LMFDB - Embedded newform 546.2.e.c.545.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,2,Mod(545,546)] 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("546.545"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,-3,2,0,-3,5,2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			545.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.545
Dual form			546.2.e.c.545.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} -1.73205i q^{5} +(-1.50000 - 0.866025i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{10} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(2.50000 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{15} +1.00000 q^{16} -3.00000 q^{17} +(1.50000 + 2.59808i) q^{18} -2.00000 q^{19} -1.73205i q^{20} +(-4.50000 - 0.866025i) q^{21} -3.46410i q^{23} +(-1.50000 - 0.866025i) q^{24} +2.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} -5.19615i q^{27} +(2.50000 - 0.866025i) q^{28} -6.92820i q^{29} +(-1.50000 + 2.59808i) q^{30} +8.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +(-1.50000 - 4.33013i) q^{35} +(1.50000 + 2.59808i) q^{36} -1.73205i q^{37} -2.00000 q^{38} +(-1.50000 + 6.06218i) q^{39} -1.73205i q^{40} +(-4.50000 - 0.866025i) q^{42} -11.0000 q^{43} +(4.50000 - 2.59808i) q^{45} -3.46410i q^{46} +12.1244i q^{47} +(-1.50000 - 0.866025i) q^{48} +(5.50000 - 4.33013i) q^{49} +2.00000 q^{50} +(4.50000 + 2.59808i) q^{51} +(-1.00000 - 3.46410i) q^{52} -3.46410i q^{53} -5.19615i q^{54} +(2.50000 - 0.866025i) q^{56} +(3.00000 + 1.73205i) q^{57} -6.92820i q^{58} +10.3923i q^{59} +(-1.50000 + 2.59808i) q^{60} +6.92820i q^{61} +8.00000 q^{62} +(6.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +13.8564i q^{67} -3.00000 q^{68} +(-3.00000 + 5.19615i) q^{69} +(-1.50000 - 4.33013i) q^{70} +9.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +2.00000 q^{73} -1.73205i q^{74} +(-3.00000 - 1.73205i) q^{75} -2.00000 q^{76} +(-1.50000 + 6.06218i) q^{78} +10.0000 q^{79} -1.73205i q^{80} +(-4.50000 + 7.79423i) q^{81} -3.46410i q^{83} +(-4.50000 - 0.866025i) q^{84} +5.19615i q^{85} -11.0000 q^{86} +(-6.00000 + 10.3923i) q^{87} -3.46410i q^{89} +(4.50000 - 2.59808i) q^{90} +(-5.50000 - 7.79423i) q^{91} -3.46410i q^{92} +(-12.0000 - 6.92820i) q^{93} +12.1244i q^{94} +3.46410i q^{95} +(-1.50000 - 0.866025i) q^{96} -8.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} + 5 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{12} - 2 q^{13} + 5 q^{14} - 3 q^{15} + 2 q^{16} - 6 q^{17} + 3 q^{18} - 4 q^{19} - 9 q^{21} - 3 q^{24} + 4 q^{25} - 2 q^{26}+ \cdots + 11 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 + 5 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^12 - 2 * q^13 + 5 * q^14 - 3 * q^15 + 2 * q^16 - 6 * q^17 + 3 * q^18 - 4 * q^19 - 9 * q^21 - 3 * q^24 + 4 * q^25 - 2 * q^26 + 5 * q^28 - 3 * q^30 + 16 * q^31 + 2 * q^32 - 6 * q^34 - 3 * q^35 + 3 * q^36 - 4 * q^38 - 3 * q^39 - 9 * q^42 - 22 * q^43 + 9 * q^45 - 3 * q^48 + 11 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 5 * q^56 + 6 * q^57 - 3 * q^60 + 16 * q^62 + 12 * q^63 + 2 * q^64 - 12 * q^65 - 6 * q^68 - 6 * q^69 - 3 * q^70 + 18 * q^71 + 3 * q^72 + 4 * q^73 - 6 * q^75 - 4 * q^76 - 3 * q^78 + 20 * q^79 - 9 * q^81 - 9 * q^84 - 22 * q^86 - 12 * q^87 + 9 * q^90 - 11 * q^91 - 24 * q^93 - 3 * q^96 - 16 * q^97 + 11 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		−	1.73205i		−	0.547723i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$	−1.50000	+	2.59808i	−0.387298	+	0.670820i
$16$	1.00000			0.250000
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$		−	1.73205i		−	0.387298i
$21$	−4.50000	−	0.866025i	−0.981981	−	0.188982i
$22$		0			0
$23$		−	3.46410i		−	0.722315i	−0.932505	−	0.361158i	$-0.882382\pi$
$23$		−	3.46410i		−	0.722315i	0.932505	−	0.361158i	$-0.117618\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	2.00000			0.400000
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$		−	5.19615i		−	1.00000i
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−3.00000			−0.514496
$35$	−1.50000	−	4.33013i	−0.253546	−	0.731925i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$		−	1.73205i		−	0.284747i	−0.989813	−	0.142374i	$-0.954527\pi$
$37$		−	1.73205i		−	0.284747i	0.989813	−	0.142374i	$-0.0454735\pi$
$38$	−2.00000			−0.324443
$39$	−1.50000	+	6.06218i	−0.240192	+	0.970725i
$40$		−	1.73205i		−	0.273861i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	−4.50000	−	0.866025i	−0.694365	−	0.133631i
$43$	−11.0000			−1.67748			−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000			−1.67748			−0.838742	+	0.544529i	$0.816708\pi$
$44$		0			0
$45$	4.50000	−	2.59808i	0.670820	−	0.387298i
$46$		−	3.46410i		−	0.510754i
$47$			12.1244i			1.76852i	0.466996	+	0.884260i	$0.345336\pi$
$47$			12.1244i			1.76852i	−0.466996	+	0.884260i	$0.654664\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	2.00000			0.282843
$51$	4.50000	+	2.59808i	0.630126	+	0.363803i
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$		−	3.46410i		−	0.475831i	−0.971286	−	0.237915i	$-0.923536\pi$
$53$		−	3.46410i		−	0.475831i	0.971286	−	0.237915i	$-0.0764641\pi$
$54$		−	5.19615i		−	0.707107i
$55$		0			0
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$	3.00000	+	1.73205i	0.397360	+	0.229416i
$58$		−	6.92820i		−	0.909718i
$59$			10.3923i			1.35296i	0.736460	+	0.676481i	$0.236496\pi$
$59$			10.3923i			1.35296i	−0.736460	+	0.676481i	$0.763504\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$			6.92820i			0.887066i	0.896258	+	0.443533i	$0.146275\pi$
$61$			6.92820i			0.887066i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	8.00000			1.01600
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$	1.00000			0.125000
$65$	−6.00000	+	1.73205i	−0.744208	+	0.214834i
$66$		0			0
$67$			13.8564i			1.69283i	0.532524	+	0.846415i	$0.321244\pi$
$67$			13.8564i			1.69283i	−0.532524	+	0.846415i	$0.678756\pi$
$68$	−3.00000			−0.363803
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	−1.50000	−	4.33013i	−0.179284	−	0.517549i
$71$	9.00000			1.06810			0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000			1.06810			0.534052	+	0.845452i	$0.320669\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		−	1.73205i		−	0.201347i
$75$	−3.00000	−	1.73205i	−0.346410	−	0.200000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	−1.50000	+	6.06218i	−0.169842	+	0.686406i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		−	1.73205i		−	0.193649i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$	−4.50000	−	0.866025i	−0.490990	−	0.0944911i
