LMFDB - Embedded newform 60.3.f.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("60.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	60.19
Dual form			60.3.f.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} -1.73205 q^{3} +(2.00000 - 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 - 1.73205i) q^{6} +10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} -1.73205 q^{3} +(2.00000 - 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 - 1.73205i) q^{6} +10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +(5.00000 + 8.66025i) q^{10} -10.3923i q^{11} +(-3.46410 + 6.00000i) q^{12} -18.0000i q^{13} +(-18.0000 + 10.3923i) q^{14} +8.66025i q^{15} +(-8.00000 - 13.8564i) q^{16} +10.0000i q^{17} +(-5.19615 + 3.00000i) q^{18} +13.8564i q^{19} +(-17.3205 - 10.0000i) q^{20} -18.0000 q^{21} +(10.3923 + 18.0000i) q^{22} -6.92820 q^{23} -13.8564i q^{24} -25.0000 q^{25} +(18.0000 + 31.1769i) q^{26} -5.19615 q^{27} +(20.7846 - 36.0000i) q^{28} +36.0000 q^{29} +(-8.66025 - 15.0000i) q^{30} +6.92820i q^{31} +(27.7128 + 16.0000i) q^{32} +18.0000i q^{33} +(-10.0000 - 17.3205i) q^{34} -51.9615i q^{35} +(6.00000 - 10.3923i) q^{36} +54.0000i q^{37} +(-13.8564 - 24.0000i) q^{38} +31.1769i q^{39} +40.0000 q^{40} +18.0000 q^{41} +(31.1769 - 18.0000i) q^{42} -20.7846 q^{43} +(-36.0000 - 20.7846i) q^{44} -15.0000i q^{45} +(12.0000 - 6.92820i) q^{46} +(13.8564 + 24.0000i) q^{48} +59.0000 q^{49} +(43.3013 - 25.0000i) q^{50} -17.3205i q^{51} +(-62.3538 - 36.0000i) q^{52} +26.0000i q^{53} +(9.00000 - 5.19615i) q^{54} -51.9615 q^{55} +83.1384i q^{56} -24.0000i q^{57} +(-62.3538 + 36.0000i) q^{58} -31.1769i q^{59} +(30.0000 + 17.3205i) q^{60} -74.0000 q^{61} +(-6.92820 - 12.0000i) q^{62} +31.1769 q^{63} -64.0000 q^{64} -90.0000 q^{65} +(-18.0000 - 31.1769i) q^{66} +41.5692 q^{67} +(34.6410 + 20.0000i) q^{68} +12.0000 q^{69} +(51.9615 + 90.0000i) q^{70} +103.923i q^{71} +24.0000i q^{72} -36.0000i q^{73} +(-54.0000 - 93.5307i) q^{74} +43.3013 q^{75} +(48.0000 + 27.7128i) q^{76} -108.000i q^{77} +(-31.1769 - 54.0000i) q^{78} +90.0666i q^{79} +(-69.2820 + 40.0000i) q^{80} +9.00000 q^{81} +(-31.1769 + 18.0000i) q^{82} +90.0666 q^{83} +(-36.0000 + 62.3538i) q^{84} +50.0000 q^{85} +(36.0000 - 20.7846i) q^{86} -62.3538 q^{87} +83.1384 q^{88} +18.0000 q^{89} +(15.0000 + 25.9808i) q^{90} -187.061i q^{91} +(-13.8564 + 24.0000i) q^{92} -12.0000i q^{93} +69.2820 q^{95} +(-48.0000 - 27.7128i) q^{96} -72.0000i q^{97} +(-102.191 + 59.0000i) q^{98} -31.1769i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 + 12 * q^6 + 12 * q^9	$ 4 q + 8 q^{4} + 12 q^{6} + 12 q^{9} + 20 q^{10} - 72 q^{14} - 32 q^{16} - 72 q^{21} - 100 q^{25} + 72 q^{26} + 144 q^{29} - 40 q^{34} + 24 q^{36} + 160 q^{40} + 72 q^{41} - 144 q^{44} + 48 q^{46} + 236 q^{49} + 36 q^{54} + 120 q^{60} - 296 q^{61} - 256 q^{64} - 360 q^{65} - 72 q^{66} + 48 q^{69} - 216 q^{74} + 192 q^{76} + 36 q^{81} - 144 q^{84} + 200 q^{85} + 144 q^{86} + 72 q^{89} + 60 q^{90} - 192 q^{96}+O(q^{100}) $ 4 * q + 8 * q^4 + 12 * q^6 + 12 * q^9 + 20 * q^10 - 72 * q^14 - 32 * q^16 - 72 * q^21 - 100 * q^25 + 72 * q^26 + 144 * q^29 - 40 * q^34 + 24 * q^36 + 160 * q^40 + 72 * q^41 - 144 * q^44 + 48 * q^46 + 236 * q^49 + 36 * q^54 + 120 * q^60 - 296 * q^61 - 256 * q^64 - 360 * q^65 - 72 * q^66 + 48 * q^69 - 216 * q^74 + 192 * q^76 + 36 * q^81 - 144 * q^84 + 200 * q^85 + 144 * q^86 + 72 * q^89 + 60 * q^90 - 192 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$2$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	2.00000	−	3.46410i	0.500000	−	0.866025i
$5$		−	5.00000i		−	1.00000i
$5$		−	5.00000i		−	1.00000i
$6$	3.00000	−	1.73205i	0.500000	−	0.288675i
$7$	10.3923			1.48461			0.742307	−	0.670059i	$-0.233731\pi$
$7$	10.3923			1.48461			0.742307	+	0.670059i	$0.233731\pi$
$8$			8.00000i			1.00000i
$9$	3.00000			0.333333
$10$	5.00000	+	8.66025i	0.500000	+	0.866025i
$11$		−	10.3923i		−	0.944755i	−0.881396	−	0.472377i	$-0.843396\pi$
$11$		−	10.3923i		−	0.944755i	0.881396	−	0.472377i	$-0.156604\pi$
$12$	−3.46410	+	6.00000i	−0.288675	+	0.500000i
$13$		−	18.0000i		−	1.38462i	−0.721602	−	0.692308i	$-0.756594\pi$
$13$		−	18.0000i		−	1.38462i	0.721602	−	0.692308i	$-0.243406\pi$
$14$	−18.0000	+	10.3923i	−1.28571	+	0.742307i
$15$			8.66025i			0.577350i
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$			10.0000i			0.588235i	0.955769	+	0.294118i	$0.0950258\pi$
$17$			10.0000i			0.588235i	−0.955769	+	0.294118i	$0.904974\pi$
$18$	−5.19615	+	3.00000i	−0.288675	+	0.166667i
$19$			13.8564i			0.729285i	0.931148	+	0.364642i	$0.118809\pi$
$19$			13.8564i			0.729285i	−0.931148	+	0.364642i	$0.881191\pi$
$20$	−17.3205	−	10.0000i	−0.866025	−	0.500000i
$21$	−18.0000			−0.857143
$22$	10.3923	+	18.0000i	0.472377	+	0.818182i
$23$	−6.92820			−0.301226			−0.150613	−	0.988593i	$-0.548125\pi$
$23$	−6.92820			−0.301226			−0.150613	+	0.988593i	$0.548125\pi$
$24$		−	13.8564i		−	0.577350i
$25$	−25.0000			−1.00000
$26$	18.0000	+	31.1769i	0.692308	+	1.19911i
$27$	−5.19615			−0.192450
$28$	20.7846	−	36.0000i	0.742307	−	1.28571i
$29$	36.0000			1.24138			0.620690	−	0.784056i	$-0.286853\pi$
$29$	36.0000			1.24138			0.620690	+	0.784056i	$0.286853\pi$
$30$	−8.66025	−	15.0000i	−0.288675	−	0.500000i
$31$			6.92820i			0.223490i	0.993737	+	0.111745i	$0.0356441\pi$
$31$			6.92820i			0.223490i	−0.993737	+	0.111745i	$0.964356\pi$
$32$	27.7128	+	16.0000i	0.866025	+	0.500000i
$33$			18.0000i			0.545455i
$34$	−10.0000	−	17.3205i	−0.294118	−	0.509427i
$35$		−	51.9615i		−	1.48461i
$36$	6.00000	−	10.3923i	0.166667	−	0.288675i
$37$			54.0000i			1.45946i	0.683736	+	0.729730i	$0.260354\pi$
$37$			54.0000i			1.45946i	−0.683736	+	0.729730i	$0.739646\pi$
$38$	−13.8564	−	24.0000i	−0.364642	−	0.631579i
$39$			31.1769i			0.799408i
$40$	40.0000			1.00000
$41$	18.0000			0.439024			0.219512	−	0.975610i	$-0.429553\pi$
$41$	18.0000			0.439024			0.219512	+	0.975610i	$0.429553\pi$
$42$	31.1769	−	18.0000i	0.742307	−	0.428571i
$43$	−20.7846			−0.483363			−0.241682	−	0.970356i	$-0.577699\pi$
$43$	−20.7846			−0.483363			−0.241682	+	0.970356i	$0.577699\pi$
$44$	−36.0000	−	20.7846i	−0.818182	−	0.472377i
$45$		−	15.0000i		−	0.333333i
$46$	12.0000	−	6.92820i	0.260870	−	0.150613i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	13.8564	+	24.0000i	0.288675	+	0.500000i
$49$	59.0000			1.20408
$50$	43.3013	−	25.0000i	0.866025	−	0.500000i
$51$		−	17.3205i		−	0.339618i
$52$	−62.3538	−	36.0000i	−1.19911	−	0.692308i
$53$			26.0000i			0.490566i	0.969452	+	0.245283i	$0.0788809\pi$
$53$			26.0000i			0.490566i	−0.969452	+	0.245283i	$0.921119\pi$
$54$	9.00000	−	5.19615i	0.166667	−	0.0962250i
$55$	−51.9615			−0.944755
$56$			83.1384i			1.48461i
$57$		−	24.0000i		−	0.421053i
$58$	−62.3538	+	36.0000i	−1.07507	+	0.620690i
$59$		−	31.1769i		−	0.528422i	−0.964465	−	0.264211i	$-0.914888\pi$
$59$		−	31.1769i		−	0.528422i	0.964465	−	0.264211i	$-0.0851116\pi$
$60$	30.0000	+	17.3205i	0.500000	+	0.288675i
$61$	−74.0000			−1.21311			−0.606557	−	0.795040i	$-0.707450\pi$
$61$	−74.0000			−1.21311			−0.606557	+	0.795040i	$0.707450\pi$
$62$	−6.92820	−	12.0000i	−0.111745	−	0.193548i
$63$	31.1769			0.494872
$64$	−64.0000			−1.00000
$65$	−90.0000			−1.38462
$66$	−18.0000	−	31.1769i	−0.272727	−	0.472377i
$67$	41.5692			0.620436			0.310218	−	0.950665i	$-0.399598\pi$
$67$	41.5692			0.620436			0.310218	+	0.950665i	$0.399598\pi$
$68$	34.6410	+	20.0000i	0.509427	+	0.294118i
$69$	12.0000			0.173913
$70$	51.9615	+	90.0000i	0.742307	+	1.28571i
$71$			103.923i			1.46370i	0.681463	+	0.731852i	$0.261344\pi$
$71$			103.923i			1.46370i	−0.681463	+	0.731852i	$0.738656\pi$
