LMFDB - Embedded newform 216.2.q.a.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	216.97
Dual form			216.2.q.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73099 + 0.0606946i) q^{3} +(-0.00848388 - 0.00308788i) q^{5} +(-0.356397 + 2.02123i) q^{7} +(2.99263 + 0.210123i) q^{9} +O(q^{10})$	\(q+(1.73099 + 0.0606946i) q^{3} +(-0.00848388 - 0.00308788i) q^{5} +(-0.356397 + 2.02123i) q^{7} +(2.99263 + 0.210123i) q^{9} +(3.47988 - 1.26657i) q^{11} +(-1.25578 + 1.05372i) q^{13} +(-0.0144981 - 0.00586000i) q^{15} +(-3.38526 - 5.86344i) q^{17} +(-1.25280 + 2.16991i) q^{19} +(-0.739596 + 3.47709i) q^{21} +(0.120050 + 0.680839i) q^{23} +(-3.83016 - 3.21389i) q^{25} +(5.16745 + 0.545357i) q^{27} +(-2.53937 - 2.13078i) q^{29} +(1.38196 + 7.83750i) q^{31} +(6.10050 - 1.98121i) q^{33} +(0.00926493 - 0.0160473i) q^{35} +(-2.92995 - 5.07482i) q^{37} +(-2.23769 + 1.74776i) q^{39} +(-3.22988 + 2.71019i) q^{41} +(-6.54298 + 2.38145i) q^{43} +(-0.0247403 - 0.0110235i) q^{45} +(1.67533 - 9.50130i) q^{47} +(2.61951 + 0.953423i) q^{49} +(-5.50396 - 10.3550i) q^{51} -6.78317 q^{53} -0.0334339 q^{55} +(-2.30028 + 3.68005i) q^{57} +(-2.68702 - 0.977994i) q^{59} +(-2.07092 + 11.7448i) q^{61} +(-1.49127 + 5.97390i) q^{63} +(0.0139076 - 0.00506196i) q^{65} +(-0.998222 + 0.837608i) q^{67} +(0.166482 + 1.18581i) q^{69} +(-1.11540 - 1.93193i) q^{71} +(7.05114 - 12.2129i) q^{73} +(-6.43489 - 5.79566i) q^{75} +(1.31981 + 7.48503i) q^{77} +(-11.0110 - 9.23932i) q^{79} +(8.91170 + 1.25764i) q^{81} +(11.5731 + 9.71102i) q^{83} +(0.0106145 + 0.0601980i) q^{85} +(-4.26629 - 3.84248i) q^{87} +(2.14879 - 3.72181i) q^{89} +(-1.68226 - 2.91375i) q^{91} +(1.91647 + 13.6505i) q^{93} +(0.0173290 - 0.0145408i) q^{95} +(6.50133 - 2.36629i) q^{97} +(10.6801 - 3.05918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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
$3$	1.73099	+	0.0606946i	0.999386	+	0.0350420i
$3$	1.73099	+	0.0606946i	0.999386	+	0.0350420i
$4$		0			0
$5$	−0.00848388	−	0.00308788i	−0.00379411	−	0.00138094i	0.340122	−	0.940381i	$-0.389531\pi$
$5$	−0.00848388	−	0.00308788i	−0.00379411	−	0.00138094i	−0.343916	+	0.939000i	$0.611754\pi$
$6$		0			0
$7$	−0.356397	+	2.02123i	−0.134705	+	0.763952i	0.840359	+	0.542030i	$0.182344\pi$
$7$	−0.356397	+	2.02123i	−0.134705	+	0.763952i	−0.975064	+	0.221922i	$0.928767\pi$
$8$		0			0
$9$	2.99263	+	0.210123i	0.997544	+	0.0700410i
$10$		0			0
$11$	3.47988	−	1.26657i	1.04922	−	0.381886i	0.240854	−	0.970561i	$-0.422573\pi$
$11$	3.47988	−	1.26657i	1.04922	−	0.381886i	0.808370	+	0.588675i	$0.200350\pi$
$12$		0			0
$13$	−1.25578	+	1.05372i	−0.348290	+	0.292250i	−0.800103	−	0.599863i	$-0.795222\pi$
$13$	−1.25578	+	1.05372i	−0.348290	+	0.292250i	0.451813	+	0.892113i	$0.350777\pi$
$14$		0			0
$15$	−0.0144981	−	0.00586000i	−0.00374338	−	0.00151305i
$16$		0			0
$17$	−3.38526	−	5.86344i	−0.821046	−	1.42209i	−0.904904	−	0.425615i	$-0.860058\pi$
$17$	−3.38526	−	5.86344i	−0.821046	−	1.42209i	0.0838587	−	0.996478i	$-0.473276\pi$
$18$		0			0
$19$	−1.25280	+	2.16991i	−0.287412	+	0.497812i	−0.973191	−	0.229997i	$-0.926128\pi$
$19$	−1.25280	+	2.16991i	−0.287412	+	0.497812i	0.685779	+	0.727810i	$0.259462\pi$
$20$		0			0
$21$	−0.739596	+	3.47709i	−0.161393	+	0.758763i
$22$		0			0
$23$	0.120050	+	0.680839i	0.0250322	+	0.141965i	0.994762	−	0.102214i	$-0.0325927\pi$
$23$	0.120050	+	0.680839i	0.0250322	+	0.141965i	−0.969730	+	0.244179i	$0.921482\pi$
$24$		0			0
$25$	−3.83016	−	3.21389i	−0.766032	−	0.642777i
$26$		0			0
$27$	5.16745	+	0.545357i	0.994477	+	0.104954i
$28$		0			0
$29$	−2.53937	−	2.13078i	−0.471549	−	0.395676i	0.375810	−	0.926697i	$-0.377364\pi$
$29$	−2.53937	−	2.13078i	−0.471549	−	0.395676i	−0.847359	+	0.531020i	$0.821809\pi$
$30$		0			0
$31$	1.38196	+	7.83750i	0.248208	+	1.40766i	0.812923	+	0.582371i	$0.197875\pi$
$31$	1.38196	+	7.83750i	0.248208	+	1.40766i	−0.564715	+	0.825286i	$0.691014\pi$
$32$		0			0
$33$	6.10050	−	1.98121i	1.06196	−	0.344885i
$34$		0			0
$35$	0.00926493	−	0.0160473i	0.00156606	−	0.00271249i
$36$		0			0
$37$	−2.92995	−	5.07482i	−0.481680	−	0.834295i	0.518099	−	0.855321i	$-0.326640\pi$
$37$	−2.92995	−	5.07482i	−0.481680	−	0.834295i	−0.999779	+	0.0210263i	$0.993307\pi$
$38$		0			0
$39$	−2.23769	+	1.74776i	−0.358317	+	0.279866i
$40$		0			0
$41$	−3.22988	+	2.71019i	−0.504423	+	0.423261i	−0.859162	−	0.511704i	$-0.829014\pi$
$41$	−3.22988	+	2.71019i	−0.504423	+	0.423261i	0.354739	+	0.934966i	$0.384570\pi$
$42$		0			0
$43$	−6.54298	+	2.38145i	−0.997795	+	0.363168i	−0.788734	−	0.614735i	$-0.789263\pi$
$43$	−6.54298	+	2.38145i	−0.997795	+	0.363168i	−0.209061	+	0.977903i	$0.567041\pi$
$44$		0			0
$45$	−0.0247403	−	0.0110235i	−0.00368806	−	0.00164329i
$46$		0			0
$47$	1.67533	−	9.50130i	0.244373	−	1.38591i	−0.577572	−	0.816340i	$-0.696000\pi$
$47$	1.67533	−	9.50130i	0.244373	−	1.38591i	0.821945	−	0.569567i	$-0.192889\pi$
$48$		0			0
$49$	2.61951	+	0.953423i	0.374215	+	0.136203i
$50$		0			0
$51$	−5.50396	−	10.3550i	−0.770708	−	1.44999i
$52$		0			0
$53$	−6.78317			−0.931741			−0.465870	−	0.884853i	$-0.654259\pi$
$53$	−6.78317			−0.931741			−0.465870	+	0.884853i	$0.654259\pi$
$54$		0			0
$55$	−0.0334339			−0.00450823
$56$		0			0
$57$	−2.30028	+	3.68005i	−0.304680	+	0.487435i
$58$		0			0
$59$	−2.68702	−	0.977994i	−0.349820	−	0.127324i	0.161133	−	0.986933i	$-0.448485\pi$
$59$	−2.68702	−	0.977994i	−0.349820	−	0.127324i	−0.510953	+	0.859609i	$0.670707\pi$
$60$		0			0
$61$	−2.07092	+	11.7448i	−0.265154	+	1.50376i	0.503443	+	0.864028i	$0.332066\pi$
$61$	−2.07092	+	11.7448i	−0.265154	+	1.50376i	−0.768597	+	0.639733i	$0.779045\pi$
$62$		0			0
$63$	−1.49127	+	5.97390i	−0.187883	+	0.752641i
$64$		0			0
$65$	0.0139076	−	0.00506196i	0.00172503	−	0.000627859i
$66$		0			0
$67$	−0.998222	+	0.837608i	−0.121952	+	0.102330i	−0.701724	−	0.712449i	$-0.747586\pi$
$67$	−0.998222	+	0.837608i	−0.121952	+	0.102330i	0.579772	+	0.814779i	$0.303142\pi$
$68$		0			0
$69$	0.166482	+	1.18581i	0.0200421	+	0.142755i
$70$		0			0
$71$	−1.11540	−	1.93193i	−0.132374	−	0.229278i	0.792217	−	0.610239i	$-0.208927\pi$
$71$	−1.11540	−	1.93193i	−0.132374	−	0.229278i	−0.924591	+	0.380961i	$0.875593\pi$
$72$		0			0
$73$	7.05114	−	12.2129i	0.825273	−	1.42942i	−0.0764371	−	0.997074i	$-0.524354\pi$
$73$	7.05114	−	12.2129i	0.825273	−	1.42942i	0.901710	−	0.432341i	$-0.142312\pi$
$74$		0			0
$75$	−6.43489	−	5.79566i	−0.743037	−	0.669226i
$76$		0			0
$77$	1.31981	+	7.48503i	0.150407	+	0.852998i
$78$		0			0
$79$	−11.0110	−	9.23932i	−1.23883	−	1.03950i	−0.997614	−	0.0690334i	$-0.978009\pi$
$79$	−11.0110	−	9.23932i	−1.23883	−	1.03950i	−0.241219	−	0.970471i	$-0.577547\pi$
$80$		0			0
$81$	8.91170	+	1.25764i	0.990189	+	0.139738i
$82$		0			0
$83$	11.5731	+	9.71102i	1.27032	+	1.06592i	0.994503	+	0.104712i	$0.0333920\pi$
