LMFDB - Embedded newform 99.2.e.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	99.67
Dual form			99.2.e.a.34.1

$q$-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} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(1.50000 - 2.59808i) q^{18} +6.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +6.92820i q^{21} +(-0.500000 + 0.866025i) q^{22} +(2.00000 - 3.46410i) q^{23} +(4.50000 + 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} -2.00000 q^{26} -5.19615i q^{27} -4.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.50000 + 6.06218i) q^{31} +(-2.50000 + 4.33013i) q^{32} +1.73205i q^{33} +(-2.00000 - 3.46410i) q^{34} +4.00000 q^{35} +3.00000 q^{36} +3.00000 q^{37} +(-3.00000 - 5.19615i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} +(1.00000 - 1.73205i) q^{41} +(6.00000 - 3.46410i) q^{42} +(-3.00000 - 5.19615i) q^{43} -1.00000 q^{44} -3.00000 q^{45} -4.00000 q^{46} +(3.50000 + 6.06218i) q^{47} -1.73205i q^{48} +(-4.50000 + 7.79423i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} -9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +1.00000 q^{55} +(6.00000 + 10.3923i) q^{56} +(-9.00000 - 5.19615i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(3.50000 - 6.06218i) q^{59} -1.73205i q^{60} +7.00000 q^{62} +(6.00000 - 10.3923i) q^{63} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.50000 - 0.866025i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(2.00000 - 3.46410i) q^{68} +(-6.00000 + 3.46410i) q^{69} +(-2.00000 - 3.46410i) q^{70} +9.00000 q^{71} +(-4.50000 - 7.79423i) q^{72} +4.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} -6.92820i q^{75} +(3.00000 - 5.19615i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(3.00000 + 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -2.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(6.00000 + 3.46410i) q^{84} +(-2.00000 + 3.46410i) q^{85} +(-3.00000 + 5.19615i) q^{86} +10.3923i q^{87} +(1.50000 + 2.59808i) q^{88} +6.00000 q^{89} +(1.50000 + 2.59808i) q^{90} -8.00000 q^{91} +(-2.00000 - 3.46410i) q^{92} +(10.5000 - 6.06218i) q^{93} +(3.50000 - 6.06218i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(7.50000 - 4.33013i) q^{96} +(9.50000 + 16.4545i) q^{97} +9.00000 q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 4 q^{7} - 6 q^{8} + 3 q^{9} + 2 q^{10} - q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{15} + q^{16} + 8 q^{17} + 3 q^{18} + 12 q^{19} + q^{20} - q^{22} + 4 q^{23}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 + q^4 - q^5 - 4 * q^7 - 6 * q^8 + 3 * q^9 + 2 * q^10 - q^11 - 3 * q^12 + 2 * q^13 - 4 * q^14 + 3 * q^15 + q^16 + 8 * q^17 + 3 * q^18 + 12 * q^19 + q^20 - q^22 + 4 * q^23 + 9 * q^24 + 4 * q^25 - 4 * q^26 - 8 * q^28 - 6 * q^29 - 3 * q^30 - 7 * q^31 - 5 * q^32 - 4 * q^34 + 8 * q^35 + 6 * q^36 + 6 * q^37 - 6 * q^38 - 6 * q^39 + 3 * q^40 + 2 * q^41 + 12 * q^42 - 6 * q^43 - 2 * q^44 - 6 * q^45 - 8 * q^46 + 7 * q^47 - 9 * q^49 + 4 * q^50 - 12 * q^51 - 2 * q^52 - 18 * q^53 - 9 * q^54 + 2 * q^55 + 12 * q^56 - 18 * q^57 - 6 * q^58 + 7 * q^59 + 14 * q^62 + 12 * q^63 + 14 * q^64 + 2 * q^65 + 3 * q^66 - 11 * q^67 + 4 * q^68 - 12 * q^69 - 4 * q^70 + 18 * q^71 - 9 * q^72 + 8 * q^73 - 3 * q^74 + 6 * q^76 - 4 * q^77 + 6 * q^78 - 8 * q^79 - 2 * q^80 - 9 * q^81 - 4 * q^82 + 12 * q^83 + 12 * q^84 - 4 * q^85 - 6 * q^86 + 3 * q^88 + 12 * q^89 + 3 * q^90 - 16 * q^91 - 4 * q^92 + 21 * q^93 + 7 * q^94 - 6 * q^95 + 15 * q^96 + 19 * q^97 + 18 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$			1.73205i			0.707107i
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	−3.00000			−1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.00000			0.316228
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$			6.92820i			1.51186i
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	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	$0.0297381\pi$
$24$	4.50000	+	2.59808i	0.918559	+	0.530330i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−2.00000			−0.392232
$27$		−	5.19615i		−	1.00000i
$28$	−4.00000			−0.755929
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	−1.50000	−	0.866025i	−0.273861	−	0.158114i
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$			1.73205i			0.301511i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$	4.00000			0.676123
$36$	3.00000			0.500000
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−3.00000	+	1.73205i	−0.480384	+	0.277350i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$	6.00000	−	3.46410i	0.925820	−	0.534522i
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	−1.00000			−0.150756
$45$	−3.00000			−0.447214
$46$	−4.00000			−0.589768
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	0.999926	+	0.0121990i	$0.00388317\pi$
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	−0.489398	+	0.872060i	$0.662783\pi$
$48$		−	1.73205i		−	0.250000i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	−6.00000	−	3.46410i	−0.840168	−	0.485071i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	1.00000			0.134840
$56$	6.00000	+	10.3923i	0.801784	+	1.38873i
$57$	−9.00000	−	5.19615i	−1.19208	−	0.688247i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	−0.543065	−	0.839691i	$-0.682736\pi$
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	0.998726	+	0.0504625i	$0.0160695\pi$
$60$		−	1.73205i		−	0.223607i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	7.00000			0.889001
$63$	6.00000	−	10.3923i	0.755929	−	1.30931i
$64$	7.00000			0.875000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$	1.50000	−	0.866025i	0.184637	−	0.106600i
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	−6.00000	+	3.46410i	−0.722315	+	0.417029i
$70$	−2.00000	−	3.46410i	−0.239046	−	0.414039i
$71$	9.00000			1.06810			0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000			1.06810			0.534052	+	0.845452i	$0.320669\pi$
$72$	−4.50000	−	7.79423i	−0.530330	−	0.918559i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$		−	6.92820i		−	0.800000i
$76$	3.00000	−	5.19615i	0.344124	−	0.596040i
$77$	−2.00000	+	3.46410i	−0.227921	+	0.394771i
$78$	3.00000	+	1.73205i	0.339683	+	0.196116i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−2.00000			−0.220863
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$	6.00000	+	3.46410i	0.654654	+	0.377964i
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$			10.3923i			1.11417i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$	−8.00000			−0.838628
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$	10.5000	−	6.06218i	1.08880	−	0.628619i
$94$	3.50000	−	6.06218i	0.360997	−	0.625266i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	9.50000	+	16.4545i	0.964579	+	1.67070i	0.710742	+	0.703452i	$0.248359\pi$
