LMFDB - Embedded newform 546.2.l.b.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.2.l.b.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-2.00000 - 3.46410i) q^{11} -1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +1.00000 q^{18} +(-2.00000 + 3.46410i) q^{19} +(-1.50000 + 2.59808i) q^{20} +1.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +(1.50000 - 2.59808i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -5.00000 q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +3.00000 q^{40} +(-3.50000 - 6.06218i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +4.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.00000 - 3.46410i) q^{46} +12.0000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +5.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +7.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-6.00000 - 10.3923i) q^{55} +(0.500000 - 0.866025i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} -3.00000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(10.5000 - 2.59808i) q^{65} -4.00000 q^{66} +(-6.00000 - 10.3923i) q^{67} +(2.50000 + 4.33013i) q^{68} +(-2.00000 + 3.46410i) q^{69} -3.00000 q^{70} +(-6.00000 + 10.3923i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.00000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-2.00000 - 3.46410i) q^{76} -4.00000 q^{77} +(1.00000 - 3.46410i) q^{78} -16.0000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.50000 + 6.06218i) q^{82} -8.00000 q^{83} +(-0.500000 + 0.866025i) q^{84} +(7.50000 - 12.9904i) q^{85} +8.00000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(1.00000 - 3.46410i) q^{91} -4.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000 q^{96} +(-9.00000 + 15.5885i) q^{97} +(-0.500000 + 0.866025i) q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 + q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} + q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 4 q^{11} - 2 q^{12} + 7 q^{13} - 2 q^{14} + 3 q^{15} - q^{16} + 5 q^{17} + 2 q^{18} - 4 q^{19} - 3 q^{20} + 2 q^{21} - 4 q^{22} + 4 q^{23} + q^{24} + 8 q^{25} - 5 q^{26} - 2 q^{27} + q^{28} + 9 q^{29} + 3 q^{30} - q^{32} + 4 q^{33} - 10 q^{34} + 3 q^{35} - q^{36} - 7 q^{37} + 8 q^{38} + 5 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} - 8 q^{43} + 8 q^{44} - 3 q^{45} + 4 q^{46} + 24 q^{47} + q^{48} - q^{49} - 4 q^{50} + 10 q^{51} - 2 q^{52} + 14 q^{53} + q^{54} - 12 q^{55} + q^{56} - 8 q^{57} + 9 q^{58} + 8 q^{59} - 6 q^{60} - 7 q^{61} + q^{63} + 2 q^{64} + 21 q^{65} - 8 q^{66} - 12 q^{67} + 5 q^{68} - 4 q^{69} - 6 q^{70} - 12 q^{71} - q^{72} - 2 q^{73} - 7 q^{74} + 4 q^{75} - 4 q^{76} - 8 q^{77} + 2 q^{78} - 32 q^{79} - 3 q^{80} - q^{81} - 7 q^{82} - 16 q^{83} - q^{84} + 15 q^{85} + 16 q^{86} - 9 q^{87} - 4 q^{88} + 6 q^{89} + 6 q^{90} + 2 q^{91} - 8 q^{92} - 12 q^{94} - 12 q^{95} - 2 q^{96} - 18 q^{97} - q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 + q^7 + 2 * q^8 - q^9 - 3 * q^10 - 4 * q^11 - 2 * q^12 + 7 * q^13 - 2 * q^14 + 3 * q^15 - q^16 + 5 * q^17 + 2 * q^18 - 4 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 4 * q^23 + q^24 + 8 * q^25 - 5 * q^26 - 2 * q^27 + q^28 + 9 * q^29 + 3 * q^30 - q^32 + 4 * q^33 - 10 * q^34 + 3 * q^35 - q^36 - 7 * q^37 + 8 * q^38 + 5 * q^39 + 6 * q^40 - 7 * q^41 - q^42 - 8 * q^43 + 8 * q^44 - 3 * q^45 + 4 * q^46 + 24 * q^47 + q^48 - q^49 - 4 * q^50 + 10 * q^51 - 2 * q^52 + 14 * q^53 + q^54 - 12 * q^55 + q^56 - 8 * q^57 + 9 * q^58 + 8 * q^59 - 6 * q^60 - 7 * q^61 + q^63 + 2 * q^64 + 21 * q^65 - 8 * q^66 - 12 * q^67 + 5 * q^68 - 4 * q^69 - 6 * q^70 - 12 * q^71 - q^72 - 2 * q^73 - 7 * q^74 + 4 * q^75 - 4 * q^76 - 8 * q^77 + 2 * q^78 - 32 * q^79 - 3 * q^80 - q^81 - 7 * q^82 - 16 * q^83 - q^84 + 15 * q^85 + 16 * q^86 - 9 * q^87 - 4 * q^88 + 6 * q^89 + 6 * q^90 + 2 * q^91 - 8 * q^92 - 12 * q^94 - 12 * q^95 - 2 * q^96 - 18 * q^97 - q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$	−1.00000			−0.288675
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	−1.00000			−0.267261
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$	1.00000			0.235702
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$	1.00000			0.218218
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.00000			0.800000
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	−1.00000			−0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$	1.50000	−	2.59808i	0.273861	−	0.474342i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	−5.00000			−0.857493
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	4.00000			0.648886
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$	3.00000			0.474342
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	−0.998504	−	0.0546823i	$-0.982585\pi$
$41$	−3.50000	−	6.06218i	−0.546608	−	0.946753i	0.451896	−	0.892071i	$-0.350748\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	4.00000			0.603023
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	5.00000			0.700140
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	7.00000			0.961524			0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000			0.961524			0.480762	+	0.876851i	$0.340360\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−6.00000	−	10.3923i	−0.809040	−	1.40130i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−4.00000			−0.529813
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$	−3.00000			−0.387298
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	10.5000	−	2.59808i	1.30236	−	0.322252i
$66$	−4.00000			−0.492366
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$	−3.00000			−0.358569
$71$	−6.00000	+	10.3923i	−0.712069	+	1.23334i	0.252010	+	0.967725i	$0.418908\pi$
$71$	−6.00000	+	10.3923i	−0.712069	+	1.23334i	−0.964079	+	0.265615i	$0.914425\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	−2.00000	−	3.46410i	−0.229416	−	0.397360i
$77$	−4.00000			−0.455842
$78$	1.00000	−	3.46410i	0.113228	−	0.392232i
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.50000	+	6.06218i	−0.386510	+	0.669456i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$	7.50000	−	12.9904i	0.813489	−	1.40900i
$86$	8.00000			0.862662
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	3.00000			0.316228
$91$	1.00000	−	3.46410i	0.104828	−	0.363137i
$92$	−4.00000			−0.417029
$93$		0			0
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$	−1.00000			−0.102062