$85$			5.19615i			0.563602i
$86$	−11.0000			−1.18616
$87$	−6.00000	+	10.3923i	−0.643268	+	1.11417i
$88$		0			0
$89$		−	3.46410i		−	0.367194i	−0.983002	−	0.183597i	$-0.941226\pi$
$89$		−	3.46410i		−	0.367194i	0.983002	−	0.183597i	$-0.0587741\pi$
$90$	4.50000	−	2.59808i	0.474342	−	0.273861i
$91$	−5.50000	−	7.79423i	−0.576557	−	0.817057i
$92$		−	3.46410i		−	0.361158i
$93$	−12.0000	−	6.92820i	−1.24434	−	0.718421i
$94$			12.1244i			1.25053i
$95$			3.46410i			0.355409i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	2.00000			0.200000
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$			3.46410i			0.341328i	0.985329	+	0.170664i	$0.0545913\pi$
$103$			3.46410i			0.341328i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	−1.00000	−	3.46410i	−0.0980581	−	0.339683i
$105$	−1.50000	+	7.79423i	−0.146385	+	0.760639i
$106$		−	3.46410i		−	0.336463i
$107$			10.3923i			1.00466i	0.864675	+	0.502331i	$0.167524\pi$
$107$			10.3923i			1.00466i	−0.864675	+	0.502331i	$0.832476\pi$
$108$		−	5.19615i		−	0.500000i
$109$			5.19615i			0.497701i	0.968542	+	0.248851i	$0.0800528\pi$
$109$			5.19615i			0.497701i	−0.968542	+	0.248851i	$0.919947\pi$
$110$		0			0
$111$	−1.50000	+	2.59808i	−0.142374	+	0.246598i
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$		−	6.92820i		−	0.651751i	−0.945413	−	0.325875i	$-0.894341\pi$
$113$		−	6.92820i		−	0.651751i	0.945413	−	0.325875i	$-0.105659\pi$
$114$	3.00000	+	1.73205i	0.280976	+	0.162221i
$115$	−6.00000			−0.559503
$116$		−	6.92820i		−	0.643268i
$117$	7.50000	−	7.79423i	0.693375	−	0.720577i
$118$			10.3923i			0.956689i
$119$	−7.50000	+	2.59808i	−0.687524	+	0.238165i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−11.0000			−1.00000
$122$			6.92820i			0.627250i
$123$		0			0
$124$	8.00000			0.718421
$125$		−	12.1244i		−	1.08444i
$126$	6.00000	+	5.19615i	0.534522	+	0.462910i
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000			0.0883883
$129$	16.5000	+	9.52628i	1.45274	+	0.838742i
$130$	−6.00000	+	1.73205i	−0.526235	+	0.151911i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$		0			0
$133$	−5.00000	+	1.73205i	−0.433555	+	0.150188i
$134$			13.8564i			1.19701i
$135$	−9.00000			−0.774597
$136$	−3.00000			−0.257248
$137$	18.0000			1.53784			0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000			1.53784			0.768922	+	0.639343i	$0.220793\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$			19.0526i			1.61602i	0.589171	+	0.808008i	$0.299454\pi$
$139$			19.0526i			1.61602i	−0.589171	+	0.808008i	$0.700546\pi$
$140$	−1.50000	−	4.33013i	−0.126773	−	0.365963i
$141$	10.5000	−	18.1865i	0.884260	−	1.53158i
$142$	9.00000			0.755263
$143$		0			0
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−12.0000			−0.996546
$146$	2.00000			0.165521
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$		−	1.73205i		−	0.142374i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−3.00000	−	1.73205i	−0.244949	−	0.141421i
$151$			19.0526i			1.55048i	0.631670	+	0.775238i	$0.282370\pi$
$151$			19.0526i			1.55048i	−0.631670	+	0.775238i	$0.717630\pi$
$152$	−2.00000			−0.162221
$153$	−4.50000	−	7.79423i	−0.363803	−	0.630126i
$154$		0			0
$155$		−	13.8564i		−	1.11297i
$156$	−1.50000	+	6.06218i	−0.120096	+	0.485363i
$157$		−	10.3923i		−	0.829396i	−0.909959	−	0.414698i	$-0.863887\pi$
$157$		−	10.3923i		−	0.829396i	0.909959	−	0.414698i	$-0.136113\pi$
$158$	10.0000			0.795557
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		−	1.73205i		−	0.136931i
$161$	−3.00000	−	8.66025i	−0.236433	−	0.682524i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$		−	17.3205i		−	1.35665i	−0.734763	−	0.678323i	$-0.762707\pi$
$163$		−	17.3205i		−	1.35665i	0.734763	−	0.678323i	$-0.237293\pi$
$164$		0			0
$165$		0			0
$166$		−	3.46410i		−	0.268866i
$167$			3.46410i			0.268060i	0.990977	+	0.134030i	$0.0427919\pi$
$167$			3.46410i			0.268060i	−0.990977	+	0.134030i	$0.957208\pi$
$168$	−4.50000	−	0.866025i	−0.347183	−	0.0668153i
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$			5.19615i			0.398527i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−11.0000			−0.838742
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	−6.00000	+	10.3923i	−0.454859	+	0.787839i
$175$	5.00000	−	1.73205i	0.377964	−	0.130931i
$176$		0			0
$177$	9.00000	−	15.5885i	0.676481	−	1.17170i
$178$		−	3.46410i		−	0.259645i
$179$			12.1244i			0.906217i	0.891455	+	0.453108i	$0.149685\pi$
$179$			12.1244i			0.906217i	−0.891455	+	0.453108i	$0.850315\pi$
$180$	4.50000	−	2.59808i	0.335410	−	0.193649i
$181$		−	3.46410i		−	0.257485i	−0.991678	−	0.128742i	$-0.958906\pi$
$181$		−	3.46410i		−	0.257485i	0.991678	−	0.128742i	$-0.0410940\pi$
$182$	−5.50000	−	7.79423i	−0.407687	−	0.577747i
$183$	6.00000	−	10.3923i	0.443533	−	0.768221i
$184$		−	3.46410i		−	0.255377i
$185$	−3.00000			−0.220564
$186$	−12.0000	−	6.92820i	−0.879883	−	0.508001i
$187$		0			0
$188$			12.1244i			0.884260i
$189$	−4.50000	−	12.9904i	−0.327327	−	0.944911i
$190$			3.46410i			0.251312i
$191$		−	20.7846i		−	1.50392i	−0.659208	−	0.751961i	$-0.729108\pi$
$191$		−	20.7846i		−	1.50392i	0.659208	−	0.751961i	$-0.270892\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$			17.3205i			1.24676i	0.781920	+	0.623379i	$0.214240\pi$
$193$			17.3205i			1.24676i	−0.781920	+	0.623379i	$0.785760\pi$
$194$	−8.00000			−0.574367
$195$	10.5000	+	2.59808i	0.751921	+	0.186052i
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		0			0
$199$		−	6.92820i		−	0.491127i	−0.969380	−	0.245564i	$-0.921027\pi$
$199$		−	6.92820i		−	0.491127i	0.969380	−	0.245564i	$-0.0789730\pi$
$200$	2.00000			0.141421
$201$	12.0000	−	20.7846i	0.846415	−	1.46603i
$202$	12.0000			0.844317
$203$	−6.00000	−	17.3205i	−0.421117	−	1.21566i
$204$	4.50000	+	2.59808i	0.315063	+	0.181902i
$205$		0			0
$206$			3.46410i			0.241355i
$207$	9.00000	−	5.19615i	0.625543	−	0.361158i
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$		0			0
$210$	−1.50000	+	7.79423i	−0.103510	+	0.537853i
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		−	3.46410i		−	0.237915i
$213$	−13.5000	−	7.79423i	−0.925005	−	0.534052i
$214$			10.3923i			0.710403i
$215$			19.0526i			1.29937i
$216$		−	5.19615i		−	0.353553i
$217$	20.0000	−	6.92820i	1.35769	−	0.470317i
$218$			5.19615i			0.351928i
$219$	−3.00000	−	1.73205i	−0.202721	−	0.117041i
$220$		0			0
$221$	3.00000	+	10.3923i	0.201802	+	0.699062i
$222$	−1.50000	+	2.59808i	−0.100673	+	0.174371i
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$	3.00000	+	5.19615i	0.200000	+	0.346410i
$226$		−	6.92820i		−	0.460857i
