LMFDB - Embedded newform 1110.2.i.b.121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1110,2,Mod(121,1110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1110.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1110, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,1,-1,-1,-2,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.b.211.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +3.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.50000 - 2.59808i) q^{21} +(1.00000 - 1.73205i) q^{22} -2.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} -5.00000 q^{29} +(0.500000 + 0.866025i) q^{30} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{35} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} +1.00000 q^{38} +(-2.50000 + 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.00000 - 8.66025i) q^{41} +(1.50000 + 2.59808i) q^{42} -6.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(1.00000 - 1.73205i) q^{46} -12.0000 q^{47} -1.00000 q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(2.50000 - 4.33013i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(0.500000 - 0.866025i) q^{57} +(2.50000 - 4.33013i) q^{58} +(-5.00000 + 8.66025i) q^{59} -1.00000 q^{60} +(2.00000 + 3.46410i) q^{61} +(2.00000 - 3.46410i) q^{62} +3.00000 q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +2.00000 q^{68} +(-1.00000 - 1.73205i) q^{69} +(-1.50000 - 2.59808i) q^{70} +(0.500000 + 0.866025i) q^{71} +(-0.500000 + 0.866025i) q^{72} +6.00000 q^{73} +(5.50000 + 2.59808i) q^{74} -1.00000 q^{75} +(-0.500000 + 0.866025i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-2.50000 - 4.33013i) q^{78} +(-5.00000 - 8.66025i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +10.0000 q^{82} +(6.50000 - 11.2583i) q^{83} -3.00000 q^{84} +2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(-2.50000 - 4.33013i) q^{87} -2.00000 q^{88} +(-8.00000 + 13.8564i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(7.50000 - 12.9904i) q^{91} +(1.00000 + 1.73205i) q^{92} +(-2.00000 - 3.46410i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.0000 q^{97} +(-1.00000 - 1.73205i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - 3 q^{7} + 2 q^{8} - q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 5 q^{13} + 6 q^{14} + q^{15} - q^{16} - 2 q^{17} - q^{18} - q^{19} - q^{20} + 3 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - 3 * q^7 + 2 * q^8 - q^9 + 2 * q^10 - 4 * q^11 + q^12 + 5 * q^13 + 6 * q^14 + q^15 - q^16 - 2 * q^17 - q^18 - q^19 - q^20 + 3 * q^21 + 2 * q^22 - 4 * q^23 + q^24 - q^25 - 10 * q^26 - 2 * q^27 - 3 * q^28 - 10 * q^29 + q^30 - 8 * q^31 - q^32 - 2 * q^33 - 2 * q^34 - 3 * q^35 + 2 * q^36 - q^37 + 2 * q^38 - 5 * q^39 - q^40 - 10 * q^41 + 3 * q^42 - 12 * q^43 + 2 * q^44 + 2 * q^45 + 2 * q^46 - 24 * q^47 - 2 * q^48 - 2 * q^49 - q^50 - 4 * q^51 + 5 * q^52 - 6 * q^53 + q^54 + 2 * q^55 - 3 * q^56 + q^57 + 5 * q^58 - 10 * q^59 - 2 * q^60 + 4 * q^61 + 4 * q^62 + 6 * q^63 + 2 * q^64 + 5 * q^65 + 4 * q^66 - 2 * q^67 + 4 * q^68 - 2 * q^69 - 3 * q^70 + q^71 - q^72 + 12 * q^73 + 11 * q^74 - 2 * q^75 - q^76 + 6 * q^77 - 5 * q^78 - 10 * q^79 + 2 * q^80 - q^81 + 20 * q^82 + 13 * q^83 - 6 * q^84 + 4 * q^85 + 6 * q^86 - 5 * q^87 - 4 * q^88 - 16 * q^89 - q^90 + 15 * q^91 + 2 * q^92 - 4 * q^93 + 12 * q^94 - q^95 + q^96 + 20 * q^97 - 2 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	3.00000			0.801784
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	1.50000	−	2.59808i	0.327327	−	0.566947i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−5.00000			−0.980581
$27$	−1.00000			−0.192450
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	1.00000			0.166667
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$38$	1.00000			0.162221
$39$	−2.50000	+	4.33013i	−0.400320	+	0.693375i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	0.150567	−	0.988600i	$-0.451890\pi$
$42$	1.50000	+	2.59808i	0.231455	+	0.400892i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	1.00000			0.149071
$46$	1.00000	−	1.73205i	0.147442	−	0.255377i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$	−1.00000			−0.144338
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−2.00000			−0.280056
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	0.500000	−	0.866025i	0.0662266	−	0.114708i
$58$	2.50000	−	4.33013i	0.328266	−	0.568574i
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$	−1.00000			−0.129099
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$	3.00000			0.377964
$64$	1.00000			0.125000
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$	2.00000			0.246183
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.00000			0.242536
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$	−1.50000	−	2.59808i	−0.179284	−	0.310530i
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	0.894169	−	0.447730i	$-0.147767\pi$
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	−0.834830	+	0.550508i	$0.814434\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	5.50000	+	2.59808i	0.639362	+	0.302020i
$75$	−1.00000			−0.115470
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$	3.00000	+	5.19615i	0.341882	+	0.592157i
$78$	−2.50000	−	4.33013i	−0.283069	−	0.490290i
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.0000			1.10432
$83$	6.50000	−	11.2583i	0.713468	−	1.23576i	−0.250080	−	0.968225i	$-0.580457\pi$
$83$	6.50000	−	11.2583i	0.713468	−	1.23576i	0.963548	−	0.267537i	$-0.0862098\pi$
$84$	−3.00000			−0.327327
$85$	2.00000			0.216930
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$	−2.00000			−0.213201
$89$	−8.00000	+	13.8564i	−0.847998	+	1.46878i	0.0349934	+	0.999388i	$0.488859\pi$
$89$	−8.00000	+	13.8564i	−0.847998	+	1.46878i	−0.882992	+	0.469389i	$0.844474\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	7.50000	−	12.9904i	0.786214	−	1.36176i
$92$	1.00000	+	1.73205i	0.104257	+	0.180579i
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$	−1.00000	−	1.73205i	−0.101015	−	0.174964i
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$	1.00000			0.100000
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	1.00000	−	1.73205i	0.0990148	−	0.171499i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	2.50000	+	4.33013i	0.245145	+	0.424604i
$105$	−3.00000			−0.292770
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	0.935695	+	0.352809i	$0.114773\pi$
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	−0.162306	+	0.986740i	$0.551893\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	−2.00000			−0.190693
$111$	5.00000	−	3.46410i	0.474579	−	0.328798i
$112$	3.00000			0.283473
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	−0.888585	−	0.458712i	$-0.848311\pi$
