LMFDB - Embedded newform 90.2.e.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(31,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("90.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	90.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:	$0.718653618192$
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			61.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	90.61
Dual form			90.2.e.b.31.1

$q$-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} +(-1.50000 + 0.866025i) q^{6} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.00000 - 3.46410i) q^{14} +1.73205i q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +3.00000 q^{18} +5.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-6.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{26} -5.19615i q^{27} -4.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(1.50000 + 0.866025i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.50000 - 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} -4.00000 q^{35} +(1.50000 - 2.59808i) q^{36} -4.00000 q^{37} +(2.50000 - 4.33013i) q^{38} -6.92820i q^{39} +(0.500000 + 0.866025i) q^{40} +(1.50000 + 2.59808i) q^{41} +6.92820i q^{42} +(-5.50000 + 9.52628i) q^{43} +3.00000 q^{44} +(1.50000 - 2.59808i) q^{45} -6.00000 q^{46} +(1.50000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +6.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} +3.00000 q^{55} +(-2.00000 + 3.46410i) q^{56} +(-7.50000 - 4.33013i) q^{57} +(3.00000 + 5.19615i) q^{58} +(1.50000 + 2.59808i) q^{59} +(1.50000 - 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +12.0000 q^{63} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} -5.19615i q^{66} +(-2.50000 - 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +10.3923i q^{69} +(-2.00000 + 3.46410i) q^{70} +6.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -7.00000 q^{73} +(-2.00000 + 3.46410i) q^{74} +(1.50000 - 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(6.00000 + 10.3923i) q^{77} +(-6.00000 - 3.46410i) q^{78} +(-7.00000 + 12.1244i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +3.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(6.00000 + 3.46410i) q^{84} +(-1.50000 - 2.59808i) q^{85} +(5.50000 + 9.52628i) q^{86} +(9.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +(-1.50000 - 2.59808i) q^{90} +16.0000 q^{91} +(-3.00000 + 5.19615i) q^{92} +3.46410i q^{93} +(-2.50000 - 4.33013i) q^{95} -1.73205i q^{96} +(-5.50000 + 9.52628i) q^{97} -9.00000 q^{98} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} - q^{5} - 3 q^{6} + 4 q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} - 3 q^{11} + 4 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 6 q^{18} + 10 q^{19} - q^{20} - 12 q^{21} + 3 q^{22}+ \cdots - 18 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 - q^5 - 3 * q^6 + 4 * q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 - 3 * q^11 + 4 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 6 * q^18 + 10 * q^19 - q^20 - 12 * q^21 + 3 * q^22 - 6 * q^23 + 3 * q^24 - q^25 + 8 * q^26 - 8 * q^28 - 6 * q^29 + 3 * q^30 - 2 * q^31 + q^32 + 9 * q^33 + 3 * q^34 - 8 * q^35 + 3 * q^36 - 8 * q^37 + 5 * q^38 + q^40 + 3 * q^41 - 11 * q^43 + 6 * q^44 + 3 * q^45 - 12 * q^46 + 3 * q^48 - 9 * q^49 + q^50 - 9 * q^51 + 4 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 - 4 * q^56 - 15 * q^57 + 6 * q^58 + 3 * q^59 + 3 * q^60 + 10 * q^61 - 4 * q^62 + 24 * q^63 + 2 * q^64 + 4 * q^65 - 5 * q^67 - 3 * q^68 - 4 * q^70 + 12 * q^71 - 3 * q^72 - 14 * q^73 - 4 * q^74 + 3 * q^75 - 5 * q^76 + 12 * q^77 - 12 * q^78 - 14 * q^79 + 2 * q^80 - 9 * q^81 + 6 * q^82 - 12 * q^83 + 12 * q^84 - 3 * q^85 + 11 * q^86 + 18 * q^87 + 3 * q^88 + 12 * q^89 - 3 * q^90 + 32 * q^91 - 6 * q^92 - 5 * q^95 - 11 * q^97 - 18 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.50000	−	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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.00000			−0.316228
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$			1.73205i			0.500000i
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$			1.73205i			0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	3.00000			0.707107
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.00000			0.784465
