LMFDB - Embedded newform 572.2.i.c.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 $ x^10 - x^9 + 9x^8 + 6x^7 + 59x^6 + 2x^5 + 47x^4 - 26x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.1
Root			$-1.09846 - 1.90260i$ of defining polynomial
Character	$\chi$	$=$	572.133
Dual form			572.2.i.c.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09846 - 1.90260i) q^{3} +0.151238 q^{5} +(2.15500 - 3.73256i) q^{7} +(-0.913248 + 1.58179i) q^{9} +O(q^{10})$	\(q+(-1.09846 - 1.90260i) q^{3} +0.151238 q^{5} +(2.15500 - 3.73256i) q^{7} +(-0.913248 + 1.58179i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(3.20357 + 1.65442i) q^{13} +(-0.166129 - 0.287744i) q^{15} +(-0.474268 + 0.821456i) q^{17} +(0.739165 - 1.28027i) q^{19} -9.46875 q^{21} +(-2.31854 - 4.01583i) q^{23} -4.97713 q^{25} -2.57810 q^{27} +(-2.41989 - 4.19138i) q^{29} +4.94473 q^{31} +(-1.09846 + 1.90260i) q^{33} +(0.325917 - 0.564504i) q^{35} +(4.11018 + 7.11904i) q^{37} +(-0.371316 - 7.91243i) q^{39} +(-1.72266 - 2.98374i) q^{41} +(-1.42438 + 2.46710i) q^{43} +(-0.138118 + 0.239227i) q^{45} -7.49363 q^{47} +(-5.78802 - 10.0251i) q^{49} +2.08386 q^{51} -3.60468 q^{53} +(-0.0756188 - 0.130976i) q^{55} -3.24779 q^{57} +(0.0689734 - 0.119465i) q^{59} +(3.02285 - 5.23572i) q^{61} +(3.93609 + 6.81751i) q^{63} +(0.484501 + 0.250211i) q^{65} +(3.07371 + 5.32383i) q^{67} +(-5.09367 + 8.82250i) q^{69} +(6.05292 - 10.4840i) q^{71} -7.66197 q^{73} +(5.46720 + 9.46946i) q^{75} -4.30999 q^{77} +15.1515 q^{79} +(5.57170 + 9.65047i) q^{81} +2.08818 q^{83} +(-0.0717272 + 0.124235i) q^{85} +(-5.31633 + 9.20816i) q^{87} +(7.72324 + 13.3770i) q^{89} +(13.0789 - 8.39227i) q^{91} +(-5.43161 - 9.40782i) q^{93} +(0.111790 - 0.193625i) q^{95} +(0.202896 - 0.351426i) q^{97} +1.82650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.09846	−	1.90260i	−0.634199	−	1.09846i	−0.986684	−	0.162647i	$-0.947997\pi$
$3$	−1.09846	−	1.90260i	−0.634199	−	1.09846i	0.352486	−	0.935817i	$-0.385337\pi$
$4$		0			0
$5$	0.151238			0.0676356			0.0338178	−	0.999428i	$-0.489233\pi$
$5$	0.151238			0.0676356			0.0338178	+	0.999428i	$0.489233\pi$
$6$		0			0
$7$	2.15500	−	3.73256i	0.814512	−	1.41078i	−0.0951656	−	0.995461i	$-0.530338\pi$
$7$	2.15500	−	3.73256i	0.814512	−	1.41078i	0.909678	−	0.415315i	$-0.136329\pi$
$8$		0			0
$9$	−0.913248	+	1.58179i	−0.304416	+	0.527264i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	3.20357	+	1.65442i	0.888512	+	0.458854i
$13$	3.20357	+	1.65442i	0.888512	+	0.458854i
$14$		0			0
$15$	−0.166129	−	0.287744i	−0.0428944	−	0.0742953i
$16$		0			0
$17$	−0.474268	+	0.821456i	−0.115027	+	0.199232i	−0.917790	−	0.397065i	$-0.870029\pi$
$17$	−0.474268	+	0.821456i	−0.115027	+	0.199232i	0.802764	+	0.596297i	$0.203362\pi$
$18$		0			0
$19$	0.739165	−	1.28027i	0.169576	−	0.293714i	−0.768695	−	0.639616i	$-0.779093\pi$
$19$	0.739165	−	1.28027i	0.169576	−	0.293714i	0.938271	+	0.345901i	$0.112427\pi$
$20$		0			0
$21$	−9.46875			−2.06625
$22$		0			0
$23$	−2.31854	−	4.01583i	−0.483450	−	0.837359i	0.516370	−	0.856366i	$-0.327283\pi$
$23$	−2.31854	−	4.01583i	−0.483450	−	0.837359i	−0.999819	+	0.0190065i	$0.993950\pi$
$24$		0			0
$25$	−4.97713			−0.995425
$26$		0			0
$27$	−2.57810			−0.496156
$28$		0			0
$29$	−2.41989	−	4.19138i	−0.449363	−	0.778320i	0.548982	−	0.835834i	$-0.315016\pi$
$29$	−2.41989	−	4.19138i	−0.449363	−	0.778320i	−0.998345	+	0.0575149i	$0.981682\pi$
$30$		0			0
$31$	4.94473			0.888099			0.444050	−	0.896002i	$-0.353541\pi$
$31$	4.94473			0.888099			0.444050	+	0.896002i	$0.353541\pi$
$32$		0			0
$33$	−1.09846	+	1.90260i	−0.191218	+	0.331199i
$34$		0			0
$35$	0.325917	−	0.564504i	0.0550900	−	0.0954186i
$36$		0			0
$37$	4.11018	+	7.11904i	0.675709	+	1.17036i	0.976261	+	0.216597i	$0.0694957\pi$
$37$	4.11018	+	7.11904i	0.675709	+	1.17036i	−0.300552	+	0.953765i	$0.597171\pi$
$38$		0			0
$39$	−0.371316	−	7.91243i	−0.0594581	−	1.26700i
$40$		0			0
$41$	−1.72266	−	2.98374i	−0.269034	−	0.465981i	0.699578	−	0.714556i	$-0.253371\pi$
$41$	−1.72266	−	2.98374i	−0.269034	−	0.465981i	−0.968613	+	0.248575i	$0.920038\pi$
$42$		0			0
$43$	−1.42438	+	2.46710i	−0.217216	+	0.376229i	−0.953956	−	0.299947i	$-0.903031\pi$
$43$	−1.42438	+	2.46710i	−0.217216	+	0.376229i	0.736740	+	0.676176i	$0.236364\pi$
$44$		0			0
$45$	−0.138118	+	0.239227i	−0.0205894	+	0.0356618i
$46$		0			0
$47$	−7.49363			−1.09306			−0.546529	−	0.837440i	$-0.684051\pi$
$47$	−7.49363			−1.09306			−0.546529	+	0.837440i	$0.684051\pi$
$48$		0			0
$49$	−5.78802	−	10.0251i	−0.826860	−	1.43216i
$50$		0			0
$51$	2.08386			0.291799
$52$		0			0
$53$	−3.60468			−0.495142			−0.247571	−	0.968870i	$-0.579632\pi$
$53$	−3.60468			−0.495142			−0.247571	+	0.968870i	$0.579632\pi$
$54$		0			0
$55$	−0.0756188	−	0.130976i	−0.0101964	−	0.0176608i
$56$		0			0
$57$	−3.24779			−0.430180
$58$		0			0
$59$	0.0689734	−	0.119465i	0.00897958	−	0.0155531i	−0.861501	−	0.507756i	$-0.830475\pi$
$59$	0.0689734	−	0.119465i	0.00897958	−	0.0155531i	0.870480	+	0.492203i	$0.163808\pi$
$60$		0			0
$61$	3.02285	−	5.23572i	0.387036	−	0.670366i	−0.605014	−	0.796215i	$-0.706832\pi$
$61$	3.02285	−	5.23572i	0.387036	−	0.670366i	0.992049	+	0.125850i	$0.0401657\pi$
$62$		0			0
$63$	3.93609	+	6.81751i	0.495901	+	0.858926i
$64$		0			0
$65$	0.484501	+	0.250211i	0.0600950	+	0.0310348i
$66$		0			0
$67$	3.07371	+	5.32383i	0.375514	+	0.650409i	0.990404	−	0.138204i	$-0.0441329\pi$
$67$	3.07371	+	5.32383i	0.375514	+	0.650409i	−0.614890	+	0.788613i	$0.710800\pi$
$68$		0			0
$69$	−5.09367	+	8.82250i	−0.613206	+	1.06210i
$70$		0			0
$71$	6.05292	−	10.4840i	0.718349	−	1.24422i	−0.243305	−	0.969950i	$-0.578231\pi$
$71$	6.05292	−	10.4840i	0.718349	−	1.24422i	0.961654	−	0.274267i	$-0.0884352\pi$
$72$		0			0
$73$	−7.66197			−0.896766			−0.448383	−	0.893842i	$-0.648000\pi$
$73$	−7.66197			−0.896766			−0.448383	+	0.893842i	$0.648000\pi$
$74$		0			0
$75$	5.46720	+	9.46946i	0.631298	+	1.09344i
$76$		0			0
$77$	−4.30999			−0.491169
$78$		0			0
$79$	15.1515			1.70468			0.852340	−	0.522988i	$-0.175183\pi$
$79$	15.1515			1.70468			0.852340	+	0.522988i	$0.175183\pi$
$80$		0			0
$81$	5.57170	+	9.65047i	0.619078	+	1.07227i
$82$		0			0
$83$	2.08818			0.229208			0.114604	−	0.993411i	$-0.463440\pi$
