LMFDB - Embedded newform 600.2.w.e.293.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(293,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.293"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,0,0,-6,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	600.293
Dual form			600.2.w.e.557.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 + 1.36603i) q^{2} +1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -3.46410 q^{11} +(-3.00000 - 1.73205i) q^{12} +(-3.46410 + 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(4.00000 + 4.00000i) q^{17} +(-1.09808 + 4.09808i) q^{18} -3.46410 q^{19} +(-5.19615 + 5.19615i) q^{21} +(1.26795 - 4.73205i) q^{22} +(1.00000 - 1.00000i) q^{23} +(3.46410 - 3.46410i) q^{24} +(-3.46410 - 6.00000i) q^{26} +5.19615 q^{27} +(8.19615 - 2.19615i) q^{28} +3.46410i q^{29} -4.00000 q^{31} +(-5.46410 + 1.46410i) q^{32} -6.00000 q^{33} +(-6.92820 + 4.00000i) q^{34} +(-5.19615 - 3.00000i) q^{36} +(1.26795 - 4.73205i) q^{38} +(-6.00000 + 6.00000i) q^{39} +6.00000i q^{41} +(-5.19615 - 9.00000i) q^{42} +(1.73205 - 1.73205i) q^{43} +(6.00000 + 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{46} +(5.00000 + 5.00000i) q^{47} +(3.46410 + 6.00000i) q^{48} -11.0000i q^{49} +(6.92820 + 6.92820i) q^{51} +(9.46410 - 2.53590i) q^{52} +(3.46410 + 3.46410i) q^{53} +(-1.90192 + 7.09808i) q^{54} +12.0000i q^{56} -6.00000 q^{57} +(-4.73205 - 1.26795i) q^{58} -10.3923i q^{59} -3.46410i q^{61} +(1.46410 - 5.46410i) q^{62} +(-9.00000 + 9.00000i) q^{63} -8.00000i q^{64} +(2.19615 - 8.19615i) q^{66} +(5.19615 + 5.19615i) q^{67} +(-2.92820 - 10.9282i) q^{68} +(1.73205 - 1.73205i) q^{69} -12.0000i q^{71} +(6.00000 - 6.00000i) q^{72} +(-6.00000 - 6.00000i) q^{73} +(6.00000 + 3.46410i) q^{76} +(10.3923 - 10.3923i) q^{77} +(-6.00000 - 10.3923i) q^{78} +8.00000i q^{79} +9.00000 q^{81} +(-8.19615 - 2.19615i) q^{82} +(-1.73205 - 1.73205i) q^{83} +(14.1962 - 3.80385i) q^{84} +(1.73205 + 3.00000i) q^{86} +6.00000i q^{87} +(-6.92820 + 6.92820i) q^{88} +12.0000 q^{89} -20.7846i q^{91} +(-2.73205 + 0.732051i) q^{92} -6.92820 q^{93} +(-8.66025 + 5.00000i) q^{94} +(-9.46410 + 2.53590i) q^{96} +(-6.00000 + 6.00000i) q^{97} +(15.0263 + 4.02628i) q^{98} -10.3923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{6} - 12 q^{7} + 8 q^{8} + 12 q^{9} - 12 q^{12} - 12 q^{14} + 8 q^{16} + 16 q^{17} + 6 q^{18} + 12 q^{22} + 4 q^{23} + 12 q^{28} - 16 q^{31} - 8 q^{32} - 24 q^{33} + 12 q^{38} - 24 q^{39}+ \cdots + 22 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^6 - 12 * q^7 + 8 * q^8 + 12 * q^9 - 12 * q^12 - 12 * q^14 + 8 * q^16 + 16 * q^17 + 6 * q^18 + 12 * q^22 + 4 * q^23 + 12 * q^28 - 16 * q^31 - 8 * q^32 - 24 * q^33 + 12 * q^38 - 24 * q^39 + 24 * q^44 + 4 * q^46 + 20 * q^47 + 24 * q^52 - 18 * q^54 - 24 * q^57 - 12 * q^58 - 8 * q^62 - 36 * q^63 - 12 * q^66 + 16 * q^68 + 24 * q^72 - 24 * q^73 + 24 * q^76 - 24 * q^78 + 36 * q^81 - 12 * q^82 + 36 * q^84 + 48 * q^89 - 4 * q^92 - 24 * q^96 - 24 * q^97 + 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$	−0.633975	+	2.36603i	−0.258819	+	0.965926i
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	3.00000			1.00000
$10$		0			0
$11$	−3.46410			−1.04447			−0.522233	−	0.852803i	$-0.674901\pi$
$11$	−3.46410			−1.04447			−0.522233	+	0.852803i	$0.674901\pi$
$12$	−3.00000	−	1.73205i	−0.866025	−	0.500000i
$13$	−3.46410	+	3.46410i	−0.960769	+	0.960769i	−0.999259	−	0.0384901i	$-0.987745\pi$
$13$	−3.46410	+	3.46410i	−0.960769	+	0.960769i	0.0384901	+	0.999259i	$0.487745\pi$
$14$	−3.00000	−	5.19615i	−0.801784	−	1.38873i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	4.00000	+	4.00000i	0.970143	+	0.970143i	0.999567	−	0.0294245i	$-0.00936746\pi$
$17$	4.00000	+	4.00000i	0.970143	+	0.970143i	−0.0294245	+	0.999567i	$0.509367\pi$
$18$	−1.09808	+	4.09808i	−0.258819	+	0.965926i
$19$	−3.46410			−0.794719			−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410			−0.794719			−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$	−5.19615	+	5.19615i	−1.13389	+	1.13389i
$22$	1.26795	−	4.73205i	0.270328	−	1.00888i
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	−0.595121	−	0.803636i	$-0.702896\pi$
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	0.803636	+	0.595121i	$0.202896\pi$
$24$	3.46410	−	3.46410i	0.707107	−	0.707107i
$25$		0			0
$26$	−3.46410	−	6.00000i	−0.679366	−	1.17670i
$27$	5.19615			1.00000
$28$	8.19615	−	2.19615i	1.54893	−	0.415034i
$29$			3.46410i			0.643268i	0.946864	+	0.321634i	$0.104232\pi$
$29$			3.46410i			0.643268i	−0.946864	+	0.321634i	$0.895768\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$	−6.00000			−1.04447
$34$	−6.92820	+	4.00000i	−1.18818	+	0.685994i
$35$		0			0
$36$	−5.19615	−	3.00000i	−0.866025	−	0.500000i
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	1.26795	−	4.73205i	0.205689	−	0.767640i
$39$	−6.00000	+	6.00000i	−0.960769	+	0.960769i
$40$		0			0
$41$			6.00000i			0.937043i	0.883452	+	0.468521i	$0.155213\pi$
$41$			6.00000i			0.937043i	−0.883452	+	0.468521i	$0.844787\pi$
$42$	−5.19615	−	9.00000i	−0.801784	−	1.38873i
$43$	1.73205	−	1.73205i	0.264135	−	0.264135i	−0.562596	−	0.826732i	$-0.690197\pi$
$43$	1.73205	−	1.73205i	0.264135	−	0.264135i	0.826732	+	0.562596i	$0.190197\pi$
$44$	6.00000	+	3.46410i	0.904534	+	0.522233i
$45$		0			0
$46$	1.00000	+	1.73205i	0.147442	+	0.255377i
$47$	5.00000	+	5.00000i	0.729325	+	0.729325i	0.970485	−	0.241160i	$-0.0775280\pi$
$47$	5.00000	+	5.00000i	0.729325	+	0.729325i	−0.241160	+	0.970485i	$0.577528\pi$
$48$	3.46410	+	6.00000i	0.500000	+	0.866025i
$49$		−	11.0000i		−	1.57143i
$50$		0			0
$51$	6.92820	+	6.92820i	0.970143	+	0.970143i
$52$	9.46410	−	2.53590i	1.31243	−	0.351666i
$53$	3.46410	+	3.46410i	0.475831	+	0.475831i	0.903796	−	0.427965i	$-0.140769\pi$
$53$	3.46410	+	3.46410i	0.475831	+	0.475831i	−0.427965	+	0.903796i	$0.640769\pi$
$54$	−1.90192	+	7.09808i	−0.258819	+	0.965926i
$55$		0			0
$56$			12.0000i			1.60357i
$57$	−6.00000			−0.794719
$58$	−4.73205	−	1.26795i	−0.621349	−	0.166490i
$59$		−	10.3923i		−	1.35296i	−0.736460	−	0.676481i	$-0.763504\pi$
$59$		−	10.3923i		−	1.35296i	0.736460	−	0.676481i	$-0.236496\pi$
$60$		0			0
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$	1.46410	−	5.46410i	0.185941	−	0.693942i
$63$	−9.00000	+	9.00000i	−1.13389	+	1.13389i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	2.19615	−	8.19615i	0.270328	−	1.00888i
$67$	5.19615	+	5.19615i	0.634811	+	0.634811i	0.949271	−	0.314460i	$-0.101823\pi$
$67$	5.19615	+	5.19615i	0.634811	+	0.634811i	−0.314460	+	0.949271i	$0.601823\pi$
$68$	−2.92820	−	10.9282i	−0.355097	−	1.32524i
$69$	1.73205	−	1.73205i	0.208514	−	0.208514i
$70$		0			0
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$	6.00000	−	6.00000i	0.707107	−	0.707107i
$73$	−6.00000	−	6.00000i	−0.702247	−	0.702247i	0.262646	−	0.964892i	$-0.415405\pi$
$73$	−6.00000	−	6.00000i	−0.702247	−	0.702247i	−0.964892	+	0.262646i	$0.915405\pi$
$74$		0			0
$75$		0			0
$76$	6.00000	+	3.46410i	0.688247	+	0.397360i
$77$	10.3923	−	10.3923i	1.18431	−	1.18431i
$78$	−6.00000	−	10.3923i	−0.679366	−	1.17670i
$79$			8.00000i			0.900070i	0.893011	+	0.450035i	$0.148589\pi$
$79$			8.00000i			0.900070i	−0.893011	+	0.450035i	$0.851411\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$	−8.19615	−	2.19615i	−0.905114	−	0.242524i
