LMFDB - Embedded newform 546.2.l.f.295.1

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			295.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.f.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} -1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} -1.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} -1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} +(1.00000 + 1.73205i) q^{20} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} -1.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 - 1.73205i) q^{37} -6.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +2.00000 q^{40} +(5.00000 - 8.66025i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.50000 - 2.59808i) q^{43} +(1.00000 + 1.73205i) q^{45} +(1.50000 + 2.59808i) q^{46} +6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} -1.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +7.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{56} -6.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(3.50000 + 6.06218i) q^{59} +2.00000 q^{60} +(-5.50000 - 9.52628i) q^{61} +(2.50000 - 4.33013i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(5.00000 + 5.19615i) q^{65} +(6.50000 - 11.2583i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(1.50000 + 2.59808i) q^{69} +2.00000 q^{70} +(1.50000 + 2.59808i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-3.00000 + 5.19615i) q^{76} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.00000 - 8.66025i) q^{82} -15.0000 q^{83} +(0.500000 + 0.866025i) q^{84} +(1.00000 + 1.73205i) q^{85} -3.00000 q^{86} +(3.00000 + 5.19615i) q^{87} +(5.50000 - 9.52628i) q^{89} +2.00000 q^{90} +(-1.00000 + 3.46410i) q^{91} +3.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +1.00000 q^{96} +(-6.00000 - 10.3923i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - 4 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - 4 * q^5 - q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} - 4 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} - 5 q^{13} - 2 q^{14} - 2 q^{15} - q^{16} - q^{17} - 2 q^{18} - 6 q^{19} + 2 q^{20} - 2 q^{21} - 3 q^{23} - q^{24} - 2 q^{25} - 7 q^{26} - 2 q^{27} - q^{28} - 6 q^{29} + 2 q^{30} + 10 q^{31} + q^{32} - 2 q^{34} + 2 q^{35} - q^{36} + 2 q^{37} - 12 q^{38} - 7 q^{39} + 4 q^{40} + 10 q^{41} - q^{42} - 3 q^{43} + 2 q^{45} + 3 q^{46} + 12 q^{47} + q^{48} - q^{49} - q^{50} - 2 q^{51} - 2 q^{52} + 14 q^{53} - q^{54} + q^{56} - 12 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 11 q^{61} + 5 q^{62} - q^{63} + 2 q^{64} + 10 q^{65} + 13 q^{67} - q^{68} + 3 q^{69} + 4 q^{70} + 3 q^{71} + q^{72} + 24 q^{73} - 2 q^{74} - q^{75} - 6 q^{76} - 2 q^{78} - 8 q^{79} + 2 q^{80} - q^{81} - 10 q^{82} - 30 q^{83} + q^{84} + 2 q^{85} - 6 q^{86} + 6 q^{87} + 11 q^{89} + 4 q^{90} - 2 q^{91} + 6 q^{92} + 5 q^{93} + 6 q^{94} + 12 q^{95} + 2 q^{96} - 12 q^{97} + q^{98}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - 4 * q^5 - q^6 - q^7 - 2 * q^8 - q^9 - 2 * q^10 - 2 * q^12 - 5 * q^13 - 2 * q^14 - 2 * q^15 - q^16 - q^17 - 2 * q^18 - 6 * q^19 + 2 * q^20 - 2 * q^21 - 3 * q^23 - q^24 - 2 * q^25 - 7 * q^26 - 2 * q^27 - q^28 - 6 * q^29 + 2 * q^30 + 10 * q^31 + q^32 - 2 * q^34 + 2 * q^35 - q^36 + 2 * q^37 - 12 * q^38 - 7 * q^39 + 4 * q^40 + 10 * q^41 - q^42 - 3 * q^43 + 2 * q^45 + 3 * q^46 + 12 * q^47 + q^48 - q^49 - q^50 - 2 * q^51 - 2 * q^52 + 14 * q^53 - q^54 + q^56 - 12 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 11 * q^61 + 5 * q^62 - q^63 + 2 * q^64 + 10 * q^65 + 13 * q^67 - q^68 + 3 * q^69 + 4 * q^70 + 3 * q^71 + q^72 + 24 * q^73 - 2 * q^74 - q^75 - 6 * q^76 - 2 * q^78 - 8 * q^79 + 2 * q^80 - q^81 - 10 * q^82 - 30 * q^83 + q^84 + 2 * q^85 - 6 * q^86 + 6 * q^87 + 11 * q^89 + 4 * q^90 - 2 * q^91 + 6 * q^92 + 5 * q^93 + 6 * q^94 + 12 * q^95 + 2 * q^96 - 12 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	−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
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−1.00000			−0.288675
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	−1.00000			−0.267261
$15$	−1.00000	+	1.73205i	−0.258199	+	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.00000			−0.200000
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$	−1.00000			−0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	1.00000	+	1.73205i	0.182574	+	0.316228i
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.00000			−0.171499
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−6.00000			−0.973329
$39$	−3.50000	+	0.866025i	−0.560449	+	0.138675i
$40$	2.00000			0.316228
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	−0.150567	−	0.988600i	$-0.548110\pi$
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	0.931436	−	0.363905i	$-0.118557\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−1.50000	−	2.59808i	−0.228748	−	0.396203i	0.728689	−	0.684844i	$-0.240130\pi$
$43$	−1.50000	−	2.59808i	−0.228748	−	0.396203i	−0.957437	+	0.288641i	$0.906796\pi$
$44$		0			0
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−1.00000			−0.140028
$52$	−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
$55$		0			0
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−6.00000			−0.794719
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$	2.00000			0.258199
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$	2.50000	−	4.33013i	0.317500	−	0.549927i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	5.00000	+	5.19615i	0.620174	+	0.644503i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	−0.500000	+	0.866025i	−0.0606339	+	0.105021i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$	2.00000			0.239046
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$		0			0
$78$	−1.00000	+	3.46410i	−0.113228	+	0.392232i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.00000	−	8.66025i	−0.552158	−	0.956365i
$83$	−15.0000			−1.64646			−0.823232	−	0.567705i	$-0.807831\pi$
$83$	−15.0000			−1.64646			−0.823232	+	0.567705i	$0.807831\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$	−3.00000			−0.323498
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	5.50000	−	9.52628i	0.582999	−	1.00978i	−0.412123	−	0.911128i	$-0.635213\pi$
$89$	5.50000	−	9.52628i	0.582999	−	1.00978i	0.995122	−	0.0986553i	$-0.0314541\pi$
$90$	2.00000			0.210819
$91$	−1.00000	+	3.46410i	−0.104828	+	0.363137i
$92$	3.00000			0.312772
$93$	2.50000	−	4.33013i	0.259238	−	0.449013i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$	1.00000			0.102062
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	−0.991371	−	0.131084i	$-0.958154\pi$
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	0.382164	−	0.924095i	$-0.375179\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	−0.948207	−	0.317653i	$-0.897105\pi$
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	0.749199	+	0.662344i	$0.230438\pi$
