LMFDB - Embedded newform 228.3.l.a.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(145,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("228.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.l (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:	$6.21255002741$
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			145.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	228.145
Dual form			228.3.l.a.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-3.00000 - 5.19615i) q^{5} -5.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-3.00000 - 5.19615i) q^{5} -5.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +(-16.5000 - 9.52628i) q^{13} +(-9.00000 - 5.19615i) q^{15} +(-3.00000 - 5.19615i) q^{17} +(-13.0000 + 13.8564i) q^{19} +(-7.50000 + 4.33013i) q^{21} +(12.0000 - 20.7846i) q^{23} +(-5.50000 + 9.52628i) q^{25} -5.19615i q^{27} +(27.0000 + 15.5885i) q^{29} -29.4449i q^{31} +(15.0000 + 25.9808i) q^{35} -60.6218i q^{37} -33.0000 q^{39} +(-36.0000 + 20.7846i) q^{41} +(12.5000 + 21.6506i) q^{43} -18.0000 q^{45} +(21.0000 - 36.3731i) q^{47} -24.0000 q^{49} +(-9.00000 - 5.19615i) q^{51} +(54.0000 + 31.1769i) q^{53} +(-7.50000 + 32.0429i) q^{57} +(63.0000 - 36.3731i) q^{59} +(-21.5000 + 37.2391i) q^{61} +(-7.50000 + 12.9904i) q^{63} +114.315i q^{65} +(49.5000 + 28.5788i) q^{67} -41.5692i q^{69} +(54.0000 - 31.1769i) q^{71} +(-5.50000 - 9.52628i) q^{73} +19.0526i q^{75} +(1.50000 - 0.866025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +126.000 q^{83} +(-18.0000 + 31.1769i) q^{85} +54.0000 q^{87} +(-9.00000 - 5.19615i) q^{89} +(82.5000 + 47.6314i) q^{91} +(-25.5000 - 44.1673i) q^{93} +(111.000 + 25.9808i) q^{95} +(-114.000 + 65.8179i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 6 q^{5} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 6 * q^5 - 10 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 6 q^{5} - 10 q^{7} + 3 q^{9} - 33 q^{13} - 18 q^{15} - 6 q^{17} - 26 q^{19} - 15 q^{21} + 24 q^{23} - 11 q^{25} + 54 q^{29} + 30 q^{35} - 66 q^{39} - 72 q^{41} + 25 q^{43} - 36 q^{45} + 42 q^{47} - 48 q^{49} - 18 q^{51} + 108 q^{53} - 15 q^{57} + 126 q^{59} - 43 q^{61} - 15 q^{63} + 99 q^{67} + 108 q^{71} - 11 q^{73} + 3 q^{79} - 9 q^{81} + 252 q^{83} - 36 q^{85} + 108 q^{87} - 18 q^{89} + 165 q^{91} - 51 q^{93} + 222 q^{95} - 228 q^{97}+O(q^{100}) $ 2 * q + 3 * q^3 - 6 * q^5 - 10 * q^7 + 3 * q^9 - 33 * q^13 - 18 * q^15 - 6 * q^17 - 26 * q^19 - 15 * q^21 + 24 * q^23 - 11 * q^25 + 54 * q^29 + 30 * q^35 - 66 * q^39 - 72 * q^41 + 25 * q^43 - 36 * q^45 + 42 * q^47 - 48 * q^49 - 18 * q^51 + 108 * q^53 - 15 * q^57 + 126 * q^59 - 43 * q^61 - 15 * q^63 + 99 * q^67 + 108 * q^71 - 11 * q^73 + 3 * q^79 - 9 * q^81 + 252 * q^83 - 36 * q^85 + 108 * q^87 - 18 * q^89 + 165 * q^91 - 51 * q^93 + 222 * q^95 - 228 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−3.00000	−	5.19615i	−0.600000	−	1.03923i	−0.992820	−	0.119615i	$-0.961834\pi$
$5$	−3.00000	−	5.19615i	−0.600000	−	1.03923i	0.392820	−	0.919615i	$-0.371499\pi$
$6$		0			0
$7$	−5.00000			−0.714286			−0.357143	−	0.934050i	$-0.616249\pi$
$7$	−5.00000			−0.714286			−0.357143	+	0.934050i	$0.616249\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	−16.5000	−	9.52628i	−1.26923	−	0.732791i	−0.294388	−	0.955686i	$-0.595116\pi$
$13$	−16.5000	−	9.52628i	−1.26923	−	0.732791i	−0.974842	+	0.222895i	$0.928449\pi$
$14$		0			0
$15$	−9.00000	−	5.19615i	−0.600000	−	0.346410i
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.176471	−	0.305656i	0.764199	−	0.644981i	$-0.223135\pi$
$17$	−3.00000	−	5.19615i	−0.176471	−	0.305656i	−0.940669	+	0.339325i	$0.889801\pi$
$18$		0			0
$19$	−13.0000	+	13.8564i	−0.684211	+	0.729285i
$19$	−13.0000	+	13.8564i	−0.684211	+	0.729285i
$20$		0			0
$21$	−7.50000	+	4.33013i	−0.357143	+	0.206197i
$22$		0			0
$23$	12.0000	−	20.7846i	0.521739	−	0.903679i	−0.477941	−	0.878392i	$-0.658617\pi$
$23$	12.0000	−	20.7846i	0.521739	−	0.903679i	0.999680	−	0.0252868i	$-0.00804990\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	27.0000	+	15.5885i	0.931034	+	0.537533i	0.887139	−	0.461503i	$-0.152690\pi$
$29$	27.0000	+	15.5885i	0.931034	+	0.537533i	0.0438959	+	0.999036i	$0.486023\pi$
$30$		0			0
$31$		−	29.4449i		−	0.949834i	−0.880031	−	0.474917i	$-0.842478\pi$
$31$		−	29.4449i		−	0.949834i	0.880031	−	0.474917i	$-0.157522\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	15.0000	+	25.9808i	0.428571	+	0.742307i
$36$		0			0
$37$		−	60.6218i		−	1.63843i	−0.573489	−	0.819213i	$-0.694410\pi$
$37$		−	60.6218i		−	1.63843i	0.573489	−	0.819213i	$-0.305590\pi$
$38$		0			0
$39$	−33.0000			−0.846154
$40$		0			0
$41$	−36.0000	+	20.7846i	−0.878049	+	0.506942i	−0.870015	−	0.493026i	$-0.835891\pi$
$41$	−36.0000	+	20.7846i	−0.878049	+	0.506942i	−0.00803422	+	0.999968i	$0.502557\pi$
$42$		0			0
$43$	12.5000	+	21.6506i	0.290698	+	0.503503i	0.973975	−	0.226656i	$-0.0727793\pi$
$43$	12.5000	+	21.6506i	0.290698	+	0.503503i	−0.683277	+	0.730159i	$0.739446\pi$
$44$		0			0
$45$	−18.0000			−0.400000
$46$		0			0
$47$	21.0000	−	36.3731i	0.446809	−	0.773895i	−0.551368	−	0.834262i	$-0.685894\pi$
$47$	21.0000	−	36.3731i	0.446809	−	0.773895i	0.998176	+	0.0603673i	$0.0192272\pi$
$48$		0			0
$49$	−24.0000			−0.489796
$50$		0			0
$51$	−9.00000	−	5.19615i	−0.176471	−	0.101885i
$52$		0			0
$53$	54.0000	+	31.1769i	1.01887	+	0.588244i	0.913776	−	0.406219i	$-0.133153\pi$
$53$	54.0000	+	31.1769i	1.01887	+	0.588244i	0.105092	+	0.994462i	$0.466486\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.50000	+	32.0429i	−0.131579	+	0.562157i
$58$		0			0
$59$	63.0000	−	36.3731i	1.06780	−	0.616493i	0.140218	−	0.990121i	$-0.455220\pi$
$59$	63.0000	−	36.3731i	1.06780	−	0.616493i	0.927579	+	0.373628i	$0.121886\pi$
$60$		0			0
$61$	−21.5000	+	37.2391i	−0.352459	+	0.610477i	−0.986680	−	0.162675i	$-0.947988\pi$
$61$	−21.5000	+	37.2391i	−0.352459	+	0.610477i	0.634221	+	0.773152i	$0.281321\pi$
$62$		0			0
$63$	−7.50000	+	12.9904i	−0.119048	+	0.206197i
$64$		0			0
$65$			114.315i			1.75870i
$66$		0			0
$67$	49.5000	+	28.5788i	0.738806	+	0.426550i	0.821635	−	0.570014i	$-0.193062\pi$
$67$	49.5000	+	28.5788i	0.738806	+	0.426550i	−0.0828290	+	0.996564i	$0.526396\pi$
$68$		0			0
$69$		−	41.5692i		−	0.602452i
$70$		0			0
$71$	54.0000	−	31.1769i	0.760563	−	0.439111i	−0.0689346	−	0.997621i	$-0.521960\pi$
