LMFDB - Embedded newform 858.2.i.h.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [858,2,Mod(133,858)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(858, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("858.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 858 = 2 \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	858.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:	$6.85116449343$
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			133.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	858.133
Dual form			858.2.i.h.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} -4.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} -1.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.00000 q^{34} +(-4.00000 + 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.00000 + 6.92820i) q^{37} +1.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} -2.00000 q^{40} +(4.00000 + 6.92820i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(0.500000 - 0.866025i) q^{43} -1.00000 q^{44} +(-1.00000 + 1.73205i) q^{45} +(3.50000 - 6.06218i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +4.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +8.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(2.00000 - 3.46410i) q^{56} +1.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(2.00000 - 3.46410i) q^{59} -2.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-2.00000 + 6.92820i) q^{65} -1.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +(3.50000 - 6.06218i) q^{69} -8.00000 q^{70} +(-1.50000 + 2.59808i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(0.500000 + 0.866025i) q^{76} -4.00000 q^{77} +(-2.50000 - 2.59808i) q^{78} -4.00000 q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.00000 + 6.92820i) q^{82} +3.00000 q^{83} +(2.00000 - 3.46410i) q^{84} +(4.00000 - 6.92820i) q^{85} +1.00000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.50000 + 6.06218i) q^{89} -2.00000 q^{90} +(-10.0000 - 10.3923i) q^{91} +7.00000 q^{92} +(-3.50000 - 6.06218i) q^{94} +(1.00000 - 1.73205i) q^{95} +1.00000 q^{96} +(6.50000 - 11.2583i) q^{97} +(4.50000 - 7.79423i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 4 * q^5 - q^6 - 4 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + q^{11} - 2 q^{12} - 2 q^{13} - 8 q^{14} + 2 q^{15} - q^{16} + 4 q^{17} - 2 q^{18} + q^{19} - 2 q^{20} - 8 q^{21} - q^{22} - 7 q^{23} - q^{24} - 2 q^{25} - 7 q^{26} - 2 q^{27} - 4 q^{28} + 5 q^{29} - 2 q^{30} + q^{32} - q^{33} + 8 q^{34} - 8 q^{35} - q^{36} + 8 q^{37} + 2 q^{38} - 7 q^{39} - 4 q^{40} + 8 q^{41} - 4 q^{42} + q^{43} - 2 q^{44} - 2 q^{45} + 7 q^{46} - 14 q^{47} + q^{48} - 9 q^{49} - q^{50} + 8 q^{51} - 5 q^{52} + 16 q^{53} - q^{54} + 2 q^{55} + 4 q^{56} + 2 q^{57} - 5 q^{58} + 4 q^{59} - 4 q^{60} + 2 q^{61} - 4 q^{63} + 2 q^{64} - 4 q^{65} - 2 q^{66} - 2 q^{67} + 4 q^{68} + 7 q^{69} - 16 q^{70} - 3 q^{71} + q^{72} + 16 q^{73} - 8 q^{74} - q^{75} + q^{76} - 8 q^{77} - 5 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} - 8 q^{82} + 6 q^{83} + 4 q^{84} + 8 q^{85} + 2 q^{86} - 5 q^{87} - q^{88} + 7 q^{89} - 4 q^{90} - 20 q^{91} + 14 q^{92} - 7 q^{94} + 2 q^{95} + 2 q^{96} + 13 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 4 * q^5 - q^6 - 4 * q^7 - 2 * q^8 - q^9 + 2 * q^10 + q^11 - 2 * q^12 - 2 * q^13 - 8 * q^14 + 2 * q^15 - q^16 + 4 * q^17 - 2 * q^18 + q^19 - 2 * q^20 - 8 * q^21 - q^22 - 7 * q^23 - q^24 - 2 * q^25 - 7 * q^26 - 2 * q^27 - 4 * q^28 + 5 * q^29 - 2 * q^30 + q^32 - q^33 + 8 * q^34 - 8 * q^35 - q^36 + 8 * q^37 + 2 * q^38 - 7 * q^39 - 4 * q^40 + 8 * q^41 - 4 * q^42 + q^43 - 2 * q^44 - 2 * q^45 + 7 * q^46 - 14 * q^47 + q^48 - 9 * q^49 - q^50 + 8 * q^51 - 5 * q^52 + 16 * q^53 - q^54 + 2 * q^55 + 4 * q^56 + 2 * q^57 - 5 * q^58 + 4 * q^59 - 4 * q^60 + 2 * q^61 - 4 * q^63 + 2 * q^64 - 4 * q^65 - 2 * q^66 - 2 * q^67 + 4 * q^68 + 7 * q^69 - 16 * q^70 - 3 * q^71 + q^72 + 16 * q^73 - 8 * q^74 - q^75 + q^76 - 8 * q^77 - 5 * q^78 - 8 * q^79 - 2 * q^80 - q^81 - 8 * q^82 + 6 * q^83 + 4 * q^84 + 8 * q^85 + 2 * q^86 - 5 * q^87 - q^88 + 7 * q^89 - 4 * q^90 - 20 * q^91 + 14 * q^92 - 7 * q^94 + 2 * q^95 + 2 * q^96 + 13 * q^97 + 9 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/858\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.00000			−0.288675
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	−4.00000			−1.06904
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	−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	$0.00546033\pi$
$18$	−1.00000			−0.235702
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$	−4.00000			−0.872872
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−3.50000	−	6.06218i	−0.729800	−	1.26405i	−0.956967	−	0.290196i	$-0.906280\pi$
$23$	−3.50000	−	6.06218i	−0.729800	−	1.26405i	0.227167	−	0.973856i	$-0.427054\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.00000			−0.200000
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$	−1.00000			−0.192450
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	4.00000			0.685994
$35$	−4.00000	+	6.92820i	−0.676123	+	1.17108i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	1.00000			0.162221
$39$	−3.50000	+	0.866025i	−0.560449	+	0.138675i
$40$	−2.00000			−0.316228
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	−0.363905	+	0.931436i	$0.618557\pi$
$42$	−2.00000	−	3.46410i	−0.308607	−	0.534522i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−1.00000			−0.150756
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$	3.50000	−	6.06218i	0.516047	−	0.893819i
$47$	−7.00000			−1.02105			−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000			−1.02105			−0.510527	+	0.859861i	$0.670550\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	4.00000			0.560112
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	8.00000			1.09888			0.549442	−	0.835532i	$-0.314840\pi$
$53$	8.00000			1.09888			0.549442	+	0.835532i	$0.314840\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	2.00000	−	3.46410i	0.267261	−	0.462910i
$57$	1.00000			0.132453
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	−2.00000			−0.258199
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$	−2.00000	+	6.92820i	−0.248069	+	0.859338i
$66$	−1.00000			−0.123091
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	3.50000	−	6.06218i	0.421350	−	0.729800i
$70$	−8.00000			−0.956183
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$	−4.00000			−0.455842
$78$	−2.50000	−	2.59808i	−0.283069	−	0.294174i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.00000	+	6.92820i	−0.441726	+	0.765092i
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$	4.00000	−	6.92820i	0.433861	−	0.751469i
$86$	1.00000			0.107833
$87$	−2.50000	+	4.33013i	−0.268028	+	0.464238i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$	−2.00000			−0.210819
$91$	−10.0000	−	10.3923i	−1.04828	−	1.08941i
$92$	7.00000			0.729800
$93$		0			0
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	1.00000			0.102062