$72$			24.0000i			0.333333i
$73$		−	36.0000i		−	0.493151i	−0.969124	−	0.246575i	$-0.920695\pi$
$73$		−	36.0000i		−	0.493151i	0.969124	−	0.246575i	$-0.0793053\pi$
$74$	−54.0000	−	93.5307i	−0.729730	−	1.26393i
$75$	43.3013			0.577350
$76$	48.0000	+	27.7128i	0.631579	+	0.364642i
$77$		−	108.000i		−	1.40260i
$78$	−31.1769	−	54.0000i	−0.399704	−	0.692308i
$79$			90.0666i			1.14008i	0.821616	+	0.570042i	$0.193073\pi$
$79$			90.0666i			1.14008i	−0.821616	+	0.570042i	$0.806927\pi$
$80$	−69.2820	+	40.0000i	−0.866025	+	0.500000i
$81$	9.00000			0.111111
$82$	−31.1769	+	18.0000i	−0.380206	+	0.219512i
$83$	90.0666			1.08514			0.542570	−	0.840011i	$-0.317451\pi$
$83$	90.0666			1.08514			0.542570	+	0.840011i	$0.317451\pi$
$84$	−36.0000	+	62.3538i	−0.428571	+	0.742307i
$85$	50.0000			0.588235
$86$	36.0000	−	20.7846i	0.418605	−	0.241682i
$87$	−62.3538			−0.716711
$88$	83.1384			0.944755
$89$	18.0000			0.202247			0.101124	−	0.994874i	$-0.467756\pi$
$89$	18.0000			0.202247			0.101124	+	0.994874i	$0.467756\pi$
$90$	15.0000	+	25.9808i	0.166667	+	0.288675i
$91$		−	187.061i		−	2.05562i
$92$	−13.8564	+	24.0000i	−0.150613	+	0.260870i
$93$		−	12.0000i		−	0.129032i
$94$		0			0
$95$	69.2820			0.729285
$96$	−48.0000	−	27.7128i	−0.500000	−	0.288675i
$97$		−	72.0000i		−	0.742268i	−0.928579	−	0.371134i	$-0.878969\pi$
$97$		−	72.0000i		−	0.742268i	0.928579	−	0.371134i	$-0.121031\pi$
$98$	−102.191	+	59.0000i	−1.04277	+	0.602041i
$99$		−	31.1769i		−	0.314918i
$100$	−50.0000	+	86.6025i	−0.500000	+	0.866025i
$101$	36.0000			0.356436			0.178218	−	0.983991i	$-0.442967\pi$
$101$	36.0000			0.356436			0.178218	+	0.983991i	$0.442967\pi$
$102$	17.3205	+	30.0000i	0.169809	+	0.294118i
$103$	−10.3923			−0.100896			−0.0504481	−	0.998727i	$-0.516065\pi$
$103$	−10.3923			−0.100896			−0.0504481	+	0.998727i	$0.516065\pi$
$104$	144.000			1.38462
$105$			90.0000i			0.857143i
$106$	−26.0000	−	45.0333i	−0.245283	−	0.424843i
$107$	−187.061			−1.74824			−0.874119	−	0.485712i	$-0.838561\pi$
$107$	−187.061			−1.74824			−0.874119	+	0.485712i	$0.838561\pi$
$108$	−10.3923	+	18.0000i	−0.0962250	+	0.166667i
$109$	26.0000			0.238532			0.119266	−	0.992862i	$-0.461946\pi$
$109$	26.0000			0.238532			0.119266	+	0.992862i	$0.461946\pi$
$110$	90.0000	−	51.9615i	0.818182	−	0.472377i
$111$		−	93.5307i		−	0.842619i
$112$	−83.1384	−	144.000i	−0.742307	−	1.28571i
$113$			10.0000i			0.0884956i	0.999021	+	0.0442478i	$0.0140891\pi$
$113$			10.0000i			0.0884956i	−0.999021	+	0.0442478i	$0.985911\pi$
$114$	24.0000	+	41.5692i	0.210526	+	0.364642i
$115$			34.6410i			0.301226i
$116$	72.0000	−	124.708i	0.620690	−	1.07507i
$117$		−	54.0000i		−	0.461538i
$118$	31.1769	+	54.0000i	0.264211	+	0.457627i
$119$			103.923i			0.873303i
$120$	−69.2820			−0.577350
$121$	13.0000			0.107438
$122$	128.172	−	74.0000i	1.05059	−	0.606557i
$123$	−31.1769			−0.253471
$124$	24.0000	+	13.8564i	0.193548	+	0.111745i
$125$			125.000i			1.00000i
$126$	−54.0000	+	31.1769i	−0.428571	+	0.247436i
$127$	218.238			1.71841			0.859206	−	0.511629i	$-0.170958\pi$
$127$	218.238			1.71841			0.859206	+	0.511629i	$0.170958\pi$
$128$	110.851	−	64.0000i	0.866025	−	0.500000i
$129$	36.0000			0.279070
$130$	155.885	−	90.0000i	1.19911	−	0.692308i
$131$			135.100i			1.03130i	0.856800	+	0.515649i	$0.172449\pi$
$131$			135.100i			1.03130i	−0.856800	+	0.515649i	$0.827551\pi$
$132$	62.3538	+	36.0000i	0.472377	+	0.272727i
$133$			144.000i			1.08271i
$134$	−72.0000	+	41.5692i	−0.537313	+	0.310218i
$135$			25.9808i			0.192450i
$136$	−80.0000			−0.588235
$137$			110.000i			0.802920i	0.915877	+	0.401460i	$0.131497\pi$
$137$			110.000i			0.802920i	−0.915877	+	0.401460i	$0.868503\pi$
$138$	−20.7846	+	12.0000i	−0.150613	+	0.0869565i
$139$		−	187.061i		−	1.34577i	−0.739749	−	0.672883i	$-0.765056\pi$
$139$		−	187.061i		−	1.34577i	0.739749	−	0.672883i	$-0.234944\pi$
$140$	−180.000	−	103.923i	−1.28571	−	0.742307i
$141$		0			0
$142$	−103.923	−	180.000i	−0.731852	−	1.26761i
$143$	−187.061			−1.30812
$144$	−24.0000	−	41.5692i	−0.166667	−	0.288675i
$145$		−	180.000i		−	1.24138i
$146$	36.0000	+	62.3538i	0.246575	+	0.427081i
$147$	−102.191			−0.695177
$148$	187.061	+	108.000i	1.26393	+	0.729730i
$149$	−288.000			−1.93289			−0.966443	−	0.256881i	$-0.917305\pi$
$149$	−288.000			−1.93289			−0.966443	+	0.256881i	$0.917305\pi$
$150$	−75.0000	+	43.3013i	−0.500000	+	0.288675i
$151$			187.061i			1.23882i	0.785069	+	0.619409i	$0.212628\pi$
$151$			187.061i			1.23882i	−0.785069	+	0.619409i	$0.787372\pi$
$152$	−110.851			−0.729285
$153$			30.0000i			0.196078i
$154$	108.000	+	187.061i	0.701299	+	1.21468i
$155$	34.6410			0.223490
$156$	108.000	+	62.3538i	0.692308	+	0.399704i
$157$			234.000i			1.49045i	0.666815	+	0.745223i	$0.267657\pi$
$157$			234.000i			1.49045i	−0.666815	+	0.745223i	$0.732343\pi$
$158$	−90.0666	−	156.000i	−0.570042	−	0.987342i
$159$		−	45.0333i		−	0.283228i
$160$	80.0000	−	138.564i	0.500000	−	0.866025i
$161$	−72.0000			−0.447205
$162$	−15.5885	+	9.00000i	−0.0962250	+	0.0555556i
$163$	−124.708			−0.765078			−0.382539	−	0.923939i	$-0.624950\pi$
$163$	−124.708			−0.765078			−0.382539	+	0.923939i	$0.624950\pi$
$164$	36.0000	−	62.3538i	0.219512	−	0.380206i
$165$	90.0000			0.545455
$166$	−156.000	+	90.0666i	−0.939759	+	0.542570i
$167$	131.636			0.788239			0.394119	−	0.919059i	$-0.371050\pi$
$167$	131.636			0.788239			0.394119	+	0.919059i	$0.371050\pi$
$168$		−	144.000i		−	0.857143i
$169$	−155.000			−0.917160
$170$	−86.6025	+	50.0000i	−0.509427	+	0.294118i
$171$			41.5692i			0.243095i
$172$	−41.5692	+	72.0000i	−0.241682	+	0.418605i
$173$		−	146.000i		−	0.843931i	−0.906612	−	0.421965i	$-0.861340\pi$
$173$		−	146.000i		−	0.843931i	0.906612	−	0.421965i	$-0.138660\pi$
$174$	108.000	−	62.3538i	0.620690	−	0.358355i
$175$	−259.808			−1.48461
$176$	−144.000	+	83.1384i	−0.818182	+	0.472377i
$177$			54.0000i			0.305085i
$178$	−31.1769	+	18.0000i	−0.175151	+	0.101124i
$179$		−	72.7461i		−	0.406403i	−0.979137	−	0.203201i	$-0.934865\pi$
$179$		−	72.7461i		−	0.406403i	0.979137	−	0.203201i	$-0.0651346\pi$
$180$	−51.9615	−	30.0000i	−0.288675	−	0.166667i
$181$	262.000			1.44751			0.723757	−	0.690055i	$-0.242414\pi$
$181$	262.000			1.44751			0.723757	+	0.690055i	$0.242414\pi$
$182$	187.061	+	324.000i	1.02781	+	1.78022i
$183$	128.172			0.700392
$184$		−	55.4256i		−	0.301226i
$185$	270.000			1.45946
$186$	12.0000	+	20.7846i	0.0645161	+	0.111745i
$187$	103.923			0.555738
$188$		0			0
$189$	−54.0000			−0.285714
$190$	−120.000	+	69.2820i	−0.631579	+	0.364642i
$191$		−	187.061i		−	0.979380i	−0.871897	−	0.489690i	$-0.837110\pi$
$191$		−	187.061i		−	0.979380i	0.871897	−	0.489690i	$-0.162890\pi$
$192$	110.851			0.577350
$193$		−	180.000i		−	0.932642i	−0.884615	−	0.466321i	$-0.845579\pi$
$193$		−	180.000i		−	0.932642i	0.884615	−	0.466321i	$-0.154421\pi$
$194$	72.0000	+	124.708i	0.371134	+	0.642823i
$195$	155.885			0.799408
$196$	118.000	−	204.382i	0.602041	−	1.04277i
$197$		−	154.000i		−	0.781726i	−0.920449	−	0.390863i	$-0.872177\pi$
$197$		−	154.000i		−	0.781726i	0.920449	−	0.390863i	$-0.127823\pi$
$198$	31.1769	+	54.0000i	0.157459	+	0.272727i
$199$		−	187.061i		−	0.940007i	−0.882664	−	0.470004i	$-0.844253\pi$
$199$		−	187.061i		−	0.940007i	0.882664	−	0.470004i	$-0.155747\pi$
$200$		−	200.000i		−	1.00000i
$201$	−72.0000			−0.358209
$202$	−62.3538	+	36.0000i	−0.308682	+	0.178218i
$203$	374.123			1.84297
$204$	−60.0000	−	34.6410i	−0.294118	−	0.169809i
$205$		−	90.0000i		−	0.439024i
$206$	18.0000	−	10.3923i	0.0873786	−	0.0504481i
$207$	−20.7846			−0.100409
$208$	−249.415	+	144.000i	−1.19911	+	0.692308i
$209$	144.000			0.688995
$210$	−90.0000	−	155.885i	−0.428571	−	0.742307i
