LMFDB - Embedded newform 336.3.bh.c.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (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:	$9.15533688251$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.3.bh.c.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(3.50000 + 6.06218i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(3.50000 + 6.06218i) q^{7} +(1.50000 + 2.59808i) q^{9} +(5.00000 - 8.66025i) q^{11} +12.1244i q^{13} -6.00000 q^{15} +(-6.00000 - 3.46410i) q^{17} +(-28.5000 + 16.4545i) q^{19} +12.1244i q^{21} +(20.0000 + 34.6410i) q^{23} +(-6.50000 + 11.2583i) q^{25} +5.19615i q^{27} +16.0000 q^{29} +(-4.50000 - 2.59808i) q^{31} +(15.0000 - 8.66025i) q^{33} +(-21.0000 - 12.1244i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(-10.5000 + 18.1865i) q^{39} +24.2487i q^{41} +19.0000 q^{43} +(-9.00000 - 5.19615i) q^{45} +(45.0000 - 25.9808i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(16.0000 - 27.7128i) q^{53} +34.6410i q^{55} -57.0000 q^{57} +(-36.0000 - 20.7846i) q^{59} +(18.0000 - 10.3923i) q^{61} +(-10.5000 + 18.1865i) q^{63} +(-21.0000 - 36.3731i) q^{65} +(29.5000 - 51.0955i) q^{67} +69.2820i q^{69} +26.0000 q^{71} +(-16.5000 - 9.52628i) q^{73} +(-19.5000 + 11.2583i) q^{75} +70.0000 q^{77} +(23.5000 + 40.7032i) q^{79} +(-4.50000 + 7.79423i) q^{81} +24.2487i q^{83} +24.0000 q^{85} +(24.0000 + 13.8564i) q^{87} +(102.000 - 58.8897i) q^{89} +(-73.5000 + 42.4352i) q^{91} +(-4.50000 - 7.79423i) q^{93} +(57.0000 - 98.7269i) q^{95} -48.4974i q^{97} +30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 6 q^{5} + 7 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 6 * q^5 + 7 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 6 q^{5} + 7 q^{7} + 3 q^{9} + 10 q^{11} - 12 q^{15} - 12 q^{17} - 57 q^{19} + 40 q^{23} - 13 q^{25} + 32 q^{29} - 9 q^{31} + 30 q^{33} - 42 q^{35} - 5 q^{37} - 21 q^{39} + 38 q^{43} - 18 q^{45} + 90 q^{47} - 49 q^{49} - 12 q^{51} + 32 q^{53} - 114 q^{57} - 72 q^{59} + 36 q^{61} - 21 q^{63} - 42 q^{65} + 59 q^{67} + 52 q^{71} - 33 q^{73} - 39 q^{75} + 140 q^{77} + 47 q^{79} - 9 q^{81} + 48 q^{85} + 48 q^{87} + 204 q^{89} - 147 q^{91} - 9 q^{93} + 114 q^{95} + 60 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 6 * q^5 + 7 * q^7 + 3 * q^9 + 10 * q^11 - 12 * q^15 - 12 * q^17 - 57 * q^19 + 40 * q^23 - 13 * q^25 + 32 * q^29 - 9 * q^31 + 30 * q^33 - 42 * q^35 - 5 * q^37 - 21 * q^39 + 38 * q^43 - 18 * q^45 + 90 * q^47 - 49 * q^49 - 12 * q^51 + 32 * q^53 - 114 * q^57 - 72 * q^59 + 36 * q^61 - 21 * q^63 - 42 * q^65 + 59 * q^67 + 52 * q^71 - 33 * q^73 - 39 * q^75 + 140 * q^77 + 47 * q^79 - 9 * q^81 + 48 * q^85 + 48 * q^87 + 204 * q^89 - 147 * q^91 - 9 * q^93 + 114 * q^95 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$		0			0
$5$	−3.00000	+	1.73205i	−0.600000	+	0.346410i	−0.769042	−	0.639199i	$-0.779266\pi$
$5$	−3.00000	+	1.73205i	−0.600000	+	0.346410i	0.169042	+	0.985609i	$0.445933\pi$
$6$		0			0
$7$	3.50000	+	6.06218i	0.500000	+	0.866025i
$7$	3.50000	+	6.06218i	0.500000	+	0.866025i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	5.00000	−	8.66025i	0.454545	−	0.787296i	−0.544116	−	0.839010i	$-0.683135\pi$
$11$	5.00000	−	8.66025i	0.454545	−	0.787296i	0.998662	+	0.0517139i	$0.0164684\pi$
$12$		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
$15$	−6.00000			−0.400000
$16$		0			0
$17$	−6.00000	−	3.46410i	−0.352941	−	0.203771i	0.313039	−	0.949740i	$-0.398653\pi$
$17$	−6.00000	−	3.46410i	−0.352941	−	0.203771i	−0.665980	+	0.745970i	$0.731986\pi$
$18$		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
$21$			12.1244i			0.577350i
$22$		0			0
$23$	20.0000	+	34.6410i	0.869565	+	1.50613i	0.862442	+	0.506157i	$0.168934\pi$
$23$	20.0000	+	34.6410i	0.869565	+	1.50613i	0.00712357	+	0.999975i	$0.497732\pi$
$24$		0			0
$25$	−6.50000	+	11.2583i	−0.260000	+	0.450333i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	16.0000			0.551724			0.275862	−	0.961197i	$-0.411037\pi$
$29$	16.0000			0.551724			0.275862	+	0.961197i	$0.411037\pi$
$30$		0			0
$31$	−4.50000	−	2.59808i	−0.145161	−	0.0838089i	0.425660	−	0.904883i	$-0.360042\pi$
$31$	−4.50000	−	2.59808i	−0.145161	−	0.0838089i	−0.570822	+	0.821074i	$0.693375\pi$
$32$		0			0
$33$	15.0000	−	8.66025i	0.454545	−	0.262432i
$34$		0			0
$35$	−21.0000	−	12.1244i	−0.600000	−	0.346410i
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.0675676	−	0.117030i	0.830262	−	0.557373i	$-0.188190\pi$
$37$	−2.50000	−	4.33013i	−0.0675676	−	0.117030i	−0.897830	+	0.440342i	$0.854857\pi$
$38$		0			0
$39$	−10.5000	+	18.1865i	−0.269231	+	0.466321i
$40$		0			0
$41$			24.2487i			0.591432i	0.955276	+	0.295716i	$0.0955582\pi$
$41$			24.2487i			0.591432i	−0.955276	+	0.295716i	$0.904442\pi$
$42$		0			0
$43$	19.0000			0.441860			0.220930	−	0.975290i	$-0.429091\pi$
$43$	19.0000			0.441860			0.220930	+	0.975290i	$0.429091\pi$
$44$		0			0
$45$	−9.00000	−	5.19615i	−0.200000	−	0.115470i
$46$		0			0
$47$	45.0000	−	25.9808i	0.957447	−	0.552782i	0.0620605	−	0.998072i	$-0.480233\pi$
$47$	45.0000	−	25.9808i	0.957447	−	0.552782i	0.895386	+	0.445290i	$0.146899\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.500000	+	0.866025i
$50$		0			0
$51$	−6.00000	−	10.3923i	−0.117647	−	0.203771i
$52$		0			0
$53$	16.0000	−	27.7128i	0.301887	−	0.522883i	−0.674677	−	0.738114i	$-0.735717\pi$
$53$	16.0000	−	27.7128i	0.301887	−	0.522883i	0.976563	+	0.215230i	$0.0690502\pi$
$54$		0			0
$55$			34.6410i			0.629837i
$56$		0			0
$57$	−57.0000			−1.00000
$58$		0			0
$59$	−36.0000	−	20.7846i	−0.610169	−	0.352282i	0.162862	−	0.986649i	$-0.447927\pi$
$59$	−36.0000	−	20.7846i	−0.610169	−	0.352282i	−0.773032	+	0.634367i	$0.781261\pi$
$60$		0			0
$61$	18.0000	−	10.3923i	0.295082	−	0.170366i	−0.345149	−	0.938548i	$-0.612172\pi$
$61$	18.0000	−	10.3923i	0.295082	−	0.170366i	0.640231	+	0.768182i	$0.278838\pi$
$62$		0			0
$63$	−10.5000	+	18.1865i	−0.166667	+	0.288675i
$64$		0			0
$65$	−21.0000	−	36.3731i	−0.323077	−	0.559586i
$66$		0			0
$67$	29.5000	−	51.0955i	0.440299	−	0.762619i	−0.557413	−	0.830235i	$-0.688206\pi$
$67$	29.5000	−	51.0955i	0.440299	−	0.762619i	0.997711	+	0.0676160i	$0.0215393\pi$
$68$		0			0
$69$			69.2820i			1.00409i
