LMFDB - Embedded newform 1110.2.i.f.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
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			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.f.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -5.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.50000 - 4.33013i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{21} +(-2.50000 + 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} -1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 - 4.33013i) q^{33} +(-2.50000 - 4.33013i) q^{34} +(1.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(0.500000 - 6.06218i) q^{37} -2.00000 q^{38} +(2.50000 - 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-1.00000 - 1.73205i) q^{42} +4.00000 q^{43} +(2.50000 + 4.33013i) q^{44} -1.00000 q^{45} +9.00000 q^{47} -1.00000 q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +5.00000 q^{51} +(-2.50000 + 4.33013i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.50000 - 4.33013i) q^{55} +(1.00000 + 1.73205i) q^{56} +(1.00000 - 1.73205i) q^{57} +(-4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +1.00000 q^{60} +(2.00000 - 3.46410i) q^{62} +2.00000 q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} -5.00000 q^{66} +(4.50000 + 7.79423i) q^{67} -5.00000 q^{68} +(-1.00000 - 1.73205i) q^{70} +(6.00000 + 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} -12.0000 q^{73} +(-5.00000 - 3.46410i) q^{74} -1.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(5.00000 + 8.66025i) q^{77} +(-2.50000 - 4.33013i) q^{78} +(-8.00000 - 13.8564i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{82} +(1.00000 - 1.73205i) q^{83} -2.00000 q^{84} +5.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.50000 - 7.79423i) q^{87} +5.00000 q^{88} +(7.00000 - 12.1244i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-5.00000 + 8.66025i) q^{91} +(2.00000 + 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} -18.0000 q^{97} +(-1.50000 - 2.59808i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} - 10 q^{11} + q^{12} - 5 q^{13} - 4 q^{14} - q^{15} - q^{16} + 5 q^{17} + q^{18} - 2 q^{19} + q^{20} + 2 q^{21} - 5 q^{22} - q^{24} - q^{25} - 10 q^{26} - 2 q^{27} - 2 q^{28} - 18 q^{29} + q^{30} + 8 q^{31} + q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 2 q^{36} + q^{37} - 4 q^{38} + 5 q^{39} - q^{40} - 6 q^{41} - 2 q^{42} + 8 q^{43} + 5 q^{44} - 2 q^{45} + 18 q^{47} - 2 q^{48} + 3 q^{49} + q^{50} + 10 q^{51} - 5 q^{52} - 6 q^{53} - q^{54} - 5 q^{55} + 2 q^{56} + 2 q^{57} - 9 q^{58} - 3 q^{59} + 2 q^{60} + 4 q^{62} + 4 q^{63} + 2 q^{64} + 5 q^{65} - 10 q^{66} + 9 q^{67} - 10 q^{68} - 2 q^{70} + 12 q^{71} + q^{72} - 24 q^{73} - 10 q^{74} - 2 q^{75} - 2 q^{76} + 10 q^{77} - 5 q^{78} - 16 q^{79} - 2 q^{80} - q^{81} - 12 q^{82} + 2 q^{83} - 4 q^{84} + 10 q^{85} + 4 q^{86} - 9 q^{87} + 10 q^{88} + 14 q^{89} - q^{90} - 10 q^{91} + 4 q^{93} + 9 q^{94} + 2 q^{95} - q^{96} - 36 q^{97} - 3 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9 + 2 * q^10 - 10 * q^11 + q^12 - 5 * q^13 - 4 * q^14 - q^15 - q^16 + 5 * q^17 + q^18 - 2 * q^19 + q^20 + 2 * q^21 - 5 * q^22 - q^24 - q^25 - 10 * q^26 - 2 * q^27 - 2 * q^28 - 18 * q^29 + q^30 + 8 * q^31 + q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 2 * q^36 + q^37 - 4 * q^38 + 5 * q^39 - q^40 - 6 * q^41 - 2 * q^42 + 8 * q^43 + 5 * q^44 - 2 * q^45 + 18 * q^47 - 2 * q^48 + 3 * q^49 + q^50 + 10 * q^51 - 5 * q^52 - 6 * q^53 - q^54 - 5 * q^55 + 2 * q^56 + 2 * q^57 - 9 * q^58 - 3 * q^59 + 2 * q^60 + 4 * q^62 + 4 * q^63 + 2 * q^64 + 5 * q^65 - 10 * q^66 + 9 * q^67 - 10 * q^68 - 2 * q^70 + 12 * q^71 + q^72 - 24 * q^73 - 10 * q^74 - 2 * q^75 - 2 * q^76 + 10 * q^77 - 5 * q^78 - 16 * q^79 - 2 * q^80 - q^81 - 12 * q^82 + 2 * q^83 - 4 * q^84 + 10 * q^85 + 4 * q^86 - 9 * q^87 + 10 * q^88 + 14 * q^89 - q^90 - 10 * q^91 + 4 * q^93 + 9 * q^94 + 2 * q^95 - q^96 - 36 * q^97 - 3 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

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
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−2.00000			−0.534522
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−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
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.50000	−	4.33013i	−0.435194	−	0.753778i
$34$	−2.50000	−	4.33013i	−0.428746	−	0.742611i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	1.00000			0.166667
$37$	0.500000	−	6.06218i	0.0821995	−	0.996616i
$37$	0.500000	−	6.06218i	0.0821995	−	0.996616i
$38$	−2.00000			−0.324443
$39$	2.50000	−	4.33013i	0.400320	−	0.693375i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−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
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$	−1.00000			−0.149071
$46$		0			0
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	−1.00000			−0.144338
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	5.00000			0.700140
$52$	−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
$55$	−2.50000	−	4.33013i	−0.337100	−	0.583874i
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	1.00000	−	1.73205i	0.132453	−	0.229416i
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$	1.00000			0.129099
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$	2.00000			0.251976
$64$	1.00000			0.125000
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$	−5.00000			−0.615457
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	0.998290	+	0.0584478i	$0.0186151\pi$
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	−0.448528	+	0.893769i	$0.648052\pi$
$68$	−5.00000			−0.606339
$69$		0			0
$70$	−1.00000	−	1.73205i	−0.119523	−	0.207020i
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−12.0000			−1.40449			−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000			−1.40449			−0.702247	+	0.711934i	$0.747820\pi$
$74$	−5.00000	−	3.46410i	−0.581238	−	0.402694i
$75$	−1.00000			−0.115470
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	5.00000	+	8.66025i	0.569803	+	0.986928i
$78$	−2.50000	−	4.33013i	−0.283069	−	0.490290i
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.827401	−	0.561611i	$-0.810182\pi$
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.0726692	−	0.997356i	$-0.523152\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000			−0.662589
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	−0.805910	−	0.592037i	$-0.798324\pi$
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	0.915675	+	0.401920i	$0.131657\pi$
$84$	−2.00000			−0.218218
$85$	5.00000			0.542326
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	−4.50000	−	7.79423i	−0.482451	−	0.835629i
$88$	5.00000			0.533002
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−5.00000	+	8.66025i	−0.524142	+	0.907841i