$83$	2.08818			0.229208			0.114604	+	0.993411i	$0.463440\pi$
$84$		0			0
$85$	−0.0717272	+	0.124235i	−0.00777990	+	0.0134752i
$86$		0			0
$87$	−5.31633	+	9.20816i	−0.569971	+	0.987219i
$88$		0			0
$89$	7.72324	+	13.3770i	0.818662	+	1.41796i	0.906668	+	0.421844i	$0.138617\pi$
$89$	7.72324	+	13.3770i	0.818662	+	1.41796i	−0.0880064	+	0.996120i	$0.528050\pi$
$90$		0			0
$91$	13.0789	−	8.39227i	1.37104	−	0.879749i
$92$		0			0
$93$	−5.43161	−	9.40782i	−0.563231	−	0.975545i
$94$		0			0
$95$	0.111790	−	0.193625i	0.0114694	−	0.0198655i
$96$		0			0
$97$	0.202896	−	0.351426i	0.0206009	−	0.0356819i	−0.855541	−	0.517735i	$-0.826775\pi$
$97$	0.202896	−	0.351426i	0.0206009	−	0.0356819i	0.876142	+	0.482053i	$0.160109\pi$
$98$		0			0
$99$	1.82650			0.183570
$100$		0			0
$101$	3.16295	+	5.47839i	0.314725	+	0.545120i	0.979379	−	0.202031i	$-0.0647543\pi$
$101$	3.16295	+	5.47839i	0.314725	+	0.545120i	−0.664654	+	0.747152i	$0.731421\pi$
$102$		0			0
$103$	3.01133			0.296715			0.148357	−	0.988934i	$-0.452601\pi$
$103$	3.01133			0.296715			0.148357	+	0.988934i	$0.452601\pi$
$104$		0			0
$105$	−1.43203			−0.139752
$106$		0			0
$107$	8.37535	+	14.5065i	0.809676	+	1.40240i	0.913089	+	0.407761i	$0.133690\pi$
$107$	8.37535	+	14.5065i	0.809676	+	1.40240i	−0.103413	+	0.994639i	$0.532976\pi$
$108$		0			0
$109$	4.98210			0.477198			0.238599	−	0.971118i	$-0.423312\pi$
$109$	4.98210			0.477198			0.238599	+	0.971118i	$0.423312\pi$
$110$		0			0
$111$	9.02977	−	15.6400i	0.857068	−	1.48448i
$112$		0			0
$113$	7.06694	−	12.2403i	0.664801	−	1.15147i	−0.314538	−	0.949245i	$-0.601849\pi$
$113$	7.06694	−	12.2403i	0.664801	−	1.15147i	0.979339	−	0.202225i	$-0.0648172\pi$
$114$		0			0
$115$	−0.350651	−	0.607345i	−0.0326984	−	0.0566353i
$116$		0			0
$117$	−5.54261	+	3.55649i	−0.512415	+	0.328798i
$118$		0			0
$119$	2.04409	+	3.54047i	0.187381	+	0.324554i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.78456	+	6.55506i	−0.341243	+	0.591050i
$124$		0			0
$125$	−1.50892			−0.134962
$126$		0			0
$127$	4.07241	+	7.05361i	0.361368	+	0.625907i	0.988186	−	0.153258i	$-0.0489766\pi$
$127$	4.07241	+	7.05361i	0.361368	+	0.625907i	−0.626819	+	0.779165i	$0.715643\pi$
$128$		0			0
$129$	6.25853			0.551033
$130$		0			0
$131$	−1.78100			−0.155607			−0.0778035	−	0.996969i	$-0.524791\pi$
$131$	−1.78100			−0.155607			−0.0778035	+	0.996969i	$0.524791\pi$
$132$		0			0
$133$	−3.18580	−	5.51796i	−0.276244	−	0.478468i
$134$		0			0
$135$	−0.389906			−0.0335578
$136$		0			0
$137$	9.18765	−	15.9135i	0.784954	−	1.35958i	−0.144073	−	0.989567i	$-0.546020\pi$
$137$	9.18765	−	15.9135i	0.784954	−	1.35958i	0.929027	−	0.370013i	$-0.120647\pi$
$138$		0			0
$139$	7.69056	−	13.3204i	0.652305	−	1.12983i	−0.330257	−	0.943891i	$-0.607136\pi$
$139$	7.69056	−	13.3204i	0.652305	−	1.12983i	0.982562	−	0.185934i	$-0.0595311\pi$
$140$		0			0
$141$	8.23149	+	14.2574i	0.693216	+	1.20069i
$142$		0			0
$143$	−0.169016	−	3.60159i	−0.0141338	−	0.301180i
$144$		0			0
$145$	−0.365979	−	0.633894i	−0.0303929	−	0.0526421i
$146$		0			0
$147$	−12.7159	+	22.0245i	−1.04879	+	1.81655i
$148$		0			0
$149$	−3.30683	+	5.72760i	−0.270906	+	0.469223i	−0.969094	−	0.246691i	$-0.920657\pi$
$149$	−3.30683	+	5.72760i	−0.270906	+	0.469223i	0.698188	+	0.715914i	$0.253990\pi$
$150$		0			0
$151$	−19.0578			−1.55090			−0.775451	−	0.631408i	$-0.782477\pi$
$151$	−19.0578			−1.55090			−0.775451	+	0.631408i	$0.782477\pi$
$152$		0			0
$153$	−0.866248	−	1.50039i	−0.0700320	−	0.121299i
$154$		0			0
$155$	0.747829			0.0600671
$156$		0			0
$157$	23.0716			1.84132			0.920658	−	0.390369i	$-0.127653\pi$
$157$	23.0716			1.84132			0.920658	+	0.390369i	$0.127653\pi$
$158$		0			0
$159$	3.95962	+	6.85826i	0.314018	+	0.543895i
$160$		0			0
$161$	−19.9858			−1.57510
$162$		0			0
$163$	1.89069	−	3.27478i	0.148091	−	0.256501i	−0.782431	−	0.622737i	$-0.786021\pi$
$163$	1.89069	−	3.27478i	0.148091	−	0.256501i	0.930522	+	0.366237i	$0.119354\pi$
$164$		0			0
$165$	−0.166129	+	0.287744i	−0.0129331	+	0.0224009i
$166$		0			0
$167$	−9.29783	−	16.1043i	−0.719488	−	1.24619i	−0.961203	−	0.275842i	$-0.911043\pi$
$167$	−9.29783	−	16.1043i	−0.719488	−	1.24619i	0.241716	−	0.970347i	$-0.422290\pi$
$168$		0			0
$169$	7.52578	+	10.6001i	0.578906	+	0.815394i
$170$		0			0
$171$	1.35008	+	2.33841i	0.103243	+	0.178823i
$172$		0			0
$173$	−12.4086	+	21.4923i	−0.943408	+	1.63403i	−0.184502	+	0.982832i	$0.559067\pi$
$173$	−12.4086	+	21.4923i	−0.943408	+	1.63403i	−0.758907	+	0.651199i	$0.774266\pi$
$174$		0			0
$175$	−10.7257	+	18.5774i	−0.810786	+	1.40432i
$176$		0			0
$177$	−0.303059			−0.0227793
$178$		0			0
$179$	5.87956	+	10.1837i	0.439459	+	0.761165i	0.997648	−	0.0685486i	$-0.0218368\pi$
$179$	5.87956	+	10.1837i	0.439459	+	0.761165i	−0.558189	+	0.829714i	$0.688503\pi$
$180$		0			0
$181$	3.18359			0.236635			0.118317	−	0.992976i	$-0.462250\pi$
$181$	3.18359			0.236635			0.118317	+	0.992976i	$0.462250\pi$
$182$		0			0
$183$	−13.2820			−0.981830
$184$		0			0
$185$	0.621614	+	1.07667i	0.0457020	+	0.0791581i
$186$		0			0
$187$	0.948535			0.0693638
$188$		0			0
$189$	−5.55580	+	9.62293i	−0.404125	+	0.699965i
$190$		0			0
$191$	−1.11195	+	1.92595i	−0.0804578	+	0.139357i	−0.903447	−	0.428701i	$-0.858972\pi$
$191$	−1.11195	+	1.92595i	−0.0804578	+	0.139357i	0.822989	+	0.568057i	$0.192305\pi$
$192$		0			0
$193$	−12.0387	−	20.8517i	−0.866568	−	1.50094i	−0.865482	−	0.500941i	$-0.832988\pi$
$193$	−12.0387	−	20.8517i	−0.866568	−	1.50094i	−0.00108640	−	0.999999i	$-0.500346\pi$
$194$		0			0
$195$	−0.0561570	−	1.19666i	−0.00402148	−	0.0856945i
$196$		0			0
$197$	9.55281	+	16.5459i	0.680609	+	1.17885i	0.974795	+	0.223102i	$0.0716182\pi$
$197$	9.55281	+	16.5459i	0.680609	+	1.17885i	−0.294186	+	0.955748i	$0.595048\pi$
$198$		0			0
$199$	7.29135	−	12.6290i	0.516870	−	0.895246i	−0.482938	−	0.875655i	$-0.660430\pi$
$199$	7.29135	−	12.6290i	0.516870	−	0.895246i	0.999808	−	0.0195910i	$-0.00623640\pi$
$200$		0			0
$201$	6.75273	−	11.6961i	0.476301	−	0.824978i
$202$		0			0
$203$	−20.8595			−1.46405
$204$		0			0
$205$	−0.260531	−	0.451253i	−0.0181963	−	0.0315169i
$206$		0			0
$207$	8.46962			0.588679
$208$		0			0
$209$	−1.47833			−0.102258
$210$		0			0
$211$	1.95717	+	3.38991i	0.134737	+	0.233371i	0.925497	−	0.378755i	$-0.123648\pi$
