LMFDB - Embedded newform 966.2.i.e.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
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			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.e.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{18} +3.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} +5.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -3.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(4.50000 - 7.79423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} +4.00000 q^{34} +(6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(6.00000 + 10.3923i) q^{37} +(1.50000 + 2.59808i) q^{40} +12.0000 q^{41} +(-0.500000 - 2.59808i) q^{42} +6.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-1.00000 - 1.73205i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(-2.50000 + 4.33013i) q^{53} +(0.500000 + 0.866025i) q^{54} -15.0000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +9.00000 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +1.00000 q^{69} +(7.50000 + 2.59808i) q^{70} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-6.00000 + 10.3923i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(12.5000 + 4.33013i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.00000 + 10.3923i) q^{82} -17.0000 q^{83} +(2.00000 - 1.73205i) q^{84} -12.0000 q^{85} +(3.00000 + 5.19615i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-5.00000 - 8.66025i) q^{89} -3.00000 q^{90} +1.00000 q^{92} +(4.50000 + 7.79423i) q^{93} +(1.00000 - 1.73205i) q^{94} +(0.500000 + 0.866025i) q^{96} -13.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 4 q^{14} + 6 q^{15} - q^{16} + 4 q^{17} + q^{18} + 6 q^{20} - 5 q^{21} + 10 q^{22} - q^{23} + q^{24} - 4 q^{25} + 2 q^{27} - 5 q^{28} - 6 q^{29} + 3 q^{30} + 9 q^{31} + q^{32} + 5 q^{33} + 8 q^{34} + 12 q^{35} + 2 q^{36} + 12 q^{37} + 3 q^{40} + 24 q^{41} - q^{42} + 12 q^{43} + 5 q^{44} - 3 q^{45} + q^{46} - 2 q^{47} + 2 q^{48} - 13 q^{49} - 8 q^{50} + 4 q^{51} - 5 q^{53} + q^{54} - 30 q^{55} - q^{56} - 3 q^{58} + 9 q^{59} - 3 q^{60} + 2 q^{61} + 18 q^{62} + 4 q^{63} + 2 q^{64} - 5 q^{66} + 2 q^{67} + 4 q^{68} + 2 q^{69} + 15 q^{70} + 12 q^{71} + q^{72} + 14 q^{73} - 12 q^{74} - 4 q^{75} + 25 q^{77} - 11 q^{79} - 3 q^{80} - q^{81} + 12 q^{82} - 34 q^{83} + 4 q^{84} - 24 q^{85} + 6 q^{86} + 3 q^{87} - 5 q^{88} - 10 q^{89} - 6 q^{90} + 2 q^{92} + 9 q^{93} + 2 q^{94} + q^{96} - 26 q^{97} - 11 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9 + 3 * q^10 + 5 * q^11 - q^12 - 4 * q^14 + 6 * q^15 - q^16 + 4 * q^17 + q^18 + 6 * q^20 - 5 * q^21 + 10 * q^22 - q^23 + q^24 - 4 * q^25 + 2 * q^27 - 5 * q^28 - 6 * q^29 + 3 * q^30 + 9 * q^31 + q^32 + 5 * q^33 + 8 * q^34 + 12 * q^35 + 2 * q^36 + 12 * q^37 + 3 * q^40 + 24 * q^41 - q^42 + 12 * q^43 + 5 * q^44 - 3 * q^45 + q^46 - 2 * q^47 + 2 * q^48 - 13 * q^49 - 8 * q^50 + 4 * q^51 - 5 * q^53 + q^54 - 30 * q^55 - q^56 - 3 * q^58 + 9 * q^59 - 3 * q^60 + 2 * q^61 + 18 * q^62 + 4 * q^63 + 2 * q^64 - 5 * q^66 + 2 * q^67 + 4 * q^68 + 2 * q^69 + 15 * q^70 + 12 * q^71 + q^72 + 14 * q^73 - 12 * q^74 - 4 * q^75 + 25 * q^77 - 11 * q^79 - 3 * q^80 - q^81 + 12 * q^82 - 34 * q^83 + 4 * q^84 - 24 * q^85 + 6 * q^86 + 3 * q^87 - 5 * q^88 - 10 * q^89 - 6 * q^90 + 2 * q^92 + 9 * q^93 + 2 * q^94 + q^96 - 26 * q^97 - 11 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	−1.00000			−0.408248
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	3.00000			0.670820
$21$	−2.50000	−	0.866025i	−0.545545	−	0.188982i
$22$	5.00000			1.06600
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$	1.00000			0.192450
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	−0.105869	−	0.994380i	$-0.533762\pi$
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	0.914093	−	0.405505i	$-0.132904\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.50000	+	4.33013i	0.435194	+	0.753778i
$34$	4.00000			0.685994
$35$	6.00000	−	5.19615i	1.01419	−	0.878310i
$36$	1.00000			0.166667
$37$	6.00000	+	10.3923i	0.986394	+	1.70848i	0.635571	+	0.772043i	$0.280765\pi$
$37$	6.00000	+	10.3923i	0.986394	+	1.70848i	0.350823	+	0.936442i	$0.385902\pi$
$38$		0			0
$39$		0			0
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$	−0.500000	−	2.59808i	−0.0771517	−	0.400892i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	0.783830	−	0.620975i	$-0.213263\pi$
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	−0.929695	+	0.368329i	$0.879930\pi$
$48$	1.00000			0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−4.00000			−0.565685
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$		0			0
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−15.0000			−2.02260
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		0			0
$58$	−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	$-0.0325726\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	9.00000			1.14300
$63$	2.00000	−	1.73205i	0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.50000	+	4.33013i	−0.307729	+	0.533002i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	1.00000			0.120386
$70$	7.50000	+	2.59808i	0.896421	+	0.310530i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	−6.00000	+	10.3923i	−0.697486	+	1.20808i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$		0			0
$77$	12.5000	+	4.33013i	1.42451	+	0.493464i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.00000	+	10.3923i	0.662589	+	1.14764i
$83$	−17.0000			−1.86599			−0.932996	−	0.359886i	$-0.882816\pi$
$83$	−17.0000			−1.86599			−0.932996	+	0.359886i	$0.882816\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$	−12.0000			−1.30158
$86$	3.00000	+	5.19615i	0.323498	+	0.560316i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	−3.00000			−0.316228
$91$		0			0
$92$	1.00000			0.104257
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$	−5.00000			−0.502519
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$	−2.00000	+	3.46410i	−0.198030	+	0.342997i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$	1.50000	+	7.79423i	0.146385	+	0.760639i
$106$	−5.00000			−0.485643
$107$	9.50000	+	16.4545i	0.918400	+	1.59071i	0.801846	+	0.597530i	$0.203851\pi$