$83$	−1.73205	−	1.73205i	−0.190117	−	0.190117i	0.605629	−	0.795747i	$-0.292921\pi$
$83$	−1.73205	−	1.73205i	−0.190117	−	0.190117i	−0.795747	+	0.605629i	$0.792921\pi$
$84$	14.1962	−	3.80385i	1.54893	−	0.415034i
$85$		0			0
$86$	1.73205	+	3.00000i	0.186772	+	0.323498i
$87$			6.00000i			0.643268i
$88$	−6.92820	+	6.92820i	−0.738549	+	0.738549i
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$		0			0
$91$		−	20.7846i		−	2.17882i
$92$	−2.73205	+	0.732051i	−0.284836	+	0.0763216i
$93$	−6.92820			−0.718421
$94$	−8.66025	+	5.00000i	−0.893237	+	0.515711i
$95$		0			0
$96$	−9.46410	+	2.53590i	−0.965926	+	0.258819i
$97$	−6.00000	+	6.00000i	−0.609208	+	0.609208i	−0.942739	−	0.333531i	$-0.891760\pi$
$97$	−6.00000	+	6.00000i	−0.609208	+	0.609208i	0.333531	+	0.942739i	$0.391760\pi$
$98$	15.0263	+	4.02628i	1.51788	+	0.406716i
$99$	−10.3923			−1.04447
$100$		0			0
$101$	3.46410			0.344691			0.172345	−	0.985037i	$-0.444865\pi$
$101$	3.46410			0.344691			0.172345	+	0.985037i	$0.444865\pi$
$102$	−12.0000	+	6.92820i	−1.18818	+	0.685994i
$103$	−3.00000	−	3.00000i	−0.295599	−	0.295599i	0.543688	−	0.839287i	$-0.317027\pi$
$103$	−3.00000	−	3.00000i	−0.295599	−	0.295599i	−0.839287	+	0.543688i	$0.817027\pi$
$104$			13.8564i			1.35873i
$105$		0			0
$106$	−6.00000	+	3.46410i	−0.582772	+	0.336463i
$107$	−5.19615	+	5.19615i	−0.502331	+	0.502331i	−0.912162	−	0.409831i	$-0.865588\pi$
$107$	−5.19615	+	5.19615i	−0.502331	+	0.502331i	0.409831	+	0.912162i	$0.365588\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	17.3205			1.65900			0.829502	−	0.558504i	$-0.188624\pi$
$109$	17.3205			1.65900			0.829502	+	0.558504i	$0.188624\pi$
$110$		0			0
$111$		0			0
$112$	−16.3923	−	4.39230i	−1.54893	−	0.415034i
$113$	2.00000	−	2.00000i	0.188144	−	0.188144i	−0.606749	−	0.794893i	$-0.707527\pi$
$113$	2.00000	−	2.00000i	0.188144	−	0.188144i	0.794893	+	0.606749i	$0.207527\pi$
$114$	2.19615	−	8.19615i	0.205689	−	0.767640i
$115$		0			0
$116$	3.46410	−	6.00000i	0.321634	−	0.557086i
$117$	−10.3923	+	10.3923i	−0.960769	+	0.960769i
$118$	14.1962	+	3.80385i	1.30686	+	0.350173i
$119$	−24.0000			−2.20008
$120$		0			0
$121$	1.00000			0.0909091
$122$	4.73205	+	1.26795i	0.428420	+	0.114795i
$123$			10.3923i			0.937043i
$124$	6.92820	+	4.00000i	0.622171	+	0.359211i
$125$		0			0
$126$	−9.00000	−	15.5885i	−0.801784	−	1.38873i
$127$	3.00000	−	3.00000i	0.266207	−	0.266207i	−0.561363	−	0.827570i	$-0.689723\pi$
$127$	3.00000	−	3.00000i	0.266207	−	0.266207i	0.827570	+	0.561363i	$0.189723\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	3.00000	−	3.00000i	0.264135	−	0.264135i
$130$		0			0
$131$	17.3205			1.51330			0.756650	−	0.653820i	$-0.226835\pi$
$131$	17.3205			1.51330			0.756650	+	0.653820i	$0.226835\pi$
$132$	10.3923	+	6.00000i	0.904534	+	0.522233i
$133$	10.3923	−	10.3923i	0.901127	−	0.901127i
$134$	−9.00000	+	5.19615i	−0.777482	+	0.448879i
$135$		0			0
$136$	16.0000			1.37199
$137$	10.0000	+	10.0000i	0.854358	+	0.854358i	0.990666	−	0.136309i	$-0.0435239\pi$
$137$	10.0000	+	10.0000i	0.854358	+	0.854358i	−0.136309	+	0.990666i	$0.543524\pi$
$138$	1.73205	+	3.00000i	0.147442	+	0.255377i
$139$	10.3923			0.881464			0.440732	−	0.897639i	$-0.354719\pi$
$139$	10.3923			0.881464			0.440732	+	0.897639i	$0.354719\pi$
$140$		0			0
$141$	8.66025	+	8.66025i	0.729325	+	0.729325i
$142$	16.3923	+	4.39230i	1.37561	+	0.368594i
$143$	12.0000	−	12.0000i	1.00349	−	1.00349i
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$		0			0
$146$	10.3923	−	6.00000i	0.860073	−	0.496564i
$147$		−	19.0526i		−	1.57143i
$148$		0			0
$149$			13.8564i			1.13516i	0.823318	+	0.567581i	$0.192120\pi$
$149$			13.8564i			1.13516i	−0.823318	+	0.567581i	$0.807880\pi$
$150$		0			0
$151$	−20.0000			−1.62758			−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000			−1.62758			−0.813788	+	0.581161i	$0.802599\pi$
$152$	−6.92820	+	6.92820i	−0.561951	+	0.561951i
$153$	12.0000	+	12.0000i	0.970143	+	0.970143i
$154$	10.3923	+	18.0000i	0.837436	+	1.45048i
$155$		0			0
$156$	16.3923	−	4.39230i	1.31243	−	0.351666i
$157$	6.92820	+	6.92820i	0.552931	+	0.552931i	0.927286	−	0.374355i	$-0.122136\pi$
$157$	6.92820	+	6.92820i	0.552931	+	0.552931i	−0.374355	+	0.927286i	$0.622136\pi$
$158$	−10.9282	−	2.92820i	−0.869401	−	0.232955i
$159$	6.00000	+	6.00000i	0.475831	+	0.475831i
$160$		0			0
$161$			6.00000i			0.472866i
$162$	−3.29423	+	12.2942i	−0.258819	+	0.965926i
$163$	−8.66025	+	8.66025i	−0.678323	+	0.678323i	−0.959621	−	0.281297i	$-0.909235\pi$
$163$	−8.66025	+	8.66025i	−0.678323	+	0.678323i	0.281297	+	0.959621i	$0.409235\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$		0			0
$166$	3.00000	−	1.73205i	0.232845	−	0.134433i
$167$	−13.0000	−	13.0000i	−1.00597	−	1.00597i	−0.999982	−	0.00598813i	$-0.998094\pi$
$167$	−13.0000	−	13.0000i	−1.00597	−	1.00597i	−0.00598813	−	0.999982i	$-0.501906\pi$
$168$			20.7846i			1.60357i
$169$		−	11.0000i		−	0.846154i
$170$		0			0
$171$	−10.3923			−0.794719
$172$	−4.73205	+	1.26795i	−0.360815	+	0.0966802i
$173$	6.92820	+	6.92820i	0.526742	+	0.526742i	0.919599	−	0.392858i	$-0.128514\pi$
$173$	6.92820	+	6.92820i	0.526742	+	0.526742i	−0.392858	+	0.919599i	$0.628514\pi$
$174$	−8.19615	−	2.19615i	−0.621349	−	0.166490i
$175$		0			0
$176$	−6.92820	−	12.0000i	−0.522233	−	0.904534i
$177$		−	18.0000i		−	1.35296i
$178$	−4.39230	+	16.3923i	−0.329217	+	1.22866i
$179$			10.3923i			0.776757i	0.921500	+	0.388379i	$0.126965\pi$
$179$			10.3923i			0.776757i	−0.921500	+	0.388379i	$0.873035\pi$
$180$		0			0
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$	28.3923	+	7.60770i	2.10458	+	0.563920i
$183$		−	6.00000i		−	0.443533i
$184$		−	4.00000i		−	0.294884i
$185$		0			0
$186$	2.53590	−	9.46410i	0.185941	−	0.693942i
$187$	−13.8564	−	13.8564i	−1.01328	−	1.01328i
$188$	−3.66025	−	13.6603i	−0.266951	−	0.996276i
$189$	−15.5885	+	15.5885i	−1.13389	+	1.13389i
$190$		0			0
$191$			12.0000i			0.868290i	0.900843	+	0.434145i	$0.142949\pi$
$191$			12.0000i			0.868290i	−0.900843	+	0.434145i	$0.857051\pi$
$192$		−	13.8564i		−	1.00000i
$193$	18.0000	+	18.0000i	1.29567	+	1.29567i	0.931226	+	0.364442i	$0.118740\pi$
$193$	18.0000	+	18.0000i	1.29567	+	1.29567i	0.364442	+	0.931226i	$0.381260\pi$
$194$	−6.00000	−	10.3923i	−0.430775	−	0.746124i
$195$		0			0
$196$	−11.0000	+	19.0526i	−0.785714	+	1.36090i
$197$	−3.46410	+	3.46410i	−0.246807	+	0.246807i	−0.819659	−	0.572852i	$-0.805837\pi$
$197$	−3.46410	+	3.46410i	−0.246807	+	0.246807i	0.572852	+	0.819659i	$0.305837\pi$
$198$	3.80385	−	14.1962i	0.270328	−	1.00888i
$199$			4.00000i			0.283552i	0.989899	+	0.141776i	$0.0452813\pi$
$199$			4.00000i			0.283552i	−0.989899	+	0.141776i	$0.954719\pi$
$200$		0			0
$201$	9.00000	+	9.00000i	0.634811	+	0.634811i
$202$	−1.26795	+	4.73205i	−0.0892126	+	0.332946i
$203$	−10.3923	−	10.3923i	−0.729397	−	0.729397i
$204$	−5.07180	−	18.9282i	−0.355097	−	1.32524i
$205$		0			0
$206$	5.19615	−	3.00000i	0.362033	−	0.209020i
$207$	3.00000	−	3.00000i	0.208514	−	0.208514i
$208$	−18.9282	−	5.07180i	−1.31243	−	0.351666i
$209$	12.0000			0.830057
$210$		0			0
$211$			3.46410i			0.238479i	0.992866	+	0.119239i	$0.0380456\pi$
$211$			3.46410i			0.238479i	−0.992866	+	0.119239i	$0.961954\pi$
$212$	−2.53590	−	9.46410i	−0.174166	−	0.649997i