$83$	11.5731	+	9.71102i	1.27032	+	1.06592i	0.275815	+	0.961211i	$0.411052\pi$
$84$		0			0
$85$	0.0106145	+	0.0601980i	0.00115131	+	0.00652939i
$86$		0			0
$87$	−4.26629	−	3.84248i	−0.457394	−	0.411957i
$88$		0			0
$89$	2.14879	−	3.72181i	0.227771	−	0.394511i	−0.729376	−	0.684113i	$-0.760190\pi$
$89$	2.14879	−	3.72181i	0.227771	−	0.394511i	0.957147	+	0.289602i	$0.0935230\pi$
$90$		0			0
$91$	−1.68226	−	2.91375i	−0.176348	−	0.305444i
$92$		0			0
$93$	1.91647	+	13.6505i	0.198728	+	1.41549i
$94$		0			0
$95$	0.0173290	−	0.0145408i	0.00177792	−	0.00149185i
$96$		0			0
$97$	6.50133	−	2.36629i	0.660110	−	0.240260i	0.00982602	−	0.999952i	$-0.496872\pi$
$97$	6.50133	−	2.36629i	0.660110	−	0.240260i	0.650284	+	0.759691i	$0.274650\pi$
$98$		0			0
$99$	10.6801	−	3.05918i	1.07339	−	0.307459i
$100$		0			0
$101$	−0.741769	+	4.20678i	−0.0738088	+	0.418590i	0.925406	+	0.378977i	$0.123724\pi$
$101$	−0.741769	+	4.20678i	−0.0738088	+	0.418590i	−0.999215	+	0.0396139i	$0.987387\pi$
$102$		0			0
$103$	18.1602	+	6.60979i	1.78938	+	0.651282i	0.999265	+	0.0383257i	$0.0122024\pi$
$103$	18.1602	+	6.60979i	1.78938	+	0.651282i	0.790117	+	0.612956i	$0.210020\pi$
$104$		0			0
$105$	0.0170115	−	0.0272154i	0.00166015	−	0.00265595i
$106$		0			0
$107$	−7.19236			−0.695312			−0.347656	−	0.937622i	$-0.613022\pi$
$107$	−7.19236			−0.695312			−0.347656	+	0.937622i	$0.613022\pi$
$108$		0			0
$109$	15.6780			1.50168			0.750838	−	0.660487i	$-0.229650\pi$
$109$	15.6780			1.50168			0.750838	+	0.660487i	$0.229650\pi$
$110$		0			0
$111$	−4.76368	−	8.96227i	−0.452149	−	0.850661i
$112$		0			0
$113$	17.3499	+	6.31485i	1.63214	+	0.594051i	0.985640	−	0.168861i	$-0.0540089\pi$
$113$	17.3499	+	6.31485i	1.63214	+	0.594051i	0.646502	+	0.762912i	$0.276231\pi$
$114$		0			0
$115$	0.00108386	−	0.00614686i	0.000101070	−	0.000573198i
$116$		0			0
$117$	−3.97949	+	2.88954i	−0.367904	+	0.267138i
$118$		0			0
$119$	13.0578	−	4.75266i	1.19701	−	0.435676i
$120$		0			0
$121$	2.07887	−	1.74438i	0.188988	−	0.158580i
$122$		0			0
$123$	−5.75538	+	4.49527i	−0.518945	+	0.405325i
$124$		0			0
$125$	0.0451414	+	0.0781872i	0.00403757	+	0.00699328i
$126$		0			0
$127$	1.11425	−	1.92993i	0.0988735	−	0.171254i	−0.812345	−	0.583177i	$-0.801809\pi$
$127$	1.11425	−	1.92993i	0.0988735	−	0.171254i	0.911219	+	0.411923i	$0.135143\pi$
$128$		0			0
$129$	−11.4704	+	3.72514i	−1.00991	+	0.327980i
$130$		0			0
$131$	2.72703	+	15.4658i	0.238262	+	1.35125i	0.835634	+	0.549287i	$0.185100\pi$
$131$	2.72703	+	15.4658i	0.238262	+	1.35125i	−0.597372	+	0.801964i	$0.703788\pi$
$132$		0			0
$133$	−3.93939	−	3.30554i	−0.341589	−	0.286627i
$134$		0			0
$135$	−0.0421561	−	0.0205832i	−0.00362822	−	0.00177152i
$136$		0			0
$137$	0.607707	+	0.509926i	0.0519199	+	0.0435660i	0.668378	−	0.743821i	$-0.266989\pi$
$137$	0.607707	+	0.509926i	0.0519199	+	0.0435660i	−0.616458	+	0.787387i	$0.711433\pi$
$138$		0			0
$139$	0.0180715	+	0.102489i	0.00153281	+	0.00869298i	0.985565	−	0.169300i	$-0.0541507\pi$
$139$	0.0180715	+	0.102489i	0.00153281	+	0.00869298i	−0.984032	+	0.177993i	$0.943040\pi$
$140$		0			0
$141$	3.47666	−	16.3449i	0.292788	−	1.37649i
$142$		0			0
$143$	−3.03534	+	5.25736i	−0.253828	+	0.439643i
$144$		0			0
$145$	0.0149641	+	0.0259186i	0.00124270	+	0.00215242i
$146$		0			0
$147$	4.47647	+	1.80935i	0.369213	+	0.149233i
$148$		0			0
$149$	−14.0830	+	11.8171i	−1.15373	+	0.968092i	−0.999800	−	0.0199900i	$-0.993637\pi$
$149$	−14.0830	+	11.8171i	−1.15373	+	0.968092i	−0.153927	+	0.988082i	$0.549192\pi$
$150$		0			0
$151$	21.7155	−	7.90378i	1.76718	−	0.643201i	0.767181	−	0.641431i	$-0.221659\pi$
$151$	21.7155	−	7.90378i	1.76718	−	0.643201i	0.999998	−	0.00176990i	$-0.000563376\pi$
$152$		0			0
$153$	−8.89879	−	18.2584i	−0.719424	−	1.47611i
$154$		0			0
$155$	0.0124769	−	0.0707597i	0.00100216	−	0.00568356i
$156$		0			0
$157$	−13.6177	−	4.95645i	−1.08681	−	0.395568i	−0.264374	−	0.964420i	$-0.585165\pi$
$157$	−13.6177	−	4.95645i	−1.08681	−	0.395568i	−0.822440	+	0.568852i	$0.807388\pi$
$158$		0			0
$159$	−11.7416	−	0.411702i	−0.931168	−	0.0326501i
$160$		0			0
$161$	−1.41892			−0.111826
$162$		0			0
$163$	−9.90188			−0.775575			−0.387788	−	0.921749i	$-0.626761\pi$
$163$	−9.90188			−0.775575			−0.387788	+	0.921749i	$0.626761\pi$
$164$		0			0
$165$	−0.0578736	−	0.00202926i	−0.00450546	−	0.000157977i
$166$		0			0
$167$	−15.3652	−	5.59247i	−1.18899	−	0.432759i	−0.329624	−	0.944112i	$-0.606922\pi$
$167$	−15.3652	−	5.59247i	−1.18899	−	0.432759i	−0.859370	+	0.511354i	$0.829144\pi$
$168$		0			0
$169$	−1.79078	+	10.1560i	−0.137752	+	0.781232i
$170$		0			0
$171$	−4.20512	+	6.23051i	−0.321573	+	0.476459i
$172$		0			0
$173$	4.42271	−	1.60973i	0.336252	−	0.122386i	−0.168375	−	0.985723i	$-0.553852\pi$
$173$	4.42271	−	1.60973i	0.336252	−	0.122386i	0.504628	+	0.863337i	$0.331630\pi$
$174$		0			0
$175$	7.86105	−	6.59620i	0.594240	−	0.498626i
$176$		0			0
$177$	−4.59183	−	1.85598i	−0.345143	−	0.139504i
$178$		0			0
$179$	7.40191	+	12.8205i	0.553245	+	0.958248i	0.998038	+	0.0626148i	$0.0199440\pi$
$179$	7.40191	+	12.8205i	0.553245	+	0.958248i	−0.444793	+	0.895633i	$0.646723\pi$
$180$		0			0
$181$	8.33215	−	14.4317i	0.619324	−	1.07270i	−0.370285	−	0.928918i	$-0.620740\pi$
$181$	8.33215	−	14.4317i	0.619324	−	1.07270i	0.989609	−	0.143782i	$-0.0459266\pi$
$182$		0			0
$183$	−4.29757	+	20.2043i	−0.317686	+	1.49355i
$184$		0			0
$185$	0.00918689	+	0.0521014i	0.000675433	+	0.00383057i
$186$		0			0
$187$	−19.2068	−	16.1164i	−1.40454	−	1.17855i
$188$		0			0
$189$	−2.94396	+	10.2502i	−0.214141	+	0.745595i
$190$		0			0
$191$	−8.43182	−	7.07514i	−0.610105	−	0.511939i	0.284571	−	0.958655i	$-0.408149\pi$
$191$	−8.43182	−	7.07514i	−0.610105	−	0.511939i	−0.894676	+	0.446716i	$0.852593\pi$
$192$		0			0
$193$	1.07135	+	6.07593i	0.0771175	+	0.437355i	0.998781	+	0.0493644i	$0.0157196\pi$
$193$	1.07135	+	6.07593i	0.0771175	+	0.437355i	−0.921663	+	0.387991i	$0.873169\pi$
$194$		0			0
$195$	0.0243812	−	0.00791807i	0.00174597	−	0.000567025i
$196$		0			0
$197$	5.58608	−	9.67538i	0.397992	−	0.689342i	−0.595486	−	0.803366i	$-0.703041\pi$
$197$	5.58608	−	9.67538i	0.397992	−	0.689342i	0.993478	+	0.114023i	$0.0363739\pi$
$198$		0			0
$199$	4.36136	+	7.55409i	0.309168	+	0.535495i	0.978181	−	0.207756i	$-0.0666160\pi$
$199$	4.36136	+	7.55409i	0.309168	+	0.535495i	−0.669012	+	0.743251i	$0.733283\pi$
$200$		0			0
$201$	−1.77875	+	1.38930i	−0.125463	+	0.0979938i
$202$		0			0
$203$	5.21182	−	4.37324i	0.365798	−	0.306941i
$204$		0			0
$205$	0.0357707	−	0.0130195i	0.00249833	−	0.000909319i
$206$		0			0
$207$	0.216206	+	2.06273i	0.0150274	+	0.143369i
$208$		0			0
$209$	−1.61124	+	9.13780i	−0.111452	+	0.632075i
$210$		0			0
$211$	1.54967	+	0.564034i	0.106684	+	0.0388297i	0.394810	−	0.918763i	$-0.370810\pi$
