LMFDB - Embedded newform 600.2.w.c.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)

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);

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")

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:	$1$
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:	$\Z[a_1, \ldots, a_{7}]$
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.c.557.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	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	$0.674901\pi$
$12$	1.73205	+	3.00000i	0.500000	+	0.866025i
$13$	3.46410	−	3.46410i	0.960769	−	0.960769i	−0.0384901	−	0.999259i	$-0.512255\pi$
$13$	3.46410	−	3.46410i	0.960769	−	0.960769i	0.999259	+	0.0384901i	$0.0122548\pi$
$14$	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	0.0294245	−	0.999567i	$-0.490633\pi$
$17$	−4.00000	−	4.00000i	−0.970143	−	0.970143i	−0.999567	+	0.0294245i	$0.990633\pi$
$18$	4.09808	−	1.09808i	0.965926	−	0.258819i
$19$	3.46410			0.794719			0.397360	−	0.917663i	$-0.369927\pi$
$19$	3.46410			0.794719			0.397360	+	0.917663i	$0.369927\pi$
$20$		0			0
$21$	−5.19615	−	5.19615i	−1.13389	−	1.13389i
$22$	4.73205	−	1.26795i	1.00888	−	0.270328i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	−3.46410	−	3.46410i	−0.707107	−	0.707107i
$25$		0			0
$26$	−3.46410	+	6.00000i	−0.679366	+	1.17670i
$27$		−	5.19615i		−	1.00000i
$28$	−2.19615	+	8.19615i	−0.415034	+	1.54893i
$29$			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	$0.616954\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		−	6.00000i		−	1.04447i
$34$	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	$0.750000\pi$
$38$	−4.73205	+	1.26795i	−0.767640	+	0.205689i
$39$	6.00000	+	6.00000i	0.960769	+	0.960769i
$40$		0			0
$41$		−	6.00000i		−	0.937043i	−0.883452	−	0.468521i	$-0.844787\pi$
$41$		−	6.00000i		−	0.937043i	0.883452	−	0.468521i	$-0.155213\pi$
$42$	9.00000	+	5.19615i	1.38873	+	0.801784i
$43$	−1.73205	+	1.73205i	−0.264135	+	0.264135i	−0.826732	−	0.562596i	$-0.809803\pi$
$43$	−1.73205	+	1.73205i	−0.264135	+	0.264135i	0.562596	+	0.826732i	$0.309803\pi$
$44$	−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	0.241160	−	0.970485i	$-0.422472\pi$
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	−0.970485	+	0.241160i	$0.922472\pi$
$48$	6.00000	+	3.46410i	0.866025	+	0.500000i
$49$		−	11.0000i		−	1.57143i
$50$		0			0
$51$	6.92820	−	6.92820i	0.970143	−	0.970143i
$52$	2.53590	−	9.46410i	0.351666	−	1.31243i
$53$	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
$57$			6.00000i			0.794719i
$58$	−1.26795	−	4.73205i	−0.166490	−	0.621349i
$59$		−	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	$0.0711822\pi$
$61$			3.46410i			0.443533i	−0.975100	+	0.221766i	$0.928818\pi$
$62$	5.46410	−	1.46410i	0.693942	−	0.185941i
$63$	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	0.314460	−	0.949271i	$-0.398177\pi$
$67$	−5.19615	−	5.19615i	−0.634811	−	0.634811i	−0.949271	+	0.314460i	$0.898177\pi$
$68$	−10.9282	−	2.92820i	−1.32524	−	0.355097i
$69$	−1.73205	−	1.73205i	−0.208514	−	0.208514i
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	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
$78$	−10.3923	−	6.00000i	−1.17670	−	0.679366i
$79$			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
$82$	2.19615	+	8.19615i	0.242524	+	0.905114i
$83$	−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
$87$	−6.00000			−0.643268
$88$	6.92820	−	6.92820i	0.738549	−	0.738549i
$89$	−12.0000			−1.27200			−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000			−1.27200			−0.635999	+	0.771690i	$0.719412\pi$
$90$		0			0
$91$			20.7846i			2.17882i
$92$	−0.732051	+	2.73205i	−0.0763216	+	0.284836i
$93$		−	6.92820i		−	0.718421i
$94$	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	$0.391760\pi$
$98$	4.02628	+	15.0263i	0.406716	+	1.51788i
$99$	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	$0.444865\pi$
$102$	−6.92820	+	12.0000i	−0.685994	+	1.18818i
$103$	−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	$0.365588\pi$
$108$	−5.19615	−	9.00000i	−0.500000	−	0.866025i