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−18.0000			−1.82762			−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000			−1.82762			−0.913812	+	0.406138i	$0.866875\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	2.50000	−	4.33013i	0.251259	−	0.435194i
$100$	1.00000			0.100000
$101$	5.00000			0.497519			0.248759	−	0.968565i	$-0.419977\pi$
$101$	5.00000			0.497519			0.248759	+	0.968565i	$0.419977\pi$
$102$	2.50000	−	4.33013i	0.247537	−	0.428746i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.50000	+	4.33013i	0.245145	+	0.424604i
$105$	2.00000			0.195180
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$	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	$0.932756\pi$
$110$	−5.00000			−0.476731
$111$	5.50000	−	2.59808i	0.522037	−	0.246598i
$112$	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
$115$		0			0
$116$	4.50000	+	7.79423i	0.417815	+	0.723676i
$117$	5.00000			0.462250
$118$	1.50000	+	2.59808i	0.138086	+	0.239172i
$119$	−10.0000			−0.916698
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	14.0000			1.27273
$122$		0			0
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−1.00000			−0.0894427
$126$	1.00000	−	1.73205i	0.0890871	−	0.154303i
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	−5.50000	+	9.52628i	−0.480537	+	0.832315i	−0.999751	−	0.0223297i	$-0.992892\pi$
$131$	−5.50000	+	9.52628i	−0.480537	+	0.832315i	0.519213	+	0.854645i	$0.326225\pi$
$132$	−2.50000	+	4.33013i	−0.217597	+	0.376889i
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$	9.00000			0.777482
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	−2.00000			−0.169031
$141$	4.50000	+	7.79423i	0.378968	+	0.656392i
$142$	12.0000			1.00702
$143$	12.5000	+	21.6506i	1.04530	+	1.81052i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	−6.00000	+	10.3923i	−0.496564	+	0.860073i
$147$	3.00000			0.247436
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	2.50000	+	4.33013i	0.202113	+	0.350070i
$154$	10.0000			0.805823
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$	−5.00000			−0.400320
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$	−16.0000			−1.27289
$159$	−6.00000			−0.475831
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	4.50000	−	7.79423i	0.352467	−	0.610491i	−0.634214	−	0.773158i	$-0.718676\pi$
$163$	4.50000	−	7.79423i	0.352467	−	0.610491i	0.986681	+	0.162667i	$0.0520095\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	8.50000	+	14.7224i	0.657750	+	1.13926i	0.981197	+	0.193010i	$0.0618249\pi$
$167$	8.50000	+	14.7224i	0.657750	+	1.13926i	−0.323447	+	0.946246i	$0.604842\pi$
$168$	−1.00000	+	1.73205i	−0.0771517	+	0.133631i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	2.50000	−	4.33013i	0.191741	−	0.332106i
$171$	2.00000			0.152944
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$	−9.00000			−0.682288
$175$	2.00000			0.151186
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$	−3.00000			−0.225494
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−7.00000	−	12.1244i	−0.520306	−	0.901196i	−0.999721	−	0.0236082i	$-0.992485\pi$
$181$	−7.00000	−	12.1244i	−0.520306	−	0.901196i	0.479415	−	0.877588i	$-0.340849\pi$
$182$	5.00000	+	8.66025i	0.370625	+	0.641941i
$183$		0			0
$184$		0			0
$185$	5.50000	−	2.59808i	0.404368	−	0.191014i
$186$	4.00000			0.293294
$187$	−12.5000	+	21.6506i	−0.914091	+	1.58325i
$188$	−4.50000	−	7.79423i	−0.328196	−	0.568453i
$189$	1.00000	+	1.73205i	0.0727393	+	0.125988i
$190$	−1.00000	−	1.73205i	−0.0725476	−	0.125656i
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	26.0000			1.87152			0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000			1.87152			0.935760	+	0.352636i	$0.114715\pi$
$194$	−9.00000	+	15.5885i	−0.646162	+	1.11919i
$195$	5.00000			0.358057
$196$	−3.00000			−0.214286
$197$	5.00000	−	8.66025i	0.356235	−	0.617018i	−0.631093	−	0.775707i	$-0.717394\pi$
$197$	5.00000	−	8.66025i	0.356235	−	0.617018i	0.987329	+	0.158689i	$0.0507268\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	7.00000			0.496217			0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000			0.496217			0.248108	+	0.968732i	$0.420191\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−4.50000	+	7.79423i	−0.317406	+	0.549762i
$202$	2.50000	−	4.33013i	0.175899	−	0.304667i
$203$	9.00000	+	15.5885i	0.631676	+	1.09410i
$204$	−2.50000	−	4.33013i	−0.175035	−	0.303170i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$		0			0
$208$	5.00000			0.346688
$209$	5.00000	+	8.66025i	0.345857	+	0.599042i
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	6.00000			0.412082
$213$	−6.00000	+	10.3923i	−0.411113	+	0.712069i
$214$	2.00000			0.136717
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	1.00000			0.0680414
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$	7.00000	+	12.1244i	0.474100	+	0.821165i
$219$	−6.00000	−	10.3923i	−0.405442	−	0.702247i
$220$	−2.50000	+	4.33013i	−0.168550	+	0.291937i
$221$	−25.0000			−1.68168
$222$	0.500000	−	6.06218i	0.0335578	−	0.406867i
$223$	12.0000			0.803579			0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	−9.00000	−	15.5885i	−0.597351	−	1.03464i	−0.993210	−	0.116331i	$-0.962887\pi$
$227$	−9.00000	−	15.5885i	−0.597351	−	1.03464i	0.395860	−	0.918311i	$-0.370447\pi$
$228$	−2.00000			−0.132453
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$	−5.00000	+	8.66025i	−0.328976	+	0.569803i
$232$	9.00000			0.590879
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	2.50000	−	4.33013i	0.163430	−	0.283069i
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	3.00000			0.195283
$237$	8.00000	−	13.8564i	0.519656	−	0.900070i
$238$	−5.00000	+	8.66025i	−0.324102	+	0.561361i
$239$	10.0000	−	17.3205i	0.646846	−	1.12037i	−0.337026	−	0.941495i	$-0.609421\pi$
$239$	10.0000	−	17.3205i	0.646846	−	1.12037i	0.983872	−	0.178875i	$-0.0572458\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	0.110963	−	0.993825i	$-0.464606\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	3.00000			0.191663
$246$	−3.00000	−	5.19615i	−0.191273	−	0.331295i
$247$	−5.00000	+	8.66025i	−0.318142	+	0.551039i
$248$	−4.00000			−0.254000
$249$	2.00000			0.126745
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−7.00000			−0.441836			−0.220918	−	0.975292i	$-0.570905\pi$
$251$	−7.00000			−0.441836			−0.220918	+	0.975292i	$0.570905\pi$
$252$	−1.00000	−	1.73205i	−0.0629941	−	0.109109i
$253$		0			0
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$	2.50000	+	4.33013i	0.156556	+	0.271163i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	−0.588916	−	0.808194i	$-0.700445\pi$
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	0.994375	+	0.105919i	$0.0337784\pi$
$258$	4.00000			0.249029
$259$	−11.0000	+	5.19615i	−0.683507	+	0.322873i
$260$	−5.00000			−0.310087
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$	5.50000	+	9.52628i	0.339791	+	0.588536i
$263$	14.0000	+	24.2487i	0.863277	+	1.49524i	0.868748	+	0.495255i	$0.164925\pi$