$211$	1.95717	+	3.38991i	0.134737	+	0.233371i	−0.790760	+	0.612126i	$0.790314\pi$
$212$		0			0
$213$	−26.5957			−1.82230
$214$		0			0
$215$	−0.215420	+	0.373119i	−0.0146915	+	0.0254465i
$216$		0			0
$217$	10.6559	−	18.4565i	0.723367	−	1.25291i
$218$		0			0
$219$	8.41640	+	14.5776i	0.568728	+	0.985065i
$220$		0			0
$221$	−2.87839	+	1.84696i	−0.193621	+	0.124240i
$222$		0			0
$223$	−9.10207	−	15.7653i	−0.609520	−	1.05572i	−0.991320	−	0.131474i	$-0.958029\pi$
$223$	−9.10207	−	15.7653i	−0.609520	−	1.05572i	0.381800	−	0.924245i	$-0.375304\pi$
$224$		0			0
$225$	4.54535	−	7.87278i	0.303024	−	0.524852i
$226$		0			0
$227$	−2.10451	+	3.64513i	−0.139682	+	0.241935i	−0.927376	−	0.374131i	$-0.877941\pi$
$227$	−2.10451	+	3.64513i	−0.139682	+	0.241935i	0.787695	+	0.616066i	$0.211275\pi$
$228$		0			0
$229$	−3.04540			−0.201246			−0.100623	−	0.994925i	$-0.532084\pi$
$229$	−3.04540			−0.201246			−0.100623	+	0.994925i	$0.532084\pi$
$230$		0			0
$231$	4.73437	+	8.20018i	0.311499	+	0.539532i
$232$		0			0
$233$	1.72464			0.112985			0.0564924	−	0.998403i	$-0.482008\pi$
$233$	1.72464			0.112985			0.0564924	+	0.998403i	$0.482008\pi$
$234$		0			0
$235$	−1.13332			−0.0739296
$236$		0			0
$237$	−16.6434	−	28.8272i	−1.08111	−	1.87253i
$238$		0			0
$239$	−22.8666			−1.47912			−0.739558	−	0.673093i	$-0.764965\pi$
$239$	−22.8666			−1.47912			−0.739558	+	0.673093i	$0.764965\pi$
$240$		0			0
$241$	8.75722	−	15.1679i	0.564102	−	0.977054i	−0.433030	−	0.901379i	$-0.642556\pi$
$241$	8.75722	−	15.1679i	0.564102	−	0.977054i	0.997133	−	0.0756742i	$-0.0241109\pi$
$242$		0			0
$243$	8.37347	−	14.5033i	0.537159	−	0.930386i
$244$		0			0
$245$	−0.875367	−	1.51618i	−0.0559251	−	0.0968652i
$246$		0			0
$247$	4.48608	−	2.87855i	0.285442	−	0.183158i
$248$		0			0
$249$	−2.29379	−	3.97297i	−0.145363	−	0.251776i
$250$		0			0
$251$	10.4402	−	18.0830i	0.658982	−	1.14139i	−0.321897	−	0.946775i	$-0.604321\pi$
$251$	10.4402	−	18.0830i	0.658982	−	1.14139i	0.980880	−	0.194616i	$-0.0623460\pi$
$252$		0			0
$253$	−2.31854	+	4.01583i	−0.145766	+	0.252473i
$254$		0			0
$255$	0.315159			0.0197360
$256$		0			0
$257$	0.635231	+	1.10025i	0.0396246	+	0.0686318i	0.885158	−	0.465291i	$-0.154050\pi$
$257$	0.635231	+	1.10025i	0.0396246	+	0.0686318i	−0.845533	+	0.533923i	$0.820717\pi$
$258$		0			0
$259$	35.4297			2.20149
$260$		0			0
$261$	8.83986			0.547173
$262$		0			0
$263$	3.44174	+	5.96127i	0.212227	+	0.367588i	0.952411	−	0.304816i	$-0.0985951\pi$
$263$	3.44174	+	5.96127i	0.212227	+	0.367588i	−0.740184	+	0.672404i	$0.765262\pi$
$264$		0			0
$265$	−0.545164			−0.0334892
$266$		0			0
$267$	16.9674	−	29.3884i	1.03839	−	1.79854i
$268$		0			0
$269$	13.3236	−	23.0772i	0.812355	−	1.40704i	−0.0988569	−	0.995102i	$-0.531519\pi$
$269$	13.3236	−	23.0772i	0.812355	−	1.40704i	0.911212	−	0.411938i	$-0.135148\pi$
$270$		0			0
$271$	8.33432	+	14.4355i	0.506274	+	0.876892i	0.999974	+	0.00725952i	$0.00231080\pi$
$271$	8.33432	+	14.4355i	0.506274	+	0.876892i	−0.493700	+	0.869632i	$0.664356\pi$
$272$		0			0
$273$	−30.3338	−	15.6653i	−1.83589	−	0.948107i
$274$		0			0
$275$	2.48856	+	4.31032i	0.150066	+	0.259922i
$276$		0			0
$277$	−10.0117	+	17.3408i	−0.601546	+	1.04191i	0.391042	+	0.920373i	$0.372115\pi$
$277$	−10.0117	+	17.3408i	−0.601546	+	1.04191i	−0.992587	+	0.121534i	$0.961219\pi$
$278$		0			0
$279$	−4.51576	+	7.82153i	−0.270352	+	0.468263i
$280$		0			0
$281$	10.0649			0.600423			0.300211	−	0.953873i	$-0.402943\pi$
$281$	10.0649			0.600423			0.300211	+	0.953873i	$0.402943\pi$
$282$		0			0
$283$	0.913093	+	1.58152i	0.0542778	+	0.0940118i	0.891888	−	0.452257i	$-0.149381\pi$
$283$	0.913093	+	1.58152i	0.0542778	+	0.0940118i	−0.837610	+	0.546269i	$0.816048\pi$
$284$		0			0
$285$	−0.491188			−0.0290954
$286$		0			0
$287$	−14.8493			−0.876527
$288$		0			0
$289$	8.05014	+	13.9433i	0.473538	+	0.820191i
$290$		0			0
$291$	−0.891495			−0.0522604
$292$		0			0
$293$	−16.1415	+	27.9579i	−0.942998	+	1.63332i	−0.183288	+	0.983059i	$0.558674\pi$
$293$	−16.1415	+	27.9579i	−0.942998	+	1.63332i	−0.759710	+	0.650262i	$0.774659\pi$
$294$		0			0
$295$	0.0104314	−	0.0180677i	0.000607339	−	0.00105194i
$296$		0			0
$297$	1.28905	+	2.23270i	0.0747984	+	0.129555i
$298$		0			0
$299$	−0.783741	−	16.7009i	−0.0453249	−	0.965836i
$300$		0			0
$301$	6.13907	+	10.6332i	0.353850	+	0.612887i
$302$		0			0
$303$	6.94878	−	12.0356i	0.399197	−	0.691429i
$304$		0			0
$305$	0.457168	−	0.791839i	0.0261774	−	0.0453405i
$306$		0			0
$307$	−8.46700			−0.483237			−0.241619	−	0.970371i	$-0.577678\pi$
$307$	−8.46700			−0.483237			−0.241619	+	0.970371i	$0.577678\pi$
$308$		0			0
$309$	−3.30783	−	5.72934i	−0.188176	−	0.325931i
$310$		0			0
$311$	−29.6715			−1.68252			−0.841258	−	0.540634i	$-0.818184\pi$
$311$	−29.6715			−1.68252			−0.841258	+	0.540634i	$0.818184\pi$
$312$		0			0
$313$	5.85388			0.330881			0.165441	−	0.986220i	$-0.447095\pi$
$313$	5.85388			0.330881			0.165441	+	0.986220i	$0.447095\pi$
$314$		0			0
$315$	0.595286	+	1.03107i	0.0335406	+	0.0580939i
$316$		0			0
$317$	14.0582			0.789586			0.394793	−	0.918770i	$-0.370816\pi$
$317$	14.0582			0.789586			0.394793	+	0.918770i	$0.370816\pi$
$318$		0			0
$319$	−2.41989	+	4.19138i	−0.135488	+	0.234672i
$320$		0			0
$321$	18.4001	−	31.8698i	1.02699	−	1.77880i
$322$		0			0
$323$	0.701124	+	1.21438i	0.0390116	+	0.0675701i
$324$		0			0
$325$	−15.9446	−	8.23427i	−0.884447	−	0.456755i
$326$		0			0
$327$	−5.47266	−	9.47892i	−0.302639	−	0.524185i
$328$		0			0
$329$	−16.1487	+	27.9705i	−0.890309	+	1.54206i
$330$		0			0
$331$	−3.05583	+	5.29285i	−0.167963	+	0.290921i	−0.937704	−	0.347436i	$-0.887052\pi$
$331$	−3.05583	+	5.29285i	−0.167963	+	0.290921i	0.769740	+	0.638357i	$0.220386\pi$
$332$		0			0
$333$	−15.0145			−0.822787
$334$		0			0
$335$	0.464861	+	0.805164i	0.0253981	+	0.0439908i
$336$		0			0
$337$	18.0759			0.984657			0.492329	−	0.870409i	$-0.336146\pi$
$337$	18.0759			0.984657			0.492329	+	0.870409i	$0.336146\pi$
$338$		0			0
$339$	−31.0511			−1.68646
$340$		0			0
$341$	−2.47236	−	4.28226i	−0.133886	−	0.231897i
$342$		0			0
$343$	−19.7227			−1.06493
$344$		0			0
$345$	−0.770355	+	1.33429i	−0.0414745	+	0.0718360i
$346$		0			0
$347$	1.49574	−	2.59070i	0.0802958	−	0.139076i	−0.823081	−	0.567924i	$-0.807747\pi$
$347$	1.49574	−	2.59070i	0.0802958	−	0.139076i	0.903377	+	0.428847i	$0.141080\pi$
