LMFDB - Embedded newform 618.2.e.a.355.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [618,2,Mod(355,618)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(618, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("618.355");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 618 = 2 \cdot 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	618.e (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:	$4.93475484492$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			355.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	618.355
Dual form			618.2.e.a.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +4.00000 q^{14} +(2.00000 - 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{21} -2.00000 q^{22} +7.00000 q^{23} -1.00000 q^{24} +(-5.50000 - 9.52628i) q^{25} +(2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} -4.00000 q^{30} -3.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} -1.00000 q^{34} +(-8.00000 - 13.8564i) q^{35} +(-0.500000 + 0.866025i) q^{36} +4.00000 q^{37} +(-3.00000 + 5.19615i) q^{38} +4.00000 q^{39} +(-2.00000 + 3.46410i) q^{40} +(-1.50000 - 2.59808i) q^{41} -4.00000 q^{42} +(3.00000 + 5.19615i) q^{43} +(1.00000 + 1.73205i) q^{44} +(-2.00000 + 3.46410i) q^{45} +(-3.50000 - 6.06218i) q^{46} +(1.50000 - 2.59808i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(4.00000 + 6.92820i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(3.00000 + 5.19615i) q^{57} +(6.00000 + 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{60} -8.00000 q^{61} +(1.50000 + 2.59808i) q^{62} +(-2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(8.00000 - 13.8564i) q^{65} +2.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(0.500000 + 0.866025i) q^{68} -7.00000 q^{69} +(-8.00000 + 13.8564i) q^{70} +(6.50000 - 11.2583i) q^{71} +1.00000 q^{72} -13.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(5.50000 + 9.52628i) q^{75} +6.00000 q^{76} +(4.00000 + 6.92820i) q^{77} +(-2.00000 - 3.46410i) q^{78} -11.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} +(-1.50000 + 2.59808i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(2.00000 + 3.46410i) q^{84} +(2.00000 + 3.46410i) q^{85} +(3.00000 - 5.19615i) q^{86} +(1.00000 - 1.73205i) q^{88} +1.00000 q^{89} +4.00000 q^{90} +(8.00000 - 13.8564i) q^{91} +(-3.50000 + 6.06218i) q^{92} +3.00000 q^{93} -3.00000 q^{94} +24.0000 q^{95} +(0.500000 - 0.866025i) q^{96} +(-6.50000 - 11.2583i) q^{97} +(-4.50000 + 7.79423i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 4 * q^5 + q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} + 8 q^{10} + 2 q^{11} + q^{12} - 8 q^{13} + 8 q^{14} + 4 q^{15} - q^{16} + q^{17} - q^{18} - 6 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{22} + 14 q^{23} - 2 q^{24} - 11 q^{25} + 4 q^{26} - 2 q^{27} - 4 q^{28} - 8 q^{30} - 6 q^{31} - q^{32} - 2 q^{33} - 2 q^{34} - 16 q^{35} - q^{36} + 8 q^{37} - 6 q^{38} + 8 q^{39} - 4 q^{40} - 3 q^{41} - 8 q^{42} + 6 q^{43} + 2 q^{44} - 4 q^{45} - 7 q^{46} + 3 q^{47} + q^{48} - 9 q^{49} - 11 q^{50} - q^{51} + 4 q^{52} - 6 q^{53} + q^{54} + 8 q^{55} - 4 q^{56} + 6 q^{57} + 12 q^{59} + 4 q^{60} - 16 q^{61} + 3 q^{62} - 4 q^{63} + 2 q^{64} + 16 q^{65} + 4 q^{66} - 2 q^{67} + q^{68} - 14 q^{69} - 16 q^{70} + 13 q^{71} + 2 q^{72} - 26 q^{73} - 4 q^{74} + 11 q^{75} + 12 q^{76} + 8 q^{77} - 4 q^{78} - 22 q^{79} + 8 q^{80} + 2 q^{81} - 3 q^{82} - 12 q^{83} + 4 q^{84} + 4 q^{85} + 6 q^{86} + 2 q^{88} + 2 q^{89} + 8 q^{90} + 16 q^{91} - 7 q^{92} + 6 q^{93} - 6 q^{94} + 48 q^{95} + q^{96} - 13 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 4 * q^5 + q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 + 8 * q^10 + 2 * q^11 + q^12 - 8 * q^13 + 8 * q^14 + 4 * q^15 - q^16 + q^17 - q^18 - 6 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^22 + 14 * q^23 - 2 * q^24 - 11 * q^25 + 4 * q^26 - 2 * q^27 - 4 * q^28 - 8 * q^30 - 6 * q^31 - q^32 - 2 * q^33 - 2 * q^34 - 16 * q^35 - q^36 + 8 * q^37 - 6 * q^38 + 8 * q^39 - 4 * q^40 - 3 * q^41 - 8 * q^42 + 6 * q^43 + 2 * q^44 - 4 * q^45 - 7 * q^46 + 3 * q^47 + q^48 - 9 * q^49 - 11 * q^50 - q^51 + 4 * q^52 - 6 * q^53 + q^54 + 8 * q^55 - 4 * q^56 + 6 * q^57 + 12 * q^59 + 4 * q^60 - 16 * q^61 + 3 * q^62 - 4 * q^63 + 2 * q^64 + 16 * q^65 + 4 * q^66 - 2 * q^67 + q^68 - 14 * q^69 - 16 * q^70 + 13 * q^71 + 2 * q^72 - 26 * q^73 - 4 * q^74 + 11 * q^75 + 12 * q^76 + 8 * q^77 - 4 * q^78 - 22 * q^79 + 8 * q^80 + 2 * q^81 - 3 * q^82 - 12 * q^83 + 4 * q^84 + 4 * q^85 + 6 * q^86 + 2 * q^88 + 2 * q^89 + 8 * q^90 + 16 * q^91 - 7 * q^92 + 6 * q^93 - 6 * q^94 + 48 * q^95 + 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 $\left(\mathbb{Z}/618\mathbb{Z}\right)^\times$.

$n$	$211$	$413$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.0599153	+	0.998203i	$0.519083\pi$
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.834512	+	0.550990i	$0.814250\pi$
$6$	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
$9$	1.00000			0.333333
$10$	4.00000			1.26491
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	4.00000			1.06904
$15$	2.00000	−	3.46410i	0.516398	−	0.894427i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	−2.00000	−	3.46410i	−0.447214	−	0.774597i
$21$	2.00000	−	3.46410i	0.436436	−	0.755929i
$22$	−2.00000			−0.426401
$23$	7.00000			1.45960			0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000			1.45960			0.729800	+	0.683660i	$0.239613\pi$
$24$	−1.00000			−0.204124
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	−1.00000			−0.192450
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	−4.00000			−0.730297
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	−1.00000			−0.171499
$35$	−8.00000	−	13.8564i	−1.35225	−	2.34216i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$	4.00000			0.640513
$40$	−2.00000	+	3.46410i	−0.316228	+	0.547723i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	−4.00000			−0.617213
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−2.00000	+	3.46410i	−0.298142	+	0.516398i
$46$	−3.50000	−	6.06218i	−0.516047	−	0.893819i
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−5.50000	+	9.52628i	−0.777817	+	1.34722i
$51$	−0.500000	+	0.866025i	−0.0700140	+	0.121268i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$	3.00000	+	5.19615i	0.397360	+	0.688247i
$58$		0			0
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	2.00000	+	3.46410i	0.258199	+	0.447214i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$	−2.00000	+	3.46410i	−0.251976	+	0.436436i
$64$	1.00000			0.125000
$65$	8.00000	−	13.8564i	0.992278	−	1.71868i
$66$	2.00000			0.246183
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	0.500000	+	0.866025i	0.0606339	+	0.105021i
$69$	−7.00000			−0.842701
$70$	−8.00000	+	13.8564i	−0.956183	+	1.65616i
$71$	6.50000	−	11.2583i	0.771408	−	1.33612i	−0.165383	−	0.986229i	$-0.552886\pi$
$71$	6.50000	−	11.2583i	0.771408	−	1.33612i	0.936791	−	0.349889i	$-0.113781\pi$
$72$	1.00000			0.117851
$73$	−13.0000			−1.52153			−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000			−1.52153			−0.760767	+	0.649025i	$0.775177\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	5.50000	+	9.52628i	0.635085	+	1.10000i
$76$	6.00000			0.688247
$77$	4.00000	+	6.92820i	0.455842	+	0.789542i
