LMFDB - Embedded newform 1014.2.i.e.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(361,1014)]

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, 5]))

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.i (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.e.823.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	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
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	−0.215615	−	0.976478i	$-0.569176\pi$
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	0.737848	+	0.674967i	$0.235842\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$			1.00000i			0.235702i
$19$	−1.73205	−	1.00000i	−0.397360	−	0.229416i	0.287984	−	0.957635i	$-0.407015\pi$
$19$	−1.73205	−	1.00000i	−0.397360	−	0.229416i	−0.685344	+	0.728219i	$0.740348\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$			2.00000i			0.436436i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	4.00000			0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	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
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$		−	5.00000i		−	0.857493i
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−9.52628	+	5.50000i	−1.56611	+	0.904194i	−0.569495	+	0.821995i	$0.692861\pi$
$37$	−9.52628	+	5.50000i	−1.56611	+	0.904194i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$	−2.00000			−0.324443
$39$		0			0
$40$	1.00000			0.158114
$41$	−4.33013	+	2.50000i	−0.676252	+	0.390434i	−0.798441	−	0.602072i	$-0.794342\pi$
$41$	−4.33013	+	2.50000i	−0.676252	+	0.390434i	0.122189	+	0.992507i	$0.461009\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$		−	2.00000i		−	0.301511i
$45$	−0.866025	−	0.500000i	−0.129099	−	0.0745356i
$46$	5.19615	+	3.00000i	0.766131	+	0.442326i
$47$			2.00000i			0.291730i	0.989305	+	0.145865i	$0.0465965\pi$
$47$			2.00000i			0.291730i	−0.989305	+	0.145865i	$0.953403\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	3.46410	−	2.00000i	0.489898	−	0.282843i
$51$	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	$0.521879\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$		−	2.00000i		−	0.264906i
$58$	7.79423	+	4.50000i	1.02343	+	0.590879i
$59$	6.92820	+	4.00000i	0.901975	+	0.520756i	0.877841	−	0.478953i	$-0.158984\pi$
$59$	6.92820	+	4.00000i	0.901975	+	0.520756i	0.0241347	+	0.999709i	$0.492317\pi$
$60$			1.00000i			0.129099i
$61$	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
$63$	−1.73205	+	1.00000i	−0.218218	+	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.00000			0.246183
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	−0.602056	−	0.798454i	$-0.705652\pi$
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	0.390453	+	0.920623i	$0.372318\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$			2.00000i			0.239046i
$71$	−12.1244	−	7.00000i	−1.43890	−	0.830747i	−0.441123	−	0.897447i	$-0.645420\pi$
$71$	−12.1244	−	7.00000i	−1.43890	−	0.830747i	−0.997773	+	0.0666994i	$0.978753\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	13.0000i		−	1.52153i	−0.649025	−	0.760767i	$-0.724823\pi$
$73$		−	13.0000i		−	1.52153i	0.649025	−	0.760767i	$-0.275177\pi$
$74$	−5.50000	+	9.52628i	−0.639362	+	1.10741i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	−1.73205	+	1.00000i	−0.198680	+	0.114708i
$77$	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	$0.572244\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.50000	+	4.33013i	−0.276079	+	0.478183i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	1.73205	+	1.00000i	0.188982	+	0.109109i
$85$	4.33013	+	2.50000i	0.469668	+	0.271163i
$86$		−	10.0000i		−	1.07833i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	1.73205	−	1.00000i	0.183597	−	0.106000i	−0.405385	−	0.914146i	$-0.632862\pi$
$89$	1.73205	−	1.00000i	0.183597	−	0.106000i	0.588982	+	0.808146i	$0.299529\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		−	1.00000i		−	0.102062i
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$			2.00000i			0.201008i
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	0.714423	−	0.699715i	$-0.246689\pi$
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	−0.963182	+	0.268851i	$0.913356\pi$
$102$	4.33013	−	2.50000i	0.428746	−	0.247537i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$	−0.866025	+	0.500000i	−0.0841158	+	0.0485643i
$107$	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
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	1.73205	+	1.00000i	0.165145	+	0.0953463i
$111$	−9.52628	−	5.50000i	−0.904194	−	0.522037i
$112$		−	2.00000i		−	0.188982i
$113$	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
$115$	−5.19615	+	3.00000i	−0.484544	+	0.279751i
$116$	9.00000			0.835629
$117$		0			0
$118$	8.00000			0.736460
$119$	8.66025	−	5.00000i	0.793884	−	0.458349i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		−	11.0000i		−	0.995893i
$123$	−4.33013	−	2.50000i	−0.390434	−	0.225417i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$			9.00000i			0.804984i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	−0.999284	−	0.0378419i	$-0.987952\pi$
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	0.466870	−	0.884326i	$-0.345382\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	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	$0.613642\pi$
$132$	1.73205	−	1.00000i	0.150756	−	0.0870388i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		−	1.00000i		−	0.0860663i
$136$	−4.33013	−	2.50000i	−0.371305	−	0.214373i
$137$	−14.7224	−	8.50000i	−1.25782	−	0.726204i	−0.285171	−	0.958477i	$-0.592051\pi$
$137$	−14.7224	−	8.50000i	−1.25782	−	0.726204i	−0.972651	+	0.232273i	$0.925384\pi$
$138$			6.00000i			0.510754i
$139$	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
$141$	−1.73205	+	1.00000i	−0.145865	+	0.0842152i
$142$	−14.0000			−1.17485
$143$		0			0
$144$	1.00000			0.0833333
$145$	−7.79423	+	4.50000i	−0.647275	+	0.373705i
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$			11.0000i			0.904194i
$149$	2.59808	+	1.50000i	0.212843	+	0.122885i	0.602632	−	0.798019i	$-0.294119\pi$
