LMFDB - Embedded newform 152.2.q.b.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(9,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	152.73
Dual form			152.2.q.b.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.26604 - 0.824773i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(0.233956 + 0.405223i) q^{7} +(2.15657 - 1.80958i) q^{9} +(0.0603074 - 0.104455i) q^{11} +(-3.85844 - 1.40436i) q^{13} +(0.564178 + 3.19961i) q^{15} +(-5.85117 - 4.90971i) q^{17} +(4.28699 - 0.788496i) q^{19} +(0.864370 + 0.725293i) q^{21} +(1.12061 + 6.35532i) q^{23} +(2.99273 + 1.08926i) q^{25} +(-0.222811 + 0.385920i) q^{27} +(-3.56418 + 2.99070i) q^{29} +(-2.79813 - 4.84651i) q^{31} +(0.0505072 - 0.286441i) q^{33} +(-0.592396 + 0.215615i) q^{35} -0.588526 q^{37} -9.90167 q^{39} +(-7.19846 + 2.62003i) q^{41} +(0.432419 - 2.45237i) q^{43} +(1.89646 + 3.28476i) q^{45} +(3.25490 - 2.73119i) q^{47} +(3.39053 - 5.87257i) q^{49} +(-17.3084 - 6.29974i) q^{51} +(1.65910 + 9.40923i) q^{53} +(0.124485 + 0.104455i) q^{55} +(9.06418 - 5.32256i) q^{57} +(6.24170 + 5.23741i) q^{59} +(0.437166 + 2.47929i) q^{61} +(1.23783 + 0.450532i) q^{63} +(2.76604 - 4.79093i) q^{65} +(-6.53983 + 5.48757i) q^{67} +(7.78106 + 13.4772i) q^{69} +(2.79561 - 15.8547i) q^{71} +(12.8229 - 4.66717i) q^{73} +7.68004 q^{75} +0.0564370 q^{77} +(15.0817 - 5.48930i) q^{79} +(-1.65317 + 9.37560i) q^{81} +(1.82635 + 3.16333i) q^{83} +(7.88326 - 6.61484i) q^{85} +(-5.60994 + 9.71670i) q^{87} +(2.27972 + 0.829748i) q^{89} +(-0.333626 - 1.89209i) q^{91} +(-10.3380 - 8.67458i) q^{93} +(0.0432332 + 5.87257i) q^{95} +(-7.17752 - 6.02265i) q^{97} +(-0.0589632 - 0.334397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} - 6 q^{5} + 6 q^{7} - 9 q^{9} + 6 q^{11} - 15 q^{13} - 15 q^{15} - 9 q^{17} + 18 q^{19} + 24 q^{21} + 18 q^{23} - 12 q^{27} - 3 q^{29} - 3 q^{31} + 3 q^{33} - 24 q^{37} - 36 q^{39} - 15 q^{41}+ \cdots - 15 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 - 6 * q^5 + 6 * q^7 - 9 * q^9 + 6 * q^11 - 15 * q^13 - 15 * q^15 - 9 * q^17 + 18 * q^19 + 24 * q^21 + 18 * q^23 - 12 * q^27 - 3 * q^29 - 3 * q^31 + 3 * q^33 - 24 * q^37 - 36 * q^39 - 15 * q^41 - 21 * q^43 + 21 * q^45 + 21 * q^47 + 3 * q^49 - 27 * q^51 - 27 * q^53 - 12 * q^55 + 36 * q^57 - 6 * q^59 + 12 * q^61 - 12 * q^63 + 12 * q^65 + 18 * q^67 + 12 * q^69 + 18 * q^71 + 36 * q^73 + 6 * q^75 + 30 * q^77 + 27 * q^79 + 54 * q^81 + 12 * q^83 + 12 * q^85 + 15 * q^87 - 12 * q^89 - 21 * q^91 + 9 * q^93 - 15 * q^95 - 18 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.26604	−	0.824773i	1.30830	−	0.476183i	0.408610	−	0.912709i	$-0.366014\pi$
$3$	2.26604	−	0.824773i	1.30830	−	0.476183i	0.899691	+	0.436526i	$0.143791\pi$
$4$		0			0
$5$	−0.233956	+	1.32683i	−0.104628	+	0.593375i	0.886740	+	0.462268i	$0.152964\pi$
$5$	−0.233956	+	1.32683i	−0.104628	+	0.593375i	−0.991368	+	0.131107i	$0.958147\pi$
$6$		0			0
$7$	0.233956	+	0.405223i	0.0884269	+	0.153160i	0.906846	−	0.421461i	$-0.138483\pi$
$7$	0.233956	+	0.405223i	0.0884269	+	0.153160i	−0.818419	+	0.574621i	$0.805149\pi$
$8$		0			0
$9$	2.15657	−	1.80958i	0.718858	−	0.603193i
$10$		0			0
$11$	0.0603074	−	0.104455i	0.0181834	−	0.0314945i	−0.856791	−	0.515665i	$-0.827545\pi$
$11$	0.0603074	−	0.104455i	0.0181834	−	0.0314945i	0.874974	+	0.484170i	$0.160878\pi$
$12$		0			0
$13$	−3.85844	−	1.40436i	−1.07014	−	0.389499i	−0.253910	−	0.967228i	$-0.581717\pi$
$13$	−3.85844	−	1.40436i	−1.07014	−	0.389499i	−0.816229	+	0.577729i	$0.803939\pi$
$14$		0			0
$15$	0.564178	+	3.19961i	0.145670	+	0.826136i
$16$		0			0
$17$	−5.85117	−	4.90971i	−1.41912	−	1.19078i	−0.951811	−	0.306684i	$-0.900781\pi$
$17$	−5.85117	−	4.90971i	−1.41912	−	1.19078i	−0.467305	−	0.884096i	$-0.654775\pi$
$18$		0			0
$19$	4.28699	−	0.788496i	0.983503	−	0.180893i
$19$	4.28699	−	0.788496i	0.983503	−	0.180893i
$20$		0			0
$21$	0.864370	+	0.725293i	0.188621	+	0.158272i
$22$		0			0
$23$	1.12061	+	6.35532i	0.233664	+	1.32518i	0.845408	+	0.534120i	$0.179357\pi$
$23$	1.12061	+	6.35532i	0.233664	+	1.32518i	−0.611744	+	0.791056i	$0.709532\pi$
$24$		0			0
$25$	2.99273	+	1.08926i	0.598545	+	0.217853i
$26$		0			0
$27$	−0.222811	+	0.385920i	−0.0428800	+	0.0742704i
$28$		0			0
$29$	−3.56418	+	2.99070i	−0.661851	+	0.555359i	−0.910641	−	0.413198i	$-0.864412\pi$
$29$	−3.56418	+	2.99070i	−0.661851	+	0.555359i	0.248790	+	0.968557i	$0.419967\pi$
$30$		0			0
$31$	−2.79813	−	4.84651i	−0.502560	−	0.870459i	−0.999996	−	0.00295808i	$-0.999058\pi$
$31$	−2.79813	−	4.84651i	−0.502560	−	0.870459i	0.497436	−	0.867501i	$-0.334275\pi$
$32$		0			0
$33$	0.0505072	−	0.286441i	0.00879217	−	0.0498629i
$34$		0			0
$35$	−0.592396	+	0.215615i	−0.100133	+	0.0364455i
$36$		0			0
$37$	−0.588526			−0.0967531			−0.0483765	−	0.998829i	$-0.515405\pi$
$37$	−0.588526			−0.0967531			−0.0483765	+	0.998829i	$0.515405\pi$
$38$		0			0
$39$	−9.90167			−1.58554
$40$		0			0
$41$	−7.19846	+	2.62003i	−1.12421	+	0.409179i	−0.836187	−	0.548444i	$-0.815220\pi$
$41$	−7.19846	+	2.62003i	−1.12421	+	0.409179i	−0.288024	+	0.957623i	$0.592998\pi$
$42$		0			0
$43$	0.432419	−	2.45237i	0.0659432	−	0.373983i	−0.933921	−	0.357480i	$-0.883636\pi$
$43$	0.432419	−	2.45237i	0.0659432	−	0.373983i	0.999864	−	0.0165021i	$-0.00525303\pi$
$44$		0			0
$45$	1.89646	+	3.28476i	0.282707	+	0.489664i
$46$		0			0
$47$	3.25490	−	2.73119i	0.474776	−	0.398384i	−0.373757	−	0.927527i	$-0.621931\pi$
$47$	3.25490	−	2.73119i	0.474776	−	0.398384i	0.848533	+	0.529142i	$0.177486\pi$
$48$		0			0
$49$	3.39053	−	5.87257i	0.484361	−	0.838939i
$50$		0			0
$51$	−17.3084	−	6.29974i	−2.42366	−	0.882140i
$52$		0			0
$53$	1.65910	+	9.40923i	0.227895	+	1.29246i	0.857073	+	0.515195i	$0.172281\pi$
$53$	1.65910	+	9.40923i	0.227895	+	1.29246i	−0.629178	+	0.777261i	$0.716608\pi$
$54$		0			0
$55$	0.124485	+	0.104455i	0.0167856	+	0.0140848i
$56$		0			0
$57$	9.06418	−	5.32256i	1.20058	−	0.704990i
$58$		0			0
$59$	6.24170	+	5.23741i	0.812600	+	0.681852i	0.951227	−	0.308493i	$-0.0998245\pi$
$59$	6.24170	+	5.23741i	0.812600	+	0.681852i	−0.138627	+	0.990345i	$0.544269\pi$
$60$		0			0
$61$	0.437166	+	2.47929i	0.0559734	+	0.317441i	0.999920	−	0.0126575i	$-0.00402912\pi$
$61$	0.437166	+	2.47929i	0.0559734	+	0.317441i	−0.943946	+	0.330099i	$0.892918\pi$
$62$		0			0
$63$	1.23783	+	0.450532i	0.155951	+	0.0567617i
$64$		0			0
$65$	2.76604	−	4.79093i	0.343086	−	0.594242i
$66$		0			0
$67$	−6.53983	+	5.48757i	−0.798967	+	0.670413i	−0.947947	−	0.318427i	$-0.896845\pi$
$67$	−6.53983	+	5.48757i	−0.798967	+	0.670413i	0.148980	+	0.988840i	$0.452401\pi$
$68$		0			0
$69$	7.78106	+	13.4772i	0.936729	+	1.62246i
$70$		0			0
$71$	2.79561	−	15.8547i	0.331778	−	1.88160i	−0.125209	−	0.992130i	$-0.539960\pi$
$71$	2.79561	−	15.8547i	0.331778	−	1.88160i	0.456987	−	0.889473i	$-0.348929\pi$
$72$		0			0
$73$	12.8229	−	4.66717i	1.50081	−	0.546251i	0.544542	−	0.838734i	$-0.316704\pi$
