LMFDB - Embedded newform 1014.2.e.d.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not 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:	$8.09683076496$
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:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.d.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} -1.00000 q^{12} +2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{20} -2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -4.00000 q^{25} -1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.50000 - 9.52628i) q^{37} +2.00000 q^{38} +1.00000 q^{40} +(2.50000 + 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} -2.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{46} -2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} -5.00000 q^{51} -1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-4.00000 + 6.92820i) q^{59} -1.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +2.00000 q^{66} +(1.00000 + 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(-7.00000 + 12.1244i) q^{71} +(-0.500000 + 0.866025i) q^{72} +13.0000 q^{73} +(-5.50000 + 9.52628i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-1.00000 - 1.73205i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{84} +(-2.50000 + 4.33013i) q^{85} +10.0000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(1.00000 + 1.73205i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} -1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + 2 * q^5 + q^6 - 2 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{14} + q^{15} - q^{16} - 5 q^{17} + 2 q^{18} - 2 q^{19} - q^{20} - 4 q^{21} + 2 q^{22} - 6 q^{23} + q^{24} - 8 q^{25} - 2 q^{27} - 2 q^{28} + 9 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 10 q^{34} - 2 q^{35} - q^{36} - 11 q^{37} + 4 q^{38} + 2 q^{40} + 5 q^{41} + 2 q^{42} - 10 q^{43} - 4 q^{44} - q^{45} - 6 q^{46} - 4 q^{47} + q^{48} + 3 q^{49} + 4 q^{50} - 10 q^{51} - 2 q^{53} + q^{54} + 2 q^{55} - 2 q^{56} - 4 q^{57} + 9 q^{58} - 8 q^{59} - 2 q^{60} + 11 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{66} + 2 q^{67} - 5 q^{68} + 6 q^{69} + 4 q^{70} - 14 q^{71} - q^{72} + 26 q^{73} - 11 q^{74} - 4 q^{75} - 2 q^{76} - 8 q^{77} - 8 q^{79} - q^{80} - q^{81} + 5 q^{82} - 12 q^{83} + 2 q^{84} - 5 q^{85} + 20 q^{86} - 9 q^{87} + 2 q^{88} + 2 q^{89} + 2 q^{90} + 12 q^{92} + 4 q^{93} + 2 q^{94} - 2 q^{95} - 2 q^{96} - 2 q^{97} + 3 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + 2 * q^5 + q^6 - 2 * q^7 + 2 * q^8 - q^9 - q^10 + 2 * q^11 - 2 * q^12 + 4 * q^14 + q^15 - q^16 - 5 * q^17 + 2 * q^18 - 2 * q^19 - q^20 - 4 * q^21 + 2 * q^22 - 6 * q^23 + q^24 - 8 * q^25 - 2 * q^27 - 2 * q^28 + 9 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 10 * q^34 - 2 * q^35 - q^36 - 11 * q^37 + 4 * q^38 + 2 * q^40 + 5 * q^41 + 2 * q^42 - 10 * q^43 - 4 * q^44 - q^45 - 6 * q^46 - 4 * q^47 + q^48 + 3 * q^49 + 4 * q^50 - 10 * q^51 - 2 * q^53 + q^54 + 2 * q^55 - 2 * q^56 - 4 * q^57 + 9 * q^58 - 8 * q^59 - 2 * q^60 + 11 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^66 + 2 * q^67 - 5 * q^68 + 6 * q^69 + 4 * q^70 - 14 * q^71 - q^72 + 26 * q^73 - 11 * q^74 - 4 * q^75 - 2 * q^76 - 8 * q^77 - 8 * q^79 - q^80 - q^81 + 5 * q^82 - 12 * q^83 + 2 * q^84 - 5 * q^85 + 20 * q^86 - 9 * q^87 + 2 * q^88 + 2 * q^89 + 2 * q^90 + 12 * q^92 + 4 * q^93 + 2 * q^94 - 2 * q^95 - 2 * q^96 - 2 * q^97 + 3 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$	1.00000			0.235702
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−2.00000			−0.436436
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	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	$0.518437\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	5.00000			0.857493
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.0821995	−	0.996616i	$-0.526194\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$	1.00000			0.158114
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$	−2.00000			−0.301511
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	−5.00000			−0.700140
$52$		0			0
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	−2.00000			−0.264906
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$	−1.00000			−0.129099
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.00000			0.246183
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	2.00000			0.239046
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	0.0666994	+	0.997773i	$0.478753\pi$
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	−0.897447	+	0.441123i	$0.854580\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	13.0000			1.52153			0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000			1.52153			0.760767	+	0.649025i	$0.224823\pi$
$74$	−5.50000	+	9.52628i	−0.639362	+	1.10741i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−4.00000			−0.455842
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.50000	−	4.33013i	0.276079	−	0.478183i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$	−2.50000	+	4.33013i	−0.271163	+	0.469668i
$86$	10.0000			1.07833
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$	−1.00000			−0.102062
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−2.00000			−0.201008
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$	2.50000	+	4.33013i	0.247537	+	0.428746i
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$	0.500000	+	0.866025i	0.0485643	+	0.0841158i
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	5.50000	−	9.52628i	0.522037	−	0.904194i
$112$	2.00000			0.188982
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−9.00000			−0.835629
$117$		0			0
$118$	8.00000			0.736460
$119$	−5.00000	−	8.66025i	−0.458349	−	0.793884i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−11.0000			−0.995893
$123$	−2.50000	+	4.33013i	−0.225417	+	0.390434i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−9.00000			−0.804984
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	6.00000	+	10.3923i	0.532414	+	0.922168i	0.999284	+	0.0378419i	$0.0120483\pi$
$127$	6.00000	+	10.3923i	0.532414	+	0.922168i	−0.466870	+	0.884326i	$0.654618\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−10.0000			−0.880451