$263$	14.0000	+	24.2487i	0.863277	+	1.49524i	−0.00547092	+	0.999985i	$0.501741\pi$
$264$	2.50000	+	4.33013i	0.153864	+	0.266501i
$265$	−6.00000			−0.368577
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$	14.0000			0.856786
$268$	4.50000	−	7.79423i	0.274881	−	0.476108i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$	−1.00000			−0.0608581
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$	2.50000	+	4.33013i	0.151585	+	0.262553i
$273$	−10.0000			−0.605228
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	−8.00000	−	13.8564i	−0.479808	−	0.831052i
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	−5.00000	+	8.66025i	−0.298275	+	0.516627i	−0.975741	−	0.218926i	$-0.929745\pi$
$281$	−5.00000	+	8.66025i	−0.298275	+	0.516627i	0.677466	+	0.735554i	$0.263078\pi$
$282$	9.00000			0.535942
$283$	7.50000	+	12.9904i	0.445829	+	0.772198i	0.998110	−	0.0614601i	$-0.0195757\pi$
$283$	7.50000	+	12.9904i	0.445829	+	0.772198i	−0.552281	+	0.833658i	$0.686242\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$	2.00000			0.118470
$286$	25.0000			1.47828
$287$	−6.00000	+	10.3923i	−0.354169	+	0.613438i
$288$	−1.00000			−0.0589256
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−9.00000			−0.528498
$291$	−9.00000	−	15.5885i	−0.527589	−	0.913812i
$292$	6.00000	+	10.3923i	0.351123	+	0.608164i
$293$	−5.00000	−	8.66025i	−0.292103	−	0.505937i	0.682204	−	0.731162i	$-0.261022\pi$
$293$	−5.00000	−	8.66025i	−0.292103	−	0.505937i	−0.974307	+	0.225225i	$0.927688\pi$
$294$	1.50000	−	2.59808i	0.0874818	−	0.151523i
$295$	−3.00000			−0.174667
$296$	−0.500000	+	6.06218i	−0.0290619	+	0.352357i
$297$	5.00000			0.290129
$298$	7.50000	−	12.9904i	0.434463	−	0.752513i
$299$		0			0
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$	−8.00000			−0.460348
$303$	2.50000	+	4.33013i	0.143621	+	0.248759i
$304$	2.00000			0.114708
$305$		0			0
$306$	5.00000			0.285831
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	5.00000	−	8.66025i	0.284901	−	0.493464i
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$	4.00000			0.227185
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	−2.50000	+	4.33013i	−0.141535	+	0.245145i
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$	−6.50000	−	11.2583i	−0.366816	−	0.635344i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	−8.00000	+	13.8564i	−0.450035	+	0.779484i
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	45.0000			2.51952
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−1.00000	+	1.73205i	−0.0558146	+	0.0966736i
$322$		0			0
$323$	−10.0000			−0.556415
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	5.00000			0.277350
$326$	−4.50000	−	7.79423i	−0.249232	−	0.431682i
$327$	−14.0000			−0.774202
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	−9.00000	−	15.5885i	−0.496186	−	0.859419i
$330$	−2.50000	−	4.33013i	−0.137620	−	0.238366i
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	−2.00000			−0.109764
$333$	5.00000	+	3.46410i	0.273998	+	0.189832i
$334$	17.0000			0.930199
$335$	−4.50000	+	7.79423i	−0.245861	+	0.425844i
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	0.609936	−	0.792451i	$-0.291195\pi$
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	−15.0000			−0.814688
$340$	−2.50000	−	4.33013i	−0.135582	−	0.234834i
$341$	−20.0000			−1.08306
$342$	1.00000	−	1.73205i	0.0540738	−	0.0936586i
$343$	−20.0000			−1.07990
$344$	−4.00000			−0.215666
$345$		0			0
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	18.0000			0.966291			0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000			0.966291			0.483145	+	0.875540i	$0.339494\pi$
$348$	−4.50000	+	7.79423i	−0.241225	+	0.417815i
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	−0.463862	−	0.885908i	$-0.653537\pi$
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	0.999149	−	0.0412379i	$-0.0131301\pi$
$350$	1.00000	−	1.73205i	0.0534522	−	0.0925820i
$351$	2.50000	+	4.33013i	0.133440	+	0.231125i
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	1.00000	−	1.73205i	0.0532246	−	0.0921878i	−0.838186	−	0.545385i	$-0.816383\pi$
$353$	1.00000	−	1.73205i	0.0532246	−	0.0921878i	0.891410	+	0.453197i	$0.149717\pi$
$354$	−1.50000	+	2.59808i	−0.0797241	+	0.138086i
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$	−14.0000			−0.741999
$357$	−5.00000	−	8.66025i	−0.264628	−	0.458349i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$	1.00000			0.0527046
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−14.0000			−0.735824
$363$	7.00000	+	12.1244i	0.367405	+	0.636364i
$364$	10.0000			0.524142
$365$	−6.00000	−	10.3923i	−0.314054	−	0.543958i
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$	0.500000	−	6.06218i	0.0259938	−	0.315158i
$371$	12.0000			0.623009
$372$	2.00000	−	3.46410i	0.103695	−	0.179605i
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	12.5000	+	21.6506i	0.646360	+	1.11953i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−9.00000			−0.464140
$377$	22.5000	+	38.9711i	1.15881	+	2.00712i
$378$	2.00000			0.102869
$379$	3.00000	−	5.19615i	0.154100	−	0.266908i	−0.778631	−	0.627482i	$-0.784086\pi$
$379$	3.00000	−	5.19615i	0.154100	−	0.266908i	0.932731	+	0.360573i	$0.117419\pi$
$380$	−2.00000			−0.102598
$381$	2.00000			0.102463
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	1.00000			0.0510310
$385$	−5.00000	+	8.66025i	−0.254824	+	0.441367i
$386$	13.0000	−	22.5167i	0.661683	−	1.14607i
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$	9.00000	+	15.5885i	0.456906	+	0.791384i
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	0.987103	−	0.160085i	$-0.0511768\pi$
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	−0.632189	+	0.774814i	$0.717843\pi$
$390$	2.50000	−	4.33013i	0.126592	−	0.219265i
$391$		0			0
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$	−11.0000			−0.554877
$394$	−5.00000	−	8.66025i	−0.251896	−	0.436297i
$395$	8.00000	−	13.8564i	0.402524	−	0.697191i
$396$	−5.00000			−0.251259
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	3.50000	−	6.06218i	0.175439	−	0.303870i
$399$	−4.00000			−0.200250
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$	4.50000	+	7.79423i	0.224440	+	0.388741i
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$	−2.50000	−	4.33013i	−0.124380	−	0.215432i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	18.0000			0.893325
$407$	−2.50000	+	30.3109i	−0.123920	+	1.50245i
$408$	−5.00000			−0.247537
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$	−3.00000	−	5.19615i	−0.148159	−	0.256620i
$411$	−1.50000	−	2.59808i	−0.0739895	−	0.128154i
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	6.00000			0.295241
$414$		0			0
$415$	2.00000			0.0981761
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	16.0000			0.783523
$418$	10.0000			0.489116
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$	−1.00000	−	1.73205i	−0.0487950	−	0.0845154i
