LMFDB - Embedded newform 105.2.i.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, 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("105.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.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:	$0.838429221223$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.2.i.b.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(-1.00000 + 1.73205i) q^{12} -3.00000 q^{13} +(-5.00000 - 1.73205i) q^{14} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(2.00000 + 3.46410i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +12.0000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +(-4.00000 + 3.46410i) q^{28} -8.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(3.00000 - 5.19615i) q^{33} +8.00000 q^{34} +(2.50000 + 0.866025i) q^{35} +2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +(1.00000 + 5.19615i) q^{42} +1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-1.00000 + 1.73205i) q^{47} -4.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -2.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(3.00000 + 5.19615i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(1.00000 - 1.73205i) q^{54} -6.00000 q^{55} +1.00000 q^{57} +(-8.00000 + 13.8564i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(7.00000 - 12.1244i) q^{61} -2.00000 q^{62} +(2.50000 + 0.866025i) q^{63} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-6.00000 - 10.3923i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(4.00000 - 6.92820i) q^{68} -4.00000 q^{69} +(4.00000 - 3.46410i) q^{70} +6.00000 q^{71} +(-0.500000 - 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(12.0000 - 10.3923i) q^{77} +6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +2.00000 q^{83} +(5.00000 + 1.73205i) q^{84} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(4.00000 + 6.92820i) q^{87} +(6.00000 - 10.3923i) q^{89} -2.00000 q^{90} +(1.50000 + 7.79423i) q^{91} -8.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(-4.00000 + 6.92820i) q^{96} -6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} - 4 q^{6} - q^{7} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 - 4 * q^6 - q^7 - q^9	$ 2 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} - 4 q^{6} - q^{7} - q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} - 6 q^{13} - 10 q^{14} + 2 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - q^{19} + 4 q^{20} - 4 q^{21} + 24 q^{22} + 4 q^{23} - q^{25} - 6 q^{26} + 2 q^{27} - 8 q^{28} - 16 q^{29} + 2 q^{30} - q^{31} - 8 q^{32} + 6 q^{33} + 16 q^{34} + 5 q^{35} + 4 q^{36} - 7 q^{37} + 2 q^{38} + 3 q^{39} - 12 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - q^{45} - 8 q^{46} - 2 q^{47} - 8 q^{48} - 13 q^{49} - 4 q^{50} + 4 q^{51} + 6 q^{52} - 4 q^{53} + 2 q^{54} - 12 q^{55} + 2 q^{57} - 16 q^{58} + 8 q^{59} - 2 q^{60} + 14 q^{61} - 4 q^{62} + 5 q^{63} - 16 q^{64} + 3 q^{65} - 12 q^{66} - 7 q^{67} + 8 q^{68} - 8 q^{69} + 8 q^{70} + 12 q^{71} - q^{73} + 14 q^{74} - q^{75} + 4 q^{76} + 24 q^{77} + 12 q^{78} + q^{79} + 4 q^{80} - q^{81} - 12 q^{82} + 4 q^{83} + 10 q^{84} - 8 q^{85} + 2 q^{86} + 8 q^{87} + 12 q^{89} - 4 q^{90} + 3 q^{91} - 16 q^{92} - q^{93} + 4 q^{94} - q^{95} - 8 q^{96} - 12 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 - 4 * q^6 - q^7 - q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 - 6 * q^13 - 10 * q^14 + 2 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^18 - q^19 + 4 * q^20 - 4 * q^21 + 24 * q^22 + 4 * q^23 - q^25 - 6 * q^26 + 2 * q^27 - 8 * q^28 - 16 * q^29 + 2 * q^30 - q^31 - 8 * q^32 + 6 * q^33 + 16 * q^34 + 5 * q^35 + 4 * q^36 - 7 * q^37 + 2 * q^38 + 3 * q^39 - 12 * q^41 + 2 * q^42 + 2 * q^43 + 12 * q^44 - q^45 - 8 * q^46 - 2 * q^47 - 8 * q^48 - 13 * q^49 - 4 * q^50 + 4 * q^51 + 6 * q^52 - 4 * q^53 + 2 * q^54 - 12 * q^55 + 2 * q^57 - 16 * q^58 + 8 * q^59 - 2 * q^60 + 14 * q^61 - 4 * q^62 + 5 * q^63 - 16 * q^64 + 3 * q^65 - 12 * q^66 - 7 * q^67 + 8 * q^68 - 8 * q^69 + 8 * q^70 + 12 * q^71 - q^73 + 14 * q^74 - q^75 + 4 * q^76 + 24 * q^77 + 12 * q^78 + q^79 + 4 * q^80 - q^81 - 12 * q^82 + 4 * q^83 + 10 * q^84 - 8 * q^85 + 2 * q^86 + 8 * q^87 + 12 * q^89 - 4 * q^90 + 3 * q^91 - 16 * q^92 - q^93 + 4 * q^94 - q^95 - 8 * q^96 - 12 * q^97 - 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−2.00000			−0.816497
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$	−5.00000	−	1.73205i	−1.33631	−	0.462910i
$15$	1.00000			0.258199
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	2.00000			0.447214
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	12.0000			2.55841
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	1.00000			0.192450
$28$	−4.00000	+	3.46410i	−0.755929	+	0.654654i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	0.817625	−	0.575751i	$-0.195290\pi$
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	−0.907428	+	0.420208i	$0.861957\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$	8.00000			1.37199
$35$	2.50000	+	0.866025i	0.422577	+	0.146385i
$36$	2.00000			0.333333
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	1.50000	+	2.59808i	0.240192	+	0.416025i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	1.00000	+	5.19615i	0.154303	+	0.801784i
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	6.00000	−	10.3923i	0.904534	−	1.56670i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	−0.929695	−	0.368329i	$-0.879930\pi$
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	0.783830	+	0.620975i	$0.213263\pi$
$48$	−4.00000			−0.577350
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−2.00000			−0.282843
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	3.00000	+	5.19615i	0.416025	+	0.720577i
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	−0.970065	+	0.242846i	$0.921919\pi$
$54$	1.00000	−	1.73205i	0.136083	−	0.235702i
$55$	−6.00000			−0.809040
$56$		0			0
$57$	1.00000			0.132453
$58$	−8.00000	+	13.8564i	−1.05045	+	1.81944i
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$	−2.00000			−0.254000
$63$	2.50000	+	0.866025i	0.314970	+	0.109109i
$64$	−8.00000			−1.00000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$	−6.00000	−	10.3923i	−0.738549	−	1.27920i
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$	4.00000	−	6.92820i	0.485071	−	0.840168i
$69$	−4.00000			−0.481543
$70$	4.00000	−	3.46410i	0.478091	−	0.414039i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−0.500000	−	0.866025i	−0.0585206	−	0.101361i	0.835281	−	0.549823i	$-0.185305\pi$
$73$	−0.500000	−	0.866025i	−0.0585206	−	0.101361i	−0.893801	+	0.448463i	$0.851972\pi$