$71$	54.0000	−	31.1769i	0.760563	−	0.439111i	0.829498	+	0.558510i	$0.188627\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.0753425	−	0.130497i	0.825893	−	0.563827i	$-0.190672\pi$
$73$	−5.50000	−	9.52628i	−0.0753425	−	0.130497i	−0.901235	+	0.433330i	$0.857338\pi$
$74$		0			0
$75$			19.0526i			0.254034i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.50000	−	0.866025i	0.0189873	−	0.0109623i	−0.490476	−	0.871455i	$-0.663177\pi$
$79$	1.50000	−	0.866025i	0.0189873	−	0.0109623i	0.509464	+	0.860492i	$0.329844\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	126.000			1.51807			0.759036	−	0.651048i	$-0.225671\pi$
$83$	126.000			1.51807			0.759036	+	0.651048i	$0.225671\pi$
$84$		0			0
$85$	−18.0000	+	31.1769i	−0.211765	+	0.366787i
$86$		0			0
$87$	54.0000			0.620690
$88$		0			0
$89$	−9.00000	−	5.19615i	−0.101124	−	0.0583837i	0.448585	−	0.893740i	$-0.351928\pi$
$89$	−9.00000	−	5.19615i	−0.101124	−	0.0583837i	−0.549709	+	0.835356i	$0.685261\pi$
$90$		0			0
$91$	82.5000	+	47.6314i	0.906593	+	0.523422i
$92$		0			0
$93$	−25.5000	−	44.1673i	−0.274194	−	0.474917i
$94$		0			0
$95$	111.000	+	25.9808i	1.16842	+	0.273482i
$96$		0			0
$97$	−114.000	+	65.8179i	−1.17526	+	0.678535i	−0.954913	−	0.296887i	$-0.904052\pi$
$97$	−114.000	+	65.8179i	−1.17526	+	0.678535i	−0.220345	+	0.975422i	$0.570718\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−78.0000	+	135.100i	−0.772277	+	1.33762i	0.164035	+	0.986455i	$0.447549\pi$
$101$	−78.0000	+	135.100i	−0.772277	+	1.33762i	−0.936312	+	0.351169i	$0.885784\pi$
$102$		0			0
$103$			36.3731i			0.353137i	0.984288	+	0.176568i	$0.0564996\pi$
$103$			36.3731i			0.353137i	−0.984288	+	0.176568i	$0.943500\pi$
$104$		0			0
$105$	45.0000	+	25.9808i	0.428571	+	0.247436i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	90.0000	−	51.9615i	0.825688	−	0.476711i	−0.0266859	−	0.999644i	$-0.508495\pi$
$109$	90.0000	−	51.9615i	0.825688	−	0.476711i	0.852374	+	0.522933i	$0.175162\pi$
$110$		0			0
$111$	−52.5000	−	90.9327i	−0.472973	−	0.819213i
$112$		0			0
$113$		−	155.885i		−	1.37951i	−0.724043	−	0.689755i	$-0.757718\pi$
$113$		−	155.885i		−	1.37951i	0.724043	−	0.689755i	$-0.242282\pi$
$114$		0			0
$115$	−144.000			−1.25217
$116$		0			0
$117$	−49.5000	+	28.5788i	−0.423077	+	0.244264i
$118$		0			0
$119$	15.0000	+	25.9808i	0.126050	+	0.218326i
$120$		0			0
$121$	−121.000			−1.00000
$122$		0			0
$123$	−36.0000	+	62.3538i	−0.292683	+	0.506942i
$124$		0			0
$125$	−84.0000			−0.672000
$126$		0			0
$127$	−36.0000	−	20.7846i	−0.283465	−	0.163658i	0.351526	−	0.936178i	$-0.385663\pi$
$127$	−36.0000	−	20.7846i	−0.283465	−	0.163658i	−0.634991	+	0.772520i	$0.718996\pi$
$128$		0			0
$129$	37.5000	+	21.6506i	0.290698	+	0.167834i
$130$		0			0
$131$	−24.0000	−	41.5692i	−0.183206	−	0.317322i	0.759764	−	0.650198i	$-0.225314\pi$
$131$	−24.0000	−	41.5692i	−0.183206	−	0.317322i	−0.942971	+	0.332876i	$0.891981\pi$
$132$		0			0
$133$	65.0000	−	69.2820i	0.488722	−	0.520918i
$134$		0			0
$135$	−27.0000	+	15.5885i	−0.200000	+	0.115470i
$136$		0			0
$137$	66.0000	−	114.315i	0.481752	−	0.834419i	−0.518029	−	0.855363i	$-0.673334\pi$
$137$	66.0000	−	114.315i	0.481752	−	0.834419i	0.999781	+	0.0209445i	$0.00666734\pi$
$138$		0			0
$139$	−0.500000	+	0.866025i	−0.00359712	+	0.00623040i	−0.867818	−	0.496882i	$-0.834478\pi$
$139$	−0.500000	+	0.866025i	−0.00359712	+	0.00623040i	0.864221	+	0.503112i	$0.167812\pi$
$140$		0			0
$141$		−	72.7461i		−	0.515930i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		−	187.061i		−	1.29008i
$146$		0			0
$147$	−36.0000	+	20.7846i	−0.244898	+	0.141392i
$148$		0			0
$149$	−90.0000	−	155.885i	−0.604027	−	1.04621i	−0.992204	−	0.124621i	$-0.960229\pi$
$149$	−90.0000	−	155.885i	−0.604027	−	1.04621i	0.388178	−	0.921585i	$-0.373105\pi$
$150$		0			0
$151$		−	235.559i		−	1.55999i	−0.625784	−	0.779996i	$-0.715221\pi$
$151$		−	235.559i		−	1.55999i	0.625784	−	0.779996i	$-0.284779\pi$
$152$		0			0
$153$	−18.0000			−0.117647
$154$		0			0
$155$	−153.000	+	88.3346i	−0.987097	+	0.569901i
$156$		0			0
$157$	38.5000	+	66.6840i	0.245223	+	0.424739i	0.962194	−	0.272364i	$-0.0878055\pi$
$157$	38.5000	+	66.6840i	0.245223	+	0.424739i	−0.716971	+	0.697103i	$0.754472\pi$
$158$		0			0
$159$	108.000			0.679245
$160$		0			0
$161$	−60.0000	+	103.923i	−0.372671	+	0.645485i
$162$		0			0
$163$	145.000			0.889571			0.444785	−	0.895637i	$-0.353280\pi$
$163$	145.000			0.889571			0.444785	+	0.895637i	$0.353280\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−261.000	−	150.688i	−1.56287	−	0.902326i	−0.996964	−	0.0778587i	$-0.975192\pi$
$167$	−261.000	−	150.688i	−1.56287	−	0.902326i	−0.565910	−	0.824467i	$-0.691475\pi$
$168$		0			0
$169$	97.0000	+	168.009i	0.573964	+	0.994136i
$170$		0			0
$171$	16.5000	+	54.5596i	0.0964912	+	0.319062i
$172$		0			0
$173$	−9.00000	+	5.19615i	−0.0520231	+	0.0300356i	−0.525786	−	0.850617i	$-0.676229\pi$
$173$	−9.00000	+	5.19615i	−0.0520231	+	0.0300356i	0.473763	+	0.880652i	$0.342895\pi$
$174$		0			0
$175$	27.5000	−	47.6314i	0.157143	−	0.272179i
$176$		0			0
$177$	63.0000	−	109.119i	0.355932	−	0.616493i
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$	−66.0000	−	38.1051i	−0.364641	−	0.210526i	0.306474	−	0.951879i	$-0.400851\pi$
$181$	−66.0000	−	38.1051i	−0.364641	−	0.210526i	−0.671115	+	0.741354i	$0.734184\pi$
$182$		0			0
$183$			74.4782i			0.406985i
$184$		0			0
$185$	−315.000	+	181.865i	−1.70270	+	0.983056i
$186$		0			0
$187$		0			0
$188$		0			0
$189$			25.9808i			0.137464i
$190$		0			0
$191$	−18.0000			−0.0942408			−0.0471204	−	0.998889i	$-0.515004\pi$
$191$	−18.0000			−0.0942408			−0.0471204	+	0.998889i	$0.515004\pi$
$192$		0			0
$193$	49.5000	−	28.5788i	0.256477	−	0.148077i	−0.366250	−	0.930517i	$-0.619358\pi$
$193$	49.5000	−	28.5788i	0.256477	−	0.148077i	0.622726	+	0.782440i	$0.286025\pi$
$194$		0			0
$195$	99.0000	+	171.473i	0.507692	+	0.879349i
$196$		0			0
$197$	−90.0000			−0.456853			−0.228426	−	0.973561i	$-0.573358\pi$
$197$	−90.0000			−0.456853			−0.228426	+	0.973561i	$0.573358\pi$
$198$		0			0
$199$	111.500	−	193.124i	0.560302	−	0.970471i	−0.437168	−	0.899380i	$-0.644019\pi$
$199$	111.500	−	193.124i	0.560302	−	0.970471i	0.997470	−	0.0710910i	$-0.0226481\pi$
$200$		0			0
$201$	99.0000			0.492537
$202$		0			0