$211$	1.54967	+	0.564034i	0.106684	+	0.0388297i	−0.288127	+	0.957592i	$0.593032\pi$
$212$		0			0
$213$	−1.81349	−	3.41185i	−0.124258	−	0.233776i
$214$		0			0
$215$	0.0628635			0.00428725
$216$		0			0
$217$	−16.3339			−1.10882
$218$		0			0
$219$	12.9467	−	20.7125i	0.874856	−	1.39962i
$220$		0			0
$221$	10.4296	+	3.79605i	0.701568	+	0.255350i
$222$		0			0
$223$	−2.10232	+	11.9229i	−0.140782	+	0.798414i	0.829876	+	0.557948i	$0.188411\pi$
$223$	−2.10232	+	11.9229i	−0.140782	+	0.798414i	−0.970658	+	0.240466i	$0.922700\pi$
$224$		0			0
$225$	−10.7869	−	10.4228i	−0.719130	−	0.694852i
$226$		0			0
$227$	−3.52456	+	1.28284i	−0.233933	+	0.0851448i	−0.456327	−	0.889812i	$-0.650835\pi$
$227$	−3.52456	+	1.28284i	−0.233933	+	0.0851448i	0.222394	+	0.974957i	$0.428613\pi$
$228$		0			0
$229$	−6.70736	+	5.62815i	−0.443235	+	0.371918i	−0.836918	−	0.547328i	$-0.815645\pi$
$229$	−6.70736	+	5.62815i	−0.443235	+	0.371918i	0.393683	+	0.919246i	$0.371201\pi$
$230$		0			0
$231$	1.83028	+	13.0366i	0.120423	+	0.857745i
$232$		0			0
$233$	−10.0591	−	17.4229i	−0.658994	−	1.14141i	−0.980876	−	0.194631i	$-0.937649\pi$
$233$	−10.0591	−	17.4229i	−0.658994	−	1.14141i	0.321883	−	0.946780i	$-0.395684\pi$
$234$		0			0
$235$	−0.0435522	+	0.0754346i	−0.00284103	+	0.00492081i
$236$		0			0
$237$	−18.4991	−	16.6614i	−1.20165	−	1.08228i
$238$		0			0
$239$	−1.74909	−	9.91957i	−0.113139	−	0.641644i	−0.987655	−	0.156646i	$-0.949932\pi$
$239$	−1.74909	−	9.91957i	−0.113139	−	0.641644i	0.874516	−	0.484997i	$-0.161179\pi$
$240$		0			0
$241$	−1.32726	−	1.11370i	−0.0854963	−	0.0717399i	0.599038	−	0.800721i	$-0.295550\pi$
$241$	−1.32726	−	1.11370i	−0.0854963	−	0.0717399i	−0.684534	+	0.728981i	$0.739994\pi$
$242$		0			0
$243$	15.3497	+	2.71785i	0.984684	+	0.174350i
$244$		0			0
$245$	−0.0192795	−	0.0161774i	−0.00123172	−	0.00103354i
$246$		0			0
$247$	−0.713248	−	4.04503i	−0.0453829	−	0.257379i
$248$		0			0
$249$	19.4435	+	17.5121i	1.23218	+	1.10978i
$250$		0			0
$251$	−11.7741	+	20.3934i	−0.743177	+	1.28722i	0.207864	+	0.978158i	$0.433349\pi$
$251$	−11.7741	+	20.3934i	−0.743177	+	1.28722i	−0.951042	+	0.309063i	$0.899985\pi$
$252$		0			0
$253$	1.28009	+	2.21719i	0.0804788	+	0.139393i
$254$		0			0
$255$	0.0147199	+	0.104846i	0.000921797	+	0.00656572i
$256$		0			0
$257$	15.3397	−	12.8716i	0.956867	−	0.802906i	−0.0235740	−	0.999722i	$-0.507505\pi$
$257$	15.3397	−	12.8716i	0.956867	−	0.802906i	0.980440	+	0.196816i	$0.0630601\pi$
$258$		0			0
$259$	11.3016	−	4.11344i	0.702246	−	0.255597i
$260$		0			0
$261$	−7.15167	−	6.91023i	−0.442677	−	0.427732i
$262$		0			0
$263$	−1.36755	+	7.75576i	−0.0843267	+	0.478240i	0.913173	+	0.407572i	$0.133624\pi$
$263$	−1.36755	+	7.75576i	−0.0843267	+	0.478240i	−0.997500	+	0.0706686i	$0.977487\pi$
$264$		0			0
$265$	0.0575476	+	0.0209456i	0.00353512	+	0.00128668i
$266$		0			0
$267$	3.94541	−	6.31198i	0.241455	−	0.386287i
$268$		0			0
$269$	18.2541			1.11297			0.556485	−	0.830858i	$-0.312150\pi$
$269$	18.2541			1.11297			0.556485	+	0.830858i	$0.312150\pi$
$270$		0			0
$271$	4.59097			0.278881			0.139441	−	0.990230i	$-0.455470\pi$
$271$	4.59097			0.278881			0.139441	+	0.990230i	$0.455470\pi$
$272$		0			0
$273$	−2.73512	−	5.14578i	−0.165537	−	0.311436i
$274$		0			0
$275$	−17.3991	−	6.33276i	−1.04921	−	0.381880i
$276$		0			0
$277$	−4.05675	+	23.0070i	−0.243746	+	1.38235i	0.579640	+	0.814873i	$0.303193\pi$
$277$	−4.05675	+	23.0070i	−0.243746	+	1.38235i	−0.823386	+	0.567482i	$0.807918\pi$
$278$		0			0
$279$	2.48887	+	23.7451i	0.149005	+	1.42158i
$280$		0			0
$281$	−29.1961	+	10.6265i	−1.74170	+	0.633926i	−0.999349	−	0.0360893i	$-0.988510\pi$
$281$	−29.1961	+	10.6265i	−1.74170	+	0.633926i	−0.742348	+	0.670015i	$0.766288\pi$
$282$		0			0
$283$	2.89410	−	2.42844i	0.172036	−	0.144356i	−0.552704	−	0.833378i	$-0.686404\pi$
$283$	2.89410	−	2.42844i	0.172036	−	0.144356i	0.724741	+	0.689022i	$0.241960\pi$
$284$		0			0
$285$	0.0308789	−	0.0241181i	0.00182911	−	0.00142863i
$286$		0			0
$287$	−4.32680	−	7.49423i	−0.255403	−	0.442371i
$288$		0			0
$289$	−14.4199	+	24.9761i	−0.848232	+	1.46918i
$290$		0			0
$291$	11.3973	−	3.70142i	0.668124	−	0.216981i
$292$		0			0
$293$	−4.93174	−	27.9693i	−0.288116	−	1.63398i	−0.693939	−	0.720033i	$-0.744126\pi$
$293$	−4.93174	−	27.9693i	−0.288116	−	1.63398i	0.405824	−	0.913951i	$-0.366985\pi$
$294$		0			0
$295$	0.0197764	+	0.0165944i	0.00115143	+	0.000966161i
$296$		0			0
$297$	18.6729	−	4.64718i	1.08351	−	0.269657i
$298$		0			0
$299$	−0.868172	−	0.728483i	−0.0502077	−	0.0421293i
$300$		0			0
$301$	−2.48155	−	14.0736i	−0.143034	−	0.811188i
$302$		0			0
$303$	−1.53932	+	7.23686i	−0.0884317	+	0.415747i
$304$		0			0
$305$	0.0538358	−	0.0932463i	0.00308263	−	0.00533927i
$306$		0			0
$307$	−1.13689	−	1.96916i	−0.0648860	−	0.112386i	0.831757	−	0.555139i	$-0.187335\pi$
$307$	−1.13689	−	1.96916i	−0.0648860	−	0.112386i	−0.896643	+	0.442753i	$0.854002\pi$
$308$		0			0
$309$	31.0340	+	12.5437i	1.76546	+	0.713585i
$310$		0			0
$311$	4.15664	−	3.48783i	0.235701	−	0.197777i	−0.517285	−	0.855813i	$-0.673057\pi$
$311$	4.15664	−	3.48783i	0.235701	−	0.197777i	0.752986	+	0.658037i	$0.228613\pi$
$312$		0			0
$313$	11.2769	−	4.10446i	0.637409	−	0.231998i	−0.00304407	−	0.999995i	$-0.500969\pi$
$313$	11.2769	−	4.10446i	0.637409	−	0.231998i	0.640453	+	0.767998i	$0.278747\pi$
$314$		0			0
$315$	0.0310985	−	0.0460770i	0.00175220	−	0.00259614i
$316$		0			0
$317$	4.94756	−	28.0590i	0.277883	−	1.57595i	−0.451771	−	0.892134i	$-0.649208\pi$
$317$	4.94756	−	28.0590i	0.277883	−	1.57595i	0.729654	−	0.683817i	$-0.239681\pi$
$318$		0			0
$319$	−11.5355	−	4.19857i	−0.645863	−	0.235075i
$320$		0			0
$321$	−12.4499	−	0.436537i	−0.694885	−	0.0243651i
$322$		0			0
$323$	16.9642			0.943914
$324$		0			0
$325$	8.19637			0.454653
$326$		0			0
$327$	27.1383	+	0.951567i	1.50075	+	0.0526218i
$328$		0			0
$329$	18.6072	+	6.77247i	1.02585	+	0.373378i
$330$		0			0
$331$	−0.721397	+	4.09124i	−0.0396516	+	0.224875i	−0.998194	−	0.0600751i	$-0.980866\pi$
$331$	−0.721397	+	4.09124i	−0.0396516	+	0.224875i	0.958542	+	0.284950i	$0.0919771\pi$
$332$		0			0
$333$	−7.70192	−	15.8027i	−0.422062	−	0.865983i
$334$		0			0
$335$	0.0110552	−	0.00402377i	0.000604012	−	0.000219842i
$336$		0			0
$337$	−13.8871	+	11.6527i	−0.756481	+	0.634763i	−0.937208	−	0.348770i	$-0.886599\pi$
$337$	−13.8871	+	11.6527i	−0.756481	+	0.634763i	0.180727	+	0.983533i	$0.442155\pi$
$338$		0			0
$339$	29.6492	+	11.9840i	1.61032	+	0.650880i
$340$		0			0
$341$	14.7358	+	25.5232i	0.797990	+	1.38216i
$342$		0			0
$343$	−10.0441	+	17.3969i	−0.542330	+	0.939343i
$344$		0			0
$345$	0.00224922	−	0.0105743i	0.000121094	−	0.000569304i
$346$		0			0
$347$	−0.453011	−	2.56915i	−0.0243189	−	0.137919i	0.970231	−	0.242182i	$-0.0778630\pi$
$347$	−0.453011	−	2.56915i	−0.0243189	−	0.137919i	−0.994550	+	0.104262i	$0.966752\pi$