$27$		−	5.19615i		−	1.00000i
$28$	−4.00000			−0.755929
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	1.50000	+	0.866025i	0.273861	+	0.158114i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.50000	−	2.59808i	0.783349	−	0.452267i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	−4.00000			−0.676123
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$		−	6.92820i		−	1.10940i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$			6.92820i			1.06904i
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	3.00000			0.452267
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	−6.00000			−0.884652
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	3.00000			0.404520
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$	−7.50000	−	4.33013i	−0.993399	−	0.573539i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$	1.50000	−	0.866025i	0.193649	−	0.111803i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	−2.00000			−0.254000
$63$	12.0000			1.51186
$64$	1.00000			0.125000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		−	5.19615i		−	0.639602i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$			10.3923i			1.25109i
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$	1.50000	−	0.866025i	0.173205	−	0.100000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	6.00000	+	10.3923i	0.683763	+	1.18431i
$78$	−6.00000	−	3.46410i	−0.679366	−	0.392232i
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	1.00000			0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	3.00000			0.331295
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$	6.00000	+	3.46410i	0.654654	+	0.377964i
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$	5.50000	+	9.52628i	0.593080	+	1.02725i
$87$	9.00000	−	5.19615i	0.964901	−	0.557086i
$88$	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
$91$	16.0000			1.67726
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$			3.46410i			0.359211i
$94$		0			0
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$		−	1.73205i		−	0.176777i
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	0.439187	+	0.898396i	$0.355267\pi$
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	−0.997627	+	0.0688512i	$0.978067\pi$
$98$	−9.00000			−0.909137
$99$	−9.00000			−0.904534
$100$	1.00000			0.100000
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$	6.00000	+	3.46410i	0.585540	+	0.338062i
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	2.00000	+	3.46410i	0.188982	+	0.327327i
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	0.0375328	−	0.999295i	$-0.488050\pi$
$114$	−7.50000	+	4.33013i	−0.702439	+	0.405554i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	6.00000			0.557086
$117$	−6.00000	+	10.3923i	−0.554700	+	0.960769i
$118$	3.00000			0.276172
$119$	6.00000	−	10.3923i	0.550019	−	0.952661i
$120$		−	1.73205i		−	0.158114i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−5.00000	−	8.66025i	−0.452679	−	0.784063i
$123$		−	5.19615i		−	0.468521i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$	6.00000	−	10.3923i	0.534522	−	0.925820i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	16.5000	−	9.52628i	1.45274	−	0.838742i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	−4.50000	−	2.59808i	−0.391675	−	0.226134i
$133$	10.0000	−	17.3205i	0.867110	−	1.50188i
$134$	−5.00000			−0.431934
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	−3.00000			−0.257248
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$	9.00000	+	5.19615i	0.766131	+	0.442326i
$139$	0.500000	+	0.866025i	0.0424094	+	0.0734553i	0.886451	−	0.462822i	$-0.153163\pi$
$139$	0.500000	+	0.866025i	0.0424094	+	0.0734553i	−0.844042	+	0.536278i	$0.819830\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	−12.0000			−1.00349
$144$	−3.00000			−0.250000
$145$	6.00000			0.498273
$146$	−3.50000	+	6.06218i	−0.289662	+	0.501709i
$147$			15.5885i			1.28571i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		−	1.73205i		−	0.141421i
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−5.00000			−0.405554
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	12.0000			0.966988
$155$	−1.00000	+	1.73205i	−0.0803219	+	0.139122i
$156$	−6.00000	+	3.46410i	−0.480384	+	0.277350i
$157$	−4.00000	−	6.92820i	−0.319235	−	0.552931i	0.661094	−	0.750303i	$-0.270093\pi$