$109$	−17.3205			−1.65900			−0.829502	−	0.558504i	$-0.811376\pi$
$109$	−17.3205			−1.65900			−0.829502	+	0.558504i	$0.811376\pi$
$110$		0			0
$111$		0			0
$112$	4.39230	+	16.3923i	0.415034	+	1.54893i
$113$	−2.00000	+	2.00000i	−0.188144	+	0.188144i	−0.794893	−	0.606749i	$-0.792473\pi$
$113$	−2.00000	+	2.00000i	−0.188144	+	0.188144i	0.606749	+	0.794893i	$0.292473\pi$
$114$	−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
$118$	3.80385	+	14.1962i	0.350173	+	1.30686i
$119$	24.0000			2.20008
$120$		0			0
$121$	1.00000			0.0909091
$122$	−1.26795	−	4.73205i	−0.114795	−	0.428420i
$123$	10.3923			0.937043
$124$	−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	$0.189723\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	−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	$0.226835\pi$
$132$	−6.00000	−	10.3923i	−0.522233	−	0.904534i
$133$	−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	0.136309	−	0.990666i	$-0.456476\pi$
$137$	−10.0000	−	10.0000i	−0.854358	−	0.854358i	−0.990666	+	0.136309i	$0.956476\pi$
$138$	3.00000	+	1.73205i	0.255377	+	0.147442i
$139$	−10.3923			−0.881464			−0.440732	−	0.897639i	$-0.645281\pi$
$139$	−10.3923			−0.881464			−0.440732	+	0.897639i	$0.645281\pi$
$140$		0			0
$141$	8.66025	−	8.66025i	0.729325	−	0.729325i
$142$	−4.39230	−	16.3923i	−0.368594	−	1.37561i
$143$	−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
$147$	19.0526			1.57143
$148$		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	0.374355	−	0.927286i	$-0.377864\pi$
$157$	−6.92820	−	6.92820i	−0.552931	−	0.552931i	−0.927286	+	0.374355i	$0.877864\pi$
$158$	−2.92820	−	10.9282i	−0.232955	−	0.869401i
$159$	−6.00000	+	6.00000i	−0.475831	+	0.475831i
$160$		0			0
$161$		−	6.00000i		−	0.472866i
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$	8.66025	−	8.66025i	0.678323	−	0.678323i	−0.281297	−	0.959621i	$-0.590765\pi$
$163$	8.66025	−	8.66025i	0.678323	−	0.678323i	0.959621	+	0.281297i	$0.0907647\pi$
$164$	−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	$0.00190609\pi$
$167$	13.0000	+	13.0000i	1.00597	+	1.00597i	0.00598813	+	0.999982i	$0.498094\pi$
$168$	20.7846			1.60357
$169$		−	11.0000i		−	0.846154i
$170$		0			0
$171$	−10.3923			−0.794719
$172$	−1.26795	+	4.73205i	−0.0966802	+	0.360815i
$173$	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
$177$	18.0000			1.35296
$178$	16.3923	−	4.39230i	1.22866	−	0.329217i
$179$			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	$0.172197\pi$
$181$			13.8564i			1.02994i	−0.857209	+	0.514969i	$0.827803\pi$
$182$	−7.60770	−	28.3923i	−0.563920	−	2.10458i
$183$	−6.00000			−0.443533
$184$		−	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
$188$	−13.6603	−	3.66025i	−0.996276	−	0.266951i
$189$	15.5885	+	15.5885i	1.13389	+	1.13389i
$190$		0			0
$191$		−	12.0000i		−	0.868290i	−0.900843	−	0.434145i	$-0.857051\pi$
$191$		−	12.0000i		−	0.868290i	0.900843	−	0.434145i	$-0.142949\pi$
$192$	13.8564			1.00000
$193$	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	$0.305837\pi$
$198$	−14.1962	+	3.80385i	−1.00888	+	0.270328i
$199$			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
$202$	−4.73205	+	1.26795i	−0.332946	+	0.0892126i
$203$	−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
$208$	−5.07180	−	18.9282i	−0.351666	−	1.31243i
$209$	−12.0000			−0.830057
$210$		0			0
$211$		−	3.46410i		−	0.238479i	−0.992866	−	0.119239i	$-0.961954\pi$
$211$		−	3.46410i		−	0.238479i	0.992866	−	0.119239i	$-0.0380456\pi$
$212$	9.46410	+	2.53590i	0.649997	+	0.174166i
$213$	−20.7846			−1.42414
$214$	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
$218$	23.6603	−	6.33975i	1.60247	−	0.429382i
$219$	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	$0.897759\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	−13.8564			−0.915657			−0.457829	−	0.889041i	$-0.651373\pi$
$229$	−13.8564			−0.915657			−0.457829	+	0.889041i	$0.651373\pi$
$230$		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	−0.563837	−	0.825886i	$-0.690675\pi$
$233$	4.00000	−	4.00000i	0.262049	−	0.262049i	0.825886	+	0.563837i	$0.190675\pi$
