LMFDB - Embedded newform 390.2.i.c.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(61,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("390.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	390.211
Dual form			390.2.i.c.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} -1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-0.500000 + 0.866025i) q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{42} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(1.50000 - 2.59808i) q^{46} -3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -6.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(1.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(2.50000 + 4.33013i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{69} +2.00000 q^{70} +(6.00000 - 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +(3.50000 + 0.866025i) q^{78} +5.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{85} +1.00000 q^{86} +(-1.50000 + 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-7.00000 - 1.73205i) q^{91} +3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{95} -1.00000 q^{96} +(-7.00000 + 12.1244i) q^{97} +(-1.50000 + 2.59808i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} - q^{16} - 6 q^{17} - 2 q^{18} - 2 q^{19} + q^{20} + 4 q^{21} - 3 q^{22} - 3 q^{23} + q^{24} + 2 q^{25} - 5 q^{26} + 2 q^{27} - 2 q^{28} - 3 q^{29} - q^{30} + 10 q^{31} + q^{32} + 3 q^{33} - 12 q^{34} + 2 q^{35} - q^{36} + 7 q^{37} - 4 q^{38} + 5 q^{39} + 2 q^{40} - 6 q^{41} + 2 q^{42} + q^{43} - 6 q^{44} + q^{45} + 3 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} + q^{50} + 12 q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 3 q^{55} + 2 q^{56} + 4 q^{57} + 3 q^{58} + 9 q^{59} - 2 q^{60} - 2 q^{61} + 5 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} - 3 q^{69} + 4 q^{70} + 12 q^{71} + q^{72} + 28 q^{73} - 7 q^{74} - q^{75} - 2 q^{76} - 12 q^{77} + 7 q^{78} + 10 q^{79} + q^{80} - q^{81} + 6 q^{82} - 12 q^{83} - 2 q^{84} + 6 q^{85} + 2 q^{86} - 3 q^{87} - 3 q^{88} + 18 q^{89} + 2 q^{90} - 14 q^{91} + 6 q^{92} - 5 q^{93} - 3 q^{94} + 2 q^{95} - 2 q^{96} - 14 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 - q^16 - 6 * q^17 - 2 * q^18 - 2 * q^19 + q^20 + 4 * q^21 - 3 * q^22 - 3 * q^23 + q^24 + 2 * q^25 - 5 * q^26 + 2 * q^27 - 2 * q^28 - 3 * q^29 - q^30 + 10 * q^31 + q^32 + 3 * q^33 - 12 * q^34 + 2 * q^35 - q^36 + 7 * q^37 - 4 * q^38 + 5 * q^39 + 2 * q^40 - 6 * q^41 + 2 * q^42 + q^43 - 6 * q^44 + q^45 + 3 * q^46 - 6 * q^47 - q^48 + 3 * q^49 + q^50 + 12 * q^51 - 7 * q^52 - 12 * q^53 + q^54 - 3 * q^55 + 2 * q^56 + 4 * q^57 + 3 * q^58 + 9 * q^59 - 2 * q^60 - 2 * q^61 + 5 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 3 * q^69 + 4 * q^70 + 12 * q^71 + q^72 + 28 * q^73 - 7 * q^74 - q^75 - 2 * q^76 - 12 * q^77 + 7 * q^78 + 10 * q^79 + q^80 - q^81 + 6 * q^82 - 12 * q^83 - 2 * q^84 + 6 * q^85 + 2 * q^86 - 3 * q^87 - 3 * q^88 + 18 * q^89 + 2 * q^90 - 14 * q^91 + 6 * q^92 - 5 * q^93 - 3 * q^94 + 2 * q^95 - 2 * q^96 - 14 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	1.00000			0.288675
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	−2.00000			−0.534522
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	−1.00000			−0.235702
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	2.00000			0.436436
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.00000			0.200000
$26$	−2.50000	+	2.59808i	−0.490290	+	0.509525i
$27$	1.00000			0.192450
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	−6.00000			−1.02899
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−2.00000			−0.324443
$39$	2.50000	−	2.59808i	0.400320	−	0.416025i
$40$	1.00000			0.158114
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−3.00000			−0.452267
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	6.00000			0.840168
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$	2.00000			0.264906
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$	−1.00000			−0.129099
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	2.50000	+	4.33013i	0.317500	+	0.549927i
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$	−1.00000	−	3.46410i	−0.124035	−	0.429669i
$66$	3.00000			0.369274
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$	2.00000			0.239046
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−6.00000			−0.683763
$78$	3.50000	+	0.866025i	0.396297	+	0.0980581i
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	1.00000			0.107833
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.736644	+	0.676280i	$0.236409\pi$
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.217354	+	0.976093i	$0.430258\pi$
$90$	1.00000			0.105409
$91$	−7.00000	−	1.73205i	−0.733799	−	0.181568i
$92$	3.00000			0.312772
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	−1.00000			−0.102062
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$	−3.00000			−0.301511
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−1.00000	−	3.46410i	−0.0980581	−	0.339683i
$105$	−2.00000			−0.195180
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	2.00000			0.188982
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	3.00000			0.278543
$117$	−3.50000	−	0.866025i	−0.323575	−	0.0800641i
$118$	9.00000			0.828517
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.00000			−0.181071
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$	−1.00000			−0.0894427
$126$	1.00000	−	1.73205i	0.0890871	−	0.154303i
$127$	−7.00000	−	12.1244i	−0.621150	−	1.07586i	−0.989272	−	0.146085i	$-0.953333\pi$
$127$	−7.00000	−	12.1244i	−0.621150	−	1.07586i	0.368122	−	0.929777i	$-0.380001\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.00000			−0.0880451