$149$	2.59808	+	1.50000i	0.212843	+	0.122885i	−0.389789	+	0.920904i	$0.627452\pi$
$150$	3.46410	+	2.00000i	0.282843	+	0.163299i
$151$		−	6.00000i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$151$		−	6.00000i		−	0.488273i	0.969741	−	0.244137i	$-0.0785045\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$	2.50000	+	4.33013i	0.202113	+	0.350070i
$154$	3.46410	−	2.00000i	0.279145	−	0.161165i
$155$	−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	$0.590112\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			12.0000i			0.945732i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.367477	−	0.930033i	$-0.619778\pi$
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.989170	+	0.146772i	$0.953112\pi$
$164$			5.00000i			0.390434i
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	20.7846	−	12.0000i	1.60836	−	0.928588i	0.618624	−	0.785687i	$-0.287690\pi$
$167$	20.7846	−	12.0000i	1.60836	−	0.928588i	0.989737	−	0.142901i	$-0.0456431\pi$
$168$	2.00000			0.154303
$169$		0			0
$170$	5.00000			0.383482
$171$	1.73205	−	1.00000i	0.132453	−	0.0764719i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	0.0566411	+	0.998395i	$0.481961\pi$
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	−0.892956	+	0.450145i	$0.851372\pi$
$174$			9.00000i			0.682288i
$175$	6.92820	+	4.00000i	0.523723	+	0.302372i
$176$	−1.73205	−	1.00000i	−0.130558	−	0.0753778i
$177$			8.00000i			0.601317i
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$	5.19615	−	3.00000i	0.383065	−	0.221163i
$185$	−5.50000	−	9.52628i	−0.404368	−	0.700386i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$		−	10.0000i		−	0.731272i
$188$	1.73205	+	1.00000i	0.126323	+	0.0729325i
$189$	−1.73205	−	1.00000i	−0.125988	−	0.0727393i
$190$		−	2.00000i		−	0.145095i
$191$	−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
$193$	−14.7224	+	8.50000i	−1.05974	+	0.611843i	−0.925361	−	0.379086i	$-0.876238\pi$
$193$	−14.7224	+	8.50000i	−1.05974	+	0.611843i	−0.134382	+	0.990930i	$0.542905\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$		−	4.00000i		−	0.282843i
$201$	−1.73205	−	1.00000i	−0.122169	−	0.0705346i
$202$	−4.33013	−	2.50000i	−0.304667	−	0.175899i
$203$			18.0000i			1.26335i
$204$	2.50000	−	4.33013i	0.175035	−	0.303170i
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$	−8.66025	+	5.00000i	−0.603388	+	0.348367i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−4.00000			−0.276686
$210$	−1.73205	+	1.00000i	−0.119523	+	0.0690066i
$211$	−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
$213$		−	14.0000i		−	0.959264i
$214$	15.5885	+	9.00000i	1.06561	+	0.615227i
$215$	8.66025	+	5.00000i	0.590624	+	0.340997i
$216$			1.00000i			0.0680414i
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	11.2583	−	6.50000i	0.760767	−	0.439229i
$220$	2.00000			0.134840
$221$		0			0
$222$	−11.0000			−0.738272
$223$	13.8564	−	8.00000i	0.927894	−	0.535720i	0.0417488	−	0.999128i	$-0.486707\pi$
$223$	13.8564	−	8.00000i	0.927894	−	0.535720i	0.886145	+	0.463409i	$0.153374\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$		−	3.00000i		−	0.199557i
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	0.845120	−	0.534577i	$-0.179529\pi$
$227$	12.1244	+	7.00000i	0.804722	+	0.464606i	−0.0403978	+	0.999184i	$0.512863\pi$
$228$	−1.73205	−	1.00000i	−0.114708	−	0.0662266i
$229$			10.0000i			0.660819i	0.943838	+	0.330409i	$0.107187\pi$
$229$			10.0000i			0.660819i	−0.943838	+	0.330409i	$0.892813\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$	2.00000	+	3.46410i	0.131590	+	0.227921i
$232$	7.79423	−	4.50000i	0.511716	−	0.295439i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	−2.00000			−0.130466
$236$	6.92820	−	4.00000i	0.450988	−	0.260378i
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	5.00000	−	8.66025i	0.324102	−	0.561361i
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	−6.06218	−	3.50000i	−0.390499	−	0.225455i	0.291877	−	0.956456i	$-0.405720\pi$
$241$	−6.06218	−	3.50000i	−0.390499	−	0.225455i	−0.682376	+	0.731001i	$0.739053\pi$
$242$			7.00000i			0.449977i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.50000	−	9.52628i	−0.352101	−	0.609858i
$245$	2.59808	−	1.50000i	0.165985	−	0.0958315i
$246$	−5.00000			−0.318788
$247$		0			0
$248$	4.00000			0.254000
$249$	5.19615	−	3.00000i	0.329293	−	0.190117i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	2.00000	−	3.46410i	0.126239	−	0.218652i	−0.795978	−	0.605326i	$-0.793043\pi$
$251$	2.00000	−	3.46410i	0.126239	−	0.218652i	0.922217	+	0.386674i	$0.126376\pi$
$252$			2.00000i			0.125988i
$253$	10.3923	+	6.00000i	0.653359	+	0.377217i
$254$	−10.3923	−	6.00000i	−0.652071	−	0.376473i
$255$			5.00000i			0.313112i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$	8.66025	−	5.00000i	0.539164	−	0.311286i
$259$	−22.0000			−1.36701
$260$		0			0
$261$	−9.00000			−0.557086
$262$	−6.92820	+	4.00000i	−0.428026	+	0.247121i
$263$	−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
$265$		−	1.00000i		−	0.0614295i
$266$	−3.46410	−	2.00000i	−0.212398	−	0.122628i
$267$	1.73205	+	1.00000i	0.106000	+	0.0611990i
$268$			2.00000i			0.122169i
$269$	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
$271$	6.92820	−	4.00000i	0.420858	−	0.242983i	−0.274586	−	0.961563i	$-0.588541\pi$
$271$	6.92820	−	4.00000i	0.420858	−	0.242983i	0.695444	+	0.718580i	$0.255208\pi$
$272$	−5.00000			−0.303170
$273$		0			0
$274$	−17.0000			−1.02701
$275$	6.92820	−	4.00000i	0.417786	−	0.241209i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	−0.982603	−	0.185720i	$-0.940538\pi$
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	0.652140	+	0.758099i	$0.273872\pi$
$278$		−	12.0000i		−	0.719712i
$279$	−3.46410	−	2.00000i	−0.207390	−	0.119737i
$280$	1.73205	+	1.00000i	0.103510	+	0.0597614i
$281$			25.0000i			1.49137i	0.666296	+	0.745687i	$0.267879\pi$
$281$			25.0000i			1.49137i	−0.666296	+	0.745687i	$0.732121\pi$
$282$	−1.00000	+	1.73205i	−0.0595491	+	0.103142i
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	0.936039	+	0.351895i	$0.114463\pi$
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	−0.163270	+	0.986581i	$0.552204\pi$