$234$	10.3923	−	18.0000i	0.679366	−	1.17670i
$235$		0			0
$236$	−10.3923	−	18.0000i	−0.676481	−	1.17170i
$237$	−13.8564			−0.900070
$238$	−32.7846	+	8.78461i	−2.12511	+	0.569422i
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−8.00000			−0.515325			−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000			−0.515325			−0.257663	+	0.966235i	$0.582952\pi$
$242$	−1.36603	+	0.366025i	−0.0878114	+	0.0235290i
$243$			15.5885i			1.00000i
$244$	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	$0.534869\pi$
$252$	6.58846	−	24.5885i	0.415034	−	1.54893i
$253$	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	0.946497	−	0.322714i	$-0.104595\pi$
$257$	10.0000	+	10.0000i	0.623783	+	0.623783i	−0.322714	+	0.946497i	$0.604595\pi$
$258$	5.19615	+	3.00000i	0.323498	+	0.186772i
$259$		0			0
$260$		0			0
$261$		−	10.3923i		−	0.643268i
$262$	−23.6603	+	6.33975i	−1.46174	+	0.391671i
$263$	7.00000	−	7.00000i	0.431638	−	0.431638i	−0.457547	−	0.889185i	$-0.651272\pi$
$263$	7.00000	−	7.00000i	0.431638	−	0.431638i	0.889185	+	0.457547i	$0.151272\pi$
$264$	12.0000	+	12.0000i	0.738549	+	0.738549i
$265$		0			0
$266$	10.3923	−	18.0000i	0.637193	−	1.10365i
$267$		−	20.7846i		−	1.27200i
$268$	−14.1962	−	3.80385i	−0.867168	−	0.232357i
$269$		−	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	$0.421874\pi$
$272$	−21.8564	+	5.85641i	−1.32524	+	0.355097i
$273$	−36.0000			−2.17882
$274$	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	$0.0945162\pi$
$277$	20.7846	+	20.7846i	1.24883	+	1.24883i	0.292587	+	0.956239i	$0.405484\pi$
$278$	14.1962	−	3.80385i	0.851429	−	0.228140i
$279$	12.0000			0.718421
$280$		0			0
$281$			18.0000i			1.07379i	0.843649	+	0.536895i	$0.180403\pi$
$281$			18.0000i			1.07379i	−0.843649	+	0.536895i	$0.819597\pi$
$282$	−8.66025	+	15.0000i	−0.515711	+	0.893237i
$283$	−5.19615	+	5.19615i	−0.308879	+	0.308879i	−0.844475	−	0.535595i	$-0.820087\pi$
$283$	−5.19615	+	5.19615i	−0.308879	+	0.308879i	0.535595	+	0.844475i	$0.320087\pi$
$284$	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
$288$	4.39230	−	16.3923i	0.258819	−	0.965926i
$289$			15.0000i			0.882353i
$290$		0			0
$291$	−10.3923	−	10.3923i	−0.609208	−	0.609208i
$292$	−16.3923	−	4.39230i	−0.959287	−	0.257040i
$293$	−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
$297$			18.0000i			1.04447i
$298$	−5.07180	−	18.9282i	−0.293801	−	1.09648i
$299$			6.92820i			0.400668i
$300$		0			0
$301$		−	10.3923i		−	0.599002i
$302$	27.3205	−	7.32051i	1.57212	−	0.421248i
$303$			6.00000i			0.344691i
$304$	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	0.655951	−	0.754804i	$-0.272268\pi$
$307$	−1.73205	−	1.73205i	−0.0988534	−	0.0988534i	−0.754804	+	0.655951i	$0.772268\pi$
$308$	7.60770	−	28.3923i	0.433489	−	1.61780i
$309$	5.19615	−	5.19615i	0.295599	−	0.295599i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	−24.0000			−1.35873
$313$	−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	$-0.163188\pi$
$318$	6.00000	−	10.3923i	0.336463	−	0.582772i
$319$		−	12.0000i		−	0.671871i
$320$		0			0
$321$	−9.00000	−	9.00000i	−0.502331	−	0.502331i
$322$	2.19615	+	8.19615i	0.122387	+	0.456754i
$323$	−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
$327$		−	30.0000i		−	1.65900i
$328$	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	$-0.907805\pi$
$331$		−	10.3923i		−	0.571213i	0.958347	−	0.285606i	$-0.0921950\pi$
$332$	−4.73205	−	1.26795i	−0.259705	−	0.0695878i
$333$		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	$0.250000\pi$
$338$	4.02628	+	15.0263i	0.219001	+	0.817322i
$339$	−3.46410	−	3.46410i	−0.188144	−	0.188144i
$340$		0			0
$341$	13.8564			0.750366
$342$	14.1962	−	3.80385i	0.767640	−	0.205689i
$343$	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	$0.451555\pi$
$348$	−10.3923	+	6.00000i	−0.557086	+	0.321634i
$349$	27.7128			1.48343			0.741716	−	0.670714i	$-0.234012\pi$
$349$	27.7128			1.48343			0.741716	+	0.670714i	$0.234012\pi$
$350$		0			0
$351$	−18.0000	−	18.0000i	−0.960769	−	0.960769i
$352$	5.07180	−	18.9282i	0.270328	−	1.00888i