$74$	7.00000	+	12.1244i	0.813733	+	1.40943i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	2.00000			0.229416
$77$	12.0000	−	10.3923i	1.36753	−	1.18431i
$78$	6.00000			0.679366
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$	5.00000	+	1.73205i	0.545545	+	0.188982i
$85$	−4.00000			−0.433861
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	4.00000	+	6.92820i	0.428845	+	0.742781i
$88$		0			0
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$	−2.00000			−0.210819
$91$	1.50000	+	7.79423i	0.157243	+	0.817057i
$92$	−8.00000			−0.834058
$93$	−0.500000	+	0.866025i	−0.0518476	+	0.0898027i
$94$	2.00000	+	3.46410i	0.206284	+	0.357295i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$	−4.00000	+	6.92820i	−0.408248	+	0.707107i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	−2.00000	+	13.8564i	−0.202031	+	1.39971i
$99$	−6.00000			−0.603023
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	−4.00000	−	6.92820i	−0.396059	−	0.685994i
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.163335	−	0.986571i	$-0.447775\pi$
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.772728	−	0.634738i	$-0.218892\pi$
$104$		0			0
$105$	−0.500000	−	2.59808i	−0.0487950	−	0.253546i
$106$	−8.00000			−0.777029
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−1.00000	−	1.73205i	−0.0962250	−	0.166667i
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	0.961645	+	0.274296i	$0.0884447\pi$
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	−0.243276	+	0.969957i	$0.578222\pi$
$110$	−6.00000	+	10.3923i	−0.572078	+	0.990867i
$111$	7.00000			0.664411
$112$	−10.0000	−	3.46410i	−0.944911	−	0.327327i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	8.00000	+	13.8564i	0.742781	+	1.28654i
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$	16.0000			1.47292
$119$	8.00000	−	6.92820i	0.733359	−	0.635107i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−14.0000	−	24.2487i	−1.26750	−	2.19538i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$	4.00000	−	3.46410i	0.356348	−	0.308607i
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$		0			0
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$	−12.0000			−1.04447
$133$	2.50000	+	0.866025i	0.216777	+	0.0750939i
$134$	−14.0000			−1.20942
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	0.643013	−	0.765855i	$-0.277684\pi$
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	−0.984757	+	0.173939i	$0.944351\pi$
$138$	−4.00000	+	6.92820i	−0.340503	+	0.589768i
$139$	21.0000			1.78120			0.890598	−	0.454791i	$-0.150286\pi$
$139$	21.0000			1.78120			0.890598	+	0.454791i	$0.150286\pi$
$140$	−1.00000	−	5.19615i	−0.0845154	−	0.439155i
$141$	2.00000			0.168430
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$	4.00000	−	6.92820i	0.332182	−	0.575356i
$146$	−2.00000			−0.165521
$147$	5.50000	+	4.33013i	0.453632	+	0.357143i
$148$	14.0000			1.15079
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$	1.00000	+	1.73205i	0.0816497	+	0.141421i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	−6.00000	−	31.1769i	−0.483494	−	2.51231i
$155$	1.00000			0.0803219
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	−2.00000	+	3.46410i	−0.158610	+	0.274721i
$160$	8.00000			0.632456
$161$	−10.0000	−	3.46410i	−0.788110	−	0.273009i
$162$	−2.00000			−0.157135
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$	−10.0000			−0.773823			−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000			−0.773823			−0.386912	+	0.922117i	$0.626458\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−12.0000	+	20.7846i	−0.912343	+	1.58022i	−0.101598	+	0.994826i	$0.532395\pi$
$173$	−12.0000	+	20.7846i	−0.912343	+	1.58022i	−0.810745	+	0.585399i	$0.800938\pi$
$174$	16.0000			1.21296
$175$	−2.00000	+	1.73205i	−0.151186	+	0.130931i
$176$	24.0000			1.80907
$177$	4.00000	−	6.92820i	0.300658	−	0.520756i
$178$	−12.0000	−	20.7846i	−0.899438	−	1.55787i
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	15.0000	+	5.19615i	1.11187	+	0.385164i
$183$	−14.0000			−1.03491
$184$		0			0
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	−12.0000	+	20.7846i	−0.877527	+	1.51992i
$188$	4.00000			0.291730
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$	−2.00000			−0.145095
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	4.50000	+	7.79423i	0.323917	+	0.561041i	0.981293	−	0.192522i	$-0.0616668\pi$
$193$	4.50000	+	7.79423i	0.323917	+	0.561041i	−0.657376	+	0.753563i	$0.728333\pi$
$194$	−6.00000	+	10.3923i	−0.430775	+	0.746124i
$195$	−3.00000			−0.214834
$196$	11.0000	+	8.66025i	0.785714	+	0.618590i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$	−6.00000	+	10.3923i	−0.426401	+	0.738549i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$	−3.50000	+	6.06218i	−0.246871	+	0.427593i
$202$	20.0000			1.40720
$203$	4.00000	+	20.7846i	0.280745	+	1.45879i
$204$	−8.00000			−0.560112
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−19.0000	−	32.9090i	−1.32379	−	2.29288i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	−6.00000	+	10.3923i	−0.416025	+	0.720577i
$209$	−6.00000			−0.415029
$210$	−5.00000	−	1.73205i	−0.345033	−	0.119523i
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	12.0000	+	20.7846i	0.820303	+	1.42081i
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$		0			0
$217$	−2.00000	+	1.73205i	−0.135769	+	0.117579i
$218$	30.0000			2.03186
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$	6.00000	+	10.3923i	0.404520	+	0.700649i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	7.00000	−	12.1244i	0.469809	−	0.813733i
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$	−16.0000	+	13.8564i	−1.06904	+	0.925820i
$225$	1.00000			0.0666667
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	0.982877	−	0.184263i	$-0.0589899\pi$
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	−0.651015	+	0.759065i	$0.725657\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$	8.00000			0.527504
$231$	−15.0000	−	5.19615i	−0.986928	−	0.341882i
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	8.00000	−	13.8564i	0.520756	−	0.901975i
$237$	−1.00000			−0.0649570
$238$	−4.00000	−	20.7846i	−0.259281	−	1.34727i
$239$	14.0000			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$240$	2.00000	−	3.46410i	0.129099	−	0.223607i
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	0.995509	+	0.0946700i	$0.0301796\pi$
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	25.0000	+	43.3013i	1.60706	+	2.78351i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−28.0000			−1.79252