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$	6.00000	+	10.3923i	0.290701	+	0.503509i
$427$		0			0
$428$	1.00000	−	1.73205i	0.0483368	−	0.0837218i
$429$	−12.5000	+	21.6506i	−0.603506	+	1.04530i
$430$	4.00000			0.192897
$431$	−18.0000	−	31.1769i	−0.867029	−	1.50174i	−0.865018	−	0.501741i	$-0.832693\pi$
$431$	−18.0000	−	31.1769i	−0.867029	−	1.50174i	−0.00201168	−	0.999998i	$-0.500640\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	24.0000			1.15337			0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000			1.15337			0.576683	+	0.816968i	$0.304347\pi$
$434$	−8.00000			−0.384012
$435$	4.50000	−	7.79423i	0.215758	−	0.373705i
$436$	14.0000			0.670478
$437$		0			0
$438$	−12.0000			−0.573382
$439$	−0.500000	−	0.866025i	−0.0238637	−	0.0413331i	0.853847	−	0.520524i	$-0.174263\pi$
$439$	−0.500000	−	0.866025i	−0.0238637	−	0.0413331i	−0.877711	+	0.479191i	$0.840930\pi$
$440$	2.50000	+	4.33013i	0.119183	+	0.206431i
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$	−12.5000	+	21.6506i	−0.594564	+	1.02982i
$443$	−10.0000			−0.475114			−0.237557	−	0.971374i	$-0.576347\pi$
$443$	−10.0000			−0.475114			−0.237557	+	0.971374i	$0.576347\pi$
$444$	−5.00000	−	3.46410i	−0.237289	−	0.164399i
$445$	14.0000			0.663664
$446$	6.00000	−	10.3923i	0.284108	−	0.492090i
$447$	7.50000	+	12.9904i	0.354738	+	0.614424i
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	−10.0000	−	17.3205i	−0.471929	−	0.817405i	0.527555	−	0.849521i	$-0.323109\pi$
$449$	−10.0000	−	17.3205i	−0.471929	−	0.817405i	−0.999484	+	0.0321156i	$0.989776\pi$
$450$	−1.00000			−0.0471405
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$	15.0000			0.705541
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	−18.0000			−0.844782
$455$	−10.0000			−0.468807
$456$	−1.00000	+	1.73205i	−0.0468293	+	0.0811107i
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	−0.948566	−	0.316579i	$-0.897466\pi$
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	0.200118	−	0.979772i	$-0.435868\pi$
$458$	4.00000			0.186908
$459$	−2.50000	+	4.33013i	−0.116690	+	0.202113i
$460$		0			0
$461$	−3.50000	+	6.06218i	−0.163011	+	0.282344i	−0.935947	−	0.352140i	$-0.885454\pi$
$461$	−3.50000	+	6.06218i	−0.163011	+	0.282344i	0.772936	+	0.634484i	$0.218787\pi$
$462$	5.00000	+	8.66025i	0.232621	+	0.402911i
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	0.992183	+	0.124788i	$0.0398251\pi$
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	−0.388022	+	0.921650i	$0.626842\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$	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	−	4.33013i	−0.115563	−	0.200160i
$469$	9.00000	−	15.5885i	0.415581	−	0.719808i
$470$	9.00000			0.415139
$471$	13.0000			0.599008
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	−20.0000			−0.919601
$474$	−8.00000	−	13.8564i	−0.367452	−	0.636446i
$475$	2.00000			0.0917663
$476$	5.00000	+	8.66025i	0.229175	+	0.396942i
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−10.0000	−	17.3205i	−0.457389	−	0.792222i
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	−0.287954	−	0.957644i	$-0.592975\pi$
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	0.973321	−	0.229447i	$-0.0736918\pi$
$480$	−1.00000			−0.0456435
$481$	−27.5000	+	12.9904i	−1.25389	+	0.592310i
$482$	−25.0000			−1.13872
$483$		0			0
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	−9.00000	−	15.5885i	−0.408669	−	0.707835i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	26.0000			1.17817			0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000			1.17817			0.589086	+	0.808070i	$0.299488\pi$
$488$		0			0
$489$	9.00000			0.406994
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	−6.00000			−0.270501
$493$	−22.5000	+	38.9711i	−1.01335	+	1.75517i
$494$	5.00000	+	8.66025i	0.224961	+	0.389643i
$495$	5.00000			0.224733
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$	1.00000	−	1.73205i	0.0448111	−	0.0776151i
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	0.246214	−	0.969216i	$-0.420813\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−8.50000	+	14.7224i	−0.379752	+	0.657750i
$502$	−3.50000	+	6.06218i	−0.156213	+	0.270568i
$503$	−2.50000	+	4.33013i	−0.111469	+	0.193071i	−0.916363	−	0.400349i	$-0.868889\pi$
$503$	−2.50000	+	4.33013i	−0.111469	+	0.193071i	0.804893	+	0.593419i	$0.202222\pi$
$504$	−2.00000			−0.0890871
$505$	2.50000	+	4.33013i	0.111249	+	0.192688i
$506$		0			0
$507$	−12.0000			−0.532939
$508$	−2.00000			−0.0887357
$509$	−13.0000	+	22.5167i	−0.576215	+	0.998033i	0.419694	+	0.907666i	$0.362138\pi$
$509$	−13.0000	+	22.5167i	−0.576215	+	0.998033i	−0.995908	+	0.0903676i	$0.971196\pi$
$510$	5.00000			0.221404
$511$	12.0000	+	20.7846i	0.530849	+	0.919457i
$512$	−1.00000			−0.0441942
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$	−6.50000	−	11.2583i	−0.286703	−	0.496584i
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−45.0000			−1.97910
$518$	−1.00000	+	12.1244i	−0.0439375	+	0.532714i
$519$	−14.0000			−0.614532
$520$	−2.50000	+	4.33013i	−0.109632	+	0.189889i
$521$	10.0000	+	17.3205i	0.438108	+	0.758825i	0.997544	−	0.0700486i	$-0.0223154\pi$
$521$	10.0000	+	17.3205i	0.438108	+	0.758825i	−0.559436	+	0.828874i	$0.688982\pi$
$522$	−4.50000	−	7.79423i	−0.196960	−	0.341144i
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$	11.0000			0.480537
$525$	1.00000	+	1.73205i	0.0436436	+	0.0755929i
$526$	28.0000			1.22086
$527$	10.0000	−	17.3205i	0.435607	−	0.754493i
$528$	5.00000			0.217597
$529$	−23.0000			−1.00000
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	−1.50000	−	2.59808i	−0.0650945	−	0.112747i
$532$	4.00000			0.173422
$533$	−15.0000	+	25.9808i	−0.649722	+	1.12535i
$534$	7.00000	−	12.1244i	0.302920	−	0.524672i
$535$	−1.00000	+	1.73205i	−0.0432338	+	0.0748831i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$	3.00000	−	5.19615i	0.129339	−	0.224022i
$539$	−7.50000	+	12.9904i	−0.323048	+	0.559535i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−32.0000			−1.37579			−0.687894	−	0.725811i	$-0.741464\pi$
$541$	−32.0000			−1.37579			−0.687894	+	0.725811i	$0.741464\pi$
$542$	−0.500000	−	0.866025i	−0.0214768	−	0.0371990i
$543$	7.00000	−	12.1244i	0.300399	−	0.520306i
$544$	5.00000			0.214373
$545$	−14.0000			−0.599694
$546$	−5.00000	+	8.66025i	−0.213980	+	0.370625i
$547$	−44.0000			−1.88130			−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000			−1.88130			−0.940652	+	0.339372i	$0.889785\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$		0			0
$550$	−2.50000	−	4.33013i	−0.106600	−	0.184637i
$551$	9.00000	+	15.5885i	0.383413	+	0.664091i
$552$		0			0
$553$	−16.0000	+	27.7128i	−0.680389	+	1.17847i
$554$	1.00000			0.0424859
$555$	5.00000	+	3.46410i	0.212238	+	0.147043i
$556$	−16.0000			−0.678551
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	−0.975356	−	0.220638i	$-0.929186\pi$