$97$	−9.00000	+	15.5885i	−0.913812	+	1.58277i	−0.105180	+	0.994453i	$0.533542\pi$
$97$	−9.00000	+	15.5885i	−0.913812	+	1.58277i	−0.808632	+	0.588315i	$0.799792\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	4.00000			0.402015
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	−2.50000	−	4.33013i	−0.247537	−	0.428746i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	3.00000			0.292770
$106$	−3.50000	−	6.06218i	−0.339950	−	0.588811i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	−6.00000	+	10.3923i	−0.572078	+	0.990867i
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	−1.00000			−0.0944911
$113$	2.50000	−	4.33013i	0.235180	−	0.407344i	−0.724145	−	0.689648i	$-0.757765\pi$
$113$	2.50000	−	4.33013i	0.235180	−	0.407344i	0.959325	+	0.282304i	$0.0910986\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$	6.00000	+	10.3923i	0.559503	+	0.969087i
$116$	−9.00000			−0.835629
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	−8.00000			−0.736460
$119$	−2.50000	−	4.33013i	−0.229175	−	0.396942i
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	7.00000			0.633750
$123$	3.50000	−	6.06218i	0.315584	−	0.546608i
$124$		0			0
$125$	−3.00000			−0.268328
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−8.00000			−0.704361
$130$	−7.50000	−	7.79423i	−0.657794	−	0.683599i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	2.00000	+	3.46410i	0.174078	+	0.301511i
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	−6.00000	+	10.3923i	−0.518321	+	0.897758i
$135$	−3.00000			−0.258199
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	4.00000			0.340503
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$	1.50000	+	2.59808i	0.126773	+	0.219578i
$141$	6.00000	+	10.3923i	0.505291	+	0.875190i
$142$	12.0000			1.00702
$143$	−10.0000	−	10.3923i	−0.836242	−	0.869048i
$144$	1.00000			0.0833333
$145$	13.5000	+	23.3827i	1.12111	+	1.94183i
$146$	0.500000	+	0.866025i	0.0413803	+	0.0716728i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	7.00000			0.575396
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	−0.973028	−	0.230689i	$-0.925902\pi$
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	0.686296	+	0.727322i	$0.259235\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	2.50000	+	4.33013i	0.202113	+	0.350070i
$154$	2.00000	+	3.46410i	0.161165	+	0.279145i
$155$		0			0
$156$	−3.50000	+	0.866025i	−0.280224	+	0.0693375i
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$	3.50000	+	6.06218i	0.277568	+	0.480762i
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$	4.00000			0.315244
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	7.00000			0.546608
$165$	6.00000	−	10.3923i	0.467099	−	0.809040i
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$	1.00000			0.0771517
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−15.0000			−1.15045
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$	9.00000			0.682288
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$	8.00000			0.601317
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$	−3.50000	+	0.866025i	−0.259437	+	0.0641941i
$183$	−7.00000			−0.517455
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$		0			0
$187$	−20.0000			−1.46254
$188$	−6.00000	+	10.3923i	−0.437595	+	0.757937i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	12.0000			0.870572
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$	18.0000			1.29232
$195$	7.50000	+	7.79423i	0.537086	+	0.558156i
$196$	1.00000			0.0714286
$197$	−11.0000	−	19.0526i	−0.783718	−	1.35744i	−0.929762	−	0.368161i	$-0.879988\pi$
$197$	−11.0000	−	19.0526i	−0.783718	−	1.35744i	0.146045	−	0.989278i	$-0.453346\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	4.00000			0.282843
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	−1.50000	+	2.59808i	−0.105540	+	0.182800i
$203$	9.00000			0.631676
$204$	−2.50000	+	4.33013i	−0.175035	+	0.303170i
$205$	−10.5000	−	18.1865i	−0.733352	−	1.27020i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$	−4.00000			−0.278019
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	16.0000			1.10674
$210$	−1.50000	−	2.59808i	−0.103510	−	0.179284i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	−3.50000	+	6.06218i	−0.240381	+	0.416352i
$213$	−12.0000			−0.822226
$214$		0			0
$215$	−12.0000	+	20.7846i	−0.818393	+	1.41750i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$	−0.500000	−	0.866025i	−0.0337869	−	0.0585206i
$220$	12.0000			0.809040
$221$	5.00000	−	17.3205i	0.336336	−	1.16510i
$222$	−7.00000			−0.469809
$223$	14.0000	+	24.2487i	0.937509	+	1.62381i	0.770097	+	0.637927i	$0.220208\pi$
$223$	14.0000	+	24.2487i	0.937509	+	1.62381i	0.167412	+	0.985887i	$0.446459\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$	−5.00000			−0.332595
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$	6.00000	−	10.3923i	0.395628	−	0.685248i
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	4.50000	+	7.79423i	0.295439	+	0.511716i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$	36.0000			2.34838
$236$	4.00000	+	6.92820i	0.260378	+	0.450988i
$237$	−8.00000	−	13.8564i	−0.519656	−	0.900070i
$238$	−2.50000	+	4.33013i	−0.162051	+	0.280680i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	1.50000	−	2.59808i	0.0968246	−	0.167705i
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	−0.683908	−	0.729568i	$-0.739721\pi$
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	0.973779	+	0.227498i	$0.0730544\pi$
$242$	5.00000			0.321412
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.50000	−	6.06218i	−0.224065	−	0.388091i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−7.00000			−0.446304
$247$	−4.00000	+	13.8564i	−0.254514	+	0.881662i
$248$		0			0
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$	−1.00000			−0.0629941
$253$	8.00000	−	13.8564i	0.502956	−	0.871145i
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$	15.0000			0.939336
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	0.735972	−	0.677012i	$-0.236726\pi$
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	−0.954296	+	0.298864i	$0.903392\pi$
$258$	4.00000	+	6.92820i	0.249029	+	0.431331i
$259$	−7.00000			−0.434959
$260$	−3.00000	+	10.3923i	−0.186052	+	0.644503i
$261$	−9.00000			−0.557086
$262$	6.00000	+	10.3923i	0.370681	+	0.642039i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	21.0000			1.29002
