LMFDB - Embedded newform 21.3.f.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,3,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$21 = 3 \cdot 7$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	21.f (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.572208555157$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.3.f.c.10.1

$q$ -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} +(-1.50000 + 0.866025i) q^{3} +(-3.00000 - 1.73205i) q^{5} +3.46410i q^{6} +(-3.50000 + 6.06218i) q^{7} +8.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-6.00000 + 3.46410i) q^{10} +(-5.00000 - 8.66025i) q^{11} -12.1244i q^{13} +(7.00000 + 12.1244i) q^{14} +6.00000 q^{15} +(8.00000 - 13.8564i) q^{16} +(-6.00000 + 3.46410i) q^{17} +(-3.00000 - 5.19615i) q^{18} +(28.5000 + 16.4545i) q^{19} -12.1244i q^{21} -20.0000 q^{22} +(-20.0000 + 34.6410i) q^{23} +(-12.0000 + 6.92820i) q^{24} +(-6.50000 - 11.2583i) q^{25} +(-21.0000 - 12.1244i) q^{26} +5.19615i q^{27} +16.0000 q^{29} +(6.00000 - 10.3923i) q^{30} +(4.50000 - 2.59808i) q^{31} +(15.0000 + 8.66025i) q^{33} +13.8564i q^{34} +(21.0000 - 12.1244i) q^{35} +(-2.50000 + 4.33013i) q^{37} +(57.0000 - 32.9090i) q^{38} +(10.5000 + 18.1865i) q^{39} +(-24.0000 - 13.8564i) q^{40} -24.2487i q^{41} +(-21.0000 - 12.1244i) q^{42} -19.0000 q^{43} +(-9.00000 + 5.19615i) q^{45} +(40.0000 + 69.2820i) q^{46} +(-45.0000 - 25.9808i) q^{47} +27.7128i q^{48} +(-24.5000 - 42.4352i) q^{49} -26.0000 q^{50} +(6.00000 - 10.3923i) q^{51} +(16.0000 + 27.7128i) q^{53} +(9.00000 + 5.19615i) q^{54} +34.6410i q^{55} +(-28.0000 + 48.4974i) q^{56} -57.0000 q^{57} +(16.0000 - 27.7128i) q^{58} +(36.0000 - 20.7846i) q^{59} +(18.0000 + 10.3923i) q^{61} -10.3923i q^{62} +(10.5000 + 18.1865i) q^{63} +64.0000 q^{64} +(-21.0000 + 36.3731i) q^{65} +(30.0000 - 17.3205i) q^{66} +(-29.5000 - 51.0955i) q^{67} -69.2820i q^{69} -48.4974i q^{70} -26.0000 q^{71} +(12.0000 - 20.7846i) q^{72} +(-16.5000 + 9.52628i) q^{73} +(5.00000 + 8.66025i) q^{74} +(19.5000 + 11.2583i) q^{75} +70.0000 q^{77} +42.0000 q^{78} +(-23.5000 + 40.7032i) q^{79} +(-48.0000 + 27.7128i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-42.0000 - 24.2487i) q^{82} +24.2487i q^{83} +24.0000 q^{85} +(-19.0000 + 32.9090i) q^{86} +(-24.0000 + 13.8564i) q^{87} +(-40.0000 - 69.2820i) q^{88} +(102.000 + 58.8897i) q^{89} +20.7846i q^{90} +(73.5000 + 42.4352i) q^{91} +(-4.50000 + 7.79423i) q^{93} +(-90.0000 + 51.9615i) q^{94} +(-57.0000 - 98.7269i) q^{95} +48.4974i q^{97} -98.0000 q^{98} -30.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + 2 q^{2} - 3 q^{3} - 6 q^{5} - 7 q^{7} + 16 q^{8} + 3 q^{9} - 12 q^{10} - 10 q^{11} + 14 q^{14} + 12 q^{15} + 16 q^{16} - 12 q^{17} - 6 q^{18} + 57 q^{19} - 40 q^{22} - 40 q^{23} - 24 q^{24} - 13 q^{25}+ \cdots - 60 q^{99}+O(q^{100})$ 2 * q + 2 * q^2 - 3 * q^3 - 6 * q^5 - 7 * q^7 + 16 * q^8 + 3 * q^9 - 12 * q^10 - 10 * q^11 + 14 * q^14 + 12 * q^15 + 16 * q^16 - 12 * q^17 - 6 * q^18 + 57 * q^19 - 40 * q^22 - 40 * q^23 - 24 * q^24 - 13 * q^25 - 42 * q^26 + 32 * q^29 + 12 * q^30 + 9 * q^31 + 30 * q^33 + 42 * q^35 - 5 * q^37 + 114 * q^38 + 21 * q^39 - 48 * q^40 - 42 * q^42 - 38 * q^43 - 18 * q^45 + 80 * q^46 - 90 * q^47 - 49 * q^49 - 52 * q^50 + 12 * q^51 + 32 * q^53 + 18 * q^54 - 56 * q^56 - 114 * q^57 + 32 * q^58 + 72 * q^59 + 36 * q^61 + 21 * q^63 + 128 * q^64 - 42 * q^65 + 60 * q^66 - 59 * q^67 - 52 * q^71 + 24 * q^72 - 33 * q^73 + 10 * q^74 + 39 * q^75 + 140 * q^77 + 84 * q^78 - 47 * q^79 - 96 * q^80 - 9 * q^81 - 84 * q^82 + 48 * q^85 - 38 * q^86 - 48 * q^87 - 80 * q^88 + 204 * q^89 + 147 * q^91 - 9 * q^93 - 180 * q^94 - 114 * q^95 - 196 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$ .

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	1.00000	−	1.73205i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	1.00000	−	1.73205i	0.500000	−	0.866025i	1.00000			$0$
$3$	−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	0.169042	−	0.985609i	$-0.445933\pi$
$5$	−3.00000	−	1.73205i	−0.600000	−	0.346410i	−0.769042	+	0.639199i	$0.779266\pi$
$6$			3.46410i			0.577350i
$7$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$7$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$8$	8.00000			1.00000
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−6.00000	+	3.46410i	−0.600000	+	0.346410i
$11$	−5.00000	−	8.66025i	−0.454545	−	0.787296i	0.544116	−	0.839010i	$-0.316865\pi$
$11$	−5.00000	−	8.66025i	−0.454545	−	0.787296i	−0.998662	+	0.0517139i	$0.983532\pi$
$12$		0			0
$13$		−	12.1244i		−	0.932643i	−0.884615	−	0.466321i	$-0.845579\pi$
$13$		−	12.1244i		−	0.932643i	0.884615	−	0.466321i	$-0.154421\pi$
$14$	7.00000	+	12.1244i	0.500000	+	0.866025i
$15$	6.00000			0.400000
$16$	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	$0.398653\pi$
$18$	−3.00000	−	5.19615i	−0.166667	−	0.288675i
$19$	28.5000	+	16.4545i	1.50000	+	0.866025i	1.00000			$0$
$19$	28.5000	+	16.4545i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$		−	12.1244i		−	0.577350i
$22$	−20.0000			−0.909091
$23$	−20.0000	+	34.6410i	−0.869565	+	1.50613i	−0.00712357	+	0.999975i	$0.502268\pi$
$23$	−20.0000	+	34.6410i	−0.869565	+	1.50613i	−0.862442	+	0.506157i	$0.831066\pi$
$24$	−12.0000	+	6.92820i	−0.500000	+	0.288675i
$25$	−6.50000	−	11.2583i	−0.260000	−	0.450333i
$26$	−21.0000	−	12.1244i	−0.807692	−	0.466321i
$27$			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	$0.411037\pi$
$30$	6.00000	−	10.3923i	0.200000	−	0.346410i
$31$	4.50000	−	2.59808i	0.145161	−	0.0838089i	−0.425660	−	0.904883i	$-0.639958\pi$
$31$	4.50000	−	2.59808i	0.145161	−	0.0838089i	0.570822	+	0.821074i	$0.306625\pi$
$32$		0			0
$33$	15.0000	+	8.66025i	0.454545	+	0.262432i
$34$			13.8564i			0.407541i
$35$	21.0000	−	12.1244i	0.600000	−	0.346410i
$36$		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
$39$	10.5000	+	18.1865i	0.269231	+	0.466321i
$40$	−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	$-0.0955582\pi$
$42$	−21.0000	−	12.1244i	−0.500000	−	0.288675i
$43$	−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
$45$	−9.00000	+	5.19615i	−0.200000	+	0.115470i