$102$	−0.500000	+	0.866025i	−0.0495074	+	0.0857493i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$	2.00000			0.195180
$106$	3.50000	−	6.06218i	0.339950	−	0.588811i
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$		0			0
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	1.00000			0.0944911
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	6.00000			0.557086
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	7.00000			0.644402
$119$	−0.500000	+	0.866025i	−0.0458349	+	0.0793884i
$120$	1.00000	−	1.73205i	0.0912871	−	0.158114i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−11.0000			−0.995893
$123$	−5.00000	−	8.66025i	−0.450835	−	0.780869i
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$	12.0000			1.07331
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	2.00000	−	3.46410i	0.177471	−	0.307389i	−0.763542	−	0.645758i	$-0.776542\pi$
$127$	2.00000	−	3.46410i	0.177471	−	0.307389i	0.941014	+	0.338368i	$0.109875\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.00000			−0.264135
$130$	7.00000	−	1.73205i	0.613941	−	0.151911i
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$	−3.00000	+	5.19615i	−0.260133	+	0.450564i
$134$	−6.50000	−	11.2583i	−0.561514	−	0.972572i
$135$	2.00000			0.172133
$136$	0.500000	+	0.866025i	0.0428746	+	0.0742611i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	3.00000			0.255377
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	3.00000			0.251754
$143$		0			0
$144$	1.00000			0.0833333
$145$	6.00000	−	10.3923i	0.498273	−	0.863034i
$146$	6.00000	−	10.3923i	0.496564	−	0.860073i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	−2.00000			−0.164399
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	−0.500000	+	0.866025i	−0.0404226	+	0.0700140i
$154$		0			0
$155$	−10.0000			−0.803219
$156$	2.50000	+	2.59808i	0.200160	+	0.208013i
$157$	22.0000			1.75579			0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000			1.75579			0.877896	+	0.478852i	$0.158947\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	3.50000	−	6.06218i	0.277568	−	0.480762i
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	3.00000			0.236433
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−2.50000	−	4.33013i	−0.195815	−	0.339162i	0.751352	−	0.659901i	$-0.229402\pi$
$163$	−2.50000	−	4.33013i	−0.195815	−	0.339162i	−0.947167	+	0.320740i	$0.896069\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	−7.50000	+	12.9904i	−0.582113	+	1.00825i
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$	1.00000			0.0771517
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	2.00000			0.153393
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	−1.50000	+	2.59808i	−0.114374	+	0.198101i
$173$	−2.00000	−	3.46410i	−0.152057	−	0.263371i	0.779926	−	0.625871i	$-0.215256\pi$
$173$	−2.00000	−	3.46410i	−0.152057	−	0.263371i	−0.931984	+	0.362500i	$0.881923\pi$
$174$	6.00000			0.454859
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$		0			0
$177$	7.00000			0.526152
$178$	−5.50000	−	9.52628i	−0.412242	−	0.714025i
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$	2.50000	+	2.59808i	0.185312	+	0.192582i
$183$	−11.0000			−0.813143
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	−2.50000	−	4.33013i	−0.183309	−	0.317500i
$187$		0			0
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	12.0000			0.870572
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	0.981635	−	0.190767i	$-0.0610975\pi$
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	−0.656027	+	0.754738i	$0.727764\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	−12.0000			−0.861550
$195$	7.00000	−	1.73205i	0.501280	−	0.124035i
$196$	1.00000			0.0714286
$197$	6.50000	−	11.2583i	0.463106	−	0.802123i	−0.536008	−	0.844213i	$-0.680068\pi$
$197$	6.50000	−	11.2583i	0.463106	−	0.802123i	0.999114	+	0.0420901i	$0.0134016\pi$
$198$		0			0
$199$	−4.50000	−	7.79423i	−0.318997	−	0.552518i	0.661282	−	0.750137i	$-0.270013\pi$
$199$	−4.50000	−	7.79423i	−0.318997	−	0.552518i	−0.980279	+	0.197619i	$0.936679\pi$
$200$	1.00000			0.0707107
$201$	−6.50000	−	11.2583i	−0.458475	−	0.794101i
$202$	2.00000	+	3.46410i	0.140720	+	0.243733i
$203$	6.00000			0.421117
$204$	0.500000	+	0.866025i	0.0350070	+	0.0606339i
$205$	−10.0000	+	17.3205i	−0.698430	+	1.20972i
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$	3.00000			0.208514
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$		0			0
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.50000	−	6.06218i	−0.240381	−	0.416352i
$213$	3.00000			0.205557
$214$	1.00000	+	1.73205i	0.0683586	+	0.118401i
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$	1.00000			0.0680414
$217$	−2.50000	−	4.33013i	−0.169711	−	0.293948i
$218$	2.00000	−	3.46410i	0.135457	−	0.234619i
$219$	6.00000	−	10.3923i	0.405442	−	0.702247i
$220$		0			0
$221$	−1.00000	+	3.46410i	−0.0672673	+	0.233021i
$222$	−2.00000			−0.134231
$223$	3.50000	−	6.06218i	0.234377	−	0.405953i	−0.724714	−	0.689050i	$-0.758028\pi$
$223$	3.50000	−	6.06218i	0.234377	−	0.405953i	0.959092	+	0.283096i	$0.0913615\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−12.0000			−0.798228
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$	3.00000	+	5.19615i	0.198680	+	0.344124i
$229$	−17.0000			−1.12339			−0.561696	−	0.827344i	$-0.689851\pi$
$229$	−17.0000			−1.12339			−0.561696	+	0.827344i	$0.689851\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−8.00000			−0.524097			−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000			−0.524097			−0.262049	+	0.965055i	$0.584398\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$	−12.0000			−0.782794
$236$	3.50000	−	6.06218i	0.227831	−	0.394614i
$237$	−2.00000	+	3.46410i	−0.129914	+	0.225018i
$238$	0.500000	+	0.866025i	0.0324102	+	0.0561361i
$239$	−29.0000			−1.87585			−0.937927	−	0.346833i	$-0.887257\pi$
$239$	−29.0000			−1.87585			−0.937927	+	0.346833i	$0.887257\pi$
$240$	−1.00000	−	1.73205i	−0.0645497	−	0.111803i
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	0.995509	+	0.0946700i	$0.0301796\pi$
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	11.0000			0.707107
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.50000	+	9.52628i	−0.352101	+	0.609858i
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	−10.0000			−0.637577
$247$	−6.00000	+	20.7846i	−0.381771	+	1.32249i
$248$	−5.00000			−0.317500
$249$	−7.50000	+	12.9904i	−0.475293	+	0.823232i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	3.50000	+	6.06218i	0.220918	+	0.382641i	0.955087	−	0.296326i	$-0.0957613\pi$
$251$	3.50000	+	6.06218i	0.220918	+	0.382641i	−0.734169	+	0.678967i	$0.762428\pi$
$252$	1.00000			0.0629941
$253$		0			0
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$	2.00000			0.125245
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.50000	−	9.52628i	0.343081	−	0.594233i	−0.641923	−	0.766769i	$-0.721863\pi$