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$	12.0000			0.765092
$247$	1.50000	−	2.59808i	0.0954427	−	0.165312i
$248$		0			0
$249$	−1.00000	−	1.73205i	−0.0633724	−	0.109764i
$250$	1.00000	−	1.73205i	0.0632456	−	0.109545i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−1.00000	−	5.19615i	−0.0629941	−	0.327327i
$253$	24.0000			1.50887
$254$	5.00000	−	8.66025i	0.313728	−	0.543393i
$255$	2.00000	+	3.46410i	0.125245	+	0.216930i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−2.00000			−0.124515
$259$	17.5000	+	6.06218i	1.08740	+	0.376685i
$260$	−6.00000			−0.372104
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	2.00000	+	3.46410i	0.123560	+	0.214013i
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	0.797752	−	0.602986i	$-0.206023\pi$
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	−0.921077	+	0.389380i	$0.872689\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$	−12.0000			−0.734388
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$	1.00000	+	1.73205i	0.0608581	+	0.105409i
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$	16.0000			0.970143
$273$	6.00000	−	5.19615i	0.363137	−	0.314485i
$274$	−16.0000			−0.966595
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	21.0000	−	36.3731i	1.25950	−	2.18151i
$279$	1.00000			0.0598684
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	2.00000	−	3.46410i	0.119098	−	0.206284i
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	0.951101	−	0.308879i	$-0.0999539\pi$
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	−0.743048	+	0.669238i	$0.766621\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−0.500000	+	0.866025i	−0.0296174	+	0.0512989i
$286$	−36.0000			−2.12872
$287$	3.00000	+	15.5885i	0.177084	+	0.920158i
$288$	8.00000			0.471405
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−8.00000	−	13.8564i	−0.469776	−	0.813676i
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$	13.0000	−	5.19615i	0.758175	−	0.303046i
$295$	−8.00000			−0.465778
$296$		0			0
$297$	3.00000	+	5.19615i	0.174078	+	0.301511i
$298$	−4.00000	−	6.92820i	−0.231714	−	0.401340i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$	2.00000			0.115470
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	−16.0000			−0.920697
$303$	5.00000	−	8.66025i	0.287242	−	0.497519i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$	3.00000			0.171219			0.0856095	−	0.996329i	$-0.472716\pi$
$307$	3.00000			0.171219			0.0856095	+	0.996329i	$0.472716\pi$
$308$	−30.0000	−	10.3923i	−1.70941	−	0.592157i
$309$	−19.0000			−1.08087
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$	−20.0000			−1.12867
$315$	−2.00000	+	1.73205i	−0.112687	+	0.0975900i
$316$	−2.00000			−0.112509
$317$	−10.0000	+	17.3205i	−0.561656	+	0.972817i	0.435696	+	0.900094i	$0.356502\pi$
$317$	−10.0000	+	17.3205i	−0.561656	+	0.972817i	−0.997352	+	0.0727229i	$0.976831\pi$
$318$	4.00000	+	6.92820i	0.224309	+	0.388514i
$319$	−24.0000	−	41.5692i	−1.34374	−	2.32743i
$320$	4.00000	−	6.92820i	0.223607	−	0.387298i
$321$	12.0000			0.669775
$322$	−16.0000	+	13.8564i	−0.891645	+	0.772187i
$323$	−4.00000			−0.222566
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$	7.50000	−	12.9904i	0.414751	−	0.718370i
$328$		0			0
$329$	5.00000	+	1.73205i	0.275659	+	0.0954911i
$330$	12.0000			0.660578
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	−0.715445	−	0.698669i	$-0.753776\pi$
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	0.962788	+	0.270259i	$0.0871094\pi$
$332$	−2.00000	−	3.46410i	−0.109764	−	0.190117i
$333$	−3.50000	−	6.06218i	−0.191799	−	0.332205i
$334$	−10.0000	+	17.3205i	−0.547176	+	0.947736i
$335$	7.00000			0.382451
$336$	2.00000	+	10.3923i	0.109109	+	0.566947i
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$	−4.00000	+	6.92820i	−0.217571	+	0.376845i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$	−2.00000			−0.108148
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	2.00000	−	3.46410i	0.107676	−	0.186501i
$346$	24.0000	+	41.5692i	1.29025	+	2.23478i
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$	8.00000	−	13.8564i	0.428845	−	0.742781i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	1.00000	+	5.19615i	0.0534522	+	0.277746i
$351$	−3.00000			−0.160128
$352$	24.0000	−	41.5692i	1.27920	−	2.21565i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	−8.00000	−	13.8564i	−0.425195	−	0.736460i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−24.0000			−1.27200
$357$	−10.0000	−	3.46410i	−0.529256	−	0.183340i
$358$	−36.0000			−1.90266
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	13.0000	−	22.5167i	0.683265	−	1.18345i
$363$	25.0000			1.31216
$364$	12.0000	−	10.3923i	0.628971	−	0.544705i
$365$	1.00000			0.0523424
$366$	−14.0000	+	24.2487i	−0.731792	+	1.26750i
$367$	−9.50000	−	16.4545i	−0.495896	−	0.858917i	0.504093	−	0.863649i	$-0.331827\pi$
$367$	−9.50000	−	16.4545i	−0.495896	−	0.858917i	−0.999989	+	0.00473247i	$0.998494\pi$
$368$	−8.00000	−	13.8564i	−0.417029	−	0.722315i
$369$	3.00000	−	5.19615i	0.156174	−	0.270501i
$370$	−14.0000			−0.727825
$371$	−8.00000	+	6.92820i	−0.415339	+	0.359694i
$372$	2.00000			0.103695
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$	24.0000	+	41.5692i	1.24101	+	2.14949i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	24.0000			1.23606
$378$	−5.00000	−	1.73205i	−0.257172	−	0.0890871i
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$	−1.00000	+	1.73205i	−0.0512989	+	0.0888523i
$381$	−2.50000	−	4.33013i	−0.128079	−	0.221839i
$382$	10.0000	+	17.3205i	0.511645	+	0.886194i
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	0.247451	+	0.968900i	$0.420407\pi$
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	−0.962818	+	0.270151i	$0.912926\pi$
$384$		0			0
$385$	3.00000	+	15.5885i	0.152894	+	0.794461i
$386$	18.0000			0.916176
$387$	−0.500000	+	0.866025i	−0.0254164	+	0.0440225i
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$	−3.00000	+	5.19615i	−0.151911	+	0.263117i
$391$	16.0000			0.809155
$392$		0			0
$393$	2.00000			0.100887
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	0.500000	+	0.866025i	0.0251577	+	0.0435745i
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	18.5000	−	32.0429i	0.928488	−	1.60819i	0.142636	−	0.989775i	$-0.454442\pi$
$397$	18.5000	−	32.0429i	0.928488	−	1.60819i	0.785853	−	0.618414i	$-0.212224\pi$
$398$	−16.0000			−0.802008
$399$	−0.500000	−	2.59808i	−0.0250313	−	0.130066i
$400$	−4.00000			−0.200000
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	7.00000	+	12.1244i	0.349128	+	0.604708i
$403$	1.50000	+	2.59808i	0.0747203	+	0.129419i