$107$	9.50000	+	16.4545i	0.918400	+	1.59071i	0.116553	+	0.993184i	$0.462815\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	−0.973176	−	0.230063i	$-0.926107\pi$
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	0.685828	+	0.727764i	$0.259440\pi$
$110$	−7.50000	−	12.9904i	−0.715097	−	1.23858i
$111$	−12.0000			−1.13899
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$		0			0
$118$	9.00000			0.828517
$119$	10.0000	+	3.46410i	0.916698	+	0.317554i
$120$	−3.00000			−0.273861
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	−6.00000	+	10.3923i	−0.541002	+	0.937043i
$124$	4.50000	+	7.79423i	0.404112	+	0.699942i
$125$	−3.00000			−0.268328
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$	−11.0000			−0.976092			−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000			−0.976092			−0.488046	+	0.872818i	$0.662290\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.00000	+	5.19615i	−0.264135	+	0.457496i
$130$		0			0
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$	−5.00000			−0.435194
$133$		0			0
$134$	2.00000			0.172774
$135$	−1.50000	−	2.59808i	−0.129099	−	0.223607i
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$	0.500000	+	0.866025i	0.0425628	+	0.0737210i
$139$	−6.00000			−0.508913			−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000			−0.508913			−0.254457	+	0.967084i	$0.581897\pi$
$140$	1.50000	+	7.79423i	0.126773	+	0.658733i
$141$	2.00000			0.168430
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	14.0000			1.15865
$147$	1.00000	−	6.92820i	0.0824786	−	0.571429i
$148$	−12.0000			−0.986394
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	0.996207	+	0.0870170i	$0.0277334\pi$
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	−0.422744	+	0.906249i	$0.638933\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	4.50000	−	7.79423i	0.366205	−	0.634285i	−0.622764	−	0.782410i	$-0.713990\pi$
$151$	4.50000	−	7.79423i	0.366205	−	0.634285i	0.988969	+	0.148124i	$0.0473236\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	2.50000	+	12.9904i	0.201456	+	1.04679i
$155$	−27.0000			−2.16869
$156$		0			0
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	−0.661094	−	0.750303i	$-0.729907\pi$
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	0.980329	+	0.197372i	$0.0632408\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	−2.50000	−	4.33013i	−0.198263	−	0.343401i
$160$	−3.00000			−0.237171
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$	−1.00000			−0.0785674
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	−6.00000	+	10.3923i	−0.468521	+	0.811503i
$165$	7.50000	−	12.9904i	0.583874	−	1.01130i
$166$	−8.50000	−	14.7224i	−0.659728	−	1.14268i
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	−13.0000			−1.00000
$170$	−6.00000	−	10.3923i	−0.460179	−	0.797053i
$171$		0			0
$172$	−3.00000	+	5.19615i	−0.228748	+	0.396203i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	3.00000			0.227429
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$	−5.00000			−0.376889
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$	5.00000	−	8.66025i	0.374766	−	0.649113i
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	−0.201613	−	0.979465i	$-0.564618\pi$
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	0.949048	−	0.315130i	$-0.102048\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	18.0000	−	31.1769i	1.32339	−	2.29217i
$186$	−4.50000	+	7.79423i	−0.329956	+	0.571501i
$187$	−10.0000	−	17.3205i	−0.731272	−	1.26660i
$188$	2.00000			0.145865
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$	−6.50000	−	11.2583i	−0.466673	−	0.808301i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	1.00000	+	1.73205i	0.0705346	+	0.122169i
$202$	2.00000			0.140720
$203$	−1.50000	−	7.79423i	−0.105279	−	0.547048i
$204$	−4.00000			−0.280056
$205$	−18.0000	−	31.1769i	−1.25717	−	2.17749i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$		0			0
$209$		0			0
$210$	−6.00000	+	5.19615i	−0.414039	+	0.358569i
$211$	6.00000			0.413057			0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000			0.413057			0.206529	+	0.978441i	$0.433783\pi$
$212$	−2.50000	−	4.33013i	−0.171701	−	0.297394i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	−9.50000	+	16.4545i	−0.649407	+	1.12481i
$215$	−9.00000	−	15.5885i	−0.613795	−	1.06312i
$216$	−1.00000			−0.0680414
$217$	22.5000	+	7.79423i	1.52740	+	0.529107i
$218$	−6.00000			−0.406371
$219$	7.00000	+	12.1244i	0.473016	+	0.819288i
$220$	7.50000	−	12.9904i	0.505650	−	0.875811i
$221$		0			0
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$	13.0000			0.870544			0.435272	−	0.900299i	$-0.356652\pi$
$223$	13.0000			0.870544			0.435272	+	0.900299i	$0.356652\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$	4.00000			0.266667
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	−2.50000	+	4.33013i	−0.165931	+	0.287401i	−0.936985	−	0.349368i	$-0.886396\pi$
$227$	−2.50000	+	4.33013i	−0.165931	+	0.287401i	0.771055	+	0.636769i	$0.219730\pi$
$228$		0			0
$229$	12.0000	+	20.7846i	0.792982	+	1.37349i	0.924113	+	0.382121i	$0.124806\pi$
$229$	12.0000	+	20.7846i	0.792982	+	1.37349i	−0.131130	+	0.991365i	$0.541861\pi$
$230$	−3.00000			−0.197814
$231$	−10.0000	+	8.66025i	−0.657952	+	0.569803i
$232$	3.00000			0.196960
$233$	−10.0000	−	17.3205i	−0.655122	−	1.13470i	−0.981863	−	0.189590i	$-0.939284\pi$
$233$	−10.0000	−	17.3205i	−0.655122	−	1.13470i	0.326741	−	0.945114i	$-0.394049\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$	4.50000	+	7.79423i	0.292925	+	0.507361i
$237$	11.0000			0.714527
$238$	2.00000	+	10.3923i	0.129641	+	0.673633i
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.00000			−0.128037
$245$	16.5000	+	12.9904i	1.05415	+	0.829925i
$246$	−12.0000			−0.765092
$247$		0			0
$248$	−4.50000	+	7.79423i	−0.285750	+	0.494934i
$249$	8.50000	−	14.7224i	0.538666	−	0.932996i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−5.00000			−0.315597			−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000			−0.315597			−0.157799	+	0.987471i	$0.550440\pi$
$252$	0.500000	+	2.59808i	0.0314970	+	0.163663i
$253$	−5.00000			−0.314347
$254$	−5.50000	−	9.52628i	−0.345101	−	0.597732i