$130$	2.50000	−	2.59808i	0.219265	−	0.227866i
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$	1.50000	+	2.59808i	0.130558	+	0.226134i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	4.00000	−	6.92820i	0.345547	−	0.598506i
$135$	−1.00000			−0.0860663
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$	−3.00000			−0.255377
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	0.399992	+	0.916519i	$0.369013\pi$
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	−0.993724	+	0.111856i	$0.964321\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	12.0000			1.00702
$143$	−7.50000	+	7.79423i	−0.627182	+	0.651786i
$144$	1.00000			0.0833333
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$	7.00000	+	12.1244i	0.579324	+	1.00342i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	−7.00000			−0.575396
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	−5.00000			−0.401610
$156$	1.00000	+	3.46410i	0.0800641	+	0.277350i
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	2.50000	+	4.33013i	0.198889	+	0.344486i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	6.00000			0.472866
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	6.50000	−	11.2583i	0.509119	−	0.881820i	−0.490825	−	0.871258i	$-0.663305\pi$
$163$	6.50000	−	11.2583i	0.509119	−	0.881820i	0.999944	−	0.0105623i	$-0.00336213\pi$
$164$	6.00000			0.468521
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	0.985933	−	0.167139i	$-0.0534527\pi$
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	−0.637713	+	0.770274i	$0.720119\pi$
$168$	−2.00000			−0.154303
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	6.00000			0.460179
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	−3.00000			−0.227429
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−9.00000			−0.676481
$178$	−9.00000	+	15.5885i	−0.674579	+	1.16840i
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−2.00000	−	6.92820i	−0.148250	−	0.513553i
$183$	2.00000			0.147844
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$	2.50000	−	4.33013i	0.183309	−	0.317500i
$187$	−18.0000			−1.31629
$188$	1.50000	−	2.59808i	0.109399	−	0.189484i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$	2.00000			0.145095
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	−14.0000			−1.00514
$195$	−2.50000	+	2.59808i	−0.179029	+	0.186052i
$196$	−3.00000			−0.214286
$197$	−12.0000	−	20.7846i	−0.854965	−	1.48084i	−0.876678	−	0.481078i	$-0.840245\pi$
$197$	−12.0000	−	20.7846i	−0.854965	−	1.48084i	0.0217133	−	0.999764i	$-0.493088\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	−1.00000			−0.0707107
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$	3.00000	−	5.19615i	0.211079	−	0.365600i
$203$	6.00000			0.421117
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	3.00000			0.208514
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	−6.00000			−0.415029
$210$	−1.00000	−	1.73205i	−0.0690066	−	0.119523i
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	−12.0000			−0.822226
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$	−1.00000			−0.0680414
$217$	−5.00000	+	8.66025i	−0.339422	+	0.587896i
$218$	7.00000	+	12.1244i	0.474100	+	0.821165i
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$	3.00000			0.202260
$221$	−21.0000	−	5.19615i	−1.41261	−	0.349531i
$222$	7.00000			0.469809
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−15.0000			−0.997785
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	−1.50000	+	2.59808i	−0.0989071	+	0.171312i
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$	−1.00000	−	3.46410i	−0.0653720	−	0.226455i
$235$	3.00000			0.195698
$236$	4.50000	+	7.79423i	0.292925	+	0.507361i
$237$	−2.50000	−	4.33013i	−0.162392	−	0.281272i
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	2.00000			0.128565
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−6.00000			−0.382546
$247$	−7.00000	−	1.73205i	−0.445399	−	0.110208i
$248$	−5.00000			−0.317500
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$	2.00000			0.125988
$253$	4.50000	−	7.79423i	0.282913	−	0.490019i
$254$	7.00000	−	12.1244i	0.439219	−	0.760750i
$255$	−6.00000			−0.375735
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	0.981901	+	0.189396i	$0.0606529\pi$
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	−0.326929	+	0.945049i	$0.606014\pi$
$258$	−0.500000	−	0.866025i	−0.0311286	−	0.0539164i
$259$	−14.0000			−0.869918
$260$	3.50000	+	0.866025i	0.217061	+	0.0537086i
$261$	3.00000			0.185695
$262$	4.50000	+	7.79423i	0.278011	+	0.481529i
$263$	7.50000	+	12.9904i	0.462470	+	0.801021i	0.999083	−	0.0428069i	$-0.0136300\pi$
$263$	7.50000	+	12.9904i	0.462470	+	0.801021i	−0.536614	+	0.843828i	$0.680297\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	6.00000			0.368577
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	9.00000	−	15.5885i	0.550791	−	0.953998i
$268$	8.00000			0.488678
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$	6.00000			0.363803
$273$	2.00000	+	6.92820i	0.121046	+	0.419314i
$274$	−9.00000			−0.543710
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	−14.0000			−0.839664
$279$	−2.50000	+	4.33013i	−0.149671	+	0.259238i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−1.50000	+	2.59808i	−0.0893237	+	0.154713i
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	−2.00000			−0.118470
$286$	−10.5000	−	2.59808i	−0.620878	−	0.153627i
$287$	12.0000			0.708338
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$	14.0000			0.820695
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	15.0000	−	25.9808i	0.876309	−	1.51781i	0.0209480	−	0.999781i	$-0.493332\pi$