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$	3.00000	+	1.73205i	0.198680	+	0.114708i
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$		−	6.92820i		−	0.454859i
$233$			8.66025i			0.567352i	0.958920	+	0.283676i	$0.0915540\pi$
$233$			8.66025i			0.567352i	−0.958920	+	0.283676i	$0.908446\pi$
$234$	7.50000	−	7.79423i	0.490290	−	0.509525i
$235$	21.0000			1.36989
$236$			10.3923i			0.676481i
$237$	−15.0000	−	8.66025i	−0.974355	−	0.562544i
$238$	−7.50000	+	2.59808i	−0.486153	+	0.168408i
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$	−1.50000	+	2.59808i	−0.0968246	+	0.167705i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	−11.0000			−0.707107
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			6.92820i			0.443533i
$245$	−7.50000	−	9.52628i	−0.479157	−	0.608612i
$246$		0			0
$247$	2.00000	+	6.92820i	0.127257	+	0.440831i
$248$	8.00000			0.508001
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$		−	12.1244i		−	0.766812i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	6.00000	+	5.19615i	0.377964	+	0.327327i
$253$		0			0
$254$	−2.00000			−0.125491
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$	1.00000			0.0625000
$257$	−21.0000			−1.30994			−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000			−1.30994			−0.654972	+	0.755653i	$0.727320\pi$
$258$	16.5000	+	9.52628i	1.02725	+	0.593080i
$259$	−1.50000	−	4.33013i	−0.0932055	−	0.269061i
$260$	−6.00000	+	1.73205i	−0.372104	+	0.107417i
$261$	18.0000	−	10.3923i	1.11417	−	0.643268i
$262$	15.0000			0.926703
$263$			13.8564i			0.854423i	0.904152	+	0.427211i	$0.140504\pi$
$263$			13.8564i			0.854423i	−0.904152	+	0.427211i	$0.859496\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	−5.00000	+	1.73205i	−0.306570	+	0.106199i
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$			13.8564i			0.846415i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	−9.00000			−0.547723
$271$	1.00000			0.0607457			0.0303728	−	0.999539i	$-0.490331\pi$
$271$	1.00000			0.0607457			0.0303728	+	0.999539i	$0.490331\pi$
$272$	−3.00000			−0.181902
$273$	1.50000	+	16.4545i	0.0907841	+	0.995871i
$274$	18.0000			1.08742
$275$		0			0
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$			19.0526i			1.14270i
$279$	12.0000	+	20.7846i	0.718421	+	1.24434i
$280$	−1.50000	−	4.33013i	−0.0896421	−	0.258775i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	10.5000	−	18.1865i	0.625266	−	1.08299i
$283$		−	10.3923i		−	0.617758i	−0.951101	−	0.308879i	$-0.900046\pi$
$283$		−	10.3923i		−	0.617758i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$	9.00000			0.534052
$285$	3.00000	−	5.19615i	0.177705	−	0.307794i
$286$		0			0
$287$		0			0
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	−8.00000			−0.470588
$290$	−12.0000			−0.704664
$291$	12.0000	+	6.92820i	0.703452	+	0.406138i
$292$	2.00000			0.117041
$293$		−	19.0526i		−	1.11306i	−0.830827	−	0.556531i	$-0.812132\pi$
$293$		−	19.0526i		−	1.11306i	0.830827	−	0.556531i	$-0.187868\pi$
$294$	−12.0000	+	1.73205i	−0.699854	+	0.101015i
$295$	18.0000			1.04800
$296$		−	1.73205i		−	0.100673i
$297$		0			0
$298$	6.00000			0.347571
$299$	−12.0000	+	3.46410i	−0.693978	+	0.200334i
$300$	−3.00000	−	1.73205i	−0.173205	−	0.100000i
$301$	−27.5000	+	9.52628i	−1.58507	+	0.549086i
$302$			19.0526i			1.09635i
$303$	−18.0000	−	10.3923i	−1.03407	−	0.597022i
$304$	−2.00000			−0.114708
$305$	12.0000			0.687118
$306$	−4.50000	−	7.79423i	−0.257248	−	0.445566i
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$		0			0
$309$	3.00000	−	5.19615i	0.170664	−	0.295599i
$310$		−	13.8564i		−	0.786991i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	−1.50000	+	6.06218i	−0.0849208	+	0.343203i
$313$			8.66025i			0.489506i	0.969585	+	0.244753i	$0.0787070\pi$
$313$			8.66025i			0.489506i	−0.969585	+	0.244753i	$0.921293\pi$
$314$		−	10.3923i		−	0.586472i
$315$	9.00000	−	10.3923i	0.507093	−	0.585540i
$316$	10.0000			0.562544
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$		0			0
$320$		−	1.73205i		−	0.0968246i
$321$	9.00000	−	15.5885i	0.502331	−	0.870063i
$322$	−3.00000	−	8.66025i	−0.167183	−	0.482617i
$323$	6.00000			0.333849
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−2.00000	−	6.92820i	−0.110940	−	0.384308i
$326$		−	17.3205i		−	0.959294i
$327$	4.50000	−	7.79423i	0.248851	−	0.431022i
$328$		0			0
$329$	10.5000	+	30.3109i	0.578884	+	1.67109i
$330$		0			0
$331$		−	17.3205i		−	0.952021i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$		−	17.3205i		−	0.952021i	0.879440	−	0.476011i	$-0.157918\pi$
$332$		−	3.46410i		−	0.190117i
$333$	4.50000	−	2.59808i	0.246598	−	0.142374i
$334$			3.46410i			0.189547i
$335$	24.0000			1.31126
$336$	−4.50000	−	0.866025i	−0.245495	−	0.0472456i
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$			5.19615i			0.281801i
$341$		0			0
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−11.0000			−0.593080
$345$	9.00000	+	5.19615i	0.484544	+	0.279751i
$346$	6.00000			0.322562
$347$			15.5885i			0.836832i	0.908255	+	0.418416i	$0.137415\pi$
$347$			15.5885i			0.836832i	−0.908255	+	0.418416i	$0.862585\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	−1.00000			−0.0535288			−0.0267644	−	0.999642i	$-0.508520\pi$
$349$	−1.00000			−0.0535288			−0.0267644	+	0.999642i	$0.508520\pi$
$350$	5.00000	−	1.73205i	0.267261	−	0.0925820i
$351$	−18.0000	+	5.19615i	−0.960769	+	0.277350i
$352$		0			0
$353$		−	10.3923i		−	0.553127i	−0.960996	−	0.276563i	$-0.910804\pi$
$353$		−	10.3923i		−	0.553127i	0.960996	−	0.276563i	$-0.0891955\pi$
$354$	9.00000	−	15.5885i	0.478345	−	0.828517i
$355$		−	15.5885i		−	0.827349i
$356$		−	3.46410i		−	0.183597i
$357$	13.5000	+	2.59808i	0.714496	+	0.137505i
$358$			12.1244i			0.640792i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	4.50000	−	2.59808i	0.237171	−	0.136931i
$361$	−15.0000			−0.789474
$362$		−	3.46410i		−	0.182069i
$363$	16.5000	+	9.52628i	0.866025	+	0.500000i
$364$	−5.50000	−	7.79423i	−0.288278	−	0.408529i
$365$		−	3.46410i		−	0.181319i
$366$	6.00000	−	10.3923i	0.313625	−	0.543214i
$367$		−	34.6410i		−	1.80825i	−0.427272	−	0.904123i	$-0.640525\pi$
$367$		−	34.6410i		−	1.80825i	0.427272	−	0.904123i	$-0.359475\pi$
$368$		−	3.46410i		−	0.180579i
$369$		0			0
$370$	−3.00000			−0.155963
$371$	−3.00000	−	8.66025i	−0.155752	−	0.449618i
$372$	−12.0000	−	6.92820i	−0.622171	−	0.359211i
$373$	16.0000			0.828449			0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000			0.828449			0.414224	+	0.910175i	$0.364053\pi$
$374$		0			0
$375$	−10.5000	+	18.1865i	−0.542218	+	0.939149i