$203$	−135.000	−	77.9423i	−0.665025	−	0.383952i
$204$		0			0
$205$	216.000	+	124.708i	1.05366	+	0.608330i
$206$		0			0
$207$	−36.0000	−	62.3538i	−0.173913	−	0.301226i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−292.500	+	168.875i	−1.38626	+	0.800355i	−0.992891	−	0.119027i	$-0.962022\pi$
$211$	−292.500	+	168.875i	−1.38626	+	0.800355i	−0.393365	+	0.919382i	$0.628689\pi$
$212$		0			0
$213$	54.0000	−	93.5307i	0.253521	−	0.439111i
$214$		0			0
$215$	75.0000	−	129.904i	0.348837	−	0.604204i
$216$		0			0
$217$			147.224i			0.678453i
$218$		0			0
$219$	−16.5000	−	9.52628i	−0.0753425	−	0.0434990i
$220$		0			0
$221$			114.315i			0.517264i
$222$		0			0
$223$	−370.500	+	213.908i	−1.66143	+	0.959230i	−0.689404	+	0.724377i	$0.742128\pi$
$223$	−370.500	+	213.908i	−1.66143	+	0.959230i	−0.972031	+	0.234853i	$0.924539\pi$
$224$		0			0
$225$	16.5000	+	28.5788i	0.0733333	+	0.127017i
$226$		0			0
$227$		−	176.669i		−	0.778278i	−0.921179	−	0.389139i	$-0.872773\pi$
$227$		−	176.669i		−	0.778278i	0.921179	−	0.389139i	$-0.127227\pi$
$228$		0			0
$229$	391.000			1.70742			0.853712	−	0.520746i	$-0.174346\pi$
$229$	391.000			1.70742			0.853712	+	0.520746i	$0.174346\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−72.0000	−	124.708i	−0.309013	−	0.535226i	0.669134	−	0.743142i	$-0.266665\pi$
$233$	−72.0000	−	124.708i	−0.309013	−	0.535226i	−0.978147	+	0.207916i	$0.933332\pi$
$234$		0			0
$235$	−252.000			−1.07234
$236$		0			0
$237$	1.50000	−	2.59808i	0.00632911	−	0.0109623i
$238$		0			0
$239$	450.000			1.88285			0.941423	−	0.337229i	$-0.109490\pi$
$239$	450.000			1.88285			0.941423	+	0.337229i	$0.109490\pi$
$240$		0			0
$241$	67.5000	+	38.9711i	0.280083	+	0.161706i	0.633461	−	0.773775i	$-0.281634\pi$
$241$	67.5000	+	38.9711i	0.280083	+	0.161706i	−0.353378	+	0.935481i	$0.614967\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	72.0000	+	124.708i	0.293878	+	0.509011i
$246$		0			0
$247$	346.500	−	104.789i	1.40283	−	0.424247i
$248$		0			0
$249$	189.000	−	109.119i	0.759036	−	0.438230i
$250$		0			0
$251$	21.0000	−	36.3731i	0.0836653	−	0.144913i	−0.821156	−	0.570703i	$-0.806671\pi$
$251$	21.0000	−	36.3731i	0.0836653	−	0.144913i	0.904822	+	0.425791i	$0.140004\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$			62.3538i			0.244525i
$256$		0			0
$257$	414.000	+	239.023i	1.61089	+	0.930051i	0.989163	+	0.146820i	$0.0469039\pi$
$257$	414.000	+	239.023i	1.61089	+	0.930051i	0.621732	+	0.783230i	$0.286429\pi$
$258$		0			0
$259$			303.109i			1.17030i
$260$		0			0
$261$	81.0000	−	46.7654i	0.310345	−	0.179178i
$262$		0			0
$263$	−78.0000	−	135.100i	−0.296578	−	0.513688i	0.678773	−	0.734348i	$-0.262512\pi$
$263$	−78.0000	−	135.100i	−0.296578	−	0.513688i	−0.975351	+	0.220660i	$0.929179\pi$
$264$		0			0
$265$		−	374.123i		−	1.41178i
$266$		0			0
$267$	−18.0000			−0.0674157
$268$		0			0
$269$	−459.000	+	265.004i	−1.70632	+	0.985144i	−0.767295	+	0.641294i	$0.778398\pi$
$269$	−459.000	+	265.004i	−1.70632	+	0.985144i	−0.939025	+	0.343850i	$0.888269\pi$
$270$		0			0
$271$	257.000	+	445.137i	0.948339	+	1.64257i	0.748923	+	0.662657i	$0.230571\pi$
$271$	257.000	+	445.137i	0.948339	+	1.64257i	0.199417	+	0.979915i	$0.436095\pi$
$272$		0			0
$273$	165.000			0.604396
$274$		0			0
$275$		0			0
$276$		0			0
$277$	238.000			0.859206			0.429603	−	0.903018i	$-0.358654\pi$
$277$	238.000			0.859206			0.429603	+	0.903018i	$0.358654\pi$
$278$		0			0
$279$	−76.5000	−	44.1673i	−0.274194	−	0.158306i
$280$		0			0
$281$	−225.000	−	129.904i	−0.800712	−	0.462291i	0.0430082	−	0.999075i	$-0.486306\pi$
$281$	−225.000	−	129.904i	−0.800712	−	0.462291i	−0.843720	+	0.536784i	$0.819639\pi$
$282$		0			0
$283$	113.000	+	195.722i	0.399293	+	0.691596i	0.993639	−	0.112613i	$-0.0359222\pi$
$283$	113.000	+	195.722i	0.399293	+	0.691596i	−0.594346	+	0.804210i	$0.702589\pi$
$284$		0			0
$285$	189.000	−	57.1577i	0.663158	−	0.200553i
$286$		0			0
$287$	180.000	−	103.923i	0.627178	−	0.362101i
$288$		0			0
$289$	126.500	−	219.104i	0.437716	−	0.758147i
$290$		0			0
$291$	−114.000	+	197.454i	−0.391753	+	0.678535i
$292$		0			0
$293$		−	31.1769i		−	0.106406i	−0.998584	−	0.0532029i	$-0.983057\pi$
$293$		−	31.1769i		−	0.106406i	0.998584	−	0.0532029i	$-0.0169430\pi$
$294$		0			0
$295$	−378.000	−	218.238i	−1.28136	−	0.739791i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−396.000	+	228.631i	−1.32441	+	0.764651i
$300$		0			0
$301$	−62.5000	−	108.253i	−0.207641	−	0.359645i
$302$		0			0
$303$			270.200i			0.891749i
$304$		0			0
$305$	258.000			0.845902
$306$		0			0
$307$	54.0000	−	31.1769i	0.175896	−	0.101553i	−0.409467	−	0.912325i	$-0.634285\pi$
$307$	54.0000	−	31.1769i	0.175896	−	0.101553i	0.585363	+	0.810771i	$0.300952\pi$
$308$		0			0
$309$	31.5000	+	54.5596i	0.101942	+	0.176568i
$310$		0			0
$311$	−534.000			−1.71704			−0.858521	−	0.512779i	$-0.828616\pi$
$311$	−534.000			−1.71704			−0.858521	+	0.512779i	$0.828616\pi$
$312$		0			0
$313$	−269.000	+	465.922i	−0.859425	+	1.48857i	0.0130534	+	0.999915i	$0.495845\pi$
$313$	−269.000	+	465.922i	−0.859425	+	1.48857i	−0.872478	+	0.488653i	$0.837488\pi$
$314$		0			0
$315$	90.0000			0.285714
$316$		0			0
$317$	81.0000	+	46.7654i	0.255521	+	0.147525i	0.622289	−	0.782787i	$-0.286203\pi$
$317$	81.0000	+	46.7654i	0.255521	+	0.147525i	−0.366769	+	0.930312i	$0.619536\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	111.000	+	25.9808i	0.343653	+	0.0804358i
$324$		0			0
$325$	181.500	−	104.789i	0.558462	−	0.322428i
$326$		0			0
$327$	90.0000	−	155.885i	0.275229	−	0.476711i
$328$		0			0
$329$	−105.000	+	181.865i	−0.319149	+	0.552782i
$330$		0			0
$331$			278.860i			0.842478i	0.906950	+	0.421239i	$0.138405\pi$
$331$			278.860i			0.842478i	−0.906950	+	0.421239i	$0.861595\pi$
$332$		0			0
$333$	−157.500	−	90.9327i	−0.472973	−	0.273071i
$334$		0			0
$335$		−	342.946i		−	1.02372i
$336$		0			0
$337$	418.500	−	241.621i	1.24184	−	0.716977i	0.272371	−	0.962192i	$-0.412192\pi$
$337$	418.500	−	241.621i	1.24184	−	0.716977i	0.969469	+	0.245216i	$0.0788588\pi$
$338$		0			0
$339$	−135.000	−	233.827i	−0.398230	−	0.689755i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	365.000			1.06414
$344$		0			0
$345$	−216.000	+	124.708i	−0.626087	+	0.361471i
$346$		0			0
$347$	267.000	+	462.458i	0.769452	+	1.33273i	0.937860	+	0.347013i	$0.112804\pi$