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	−1.00000	−	1.73205i	−0.0870388	−	0.150756i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	−1.00000			−0.0860663
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$	−6.00000			−0.510754
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	−1.00000	−	1.73205i	−0.0842152	−	0.145865i
$142$	14.0000			1.17485
$143$		0			0
$144$	1.00000			0.0833333
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	11.0000			0.904194
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	6.00000			0.488273			0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000			0.488273			0.244137	+	0.969741i	$0.421495\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$	−2.50000	−	4.33013i	−0.202113	−	0.350070i
$154$	2.00000	+	3.46410i	0.161165	+	0.279145i
$155$	4.00000			0.321288
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.0000			0.945732
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	−5.00000			−0.390434
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.785687	+	0.618624i	$0.212310\pi$
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.142901	+	0.989737i	$0.454357\pi$
$168$	−2.00000			−0.154303
$169$		0			0
$170$	5.00000			0.383482
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	−0.0566411	−	0.998395i	$-0.518039\pi$
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	0.892956	−	0.450145i	$-0.148628\pi$
$174$	9.00000			0.682288
$175$	4.00000	−	6.92820i	0.302372	−	0.523723i
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$	−8.00000			−0.601317
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	−5.50000	−	9.52628i	−0.404368	−	0.700386i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	−10.0000			−0.731272
$188$	1.00000	−	1.73205i	0.0729325	−	0.126323i
$189$	1.00000	−	1.73205i	0.0727393	−	0.125988i
$190$	2.00000			0.145095
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$	−4.00000			−0.282843
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	2.50000	−	4.33013i	0.175899	−	0.304667i
$203$	−18.0000			−1.26335
$204$	2.50000	−	4.33013i	0.175035	−	0.303170i
$205$	2.50000	+	4.33013i	0.174608	+	0.302429i
$206$	−5.00000	−	8.66025i	−0.348367	−	0.603388i
$207$	6.00000			0.417029
$208$		0			0
$209$	−4.00000			−0.276686
$210$	1.00000	+	1.73205i	0.0690066	+	0.119523i
$211$	−12.0000	−	20.7846i	−0.826114	−	1.43087i	−0.901065	−	0.433684i	$-0.857213\pi$
$211$	−12.0000	−	20.7846i	−0.826114	−	1.43087i	0.0749508	−	0.997187i	$-0.476120\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$	−14.0000			−0.959264
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$	−1.00000			−0.0680414
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$	6.50000	+	11.2583i	0.439229	+	0.760767i
$220$	−2.00000			−0.134840
$221$		0			0
$222$	−11.0000			−0.738272
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	−3.00000			−0.199557
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$	−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	$0.562969\pi$
$234$		0			0
$235$	−2.00000			−0.130466
$236$	−4.00000	−	6.92820i	−0.260378	−	0.450988i
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	−5.00000	+	8.66025i	−0.324102	+	0.561361i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	−7.00000			−0.449977
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.50000	+	9.52628i	0.352101	+	0.609858i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$	5.00000			0.318788
$247$		0			0
$248$	4.00000			0.254000
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	−0.922217	−	0.386674i	$-0.873624\pi$
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	0.795978	+	0.605326i	$0.206957\pi$
$252$	2.00000			0.125988
$253$	6.00000	−	10.3923i	0.377217	−	0.653359i
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$	−5.00000			−0.313112
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	5.00000	+	8.66025i	0.311286	+	0.539164i
$259$	22.0000			1.36701
$260$		0			0
$261$	−9.00000			−0.557086
$262$	4.00000	+	6.92820i	0.247121	+	0.428026i
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	0.565376	−	0.824833i	$-0.308731\pi$
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	−0.997015	+	0.0772134i	$0.975398\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	−1.00000			−0.0614295
$266$	−2.00000	+	3.46410i	−0.122628	+	0.212398i
$267$	−1.00000	+	1.73205i	−0.0611990	+	0.106000i
$268$	−2.00000			−0.122169
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	5.00000			0.303170
$273$		0			0
$274$	−17.0000			−1.02701
$275$	−4.00000	−	6.92820i	−0.241209	−	0.417786i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	−0.652140	−	0.758099i	$-0.726128\pi$
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	0.982603	+	0.185720i	$0.0594618\pi$
$278$	−12.0000			−0.719712
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	−25.0000			−1.49137			−0.745687	−	0.666296i	$-0.767879\pi$
$281$	−25.0000			−1.49137			−0.745687	+	0.666296i	$0.767879\pi$
$282$	−1.00000	+	1.73205i	−0.0595491	+	0.103142i
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	−0.936039	−	0.351895i	$-0.885537\pi$
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	0.163270	−	0.986581i	$-0.447796\pi$
$284$	−7.00000	−	12.1244i	−0.415374	−	0.719448i
$285$	−2.00000			−0.118470
$286$		0			0
$287$	−10.0000			−0.590281
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	−2.00000			−0.117242
$292$	−6.50000	+	11.2583i	−0.380384	+	0.658844i
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	−0.880261	−	0.474490i	$-0.842633\pi$
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	0.851051	+	0.525084i	$0.175966\pi$
$294$	3.00000			0.174964
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	−5.50000	−	9.52628i	−0.319681	−	0.553704i
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	−3.00000			−0.173785
$299$		0			0
$300$	4.00000			0.230940
$301$	−10.0000	−	17.3205i	−0.576390	−	0.998337i
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$	−2.50000	+	4.33013i	−0.143621	+	0.248759i
$304$	2.00000			0.114708
$305$	5.50000	−	9.52628i	0.314929	−	0.545473i
$306$	−2.50000	+	4.33013i	−0.142915	+	0.247537i
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	5.00000	+	8.66025i	0.284440	+	0.492665i