$348$		0			0
$349$	3.20041	+	5.54327i	0.171314	+	0.296725i	0.938880	−	0.344246i	$-0.111865\pi$
$349$	3.20041	+	5.54327i	0.171314	+	0.296725i	−0.767565	+	0.640971i	$0.778532\pi$
$350$		0			0
$351$	−8.25915	−	4.26527i	−0.440841	−	0.227663i
$352$		0			0
$353$	−7.98104	−	13.8236i	−0.424788	−	0.735754i	0.571613	−	0.820524i	$-0.306318\pi$
$353$	−7.98104	−	13.8236i	−0.424788	−	0.735754i	−0.996401	+	0.0847693i	$0.972985\pi$
$354$		0			0
$355$	0.915429	−	1.58557i	0.0485859	−	0.0841533i
$356$		0			0
$357$	4.49072	−	7.77816i	0.237674	−	0.411664i
$358$		0			0
$359$	25.9887			1.37163			0.685816	−	0.727775i	$-0.259446\pi$
$359$	25.9887			1.37163			0.685816	+	0.727775i	$0.259446\pi$
$360$		0			0
$361$	8.40727	+	14.5618i	0.442488	+	0.766412i
$362$		0			0
$363$	2.19693			0.115309
$364$		0			0
$365$	−1.15878			−0.0606532
$366$		0			0
$367$	−3.86696	−	6.69777i	−0.201854	−	0.349621i	0.747272	−	0.664518i	$-0.231363\pi$
$367$	−3.86696	−	6.69777i	−0.201854	−	0.349621i	−0.949126	+	0.314897i	$0.898030\pi$
$368$		0			0
$369$	6.29287			0.327594
$370$		0			0
$371$	−7.76808	+	13.4547i	−0.403299	+	0.698534i
$372$		0			0
$373$	−7.16398	+	12.4084i	−0.370937	+	0.642481i	−0.989710	−	0.143088i	$-0.954297\pi$
$373$	−7.16398	+	12.4084i	−0.370937	+	0.642481i	0.618773	+	0.785570i	$0.287630\pi$
$374$		0			0
$375$	1.65749	+	2.87086i	0.0855925	+	0.148251i
$376$		0			0
$377$	−0.818001	−	17.4309i	−0.0421292	−	0.897738i
$378$		0			0
$379$	3.69939	+	6.40753i	0.190025	+	0.329133i	0.945258	−	0.326323i	$-0.105810\pi$
$379$	3.69939	+	6.40753i	0.190025	+	0.329133i	−0.755233	+	0.655456i	$0.772476\pi$
$380$		0			0
$381$	8.94679	−	15.4963i	0.458358	−	0.793899i
$382$		0			0
$383$	4.09974	−	7.10096i	0.209487	−	0.362842i	−0.742066	−	0.670327i	$-0.766154\pi$
$383$	4.09974	−	7.10096i	0.209487	−	0.362842i	0.951553	+	0.307485i	$0.0994873\pi$
$384$		0			0
$385$	−0.651833			−0.0332205
$386$		0			0
$387$	−2.60163	−	4.50615i	−0.132248	−	0.229061i
$388$		0			0
$389$	2.29767			0.116497			0.0582483	−	0.998302i	$-0.481448\pi$
$389$	2.29767			0.116497			0.0582483	+	0.998302i	$0.481448\pi$
$390$		0			0
$391$	4.39844			0.222439
$392$		0			0
$393$	1.95637	+	3.38853i	0.0986857	+	0.170929i
$394$		0			0
$395$	2.29148			0.115297
$396$		0			0
$397$	6.28037	−	10.8779i	0.315203	−	0.545947i	−0.664278	−	0.747486i	$-0.731261\pi$
$397$	6.28037	−	10.8779i	0.315203	−	0.545947i	0.979481	+	0.201539i	$0.0645942\pi$
$398$		0			0
$399$	−6.99897	+	12.1226i	−0.350387	+	0.606887i
$400$		0			0
$401$	6.77773	+	11.7394i	0.338463	+	0.586236i	0.984144	−	0.177372i	$-0.0567595\pi$
$401$	6.77773	+	11.7394i	0.338463	+	0.586236i	−0.645680	+	0.763608i	$0.723426\pi$
$402$		0			0
$403$	15.8408	+	8.18066i	0.789086	+	0.407508i
$404$		0			0
$405$	0.842651	+	1.45951i	0.0418717	+	0.0725239i
$406$		0			0
$407$	4.11018	−	7.11904i	0.203734	−	0.352878i
$408$		0			0
$409$	3.13507	−	5.43010i	0.155019	−	0.268501i	−0.778047	−	0.628206i	$-0.783789\pi$
$409$	3.13507	−	5.43010i	0.155019	−	0.268501i	0.933066	+	0.359705i	$0.117123\pi$
$410$		0			0
$411$	−40.3692			−1.99127
$412$		0			0
$413$	−0.297275	−	0.514895i	−0.0146279	−	0.0253363i
$414$		0			0
$415$	0.315812			0.0155026
$416$		0			0
$417$	−33.7912			−1.65476
$418$		0			0
$419$	−12.0739	−	20.9126i	−0.589848	−	1.02165i	−0.994252	−	0.107066i	$-0.965854\pi$
$419$	−12.0739	−	20.9126i	−0.589848	−	1.02165i	0.404404	−	0.914581i	$-0.367479\pi$
$420$		0			0
$421$	12.7932			0.623504			0.311752	−	0.950164i	$-0.399084\pi$
$421$	12.7932			0.623504			0.311752	+	0.950164i	$0.399084\pi$
$422$		0			0
$423$	6.84355	−	11.8534i	0.332745	−	0.576331i
$424$		0			0
$425$	2.36049	−	4.08849i	0.114501	−	0.198321i
$426$		0			0
$427$	−13.0284	−	22.5659i	−0.630491	−	1.09204i
$428$		0			0
$429$	−6.66671	+	4.27779i	−0.321872	+	0.206533i
$430$		0			0
$431$	−13.0307	−	22.5699i	−0.627668	−	1.08715i	−0.988018	−	0.154336i	$-0.950676\pi$
$431$	−13.0307	−	22.5699i	−0.627668	−	1.08715i	0.360350	−	0.932817i	$-0.382657\pi$
$432$		0			0
$433$	2.17254	−	3.76296i	0.104406	−	0.180836i	−0.809090	−	0.587685i	$-0.800039\pi$
$433$	2.17254	−	3.76296i	0.104406	−	0.180836i	0.913495	+	0.406849i	$0.133373\pi$
$434$		0			0
$435$	−0.804030	+	1.39262i	−0.0385503	+	0.0667711i
$436$		0			0
$437$	−6.85514			−0.327926
$438$		0			0
$439$	11.5022	+	19.9224i	0.548970	+	0.950843i	0.998345	+	0.0575005i	$0.0183131\pi$
$439$	11.5022	+	19.9224i	0.548970	+	0.950843i	−0.449376	+	0.893343i	$0.648354\pi$
$440$		0			0
$441$	21.1436			1.00684
$442$		0			0
$443$	−34.9959			−1.66270			−0.831352	−	0.555746i	$-0.812433\pi$
$443$	−34.9959			−1.66270			−0.831352	+	0.555746i	$0.812433\pi$
$444$		0			0
$445$	1.16805	+	2.02311i	0.0553707	+	0.0959048i
$446$		0			0
$447$	14.5297			0.687233
$448$		0			0
$449$	−19.5030	+	33.7802i	−0.920403	+	1.59418i	−0.121610	+	0.992578i	$0.538806\pi$
$449$	−19.5030	+	33.7802i	−0.920403	+	1.59418i	−0.798793	+	0.601606i	$0.794528\pi$
$450$		0			0
$451$	−1.72266	+	2.98374i	−0.0811169	+	0.140499i
$452$		0			0
$453$	20.9343	+	36.2593i	0.983579	+	1.70361i
$454$		0			0
$455$	1.97803	−	1.26923i	0.0927313	−	0.0595023i
$456$		0			0
$457$	18.0031	+	31.1823i	0.842149	+	1.45865i	0.888074	+	0.459701i	$0.152043\pi$
$457$	18.0031	+	31.1823i	0.842149	+	1.45865i	−0.0459246	+	0.998945i	$0.514623\pi$
$458$		0			0
$459$	1.22271	−	2.11780i	0.0570713	−	0.0988503i
$460$		0			0
$461$	−6.61490	+	11.4573i	−0.308086	+	0.533621i	−0.977944	−	0.208869i	$-0.933022\pi$
$461$	−6.61490	+	11.4573i	−0.308086	+	0.533621i	0.669857	+	0.742490i	$0.266355\pi$
$462$		0			0
$463$	−13.2667			−0.616554			−0.308277	−	0.951297i	$-0.599752\pi$
$463$	−13.2667			−0.616554			−0.308277	+	0.951297i	$0.599752\pi$
$464$		0			0
$465$	−0.821464	−	1.42282i	−0.0380945	−	0.0659815i
$466$		0			0
$467$	29.3401			1.35770			0.678849	−	0.734278i	$-0.262479\pi$
$467$	29.3401			1.35770			0.678849	+	0.734278i	$0.262479\pi$
$468$		0			0
$469$	26.4954			1.22344
$470$		0			0
$471$	−25.3434	−	43.8960i	−1.16776	−	2.02262i
$472$		0			0
$473$	2.84876			0.130986
$474$		0			0
$475$	−3.67892	+	6.37207i	−0.168800	+	0.292371i
$476$		0			0
$477$	3.29197	−	5.70186i	0.150729	−	0.261070i
$478$		0			0
$479$	3.72784	+	6.45681i	0.170329	+	0.295019i	0.938535	−	0.345184i	$-0.112184\pi$
