0.639413\pi$
$797$	14.5713	−	35.1783i	0.516144	−	1.24608i	0.940255	−	0.340471i	$-0.110587\pi$
$798$		0			0
$799$			18.2526i			0.645729i
$800$	23.8291	+	15.2059i	0.842484	+	0.537608i
$801$		0			0
$802$	−1.08114	+	0.404036i	−0.0381763	+	0.0142670i
$803$	−0.781758	−	0.323815i	−0.0275877	−	0.0114272i
$804$		0			0
$805$	0.183249	+	0.442401i	0.00645866	+	0.0155926i
$806$	12.1258	+	0.425259i	0.427113	+	0.0149791i
$807$		0			0
$808$	5.70872	−	54.0813i	0.200832	−	1.90257i
$809$	−20.5126	+	20.5126i	−0.721186	+	0.721186i	−0.968847	−	0.247661i	$-0.920338\pi$
$809$	−20.5126	+	20.5126i	−0.721186	+	0.721186i	0.247661	+	0.968847i	$0.420338\pi$
$810$		0			0
$811$	0.939648	+	2.26851i	0.0329955	+	0.0796582i	0.939518	−	0.342499i	$-0.111273\pi$
$811$	0.939648	+	2.26851i	0.0329955	+	0.0796582i	−0.906523	+	0.422157i	$0.861273\pi$
$812$	−3.43345	+	6.88127i	−0.120490	+	0.241485i
$813$		0			0
$814$	−1.54255	−	0.703259i	−0.0540663	−	0.0246492i
$815$			1.06244i			0.0372157i
$816$		0			0
$817$			39.7439i			1.39046i
$818$	14.3704	−	31.5204i	0.502448	−	1.10209i
$819$		0			0
$820$	−0.339127	−	1.01455i	−0.0118428	−	0.0354298i
$821$	−10.2442	−	24.7317i	−0.357526	−	0.863143i	−0.995647	−	0.0932071i	$-0.970288\pi$
$821$	−10.2442	−	24.7317i	−0.357526	−	0.863143i	0.638121	−	0.769936i	$-0.279712\pi$
$822$		0			0
$823$	8.04412	−	8.04412i	0.280400	−	0.280400i	−0.552868	−	0.833269i	$-0.686467\pi$
$823$	8.04412	−	8.04412i	0.280400	−	0.280400i	0.833269	+	0.552868i	$0.186467\pi$
$824$	26.7666	−	7.91557i	0.932459	−	0.275752i
$825$		0			0
$826$	−1.11412	+	31.7679i	−0.0387651	+	1.10535i
$827$	14.8516	+	35.8550i	0.516441	+	1.24680i	0.940076	+	0.340966i	$0.110754\pi$
$827$	14.8516	+	35.8550i	0.516441	+	1.24680i	−0.423634	+	0.905833i	$0.639246\pi$
$828$		0			0
$829$	48.7703	+	20.2013i	1.69386	+	0.701620i	0.999832	−	0.0183260i	$-0.00583367\pi$
$829$	48.7703	+	20.2013i	1.69386	+	0.701620i	0.694030	+	0.719946i	$0.255834\pi$
$830$	−0.176038	−	0.471050i	−0.00611037	−	0.0163504i
$831$		0			0
$832$	−12.8215	+	2.36443i	−0.444507	+	0.0819718i
$833$			16.0701i			0.556796i
$834$		0			0
$835$	−0.184858	+	0.446287i	−0.00639728	+	0.0154444i
$836$	2.34560	−	2.03777i	0.0811243	−	0.0704777i
$837$		0			0
$838$	18.0559	+	0.633232i	0.623732	+	0.0218746i
$839$	−36.5267	+	36.5267i	−1.26104	+	1.26104i	−0.310451	+	0.950589i	$0.600480\pi$
$839$	−36.5267	+	36.5267i	−1.26104	+	1.26104i	−0.950589	+	0.310451i	$0.899520\pi$
$840$		0			0
$841$	17.9905	+	17.9905i	0.620361	+	0.620361i
$842$	2.03296	+	2.18074i	0.0700606	+	0.0751533i
$843$		0			0
$844$	−30.0396	+	10.0411i	−1.03400	+	0.345629i
$845$	−0.523074	−	0.216664i	−0.0179943	−	0.00745348i
$846$		0			0