$73$	12.8229	−	4.66717i	1.50081	−	0.546251i	0.956271	+	0.292483i	$0.0944814\pi$
$74$		0			0
$75$	7.68004			0.886815
$76$		0			0
$77$	0.0564370			0.00643159
$78$		0			0
$79$	15.0817	−	5.48930i	1.69683	−	0.617594i	0.701368	−	0.712799i	$-0.252573\pi$
$79$	15.0817	−	5.48930i	1.69683	−	0.617594i	0.995458	+	0.0952050i	$0.0303507\pi$
$80$		0			0
$81$	−1.65317	+	9.37560i	−0.183686	+	1.04173i
$82$		0			0
$83$	1.82635	+	3.16333i	0.200468	+	0.347221i	0.948679	−	0.316240i	$-0.102420\pi$
$83$	1.82635	+	3.16333i	0.200468	+	0.347221i	−0.748211	+	0.663461i	$0.769087\pi$
$84$		0			0
$85$	7.88326	−	6.61484i	0.855059	−	0.717480i
$86$		0			0
$87$	−5.60994	+	9.71670i	−0.601448	+	1.04174i
$88$		0			0
$89$	2.27972	+	0.829748i	0.241649	+	0.0879532i	0.460006	−	0.887916i	$-0.347847\pi$
$89$	2.27972	+	0.829748i	0.241649	+	0.0879532i	−0.218356	+	0.975869i	$0.570070\pi$
$90$		0			0
$91$	−0.333626	−	1.89209i	−0.0349735	−	0.198344i
$92$		0			0
$93$	−10.3380	−	8.67458i	−1.07200	−	0.899512i
$94$		0			0
$95$	0.0432332	+	5.87257i	0.00443564	+	0.602513i
$96$		0			0
$97$	−7.17752	−	6.02265i	−0.728767	−	0.611508i	0.201028	−	0.979585i	$-0.435572\pi$
$97$	−7.17752	−	6.02265i	−0.728767	−	0.611508i	−0.929795	+	0.368078i	$0.880016\pi$
$98$		0			0
$99$	−0.0589632	−	0.334397i	−0.00592603	−	0.0336082i
$100$		0			0
$101$	−5.79813	−	2.11035i	−0.576936	−	0.209987i	0.0370380	−	0.999314i	$-0.488208\pi$
$101$	−5.79813	−	2.11035i	−0.576936	−	0.209987i	−0.613974	+	0.789326i	$0.710430\pi$
$102$		0			0
$103$	3.76991	−	6.52968i	0.371461	−	0.643389i	−0.618330	−	0.785919i	$-0.712190\pi$
$103$	3.76991	−	6.52968i	0.371461	−	0.643389i	0.989790	+	0.142530i	$0.0455237\pi$
$104$		0			0
$105$	−1.16456	+	0.977185i	−0.113650	+	0.0953634i
$106$		0			0
$107$	2.70961	+	4.69318i	0.261948	+	0.453707i	0.966759	−	0.255688i	$-0.0823019\pi$
$107$	2.70961	+	4.69318i	0.261948	+	0.453707i	−0.704812	+	0.709394i	$0.748969\pi$
$108$		0			0
$109$	1.48411	−	8.41679i	0.142152	−	0.806183i	−0.827458	−	0.561527i	$-0.810214\pi$
$109$	1.48411	−	8.41679i	0.142152	−	0.806183i	0.969610	−	0.244656i	$-0.0786749\pi$
$110$		0			0
$111$	−1.33363	+	0.485400i	−0.126582	+	0.0460721i
$112$		0			0
$113$	−6.37464			−0.599675			−0.299838	−	0.953990i	$-0.596933\pi$
$113$	−6.37464			−0.599675			−0.299838	+	0.953990i	$0.596933\pi$
$114$		0			0
$115$	−8.69459			−0.810775
$116$		0			0
$117$	−10.8623	+	3.95356i	−1.00422	+	0.365507i
$118$		0			0
$119$	0.620615	−	3.51968i	0.0568917	−	0.322649i
$120$		0			0
$121$	5.49273	+	9.51368i	0.499339	+	0.864880i
$122$		0			0
$123$	−14.1511	+	11.8742i	−1.27596	+	1.07066i
$124$		0			0
$125$	−5.51367	+	9.54996i	−0.493158	+	0.854174i
$126$		0			0
$127$	0.152704	+	0.0555796i	0.0135503	+	0.00493189i	0.348786	−	0.937202i	$-0.386594\pi$
$127$	0.152704	+	0.0555796i	0.0135503	+	0.00493189i	−0.335236	+	0.942134i	$0.608816\pi$
$128$		0			0
$129$	−1.04277	−	5.91382i	−0.0918105	−	0.520683i
$130$		0			0
$131$	−0.754900	−	0.633436i	−0.0659559	−	0.0553436i	0.609214	−	0.793006i	$-0.291485\pi$
$131$	−0.754900	−	0.633436i	−0.0659559	−	0.0553436i	−0.675170	+	0.737662i	$0.735930\pi$
$132$		0			0
$133$	1.32248	+	1.55271i	0.114674	+	0.134637i
$134$		0			0
$135$	−0.459922	−	0.385920i	−0.0395838	−	0.0332147i
$136$		0			0
$137$	−0.340900	−	1.93334i	−0.0291250	−	0.165176i	0.966776	−	0.255625i	$-0.0822811\pi$
$137$	−0.340900	−	1.93334i	−0.0291250	−	0.165176i	−0.995901	+	0.0904484i	$0.971170\pi$
$138$		0			0
$139$	12.9572	+	4.71605i	1.09902	+	0.400010i	0.826954	−	0.562269i	$-0.190072\pi$
$139$	12.9572	+	4.71605i	1.09902	+	0.400010i	0.272064	+	0.962279i	$0.412294\pi$
$140$		0			0
$141$	5.12314	−	8.87354i	0.431446	−	0.747287i
$142$		0			0
$143$	−0.379385	+	0.318342i	−0.0317258	+	0.0266211i
$144$		0			0
$145$	−3.13429	−	5.42874i	−0.260288	−	0.450832i
$146$		0			0
$147$	2.83956	−	16.1039i	0.234203	−	1.32823i
$148$		0			0
$149$	7.65183	−	2.78504i	0.626862	−	0.228159i	−0.00900290	−	0.999959i	$-0.502866\pi$
$149$	7.65183	−	2.78504i	0.626862	−	0.228159i	0.635865	+	0.771800i	$0.280644\pi$
$150$		0			0
$151$	−17.6236			−1.43419			−0.717094	−	0.696976i	$-0.754528\pi$
$151$	−17.6236			−1.43419			−0.717094	+	0.696976i	$0.754528\pi$
$152$		0			0
$153$	−21.5030			−1.73841
$154$		0			0
$155$	7.08512	−	2.57877i	0.569091	−	0.207132i
$156$		0			0
$157$	−3.48024	+	19.7374i	−0.277753	+	1.57522i	0.452325	+	0.891853i	$0.350595\pi$
$157$	−3.48024	+	19.7374i	−0.277753	+	1.57522i	−0.730078	+	0.683364i	$0.760516\pi$
$158$		0			0
$159$	11.5201	+	19.9533i	0.913601	+	1.58240i
$160$		0			0
$161$	−2.31315	+	1.94096i	−0.182302	+	0.152969i
$162$		0			0
$163$	−4.64203	+	8.04023i	−0.363592	+	0.629759i	−0.988549	−	0.150900i	$-0.951783\pi$
$163$	−4.64203	+	8.04023i	−0.363592	+	0.629759i	0.624958	+	0.780659i	$0.285116\pi$
$164$		0			0
$165$	0.368241	+	0.134029i	0.0286675	+	0.0104341i
$166$		0			0
$167$	−2.05303	−	11.6433i	−0.158868	−	0.900988i	−0.955163	−	0.296079i	$-0.904321\pi$
$167$	−2.05303	−	11.6433i	−0.158868	−	0.900988i	0.796295	−	0.604909i	$-0.206790\pi$
$168$		0			0
$169$	2.95677	+	2.48102i	0.227444	+	0.190848i
$170$		0			0
$171$	7.81836	−	9.45810i	0.597885	−	0.723279i
$172$		0			0
$173$	−17.2121	−	14.4427i	−1.30861	−	1.09806i	−0.988587	−	0.150649i	$-0.951864\pi$
$173$	−17.2121	−	14.4427i	−1.30861	−	1.09806i	−0.320027	−	0.947408i	$-0.603692\pi$
$174$		0			0
$175$	0.258770	+	1.46756i	0.0195612	+	0.110937i
$176$		0			0
$177$	18.4636	+	6.72021i	1.38781	+	0.505122i
$178$		0			0
$179$	−1.51842	+	2.62998i	−0.113492	+	0.196574i	−0.917176	−	0.398483i	$-0.869537\pi$
$179$	−1.51842	+	2.62998i	−0.113492	+	0.196574i	0.803684	+	0.595056i	$0.202870\pi$
$180$		0			0
$181$	8.75877	−	7.34948i	0.651034	−	0.546283i	−0.256350	−	0.966584i	$-0.582520\pi$
$181$	8.75877	−	7.34948i	0.651034	−	0.546283i	0.907385	+	0.420301i	$0.138076\pi$
$182$		0			0
$183$	3.03549	+	5.25763i	0.224390	+	0.388655i
$184$		0			0
$185$	0.137689	−	0.780873i	0.0101231	−	0.0574109i
$186$		0			0
$187$	−0.865715	+	0.315094i	−0.0633073	+	0.0230420i
$188$		0			0
$189$	−0.208512			−0.0151670
$190$		0			0
$191$	4.02734			0.291408			0.145704	−	0.989328i	$-0.453455\pi$
$191$	4.02734			0.291408			0.145704	+	0.989328i	$0.453455\pi$
$192$		0			0
$193$	−15.5792	+	5.67036i	−1.12141	+	0.408162i	−0.835168	−	0.549994i	$-0.814630\pi$
$193$	−15.5792	+	5.67036i	−1.12141	+	0.408162i	−0.286246	+	0.958156i	$0.592408\pi$
$194$		0			0
$195$	2.31655	−	13.1378i	0.165892	−	0.940819i
$196$		0			0
$197$	−3.74376	−	6.48438i	−0.266732	−	0.461993i	0.701284	−	0.712882i	$-0.252610\pi$
$197$	−3.74376	−	6.48438i	−0.266732	−	0.461993i	−0.968016	+	0.250889i	$0.919277\pi$
$198$		0			0
$199$	−18.2121	+	15.2818i	−1.29102	+	1.08330i	−0.299402	+	0.954127i	$0.596787\pi$
$199$	−18.2121	+	15.2818i	−1.29102	+	1.08330i	−0.991622	+	0.129170i	$0.958769\pi$
$200$		0			0
$201$	−10.2935	+	17.8289i	−0.726051	+	1.25756i
$202$		0			0
$203$	−2.04576	−	0.744596i	−0.143584	−	0.0522604i