$157$	−4.00000	−	6.92820i	−0.319235	−	0.552931i	−0.980329	+	0.197372i	$0.936759\pi$
$158$	7.00000	+	12.1244i	0.556890	+	0.964562i
$159$	−9.00000	−	5.19615i	−0.713746	−	0.412082i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−24.0000			−1.89146
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	−4.50000	−	2.59808i	−0.350325	−	0.202260i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$	6.00000	−	3.46410i	0.462910	−	0.267261i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	−3.00000			−0.230089
$171$	7.50000	+	12.9904i	0.573539	+	0.993399i
$172$	11.0000			0.838742
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$		−	10.3923i		−	0.787839i
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		−	5.19615i		−	0.390567i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−3.00000			−0.223607
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	8.00000	−	13.8564i	0.592999	−	1.02711i
$183$	−15.0000	+	8.66025i	−1.10883	+	0.640184i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$		0			0
$189$	−18.0000	−	10.3923i	−1.30931	−	0.755929i
$190$	−5.00000			−0.362738
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$	5.50000	+	9.52628i	0.394877	+	0.683947i
$195$	−6.00000	+	3.46410i	−0.429669	+	0.248069i
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−4.50000	+	7.79423i	−0.319801	+	0.553912i
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$			8.66025i			0.610847i
$202$	−6.00000	−	10.3923i	−0.422159	−	0.731200i
$203$	12.0000	+	20.7846i	0.842235	+	1.45879i
$204$			5.19615i			0.363803i
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$	4.00000			0.278693
$207$	9.00000	−	15.5885i	0.625543	−	1.08347i
$208$	−4.00000			−0.277350
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$	6.00000	−	3.46410i	0.414039	−	0.239046i
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−9.00000	−	5.19615i	−0.616670	−	0.356034i
$214$	−4.50000	+	7.79423i	−0.307614	+	0.532803i
$215$	11.0000			0.750194
$216$			5.19615i			0.353553i
$217$	−8.00000			−0.543075
$218$	−2.00000	+	3.46410i	−0.135457	+	0.234619i
$219$	10.5000	+	6.06218i	0.709524	+	0.409644i
$220$	−1.50000	−	2.59808i	−0.101130	−	0.175162i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	6.00000	−	3.46410i	0.402694	−	0.232495i
$223$	11.0000	−	19.0526i	0.736614	−	1.27585i	−0.217397	−	0.976083i	$-0.569757\pi$
$223$	11.0000	−	19.0526i	0.736614	−	1.27585i	0.954011	−	0.299770i	$-0.0969101\pi$
$224$	4.00000			0.267261
$225$	−3.00000			−0.200000
$226$	−18.0000			−1.19734
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$			8.66025i			0.573539i
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$		−	20.7846i		−	1.36753i
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$		0			0
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$	21.0000	−	12.1244i	1.36410	−	0.787562i
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	2.00000			0.128565
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−10.0000			−0.640184
$245$	−4.50000	+	7.79423i	−0.287494	+	0.497955i
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	10.0000	+	17.3205i	0.636285	+	1.10208i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	18.0000	−	10.3923i	1.14070	−	0.658586i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$	−6.00000	−	10.3923i	−0.377964	−	0.654654i
$253$	18.0000			1.13165
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$			5.19615i			0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	0.690856	−	0.722993i	$-0.257234\pi$
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	−0.971558	+	0.236802i	$0.923901\pi$
$258$		−	19.0526i		−	1.18616i
$259$	−8.00000	+	13.8564i	−0.497096	+	0.860995i
$260$	−4.00000			−0.248069
$261$	−18.0000			−1.11417
$262$	−12.0000			−0.741362
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	−4.50000	+	2.59808i	−0.276956	+	0.159901i
$265$	−3.00000	−	5.19615i	−0.184289	−	0.319197i
$266$	−10.0000	−	17.3205i	−0.613139	−	1.06199i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$			5.19615i			0.316228i
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	−24.0000	−	13.8564i	−1.45255	−	0.838628i
$274$	−4.50000	−	7.79423i	−0.271855	−	0.470867i
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$	9.00000	−	5.19615i	0.541736	−	0.312772i
