LMFDB - Embedded newform 441.3.m.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(19,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("441.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.m (of order $6$, degree $2$, not 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.19
Dual form			441.3.m.b.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-3.00000 - 1.73205i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-3.00000 - 1.73205i) q^{5} -8.00000 q^{8} +(6.00000 - 3.46410i) q^{10} +(5.00000 + 8.66025i) q^{11} +12.1244i q^{13} +(8.00000 - 13.8564i) q^{16} +(-6.00000 + 3.46410i) q^{17} +(-28.5000 - 16.4545i) q^{19} -20.0000 q^{22} +(20.0000 - 34.6410i) q^{23} +(-6.50000 - 11.2583i) q^{25} +(-21.0000 - 12.1244i) q^{26} -16.0000 q^{29} +(-4.50000 + 2.59808i) q^{31} -13.8564i q^{34} +(-2.50000 + 4.33013i) q^{37} +(57.0000 - 32.9090i) q^{38} +(24.0000 + 13.8564i) q^{40} -24.2487i q^{41} -19.0000 q^{43} +(40.0000 + 69.2820i) q^{46} +(-45.0000 - 25.9808i) q^{47} +26.0000 q^{50} +(-16.0000 - 27.7128i) q^{53} -34.6410i q^{55} +(16.0000 - 27.7128i) q^{58} +(36.0000 - 20.7846i) q^{59} +(-18.0000 - 10.3923i) q^{61} -10.3923i q^{62} +64.0000 q^{64} +(21.0000 - 36.3731i) q^{65} +(-29.5000 - 51.0955i) q^{67} +26.0000 q^{71} +(16.5000 - 9.52628i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-23.5000 + 40.7032i) q^{79} +(-48.0000 + 27.7128i) q^{80} +(42.0000 + 24.2487i) q^{82} +24.2487i q^{83} +24.0000 q^{85} +(19.0000 - 32.9090i) q^{86} +(-40.0000 - 69.2820i) q^{88} +(102.000 + 58.8897i) q^{89} +(90.0000 - 51.9615i) q^{94} +(57.0000 + 98.7269i) q^{95} -48.4974i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 6 q^{5} - 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 6 * q^5 - 16 * q^8	$ 2 q - 2 q^{2} - 6 q^{5} - 16 q^{8} + 12 q^{10} + 10 q^{11} + 16 q^{16} - 12 q^{17} - 57 q^{19} - 40 q^{22} + 40 q^{23} - 13 q^{25} - 42 q^{26} - 32 q^{29} - 9 q^{31} - 5 q^{37} + 114 q^{38} + 48 q^{40} - 38 q^{43} + 80 q^{46} - 90 q^{47} + 52 q^{50} - 32 q^{53} + 32 q^{58} + 72 q^{59} - 36 q^{61} + 128 q^{64} + 42 q^{65} - 59 q^{67} + 52 q^{71} + 33 q^{73} - 10 q^{74} - 47 q^{79} - 96 q^{80} + 84 q^{82} + 48 q^{85} + 38 q^{86} - 80 q^{88} + 204 q^{89} + 180 q^{94} + 114 q^{95}+O(q^{100}) $ 2 * q - 2 * q^2 - 6 * q^5 - 16 * q^8 + 12 * q^10 + 10 * q^11 + 16 * q^16 - 12 * q^17 - 57 * q^19 - 40 * q^22 + 40 * q^23 - 13 * q^25 - 42 * q^26 - 32 * q^29 - 9 * q^31 - 5 * q^37 + 114 * q^38 + 48 * q^40 - 38 * q^43 + 80 * q^46 - 90 * q^47 + 52 * q^50 - 32 * q^53 + 32 * q^58 + 72 * q^59 - 36 * q^61 + 128 * q^64 + 42 * q^65 - 59 * q^67 + 52 * q^71 + 33 * q^73 - 10 * q^74 - 47 * q^79 - 96 * q^80 + 84 * q^82 + 48 * q^85 + 38 * q^86 - 80 * q^88 + 204 * q^89 + 180 * q^94 + 114 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i	−1.00000			$\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.00000	−	1.73205i	−0.600000	−	0.346410i	0.169042	−	0.985609i	$-0.445933\pi$
$5$	−3.00000	−	1.73205i	−0.600000	−	0.346410i	−0.769042	+	0.639199i	$0.779266\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−1.00000
$9$		0			0
$10$	6.00000	−	3.46410i	0.600000	−	0.346410i
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	0.998662	−	0.0517139i	$-0.0164684\pi$
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	−0.544116	+	0.839010i	$0.683135\pi$
$12$		0			0
$13$			12.1244i			0.932643i	0.884615	+	0.466321i	$0.154421\pi$
$13$			12.1244i			0.932643i	−0.884615	+	0.466321i	$0.845579\pi$
$14$		0			0
$15$		0			0
$16$	8.00000	−	13.8564i	0.500000	−	0.866025i
$17$	−6.00000	+	3.46410i	−0.352941	+	0.203771i	−0.665980	−	0.745970i	$-0.731986\pi$
$17$	−6.00000	+	3.46410i	−0.352941	+	0.203771i	0.313039	+	0.949740i	$0.398653\pi$
$18$		0			0
$19$	−28.5000	−	16.4545i	−1.50000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−28.5000	−	16.4545i	−1.50000	−	0.866025i	−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$	−20.0000			−0.909091
$23$	20.0000	−	34.6410i	0.869565	−	1.50613i	0.00712357	−	0.999975i	$-0.497732\pi$
$23$	20.0000	−	34.6410i	0.869565	−	1.50613i	0.862442	−	0.506157i	$-0.168934\pi$
$24$		0			0
$25$	−6.50000	−	11.2583i	−0.260000	−	0.450333i
$26$	−21.0000	−	12.1244i	−0.807692	−	0.466321i
$27$		0			0
$28$		0			0
$29$	−16.0000			−0.551724			−0.275862	−	0.961197i	$-0.588963\pi$
$29$	−16.0000			−0.551724			−0.275862	+	0.961197i	$0.588963\pi$
$30$		0			0
$31$	−4.50000	+	2.59808i	−0.145161	+	0.0838089i	−0.570822	−	0.821074i	$-0.693375\pi$
$31$	−4.50000	+	2.59808i	−0.145161	+	0.0838089i	0.425660	+	0.904883i	$0.360042\pi$
$32$		0			0
$33$		0			0
$34$		−	13.8564i		−	0.407541i
$35$		0			0
$36$		0			0
$37$	−2.50000	+	4.33013i	−0.0675676	+	0.117030i	−0.897830	−	0.440342i	$-0.854857\pi$
$37$	−2.50000	+	4.33013i	−0.0675676	+	0.117030i	0.830262	+	0.557373i	$0.188190\pi$
$38$	57.0000	−	32.9090i	1.50000	−	0.866025i
$39$		0			0
$40$	24.0000	+	13.8564i	0.600000	+	0.346410i
$41$		−	24.2487i		−	0.591432i	−0.955276	−	0.295716i	$-0.904442\pi$
$41$		−	24.2487i		−	0.591432i	0.955276	−	0.295716i	$-0.0955582\pi$
$42$		0			0
$43$	−19.0000			−0.441860			−0.220930	−	0.975290i	$-0.570909\pi$
$43$	−19.0000			−0.441860			−0.220930	+	0.975290i	$0.570909\pi$
$44$		0			0
$45$		0			0
$46$	40.0000	+	69.2820i	0.869565	+	1.50613i
$47$	−45.0000	−	25.9808i	−0.957447	−	0.552782i	−0.0620605	−	0.998072i	$-0.519767\pi$
$47$	−45.0000	−	25.9808i	−0.957447	−	0.552782i	−0.895386	+	0.445290i	$0.853101\pi$
$48$		0			0
$49$		0			0
$50$	26.0000			0.520000
$51$		0			0
$52$		0			0
$53$	−16.0000	−	27.7128i	−0.301887	−	0.522883i	0.674677	−	0.738114i	$-0.264283\pi$
$53$	−16.0000	−	27.7128i	−0.301887	−	0.522883i	−0.976563	+	0.215230i	$0.930950\pi$
$54$		0			0
$55$		−	34.6410i		−	0.629837i
$56$		0			0
$57$		0			0
$58$	16.0000	−	27.7128i	0.275862	−	0.477807i
$59$	36.0000	−	20.7846i	0.610169	−	0.352282i	−0.162862	−	0.986649i	$-0.552073\pi$
$59$	36.0000	−	20.7846i	0.610169	−	0.352282i	0.773032	+	0.634367i	$0.218739\pi$
$60$		0			0
$61$	−18.0000	−	10.3923i	−0.295082	−	0.170366i	0.345149	−	0.938548i	$-0.387828\pi$
$61$	−18.0000	−	10.3923i	−0.295082	−	0.170366i	−0.640231	+	0.768182i	$0.721162\pi$
$62$		−	10.3923i		−	0.167618i
$63$		0			0
$64$	64.0000			1.00000
$65$	21.0000	−	36.3731i	0.323077	−	0.559586i
$66$		0			0
$67$	−29.5000	−	51.0955i	−0.440299	−	0.762619i	0.557413	−	0.830235i	$-0.311794\pi$
$67$	−29.5000	−	51.0955i	−0.440299	−	0.762619i	−0.997711	+	0.0676160i	$0.978461\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	26.0000			0.366197			0.183099	−	0.983095i	$-0.441387\pi$
$71$	26.0000			0.366197			0.183099	+	0.983095i	$0.441387\pi$
$72$		0			0