$847$	−22.1785			−0.762061
$848$	5.86997	−	1.51433i	0.201576	−	0.0520023i
$849$		0			0
$850$	16.5639	−	36.3318i	0.568138	−	1.24617i
$851$	−5.66643	+	13.6800i	−0.194243	+	0.468944i
$852$		0			0
$853$	8.47051	−	3.50860i	0.290025	−	0.120132i	−0.232928	−	0.972494i	$-0.574831\pi$
$853$	8.47051	−	3.50860i	0.290025	−	0.120132i	0.522952	+	0.852362i	$0.324831\pi$
$854$	−25.8459	−	27.7247i	−0.884429	−	0.948718i
$855$		0			0
$856$	4.22642	−	40.0388i	0.144456	−	1.36850i
$857$	−30.1040	−	30.1040i	−1.02833	−	1.02833i	−0.999587	−	0.0287458i	$-0.990849\pi$
$857$	−30.1040	−	30.1040i	−1.02833	−	1.02833i	−0.0287458	−	0.999587i	$-0.509151\pi$
$858$		0			0
$859$	−25.2414	+	10.4553i	−0.861225	+	0.356731i	−0.769186	−	0.639025i	$-0.779338\pi$
$859$	−25.2414	+	10.4553i	−0.861225	+	0.356731i	−0.0920383	+	0.995755i	$0.529338\pi$
$860$	−0.970580	−	0.0681615i	−0.0330965	−	0.00232429i
$861$		0			0
$862$	16.4302	+	43.9647i	0.559616	+	1.49745i
$863$	−37.4443			−1.27462			−0.637309	−	0.770608i	$-0.719952\pi$
$863$	−37.4443			−1.27462			−0.637309	+	0.770608i	$0.719952\pi$
$864$		0			0
$865$	−0.572618			−0.0194696
$866$	−6.96864	−	18.6470i	−0.236804	−	0.633650i
$867$		0			0
$868$	−1.50366	+	21.4113i	−0.0510376	+	0.726746i
$869$	−4.85410	+	2.01063i	−0.164664	+	0.0682061i
$870$		0			0
$871$	−10.0792	−	10.0792i	−0.341520	−	0.341520i
$872$	−32.2862	−	39.9068i	−1.09335	−	1.35141i
$873$		0			0
$874$	−18.5055	−	19.8506i	−0.625956	−	0.671457i
$875$	1.03056	−	0.426873i	0.0348394	−	0.0144309i
$876$		0			0
$877$	−9.67707	+	23.3625i	−0.326772	+	0.788896i	0.672057	+	0.740500i	$0.265411\pi$
$877$	−9.67707	+	23.3625i	−0.326772	+	0.788896i	−0.998828	+	0.0483966i	$0.984589\pi$
$878$	1.25033	−	2.74252i	0.0421967	−	0.0925555i
$879$		0			0
$880$	0.0457413	+	0.0607764i	0.00154194	+	0.00204877i
$881$	−21.5129			−0.724789			−0.362394	−	0.932025i	$-0.618041\pi$
$881$	−21.5129			−0.724789			−0.362394	+	0.932025i	$0.618041\pi$
$882$		0			0
$883$	43.7878	+	18.1375i	1.47358	+	0.610376i	0.967672	−	0.252213i	$-0.0811584\pi$
$883$	43.7878	+	18.1375i	1.47358	+	0.610376i	0.505906	+	0.862589i	$0.331158\pi$
$884$	5.83846	+	17.4667i	0.196369	+	0.587469i
$885$		0			0
$886$	−26.3989	−	28.3178i	−0.886887	−	0.951355i
$887$	−0.105277	−	0.105277i	−0.00353486	−	0.00353486i	0.705337	−	0.708872i	$-0.250796\pi$
$887$	−0.105277	−	0.105277i	−0.00353486	−	0.00353486i	−0.708872	+	0.705337i	$0.750796\pi$
$888$		0			0
$889$	16.6363	−	16.6363i	0.557963	−	0.557963i
$890$	−0.295784	−	0.0103733i	−0.00991470	−	0.000347714i
$891$		0			0
$892$	−0.0962640	−	0.110806i	−0.00322316	−	0.00371006i
$893$	5.52782	−	13.3453i	0.184981	−	0.446584i
$894$		0			0
$895$		−	0.451704i		−	0.0150988i