$211$			242.487i			1.14923i	0.818425	+	0.574614i	$0.194848\pi$
$211$			242.487i			1.14923i	−0.818425	+	0.574614i	$0.805152\pi$
$212$	90.0666	+	52.0000i	0.424843	+	0.245283i
$213$		−	180.000i		−	0.845070i
$214$	324.000	−	187.061i	1.51402	−	0.874119i
$215$			103.923i			0.483363i
$216$		−	41.5692i		−	0.192450i
$217$			72.0000i			0.331797i
$218$	−45.0333	+	26.0000i	−0.206575	+	0.119266i
$219$			62.3538i			0.284721i
$220$	−103.923	+	180.000i	−0.472377	+	0.818182i
$221$	180.000			0.814480
$222$	93.5307	+	162.000i	0.421310	+	0.729730i
$223$	−93.5307			−0.419420			−0.209710	−	0.977764i	$-0.567252\pi$
$223$	−93.5307			−0.419420			−0.209710	+	0.977764i	$0.567252\pi$
$224$	288.000	+	166.277i	1.28571	+	0.742307i
$225$	−75.0000			−0.333333
$226$	−10.0000	−	17.3205i	−0.0442478	−	0.0766394i
$227$	−214.774			−0.946142			−0.473071	−	0.881024i	$-0.656855\pi$
$227$	−214.774			−0.946142			−0.473071	+	0.881024i	$0.656855\pi$
$228$	−83.1384	−	48.0000i	−0.364642	−	0.210526i
$229$	−338.000			−1.47598			−0.737991	−	0.674810i	$-0.764225\pi$
$229$	−338.000			−1.47598			−0.737991	+	0.674810i	$0.764225\pi$
$230$	−34.6410	−	60.0000i	−0.150613	−	0.260870i
$231$			187.061i			0.809790i
$232$			288.000i			1.24138i
$233$			182.000i			0.781116i	0.920578	+	0.390558i	$0.127718\pi$
$233$			182.000i			0.781116i	−0.920578	+	0.390558i	$0.872282\pi$
$234$	54.0000	+	93.5307i	0.230769	+	0.399704i
$235$		0			0
$236$	−108.000	−	62.3538i	−0.457627	−	0.264211i
$237$		−	156.000i		−	0.658228i
$238$	−103.923	−	180.000i	−0.436651	−	0.756303i
$239$		−	353.338i		−	1.47840i	−0.673484	−	0.739202i	$-0.735203\pi$
$239$		−	353.338i		−	1.47840i	0.673484	−	0.739202i	$-0.264797\pi$
$240$	120.000	−	69.2820i	0.500000	−	0.288675i
$241$	−106.000			−0.439834			−0.219917	−	0.975519i	$-0.570579\pi$
$241$	−106.000			−0.439834			−0.219917	+	0.975519i	$0.570579\pi$
$242$	−22.5167	+	13.0000i	−0.0930441	+	0.0537190i
$243$	−15.5885			−0.0641500
$244$	−148.000	+	256.344i	−0.606557	+	1.05059i
$245$		−	295.000i		−	1.20408i
$246$	54.0000	−	31.1769i	0.219512	−	0.126735i
$247$	249.415			1.00978
$248$	−55.4256			−0.223490
$249$	−156.000			−0.626506
$250$	−125.000	−	216.506i	−0.500000	−	0.866025i
$251$		−	322.161i		−	1.28351i	−0.766909	−	0.641756i	$-0.778206\pi$
$251$		−	322.161i		−	1.28351i	0.766909	−	0.641756i	$-0.221794\pi$
$252$	62.3538	−	108.000i	0.247436	−	0.428571i
$253$			72.0000i			0.284585i
$254$	−378.000	+	218.238i	−1.48819	+	0.859206i
$255$	−86.6025			−0.339618
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$			14.0000i			0.0544747i	0.999629	+	0.0272374i	$0.00867099\pi$
$257$			14.0000i			0.0544747i	−0.999629	+	0.0272374i	$0.991329\pi$
$258$	−62.3538	+	36.0000i	−0.241682	+	0.139535i
$259$			561.184i			2.16674i
$260$	−180.000	+	311.769i	−0.692308	+	1.19911i
$261$	108.000			0.413793
$262$	−135.100	−	234.000i	−0.515649	−	0.893130i
$263$	−187.061			−0.711260			−0.355630	−	0.934627i	$-0.615734\pi$
$263$	−187.061			−0.711260			−0.355630	+	0.934627i	$0.615734\pi$
$264$	−144.000			−0.545455
$265$	130.000			0.490566
$266$	−144.000	−	249.415i	−0.541353	−	0.937652i
$267$	−31.1769			−0.116767
$268$	83.1384	−	144.000i	0.310218	−	0.537313i
$269$	108.000			0.401487			0.200743	−	0.979644i	$-0.435664\pi$
$269$	108.000			0.401487			0.200743	+	0.979644i	$0.435664\pi$
$270$	−25.9808	−	45.0000i	−0.0962250	−	0.166667i
$271$		−	325.626i		−	1.20157i	−0.799411	−	0.600785i	$-0.794855\pi$
$271$		−	325.626i		−	1.20157i	0.799411	−	0.600785i	$-0.205145\pi$
$272$	138.564	−	80.0000i	0.509427	−	0.294118i
$273$			324.000i			1.18681i
$274$	−110.000	−	190.526i	−0.401460	−	0.695349i
$275$			259.808i			0.944755i
$276$	24.0000	−	41.5692i	0.0869565	−	0.150613i
$277$			270.000i			0.974729i	0.873199	+	0.487365i	$0.162042\pi$
$277$			270.000i			0.974729i	−0.873199	+	0.487365i	$0.837958\pi$
$278$	187.061	+	324.000i	0.672883	+	1.16547i
$279$			20.7846i			0.0744968i
$280$	415.692			1.48461
$281$	−234.000			−0.832740			−0.416370	−	0.909195i	$-0.636698\pi$
$281$	−234.000			−0.832740			−0.416370	+	0.909195i	$0.636698\pi$
$282$		0			0
$283$	83.1384			0.293775			0.146888	−	0.989153i	$-0.453074\pi$
$283$	83.1384			0.293775			0.146888	+	0.989153i	$0.453074\pi$
$284$	360.000	+	207.846i	1.26761	+	0.731852i
$285$	−120.000			−0.421053
$286$	324.000	−	187.061i	1.13287	−	0.654061i
$287$	187.061			0.651782
$288$	83.1384	+	48.0000i	0.288675	+	0.166667i
$289$	189.000			0.653979
$290$	180.000	+	311.769i	0.620690	+	1.07507i
$291$			124.708i			0.428549i
$292$	−124.708	−	72.0000i	−0.427081	−	0.246575i
$293$			58.0000i			0.197952i	0.995090	+	0.0989761i	$0.0315567\pi$
$293$			58.0000i			0.197952i	−0.995090	+	0.0989761i	$0.968443\pi$
$294$	177.000	−	102.191i	0.602041	−	0.347588i
$295$	−155.885			−0.528422
$296$	−432.000			−1.45946
$297$			54.0000i			0.181818i
$298$	498.831	−	288.000i	1.67393	−	0.966443i
$299$			124.708i			0.417082i
$300$	86.6025	−	150.000i	0.288675	−	0.500000i
$301$	−216.000			−0.717608
$302$	−187.061	−	324.000i	−0.619409	−	1.07285i
$303$	−62.3538			−0.205788
$304$	192.000	−	110.851i	0.631579	−	0.364642i
$305$			370.000i			1.21311i
$306$	−30.0000	−	51.9615i	−0.0980392	−	0.169809i
$307$	−270.200			−0.880130			−0.440065	−	0.897966i	$-0.645045\pi$
$307$	−270.200			−0.880130			−0.440065	+	0.897966i	$0.645045\pi$
$308$	−374.123	−	216.000i	−1.21468	−	0.701299i
$309$	18.0000			0.0582524
$310$	−60.0000	+	34.6410i	−0.193548	+	0.111745i
$311$		−	270.200i		−	0.868810i	−0.900718	−	0.434405i	$-0.856959\pi$
$311$		−	270.200i		−	0.868810i	0.900718	−	0.434405i	$-0.143041\pi$
$312$	−249.415			−0.799408
$313$		−	468.000i		−	1.49521i	−0.664145	−	0.747604i	$-0.731204\pi$
$313$		−	468.000i		−	1.49521i	0.664145	−	0.747604i	$-0.268796\pi$
$314$	−234.000	−	405.300i	−0.745223	−	1.29076i
$315$		−	155.885i		−	0.494872i
$316$	312.000	+	180.133i	0.987342	+	0.570042i
$317$			250.000i			0.788644i	0.918972	+	0.394322i	$0.129020\pi$
$317$			250.000i			0.788644i	−0.918972	+	0.394322i	$0.870980\pi$
$318$	45.0333	+	78.0000i	0.141614	+	0.245283i
$319$		−	374.123i		−	1.17280i
$320$			320.000i			1.00000i
$321$	324.000			1.00935
$322$	124.708	−	72.0000i	0.387291	−	0.223602i
$323$	−138.564			−0.428991
$324$	18.0000	−	31.1769i	0.0555556	−	0.0962250i
$325$			450.000i			1.38462i
$326$	216.000	−	124.708i	0.662577	−	0.382539i
$327$	−45.0333			−0.137717
$328$			144.000i			0.439024i
$329$		0			0
$330$	−155.885	+	90.0000i	−0.472377	+	0.272727i
$331$			374.123i			1.13028i	0.824995	+	0.565140i	$0.191178\pi$
$331$			374.123i			1.13028i	−0.824995	+	0.565140i	$0.808822\pi$
$332$	180.133	−	312.000i	0.542570	−	0.939759i
$333$			162.000i			0.486486i
$334$	−228.000	+	131.636i	−0.682635	+	0.394119i
$335$		−	207.846i		−	0.620436i
$336$	144.000	+	249.415i	0.428571	+	0.742307i
$337$		−	468.000i		−	1.38872i	−0.719626	−	0.694362i	$-0.755687\pi$
$337$		−	468.000i		−	1.38872i	0.719626	−	0.694362i	$-0.244313\pi$
$338$	268.468	−	155.000i	0.794284	−	0.458580i
$339$		−	17.3205i		−	0.0510929i
$340$	100.000	−	173.205i	0.294118	−	0.509427i
$341$	72.0000			0.211144
$342$	−41.5692	−	72.0000i	−0.121547	−	0.210526i
$343$	103.923			0.302983
$344$		−	166.277i		−	0.483363i
$345$		−	60.0000i		−	0.173913i
$346$	146.000	+	252.879i	0.421965	+	0.730865i
$347$	−561.184			−1.61725			−0.808623	−	0.588327i	$-0.799787\pi$
$347$	−561.184			−1.61725			−0.808623	+	0.588327i	$0.799787\pi$
$348$	−124.708	+	216.000i	−0.358355	+	0.620690i
$349$	434.000			1.24355			0.621777	−	0.783195i	$-0.286411\pi$
$349$	434.000			1.24355			0.621777	+	0.783195i	$0.286411\pi$
$350$	450.000	−	259.808i	1.28571	−	0.742307i
$351$			93.5307i			0.266469i
$352$	166.277	−	288.000i	0.472377	−	0.818182i