$404$	10.0000	−	17.3205i	0.497519	−	0.861727i
$405$	1.00000			0.0496904
$406$	40.0000	+	13.8564i	1.98517	+	0.687682i
$407$	−42.0000			−2.08186
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	−4.00000	+	6.92820i	−0.197305	+	0.341743i
$412$	−38.0000			−1.87213
$413$	16.0000	−	13.8564i	0.787309	−	0.681829i
$414$	8.00000			0.393179
$415$	−1.00000	+	1.73205i	−0.0490881	+	0.0850230i
$416$	12.0000	+	20.7846i	0.588348	+	1.01905i
$417$	−10.5000	−	18.1865i	−0.514187	−	0.890598i
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$	−4.00000	+	3.46410i	−0.195180	+	0.169031i
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	−20.0000	+	34.6410i	−0.973585	+	1.68630i
$423$	−1.00000	−	1.73205i	−0.0486217	−	0.0842152i
$424$		0			0
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	−12.0000			−0.581402
$427$	−35.0000	−	12.1244i	−1.69377	−	0.586739i
$428$	24.0000			1.16008
$429$	−9.00000	+	15.5885i	−0.434524	+	0.752618i
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−5.00000			−0.240285			−0.120142	−	0.992757i	$-0.538335\pi$
$433$	−5.00000			−0.240285			−0.120142	+	0.992757i	$0.538335\pi$
$434$	1.00000	+	5.19615i	0.0480015	+	0.249423i
$435$	−8.00000			−0.383571
$436$	15.0000	−	25.9808i	0.718370	−	1.24425i
$437$	2.00000	+	3.46410i	0.0956730	+	0.165710i
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	−24.0000			−1.14156
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$	−7.00000	−	12.1244i	−0.332205	−	0.575396i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−24.0000	+	41.5692i	−1.13643	+	1.96836i
$447$	−4.00000			−0.189194
$448$	4.00000	+	20.7846i	0.188982	+	0.981981i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	−18.0000	−	31.1769i	−0.847587	−	1.46806i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	20.0000			0.938647
$455$	−7.50000	−	2.59808i	−0.351605	−	0.121800i
$456$		0			0
$457$	7.50000	−	12.9904i	0.350835	−	0.607664i	−0.635561	−	0.772051i	$-0.719231\pi$
$457$	7.50000	−	12.9904i	0.350835	−	0.607664i	0.986396	+	0.164386i	$0.0525644\pi$
$458$	13.0000	+	22.5167i	0.607450	+	1.05213i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	−8.00000			−0.372597			−0.186299	−	0.982493i	$-0.559649\pi$
$461$	−8.00000			−0.372597			−0.186299	+	0.982493i	$0.559649\pi$
$462$	−24.0000	+	20.7846i	−1.11658	+	0.966988i
$463$	3.00000			0.139422			0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000			0.139422			0.0697109	+	0.997567i	$0.477792\pi$
$464$	−16.0000	+	27.7128i	−0.742781	+	1.28654i
$465$	−0.500000	−	0.866025i	−0.0231869	−	0.0401610i
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	−11.0000	+	19.0526i	−0.509019	+	0.881647i	0.490926	+	0.871201i	$0.336658\pi$
$467$	−11.0000	+	19.0526i	−0.509019	+	0.881647i	−0.999945	+	0.0104461i	$0.996675\pi$
$468$	−6.00000			−0.277350
$469$	−14.0000	+	12.1244i	−0.646460	+	0.559851i
$470$	−4.00000			−0.184506
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$	1.00000			0.0458831
$476$	−20.0000	−	6.92820i	−0.916698	−	0.317554i
$477$	4.00000			0.183147
$478$	14.0000	−	24.2487i	0.640345	−	1.10911i
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	0.908093	−	0.418769i	$-0.137538\pi$
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	−0.816711	+	0.577047i	$0.804205\pi$
$480$	−4.00000	−	6.92820i	−0.182574	−	0.316228i
$481$	10.5000	−	18.1865i	0.478759	−	0.829235i
$482$	36.0000			1.63976
$483$	2.00000	+	10.3923i	0.0910032	+	0.472866i
$484$	50.0000			2.27273
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$	1.00000	+	1.73205i	0.0453609	+	0.0785674i
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	0.974879	−	0.222737i	$-0.0714992\pi$
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	−0.680335	+	0.732901i	$0.738166\pi$
$488$		0			0
$489$	−12.0000			−0.542659
$490$	−11.0000	−	8.66025i	−0.496929	−	0.391230i
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	−16.0000	−	27.7128i	−0.720604	−	1.24812i
$494$	−3.00000	−	5.19615i	−0.134976	−	0.233786i
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$	−4.00000			−0.179605
$497$	−3.00000	−	15.5885i	−0.134568	−	0.699238i
$498$	−4.00000			−0.179244
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$	5.00000	+	8.66025i	0.223384	+	0.386912i
$502$	12.0000	−	20.7846i	0.535586	−	0.927663i
$503$	−2.00000			−0.0891756			−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000			−0.0891756			−0.0445878	+	0.999005i	$0.514197\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	24.0000	−	41.5692i	1.06693	−	1.84798i
$507$	2.00000	+	3.46410i	0.0888231	+	0.153846i
$508$	−5.00000	−	8.66025i	−0.221839	−	0.384237i
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	−0.955300	−	0.295637i	$-0.904468\pi$
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	0.733679	+	0.679496i	$0.237801\pi$
$510$	8.00000			0.354246
$511$	−2.00000	+	1.73205i	−0.0884748	+	0.0766214i
$512$	−32.0000			−1.41421
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	−18.0000	−	31.1769i	−0.793946	−	1.37515i
$515$	9.50000	+	16.4545i	0.418620	+	0.725071i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	−12.0000			−0.527759
$518$	28.0000	−	24.2487i	1.23025	−	1.06543i
$519$	24.0000			1.05348
$520$		0			0
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	0.818884	−	0.573959i	$-0.194593\pi$
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	−0.906505	+	0.422194i	$0.861260\pi$
$522$	−8.00000	−	13.8564i	−0.350150	−	0.606478i
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	−0.960856	−	0.277047i	$-0.910644\pi$
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	0.720358	+	0.693602i	$0.243977\pi$
$524$	4.00000			0.174741
$525$	2.50000	+	0.866025i	0.109109	+	0.0377964i
$526$	−8.00000			−0.348817
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$	−12.0000	−	20.7846i	−0.522233	−	0.904534i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	4.00000	−	6.92820i	0.173749	−	0.300942i
$531$	−8.00000			−0.347170
$532$	−1.00000	−	5.19615i	−0.0433555	−	0.225282i
$533$	18.0000			0.779667
$534$	−12.0000	+	20.7846i	−0.519291	+	0.899438i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$		0			0
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$	20.0000			0.862261
$539$	−33.0000	−	25.9808i	−1.42141	−	1.11907i
$540$	2.00000			0.0860663
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$	−24.0000	−	41.5692i	−1.03089	−	1.78555i
$543$	−6.50000	−	11.2583i	−0.278942	−	0.483141i
$544$	16.0000	−	27.7128i	0.685994	−	1.18818i
$545$	−15.0000			−0.642529
$546$	−3.00000	−	15.5885i	−0.128388	−	0.667124i
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	−8.00000	+	13.8564i	−0.341743	+	0.591916i