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	0.841549	+	0.540181i	$0.181644\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$	2.50000	+	4.33013i	0.232119	+	0.402042i
$117$	−5.00000			−0.462250
$118$	−5.00000	−	8.66025i	−0.460287	−	0.797241i
$119$	6.00000			0.550019
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−7.00000			−0.636364
$122$	−4.00000			−0.362143
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	−0.511859	−	0.859069i	$-0.671043\pi$
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	0.999905	+	0.0137486i	$0.00437646\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$	2.50000	+	4.33013i	0.219265	+	0.379777i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	−1.50000	+	2.59808i	−0.130066	+	0.225282i
$134$	2.00000			0.172774
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	11.0000			0.939793			0.469897	−	0.882721i	$-0.344291\pi$
$137$	11.0000			0.939793			0.469897	+	0.882721i	$0.344291\pi$
$138$	2.00000			0.170251
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	3.00000			0.253546
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$	−1.00000			−0.0839181
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$	−3.00000	+	5.19615i	−0.248282	+	0.430037i
$147$	−2.00000			−0.164957
$148$	−5.00000	+	3.46410i	−0.410997	+	0.284747i
$149$	−9.00000			−0.737309			−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000			−0.737309			−0.368654	+	0.929567i	$0.620181\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$	−6.00000			−0.483494
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$	5.00000			0.400320
$157$	11.5000	−	19.9186i	0.917800	−	1.58968i	0.115050	−	0.993360i	$-0.463297\pi$
$157$	11.5000	−	19.9186i	0.917800	−	1.58968i	0.802749	−	0.596316i	$-0.203370\pi$
$158$	10.0000			0.795557
$159$	−6.00000			−0.475831
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	3.00000	+	5.19615i	0.236433	+	0.409514i
$162$	1.00000			0.0785674
$163$	12.0000	−	20.7846i	0.939913	−	1.62798i	0.174282	−	0.984696i	$-0.444240\pi$
$163$	12.0000	−	20.7846i	0.939913	−	1.62798i	0.765631	−	0.643280i	$-0.222427\pi$
$164$	−5.00000	+	8.66025i	−0.390434	+	0.676252i
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	6.50000	+	11.2583i	0.504498	+	0.873816i
$167$	5.00000	+	8.66025i	0.386912	+	0.670151i	0.992032	−	0.125983i	$-0.0402085\pi$
$167$	5.00000	+	8.66025i	0.386912	+	0.670151i	−0.605121	+	0.796134i	$0.706875\pi$
$168$	1.50000	−	2.59808i	0.115728	−	0.200446i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−1.00000	+	1.73205i	−0.0766965	+	0.132842i
$171$	1.00000			0.0764719
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	0.779926	+	0.625871i	$0.215256\pi$
$174$	5.00000			0.379049
$175$	3.00000			0.226779
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$	−10.0000			−0.751646
$178$	−8.00000	−	13.8564i	−0.599625	−	1.03858i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	0.989819	−	0.142331i	$-0.0454598\pi$
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	−0.618172	+	0.786043i	$0.712126\pi$
$182$	7.50000	+	12.9904i	0.555937	+	0.962911i
$183$	−2.00000	+	3.46410i	−0.147844	+	0.256074i
$184$	−2.00000			−0.147442
$185$	−5.00000	+	3.46410i	−0.367607	+	0.254686i
$186$	4.00000			0.293294
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	6.00000	+	10.3923i	0.437595	+	0.757937i
$189$	1.50000	+	2.59808i	0.109109	+	0.188982i
$190$	−0.500000	−	0.866025i	−0.0362738	−	0.0628281i
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$	5.00000			0.358057
$196$	2.00000			0.142857
$197$	1.00000	−	1.73205i	0.0712470	−	0.123404i	−0.828201	−	0.560431i	$-0.810635\pi$
$197$	1.00000	−	1.73205i	0.0712470	−	0.123404i	0.899448	+	0.437028i	$0.143969\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	3.00000	−	5.19615i	0.211079	−	0.365600i
$203$	7.50000	+	12.9904i	0.526397	+	0.911746i
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$	1.00000	−	1.73205i	0.0695048	−	0.120386i
$208$	−5.00000			−0.346688
$209$	1.00000	+	1.73205i	0.0691714	+	0.119808i
$210$	1.50000	−	2.59808i	0.103510	−	0.179284i
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	6.00000			0.412082
$213$	−0.500000	+	0.866025i	−0.0342594	+	0.0593391i
$214$	−16.0000			−1.09374
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$	−1.00000			−0.0680414
$217$	6.00000	+	10.3923i	0.407307	+	0.705476i
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	−10.0000			−0.672673
$222$	0.500000	+	6.06218i	0.0335578	+	0.406867i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−0.500000	−	0.866025i	−0.0332595	−	0.0576072i
$227$	−8.50000	−	14.7224i	−0.564165	−	0.977162i	−0.997127	−	0.0757500i	$-0.975865\pi$
$227$	−8.50000	−	14.7224i	−0.564165	−	0.977162i	0.432962	−	0.901412i	$-0.357468\pi$
$228$	−1.00000			−0.0662266
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$	−2.00000			−0.131876
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−5.00000			−0.328266
$233$	−17.0000			−1.11371			−0.556854	−	0.830611i	$-0.687992\pi$
$233$	−17.0000			−1.11371			−0.556854	+	0.830611i	$0.687992\pi$
$234$	2.50000	−	4.33013i	0.163430	−	0.283069i
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$	10.0000			0.650945
$237$	5.00000	−	8.66025i	0.324785	−	0.562544i
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	6.50000	−	11.2583i	0.420450	−	0.728241i	−0.575533	−	0.817778i	$-0.695206\pi$
$239$	6.50000	−	11.2583i	0.420450	−	0.728241i	0.995983	+	0.0895374i	$0.0285389\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.00000	−	3.46410i	0.128037	−	0.221766i
$245$	2.00000			0.127775
$246$	5.00000	+	8.66025i	0.318788	+	0.552158i
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$	−4.00000			−0.254000
$249$	13.0000			0.823842
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$	−1.50000	−	2.59808i	−0.0944911	−	0.163663i
$253$	4.00000			0.251478
$254$	5.50000	+	9.52628i	0.345101	+	0.597732i
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.0828783	+	0.996560i	$0.526411\pi$
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.821607	+	0.570055i	$0.806922\pi$
$258$	6.00000			0.373544
$259$	−15.0000	+	10.3923i	−0.932055	+	0.645746i
$260$	−5.00000			−0.310087
$261$	2.50000	−	4.33013i	0.154746	−	0.268028i
$262$		0			0
$263$	−1.00000	−	1.73205i	−0.0616626	−	0.106803i	0.833546	−	0.552450i	$-0.186307\pi$
$263$	−1.00000	−	1.73205i	−0.0616626	−	0.106803i	−0.895209	+	0.445647i	$0.852974\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$	6.00000			0.368577
$266$	−1.50000	−	2.59808i	−0.0919709	−	0.159298i
$267$	−16.0000			−0.979184
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	13.0000			0.792624			0.396312	−	0.918116i	$-0.370290\pi$
$269$	13.0000			0.792624			0.396312	+	0.918116i	$0.370290\pi$
$270$	−1.00000			−0.0608581
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	−0.798865	−	0.601511i	$-0.794566\pi$