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	−0.320647	−	0.947199i	$-0.603900\pi$
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	0.980622	−	0.195911i	$-0.0627665\pi$
$98$	4.50000	−	7.79423i	0.454569	−	0.787336i
$99$	−1.00000			−0.100504
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	1.00000	−	3.46410i	0.0980581	−	0.339683i
$105$	−8.00000			−0.780720
$106$	4.00000	+	6.92820i	0.388514	+	0.672927i
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	0.935695	+	0.352809i	$0.114773\pi$
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	−0.162306	+	0.986740i	$0.551893\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−4.00000	+	6.92820i	−0.379663	+	0.657596i
$112$	4.00000			0.377964
$113$	8.50000	−	14.7224i	0.799613	−	1.38497i	−0.120256	−	0.992743i	$-0.538371\pi$
$113$	8.50000	−	14.7224i	0.799613	−	1.38497i	0.919868	−	0.392227i	$-0.128295\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$	−7.00000	−	12.1244i	−0.652753	−	1.13060i
$116$	−5.00000			−0.464238
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	4.00000			0.368230
$119$	8.00000	+	13.8564i	0.733359	+	1.27021i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.00000			0.181071
$123$	−4.00000	+	6.92820i	−0.360668	+	0.624695i
$124$		0			0
$125$	−12.0000			−1.07331
$126$	2.00000	−	3.46410i	0.178174	−	0.308607i
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	0.554281	−	0.832330i	$-0.312993\pi$
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	−0.997959	+	0.0638564i	$0.979660\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.00000			0.0880451
$130$	−7.00000	+	1.73205i	−0.613941	+	0.151911i
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$	−0.500000	−	0.866025i	−0.0435194	−	0.0753778i
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	−2.00000			−0.172133
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	7.00000	−	12.1244i	0.598050	−	1.03585i	−0.395058	−	0.918656i	$-0.629276\pi$
$137$	7.00000	−	12.1244i	0.598050	−	1.03585i	0.993109	−	0.117198i	$-0.0373911\pi$
$138$	7.00000			0.595880
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$	−3.50000	−	6.06218i	−0.294753	−	0.510527i
$142$	−3.00000			−0.251754
$143$	−3.50000	+	0.866025i	−0.292685	+	0.0724207i
$144$	1.00000			0.0833333
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$	4.00000	+	6.92820i	0.331042	+	0.573382i
$147$	4.50000	−	7.79423i	0.371154	−	0.642857i
$148$	−8.00000			−0.657596
$149$	−5.50000	+	9.52628i	−0.450578	+	0.780423i	−0.998422	−	0.0561570i	$-0.982115\pi$
$149$	−5.50000	+	9.52628i	−0.450578	+	0.780423i	0.547844	+	0.836580i	$0.315449\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	22.0000			1.79033			0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000			1.79033			0.895167	+	0.445730i	$0.147056\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	2.00000	+	3.46410i	0.161690	+	0.280056i
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	4.00000	+	6.92820i	0.317221	+	0.549442i
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	28.0000			2.20671
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$	−8.00000			−0.624695
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	1.50000	+	2.59808i	0.116423	+	0.201650i
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	0.902120	−	0.431486i	$-0.142010\pi$
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	−0.824737	+	0.565516i	$0.808677\pi$
$168$	4.00000			0.308607
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	8.00000			0.613572
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	5.50000	−	9.52628i	0.418157	−	0.724270i	−0.577597	−	0.816322i	$-0.696009\pi$
$173$	5.50000	−	9.52628i	0.418157	−	0.724270i	0.995754	+	0.0920525i	$0.0293428\pi$
$174$	−5.00000			−0.379049
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	4.00000			0.300658
$178$	−3.50000	+	6.06218i	−0.262336	+	0.454379i
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$	4.00000	−	13.8564i	0.296500	−	1.02711i
$183$	2.00000			0.147844
$184$	3.50000	+	6.06218i	0.258023	+	0.446910i
$185$	8.00000	+	13.8564i	0.588172	+	1.01874i
$186$		0			0
$187$	4.00000			0.292509
$188$	3.50000	−	6.06218i	0.255264	−	0.442130i
$189$	2.00000	−	3.46410i	0.145479	−	0.251976i
$190$	2.00000			0.145095
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	0.737620	−	0.675216i	$-0.235950\pi$
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	−0.953564	+	0.301189i	$0.902616\pi$
$194$	13.0000			0.933346
$195$	−7.00000	+	1.73205i	−0.501280	+	0.124035i
$196$	9.00000			0.642857
$197$	0.500000	+	0.866025i	0.0356235	+	0.0617018i	0.883287	−	0.468832i	$-0.155325\pi$
$197$	0.500000	+	0.866025i	0.0356235	+	0.0617018i	−0.847664	+	0.530534i	$0.821992\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	1.00000			0.0707107
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−4.50000	+	7.79423i	−0.316619	+	0.548400i
$203$	−20.0000			−1.40372
$204$	−2.00000	+	3.46410i	−0.140028	+	0.242536i
$205$	8.00000	+	13.8564i	0.558744	+	0.967773i
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	7.00000			0.486534
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$	1.00000			0.0691714
$210$	−4.00000	−	6.92820i	−0.276026	−	0.478091i
$211$	1.50000	+	2.59808i	0.103264	+	0.178859i	0.913028	−	0.407898i	$-0.133738\pi$
$211$	1.50000	+	2.59808i	0.103264	+	0.178859i	−0.809763	+	0.586756i	$0.800405\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	−3.00000			−0.205557
$214$	−8.00000	+	13.8564i	−0.546869	+	0.947204i
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	1.00000			0.0680414
$217$		0			0
$218$	3.50000	+	6.06218i	0.237050	+	0.410582i
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$	−2.00000			−0.134840
$221$	10.0000	+	10.3923i	0.672673	+	0.699062i
$222$	−8.00000			−0.536925
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	17.0000			1.13082
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$	−0.500000	+	0.866025i	−0.0331133	+	0.0573539i
$229$	−24.0000			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$230$	7.00000	−	12.1244i	0.461566	−	0.799456i
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	−2.50000	−	4.33013i	−0.164133	−	0.284287i
$233$	−22.0000			−1.44127			−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000			−1.44127			−0.720634	+	0.693316i	$0.756149\pi$
$234$	1.00000	−	3.46410i	0.0653720	−	0.226455i
$235$	−14.0000			−0.913259
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	−8.00000	+	13.8564i	−0.518563	+	0.898177i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−1.00000			−0.0642824
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$	−8.00000			−0.510061
$247$	2.50000	+	2.59808i	0.159071	+	0.165312i
$248$		0			0
$249$	1.50000	+	2.59808i	0.0950586	+	0.164646i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	4.00000			0.251976
$253$	3.50000	−	6.06218i	0.220043	−	0.381126i
$254$	5.00000	−	8.66025i	0.313728	−	0.543393i
$255$	8.00000			0.500979
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	0.500000	+	0.866025i	0.0311286	+	0.0539164i
$259$	−32.0000			−1.98838
$260$	−5.00000	−	5.19615i	−0.310087	−	0.322252i