$257$	5.50000	−	9.52628i	0.343081	−	0.594233i	0.985003	+	0.172536i	$0.0551963\pi$
$258$	−1.50000	+	2.59808i	−0.0933859	+	0.161749i
$259$	−2.00000			−0.124274
$260$	2.00000	−	6.92820i	0.124035	−	0.429669i
$261$	6.00000			0.371391
$262$	−7.50000	+	12.9904i	−0.463352	+	0.802548i
$263$	−14.0000	+	24.2487i	−0.863277	+	1.49524i	0.00547092	+	0.999985i	$0.498259\pi$
$263$	−14.0000	+	24.2487i	−0.863277	+	1.49524i	−0.868748	+	0.495255i	$0.835075\pi$
$264$		0			0
$265$	−14.0000			−0.860013
$266$	3.00000	+	5.19615i	0.183942	+	0.318597i
$267$	−5.50000	−	9.52628i	−0.336595	−	0.582999i
$268$	−13.0000			−0.794101
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	1.00000	−	1.73205i	0.0608581	−	0.105409i
$271$	−13.5000	+	23.3827i	−0.820067	+	1.42040i	0.0855654	+	0.996333i	$0.472730\pi$
$271$	−13.5000	+	23.3827i	−0.820067	+	1.42040i	−0.905632	+	0.424064i	$0.860603\pi$
$272$	1.00000			0.0606339
$273$	2.50000	+	2.59808i	0.151307	+	0.157243i
$274$	12.0000			0.724947
$275$		0			0
$276$	1.50000	−	2.59808i	0.0902894	−	0.156386i
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	0.919834	−	0.392308i	$-0.128323\pi$
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	−0.799666	+	0.600446i	$0.794990\pi$
$278$	−4.00000			−0.239904
$279$	−2.50000	−	4.33013i	−0.149671	−	0.259238i
$280$	−1.00000	−	1.73205i	−0.0597614	−	0.103510i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	1.50000	−	2.59808i	0.0890086	−	0.154167i
$285$	12.0000			0.710819
$286$		0			0
$287$	−10.0000			−0.590281
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$	−6.00000	−	10.3923i	−0.352332	−	0.610257i
$291$	−12.0000			−0.703452
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	−0.968099	−	0.250568i	$-0.919383\pi$
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	0.267052	−	0.963682i	$-0.413951\pi$
$294$	1.00000			0.0583212
$295$	−7.00000	−	12.1244i	−0.407556	−	0.705907i
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$		0			0
$298$	15.0000			0.868927
$299$	10.5000	−	2.59808i	0.607231	−	0.150251i
$300$	1.00000			0.0577350
$301$	−1.50000	+	2.59808i	−0.0864586	+	0.149751i
$302$	2.00000	−	3.46410i	0.115087	−	0.199337i
$303$	2.00000	+	3.46410i	0.114897	+	0.199007i
$304$	6.00000			0.344124
$305$	11.0000	+	19.0526i	0.629858	+	1.09095i
$306$	0.500000	+	0.866025i	0.0285831	+	0.0495074i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$		0			0
$309$	−0.500000	+	0.866025i	−0.0284440	+	0.0492665i
$310$	−5.00000	+	8.66025i	−0.283981	+	0.491869i
$311$	14.0000			0.793867			0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000			0.793867			0.396934	+	0.917847i	$0.370074\pi$
$312$	3.50000	−	0.866025i	0.198148	−	0.0490290i
$313$	−32.0000			−1.80875			−0.904373	−	0.426742i	$-0.859661\pi$
$313$	−32.0000			−1.80875			−0.904373	+	0.426742i	$0.859661\pi$
$314$	11.0000	−	19.0526i	0.620766	−	1.07520i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	3.00000			0.168497			0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000			0.168497			0.0842484	+	0.996445i	$0.473151\pi$
$318$	−3.50000	−	6.06218i	−0.196270	−	0.339950i
$319$		0			0
$320$	−2.00000			−0.111803
$321$	1.00000	+	1.73205i	0.0558146	+	0.0966736i
$322$	1.50000	−	2.59808i	0.0835917	−	0.144785i
$323$	−3.00000	+	5.19615i	−0.166924	+	0.289122i
$324$	1.00000			0.0555556
$325$	2.50000	+	2.59808i	0.138675	+	0.144115i
$326$	−5.00000			−0.276924
$327$	2.00000	−	3.46410i	0.110600	−	0.191565i
$328$	−5.00000	+	8.66025i	−0.276079	+	0.478183i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	7.50000	+	12.9904i	0.411616	+	0.712940i
$333$	−2.00000			−0.109599
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	−13.0000	+	22.5167i	−0.710266	+	1.23022i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	34.0000			1.85210			0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000			1.85210			0.926049	+	0.377403i	$0.123183\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$	−12.0000			−0.651751
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$		0			0
$342$	3.00000	+	5.19615i	0.162221	+	0.280976i
$343$	1.00000			0.0539949
$344$	1.50000	+	2.59808i	0.0808746	+	0.140079i
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	−4.00000			−0.215041
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	−0.969201	−	0.246270i	$-0.920795\pi$
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	0.271325	−	0.962488i	$-0.412538\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	−14.5000	+	25.1147i	−0.776167	+	1.34436i	0.157969	+	0.987444i	$0.449505\pi$
$349$	−14.5000	+	25.1147i	−0.776167	+	1.34436i	−0.934136	+	0.356917i	$0.883828\pi$
$350$	1.00000			0.0534522
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$		0			0
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$	3.50000	−	6.06218i	0.186023	−	0.322201i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	−11.0000			−0.582999
$357$	0.500000	+	0.866025i	0.0264628	+	0.0458349i
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	11.0000			0.577350
$364$	3.50000	−	0.866025i	0.183450	−	0.0453921i
$365$	−24.0000			−1.25622
$366$	−5.50000	+	9.52628i	−0.287490	+	0.497947i
$367$	−7.50000	+	12.9904i	−0.391497	+	0.678092i	−0.992647	−	0.121044i	$-0.961376\pi$
$367$	−7.50000	+	12.9904i	−0.391497	+	0.678092i	0.601150	+	0.799136i	$0.294709\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$	−10.0000			−0.520579
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$	−3.50000	−	6.06218i	−0.181711	−	0.314733i
$372$	−5.00000			−0.259238
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	0.950804	−	0.309794i	$-0.100260\pi$
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	−0.743691	+	0.668523i	$0.766927\pi$
$374$		0			0
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$	−6.00000			−0.309426
$377$	21.0000	−	5.19615i	1.08156	−	0.267615i
$378$	1.00000			0.0514344
$379$	−6.00000	+	10.3923i	−0.308199	+	0.533817i	−0.977969	−	0.208752i	$-0.933060\pi$
$379$	−6.00000	+	10.3923i	−0.308199	+	0.533817i	0.669769	+	0.742569i	$0.266393\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$	−2.00000	−	3.46410i	−0.102463	−	0.177471i
$382$	9.00000			0.460480
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	0.810394	−	0.585886i	$-0.199253\pi$
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	−0.912589	+	0.408879i	$0.865920\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	5.00000	+	8.66025i	0.254493	+	0.440795i
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	−6.00000	+	10.3923i	−0.304604	+	0.527589i
$389$	−5.00000			−0.253510			−0.126755	−	0.991934i	$-0.540456\pi$
$389$	−5.00000			−0.253510			−0.126755	+	0.991934i	$0.540456\pi$
$390$	2.00000	−	6.92820i	0.101274	−	0.350823i
$391$	3.00000			0.151717
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$	−7.50000	+	12.9904i	−0.378325	+	0.655278i
$394$	−6.50000	−	11.2583i	−0.327465	−	0.567186i
$395$	8.00000			0.402524
$396$		0			0