$213$		−	20.7846i		−	1.42414i
$214$	−5.19615	−	9.00000i	−0.355202	−	0.615227i
$215$		0			0
$216$	10.3923	−	10.3923i	0.707107	−	0.707107i
$217$	12.0000	−	12.0000i	0.814613	−	0.814613i
$218$	−6.33975	+	23.6603i	−0.429382	+	1.60247i
$219$	−10.3923	−	10.3923i	−0.702247	−	0.702247i
$220$		0			0
$221$	−27.7128			−1.86417
$222$		0			0
$223$	3.00000	+	3.00000i	0.200895	+	0.200895i	0.800383	−	0.599489i	$-0.204629\pi$
$223$	3.00000	+	3.00000i	0.200895	+	0.200895i	−0.599489	+	0.800383i	$0.704629\pi$
$224$	12.0000	−	20.7846i	0.801784	−	1.38873i
$225$		0			0
$226$	2.00000	+	3.46410i	0.133038	+	0.230429i
$227$	−19.0526	+	19.0526i	−1.26456	+	1.26456i	−0.315706	+	0.948857i	$0.602241\pi$
$227$	−19.0526	+	19.0526i	−1.26456	+	1.26456i	−0.948857	+	0.315706i	$0.897759\pi$
$228$	10.3923	+	6.00000i	0.688247	+	0.397360i
$229$	13.8564			0.915657			0.457829	−	0.889041i	$-0.348627\pi$
$229$	13.8564			0.915657			0.457829	+	0.889041i	$0.348627\pi$
$230$		0			0
$231$	18.0000	−	18.0000i	1.18431	−	1.18431i
$232$	6.92820	+	6.92820i	0.454859	+	0.454859i
$233$	−4.00000	+	4.00000i	−0.262049	+	0.262049i	−0.825886	−	0.563837i	$-0.809325\pi$
$233$	−4.00000	+	4.00000i	−0.262049	+	0.262049i	0.563837	+	0.825886i	$0.309325\pi$
$234$	−10.3923	−	18.0000i	−0.679366	−	1.17670i
$235$		0			0
$236$	−10.3923	+	18.0000i	−0.676481	+	1.17170i
$237$			13.8564i			0.900070i
$238$	8.78461	−	32.7846i	0.569422	−	2.12511i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$	−0.366025	+	1.36603i	−0.0235290	+	0.0878114i
$243$	15.5885			1.00000
$244$	−3.46410	+	6.00000i	−0.221766	+	0.384111i
$245$		0			0
$246$	−14.1962	−	3.80385i	−0.905114	−	0.242524i
$247$	12.0000	−	12.0000i	0.763542	−	0.763542i
$248$	−8.00000	+	8.00000i	−0.508001	+	0.508001i
$249$	−3.00000	−	3.00000i	−0.190117	−	0.190117i
$250$		0			0
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$	24.5885	−	6.58846i	1.54893	−	0.415034i
$253$	−3.46410	+	3.46410i	−0.217786	+	0.217786i
$254$	3.00000	+	5.19615i	0.188237	+	0.326036i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−10.0000	−	10.0000i	−0.623783	−	0.623783i	0.322714	−	0.946497i	$-0.395405\pi$
$257$	−10.0000	−	10.0000i	−0.623783	−	0.623783i	−0.946497	+	0.322714i	$0.895405\pi$
$258$	3.00000	+	5.19615i	0.186772	+	0.323498i
$259$		0			0
$260$		0			0
$261$			10.3923i			0.643268i
$262$	−6.33975	+	23.6603i	−0.391671	+	1.46174i
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	−0.889185	−	0.457547i	$-0.848728\pi$
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	0.457547	+	0.889185i	$0.348728\pi$
$264$	−12.0000	+	12.0000i	−0.738549	+	0.738549i
$265$		0			0
$266$	10.3923	+	18.0000i	0.637193	+	1.10365i
$267$	20.7846			1.27200
$268$	−3.80385	−	14.1962i	−0.232357	−	0.867168i
$269$		−	27.7128i		−	1.68968i	−0.535019	−	0.844840i	$-0.679696\pi$
$269$		−	27.7128i		−	1.68968i	0.535019	−	0.844840i	$-0.320304\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−5.85641	+	21.8564i	−0.355097	+	1.32524i
$273$		−	36.0000i		−	2.17882i
$274$	−17.3205	+	10.0000i	−1.04637	+	0.604122i
$275$		0			0
$276$	−4.73205	+	1.26795i	−0.284836	+	0.0763216i
$277$	−20.7846	−	20.7846i	−1.24883	−	1.24883i	−0.956239	−	0.292587i	$-0.905484\pi$
$277$	−20.7846	−	20.7846i	−1.24883	−	1.24883i	−0.292587	−	0.956239i	$-0.594516\pi$
$278$	−3.80385	+	14.1962i	−0.228140	+	0.851429i
$279$	−12.0000			−0.718421
$280$		0			0
$281$		−	18.0000i		−	1.07379i	−0.843649	−	0.536895i	$-0.819597\pi$
$281$		−	18.0000i		−	1.07379i	0.843649	−	0.536895i	$-0.180403\pi$
$282$	−15.0000	+	8.66025i	−0.893237	+	0.515711i
$283$	5.19615	−	5.19615i	0.308879	−	0.308879i	−0.535595	−	0.844475i	$-0.679913\pi$
$283$	5.19615	−	5.19615i	0.308879	−	0.308879i	0.844475	+	0.535595i	$0.179913\pi$
$284$	−12.0000	+	20.7846i	−0.712069	+	1.23334i
$285$		0			0
$286$	12.0000	+	20.7846i	0.709575	+	1.22902i
$287$	−18.0000	−	18.0000i	−1.06251	−	1.06251i
$288$	−16.3923	+	4.39230i	−0.965926	+	0.258819i
$289$			15.0000i			0.882353i
$290$		0			0
$291$	−10.3923	+	10.3923i	−0.609208	+	0.609208i
$292$	4.39230	+	16.3923i	0.257040	+	0.959287i
$293$	−6.92820	−	6.92820i	−0.404750	−	0.404750i	0.475153	−	0.879903i	$-0.342393\pi$
$293$	−6.92820	−	6.92820i	−0.404750	−	0.404750i	−0.879903	+	0.475153i	$0.842393\pi$
$294$	26.0263	+	6.97372i	1.51788	+	0.406716i
$295$		0			0
$296$		0			0
$297$	−18.0000			−1.04447
$298$	−18.9282	−	5.07180i	−1.09648	−	0.293801i
$299$			6.92820i			0.400668i
$300$		0			0
$301$			10.3923i			0.599002i
$302$	7.32051	−	27.3205i	0.421248	−	1.57212i
$303$	6.00000			0.344691
$304$	−6.92820	−	12.0000i	−0.397360	−	0.688247i
$305$		0			0
$306$	−20.7846	+	12.0000i	−1.18818	+	0.685994i
$307$	1.73205	+	1.73205i	0.0988534	+	0.0988534i	0.754804	−	0.655951i	$-0.227732\pi$
$307$	1.73205	+	1.73205i	0.0988534	+	0.0988534i	−0.655951	+	0.754804i	$0.727732\pi$
$308$	−28.3923	+	7.60770i	−1.61780	+	0.433489i
$309$	−5.19615	−	5.19615i	−0.295599	−	0.295599i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$			24.0000i			1.35873i
$313$	−12.0000	−	12.0000i	−0.678280	−	0.678280i	0.281331	−	0.959611i	$-0.409224\pi$
$313$	−12.0000	−	12.0000i	−0.678280	−	0.678280i	−0.959611	+	0.281331i	$0.909224\pi$
$314$	−12.0000	+	6.92820i	−0.677199	+	0.390981i
$315$		0			0
$316$	8.00000	−	13.8564i	0.450035	−	0.779484i
$317$	24.2487	−	24.2487i	1.36194	−	1.36194i	0.490505	−	0.871438i	$-0.336812\pi$
$317$	24.2487	−	24.2487i	1.36194	−	1.36194i	0.871438	−	0.490505i	$-0.163188\pi$
$318$	−10.3923	+	6.00000i	−0.582772	+	0.336463i
$319$		−	12.0000i		−	0.671871i
$320$		0			0
$321$	−9.00000	+	9.00000i	−0.502331	+	0.502331i
$322$	−8.19615	−	2.19615i	−0.456754	−	0.122387i
$323$	−13.8564	−	13.8564i	−0.770991	−	0.770991i
$324$	−15.5885	−	9.00000i	−0.866025	−	0.500000i
$325$		0			0
$326$	−8.66025	−	15.0000i	−0.479647	−	0.830773i
$327$	30.0000			1.65900
$328$	12.0000	+	12.0000i	0.662589	+	0.662589i
$329$	−30.0000			−1.65395
$330$		0			0
$331$			10.3923i			0.571213i	0.958347	+	0.285606i	$0.0921950\pi$
$331$			10.3923i			0.571213i	−0.958347	+	0.285606i	$0.907805\pi$
$332$	1.26795	+	4.73205i	0.0695878	+	0.259705i
$333$		0			0
$334$	22.5167	−	13.0000i	1.23206	−	0.711328i
$335$		0			0
$336$	−28.3923	−	7.60770i	−1.54893	−	0.415034i
$337$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$337$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$338$	15.0263	+	4.02628i	0.817322	+	0.219001i
$339$	3.46410	−	3.46410i	0.188144	−	0.188144i
$340$		0			0
$341$	13.8564			0.750366
$342$	3.80385	−	14.1962i	0.205689	−	0.767640i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$		−	6.92820i		−	0.373544i
$345$		0			0
$346$	−12.0000	+	6.92820i	−0.645124	+	0.372463i
$347$	−15.5885	+	15.5885i	−0.836832	+	0.836832i	−0.988441	−	0.151608i	$-0.951555\pi$
$347$	−15.5885	+	15.5885i	−0.836832	+	0.836832i	0.151608	+	0.988441i	$0.451555\pi$
$348$	6.00000	−	10.3923i	0.321634	−	0.557086i
$349$	−27.7128			−1.48343			−0.741716	−	0.670714i	$-0.765988\pi$
$349$	−27.7128			−1.48343			−0.741716	+	0.670714i	$0.765988\pi$
$350$		0			0
$351$	−18.0000	+	18.0000i	−0.960769	+	0.960769i
$352$	18.9282	−	5.07180i	1.00888	−	0.270328i
$353$	−14.0000	+	14.0000i	−0.745145	+	0.745145i	−0.973563	−	0.228418i	$-0.926645\pi$
$353$	−14.0000	+	14.0000i	−0.745145	+	0.745145i	0.228418	+	0.973563i	$0.426645\pi$
$354$	24.5885	+	6.58846i	1.30686	+	0.350173i