$479$	3.72784	+	6.45681i	0.170329	+	0.295019i	−0.768206	+	0.640203i	$0.778850\pi$
$480$		0			0
$481$	1.38937	+	29.6063i	0.0633498	+	1.34993i
$482$		0			0
$483$	21.9537	+	38.0249i	0.998928	+	1.73019i
$484$		0			0
$485$	0.0306855	−	0.0531488i	0.00139336	−	0.00241336i
$486$		0			0
$487$	−16.6278	+	28.8002i	−0.753477	+	1.30506i	0.192651	+	0.981267i	$0.438291\pi$
$487$	−16.6278	+	28.8002i	−0.753477	+	1.30506i	−0.946128	+	0.323793i	$0.895042\pi$
$488$		0			0
$489$	−8.30744			−0.375676
$490$		0			0
$491$	14.1155	+	24.4488i	0.637024	+	1.10336i	0.986083	+	0.166256i	$0.0531679\pi$
$491$	14.1155	+	24.4488i	0.637024	+	1.10336i	−0.349059	+	0.937101i	$0.613499\pi$
$492$		0			0
$493$	4.59071			0.206755
$494$		0			0
$495$	0.276235			0.0124158
$496$		0			0
$497$	−26.0880	−	45.1858i	−1.17021	−	2.02686i
$498$		0			0
$499$	−1.31861			−0.0590292			−0.0295146	−	0.999564i	$-0.509396\pi$
$499$	−1.31861			−0.0590292			−0.0295146	+	0.999564i	$0.509396\pi$
$500$		0			0
$501$	−20.4267	+	35.3800i	−0.912596	+	1.58066i
$502$		0			0
$503$	−13.9365	+	24.1388i	−0.621398	+	1.07629i	0.367827	+	0.929894i	$0.380102\pi$
$503$	−13.9365	+	24.1388i	−0.621398	+	1.07629i	−0.989226	+	0.146399i	$0.953232\pi$
$504$		0			0
$505$	0.478357	+	0.828539i	0.0212866	+	0.0368695i
$506$		0			0
$507$	11.9010	−	25.9624i	0.528540	−	1.15303i
$508$		0			0
$509$	18.1375	+	31.4151i	0.803931	+	1.39245i	0.917011	+	0.398863i	$0.130595\pi$
$509$	18.1375	+	31.4151i	0.803931	+	1.39245i	−0.113080	+	0.993586i	$0.536072\pi$
$510$		0			0
$511$	−16.5115	+	28.5988i	−0.730426	+	1.26514i
$512$		0			0
$513$	−1.90564	+	3.30067i	−0.0841362	+	0.145728i
$514$		0			0
$515$	0.455426			0.0200685
$516$		0			0
$517$	3.74682	+	6.48967i	0.164785	+	0.285416i
$518$		0			0
$519$	54.5216			2.39323
$520$		0			0
$521$	41.6407			1.82431			0.912156	−	0.409843i	$-0.134416\pi$
$521$	41.6407			1.82431			0.912156	+	0.409843i	$0.134416\pi$
$522$		0			0
$523$	−19.3056	−	33.4382i	−0.844173	−	1.46215i	−0.886337	−	0.463040i	$-0.846759\pi$
$523$	−19.3056	−	33.4382i	−0.844173	−	1.46215i	0.0421640	−	0.999111i	$-0.486575\pi$
$524$		0			0
$525$	47.1272			2.05680
$526$		0			0
$527$	−2.34512	+	4.06187i	−0.102155	+	0.176938i
$528$		0			0
$529$	0.748720	−	1.29682i	0.0325530	−	0.0563835i
$530$		0			0
$531$	0.125980	+	0.218203i	0.00546706	+	0.00946922i
$532$		0			0
$533$	−0.582314	−	12.4086i	−0.0252228	−	0.537477i
$534$		0			0
$535$	1.26667	+	2.19393i	0.0547629	+	0.0948521i
$536$		0			0
$537$	12.9170	−	22.3729i	0.557409	−	0.965460i
$538$		0			0
$539$	−5.78802	+	10.0251i	−0.249308	+	0.431814i
$540$		0			0
$541$	14.2454			0.612456			0.306228	−	0.951958i	$-0.400933\pi$
$541$	14.2454			0.612456			0.306228	+	0.951958i	$0.400933\pi$
$542$		0			0
$543$	−3.49706	−	6.05709i	−0.150073	−	0.259935i
$544$		0			0
$545$	0.753481			0.0322756
$546$		0			0
$547$	15.6344			0.668479			0.334240	−	0.942488i	$-0.391521\pi$
$547$	15.6344			0.668479			0.334240	+	0.942488i	$0.391521\pi$
$548$		0			0
$549$	5.52122	+	9.56303i	0.235640	+	0.408140i
$550$		0			0
$551$	−7.15480			−0.304805
$552$		0			0
$553$	32.6515	−	56.5540i	1.38848	−	2.40492i
$554$		0			0
$555$	1.36564	−	2.36536i	0.0579682	−	0.100404i
$556$		0			0
$557$	13.7441	+	23.8054i	0.582354	+	1.00867i	0.995200	+	0.0978662i	$0.0312017\pi$
$557$	13.7441	+	23.8054i	0.582354	+	1.00867i	−0.412845	+	0.910801i	$0.635465\pi$
$558$		0			0
$559$	−8.64474	+	5.54701i	−0.365633	+	0.234614i
$560$		0			0
$561$	−1.04193	−	1.80468i	−0.0439904	−	0.0761936i
$562$		0			0
$563$	4.64552	−	8.04628i	0.195786	−	0.339110i	−0.751372	−	0.659879i	$-0.770608\pi$
$563$	4.64552	−	8.04628i	0.195786	−	0.339110i	0.947158	+	0.320768i	$0.103941\pi$
$564$		0			0
$565$	1.06879	−	1.85119i	0.0449642	−	0.0778803i
$566$		0			0
$567$	48.0280			2.01699
$568$		0			0
$569$	−2.23410	−	3.86958i	−0.0936585	−	0.162221i	0.815389	−	0.578913i	$-0.196523\pi$
$569$	−2.23410	−	3.86958i	−0.0936585	−	0.162221i	−0.909048	+	0.416692i	$0.863190\pi$
$570$		0			0
$571$	−19.7999			−0.828600			−0.414300	−	0.910140i	$-0.635974\pi$
$571$	−19.7999			−0.828600			−0.414300	+	0.910140i	$0.635974\pi$
$572$		0			0
$573$	4.88574			0.204105
$574$		0			0
$575$	11.5397	+	19.9873i	0.481238	+	0.833529i
$576$		0			0
$577$	15.0858			0.628031			0.314016	−	0.949418i	$-0.398326\pi$
$577$	15.0858			0.628031			0.314016	+	0.949418i	$0.398326\pi$
$578$		0			0
$579$	−26.4483	+	45.8098i	−1.09915	+	1.90379i
$580$		0			0
$581$	4.50002	−	7.79427i	0.186692	−	0.323361i
$582$		0			0
$583$	1.80234	+	3.12175i	0.0746454	+	0.129290i
$584$		0			0
$585$	−0.838252	+	0.537876i	−0.0346574	+	0.0222384i
$586$		0			0
$587$	−19.5739	−	33.9030i	−0.807901	−	1.39933i	−0.914315	−	0.405004i	$-0.867270\pi$
$587$	−19.5739	−	33.9030i	−0.807901	−	1.39933i	0.106414	−	0.994322i	$-0.466063\pi$
$588$		0			0
$589$	3.65497	−	6.33059i	0.150600	−	0.260848i
$590$		0			0
$591$	20.9868	−	36.3503i	0.863283	−	1.49525i
$592$		0			0
$593$	15.3769			0.631452			0.315726	−	0.948850i	$-0.397752\pi$
$593$	15.3769			0.631452			0.315726	+	0.948850i	$0.397752\pi$
$594$		0			0
$595$	0.309144	+	0.535452i	0.0126736	+	0.0219514i
$596$		0			0
$597$	−32.0372			−1.31119
$598$		0			0
$599$	34.1546			1.39552			0.697760	−	0.716331i	$-0.254180\pi$
$599$	34.1546			1.39552			0.697760	+	0.716331i	$0.254180\pi$
$600$		0			0
$601$	−20.5133	−	35.5300i	−0.836754	−	1.44930i	−0.892594	−	0.450861i	$-0.851117\pi$
$601$	−20.5133	−	35.5300i	−0.836754	−	1.44930i	0.0558400	−	0.998440i	$-0.482216\pi$
$602$		0			0
$603$	−11.2283			−0.457250
$604$		0			0
$605$	−0.0756188	+	0.130976i	−0.00307434	+	0.00532492i
$606$		0			0
$607$	−18.4466	+	31.9504i	−0.748723	+	1.29683i	0.199712	+	0.979855i	$0.435999\pi$
$607$	−18.4466	+	31.9504i	−0.748723	+	1.29683i	−0.948435	+	0.316972i	$0.897334\pi$
$608$		0			0
$609$	22.9134	+	39.6871i	0.928496	+	1.60820i
$610$		0			0
$611$	−24.0064	−	12.3976i	−0.971195	−	0.501554i
$612$		0			0
$613$	−7.38792	−	12.7962i	−0.298395	−	0.516836i	0.677374	−	0.735639i	$-0.263118\pi$
$613$	−7.38792	−	12.7962i	−0.298395	−	0.516836i	−0.975769	+	0.218803i	$0.929785\pi$
$614$		0			0
$615$	−0.572369	+	0.991372i	−0.0230801	+	0.0399760i
$616$		0			0
$617$	−17.1197	+	29.6521i	−0.689212	+	1.19375i	0.282882	+	0.959155i	$0.408710\pi$
$617$	−17.1197	+	29.6521i	−0.689212	+	1.19375i	−0.972093	+	0.234595i	$0.924624\pi$
$618$		0			0