$896$	−3.38519	−	22.8143i	−0.113091	−	0.762172i
$897$		0			0
$898$	−6.70465	−	17.9406i	−0.223737	−	0.598685i
$899$	−9.17374	−	3.79989i	−0.305961	−	0.126733i
$900$		0			0
$901$	−3.27699	−	7.91136i	−0.109173	−	0.263566i
$902$	−0.168287	+	4.79852i	−0.00560334	+	0.159773i
$903$		0			0
$904$	−15.6498	+	28.7924i	−0.520503	+	0.957622i
$905$	−0.430024	+	0.430024i	−0.0142945	+	0.0142945i
$906$		0			0
$907$	−8.71193	−	21.0325i	−0.289275	−	0.698371i	0.710712	−	0.703483i	$-0.248373\pi$
$907$	−8.71193	−	21.0325i	−0.289275	−	0.698371i	−0.999987	+	0.00511165i	$0.998373\pi$
$908$	−29.5070	+	9.86309i	−0.979225	+	0.327318i
$909$		0			0
$910$	−0.106681	+	0.233996i	−0.00353643	+	0.00775691i
$911$		−	45.6074i		−	1.51104i	−0.655125	−	0.755521i	$-0.727384\pi$
$911$		−	45.6074i		−	1.51104i	0.655125	−	0.755521i	$-0.272616\pi$
$912$		0			0
$913$			2.25712i			0.0746997i
$914$	−26.2627	−	11.9733i	−0.868692	−	0.396043i
$915$		0			0
$916$	46.8717	+	23.3869i	1.54868	+	0.772724i
$917$	1.23707	+	2.98655i	0.0408517	+	0.0986246i
$918$		0			0
$919$	−24.4249	+	24.4249i	−0.805703	+	0.805703i	−0.983980	−	0.178277i	$-0.942948\pi$
$919$	−24.4249	+	24.4249i	−0.805703	+	0.805703i	0.178277	+	0.983980i	$0.442948\pi$
$920$	0.516506	−	0.417875i	0.0170287	−	0.0137769i
$921$		0			0
$922$	14.2799	+	0.500805i	0.470284	+	0.0164931i
$923$	−8.26148	−	19.9450i	−0.271930	−	0.656497i
$924$		0			0
$925$	15.9288	+	6.59793i	0.523736	+	0.216938i
$926$	44.2128	−	16.5229i	1.45292	−	0.542978i
$927$		0			0
$928$	10.5063	+	1.86065i	0.344887	+	0.0610789i
$929$			14.0133i			0.459760i	0.973219	+	0.229880i	$0.0738334\pi$
$929$			14.0133i			0.459760i	−0.973219	+	0.229880i	$0.926167\pi$
$930$		0			0
$931$	4.86686	−	11.7496i	0.159505	−	0.385079i
$932$	−0.968101	+	13.7852i	−0.0317112	+	0.451549i
$933$		0			0
$934$	1.75278	−	49.9786i	0.0573527	−	1.63535i
$935$	0.0759774	−	0.0759774i	0.00248473	−	0.00248473i
$936$		0			0
$937$	13.8787	+	13.8787i	0.453398	+	0.453398i	0.896481	−	0.443083i	$-0.146115\pi$
$937$	13.8787	+	13.8787i	0.453398	+	0.453398i	−0.443083	+	0.896481i	$0.646115\pi$
$938$	18.4443	−	17.1944i	0.602228	−	0.561418i
$939$		0			0
$940$	0.316424	+	0.157881i	0.0103206	+	0.00514952i
$941$	−3.58022	−	1.48297i	−0.116712	−	0.0483436i	0.323563	−	0.946206i	$-0.395119\pi$
$941$	−3.58022	−	1.48297i	−0.116712	−	0.0483436i	−0.440275	+	0.897863i	$0.645119\pi$
$942$		0			0
$943$	41.9372			1.36566
$944$	42.7050	−	11.0170i	1.38993	−	0.358572i
$945$		0			0
$946$	3.97368	+	1.81163i	0.129195	+	0.0589011i
$947$	1.90171	−	4.59114i	0.0617974	−	0.149192i	−0.889964	−	0.456030i	$-0.849271\pi$
$947$	1.90171	−	4.59114i	0.0617974	−	0.149192i	0.951762	+	0.306838i	$0.0992710\pi$
$948$		0			0