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	0.678756	+	0.734364i	$0.262519\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	−10.0000	−	17.3205i	−0.422955	−	0.732579i
$560$	1.00000	+	1.73205i	0.0422577	+	0.0731925i
$561$	−25.0000			−1.05550
$562$	5.00000	+	8.66025i	0.210912	+	0.365311i
$563$	24.0000			1.01148			0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000			1.01148			0.505740	+	0.862686i	$0.331220\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$	−15.0000			−0.631055
$566$	15.0000			0.630497
$567$	−1.00000	+	1.73205i	−0.0419961	+	0.0727393i
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	−1.00000	+	1.73205i	−0.0418487	+	0.0724841i	−0.886191	−	0.463320i	$-0.846658\pi$
$571$	−1.00000	+	1.73205i	−0.0418487	+	0.0724841i	0.844342	+	0.535804i	$0.179991\pi$
$572$	12.5000	−	21.6506i	0.522651	−	0.905259i
$573$	9.00000	+	15.5885i	0.375980	+	0.651217i
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.00000	+	10.3923i	−0.249783	+	0.432637i	−0.963466	−	0.267832i	$-0.913693\pi$
$577$	−6.00000	+	10.3923i	−0.249783	+	0.432637i	0.713682	+	0.700470i	$0.247026\pi$
$578$	−8.00000			−0.332756
$579$	13.0000	+	22.5167i	0.540262	+	0.935760i
$580$	−4.50000	+	7.79423i	−0.186852	+	0.323638i
$581$	−4.00000			−0.165948
$582$	−18.0000			−0.746124
$583$	15.0000	−	25.9808i	0.621237	−	1.07601i
$584$	12.0000			0.496564
$585$	2.50000	+	4.33013i	0.103362	+	0.179029i
$586$	−10.0000			−0.413096
$587$	−21.0000	−	36.3731i	−0.866763	−	1.50128i	−0.865286	−	0.501278i	$-0.832863\pi$
$587$	−21.0000	−	36.3731i	−0.866763	−	1.50128i	−0.00147660	−	0.999999i	$-0.500470\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	−4.00000	−	6.92820i	−0.164817	−	0.285472i
$590$	−1.50000	+	2.59808i	−0.0617540	+	0.106961i
$591$	10.0000			0.411345
$592$	5.00000	+	3.46410i	0.205499	+	0.142374i
$593$	11.0000			0.451716			0.225858	−	0.974160i	$-0.427481\pi$
$593$	11.0000			0.451716			0.225858	+	0.974160i	$0.427481\pi$
$594$	2.50000	−	4.33013i	0.102576	−	0.177667i
$595$	−5.00000	−	8.66025i	−0.204980	−	0.355036i
$596$	−7.50000	−	12.9904i	−0.307212	−	0.532107i
$597$	3.50000	+	6.06218i	0.143245	+	0.248108i
$598$		0			0
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	0.949908	−	0.312531i	$-0.101177\pi$
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	−0.745613	+	0.666379i	$0.767843\pi$
$600$	1.00000			0.0408248
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	−0.967600	−	0.252486i	$-0.918752\pi$
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	0.702460	+	0.711723i	$0.252085\pi$
$602$	−8.00000			−0.326056
$603$	−9.00000			−0.366508
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	5.00000			0.203111
$607$	−17.0000	+	29.4449i	−0.690009	+	1.19513i	0.281826	+	0.959466i	$0.409060\pi$
$607$	−17.0000	+	29.4449i	−0.690009	+	1.19513i	−0.971834	+	0.235665i	$0.924273\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	−9.00000	+	15.5885i	−0.364698	+	0.631676i
$610$		0			0
$611$	−22.5000	−	38.9711i	−0.910253	−	1.57660i
$612$	2.50000	−	4.33013i	0.101057	−	0.175035i
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.00472215	−	0.999989i	$-0.498497\pi$
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.863655	−	0.504084i	$-0.168170\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$	6.00000			0.241943
$616$	−5.00000	−	8.66025i	−0.201456	−	0.348932i
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	−0.834251	−	0.551385i	$-0.814100\pi$
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	0.894639	+	0.446790i	$0.147433\pi$
$618$	−4.00000			−0.160904
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$		0			0
$622$	−12.0000	−	20.7846i	−0.481156	−	0.833387i
$623$	−28.0000			−1.12180
$624$	2.50000	+	4.33013i	0.100080	+	0.173344i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$	−5.00000	+	8.66025i	−0.199681	+	0.345857i
$628$	−13.0000			−0.518756
$629$	−25.0000	−	17.3205i	−0.996815	−	0.690614i
$630$	2.00000			0.0796819
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	−0.999996	−	0.00274930i	$-0.999125\pi$
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	0.502379	+	0.864647i	$0.332458\pi$
$632$	8.00000	+	13.8564i	0.318223	+	0.551178i
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	2.00000			0.0793676
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	−15.0000			−0.594322
$638$	22.5000	−	38.9711i	0.890784	−	1.54288i
$639$	−12.0000			−0.474713
$640$	1.00000			0.0395285
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$	1.00000	+	1.73205i	0.0394669	+	0.0683586i
$643$	19.0000			0.749287			0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000			0.749287			0.374643	+	0.927169i	$0.377765\pi$
$644$		0			0
$645$	−2.00000	+	3.46410i	−0.0787499	+	0.136399i
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$	−9.50000	−	16.4545i	−0.373484	−	0.646892i	0.616615	−	0.787265i	$-0.288503\pi$
$647$	−9.50000	−	16.4545i	−0.373484	−	0.646892i	−0.990099	+	0.140372i	$0.955170\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	7.50000	−	12.9904i	0.294401	−	0.509917i
$650$	2.50000	−	4.33013i	0.0980581	−	0.169842i
$651$	4.00000	−	6.92820i	0.156772	−	0.271538i
$652$	−9.00000			−0.352467
$653$	−14.0000	−	24.2487i	−0.547862	−	0.948925i	−0.998421	−	0.0561784i	$-0.982108\pi$
$653$	−14.0000	−	24.2487i	−0.547862	−	0.948925i	0.450558	−	0.892747i	$-0.351225\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$	−11.0000			−0.429806
$656$	6.00000			0.234261
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$	−18.0000			−0.701713
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	0.999545	+	0.0301523i	$0.00959924\pi$
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	−0.473660	+	0.880708i	$0.657067\pi$
$660$	−5.00000			−0.194625
$661$	−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	$-0.380480\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$	−12.5000	−	21.6506i	−0.485460	−	0.840841i
$664$	−1.00000	+	1.73205i	−0.0388075	+	0.0672166i
$665$	−4.00000			−0.155113
$666$	5.50000	−	2.59808i	0.213121	−	0.100673i
$667$		0			0
$668$	8.50000	−	14.7224i	0.328875	−	0.569628i
$669$	6.00000	+	10.3923i	0.231973	+	0.401790i
$670$	4.50000	+	7.79423i	0.173850	+	0.301117i
$671$		0			0
$672$	2.00000			0.0771517
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	0.802395	−	0.596794i	$-0.203559\pi$
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	−0.918036	+	0.396497i	$0.870226\pi$
$674$	−14.0000			−0.539260
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	12.0000			0.461538
$677$	−20.0000			−0.768662			−0.384331	−	0.923195i	$-0.625568\pi$
$677$	−20.0000			−0.768662			−0.384331	+	0.923195i	$0.625568\pi$
$678$	−7.50000	+	12.9904i	−0.288036	+	0.498893i
$679$	18.0000	+	31.1769i	0.690777	+	1.19646i
$680$	−5.00000			−0.191741
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	−10.0000	+	17.3205i	−0.382920	+	0.663237i
$683$	17.0000	−	29.4449i	0.650487	−	1.12668i	−0.332518	−	0.943097i	$-0.607898\pi$