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$	−2.50000	−	0.866025i	−0.106311	−	0.0368271i
$554$	14.0000			0.594803
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$	−21.0000	−	36.3731i	−0.890598	−	1.54256i
$557$	5.00000	+	8.66025i	0.211857	+	0.366947i	0.952296	−	0.305177i	$-0.0987156\pi$
$557$	5.00000	+	8.66025i	0.211857	+	0.366947i	−0.740439	+	0.672124i	$0.765382\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	−3.00000			−0.126886
$560$	8.00000	−	6.92820i	0.338062	−	0.292770i
$561$	24.0000			1.01328
$562$	−12.0000	+	20.7846i	−0.506189	+	0.876746i
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	0.998419	+	0.0562051i	$0.0179001\pi$
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	−0.450535	+	0.892759i	$0.648767\pi$
$564$	−2.00000	−	3.46410i	−0.0842152	−	0.145865i
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$	14.0000			0.588464
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$	1.00000	+	1.73205i	0.0418854	+	0.0725476i
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	0.895704	−	0.444651i	$-0.146672\pi$
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	−0.832931	+	0.553377i	$0.813339\pi$
$572$	−18.0000	+	31.1769i	−0.752618	+	1.30357i
$573$	10.0000			0.417756
$574$	30.0000	+	10.3923i	1.25218	+	0.433766i
$575$	−4.00000			−0.166812
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	14.5000	+	25.1147i	0.603643	+	1.04554i	0.992264	+	0.124143i	$0.0396180\pi$
$577$	14.5000	+	25.1147i	0.603643	+	1.04554i	−0.388621	+	0.921397i	$0.627049\pi$
$578$	−1.00000	−	1.73205i	−0.0415945	−	0.0720438i
$579$	4.50000	−	7.79423i	0.187014	−	0.323917i
$580$	−16.0000			−0.664364
$581$	−1.00000	−	5.19615i	−0.0414870	−	0.215573i
$582$	12.0000			0.497416
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$	−16.0000	+	27.7128i	−0.660954	+	1.14481i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$	2.00000	−	13.8564i	0.0824786	−	0.571429i
$589$	1.00000			0.0412043
$590$	−8.00000	+	13.8564i	−0.329355	+	0.570459i
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	14.0000	+	24.2487i	0.575396	+	0.996616i
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	−0.619915	−	0.784669i	$-0.712833\pi$
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	0.989501	+	0.144528i	$0.0461663\pi$
$594$	12.0000			0.492366
$595$	2.00000	+	10.3923i	0.0819920	+	0.426043i
$596$	−8.00000			−0.327693
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$	12.0000	+	20.7846i	0.490716	+	0.849946i
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	0.903988	−	0.427558i	$-0.140626\pi$
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	−0.822270	+	0.569097i	$0.807293\pi$
$600$		0			0
$601$	−33.0000			−1.34610			−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000			−1.34610			−0.673049	+	0.739598i	$0.735016\pi$
$602$	−5.00000	−	1.73205i	−0.203785	−	0.0705931i
$603$	7.00000			0.285062
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	−12.5000	−	21.6506i	−0.508197	−	0.880223i
$606$	−10.0000	−	17.3205i	−0.406222	−	0.703598i
$607$	−17.5000	+	30.3109i	−0.710303	+	1.23028i	0.254440	+	0.967088i	$0.418109\pi$
$607$	−17.5000	+	30.3109i	−0.710303	+	1.23028i	−0.964743	+	0.263193i	$0.915225\pi$
$608$	8.00000			0.324443
$609$	16.0000	−	13.8564i	0.648353	−	0.561490i
$610$	28.0000			1.13369
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	4.00000	+	6.92820i	0.161690	+	0.280056i
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$	3.00000	−	5.19615i	0.121070	−	0.209700i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−19.0000	+	32.9090i	−0.764292	+	1.32379i
$619$	−1.50000	−	2.59808i	−0.0602901	−	0.104425i	0.834305	−	0.551303i	$-0.185869\pi$
$619$	−1.50000	−	2.59808i	−0.0602901	−	0.104425i	−0.894595	+	0.446878i	$0.852536\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$	−12.0000			−0.481156
$623$	−30.0000	−	10.3923i	−1.20192	−	0.416359i
$624$	12.0000			0.480384
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	−10.0000	+	17.3205i	−0.399043	+	0.691164i
$629$	−28.0000			−1.11643
$630$	1.00000	+	5.19615i	0.0398410	+	0.207020i
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	10.0000	+	17.3205i	0.397464	+	0.688428i
$634$	20.0000	+	34.6410i	0.794301	+	1.37577i
$635$	−2.50000	+	4.33013i	−0.0992095	+	0.171836i
$636$	8.00000			0.317221
$637$	19.5000	−	7.79423i	0.772618	−	0.308819i
$638$	−96.0000			−3.80068
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$	12.0000	−	20.7846i	0.473602	−	0.820303i
$643$	1.00000			0.0394362			0.0197181	−	0.999806i	$-0.493723\pi$
$643$	1.00000			0.0394362			0.0197181	+	0.999806i	$0.493723\pi$
$644$	4.00000	+	20.7846i	0.157622	+	0.819028i
$645$	1.00000			0.0393750
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	−15.0000	−	25.9808i	−0.589711	−	1.02141i	−0.994270	−	0.106897i	$-0.965908\pi$
$647$	−15.0000	−	25.9808i	−0.589711	−	1.02141i	0.404559	−	0.914512i	$-0.367425\pi$
$648$		0			0
$649$	−24.0000	+	41.5692i	−0.942082	+	1.63173i
$650$	6.00000			0.235339
$651$	2.50000	+	0.866025i	0.0979827	+	0.0339422i
$652$	−24.0000			−0.939913
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	−15.0000	−	25.9808i	−0.586546	−	1.01593i
$655$	−1.00000	−	1.73205i	−0.0390732	−	0.0676768i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	1.00000			0.0390137
$658$	8.00000	−	6.92820i	0.311872	−	0.270089i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	6.00000	−	10.3923i	0.233550	−	0.404520i
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$662$	−9.00000	−	15.5885i	−0.349795	−	0.605863i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$		0			0
$665$	−2.00000	+	1.73205i	−0.0775567	+	0.0671660i
$666$	−14.0000			−0.542489
$667$	−16.0000	+	27.7128i	−0.619522	+	1.07304i
$668$	10.0000	+	17.3205i	0.386912	+	0.670151i
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$	7.00000	−	12.1244i	0.270434	−	0.468405i
$671$	84.0000			3.24278
$672$	20.0000	+	6.92820i	0.771517	+	0.267261i
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$	25.0000	−	43.3013i	0.962964	−	1.66790i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	4.00000	+	6.92820i	0.153846	+	0.266469i
$677$	−8.00000	+	13.8564i	−0.307465	+	0.532545i	−0.977807	−	0.209507i	$-0.932814\pi$
$677$	−8.00000	+	13.8564i	−0.307465	+	0.532545i	0.670342	+	0.742052i	$0.266147\pi$
$678$	12.0000			0.460857
$679$	3.00000	+	15.5885i	0.115129	+	0.598230i
$680$		0			0
$681$	5.00000	−	8.66025i	0.191600	−	0.331862i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	24.0000	+	41.5692i	0.918334	+	1.59060i	0.801945	+	0.597398i	$0.203799\pi$