$949$	−3.66701	+	1.51893i	−0.119036	+	0.0493064i
$950$	−23.1138	+	21.5475i	−0.749911	+	0.699094i
$951$		0			0
$952$	−31.2420	+	9.23906i	−1.01256	+	0.299440i
$953$	16.0973	+	16.0973i	0.521441	+	0.521441i	0.918007	−	0.396565i	$-0.129798\pi$
$953$	16.0973	+	16.0973i	0.521441	+	0.521441i	−0.396565	+	0.918007i	$0.629798\pi$
$954$		0			0
$955$	0.309451	−	0.128179i	0.0100136	−	0.00414776i
$956$	31.9182	+	36.7399i	1.03231	+	1.18825i
$957$		0			0
$958$	−21.8217	+	8.15509i	−0.705028	+	0.263479i
$959$	7.96526			0.257212
$960$		0			0
$961$	3.28596			0.105999
$962$	−7.44899	+	2.78379i	−0.240165	+	0.0897530i
$963$		0			0
$964$	4.21034	+	4.84637i	0.135606	+	0.156091i
$965$	−0.740881	+	0.306883i	−0.0238498	+	0.00987891i
$966$		0			0
$967$	−13.6682	−	13.6682i	−0.439540	−	0.439540i	0.452317	−	0.891857i	$-0.350597\pi$
$967$	−13.6682	−	13.6682i	−0.439540	−	0.439540i	−0.891857	+	0.452317i	$0.850597\pi$
$968$	8.72627	+	29.5080i	0.280473	+	0.948424i
$969$		0			0
$970$	−0.364513	+	0.339812i	−0.0117038	+	0.0109107i
$971$	−35.7127	+	14.7927i	−1.14608	+	0.474720i	−0.873216	−	0.487333i	$-0.837970\pi$
$971$	−35.7127	+	14.7927i	−1.14608	+	0.474720i	−0.272860	+	0.962054i	$0.587970\pi$
$972$		0			0
$973$	−5.13740	+	12.4028i	−0.164698	+	0.397615i
$974$	−5.82865	−	2.65732i	−0.186762	−	0.0851462i
$975$		0			0
$976$	−26.7179	+	45.2960i	−0.855219	+	1.44989i
$977$	−3.99623			−0.127851			−0.0639254	−	0.997955i	$-0.520362\pi$
$977$	−3.99623			−0.127851			−0.0639254	+	0.997955i	$0.520362\pi$
$978$		0			0
$979$	1.22732	+	0.508371i	0.0392252	+	0.0162476i
$980$	0.278589	+	0.139004i	0.00889920	+	0.00444031i
$981$		0			0
$982$	40.8062	−	38.0410i	1.30218	−	1.21394i
$983$	−5.05054	−	5.05054i	−0.161087	−	0.161087i	0.621961	−	0.783048i	$-0.286336\pi$
$983$	−5.05054	−	5.05054i	−0.161087	−	0.161087i	−0.783048	+	0.621961i	$0.786336\pi$
$984$		0			0
$985$	−0.844804	+	0.844804i	−0.0269177	+	0.0269177i
$986$	0.528252	−	15.0625i	0.0168230	−	0.479689i
$987$		0			0
$988$	1.02103	−	14.5389i	0.0324834	−	0.462545i
$989$	14.5970	−	35.2403i	0.464158	−	1.12058i
$990$		0			0
$991$			45.1460i			1.43411i	0.697017	+	0.717055i	$0.254510\pi$
$991$			45.1460i			1.43411i	−0.697017	+	0.717055i	$0.745490\pi$
$992$	29.0789	−	6.42382i	0.923257	−	0.203957i
$993$		0			0
$994$	35.7737	−	13.3691i	1.13467	−	0.424043i
$995$	0.0960513	+	0.0397858i	0.00304503	+	0.00126129i
$996$		0			0
$997$	−17.6186	−	42.5351i	−0.557987	−	1.34710i	−0.911357	−	0.411616i	$-0.864964\pi$
$997$	−17.6186	−	42.5351i	−0.557987	−	1.34710i	0.353370	−	0.935484i	$-0.385036\pi$
$998$	−27.2152	−	0.954453i	−0.861482	−	0.0302127i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.35.8	✓	32