$97$	9.50000	+	16.4545i	0.964579	+	1.67070i	0.253837	+	0.967247i	$0.418307\pi$
$98$	9.00000			0.909137
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	4.00000			0.400000
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	0.948207	−	0.317653i	$-0.102895\pi$
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	−0.749199	+	0.662344i	$0.769562\pi$
$102$			6.92820i			0.685994i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−3.00000	+	5.19615i	−0.294174	+	0.509525i
$105$	−6.00000	−	3.46410i	−0.585540	−	0.338062i
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	−4.50000	−	2.59808i	−0.427121	−	0.246598i
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$			10.3923i			0.973329i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	−6.00000			−0.557086
$117$	6.00000			0.554700
$118$	−7.00000			−0.644402
$119$	−8.00000	−	13.8564i	−0.733359	−	1.27021i
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.00000	+	1.73205i	−0.270501	+	0.156174i
$124$	3.50000	+	6.06218i	0.314309	+	0.544400i
$125$	−9.00000			−0.804984
$126$	−12.0000			−1.06904
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$			10.3923i			0.914991i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	1.50000	+	0.866025i	0.130558	+	0.0753778i
$133$	−12.0000	−	20.7846i	−1.04053	−	1.80225i
$134$	11.0000			0.950255
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	−12.0000			−1.02899
$137$	−2.50000	−	4.33013i	−0.213589	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$137$	−2.50000	−	4.33013i	−0.213589	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$138$	6.00000	+	3.46410i	0.510754	+	0.294884i
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	−0.820495	−	0.571654i	$-0.806302\pi$
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	0.905314	+	0.424743i	$0.139635\pi$
$140$	2.00000	−	3.46410i	0.169031	−	0.292770i
$141$		−	12.1244i		−	1.02105i
$142$	−4.50000	−	7.79423i	−0.377632	−	0.654077i
$143$	−2.00000			−0.167248
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	6.00000			0.498273
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	13.5000	−	7.79423i	1.11346	−	0.642857i
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	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	$0.114277\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	−18.0000			−1.45999
$153$	6.00000	+	10.3923i	0.485071	+	0.840168i
$154$	4.00000			0.322329
$155$	−3.50000	−	6.06218i	−0.281127	−	0.486926i
$156$			3.46410i			0.277350i
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$	13.5000	+	7.79423i	1.07062	+	0.618123i
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$	−16.0000			−1.26098
$162$	9.00000			0.707107
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	−1.50000	−	0.866025i	−0.116775	−	0.0674200i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		−	20.7846i		−	1.60357i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	4.00000			0.306786
$171$	9.00000	+	15.5885i	0.688247	+	1.19208i
$172$	−6.00000			−0.457496
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	9.00000	−	5.19615i	0.682288	−	0.393919i
$175$	8.00000	−	13.8564i	0.604743	−	1.04745i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	−10.5000	+	6.06218i	−0.789228	+	0.455661i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	4.00000	+	6.92820i	0.296500	+	0.513553i
$183$		0			0
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$	−10.5000	−	6.06218i	−0.769897	−	0.444500i
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	7.00000			0.510527
$189$	−18.0000	+	10.3923i	−1.30931	+	0.755929i
$190$	6.00000			0.435286
$191$	6.50000	+	11.2583i	0.470323	+	0.814624i	0.999424	−	0.0339349i	$-0.0108039\pi$
$191$	6.50000	+	11.2583i	0.470323	+	0.814624i	−0.529101	+	0.848559i	$0.677471\pi$
$192$	−10.5000	−	6.06218i	−0.757772	−	0.437500i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	9.50000	−	16.4545i	0.682060	−	1.18136i
$195$		−	3.46410i		−	0.248069i
$196$	4.50000	+	7.79423i	0.321429	+	0.556731i
$197$	16.0000			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$198$	−3.00000			−0.213201
$199$	−3.00000			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$200$	−6.00000	−	10.3923i	−0.424264	−	0.734847i
$201$	16.5000	−	9.52628i	1.16382	−	0.671932i
$202$	2.00000	−	3.46410i	0.140720	−	0.243733i
$203$	−12.0000	+	20.7846i	−0.842235	+	1.45879i
$204$	−6.00000	+	3.46410i	−0.420084	+	0.242536i
$205$	1.00000	+	1.73205i	0.0698430	+	0.120972i
$206$	−13.0000			−0.905753
$207$	12.0000			0.834058
$208$	2.00000			0.138675
$209$	−3.00000	−	5.19615i	−0.207514	−	0.359425i
$210$			6.92820i			0.478091i
$211$	−3.00000	+	5.19615i	−0.206529	+	0.357718i	−0.950619	−	0.310361i	$-0.899550\pi$
$211$	−3.00000	+	5.19615i	−0.206529	+	0.357718i	0.744090	+	0.668079i	$0.232883\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$	−13.5000	−	7.79423i	−0.925005	−	0.534052i
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$	6.00000			0.409197
$216$			15.5885i			1.06066i
$217$	28.0000			1.90076
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$			5.19615i			0.348743i
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	20.0000			1.33631
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	−15.0000			−0.997785
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$	−9.00000	+	5.19615i	−0.596040	+	0.344124i
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	−0.749714	−	0.661762i	$-0.769809\pi$
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	0.947960	+	0.318390i	$0.103142\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$	6.00000	−	3.46410i	0.394771	−	0.227921i
$232$	9.00000	+	15.5885i	0.590879	+	1.02343i
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	−7.00000			−0.456630
$236$	−3.50000	−	6.06218i	−0.227831	−	0.394614i
$237$			13.8564i			0.900070i
$238$	−8.00000	+	13.8564i	−0.518563	+	0.898177i
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	1.50000	+	0.866025i	0.0968246	+	0.0559017i
$241$	−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	$0.937715\pi$
$242$	1.00000			0.0642824
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		0			0
$245$	−4.50000	−	7.79423i	−0.287494	−	0.497955i
$246$	3.00000	+	1.73205i	0.191273	+	0.110432i
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$	10.5000	−	18.1865i	0.666751	−	1.15485i
$249$		−	20.7846i		−	1.31717i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	28.0000			1.76734			0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000			1.76734			0.883672	+	0.468106i	$0.155064\pi$
$252$	−6.00000	−	10.3923i	−0.377964	−	0.654654i
$253$	−4.00000			−0.251478
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$	6.00000	−	3.46410i	0.375735	−	0.216930i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$	9.00000	−	5.19615i	0.560316	−	0.323498i