$78$	−2.00000	−	3.46410i	−0.226455	−	0.392232i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$	4.00000			0.447214
$81$	1.00000			0.111111
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$	2.00000	+	3.46410i	0.218218	+	0.377964i
$85$	2.00000	+	3.46410i	0.216930	+	0.375735i
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$		0			0
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$	4.00000			0.421637
$91$	8.00000	−	13.8564i	0.838628	−	1.45255i
$92$	−3.50000	+	6.06218i	−0.364900	+	0.632026i
$93$	3.00000			0.311086
$94$	−3.00000			−0.309426
$95$	24.0000			2.46235
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	−0.980622	−	0.195911i	$-0.937234\pi$
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	0.320647	−	0.947199i	$-0.396100\pi$
$98$	−4.50000	+	7.79423i	−0.454569	+	0.787336i
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$	11.0000			1.10000
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	1.00000			0.0990148
$103$	10.0000	+	1.73205i	0.985329	+	0.170664i
$103$	10.0000	+	1.73205i	0.985329	+	0.170664i
$104$	−4.00000			−0.392232
$105$	8.00000	+	13.8564i	0.780720	+	1.35225i
$106$	6.00000			0.582772
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−10.0000	−	17.3205i	−0.957826	−	1.65900i	−0.727764	−	0.685828i	$-0.759440\pi$
$109$	−10.0000	−	17.3205i	−0.957826	−	1.65900i	−0.230063	−	0.973176i	$-0.573893\pi$
$110$	4.00000	−	6.92820i	0.381385	−	0.660578i
$111$	−4.00000			−0.379663
$112$	4.00000			0.377964
$113$	−11.0000			−1.03479			−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000			−1.03479			−0.517396	+	0.855746i	$0.673099\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$	−14.0000	+	24.2487i	−1.30551	+	2.26120i
$116$		0			0
$117$	−4.00000			−0.369800
$118$	6.00000	−	10.3923i	0.552345	−	0.956689i
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$	2.00000	−	3.46410i	0.182574	−	0.316228i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	4.00000	+	6.92820i	0.362143	+	0.627250i
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$	1.50000	−	2.59808i	0.134704	−	0.233314i
$125$	24.0000			2.14663
$126$	4.00000			0.356348
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$	−16.0000			−1.40329
$131$	−11.0000	−	19.0526i	−0.961074	−	1.66463i	−0.719811	−	0.694170i	$-0.755772\pi$
$131$	−11.0000	−	19.0526i	−0.961074	−	1.66463i	−0.241264	−	0.970460i	$-0.577562\pi$
$132$	−1.00000	−	1.73205i	−0.0870388	−	0.150756i
$133$	24.0000			2.08106
$134$	2.00000			0.172774
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$	0.500000	−	0.866025i	0.0428746	−	0.0742611i
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$	3.50000	+	6.06218i	0.297940	+	0.516047i
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	0.399992	+	0.916519i	$0.369013\pi$
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	−0.993724	+	0.111856i	$0.964321\pi$
$140$	16.0000			1.35225
$141$	−1.50000	+	2.59808i	−0.126323	+	0.218797i
$142$	−13.0000			−1.09094
$143$	−4.00000	+	6.92820i	−0.334497	+	0.579365i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	6.50000	+	11.2583i	0.537944	+	0.931746i
$147$	4.50000	+	7.79423i	0.371154	+	0.642857i
$148$	−2.00000	+	3.46410i	−0.164399	+	0.284747i
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$	5.50000	−	9.52628i	0.449073	−	0.777817i
$151$	4.50000	+	7.79423i	0.366205	+	0.634285i	0.988969	−	0.148124i	$-0.0473236\pi$
$151$	4.50000	+	7.79423i	0.366205	+	0.634285i	−0.622764	+	0.782410i	$0.713990\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	0.500000	−	0.866025i	0.0404226	−	0.0700140i
$154$	4.00000	−	6.92820i	0.322329	−	0.558291i
$155$	6.00000	−	10.3923i	0.481932	−	0.834730i
$156$	−2.00000	+	3.46410i	−0.160128	+	0.277350i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	5.50000	+	9.52628i	0.437557	+	0.757870i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	−2.00000	−	3.46410i	−0.158114	−	0.273861i
$161$	−14.0000	+	24.2487i	−1.10335	+	1.91107i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−7.00000	−	12.1244i	−0.548282	−	0.949653i	−0.998392	−	0.0566798i	$-0.981949\pi$
$163$	−7.00000	−	12.1244i	−0.548282	−	0.949653i	0.450110	−	0.892973i	$-0.351385\pi$
$164$	3.00000			0.234261
$165$	−4.00000	−	6.92820i	−0.311400	−	0.539360i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$	2.00000	−	3.46410i	0.154303	−	0.267261i
$169$	3.00000			0.230769
$170$	2.00000	−	3.46410i	0.153393	−	0.265684i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−6.00000			−0.457496
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	0.779926	+	0.625871i	$0.215256\pi$
$174$		0			0
$175$	44.0000			3.32609
$176$	−2.00000			−0.150756
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	−0.500000	−	0.866025i	−0.0374766	−	0.0649113i
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$	−2.00000	−	3.46410i	−0.149071	−	0.258199i
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	−0.993598	−	0.112972i	$-0.963963\pi$
$181$	−8.00000	−	13.8564i	−0.594635	−	1.02994i	0.398963	−	0.916967i	$-0.369370\pi$
$182$	−16.0000			−1.18600
$183$	8.00000			0.591377
$184$	7.00000			0.516047
$185$	−8.00000	+	13.8564i	−0.588172	+	1.01874i
$186$	−1.50000	−	2.59808i	−0.109985	−	0.190500i
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	2.00000	−	3.46410i	0.145479	−	0.251976i
$190$	−12.0000	−	20.7846i	−0.870572	−	1.50787i
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	−1.00000			−0.0721688
$193$	2.00000			0.143963			0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000			0.143963			0.0719816	+	0.997406i	$0.477068\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$	−8.00000	+	13.8564i	−0.572892	+	0.992278i
$196$	9.00000			0.642857
$197$	−26.0000			−1.85242			−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$	−2.00000			−0.142134
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	0.206184	+	0.978513i	$0.433895\pi$
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	−0.950509	+	0.310696i	$0.899438\pi$
$200$	−5.50000	−	9.52628i	−0.388909	−	0.673610i
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−5.00000	+	8.66025i	−0.351799	+	0.609333i
$203$		0			0
$204$	−0.500000	−	0.866025i	−0.0350070	−	0.0606339i
$205$	12.0000			0.838116
$206$	−3.50000	−	9.52628i	−0.243857	−	0.663727i
$207$	7.00000			0.486534
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−12.0000			−0.830057
$210$	8.00000	−	13.8564i	0.552052	−	0.956183i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−6.50000	+	11.2583i	−0.445373	+	0.771408i
$214$	18.0000			1.23045
$215$	−24.0000			−1.63679
$216$	−1.00000			−0.0680414
$217$	6.00000	−	10.3923i	0.407307	−	0.705476i
$218$	−10.0000	+	17.3205i	−0.677285	+	1.17309i
$219$	13.0000			0.878459
$220$	−8.00000			−0.539360
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$	2.00000	+	3.46410i	0.134231	+	0.232495i
$223$	2.50000	−	4.33013i	0.167412	−	0.289967i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	2.50000	−	4.33013i	0.167412	−	0.289967i	0.937509	+	0.347960i	$0.113126\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$	−5.50000	−	9.52628i	−0.366667	−	0.635085i
$226$	5.50000	+	9.52628i	0.365855	+	0.633679i
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$	−6.00000			−0.397360
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$	28.0000			1.84627