$347$	267.000	+	462.458i	0.769452	+	1.33273i	−0.168408	+	0.985717i	$0.553863\pi$
$348$		0			0
$349$	−187.000			−0.535817			−0.267908	−	0.963444i	$-0.586332\pi$
$349$	−187.000			−0.535817			−0.267908	+	0.963444i	$0.586332\pi$
$350$		0			0
$351$	−49.5000	+	85.7365i	−0.141026	+	0.244264i
$352$		0			0
$353$	438.000			1.24079			0.620397	−	0.784288i	$-0.286972\pi$
$353$	438.000			1.24079			0.620397	+	0.784288i	$0.286972\pi$
$354$		0			0
$355$	−324.000	−	187.061i	−0.912676	−	0.526934i
$356$		0			0
$357$	45.0000	+	25.9808i	0.126050	+	0.0727752i
$358$		0			0
$359$	168.000	+	290.985i	0.467967	+	0.810542i	0.999330	−	0.0366021i	$-0.0116534\pi$
$359$	168.000	+	290.985i	0.467967	+	0.810542i	−0.531363	+	0.847144i	$0.678320\pi$
$360$		0			0
$361$	−23.0000	−	360.267i	−0.0637119	−	0.997968i
$362$		0			0
$363$	−181.500	+	104.789i	−0.500000	+	0.288675i
$364$		0			0
$365$	−33.0000	+	57.1577i	−0.0904110	+	0.156596i
$366$		0			0
$367$	−50.5000	+	87.4686i	−0.137602	+	0.238334i	−0.926588	−	0.376077i	$-0.877273\pi$
$367$	−50.5000	+	87.4686i	−0.137602	+	0.238334i	0.788986	+	0.614411i	$0.210606\pi$
$368$		0			0
$369$			124.708i			0.337961i
$370$		0			0
$371$	−270.000	−	155.885i	−0.727763	−	0.420174i
$372$		0			0
$373$		−	547.328i		−	1.46737i	−0.679491	−	0.733684i	$-0.737799\pi$
$373$		−	547.328i		−	1.46737i	0.679491	−	0.733684i	$-0.262201\pi$
$374$		0			0
$375$	−126.000	+	72.7461i	−0.336000	+	0.193990i
$376$		0			0
$377$	−297.000	−	514.419i	−0.787798	−	1.36451i
$378$		0			0
$379$		−	46.7654i		−	0.123391i	−0.998095	−	0.0616957i	$-0.980349\pi$
$379$		−	46.7654i		−	0.123391i	0.998095	−	0.0616957i	$-0.0196508\pi$
$380$		0			0
$381$	−72.0000			−0.188976
$382$		0			0
$383$	342.000	−	197.454i	0.892950	−	0.515545i	0.0180440	−	0.999837i	$-0.494256\pi$
$383$	342.000	−	197.454i	0.892950	−	0.515545i	0.874906	+	0.484292i	$0.160923\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	75.0000			0.193798
$388$		0			0
$389$	228.000	−	394.908i	0.586118	−	1.01519i	−0.408617	−	0.912706i	$-0.633989\pi$
$389$	228.000	−	394.908i	0.586118	−	1.01519i	0.994735	−	0.102481i	$-0.0326779\pi$
$390$		0			0
$391$	−144.000			−0.368286
$392$		0			0
$393$	−72.0000	−	41.5692i	−0.183206	−	0.105774i
$394$		0			0
$395$	−9.00000	−	5.19615i	−0.0227848	−	0.0131548i
$396$		0			0
$397$	−116.500	−	201.784i	−0.293451	−	0.508272i	0.681172	−	0.732123i	$-0.261470\pi$
$397$	−116.500	−	201.784i	−0.293451	−	0.508272i	−0.974623	+	0.223851i	$0.928137\pi$
$398$		0			0
$399$	37.5000	−	160.215i	0.0939850	−	0.401541i
$400$		0			0
$401$	63.0000	−	36.3731i	0.157107	−	0.0907059i	−0.419385	−	0.907808i	$-0.637754\pi$
$401$	63.0000	−	36.3731i	0.157107	−	0.0907059i	0.576492	+	0.817102i	$0.304421\pi$
$402$		0			0
$403$	−280.500	+	485.840i	−0.696030	+	1.20556i
$404$		0			0
$405$	−27.0000	+	46.7654i	−0.0666667	+	0.115470i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−210.000	−	121.244i	−0.513447	−	0.296439i	0.220802	−	0.975319i	$-0.429132\pi$
$409$	−210.000	−	121.244i	−0.513447	−	0.296439i	−0.734250	+	0.678880i	$0.762466\pi$
$410$		0			0
$411$		−	228.631i		−	0.556279i
$412$		0			0
$413$	−315.000	+	181.865i	−0.762712	+	0.440352i
$414$		0			0
$415$	−378.000	−	654.715i	−0.910843	−	1.57763i
$416$		0			0
$417$			1.73205i			0.00415360i
$418$		0			0
$419$	84.0000			0.200477			0.100239	−	0.994963i	$-0.468039\pi$
$419$	84.0000			0.200477			0.100239	+	0.994963i	$0.468039\pi$
$420$		0			0
$421$	−678.000	+	391.443i	−1.61045	+	0.929794i	−0.621186	+	0.783663i	$0.713349\pi$
$421$	−678.000	+	391.443i	−1.61045	+	0.929794i	−0.989265	+	0.146131i	$0.953318\pi$
$422$		0			0
$423$	−63.0000	−	109.119i	−0.148936	−	0.257965i
$424$		0			0
$425$	66.0000			0.155294
$426$		0			0
$427$	107.500	−	186.195i	0.251756	−	0.436055i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−333.000	−	192.258i	−0.772622	−	0.446073i	0.0611873	−	0.998126i	$-0.480511\pi$
$431$	−333.000	−	192.258i	−0.772622	−	0.446073i	−0.833809	+	0.552053i	$0.813845\pi$
$432$		0			0
$433$	253.500	+	146.358i	0.585450	+	0.338010i	0.763296	−	0.646048i	$-0.223580\pi$
$433$	253.500	+	146.358i	0.585450	+	0.338010i	−0.177846	+	0.984058i	$0.556913\pi$
$434$		0			0
$435$	−162.000	−	280.592i	−0.372414	−	0.645040i
$436$		0			0
$437$	132.000	+	436.477i	0.302059	+	0.998803i
$438$		0			0
$439$	−97.5000	+	56.2917i	−0.222096	+	0.128227i	−0.606920	−	0.794763i	$-0.707595\pi$
$439$	−97.5000	+	56.2917i	−0.222096	+	0.128227i	0.384825	+	0.922990i	$0.374262\pi$
$440$		0			0
$441$	−36.0000	+	62.3538i	−0.0816327	+	0.141392i
$442$		0			0
$443$	−93.0000	+	161.081i	−0.209932	+	0.363613i	−0.951693	−	0.307051i	$-0.900658\pi$
$443$	−93.0000	+	161.081i	−0.209932	+	0.363613i	0.741761	+	0.670665i	$0.233991\pi$
$444$		0			0
$445$			62.3538i			0.140121i
$446$		0			0
$447$	−270.000	−	155.885i	−0.604027	−	0.348735i
$448$		0			0
$449$		−	135.100i		−	0.300891i	−0.988618	−	0.150445i	$-0.951929\pi$
$449$		−	135.100i		−	0.300891i	0.988618	−	0.150445i	$-0.0480708\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−204.000	−	353.338i	−0.450331	−	0.779996i
$454$		0			0
$455$		−	571.577i		−	1.25621i
$456$		0			0
$457$	−565.000			−1.23632			−0.618162	−	0.786051i	$-0.712122\pi$
$457$	−565.000			−1.23632			−0.618162	+	0.786051i	$0.712122\pi$
$458$		0			0
$459$	−27.0000	+	15.5885i	−0.0588235	+	0.0339618i
$460$		0			0
$461$	69.0000	+	119.512i	0.149675	+	0.259244i	0.931107	−	0.364746i	$-0.118844\pi$
$461$	69.0000	+	119.512i	0.149675	+	0.259244i	−0.781433	+	0.623990i	$0.785511\pi$
$462$		0			0
$463$	−139.000			−0.300216			−0.150108	−	0.988670i	$-0.547962\pi$
$463$	−139.000			−0.300216			−0.150108	+	0.988670i	$0.547962\pi$
$464$		0			0
$465$	−153.000	+	265.004i	−0.329032	+	0.569901i
$466$		0			0
$467$	888.000			1.90150			0.950749	−	0.309960i	$-0.100316\pi$
$467$	888.000			1.90150			0.950749	+	0.309960i	$0.100316\pi$
$468$		0			0
$469$	−247.500	−	142.894i	−0.527719	−	0.304678i
$470$		0			0
$471$	115.500	+	66.6840i	0.245223	+	0.141580i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−60.5000	−	200.052i	−0.127368	−	0.421162i
$476$		0			0
$477$	162.000	−	93.5307i	0.339623	−	0.196081i
$478$		0			0
$479$	348.000	−	602.754i	0.726514	−	1.25836i	−0.231834	−	0.972755i	$-0.574473\pi$
$479$	348.000	−	602.754i	0.726514	−	1.25836i	0.958348	−	0.285603i	$-0.0921939\pi$
$480$		0			0