$619$	−23.6164			−0.949225			−0.474612	−	0.880195i	$-0.657412\pi$
$619$	−23.6164			−0.949225			−0.474612	+	0.880195i	$0.657412\pi$
$620$		0			0
$621$	5.97744	+	10.3532i	0.239867	+	0.415461i
$622$		0			0
$623$	66.5742			2.66724
$624$		0			0
$625$	24.6574			0.986297
$626$		0			0
$627$	1.62389	+	2.81267i	0.0648520	+	0.112327i
$628$		0			0
$629$	−7.79730			−0.310899
$630$		0			0
$631$	−8.55599	+	14.8194i	−0.340609	+	0.589952i	−0.984546	−	0.175127i	$-0.943966\pi$
$631$	−8.55599	+	14.8194i	−0.340609	+	0.589952i	0.643937	+	0.765078i	$0.277300\pi$
$632$		0			0
$633$	4.29976	−	7.44740i	0.170900	−	0.296008i
$634$		0			0
$635$	0.615901	+	1.06677i	0.0244413	+	0.0423336i
$636$		0			0
$637$	−1.95653	−	41.6921i	−0.0775207	−	1.65190i
$638$		0			0
$639$	11.0556	+	19.1489i	0.437354	+	0.757519i
$640$		0			0
$641$	13.2197	−	22.8972i	0.522148	−	0.904386i	−0.477520	−	0.878621i	$-0.658464\pi$
$641$	13.2197	−	22.8972i	0.522148	−	0.904386i	0.999668	−	0.0257657i	$-0.00820237\pi$
$642$		0			0
$643$	10.8136	−	18.7297i	0.426446	−	0.738626i	−0.570108	−	0.821570i	$-0.693099\pi$
$643$	10.8136	−	18.7297i	0.426446	−	0.738626i	0.996554	+	0.0829434i	$0.0264321\pi$
$644$		0			0
$645$	0.946525			0.0372694
$646$		0			0
$647$	19.9635	+	34.5778i	0.784847	+	1.35939i	0.929091	+	0.369852i	$0.120592\pi$
$647$	19.9635	+	34.5778i	0.784847	+	1.35939i	−0.144244	+	0.989542i	$0.546075\pi$
$648$		0			0
$649$	−0.137947			−0.00541489
$650$		0			0
$651$	−46.8204			−1.83504
$652$		0			0
$653$	5.66357	+	9.80959i	0.221633	+	0.383879i	0.955304	−	0.295626i	$-0.0955281\pi$
$653$	5.66357	+	9.80959i	0.221633	+	0.383879i	−0.733671	+	0.679505i	$0.762195\pi$
$654$		0			0
$655$	−0.269355			−0.0105246
$656$		0			0
$657$	6.99728	−	12.1196i	0.272990	−	0.472832i
$658$		0			0
$659$	9.42568	−	16.3258i	0.367173	−	0.635962i	−0.621950	−	0.783057i	$-0.713659\pi$
$659$	9.42568	−	16.3258i	0.367173	−	0.635962i	0.989122	+	0.147096i	$0.0469925\pi$
$660$		0			0
$661$	−16.2650	−	28.1719i	−0.632636	−	1.09576i	−0.987011	−	0.160654i	$-0.948640\pi$
$661$	−16.2650	−	28.1719i	−0.632636	−	1.09576i	0.354375	−	0.935104i	$-0.384694\pi$
$662$		0			0
$663$	6.67582	+	3.44759i	0.259267	+	0.133893i
$664$		0			0
$665$	−0.481812	−	0.834524i	−0.0186839	−	0.0323614i
$666$		0			0
$667$	−11.2213	+	19.4358i	−0.434489	+	0.752556i
$668$		0			0
$669$	−19.9966	+	34.6351i	−0.773114	+	1.33907i
$670$		0			0
$671$	−6.04569			−0.233391
$672$		0			0
$673$	−16.3195	−	28.2663i	−0.629072	−	1.08959i	−0.987738	−	0.156119i	$-0.950102\pi$
$673$	−16.3195	−	28.2663i	−0.629072	−	1.08959i	0.358666	−	0.933466i	$-0.383232\pi$
$674$		0			0
$675$	12.8315			0.493887
$676$		0			0
$677$	−34.3235			−1.31916			−0.659580	−	0.751634i	$-0.729266\pi$
$677$	−34.3235			−1.31916			−0.659580	+	0.751634i	$0.729266\pi$
$678$		0			0
$679$	−0.874479	−	1.51464i	−0.0335594	−	0.0581266i
$680$		0			0
$681$	9.24694			0.354343
$682$		0			0
$683$	−18.3779	+	31.8315i	−0.703213	+	1.21800i	0.264120	+	0.964490i	$0.414918\pi$
$683$	−18.3779	+	31.8315i	−0.703213	+	1.21800i	−0.967333	+	0.253510i	$0.918415\pi$
$684$		0			0
$685$	1.38952	−	2.40672i	0.0530908	−	0.0919560i
$686$		0			0
$687$	3.34527	+	5.79417i	0.127630	+	0.221062i
$688$		0			0
$689$	−11.5479	−	5.96367i	−0.439939	−	0.227198i
$690$		0			0
$691$	−8.09435	−	14.0198i	−0.307923	−	0.533339i	0.669985	−	0.742375i	$-0.266301\pi$
$691$	−8.09435	−	14.0198i	−0.307923	−	0.533339i	−0.977908	+	0.209036i	$0.932967\pi$
$692$		0			0
$693$	3.93609	−	6.81751i	0.149520	−	0.258976i
$694$		0			0
$695$	1.16310	−	2.01455i	0.0441190	−	0.0764163i
$696$		0			0
$697$	3.26801			0.123785
$698$		0			0
$699$	−1.89445	−	3.28129i	−0.0716548	−	0.124110i
$700$		0			0
$701$	−22.6393			−0.855074			−0.427537	−	0.903998i	$-0.640619\pi$
$701$	−22.6393			−0.855074			−0.427537	+	0.903998i	$0.640619\pi$
$702$		0			0
$703$	12.1524			0.458336
$704$		0			0
$705$	1.24491	+	2.15625i	0.0468861	+	0.0812090i
$706$		0			0
$707$	27.2646			1.02539
$708$		0			0
$709$	−7.44263	+	12.8910i	−0.279514	+	0.484132i	−0.971264	−	0.238005i	$-0.923507\pi$
$709$	−7.44263	+	12.8910i	−0.279514	+	0.484132i	0.691750	+	0.722137i	$0.256840\pi$
$710$		0			0
$711$	−13.8371	+	23.9666i	−0.518932	+	0.898817i
$712$		0			0
$713$	−11.4646	−	19.8572i	−0.429351	−	0.743658i
$714$		0			0
$715$	−0.0255616	−	0.544696i	−0.000955949	−	0.0203705i
$716$		0			0
$717$	25.1181	+	43.5059i	0.938054	+	1.62476i
$718$		0			0
$719$	−12.6862	+	21.9731i	−0.473115	+	0.819460i	−0.999526	−	0.0307705i	$-0.990204\pi$
$719$	−12.6862	+	21.9731i	−0.473115	+	0.819460i	0.526411	+	0.850230i	$0.323537\pi$
$720$		0			0
$721$	6.48940	−	11.2400i	0.241678	−	0.418598i
$722$		0			0
$723$	−38.4780			−1.43101
$724$		0			0
$725$	12.0441	+	20.8610i	0.447307	+	0.774759i
$726$		0			0
$727$	−52.7515			−1.95645			−0.978223	−	0.207558i	$-0.933448\pi$
$727$	−52.7515			−1.95645			−0.978223	+	0.207558i	$0.933448\pi$
$728$		0			0
$729$	−3.36165			−0.124506
$730$		0			0
$731$	−1.35108	−	2.34013i	−0.0499714	−	0.0865529i
$732$		0			0
$733$	−42.4824			−1.56912			−0.784561	−	0.620051i	$-0.787112\pi$
$733$	−42.4824			−1.56912			−0.784561	+	0.620051i	$0.787112\pi$
$734$		0			0
$735$	−1.92312	+	3.33094i	−0.0709353	+	0.122864i
$736$		0			0
$737$	3.07371	−	5.32383i	0.113222	−	0.196106i
$738$		0			0
$739$	4.32128	+	7.48468i	0.158961	+	0.275329i	0.934494	−	0.355978i	$-0.115852\pi$
$739$	4.32128	+	7.48468i	0.158961	+	0.275329i	−0.775533	+	0.631307i	$0.782519\pi$
$740$		0			0
$741$	−10.4045	−	5.37321i	−0.382220	−	0.197390i
$742$		0			0
$743$	−9.12153	−	15.7989i	−0.334636	−	0.579607i	0.648779	−	0.760977i	$-0.275280\pi$
$743$	−9.12153	−	15.7989i	−0.334636	−	0.579607i	−0.983415	+	0.181370i	$0.941947\pi$
$744$		0			0
$745$	−0.500117	+	0.866229i	−0.0183229	+	0.0317362i
$746$		0			0
$747$	−1.90703	+	3.30307i	−0.0697745	+	0.120853i
$748$		0			0
$749$	72.1954			2.63796
$750$		0			0
$751$	15.3297	+	26.5517i	0.559387	+	0.968887i	0.997548	+	0.0699901i	$0.0222968\pi$
$751$	15.3297	+	26.5517i	0.559387	+	0.968887i	−0.438161	+	0.898897i	$0.644370\pi$
$752$		0			0
$753$	−45.8729			−1.67170
$754$		0			0
$755$	−2.88226			−0.104896
$756$		0			0
$757$	0.863776	+	1.49610i	0.0313945	+	0.0543768i	0.881296	−	0.472565i	$-0.156672\pi$
$757$	0.863776	+	1.49610i	0.0313945	+	0.0543768i	−0.849901	+	0.526942i	$0.823339\pi$