$271$	2.00000	−	3.46410i	0.121491	−	0.210429i	0.920356	+	0.391082i	$0.127899\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$	15.0000			0.907841
$274$	−5.50000	+	9.52628i	−0.332267	+	0.575504i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	−1.00000	+	1.73205i	−0.0601929	+	0.104257i
$277$	5.50000	+	9.52628i	0.330463	+	0.572379i	0.982603	−	0.185720i	$-0.0594618\pi$
$277$	5.50000	+	9.52628i	0.330463	+	0.572379i	−0.652140	+	0.758099i	$0.726128\pi$
$278$	−6.00000	−	10.3923i	−0.359856	−	0.623289i
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	−1.50000	+	2.59808i	−0.0896421	+	0.155265i
$281$	4.00000	−	6.92820i	0.238620	−	0.413302i	−0.721699	−	0.692207i	$-0.756638\pi$
$281$	4.00000	−	6.92820i	0.238620	−	0.413302i	0.960319	+	0.278906i	$0.0899716\pi$
$282$	12.0000			0.714590
$283$	15.0000	+	25.9808i	0.891657	+	1.54440i	0.837888	+	0.545843i	$0.183790\pi$
$283$	15.0000	+	25.9808i	0.891657	+	1.54440i	0.0537697	+	0.998553i	$0.482876\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$	−1.00000			−0.0592349
$286$	10.0000			0.591312
$287$	−15.0000	+	25.9808i	−0.885422	+	1.53360i
$288$	1.00000			0.0589256
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−5.00000			−0.293610
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$	1.00000	−	1.73205i	0.0583212	−	0.101015i
$295$	10.0000			0.582223
$296$	−0.500000	−	6.06218i	−0.0290619	−	0.352357i
$297$	2.00000			0.116052
$298$	4.50000	−	7.79423i	0.260678	−	0.451508i
$299$	−5.00000	−	8.66025i	−0.289157	−	0.500835i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	9.00000	+	15.5885i	0.518751	+	0.898504i
$302$	10.0000			0.575435
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	1.00000			0.0573539
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$	2.00000			0.114332
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$	−0.500000	−	0.866025i	−0.0284440	−	0.0492665i
$310$	−4.00000			−0.227185
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$	−2.50000	+	4.33013i	−0.141535	+	0.245145i
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	−0.956647	−	0.291250i	$-0.905929\pi$
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	0.730554	+	0.682855i	$0.239262\pi$
$314$	11.5000	+	19.9186i	0.648983	+	1.12407i
$315$	−1.50000	−	2.59808i	−0.0845154	−	0.146385i
$316$	−5.00000	+	8.66025i	−0.281272	+	0.487177i
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$	10.0000			0.559893
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−8.00000	+	13.8564i	−0.446516	+	0.773389i
$322$	−6.00000			−0.334367
$323$	2.00000			0.111283
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−5.00000			−0.277350
$326$	12.0000	+	20.7846i	0.664619	+	1.15115i
$327$	−14.0000			−0.774202
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	18.0000	+	31.1769i	0.992372	+	1.71884i
$330$	−1.00000	−	1.73205i	−0.0550482	−	0.0953463i
$331$	1.50000	−	2.59808i	0.0824475	−	0.142803i	−0.821853	−	0.569699i	$-0.807060\pi$
$331$	1.50000	−	2.59808i	0.0824475	−	0.142803i	0.904301	+	0.426896i	$0.140393\pi$
$332$	−13.0000			−0.713468
$333$	5.50000	+	2.59808i	0.301398	+	0.142374i
$334$	−10.0000			−0.547176
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$	1.50000	+	2.59808i	0.0818317	+	0.141737i
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−1.00000			−0.0543125
$340$	−1.00000	−	1.73205i	−0.0542326	−	0.0939336i
$341$	8.00000			0.433224
$342$	−0.500000	+	0.866025i	−0.0270369	+	0.0468293i
$343$	−15.0000			−0.809924
$344$	−6.00000			−0.323498
$345$	−1.00000	+	1.73205i	−0.0538382	+	0.0932505i
$346$	−2.00000	−	3.46410i	−0.107521	−	0.186231i
$347$	27.0000			1.44944			0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000			1.44944			0.724718	+	0.689046i	$0.241970\pi$
$348$	−2.50000	+	4.33013i	−0.134014	+	0.232119i
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$	−1.50000	+	2.59808i	−0.0801784	+	0.138873i
$351$	−2.50000	−	4.33013i	−0.133440	−	0.231125i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	6.50000	−	11.2583i	0.345960	−	0.599220i	−0.639568	−	0.768735i	$-0.720887\pi$
$353$	6.50000	−	11.2583i	0.345960	−	0.599220i	0.985528	+	0.169514i	$0.0542199\pi$
$354$	5.00000	−	8.66025i	0.265747	−	0.460287i
$355$	0.500000	−	0.866025i	0.0265372	−	0.0459639i
$356$	16.0000			0.847998
$357$	3.00000	+	5.19615i	0.158777	+	0.275010i
$358$		0			0
$359$	−17.0000			−0.897226			−0.448613	−	0.893726i	$-0.648082\pi$
$359$	−17.0000			−0.897226			−0.448613	+	0.893726i	$0.648082\pi$
$360$	1.00000			0.0527046
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−10.0000			−0.525588
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$	−15.0000			−0.786214
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$	−2.00000	−	3.46410i	−0.104542	−	0.181071i
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	1.00000	−	1.73205i	0.0521286	−	0.0902894i
$369$	10.0000			0.520579
$370$	−0.500000	−	6.06218i	−0.0259938	−	0.315158i
$371$	18.0000			0.934513
$372$	−2.00000	+	3.46410i	−0.103695	+	0.179605i
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	0.647225	−	0.762299i	$-0.275929\pi$
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	−0.983783	+	0.179364i	$0.942596\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−12.0000			−0.618853
$377$	−12.5000	−	21.6506i	−0.643783	−	1.11506i
$378$	−3.00000			−0.154303
$379$	5.50000	−	9.52628i	0.282516	−	0.489332i	−0.689488	−	0.724297i	$-0.742164\pi$
$379$	5.50000	−	9.52628i	0.282516	−	0.489332i	0.972004	+	0.234965i	$0.0754976\pi$
$380$	1.00000			0.0512989
$381$	11.0000			0.563547
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	0.987573	−	0.157159i	$-0.0502334\pi$
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	−0.629890	+	0.776684i	$0.716900\pi$
$384$	−1.00000			−0.0510310
$385$	3.00000	−	5.19615i	0.152894	−	0.264820i
$386$	−7.00000	+	12.1244i	−0.356291	+	0.617113i
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−5.50000	−	9.52628i	−0.278861	−	0.483002i	0.692241	−	0.721666i	$-0.256624\pi$
$389$	−5.50000	−	9.52628i	−0.278861	−	0.483002i	−0.971102	+	0.238665i	$0.923290\pi$
$390$	−2.50000	+	4.33013i	−0.126592	+	0.219265i
$391$	2.00000	−	3.46410i	0.101144	−	0.175187i
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$		0			0
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$	−2.00000			−0.100504
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$	4.00000	−	6.92820i	0.200502	−	0.347279i
$399$	−3.00000			−0.150188
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$	1.00000	+	1.73205i	0.0498755	+	0.0863868i
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−15.0000			−0.744438
$407$	1.00000	+	12.1244i	0.0495682	+	0.600982i
$408$	−2.00000			−0.0990148
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−5.00000	−	8.66025i	−0.246932	−	0.427699i
$411$	5.50000	+	9.52628i	0.271295	+	0.469897i
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	30.0000			1.47620