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$	1.00000			0.0599760
$279$	3.00000	−	5.19615i	0.179605	−	0.311086i
$280$	4.00000			0.239046
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	−0.762561	−	0.646916i	$-0.776058\pi$
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	0.941526	+	0.336939i	$0.109392\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$			8.66025i			0.512989i
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$	12.0000			0.708338
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	−8.00000			−0.470588
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$	16.5000	−	9.52628i	0.967247	−	0.558440i
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$	13.5000	+	7.79423i	0.787336	+	0.454569i
$295$	1.50000	−	2.59808i	0.0873334	−	0.151266i
$296$	4.00000			0.232495
$297$	13.5000	+	7.79423i	0.783349	+	0.452267i
$298$		0			0
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$	−1.50000	−	0.866025i	−0.0866025	−	0.0500000i
$301$	22.0000	+	38.1051i	1.26806	+	2.19634i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$	−18.0000	+	10.3923i	−1.03407	+	0.597022i
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	−10.0000			−0.572598
$306$	9.00000			0.514496
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	6.00000	−	10.3923i	0.341882	−	0.592157i
$309$		−	6.92820i		−	0.394132i
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$			6.92820i			0.392232i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−8.00000			−0.451466
$315$	−6.00000	−	10.3923i	−0.338062	−	0.585540i
$316$	14.0000			0.787562
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	0.302777	+	0.953062i	$0.402086\pi$
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	−0.976764	+	0.214318i	$0.931247\pi$
$318$	−9.00000	+	5.19615i	−0.504695	+	0.291386i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	13.5000	+	7.79423i	0.753497	+	0.435031i
$322$	−12.0000	+	20.7846i	−0.668734	+	1.15828i
$323$	15.0000			0.834622
$324$	9.00000			0.500000
$325$	−4.00000			−0.221880
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	6.00000	+	3.46410i	0.331801	+	0.191565i
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$		0			0
$330$	−4.50000	+	2.59808i	−0.247717	+	0.143019i
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	12.0000			0.658586
$333$	−6.00000	−	10.3923i	−0.328798	−	0.569495i
$334$	18.0000			0.984916
$335$	−2.50000	+	4.33013i	−0.136590	+	0.236580i
$336$		−	6.92820i		−	0.377964i
$337$	15.5000	+	26.8468i	0.844339	+	1.46244i	0.886194	+	0.463314i	$0.153340\pi$
$337$	15.5000	+	26.8468i	0.844339	+	1.46244i	−0.0418554	+	0.999124i	$0.513327\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$			31.1769i			1.69330i
$340$	−1.50000	+	2.59808i	−0.0813489	+	0.140900i
$341$	6.00000			0.324918
$342$	15.0000			0.811107
$343$	−8.00000			−0.431959
$344$	5.50000	−	9.52628i	0.296540	−	0.513623i
$345$	9.00000	−	5.19615i	0.484544	−	0.279751i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−10.5000	−	18.1865i	−0.563670	−	0.976304i	−0.997172	−	0.0751519i	$-0.976056\pi$
$347$	−10.5000	−	18.1865i	−0.563670	−	0.976304i	0.433503	−	0.901152i	$-0.357278\pi$
$348$	−9.00000	−	5.19615i	−0.482451	−	0.278543i
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	−0.568486	−	0.822693i	$-0.692471\pi$
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	0.996716	+	0.0809766i	$0.0258039\pi$
$350$	4.00000			0.213809
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$	−3.00000			−0.159901
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$	−4.50000	−	2.59808i	−0.239172	−	0.138086i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−18.0000	+	10.3923i	−0.952661	+	0.550019i
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	6.00000			0.315789
$362$	−8.00000	+	13.8564i	−0.420471	+	0.728277i
$363$		−	3.46410i		−	0.181818i
$364$	−8.00000	−	13.8564i	−0.419314	−	0.726273i
$365$	3.50000	+	6.06218i	0.183198	+	0.317309i
$366$			17.3205i			0.905357i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	6.00000			0.312772
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$	4.00000			0.207950
$371$	12.0000	−	20.7846i	0.623009	−	1.07908i
$372$	3.00000	−	1.73205i	0.155543	−	0.0898027i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$		0			0
$377$	−24.0000			−1.23606