$353$			158.000i			0.447592i	0.974636	+	0.223796i	$0.0718449\pi$
$353$			158.000i			0.447592i	−0.974636	+	0.223796i	$0.928155\pi$
$354$	−54.0000	−	93.5307i	−0.152542	−	0.264211i
$355$	519.615			1.46370
$356$	36.0000	−	62.3538i	0.101124	−	0.175151i
$357$		−	180.000i		−	0.504202i
$358$	72.7461	+	126.000i	0.203201	+	0.351955i
$359$			457.261i			1.27371i	0.770984	+	0.636854i	$0.219765\pi$
$359$			457.261i			1.27371i	−0.770984	+	0.636854i	$0.780235\pi$
$360$	120.000			0.333333
$361$	169.000			0.468144
$362$	−453.797	+	262.000i	−1.25358	+	0.723757i
$363$	−22.5167			−0.0620294
$364$	−648.000	−	374.123i	−1.78022	−	1.02781i
$365$	−180.000			−0.493151
$366$	−222.000	+	128.172i	−0.606557	+	0.350196i
$367$	218.238			0.594655			0.297328	−	0.954776i	$-0.403905\pi$
$367$	218.238			0.594655			0.297328	+	0.954776i	$0.403905\pi$
$368$	55.4256	+	96.0000i	0.150613	+	0.260870i
$369$	54.0000			0.146341
$370$	−467.654	+	270.000i	−1.26393	+	0.729730i
$371$			270.200i			0.728302i
$372$	−41.5692	−	24.0000i	−0.111745	−	0.0645161i
$373$			270.000i			0.723861i	0.932205	+	0.361930i	$0.117882\pi$
$373$			270.000i			0.723861i	−0.932205	+	0.361930i	$0.882118\pi$
$374$	−180.000	+	103.923i	−0.481283	+	0.277869i
$375$		−	216.506i		−	0.577350i
$376$		0			0
$377$		−	648.000i		−	1.71883i
$378$	93.5307	−	54.0000i	0.247436	−	0.142857i
$379$		−	325.626i		−	0.859170i	−0.903026	−	0.429585i	$-0.858660\pi$
$379$		−	325.626i		−	0.859170i	0.903026	−	0.429585i	$-0.141340\pi$
$380$	138.564	−	240.000i	0.364642	−	0.631579i
$381$	−378.000			−0.992126
$382$	187.061	+	324.000i	0.489690	+	0.848168i
$383$	55.4256			0.144714			0.0723572	−	0.997379i	$-0.476948\pi$
$383$	55.4256			0.144714			0.0723572	+	0.997379i	$0.476948\pi$
$384$	−192.000	+	110.851i	−0.500000	+	0.288675i
$385$	−540.000			−1.40260
$386$	180.000	+	311.769i	0.466321	+	0.807692i
$387$	−62.3538			−0.161121
$388$	−249.415	−	144.000i	−0.642823	−	0.371134i
$389$	288.000			0.740360			0.370180	−	0.928960i	$-0.379296\pi$
$389$	288.000			0.740360			0.370180	+	0.928960i	$0.379296\pi$
$390$	−270.000	+	155.885i	−0.692308	+	0.399704i
$391$		−	69.2820i		−	0.177192i
$392$			472.000i			1.20408i
$393$		−	234.000i		−	0.595420i
$394$	154.000	+	266.736i	0.390863	+	0.676994i
$395$	450.333			1.14008
$396$	−108.000	−	62.3538i	−0.272727	−	0.157459i
$397$		−	306.000i		−	0.770781i	−0.922754	−	0.385390i	$-0.874067\pi$
$397$		−	306.000i		−	0.770781i	0.922754	−	0.385390i	$-0.125933\pi$
$398$	187.061	+	324.000i	0.470004	+	0.814070i
$399$		−	249.415i		−	0.625101i
$400$	200.000	+	346.410i	0.500000	+	0.866025i
$401$	−450.000			−1.12219			−0.561097	−	0.827750i	$-0.689621\pi$
$401$	−450.000			−1.12219			−0.561097	+	0.827750i	$0.689621\pi$
$402$	124.708	−	72.0000i	0.310218	−	0.179104i
$403$	124.708			0.309448
$404$	72.0000	−	124.708i	0.178218	−	0.308682i
$405$		−	45.0000i		−	0.111111i
$406$	−648.000	+	374.123i	−1.59606	+	0.921485i
$407$	561.184			1.37883
$408$	138.564			0.339618
$409$	50.0000			0.122249			0.0611247	−	0.998130i	$-0.480531\pi$
$409$	50.0000			0.122249			0.0611247	+	0.998130i	$0.480531\pi$
$410$	90.0000	+	155.885i	0.219512	+	0.380206i
$411$		−	190.526i		−	0.463566i
$412$	−20.7846	+	36.0000i	−0.0504481	+	0.0873786i
$413$		−	324.000i		−	0.784504i
$414$	36.0000	−	20.7846i	0.0869565	−	0.0502044i
$415$		−	450.333i		−	1.08514i
$416$	288.000	−	498.831i	0.692308	−	1.19911i
$417$			324.000i			0.776978i
$418$	−249.415	+	144.000i	−0.596687	+	0.344498i
$419$			737.854i			1.76099i	0.474058	+	0.880494i	$0.342789\pi$
$419$			737.854i			1.76099i	−0.474058	+	0.880494i	$0.657211\pi$
$420$	311.769	+	180.000i	0.742307	+	0.428571i
$421$	−286.000			−0.679335			−0.339667	−	0.940546i	$-0.610315\pi$
$421$	−286.000			−0.679335			−0.339667	+	0.940546i	$0.610315\pi$
$422$	−242.487	−	420.000i	−0.574614	−	0.995261i
$423$		0			0
$424$	−208.000			−0.490566
$425$		−	250.000i		−	0.588235i
$426$	180.000	+	311.769i	0.422535	+	0.731852i
$427$	−769.031			−1.80101
$428$	−374.123	+	648.000i	−0.874119	+	1.51402i
$429$	324.000			0.755245
$430$	−103.923	−	180.000i	−0.241682	−	0.418605i
$431$			124.708i			0.289345i	0.989480	+	0.144672i	$0.0462128\pi$
$431$			124.708i			0.289345i	−0.989480	+	0.144672i	$0.953787\pi$
$432$	41.5692	+	72.0000i	0.0962250	+	0.166667i
$433$			36.0000i			0.0831409i	0.999136	+	0.0415704i	$0.0132361\pi$
$433$			36.0000i			0.0831409i	−0.999136	+	0.0415704i	$0.986764\pi$
$434$	−72.0000	−	124.708i	−0.165899	−	0.287345i
$435$			311.769i			0.716711i
$436$	52.0000	−	90.0666i	0.119266	−	0.206575i
$437$		−	96.0000i		−	0.219680i
$438$	−62.3538	−	108.000i	−0.142360	−	0.246575i
$439$			782.887i			1.78334i	0.452684	+	0.891671i	$0.350466\pi$
$439$			782.887i			1.78334i	−0.452684	+	0.891671i	$0.649534\pi$
$440$		−	415.692i		−	0.944755i
$441$	177.000			0.401361
$442$	−311.769	+	180.000i	−0.705360	+	0.407240i
$443$	214.774			0.484818			0.242409	−	0.970174i	$-0.422062\pi$
$443$	214.774			0.484818			0.242409	+	0.970174i	$0.422062\pi$
$444$	−324.000	−	187.061i	−0.729730	−	0.421310i
$445$		−	90.0000i		−	0.202247i
$446$	162.000	−	93.5307i	0.363229	−	0.209710i
$447$	498.831			1.11595
$448$	−665.108			−1.48461
$449$	−54.0000			−0.120267			−0.0601336	−	0.998190i	$-0.519153\pi$
$449$	−54.0000			−0.120267			−0.0601336	+	0.998190i	$0.519153\pi$
$450$	129.904	−	75.0000i	0.288675	−	0.166667i
$451$		−	187.061i		−	0.414770i
$452$	34.6410	+	20.0000i	0.0766394	+	0.0442478i
$453$		−	324.000i		−	0.715232i
$454$	372.000	−	214.774i	0.819383	−	0.473071i
$455$	−935.307			−2.05562
$456$	192.000			0.421053
$457$			288.000i			0.630197i	0.949059	+	0.315098i	$0.102038\pi$
$457$			288.000i			0.630197i	−0.949059	+	0.315098i	$0.897962\pi$
$458$	585.433	−	338.000i	1.27824	−	0.737991i
$459$		−	51.9615i		−	0.113206i
$460$	120.000	+	69.2820i	0.260870	+	0.150613i
$461$	−288.000			−0.624729			−0.312364	−	0.949962i	$-0.601121\pi$
$461$	−288.000			−0.624729			−0.312364	+	0.949962i	$0.601121\pi$
$462$	−187.061	−	324.000i	−0.404895	−	0.701299i
$463$	−405.300			−0.875378			−0.437689	−	0.899126i	$-0.644203\pi$
$463$	−405.300			−0.875378			−0.437689	+	0.899126i	$0.644203\pi$
$464$	−288.000	−	498.831i	−0.620690	−	1.07507i
$465$	−60.0000			−0.129032
$466$	−182.000	−	315.233i	−0.390558	−	0.676466i
$467$	575.041			1.23135			0.615675	−	0.788000i	$-0.288883\pi$
$467$	575.041			1.23135			0.615675	+	0.788000i	$0.288883\pi$
$468$	−187.061	−	108.000i	−0.399704	−	0.230769i
$469$	432.000			0.921109
$470$		0			0
$471$		−	405.300i		−	0.860509i
$472$	249.415			0.528422
$473$			216.000i			0.456660i
$474$	156.000	+	270.200i	0.329114	+	0.570042i
$475$		−	346.410i		−	0.729285i
$476$	360.000	+	207.846i	0.756303	+	0.436651i
$477$			78.0000i			0.163522i
$478$	353.338	+	612.000i	0.739202	+	1.28033i
$479$		−	145.492i		−	0.303742i	−0.988400	−	0.151871i	$-0.951470\pi$
$479$		−	145.492i		−	0.303742i	0.988400	−	0.151871i	$-0.0485298\pi$
$480$	−138.564	+	240.000i	−0.288675	+	0.500000i
$481$	972.000			2.02079
$482$	183.597	−	106.000i	0.380907	−	0.219917i
$483$	124.708			0.258194
$484$	26.0000	−	45.0333i	0.0537190	−	0.0930441i
$485$	−360.000			−0.742268
$486$	27.0000	−	15.5885i	0.0555556	−	0.0320750i
$487$	−259.808			−0.533486			−0.266743	−	0.963768i	$-0.585947\pi$
$487$	−259.808			−0.533486			−0.266743	+	0.963768i	$0.585947\pi$
$488$		−	592.000i		−	1.21311i
$489$	216.000			0.441718
$490$	295.000	+	510.955i	0.602041	+	1.04277i
$491$		−	72.7461i		−	0.148159i	−0.997252	−	0.0740796i	$-0.976398\pi$
$491$		−	72.7461i		−	0.148159i	0.997252	−	0.0740796i	$-0.0236019\pi$
$492$	−62.3538	+	108.000i	−0.126735	+	0.219512i
$493$			360.000i			0.730223i
$494$	−432.000	+	249.415i	−0.874494	+	0.504889i