$46$	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	$0.853101\pi$
$48$			27.7128i			0.577350i
$49$	−24.5000	−	42.4352i	−0.500000	−	0.866025i
$50$	−26.0000			−0.520000
$51$	6.00000	−	10.3923i	0.117647	−	0.203771i
$52$		0			0
$53$	16.0000	+	27.7128i	0.301887	+	0.522883i	0.976563	−	0.215230i	$-0.0690502\pi$
$53$	16.0000	+	27.7128i	0.301887	+	0.522883i	−0.674677	+	0.738114i	$0.735717\pi$
$54$	9.00000	+	5.19615i	0.166667	+	0.0962250i
$55$			34.6410i			0.629837i
$56$	−28.0000	+	48.4974i	−0.500000	+	0.866025i
$57$	−57.0000			−1.00000
$58$	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	0.640231	−	0.768182i	$-0.278838\pi$
$61$	18.0000	+	10.3923i	0.295082	+	0.170366i	−0.345149	+	0.938548i	$0.612172\pi$
$62$		−	10.3923i		−	0.167618i
$63$	10.5000	+	18.1865i	0.166667	+	0.288675i
$64$	64.0000			1.00000
$65$	−21.0000	+	36.3731i	−0.323077	+	0.559586i
$66$	30.0000	−	17.3205i	0.454545	−	0.262432i
$67$	−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
$69$		−	69.2820i		−	1.00409i
$70$		−	48.4974i		−	0.692820i
$71$	−26.0000			−0.366197			−0.183099	−	0.983095i	$-0.558613\pi$
$71$	−26.0000			−0.366197			−0.183099	+	0.983095i	$0.558613\pi$
$72$	12.0000	−	20.7846i	0.166667	−	0.288675i
$73$	−16.5000	+	9.52628i	−0.226027	+	0.130497i	−0.608738	−	0.793371i	$-0.708324\pi$
$73$	−16.5000	+	9.52628i	−0.226027	+	0.130497i	0.382711	+	0.923868i	$0.374991\pi$
$74$	5.00000	+	8.66025i	0.0675676	+	0.117030i
$75$	19.5000	+	11.2583i	0.260000	+	0.150111i
$76$		0			0
$77$	70.0000			0.909091
$78$	42.0000			0.538462
$79$	−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
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−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
$87$	−24.0000	+	13.8564i	−0.275862	+	0.159269i
$88$	−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	$0.436509\pi$
$90$			20.7846i			0.230940i
$91$	73.5000	+	42.4352i	0.807692	+	0.466321i
$92$		0			0
$93$	−4.50000	+	7.79423i	−0.0483871	+	0.0838089i
$94$	−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	$0.0804263\pi$
$97$			48.4974i			0.499973i	−0.968249	+	0.249987i	$0.919574\pi$
$98$	−98.0000			−1.00000
$99$	−30.0000			−0.303030
$100$		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	$0.552133\pi$
$102$	−12.0000	−	20.7846i	−0.117647	−	0.203771i
$103$	7.50000	+	4.33013i	0.0728155	+	0.0420401i	0.535966	−	0.844240i	$-0.319948\pi$
$103$	7.50000	+	4.33013i	0.0728155	+	0.0420401i	−0.463150	+	0.886280i	$0.653281\pi$
$104$		−	96.9948i		−	0.932643i
$105$	−21.0000	+	36.3731i	−0.200000	+	0.346410i
$106$	64.0000			0.603774
$107$	106.000	−	183.597i	0.990654	−	1.71586i	0.377204	−	0.926130i	$-0.376886\pi$
$107$	106.000	−	183.597i	0.990654	−	1.71586i	0.613451	−	0.789733i	$-0.289781\pi$
$108$		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
$111$		−	8.66025i		−	0.0780203i
$112$	56.0000	+	96.9948i	0.500000	+	0.866025i
$113$	142.000			1.25664			0.628319	−	0.777956i	$-0.283743\pi$
$113$	142.000			1.25664			0.628319	+	0.777956i	$0.283743\pi$
$114$	−57.0000	+	98.7269i	−0.500000	+	0.866025i
$115$	120.000	−	69.2820i	1.04348	−	0.602452i
$116$		0			0
$117$	−31.5000	−	18.1865i	−0.269231	−	0.155440i
$118$		−	83.1384i		−	0.704563i
$119$		−	48.4974i		−	0.407541i
$120$	48.0000			0.400000
$121$	10.5000	−	18.1865i	0.0867769	−	0.150302i
$122$	36.0000	−	20.7846i	0.295082	−	0.170366i
$123$	21.0000	+	36.3731i	0.170732	+	0.295716i
$124$		0			0
$125$			131.636i			1.05309i
$126$	42.0000			0.333333
$127$	−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
$129$	28.5000	−	16.4545i	0.220930	−	0.127554i
$130$	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
$133$	−199.500	+	115.181i	−1.50000	+	0.866025i
$134$	−118.000			−0.880597
$135$	9.00000	−	15.5885i	0.0666667	−	0.115470i
$136$	−48.0000	+	27.7128i	−0.352941	+	0.203771i
$137$	58.0000	+	100.459i	0.423358	+	0.733277i	0.996265	−	0.0863428i	$-0.0275180\pi$
$137$	58.0000	+	100.459i	0.423358	+	0.733277i	−0.572908	+	0.819620i	$0.694185\pi$
$138$	−120.000	−	69.2820i	−0.869565	−	0.502044i
$139$		−	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
$142$	−26.0000	+	45.0333i	−0.183099	+	0.317136i
$143$	−105.000	+	60.6218i	−0.734266	+	0.423929i
$144$	−24.0000	−	41.5692i	−0.166667	−	0.288675i
$145$	−48.0000	−	27.7128i	−0.331034	−	0.191123i
$146$			38.1051i			0.260994i
$147$	73.5000	+	42.4352i	0.500000	+	0.288675i
$148$		0			0
$149$	−62.0000	+	107.387i	−0.416107	+	0.720719i	−0.995544	−	0.0942982i	$-0.969939\pi$
$149$	−62.0000	+	107.387i	−0.416107	+	0.720719i	0.579437	+	0.815017i	$0.303273\pi$
$150$	39.0000	−	22.5167i	0.260000	−	0.150111i
$151$	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
$153$			20.7846i			0.135847i
$154$	70.0000	−	121.244i	0.454545	−	0.787296i
$155$	−18.0000			−0.116129
$156$		0			0
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.114334	−	0.993442i	$-0.463527\pi$
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.917513	+	0.397705i	$0.130193\pi$
$158$	47.0000	+	81.4064i	0.297468	+	0.515230i
$159$	−48.0000	−	27.7128i	−0.301887	−	0.174294i
$160$		0			0
$161$	−140.000	−	242.487i	−0.869565	−	1.50613i
$162$	−18.0000			−0.111111
$163$	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
$165$	−30.0000	−	51.9615i	−0.181818	−	0.314918i
$166$	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	$0.705569\pi$
$168$		−	96.9948i		−	0.577350i
$169$	22.0000			0.130178
$170$	24.0000	−	41.5692i	0.141176	−	0.244525i
$171$	85.5000	−	49.3634i	0.500000	−	0.288675i
$172$		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	$0.784036\pi$
$174$			55.4256i			0.318538i
$175$	91.0000			0.520000
$176$	−160.000			−0.909091
$177$	−36.0000	+	62.3538i	−0.203390	+	0.352282i
$178$	204.000	−	117.779i	1.14607	−	0.661682i
$179$	−5.00000	−	8.66025i	−0.0279330	−	0.0483813i	0.851721	−	0.523996i	$-0.175559\pi$
$179$	−5.00000	−	8.66025i	−0.0279330	−	0.0483813i	−0.879654	+	0.475614i	$0.842226\pi$
$180$		0			0
$181$		−	327.358i		−	1.80861i	−0.426892	−	0.904303i	$-0.640391\pi$
$181$		−	327.358i		−	1.80861i	0.426892	−	0.904303i	$-0.359609\pi$
$182$	147.000	−	84.8705i	0.807692	−	0.466321i
$183$	−36.0000			−0.196721
$184$	−160.000	+	277.128i	−0.869565	+	1.50613i
$185$	15.0000	−	8.66025i	0.0810811	−	0.0468122i