$758$		0			0
$759$	10.1873			0.369777
$760$		0			0
$761$	−0.119357	+	0.206733i	−0.00432669	+	0.00749405i	−0.868181	−	0.496248i	$-0.834711\pi$
$761$	−0.119357	+	0.206733i	−0.00432669	+	0.00749405i	0.863854	+	0.503742i	$0.168044\pi$
$762$		0			0
$763$	10.7364	−	18.5960i	0.388684	−	0.673220i
$764$		0			0
$765$	−0.131009	−	0.226915i	−0.00473666	−	0.00820413i
$766$		0			0
$767$	0.418608	−	0.268605i	0.0151151	−	0.00969878i
$768$		0			0
$769$	−1.19637	−	2.07218i	−0.0431422	−	0.0747246i	0.843648	−	0.536897i	$-0.180404\pi$
$769$	−1.19637	−	2.07218i	−0.0431422	−	0.0747246i	−0.886790	+	0.462172i	$0.847070\pi$
$770$		0			0
$771$	1.39556	−	2.41718i	0.0502598	−	0.0870525i
$772$		0			0
$773$	2.91610	−	5.05083i	0.104885	−	0.181666i	−0.808806	−	0.588075i	$-0.799886\pi$
$773$	2.91610	−	5.05083i	0.104885	−	0.181666i	0.913691	+	0.406409i	$0.133219\pi$
$774$		0			0
$775$	−24.6105			−0.884036
$776$		0			0
$777$	−38.9182	−	67.4084i	−1.39618	−	2.41826i
$778$		0			0
$779$	−5.09332			−0.182487
$780$		0			0
$781$	−12.1058			−0.433181
$782$		0			0
$783$	6.23874	+	10.8058i	0.222954	+	0.386168i
$784$		0			0
$785$	3.48930			0.124538
$786$		0			0
$787$	−13.5596	+	23.4858i	−0.483346	+	0.837180i	−0.999817	−	0.0191248i	$-0.993912\pi$
$787$	−13.5596	+	23.4858i	−0.483346	+	0.837180i	0.516471	+	0.856305i	$0.327245\pi$
$788$		0			0
$789$	7.56126	−	13.0965i	0.269188	−	0.466247i
$790$		0			0
$791$	−30.4584	−	52.7556i	−1.08298	−	1.87577i
$792$		0			0
$793$	18.3460	−	11.7720i	0.651486	−	0.418035i
$794$		0			0
$795$	0.598844	+	1.03723i	0.0212388	+	0.0367867i
$796$		0			0
$797$	−4.23685	+	7.33843i	−0.150077	+	0.259941i	−0.931256	−	0.364367i	$-0.881285\pi$
$797$	−4.23685	+	7.33843i	−0.150077	+	0.259941i	0.781179	+	0.624308i	$0.214619\pi$
$798$		0			0
$799$	3.55399	−	6.15569i	0.125731	−	0.217773i
$800$		0			0
$801$	−28.2130			−0.996856
$802$		0			0
$803$	3.83098	+	6.63546i	0.135192	+	0.234160i
$804$		0			0
$805$	−3.02261			−0.106533
$806$		0			0
$807$	−58.5420			−2.06078
$808$		0			0
$809$	5.81414	+	10.0704i	0.204414	+	0.354056i	0.949946	−	0.312414i	$-0.101138\pi$
$809$	5.81414	+	10.0704i	0.204414	+	0.354056i	−0.745532	+	0.666470i	$0.767804\pi$
$810$		0			0
$811$	−43.7551			−1.53645			−0.768224	−	0.640181i	$-0.778859\pi$
$811$	−43.7551			−1.53645			−0.768224	+	0.640181i	$0.778859\pi$
$812$		0			0
$813$	18.3099	−	31.7137i	0.642156	−	1.11225i
$814$		0			0
$815$	0.285944	−	0.495270i	0.0100162	−	0.0173486i
$816$		0			0
$817$	2.10571	+	3.64719i	0.0736693	+	0.127599i
$818$		0			0
$819$	1.33052	+	28.3524i	0.0464923	+	0.990712i
$820$		0			0
$821$	−26.5277	−	45.9473i	−0.925823	−	1.60357i	−0.790231	−	0.612809i	$-0.790040\pi$
$821$	−26.5277	−	45.9473i	−0.925823	−	1.60357i	−0.135592	−	0.990765i	$-0.543294\pi$
$822$		0			0
$823$	7.94924	−	13.7685i	0.277093	−	0.479939i	−0.693568	−	0.720391i	$-0.743962\pi$
$823$	7.94924	−	13.7685i	0.277093	−	0.479939i	0.970661	+	0.240452i	$0.0772956\pi$
$824$		0			0
$825$	5.46720	−	9.46946i	0.190343	−	0.329684i
$826$		0			0
$827$	−7.77095			−0.270222			−0.135111	−	0.990830i	$-0.543139\pi$
$827$	−7.77095			−0.270222			−0.135111	+	0.990830i	$0.543139\pi$
$828$		0			0
$829$	−21.6929	−	37.5732i	−0.753426	−	1.30497i	−0.946153	−	0.323719i	$-0.895067\pi$
$829$	−21.6929	−	37.5732i	−0.753426	−	1.30497i	0.192728	−	0.981252i	$-0.438267\pi$
$830$		0			0
$831$	43.9900			1.52600
$832$		0			0
$833$	10.9803			0.380444
$834$		0			0
$835$	−1.40618	−	2.43558i	−0.0486629	−	0.0842867i
$836$		0			0
$837$	−12.7480			−0.440636
$838$		0			0
$839$	27.7824	−	48.1206i	0.959156	−	1.66131i	0.234599	−	0.972092i	$-0.424622\pi$
$839$	27.7824	−	48.1206i	0.959156	−	1.66131i	0.724557	−	0.689215i	$-0.242044\pi$
$840$		0			0
$841$	2.78823	−	4.82935i	0.0961458	−	0.166529i
$842$		0			0
$843$	−11.0560	−	19.1495i	−0.380787	−	0.659543i
$844$		0			0
$845$	1.13818	+	1.60314i	0.0391546	+	0.0551496i
$846$		0			0
$847$	2.15500	+	3.73256i	0.0740466	+	0.128252i
$848$		0			0
$849$	2.00600	−	3.47450i	0.0688458	−	0.119244i
$850$		0			0
$851$	19.0592	−	33.0116i	0.653342	−	1.13162i
$852$		0			0
$853$	5.13239			0.175730			0.0878649	−	0.996132i	$-0.471996\pi$
$853$	5.13239			0.175730			0.0878649	+	0.996132i	$0.471996\pi$
$854$		0			0
$855$	0.204183	+	0.353656i	0.00698292	+	0.0120948i
$856$		0			0
$857$	−26.9653			−0.921118			−0.460559	−	0.887629i	$-0.652351\pi$
$857$	−26.9653			−0.921118			−0.460559	+	0.887629i	$0.652351\pi$
$858$		0			0
$859$	3.93622			0.134302			0.0671510	−	0.997743i	$-0.478609\pi$
$859$	3.93622			0.134302			0.0671510	+	0.997743i	$0.478609\pi$
$860$		0			0
$861$	16.3114	+	28.2523i	0.555893	+	0.962834i
$862$		0			0
$863$	−14.1075			−0.480225			−0.240113	−	0.970745i	$-0.577184\pi$
$863$	−14.1075			−0.480225			−0.240113	+	0.970745i	$0.577184\pi$
$864$		0			0
$865$	−1.87665	+	3.25045i	−0.0638080	+	0.110519i
$866$		0			0
$867$	17.6856	−	30.6323i	0.600634	−	1.04033i
$868$		0			0
$869$	−7.57576	−	13.1216i	−0.256990	−	0.445120i
$870$		0			0
$871$	1.03901	+	22.1405i	0.0352056	+	0.750202i
$872$		0			0
$873$	0.370588	+	0.641878i	0.0125425	+	0.0217243i
$874$		0			0
$875$	−3.25171	+	5.63213i	−0.109928	+	0.190401i
$876$		0			0
$877$	−6.92118	+	11.9878i	−0.233711	+	0.404800i	−0.958897	−	0.283753i	$-0.908420\pi$
$877$	−6.92118	+	11.9878i	−0.233711	+	0.404800i	0.725186	+	0.688553i	$0.241754\pi$
$878$		0			0
$879$	70.9236			2.39219
$880$		0			0
$881$	21.1005	+	36.5471i	0.710894	+	1.23130i	0.964522	+	0.264002i	$0.0850426\pi$
$881$	21.1005	+	36.5471i	0.710894	+	1.23130i	−0.253628	+	0.967302i	$0.581624\pi$
$882$		0			0
$883$	−6.14690			−0.206860			−0.103430	−	0.994637i	$-0.532982\pi$
$883$	−6.14690			−0.206860			−0.103430	+	0.994637i	$0.532982\pi$
$884$		0			0
$885$	−0.0458340			−0.00154069
$886$		0			0
$887$	−5.58834	−	9.67928i	−0.187638	−	0.324999i	0.756824	−	0.653618i	$-0.226750\pi$
$887$	−5.58834	−	9.67928i	−0.187638	−	0.324999i	−0.944462	+	0.328620i	$0.893417\pi$
$888$		0			0
$889$	35.1041			1.17735
$890$		0			0
$891$	5.57170	−	9.65047i	0.186659	−	0.323303i
$892$		0			0
$893$	−5.53903	+	9.59388i	−0.185357	+	0.321047i
$894$		0			0
$895$	0.889211	+	1.54016i	0.0297231	+	0.0514818i
$896$		0			0
$897$	−30.9141	+	19.8365i	−1.03219	+	0.662320i
$898$		0			0
$899$	−11.9657	−	20.7252i	−0.399079	−	0.691225i
$900$		0			0