$414$	1.00000	+	1.73205i	0.0491473	+	0.0851257i
$415$	−13.0000			−0.638145
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	−12.0000			−0.587643
$418$	−2.00000			−0.0978232
$419$	14.0000	−	24.2487i	0.683945	−	1.18463i	−0.289822	−	0.957080i	$-0.593596\pi$
$419$	14.0000	−	24.2487i	0.683945	−	1.18463i	0.973767	−	0.227547i	$-0.0730704\pi$
$420$	1.50000	+	2.59808i	0.0731925	+	0.126773i
$421$	4.00000			0.194948			0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000			0.194948			0.0974740	+	0.995238i	$0.468924\pi$
$422$	−2.50000	+	4.33013i	−0.121698	+	0.210787i
$423$	6.00000	−	10.3923i	0.291730	−	0.505291i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	−0.500000	−	0.866025i	−0.0242251	−	0.0419591i
$427$	6.00000	−	10.3923i	0.290360	−	0.502919i
$428$	8.00000	−	13.8564i	0.386695	−	0.669775i
$429$	5.00000	−	8.66025i	0.241402	−	0.418121i
$430$	−6.00000			−0.289346
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	0.737057	−	0.675830i	$-0.236215\pi$
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	−0.953815	+	0.300395i	$0.902881\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	−12.0000			−0.576018
$435$	−2.50000	+	4.33013i	−0.119866	+	0.207614i
$436$	14.0000			0.670478
$437$	1.00000	+	1.73205i	0.0478365	+	0.0828552i
$438$	−6.00000			−0.286691
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	1.00000	+	1.73205i	0.0476731	+	0.0825723i
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$	5.00000	−	8.66025i	0.237826	−	0.411926i
$443$	−15.0000			−0.712672			−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000			−0.712672			−0.356336	+	0.934358i	$0.615974\pi$
$444$	−5.50000	−	2.59808i	−0.261018	−	0.123299i
$445$	16.0000			0.758473
$446$		0			0
$447$	−4.50000	−	7.79423i	−0.212843	−	0.368654i
$448$	−1.50000	−	2.59808i	−0.0708683	−	0.122748i
$449$	12.0000	+	20.7846i	0.566315	+	0.980886i	0.996926	+	0.0783487i	$0.0249648\pi$
$449$	12.0000	+	20.7846i	0.566315	+	0.980886i	−0.430611	+	0.902538i	$0.641702\pi$
$450$	1.00000			0.0471405
$451$	10.0000	+	17.3205i	0.470882	+	0.815591i
$452$	1.00000			0.0470360
$453$	5.00000	−	8.66025i	0.234920	−	0.406894i
$454$	17.0000			0.797850
$455$	−15.0000			−0.703211
$456$	0.500000	−	0.866025i	0.0234146	−	0.0405554i
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	0.927622	−	0.373519i	$-0.121849\pi$
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	−0.787288	+	0.616585i	$0.788516\pi$
$458$	−16.0000			−0.747631
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$	1.00000	−	1.73205i	0.0466252	−	0.0807573i
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	−0.510887	−	0.859648i	$-0.670683\pi$
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	0.999920	+	0.0126168i	$0.00401615\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	−19.5000	−	33.7750i	−0.906242	−	1.56966i	−0.819242	−	0.573449i	$-0.805605\pi$
$463$	−19.5000	−	33.7750i	−0.906242	−	1.56966i	−0.0870004	−	0.996208i	$-0.527728\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	8.50000	−	14.7224i	0.393755	−	0.682003i
$467$	−21.0000			−0.971764			−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000			−0.971764			−0.485882	+	0.874024i	$0.661502\pi$
$468$	2.50000	+	4.33013i	0.115563	+	0.200160i
$469$	−3.00000	+	5.19615i	−0.138527	+	0.239936i
$470$	−12.0000			−0.553519
$471$	23.0000			1.05978
$472$	−5.00000	+	8.66025i	−0.230144	+	0.398621i
$473$	12.0000			0.551761
$474$	5.00000	+	8.66025i	0.229658	+	0.397779i
$475$	1.00000			0.0458831
$476$	−3.00000	−	5.19615i	−0.137505	−	0.238165i
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	6.50000	+	11.2583i	0.297303	+	0.514944i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	−1.00000			−0.0456435
$481$	25.0000	−	17.3205i	1.13990	−	0.789747i
$482$	10.0000			0.455488
$483$	−3.00000	+	5.19615i	−0.136505	+	0.236433i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−3.00000			−0.135943			−0.0679715	−	0.997687i	$-0.521653\pi$
$487$	−3.00000			−0.135943			−0.0679715	+	0.997687i	$0.521653\pi$
$488$	2.00000	+	3.46410i	0.0905357	+	0.156813i
$489$	24.0000			1.08532
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	−38.0000			−1.71492			−0.857458	−	0.514554i	$-0.827958\pi$
$491$	−38.0000			−1.71492			−0.857458	+	0.514554i	$0.827958\pi$
$492$	−10.0000			−0.450835
$493$	5.00000	−	8.66025i	0.225189	−	0.390038i
$494$	2.50000	+	4.33013i	0.112480	+	0.194822i
$495$	−2.00000			−0.0898933
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	1.50000	−	2.59808i	0.0672842	−	0.116540i
$498$	−6.50000	+	11.2583i	−0.291272	+	0.504498i
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−5.00000	+	8.66025i	−0.223384	+	0.386912i
$502$	−3.00000	+	5.19615i	−0.133897	+	0.231916i
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$	3.00000			0.133631
$505$	3.00000	+	5.19615i	0.133498	+	0.231226i
$506$	−2.00000	+	3.46410i	−0.0889108	+	0.153998i
$507$	−12.0000			−0.532939
$508$	−11.0000			−0.488046
$509$	14.5000	−	25.1147i	0.642701	−	1.11319i	−0.342126	−	0.939654i	$-0.611147\pi$
$509$	14.5000	−	25.1147i	0.642701	−	1.11319i	0.984827	−	0.173537i	$-0.0555197\pi$
$510$	−2.00000			−0.0885615
$511$	−9.00000	−	15.5885i	−0.398137	−	0.689593i
$512$	1.00000			0.0441942
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−14.5000	−	25.1147i	−0.639568	−	1.10776i
$515$	0.500000	+	0.866025i	0.0220326	+	0.0381616i
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	24.0000			1.05552
$518$	−1.50000	−	18.1865i	−0.0659062	−	0.799070i
$519$	−4.00000			−0.175581
$520$	2.50000	−	4.33013i	0.109632	−	0.189889i
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	0.704137	−	0.710064i	$-0.251334\pi$
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	−0.967002	+	0.254769i	$0.918001\pi$
$522$	2.50000	+	4.33013i	0.109422	+	0.189525i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$		0			0
$525$	1.50000	+	2.59808i	0.0654654	+	0.113389i
$526$	2.00000			0.0872041
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$	2.00000			0.0870388
$529$	−19.0000			−0.826087
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	−5.00000	−	8.66025i	−0.216982	−	0.375823i
$532$	3.00000			0.130066
$533$	25.0000	−	43.3013i	1.08287	−	1.87559i
$534$	8.00000	−	13.8564i	0.346194	−	0.599625i
$535$	8.00000	−	13.8564i	0.345870	−	0.599065i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	−6.50000	+	11.2583i	−0.280235	+	0.485381i
$539$	2.00000	−	3.46410i	0.0861461	−	0.149209i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−36.0000			−1.54776			−0.773880	−	0.633332i	$-0.781687\pi$
$541$	−36.0000			−1.54776			−0.773880	+	0.633332i	$0.781687\pi$
$542$	2.00000	+	3.46410i	0.0859074	+	0.148796i
$543$	−5.00000	+	8.66025i	−0.214571	+	0.371647i
$544$	2.00000			0.0857493
$545$	14.0000			0.599694
$546$	−7.50000	+	12.9904i	−0.320970	+	0.555937i