$355$		0			0
$356$	−20.7846	−	12.0000i	−1.10158	−	0.635999i
$357$	−41.5692			−2.20008
$358$	−14.1962	−	3.80385i	−0.750290	−	0.201040i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	−7.00000			−0.368421
$362$	18.9282	+	5.07180i	0.994844	+	0.266568i
$363$	1.73205			0.0909091
$364$	−20.7846	+	36.0000i	−1.08941	+	1.88691i
$365$		0			0
$366$	8.19615	+	2.19615i	0.428420	+	0.114795i
$367$	−9.00000	+	9.00000i	−0.469796	+	0.469796i	−0.901849	−	0.432052i	$-0.857790\pi$
$367$	−9.00000	+	9.00000i	−0.469796	+	0.469796i	0.432052	+	0.901849i	$0.357790\pi$
$368$	5.46410	+	1.46410i	0.284836	+	0.0763216i
$369$			18.0000i			0.937043i
$370$		0			0
$371$	−20.7846			−1.07908
$372$	12.0000	+	6.92820i	0.622171	+	0.359211i
$373$	−6.92820	+	6.92820i	−0.358729	+	0.358729i	−0.863344	−	0.504615i	$-0.831634\pi$
$373$	−6.92820	+	6.92820i	−0.358729	+	0.358729i	0.504615	+	0.863344i	$0.331634\pi$
$374$	24.0000	−	13.8564i	1.24101	−	0.716498i
$375$		0			0
$376$	20.0000			1.03142
$377$	−12.0000	−	12.0000i	−0.618031	−	0.618031i
$378$	−15.5885	−	27.0000i	−0.801784	−	1.38873i
$379$	−3.46410			−0.177939			−0.0889695	−	0.996034i	$-0.528357\pi$
$379$	−3.46410			−0.177939			−0.0889695	+	0.996034i	$0.528357\pi$
$380$		0			0
$381$	5.19615	−	5.19615i	0.266207	−	0.266207i
$382$	−16.3923	−	4.39230i	−0.838703	−	0.224730i
$383$	1.00000	−	1.00000i	0.0510976	−	0.0510976i	−0.681096	−	0.732194i	$-0.738496\pi$
$383$	1.00000	−	1.00000i	0.0510976	−	0.0510976i	0.732194	+	0.681096i	$0.238496\pi$
$384$	18.9282	+	5.07180i	0.965926	+	0.258819i
$385$		0			0
$386$	−31.1769	+	18.0000i	−1.58686	+	0.916176i
$387$	5.19615	−	5.19615i	0.264135	−	0.264135i
$388$	16.3923	−	4.39230i	0.832193	−	0.222985i
$389$		−	13.8564i		−	0.702548i	−0.936273	−	0.351274i	$-0.885749\pi$
$389$		−	13.8564i		−	0.702548i	0.936273	−	0.351274i	$-0.114251\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$	−22.0000	−	22.0000i	−1.11117	−	1.11117i
$393$	30.0000			1.51330
$394$	−3.46410	−	6.00000i	−0.174519	−	0.302276i
$395$		0			0
$396$	18.0000	+	10.3923i	0.904534	+	0.522233i
$397$	17.3205	+	17.3205i	0.869291	+	0.869291i	0.992394	−	0.123103i	$-0.0392844\pi$
$397$	17.3205	+	17.3205i	0.869291	+	0.869291i	−0.123103	+	0.992394i	$0.539284\pi$
$398$	−5.46410	−	1.46410i	−0.273891	−	0.0733888i
$399$	18.0000	−	18.0000i	0.901127	−	0.901127i
$400$		0			0
$401$		−	12.0000i		−	0.599251i	−0.954057	−	0.299626i	$-0.903138\pi$
$401$		−	12.0000i		−	0.599251i	0.954057	−	0.299626i	$-0.0968618\pi$
$402$	−15.5885	+	9.00000i	−0.777482	+	0.448879i
$403$	13.8564	−	13.8564i	0.690237	−	0.690237i
$404$	−6.00000	−	3.46410i	−0.298511	−	0.172345i
$405$		0			0
$406$	18.0000	−	10.3923i	0.893325	−	0.515761i
$407$		0			0
$408$	27.7128			1.37199
$409$			4.00000i			0.197787i	0.995098	+	0.0988936i	$0.0315304\pi$
$409$			4.00000i			0.197787i	−0.995098	+	0.0988936i	$0.968470\pi$
$410$		0			0
$411$	17.3205	+	17.3205i	0.854358	+	0.854358i
$412$	2.19615	+	8.19615i	0.108197	+	0.403795i
$413$	31.1769	+	31.1769i	1.53412	+	1.53412i
$414$	3.00000	+	5.19615i	0.147442	+	0.255377i
$415$		0			0
$416$	13.8564	−	24.0000i	0.679366	−	1.17670i
$417$	18.0000			0.881464
$418$	−4.39230	+	16.3923i	−0.214835	+	0.801774i
$419$		−	24.2487i		−	1.18463i	−0.805708	−	0.592314i	$-0.798215\pi$
$419$		−	24.2487i		−	1.18463i	0.805708	−	0.592314i	$-0.201785\pi$
$420$		0			0
$421$			3.46410i			0.168830i	0.996431	+	0.0844150i	$0.0269021\pi$
$421$			3.46410i			0.168830i	−0.996431	+	0.0844150i	$0.973098\pi$
$422$	−4.73205	−	1.26795i	−0.230353	−	0.0617228i
$423$	15.0000	+	15.0000i	0.729325	+	0.729325i
$424$	13.8564			0.672927
$425$		0			0
$426$	28.3923	+	7.60770i	1.37561	+	0.368594i
$427$	10.3923	+	10.3923i	0.502919	+	0.502919i
$428$	14.1962	−	3.80385i	0.686197	−	0.183866i
$429$	20.7846	−	20.7846i	1.00349	−	1.00349i
$430$		0			0
$431$			12.0000i			0.578020i	0.957326	+	0.289010i	$0.0933260\pi$
$431$			12.0000i			0.578020i	−0.957326	+	0.289010i	$0.906674\pi$
$432$	10.3923	+	18.0000i	0.500000	+	0.866025i
$433$	6.00000	+	6.00000i	0.288342	+	0.288342i	0.836424	−	0.548083i	$-0.184642\pi$
$433$	6.00000	+	6.00000i	0.288342	+	0.288342i	−0.548083	+	0.836424i	$0.684642\pi$
$434$	12.0000	+	20.7846i	0.576018	+	0.997693i
$435$		0			0
$436$	−30.0000	−	17.3205i	−1.43674	−	0.829502i
$437$	−3.46410	+	3.46410i	−0.165710	+	0.165710i
$438$	18.0000	−	10.3923i	0.860073	−	0.496564i
$439$		−	32.0000i		−	1.52728i	−0.645644	−	0.763638i	$-0.723411\pi$
$439$		−	32.0000i		−	1.52728i	0.645644	−	0.763638i	$-0.276589\pi$
$440$		0			0
$441$		−	33.0000i		−	1.57143i
$442$	10.1436	−	37.8564i	0.482482	−	1.80065i
$443$	8.66025	+	8.66025i	0.411461	+	0.411461i	0.882247	−	0.470786i	$-0.156030\pi$
$443$	8.66025	+	8.66025i	0.411461	+	0.411461i	−0.470786	+	0.882247i	$0.656030\pi$
$444$		0			0
$445$		0			0
$446$	−5.19615	+	3.00000i	−0.246045	+	0.142054i
$447$			24.0000i			1.13516i
$448$	24.0000	+	24.0000i	1.13389	+	1.13389i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		−	20.7846i		−	0.978709i
$452$	−5.46410	+	1.46410i	−0.257010	+	0.0688655i
$453$	−34.6410			−1.62758
$454$	−19.0526	−	33.0000i	−0.894181	−	1.54877i
$455$		0			0
$456$	−12.0000	+	12.0000i	−0.561951	+	0.561951i
$457$	12.0000	−	12.0000i	0.561336	−	0.561336i	−0.368351	−	0.929687i	$-0.620077\pi$
$457$	12.0000	−	12.0000i	0.561336	−	0.561336i	0.929687	+	0.368351i	$0.120077\pi$
$458$	−5.07180	+	18.9282i	−0.236989	+	0.884457i
$459$	20.7846	+	20.7846i	0.970143	+	0.970143i
$460$		0			0
$461$	31.1769			1.45205			0.726027	−	0.687666i	$-0.241365\pi$
$461$	31.1769			1.45205			0.726027	+	0.687666i	$0.241365\pi$
$462$	18.0000	+	31.1769i	0.837436	+	1.45048i
$463$	−9.00000	−	9.00000i	−0.418265	−	0.418265i	0.466340	−	0.884606i	$-0.345572\pi$
$463$	−9.00000	−	9.00000i	−0.418265	−	0.418265i	−0.884606	+	0.466340i	$0.845572\pi$
$464$	−12.0000	+	6.92820i	−0.557086	+	0.321634i
$465$		0			0
$466$	−4.00000	−	6.92820i	−0.185296	−	0.320943i
$467$	8.66025	−	8.66025i	0.400749	−	0.400749i	−0.477748	−	0.878497i	$-0.658547\pi$
$467$	8.66025	−	8.66025i	0.400749	−	0.400749i	0.878497	+	0.477748i	$0.158547\pi$
$468$	28.3923	−	7.60770i	1.31243	−	0.351666i
$469$	−31.1769			−1.43962
$470$		0			0
$471$	12.0000	+	12.0000i	0.552931	+	0.552931i
$472$	−20.7846	−	20.7846i	−0.956689	−	0.956689i
$473$	−6.00000	+	6.00000i	−0.275880	+	0.275880i
$474$	−18.9282	−	5.07180i	−0.869401	−	0.232955i
$475$		0			0
$476$	41.5692	+	24.0000i	1.90532	+	1.10004i
$477$	10.3923	+	10.3923i	0.475831	+	0.475831i
$478$	−8.78461	+	32.7846i	−0.401799	+	1.49953i
$479$	36.0000			1.64488			0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000			1.64488			0.822441	+	0.568850i	$0.192612\pi$
$480$		0			0
$481$		0			0
$482$	2.92820	−	10.9282i	0.133376	−	0.497766i
$483$			10.3923i			0.472866i
$484$	−1.73205	−	1.00000i	−0.0787296	−	0.0454545i
$485$		0			0
$486$	−5.70577	+	21.2942i	−0.258819	+	0.965926i
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	−0.959936	−	0.280221i	$-0.909592\pi$
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	0.280221	+	0.959936i	$0.409592\pi$
$488$	−6.92820	−	6.92820i	−0.313625	−	0.313625i
$489$	−15.0000	+	15.0000i	−0.678323	+	0.678323i
$490$		0			0
$491$	10.3923			0.468998			0.234499	−	0.972116i	$-0.424655\pi$
$491$	10.3923			0.468998			0.234499	+	0.972116i	$0.424655\pi$
$492$	10.3923	−	18.0000i	0.468521	−	0.811503i