$353$	14.0000	−	14.0000i	0.745145	−	0.745145i	−0.228418	−	0.973563i	$-0.573355\pi$
$353$	14.0000	−	14.0000i	0.745145	−	0.745145i	0.973563	+	0.228418i	$0.0733554\pi$
$354$	−24.5885	+	6.58846i	−1.30686	+	0.350173i
$355$		0			0
$356$	−20.7846	+	12.0000i	−1.10158	+	0.635999i
$357$			41.5692i			2.20008i
$358$	−3.80385	−	14.1962i	−0.201040	−	0.750290i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−7.00000			−0.368421
$362$	−5.07180	−	18.9282i	−0.266568	−	0.994844i
$363$			1.73205i			0.0909091i
$364$	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	$0.357790\pi$
$368$	1.46410	+	5.46410i	0.0763216	+	0.284836i
$369$			18.0000i			0.937043i
$370$		0			0
$371$	−20.7846			−1.07908
$372$	−6.92820	−	12.0000i	−0.359211	−	0.622171i
$373$	6.92820	−	6.92820i	0.358729	−	0.358729i	−0.504615	−	0.863344i	$-0.668366\pi$
$373$	6.92820	−	6.92820i	0.358729	−	0.358729i	0.863344	+	0.504615i	$0.168366\pi$
$374$	−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
$378$	−27.0000	−	15.5885i	−1.38873	−	0.801784i
$379$	3.46410			0.177939			0.0889695	−	0.996034i	$-0.471643\pi$
$379$	3.46410			0.177939			0.0889695	+	0.996034i	$0.471643\pi$
$380$		0			0
$381$	5.19615	+	5.19615i	0.266207	+	0.266207i
$382$	4.39230	+	16.3923i	0.224730	+	0.838703i
$383$	−1.00000	+	1.00000i	−0.0510976	+	0.0510976i	−0.732194	−	0.681096i	$-0.761504\pi$
$383$	−1.00000	+	1.00000i	−0.0510976	+	0.0510976i	0.681096	+	0.732194i	$0.261504\pi$
$384$	−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
$388$	−4.39230	+	16.3923i	−0.222985	+	0.832193i
$389$		−	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
$393$			30.0000i			1.51330i
$394$	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	0.123103	−	0.992394i	$-0.460716\pi$
$397$	−17.3205	−	17.3205i	−0.869291	−	0.869291i	−0.992394	+	0.123103i	$0.960716\pi$
$398$	−1.46410	−	5.46410i	−0.0733888	−	0.273891i
$399$	−18.0000	−	18.0000i	−0.901127	−	0.901127i
$400$		0			0
$401$			12.0000i			0.599251i	0.954057	+	0.299626i	$0.0968618\pi$
$401$			12.0000i			0.599251i	−0.954057	+	0.299626i	$0.903138\pi$
$402$	−9.00000	+	15.5885i	−0.448879	+	0.777482i
$403$	−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
$408$			27.7128i			1.37199i
$409$			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
$412$	−8.19615	−	2.19615i	−0.403795	−	0.108197i
$413$	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
$417$		−	18.0000i		−	0.881464i
$418$	16.3923	−	4.39230i	0.801774	−	0.214835i
$419$		−	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	$-0.973098\pi$
$421$		−	3.46410i		−	0.168830i	0.996431	−	0.0844150i	$-0.0269021\pi$
$422$	1.26795	+	4.73205i	0.0617228	+	0.230353i
$423$	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
$428$	−3.80385	+	14.1962i	−0.183866	+	0.686197i
$429$	−20.7846	−	20.7846i	−1.00349	−	1.00349i
$430$		0			0
$431$		−	12.0000i		−	0.578020i	−0.957326	−	0.289010i	$-0.906674\pi$
$431$		−	12.0000i		−	0.578020i	0.957326	−	0.289010i	$-0.0933260\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	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
$438$	−10.3923	+	18.0000i	−0.496564	+	0.860073i
$439$		−	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
$442$	37.8564	−	10.1436i	1.80065	−	0.482482i
$443$	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
$447$	−24.0000			−1.13516
$448$	24.0000	+	24.0000i	1.13389	+	1.13389i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$			20.7846i			0.978709i
$452$	−1.46410	+	5.46410i	−0.0688655	+	0.257010i
$453$		−	34.6410i		−	1.62758i
$454$	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	$0.120077\pi$
$458$	18.9282	−	5.07180i	0.884457	−	0.236989i
$459$	−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	$0.241365\pi$
$462$	−31.1769	−	18.0000i	−1.45048	−	0.837436i
$463$	−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	$0.158547\pi$
$468$	−7.60770	+	28.3923i	−0.351666	+	1.31243i
$469$	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
$478$	32.7846	−	8.78461i	1.49953	−	0.401799i
$479$	−36.0000			−1.64488			−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000			−1.64488			−0.822441	+	0.568850i	$0.807388\pi$