$73$	16.5000	−	9.52628i	0.226027	−	0.130497i	−0.382711	−	0.923868i	$-0.625009\pi$
$73$	16.5000	−	9.52628i	0.226027	−	0.130497i	0.608738	+	0.793371i	$0.291676\pi$
$74$	−5.00000	−	8.66025i	−0.0675676	−	0.117030i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−23.5000	+	40.7032i	−0.297468	+	0.515230i	−0.975556	−	0.219751i	$-0.929476\pi$
$79$	−23.5000	+	40.7032i	−0.297468	+	0.515230i	0.678088	+	0.734981i	$0.262809\pi$
$80$	−48.0000	+	27.7128i	−0.600000	+	0.346410i
$81$		0			0
$82$	42.0000	+	24.2487i	0.512195	+	0.295716i
$83$			24.2487i			0.292153i	0.989273	+	0.146077i	$0.0466646\pi$
$83$			24.2487i			0.292153i	−0.989273	+	0.146077i	$0.953335\pi$
$84$		0			0
$85$	24.0000			0.282353
$86$	19.0000	−	32.9090i	0.220930	−	0.382662i
$87$		0			0
$88$	−40.0000	−	69.2820i	−0.454545	−	0.787296i
$89$	102.000	+	58.8897i	1.14607	+	0.661682i	0.947926	−	0.318491i	$-0.103176\pi$
$89$	102.000	+	58.8897i	1.14607	+	0.661682i	0.198142	+	0.980173i	$0.436509\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	90.0000	−	51.9615i	0.957447	−	0.552782i
$95$	57.0000	+	98.7269i	0.600000	+	1.03923i
$96$		0			0
$97$		−	48.4974i		−	0.499973i	−0.968249	−	0.249987i	$-0.919574\pi$
$97$		−	48.4974i		−	0.499973i	0.968249	−	0.249987i	$-0.0804263\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−111.000	+	64.0859i	−1.09901	+	0.634514i	−0.935961	−	0.352104i	$-0.885466\pi$
$101$	−111.000	+	64.0859i	−1.09901	+	0.634514i	−0.163049	+	0.986618i	$0.552133\pi$
$102$		0			0
$103$	−7.50000	−	4.33013i	−0.0728155	−	0.0420401i	0.463150	−	0.886280i	$-0.346719\pi$
$103$	−7.50000	−	4.33013i	−0.0728155	−	0.0420401i	−0.535966	+	0.844240i	$0.680052\pi$
$104$		−	96.9948i		−	0.932643i
$105$		0			0
$106$	64.0000			0.603774
$107$	−106.000	+	183.597i	−0.990654	+	1.71586i	−0.377204	+	0.926130i	$0.623114\pi$
$107$	−106.000	+	183.597i	−0.990654	+	1.71586i	−0.613451	+	0.789733i	$0.710219\pi$
$108$		0			0
$109$	−8.50000	−	14.7224i	−0.0779817	−	0.135068i	0.824397	−	0.566011i	$-0.191514\pi$
$109$	−8.50000	−	14.7224i	−0.0779817	−	0.135068i	−0.902379	+	0.430943i	$0.858181\pi$
$110$	60.0000	+	34.6410i	0.545455	+	0.314918i
$111$		0			0
$112$		0			0
$113$	−142.000			−1.25664			−0.628319	−	0.777956i	$-0.716257\pi$
$113$	−142.000			−1.25664			−0.628319	+	0.777956i	$0.716257\pi$
$114$		0			0
$115$	−120.000	+	69.2820i	−1.04348	+	0.602452i
$116$		0			0
$117$		0			0
$118$			83.1384i			0.704563i
$119$		0			0
$120$		0			0
$121$	10.5000	−	18.1865i	0.0867769	−	0.150302i
$122$	36.0000	−	20.7846i	0.295082	−	0.170366i
$123$		0			0
$124$		0			0
$125$			131.636i			1.05309i
$126$		0			0
$127$	−145.000			−1.14173			−0.570866	−	0.821043i	$-0.693392\pi$
$127$	−145.000			−1.14173			−0.570866	+	0.821043i	$0.693392\pi$
$128$	−64.0000	+	110.851i	−0.500000	+	0.866025i
$129$		0			0
$130$	42.0000	+	72.7461i	0.323077	+	0.559586i
$131$	−129.000	−	74.4782i	−0.984733	−	0.568536i	−0.0810371	−	0.996711i	$-0.525823\pi$
$131$	−129.000	−	74.4782i	−0.984733	−	0.568536i	−0.903696	+	0.428175i	$0.859157\pi$
$132$		0			0
$133$		0			0
$134$	118.000			0.880597
$135$		0			0
$136$	48.0000	−	27.7128i	0.352941	−	0.203771i
$137$	−58.0000	−	100.459i	−0.423358	−	0.733277i	0.572908	−	0.819620i	$-0.305815\pi$
$137$	−58.0000	−	100.459i	−0.423358	−	0.733277i	−0.996265	+	0.0863428i	$0.972482\pi$
$138$		0			0
$139$			84.8705i			0.610579i	0.952260	+	0.305290i	$0.0987532\pi$
$139$			84.8705i			0.610579i	−0.952260	+	0.305290i	$0.901247\pi$
$140$		0			0
$141$		0			0
$142$	−26.0000	+	45.0333i	−0.183099	+	0.317136i
$143$	−105.000	+	60.6218i	−0.734266	+	0.423929i
$144$		0			0
$145$	48.0000	+	27.7128i	0.331034	+	0.191123i
$146$			38.1051i			0.260994i
$147$		0			0
$148$		0			0
$149$	62.0000	−	107.387i	0.416107	−	0.720719i	−0.579437	−	0.815017i	$-0.696727\pi$
$149$	62.0000	−	107.387i	0.416107	−	0.720719i	0.995544	+	0.0942982i	$0.0300607\pi$
$150$		0			0
$151$	23.0000	+	39.8372i	0.152318	+	0.263822i	0.932079	−	0.362255i	$-0.117993\pi$
$151$	23.0000	+	39.8372i	0.152318	+	0.263822i	−0.779761	+	0.626077i	$0.784660\pi$
$152$	228.000	+	131.636i	1.50000	+	0.866025i
$153$		0			0
$154$		0			0
$155$	18.0000			0.116129
$156$		0			0
$157$	−162.000	+	93.5307i	−1.03185	+	0.595737i	−0.917513	−	0.397705i	$-0.869807\pi$
$157$	−162.000	+	93.5307i	−1.03185	+	0.595737i	−0.114334	+	0.993442i	$0.536473\pi$
$158$	−47.0000	−	81.4064i	−0.297468	−	0.515230i
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	29.0000	−	50.2295i	0.177914	−	0.308156i	−0.763252	−	0.646101i	$-0.776398\pi$
$163$	29.0000	−	50.2295i	0.177914	−	0.308156i	0.941166	+	0.337945i	$0.109732\pi$
$164$		0			0
$165$		0			0
$166$	−42.0000	−	24.2487i	−0.253012	−	0.146077i
$167$			266.736i			1.59722i	0.601849	+	0.798610i	$0.294431\pi$
$167$			266.736i			1.59722i	−0.601849	+	0.798610i	$0.705569\pi$
$168$		0			0
$169$	22.0000			0.130178
$170$	−24.0000	+	41.5692i	−0.141176	+	0.244525i
$171$		0			0
$172$		0			0
$173$	−108.000	−	62.3538i	−0.624277	−	0.360427i	0.154255	−	0.988031i	$-0.450702\pi$
$173$	−108.000	−	62.3538i	−0.624277	−	0.360427i	−0.778532	+	0.627604i	$0.784036\pi$
$174$		0			0
$175$		0			0
$176$	160.000			0.909091
$177$		0			0
$178$	−204.000	+	117.779i	−1.14607	+	0.661682i
$179$	5.00000	+	8.66025i	0.0279330	+	0.0483813i	0.879654	−	0.475614i	$-0.157774\pi$
$179$	5.00000	+	8.66025i	0.0279330	+	0.0483813i	−0.851721	+	0.523996i	$0.824441\pi$
$180$		0			0
$181$			327.358i			1.80861i	0.426892	+	0.904303i	$0.359609\pi$
$181$			327.358i			1.80861i	−0.426892	+	0.904303i	$0.640391\pi$
$182$		0			0
$183$		0			0
$184$	−160.000	+	277.128i	−0.869565	+	1.50613i
$185$	15.0000	−	8.66025i	0.0810811	−	0.0468122i
$186$		0			0
$187$	−60.0000	−	34.6410i	−0.320856	−	0.185246i
$188$		0			0
$189$		0			0
$190$	−228.000			−1.20000
$191$	−1.00000	+	1.73205i	−0.00523560	+	0.00906833i	−0.868631	−	0.495459i	$-0.835000\pi$
$191$	−1.00000	+	1.73205i	−0.00523560	+	0.00906833i	0.863396	+	0.504527i	$0.168333\pi$
$192$		0			0
$193$	117.500	+	203.516i	0.608808	+	1.05449i	0.991437	+	0.130585i	$0.0416855\pi$
$193$	117.500	+	203.516i	0.608808	+	1.05449i	−0.382629	+	0.923902i	$0.624981\pi$
$194$	84.0000	+	48.4974i	0.432990	+	0.249987i
$195$		0			0
$196$		0			0
$197$	−100.000			−0.507614			−0.253807	−	0.967255i	$-0.581683\pi$
$197$	−100.000			−0.507614			−0.253807	+	0.967255i	$0.581683\pi$
$198$		0			0
$199$	174.000	−	100.459i	0.874372	−	0.504819i	0.00557327	−	0.999984i	$-0.498226\pi$
$199$	174.000	−	100.459i	0.874372	−	0.504819i	0.868799	+	0.495166i	$0.164893\pi$
$200$	52.0000	+	90.0666i	0.260000	+	0.450333i
$201$		0			0
$202$		−	256.344i		−	1.26903i
$203$		0			0
$204$		0			0