$683$	17.0000	−	29.4449i	0.650487	−	1.12668i	0.983005	−	0.183579i	$-0.0587685\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$	−1.50000	−	2.59808i	−0.0573121	−	0.0992674i
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	−2.00000	+	3.46410i	−0.0763048	+	0.132164i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	30.0000			1.14291
$690$		0			0
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	−0.755110	−	0.655598i	$-0.772417\pi$
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	0.945319	+	0.326146i	$0.105750\pi$
$692$	14.0000			0.532200
$693$	−10.0000			−0.379869
$694$	9.00000	−	15.5885i	0.341635	−	0.591730i
$695$	16.0000			0.606915
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$	−30.0000			−1.13633
$698$	−10.0000	−	17.3205i	−0.378506	−	0.655591i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	2.50000	−	4.33013i	0.0944237	−	0.163547i	−0.814944	−	0.579539i	$-0.803232\pi$
$701$	2.50000	−	4.33013i	0.0944237	−	0.163547i	0.909368	+	0.415993i	$0.136566\pi$
$702$	5.00000			0.188713
$703$	−11.0000	+	5.19615i	−0.414873	+	0.195977i
$704$	−5.00000			−0.188445
$705$	−4.50000	+	7.79423i	−0.169480	+	0.293548i
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$	−5.00000	−	8.66025i	−0.188044	−	0.325702i
$708$	1.50000	+	2.59808i	0.0563735	+	0.0976417i
$709$	24.0000			0.901339			0.450669	−	0.892691i	$-0.351185\pi$
$709$	24.0000			0.901339			0.450669	+	0.892691i	$0.351185\pi$
$710$	6.00000	+	10.3923i	0.225176	+	0.390016i
$711$	16.0000			0.600047
$712$	−7.00000	+	12.1244i	−0.262336	+	0.454379i
$713$		0			0
$714$	−10.0000			−0.374241
$715$	−12.5000	+	21.6506i	−0.467473	+	0.809688i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	20.0000			0.746914
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	12.5000	−	21.6506i	0.464880	−	0.805196i
$724$	−7.00000	+	12.1244i	−0.260153	+	0.450598i
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$	14.0000			0.519589
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	0.999750	+	0.0223506i	$0.00711500\pi$
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	−0.480519	+	0.876984i	$0.659552\pi$
$728$	5.00000	−	8.66025i	0.185312	−	0.320970i
$729$	1.00000			0.0370370
$730$	−12.0000			−0.444140
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$		0			0
$733$	16.5000	+	28.5788i	0.609441	+	1.05558i	0.991333	+	0.131376i	$0.0419396\pi$
$733$	16.5000	+	28.5788i	0.609441	+	1.05558i	−0.381891	+	0.924207i	$0.624727\pi$
$734$	4.00000			0.147643
$735$	1.50000	+	2.59808i	0.0553283	+	0.0958315i
$736$		0			0
$737$	−22.5000	−	38.9711i	−0.828798	−	1.43552i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	10.0000			0.367856			0.183928	−	0.982940i	$-0.441119\pi$
$739$	10.0000			0.367856			0.183928	+	0.982940i	$0.441119\pi$
$740$	−5.00000	−	3.46410i	−0.183804	−	0.127343i
$741$	−10.0000			−0.367359
$742$	6.00000	−	10.3923i	0.220267	−	0.381514i
$743$	−13.5000	−	23.3827i	−0.495267	−	0.857828i	0.504718	−	0.863284i	$-0.331596\pi$
$743$	−13.5000	−	23.3827i	−0.495267	−	0.857828i	−0.999985	+	0.00545664i	$0.998263\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$	−10.0000			−0.366126
$747$	1.00000	+	1.73205i	0.0365881	+	0.0633724i
$748$	25.0000			0.914091
$749$	2.00000	−	3.46410i	0.0730784	−	0.126576i
$750$	−1.00000			−0.0365148
$751$	3.00000			0.109472			0.0547358	−	0.998501i	$-0.482568\pi$
$751$	3.00000			0.109472			0.0547358	+	0.998501i	$0.482568\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−3.50000	−	6.06218i	−0.127547	−	0.220918i
$754$	45.0000			1.63880
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$	1.00000	−	1.73205i	0.0363696	−	0.0629941i
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	−0.993701	−	0.112062i	$-0.964254\pi$
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	0.593899	+	0.804539i	$0.297588\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$		0			0
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	24.0000	−	41.5692i	0.869999	−	1.50688i	0.00800331	−	0.999968i	$-0.497452\pi$
$761$	24.0000	−	41.5692i	0.869999	−	1.50688i	0.861996	−	0.506915i	$-0.169214\pi$
$762$	1.00000	−	1.73205i	0.0362262	−	0.0627456i
$763$	28.0000			1.01367
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$	−2.50000	+	4.33013i	−0.0903877	+	0.156556i
$766$	15.0000			0.541972
$767$	15.0000			0.541619
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	15.0000			0.540914			0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000			0.540914			0.270457	+	0.962732i	$0.412825\pi$
$770$	5.00000	+	8.66025i	0.180187	+	0.312094i
$771$	13.0000			0.468184
$772$	−13.0000	−	22.5167i	−0.467880	−	0.810392i
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$	18.0000			0.646162
$777$	−10.0000	−	6.92820i	−0.358748	−	0.248548i
$778$	14.0000			0.501924
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	−2.50000	−	4.33013i	−0.0895144	−	0.155043i
$781$	−30.0000	−	51.9615i	−1.07348	−	1.85933i
$782$		0			0
$783$	9.00000			0.321634
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$	13.0000			0.463990
$786$	−5.50000	+	9.52628i	−0.196179	+	0.339791i
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$	−10.0000			−0.356235
$789$	−14.0000	+	24.2487i	−0.498413	+	0.863277i
$790$	−8.00000	−	13.8564i	−0.284627	−	0.492989i
$791$	30.0000			1.06668
$792$	−2.50000	+	4.33013i	−0.0888336	+	0.153864i
$793$		0			0
$794$	−11.5000	+	19.9186i	−0.408120	+	0.706884i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$	−3.50000	−	6.06218i	−0.124054	−	0.214868i
$797$	−16.0000	+	27.7128i	−0.566749	+	0.981638i	0.430136	+	0.902764i	$0.358466\pi$
$797$	−16.0000	+	27.7128i	−0.566749	+	0.981638i	−0.996885	+	0.0788739i	$0.974868\pi$
$798$	−2.00000	+	3.46410i	−0.0707992	+	0.122628i
$799$	22.5000	−	38.9711i	0.795993	−	1.37870i
$800$	−1.00000			−0.0353553
$801$	7.00000	+	12.1244i	0.247333	+	0.428393i
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$	60.0000			2.11735
$804$	9.00000			0.317406
$805$		0			0
$806$	−20.0000			−0.704470
$807$	3.00000	+	5.19615i	0.105605	+	0.182913i
$808$	−5.00000			−0.175899
$809$	−25.0000	−	43.3013i	−0.878953	−	1.52239i	−0.852491	−	0.522742i	$-0.824909\pi$
$809$	−25.0000	−	43.3013i	−0.878953	−	1.52239i	−0.0264621	−	0.999650i	$-0.508424\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	8.00000	+	13.8564i	0.280918	+	0.486564i	0.971611	−	0.236584i	$-0.0760278\pi$
$811$	8.00000	+	13.8564i	0.280918	+	0.486564i	−0.690693	+	0.723148i	$0.742694\pi$
$812$	9.00000	−	15.5885i	0.315838	−	0.547048i
$813$	1.00000			0.0350715
$814$	25.0000	+	17.3205i	0.876250	+	0.607083i
$815$	9.00000			0.315256
$816$	−2.50000	+	4.33013i	−0.0875175	+	0.151585i
$817$	−4.00000	−	6.92820i	−0.139942	−	0.242387i
$818$	−12.5000	−	21.6506i	−0.437052	−	0.756997i
$819$	−5.00000	−	8.66025i	−0.174714	−	0.302614i
$820$	−6.00000			−0.209529
$821$	16.5000	+	28.5788i	0.575854	+	0.997408i	0.995948	+	0.0899279i	$0.0286637\pi$