$261$	−5.00000			−0.309492
$262$	4.50000	+	7.79423i	0.278011	+	0.481529i
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$	16.0000			0.982872
$266$	−2.00000	+	3.46410i	−0.122628	+	0.212398i
$267$	−3.50000	+	6.06218i	−0.214197	+	0.370999i
$268$	2.00000			0.122169
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$	−1.00000	−	1.73205i	−0.0608581	−	0.105409i
$271$	−5.00000	−	8.66025i	−0.303728	−	0.526073i	0.673249	−	0.739416i	$-0.264898\pi$
$271$	−5.00000	−	8.66025i	−0.303728	−	0.526073i	−0.976977	+	0.213343i	$0.931565\pi$
$272$	−4.00000			−0.242536
$273$	4.00000	−	13.8564i	0.242091	−	0.838628i
$274$	14.0000			0.845771
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	3.50000	+	6.06218i	0.210675	+	0.364900i
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$		0			0
$279$		0			0
$280$	4.00000	−	6.92820i	0.239046	−	0.414039i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	3.50000	−	6.06218i	0.208422	−	0.360997i
$283$	−10.5000	−	18.1865i	−0.624160	−	1.08108i	−0.988703	−	0.149890i	$-0.952108\pi$
$283$	−10.5000	−	18.1865i	−0.624160	−	1.08108i	0.364542	−	0.931187i	$-0.381225\pi$
$284$	−1.50000	−	2.59808i	−0.0890086	−	0.154167i
$285$	2.00000			0.118470
$286$	−2.50000	−	2.59808i	−0.147828	−	0.153627i
$287$	−32.0000			−1.88890
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−5.00000	+	8.66025i	−0.293610	+	0.508548i
$291$	13.0000			0.762073
$292$	−4.00000	+	6.92820i	−0.234082	+	0.405442i
$293$	3.50000	−	6.06218i	0.204472	−	0.354156i	−0.745492	−	0.666514i	$-0.767786\pi$
$293$	3.50000	−	6.06218i	0.204472	−	0.354156i	0.949964	+	0.312358i	$0.101119\pi$
$294$	9.00000			0.524891
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	−11.0000			−0.637213
$299$	24.5000	−	6.06218i	1.41687	−	0.350585i
$300$	1.00000			0.0577350
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$	11.0000	+	19.0526i	0.632979	+	1.09635i
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$	−1.00000			−0.0573539
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	21.0000			1.19853			0.599267	−	0.800549i	$-0.295459\pi$
$307$	21.0000			1.19853			0.599267	+	0.800549i	$0.295459\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$	−6.50000	−	11.2583i	−0.369772	−	0.640464i
$310$		0			0
$311$	5.00000			0.283524			0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000			0.283524			0.141762	+	0.989901i	$0.454723\pi$
$312$	3.50000	−	0.866025i	0.198148	−	0.0490290i
$313$	21.0000			1.18699			0.593495	−	0.804838i	$-0.297748\pi$
$313$	21.0000			1.18699			0.593495	+	0.804838i	$0.297748\pi$
$314$	−5.00000	−	8.66025i	−0.282166	−	0.488726i
$315$	−4.00000	−	6.92820i	−0.225374	−	0.390360i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	32.0000			1.79730			0.898650	−	0.438667i	$-0.144549\pi$
$317$	32.0000			1.79730			0.898650	+	0.438667i	$0.144549\pi$
$318$	−4.00000	+	6.92820i	−0.224309	+	0.388514i
$319$	−2.50000	+	4.33013i	−0.139973	+	0.242441i
$320$	2.00000			0.111803
$321$	−8.00000	+	13.8564i	−0.446516	+	0.773389i
$322$	14.0000	+	24.2487i	0.780189	+	1.35133i
$323$	−2.00000	−	3.46410i	−0.111283	−	0.192748i
$324$	1.00000			0.0555556
$325$	1.00000	−	3.46410i	0.0554700	−	0.192154i
$326$	10.0000			0.553849
$327$	3.50000	+	6.06218i	0.193550	+	0.335239i
$328$	−4.00000	−	6.92820i	−0.220863	−	0.382546i
$329$	14.0000	−	24.2487i	0.771845	−	1.33687i
$330$	−2.00000			−0.110096
$331$	−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	$0.887167\pi$
$332$	−1.50000	+	2.59808i	−0.0823232	+	0.142588i
$333$	−8.00000			−0.438397
$334$	−1.00000	+	1.73205i	−0.0547176	+	0.0947736i
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$	2.00000	+	3.46410i	0.109109	+	0.188982i
$337$	−32.0000			−1.74315			−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−32.0000			−1.74315			−0.871576	+	0.490261i	$0.836901\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$	17.0000			0.923313
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$		0			0
$342$	−0.500000	+	0.866025i	−0.0270369	+	0.0468293i
$343$	8.00000			0.431959
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$	7.00000	−	12.1244i	0.376867	−	0.652753i
$346$	11.0000			0.591364
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	−0.903475	−	0.428640i	$-0.858993\pi$
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	0.822951	+	0.568112i	$0.192326\pi$
$348$	−2.50000	−	4.33013i	−0.134014	−	0.232119i
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	−0.994388	−	0.105797i	$-0.966261\pi$
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	0.405571	−	0.914063i	$-0.367073\pi$
$350$	4.00000			0.213809
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$	1.00000			0.0533002
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−7.00000			−0.370999
$357$	−8.00000	+	13.8564i	−0.423405	+	0.733359i
$358$	−12.0000	+	20.7846i	−0.634220	+	1.09850i
$359$	4.00000			0.211112			0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000			0.211112			0.105556	+	0.994413i	$0.466338\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	8.00000	+	13.8564i	0.420471	+	0.728277i
$363$	−1.00000			−0.0524864
$364$	14.0000	−	3.46410i	0.733799	−	0.181568i
$365$	16.0000			0.837478
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	−0.988269	−	0.152721i	$-0.951196\pi$
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	0.361874	−	0.932227i	$-0.382137\pi$
$368$	−3.50000	+	6.06218i	−0.182450	+	0.316013i
$369$	−8.00000			−0.416463
$370$	−8.00000	+	13.8564i	−0.415900	+	0.720360i
$371$	−16.0000	+	27.7128i	−0.830679	+	1.43878i
$372$		0			0
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$	7.00000			0.360997
$377$	−17.5000	+	4.33013i	−0.901296	+	0.223013i
$378$	4.00000			0.205738
$379$	−17.0000	−	29.4449i	−0.873231	−	1.51248i	−0.858635	−	0.512588i	$-0.828687\pi$
$379$	−17.0000	−	29.4449i	−0.873231	−	1.51248i	−0.0145964	−	0.999893i	$-0.504646\pi$
$380$	1.00000	+	1.73205i	0.0512989	+	0.0888523i
$381$	5.00000	−	8.66025i	0.256158	−	0.443678i
$382$	24.0000			1.22795
$383$	0.500000	−	0.866025i	0.0255488	−	0.0442518i	−0.852968	−	0.521963i	$-0.825200\pi$
$383$	0.500000	−	0.866025i	0.0255488	−	0.0442518i	0.878517	+	0.477711i	$0.158533\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−8.00000			−0.407718
$386$	3.00000	−	5.19615i	0.152696	−	0.264477i
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$	6.50000	+	11.2583i	0.329988	+	0.571555i
$389$	−36.0000			−1.82527			−0.912636	−	0.408773i	$-0.865957\pi$
$389$	−36.0000			−1.82527			−0.912636	+	0.408773i	$0.865957\pi$
$390$	−5.00000	−	5.19615i	−0.253185	−	0.263117i
$391$	−28.0000			−1.41602
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$	4.50000	+	7.79423i	0.226995	+	0.393167i
$394$	−0.500000	+	0.866025i	−0.0251896	+	0.0436297i
$395$	−8.00000			−0.402524
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	3.00000	−	5.19615i	0.150566	−	0.260787i	−0.780870	−	0.624694i	$-0.785224\pi$
$397$	3.00000	−	5.19615i	0.150566	−	0.260787i	0.931436	+	0.363906i	$0.118557\pi$
$398$	7.00000			0.350878
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	0.731516	−	0.681824i	$-0.238813\pi$