$547$	−16.0000			−0.684111			−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000			−0.684111			−0.342055	+	0.939680i	$0.611123\pi$
$548$	−5.50000	−	9.52628i	−0.234948	−	0.406942i
$549$	−4.00000			−0.170716
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	2.50000	+	4.33013i	0.106504	+	0.184470i
$552$	−1.00000	−	1.73205i	−0.0425628	−	0.0737210i
$553$	−15.0000	+	25.9808i	−0.637865	+	1.10481i
$554$	−11.0000			−0.467345
$555$	−5.50000	−	2.59808i	−0.233462	−	0.110282i
$556$	12.0000			0.508913
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	−15.0000	−	25.9808i	−0.634432	−	1.09887i
$560$	−1.50000	−	2.59808i	−0.0633866	−	0.109789i
$561$	4.00000			0.168880
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	−15.0000			−0.632175			−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000			−0.632175			−0.316087	+	0.948730i	$0.602369\pi$
$564$	−6.00000	+	10.3923i	−0.252646	+	0.437595i
$565$	1.00000			0.0420703
$566$	−30.0000			−1.26099
$567$	−1.50000	+	2.59808i	−0.0629941	+	0.109109i
$568$	0.500000	+	0.866025i	0.0209795	+	0.0363376i
$569$	38.0000			1.59304			0.796521	−	0.604610i	$-0.206671\pi$
$569$	38.0000			1.59304			0.796521	+	0.604610i	$0.206671\pi$
$570$	0.500000	−	0.866025i	0.0209427	−	0.0362738i
$571$	−19.5000	+	33.7750i	−0.816050	+	1.41344i	0.0925222	+	0.995711i	$0.470507\pi$
$571$	−19.5000	+	33.7750i	−0.816050	+	1.41344i	−0.908572	+	0.417729i	$0.862826\pi$
$572$	−5.00000	+	8.66025i	−0.209061	+	0.362103i
$573$	−8.00000	−	13.8564i	−0.334205	−	0.578860i
$574$	−15.0000	−	25.9808i	−0.626088	−	1.08442i
$575$	1.00000	−	1.73205i	0.0417029	−	0.0722315i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.00000	−	6.92820i	0.166522	−	0.288425i	−0.770673	−	0.637231i	$-0.780080\pi$
$577$	4.00000	−	6.92820i	0.166522	−	0.288425i	0.937195	+	0.348806i	$0.113413\pi$
$578$	−13.0000			−0.540729
$579$	7.00000	+	12.1244i	0.290910	+	0.503871i
$580$	2.50000	−	4.33013i	0.103807	−	0.179799i
$581$	−39.0000			−1.61799
$582$	−10.0000			−0.414513
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$	6.00000			0.248282
$585$	2.50000	+	4.33013i	0.103362	+	0.179029i
$586$	−18.0000			−0.743573
$587$	−13.5000	−	23.3827i	−0.557205	−	0.965107i	−0.997728	−	0.0673658i	$-0.978541\pi$
$587$	−13.5000	−	23.3827i	−0.557205	−	0.965107i	0.440524	−	0.897741i	$-0.354793\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$	−5.00000	+	8.66025i	−0.205847	+	0.356537i
$591$	2.00000			0.0822690
$592$	5.50000	+	2.59808i	0.226049	+	0.106780i
$593$	−2.00000			−0.0821302			−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000			−0.0821302			−0.0410651	+	0.999156i	$0.513075\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	−3.00000	−	5.19615i	−0.122988	−	0.213021i
$596$	4.50000	+	7.79423i	0.184327	+	0.319264i
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$	10.0000			0.408930
$599$	−22.5000	−	38.9711i	−0.919325	−	1.59232i	−0.800443	−	0.599409i	$-0.795402\pi$
$599$	−22.5000	−	38.9711i	−0.919325	−	1.59232i	−0.118882	−	0.992908i	$-0.537931\pi$
$600$	−1.00000			−0.0408248
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$	−18.0000			−0.733625
$603$	2.00000			0.0814463
$604$	−5.00000	+	8.66025i	−0.203447	+	0.352381i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	6.00000			0.243733
$607$	8.50000	−	14.7224i	0.345004	−	0.597565i	−0.640350	−	0.768083i	$-0.721211\pi$
$607$	8.50000	−	14.7224i	0.345004	−	0.597565i	0.985355	+	0.170518i	$0.0545441\pi$
$608$	−0.500000	+	0.866025i	−0.0202777	+	0.0351220i
$609$	−7.50000	+	12.9904i	−0.303915	+	0.526397i
$610$	2.00000	+	3.46410i	0.0809776	+	0.140257i
$611$	−30.0000	−	51.9615i	−1.21367	−	2.10214i
$612$	−1.00000	+	1.73205i	−0.0404226	+	0.0700140i
$613$	−21.5000	+	37.2391i	−0.868377	+	1.50407i	−0.00472215	+	0.999989i	$0.501503\pi$
$613$	−21.5000	+	37.2391i	−0.868377	+	1.50407i	−0.863655	+	0.504084i	$0.831830\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	−10.0000			−0.403239
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$	1.00000			0.0402259
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$	2.00000			0.0802572
$622$	6.00000	+	10.3923i	0.240578	+	0.416693i
$623$	48.0000			1.92308
$624$	−2.50000	−	4.33013i	−0.100080	−	0.173344i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$	−1.00000	+	1.73205i	−0.0399362	+	0.0691714i
$628$	−23.0000			−0.917800
$629$	11.0000	+	5.19615i	0.438599	+	0.207184i
$630$	3.00000			0.119523
$631$	−7.00000	+	12.1244i	−0.278666	+	0.482663i	−0.971053	−	0.238863i	$-0.923225\pi$
$631$	−7.00000	+	12.1244i	−0.278666	+	0.482663i	0.692388	+	0.721526i	$0.256559\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	2.50000	+	4.33013i	0.0993661	+	0.172107i
$634$	15.0000	+	25.9808i	0.595726	+	1.03183i
$635$	−11.0000			−0.436522
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	−10.0000			−0.396214
$638$	−5.00000	+	8.66025i	−0.197952	+	0.342863i
$639$	−1.00000			−0.0395594
$640$	1.00000			0.0395285
$641$	−16.0000	+	27.7128i	−0.631962	+	1.09459i	0.355188	+	0.934795i	$0.384417\pi$
$641$	−16.0000	+	27.7128i	−0.631962	+	1.09459i	−0.987150	+	0.159795i	$0.948917\pi$
$642$	−8.00000	−	13.8564i	−0.315735	−	0.546869i
$643$	44.0000			1.73519			0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000			1.73519			0.867595	+	0.497271i	$0.165665\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$	−3.00000	+	5.19615i	−0.118125	+	0.204598i
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	0.885013	−	0.465566i	$-0.154149\pi$
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$	2.50000	−	4.33013i	0.0980581	−	0.169842i
$651$	−6.00000	+	10.3923i	−0.235159	+	0.407307i
$652$	−24.0000			−0.939913
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$	10.0000			0.390434
$657$	−3.00000	+	5.19615i	−0.117041	+	0.202721i
$658$	−36.0000			−1.40343
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$	2.00000			0.0778499
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	1.50000	+	2.59808i	0.0582992	+	0.100977i
$663$	−5.00000	−	8.66025i	−0.194184	−	0.336336i
$664$	6.50000	−	11.2583i	0.252249	−	0.436908i
$665$	3.00000			0.116335
$666$	−5.00000	+	3.46410i	−0.193746	+	0.134231i
$667$	10.0000			0.387202
$668$	5.00000	−	8.66025i	0.193456	−	0.335075i
$669$		0			0
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	−4.00000	−	6.92820i	−0.154418	−	0.267460i
$672$	−3.00000			−0.115728
$673$	25.0000	+	43.3013i	0.963679	+	1.66914i	0.713123	+	0.701039i	$0.247280\pi$
$673$	25.0000	+	43.3013i	0.963679	+	1.66914i	0.250557	+	0.968102i	$0.419386\pi$
$674$	−22.0000			−0.847408
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	12.0000			0.461538
$677$	−48.0000			−1.84479			−0.922395	−	0.386248i	$-0.873771\pi$
$677$	−48.0000			−1.84479			−0.922395	+	0.386248i	$0.873771\pi$
$678$	0.500000	−	0.866025i	0.0192024	−	0.0332595i