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$	12.0000			0.733017
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$	1.50000	+	2.59808i	0.0912871	+	0.158114i
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$	−5.00000			−0.303170
$273$	3.50000	−	0.866025i	0.211830	−	0.0524142i
$274$	3.00000			0.181237
$275$	−8.00000	−	13.8564i	−0.482418	−	0.835573i
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$	4.00000			0.239904
$279$		0			0
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	15.0000			0.894825			0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000			0.894825			0.447412	+	0.894328i	$0.352346\pi$
$282$	6.00000	−	10.3923i	0.357295	−	0.618853i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−12.0000			−0.710819
$286$	−4.00000	+	13.8564i	−0.236525	+	0.819346i
$287$	−7.00000			−0.413197
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	13.5000	−	23.3827i	0.792747	−	1.37308i
$291$	−18.0000			−1.05518
$292$	0.500000	−	0.866025i	0.0292603	−	0.0506803i
$293$	16.5000	−	28.5788i	0.963940	−	1.66959i	0.251505	−	0.967856i	$-0.419075\pi$
$293$	16.5000	−	28.5788i	0.963940	−	1.66959i	0.712436	−	0.701737i	$-0.247592\pi$
$294$	−1.00000			−0.0583212
$295$	12.0000	−	20.7846i	0.698667	−	1.21013i
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	7.00000			0.405499
$299$	10.0000	+	10.3923i	0.578315	+	0.601003i
$300$	−4.00000			−0.230940
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	4.00000	+	6.92820i	0.230174	+	0.398673i
$303$	1.50000	−	2.59808i	0.0861727	−	0.149256i
$304$	4.00000			0.229416
$305$	−10.5000	+	18.1865i	−0.601228	+	1.04136i
$306$	2.50000	−	4.33013i	0.142915	−	0.247537i
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$	2.50000	+	2.59808i	0.141535	+	0.147087i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	6.50000	+	11.2583i	0.366816	+	0.635344i
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	8.00000	−	13.8564i	0.450035	−	0.779484i
$317$	35.0000			1.96580			0.982898	−	0.184151i	$-0.0589536\pi$
$317$	35.0000			1.96580			0.982898	+	0.184151i	$0.0589536\pi$
$318$	3.50000	−	6.06218i	0.196270	−	0.339950i
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	3.00000			0.167705
$321$		0			0
$322$	−2.00000	−	3.46410i	−0.111456	−	0.193047i
$323$	10.0000	+	17.3205i	0.556415	+	0.963739i
$324$	1.00000			0.0555556
$325$	14.0000	−	3.46410i	0.776580	−	0.192154i
$326$	4.00000			0.221540
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	−12.0000			−0.660578
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	4.00000	−	6.92820i	0.219529	−	0.380235i
$333$	7.00000			0.383598
$334$	4.00000	−	6.92820i	0.218870	−	0.379094i
$335$	−18.0000	−	31.1769i	−0.983445	−	1.70338i
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−9.00000			−0.490261			−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000			−0.490261			−0.245131	+	0.969490i	$0.578831\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$	5.00000			0.271563
$340$	7.50000	+	12.9904i	0.406745	+	0.704502i
$341$		0			0
$342$	−2.00000	+	3.46410i	−0.108148	+	0.187317i
$343$	−1.00000			−0.0539949
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$	−6.00000	+	10.3923i	−0.323029	+	0.559503i
$346$	14.0000			0.752645
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	0.462244	+	0.886753i	$0.347044\pi$
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	−0.999072	+	0.0430610i	$0.986289\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	−4.00000			−0.213809
$351$	−3.50000	+	0.866025i	−0.186816	+	0.0462250i
$352$	4.00000			0.213201
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	0.979202	+	0.202889i	$0.0650330\pi$
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	−0.313894	+	0.949458i	$0.601634\pi$
$354$	−4.00000	−	6.92820i	−0.212598	−	0.368230i
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$	−6.00000			−0.317999
$357$	2.50000	−	4.33013i	0.132314	−	0.229175i
$358$	−10.0000	+	17.3205i	−0.528516	+	0.915417i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	2.50000	+	4.33013i	0.131397	+	0.227586i
$363$	−5.00000			−0.262432
$364$	2.50000	+	2.59808i	0.131036	+	0.136176i
$365$	−3.00000			−0.157027
$366$	3.50000	+	6.06218i	0.182948	+	0.316875i
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	7.00000			0.364405
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$	3.50000	−	6.06218i	0.181711	−	0.314733i
$372$		0			0
$373$	−7.50000	+	12.9904i	−0.388335	+	0.672616i	−0.992226	−	0.124451i	$-0.960283\pi$
$373$	−7.50000	+	12.9904i	−0.388335	+	0.672616i	0.603890	+	0.797067i	$0.293616\pi$
$374$	10.0000	+	17.3205i	0.517088	+	0.895622i
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$	12.0000			0.618853
$377$	22.5000	+	23.3827i	1.15881	+	1.20427i
$378$	1.00000			0.0514344
$379$	14.0000	+	24.2487i	0.719132	+	1.24557i	0.961344	+	0.275349i	$0.0887935\pi$
$379$	14.0000	+	24.2487i	0.719132	+	1.24557i	−0.242213	+	0.970223i	$0.577873\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	−24.0000			−1.22795
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−12.0000			−0.611577
$386$	−9.50000	+	16.4545i	−0.483537	+	0.837511i
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−9.00000	−	15.5885i	−0.456906	−	0.791384i
$389$	7.00000			0.354914			0.177457	−	0.984129i	$-0.443213\pi$
$389$	7.00000			0.354914			0.177457	+	0.984129i	$0.443213\pi$
$390$	3.00000	−	10.3923i	0.151911	−	0.526235i
$391$	20.0000			1.01144
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	−6.00000	−	10.3923i	−0.302660	−	0.524222i
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	−48.0000			−2.41514
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$		0			0
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	8.50000	+	14.7224i	0.424470	+	0.735203i	0.996371	−	0.0851195i	$-0.0271272\pi$
$401$	8.50000	+	14.7224i	0.424470	+	0.735203i	−0.571901	+	0.820323i	$0.693794\pi$
$402$	−12.0000			−0.598506
$403$		0			0
$404$	3.00000			0.149256
$405$	−1.50000	−	2.59808i	−0.0745356	−	0.129099i
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	−14.0000	+	24.2487i	−0.693954	+	1.20196i
$408$	5.00000			0.247537
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	−0.659374	−	0.751815i	$-0.729178\pi$
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	0.980778	+	0.195127i	$0.0625118\pi$
$410$	−10.5000	+	18.1865i	−0.518558	+	0.898169i
$411$	−3.00000			−0.147979