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$	2.00000			0.124035
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	−6.00000			−0.370681
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		−	5.19615i		−	0.319801i
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$	−12.0000	+	20.7846i	−0.735767	+	1.27439i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	5.50000	+	9.52628i	0.335966	+	0.581910i
$269$	−17.0000			−1.03651			−0.518254	−	0.855227i	$-0.673418\pi$
$269$	−17.0000			−1.03651			−0.518254	+	0.855227i	$0.673418\pi$
$270$		−	5.19615i		−	0.316228i
$271$	−22.0000			−1.33640			−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000			−1.33640			−0.668202	+	0.743980i	$0.732936\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$	12.0000	+	6.92820i	0.726273	+	0.419314i
$274$	−2.50000	+	4.33013i	−0.151031	+	0.261593i
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$			6.92820i			0.417029i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−2.00000			−0.119952
$279$	−21.0000			−1.25724
$280$	−12.0000			−0.717137
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$	−10.5000	+	6.06218i	−0.625266	+	0.360997i
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	4.50000	−	7.79423i	0.267026	−	0.462502i
$285$	9.00000	−	5.19615i	0.533114	−	0.307794i
$286$	1.00000	+	1.73205i	0.0591312	+	0.102418i
$287$	−8.00000			−0.472225
$288$	−15.0000			−0.883883
$289$	−1.00000			−0.0588235
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$		−	32.9090i		−	1.92916i
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$	−13.5000	−	7.79423i	−0.787336	−	0.454569i
$295$	3.50000	+	6.06218i	0.203778	+	0.352954i
$296$	−9.00000			−0.523114
$297$	−4.50000	+	2.59808i	−0.261116	+	0.150756i
$298$	−4.00000			−0.231714
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$	−6.00000	−	3.46410i	−0.346410	−	0.200000i
$301$	−12.0000	+	20.7846i	−0.691669	+	1.19800i
$302$	8.00000	−	13.8564i	0.460348	−	0.797347i
$303$		−	6.92820i		−	0.398015i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$		0			0
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	2.00000	+	3.46410i	0.113961	+	0.197386i
$309$	−19.5000	+	11.2583i	−1.10932	+	0.640464i
$310$	−3.50000	+	6.06218i	−0.198787	+	0.344309i
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	−0.398090	−	0.917346i	$-0.630327\pi$
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	0.993490	−	0.113917i	$-0.0363399\pi$
$312$	9.00000	−	5.19615i	0.509525	−	0.294174i
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	−7.00000			−0.395033
$315$	6.00000	+	10.3923i	0.338062	+	0.585540i
$316$	−8.00000			−0.450035
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	−0.989882	−	0.141890i	$-0.954682\pi$
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	0.372061	−	0.928208i	$-0.378651\pi$
$318$		−	15.5885i		−	0.874157i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	−3.50000	+	6.06218i	−0.195656	+	0.338886i
$321$	27.0000	+	15.5885i	1.50699	+	0.870063i
$322$	8.00000	+	13.8564i	0.445823	+	0.772187i
$323$	24.0000			1.33540
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	8.00000			0.443760
$326$	5.50000	+	9.52628i	0.304617	+	0.527612i
$327$	3.00000	+	1.73205i	0.165900	+	0.0957826i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	14.0000	−	24.2487i	0.771845	−	1.33687i
$330$			1.73205i			0.0953463i
$331$	−0.500000	−	0.866025i	−0.0274825	−	0.0476011i	0.851957	−	0.523612i	$-0.175416\pi$
$331$	−0.500000	−	0.866025i	−0.0274825	−	0.0476011i	−0.879440	+	0.476011i	$0.842082\pi$
$332$	12.0000			0.658586
$333$	4.50000	+	7.79423i	0.246598	+	0.427121i
$334$	12.0000			0.656611
$335$	−5.50000	−	9.52628i	−0.300497	−	0.520476i
$336$	−6.00000	+	3.46410i	−0.327327	+	0.188982i
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−22.5000	+	12.9904i	−1.22203	+	0.705541i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	7.00000			0.379071
$342$	9.00000	−	15.5885i	0.486664	−	0.842927i
$343$	8.00000			0.431959
$344$	9.00000	+	15.5885i	0.485247	+	0.840473i
$345$		−	6.92820i		−	0.373002i
$346$		0			0
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$	9.00000	+	5.19615i	0.482451	+	0.278543i
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$	−16.0000			−0.855236
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$	5.00000			0.266501
$353$	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	$0.674325\pi$
$354$	10.5000	+	6.06218i	0.558069	+	0.322201i
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	3.00000	−	5.19615i	0.159000	−	0.275396i
$357$			27.7128i			1.46672i
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	−32.0000			−1.68890			−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000			−1.68890			−0.844448	+	0.535638i	$0.820071\pi$
$360$	9.00000			0.474342
$361$	17.0000			0.894737
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	1.50000	−	0.866025i	0.0787296	−	0.0454545i
$364$	−4.00000	+	6.92820i	−0.209657	+	0.363137i
$365$	−2.00000	+	3.46410i	−0.104685	+	0.181319i
$366$		0			0
$367$	5.50000	+	9.52628i	0.287098	+	0.497268i	0.973116	−	0.230317i	$-0.0739762\pi$
$367$	5.50000	+	9.52628i	0.287098	+	0.497268i	−0.686018	+	0.727585i	$0.740643\pi$
$368$	4.00000			0.208514
$369$	6.00000			0.312348
$370$	3.00000			0.155963
$371$	18.0000	+	31.1769i	0.934513	+	1.61862i
$372$		−	12.1244i		−	0.628619i
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	−0.965945	−	0.258748i	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$	13.5000	+	7.79423i	0.697137	+	0.402492i
$376$	−10.5000	−	18.1865i	−0.541496	−	0.937899i
$377$	−12.0000			−0.618031
$378$	18.0000	+	10.3923i	0.925820	+	0.534522i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$	6.50000	−	11.2583i	0.332569	−	0.576026i
$383$	−14.5000	+	25.1147i	−0.740915	+	1.28330i	0.211164	+	0.977451i	$0.432275\pi$
$383$	−14.5000	+	25.1147i	−0.740915	+	1.28330i	−0.952079	+	0.305852i	$0.901059\pi$
$384$		−	5.19615i		−	0.265165i
$385$	−2.00000	−	3.46410i	−0.101929	−	0.176547i
$386$	4.00000			0.203595
$387$	9.00000	−	15.5885i	0.457496	−	0.792406i
$388$	19.0000			0.964579
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	−0.892735	−	0.450582i	$-0.851216\pi$
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	0.0561516	−	0.998422i	$-0.482117\pi$
$390$	−3.00000	+	1.73205i	−0.151911	+	0.0877058i
$391$	8.00000	−	13.8564i	0.404577	−	0.700749i
$392$	13.5000	−	23.3827i	0.681853	−	1.18100i
$393$	−9.00000	+	5.19615i	−0.453990	+	0.262111i
$394$	−8.00000	−	13.8564i	−0.403034	−	0.698076i
$395$	8.00000			0.402524
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	1.50000	+	2.59808i	0.0751882	+	0.130230i
$399$			41.5692i			2.08106i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	−0.996371	−	0.0851195i	$-0.972873\pi$
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	0.571901	+	0.820323i	$0.306206\pi$