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	3.50000	+	6.06218i	0.197516	+	0.342108i
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	33.0000			1.85346			0.926732	−	0.375722i	$-0.122605\pi$
$317$	33.0000			1.85346			0.926732	+	0.375722i	$0.122605\pi$
$318$	−0.500000	+	0.866025i	−0.0280386	+	0.0485643i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	1.00000			0.0559017
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$	−5.00000	−	8.66025i	−0.278207	−	0.481869i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−20.0000			−1.10770
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	2.50000	+	4.33013i	0.138039	+	0.239091i
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$	2.00000			0.110096
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	11.0000			0.602796
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	−9.00000			−0.490261			−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000			−0.490261			−0.245131	+	0.969490i	$0.578831\pi$
$338$		0			0
$339$	3.00000			0.162938
$340$	−2.50000	−	4.33013i	−0.135582	−	0.234834i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	−1.00000	+	1.73205i	−0.0540738	+	0.0936586i
$343$	−20.0000			−1.07990
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$	3.00000	−	5.19615i	0.161515	−	0.279751i
$346$	−22.0000			−1.18273
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	3.00000	+	5.19615i	0.160586	+	0.278144i	0.935079	−	0.354439i	$-0.115328\pi$
$349$	3.00000	+	5.19615i	0.160586	+	0.278144i	−0.774493	+	0.632583i	$0.781995\pi$
$350$	−8.00000			−0.427618
$351$		0			0
$352$	−2.00000			−0.106600
$353$	8.50000	+	14.7224i	0.452409	+	0.783596i	0.998535	−	0.0541072i	$-0.0172313\pi$
$353$	8.50000	+	14.7224i	0.452409	+	0.783596i	−0.546126	+	0.837703i	$0.683898\pi$
$354$	4.00000	+	6.92820i	0.212598	+	0.368230i
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$	−2.00000			−0.106000
$357$	5.00000	−	8.66025i	0.264628	−	0.458349i
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	30.0000			1.58334			0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000			1.58334			0.791670	+	0.610949i	$0.209212\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−2.50000	−	4.33013i	−0.131397	−	0.227586i
$363$	7.00000			0.367405
$364$		0			0
$365$	13.0000			0.680451
$366$	−5.50000	−	9.52628i	−0.287490	−	0.497947i
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	0.890945	−	0.454112i	$-0.150043\pi$
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	−0.838745	+	0.544524i	$0.816710\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	−5.00000			−0.260290
$370$	−5.50000	+	9.52628i	−0.285931	+	0.495248i
$371$	1.00000	−	1.73205i	0.0519174	−	0.0899236i
$372$	−4.00000			−0.207390
$373$	−4.50000	+	7.79423i	−0.233001	+	0.403570i	−0.958690	−	0.284453i	$-0.908188\pi$
$373$	−4.50000	+	7.79423i	−0.233001	+	0.403570i	0.725689	+	0.688023i	$0.241521\pi$
$374$	5.00000	+	8.66025i	0.258544	+	0.447811i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−2.00000			−0.103142
$377$		0			0
$378$	−2.00000			−0.102869
$379$	6.00000	+	10.3923i	0.308199	+	0.533817i	0.977969	−	0.208752i	$-0.0669403\pi$
$379$	6.00000	+	10.3923i	0.308199	+	0.533817i	−0.669769	+	0.742569i	$0.733607\pi$
$380$	−1.00000	−	1.73205i	−0.0512989	−	0.0888523i
$381$	−6.00000	+	10.3923i	−0.307389	+	0.532414i
$382$	4.00000			0.204658
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−4.00000			−0.203859
$386$	−8.50000	+	14.7224i	−0.432639	+	0.749352i
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$	−4.00000	−	6.92820i	−0.201773	−	0.349482i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−4.00000			−0.201262
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	−0.998492	−	0.0549046i	$-0.982515\pi$
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	0.546795	+	0.837267i	$0.315848\pi$
$398$	10.0000			0.501255
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$	2.00000			0.0997509
$403$		0			0
$404$	−5.00000			−0.248759
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	9.00000	+	15.5885i	0.446663	+	0.773642i
$407$	11.0000	−	19.0526i	0.545250	−	0.944400i
$408$	−5.00000			−0.247537
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	−0.428063	−	0.903749i	$-0.640804\pi$
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	0.996701	−	0.0811615i	$-0.0258630\pi$
$410$	2.50000	−	4.33013i	0.123466	−	0.213850i
$411$	17.0000			0.838548
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$	−8.00000	−	13.8564i	−0.393654	−	0.681829i
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$	−6.00000			−0.294528
$416$		0			0
$417$	12.0000			0.587643
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	16.0000	+	27.7128i	0.781651	+	1.35386i	0.930979	+	0.365072i	$0.118956\pi$
$419$	16.0000	+	27.7128i	0.781651	+	1.35386i	−0.149328	+	0.988788i	$0.547711\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$	−12.0000	+	20.7846i	−0.584151	+	1.01178i
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$	−1.00000			−0.0485643
$425$	10.0000	−	17.3205i	0.485071	−	0.840168i
$426$	7.00000	+	12.1244i	0.339151	+	0.587427i
$427$	11.0000	+	19.0526i	0.532327	+	0.922018i
$428$	−18.0000			−0.870063
$429$		0			0
$430$	10.0000			0.482243
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	0.840936	−	0.541135i	$-0.182005\pi$
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	−0.889104	+	0.457705i	$0.848672\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	−0.495388	−	0.868672i	$-0.664974\pi$
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	0.999986	−	0.00531724i	$-0.00169254\pi$
$434$	8.00000			0.384012
$435$	−4.50000	+	7.79423i	−0.215758	+	0.373705i
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	12.0000			0.574038
$438$	6.50000	−	11.2583i	0.310582	−	0.537944i
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$	1.00000	+	1.73205i	0.0476731	+	0.0825723i
$441$	−3.00000			−0.142857
$442$		0			0
$443$	20.0000			0.950229			0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000			0.950229			0.475114	+	0.879924i	$0.342407\pi$
$444$	5.50000	+	9.52628i	0.261018	+	0.452097i
$445$	1.00000	+	1.73205i	0.0474045	+	0.0821071i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	3.00000			0.141895