$231$	−4.00000	−	6.92820i	−0.263181	−	0.455842i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$	−12.0000			−0.781133
$237$	11.0000			0.714527
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	−9.50000	+	16.4545i	−0.614504	+	1.06435i	0.375967	+	0.926633i	$0.377310\pi$
$239$	−9.50000	+	16.4545i	−0.614504	+	1.06435i	−0.990471	+	0.137719i	$0.956023\pi$
$240$	−4.00000			−0.258199
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	−1.00000			−0.0641500
$244$	4.00000	−	6.92820i	0.256074	−	0.443533i
$245$	36.0000			2.29996
$246$	1.50000	−	2.59808i	0.0956365	−	0.165647i
$247$	12.0000	+	20.7846i	0.763542	+	1.32249i
$248$	−3.00000			−0.190500
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	4.00000	−	6.92820i	0.252478	−	0.437304i	−0.711730	−	0.702454i	$-0.752088\pi$
$251$	4.00000	−	6.92820i	0.252478	−	0.437304i	0.964207	+	0.265149i	$0.0854212\pi$
$252$	−2.00000	−	3.46410i	−0.125988	−	0.218218i
$253$	7.00000	−	12.1244i	0.440086	−	0.762252i
$254$	−6.50000	−	11.2583i	−0.407846	−	0.706410i
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	−0.994375	−	0.105919i	$-0.966222\pi$
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	0.588916	+	0.808194i	$0.299555\pi$
$258$	−3.00000	+	5.19615i	−0.186772	+	0.323498i
$259$	−8.00000	+	13.8564i	−0.497096	+	0.860995i
$260$	8.00000	+	13.8564i	0.496139	+	0.859338i
$261$		0			0
$262$	−11.0000	+	19.0526i	−0.679582	+	1.17707i
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	0.984272	−	0.176659i	$-0.0565291\pi$
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	−0.645128	+	0.764075i	$0.723196\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	−12.0000	−	20.7846i	−0.737154	−	1.27679i
$266$	−12.0000	−	20.7846i	−0.735767	−	1.27439i
$267$	−1.00000			−0.0611990
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	−4.00000			−0.243432
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−1.00000			−0.0606339
$273$	−8.00000	+	13.8564i	−0.484182	+	0.838628i
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	−22.0000			−1.32665
$276$	3.50000	−	6.06218i	0.210675	−	0.364900i
$277$	−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	$0.243925\pi$
$278$	14.0000			0.839664
$279$	−3.00000			−0.179605
$280$	−8.00000	−	13.8564i	−0.478091	−	0.828079i
$281$	−10.5000	−	18.1865i	−0.626377	−	1.08492i	−0.988273	−	0.152699i	$-0.951204\pi$
$281$	−10.5000	−	18.1865i	−0.626377	−	1.08492i	0.361895	−	0.932219i	$-0.382130\pi$
$282$	3.00000			0.178647
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	0.975499	−	0.220005i	$-0.0706075\pi$
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	−0.678280	+	0.734804i	$0.737274\pi$
$284$	6.50000	+	11.2583i	0.385704	+	0.668059i
$285$	−24.0000			−1.42164
$286$	8.00000			0.473050
$287$	12.0000			0.708338
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$	6.50000	+	11.2583i	0.381037	+	0.659975i
$292$	6.50000	−	11.2583i	0.380384	−	0.658844i
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.855361	−	0.518032i	$-0.826665\pi$
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.0209480	−	0.999781i	$-0.506668\pi$
$294$	4.50000	−	7.79423i	0.262445	−	0.454569i
$295$	−48.0000			−2.79467
$296$	4.00000			0.232495
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	5.00000	−	8.66025i	0.289642	−	0.501675i
$299$	−28.0000			−1.61928
$300$	−11.0000			−0.635085
$301$	−24.0000			−1.38334
$302$	4.50000	−	7.79423i	0.258946	−	0.448507i
$303$	5.00000	+	8.66025i	0.287242	+	0.497519i
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$	16.0000	−	27.7128i	0.916157	−	1.58683i
$306$	−1.00000			−0.0571662
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	0.836077	−	0.548612i	$-0.184843\pi$
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	−0.893150	+	0.449758i	$0.851510\pi$
$308$	−8.00000			−0.455842
$309$	−10.0000	−	1.73205i	−0.568880	−	0.0985329i
$310$	−12.0000			−0.681554
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	0.571161	−	0.820838i	$-0.306493\pi$
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	−0.996447	+	0.0842210i	$0.973160\pi$
$312$	4.00000			0.226455
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	5.00000	−	8.66025i	0.282166	−	0.488726i
$315$	−8.00000	−	13.8564i	−0.450749	−	0.780720i
$316$	5.50000	−	9.52628i	0.309399	−	0.535895i
$317$	−10.0000			−0.561656			−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000			−0.561656			−0.280828	+	0.959758i	$0.590609\pi$
$318$	−6.00000			−0.336463
$319$		0			0
$320$	−2.00000	+	3.46410i	−0.111803	+	0.193649i
$321$	9.00000	−	15.5885i	0.502331	−	0.870063i
$322$	28.0000			1.56038
$323$	−6.00000			−0.333849
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	22.0000	+	38.1051i	1.22034	+	2.11369i
$326$	−7.00000	+	12.1244i	−0.387694	+	0.671506i
$327$	10.0000	+	17.3205i	0.553001	+	0.957826i
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$	−4.00000	+	6.92820i	−0.220193	+	0.381385i
$331$	−2.00000			−0.109930			−0.0549650	−	0.998488i	$-0.517505\pi$
$331$	−2.00000			−0.109930			−0.0549650	+	0.998488i	$0.517505\pi$
$332$	12.0000			0.658586
$333$	4.00000			0.219199
$334$	−10.5000	−	18.1865i	−0.574534	−	0.995123i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	−4.00000			−0.218218
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	−0.999793	−	0.0203242i	$-0.993530\pi$
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	0.482295	−	0.876009i	$-0.339803\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	11.0000			0.597438
$340$	−4.00000			−0.216930
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$	8.00000			0.431959
$344$	3.00000	+	5.19615i	0.161749	+	0.280158i
$345$	14.0000	−	24.2487i	0.753735	−	1.30551i
$346$	4.00000			0.215041
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$		0			0
$349$	−14.0000	+	24.2487i	−0.749403	+	1.29800i	0.198706	+	0.980059i	$0.436326\pi$
$349$	−14.0000	+	24.2487i	−0.749403	+	1.29800i	−0.948109	+	0.317945i	$0.897007\pi$
$350$	−22.0000	−	38.1051i	−1.17595	−	2.03680i
$351$	4.00000			0.213504
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	26.0000	+	45.0333i	1.37994	+	2.39012i
$356$	−0.500000	+	0.866025i	−0.0264999	+	0.0458993i
$357$	−2.00000	−	3.46410i	−0.105851	−	0.183340i
$358$	2.00000	+	3.46410i	0.105703	+	0.183083i
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$	−2.00000	+	3.46410i	−0.105409	+	0.182574i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−8.00000	+	13.8564i	−0.420471	+	0.728277i
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$	8.00000	+	13.8564i	0.419314	+	0.726273i
$365$	26.0000	−	45.0333i	1.36090	−	2.35715i
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	−1.50000	+	2.59808i	−0.0782994	+	0.135618i	−0.902516	−	0.430656i	$-0.858282\pi$
$367$	−1.50000	+	2.59808i	−0.0782994	+	0.135618i	0.824217	+	0.566274i	$0.191616\pi$
$368$	−3.50000	−	6.06218i	−0.182450	−	0.316013i
$369$	−1.50000	−	2.59808i	−0.0780869	−	0.135250i
$370$	16.0000			0.831800
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$	−1.50000	+	2.59808i	−0.0777714	+	0.134704i
$373$	16.0000			0.828449			0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000			0.828449			0.414224	+	0.910175i	$0.364053\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$	−24.0000			−1.23935
$376$	1.50000	−	2.59808i	0.0773566	−	0.133986i