$293$	15.0000	−	25.9808i	0.876309	−	1.51781i	0.855361	−	0.518032i	$-0.173335\pi$
$294$	3.00000			0.174964
$295$	−4.50000	+	7.79423i	−0.262000	+	0.453798i
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$	9.00000			0.521356
$299$	7.50000	−	7.79423i	0.433736	−	0.450752i
$300$	1.00000			0.0577350
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	4.00000	+	6.92820i	0.230174	+	0.398673i
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$	2.00000			0.114708
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$	−2.50000	−	4.33013i	−0.141990	−	0.245935i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$	−2.50000	+	2.59808i	−0.141535	+	0.147087i
$313$	8.00000			0.452187			0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000			0.452187			0.226093	+	0.974106i	$0.427405\pi$
$314$	−6.50000	−	11.2583i	−0.366816	−	0.635344i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$	−1.00000			−0.0559017
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$	3.00000	+	5.19615i	0.167183	+	0.289570i
$323$	−6.00000	−	10.3923i	−0.333849	−	0.578243i
$324$	1.00000			0.0555556
$325$	1.00000	+	3.46410i	0.0554700	+	0.192154i
$326$	13.0000			0.720003
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$	−3.00000			−0.165145
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.0274825	+	0.999622i	$0.508749\pi$
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−7.00000			−0.383598
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$	4.00000	+	6.92820i	0.218543	+	0.378528i
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−11.5000	−	6.06218i	−0.625518	−	0.329739i
$339$	15.0000			0.814688
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$	1.00000	−	1.73205i	0.0540738	−	0.0936586i
$343$	−20.0000			−1.07990
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$	1.50000	−	2.59808i	0.0807573	−	0.139876i
$346$	−12.0000			−0.645124
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	0.738883	−	0.673833i	$-0.235353\pi$
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	−0.952998	+	0.302975i	$0.902020\pi$
$350$	−2.00000			−0.106904
$351$	1.00000	+	3.46410i	0.0533761	+	0.184900i
$352$	3.00000			0.159901
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$	−18.0000			−0.953998
$357$	−6.00000	+	10.3923i	−0.317554	+	0.550019i
$358$	−1.50000	+	2.59808i	−0.0792775	+	0.137313i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−8.00000	−	13.8564i	−0.420471	−	0.728277i
$363$	−2.00000			−0.104973
$364$	5.00000	−	5.19615i	0.262071	−	0.272352i
$365$	−14.0000			−0.732793
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−10.0000	−	17.3205i	−0.521996	−	0.904123i	−0.999673	−	0.0255875i	$-0.991854\pi$
$367$	−10.0000	−	17.3205i	−0.521996	−	0.904123i	0.477677	−	0.878536i	$-0.341479\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$	6.00000			0.312348
$370$	3.50000	−	6.06218i	0.181956	−	0.315158i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$	5.00000			0.259238
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	3.00000			0.154713
$377$	7.50000	−	7.79423i	0.386270	−	0.401423i
$378$	−2.00000			−0.102869
$379$	−19.0000	−	32.9090i	−0.975964	−	1.69042i	−0.676715	−	0.736245i	$-0.736597\pi$
$379$	−19.0000	−	32.9090i	−0.975964	−	1.69042i	−0.299249	−	0.954175i	$-0.596736\pi$
$380$	1.00000	+	1.73205i	0.0512989	+	0.0888523i
$381$	−7.00000	+	12.1244i	−0.358621	+	0.621150i
$382$	12.0000			0.613973
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	6.00000			0.305788
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$	−7.00000	−	12.1244i	−0.355371	−	0.615521i
$389$	3.00000			0.152106			0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000			0.152106			0.0760530	+	0.997104i	$0.475768\pi$
$390$	−3.50000	−	0.866025i	−0.177229	−	0.0438529i
$391$	18.0000			0.910299
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$	−4.50000	−	7.79423i	−0.226995	−	0.393167i
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	−5.00000			−0.251577
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	15.5000	−	26.8468i	0.777923	−	1.34740i	−0.155214	−	0.987881i	$-0.549607\pi$
$397$	15.5000	−	26.8468i	0.777923	−	1.34740i	0.933137	−	0.359521i	$-0.117060\pi$
$398$	−8.00000			−0.401004
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$	−8.00000			−0.399004
$403$	5.00000	+	17.3205i	0.249068	+	0.862796i
$404$	6.00000			0.298511
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	3.00000	+	5.19615i	0.148888	+	0.257881i
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$	−6.00000			−0.297044
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$	−3.00000	+	5.19615i	−0.148159	+	0.256620i
$411$	9.00000			0.443937
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$	9.00000	+	15.5885i	0.442861	+	0.767058i
$414$	1.50000	+	2.59808i	0.0737210	+	0.127688i
$415$	6.00000			0.294528
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$	14.0000			0.685583
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	6.00000			0.291386
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	−6.00000	−	10.3923i	−0.290701	−	0.503509i
$427$	−2.00000	−	3.46410i	−0.0967868	−	0.167640i
$428$	−6.00000			−0.290021
$429$	10.5000	+	2.59808i	0.506945	+	0.125436i
$430$	−1.00000			−0.0482243
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	20.0000	−	34.6410i	0.961139	−	1.66474i	0.241489	−	0.970404i	$-0.422364\pi$
$433$	20.0000	−	34.6410i	0.961139	−	1.66474i	0.719650	−	0.694337i	$-0.244302\pi$
$434$	−10.0000			−0.480015
$435$	1.50000	−	2.59808i	0.0719195	−	0.124568i
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	6.00000			0.287019
$438$	7.00000	−	12.1244i	0.334473	−	0.579324i