$205$	−42.0000	+	72.7461i	−0.204878	+	0.354859i
$206$	15.0000	−	8.66025i	0.0728155	−	0.0420401i
$207$		0			0
$208$	168.000	+	96.9948i	0.807692	+	0.466321i
$209$		−	329.090i		−	1.57459i
$210$		0			0
$211$	2.00000			0.00947867			0.00473934	−	0.999989i	$-0.498491\pi$
$211$	2.00000			0.00947867			0.00473934	+	0.999989i	$0.498491\pi$
$212$		0			0
$213$		0			0
$214$	−212.000	−	367.195i	−0.990654	−	1.71586i
$215$	57.0000	+	32.9090i	0.265116	+	0.153065i
$216$		0			0
$217$		0			0
$218$	34.0000			0.155963
$219$		0			0
$220$		0			0
$221$	−42.0000	−	72.7461i	−0.190045	−	0.329168i
$222$		0			0
$223$		−	339.482i		−	1.52234i	−0.648552	−	0.761170i	$-0.724625\pi$
$223$		−	339.482i		−	1.52234i	0.648552	−	0.761170i	$-0.275375\pi$
$224$		0			0
$225$		0			0
$226$	142.000	−	245.951i	0.628319	−	1.08828i
$227$	141.000	−	81.4064i	0.621145	−	0.358618i	−0.156169	−	0.987730i	$-0.549915\pi$
$227$	141.000	−	81.4064i	0.621145	−	0.358618i	0.777315	+	0.629112i	$0.216581\pi$
$228$		0			0
$229$	−7.50000	−	4.33013i	−0.0327511	−	0.0189089i	0.483535	−	0.875325i	$-0.339353\pi$
$229$	−7.50000	−	4.33013i	−0.0327511	−	0.0189089i	−0.516286	+	0.856416i	$0.672686\pi$
$230$		−	277.128i		−	1.20490i
$231$		0			0
$232$	128.000			0.551724
$233$	−85.0000	+	147.224i	−0.364807	+	0.631864i	−0.988745	−	0.149610i	$-0.952198\pi$
$233$	−85.0000	+	147.224i	−0.364807	+	0.631864i	0.623938	+	0.781474i	$0.285532\pi$
$234$		0			0
$235$	90.0000	+	155.885i	0.382979	+	0.663339i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−142.000			−0.594142			−0.297071	−	0.954855i	$-0.596010\pi$
$239$	−142.000			−0.594142			−0.297071	+	0.954855i	$0.596010\pi$
$240$		0			0
$241$	132.000	−	76.2102i	0.547718	−	0.316225i	−0.200483	−	0.979697i	$-0.564251\pi$
$241$	132.000	−	76.2102i	0.547718	−	0.316225i	0.748201	+	0.663472i	$0.230918\pi$
$242$	21.0000	+	36.3731i	0.0867769	+	0.150302i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	199.500	−	345.544i	0.807692	−	1.39896i
$248$	36.0000	−	20.7846i	0.145161	−	0.0838089i
$249$		0			0
$250$	−228.000	−	131.636i	−0.912000	−	0.526543i
$251$			290.985i			1.15930i	0.814865	+	0.579650i	$0.196811\pi$
$251$			290.985i			1.15930i	−0.814865	+	0.579650i	$0.803189\pi$
$252$		0			0
$253$	400.000			1.58103
$254$	145.000	−	251.147i	0.570866	−	0.988769i
$255$		0			0
$256$		0			0
$257$	−381.000	−	219.970i	−1.48249	−	0.855916i	−0.482688	−	0.875792i	$-0.660339\pi$
$257$	−381.000	−	219.970i	−1.48249	−	0.855916i	−0.999802	+	0.0198763i	$0.993673\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	258.000	−	148.956i	0.984733	−	0.568536i
$263$	68.0000	+	117.779i	0.258555	+	0.447831i	0.965855	−	0.259083i	$-0.0834203\pi$
$263$	68.0000	+	117.779i	0.258555	+	0.447831i	−0.707300	+	0.706914i	$0.750087\pi$
$264$		0			0
$265$			110.851i			0.418307i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−195.000	+	112.583i	−0.724907	+	0.418525i	−0.816556	−	0.577266i	$-0.804120\pi$
$269$	−195.000	+	112.583i	−0.724907	+	0.418525i	0.0916490	+	0.995791i	$0.470786\pi$
$270$		0			0
$271$	318.000	+	183.597i	1.17343	+	0.677481i	0.954486	−	0.298256i	$-0.0964049\pi$
$271$	318.000	+	183.597i	1.17343	+	0.677481i	0.218946	+	0.975737i	$0.429738\pi$
$272$			110.851i			0.407541i
$273$		0			0
$274$	232.000			0.846715
$275$	65.0000	−	112.583i	0.236364	−	0.409394i
$276$		0			0
$277$	−197.500	−	342.080i	−0.712996	−	1.23495i	−0.963727	−	0.266889i	$-0.914004\pi$
$277$	−197.500	−	342.080i	−0.712996	−	1.23495i	0.250731	−	0.968057i	$-0.419329\pi$
$278$	−147.000	−	84.8705i	−0.528777	−	0.305290i
$279$		0			0
$280$		0			0
$281$	−100.000			−0.355872			−0.177936	−	0.984042i	$-0.556942\pi$
$281$	−100.000			−0.355872			−0.177936	+	0.984042i	$0.556942\pi$
$282$		0			0
$283$	310.500	−	179.267i	1.09717	−	0.633453i	0.161696	−	0.986841i	$-0.448304\pi$
$283$	310.500	−	179.267i	1.09717	−	0.633453i	0.935477	+	0.353387i	$0.114970\pi$
$284$		0			0
$285$		0			0
$286$		−	242.487i		−	0.847857i
$287$		0			0
$288$		0			0
$289$	−120.500	+	208.712i	−0.416955	+	0.722187i
$290$	−96.0000	+	55.4256i	−0.331034	+	0.191123i
$291$		0			0
$292$		0			0
$293$		−	242.487i		−	0.827601i	−0.910368	−	0.413801i	$-0.864201\pi$
$293$		−	242.487i		−	0.827601i	0.910368	−	0.413801i	$-0.135799\pi$
$294$		0			0
$295$	−144.000			−0.488136
$296$	20.0000	−	34.6410i	0.0675676	−	0.117030i
$297$		0			0
$298$	124.000	+	214.774i	0.416107	+	0.720719i
$299$	420.000	+	242.487i	1.40468	+	0.810994i
$300$		0			0
$301$		0			0
$302$	−92.0000			−0.304636
$303$		0			0
$304$	−456.000	+	263.272i	−1.50000	+	0.866025i
$305$	36.0000	+	62.3538i	0.118033	+	0.204439i
$306$		0			0
$307$			181.865i			0.592395i	0.955127	+	0.296198i	$0.0957187\pi$
$307$			181.865i			0.592395i	−0.955127	+	0.296198i	$0.904281\pi$
$308$		0			0
$309$		0			0
$310$	−18.0000	+	31.1769i	−0.0580645	+	0.100571i
$311$	477.000	−	275.396i	1.53376	−	0.885518i	0.534578	−	0.845119i	$-0.320470\pi$
$311$	477.000	−	275.396i	1.53376	−	0.885518i	0.999184	−	0.0403991i	$-0.0128629\pi$
$312$		0			0
$313$	−175.500	−	101.325i	−0.560703	−	0.323722i	0.192725	−	0.981253i	$-0.438268\pi$
$313$	−175.500	−	101.325i	−0.560703	−	0.323722i	−0.753428	+	0.657531i	$0.771601\pi$
$314$		−	374.123i		−	1.19147i
$315$		0			0
$316$		0			0
$317$	146.000	−	252.879i	0.460568	−	0.797727i	−0.538421	−	0.842676i	$-0.680979\pi$
$317$	146.000	−	252.879i	0.460568	−	0.797727i	0.998989	+	0.0449488i	$0.0143125\pi$
$318$		0			0
$319$	−80.0000	−	138.564i	−0.250784	−	0.434370i
$320$	−192.000	−	110.851i	−0.600000	−	0.346410i
$321$		0			0
$322$		0			0
$323$	228.000			0.705882
$324$		0			0
$325$	136.500	−	78.8083i	0.420000	−	0.242487i
$326$	58.0000	+	100.459i	0.177914	+	0.308156i
$327$		0			0
$328$			193.990i			0.591432i
$329$		0			0
$330$		0			0
$331$	−2.50000	+	4.33013i	−0.00755287	+	0.0130820i	−0.869777	−	0.493445i	$-0.835738\pi$
$331$	−2.50000	+	4.33013i	−0.00755287	+	0.0130820i	0.862224	+	0.506527i	$0.169071\pi$
$332$		0			0
$333$		0			0
$334$	−462.000	−	266.736i	−1.38323	−	0.798610i
$335$			204.382i			0.610096i
$336$		0			0
$337$	−439.000			−1.30267			−0.651335	−	0.758790i	$-0.725791\pi$
$337$	−439.000			−1.30267			−0.651335	+	0.758790i	$0.725791\pi$
$338$	−22.0000	+	38.1051i	−0.0650888	+	0.112737i
$339$		0			0
$340$		0			0
$341$	−45.0000	−	25.9808i	−0.131965	−	0.0761899i
$342$		0			0
$343$		0			0
$344$	152.000			0.441860
$345$		0			0
$346$	216.000	−	124.708i	0.624277	−	0.360427i
$347$	110.000	+	190.526i	0.317003	+	0.549065i	0.979861	−	0.199680i	$-0.0639902\pi$
$347$	110.000	+	190.526i	0.317003	+	0.549065i	−0.662858	+	0.748745i	$0.730657\pi$
$348$		0			0
$349$		−	339.482i		−	0.972728i	−0.873756	−	0.486364i	$-0.838323\pi$