3.2	odd	2		288.2.w.b.35.1	yes	32
4.3	odd	2		1152.2.w.b.431.5		32
12.11	even	2		1152.2.w.a.431.4		32
32.11	odd	8		288.2.w.b.107.1	yes	32
32.21	even	8		1152.2.w.a.719.4		32
96.11	even	8	inner	288.2.w.a.107.8	yes	32
96.53	odd	8		1152.2.w.b.719.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.8	✓	32	1.1	even	1	trivial
288.2.w.a.107.8	yes	32	96.11	even	8	inner
288.2.w.b.35.1	yes	32	3.2	odd	2
288.2.w.b.107.1	yes	32	32.11	odd	8
1152.2.w.a.431.4		32	12.11	even	2
1152.2.w.a.719.4		32	32.21	even	8
1152.2.w.b.431.5		32	4.3	odd	2
1152.2.w.b.719.5		32	96.53	odd	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32473 - 0.495070i) q^{2} +(1.50981 - 1.31167i) q^{4} +(-0.0505677 + 0.0209458i) q^{5} +(1.44150 + 1.44150i) q^{7} +(1.35072 - 2.48506i) q^{8} +(-0.0566189 + 0.0527821i) q^{10} +(0.320987 - 0.132957i) q^{11} +(0.623666 - 1.50566i) q^{13} +(2.62325 + 1.19596i) q^{14} +(0.559063 - 3.96074i) q^{16} -5.65026 q^{17} +(4.13118 + 1.71119i) q^{19} +(-0.0488738 + 0.0979522i) q^{20} +(0.359398 - 0.335043i) q^{22} +(-3.03457 - 3.03457i) q^{23} +(-3.53342 + 3.53342i) q^{25} +(0.0807799 - 2.30335i) q^{26} +(4.06717 + 0.285627i) q^{28} +(-0.721807 + 1.74260i) q^{29} +5.26441i q^{31} +(-1.22024 - 5.52368i) q^{32} +(-7.48507 + 2.79728i) q^{34} +(-0.103087 - 0.0427001i) q^{35} +(-1.32038 - 3.18767i) q^{37} +(6.31986 + 0.221641i) q^{38} +(-0.0162513 + 0.153956i) q^{40} +(-6.90990 + 6.90990i) q^{41} +(3.40135 + 8.21159i) q^{43} +(0.310235 - 0.621769i) q^{44} +(-5.52231 - 2.51766i) q^{46} -3.23039i q^{47} -2.84413i q^{49} +(-2.93153 + 6.43010i) q^{50} +(-1.03331 - 3.09131i) q^{52} +(0.579972 + 1.40018i) q^{53} +(-0.0134467 + 0.0134467i) q^{55} +(5.52930 - 1.63516i) q^{56} +(-0.0934916 + 2.66581i) q^{58} +(4.21939 + 10.1865i) q^{59} +(-12.1464 - 5.03120i) q^{61} +(2.60625 + 6.97392i) q^{62} +(-4.35109 - 6.71327i) q^{64} +0.0892011i q^{65} +(3.34709 - 8.08060i) q^{67} +(-8.53083 + 7.41126i) q^{68} +(-0.157702 - 0.00553070i) q^{70} +(9.36679 - 9.36679i) q^{71} +(-1.72215 - 1.72215i) q^{73} +(-3.32726 - 3.56912i) q^{74} +(8.48182 - 2.83516i) q^{76} +(0.654363 + 0.271046i) q^{77} -15.1224 q^{79} +(0.0546904 + 0.211996i) q^{80} +(-5.73286 + 12.5746i) q^{82} +(-2.48612 + 6.00202i) q^{83} +(0.285721 - 0.118349i) q^{85} +(8.57118 + 9.19422i) q^{86} +(0.103158 - 0.977262i) q^{88} +(2.70367 + 2.70367i) q^{89} +(3.06943 - 1.27140i) q^{91} +(-8.56197 - 0.601286i) q^{92} +(-1.59927 - 4.27939i) q^{94} -0.244747 q^{95} +6.43802 q^{97} +(-1.40804 - 3.76770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52}+ \cdots - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

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