$348$		0			0
$349$	11.4687	+	9.62341i	0.613907	+	0.515129i	0.895882	−	0.444293i	$-0.146545\pi$
$349$	11.4687	+	9.62341i	0.613907	+	0.515129i	−0.281975	+	0.959422i	$0.590989\pi$
$350$		0			0
$351$	−7.06383	+	4.76021i	−0.377039	+	0.254081i
$352$		0			0
$353$	2.61951	+	2.19803i	0.139422	+	0.116989i	0.709832	−	0.704371i	$-0.248771\pi$
$353$	2.61951	+	2.19803i	0.139422	+	0.116989i	−0.570409	+	0.821361i	$0.693215\pi$
$354$		0			0
$355$	0.00349736	+	0.0198345i	0.000185620	+	0.00105271i
$356$		0			0
$357$	22.8914	−	7.43426i	1.21154	−	0.393463i
$358$		0			0
$359$	9.89460	−	17.1380i	0.522217	−	0.904507i	−0.477449	−	0.878660i	$-0.658438\pi$
$359$	9.89460	−	17.1380i	0.522217	−	0.904507i	0.999666	−	0.0258470i	$-0.00822826\pi$
$360$		0			0
$361$	6.36098	+	11.0175i	0.334789	+	0.579871i
$362$		0			0
$363$	3.70437	−	2.89332i	0.194429	−	0.151860i
$364$		0			0
$365$	−0.0975330	+	0.0818399i	−0.00510511	+	0.00428370i
$366$		0			0
$367$	17.4071	−	6.33566i	0.908643	−	0.330719i	0.154932	−	0.987925i	$-0.450484\pi$
$367$	17.4071	−	6.33566i	0.908643	−	0.330719i	0.753711	+	0.657206i	$0.228262\pi$
$368$		0			0
$369$	−10.2353	+	7.43194i	−0.532830	+	0.386891i
$370$		0			0
$371$	2.41750	−	13.7103i	0.125510	−	0.711805i
$372$		0			0
$373$	−9.60952	−	3.49758i	−0.497562	−	0.181098i	0.0810349	−	0.996711i	$-0.474177\pi$
$373$	−9.60952	−	3.49758i	−0.497562	−	0.181098i	−0.578597	+	0.815613i	$0.696400\pi$
$374$		0			0
$375$	0.0733936	+	0.138081i	0.00379003	+	0.00713047i
$376$		0			0
$377$	5.43413			0.279872
$378$		0			0
$379$	−10.0913			−0.518353			−0.259177	−	0.965830i	$-0.583451\pi$
$379$	−10.0913			−0.518353			−0.259177	+	0.965830i	$0.583451\pi$
$380$		0			0
$381$	2.04589	−	3.27306i	0.104814	−	0.167684i
$382$		0			0
$383$	−28.9473	−	10.5359i	−1.47914	−	0.538362i	−0.528572	−	0.848888i	$-0.677272\pi$
$383$	−28.9473	−	10.5359i	−1.47914	−	0.538362i	−0.950565	+	0.310526i	$0.899495\pi$
$384$		0			0
$385$	0.0119157	−	0.0675775i	0.000607282	−	0.00344407i
$386$		0			0
$387$	−20.0811	+	5.75197i	−1.02078	+	0.292389i
$388$		0			0
$389$	1.30592	−	0.475315i	0.0662126	−	0.0240994i	−0.308702	−	0.951159i	$-0.599894\pi$
$389$	1.30592	−	0.475315i	0.0662126	−	0.0240994i	0.374914	+	0.927060i	$0.377672\pi$
$390$		0			0
$391$	3.58566	−	3.00872i	0.181335	−	0.152158i
$392$		0			0
$393$	3.78177	+	26.9366i	0.190765	+	1.35877i
$394$		0			0
$395$	0.0648860	+	0.112386i	0.00326477	+	0.00565474i
$396$		0			0
$397$	−12.1396	+	21.0264i	−0.609269	+	1.05528i	0.382092	+	0.924124i	$0.375204\pi$
$397$	−12.1396	+	21.0264i	−0.609269	+	1.05528i	−0.991361	+	0.131160i	$0.958130\pi$
$398$		0			0
$399$	−6.61841	−	5.96095i	−0.331335	−	0.298421i
$400$		0			0
$401$	−1.96102	−	11.1215i	−0.0979284	−	0.555380i	−0.993811	−	0.111088i	$-0.964566\pi$
$401$	−1.96102	−	11.1215i	−0.0979284	−	0.555380i	0.895882	−	0.444292i	$-0.146545\pi$
$402$		0			0
$403$	−9.99399	−	8.38595i	−0.497836	−	0.417734i
$404$		0			0
$405$	−0.0717223	−	0.0381879i	−0.00356391	−	0.00189757i
$406$		0			0
$407$	−16.6235	−	13.9488i	−0.823995	−	0.691414i
$408$		0			0
$409$	0.600991	+	3.40839i	0.0297171	+	0.168534i	0.996054	−	0.0887443i	$-0.0282854\pi$
$409$	0.600991	+	3.40839i	0.0297171	+	0.168534i	−0.966337	+	0.257278i	$0.917174\pi$
$410$		0			0
$411$	1.02098	+	0.919561i	0.0503614	+	0.0453586i
$412$		0			0
$413$	2.93439	−	5.08252i	0.144392	−	0.250094i
$414$		0			0
$415$	−0.0681987	−	0.118124i	−0.00334774	−	0.00579846i
$416$		0			0
$417$	0.0250611	+	0.178504i	0.00122725	+	0.00874135i
$418$		0			0
$419$	11.0677	−	9.28692i	0.540694	−	0.453696i	−0.331081	−	0.943602i	$-0.607413\pi$
$419$	11.0677	−	9.28692i	0.540694	−	0.453696i	0.871775	+	0.489906i	$0.162969\pi$
$420$		0			0
$421$	22.3041	−	8.11803i	1.08704	−	0.395649i	0.264514	−	0.964382i	$-0.414789\pi$
$421$	22.3041	−	8.11803i	1.08704	−	0.395649i	0.822522	+	0.568733i	$0.192566\pi$
$422$		0			0
$423$	7.01010	−	28.0819i	0.340843	−	1.36539i
$424$		0			0
$425$	−5.87834	+	33.3377i	−0.285141	+	1.61712i
$426$		0			0
$427$	−23.0007	−	8.37159i	−1.11308	−	0.405129i
$428$		0			0
$429$	−5.57322	+	8.91619i	−0.269078	+	0.430478i
$430$		0			0
$431$	−18.4234			−0.887422			−0.443711	−	0.896170i	$-0.646338\pi$
$431$	−18.4234			−0.887422			−0.443711	+	0.896170i	$0.646338\pi$
$432$		0			0
$433$	−15.6349			−0.751364			−0.375682	−	0.926749i	$-0.622592\pi$
$433$	−15.6349			−0.751364			−0.375682	+	0.926749i	$0.622592\pi$
$434$		0			0
$435$	0.0243295	+	0.0457729i	0.00116651	+	0.00219464i
$436$		0			0
$437$	−1.62776	−	0.592457i	−0.0778664	−	0.0283410i
$438$		0			0
$439$	1.20585	−	6.83869i	0.0575519	−	0.326393i	−0.942416	−	0.334444i	$-0.891452\pi$
$439$	1.20585	−	6.83869i	0.0575519	−	0.326393i	0.999968	+	0.00805081i	$0.00256268\pi$
$440$		0			0
$441$	7.63889	+	3.40366i	0.363757	+	0.162079i
$442$		0			0
$443$	−24.3559	+	8.86481i	−1.15718	+	0.421180i	−0.848090	−	0.529852i	$-0.822247\pi$
$443$	−24.3559	+	8.86481i	−1.15718	+	0.421180i	−0.309092	+	0.951032i	$0.600025\pi$
$444$		0			0
$445$	−0.0297225	+	0.0249402i	−0.00140898	+	0.00118228i
$446$		0			0
$447$	−25.0948	+	19.6004i	−1.18694	+	0.927069i
$448$		0			0
$449$	−3.72425	−	6.45058i	−0.175758	−	0.304422i	0.764665	−	0.644428i	$-0.222904\pi$
$449$	−3.72425	−	6.45058i	−0.175758	−	0.304422i	−0.940423	+	0.340006i	$0.889571\pi$
$450$		0			0
$451$	−7.80695	+	13.5220i	−0.367615	+	0.636728i
$452$		0			0
$453$	38.0689	−	12.3633i	1.78863	−	0.580880i
$454$		0			0
$455$	0.00527474	+	0.0299145i	0.000247284	+	0.00140242i
$456$		0			0
$457$	−21.1948	−	17.7845i	−0.991451	−	0.831926i	−0.00567382	−	0.999984i	$-0.501806\pi$
$457$	−21.1948	−	17.7845i	−0.991451	−	0.831926i	−0.985777	+	0.168058i	$0.946250\pi$
$458$		0			0
$459$	−14.2955	−	32.1452i	−0.667257	−	1.50041i
$460$		0			0
$461$	−6.09589	−	5.11506i	−0.283914	−	0.238232i	0.489697	−	0.871892i	$-0.337107\pi$
$461$	−6.09589	−	5.11506i	−0.283914	−	0.238232i	−0.773611	+	0.633660i	$0.781552\pi$
$462$		0			0
$463$	−2.91081	−	16.5080i	−0.135277	−	0.767193i	−0.974667	−	0.223663i	$-0.928199\pi$
$463$	−2.91081	−	16.5080i	−0.135277	−	0.767193i	0.839390	−	0.543530i	$-0.182913\pi$
$464$		0			0
$465$	0.0258920	−	0.121727i	0.00120071	−	0.00564495i
$466$		0			0
$467$	0.868873	−	1.50493i	0.0402067	−	0.0696400i	−0.845222	−	0.534416i	$-0.820532\pi$
$467$	0.868873	−	1.50493i	0.0402067	−	0.0696400i	0.885428	+	0.464776i	$0.153865\pi$
$468$		0			0
$469$	−1.33723	−	2.31615i	−0.0617477	−	0.106950i
$470$		0			0
$471$	−23.2713	−	9.40607i	−1.07228	−	0.433409i
$472$		0			0
$473$	−19.7525	+	16.5743i	−0.908221	+	0.762088i
$474$		0			0
$475$	11.7723	−	4.28476i	0.540149	−	0.196598i
$476$		0			0
$477$	−20.2995	−	1.42530i	−0.929452	−	0.0652601i
$478$		0			0
$479$	−5.53147	+	31.3706i	−0.252740	+	1.43336i	0.549069	+	0.835777i	$0.314982\pi$
$479$	−5.53147	+	31.3706i	−0.252740	+	1.43336i	−0.801809	+	0.597580i	$0.796129\pi$