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$	−9.00000			−0.451129
$399$	3.00000	+	5.19615i	0.150188	+	0.260133i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$	−13.0000			−0.648381
$403$	−12.5000	−	12.9904i	−0.622669	−	0.647097i
$404$	4.00000			0.199007
$405$	1.00000	−	1.73205i	0.0496904	−	0.0860663i
$406$	3.00000	−	5.19615i	0.148888	−	0.257881i
$407$		0			0
$408$	1.00000			0.0495074
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	0.889689	−	0.456566i	$-0.150921\pi$
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	−0.840243	+	0.542211i	$0.817588\pi$
$410$	10.0000	+	17.3205i	0.493865	+	0.855399i
$411$	12.0000			0.591916
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	3.50000	−	6.06218i	0.172224	−	0.298300i
$414$	1.50000	−	2.59808i	0.0737210	−	0.127688i
$415$	30.0000			1.47264
$416$	1.00000	−	3.46410i	0.0490290	−	0.169842i
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	−0.989000	−	0.147918i	$-0.952743\pi$
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	0.622601	+	0.782540i	$0.286076\pi$
$420$	−1.00000	−	1.73205i	−0.0487950	−	0.0845154i
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	−7.00000			−0.339950
$425$	0.500000	+	0.866025i	0.0242536	+	0.0420084i
$426$	1.50000	−	2.59808i	0.0726752	−	0.125877i
$427$	−5.50000	+	9.52628i	−0.266164	+	0.461009i
$428$	2.00000			0.0966736
$429$		0			0
$430$	6.00000			0.289346
$431$	6.50000	−	11.2583i	0.313094	−	0.542295i	−0.665937	−	0.746008i	$-0.731968\pi$
$431$	6.50000	−	11.2583i	0.313094	−	0.542295i	0.979030	+	0.203714i	$0.0653012\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	0.607238	−	0.794520i	$-0.292277\pi$
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	−0.991693	+	0.128624i	$0.958944\pi$
$434$	−5.00000			−0.240008
$435$	−6.00000	−	10.3923i	−0.287678	−	0.498273i
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	18.0000			0.861057
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$	2.50000	+	2.59808i	0.118913	+	0.123578i
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	−11.0000	+	19.0526i	−0.521450	+	0.903178i
$446$	−3.50000	−	6.06218i	−0.165730	−	0.287052i
$447$	15.0000			0.709476
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	0.652230	−	0.758021i	$-0.273834\pi$
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	−0.982581	+	0.185837i	$0.940500\pi$
$450$	1.00000			0.0471405
$451$		0			0
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	2.00000	−	3.46410i	0.0939682	−	0.162758i
$454$	−20.0000			−0.938647
$455$	2.00000	−	6.92820i	0.0937614	−	0.324799i
$456$	6.00000			0.280976
$457$	20.5000	−	35.5070i	0.958950	−	1.66095i	0.233890	−	0.972263i	$-0.424854\pi$
$457$	20.5000	−	35.5070i	0.958950	−	1.66095i	0.725059	−	0.688686i	$-0.241812\pi$
$458$	−8.50000	+	14.7224i	−0.397179	+	0.687934i
$459$	0.500000	+	0.866025i	0.0233380	+	0.0404226i
$460$	−6.00000			−0.279751
$461$	−8.00000	−	13.8564i	−0.372597	−	0.645357i	0.617367	−	0.786675i	$-0.288199\pi$
$461$	−8.00000	−	13.8564i	−0.372597	−	0.645357i	−0.989964	+	0.141318i	$0.954866\pi$
$462$		0			0
$463$	34.0000			1.58011			0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000			1.58011			0.790057	+	0.613033i	$0.210051\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	−5.00000	+	8.66025i	−0.231869	+	0.401610i
$466$	−4.00000	+	6.92820i	−0.185296	+	0.320943i
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$	3.50000	−	0.866025i	0.161788	−	0.0400320i
$469$	−13.0000			−0.600284
$470$	−6.00000	+	10.3923i	−0.276759	+	0.479361i
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	−3.50000	−	6.06218i	−0.161101	−	0.279034i
$473$		0			0
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$	3.00000	+	5.19615i	0.137649	+	0.238416i
$476$	1.00000			0.0458349
$477$	−3.50000	−	6.06218i	−0.160254	−	0.277568i
$478$	−14.5000	+	25.1147i	−0.663215	+	1.14872i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	−2.00000			−0.0912871
$481$	−7.00000	+	1.73205i	−0.319173	+	0.0789747i
$482$	18.0000			0.819878
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	12.0000	+	20.7846i	0.544892	+	0.943781i
$486$	1.00000			0.0453609
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	0.697459	−	0.716625i	$-0.254314\pi$
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	−0.969345	+	0.245705i	$0.920981\pi$
$488$	5.50000	+	9.52628i	0.248973	+	0.431234i
$489$	−5.00000			−0.226108
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	−0.761539	−	0.648119i	$-0.775556\pi$
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	0.942057	+	0.335453i	$0.108889\pi$
$492$	−5.00000	+	8.66025i	−0.225417	+	0.390434i
$493$	6.00000			0.270226
$494$	15.0000	+	15.5885i	0.674882	+	0.701358i
$495$		0			0
$496$	−2.50000	+	4.33013i	−0.112253	+	0.194428i
$497$	1.50000	−	2.59808i	0.0672842	−	0.116540i
$498$	7.50000	+	12.9904i	0.336083	+	0.582113i
$499$	−17.0000			−0.761025			−0.380512	−	0.924776i	$-0.624252\pi$
$499$	−17.0000			−0.761025			−0.380512	+	0.924776i	$0.624252\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	4.00000	+	6.92820i	0.178707	+	0.309529i
$502$	7.00000			0.312425
$503$	4.00000	+	6.92820i	0.178351	+	0.308913i	0.941316	−	0.337527i	$-0.109590\pi$
$503$	4.00000	+	6.92820i	0.178351	+	0.308913i	−0.762965	+	0.646440i	$0.776257\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	4.00000	−	6.92820i	0.177998	−	0.308301i
$506$		0			0
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$	−4.00000			−0.177471
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$	1.00000	−	1.73205i	0.0442807	−	0.0766965i
$511$	−6.00000	−	10.3923i	−0.265424	−	0.459728i
$512$	−1.00000			−0.0441942
$513$	3.00000	+	5.19615i	0.132453	+	0.229416i
$514$	−5.50000	−	9.52628i	−0.242595	−	0.420186i
$515$	2.00000			0.0881305
$516$	1.50000	+	2.59808i	0.0660338	+	0.114374i
$517$		0			0
$518$	−1.00000	+	1.73205i	−0.0439375	+	0.0761019i
$519$	−4.00000			−0.175581
$520$	−5.00000	−	5.19615i	−0.219265	−	0.227866i
$521$	34.0000			1.48957			0.744784	−	0.667306i	$-0.232553\pi$
$521$	34.0000			1.48957			0.744784	+	0.667306i	$0.232553\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	18.0000	−	31.1769i	0.787085	−	1.36327i	−0.140660	−	0.990058i	$-0.544923\pi$
$523$	18.0000	−	31.1769i	0.787085	−	1.36327i	0.927746	−	0.373213i	$-0.121744\pi$
$524$	7.50000	+	12.9904i	0.327639	+	0.567487i
$525$	1.00000			0.0436436
$526$	14.0000	+	24.2487i	0.610429	+	1.05729i
$527$	−2.50000	−	4.33013i	−0.108902	−	0.188623i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−7.00000	+	12.1244i	−0.304061	+	0.526648i
$531$	3.50000	−	6.06218i	0.151887	−	0.263076i
$532$	6.00000			0.260133
$533$	−35.0000	+	8.66025i	−1.51602	+	0.375117i
$534$	−11.0000			−0.476017
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$	−6.50000	+	11.2583i	−0.280757	+	0.486286i
$537$	3.00000	+	5.19615i	0.129460	+	0.224231i
$538$	6.00000			0.258678
$539$		0			0