$493$	−13.8564	+	13.8564i	−0.624061	+	0.624061i
$494$	12.0000	+	20.7846i	0.539906	+	0.935144i
$495$		0			0
$496$	−8.00000	−	13.8564i	−0.359211	−	0.622171i
$497$	36.0000	+	36.0000i	1.61482	+	1.61482i
$498$	5.19615	−	3.00000i	0.232845	−	0.134433i
$499$	24.2487			1.08552			0.542761	−	0.839887i	$-0.317379\pi$
$499$	24.2487			1.08552			0.542761	+	0.839887i	$0.317379\pi$
$500$		0			0
$501$	−22.5167	−	22.5167i	−1.00597	−	1.00597i
$502$	1.26795	−	4.73205i	0.0565913	−	0.211202i
$503$	5.00000	−	5.00000i	0.222939	−	0.222939i	−0.586796	−	0.809735i	$-0.699611\pi$
$503$	5.00000	−	5.00000i	0.222939	−	0.222939i	0.809735	+	0.586796i	$0.199611\pi$
$504$			36.0000i			1.60357i
$505$		0			0
$506$	−3.46410	−	6.00000i	−0.153998	−	0.266733i
$507$		−	19.0526i		−	0.846154i
$508$	−8.19615	+	2.19615i	−0.363645	+	0.0974385i
$509$			38.1051i			1.68898i	0.535572	+	0.844490i	$0.320096\pi$
$509$			38.1051i			1.68898i	−0.535572	+	0.844490i	$0.679904\pi$
$510$		0			0
$511$	36.0000			1.59255
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−18.0000			−0.794719
$514$	17.3205	−	10.0000i	0.763975	−	0.441081i
$515$		0			0
$516$	−8.19615	+	2.19615i	−0.360815	+	0.0966802i
$517$	−17.3205	−	17.3205i	−0.761755	−	0.761755i
$518$		0			0
$519$	12.0000	+	12.0000i	0.526742	+	0.526742i
$520$		0			0
$521$			24.0000i			1.05146i	0.850652	+	0.525730i	$0.176208\pi$
$521$			24.0000i			1.05146i	−0.850652	+	0.525730i	$0.823792\pi$
$522$	−14.1962	−	3.80385i	−0.621349	−	0.166490i
$523$	8.66025	−	8.66025i	0.378686	−	0.378686i	−0.491942	−	0.870628i	$-0.663713\pi$
$523$	8.66025	−	8.66025i	0.378686	−	0.378686i	0.870628	+	0.491942i	$0.163713\pi$
$524$	−30.0000	−	17.3205i	−1.31056	−	0.756650i
$525$		0			0
$526$	−7.00000	−	12.1244i	−0.305215	−	0.528647i
$527$	−16.0000	−	16.0000i	−0.696971	−	0.696971i
$528$	−12.0000	−	20.7846i	−0.522233	−	0.904534i
$529$			21.0000i			0.913043i
$530$		0			0
$531$		−	31.1769i		−	1.35296i
$532$	−28.3923	+	7.60770i	−1.23096	+	0.329835i
$533$	−20.7846	−	20.7846i	−0.900281	−	0.900281i
$534$	−7.60770	+	28.3923i	−0.329217	+	1.22866i
$535$		0			0
$536$	20.7846			0.897758
$537$			18.0000i			0.776757i
$538$	37.8564	+	10.1436i	1.63211	+	0.437321i
$539$			38.1051i			1.64130i
$540$		0			0
$541$		−	41.5692i		−	1.78720i	−0.448864	−	0.893600i	$-0.648171\pi$
$541$		−	41.5692i		−	1.78720i	0.448864	−	0.893600i	$-0.351829\pi$
$542$	−2.92820	+	10.9282i	−0.125777	+	0.469407i
$543$		−	24.0000i		−	1.02994i
$544$	−27.7128	−	16.0000i	−1.18818	−	0.685994i
$545$		0			0
$546$	49.1769	+	13.1769i	2.10458	+	0.563920i
$547$	8.66025	+	8.66025i	0.370286	+	0.370286i	0.867581	−	0.497296i	$-0.165674\pi$
$547$	8.66025	+	8.66025i	0.370286	+	0.370286i	−0.497296	+	0.867581i	$0.665674\pi$
$548$	−7.32051	−	27.3205i	−0.312717	−	1.16707i
$549$		−	10.3923i		−	0.443533i
$550$		0			0
$551$		−	12.0000i		−	0.511217i
$552$		−	6.92820i		−	0.294884i
$553$	−24.0000	−	24.0000i	−1.02058	−	1.02058i
$554$	36.0000	−	20.7846i	1.52949	−	0.883053i
$555$		0			0
$556$	−18.0000	−	10.3923i	−0.763370	−	0.440732i
$557$	20.7846	−	20.7846i	0.880672	−	0.880672i	−0.112931	−	0.993603i	$-0.536024\pi$
$557$	20.7846	−	20.7846i	0.880672	−	0.880672i	0.993603	+	0.112931i	$0.0360238\pi$
$558$	4.39230	−	16.3923i	0.185941	−	0.693942i
$559$			12.0000i			0.507546i
$560$		0			0
$561$	−24.0000	−	24.0000i	−1.01328	−	1.01328i
$562$	24.5885	+	6.58846i	1.03720	+	0.277917i
$563$	5.19615	+	5.19615i	0.218992	+	0.218992i	0.808073	−	0.589082i	$-0.200510\pi$
$563$	5.19615	+	5.19615i	0.218992	+	0.218992i	−0.589082	+	0.808073i	$0.700510\pi$
$564$	−6.33975	−	23.6603i	−0.266951	−	0.996276i
$565$		0			0
$566$	5.19615	+	9.00000i	0.218411	+	0.378298i
$567$	−27.0000	+	27.0000i	−1.13389	+	1.13389i
$568$	−24.0000	−	24.0000i	−1.00702	−	1.00702i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$			45.0333i			1.88459i	0.334790	+	0.942293i	$0.391335\pi$
$571$			45.0333i			1.88459i	−0.334790	+	0.942293i	$0.608665\pi$
$572$	−32.7846	+	8.78461i	−1.37079	+	0.367303i
$573$			20.7846i			0.868290i
$574$	31.1769	−	18.0000i	1.30130	−	0.751305i
$575$		0			0
$576$		−	24.0000i		−	1.00000i
$577$	−24.0000	+	24.0000i	−0.999133	+	0.999133i	−1.00000		0.000866551i	$-0.999724\pi$
$577$	−24.0000	+	24.0000i	−0.999133	+	0.999133i	0.000866551		1.00000i	$0.499724\pi$
$578$	−20.4904	−	5.49038i	−0.852287	−	0.228370i
$579$	31.1769	+	31.1769i	1.29567	+	1.29567i
$580$		0			0
$581$	10.3923			0.431145
$582$	−10.3923	−	18.0000i	−0.430775	−	0.746124i
$583$	−12.0000	−	12.0000i	−0.496989	−	0.496989i
$584$	−24.0000			−0.993127
$585$		0			0
$586$	12.0000	−	6.92820i	0.495715	−	0.286201i
$587$	1.73205	−	1.73205i	0.0714894	−	0.0714894i	−0.670458	−	0.741947i	$-0.733902\pi$
$587$	1.73205	−	1.73205i	0.0714894	−	0.0714894i	0.741947	+	0.670458i	$0.233902\pi$
$588$	−19.0526	+	33.0000i	−0.785714	+	1.36090i
$589$	13.8564			0.570943
$590$		0			0
$591$	−6.00000	+	6.00000i	−0.246807	+	0.246807i
$592$		0			0
$593$	−14.0000	+	14.0000i	−0.574911	+	0.574911i	−0.933497	−	0.358586i	$-0.883259\pi$
$593$	−14.0000	+	14.0000i	−0.574911	+	0.574911i	0.358586	+	0.933497i	$0.383259\pi$
$594$	6.58846	−	24.5885i	0.270328	−	1.00888i
$595$		0			0
$596$	13.8564	−	24.0000i	0.567581	−	0.983078i
$597$			6.92820i			0.283552i
$598$	−9.46410	−	2.53590i	−0.387016	−	0.103701i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	−8.00000			−0.326327			−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000			−0.326327			−0.163163	+	0.986599i	$0.552170\pi$
$602$	−14.1962	−	3.80385i	−0.578592	−	0.155033i
$603$	15.5885	+	15.5885i	0.634811	+	0.634811i
$604$	34.6410	+	20.0000i	1.40952	+	0.813788i
$605$		0			0
$606$	−2.19615	+	8.19615i	−0.0892126	+	0.332946i
$607$	3.00000	−	3.00000i	0.121766	−	0.121766i	−0.643598	−	0.765364i	$-0.722559\pi$
$607$	3.00000	−	3.00000i	0.121766	−	0.121766i	0.765364	+	0.643598i	$0.222559\pi$
$608$	18.9282	−	5.07180i	0.767640	−	0.205689i
$609$	−18.0000	−	18.0000i	−0.729397	−	0.729397i
$610$		0			0
$611$	−34.6410			−1.40143
$612$	−8.78461	−	32.7846i	−0.355097	−	1.32524i
$613$	24.2487	−	24.2487i	0.979396	−	0.979396i	−0.0203958	−	0.999792i	$-0.506493\pi$
$613$	24.2487	−	24.2487i	0.979396	−	0.979396i	0.999792	+	0.0203958i	$0.00649262\pi$
$614$	−3.00000	+	1.73205i	−0.121070	+	0.0698999i
$615$		0			0
$616$		−	41.5692i		−	1.67487i
$617$	8.00000	+	8.00000i	0.322068	+	0.322068i	0.849560	−	0.527492i	$-0.176868\pi$
$617$	8.00000	+	8.00000i	0.322068	+	0.322068i	−0.527492	+	0.849560i	$0.676868\pi$
$618$	9.00000	−	5.19615i	0.362033	−	0.209020i
$619$	−31.1769			−1.25311			−0.626553	−	0.779379i	$-0.715535\pi$
$619$	−31.1769			−1.25311			−0.626553	+	0.779379i	$0.715535\pi$
$620$		0			0
$621$	5.19615	−	5.19615i	0.208514	−	0.208514i
$622$		0			0
$623$	−36.0000	+	36.0000i	−1.44231	+	1.44231i
$624$	−32.7846	−	8.78461i	−1.31243	−	0.351666i
$625$		0			0
$626$	20.7846	−	12.0000i	0.830720	−	0.479616i
$627$	20.7846			0.830057
$628$	−5.07180	−	18.9282i	−0.202387	−	0.755318i
$629$		0			0
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	16.0000	+	16.0000i	0.636446	+	0.636446i
$633$			6.00000i			0.238479i
$634$	24.2487	+	42.0000i	0.963039	+	1.66803i
$635$		0			0
$636$	−4.39230	−	16.3923i	−0.174166	−	0.649997i
$637$	38.1051	+	38.1051i	1.50978	+	1.50978i
$638$	16.3923	+	4.39230i	0.648978	+	0.173893i
$639$		−	36.0000i		−	1.42414i