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	−0.965637	+	0.259895i	$0.916312\pi$
$450$	−4.00000			−0.188562
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	1.50000	+	2.59808i	0.0705541	+	0.122203i
$453$	3.00000	+	5.19615i	0.140952	+	0.244137i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	1.50000	+	2.59808i	0.0701670	+	0.121533i	0.898974	−	0.438001i	$-0.144313\pi$
$457$	1.50000	+	2.59808i	0.0701670	+	0.121533i	−0.828807	+	0.559534i	$0.810980\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$	6.00000			0.279751
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	−0.828978	−	0.559281i	$-0.811077\pi$
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	0.898840	+	0.438276i	$0.144411\pi$
$462$	−2.00000	+	3.46410i	−0.0930484	+	0.161165i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	2.00000	+	3.46410i	0.0927478	+	0.160644i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−22.0000			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	1.00000	+	1.73205i	0.0461266	+	0.0798935i
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−4.00000	+	6.92820i	−0.184115	+	0.318896i
$473$	−20.0000			−0.919601
$474$	−2.00000	+	3.46410i	−0.0918630	+	0.159111i
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$	10.0000			0.458349
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	0.956431	+	0.291958i	$0.0943068\pi$
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	−0.225372	+	0.974273i	$0.572360\pi$
$480$	−1.00000			−0.0456435
$481$		0			0
$482$	−7.00000			−0.318841
$483$	6.00000	+	10.3923i	0.273009	+	0.472866i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	−1.00000			−0.0453609
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	0.405266	+	0.914199i	$0.367179\pi$
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	−0.994352	+	0.106129i	$0.966154\pi$
$488$	5.50000	−	9.52628i	0.248973	−	0.431234i
$489$	20.0000			0.904431
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	0.975898	+	0.218229i	$0.0700279\pi$
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	−0.298957	+	0.954267i	$0.596639\pi$
$492$	−2.50000	−	4.33013i	−0.112709	−	0.195217i
$493$	−45.0000			−2.02670
$494$		0			0
$495$	−2.00000			−0.0898933
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−14.0000	−	24.2487i	−0.627986	−	1.08770i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	−12.0000	+	20.7846i	−0.536120	+	0.928588i
$502$	4.00000			0.178529
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	−0.666705	−	0.745321i	$-0.732296\pi$
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	0.978820	+	0.204723i	$0.0656294\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	2.50000	+	4.33013i	0.111249	+	0.192688i
$506$	−12.0000			−0.533465
$507$		0			0
$508$	−12.0000			−0.532414
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$	2.50000	+	4.33013i	0.110702	+	0.191741i
$511$	−13.0000	+	22.5167i	−0.575086	+	0.996078i
$512$	1.00000			0.0441942
$513$	1.00000	−	1.73205i	0.0441511	−	0.0764719i
$514$	1.50000	−	2.59808i	0.0661622	−	0.114596i
$515$	10.0000			0.440653
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−2.00000	−	3.46410i	−0.0879599	−	0.152351i
$518$	−11.0000	−	19.0526i	−0.483312	−	0.837121i
$519$	22.0000			0.965693
$520$		0			0
$521$	25.0000			1.09527			0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000			1.09527			0.547635	+	0.836717i	$0.315528\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	19.0000	+	32.9090i	0.830812	+	1.43901i	0.897395	+	0.441228i	$0.145457\pi$
$523$	19.0000	+	32.9090i	0.830812	+	1.43901i	−0.0665832	+	0.997781i	$0.521210\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$	8.00000			0.349149
$526$	−7.00000	+	12.1244i	−0.305215	+	0.528647i
$527$	−10.0000	+	17.3205i	−0.435607	+	0.754493i
$528$	2.00000			0.0870388
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	0.500000	+	0.866025i	0.0217186	+	0.0376177i
$531$	−4.00000	−	6.92820i	−0.173585	−	0.300658i
$532$	4.00000			0.173422
$533$		0			0
$534$	2.00000			0.0865485
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$	−14.0000			−0.603583
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	7.00000			0.300954			0.150477	−	0.988614i	$-0.451919\pi$
$541$	7.00000			0.300954			0.150477	+	0.988614i	$0.451919\pi$
$542$	4.00000	−	6.92820i	0.171815	−	0.297592i
$543$	2.50000	+	4.33013i	0.107285	+	0.185824i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	2.00000			0.0856706
$546$		0			0
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	8.50000	+	14.7224i	0.363102	+	0.628911i
$549$	5.50000	+	9.52628i	0.234734	+	0.406572i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	−18.0000			−0.766826
$552$	3.00000	−	5.19615i	0.127688	−	0.221163i
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$	−11.0000			−0.467345
$555$	5.50000	−	9.52628i	0.233462	−	0.404368i
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	2.00000			0.0845154
$561$	−5.00000	−	8.66025i	−0.211100	−	0.365636i
$562$	12.5000	+	21.6506i	0.527281	+	0.913277i
$563$	−20.0000	+	34.6410i	−0.842900	+	1.45994i	0.0445334	+	0.999008i	$0.485820\pi$
$563$	−20.0000	+	34.6410i	−0.842900	+	1.45994i	−0.887433	+	0.460937i	$0.847513\pi$
$564$	2.00000			0.0842152
$565$	1.50000	−	2.59808i	0.0631055	−	0.109302i
$566$	−13.0000	+	22.5167i	−0.546431	+	0.946446i
$567$	2.00000			0.0839921
$568$	−7.00000	+	12.1244i	−0.293713	+	0.508727i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$		0			0
$573$	−4.00000			−0.167102
$574$	5.00000	+	8.66025i	0.208696	+	0.361472i
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−27.0000			−1.12402			−0.562012	−	0.827129i	$-0.689973\pi$
$577$	−27.0000			−1.12402			−0.562012	+	0.827129i	$0.689973\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	8.50000	−	14.7224i	0.353248	−	0.611843i
$580$	−9.00000			−0.373705
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	1.00000	+	1.73205i	0.0414513	+	0.0717958i
$583$	−1.00000	−	1.73205i	−0.0414158	−	0.0717342i
$584$	13.0000			0.537944
$585$		0			0
$586$	1.00000			0.0413096
$587$	−16.0000	−	27.7128i	−0.660391	−	1.14383i	−0.980513	−	0.196454i	$-0.937057\pi$