$679$	−15.0000	−	25.9808i	−0.575647	−	0.997050i
$680$	2.00000			0.0766965
$681$	8.50000	−	14.7224i	0.325721	−	0.564165i
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	4.00000	−	6.92820i	0.153056	−	0.265100i	−0.779294	−	0.626659i	$-0.784422\pi$
$683$	4.00000	−	6.92820i	0.153056	−	0.265100i	0.932349	+	0.361559i	$0.117755\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$	−5.50000	−	9.52628i	−0.210144	−	0.363980i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	−8.00000	+	13.8564i	−0.305219	+	0.528655i
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−30.0000			−1.14291
$690$	−1.00000	−	1.73205i	−0.0380693	−	0.0659380i
$691$	−0.500000	+	0.866025i	−0.0190209	+	0.0329452i	−0.875379	−	0.483437i	$-0.839388\pi$
$691$	−0.500000	+	0.866025i	−0.0190209	+	0.0329452i	0.856358	+	0.516382i	$0.172722\pi$
$692$	4.00000			0.152057
$693$	−6.00000			−0.227921
$694$	−13.5000	+	23.3827i	−0.512453	+	0.887595i
$695$	12.0000			0.455186
$696$	−2.50000	−	4.33013i	−0.0947623	−	0.164133i
$697$	20.0000			0.757554
$698$	−4.00000	−	6.92820i	−0.151402	−	0.262236i
$699$	−8.50000	−	14.7224i	−0.321500	−	0.556854i
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	−0.580013	−	0.814607i	$-0.696952\pi$
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	0.995477	+	0.0950021i	$0.0302858\pi$
$702$	5.00000			0.188713
$703$	−5.00000	+	3.46410i	−0.188579	+	0.130651i
$704$	−2.00000			−0.0753778
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$	6.50000	+	11.2583i	0.244631	+	0.423713i
$707$	9.00000	+	15.5885i	0.338480	+	0.586264i
$708$	5.00000	+	8.66025i	0.187912	+	0.325472i
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	0.500000	+	0.866025i	0.0187647	+	0.0325014i
$711$	10.0000			0.375029
$712$	−8.00000	+	13.8564i	−0.299813	+	0.519291i
$713$	8.00000			0.299602
$714$	−6.00000			−0.224544
$715$	−5.00000	+	8.66025i	−0.186989	+	0.323875i
$716$		0			0
$717$	13.0000			0.485494
$718$	8.50000	−	14.7224i	0.317217	−	0.549436i
$719$	26.5000	−	45.8993i	0.988283	−	1.71176i	0.361959	−	0.932194i	$-0.382108\pi$
$719$	26.5000	−	45.8993i	0.988283	−	1.71176i	0.626324	−	0.779563i	$-0.284559\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	1.50000	+	2.59808i	0.0558629	+	0.0967574i
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	2.50000	−	4.33013i	0.0928477	−	0.160817i
$726$	7.00000			0.259794
$727$	22.5000	+	38.9711i	0.834479	+	1.44536i	0.894454	+	0.447160i	$0.147564\pi$
$727$	22.5000	+	38.9711i	0.834479	+	1.44536i	−0.0599753	+	0.998200i	$0.519102\pi$
$728$	7.50000	−	12.9904i	0.277968	−	0.481456i
$729$	1.00000			0.0370370
$730$	6.00000			0.222070
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$	4.00000			0.147844
$733$	−19.0000	−	32.9090i	−0.701781	−	1.21552i	−0.967841	−	0.251564i	$-0.919055\pi$
$733$	−19.0000	−	32.9090i	−0.701781	−	1.21552i	0.266060	−	0.963957i	$-0.414278\pi$
$734$	17.0000			0.627481
$735$	1.00000	+	1.73205i	0.0368856	+	0.0638877i
$736$	1.00000	+	1.73205i	0.0368605	+	0.0638442i
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$	−5.00000	+	8.66025i	−0.184053	+	0.318788i
$739$	15.0000			0.551784			0.275892	−	0.961189i	$-0.411027\pi$
$739$	15.0000			0.551784			0.275892	+	0.961189i	$0.411027\pi$
$740$	5.50000	+	2.59808i	0.202184	+	0.0955072i
$741$	5.00000			0.183680
$742$	−9.00000	+	15.5885i	−0.330400	+	0.572270i
$743$	26.0000	+	45.0333i	0.953847	+	1.65211i	0.736984	+	0.675910i	$0.236249\pi$
$743$	26.0000	+	45.0333i	0.953847	+	1.65211i	0.216864	+	0.976202i	$0.430417\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	4.50000	+	7.79423i	0.164867	+	0.285558i
$746$	13.0000			0.475964
$747$	6.50000	+	11.2583i	0.237823	+	0.411921i
$748$	−4.00000			−0.146254
$749$	24.0000	−	41.5692i	0.876941	−	1.51891i
$750$	−1.00000			−0.0365148
$751$	−28.0000			−1.02173			−0.510867	−	0.859660i	$-0.670676\pi$
$751$	−28.0000			−1.02173			−0.510867	+	0.859660i	$0.670676\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$	25.0000			0.910446
$755$	−5.00000	+	8.66025i	−0.181969	+	0.315179i
$756$	1.50000	−	2.59808i	0.0545545	−	0.0944911i
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	−0.577761	−	0.816206i	$-0.696073\pi$
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	0.995736	+	0.0922527i	$0.0294068\pi$
$758$	5.50000	+	9.52628i	0.199769	+	0.346010i
$759$	2.00000	+	3.46410i	0.0725954	+	0.125739i
$760$	−0.500000	+	0.866025i	−0.0181369	+	0.0314140i
$761$	7.00000	−	12.1244i	0.253750	−	0.439508i	−0.710805	−	0.703389i	$-0.751669\pi$
$761$	7.00000	−	12.1244i	0.253750	−	0.439508i	0.964555	+	0.263881i	$0.0850027\pi$
$762$	−5.50000	+	9.52628i	−0.199244	+	0.345101i
$763$	42.0000			1.52050
$764$	8.00000	+	13.8564i	0.289430	+	0.501307i
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$	−14.0000			−0.505841
$767$	−50.0000			−1.80540
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	23.0000			0.829401			0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000			0.829401			0.414701	+	0.909958i	$0.363886\pi$
$770$	3.00000	+	5.19615i	0.108112	+	0.187256i
$771$	−29.0000			−1.04441
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	6.00000	+	10.3923i	0.215805	+	0.373785i	0.953521	−	0.301326i	$-0.0974291\pi$
$773$	6.00000	+	10.3923i	0.215805	+	0.373785i	−0.737716	+	0.675111i	$0.764096\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	10.0000			0.358979
$777$	−16.5000	−	7.79423i	−0.591934	−	0.279616i
$778$	11.0000			0.394369
$779$	−5.00000	+	8.66025i	−0.179144	+	0.310286i
$780$	−2.50000	−	4.33013i	−0.0895144	−	0.155043i
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$	2.00000	+	3.46410i	0.0715199	+	0.123876i
$783$	5.00000			0.178685
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	−23.0000			−0.820905
$786$		0			0
$787$	50.0000			1.78231			0.891154	−	0.453701i	$-0.149897\pi$
$787$	50.0000			1.78231			0.891154	+	0.453701i	$0.149897\pi$
$788$	−2.00000			−0.0712470
$789$	1.00000	−	1.73205i	0.0356009	−	0.0616626i
$790$	−5.00000	−	8.66025i	−0.177892	−	0.308118i
$791$	3.00000			0.106668
$792$	1.00000	−	1.73205i	0.0355335	−	0.0615457i
$793$	−10.0000	+	17.3205i	−0.355110	+	0.615069i
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	−0.602761	−	0.797922i	$-0.705933\pi$
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	0.992401	+	0.123045i	$0.0392661\pi$
$798$	1.50000	−	2.59808i	0.0530994	−	0.0919709i
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$	1.00000			0.0353553
$801$	−8.00000	−	13.8564i	−0.282666	−	0.489592i
$802$	1.00000	−	1.73205i	0.0353112	−	0.0611608i
$803$	−12.0000			−0.423471
$804$	−2.00000			−0.0705346
$805$	3.00000	−	5.19615i	0.105736	−	0.183140i
$806$	20.0000			0.704470
$807$	6.50000	+	11.2583i	0.228811	+	0.396312i
$808$	−6.00000			−0.211079
$809$	14.0000	+	24.2487i	0.492214	+	0.852539i	0.999960	−	0.00896753i	$-0.00285449\pi$