$284$	−12.1244	+	7.00000i	−0.719448	+	0.415374i
$285$	2.00000			0.118470
$286$		0			0
$287$	−10.0000			−0.590281
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$		−	2.00000i		−	0.117242i
$292$	−11.2583	−	6.50000i	−0.658844	−	0.380384i
$293$	0.866025	+	0.500000i	0.0505937	+	0.0292103i	0.525084	−	0.851051i	$-0.324034\pi$
$293$	0.866025	+	0.500000i	0.0505937	+	0.0292103i	−0.474490	+	0.880261i	$0.657367\pi$
$294$		−	3.00000i		−	0.174964i
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	5.50000	+	9.52628i	0.319681	+	0.553704i
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$	3.00000			0.173785
$299$		0			0
$300$	4.00000			0.230940
$301$	17.3205	−	10.0000i	0.998337	−	0.576390i
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$	2.50000	−	4.33013i	0.143621	−	0.248759i
$304$			2.00000i			0.114708i
$305$	9.52628	+	5.50000i	0.545473	+	0.314929i
$306$	4.33013	+	2.50000i	0.247537	+	0.142915i
$307$		−	14.0000i		−	0.799022i	−0.916728	−	0.399511i	$-0.869180\pi$
$307$		−	14.0000i		−	0.799022i	0.916728	−	0.399511i	$-0.130820\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	−5.00000	−	8.66025i	−0.284440	−	0.492665i
$310$	−3.46410	+	2.00000i	−0.196748	+	0.113592i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−6.06218	+	3.50000i	−0.342108	+	0.197516i
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$			33.0000i			1.85346i	0.375722	+	0.926732i	$0.377395\pi$
$317$			33.0000i			1.85346i	−0.375722	+	0.926732i	$0.622605\pi$
$318$	−0.866025	−	0.500000i	−0.0485643	−	0.0280386i
$319$	15.5885	+	9.00000i	0.872786	+	0.503903i
$320$		−	1.00000i		−	0.0559017i
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$	6.00000	+	10.3923i	0.334367	+	0.579141i
$323$	−8.66025	+	5.00000i	−0.481869	+	0.278207i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−20.0000			−1.10770
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$	2.50000	+	4.33013i	0.138039	+	0.239091i
$329$	−2.00000	+	3.46410i	−0.110264	+	0.190982i
$330$			2.00000i			0.110096i
$331$	−24.2487	−	14.0000i	−1.33283	−	0.769510i	−0.347097	−	0.937829i	$-0.612833\pi$
$331$	−24.2487	−	14.0000i	−1.33283	−	0.769510i	−0.985732	+	0.168320i	$0.946166\pi$
$332$	−5.19615	−	3.00000i	−0.285176	−	0.164646i
$333$		−	11.0000i		−	0.602796i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$	−1.00000	−	1.73205i	−0.0546358	−	0.0946320i
$336$	1.73205	−	1.00000i	0.0944911	−	0.0545545i
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$		0			0
$339$	3.00000			0.162938
$340$	4.33013	−	2.50000i	0.234834	−	0.135582i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	1.00000	−	1.73205i	0.0540738	−	0.0936586i
$343$		−	20.0000i		−	1.07990i
$344$	−8.66025	−	5.00000i	−0.466930	−	0.269582i
$345$	−5.19615	−	3.00000i	−0.279751	−	0.161515i
$346$			22.0000i			1.18273i
$347$	−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
$349$	5.19615	−	3.00000i	0.278144	−	0.160586i	−0.354439	−	0.935079i	$-0.615328\pi$
$349$	5.19615	−	3.00000i	0.278144	−	0.160586i	0.632583	+	0.774493i	$0.281995\pi$
$350$	8.00000			0.427618
$351$		0			0
$352$	−2.00000			−0.106600
$353$	−14.7224	+	8.50000i	−0.783596	+	0.452409i	−0.837703	−	0.546126i	$-0.816102\pi$
$353$	−14.7224	+	8.50000i	−0.783596	+	0.452409i	0.0541072	+	0.998535i	$0.482769\pi$
$354$	4.00000	+	6.92820i	0.212598	+	0.368230i
$355$	7.00000	−	12.1244i	0.371521	−	0.643494i
$356$		−	2.00000i		−	0.106000i
$357$	8.66025	+	5.00000i	0.458349	+	0.264628i
$358$	−5.19615	−	3.00000i	−0.274625	−	0.158555i
$359$		−	30.0000i		−	1.58334i	−0.610949	−	0.791670i	$-0.709212\pi$
$359$		−	30.0000i		−	1.58334i	0.610949	−	0.791670i	$-0.290788\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$	−4.33013	+	2.50000i	−0.227586	+	0.131397i
$363$	−7.00000			−0.367405
$364$		0			0
$365$	13.0000			0.680451
$366$	9.52628	−	5.50000i	0.497947	−	0.287490i
$367$	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
$369$		−	5.00000i		−	0.260290i
$370$	−9.52628	−	5.50000i	−0.495248	−	0.285931i
$371$	−1.73205	−	1.00000i	−0.0899236	−	0.0519174i
$372$			4.00000i			0.207390i
$373$	−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
$375$	−7.79423	+	4.50000i	−0.402492	+	0.232379i
$376$	2.00000			0.103142
$377$		0			0
$378$	−2.00000			−0.102869
$379$	−10.3923	+	6.00000i	−0.533817	+	0.308199i	−0.742569	−	0.669769i	$-0.766393\pi$
$379$	−10.3923	+	6.00000i	−0.533817	+	0.308199i	0.208752	+	0.977969i	$0.433060\pi$
$380$	−1.00000	−	1.73205i	−0.0512989	−	0.0888523i
$381$	6.00000	−	10.3923i	0.307389	−	0.532414i
$382$			4.00000i			0.204658i
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.925997	−	0.377531i	$-0.123227\pi$
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.136047	+	0.990702i	$0.456560\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$			4.00000i			0.203859i
$386$	−8.50000	+	14.7224i	−0.432639	+	0.749352i
$387$	5.00000	+	8.66025i	0.254164	+	0.440225i
$388$	−1.73205	+	1.00000i	−0.0879316	+	0.0507673i
$389$	−19.0000			−0.963338			−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000			−0.963338			−0.481669	+	0.876353i	$0.659969\pi$
$390$		0			0
$391$	30.0000			1.51717
$392$	−2.59808	+	1.50000i	−0.131223	+	0.0757614i
$393$	−4.00000	−	6.92820i	−0.201773	−	0.349482i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$		−	4.00000i		−	0.201262i
$396$	1.73205	+	1.00000i	0.0870388	+	0.0502519i
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	0.837267	−	0.546795i	$-0.184152\pi$
$397$	15.5885	+	9.00000i	0.782362	+	0.451697i	−0.0549046	+	0.998492i	$0.517485\pi$
$398$		−	10.0000i		−	0.501255i
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−23.3827	+	13.5000i	−1.16768	+	0.674158i	−0.953131	−	0.302556i	$-0.902160\pi$
$401$	−23.3827	+	13.5000i	−1.16768	+	0.674158i	−0.214544	+	0.976714i	$0.568827\pi$
$402$	−2.00000			−0.0997509
$403$		0			0
$404$	−5.00000			−0.248759
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	9.00000	+	15.5885i	0.446663	+	0.773642i
$407$	−11.0000	+	19.0526i	−0.545250	+	0.944400i
$408$		−	5.00000i		−	0.247537i
$409$	19.9186	+	11.5000i	0.984911	+	0.568638i	0.903749	−	0.428063i	$-0.140804\pi$