$481$	−577.500	+	1000.26i	−1.20062	+	2.07954i
$482$		0			0
$483$			207.846i			0.430323i
$484$		0			0
$485$	684.000	+	394.908i	1.41031	+	0.814242i
$486$		0			0
$487$		−	214.774i		−	0.441015i	−0.975385	−	0.220507i	$-0.929229\pi$
$487$		−	214.774i		−	0.441015i	0.975385	−	0.220507i	$-0.0707713\pi$
$488$		0			0
$489$	217.500	−	125.574i	0.444785	−	0.256797i
$490$		0			0
$491$	468.000	+	810.600i	0.953157	+	1.65092i	0.738531	+	0.674220i	$0.235520\pi$
$491$	468.000	+	810.600i	0.953157	+	1.65092i	0.214626	+	0.976696i	$0.431147\pi$
$492$		0			0
$493$		−	187.061i		−	0.379435i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−270.000	+	155.885i	−0.543260	+	0.313651i
$498$		0			0
$499$	263.500	+	456.395i	0.528056	+	0.914620i	0.999465	+	0.0327053i	$0.0104123\pi$
$499$	263.500	+	456.395i	0.528056	+	0.914620i	−0.471409	+	0.881915i	$0.656254\pi$
$500$		0			0
$501$	−522.000			−1.04192
$502$		0			0
$503$	195.000	−	337.750i	0.387674	−	0.671471i	−0.604462	−	0.796634i	$-0.706612\pi$
$503$	195.000	−	337.750i	0.387674	−	0.671471i	0.992136	+	0.125163i	$0.0399453\pi$
$504$		0			0
$505$	936.000			1.85347
$506$		0			0
$507$	291.000	+	168.009i	0.573964	+	0.331379i
$508$		0			0
$509$	513.000	+	296.181i	1.00786	+	0.581887i	0.910564	−	0.413368i	$-0.135648\pi$
$509$	513.000	+	296.181i	1.00786	+	0.581887i	0.0972946	+	0.995256i	$0.468981\pi$
$510$		0			0
$511$	27.5000	+	47.6314i	0.0538160	+	0.0932121i
$512$		0			0
$513$	72.0000	+	67.5500i	0.140351	+	0.131676i
$514$		0			0
$515$	189.000	−	109.119i	0.366990	−	0.211882i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−9.00000	+	15.5885i	−0.0173410	+	0.0300356i
$520$		0			0
$521$		−	103.923i		−	0.199468i	−0.995014	−	0.0997342i	$-0.968201\pi$
$521$		−	103.923i		−	0.199468i	0.995014	−	0.0997342i	$-0.0317993\pi$
$522$		0			0
$523$	118.500	+	68.4160i	0.226577	+	0.130815i	0.608992	−	0.793176i	$-0.291574\pi$
$523$	118.500	+	68.4160i	0.226577	+	0.130815i	−0.382415	+	0.923991i	$0.624907\pi$
$524$		0			0
$525$		−	95.2628i		−	0.181453i
$526$		0			0
$527$	−153.000	+	88.3346i	−0.290323	+	0.167618i
$528$		0			0
$529$	−23.5000	−	40.7032i	−0.0444234	−	0.0769437i
$530$		0			0
$531$		−	218.238i		−	0.410995i
$532$		0			0
$533$	792.000			1.48593
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	99.5000	−	172.339i	0.183919	−	0.318556i	−0.759293	−	0.650749i	$-0.774455\pi$
$541$	99.5000	−	172.339i	0.183919	−	0.318556i	0.943212	+	0.332192i	$0.107788\pi$
$542$		0			0
$543$	−132.000			−0.243094
$544$		0			0
$545$	−540.000	−	311.769i	−0.990826	−	0.572053i
$546$		0			0
$547$	532.500	+	307.439i	0.973492	+	0.562046i	0.900299	−	0.435272i	$-0.143348\pi$
$547$	532.500	+	307.439i	0.973492	+	0.562046i	0.0731928	+	0.997318i	$0.476681\pi$
$548$		0			0
$549$	64.5000	+	111.717i	0.117486	+	0.203492i
$550$		0			0
$551$	−567.000	+	171.473i	−1.02904	+	0.311203i
$552$		0			0
$553$	−7.50000	+	4.33013i	−0.0135624	+	0.00783025i
$554$		0			0
$555$	−315.000	+	545.596i	−0.567568	+	0.983056i
$556$		0			0
$557$	−360.000	+	623.538i	−0.646320	+	1.11946i	0.337675	+	0.941263i	$0.390359\pi$
$557$	−360.000	+	623.538i	−0.646320	+	1.11946i	−0.983995	+	0.178196i	$0.942974\pi$
$558$		0			0
$559$		−	476.314i		−	0.852082i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			374.123i			0.664517i	0.943188	+	0.332258i	$0.107811\pi$
$563$			374.123i			0.664517i	−0.943188	+	0.332258i	$0.892189\pi$
$564$		0			0
$565$	−810.000	+	467.654i	−1.43363	+	0.827706i
$566$		0			0
$567$	22.5000	+	38.9711i	0.0396825	+	0.0687322i
$568$		0			0
$569$		−	290.985i		−	0.511396i	−0.966757	−	0.255698i	$-0.917695\pi$
$569$		−	290.985i		−	0.511396i	0.966757	−	0.255698i	$-0.0823053\pi$
$570$		0			0
$571$	95.0000			0.166375			0.0831874	−	0.996534i	$-0.473490\pi$
$571$	95.0000			0.166375			0.0831874	+	0.996534i	$0.473490\pi$
$572$		0			0
$573$	−27.0000	+	15.5885i	−0.0471204	+	0.0272050i
$574$		0			0
$575$	132.000	+	228.631i	0.229565	+	0.397619i
$576$		0			0
$577$	874.000			1.51473			0.757366	−	0.652991i	$-0.226486\pi$
$577$	874.000			1.51473			0.757366	+	0.652991i	$0.226486\pi$
$578$		0			0
$579$	49.5000	−	85.7365i	0.0854922	−	0.148077i
$580$		0			0
$581$	−630.000			−1.08434
$582$		0			0
$583$		0			0
$584$		0			0
$585$	297.000	+	171.473i	0.507692	+	0.293116i
$586$		0			0
$587$	327.000	+	566.381i	0.557070	+	0.964873i	0.997739	+	0.0672038i	$0.0214078\pi$
$587$	327.000	+	566.381i	0.557070	+	0.964873i	−0.440669	+	0.897669i	$0.645259\pi$
$588$		0			0
$589$	408.000	+	382.783i	0.692699	+	0.649887i
$590$		0			0
$591$	−135.000	+	77.9423i	−0.228426	+	0.131882i
$592$		0			0
$593$	471.000	−	815.796i	0.794266	−	1.37571i	−0.129037	−	0.991640i	$-0.541189\pi$
$593$	471.000	−	815.796i	0.794266	−	1.37571i	0.923304	−	0.384070i	$-0.125478\pi$
$594$		0			0
$595$	90.0000	−	155.885i	0.151261	−	0.261991i
$596$		0			0
$597$		−	386.247i		−	0.646980i
$598$		0			0
$599$	324.000	+	187.061i	0.540902	+	0.312290i	0.745444	−	0.666568i	$-0.232237\pi$
$599$	324.000	+	187.061i	0.540902	+	0.312290i	−0.204543	+	0.978858i	$0.565571\pi$
$600$		0			0
$601$		−	646.055i		−	1.07497i	−0.843274	−	0.537483i	$-0.819375\pi$
$601$		−	646.055i		−	1.07497i	0.843274	−	0.537483i	$-0.180625\pi$
$602$		0			0
$603$	148.500	−	85.7365i	0.246269	−	0.142183i
$604$		0			0
$605$	363.000	+	628.734i	0.600000	+	1.03923i
$606$		0			0
$607$			358.535i			0.590666i	0.955394	+	0.295333i	$0.0954307\pi$
$607$			358.535i			0.590666i	−0.955394	+	0.295333i	$0.904569\pi$
$608$		0			0
$609$	−270.000			−0.443350
$610$		0			0
$611$	−693.000	+	400.104i	−1.13421	+	0.654834i
$612$		0			0
$613$	−383.000	−	663.375i	−0.624796	−	1.08218i	−0.988580	−	0.150695i	$-0.951849\pi$
$613$	−383.000	−	663.375i	−0.624796	−	1.08218i	0.363784	−	0.931483i	$-0.381485\pi$
$614$		0			0
$615$	432.000			0.702439
$616$		0			0
$617$	270.000	−	467.654i	0.437601	−	0.757948i	−0.559903	−	0.828558i	$-0.689161\pi$
$617$	270.000	−	467.654i	0.437601	−	0.757948i	0.997504	+	0.0706107i	$0.0224948\pi$
$618$		0			0
$619$	97.0000			0.156704			0.0783522	−	0.996926i	$-0.475034\pi$
$619$	97.0000			0.156704			0.0783522	+	0.996926i	$0.475034\pi$
$620$		0			0
$621$	−108.000	−	62.3538i	−0.173913	−	0.100409i
$622$		0			0
$623$	45.0000	+	25.9808i	0.0722311	+	0.0417027i
$624$		0			0
$625$	389.500	+	674.634i	0.623200	+	1.07941i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−315.000	+	181.865i	−0.500795	+	0.289134i