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	0.666880	−	0.745165i	$-0.267629\pi$
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	−0.978772	+	0.204953i	$0.934296\pi$
$258$	−6.00000			−0.373544
$259$	−24.0000	+	20.7846i	−1.49129	+	1.29149i
$260$		0			0
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	−2.50000	−	4.33013i	−0.153864	−	0.266501i
$265$	15.0000			0.921443
$266$		0			0
$267$	10.0000			0.611990
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$	1.50000	−	2.59808i	0.0912871	−	0.158114i
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	6.00000			0.362473
$275$	10.0000	+	17.3205i	0.603023	+	1.04447i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−3.00000	−	5.19615i	−0.179928	−	0.311645i
$279$	−9.00000			−0.538816
$280$	−6.00000	+	5.19615i	−0.358569	+	0.310530i
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	1.00000	+	1.73205i	0.0595491	+	0.103142i
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	−0.941309	−	0.337546i	$-0.890403\pi$
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	0.762978	+	0.646425i	$0.223737\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$		0			0
$287$	6.00000	+	31.1769i	0.354169	+	1.84032i
$288$	−1.00000			−0.0589256
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	6.50000	−	11.2583i	0.381037	−	0.659975i
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	33.0000			1.92788			0.963940	−	0.266119i	$-0.0857413\pi$
$293$	33.0000			1.92788			0.963940	+	0.266119i	$0.0857413\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$	−27.0000			−1.57200
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$	−7.00000	+	12.1244i	−0.405499	+	0.702345i
$299$		0			0
$300$	4.00000			0.230940
$301$	3.00000	+	15.5885i	0.172917	+	0.898504i
$302$	9.00000			0.517892
$303$	1.00000	+	1.73205i	0.0574485	+	0.0995037i
$304$		0			0
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	−2.00000	−	3.46410i	−0.114332	−	0.198030i
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	−10.0000	+	8.66025i	−0.569803	+	0.493464i
$309$	8.00000			0.455104
$310$	−13.5000	−	23.3827i	−0.766748	−	1.32805i
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	0.429808	+	0.902920i	$0.358581\pi$
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	−0.996856	+	0.0792356i	$0.974752\pi$
$312$		0			0
$313$	5.50000	+	9.52628i	0.310878	+	0.538457i	0.978553	−	0.205996i	$-0.0660435\pi$
$313$	5.50000	+	9.52628i	0.310878	+	0.538457i	−0.667674	+	0.744453i	$0.732710\pi$
$314$	8.00000			0.451466
$315$	−7.50000	−	2.59808i	−0.422577	−	0.146385i
$316$	11.0000			0.618798
$317$	−2.50000	−	4.33013i	−0.140414	−	0.243204i	0.787239	−	0.616649i	$-0.211510\pi$
$317$	−2.50000	−	4.33013i	−0.140414	−	0.243204i	−0.927653	+	0.373444i	$0.878177\pi$
$318$	2.50000	−	4.33013i	0.140193	−	0.242821i
$319$	−7.50000	+	12.9904i	−0.419919	+	0.727322i
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$	−19.0000			−1.06048
$322$	2.50000	+	0.866025i	0.139320	+	0.0482617i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−10.0000	+	17.3205i	−0.553849	+	0.959294i
$327$	−3.00000	−	5.19615i	−0.165900	−	0.287348i
$328$	−12.0000			−0.662589
$329$	4.00000	−	3.46410i	0.220527	−	0.190982i
$330$	15.0000			0.825723
$331$	8.00000	+	13.8564i	0.439720	+	0.761617i	0.997668	−	0.0682590i	$-0.0217444\pi$
$331$	8.00000	+	13.8564i	0.439720	+	0.761617i	−0.557948	+	0.829876i	$0.688411\pi$
$332$	8.50000	−	14.7224i	0.466498	−	0.807998i
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$	−1.00000	−	1.73205i	−0.0547176	−	0.0947736i
$335$	−6.00000			−0.327815
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$	21.0000			1.14394			0.571971	−	0.820274i	$-0.306179\pi$
$337$	21.0000			1.14394			0.571971	+	0.820274i	$0.306179\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$	−22.5000	−	38.9711i	−1.21844	−	2.11041i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−6.00000			−0.323498
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$	−2.00000	−	10.3923i	−0.106904	−	0.555492i
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	−2.00000	+	3.46410i	−0.106449	+	0.184376i	−0.914329	−	0.404971i	$-0.867282\pi$
$353$	−2.00000	+	3.46410i	−0.106449	+	0.184376i	0.807880	+	0.589347i	$0.200615\pi$
$354$	−4.50000	+	7.79423i	−0.239172	+	0.414259i
$355$	−9.00000	−	15.5885i	−0.477670	−	0.827349i
$356$	10.0000			0.529999
$357$	−8.00000	+	6.92820i	−0.423405	+	0.366679i
$358$	20.0000			1.05703
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$	14.0000			0.734809
$364$		0			0
$365$	−42.0000			−2.19838
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−12.5000	+	21.6506i	−0.652495	+	1.13015i	0.330021	+	0.943974i	$0.392944\pi$
$367$	−12.5000	+	21.6506i	−0.652495	+	1.13015i	−0.982516	+	0.186180i	$0.940389\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	−6.00000	−	10.3923i	−0.312348	−	0.541002i
$370$	36.0000			1.87155
$371$	−12.5000	−	4.33013i	−0.648968	−	0.224809i
$372$	−9.00000			−0.466628
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	0.950804	−	0.309794i	$-0.100260\pi$
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	−0.743691	+	0.668523i	$0.766927\pi$
$374$	10.0000	−	17.3205i	0.517088	−	0.895622i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	1.00000	+	1.73205i	0.0515711	+	0.0893237i
$377$		0			0
$378$	−2.00000	+	1.73205i	−0.102869	+	0.0890871i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	5.50000	−	9.52628i	0.281774	−	0.488046i
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$	−1.00000			−0.0510310
$385$	−7.50000	−	38.9711i	−0.382235	−	1.98615i
$386$	−13.0000			−0.661683
$387$	−3.00000	−	5.19615i	−0.152499	−	0.264135i
$388$	6.50000	−	11.2583i	0.329988	−	0.571555i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	3.00000			0.151330
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−16.5000	+	28.5788i	−0.830205	+	1.43796i
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	4.00000	+	6.92820i	0.200754	+	0.347717i	0.948772	−	0.315963i	$-0.102327\pi$
$397$	4.00000	+	6.92820i	0.200754	+	0.347717i	−0.748017	+	0.663679i	$0.768994\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	4.00000			0.200000
$401$	−16.0000	−	27.7128i	−0.799002	−	1.38391i	−0.920267	−	0.391292i	$-0.872028\pi$