$540$	−1.00000	−	1.73205i	−0.0430331	−	0.0745356i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	13.5000	+	23.3827i	0.579875	+	1.00437i
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$	0.500000	−	0.866025i	0.0214373	−	0.0371305i
$545$	−8.00000			−0.342682
$546$	3.50000	−	0.866025i	0.149786	−	0.0370625i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−5.50000	+	9.52628i	−0.234734	+	0.406572i
$550$		0			0
$551$	36.0000			1.53365
$552$	−1.50000	−	2.59808i	−0.0638442	−	0.110581i
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$	4.00000			0.169944
$555$	2.00000	+	3.46410i	0.0848953	+	0.147043i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	15.5000	−	26.8468i	0.656756	−	1.13753i	−0.324694	−	0.945819i	$-0.605261\pi$
$557$	15.5000	−	26.8468i	0.656756	−	1.13753i	0.981450	−	0.191716i	$-0.0614052\pi$
$558$	−5.00000			−0.211667
$559$	−3.00000	+	10.3923i	−0.126886	+	0.439548i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	−6.00000			−0.252646
$565$	12.0000	+	20.7846i	0.504844	+	0.874415i
$566$	7.00000	+	12.1244i	0.294232	+	0.509625i
$567$	1.00000			0.0419961
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$	6.00000	−	10.3923i	0.251312	−	0.435286i
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$		0			0
$573$	9.00000			0.375980
$574$	−5.00000	+	8.66025i	−0.208696	+	0.361472i
$575$	1.50000	−	2.59808i	0.0625543	−	0.108347i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	42.0000			1.74848			0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000			1.74848			0.874241	+	0.485491i	$0.161359\pi$
$578$	−8.00000	−	13.8564i	−0.332756	−	0.576351i
$579$	5.00000	+	8.66025i	0.207793	+	0.359908i
$580$	−12.0000			−0.498273
$581$	7.50000	+	12.9904i	0.311152	+	0.538932i
$582$	−6.00000	+	10.3923i	−0.248708	+	0.430775i
$583$		0			0
$584$	−12.0000			−0.496564
$585$	2.00000	−	6.92820i	0.0826898	−	0.286446i
$586$	−24.0000			−0.991431
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$	−15.0000	−	25.9808i	−0.618064	−	1.07052i
$590$	−14.0000			−0.576371
$591$	−6.50000	−	11.2583i	−0.267374	−	0.463106i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	35.0000			1.43728			0.718639	−	0.695383i	$-0.244765\pi$
$593$	35.0000			1.43728			0.718639	+	0.695383i	$0.244765\pi$
$594$		0			0
$595$	1.00000	−	1.73205i	0.0409960	−	0.0710072i
$596$	7.50000	−	12.9904i	0.307212	−	0.532107i
$597$	−9.00000			−0.368345
$598$	3.00000	−	10.3923i	0.122679	−	0.424973i
$599$	−27.0000			−1.10319			−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000			−1.10319			−0.551595	+	0.834112i	$0.685981\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−23.0000	+	39.8372i	−0.938190	+	1.62499i	−0.169344	+	0.985557i	$0.554165\pi$
$601$	−23.0000	+	39.8372i	−0.938190	+	1.62499i	−0.768845	+	0.639435i	$0.779168\pi$
$602$	1.50000	+	2.59808i	0.0611354	+	0.105890i
$603$	−13.0000			−0.529401
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$	−11.0000	−	19.0526i	−0.447214	−	0.774597i
$606$	4.00000			0.162489
$607$	17.5000	+	30.3109i	0.710303	+	1.23028i	0.964743	+	0.263193i	$0.0847754\pi$
$607$	17.5000	+	30.3109i	0.710303	+	1.23028i	−0.254440	+	0.967088i	$0.581891\pi$
$608$	3.00000	−	5.19615i	0.121666	−	0.210732i
$609$	3.00000	−	5.19615i	0.121566	−	0.210559i
$610$	22.0000			0.890754
$611$	−15.0000	−	15.5885i	−0.606835	−	0.630641i
$612$	1.00000			0.0404226
$613$	11.0000	−	19.0526i	0.444286	−	0.769526i	−0.553716	−	0.832705i	$-0.686791\pi$
$613$	11.0000	−	19.0526i	0.444286	−	0.769526i	0.998002	+	0.0631797i	$0.0201241\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$	10.0000	+	17.3205i	0.403239	+	0.698430i
$616$		0			0
$617$	4.00000	+	6.92820i	0.161034	+	0.278919i	0.935240	−	0.354015i	$-0.115184\pi$
$617$	4.00000	+	6.92820i	0.161034	+	0.278919i	−0.774206	+	0.632934i	$0.781850\pi$
$618$	0.500000	+	0.866025i	0.0201129	+	0.0348367i
$619$	38.0000			1.52735			0.763674	−	0.645601i	$-0.223393\pi$
$619$	38.0000			1.52735			0.763674	+	0.645601i	$0.223393\pi$
$620$	5.00000	+	8.66025i	0.200805	+	0.347804i
$621$	1.50000	−	2.59808i	0.0601929	−	0.104257i
$622$	7.00000	−	12.1244i	0.280674	−	0.486142i
$623$	−11.0000			−0.440706
$624$	1.00000	−	3.46410i	0.0400320	−	0.138675i
$625$	−19.0000			−0.760000
$626$	−16.0000	+	27.7128i	−0.639489	+	1.10763i
$627$		0			0
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$	−2.00000			−0.0797452
$630$	−1.00000	−	1.73205i	−0.0398410	−	0.0690066i
$631$	20.0000	+	34.6410i	0.796187	+	1.37904i	0.922082	+	0.386994i	$0.126486\pi$
$631$	20.0000	+	34.6410i	0.796187	+	1.37904i	−0.125895	+	0.992044i	$0.540180\pi$
$632$	4.00000			0.159111
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	1.50000	−	2.59808i	0.0595726	−	0.103183i
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$	−7.00000			−0.277568
$637$	3.50000	−	0.866025i	0.138675	−	0.0343132i
$638$		0			0
$639$	1.50000	−	2.59808i	0.0593391	−	0.102778i
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−18.0000	−	31.1769i	−0.710957	−	1.23141i	−0.964498	−	0.264089i	$-0.914929\pi$
$641$	−18.0000	−	31.1769i	−0.710957	−	1.23141i	0.253541	−	0.967325i	$-0.418405\pi$
$642$	2.00000			0.0789337
$643$	7.00000	+	12.1244i	0.276053	+	0.478138i	0.970400	−	0.241502i	$-0.0776401\pi$
$643$	7.00000	+	12.1244i	0.276053	+	0.478138i	−0.694347	+	0.719640i	$0.744307\pi$
$644$	−1.50000	−	2.59808i	−0.0591083	−	0.102379i
$645$	6.00000			0.236250
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	3.00000	−	5.19615i	0.117942	−	0.204282i	−0.801010	−	0.598651i	$-0.795704\pi$
$647$	3.00000	−	5.19615i	0.117942	−	0.204282i	0.918952	+	0.394369i	$0.129037\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$		0			0
$650$	3.50000	−	0.866025i	0.137281	−	0.0339683i
$651$	−5.00000			−0.195965
$652$	−2.50000	+	4.33013i	−0.0979076	+	0.169581i
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	−0.974634	−	0.223803i	$-0.928153\pi$
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	0.681137	+	0.732156i	$0.261486\pi$
$654$	−2.00000	−	3.46410i	−0.0782062	−	0.135457i
$655$	30.0000			1.17220
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$	−6.00000	−	10.3923i	−0.234082	−	0.405442i
$658$	−6.00000			−0.233904
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$	−20.0000			−0.777322
$663$	2.50000	+	2.59808i	0.0970920	+	0.100901i
$664$	15.0000			0.582113
$665$	6.00000	−	10.3923i	0.232670	−	0.402996i
$666$	−1.00000	+	1.73205i	−0.0387492	+	0.0671156i
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$	8.00000			0.309529
$669$	−3.50000	−	6.06218i	−0.135318	−	0.234377i
$670$	13.0000	+	22.5167i	0.502234	+	0.869894i
$671$		0			0
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	12.5000	−	21.6506i	0.481840	−	0.834571i	−0.517943	−	0.855415i	$-0.673302\pi$
$673$	12.5000	−	21.6506i	0.481840	−	0.834571i	0.999783	+	0.0208444i	$0.00663546\pi$
$674$	17.0000	−	29.4449i	0.654816	−	1.13417i
$675$	1.00000			0.0384900
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	4.00000			0.153732			0.0768662	−	0.997041i	$-0.475509\pi$