$186$	9.00000	+	15.5885i	0.0483871	+	0.0838089i
$187$	60.0000	+	34.6410i	0.320856	+	0.185246i
$188$		0			0
$189$	−31.5000	−	18.1865i	−0.166667	−	0.0962250i
$190$	−228.000			−1.20000
$191$	1.00000	−	1.73205i	0.00523560	−	0.00906833i	−0.863396	−	0.504527i	$-0.831667\pi$
$191$	1.00000	−	1.73205i	0.00523560	−	0.00906833i	0.868631	+	0.495459i	$0.165000\pi$
$192$	−96.0000	+	55.4256i	−0.500000	+	0.288675i
$193$	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
$195$		−	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	$0.418317\pi$
$198$	−30.0000	+	51.9615i	−0.151515	+	0.262432i
$199$	−174.000	+	100.459i	−0.874372	+	0.504819i	−0.868799	−	0.495166i	$-0.835107\pi$
$199$	−174.000	+	100.459i	−0.874372	+	0.504819i	−0.00557327	+	0.999984i	$0.501774\pi$
$200$	−52.0000	−	90.0666i	−0.260000	−	0.450333i
$201$	88.5000	+	51.0955i	0.440299	+	0.254206i
$202$			256.344i			1.26903i
$203$	−56.0000	+	96.9948i	−0.275862	+	0.477807i
$204$		0			0
$205$	−42.0000	+	72.7461i	−0.204878	+	0.354859i
$206$	15.0000	−	8.66025i	0.0728155	−	0.0420401i
$207$	60.0000	+	103.923i	0.289855	+	0.502044i
$208$	−168.000	−	96.9948i	−0.807692	−	0.466321i
$209$		−	329.090i		−	1.57459i
$210$	42.0000	+	72.7461i	0.200000	+	0.346410i
$211$	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
$213$	39.0000	−	22.5167i	0.183099	−	0.105712i
$214$	−212.000	−	367.195i	−0.990654	−	1.71586i
$215$	57.0000	+	32.9090i	0.265116	+	0.153065i
$216$			41.5692i			0.192450i
$217$			36.3731i			0.167618i
$218$	−34.0000			−0.155963
$219$	16.5000	−	28.5788i	0.0753425	−	0.130497i
$220$		0			0
$221$	42.0000	+	72.7461i	0.190045	+	0.329168i
$222$	−15.0000	−	8.66025i	−0.0675676	−	0.0390102i
$223$			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
$226$	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	0.516286	−	0.856416i	$-0.327314\pi$
$229$	7.50000	+	4.33013i	0.0327511	+	0.0189089i	−0.483535	+	0.875325i	$0.660647\pi$
$230$		−	277.128i		−	1.20490i
$231$	−105.000	+	60.6218i	−0.454545	+	0.262432i
$232$	128.000			0.551724
$233$	85.0000	−	147.224i	0.364807	−	0.631864i	−0.623938	−	0.781474i	$-0.714468\pi$
$233$	85.0000	−	147.224i	0.364807	−	0.631864i	0.988745	+	0.149610i	$0.0478017\pi$
$234$	−63.0000	+	36.3731i	−0.269231	+	0.155440i
$235$	90.0000	+	155.885i	0.382979	+	0.663339i
$236$		0			0
$237$		−	81.4064i		−	0.343487i
$238$	−84.0000	−	48.4974i	−0.352941	−	0.203771i
$239$	142.000			0.594142			0.297071	−	0.954855i	$-0.403990\pi$
$239$	142.000			0.594142			0.297071	+	0.954855i	$0.403990\pi$
$240$	48.0000	−	83.1384i	0.200000	−	0.346410i
$241$	−132.000	+	76.2102i	−0.547718	+	0.316225i	−0.748201	−	0.663472i	$-0.769082\pi$
$241$	−132.000	+	76.2102i	−0.547718	+	0.316225i	0.200483	+	0.979697i	$0.435749\pi$
$242$	−21.0000	−	36.3731i	−0.0867769	−	0.150302i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$			169.741i			0.692820i
$246$	84.0000			0.341463
$247$	199.500	−	345.544i	0.807692	−	1.39896i
$248$	36.0000	−	20.7846i	0.145161	−	0.0838089i
$249$	−21.0000	−	36.3731i	−0.0843373	−	0.146077i
$250$	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
$255$	−36.0000	+	20.7846i	−0.141176	+	0.0815083i
$256$		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	$0.993673\pi$
$258$		−	65.8179i		−	0.255108i
$259$	−17.5000	−	30.3109i	−0.0675676	−	0.117030i
$260$		0			0
$261$	24.0000	−	41.5692i	0.0919540	−	0.159269i
$262$	−258.000	+	148.956i	−0.984733	+	0.568536i
$263$	−68.0000	−	117.779i	−0.258555	−	0.447831i	0.707300	−	0.706914i	$-0.249913\pi$
$263$	−68.0000	−	117.779i	−0.258555	−	0.447831i	−0.965855	+	0.259083i	$0.916580\pi$
$264$	120.000	+	69.2820i	0.454545	+	0.262432i
$265$		−	110.851i		−	0.418307i
$266$			460.726i			1.73205i
$267$	−204.000			−0.764045
$268$		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	$0.470786\pi$
$270$	−18.0000	−	31.1769i	−0.0666667	−	0.115470i
$271$	−318.000	−	183.597i	−1.17343	−	0.677481i	−0.218946	−	0.975737i	$-0.570262\pi$
$271$	−318.000	−	183.597i	−1.17343	−	0.677481i	−0.954486	+	0.298256i	$0.903595\pi$
$272$			110.851i			0.407541i
$273$	−147.000			−0.538462
$274$	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
$279$		−	15.5885i		−	0.0558726i
$280$	168.000	−	96.9948i	0.600000	−	0.346410i
$281$	100.000			0.355872			0.177936	−	0.984042i	$-0.443058\pi$
$281$	100.000			0.355872			0.177936	+	0.984042i	$0.443058\pi$
$282$	90.0000	−	155.885i	0.319149	−	0.552782i
$283$	−310.500	+	179.267i	−1.09717	+	0.633453i	−0.935477	−	0.353387i	$-0.885030\pi$
$283$	−310.500	+	179.267i	−1.09717	+	0.633453i	−0.161696	+	0.986841i	$0.551696\pi$
$284$		0			0
$285$	171.000	+	98.7269i	0.600000	+	0.346410i
$286$			242.487i			0.847857i
$287$	147.000	+	84.8705i	0.512195	+	0.295716i
$288$		0			0
$289$	−120.500	+	208.712i	−0.416955	+	0.722187i
$290$	−96.0000	+	55.4256i	−0.331034	+	0.191123i
$291$	−42.0000	−	72.7461i	−0.144330	−	0.249987i
$292$		0			0
$293$		−	242.487i		−	0.827601i	−0.910368	−	0.413801i	$-0.864201\pi$
$293$		−	242.487i		−	0.827601i	0.910368	−	0.413801i	$-0.135799\pi$
$294$	147.000	−	84.8705i	0.500000	−	0.288675i
$295$	−144.000			−0.488136
$296$	−20.0000	+	34.6410i	−0.0675676	+	0.117030i
$297$	45.0000	−	25.9808i	0.151515	−	0.0874773i
$298$	124.000	+	214.774i	0.416107	+	0.720719i
$299$	420.000	+	242.487i	1.40468	+	0.810994i
$300$		0			0
$301$	66.5000	−	115.181i	0.220930	−	0.382662i
$302$	92.0000			0.304636
$303$	111.000	−	192.258i	0.366337	−	0.634514i
$304$	456.000	−	263.272i	1.50000	−	0.866025i
$305$	−36.0000	−	62.3538i	−0.118033	−	0.204439i
$306$	36.0000	+	20.7846i	0.117647	+	0.0679236i
$307$		−	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
$310$	−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	$-0.0128629\pi$
$312$	84.0000	+	145.492i	0.269231	+	0.466321i
$313$	175.500	+	101.325i	0.560703	+	0.323722i	0.753428	−	0.657531i	$-0.228399\pi$
$313$	175.500	+	101.325i	0.560703	+	0.323722i	−0.192725	+	0.981253i	$0.561732\pi$
$314$		−	374.123i		−	1.19147i
$315$		−	72.7461i		−	0.230940i
$316$		0			0
$317$	−146.000	+	252.879i	−0.460568	+	0.797727i	−0.998989	−	0.0449488i	$-0.985688\pi$
$317$	−146.000	+	252.879i	−0.460568	+	0.797727i	0.538421	+	0.842676i	$0.319021\pi$