$401$	−16.0000	−	27.7128i	−0.799002	−	1.38391i	0.121265	−	0.992620i	$-0.461305\pi$
$402$	−1.00000	+	1.73205i	−0.0498755	+	0.0863868i
$403$		0			0
$404$	1.00000	+	1.73205i	0.0497519	+	0.0861727i
$405$	3.00000			0.149071
$406$	6.00000	−	5.19615i	0.297775	−	0.257881i
$407$	60.0000			2.97409
$408$	−2.00000	−	3.46410i	−0.0990148	−	0.171499i
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	0.766426	+	0.642333i	$0.222033\pi$
$410$	18.0000	−	31.1769i	0.888957	−	1.53972i
$411$	3.00000	+	5.19615i	0.147979	+	0.256307i
$412$	8.00000			0.394132
$413$	22.5000	+	7.79423i	1.10715	+	0.383529i
$414$	−1.00000			−0.0491473
$415$	25.5000	+	44.1673i	1.25175	+	2.16809i
$416$		0			0
$417$	3.00000	−	5.19615i	0.146911	−	0.254457i
$418$		0			0
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$	−7.50000	−	2.59808i	−0.365963	−	0.126773i
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	3.00000	+	5.19615i	0.146038	+	0.252945i
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	2.50000	−	4.33013i	0.121411	−	0.210290i
$425$	8.00000	+	13.8564i	0.388057	+	0.672134i
$426$	−6.00000			−0.290701
$427$	−4.00000	+	3.46410i	−0.193574	+	0.167640i
$428$	−19.0000			−0.918400
$429$		0			0
$430$	9.00000	−	15.5885i	0.434019	−	0.751742i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	4.50000	+	23.3827i	0.216007	+	1.12240i
$435$	−9.00000			−0.431517
$436$	−3.00000	−	5.19615i	−0.143674	−	0.248851i
$437$		0			0
$438$	−7.00000	+	12.1244i	−0.334473	+	0.579324i
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	−0.668184	+	0.743996i	$0.732928\pi$
$440$	15.0000			0.715097
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	14.5000	+	25.1147i	0.688916	+	1.19324i	0.972189	+	0.234198i	$0.0752464\pi$
$443$	14.5000	+	25.1147i	0.688916	+	1.19324i	−0.283273	+	0.959039i	$0.591420\pi$
$444$	6.00000	−	10.3923i	0.284747	−	0.493197i
$445$	−15.0000	+	25.9808i	−0.711068	+	1.23161i
$446$	6.50000	+	11.2583i	0.307784	+	0.533097i
$447$	−14.0000			−0.662177
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	30.0000	−	51.9615i	1.41264	−	2.44677i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	4.50000	+	7.79423i	0.211428	+	0.366205i
$454$	−5.00000			−0.234662
$455$		0			0
$456$		0			0
$457$	10.5000	+	18.1865i	0.491169	+	0.850730i	0.999948	−	0.0101670i	$-0.00323631\pi$
$457$	10.5000	+	18.1865i	0.491169	+	0.850730i	−0.508779	+	0.860897i	$0.669903\pi$
$458$	−12.0000	+	20.7846i	−0.560723	+	0.971201i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$	−12.5000	−	4.33013i	−0.581553	−	0.201456i
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	13.5000	−	23.3827i	0.626048	−	1.08435i
$466$	10.0000	−	17.3205i	0.463241	−	0.802357i
$467$	−14.0000	−	24.2487i	−0.647843	−	1.12210i	−0.983637	−	0.180161i	$-0.942338\pi$
$467$	−14.0000	−	24.2487i	−0.647843	−	1.12210i	0.335794	−	0.941935i	$-0.390995\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$	−6.00000			−0.276759
$471$	4.00000	+	6.92820i	0.184310	+	0.319235i
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$	15.0000	−	25.9808i	0.689701	−	1.19460i
$474$	5.50000	+	9.52628i	0.252623	+	0.437557i
$475$		0			0
$476$	−8.00000	+	6.92820i	−0.366679	+	0.317554i
$477$	5.00000			0.228934
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$		0			0
$482$	−19.0000			−0.865426
$483$	0.500000	+	2.59808i	0.0227508	+	0.118217i
$484$	14.0000			0.636364
$485$	19.5000	+	33.7750i	0.885449	+	1.53364i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	−0.478584	−	0.878042i	$-0.658850\pi$
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	0.999698	−	0.0245553i	$-0.00781698\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	−20.0000			−0.904431
$490$	−3.00000	+	20.7846i	−0.135526	+	0.938953i
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$		0			0
$495$	7.50000	+	12.9904i	0.337100	+	0.583874i
$496$	−9.00000			−0.404112
$497$	3.00000	+	15.5885i	0.134568	+	0.699238i
$498$	17.0000			0.761788
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	1.00000	−	1.73205i	0.0446767	−	0.0773823i
$502$	−2.50000	−	4.33013i	−0.111580	−	0.193263i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$	−2.00000	+	1.73205i	−0.0890871	+	0.0771517i
$505$	−6.00000			−0.266996
$506$	−2.50000	−	4.33013i	−0.111139	−	0.192498i
$507$	6.50000	−	11.2583i	0.288675	−	0.500000i
$508$	5.50000	−	9.52628i	0.244023	−	0.422660i
$509$	15.5000	+	26.8468i	0.687025	+	1.18996i	0.972796	+	0.231665i	$0.0744172\pi$
$509$	15.5000	+	26.8468i	0.687025	+	1.18996i	−0.285770	+	0.958298i	$0.592249\pi$
$510$	12.0000			0.531369
$511$	35.0000	+	12.1244i	1.54831	+	0.536350i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.00000	−	8.66025i	0.220541	−	0.381987i
$515$	−12.0000	+	20.7846i	−0.528783	+	0.915879i
$516$	−3.00000	−	5.19615i	−0.132068	−	0.228748i
$517$	−10.0000			−0.439799
$518$	−30.0000	−	10.3923i	−1.31812	−	0.456612i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	−0.927746	−	0.373213i	$-0.878256\pi$
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	0.140660	−	0.990058i	$-0.455077\pi$
$524$	3.00000			0.131056
$525$	8.00000	−	6.92820i	0.349149	−	0.302372i
$526$	−18.0000			−0.784837
$527$	−18.0000	−	31.1769i	−0.784092	−	1.35809i
$528$	2.50000	−	4.33013i	0.108799	−	0.188445i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	7.50000	+	12.9904i	0.325779	+	0.564266i
$531$	−9.00000			−0.390567
$532$		0			0
$533$		0			0
$534$	5.00000	+	8.66025i	0.216371	+	0.374766i
$535$	28.5000	−	49.3634i	1.23216	−	2.13417i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	10.0000	+	17.3205i	0.431532	+	0.747435i
$538$	−9.00000			−0.388018
$539$	−5.00000	+	34.6410i	−0.215365	+	1.49209i
$540$	3.00000			0.129099
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	0.956504	+	0.291718i	$0.0942267\pi$
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	−0.225617	+	0.974216i	$0.572440\pi$
$542$	−6.50000	+	11.2583i	−0.279199	+	0.483587i
$543$	4.00000	−	6.92820i	0.171656	−	0.297318i
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$	18.0000			0.771035
$546$		0			0
$547$	−44.0000			−1.88130			−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000			−1.88130			−0.940652	+	0.339372i	$0.889785\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−10.0000	+	17.3205i	−0.426401	+	0.738549i