$70$		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	$-0.374991\pi$
$73$	−16.5000	−	9.52628i	−0.226027	−	0.130497i	−0.608738	+	0.793371i	$0.708324\pi$
$74$		0			0
$75$	−19.5000	+	11.2583i	−0.260000	+	0.150111i
$76$		0			0
$77$	70.0000			0.909091
$78$		0			0
$79$	23.5000	+	40.7032i	0.297468	+	0.515230i	0.975556	−	0.219751i	$-0.0705244\pi$
$79$	23.5000	+	40.7032i	0.297468	+	0.515230i	−0.678088	+	0.734981i	$0.737191\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			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
$86$		0			0
$87$	24.0000	+	13.8564i	0.275862	+	0.159269i
$88$		0			0
$89$	102.000	−	58.8897i	1.14607	−	0.661682i	0.198142	−	0.980173i	$-0.436509\pi$
$89$	102.000	−	58.8897i	1.14607	−	0.661682i	0.947926	+	0.318491i	$0.103176\pi$
$90$		0			0
$91$	−73.5000	+	42.4352i	−0.807692	+	0.466321i
$92$		0			0
$93$	−4.50000	−	7.79423i	−0.0483871	−	0.0838089i
$94$		0			0
$95$	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
$99$	30.0000			0.303030
$100$		0			0
$101$	−111.000	−	64.0859i	−1.09901	−	0.634514i	−0.163049	−	0.986618i	$-0.552133\pi$
$101$	−111.000	−	64.0859i	−1.09901	−	0.634514i	−0.935961	+	0.352104i	$0.885466\pi$
$102$		0			0
$103$	−7.50000	+	4.33013i	−0.0728155	+	0.0420401i	−0.535966	−	0.844240i	$-0.680052\pi$
$103$	−7.50000	+	4.33013i	−0.0728155	+	0.0420401i	0.463150	+	0.886280i	$0.346719\pi$
$104$		0			0
$105$	−21.0000	−	36.3731i	−0.200000	−	0.346410i
$106$		0			0
$107$	−106.000	−	183.597i	−0.990654	−	1.71586i	−0.613451	−	0.789733i	$-0.710219\pi$
$107$	−106.000	−	183.597i	−0.990654	−	1.71586i	−0.377204	−	0.926130i	$-0.623114\pi$
$108$		0			0
$109$	−8.50000	+	14.7224i	−0.0779817	+	0.135068i	−0.902379	−	0.430943i	$-0.858181\pi$
$109$	−8.50000	+	14.7224i	−0.0779817	+	0.135068i	0.824397	+	0.566011i	$0.191514\pi$
$110$		0			0
$111$		−	8.66025i		−	0.0780203i
$112$		0			0
$113$	142.000			1.25664			0.628319	−	0.777956i	$-0.283743\pi$
$113$	142.000			1.25664			0.628319	+	0.777956i	$0.283743\pi$
$114$		0			0
$115$	−120.000	−	69.2820i	−1.04348	−	0.602452i
$116$		0			0
$117$	−31.5000	+	18.1865i	−0.269231	+	0.155440i
$118$		0			0
$119$		−	48.4974i		−	0.407541i
$120$		0			0
$121$	10.5000	+	18.1865i	0.0867769	+	0.150302i
$122$		0			0
$123$	−21.0000	+	36.3731i	−0.170732	+	0.295716i
$124$		0			0
$125$		−	131.636i		−	1.05309i
$126$		0			0
$127$	145.000			1.14173			0.570866	−	0.821043i	$-0.306608\pi$
$127$	145.000			1.14173			0.570866	+	0.821043i	$0.306608\pi$
$128$		0			0
$129$	28.5000	+	16.4545i	0.220930	+	0.127554i
$130$		0			0
$131$	129.000	−	74.4782i	0.984733	−	0.568536i	0.0810371	−	0.996711i	$-0.474177\pi$
$131$	129.000	−	74.4782i	0.984733	−	0.568536i	0.903696	+	0.428175i	$0.140843\pi$
$132$		0			0
$133$	−199.500	−	115.181i	−1.50000	−	0.866025i
$134$		0			0
$135$	−9.00000	−	15.5885i	−0.0666667	−	0.115470i
$136$		0			0
$137$	58.0000	−	100.459i	0.423358	−	0.733277i	−0.572908	−	0.819620i	$-0.694185\pi$
$137$	58.0000	−	100.459i	0.423358	−	0.733277i	0.996265	+	0.0863428i	$0.0275180\pi$
$138$		0			0
$139$		−	84.8705i		−	0.610579i	−0.952260	−	0.305290i	$-0.901247\pi$
$139$		−	84.8705i		−	0.610579i	0.952260	−	0.305290i	$-0.0987532\pi$
$140$		0			0
$141$	90.0000			0.638298
$142$		0			0
$143$	105.000	+	60.6218i	0.734266	+	0.423929i
$144$		0			0
$145$	−48.0000	+	27.7128i	−0.331034	+	0.191123i
$146$		0			0
$147$	−73.5000	+	42.4352i	−0.500000	+	0.288675i
$148$		0			0
$149$	−62.0000	−	107.387i	−0.416107	−	0.720719i	0.579437	−	0.815017i	$-0.303273\pi$
$149$	−62.0000	−	107.387i	−0.416107	−	0.720719i	−0.995544	+	0.0942982i	$0.969939\pi$
$150$		0			0
$151$	−23.0000	+	39.8372i	−0.152318	+	0.263822i	−0.932079	−	0.362255i	$-0.882007\pi$
$151$	−23.0000	+	39.8372i	−0.152318	+	0.263822i	0.779761	+	0.626077i	$0.215340\pi$
$152$		0			0
$153$		−	20.7846i		−	0.135847i
$154$		0			0
$155$	18.0000			0.116129
$156$		0			0
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.917513	−	0.397705i	$-0.130193\pi$
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.114334	+	0.993442i	$0.463527\pi$
$158$		0			0
$159$	48.0000	−	27.7128i	0.301887	−	0.174294i
$160$		0			0
$161$	−140.000	+	242.487i	−0.869565	+	1.50613i
$162$		0			0
$163$	−29.0000	−	50.2295i	−0.177914	−	0.308156i	0.763252	−	0.646101i	$-0.223602\pi$
$163$	−29.0000	−	50.2295i	−0.177914	−	0.308156i	−0.941166	+	0.337945i	$0.890268\pi$
$164$		0			0
$165$	−30.0000	+	51.9615i	−0.181818	+	0.314918i
$166$		0			0
$167$			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
$170$		0			0
$171$	−85.5000	−	49.3634i	−0.500000	−	0.288675i
$172$		0			0
$173$	−108.000	+	62.3538i	−0.624277	+	0.360427i	−0.778532	−	0.627604i	$-0.784036\pi$
$173$	−108.000	+	62.3538i	−0.624277	+	0.360427i	0.154255	+	0.988031i	$0.450702\pi$
$174$		0			0
$175$	−91.0000			−0.520000
$176$		0			0
$177$	−36.0000	−	62.3538i	−0.203390	−	0.352282i
$178$		0			0
$179$	5.00000	−	8.66025i	0.0279330	−	0.0483813i	−0.851721	−	0.523996i	$-0.824441\pi$
$179$	5.00000	−	8.66025i	0.0279330	−	0.0483813i	0.879654	+	0.475614i	$0.157774\pi$
$180$		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
$183$	36.0000			0.196721
$184$		0			0
$185$	15.0000	+	8.66025i	0.0810811	+	0.0468122i
$186$		0			0
$187$	−60.0000	+	34.6410i	−0.320856	+	0.185246i
$188$		0			0
$189$	−31.5000	+	18.1865i	−0.166667	+	0.0962250i
$190$		0			0
$191$	−1.00000	−	1.73205i	−0.00523560	−	0.00906833i	0.863396	−	0.504527i	$-0.168333\pi$
$191$	−1.00000	−	1.73205i	−0.00523560	−	0.00906833i	−0.868631	+	0.495459i	$0.835000\pi$
$192$		0			0
$193$	117.500	−	203.516i	0.608808	−	1.05449i	−0.382629	−	0.923902i	$-0.624981\pi$
$193$	117.500	−	203.516i	0.608808	−	1.05449i	0.991437	−	0.130585i	$-0.0416855\pi$
$194$		0			0
$195$		−	72.7461i		−	0.373057i
$196$		0			0
$197$	100.000			0.507614			0.253807	−	0.967255i	$-0.418317\pi$
$197$	100.000			0.507614			0.253807	+	0.967255i	$0.418317\pi$
$198$		0			0
$199$	174.000	+	100.459i	0.874372	+	0.504819i	0.868799	−	0.495166i	$-0.164893\pi$
$199$	174.000	+	100.459i	0.874372	+	0.504819i	0.00557327	+	0.999984i	$0.498226\pi$
$200$		0			0
$201$	88.5000	−	51.0955i	0.440299	−	0.254206i
$202$		0			0
$203$	56.0000	+	96.9948i	0.275862	+	0.477807i
$204$		0			0
$205$	−42.0000	−	72.7461i	−0.204878	−	0.354859i