$402$	−16.5000	−	9.52628i	−0.822945	−	0.475128i
$403$	7.00000	+	12.1244i	0.348695	+	0.603957i
$404$	4.00000			0.199007
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$	24.0000			1.19110
$407$	−1.50000	−	2.59808i	−0.0743522	−	0.128782i
$408$	18.0000	+	10.3923i	0.891133	+	0.514496i
$409$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$			8.66025i			0.427179i
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$	−28.0000			−1.37779
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$	−12.0000			−0.589057
$416$	5.00000	+	8.66025i	0.245145	+	0.424604i
$417$	−3.00000	+	1.73205i	−0.146911	+	0.0848189i
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	−2.50000	+	4.33013i	−0.122133	+	0.211541i	−0.920609	−	0.390487i	$-0.872307\pi$
$419$	−2.50000	+	4.33013i	−0.122133	+	0.211541i	0.798476	+	0.602027i	$0.205640\pi$
$420$	−6.00000	+	3.46410i	−0.292770	+	0.169031i
$421$	−6.50000	−	11.2583i	−0.316791	−	0.548697i	0.663026	−	0.748596i	$-0.269272\pi$
$421$	−6.50000	−	11.2583i	−0.316791	−	0.548697i	−0.979817	+	0.199899i	$0.935939\pi$
$422$	6.00000			0.292075
$423$	−10.5000	+	18.1865i	−0.510527	+	0.884260i
$424$	27.0000			1.31124
$425$	8.00000	+	13.8564i	0.388057	+	0.672134i
$426$			15.5885i			0.755263i
$427$		0			0
$428$	−9.00000	+	15.5885i	−0.435031	+	0.753497i
$429$	3.00000	+	1.73205i	0.144841	+	0.0836242i
$430$	−3.00000	−	5.19615i	−0.144673	−	0.250581i
$431$	−30.0000			−1.44505			−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000			−1.44505			−0.722525	+	0.691345i	$0.757018\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−14.0000	−	24.2487i	−0.672022	−	1.16398i
$435$	−9.00000	−	5.19615i	−0.431517	−	0.249136i
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$			6.92820i			0.331042i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$	−3.00000			−0.143019
$441$	−27.0000			−1.28571
$442$	−8.00000			−0.380521
$443$	−0.500000	−	0.866025i	−0.0237557	−	0.0411461i	0.853903	−	0.520432i	$-0.174229\pi$
$443$	−0.500000	−	0.866025i	−0.0237557	−	0.0411461i	−0.877659	+	0.479286i	$0.840896\pi$
$444$	−4.50000	+	2.59808i	−0.213561	+	0.123299i
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	−6.00000	+	3.46410i	−0.283790	+	0.163846i
$448$	−14.0000	−	24.2487i	−0.661438	−	1.14564i
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$	12.0000			0.565685
$451$	−2.00000			−0.0941763
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$		−	27.7128i		−	1.30206i
$454$	9.00000	−	15.5885i	0.422391	−	0.731603i
$455$	4.00000	−	6.92820i	0.187523	−	0.324799i
$456$	27.0000	+	15.5885i	1.26439	+	0.729996i
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	0.927622	−	0.373519i	$-0.121849\pi$
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	−0.787288	+	0.616585i	$0.788516\pi$
$458$	−6.00000			−0.280362
$459$		−	20.7846i		−	0.970143i
$460$	4.00000			0.186501
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$	−6.00000	−	3.46410i	−0.279145	−	0.161165i
$463$	4.00000	−	6.92820i	0.185896	−	0.321981i	−0.757982	−	0.652275i	$-0.773815\pi$
$463$	4.00000	−	6.92820i	0.185896	−	0.321981i	0.943878	+	0.330294i	$0.107148\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$			12.1244i			0.562254i
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$	3.00000	−	5.19615i	0.138675	−	0.240192i
$469$	44.0000			2.03173
$470$	3.50000	+	6.06218i	0.161443	+	0.279627i
$471$	−10.5000	+	6.06218i	−0.483814	+	0.279330i
$472$	−10.5000	+	18.1865i	−0.483302	+	0.837103i
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$	12.0000	−	6.92820i	0.551178	−	0.318223i
$475$	12.0000	+	20.7846i	0.550598	+	0.953663i
$476$	−16.0000			−0.733359
$477$	−13.5000	−	23.3827i	−0.618123	−	1.07062i
$478$	6.00000			0.274434
$479$	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	$0.804205\pi$
$480$			8.66025i			0.395285i
$481$	3.00000	−	5.19615i	0.136788	−	0.236924i
$482$	−5.00000	+	8.66025i	−0.227744	+	0.394464i
$483$	24.0000	+	13.8564i	1.09204	+	0.630488i
$484$	0.500000	+	0.866025i	0.0227273	+	0.0393648i
$485$	−19.0000			−0.862746
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−37.0000			−1.67663			−0.838315	−	0.545186i	$-0.816459\pi$
$487$	−37.0000			−1.67663			−0.838315	+	0.545186i	$0.816459\pi$
$488$		0			0
$489$	16.5000	+	9.52628i	0.746156	+	0.430793i
$490$	−4.50000	+	7.79423i	−0.203289	+	0.352107i
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	−0.761539	−	0.648119i	$-0.775556\pi$
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	0.942057	+	0.335453i	$0.108889\pi$
$492$			3.46410i			0.156174i
$493$	−12.0000	−	20.7846i	−0.540453	−	0.936092i
$494$	−12.0000			−0.539906
$495$	1.50000	+	2.59808i	0.0674200	+	0.116775i
$496$	−7.00000			−0.314309
$497$	−18.0000	−	31.1769i	−0.807410	−	1.39848i
$498$	−18.0000	+	10.3923i	−0.806599	+	0.465690i
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	18.0000	−	10.3923i	0.804181	−	0.464294i
$502$	−14.0000	−	24.2487i	−0.624851	−	1.08227i
$503$	−14.0000			−0.624229			−0.312115	−	0.950044i	$-0.601037\pi$
$503$	−14.0000			−0.624229			−0.312115	+	0.950044i	$0.601037\pi$
$504$	−18.0000	+	31.1769i	−0.801784	+	1.38873i
$505$	−4.00000			−0.177998
$506$	2.00000	+	3.46410i	0.0889108	+	0.153998i
$507$		−	15.5885i		−	0.692308i
$508$	1.00000	−	1.73205i	0.0443678	−	0.0768473i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$	−6.00000	−	3.46410i	−0.265684	−	0.153393i
$511$	−8.00000	−	13.8564i	−0.353899	−	0.612971i
$512$	−11.0000			−0.486136
$513$		−	31.1769i		−	1.37649i
$514$	22.0000			0.970378
$515$	6.50000	+	11.2583i	0.286424	+	0.496101i
$516$	9.00000	+	5.19615i	0.396203	+	0.228748i
$517$	3.50000	−	6.06218i	0.153930	−	0.266614i
$518$	−6.00000	+	10.3923i	−0.263625	+	0.456612i
$519$		0			0
$520$	−3.00000	−	5.19615i	−0.131559	−	0.227866i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−18.0000			−0.787839
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−3.00000	−	5.19615i	−0.131056	−	0.226995i
$525$	−24.0000	+	13.8564i	−1.04745	+	0.604743i
$526$	8.00000	−	13.8564i	0.348817	−	0.604168i
$527$	−14.0000	+	24.2487i	−0.609850	+	1.05629i
$528$	−1.50000	+	0.866025i	−0.0652791	+	0.0376889i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−9.00000			−0.390935
$531$	21.0000			0.911322
$532$	−24.0000			−1.04053
$533$	−2.00000	−	3.46410i	−0.0866296	−	0.150047i
$534$			10.3923i			0.449719i
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$	16.5000	−	28.5788i	0.712691	−	1.23442i
$537$	13.5000	+	7.79423i	0.582568	+	0.336346i
$538$	8.50000	+	14.7224i	0.366461	+	0.634729i
$539$	9.00000			0.387657
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$	11.0000	+	19.0526i	0.472490	+	0.818377i
$543$	−10.5000	−	6.06218i	−0.450598	−	0.260153i
$544$	−10.0000	+	17.3205i	−0.428746	+	0.742611i
$545$	1.00000	−	1.73205i	0.0428353	−	0.0741929i