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	−0.956235	+	0.292599i	$0.905480\pi$
$402$	2.00000			0.0997509
$403$		0			0
$404$	−9.00000			−0.447767
$405$	−1.00000	−	1.73205i	−0.0496904	−	0.0860663i
$406$	−10.0000	−	17.3205i	−0.496292	−	0.859602i
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$	−4.00000			−0.198030
$409$	−12.0000	+	20.7846i	−0.593362	+	1.02773i	0.400414	+	0.916334i	$0.368866\pi$
$409$	−12.0000	+	20.7846i	−0.593362	+	1.02773i	−0.993776	+	0.111398i	$0.964467\pi$
$410$	−8.00000	+	13.8564i	−0.395092	+	0.684319i
$411$	14.0000			0.690569
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	8.00000	+	13.8564i	0.393654	+	0.681829i
$414$	3.50000	+	6.06218i	0.172016	+	0.297940i
$415$	6.00000			0.294528
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$		0			0
$418$	0.500000	+	0.866025i	0.0244558	+	0.0423587i
$419$	−1.00000	−	1.73205i	−0.0488532	−	0.0846162i	0.840565	−	0.541711i	$-0.182223\pi$
$419$	−1.00000	−	1.73205i	−0.0488532	−	0.0846162i	−0.889418	+	0.457095i	$0.848890\pi$
$420$	4.00000	−	6.92820i	0.195180	−	0.338062i
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	−1.50000	+	2.59808i	−0.0730189	+	0.126472i
$423$	3.50000	−	6.06218i	0.170176	−	0.294753i
$424$	−8.00000			−0.388514
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	−1.50000	−	2.59808i	−0.0726752	−	0.125877i
$427$	4.00000	+	6.92820i	0.193574	+	0.335279i
$428$	−16.0000			−0.773389
$429$	−2.50000	−	2.59808i	−0.120701	−	0.125436i
$430$	2.00000			0.0964486
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	0.840936	−	0.541135i	$-0.182005\pi$
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	−0.889104	+	0.457705i	$0.848672\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−7.50000	+	12.9904i	−0.360427	+	0.624278i	−0.988031	−	0.154255i	$-0.950702\pi$
$433$	−7.50000	+	12.9904i	−0.360427	+	0.624278i	0.627604	+	0.778533i	$0.284036\pi$
$434$		0			0
$435$	−5.00000	+	8.66025i	−0.239732	+	0.415227i
$436$	−3.50000	+	6.06218i	−0.167620	+	0.290326i
$437$	−7.00000			−0.334855
$438$	−4.00000	+	6.92820i	−0.191127	+	0.331042i
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	0.996284	+	0.0861252i	$0.0274485\pi$
$439$	12.0000	+	20.7846i	0.572729	+	0.991995i	−0.423556	+	0.905870i	$0.639218\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$	9.00000			0.428571
$442$	−4.00000	+	13.8564i	−0.190261	+	0.659082i
$443$	−2.00000			−0.0950229			−0.0475114	−	0.998871i	$-0.515129\pi$
$443$	−2.00000			−0.0950229			−0.0475114	+	0.998871i	$0.515129\pi$
$444$	−4.00000	−	6.92820i	−0.189832	−	0.328798i
$445$	7.00000	+	12.1244i	0.331832	+	0.574750i
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$	−11.0000			−0.520282
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	9.00000	−	15.5885i	0.424736	−	0.735665i	−0.571660	−	0.820491i	$-0.693700\pi$
$449$	9.00000	−	15.5885i	0.424736	−	0.735665i	0.996396	+	0.0848262i	$0.0270335\pi$
$450$	1.00000			0.0471405
$451$	−4.00000	+	6.92820i	−0.188353	+	0.326236i
$452$	8.50000	+	14.7224i	0.399806	+	0.692485i
$453$	11.0000	+	19.0526i	0.516825	+	0.895167i
$454$	3.00000			0.140797
$455$	−20.0000	−	20.7846i	−0.937614	−	0.974398i
$456$	−1.00000			−0.0468293
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.841316	−	0.540544i	$-0.818219\pi$
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$458$	−12.0000	−	20.7846i	−0.560723	−	0.971201i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	14.0000			0.652753
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	−0.997871	−	0.0652135i	$-0.979227\pi$
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	0.555412	+	0.831575i	$0.312560\pi$
$462$	2.00000	−	3.46410i	0.0930484	−	0.161165i
$463$	−9.00000			−0.418265			−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000			−0.418265			−0.209133	+	0.977887i	$0.567064\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$		0			0
$466$	−11.0000	−	19.0526i	−0.509565	−	0.882593i
$467$	−26.0000			−1.20314			−0.601568	−	0.798821i	$-0.705457\pi$
$467$	−26.0000			−1.20314			−0.601568	+	0.798821i	$0.705457\pi$
$468$	3.50000	−	0.866025i	0.161788	−	0.0400320i
$469$	8.00000			0.369406
$470$	−7.00000	−	12.1244i	−0.322886	−	0.559255i
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	1.00000			0.0459800
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$	−16.0000			−0.733359
$477$	−4.00000	+	6.92820i	−0.183147	+	0.317221i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	0.973321	+	0.229447i	$0.0736918\pi$
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	−0.287954	+	0.957644i	$0.592975\pi$
$480$	2.00000			0.0912871
$481$	−28.0000	+	6.92820i	−1.27669	+	0.315899i
$482$	10.0000			0.455488
$483$	14.0000	+	24.2487i	0.637022	+	1.10335i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	13.0000	−	22.5167i	0.590300	−	1.02243i
$486$	1.00000			0.0453609
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	10.0000			0.452216
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	−0.991365	−	0.131132i	$-0.958139\pi$
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	0.382118	−	0.924113i	$-0.375195\pi$
$492$	−4.00000	−	6.92820i	−0.180334	−	0.312348i
$493$	20.0000			0.900755
$494$	−1.00000	+	3.46410i	−0.0449921	+	0.155857i
$495$	−2.00000			−0.0898933
$496$		0			0
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$	−1.50000	+	2.59808i	−0.0672166	+	0.116423i
$499$	−26.0000			−1.16392			−0.581960	−	0.813217i	$-0.697714\pi$
$499$	−26.0000			−1.16392			−0.581960	+	0.813217i	$0.697714\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	−1.00000	+	1.73205i	−0.0446767	+	0.0773823i
$502$	−12.0000			−0.535586
$503$	−18.0000	+	31.1769i	−0.802580	+	1.39011i	0.115332	+	0.993327i	$0.463207\pi$
$503$	−18.0000	+	31.1769i	−0.802580	+	1.39011i	−0.917912	+	0.396783i	$0.870127\pi$
$504$	2.00000	+	3.46410i	0.0890871	+	0.154303i
$505$	9.00000	+	15.5885i	0.400495	+	0.693677i
$506$	7.00000			0.311188
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	10.0000			0.443678
$509$	−18.0000	−	31.1769i	−0.797836	−	1.38189i	−0.921023	−	0.389509i	$-0.872645\pi$
$509$	−18.0000	−	31.1769i	−0.797836	−	1.38189i	0.123187	−	0.992384i	$-0.460689\pi$
$510$	4.00000	+	6.92820i	0.177123	+	0.306786i
$511$	−16.0000	+	27.7128i	−0.707798	+	1.22594i
$512$	−1.00000			−0.0441942
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	−26.0000			−1.14570
$516$	−0.500000	+	0.866025i	−0.0220113	+	0.0381246i
$517$	−3.50000	−	6.06218i	−0.153930	−	0.266614i
$518$	−16.0000	−	27.7128i	−0.703000	−	1.21763i
$519$	11.0000			0.482846
$520$	2.00000	−	6.92820i	0.0877058	−	0.303822i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$	−2.50000	−	4.33013i	−0.109422	−	0.189525i
$523$	−18.5000	−	32.0429i	−0.808949	−	1.40114i	−0.913593	−	0.406630i	$-0.866704\pi$
$523$	−18.5000	−	32.0429i	−0.808949	−	1.40114i	0.104644	−	0.994510i	$-0.466630\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$	4.00000			0.174574
$526$	−3.00000	+	5.19615i	−0.130806	+	0.226563i
$527$		0			0
$528$	1.00000			0.0435194
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$	8.00000	+	13.8564i	0.347498	+	0.601884i