$409$	19.9186	+	11.5000i	0.984911	+	0.568638i	0.0811615	+	0.996701i	$0.474137\pi$
$410$	−4.33013	−	2.50000i	−0.213850	−	0.123466i
$411$		−	17.0000i		−	0.838548i
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$	8.00000	+	13.8564i	0.393654	+	0.681829i
$414$	−5.19615	+	3.00000i	−0.255377	+	0.147442i
$415$	6.00000			0.294528
$416$		0			0
$417$	12.0000			0.587643
$418$	−3.46410	+	2.00000i	−0.169435	+	0.0978232i
$419$	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
$421$			23.0000i			1.12095i	0.828171	+	0.560476i	$0.189382\pi$
$421$			23.0000i			1.12095i	−0.828171	+	0.560476i	$0.810618\pi$
$422$	−20.7846	−	12.0000i	−1.01178	−	0.584151i
$423$	−1.73205	−	1.00000i	−0.0842152	−	0.0486217i
$424$			1.00000i			0.0485643i
$425$	10.0000	−	17.3205i	0.485071	−	0.840168i
$426$	−7.00000	−	12.1244i	−0.339151	−	0.587427i
$427$	19.0526	−	11.0000i	0.922018	−	0.532327i
$428$	18.0000			0.870063
$429$		0			0
$430$	10.0000			0.482243
$431$	1.73205	−	1.00000i	0.0834300	−	0.0481683i	−0.457705	−	0.889104i	$-0.651328\pi$
$431$	1.73205	−	1.00000i	0.0834300	−	0.0481683i	0.541135	+	0.840936i	$0.317995\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−10.5000	+	18.1865i	−0.504598	+	0.873989i	0.495388	+	0.868672i	$0.335026\pi$
$433$	−10.5000	+	18.1865i	−0.504598	+	0.873989i	−0.999986	+	0.00531724i	$0.998307\pi$
$434$			8.00000i			0.384012i
$435$	−7.79423	−	4.50000i	−0.373705	−	0.215758i
$436$	1.73205	+	1.00000i	0.0829502	+	0.0478913i
$437$		−	12.0000i		−	0.574038i
$438$	6.50000	−	11.2583i	0.310582	−	0.537944i
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$	1.73205	−	1.00000i	0.0825723	−	0.0476731i
$441$	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	$0.342407\pi$
$444$	−9.52628	+	5.50000i	−0.452097	+	0.261018i
$445$	1.00000	+	1.73205i	0.0474045	+	0.0821071i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$			3.00000i			0.141895i
$448$	−1.73205	−	1.00000i	−0.0818317	−	0.0472456i
$449$	25.9808	+	15.0000i	1.22611	+	0.707894i	0.966213	−	0.257743i	$-0.0829789\pi$
$449$	25.9808	+	15.0000i	1.22611	+	0.707894i	0.259895	+	0.965637i	$0.416312\pi$
$450$			4.00000i			0.188562i
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$	5.19615	−	3.00000i	0.244137	−	0.140952i
$454$	14.0000			0.657053
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−2.59808	+	1.50000i	−0.121533	+	0.0701670i	−0.559534	−	0.828807i	$-0.689020\pi$
$457$	−2.59808	+	1.50000i	−0.121533	+	0.0701670i	0.438001	+	0.898974i	$0.355687\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$	−2.50000	+	4.33013i	−0.116690	+	0.202113i
$460$			6.00000i			0.279751i
$461$	2.59808	+	1.50000i	0.121004	+	0.0698620i	0.559281	−	0.828978i	$-0.311077\pi$
$461$	2.59808	+	1.50000i	0.121004	+	0.0698620i	−0.438276	+	0.898840i	$0.644411\pi$
$462$	3.46410	+	2.00000i	0.161165	+	0.0930484i
$463$		−	14.0000i		−	0.650635i	−0.945605	−	0.325318i	$-0.894529\pi$
$463$		−	14.0000i		−	0.650635i	0.945605	−	0.325318i	$-0.105471\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	5.19615	−	3.00000i	0.240707	−	0.138972i
$467$	22.0000			1.01804			0.509019	−	0.860755i	$-0.330008\pi$
$467$	22.0000			1.01804			0.509019	+	0.860755i	$0.330008\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	−1.73205	+	1.00000i	−0.0798935	+	0.0461266i
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	4.00000	−	6.92820i	0.184115	−	0.318896i
$473$		−	20.0000i		−	0.919601i
$474$	−3.46410	−	2.00000i	−0.159111	−	0.0918630i
$475$	−6.92820	−	4.00000i	−0.317888	−	0.183533i
$476$		−	10.0000i		−	0.458349i
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	27.7128	−	16.0000i	1.26623	−	0.731059i	0.291958	−	0.956431i	$-0.405693\pi$
$479$	27.7128	−	16.0000i	1.26623	−	0.731059i	0.974273	+	0.225372i	$0.0723599\pi$
$480$	1.00000			0.0456435
$481$		0			0
$482$	−7.00000			−0.318841
$483$	−10.3923	+	6.00000i	−0.472866	+	0.273009i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		−	1.00000i		−	0.0453609i
$487$	−22.5167	−	13.0000i	−1.02033	−	0.589086i	−0.106129	−	0.994352i	$-0.533846\pi$
$487$	−22.5167	−	13.0000i	−1.02033	−	0.589086i	−0.914199	+	0.405266i	$0.867179\pi$
$488$	−9.52628	−	5.50000i	−0.431234	−	0.248973i
$489$		−	20.0000i		−	0.904431i
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$	−4.33013	+	2.50000i	−0.195217	+	0.112709i
$493$	45.0000			2.02670
$494$		0			0
$495$	−2.00000			−0.0898933
$496$	3.46410	−	2.00000i	0.155543	−	0.0898027i
$497$	−14.0000	−	24.2487i	−0.627986	−	1.08770i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	7.79423	+	4.50000i	0.348569	+	0.201246i
$501$	20.7846	+	12.0000i	0.928588	+	0.536120i
$502$		−	4.00000i		−	0.178529i
$503$	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
$505$	4.33013	−	2.50000i	0.192688	−	0.111249i
$506$	12.0000			0.533465
$507$		0			0
$508$	−12.0000			−0.532414
$509$	−12.9904	+	7.50000i	−0.575789	+	0.332432i	−0.759458	−	0.650556i	$-0.774536\pi$
$509$	−12.9904	+	7.50000i	−0.575789	+	0.332432i	0.183669	+	0.982988i	$0.441202\pi$
$510$	2.50000	+	4.33013i	0.110702	+	0.191741i
$511$	13.0000	−	22.5167i	0.575086	−	0.996078i
$512$			1.00000i			0.0441942i
$513$	1.73205	+	1.00000i	0.0764719	+	0.0441511i
$514$	−2.59808	−	1.50000i	−0.114596	−	0.0661622i
$515$		−	10.0000i		−	0.440653i
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	2.00000	+	3.46410i	0.0879599	+	0.152351i
$518$	−19.0526	+	11.0000i	−0.837121	+	0.483312i
$519$	−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	$0.315528\pi$
$522$	−7.79423	+	4.50000i	−0.341144	+	0.196960i
$523$	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
$525$			8.00000i			0.349149i
$526$	−12.1244	−	7.00000i	−0.528647	−	0.305215i
$527$	17.3205	+	10.0000i	0.754493	+	0.435607i
$528$		−	2.00000i		−	0.0870388i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−0.500000	−	0.866025i	−0.0217186	−	0.0376177i
$531$	−6.92820	+	4.00000i	−0.300658	+	0.173585i
$532$	−4.00000			−0.173422
$533$		0			0
$534$	2.00000			0.0865485
$535$	−15.5885	+	9.00000i	−0.673948	+	0.389104i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$		−	14.0000i		−	0.603583i
$539$	−5.19615	−	3.00000i	−0.223814	−	0.129219i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$		−	7.00000i		−	0.300954i	−0.988614	−	0.150477i	$-0.951919\pi$