$349$		−	339.482i		−	0.972728i	0.873756	−	0.486364i	$-0.161677\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	267.000	−	154.153i	0.756374	−	0.436693i	−0.0716184	−	0.997432i	$-0.522816\pi$
$353$	267.000	−	154.153i	0.756374	−	0.436693i	0.827992	+	0.560739i	$0.189483\pi$
$354$		0			0
$355$	−78.0000	−	45.0333i	−0.219718	−	0.126854i
$356$		0			0
$357$		0			0
$358$	−20.0000			−0.0558659
$359$	146.000	−	252.879i	0.406685	−	0.704399i	−0.587831	−	0.808984i	$-0.700018\pi$
$359$	146.000	−	252.879i	0.406685	−	0.704399i	0.994516	+	0.104584i	$0.0333512\pi$
$360$		0			0
$361$	361.000	+	625.270i	1.00000	+	1.73205i
$362$	−567.000	−	327.358i	−1.56630	−	0.904303i
$363$		0			0
$364$		0			0
$365$	−66.0000			−0.180822
$366$		0			0
$367$	−466.500	+	269.334i	−1.27112	+	0.733880i	−0.975198	−	0.221333i	$-0.928959\pi$
$367$	−466.500	+	269.334i	−1.27112	+	0.733880i	−0.295919	+	0.955213i	$0.595626\pi$
$368$	−320.000	−	554.256i	−0.869565	−	1.50613i
$369$		0			0
$370$			34.6410i			0.0936244i
$371$		0			0
$372$		0			0
$373$	102.500	−	177.535i	0.274799	−	0.475966i	−0.695285	−	0.718734i	$-0.744722\pi$
$373$	102.500	−	177.535i	0.274799	−	0.475966i	0.970084	+	0.242768i	$0.0780554\pi$
$374$	120.000	−	69.2820i	0.320856	−	0.185246i
$375$		0			0
$376$	360.000	+	207.846i	0.957447	+	0.552782i
$377$		−	193.990i		−	0.514562i
$378$		0			0
$379$	−523.000			−1.37995			−0.689974	−	0.723835i	$-0.742378\pi$
$379$	−523.000			−1.37995			−0.689974	+	0.723835i	$0.742378\pi$
$380$		0			0
$381$		0			0
$382$	−2.00000	−	3.46410i	−0.00523560	−	0.00906833i
$383$	−66.0000	−	38.1051i	−0.172324	−	0.0994912i	0.411357	−	0.911474i	$-0.365055\pi$
$383$	−66.0000	−	38.1051i	−0.172324	−	0.0994912i	−0.583681	+	0.811983i	$0.698388\pi$
$384$		0			0
$385$		0			0
$386$	−470.000			−1.21762
$387$		0			0
$388$		0			0
$389$	−37.0000	−	64.0859i	−0.0951157	−	0.164745i	0.814541	−	0.580106i	$-0.196989\pi$
$389$	−37.0000	−	64.0859i	−0.0951157	−	0.164745i	−0.909657	+	0.415361i	$0.863655\pi$
$390$		0			0
$391$			277.128i			0.708768i
$392$		0			0
$393$		0			0
$394$	100.000	−	173.205i	0.253807	−	0.439607i
$395$	141.000	−	81.4064i	0.356962	−	0.206092i
$396$		0			0
$397$	−280.500	−	161.947i	−0.706549	−	0.407926i	0.103233	−	0.994657i	$-0.467081\pi$
$397$	−280.500	−	161.947i	−0.706549	−	0.407926i	−0.809782	+	0.586731i	$0.800415\pi$
$398$			401.836i			1.00964i
$399$		0			0
$400$	−208.000			−0.520000
$401$	−64.0000	+	110.851i	−0.159601	+	0.276437i	−0.934725	−	0.355372i	$-0.884354\pi$
$401$	−64.0000	+	110.851i	−0.159601	+	0.276437i	0.775124	+	0.631809i	$0.217687\pi$
$402$		0			0
$403$	−31.5000	−	54.5596i	−0.0781638	−	0.135384i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−50.0000			−0.122850
$408$		0			0
$409$	−256.500	+	148.090i	−0.627139	+	0.362079i	−0.779643	−	0.626224i	$-0.784600\pi$
$409$	−256.500	+	148.090i	−0.627139	+	0.362079i	0.152504	+	0.988303i	$0.451266\pi$
$410$	−84.0000	−	145.492i	−0.204878	−	0.354859i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	42.0000	−	72.7461i	0.101205	−	0.175292i
$416$		0			0
$417$		0			0
$418$	570.000	+	329.090i	1.36364	+	0.787296i
$419$			412.228i			0.983838i	0.870641	+	0.491919i	$0.163704\pi$
$419$			412.228i			0.983838i	−0.870641	+	0.491919i	$0.836296\pi$
$420$		0			0
$421$	107.000			0.254157			0.127078	−	0.991893i	$-0.459440\pi$
$421$	107.000			0.254157			0.127078	+	0.991893i	$0.459440\pi$
$422$	−2.00000	+	3.46410i	−0.00473934	+	0.00820877i
$423$		0			0
$424$	128.000	+	221.703i	0.301887	+	0.522883i
$425$	78.0000	+	45.0333i	0.183529	+	0.105961i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−114.000	+	65.8179i	−0.265116	+	0.153065i
$431$	131.000	+	226.899i	0.303944	+	0.526447i	0.977026	−	0.213121i	$-0.0683630\pi$
$431$	131.000	+	226.899i	0.303944	+	0.526447i	−0.673081	+	0.739568i	$0.735030\pi$
$432$		0			0
$433$		−	36.3731i		−	0.0840025i	−0.999118	−	0.0420012i	$-0.986627\pi$
$433$		−	36.3731i		−	0.0840025i	0.999118	−	0.0420012i	$-0.0133733\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1140.00	+	658.179i	−2.60870	+	1.50613i
$438$		0			0
$439$	−270.000	−	155.885i	−0.615034	−	0.355090i	0.159899	−	0.987133i	$-0.448883\pi$
$439$	−270.000	−	155.885i	−0.615034	−	0.355090i	−0.774933	+	0.632043i	$0.782216\pi$
$440$			277.128i			0.629837i
$441$		0			0
$442$	168.000			0.380090
$443$	−106.000	+	183.597i	−0.239278	+	0.414441i	−0.960507	−	0.278255i	$-0.910244\pi$
$443$	−106.000	+	183.597i	−0.239278	+	0.414441i	0.721230	+	0.692696i	$0.243577\pi$
$444$		0			0
$445$	−204.000	−	353.338i	−0.458427	−	0.794019i
$446$	588.000	+	339.482i	1.31839	+	0.761170i
$447$		0			0
$448$		0			0
$449$	782.000			1.74165			0.870824	−	0.491595i	$-0.163586\pi$
$449$	782.000			1.74165			0.870824	+	0.491595i	$0.163586\pi$
$450$		0			0
$451$	210.000	−	121.244i	0.465632	−	0.268833i
$452$		0			0
$453$		0			0
$454$			325.626i			0.717237i
$455$		0			0
$456$		0			0
$457$	−338.500	+	586.299i	−0.740700	+	1.28293i	0.211477	+	0.977383i	$0.432173\pi$
$457$	−338.500	+	586.299i	−0.740700	+	1.28293i	−0.952177	+	0.305547i	$0.901161\pi$
$458$	15.0000	−	8.66025i	0.0327511	−	0.0189089i
$459$		0			0
$460$		0			0
$461$		−	484.974i		−	1.05200i	−0.850483	−	0.526002i	$-0.823690\pi$
$461$		−	484.974i		−	1.05200i	0.850483	−	0.526002i	$-0.176310\pi$
$462$		0			0
$463$	443.000			0.956803			0.478402	−	0.878141i	$-0.341216\pi$
$463$	443.000			0.956803			0.478402	+	0.878141i	$0.341216\pi$
$464$	−128.000	+	221.703i	−0.275862	+	0.477807i
$465$		0			0
$466$	−170.000	−	294.449i	−0.364807	−	0.631864i
$467$	39.0000	+	22.5167i	0.0835118	+	0.0482155i	0.541174	−	0.840910i	$-0.317980\pi$
$467$	39.0000	+	22.5167i	0.0835118	+	0.0482155i	−0.457663	+	0.889126i	$0.651313\pi$
$468$		0			0
$469$		0			0
$470$	−360.000			−0.765957
$471$		0			0
$472$	−288.000	+	166.277i	−0.610169	+	0.352282i
$473$	−95.0000	−	164.545i	−0.200846	−	0.347875i
$474$		0			0
$475$			427.817i			0.900666i
$476$		0			0
$477$		0			0
$478$	142.000	−	245.951i	0.297071	−	0.514542i
$479$	−48.0000	+	27.7128i	−0.100209	+	0.0578556i	−0.549267	−	0.835647i	$-0.685093\pi$
$479$	−48.0000	+	27.7128i	−0.100209	+	0.0578556i	0.449058	+	0.893503i	$0.351760\pi$
$480$		0			0
$481$	−52.5000	−	30.3109i	−0.109148	−	0.0630164i
$482$			304.841i			0.632450i
$483$		0			0
$484$		0			0
$485$	−84.0000	+	145.492i	−0.173196	+	0.299984i
$486$		0			0
$487$	33.5000	+	58.0237i	0.0687885	+	0.119145i	0.898368	−	0.439243i	$-0.144753\pi$
$487$	33.5000	+	58.0237i	0.0687885	+	0.119145i	−0.829580	+	0.558388i	$0.811420\pi$
$488$	144.000	+	83.1384i	0.295082	+	0.170366i
$489$		0			0
$490$		0			0
$491$	68.0000			0.138493			0.0692464	−	0.997600i	$-0.477941\pi$