$377$		0			0
$378$	−4.00000			−0.205738
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	−12.0000	+	20.7846i	−0.615587	+	1.06623i
$381$	−13.0000			−0.666010
$382$	−8.00000			−0.409316
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−32.0000			−1.63087
$386$	−1.00000	−	1.73205i	−0.0508987	−	0.0881591i
$387$	3.00000	+	5.19615i	0.152499	+	0.264135i
$388$	13.0000			0.659975
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$	16.0000			0.810191
$391$	3.50000	−	6.06218i	0.177003	−	0.306578i
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$	11.0000	+	19.0526i	0.554877	+	0.961074i
$394$	13.0000	+	22.5167i	0.654931	+	1.13437i
$395$	22.0000	−	38.1051i	1.10694	−	1.91728i
$396$	1.00000	+	1.73205i	0.0502519	+	0.0870388i
$397$	−14.0000	+	24.2487i	−0.702640	+	1.21701i	0.264897	+	0.964277i	$0.414662\pi$
$397$	−14.0000	+	24.2487i	−0.702640	+	1.21701i	−0.967537	+	0.252731i	$0.918671\pi$
$398$	21.0000			1.05263
$399$	−24.0000			−1.20150
$400$	−5.50000	+	9.52628i	−0.275000	+	0.476314i
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$	−2.00000			−0.0997509
$403$	12.0000			0.597763
$404$	10.0000			0.497519
$405$	−2.00000	+	3.46410i	−0.0993808	+	0.172133i
$406$		0			0
$407$	4.00000	−	6.92820i	0.198273	−	0.343418i
$408$	−0.500000	+	0.866025i	−0.0247537	+	0.0428746i
$409$	1.00000			0.0494468			0.0247234	−	0.999694i	$-0.492129\pi$
$409$	1.00000			0.0494468			0.0247234	+	0.999694i	$0.492129\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	−3.00000			−0.147979
$412$	−6.50000	+	7.79423i	−0.320232	+	0.383994i
$413$	−48.0000			−2.36193
$414$	−3.50000	−	6.06218i	−0.172016	−	0.297940i
$415$	48.0000			2.35623
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$	7.00000	−	12.1244i	0.342791	−	0.593732i
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$	−16.0000			−0.780720
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	−8.00000			−0.389434
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−11.0000			−0.533578
$426$	13.0000			0.629852
$427$	16.0000	−	27.7128i	0.774294	−	1.34112i
$428$	−9.00000	−	15.5885i	−0.435031	−	0.753497i
$429$	4.00000	−	6.92820i	0.193122	−	0.334497i
$430$	12.0000	+	20.7846i	0.578691	+	1.00232i
$431$	−0.500000	−	0.866025i	−0.0240842	−	0.0417150i	0.853732	−	0.520712i	$-0.174334\pi$
$431$	−0.500000	−	0.866025i	−0.0240842	−	0.0417150i	−0.877816	+	0.478997i	$0.841000\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	0.363851	+	0.931457i	$0.381462\pi$
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	−0.988591	+	0.150624i	$0.951872\pi$
$434$	−12.0000			−0.576018
$435$		0			0
$436$	20.0000			0.957826
$437$	−21.0000	−	36.3731i	−1.00457	−	1.73996i
$438$	−6.50000	−	11.2583i	−0.310582	−	0.537944i
$439$	1.00000			0.0477274			0.0238637	−	0.999715i	$-0.492403\pi$
$439$	1.00000			0.0477274			0.0238637	+	0.999715i	$0.492403\pi$
$440$	4.00000	+	6.92820i	0.190693	+	0.330289i
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$	4.00000			0.190261
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$	−2.00000	+	3.46410i	−0.0948091	+	0.164214i
$446$	−5.00000			−0.236757
$447$	−5.00000	−	8.66025i	−0.236492	−	0.409616i
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$	−5.50000	+	9.52628i	−0.259272	+	0.449073i
$451$	−6.00000			−0.282529
$452$	5.50000	−	9.52628i	0.258698	−	0.448078i
$453$	−4.50000	−	7.79423i	−0.211428	−	0.366205i
$454$	6.00000			0.281594
$455$	32.0000	+	55.4256i	1.50018	+	2.59839i
$456$	3.00000	+	5.19615i	0.140488	+	0.243332i
$457$	−10.5000	+	18.1865i	−0.491169	+	0.850730i	−0.999948	−	0.0101670i	$-0.996764\pi$
$457$	−10.5000	+	18.1865i	−0.491169	+	0.850730i	0.508779	+	0.860897i	$0.330097\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$	−14.0000	−	24.2487i	−0.652753	−	1.13060i
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$	−4.00000	+	6.92820i	−0.186097	+	0.322329i
$463$	20.5000	−	35.5070i	0.952716	−	1.65015i	0.213205	−	0.977007i	$-0.431610\pi$
$463$	20.5000	−	35.5070i	0.952716	−	1.65015i	0.739511	−	0.673145i	$-0.235057\pi$
$464$		0			0
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$	2.00000	−	3.46410i	0.0924500	−	0.160128i
$469$	−4.00000	−	6.92820i	−0.184703	−	0.319915i
$470$	6.00000	−	10.3923i	0.276759	−	0.479361i
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	12.0000			0.551761
$474$	−5.50000	−	9.52628i	−0.252623	−	0.437557i
$475$	−33.0000	+	57.1577i	−1.51414	+	2.62257i
$476$	−4.00000			−0.183340
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$	19.0000			0.869040
$479$	11.5000	−	19.9186i	0.525448	−	0.910103i	−0.474112	−	0.880464i	$-0.657231\pi$
$479$	11.5000	−	19.9186i	0.525448	−	0.910103i	0.999561	−	0.0296389i	$-0.00943575\pi$
$480$	2.00000	+	3.46410i	0.0912871	+	0.158114i
$481$	−16.0000			−0.729537
$482$	−5.00000	+	8.66025i	−0.227744	+	0.394464i
$483$	14.0000	−	24.2487i	0.637022	−	1.10335i
$484$	−7.00000			−0.318182
$485$	52.0000			2.36120
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	−8.00000			−0.362143
$489$	7.00000	+	12.1244i	0.316551	+	0.548282i
$490$	−18.0000	−	31.1769i	−0.813157	−	1.40843i
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	−3.00000			−0.135250
$493$		0			0
$494$	12.0000	−	20.7846i	0.539906	−	0.935144i
$495$	4.00000	+	6.92820i	0.179787	+	0.311400i
$496$	1.50000	+	2.59808i	0.0673520	+	0.116657i
$497$	26.0000	+	45.0333i	1.16626	+	2.02002i
$498$	6.00000	−	10.3923i	0.268866	−	0.465690i
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$	−21.0000			−0.938211
$502$	−8.00000			−0.357057
$503$	1.50000	−	2.59808i	0.0668817	−	0.115842i	−0.830645	−	0.556802i	$-0.812028\pi$
$503$	1.50000	−	2.59808i	0.0668817	−	0.115842i	0.897527	+	0.440959i	$0.145362\pi$
$504$	−2.00000	+	3.46410i	−0.0890871	+	0.154303i
$505$	40.0000			1.77998
$506$	−14.0000			−0.622376
$507$	−3.00000			−0.133235
$508$	−6.50000	+	11.2583i	−0.288391	+	0.499508i
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	−0.733679	+	0.679496i	$0.762199\pi$
$510$	−2.00000	+	3.46410i	−0.0885615	+	0.153393i
$511$	26.0000	−	45.0333i	1.15017	−	1.99216i
$512$	1.00000			0.0441942
$513$	3.00000	+	5.19615i	0.132453	+	0.229416i
$514$	13.0000			0.573405
$515$	−26.0000	+	31.1769i	−1.14570	+	1.37382i
$516$	6.00000			0.264135
$517$	−3.00000	−	5.19615i	−0.131940	−	0.228527i
$518$	16.0000			0.703000
$519$	2.00000	−	3.46410i	0.0877903	−	0.152057i
$520$	8.00000	−	13.8564i	0.350823	−	0.607644i
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	0.924229	−	0.381839i	$-0.124709\pi$
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	−0.792797	+	0.609486i	$0.791376\pi$
$522$		0			0
$523$	16.0000			0.699631			0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000			0.699631			0.349816	+	0.936819i	$0.386244\pi$
$524$	22.0000			0.961074
$525$	−44.0000			−1.92032
$526$	5.50000	−	9.52628i	0.239811	−	0.415366i
$527$	−1.50000	+	2.59808i	−0.0653410	+	0.113174i
$528$	2.00000			0.0870388
$529$	26.0000			1.13043
$530$	−12.0000	+	20.7846i	−0.521247	+	0.902826i
$531$	6.00000	+	10.3923i	0.260378	+	0.450988i
$532$	−12.0000	+	20.7846i	−0.520266	+	0.901127i
$533$	6.00000	+	10.3923i	0.259889	+	0.450141i
$534$	0.500000	+	0.866025i	0.0216371	+	0.0374766i
$535$	−36.0000	−	62.3538i	−1.55642	−	2.69579i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	4.00000			0.172613
$538$		0			0
$539$	−18.0000			−0.775315