$901$	1.70959	−	2.96109i	0.0569546	−	0.0986482i
$902$		0			0
$903$	13.4871	−	23.3604i	0.448823	−	0.777384i
$904$		0			0
$905$	0.481479			0.0160049
$906$		0			0
$907$	14.1027	+	24.4265i	0.468271	+	0.811069i	0.999342	−	0.0362578i	$-0.0115437\pi$
$907$	14.1027	+	24.4265i	0.468271	+	0.811069i	−0.531071	+	0.847327i	$0.678210\pi$
$908$		0			0
$909$	−11.5542			−0.383230
$910$		0			0
$911$	43.5478			1.44280			0.721402	−	0.692517i	$-0.243498\pi$
$911$	43.5478			1.44280			0.721402	+	0.692517i	$0.243498\pi$
$912$		0			0
$913$	−1.04409	−	1.80842i	−0.0345544	−	0.0598499i
$914$		0			0
$915$	−2.00873			−0.0664066
$916$		0			0
$917$	−3.83805	+	6.64771i	−0.126744	+	0.219527i
$918$		0			0
$919$	−8.88587	+	15.3908i	−0.293118	+	0.507695i	−0.974545	−	0.224191i	$-0.928026\pi$
$919$	−8.88587	+	15.3908i	−0.293118	+	0.507695i	0.681428	+	0.731886i	$0.261359\pi$
$920$		0			0
$921$	9.30070	+	16.1093i	0.306469	+	0.530819i
$922$		0			0
$923$	36.7359	−	23.5721i	1.20918	−	0.775884i
$924$		0			0
$925$	−20.4569	−	35.4323i	−0.672618	−	1.16501i
$926$		0			0
$927$	−2.75009	+	4.76329i	−0.0903248	+	0.156447i
$928$		0			0
$929$	−12.8757	+	22.3014i	−0.422439	+	0.731686i	−0.996177	−	0.0873529i	$-0.972159\pi$
$929$	−12.8757	+	22.3014i	−0.422439	+	0.731686i	0.573739	+	0.819039i	$0.305493\pi$
$930$		0			0
$931$	−17.1132			−0.560863
$932$		0			0
$933$	32.5931	+	56.4529i	1.06705	+	1.84818i
$934$		0			0
$935$	0.143454			0.00469146
$936$		0			0
$937$	7.98935			0.261001			0.130500	−	0.991448i	$-0.458342\pi$
$937$	7.98935			0.261001			0.130500	+	0.991448i	$0.458342\pi$
$938$		0			0
$939$	−6.43028	−	11.1376i	−0.209844	−	0.363461i
$940$		0			0
$941$	−4.60320			−0.150060			−0.0750301	−	0.997181i	$-0.523905\pi$
$941$	−4.60320			−0.150060			−0.0750301	+	0.997181i	$0.523905\pi$
$942$		0			0
$943$	−7.98813	+	13.8358i	−0.260129	+	0.450557i
$944$		0			0
$945$	−0.840247	+	1.45535i	−0.0273332	+	0.0473425i
$946$		0			0
$947$	1.12626	+	1.95073i	0.0365984	+	0.0633903i	0.883744	−	0.467970i	$-0.155014\pi$
$947$	1.12626	+	1.95073i	0.0365984	+	0.0633903i	−0.847146	+	0.531360i	$0.821681\pi$
$948$		0			0
$949$	−24.5457	−	12.6761i	−0.796787	−	0.411484i
$950$		0			0
$951$	−15.4424	−	26.7470i	−0.500754	−	0.867332i
$952$		0			0
$953$	7.58355	−	13.1351i	0.245655	−	0.425487i	−0.716660	−	0.697422i	$-0.754330\pi$
$953$	7.58355	−	13.1351i	0.245655	−	0.425487i	0.962316	+	0.271935i	$0.0876635\pi$
$954$		0			0
$955$	−0.168169	+	0.291276i	−0.00544181	+	0.00942549i
$956$		0			0
$957$	10.6327			0.343705
$958$		0			0
$959$	−39.5987	−	68.5870i	−1.27871	−	2.21479i
$960$		0			0
$961$	−6.54968			−0.211280
$962$		0			0
$963$	−30.5951			−0.985913
$964$		0			0
$965$	−1.82071	−	3.15357i	−0.0586108	−	0.101517i
$966$		0			0
$967$	−33.3320			−1.07188			−0.535942	−	0.844255i	$-0.680043\pi$
$967$	−33.3320			−1.07188			−0.535942	+	0.844255i	$0.680043\pi$
$968$		0			0
$969$	1.54032	−	2.66791i	0.0494822	−	0.0857057i
$970$		0			0
$971$	−1.03438	+	1.79160i	−0.0331949	+	0.0574952i	−0.882146	−	0.470977i	$-0.843902\pi$
$971$	−1.03438	+	1.79160i	−0.0331949	+	0.0574952i	0.848951	+	0.528472i	$0.177235\pi$
$972$		0			0
$973$	−33.1463	−	57.4110i	−1.06262	−	1.84051i
$974$		0			0
$975$	1.84809	+	39.3812i	0.0591861	+	1.26121i
$976$		0			0
$977$	15.0195	+	26.0145i	0.480516	+	0.832279i	0.999750	−	0.0223534i	$-0.00711591\pi$
$977$	15.0195	+	26.0145i	0.480516	+	0.832279i	−0.519234	+	0.854632i	$0.673783\pi$
$978$		0			0
$979$	7.72324	−	13.3770i	0.246836	−	0.427532i
$980$		0			0
$981$	−4.54989	+	7.88064i	−0.145267	+	0.251610i
$982$		0			0
$983$	43.6884			1.39344			0.696722	−	0.717341i	$-0.254641\pi$
$983$	43.6884			1.39344			0.696722	+	0.717341i	$0.254641\pi$
$984$		0			0
$985$	1.44474	+	2.50237i	0.0460334	+	0.0797322i
$986$		0			0
$987$	70.9553			2.25853
$988$		0			0
$989$	13.2100			0.420052
$990$		0			0
$991$	19.3072	+	33.4410i	0.613313	+	1.06229i	0.990678	+	0.136224i	$0.0434967\pi$
$991$	19.3072	+	33.4410i	0.613313	+	1.06229i	−0.377365	+	0.926064i	$0.623170\pi$
$992$		0			0
$993$	13.4269			0.426089
$994$		0			0
$995$	1.10273	−	1.90998i	0.0349588	−	0.0605504i
$996$		0			0
$997$	17.6879	−	30.6363i	0.560180	−	0.970261i	−0.437300	−	0.899316i	$-0.644065\pi$
$997$	17.6879	−	30.6363i	0.560180	−	0.970261i	0.997480	−	0.0709452i	$-0.0226015\pi$
$998$		0			0
$999$	−10.5965	−	18.3536i	−0.335257	−	0.580683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.c.133.1	✓	10
13.3	even	3		7436.2.a.r.1.5		5
13.9	even	3	inner	572.2.i.c.529.1	yes	10
13.10	even	6		7436.2.a.q.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.c.133.1	✓	10	1.1	even	1	trivial
572.2.i.c.529.1	yes	10	13.9	even	3	inner
7436.2.a.q.1.5		5	13.10	even	6
7436.2.a.r.1.5		5	13.3	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09846 - 1.90260i) q^{3} +0.151238 q^{5} +(2.15500 - 3.73256i) q^{7} +(-0.913248 + 1.58179i) q^{9} +O(q^{10})\)	\(q+(-1.09846 - 1.90260i) q^{3} +0.151238 q^{5} +(2.15500 - 3.73256i) q^{7} +(-0.913248 + 1.58179i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(3.20357 + 1.65442i) q^{13} +(-0.166129 - 0.287744i) q^{15} +(-0.474268 + 0.821456i) q^{17} +(0.739165 - 1.28027i) q^{19} -9.46875 q^{21} +(-2.31854 - 4.01583i) q^{23} -4.97713 q^{25} -2.57810 q^{27} +(-2.41989 - 4.19138i) q^{29} +4.94473 q^{31} +(-1.09846 + 1.90260i) q^{33} +(0.325917 - 0.564504i) q^{35} +(4.11018 + 7.11904i) q^{37} +(-0.371316 - 7.91243i) q^{39} +(-1.72266 - 2.98374i) q^{41} +(-1.42438 + 2.46710i) q^{43} +(-0.138118 + 0.239227i) q^{45} -7.49363 q^{47} +(-5.78802 - 10.0251i) q^{49} +2.08386 q^{51} -3.60468 q^{53} +(-0.0756188 - 0.130976i) q^{55} -3.24779 q^{57} +(0.0689734 - 0.119465i) q^{59} +(3.02285 - 5.23572i) q^{61} +(3.93609 + 6.81751i) q^{63} +(0.484501 + 0.250211i) q^{65} +(3.07371 + 5.32383i) q^{67} +(-5.09367 + 8.82250i) q^{69} +(6.05292 - 10.4840i) q^{71} -7.66197 q^{73} +(5.46720 + 9.46946i) q^{75} -4.30999 q^{77} +15.1515 q^{79} +(5.57170 + 9.65047i) q^{81} +2.08818 q^{83} +(-0.0717272 + 0.124235i) q^{85} +(-5.31633 + 9.20816i) q^{87} +(7.72324 + 13.3770i) q^{89} +(13.0789 - 8.39227i) q^{91} +(-5.43161 - 9.40782i) q^{93} +(0.111790 - 0.193625i) q^{95} +(0.202896 - 0.351426i) q^{97} +1.82650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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