$480$		0			0
$481$		0			0
$482$	10.9282	−	2.92820i	0.497766	−	0.133376i
$483$	10.3923			0.472866
$484$	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	$0.424655\pi$
$492$	18.0000	−	10.3923i	0.811503	−	0.468521i
$493$	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
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	−24.2487			−1.08552			−0.542761	−	0.839887i	$-0.682621\pi$
$499$	−24.2487			−1.08552			−0.542761	+	0.839887i	$0.682621\pi$
$500$		0			0
$501$	−22.5167	+	22.5167i	−1.00597	+	1.00597i
$502$	4.73205	−	1.26795i	0.211202	−	0.0565913i
$503$	−5.00000	+	5.00000i	−0.222939	+	0.222939i	−0.809735	−	0.586796i	$-0.800389\pi$
$503$	−5.00000	+	5.00000i	−0.222939	+	0.222939i	0.586796	+	0.809735i	$0.300389\pi$
$504$			36.0000i			1.60357i
$505$		0			0
$506$	−3.46410	+	6.00000i	−0.153998	+	0.266733i
$507$	19.0526			0.846154
$508$	2.19615	−	8.19615i	0.0974385	−	0.363645i
$509$			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
$513$		−	18.0000i		−	0.794719i
$514$	−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	$-0.823792\pi$
$521$		−	24.0000i		−	1.05146i	0.850652	−	0.525730i	$-0.176208\pi$
$522$	3.80385	+	14.1962i	0.166490	+	0.621349i
$523$	−8.66025	+	8.66025i	−0.378686	+	0.378686i	−0.870628	−	0.491942i	$-0.836287\pi$
$523$	−8.66025	+	8.66025i	−0.378686	+	0.378686i	0.491942	+	0.870628i	$0.336287\pi$
$524$	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
$528$	−20.7846	−	12.0000i	−0.904534	−	0.522233i
$529$			21.0000i			0.913043i
$530$		0			0
$531$			31.1769i			1.35296i
$532$	−7.60770	+	28.3923i	−0.329835	+	1.23096i
$533$	−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
$537$	−18.0000			−0.776757
$538$	10.1436	+	37.8564i	0.437321	+	1.63211i
$539$			38.1051i			1.64130i
$540$		0			0
$541$			41.5692i			1.78720i	0.448864	+	0.893600i	$0.351829\pi$
$541$			41.5692i			1.78720i	−0.448864	+	0.893600i	$0.648171\pi$
$542$	−10.9282	+	2.92820i	−0.469407	+	0.125777i
$543$	−24.0000			−1.02994
$544$	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	0.497296	−	0.867581i	$-0.334326\pi$
$547$	−8.66025	−	8.66025i	−0.370286	−	0.370286i	−0.867581	+	0.497296i	$0.834326\pi$
$548$	−27.3205	−	7.32051i	−1.16707	−	0.312717i
$549$		−	10.3923i		−	0.443533i
$550$		0			0
$551$			12.0000i			0.511217i
$552$	6.92820			0.294884
$553$	−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	$0.0360238\pi$
$558$	−16.3923	+	4.39230i	−0.693942	+	0.185941i
$559$			12.0000i			0.507546i
$560$		0			0
$561$	−24.0000	+	24.0000i	−1.01328	+	1.01328i
$562$	−6.58846	−	24.5885i	−0.277917	−	1.03720i
$563$	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	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$		−	45.0333i		−	1.88459i	−0.334790	−	0.942293i	$-0.608665\pi$
$571$		−	45.0333i		−	1.88459i	0.334790	−	0.942293i	$-0.391335\pi$
$572$	−8.78461	+	32.7846i	−0.367303	+	1.37079i
$573$	20.7846			0.868290
$574$	−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	$0.499724\pi$
$578$	−5.49038	−	20.4904i	−0.228370	−	0.852287i
$579$	−31.1769	+	31.1769i	−1.29567	+	1.29567i
$580$		0			0
$581$	10.3923			0.431145
$582$	18.0000	+	10.3923i	0.746124	+	0.430775i
$583$	−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	$0.233902\pi$
$588$	33.0000	−	19.0526i	1.36090	−	0.785714i
$589$	−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	−0.358586	−	0.933497i	$-0.616741\pi$
$593$	14.0000	−	14.0000i	0.574911	−	0.574911i	0.933497	+	0.358586i	$0.116741\pi$
$594$	−6.58846	−	24.5885i	−0.270328	−	1.00888i
$595$		0			0
$596$	13.8564	+	24.0000i	0.567581	+	0.983078i
$597$	−6.92820			−0.283552
$598$	−2.53590	−	9.46410i	−0.103701	−	0.387016i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−8.00000			−0.326327			−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000			−0.326327			−0.163163	+	0.986599i	$0.552170\pi$
$602$	3.80385	+	14.1962i	0.155033	+	0.578592i
$603$	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	$0.222559\pi$
$608$	−5.07180	+	18.9282i	−0.205689	+	0.767640i
$609$	18.0000	−	18.0000i	0.729397	−	0.729397i
$610$		0			0
$611$	−34.6410			−1.40143
$612$	32.7846	+	8.78461i	1.32524	+	0.355097i