$809$	14.0000	+	24.2487i	0.492214	+	0.852539i	−0.507746	+	0.861507i	$0.669521\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	0.635303	−	0.772263i	$-0.280875\pi$
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	−0.986451	+	0.164057i	$0.947542\pi$
$812$	7.50000	−	12.9904i	0.263198	−	0.455873i
$813$	4.00000			0.140286
$814$	−11.0000	−	5.19615i	−0.385550	−	0.182125i
$815$	−24.0000			−0.840683
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	3.00000	+	5.19615i	0.104957	+	0.181790i
$818$	−15.5000	−	26.8468i	−0.541945	−	0.938676i
$819$	7.50000	+	12.9904i	0.262071	+	0.453921i
$820$	10.0000			0.349215
$821$	4.50000	+	7.79423i	0.157051	+	0.272020i	0.933804	−	0.357785i	$-0.116468\pi$
$821$	4.50000	+	7.79423i	0.157051	+	0.272020i	−0.776753	+	0.629805i	$0.783135\pi$
$822$	−11.0000			−0.383669
$823$	−12.5000	+	21.6506i	−0.435723	+	0.754694i	−0.997354	−	0.0726937i	$-0.976840\pi$
$823$	−12.5000	+	21.6506i	−0.435723	+	0.754694i	0.561632	+	0.827387i	$0.310174\pi$
$824$	−1.00000			−0.0348367
$825$	2.00000			0.0696311
$826$	−15.0000	+	25.9808i	−0.521917	+	0.903986i
$827$	4.50000	+	7.79423i	0.156480	+	0.271032i	0.933597	−	0.358325i	$-0.116652\pi$
$827$	4.50000	+	7.79423i	0.156480	+	0.271032i	−0.777117	+	0.629356i	$0.783319\pi$
$828$	−2.00000			−0.0695048
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	−0.985771	−	0.168091i	$-0.946240\pi$
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	0.638457	+	0.769657i	$0.279573\pi$
$830$	6.50000	−	11.2583i	0.225618	−	0.390782i
$831$	−5.50000	+	9.52628i	−0.190793	+	0.330463i
$832$	2.50000	+	4.33013i	0.0866719	+	0.150120i
$833$	−2.00000	−	3.46410i	−0.0692959	−	0.120024i
$834$	6.00000	−	10.3923i	0.207763	−	0.359856i
$835$	5.00000	−	8.66025i	0.173032	−	0.299700i
$836$	1.00000	−	1.73205i	0.0345857	−	0.0599042i
$837$	4.00000			0.138260
$838$	14.0000	+	24.2487i	0.483622	+	0.837658i
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	−0.995353	−	0.0962912i	$-0.969302\pi$
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	0.581067	+	0.813856i	$0.302635\pi$
$840$	−3.00000			−0.103510
$841$	−4.00000			−0.137931
$842$	−2.00000	+	3.46410i	−0.0689246	+	0.119381i
$843$	8.00000			0.275535
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	12.0000			0.412813
$846$	6.00000	+	10.3923i	0.206284	+	0.357295i
$847$	10.5000	+	18.1865i	0.360784	+	0.624897i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$	−15.0000	+	25.9808i	−0.514799	+	0.891657i
$850$	2.00000			0.0685994
$851$	1.00000	+	12.1244i	0.0342796	+	0.415618i
$852$	1.00000			0.0342594
$853$	15.0000	−	25.9808i	0.513590	−	0.889564i	−0.486286	−	0.873800i	$-0.661649\pi$
$853$	15.0000	−	25.9808i	0.513590	−	0.889564i	0.999876	−	0.0157644i	$-0.00501816\pi$
$854$	6.00000	+	10.3923i	0.205316	+	0.355617i
$855$	−0.500000	−	0.866025i	−0.0170996	−	0.0296174i
$856$	8.00000	+	13.8564i	0.273434	+	0.473602i
$857$	21.0000			0.717346			0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000			0.717346			0.358673	+	0.933463i	$0.383229\pi$
$858$	5.00000	+	8.66025i	0.170697	+	0.295656i
$859$	−33.0000			−1.12595			−0.562973	−	0.826475i	$-0.690342\pi$
$859$	−33.0000			−1.12595			−0.562973	+	0.826475i	$0.690342\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$	−30.0000			−1.02240
$862$	9.00000			0.306541
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	4.00000			0.136004
$866$	8.00000	−	13.8564i	0.271851	−	0.470860i
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$	6.00000	−	10.3923i	0.203653	−	0.352738i
$869$	10.0000	+	17.3205i	0.339227	+	0.587558i
$870$	−2.50000	−	4.33013i	−0.0847579	−	0.146805i
$871$	5.00000	−	8.66025i	0.169419	−	0.293442i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$	−2.00000			−0.0676510
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$	3.00000	−	5.19615i	0.101361	−	0.175562i
$877$	21.0000			0.709120			0.354560	−	0.935033i	$-0.384631\pi$
$877$	21.0000			0.709120			0.354560	+	0.935033i	$0.384631\pi$
$878$		0			0
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$	−2.00000			−0.0674200
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	0.976863	−	0.213866i	$-0.0686057\pi$
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	−0.673645	+	0.739055i	$0.735272\pi$
$882$	2.00000			0.0673435
$883$	−10.0000	−	17.3205i	−0.336527	−	0.582882i	0.647250	−	0.762278i	$-0.275919\pi$
$883$	−10.0000	−	17.3205i	−0.336527	−	0.582882i	−0.983777	+	0.179396i	$0.942586\pi$
$884$	5.00000	+	8.66025i	0.168168	+	0.291276i
$885$	5.00000	+	8.66025i	0.168073	+	0.291111i
$886$	7.50000	−	12.9904i	0.251967	−	0.436420i
$887$	−12.0000			−0.402921			−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000			−0.402921			−0.201460	+	0.979497i	$0.564569\pi$
$888$	5.00000	−	3.46410i	0.167789	−	0.116248i
$889$	−33.0000			−1.10678
$890$	−8.00000	+	13.8564i	−0.268161	+	0.464468i
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$	9.00000			0.301005
$895$		0			0
$896$	3.00000			0.100223
$897$	5.00000	−	8.66025i	0.166945	−	0.289157i
$898$	−24.0000			−0.800890
$899$	20.0000			0.667037
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$	−20.0000			−0.665927
$903$	−9.00000	+	15.5885i	−0.299501	+	0.518751i
$904$	−0.500000	+	0.866025i	−0.0166298	+	0.0288036i
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	5.00000	+	8.66025i	0.166114	+	0.287718i
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	−8.50000	+	14.7224i	−0.282082	+	0.488581i
$909$	3.00000	−	5.19615i	0.0995037	−	0.172345i
$910$	7.50000	−	12.9904i	0.248623	−	0.430627i
$911$	23.0000			0.762024			0.381012	−	0.924570i	$-0.375576\pi$
$911$	23.0000			0.762024			0.381012	+	0.924570i	$0.375576\pi$
$912$	0.500000	+	0.866025i	0.0165567	+	0.0286770i
$913$	−13.0000	+	22.5167i	−0.430237	+	0.745193i
$914$	−6.00000			−0.198462
$915$	4.00000			0.132236
$916$	8.00000	−	13.8564i	0.264327	−	0.457829i
$917$		0			0
$918$	1.00000	+	1.73205i	0.0330049	+	0.0571662i
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$	1.00000	+	1.73205i	0.0329690	+	0.0571040i
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$	10.5000	+	18.1865i	0.345799	+	0.598942i
$923$	−2.50000	+	4.33013i	−0.0822885	+	0.142528i
$924$	6.00000			0.197386
$925$	5.50000	+	2.59808i	0.180839	+	0.0854242i
$926$	39.0000			1.28162
$927$	0.500000	−	0.866025i	0.0164222	−	0.0284440i
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	−5.00000	−	8.66025i	−0.164045	−	0.284134i	0.772271	−	0.635293i	$-0.219121\pi$
$929$	−5.00000	−	8.66025i	−0.164045	−	0.284134i	−0.936316	+	0.351160i	$0.885787\pi$
$930$	−2.00000	−	3.46410i	−0.0655826	−	0.113592i
$931$	2.00000			0.0655474
$932$	8.50000	+	14.7224i	0.278427	+	0.482249i
$933$	12.0000			0.392862
$934$	10.5000	−	18.1865i	0.343570	−	0.595082i
$935$	−4.00000			−0.130814
$936$	−5.00000			−0.163430
$937$	−4.00000	+	6.92820i	−0.130674	+	0.226335i	−0.923937	−	0.382545i	$-0.875048\pi$