$204$		0			0
$205$	−1.79220	−	10.1641i	−0.125173	−	0.709891i
$206$		0			0
$207$	13.9172	+	11.6779i	0.967309	+	0.811669i
$208$		0			0
$209$	0.176174	−	0.495351i	0.0121862	−	0.0342642i
$210$		0			0
$211$	2.32635	+	1.95204i	0.160153	+	0.134384i	0.719342	−	0.694656i	$-0.244443\pi$
$211$	2.32635	+	1.95204i	0.160153	+	0.134384i	−0.559190	+	0.829040i	$0.688888\pi$
$212$		0			0
$213$	−6.74153	−	38.2331i	−0.461922	−	2.61969i
$214$		0			0
$215$	3.15270	+	1.14749i	0.215013	+	0.0782582i
$216$		0			0
$217$	1.30928	−	2.26774i	0.0888796	−	0.153944i
$218$		0			0
$219$	25.2080	−	21.1520i	1.70340	−	1.42932i
$220$		0			0
$221$	15.6814	+	27.1610i	1.05484	+	1.82704i
$222$		0			0
$223$	1.09105	−	6.18766i	0.0730623	−	0.414357i	−0.926238	−	0.376940i	$-0.876976\pi$
$223$	1.09105	−	6.18766i	0.0730623	−	0.414357i	0.999300	−	0.0374162i	$-0.0119127\pi$
$224$		0			0
$225$	8.42514	−	3.06650i	0.561676	−	0.204433i
$226$		0			0
$227$	4.09833			0.272015			0.136008	−	0.990708i	$-0.456573\pi$
$227$	4.09833			0.272015			0.136008	+	0.990708i	$0.456573\pi$
$228$		0			0
$229$	−1.21213			−0.0801000			−0.0400500	−	0.999198i	$-0.512752\pi$
$229$	−1.21213			−0.0801000			−0.0400500	+	0.999198i	$0.512752\pi$
$230$		0			0
$231$	0.127889	−	0.0465477i	0.00841446	−	0.00306261i
$232$		0			0
$233$	1.08079	−	6.12944i	0.0708046	−	0.401553i	−0.928722	−	0.370777i	$-0.879091\pi$
$233$	1.08079	−	6.12944i	0.0708046	−	0.401553i	0.999526	−	0.0307753i	$-0.00979763\pi$
$234$		0			0
$235$	2.86231	+	4.95767i	0.186717	+	0.323403i
$236$		0			0
$237$	29.6484	−	24.8780i	1.92587	−	1.61600i
$238$		0			0
$239$	−6.36824	+	11.0301i	−0.411927	+	0.713479i	−0.995100	−	0.0988689i	$-0.968478\pi$
$239$	−6.36824	+	11.0301i	−0.411927	+	0.713479i	0.583173	+	0.812348i	$0.301811\pi$
$240$		0			0
$241$	19.4932	+	7.09494i	1.25567	+	0.457025i	0.882313	−	0.470664i	$-0.155985\pi$
$241$	19.4932	+	7.09494i	1.25567	+	0.457025i	0.373354	+	0.927689i	$0.378208\pi$
$242$		0			0
$243$	3.75443	+	21.2924i	0.240847	+	1.36591i
$244$		0			0
$245$	6.99866	+	5.87257i	0.447128	+	0.375185i
$246$		0			0
$247$	−17.6484	−	2.97810i	−1.12294	−	0.189492i
$248$		0			0
$249$	6.74763	+	5.66193i	0.427613	+	0.358810i
$250$		0			0
$251$	1.22281	+	6.93491i	0.0771832	+	0.437727i	0.998771	+	0.0495581i	$0.0157813\pi$
$251$	1.22281	+	6.93491i	0.0771832	+	0.437727i	−0.921588	+	0.388169i	$0.873108\pi$
$252$		0			0
$253$	0.731429	+	0.266219i	0.0459846	+	0.0167370i
$254$		0			0
$255$	12.4081	−	21.4914i	0.777024	−	1.34584i
$256$		0			0
$257$	−12.8969	+	10.8218i	−0.804488	+	0.675046i	−0.949285	−	0.314416i	$-0.898191\pi$
$257$	−12.8969	+	10.8218i	−0.804488	+	0.675046i	0.144797	+	0.989461i	$0.453747\pi$
$258$		0			0
$259$	−0.137689	−	0.238484i	−0.00855557	−	0.0148187i
$260$		0			0
$261$	−2.27450	+	12.8993i	−0.140788	+	0.798449i
$262$		0			0
$263$	7.38578	−	2.68820i	0.455427	−	0.165762i	−0.104113	−	0.994566i	$-0.533200\pi$
$263$	7.38578	−	2.68820i	0.455427	−	0.165762i	0.559539	+	0.828804i	$0.310978\pi$
$264$		0			0
$265$	−12.8726			−0.790756
$266$		0			0
$267$	5.85029			0.358032
$268$		0			0
$269$	30.5035	−	11.1024i	1.85983	−	0.676922i	0.880702	−	0.473670i	$-0.157071\pi$
$269$	30.5035	−	11.1024i	1.85983	−	0.676922i	0.979126	−	0.203252i	$-0.0651511\pi$
$270$		0			0
$271$	0.251030	−	1.42366i	0.0152490	−	0.0864812i	−0.976234	−	0.216721i	$-0.930464\pi$
$271$	0.251030	−	1.42366i	0.0152490	−	0.0864812i	0.991482	+	0.130240i	$0.0415748\pi$
$272$		0			0
$273$	−2.31655	−	4.01239i	−0.140204	−	0.242841i
$274$		0			0
$275$	0.294263	−	0.246916i	0.0177447	−	0.0148896i
$276$		0			0
$277$	−8.53849	+	14.7891i	−0.513028	+	0.888590i	0.486858	+	0.873481i	$0.338143\pi$
$277$	−8.53849	+	14.7891i	−0.513028	+	0.888590i	−0.999886	+	0.0151092i	$0.995190\pi$
$278$		0			0
$279$	−14.8045	−	5.38841i	−0.886324	−	0.322596i
$280$		0			0
$281$	−3.08125	−	17.4746i	−0.183812	−	1.04245i	−0.927472	−	0.373892i	$-0.878023\pi$
$281$	−3.08125	−	17.4746i	−0.183812	−	1.04245i	0.743660	−	0.668558i	$-0.233088\pi$
$282$		0			0
$283$	−20.0194	−	16.7982i	−1.19003	−	0.998551i	−0.999859	−	0.0167996i	$-0.994652\pi$
$283$	−20.0194	−	16.7982i	−1.19003	−	0.998551i	−0.190168	−	0.981752i	$-0.560903\pi$
$284$		0			0
$285$	4.94150	+	13.2718i	0.292709	+	0.786156i
$286$		0			0
$287$	−2.74582	−	2.30401i	−0.162080	−	0.136002i
$288$		0			0
$289$	7.17886	+	40.7134i	0.422286	+	2.39490i
$290$		0			0
$291$	−21.2319	−	7.72778i	−1.24464	−	0.453010i
$292$		0			0
$293$	−3.33868	+	5.78276i	−0.195048	+	0.337832i	−0.946916	−	0.321481i	$-0.895819\pi$
$293$	−3.33868	+	5.78276i	−0.195048	+	0.337832i	0.751868	+	0.659313i	$0.229153\pi$
$294$		0			0
$295$	−8.40941	+	7.05634i	−0.489615	+	0.410836i
$296$		0			0
$297$	0.0268743	+	0.0465477i	0.00155941	+	0.00270097i
$298$		0			0
$299$	4.60132	−	26.0954i	0.266101	−	1.50913i
$300$		0			0
$301$	1.09492	−	0.398519i	0.0631103	−	0.0229703i
$302$		0			0
$303$	−14.8794			−0.854798
$304$		0			0
$305$	−3.39187			−0.194218
$306$		0			0
$307$	−19.3935	+	7.05866i	−1.10685	+	0.402859i	−0.829836	−	0.558007i	$-0.811566\pi$
$307$	−19.3935	+	7.05866i	−1.10685	+	0.402859i	−0.277011	+	0.960867i	$0.589344\pi$
$308$		0			0
$309$	3.15729	−	17.9059i	0.179612	−	1.01863i
$310$		0			0
$311$	0.333626	+	0.577857i	0.0189182	+	0.0327673i	0.875330	−	0.483527i	$-0.160644\pi$
$311$	0.333626	+	0.577857i	0.0189182	+	0.0327673i	−0.856411	+	0.516294i	$0.827311\pi$
$312$		0			0
$313$	−16.9684	+	14.2382i	−0.959109	+	0.804788i	−0.980808	−	0.194976i	$-0.937537\pi$
$313$	−16.9684	+	14.2382i	−0.959109	+	0.804788i	0.0216985	+	0.999765i	$0.493093\pi$
$314$		0			0
$315$	−0.887374	+	1.53698i	−0.0499979	+	0.0865989i
$316$		0			0
$317$	−7.99273	−	2.90911i	−0.448916	−	0.163392i	0.107662	−	0.994188i	$-0.465664\pi$
$317$	−7.99273	−	2.90911i	−0.448916	−	0.163392i	−0.556578	+	0.830795i	$0.687886\pi$
$318$		0			0
$319$	0.0974487	+	0.552659i	0.00545608	+	0.0309430i
$320$		0			0
$321$	10.0109	+	8.40014i	0.558754	+	0.468850i
$322$		0			0
$323$	−28.9552	−	16.4343i	−1.61111	−	0.914427i
$324$		0			0
$325$	−10.0175	−	8.40571i	−0.555673	−	0.466265i
$326$		0			0
$327$	−3.57889	−	20.2969i	−0.197913	−	1.12242i
$328$		0			0
$329$	1.86824	+	0.679984i	0.102999	+	0.0374887i
$330$		0			0
$331$	−6.95336	+	12.0436i	−0.382191	+	0.661975i	−0.991375	−	0.131054i	$-0.958164\pi$
$331$	−6.95336	+	12.0436i	−0.382191	+	0.661975i	0.609184	+	0.793029i	$0.291497\pi$
$332$		0			0
$333$	−1.26920	+	1.06498i	−0.0695517	+	0.0583608i
$334$		0			0
$335$	−5.75103	−	9.96108i	−0.314212	−	0.544232i
$336$		0			0
$337$	−3.29039	+	18.6607i	−0.179239	+	1.01652i	0.753897	+	0.656992i	$0.228172\pi$
$337$	−3.29039	+	18.6607i	−0.179239	+	1.01652i	−0.933136	+	0.359523i	$0.882939\pi$
$338$		0			0
$339$	−14.4452	+	5.25763i	−0.784556	+	0.285555i
$340$		0			0
$341$	−0.674992			−0.0365529
$342$		0			0
$343$	6.44831			0.348176
$344$		0			0
$345$	−19.7023	+	7.17106i	−1.06074	+	0.386077i
$346$		0			0