$546$		−	13.8564i		−	0.592999i
$547$	11.0000	+	19.0526i	0.470326	+	0.814629i	0.999424	−	0.0339321i	$-0.0108030\pi$
$547$	11.0000	+	19.0526i	0.470326	+	0.814629i	−0.529098	+	0.848561i	$0.677470\pi$
$548$	−5.00000			−0.213589
$549$		0			0
$550$	−4.00000			−0.170561
$551$	−18.0000	−	31.1769i	−0.766826	−	1.32818i
$552$	18.0000	−	10.3923i	0.766131	−	0.442326i
$553$	−16.0000	+	27.7128i	−0.680389	+	1.17847i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$	4.50000	−	2.59808i	0.191014	−	0.110282i
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	40.0000			1.69485			0.847427	−	0.530912i	$-0.178150\pi$
$557$	40.0000			1.69485			0.847427	+	0.530912i	$0.178150\pi$
$558$	10.5000	+	18.1865i	0.444500	+	0.769897i
$559$	−12.0000			−0.507546
$560$	2.00000	+	3.46410i	0.0845154	+	0.146385i
$561$			6.92820i			0.292509i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	−0.679974	−	0.733237i	$-0.738009\pi$
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	0.974988	+	0.222256i	$0.0713421\pi$
$564$	−10.5000	−	6.06218i	−0.442130	−	0.255264i
$565$	7.50000	+	12.9904i	0.315527	+	0.546509i
$566$	28.0000			1.17693
$567$	36.0000			1.51186
$568$	−27.0000			−1.13289
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−9.00000	−	5.19615i	−0.376969	−	0.217643i
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−1.00000	+	1.73205i	−0.0418121	+	0.0724207i
$573$		−	22.5167i		−	0.940647i
$574$	4.00000	+	6.92820i	0.166957	+	0.289178i
$575$	16.0000			0.667246
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	−3.00000			−0.124892			−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000			−0.124892			−0.0624458	+	0.998048i	$0.519890\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	6.00000	−	3.46410i	0.249351	−	0.143963i
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	24.0000	−	41.5692i	0.995688	−	1.72458i
$582$	−28.5000	+	16.4545i	−1.18136	+	0.682060i
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	−12.0000			−0.496564
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	12.0000			0.495715
$587$	2.50000	+	4.33013i	0.103186	+	0.178723i	0.912996	−	0.407969i	$-0.133763\pi$
$587$	2.50000	+	4.33013i	0.103186	+	0.178723i	−0.809810	+	0.586693i	$0.800430\pi$
$588$		−	15.5885i		−	0.642857i
$589$	−21.0000	+	36.3731i	−0.865290	+	1.49873i
$590$	3.50000	−	6.06218i	0.144093	−	0.249576i
$591$	−24.0000	−	13.8564i	−0.987228	−	0.569976i
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$	4.50000	+	2.59808i	0.184637	+	0.106600i
$595$	16.0000			0.655936
$596$	−2.00000	−	3.46410i	−0.0819232	−	0.141895i
$597$	4.50000	+	2.59808i	0.184173	+	0.106332i
$598$	−4.00000	+	6.92820i	−0.163572	+	0.283315i
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	−0.903988	−	0.427558i	$-0.859374\pi$
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	0.822270	+	0.569097i	$0.192707\pi$
$600$			20.7846i			0.848528i
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$	24.0000			0.978167
$603$	−33.0000			−1.34386
$604$	16.0000			0.651031
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	−6.00000	+	3.46410i	−0.243733	+	0.140720i
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	−15.0000	+	25.9808i	−0.608330	+	1.05366i
$609$	36.0000	−	20.7846i	1.45879	−	0.842235i
$610$		0			0
$611$	14.0000			0.566379
$612$	12.0000			0.485071
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		−	3.46410i		−	0.139686i
$616$	6.00000	−	10.3923i	0.241747	−	0.418718i
$617$	7.50000	−	12.9904i	0.301939	−	0.522973i	−0.674636	−	0.738150i	$-0.735700\pi$
$617$	7.50000	−	12.9904i	0.301939	−	0.522973i	0.976575	+	0.215177i	$0.0690329\pi$
$618$	19.5000	+	11.2583i	0.784405	+	0.452876i
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	0.999996	+	0.00279365i	$0.000889247\pi$
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	−0.497579	+	0.867419i	$0.665777\pi$
$620$	−7.00000			−0.281127
$621$	−18.0000	−	10.3923i	−0.722315	−	0.417029i
$622$	−21.0000			−0.842023
$623$	−12.0000	−	20.7846i	−0.480770	−	0.832718i
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$			10.3923i			0.415029i
$628$	−3.50000	−	6.06218i	−0.139665	−	0.241907i
$629$	12.0000			0.478471
$630$	6.00000	−	10.3923i	0.239046	−	0.414039i
$631$	37.0000			1.47295			0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000			1.47295			0.736473	+	0.676467i	$0.236490\pi$
$632$	12.0000	+	20.7846i	0.477334	+	0.826767i
$633$	9.00000	−	5.19615i	0.357718	−	0.206529i
$634$	−11.0000	+	19.0526i	−0.436866	+	0.756674i
$635$	−1.00000	+	1.73205i	−0.0396838	+	0.0687343i
$636$	13.5000	−	7.79423i	0.535310	−	0.309061i
$637$	9.00000	+	15.5885i	0.356593	+	0.617637i
$638$	6.00000			0.237542
$639$	13.5000	+	23.3827i	0.534052	+	0.925005i
$640$	−3.00000			−0.118585
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		−	31.1769i		−	1.23045i
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$	−8.00000	+	13.8564i	−0.315244	+	0.546019i
$645$	−9.00000	−	5.19615i	−0.354375	−	0.204598i
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	13.5000	−	23.3827i	0.530330	−	0.918559i
$649$	−7.00000			−0.274774
$650$	−4.00000	−	6.92820i	−0.156893	−	0.271746i
$651$	−42.0000	−	24.2487i	−1.64611	−	0.950382i
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	−15.5000	+	26.8468i	−0.606562	+	1.05060i	0.385241	+	0.922816i	$0.374118\pi$
$653$	−15.5000	+	26.8468i	−0.606562	+	1.05060i	−0.991803	+	0.127780i	$0.959215\pi$
$654$		−	3.46410i		−	0.135457i
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	2.00000			0.0780869
$657$	6.00000	+	10.3923i	0.234082	+	0.405442i
$658$	−28.0000			−1.09155
$659$	−17.0000	−	29.4449i	−0.662226	−	1.14701i	−0.980029	−	0.198852i	$-0.936279\pi$
$659$	−17.0000	−	29.4449i	−0.662226	−	1.14701i	0.317803	−	0.948157i	$-0.397055\pi$
$660$	−1.50000	+	0.866025i	−0.0583874	+	0.0337100i
$661$	−24.5000	+	42.4352i	−0.952940	+	1.65054i	−0.213925	+	0.976850i	$0.568625\pi$
$661$	−24.5000	+	42.4352i	−0.952940	+	1.65054i	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−0.500000	+	0.866025i	−0.0194331	+	0.0336590i
$663$	−12.0000	+	6.92820i	−0.466041	+	0.269069i
$664$	−18.0000	−	31.1769i	−0.698535	−	1.20990i
$665$	24.0000			0.930680
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$	−24.0000			−0.929284
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$			27.7128i			1.07144i
$670$	−5.50000	+	9.52628i	−0.212484	+	0.368032i
$671$		0			0
$672$	−30.0000	−	17.3205i	−1.15728	−	0.668153i
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	0.996328	−	0.0856156i	$-0.0272857\pi$
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	−0.572309	+	0.820038i	$0.693952\pi$
$674$	−22.0000			−0.847408
$675$	18.0000	−	10.3923i	0.692820	−	0.400000i
$676$	9.00000			0.346154
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$	22.5000	+	12.9904i	0.864107	+	0.498893i