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	−4.00000	−	6.92820i	−0.196827	−	0.340915i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$	−24.0000			−1.17811
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	−4.00000			−0.195881
$418$	−8.00000	−	13.8564i	−0.391293	−	0.677739i
$419$	8.00000	+	13.8564i	0.390826	+	0.676930i	0.992559	−	0.121768i	$-0.0388562\pi$
$419$	8.00000	+	13.8564i	0.390826	+	0.676930i	−0.601733	+	0.798697i	$0.705523\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$	4.00000	−	6.92820i	0.194717	−	0.337260i
$423$	−6.00000	+	10.3923i	−0.291730	+	0.505291i
$424$	7.00000			0.339950
$425$	10.0000	−	17.3205i	0.485071	−	0.840168i
$426$	6.00000	+	10.3923i	0.290701	+	0.503509i
$427$	3.50000	+	6.06218i	0.169377	+	0.293369i
$428$		0			0
$429$	4.00000	−	13.8564i	0.193122	−	0.668994i
$430$	24.0000			1.15738
$431$	2.00000	+	3.46410i	0.0963366	+	0.166860i	0.910166	−	0.414244i	$-0.135954\pi$
$431$	2.00000	+	3.46410i	0.0963366	+	0.166860i	−0.813829	+	0.581104i	$0.802621\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−15.5000	+	26.8468i	−0.744882	+	1.29017i	0.205367	+	0.978685i	$0.434161\pi$
$433$	−15.5000	+	26.8468i	−0.744882	+	1.29017i	−0.950250	+	0.311489i	$0.899172\pi$
$434$		0			0
$435$	−13.5000	+	23.3827i	−0.647275	+	1.12111i
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	−16.0000			−0.765384
$438$	−0.500000	+	0.866025i	−0.0238909	+	0.0413803i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−6.00000	−	10.3923i	−0.286039	−	0.495434i
$441$	1.00000			0.0476190
$442$	−17.5000	+	4.33013i	−0.832390	+	0.205963i
$443$	−16.0000			−0.760183			−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000			−0.760183			−0.380091	+	0.924949i	$0.624107\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	14.0000	−	24.2487i	0.662919	−	1.14821i
$447$	−7.00000			−0.331089
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	7.00000	−	12.1244i	0.330350	−	0.572184i	−0.652230	−	0.758021i	$-0.726166\pi$
$449$	7.00000	−	12.1244i	0.330350	−	0.572184i	0.982581	+	0.185837i	$0.0594997\pi$
$450$	4.00000			0.188562
$451$	−14.0000	+	24.2487i	−0.659234	+	1.14183i
$452$	2.50000	+	4.33013i	0.117590	+	0.203672i
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$	24.0000			1.12638
$455$	3.00000	−	10.3923i	0.140642	−	0.487199i
$456$	−4.00000			−0.187317
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	−3.00000	−	5.19615i	−0.140181	−	0.242800i
$459$	−2.50000	+	4.33013i	−0.116690	+	0.202113i
$460$	−12.0000			−0.559503
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	−0.997871	−	0.0652135i	$-0.979227\pi$
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	0.555412	+	0.831575i	$0.312560\pi$
$462$	−2.00000	+	3.46410i	−0.0930484	+	0.161165i
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	−12.0000			−0.554109
$470$	−18.0000	−	31.1769i	−0.830278	−	1.43808i
$471$	−6.50000	−	11.2583i	−0.299504	−	0.518756i
$472$	4.00000	−	6.92820i	0.184115	−	0.318896i
$473$	32.0000			1.47136
$474$	−8.00000	+	13.8564i	−0.367452	+	0.636446i
$475$	−8.00000	+	13.8564i	−0.367065	+	0.635776i
$476$	5.00000			0.229175
$477$	−3.50000	+	6.06218i	−0.160254	+	0.277568i
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$	−3.00000			−0.136931
$481$	−17.5000	−	18.1865i	−0.797931	−	0.829235i
$482$	−9.00000			−0.409939
$483$	2.00000	+	3.46410i	0.0910032	+	0.157622i
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−27.0000	+	46.7654i	−1.22601	+	2.12351i
$486$	−1.00000			−0.0453609
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$	−4.00000			−0.180886
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−10.0000	−	17.3205i	−0.451294	−	0.781664i	0.547173	−	0.837020i	$-0.315704\pi$
$491$	−10.0000	−	17.3205i	−0.451294	−	0.781664i	−0.998467	+	0.0553560i	$0.982371\pi$
$492$	3.50000	+	6.06218i	0.157792	+	0.273304i
$493$	45.0000			2.02670
$494$	14.0000	−	3.46410i	0.629890	−	0.155857i
$495$	12.0000			0.539360
$496$		0			0
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$	−4.00000	+	6.92820i	−0.179244	+	0.310460i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$	−12.0000			−0.535586
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	−0.464107	−	0.885779i	$-0.653625\pi$
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	0.999161	−	0.0409609i	$-0.0130419\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$	−4.50000	−	7.79423i	−0.200247	−	0.346839i
$506$	−16.0000			−0.711287
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$	−8.00000			−0.354943
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$	−7.50000	−	12.9904i	−0.332106	−	0.575224i
$511$	−0.500000	+	0.866025i	−0.0221187	+	0.0383107i
$512$	1.00000			0.0441942
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$	−3.50000	+	6.06218i	−0.154378	+	0.267391i
$515$	−12.0000			−0.528783
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	−24.0000	−	41.5692i	−1.05552	−	1.82821i
$518$	3.50000	+	6.06218i	0.153781	+	0.266357i
$519$	−14.0000			−0.614532
$520$	10.5000	−	2.59808i	0.460455	−	0.113933i
$521$	−17.0000			−0.744784			−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000			−0.744784			−0.372392	+	0.928076i	$0.621462\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$	4.00000			0.174574
$526$	−4.00000	+	6.92820i	−0.174408	+	0.302084i
$527$		0			0
$528$	−4.00000			−0.174078
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−10.5000	−	18.1865i	−0.456091	−	0.789973i
$531$	4.00000	+	6.92820i	0.173585	+	0.300658i
$532$	−4.00000			−0.173422
$533$	−17.5000	−	18.1865i	−0.758009	−	0.787746i
$534$	6.00000			0.259645
$535$		0			0
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	10.0000	−	17.3205i	0.431532	−	0.747435i
$538$	14.0000			0.603583
$539$	−2.00000	+	3.46410i	−0.0861461	+	0.149209i
$540$	1.50000	−	2.59808i	0.0645497	−	0.111803i
$541$	43.0000			1.84871			0.924357	−	0.381528i	$-0.124602\pi$
$541$	43.0000			1.84871			0.924357	+	0.381528i	$0.124602\pi$
$542$	−12.0000	+	20.7846i	−0.515444	+	0.892775i
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	42.0000			1.79908
$546$	−2.50000	−	2.59808i	−0.106990	−	0.111187i
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$	−3.50000	−	6.06218i	−0.149376	−	0.258727i
$550$	−8.00000	+	13.8564i	−0.341121	+	0.590839i
$551$	−36.0000			−1.53365
$552$	−2.00000	+	3.46410i	−0.0851257	+	0.147442i
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$	19.0000			0.807233