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	0.909798	−	0.415051i	$-0.136236\pi$
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	−0.814344	+	0.580383i	$0.802903\pi$
$440$	1.50000	+	2.59808i	0.0715097	+	0.123858i
$441$	−3.00000			−0.142857
$442$	−6.00000	−	20.7846i	−0.285391	−	0.988623i
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	−5.00000	+	8.66025i	−0.236757	+	0.410075i
$447$	−9.00000			−0.425685
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	−18.0000	+	31.1769i	−0.849473	+	1.47133i	0.0322072	+	0.999481i	$0.489746\pi$
$449$	−18.0000	+	31.1769i	−0.849473	+	1.47133i	−0.881680	+	0.471848i	$0.843587\pi$
$450$	−1.00000			−0.0471405
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$		0			0
$455$	7.00000	+	1.73205i	0.328165	+	0.0811998i
$456$	−2.00000			−0.0936586
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$	−3.00000			−0.139876
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	−0.986127	−	0.165992i	$-0.946917\pi$
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	0.636817	+	0.771015i	$0.280251\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$	2.50000	+	4.33013i	0.115935	+	0.200805i
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	2.50000	−	2.59808i	0.115563	−	0.120096i
$469$	16.0000			0.738811
$470$	1.50000	+	2.59808i	0.0691898	+	0.119840i
$471$	6.50000	+	11.2583i	0.299504	+	0.518756i
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$	3.00000			0.137940
$474$	2.50000	−	4.33013i	0.114829	−	0.198889i
$475$	−1.00000	+	1.73205i	−0.0458831	+	0.0794719i
$476$	12.0000			0.550019
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	1.00000			0.0456435
$481$	−17.5000	+	18.1865i	−0.797931	+	0.829235i
$482$	−17.0000			−0.774329
$483$	−3.00000	−	5.19615i	−0.136505	−	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$	−1.00000			−0.0453609
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	−0.887793	−	0.460243i	$-0.847762\pi$
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	0.842479	+	0.538730i	$0.181096\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−13.0000			−0.587880
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$	18.0000			0.810679
$494$	−2.00000	−	6.92820i	−0.0899843	−	0.311715i
$495$	3.00000			0.134840
$496$	−2.50000	−	4.33013i	−0.112253	−	0.194428i
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	4.50000	−	7.79423i	0.201045	−	0.348220i
$502$	−15.0000			−0.669483
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$	3.00000	+	5.19615i	0.133498	+	0.231226i
$506$	9.00000			0.400099
$507$	11.5000	+	6.06218i	0.510733	+	0.269231i
$508$	14.0000			0.621150
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$	−3.00000	−	5.19615i	−0.132842	−	0.230089i
$511$	−14.0000	+	24.2487i	−0.619324	+	1.07270i
$512$	−1.00000			−0.0441942
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$	−10.5000	+	18.1865i	−0.463135	+	0.802174i
$515$	−14.0000			−0.616914
$516$	0.500000	−	0.866025i	0.0220113	−	0.0381246i
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$	−7.00000	−	12.1244i	−0.307562	−	0.532714i
$519$	12.0000			0.526742
$520$	1.00000	+	3.46410i	0.0438529	+	0.151911i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	1.50000	+	2.59808i	0.0656532	+	0.113715i
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	0.720358	−	0.693602i	$-0.243977\pi$
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	−0.960856	+	0.277047i	$0.910644\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$	2.00000			0.0872872
$526$	−7.50000	+	12.9904i	−0.327016	+	0.566408i
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$	−3.00000			−0.130558
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	4.50000	+	7.79423i	0.195283	+	0.338241i
$532$	4.00000			0.173422
$533$	15.0000	−	15.5885i	0.649722	−	0.675211i
$534$	18.0000			0.778936
$535$	−3.00000	−	5.19615i	−0.129701	−	0.224649i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	1.50000	−	2.59808i	0.0647298	−	0.112115i
$538$	−18.0000			−0.776035
$539$	−4.50000	+	7.79423i	−0.193829	+	0.335721i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	5.50000	−	9.52628i	0.236245	−	0.409189i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	−14.0000			−0.599694
$546$	−5.00000	+	5.19615i	−0.213980	+	0.222375i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	−1.50000	+	2.59808i	−0.0639602	+	0.110782i
$551$	6.00000			0.255609
$552$	1.50000	−	2.59808i	0.0638442	−	0.110581i
$553$	−5.00000	+	8.66025i	−0.212622	+	0.368271i
$554$	1.00000			0.0424859
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	0.922557	−	0.385860i	$-0.126095\pi$
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	−0.795443	+	0.606028i	$0.792762\pi$
$558$	−5.00000			−0.211667
$559$	3.50000	+	0.866025i	0.148034	+	0.0366290i
$560$	−2.00000			−0.0845154
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	−3.00000			−0.126323
$565$	7.50000	−	12.9904i	0.315527	−	0.546509i
$566$	−15.5000	+	26.8468i	−0.651514	+	1.12845i
$567$	2.00000			0.0839921
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	−3.00000	−	10.3923i	−0.125436	−	0.434524i
$573$	−12.0000			−0.501307
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$	−1.50000	−	2.59808i	−0.0625543	−	0.108347i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$	−3.00000			−0.124568
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	7.00000	+	12.1244i	0.290159	+	0.502571i
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	−14.0000			−0.579324
$585$	3.50000	+	0.866025i	0.144707	+	0.0358057i
$586$	30.0000			1.23929
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	−9.00000			−0.370524
$591$	−12.0000	+	20.7846i	−0.493614	+	0.854965i