$640$		0			0
$641$			6.00000i			0.236986i	0.992955	+	0.118493i	$0.0378063\pi$
$641$			6.00000i			0.236986i	−0.992955	+	0.118493i	$0.962194\pi$
$642$	−9.00000	−	15.5885i	−0.355202	−	0.615227i
$643$	−19.0526	+	19.0526i	−0.751360	+	0.751360i	−0.974733	−	0.223373i	$-0.928293\pi$
$643$	−19.0526	+	19.0526i	−0.751360	+	0.751360i	0.223373	+	0.974733i	$0.428293\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$	24.0000	−	13.8564i	0.944267	−	0.545173i
$647$	25.0000	+	25.0000i	0.982851	+	0.982851i	0.999855	−	0.0170040i	$-0.00541280\pi$
$647$	25.0000	+	25.0000i	0.982851	+	0.982851i	−0.0170040	+	0.999855i	$0.505413\pi$
$648$	18.0000	−	18.0000i	0.707107	−	0.707107i
$649$			36.0000i			1.41312i
$650$		0			0
$651$	20.7846	−	20.7846i	0.814613	−	0.814613i
$652$	23.6603	−	6.33975i	0.926607	−	0.248284i
$653$	17.3205	+	17.3205i	0.677804	+	0.677804i	0.959503	−	0.281699i	$-0.0908980\pi$
$653$	17.3205	+	17.3205i	0.677804	+	0.677804i	−0.281699	+	0.959503i	$0.590898\pi$
$654$	−10.9808	+	40.9808i	−0.429382	+	1.60247i
$655$		0			0
$656$	−20.7846	+	12.0000i	−0.811503	+	0.468521i
$657$	−18.0000	−	18.0000i	−0.702247	−	0.702247i
$658$	10.9808	−	40.9808i	0.428075	−	1.59760i
$659$			10.3923i			0.404827i	0.979300	+	0.202413i	$0.0648785\pi$
$659$			10.3923i			0.404827i	−0.979300	+	0.202413i	$0.935122\pi$
$660$		0			0
$661$			31.1769i			1.21264i	0.795220	+	0.606321i	$0.207355\pi$
$661$			31.1769i			1.21264i	−0.795220	+	0.606321i	$0.792645\pi$
$662$	−14.1962	−	3.80385i	−0.551749	−	0.147841i
$663$	−48.0000			−1.86417
$664$	−6.92820			−0.268866
$665$		0			0
$666$		0			0
$667$	3.46410	+	3.46410i	0.134131	+	0.134131i
$668$	9.51666	+	35.5167i	0.368211	+	1.37418i
$669$	5.19615	+	5.19615i	0.200895	+	0.200895i
$670$		0			0
$671$			12.0000i			0.463255i
$672$	20.7846	−	36.0000i	0.801784	−	1.38873i
$673$	6.00000	+	6.00000i	0.231283	+	0.231283i	0.813228	−	0.581945i	$-0.197708\pi$
$673$	6.00000	+	6.00000i	0.231283	+	0.231283i	−0.581945	+	0.813228i	$0.697708\pi$
$674$		0			0
$675$		0			0
$676$	−11.0000	+	19.0526i	−0.423077	+	0.732791i
$677$	−10.3923	+	10.3923i	−0.399409	+	0.399409i	−0.878024	−	0.478616i	$-0.841139\pi$
$677$	−10.3923	+	10.3923i	−0.399409	+	0.399409i	0.478616	+	0.878024i	$0.341139\pi$
$678$	3.46410	+	6.00000i	0.133038	+	0.230429i
$679$		−	36.0000i		−	1.38155i
$680$		0			0
$681$	−33.0000	+	33.0000i	−1.26456	+	1.26456i
$682$	−5.07180	+	18.9282i	−0.194209	+	0.724798i
$683$	−29.4449	−	29.4449i	−1.12668	−	1.12668i	−0.990714	−	0.135962i	$-0.956587\pi$
$683$	−29.4449	−	29.4449i	−1.12668	−	1.12668i	−0.135962	−	0.990714i	$-0.543413\pi$
$684$	18.0000	+	10.3923i	0.688247	+	0.397360i
$685$		0			0
$686$	−20.7846	+	12.0000i	−0.793560	+	0.458162i
$687$	24.0000			0.915657
$688$	9.46410	+	2.53590i	0.360815	+	0.0966802i
$689$	−24.0000			−0.914327
$690$		0			0
$691$			3.46410i			0.131781i	0.997827	+	0.0658903i	$0.0209887\pi$
$691$			3.46410i			0.131781i	−0.997827	+	0.0658903i	$0.979011\pi$
$692$	−5.07180	−	18.9282i	−0.192801	−	0.719542i
$693$	31.1769	−	31.1769i	1.18431	−	1.18431i
$694$	−15.5885	−	27.0000i	−0.591730	−	1.02491i
$695$		0			0
$696$	12.0000	+	12.0000i	0.454859	+	0.454859i
$697$	−24.0000	+	24.0000i	−0.909065	+	0.909065i
$698$	10.1436	−	37.8564i	0.383941	−	1.43289i
$699$	−6.92820	+	6.92820i	−0.262049	+	0.262049i
$700$		0			0
$701$	13.8564			0.523349			0.261675	−	0.965156i	$-0.415725\pi$
$701$	13.8564			0.523349			0.261675	+	0.965156i	$0.415725\pi$
$702$	−18.0000	−	31.1769i	−0.679366	−	1.17670i
$703$		0			0
$704$			27.7128i			1.04447i
$705$		0			0
$706$	−14.0000	−	24.2487i	−0.526897	−	0.912612i
$707$	−10.3923	+	10.3923i	−0.390843	+	0.390843i
$708$	−18.0000	+	31.1769i	−0.676481	+	1.17170i
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$		0			0
$711$			24.0000i			0.900070i
$712$	24.0000	−	24.0000i	0.899438	−	0.899438i
$713$	−4.00000	+	4.00000i	−0.149801	+	0.149801i
$714$	15.2154	−	56.7846i	0.569422	−	2.12511i
$715$		0			0
$716$	10.3923	−	18.0000i	0.388379	−	0.672692i
$717$	41.5692			1.55243
$718$	4.39230	−	16.3923i	0.163919	−	0.611755i
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$		0			0
$721$	18.0000			0.670355
$722$	2.56218	−	9.56218i	0.0953544	−	0.355867i
$723$	−13.8564			−0.515325
$724$	−13.8564	+	24.0000i	−0.514969	+	0.891953i
$725$		0			0
$726$	−0.633975	+	2.36603i	−0.0235290	+	0.0878114i
$727$	15.0000	−	15.0000i	0.556319	−	0.556319i	−0.371938	−	0.928257i	$-0.621307\pi$
$727$	15.0000	−	15.0000i	0.556319	−	0.556319i	0.928257	+	0.371938i	$0.121307\pi$
$728$	−41.5692	−	41.5692i	−1.54066	−	1.54066i
$729$	27.0000			1.00000
$730$		0			0
$731$	13.8564			0.512498
$732$	−6.00000	+	10.3923i	−0.221766	+	0.384111i
$733$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$733$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$734$	−9.00000	−	15.5885i	−0.332196	−	0.575380i
$735$		0			0
$736$	−4.00000	+	6.92820i	−0.147442	+	0.255377i
$737$	−18.0000	−	18.0000i	−0.663039	−	0.663039i
$738$	−24.5885	−	6.58846i	−0.905114	−	0.242524i
$739$	3.46410			0.127429			0.0637145	−	0.997968i	$-0.479705\pi$
$739$	3.46410			0.127429			0.0637145	+	0.997968i	$0.479705\pi$
$740$		0			0
$741$	20.7846	−	20.7846i	0.763542	−	0.763542i
$742$	7.60770	−	28.3923i	0.279287	−	1.04231i
$743$	25.0000	−	25.0000i	0.917161	−	0.917161i	−0.0796610	−	0.996822i	$-0.525384\pi$
$743$	25.0000	−	25.0000i	0.917161	−	0.917161i	0.996822	+	0.0796610i	$0.0253838\pi$
$744$	−13.8564	+	13.8564i	−0.508001	+	0.508001i
$745$		0			0
$746$	−6.92820	−	12.0000i	−0.253660	−	0.439351i
$747$	−5.19615	−	5.19615i	−0.190117	−	0.190117i
$748$	10.1436	+	37.8564i	0.370887	+	1.38417i
$749$		−	31.1769i		−	1.13918i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	−7.32051	+	27.3205i	−0.266951	+	0.996276i
$753$	−6.00000			−0.218652
$754$	20.7846	−	12.0000i	0.756931	−	0.437014i
$755$		0			0
$756$	42.5885	−	11.4115i	1.54893	−	0.415034i
$757$	−27.7128	−	27.7128i	−1.00724	−	1.00724i	−0.999974	−	0.00726571i	$-0.997687\pi$
$757$	−27.7128	−	27.7128i	−1.00724	−	1.00724i	−0.00726571	−	0.999974i	$-0.502313\pi$
$758$	1.26795	−	4.73205i	0.0460540	−	0.171876i
$759$	−6.00000	+	6.00000i	−0.217786	+	0.217786i
$760$		0			0
$761$		−	48.0000i		−	1.74000i	−0.493053	−	0.869999i	$-0.664119\pi$
$761$		−	48.0000i		−	1.74000i	0.493053	−	0.869999i	$-0.335881\pi$
$762$	5.19615	+	9.00000i	0.188237	+	0.326036i
$763$	−51.9615	+	51.9615i	−1.88113	+	1.88113i
$764$	12.0000	−	20.7846i	0.434145	−	0.751961i
$765$		0			0
$766$	1.00000	+	1.73205i	0.0361315	+	0.0625815i
$767$	36.0000	+	36.0000i	1.29988	+	1.29988i
$768$	−13.8564	+	24.0000i	−0.500000	+	0.866025i
$769$		−	14.0000i		−	0.504853i	−0.967616	−	0.252426i	$-0.918771\pi$
$769$		−	14.0000i		−	0.504853i	0.967616	−	0.252426i	$-0.0812286\pi$
$770$		0			0
$771$	−17.3205	−	17.3205i	−0.623783	−	0.623783i
$772$	−13.1769	−	49.1769i	−0.474248	−	1.76992i
$773$	3.46410	+	3.46410i	0.124595	+	0.124595i	0.766655	−	0.642060i	$-0.221920\pi$
$773$	3.46410	+	3.46410i	0.124595	+	0.124595i	−0.642060	+	0.766655i	$0.721920\pi$
$774$	5.19615	+	9.00000i	0.186772	+	0.323498i
$775$		0			0
$776$			24.0000i			0.861550i
$777$		0			0
$778$	18.9282	+	5.07180i	0.678609	+	0.181833i
$779$		−	20.7846i		−	0.744686i
$780$		0			0
$781$			41.5692i			1.48746i
$782$	−2.92820	+	10.9282i	−0.104712	+	0.390792i
$783$			18.0000i			0.643268i