$551$		0			0
$552$	−1.00000			−0.0425628
$553$	22.0000	−	19.0526i	0.935535	−	0.810197i
$554$	−8.00000			−0.339887
$555$	18.0000	+	31.1769i	0.764057	+	1.32339i
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	−0.896053	−	0.443947i	$-0.853578\pi$
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	0.832496	+	0.554031i	$0.186911\pi$
$558$	−4.50000	−	7.79423i	−0.190500	−	0.329956i
$559$		0			0
$560$	−7.50000	−	2.59808i	−0.316933	−	0.109789i
$561$	20.0000			0.844401
$562$	1.00000	+	1.73205i	0.0421825	+	0.0730622i
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$	−1.00000	+	1.73205i	−0.0421076	+	0.0729325i
$565$	−18.0000	−	31.1769i	−0.757266	−	1.31162i
$566$	−6.00000			−0.252199
$567$	−2.50000	−	0.866025i	−0.104990	−	0.0363696i
$568$	−6.00000			−0.251754
$569$	−10.0000	−	17.3205i	−0.419222	−	0.726113i	0.576640	−	0.816999i	$-0.304364\pi$
$569$	−10.0000	−	17.3205i	−0.419222	−	0.726113i	−0.995861	+	0.0908852i	$0.971030\pi$
$570$		0			0
$571$	−5.00000	+	8.66025i	−0.209243	+	0.362420i	−0.951476	−	0.307722i	$-0.900433\pi$
$571$	−5.00000	+	8.66025i	−0.209243	+	0.362420i	0.742233	+	0.670142i	$0.233767\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$	−24.0000	+	20.7846i	−1.00174	+	0.867533i
$575$	4.00000			0.166812
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	0.0998105	+	0.995006i	$0.468176\pi$
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	−0.911606	+	0.411065i	$0.865157\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	−6.50000	−	11.2583i	−0.270131	−	0.467880i
$580$	−9.00000			−0.373705
$581$	−8.50000	−	44.1673i	−0.352639	−	1.83237i
$582$	13.0000			0.538867
$583$	12.5000	+	21.6506i	0.517697	+	0.896678i
$584$	−7.00000	+	12.1244i	−0.289662	+	0.501709i
$585$		0			0
$586$	16.5000	+	28.5788i	0.681609	+	1.18058i
$587$	−15.0000			−0.619116			−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000			−0.619116			−0.309558	+	0.950881i	$0.600181\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$		0			0
$590$	−13.5000	−	23.3827i	−0.555786	−	0.962650i
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	−4.00000	−	6.92820i	−0.164260	−	0.284507i	0.772132	−	0.635462i	$-0.219190\pi$
$593$	−4.00000	−	6.92820i	−0.164260	−	0.284507i	−0.936392	+	0.350955i	$0.885857\pi$
$594$	5.00000			0.205152
$595$	−6.00000	−	31.1769i	−0.245976	−	1.27813i
$596$	−14.0000			−0.573462
$597$	10.0000	+	17.3205i	0.409273	+	0.708881i
$598$		0			0
$599$	11.0000	−	19.0526i	0.449448	−	0.778466i	−0.548902	−	0.835887i	$-0.684954\pi$
$599$	11.0000	−	19.0526i	0.449448	−	0.778466i	0.998350	+	0.0574201i	$0.0182874\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$	−12.0000	+	10.3923i	−0.489083	+	0.423559i
$603$	−2.00000			−0.0814463
$604$	4.50000	+	7.79423i	0.183102	+	0.317143i
$605$	−21.0000	+	36.3731i	−0.853771	+	1.47878i
$606$	−1.00000	+	1.73205i	−0.0406222	+	0.0703598i
$607$	7.50000	+	12.9904i	0.304416	+	0.527263i	0.977131	−	0.212638i	$-0.0682055\pi$
$607$	7.50000	+	12.9904i	0.304416	+	0.527263i	−0.672715	+	0.739901i	$0.734872\pi$
$608$		0			0
$609$	7.50000	+	2.59808i	0.303915	+	0.105279i
$610$	6.00000			0.242933
$611$		0			0
$612$	2.00000	−	3.46410i	0.0808452	−	0.140028i
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	−0.981129	−	0.193352i	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$	36.0000			1.45166
$616$	−12.5000	−	4.33013i	−0.503639	−	0.174466i
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.132002	−	0.991250i	$-0.457860\pi$
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.792446	−	0.609941i	$-0.208807\pi$
$620$	13.5000	−	23.3827i	0.542173	−	0.939071i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	−20.0000			−0.801927
$623$	20.0000	−	17.3205i	0.801283	−	0.693932i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−5.50000	+	9.52628i	−0.219824	+	0.380747i
$627$		0			0
$628$	4.00000	+	6.92820i	0.159617	+	0.276465i
$629$	48.0000			1.91389
$630$	−1.50000	−	7.79423i	−0.0597614	−	0.310530i
$631$	37.0000			1.47295			0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000			1.47295			0.736473	+	0.676467i	$0.236490\pi$
$632$	5.50000	+	9.52628i	0.218778	+	0.378935i
$633$	−3.00000	+	5.19615i	−0.119239	+	0.206529i
$634$	2.50000	−	4.33013i	0.0992877	−	0.171971i
$635$	16.5000	+	28.5788i	0.654783	+	1.13412i
$636$	5.00000			0.198263
$637$		0			0
$638$	−15.0000			−0.593856
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$	−9.50000	−	16.4545i	−0.374935	−	0.649407i
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$	0.500000	+	2.59808i	0.0197028	+	0.102379i
$645$	18.0000			0.708749
$646$		0			0
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−22.5000	−	38.9711i	−0.883202	−	1.52975i
$650$		0			0
$651$	−18.0000	+	15.5885i	−0.705476	+	0.610960i
$652$	−20.0000			−0.783260
$653$	8.50000	+	14.7224i	0.332631	+	0.576133i	0.983027	−	0.183462i	$-0.0587304\pi$
$653$	8.50000	+	14.7224i	0.332631	+	0.576133i	−0.650396	+	0.759595i	$0.725397\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$	−4.50000	+	7.79423i	−0.175830	+	0.304546i
$656$	−6.00000	−	10.3923i	−0.234261	−	0.405751i
$657$	−14.0000			−0.546192
$658$	5.00000	+	1.73205i	0.194920	+	0.0675224i
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$	7.50000	+	12.9904i	0.291937	+	0.505650i
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−8.00000	+	13.8564i	−0.310929	+	0.538545i
$663$		0			0
$664$	17.0000			0.659728
$665$		0			0
$666$	12.0000			0.464991
$667$	1.50000	+	2.59808i	0.0580802	+	0.100598i
$668$	1.00000	−	1.73205i	0.0386912	−	0.0670151i
$669$	−6.50000	+	11.2583i	−0.251305	+	0.435272i
$670$	−3.00000	−	5.19615i	−0.115900	−	0.200745i
$671$	10.0000			0.386046
$672$	−2.00000	+	1.73205i	−0.0771517	+	0.0668153i
$673$	13.0000			0.501113			0.250557	−	0.968102i	$-0.419386\pi$
$673$	13.0000			0.501113			0.250557	+	0.968102i	$0.419386\pi$
$674$	10.5000	+	18.1865i	0.404445	+	0.700519i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−15.5000	−	26.8468i	−0.595713	−	1.03181i	−0.993446	−	0.114304i	$-0.963536\pi$
$677$	−15.5000	−	26.8468i	−0.595713	−	1.03181i	0.397732	−	0.917501i	$-0.369797\pi$
$678$	−12.0000			−0.460857