$683$	24.0000	+	41.5692i	0.918334	+	1.59060i	0.116390	+	0.993204i	$0.462868\pi$
$684$	−1.00000	+	1.73205i	−0.0382360	+	0.0662266i
$685$	8.00000			0.305664
$686$	37.0000	−	1.73205i	1.41267	−	0.0661300i
$687$	13.0000			0.495981
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$	−4.00000	−	6.92820i	−0.152277	−	0.263752i
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	0.486312	+	0.873785i	$0.338342\pi$
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	−0.999876	+	0.0157341i	$0.994991\pi$
$692$	48.0000			1.82469
$693$	3.00000	+	15.5885i	0.113961	+	0.592157i
$694$	−32.0000			−1.21470
$695$	−10.5000	+	18.1865i	−0.398288	+	0.689855i
$696$		0			0
$697$	−12.0000	−	20.7846i	−0.454532	−	0.787273i
$698$	2.00000	−	3.46410i	0.0757011	−	0.131118i
$699$	6.00000			0.226941
$700$	5.00000	+	1.73205i	0.188982	+	0.0654654i
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$	−3.00000	+	5.19615i	−0.113228	+	0.196116i
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$	−24.0000	−	41.5692i	−0.904534	−	1.56670i
$705$	−1.00000	+	1.73205i	−0.0376622	+	0.0652328i
$706$	36.0000			1.35488
$707$	20.0000	−	17.3205i	0.752177	−	0.651405i
$708$	−16.0000			−0.601317
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	6.00000	+	10.3923i	0.225176	+	0.390016i
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$	−4.00000			−0.149801
$714$	−16.0000	+	13.8564i	−0.598785	+	0.518563i
$715$	18.0000			0.673162
$716$	−18.0000	+	31.1769i	−0.672692	+	1.16514i
$717$	−7.00000	−	12.1244i	−0.261420	−	0.452792i
$718$	−24.0000	−	41.5692i	−0.895672	−	1.55135i
$719$	17.0000	−	29.4449i	0.633993	−	1.09811i	−0.352735	−	0.935723i	$-0.614748\pi$
$719$	17.0000	−	29.4449i	0.633993	−	1.09811i	0.986728	−	0.162385i	$-0.0519185\pi$
$720$	−4.00000			−0.149071
$721$	−47.5000	−	16.4545i	−1.76899	−	0.612797i
$722$	36.0000			1.33978
$723$	9.00000	−	15.5885i	0.334714	−	0.579741i
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$	25.0000	−	43.3013i	0.927837	−	1.60706i
$727$	7.00000			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$	14.0000	+	24.2487i	0.517455	+	0.896258i
$733$	21.5000	−	37.2391i	0.794121	−	1.37546i	−0.129275	−	0.991609i	$-0.541265\pi$
$733$	21.5000	−	37.2391i	0.794121	−	1.37546i	0.923396	−	0.383849i	$-0.125402\pi$
$734$	−38.0000			−1.40261
$735$	−6.50000	+	2.59808i	−0.239756	+	0.0958315i
$736$	−32.0000			−1.17954
$737$	21.0000	−	36.3731i	0.773545	−	1.33982i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$	−7.00000	+	12.1244i	−0.257325	+	0.445700i
$741$	−3.00000			−0.110208
$742$	4.00000	+	20.7846i	0.146845	+	0.763027i
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$	−1.00000	+	1.73205i	−0.0365881	+	0.0633724i
$748$	48.0000			1.75505
$749$	30.0000	+	10.3923i	1.09618	+	0.379727i
$750$	−2.00000			−0.0730297
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$	24.0000	−	41.5692i	0.874028	−	1.51386i
$755$	8.00000			0.291150
$756$	−4.00000	+	3.46410i	−0.145479	+	0.125988i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	11.0000	−	19.0526i	0.399538	−	0.692020i
$759$	−12.0000	−	20.7846i	−0.435572	−	0.754434i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	−10.0000			−0.362262
$763$	30.0000	−	25.9808i	1.08607	−	0.940567i
$764$	20.0000			0.723575
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	28.0000	+	48.4974i	1.01168	+	1.75228i
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$	−8.00000	+	13.8564i	−0.288675	+	0.500000i
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$	30.0000	+	10.3923i	1.08112	+	0.374513i
$771$	−18.0000			−0.648254
$772$	9.00000	−	15.5885i	0.323917	−	0.561041i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	−0.500000	+	0.866025i	−0.0179605	+	0.0311086i
$776$		0			0
$777$	−3.50000	−	18.1865i	−0.125562	−	0.652438i
$778$	−12.0000			−0.430221
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	3.00000	+	5.19615i	0.107417	+	0.186052i
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	16.0000	−	27.7128i	0.572159	−	0.991008i
$783$	−8.00000			−0.285897
$784$	−4.00000	+	27.7128i	−0.142857	+	0.989743i
$785$	10.0000			0.356915
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	0.996531	+	0.0832226i	$0.0265213\pi$
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	−0.426193	+	0.904632i	$0.640145\pi$
$788$	−12.0000	−	20.7846i	−0.427482	−	0.740421i
$789$	−2.00000	+	3.46410i	−0.0712019	+	0.123325i
$790$	2.00000			0.0711568
$791$	3.00000	+	15.5885i	0.106668	+	0.554262i
$792$		0			0
$793$	−21.0000	+	36.3731i	−0.745732	+	1.29165i
$794$	−37.0000	−	64.0859i	−1.31308	−	2.27432i
$795$	−2.00000	−	3.46410i	−0.0709327	−	0.122859i
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−36.0000			−1.27519			−0.637593	−	0.770374i	$-0.720070\pi$
$797$	−36.0000			−1.27519			−0.637593	+	0.770374i	$0.720070\pi$
$798$	−5.00000	−	1.73205i	−0.176998	−	0.0613139i
$799$	−8.00000			−0.283020
$800$	−4.00000	+	6.92820i	−0.141421	+	0.244949i
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$	14.0000			0.493742
$805$	8.00000	−	6.92820i	0.281963	−	0.244187i
$806$	6.00000			0.211341
$807$	5.00000	−	8.66025i	0.176008	−	0.304855i
$808$		0			0
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$	−48.0000			−1.68551			−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000			−1.68551			−0.842754	+	0.538299i	$0.819067\pi$
$812$	32.0000	−	27.7128i	1.12298	−	0.972529i
$813$	−24.0000			−0.841717
$814$	−42.0000	+	72.7461i	−1.47210	+	2.54975i
$815$	6.00000	+	10.3923i	0.210171	+	0.364027i
$816$	−8.00000	−	13.8564i	−0.280056	−	0.485071i
$817$	−0.500000	+	0.866025i	−0.0174928	+	0.0302984i
$818$	−10.0000			−0.349642
$819$	−7.50000	−	2.59808i	−0.262071	−	0.0907841i
$820$	−12.0000			−0.419058
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$	8.00000	+	13.8564i	0.279032	+	0.483298i
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$	−8.00000	−	41.5692i	−0.278356	−	1.44638i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$	4.00000	−	6.92820i	0.139010	−	0.240772i
$829$	−28.5000	−	49.3634i	−0.989846	−	1.71446i	−0.618024	−	0.786159i	$-0.712066\pi$
$829$	−28.5000	−	49.3634i	−0.989846	−	1.71446i	−0.371822	−	0.928304i	$-0.621267\pi$
$830$	2.00000	+	3.46410i	0.0694210	+	0.120241i
$831$	3.50000	−	6.06218i	0.121414	−	0.210295i
$832$	24.0000			0.832050
$833$	−22.0000	−	17.3205i	−0.762255	−	0.600120i
$834$	−42.0000			−1.45434
$835$	5.00000	−	8.66025i	0.173032	−	0.299700i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	−0.500000	−	0.866025i	−0.0172825	−	0.0299342i
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	1.00000	−	1.73205i	0.0344623	−	0.0596904i
$843$	6.00000	+	10.3923i	0.206651	+	0.357930i