$784$	38.1051	−	22.0000i	1.36090	−	0.785714i
$785$		0			0
$786$	−10.9808	+	40.9808i	−0.391671	+	1.46174i
$787$	−29.4449	−	29.4449i	−1.04960	−	1.04960i	−0.998704	−	0.0508919i	$-0.983794\pi$
$787$	−29.4449	−	29.4449i	−1.04960	−	1.04960i	−0.0508919	−	0.998704i	$-0.516206\pi$
$788$	9.46410	−	2.53590i	0.337145	−	0.0903376i
$789$	−12.1244	+	12.1244i	−0.431638	+	0.431638i
$790$		0			0
$791$			12.0000i			0.426671i
$792$	−20.7846	+	20.7846i	−0.738549	+	0.738549i
$793$	12.0000	+	12.0000i	0.426132	+	0.426132i
$794$	−30.0000	+	17.3205i	−1.06466	+	0.614682i
$795$		0			0
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	24.2487	−	24.2487i	0.858933	−	0.858933i	−0.132279	−	0.991213i	$-0.542230\pi$
$797$	24.2487	−	24.2487i	0.858933	−	0.858933i	0.991213	+	0.132279i	$0.0422295\pi$
$798$	18.0000	+	31.1769i	0.637193	+	1.10365i
$799$			40.0000i			1.41510i
$800$		0			0
$801$	36.0000			1.27200
$802$	16.3923	+	4.39230i	0.578832	+	0.155098i
$803$	20.7846	+	20.7846i	0.733473	+	0.733473i
$804$	−6.58846	−	24.5885i	−0.232357	−	0.867168i
$805$		0			0
$806$	13.8564	+	24.0000i	0.488071	+	0.845364i
$807$		−	48.0000i		−	1.68968i
$808$	6.92820	−	6.92820i	0.243733	−	0.243733i
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	7.60770	+	28.3923i	0.266978	+	0.996375i
$813$	13.8564			0.485965
$814$		0			0
$815$		0			0
$816$	−10.1436	+	37.8564i	−0.355097	+	1.32524i
$817$	−6.00000	+	6.00000i	−0.209913	+	0.209913i
$818$	−5.46410	−	1.46410i	−0.191048	−	0.0511911i
$819$		−	62.3538i		−	2.17882i
$820$		0			0
$821$	−41.5692			−1.45078			−0.725388	−	0.688340i	$-0.758340\pi$
$821$	−41.5692			−1.45078			−0.725388	+	0.688340i	$0.758340\pi$
$822$	−30.0000	+	17.3205i	−1.04637	+	0.604122i
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	0.757458	−	0.652884i	$-0.226441\pi$
$823$	3.00000	+	3.00000i	0.104573	+	0.104573i	−0.652884	+	0.757458i	$0.726441\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$	−54.0000	+	31.1769i	−1.87890	+	1.08478i
$827$	8.66025	−	8.66025i	0.301147	−	0.301147i	−0.540316	−	0.841462i	$-0.681695\pi$
$827$	8.66025	−	8.66025i	0.301147	−	0.301147i	0.841462	+	0.540316i	$0.181695\pi$
$828$	−8.19615	+	2.19615i	−0.284836	+	0.0763216i
$829$	−51.9615			−1.80470			−0.902349	−	0.431006i	$-0.858159\pi$
$829$	−51.9615			−1.80470			−0.902349	+	0.431006i	$0.858159\pi$
$830$		0			0
$831$	−36.0000	−	36.0000i	−1.24883	−	1.24883i
$832$	27.7128	+	27.7128i	0.960769	+	0.960769i
$833$	44.0000	−	44.0000i	1.52451	−	1.52451i
$834$	−6.58846	+	24.5885i	−0.228140	+	0.851429i
$835$		0			0
$836$	−20.7846	−	12.0000i	−0.718851	−	0.415029i
$837$	−20.7846			−0.718421
$838$	33.1244	+	8.87564i	1.14426	+	0.306604i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$	−4.73205	−	1.26795i	−0.163077	−	0.0436964i
$843$		−	31.1769i		−	1.07379i
$844$	3.46410	−	6.00000i	0.119239	−	0.206529i
$845$		0			0
$846$	−25.9808	+	15.0000i	−0.893237	+	0.515711i
$847$	−3.00000	+	3.00000i	−0.103081	+	0.103081i
$848$	−5.07180	+	18.9282i	−0.174166	+	0.649997i
$849$	9.00000	−	9.00000i	0.308879	−	0.308879i
$850$		0			0
$851$		0			0
$852$	−20.7846	+	36.0000i	−0.712069	+	1.23334i
$853$	3.46410	−	3.46410i	0.118609	−	0.118609i	−0.645311	−	0.763920i	$-0.723272\pi$
$853$	3.46410	−	3.46410i	0.118609	−	0.118609i	0.763920	+	0.645311i	$0.223272\pi$
$854$	−18.0000	+	10.3923i	−0.615947	+	0.355617i
$855$		0			0
$856$			20.7846i			0.710403i
$857$	26.0000	+	26.0000i	0.888143	+	0.888143i	0.994345	−	0.106202i	$-0.0338689\pi$
$857$	26.0000	+	26.0000i	0.888143	+	0.888143i	−0.106202	+	0.994345i	$0.533869\pi$
$858$	20.7846	+	36.0000i	0.709575	+	1.22902i
$859$	24.2487			0.827355			0.413678	−	0.910423i	$-0.364244\pi$
$859$	24.2487			0.827355			0.413678	+	0.910423i	$0.364244\pi$
$860$		0			0
$861$	−31.1769	−	31.1769i	−1.06251	−	1.06251i
$862$	−16.3923	−	4.39230i	−0.558324	−	0.149602i
$863$	23.0000	−	23.0000i	0.782929	−	0.782929i	−0.197395	−	0.980324i	$-0.563248\pi$
$863$	23.0000	−	23.0000i	0.782929	−	0.782929i	0.980324	+	0.197395i	$0.0632481\pi$
$864$	−28.3923	+	7.60770i	−0.965926	+	0.258819i
$865$		0			0
$866$	−10.3923	+	6.00000i	−0.353145	+	0.203888i
$867$			25.9808i			0.882353i
$868$	−32.7846	+	8.78461i	−1.11278	+	0.298169i
$869$		−	27.7128i		−	0.940093i
$870$		0			0
$871$	−36.0000			−1.21981
$872$	34.6410	−	34.6410i	1.17309	−	1.17309i
$873$	−18.0000	+	18.0000i	−0.609208	+	0.609208i
$874$	−3.46410	−	6.00000i	−0.117175	−	0.202953i
$875$		0			0
$876$	7.60770	+	28.3923i	0.257040	+	0.959287i
$877$	13.8564	+	13.8564i	0.467898	+	0.467898i	0.901233	−	0.433335i	$-0.142663\pi$
$877$	13.8564	+	13.8564i	0.467898	+	0.467898i	−0.433335	+	0.901233i	$0.642663\pi$
$878$	43.7128	+	11.7128i	1.47524	+	0.395288i
$879$	−12.0000	−	12.0000i	−0.404750	−	0.404750i
$880$		0			0
$881$		−	30.0000i		−	1.01073i	−0.862907	−	0.505363i	$-0.831359\pi$
$881$		−	30.0000i		−	1.01073i	0.862907	−	0.505363i	$-0.168641\pi$
$882$	45.0788	+	12.0788i	1.51788	+	0.406716i
$883$	15.5885	−	15.5885i	0.524593	−	0.524593i	−0.394362	−	0.918955i	$-0.629034\pi$
$883$	15.5885	−	15.5885i	0.524593	−	0.524593i	0.918955	+	0.394362i	$0.129034\pi$
$884$	48.0000	+	27.7128i	1.61441	+	0.932083i
$885$		0			0
$886$	−15.0000	+	8.66025i	−0.503935	+	0.290947i
$887$	−17.0000	−	17.0000i	−0.570804	−	0.570804i	0.361549	−	0.932353i	$-0.382248\pi$
$887$	−17.0000	−	17.0000i	−0.570804	−	0.570804i	−0.932353	+	0.361549i	$0.882248\pi$
$888$		0			0
$889$			18.0000i			0.603701i
$890$		0			0
$891$	−31.1769			−1.04447
$892$	−2.19615	−	8.19615i	−0.0735326	−	0.274427i
$893$	−17.3205	−	17.3205i	−0.579609	−	0.579609i
$894$	−32.7846	−	8.78461i	−1.09648	−	0.293801i
$895$		0			0
$896$	−41.5692	+	24.0000i	−1.38873	+	0.801784i
$897$			12.0000i			0.400668i
$898$	6.58846	−	24.5885i	0.219860	−	0.820527i
$899$		−	13.8564i		−	0.462137i
$900$		0			0
$901$			27.7128i			0.923248i
$902$	28.3923	+	7.60770i	0.945360	+	0.253309i
$903$			18.0000i			0.599002i
$904$		−	8.00000i		−	0.266076i
$905$		0			0
$906$	12.6795	−	47.3205i	0.421248	−	1.57212i
$907$	19.0526	+	19.0526i	0.632630	+	0.632630i	0.948727	−	0.316097i	$-0.102373\pi$
$907$	19.0526	+	19.0526i	0.632630	+	0.632630i	−0.316097	+	0.948727i	$0.602373\pi$
$908$	52.0526	−	13.9474i	1.72742	−	0.462862i
$909$	10.3923			0.344691
$910$		0			0
$911$		−	12.0000i		−	0.397578i	−0.980042	−	0.198789i	$-0.936299\pi$
$911$		−	12.0000i		−	0.397578i	0.980042	−	0.198789i	$-0.0637008\pi$
$912$	−12.0000	−	20.7846i	−0.397360	−	0.688247i
$913$	6.00000	+	6.00000i	0.198571	+	0.198571i
$914$	12.0000	+	20.7846i	0.396925	+	0.687494i
$915$		0			0
$916$	−24.0000	−	13.8564i	−0.792982	−	0.457829i
$917$	−51.9615	+	51.9615i	−1.71592	+	1.71592i
$918$	−36.0000	+	20.7846i	−1.18818	+	0.685994i
$919$			40.0000i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$919$			40.0000i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$920$		0			0
$921$	3.00000	+	3.00000i	0.0988534	+	0.0988534i
$922$	−11.4115	+	42.5885i	−0.375819	+	1.40258i
$923$	41.5692	+	41.5692i	1.36827	+	1.36827i
$924$	−49.1769	+	13.1769i	−1.61780	+	0.433489i
$925$		0			0
$926$	15.5885	−	9.00000i	0.512268	−	0.295758i
$927$	−9.00000	−	9.00000i	−0.295599	−	0.295599i
$928$	−5.07180	−	18.9282i	−0.166490	−	0.621349i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$			38.1051i			1.24884i
$932$	10.9282	−	2.92820i	0.357965	−	0.0959165i
$933$		0			0