$376$			12.1244i			0.625266i
$377$	−24.0000	+	6.92820i	−1.23606	+	0.356821i
$378$	−4.50000	−	12.9904i	−0.231455	−	0.668153i
$379$		−	17.3205i		−	0.889695i	−0.895606	−	0.444847i	$-0.853258\pi$
$379$		−	17.3205i		−	0.889695i	0.895606	−	0.444847i	$-0.146742\pi$
$380$			3.46410i			0.177705i
$381$	3.00000	+	1.73205i	0.153695	+	0.0887357i
$382$		−	20.7846i		−	1.06343i
$383$			5.19615i			0.265511i	0.991149	+	0.132755i	$0.0423825\pi$
$383$			5.19615i			0.265511i	−0.991149	+	0.132755i	$0.957617\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$		0			0
$386$			17.3205i			0.881591i
$387$	−16.5000	−	28.5788i	−0.838742	−	1.45274i
$388$	−8.00000			−0.406138
$389$		−	10.3923i		−	0.526911i	−0.964672	−	0.263455i	$-0.915138\pi$
$389$		−	10.3923i		−	0.526911i	0.964672	−	0.263455i	$-0.0848622\pi$
$390$	10.5000	+	2.59808i	0.531688	+	0.131559i
$391$			10.3923i			0.525561i
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	−22.5000	−	12.9904i	−1.13497	−	0.655278i
$394$	−15.0000			−0.755689
$395$		−	17.3205i		−	0.871489i
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$		−	6.92820i		−	0.347279i
$399$	9.00000	+	1.73205i	0.450564	+	0.0867110i
$400$	2.00000			0.100000
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	12.0000	−	20.7846i	0.598506	−	1.03664i
$403$	−8.00000	−	27.7128i	−0.398508	−	1.38047i
$404$	12.0000			0.597022
$405$	13.5000	+	7.79423i	0.670820	+	0.387298i
$406$	−6.00000	−	17.3205i	−0.297775	−	0.859602i
$407$		0			0
$408$	4.50000	+	2.59808i	0.222783	+	0.128624i
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$		0			0
$411$	−27.0000	−	15.5885i	−1.33181	−	0.768922i
$412$			3.46410i			0.170664i
$413$	9.00000	+	25.9808i	0.442861	+	1.27843i
$414$	9.00000	−	5.19615i	0.442326	−	0.255377i
$415$	−6.00000			−0.294528
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$	16.5000	−	28.5788i	0.808008	−	1.39951i
$418$		0			0
$419$	27.0000			1.31904			0.659518	−	0.751689i	$-0.270760\pi$
$419$	27.0000			1.31904			0.659518	+	0.751689i	$0.270760\pi$
$420$	−1.50000	+	7.79423i	−0.0731925	+	0.380319i
$421$			32.9090i			1.60388i	0.597401	+	0.801942i	$0.296200\pi$
$421$			32.9090i			1.60388i	−0.597401	+	0.801942i	$0.703800\pi$
$422$	−13.0000			−0.632830
$423$	−31.5000	+	18.1865i	−1.53158	+	0.884260i
$424$		−	3.46410i		−	0.168232i
$425$	−6.00000			−0.291043
$426$	−13.5000	−	7.79423i	−0.654077	−	0.377632i
$427$	6.00000	+	17.3205i	0.290360	+	0.838198i
$428$			10.3923i			0.502331i
$429$		0			0
$430$			19.0526i			0.918796i
$431$	−33.0000			−1.58955			−0.794777	−	0.606902i	$-0.792412\pi$
$431$	−33.0000			−1.58955			−0.794777	+	0.606902i	$0.792412\pi$
$432$		−	5.19615i		−	0.250000i
$433$		−	5.19615i		−	0.249711i	−0.992175	−	0.124856i	$-0.960153\pi$
$433$		−	5.19615i		−	0.249711i	0.992175	−	0.124856i	$-0.0398468\pi$
$434$	20.0000	−	6.92820i	0.960031	−	0.332564i
$435$	18.0000	+	10.3923i	0.863034	+	0.498273i
$436$			5.19615i			0.248851i
$437$			6.92820i			0.331421i
$438$	−3.00000	−	1.73205i	−0.143346	−	0.0827606i
$439$			31.1769i			1.48799i	0.668184	+	0.743996i	$0.267072\pi$
$439$			31.1769i			1.48799i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$	19.5000	+	7.79423i	0.928571	+	0.371154i
$442$	3.00000	+	10.3923i	0.142695	+	0.494312i
$443$		−	22.5167i		−	1.06980i	−0.844916	−	0.534899i	$-0.820349\pi$
$443$		−	22.5167i		−	1.06980i	0.844916	−	0.534899i	$-0.179651\pi$
$444$	−1.50000	+	2.59808i	−0.0711868	+	0.123299i
$445$	−6.00000			−0.284427
$446$	7.00000			0.331460
$447$	−9.00000	−	5.19615i	−0.425685	−	0.245770i
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	3.00000	+	5.19615i	0.141421	+	0.244949i
$451$		0			0
$452$		−	6.92820i		−	0.325875i
$453$	16.5000	−	28.5788i	0.775238	−	1.34275i
$454$		0			0
$455$	−13.5000	+	9.52628i	−0.632890	+	0.446599i
$456$	3.00000	+	1.73205i	0.140488	+	0.0811107i
$457$			10.3923i			0.486132i	0.970010	+	0.243066i	$0.0781531\pi$
$457$			10.3923i			0.486132i	−0.970010	+	0.243066i	$0.921847\pi$
$458$	5.00000			0.233635
$459$			15.5885i			0.727607i
$460$	−6.00000			−0.279751
$461$		−	5.19615i		−	0.242009i	−0.992652	−	0.121004i	$-0.961388\pi$
$461$		−	5.19615i		−	0.242009i	0.992652	−	0.121004i	$-0.0386115\pi$
$462$		0			0
$463$		−	24.2487i		−	1.12693i	−0.826139	−	0.563467i	$-0.809467\pi$
$463$		−	24.2487i		−	1.12693i	0.826139	−	0.563467i	$-0.190533\pi$
$464$		−	6.92820i		−	0.321634i
$465$	−12.0000	+	20.7846i	−0.556487	+	0.963863i
$466$			8.66025i			0.401179i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$	7.50000	−	7.79423i	0.346688	−	0.360288i
$469$	12.0000	+	34.6410i	0.554109	+	1.59957i
$470$	21.0000			0.968658
$471$	−9.00000	+	15.5885i	−0.414698	+	0.718278i
$472$			10.3923i			0.478345i
$473$		0			0
$474$	−15.0000	−	8.66025i	−0.688973	−	0.397779i
$475$	−4.00000			−0.183533
$476$	−7.50000	+	2.59808i	−0.343762	+	0.119083i
$477$	9.00000	−	5.19615i	0.412082	−	0.237915i
$478$	−15.0000			−0.686084
$479$			32.9090i			1.50365i	0.659363	+	0.751825i	$0.270826\pi$
$479$			32.9090i			1.50365i	−0.659363	+	0.751825i	$0.729174\pi$
$480$	−1.50000	+	2.59808i	−0.0684653	+	0.118585i
$481$	−6.00000	+	1.73205i	−0.273576	+	0.0789747i
$482$	−10.0000			−0.455488
$483$	−3.00000	+	15.5885i	−0.136505	+	0.709299i
$484$	−11.0000			−0.500000
$485$			13.8564i			0.629187i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$		−	24.2487i		−	1.09881i	−0.835555	−	0.549407i	$-0.814854\pi$
$487$		−	24.2487i		−	1.09881i	0.835555	−	0.549407i	$-0.185146\pi$
$488$			6.92820i			0.313625i
$489$	−15.0000	+	25.9808i	−0.678323	+	1.17489i
$490$	−7.50000	−	9.52628i	−0.338815	−	0.430353i
$491$			36.3731i			1.64149i	0.571292	+	0.820747i	$0.306442\pi$
$491$			36.3731i			1.64149i	−0.571292	+	0.820747i	$0.693558\pi$
$492$		0			0
$493$			20.7846i			0.936092i
$494$	2.00000	+	6.92820i	0.0899843	+	0.311715i
$495$		0			0
$496$	8.00000			0.359211
$497$	22.5000	−	7.79423i	1.00926	−	0.349619i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$			20.7846i			0.930447i	0.885193	+	0.465223i	$0.154026\pi$
$499$			20.7846i			0.930447i	−0.885193	+	0.465223i	$0.845974\pi$
$500$		−	12.1244i		−	0.542218i
$501$	3.00000	−	5.19615i	0.134030	−	0.232147i
$502$	−12.0000			−0.535586
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	6.00000	+	5.19615i	0.267261	+	0.231455i
$505$		−	20.7846i		−	0.924903i
$506$		0			0
$507$	22.5000	−	0.866025i	0.999260	−	0.0384615i
$508$	−2.00000			−0.0887357
$509$			27.7128i			1.22835i	0.789170	+	0.614174i	$0.210511\pi$
$509$			27.7128i			1.22835i	−0.789170	+	0.614174i	$0.789489\pi$
$510$	4.50000	−	7.79423i	0.199263	−	0.345134i