$821$	16.5000	+	28.5788i	0.575854	+	0.997408i	−0.420094	+	0.907480i	$0.638003\pi$
$822$	−3.00000			−0.104637
$823$	−17.0000	+	29.4449i	−0.592583	+	1.02638i	0.401300	+	0.915947i	$0.368558\pi$
$823$	−17.0000	+	29.4449i	−0.592583	+	1.02638i	−0.993883	+	0.110437i	$0.964775\pi$
$824$	4.00000			0.139347
$825$	5.00000			0.174078
$826$	3.00000	−	5.19615i	0.104383	−	0.180797i
$827$	−11.0000	−	19.0526i	−0.382507	−	0.662522i	0.608913	−	0.793237i	$-0.291606\pi$
$827$	−11.0000	−	19.0526i	−0.382507	−	0.662522i	−0.991420	+	0.130715i	$0.958273\pi$
$828$		0			0
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	−0.998480	−	0.0551154i	$-0.982447\pi$
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	0.546971	+	0.837151i	$0.315781\pi$
$830$	1.00000	−	1.73205i	0.0347105	−	0.0601204i
$831$	−0.500000	+	0.866025i	−0.0173448	+	0.0300421i
$832$	−2.50000	−	4.33013i	−0.0866719	−	0.150120i
$833$	−7.50000	−	12.9904i	−0.259860	−	0.450090i
$834$	8.00000	−	13.8564i	0.277017	−	0.479808i
$835$	−8.50000	+	14.7224i	−0.294155	+	0.509491i
$836$	5.00000	−	8.66025i	0.172929	−	0.299521i
$837$	−4.00000			−0.138260
$838$	−18.0000	−	31.1769i	−0.621800	−	1.07699i
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	−0.898482	−	0.439010i	$-0.855329\pi$
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	0.829435	+	0.558604i	$0.188663\pi$
$840$	−2.00000			−0.0690066
$841$	52.0000			1.79310
$842$	10.0000	−	17.3205i	0.344623	−	0.596904i
$843$	−10.0000			−0.344418
$844$	−2.00000	−	3.46410i	−0.0688428	−	0.119239i
$845$	−12.0000			−0.412813
$846$	4.50000	+	7.79423i	0.154713	+	0.267971i
$847$	−14.0000	−	24.2487i	−0.481046	−	0.833196i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$	−7.50000	+	12.9904i	−0.257399	+	0.445829i
$850$	5.00000			0.171499
$851$		0			0
$852$	12.0000			0.411113
$853$	23.5000	−	40.7032i	0.804625	−	1.39365i	−0.111919	−	0.993717i	$-0.535700\pi$
$853$	23.5000	−	40.7032i	0.804625	−	1.39365i	0.916544	−	0.399934i	$-0.130967\pi$
$854$		0			0
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	−1.00000	−	1.73205i	−0.0341793	−	0.0592003i
$857$	43.0000			1.46885			0.734426	−	0.678689i	$-0.237451\pi$
$857$	43.0000			1.46885			0.734426	+	0.678689i	$0.237451\pi$
$858$	12.5000	+	21.6506i	0.426743	+	0.739140i
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$	−12.0000			−0.408959
$862$	−36.0000			−1.22616
$863$	−10.5000	+	18.1865i	−0.357424	+	0.619077i	−0.987530	−	0.157433i	$-0.949678\pi$
$863$	−10.5000	+	18.1865i	−0.357424	+	0.619077i	0.630106	+	0.776509i	$0.283012\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−14.0000			−0.476014
$866$	12.0000	−	20.7846i	0.407777	−	0.706290i
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	−4.00000	+	6.92820i	−0.135769	+	0.235159i
$869$	40.0000	+	69.2820i	1.35691	+	2.35023i
$870$	−4.50000	−	7.79423i	−0.152564	−	0.264249i
$871$	22.5000	−	38.9711i	0.762383	−	1.32049i
$872$	7.00000	−	12.1244i	0.237050	−	0.410582i
$873$	9.00000	−	15.5885i	0.304604	−	0.527589i
$874$		0			0
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$	−6.00000	+	10.3923i	−0.202721	+	0.351123i
$877$	43.0000			1.45201			0.726003	−	0.687691i	$-0.241376\pi$
$877$	43.0000			1.45201			0.726003	+	0.687691i	$0.241376\pi$
$878$	−1.00000			−0.0337484
$879$	5.00000	−	8.66025i	0.168646	−	0.292103i
$880$	5.00000			0.168550
$881$	16.0000	+	27.7128i	0.539054	+	0.933668i	0.998955	+	0.0456985i	$0.0145514\pi$
$881$	16.0000	+	27.7128i	0.539054	+	0.933668i	−0.459902	+	0.887970i	$0.652115\pi$
$882$	3.00000			0.101015
$883$	−23.5000	−	40.7032i	−0.790838	−	1.36977i	−0.925449	−	0.378873i	$-0.876312\pi$
$883$	−23.5000	−	40.7032i	−0.790838	−	1.36977i	0.134611	−	0.990899i	$-0.457022\pi$
$884$	12.5000	+	21.6506i	0.420420	+	0.728190i
$885$	−1.50000	−	2.59808i	−0.0504219	−	0.0873334i
$886$	−5.00000	+	8.66025i	−0.167978	+	0.290947i
$887$	8.00000			0.268614			0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$	−5.50000	+	2.59808i	−0.184568	+	0.0871857i
$889$	−4.00000			−0.134156
$890$	7.00000	−	12.1244i	0.234641	−	0.406409i
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	−6.00000	−	10.3923i	−0.200895	−	0.347960i
$893$	−9.00000	−	15.5885i	−0.301174	−	0.521648i
$894$	15.0000			0.501675
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$	−20.0000			−0.667409
$899$	−36.0000			−1.20067
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	15.0000	+	25.9808i	0.499722	+	0.865545i
$902$	30.0000			0.998891
$903$	4.00000	−	6.92820i	0.133112	−	0.230556i
$904$	7.50000	−	12.9904i	0.249446	−	0.432054i
$905$	7.00000	−	12.1244i	0.232688	−	0.403027i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	0.897318	−	0.441384i	$-0.145512\pi$
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	−0.830909	+	0.556408i	$0.812179\pi$
$908$	−9.00000	+	15.5885i	−0.298675	+	0.517321i
$909$	−2.50000	+	4.33013i	−0.0829198	+	0.143621i
$910$	−5.00000	+	8.66025i	−0.165748	+	0.287085i
$911$	−34.0000			−1.12647			−0.563235	−	0.826297i	$-0.690443\pi$
$911$	−34.0000			−1.12647			−0.563235	+	0.826297i	$0.690443\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$	−5.00000	+	8.66025i	−0.165476	+	0.286613i
$914$	−32.0000			−1.05847
$915$		0			0
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$	22.0000			0.726504
$918$	2.50000	+	4.33013i	0.0825123	+	0.142915i
$919$	−25.0000			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$920$		0			0
$921$	−8.00000	−	13.8564i	−0.263609	−	0.456584i
$922$	3.50000	+	6.06218i	0.115266	+	0.199647i
$923$	30.0000	−	51.9615i	0.987462	−	1.71033i
$924$	10.0000			0.328976
$925$	5.00000	+	3.46410i	0.164399	+	0.113899i
$926$	26.0000			0.854413
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	2.00000	+	3.46410i	0.0656179	+	0.113653i	0.896968	−	0.442096i	$-0.145765\pi$
$929$	2.00000	+	3.46410i	0.0656179	+	0.113653i	−0.831350	+	0.555749i	$0.812431\pi$
$930$	2.00000	+	3.46410i	0.0655826	+	0.113592i
$931$	−6.00000			−0.196642
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$	24.0000			0.785725
$934$	9.00000	−	15.5885i	0.294489	−	0.510070i
$935$	−25.0000			−0.817587
$936$	−5.00000			−0.163430
$937$	17.0000	−	29.4449i	0.555366	−	0.961922i	−0.442509	−	0.896764i	$-0.645912\pi$
$937$	17.0000	−	29.4449i	0.555366	−	0.961922i	0.997875	−	0.0651578i	$-0.0207551\pi$
$938$	−9.00000	−	15.5885i	−0.293860	−	0.508981i
$939$	14.0000			0.456873
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	−0.957273	−	0.289187i	$-0.906615\pi$
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	0.729079	+	0.684429i	$0.239949\pi$
$942$	6.50000	−	11.2583i	0.211781	−	0.366816i
$943$		0			0
$944$	−1.50000	−	2.59808i	−0.0488208	−	0.0845602i
$945$	−1.00000	+	1.73205i	−0.0325300	+	0.0563436i
$946$	−10.0000	+	17.3205i	−0.325128	+	0.563138i
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	−0.813157	−	0.582045i	$-0.802253\pi$
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	0.910644	+	0.413192i	$0.135586\pi$
$948$	−16.0000			−0.519656