$531$	2.00000	+	3.46410i	0.0867926	+	0.150329i
$532$	−4.00000			−0.173422
$533$	−28.0000	+	6.92820i	−1.21281	+	0.300094i
$534$	−7.00000			−0.302920
$535$	16.0000	+	27.7128i	0.691740	+	1.19813i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	−24.0000			−1.03471
$539$	4.50000	−	7.79423i	0.193829	−	0.335721i
$540$	1.00000	−	1.73205i	0.0430331	−	0.0745356i
$541$	15.0000			0.644900			0.322450	−	0.946586i	$-0.395494\pi$
$541$	15.0000			0.644900			0.322450	+	0.946586i	$0.395494\pi$
$542$	5.00000	−	8.66025i	0.214768	−	0.371990i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$	14.0000			0.599694
$546$	14.0000	−	3.46410i	0.599145	−	0.148250i
$547$	−37.0000			−1.58201			−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000			−1.58201			−0.791003	+	0.611812i	$0.790441\pi$
$548$	7.00000	+	12.1244i	0.299025	+	0.517927i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	5.00000			0.213007
$552$	−3.50000	+	6.06218i	−0.148970	+	0.258023i
$553$	8.00000	−	13.8564i	0.340195	−	0.589234i
$554$	−14.0000			−0.594803
$555$	−8.00000	+	13.8564i	−0.339581	+	0.588172i
$556$		0			0
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	2.50000	+	2.59808i	0.105739	+	0.109887i
$560$	8.00000			0.338062
$561$	2.00000	+	3.46410i	0.0844401	+	0.146254i
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	7.00000			0.294753
$565$	17.0000	−	29.4449i	0.715195	−	1.23875i
$566$	10.5000	−	18.1865i	0.441348	−	0.764437i
$567$	4.00000			0.167984
$568$	1.50000	−	2.59808i	0.0629386	−	0.109013i
$569$	16.0000	+	27.7128i	0.670755	+	1.16178i	0.977690	+	0.210051i	$0.0673631\pi$
$569$	16.0000	+	27.7128i	0.670755	+	1.16178i	−0.306935	+	0.951730i	$0.599304\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$	1.00000	−	3.46410i	0.0418121	−	0.144841i
$573$	24.0000			1.00261
$574$	−16.0000	−	27.7128i	−0.667827	−	1.15671i
$575$	3.50000	+	6.06218i	0.145960	+	0.252810i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	25.0000			1.04076			0.520382	−	0.853934i	$-0.325790\pi$
$577$	25.0000			1.04076			0.520382	+	0.853934i	$0.325790\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	3.00000	−	5.19615i	0.124676	−	0.215945i
$580$	−10.0000			−0.415227
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$	6.50000	+	11.2583i	0.269434	+	0.466673i
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$	−8.00000			−0.331042
$585$	−5.00000	−	5.19615i	−0.206725	−	0.214834i
$586$	7.00000			0.289167
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	4.50000	+	7.79423i	0.185577	+	0.321429i
$589$		0			0
$590$	8.00000			0.329355
$591$	−0.500000	+	0.866025i	−0.0205673	+	0.0356235i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	12.0000			0.492781			0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000			0.492781			0.246390	+	0.969171i	$0.420755\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$	16.0000	+	27.7128i	0.655936	+	1.13611i
$596$	−5.50000	−	9.52628i	−0.225289	−	0.390212i
$597$	7.00000			0.286491
$598$	17.5000	+	18.1865i	0.715628	+	0.743703i
$599$	−27.0000			−1.10319			−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000			−1.10319			−0.551595	+	0.834112i	$0.685981\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	8.00000	+	13.8564i	0.326327	+	0.565215i	0.981780	−	0.190021i	$-0.0608557\pi$
$601$	8.00000	+	13.8564i	0.326327	+	0.565215i	−0.655453	+	0.755236i	$0.727522\pi$
$602$	−2.00000	+	3.46410i	−0.0815139	+	0.141186i
$603$	2.00000			0.0814463
$604$	−11.0000	+	19.0526i	−0.447584	+	0.775238i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	−9.00000			−0.365600
$607$	−1.00000	+	1.73205i	−0.0405887	+	0.0703018i	−0.885606	−	0.464437i	$-0.846257\pi$
$607$	−1.00000	+	1.73205i	−0.0405887	+	0.0703018i	0.845017	+	0.534739i	$0.179590\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$	−10.0000	−	17.3205i	−0.405220	−	0.701862i
$610$	4.00000			0.161955
$611$	7.00000	−	24.2487i	0.283190	−	0.980998i
$612$	−4.00000			−0.161690
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	10.5000	+	18.1865i	0.423746	+	0.733949i
$615$	−8.00000	+	13.8564i	−0.322591	+	0.558744i
$616$	4.00000			0.161165
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$	6.50000	−	11.2583i	0.261468	−	0.452876i
$619$	26.0000			1.04503			0.522514	−	0.852631i	$-0.324994\pi$
$619$	26.0000			1.04503			0.522514	+	0.852631i	$0.324994\pi$
$620$		0			0
$621$	3.50000	+	6.06218i	0.140450	+	0.243267i
$622$	2.50000	+	4.33013i	0.100241	+	0.173622i
$623$	−28.0000			−1.12180
$624$	2.50000	+	2.59808i	0.100080	+	0.104006i
$625$	−19.0000			−0.760000
$626$	10.5000	+	18.1865i	0.419664	+	0.726880i
$627$	0.500000	+	0.866025i	0.0199681	+	0.0345857i
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	32.0000			1.27592
$630$	4.00000	−	6.92820i	0.159364	−	0.276026i
$631$	22.5000	−	38.9711i	0.895711	−	1.55142i	0.0627885	−	0.998027i	$-0.480001\pi$
$631$	22.5000	−	38.9711i	0.895711	−	1.55142i	0.832922	−	0.553390i	$-0.186666\pi$
$632$	4.00000			0.159111
$633$	−1.50000	+	2.59808i	−0.0596196	+	0.103264i
$634$	16.0000	+	27.7128i	0.635441	+	1.10062i
$635$	−10.0000	−	17.3205i	−0.396838	−	0.687343i
$636$	−8.00000			−0.317221
$637$	31.5000	−	7.79423i	1.24808	−	0.308819i
$638$	−5.00000			−0.197952
$639$	−1.50000	−	2.59808i	−0.0593391	−	0.102778i
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.0472793	−	0.998882i	$-0.484945\pi$
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.841417	−	0.540386i	$-0.181722\pi$
$642$	−16.0000			−0.631470
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	−0.307372	−	0.951589i	$-0.599450\pi$
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	0.977787	−	0.209603i	$-0.0672170\pi$
$644$	−14.0000	+	24.2487i	−0.551677	+	0.955533i
$645$	2.00000			0.0787499
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	4.00000			0.157014
$650$	3.50000	−	0.866025i	0.137281	−	0.0339683i
$651$		0			0
$652$	5.00000	+	8.66025i	0.195815	+	0.339162i
$653$	−4.00000	−	6.92820i	−0.156532	−	0.271122i	0.777084	−	0.629397i	$-0.216698\pi$
$653$	−4.00000	−	6.92820i	−0.156532	−	0.271122i	−0.933616	+	0.358276i	$0.883365\pi$
$654$	−3.50000	+	6.06218i	−0.136861	+	0.237050i
$655$	18.0000			0.703318
$656$	4.00000	−	6.92820i	0.156174	−	0.270501i
$657$	−4.00000	+	6.92820i	−0.156055	+	0.270295i
$658$	28.0000			1.09155
$659$	−20.0000	+	34.6410i	−0.779089	+	1.34942i	0.153378	+	0.988168i	$0.450985\pi$
$659$	−20.0000	+	34.6410i	−0.779089	+	1.34942i	−0.932467	+	0.361255i	$0.882348\pi$
$660$	−1.00000	−	1.73205i	−0.0389249	−	0.0674200i
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$	−28.0000			−1.08825
$663$	−4.00000	+	13.8564i	−0.155347	+	0.538138i
$664$	−3.00000			−0.116423
$665$	4.00000	+	6.92820i	0.155113	+	0.268664i
$666$	−4.00000	−	6.92820i	−0.154997	−	0.268462i
$667$	17.5000	−	30.3109i	0.677603	−	1.17364i
$668$	−2.00000			−0.0773823
$669$	−9.50000	+	16.4545i	−0.367291	+	0.636167i
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	2.00000			0.0772091
$672$	−2.00000	+	3.46410i	−0.0771517	+	0.133631i
$673$	−8.00000	−	13.8564i	−0.308377	−	0.534125i	0.669630	−	0.742695i	$-0.266453\pi$