$679$	38.0000	−	65.8179i	1.45831	−	2.52586i
$680$	6.00000	−	10.3923i	0.230089	−	0.398527i
$681$		−	31.1769i		−	1.19470i
$682$	−3.50000	−	6.06218i	−0.134022	−	0.232133i
$683$	5.00000			0.191320			0.0956598	−	0.995414i	$-0.469504\pi$
$683$	5.00000			0.191320			0.0956598	+	0.995414i	$0.469504\pi$
$684$	18.0000			0.688247
$685$	5.00000			0.191040
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	−9.00000	+	5.19615i	−0.343371	+	0.198246i
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−9.00000	+	15.5885i	−0.342873	+	0.593873i
$690$	−6.00000	+	3.46410i	−0.228416	+	0.131876i
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	−0.979086	−	0.203445i	$-0.934786\pi$
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	0.313355	−	0.949636i	$-0.398547\pi$
$692$		0			0
$693$	−12.0000			−0.455842
$694$	4.00000			0.151838
$695$	1.00000	+	1.73205i	0.0379322	+	0.0657004i
$696$		−	31.1769i		−	1.18176i
$697$	4.00000	−	6.92820i	0.151511	−	0.262424i
$698$	−15.0000	+	25.9808i	−0.567758	+	0.983386i
$699$	−36.0000	−	20.7846i	−1.36165	−	0.786146i
$700$	−8.00000	−	13.8564i	−0.302372	−	0.523723i
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$			10.3923i			0.392232i
$703$	18.0000			0.678883
$704$	−3.50000	−	6.06218i	−0.131911	−	0.228477i
$705$	10.5000	+	6.06218i	0.395453	+	0.228315i
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$	8.00000	−	13.8564i	0.300871	−	0.521124i
$708$			12.1244i			0.455661i
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	0.961882	−	0.273466i	$-0.0881700\pi$
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	−0.717769	+	0.696281i	$0.754837\pi$
$710$	9.00000			0.337764
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$	−18.0000			−0.674579
$713$	14.0000	+	24.2487i	0.524304	+	0.908121i
$714$	24.0000	−	13.8564i	0.898177	−	0.518563i
$715$	1.00000	−	1.73205i	0.0373979	−	0.0647750i
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$	9.00000	−	5.19615i	0.336111	−	0.194054i
$718$	16.0000	+	27.7128i	0.597115	+	1.03423i
$719$	−15.0000			−0.559406			−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000			−0.559406			−0.279703	+	0.960087i	$0.590236\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$	−52.0000			−1.93658
$722$	−8.50000	−	14.7224i	−0.316337	−	0.547912i
$723$			17.3205i			0.644157i
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$	12.0000	−	20.7846i	0.445669	−	0.771921i
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$	16.5000	+	28.5788i	0.611951	+	1.05993i	0.990911	+	0.134517i	$0.0429484\pi$
$727$	16.5000	+	28.5788i	0.611951	+	1.05993i	−0.378960	+	0.925413i	$0.623718\pi$
$728$	24.0000			0.889499
$729$	−27.0000			−1.00000
$730$	4.00000			0.148047
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	3.00000	−	5.19615i	0.110808	−	0.191924i	−0.805289	−	0.592883i	$-0.797990\pi$
$733$	3.00000	−	5.19615i	0.110808	−	0.191924i	0.916096	+	0.400959i	$0.131323\pi$
$734$	5.50000	−	9.52628i	0.203009	−	0.351621i
$735$			15.5885i			0.574989i
$736$	10.0000	+	17.3205i	0.368605	+	0.638442i
$737$	11.0000			0.405190
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$	1.50000	+	2.59808i	0.0551411	+	0.0955072i
$741$	−18.0000	+	10.3923i	−0.661247	+	0.381771i
$742$	18.0000	−	31.1769i	0.660801	−	1.14454i
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.113455	−	0.993543i	$-0.463808\pi$
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.803706	−	0.595026i	$-0.202858\pi$
$744$	−31.5000	+	18.1865i	−1.15485	+	0.666751i
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$	10.0000			0.366126
$747$	−18.0000	+	31.1769i	−0.658586	+	1.14070i
$748$	−4.00000			−0.146254
$749$	36.0000	+	62.3538i	1.31541	+	2.27836i
$750$		−	15.5885i		−	0.569210i
$751$	5.50000	−	9.52628i	0.200698	−	0.347619i	−0.748056	−	0.663636i	$-0.769012\pi$
$751$	5.50000	−	9.52628i	0.200698	−	0.347619i	0.948753	+	0.316017i	$0.102346\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$	−42.0000	−	24.2487i	−1.53057	−	0.883672i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	−16.0000			−0.582300
$756$			20.7846i			0.755929i
$757$	−19.0000			−0.690567			−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000			−0.690567			−0.345283	+	0.938498i	$0.612217\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	6.00000	+	3.46410i	0.217786	+	0.125739i
$760$	9.00000	−	15.5885i	0.326464	−	0.565453i
$761$	−18.0000	+	31.1769i	−0.652499	+	1.13016i	0.330015	+	0.943976i	$0.392946\pi$
$761$	−18.0000	+	31.1769i	−0.652499	+	1.13016i	−0.982514	+	0.186187i	$0.940387\pi$
$762$			3.46410i			0.125491i
$763$	4.00000	+	6.92820i	0.144810	+	0.250818i
$764$	13.0000			0.470323
$765$	−12.0000			−0.433861
$766$	29.0000			1.04781
$767$	−7.00000	−	12.1244i	−0.252755	−	0.437785i
$768$	−25.5000	+	14.7224i	−0.920152	+	0.531250i
$769$	8.00000	−	13.8564i	0.288487	−	0.499675i	−0.684962	−	0.728579i	$-0.740181\pi$
$769$	8.00000	−	13.8564i	0.288487	−	0.499675i	0.973449	+	0.228904i	$0.0735143\pi$
$770$	−2.00000	+	3.46410i	−0.0720750	+	0.124838i
$771$	33.0000	−	19.0526i	1.18847	−	0.686161i
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	−18.0000			−0.646997
$775$	−28.0000			−1.00579
$776$	−28.5000	−	49.3634i	−1.02309	−	1.77204i
$777$			20.7846i			0.745644i
$778$	−16.5000	+	28.5788i	−0.591554	+	1.02460i
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$	−3.00000	−	1.73205i	−0.107417	−	0.0620174i
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$	−16.0000			−0.572159
$783$	−27.0000	+	15.5885i	−0.964901	+	0.557086i
$784$	−9.00000			−0.321429
$785$	3.50000	+	6.06218i	0.124920	+	0.216368i
$786$	9.00000	+	5.19615i	0.321019	+	0.185341i
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	−0.713871	−	0.700278i	$-0.753059\pi$
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	0.963394	+	0.268091i	$0.0863928\pi$
$788$	8.00000	−	13.8564i	0.284988	−	0.493614i
$789$		−	27.7128i		−	0.986602i
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$	−60.0000			−2.13335
$792$	−4.50000	+	7.79423i	−0.159901	+	0.276956i
$793$		0			0
$794$	−6.50000	−	11.2583i	−0.230676	−	0.399543i
$795$	−13.5000	+	7.79423i	−0.478796	+	0.276433i
$796$	−1.50000	+	2.59808i	−0.0531661	+	0.0920864i
$797$	−2.50000	+	4.33013i	−0.0885545	+	0.153381i	−0.906900	−	0.421345i	$-0.861558\pi$
$797$	−2.50000	+	4.33013i	−0.0885545	+	0.153381i	0.818346	+	0.574726i	$0.194891\pi$
$798$	36.0000	−	20.7846i	1.27439	−	0.735767i
$799$	14.0000	+	24.2487i	0.495284	+	0.857858i
$800$	−20.0000			−0.707107
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	17.0000			0.600291
$803$	−2.00000	−	3.46410i	−0.0705785	−	0.122245i
$804$		−	19.0526i		−	0.671932i
$805$	8.00000	−	13.8564i	0.281963	−	0.488374i
$806$	7.00000	−	12.1244i	0.246564	−	0.427062i
$807$	25.5000	+	14.7224i	0.897643	+	0.518254i