$511$	5.00000	−	1.73205i	0.221187	−	0.0766214i
$512$	1.00000			0.0441942
$513$			10.3923i			0.458831i
$514$	−21.0000			−0.926270
$515$	6.00000			0.264392
$516$	16.5000	+	9.52628i	0.726372	+	0.419371i
$517$		0			0
$518$	−1.50000	−	4.33013i	−0.0659062	−	0.190255i
$519$	−9.00000	−	5.19615i	−0.395056	−	0.228086i
$520$	−6.00000	+	1.73205i	−0.263117	+	0.0759555i
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$	18.0000	−	10.3923i	0.787839	−	0.454859i
$523$			17.3205i			0.757373i	0.925525	+	0.378686i	$0.123624\pi$
$523$			17.3205i			0.757373i	−0.925525	+	0.378686i	$0.876376\pi$
$524$	15.0000			0.655278
$525$	−9.00000	−	1.73205i	−0.392792	−	0.0755929i
$526$			13.8564i			0.604168i
$527$	−24.0000			−1.04546
$528$		0			0
$529$	11.0000			0.478261
$530$	−6.00000			−0.260623
$531$	−27.0000	+	15.5885i	−1.17170	+	0.676481i
$532$	−5.00000	+	1.73205i	−0.216777	+	0.0750939i
$533$		0			0
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	18.0000			0.778208
$536$			13.8564i			0.598506i
$537$	10.5000	−	18.1865i	0.453108	−	0.784807i
$538$		0			0
$539$		0			0
$540$	−9.00000			−0.387298
$541$		−	19.0526i		−	0.819133i	−0.912280	−	0.409567i	$-0.865680\pi$
$541$		−	19.0526i		−	0.819133i	0.912280	−	0.409567i	$-0.134320\pi$
$542$	1.00000			0.0429537
$543$	−3.00000	+	5.19615i	−0.128742	+	0.222988i
$544$	−3.00000			−0.128624
$545$	9.00000			0.385518
$546$	1.50000	+	16.4545i	0.0641941	+	0.704187i
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$	18.0000			0.768922
$549$	−18.0000	+	10.3923i	−0.768221	+	0.443533i
$550$		0			0
$551$			13.8564i			0.590303i
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	25.0000	−	8.66025i	1.06311	−	0.368271i
$554$	−16.0000			−0.679775
$555$	4.50000	+	2.59808i	0.191014	+	0.110282i
$556$			19.0526i			0.808008i
$557$	−33.0000			−1.39825			−0.699127	−	0.714997i	$-0.746428\pi$
$557$	−33.0000			−1.39825			−0.699127	+	0.714997i	$0.746428\pi$
$558$	12.0000	+	20.7846i	0.508001	+	0.879883i
$559$	11.0000	+	38.1051i	0.465250	+	1.61167i
$560$	−1.50000	−	4.33013i	−0.0633866	−	0.182981i
$561$		0			0
$562$	30.0000			1.26547
$563$	21.0000			0.885044			0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000			0.885044			0.442522	+	0.896758i	$0.354084\pi$
$564$	10.5000	−	18.1865i	0.442130	−	0.765791i
$565$	−12.0000			−0.504844
$566$		−	10.3923i		−	0.436821i
$567$	−4.50000	+	23.3827i	−0.188982	+	0.981981i
$568$	9.00000			0.377632
$569$		−	32.9090i		−	1.37962i	−0.723993	−	0.689808i	$-0.757695\pi$
$569$		−	32.9090i		−	1.37962i	0.723993	−	0.689808i	$-0.242305\pi$
$570$	3.00000	−	5.19615i	0.125656	−	0.217643i
$571$	13.0000			0.544033			0.272017	−	0.962293i	$-0.412309\pi$
$571$	13.0000			0.544033			0.272017	+	0.962293i	$0.412309\pi$
$572$		0			0
$573$	−18.0000	+	31.1769i	−0.751961	+	1.30243i
$574$		0			0
$575$		−	6.92820i		−	0.288926i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$	−8.00000			−0.332756
$579$	15.0000	−	25.9808i	0.623379	−	1.07972i
$580$	−12.0000			−0.498273
$581$	−3.00000	−	8.66025i	−0.124461	−	0.359288i
$582$	12.0000	+	6.92820i	0.497416	+	0.287183i
$583$		0			0
$584$	2.00000			0.0827606
$585$	−13.5000	−	12.9904i	−0.558156	−	0.537086i
$586$		−	19.0526i		−	0.787054i
$587$		−	38.1051i		−	1.57277i	−0.617739	−	0.786383i	$-0.711951\pi$
$587$		−	38.1051i		−	1.57277i	0.617739	−	0.786383i	$-0.288049\pi$
$588$	−12.0000	+	1.73205i	−0.494872	+	0.0714286i
$589$	−16.0000			−0.659269
$590$	18.0000			0.741048
$591$	22.5000	+	12.9904i	0.925526	+	0.534353i
$592$		−	1.73205i		−	0.0711868i
$593$			48.4974i			1.99155i	0.0918243	+	0.995775i	$0.470730\pi$
$593$			48.4974i			1.99155i	−0.0918243	+	0.995775i	$0.529270\pi$
$594$		0			0
$595$	4.50000	+	12.9904i	0.184482	+	0.532554i
$596$	6.00000			0.245770
$597$	−6.00000	+	10.3923i	−0.245564	+	0.425329i
$598$	−12.0000	+	3.46410i	−0.490716	+	0.141658i
$599$			24.2487i			0.990775i	0.868672	+	0.495388i	$0.164974\pi$
$599$			24.2487i			0.990775i	−0.868672	+	0.495388i	$0.835026\pi$
$600$	−3.00000	−	1.73205i	−0.122474	−	0.0707107i
$601$			5.19615i			0.211955i	0.994369	+	0.105978i	$0.0337972\pi$
$601$			5.19615i			0.211955i	−0.994369	+	0.105978i	$0.966203\pi$
$602$	−27.5000	+	9.52628i	−1.12082	+	0.388262i
$603$	−36.0000	+	20.7846i	−1.46603	+	0.846415i
$604$			19.0526i			0.775238i
$605$			19.0526i			0.774597i
$606$	−18.0000	−	10.3923i	−0.731200	−	0.422159i
$607$		−	24.2487i		−	0.984225i	−0.870532	−	0.492112i	$-0.836225\pi$
$607$		−	24.2487i		−	0.984225i	0.870532	−	0.492112i	$-0.163775\pi$
$608$	−2.00000			−0.0811107
$609$	−6.00000	+	31.1769i	−0.243132	+	1.26335i
$610$	12.0000			0.485866
$611$	42.0000	−	12.1244i	1.69914	−	0.490499i
$612$	−4.50000	−	7.79423i	−0.181902	−	0.315063i
$613$		−	6.92820i		−	0.279827i	−0.990164	−	0.139914i	$-0.955317\pi$
$613$		−	6.92820i		−	0.279827i	0.990164	−	0.139914i	$-0.0446825\pi$
$614$	14.0000			0.564994
$615$		0			0
$616$		0			0
$617$	−36.0000			−1.44931			−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000			−1.44931			−0.724653	+	0.689114i	$0.758000\pi$
$618$	3.00000	−	5.19615i	0.120678	−	0.209020i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		−	13.8564i		−	0.556487i
$621$	−18.0000			−0.722315
$622$	−30.0000			−1.20289
$623$	−3.00000	−	8.66025i	−0.120192	−	0.346966i
$624$	−1.50000	+	6.06218i	−0.0600481	+	0.242681i
$625$	−11.0000			−0.440000
$626$			8.66025i			0.346133i
$627$		0			0
$628$		−	10.3923i		−	0.414698i
$629$			5.19615i			0.207184i
$630$	9.00000	−	10.3923i	0.358569	−	0.414039i
$631$			22.5167i			0.896374i	0.893940	+	0.448187i	$0.147930\pi$
$631$			22.5167i			0.896374i	−0.893940	+	0.448187i	$0.852070\pi$
$632$	10.0000			0.397779
$633$	19.5000	+	11.2583i	0.775055	+	0.447478i
$634$	−6.00000			−0.238290
$635$			3.46410i			0.137469i
$636$	−3.00000	+	5.19615i	−0.118958	+	0.206041i
$637$	−20.5000	−	14.7224i	−0.812240	−	0.583324i
$638$		0			0
$639$	13.5000	+	23.3827i	0.534052	+	0.925005i
$640$		−	1.73205i		−	0.0684653i
$641$		−	34.6410i		−	1.36824i	−0.729370	−	0.684119i	$-0.760187\pi$
$641$		−	34.6410i		−	1.36824i	0.729370	−	0.684119i	$-0.239813\pi$
$642$	9.00000	−	15.5885i	0.355202	−	0.615227i
$643$	−40.0000			−1.57745			−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000			−1.57745			−0.788723	+	0.614749i	$0.789257\pi$
$644$	−3.00000	−	8.66025i	−0.118217	−	0.341262i
$645$	16.5000	−	28.5788i	0.649687	−	1.12529i
$646$	6.00000			0.236067
$647$	−30.0000			−1.17942			−0.589711	−	0.807614i	$-0.700758\pi$
$647$	−30.0000			−1.17942			−0.589711	+	0.807614i	$0.700758\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$		0			0