$347$	−4.27719	+	24.2571i	−0.229612	+	1.30219i	0.624059	+	0.781378i	$0.285483\pi$
$347$	−4.27719	+	24.2571i	−0.229612	+	1.30219i	−0.853670	+	0.520814i	$0.825628\pi$
$348$		0			0
$349$	−11.5522	−	20.0089i	−0.618373	−	1.07105i	−0.989783	−	0.142584i	$-0.954459\pi$
$349$	−11.5522	−	20.0089i	−0.618373	−	1.07105i	0.371410	−	0.928469i	$-0.378874\pi$
$350$		0			0
$351$	1.40167	−	1.17614i	0.0748158	−	0.0627779i
$352$		0			0
$353$	14.4559	−	25.0383i	0.769409	−	1.33266i	−0.168474	−	0.985706i	$-0.553884\pi$
$353$	14.4559	−	25.0383i	0.769409	−	1.33266i	0.937884	−	0.346950i	$-0.112783\pi$
$354$		0			0
$355$	20.3824	+	7.41858i	1.08178	+	0.393737i
$356$		0			0
$357$	−1.49660	−	8.48762i	−0.0792083	−	0.449212i
$358$		0			0
$359$	12.1231	+	10.1725i	0.639835	+	0.536885i	0.903968	−	0.427601i	$-0.140641\pi$
$359$	12.1231	+	10.1725i	0.639835	+	0.536885i	−0.264133	+	0.964486i	$0.585086\pi$
$360$		0			0
$361$	17.7565	−	6.76055i	0.934555	−	0.355818i
$362$		0			0
$363$	20.2934	+	17.0282i	1.06513	+	0.893747i
$364$		0			0
$365$	3.19253	+	18.1058i	0.167105	+	0.947699i
$366$		0			0
$367$	18.6370	+	6.78330i	0.972842	+	0.354086i	0.779053	−	0.626958i	$-0.215700\pi$
$367$	18.6370	+	6.78330i	0.972842	+	0.354086i	0.193789	+	0.981043i	$0.437922\pi$
$368$		0			0
$369$	−10.7829	+	18.6765i	−0.561334	+	0.972259i
$370$		0			0
$371$	−3.42468	+	2.87365i	−0.177800	+	0.149192i
$372$		0			0
$373$	−8.98932	−	15.5700i	−0.465449	−	0.806182i	0.533772	−	0.845628i	$-0.320774\pi$
$373$	−8.98932	−	15.5700i	−0.465449	−	0.806182i	−0.999222	+	0.0394462i	$0.987441\pi$
$374$		0			0
$375$	−4.61768	+	26.1882i	−0.238456	+	1.35235i
$376$		0			0
$377$	17.9522	−	6.53406i	0.924584	−	0.336521i
$378$		0			0
$379$	3.35504			0.172337			0.0861683	−	0.996281i	$-0.472538\pi$
$379$	3.35504			0.172337			0.0861683	+	0.996281i	$0.472538\pi$
$380$		0			0
$381$	0.391874			0.0200763
$382$		0			0
$383$	10.3991	−	3.78498i	0.531372	−	0.193403i	−0.0623790	−	0.998053i	$-0.519869\pi$
$383$	10.3991	−	3.78498i	0.531372	−	0.193403i	0.593751	+	0.804649i	$0.297647\pi$
$384$		0			0
$385$	−0.0132037	+	0.0748822i	−0.000672925	+	0.00381635i
$386$		0			0
$387$	−3.50521	−	6.07121i	−0.178180	−	0.308617i
$388$		0			0
$389$	4.63223	−	3.88690i	0.234863	−	0.197074i	−0.517758	−	0.855527i	$-0.673233\pi$
$389$	4.63223	−	3.88690i	0.234863	−	0.197074i	0.752622	+	0.658453i	$0.228789\pi$
$390$		0			0
$391$	24.6459	−	42.6879i	1.24640	−	2.15882i
$392$		0			0
$393$	−2.23308	−	0.812774i	−0.112644	−	0.0409990i
$394$		0			0
$395$	3.75490	+	21.2951i	0.188930	+	1.07147i
$396$		0			0
$397$	−11.4868	−	9.63857i	−0.576506	−	0.483746i	0.307292	−	0.951615i	$-0.400577\pi$
$397$	−11.4868	−	9.63857i	−0.576506	−	0.483746i	−0.883798	+	0.467870i	$0.845022\pi$
$398$		0			0
$399$	4.27744	+	2.42777i	0.214140	+	0.121541i
$400$		0			0
$401$	−12.7326	−	10.6839i	−0.635836	−	0.533530i	0.266900	−	0.963724i	$-0.414001\pi$
$401$	−12.7326	−	10.6839i	−0.635836	−	0.533530i	−0.902736	+	0.430194i	$0.858445\pi$
$402$		0			0
$403$	3.99020	+	22.6295i	0.198766	+	1.12726i
$404$		0			0
$405$	−12.0530	−	4.38695i	−0.598920	−	0.217989i
$406$		0			0
$407$	−0.0354925	+	0.0614747i	−0.00175930	+	0.00304719i
$408$		0			0
$409$	−9.74376	+	8.17598i	−0.481798	+	0.404276i	−0.851076	−	0.525043i	$-0.824049\pi$
$409$	−9.74376	+	8.17598i	−0.481798	+	0.404276i	0.369278	+	0.929319i	$0.379605\pi$
$410$		0			0
$411$	−2.36706	−	4.09987i	−0.116758	−	0.202231i
$412$		0			0
$413$	−0.662037	+	3.75460i	−0.0325767	+	0.184752i
$414$		0			0
$415$	−4.62449	+	1.68317i	−0.227007	+	0.0826238i
$416$		0			0
$417$	33.2513			1.62832
$418$		0			0
$419$	26.5990			1.29944			0.649722	−	0.760172i	$-0.274885\pi$
$419$	26.5990			1.29944			0.649722	+	0.760172i	$0.274885\pi$
$420$		0			0
$421$	10.0496	−	3.65777i	0.489789	−	0.178269i	−0.0853067	−	0.996355i	$-0.527187\pi$
$421$	10.0496	−	3.65777i	0.489789	−	0.178269i	0.575096	+	0.818086i	$0.304965\pi$
$422$		0			0
$423$	2.07713	−	11.7800i	0.100994	−	0.572764i
$424$		0			0
$425$	−12.1630	−	21.0669i	−0.589991	−	1.02189i
$426$		0			0
$427$	−0.902389	+	0.757194i	−0.0436697	+	0.0366432i
$428$		0			0
$429$	−0.597144	+	1.03428i	−0.0288304	+	0.0499357i
$430$		0			0
$431$	−13.1814	−	4.79763i	−0.634925	−	0.231094i	0.00444841	−	0.999990i	$-0.498584\pi$
$431$	−13.1814	−	4.79763i	−0.634925	−	0.231094i	−0.639374	+	0.768896i	$0.720806\pi$
$432$		0			0
$433$	−2.23261	−	12.6618i	−0.107292	−	0.608486i	−0.990280	−	0.139089i	$-0.955583\pi$
$433$	−2.23261	−	12.6618i	−0.107292	−	0.608486i	0.882987	−	0.469397i	$-0.155529\pi$
$434$		0			0
$435$	−11.5799	−	9.71670i	−0.555214	−	0.465880i
$436$		0			0
$437$	9.81521	+	26.3616i	0.469525	+	1.26105i
$438$		0			0
$439$	12.3439	+	10.3578i	0.589142	+	0.494349i	0.887935	−	0.459969i	$-0.152140\pi$
$439$	12.3439	+	10.3578i	0.589142	+	0.494349i	−0.298793	+	0.954318i	$0.596584\pi$
$440$		0			0
$441$	−3.31496	−	18.8001i	−0.157855	−	0.895241i
$442$		0			0
$443$	−3.32383	−	1.20977i	−0.157920	−	0.0574781i	0.261851	−	0.965108i	$-0.415667\pi$
$443$	−3.32383	−	1.20977i	−0.157920	−	0.0574781i	−0.419770	+	0.907630i	$0.637889\pi$
$444$		0			0
$445$	−1.63429	+	2.83067i	−0.0774726	+	0.134186i
$446$		0			0
$447$	15.0424	−	12.6220i	0.711479	−	0.597002i
$448$		0			0
$449$	−11.6853	−	20.2395i	−0.551461	−	0.955159i	−0.998169	−	0.0604795i	$-0.980737\pi$
$449$	−11.6853	−	20.2395i	−0.551461	−	0.955159i	0.446708	−	0.894680i	$-0.352596\pi$
$450$		0			0
$451$	−0.160444	+	0.909926i	−0.00755503	+	0.0428467i
$452$		0			0
$453$	−39.9359	+	14.5355i	−1.87635	+	0.682936i
$454$		0			0
$455$	2.58853			0.121352
$456$		0			0
$457$	−7.53890			−0.352655			−0.176327	−	0.984332i	$-0.556422\pi$
$457$	−7.53890			−0.352655			−0.176327	+	0.984332i	$0.556422\pi$
$458$		0			0
$459$	3.19846	−	1.16415i	0.149291	−	0.0543377i
$460$		0			0
$461$	−1.60900	+	9.12511i	−0.0749388	+	0.424999i	0.924139	+	0.382057i	$0.124784\pi$
$461$	−1.60900	+	9.12511i	−0.0749388	+	0.424999i	−0.999078	+	0.0429420i	$0.986327\pi$
$462$		0			0
$463$	20.3111	+	35.1798i	0.943936	+	1.63495i	0.757867	+	0.652409i	$0.226242\pi$
$463$	20.3111	+	35.1798i	0.943936	+	1.63495i	0.186069	+	0.982537i	$0.440425\pi$
$464$		0			0
$465$	13.9283	−	11.6872i	0.645909	−	0.541982i
$466$		0			0
$467$	13.8735	−	24.0295i	0.641987	−	1.11195i	−0.343002	−	0.939335i	$-0.611444\pi$
$467$	13.8735	−	24.0295i	0.641987	−	1.11195i	0.984989	−	0.172619i	$-0.0552230\pi$
$468$		0			0
$469$	−3.75372	−	1.36624i	−0.173331	−	0.0630872i
$470$		0			0
$471$	8.39250	+	47.5962i	0.386706	+	2.19312i
$472$		0			0
$473$	−0.230085	−	0.193064i	−0.0105793	−	0.00887711i
$474$		0			0
$475$	13.6887	+	2.30991i	0.628079	+	0.105986i
$476$		0			0
$477$	20.6047	+	17.2894i	0.943425	+	0.791628i
$478$		0			0
$479$	−6.00521	−	34.0573i	−0.274385	−	1.55612i	−0.740908	−	0.671607i	$-0.765604\pi$
$479$	−6.00521	−	34.0573i	−0.274385	−	1.55612i	0.466523	−	0.884509i	$-0.345507\pi$
$480$		0			0