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	27.0000			1.10876			0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000			1.10876			0.554379	+	0.832265i	$0.312956\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$	4.50000	+	7.79423i	0.184327	+	0.319264i
$597$	8.00000			0.327418
$598$	10.5000	+	2.59808i	0.429377	+	0.106243i
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$	−1.00000	+	1.73205i	−0.0407570	+	0.0705931i
$603$	8.00000			0.325785
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	−6.00000			−0.243733
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	−3.00000	−	5.19615i	−0.121566	−	0.210559i
$610$	2.00000			0.0809776
$611$	−3.00000	−	10.3923i	−0.121367	−	0.420428i
$612$	6.00000			0.242536
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$	3.00000	−	5.19615i	0.120972	−	0.209529i
$616$	6.00000			0.241747
$617$	−10.5000	+	18.1865i	−0.422714	+	0.732162i	−0.996204	−	0.0870504i	$-0.972256\pi$
$617$	−10.5000	+	18.1865i	−0.422714	+	0.732162i	0.573490	+	0.819213i	$0.305589\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	−46.0000			−1.84890			−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000			−1.84890			−0.924448	+	0.381308i	$0.875474\pi$
$620$	2.50000	−	4.33013i	0.100402	−	0.173902i
$621$	−1.50000	−	2.59808i	−0.0601929	−	0.104257i
$622$	−6.00000	−	10.3923i	−0.240578	−	0.416693i
$623$	−36.0000			−1.44231
$624$	−3.50000	−	0.866025i	−0.140112	−	0.0346688i
$625$	1.00000			0.0400000
$626$	4.00000	+	6.92820i	0.159872	+	0.276907i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$	−42.0000			−1.67465
$630$	−1.00000	+	1.73205i	−0.0398410	+	0.0690066i
$631$	8.00000	−	13.8564i	0.318475	−	0.551615i	−0.661695	−	0.749773i	$-0.730163\pi$
$631$	8.00000	−	13.8564i	0.318475	−	0.551615i	0.980170	+	0.198158i	$0.0634960\pi$
$632$	−5.00000			−0.198889
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	7.00000	+	12.1244i	0.277787	+	0.481140i
$636$	−6.00000			−0.237915
$637$	−7.50000	+	7.79423i	−0.297161	+	0.308819i
$638$	9.00000			0.356313
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$	6.00000			0.236801
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$	1.00000			0.0393750
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	0.527710	−	0.849425i	$-0.323051\pi$
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	−0.999478	+	0.0322975i	$0.989718\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	27.0000			1.05984
$650$	−2.50000	+	2.59808i	−0.0980581	+	0.101905i
$651$	10.0000			0.391931
$652$	6.50000	+	11.2583i	0.254560	+	0.440910i
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$	−9.00000			−0.351659
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	−7.00000	+	12.1244i	−0.273096	+	0.473016i
$658$	6.00000			0.233904
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$	−1.50000	−	2.59808i	−0.0583874	−	0.101130i
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−32.0000			−1.24372
$663$	6.00000	+	20.7846i	0.233021	+	0.807207i
$664$	6.00000			0.232845
$665$	2.00000	+	3.46410i	0.0775567	+	0.134332i
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$	−9.00000			−0.348220
$669$	5.00000	−	8.66025i	0.193311	−	0.334825i
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	−6.00000			−0.231627
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	2.00000	+	3.46410i	0.0770943	+	0.133531i	0.901995	−	0.431746i	$-0.142102\pi$
$673$	2.00000	+	3.46410i	0.0770943	+	0.133531i	−0.824901	+	0.565278i	$0.808769\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	1.00000			0.0384900
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	−36.0000			−1.38359			−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000			−1.38359			−0.691796	+	0.722093i	$0.743180\pi$
$678$	7.50000	+	12.9904i	0.288036	+	0.498893i
$679$	−14.0000	−	24.2487i	−0.537271	−	0.930580i
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$		0			0
$682$	−7.50000	+	12.9904i	−0.287190	+	0.497427i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	2.00000			0.0764719
$685$	4.50000	−	7.79423i	0.171936	−	0.297802i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−7.00000	−	12.1244i	−0.267067	−	0.462573i
$688$	−1.00000			−0.0381246
$689$	−6.00000	−	20.7846i	−0.228582	−	0.791831i
$690$	3.00000			0.114208
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.856804	+	0.515642i	$0.172447\pi$
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.0181572	+	0.999835i	$0.494220\pi$
$692$	−6.00000	−	10.3923i	−0.228086	−	0.395056i
$693$	3.00000	−	5.19615i	0.113961	−	0.197386i
$694$	30.0000			1.13878
$695$	7.00000	−	12.1244i	0.265525	−	0.459903i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	36.0000			1.36360
$698$	4.00000	−	6.92820i	0.151402	−	0.262236i
$699$	−10.5000	−	18.1865i	−0.397146	−	0.687878i
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	−21.0000			−0.793159			−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000			−0.793159			−0.396580	+	0.918000i	$0.629803\pi$
$702$	−2.50000	+	2.59808i	−0.0943564	+	0.0980581i
$703$	−14.0000			−0.528020
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	−1.50000	−	2.59808i	−0.0564933	−	0.0978492i
$706$	15.0000	−	25.9808i	0.564532	−	0.977799i
$707$	12.0000			0.451306
$708$	4.50000	−	7.79423i	0.169120	−	0.292925i
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	0.391794	+	0.920053i	$0.371855\pi$
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	−0.992686	+	0.120723i	$0.961479\pi$
$710$	−12.0000			−0.450352
$711$	−2.50000	+	4.33013i	−0.0937573	+	0.162392i
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	−7.50000	−	12.9904i	−0.280877	−	0.486494i
$714$	−12.0000			−0.449089