$679$	−6.50000	−	33.7750i	−0.249447	−	1.29617i
$680$	12.0000			0.460179
$681$	−2.50000	−	4.33013i	−0.0958002	−	0.165931i
$682$	22.5000	−	38.9711i	0.861570	−	1.49228i
$683$	21.5000	−	37.2391i	0.822675	−	1.42491i	−0.0810089	−	0.996713i	$-0.525814\pi$
$683$	21.5000	−	37.2391i	0.822675	−	1.42491i	0.903684	−	0.428201i	$-0.140852\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	−24.0000			−0.915657
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$		0			0
$690$	1.50000	−	2.59808i	0.0571040	−	0.0989071i
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$	−6.00000			−0.228086
$693$	−2.50000	−	12.9904i	−0.0949671	−	0.493464i
$694$	4.00000			0.151838
$695$	9.00000	+	15.5885i	0.341389	+	0.591304i
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$	24.0000	−	41.5692i	0.909065	−	1.57455i
$698$	11.0000	+	19.0526i	0.416356	+	0.721150i
$699$	20.0000			0.756469
$700$	8.00000	−	6.92820i	0.302372	−	0.261861i
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$		0			0
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$	−4.00000			−0.150542
$707$	5.00000	+	1.73205i	0.188044	+	0.0651405i
$708$	−9.00000			−0.338241
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	0.995228	−	0.0975728i	$-0.0311079\pi$
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	−0.582115	+	0.813107i	$0.697775\pi$
$710$	9.00000	−	15.5885i	0.337764	−	0.585024i
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$	5.00000	+	8.66025i	0.187383	+	0.324557i
$713$	−9.00000			−0.337053
$714$	−10.0000	−	3.46410i	−0.374241	−	0.129641i
$715$		0			0
$716$	10.0000	+	17.3205i	0.373718	+	0.647298i
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	−7.00000	−	12.1244i	−0.261056	−	0.452162i	0.705467	−	0.708743i	$-0.250737\pi$
$719$	−7.00000	−	12.1244i	−0.261056	−	0.452162i	−0.966523	+	0.256581i	$0.917404\pi$
$720$	3.00000			0.111803
$721$	16.0000	−	13.8564i	0.595871	−	0.516040i
$722$	19.0000			0.707107
$723$	−9.50000	−	16.4545i	−0.353309	−	0.611949i
$724$	4.00000	−	6.92820i	0.148659	−	0.257485i
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$	7.00000			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−21.0000	−	36.3731i	−0.777245	−	1.34623i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$	23.0000	+	39.8372i	0.849524	+	1.47142i	0.881633	+	0.471935i	$0.156444\pi$
$733$	23.0000	+	39.8372i	0.849524	+	1.47142i	−0.0321090	+	0.999484i	$0.510222\pi$
$734$	−25.0000			−0.922767
$735$	−19.5000	+	7.79423i	−0.719268	+	0.287494i
$736$	−1.00000			−0.0368605
$737$	−5.00000	−	8.66025i	−0.184177	−	0.319005i
$738$	6.00000	−	10.3923i	0.220863	−	0.382546i
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	−0.883832	−	0.467804i	$-0.845045\pi$
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	0.847046	+	0.531519i	$0.178379\pi$
$740$	18.0000	+	31.1769i	0.661693	+	1.14609i
$741$		0			0
$742$	−2.50000	−	12.9904i	−0.0917779	−	0.476892i
$743$	−26.0000			−0.953847			−0.476924	−	0.878945i	$-0.658248\pi$
$743$	−26.0000			−0.953847			−0.476924	+	0.878945i	$0.658248\pi$
$744$	−4.50000	−	7.79423i	−0.164978	−	0.285750i
$745$	21.0000	−	36.3731i	0.769380	−	1.33261i
$746$	−4.00000	+	6.92820i	−0.146450	+	0.253660i
$747$	8.50000	+	14.7224i	0.310999	+	0.538666i
$748$	20.0000			0.731272
$749$	−38.0000	+	32.9090i	−1.38849	+	1.20247i
$750$	3.00000			0.109545
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	0.816801	−	0.576919i	$-0.195745\pi$
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	−0.908027	+	0.418911i	$0.862412\pi$
$752$	−1.00000	+	1.73205i	−0.0364662	+	0.0631614i
$753$	2.50000	−	4.33013i	0.0911051	−	0.157799i
$754$		0			0
$755$	−27.0000			−0.982631
$756$	−2.50000	−	0.866025i	−0.0909241	−	0.0314970i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	2.50000	−	4.33013i	0.0907443	−	0.157174i
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$	11.0000			0.398488
$763$	−15.0000	−	5.19615i	−0.543036	−	0.188113i
$764$	12.0000			0.434145
$765$	6.00000	+	10.3923i	0.216930	+	0.375735i
$766$	−9.00000	+	15.5885i	−0.325183	+	0.563234i
$767$		0			0
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−31.0000			−1.11789			−0.558944	−	0.829205i	$-0.688793\pi$
$769$	−31.0000			−1.11789			−0.558944	+	0.829205i	$0.688793\pi$
$770$	30.0000	−	25.9808i	1.08112	−	0.936282i
$771$	10.0000			0.360141
$772$	−6.50000	−	11.2583i	−0.233940	−	0.405196i
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	0.0729331	+	0.997337i	$0.476764\pi$
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	−0.900186	+	0.435507i	$0.856569\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$	18.0000	+	31.1769i	0.646579	+	1.11991i
$776$	13.0000			0.466673
$777$	−6.00000	−	31.1769i	−0.215249	−	1.11847i
$778$	−18.0000			−0.645331
$779$		0			0
$780$		0			0
$781$	15.0000	−	25.9808i	0.536742	−	0.929665i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$	−3.00000			−0.107211
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−24.0000			−0.856597
$786$	1.50000	+	2.59808i	0.0535032	+	0.0926703i
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$	−9.00000	−	15.5885i	−0.320408	−	0.554964i
$790$	−33.0000			−1.17409
$791$	6.00000	+	31.1769i	0.213335	+	1.10852i
$792$	5.00000			0.177667
$793$		0			0
$794$	−4.00000	+	6.92820i	−0.141955	+	0.245873i
$795$	−7.50000	+	12.9904i	−0.265998	+	0.460721i
$796$	10.0000	+	17.3205i	0.354441	+	0.613909i
$797$	−49.0000			−1.73567			−0.867835	−	0.496853i	$-0.834489\pi$
$797$	−49.0000			−1.73567			−0.867835	+	0.496853i	$0.834489\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	−5.00000	+	8.66025i	−0.176666	+	0.305995i
$802$	16.0000	−	27.7128i	0.564980	−	0.978573i
$803$	−35.0000	−	60.6218i	−1.23512	−	2.13930i
$804$	−2.00000			−0.0705346
$805$	−7.50000	−	2.59808i	−0.264340	−	0.0915702i
$806$		0			0
$807$	−4.50000	−	7.79423i	−0.158408	−	0.274370i
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	−22.0000	+	38.1051i	−0.773479	+	1.33970i	0.162167	+	0.986763i	$0.448152\pi$
$809$	−22.0000	+	38.1051i	−0.773479	+	1.33970i	−0.935645	+	0.352941i	$0.885182\pi$
$810$	1.50000	+	2.59808i	0.0527046	+	0.0912871i
$811$	42.0000			1.47482			0.737410	−	0.675446i	$-0.236049\pi$
$811$	42.0000			1.47482			0.737410	+	0.675446i	$0.236049\pi$