$206$		0			0
$207$	−60.0000	+	103.923i	−0.289855	+	0.502044i
$208$		0			0
$209$			329.090i			1.57459i
$210$		0			0
$211$	−2.00000			−0.00947867			−0.00473934	−	0.999989i	$-0.501509\pi$
$211$	−2.00000			−0.00947867			−0.00473934	+	0.999989i	$0.501509\pi$
$212$		0			0
$213$	39.0000	+	22.5167i	0.183099	+	0.105712i
$214$		0			0
$215$	−57.0000	+	32.9090i	−0.265116	+	0.153065i
$216$		0			0
$217$		−	36.3731i		−	0.167618i
$218$		0			0
$219$	−16.5000	−	28.5788i	−0.0753425	−	0.130497i
$220$		0			0
$221$	42.0000	−	72.7461i	0.190045	−	0.329168i
$222$		0			0
$223$			339.482i			1.52234i	0.648552	+	0.761170i	$0.275375\pi$
$223$			339.482i			1.52234i	−0.648552	+	0.761170i	$0.724625\pi$
$224$		0			0
$225$	−39.0000			−0.173333
$226$		0			0
$227$	−141.000	−	81.4064i	−0.621145	−	0.358618i	0.156169	−	0.987730i	$-0.450085\pi$
$227$	−141.000	−	81.4064i	−0.621145	−	0.358618i	−0.777315	+	0.629112i	$0.783419\pi$
$228$		0			0
$229$	7.50000	−	4.33013i	0.0327511	−	0.0189089i	−0.483535	−	0.875325i	$-0.660647\pi$
$229$	7.50000	−	4.33013i	0.0327511	−	0.0189089i	0.516286	+	0.856416i	$0.327314\pi$
$230$		0			0
$231$	105.000	+	60.6218i	0.454545	+	0.262432i
$232$		0			0
$233$	85.0000	+	147.224i	0.364807	+	0.631864i	0.988745	−	0.149610i	$-0.0478017\pi$
$233$	85.0000	+	147.224i	0.364807	+	0.631864i	−0.623938	+	0.781474i	$0.714468\pi$
$234$		0			0
$235$	−90.0000	+	155.885i	−0.382979	+	0.663339i
$236$		0			0
$237$			81.4064i			0.343487i
$238$		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	$-0.435749\pi$
$241$	−132.000	−	76.2102i	−0.547718	−	0.316225i	−0.748201	+	0.663472i	$0.769082\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		−	169.741i		−	0.692820i
$246$		0			0
$247$	−199.500	−	345.544i	−0.807692	−	1.39896i
$248$		0			0
$249$	−21.0000	+	36.3731i	−0.0843373	+	0.146077i
$250$		0			0
$251$			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
$254$		0			0
$255$	36.0000	+	20.7846i	0.141176	+	0.0815083i
$256$		0			0
$257$	−381.000	+	219.970i	−1.48249	+	0.855916i	−0.999802	−	0.0198763i	$-0.993673\pi$
$257$	−381.000	+	219.970i	−1.48249	+	0.855916i	−0.482688	+	0.875792i	$0.660339\pi$
$258$		0			0
$259$	17.5000	−	30.3109i	0.0675676	−	0.117030i
$260$		0			0
$261$	24.0000	+	41.5692i	0.0919540	+	0.159269i
$262$		0			0
$263$	68.0000	−	117.779i	0.258555	−	0.447831i	−0.707300	−	0.706914i	$-0.750087\pi$
$263$	68.0000	−	117.779i	0.258555	−	0.447831i	0.965855	+	0.259083i	$0.0834203\pi$
$264$		0			0
$265$			110.851i			0.418307i
$266$		0			0
$267$	204.000			0.764045
$268$		0			0
$269$	−195.000	−	112.583i	−0.724907	−	0.418525i	0.0916490	−	0.995791i	$-0.470786\pi$
$269$	−195.000	−	112.583i	−0.724907	−	0.418525i	−0.816556	+	0.577266i	$0.804120\pi$
$270$		0			0
$271$	318.000	−	183.597i	1.17343	−	0.677481i	0.218946	−	0.975737i	$-0.429738\pi$
$271$	318.000	−	183.597i	1.17343	−	0.677481i	0.954486	+	0.298256i	$0.0964049\pi$
$272$		0			0
$273$	−147.000			−0.538462
$274$		0			0
$275$	65.0000	+	112.583i	0.236364	+	0.409394i
$276$		0			0
$277$	−197.500	+	342.080i	−0.712996	+	1.23495i	0.250731	+	0.968057i	$0.419329\pi$
$277$	−197.500	+	342.080i	−0.712996	+	1.23495i	−0.963727	+	0.266889i	$0.914004\pi$
$278$		0			0
$279$		−	15.5885i		−	0.0558726i
$280$		0			0
$281$	100.000			0.355872			0.177936	−	0.984042i	$-0.443058\pi$
$281$	100.000			0.355872			0.177936	+	0.984042i	$0.443058\pi$
$282$		0			0
$283$	310.500	+	179.267i	1.09717	+	0.633453i	0.935477	−	0.353387i	$-0.114970\pi$
$283$	310.500	+	179.267i	1.09717	+	0.633453i	0.161696	+	0.986841i	$0.448304\pi$
$284$		0			0
$285$	171.000	−	98.7269i	0.600000	−	0.346410i
$286$		0			0
$287$	−147.000	+	84.8705i	−0.512195	+	0.295716i
$288$		0			0
$289$	−120.500	−	208.712i	−0.416955	−	0.722187i
$290$		0			0
$291$	42.0000	−	72.7461i	0.144330	−	0.249987i
$292$		0			0
$293$			242.487i			0.827601i	0.910368	+	0.413801i	$0.135799\pi$
$293$			242.487i			0.827601i	−0.910368	+	0.413801i	$0.864201\pi$
$294$		0			0
$295$	144.000			0.488136
$296$		0			0
$297$	45.0000	+	25.9808i	0.151515	+	0.0874773i
$298$		0			0
$299$	−420.000	+	242.487i	−1.40468	+	0.810994i
$300$		0			0
$301$	66.5000	+	115.181i	0.220930	+	0.382662i
$302$		0			0
$303$	−111.000	−	192.258i	−0.366337	−	0.634514i
$304$		0			0
$305$	−36.0000	+	62.3538i	−0.118033	+	0.204439i
$306$		0			0
$307$		−	181.865i		−	0.592395i	−0.955127	−	0.296198i	$-0.904281\pi$
$307$		−	181.865i		−	0.592395i	0.955127	−	0.296198i	$-0.0957187\pi$
$308$		0			0
$309$	−15.0000			−0.0485437
$310$		0			0
$311$	−477.000	−	275.396i	−1.53376	−	0.885518i	−0.999184	−	0.0403991i	$-0.987137\pi$
$311$	−477.000	−	275.396i	−1.53376	−	0.885518i	−0.534578	−	0.845119i	$-0.679530\pi$
$312$		0			0
$313$	175.500	−	101.325i	0.560703	−	0.323722i	−0.192725	−	0.981253i	$-0.561732\pi$
$313$	175.500	−	101.325i	0.560703	−	0.323722i	0.753428	+	0.657531i	$0.228399\pi$
$314$		0			0
$315$		−	72.7461i		−	0.230940i
$316$		0			0
$317$	−146.000	−	252.879i	−0.460568	−	0.797727i	0.538421	−	0.842676i	$-0.319021\pi$
$317$	−146.000	−	252.879i	−0.460568	−	0.797727i	−0.998989	+	0.0449488i	$0.985688\pi$
$318$		0			0
$319$	80.0000	−	138.564i	0.250784	−	0.434370i
$320$		0			0
$321$		−	367.195i		−	1.14391i
$322$		0			0
$323$	228.000			0.705882
$324$		0			0
$325$	−136.500	−	78.8083i	−0.420000	−	0.242487i
$326$		0			0
$327$	−25.5000	+	14.7224i	−0.0779817	+	0.0450227i
$328$		0			0
$329$	315.000	+	181.865i	0.957447	+	0.552782i
$330$		0			0
$331$	2.50000	+	4.33013i	0.00755287	+	0.0130820i	0.869777	−	0.493445i	$-0.164262\pi$
$331$	2.50000	+	4.33013i	0.00755287	+	0.0130820i	−0.862224	+	0.506527i	$0.830929\pi$
$332$		0			0
$333$	7.50000	−	12.9904i	0.0225225	−	0.0390102i
$334$		0			0
$335$			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	$0.725791\pi$
$338$		0			0
$339$	213.000	+	122.976i	0.628319	+	0.362760i
$340$		0			0
$341$	−45.0000	+	25.9808i	−0.131965	+	0.0761899i
$342$		0			0
$343$	−343.000			−1.00000
$344$		0			0
$345$	−120.000	−	207.846i	−0.347826	−	0.602452i
$346$		0			0
$347$	110.000	−	190.526i	0.317003	−	0.549065i	−0.662858	−	0.748745i	$-0.730657\pi$
$347$	110.000	−	190.526i	0.317003	−	0.549065i	0.979861	+	0.199680i	$0.0639902\pi$
$348$		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