$491$	68.0000			0.138493			0.0692464	+	0.997600i	$0.477941\pi$
$492$		0			0
$493$	96.0000	−	55.4256i	0.194726	−	0.112425i
$494$	399.000	+	691.088i	0.807692	+	1.39896i
$495$		0			0
$496$			83.1384i			0.167618i
$497$		0			0
$498$		0			0
$499$	−254.500	+	440.807i	−0.510020	+	0.883381i	0.489913	+	0.871772i	$0.337029\pi$
$499$	−254.500	+	440.807i	−0.510020	+	0.883381i	−0.999933	+	0.0116091i	$0.996305\pi$
$500$		0			0
$501$		0			0
$502$	−504.000	−	290.985i	−1.00398	−	0.579650i
$503$		−	654.715i		−	1.30162i	−0.759240	−	0.650810i	$-0.774429\pi$
$503$		−	654.715i		−	1.30162i	0.759240	−	0.650810i	$-0.225571\pi$
$504$		0			0
$505$	444.000			0.879208
$506$	−400.000	+	692.820i	−0.790514	+	1.36921i
$507$		0			0
$508$		0			0
$509$	753.000	+	434.745i	1.47937	+	0.854115i	0.999727	−	0.0233478i	$-0.00743251\pi$
$509$	753.000	+	434.745i	1.47937	+	0.854115i	0.479644	+	0.877463i	$0.340766\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−1.00000
$513$		0			0
$514$	762.000	−	439.941i	1.48249	−	0.855916i
$515$	15.0000	+	25.9808i	0.0291262	+	0.0504481i
$516$		0			0
$517$		−	519.615i		−	1.00506i
$518$		0			0
$519$		0			0
$520$	−168.000	+	290.985i	−0.323077	+	0.559586i
$521$	372.000	−	214.774i	0.714012	−	0.412235i	−0.0985331	−	0.995134i	$-0.531415\pi$
$521$	372.000	−	214.774i	0.714012	−	0.412235i	0.812545	+	0.582899i	$0.198082\pi$
$522$		0			0
$523$	853.500	+	492.768i	1.63193	+	0.942196i	0.983497	+	0.180925i	$0.0579092\pi$
$523$	853.500	+	492.768i	1.63193	+	0.942196i	0.648434	+	0.761271i	$0.275424\pi$
$524$		0			0
$525$		0			0
$526$	−272.000			−0.517110
$527$	18.0000	−	31.1769i	0.0341556	−	0.0591592i
$528$		0			0
$529$	−535.500	−	927.513i	−1.01229	−	1.75333i
$530$	−192.000	−	110.851i	−0.362264	−	0.209153i
$531$		0			0
$532$		0			0
$533$	294.000			0.551595
$534$		0			0
$535$	636.000	−	367.195i	1.18879	−	0.686345i
$536$	236.000	+	408.764i	0.440299	+	0.762619i
$537$		0			0
$538$		−	450.333i		−	0.837051i
$539$		0			0
$540$		0			0
$541$	60.5000	−	104.789i	0.111830	−	0.193695i	−0.804678	−	0.593711i	$-0.797662\pi$
$541$	60.5000	−	104.789i	0.111830	−	0.193695i	0.916508	+	0.400016i	$0.130995\pi$
$542$	−636.000	+	367.195i	−1.17343	+	0.677481i
$543$		0			0
$544$		0			0
$545$			58.8897i			0.108055i
$546$		0			0
$547$	926.000			1.69287			0.846435	−	0.532492i	$-0.178744\pi$
$547$	926.000			1.69287			0.846435	+	0.532492i	$0.178744\pi$
$548$		0			0
$549$		0			0
$550$	130.000	+	225.167i	0.236364	+	0.409394i
$551$	456.000	+	263.272i	0.827586	+	0.477807i
$552$		0			0
$553$		0			0
$554$	790.000			1.42599
$555$		0			0
$556$		0			0
$557$	−331.000	−	573.309i	−0.594255	−	1.02928i	−0.993652	−	0.112502i	$-0.964114\pi$
$557$	−331.000	−	573.309i	−0.594255	−	1.02928i	0.399397	−	0.916778i	$-0.369220\pi$
$558$		0			0
$559$		−	230.363i		−	0.412098i
$560$		0			0
$561$		0			0
$562$	100.000	−	173.205i	0.177936	−	0.308194i
$563$	−279.000	+	161.081i	−0.495560	+	0.286111i	−0.726878	−	0.686767i	$-0.759029\pi$
$563$	−279.000	+	161.081i	−0.495560	+	0.286111i	0.231318	+	0.972878i	$0.425696\pi$
$564$		0			0
$565$	426.000	+	245.951i	0.753982	+	0.435312i
$566$			717.069i			1.26691i
$567$		0			0
$568$	−208.000			−0.366197
$569$	−379.000	+	656.447i	−0.666081	+	1.15369i	0.312910	+	0.949783i	$0.398696\pi$
$569$	−379.000	+	656.447i	−0.666081	+	1.15369i	−0.978991	+	0.203903i	$0.934637\pi$
$570$		0			0
$571$	432.500	+	749.112i	0.757443	+	1.31193i	0.944151	+	0.329514i	$0.106885\pi$
$571$	432.500	+	749.112i	0.757443	+	1.31193i	−0.186707	+	0.982416i	$0.559782\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−520.000			−0.904348
$576$		0			0
$577$	−928.500	+	536.070i	−1.60919	+	0.929064i	−0.619633	+	0.784892i	$0.712718\pi$
$577$	−928.500	+	536.070i	−1.60919	+	0.929064i	−0.989553	+	0.144172i	$0.953948\pi$
$578$	−241.000	−	417.424i	−0.416955	−	0.722187i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	160.000	−	277.128i	0.274443	−	0.475348i
$584$	−132.000	+	76.2102i	−0.226027	+	0.130497i
$585$		0			0
$586$	420.000	+	242.487i	0.716724	+	0.413801i
$587$		−	339.482i		−	0.578334i	−0.957279	−	0.289167i	$-0.906622\pi$
$587$		−	339.482i		−	0.578334i	0.957279	−	0.289167i	$-0.0933783\pi$
$588$		0			0
$589$	171.000			0.290323
$590$	144.000	−	249.415i	0.244068	−	0.422738i
$591$		0			0
$592$	40.0000	+	69.2820i	0.0675676	+	0.117030i
$593$	−213.000	−	122.976i	−0.359191	−	0.207379i	0.309535	−	0.950888i	$-0.399827\pi$
$593$	−213.000	−	122.976i	−0.359191	−	0.207379i	−0.668726	+	0.743509i	$0.733160\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−840.000	+	484.974i	−1.40468	+	0.810994i
$599$	−142.000	−	245.951i	−0.237062	−	0.410603i	0.722808	−	0.691049i	$-0.242851\pi$
$599$	−142.000	−	245.951i	−0.237062	−	0.410603i	−0.959870	+	0.280446i	$0.909518\pi$
$600$		0			0
$601$		−	594.093i		−	0.988508i	−0.869317	−	0.494254i	$-0.835441\pi$
$601$		−	594.093i		−	0.988508i	0.869317	−	0.494254i	$-0.164559\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−63.0000	+	36.3731i	−0.104132	+	0.0601208i
$606$		0			0
$607$	−7.50000	−	4.33013i	−0.0123558	−	0.00713365i	0.493809	−	0.869570i	$-0.335604\pi$
$607$	−7.50000	−	4.33013i	−0.0123558	−	0.00713365i	−0.506165	+	0.862437i	$0.668937\pi$
$608$		0			0
$609$		0			0
$610$	−144.000			−0.236066
$611$	315.000	−	545.596i	0.515548	−	0.892956i
$612$		0			0
$613$	−439.000	−	760.370i	−0.716150	−	1.24041i	−0.962514	−	0.271231i	$-0.912569\pi$
$613$	−439.000	−	760.370i	−0.716150	−	1.24041i	0.246364	−	0.969177i	$-0.420764\pi$
$614$	−315.000	−	181.865i	−0.513029	−	0.296198i
$615$		0			0
$616$		0			0
$617$	194.000			0.314425			0.157212	−	0.987565i	$-0.449749\pi$
$617$	194.000			0.314425			0.157212	+	0.987565i	$0.449749\pi$
$618$		0			0
$619$	−529.500	+	305.707i	−0.855412	+	0.493872i	−0.862473	−	0.506103i	$-0.831086\pi$
$619$	−529.500	+	305.707i	−0.855412	+	0.493872i	0.00706124	+	0.999975i	$0.497752\pi$
$620$		0			0
$621$		0			0
$622$			1101.58i			1.77104i
$623$		0			0
$624$		0			0
$625$	65.5000	−	113.449i	0.104800	−	0.181519i
$626$	351.000	−	202.650i	0.560703	−	0.323722i
$627$		0			0
$628$		0			0
$629$		−	34.6410i		−	0.0550732i
$630$		0			0
$631$	−250.000			−0.396197			−0.198098	−	0.980182i	$-0.563477\pi$
$631$	−250.000			−0.396197			−0.198098	+	0.980182i	$0.563477\pi$
$632$	188.000	−	325.626i	0.297468	−	0.515230i
$633$		0			0
$634$	292.000	+	505.759i	0.460568	+	0.797727i
$635$	435.000	+	251.147i	0.685039	+	0.395508i
$636$		0			0
$637$		0			0
$638$	320.000			0.501567
$639$		0			0
$640$	384.000	−	221.703i	0.600000	−	0.346410i
$641$	−562.000	−	973.413i	−0.876755	−	1.51858i	−0.854881	−	0.518824i	$-0.826370\pi$