$378$	−18.0000	+	10.3923i	−0.925820	+	0.534522i
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	−2.50000	+	4.33013i	−0.128247	+	0.222131i
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$		0			0
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	6.00000	−	10.3923i	0.305788	−	0.529641i
$386$	13.0000			0.661683
$387$	−33.0000			−1.67748
$388$	11.0000			0.558440
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.102311	+	0.994753i	$0.532624\pi$
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.810326	+	0.585980i	$0.800710\pi$
$390$			6.92820i			0.350823i
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$			20.7846i			1.04844i
$394$		0			0
$395$	14.0000			0.704416
$396$	4.50000	+	7.79423i	0.226134	+	0.391675i
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$	10.0000	−	17.3205i	0.501255	−	0.868199i
$399$	−30.0000	+	17.3205i	−1.50188	+	0.867110i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	−0.902703	−	0.430263i	$-0.858421\pi$
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	0.0787327	−	0.996896i	$-0.474913\pi$
$402$	7.50000	+	4.33013i	0.374066	+	0.215967i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−12.0000			−0.597022
$405$	9.00000			0.447214
$406$	24.0000			1.19110
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	4.50000	+	2.59808i	0.222783	+	0.128624i
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	0.939490	+	0.342578i	$0.111300\pi$
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	−0.173064	+	0.984911i	$0.555367\pi$
$410$	−1.50000	−	2.59808i	−0.0740797	−	0.128310i
$411$	−13.5000	+	7.79423i	−0.665906	+	0.384461i
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	12.0000			0.590481
$414$	−9.00000	−	15.5885i	−0.442326	−	0.766131i
$415$	12.0000			0.589057
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$		−	1.73205i		−	0.0848189i
$418$	7.50000	+	12.9904i	0.366837	+	0.635380i
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		−	6.92820i		−	0.338062i
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	−0.889365	−	0.457198i	$-0.848853\pi$
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	0.840628	+	0.541613i	$0.182186\pi$
$422$	4.00000			0.194717
$423$		0			0
$424$	−6.00000			−0.291386
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$	−9.00000	+	5.19615i	−0.436051	+	0.251754i
$427$	−20.0000	−	34.6410i	−0.967868	−	1.67640i
$428$	4.50000	+	7.79423i	0.217516	+	0.376748i
$429$	18.0000	+	10.3923i	0.869048	+	0.501745i
$430$	5.50000	−	9.52628i	0.265234	−	0.459398i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−13.0000			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$434$	−4.00000	+	6.92820i	−0.192006	+	0.332564i
$435$	−9.00000	−	5.19615i	−0.431517	−	0.249136i
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−15.0000	−	25.9808i	−0.717547	−	1.24283i
$438$	10.5000	−	6.06218i	0.501709	−	0.289662i
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	−0.721686	−	0.692220i	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$	−3.00000			−0.143019
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$	12.0000			0.570782
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$		−	6.92820i		−	0.328798i
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	−11.0000	−	19.0526i	−0.520865	−	0.902165i
$447$		0			0
$448$	2.00000	−	3.46410i	0.0944911	−	0.163663i
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$	−1.50000	+	2.59808i	−0.0707107	+	0.122474i
$451$	−9.00000			−0.423793
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$	−15.0000	+	8.66025i	−0.704761	+	0.406894i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$	−8.00000	−	13.8564i	−0.375046	−	0.649598i
$456$	7.50000	+	4.33013i	0.351220	+	0.202777i
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$	−20.0000			−0.934539
$459$		−	15.5885i		−	0.727607i
$460$	6.00000			0.279751
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$	−18.0000	−	10.3923i	−0.837436	−	0.483494i
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	0.534450	−	0.845200i	$-0.320519\pi$
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	3.00000	−	1.73205i	0.139122	−	0.0803219i
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	21.0000			0.971764			0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000			0.971764			0.485882	+	0.874024i	$0.338498\pi$