$540$	2.00000	+	3.46410i	0.0860663	+	0.149071i
$541$	20.0000	+	34.6410i	0.859867	+	1.48933i	0.872055	+	0.489408i	$0.162787\pi$
$541$	20.0000	+	34.6410i	0.859867	+	1.48933i	−0.0121878	+	0.999926i	$0.503880\pi$
$542$		0			0
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	80.0000			3.42682
$546$	16.0000			0.684737
$547$	−8.00000	+	13.8564i	−0.342055	+	0.592457i	−0.984814	−	0.173611i	$-0.944456\pi$
$547$	−8.00000	+	13.8564i	−0.342055	+	0.592457i	0.642759	+	0.766068i	$0.277790\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	−8.00000			−0.341432
$550$	11.0000	+	19.0526i	0.469042	+	0.812404i
$551$		0			0
$552$	−7.00000			−0.297940
$553$	22.0000	−	38.1051i	0.935535	−	1.62039i
$554$	8.00000			0.339887
$555$	8.00000	−	13.8564i	0.339581	−	0.588172i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	−42.0000			−1.77960			−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000			−1.77960			−0.889799	+	0.456354i	$0.849155\pi$
$558$	1.50000	+	2.59808i	0.0635001	+	0.109985i
$559$	−12.0000	−	20.7846i	−0.507546	−	0.879095i
$560$	−8.00000	+	13.8564i	−0.338062	+	0.585540i
$561$	1.00000	+	1.73205i	0.0422200	+	0.0731272i
$562$	−10.5000	+	18.1865i	−0.442916	+	0.767153i
$563$	15.0000	+	25.9808i	0.632175	+	1.09496i	0.987106	+	0.160066i	$0.0511708\pi$
$563$	15.0000	+	25.9808i	0.632175	+	1.09496i	−0.354932	+	0.934892i	$0.615496\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$	22.0000	−	38.1051i	0.925547	−	1.60309i
$566$	5.00000	−	8.66025i	0.210166	−	0.364018i
$567$	−2.00000	+	3.46410i	−0.0839921	+	0.145479i
$568$	6.50000	−	11.2583i	0.272734	−	0.472389i
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	0.971275	+	0.237959i	$0.0764783\pi$
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	−0.279559	+	0.960128i	$0.590188\pi$
$570$	12.0000	+	20.7846i	0.502625	+	0.870572i
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	−0.192950	−	0.981209i	$-0.561806\pi$
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	0.946227	−	0.323505i	$-0.104861\pi$
$572$	−4.00000	−	6.92820i	−0.167248	−	0.289683i
$573$	−4.00000	+	6.92820i	−0.167102	+	0.289430i
$574$	−6.00000	−	10.3923i	−0.250435	−	0.433766i
$575$	−38.5000	−	66.6840i	−1.60556	−	2.78091i
$576$	1.00000			0.0416667
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	−2.00000			−0.0831172
$580$		0			0
$581$	48.0000			1.99138
$582$	6.50000	−	11.2583i	0.269434	−	0.466673i
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$	−13.0000			−0.537944
$585$	8.00000	−	13.8564i	0.330759	−	0.572892i
$586$	−15.0000	+	25.9808i	−0.619644	+	1.07326i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$	−9.00000			−0.371154
$589$	9.00000	+	15.5885i	0.370839	+	0.642311i
$590$	24.0000	+	41.5692i	0.988064	+	1.71138i
$591$	26.0000			1.06950
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	−8.50000	−	14.7224i	−0.349053	−	0.604578i	0.637028	−	0.770840i	$-0.280163\pi$
$593$	−8.50000	−	14.7224i	−0.349053	−	0.604578i	−0.986082	+	0.166263i	$0.946830\pi$
$594$	2.00000			0.0820610
$595$	−16.0000			−0.655936
$596$	−10.0000			−0.409616
$597$	10.5000	−	18.1865i	0.429736	−	0.744325i
$598$	14.0000	+	24.2487i	0.572503	+	0.991604i
$599$	0.500000	+	0.866025i	0.0204294	+	0.0353848i	0.876059	−	0.482203i	$-0.160163\pi$
$599$	0.500000	+	0.866025i	0.0204294	+	0.0353848i	−0.855630	+	0.517588i	$0.826830\pi$
$600$	5.50000	+	9.52628i	0.224537	+	0.388909i
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	−0.190927	−	0.981604i	$-0.561149\pi$
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	0.945558	−	0.325455i	$-0.105517\pi$
$602$	12.0000	+	20.7846i	0.489083	+	0.847117i
$603$	−1.00000	+	1.73205i	−0.0407231	+	0.0705346i
$604$	−9.00000			−0.366205
$605$	−28.0000			−1.13836
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	−24.5000	+	42.4352i	−0.994424	+	1.72239i	−0.405887	+	0.913923i	$0.633038\pi$
$607$	−24.5000	+	42.4352i	−0.994424	+	1.72239i	−0.588537	+	0.808470i	$0.700296\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−32.0000			−1.29564
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	0.500000	+	0.866025i	0.0202113	+	0.0350070i
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	0.286300	+	0.958140i	$0.407575\pi$
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	−0.972924	+	0.231127i	$0.925759\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$	−12.0000			−0.483887
$616$	4.00000	+	6.92820i	0.161165	+	0.279145i
$617$	−23.0000			−0.925945			−0.462973	−	0.886373i	$-0.653217\pi$
$617$	−23.0000			−0.925945			−0.462973	+	0.886373i	$0.653217\pi$
$618$	3.50000	+	9.52628i	0.140791	+	0.383203i
$619$	−46.0000			−1.84890			−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000			−1.84890			−0.924448	+	0.381308i	$0.875474\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$	−7.00000			−0.280900
$622$	−7.50000	+	12.9904i	−0.300723	+	0.520867i
$623$	−2.00000	+	3.46410i	−0.0801283	+	0.138786i
$624$	−2.00000	−	3.46410i	−0.0800641	−	0.138675i
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	−22.0000			−0.879297
$627$	12.0000			0.479234
$628$	−10.0000			−0.399043
$629$	2.00000	−	3.46410i	0.0797452	−	0.138123i
$630$	−8.00000	+	13.8564i	−0.318728	+	0.552052i
$631$	−25.0000			−0.995234			−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000			−0.995234			−0.497617	+	0.867397i	$0.665792\pi$
$632$	−11.0000			−0.437557
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	5.00000	+	8.66025i	0.198575	+	0.343943i
$635$	−26.0000	+	45.0333i	−1.03178	+	1.78709i
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	18.0000	+	31.1769i	0.713186	+	1.23527i
$638$		0			0
$639$	6.50000	−	11.2583i	0.257136	−	0.445373i
$640$	4.00000			0.158114
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$	−18.0000			−0.710403
$643$	−15.0000	−	25.9808i	−0.591542	−	1.02458i	−0.994025	−	0.109154i	$-0.965186\pi$
$643$	−15.0000	−	25.9808i	−0.591542	−	1.02458i	0.402483	−	0.915428i	$-0.368147\pi$
$644$	−14.0000	−	24.2487i	−0.551677	−	0.955533i
$645$	24.0000			0.944999
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	22.0000	+	38.1051i	0.864909	+	1.49807i	0.867137	+	0.498069i	$0.165957\pi$
$647$	22.0000	+	38.1051i	0.864909	+	1.49807i	−0.00222801	+	0.999998i	$0.500709\pi$
$648$	1.00000			0.0392837
$649$	24.0000			0.942082
$650$	22.0000	−	38.1051i	0.862911	−	1.49461i
$651$	−6.00000	+	10.3923i	−0.235159	+	0.407307i
$652$	14.0000			0.548282
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	0.824236	−	0.566247i	$-0.191605\pi$
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	−0.902502	+	0.430686i	$0.858272\pi$
$654$	10.0000	−	17.3205i	0.391031	−	0.677285i
$655$	88.0000			3.43844
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	−13.0000			−0.507178
$658$	6.00000	−	10.3923i	0.233904	−	0.405134i
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	0.918523	−	0.395367i	$-0.129383\pi$
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	−0.801660	+	0.597781i	$0.796049\pi$
$660$	8.00000			0.311400
$661$	9.00000	+	15.5885i	0.350059	+	0.606321i	0.986260	−	0.165203i	$-0.0528281\pi$
$661$	9.00000	+	15.5885i	0.350059	+	0.606321i	−0.636200	+	0.771524i	$0.719495\pi$
$662$	1.00000	+	1.73205i	0.0388661	+	0.0673181i
$663$	2.00000	−	3.46410i	0.0776736	−	0.134535i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	−48.0000	+	83.1384i	−1.86136	+	3.22397i