$587$	−16.0000	−	27.7128i	−0.660391	−	1.14383i	0.320122	−	0.947376i	$-0.396276\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	−4.00000	+	6.92820i	−0.164817	+	0.285472i
$590$	8.00000			0.329355
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	−5.50000	+	9.52628i	−0.226049	+	0.391528i
$593$	39.0000			1.60154			0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000			1.60154			0.800769	+	0.598973i	$0.204424\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	−5.00000	−	8.66025i	−0.204980	−	0.355036i
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$	−10.0000			−0.409273
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−2.00000	−	3.46410i	−0.0816497	−	0.141421i
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	0.731774	−	0.681547i	$-0.238692\pi$
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	−0.956124	+	0.292962i	$0.905359\pi$
$602$	−10.0000	+	17.3205i	−0.407570	+	0.705931i
$603$	−2.00000			−0.0814463
$604$	−3.00000	+	5.19615i	−0.122068	+	0.211428i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	5.00000			0.203111
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	−9.00000	−	15.5885i	−0.364698	−	0.631676i
$610$	−11.0000			−0.445377
$611$		0			0
$612$	5.00000			0.202113
$613$	6.50000	+	11.2583i	0.262533	+	0.454720i	0.966914	−	0.255102i	$-0.0821090\pi$
$613$	6.50000	+	11.2583i	0.262533	+	0.454720i	−0.704382	+	0.709821i	$0.748776\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$	−2.50000	+	4.33013i	−0.100810	+	0.174608i
$616$	−4.00000			−0.161165
$617$	−7.50000	+	12.9904i	−0.301939	+	0.522973i	−0.976575	−	0.215177i	$-0.930967\pi$
$617$	−7.50000	+	12.9904i	−0.301939	+	0.522973i	0.674636	+	0.738150i	$0.264300\pi$
$618$	5.00000	−	8.66025i	0.201129	−	0.348367i
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	−3.00000	−	5.19615i	−0.120289	−	0.208347i
$623$	−4.00000			−0.160257
$624$		0			0
$625$	11.0000			0.440000
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	−2.00000	−	3.46410i	−0.0798723	−	0.138343i
$628$	3.50000	−	6.06218i	0.139665	−	0.241907i
$629$	55.0000			2.19299
$630$	−1.00000	+	1.73205i	−0.0398410	+	0.0690066i
$631$	6.00000	−	10.3923i	0.238856	−	0.413711i	−0.721530	−	0.692383i	$-0.756561\pi$
$631$	6.00000	−	10.3923i	0.238856	−	0.413711i	0.960386	+	0.278672i	$0.0898942\pi$
$632$	−4.00000			−0.159111
$633$	12.0000	−	20.7846i	0.476957	−	0.826114i
$634$	−16.5000	−	28.5788i	−0.655299	−	1.13501i
$635$	6.00000	+	10.3923i	0.238103	+	0.412406i
$636$	1.00000			0.0396526
$637$		0			0
$638$	18.0000			0.712627
$639$	−7.00000	−	12.1244i	−0.276916	−	0.479632i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$	18.0000			0.710403
$643$	4.00000	−	6.92820i	0.157745	−	0.273222i	−0.776310	−	0.630351i	$-0.782911\pi$
$643$	4.00000	−	6.92820i	0.157745	−	0.273222i	0.934055	+	0.357129i	$0.116244\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$	−10.0000			−0.393750
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−16.0000			−0.628055
$650$		0			0
$651$	−8.00000			−0.313545
$652$	10.0000	+	17.3205i	0.391630	+	0.678323i
$653$	11.0000	+	19.0526i	0.430463	+	0.745584i	0.996913	−	0.0785119i	$-0.0250169\pi$
$653$	11.0000	+	19.0526i	0.430463	+	0.745584i	−0.566450	+	0.824096i	$0.691684\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	−8.00000			−0.312586
$656$	2.50000	−	4.33013i	0.0976086	−	0.169063i
$657$	−6.50000	+	11.2583i	−0.253589	+	0.439229i
$658$	−4.00000			−0.155936
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	−0.999309	−	0.0371821i	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$	−1.00000	−	1.73205i	−0.0389249	−	0.0674200i
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	0.999874	−	0.0158695i	$-0.00505163\pi$
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	−0.513680	+	0.857982i	$0.671718\pi$
$662$	28.0000			1.08825
$663$		0			0
$664$	−6.00000			−0.232845
$665$	−2.00000	−	3.46410i	−0.0775567	−	0.134332i
$666$	−5.50000	−	9.52628i	−0.213121	−	0.369136i
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	−24.0000			−0.928588
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	1.00000	−	1.73205i	0.0386334	−	0.0669150i
$671$	22.0000			0.849301
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	−21.5000	−	37.2391i	−0.828764	−	1.43546i	−0.899008	−	0.437932i	$-0.855711\pi$
$673$	−21.5000	−	37.2391i	−0.828764	−	1.43546i	0.0702442	−	0.997530i	$-0.477622\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$	4.00000			0.153960
$676$		0			0
$677$	−46.0000			−1.76792			−0.883962	−	0.467559i	$-0.845134\pi$
$677$	−46.0000			−1.76792			−0.883962	+	0.467559i	$0.845134\pi$
$678$	−1.50000	−	2.59808i	−0.0576072	−	0.0997785i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	−2.50000	+	4.33013i	−0.0958706	+	0.166053i
$681$	14.0000			0.536481
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	−20.0000	+	34.6410i	−0.765279	+	1.32550i	0.174820	+	0.984600i	$0.444066\pi$
$683$	−20.0000	+	34.6410i	−0.765279	+	1.32550i	−0.940099	+	0.340901i	$0.889268\pi$
$684$	2.00000			0.0764719
$685$	8.50000	−	14.7224i	0.324768	−	0.562515i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−5.00000	−	8.66025i	−0.190762	−	0.330409i
$688$	10.0000			0.381246
$689$		0			0
$690$	−6.00000			−0.228416
$691$	−1.00000	−	1.73205i	−0.0380418	−	0.0658903i	0.846378	−	0.532583i	$-0.178779\pi$
$691$	−1.00000	−	1.73205i	−0.0380418	−	0.0658903i	−0.884419	+	0.466693i	$0.845445\pi$
$692$	11.0000	+	19.0526i	0.418157	+	0.724270i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$	6.00000			0.227757
$695$	6.00000	−	10.3923i	0.227593	−	0.394203i
$696$	−4.50000	+	7.79423i	−0.170572	+	0.295439i
$697$	−25.0000			−0.946943
$698$	3.00000	−	5.19615i	0.113552	−	0.196677i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$	22.0000			0.829746
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$	8.50000	−	14.7224i	0.319902	−	0.554086i
$707$	−10.0000			−0.376089
$708$	4.00000	−	6.92820i	0.150329	−	0.260378i
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	−0.971796	−	0.235824i	$-0.924221\pi$
$709$	−7.50000	+	12.9904i	−0.281668	+	0.487864i	0.690127	+	0.723688i	$0.257554\pi$
$710$	14.0000			0.525411
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$	−10.0000			−0.374241
$715$		0			0
$716$	−6.00000			−0.224231