$351$	−63.0000			−0.179487
$352$		0			0
$353$	267.000	+	154.153i	0.756374	+	0.436693i	0.827992	−	0.560739i	$-0.189483\pi$
$353$	267.000	+	154.153i	0.756374	+	0.436693i	−0.0716184	+	0.997432i	$0.522816\pi$
$354$		0			0
$355$	−78.0000	+	45.0333i	−0.219718	+	0.126854i
$356$		0			0
$357$	42.0000	−	72.7461i	0.117647	−	0.203771i
$358$		0			0
$359$	146.000	+	252.879i	0.406685	+	0.704399i	0.994516	−	0.104584i	$-0.0333512\pi$
$359$	146.000	+	252.879i	0.406685	+	0.704399i	−0.587831	+	0.808984i	$0.700018\pi$
$360$		0			0
$361$	361.000	−	625.270i	1.00000	−	1.73205i
$362$		0			0
$363$			36.3731i			0.100201i
$364$		0			0
$365$	66.0000			0.180822
$366$		0			0
$367$	−466.500	−	269.334i	−1.27112	−	0.733880i	−0.295919	−	0.955213i	$-0.595626\pi$
$367$	−466.500	−	269.334i	−1.27112	−	0.733880i	−0.975198	+	0.221333i	$0.928959\pi$
$368$		0			0
$369$	−63.0000	+	36.3731i	−0.170732	+	0.0985720i
$370$		0			0
$371$	224.000			0.603774
$372$		0			0
$373$	102.500	+	177.535i	0.274799	+	0.475966i	0.970084	−	0.242768i	$-0.0780554\pi$
$373$	102.500	+	177.535i	0.274799	+	0.475966i	−0.695285	+	0.718734i	$0.744722\pi$
$374$		0			0
$375$	114.000	−	197.454i	0.304000	−	0.526543i
$376$		0			0
$377$			193.990i			0.514562i
$378$		0			0
$379$	523.000			1.37995			0.689974	−	0.723835i	$-0.257622\pi$
$379$	523.000			1.37995			0.689974	+	0.723835i	$0.257622\pi$
$380$		0			0
$381$	217.500	+	125.574i	0.570866	+	0.329590i
$382$		0			0
$383$	66.0000	−	38.1051i	0.172324	−	0.0994912i	−0.411357	−	0.911474i	$-0.634945\pi$
$383$	66.0000	−	38.1051i	0.172324	−	0.0994912i	0.583681	+	0.811983i	$0.301612\pi$
$384$		0			0
$385$	−210.000	+	121.244i	−0.545455	+	0.314918i
$386$		0			0
$387$	28.5000	+	49.3634i	0.0736434	+	0.127554i
$388$		0			0
$389$	37.0000	−	64.0859i	0.0951157	−	0.164745i	−0.814541	−	0.580106i	$-0.803011\pi$
$389$	37.0000	−	64.0859i	0.0951157	−	0.164745i	0.909657	+	0.415361i	$0.136345\pi$
$390$		0			0
$391$		−	277.128i		−	0.708768i
$392$		0			0
$393$	258.000			0.656489
$394$		0			0
$395$	−141.000	−	81.4064i	−0.356962	−	0.206092i
$396$		0			0
$397$	280.500	−	161.947i	0.706549	−	0.407926i	−0.103233	−	0.994657i	$-0.532919\pi$
$397$	280.500	−	161.947i	0.706549	−	0.407926i	0.809782	+	0.586731i	$0.199585\pi$
$398$		0			0
$399$	−199.500	−	345.544i	−0.500000	−	0.866025i
$400$		0			0
$401$	64.0000	+	110.851i	0.159601	+	0.276437i	0.934725	−	0.355372i	$-0.115646\pi$
$401$	64.0000	+	110.851i	0.159601	+	0.276437i	−0.775124	+	0.631809i	$0.782313\pi$
$402$		0			0
$403$	31.5000	−	54.5596i	0.0781638	−	0.135384i
$404$		0			0
$405$		−	31.1769i		−	0.0769800i
$406$		0			0
$407$	−50.0000			−0.122850
$408$		0			0
$409$	256.500	+	148.090i	0.627139	+	0.362079i	0.779643	−	0.626224i	$-0.215400\pi$
$409$	256.500	+	148.090i	0.627139	+	0.362079i	−0.152504	+	0.988303i	$0.548734\pi$
$410$		0			0
$411$	174.000	−	100.459i	0.423358	−	0.244426i
$412$		0			0
$413$		−	290.985i		−	0.704563i
$414$		0			0
$415$	−42.0000	−	72.7461i	−0.101205	−	0.175292i
$416$		0			0
$417$	73.5000	−	127.306i	0.176259	−	0.305290i
$418$		0			0
$419$			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	$0.459440\pi$
$422$		0			0
$423$	135.000	+	77.9423i	0.319149	+	0.184261i
$424$		0			0
$425$	78.0000	−	45.0333i	0.183529	−	0.105961i
$426$		0			0
$427$	126.000	+	72.7461i	0.295082	+	0.170366i
$428$		0			0
$429$	105.000	+	181.865i	0.244755	+	0.423929i
$430$		0			0
$431$	131.000	−	226.899i	0.303944	−	0.526447i	−0.673081	−	0.739568i	$-0.735030\pi$
$431$	131.000	−	226.899i	0.303944	−	0.526447i	0.977026	+	0.213121i	$0.0683630\pi$
$432$		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
$435$	−96.0000			−0.220690
$436$		0			0
$437$	−1140.00	−	658.179i	−2.60870	−	1.50613i
$438$		0			0
$439$	−270.000	+	155.885i	−0.615034	+	0.355090i	−0.774933	−	0.632043i	$-0.782216\pi$
$439$	−270.000	+	155.885i	−0.615034	+	0.355090i	0.159899	+	0.987133i	$0.448883\pi$
$440$		0			0
$441$	−147.000			−0.333333
$442$		0			0
$443$	−106.000	−	183.597i	−0.239278	−	0.414441i	0.721230	−	0.692696i	$-0.243577\pi$
$443$	−106.000	−	183.597i	−0.239278	−	0.414441i	−0.960507	+	0.278255i	$0.910244\pi$
$444$		0			0
$445$	−204.000	+	353.338i	−0.458427	+	0.794019i
$446$		0			0
$447$		−	214.774i		−	0.480479i
$448$		0			0
$449$	−782.000			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$449$	−782.000			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$450$		0			0
$451$	210.000	+	121.244i	0.465632	+	0.268833i
$452$		0			0
$453$	−69.0000	+	39.8372i	−0.152318	+	0.0879408i
$454$		0			0
$455$	147.000	−	254.611i	0.323077	−	0.559586i
$456$		0			0
$457$	−338.500	−	586.299i	−0.740700	−	1.28293i	−0.952177	−	0.305547i	$-0.901161\pi$
$457$	−338.500	−	586.299i	−0.740700	−	1.28293i	0.211477	−	0.977383i	$-0.432173\pi$
$458$		0			0
$459$	18.0000	−	31.1769i	0.0392157	−	0.0679236i
$460$		0			0
$461$			484.974i			1.05200i	0.850483	+	0.526002i	$0.176310\pi$
$461$			484.974i			1.05200i	−0.850483	+	0.526002i	$0.823690\pi$
$462$		0			0
$463$	−443.000			−0.956803			−0.478402	−	0.878141i	$-0.658784\pi$
$463$	−443.000			−0.956803			−0.478402	+	0.878141i	$0.658784\pi$
$464$		0			0
$465$	27.0000	+	15.5885i	0.0580645	+	0.0335236i
$466$		0			0
$467$	−39.0000	+	22.5167i	−0.0835118	+	0.0482155i	−0.541174	−	0.840910i	$-0.682020\pi$
$467$	−39.0000	+	22.5167i	−0.0835118	+	0.0482155i	0.457663	+	0.889126i	$0.348687\pi$
$468$		0			0
$469$	413.000			0.880597
$470$		0			0
$471$	162.000	+	280.592i	0.343949	+	0.595737i
$472$		0			0
$473$	95.0000	−	164.545i	0.200846	−	0.347875i
$474$		0			0
$475$		−	427.817i		−	0.900666i
$476$		0			0
$477$	96.0000			0.201258
$478$		0			0
$479$	48.0000	+	27.7128i	0.100209	+	0.0578556i	0.549267	−	0.835647i	$-0.314907\pi$
$479$	48.0000	+	27.7128i	0.100209	+	0.0578556i	−0.449058	+	0.893503i	$0.648240\pi$
$480$		0			0
$481$	52.5000	−	30.3109i	0.109148	−	0.0630164i
$482$		0			0
$483$	−420.000	+	242.487i	−0.869565	+	0.502044i
$484$		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	$-0.855247\pi$
$487$	−33.5000	+	58.0237i	−0.0687885	+	0.119145i	0.829580	+	0.558388i	$0.188580\pi$
$488$		0			0
$489$		−	100.459i		−	0.205438i
$490$		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
$494$		0			0