$666$	−2.00000	−	3.46410i	−0.0774984	−	0.134231i
$667$		0			0
$668$	−10.5000	+	18.1865i	−0.406257	+	0.703658i
$669$	−2.50000	+	4.33013i	−0.0966556	+	0.167412i
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	−8.00000	+	13.8564i	−0.308837	+	0.534921i
$672$	2.00000	+	3.46410i	0.0771517	+	0.133631i
$673$	−2.50000	−	4.33013i	−0.0963679	−	0.166914i	0.813811	−	0.581130i	$-0.197389\pi$
$673$	−2.50000	−	4.33013i	−0.0963679	−	0.166914i	−0.910179	+	0.414216i	$0.864056\pi$
$674$	−9.50000	+	16.4545i	−0.365926	+	0.633803i
$675$	5.50000	+	9.52628i	0.211695	+	0.366667i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	10.0000	+	17.3205i	0.384331	+	0.665681i	0.991676	−	0.128757i	$-0.0410987\pi$
$677$	10.0000	+	17.3205i	0.384331	+	0.665681i	−0.607345	+	0.794438i	$0.707765\pi$
$678$	−5.50000	−	9.52628i	−0.211226	−	0.365855i
$679$	52.0000			1.99558
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$	6.00000			0.229752
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	−0.283491	−	0.958975i	$-0.591493\pi$
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	0.972242	−	0.233977i	$-0.0751739\pi$
$684$	6.00000			0.229416
$685$	−6.00000	+	10.3923i	−0.229248	+	0.397070i
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	20.0000			0.763048
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$	−28.0000			−1.06594
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$	−2.00000	−	3.46410i	−0.0760286	−	0.131685i
$693$	4.00000	+	6.92820i	0.151947	+	0.263181i
$694$	30.0000			1.13878
$695$	−28.0000	−	48.4974i	−1.06210	−	1.83961i
$696$		0			0
$697$	−3.00000			−0.113633
$698$	28.0000			1.05982
$699$	−18.0000			−0.680823
$700$	−22.0000	+	38.1051i	−0.831522	+	1.44024i
$701$	3.00000	+	5.19615i	0.113308	+	0.196256i	0.917102	−	0.398652i	$-0.130522\pi$
$701$	3.00000	+	5.19615i	0.113308	+	0.196256i	−0.803794	+	0.594908i	$0.797189\pi$
$702$	−2.00000	−	3.46410i	−0.0754851	−	0.130744i
$703$	−12.0000	−	20.7846i	−0.452589	−	0.783906i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$	40.0000			1.50435
$708$	12.0000			0.450988
$709$	11.0000	−	19.0526i	0.413114	−	0.715534i	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	11.0000	−	19.0526i	0.413114	−	0.715534i	0.995228	+	0.0975728i	$0.0311079\pi$
$710$	26.0000	−	45.0333i	0.975763	−	1.69007i
$711$	−11.0000			−0.412532
$712$	1.00000			0.0374766
$713$	−21.0000			−0.786456
$714$	−2.00000	+	3.46410i	−0.0748481	+	0.129641i
$715$	−16.0000	−	27.7128i	−0.598366	−	1.03640i
$716$	2.00000	−	3.46410i	0.0747435	−	0.129460i
$717$	9.50000	−	16.4545i	0.354784	−	0.614504i
$718$	20.0000			0.746393
$719$	−5.50000	−	9.52628i	−0.205115	−	0.355270i	0.745054	−	0.667004i	$-0.232424\pi$
$719$	−5.50000	−	9.52628i	−0.205115	−	0.355270i	−0.950169	+	0.311734i	$0.899090\pi$
$720$	4.00000			0.149071
$721$	−26.0000	+	31.1769i	−0.968291	+	1.16109i
$722$	17.0000			0.632674
$723$	5.00000	+	8.66025i	0.185952	+	0.322078i
$724$	16.0000			0.594635
$725$		0			0
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$	−8.00000	−	13.8564i	−0.296704	−	0.513906i	0.678676	−	0.734438i	$-0.262554\pi$
$727$	−8.00000	−	13.8564i	−0.296704	−	0.513906i	−0.975380	+	0.220532i	$0.929221\pi$
$728$	8.00000	−	13.8564i	0.296500	−	0.513553i
$729$	1.00000			0.0370370
$730$	−52.0000			−1.92461
$731$	6.00000			0.221918
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	−25.0000	+	43.3013i	−0.923396	+	1.59937i	−0.129275	+	0.991609i	$0.541265\pi$
$733$	−25.0000	+	43.3013i	−0.923396	+	1.59937i	−0.794121	+	0.607760i	$0.792068\pi$
$734$	3.00000			0.110732
$735$	−36.0000			−1.32788
$736$	−3.50000	+	6.06218i	−0.129012	+	0.223455i
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$	−1.50000	+	2.59808i	−0.0552158	+	0.0956365i
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	0.783028	−	0.621987i	$-0.213674\pi$
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	−0.930170	+	0.367129i	$0.880341\pi$
$740$	−8.00000	−	13.8564i	−0.294086	−	0.509372i
$741$	−12.0000	−	20.7846i	−0.440831	−	0.763542i
$742$	−12.0000	+	20.7846i	−0.440534	+	0.763027i
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	3.00000			0.109985
$745$	−40.0000			−1.46549
$746$	−8.00000	−	13.8564i	−0.292901	−	0.507319i
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$	2.00000			0.0731272
$749$	−36.0000	−	62.3538i	−1.31541	−	2.27836i
$750$	12.0000	+	20.7846i	0.438178	+	0.758947i
$751$	−15.0000			−0.547358			−0.273679	−	0.961821i	$-0.588241\pi$
$751$	−15.0000			−0.547358			−0.273679	+	0.961821i	$0.588241\pi$
$752$	−3.00000			−0.109399
$753$	−4.00000	+	6.92820i	−0.145768	+	0.252478i
$754$		0			0
$755$	−36.0000			−1.31017
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	6.00000	−	10.3923i	0.218074	−	0.377715i	−0.736145	−	0.676824i	$-0.763356\pi$
$757$	6.00000	−	10.3923i	0.218074	−	0.377715i	0.954219	+	0.299109i	$0.0966893\pi$
$758$	−20.0000			−0.726433
$759$	−7.00000	+	12.1244i	−0.254084	+	0.440086i
$760$	24.0000			0.870572
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	−0.394973	−	0.918693i	$-0.629246\pi$
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	0.993098	−	0.117289i	$-0.0374205\pi$
$762$	6.50000	+	11.2583i	0.235470	+	0.407846i
$763$	80.0000			2.89619
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$	10.5000	−	18.1865i	0.379380	−	0.657106i
$767$	−24.0000	−	41.5692i	−0.866590	−	1.50098i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−13.0000	−	22.5167i	−0.468792	−	0.811972i	0.530572	−	0.847640i	$-0.321977\pi$
$769$	−13.0000	−	22.5167i	−0.468792	−	0.811972i	−0.999364	+	0.0356685i	$0.988644\pi$
$770$	16.0000	+	27.7128i	0.576600	+	0.998700i
$771$	6.50000	−	11.2583i	0.234092	−	0.405459i
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	−0.953521	−	0.301326i	$-0.902571\pi$
$773$	−6.00000	+	10.3923i	−0.215805	+	0.373785i	0.737716	+	0.675111i	$0.235904\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$	16.5000	+	28.5788i	0.592697	+	1.02658i
$776$	−6.50000	−	11.2583i	−0.233336	−	0.404151i
$777$	8.00000	−	13.8564i	0.286998	−	0.497096i
$778$	−6.00000	−	10.3923i	−0.215110	−	0.372582i
$779$	−9.00000	+	15.5885i	−0.322458	+	0.558514i
$780$	−8.00000	−	13.8564i	−0.286446	−	0.496139i
$781$	−13.0000	−	22.5167i	−0.465177	−	0.805709i
$782$	−7.00000			−0.250319
$783$		0			0
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	−40.0000			−1.42766
$786$	11.0000	−	19.0526i	0.392357	−	0.679582i
$787$	−22.0000			−0.784215			−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000			−0.784215			−0.392108	+	0.919919i	$0.628254\pi$
$788$	13.0000	−	22.5167i	0.463106	−	0.802123i
$789$	−5.50000	−	9.52628i	−0.195805	−	0.339145i
$790$	−44.0000			−1.56545
$791$	22.0000	−	38.1051i	0.782230	−	1.35486i
$792$	1.00000	−	1.73205i	0.0355335	−	0.0615457i
$793$	32.0000			1.13635
$794$	28.0000			0.993683
$795$	12.0000	+	20.7846i	0.425596	+	0.737154i
$796$	−10.5000	−	18.1865i	−0.372163	−	0.644605i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$	12.0000	+	20.7846i	0.424795	+	0.735767i
$799$	−1.50000	−	2.59808i	−0.0530662	−	0.0919133i
$800$	11.0000			0.388909
$801$	1.00000			0.0353333
$802$	6.00000			0.211867
$803$	−13.0000	+	22.5167i	−0.458760	+	0.794596i
$804$	1.00000	+	1.73205i	0.0352673	+	0.0610847i
$805$	−56.0000	−	96.9948i	−1.97374	−	3.41862i