$480$		0			0
$481$	9.02681	+	3.28549i	0.411587	+	0.149805i
$482$		0			0
$483$	−2.45613	−	0.0861206i	−0.111758	−	0.00391862i
$484$		0			0
$485$	−0.0624633			−0.00283631
$486$		0			0
$487$	5.12802			0.232373			0.116186	−	0.993227i	$-0.462933\pi$
$487$	5.12802			0.232373			0.116186	+	0.993227i	$0.462933\pi$
$488$		0			0
$489$	−17.1400	−	0.600991i	−0.775099	−	0.0271777i
$490$		0			0
$491$	4.30464	+	1.56676i	0.194266	+	0.0707069i	0.437321	−	0.899306i	$-0.355927\pi$
$491$	4.30464	+	1.56676i	0.194266	+	0.0707069i	−0.243055	+	0.970012i	$0.578150\pi$
$492$		0			0
$493$	−3.89730	+	22.1027i	−0.175525	+	0.995454i
$494$		0			0
$495$	−0.100055	−	0.00702523i	−0.00449715	−	0.000315761i
$496$		0			0
$497$	4.30240	−	1.56595i	0.192989	−	0.0702422i
$498$		0			0
$499$	−9.12857	+	7.65978i	−0.408651	+	0.342899i	−0.823826	−	0.566843i	$-0.808165\pi$
$499$	−9.12857	+	7.65978i	−0.408651	+	0.342899i	0.415175	+	0.909741i	$0.363720\pi$
$500$		0			0
$501$	−26.2575	−	10.6131i	−1.17310	−	0.474158i
$502$		0			0
$503$	14.7483	+	25.5448i	0.657593	+	1.13898i	0.981237	+	0.192806i	$0.0617588\pi$
$503$	14.7483	+	25.5448i	0.657593	+	1.13898i	−0.323644	+	0.946179i	$0.604908\pi$
$504$		0			0
$505$	0.0192831	−	0.0333993i	0.000858087	−	0.00148625i
$506$		0			0
$507$	−3.71623	+	17.4712i	−0.165044	+	0.775925i
$508$		0			0
$509$	−4.48842	−	25.4551i	−0.198946	−	1.12828i	−0.906686	−	0.421805i	$-0.861397\pi$
$509$	−4.48842	−	25.4551i	−0.198946	−	1.12828i	0.707741	−	0.706472i	$-0.249715\pi$
$510$		0			0
$511$	22.1721	+	18.6046i	0.980836	+	0.823019i
$512$		0			0
$513$	−7.65716	+	10.5297i	−0.338072	+	0.464898i
$514$		0			0
$515$	−0.133659	−	0.112153i	−0.00588972	−	0.00494206i
$516$		0			0
$517$	−6.20412	−	35.1853i	−0.272857	−	1.54745i
$518$		0			0
$519$	7.75335	−	2.51799i	0.340334	−	0.110528i
$520$		0			0
$521$	−4.14931	+	7.18682i	−0.181785	+	0.314860i	−0.942488	−	0.334239i	$-0.891521\pi$
$521$	−4.14931	+	7.18682i	−0.181785	+	0.314860i	0.760704	+	0.649099i	$0.224854\pi$
$522$		0			0
$523$	1.68608	+	2.92038i	0.0737273	+	0.127699i	0.900532	−	0.434790i	$-0.143177\pi$
$523$	1.68608	+	2.92038i	0.0737273	+	0.127699i	−0.826805	+	0.562489i	$0.809844\pi$
$524$		0			0
$525$	14.0077	−	10.9408i	0.611347	−	0.477497i
$526$		0			0
$527$	41.2764	−	34.6350i	1.79803	−	1.50873i
$528$		0			0
$529$	21.1638	−	7.70299i	0.920165	−	0.334913i
$530$		0			0
$531$	−7.83576	−	3.49138i	−0.340043	−	0.151513i
$532$		0			0
$533$	1.20022	−	6.80680i	0.0519874	−	0.294835i
$534$		0			0
$535$	0.0610191	+	0.0222091i	0.00263809	+	0.000960185i
$536$		0			0
$537$	12.0345	+	22.6414i	0.519326	+	0.977047i
$538$		0			0
$539$	10.3232			0.444650
$540$		0			0
$541$	23.7788			1.02233			0.511166	−	0.859482i	$-0.329214\pi$
$541$	23.7788			1.02233			0.511166	+	0.859482i	$0.329214\pi$
$542$		0			0
$543$	15.2988	−	24.4754i	0.656533	−	1.05034i
$544$		0			0
$545$	−0.133010	−	0.0484116i	−0.00569752	−	0.00207373i
$546$		0			0
$547$	−1.15310	+	6.53956i	−0.0493030	+	0.279611i	−0.999485	−	0.0320838i	$-0.989786\pi$
$547$	−1.15310	+	6.53956i	−0.0493030	+	0.279611i	0.950182	+	0.311695i	$0.100897\pi$
$548$		0			0
$549$	−8.66533	+	34.7126i	−0.369827	+	1.48150i
$550$		0			0
$551$	7.80493	−	2.84076i	0.332501	−	0.121021i
$552$		0			0
$553$	22.5990	−	18.9628i	0.961009	−	0.806382i
$554$		0			0
$555$	0.0127401	+	0.0907445i	0.000540788	+	0.00385189i
$556$		0			0
$557$	14.9195	+	25.8413i	0.632160	+	1.09493i	0.987109	+	0.160047i	$0.0511647\pi$
$557$	14.9195	+	25.8413i	0.632160	+	1.09493i	−0.354950	+	0.934885i	$0.615502\pi$
$558$		0			0
$559$	5.70714	−	9.88506i	0.241386	−	0.418093i
$560$		0			0
$561$	−32.2685	−	29.0630i	−1.36238	−	1.22704i
$562$		0			0
$563$	5.19846	+	29.4819i	0.219089	+	1.24252i	0.873668	+	0.486522i	$0.161735\pi$
$563$	5.19846	+	29.4819i	0.219089	+	1.24252i	−0.654579	+	0.755993i	$0.727154\pi$
$564$		0			0
$565$	−0.127695	−	0.107149i	−0.00537217	−	0.00450778i
$566$		0			0
$567$	−5.71808	+	17.5643i	−0.240137	+	0.737633i
$568$		0			0
$569$	1.98163	+	1.66278i	0.0830742	+	0.0697075i	0.683379	−	0.730064i	$-0.260510\pi$
$569$	1.98163	+	1.66278i	0.0830742	+	0.0697075i	−0.600305	+	0.799771i	$0.704954\pi$
$570$		0			0
$571$	−2.14782	−	12.1809i	−0.0898836	−	0.509755i	−0.996196	−	0.0871460i	$-0.972225\pi$
$571$	−2.14782	−	12.1809i	−0.0898836	−	0.509755i	0.906312	−	0.422609i	$-0.138886\pi$
$572$		0			0
$573$	−14.1659	−	12.7587i	−0.591791	−	0.533004i
$574$		0			0
$575$	1.72833	−	2.99355i	0.0720763	−	0.124840i
$576$		0			0
$577$	−1.91640	−	3.31931i	−0.0797808	−	0.138184i	0.823374	−	0.567498i	$-0.192089\pi$
$577$	−1.91640	−	3.31931i	−0.0797808	−	0.138184i	−0.903155	+	0.429314i	$0.858755\pi$
$578$		0			0
$579$	1.48572	+	10.5824i	0.0617443	+	0.439789i
$580$		0			0
$581$	−23.7528	+	19.9310i	−0.985432	+	0.826876i
$582$		0			0
$583$	−23.6046	+	8.59138i	−0.977604	+	0.355819i
$584$		0			0
$585$	0.0426841	−	0.0122263i	0.00176477	−	0.000505494i
$586$		0			0
$587$	−2.63559	+	14.9472i	−0.108783	+	0.616937i	0.880859	+	0.473378i	$0.156966\pi$
$587$	−2.63559	+	14.9472i	−0.108783	+	0.616937i	−0.989642	+	0.143559i	$0.954145\pi$
$588$		0			0
$589$	−18.7380	−	6.82008i	−0.772087	−	0.281017i
$590$		0			0
$591$	10.2567	−	16.4089i	0.421903	−	0.674972i
$592$		0			0
$593$	−0.889100			−0.0365110			−0.0182555	−	0.999833i	$-0.505811\pi$
$593$	−0.889100			−0.0365110			−0.0182555	+	0.999833i	$0.505811\pi$
$594$		0			0
$595$	−0.125457			−0.00514322
$596$		0			0
$597$	7.09096	+	13.3407i	0.290214	+	0.546000i
$598$		0			0
$599$	30.6477	+	11.1548i	1.25223	+	0.455774i	0.881155	−	0.472828i	$-0.156767\pi$
$599$	30.6477	+	11.1548i	1.25223	+	0.455774i	0.371075	+	0.928603i	$0.378989\pi$
$600$		0			0
$601$	7.96466	−	45.1698i	0.324885	−	1.84252i	−0.185594	−	0.982626i	$-0.559421\pi$
$601$	7.96466	−	45.1698i	0.324885	−	1.84252i	0.510480	−	0.859890i	$-0.329468\pi$
$602$		0			0
$603$	−3.16331	+	2.29690i	−0.128820	+	0.0935371i
$604$		0			0
$605$	−0.0230233	+	0.00837979i	−0.000936030	+	0.000340687i
$606$		0			0
$607$	−3.59603	+	3.01742i	−0.145958	+	0.122473i	−0.712843	−	0.701324i	$-0.752593\pi$
$607$	−3.59603	+	3.01742i	−0.145958	+	0.122473i	0.566885	+	0.823797i	$0.308148\pi$
$608$		0			0
$609$	9.28702	−	7.25368i	0.376329	−	0.293934i
$610$		0			0
$611$	7.90788	+	13.6968i	0.319919	+	0.554115i
$612$		0			0
$613$	21.0007	−	36.3743i	0.848210	−	1.46914i	−0.0345948	−	0.999401i	$-0.511014\pi$
$613$	21.0007	−	36.3743i	0.848210	−	1.46914i	0.882804	−	0.469741i	$-0.155653\pi$
$614$		0			0
$615$	0.0627088	−	0.0203654i	0.00252866	−	0.000821214i
$616$		0			0
$617$	−4.28309	−	24.2906i	−0.172431	−	0.977902i	−0.941068	−	0.338218i	$-0.890176\pi$
$617$	−4.28309	−	24.2906i	−0.172431	−	0.977902i	0.768637	−	0.639685i	$-0.220935\pi$
$618$		0			0
$619$	20.6288	+	17.3096i	0.829140	+	0.695731i	0.955093	−	0.296305i	$-0.0957545\pi$