$541$		−	7.00000i		−	0.300954i	0.988614	−	0.150477i	$-0.0480809\pi$
$542$	4.00000	−	6.92820i	0.171815	−	0.297592i
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$	−4.33013	+	2.50000i	−0.185653	+	0.107187i
$545$	−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	$0.486386\pi$
$548$	−14.7224	+	8.50000i	−0.628911	+	0.363102i
$549$	5.50000	+	9.52628i	0.234734	+	0.406572i
$550$	4.00000	−	6.92820i	0.170561	−	0.295420i
$551$		−	18.0000i		−	0.766826i
$552$	5.19615	+	3.00000i	0.221163	+	0.127688i
$553$	−6.92820	−	4.00000i	−0.294617	−	0.170097i
$554$			11.0000i			0.467345i
$555$	5.50000	−	9.52628i	0.233462	−	0.404368i
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	−0.655953	−	0.754802i	$-0.727733\pi$
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	0.325701	+	0.945473i	$0.394400\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	2.00000			0.0845154
$561$	8.66025	−	5.00000i	0.365636	−	0.211100i
$562$	12.5000	+	21.6506i	0.527281	+	0.913277i
$563$	20.0000	−	34.6410i	0.842900	−	1.45994i	−0.0445334	−	0.999008i	$-0.514180\pi$
$563$	20.0000	−	34.6410i	0.842900	−	1.45994i	0.887433	−	0.460937i	$-0.152487\pi$
$564$			2.00000i			0.0842152i
$565$	2.59808	+	1.50000i	0.109302	+	0.0631055i
$566$	22.5167	+	13.0000i	0.946446	+	0.546431i
$567$		−	2.00000i		−	0.0839921i
$568$	−7.00000	+	12.1244i	−0.293713	+	0.508727i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	1.73205	−	1.00000i	0.0725476	−	0.0418854i
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$		0			0
$573$	−4.00000			−0.167102
$574$	−8.66025	+	5.00000i	−0.361472	+	0.208696i
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	27.0000i		−	1.12402i	−0.827129	−	0.562012i	$-0.810027\pi$
$577$		−	27.0000i		−	1.12402i	0.827129	−	0.562012i	$-0.189973\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$	−14.7224	−	8.50000i	−0.611843	−	0.353248i
$580$			9.00000i			0.373705i
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−1.00000	−	1.73205i	−0.0414513	−	0.0717958i
$583$	−1.73205	+	1.00000i	−0.0717342	+	0.0414158i
$584$	−13.0000			−0.537944
$585$		0			0
$586$	1.00000			0.0413096
$587$	27.7128	−	16.0000i	1.14383	−	0.660391i	0.196454	−	0.980513i	$-0.437057\pi$
$587$	27.7128	−	16.0000i	1.14383	−	0.660391i	0.947376	+	0.320122i	$0.103724\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	4.00000	−	6.92820i	0.164817	−	0.285472i
$590$			8.00000i			0.329355i
$591$	−5.19615	−	3.00000i	−0.213741	−	0.123404i
$592$	9.52628	+	5.50000i	0.391528	+	0.226049i
$593$		−	39.0000i		−	1.60154i	−0.598973	−	0.800769i	$-0.704424\pi$
$593$		−	39.0000i		−	1.60154i	0.598973	−	0.800769i	$-0.295576\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	5.00000	+	8.66025i	0.204980	+	0.355036i
$596$	2.59808	−	1.50000i	0.106421	−	0.0614424i
$597$	10.0000			0.409273
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	3.46410	−	2.00000i	0.141421	−	0.0816497i
$601$	−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
$603$		−	2.00000i		−	0.0814463i
$604$	−5.19615	−	3.00000i	−0.211428	−	0.122068i
$605$	−6.06218	−	3.50000i	−0.246463	−	0.142295i
$606$		−	5.00000i		−	0.203111i
$607$	−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
$609$	−15.5885	+	9.00000i	−0.631676	+	0.364698i
$610$	11.0000			0.445377
$611$		0			0
$612$	5.00000			0.202113
$613$	−11.2583	+	6.50000i	−0.454720	+	0.262533i	−0.709821	−	0.704382i	$-0.751224\pi$
$613$	−11.2583	+	6.50000i	−0.454720	+	0.262533i	0.255102	+	0.966914i	$0.417891\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$	2.50000	−	4.33013i	0.100810	−	0.174608i
$616$		−	4.00000i		−	0.161165i
$617$	−12.9904	−	7.50000i	−0.522973	−	0.301939i	0.215177	−	0.976575i	$-0.430967\pi$
$617$	−12.9904	−	7.50000i	−0.522973	−	0.301939i	−0.738150	+	0.674636i	$0.764300\pi$
$618$	−8.66025	−	5.00000i	−0.348367	−	0.201129i
$619$			32.0000i			1.28619i	0.765787	+	0.643094i	$0.222350\pi$
$619$			32.0000i			1.28619i	−0.765787	+	0.643094i	$0.777650\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	−5.19615	+	3.00000i	−0.208347	+	0.120289i
$623$	4.00000			0.160257
$624$		0			0
$625$	11.0000			0.440000
$626$	5.19615	−	3.00000i	0.207680	−	0.119904i
$627$	−2.00000	−	3.46410i	−0.0798723	−	0.138343i
$628$	−3.50000	+	6.06218i	−0.139665	+	0.241907i
$629$			55.0000i			2.19299i
$630$	−1.73205	−	1.00000i	−0.0690066	−	0.0398410i
$631$	−10.3923	−	6.00000i	−0.413711	−	0.238856i	0.278672	−	0.960386i	$-0.410106\pi$
$631$	−10.3923	−	6.00000i	−0.413711	−	0.238856i	−0.692383	+	0.721530i	$0.743439\pi$
$632$			4.00000i			0.159111i
$633$	12.0000	−	20.7846i	0.476957	−	0.826114i
$634$	16.5000	+	28.5788i	0.655299	+	1.13501i
$635$	10.3923	−	6.00000i	0.412406	−	0.238103i
$636$	−1.00000			−0.0396526
$637$		0			0
$638$	18.0000			0.712627
$639$	12.1244	−	7.00000i	0.479632	−	0.276916i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	−0.812421	−	0.583071i	$-0.801851\pi$
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	0.911165	+	0.412042i	$0.135184\pi$
$642$			18.0000i			0.710403i
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	0.630351	−	0.776310i	$-0.282911\pi$
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	−0.357129	+	0.934055i	$0.616244\pi$
$644$	10.3923	+	6.00000i	0.409514	+	0.236433i
$645$			10.0000i			0.393750i
$646$	−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	$0.833333\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	16.0000			0.628055
$650$		0			0
$651$	−8.00000			−0.313545
$652$	−17.3205	+	10.0000i	−0.678323	+	0.391630i
$653$	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
$655$		−	8.00000i		−	0.312586i
$656$	4.33013	+	2.50000i	0.169063	+	0.0976086i
$657$	11.2583	+	6.50000i	0.439229	+	0.253589i
$658$			4.00000i			0.155936i
$659$	−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
$661$	21.6506	−	12.5000i	0.842112	−	0.486194i	−0.0158695	−	0.999874i	$-0.505052\pi$
$661$	21.6506	−	12.5000i	0.842112	−	0.486194i	0.857982	+	0.513680i	$0.171718\pi$
$662$	−28.0000			−1.08825
$663$		0			0
$664$	−6.00000			−0.232845
$665$	3.46410	−	2.00000i	0.134332	−	0.0775567i