$673$	−8.00000	−	13.8564i	−0.308377	−	0.534125i	−0.978008	+	0.208569i	$0.933119\pi$
$674$	−16.0000	−	27.7128i	−0.616297	−	1.06746i
$675$	1.00000			0.0384900
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	−27.0000			−1.03769			−0.518847	−	0.854867i	$-0.673639\pi$
$677$	−27.0000			−1.03769			−0.518847	+	0.854867i	$0.673639\pi$
$678$	8.50000	+	14.7224i	0.326441	+	0.565412i
$679$	26.0000	+	45.0333i	0.997788	+	1.72822i
$680$	−4.00000	+	6.92820i	−0.153393	+	0.265684i
$681$	3.00000			0.114960
$682$		0			0
$683$	23.0000	−	39.8372i	0.880071	−	1.52433i	0.0288092	−	0.999585i	$-0.490828\pi$
$683$	23.0000	−	39.8372i	0.880071	−	1.52433i	0.851261	−	0.524742i	$-0.175838\pi$
$684$	−1.00000			−0.0382360
$685$	14.0000	−	24.2487i	0.534913	−	0.926496i
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$	−12.0000	−	20.7846i	−0.457829	−	0.792982i
$688$	−1.00000			−0.0381246
$689$	−8.00000	+	27.7128i	−0.304776	+	1.05577i
$690$	14.0000			0.532971
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	5.50000	+	9.52628i	0.209079	+	0.362135i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$	−3.00000			−0.113878
$695$		0			0
$696$	2.50000	−	4.33013i	0.0947623	−	0.164133i
$697$	32.0000			1.21209
$698$	11.0000	−	19.0526i	0.416356	−	0.721150i
$699$	−11.0000	−	19.0526i	−0.416058	−	0.720634i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	38.0000			1.43524			0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000			1.43524			0.717620	+	0.696435i	$0.245231\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	8.00000			0.301726
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−7.00000	−	12.1244i	−0.263635	−	0.456630i
$706$	15.0000	−	25.9808i	0.564532	−	0.977799i
$707$	−36.0000			−1.35392
$708$	−2.00000	+	3.46410i	−0.0751646	+	0.130189i
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	−0.614852	−	0.788642i	$-0.710784\pi$
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	0.990410	+	0.138157i	$0.0441178\pi$
$710$	−6.00000			−0.225176
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−3.50000	−	6.06218i	−0.131168	−	0.227190i
$713$		0			0
$714$	−16.0000			−0.598785
$715$	−7.00000	+	1.73205i	−0.261785	+	0.0647750i
$716$	−24.0000			−0.896922
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	−0.781748	−	0.623595i	$-0.785672\pi$
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	0.930923	+	0.365216i	$0.119005\pi$
$720$	2.00000			0.0745356
$721$	26.0000	−	45.0333i	0.968291	−	1.67713i
$722$	−9.00000	+	15.5885i	−0.334945	+	0.580142i
$723$	10.0000			0.371904
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$	−2.50000	−	4.33013i	−0.0928477	−	0.160817i
$726$	−0.500000	−	0.866025i	−0.0185567	−	0.0321412i
$727$	−47.0000			−1.74313			−0.871567	−	0.490277i	$-0.836896\pi$
$727$	−47.0000			−1.74313			−0.871567	+	0.490277i	$0.836896\pi$
$728$	10.0000	+	10.3923i	0.370625	+	0.385164i
$729$	1.00000			0.0370370
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	47.0000			1.73598			0.867992	−	0.496578i	$-0.165410\pi$
$733$	47.0000			1.73598			0.867992	+	0.496578i	$0.165410\pi$
$734$	12.0000	−	20.7846i	0.442928	−	0.767174i
$735$	9.00000	−	15.5885i	0.331970	−	0.574989i
$736$	−7.00000			−0.258023
$737$	1.00000	−	1.73205i	0.0368355	−	0.0638009i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	23.5000	+	40.7032i	0.864461	+	1.49729i	0.867581	+	0.497296i	$0.165674\pi$
$739$	23.5000	+	40.7032i	0.864461	+	1.49729i	−0.00311943	+	0.999995i	$0.500993\pi$
$740$	−16.0000			−0.588172
$741$	−1.00000	+	3.46410i	−0.0367359	+	0.127257i
$742$	−32.0000			−1.17476
$743$	15.0000	+	25.9808i	0.550297	+	0.953142i	0.998253	+	0.0590862i	$0.0188187\pi$
$743$	15.0000	+	25.9808i	0.550297	+	0.953142i	−0.447956	+	0.894055i	$0.647848\pi$
$744$		0			0
$745$	−11.0000	+	19.0526i	−0.403009	+	0.698032i
$746$	31.0000			1.13499
$747$	−1.50000	+	2.59808i	−0.0548821	+	0.0950586i
$748$	−2.00000	+	3.46410i	−0.0731272	+	0.126660i
$749$	−64.0000			−2.33851
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$	3.50000	+	6.06218i	0.127632	+	0.221065i
$753$	−12.0000			−0.437304
$754$	−12.5000	−	12.9904i	−0.455223	−	0.473082i
$755$	44.0000			1.60132
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	−18.0000	−	31.1769i	−0.654221	−	1.13314i	−0.982088	−	0.188420i	$-0.939663\pi$
$757$	−18.0000	−	31.1769i	−0.654221	−	1.13314i	0.327867	−	0.944724i	$-0.393670\pi$
$758$	17.0000	−	29.4449i	0.617468	−	1.06949i
$759$	7.00000			0.254084
$760$	−1.00000	+	1.73205i	−0.0362738	+	0.0628281i
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	−0.883581	−	0.468278i	$-0.844875\pi$
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	0.847331	+	0.531065i	$0.178208\pi$
$762$	10.0000			0.362262
$763$	−14.0000	+	24.2487i	−0.506834	+	0.877862i
$764$	12.0000	+	20.7846i	0.434145	+	0.751961i
$765$	4.00000	+	6.92820i	0.144620	+	0.250490i
$766$	1.00000			0.0361315
$767$	10.0000	+	10.3923i	0.361079	+	0.375244i
$768$	−1.00000			−0.0360844
$769$	−3.00000	−	5.19615i	−0.108183	−	0.187378i	0.806851	−	0.590755i	$-0.201170\pi$
$769$	−3.00000	−	5.19615i	−0.108183	−	0.187378i	−0.915034	+	0.403376i	$0.867837\pi$
$770$	−4.00000	−	6.92820i	−0.144150	−	0.249675i
$771$	9.00000	−	15.5885i	0.324127	−	0.561405i
$772$	6.00000			0.215945
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	0.336323	+	0.941747i	$0.390817\pi$
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	−0.983738	+	0.179609i	$0.942517\pi$
$774$	−0.500000	+	0.866025i	−0.0179721	+	0.0311286i
$775$		0			0
$776$	−6.50000	+	11.2583i	−0.233336	+	0.404151i
$777$	−16.0000	−	27.7128i	−0.573997	−	0.994192i
$778$	−18.0000	−	31.1769i	−0.645331	−	1.11775i
$779$	8.00000			0.286630
$780$	2.00000	−	6.92820i	0.0716115	−	0.248069i
$781$	−3.00000			−0.107348
$782$	−14.0000	−	24.2487i	−0.500639	−	0.867132i
$783$	−2.50000	−	4.33013i	−0.0893427	−	0.154746i
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	−20.0000			−0.713831
$786$	−4.50000	+	7.79423i	−0.160510	+	0.278011i
$787$	19.5000	−	33.7750i	0.695100	−	1.20395i	−0.275047	−	0.961431i	$-0.588693\pi$
$787$	19.5000	−	33.7750i	0.695100	−	1.20395i	0.970147	−	0.242518i	$-0.0779732\pi$
$788$	−1.00000			−0.0356235
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$	34.0000	+	58.8897i	1.20890	+	2.09388i
$792$	1.00000			0.0355335
$793$	5.00000	+	5.19615i	0.177555	+	0.184521i
$794$	6.00000			0.212932
$795$	8.00000	+	13.8564i	0.283731	+	0.491436i
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	−0.602761	−	0.797922i	$-0.705933\pi$
$797$	11.0000	−	19.0526i	0.389640	−	0.674876i	0.992401	+	0.123045i	$0.0392661\pi$
$798$	−4.00000			−0.141598
$799$	−14.0000	+	24.2487i	−0.495284	+	0.857858i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−7.00000			−0.247333
$802$	4.50000	−	7.79423i	0.158901	−	0.275224i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	1.00000	+	1.73205i	0.0352673	+	0.0610847i
$805$	56.0000			1.97374
$806$		0			0
$807$	−24.0000			−0.844840
$808$	−4.50000	−	7.79423i	−0.158309	−	0.274200i
$809$	−12.0000	−	20.7846i	−0.421898	−	0.730748i	0.574228	−	0.818696i	$-0.305302\pi$