$806$	−6.00000	−	10.3923i	−0.211341	−	0.366053i
$807$		0			0
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	−0.940435	−	0.339975i	$-0.889582\pi$
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	0.764644	+	0.644453i	$0.222915\pi$
$810$	4.00000			0.140546
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$		0			0
$813$		0			0
$814$	−8.00000			−0.280400
$815$	56.0000			1.96159
$816$	1.00000			0.0350070
$817$	18.0000	−	31.1769i	0.629740	−	1.09074i
$818$	−0.500000	−	0.866025i	−0.0174821	−	0.0302799i
$819$	8.00000	−	13.8564i	0.279543	−	0.484182i
$820$	−6.00000	+	10.3923i	−0.209529	+	0.362915i
$821$	−34.0000			−1.18661			−0.593304	−	0.804978i	$-0.702177\pi$
$821$	−34.0000			−1.18661			−0.593304	+	0.804978i	$0.702177\pi$
$822$	1.50000	+	2.59808i	0.0523185	+	0.0906183i
$823$	−15.0000			−0.522867			−0.261434	−	0.965221i	$-0.584195\pi$
$823$	−15.0000			−0.522867			−0.261434	+	0.965221i	$0.584195\pi$
$824$	10.0000	+	1.73205i	0.348367	+	0.0603388i
$825$	22.0000			0.765942
$826$	24.0000	+	41.5692i	0.835067	+	1.44638i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	−3.50000	+	6.06218i	−0.121633	+	0.210675i
$829$	−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	$0.279573\pi$
$830$	−24.0000	−	41.5692i	−0.833052	−	1.44289i
$831$	4.00000	−	6.92820i	0.138758	−	0.240337i
$832$	−4.00000			−0.138675
$833$	−9.00000			−0.311832
$834$	−14.0000			−0.484780
$835$	−42.0000	+	72.7461i	−1.45347	+	2.51748i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	3.00000			0.103695
$838$	−24.0000			−0.829066
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$	8.00000	+	13.8564i	0.276026	+	0.478091i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	3.00000	+	5.19615i	0.103387	+	0.179071i
$843$	10.5000	+	18.1865i	0.361639	+	0.626377i
$844$	4.00000	+	6.92820i	0.137686	+	0.238479i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$	−3.00000			−0.103142
$847$	−28.0000			−0.962091
$848$	6.00000			0.206041
$849$	−5.00000	−	8.66025i	−0.171600	−	0.297219i
$850$	5.50000	+	9.52628i	0.188648	+	0.326749i
$851$	28.0000			0.959828
$852$	−6.50000	−	11.2583i	−0.222686	−	0.385704i
$853$	9.00000	+	15.5885i	0.308154	+	0.533739i	0.977959	−	0.208799i	$-0.0669554\pi$
$853$	9.00000	+	15.5885i	0.308154	+	0.533739i	−0.669804	+	0.742538i	$0.733622\pi$
$854$	−32.0000			−1.09502
$855$	24.0000			0.820783
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	−11.5000	+	19.9186i	−0.392833	+	0.680406i	−0.992822	−	0.119602i	$-0.961838\pi$
$857$	−11.5000	+	19.9186i	−0.392833	+	0.680406i	0.599989	+	0.800008i	$0.295171\pi$
$858$	−8.00000			−0.273115
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$	12.0000	−	20.7846i	0.409197	−	0.708749i
$861$	−12.0000			−0.408959
$862$	−0.500000	+	0.866025i	−0.0170301	+	0.0294969i
$863$	−15.0000			−0.510606			−0.255303	−	0.966861i	$-0.582175\pi$
$863$	−15.0000			−0.510606			−0.255303	+	0.966861i	$0.582175\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−8.00000	−	13.8564i	−0.272008	−	0.471132i
$866$	26.0000			0.883516
$867$	−8.00000	−	13.8564i	−0.271694	−	0.470588i
$868$	6.00000	+	10.3923i	0.203653	+	0.352738i
$869$	−11.0000	+	19.0526i	−0.373149	+	0.646314i
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	−10.0000	−	17.3205i	−0.338643	−	0.586546i
$873$	−6.50000	−	11.2583i	−0.219992	−	0.381037i
$874$	−21.0000	+	36.3731i	−0.710336	+	1.23034i
$875$	−48.0000	+	83.1384i	−1.62270	+	2.81059i
$876$	−6.50000	+	11.2583i	−0.219615	+	0.380384i
$877$	24.0000	−	41.5692i	0.810422	−	1.40369i	−0.102146	−	0.994769i	$-0.532571\pi$
$877$	24.0000	−	41.5692i	0.810422	−	1.40369i	0.912569	−	0.408923i	$-0.134096\pi$
$878$	−0.500000	−	0.866025i	−0.0168742	−	0.0292269i
$879$	15.0000	+	25.9808i	0.505937	+	0.876309i
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	−8.50000	−	14.7224i	−0.286372	−	0.496011i	0.686569	−	0.727065i	$-0.259116\pi$
$881$	−8.50000	−	14.7224i	−0.286372	−	0.496011i	−0.972941	+	0.231054i	$0.925783\pi$
$882$	−4.50000	+	7.79423i	−0.151523	+	0.262445i
$883$	−10.0000	−	17.3205i	−0.336527	−	0.582882i	0.647250	−	0.762278i	$-0.275919\pi$
$883$	−10.0000	−	17.3205i	−0.336527	−	0.582882i	−0.983777	+	0.179396i	$0.942586\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$	48.0000			1.61350
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$	15.5000	−	26.8468i	0.520439	−	0.901427i	−0.479279	−	0.877663i	$-0.659102\pi$
$887$	15.5000	−	26.8468i	0.520439	−	0.901427i	0.999718	−	0.0237640i	$-0.00756504\pi$
$888$	−4.00000			−0.134231
$889$	−26.0000	+	45.0333i	−0.872012	+	1.51037i
$890$	4.00000			0.134080
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	2.50000	+	4.33013i	0.0837062	+	0.144983i
$893$	−18.0000			−0.602347
$894$	−5.00000	+	8.66025i	−0.167225	+	0.289642i
$895$	8.00000	−	13.8564i	0.267411	−	0.463169i
$896$	4.00000			0.133631
$897$	28.0000			0.934893
$898$	−11.5000	−	19.9186i	−0.383760	−	0.664692i
$899$		0			0
$900$	11.0000			0.366667
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$	3.00000	+	5.19615i	0.0998891	+	0.173013i
$903$	24.0000			0.798670
$904$	−11.0000			−0.365855
$905$	64.0000			2.12743
$906$	−4.50000	+	7.79423i	−0.149502	+	0.258946i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$	−5.00000	−	8.66025i	−0.165840	−	0.287242i
$910$	32.0000	−	55.4256i	1.06079	−	1.83734i
$911$	−12.0000	−	20.7846i	−0.397578	−	0.688625i	0.595849	−	0.803097i	$-0.296816\pi$
$911$	−12.0000	−	20.7846i	−0.397578	−	0.688625i	−0.993426	+	0.114472i	$0.963482\pi$
$912$	3.00000	−	5.19615i	0.0993399	−	0.172062i
$913$	−24.0000			−0.794284
$914$	21.0000			0.694618
$915$	−16.0000	+	27.7128i	−0.528944	+	0.916157i
$916$	10.0000	−	17.3205i	0.330409	−	0.572286i
$917$	88.0000			2.90602
$918$	1.00000			0.0330049
$919$	−51.0000			−1.68233			−0.841167	−	0.540775i	$-0.818131\pi$
$919$	−51.0000			−1.68233			−0.841167	+	0.540775i	$0.818131\pi$
$920$	−14.0000	+	24.2487i	−0.461566	+	0.799456i
$921$	1.00000	+	1.73205i	0.0329511	+	0.0570730i
$922$		0			0
$923$	−26.0000	+	45.0333i	−0.855800	+	1.48229i
$924$	8.00000			0.263181
$925$	−22.0000	−	38.1051i	−0.723356	−	1.25289i
$926$	−41.0000			−1.34734
$927$	10.0000	+	1.73205i	0.328443	+	0.0568880i
$928$		0			0
$929$	8.50000	+	14.7224i	0.278876	+	0.483027i	0.971106	−	0.238650i	$-0.0767048\pi$
$929$	8.50000	+	14.7224i	0.278876	+	0.483027i	−0.692230	+	0.721677i	$0.743372\pi$
$930$	12.0000			0.393496
$931$	−27.0000	+	46.7654i	−0.884889	+	1.53267i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$	7.50000	+	12.9904i	0.245539	+	0.425286i
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	8.00000			0.261628
$936$	−4.00000			−0.130744
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$	−4.00000	+	6.92820i	−0.130605	+	0.226214i
$939$	−11.0000	+	19.0526i	−0.358971	+	0.621757i
$940$	−12.0000			−0.391397
$941$	58.0000			1.89075			0.945373	−	0.325991i	$-0.105698\pi$
$941$	58.0000			1.89075			0.945373	+	0.325991i	$0.105698\pi$
$942$	−5.00000	+	8.66025i	−0.162909	+	0.282166i
$943$	−10.5000	−	18.1865i	−0.341927	−	0.592235i
$944$	6.00000	−	10.3923i	0.195283	−	0.338241i
$945$	8.00000	+	13.8564i	0.260240	+	0.450749i
$946$	−6.00000	−	10.3923i	−0.195077	−	0.337883i
$947$	−1.00000	−	1.73205i	−0.0324956	−	0.0562841i	0.849320	−	0.527878i	$-0.177012\pi$