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$	1.00000			0.0372678
$721$	−10.0000	+	17.3205i	−0.372419	+	0.645049i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	7.00000			0.260333
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	−18.0000	−	31.1769i	−0.668503	−	1.15788i
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	2.00000			0.0741759			0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000			0.0741759			0.0370879	+	0.999312i	$0.488192\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−6.50000	−	11.2583i	−0.240576	−	0.416689i
$731$	−25.0000	−	43.3013i	−0.924658	−	1.60156i
$732$	−5.50000	+	9.52628i	−0.203286	+	0.352101i
$733$	−13.0000			−0.480166			−0.240083	−	0.970752i	$-0.577175\pi$
$733$	−13.0000			−0.480166			−0.240083	+	0.970752i	$0.577175\pi$
$734$	1.00000	−	1.73205i	0.0369107	−	0.0639312i
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$	6.00000			0.221163
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$	2.50000	+	4.33013i	0.0920263	+	0.159394i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	11.0000			0.404368
$741$		0			0
$742$	−2.00000			−0.0734223
$743$	−6.00000	−	10.3923i	−0.220119	−	0.381257i	0.734725	−	0.678365i	$-0.237311\pi$
$743$	−6.00000	−	10.3923i	−0.220119	−	0.381257i	−0.954844	+	0.297108i	$0.903978\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	9.00000			0.329513
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	5.00000	−	8.66025i	0.182818	−	0.316650i
$749$	−36.0000			−1.31541
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$	−4.00000			−0.145768
$754$		0			0
$755$	6.00000			0.218362
$756$	1.00000	+	1.73205i	0.0363696	+	0.0629941i
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	−0.654827	+	0.755779i	$0.727258\pi$
$758$	6.00000	−	10.3923i	0.217930	−	0.377466i
$759$	12.0000			0.435572
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	17.0000	−	29.4449i	0.616250	−	1.06738i	−0.373914	−	0.927463i	$-0.621985\pi$
$761$	17.0000	−	29.4449i	0.616250	−	1.06738i	0.990164	−	0.139912i	$-0.0446820\pi$
$762$	12.0000			0.434714
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	−2.50000	−	4.33013i	−0.0903877	−	0.156556i
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	−0.990726	−	0.135877i	$-0.956615\pi$
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	0.377690	−	0.925932i	$-0.376718\pi$
$770$	2.00000	+	3.46410i	0.0720750	+	0.124838i
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$	17.0000			0.611843
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	−16.0000			−0.574737
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$	11.0000	+	19.0526i	0.394623	+	0.683507i
$778$	−9.50000	−	16.4545i	−0.340592	−	0.589922i
$779$	−10.0000			−0.358287
$780$		0			0
$781$	−28.0000			−1.00192
$782$	−15.0000	−	25.9808i	−0.536399	−	0.929070i
$783$	−4.50000	−	7.79423i	−0.160817	−	0.278543i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	−7.00000			−0.249841
$786$	−4.00000	+	6.92820i	−0.142675	+	0.247121i
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	−6.00000			−0.213741
$789$	7.00000	−	12.1244i	0.249207	−	0.431638i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	3.00000	+	5.19615i	0.106668	+	0.184754i
$792$	−2.00000			−0.0710669
$793$		0			0
$794$	18.0000			0.638796
$795$	−0.500000	−	0.866025i	−0.0177332	−	0.0307148i
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	−0.847771	−	0.530362i	$-0.822056\pi$
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	0.883193	+	0.469010i	$0.155389\pi$
$798$	−4.00000			−0.141598
$799$	5.00000	−	8.66025i	0.176887	−	0.306378i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−2.00000			−0.0706665
$802$	−13.5000	+	23.3827i	−0.476702	+	0.825671i
$803$	13.0000	+	22.5167i	0.458760	+	0.794596i
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$	12.0000			0.422944
$806$		0			0
$807$	14.0000			0.492823
$808$	2.50000	+	4.33013i	0.0879497	+	0.152333i
$809$	−2.50000	−	4.33013i	−0.0878953	−	0.152239i	0.818726	−	0.574184i	$-0.194681\pi$
$809$	−2.50000	−	4.33013i	−0.0878953	−	0.152239i	−0.906621	+	0.421945i	$0.861347\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	36.0000			1.26413			0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000			1.26413			0.632065	+	0.774915i	$0.282207\pi$
$812$	9.00000	−	15.5885i	0.315838	−	0.547048i
$813$	−4.00000	+	6.92820i	−0.140286	+	0.242983i
$814$	−22.0000			−0.771100
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$	2.50000	+	4.33013i	0.0875175	+	0.151585i
$817$	−10.0000	−	17.3205i	−0.349856	−	0.605968i
$818$	−23.0000			−0.804176
$819$		0			0
$820$	−5.00000			−0.174608
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$	−8.50000	−	14.7224i	−0.296472	−	0.513504i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	10.0000			0.348367
$825$	4.00000	−	6.92820i	0.139262	−	0.241209i
$826$	−8.00000	+	13.8564i	−0.278356	+	0.482126i
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	17.5000	+	30.3109i	0.607800	+	1.05274i	0.991602	+	0.129325i	$0.0412811\pi$
$829$	17.5000	+	30.3109i	0.607800	+	1.05274i	−0.383802	+	0.923415i	$0.625386\pi$
$830$	3.00000	+	5.19615i	0.104132	+	0.180361i
$831$	11.0000			0.381586
$832$		0			0
$833$	−15.0000			−0.519719
$834$	−6.00000	−	10.3923i	−0.207763	−	0.359856i
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	2.00000	−	3.46410i	0.0691714	−	0.119808i
$837$	−4.00000			−0.138260
$838$	16.0000	−	27.7128i	0.552711	−	0.957323i
$839$	22.0000	−	38.1051i	0.759524	−	1.31553i	−0.183569	−	0.983007i	$-0.558765\pi$
$839$	22.0000	−	38.1051i	0.759524	−	1.31553i	0.943093	−	0.332528i	$-0.107902\pi$
$840$	−2.00000			−0.0690066
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	−11.5000	−	19.9186i	−0.396316	−	0.686440i
$843$	−12.5000	−	21.6506i	−0.430523	−	0.745687i
$844$	24.0000			0.826114
$845$		0			0
$846$	−2.00000			−0.0687614
$847$	7.00000	+	12.1244i	0.240523	+	0.416598i
$848$	0.500000	+	0.866025i	0.0171701	+	0.0297394i
$849$	13.0000	−	22.5167i	0.446159	−	0.772770i
$850$	−20.0000			−0.685994
$851$	−33.0000	+	57.1577i	−1.13123	+	1.95934i
$852$	7.00000	−	12.1244i	0.239816	−	0.415374i
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	11.0000	−	19.0526i	0.376412	−	0.651965i