$495$	−155.885			−0.314918
$496$	96.0000	−	55.4256i	0.193548	−	0.111745i
$497$			1080.00i			2.17304i
$498$	270.200	−	156.000i	0.542570	−	0.313253i
$499$		−	443.405i		−	0.888587i	−0.895881	−	0.444294i	$-0.853455\pi$
$499$		−	443.405i		−	0.888587i	0.895881	−	0.444294i	$-0.146545\pi$
$500$	433.013	+	250.000i	0.866025	+	0.500000i
$501$	−228.000			−0.455090
$502$	322.161	+	558.000i	0.641756	+	1.11155i
$503$	−110.851			−0.220380			−0.110190	−	0.993911i	$-0.535146\pi$
$503$	−110.851			−0.220380			−0.110190	+	0.993911i	$0.535146\pi$
$504$			249.415i			0.494872i
$505$		−	180.000i		−	0.356436i
$506$	−72.0000	−	124.708i	−0.142292	−	0.246458i
$507$	268.468			0.529522
$508$	436.477	−	756.000i	0.859206	−	1.48819i
$509$	252.000			0.495088			0.247544	−	0.968877i	$-0.420376\pi$
$509$	252.000			0.495088			0.247544	+	0.968877i	$0.420376\pi$
$510$	150.000	−	86.6025i	0.294118	−	0.169809i
$511$		−	374.123i		−	0.732139i
$512$		−	512.000i		−	1.00000i
$513$		−	72.0000i		−	0.140351i
$514$	−14.0000	−	24.2487i	−0.0272374	−	0.0471765i
$515$			51.9615i			0.100896i
$516$	72.0000	−	124.708i	0.139535	−	0.241682i
$517$		0			0
$518$	−561.184	−	972.000i	−1.08337	−	1.87645i
$519$			252.879i			0.487244i
$520$		−	720.000i		−	1.38462i
$521$	54.0000			0.103647			0.0518234	−	0.998656i	$-0.483497\pi$
$521$	54.0000			0.103647			0.0518234	+	0.998656i	$0.483497\pi$
$522$	−187.061	+	108.000i	−0.358355	+	0.206897i
$523$	623.538			1.19223			0.596117	−	0.802898i	$-0.296709\pi$
$523$	623.538			1.19223			0.596117	+	0.802898i	$0.296709\pi$
$524$	468.000	+	270.200i	0.893130	+	0.515649i
$525$	450.000			0.857143
$526$	324.000	−	187.061i	0.615970	−	0.355630i
$527$	−69.2820			−0.131465
$528$	249.415	−	144.000i	0.472377	−	0.272727i
$529$	−481.000			−0.909263
$530$	−225.167	+	130.000i	−0.424843	+	0.245283i
$531$		−	93.5307i		−	0.176141i
$532$	498.831	+	288.000i	0.937652	+	0.541353i
$533$		−	324.000i		−	0.607880i
$534$	54.0000	−	31.1769i	0.101124	−	0.0583837i
$535$			935.307i			1.74824i
$536$			332.554i			0.620436i
$537$			126.000i			0.234637i
$538$	−187.061	+	108.000i	−0.347698	+	0.200743i
$539$		−	613.146i		−	1.13756i
$540$	90.0000	+	51.9615i	0.166667	+	0.0962250i
$541$	−650.000			−1.20148			−0.600739	−	0.799445i	$-0.705127\pi$
$541$	−650.000			−1.20148			−0.600739	+	0.799445i	$0.705127\pi$
$542$	325.626	+	564.000i	0.600785	+	1.04059i
$543$	−453.797			−0.835722
$544$	−160.000	+	277.128i	−0.294118	+	0.509427i
$545$		−	130.000i		−	0.238532i
$546$	−324.000	−	561.184i	−0.593407	−	1.02781i
$547$	−685.892			−1.25392			−0.626958	−	0.779053i	$-0.715700\pi$
$547$	−685.892			−1.25392			−0.626958	+	0.779053i	$0.715700\pi$
$548$	381.051	+	220.000i	0.695349	+	0.401460i
$549$	−222.000			−0.404372
$550$	−259.808	−	450.000i	−0.472377	−	0.818182i
$551$			498.831i			0.905319i
$552$			96.0000i			0.173913i
$553$			936.000i			1.69259i
$554$	−270.000	−	467.654i	−0.487365	−	0.844140i
$555$	−467.654			−0.842619
$556$	−648.000	−	374.123i	−1.16547	−	0.672883i
$557$			574.000i			1.03052i	0.857034	+	0.515260i	$0.172305\pi$
$557$			574.000i			1.03052i	−0.857034	+	0.515260i	$0.827695\pi$
$558$	−20.7846	−	36.0000i	−0.0372484	−	0.0645161i
$559$			374.123i			0.669272i
$560$	−720.000	+	415.692i	−1.28571	+	0.742307i
$561$	−180.000			−0.320856
$562$	405.300	−	234.000i	0.721174	−	0.416370i
$563$	−561.184			−0.996775			−0.498388	−	0.866954i	$-0.666074\pi$
$563$	−561.184			−0.996775			−0.498388	+	0.866954i	$0.666074\pi$
$564$		0			0
$565$	50.0000			0.0884956
$566$	−144.000	+	83.1384i	−0.254417	+	0.146888i
$567$	93.5307			0.164957
$568$	−831.384			−1.46370
$569$	−198.000			−0.347979			−0.173989	−	0.984748i	$-0.555666\pi$
$569$	−198.000			−0.347979			−0.173989	+	0.984748i	$0.555666\pi$
$570$	207.846	−	120.000i	0.364642	−	0.210526i
$571$		−	180.133i		−	0.315470i	−0.987481	−	0.157735i	$-0.949581\pi$
$571$		−	180.133i		−	0.315470i	0.987481	−	0.157735i	$-0.0504192\pi$
$572$	−374.123	+	648.000i	−0.654061	+	1.13287i
$573$			324.000i			0.565445i
$574$	−324.000	+	187.061i	−0.564460	+	0.325891i
$575$	173.205			0.301226
$576$	−192.000			−0.333333
$577$		−	504.000i		−	0.873484i	−0.899587	−	0.436742i	$-0.856132\pi$
$577$		−	504.000i		−	0.873484i	0.899587	−	0.436742i	$-0.143868\pi$
$578$	−327.358	+	189.000i	−0.566363	+	0.326990i
$579$			311.769i			0.538461i
$580$	−623.538	−	360.000i	−1.07507	−	0.620690i
$581$	936.000			1.61102
$582$	−124.708	−	216.000i	−0.214274	−	0.371134i
$583$	270.200			0.463465
$584$	288.000			0.493151
$585$	−270.000			−0.461538
$586$	−58.0000	−	100.459i	−0.0989761	−	0.171432i
$587$	−408.764			−0.696361			−0.348181	−	0.937427i	$-0.613200\pi$
$587$	−408.764			−0.696361			−0.348181	+	0.937427i	$0.613200\pi$
$588$	−204.382	+	354.000i	−0.347588	+	0.602041i
$589$	−96.0000			−0.162988
$590$	270.000	−	155.885i	0.457627	−	0.264211i
$591$			266.736i			0.451330i
$592$	748.246	−	432.000i	1.26393	−	0.729730i
$593$		−	998.000i		−	1.68297i	−0.540282	−	0.841484i	$-0.681682\pi$
$593$		−	998.000i		−	1.68297i	0.540282	−	0.841484i	$-0.318318\pi$
$594$	−54.0000	−	93.5307i	−0.0909091	−	0.157459i
$595$	519.615			0.873303
$596$	−576.000	+	997.661i	−0.966443	+	1.67393i
$597$			324.000i			0.542714i
$598$	−124.708	−	216.000i	−0.208541	−	0.361204i
$599$		−	540.400i		−	0.902170i	−0.892481	−	0.451085i	$-0.851037\pi$
$599$		−	540.400i		−	0.902170i	0.892481	−	0.451085i	$-0.148963\pi$
$600$			346.410i			0.577350i
$601$	−614.000			−1.02163			−0.510815	−	0.859690i	$-0.670656\pi$
$601$	−614.000			−1.02163			−0.510815	+	0.859690i	$0.670656\pi$
$602$	374.123	−	216.000i	0.621467	−	0.358804i
$603$	124.708			0.206812
$604$	648.000	+	374.123i	1.07285	+	0.619409i
$605$		−	65.0000i		−	0.107438i
$606$	108.000	−	62.3538i	0.178218	−	0.102894i
$607$	654.715			1.07861			0.539304	−	0.842111i	$-0.318687\pi$
$607$	654.715			1.07861			0.539304	+	0.842111i	$0.318687\pi$
$608$	−221.703	+	384.000i	−0.364642	+	0.631579i
$609$	−648.000			−1.06404
$610$	−370.000	−	640.859i	−0.606557	−	1.05059i
$611$		0			0
$612$	103.923	+	60.0000i	0.169809	+	0.0980392i
$613$		−	414.000i		−	0.675367i	−0.941260	−	0.337684i	$-0.890357\pi$
$613$		−	414.000i		−	0.675367i	0.941260	−	0.337684i	$-0.109643\pi$
$614$	468.000	−	270.200i	0.762215	−	0.440065i
$615$			155.885i			0.253471i
$616$	864.000			1.40260
$617$			58.0000i			0.0940032i	0.998895	+	0.0470016i	$0.0149666\pi$
$617$			58.0000i			0.0940032i	−0.998895	+	0.0470016i	$0.985033\pi$
$618$	−31.1769	+	18.0000i	−0.0504481	+	0.0291262i
$619$			187.061i			0.302199i	0.988519	+	0.151100i	$0.0482815\pi$
$619$			187.061i			0.302199i	−0.988519	+	0.151100i	$0.951719\pi$
$620$	69.2820	−	120.000i	0.111745	−	0.193548i
$621$	36.0000			0.0579710
$622$	270.200	+	468.000i	0.434405	+	0.752412i
$623$	187.061			0.300259
$624$	432.000	−	249.415i	0.692308	−	0.399704i
$625$	625.000			1.00000
$626$	468.000	+	810.600i	0.747604	+	1.29489i
$627$	−249.415			−0.397792
$628$	810.600	+	468.000i	1.29076	+	0.745223i
$629$	−540.000			−0.858506
$630$	155.885	+	270.000i	0.247436	+	0.428571i
$631$			824.456i			1.30659i	0.757105	+	0.653293i	$0.226613\pi$
$631$			824.456i			1.30659i	−0.757105	+	0.653293i	$0.773387\pi$
$632$	−720.533			−1.14008
$633$		−	420.000i		−	0.663507i
$634$	−250.000	−	433.013i	−0.394322	−	0.682985i
$635$		−	1091.19i		−	1.71841i
$636$	−156.000	−	90.0666i	−0.245283	−	0.141614i
$637$		−	1062.00i		−	1.66719i
$638$	374.123	+	648.000i	0.586400	+	1.01567i
$639$			311.769i			0.487902i
$640$	−320.000	−	554.256i	−0.500000	−	0.866025i
$641$	810.000			1.26365			0.631825	−	0.775111i	$-0.282306\pi$
$641$	810.000			1.26365			0.631825	+	0.775111i	$0.282306\pi$
$642$	−561.184	+	324.000i	−0.874119	+	0.504673i