$468$	12.0000			0.554700
$469$	−20.0000			−0.923514
$470$		0			0
$471$			13.8564i			0.638470i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	−16.5000	−	28.5788i	−0.758671	−	1.31406i
$474$		−	24.2487i		−	1.11378i
$475$	−2.50000	+	4.33013i	−0.114708	+	0.198680i
$476$	−12.0000			−0.550019
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	−6.00000			−0.274434
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$	−1.50000	+	0.866025i	−0.0684653	+	0.0395285i
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	8.50000	+	14.7224i	0.387164	+	0.670588i
$483$	36.0000	+	20.7846i	1.63806	+	0.945732i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	11.0000			0.499484
$486$		−	15.5885i		−	0.707107i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−5.00000	+	8.66025i	−0.226339	+	0.392031i
$489$	24.0000	+	13.8564i	1.08532	+	0.626608i
$490$	4.50000	+	7.79423i	0.203289	+	0.352107i
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$	−4.50000	+	2.59808i	−0.202876	+	0.117130i
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	20.0000			0.899843
$495$	4.50000	+	7.79423i	0.202260	+	0.350325i
$496$	2.00000			0.0898027
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$		−	20.7846i		−	0.931381i
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	0.970558	+	0.240866i	$0.0774314\pi$
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	−0.276683	+	0.960961i	$0.589235\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		−	31.1769i		−	1.39288i
$502$	−10.5000	+	18.1865i	−0.468638	+	0.811705i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	−12.0000			−0.534522
$505$	−12.0000			−0.533993
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$	4.50000	−	2.59808i	0.199852	−	0.115385i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$	4.50000	+	2.59808i	0.199263	+	0.115045i
$511$	−14.0000	+	24.2487i	−0.619324	+	1.07270i
$512$	−1.00000			−0.0441942
$513$		−	25.9808i		−	1.14708i
$514$	−9.00000			−0.396973
$515$	2.00000	−	3.46410i	0.0881305	−	0.152647i
$516$	−16.5000	−	9.52628i	−0.726372	−	0.419371i
$517$		0			0
$518$	8.00000	+	13.8564i	0.351500	+	0.608816i
$519$	−27.0000	+	15.5885i	−1.18517	+	0.684257i
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		−	6.92820i		−	0.302372i
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$			5.19615i			0.226134i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−6.00000			−0.260623
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$	−20.0000			−0.867110
$533$	−6.00000	+	10.3923i	−0.259889	+	0.450141i
$534$	−9.00000	+	5.19615i	−0.389468	+	0.224860i
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$	2.50000	+	4.33013i	0.107984	+	0.187033i
$537$		0			0
$538$	3.00000	−	5.19615i	0.129339	−	0.224022i
$539$	27.0000			1.16297
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	24.0000	+	13.8564i	1.02994	+	0.594635i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$	−24.0000	+	13.8564i	−1.02711	+	0.592999i
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	0.876517	+	0.481371i	$0.159861\pi$
$548$	−9.00000			−0.384461
$549$	30.0000			1.28037
$550$	−3.00000			−0.127920
$551$	−15.0000	+	25.9808i	−0.639021	+	1.10682i
$552$		−	10.3923i		−	0.442326i
$553$	28.0000	+	48.4974i	1.19068	+	2.06232i
$554$	−11.0000	−	19.0526i	−0.467345	−	0.809466i
$555$		−	6.92820i		−	0.294086i
$556$	0.500000	−	0.866025i	0.0212047	−	0.0367277i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$	−3.00000	−	5.19615i	−0.127000	−	0.219971i
$559$	−44.0000			−1.86100
$560$	2.00000	−	3.46410i	0.0845154	−	0.146385i
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	0.895902	−	0.444252i	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$		0			0
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$	−20.0000			−0.840663
$567$	18.0000	+	31.1769i	0.755929	+	1.30931i
$568$	−6.00000			−0.251754
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	−0.0900490	−	0.995937i	$-0.528702\pi$
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	0.907532	−	0.419984i	$-0.137964\pi$
$570$	7.50000	+	4.33013i	0.314140	+	0.181369i
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	−0.991763	−	0.128085i	$-0.959117\pi$
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	0.384957	−	0.922934i	$-0.374216\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$		0			0