$677$	4.00000			0.153732			0.0768662	+	0.997041i	$0.475509\pi$
$678$	−6.00000	+	10.3923i	−0.230429	+	0.399114i
$679$	−6.00000	+	10.3923i	−0.230259	+	0.398820i
$680$	−1.00000	−	1.73205i	−0.0383482	−	0.0664211i
$681$	−20.0000			−0.766402
$682$		0			0
$683$	−23.0000	−	39.8372i	−0.880071	−	1.52433i	−0.851261	−	0.524742i	$-0.824162\pi$
$683$	−23.0000	−	39.8372i	−0.880071	−	1.52433i	−0.0288092	−	0.999585i	$-0.509172\pi$
$684$	6.00000			0.229416
$685$	−12.0000	−	20.7846i	−0.458496	−	0.794139i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−8.50000	+	14.7224i	−0.324295	+	0.561696i
$688$	3.00000			0.114374
$689$	−17.5000	−	18.1865i	−0.666697	−	0.692852i
$690$	−6.00000			−0.228416
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	−2.00000	+	3.46410i	−0.0760286	+	0.131685i
$693$		0			0
$694$	−26.0000			−0.986947
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	−10.0000			−0.378777
$698$	14.5000	+	25.1147i	0.548833	+	0.950607i
$699$	−4.00000	+	6.92820i	−0.151294	+	0.262049i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	−12.0000			−0.452589
$704$		0			0
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$	−10.5000	−	18.1865i	−0.395173	−	0.684459i
$707$	4.00000			0.150435
$708$	−3.50000	−	6.06218i	−0.131538	−	0.227831i
$709$	−20.0000	−	34.6410i	−0.751116	−	1.30097i	−0.947282	−	0.320400i	$-0.896183\pi$
$709$	−20.0000	−	34.6410i	−0.751116	−	1.30097i	0.196167	−	0.980571i	$-0.437151\pi$
$710$	−6.00000			−0.225176
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	−5.50000	+	9.52628i	−0.206121	+	0.357012i
$713$	−7.50000	+	12.9904i	−0.280877	+	0.486494i
$714$	1.00000			0.0374241
$715$		0			0
$716$	6.00000			0.224231
$717$	−14.5000	+	25.1147i	−0.541512	+	0.937927i
$718$	8.00000	−	13.8564i	0.298557	−	0.517116i
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	0.999669	+	0.0257237i	$0.00818900\pi$
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	−0.477557	+	0.878601i	$0.658478\pi$
$720$	−2.00000			−0.0745356
$721$	0.500000	+	0.866025i	0.0186210	+	0.0322525i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$	18.0000			0.669427
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	5.50000	−	9.52628i	0.204124	−	0.353553i
$727$	33.0000			1.22390			0.611951	−	0.790896i	$-0.290385\pi$
$727$	33.0000			1.22390			0.611951	+	0.790896i	$0.290385\pi$
$728$	1.00000	−	3.46410i	0.0370625	−	0.128388i
$729$	1.00000			0.0370370
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	5.50000	+	9.52628i	0.203286	+	0.352101i
$733$	25.0000			0.923396			0.461698	−	0.887037i	$-0.347240\pi$
$733$	25.0000			0.923396			0.461698	+	0.887037i	$0.347240\pi$
$734$	7.50000	+	12.9904i	0.276830	+	0.479484i
$735$	−1.00000	−	1.73205i	−0.0368856	−	0.0638877i
$736$	−3.00000			−0.110581
$737$		0			0
$738$	−5.00000	+	8.66025i	−0.184053	+	0.318788i
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	−0.936845	−	0.349744i	$-0.886268\pi$
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	0.771310	+	0.636460i	$0.219602\pi$
$740$	4.00000			0.147043
$741$	15.0000	+	15.5885i	0.551039	+	0.572656i
$742$	−7.00000			−0.256978
$743$	−21.5000	+	37.2391i	−0.788759	+	1.36617i	0.137969	+	0.990437i	$0.455942\pi$
$743$	−21.5000	+	37.2391i	−0.788759	+	1.36617i	−0.926728	+	0.375733i	$0.877391\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$	−15.0000	−	25.9808i	−0.549557	−	0.951861i
$746$	8.00000			0.292901
$747$	7.50000	+	12.9904i	0.274411	+	0.475293i
$748$		0			0
$749$	2.00000			0.0730784
$750$	−6.00000	−	10.3923i	−0.219089	−	0.379473i
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	−0.277424	−	0.960748i	$-0.589481\pi$
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	0.970744	−	0.240118i	$-0.0771860\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	7.00000			0.255094
$754$	6.00000	−	20.7846i	0.218507	−	0.756931i
$755$	−8.00000			−0.291150
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	−0.847280	−	0.531146i	$-0.821762\pi$
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	0.883626	+	0.468193i	$0.155095\pi$
$758$	6.00000	+	10.3923i	0.217930	+	0.377466i
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	0.594822	−	0.803857i	$-0.297222\pi$
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	−0.993572	+	0.113203i	$0.963889\pi$
$762$	−4.00000			−0.144905
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	4.50000	−	7.79423i	0.162804	−	0.281985i
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−4.00000			−0.144526
$767$	7.00000	−	24.2487i	0.252755	−	0.875570i
$768$	−1.00000			−0.0360844
$769$	20.0000	−	34.6410i	0.721218	−	1.24919i	−0.239293	−	0.970947i	$-0.576916\pi$
$769$	20.0000	−	34.6410i	0.721218	−	1.24919i	0.960512	−	0.278240i	$-0.0897509\pi$
$770$		0			0
$771$	−5.50000	−	9.52628i	−0.198078	−	0.343081i
$772$	10.0000			0.359908
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	−0.998930	−	0.0462427i	$-0.985275\pi$
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	0.459418	−	0.888220i	$-0.348058\pi$
$774$	1.50000	+	2.59808i	0.0539164	+	0.0933859i
$775$	−5.00000			−0.179605
$776$	6.00000	+	10.3923i	0.215387	+	0.373062i
$777$	−1.00000	+	1.73205i	−0.0358748	+	0.0621370i
$778$	−2.50000	+	4.33013i	−0.0896293	+	0.155243i
$779$	−60.0000			−2.14972
$780$	−5.00000	−	5.19615i	−0.179029	−	0.186052i
$781$		0			0
$782$	1.50000	−	2.59808i	0.0536399	−	0.0929070i
$783$	3.00000	−	5.19615i	0.107211	−	0.185695i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−44.0000			−1.57043
$786$	7.50000	+	12.9904i	0.267516	+	0.463352i
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	−13.0000			−0.463106
$789$	14.0000	+	24.2487i	0.498413	+	0.863277i
$790$	4.00000	−	6.92820i	0.142314	−	0.246494i
$791$	−6.00000	+	10.3923i	−0.213335	+	0.369508i
$792$		0			0
$793$	−11.0000	+	38.1051i	−0.390621	+	1.35315i
$794$	−13.0000			−0.461353
$795$	−7.00000	+	12.1244i	−0.248264	+	0.430007i
$796$	−4.50000	+	7.79423i	−0.159498	+	0.276259i
$797$	10.0000	+	17.3205i	0.354218	+	0.613524i	0.986984	−	0.160819i	$-0.0514137\pi$
$797$	10.0000	+	17.3205i	0.354218	+	0.613524i	−0.632766	+	0.774343i	$0.718080\pi$
$798$	6.00000			0.212398
$799$	−3.00000	−	5.19615i	−0.106132	−	0.183827i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−11.0000			−0.388666
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$		0			0
$804$	−6.50000	+	11.2583i	−0.229237	+	0.397051i
$805$	−6.00000			−0.211472
$806$	−17.5000	+	4.33013i	−0.616411	+	0.152522i
$807$	6.00000			0.211210
$808$	2.00000	−	3.46410i	0.0703598	−	0.121867i
$809$	−14.0000	+	24.2487i	−0.492214	+	0.852539i	−0.999960	−	0.00896753i	$-0.997146\pi$
$809$	−14.0000	+	24.2487i	−0.492214	+	0.852539i	0.507746	+	0.861507i	$0.330479\pi$
$810$	−1.00000	−	1.73205i	−0.0351364	−	0.0608581i
$811$	−24.0000			−0.842754			−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000			−0.842754			−0.421377	+	0.906886i	$0.638453\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$	13.5000	+	23.3827i	0.473466	+	0.820067i