$619$	20.6288	+	17.3096i	0.829140	+	0.695731i	−0.125953	+	0.992036i	$0.540199\pi$
$620$		0			0
$621$	0.249054	+	3.58368i	0.00999420	+	0.143808i
$622$		0			0
$623$	6.75679	+	5.66962i	0.270705	+	0.227149i
$624$		0			0
$625$	4.34099	+	24.6190i	0.173640	+	0.984760i
$626$		0			0
$627$	−3.34365	+	15.7196i	−0.133533	+	0.627781i
$628$		0			0
$629$	−19.8372	+	34.3591i	−0.790963	+	1.36999i
$630$		0			0
$631$	1.07564	+	1.86306i	0.0428204	+	0.0741671i	0.886641	−	0.462458i	$-0.153032\pi$
$631$	1.07564	+	1.86306i	0.0428204	+	0.0741671i	−0.843821	+	0.536625i	$0.819699\pi$
$632$		0			0
$633$	2.64822	+	1.07039i	0.105257	+	0.0425442i
$634$		0			0
$635$	−0.0154125	+	0.0129327i	−0.000611628	+	0.000513217i
$636$		0			0
$637$	−4.29416	+	1.56295i	−0.170141	+	0.0619262i
$638$		0			0
$639$	−2.93204	−	6.01593i	−0.115990	−	0.237987i
$640$		0			0
$641$	0.105240	−	0.596848i	0.00415675	−	0.0235741i	−0.982659	−	0.185423i	$-0.940635\pi$
$641$	0.105240	−	0.596848i	0.00415675	−	0.0235741i	0.986816	+	0.161849i	$0.0517457\pi$
$642$		0			0
$643$	35.5046	+	12.9226i	1.40017	+	0.509618i	0.928227	−	0.372013i	$-0.121332\pi$
$643$	35.5046	+	12.9226i	1.40017	+	0.509618i	0.471938	+	0.881632i	$0.343555\pi$
$644$		0			0
$645$	0.108816	+	0.00381547i	0.00428462	+	0.000150234i
$646$		0			0
$647$	26.1063			1.02634			0.513172	−	0.858286i	$-0.328470\pi$
$647$	26.1063			1.02634			0.513172	+	0.858286i	$0.328470\pi$
$648$		0			0
$649$	−10.5892			−0.415662
$650$		0			0
$651$	−28.2738	−	0.991379i	−1.10814	−	0.0388552i
$652$		0			0
$653$	−14.7315	−	5.36184i	−0.576490	−	0.209825i	0.0372873	−	0.999305i	$-0.488128\pi$
$653$	−14.7315	−	5.36184i	−0.576490	−	0.209825i	−0.613777	+	0.789480i	$0.710351\pi$
$654$		0			0
$655$	0.0246206	−	0.139630i	0.000962007	−	0.00545581i
$656$		0			0
$657$	23.6677	−	35.0672i	0.923364	−	1.36810i
$658$		0			0
$659$	−12.2589	+	4.46189i	−0.477541	+	0.173811i	−0.569565	−	0.821946i	$-0.692888\pi$
$659$	−12.2589	+	4.46189i	−0.477541	+	0.173811i	0.0920245	+	0.995757i	$0.470666\pi$
$660$		0			0
$661$	23.3640	−	19.6047i	0.908752	−	0.762534i	−0.0631288	−	0.998005i	$-0.520108\pi$
$661$	23.3640	−	19.6047i	0.908752	−	0.762534i	0.971881	+	0.235472i	$0.0756634\pi$
$662$		0			0
$663$	17.8230	+	7.20393i	0.692190	+	0.279778i
$664$		0			0
$665$	0.0232142	+	0.0402082i	0.000900209	+	0.00155921i
$666$		0			0
$667$	1.14587	−	1.98470i	0.0443682	−	0.0768480i
$668$		0			0
$669$	−4.36275	+	20.5107i	−0.168673	+	0.792990i
$670$		0			0
$671$	7.66904	+	43.4933i	0.296060	+	1.67904i
$672$		0			0
$673$	−6.49892	−	5.45324i	−0.250515	−	0.210207i	0.508879	−	0.860838i	$-0.330060\pi$
$673$	−6.49892	−	5.45324i	−0.250515	−	0.210207i	−0.759394	+	0.650631i	$0.774504\pi$
$674$		0			0
$675$	−18.0395	−	18.6964i	−0.694339	−	0.719625i
$676$		0			0
$677$	−0.222584	−	0.186770i	−0.00855461	−	0.00717817i	0.638500	−	0.769622i	$-0.279555\pi$
$677$	−0.222584	−	0.186770i	−0.00855461	−	0.00717817i	−0.647055	+	0.762443i	$0.724000\pi$
$678$		0			0
$679$	2.46576	+	13.9840i	0.0946270	+	0.536657i
$680$		0			0
$681$	−6.17883	+	2.00665i	−0.236773	+	0.0768950i
$682$		0			0
$683$	18.6164	−	32.2446i	0.712339	−	1.23381i	−0.251638	−	0.967821i	$-0.580969\pi$
$683$	18.6164	−	32.2446i	0.712339	−	1.23381i	0.963977	−	0.265985i	$-0.0856973\pi$
$684$		0			0
$685$	−0.00358112	−	0.00620268i	−0.000136827	−	0.000236992i
$686$		0			0
$687$	−11.9520	+	9.33515i	−0.455996	+	0.356158i
$688$		0			0
$689$	8.51816	−	7.14758i	0.324516	−	0.272301i
$690$		0			0
$691$	21.9897	−	8.00361i	0.836529	−	0.304472i	0.111993	−	0.993709i	$-0.464276\pi$
$691$	21.9897	−	8.00361i	0.836529	−	0.304472i	0.724536	+	0.689237i	$0.242054\pi$
$692$		0			0
$693$	2.37694	+	22.6773i	0.0902924	+	0.861438i
$694$		0			0
$695$	0.000163156	0	0.000925305i	6.18887e−6	0	3.50988e-5i
$696$		0			0
$697$	26.8250	+	9.76352i	1.01607	+	0.369820i
$698$		0			0
$699$	−16.3547	−	30.7693i	−0.618592	−	1.16380i
$700$		0			0
$701$	4.89418			0.184851			0.0924253	−	0.995720i	$-0.470538\pi$
$701$	4.89418			0.184851			0.0924253	+	0.995720i	$0.470538\pi$
$702$		0			0
$703$	14.6825			0.553763
$704$		0			0
$705$	−0.0799667	+	0.127933i	−0.00301172	+	0.00481823i
$706$		0			0
$707$	−8.23850	−	2.99857i	−0.309841	−	0.112773i
$708$		0			0
$709$	6.22367	−	35.2962i	0.233735	−	1.32558i	−0.611527	−	0.791224i	$-0.709444\pi$
$709$	6.22367	−	35.2962i	0.233735	−	1.32558i	0.845262	−	0.534353i	$-0.179445\pi$
$710$		0			0
$711$	−31.0104	−	29.9635i	−1.16298	−	1.12372i
$712$		0			0
$713$	−5.17018	+	1.88179i	−0.193625	+	0.0704736i
$714$		0			0
$715$	0.0419855	−	0.0352300i	0.00157017	−	0.00131753i
$716$		0			0
$717$	−2.42558	−	17.2768i	−0.0905851	−	0.645214i
$718$		0			0
$719$	−19.7374	−	34.1863i	−0.736083	−	1.27493i	−0.954247	−	0.299020i	$-0.903340\pi$
$719$	−19.7374	−	34.1863i	−0.736083	−	1.27493i	0.218164	−	0.975912i	$-0.429993\pi$
$720$		0			0
$721$	−19.8321	+	34.3503i	−0.738588	+	1.27927i
$722$		0			0
$723$	−2.22987	−	2.00836i	−0.0829298	−	0.0746918i
$724$		0			0
$725$	2.87809	+	16.3225i	0.106890	+	0.606202i
$726$		0			0
$727$	2.53124	+	2.12397i	0.0938786	+	0.0787735i	0.688519	−	0.725218i	$-0.258261\pi$
$727$	2.53124	+	2.12397i	0.0938786	+	0.0787735i	−0.594640	+	0.803992i	$0.702706\pi$
$728$		0			0
$729$	26.4052	+	5.63621i	0.977969	+	0.208749i
$730$		0			0
$731$	36.1132	+	30.3025i	1.33569	+	1.12078i
$732$		0			0
$733$	4.01650	+	22.7787i	0.148353	+	0.841350i	0.964614	+	0.263667i	$0.0849320\pi$
$733$	4.01650	+	22.7787i	0.148353	+	0.841350i	−0.816261	+	0.577683i	$0.803957\pi$
$734$		0			0
$735$	−0.0323907	−	0.0291731i	−0.00119475	−	0.00107607i
$736$		0			0
$737$	−2.41280	+	4.17910i	−0.0888767	+	0.153939i
$738$		0			0
$739$	1.15368	+	1.99824i	0.0424390	+	0.0735064i	0.886465	−	0.462796i	$-0.153154\pi$
$739$	1.15368	+	1.99824i	0.0424390	+	0.0735064i	−0.844026	+	0.536303i	$0.819821\pi$
$740$		0			0
$741$	−0.989112	−	7.04519i	−0.0363359	−	0.258811i
$742$		0			0
$743$	−9.70414	+	8.14274i	−0.356010	+	0.298728i	−0.803198	−	0.595712i	$-0.796870\pi$
$743$	−9.70414	+	8.14274i	−0.356010	+	0.298728i	0.447188	+	0.894440i	$0.352426\pi$
$744$		0			0
$745$	0.155968	−	0.0567679i	0.00571424	−	0.00207981i
$746$		0			0
$747$	32.5936	+	31.4933i	1.19254	+	1.15228i
$748$		0			0
$749$	2.56334	−	14.5374i	0.0936622	−	0.531185i
$750$		0			0
$751$	−29.9861	−	10.9140i	−1.09421	−	0.398259i	−0.269030	−	0.963132i	$-0.586703\pi$
$751$	−29.9861	−	10.9140i	−1.09421	−	0.398259i	−0.825178	+	0.564873i	$0.808925\pi$
$752$		0			0
$753$	−21.6187	+	34.5861i	−0.787828	+	1.26039i
$754$		0			0
$755$	−0.208637			−0.00759309
$756$		0			0
$757$	−33.2146			−1.20721			−0.603603	−	0.797285i	$-0.706269\pi$
$757$	−33.2146			−1.20721			−0.603603	+	0.797285i	$0.706269\pi$
$758$		0			0
$759$	2.08125	+	3.91562i	0.0755447	+	0.142128i
$760$		0			0
$761$	28.4090	+	10.3400i	1.02982	+	0.374825i	0.801014	−	0.598646i	$-0.204294\pi$