$934$	8.66025	+	15.0000i	0.283372	+	0.490815i
$935$		0			0
$936$			41.5692i			1.35873i
$937$	18.0000	−	18.0000i	0.588034	−	0.588034i	−0.349064	−	0.937099i	$-0.613501\pi$
$937$	18.0000	−	18.0000i	0.588034	−	0.588034i	0.937099	+	0.349064i	$0.113501\pi$
$938$	11.4115	−	42.5885i	0.372600	−	1.39056i
$939$	−20.7846	−	20.7846i	−0.678280	−	0.678280i
$940$		0			0
$941$	−17.3205			−0.564632			−0.282316	−	0.959321i	$-0.591103\pi$
$941$	−17.3205			−0.564632			−0.282316	+	0.959321i	$0.591103\pi$
$942$	−20.7846	+	12.0000i	−0.677199	+	0.390981i
$943$	6.00000	+	6.00000i	0.195387	+	0.195387i
$944$	36.0000	−	20.7846i	1.17170	−	0.676481i
$945$		0			0
$946$	−6.00000	−	10.3923i	−0.195077	−	0.337883i
$947$	8.66025	−	8.66025i	0.281420	−	0.281420i	−0.552255	−	0.833675i	$-0.686232\pi$
$947$	8.66025	−	8.66025i	0.281420	−	0.281420i	0.833675	+	0.552255i	$0.186232\pi$
$948$	13.8564	−	24.0000i	0.450035	−	0.779484i
$949$	41.5692			1.34939
$950$		0			0
$951$	42.0000	−	42.0000i	1.36194	−	1.36194i
$952$	−48.0000	+	48.0000i	−1.55569	+	1.55569i
$953$	10.0000	−	10.0000i	0.323932	−	0.323932i	−0.526341	−	0.850273i	$-0.676437\pi$
$953$	10.0000	−	10.0000i	0.323932	−	0.323932i	0.850273	+	0.526341i	$0.176437\pi$
$954$	−18.0000	+	10.3923i	−0.582772	+	0.336463i
$955$		0			0
$956$	−41.5692	−	24.0000i	−1.34444	−	0.776215i
$957$		−	20.7846i		−	0.671871i
$958$	−13.1769	+	49.1769i	−0.425727	+	1.58883i
$959$	−60.0000			−1.93750
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−15.5885	+	15.5885i	−0.502331	+	0.502331i
$964$	13.8564	+	8.00000i	0.446285	+	0.257663i
$965$		0			0
$966$	−14.1962	−	3.80385i	−0.456754	−	0.122387i
$967$	−39.0000	+	39.0000i	−1.25416	+	1.25416i	−0.300316	+	0.953840i	$0.597092\pi$
$967$	−39.0000	+	39.0000i	−1.25416	+	1.25416i	−0.953840	+	0.300316i	$0.902908\pi$
$968$	2.00000	−	2.00000i	0.0642824	−	0.0642824i
$969$	−24.0000	−	24.0000i	−0.770991	−	0.770991i
$970$		0			0
$971$	24.2487			0.778178			0.389089	−	0.921200i	$-0.372790\pi$
$971$	24.2487			0.778178			0.389089	+	0.921200i	$0.372790\pi$
$972$	−27.0000	−	15.5885i	−0.866025	−	0.500000i
$973$	−31.1769	+	31.1769i	−0.999486	+	0.999486i
$974$	−15.0000	−	25.9808i	−0.480631	−	0.832477i
$975$		0			0
$976$	12.0000	−	6.92820i	0.384111	−	0.221766i
$977$	−16.0000	−	16.0000i	−0.511885	−	0.511885i	0.403218	−	0.915104i	$-0.367891\pi$
$977$	−16.0000	−	16.0000i	−0.511885	−	0.511885i	−0.915104	+	0.403218i	$0.867891\pi$
$978$	−15.0000	−	25.9808i	−0.479647	−	0.830773i
$979$	−41.5692			−1.32856
$980$		0			0
$981$	51.9615			1.65900
$982$	−3.80385	+	14.1962i	−0.121386	+	0.453017i
$983$	11.0000	−	11.0000i	0.350846	−	0.350846i	−0.509579	−	0.860424i	$-0.670199\pi$
$983$	11.0000	−	11.0000i	0.350846	−	0.350846i	0.860424	+	0.509579i	$0.170199\pi$
$984$	20.7846	+	20.7846i	0.662589	+	0.662589i
$985$		0			0
$986$	−13.8564	−	24.0000i	−0.441278	−	0.764316i
$987$	−51.9615			−1.65395
$988$	−32.7846	+	8.78461i	−1.04302	+	0.279476i
$989$		−	3.46410i		−	0.110152i
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	21.8564	−	5.85641i	0.693942	−	0.185941i
$993$			18.0000i			0.571213i
$994$	−62.3538	+	36.0000i	−1.97774	+	1.14185i
$995$		0			0
$996$	2.19615	+	8.19615i	0.0695878	+	0.259705i
$997$	3.46410	+	3.46410i	0.109709	+	0.109709i	0.759830	−	0.650121i	$-0.225282\pi$
$997$	3.46410	+	3.46410i	0.109709	+	0.109709i	−0.650121	+	0.759830i	$0.725282\pi$
$998$	−8.87564	+	33.1244i	−0.280954	+	1.04853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.e.293.1	yes	4
3.2	odd	2		600.2.w.c.293.2	yes	4
5.2	odd	4		600.2.w.c.557.1	yes	4
5.3	odd	4		600.2.w.f.557.2	yes	4
5.4	even	2		600.2.w.d.293.2	yes	4
8.5	even	2	inner	600.2.w.e.293.2	yes	4
15.2	even	4	inner	600.2.w.e.557.2	yes	4
15.8	even	4		600.2.w.d.557.1	yes	4
15.14	odd	2		600.2.w.f.293.1	yes	4
24.5	odd	2		600.2.w.c.293.1	✓	4
40.13	odd	4		600.2.w.f.557.1	yes	4
40.29	even	2		600.2.w.d.293.1	yes	4
40.37	odd	4		600.2.w.c.557.2	yes	4
120.29	odd	2		600.2.w.f.293.2	yes	4
120.53	even	4		600.2.w.d.557.2	yes	4
120.77	even	4	inner	600.2.w.e.557.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.w.c.293.1	✓	4	24.5	odd	2
600.2.w.c.293.2	yes	4	3.2	odd	2
600.2.w.c.557.1	yes	4	5.2	odd	4
600.2.w.c.557.2	yes	4	40.37	odd	4
600.2.w.d.293.1	yes	4	40.29	even	2
600.2.w.d.293.2	yes	4	5.4	even	2
600.2.w.d.557.1	yes	4	15.8	even	4
600.2.w.d.557.2	yes	4	120.53	even	4
600.2.w.e.293.1	yes	4	1.1	even	1	trivial
600.2.w.e.293.2	yes	4	8.5	even	2	inner
600.2.w.e.557.1	yes	4	120.77	even	4	inner
600.2.w.e.557.2	yes	4	15.2	even	4	inner
600.2.w.f.293.1	yes	4	15.14	odd	2
600.2.w.f.293.2	yes	4	120.29	odd	2
600.2.w.f.557.1	yes	4	40.13	odd	4
600.2.w.f.557.2	yes	4	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -3.46410 q^{11} +(-3.00000 - 1.73205i) q^{12} +(-3.46410 + 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(4.00000 + 4.00000i) q^{17} +(-1.09808 + 4.09808i) q^{18} -3.46410 q^{19} +(-5.19615 + 5.19615i) q^{21} +(1.26795 - 4.73205i) q^{22} +(1.00000 - 1.00000i) q^{23} +(3.46410 - 3.46410i) q^{24} +(-3.46410 - 6.00000i) q^{26} +5.19615 q^{27} +(8.19615 - 2.19615i) q^{28} +3.46410i q^{29} -4.00000 q^{31} +(-5.46410 + 1.46410i) q^{32} -6.00000 q^{33} +(-6.92820 + 4.00000i) q^{34} +(-5.19615 - 3.00000i) q^{36} +(1.26795 - 4.73205i) q^{38} +(-6.00000 + 6.00000i) q^{39} +6.00000i q^{41} +(-5.19615 - 9.00000i) q^{42} +(1.73205 - 1.73205i) q^{43} +(6.00000 + 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{46} +(5.00000 + 5.00000i) q^{47} +(3.46410 + 6.00000i) q^{48} -11.0000i q^{49} +(6.92820 + 6.92820i) q^{51} +(9.46410 - 2.53590i) q^{52} +(3.46410 + 3.46410i) q^{53} +(-1.90192 + 7.09808i) q^{54} +12.0000i q^{56} -6.00000 q^{57} +(-4.73205 - 1.26795i) q^{58} -10.3923i q^{59} -3.46410i q^{61} +(1.46410 - 5.46410i) q^{62} +(-9.00000 + 9.00000i) q^{63} -8.00000i q^{64} +(2.19615 - 8.19615i) q^{66} +(5.19615 + 5.19615i) q^{67} +(-2.92820 - 10.9282i) q^{68} +(1.73205 - 1.73205i) q^{69} -12.0000i q^{71} +(6.00000 - 6.00000i) q^{72} +(-6.00000 - 6.00000i) q^{73} +(6.00000 + 3.46410i) q^{76} +(10.3923 - 10.3923i) q^{77} +(-6.00000 - 10.3923i) q^{78} +8.00000i q^{79} +9.00000 q^{81} +(-8.19615 - 2.19615i) q^{82} +(-1.73205 - 1.73205i) q^{83} +(14.1962 - 3.80385i) q^{84} +(1.73205 + 3.00000i) q^{86} +6.00000i q^{87} +(-6.92820 + 6.92820i) q^{88} +12.0000 q^{89} -20.7846i q^{91} +(-2.73205 + 0.732051i) q^{92} -6.92820 q^{93} +(-8.66025 + 5.00000i) q^{94} +(-9.46410 + 2.53590i) q^{96} +(-6.00000 + 6.00000i) q^{97} +(15.0263 + 4.02628i) q^{98} -10.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{6} - 12 q^{7} + 8 q^{8} + 12 q^{9} - 12 q^{12} - 12 q^{14} + 8 q^{16} + 16 q^{17} + 6 q^{18} + 12 q^{22} + 4 q^{23} + 12 q^{28} - 16 q^{31} - 8 q^{32} - 24 q^{33} + 12 q^{38} - 24 q^{39}+ \cdots + 22 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^6 - 12 * q^7 + 8 * q^8 + 12 * q^9 - 12 * q^12 - 12 * q^14 + 8 * q^16 + 16 * q^17 + 6 * q^18 + 12 * q^22 + 4 * q^23 + 12 * q^28 - 16 * q^31 - 8 * q^32 - 24 * q^33 + 12 * q^38 - 24 * q^39 + 24 * q^44 + 4 * q^46 + 20 * q^47 + 24 * q^52 - 18 * q^54 - 24 * q^57 - 12 * q^58 - 8 * q^62 - 36 * q^63 - 12 * q^66 + 16 * q^68 + 24 * q^72 - 24 * q^73 + 24 * q^76 - 24 * q^78 + 36 * q^81 - 12 * q^82 + 36 * q^84 + 48 * q^89 - 4 * q^92 - 24 * q^96 - 24 * q^97 + 22 * q^98

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