$844$	20.0000	+	34.6410i	0.688428	+	1.19239i
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$	−4.00000			−0.137523
$847$	62.5000	+	21.6506i	2.14753	+	0.743925i
$848$	−16.0000			−0.549442
$849$	3.50000	−	6.06218i	0.120120	−	0.208053i
$850$	−4.00000	−	6.92820i	−0.137199	−	0.237635i
$851$	14.0000	+	24.2487i	0.479914	+	0.831235i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	−9.00000			−0.308154			−0.154077	−	0.988059i	$-0.549240\pi$
$853$	−9.00000			−0.308154			−0.154077	+	0.988059i	$0.549240\pi$
$854$	−56.0000	+	48.4974i	−1.91628	+	1.65955i
$855$	1.00000			0.0341993
$856$		0			0
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$	18.0000	+	31.1769i	0.614510	+	1.06436i
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$	2.00000			0.0681994
$861$	12.0000	−	10.3923i	0.408959	−	0.354169i
$862$	4.00000			0.136241
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$	−4.00000	−	6.92820i	−0.136083	−	0.235702i
$865$	−12.0000	−	20.7846i	−0.408012	−	0.706698i
$866$	−5.00000	+	8.66025i	−0.169907	+	0.294287i
$867$	−1.00000			−0.0339618
$868$	5.00000	+	1.73205i	0.169711	+	0.0587896i
$869$	6.00000			0.203536
$870$	−8.00000	+	13.8564i	−0.271225	+	0.469776i
$871$	10.5000	+	18.1865i	0.355779	+	0.616227i
$872$		0			0
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$	8.00000			0.270604
$875$	−0.500000	−	2.59808i	−0.0169031	−	0.0878310i
$876$	2.00000			0.0675737
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	16.0000	+	27.7128i	0.539974	+	0.935262i
$879$	8.00000	+	13.8564i	0.269833	+	0.467365i
$880$	−12.0000	+	20.7846i	−0.404520	+	0.700649i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−11.0000	−	8.66025i	−0.370389	−	0.291606i
$883$	7.00000			0.235569			0.117784	−	0.993039i	$-0.462421\pi$
$883$	7.00000			0.235569			0.117784	+	0.993039i	$0.462421\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$	4.00000	+	6.92820i	0.134459	+	0.232889i
$886$	−36.0000	−	62.3538i	−1.20944	−	2.09482i
$887$	−5.00000	+	8.66025i	−0.167884	+	0.290783i	−0.937676	−	0.347512i	$-0.887027\pi$
$887$	−5.00000	+	8.66025i	−0.167884	+	0.290783i	0.769792	+	0.638295i	$0.220360\pi$
$888$		0			0
$889$	−2.50000	−	12.9904i	−0.0838473	−	0.435683i
$890$	24.0000			0.804482
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	24.0000	+	41.5692i	0.803579	+	1.39184i
$893$	−1.00000	−	1.73205i	−0.0334637	−	0.0579609i
$894$	−4.00000	+	6.92820i	−0.133780	+	0.231714i
$895$	18.0000			0.601674
$896$		0			0
$897$	12.0000			0.400668
$898$	30.0000	−	51.9615i	1.00111	−	1.73398i
$899$	4.00000	+	6.92820i	0.133407	+	0.231069i
$900$	−1.00000	−	1.73205i	−0.0333333	−	0.0577350i
$901$	8.00000	−	13.8564i	0.266519	−	0.461624i
$902$	−72.0000			−2.39734
$903$	−2.00000	+	1.73205i	−0.0665558	+	0.0576390i
$904$		0			0
$905$	−6.50000	+	11.2583i	−0.216067	+	0.374240i
$906$	8.00000	+	13.8564i	0.265782	+	0.460348i
$907$	−15.5000	−	26.8468i	−0.514669	−	0.891433i	−0.999855	−	0.0170220i	$-0.994581\pi$
$907$	−15.5000	−	26.8468i	−0.514669	−	0.891433i	0.485186	−	0.874411i	$-0.338752\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	−10.0000			−0.331679
$910$	−12.0000	+	10.3923i	−0.397796	+	0.344502i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$	−15.0000	−	25.9808i	−0.496156	−	0.859367i
$915$	7.00000	−	12.1244i	0.231413	−	0.400819i
$916$	26.0000			0.859064
$917$	5.00000	+	1.73205i	0.165115	+	0.0571974i
$918$	8.00000			0.264039
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	−0.782210	−	0.623015i	$-0.785908\pi$
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	0.930652	+	0.365907i	$0.119241\pi$
$920$		0			0
$921$	−1.50000	−	2.59808i	−0.0494267	−	0.0856095i
$922$	−8.00000	+	13.8564i	−0.263466	+	0.456336i
$923$	−18.0000			−0.592477
$924$	6.00000	+	31.1769i	0.197386	+	1.02565i
$925$	7.00000			0.230159
$926$	3.00000	−	5.19615i	0.0985861	−	0.170756i
$927$	9.50000	+	16.4545i	0.312021	+	0.540436i
$928$	32.0000	+	55.4256i	1.05045	+	1.81944i
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$	−2.00000			−0.0655826
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$	12.0000			0.393073
$933$	−3.00000	+	5.19615i	−0.0982156	+	0.170114i
$934$	22.0000	+	38.1051i	0.719862	+	1.24684i
$935$	−12.0000	−	20.7846i	−0.392442	−	0.679729i
$936$		0			0
$937$	−29.0000			−0.947389			−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000			−0.947389			−0.473694	+	0.880689i	$0.657080\pi$
$938$	7.00000	+	36.3731i	0.228558	+	1.18762i
$939$	11.0000			0.358971
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	10.0000	+	17.3205i	0.325818	+	0.564333i
$943$	−12.0000	+	20.7846i	−0.390774	+	0.676840i
$944$	32.0000			1.04151
$945$	2.50000	+	0.866025i	0.0813250	+	0.0281718i
$946$	12.0000			0.390154
$947$	−13.0000	+	22.5167i	−0.422443	+	0.731693i	−0.996178	−	0.0873481i	$-0.972161\pi$
$947$	−13.0000	+	22.5167i	−0.422443	+	0.731693i	0.573735	+	0.819041i	$0.305494\pi$
$948$	1.00000	+	1.73205i	0.0324785	+	0.0562544i
$949$	1.50000	+	2.59808i	0.0486921	+	0.0843371i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	20.0000			0.648544
$952$		0			0
$953$	4.00000			0.129573			0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000			0.129573			0.0647864	+	0.997899i	$0.479363\pi$
$954$	4.00000	−	6.92820i	0.129505	−	0.224309i
$955$	−5.00000	−	8.66025i	−0.161796	−	0.280239i
$956$	−14.0000	−	24.2487i	−0.452792	−	0.784259i
$957$	−24.0000	+	41.5692i	−0.775810	+	1.34374i
$958$	8.00000			0.258468
$959$	−16.0000	+	13.8564i	−0.516667	+	0.447447i
$960$	−8.00000			−0.258199
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	−21.0000	−	36.3731i	−0.677067	−	1.17271i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	18.0000	−	31.1769i	0.579741	−	1.00414i
$965$	−9.00000			−0.289720
$966$	20.0000	+	6.92820i	0.643489	+	0.222911i
$967$	55.0000			1.76868			0.884340	−	0.466843i	$-0.154609\pi$
$967$	55.0000			1.76868			0.884340	+	0.466843i	$0.154609\pi$
$968$		0			0
$969$	2.00000	+	3.46410i	0.0642493	+	0.111283i
$970$	−6.00000	−	10.3923i	−0.192648	−	0.333677i
$971$	26.0000	−	45.0333i	0.834380	−	1.44519i	−0.0601548	−	0.998189i	$-0.519159\pi$
$971$	26.0000	−	45.0333i	0.834380	−	1.44519i	0.894534	−	0.446999i	$-0.147507\pi$
$972$	2.00000			0.0641500
$973$	−10.5000	−	54.5596i	−0.336615	−	1.74910i
$974$	26.0000			0.833094
$975$	1.50000	−	2.59808i	0.0480384	−	0.0832050i
$976$	−28.0000	−	48.4974i	−0.896258	−	1.55236i
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	0.986586	−	0.163242i	$-0.0521952\pi$
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	−0.634665	+	0.772787i	$0.718862\pi$
$978$	−12.0000	+	20.7846i	−0.383718	+	0.664619i