$666$	−5.50000	−	9.52628i	−0.213121	−	0.369136i
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$		−	24.0000i		−	0.928588i
$669$	13.8564	+	8.00000i	0.535720	+	0.309298i
$670$	−1.73205	−	1.00000i	−0.0669150	−	0.0386334i
$671$		−	22.0000i		−	0.849301i
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	21.5000	+	37.2391i	0.828764	+	1.43546i	0.899008	+	0.437932i	$0.144289\pi$
$673$	21.5000	+	37.2391i	0.828764	+	1.43546i	−0.0702442	+	0.997530i	$0.522378\pi$
$674$	7.79423	−	4.50000i	0.300222	−	0.173334i
$675$	−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	$0.845134\pi$
$678$	2.59808	−	1.50000i	0.0997785	−	0.0576072i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	2.50000	−	4.33013i	0.0958706	−	0.166053i
$681$			14.0000i			0.536481i
$682$	6.92820	+	4.00000i	0.265295	+	0.153168i
$683$	34.6410	+	20.0000i	1.32550	+	0.765279i	0.984600	−	0.174820i	$-0.0559345\pi$
$683$	34.6410	+	20.0000i	1.32550	+	0.765279i	0.340901	+	0.940099i	$0.389268\pi$
$684$		−	2.00000i		−	0.0764719i
$685$	8.50000	−	14.7224i	0.324768	−	0.562515i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−8.66025	+	5.00000i	−0.330409	+	0.190762i
$688$	−10.0000			−0.381246
$689$		0			0
$690$	−6.00000			−0.228416
$691$	1.73205	−	1.00000i	0.0658903	−	0.0380418i	−0.466693	−	0.884419i	$-0.654555\pi$
$691$	1.73205	−	1.00000i	0.0658903	−	0.0380418i	0.532583	+	0.846378i	$0.321221\pi$
$692$	11.0000	+	19.0526i	0.418157	+	0.724270i
$693$	−2.00000	+	3.46410i	−0.0759737	+	0.131590i
$694$			6.00000i			0.227757i
$695$	10.3923	+	6.00000i	0.394203	+	0.227593i
$696$	7.79423	+	4.50000i	0.295439	+	0.170572i
$697$			25.0000i			0.946943i
$698$	3.00000	−	5.19615i	0.113552	−	0.196677i
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$	6.92820	−	4.00000i	0.261861	−	0.151186i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		0			0
$703$	22.0000			0.829746
$704$	−1.73205	+	1.00000i	−0.0652791	+	0.0376889i
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$	−8.50000	+	14.7224i	−0.319902	+	0.554086i
$707$		−	10.0000i		−	0.376089i
$708$	6.92820	+	4.00000i	0.260378	+	0.150329i
$709$	12.9904	+	7.50000i	0.487864	+	0.281668i	0.723688	−	0.690127i	$-0.242446\pi$
$709$	12.9904	+	7.50000i	0.487864	+	0.281668i	−0.235824	+	0.971796i	$0.575779\pi$
$710$		−	14.0000i		−	0.525411i
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−1.00000	−	1.73205i	−0.0374766	−	0.0649113i
$713$	−20.7846	+	12.0000i	−0.778390	+	0.449404i
$714$	10.0000			0.374241
$715$		0			0
$716$	−6.00000			−0.224231
$717$	−5.19615	+	3.00000i	−0.194054	+	0.112037i
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$			1.00000i			0.0372678i
$721$	−17.3205	−	10.0000i	−0.645049	−	0.372419i
$722$	−12.9904	−	7.50000i	−0.483452	−	0.279121i
$723$		−	7.00000i		−	0.260333i
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$	−6.06218	+	3.50000i	−0.224989	+	0.129897i
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	11.2583	−	6.50000i	0.416689	−	0.240576i
$731$	−25.0000	−	43.3013i	−0.924658	−	1.60156i
$732$	5.50000	−	9.52628i	0.203286	−	0.352101i
$733$		−	13.0000i		−	0.480166i	−0.970752	−	0.240083i	$-0.922825\pi$
$733$		−	13.0000i		−	0.480166i	0.970752	−	0.240083i	$-0.0771747\pi$
$734$	1.73205	+	1.00000i	0.0639312	+	0.0369107i
$735$	2.59808	+	1.50000i	0.0958315	+	0.0553283i
$736$		−	6.00000i		−	0.221163i
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$	−2.50000	−	4.33013i	−0.0920263	−	0.159394i
$739$	13.8564	−	8.00000i	0.509716	−	0.294285i	−0.223001	−	0.974818i	$-0.571585\pi$
$739$	13.8564	−	8.00000i	0.509716	−	0.294285i	0.732717	+	0.680534i	$0.238252\pi$
$740$	−11.0000			−0.404368
$741$		0			0
$742$	−2.00000			−0.0734223
$743$	10.3923	−	6.00000i	0.381257	−	0.220119i	−0.297108	−	0.954844i	$-0.596022\pi$
$743$	10.3923	−	6.00000i	0.381257	−	0.220119i	0.678365	+	0.734725i	$0.262689\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$			9.00000i			0.329513i
$747$	5.19615	+	3.00000i	0.190117	+	0.109764i
$748$	−8.66025	−	5.00000i	−0.316650	−	0.182818i
$749$			36.0000i			1.31541i
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	0.999570	−	0.0293387i	$-0.00934013\pi$
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	−0.525193	+	0.850983i	$0.676007\pi$
$752$	1.73205	−	1.00000i	0.0631614	−	0.0364662i
$753$	4.00000			0.145768
$754$		0			0
$755$	6.00000			0.218362
$756$	−1.73205	+	1.00000i	−0.0629941	+	0.0363696i
$757$	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
$759$			12.0000i			0.435572i
$760$	−1.73205	−	1.00000i	−0.0628281	−	0.0362738i
$761$	−29.4449	−	17.0000i	−1.06738	−	0.616250i	−0.139912	−	0.990164i	$-0.544682\pi$
$761$	−29.4449	−	17.0000i	−1.06738	−	0.616250i	−0.927463	+	0.373914i	$0.878015\pi$
$762$		−	12.0000i		−	0.434714i
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$	−4.33013	+	2.50000i	−0.156556	+	0.0903877i
$766$	24.0000			0.867155
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	29.4449	−	17.0000i	1.06181	−	0.613036i	0.135877	−	0.990726i	$-0.456615\pi$
$769$	29.4449	−	17.0000i	1.06181	−	0.613036i	0.925932	+	0.377690i	$0.123282\pi$
$770$	2.00000	+	3.46410i	0.0720750	+	0.124838i
$771$	1.50000	−	2.59808i	0.0540212	−	0.0935674i
$772$			17.0000i			0.611843i
$773$	15.5885	+	9.00000i	0.560678	+	0.323708i	0.753418	−	0.657542i	$-0.228404\pi$
$773$	15.5885	+	9.00000i	0.560678	+	0.323708i	−0.192740	+	0.981250i	$0.561737\pi$
$774$	8.66025	+	5.00000i	0.311286	+	0.179721i
$775$			16.0000i			0.574737i
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$	−11.0000	−	19.0526i	−0.394623	−	0.683507i
$778$	−16.4545	+	9.50000i	−0.589922	+	0.340592i
$779$	10.0000			0.358287
$780$		0			0
$781$	−28.0000			−1.00192
$782$	25.9808	−	15.0000i	0.929070	−	0.536399i
$783$	−4.50000	−	7.79423i	−0.160817	−	0.278543i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		−	7.00000i		−	0.249841i
$786$	−6.92820	−	4.00000i	−0.247121	−	0.142675i
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	0.436987	−	0.899468i	$-0.356046\pi$
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	−0.560469	+	0.828176i	$0.689379\pi$
$788$			6.00000i			0.213741i
$789$	7.00000	−	12.1244i	0.249207	−	0.431638i