$715$	7.50000	−	7.79423i	0.280484	−	0.291488i
$716$	−3.00000			−0.112115
$717$	−12.0000	−	20.7846i	−0.448148	−	0.776215i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$	−1.00000			−0.0372678
$721$	−14.0000	+	24.2487i	−0.521387	+	0.903069i
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	17.0000			0.632237
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−4.00000			−0.148352			−0.0741759	−	0.997245i	$-0.523633\pi$
$727$	−4.00000			−0.148352			−0.0741759	+	0.997245i	$0.523633\pi$
$728$	7.00000	+	1.73205i	0.259437	+	0.0641941i
$729$	1.00000			0.0370370
$730$	−7.00000	−	12.1244i	−0.259082	−	0.448743i
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	10.0000	−	17.3205i	0.369107	−	0.639312i
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$	−3.00000			−0.110581
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	7.00000			0.257325
$741$	2.00000	+	6.92820i	0.0734718	+	0.254514i
$742$	12.0000			0.440534
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	0.936687	−	0.350168i	$-0.113876\pi$
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	−0.771598	+	0.636111i	$0.780542\pi$
$744$	2.50000	+	4.33013i	0.0916544	+	0.158750i
$745$	−4.50000	+	7.79423i	−0.164867	+	0.285558i
$746$	25.0000			0.915315
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	9.00000	−	15.5885i	0.329073	−	0.569970i
$749$	−12.0000			−0.438470
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−20.5000	−	35.5070i	−0.748056	−	1.29567i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−20.5000	−	35.5070i	−0.748056	−	1.29567i	0.200698	−	0.979653i	$-0.435679\pi$
$752$	1.50000	+	2.59808i	0.0546994	+	0.0947421i
$753$	15.0000			0.546630
$754$	10.5000	+	2.59808i	0.382387	+	0.0946164i
$755$	−8.00000			−0.291150
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$	19.0000	−	32.9090i	0.690111	−	1.19531i
$759$	−9.00000			−0.326679
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	−14.0000			−0.507166
$763$	−14.0000	+	24.2487i	−0.506834	+	0.877862i
$764$	6.00000	+	10.3923i	0.217072	+	0.375980i
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$	21.0000			0.758761
$767$	31.5000	+	7.79423i	1.13740	+	0.281433i
$768$	1.00000			0.0360844
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	0.959097	−	0.283078i	$-0.0913554\pi$
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	−0.724701	+	0.689063i	$0.758022\pi$
$770$	3.00000	+	5.19615i	0.108112	+	0.187256i
$771$	10.5000	−	18.1865i	0.378148	−	0.654972i
$772$	−4.00000			−0.143963
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	−0.00558380	−	0.999984i	$-0.501777\pi$
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	0.868804	−	0.495156i	$-0.164889\pi$
$774$	−0.500000	+	0.866025i	−0.0179721	+	0.0311286i
$775$	5.00000			0.179605
$776$	7.00000	−	12.1244i	0.251285	−	0.435239i
$777$	7.00000	+	12.1244i	0.251124	+	0.434959i
$778$	1.50000	+	2.59808i	0.0537776	+	0.0931455i
$779$	12.0000			0.429945
$780$	−1.00000	−	3.46410i	−0.0358057	−	0.124035i
$781$	36.0000			1.28818
$782$	9.00000	+	15.5885i	0.321839	+	0.557442i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	13.0000			0.463990
$786$	4.50000	−	7.79423i	0.160510	−	0.278011i
$787$	−17.5000	+	30.3109i	−0.623808	+	1.08047i	0.364963	+	0.931022i	$0.381082\pi$
$787$	−17.5000	+	30.3109i	−0.623808	+	1.08047i	−0.988770	+	0.149444i	$0.952252\pi$
$788$	24.0000			0.854965
$789$	7.50000	−	12.9904i	0.267007	−	0.462470i
$790$	−2.50000	−	4.33013i	−0.0889460	−	0.154059i
$791$	−15.0000	−	25.9808i	−0.533339	−	0.923770i
$792$	3.00000			0.106600
$793$	−7.00000	−	1.73205i	−0.248577	−	0.0615069i
$794$	31.0000			1.10015
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	12.0000	−	20.7846i	0.425062	−	0.736229i	−0.571364	−	0.820696i	$-0.693586\pi$
$797$	12.0000	−	20.7846i	0.425062	−	0.736229i	0.996426	+	0.0844678i	$0.0269190\pi$
$798$	−4.00000			−0.141598
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−18.0000			−0.635999
$802$	−6.00000	+	10.3923i	−0.211867	+	0.366965i
$803$	21.0000	+	36.3731i	0.741074	+	1.28358i
$804$	−4.00000	−	6.92820i	−0.141069	−	0.244339i
$805$	−6.00000			−0.211472
$806$	−12.5000	+	12.9904i	−0.440294	+	0.457567i
$807$	18.0000			0.633630
$808$	3.00000	+	5.19615i	0.105540	+	0.182800i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	−3.00000	+	5.19615i	−0.105279	+	0.182349i
$813$	−5.50000	+	9.52628i	−0.192893	+	0.334101i
$814$	−21.0000			−0.736050
$815$	−6.50000	+	11.2583i	−0.227685	+	0.394362i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	1.00000	+	1.73205i	0.0349856	+	0.0605968i
$818$	10.0000			0.349642
$819$	5.00000	−	5.19615i	0.174714	−	0.181568i
$820$	−6.00000			−0.209529
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	0.528302	−	0.849056i	$-0.322829\pi$
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	−0.999456	+	0.0329950i	$0.989495\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−14.0000			−0.487713
$825$	1.50000	−	2.59808i	0.0522233	−	0.0904534i
$826$	−9.00000	+	15.5885i	−0.313150	+	0.542392i
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$	−1.50000	+	2.59808i	−0.0521286	+	0.0902894i
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	0.546971	−	0.837151i	$-0.315781\pi$
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	−0.998480	+	0.0551154i	$0.982447\pi$
$830$	3.00000	+	5.19615i	0.104132	+	0.180361i
$831$	−1.00000			−0.0346896
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$	−18.0000			−0.623663
$834$	7.00000	+	12.1244i	0.242390	+	0.419832i
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	5.00000			0.172825
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	0.233973	+	0.972243i	$0.424827\pi$