$481$	2.27079	+	0.826501i	0.103539	+	0.0376852i
$482$		0			0
$483$	−3.64084	+	6.30613i	−0.165664	+	0.286939i
$484$		0			0
$485$	9.67024	−	8.11430i	0.439103	−	0.368451i
$486$		0			0
$487$	−8.64409	−	14.9720i	−0.391701	−	0.678446i	0.600973	−	0.799269i	$-0.294780\pi$
$487$	−8.64409	−	14.9720i	−0.391701	−	0.678446i	−0.992674	+	0.120823i	$0.961447\pi$
$488$		0			0
$489$	−3.88768	+	22.0481i	−0.175807	+	0.997051i
$490$		0			0
$491$	−22.9739	+	8.36181i	−1.03680	+	0.377363i	−0.803665	−	0.595082i	$-0.797120\pi$
$491$	−22.9739	+	8.36181i	−1.03680	+	0.377363i	−0.233132	+	0.972445i	$0.574897\pi$
$492$		0			0
$493$	35.5381			1.60055
$494$		0			0
$495$	0.457482			0.0205623
$496$		0			0
$497$	7.07873	−	2.57645i	0.317524	−	0.115569i
$498$		0			0
$499$	3.68438	−	20.8952i	0.164936	−	0.935396i	−0.784195	−	0.620514i	$-0.786924\pi$
$499$	3.68438	−	20.8952i	0.164936	−	0.935396i	0.949131	−	0.314882i	$-0.101965\pi$
$500$		0			0
$501$	−14.2554	−	24.6910i	−0.636883	−	1.10311i
$502$		0			0
$503$	24.8824	−	20.8788i	1.10945	−	0.930939i	0.111426	−	0.993773i	$-0.464458\pi$
$503$	24.8824	−	20.8788i	1.10945	−	0.930939i	0.998024	+	0.0628333i	$0.0200136\pi$
$504$		0			0
$505$	4.15657	−	7.19940i	0.184965	−	0.320369i
$506$		0			0
$507$	8.74644	+	3.18345i	0.388443	+	0.141382i
$508$		0			0
$509$	4.56300	+	25.8780i	0.202251	+	1.14702i	0.901707	+	0.432348i	$0.142315\pi$
$509$	4.56300	+	25.8780i	0.202251	+	1.14702i	−0.699456	+	0.714676i	$0.746574\pi$
$510$		0			0
$511$	4.89124	+	4.10424i	0.216376	+	0.181561i
$512$		0			0
$513$	−0.650893	+	1.83012i	−0.0287376	+	0.0808019i
$514$		0			0
$515$	7.78177	+	6.52968i	0.342906	+	0.287732i
$516$		0			0
$517$	−0.0889927	−	0.504703i	−0.00391389	−	0.0221968i
$518$		0			0
$519$	−50.9154	−	18.5317i	−2.23494	−	0.813451i
$520$		0			0
$521$	0.305407	−	0.528981i	0.0133801	−	0.0231751i	−0.859258	−	0.511543i	$-0.829074\pi$
$521$	0.305407	−	0.528981i	0.0133801	−	0.0231751i	0.872638	+	0.488368i	$0.162408\pi$
$522$		0			0
$523$	−6.90348	+	5.79271i	−0.301868	+	0.253298i	−0.781121	−	0.624379i	$-0.785352\pi$
$523$	−6.90348	+	5.79271i	−0.301868	+	0.253298i	0.479253	+	0.877677i	$0.340908\pi$
$524$		0			0
$525$	1.79679	+	3.11213i	0.0784183	+	0.135824i
$526$		0			0
$527$	−7.42262	+	42.0958i	−0.323334	+	1.83372i
$528$		0			0
$529$	−17.5214	+	6.37727i	−0.761800	+	0.277273i
$530$		0			0
$531$	22.9382			0.995432
$532$		0			0
$533$	31.4543			1.36244
$534$		0			0
$535$	−6.86097	+	2.49719i	−0.296625	+	0.107963i
$536$		0			0
$537$	−1.27167	+	7.21200i	−0.0548766	+	0.311221i
$538$		0			0
$539$	−0.408948	−	0.708319i	−0.0176146	−	0.0305094i
$540$		0			0
$541$	−12.5489	+	10.5298i	−0.539520	+	0.452711i	−0.871374	−	0.490620i	$-0.836770\pi$
$541$	−12.5489	+	10.5298i	−0.539520	+	0.452711i	0.331854	+	0.943331i	$0.392326\pi$
$542$		0			0
$543$	13.7861	−	23.8782i	0.591619	−	1.02471i
$544$		0			0
$545$	10.8204	+	3.93831i	0.463496	+	0.168699i
$546$		0			0
$547$	−6.84760	−	38.8347i	−0.292782	−	1.66045i	−0.676082	−	0.736827i	$-0.736323\pi$
$547$	−6.84760	−	38.8347i	−0.292782	−	1.66045i	0.383299	−	0.923624i	$-0.374788\pi$
$548$		0			0
$549$	5.42926	+	4.55569i	0.231715	+	0.194432i
$550$		0			0
$551$	−12.9214	+	15.6314i	−0.550472	+	0.665922i
$552$		0			0
$553$	5.75284	+	4.82721i	0.244636	+	0.205274i
$554$		0			0
$555$	−0.332033	−	1.88305i	−0.0140940	−	0.0799312i
$556$		0			0
$557$	−38.4568	−	13.9971i	−1.62947	−	0.593078i	−0.644315	−	0.764760i	$-0.722858\pi$
$557$	−38.4568	−	13.9971i	−1.62947	−	0.593078i	−0.985152	+	0.171682i	$0.945080\pi$
$558$		0			0
$559$	−5.11246	+	8.85505i	−0.216234	+	0.374529i
$560$		0			0
$561$	−1.70187	+	1.42804i	−0.0718529	+	0.0602917i
$562$		0			0
$563$	3.57650	+	6.19469i	0.150732	+	0.261075i	0.931497	−	0.363750i	$-0.118504\pi$
$563$	3.57650	+	6.19469i	0.150732	+	0.261075i	−0.780765	+	0.624825i	$0.785170\pi$
$564$		0			0
$565$	1.49138	−	8.45805i	0.0627429	−	0.355833i
$566$		0			0
$567$	−4.18597	+	1.52357i	−0.175794	+	0.0639839i
$568$		0			0
$569$	4.13516			0.173355			0.0866775	−	0.996236i	$-0.472375\pi$
$569$	4.13516			0.173355			0.0866775	+	0.996236i	$0.472375\pi$
$570$		0			0
$571$	36.9513			1.54636			0.773182	−	0.634184i	$-0.218664\pi$
$571$	36.9513			1.54636			0.773182	+	0.634184i	$0.218664\pi$
$572$		0			0
$573$	9.12613	−	3.32164i	0.381250	−	0.138764i
$574$		0			0
$575$	−3.56893	+	20.2404i	−0.148834	+	0.844082i
$576$		0			0
$577$	−14.8097	−	25.6512i	−0.616538	−	1.06787i	−0.990113	−	0.140275i	$-0.955201\pi$
$577$	−14.8097	−	25.6512i	−0.616538	−	1.06787i	0.373575	−	0.927600i	$-0.378132\pi$
$578$		0			0
$579$	−30.6264	+	25.6986i	−1.27279	+	1.06800i
$580$		0			0
$581$	−0.854570	+	1.48016i	−0.0354536	+	0.0614074i
$582$		0			0
$583$	1.08290	+	0.394144i	0.0448492	+	0.0163238i
$584$		0			0
$585$	−2.70439	−	15.3374i	−0.111813	−	0.634122i
$586$		0			0
$587$	−33.8810	−	28.4296i	−1.39842	−	1.17341i	−0.961795	−	0.273770i	$-0.911729\pi$
$587$	−33.8810	−	28.4296i	−1.39842	−	1.17341i	−0.436625	−	0.899644i	$-0.643826\pi$
$588$		0			0
$589$	−15.8170	−	18.5706i	−0.651729	−	0.765189i
$590$		0			0
$591$	−13.8317	−	11.6061i	−0.568958	−	0.477413i
$592$		0			0
$593$	3.19759	+	18.1344i	0.131309	+	0.744691i	0.977359	+	0.211587i	$0.0678633\pi$
$593$	3.19759	+	18.1344i	0.131309	+	0.744691i	−0.846050	+	0.533104i	$0.821026\pi$
$594$		0			0
$595$	4.52481	+	1.64690i	0.185499	+	0.0675162i
$596$		0			0
$597$	−28.6655	+	49.6501i	−1.17320	+	2.03204i
$598$		0			0
$599$	−32.4085	+	27.1940i	−1.32418	+	1.11112i	−0.338776	+	0.940867i	$0.610013\pi$
$599$	−32.4085	+	27.1940i	−1.32418	+	1.11112i	−0.985401	+	0.170249i	$0.945543\pi$
$600$		0			0
$601$	−21.5005	−	37.2399i	−0.877022	−	1.51905i	−0.854593	−	0.519299i	$-0.826193\pi$
$601$	−21.5005	−	37.2399i	−0.877022	−	1.51905i	−0.0224296	−	0.999748i	$-0.507140\pi$
$602$		0			0
$603$	−4.17343	+	23.6687i	−0.169955	+	0.963864i
$604$		0			0
$605$	−13.9081	+	5.06212i	−0.565443	+	0.205805i
$606$		0			0
$607$	−13.0787			−0.530849			−0.265425	−	0.964132i	$-0.585512\pi$
$607$	−13.0787			−0.530849			−0.265425	+	0.964132i	$0.585512\pi$
$608$		0			0
$609$	−5.24990			−0.212737
$610$		0			0
$611$	−16.3944	+	5.96707i	−0.663246	+	0.241402i
$612$		0			0
$613$	−2.33450	+	13.2396i	−0.0942897	+	0.534743i	0.900673	+	0.434498i	$0.143074\pi$
$613$	−2.33450	+	13.2396i	−0.0942897	+	0.534743i	−0.994963	+	0.100246i	$0.968037\pi$
$614$		0			0
$615$	−12.4443	−	21.5541i	−0.501802	−	0.869146i
$616$		0			0
$617$	9.28177	−	7.78833i	0.373670	−	0.313546i	−0.436541	−	0.899684i	$-0.643797\pi$
$617$	9.28177	−	7.78833i	0.373670	−	0.313546i	0.810211	+	0.586138i	$0.199352\pi$
$618$		0			0
$619$	13.5672	−	23.4990i	0.545311	−	0.944506i	−0.453277	−	0.891370i	$-0.649745\pi$
$619$	13.5672	−	23.4990i	0.545311	−	0.944506i	0.998587	−	0.0531358i	$-0.0169216\pi$
$620$		0			0
$621$	−2.70233	−	0.983569i	−0.108441	−	0.0394693i
$622$		0			0
$623$	0.197119	+	1.11792i	0.00789740	+	0.0447884i
$624$		0			0