$495$	−90.0000	+	51.9615i	−0.181818	+	0.104973i
$496$		0			0
$497$	91.0000	+	157.617i	0.183099	+	0.317136i
$498$		0			0
$499$	254.500	+	440.807i	0.510020	+	0.883381i	0.999933	+	0.0116091i	$0.00369536\pi$
$499$	254.500	+	440.807i	0.510020	+	0.883381i	−0.489913	+	0.871772i	$0.662971\pi$
$500$		0			0
$501$	−231.000	+	400.104i	−0.461078	+	0.798610i
$502$		0			0
$503$		−	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
$506$		0			0
$507$	33.0000	+	19.0526i	0.0650888	+	0.0375790i
$508$		0			0
$509$	753.000	−	434.745i	1.47937	−	0.854115i	0.479644	−	0.877463i	$-0.340766\pi$
$509$	753.000	−	434.745i	1.47937	−	0.854115i	0.999727	+	0.0233478i	$0.00743251\pi$
$510$		0			0
$511$		−	133.368i		−	0.260994i
$512$		0			0
$513$	−85.5000	−	148.090i	−0.166667	−	0.288675i
$514$		0			0
$515$	15.0000	−	25.9808i	0.0291262	−	0.0504481i
$516$		0			0
$517$		−	519.615i		−	1.00506i
$518$		0			0
$519$	−216.000			−0.416185
$520$		0			0
$521$	372.000	+	214.774i	0.714012	+	0.412235i	0.812545	−	0.582899i	$-0.198082\pi$
$521$	372.000	+	214.774i	0.714012	+	0.412235i	−0.0985331	+	0.995134i	$0.531415\pi$
$522$		0			0
$523$	853.500	−	492.768i	1.63193	−	0.942196i	0.648434	−	0.761271i	$-0.275424\pi$
$523$	853.500	−	492.768i	1.63193	−	0.942196i	0.983497	−	0.180925i	$-0.0579092\pi$
$524$		0			0
$525$	−136.500	−	78.8083i	−0.260000	−	0.150111i
$526$		0			0
$527$	18.0000	+	31.1769i	0.0341556	+	0.0591592i
$528$		0			0
$529$	−535.500	+	927.513i	−1.01229	+	1.75333i
$530$		0			0
$531$		−	124.708i		−	0.234854i
$532$		0			0
$533$	−294.000			−0.551595
$534$		0			0
$535$	636.000	+	367.195i	1.18879	+	0.686345i
$536$		0			0
$537$	15.0000	−	8.66025i	0.0279330	−	0.0161271i
$538$		0			0
$539$	245.000	+	424.352i	0.454545	+	0.787296i
$540$		0			0
$541$	60.5000	+	104.789i	0.111830	+	0.193695i	0.916508	−	0.400016i	$-0.130995\pi$
$541$	60.5000	+	104.789i	0.111830	+	0.193695i	−0.804678	+	0.593711i	$0.797662\pi$
$542$		0			0
$543$	−283.500	+	491.036i	−0.522099	+	0.904303i
$544$		0			0
$545$		−	58.8897i		−	0.108055i
$546$		0			0
$547$	−926.000			−1.69287			−0.846435	−	0.532492i	$-0.821256\pi$
$547$	−926.000			−1.69287			−0.846435	+	0.532492i	$0.821256\pi$
$548$		0			0
$549$	54.0000	+	31.1769i	0.0983607	+	0.0567886i
$550$		0			0
$551$	−456.000	+	263.272i	−0.827586	+	0.477807i
$552$		0			0
$553$	−164.500	+	284.922i	−0.297468	+	0.515230i
$554$		0			0
$555$	15.0000	+	25.9808i	0.0270270	+	0.0468122i
$556$		0			0
$557$	331.000	−	573.309i	0.594255	−	1.02928i	−0.399397	−	0.916778i	$-0.630780\pi$
$557$	331.000	−	573.309i	0.594255	−	1.02928i	0.993652	−	0.112502i	$-0.0358863\pi$
$558$		0			0
$559$			230.363i			0.412098i
$560$		0			0
$561$	−120.000			−0.213904
$562$		0			0
$563$	279.000	+	161.081i	0.495560	+	0.286111i	0.726878	−	0.686767i	$-0.240971\pi$
$563$	279.000	+	161.081i	0.495560	+	0.286111i	−0.231318	+	0.972878i	$0.574304\pi$
$564$		0			0
$565$	−426.000	+	245.951i	−0.753982	+	0.435312i
$566$		0			0
$567$	−63.0000			−0.111111
$568$		0			0
$569$	379.000	+	656.447i	0.666081	+	1.15369i	0.978991	+	0.203903i	$0.0653628\pi$
$569$	379.000	+	656.447i	0.666081	+	1.15369i	−0.312910	+	0.949783i	$0.601304\pi$
$570$		0			0
$571$	−432.500	+	749.112i	−0.757443	+	1.31193i	0.186707	+	0.982416i	$0.440218\pi$
$571$	−432.500	+	749.112i	−0.757443	+	1.31193i	−0.944151	+	0.329514i	$0.893115\pi$
$572$		0			0
$573$		−	3.46410i		−	0.00604555i
$574$		0			0
$575$	−520.000			−0.904348
$576$		0			0
$577$	928.500	+	536.070i	1.60919	+	0.929064i	0.989553	+	0.144172i	$0.0460518\pi$
$577$	928.500	+	536.070i	1.60919	+	0.929064i	0.619633	+	0.784892i	$0.287282\pi$
$578$		0			0
$579$	352.500	−	203.516i	0.608808	−	0.351496i
$580$		0			0
$581$	−147.000	+	84.8705i	−0.253012	+	0.146077i
$582$		0			0
$583$	−160.000	−	277.128i	−0.274443	−	0.475348i
$584$		0			0
$585$	63.0000	−	109.119i	0.107692	−	0.186529i
$586$		0			0
$587$		−	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
$590$		0			0
$591$	150.000	+	86.6025i	0.253807	+	0.146536i
$592$		0			0
$593$	−213.000	+	122.976i	−0.359191	+	0.207379i	−0.668726	−	0.743509i	$-0.733160\pi$
$593$	−213.000	+	122.976i	−0.359191	+	0.207379i	0.309535	+	0.950888i	$0.399827\pi$
$594$		0			0
$595$	84.0000	+	145.492i	0.141176	+	0.244525i
$596$		0			0
$597$	174.000	+	301.377i	0.291457	+	0.504819i
$598$		0			0
$599$	−142.000	+	245.951i	−0.237062	+	0.410603i	−0.959870	−	0.280446i	$-0.909518\pi$
$599$	−142.000	+	245.951i	−0.237062	+	0.410603i	0.722808	+	0.691049i	$0.242851\pi$
$600$		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
$603$	177.000			0.293532
$604$		0			0
$605$	−63.0000	−	36.3731i	−0.104132	−	0.0601208i
$606$		0			0
$607$	−7.50000	+	4.33013i	−0.0123558	+	0.00713365i	−0.506165	−	0.862437i	$-0.668937\pi$
$607$	−7.50000	+	4.33013i	−0.0123558	+	0.00713365i	0.493809	+	0.869570i	$0.335604\pi$
$608$		0			0
$609$			193.990i			0.318538i
$610$		0			0
$611$	315.000	+	545.596i	0.515548	+	0.892956i
$612$		0			0
$613$	−439.000	+	760.370i	−0.716150	+	1.24041i	0.246364	+	0.969177i	$0.420764\pi$
$613$	−439.000	+	760.370i	−0.716150	+	1.24041i	−0.962514	+	0.271231i	$0.912569\pi$
$614$		0			0
$615$		−	145.492i		−	0.236573i
$616$		0			0
$617$	−194.000			−0.314425			−0.157212	−	0.987565i	$-0.550251\pi$
$617$	−194.000			−0.314425			−0.157212	+	0.987565i	$0.550251\pi$
$618$		0			0
$619$	−529.500	−	305.707i	−0.855412	−	0.493872i	0.00706124	−	0.999975i	$-0.497752\pi$
$619$	−529.500	−	305.707i	−0.855412	−	0.493872i	−0.862473	+	0.506103i	$0.831086\pi$
$620$		0			0
$621$	−180.000	+	103.923i	−0.289855	+	0.167348i
$622$		0			0
$623$	714.000	+	412.228i	1.14607	+	0.661682i
$624$		0			0
$625$	65.5000	+	113.449i	0.104800	+	0.181519i
$626$		0			0
$627$	−285.000	+	493.634i	−0.454545	+	0.787296i
$628$		0			0
$629$			34.6410i			0.0550732i
$630$		0			0
$631$	250.000			0.396197			0.198098	−	0.980182i	$-0.436523\pi$
$631$	250.000			0.396197			0.198098	+	0.980182i	$0.436523\pi$
$632$		0			0
$633$	−3.00000	−	1.73205i	−0.00473934	−	0.00273626i
$634$		0			0
$635$	−435.000	+	251.147i	−0.685039	+	0.395508i
$636$		0			0
$637$	−514.500	−	297.047i	−0.807692	−	0.466321i
$638$		0			0
$639$	39.0000	+	67.5500i	0.0610329	+	0.105712i
$640$		0			0
$641$	562.000	−	973.413i	0.876755	−	1.51858i	0.0218737	−	0.999761i	$-0.493037\pi$