$574$	6.00000	−	10.3923i	0.250435	−	0.433766i
$575$	6.00000			0.250217
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		−	22.5167i		−	0.935760i
$580$	−3.00000	−	5.19615i	−0.124568	−	0.215758i
$581$	24.0000	+	41.5692i	0.995688	+	1.72458i
$582$		−	19.0526i		−	0.789754i
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$	7.00000			0.289662
$585$	12.0000			0.496139
$586$	18.0000			0.743573
$587$	−19.5000	+	33.7750i	−0.804851	+	1.39404i	0.111540	+	0.993760i	$0.464422\pi$
$587$	−19.5000	+	33.7750i	−0.804851	+	1.39404i	−0.916392	+	0.400283i	$0.868912\pi$
$588$	13.5000	−	7.79423i	0.556731	−	0.321429i
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	−1.50000	−	2.59808i	−0.0617540	−	0.106961i
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$	−12.0000			−0.491952
$596$		0			0
$597$	−30.0000	−	17.3205i	−1.22782	−	0.708881i
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	−1.50000	+	0.866025i	−0.0612372	+	0.0353553i
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	−0.490049	−	0.871695i	$-0.663021\pi$
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	0.999934	−	0.0114528i	$-0.00364562\pi$
$602$	44.0000			1.79331
$603$	7.50000	−	12.9904i	0.305424	−	0.529009i
$604$	−10.0000			−0.406894
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$			20.7846i			0.844317i
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$		−	41.5692i		−	1.68447i
$610$	−5.00000	+	8.66025i	−0.202444	+	0.350643i
$611$		0			0
$612$	4.50000	−	7.79423i	0.181902	−	0.315063i
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$	−4.50000	+	2.59808i	−0.181458	+	0.104765i
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	19.5000	+	33.7750i	0.785040	+	1.35973i	0.928975	+	0.370143i	$0.120691\pi$
$617$	19.5000	+	33.7750i	0.785040	+	1.35973i	−0.143934	+	0.989587i	$0.545975\pi$
$618$	−6.00000	−	3.46410i	−0.241355	−	0.139347i
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	−0.609488	−	0.792796i	$-0.708625\pi$
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	0.991325	+	0.131434i	$0.0419582\pi$
$620$	2.00000			0.0803219
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$	6.00000			0.240578
$623$	12.0000	−	20.7846i	0.480770	−	0.832718i
$624$	6.00000	+	3.46410i	0.240192	+	0.138675i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	22.5000	−	12.9904i	0.898563	−	0.518786i
$628$	−4.00000	+	6.92820i	−0.159617	+	0.276465i
$629$	−12.0000			−0.478471
$630$	−12.0000			−0.478091
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	7.00000	−	12.1244i	0.278445	−	0.482281i
$633$		−	6.92820i		−	0.275371i
$634$	12.0000	+	20.7846i	0.476581	+	0.825462i
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$			10.3923i			0.412082i
$637$	18.0000	−	31.1769i	0.713186	−	1.23527i
$638$	−18.0000			−0.712627
$639$	9.00000	+	15.5885i	0.356034	+	0.616670i
$640$	−1.00000			−0.0395285
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$	13.5000	−	7.79423i	0.532803	−	0.307614i
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$	−16.5000	−	9.52628i	−0.649687	−	0.375097i
$646$	7.50000	−	12.9904i	0.295084	−	0.511100i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−9.00000			−0.353281
$650$	−2.00000	+	3.46410i	−0.0784465	+	0.135873i
$651$	12.0000	+	6.92820i	0.470317	+	0.271538i
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$	6.00000	−	3.46410i	0.234619	−	0.135457i
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$	−3.00000			−0.117130
$657$	−10.5000	−	18.1865i	−0.409644	−	0.709524i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$			5.19615i			0.202260i
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		−	20.7846i		−	0.807207i
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$	−20.0000			−0.775567
$666$	−12.0000			−0.464991
$667$	36.0000			1.39393
$668$	9.00000	−	15.5885i	0.348220	−	0.603136i
$669$	−33.0000	+	19.0526i	−1.27585	+	0.736614i
$670$	2.50000	+	4.33013i	0.0965834	+	0.167287i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$	−6.00000	−	3.46410i	−0.231455	−	0.133631i
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	31.0000			1.19408
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	3.00000			0.115385
$677$	18.0000	−	31.1769i	0.691796	−	1.19823i	−0.279453	−	0.960159i	$-0.590153\pi$