$613$	−24.2487	+	24.2487i	−0.979396	+	0.979396i	−0.999792	−	0.0203958i	$-0.993507\pi$
$613$	−24.2487	+	24.2487i	−0.979396	+	0.979396i	0.0203958	+	0.999792i	$0.493507\pi$
$614$	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	0.527492	−	0.849560i	$-0.323132\pi$
$617$	−8.00000	−	8.00000i	−0.322068	−	0.322068i	−0.849560	+	0.527492i	$0.823132\pi$
$618$	−5.19615	+	9.00000i	−0.209020	+	0.362033i
$619$	31.1769			1.25311			0.626553	−	0.779379i	$-0.284465\pi$
$619$	31.1769			1.25311			0.626553	+	0.779379i	$0.284465\pi$
$620$		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
$627$		−	20.7846i		−	0.830057i
$628$	−18.9282	−	5.07180i	−0.755318	−	0.202387i
$629$		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
$633$	6.00000			0.238479
$634$	−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
$638$	4.39230	+	16.3923i	0.173893	+	0.648978i
$639$		−	36.0000i		−	1.42414i
$640$		0			0
$641$		−	6.00000i		−	0.236986i	−0.992955	−	0.118493i	$-0.962194\pi$
$641$		−	6.00000i		−	0.236986i	0.992955	−	0.118493i	$-0.0378063\pi$
$642$	15.5885	+	9.00000i	0.615227	+	0.355202i
$643$	19.0526	−	19.0526i	0.751360	−	0.751360i	−0.223373	−	0.974733i	$-0.571707\pi$
$643$	19.0526	−	19.0526i	0.751360	−	0.751360i	0.974733	+	0.223373i	$0.0717069\pi$
$644$	−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	0.0170040	−	0.999855i	$-0.494587\pi$
$647$	−25.0000	−	25.0000i	−0.982851	−	0.982851i	−0.999855	+	0.0170040i	$0.994587\pi$
$648$	−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
$652$	6.33975	−	23.6603i	0.248284	−	0.926607i
$653$	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
$658$	−40.9808	+	10.9808i	−1.59760	+	0.428075i
$659$			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	$-0.792645\pi$
$661$		−	31.1769i		−	1.21264i	0.795220	−	0.606321i	$-0.207355\pi$
$662$	3.80385	+	14.1962i	0.147841	+	0.551749i
$663$		−	48.0000i		−	1.86417i
$664$	6.92820			0.268866
$665$		0			0
$666$		0			0
$667$	−3.46410	−	3.46410i	−0.134131	−	0.134131i
$668$	35.5167	+	9.51666i	1.37418	+	0.368211i
$669$	−5.19615	+	5.19615i	−0.200895	+	0.200895i
$670$		0			0
$671$		−	12.0000i		−	0.463255i
$672$	36.0000	−	20.7846i	1.38873	−	0.801784i
$673$	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	$0.341139\pi$
$678$	6.00000	+	3.46410i	0.230429	+	0.133038i
$679$		−	36.0000i		−	1.38155i
$680$		0			0
$681$	−33.0000	−	33.0000i	−1.26456	−	1.26456i
$682$	−18.9282	+	5.07180i	−0.724798	+	0.194209i
$683$	−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
$687$		−	24.0000i		−	0.915657i
$688$	2.53590	+	9.46410i	0.0966802	+	0.360815i
$689$	24.0000			0.914327
$690$		0			0
$691$		−	3.46410i		−	0.131781i	−0.997827	−	0.0658903i	$-0.979011\pi$
$691$		−	3.46410i		−	0.131781i	0.997827	−	0.0658903i	$-0.0209887\pi$
$692$	18.9282	+	5.07180i	0.719542	+	0.192801i
$693$	−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
$698$	−37.8564	+	10.1436i	−1.43289	+	0.383941i
$699$	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	$0.415725\pi$
$702$	31.1769	+	18.0000i	1.17670	+	0.679366i
$703$		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
$708$	31.1769	−	18.0000i	1.17170	−	0.676481i
$709$		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
$717$		−	41.5692i		−	1.55243i
$718$	−16.3923	+	4.39230i	−0.611755	+	0.163919i
$719$	12.0000			0.447524			0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000			0.447524			0.223762	+	0.974644i	$0.428166\pi$
$720$		0			0
$721$	18.0000			0.670355
$722$	9.56218	−	2.56218i	0.355867	−	0.0953544i
$723$		−	13.8564i		−	0.515325i
$724$	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
$732$	−10.3923	+	6.00000i	−0.384111	+	0.221766i
$733$		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
$738$	−6.58846	−	24.5885i	−0.242524	−	0.905114i
$739$	−3.46410			−0.127429			−0.0637145	−	0.997968i	$-0.520295\pi$
$739$	−3.46410			−0.127429			−0.0637145	+	0.997968i	$0.520295\pi$
$740$		0			0
$741$	20.7846	+	20.7846i	0.763542	+	0.763542i
$742$	28.3923	−	7.60770i	1.04231	−	0.279287i
$743$	−25.0000	+	25.0000i	−0.917161	+	0.917161i	−0.996822	−	0.0796610i	$-0.974616\pi$