$630$		0			0
$631$	224.500	−	388.845i	0.355784	−	0.616237i	−0.631467	−	0.775402i	$-0.717547\pi$
$631$	224.500	−	388.845i	0.355784	−	0.616237i	0.987252	+	0.159166i	$0.0508804\pi$
$632$		0			0
$633$	−292.500	+	506.625i	−0.462085	+	0.800355i
$634$		0			0
$635$			249.415i			0.392780i
$636$		0			0
$637$	396.000	+	228.631i	0.621664	+	0.358918i
$638$		0			0
$639$		−	187.061i		−	0.292741i
$640$		0			0
$641$	−513.000	+	296.181i	−0.800312	+	0.462060i	−0.843580	−	0.537003i	$-0.819556\pi$
$641$	−513.000	+	296.181i	−0.800312	+	0.462060i	0.0432682	+	0.999063i	$0.486223\pi$
$642$		0			0
$643$	−461.500	−	799.341i	−0.717729	−	1.24314i	−0.961897	−	0.273411i	$-0.911848\pi$
$643$	−461.500	−	799.341i	−0.717729	−	1.24314i	0.244168	−	0.969733i	$-0.421485\pi$
$644$		0			0
$645$		−	259.808i		−	0.402803i
$646$		0			0
$647$	594.000			0.918083			0.459042	−	0.888415i	$-0.348193\pi$
$647$	594.000			0.918083			0.459042	+	0.888415i	$0.348193\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	127.500	+	220.836i	0.195853	+	0.339227i
$652$		0			0
$653$	936.000			1.43338			0.716692	−	0.697390i	$-0.245655\pi$
$653$	936.000			1.43338			0.716692	+	0.697390i	$0.245655\pi$
$654$		0			0
$655$	−144.000	+	249.415i	−0.219847	+	0.380787i
$656$		0			0
$657$	−33.0000			−0.0502283
$658$		0			0
$659$	−252.000	−	145.492i	−0.382398	−	0.220777i	0.296463	−	0.955044i	$-0.404193\pi$
$659$	−252.000	−	145.492i	−0.382398	−	0.220777i	−0.678861	+	0.734267i	$0.737526\pi$
$660$		0			0
$661$	−672.000	−	387.979i	−1.01664	−	0.586958i	−0.103512	−	0.994628i	$-0.533008\pi$
$661$	−672.000	−	387.979i	−1.01664	−	0.586958i	−0.913129	+	0.407670i	$0.866341\pi$
$662$		0			0
$663$	99.0000	+	171.473i	0.149321	+	0.258632i
$664$		0			0
$665$	−555.000	−	129.904i	−0.834586	−	0.195344i
$666$		0			0
$667$	648.000	−	374.123i	0.971514	−	0.560904i
$668$		0			0
$669$	−370.500	+	641.725i	−0.553812	+	0.959230i
$670$		0			0
$671$		0			0
$672$		0			0
$673$			961.288i			1.42836i	0.699961	+	0.714181i	$0.253201\pi$
$673$			961.288i			1.42836i	−0.699961	+	0.714181i	$0.746799\pi$
$674$		0			0
$675$	49.5000	+	28.5788i	0.0733333	+	0.0423390i
$676$		0			0
$677$		−	259.808i		−	0.383763i	−0.981418	−	0.191882i	$-0.938541\pi$
$677$		−	259.808i		−	0.383763i	0.981418	−	0.191882i	$-0.0614589\pi$
$678$		0			0
$679$	570.000	−	329.090i	0.839470	−	0.484668i
$680$		0			0
$681$	−153.000	−	265.004i	−0.224670	−	0.389139i
$682$		0			0
$683$		−	1132.76i		−	1.65851i	−0.558872	−	0.829254i	$-0.688766\pi$
$683$		−	1132.76i		−	1.65851i	0.558872	−	0.829254i	$-0.311234\pi$
$684$		0			0
$685$	−792.000			−1.15620
$686$		0			0
$687$	586.500	−	338.616i	0.853712	−	0.492891i
$688$		0			0
$689$	−594.000	−	1028.84i	−0.862119	−	1.49323i
$690$		0			0
$691$	−58.0000			−0.0839363			−0.0419682	−	0.999119i	$-0.513363\pi$
$691$	−58.0000			−0.0839363			−0.0419682	+	0.999119i	$0.513363\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.00000			0.00863309
$696$		0			0
$697$	216.000	+	124.708i	0.309900	+	0.178921i
$698$		0			0
$699$	−216.000	−	124.708i	−0.309013	−	0.178409i
$700$		0			0
$701$	171.000	+	296.181i	0.243937	+	0.422512i	0.961832	−	0.273640i	$-0.0882276\pi$
$701$	171.000	+	296.181i	0.243937	+	0.422512i	−0.717895	+	0.696151i	$0.754894\pi$
$702$		0			0
$703$	840.000	+	788.083i	1.19488	+	1.12103i
$704$		0			0
$705$	−378.000	+	218.238i	−0.536170	+	0.309558i
$706$		0			0
$707$	390.000	−	675.500i	0.551627	−	0.955445i
$708$		0			0
$709$	−272.500	+	471.984i	−0.384344	+	0.665704i	−0.991678	−	0.128743i	$-0.958906\pi$
$709$	−272.500	+	471.984i	−0.384344	+	0.665704i	0.607334	+	0.794447i	$0.292239\pi$
$710$		0			0
$711$		−	5.19615i		−	0.00730823i
$712$		0			0
$713$	−612.000	−	353.338i	−0.858345	−	0.495566i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	675.000	−	389.711i	0.941423	−	0.543531i
$718$		0			0
$719$	534.000	+	924.915i	0.742698	+	1.28639i	0.951262	+	0.308382i	$0.0997876\pi$
$719$	534.000	+	924.915i	0.742698	+	1.28639i	−0.208564	+	0.978009i	$0.566879\pi$
$720$		0			0
$721$		−	181.865i		−	0.252240i
$722$		0			0
$723$	135.000			0.186722
$724$		0			0
$725$	−297.000	+	171.473i	−0.409655	+	0.236515i
$726$		0			0
$727$	57.5000	+	99.5929i	0.0790922	+	0.136992i	0.902858	−	0.429938i	$-0.141465\pi$
$727$	57.5000	+	99.5929i	0.0790922	+	0.136992i	−0.823766	+	0.566929i	$0.808131\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	75.0000	−	129.904i	0.102599	−	0.177707i
$732$		0			0
$733$	−298.000			−0.406548			−0.203274	−	0.979122i	$-0.565158\pi$
$733$	−298.000			−0.406548			−0.203274	+	0.979122i	$0.565158\pi$
$734$		0			0
$735$	216.000	+	124.708i	0.293878	+	0.169670i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−666.500	−	1154.41i	−0.901894	−	1.56213i	−0.825033	−	0.565085i	$-0.808843\pi$
$739$	−666.500	−	1154.41i	−0.901894	−	1.56213i	−0.0768619	−	0.997042i	$-0.524490\pi$
$740$		0			0
$741$	429.000	−	457.261i	0.578947	−	0.617087i
$742$		0			0
$743$	−738.000	+	426.084i	−0.993271	+	0.573465i	−0.906250	−	0.422742i	$-0.861068\pi$
$743$	−738.000	+	426.084i	−0.993271	+	0.573465i	−0.0870202	+	0.996207i	$0.527734\pi$
$744$		0			0
$745$	−540.000	+	935.307i	−0.724832	+	1.25545i
$746$		0			0
$747$	189.000	−	327.358i	0.253012	−	0.438230i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−343.500	−	198.320i	−0.457390	−	0.264074i	0.253556	−	0.967321i	$-0.418400\pi$
$751$	−343.500	−	198.320i	−0.457390	−	0.264074i	−0.710946	+	0.703246i	$0.751733\pi$
$752$		0			0
$753$		−	72.7461i		−	0.0966084i
$754$		0			0
$755$	−1224.00	+	706.677i	−1.62119	+	0.935996i
$756$		0			0
$757$	−117.500	−	203.516i	−0.155218	−	0.268845i	0.777920	−	0.628363i	$-0.216275\pi$
$757$	−117.500	−	203.516i	−0.155218	−	0.268845i	−0.933138	+	0.359517i	$0.882941\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1158.00			−1.52168			−0.760841	−	0.648938i	$-0.775213\pi$
$761$	−1158.00			−1.52168			−0.760841	+	0.648938i	$0.775213\pi$
$762$		0			0
$763$	−450.000	+	259.808i	−0.589777	+	0.340508i
$764$		0			0
$765$	54.0000	+	93.5307i	0.0705882	+	0.122262i
$766$		0			0
$767$	−1386.00			−1.80704
$768$		0			0
$769$	−492.500	+	853.035i	−0.640442	+	1.10928i	0.344892	+	0.938642i	$0.387916\pi$
$769$	−492.500	+	853.035i	−0.640442	+	1.10928i	−0.985334	+	0.170636i	$0.945418\pi$
$770$		0			0
$771$	828.000			1.07393
$772$		0			0