$318$	−96.0000	+	55.4256i	−0.301887	+	0.174294i
$319$	−80.0000	−	138.564i	−0.250784	−	0.434370i
$320$	−192.000	−	110.851i	−0.600000	−	0.346410i
$321$			367.195i			1.14391i
$322$	−560.000			−1.73913
$323$	−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
$327$	25.5000	+	14.7224i	0.0779817	+	0.0450227i
$328$		−	193.990i		−	0.591432i
$329$	315.000	−	181.865i	0.957447	−	0.552782i
$330$	−120.000			−0.363636
$331$	−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
$333$	7.50000	+	12.9904i	0.0225225	+	0.0390102i
$334$	462.000	+	266.736i	1.38323	+	0.798610i
$335$			204.382i			0.610096i
$336$	−168.000	−	96.9948i	−0.500000	−	0.288675i
$337$	−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
$339$	−213.000	+	122.976i	−0.628319	+	0.362760i
$340$		0			0
$341$	−45.0000	−	25.9808i	−0.131965	−	0.0761899i
$342$		−	197.454i		−	0.577350i
$343$	343.000			1.00000
$344$	−152.000			−0.441860
$345$	−120.000	+	207.846i	−0.347826	+	0.602452i
$346$	−216.000	+	124.708i	−0.624277	+	0.360427i
$347$	−110.000	−	190.526i	−0.317003	−	0.549065i	0.662858	−	0.748745i	$-0.269343\pi$
$347$	−110.000	−	190.526i	−0.317003	−	0.549065i	−0.979861	+	0.199680i	$0.936010\pi$
$348$		0			0
$349$			339.482i			0.972728i	0.873756	+	0.486364i	$0.161677\pi$
$349$			339.482i			0.972728i	−0.873756	+	0.486364i	$0.838323\pi$
$350$	91.0000	−	157.617i	0.260000	−	0.450333i
$351$	63.0000			0.179487
$352$		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	$0.189483\pi$
$354$	72.0000	+	124.708i	0.203390	+	0.352282i
$355$	78.0000	+	45.0333i	0.219718	+	0.126854i
$356$		0			0
$357$	42.0000	+	72.7461i	0.117647	+	0.203771i
$358$	−20.0000			−0.0558659
$359$	−146.000	+	252.879i	−0.406685	+	0.704399i	−0.994516	−	0.104584i	$-0.966649\pi$
$359$	−146.000	+	252.879i	−0.406685	+	0.704399i	0.587831	+	0.808984i	$0.299982\pi$
$360$	−72.0000	+	41.5692i	−0.200000	+	0.115470i
$361$	361.000	+	625.270i	1.00000	+	1.73205i
$362$	−567.000	−	327.358i	−1.56630	−	0.904303i
$363$			36.3731i			0.100201i
$364$		0			0
$365$	66.0000			0.180822
$366$	−36.0000	+	62.3538i	−0.0983607	+	0.170366i
$367$	466.500	−	269.334i	1.27112	−	0.733880i	0.295919	−	0.955213i	$-0.404374\pi$
$367$	466.500	−	269.334i	1.27112	−	0.733880i	0.975198	+	0.221333i	$0.0710408\pi$
$368$	320.000	+	554.256i	0.869565	+	1.50613i
$369$	−63.0000	−	36.3731i	−0.170732	−	0.0985720i
$370$		−	34.6410i		−	0.0936244i
$371$	−224.000			−0.603774
$372$		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
$375$	−114.000	−	197.454i	−0.304000	−	0.526543i
$376$	−360.000	−	207.846i	−0.957447	−	0.552782i
$377$		−	193.990i		−	0.514562i
$378$	−63.0000	+	36.3731i	−0.166667	+	0.0962250i
$379$	−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
$381$	217.500	−	125.574i	0.570866	−	0.329590i
$382$	−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	$0.698388\pi$
$384$			221.703i			0.577350i
$385$	−210.000	−	121.244i	−0.545455	−	0.314918i
$386$	470.000			1.21762
$387$	−28.5000	+	49.3634i	−0.0736434	+	0.127554i
$388$		0			0
$389$	37.0000	+	64.0859i	0.0951157	+	0.164745i	0.909657	−	0.415361i	$-0.136345\pi$
$389$	37.0000	+	64.0859i	0.0951157	+	0.164745i	−0.814541	+	0.580106i	$0.803011\pi$
$390$	−126.000	−	72.7461i	−0.323077	−	0.186529i
$391$		−	277.128i		−	0.708768i
$392$	−196.000	−	339.482i	−0.500000	−	0.866025i
$393$	258.000			0.656489
$394$	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	0.809782	−	0.586731i	$-0.199585\pi$
$397$	280.500	+	161.947i	0.706549	+	0.407926i	−0.103233	+	0.994657i	$0.532919\pi$
$398$			401.836i			1.00964i
$399$	199.500	−	345.544i	0.500000	−	0.866025i
$400$	−208.000			−0.520000
$401$	64.0000	−	110.851i	0.159601	−	0.276437i	−0.775124	−	0.631809i	$-0.782313\pi$
$401$	64.0000	−	110.851i	0.159601	−	0.276437i	0.934725	+	0.355372i	$0.115646\pi$
$402$	177.000	−	102.191i	0.440299	−	0.254206i
$403$	−31.5000	−	54.5596i	−0.0781638	−	0.135384i
$404$		0			0
$405$			31.1769i			0.0769800i
$406$	112.000	+	193.990i	0.275862	+	0.477807i
$407$	50.0000			0.122850
$408$	48.0000	−	83.1384i	0.117647	−	0.203771i
$409$	256.500	−	148.090i	0.627139	−	0.362079i	−0.152504	−	0.988303i	$-0.548734\pi$
$409$	256.500	−	148.090i	0.627139	−	0.362079i	0.779643	+	0.626224i	$0.215400\pi$
$410$	84.0000	+	145.492i	0.204878	+	0.354859i
$411$	−174.000	−	100.459i	−0.423358	−	0.244426i
$412$		0			0
$413$			290.985i			0.704563i
$414$	240.000			0.579710
$415$	42.0000	−	72.7461i	0.101205	−	0.175292i
$416$		0			0
$417$	73.5000	+	127.306i	0.176259	+	0.305290i
$418$	−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
$423$	−135.000	+	77.9423i	−0.319149	+	0.184261i
$424$	128.000	+	221.703i	0.301887	+	0.522883i
$425$	78.0000	+	45.0333i	0.183529	+	0.105961i
$426$		−	90.0666i		−	0.211424i
$427$	−126.000	+	72.7461i	−0.295082	+	0.170366i
$428$		0			0
$429$	105.000	−	181.865i	0.244755	−	0.423929i
$430$	114.000	−	65.8179i	0.265116	−	0.153065i
$431$	−131.000	−	226.899i	−0.303944	−	0.526447i	0.673081	−	0.739568i	$-0.264970\pi$
$431$	−131.000	−	226.899i	−0.303944	−	0.526447i	−0.977026	+	0.213121i	$0.931637\pi$
$432$	72.0000	+	41.5692i	0.166667	+	0.0962250i
$433$			36.3731i			0.0840025i	0.999118	+	0.0420012i	$0.0133733\pi$
$433$			36.3731i			0.0840025i	−0.999118	+	0.0420012i	$0.986627\pi$
$434$	63.0000	+	36.3731i	0.145161	+	0.0838089i
$435$	96.0000			0.220690
$436$		0			0
$437$	−1140.00	+	658.179i	−2.60870	+	1.50613i
$438$	−33.0000	−	57.1577i	−0.0753425	−	0.130497i
$439$	270.000	+	155.885i	0.615034	+	0.355090i	0.774933	−	0.632043i	$-0.217784\pi$
$439$	270.000	+	155.885i	0.615034	+	0.355090i	−0.159899	+	0.987133i	$0.551117\pi$
$440$			277.128i			0.629837i
$441$	−147.000			−0.333333
$442$	168.000			0.380090
$443$	106.000	−	183.597i	0.239278	−	0.414441i	−0.721230	−	0.692696i	$-0.756423\pi$
$443$	106.000	−	183.597i	0.239278	−	0.414441i	0.960507	+	0.278255i	$0.0897561\pi$
$444$		0			0
$445$	−204.000	−	353.338i	−0.458427	−	0.794019i
$446$	588.000	+	339.482i	1.31839	+	0.761170i
$447$		−	214.774i		−	0.480479i
$448$	−224.000	+	387.979i	−0.500000	+	0.866025i
$449$	−782.000			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$449$	−782.000			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$450$	−39.0000	+	67.5500i	−0.0866667	+	0.150111i