$949$	30.0000	+	51.9615i	0.973841	+	1.68674i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	−18.0000			−0.583690
$952$	10.0000			0.324102
$953$	15.5000	−	26.8468i	0.502094	−	0.869653i	−0.497903	−	0.867233i	$-0.665896\pi$
$953$	15.5000	−	26.8468i	0.502094	−	0.869653i	0.999997	−	0.00241992i	$-0.000770286\pi$
$954$	−6.00000			−0.194257
$955$	9.00000	+	15.5885i	0.291233	+	0.504431i
$956$	−20.0000			−0.646846
$957$	22.5000	+	38.9711i	0.727322	+	1.25976i
$958$	−15.0000	−	25.9808i	−0.484628	−	0.839400i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	−15.0000			−0.483871
$962$	−2.50000	+	30.3109i	−0.0806032	+	0.977262i
$963$	−2.00000			−0.0644491
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$	13.0000	+	22.5167i	0.418485	+	0.724837i
$966$		0			0
$967$	3.00000	+	5.19615i	0.0964735	+	0.167097i	0.910223	−	0.414119i	$-0.135910\pi$
$967$	3.00000	+	5.19615i	0.0964735	+	0.167097i	−0.813749	+	0.581216i	$0.802577\pi$
$968$	−14.0000			−0.449977
$969$	−5.00000	−	8.66025i	−0.160623	−	0.278207i
$970$	−18.0000			−0.577945
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	0.0601548	+	0.998189i	$0.480841\pi$
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	−0.894534	+	0.446999i	$0.852493\pi$
$972$	−1.00000			−0.0320750
$973$	−32.0000			−1.02587
$974$	13.0000	−	22.5167i	0.416547	−	0.721480i
$975$	2.50000	+	4.33013i	0.0800641	+	0.138675i
$976$		0			0
$977$	20.5000	−	35.5070i	0.655853	−	1.13597i	−0.325826	−	0.945430i	$-0.605642\pi$
$977$	20.5000	−	35.5070i	0.655853	−	1.13597i	0.981679	−	0.190541i	$-0.0610243\pi$
$978$	4.50000	−	7.79423i	0.143894	−	0.249232i
$979$	−35.0000	+	60.6218i	−1.11860	+	1.93748i
$980$	−1.50000	−	2.59808i	−0.0479157	−	0.0829925i
$981$	−7.00000	−	12.1244i	−0.223493	−	0.387101i
$982$	−18.0000	+	31.1769i	−0.574403	+	0.994895i
$983$	−24.0000	+	41.5692i	−0.765481	+	1.32585i	0.174511	+	0.984655i	$0.444166\pi$
$983$	−24.0000	+	41.5692i	−0.765481	+	1.32585i	−0.939992	+	0.341197i	$0.889168\pi$
$984$	−3.00000	+	5.19615i	−0.0956365	+	0.165647i
$985$	10.0000			0.318626
$986$	22.5000	+	38.9711i	0.716546	+	1.24109i
$987$	9.00000	−	15.5885i	0.286473	−	0.496186i
$988$	10.0000			0.318142
$989$		0			0
$990$	2.50000	−	4.33013i	0.0794552	−	0.137620i
$991$	−3.00000			−0.0952981			−0.0476491	−	0.998864i	$-0.515173\pi$
$991$	−3.00000			−0.0952981			−0.0476491	+	0.998864i	$0.515173\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	−28.0000			−0.888553
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$	3.50000	+	6.06218i	0.110957	+	0.192184i
$996$	−1.00000	−	1.73205i	−0.0316862	−	0.0548821i
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	−0.888800	−	0.458295i	$-0.848460\pi$
$997$	−1.50000	+	2.59808i	−0.0475055	+	0.0822819i	0.841295	+	0.540576i	$0.181794\pi$
$998$	−32.0000			−1.01294
$999$	−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.f.121.1	✓	2
37.26	even	3	inner	1110.2.i.f.211.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.f.121.1	✓	2	1.1	even	1	trivial
1110.2.i.f.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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -5.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.50000 - 4.33013i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{21} +(-2.50000 + 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} -1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 - 4.33013i) q^{33} +(-2.50000 - 4.33013i) q^{34} +(1.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(0.500000 - 6.06218i) q^{37} -2.00000 q^{38} +(2.50000 - 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-1.00000 - 1.73205i) q^{42} +4.00000 q^{43} +(2.50000 + 4.33013i) q^{44} -1.00000 q^{45} +9.00000 q^{47} -1.00000 q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +5.00000 q^{51} +(-2.50000 + 4.33013i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.50000 - 4.33013i) q^{55} +(1.00000 + 1.73205i) q^{56} +(1.00000 - 1.73205i) q^{57} +(-4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +1.00000 q^{60} +(2.00000 - 3.46410i) q^{62} +2.00000 q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} -5.00000 q^{66} +(4.50000 + 7.79423i) q^{67} -5.00000 q^{68} +(-1.00000 - 1.73205i) q^{70} +(6.00000 + 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} -12.0000 q^{73} +(-5.00000 - 3.46410i) q^{74} -1.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(5.00000 + 8.66025i) q^{77} +(-2.50000 - 4.33013i) q^{78} +(-8.00000 - 13.8564i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{82} +(1.00000 - 1.73205i) q^{83} -2.00000 q^{84} +5.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.50000 - 7.79423i) q^{87} +5.00000 q^{88} +(7.00000 - 12.1244i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-5.00000 + 8.66025i) q^{91} +(2.00000 + 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} -18.0000 q^{97} +(-1.50000 - 2.59808i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} - 10 q^{11} + q^{12} - 5 q^{13} - 4 q^{14} - q^{15} - q^{16} + 5 q^{17} + q^{18} - 2 q^{19} + q^{20} + 2 q^{21} - 5 q^{22} - q^{24} - q^{25} - 10 q^{26} - 2 q^{27} - 2 q^{28} - 18 q^{29} + q^{30} + 8 q^{31} + q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 2 q^{36} + q^{37} - 4 q^{38} + 5 q^{39} - q^{40} - 6 q^{41} - 2 q^{42} + 8 q^{43} + 5 q^{44} - 2 q^{45} + 18 q^{47} - 2 q^{48} + 3 q^{49} + q^{50} + 10 q^{51} - 5 q^{52} - 6 q^{53} - q^{54} - 5 q^{55} + 2 q^{56} + 2 q^{57} - 9 q^{58} - 3 q^{59} + 2 q^{60} + 4 q^{62} + 4 q^{63} + 2 q^{64} + 5 q^{65} - 10 q^{66} + 9 q^{67} - 10 q^{68} - 2 q^{70} + 12 q^{71} + q^{72} - 24 q^{73} - 10 q^{74} - 2 q^{75} - 2 q^{76} + 10 q^{77} - 5 q^{78} - 16 q^{79} - 2 q^{80} - q^{81} - 12 q^{82} + 2 q^{83} - 4 q^{84} + 10 q^{85} + 4 q^{86} - 9 q^{87} + 10 q^{88} + 14 q^{89} - q^{90} - 10 q^{91} + 4 q^{93} + 9 q^{94} + 2 q^{95} - q^{96} - 36 q^{97} - 3 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9 + 2 * q^10 - 10 * q^11 + q^12 - 5 * q^13 - 4 * q^14 - q^15 - q^16 + 5 * q^17 + q^18 - 2 * q^19 + q^20 + 2 * q^21 - 5 * q^22 - q^24 - q^25 - 10 * q^26 - 2 * q^27 - 2 * q^28 - 18 * q^29 + q^30 + 8 * q^31 + q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 2 * q^36 + q^37 - 4 * q^38 + 5 * q^39 - q^40 - 6 * q^41 - 2 * q^42 + 8 * q^43 + 5 * q^44 - 2 * q^45 + 18 * q^47 - 2 * q^48 + 3 * q^49 + q^50 + 10 * q^51 - 5 * q^52 - 6 * q^53 - q^54 - 5 * q^55 + 2 * q^56 + 2 * q^57 - 9 * q^58 - 3 * q^59 + 2 * q^60 + 4 * q^62 + 4 * q^63 + 2 * q^64 + 5 * q^65 - 10 * q^66 + 9 * q^67 - 10 * q^68 - 2 * q^70 + 12 * q^71 + q^72 - 24 * q^73 - 10 * q^74 - 2 * q^75 - 2 * q^76 + 10 * q^77 - 5 * q^78 - 16 * q^79 - 2 * q^80 - q^81 - 12 * q^82 + 2 * q^83 - 4 * q^84 + 10 * q^85 + 4 * q^86 - 9 * q^87 + 10 * q^88 + 14 * q^89 - q^90 - 10 * q^91 + 4 * q^93 + 9 * q^94 + 2 * q^95 - q^96 - 36 * q^97 - 3 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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