$814$		0			0
$815$	5.00000	+	8.66025i	0.175142	+	0.303355i
$816$	0.500000	−	0.866025i	0.0175035	−	0.0303170i
$817$	−9.00000	+	15.5885i	−0.314870	+	0.545371i
$818$	2.00000			0.0699284
$819$	3.50000	−	0.866025i	0.122300	−	0.0302614i
$820$	20.0000			0.698430
$821$	16.5000	−	28.5788i	0.575854	−	0.997408i	−0.420094	−	0.907480i	$-0.638003\pi$
$821$	16.5000	−	28.5788i	0.575854	−	0.997408i	0.995948	−	0.0899279i	$-0.0286637\pi$
$822$	6.00000	−	10.3923i	0.209274	−	0.362473i
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	1.00000			0.0348367
$825$		0			0
$826$	−3.50000	−	6.06218i	−0.121781	−	0.210930i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$	−1.50000	−	2.59808i	−0.0521286	−	0.0902894i
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	−0.766039	−	0.642795i	$-0.777775\pi$
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	0.939696	+	0.342012i	$0.111108\pi$
$830$	15.0000	−	25.9808i	0.520658	−	0.901805i
$831$	4.00000			0.138758
$832$	−2.50000	−	2.59808i	−0.0866719	−	0.0900721i
$833$	1.00000			0.0346479
$834$	−2.00000	+	3.46410i	−0.0692543	+	0.119952i
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$		0			0
$837$	−5.00000			−0.172825
$838$	7.50000	+	12.9904i	0.259083	+	0.448745i
$839$	17.0000	+	29.4449i	0.586905	+	1.01655i	0.994635	+	0.103447i	$0.0329872\pi$
$839$	17.0000	+	29.4449i	0.586905	+	1.01655i	−0.407730	+	0.913103i	$0.633679\pi$
$840$	−2.00000			−0.0690066
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	3.00000	−	5.19615i	0.103387	−	0.179071i
$843$	9.00000	−	15.5885i	0.309976	−	0.536895i
$844$	−4.00000			−0.137686
$845$	1.00000	−	25.9808i	0.0344010	−	0.893765i
$846$	−6.00000			−0.206284
$847$	5.50000	−	9.52628i	0.188982	−	0.327327i
$848$	−3.50000	+	6.06218i	−0.120190	+	0.208176i
$849$	7.00000	+	12.1244i	0.240239	+	0.416107i
$850$	1.00000			0.0342997
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$	−1.50000	−	2.59808i	−0.0513892	−	0.0890086i
$853$	−23.0000			−0.787505			−0.393753	−	0.919216i	$-0.628823\pi$
$853$	−23.0000			−0.787505			−0.393753	+	0.919216i	$0.628823\pi$
$854$	5.50000	+	9.52628i	0.188206	+	0.325983i
$855$	6.00000	−	10.3923i	0.205196	−	0.355409i
$856$	1.00000	−	1.73205i	0.0341793	−	0.0592003i
$857$	−38.0000			−1.29806			−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000			−1.29806			−0.649028	+	0.760765i	$0.724824\pi$
$858$		0			0
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$	−5.00000	+	8.66025i	−0.170400	+	0.295141i
$862$	−6.50000	−	11.2583i	−0.221391	−	0.383460i
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	4.00000	+	6.92820i	0.136004	+	0.235566i
$866$	−16.0000			−0.543702
$867$	−8.00000	−	13.8564i	−0.271694	−	0.470588i
$868$	−2.50000	+	4.33013i	−0.0848555	+	0.146974i
$869$		0			0
$870$	−12.0000			−0.406838
$871$	−45.5000	+	11.2583i	−1.54171	+	0.381474i
$872$	−4.00000			−0.135457
$873$	−6.00000	+	10.3923i	−0.203069	+	0.351726i
$874$	9.00000	−	15.5885i	0.304430	−	0.527287i
$875$	−6.00000	−	10.3923i	−0.202837	−	0.351324i
$876$	−12.0000			−0.405442
$877$	21.0000	+	36.3731i	0.709120	+	1.22823i	0.965184	+	0.261571i	$0.0842407\pi$
$877$	21.0000	+	36.3731i	0.709120	+	1.22823i	−0.256064	+	0.966660i	$0.582426\pi$
$878$	2.00000	+	3.46410i	0.0674967	+	0.116908i
$879$	−24.0000			−0.809500
$880$		0			0
$881$	0.500000	−	0.866025i	0.0168454	−	0.0291771i	−0.857480	−	0.514518i	$-0.827971\pi$
$881$	0.500000	−	0.866025i	0.0168454	−	0.0291771i	0.874325	+	0.485340i	$0.161304\pi$
$882$	0.500000	−	0.866025i	0.0168359	−	0.0291606i
$883$	25.0000			0.841317			0.420658	−	0.907219i	$-0.361799\pi$
$883$	25.0000			0.841317			0.420658	+	0.907219i	$0.361799\pi$
$884$	3.50000	−	0.866025i	0.117718	−	0.0291276i
$885$	−14.0000			−0.470605
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	0.261540	+	0.965193i	$0.415770\pi$
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	−0.966651	+	0.256096i	$0.917564\pi$
$888$	1.00000	+	1.73205i	0.0335578	+	0.0581238i
$889$	−4.00000			−0.134156
$890$	11.0000	+	19.0526i	0.368721	+	0.638643i
$891$		0			0
$892$	−7.00000			−0.234377
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$	7.50000	−	12.9904i	0.250838	−	0.434463i
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$	−1.00000			−0.0334077
$897$	3.00000	−	10.3923i	0.100167	−	0.346989i
$898$	−14.0000			−0.467186
$899$	−15.0000	+	25.9808i	−0.500278	+	0.866507i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	−3.50000	−	6.06218i	−0.116602	−	0.201960i
$902$		0			0
$903$	1.50000	+	2.59808i	0.0499169	+	0.0864586i
$904$	6.00000	+	10.3923i	0.199557	+	0.345643i
$905$	−20.0000			−0.664822
$906$	−2.00000	−	3.46410i	−0.0664455	−	0.115087i
$907$	20.5000	−	35.5070i	0.680691	−	1.17899i	−0.294079	−	0.955781i	$-0.595013\pi$
$907$	20.5000	−	35.5070i	0.680691	−	1.17899i	0.974770	−	0.223211i	$-0.0716538\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$	4.00000			0.132672
$910$	−5.00000	−	5.19615i	−0.165748	−	0.172251i
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	3.00000	−	5.19615i	0.0993399	−	0.172062i
$913$		0			0
$914$	−20.5000	−	35.5070i	−0.678080	−	1.17447i
$915$	22.0000			0.727298
$916$	8.50000	+	14.7224i	0.280848	+	0.486443i
$917$	7.50000	+	12.9904i	0.247672	+	0.428980i
$918$	1.00000			0.0330049
$919$	−29.0000	−	50.2295i	−0.956622	−	1.65692i	−0.730613	−	0.682792i	$-0.760765\pi$
$919$	−29.0000	−	50.2295i	−0.956622	−	1.65692i	−0.226009	−	0.974125i	$-0.572568\pi$
$920$	−3.00000	+	5.19615i	−0.0989071	+	0.171312i
$921$	−9.00000	+	15.5885i	−0.296560	+	0.513657i
$922$	−16.0000			−0.526932
$923$	3.00000	−	10.3923i	0.0987462	−	0.342067i
$924$		0			0
$925$	−1.00000	+	1.73205i	−0.0328798	+	0.0569495i
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$	0.500000	+	0.866025i	0.0164222	+	0.0284440i
$928$	−6.00000			−0.196960
$929$	−21.5000	−	37.2391i	−0.705392	−	1.22177i	−0.966550	−	0.256479i	$-0.917438\pi$
$929$	−21.5000	−	37.2391i	−0.705392	−	1.22177i	0.261158	−	0.965296i	$-0.415896\pi$
$930$	5.00000	+	8.66025i	0.163956	+	0.283981i
$931$	6.00000			0.196642
$932$	4.00000	+	6.92820i	0.131024	+	0.226941i
$933$	7.00000	−	12.1244i	0.229170	−	0.396934i
$934$	13.5000	−	23.3827i	0.441733	−	0.765105i
$935$		0			0
$936$	1.00000	−	3.46410i	0.0326860	−	0.113228i
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	−6.50000	+	11.2583i	−0.212233	+	0.367598i
$939$	−16.0000	+	27.7128i	−0.522140	+	0.904373i
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	−11.0000	−	19.0526i	−0.358399	−	0.620766i
$943$	15.0000	+	25.9808i	0.488467	+	0.846050i
$944$	−7.00000			−0.227831
$945$	−1.00000	−	1.73205i	−0.0325300	−	0.0563436i
$946$		0			0
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	4.00000			0.129914
$949$	−30.0000	−	31.1769i	−0.973841	−	1.01205i
$950$	6.00000			0.194666
$951$	1.50000	−	2.59808i	0.0486408	−	0.0842484i