$761$	28.4090	+	10.3400i	1.02982	+	0.374825i	0.228810	+	0.973471i	$0.426516\pi$
$762$		0			0
$763$	−5.58757	+	31.6887i	−0.202284	+	1.14721i
$764$		0			0
$765$	0.0191164	+	0.182381i	0.000691154	+	0.00659399i
$766$		0			0
$767$	4.40483	−	1.60323i	0.159049	−	0.0578892i
$768$		0			0
$769$	15.7530	−	13.2183i	0.568068	−	0.476666i	−0.312936	−	0.949774i	$-0.601313\pi$
$769$	15.7530	−	13.2183i	0.568068	−	0.476666i	0.881004	+	0.473109i	$0.156868\pi$
$770$		0			0
$771$	27.3341	−	21.3495i	0.984414	−	0.768883i
$772$		0			0
$773$	1.11051	+	1.92346i	0.0399424	+	0.0691822i	0.885305	−	0.465010i	$-0.153949\pi$
$773$	1.11051	+	1.92346i	0.0399424	+	0.0691822i	−0.845363	+	0.534192i	$0.820616\pi$
$774$		0			0
$775$	19.8957	−	34.4604i	0.714675	−	1.23785i
$776$		0			0
$777$	19.8125	−	6.43436i	0.710771	−	0.230832i
$778$		0			0
$779$	−1.83449	−	10.4039i	−0.0657274	−	0.372758i
$780$		0			0
$781$	−6.32840	−	5.31015i	−0.226448	−	0.190012i
$782$		0			0
$783$	−11.9600	−	12.3956i	−0.427417	−	0.442982i
$784$		0			0
$785$	0.100226	+	0.0840998i	0.00357723	+	0.00300165i
$786$		0			0
$787$	0.984197	+	5.58166i	0.0350828	+	0.198965i	0.997312	−	0.0732776i	$-0.0233459\pi$
$787$	0.984197	+	5.58166i	0.0350828	+	0.198965i	−0.962229	+	0.272242i	$0.912235\pi$
$788$		0			0
$789$	−2.83794	+	13.3421i	−0.101033	+	0.474992i
$790$		0			0
$791$	−18.9472	+	32.8175i	−0.673685	+	1.16686i
$792$		0			0
$793$	−9.77510	−	16.9310i	−0.347124	−	0.601236i
$794$		0			0
$795$	0.0983429	+	0.0397494i	0.00348786	+	0.00140977i
$796$		0			0
$797$	−29.8828	+	25.0746i	−1.05850	+	0.888189i	−0.993962	−	0.109726i	$-0.965003\pi$
$797$	−29.8828	+	25.0746i	−1.05850	+	0.888189i	−0.0645410	+	0.997915i	$0.520558\pi$
$798$		0			0
$799$	−61.3817	+	22.3411i	−2.17153	+	0.790372i
$800$		0			0
$801$	7.21256	−	10.6865i	0.254843	−	0.377588i
$802$		0			0
$803$	9.06855	−	51.4303i	0.320022	−	1.81494i
$804$		0			0
$805$	0.0120379	+	0.00438144i	0.000424281	+	0.000154426i
$806$		0			0
$807$	31.5976	+	1.10792i	1.11229	+	0.0390007i
$808$		0			0
$809$	−40.9853			−1.44097			−0.720484	−	0.693472i	$-0.756080\pi$
$809$	−40.9853			−1.44097			−0.720484	+	0.693472i	$0.756080\pi$
$810$		0			0
$811$	24.2369			0.851072			0.425536	−	0.904942i	$-0.360086\pi$
$811$	24.2369			0.851072			0.425536	+	0.904942i	$0.360086\pi$
$812$		0			0
$813$	7.94691	+	0.278647i	0.278710	+	0.00977258i
$814$		0			0
$815$	0.0840063	+	0.0305758i	0.00294261	+	0.00107102i
$816$		0			0
$817$	3.02951	−	17.1812i	0.105989	−	0.601094i
$818$		0			0
$819$	−4.42213	−	9.07328i	−0.154522	−	0.317046i
$820$		0			0
$821$	23.8003	−	8.66260i	0.830636	−	0.302327i	0.108516	−	0.994095i	$-0.465390\pi$
$821$	23.8003	−	8.66260i	0.830636	−	0.302327i	0.722120	+	0.691768i	$0.243168\pi$
$822$		0			0
$823$	−34.9722	+	29.3452i	−1.21906	+	1.02291i	−0.220182	+	0.975459i	$0.570665\pi$
$823$	−34.9722	+	29.3452i	−1.21906	+	1.02291i	−0.998874	+	0.0474499i	$0.984891\pi$
$824$		0			0
$825$	−29.7333	−	12.0180i	−1.03518	−	0.418412i
$826$		0			0
$827$	−27.1400	−	47.0079i	−0.943752	−	1.63463i	−0.758232	−	0.651985i	$-0.773936\pi$
$827$	−27.1400	−	47.0079i	−0.943752	−	1.63463i	−0.185520	−	0.982640i	$-0.559397\pi$
$828$		0			0
$829$	11.2155	−	19.4259i	0.389531	−	0.674688i	−0.602855	−	0.797851i	$-0.705970\pi$
$829$	11.2155	−	19.4259i	0.389531	−	0.674688i	0.992387	+	0.123163i	$0.0393037\pi$
$830$		0			0
$831$	−8.41858	+	39.5785i	−0.292037	+	1.37296i
$832$		0			0
$833$	−3.27737	−	18.5869i	−0.113554	−	0.643998i
$834$		0			0
$835$	0.113088	+	0.0948917i	0.00391356	+	0.00328386i
$836$		0			0
$837$	2.86699	+	41.2536i	0.0990978	+	1.42593i
$838$		0			0
$839$	−20.8322	−	17.4803i	−0.719206	−	0.603486i	0.207959	−	0.978137i	$-0.433318\pi$
$839$	−20.8322	−	17.4803i	−0.719206	−	0.603486i	−0.927166	+	0.374652i	$0.877762\pi$
$840$		0			0
$841$	−3.12764	−	17.7377i	−0.107850	−	0.611646i
$842$		0			0
$843$	−51.1831	+	16.6223i	−1.76284	+	0.572504i
$844$		0			0
$845$	0.0465533	−	0.0806327i	0.00160148	−	0.00277385i
$846$		0			0
$847$	2.78488	+	4.82356i	0.0956897	+	0.165739i
$848$		0			0
$849$	5.15704	−	4.02794i	0.176989	−	0.138238i
$850$		0			0
$851$	3.10339	−	2.60406i	0.106383	−	0.0892659i
$852$		0			0
$853$	−42.2708	+	15.3853i	−1.44733	+	0.526784i	−0.941843	−	0.336053i	$-0.890908\pi$
$853$	−42.2708	+	15.3853i	−1.44733	+	0.526784i	−0.505483	+	0.862837i	$0.668686\pi$
$854$		0			0
$855$	0.0549148	−	0.0398740i	0.00187805	−	0.00136366i
$856$		0			0
$857$	2.11847	−	12.0145i	0.0723656	−	0.410406i	−0.927009	−	0.375040i	$-0.877629\pi$
$857$	2.11847	−	12.0145i	0.0723656	−	0.410406i	0.999374	−	0.0353663i	$-0.0112598\pi$
$858$		0			0
$859$	−42.6476	−	15.5224i	−1.45512	−	0.529619i	−0.511101	−	0.859521i	$-0.670762\pi$
$859$	−42.6476	−	15.5224i	−1.45512	−	0.529619i	−0.944015	+	0.329902i	$0.892984\pi$
$860$		0			0
$861$	−7.03477	−	13.2350i	−0.239744	−	0.451049i
$862$		0			0
$863$	6.90855			0.235170			0.117585	−	0.993063i	$-0.462485\pi$
$863$	6.90855			0.235170			0.117585	+	0.993063i	$0.462485\pi$
$864$		0			0
$865$	−0.0424924			−0.00144478
$866$		0			0
$867$	−26.4766	+	42.3580i	−0.899194	+	1.43855i
$868$		0			0
$869$	−50.0192	−	18.2055i	−1.69678	−	0.617579i
$870$		0			0
$871$	0.370939	−	2.10370i	0.0125688	−	0.0712811i
$872$		0			0
$873$	19.9533	−	5.71536i	0.675317	−	0.193435i
$874$		0			0
$875$	−0.174122	+	0.0633754i	−0.00588641	+	0.00214248i
$876$		0			0
$877$	−31.5767	+	26.4960i	−1.06627	+	0.894708i	−0.994709	−	0.102729i	$-0.967243\pi$
$877$	−31.5767	+	26.4960i	−1.06627	+	0.894708i	−0.0715616	+	0.997436i	$0.522798\pi$
$878$		0			0
$879$	−6.83920	−	48.7138i	−0.230680	−	1.64308i
$880$		0			0
$881$	−18.7930	−	32.5505i	−0.633153	−	1.09665i	−0.986903	−	0.161313i	$-0.948427\pi$
$881$	−18.7930	−	32.5505i	−0.633153	−	1.09665i	0.353751	−	0.935340i	$-0.384906\pi$
$882$		0			0
$883$	15.6493	−	27.1054i	0.526642	−	0.912171i	−0.472876	−	0.881129i	$-0.656784\pi$
$883$	15.6493	−	27.1054i	0.526642	−	0.912171i	0.999518	−	0.0310417i	$-0.00988247\pi$
$884$		0			0
$885$	0.0332255	+	0.0299250i	0.00111686	+	0.00100592i
$886$		0			0
$887$	5.95465	+	33.7705i	0.199938	+	1.13390i	0.905210	+	0.424966i	$0.139714\pi$
$887$	5.95465	+	33.7705i	0.199938	+	1.13390i	−0.705272	+	0.708937i	$0.749175\pi$
$888$		0			0
$889$	3.50372	+	2.93997i	0.117511	+	0.0986034i
$890$		0			0
$891$	32.6045	−	6.91087i	1.09229	−	0.231523i
$892$		0			0
$893$	18.5181	+	15.5386i	0.619686	+	0.519978i
$894$		0			0
$895$	−0.0232088	−	0.131624i	−0.000775785	−	0.00439969i
$896$		0			0
$897$	−1.45858	−	1.31369i	−0.0487006	−	0.0438628i
$898$		0			0
$899$	13.1907	−	22.8470i	0.439935	−	0.761989i
$900$		0			0
$901$	22.9628	+	39.7727i	0.765002	+	1.32502i
$902$		0			0
$903$	−3.44135	−	24.5118i	−0.114521	−	0.815703i
$904$		0			0
$905$	−0.115252	+	0.0967082i	−0.00383112	+	0.00321469i
$906$		0			0
$907$	−20.3753	+	7.41602i	−0.676552	+	0.246245i	−0.657366	−	0.753571i	$-0.728330\pi$