$650$	−2.00000	−	6.92820i	−0.0784465	−	0.271746i
$651$	−36.0000	−	6.92820i	−1.41095	−	0.271538i
$652$		−	17.3205i		−	0.678323i
$653$			41.5692i			1.62673i	0.581754	+	0.813365i	$0.302367\pi$
$653$			41.5692i			1.62673i	−0.581754	+	0.813365i	$0.697633\pi$
$654$	4.50000	−	7.79423i	0.175964	−	0.304778i
$655$		−	25.9808i		−	1.01515i
$656$		0			0
$657$	3.00000	+	5.19615i	0.117041	+	0.202721i
$658$	10.5000	+	30.3109i	0.409333	+	1.18164i
$659$		−	24.2487i		−	0.944596i	−0.881439	−	0.472298i	$-0.843425\pi$
$659$		−	24.2487i		−	0.944596i	0.881439	−	0.472298i	$-0.156575\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$		−	17.3205i		−	0.673181i
$663$	4.50000	−	18.1865i	0.174766	−	0.706306i
$664$		−	3.46410i		−	0.134433i
$665$	3.00000	+	8.66025i	0.116335	+	0.335830i
$666$	4.50000	−	2.59808i	0.174371	−	0.100673i
$667$	−24.0000			−0.929284
$668$			3.46410i			0.134030i
$669$	−10.5000	−	6.06218i	−0.405953	−	0.234377i
$670$	24.0000			0.927201
$671$		0			0
$672$	−4.50000	−	0.866025i	−0.173591	−	0.0334077i
$673$	−17.0000			−0.655302			−0.327651	−	0.944799i	$-0.606257\pi$
$673$	−17.0000			−0.655302			−0.327651	+	0.944799i	$0.606257\pi$
$674$	5.00000			0.192593
$675$		−	10.3923i		−	0.400000i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−6.00000	+	10.3923i	−0.230429	+	0.399114i
$679$	−20.0000	+	6.92820i	−0.767530	+	0.265880i
$680$			5.19615i			0.199263i
$681$		0			0
$682$		0			0
$683$	−30.0000			−1.14792			−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000			−1.14792			−0.573959	+	0.818884i	$0.694593\pi$
$684$	−3.00000	−	5.19615i	−0.114708	−	0.198680i
$685$		−	31.1769i		−	1.19121i
$686$	10.0000	−	15.5885i	0.381802	−	0.595170i
$687$	−7.50000	−	4.33013i	−0.286143	−	0.165205i
$688$	−11.0000			−0.419371
$689$	−12.0000	+	3.46410i	−0.457164	+	0.131972i
$690$	9.00000	+	5.19615i	0.342624	+	0.197814i
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$			15.5885i			0.591730i
$695$	33.0000			1.25176
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$		0			0
$698$	−1.00000			−0.0378506
$699$	7.50000	−	12.9904i	0.283676	−	0.491341i
$700$	5.00000	−	1.73205i	0.188982	−	0.0654654i
$701$		−	38.1051i		−	1.43921i	−0.694383	−	0.719605i	$-0.744323\pi$
$701$		−	38.1051i		−	1.43921i	0.694383	−	0.719605i	$-0.255677\pi$
$702$	−18.0000	+	5.19615i	−0.679366	+	0.196116i
$703$			3.46410i			0.130651i
$704$		0			0
$705$	−31.5000	−	18.1865i	−1.18636	−	0.684944i
$706$		−	10.3923i		−	0.391120i
$707$	30.0000	−	10.3923i	1.12827	−	0.390843i
$708$	9.00000	−	15.5885i	0.338241	−	0.585850i
$709$			34.6410i			1.30097i	0.759519	+	0.650485i	$0.225434\pi$
$709$			34.6410i			1.30097i	−0.759519	+	0.650485i	$0.774566\pi$
$710$		−	15.5885i		−	0.585024i
$711$	15.0000	+	25.9808i	0.562544	+	0.974355i
$712$		−	3.46410i		−	0.129823i
$713$		−	27.7128i		−	1.03785i
$714$	13.5000	+	2.59808i	0.505225	+	0.0972306i
$715$		0			0
$716$			12.1244i			0.453108i
$717$	22.5000	+	12.9904i	0.840278	+	0.485135i
$718$		0			0
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$	4.50000	−	2.59808i	0.167705	−	0.0968246i
$721$	3.00000	+	8.66025i	0.111726	+	0.322525i
$722$	−15.0000			−0.558242
$723$	15.0000	+	8.66025i	0.557856	+	0.322078i
$724$		−	3.46410i		−	0.128742i
$725$		−	13.8564i		−	0.514614i
$726$	16.5000	+	9.52628i	0.612372	+	0.353553i
$727$		−	41.5692i		−	1.54172i	−0.637006	−	0.770859i	$-0.719828\pi$
$727$		−	41.5692i		−	1.54172i	0.637006	−	0.770859i	$-0.280172\pi$
$728$	−5.50000	−	7.79423i	−0.203844	−	0.288873i
$729$	−27.0000			−1.00000
$730$		−	3.46410i		−	0.128212i
$731$	33.0000			1.22055
$732$	6.00000	−	10.3923i	0.221766	−	0.384111i
$733$	−19.0000			−0.701781			−0.350891	−	0.936416i	$-0.614121\pi$
$733$	−19.0000			−0.701781			−0.350891	+	0.936416i	$0.614121\pi$
$734$		−	34.6410i		−	1.27862i
$735$	3.00000	+	20.7846i	0.110657	+	0.766652i
$736$		−	3.46410i		−	0.127688i
$737$		0			0
$738$		0			0
$739$		−	20.7846i		−	0.764574i	−0.924044	−	0.382287i	$-0.875137\pi$
$739$		−	20.7846i		−	0.764574i	0.924044	−	0.382287i	$-0.124863\pi$
$740$	−3.00000			−0.110282
$741$	3.00000	−	12.1244i	0.110208	−	0.445399i
$742$	−3.00000	−	8.66025i	−0.110133	−	0.317928i
$743$	33.0000			1.21065			0.605326	−	0.795977i	$-0.293043\pi$
$743$	33.0000			1.21065			0.605326	+	0.795977i	$0.293043\pi$
$744$	−12.0000	−	6.92820i	−0.439941	−	0.254000i
$745$		−	10.3923i		−	0.380745i
$746$	16.0000			0.585802
$747$	9.00000	−	5.19615i	0.329293	−	0.190117i
$748$		0			0
$749$	9.00000	+	25.9808i	0.328853	+	0.949316i
$750$	−10.5000	+	18.1865i	−0.383406	+	0.664078i
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$			12.1244i			0.442130i
$753$	18.0000	+	10.3923i	0.655956	+	0.378717i
$754$	−24.0000	+	6.92820i	−0.874028	+	0.252310i
$755$	33.0000			1.20099
$756$	−4.50000	−	12.9904i	−0.163663	−	0.472456i
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		−	17.3205i		−	0.629109i
$759$		0			0
$760$			3.46410i			0.125656i
$761$		−	38.1051i		−	1.38131i	−0.723185	−	0.690655i	$-0.757322\pi$
$761$		−	38.1051i		−	1.38131i	0.723185	−	0.690655i	$-0.242678\pi$
$762$	3.00000	+	1.73205i	0.108679	+	0.0627456i
$763$	4.50000	+	12.9904i	0.162911	+	0.470283i
$764$		−	20.7846i		−	0.751961i
$765$	−13.5000	+	7.79423i	−0.488094	+	0.281801i
$766$			5.19615i			0.187745i
$767$	36.0000	−	10.3923i	1.29988	−	0.375244i
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$		0			0
$771$	31.5000	+	18.1865i	1.13444	+	0.654972i
$772$			17.3205i			0.623379i
$773$		−	15.5885i		−	0.560678i	−0.959901	−	0.280339i	$-0.909553\pi$
$773$		−	15.5885i		−	0.560678i	0.959901	−	0.280339i	$-0.0904469\pi$
$774$	−16.5000	−	28.5788i	−0.593080	−	1.02725i
$775$	16.0000			0.574737
$776$	−8.00000			−0.287183
$777$	−1.50000	+	7.79423i	−0.0538122	+	0.279616i
$778$		−	10.3923i		−	0.372582i
$779$		0			0
$780$	10.5000	+	2.59808i	0.375960	+	0.0930261i
$781$		0			0
$782$			10.3923i			0.371628i
$783$	−36.0000			−1.28654
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−18.0000			−0.642448
$786$	−22.5000	−	12.9904i	−0.802548	−	0.463352i
$787$	−32.0000			−1.14068			−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000			−1.14068			−0.570338	+	0.821410i	$0.693188\pi$
$788$	−15.0000			−0.534353
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		−	17.3205i		−	0.616236i
$791$	−6.00000	−	17.3205i	−0.213335	−	0.615846i
$792$		0			0
$793$	24.0000	−	6.92820i	0.852265	−	0.246028i
$794$	22.0000			0.780751
$795$	9.00000	+	5.19615i	0.319197	+	0.184289i
$796$		−	6.92820i		−	0.245564i
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$	9.00000	+	1.73205i	0.318597	+	0.0613139i