$451$	−210.000	+	121.244i	−0.465632	+	0.268833i
$452$		0			0
$453$	−69.0000	−	39.8372i	−0.152318	−	0.0879408i
$454$		−	325.626i		−	0.717237i
$455$	−147.000	−	254.611i	−0.323077	−	0.559586i
$456$	−456.000			−1.00000
$457$	−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
$459$	−18.0000	−	31.1769i	−0.0392157	−	0.0679236i
$460$		0			0
$461$		−	484.974i		−	1.05200i	−0.850483	−	0.526002i	$-0.823690\pi$
$461$		−	484.974i		−	1.05200i	0.850483	−	0.526002i	$-0.176310\pi$
$462$			242.487i			0.524864i
$463$	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
$465$	27.0000	−	15.5885i	0.0580645	−	0.0335236i
$466$	−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
$469$	413.000			0.880597
$470$	360.000			0.765957
$471$	−162.000	+	280.592i	−0.343949	+	0.595737i
$472$	288.000	−	166.277i	0.610169	−	0.352282i
$473$	95.0000	+	164.545i	0.200846	+	0.347875i
$474$	−141.000	−	81.4064i	−0.297468	−	0.171743i
$475$		−	427.817i		−	0.900666i
$476$		0			0
$477$	96.0000			0.201258
$478$	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
$483$	420.000	+	242.487i	0.869565	+	0.502044i
$484$		0			0
$485$	84.0000	−	145.492i	0.173196	−	0.299984i
$486$	27.0000	−	15.5885i	0.0555556	−	0.0320750i
$487$	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
$489$			100.459i			0.205438i
$490$	294.000	+	169.741i	0.600000	+	0.346410i
$491$	−68.0000			−0.138493			−0.0692464	−	0.997600i	$-0.522059\pi$
$491$	−68.0000			−0.138493			−0.0692464	+	0.997600i	$0.522059\pi$
$492$		0			0
$493$	−96.0000	+	55.4256i	−0.194726	+	0.112425i
$494$	−399.000	−	691.088i	−0.807692	−	1.39896i
$495$	90.0000	+	51.9615i	0.181818	+	0.104973i
$496$		−	83.1384i		−	0.167618i
$497$	91.0000	−	157.617i	0.183099	−	0.317136i
$498$	−84.0000			−0.168675
$499$	−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
$501$	−231.000	−	400.104i	−0.461078	−	0.798610i
$502$	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	$-0.225571\pi$
$504$	84.0000	+	145.492i	0.166667	+	0.288675i
$505$	444.000			0.879208
$506$	400.000	−	692.820i	0.790514	−	1.36921i
$507$	−33.0000	+	19.0526i	−0.0650888	+	0.0375790i
$508$		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	$0.340766\pi$
$510$			83.1384i			0.163017i
$511$		−	133.368i		−	0.260994i
$512$	512.000			1.00000
$513$	−85.5000	+	148.090i	−0.166667	+	0.288675i
$514$	−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
$518$	−70.0000			−0.135135
$519$	216.000			0.416185
$520$	−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	$0.198082\pi$
$522$	−48.0000	−	83.1384i	−0.0919540	−	0.159269i
$523$	−853.500	−	492.768i	−1.63193	−	0.942196i	−0.983497	−	0.180925i	$-0.942091\pi$
$523$	−853.500	−	492.768i	−1.63193	−	0.942196i	−0.648434	−	0.761271i	$-0.724576\pi$
$524$		0			0
$525$	−136.500	+	78.8083i	−0.260000	+	0.150111i
$526$	−272.000			−0.517110
$527$	−18.0000	+	31.1769i	−0.0341556	+	0.0591592i
$528$	240.000	−	138.564i	0.454545	−	0.262432i
$529$	−535.500	−	927.513i	−1.01229	−	1.75333i
$530$	−192.000	−	110.851i	−0.362264	−	0.209153i
$531$		−	124.708i		−	0.234854i
$532$		0			0
$533$	−294.000			−0.551595
$534$	−204.000	+	353.338i	−0.382022	+	0.661682i
$535$	−636.000	+	367.195i	−1.18879	+	0.686345i
$536$	−236.000	−	408.764i	−0.440299	−	0.762619i
$537$	15.0000	+	8.66025i	0.0279330	+	0.0161271i
$538$			450.333i			0.837051i
$539$	−245.000	+	424.352i	−0.454545	+	0.787296i
$540$		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
$543$	283.500	+	491.036i	0.522099	+	0.904303i
$544$		0			0
$545$			58.8897i			0.108055i
$546$	−147.000	+	254.611i	−0.269231	+	0.466321i
$547$	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
$549$	54.0000	−	31.1769i	0.0983607	−	0.0567886i
$550$	130.000	+	225.167i	0.236364	+	0.409394i
$551$	456.000	+	263.272i	0.827586	+	0.477807i
$552$		−	554.256i		−	1.00409i
$553$	−164.500	−	284.922i	−0.297468	−	0.515230i
$554$	−790.000			−1.42599
$555$	−15.0000	+	25.9808i	−0.0270270	+	0.0468122i
$556$		0			0
$557$	331.000	+	573.309i	0.594255	+	1.02928i	0.993652	+	0.112502i	$0.0358863\pi$
$557$	331.000	+	573.309i	0.594255	+	1.02928i	−0.399397	+	0.916778i	$0.630780\pi$
$558$	−27.0000	−	15.5885i	−0.0483871	−	0.0279363i
$559$			230.363i			0.412098i
$560$		−	387.979i		−	0.692820i
$561$	−120.000			−0.213904
$562$	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
$567$	63.0000			0.111111
$568$	−208.000			−0.366197
$569$	379.000	−	656.447i	0.666081	−	1.15369i	−0.312910	−	0.949783i	$-0.601304\pi$
$569$	379.000	−	656.447i	0.666081	−	1.15369i	0.978991	−	0.203903i	$-0.0653628\pi$
$570$	342.000	−	197.454i	0.600000	−	0.346410i
$571$	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
$573$			3.46410i			0.00604555i
$574$	294.000	−	169.741i	0.512195	−	0.295716i
$575$	520.000			0.904348
$576$	96.0000	−	166.277i	0.166667	−	0.288675i
$577$	928.500	−	536.070i	1.60919	−	0.929064i	0.619633	−	0.784892i	$-0.287282\pi$
$577$	928.500	−	536.070i	1.60919	−	0.929064i	0.989553	−	0.144172i	$-0.0460518\pi$
$578$	241.000	+	417.424i	0.416955	+	0.722187i
$579$	−352.500	−	203.516i	−0.608808	−	0.351496i
$580$		0			0
$581$	−147.000	−	84.8705i	−0.253012	−	0.146077i
$582$	−168.000			−0.288660
$583$	160.000	−	277.128i	0.274443	−	0.475348i
$584$	−132.000	+	76.2102i	−0.226027	+	0.130497i
$585$	63.0000	+	109.119i	0.107692	+	0.186529i
$586$	−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
$591$	−150.000	+	86.6025i	−0.253807	+	0.146536i
$592$	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	$0.733160\pi$
$594$		−	103.923i		−	0.174955i
$595$	−84.0000	+	145.492i	−0.141176	+	0.244525i
$596$		0			0
$597$	174.000	−	301.377i	0.291457	−	0.504819i
$598$	840.000	−	484.974i	1.40468	−	0.810994i
$599$	142.000	+	245.951i	0.237062	+	0.410603i	0.959870	−	0.280446i	$-0.0904823\pi$
$599$	142.000	+	245.951i	0.237062	+	0.410603i	−0.722808	+	0.691049i	$0.757149\pi$
$600$	156.000	+	90.0666i	0.260000	+	0.150111i
$601$			594.093i			0.988508i	0.869317	+	0.494254i	$0.164559\pi$
$601$			594.093i			0.988508i	−0.869317	+	0.494254i	$0.835441\pi$
$602$	−133.000	−	230.363i	−0.220930	−	0.382662i
$603$	−177.000			−0.293532
$604$		0			0
$605$	−63.0000	+	36.3731i	−0.104132	+	0.0601208i