$855$	−1.00000	−	1.73205i	−0.0341993	−	0.0592349i
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	45.0000			1.53717			0.768585	−	0.639747i	$-0.220961\pi$
$857$	45.0000			1.53717			0.768585	+	0.639747i	$0.220961\pi$
$858$		0			0
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$	−5.00000	−	8.66025i	−0.170499	−	0.295312i
$861$	−5.00000	−	8.66025i	−0.170400	−	0.295141i
$862$	−1.00000	+	1.73205i	−0.0340601	+	0.0589939i
$863$	−46.0000			−1.56586			−0.782929	−	0.622111i	$-0.786275\pi$
$863$	−46.0000			−1.56586			−0.782929	+	0.622111i	$0.786275\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	11.0000	−	19.0526i	0.374011	−	0.647806i
$866$	−21.0000			−0.713609
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	−4.00000	−	6.92820i	−0.135691	−	0.235023i
$870$	9.00000			0.305129
$871$		0			0
$872$	2.00000			0.0677285
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	9.00000	−	15.5885i	0.304256	−	0.526986i
$876$	−13.0000			−0.439229
$877$	18.5000	−	32.0429i	0.624701	−	1.08201i	−0.363898	−	0.931439i	$-0.618554\pi$
$877$	18.5000	−	32.0429i	0.624701	−	1.08201i	0.988599	−	0.150574i	$-0.0481123\pi$
$878$	−5.00000	+	8.66025i	−0.168742	+	0.292269i
$879$	−1.00000			−0.0337292
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	−8.50000	−	14.7224i	−0.286372	−	0.496011i	0.686569	−	0.727065i	$-0.259116\pi$
$881$	−8.50000	−	14.7224i	−0.286372	−	0.496011i	−0.972941	+	0.231054i	$0.925783\pi$
$882$	1.50000	+	2.59808i	0.0505076	+	0.0874818i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$	−8.00000			−0.268917
$886$	−10.0000	−	17.3205i	−0.335957	−	0.581894i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$	5.50000	−	9.52628i	0.184568	−	0.319681i
$889$	−24.0000			−0.804934
$890$	1.00000	−	1.73205i	0.0335201	−	0.0580585i
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	16.0000			0.535720
$893$	2.00000	−	3.46410i	0.0669274	−	0.115922i
$894$	−1.50000	−	2.59808i	−0.0501675	−	0.0868927i
$895$	3.00000	+	5.19615i	0.100279	+	0.173688i
$896$	2.00000			0.0668153
$897$		0			0
$898$	30.0000			1.00111
$899$	18.0000	+	31.1769i	0.600334	+	1.03981i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	2.50000	−	4.33013i	0.0832871	−	0.144257i
$902$	10.0000			0.332964
$903$	10.0000	−	17.3205i	0.332779	−	0.576390i
$904$	1.50000	−	2.59808i	0.0498893	−	0.0864107i
$905$	5.00000			0.166206
$906$	3.00000	−	5.19615i	0.0996683	−	0.172631i
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$	7.00000	+	12.1244i	0.232303	+	0.402361i
$909$	−5.00000			−0.165840
$910$		0			0
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	1.50000	−	2.59808i	0.0496156	−	0.0859367i
$915$	11.0000			0.363649
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	8.00000	−	13.8564i	0.264183	−	0.457579i
$918$	−5.00000			−0.165025
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	−3.00000	−	5.19615i	−0.0989071	−	0.171312i
$921$	7.00000	+	12.1244i	0.230658	+	0.399511i
$922$	−3.00000			−0.0987997
$923$		0			0
$924$	4.00000			0.131590
$925$	22.0000	+	38.1051i	0.723356	+	1.25289i
$926$	−7.00000	−	12.1244i	−0.230034	−	0.398431i
$927$	−5.00000	+	8.66025i	−0.164222	+	0.284440i
$928$	−9.00000			−0.295439
$929$	−11.5000	+	19.9186i	−0.377303	+	0.653508i	−0.990669	−	0.136291i	$-0.956482\pi$
$929$	−11.5000	+	19.9186i	−0.377303	+	0.653508i	0.613366	+	0.789799i	$0.289815\pi$
$930$	2.00000	−	3.46410i	0.0655826	−	0.113592i
$931$	−6.00000			−0.196642
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	3.00000	+	5.19615i	0.0982156	+	0.170114i
$934$	11.0000	+	19.0526i	0.359931	+	0.623419i
$935$	−10.0000			−0.327035
$936$		0			0
$937$	−1.00000			−0.0326686			−0.0163343	−	0.999867i	$-0.505200\pi$
$937$	−1.00000			−0.0326686			−0.0163343	+	0.999867i	$0.505200\pi$
$938$	2.00000	+	3.46410i	0.0653023	+	0.113107i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$	1.00000	−	1.73205i	0.0326164	−	0.0564933i
$941$	22.0000			0.717180			0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000			0.717180			0.358590	+	0.933495i	$0.383258\pi$
$942$	−3.50000	+	6.06218i	−0.114036	+	0.197516i
$943$	15.0000	−	25.9808i	0.488467	−	0.846050i
$944$	8.00000			0.260378
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$	10.0000	+	17.3205i	0.325128	+	0.563138i
$947$	4.00000	+	6.92820i	0.129983	+	0.225136i	0.923670	−	0.383190i	$-0.125175\pi$
$947$	4.00000	+	6.92820i	0.129983	+	0.225136i	−0.793687	+	0.608326i	$0.791841\pi$
$948$	4.00000			0.129914
$949$		0			0
$950$	−8.00000			−0.259554
$951$	16.5000	+	28.5788i	0.535049	+	0.926732i
$952$	−5.00000	−	8.66025i	−0.162051	−	0.280680i
$953$	−27.0000	+	46.7654i	−0.874616	+	1.51488i	−0.0174443	+	0.999848i	$0.505553\pi$
$953$	−27.0000	+	46.7654i	−0.874616	+	1.51488i	−0.857171	+	0.515031i	$0.827780\pi$
$954$	−1.00000			−0.0323762
$955$	−2.00000	+	3.46410i	−0.0647185	+	0.112096i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	−18.0000			−0.581857
$958$	16.0000	−	27.7128i	0.516937	−	0.895360i
$959$	17.0000	+	29.4449i	0.548959	+	0.950824i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−18.0000			−0.580042
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$	−8.50000	−	14.7224i	−0.273625	−	0.473932i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$	50.0000			1.60789			0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000			1.60789			0.803946	+	0.594703i	$0.202730\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	5.00000	−	8.66025i	0.160623	−	0.278207i
$970$	2.00000			0.0642161
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	−0.980677	−	0.195633i	$-0.937324\pi$
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	0.659762	+	0.751475i	$0.270657\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	12.0000	+	20.7846i	0.384702	+	0.666324i
$974$	26.0000			0.833094
$975$		0			0
$976$	−11.0000			−0.352101
$977$	10.5000	+	18.1865i	0.335925	+	0.581839i	0.983662	−	0.180025i	$-0.0576179\pi$
$977$	10.5000	+	18.1865i	0.335925	+	0.581839i	−0.647737	+	0.761864i	$0.724285\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	−2.00000	+	3.46410i	−0.0639203	+	0.110713i
$980$	−3.00000			−0.0958315
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$	15.0000	−	25.9808i	0.478669	−	0.829079i