$790$	−2.00000	−	3.46410i	−0.0711568	−	0.123247i
$791$	5.19615	−	3.00000i	0.184754	−	0.106668i
$792$	2.00000			0.0710669
$793$		0			0
$794$	18.0000			0.638796
$795$	0.866025	−	0.500000i	0.0307148	−	0.0177332i
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$		−	4.00000i		−	0.141598i
$799$	8.66025	+	5.00000i	0.306378	+	0.176887i
$800$	−3.46410	−	2.00000i	−0.122474	−	0.0707107i
$801$			2.00000i			0.0706665i
$802$	−13.5000	+	23.3827i	−0.476702	+	0.825671i
$803$	−13.0000	−	22.5167i	−0.458760	−	0.794596i
$804$	−1.73205	+	1.00000i	−0.0610847	+	0.0352673i
$805$	−12.0000			−0.422944
$806$		0			0
$807$	14.0000			0.492823
$808$	−4.33013	+	2.50000i	−0.152333	+	0.0879497i
$809$	−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
$811$			36.0000i			1.26413i	0.774915	+	0.632065i	$0.217793\pi$
$811$			36.0000i			1.26413i	−0.774915	+	0.632065i	$0.782207\pi$
$812$	15.5885	+	9.00000i	0.547048	+	0.315838i
$813$	6.92820	+	4.00000i	0.242983	+	0.140286i
$814$			22.0000i			0.771100i
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$	−2.50000	−	4.33013i	−0.0875175	−	0.151585i
$817$	−17.3205	+	10.0000i	−0.605968	+	0.349856i
$818$	23.0000			0.804176
$819$		0			0
$820$	−5.00000			−0.174608
$821$	25.9808	−	15.0000i	0.906735	−	0.523504i	0.0273557	−	0.999626i	$-0.491291\pi$
$821$	25.9808	−	15.0000i	0.906735	−	0.523504i	0.879379	+	0.476122i	$0.157958\pi$
$822$	−8.50000	−	14.7224i	−0.296472	−	0.513504i
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$			10.0000i			0.348367i
$825$	6.92820	+	4.00000i	0.241209	+	0.139262i
$826$	13.8564	+	8.00000i	0.482126	+	0.278356i
$827$		−	8.00000i		−	0.278187i	−0.990279	−	0.139094i	$-0.955581\pi$
$827$		−	8.00000i		−	0.278187i	0.990279	−	0.139094i	$-0.0444189\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	−0.991602	−	0.129325i	$-0.958719\pi$
$829$	−17.5000	−	30.3109i	−0.607800	−	1.05274i	0.383802	−	0.923415i	$-0.374614\pi$
$830$	5.19615	−	3.00000i	0.180361	−	0.104132i
$831$	−11.0000			−0.381586
$832$		0			0
$833$	−15.0000			−0.519719
$834$	10.3923	−	6.00000i	0.359856	−	0.207763i
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	−2.00000	+	3.46410i	−0.0691714	+	0.119808i
$837$		−	4.00000i		−	0.138260i
$838$	27.7128	+	16.0000i	0.957323	+	0.552711i
$839$	−38.1051	−	22.0000i	−1.31553	−	0.759524i	−0.332528	−	0.943093i	$-0.607902\pi$
$839$	−38.1051	−	22.0000i	−1.31553	−	0.759524i	−0.983007	+	0.183569i	$0.941235\pi$
$840$			2.00000i			0.0690066i
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	11.5000	+	19.9186i	0.396316	+	0.686440i
$843$	−21.6506	+	12.5000i	−0.745687	+	0.430523i
$844$	−24.0000			−0.826114
$845$		0			0
$846$	−2.00000			−0.0687614
$847$	−12.1244	+	7.00000i	−0.416598	+	0.240523i
$848$	0.500000	+	0.866025i	0.0171701	+	0.0297394i
$849$	−13.0000	+	22.5167i	−0.446159	+	0.772770i
$850$		−	20.0000i		−	0.685994i
$851$	−57.1577	−	33.0000i	−1.95934	−	1.13123i
$852$	−12.1244	−	7.00000i	−0.415374	−	0.239816i
$853$			49.0000i			1.67773i	0.544341	+	0.838864i	$0.316780\pi$
$853$			49.0000i			1.67773i	−0.544341	+	0.838864i	$0.683220\pi$
$854$	11.0000	−	19.0526i	0.376412	−	0.651965i
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	15.5885	−	9.00000i	0.532803	−	0.307614i
$857$	−45.0000			−1.53717			−0.768585	−	0.639747i	$-0.779039\pi$
$857$	−45.0000			−1.53717			−0.768585	+	0.639747i	$0.779039\pi$
$858$		0			0
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$	8.66025	−	5.00000i	0.295312	−	0.170499i
$861$	−5.00000	−	8.66025i	−0.170400	−	0.295141i
$862$	1.00000	−	1.73205i	0.0340601	−	0.0589939i
$863$		−	46.0000i		−	1.56586i	−0.622111	−	0.782929i	$-0.713725\pi$
$863$		−	46.0000i		−	1.56586i	0.622111	−	0.782929i	$-0.286275\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−19.0526	−	11.0000i	−0.647806	−	0.374011i
$866$			21.0000i			0.713609i
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	4.00000	+	6.92820i	0.135769	+	0.235159i
$869$	−6.92820	+	4.00000i	−0.235023	+	0.135691i
$870$	−9.00000			−0.305129
$871$		0			0
$872$	2.00000			0.0677285
$873$	1.73205	−	1.00000i	0.0586210	−	0.0338449i
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−9.00000	+	15.5885i	−0.304256	+	0.526986i
$876$		−	13.0000i		−	0.439229i
$877$	32.0429	+	18.5000i	1.08201	+	0.624701i	0.931439	−	0.363898i	$-0.118554\pi$
$877$	32.0429	+	18.5000i	1.08201	+	0.624701i	0.150574	+	0.988599i	$0.451888\pi$
$878$	8.66025	+	5.00000i	0.292269	+	0.168742i
$879$			1.00000i			0.0337292i
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	8.50000	+	14.7224i	0.286372	+	0.496011i	0.972941	−	0.231054i	$-0.0742173\pi$
$881$	8.50000	+	14.7224i	0.286372	+	0.496011i	−0.686569	+	0.727065i	$0.740884\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$		0			0
$885$	−8.00000			−0.268917
$886$	17.3205	−	10.0000i	0.581894	−	0.335957i
$887$	−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
$889$		−	24.0000i		−	0.804934i
$890$	1.73205	+	1.00000i	0.0580585	+	0.0335201i
$891$	−1.73205	−	1.00000i	−0.0580259	−	0.0335013i
$892$		−	16.0000i		−	0.535720i
$893$	2.00000	−	3.46410i	0.0669274	−	0.115922i
$894$	1.50000	+	2.59808i	0.0501675	+	0.0868927i
$895$	5.19615	−	3.00000i	0.173688	−	0.100279i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$	30.0000			1.00111
$899$	−31.1769	+	18.0000i	−1.03981	+	0.600334i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	−2.50000	+	4.33013i	−0.0832871	+	0.144257i
$902$			10.0000i			0.332964i
$903$	17.3205	+	10.0000i	0.576390	+	0.332779i
$904$	−2.59808	−	1.50000i	−0.0864107	−	0.0498893i
$905$		−	5.00000i		−	0.166206i
$906$	3.00000	−	5.19615i	0.0996683	−	0.172631i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$	12.1244	−	7.00000i	0.402361	−	0.232303i
$909$	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	$0.677847\pi$
$912$	−1.73205	+	1.00000i	−0.0573539	+	0.0331133i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−1.50000	+	2.59808i	−0.0496156	+	0.0859367i
$915$			11.0000i			0.363649i
$916$	8.66025	+	5.00000i	0.286143	+	0.165205i
$917$	−13.8564	−	8.00000i	−0.457579	−	0.264183i
$918$			5.00000i			0.165025i
$919$	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