$643$	415.692			0.646489			0.323244	−	0.946316i	$-0.395226\pi$
$643$	415.692			0.646489			0.323244	+	0.946316i	$0.395226\pi$
$644$	−144.000	+	249.415i	−0.223602	+	0.387291i
$645$		−	180.000i		−	0.279070i
$646$	240.000	−	138.564i	0.371517	−	0.214495i
$647$	983.805			1.52056			0.760282	−	0.649593i	$-0.225061\pi$
$647$	983.805			1.52056			0.760282	+	0.649593i	$0.225061\pi$
$648$			72.0000i			0.111111i
$649$	−324.000			−0.499230
$650$	−450.000	−	779.423i	−0.692308	−	1.19911i
$651$		−	124.708i		−	0.191563i
$652$	−249.415	+	432.000i	−0.382539	+	0.662577i
$653$			950.000i			1.45482i	0.686201	+	0.727412i	$0.259277\pi$
$653$			950.000i			1.45482i	−0.686201	+	0.727412i	$0.740723\pi$
$654$	78.0000	−	45.0333i	0.119266	−	0.0688583i
$655$	675.500			1.03130
$656$	−144.000	−	249.415i	−0.219512	−	0.380206i
$657$		−	108.000i		−	0.164384i
$658$		0			0
$659$		−	1132.76i		−	1.71891i	−0.511212	−	0.859455i	$-0.670803\pi$
$659$		−	1132.76i		−	1.71891i	0.511212	−	0.859455i	$-0.329197\pi$
$660$	180.000	−	311.769i	0.272727	−	0.472377i
$661$	−242.000			−0.366112			−0.183056	−	0.983102i	$-0.558599\pi$
$661$	−242.000			−0.366112			−0.183056	+	0.983102i	$0.558599\pi$
$662$	−374.123	−	648.000i	−0.565140	−	0.978852i
$663$	−311.769			−0.470240
$664$			720.533i			1.08514i
$665$	720.000			1.08271
$666$	−162.000	−	280.592i	−0.243243	−	0.421310i
$667$	−249.415			−0.373936
$668$	263.272	−	456.000i	0.394119	−	0.682635i
$669$	162.000			0.242152
$670$	207.846	+	360.000i	0.310218	+	0.537313i
$671$			769.031i			1.14610i
$672$	−498.831	−	288.000i	−0.742307	−	0.428571i
$673$		−	324.000i		−	0.481426i	−0.970596	−	0.240713i	$-0.922619\pi$
$673$		−	324.000i		−	0.481426i	0.970596	−	0.240713i	$-0.0773813\pi$
$674$	468.000	+	810.600i	0.694362	+	1.20267i
$675$	129.904			0.192450
$676$	−310.000	+	536.936i	−0.458580	+	0.794284i
$677$		−	806.000i		−	1.19055i	−0.803523	−	0.595273i	$-0.797044\pi$
$677$		−	806.000i		−	1.19055i	0.803523	−	0.595273i	$-0.202956\pi$
$678$	17.3205	+	30.0000i	0.0255465	+	0.0442478i
$679$		−	748.246i		−	1.10198i
$680$			400.000i			0.588235i
$681$	372.000			0.546256
$682$	−124.708	+	72.0000i	−0.182856	+	0.105572i
$683$	−575.041			−0.841934			−0.420967	−	0.907076i	$-0.638309\pi$
$683$	−575.041			−0.841934			−0.420967	+	0.907076i	$0.638309\pi$
$684$	144.000	+	83.1384i	0.210526	+	0.121547i
$685$	550.000			0.802920
$686$	−180.000	+	103.923i	−0.262391	+	0.151491i
$687$	585.433			0.852159
$688$	166.277	+	288.000i	0.241682	+	0.418605i
$689$	468.000			0.679245
$690$	60.0000	+	103.923i	0.0869565	+	0.150613i
$691$		−	775.959i		−	1.12295i	−0.827494	−	0.561475i	$-0.810234\pi$
$691$		−	775.959i		−	1.12295i	0.827494	−	0.561475i	$-0.189766\pi$
$692$	−505.759	−	292.000i	−0.730865	−	0.421965i
$693$		−	324.000i		−	0.467532i
$694$	972.000	−	561.184i	1.40058	−	0.808623i
$695$	−935.307			−1.34577
$696$		−	498.831i		−	0.716711i
$697$			180.000i			0.258250i
$698$	−751.710	+	434.000i	−1.07695	+	0.621777i
$699$		−	315.233i		−	0.450977i
$700$	−519.615	+	900.000i	−0.742307	+	1.28571i
$701$	756.000			1.07846			0.539230	−	0.842159i	$-0.318715\pi$
$701$	756.000			1.07846			0.539230	+	0.842159i	$0.318715\pi$
$702$	−93.5307	−	162.000i	−0.133235	−	0.230769i
$703$	−748.246			−1.06436
$704$			665.108i			0.944755i
$705$		0			0
$706$	−158.000	−	273.664i	−0.223796	−	0.387626i
$707$	374.123			0.529170
$708$	187.061	+	108.000i	0.264211	+	0.152542i
$709$	310.000			0.437236			0.218618	−	0.975811i	$-0.429845\pi$
$709$	310.000			0.437236			0.218618	+	0.975811i	$0.429845\pi$
$710$	−900.000	+	519.615i	−1.26761	+	0.731852i
$711$			270.200i			0.380028i
$712$			144.000i			0.202247i
$713$		−	48.0000i		−	0.0673212i
$714$	180.000	+	311.769i	0.252101	+	0.436651i
$715$			935.307i			1.30812i
$716$	−252.000	−	145.492i	−0.351955	−	0.203201i
$717$			612.000i			0.853556i
$718$	−457.261	−	792.000i	−0.636854	−	1.10306i
$719$			83.1384i			0.115631i	0.998327	+	0.0578153i	$0.0184135\pi$
$719$			83.1384i			0.115631i	−0.998327	+	0.0578153i	$0.981587\pi$
$720$	−207.846	+	120.000i	−0.288675	+	0.166667i
$721$	−108.000			−0.149792
$722$	−292.717	+	169.000i	−0.405425	+	0.234072i
$723$	183.597			0.253938
$724$	524.000	−	907.595i	0.723757	−	1.25358i
$725$	−900.000			−1.24138
$726$	39.0000	−	22.5167i	0.0537190	−	0.0310147i
$727$	−1091.19			−1.50095			−0.750476	−	0.660898i	$-0.770176\pi$
$727$	−1091.19			−1.50095			−0.750476	+	0.660898i	$0.770176\pi$
$728$	1496.49			2.05562
$729$	27.0000			0.0370370
$730$	311.769	−	180.000i	0.427081	−	0.246575i
$731$		−	207.846i		−	0.284331i
$732$	256.344	−	444.000i	0.350196	−	0.606557i
$733$		−	1206.00i		−	1.64529i	−0.568553	−	0.822647i	$-0.692497\pi$
$733$		−	1206.00i		−	1.64529i	0.568553	−	0.822647i	$-0.307503\pi$
$734$	−378.000	+	218.238i	−0.514986	+	0.297328i
$735$			510.955i			0.695177i
$736$	−192.000	−	110.851i	−0.260870	−	0.150613i
$737$		−	432.000i		−	0.586160i
$738$	−93.5307	+	54.0000i	−0.126735	+	0.0731707i
$739$			484.974i			0.656257i	0.944633	+	0.328129i	$0.106418\pi$
$739$			484.974i			0.656257i	−0.944633	+	0.328129i	$0.893582\pi$
$740$	540.000	−	935.307i	0.729730	−	1.26393i
$741$	−432.000			−0.582996
$742$	−270.200	−	468.000i	−0.364151	−	0.630728i
$743$	1122.37			1.51059			0.755295	−	0.655385i	$-0.227493\pi$
$743$	1122.37			1.51059			0.755295	+	0.655385i	$0.227493\pi$
$744$	96.0000			0.129032
$745$			1440.00i			1.93289i
$746$	−270.000	−	467.654i	−0.361930	−	0.626882i
$747$	270.200			0.361713
$748$	207.846	−	360.000i	0.277869	−	0.481283i
$749$	−1944.00			−2.59546
$750$	216.506	+	375.000i	0.288675	+	0.500000i
$751$			242.487i			0.322886i	0.986882	+	0.161443i	$0.0516147\pi$
$751$			242.487i			0.322886i	−0.986882	+	0.161443i	$0.948385\pi$
$752$		0			0
$753$			558.000i			0.741036i
$754$	648.000	+	1122.37i	0.859416	+	1.48855i
$755$	935.307			1.23882
$756$	−108.000	+	187.061i	−0.142857	+	0.247436i
$757$			846.000i			1.11757i	0.829313	+	0.558785i	$0.188732\pi$
$757$			846.000i			1.11757i	−0.829313	+	0.558785i	$0.811268\pi$
$758$	325.626	+	564.000i	0.429585	+	0.744063i
$759$		−	124.708i		−	0.164305i
$760$			554.256i			0.729285i
$761$	−1458.00			−1.91590			−0.957950	−	0.286935i	$-0.907364\pi$
$761$	−1458.00			−1.91590			−0.957950	+	0.286935i	$0.907364\pi$
$762$	654.715	−	378.000i	0.859206	−	0.496063i
$763$	270.200			0.354128
$764$	−648.000	−	374.123i	−0.848168	−	0.489690i
$765$	150.000			0.196078
$766$	−96.0000	+	55.4256i	−0.125326	+	0.0723572i
$767$	−561.184			−0.731662
$768$	221.703	−	384.000i	0.288675	−	0.500000i
$769$	−1282.00			−1.66710			−0.833550	−	0.552444i	$-0.813695\pi$
$769$	−1282.00			−1.66710			−0.833550	+	0.552444i	$0.813695\pi$
$770$	935.307	−	540.000i	1.21468	−	0.701299i
$771$		−	24.2487i		−	0.0314510i
$772$	−623.538	−	360.000i	−0.807692	−	0.466321i
$773$			422.000i			0.545925i	0.962025	+	0.272962i	$0.0880035\pi$
$773$			422.000i			0.545925i	−0.962025	+	0.272962i	$0.911997\pi$
$774$	108.000	−	62.3538i	0.139535	−	0.0805605i
$775$		−	173.205i		−	0.223490i
$776$	576.000			0.742268
$777$		−	972.000i		−	1.25097i
$778$	−498.831	+	288.000i	−0.641170	+	0.370180i
$779$			249.415i			0.320174i
$780$	311.769	−	540.000i	0.399704	−	0.692308i
$781$	1080.00			1.38284
$782$	69.2820	+	120.000i	0.0885959	+	0.153453i
$783$	−187.061			−0.238904
$784$	−472.000	−	817.528i	−0.602041	−	1.04277i
$785$	1170.00			1.49045
$786$	234.000	+	405.300i	0.297710	+	0.515649i
$787$	−1205.51			−1.53178			−0.765888	−	0.642974i	$-0.777700\pi$
$787$	−1205.51			−1.53178			−0.765888	+	0.642974i	$0.777700\pi$
$788$	−533.472	−	308.000i	−0.676994	−	0.390863i
$789$	324.000			0.410646
$790$	−780.000	+	450.333i	−0.987342	+	0.570042i
$791$			103.923i			0.131382i