$773$	−873.000	−	504.027i	−1.12937	−	0.652040i	−0.185591	−	0.982627i	$-0.559420\pi$
$773$	−873.000	−	504.027i	−1.12937	−	0.652040i	−0.943775	+	0.330587i	$0.892753\pi$
$774$		0			0
$775$	280.500	+	161.947i	0.361935	+	0.208964i
$776$		0			0
$777$	262.500	+	454.663i	0.337838	+	0.585152i
$778$		0			0
$779$	180.000	−	769.031i	0.231065	−	0.987202i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	81.0000	−	140.296i	0.103448	−	0.179178i
$784$		0			0
$785$	231.000	−	400.104i	0.294268	−	0.509686i
$786$		0			0
$787$		−	1404.69i		−	1.78487i	−0.451175	−	0.892435i	$-0.648995\pi$
$787$		−	1404.69i		−	1.78487i	0.451175	−	0.892435i	$-0.351005\pi$
$788$		0			0
$789$	−234.000	−	135.100i	−0.296578	−	0.171229i
$790$		0			0
$791$			779.423i			0.985364i
$792$		0			0
$793$	709.500	−	409.630i	0.894704	−	0.516557i
$794$		0			0
$795$	−324.000	−	561.184i	−0.407547	−	0.705892i
$796$		0			0
$797$		−	1267.86i		−	1.59079i	−0.606090	−	0.795396i	$-0.707263\pi$
$797$		−	1267.86i		−	1.59079i	0.606090	−	0.795396i	$-0.292737\pi$
$798$		0			0
$799$	−252.000			−0.315394
$800$		0			0
$801$	−27.0000	+	15.5885i	−0.0337079	+	0.0194612i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	720.000			0.894410
$806$		0			0
$807$	−459.000	+	795.011i	−0.568773	+	0.985144i
$808$		0			0
$809$	−546.000			−0.674907			−0.337454	−	0.941342i	$-0.609566\pi$
$809$	−546.000			−0.674907			−0.337454	+	0.941342i	$0.609566\pi$
$810$		0			0
$811$	936.000	+	540.400i	1.15413	+	0.666338i	0.949890	−	0.312583i	$-0.101194\pi$
$811$	936.000	+	540.400i	1.15413	+	0.666338i	0.204240	+	0.978921i	$0.434528\pi$
$812$		0			0
$813$	771.000	+	445.137i	0.948339	+	0.547524i
$814$		0			0
$815$	−435.000	−	753.442i	−0.533742	−	0.924469i
$816$		0			0
$817$	−462.500	−	108.253i	−0.566095	−	0.132501i
$818$		0			0
$819$	247.500	−	142.894i	0.302198	−	0.174474i
$820$		0			0
$821$	−477.000	+	826.188i	−0.580999	+	1.00632i	0.414363	+	0.910112i	$0.364005\pi$
$821$	−477.000	+	826.188i	−0.580999	+	1.00632i	−0.995361	+	0.0962075i	$0.969329\pi$
$822$		0			0
$823$	349.000	−	604.486i	0.424058	−	0.734491i	−0.572274	−	0.820063i	$-0.693938\pi$
$823$	349.000	−	604.486i	0.424058	−	0.734491i	0.996332	+	0.0855722i	$0.0272718\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−333.000	−	192.258i	−0.402660	−	0.232476i	0.284971	−	0.958536i	$-0.408016\pi$
$827$	−333.000	−	192.258i	−0.402660	−	0.232476i	−0.687631	+	0.726060i	$0.741349\pi$
$828$		0			0
$829$		−	57.1577i		−	0.0689477i	−0.999406	−	0.0344739i	$-0.989024\pi$
$829$		−	57.1577i		−	0.0689477i	0.999406	−	0.0344739i	$-0.0109755\pi$
$830$		0			0
$831$	357.000	−	206.114i	0.429603	−	0.248031i
$832$		0			0
$833$	72.0000	+	124.708i	0.0864346	+	0.149709i
$834$		0			0
$835$			1808.26i			2.16558i
$836$		0			0
$837$	−153.000			−0.182796
$838$		0			0
$839$	−9.00000	+	5.19615i	−0.0107271	+	0.00619327i	−0.505354	−	0.862912i	$-0.668638\pi$
$839$	−9.00000	+	5.19615i	−0.0107271	+	0.00619327i	0.494627	+	0.869105i	$0.335305\pi$
$840$		0			0
$841$	65.5000	+	113.449i	0.0778835	+	0.134898i
$842$		0			0
$843$	−450.000			−0.533808
$844$		0			0
$845$	582.000	−	1008.05i	0.688757	−	1.19296i
$846$		0			0
$847$	605.000			0.714286
$848$		0			0
$849$	339.000	+	195.722i	0.399293	+	0.230532i
$850$		0			0
$851$	−1260.00	−	727.461i	−1.48061	−	0.854831i
$852$		0			0
$853$	−794.500	−	1376.11i	−0.931419	−	1.61326i	−0.780899	−	0.624657i	$-0.785239\pi$
$853$	−794.500	−	1376.11i	−0.931419	−	1.61326i	−0.150519	−	0.988607i	$-0.548095\pi$
$854$		0			0
$855$	234.000	−	249.415i	0.273684	−	0.291714i
$856$		0			0
$857$	747.000	−	431.281i	0.871645	−	0.503245i	0.00375064	−	0.999993i	$-0.498806\pi$
$857$	747.000	−	431.281i	0.871645	−	0.503245i	0.867895	+	0.496748i	$0.165473\pi$
$858$		0			0
$859$	461.500	−	799.341i	0.537253	−	0.930549i	−0.461798	−	0.886985i	$-0.652796\pi$
$859$	461.500	−	799.341i	0.537253	−	0.930549i	0.999051	−	0.0435637i	$-0.0138712\pi$
$860$		0			0
$861$	180.000	−	311.769i	0.209059	−	0.362101i
$862$		0			0
$863$			197.454i			0.228799i	0.993435	+	0.114400i	$0.0364944\pi$
$863$			197.454i			0.228799i	−0.993435	+	0.114400i	$0.963506\pi$
$864$		0			0
$865$	54.0000	+	31.1769i	0.0624277	+	0.0360427i
$866$		0			0
$867$		−	438.209i		−	0.505431i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−544.500	−	943.102i	−0.625144	−	1.08278i
$872$		0			0
$873$			394.908i			0.452357i
$874$		0			0
$875$	420.000			0.480000
$876$		0			0
$877$	736.500	−	425.218i	0.839795	−	0.484856i	−0.0173997	−	0.999849i	$-0.505539\pi$
$877$	736.500	−	425.218i	0.839795	−	0.484856i	0.857194	+	0.514993i	$0.172205\pi$
$878$		0			0
$879$	−27.0000	−	46.7654i	−0.0307167	−	0.0532029i
$880$		0			0
$881$	−402.000			−0.456300			−0.228150	−	0.973626i	$-0.573268\pi$
$881$	−402.000			−0.456300			−0.228150	+	0.973626i	$0.573268\pi$
$882$		0			0
$883$	−630.500	+	1092.06i	−0.714043	+	1.23676i	0.249284	+	0.968430i	$0.419805\pi$
$883$	−630.500	+	1092.06i	−0.714043	+	1.23676i	−0.963327	+	0.268329i	$0.913529\pi$
$884$		0			0
$885$	−756.000			−0.854237
$886$		0			0
$887$	189.000	+	109.119i	0.213078	+	0.123021i	0.602741	−	0.797937i	$-0.294075\pi$
$887$	189.000	+	109.119i	0.213078	+	0.123021i	−0.389663	+	0.920957i	$0.627409\pi$
$888$		0			0
$889$	180.000	+	103.923i	0.202475	+	0.116899i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	231.000	+	763.834i	0.258679	+	0.855358i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−396.000	+	685.892i	−0.441472	+	0.764651i
$898$		0			0
$899$	459.000	−	795.011i	0.510567	−	0.884328i
$900$		0			0
$901$		−	374.123i		−	0.415231i
$902$		0			0
$903$	−187.500	−	108.253i	−0.207641	−	0.119882i
$904$		0			0
$905$			457.261i			0.505261i
$906$		0			0
$907$	60.0000	−	34.6410i	0.0661521	−	0.0381930i	−0.466559	−	0.884490i	$-0.654507\pi$
$907$	60.0000	−	34.6410i	0.0661521	−	0.0381930i	0.532711	+	0.846297i	$0.321173\pi$
$908$		0			0
$909$	234.000	+	405.300i	0.257426	+	0.445874i
$910$		0			0
$911$			1184.72i			1.30046i	0.759736	+	0.650232i	$0.225328\pi$
$911$			1184.72i			1.30046i	−0.759736	+	0.650232i	$0.774672\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	387.000	−	223.435i	0.422951	−	0.244191i
$916$		0			0
$917$	120.000	+	207.846i	0.130862	+	0.226659i
$918$		0			0
$919$	955.000			1.03917			0.519587	−	0.854418i	$-0.326086\pi$
$919$	955.000			1.03917			0.519587	+	0.854418i	$0.326086\pi$
$920$		0			0