$937$	−4.00000	+	6.92820i	−0.130674	+	0.226335i	0.793262	+	0.608880i	$0.208381\pi$
$938$	−3.00000	−	5.19615i	−0.0979535	−	0.169660i
$939$	−8.00000			−0.261070
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	−7.50000	+	12.9904i	−0.244493	+	0.423474i	−0.961989	−	0.273088i	$-0.911955\pi$
$941$	−7.50000	+	12.9904i	−0.244493	+	0.423474i	0.717496	+	0.696563i	$0.245288\pi$
$942$	−11.5000	+	19.9186i	−0.374690	+	0.648983i
$943$	10.0000	+	17.3205i	0.325645	+	0.564033i
$944$	−5.00000	−	8.66025i	−0.162736	−	0.281867i
$945$	1.50000	−	2.59808i	0.0487950	−	0.0845154i
$946$	−6.00000	+	10.3923i	−0.195077	+	0.337883i
$947$	−15.5000	+	26.8468i	−0.503682	+	0.872403i	0.496309	+	0.868146i	$0.334688\pi$
$947$	−15.5000	+	26.8468i	−0.503682	+	0.872403i	−0.999991	+	0.00425721i	$0.998645\pi$
$948$	−10.0000			−0.324785
$949$	15.0000	+	25.9808i	0.486921	+	0.843371i
$950$	−0.500000	+	0.866025i	−0.0162221	+	0.0280976i
$951$	30.0000			0.972817
$952$	6.00000			0.194461
$953$	−23.5000	+	40.7032i	−0.761240	+	1.31851i	0.180972	+	0.983488i	$0.442076\pi$
$953$	−23.5000	+	40.7032i	−0.761240	+	1.31851i	−0.942212	+	0.335018i	$0.891258\pi$
$954$	6.00000			0.194257
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	−13.0000			−0.420450
$957$	5.00000	+	8.66025i	0.161627	+	0.279946i
$958$		0			0
$959$	−16.5000	−	28.5788i	−0.532813	−	0.922859i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−15.0000			−0.483871
$962$	2.50000	+	30.3109i	0.0806032	+	0.977262i
$963$	−16.0000			−0.515593
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	−7.00000	−	12.1244i	−0.225338	−	0.390297i
$966$	−3.00000	−	5.19615i	−0.0965234	−	0.167183i
$967$	15.5000	+	26.8468i	0.498446	+	0.863334i	0.999998	−	0.00179302i	$-0.000570736\pi$
$967$	15.5000	+	26.8468i	0.498446	+	0.863334i	−0.501552	+	0.865128i	$0.667237\pi$
$968$	−7.00000			−0.224989
$969$	1.00000	+	1.73205i	0.0321246	+	0.0556415i
$970$	10.0000			0.321081
$971$	−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	$0.270657\pi$
$972$	−1.00000			−0.0320750
$973$	36.0000			1.15411
$974$	1.50000	−	2.59808i	0.0480631	−	0.0832477i
$975$	−2.50000	−	4.33013i	−0.0800641	−	0.138675i
$976$	−4.00000			−0.128037
$977$	21.5000	−	37.2391i	0.687846	−	1.19138i	−0.284687	−	0.958620i	$-0.591890\pi$
$977$	21.5000	−	37.2391i	0.687846	−	1.19138i	0.972533	−	0.232764i	$-0.0747769\pi$
$978$	−12.0000	+	20.7846i	−0.383718	+	0.664619i
$979$	16.0000	−	27.7128i	0.511362	−	0.885705i
$980$	−1.00000	−	1.73205i	−0.0319438	−	0.0553283i
$981$	−7.00000	−	12.1244i	−0.223493	−	0.387101i
$982$	19.0000	−	32.9090i	0.606314	−	1.05017i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$	5.00000	−	8.66025i	0.159394	−	0.276079i
$985$	−2.00000			−0.0637253
$986$	5.00000	+	8.66025i	0.159232	+	0.275799i
$987$	−18.0000	+	31.1769i	−0.572946	+	0.992372i
$988$	−5.00000			−0.159071
$989$	12.0000			0.381578
$990$	1.00000	−	1.73205i	0.0317821	−	0.0550482i
$991$	34.0000			1.08005			0.540023	−	0.841650i	$-0.318416\pi$
$991$	34.0000			1.08005			0.540023	+	0.841650i	$0.318416\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	3.00000			0.0952021
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$	4.00000	+	6.92820i	0.126809	+	0.219639i
$996$	−6.50000	−	11.2583i	−0.205960	−	0.356734i
$997$	1.50000	−	2.59808i	0.0475055	−	0.0822819i	−0.841295	−	0.540576i	$-0.818206\pi$
$997$	1.50000	−	2.59808i	0.0475055	−	0.0822819i	0.888800	+	0.458295i	$0.151540\pi$
$998$	−29.0000			−0.917979
$999$	0.500000	+	6.06218i	0.0158193	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.b.121.1	✓	2
37.26	even	3	inner	1110.2.i.b.211.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.b.121.1	✓	2	1.1	even	1	trivial
1110.2.i.b.211.1	yes	2	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +3.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.50000 - 2.59808i) q^{21} +(1.00000 - 1.73205i) q^{22} -2.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} -5.00000 q^{29} +(0.500000 + 0.866025i) q^{30} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{35} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} +1.00000 q^{38} +(-2.50000 + 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.00000 - 8.66025i) q^{41} +(1.50000 + 2.59808i) q^{42} -6.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(1.00000 - 1.73205i) q^{46} -12.0000 q^{47} -1.00000 q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(2.50000 - 4.33013i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(0.500000 - 0.866025i) q^{57} +(2.50000 - 4.33013i) q^{58} +(-5.00000 + 8.66025i) q^{59} -1.00000 q^{60} +(2.00000 + 3.46410i) q^{61} +(2.00000 - 3.46410i) q^{62} +3.00000 q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +2.00000 q^{68} +(-1.00000 - 1.73205i) q^{69} +(-1.50000 - 2.59808i) q^{70} +(0.500000 + 0.866025i) q^{71} +(-0.500000 + 0.866025i) q^{72} +6.00000 q^{73} +(5.50000 + 2.59808i) q^{74} -1.00000 q^{75} +(-0.500000 + 0.866025i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-2.50000 - 4.33013i) q^{78} +(-5.00000 - 8.66025i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +10.0000 q^{82} +(6.50000 - 11.2583i) q^{83} -3.00000 q^{84} +2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(-2.50000 - 4.33013i) q^{87} -2.00000 q^{88} +(-8.00000 + 13.8564i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(7.50000 - 12.9904i) q^{91} +(1.00000 + 1.73205i) q^{92} +(-2.00000 - 3.46410i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.0000 q^{97} +(-1.00000 - 1.73205i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - 3 q^{7} + 2 q^{8} - q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 5 q^{13} + 6 q^{14} + q^{15} - q^{16} - 2 q^{17} - q^{18} - q^{19} - q^{20} + 3 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - 3 * q^7 + 2 * q^8 - q^9 + 2 * q^10 - 4 * q^11 + q^12 + 5 * q^13 + 6 * q^14 + q^15 - q^16 - 2 * q^17 - q^18 - q^19 - q^20 + 3 * q^21 + 2 * q^22 - 4 * q^23 + q^24 - q^25 - 10 * q^26 - 2 * q^27 - 3 * q^28 - 10 * q^29 + q^30 - 8 * q^31 - q^32 - 2 * q^33 - 2 * q^34 - 3 * q^35 + 2 * q^36 - q^37 + 2 * q^38 - 5 * q^39 - q^40 - 10 * q^41 + 3 * q^42 - 12 * q^43 + 2 * q^44 + 2 * q^45 + 2 * q^46 - 24 * q^47 - 2 * q^48 - 2 * q^49 - q^50 - 4 * q^51 + 5 * q^52 - 6 * q^53 + q^54 + 2 * q^55 - 3 * q^56 + q^57 + 5 * q^58 - 10 * q^59 - 2 * q^60 + 4 * q^61 + 4 * q^62 + 6 * q^63 + 2 * q^64 + 5 * q^65 + 4 * q^66 - 2 * q^67 + 4 * q^68 - 2 * q^69 - 3 * q^70 + q^71 - q^72 + 12 * q^73 + 11 * q^74 - 2 * q^75 - q^76 + 6 * q^77 - 5 * q^78 - 10 * q^79 + 2 * q^80 - q^81 + 20 * q^82 + 13 * q^83 - 6 * q^84 + 4 * q^85 + 6 * q^86 - 5 * q^87 - 4 * q^88 - 16 * q^89 - q^90 + 15 * q^91 + 2 * q^92 - 4 * q^93 + 12 * q^94 - q^95 + q^96 + 20 * q^97 - 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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