$792$	249.415			0.314918
$793$			1332.00i			1.67970i
$794$	306.000	+	530.008i	0.385390	+	0.667516i
$795$	−225.167			−0.283228
$796$	−648.000	−	374.123i	−0.814070	−	0.470004i
$797$		−	94.0000i		−	0.117942i	−0.998260	−	0.0589711i	$-0.981218\pi$
$797$		−	94.0000i		−	0.117942i	0.998260	−	0.0589711i	$-0.0187820\pi$
$798$	249.415	+	432.000i	0.312551	+	0.541353i
$799$		0			0
$800$	−692.820	−	400.000i	−0.866025	−	0.500000i
$801$	54.0000			0.0674157
$802$	779.423	−	450.000i	0.971849	−	0.561097i
$803$	−374.123			−0.465907
$804$	−144.000	+	249.415i	−0.179104	+	0.310218i
$805$			360.000i			0.447205i
$806$	−216.000	+	124.708i	−0.267990	+	0.154724i
$807$	−187.061			−0.231799
$808$			288.000i			0.356436i
$809$	270.000			0.333745			0.166873	−	0.985978i	$-0.446633\pi$
$809$	270.000			0.333745			0.166873	+	0.985978i	$0.446633\pi$
$810$	45.0000	+	77.9423i	0.0555556	+	0.0962250i
$811$			187.061i			0.230655i	0.993328	+	0.115328i	$0.0367918\pi$
$811$			187.061i			0.230655i	−0.993328	+	0.115328i	$0.963208\pi$
$812$	748.246	−	1296.00i	0.921485	−	1.59606i
$813$			564.000i			0.693727i
$814$	−972.000	+	561.184i	−1.19410	+	0.689416i
$815$			623.538i			0.765078i
$816$	−240.000	+	138.564i	−0.294118	+	0.169809i
$817$		−	288.000i		−	0.352509i
$818$	−86.6025	+	50.0000i	−0.105871	+	0.0611247i
$819$		−	561.184i		−	0.685207i
$820$	−311.769	−	180.000i	−0.380206	−	0.219512i
$821$	1188.00			1.44702			0.723508	−	0.690316i	$-0.242529\pi$
$821$	1188.00			1.44702			0.723508	+	0.690316i	$0.242529\pi$
$822$	190.526	+	330.000i	0.231783	+	0.401460i
$823$	384.515			0.467212			0.233606	−	0.972331i	$-0.424947\pi$
$823$	384.515			0.467212			0.233606	+	0.972331i	$0.424947\pi$
$824$		−	83.1384i		−	0.100896i
$825$		−	450.000i		−	0.545455i
$826$	324.000	+	561.184i	0.392252	+	0.679400i
$827$	−450.333			−0.544538			−0.272269	−	0.962221i	$-0.587774\pi$
$827$	−450.333			−0.544538			−0.272269	+	0.962221i	$0.587774\pi$
$828$	−41.5692	+	72.0000i	−0.0502044	+	0.0869565i
$829$	−718.000			−0.866104			−0.433052	−	0.901369i	$-0.642563\pi$
$829$	−718.000			−0.866104			−0.433052	+	0.901369i	$0.642563\pi$
$830$	450.333	+	780.000i	0.542570	+	0.939759i
$831$		−	467.654i		−	0.562760i
$832$			1152.00i			1.38462i
$833$			590.000i			0.708283i
$834$	−324.000	−	561.184i	−0.388489	−	0.672883i
$835$		−	658.179i		−	0.788239i
$836$	288.000	−	498.831i	0.344498	−	0.596687i
$837$		−	36.0000i		−	0.0430108i
$838$	−737.854	−	1278.00i	−0.880494	−	1.52506i
$839$			914.523i			1.09002i	0.838431	+	0.545008i	$0.183473\pi$
$839$			914.523i			1.09002i	−0.838431	+	0.545008i	$0.816527\pi$
$840$	−720.000			−0.857143
$841$	455.000			0.541023
$842$	495.367	−	286.000i	0.588321	−	0.339667i
$843$	405.300			0.480783
$844$	840.000	+	484.974i	0.995261	+	0.574614i
$845$			775.000i			0.917160i
$846$		0			0
$847$	135.100			0.159504
$848$	360.267	−	208.000i	0.424843	−	0.245283i
$849$	−144.000			−0.169611
$850$	250.000	+	433.013i	0.294118	+	0.509427i
$851$		−	374.123i		−	0.439627i
$852$	−623.538	−	360.000i	−0.731852	−	0.422535i
$853$			666.000i			0.780774i	0.920651	+	0.390387i	$0.127659\pi$
$853$			666.000i			0.780774i	−0.920651	+	0.390387i	$0.872341\pi$
$854$	1332.00	−	769.031i	1.55972	−	0.900504i
$855$	207.846			0.243095
$856$		−	1496.49i		−	1.74824i
$857$		−	182.000i		−	0.212369i	−0.994346	−	0.106184i	$-0.966137\pi$
$857$		−	182.000i		−	0.212369i	0.994346	−	0.106184i	$-0.0338634\pi$
$858$	−561.184	+	324.000i	−0.654061	+	0.377622i
$859$		−	990.733i		−	1.15336i	−0.816971	−	0.576678i	$-0.804349\pi$
$859$		−	990.733i		−	1.15336i	0.816971	−	0.576678i	$-0.195651\pi$
$860$	360.000	+	207.846i	0.418605	+	0.241682i
$861$	−324.000			−0.376307
$862$	−124.708	−	216.000i	−0.144672	−	0.250580i
$863$	−1170.87			−1.35674			−0.678370	−	0.734721i	$-0.737313\pi$
$863$	−1170.87			−1.35674			−0.678370	+	0.734721i	$0.737313\pi$
$864$	−144.000	−	83.1384i	−0.166667	−	0.0962250i
$865$	−730.000			−0.843931
$866$	−36.0000	−	62.3538i	−0.0415704	−	0.0720021i
$867$	−327.358			−0.377575
$868$	249.415	+	144.000i	0.287345	+	0.165899i
$869$	936.000			1.07710
$870$	−311.769	−	540.000i	−0.358355	−	0.620690i
$871$		−	748.246i		−	0.859065i
$872$			208.000i			0.238532i
$873$		−	216.000i		−	0.247423i
$874$	96.0000	+	166.277i	0.109840	+	0.190248i
$875$			1299.04i			1.48461i
$876$	216.000	+	124.708i	0.246575	+	0.142360i
$877$		−	774.000i		−	0.882554i	−0.897371	−	0.441277i	$-0.854526\pi$
$877$		−	774.000i		−	0.882554i	0.897371	−	0.441277i	$-0.145474\pi$
$878$	−782.887	−	1356.00i	−0.891671	−	1.54442i
$879$		−	100.459i		−	0.114288i
$880$	415.692	+	720.000i	0.472377	+	0.818182i
$881$	−1602.00			−1.81839			−0.909194	−	0.416373i	$-0.863301\pi$
$881$	−1602.00			−1.81839			−0.909194	+	0.416373i	$0.863301\pi$
$882$	−306.573	+	177.000i	−0.347588	+	0.200680i
$883$	−415.692			−0.470773			−0.235386	−	0.971902i	$-0.575636\pi$
$883$	−415.692			−0.470773			−0.235386	+	0.971902i	$0.575636\pi$
$884$	360.000	−	623.538i	0.407240	−	0.705360i
$885$	270.000			0.305085
$886$	−372.000	+	214.774i	−0.419865	+	0.242409i
$887$	−367.195			−0.413974			−0.206987	−	0.978344i	$-0.566366\pi$
$887$	−367.195			−0.413974			−0.206987	+	0.978344i	$0.566366\pi$
$888$	748.246			0.842619
$889$	2268.00			2.55118
$890$	90.0000	+	155.885i	0.101124	+	0.175151i
$891$		−	93.5307i		−	0.104973i
$892$	−187.061	+	324.000i	−0.209710	+	0.363229i
$893$		0			0
$894$	−864.000	+	498.831i	−0.966443	+	0.557976i
$895$	−363.731			−0.406403
$896$	1152.00	−	665.108i	1.28571	−	0.742307i
$897$		−	216.000i		−	0.240803i
$898$	93.5307	−	54.0000i	0.104155	−	0.0601336i
$899$			249.415i			0.277436i
$900$	−150.000	+	259.808i	−0.166667	+	0.288675i
$901$	−260.000			−0.288568
$902$	187.061	+	324.000i	0.207385	+	0.359202i
$903$	374.123			0.414311
$904$	−80.0000			−0.0884956
$905$		−	1310.00i		−	1.44751i
$906$	324.000	+	561.184i	0.357616	+	0.619409i
$907$	1434.14			1.58119			0.790594	−	0.612340i	$-0.209772\pi$
$907$	1434.14			1.58119			0.790594	+	0.612340i	$0.209772\pi$
$908$	−429.549	+	744.000i	−0.473071	+	0.819383i
$909$	108.000			0.118812
$910$	1620.00	−	935.307i	1.78022	−	1.02781i
$911$		−	1080.80i		−	1.18639i	−0.805059	−	0.593194i	$-0.797867\pi$
$911$		−	1080.80i		−	1.18639i	0.805059	−	0.593194i	$-0.202133\pi$
$912$	−332.554	+	192.000i	−0.364642	+	0.210526i
$913$		−	936.000i		−	1.02519i
$914$	−288.000	−	498.831i	−0.315098	−	0.545767i
$915$		−	640.859i		−	0.700392i
$916$	−676.000	+	1170.87i	−0.737991	+	1.27824i
$917$			1404.00i			1.53108i
$918$	51.9615	+	90.0000i	0.0566030	+	0.0980392i
$919$		−	187.061i		−	0.203549i	−0.994807	−	0.101774i	$-0.967548\pi$
$919$		−	187.061i		−	0.203549i	0.994807	−	0.101774i	$-0.0324520\pi$
$920$	−277.128			−0.301226
$921$	468.000			0.508143
$922$	498.831	−	288.000i	0.541031	−	0.312364i
$923$	1870.61			2.02667
$924$	648.000	+	374.123i	0.701299	+	0.404895i
$925$		−	1350.00i		−	1.45946i
$926$	702.000	−	405.300i	0.758099	−	0.437689i
$927$	−31.1769			−0.0336321
$928$	997.661	+	576.000i	1.07507	+	0.620690i
$929$	−54.0000			−0.0581270			−0.0290635	−	0.999578i	$-0.509253\pi$
$929$	−54.0000			−0.0581270			−0.0290635	+	0.999578i	$0.509253\pi$
$930$	103.923	−	60.0000i	0.111745	−	0.0645161i
$931$			817.528i			0.878118i
$932$	630.466	+	364.000i	0.676466	+	0.390558i
$933$			468.000i			0.501608i
$934$	−996.000	+	575.041i	−1.06638	+	0.615675i
$935$		−	519.615i		−	0.555738i
$936$	432.000			0.461538
$937$			936.000i			0.998933i	0.866333	+	0.499466i	$0.166471\pi$
$937$			936.000i			0.998933i	−0.866333	+	0.499466i	$0.833529\pi$
$938$	−748.246	+	432.000i	−0.797704	+	0.460554i
$939$			810.600i			0.863259i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	405.300	+	702.000i	0.430255	+	0.745223i