$921$	54.0000	−	93.5307i	0.0586319	−	0.101553i
$922$		0			0
$923$	−1188.00			−1.28711
$924$		0			0
$925$	577.500	+	333.420i	0.624324	+	0.360454i
$926$		0			0
$927$	94.5000	+	54.5596i	0.101942	+	0.0588561i
$928$		0			0
$929$	537.000	+	930.111i	0.578041	+	1.00120i	0.995704	+	0.0925942i	$0.0295159\pi$
$929$	537.000	+	930.111i	0.578041	+	1.00120i	−0.417663	+	0.908602i	$0.637151\pi$
$930$		0			0
$931$	312.000	−	332.554i	0.335124	−	0.357201i
$932$		0			0
$933$	−801.000	+	462.458i	−0.858521	+	0.495667i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	324.500	−	562.050i	0.346318	−	0.599840i	−0.639274	−	0.768979i	$-0.720765\pi$
$937$	324.500	−	562.050i	0.346318	−	0.599840i	0.985592	+	0.169138i	$0.0540985\pi$
$938$		0			0
$939$			931.843i			0.992378i
$940$		0			0
$941$	1188.00	+	685.892i	1.26249	+	0.728897i	0.973555	−	0.228453i	$-0.0733666\pi$
$941$	1188.00	+	685.892i	1.26249	+	0.728897i	0.288932	+	0.957350i	$0.406700\pi$
$942$		0			0
$943$			997.661i			1.05797i
$944$		0			0
$945$	135.000	−	77.9423i	0.142857	−	0.0824786i
$946$		0			0
$947$	282.000	+	488.438i	0.297782	+	0.515774i	0.975628	−	0.219430i	$-0.0704197\pi$
$947$	282.000	+	488.438i	0.297782	+	0.515774i	−0.677846	+	0.735204i	$0.737086\pi$
$948$		0			0
$949$			209.578i			0.220841i
$950$		0			0
$951$	162.000			0.170347
$952$		0			0
$953$	1530.00	−	883.346i	1.60546	−	0.926911i	0.615087	−	0.788459i	$-0.289121\pi$
$953$	1530.00	−	883.346i	1.60546	−	0.926911i	0.990369	−	0.138452i	$-0.0442126\pi$
$954$		0			0
$955$	54.0000	+	93.5307i	0.0565445	+	0.0979380i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−330.000	+	571.577i	−0.344108	+	0.596013i
$960$		0			0
$961$	94.0000			0.0978148
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−297.000	−	171.473i	−0.307772	−	0.177692i
$966$		0			0
$967$	530.500	+	918.853i	0.548604	+	0.950210i	0.998371	+	0.0570638i	$0.0181738\pi$
$967$	530.500	+	918.853i	0.548604	+	0.950210i	−0.449767	+	0.893146i	$0.648493\pi$
$968$		0			0
$969$	189.000	−	57.1577i	0.195046	−	0.0589863i
$970$		0			0
$971$	−477.000	+	275.396i	−0.491246	+	0.283621i	−0.725091	−	0.688653i	$-0.758202\pi$
$971$	−477.000	+	275.396i	−0.491246	+	0.283621i	0.233845	+	0.972274i	$0.424869\pi$
$972$		0			0
$973$	2.50000	−	4.33013i	0.00256937	−	0.00445028i
$974$		0			0
$975$	181.500	−	314.367i	0.186154	−	0.322428i
$976$		0			0
$977$			737.854i			0.755224i	0.925964	+	0.377612i	$0.123255\pi$
$977$			737.854i			0.755224i	−0.925964	+	0.377612i	$0.876745\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		−	311.769i		−	0.317807i
$982$		0			0
$983$	−630.000	+	363.731i	−0.640895	+	0.370021i	−0.784959	−	0.619547i	$-0.787316\pi$
$983$	−630.000	+	363.731i	−0.640895	+	0.370021i	0.144064	+	0.989568i	$0.453983\pi$
$984$		0			0
$985$	270.000	+	467.654i	0.274112	+	0.474775i
$986$		0			0
$987$			363.731i			0.368521i
$988$		0			0
$989$	600.000			0.606673
$990$		0			0
$991$	−1042.50	+	601.888i	−1.05197	+	0.607354i	−0.923200	−	0.384321i	$-0.874436\pi$
$991$	−1042.50	+	601.888i	−1.05197	+	0.607354i	−0.128768	+	0.991675i	$0.541102\pi$
$992$		0			0
$993$	241.500	+	418.290i	0.243202	+	0.421239i
$994$		0			0
$995$	−1338.00			−1.34472
$996$		0			0
$997$	104.500	−	180.999i	0.104814	−	0.181544i	−0.808848	−	0.588018i	$-0.799908\pi$
$997$	104.500	−	180.999i	0.104814	−	0.181544i	0.913662	+	0.406474i	$0.133242\pi$
$998$		0			0
$999$	−315.000			−0.315315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.l.a.145.1	✓	2
3.2	odd	2		684.3.y.e.145.1		2
4.3	odd	2		912.3.be.a.145.1		2
19.8	odd	6	inner	228.3.l.a.217.1	yes	2
57.8	even	6		684.3.y.e.217.1		2
76.27	even	6		912.3.be.a.673.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.l.a.145.1	✓	2	1.1	even	1	trivial
228.3.l.a.217.1	yes	2	19.8	odd	6	inner
684.3.y.e.145.1		2	3.2	odd	2
684.3.y.e.217.1		2	57.8	even	6
912.3.be.a.145.1		2	4.3	odd	2
912.3.be.a.673.1		2	76.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.00000 - 5.19615i) q^{5} -5.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.00000 - 5.19615i) q^{5} -5.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +(-16.5000 - 9.52628i) q^{13} +(-9.00000 - 5.19615i) q^{15} +(-3.00000 - 5.19615i) q^{17} +(-13.0000 + 13.8564i) q^{19} +(-7.50000 + 4.33013i) q^{21} +(12.0000 - 20.7846i) q^{23} +(-5.50000 + 9.52628i) q^{25} -5.19615i q^{27} +(27.0000 + 15.5885i) q^{29} -29.4449i q^{31} +(15.0000 + 25.9808i) q^{35} -60.6218i q^{37} -33.0000 q^{39} +(-36.0000 + 20.7846i) q^{41} +(12.5000 + 21.6506i) q^{43} -18.0000 q^{45} +(21.0000 - 36.3731i) q^{47} -24.0000 q^{49} +(-9.00000 - 5.19615i) q^{51} +(54.0000 + 31.1769i) q^{53} +(-7.50000 + 32.0429i) q^{57} +(63.0000 - 36.3731i) q^{59} +(-21.5000 + 37.2391i) q^{61} +(-7.50000 + 12.9904i) q^{63} +114.315i q^{65} +(49.5000 + 28.5788i) q^{67} -41.5692i q^{69} +(54.0000 - 31.1769i) q^{71} +(-5.50000 - 9.52628i) q^{73} +19.0526i q^{75} +(1.50000 - 0.866025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +126.000 q^{83} +(-18.0000 + 31.1769i) q^{85} +54.0000 q^{87} +(-9.00000 - 5.19615i) q^{89} +(82.5000 + 47.6314i) q^{91} +(-25.5000 - 44.1673i) q^{93} +(111.000 + 25.9808i) q^{95} +(-114.000 + 65.8179i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 6 q^{5} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 6 * q^5 - 10 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 6 q^{5} - 10 q^{7} + 3 q^{9} - 33 q^{13} - 18 q^{15} - 6 q^{17} - 26 q^{19} - 15 q^{21} + 24 q^{23} - 11 q^{25} + 54 q^{29} + 30 q^{35} - 66 q^{39} - 72 q^{41} + 25 q^{43} - 36 q^{45} + 42 q^{47} - 48 q^{49} - 18 q^{51} + 108 q^{53} - 15 q^{57} + 126 q^{59} - 43 q^{61} - 15 q^{63} + 99 q^{67} + 108 q^{71} - 11 q^{73} + 3 q^{79} - 9 q^{81} + 252 q^{83} - 36 q^{85} + 108 q^{87} - 18 q^{89} + 165 q^{91} - 51 q^{93} + 222 q^{95} - 228 q^{97}+O(q^{100}) \) 2 * q + 3 * q^3 - 6 * q^5 - 10 * q^7 + 3 * q^9 - 33 * q^13 - 18 * q^15 - 6 * q^17 - 26 * q^19 - 15 * q^21 + 24 * q^23 - 11 * q^25 + 54 * q^29 + 30 * q^35 - 66 * q^39 - 72 * q^41 + 25 * q^43 - 36 * q^45 + 42 * q^47 - 48 * q^49 - 18 * q^51 + 108 * q^53 - 15 * q^57 + 126 * q^59 - 43 * q^61 - 15 * q^63 + 99 * q^67 + 108 * q^71 - 11 * q^73 + 3 * q^79 - 9 * q^81 + 252 * q^83 - 36 * q^85 + 108 * q^87 - 18 * q^89 + 165 * q^91 - 51 * q^93 + 222 * q^95 - 228 * q^97

Introduction

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