$606$	−222.000	−	384.515i	−0.366337	−	0.634514i
$607$	7.50000	+	4.33013i	0.0123558	+	0.00713365i	0.506165	−	0.862437i	$-0.331063\pi$
$607$	7.50000	+	4.33013i	0.0123558	+	0.00713365i	−0.493809	+	0.869570i	$0.664396\pi$
$608$		0			0
$609$		−	193.990i		−	0.318538i
$610$	−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
$615$		−	145.492i		−	0.236573i
$616$	560.000			0.909091
$617$	−194.000			−0.314425			−0.157212	−	0.987565i	$-0.550251\pi$
$617$	−194.000			−0.314425			−0.157212	+	0.987565i	$0.550251\pi$
$618$	−15.0000	+	25.9808i	−0.0242718	+	0.0420401i
$619$	529.500	−	305.707i	0.855412	−	0.493872i	−0.00706124	−	0.999975i	$-0.502248\pi$
$619$	529.500	−	305.707i	0.855412	−	0.493872i	0.862473	+	0.506103i	$0.168914\pi$
$620$		0			0
$621$	−180.000	−	103.923i	−0.289855	−	0.167348i
$622$		−	1101.58i		−	1.77104i
$623$	−714.000	+	412.228i	−1.14607	+	0.661682i
$624$	336.000			0.538462
$625$	65.5000	−	113.449i	0.104800	−	0.181519i
$626$	351.000	−	202.650i	0.560703	−	0.323722i
$627$	285.000	+	493.634i	0.454545	+	0.787296i
$628$		0			0
$629$		−	34.6410i		−	0.0550732i
$630$	−126.000	−	72.7461i	−0.200000	−	0.115470i
$631$	−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
$633$	−3.00000	+	1.73205i	−0.00473934	+	0.00273626i
$634$	292.000	+	505.759i	0.460568	+	0.797727i
$635$	435.000	+	251.147i	0.685039	+	0.395508i
$636$		0			0
$637$	−514.500	+	297.047i	−0.807692	+	0.466321i
$638$	−320.000			−0.501567
$639$	−39.0000	+	67.5500i	−0.0610329	+	0.105712i
$640$	−384.000	+	221.703i	−0.600000	+	0.346410i
$641$	562.000	+	973.413i	0.876755	+	1.51858i	0.854881	+	0.518824i	$0.173630\pi$
$641$	562.000	+	973.413i	0.876755	+	1.51858i	0.0218737	+	0.999761i	$0.493037\pi$
$642$	636.000	+	367.195i	0.990654	+	0.571954i
$643$			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
$646$	−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	$0.0171070\pi$
$648$	−36.0000	−	62.3538i	−0.0555556	−	0.0962250i
$649$	−360.000	−	207.846i	−0.554700	−	0.320256i
$650$			315.233i			0.484974i
$651$	−31.5000	−	54.5596i	−0.0483871	−	0.0838089i
$652$		0			0
$653$	505.000	−	874.686i	0.773354	−	1.33949i	−0.162361	−	0.986731i	$-0.551911\pi$
$653$	505.000	−	874.686i	0.773354	−	1.33949i	0.935715	−	0.352757i	$-0.114756\pi$
$654$	51.0000	−	29.4449i	0.0779817	−	0.0450227i
$655$	258.000	+	446.869i	0.393893	+	0.682243i
$656$	−336.000	−	193.990i	−0.512195	−	0.295716i
$657$			57.1577i			0.0869980i
$658$		−	727.461i		−	1.10556i
$659$	−908.000			−1.37785			−0.688923	−	0.724835i	$-0.741916\pi$
$659$	−908.000			−1.37785			−0.688923	+	0.724835i	$0.741916\pi$
$660$		0			0
$661$	−625.500	+	361.133i	−0.946293	+	0.546343i	−0.891928	−	0.452178i	$-0.850647\pi$
$661$	−625.500	+	361.133i	−0.946293	+	0.546343i	−0.0543659	+	0.998521i	$0.517314\pi$
$662$	5.00000	+	8.66025i	0.00755287	+	0.0130820i
$663$	−126.000	−	72.7461i	−0.190045	−	0.109723i
$664$			193.990i			0.292153i
$665$	798.000			1.20000
$666$	30.0000			0.0450450
$667$	−320.000	+	554.256i	−0.479760	+	0.830969i
$668$		0			0
$669$	−294.000	−	509.223i	−0.439462	−	0.761170i
$670$	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
$675$	58.5000	−	33.7750i	0.0866667	−	0.0500370i
$676$		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	$0.802698\pi$
$678$			491.902i			0.725520i
$679$	−294.000	−	169.741i	−0.432990	−	0.249987i
$680$	192.000			0.282353
$681$	−141.000	+	244.219i	−0.207048	+	0.358618i
$682$	−90.0000	+	51.9615i	−0.131965	+	0.0761899i
$683$	−488.000	−	845.241i	−0.714495	−	1.23754i	−0.963154	−	0.268950i	$-0.913323\pi$
$683$	−488.000	−	845.241i	−0.714495	−	1.23754i	0.248659	−	0.968591i	$-0.420010\pi$
$684$		0			0
$685$		−	401.836i		−	0.586622i
$686$	343.000	−	594.093i	0.500000	−	0.866025i
$687$	−15.0000			−0.0218341
$688$	−152.000	+	263.272i	−0.220930	+	0.382662i
$689$	336.000	−	193.990i	0.487663	−	0.281553i
$690$	240.000	+	415.692i	0.347826	+	0.602452i
$691$	490.500	+	283.190i	0.709841	+	0.409827i	0.811002	−	0.585043i	$-0.198922\pi$
$691$	490.500	+	283.190i	0.709841	+	0.409827i	−0.101161	+	0.994870i	$0.532256\pi$
$692$		0			0
$693$	105.000	−	181.865i	0.151515	−	0.262432i
$694$	−440.000			−0.634006
$695$	−147.000	+	254.611i	−0.211511	+	0.366347i
$696$	−192.000	+	110.851i	−0.275862	+	0.159269i
$697$	84.0000	+	145.492i	0.120516	+	0.208741i
$698$	588.000	+	339.482i	0.842407	+	0.486364i
$699$			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	$0.419218\pi$
$702$	63.0000	−	109.119i	0.0897436	−	0.155440i
$703$	−142.500	+	82.2724i	−0.202703	+	0.117030i
$704$	−320.000	−	554.256i	−0.454545	−	0.787296i
$705$	−270.000	−	155.885i	−0.382979	−	0.221113i
$706$		−	616.610i		−	0.873385i
$707$		−	897.202i		−	1.26903i
$708$		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
$711$	70.5000	+	122.110i	0.0991561	+	0.171743i
$712$	816.000	+	471.118i	1.14607	+	0.661682i
$713$			207.846i			0.291509i
$714$	168.000			0.235294
$715$	420.000			0.587413
$716$		0			0
$717$	−213.000	+	122.976i	−0.297071	+	0.171514i
$718$	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	$0.903353\pi$
$720$			166.277i			0.230940i
$721$	−52.5000	+	30.3109i	−0.0728155	+	0.0420401i
$722$	1444.00			2.00000
$723$	132.000	−	228.631i	0.182573	−	0.316225i
$724$		0			0
$725$	−104.000	−	180.133i	−0.143448	−	0.248460i
$726$	63.0000	+	36.3731i	0.0867769	+	0.0501006i
$727$		−	206.114i		−	0.283513i	−0.989902	−	0.141757i	$-0.954725\pi$
$727$		−	206.114i		−	0.283513i	0.989902	−	0.141757i	$-0.0452750\pi$
$728$	588.000	+	339.482i	0.807692	+	0.466321i
$729$	−27.0000			−0.0370370
$730$	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	0.999482	−	0.0321842i	$-0.0102463\pi$
$733$	1078.50	+	622.672i	1.47135	+	0.849485i	0.471869	+	0.881669i	$0.343580\pi$
$734$		−	1077.34i		−	1.46776i
$735$	−147.000	−	254.611i	−0.200000	−	0.346410i
$736$		0			0
$737$	−295.000	+	510.955i	−0.400271	+	0.693290i
$738$	−126.000	+	72.7461i	−0.170732	+	0.0985720i
$739$	−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
$741$			691.088i			0.932643i
$742$	−224.000	+	387.979i	−0.301887	+	0.522883i
$743$	394.000			0.530283			0.265141	−	0.964210i	$-0.414581\pi$
$743$	394.000			0.530283			0.265141	+	0.964210i	$0.414581\pi$