$743$	−25.0000	+	25.0000i	−0.917161	+	0.917161i	0.0796610	+	0.996822i	$0.474616\pi$
$744$	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
$748$	37.8564	+	10.1436i	1.38417	+	0.370887i
$749$		−	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	$0.301546\pi$
$752$	−27.3205	+	7.32051i	−0.996276	+	0.266951i
$753$		−	6.00000i		−	0.218652i
$754$	−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	$0.00231277\pi$
$757$	27.7128	+	27.7128i	1.00724	+	1.00724i	0.00726571	+	0.999974i	$0.497687\pi$
$758$	−4.73205	+	1.26795i	−0.171876	+	0.0460540i
$759$	6.00000	+	6.00000i	0.217786	+	0.217786i
$760$		0			0
$761$			48.0000i			1.74000i	0.493053	+	0.869999i	$0.335881\pi$
$761$			48.0000i			1.74000i	−0.493053	+	0.869999i	$0.664119\pi$
$762$	−9.00000	−	5.19615i	−0.326036	−	0.188237i
$763$	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
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$		−	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
$772$	49.1769	+	13.1769i	1.76992	+	0.474248i
$773$	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
$778$	5.07180	+	18.9282i	0.181833	+	0.678609i
$779$		−	20.7846i		−	0.744686i
$780$		0			0
$781$		−	41.5692i		−	1.48746i
$782$	−10.9282	+	2.92820i	−0.390792	+	0.104712i
$783$	18.0000			0.643268
$784$	−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	$0.0162064\pi$
$787$	29.4449	+	29.4449i	1.04960	+	1.04960i	0.0508919	+	0.998704i	$0.483794\pi$
$788$	−2.53590	+	9.46410i	−0.0903376	+	0.337145i
$789$	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	$0.0422295\pi$
$798$	31.1769	+	18.0000i	1.10365	+	0.637193i
$799$			40.0000i			1.41510i
$800$		0			0
$801$	36.0000			1.27200
$802$	−4.39230	−	16.3923i	−0.155098	−	0.578832i
$803$	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
$807$	48.0000			1.68968
$808$	−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	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	−28.3923	−	7.60770i	−0.996375	−	0.266978i
$813$			13.8564i			0.485965i
$814$		0			0
$815$		0			0
$816$	−10.1436	−	37.8564i	−0.355097	−	1.32524i
$817$	−6.00000	+	6.00000i	−0.209913	+	0.209913i
$818$	−1.46410	−	5.46410i	−0.0511911	−	0.191048i
$819$		−	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	$0.758340\pi$
$822$	−17.3205	+	30.0000i	−0.604122	+	1.04637i
$823$	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	$0.181695\pi$
$828$	2.19615	−	8.19615i	0.0763216	−	0.284836i
$829$	51.9615			1.80470			0.902349	−	0.431006i	$-0.141841\pi$
$829$	51.9615			1.80470			0.902349	+	0.431006i	$0.141841\pi$
$830$		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
$837$			20.7846i			0.718421i
$838$	8.87564	+	33.1244i	0.306604	+	1.14426i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$	1.26795	+	4.73205i	0.0436964	+	0.163077i
$843$	−31.1769			−1.07379
$844$	−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
$848$	18.9282	−	5.07180i	0.649997	−	0.174166i
$849$	−9.00000	−	9.00000i	−0.308879	−	0.308879i
$850$		0			0
$851$		0			0
$852$	−36.0000	+	20.7846i	−1.23334	+	0.712069i
$853$	−3.46410	+	3.46410i	−0.118609	+	0.118609i	−0.763920	−	0.645311i	$-0.776728\pi$
$853$	−3.46410	+	3.46410i	−0.118609	+	0.118609i	0.645311	+	0.763920i	$0.276728\pi$
$854$	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	0.106202	−	0.994345i	$-0.466131\pi$
$857$	−26.0000	−	26.0000i	−0.888143	−	0.888143i	−0.994345	+	0.106202i	$0.966131\pi$
$858$	36.0000	+	20.7846i	1.22902	+	0.709575i
$859$	−24.2487			−0.827355			−0.413678	−	0.910423i	$-0.635756\pi$
$859$	−24.2487			−0.827355			−0.413678	+	0.910423i	$0.635756\pi$
$860$		0			0
$861$	−31.1769	+	31.1769i	−1.06251	+	1.06251i
$862$	4.39230	+	16.3923i	0.149602	+	0.558324i
$863$	−23.0000	+	23.0000i	−0.782929	+	0.782929i	−0.980324	−	0.197395i	$-0.936752\pi$
$863$	−23.0000	+	23.0000i	−0.782929	+	0.782929i	0.197395	+	0.980324i	$0.436752\pi$
$864$	28.3923	+	7.60770i	0.965926	+	0.258819i
$865$		0			0
$866$	−10.3923	−	6.00000i	−0.353145	−	0.203888i
$867$	−25.9808			−0.882353
$868$	8.78461	−	32.7846i	0.298169	−	1.11278i
$869$		−	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	0.433335	−	0.901233i	$-0.357337\pi$