$641$	562.000	−	973.413i	0.876755	−	1.51858i	0.854881	−	0.518824i	$-0.173630\pi$
$642$		0			0
$643$			569.845i			0.886228i	0.896465	+	0.443114i	$0.146126\pi$
$643$			569.845i			0.886228i	−0.896465	+	0.443114i	$0.853874\pi$
$644$		0			0
$645$	−114.000			−0.176744
$646$		0			0
$647$	−939.000	−	542.132i	−1.45131	−	0.837916i	−0.452758	−	0.891634i	$-0.649560\pi$
$647$	−939.000	−	542.132i	−1.45131	−	0.837916i	−0.998556	+	0.0537173i	$0.982893\pi$
$648$		0			0
$649$	−360.000	+	207.846i	−0.554700	+	0.320256i
$650$		0			0
$651$	31.5000	−	54.5596i	0.0483871	−	0.0838089i
$652$		0			0
$653$	505.000	+	874.686i	0.773354	+	1.33949i	0.935715	+	0.352757i	$0.114756\pi$
$653$	505.000	+	874.686i	0.773354	+	1.33949i	−0.162361	+	0.986731i	$0.551911\pi$
$654$		0			0
$655$	−258.000	+	446.869i	−0.393893	+	0.682243i
$656$		0			0
$657$		−	57.1577i		−	0.0869980i
$658$		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	$-0.517314\pi$
$661$	−625.500	−	361.133i	−0.946293	−	0.546343i	−0.891928	+	0.452178i	$0.850647\pi$
$662$		0			0
$663$	126.000	−	72.7461i	0.190045	−	0.109723i
$664$		0			0
$665$	798.000			1.20000
$666$		0			0
$667$	320.000	+	554.256i	0.479760	+	0.830969i
$668$		0			0
$669$	−294.000	+	509.223i	−0.439462	+	0.761170i
$670$		0			0
$671$		−	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	$0.776275\pi$
$674$		0			0
$675$	−58.5000	−	33.7750i	−0.0866667	−	0.0500370i
$676$		0			0
$677$	−486.000	+	280.592i	−0.717873	+	0.414464i	−0.813969	−	0.580908i	$-0.802698\pi$
$677$	−486.000	+	280.592i	−0.717873	+	0.414464i	0.0960963	+	0.995372i	$0.469364\pi$
$678$		0			0
$679$	294.000	−	169.741i	0.432990	−	0.249987i
$680$		0			0
$681$	−141.000	−	244.219i	−0.207048	−	0.358618i
$682$		0			0
$683$	488.000	−	845.241i	0.714495	−	1.23754i	−0.248659	−	0.968591i	$-0.579990\pi$
$683$	488.000	−	845.241i	0.714495	−	1.23754i	0.963154	−	0.268950i	$-0.0866768\pi$
$684$		0			0
$685$			401.836i			0.586622i
$686$		0			0
$687$	15.0000			0.0218341
$688$		0			0
$689$	336.000	+	193.990i	0.487663	+	0.281553i
$690$		0			0
$691$	−490.500	+	283.190i	−0.709841	+	0.409827i	−0.811002	−	0.585043i	$-0.801078\pi$
$691$	−490.500	+	283.190i	−0.709841	+	0.409827i	0.101161	+	0.994870i	$0.467744\pi$
$692$		0			0
$693$	105.000	+	181.865i	0.151515	+	0.262432i
$694$		0			0
$695$	147.000	+	254.611i	0.211511	+	0.366347i
$696$		0			0
$697$	84.0000	−	145.492i	0.120516	−	0.208741i
$698$		0			0
$699$			294.449i			0.421243i
$700$		0			0
$701$	352.000			0.502140			0.251070	−	0.967969i	$-0.419218\pi$
$701$	352.000			0.502140			0.251070	+	0.967969i	$0.419218\pi$
$702$		0			0
$703$	142.500	+	82.2724i	0.202703	+	0.117030i
$704$		0			0
$705$	−270.000	+	155.885i	−0.382979	+	0.221113i
$706$		0			0
$707$		−	897.202i		−	1.26903i
$708$		0			0
$709$	575.000	+	995.929i	0.811001	+	1.40470i	0.912164	+	0.409826i	$0.134410\pi$
$709$	575.000	+	995.929i	0.811001	+	1.40470i	−0.101162	+	0.994870i	$0.532256\pi$
$710$		0			0
$711$	−70.5000	+	122.110i	−0.0991561	+	0.171743i
$712$		0			0
$713$		−	207.846i		−	0.291509i
$714$		0			0
$715$	−420.000			−0.587413
$716$		0			0
$717$	−213.000	−	122.976i	−0.297071	−	0.171514i
$718$		0			0
$719$	843.000	−	486.706i	1.17246	−	0.676921i	0.218203	−	0.975903i	$-0.429980\pi$
$719$	843.000	−	486.706i	1.17246	−	0.676921i	0.954259	+	0.298982i	$0.0966471\pi$
$720$		0			0
$721$	−52.5000	−	30.3109i	−0.0728155	−	0.0420401i
$722$		0			0
$723$	−132.000	−	228.631i	−0.182573	−	0.316225i
$724$		0			0
$725$	−104.000	+	180.133i	−0.143448	+	0.248460i
$726$		0			0
$727$		−	206.114i		−	0.283513i	−0.989902	−	0.141757i	$-0.954725\pi$
$727$		−	206.114i		−	0.283513i	0.989902	−	0.141757i	$-0.0452750\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−114.000	−	65.8179i	−0.155951	−	0.0900382i
$732$		0			0
$733$	1078.50	−	622.672i	1.47135	−	0.849485i	0.471869	−	0.881669i	$-0.343580\pi$
$733$	1078.50	−	622.672i	1.47135	−	0.849485i	0.999482	+	0.0321842i	$0.0102463\pi$
$734$		0			0
$735$	147.000	−	254.611i	0.200000	−	0.346410i
$736$		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	$-0.765850\pi$
$739$	155.500	−	269.334i	0.210419	−	0.364457i	0.951846	+	0.306577i	$0.0991837\pi$
$740$		0			0
$741$		−	691.088i		−	0.932643i
$742$		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
$746$		0			0
$747$	−63.0000	+	36.3731i	−0.0843373	+	0.0486922i
$748$		0			0
$749$	742.000	−	1285.18i	0.990654	−	1.71586i
$750$		0			0
$751$	−39.5000	−	68.4160i	−0.0525965	−	0.0910999i	0.838528	−	0.544858i	$-0.183416\pi$
$751$	−39.5000	−	68.4160i	−0.0525965	−	0.0910999i	−0.891125	+	0.453758i	$0.850083\pi$
$752$		0			0
$753$	−252.000	+	436.477i	−0.334661	+	0.579650i
$754$		0			0
$755$		−	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	$0.552803\pi$
$758$		0			0
$759$	600.000	+	346.410i	0.790514	+	0.456403i
$760$		0			0
$761$	−822.000	+	474.582i	−1.08016	+	0.623629i	−0.930939	−	0.365175i	$-0.881009\pi$
$761$	−822.000	+	474.582i	−1.08016	+	0.623629i	−0.149219	+	0.988804i	$0.547676\pi$
$762$		0			0
$763$	−119.000			−0.155963
$764$		0			0
$765$	36.0000	+	62.3538i	0.0470588	+	0.0815083i
$766$		0			0
$767$	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
$771$	−762.000			−0.988327
$772$		0			0
$773$	−195.000	−	112.583i	−0.252264	−	0.145645i	0.368537	−	0.929613i	$-0.379859\pi$
$773$	−195.000	−	112.583i	−0.252264	−	0.145645i	−0.620800	+	0.783969i	$0.713192\pi$
$774$		0			0
$775$	58.5000	−	33.7750i	0.0754839	−	0.0435806i
$776$		0			0
$777$	52.5000	−	30.3109i	0.0675676	−	0.0390102i
$778$		0			0
$779$	−399.000	−	691.088i	−0.512195	−	0.887148i
$780$		0			0
$781$	130.000	−	225.167i	0.166453	−	0.288306i
$782$		0			0
$783$			83.1384i			0.106179i
$784$		0			0
$785$	−648.000			−0.825478
$786$		0			0
$787$	216.000	+	124.708i	0.274460	+	0.158460i	0.630913	−	0.775854i	$-0.282681\pi$
$787$	216.000	+	124.708i	0.274460	+	0.158460i	−0.356453	+	0.934313i	$0.616014\pi$
$788$		0			0
$789$	204.000	−	117.779i	0.258555	−	0.149277i
$790$		0			0
$791$	497.000	+	860.829i	0.628319	+	1.08828i
$792$		0			0
$793$	126.000	+	218.238i	0.158890	+	0.275206i
$794$		0			0
$795$	−96.0000	+	166.277i	−0.120755	+	0.209153i
$796$		0			0
$797$		−	1357.93i		−	1.70380i	−0.523705	−	0.851900i	$-0.675451\pi$