$641$	−562.000	−	973.413i	−0.876755	−	1.51858i	−0.0218737	−	0.999761i	$-0.506963\pi$
$642$		0			0
$643$		−	569.845i		−	0.886228i	−0.896465	−	0.443114i	$-0.853874\pi$
$643$		−	569.845i		−	0.886228i	0.896465	−	0.443114i	$-0.146126\pi$
$644$		0			0
$645$		0			0
$646$	−228.000	+	394.908i	−0.352941	+	0.611312i
$647$	939.000	−	542.132i	1.45131	−	0.837916i	0.452758	−	0.891634i	$-0.350440\pi$
$647$	939.000	−	542.132i	1.45131	−	0.837916i	0.998556	+	0.0537173i	$0.0171070\pi$
$648$		0			0
$649$	360.000	+	207.846i	0.554700	+	0.320256i
$650$			315.233i			0.484974i
$651$		0			0
$652$		0			0
$653$	−505.000	+	874.686i	−0.773354	+	1.33949i	0.162361	+	0.986731i	$0.448089\pi$
$653$	−505.000	+	874.686i	−0.773354	+	1.33949i	−0.935715	+	0.352757i	$0.885244\pi$
$654$		0			0
$655$	258.000	+	446.869i	0.393893	+	0.682243i
$656$	−336.000	−	193.990i	−0.512195	−	0.295716i
$657$		0			0
$658$		0			0
$659$	908.000			1.37785			0.688923	−	0.724835i	$-0.258084\pi$
$659$	908.000			1.37785			0.688923	+	0.724835i	$0.258084\pi$
$660$		0			0
$661$	625.500	−	361.133i	0.946293	−	0.546343i	0.0543659	−	0.998521i	$-0.482686\pi$
$661$	625.500	−	361.133i	0.946293	−	0.546343i	0.891928	+	0.452178i	$0.149353\pi$
$662$	−5.00000	−	8.66025i	−0.00755287	−	0.0130820i
$663$		0			0
$664$		−	193.990i		−	0.292153i
$665$		0			0
$666$		0			0
$667$	−320.000	+	554.256i	−0.479760	+	0.830969i
$668$		0			0
$669$		0			0
$670$	−354.000	−	204.382i	−0.528358	−	0.305048i
$671$		−	207.846i		−	0.309756i
$672$		0			0
$673$	−1027.00			−1.52600			−0.763001	−	0.646397i	$-0.776275\pi$
$673$	−1027.00			−1.52600			−0.763001	+	0.646397i	$0.776275\pi$
$674$	439.000	−	760.370i	0.651335	−	1.12815i
$675$		0			0
$676$		0			0
$677$	−486.000	−	280.592i	−0.717873	−	0.414464i	0.0960963	−	0.995372i	$-0.469364\pi$
$677$	−486.000	−	280.592i	−0.717873	−	0.414464i	−0.813969	+	0.580908i	$0.802698\pi$
$678$		0			0
$679$		0			0
$680$	−192.000			−0.282353
$681$		0			0
$682$	90.0000	−	51.9615i	0.131965	−	0.0761899i
$683$	488.000	+	845.241i	0.714495	+	1.23754i	0.963154	+	0.268950i	$0.0866768\pi$
$683$	488.000	+	845.241i	0.714495	+	1.23754i	−0.248659	+	0.968591i	$0.579990\pi$
$684$		0			0
$685$			401.836i			0.586622i
$686$		0			0
$687$		0			0
$688$	−152.000	+	263.272i	−0.220930	+	0.382662i
$689$	336.000	−	193.990i	0.487663	−	0.281553i
$690$		0			0
$691$	−490.500	−	283.190i	−0.709841	−	0.409827i	0.101161	−	0.994870i	$-0.467744\pi$
$691$	−490.500	−	283.190i	−0.709841	−	0.409827i	−0.811002	+	0.585043i	$0.801078\pi$
$692$		0			0
$693$		0			0
$694$	−440.000			−0.634006
$695$	147.000	−	254.611i	0.211511	−	0.366347i
$696$		0			0
$697$	84.0000	+	145.492i	0.120516	+	0.208741i
$698$	588.000	+	339.482i	0.842407	+	0.486364i
$699$		0			0
$700$		0			0
$701$	−352.000			−0.502140			−0.251070	−	0.967969i	$-0.580782\pi$
$701$	−352.000			−0.502140			−0.251070	+	0.967969i	$0.580782\pi$
$702$		0			0
$703$	142.500	−	82.2724i	0.202703	−	0.117030i
$704$	320.000	+	554.256i	0.454545	+	0.787296i
$705$		0			0
$706$			616.610i			0.873385i
$707$		0			0
$708$		0			0
$709$	575.000	−	995.929i	0.811001	−	1.40470i	−0.101162	−	0.994870i	$-0.532256\pi$
$709$	575.000	−	995.929i	0.811001	−	1.40470i	0.912164	−	0.409826i	$-0.134410\pi$
$710$	156.000	−	90.0666i	0.219718	−	0.126854i
$711$		0			0
$712$	−816.000	−	471.118i	−1.14607	−	0.661682i
$713$			207.846i			0.291509i
$714$		0			0
$715$	420.000			0.587413
$716$		0			0
$717$		0			0
$718$	292.000	+	505.759i	0.406685	+	0.704399i
$719$	−843.000	−	486.706i	−1.17246	−	0.676921i	−0.218203	−	0.975903i	$-0.570020\pi$
$719$	−843.000	−	486.706i	−1.17246	−	0.676921i	−0.954259	+	0.298982i	$0.903353\pi$
$720$		0			0
$721$		0			0
$722$	−1444.00			−2.00000
$723$		0			0
$724$		0			0
$725$	104.000	+	180.133i	0.143448	+	0.248460i
$726$		0			0
$727$			206.114i			0.283513i	0.989902	+	0.141757i	$0.0452750\pi$
$727$			206.114i			0.283513i	−0.989902	+	0.141757i	$0.954725\pi$
$728$		0			0
$729$		0			0
$730$	66.0000	−	114.315i	0.0904110	−	0.156596i
$731$	114.000	−	65.8179i	0.155951	−	0.0900382i
$732$		0			0
$733$	−1078.50	−	622.672i	−1.47135	−	0.849485i	−0.471869	−	0.881669i	$-0.656420\pi$
$733$	−1078.50	−	622.672i	−1.47135	−	0.849485i	−0.999482	+	0.0321842i	$0.989754\pi$
$734$		−	1077.34i		−	1.46776i
$735$		0			0
$736$		0			0
$737$	295.000	−	510.955i	0.400271	−	0.693290i
$738$		0			0
$739$	−155.500	−	269.334i	−0.210419	−	0.364457i	0.741426	−	0.671034i	$-0.234150\pi$
$739$	−155.500	−	269.334i	−0.210419	−	0.364457i	−0.951846	+	0.306577i	$0.900816\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−394.000			−0.530283			−0.265141	−	0.964210i	$-0.585419\pi$
$743$	−394.000			−0.530283			−0.265141	+	0.964210i	$0.585419\pi$
$744$		0			0
$745$	−372.000	+	214.774i	−0.499329	+	0.288288i
$746$	205.000	+	355.070i	0.274799	+	0.475966i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	39.5000	−	68.4160i	0.0525965	−	0.0910999i	−0.838528	−	0.544858i	$-0.816584\pi$
$751$	39.5000	−	68.4160i	0.0525965	−	0.0910999i	0.891125	+	0.453758i	$0.149917\pi$
$752$	−720.000	+	415.692i	−0.957447	+	0.552782i
$753$		0			0
$754$	336.000	+	193.990i	0.445623	+	0.257281i
$755$		−	159.349i		−	0.211058i
$756$		0			0
$757$	−250.000			−0.330251			−0.165125	−	0.986273i	$-0.552803\pi$
$757$	−250.000			−0.330251			−0.165125	+	0.986273i	$0.552803\pi$
$758$	523.000	−	905.863i	0.689974	−	1.19507i
$759$		0			0
$760$	−456.000	−	789.815i	−0.600000	−	1.03923i
$761$	−822.000	−	474.582i	−1.08016	−	0.623629i	−0.149219	−	0.988804i	$-0.547676\pi$
$761$	−822.000	−	474.582i	−1.08016	−	0.623629i	−0.930939	+	0.365175i	$0.881009\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	132.000	−	76.2102i	0.172324	−	0.0994912i
$767$	252.000	+	436.477i	0.328553	+	0.569070i
$768$		0			0
$769$		−	860.829i		−	1.11941i	−0.828691	−	0.559707i	$-0.810914\pi$
$769$		−	860.829i		−	1.11941i	0.828691	−	0.559707i	$-0.189086\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−195.000	+	112.583i	−0.252264	+	0.145645i	−0.620800	−	0.783969i	$-0.713192\pi$
$773$	−195.000	+	112.583i	−0.252264	+	0.145645i	0.368537	+	0.929613i	$0.379859\pi$
$774$		0			0
$775$	58.5000	+	33.7750i	0.0754839	+	0.0435806i
$776$			387.979i			0.499973i
$777$		0			0
$778$	148.000			0.190231
$779$	−399.000	+	691.088i	−0.512195	+	0.887148i
$780$		0			0
$781$	130.000	+	225.167i	0.166453	+	0.288306i
$782$	−480.000	−	277.128i	−0.613811	−	0.354384i
$783$		0			0
$784$		0			0
$785$	648.000			0.825478
$786$		0			0
$787$	216.000	−	124.708i	0.274460	−	0.158460i	−0.356453	−	0.934313i	$-0.616014\pi$
$787$	216.000	−	124.708i	0.274460	−	0.158460i	0.630913	+	0.775854i	$0.282681\pi$
$788$		0			0
$789$		0			0