$625$	0.817267	+	0.685768i	0.0326907	+	0.0274307i
$626$		0			0
$627$	−0.00933335	−	1.26779i	−0.000372738	−	0.0506307i
$628$		0			0
$629$	3.44356	+	2.88949i	0.137304	+	0.115212i
$630$		0			0
$631$	4.68004	+	26.5419i	0.186310	+	1.05661i	0.924261	+	0.381761i	$0.124682\pi$
$631$	4.68004	+	26.5419i	0.186310	+	1.05661i	−0.737952	+	0.674854i	$0.764207\pi$
$632$		0			0
$633$	6.88161	+	2.50470i	0.273519	+	0.0995529i
$634$		0			0
$635$	−0.109470	+	0.189608i	−0.00434420	+	0.00752438i
$636$		0			0
$637$	−21.3293	+	17.8974i	−0.845099	+	0.709123i
$638$		0			0
$639$	−22.6614	−	39.2507i	−0.896470	−	1.55273i
$640$		0			0
$641$	−0.0812519	+	0.460802i	−0.00320926	+	0.0182006i	−0.986370	−	0.164540i	$-0.947386\pi$
$641$	−0.0812519	+	0.460802i	−0.00320926	+	0.0182006i	0.983161	+	0.182741i	$0.0584970\pi$
$642$		0			0
$643$	30.0035	−	10.9204i	1.18322	−	0.430657i	0.325882	−	0.945410i	$-0.394339\pi$
$643$	30.0035	−	10.9204i	1.18322	−	0.430657i	0.857338	+	0.514753i	$0.172116\pi$
$644$		0			0
$645$	8.09059			0.318566
$646$		0			0
$647$	−24.2594			−0.953735			−0.476868	−	0.878975i	$-0.658228\pi$
$647$	−24.2594			−0.953735			−0.476868	+	0.878975i	$0.658228\pi$
$648$		0			0
$649$	0.923496	−	0.336125i	0.0362504	−	0.0131941i
$650$		0			0
$651$	1.09652	−	6.21865i	0.0429758	−	0.243728i
$652$		0			0
$653$	12.7567	+	22.0953i	0.499209	+	0.864655i	1.00000		0.000913495i	$-0.000290775\pi$
$653$	12.7567	+	22.0953i	0.499209	+	0.864655i	−0.500791	+	0.865568i	$0.666957\pi$
$654$		0			0
$655$	1.01707	−	0.853427i	0.0397404	−	0.0333461i
$656$		0			0
$657$	19.2080	−	33.2693i	0.749376	−	1.29796i
$658$		0			0
$659$	3.94697	+	1.43658i	0.153752	+	0.0559611i	0.417750	−	0.908562i	$-0.362819\pi$
$659$	3.94697	+	1.43658i	0.153752	+	0.0559611i	−0.263998	+	0.964523i	$0.585041\pi$
$660$		0			0
$661$	2.97889	+	16.8941i	0.115866	+	0.657106i	0.986318	+	0.164854i	$0.0527152\pi$
$661$	2.97889	+	16.8941i	0.115866	+	0.657106i	−0.870453	+	0.492252i	$0.836174\pi$
$662$		0			0
$663$	57.9363	+	48.6144i	2.25006	+	1.88803i
$664$		0			0
$665$	−2.36959	+	1.39144i	−0.0918886	+	0.0539577i
$666$		0			0
$667$	−23.0009	−	19.3001i	−0.890600	−	0.747302i
$668$		0			0
$669$	−2.63104	−	14.9214i	−0.101722	−	0.576894i
$670$		0			0
$671$	0.285340	+	0.103855i	0.0110154	+	0.00400929i
$672$		0			0
$673$	0.124485	−	0.215615i	0.00479855	−	0.00831133i	−0.863616	−	0.504150i	$-0.831806\pi$
$673$	0.124485	−	0.215615i	0.00479855	−	0.00831133i	0.868415	+	0.495839i	$0.165139\pi$
$674$		0			0
$675$	−1.08718	+	0.912254i	−0.0418456	+	0.0351127i
$676$		0			0
$677$	17.1150	+	29.6440i	0.657782	+	1.13931i	0.981188	+	0.193052i	$0.0618387\pi$
$677$	17.1150	+	29.6440i	0.657782	+	1.13931i	−0.323406	+	0.946260i	$0.604828\pi$
$678$		0			0
$679$	0.761297	−	4.31753i	0.0292159	−	0.165692i
$680$		0			0
$681$	9.28699	−	3.38019i	0.355878	−	0.129529i
$682$		0			0
$683$	−1.97771			−0.0756750			−0.0378375	−	0.999284i	$-0.512047\pi$
$683$	−1.97771			−0.0756750			−0.0378375	+	0.999284i	$0.512047\pi$
$684$		0			0
$685$	2.64496			0.101059
$686$		0			0
$687$	−2.74675	+	0.999735i	−0.104795	+	0.0381423i
$688$		0			0
$689$	6.81238	−	38.6349i	0.259531	−	1.47187i
$690$		0			0
$691$	−18.4243	−	31.9118i	−0.700892	−	1.21398i	−0.968154	−	0.250357i	$-0.919452\pi$
$691$	−18.4243	−	31.9118i	−0.700892	−	1.21398i	0.267261	−	0.963624i	$-0.413881\pi$
$692$		0			0
$693$	0.121711	−	0.102127i	0.00462340	−	0.00387949i
$694$		0			0
$695$	−9.28880	+	16.0887i	−0.352344	+	0.610278i
$696$		0			0
$697$	54.9830	+	20.0122i	2.08263	+	0.758015i
$698$		0			0
$699$	−2.60629	−	14.7810i	−0.0985788	−	0.559068i
$700$		0			0
$701$	4.82429	+	4.04806i	0.182211	+	0.152893i	0.729331	−	0.684161i	$-0.239831\pi$
$701$	4.82429	+	4.04806i	0.182211	+	0.152893i	−0.547120	+	0.837054i	$0.684276\pi$
$702$		0			0
$703$	−2.52300	+	0.464050i	−0.0951569	+	0.0175020i
$704$		0			0
$705$	10.5751	+	8.87354i	0.398280	+	0.334197i
$706$		0			0
$707$	−0.501344	−	2.84326i	−0.0188550	−	0.106932i
$708$		0			0
$709$	17.6557	+	6.42615i	0.663074	+	0.241339i	0.651563	−	0.758595i	$-0.274114\pi$
$709$	17.6557	+	6.42615i	0.663074	+	0.241339i	0.0115108	+	0.999934i	$0.496336\pi$
$710$		0			0
$711$	22.5915	−	39.1297i	0.847248	−	1.46748i
$712$		0			0
$713$	27.6655	−	23.2141i	1.03608	−	0.869375i
$714$		0			0
$715$	−0.333626	−	0.577857i	−0.0124769	−	0.0216106i
$716$		0			0
$717$	−5.33338	+	30.2471i	−0.199179	+	1.12960i
$718$		0			0
$719$	−29.1232	+	10.6000i	−1.08611	+	0.395312i	−0.822179	−	0.569229i	$-0.807242\pi$
$719$	−29.1232	+	10.6000i	−1.08611	+	0.395312i	−0.263933	+	0.964541i	$0.585020\pi$
$720$		0			0
$721$	3.52797			0.131388
$722$		0			0
$723$	50.0242			1.86042
$724$		0			0
$725$	−13.9243	+	5.06802i	−0.517134	+	0.188221i
$726$		0			0
$727$	2.28106	−	12.9365i	0.0845998	−	0.479789i	−0.912842	−	0.408312i	$-0.866118\pi$
$727$	2.28106	−	12.9365i	0.0845998	−	0.479789i	0.997442	−	0.0714773i	$-0.0227713\pi$
$728$		0			0
$729$	11.7888	+	20.4188i	0.436622	+	0.756252i
$730$		0			0
$731$	−14.5706	+	12.2262i	−0.538912	+	0.452201i
$732$		0			0
$733$	14.9834	−	25.9520i	0.553424	−	0.958559i	−0.444600	−	0.895729i	$-0.646654\pi$
$733$	14.9834	−	25.9520i	0.553424	−	0.958559i	0.998024	−	0.0628297i	$-0.0200125\pi$
$734$		0			0
$735$	20.7028	+	7.53520i	0.763634	+	0.277940i
$736$		0			0
$737$	0.178806	+	1.01406i	0.00658642	+	0.0373534i
$738$		0			0
$739$	19.9388	+	16.7307i	0.733461	+	0.615447i	0.931073	−	0.364833i	$-0.118874\pi$
$739$	19.9388	+	16.7307i	0.733461	+	0.615447i	−0.197612	+	0.980280i	$0.563318\pi$
$740$		0			0
$741$	−42.4484	+	7.80743i	−1.55938	+	0.286813i
$742$		0			0
$743$	16.3478	+	13.7174i	0.599741	+	0.503243i	0.891362	−	0.453291i	$-0.149750\pi$
$743$	16.3478	+	13.7174i	0.599741	+	0.503243i	−0.291621	+	0.956534i	$0.594195\pi$
$744$		0			0
$745$	1.90508	+	10.8042i	0.0697966	+	0.395836i
$746$		0			0
$747$	9.66297	+	3.51703i	0.353550	+	0.128682i
$748$		0			0
$749$	−1.26786	+	2.19599i	−0.0463264	+	0.0802397i
$750$		0			0
$751$	17.0183	−	14.2800i	0.621005	−	0.521085i	−0.277114	−	0.960837i	$-0.589378\pi$
$751$	17.0183	−	14.2800i	0.621005	−	0.521085i	0.898119	+	0.439752i	$0.144934\pi$
$752$		0			0
$753$	8.49067	+	14.7063i	0.309417	+	0.535926i
$754$		0			0
$755$	4.12314	−	23.3835i	0.150056	−	0.851012i
$756$		0			0
$757$	38.1575	−	13.8882i	1.38686	−	0.504775i	0.462608	−	0.886563i	$-0.346914\pi$
$757$	38.1575	−	13.8882i	1.38686	−	0.504775i	0.924250	+	0.381788i	$0.124691\pi$
$758$		0			0
$759$	1.87702			0.0681316
$760$		0			0
$761$	39.0455			1.41540			0.707699	−	0.706514i	$-0.249733\pi$
$761$	39.0455			1.41540			0.707699	+	0.706514i	$0.249733\pi$
$762$		0			0
$763$	3.75789	−	1.36776i	0.136045	−	0.0495163i
$764$		0			0
$765$	5.03074	−	28.5308i	0.181887	−	1.03153i
$766$		0			0
$767$	−16.7280	−	28.9738i	−0.604014	−	1.04618i
$768$		0			0
$769$	−22.6208	+	18.9811i	−0.815728	+	0.684477i	−0.951968	−	0.306199i	$-0.900943\pi$
$769$	−22.6208	+	18.9811i	−0.815728	+	0.684477i	0.136239	+	0.990676i	$0.456498\pi$