$555$	10.5000	−	18.1865i	0.445700	−	0.771975i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	0.968769	+	0.247964i	$0.0797613\pi$
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	−0.269642	+	0.962961i	$0.586905\pi$
$558$		0			0
$559$	−8.00000	+	27.7128i	−0.338364	+	1.17213i
$560$	−3.00000			−0.126773
$561$	−10.0000	−	17.3205i	−0.422200	−	0.731272i
$562$	−7.50000	−	12.9904i	−0.316368	−	0.547966i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	−12.0000			−0.505291
$565$	7.50000	−	12.9904i	0.315527	−	0.546509i
$566$	2.00000	−	3.46410i	0.0840663	−	0.145607i
$567$	−1.00000			−0.0419961
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	0.999018	−	0.0443003i	$-0.0141058\pi$
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	−0.537874	+	0.843025i	$0.680772\pi$
$570$	6.00000	+	10.3923i	0.251312	+	0.435286i
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$	14.0000	−	3.46410i	0.585369	−	0.144841i
$573$	24.0000			1.00261
$574$	3.50000	+	6.06218i	0.146087	+	0.253030i
$575$	8.00000	+	13.8564i	0.333623	+	0.577852i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−5.00000			−0.208153			−0.104076	−	0.994569i	$-0.533189\pi$
$577$	−5.00000			−0.208153			−0.104076	+	0.994569i	$0.533189\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	9.50000	−	16.4545i	0.394807	−	0.683825i
$580$	−27.0000			−1.12111
$581$	−4.00000	+	6.92820i	−0.165948	+	0.287430i
$582$	9.00000	+	15.5885i	0.373062	+	0.646162i
$583$	−14.0000	−	24.2487i	−0.579821	−	1.00428i
$584$	−1.00000			−0.0413803
$585$	−3.00000	+	10.3923i	−0.124035	+	0.429669i
$586$	−33.0000			−1.36322
$587$	12.0000	+	20.7846i	0.495293	+	0.857873i	0.999985	−	0.00542667i	$-0.00172737\pi$
$587$	12.0000	+	20.7846i	0.495293	+	0.857873i	−0.504692	+	0.863299i	$0.668394\pi$
$588$	0.500000	+	0.866025i	0.0206197	+	0.0357143i
$589$		0			0
$590$	−24.0000			−0.988064
$591$	11.0000	−	19.0526i	0.452480	−	0.783718i
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	−33.0000			−1.35515			−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000			−1.35515			−0.677574	+	0.735455i	$0.736969\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	−7.50000	−	12.9904i	−0.307470	−	0.532554i
$596$	−3.50000	−	6.06218i	−0.143366	−	0.248316i
$597$		0			0
$598$	4.00000	−	13.8564i	0.163572	−	0.566631i
$599$	−4.00000			−0.163436			−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000			−0.163436			−0.0817178	+	0.996656i	$0.526041\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	8.50000	+	14.7224i	0.346722	+	0.600541i	0.985665	−	0.168714i	$-0.0539613\pi$
$601$	8.50000	+	14.7224i	0.346722	+	0.600541i	−0.638943	+	0.769254i	$0.720628\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	12.0000			0.488678
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	−7.50000	+	12.9904i	−0.304918	+	0.528134i
$606$	−3.00000			−0.121867
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$	4.50000	+	7.79423i	0.182349	+	0.315838i
$610$	21.0000			0.850265
$611$	42.0000	−	10.3923i	1.69914	−	0.420428i
$612$	−5.00000			−0.202113
$613$	0.500000	+	0.866025i	0.0201948	+	0.0349784i	0.875946	−	0.482409i	$-0.160238\pi$
$613$	0.500000	+	0.866025i	0.0201948	+	0.0349784i	−0.855751	+	0.517387i	$0.826905\pi$
$614$	−2.00000	−	3.46410i	−0.0807134	−	0.139800i
$615$	10.5000	−	18.1865i	0.423401	−	0.733352i
$616$	−4.00000			−0.161165
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	−0.315219	−	0.949019i	$-0.602078\pi$
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	0.979484	−	0.201522i	$-0.0645887\pi$
$618$	−2.00000	+	3.46410i	−0.0804518	+	0.139347i
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	−4.00000	−	6.92820i	−0.160385	−	0.277796i
$623$	6.00000			0.240385
$624$	1.00000	−	3.46410i	0.0400320	−	0.138675i
$625$	−29.0000			−1.16000
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	8.00000	+	13.8564i	0.319489	+	0.553372i
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$	−35.0000			−1.39554
$630$	1.50000	−	2.59808i	0.0597614	−	0.103510i
$631$	20.0000	−	34.6410i	0.796187	−	1.37904i	−0.125895	−	0.992044i	$-0.540180\pi$
$631$	20.0000	−	34.6410i	0.796187	−	1.37904i	0.922082	−	0.386994i	$-0.126486\pi$
$632$	−16.0000			−0.636446
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	−17.5000	−	30.3109i	−0.695014	−	1.20380i
$635$	12.0000	+	20.7846i	0.476205	+	0.824812i
$636$	−7.00000			−0.277568
$637$	−2.50000	−	2.59808i	−0.0990536	−	0.102940i
$638$	−36.0000			−1.42525
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		0			0
$643$	−6.00000	+	10.3923i	−0.236617	+	0.409832i	−0.959741	−	0.280885i	$-0.909372\pi$
$643$	−6.00000	+	10.3923i	−0.236617	+	0.409832i	0.723124	+	0.690718i	$0.242705\pi$
$644$	−2.00000	+	3.46410i	−0.0788110	+	0.136505i
$645$	−24.0000			−0.944999
$646$	10.0000	−	17.3205i	0.393445	−	0.681466i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−32.0000			−1.25611
$650$	−10.0000	−	10.3923i	−0.392232	−	0.407620i
$651$		0			0
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	17.0000	+	29.4449i	0.665261	+	1.15227i	0.979214	+	0.202828i	$0.0650132\pi$
$653$	17.0000	+	29.4449i	0.665261	+	1.15227i	−0.313953	+	0.949439i	$0.601653\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$	−36.0000			−1.40664
$656$	−3.50000	+	6.06218i	−0.136652	+	0.236688i
$657$	0.500000	−	0.866025i	0.0195069	−	0.0337869i
$658$	−12.0000			−0.467809
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	6.00000	+	10.3923i	0.233550	+	0.404520i
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	0.875585	−	0.483063i	$-0.160476\pi$
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	−0.856138	+	0.516748i	$0.827143\pi$
$662$	−20.0000			−0.777322
$663$	17.5000	−	4.33013i	0.679644	−	0.168168i
$664$	−8.00000			−0.310460
$665$	6.00000	+	10.3923i	0.232670	+	0.402996i
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	−18.0000	+	31.1769i	−0.696963	+	1.20717i
$668$	−8.00000			−0.309529
$669$	−14.0000	+	24.2487i	−0.541271	+	0.937509i
$670$	−18.0000	+	31.1769i	−0.695401	+	1.20447i
$671$	28.0000			1.08093
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	0.622770	−	0.782405i	$-0.286007\pi$
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	−0.988968	+	0.148132i	$0.952674\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$	−4.00000			−0.153960
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$	−2.50000	−	4.33013i	−0.0960119	−	0.166298i
$679$	9.00000	+	15.5885i	0.345388	+	0.598230i