$799$		−	36.3731i		−	1.28679i
$800$	2.00000			0.0707107
$801$	9.00000	−	5.19615i	0.317999	−	0.183597i
$802$	6.00000			0.211867
$803$		0			0
$804$	12.0000	−	20.7846i	0.423207	−	0.733017i
$805$	−15.0000	+	5.19615i	−0.528681	+	0.183140i
$806$	−8.00000	−	27.7128i	−0.281788	−	0.976142i
$807$		0			0
$808$	12.0000			0.422159
$809$			1.73205i			0.0608957i	0.999536	+	0.0304478i	$0.00969334\pi$
$809$			1.73205i			0.0608957i	−0.999536	+	0.0304478i	$0.990307\pi$
$810$	13.5000	+	7.79423i	0.474342	+	0.273861i
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	−6.00000	−	17.3205i	−0.210559	−	0.607831i
$813$	−1.50000	−	0.866025i	−0.0526073	−	0.0303728i
$814$		0			0
$815$	−30.0000			−1.05085
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	22.0000			0.769683
$818$	−14.0000			−0.489499
$819$	12.0000	−	25.9808i	0.419314	−	0.907841i
$820$		0			0
$821$	−15.0000			−0.523504			−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000			−0.523504			−0.261752	+	0.965135i	$0.584300\pi$
$822$	−27.0000	−	15.5885i	−0.941733	−	0.543710i
$823$	38.0000			1.32460			0.662298	−	0.749240i	$-0.269581\pi$
$823$	38.0000			1.32460			0.662298	+	0.749240i	$0.269581\pi$
$824$			3.46410i			0.120678i
$825$		0			0
$826$	9.00000	+	25.9808i	0.313150	+	0.903986i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$	9.00000	−	5.19615i	0.312772	−	0.180579i
$829$		−	27.7128i		−	0.962506i	−0.876582	−	0.481253i	$-0.840182\pi$
$829$		−	27.7128i		−	0.962506i	0.876582	−	0.481253i	$-0.159818\pi$
$830$	−6.00000			−0.208263
$831$	24.0000	+	13.8564i	0.832551	+	0.480673i
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$	−16.5000	+	12.9904i	−0.571691	+	0.450090i
$834$	16.5000	−	28.5788i	0.571348	−	0.989604i
$835$	6.00000			0.207639
$836$		0			0
$837$		−	41.5692i		−	1.43684i
$838$	27.0000			0.932700
$839$			10.3923i			0.358782i	0.983778	+	0.179391i	$0.0574128\pi$
$839$			10.3923i			0.358782i	−0.983778	+	0.179391i	$0.942587\pi$
$840$	−1.50000	+	7.79423i	−0.0517549	+	0.268926i
$841$	−19.0000			−0.655172
$842$			32.9090i			1.13412i
$843$	−45.0000	−	25.9808i	−1.54988	−	0.894825i
$844$	−13.0000			−0.447478
$845$	12.0000	+	19.0526i	0.412813	+	0.655428i
$846$	−31.5000	+	18.1865i	−1.08299	+	0.625266i
$847$	−27.5000	+	9.52628i	−0.944911	+	0.327327i
$848$		−	3.46410i		−	0.118958i
$849$	−9.00000	+	15.5885i	−0.308879	+	0.534994i
$850$	−6.00000			−0.205798
$851$	−6.00000			−0.205677
$852$	−13.5000	−	7.79423i	−0.462502	−	0.267026i
$853$	19.0000			0.650548			0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000			0.650548			0.325274	+	0.945620i	$0.394544\pi$
$854$	6.00000	+	17.3205i	0.205316	+	0.592696i
$855$	−9.00000	+	5.19615i	−0.307794	+	0.177705i
$856$			10.3923i			0.355202i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$		−	17.3205i		−	0.590968i	−0.955348	−	0.295484i	$-0.904519\pi$
$859$		−	17.3205i		−	0.590968i	0.955348	−	0.295484i	$-0.0954809\pi$
$860$			19.0526i			0.649687i
$861$		0			0
$862$	−33.0000			−1.12398
$863$	−33.0000			−1.12333			−0.561667	−	0.827364i	$-0.689840\pi$
$863$	−33.0000			−1.12333			−0.561667	+	0.827364i	$0.689840\pi$
$864$		−	5.19615i		−	0.176777i
$865$		−	10.3923i		−	0.353349i
$866$		−	5.19615i		−	0.176572i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$	20.0000	−	6.92820i	0.678844	−	0.235159i
$869$		0			0
$870$	18.0000	+	10.3923i	0.610257	+	0.352332i
$871$	48.0000	−	13.8564i	1.62642	−	0.469506i
$872$			5.19615i			0.175964i
$873$	−12.0000	−	20.7846i	−0.406138	−	0.703452i
$874$			6.92820i			0.234350i
$875$	−10.5000	−	30.3109i	−0.354965	−	1.02470i
$876$	−3.00000	−	1.73205i	−0.101361	−	0.0585206i
$877$			53.6936i			1.81310i	0.422095	+	0.906552i	$0.361295\pi$
$877$			53.6936i			1.81310i	−0.422095	+	0.906552i	$0.638705\pi$
$878$			31.1769i			1.05217i
$879$	−16.5000	+	28.5788i	−0.556531	+	0.963940i
$880$		0			0
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$	19.5000	+	7.79423i	0.656599	+	0.262445i
$883$	17.0000			0.572096			0.286048	−	0.958215i	$-0.407658\pi$
$883$	17.0000			0.572096			0.286048	+	0.958215i	$0.407658\pi$
$884$	3.00000	+	10.3923i	0.100901	+	0.349531i
$885$	−27.0000	−	15.5885i	−0.907595	−	0.524000i
$886$		−	22.5167i		−	0.756462i
$887$	24.0000			0.805841			0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000			0.805841			0.402921	+	0.915235i	$0.367995\pi$
$888$	−1.50000	+	2.59808i	−0.0503367	+	0.0871857i
$889$	−5.00000	+	1.73205i	−0.167695	+	0.0580911i
$890$	−6.00000			−0.201120
$891$		0			0
$892$	7.00000			0.234377
$893$		−	24.2487i		−	0.811452i
$894$	−9.00000	−	5.19615i	−0.301005	−	0.173785i
$895$	21.0000			0.701953
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$	21.0000	+	5.19615i	0.701170	+	0.173494i
$898$		0			0
$899$		−	55.4256i		−	1.84855i
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$			10.3923i			0.346218i
$902$		0			0
$903$	49.5000	+	9.52628i	1.64726	+	0.317015i
$904$		−	6.92820i		−	0.230429i
$905$	−6.00000			−0.199447
$906$	16.5000	−	28.5788i	0.548176	−	0.949468i
$907$	53.0000			1.75984			0.879918	−	0.475125i	$-0.157597\pi$
$907$	53.0000			1.75984			0.879918	+	0.475125i	$0.157597\pi$
$908$		0			0
$909$	18.0000	+	31.1769i	0.597022	+	1.03407i
$910$	−13.5000	+	9.52628i	−0.447521	+	0.315793i
$911$		−	6.92820i		−	0.229542i	−0.993392	−	0.114771i	$-0.963387\pi$
$911$		−	6.92820i		−	0.229542i	0.993392	−	0.114771i	$-0.0366134\pi$
$912$	3.00000	+	1.73205i	0.0993399	+	0.0573539i
$913$		0			0
$914$			10.3923i			0.343747i
$915$	−18.0000	−	10.3923i	−0.595062	−	0.343559i
$916$	5.00000			0.165205
$917$	37.5000	−	12.9904i	1.23836	−	0.428980i
$918$			15.5885i			0.514496i
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$	−6.00000			−0.197814
$921$	−21.0000	−	12.1244i	−0.691974	−	0.399511i
$922$		−	5.19615i		−	0.171126i
$923$	−9.00000	−	31.1769i	−0.296239	−	1.02620i
$924$		0			0
$925$		−	3.46410i		−	0.113899i
$926$		−	24.2487i		−	0.796862i
$927$	−9.00000	+	5.19615i	−0.295599	+	0.170664i
$928$		−	6.92820i		−	0.227429i
$929$			34.6410i			1.13653i	0.822844	+	0.568267i	$0.192386\pi$
$929$			34.6410i			1.13653i	−0.822844	+	0.568267i	$0.807614\pi$
$930$	−12.0000	+	20.7846i	−0.393496	+	0.681554i
$931$	−11.0000	+	8.66025i	−0.360510	+	0.283828i
$932$			8.66025i			0.283676i
$933$	45.0000	+	25.9808i	1.47323	+	0.850572i
$934$	−36.0000			−1.17796
$935$		0			0
$936$	7.50000	−	7.79423i	0.245145	−	0.254762i
$937$		−	34.6410i		−	1.13167i	−0.824518	−	0.565836i	$-0.808553\pi$
$937$		−	34.6410i		−	1.13167i	0.824518	−	0.565836i	$-0.191447\pi$
$938$	12.0000	+	34.6410i	0.391814	+	1.13107i
$939$	7.50000	−	12.9904i	0.244753	−	0.423925i