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	−0.958974	+	0.283495i	$0.908506\pi$
$840$	2.00000			0.0690066
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−8.00000	−	13.8564i	−0.275698	−	0.477523i
$843$	−9.00000	−	15.5885i	−0.309976	−	0.536895i
$844$	20.0000			0.688428
$845$	11.0000	−	6.92820i	0.378412	−	0.238337i
$846$	3.00000			0.103142
$847$	2.00000	+	3.46410i	0.0687208	+	0.119028i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	15.5000	−	26.8468i	0.531959	−	0.921379i
$850$	−6.00000			−0.205798
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	−19.0000			−0.650548			−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000			−0.650548			−0.325274	+	0.945620i	$0.605456\pi$
$854$	2.00000	−	3.46410i	0.0684386	−	0.118539i
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$	3.00000			0.102478			0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000			0.102478			0.0512390	+	0.998686i	$0.483683\pi$
$858$	3.00000	+	10.3923i	0.102418	+	0.354787i
$859$	−46.0000			−1.56950			−0.784750	−	0.619813i	$-0.787209\pi$
$859$	−46.0000			−1.56950			−0.784750	+	0.619813i	$0.787209\pi$
$860$	−0.500000	−	0.866025i	−0.0170499	−	0.0295312i
$861$	−6.00000	−	10.3923i	−0.204479	−	0.354169i
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	−45.0000			−1.53182			−0.765909	−	0.642949i	$-0.777711\pi$
$863$	−45.0000			−1.53182			−0.765909	+	0.642949i	$0.777711\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$	40.0000			1.35926
$867$	−9.50000	+	16.4545i	−0.322637	+	0.558824i
$868$	−5.00000	−	8.66025i	−0.169711	−	0.293948i
$869$	7.50000	+	12.9904i	0.254420	+	0.440668i
$870$	3.00000			0.101710
$871$	20.0000	−	20.7846i	0.677674	−	0.704260i
$872$	−14.0000			−0.474100
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$	3.00000	+	5.19615i	0.101477	+	0.175762i
$875$	1.00000	−	1.73205i	0.0338062	−	0.0585540i
$876$	14.0000			0.473016
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	−2.00000	+	3.46410i	−0.0674967	+	0.116908i
$879$	−30.0000			−1.01187
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	15.0000	−	15.5885i	0.504505	−	0.524297i
$885$	9.00000			0.302532
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	28.5000	+	49.3634i	0.956936	+	1.65746i	0.729873	+	0.683582i	$0.239579\pi$
$887$	28.5000	+	49.3634i	0.956936	+	1.65746i	0.227063	+	0.973880i	$0.427088\pi$
$888$	−3.50000	+	6.06218i	−0.117452	+	0.203433i
$889$	28.0000			0.939090
$890$	9.00000	−	15.5885i	0.301681	−	0.522526i
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−10.0000			−0.334825
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$	−4.50000	−	7.79423i	−0.150503	−	0.260678i
$895$	−1.50000	−	2.59808i	−0.0501395	−	0.0868441i
$896$	−2.00000			−0.0668153
$897$	−10.5000	−	2.59808i	−0.350585	−	0.0867472i
$898$	−36.0000			−1.20134
$899$	−7.50000	−	12.9904i	−0.250139	−	0.433253i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$	18.0000			0.599334
$903$	1.00000	−	1.73205i	0.0332779	−	0.0576390i
$904$	7.50000	−	12.9904i	0.249446	−	0.432054i
$905$	16.0000			0.531858
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$	2.00000	+	6.92820i	0.0662994	+	0.229668i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	−9.00000	−	15.5885i	−0.297857	−	0.515903i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$	−2.00000			−0.0661180
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	−9.00000	+	15.5885i	−0.297206	+	0.514776i
$918$	−6.00000			−0.198030
$919$	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	$0.0816592\pi$
$920$	−1.50000	−	2.59808i	−0.0494535	−	0.0856560i
$921$	−4.00000	−	6.92820i	−0.131804	−	0.228292i
$922$	−15.0000			−0.493999
$923$	42.0000	+	10.3923i	1.38245	+	0.342067i
$924$	−6.00000			−0.197386
$925$	3.50000	+	6.06218i	0.115079	+	0.199323i
$926$	−17.0000	−	29.4449i	−0.558655	−	0.967618i
$927$	−7.00000	+	12.1244i	−0.229910	+	0.398216i
$928$	−3.00000			−0.0984798
$929$	6.00000	−	10.3923i	0.196854	−	0.340960i	−0.750653	−	0.660697i	$-0.770261\pi$
$929$	6.00000	−	10.3923i	0.196854	−	0.340960i	0.947507	+	0.319736i	$0.103594\pi$
$930$	−2.50000	+	4.33013i	−0.0819782	+	0.141990i
$931$	−6.00000			−0.196642
$932$	−10.5000	+	18.1865i	−0.343939	+	0.595720i
$933$	6.00000	+	10.3923i	0.196431	+	0.340229i
$934$	9.00000	+	15.5885i	0.294489	+	0.510070i
$935$	18.0000			0.588663
$936$	3.50000	+	0.866025i	0.114401	+	0.0283069i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$	8.00000	+	13.8564i	0.261209	+	0.452428i
$939$	−4.00000	−	6.92820i	−0.130535	−	0.226093i
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	−6.50000	+	11.2583i	−0.211781	+	0.366816i
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$	−9.00000			−0.292925
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$	1.50000	+	2.59808i	0.0487692	+	0.0844707i
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$	5.00000			0.162392
$949$	14.0000	+	48.4974i	0.454459	+	1.57429i
$950$	−2.00000			−0.0648886
$951$	−6.00000	−	10.3923i	−0.194563	−	0.336994i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	−4.50000	+	7.79423i	−0.145769	+	0.252480i	−0.929660	−	0.368419i	$-0.879899\pi$
$953$	−4.50000	+	7.79423i	−0.145769	+	0.252480i	0.783890	+	0.620899i	$0.213232\pi$
$954$	6.00000			0.194257
$955$	−6.00000	+	10.3923i	−0.194155	+	0.336287i
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$	−9.00000			−0.290929
$958$		0			0
$959$	−9.00000	−	15.5885i	−0.290625	−	0.503378i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−6.00000			−0.193548
$962$	−24.5000	−	6.06218i	−0.789912	−	0.195452i
$963$	−6.00000			−0.193347
$964$	−8.50000	−	14.7224i	−0.273767	−	0.474178i
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$	14.0000			0.449513