$790$			325.626i			0.412184i
$791$		0			0
$792$		0			0
$793$	126.000	−	218.238i	0.158890	−	0.275206i
$794$	561.000	−	323.894i	0.706549	−	0.407926i
$795$		0			0
$796$		0			0
$797$			1357.93i			1.70380i	0.523705	+	0.851900i	$0.324549\pi$
$797$			1357.93i			1.70380i	−0.523705	+	0.851900i	$0.675451\pi$
$798$		0			0
$799$	360.000			0.450563
$800$		0			0
$801$		0			0
$802$	−128.000	−	221.703i	−0.159601	−	0.276437i
$803$	165.000	+	95.2628i	0.205479	+	0.118634i
$804$		0			0
$805$		0			0
$806$	126.000			0.156328
$807$		0			0
$808$	888.000	−	512.687i	1.09901	−	0.634514i
$809$	−709.000	−	1228.02i	−0.876391	−	1.51795i	−0.855274	−	0.518176i	$-0.826611\pi$
$809$	−709.000	−	1228.02i	−0.876391	−	1.51795i	−0.0211166	−	0.999777i	$-0.506722\pi$
$810$		0			0
$811$			872.954i			1.07639i	0.842820	+	0.538196i	$0.180894\pi$
$811$			872.954i			1.07639i	−0.842820	+	0.538196i	$0.819106\pi$
$812$		0			0
$813$		0			0
$814$	50.0000	−	86.6025i	0.0614251	−	0.106391i
$815$	−174.000	+	100.459i	−0.213497	+	0.123263i
$816$		0			0
$817$	541.500	+	312.635i	0.662791	+	0.382662i
$818$		−	592.361i		−	0.724158i
$819$		0			0
$820$		0			0
$821$	125.000	−	216.506i	0.152253	−	0.263711i	−0.779802	−	0.626026i	$-0.784680\pi$
$821$	125.000	−	216.506i	0.152253	−	0.263711i	0.932056	+	0.362315i	$0.118014\pi$
$822$		0			0
$823$	−103.000	−	178.401i	−0.125152	−	0.216769i	0.796640	−	0.604454i	$-0.206608\pi$
$823$	−103.000	−	178.401i	−0.125152	−	0.216769i	−0.921792	+	0.387684i	$0.873275\pi$
$824$	60.0000	+	34.6410i	0.0728155	+	0.0420401i
$825$		0			0
$826$		0			0
$827$	−1234.00			−1.49214			−0.746070	−	0.665867i	$-0.768062\pi$
$827$	−1234.00			−1.49214			−0.746070	+	0.665867i	$0.768062\pi$
$828$		0			0
$829$	−298.500	+	172.339i	−0.360072	+	0.207888i	−0.669113	−	0.743161i	$-0.733326\pi$
$829$	−298.500	+	172.339i	−0.360072	+	0.207888i	0.309040	+	0.951049i	$0.399992\pi$
$830$	84.0000	+	145.492i	0.101205	+	0.175292i
$831$		0			0
$832$			775.959i			0.932643i
$833$		0			0
$834$		0			0
$835$	462.000	−	800.207i	0.553293	−	0.958332i
$836$		0			0
$837$		0			0
$838$	−714.000	−	412.228i	−0.852029	−	0.491919i
$839$		−	484.974i		−	0.578038i	−0.957323	−	0.289019i	$-0.906671\pi$
$839$		−	484.974i		−	0.578038i	0.957323	−	0.289019i	$-0.0933291\pi$
$840$		0			0
$841$	−585.000			−0.695600
$842$	−107.000	+	185.329i	−0.127078	+	0.220106i
$843$		0			0
$844$		0			0
$845$	−66.0000	−	38.1051i	−0.0781065	−	0.0450948i
$846$		0			0
$847$		0			0
$848$	−512.000			−0.603774
$849$		0			0
$850$	−156.000	+	90.0666i	−0.183529	+	0.105961i
$851$	100.000	+	173.205i	0.117509	+	0.203531i
$852$		0			0
$853$			278.860i			0.326917i	0.986550	+	0.163458i	$0.0522650\pi$
$853$			278.860i			0.326917i	−0.986550	+	0.163458i	$0.947735\pi$
$854$		0			0
$855$		0			0
$856$	848.000	−	1468.78i	0.990654	−	1.71586i
$857$	−552.000	+	318.697i	−0.644107	+	0.371876i	−0.786195	−	0.617979i	$-0.787952\pi$
$857$	−552.000	+	318.697i	−0.644107	+	0.371876i	0.142088	+	0.989854i	$0.454619\pi$
$858$		0			0
$859$	528.000	+	304.841i	0.614668	+	0.354879i	0.774790	−	0.632218i	$-0.217855\pi$
$859$	528.000	+	304.841i	0.614668	+	0.354879i	−0.160122	+	0.987097i	$0.551189\pi$
$860$		0			0
$861$		0			0
$862$	−524.000			−0.607889
$863$	335.000	−	580.237i	0.388181	−	0.672349i	−0.604024	−	0.796966i	$-0.706437\pi$
$863$	335.000	−	580.237i	0.388181	−	0.672349i	0.992205	+	0.124617i	$0.0397703\pi$
$864$		0			0
$865$	216.000	+	374.123i	0.249711	+	0.432512i
$866$	63.0000	+	36.3731i	0.0727483	+	0.0420012i
$867$		0			0
$868$		0			0
$869$	−470.000			−0.540852
$870$		0			0
$871$	619.500	−	357.668i	0.711251	−	0.410641i
$872$	68.0000	+	117.779i	0.0779817	+	0.135068i
$873$		0			0
$874$		−	2632.72i		−	3.01226i
$875$		0			0
$876$		0			0
$877$	197.000	−	341.214i	0.224629	−	0.389070i	−0.731579	−	0.681757i	$-0.761216\pi$
$877$	197.000	−	341.214i	0.224629	−	0.389070i	0.956208	+	0.292687i	$0.0945495\pi$
$878$	540.000	−	311.769i	0.615034	−	0.355090i
$879$		0			0
$880$	−480.000	−	277.128i	−0.545455	−	0.314918i
$881$		−	1163.94i		−	1.32116i	−0.750758	−	0.660578i	$-0.770311\pi$
$881$		−	1163.94i		−	1.32116i	0.750758	−	0.660578i	$-0.229689\pi$
$882$		0			0
$883$	737.000			0.834655			0.417327	−	0.908756i	$-0.362967\pi$
$883$	737.000			0.834655			0.417327	+	0.908756i	$0.362967\pi$
$884$		0			0
$885$		0			0
$886$	−212.000	−	367.195i	−0.239278	−	0.414441i
$887$	−633.000	−	365.463i	−0.713641	−	0.412021i	0.0987664	−	0.995111i	$-0.468510\pi$
$887$	−633.000	−	365.463i	−0.713641	−	0.412021i	−0.812408	+	0.583090i	$0.801844\pi$
$888$		0			0
$889$		0			0
$890$	816.000			0.916854
$891$		0			0
$892$		0			0
$893$	855.000	+	1480.90i	0.957447	+	1.65835i
$894$		0			0
$895$		−	34.6410i		−	0.0387050i
$896$		0			0
$897$		0			0
$898$	−782.000	+	1354.46i	−0.870824	+	1.50831i
$899$	72.0000	−	41.5692i	0.0800890	−	0.0462394i
$900$		0			0
$901$	192.000	+	110.851i	0.213097	+	0.123031i
$902$			484.974i			0.537665i
$903$		0			0
$904$	1136.00			1.25664
$905$	567.000	−	982.073i	0.626519	−	1.08516i
$906$		0			0
$907$	117.500	+	203.516i	0.129548	+	0.224384i	0.923502	−	0.383595i	$-0.125314\pi$
$907$	117.500	+	203.516i	0.129548	+	0.224384i	−0.793954	+	0.607978i	$0.791981\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	740.000			0.812294			0.406147	−	0.913808i	$-0.366872\pi$
$911$	740.000			0.812294			0.406147	+	0.913808i	$0.366872\pi$
$912$		0			0
$913$	−210.000	+	121.244i	−0.230011	+	0.132797i
$914$	−677.000	−	1172.60i	−0.740700	−	1.28293i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−758.500	+	1313.76i	−0.825354	+	1.42955i	0.0762951	+	0.997085i	$0.475691\pi$
$919$	−758.500	+	1313.76i	−0.825354	+	1.42955i	−0.901649	+	0.432469i	$0.857642\pi$
$920$	960.000	−	554.256i	1.04348	−	0.602452i
$921$		0			0
$922$	840.000	+	484.974i	0.911063	+	0.526002i
$923$			315.233i			0.341531i
$924$		0			0
$925$	65.0000			0.0702703
$926$	−443.000	+	767.299i	−0.478402	+	0.828616i
$927$		0			0
$928$		0			0
$929$	963.000	+	555.988i	1.03660	+	0.598480i	0.918868	−	0.394565i	$-0.129105\pi$
$929$	963.000	+	555.988i	1.03660	+	0.598480i	0.117731	+	0.993046i	$0.462438\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−78.0000	+	45.0333i	−0.0835118	+	0.0482155i
$935$	120.000	+	207.846i	0.128342	+	0.222295i
$936$		0			0
$937$		−	836.581i		−	0.892829i	−0.894826	−	0.446414i	$-0.852701\pi$
$937$		−	836.581i		−	0.892829i	0.894826	−	0.446414i	$-0.147299\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−342.000	+	197.454i	−0.363443	+	0.209834i	−0.670590	−	0.741828i	$-0.733959\pi$
$941$	−342.000	+	197.454i	−0.363443	+	0.209834i	0.307147	+	0.951662i	$0.400626\pi$
$942$		0			0