$952$	0.500000	−	0.866025i	0.0162051	−	0.0280680i
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	0.999869	−	0.0162081i	$-0.00515944\pi$
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	−0.513971	+	0.857808i	$0.671826\pi$
$954$	−7.00000			−0.226633
$955$	−9.00000	−	15.5885i	−0.291233	−	0.504431i
$956$	14.5000	+	25.1147i	0.468964	+	0.812269i
$957$		0			0
$958$		0			0
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$	−1.00000	+	1.73205i	−0.0322749	+	0.0559017i
$961$	−6.00000			−0.193548
$962$	−2.00000	+	6.92820i	−0.0644826	+	0.223374i
$963$	2.00000			0.0644491
$964$	9.00000	−	15.5885i	0.289870	−	0.502070i
$965$	10.0000	−	17.3205i	0.321911	−	0.557567i
$966$	−1.50000	−	2.59808i	−0.0482617	−	0.0835917i
$967$	54.0000			1.73652			0.868261	−	0.496107i	$-0.165238\pi$
$967$	54.0000			1.73652			0.868261	+	0.496107i	$0.165238\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$	24.0000			0.770594
$971$	23.5000	+	40.7032i	0.754151	+	1.30623i	0.945795	+	0.324763i	$0.105285\pi$
$971$	23.5000	+	40.7032i	0.754151	+	1.30623i	−0.191644	+	0.981464i	$0.561382\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−2.00000	+	3.46410i	−0.0641171	+	0.111054i
$974$	−12.0000			−0.384505
$975$	3.50000	−	0.866025i	0.112090	−	0.0277350i
$976$	11.0000			0.352101
$977$	−22.0000	+	38.1051i	−0.703842	+	1.21909i	0.263265	+	0.964723i	$0.415201\pi$
$977$	−22.0000	+	38.1051i	−0.703842	+	1.21909i	−0.967108	+	0.254367i	$0.918133\pi$
$978$	−2.50000	+	4.33013i	−0.0799412	+	0.138462i
$979$		0			0
$980$	−2.00000			−0.0638877
$981$	−2.00000	−	3.46410i	−0.0638551	−	0.110600i
$982$	−4.00000	−	6.92820i	−0.127645	−	0.221088i
$983$	30.0000			0.956851			0.478426	−	0.878128i	$-0.341208\pi$
$983$	30.0000			0.956851			0.478426	+	0.878128i	$0.341208\pi$
$984$	5.00000	+	8.66025i	0.159394	+	0.276079i
$985$	−13.0000	+	22.5167i	−0.414214	+	0.717440i
$986$	3.00000	−	5.19615i	0.0955395	−	0.165479i
$987$	−6.00000			−0.190982
$988$	21.0000	−	5.19615i	0.668099	−	0.165312i
$989$	9.00000			0.286183
$990$		0			0
$991$	9.00000	−	15.5885i	0.285894	−	0.495184i	−0.686931	−	0.726722i	$-0.741043\pi$
$991$	9.00000	−	15.5885i	0.285894	−	0.495184i	0.972826	+	0.231539i	$0.0743760\pi$
$992$	2.50000	+	4.33013i	0.0793751	+	0.137482i
$993$	−20.0000			−0.634681
$994$	−1.50000	−	2.59808i	−0.0475771	−	0.0824060i
$995$	9.00000	+	15.5885i	0.285319	+	0.494187i
$996$	15.0000			0.475293
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	0.993213	−	0.116310i	$-0.0371066\pi$
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	−0.597334	+	0.801993i	$0.703773\pi$
$998$	−8.50000	+	14.7224i	−0.269063	+	0.466030i
$999$	−1.00000	+	1.73205i	−0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.f.295.1	yes	2
3.2	odd	2		1638.2.r.j.1387.1		2
13.3	even	3	inner	546.2.l.f.211.1	✓	2
13.4	even	6		7098.2.a.u.1.1		1
13.9	even	3		7098.2.a.c.1.1		1
39.29	odd	6		1638.2.r.j.757.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.f.211.1	✓	2	13.3	even	3	inner
546.2.l.f.295.1	yes	2	1.1	even	1	trivial
1638.2.r.j.757.1		2	39.29	odd	6
1638.2.r.j.1387.1		2	3.2	odd	2
7098.2.a.c.1.1		1	13.9	even	3
7098.2.a.u.1.1		1	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} -1.00000 q^{12} +(-2.50000 - 2.59808i) q^{13} -1.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} -1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} +(1.00000 + 1.73205i) q^{20} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} -1.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 - 1.73205i) q^{37} -6.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +2.00000 q^{40} +(5.00000 - 8.66025i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.50000 - 2.59808i) q^{43} +(1.00000 + 1.73205i) q^{45} +(1.50000 + 2.59808i) q^{46} +6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} -1.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +7.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{56} -6.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(3.50000 + 6.06218i) q^{59} +2.00000 q^{60} +(-5.50000 - 9.52628i) q^{61} +(2.50000 - 4.33013i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(5.00000 + 5.19615i) q^{65} +(6.50000 - 11.2583i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(1.50000 + 2.59808i) q^{69} +2.00000 q^{70} +(1.50000 + 2.59808i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-3.00000 + 5.19615i) q^{76} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.00000 - 8.66025i) q^{82} -15.0000 q^{83} +(0.500000 + 0.866025i) q^{84} +(1.00000 + 1.73205i) q^{85} -3.00000 q^{86} +(3.00000 + 5.19615i) q^{87} +(5.50000 - 9.52628i) q^{89} +2.00000 q^{90} +(-1.00000 + 3.46410i) q^{91} +3.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +1.00000 q^{96} +(-6.00000 - 10.3923i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - 4 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - 4 * q^5 - q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} - 4 q^{5} - q^{6} - q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} - 5 q^{13} - 2 q^{14} - 2 q^{15} - q^{16} - q^{17} - 2 q^{18} - 6 q^{19} + 2 q^{20} - 2 q^{21} - 3 q^{23} - q^{24} - 2 q^{25} - 7 q^{26} - 2 q^{27} - q^{28} - 6 q^{29} + 2 q^{30} + 10 q^{31} + q^{32} - 2 q^{34} + 2 q^{35} - q^{36} + 2 q^{37} - 12 q^{38} - 7 q^{39} + 4 q^{40} + 10 q^{41} - q^{42} - 3 q^{43} + 2 q^{45} + 3 q^{46} + 12 q^{47} + q^{48} - q^{49} - q^{50} - 2 q^{51} - 2 q^{52} + 14 q^{53} - q^{54} + q^{56} - 12 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 11 q^{61} + 5 q^{62} - q^{63} + 2 q^{64} + 10 q^{65} + 13 q^{67} - q^{68} + 3 q^{69} + 4 q^{70} + 3 q^{71} + q^{72} + 24 q^{73} - 2 q^{74} - q^{75} - 6 q^{76} - 2 q^{78} - 8 q^{79} + 2 q^{80} - q^{81} - 10 q^{82} - 30 q^{83} + q^{84} + 2 q^{85} - 6 q^{86} + 6 q^{87} + 11 q^{89} + 4 q^{90} - 2 q^{91} + 6 q^{92} + 5 q^{93} + 6 q^{94} + 12 q^{95} + 2 q^{96} - 12 q^{97} + q^{98}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - 4 * q^5 - q^6 - q^7 - 2 * q^8 - q^9 - 2 * q^10 - 2 * q^12 - 5 * q^13 - 2 * q^14 - 2 * q^15 - q^16 - q^17 - 2 * q^18 - 6 * q^19 + 2 * q^20 - 2 * q^21 - 3 * q^23 - q^24 - 2 * q^25 - 7 * q^26 - 2 * q^27 - q^28 - 6 * q^29 + 2 * q^30 + 10 * q^31 + q^32 - 2 * q^34 + 2 * q^35 - q^36 + 2 * q^37 - 12 * q^38 - 7 * q^39 + 4 * q^40 + 10 * q^41 - q^42 - 3 * q^43 + 2 * q^45 + 3 * q^46 + 12 * q^47 + q^48 - q^49 - q^50 - 2 * q^51 - 2 * q^52 + 14 * q^53 - q^54 + q^56 - 12 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 11 * q^61 + 5 * q^62 - q^63 + 2 * q^64 + 10 * q^65 + 13 * q^67 - q^68 + 3 * q^69 + 4 * q^70 + 3 * q^71 + q^72 + 24 * q^73 - 2 * q^74 - q^75 - 6 * q^76 - 2 * q^78 - 8 * q^79 + 2 * q^80 - q^81 - 10 * q^82 - 30 * q^83 + q^84 + 2 * q^85 - 6 * q^86 + 6 * q^87 + 11 * q^89 + 4 * q^90 - 2 * q^91 + 6 * q^92 + 5 * q^93 + 6 * q^94 + 12 * q^95 + 2 * q^96 - 12 * q^97 + q^98

Introduction

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