$809$	−12.0000	−	20.7846i	−0.421898	−	0.730748i	−0.996125	+	0.0879478i	$0.971969\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$	9.00000			0.316033			0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000			0.316033			0.158016	+	0.987436i	$0.449490\pi$
$812$	10.0000	−	17.3205i	0.350931	−	0.607831i
$813$	5.00000	−	8.66025i	0.175358	−	0.303728i
$814$	−8.00000			−0.280400
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	−0.500000	−	0.866025i	−0.0174928	−	0.0302984i
$818$	−24.0000			−0.839140
$819$	14.0000	−	3.46410i	0.489200	−	0.121046i
$820$	−16.0000			−0.558744
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	0.528302	−	0.849056i	$-0.322829\pi$
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	−0.999456	+	0.0329950i	$0.989495\pi$
$822$	7.00000	+	12.1244i	0.244153	+	0.422885i
$823$	−21.5000	+	37.2391i	−0.749443	+	1.29807i	0.198647	+	0.980071i	$0.436345\pi$
$823$	−21.5000	+	37.2391i	−0.749443	+	1.29807i	−0.948090	+	0.318002i	$0.896988\pi$
$824$	13.0000			0.452876
$825$	0.500000	−	0.866025i	0.0174078	−	0.0301511i
$826$	−8.00000	+	13.8564i	−0.278356	+	0.482126i
$827$	23.0000			0.799788			0.399894	−	0.916561i	$-0.369047\pi$
$827$	23.0000			0.799788			0.399894	+	0.916561i	$0.369047\pi$
$828$	−3.50000	+	6.06218i	−0.121633	+	0.210675i
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	0.638457	−	0.769657i	$-0.279573\pi$
$829$	−10.0000	−	17.3205i	−0.347314	−	0.601566i	−0.985771	+	0.168091i	$0.946240\pi$
$830$	3.00000	+	5.19615i	0.104132	+	0.180361i
$831$	−14.0000			−0.485655
$832$	−1.00000	+	3.46410i	−0.0346688	+	0.120096i
$833$	−36.0000			−1.24733
$834$		0			0
$835$	2.00000	+	3.46410i	0.0692129	+	0.119880i
$836$	−0.500000	+	0.866025i	−0.0172929	+	0.0299521i
$837$		0			0
$838$	1.00000	−	1.73205i	0.0345444	−	0.0598327i
$839$	3.50000	−	6.06218i	0.120833	−	0.209290i	−0.799263	−	0.600981i	$-0.794777\pi$
$839$	3.50000	−	6.06218i	0.120833	−	0.209290i	0.920097	+	0.391692i	$0.128110\pi$
$840$	8.00000			0.276026
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$	−3.00000			−0.103264
$845$	−22.0000	−	13.8564i	−0.756823	−	0.476675i
$846$	7.00000			0.240665
$847$	−2.00000	−	3.46410i	−0.0687208	−	0.119028i
$848$	−4.00000	−	6.92820i	−0.137361	−	0.237915i
$849$	10.5000	−	18.1865i	0.360359	−	0.624160i
$850$	−4.00000			−0.137199
$851$	28.0000	−	48.4974i	0.959828	−	1.66247i
$852$	1.50000	−	2.59808i	0.0513892	−	0.0890086i
$853$	31.0000			1.06142			0.530710	−	0.847554i	$-0.321925\pi$
$853$	31.0000			1.06142			0.530710	+	0.847554i	$0.321925\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	−8.00000	−	13.8564i	−0.273434	−	0.473602i
$857$	−32.0000			−1.09310			−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000			−1.09310			−0.546550	+	0.837427i	$0.684059\pi$
$858$	1.00000	−	3.46410i	0.0341394	−	0.118262i
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$	−16.0000	−	27.7128i	−0.545279	−	0.944450i
$862$	1.00000	−	1.73205i	0.0340601	−	0.0589939i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	11.0000	−	19.0526i	0.374011	−	0.647806i
$866$	−15.0000			−0.509721
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$		0			0
$869$	−2.00000	−	3.46410i	−0.0678454	−	0.117512i
$870$	−10.0000			−0.339032
$871$	7.00000	−	1.73205i	0.237186	−	0.0586883i
$872$	−7.00000			−0.237050
$873$	6.50000	+	11.2583i	0.219992	+	0.381037i
$874$	−3.50000	−	6.06218i	−0.118389	−	0.205056i
$875$	24.0000	−	41.5692i	0.811348	−	1.40530i
$876$	−8.00000			−0.270295
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$	−12.0000	+	20.7846i	−0.404980	+	0.701447i
$879$	7.00000			0.236104
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	0.997833	+	0.0657979i	$0.0209593\pi$
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	−0.441934	+	0.897048i	$0.645707\pi$
$882$	4.50000	+	7.79423i	0.151523	+	0.262445i
$883$	22.0000			0.740359			0.370179	−	0.928960i	$-0.379296\pi$
$883$	22.0000			0.740359			0.370179	+	0.928960i	$0.379296\pi$
$884$	−14.0000	+	3.46410i	−0.470871	+	0.116510i
$885$	8.00000			0.268917
$886$	−1.00000	−	1.73205i	−0.0335957	−	0.0581894i
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$	4.00000	−	6.92820i	0.134231	−	0.232495i
$889$	40.0000			1.34156
$890$	−7.00000	+	12.1244i	−0.234641	+	0.406409i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−19.0000			−0.636167
$893$	−3.50000	+	6.06218i	−0.117123	+	0.202863i
$894$	−5.50000	−	9.52628i	−0.183948	−	0.318606i
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$	−4.00000			−0.133631
$897$	17.5000	+	18.1865i	0.584308	+	0.607231i
$898$	18.0000			0.600668
$899$		0			0
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	16.0000	−	27.7128i	0.533037	−	0.923248i
$902$	−8.00000			−0.266371
$903$	−2.00000	+	3.46410i	−0.0665558	+	0.115278i
$904$	−8.50000	+	14.7224i	−0.282706	+	0.489661i
$905$	32.0000			1.06372
$906$	−11.0000	+	19.0526i	−0.365451	+	0.632979i
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	0.702094	−	0.712084i	$-0.252248\pi$
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	−0.967730	+	0.251990i	$0.918915\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$	−9.00000			−0.298511
$910$	8.00000	−	27.7128i	0.265197	−	0.918671i
$911$	13.0000			0.430709			0.215355	−	0.976536i	$-0.430909\pi$
$911$	13.0000			0.430709			0.215355	+	0.976536i	$0.430909\pi$
$912$	−0.500000	−	0.866025i	−0.0165567	−	0.0286770i
$913$	1.50000	+	2.59808i	0.0496428	+	0.0859838i
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$	4.00000			0.132236
$916$	12.0000	−	20.7846i	0.396491	−	0.686743i
$917$	−18.0000	+	31.1769i	−0.594412	+	1.02955i
$918$	−4.00000			−0.132020
$919$	−23.0000	+	39.8372i	−0.758700	+	1.31411i	0.184814	+	0.982774i	$0.440832\pi$
$919$	−23.0000	+	39.8372i	−0.758700	+	1.31411i	−0.943514	+	0.331333i	$0.892502\pi$
$920$	7.00000	+	12.1244i	0.230783	+	0.399728i
$921$	10.5000	+	18.1865i	0.345987	+	0.599267i
$922$	−19.0000			−0.625732
$923$	−7.50000	−	7.79423i	−0.246866	−	0.256550i
$924$	4.00000			0.131590
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	−4.50000	−	7.79423i	−0.147879	−	0.256134i
$927$	6.50000	−	11.2583i	0.213488	−	0.369772i
$928$	5.00000			0.164133
$929$	1.50000	−	2.59808i	0.0492134	−	0.0852401i	−0.840369	−	0.542014i	$-0.817662\pi$
$929$	1.50000	−	2.59808i	0.0492134	−	0.0852401i	0.889583	+	0.456774i	$0.150995\pi$
$930$		0			0
$931$	−9.00000			−0.294963
$932$	11.0000	−	19.0526i	0.360317	−	0.624087i
$933$	2.50000	+	4.33013i	0.0818463	+	0.141762i
$934$	−13.0000	−	22.5167i	−0.425373	−	0.736768i
$935$	8.00000			0.261628
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	4.00000	+	6.92820i	0.130605	+	0.226214i
$939$	10.5000	+	18.1865i	0.342655	+	0.593495i
$940$	7.00000	−	12.1244i	0.228315	−	0.395453i
$941$	−3.00000			−0.0977972			−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000			−0.0977972			−0.0488986	+	0.998804i	$0.515571\pi$
$942$	5.00000	−	8.66025i	0.162909	−	0.282166i
$943$	28.0000	−	48.4974i	0.911805	−	1.57929i
$944$	−4.00000			−0.130189
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	0.500000	+	0.866025i	0.0162564	+	0.0281569i