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	−0.167258	−	0.985913i	$-0.553491\pi$
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	0.937455	−	0.348107i	$-0.113175\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−14.0000	−	24.2487i	−0.448819	−	0.777378i
$974$	−2.00000			−0.0640841
$975$	2.50000	−	2.59808i	0.0800641	−	0.0832050i
$976$	2.00000			0.0640184
$977$	28.5000	+	49.3634i	0.911796	+	1.57928i	0.811526	+	0.584316i	$0.198637\pi$
$977$	28.5000	+	49.3634i	0.911796	+	1.57928i	0.100270	+	0.994960i	$0.468029\pi$
$978$	−6.50000	−	11.2583i	−0.207847	−	0.360002i
$979$	−27.0000	+	46.7654i	−0.862924	+	1.49463i
$980$	3.00000			0.0958315
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$		0			0
$983$	9.00000			0.287055			0.143528	−	0.989646i	$-0.454155\pi$
$983$	9.00000			0.287055			0.143528	+	0.989646i	$0.454155\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	12.0000	+	20.7846i	0.382352	+	0.662253i
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$	−6.00000			−0.190982
$988$	5.00000	−	5.19615i	0.159071	−	0.165312i
$989$	−3.00000			−0.0953945
$990$	1.50000	+	2.59808i	0.0476731	+	0.0825723i
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	0.993364	−	0.115015i	$-0.0366917\pi$
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	−0.596288	+	0.802771i	$0.703358\pi$
$992$	2.50000	−	4.33013i	0.0793751	−	0.137482i
$993$	32.0000			1.01549
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$	4.00000	−	6.92820i	0.126809	−	0.219639i
$996$	−6.00000			−0.190117
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	−0.637587	−	0.770378i	$-0.720067\pi$
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	0.985961	+	0.166978i	$0.0534008\pi$
$998$	16.0000	+	27.7128i	0.506471	+	0.877234i
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.i.c.211.1	yes	2
3.2	odd	2		1170.2.i.d.991.1		2
5.2	odd	4		1950.2.z.k.1849.1		4
5.3	odd	4		1950.2.z.k.1849.2		4
5.4	even	2		1950.2.i.n.601.1		2
13.2	odd	12		5070.2.b.j.1351.2		2
13.3	even	3		5070.2.a.j.1.1		1
13.9	even	3	inner	390.2.i.c.61.1	✓	2
13.10	even	6		5070.2.a.v.1.1		1
13.11	odd	12		5070.2.b.j.1351.1		2
39.35	odd	6		1170.2.i.d.451.1		2
65.9	even	6		1950.2.i.n.451.1		2
65.22	odd	12		1950.2.z.k.1699.2		4
65.48	odd	12		1950.2.z.k.1699.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.c.61.1	✓	2	13.9	even	3	inner
390.2.i.c.211.1	yes	2	1.1	even	1	trivial
1170.2.i.d.451.1		2	39.35	odd	6
1170.2.i.d.991.1		2	3.2	odd	2
1950.2.i.n.451.1		2	65.9	even	6
1950.2.i.n.601.1		2	5.4	even	2
1950.2.z.k.1699.1		4	65.48	odd	12
1950.2.z.k.1699.2		4	65.22	odd	12
1950.2.z.k.1849.1		4	5.2	odd	4
1950.2.z.k.1849.2		4	5.3	odd	4
5070.2.a.j.1.1		1	13.3	even	3
5070.2.a.v.1.1		1	13.10	even	6
5070.2.b.j.1351.1		2	13.11	odd	12
5070.2.b.j.1351.2		2	13.2	odd	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} -1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-0.500000 + 0.866025i) q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{42} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(1.50000 - 2.59808i) q^{46} -3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -6.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(1.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(2.50000 + 4.33013i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{69} +2.00000 q^{70} +(6.00000 - 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +(3.50000 + 0.866025i) q^{78} +5.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{85} +1.00000 q^{86} +(-1.50000 + 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-7.00000 - 1.73205i) q^{91} +3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{95} -1.00000 q^{96} +(-7.00000 + 12.1244i) q^{97} +(-1.50000 + 2.59808i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} - q^{16} - 6 q^{17} - 2 q^{18} - 2 q^{19} + q^{20} + 4 q^{21} - 3 q^{22} - 3 q^{23} + q^{24} + 2 q^{25} - 5 q^{26} + 2 q^{27} - 2 q^{28} - 3 q^{29} - q^{30} + 10 q^{31} + q^{32} + 3 q^{33} - 12 q^{34} + 2 q^{35} - q^{36} + 7 q^{37} - 4 q^{38} + 5 q^{39} + 2 q^{40} - 6 q^{41} + 2 q^{42} + q^{43} - 6 q^{44} + q^{45} + 3 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} + q^{50} + 12 q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 3 q^{55} + 2 q^{56} + 4 q^{57} + 3 q^{58} + 9 q^{59} - 2 q^{60} - 2 q^{61} + 5 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} - 3 q^{69} + 4 q^{70} + 12 q^{71} + q^{72} + 28 q^{73} - 7 q^{74} - q^{75} - 2 q^{76} - 12 q^{77} + 7 q^{78} + 10 q^{79} + q^{80} - q^{81} + 6 q^{82} - 12 q^{83} - 2 q^{84} + 6 q^{85} + 2 q^{86} - 3 q^{87} - 3 q^{88} + 18 q^{89} + 2 q^{90} - 14 q^{91} + 6 q^{92} - 5 q^{93} - 3 q^{94} + 2 q^{95} - 2 q^{96} - 14 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 - q^16 - 6 * q^17 - 2 * q^18 - 2 * q^19 + q^20 + 4 * q^21 - 3 * q^22 - 3 * q^23 + q^24 + 2 * q^25 - 5 * q^26 + 2 * q^27 - 2 * q^28 - 3 * q^29 - q^30 + 10 * q^31 + q^32 + 3 * q^33 - 12 * q^34 + 2 * q^35 - q^36 + 7 * q^37 - 4 * q^38 + 5 * q^39 + 2 * q^40 - 6 * q^41 + 2 * q^42 + q^43 - 6 * q^44 + q^45 + 3 * q^46 - 6 * q^47 - q^48 + 3 * q^49 + q^50 + 12 * q^51 - 7 * q^52 - 12 * q^53 + q^54 - 3 * q^55 + 2 * q^56 + 4 * q^57 + 3 * q^58 + 9 * q^59 - 2 * q^60 - 2 * q^61 + 5 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 3 * q^69 + 4 * q^70 + 12 * q^71 + q^72 + 28 * q^73 - 7 * q^74 - q^75 - 2 * q^76 - 12 * q^77 + 7 * q^78 + 10 * q^79 + q^80 - q^81 + 6 * q^82 - 12 * q^83 - 2 * q^84 + 6 * q^85 + 2 * q^86 - 3 * q^87 - 3 * q^88 + 18 * q^89 + 2 * q^90 - 14 * q^91 + 6 * q^92 - 5 * q^93 - 3 * q^94 + 2 * q^95 - 2 * q^96 - 14 * q^97 - 3 * q^98 - 6 * q^99

Introduction

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