$943$	−840.000	−	484.974i	−0.890774	−	0.514289i
$944$		−	665.108i		−	0.704563i
$945$		0			0
$946$	380.000			0.401691
$947$	−169.000	+	292.717i	−0.178458	+	0.309099i	−0.941353	−	0.337424i	$-0.890444\pi$
$947$	−169.000	+	292.717i	−0.178458	+	0.309099i	0.762894	+	0.646523i	$0.223778\pi$
$948$		0			0
$949$	115.500	+	200.052i	0.121707	+	0.210803i
$950$	−741.000	−	427.817i	−0.780000	−	0.450333i
$951$		0			0
$952$		0			0
$953$	1244.00			1.30535			0.652676	−	0.757637i	$-0.273646\pi$
$953$	1244.00			1.30535			0.652676	+	0.757637i	$0.273646\pi$
$954$		0			0
$955$	6.00000	−	3.46410i	0.00628272	−	0.00362733i
$956$		0			0
$957$		0			0
$958$		−	110.851i		−	0.115711i
$959$		0			0
$960$		0			0
$961$	−467.000	+	808.868i	−0.485952	+	0.841694i
$962$	105.000	−	60.6218i	0.109148	−	0.0630164i
$963$		0			0
$964$		0			0
$965$		−	814.064i		−	0.843590i
$966$		0			0
$967$	−1741.00			−1.80041			−0.900207	−	0.435463i	$-0.856585\pi$
$967$	−1741.00			−1.80041			−0.900207	+	0.435463i	$0.856585\pi$
$968$	−84.0000	+	145.492i	−0.0867769	+	0.150302i
$969$		0			0
$970$	−168.000	−	290.985i	−0.173196	−	0.299984i
$971$	1110.00	+	640.859i	1.14315	+	0.659999i	0.947209	−	0.320617i	$-0.103890\pi$
$971$	1110.00	+	640.859i	1.14315	+	0.659999i	0.195942	+	0.980615i	$0.437223\pi$
$972$		0			0
$973$		0			0
$974$	−134.000			−0.137577
$975$		0			0
$976$	−288.000	+	166.277i	−0.295082	+	0.170366i
$977$	131.000	+	226.899i	0.134084	+	0.232240i	0.925247	−	0.379365i	$-0.123857\pi$
$977$	131.000	+	226.899i	0.134084	+	0.232240i	−0.791163	+	0.611605i	$0.790524\pi$
$978$		0			0
$979$			1177.79i			1.20306i
$980$		0			0
$981$		0			0
$982$	−68.0000	+	117.779i	−0.0692464	+	0.119938i
$983$	960.000	−	554.256i	0.976602	−	0.563842i	0.0753596	−	0.997156i	$-0.475990\pi$
$983$	960.000	−	554.256i	0.976602	−	0.563842i	0.901243	+	0.433315i	$0.142656\pi$
$984$		0			0
$985$	300.000	+	173.205i	0.304569	+	0.175843i
$986$			221.703i			0.224850i
$987$		0			0
$988$		0			0
$989$	−380.000	+	658.179i	−0.384226	+	0.665500i
$990$		0			0
$991$	33.5000	+	58.0237i	0.0338042	+	0.0585507i	0.882433	−	0.470439i	$-0.155904\pi$
$991$	33.5000	+	58.0237i	0.0338042	+	0.0585507i	−0.848628	+	0.528990i	$0.822571\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−696.000			−0.699497
$996$		0			0
$997$	856.500	−	494.501i	0.859077	−	0.495988i	−0.00462594	−	0.999989i	$-0.501472\pi$
$997$	856.500	−	494.501i	0.859077	−	0.495988i	0.863703	+	0.504001i	$0.168139\pi$
$998$	−509.000	−	881.614i	−0.510020	−	0.883381i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.m.b.19.1		2
3.2	odd	2		147.3.f.e.19.1		2
7.2	even	3		441.3.d.d.244.2		2
7.3	odd	6	inner	441.3.m.b.325.1		2
7.4	even	3		63.3.m.a.10.1		2
7.5	odd	6		441.3.d.d.244.1		2
7.6	odd	2		63.3.m.a.19.1		2
21.2	odd	6		147.3.d.a.97.2		2
21.5	even	6		147.3.d.a.97.1		2
21.11	odd	6		21.3.f.c.10.1	✓	2
21.17	even	6		147.3.f.e.31.1		2
21.20	even	2		21.3.f.c.19.1	yes	2
28.11	odd	6		1008.3.cg.f.577.1		2
28.27	even	2		1008.3.cg.f.145.1		2
84.11	even	6		336.3.bh.c.241.1		2
84.23	even	6		2352.3.f.b.97.1		2
84.47	odd	6		2352.3.f.b.97.2		2
84.83	odd	2		336.3.bh.c.145.1		2
105.32	even	12		525.3.s.d.199.1		4
105.53	even	12		525.3.s.d.199.2		4
105.62	odd	4		525.3.s.d.124.2		4
105.74	odd	6		525.3.o.b.451.1		2
105.83	odd	4		525.3.s.d.124.1		4
105.104	even	2		525.3.o.b.376.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.c.10.1	✓	2	21.11	odd	6
21.3.f.c.19.1	yes	2	21.20	even	2
63.3.m.a.10.1		2	7.4	even	3
63.3.m.a.19.1		2	7.6	odd	2
147.3.d.a.97.1		2	21.5	even	6
147.3.d.a.97.2		2	21.2	odd	6
147.3.f.e.19.1		2	3.2	odd	2
147.3.f.e.31.1		2	21.17	even	6
336.3.bh.c.145.1		2	84.83	odd	2
336.3.bh.c.241.1		2	84.11	even	6
441.3.d.d.244.1		2	7.5	odd	6
441.3.d.d.244.2		2	7.2	even	3
441.3.m.b.19.1		2	1.1	even	1	trivial
441.3.m.b.325.1		2	7.3	odd	6	inner
525.3.o.b.376.1		2	105.104	even	2
525.3.o.b.451.1		2	105.74	odd	6
525.3.s.d.124.1		4	105.83	odd	4
525.3.s.d.124.2		4	105.62	odd	4
525.3.s.d.199.1		4	105.32	even	12
525.3.s.d.199.2		4	105.53	even	12
1008.3.cg.f.145.1		2	28.27	even	2
1008.3.cg.f.577.1		2	28.11	odd	6
2352.3.f.b.97.1		2	84.23	even	6
2352.3.f.b.97.2		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-3.00000 - 1.73205i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-3.00000 - 1.73205i) q^{5} -8.00000 q^{8} +(6.00000 - 3.46410i) q^{10} +(5.00000 + 8.66025i) q^{11} +12.1244i q^{13} +(8.00000 - 13.8564i) q^{16} +(-6.00000 + 3.46410i) q^{17} +(-28.5000 - 16.4545i) q^{19} -20.0000 q^{22} +(20.0000 - 34.6410i) q^{23} +(-6.50000 - 11.2583i) q^{25} +(-21.0000 - 12.1244i) q^{26} -16.0000 q^{29} +(-4.50000 + 2.59808i) q^{31} -13.8564i q^{34} +(-2.50000 + 4.33013i) q^{37} +(57.0000 - 32.9090i) q^{38} +(24.0000 + 13.8564i) q^{40} -24.2487i q^{41} -19.0000 q^{43} +(40.0000 + 69.2820i) q^{46} +(-45.0000 - 25.9808i) q^{47} +26.0000 q^{50} +(-16.0000 - 27.7128i) q^{53} -34.6410i q^{55} +(16.0000 - 27.7128i) q^{58} +(36.0000 - 20.7846i) q^{59} +(-18.0000 - 10.3923i) q^{61} -10.3923i q^{62} +64.0000 q^{64} +(21.0000 - 36.3731i) q^{65} +(-29.5000 - 51.0955i) q^{67} +26.0000 q^{71} +(16.5000 - 9.52628i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-23.5000 + 40.7032i) q^{79} +(-48.0000 + 27.7128i) q^{80} +(42.0000 + 24.2487i) q^{82} +24.2487i q^{83} +24.0000 q^{85} +(19.0000 - 32.9090i) q^{86} +(-40.0000 - 69.2820i) q^{88} +(102.000 + 58.8897i) q^{89} +(90.0000 - 51.9615i) q^{94} +(57.0000 + 98.7269i) q^{95} -48.4974i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 6 q^{5} - 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 6 * q^5 - 16 * q^8	\( 2 q - 2 q^{2} - 6 q^{5} - 16 q^{8} + 12 q^{10} + 10 q^{11} + 16 q^{16} - 12 q^{17} - 57 q^{19} - 40 q^{22} + 40 q^{23} - 13 q^{25} - 42 q^{26} - 32 q^{29} - 9 q^{31} - 5 q^{37} + 114 q^{38} + 48 q^{40} - 38 q^{43} + 80 q^{46} - 90 q^{47} + 52 q^{50} - 32 q^{53} + 32 q^{58} + 72 q^{59} - 36 q^{61} + 128 q^{64} + 42 q^{65} - 59 q^{67} + 52 q^{71} + 33 q^{73} - 10 q^{74} - 47 q^{79} - 96 q^{80} + 84 q^{82} + 48 q^{85} + 38 q^{86} - 80 q^{88} + 204 q^{89} + 180 q^{94} + 114 q^{95}+O(q^{100}) \) 2 * q - 2 * q^2 - 6 * q^5 - 16 * q^8 + 12 * q^10 + 10 * q^11 + 16 * q^16 - 12 * q^17 - 57 * q^19 - 40 * q^22 + 40 * q^23 - 13 * q^25 - 42 * q^26 - 32 * q^29 - 9 * q^31 - 5 * q^37 + 114 * q^38 + 48 * q^40 - 38 * q^43 + 80 * q^46 - 90 * q^47 + 52 * q^50 - 32 * q^53 + 32 * q^58 + 72 * q^59 - 36 * q^61 + 128 * q^64 + 42 * q^65 - 59 * q^67 + 52 * q^71 + 33 * q^73 - 10 * q^74 - 47 * q^79 - 96 * q^80 + 84 * q^82 + 48 * q^85 + 38 * q^86 - 80 * q^88 + 204 * q^89 + 180 * q^94 + 114 * q^95

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