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	12.0000	+	20.7846i	0.421117	+	0.729397i
$813$	33.0000	+	19.0526i	1.15736	+	0.668202i
$814$	−1.50000	+	2.59808i	−0.0525750	+	0.0910625i
$815$	5.50000	−	9.52628i	0.192657	−	0.333691i
$816$		−	6.92820i		−	0.242536i
$817$	−18.0000	−	31.1769i	−0.629740	−	1.09074i
$818$		0			0
$819$	−12.0000	−	20.7846i	−0.419314	−	0.726273i
$820$	2.00000			0.0698430
$821$	10.0000	+	17.3205i	0.349002	+	0.604490i	0.986073	−	0.166316i	$-0.0531872\pi$
$821$	10.0000	+	17.3205i	0.349002	+	0.604490i	−0.637070	+	0.770806i	$0.719854\pi$
$822$	7.50000	−	4.33013i	0.261593	−	0.151031i
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	−19.5000	+	33.7750i	−0.679315	+	1.17661i
$825$	−6.00000	+	3.46410i	−0.208893	+	0.120605i
$826$	14.0000	+	24.2487i	0.487122	+	0.843721i
$827$	−40.0000			−1.39094			−0.695468	−	0.718557i	$-0.744803\pi$
$827$	−40.0000			−1.39094			−0.695468	+	0.718557i	$0.744803\pi$
$828$	6.00000	−	10.3923i	0.208514	−	0.361158i
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$		−	3.46410i		−	0.120168i
$832$	7.00000	−	12.1244i	0.242681	−	0.420336i
$833$	−18.0000	+	31.1769i	−0.623663	+	1.08022i
$834$	3.00000	+	1.73205i	0.103882	+	0.0599760i
$835$	−6.00000	−	10.3923i	−0.207639	−	0.359641i
$836$	−6.00000			−0.207514
$837$	31.5000	+	18.1865i	1.08880	+	0.628619i
$838$	5.00000			0.172722
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	0.694244	−	0.719740i	$-0.255739\pi$
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	−0.970435	+	0.241363i	$0.922405\pi$
$840$	18.0000	+	10.3923i	0.621059	+	0.358569i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−6.50000	+	11.2583i	−0.224005	+	0.387988i
$843$			10.3923i			0.357930i
$844$	3.00000	+	5.19615i	0.103264	+	0.178859i
$845$	−9.00000			−0.309609
$846$	21.0000			0.721995
$847$	4.00000			0.137442
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	42.0000	−	24.2487i	1.44144	−	0.832214i
$850$	8.00000	−	13.8564i	0.274398	−	0.475271i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	−13.5000	+	7.79423i	−0.462502	+	0.267026i
$853$	−1.00000	−	1.73205i	−0.0342393	−	0.0593043i	0.848398	−	0.529359i	$-0.177568\pi$
$853$	−1.00000	−	1.73205i	−0.0342393	−	0.0593043i	−0.882637	+	0.470055i	$0.844234\pi$
$854$		0			0
$855$	−18.0000			−0.615587
$856$	54.0000			1.84568
$857$	−19.0000	−	32.9090i	−0.649028	−	1.12415i	−0.983355	−	0.181692i	$-0.941843\pi$
$857$	−19.0000	−	32.9090i	−0.649028	−	1.12415i	0.334328	−	0.942457i	$-0.391491\pi$
$858$		−	3.46410i		−	0.118262i
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	−0.965139	−	0.261739i	$-0.915704\pi$
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	0.709242	+	0.704965i	$0.249037\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$	12.0000	+	6.92820i	0.408959	+	0.236113i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	22.5000	+	12.9904i	0.765466	+	0.441942i
$865$		0			0
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$	1.50000	+	0.866025i	0.0509427	+	0.0294118i
$868$	14.0000	−	24.2487i	0.475191	−	0.823055i
$869$	−4.00000	+	6.92820i	−0.135691	+	0.235023i
$870$			10.3923i			0.352332i
$871$	11.0000	+	19.0526i	0.372721	+	0.645571i
$872$	6.00000			0.203186
$873$	−28.5000	+	49.3634i	−0.964579	+	1.67070i
$874$	−24.0000			−0.811812
$875$	18.0000	+	31.1769i	0.608511	+	1.05397i
$876$	−6.00000	+	3.46410i	−0.202721	+	0.117041i
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$	7.00000	−	12.1244i	0.236239	−	0.409177i
$879$	18.0000	−	10.3923i	0.607125	−	0.350524i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	13.5000	+	23.3827i	0.454569	+	0.787336i
$883$	−5.00000			−0.168263			−0.0841317	−	0.996455i	$-0.526812\pi$
$883$	−5.00000			−0.168263			−0.0841317	+	0.996455i	$0.526812\pi$
$884$	−4.00000	−	6.92820i	−0.134535	−	0.233021i
$885$		−	12.1244i		−	0.407556i
$886$	−0.500000	+	0.866025i	−0.0167978	+	0.0290947i
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	−0.925332	−	0.379157i	$-0.876214\pi$
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	0.791026	+	0.611783i	$0.209547\pi$
$888$	13.5000	+	7.79423i	0.453030	+	0.261557i
$889$	−4.00000	−	6.92820i	−0.134156	−	0.232364i
$890$	6.00000			0.201120
$891$	9.00000			0.301511
$892$	−16.0000			−0.535720
$893$	21.0000	+	36.3731i	0.702738	+	1.21718i
$894$	6.00000	+	3.46410i	0.200670	+	0.115857i
$895$	4.50000	−	7.79423i	0.150418	−	0.260532i
$896$	6.00000	−	10.3923i	0.200446	−	0.347183i
$897$			13.8564i			0.462652i
$898$	−11.5000	−	19.9186i	−0.383760	−	0.664692i
$899$	42.0000			1.40078
$900$	6.00000	+	10.3923i	0.200000	+	0.346410i
$901$	−36.0000			−1.19933
$902$	1.00000	+	1.73205i	0.0332964	+	0.0576710i
$903$	36.0000	−	20.7846i	1.19800	−	0.691669i
$904$	−22.5000	+	38.9711i	−0.748339	+	1.29616i
$905$	−3.50000	+	6.06218i	−0.116344	+	0.201514i
$906$	−24.0000	+	13.8564i	−0.797347	+	0.460348i
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	18.0000			0.597351
$909$	−6.00000	+	10.3923i	−0.199007	+	0.344691i
$910$	−8.00000			−0.265197
$911$	−13.5000	−	23.3827i	−0.447275	−	0.774703i	0.550933	−	0.834550i	$-0.314272\pi$
$911$	−13.5000	−	23.3827i	−0.447275	−	0.774703i	−0.998208	+	0.0598468i	$0.980939\pi$
$912$		−	10.3923i		−	0.344124i
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	3.00000	−	5.19615i	0.0992312	−	0.171873i
$915$		0			0
$916$	−3.00000	−	5.19615i	−0.0991228	−	0.171686i
$917$	−24.0000			−0.792550
$918$	−18.0000	+	10.3923i	−0.594089	+	0.342997i
$919$	52.0000			1.71532			0.857661	−	0.514216i	$-0.171917\pi$
$919$	52.0000			1.71532			0.857661	+	0.514216i	$0.171917\pi$
$920$	−6.00000	−	10.3923i	−0.197814	−	0.342624i
$921$	42.0000	+	24.2487i	1.38395	+	0.799022i
$922$	6.00000	−	10.3923i	0.197599	−	0.342252i
$923$	9.00000	−	15.5885i	0.296239	−	0.513100i
$924$		−	6.92820i		−	0.227921i
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	−8.00000			−0.262896
$927$	39.0000			1.28093
$928$	30.0000			0.984798
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$	10.5000	−	6.06218i	0.344309	−	0.198787i
$931$	−27.0000	+	46.7654i	−0.884889	+	1.53267i
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$	−31.5000	+	18.1865i	−1.03126	+	0.595400i
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$	4.00000			0.130814
$936$	−18.0000			−0.588348
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$	−22.0000	−	38.1051i	−0.718325	−	1.24418i
$939$			24.2487i			0.791327i
$940$	−3.50000	+	6.06218i	−0.114157	+	0.197726i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$	10.5000	+	6.06218i	0.342108	+	0.197516i
$943$	−4.00000	−	6.92820i	−0.130258	−	0.225613i
$944$	7.00000			0.227831
$945$		−	20.7846i		−	0.676123i
$946$	6.00000			0.195077
$947$	−7.50000	−	12.9904i	−0.243717	−	0.422131i	0.718053	−	0.695988i	$-0.245034\pi$
$947$	−7.50000	−	12.9904i	−0.243717	−	0.422131i	−0.961770	+	0.273858i	$0.911700\pi$