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	0.974244	+	0.225497i	$0.0724007\pi$
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	−0.291835	+	0.956469i	$0.594266\pi$
$948$	4.00000			0.129914
$949$	−8.00000	+	27.7128i	−0.259691	+	0.899596i
$950$	−1.00000			−0.0324443
$951$	16.0000	+	27.7128i	0.518836	+	0.898650i
$952$	−8.00000	−	13.8564i	−0.259281	−	0.449089i
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	−0.603559	−	0.797318i	$-0.706251\pi$
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	0.992277	+	0.124039i	$0.0395847\pi$
$954$	−8.00000			−0.259010
$955$	24.0000	−	41.5692i	0.776622	−	1.34515i
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$	−5.00000			−0.161627
$958$	−15.0000	+	25.9808i	−0.484628	+	0.839400i
$959$	28.0000	+	48.4974i	0.904167	+	1.56606i
$960$	1.00000	+	1.73205i	0.0322749	+	0.0559017i
$961$	−31.0000			−1.00000
$962$	−20.0000	−	20.7846i	−0.644826	−	0.670123i
$963$	−16.0000			−0.515593
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	−6.00000	−	10.3923i	−0.193147	−	0.334540i
$966$	−14.0000	+	24.2487i	−0.450443	+	0.780189i
$967$	−56.0000			−1.80084			−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000			−1.80084			−0.900419	+	0.435023i	$0.856740\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	2.00000	−	3.46410i	0.0642493	−	0.111283i
$970$	26.0000			0.834810
$971$	20.0000	−	34.6410i	0.641831	−	1.11168i	−0.343193	−	0.939265i	$-0.611509\pi$
$971$	20.0000	−	34.6410i	0.641831	−	1.11168i	0.985024	−	0.172418i	$-0.0551581\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$		0			0
$974$	−16.0000			−0.512673
$975$	3.50000	−	0.866025i	0.112090	−	0.0277350i
$976$	−2.00000			−0.0640184
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$	5.00000	+	8.66025i	0.159882	+	0.276924i
$979$	−3.50000	+	6.06218i	−0.111860	+	0.193748i
$980$	18.0000			0.574989
$981$	−3.50000	+	6.06218i	−0.111746	+	0.193550i
$982$	13.5000	−	23.3827i	0.430802	−	0.746171i
$983$	11.0000			0.350846			0.175423	−	0.984493i	$-0.443871\pi$
$983$	11.0000			0.350846			0.175423	+	0.984493i	$0.443871\pi$
$984$	4.00000	−	6.92820i	0.127515	−	0.220863i
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$	10.0000	+	17.3205i	0.318465	+	0.551597i
$987$	28.0000			0.891250
$988$	−3.50000	+	0.866025i	−0.111350	+	0.0275519i
$989$	−7.00000			−0.222587
$990$	−1.00000	−	1.73205i	−0.0317821	−	0.0550482i
$991$	24.5000	+	42.4352i	0.778268	+	1.34800i	0.932939	+	0.360034i	$0.117235\pi$
$991$	24.5000	+	42.4352i	0.778268	+	1.34800i	−0.154671	+	0.987966i	$0.549432\pi$
$992$		0			0
$993$	−28.0000			−0.888553
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$	7.00000	−	12.1244i	0.221915	−	0.384368i
$996$	−3.00000			−0.0950586
$997$	−16.5000	+	28.5788i	−0.522560	+	0.905101i	0.477095	+	0.878852i	$0.341690\pi$
$997$	−16.5000	+	28.5788i	−0.522560	+	0.905101i	−0.999655	+	0.0262493i	$0.991644\pi$
$998$	−13.0000	−	22.5167i	−0.411508	−	0.712752i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	858.2.i.h.133.1	✓	2
13.9	even	3	inner	858.2.i.h.529.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
858.2.i.h.133.1	✓	2	1.1	even	1	trivial
858.2.i.h.529.1	yes	2	13.9	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:	\( N \)	\(=\)	\( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	858.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} -4.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} -1.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +4.00000 q^{34} +(-4.00000 + 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.00000 + 6.92820i) q^{37} +1.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} -2.00000 q^{40} +(4.00000 + 6.92820i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(0.500000 - 0.866025i) q^{43} -1.00000 q^{44} +(-1.00000 + 1.73205i) q^{45} +(3.50000 - 6.06218i) q^{46} -7.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +4.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +8.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(2.00000 - 3.46410i) q^{56} +1.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(2.00000 - 3.46410i) q^{59} -2.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-2.00000 + 6.92820i) q^{65} -1.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +(3.50000 - 6.06218i) q^{69} -8.00000 q^{70} +(-1.50000 + 2.59808i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(0.500000 + 0.866025i) q^{76} -4.00000 q^{77} +(-2.50000 - 2.59808i) q^{78} -4.00000 q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.00000 + 6.92820i) q^{82} +3.00000 q^{83} +(2.00000 - 3.46410i) q^{84} +(4.00000 - 6.92820i) q^{85} +1.00000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.50000 + 6.06218i) q^{89} -2.00000 q^{90} +(-10.0000 - 10.3923i) q^{91} +7.00000 q^{92} +(-3.50000 - 6.06218i) q^{94} +(1.00000 - 1.73205i) q^{95} +1.00000 q^{96} +(6.50000 - 11.2583i) q^{97} +(4.50000 - 7.79423i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 4 * q^5 - q^6 - 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + q^{11} - 2 q^{12} - 2 q^{13} - 8 q^{14} + 2 q^{15} - q^{16} + 4 q^{17} - 2 q^{18} + q^{19} - 2 q^{20} - 8 q^{21} - q^{22} - 7 q^{23} - q^{24} - 2 q^{25} - 7 q^{26} - 2 q^{27} - 4 q^{28} + 5 q^{29} - 2 q^{30} + q^{32} - q^{33} + 8 q^{34} - 8 q^{35} - q^{36} + 8 q^{37} + 2 q^{38} - 7 q^{39} - 4 q^{40} + 8 q^{41} - 4 q^{42} + q^{43} - 2 q^{44} - 2 q^{45} + 7 q^{46} - 14 q^{47} + q^{48} - 9 q^{49} - q^{50} + 8 q^{51} - 5 q^{52} + 16 q^{53} - q^{54} + 2 q^{55} + 4 q^{56} + 2 q^{57} - 5 q^{58} + 4 q^{59} - 4 q^{60} + 2 q^{61} - 4 q^{63} + 2 q^{64} - 4 q^{65} - 2 q^{66} - 2 q^{67} + 4 q^{68} + 7 q^{69} - 16 q^{70} - 3 q^{71} + q^{72} + 16 q^{73} - 8 q^{74} - q^{75} + q^{76} - 8 q^{77} - 5 q^{78} - 8 q^{79} - 2 q^{80} - q^{81} - 8 q^{82} + 6 q^{83} + 4 q^{84} + 8 q^{85} + 2 q^{86} - 5 q^{87} - q^{88} + 7 q^{89} - 4 q^{90} - 20 q^{91} + 14 q^{92} - 7 q^{94} + 2 q^{95} + 2 q^{96} + 13 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 4 * q^5 - q^6 - 4 * q^7 - 2 * q^8 - q^9 + 2 * q^10 + q^11 - 2 * q^12 - 2 * q^13 - 8 * q^14 + 2 * q^15 - q^16 + 4 * q^17 - 2 * q^18 + q^19 - 2 * q^20 - 8 * q^21 - q^22 - 7 * q^23 - q^24 - 2 * q^25 - 7 * q^26 - 2 * q^27 - 4 * q^28 + 5 * q^29 - 2 * q^30 + q^32 - q^33 + 8 * q^34 - 8 * q^35 - q^36 + 8 * q^37 + 2 * q^38 - 7 * q^39 - 4 * q^40 + 8 * q^41 - 4 * q^42 + q^43 - 2 * q^44 - 2 * q^45 + 7 * q^46 - 14 * q^47 + q^48 - 9 * q^49 - q^50 + 8 * q^51 - 5 * q^52 + 16 * q^53 - q^54 + 2 * q^55 + 4 * q^56 + 2 * q^57 - 5 * q^58 + 4 * q^59 - 4 * q^60 + 2 * q^61 - 4 * q^63 + 2 * q^64 - 4 * q^65 - 2 * q^66 - 2 * q^67 + 4 * q^68 + 7 * q^69 - 16 * q^70 - 3 * q^71 + q^72 + 16 * q^73 - 8 * q^74 - q^75 + q^76 - 8 * q^77 - 5 * q^78 - 8 * q^79 - 2 * q^80 - q^81 - 8 * q^82 + 6 * q^83 + 4 * q^84 + 8 * q^85 + 2 * q^86 - 5 * q^87 - q^88 + 7 * q^89 - 4 * q^90 - 20 * q^91 + 14 * q^92 - 7 * q^94 + 2 * q^95 + 2 * q^96 + 13 * q^97 + 9 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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