$812$	7.50000	+	2.59808i	0.263198	+	0.0911746i
$813$	−13.0000			−0.455930
$814$	30.0000	+	51.9615i	1.05150	+	1.82125i
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$		0			0
$818$	−7.00000			−0.244749
$819$		0			0
$820$	36.0000			1.25717
$821$	−28.5000	−	49.3634i	−0.994657	−	1.72280i	−0.586734	−	0.809780i	$-0.699586\pi$
$821$	−28.5000	−	49.3634i	−0.994657	−	1.72280i	−0.407923	−	0.913016i	$-0.633747\pi$
$822$	−3.00000	+	5.19615i	−0.104637	+	0.181237i
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$	−20.0000			−0.696311
$826$	4.50000	+	23.3827i	0.156575	+	0.813588i
$827$	−33.0000			−1.14752			−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000			−1.14752			−0.573761	+	0.819023i	$0.694516\pi$
$828$	−0.500000	−	0.866025i	−0.0173762	−	0.0300965i
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	−0.985771	−	0.168091i	$-0.946240\pi$
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	0.638457	+	0.769657i	$0.279573\pi$
$830$	−25.5000	+	44.1673i	−0.885118	+	1.53307i
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$		0			0
$833$	−4.00000	+	27.7128i	−0.138592	+	0.960192i
$834$	6.00000			0.207763
$835$	3.00000	+	5.19615i	0.103819	+	0.179820i
$836$		0			0
$837$	4.50000	−	7.79423i	0.155543	−	0.269408i
$838$	−8.00000	−	13.8564i	−0.276355	−	0.478662i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$	−1.50000	−	7.79423i	−0.0517549	−	0.268926i
$841$	−20.0000			−0.689655
$842$	−3.00000	−	5.19615i	−0.103387	−	0.179071i
$843$	−1.00000	+	1.73205i	−0.0344418	+	0.0596550i
$844$	−3.00000	+	5.19615i	−0.103264	+	0.178859i
$845$	19.5000	+	33.7750i	0.670820	+	1.16190i
$846$	−2.00000			−0.0687614
$847$	28.0000	−	24.2487i	0.962091	−	0.833196i
$848$	5.00000			0.171701
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$	−8.00000	+	13.8564i	−0.274398	+	0.475271i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	−3.00000	−	5.19615i	−0.102778	−	0.178017i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	−5.00000	−	1.73205i	−0.171096	−	0.0592696i
$855$		0			0
$856$	−9.50000	−	16.4545i	−0.324703	−	0.562403i
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.126459	−	0.991972i	$-0.459639\pi$
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.795843	−	0.605503i	$-0.207028\pi$
$858$		0			0
$859$	−11.0000	−	19.0526i	−0.375315	−	0.650065i	0.615059	−	0.788481i	$-0.289132\pi$
$859$	−11.0000	−	19.0526i	−0.375315	−	0.650065i	−0.990374	+	0.138416i	$0.955799\pi$
$860$	18.0000			0.613795
$861$	−30.0000	−	10.3923i	−1.02240	−	0.354169i
$862$	12.0000			0.408722
$863$	7.00000	+	12.1244i	0.238283	+	0.412718i	0.960222	−	0.279239i	$-0.0900822\pi$
$863$	7.00000	+	12.1244i	0.238283	+	0.412718i	−0.721939	+	0.691957i	$0.756749\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$	−1.00000			−0.0339618
$868$	−18.0000	+	15.5885i	−0.610960	+	0.529107i
$869$	−55.0000			−1.86575
$870$	−4.50000	−	7.79423i	−0.152564	−	0.264249i
$871$		0			0
$872$	3.00000	−	5.19615i	0.101593	−	0.175964i
$873$	6.50000	+	11.2583i	0.219992	+	0.381037i
$874$		0			0
$875$	−1.50000	−	7.79423i	−0.0507093	−	0.263493i
$876$	−14.0000			−0.473016
$877$	6.00000	+	10.3923i	0.202606	+	0.350923i	0.949367	−	0.314169i	$-0.101726\pi$
$877$	6.00000	+	10.3923i	0.202606	+	0.350923i	−0.746762	+	0.665092i	$0.768392\pi$
$878$	−6.50000	+	11.2583i	−0.219364	+	0.379950i
$879$	−16.5000	+	28.5788i	−0.556531	+	0.963940i
$880$	7.50000	+	12.9904i	0.252825	+	0.437906i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	−1.00000	+	6.92820i	−0.0336718	+	0.233285i
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$		0			0
$885$	13.5000	−	23.3827i	0.453798	−	0.786000i
$886$	−14.5000	+	25.1147i	−0.487137	+	0.843746i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$	12.0000			0.402694
$889$	−5.50000	−	28.5788i	−0.184464	−	0.958503i
$890$	−30.0000			−1.00560
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	−6.50000	+	11.2583i	−0.217636	+	0.376957i
$893$		0			0
$894$	−7.00000	−	12.1244i	−0.234115	−	0.405499i
$895$	−60.0000			−2.00558
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		0			0
$898$		0			0
$899$	−13.5000	+	23.3827i	−0.450250	+	0.779856i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$	60.0000			1.99778
$903$	−15.0000	−	5.19615i	−0.499169	−	0.172917i
$904$	−12.0000			−0.399114
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$	−4.50000	+	7.79423i	−0.149502	+	0.258946i
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	−0.226173	−	0.974087i	$-0.572621\pi$
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	0.956671	−	0.291172i	$-0.0940453\pi$
$908$	−2.50000	−	4.33013i	−0.0829654	−	0.143700i
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	−10.0000			−0.331315			−0.165657	−	0.986183i	$-0.552975\pi$
$911$	−10.0000			−0.331315			−0.165657	+	0.986183i	$0.552975\pi$
$912$		0			0
$913$	−42.5000	+	73.6122i	−1.40654	+	2.43621i
$914$	−10.5000	+	18.1865i	−0.347309	+	0.601557i
$915$	3.00000	+	5.19615i	0.0991769	+	0.171780i
$916$	−24.0000			−0.792982
$917$	6.00000	−	5.19615i	0.198137	−	0.171592i
$918$	4.00000			0.132020
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	0.993208	−	0.116348i	$-0.0371189\pi$
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	−0.597365	+	0.801970i	$0.703786\pi$
$920$	1.50000	−	2.59808i	0.0494535	−	0.0856560i
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$		0			0
$924$	−2.50000	−	12.9904i	−0.0822440	−	0.427352i
$925$	−48.0000			−1.57823
$926$	−16.0000	−	27.7128i	−0.525793	−	0.910700i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$	27.0000			0.885365
$931$		0			0
$932$	20.0000			0.655122
$933$	−10.0000	−	17.3205i	−0.327385	−	0.567048i
$934$	14.0000	−	24.2487i	0.458094	−	0.793442i
$935$	−30.0000	+	51.9615i	−0.981105	+	1.69932i
$936$		0			0
$937$	7.00000			0.228680			0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000			0.228680			0.114340	+	0.993442i	$0.463525\pi$
$938$	1.00000	+	5.19615i	0.0326512	+	0.169660i
$939$	−11.0000			−0.358971
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−7.50000	+	12.9904i	−0.244493	+	0.423474i	−0.961989	−	0.273088i	$-0.911955\pi$
$941$	−7.50000	+	12.9904i	−0.244493	+	0.423474i	0.717496	+	0.696563i	$0.245288\pi$