$770$		0			0
$771$	−20.2995	+	35.1597i	−0.731068	+	1.26625i
$772$		0			0
$773$	23.4111	+	8.52093i	0.842037	+	0.306477i	0.726790	−	0.686860i	$-0.241012\pi$
$773$	23.4111	+	8.52093i	0.842037	+	0.306477i	0.115248	+	0.993337i	$0.463234\pi$
$774$		0			0
$775$	−3.09492	−	17.5522i	−0.111173	−	0.630493i
$776$		0			0
$777$	−0.508704	−	0.426854i	−0.0182497	−	0.0153133i
$778$		0			0
$779$	−28.7939	+	16.9080i	−1.03165	+	0.605791i
$780$		0			0
$781$	−1.48751	−	1.24817i	−0.0532273	−	0.0446630i
$782$		0			0
$783$	−0.360033	−	2.04185i	−0.0128665	−	0.0729698i
$784$		0			0
$785$	−25.3739	−	9.23535i	−0.905634	−	0.329624i
$786$		0			0
$787$	−21.7430	+	37.6601i	−0.775056	+	1.34244i	0.159707	+	0.987164i	$0.448945\pi$
$787$	−21.7430	+	37.6601i	−0.775056	+	1.34244i	−0.934763	+	0.355271i	$0.884388\pi$
$788$		0			0
$789$	14.5194	−	12.1832i	0.516903	−	0.433733i
$790$		0			0
$791$	−1.49138	−	2.58315i	−0.0530274	−	0.0918462i
$792$		0			0
$793$	1.79503	−	10.1801i	0.0637435	−	0.361508i
$794$		0			0
$795$	−29.1698	+	10.6170i	−1.03455	+	0.376544i
$796$		0			0
$797$	−36.2158			−1.28283			−0.641414	−	0.767195i	$-0.721652\pi$
$797$	−36.2158			−1.28283			−0.641414	+	0.767195i	$0.721652\pi$
$798$		0			0
$799$	−32.4543			−1.14815
$800$		0			0
$801$	6.41787	−	2.33591i	0.226764	−	0.0825355i
$802$		0			0
$803$	0.285807	−	1.62089i	0.0100859	−	0.0572000i
$804$		0			0
$805$	−2.03415	−	3.52325i	−0.0716943	−	0.124178i
$806$		0			0
$807$	59.9653	−	50.3168i	2.11088	−	1.77124i
$808$		0			0
$809$	−14.2515	+	24.6843i	−0.501056	+	0.867854i	0.498943	+	0.866635i	$0.333722\pi$
$809$	−14.2515	+	24.6843i	−0.501056	+	0.867854i	−0.999999	+	0.00121972i	$0.999612\pi$
$810$		0			0
$811$	8.90255	+	3.24026i	0.312611	+	0.113781i	0.493561	−	0.869711i	$-0.335695\pi$
$811$	8.90255	+	3.24026i	0.312611	+	0.113781i	−0.180950	+	0.983492i	$0.557917\pi$
$812$		0			0
$813$	−0.605352	−	3.43312i	−0.0212306	−	0.120405i
$814$		0			0
$815$	−9.58197	−	8.04023i	−0.335642	−	0.281637i
$816$		0			0
$817$	−0.0799077	−	10.8542i	−0.00279562	−	0.379742i
$818$		0			0
$819$	−4.14337	−	3.47670i	−0.144781	−	0.121486i
$820$		0			0
$821$	−1.58482	−	8.98795i	−0.0553105	−	0.313682i	0.944583	−	0.328273i	$-0.106466\pi$
$821$	−1.58482	−	8.98795i	−0.0553105	−	0.313682i	−0.999894	+	0.0145911i	$0.995355\pi$
$822$		0			0
$823$	1.75150	+	0.637493i	0.0610533	+	0.0222216i	0.372366	−	0.928086i	$-0.378547\pi$
$823$	1.75150	+	0.637493i	0.0610533	+	0.0222216i	−0.311313	+	0.950307i	$0.600769\pi$
$824$		0			0
$825$	0.463163	−	0.802222i	0.0161253	−	0.0279298i
$826$		0			0
$827$	31.1366	−	26.1267i	1.08272	−	0.908514i	0.0865802	−	0.996245i	$-0.472406\pi$
$827$	31.1366	−	26.1267i	1.08272	−	0.908514i	0.996144	+	0.0877312i	$0.0279617\pi$
$828$		0			0
$829$	−14.2677	−	24.7124i	−0.495537	−	0.858296i	0.504449	−	0.863441i	$-0.331696\pi$
$829$	−14.2677	−	24.7124i	−0.495537	−	0.858296i	−0.999987	+	0.00514524i	$0.998362\pi$
$830$		0			0
$831$	−7.15095	+	40.5550i	−0.248064	+	1.40684i
$832$		0			0
$833$	−48.6712	+	17.7149i	−1.68636	+	0.613784i
$834$		0			0
$835$	15.9290			0.551246
$836$		0			0
$837$	2.49382			0.0861991
$838$		0			0
$839$	25.6180	−	9.32418i	0.884431	−	0.321907i	0.140434	−	0.990090i	$-0.455150\pi$
$839$	25.6180	−	9.32418i	0.884431	−	0.321907i	0.743997	+	0.668183i	$0.232928\pi$
$840$		0			0
$841$	−1.27672	+	7.24065i	−0.0440249	+	0.249678i
$842$		0			0
$843$	−21.3949	−	37.0570i	−0.736878	−	1.27631i
$844$		0			0
$845$	−3.98364	+	3.34267i	−0.137041	+	0.114991i
$846$		0			0
$847$	−2.57011	+	4.45156i	−0.0883099	+	0.152957i
$848$		0			0
$849$	−59.2195	−	21.5541i	−2.03241	−	0.739736i
$850$		0			0
$851$	−0.659511	−	3.74027i	−0.0226077	−	0.128215i
$852$		0			0
$853$	35.0337	+	29.3968i	1.19953	+	1.00653i	0.999643	+	0.0267086i	$0.00850262\pi$
$853$	35.0337	+	29.3968i	1.19953	+	1.00653i	0.199889	+	0.979819i	$0.435942\pi$
$854$		0			0
$855$	10.7201	+	12.5864i	0.366620	+	0.430446i
$856$		0			0
$857$	−12.1250	−	10.1740i	−0.414180	−	0.347539i	0.411764	−	0.911291i	$-0.364913\pi$
$857$	−12.1250	−	10.1740i	−0.414180	−	0.347539i	−0.825944	+	0.563752i	$0.809357\pi$
$858$		0			0
$859$	−6.48782	−	36.7942i	−0.221361	−	1.25540i	−0.869520	−	0.493898i	$-0.835572\pi$
$859$	−6.48782	−	36.7942i	−0.221361	−	1.25540i	0.648159	−	0.761505i	$-0.275539\pi$
$860$		0			0
$861$	−8.12243	−	2.95632i	−0.276812	−	0.100751i
$862$		0			0
$863$	−7.61246	+	13.1852i	−0.259131	+	0.448829i	−0.966009	−	0.258507i	$-0.916770\pi$
$863$	−7.61246	+	13.1852i	−0.259131	+	0.448829i	0.706878	+	0.707335i	$0.250103\pi$
$864$		0			0
$865$	23.1898	−	19.4586i	0.788478	−	0.661612i
$866$		0			0
$867$	49.8469	+	86.3373i	1.69289	+	2.93217i
$868$		0			0
$869$	0.336152	−	1.90641i	0.0114032	−	0.0646706i
$870$		0			0
$871$	32.9401	−	11.9892i	1.11613	−	0.406239i
$872$		0			0
$873$	−26.3773			−0.892737
$874$		0			0
$875$	−5.15982			−0.174434
$876$		0			0
$877$	−47.5338	+	17.3009i	−1.60510	+	0.584209i	−0.980463	−	0.196704i	$-0.936976\pi$
$877$	−47.5338	+	17.3009i	−1.60510	+	0.584209i	−0.624639	+	0.780913i	$0.714754\pi$
$878$		0			0
$879$	−2.79613	+	15.8576i	−0.0943111	+	0.534865i
$880$		0			0
$881$	10.7724	+	18.6584i	0.362933	+	0.628618i	0.988442	−	0.151599i	$-0.0484421\pi$
$881$	10.7724	+	18.6584i	0.362933	+	0.628618i	−0.625509	+	0.780217i	$0.715109\pi$
$882$		0			0
$883$	−14.0981	+	11.8297i	−0.474438	+	0.398101i	−0.848410	−	0.529339i	$-0.822440\pi$
$883$	−14.0981	+	11.8297i	−0.474438	+	0.398101i	0.373972	+	0.927440i	$0.377996\pi$
$884$		0			0
$885$	−13.2362	+	22.9258i	−0.444931	+	0.770643i
$886$		0			0
$887$	25.8354	+	9.40333i	0.867469	+	0.315733i	0.737142	−	0.675738i	$-0.236175\pi$
$887$	25.8354	+	9.40333i	0.867469	+	0.315733i	0.130327	+	0.991471i	$0.458397\pi$
$888$		0			0
$889$	0.0132037	+	0.0748822i	0.000442839	+	0.00251147i
$890$		0			0
$891$	0.879634	+	0.738100i	0.0294688	+	0.0247273i
$892$		0			0
$893$	11.8002	−	14.2750i	0.394878	−	0.477696i
$894$		0			0
$895$	−3.13429	−	2.62998i	−0.104768	−	0.0879105i
$896$		0			0
$897$	−11.0960	−	62.9283i	−0.370483	−	2.10112i
$898$		0			0
$899$	24.4675	+	8.90544i	0.816037	+	0.297013i
$900$		0			0
$901$	36.4889	−	63.2006i	1.21562	−	2.10552i
$902$		0			0
$903$	2.15246	−	1.80612i	0.0716292	−	0.0601041i
$904$		0			0
$905$	7.70233	+	13.3408i	0.256034	+	0.443464i
$906$		0			0
$907$	−7.55913	+	42.8699i	−0.250997	+	1.42347i	0.555147	+	0.831752i	$0.312662\pi$
$907$	−7.55913	+	42.8699i	−0.250997	+	1.42347i	−0.806143	+	0.591720i	$0.798449\pi$
$908$		0			0
$909$	−16.3229	+	5.94107i	−0.541398	+	0.197053i
$910$		0			0
$911$	0.662199			0.0219396			0.0109698	−	0.999940i	$-0.496508\pi$
$911$	0.662199			0.0219396			0.0109698	+	0.999940i	$0.496508\pi$
$912$		0			0
$913$	0.440570			0.0145807
$914$		0			0
$915$	−7.68614	+	2.79752i	−0.254096	+	0.0924833i
$916$		0			0
$917$	0.0800699	−	0.454099i	0.00264414	−	0.0149957i
$918$		0			0
$919$	24.4586	+	42.3635i	0.806814	+	1.39744i	0.915060	+	0.403319i	$0.132143\pi$