$797$		−	1357.93i		−	1.70380i	0.523705	−	0.851900i	$-0.324549\pi$
$798$		0			0
$799$	−360.000			−0.450563
$800$		0			0
$801$	306.000	+	176.669i	0.382022	+	0.220561i
$802$		0			0
$803$	−165.000	+	95.2628i	−0.205479	+	0.118634i
$804$		0			0
$805$		−	969.948i		−	1.20490i
$806$		0			0
$807$	−195.000	−	337.750i	−0.241636	−	0.418525i
$808$		0			0
$809$	709.000	−	1228.02i	0.876391	−	1.51795i	0.0211166	−	0.999777i	$-0.493278\pi$
$809$	709.000	−	1228.02i	0.876391	−	1.51795i	0.855274	−	0.518176i	$-0.173389\pi$
$810$		0			0
$811$		−	872.954i		−	1.07639i	−0.842820	−	0.538196i	$-0.819106\pi$
$811$		−	872.954i		−	1.07639i	0.842820	−	0.538196i	$-0.180894\pi$
$812$		0			0
$813$	636.000			0.782288
$814$		0			0
$815$	174.000	+	100.459i	0.213497	+	0.123263i
$816$		0			0
$817$	−541.500	+	312.635i	−0.662791	+	0.382662i
$818$		0			0
$819$	−220.500	−	127.306i	−0.269231	−	0.155440i
$820$		0			0
$821$	−125.000	−	216.506i	−0.152253	−	0.263711i	0.779802	−	0.626026i	$-0.215320\pi$
$821$	−125.000	−	216.506i	−0.152253	−	0.263711i	−0.932056	+	0.362315i	$0.881986\pi$
$822$		0			0
$823$	103.000	−	178.401i	0.125152	−	0.216769i	−0.796640	−	0.604454i	$-0.793392\pi$
$823$	103.000	−	178.401i	0.125152	−	0.216769i	0.921792	+	0.387684i	$0.126725\pi$
$824$		0			0
$825$			225.167i			0.272929i
$826$		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	$-0.266674\pi$
$829$	298.500	+	172.339i	0.360072	+	0.207888i	−0.309040	+	0.951049i	$0.600008\pi$
$830$		0			0
$831$	−592.500	+	342.080i	−0.712996	+	0.411649i
$832$		0			0
$833$	294.000	−	169.741i	0.352941	−	0.203771i
$834$		0			0
$835$	−462.000	−	800.207i	−0.553293	−	0.958332i
$836$		0			0
$837$	13.5000	−	23.3827i	0.0161290	−	0.0279363i
$838$		0			0
$839$		−	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
$842$		0			0
$843$	150.000	+	86.6025i	0.177936	+	0.102731i
$844$		0			0
$845$	−66.0000	+	38.1051i	−0.0781065	+	0.0450948i
$846$		0			0
$847$	−73.5000	+	127.306i	−0.0867769	+	0.150302i
$848$		0			0
$849$	310.500	+	537.802i	0.365724	+	0.633453i
$850$		0			0
$851$	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
$855$	342.000			0.400000
$856$		0			0
$857$	−552.000	−	318.697i	−0.644107	−	0.371876i	0.142088	−	0.989854i	$-0.454619\pi$
$857$	−552.000	−	318.697i	−0.644107	−	0.371876i	−0.786195	+	0.617979i	$0.787952\pi$
$858$		0			0
$859$	528.000	−	304.841i	0.614668	−	0.354879i	−0.160122	−	0.987097i	$-0.551189\pi$
$859$	528.000	−	304.841i	0.614668	−	0.354879i	0.774790	+	0.632218i	$0.217855\pi$
$860$		0			0
$861$	−294.000			−0.341463
$862$		0			0
$863$	335.000	+	580.237i	0.388181	+	0.672349i	0.992205	−	0.124617i	$-0.0397703\pi$
$863$	335.000	+	580.237i	0.388181	+	0.672349i	−0.604024	+	0.796966i	$0.706437\pi$
$864$		0			0
$865$	216.000	−	374.123i	0.249711	−	0.432512i
$866$		0			0
$867$		−	417.424i		−	0.481458i
$868$		0			0
$869$	470.000			0.540852
$870$		0			0
$871$	619.500	+	357.668i	0.711251	+	0.410641i
$872$		0			0
$873$	126.000	−	72.7461i	0.144330	−	0.0833289i
$874$		0			0
$875$	798.000	−	460.726i	0.912000	−	0.526543i
$876$		0			0
$877$	197.000	+	341.214i	0.224629	+	0.389070i	0.956208	−	0.292687i	$-0.0945495\pi$
$877$	197.000	+	341.214i	0.224629	+	0.389070i	−0.731579	+	0.681757i	$0.761216\pi$
$878$		0			0
$879$	−210.000	+	363.731i	−0.238908	+	0.413801i
$880$		0			0
$881$			1163.94i			1.32116i	0.750758	+	0.660578i	$0.229689\pi$
$881$			1163.94i			1.32116i	−0.750758	+	0.660578i	$0.770311\pi$
$882$		0			0
$883$	−737.000			−0.834655			−0.417327	−	0.908756i	$-0.637033\pi$
$883$	−737.000			−0.834655			−0.417327	+	0.908756i	$0.637033\pi$
$884$		0			0
$885$	216.000	+	124.708i	0.244068	+	0.140913i
$886$		0			0
$887$	633.000	−	365.463i	0.713641	−	0.412021i	−0.0987664	−	0.995111i	$-0.531490\pi$
$887$	633.000	−	365.463i	0.713641	−	0.412021i	0.812408	+	0.583090i	$0.198156\pi$
$888$		0			0
$889$	507.500	+	879.016i	0.570866	+	0.988769i
$890$		0			0
$891$	45.0000	+	77.9423i	0.0505051	+	0.0874773i
$892$		0			0
$893$	−855.000	+	1480.90i	−0.957447	+	1.65835i
$894$		0			0
$895$			34.6410i			0.0387050i
$896$		0			0
$897$	−840.000			−0.936455
$898$		0			0
$899$	−72.0000	−	41.5692i	−0.0800890	−	0.0462394i
$900$		0			0
$901$	−192.000	+	110.851i	−0.213097	+	0.123031i
$902$		0			0
$903$			230.363i			0.255108i
$904$		0			0
$905$	−567.000	−	982.073i	−0.626519	−	1.08516i
$906$		0			0
$907$	−117.500	+	203.516i	−0.129548	+	0.224384i	−0.923502	−	0.383595i	$-0.874686\pi$
$907$	−117.500	+	203.516i	−0.129548	+	0.224384i	0.793954	+	0.607978i	$0.208019\pi$
$908$		0			0
$909$		−	384.515i		−	0.423009i
$910$		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
$914$		0			0
$915$	−108.000	+	62.3538i	−0.118033	+	0.0681463i
$916$		0			0
$917$	903.000	+	521.347i	0.984733	+	0.568536i
$918$		0			0
$919$	758.500	+	1313.76i	0.825354	+	1.42955i	0.901649	+	0.432469i	$0.142358\pi$
$919$	758.500	+	1313.76i	0.825354	+	1.42955i	−0.0762951	+	0.997085i	$0.524309\pi$
$920$		0			0
$921$	157.500	−	272.798i	0.171010	−	0.296198i
$922$		0			0
$923$			315.233i			0.341531i
$924$		0			0
$925$	65.0000			0.0702703
$926$		0			0
$927$	−22.5000	−	12.9904i	−0.0242718	−	0.0140134i
$928$		0			0
$929$	963.000	−	555.988i	1.03660	−	0.598480i	0.117731	−	0.993046i	$-0.462438\pi$
$929$	963.000	−	555.988i	1.03660	−	0.598480i	0.918868	+	0.394565i	$0.129105\pi$
$930$		0			0
$931$		−	1612.54i		−	1.73205i
$932$		0			0
$933$	−477.000	−	826.188i	−0.511254	−	0.885518i
$934$		0			0
$935$	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
$939$	351.000			0.373802
$940$		0			0
$941$	−342.000	−	197.454i	−0.363443	−	0.209834i	0.307147	−	0.951662i	$-0.400626\pi$
$941$	−342.000	−	197.454i	−0.363443	−	0.209834i	−0.670590	+	0.741828i	$0.733959\pi$
$942$		0			0
$943$	−840.000	+	484.974i	−0.890774	+	0.514289i
$944$		0			0
$945$	63.0000	−	109.119i	0.0666667	−	0.115470i
$946$		0			0
$947$	−169.000	−	292.717i	−0.178458	−	0.309099i	0.762894	−	0.646523i	$-0.223778\pi$
$947$	−169.000	−	292.717i	−0.178458	−	0.309099i	−0.941353	+	0.337424i	$0.890444\pi$
$948$		0			0
$949$	115.500	−	200.052i	0.121707	−	0.210803i
$950$		0			0
$951$		−	505.759i		−	0.531818i
$952$		0			0
$953$	−1244.00			−1.30535			−0.652676	−	0.757637i	$-0.726354\pi$