$680$	7.50000	−	12.9904i	0.287612	−	0.498158i
$681$	−24.0000			−0.919682
$682$		0			0
$683$	−10.0000	+	17.3205i	−0.382639	+	0.662751i	−0.991439	−	0.130573i	$-0.958318\pi$
$683$	−10.0000	+	17.3205i	−0.382639	+	0.662751i	0.608799	+	0.793324i	$0.291651\pi$
$684$	4.00000			0.152944
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	3.00000	+	5.19615i	0.114457	+	0.198246i
$688$	8.00000			0.304997
$689$	24.5000	−	6.06218i	0.933376	−	0.230951i
$690$	12.0000			0.456832
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	0.942420	+	0.334431i	$0.108544\pi$
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	−0.181584	+	0.983375i	$0.558123\pi$
$692$	−7.00000	−	12.1244i	−0.266100	−	0.460899i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$	20.0000			0.759190
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$	−4.50000	+	7.79423i	−0.170572	+	0.295439i
$697$	−35.0000			−1.32572
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	2.50000	+	2.59808i	0.0943564	+	0.0980581i
$703$	28.0000			1.05604
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$	18.0000	+	31.1769i	0.677919	+	1.17419i
$706$	12.5000	−	21.6506i	0.470444	−	0.814832i
$707$	−3.00000			−0.112827
$708$	−4.00000	+	6.92820i	−0.150329	+	0.260378i
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	−0.856484	−	0.516174i	$-0.827356\pi$
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	0.875262	+	0.483650i	$0.160689\pi$
$710$	36.0000			1.35106
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$		0			0
$714$	−5.00000			−0.187120
$715$	−30.0000	−	31.1769i	−1.12194	−	1.16595i
$716$	20.0000			0.747435
$717$	−2.00000	−	3.46410i	−0.0746914	−	0.129369i
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$	3.00000			0.111803
$721$	−2.00000	+	3.46410i	−0.0744839	+	0.129010i
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$	9.00000			0.334714
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$	2.50000	+	4.33013i	0.0927837	+	0.160706i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	1.00000	−	3.46410i	0.0370625	−	0.128388i
$729$	1.00000			0.0370370
$730$	1.50000	+	2.59808i	0.0555175	+	0.0961591i
$731$	20.0000	+	34.6410i	0.739727	+	1.28124i
$732$	3.50000	−	6.06218i	0.129364	−	0.224065i
$733$	23.0000			0.849524			0.424762	−	0.905305i	$-0.360358\pi$
$733$	23.0000			0.849524			0.424762	+	0.905305i	$0.360358\pi$
$734$	2.00000	−	3.46410i	0.0738213	−	0.127862i
$735$	1.50000	−	2.59808i	0.0553283	−	0.0958315i
$736$	−4.00000			−0.147442
$737$	−24.0000	+	41.5692i	−0.884051	+	1.53122i
$738$	−3.50000	−	6.06218i	−0.128837	−	0.223152i
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	0.783028	−	0.621987i	$-0.213674\pi$
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	−0.930170	+	0.367129i	$0.880341\pi$
$740$	21.0000			0.771975
$741$	−14.0000	+	3.46410i	−0.514303	+	0.127257i
$742$	−7.00000			−0.256978
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	0.681141	−	0.732152i	$-0.261484\pi$
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	−0.974633	+	0.223810i	$0.928151\pi$
$744$		0			0
$745$	−10.5000	+	18.1865i	−0.384690	+	0.666303i
$746$	15.0000			0.549189
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$	10.0000	−	17.3205i	0.365636	−	0.633300i
$749$		0			0
$750$	−1.50000	+	2.59808i	−0.0547723	+	0.0948683i
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$	12.0000			0.437304
$754$	9.00000	−	31.1769i	0.327761	−	1.13540i
$755$	−24.0000			−0.873449
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$	16.0000			0.580763
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	−0.942306	−	0.334752i	$-0.891348\pi$
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	0.761057	+	0.648686i	$0.224681\pi$
$762$	8.00000			0.289809
$763$	7.00000	−	12.1244i	0.253417	−	0.438931i
$764$	12.0000	+	20.7846i	0.434145	+	0.751961i
$765$	7.50000	+	12.9904i	0.271163	+	0.469668i
$766$	−28.0000			−1.01168
$767$	8.00000	−	27.7128i	0.288863	−	1.00065i
$768$	−1.00000			−0.0360844
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.0760054	−	0.997107i	$-0.524217\pi$
$770$	6.00000	+	10.3923i	0.216225	+	0.374513i
$771$	3.50000	−	6.06218i	0.126049	−	0.218324i
$772$	19.0000			0.683825
$773$	−19.0000	+	32.9090i	−0.683383	+	1.18365i	0.290560	+	0.956857i	$0.406159\pi$
$773$	−19.0000	+	32.9090i	−0.683383	+	1.18365i	−0.973942	+	0.226796i	$0.927175\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$		0			0
$776$	−9.00000	+	15.5885i	−0.323081	+	0.559593i
$777$	−3.50000	−	6.06218i	−0.125562	−	0.217479i
$778$	−3.50000	−	6.06218i	−0.125481	−	0.217340i
$779$	28.0000			1.00320
$780$	−10.5000	+	2.59808i	−0.375960	+	0.0930261i
$781$	48.0000			1.71758
$782$	−10.0000	−	17.3205i	−0.357599	−	0.619380i
$783$	−4.50000	−	7.79423i	−0.160817	−	0.278543i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−39.0000			−1.39197
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	−0.250832	−	0.968031i	$-0.580704\pi$
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	0.963755	−	0.266788i	$-0.0859624\pi$
$788$	22.0000			0.783718
$789$	4.00000	−	6.92820i	0.142404	−	0.246651i
$790$	24.0000	+	41.5692i	0.853882	+	1.47897i
$791$	−2.50000	−	4.33013i	−0.0888898	−	0.153962i
$792$	4.00000			0.142134
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$	−2.00000			−0.0709773
$795$	10.5000	+	18.1865i	0.372397	+	0.645010i
$796$		0			0
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$	4.00000			0.141598
$799$	30.0000	−	51.9615i	1.06132	−	1.83827i
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	−6.00000			−0.212000
$802$	8.50000	−	14.7224i	0.300145	−	0.519867i
$803$	2.00000	+	3.46410i	0.0705785	+	0.122245i
$804$	6.00000	+	10.3923i	0.211604	+	0.366508i
$805$	12.0000			0.422944
$806$		0			0
$807$	−14.0000			−0.492823
$808$	−1.50000	−	2.59808i	−0.0527698	−	0.0914000i
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	0.906621	−	0.421945i	$-0.138653\pi$
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	−0.818726	+	0.574184i	$0.805319\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	−4.50000	+	7.79423i	−0.157919	+	0.273524i
$813$	12.0000	−	20.7846i	0.420858	−	0.728948i
$814$	28.0000			0.981399
$815$	−6.00000	+	10.3923i	−0.210171	+	0.364027i
$816$	−2.50000	−	4.33013i	−0.0875175	−	0.151585i
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	−13.0000			−0.454534
$819$	2.50000	+	2.59808i	0.0873571	+	0.0907841i