$948$	12.0000	+	6.92820i	0.389742	+	0.225018i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	12.0000	−	20.7846i	0.389331	−	0.674342i
$951$			38.1051i			1.23564i
$952$	24.0000	+	41.5692i	0.777844	+	1.34727i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	−13.5000	+	23.3827i	−0.437079	+	0.757042i
$955$	−13.0000			−0.420670
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	9.00000	−	5.19615i	0.290929	−	0.167968i
$958$	2.00000	−	3.46410i	0.0646171	−	0.111920i
$959$	−10.0000	+	17.3205i	−0.322917	+	0.559308i
$960$	10.5000	−	6.06218i	0.338886	−	0.195656i
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$	−6.00000			−0.193448
$963$	−27.0000	−	46.7654i	−0.870063	−	1.50699i
$964$	−10.0000			−0.322078
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$		−	27.7128i		−	0.891645i
$967$	25.0000	−	43.3013i	0.803946	−	1.39247i	−0.113055	−	0.993589i	$-0.536064\pi$
$967$	25.0000	−	43.3013i	0.803946	−	1.39247i	0.917000	−	0.398886i	$-0.130603\pi$
$968$	1.50000	−	2.59808i	0.0482118	−	0.0835053i
$969$	−36.0000	−	20.7846i	−1.15649	−	0.667698i
$970$	9.50000	+	16.4545i	0.305027	+	0.528322i
$971$	20.0000			0.641831			0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000			0.641831			0.320915	+	0.947108i	$0.396010\pi$
$972$		−	15.5885i		−	0.500000i
$973$	−8.00000			−0.256468
$974$	18.5000	+	32.0429i	0.592778	+	1.02672i
$975$	−12.0000	−	6.92820i	−0.384308	−	0.221880i
$976$		0			0
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		−	19.0526i		−	0.609234i
$979$	−3.00000	−	5.19615i	−0.0958804	−	0.166070i
$980$	−9.00000			−0.287494
$981$	−3.00000	−	5.19615i	−0.0957826	−	0.165900i
$982$	−8.00000			−0.255290
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$	9.00000	−	5.19615i	0.286910	−	0.165647i
$985$	−8.00000	+	13.8564i	−0.254901	+	0.441502i
$986$	−12.0000	+	20.7846i	−0.382158	+	0.661917i
$987$	−42.0000	+	24.2487i	−1.33687	+	0.771845i
$988$	−6.00000	−	10.3923i	−0.190885	−	0.330623i
$989$	−24.0000			−0.763156
$990$	1.50000	−	2.59808i	0.0476731	−	0.0825723i
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$	−17.5000	−	30.3109i	−0.555626	−	0.962372i
$993$			1.73205i			0.0549650i
$994$	−18.0000	+	31.1769i	−0.570925	+	0.988872i
$995$	1.50000	−	2.59808i	0.0475532	−	0.0823646i
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	2.00000	+	3.46410i	0.0633406	+	0.109709i	0.895957	−	0.444141i	$-0.146491\pi$
$997$	2.00000	+	3.46410i	0.0633406	+	0.109709i	−0.832616	+	0.553851i	$0.813158\pi$
$998$	−25.0000			−0.791361
$999$		−	15.5885i		−	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.a.67.1	yes	2
3.2	odd	2		297.2.e.c.199.1		2
9.2	odd	6		297.2.e.c.100.1		2
9.4	even	3		891.2.a.g.1.1		1
9.5	odd	6		891.2.a.c.1.1		1
9.7	even	3	inner	99.2.e.a.34.1	✓	2
11.10	odd	2		1089.2.e.c.364.1		2
99.32	even	6		9801.2.a.i.1.1		1
99.43	odd	6		1089.2.e.c.727.1		2
99.76	odd	6		9801.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.a.34.1	✓	2	9.7	even	3	inner
99.2.e.a.67.1	yes	2	1.1	even	1	trivial
297.2.e.c.100.1		2	9.2	odd	6
297.2.e.c.199.1		2	3.2	odd	2
891.2.a.c.1.1		1	9.5	odd	6
891.2.a.g.1.1		1	9.4	even	3
1089.2.e.c.364.1		2	11.10	odd	2
1089.2.e.c.727.1		2	99.43	odd	6
9801.2.a.c.1.1		1	99.76	odd	6
9801.2.a.i.1.1		1	99.32	even	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} +(-2.00000 - 3.46410i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +4.00000 q^{17} +(1.50000 - 2.59808i) q^{18} +6.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +6.92820i q^{21} +(-0.500000 + 0.866025i) q^{22} +(2.00000 - 3.46410i) q^{23} +(4.50000 + 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} -2.00000 q^{26} -5.19615i q^{27} -4.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-3.50000 + 6.06218i) q^{31} +(-2.50000 + 4.33013i) q^{32} +1.73205i q^{33} +(-2.00000 - 3.46410i) q^{34} +4.00000 q^{35} +3.00000 q^{36} +3.00000 q^{37} +(-3.00000 - 5.19615i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} +(1.00000 - 1.73205i) q^{41} +(6.00000 - 3.46410i) q^{42} +(-3.00000 - 5.19615i) q^{43} -1.00000 q^{44} -3.00000 q^{45} -4.00000 q^{46} +(3.50000 + 6.06218i) q^{47} -1.73205i q^{48} +(-4.50000 + 7.79423i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} -9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +1.00000 q^{55} +(6.00000 + 10.3923i) q^{56} +(-9.00000 - 5.19615i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(3.50000 - 6.06218i) q^{59} -1.73205i q^{60} +7.00000 q^{62} +(6.00000 - 10.3923i) q^{63} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.50000 - 0.866025i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(2.00000 - 3.46410i) q^{68} +(-6.00000 + 3.46410i) q^{69} +(-2.00000 - 3.46410i) q^{70} +9.00000 q^{71} +(-4.50000 - 7.79423i) q^{72} +4.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} -6.92820i q^{75} +(3.00000 - 5.19615i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(3.00000 + 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -2.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(6.00000 + 3.46410i) q^{84} +(-2.00000 + 3.46410i) q^{85} +(-3.00000 + 5.19615i) q^{86} +10.3923i q^{87} +(1.50000 + 2.59808i) q^{88} +6.00000 q^{89} +(1.50000 + 2.59808i) q^{90} -8.00000 q^{91} +(-2.00000 - 3.46410i) q^{92} +(10.5000 - 6.06218i) q^{93} +(3.50000 - 6.06218i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(7.50000 - 4.33013i) q^{96} +(9.50000 + 16.4545i) q^{97} +9.00000 q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} + q^{4} - q^{5} - 4 q^{7} - 6 q^{8} + 3 q^{9} + 2 q^{10} - q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{15} + q^{16} + 8 q^{17} + 3 q^{18} + 12 q^{19} + q^{20} - q^{22} + 4 q^{23}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 + q^4 - q^5 - 4 * q^7 - 6 * q^8 + 3 * q^9 + 2 * q^10 - q^11 - 3 * q^12 + 2 * q^13 - 4 * q^14 + 3 * q^15 + q^16 + 8 * q^17 + 3 * q^18 + 12 * q^19 + q^20 - q^22 + 4 * q^23 + 9 * q^24 + 4 * q^25 - 4 * q^26 - 8 * q^28 - 6 * q^29 - 3 * q^30 - 7 * q^31 - 5 * q^32 - 4 * q^34 + 8 * q^35 + 6 * q^36 + 6 * q^37 - 6 * q^38 - 6 * q^39 + 3 * q^40 + 2 * q^41 + 12 * q^42 - 6 * q^43 - 2 * q^44 - 6 * q^45 - 8 * q^46 + 7 * q^47 - 9 * q^49 + 4 * q^50 - 12 * q^51 - 2 * q^52 - 18 * q^53 - 9 * q^54 + 2 * q^55 + 12 * q^56 - 18 * q^57 - 6 * q^58 + 7 * q^59 + 14 * q^62 + 12 * q^63 + 14 * q^64 + 2 * q^65 + 3 * q^66 - 11 * q^67 + 4 * q^68 - 12 * q^69 - 4 * q^70 + 18 * q^71 - 9 * q^72 + 8 * q^73 - 3 * q^74 + 6 * q^76 - 4 * q^77 + 6 * q^78 - 8 * q^79 - 2 * q^80 - 9 * q^81 - 4 * q^82 + 12 * q^83 + 12 * q^84 - 4 * q^85 - 6 * q^86 + 3 * q^88 + 12 * q^89 + 3 * q^90 - 16 * q^91 - 4 * q^92 + 21 * q^93 + 7 * q^94 - 6 * q^95 + 15 * q^96 + 19 * q^97 + 18 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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