$943$	−124.708			−0.132246
$944$	−432.000	+	249.415i	−0.457627	+	0.264211i
$945$			270.000i			0.285714i
$946$	−216.000	−	374.123i	−0.228330	−	0.395479i
$947$	1032.30			1.09008			0.545038	−	0.838411i	$-0.316515\pi$
$947$	1032.30			1.09008			0.545038	+	0.838411i	$0.316515\pi$
$948$	−540.400	−	312.000i	−0.570042	−	0.329114i
$949$	−648.000			−0.682824
$950$	346.410	+	600.000i	0.364642	+	0.631579i
$951$		−	433.013i		−	0.455324i
$952$	−831.384			−0.873303
$953$		−	1550.00i		−	1.62644i	−0.581954	−	0.813221i	$-0.697712\pi$
$953$		−	1550.00i		−	1.62644i	0.581954	−	0.813221i	$-0.302288\pi$
$954$	−78.0000	−	135.100i	−0.0817610	−	0.141614i
$955$	−935.307			−0.979380
$956$	−1224.00	−	706.677i	−1.28033	−	0.739202i
$957$			648.000i			0.677116i
$958$	145.492	+	252.000i	0.151871	+	0.263048i
$959$			1143.15i			1.19203i
$960$		−	554.256i		−	0.577350i
$961$	913.000			0.950052
$962$	−1683.55	+	972.000i	−1.75006	+	1.01040i
$963$	−561.184			−0.582746
$964$	−212.000	+	367.195i	−0.219917	+	0.380907i
$965$	−900.000			−0.932642
$966$	−216.000	+	124.708i	−0.223602	+	0.129097i
$967$	1215.90			1.25739			0.628697	−	0.777650i	$-0.283589\pi$
$967$	1215.90			1.25739			0.628697	+	0.777650i	$0.283589\pi$
$968$			104.000i			0.107438i
$969$	240.000			0.247678
$970$	623.538	−	360.000i	0.642823	−	0.371134i
$971$			1839.44i			1.89437i	0.320681	+	0.947187i	$0.396088\pi$
$971$			1839.44i			1.89437i	−0.320681	+	0.947187i	$0.603912\pi$
$972$	−31.1769	+	54.0000i	−0.0320750	+	0.0555556i
$973$		−	1944.00i		−	1.99794i
$974$	450.000	−	259.808i	0.462012	−	0.266743i
$975$		−	779.423i		−	0.799408i
$976$	592.000	+	1025.37i	0.606557	+	1.05059i
$977$		−	206.000i		−	0.210850i	−0.994427	−	0.105425i	$-0.966380\pi$
$977$		−	206.000i		−	0.210850i	0.994427	−	0.105425i	$-0.0336202\pi$
$978$	−374.123	+	216.000i	−0.382539	+	0.220859i
$979$		−	187.061i		−	0.191074i
$980$	−1021.91	−	590.000i	−1.04277	−	0.602041i
$981$	78.0000			0.0795107
$982$	72.7461	+	126.000i	0.0740796	+	0.128310i
$983$	720.533			0.732994			0.366497	−	0.930419i	$-0.380557\pi$
$983$	720.533			0.732994			0.366497	+	0.930419i	$0.380557\pi$
$984$		−	249.415i		−	0.253471i
$985$	−770.000			−0.781726
$986$	−360.000	−	623.538i	−0.365112	−	0.632392i
$987$		0			0
$988$	498.831	−	864.000i	0.504889	−	0.874494i
$989$	144.000			0.145602
$990$	270.000	−	155.885i	0.272727	−	0.157459i
$991$			1323.29i			1.33530i	0.744473	+	0.667652i	$0.232701\pi$
$991$			1323.29i			1.33530i	−0.744473	+	0.667652i	$0.767299\pi$
$992$	−110.851	+	192.000i	−0.111745	+	0.193548i
$993$		−	648.000i		−	0.652568i
$994$	−1080.00	−	1870.61i	−1.08652	−	1.88191i
$995$	−935.307			−0.940007
$996$	−312.000	+	540.400i	−0.313253	+	0.542570i
$997$		−	198.000i		−	0.198596i	−0.995058	−	0.0992979i	$-0.968340\pi$
$997$		−	198.000i		−	0.198596i	0.995058	−	0.0992979i	$-0.0316597\pi$
$998$	443.405	+	768.000i	0.444294	+	0.769539i
$999$		−	280.592i		−	0.280873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.f.a.19.2	yes	4
3.2	odd	2		180.3.f.e.19.3		4
4.3	odd	2	inner	60.3.f.a.19.4	yes	4
5.2	odd	4		300.3.c.a.151.1		2
5.3	odd	4		300.3.c.c.151.2		2
5.4	even	2	inner	60.3.f.a.19.3	yes	4
8.3	odd	2		960.3.j.b.319.2		4
8.5	even	2		960.3.j.b.319.4		4
12.11	even	2		180.3.f.e.19.1		4
15.2	even	4		900.3.c.j.451.2		2
15.8	even	4		900.3.c.f.451.1		2
15.14	odd	2		180.3.f.e.19.2		4
20.3	even	4		300.3.c.c.151.1		2
20.7	even	4		300.3.c.a.151.2		2
20.19	odd	2	inner	60.3.f.a.19.1	✓	4
40.19	odd	2		960.3.j.b.319.3		4
40.29	even	2		960.3.j.b.319.1		4
60.23	odd	4		900.3.c.f.451.2		2
60.47	odd	4		900.3.c.j.451.1		2
60.59	even	2		180.3.f.e.19.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.a.19.1	✓	4	20.19	odd	2	inner
60.3.f.a.19.2	yes	4	1.1	even	1	trivial
60.3.f.a.19.3	yes	4	5.4	even	2	inner
60.3.f.a.19.4	yes	4	4.3	odd	2	inner
180.3.f.e.19.1		4	12.11	even	2
180.3.f.e.19.2		4	15.14	odd	2
180.3.f.e.19.3		4	3.2	odd	2
180.3.f.e.19.4		4	60.59	even	2
300.3.c.a.151.1		2	5.2	odd	4
300.3.c.a.151.2		2	20.7	even	4
300.3.c.c.151.1		2	20.3	even	4
300.3.c.c.151.2		2	5.3	odd	4
900.3.c.f.451.1		2	15.8	even	4
900.3.c.f.451.2		2	60.23	odd	4
900.3.c.j.451.1		2	60.47	odd	4
900.3.c.j.451.2		2	15.2	even	4
960.3.j.b.319.1		4	40.29	even	2
960.3.j.b.319.2		4	8.3	odd	2
960.3.j.b.319.3		4	40.19	odd	2
960.3.j.b.319.4		4	8.5	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} -1.73205 q^{3} +(2.00000 - 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 - 1.73205i) q^{6} +10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} -1.73205 q^{3} +(2.00000 - 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 - 1.73205i) q^{6} +10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +(5.00000 + 8.66025i) q^{10} -10.3923i q^{11} +(-3.46410 + 6.00000i) q^{12} -18.0000i q^{13} +(-18.0000 + 10.3923i) q^{14} +8.66025i q^{15} +(-8.00000 - 13.8564i) q^{16} +10.0000i q^{17} +(-5.19615 + 3.00000i) q^{18} +13.8564i q^{19} +(-17.3205 - 10.0000i) q^{20} -18.0000 q^{21} +(10.3923 + 18.0000i) q^{22} -6.92820 q^{23} -13.8564i q^{24} -25.0000 q^{25} +(18.0000 + 31.1769i) q^{26} -5.19615 q^{27} +(20.7846 - 36.0000i) q^{28} +36.0000 q^{29} +(-8.66025 - 15.0000i) q^{30} +6.92820i q^{31} +(27.7128 + 16.0000i) q^{32} +18.0000i q^{33} +(-10.0000 - 17.3205i) q^{34} -51.9615i q^{35} +(6.00000 - 10.3923i) q^{36} +54.0000i q^{37} +(-13.8564 - 24.0000i) q^{38} +31.1769i q^{39} +40.0000 q^{40} +18.0000 q^{41} +(31.1769 - 18.0000i) q^{42} -20.7846 q^{43} +(-36.0000 - 20.7846i) q^{44} -15.0000i q^{45} +(12.0000 - 6.92820i) q^{46} +(13.8564 + 24.0000i) q^{48} +59.0000 q^{49} +(43.3013 - 25.0000i) q^{50} -17.3205i q^{51} +(-62.3538 - 36.0000i) q^{52} +26.0000i q^{53} +(9.00000 - 5.19615i) q^{54} -51.9615 q^{55} +83.1384i q^{56} -24.0000i q^{57} +(-62.3538 + 36.0000i) q^{58} -31.1769i q^{59} +(30.0000 + 17.3205i) q^{60} -74.0000 q^{61} +(-6.92820 - 12.0000i) q^{62} +31.1769 q^{63} -64.0000 q^{64} -90.0000 q^{65} +(-18.0000 - 31.1769i) q^{66} +41.5692 q^{67} +(34.6410 + 20.0000i) q^{68} +12.0000 q^{69} +(51.9615 + 90.0000i) q^{70} +103.923i q^{71} +24.0000i q^{72} -36.0000i q^{73} +(-54.0000 - 93.5307i) q^{74} +43.3013 q^{75} +(48.0000 + 27.7128i) q^{76} -108.000i q^{77} +(-31.1769 - 54.0000i) q^{78} +90.0666i q^{79} +(-69.2820 + 40.0000i) q^{80} +9.00000 q^{81} +(-31.1769 + 18.0000i) q^{82} +90.0666 q^{83} +(-36.0000 + 62.3538i) q^{84} +50.0000 q^{85} +(36.0000 - 20.7846i) q^{86} -62.3538 q^{87} +83.1384 q^{88} +18.0000 q^{89} +(15.0000 + 25.9808i) q^{90} -187.061i q^{91} +(-13.8564 + 24.0000i) q^{92} -12.0000i q^{93} +69.2820 q^{95} +(-48.0000 - 27.7128i) q^{96} -72.0000i q^{97} +(-102.191 + 59.0000i) q^{98} -31.1769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 + 12 * q^6 + 12 * q^9	\( 4 q + 8 q^{4} + 12 q^{6} + 12 q^{9} + 20 q^{10} - 72 q^{14} - 32 q^{16} - 72 q^{21} - 100 q^{25} + 72 q^{26} + 144 q^{29} - 40 q^{34} + 24 q^{36} + 160 q^{40} + 72 q^{41} - 144 q^{44} + 48 q^{46} + 236 q^{49} + 36 q^{54} + 120 q^{60} - 296 q^{61} - 256 q^{64} - 360 q^{65} - 72 q^{66} + 48 q^{69} - 216 q^{74} + 192 q^{76} + 36 q^{81} - 144 q^{84} + 200 q^{85} + 144 q^{86} + 72 q^{89} + 60 q^{90} - 192 q^{96}+O(q^{100}) \) 4 * q + 8 * q^4 + 12 * q^6 + 12 * q^9 + 20 * q^10 - 72 * q^14 - 32 * q^16 - 72 * q^21 - 100 * q^25 + 72 * q^26 + 144 * q^29 - 40 * q^34 + 24 * q^36 + 160 * q^40 + 72 * q^41 - 144 * q^44 + 48 * q^46 + 236 * q^49 + 36 * q^54 + 120 * q^60 - 296 * q^61 - 256 * q^64 - 360 * q^65 - 72 * q^66 + 48 * q^69 - 216 * q^74 + 192 * q^76 + 36 * q^81 - 144 * q^84 + 200 * q^85 + 144 * q^86 + 72 * q^89 + 60 * q^90 - 192 * q^96

Introduction

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