$820$	21.0000			0.733352
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$	1.50000	+	2.59808i	0.0523185	+	0.0906183i
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	−0.172379	−	0.985031i	$-0.555146\pi$
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	0.939251	−	0.343230i	$-0.111521\pi$
$824$	−4.00000			−0.139347
$825$	8.00000	−	13.8564i	0.278524	−	0.482418i
$826$	−4.00000	+	6.92820i	−0.139178	+	0.241063i
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	−15.5000	−	26.8468i	−0.538337	−	0.932427i	−0.998994	−	0.0448490i	$-0.985719\pi$
$829$	−15.5000	−	26.8468i	−0.538337	−	0.932427i	0.460657	−	0.887578i	$-0.347614\pi$
$830$	12.0000	+	20.7846i	0.416526	+	0.721444i
$831$	−19.0000			−0.659103
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−5.00000			−0.173240
$834$	2.00000	+	3.46410i	0.0692543	+	0.119952i
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	−8.00000	+	13.8564i	−0.276686	+	0.479234i
$837$		0			0
$838$	8.00000	−	13.8564i	0.276355	−	0.478662i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$	3.00000			0.103510
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	0.500000	+	0.866025i	0.0172311	+	0.0298452i
$843$	7.50000	+	12.9904i	0.258314	+	0.447412i
$844$	−8.00000			−0.275371
$845$	34.5000	−	18.1865i	1.18684	−	0.625636i
$846$	12.0000			0.412568
$847$	2.50000	+	4.33013i	0.0859010	+	0.148785i
$848$	−3.50000	−	6.06218i	−0.120190	−	0.208176i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$	−20.0000			−0.685994
$851$	14.0000	−	24.2487i	0.479914	−	0.831235i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	3.50000	−	6.06218i	0.119768	−	0.207443i
$855$	−6.00000	−	10.3923i	−0.205196	−	0.355409i
$856$		0			0
$857$	31.0000			1.05894			0.529470	−	0.848329i	$-0.322391\pi$
$857$	31.0000			1.05894			0.529470	+	0.848329i	$0.322391\pi$
$858$	−14.0000	+	3.46410i	−0.477952	+	0.118262i
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−12.0000	−	20.7846i	−0.409197	−	0.708749i
$861$	−3.50000	−	6.06218i	−0.119280	−	0.206598i
$862$	2.00000	−	3.46410i	0.0681203	−	0.117988i
$863$	12.0000			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−21.0000	+	36.3731i	−0.714021	+	1.23672i
$866$	31.0000			1.05342
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$		0			0
$869$	32.0000	+	55.4256i	1.08553	+	1.88019i
$870$	27.0000			0.915386
$871$	−30.0000	−	31.1769i	−1.01651	−	1.05639i
$872$	14.0000			0.474100
$873$	−9.00000	−	15.5885i	−0.304604	−	0.527589i
$874$	8.00000	+	13.8564i	0.270604	+	0.468700i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$	1.00000			0.0337869
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	−0.890239	−	0.455493i	$-0.849463\pi$
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	0.839588	+	0.543224i	$0.182796\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$	33.0000			1.11306
$880$	−6.00000	+	10.3923i	−0.202260	+	0.350325i
$881$	20.5000	+	35.5070i	0.690663	+	1.19626i	0.971621	+	0.236543i	$0.0760143\pi$
$881$	20.5000	+	35.5070i	0.690663	+	1.19626i	−0.280959	+	0.959720i	$0.590652\pi$
$882$	−0.500000	−	0.866025i	−0.0168359	−	0.0291606i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	12.5000	+	12.9904i	0.420420	+	0.436914i
$885$	24.0000			0.806751
$886$	8.00000	+	13.8564i	0.268765	+	0.465515i
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$	3.50000	−	6.06218i	0.117452	−	0.203433i
$889$	8.00000			0.268311
$890$	9.00000	−	15.5885i	0.301681	−	0.522526i
$891$	−2.00000	+	3.46410i	−0.0670025	+	0.116052i
$892$	−28.0000			−0.937509
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$	3.50000	+	6.06218i	0.117058	+	0.202750i
$895$	−30.0000	−	51.9615i	−1.00279	−	1.73688i
$896$	−1.00000			−0.0334077
$897$	−4.00000	+	13.8564i	−0.133556	+	0.462652i
$898$	−14.0000			−0.467186
$899$		0			0
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	17.5000	−	30.3109i	0.583010	−	1.00980i
$902$	28.0000			0.932298
$903$	−4.00000	+	6.92820i	−0.133112	+	0.230556i
$904$	2.50000	−	4.33013i	0.0831488	−	0.144018i
$905$	−15.0000			−0.498617
$906$	−4.00000	+	6.92820i	−0.132891	+	0.230174i
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	3.00000			0.0995037
$910$	−10.5000	+	2.59808i	−0.348072	+	0.0861254i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	16.0000	+	27.7128i	0.529523	+	0.917160i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$	−21.0000			−0.694239
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$	−6.00000	+	10.3923i	−0.198137	+	0.343184i
$918$	5.00000			0.165025
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$	6.00000	+	10.3923i	0.197814	+	0.342624i
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	19.0000			0.625732
$923$	−12.0000	+	41.5692i	−0.394985	+	1.36827i
$924$	4.00000			0.131590
$925$	−14.0000	−	24.2487i	−0.460317	−	0.797293i
$926$	−16.0000	−	27.7128i	−0.525793	−	0.910700i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	−9.00000			−0.295439
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$		0			0
$931$	4.00000			0.131095
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	4.00000	+	6.92820i	0.130954	+	0.226819i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	−60.0000			−1.96221
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$	−49.0000			−1.60076			−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000			−1.60076			−0.800380	+	0.599493i	$0.795369\pi$
$938$	6.00000	+	10.3923i	0.195907	+	0.339321i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$	−18.0000	+	31.1769i	−0.587095	+	1.01688i
$941$	−50.0000			−1.62995			−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000			−1.62995			−0.814977	+	0.579494i	$0.803250\pi$
$942$	−6.50000	+	11.2583i	−0.211781	+	0.366816i
$943$	14.0000	−	24.2487i	0.455903	−	0.789647i
$944$	−8.00000			−0.260378
$945$	−1.50000	+	2.59808i	−0.0487950	+	0.0845154i
$946$	−16.0000	−	27.7128i	−0.520205	−	0.901021i
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	0.831699	−	0.555227i	$-0.187369\pi$
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	−0.896690	+	0.442659i	$0.854035\pi$
$948$	16.0000			0.519656
$949$	−3.50000	+	0.866025i	−0.113615	+	0.0281124i
$950$	16.0000			0.519109
$951$	17.5000	+	30.3109i	0.567476	+	0.982898i
$952$	−2.50000	−	4.33013i	−0.0810255	−	0.140340i
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$	7.00000			0.226633
$955$	36.0000	−	62.3538i	1.16493	−	2.01772i