$744$	−36.0000	+	62.3538i	−0.0483871	+	0.0838089i
$745$	372.000	−	214.774i	0.499329	−	0.288288i
$746$	−205.000	−	355.070i	−0.274799	−	0.475966i
$747$	63.0000	+	36.3731i	0.0843373	+	0.0486922i
$748$		0			0
$749$	742.000	+	1285.18i	0.990654	+	1.71586i
$750$	−456.000			−0.608000
$751$	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
$753$	−252.000	−	436.477i	−0.334661	−	0.579650i
$754$	−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
$759$	−600.000	+	346.410i	−0.790514	+	0.456403i
$760$	−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	$0.881009\pi$
$762$		−	502.295i		−	0.659179i
$763$	119.000			0.155963
$764$		0			0
$765$	36.0000	−	62.3538i	0.0470588	−	0.0815083i
$766$	−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	$0.189086\pi$
$769$			860.829i			1.11941i	−0.828691	+	0.559707i	$0.810914\pi$
$770$	−420.000	+	242.487i	−0.545455	+	0.314918i
$771$	762.000			0.988327
$772$		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	$0.379859\pi$
$774$	57.0000	+	98.7269i	0.0736434	+	0.127554i
$775$	−58.5000	−	33.7750i	−0.0754839	−	0.0435806i
$776$			387.979i			0.499973i
$777$	52.5000	+	30.3109i	0.0675676	+	0.0390102i
$778$	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
$783$			83.1384i			0.106179i
$784$	−784.000			−1.00000
$785$	−648.000			−0.825478
$786$	258.000	−	446.869i	0.328244	−	0.568536i
$787$	−216.000	+	124.708i	−0.274460	+	0.158460i	−0.630913	−	0.775854i	$-0.717319\pi$
$787$	−216.000	+	124.708i	−0.274460	+	0.158460i	0.356453	+	0.934313i	$0.383986\pi$
$788$		0			0
$789$	204.000	+	117.779i	0.258555	+	0.149277i
$790$		−	325.626i		−	0.412184i
$791$	−497.000	+	860.829i	−0.628319	+	1.08828i
$792$	−240.000			−0.303030
$793$	126.000	−	218.238i	0.158890	−	0.275206i
$794$	561.000	−	323.894i	0.706549	−	0.407926i
$795$	96.0000	+	166.277i	0.120755	+	0.209153i
$796$		0			0
$797$			1357.93i			1.70380i	0.523705	+	0.851900i	$0.324549\pi$
$797$			1357.93i			1.70380i	−0.523705	+	0.851900i	$0.675451\pi$
$798$	−399.000	−	691.088i	−0.500000	−	0.866025i
$799$	360.000			0.450563
$800$		0			0
$801$	306.000	−	176.669i	0.382022	−	0.220561i
$802$	−128.000	−	221.703i	−0.159601	−	0.276437i
$803$	165.000	+	95.2628i	0.205479	+	0.118634i
$804$		0			0
$805$			969.948i			1.20490i
$806$	−126.000			−0.156328
$807$	195.000	−	337.750i	0.241636	−	0.418525i
$808$	−888.000	+	512.687i	−1.09901	+	0.634514i
$809$	709.000	+	1228.02i	0.876391	+	1.51795i	0.855274	+	0.518176i	$0.173389\pi$
$809$	709.000	+	1228.02i	0.876391	+	1.51795i	0.0211166	+	0.999777i	$0.493278\pi$
$810$	54.0000	+	31.1769i	0.0666667	+	0.0384900i
$811$		−	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
$814$	50.0000	−	86.6025i	0.0614251	−	0.106391i
$815$	−174.000	+	100.459i	−0.213497	+	0.123263i
$816$	−96.0000	−	166.277i	−0.117647	−	0.203771i
$817$	−541.500	−	312.635i	−0.662791	−	0.382662i
$818$		−	592.361i		−	0.724158i
$819$	220.500	−	127.306i	0.269231	−	0.155440i
$820$		0			0
$821$	−125.000	+	216.506i	−0.152253	+	0.263711i	−0.932056	−	0.362315i	$-0.881986\pi$
$821$	−125.000	+	216.506i	−0.152253	+	0.263711i	0.779802	+	0.626026i	$0.215320\pi$
$822$	−348.000	+	200.918i	−0.423358	+	0.244426i
$823$	−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
$825$		−	225.167i		−	0.272929i
$826$	504.000	+	290.985i	0.610169	+	0.352282i
$827$	1234.00			1.49214			0.746070	−	0.665867i	$-0.231938\pi$
$827$	1234.00			1.49214			0.746070	+	0.665867i	$0.231938\pi$
$828$		0			0
$829$	298.500	−	172.339i	0.360072	−	0.207888i	−0.309040	−	0.951049i	$-0.600008\pi$
$829$	298.500	−	172.339i	0.360072	−	0.207888i	0.669113	+	0.743161i	$0.266674\pi$
$830$	−84.0000	−	145.492i	−0.101205	−	0.175292i
$831$	592.500	+	342.080i	0.712996	+	0.411649i
$832$		−	775.959i		−	0.932643i
$833$	294.000	+	169.741i	0.352941	+	0.203771i
$834$	294.000			0.352518
$835$	462.000	−	800.207i	0.553293	−	0.958332i
$836$		0			0
$837$	13.5000	+	23.3827i	0.0161290	+	0.0279363i
$838$	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	$-0.0933291\pi$
$840$	−168.000	+	290.985i	−0.200000	+	0.346410i
$841$	−585.000			−0.695600
$842$	107.000	−	185.329i	0.127078	−	0.220106i
$843$	−150.000	+	86.6025i	−0.177936	+	0.102731i
$844$		0			0
$845$	−66.0000	−	38.1051i	−0.0781065	−	0.0450948i
$846$			311.769i			0.368521i
$847$	73.5000	+	127.306i	0.0867769	+	0.150302i
$848$	512.000			0.603774
$849$	310.500	−	537.802i	0.365724	−	0.633453i
$850$	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	$-0.947735\pi$
$853$		−	278.860i		−	0.326917i	0.986550	−	0.163458i	$-0.0522650\pi$
$854$			290.985i			0.340731i
$855$	−342.000			−0.400000
$856$	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	$0.454619\pi$
$858$	−210.000	−	363.731i	−0.244755	−	0.423929i
$859$	−528.000	−	304.841i	−0.614668	−	0.354879i	0.160122	−	0.987097i	$-0.448811\pi$
$859$	−528.000	−	304.841i	−0.614668	−	0.354879i	−0.774790	+	0.632218i	$0.782145\pi$
$860$		0			0
$861$	−294.000			−0.341463
$862$	−524.000			−0.607889
$863$	−335.000	+	580.237i	−0.388181	+	0.672349i	−0.992205	−	0.124617i	$-0.960230\pi$
$863$	−335.000	+	580.237i	−0.388181	+	0.672349i	0.604024	+	0.796966i	$0.293563\pi$
$864$		0			0
$865$	216.000	+	374.123i	0.249711	+	0.432512i
$866$	63.0000	+	36.3731i	0.0727483	+	0.0420012i
$867$		−	417.424i		−	0.481458i
$868$		0			0
$869$	470.000			0.540852
$870$	96.0000	−	166.277i	0.110345	−	0.191123i
$871$	−619.500	+	357.668i	−0.711251	+	0.410641i
$872$	−68.0000	−	117.779i	−0.0779817	−	0.135068i
$873$	126.000	+	72.7461i	0.144330	+	0.0833289i
$874$			2632.72i			3.01226i
$875$	−798.000	−	460.726i	−0.912000	−	0.526543i
$876$		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
$879$	210.000	+	363.731i	0.238908	+	0.413801i
$880$	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	$-0.229689\pi$
$882$	−147.000	+	254.611i	−0.166667	+	0.288675i
$883$	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
$885$	216.000	−	124.708i	0.244068	−	0.140913i
$886$	−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	$0.801844\pi$
$888$		−	69.2820i		−	0.0780203i
$889$	507.500	−	879.016i	0.570866	−	0.988769i
$890$	−816.000			−0.916854
$891$	−45.0000	+	77.9423i	−0.0505051	+	0.0874773i
$892$		0			0