$907$	−20.3753	+	7.41602i	−0.676552	+	0.246245i	−0.0191857	+	0.999816i	$0.506107\pi$
$908$		0			0
$909$	−3.10378	+	12.4335i	−0.102946	+	0.412393i
$910$		0			0
$911$	−4.81687	+	27.3178i	−0.159590	+	0.905080i	0.794879	+	0.606768i	$0.207534\pi$
$911$	−4.81687	+	27.3178i	−0.159590	+	0.905080i	−0.954469	+	0.298311i	$0.903577\pi$
$912$		0			0
$913$	52.5728	+	19.1350i	1.73991	+	0.633274i
$914$		0			0
$915$	0.0988486	−	0.158141i	0.00326783	−	0.00522797i
$916$		0			0
$917$	−32.2317			−1.06439
$918$		0			0
$919$	−34.2970			−1.13135			−0.565676	−	0.824628i	$-0.691385\pi$
$919$	−34.2970			−1.13135			−0.565676	+	0.824628i	$0.691385\pi$
$920$		0			0
$921$	−1.84843	−	3.47759i	−0.0609079	−	0.114591i
$922$		0			0
$923$	3.43642	+	1.25075i	0.113111	+	0.0411690i
$924$		0			0
$925$	−5.08771	+	28.8539i	−0.167283	+	0.948709i
$926$		0			0
$927$	52.9581	+	23.5966i	1.73937	+	0.775013i
$928$		0			0
$929$	33.7239	−	12.2745i	1.10645	−	0.402714i	0.276758	−	0.960940i	$-0.410740\pi$
$929$	33.7239	−	12.2745i	1.10645	−	0.402714i	0.829689	+	0.558226i	$0.188518\pi$
$930$		0			0
$931$	−5.35056	+	4.48966i	−0.175358	+	0.147143i
$932$		0			0
$933$	7.40678	−	5.78511i	0.242487	−	0.189396i
$934$		0			0
$935$	0.113182	+	0.196038i	0.00370146	+	0.00641111i
$936$		0			0
$937$	−9.97725	+	17.2811i	−0.325943	+	0.564549i	−0.981703	−	0.190420i	$-0.939015\pi$
$937$	−9.97725	+	17.2811i	−0.325943	+	0.564549i	0.655760	+	0.754969i	$0.272348\pi$
$938$		0			0
$939$	19.7693	−	6.42032i	0.645147	−	0.209519i
$940$		0			0
$941$	−0.559581	−	3.17354i	−0.0182418	−	0.103454i	0.974327	−	0.225136i	$-0.0722825\pi$
$941$	−0.559581	−	3.17354i	−0.0182418	−	0.103454i	−0.992569	+	0.121681i	$0.961171\pi$
$942$		0			0
$943$	−2.23296	−	1.87367i	−0.0727150	−	0.0610152i
$944$		0			0
$945$	0.0566276	−	0.0778712i	0.00184210	−	0.00253315i
$946$		0			0
$947$	−23.3769	−	19.6156i	−0.759648	−	0.637420i	0.178387	−	0.983960i	$-0.442912\pi$
$947$	−23.3769	−	19.6156i	−0.759648	−	0.637420i	−0.938035	+	0.346540i	$0.887356\pi$
$948$		0			0
$949$	4.01438	+	22.7667i	0.130312	+	0.739037i
$950$		0			0
$951$	10.2672	−	48.2695i	0.332937	−	1.56525i
$952$		0			0
$953$	9.91496	−	17.1732i	0.321177	−	0.556295i	−0.659554	−	0.751657i	$-0.729255\pi$
$953$	9.91496	−	17.1732i	0.321177	−	0.556295i	0.980731	+	0.195362i	$0.0625883\pi$
$954$		0			0
$955$	0.0496874	+	0.0860610i	0.00160785	+	0.00278487i
$956$		0			0
$957$	−19.7129	−	7.96782i	−0.637229	−	0.257563i
$958$		0			0
$959$	−1.24726	+	1.04658i	−0.0402762	+	0.0337957i
$960$		0			0
$961$	−30.3861	+	11.0597i	−0.980198	+	0.356763i
$962$		0			0
$963$	−21.5241	−	1.51128i	−0.693604	−	0.0487004i
$964$		0			0
$965$	0.00967253	−	0.0548556i	0.000311370	−	0.00176587i
$966$		0			0
$967$	15.9594	+	5.80873i	0.513218	+	0.186796i	0.585630	−	0.810579i	$-0.300847\pi$
$967$	15.9594	+	5.80873i	0.513218	+	0.186796i	−0.0724115	+	0.997375i	$0.523069\pi$
$968$		0			0
$969$	29.3648	+	1.02964i	0.943334	+	0.0330767i
$970$		0			0
$971$	−36.8069			−1.18119			−0.590595	−	0.806968i	$-0.701107\pi$
$971$	−36.8069			−1.18119			−0.590595	+	0.806968i	$0.701107\pi$
$972$		0			0
$973$	−0.213594			−0.00684750
$974$		0			0
$975$	14.1878	+	0.497475i	0.454374	+	0.0159320i
$976$		0			0
$977$	43.1112	+	15.6912i	1.37925	+	0.502006i	0.921951	−	0.387307i	$-0.126595\pi$
$977$	43.1112	+	15.6912i	1.37925	+	0.502006i	0.457299	+	0.889313i	$0.348817\pi$
$978$		0			0
$979$	2.76358	−	15.6730i	0.0883243	−	0.500912i
$980$		0			0
$981$	46.9184	+	3.29430i	1.49799	+	0.105179i
$982$		0			0
$983$	7.30989	−	2.66058i	0.233149	−	0.0848594i	−0.222803	−	0.974863i	$-0.571521\pi$
$983$	7.30989	−	2.66058i	0.233149	−	0.0848594i	0.455953	+	0.890004i	$0.349299\pi$
$984$		0			0
$985$	−0.0772680	+	0.0648356i	−0.00246196	+	0.00206583i
$986$		0			0
$987$	31.7978	+	12.8524i	1.01213	+	0.409097i
$988$		0			0
$989$	−2.40687	−	4.16883i	−0.0765341	−	0.132561i
$990$		0			0
$991$	−3.87090	+	6.70460i	−0.122963	+	0.212979i	−0.920935	−	0.389716i	$-0.872573\pi$
$991$	−3.87090	+	6.70460i	−0.122963	+	0.212979i	0.797972	+	0.602695i	$0.205906\pi$
$992$		0			0
$993$	−1.49704	+	7.03811i	−0.0475073	+	0.223348i
$994$		0			0
$995$	−0.0136751	−	0.0775553i	−0.000433530	−	0.00245867i
$996$		0			0
$997$	7.97977	+	6.69582i	0.252722	+	0.212059i	0.760343	−	0.649521i	$-0.225031\pi$
$997$	7.97977	+	6.69582i	0.252722	+	0.212059i	−0.507622	+	0.861580i	$0.669475\pi$
$998$		0			0
$999$	−12.3728	−	27.8217i	−0.391457	−	0.880241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.97.4	yes	24
3.2	odd	2		648.2.q.a.289.3		24
4.3	odd	2		432.2.u.e.97.1		24
27.5	odd	18		648.2.q.a.361.3		24
27.7	even	9		5832.2.a.h.1.7		12
27.20	odd	18		5832.2.a.i.1.6		12
27.22	even	9	inner	216.2.q.a.49.4	✓	24
108.103	odd	18		432.2.u.e.49.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.49.4	✓	24	27.22	even	9	inner
216.2.q.a.97.4	yes	24	1.1	even	1	trivial
432.2.u.e.49.1		24	108.103	odd	18
432.2.u.e.97.1		24	4.3	odd	2
648.2.q.a.289.3		24	3.2	odd	2
648.2.q.a.361.3		24	27.5	odd	18
5832.2.a.h.1.7		12	27.7	even	9
5832.2.a.i.1.6		12	27.20	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73099 + 0.0606946i) q^{3} +(-0.00848388 - 0.00308788i) q^{5} +(-0.356397 + 2.02123i) q^{7} +(2.99263 + 0.210123i) q^{9} +O(q^{10})\)	\(q+(1.73099 + 0.0606946i) q^{3} +(-0.00848388 - 0.00308788i) q^{5} +(-0.356397 + 2.02123i) q^{7} +(2.99263 + 0.210123i) q^{9} +(3.47988 - 1.26657i) q^{11} +(-1.25578 + 1.05372i) q^{13} +(-0.0144981 - 0.00586000i) q^{15} +(-3.38526 - 5.86344i) q^{17} +(-1.25280 + 2.16991i) q^{19} +(-0.739596 + 3.47709i) q^{21} +(0.120050 + 0.680839i) q^{23} +(-3.83016 - 3.21389i) q^{25} +(5.16745 + 0.545357i) q^{27} +(-2.53937 - 2.13078i) q^{29} +(1.38196 + 7.83750i) q^{31} +(6.10050 - 1.98121i) q^{33} +(0.00926493 - 0.0160473i) q^{35} +(-2.92995 - 5.07482i) q^{37} +(-2.23769 + 1.74776i) q^{39} +(-3.22988 + 2.71019i) q^{41} +(-6.54298 + 2.38145i) q^{43} +(-0.0247403 - 0.0110235i) q^{45} +(1.67533 - 9.50130i) q^{47} +(2.61951 + 0.953423i) q^{49} +(-5.50396 - 10.3550i) q^{51} -6.78317 q^{53} -0.0334339 q^{55} +(-2.30028 + 3.68005i) q^{57} +(-2.68702 - 0.977994i) q^{59} +(-2.07092 + 11.7448i) q^{61} +(-1.49127 + 5.97390i) q^{63} +(0.0139076 - 0.00506196i) q^{65} +(-0.998222 + 0.837608i) q^{67} +(0.166482 + 1.18581i) q^{69} +(-1.11540 - 1.93193i) q^{71} +(7.05114 - 12.2129i) q^{73} +(-6.43489 - 5.79566i) q^{75} +(1.31981 + 7.48503i) q^{77} +(-11.0110 - 9.23932i) q^{79} +(8.91170 + 1.25764i) q^{81} +(11.5731 + 9.71102i) q^{83} +(0.0106145 + 0.0601980i) q^{85} +(-4.26629 - 3.84248i) q^{87} +(2.14879 - 3.72181i) q^{89} +(-1.68226 - 2.91375i) q^{91} +(1.91647 + 13.6505i) q^{93} +(0.0173290 - 0.0145408i) q^{95} +(6.50133 - 2.36629i) q^{97} +(10.6801 - 3.05918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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