$956$	2.00000	−	3.46410i	0.0646846	−	0.112037i
$957$	36.0000			1.16371
$958$	−14.0000	+	24.2487i	−0.452319	+	0.783440i
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$	1.50000	+	2.59808i	0.0484123	+	0.0838525i
$961$	−31.0000			−1.00000
$962$	−7.00000	+	24.2487i	−0.225689	+	0.781810i
$963$		0			0
$964$	4.50000	+	7.79423i	0.144935	+	0.251035i
$965$	−28.5000	−	49.3634i	−0.917447	−	1.58907i
$966$	2.00000	−	3.46410i	0.0643489	−	0.111456i
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	−10.0000	+	17.3205i	−0.321246	+	0.556415i
$970$	54.0000			1.73384
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	2.00000	+	3.46410i	0.0641171	+	0.111054i
$974$	4.00000			0.128168
$975$	10.0000	+	10.3923i	0.320256	+	0.332820i
$976$	7.00000			0.224065
$977$	−23.5000	−	40.7032i	−0.751832	−	1.30221i	−0.946934	−	0.321428i	$-0.895837\pi$
$977$	−23.5000	−	40.7032i	−0.751832	−	1.30221i	0.195103	−	0.980783i	$-0.437496\pi$
$978$	2.00000	+	3.46410i	0.0639529	+	0.110770i
$979$	12.0000	−	20.7846i	0.383522	−	0.664279i
$980$	3.00000			0.0958315
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	−10.0000	+	17.3205i	−0.319113	+	0.552720i
$983$	−28.0000			−0.893061			−0.446531	−	0.894768i	$-0.647341\pi$
$983$	−28.0000			−0.893061			−0.446531	+	0.894768i	$0.647341\pi$
$984$	3.50000	−	6.06218i	0.111576	−	0.193255i
$985$	−33.0000	−	57.1577i	−1.05147	−	1.82120i
$986$	−22.5000	−	38.9711i	−0.716546	−	1.24109i
$987$	12.0000			0.381964
$988$	−10.0000	−	10.3923i	−0.318142	−	0.330623i
$989$	−32.0000			−1.01754
$990$	−6.00000	−	10.3923i	−0.190693	−	0.330289i
$991$	16.0000	+	27.7128i	0.508257	+	0.880327i	0.999954	+	0.00956046i	$0.00304324\pi$
$991$	16.0000	+	27.7128i	0.508257	+	0.880327i	−0.491698	+	0.870766i	$0.663623\pi$
$992$		0			0
$993$	20.0000			0.634681
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$		0			0
$996$	8.00000			0.253490
$997$	−19.5000	+	33.7750i	−0.617571	+	1.06966i	0.372356	+	0.928090i	$0.378550\pi$
$997$	−19.5000	+	33.7750i	−0.617571	+	1.06966i	−0.989928	+	0.141575i	$0.954783\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.b.211.1	✓	2
3.2	odd	2		1638.2.r.o.757.1		2
13.3	even	3		7098.2.a.v.1.1		1
13.9	even	3	inner	546.2.l.b.295.1	yes	2
13.10	even	6		7098.2.a.a.1.1		1
39.35	odd	6		1638.2.r.o.1387.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.b.211.1	✓	2	1.1	even	1	trivial
546.2.l.b.295.1	yes	2	13.9	even	3	inner
1638.2.r.o.757.1		2	3.2	odd	2
1638.2.r.o.1387.1		2	39.35	odd	6
7098.2.a.a.1.1		1	13.10	even	6
7098.2.a.v.1.1		1	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-2.00000 - 3.46410i) q^{11} -1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +1.00000 q^{18} +(-2.00000 + 3.46410i) q^{19} +(-1.50000 + 2.59808i) q^{20} +1.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +(1.50000 - 2.59808i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -5.00000 q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +3.00000 q^{40} +(-3.50000 - 6.06218i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +4.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.00000 - 3.46410i) q^{46} +12.0000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +5.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +7.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-6.00000 - 10.3923i) q^{55} +(0.500000 - 0.866025i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} -3.00000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(10.5000 - 2.59808i) q^{65} -4.00000 q^{66} +(-6.00000 - 10.3923i) q^{67} +(2.50000 + 4.33013i) q^{68} +(-2.00000 + 3.46410i) q^{69} -3.00000 q^{70} +(-6.00000 + 10.3923i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.00000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-2.00000 - 3.46410i) q^{76} -4.00000 q^{77} +(1.00000 - 3.46410i) q^{78} -16.0000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.50000 + 6.06218i) q^{82} -8.00000 q^{83} +(-0.500000 + 0.866025i) q^{84} +(7.50000 - 12.9904i) q^{85} +8.00000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(1.00000 - 3.46410i) q^{91} -4.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000 q^{96} +(-9.00000 + 15.5885i) q^{97} +(-0.500000 + 0.866025i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 + q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + 6 q^{5} + q^{6} + q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 4 q^{11} - 2 q^{12} + 7 q^{13} - 2 q^{14} + 3 q^{15} - q^{16} + 5 q^{17} + 2 q^{18} - 4 q^{19} - 3 q^{20} + 2 q^{21} - 4 q^{22} + 4 q^{23} + q^{24} + 8 q^{25} - 5 q^{26} - 2 q^{27} + q^{28} + 9 q^{29} + 3 q^{30} - q^{32} + 4 q^{33} - 10 q^{34} + 3 q^{35} - q^{36} - 7 q^{37} + 8 q^{38} + 5 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} - 8 q^{43} + 8 q^{44} - 3 q^{45} + 4 q^{46} + 24 q^{47} + q^{48} - q^{49} - 4 q^{50} + 10 q^{51} - 2 q^{52} + 14 q^{53} + q^{54} - 12 q^{55} + q^{56} - 8 q^{57} + 9 q^{58} + 8 q^{59} - 6 q^{60} - 7 q^{61} + q^{63} + 2 q^{64} + 21 q^{65} - 8 q^{66} - 12 q^{67} + 5 q^{68} - 4 q^{69} - 6 q^{70} - 12 q^{71} - q^{72} - 2 q^{73} - 7 q^{74} + 4 q^{75} - 4 q^{76} - 8 q^{77} + 2 q^{78} - 32 q^{79} - 3 q^{80} - q^{81} - 7 q^{82} - 16 q^{83} - q^{84} + 15 q^{85} + 16 q^{86} - 9 q^{87} - 4 q^{88} + 6 q^{89} + 6 q^{90} + 2 q^{91} - 8 q^{92} - 12 q^{94} - 12 q^{95} - 2 q^{96} - 18 q^{97} - q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + 6 * q^5 + q^6 + q^7 + 2 * q^8 - q^9 - 3 * q^10 - 4 * q^11 - 2 * q^12 + 7 * q^13 - 2 * q^14 + 3 * q^15 - q^16 + 5 * q^17 + 2 * q^18 - 4 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 4 * q^23 + q^24 + 8 * q^25 - 5 * q^26 - 2 * q^27 + q^28 + 9 * q^29 + 3 * q^30 - q^32 + 4 * q^33 - 10 * q^34 + 3 * q^35 - q^36 - 7 * q^37 + 8 * q^38 + 5 * q^39 + 6 * q^40 - 7 * q^41 - q^42 - 8 * q^43 + 8 * q^44 - 3 * q^45 + 4 * q^46 + 24 * q^47 + q^48 - q^49 - 4 * q^50 + 10 * q^51 - 2 * q^52 + 14 * q^53 + q^54 - 12 * q^55 + q^56 - 8 * q^57 + 9 * q^58 + 8 * q^59 - 6 * q^60 - 7 * q^61 + q^63 + 2 * q^64 + 21 * q^65 - 8 * q^66 - 12 * q^67 + 5 * q^68 - 4 * q^69 - 6 * q^70 - 12 * q^71 - q^72 - 2 * q^73 - 7 * q^74 + 4 * q^75 - 4 * q^76 - 8 * q^77 + 2 * q^78 - 32 * q^79 - 3 * q^80 - q^81 - 7 * q^82 - 16 * q^83 - q^84 + 15 * q^85 + 16 * q^86 - 9 * q^87 - 4 * q^88 + 6 * q^89 + 6 * q^90 + 2 * q^91 - 8 * q^92 - 12 * q^94 - 12 * q^95 - 2 * q^96 - 18 * q^97 - q^98 + 8 * q^99

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