$983$	−60.0000			−1.91370			−0.956851	−	0.290578i	$-0.906153\pi$
$983$	−60.0000			−1.91370			−0.956851	+	0.290578i	$0.906153\pi$
$984$	−2.50000	+	4.33013i	−0.0796971	+	0.138039i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	22.5000	+	38.9711i	0.716546	+	1.24109i
$987$	4.00000			0.127321
$988$		0			0
$989$	60.0000			1.90789
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	0.686931	−	0.726722i	$-0.258957\pi$
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	−0.972826	+	0.231539i	$0.925624\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−28.0000			−0.888553
$994$	−14.0000	+	24.2487i	−0.444053	+	0.769122i
$995$	−5.00000	+	8.66025i	−0.158511	+	0.274549i
$996$	6.00000			0.190117
$997$	11.5000	−	19.9186i	0.364209	−	0.630828i	−0.624440	−	0.781073i	$-0.714673\pi$
$997$	11.5000	−	19.9186i	0.364209	−	0.630828i	0.988649	+	0.150245i	$0.0480062\pi$
$998$		0			0
$999$	5.50000	+	9.52628i	0.174012	+	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.d.991.1		2
13.2	odd	12		1014.2.b.a.337.1		2
13.3	even	3		1014.2.a.e.1.1		1
13.4	even	6		78.2.e.b.61.1	yes	2
13.5	odd	4		1014.2.i.e.361.1		4
13.6	odd	12		1014.2.i.e.823.2		4
13.7	odd	12		1014.2.i.e.823.1		4
13.8	odd	4		1014.2.i.e.361.2		4
13.9	even	3	inner	1014.2.e.d.529.1		2
13.10	even	6		1014.2.a.a.1.1		1
13.11	odd	12		1014.2.b.a.337.2		2
13.12	even	2		78.2.e.b.55.1	✓	2
39.2	even	12		3042.2.b.d.1351.2		2
39.11	even	12		3042.2.b.d.1351.1		2
39.17	odd	6		234.2.h.b.217.1		2
39.23	odd	6		3042.2.a.m.1.1		1
39.29	odd	6		3042.2.a.d.1.1		1
39.38	odd	2		234.2.h.b.55.1		2
52.3	odd	6		8112.2.a.bb.1.1		1
52.23	odd	6		8112.2.a.x.1.1		1
52.43	odd	6		624.2.q.b.529.1		2
52.51	odd	2		624.2.q.b.289.1		2
65.4	even	6		1950.2.i.b.451.1		2
65.12	odd	4		1950.2.z.b.1849.1		4
65.17	odd	12		1950.2.z.b.1699.2		4
65.38	odd	4		1950.2.z.b.1849.2		4
65.43	odd	12		1950.2.z.b.1699.1		4
65.64	even	2		1950.2.i.b.601.1		2
156.95	even	6		1872.2.t.i.1153.1		2
156.155	even	2		1872.2.t.i.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.b.55.1	✓	2	13.12	even	2
78.2.e.b.61.1	yes	2	13.4	even	6
234.2.h.b.55.1		2	39.38	odd	2
234.2.h.b.217.1		2	39.17	odd	6
624.2.q.b.289.1		2	52.51	odd	2
624.2.q.b.529.1		2	52.43	odd	6
1014.2.a.a.1.1		1	13.10	even	6
1014.2.a.e.1.1		1	13.3	even	3
1014.2.b.a.337.1		2	13.2	odd	12
1014.2.b.a.337.2		2	13.11	odd	12
1014.2.e.d.529.1		2	13.9	even	3	inner
1014.2.e.d.991.1		2	1.1	even	1	trivial
1014.2.i.e.361.1		4	13.5	odd	4
1014.2.i.e.361.2		4	13.8	odd	4
1014.2.i.e.823.1		4	13.7	odd	12
1014.2.i.e.823.2		4	13.6	odd	12
1872.2.t.i.289.1		2	156.155	even	2
1872.2.t.i.1153.1		2	156.95	even	6
1950.2.i.b.451.1		2	65.4	even	6
1950.2.i.b.601.1		2	65.64	even	2
1950.2.z.b.1699.1		4	65.43	odd	12
1950.2.z.b.1699.2		4	65.17	odd	12
1950.2.z.b.1849.1		4	65.12	odd	4
1950.2.z.b.1849.2		4	65.38	odd	4
3042.2.a.d.1.1		1	39.29	odd	6
3042.2.a.m.1.1		1	39.23	odd	6
3042.2.b.d.1351.1		2	39.11	even	12
3042.2.b.d.1351.2		2	39.2	even	12
8112.2.a.x.1.1		1	52.23	odd	6
8112.2.a.bb.1.1		1	52.3	odd	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} -1.00000 q^{12} +2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(-0.500000 + 0.866025i) q^{20} -2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -4.00000 q^{25} -1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.50000 - 9.52628i) q^{37} +2.00000 q^{38} +1.00000 q^{40} +(2.50000 + 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} -2.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{46} -2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} -5.00000 q^{51} -1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-4.00000 + 6.92820i) q^{59} -1.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +2.00000 q^{66} +(1.00000 + 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(-7.00000 + 12.1244i) q^{71} +(-0.500000 + 0.866025i) q^{72} +13.0000 q^{73} +(-5.50000 + 9.52628i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-1.00000 - 1.73205i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{84} +(-2.50000 + 4.33013i) q^{85} +10.0000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(1.00000 + 1.73205i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} -1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + 2 * q^5 + q^6 - 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{14} + q^{15} - q^{16} - 5 q^{17} + 2 q^{18} - 2 q^{19} - q^{20} - 4 q^{21} + 2 q^{22} - 6 q^{23} + q^{24} - 8 q^{25} - 2 q^{27} - 2 q^{28} + 9 q^{29} + q^{30} + 8 q^{31} - q^{32} - 2 q^{33} + 10 q^{34} - 2 q^{35} - q^{36} - 11 q^{37} + 4 q^{38} + 2 q^{40} + 5 q^{41} + 2 q^{42} - 10 q^{43} - 4 q^{44} - q^{45} - 6 q^{46} - 4 q^{47} + q^{48} + 3 q^{49} + 4 q^{50} - 10 q^{51} - 2 q^{53} + q^{54} + 2 q^{55} - 2 q^{56} - 4 q^{57} + 9 q^{58} - 8 q^{59} - 2 q^{60} + 11 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{66} + 2 q^{67} - 5 q^{68} + 6 q^{69} + 4 q^{70} - 14 q^{71} - q^{72} + 26 q^{73} - 11 q^{74} - 4 q^{75} - 2 q^{76} - 8 q^{77} - 8 q^{79} - q^{80} - q^{81} + 5 q^{82} - 12 q^{83} + 2 q^{84} - 5 q^{85} + 20 q^{86} - 9 q^{87} + 2 q^{88} + 2 q^{89} + 2 q^{90} + 12 q^{92} + 4 q^{93} + 2 q^{94} - 2 q^{95} - 2 q^{96} - 2 q^{97} + 3 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + 2 * q^5 + q^6 - 2 * q^7 + 2 * q^8 - q^9 - q^10 + 2 * q^11 - 2 * q^12 + 4 * q^14 + q^15 - q^16 - 5 * q^17 + 2 * q^18 - 2 * q^19 - q^20 - 4 * q^21 + 2 * q^22 - 6 * q^23 + q^24 - 8 * q^25 - 2 * q^27 - 2 * q^28 + 9 * q^29 + q^30 + 8 * q^31 - q^32 - 2 * q^33 + 10 * q^34 - 2 * q^35 - q^36 - 11 * q^37 + 4 * q^38 + 2 * q^40 + 5 * q^41 + 2 * q^42 - 10 * q^43 - 4 * q^44 - q^45 - 6 * q^46 - 4 * q^47 + q^48 + 3 * q^49 + 4 * q^50 - 10 * q^51 - 2 * q^53 + q^54 + 2 * q^55 - 2 * q^56 - 4 * q^57 + 9 * q^58 - 8 * q^59 - 2 * q^60 + 11 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^66 + 2 * q^67 - 5 * q^68 + 6 * q^69 + 4 * q^70 - 14 * q^71 - q^72 + 26 * q^73 - 11 * q^74 - 4 * q^75 - 2 * q^76 - 8 * q^77 - 8 * q^79 - q^80 - q^81 + 5 * q^82 - 12 * q^83 + 2 * q^84 - 5 * q^85 + 20 * q^86 - 9 * q^87 + 2 * q^88 + 2 * q^89 + 2 * q^90 + 12 * q^92 + 4 * q^93 + 2 * q^94 - 2 * q^95 - 2 * q^96 - 2 * q^97 + 3 * q^98 - 4 * q^99

Introduction

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