$919$	24.4586	+	42.3635i	0.806814	+	1.39744i	−0.108246	+	0.994124i	$0.534523\pi$
$920$		0			0
$921$	−38.1248	+	31.9905i	−1.25625	+	1.05412i
$922$		0			0
$923$	−33.0523	+	57.2483i	−1.08793	+	1.88435i
$924$		0			0
$925$	−1.76130	−	0.641060i	−0.0579111	−	0.0210779i
$926$		0			0
$927$	−3.68589	−	20.9037i	−0.121060	−	0.686568i
$928$		0			0
$929$	−7.52410	−	6.31347i	−0.246858	−	0.207138i	0.510960	−	0.859604i	$-0.329290\pi$
$929$	−7.52410	−	6.31347i	−0.246858	−	0.207138i	−0.757818	+	0.652466i	$0.773734\pi$
$930$		0			0
$931$	9.90467	−	27.8491i	0.324612	−	0.912716i
$932$		0			0
$933$	1.23261	+	1.03428i	0.0403539	+	0.0338609i
$934$		0			0
$935$	−0.215537	−	1.22237i	−0.00704882	−	0.0399759i
$936$		0			0
$937$	18.5479	+	6.75087i	0.605933	+	0.220541i	0.626723	−	0.779242i	$-0.284396\pi$
$937$	18.5479	+	6.75087i	0.605933	+	0.220541i	−0.0207900	+	0.999784i	$0.506618\pi$
$938$		0			0
$939$	−26.7079	+	46.2594i	−0.871578	+	1.50962i
$940$		0			0
$941$	14.4907	−	12.1591i	0.472382	−	0.396376i	−0.375280	−	0.926911i	$-0.622454\pi$
$941$	14.4907	−	12.1591i	0.472382	−	0.396376i	0.847663	+	0.530536i	$0.178009\pi$
$942$		0			0
$943$	−24.7178	−	42.8125i	−0.804923	−	1.39417i
$944$		0			0
$945$	0.0487825	−	0.276659i	0.00158689	−	0.00899972i
$946$		0			0
$947$	33.9842	−	12.3692i	1.10434	−	0.401946i	0.275424	−	0.961323i	$-0.411182\pi$
$947$	33.9842	−	12.3692i	1.10434	−	0.401946i	0.828913	+	0.559377i	$0.188960\pi$
$948$		0			0
$949$	−56.0310			−1.81884
$950$		0			0
$951$	−20.5112			−0.665122
$952$		0			0
$953$	21.3246	−	7.76152i	0.690771	−	0.251420i	0.0273060	−	0.999627i	$-0.491307\pi$
$953$	21.3246	−	7.76152i	0.690771	−	0.251420i	0.663466	+	0.748207i	$0.269085\pi$
$954$		0			0
$955$	−0.942219	+	5.34359i	−0.0304895	+	0.172914i
$956$		0			0
$957$	0.676641	+	1.17198i	0.0218727	+	0.0378846i
$958$		0			0
$959$	0.703678	−	0.590456i	0.0227229	−	0.0190668i
$960$		0			0
$961$	−0.159100	+	0.275570i	−0.00513227	+	0.00888935i
$962$		0			0
$963$	14.3362	+	5.21793i	0.461976	+	0.168146i
$964$		0			0
$965$	−3.87876	−	21.9975i	−0.124862	−	0.708125i
$966$		0			0
$967$	13.0797	+	10.9751i	0.420613	+	0.352937i	0.828396	−	0.560142i	$-0.189254\pi$
$967$	13.0797	+	10.9751i	0.420613	+	0.352937i	−0.407783	+	0.913079i	$0.633698\pi$
$968$		0			0
$969$	−79.1682	−	13.3593i	−2.54325	−	0.429163i
$970$		0			0
$971$	−23.5713	−	19.7787i	−0.756439	−	0.634727i	0.180758	−	0.983528i	$-0.442145\pi$
$971$	−23.5713	−	19.7787i	−0.756439	−	0.634727i	−0.937197	+	0.348800i	$0.886589\pi$
$972$		0			0
$973$	1.12037	+	6.35391i	0.0359173	+	0.203697i
$974$		0			0
$975$	−29.6330	−	10.7855i	−0.949015	−	0.345413i
$976$		0			0
$977$	4.76857	−	8.25941i	0.152560	−	0.264242i	−0.779608	−	0.626268i	$-0.784582\pi$
$977$	4.76857	−	8.25941i	0.152560	−	0.264242i	0.932168	+	0.362026i	$0.117915\pi$
$978$		0			0
$979$	0.224155	−	0.188089i	0.00716404	−	0.00601134i
$980$		0			0
$981$	−12.0303	−	20.8371i	−0.384097	−	0.665276i
$982$		0			0
$983$	0.267332	−	1.51612i	0.00852658	−	0.0483566i	−0.980248	−	0.197774i	$-0.936629\pi$
$983$	0.267332	−	1.51612i	0.00852658	−	0.0483566i	0.988774	+	0.149418i	$0.0477398\pi$
$984$		0			0
$985$	9.47952	−	3.45026i	0.302043	−	0.109935i
$986$		0			0
$987$	4.79435			0.152606
$988$		0			0
$989$	16.0702			0.511001
$990$		0			0
$991$	18.3665	−	6.68485i	0.583431	−	0.212351i	−0.0334070	−	0.999442i	$-0.510636\pi$
$991$	18.3665	−	6.68485i	0.583431	−	0.212351i	0.616838	+	0.787090i	$0.288414\pi$
$992$		0			0
$993$	−5.82342	+	33.0262i	−0.184800	+	1.04806i
$994$		0			0
$995$	−16.0155	−	27.7396i	−0.507725	−	0.879405i
$996$		0			0
$997$	−20.5346	+	17.2306i	−0.650338	+	0.545698i	−0.907173	−	0.420757i	$-0.861765\pi$
$997$	−20.5346	+	17.2306i	−0.650338	+	0.545698i	0.256836	+	0.966455i	$0.417320\pi$
$998$		0			0
$999$	0.131130	−	0.227124i	0.00414877	−	0.00718589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.b.73.1	yes	6
4.3	odd	2		304.2.u.a.225.1		6
19.5	even	9		2888.2.a.s.1.1		3
19.6	even	9	inner	152.2.q.b.25.1	✓	6
19.14	odd	18		2888.2.a.m.1.3		3
76.43	odd	18		5776.2.a.bj.1.3		3
76.63	odd	18		304.2.u.a.177.1		6
76.71	even	18		5776.2.a.bs.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.b.25.1	✓	6	19.6	even	9	inner
152.2.q.b.73.1	yes	6	1.1	even	1	trivial
304.2.u.a.177.1		6	76.63	odd	18
304.2.u.a.225.1		6	4.3	odd	2
2888.2.a.m.1.3		3	19.14	odd	18
2888.2.a.s.1.1		3	19.5	even	9
5776.2.a.bj.1.3		3	76.43	odd	18
5776.2.a.bs.1.1		3	76.71	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.26604 - 0.824773i) q^{3} +(-0.233956 + 1.32683i) q^{5} +(0.233956 + 0.405223i) q^{7} +(2.15657 - 1.80958i) q^{9} +(0.0603074 - 0.104455i) q^{11} +(-3.85844 - 1.40436i) q^{13} +(0.564178 + 3.19961i) q^{15} +(-5.85117 - 4.90971i) q^{17} +(4.28699 - 0.788496i) q^{19} +(0.864370 + 0.725293i) q^{21} +(1.12061 + 6.35532i) q^{23} +(2.99273 + 1.08926i) q^{25} +(-0.222811 + 0.385920i) q^{27} +(-3.56418 + 2.99070i) q^{29} +(-2.79813 - 4.84651i) q^{31} +(0.0505072 - 0.286441i) q^{33} +(-0.592396 + 0.215615i) q^{35} -0.588526 q^{37} -9.90167 q^{39} +(-7.19846 + 2.62003i) q^{41} +(0.432419 - 2.45237i) q^{43} +(1.89646 + 3.28476i) q^{45} +(3.25490 - 2.73119i) q^{47} +(3.39053 - 5.87257i) q^{49} +(-17.3084 - 6.29974i) q^{51} +(1.65910 + 9.40923i) q^{53} +(0.124485 + 0.104455i) q^{55} +(9.06418 - 5.32256i) q^{57} +(6.24170 + 5.23741i) q^{59} +(0.437166 + 2.47929i) q^{61} +(1.23783 + 0.450532i) q^{63} +(2.76604 - 4.79093i) q^{65} +(-6.53983 + 5.48757i) q^{67} +(7.78106 + 13.4772i) q^{69} +(2.79561 - 15.8547i) q^{71} +(12.8229 - 4.66717i) q^{73} +7.68004 q^{75} +0.0564370 q^{77} +(15.0817 - 5.48930i) q^{79} +(-1.65317 + 9.37560i) q^{81} +(1.82635 + 3.16333i) q^{83} +(7.88326 - 6.61484i) q^{85} +(-5.60994 + 9.71670i) q^{87} +(2.27972 + 0.829748i) q^{89} +(-0.333626 - 1.89209i) q^{91} +(-10.3380 - 8.67458i) q^{93} +(0.0432332 + 5.87257i) q^{95} +(-7.17752 - 6.02265i) q^{97} +(-0.0589632 - 0.334397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} - 6 q^{5} + 6 q^{7} - 9 q^{9} + 6 q^{11} - 15 q^{13} - 15 q^{15} - 9 q^{17} + 18 q^{19} + 24 q^{21} + 18 q^{23} - 12 q^{27} - 3 q^{29} - 3 q^{31} + 3 q^{33} - 24 q^{37} - 36 q^{39} - 15 q^{41}+ \cdots - 15 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 - 6 * q^5 + 6 * q^7 - 9 * q^9 + 6 * q^11 - 15 * q^13 - 15 * q^15 - 9 * q^17 + 18 * q^19 + 24 * q^21 + 18 * q^23 - 12 * q^27 - 3 * q^29 - 3 * q^31 + 3 * q^33 - 24 * q^37 - 36 * q^39 - 15 * q^41 - 21 * q^43 + 21 * q^45 + 21 * q^47 + 3 * q^49 - 27 * q^51 - 27 * q^53 - 12 * q^55 + 36 * q^57 - 6 * q^59 + 12 * q^61 - 12 * q^63 + 12 * q^65 + 18 * q^67 + 12 * q^69 + 18 * q^71 + 36 * q^73 + 6 * q^75 + 30 * q^77 + 27 * q^79 + 54 * q^81 + 12 * q^83 + 12 * q^85 + 15 * q^87 - 12 * q^89 - 21 * q^91 + 9 * q^93 - 15 * q^95 - 18 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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