$877$	−13.8564	−	13.8564i	−0.467898	−	0.467898i	−0.901233	+	0.433335i	$0.857337\pi$
$878$	11.7128	+	43.7128i	0.395288	+	1.47524i
$879$	12.0000	−	12.0000i	0.404750	−	0.404750i
$880$		0			0
$881$			30.0000i			1.01073i	0.862907	+	0.505363i	$0.168641\pi$
$881$			30.0000i			1.01073i	−0.862907	+	0.505363i	$0.831359\pi$
$882$	−12.0788	−	45.0788i	−0.406716	−	1.51788i
$883$	−15.5885	+	15.5885i	−0.524593	+	0.524593i	−0.918955	−	0.394362i	$-0.870966\pi$
$883$	−15.5885	+	15.5885i	−0.524593	+	0.524593i	0.394362	+	0.918955i	$0.370966\pi$
$884$	−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	0.932353	−	0.361549i	$-0.117752\pi$
$887$	17.0000	+	17.0000i	0.570804	+	0.570804i	−0.361549	+	0.932353i	$0.617752\pi$
$888$		0			0
$889$			18.0000i			0.603701i
$890$		0			0
$891$	−31.1769			−1.04447
$892$	8.19615	+	2.19615i	0.274427	+	0.0735326i
$893$	−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
$897$	−12.0000			−0.400668
$898$	−24.5885	+	6.58846i	−0.820527	+	0.219860i
$899$		−	13.8564i		−	0.462137i
$900$		0			0
$901$		−	27.7128i		−	0.923248i
$902$	−7.60770	−	28.3923i	−0.253309	−	0.945360i
$903$	18.0000			0.599002
$904$		−	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	0.316097	−	0.948727i	$-0.397627\pi$
$907$	−19.0526	−	19.0526i	−0.632630	−	0.632630i	−0.948727	+	0.316097i	$0.897627\pi$
$908$	−13.9474	+	52.0526i	−0.462862	+	1.72742i
$909$	−10.3923			−0.344691
$910$		0			0
$911$			12.0000i			0.397578i	0.980042	+	0.198789i	$0.0637008\pi$
$911$			12.0000i			0.397578i	−0.980042	+	0.198789i	$0.936299\pi$
$912$	20.7846	+	12.0000i	0.688247	+	0.397360i
$913$	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
$918$	20.7846	−	36.0000i	0.685994	−	1.18818i
$919$			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
$922$	−42.5885	+	11.4115i	−1.40258	+	0.375819i
$923$	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
$928$	−18.9282	−	5.07180i	−0.621349	−	0.166490i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$		−	38.1051i		−	1.24884i
$932$	2.92820	−	10.9282i	0.0959165	−	0.357965i
$933$		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	$0.113501\pi$
$938$	−42.5885	+	11.4115i	−1.39056	+	0.372600i
$939$	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	$0.591103\pi$
$942$	−12.0000	+	20.7846i	−0.390981	+	0.677199i
$943$	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	$0.186232\pi$
$948$	−24.0000	+	13.8564i	−0.779484	+	0.450035i
$949$	−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	−0.850273	−	0.526341i	$-0.823563\pi$
$953$	−10.0000	+	10.0000i	−0.323932	+	0.323932i	0.526341	+	0.850273i	$0.323563\pi$
$954$	18.0000	+	10.3923i	0.582772	+	0.336463i
$955$		0			0
$956$	−41.5692	+	24.0000i	−1.34444	+	0.776215i
$957$	20.7846			0.671871
$958$	49.1769	−	13.1769i	1.58883	−	0.425727i
$959$	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	$0.372790\pi$
$972$	15.5885	+	27.0000i	0.500000	+	0.866025i
$973$	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	0.915104	−	0.403218i	$-0.132109\pi$
$977$	16.0000	+	16.0000i	0.511885	+	0.511885i	−0.403218	+	0.915104i	$0.632109\pi$
$978$	−25.9808	−	15.0000i	−0.830773	−	0.479647i
$979$	41.5692			1.32856
$980$		0			0
$981$	51.9615			1.65900
$982$	−14.1962	+	3.80385i	−0.453017	+	0.121386i
$983$	−11.0000	+	11.0000i	−0.350846	+	0.350846i	−0.860424	−	0.509579i	$-0.829801\pi$
$983$	−11.0000	+	11.0000i	−0.350846	+	0.350846i	0.509579	+	0.860424i	$0.329801\pi$
$984$	−20.7846	+	20.7846i	−0.662589	+	0.662589i
$985$		0			0
$986$	−13.8564	+	24.0000i	−0.441278	+	0.764316i
$987$			51.9615i			1.65395i
$988$	8.78461	−	32.7846i	0.279476	−	1.04302i
$989$		−	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	$0.397103\pi$
$992$	5.85641	−	21.8564i	0.185941	−	0.693942i
$993$	18.0000			0.571213
$994$	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	0.650121	−	0.759830i	$-0.274718\pi$
$997$	−3.46410	−	3.46410i	−0.109709	−	0.109709i	−0.759830	+	0.650121i	$0.774718\pi$
$998$	33.1244	−	8.87564i	1.04853	−	0.280954i
$999$		0			0

Twists

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more