$921$	12.1244	−	7.00000i	0.399511	−	0.230658i
$922$	3.00000			0.0987997
$923$		0			0
$924$	4.00000			0.131590
$925$	−38.1051	+	22.0000i	−1.25289	+	0.723356i
$926$	−7.00000	−	12.1244i	−0.230034	−	0.398431i
$927$	5.00000	−	8.66025i	0.164222	−	0.284440i
$928$		−	9.00000i		−	0.295439i
$929$	−19.9186	−	11.5000i	−0.653508	−	0.377303i	0.136291	−	0.990669i	$-0.456482\pi$
$929$	−19.9186	−	11.5000i	−0.653508	−	0.377303i	−0.789799	+	0.613366i	$0.789815\pi$
$930$	−3.46410	−	2.00000i	−0.113592	−	0.0655826i
$931$			6.00000i			0.196642i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	−3.00000	−	5.19615i	−0.0982156	−	0.170114i
$934$	19.0526	−	11.0000i	0.623419	−	0.359931i
$935$	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	$0.505200\pi$
$938$	−3.46410	+	2.00000i	−0.113107	+	0.0653023i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$	−1.00000	+	1.73205i	−0.0326164	+	0.0564933i
$941$			22.0000i			0.717180i	0.933495	+	0.358590i	$0.116742\pi$
$941$			22.0000i			0.717180i	−0.933495	+	0.358590i	$0.883258\pi$
$942$	−6.06218	−	3.50000i	−0.197516	−	0.114036i
$943$	−25.9808	−	15.0000i	−0.846050	−	0.488467i
$944$		−	8.00000i		−	0.260378i
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$	−10.0000	−	17.3205i	−0.325128	−	0.563138i
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	−0.383190	−	0.923670i	$-0.625175\pi$
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	0.608326	+	0.793687i	$0.291841\pi$
$948$	−4.00000			−0.129914
$949$		0			0
$950$	−8.00000			−0.259554
$951$	−28.5788	+	16.5000i	−0.926732	+	0.535049i
$952$	−5.00000	−	8.66025i	−0.162051	−	0.280680i
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.0174443	−	0.999848i	$-0.494447\pi$
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.857171	−	0.515031i	$-0.172220\pi$
$954$		−	1.00000i		−	0.0323762i
$955$	−3.46410	−	2.00000i	−0.112096	−	0.0647185i
$956$	5.19615	+	3.00000i	0.168056	+	0.0970269i
$957$			18.0000i			0.581857i
$958$	16.0000	−	27.7128i	0.516937	−	0.895360i
$959$	−17.0000	−	29.4449i	−0.548959	−	0.950824i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	15.0000			0.483871
$962$		0			0
$963$	−18.0000			−0.580042
$964$	−6.06218	+	3.50000i	−0.195250	+	0.112727i
$965$	−8.50000	−	14.7224i	−0.273625	−	0.473932i
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$			50.0000i			1.60789i	0.594703	+	0.803946i	$0.297270\pi$
$967$			50.0000i			1.60789i	−0.594703	+	0.803946i	$0.702730\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$	−8.66025	−	5.00000i	−0.278207	−	0.160623i
$970$		−	2.00000i		−	0.0642161i
$971$	−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
$973$	20.7846	−	12.0000i	0.666324	−	0.384702i
$974$	−26.0000			−0.833094
$975$		0			0
$976$	−11.0000			−0.352101
$977$	−18.1865	+	10.5000i	−0.581839	+	0.335925i	−0.761864	−	0.647737i	$-0.775715\pi$
$977$	−18.1865	+	10.5000i	−0.581839	+	0.335925i	0.180025	+	0.983662i	$0.442382\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	2.00000	−	3.46410i	0.0639203	−	0.110713i
$980$		−	3.00000i		−	0.0958315i
$981$	−1.73205	−	1.00000i	−0.0553001	−	0.0319275i
$982$	−25.9808	−	15.0000i	−0.829079	−	0.478669i
$983$			60.0000i			1.91370i	0.290578	+	0.956851i	$0.406153\pi$
$983$			60.0000i			1.91370i	−0.290578	+	0.956851i	$0.593847\pi$
$984$	−2.50000	+	4.33013i	−0.0796971	+	0.138039i
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	38.9711	−	22.5000i	1.24109	−	0.716546i
$987$	−4.00000			−0.127321
$988$		0			0
$989$	60.0000			1.90789
$990$	−1.73205	+	1.00000i	−0.0550482	+	0.0317821i
$991$	−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
$993$		−	28.0000i		−	0.888553i
$994$	−24.2487	−	14.0000i	−0.769122	−	0.444053i
$995$	8.66025	+	5.00000i	0.274549	+	0.158511i
$996$		−	6.00000i		−	0.190117i
$997$	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
$999$	9.52628	−	5.50000i	0.301398	−	0.174012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.e.361.2		4
13.2	odd	12		1014.2.a.e.1.1		1
13.3	even	3		1014.2.b.a.337.2		2
13.4	even	6	inner	1014.2.i.e.823.2		4
13.5	odd	4		1014.2.e.d.991.1		2
13.6	odd	12		1014.2.e.d.529.1		2
13.7	odd	12		78.2.e.b.61.1	yes	2
13.8	odd	4		78.2.e.b.55.1	✓	2
13.9	even	3	inner	1014.2.i.e.823.1		4
13.10	even	6		1014.2.b.a.337.1		2
13.11	odd	12		1014.2.a.a.1.1		1
13.12	even	2	inner	1014.2.i.e.361.1		4
39.2	even	12		3042.2.a.d.1.1		1
39.8	even	4		234.2.h.b.55.1		2
39.11	even	12		3042.2.a.m.1.1		1
39.20	even	12		234.2.h.b.217.1		2
39.23	odd	6		3042.2.b.d.1351.2		2
39.29	odd	6		3042.2.b.d.1351.1		2
52.7	even	12		624.2.q.b.529.1		2
52.11	even	12		8112.2.a.x.1.1		1
52.15	even	12		8112.2.a.bb.1.1		1
52.47	even	4		624.2.q.b.289.1		2
65.7	even	12		1950.2.z.b.1699.2		4
65.8	even	4		1950.2.z.b.1849.2		4
65.33	even	12		1950.2.z.b.1699.1		4
65.34	odd	4		1950.2.i.b.601.1		2
65.47	even	4		1950.2.z.b.1849.1		4
65.59	odd	12		1950.2.i.b.451.1		2
156.47	odd	4		1872.2.t.i.289.1		2
156.59	odd	12		1872.2.t.i.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.b.55.1	✓	2	13.8	odd	4
78.2.e.b.61.1	yes	2	13.7	odd	12
234.2.h.b.55.1		2	39.8	even	4
234.2.h.b.217.1		2	39.20	even	12
624.2.q.b.289.1		2	52.47	even	4
624.2.q.b.529.1		2	52.7	even	12
1014.2.a.a.1.1		1	13.11	odd	12
1014.2.a.e.1.1		1	13.2	odd	12
1014.2.b.a.337.1		2	13.10	even	6
1014.2.b.a.337.2		2	13.3	even	3
1014.2.e.d.529.1		2	13.6	odd	12
1014.2.e.d.991.1		2	13.5	odd	4
1014.2.i.e.361.1		4	13.12	even	2	inner
1014.2.i.e.361.2		4	1.1	even	1	trivial
1014.2.i.e.823.1		4	13.9	even	3	inner
1014.2.i.e.823.2		4	13.4	even	6	inner
1872.2.t.i.289.1		2	156.47	odd	4
1872.2.t.i.1153.1		2	156.59	odd	12
1950.2.i.b.451.1		2	65.59	odd	12
1950.2.i.b.601.1		2	65.34	odd	4
1950.2.z.b.1699.1		4	65.33	even	12
1950.2.z.b.1699.2		4	65.7	even	12
1950.2.z.b.1849.1		4	65.47	even	4
1950.2.z.b.1849.2		4	65.8	even	4
3042.2.a.d.1.1		1	39.2	even	12
3042.2.a.m.1.1		1	39.11	even	12
3042.2.b.d.1351.1		2	39.29	odd	6
3042.2.b.d.1351.2		2	39.23	odd	6
8112.2.a.x.1.1		1	52.11	even	12
8112.2.a.bb.1.1		1	52.15	even	12

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.i (of order \(6\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more