$942$	−4.00000	+	6.92820i	−0.130327	+	0.225733i
$943$	−6.00000	−	10.3923i	−0.195387	−	0.338420i
$944$	−9.00000			−0.292925
$945$	6.00000	−	5.19615i	0.195180	−	0.169031i
$946$	30.0000			0.975384
$947$	−4.00000	−	6.92820i	−0.129983	−	0.225136i	0.793687	−	0.608326i	$-0.208159\pi$
$947$	−4.00000	−	6.92820i	−0.129983	−	0.225136i	−0.923670	+	0.383190i	$0.874825\pi$
$948$	−5.50000	+	9.52628i	−0.178632	+	0.309399i
$949$		0			0
$950$		0			0
$951$	5.00000			0.162136
$952$	−10.0000	−	3.46410i	−0.324102	−	0.112272i
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	2.50000	+	4.33013i	0.0809405	+	0.140193i
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$	−7.50000	−	12.9904i	−0.242441	−	0.419919i
$958$	−18.0000			−0.581554
$959$	15.0000	+	5.19615i	0.484375	+	0.167793i
$960$	3.00000			0.0968246
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$		0			0
$963$	9.50000	−	16.4545i	0.306133	−	0.530238i
$964$	−9.50000	−	16.4545i	−0.305974	−	0.529963i
$965$	39.0000			1.25545
$966$	−2.00000	+	1.73205i	−0.0643489	+	0.0557278i
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$		0			0
$970$	−19.5000	+	33.7750i	−0.626107	+	1.08445i
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$	1.00000			0.0320750
$973$	−3.00000	−	15.5885i	−0.0961756	−	0.499743i
$974$	23.0000			0.736968
$975$		0			0
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	31.0000	−	53.6936i	0.991778	−	1.71781i	0.385063	−	0.922890i	$-0.374180\pi$
$977$	31.0000	−	53.6936i	0.991778	−	1.71781i	0.606715	−	0.794919i	$-0.292487\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	−50.0000			−1.59801
$980$	−19.5000	+	7.79423i	−0.622905	+	0.248978i
$981$	6.00000			0.191565
$982$	13.5000	+	23.3827i	0.430802	+	0.746171i
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$	6.00000	−	10.3923i	0.191273	−	0.331295i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	−12.0000			−0.382158
$987$	1.00000	+	5.19615i	0.0318304	+	0.165395i
$988$		0			0
$989$	−3.00000	−	5.19615i	−0.0953945	−	0.165228i
$990$	−7.50000	+	12.9904i	−0.238366	+	0.412861i
$991$	−25.5000	+	44.1673i	−0.810034	+	1.40302i	0.102805	+	0.994702i	$0.467218\pi$
$991$	−25.5000	+	44.1673i	−0.810034	+	1.40302i	−0.912839	+	0.408319i	$0.866115\pi$
$992$	−4.50000	−	7.79423i	−0.142875	−	0.247467i
$993$	−16.0000			−0.507745
$994$	−12.0000	+	10.3923i	−0.380617	+	0.329624i
$995$	−60.0000			−1.90213
$996$	8.50000	+	14.7224i	0.269333	+	0.466498i
$997$	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	$0.0534008\pi$
$998$	5.00000	−	8.66025i	0.158272	−	0.274136i
$999$	6.00000	+	10.3923i	0.189832	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.e.277.1	✓	2
7.2	even	3	inner	966.2.i.e.415.1	yes	2
7.3	odd	6		6762.2.a.a.1.1		1
7.4	even	3		6762.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.e.277.1	✓	2	1.1	even	1	trivial
966.2.i.e.415.1	yes	2	7.2	even	3	inner
6762.2.a.a.1.1		1	7.3	odd	6
6762.2.a.t.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{18} +3.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} +5.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -3.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(4.50000 - 7.79423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} +4.00000 q^{34} +(6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(6.00000 + 10.3923i) q^{37} +(1.50000 + 2.59808i) q^{40} +12.0000 q^{41} +(-0.500000 - 2.59808i) q^{42} +6.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-1.00000 - 1.73205i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(-2.50000 + 4.33013i) q^{53} +(0.500000 + 0.866025i) q^{54} -15.0000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +9.00000 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +1.00000 q^{69} +(7.50000 + 2.59808i) q^{70} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-6.00000 + 10.3923i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(12.5000 + 4.33013i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.00000 + 10.3923i) q^{82} -17.0000 q^{83} +(2.00000 - 1.73205i) q^{84} -12.0000 q^{85} +(3.00000 + 5.19615i) q^{86} +(1.50000 - 2.59808i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-5.00000 - 8.66025i) q^{89} -3.00000 q^{90} +1.00000 q^{92} +(4.50000 + 7.79423i) q^{93} +(1.00000 - 1.73205i) q^{94} +(0.500000 + 0.866025i) q^{96} -13.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 4 q^{14} + 6 q^{15} - q^{16} + 4 q^{17} + q^{18} + 6 q^{20} - 5 q^{21} + 10 q^{22} - q^{23} + q^{24} - 4 q^{25} + 2 q^{27} - 5 q^{28} - 6 q^{29} + 3 q^{30} + 9 q^{31} + q^{32} + 5 q^{33} + 8 q^{34} + 12 q^{35} + 2 q^{36} + 12 q^{37} + 3 q^{40} + 24 q^{41} - q^{42} + 12 q^{43} + 5 q^{44} - 3 q^{45} + q^{46} - 2 q^{47} + 2 q^{48} - 13 q^{49} - 8 q^{50} + 4 q^{51} - 5 q^{53} + q^{54} - 30 q^{55} - q^{56} - 3 q^{58} + 9 q^{59} - 3 q^{60} + 2 q^{61} + 18 q^{62} + 4 q^{63} + 2 q^{64} - 5 q^{66} + 2 q^{67} + 4 q^{68} + 2 q^{69} + 15 q^{70} + 12 q^{71} + q^{72} + 14 q^{73} - 12 q^{74} - 4 q^{75} + 25 q^{77} - 11 q^{79} - 3 q^{80} - q^{81} + 12 q^{82} - 34 q^{83} + 4 q^{84} - 24 q^{85} + 6 q^{86} + 3 q^{87} - 5 q^{88} - 10 q^{89} - 6 q^{90} + 2 q^{92} + 9 q^{93} + 2 q^{94} + q^{96} - 26 q^{97} - 11 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9 + 3 * q^10 + 5 * q^11 - q^12 - 4 * q^14 + 6 * q^15 - q^16 + 4 * q^17 + q^18 + 6 * q^20 - 5 * q^21 + 10 * q^22 - q^23 + q^24 - 4 * q^25 + 2 * q^27 - 5 * q^28 - 6 * q^29 + 3 * q^30 + 9 * q^31 + q^32 + 5 * q^33 + 8 * q^34 + 12 * q^35 + 2 * q^36 + 12 * q^37 + 3 * q^40 + 24 * q^41 - q^42 + 12 * q^43 + 5 * q^44 - 3 * q^45 + q^46 - 2 * q^47 + 2 * q^48 - 13 * q^49 - 8 * q^50 + 4 * q^51 - 5 * q^53 + q^54 - 30 * q^55 - q^56 - 3 * q^58 + 9 * q^59 - 3 * q^60 + 2 * q^61 + 18 * q^62 + 4 * q^63 + 2 * q^64 - 5 * q^66 + 2 * q^67 + 4 * q^68 + 2 * q^69 + 15 * q^70 + 12 * q^71 + q^72 + 14 * q^73 - 12 * q^74 - 4 * q^75 + 25 * q^77 - 11 * q^79 - 3 * q^80 - q^81 + 12 * q^82 - 34 * q^83 + 4 * q^84 - 24 * q^85 + 6 * q^86 + 3 * q^87 - 5 * q^88 - 10 * q^89 - 6 * q^90 + 2 * q^92 + 9 * q^93 + 2 * q^94 + q^96 - 26 * q^97 - 11 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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