$979$	72.0000			2.30113
$980$	−13.0000	+	5.19615i	−0.415270	+	0.165985i
$981$	−15.0000			−0.478913
$982$	−12.0000	+	20.7846i	−0.382935	+	0.663264i
$983$	−16.0000	−	27.7128i	−0.510321	−	0.883901i	−0.999928	−	0.0119587i	$-0.996193\pi$
$983$	−16.0000	−	27.7128i	−0.510321	−	0.883901i	0.489608	−	0.871943i	$-0.337140\pi$
$984$		0			0
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$	−64.0000			−2.03818
$987$	−1.00000	−	5.19615i	−0.0318304	−	0.165395i
$988$	−6.00000			−0.190885
$989$	2.00000	−	3.46410i	0.0635963	−	0.110152i
$990$	−6.00000	−	10.3923i	−0.190693	−	0.330289i
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	0.960211	−	0.279276i	$-0.0900944\pi$
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	−0.721966	+	0.691929i	$0.756761\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$	−9.00000			−0.285606
$994$	−30.0000	−	10.3923i	−0.951542	−	0.329624i
$995$	8.00000			0.253617
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	0.993213	−	0.116310i	$-0.0371066\pi$
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	−0.597334	+	0.801993i	$0.703773\pi$
$998$	29.0000	+	50.2295i	0.917979	+	1.58999i
$999$	−3.50000	+	6.06218i	−0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.i.b.16.1	✓	2
3.2	odd	2		315.2.j.a.226.1		2
4.3	odd	2		1680.2.bg.l.961.1		2
5.2	odd	4		525.2.r.d.499.2		4
5.3	odd	4		525.2.r.d.499.1		4
5.4	even	2		525.2.i.a.226.1		2
7.2	even	3		735.2.a.b.1.1		1
7.3	odd	6		735.2.i.f.361.1		2
7.4	even	3	inner	105.2.i.b.46.1	yes	2
7.5	odd	6		735.2.a.a.1.1		1
7.6	odd	2		735.2.i.f.226.1		2
21.2	odd	6		2205.2.a.k.1.1		1
21.5	even	6		2205.2.a.m.1.1		1
21.11	odd	6		315.2.j.a.46.1		2
28.11	odd	6		1680.2.bg.l.1201.1		2
35.4	even	6		525.2.i.a.151.1		2
35.9	even	6		3675.2.a.o.1.1		1
35.18	odd	12		525.2.r.d.424.2		4
35.19	odd	6		3675.2.a.p.1.1		1
35.32	odd	12		525.2.r.d.424.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.b.16.1	✓	2	1.1	even	1	trivial
105.2.i.b.46.1	yes	2	7.4	even	3	inner
315.2.j.a.46.1		2	21.11	odd	6
315.2.j.a.226.1		2	3.2	odd	2
525.2.i.a.151.1		2	35.4	even	6
525.2.i.a.226.1		2	5.4	even	2
525.2.r.d.424.1		4	35.32	odd	12
525.2.r.d.424.2		4	35.18	odd	12
525.2.r.d.499.1		4	5.3	odd	4
525.2.r.d.499.2		4	5.2	odd	4
735.2.a.a.1.1		1	7.5	odd	6
735.2.a.b.1.1		1	7.2	even	3
735.2.i.f.226.1		2	7.6	odd	2
735.2.i.f.361.1		2	7.3	odd	6
1680.2.bg.l.961.1		2	4.3	odd	2
1680.2.bg.l.1201.1		2	28.11	odd	6
2205.2.a.k.1.1		1	21.2	odd	6
2205.2.a.m.1.1		1	21.5	even	6
3675.2.a.o.1.1		1	35.9	even	6
3675.2.a.p.1.1		1	35.19	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(-1.00000 + 1.73205i) q^{12} -3.00000 q^{13} +(-5.00000 - 1.73205i) q^{14} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(2.00000 + 3.46410i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +12.0000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +(-4.00000 + 3.46410i) q^{28} -8.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(3.00000 - 5.19615i) q^{33} +8.00000 q^{34} +(2.50000 + 0.866025i) q^{35} +2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +(1.00000 + 5.19615i) q^{42} +1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-1.00000 + 1.73205i) q^{47} -4.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -2.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(3.00000 + 5.19615i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(1.00000 - 1.73205i) q^{54} -6.00000 q^{55} +1.00000 q^{57} +(-8.00000 + 13.8564i) q^{58} +(4.00000 + 6.92820i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(7.00000 - 12.1244i) q^{61} -2.00000 q^{62} +(2.50000 + 0.866025i) q^{63} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-6.00000 - 10.3923i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(4.00000 - 6.92820i) q^{68} -4.00000 q^{69} +(4.00000 - 3.46410i) q^{70} +6.00000 q^{71} +(-0.500000 - 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(12.0000 - 10.3923i) q^{77} +6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +2.00000 q^{83} +(5.00000 + 1.73205i) q^{84} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(4.00000 + 6.92820i) q^{87} +(6.00000 - 10.3923i) q^{89} -2.00000 q^{90} +(1.50000 + 7.79423i) q^{91} -8.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(-4.00000 + 6.92820i) q^{96} -6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} - 4 q^{6} - q^{7} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 - 4 * q^6 - q^7 - q^9	\( 2 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} - 4 q^{6} - q^{7} - q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} - 6 q^{13} - 10 q^{14} + 2 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - q^{19} + 4 q^{20} - 4 q^{21} + 24 q^{22} + 4 q^{23} - q^{25} - 6 q^{26} + 2 q^{27} - 8 q^{28} - 16 q^{29} + 2 q^{30} - q^{31} - 8 q^{32} + 6 q^{33} + 16 q^{34} + 5 q^{35} + 4 q^{36} - 7 q^{37} + 2 q^{38} + 3 q^{39} - 12 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - q^{45} - 8 q^{46} - 2 q^{47} - 8 q^{48} - 13 q^{49} - 4 q^{50} + 4 q^{51} + 6 q^{52} - 4 q^{53} + 2 q^{54} - 12 q^{55} + 2 q^{57} - 16 q^{58} + 8 q^{59} - 2 q^{60} + 14 q^{61} - 4 q^{62} + 5 q^{63} - 16 q^{64} + 3 q^{65} - 12 q^{66} - 7 q^{67} + 8 q^{68} - 8 q^{69} + 8 q^{70} + 12 q^{71} - q^{73} + 14 q^{74} - q^{75} + 4 q^{76} + 24 q^{77} + 12 q^{78} + q^{79} + 4 q^{80} - q^{81} - 12 q^{82} + 4 q^{83} + 10 q^{84} - 8 q^{85} + 2 q^{86} + 8 q^{87} + 12 q^{89} - 4 q^{90} + 3 q^{91} - 16 q^{92} - q^{93} + 4 q^{94} - q^{95} - 8 q^{96} - 12 q^{97} - 4 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 - 4 * q^6 - q^7 - q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 - 6 * q^13 - 10 * q^14 + 2 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^18 - q^19 + 4 * q^20 - 4 * q^21 + 24 * q^22 + 4 * q^23 - q^25 - 6 * q^26 + 2 * q^27 - 8 * q^28 - 16 * q^29 + 2 * q^30 - q^31 - 8 * q^32 + 6 * q^33 + 16 * q^34 + 5 * q^35 + 4 * q^36 - 7 * q^37 + 2 * q^38 + 3 * q^39 - 12 * q^41 + 2 * q^42 + 2 * q^43 + 12 * q^44 - q^45 - 8 * q^46 - 2 * q^47 - 8 * q^48 - 13 * q^49 - 4 * q^50 + 4 * q^51 + 6 * q^52 - 4 * q^53 + 2 * q^54 - 12 * q^55 + 2 * q^57 - 16 * q^58 + 8 * q^59 - 2 * q^60 + 14 * q^61 - 4 * q^62 + 5 * q^63 - 16 * q^64 + 3 * q^65 - 12 * q^66 - 7 * q^67 + 8 * q^68 - 8 * q^69 + 8 * q^70 + 12 * q^71 - q^73 + 14 * q^74 - q^75 + 4 * q^76 + 24 * q^77 + 12 * q^78 + q^79 + 4 * q^80 - q^81 - 12 * q^82 + 4 * q^83 + 10 * q^84 - 8 * q^85 + 2 * q^86 + 8 * q^87 + 12 * q^89 - 4 * q^90 + 3 * q^91 - 16 * q^92 - q^93 + 4 * q^94 - q^95 - 8 * q^96 - 12 * q^97 - 4 * q^98 - 12 * q^99

Introduction

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