$947$	−1.00000	−	1.73205i	−0.0324956	−	0.0562841i	−0.881816	+	0.471594i	$0.843679\pi$
$948$	−5.50000	+	9.52628i	−0.178632	+	0.309399i
$949$	52.0000			1.68799
$950$	66.0000			2.14132
$951$	10.0000			0.324272
$952$	2.00000	+	3.46410i	0.0648204	+	0.112272i
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$	6.00000			0.194257
$955$	16.0000	+	27.7128i	0.517748	+	0.896766i
$956$	−9.50000	−	16.4545i	−0.307252	−	0.532176i
$957$		0			0
$958$	−23.0000			−0.743096
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$	2.00000	−	3.46410i	0.0645497	−	0.111803i
$961$	−22.0000			−0.709677
$962$	8.00000	+	13.8564i	0.257930	+	0.446748i
$963$	−9.00000	+	15.5885i	−0.290021	+	0.502331i
$964$	10.0000			0.322078
$965$	−4.00000	+	6.92820i	−0.128765	+	0.223027i
$966$	−28.0000			−0.900885
$967$	−12.5000	+	21.6506i	−0.401973	+	0.696237i	−0.993964	−	0.109707i	$-0.965009\pi$
$967$	−12.5000	+	21.6506i	−0.401973	+	0.696237i	0.591991	+	0.805945i	$0.298342\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	6.00000			0.192748
$970$	−26.0000	−	45.0333i	−0.834810	−	1.44593i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−28.0000	−	48.4974i	−0.897639	−	1.55476i
$974$	−8.00000	+	13.8564i	−0.256337	+	0.443988i
$975$	−22.0000	−	38.1051i	−0.704564	−	1.22034i
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	−19.0000	+	32.9090i	−0.607864	+	1.05285i	0.383728	+	0.923446i	$0.374640\pi$
$977$	−19.0000	+	32.9090i	−0.607864	+	1.05285i	−0.991592	+	0.129405i	$0.958693\pi$
$978$	7.00000	−	12.1244i	0.223835	−	0.387694i
$979$	1.00000	−	1.73205i	0.0319601	−	0.0553566i
$980$	−18.0000	+	31.1769i	−0.574989	+	0.995910i
$981$	−10.0000	−	17.3205i	−0.319275	−	0.553001i
$982$	9.00000	+	15.5885i	0.287202	+	0.497448i
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	−0.489608	−	0.871943i	$-0.662860\pi$
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	0.999928	−	0.0119587i	$-0.00380665\pi$
$984$	1.50000	+	2.59808i	0.0478183	+	0.0828236i
$985$	52.0000	−	90.0666i	1.65686	−	2.86976i
$986$		0			0
$987$	−6.00000	−	10.3923i	−0.190982	−	0.330791i
$988$	−24.0000			−0.763542
$989$	21.0000	+	36.3731i	0.667761	+	1.15660i
$990$	4.00000	−	6.92820i	0.127128	−	0.220193i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	1.50000	−	2.59808i	0.0476250	−	0.0824890i
$993$	2.00000			0.0634681
$994$	26.0000	−	45.0333i	0.824670	−	1.42837i
$995$	−42.0000	−	72.7461i	−1.33149	−	2.30621i
$996$	−12.0000			−0.380235
$997$	8.00000	−	13.8564i	0.253363	−	0.438837i	−0.711087	−	0.703104i	$-0.751797\pi$
$997$	8.00000	−	13.8564i	0.253363	−	0.438837i	0.964449	+	0.264267i	$0.0851301\pi$
$998$	−11.0000	+	19.0526i	−0.348199	+	0.603098i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	618.2.e.a.355.1	✓	2
3.2	odd	2		1854.2.f.e.973.1		2
103.56	even	3	inner	618.2.e.a.571.1	yes	2
309.56	odd	6		1854.2.f.e.1189.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
618.2.e.a.355.1	✓	2	1.1	even	1	trivial
618.2.e.a.571.1	yes	2	103.56	even	3	inner
1854.2.f.e.973.1		2	3.2	odd	2
1854.2.f.e.1189.1		2	309.56	odd	6

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:	\( N \)	\(=\)	\( 618 = 2 \cdot 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	618.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +4.00000 q^{14} +(2.00000 - 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{21} -2.00000 q^{22} +7.00000 q^{23} -1.00000 q^{24} +(-5.50000 - 9.52628i) q^{25} +(2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} -4.00000 q^{30} -3.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} -1.00000 q^{34} +(-8.00000 - 13.8564i) q^{35} +(-0.500000 + 0.866025i) q^{36} +4.00000 q^{37} +(-3.00000 + 5.19615i) q^{38} +4.00000 q^{39} +(-2.00000 + 3.46410i) q^{40} +(-1.50000 - 2.59808i) q^{41} -4.00000 q^{42} +(3.00000 + 5.19615i) q^{43} +(1.00000 + 1.73205i) q^{44} +(-2.00000 + 3.46410i) q^{45} +(-3.50000 - 6.06218i) q^{46} +(1.50000 - 2.59808i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(4.00000 + 6.92820i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(3.00000 + 5.19615i) q^{57} +(6.00000 + 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{60} -8.00000 q^{61} +(1.50000 + 2.59808i) q^{62} +(-2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(8.00000 - 13.8564i) q^{65} +2.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(0.500000 + 0.866025i) q^{68} -7.00000 q^{69} +(-8.00000 + 13.8564i) q^{70} +(6.50000 - 11.2583i) q^{71} +1.00000 q^{72} -13.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(5.50000 + 9.52628i) q^{75} +6.00000 q^{76} +(4.00000 + 6.92820i) q^{77} +(-2.00000 - 3.46410i) q^{78} -11.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} +(-1.50000 + 2.59808i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(2.00000 + 3.46410i) q^{84} +(2.00000 + 3.46410i) q^{85} +(3.00000 - 5.19615i) q^{86} +(1.00000 - 1.73205i) q^{88} +1.00000 q^{89} +4.00000 q^{90} +(8.00000 - 13.8564i) q^{91} +(-3.50000 + 6.06218i) q^{92} +3.00000 q^{93} -3.00000 q^{94} +24.0000 q^{95} +(0.500000 - 0.866025i) q^{96} +(-6.50000 - 11.2583i) q^{97} +(-4.50000 + 7.79423i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 4 * q^5 + q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} + 8 q^{10} + 2 q^{11} + q^{12} - 8 q^{13} + 8 q^{14} + 4 q^{15} - q^{16} + q^{17} - q^{18} - 6 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{22} + 14 q^{23} - 2 q^{24} - 11 q^{25} + 4 q^{26} - 2 q^{27} - 4 q^{28} - 8 q^{30} - 6 q^{31} - q^{32} - 2 q^{33} - 2 q^{34} - 16 q^{35} - q^{36} + 8 q^{37} - 6 q^{38} + 8 q^{39} - 4 q^{40} - 3 q^{41} - 8 q^{42} + 6 q^{43} + 2 q^{44} - 4 q^{45} - 7 q^{46} + 3 q^{47} + q^{48} - 9 q^{49} - 11 q^{50} - q^{51} + 4 q^{52} - 6 q^{53} + q^{54} + 8 q^{55} - 4 q^{56} + 6 q^{57} + 12 q^{59} + 4 q^{60} - 16 q^{61} + 3 q^{62} - 4 q^{63} + 2 q^{64} + 16 q^{65} + 4 q^{66} - 2 q^{67} + q^{68} - 14 q^{69} - 16 q^{70} + 13 q^{71} + 2 q^{72} - 26 q^{73} - 4 q^{74} + 11 q^{75} + 12 q^{76} + 8 q^{77} - 4 q^{78} - 22 q^{79} + 8 q^{80} + 2 q^{81} - 3 q^{82} - 12 q^{83} + 4 q^{84} + 4 q^{85} + 6 q^{86} + 2 q^{88} + 2 q^{89} + 8 q^{90} + 16 q^{91} - 7 q^{92} + 6 q^{93} - 6 q^{94} + 48 q^{95} + q^{96} - 13 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 4 * q^5 + q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 + 8 * q^10 + 2 * q^11 + q^12 - 8 * q^13 + 8 * q^14 + 4 * q^15 - q^16 + q^17 - q^18 - 6 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^22 + 14 * q^23 - 2 * q^24 - 11 * q^25 + 4 * q^26 - 2 * q^27 - 4 * q^28 - 8 * q^30 - 6 * q^31 - q^32 - 2 * q^33 - 2 * q^34 - 16 * q^35 - q^36 + 8 * q^37 - 6 * q^38 + 8 * q^39 - 4 * q^40 - 3 * q^41 - 8 * q^42 + 6 * q^43 + 2 * q^44 - 4 * q^45 - 7 * q^46 + 3 * q^47 + q^48 - 9 * q^49 - 11 * q^50 - q^51 + 4 * q^52 - 6 * q^53 + q^54 + 8 * q^55 - 4 * q^56 + 6 * q^57 + 12 * q^59 + 4 * q^60 - 16 * q^61 + 3 * q^62 - 4 * q^63 + 2 * q^64 + 16 * q^65 + 4 * q^66 - 2 * q^67 + q^68 - 14 * q^69 - 16 * q^70 + 13 * q^71 + 2 * q^72 - 26 * q^73 - 4 * q^74 + 11 * q^75 + 12 * q^76 + 8 * q^77 - 4 * q^78 - 22 * q^79 + 8 * q^80 + 2 * q^81 - 3 * q^82 - 12 * q^83 + 4 * q^84 + 4 * q^85 + 6 * q^86 + 2 * q^88 + 2 * q^89 + 8 * q^90 + 16 * q^91 - 7 * q^92 + 6 * q^93 - 6 * q^94 + 48 * q^95 + q^96 - 13 * q^97 - 9 * q^98 + 2 * q^99

Introduction

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