$940$	21.0000			0.684944
$941$			43.3013i			1.41158i	0.708421	+	0.705791i	$0.249408\pi$
$941$			43.3013i			1.41158i	−0.708421	+	0.705791i	$0.750592\pi$
$942$	−9.00000	+	15.5885i	−0.293236	+	0.507899i
$943$		0			0
$944$			10.3923i			0.338241i
$945$	−22.5000	+	7.79423i	−0.731925	+	0.253546i
$946$		0			0
$947$	36.0000			1.16984			0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000			1.16984			0.584921	+	0.811090i	$0.301125\pi$
$948$	−15.0000	−	8.66025i	−0.487177	−	0.281272i
$949$	−2.00000	−	6.92820i	−0.0649227	−	0.224899i
$950$	−4.00000			−0.129777
$951$	9.00000	+	5.19615i	0.291845	+	0.168497i
$952$	−7.50000	+	2.59808i	−0.243076	+	0.0842041i
$953$			1.73205i			0.0561066i	0.999606	+	0.0280533i	$0.00893082\pi$
$953$			1.73205i			0.0561066i	−0.999606	+	0.0280533i	$0.991069\pi$
$954$	9.00000	−	5.19615i	0.291386	−	0.168232i
$955$	−36.0000			−1.16493
$956$	−15.0000			−0.485135
$957$		0			0
$958$			32.9090i			1.06324i
$959$	45.0000	−	15.5885i	1.45313	−	0.503378i
$960$	−1.50000	+	2.59808i	−0.0484123	+	0.0838525i
$961$	33.0000			1.06452
$962$	−6.00000	+	1.73205i	−0.193448	+	0.0558436i
$963$	−27.0000	+	15.5885i	−0.870063	+	0.502331i
$964$	−10.0000			−0.322078
$965$	30.0000			0.965734
$966$	−3.00000	+	15.5885i	−0.0965234	+	0.501550i
$967$			43.3013i			1.39247i	0.717812	+	0.696237i	$0.245144\pi$
$967$			43.3013i			1.39247i	−0.717812	+	0.696237i	$0.754856\pi$
$968$	−11.0000			−0.353553
$969$	−9.00000	−	5.19615i	−0.289122	−	0.166924i
$970$			13.8564i			0.444902i
$971$	−9.00000			−0.288824			−0.144412	−	0.989518i	$-0.546129\pi$
$971$	−9.00000			−0.288824			−0.144412	+	0.989518i	$0.546129\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	16.5000	+	47.6314i	0.528966	+	1.52699i
$974$		−	24.2487i		−	0.776979i
$975$	−3.00000	+	12.1244i	−0.0960769	+	0.388290i
$976$			6.92820i			0.221766i
$977$	−24.0000			−0.767828			−0.383914	−	0.923369i	$-0.625424\pi$
$977$	−24.0000			−0.767828			−0.383914	+	0.923369i	$0.625424\pi$
$978$	−15.0000	+	25.9808i	−0.479647	+	0.830773i
$979$		0			0
$980$	−7.50000	−	9.52628i	−0.239579	−	0.304306i
$981$	−13.5000	+	7.79423i	−0.431022	+	0.248851i
$982$			36.3731i			1.16071i
$983$		−	32.9090i		−	1.04963i	−0.851215	−	0.524816i	$-0.824134\pi$
$983$		−	32.9090i		−	1.04963i	0.851215	−	0.524816i	$-0.175866\pi$
$984$		0			0
$985$			25.9808i			0.827816i
$986$			20.7846i			0.661917i
$987$	10.5000	−	54.5596i	0.334219	−	1.73665i
$988$	2.00000	+	6.92820i	0.0636285	+	0.220416i
$989$			38.1051i			1.21167i
$990$		0			0
$991$	10.0000			0.317660			0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000			0.317660			0.158830	+	0.987306i	$0.449228\pi$
$992$	8.00000			0.254000
$993$	−15.0000	+	25.9808i	−0.476011	+	0.824475i
$994$	22.5000	−	7.79423i	0.713657	−	0.247218i
$995$	−12.0000			−0.380426
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$			20.7846i			0.657925i
$999$	−9.00000			−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.e.c.545.1	yes	2
3.2	odd	2		546.2.e.b.545.1	yes	2
7.6	odd	2		546.2.e.d.545.2	yes	2
13.12	even	2		546.2.e.a.545.1	✓	2
21.20	even	2		546.2.e.a.545.2	yes	2
39.38	odd	2		546.2.e.d.545.1	yes	2
91.90	odd	2		546.2.e.b.545.2	yes	2
273.272	even	2	inner	546.2.e.c.545.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.e.a.545.1	✓	2	13.12	even	2
546.2.e.a.545.2	yes	2	21.20	even	2
546.2.e.b.545.1	yes	2	3.2	odd	2
546.2.e.b.545.2	yes	2	91.90	odd	2
546.2.e.c.545.1	yes	2	1.1	even	1	trivial
546.2.e.c.545.2	yes	2	273.272	even	2	inner
546.2.e.d.545.1	yes	2	39.38	odd	2
546.2.e.d.545.2	yes	2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} -1.73205i q^{5} +(-1.50000 - 0.866025i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{10} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(2.50000 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{15} +1.00000 q^{16} -3.00000 q^{17} +(1.50000 + 2.59808i) q^{18} -2.00000 q^{19} -1.73205i q^{20} +(-4.50000 - 0.866025i) q^{21} -3.46410i q^{23} +(-1.50000 - 0.866025i) q^{24} +2.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} -5.19615i q^{27} +(2.50000 - 0.866025i) q^{28} -6.92820i q^{29} +(-1.50000 + 2.59808i) q^{30} +8.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +(-1.50000 - 4.33013i) q^{35} +(1.50000 + 2.59808i) q^{36} -1.73205i q^{37} -2.00000 q^{38} +(-1.50000 + 6.06218i) q^{39} -1.73205i q^{40} +(-4.50000 - 0.866025i) q^{42} -11.0000 q^{43} +(4.50000 - 2.59808i) q^{45} -3.46410i q^{46} +12.1244i q^{47} +(-1.50000 - 0.866025i) q^{48} +(5.50000 - 4.33013i) q^{49} +2.00000 q^{50} +(4.50000 + 2.59808i) q^{51} +(-1.00000 - 3.46410i) q^{52} -3.46410i q^{53} -5.19615i q^{54} +(2.50000 - 0.866025i) q^{56} +(3.00000 + 1.73205i) q^{57} -6.92820i q^{58} +10.3923i q^{59} +(-1.50000 + 2.59808i) q^{60} +6.92820i q^{61} +8.00000 q^{62} +(6.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +13.8564i q^{67} -3.00000 q^{68} +(-3.00000 + 5.19615i) q^{69} +(-1.50000 - 4.33013i) q^{70} +9.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +2.00000 q^{73} -1.73205i q^{74} +(-3.00000 - 1.73205i) q^{75} -2.00000 q^{76} +(-1.50000 + 6.06218i) q^{78} +10.0000 q^{79} -1.73205i q^{80} +(-4.50000 + 7.79423i) q^{81} -3.46410i q^{83} +(-4.50000 - 0.866025i) q^{84} +5.19615i q^{85} -11.0000 q^{86} +(-6.00000 + 10.3923i) q^{87} -3.46410i q^{89} +(4.50000 - 2.59808i) q^{90} +(-5.50000 - 7.79423i) q^{91} -3.46410i q^{92} +(-12.0000 - 6.92820i) q^{93} +12.1244i q^{94} +3.46410i q^{95} +(-1.50000 - 0.866025i) q^{96} -8.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} + 5 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{12} - 2 q^{13} + 5 q^{14} - 3 q^{15} + 2 q^{16} - 6 q^{17} + 3 q^{18} - 4 q^{19} - 9 q^{21} - 3 q^{24} + 4 q^{25} - 2 q^{26}+ \cdots + 11 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 + 5 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^12 - 2 * q^13 + 5 * q^14 - 3 * q^15 + 2 * q^16 - 6 * q^17 + 3 * q^18 - 4 * q^19 - 9 * q^21 - 3 * q^24 + 4 * q^25 - 2 * q^26 + 5 * q^28 - 3 * q^30 + 16 * q^31 + 2 * q^32 - 6 * q^34 - 3 * q^35 + 3 * q^36 - 4 * q^38 - 3 * q^39 - 9 * q^42 - 22 * q^43 + 9 * q^45 - 3 * q^48 + 11 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 5 * q^56 + 6 * q^57 - 3 * q^60 + 16 * q^62 + 12 * q^63 + 2 * q^64 - 12 * q^65 - 6 * q^68 - 6 * q^69 - 3 * q^70 + 18 * q^71 + 3 * q^72 + 4 * q^73 - 6 * q^75 - 4 * q^76 - 3 * q^78 + 20 * q^79 - 9 * q^81 - 9 * q^84 - 22 * q^86 - 12 * q^87 + 9 * q^90 - 11 * q^91 - 24 * q^93 - 3 * q^96 - 16 * q^97 + 11 * q^98

Introduction

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