$953$	−1244.00			−1.30535			−0.652676	+	0.757637i	$0.726354\pi$
$954$		0			0
$955$	6.00000	+	3.46410i	0.00628272	+	0.00362733i
$956$		0			0
$957$	240.000	−	138.564i	0.250784	−	0.144790i
$958$		0			0
$959$	812.000			0.846715
$960$		0			0
$961$	−467.000	−	808.868i	−0.485952	−	0.841694i
$962$		0			0
$963$	318.000	−	550.792i	0.330218	−	0.571954i
$964$		0			0
$965$			814.064i			0.843590i
$966$		0			0
$967$	1741.00			1.80041			0.900207	−	0.435463i	$-0.143415\pi$
$967$	1741.00			1.80041			0.900207	+	0.435463i	$0.143415\pi$
$968$		0			0
$969$	342.000	+	197.454i	0.352941	+	0.203771i
$970$		0			0
$971$	−1110.00	+	640.859i	−1.14315	+	0.659999i	−0.947209	−	0.320617i	$-0.896110\pi$
$971$	−1110.00	+	640.859i	−1.14315	+	0.659999i	−0.195942	+	0.980615i	$0.562777\pi$
$972$		0			0
$973$	514.500	−	297.047i	0.528777	−	0.305290i
$974$		0			0
$975$	−136.500	−	236.425i	−0.140000	−	0.242487i
$976$		0			0
$977$	−131.000	+	226.899i	−0.134084	+	0.232240i	−0.925247	−	0.379365i	$-0.876143\pi$
$977$	−131.000	+	226.899i	−0.134084	+	0.232240i	0.791163	+	0.611605i	$0.209476\pi$
$978$		0			0
$979$		−	1177.79i		−	1.20306i
$980$		0			0
$981$	−51.0000			−0.0519878
$982$		0			0
$983$	−960.000	−	554.256i	−0.976602	−	0.563842i	−0.0753596	−	0.997156i	$-0.524010\pi$
$983$	−960.000	−	554.256i	−0.976602	−	0.563842i	−0.901243	+	0.433315i	$0.857344\pi$
$984$		0			0
$985$	−300.000	+	173.205i	−0.304569	+	0.175843i
$986$		0			0
$987$	315.000	+	545.596i	0.319149	+	0.552782i
$988$		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	$-0.844096\pi$
$991$	−33.5000	+	58.0237i	−0.0338042	+	0.0585507i	0.848628	+	0.528990i	$0.177429\pi$
$992$		0			0
$993$			8.66025i			0.00872130i
$994$		0			0
$995$	−696.000			−0.699497
$996$		0			0
$997$	−856.500	−	494.501i	−0.859077	−	0.495988i	0.00462594	−	0.999989i	$-0.498528\pi$
$997$	−856.500	−	494.501i	−0.859077	−	0.495988i	−0.863703	+	0.504001i	$0.831861\pi$
$998$		0			0
$999$	22.5000	−	12.9904i	0.0225225	−	0.0130034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.c.241.1		2
3.2	odd	2		1008.3.cg.f.577.1		2
4.3	odd	2		21.3.f.c.10.1	✓	2
7.3	odd	6		2352.3.f.b.97.2		2
7.4	even	3		2352.3.f.b.97.1		2
7.5	odd	6	inner	336.3.bh.c.145.1		2
12.11	even	2		63.3.m.a.10.1		2
20.3	even	4		525.3.s.d.199.2		4
20.7	even	4		525.3.s.d.199.1		4
20.19	odd	2		525.3.o.b.451.1		2
21.5	even	6		1008.3.cg.f.145.1		2
28.3	even	6		147.3.d.a.97.1		2
28.11	odd	6		147.3.d.a.97.2		2
28.19	even	6		21.3.f.c.19.1	yes	2
28.23	odd	6		147.3.f.e.19.1		2
28.27	even	2		147.3.f.e.31.1		2
84.11	even	6		441.3.d.d.244.2		2
84.23	even	6		441.3.m.b.19.1		2
84.47	odd	6		63.3.m.a.19.1		2
84.59	odd	6		441.3.d.d.244.1		2
84.83	odd	2		441.3.m.b.325.1		2
140.19	even	6		525.3.o.b.376.1		2
140.47	odd	12		525.3.s.d.124.2		4
140.103	odd	12		525.3.s.d.124.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.c.10.1	✓	2	4.3	odd	2
21.3.f.c.19.1	yes	2	28.19	even	6
63.3.m.a.10.1		2	12.11	even	2
63.3.m.a.19.1		2	84.47	odd	6
147.3.d.a.97.1		2	28.3	even	6
147.3.d.a.97.2		2	28.11	odd	6
147.3.f.e.19.1		2	28.23	odd	6
147.3.f.e.31.1		2	28.27	even	2
336.3.bh.c.145.1		2	7.5	odd	6	inner
336.3.bh.c.241.1		2	1.1	even	1	trivial
441.3.d.d.244.1		2	84.59	odd	6
441.3.d.d.244.2		2	84.11	even	6
441.3.m.b.19.1		2	84.23	even	6
441.3.m.b.325.1		2	84.83	odd	2
525.3.o.b.376.1		2	140.19	even	6
525.3.o.b.451.1		2	20.19	odd	2
525.3.s.d.124.1		4	140.103	odd	12
525.3.s.d.124.2		4	140.47	odd	12
525.3.s.d.199.1		4	20.7	even	4
525.3.s.d.199.2		4	20.3	even	4
1008.3.cg.f.145.1		2	21.5	even	6
1008.3.cg.f.577.1		2	3.2	odd	2
2352.3.f.b.97.1		2	7.4	even	3
2352.3.f.b.97.2		2	7.3	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(3.50000 + 6.06218i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(3.50000 + 6.06218i) q^{7} +(1.50000 + 2.59808i) q^{9} +(5.00000 - 8.66025i) q^{11} +12.1244i q^{13} -6.00000 q^{15} +(-6.00000 - 3.46410i) q^{17} +(-28.5000 + 16.4545i) q^{19} +12.1244i q^{21} +(20.0000 + 34.6410i) q^{23} +(-6.50000 + 11.2583i) q^{25} +5.19615i q^{27} +16.0000 q^{29} +(-4.50000 - 2.59808i) q^{31} +(15.0000 - 8.66025i) q^{33} +(-21.0000 - 12.1244i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(-10.5000 + 18.1865i) q^{39} +24.2487i q^{41} +19.0000 q^{43} +(-9.00000 - 5.19615i) q^{45} +(45.0000 - 25.9808i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(16.0000 - 27.7128i) q^{53} +34.6410i q^{55} -57.0000 q^{57} +(-36.0000 - 20.7846i) q^{59} +(18.0000 - 10.3923i) q^{61} +(-10.5000 + 18.1865i) q^{63} +(-21.0000 - 36.3731i) q^{65} +(29.5000 - 51.0955i) q^{67} +69.2820i q^{69} +26.0000 q^{71} +(-16.5000 - 9.52628i) q^{73} +(-19.5000 + 11.2583i) q^{75} +70.0000 q^{77} +(23.5000 + 40.7032i) q^{79} +(-4.50000 + 7.79423i) q^{81} +24.2487i q^{83} +24.0000 q^{85} +(24.0000 + 13.8564i) q^{87} +(102.000 - 58.8897i) q^{89} +(-73.5000 + 42.4352i) q^{91} +(-4.50000 - 7.79423i) q^{93} +(57.0000 - 98.7269i) q^{95} -48.4974i q^{97} +30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 6 q^{5} + 7 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 6 * q^5 + 7 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 6 q^{5} + 7 q^{7} + 3 q^{9} + 10 q^{11} - 12 q^{15} - 12 q^{17} - 57 q^{19} + 40 q^{23} - 13 q^{25} + 32 q^{29} - 9 q^{31} + 30 q^{33} - 42 q^{35} - 5 q^{37} - 21 q^{39} + 38 q^{43} - 18 q^{45} + 90 q^{47} - 49 q^{49} - 12 q^{51} + 32 q^{53} - 114 q^{57} - 72 q^{59} + 36 q^{61} - 21 q^{63} - 42 q^{65} + 59 q^{67} + 52 q^{71} - 33 q^{73} - 39 q^{75} + 140 q^{77} + 47 q^{79} - 9 q^{81} + 48 q^{85} + 48 q^{87} + 204 q^{89} - 147 q^{91} - 9 q^{93} + 114 q^{95} + 60 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 6 * q^5 + 7 * q^7 + 3 * q^9 + 10 * q^11 - 12 * q^15 - 12 * q^17 - 57 * q^19 + 40 * q^23 - 13 * q^25 + 32 * q^29 - 9 * q^31 + 30 * q^33 - 42 * q^35 - 5 * q^37 - 21 * q^39 + 38 * q^43 - 18 * q^45 + 90 * q^47 - 49 * q^49 - 12 * q^51 + 32 * q^53 - 114 * q^57 - 72 * q^59 + 36 * q^61 - 21 * q^63 - 42 * q^65 + 59 * q^67 + 52 * q^71 - 33 * q^73 - 39 * q^75 + 140 * q^77 + 47 * q^79 - 9 * q^81 + 48 * q^85 + 48 * q^87 + 204 * q^89 - 147 * q^91 - 9 * q^93 + 114 * q^95 + 60 * q^99

Introduction

L-functions

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