$893$	−855.000	−	1480.90i	−0.957447	−	1.65835i
$894$	−372.000	−	214.774i	−0.416107	−	0.240240i
$895$			34.6410i			0.0387050i
$896$	448.000	+	775.959i	0.500000	+	0.866025i
$897$	−840.000			−0.936455
$898$	−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
$903$			230.363i			0.255108i
$904$	1136.00			1.25664
$905$	−567.000	+	982.073i	−0.626519	+	1.08516i
$906$	−138.000	+	79.6743i	−0.152318	+	0.0879408i
$907$	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
$909$			384.515i			0.423009i
$910$	−588.000			−0.646154
$911$	−740.000			−0.812294			−0.406147	−	0.913808i	$-0.633128\pi$
$911$	−740.000			−0.812294			−0.406147	+	0.913808i	$0.633128\pi$
$912$	−456.000	+	789.815i	−0.500000	+	0.866025i
$913$	210.000	−	121.244i	0.230011	−	0.132797i
$914$	677.000	+	1172.60i	0.740700	+	1.28293i
$915$	108.000	+	62.3538i	0.118033	+	0.0681463i
$916$		0			0
$917$	903.000	−	521.347i	0.984733	−	0.568536i
$918$	−72.0000			−0.0784314
$919$	−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
$921$	157.500	+	272.798i	0.171010	+	0.296198i
$922$	−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
$927$	22.5000	−	12.9904i	0.0242718	−	0.0140134i
$928$		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	$0.462438\pi$
$930$		−	62.3538i		−	0.0670471i
$931$		−	1612.54i		−	1.73205i
$932$		0			0
$933$	−477.000	+	826.188i	−0.511254	+	0.885518i
$934$	78.0000	−	45.0333i	0.0835118	−	0.0482155i
$935$	−120.000	−	207.846i	−0.128342	−	0.222295i
$936$	−252.000	−	145.492i	−0.269231	−	0.155440i
$937$			836.581i			0.892829i	0.894826	+	0.446414i	$0.147299\pi$
$937$			836.581i			0.892829i	−0.894826	+	0.446414i	$0.852701\pi$
$938$	413.000	−	715.337i	0.440299	−	0.762619i
$939$	−351.000			−0.373802
$940$		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	$0.400626\pi$
$942$	324.000	+	561.184i	0.343949	+	0.595737i
$943$	840.000	+	484.974i	0.890774	+	0.514289i
$944$		−	665.108i		−	0.704563i
$945$	63.0000	+	109.119i	0.0666667	+	0.115470i
$946$	380.000			0.401691
$947$	169.000	−	292.717i	0.178458	−	0.309099i	−0.762894	−	0.646523i	$-0.776222\pi$
$947$	169.000	−	292.717i	0.178458	−	0.309099i	0.941353	+	0.337424i	$0.109556\pi$
$948$		0			0
$949$	115.500	+	200.052i	0.121707	+	0.210803i
$950$	−741.000	−	427.817i	−0.780000	−	0.450333i
$951$		−	505.759i		−	0.531818i
$952$		−	387.979i		−	0.407541i
$953$	−1244.00			−1.30535			−0.652676	−	0.757637i	$-0.726354\pi$
$953$	−1244.00			−1.30535			−0.652676	+	0.757637i	$0.726354\pi$
$954$	96.0000	−	166.277i	0.100629	−	0.174294i
$955$	−6.00000	+	3.46410i	−0.00628272	+	0.00362733i
$956$		0			0
$957$	240.000	+	138.564i	0.250784	+	0.144790i
$958$			110.851i			0.115711i
$959$	−812.000			−0.846715
$960$	384.000			0.400000
$961$	−467.000	+	808.868i	−0.485952	+	0.841694i
$962$	105.000	−	60.6218i	0.109148	−	0.0630164i
$963$	−318.000	−	550.792i	−0.330218	−	0.571954i
$964$		0			0
$965$		−	814.064i		−	0.843590i
$966$	840.000	−	484.974i	0.869565	−	0.502044i
$967$	−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
$969$	342.000	−	197.454i	0.352941	−	0.203771i
$970$	−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
$973$	514.500	+	297.047i	0.528777	+	0.305290i
$974$	134.000			0.137577
$975$	136.500	−	236.425i	0.140000	−	0.242487i
$976$	288.000	−	166.277i	0.295082	−	0.170366i
$977$	−131.000	−	226.899i	−0.134084	−	0.232240i	0.791163	−	0.611605i	$-0.209476\pi$
$977$	−131.000	−	226.899i	−0.134084	−	0.232240i	−0.925247	+	0.379365i	$0.876143\pi$
$978$	174.000	+	100.459i	0.177914	+	0.102719i
$979$		−	1177.79i		−	1.20306i
$980$		0			0
$981$	−51.0000			−0.0519878
$982$	−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	$0.142656\pi$
$984$	168.000	+	290.985i	0.170732	+	0.295716i
$985$	−300.000	−	173.205i	−0.304569	−	0.175843i
$986$			221.703i			0.224850i
$987$	−315.000	+	545.596i	−0.319149	+	0.552782i
$988$		0			0
$989$	380.000	−	658.179i	0.384226	−	0.665500i
$990$	180.000	−	103.923i	0.181818	−	0.104973i
$991$	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
$993$		−	8.66025i		−	0.00872130i
$994$	−182.000	−	315.233i	−0.183099	−	0.317136i
$995$	696.000			0.699497
$996$		0			0
$997$	−856.500	+	494.501i	−0.859077	+	0.495988i	−0.863703	−	0.504001i	$-0.831861\pi$
$997$	−856.500	+	494.501i	−0.859077	+	0.495988i	0.00462594	+	0.999989i	$0.498528\pi$
$998$	509.000	+	881.614i	0.510020	+	0.883381i
$999$	−22.5000	−	12.9904i	−0.0225225	−	0.0130034i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.3.f.c.19.1	yes	2
3.2	odd	2		63.3.m.a.19.1		2
4.3	odd	2		336.3.bh.c.145.1		2
5.2	odd	4		525.3.s.d.124.2		4
5.3	odd	4		525.3.s.d.124.1		4
5.4	even	2		525.3.o.b.376.1		2
7.2	even	3		147.3.d.a.97.1		2
7.3	odd	6	inner	21.3.f.c.10.1	✓	2
7.4	even	3		147.3.f.e.31.1		2
7.5	odd	6		147.3.d.a.97.2		2
7.6	odd	2		147.3.f.e.19.1		2
12.11	even	2		1008.3.cg.f.145.1		2
21.2	odd	6		441.3.d.d.244.1		2
21.5	even	6		441.3.d.d.244.2		2
21.11	odd	6		441.3.m.b.325.1		2
21.17	even	6		63.3.m.a.10.1		2
21.20	even	2		441.3.m.b.19.1		2
28.3	even	6		336.3.bh.c.241.1		2
28.19	even	6		2352.3.f.b.97.1		2
28.23	odd	6		2352.3.f.b.97.2		2
35.3	even	12		525.3.s.d.199.2		4
35.17	even	12		525.3.s.d.199.1		4
35.24	odd	6		525.3.o.b.451.1		2
84.59	odd	6		1008.3.cg.f.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.c.10.1	✓	2	7.3	odd	6	inner
21.3.f.c.19.1	yes	2	1.1	even	1	trivial
63.3.m.a.10.1		2	21.17	even	6
63.3.m.a.19.1		2	3.2	odd	2
147.3.d.a.97.1		2	7.2	even	3
147.3.d.a.97.2		2	7.5	odd	6
147.3.f.e.19.1		2	7.6	odd	2
147.3.f.e.31.1		2	7.4	even	3
336.3.bh.c.145.1		2	4.3	odd	2
336.3.bh.c.241.1		2	28.3	even	6
441.3.d.d.244.1		2	21.2	odd	6
441.3.d.d.244.2		2	21.5	even	6
441.3.m.b.19.1		2	21.20	even	2
441.3.m.b.325.1		2	21.11	odd	6
525.3.o.b.376.1		2	5.4	even	2
525.3.o.b.451.1		2	35.24	odd	6
525.3.s.d.124.1		4	5.3	odd	4
525.3.s.d.124.2		4	5.2	odd	4
525.3.s.d.199.1		4	35.17	even	12
525.3.s.d.199.2		4	35.3	even	12
1008.3.cg.f.145.1		2	12.11	even	2
1008.3.cg.f.577.1		2	84.59	odd	6
2352.3.f.b.97.1		2	28.19	even	6
2352.3.f.b.97.2		2	28.23	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	21.3.f.c.19.1

Level	$21$
Weight	$3$
Character	21.19
Analytic conductor	$0.572$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$