$677$	18.0000	−	31.1769i	0.691796	−	1.19823i	0.971249	−	0.238067i	$-0.0765137\pi$
$678$	27.0000	+	15.5885i	1.03693	+	0.598671i
$679$	22.0000	+	38.1051i	0.844283	+	1.46234i
$680$	1.50000	+	2.59808i	0.0575224	+	0.0996317i
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	−21.0000			−0.803543			−0.401771	−	0.915740i	$-0.631605\pi$
$683$	−21.0000			−0.803543			−0.401771	+	0.915740i	$0.631605\pi$
$684$	7.50000	−	12.9904i	0.286770	−	0.496700i
$685$	−9.00000			−0.343872
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$			34.6410i			1.32164i
$688$	−5.50000	−	9.52628i	−0.209686	−	0.363186i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		−	10.3923i		−	0.395628i
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−18.0000			−0.684257
$693$	−18.0000	+	31.1769i	−0.683763	+	1.18431i
$694$	−21.0000			−0.797149
$695$	0.500000	−	0.866025i	0.0189661	−	0.0328502i
$696$	−9.00000	+	5.19615i	−0.341144	+	0.196960i
$697$	4.50000	+	7.79423i	0.170450	+	0.295227i
$698$	−8.00000	−	13.8564i	−0.302804	−	0.524473i
$699$	−31.5000	−	18.1865i	−1.19144	−	0.687878i
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		−	20.7846i		−	0.784465i
$703$	−20.0000			−0.754314
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	−24.0000	−	41.5692i	−0.902613	−	1.56337i
$708$	−4.50000	+	2.59808i	−0.169120	+	0.0976417i
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	−0.347325	−	0.937745i	$-0.612910\pi$
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	0.985773	−	0.168080i	$-0.0537568\pi$
$710$	−6.00000			−0.225176
$711$	−42.0000			−1.57512
$712$	−6.00000			−0.224860
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$			20.7846i			0.777844i
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$		0			0
$717$			10.3923i			0.388108i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	1.50000	+	2.59808i	0.0559017	+	0.0968246i
$721$	16.0000			0.595871
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	25.5000	−	14.7224i	0.948355	−	0.547533i
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−3.00000	−	1.73205i	−0.111340	−	0.0642824i
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$	−16.0000			−0.592999
$729$	−27.0000			−1.00000
$730$	7.00000			0.259082
$731$	−16.5000	+	28.5788i	−0.610275	+	1.05703i
$732$	15.0000	+	8.66025i	0.554416	+	0.320092i
$733$	−16.0000	−	27.7128i	−0.590973	−	1.02360i	−0.994102	−	0.108453i	$-0.965410\pi$
$733$	−16.0000	−	27.7128i	−0.590973	−	1.02360i	0.403128	−	0.915144i	$-0.367923\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$	13.5000	−	7.79423i	0.497955	−	0.287494i
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	15.0000			0.552532
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	29.0000			1.06678			0.533391	−	0.845869i	$-0.320917\pi$
$739$	29.0000			1.06678			0.533391	+	0.845869i	$0.320917\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$		−	34.6410i		−	1.27257i
$742$	−12.0000	−	20.7846i	−0.440534	−	0.763027i
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		−	3.46410i		−	0.127000i
$745$		0			0
$746$	10.0000			0.366126
$747$	−36.0000			−1.31717
$748$	9.00000			0.329073
$749$	−18.0000	+	31.1769i	−0.657706	+	1.13918i
$750$	−1.50000	+	0.866025i	−0.0547723	+	0.0316228i
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$		0			0
$753$	31.5000	+	18.1865i	1.14792	+	0.662754i
$754$	−12.0000	+	20.7846i	−0.437014	+	0.756931i
$755$	−10.0000			−0.363937
$756$			20.7846i			0.755929i
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	14.5000	−	25.1147i	0.526664	−	0.912208i
$759$	−27.0000	−	15.5885i	−0.980038	−	0.565825i
$760$	2.50000	+	4.33013i	0.0906845	+	0.157070i
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$	−3.00000	+	1.73205i	−0.108679	+	0.0627456i
$763$	−8.00000	+	13.8564i	−0.289619	+	0.501636i
$764$		0			0
$765$	4.50000	−	7.79423i	0.162698	−	0.281801i
$766$	−12.0000			−0.433578
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$			1.73205i			0.0625000i
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.0760054	−	0.997107i	$-0.524217\pi$
$770$	−6.00000	−	10.3923i	−0.216225	−	0.374513i
$771$			15.5885i			0.561405i
$772$	6.50000	−	11.2583i	0.233940	−	0.405196i
$773$	−30.0000			−1.07903			−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000			−1.07903			−0.539513	+	0.841978i	$0.681391\pi$
$774$	−16.5000	+	28.5788i	−0.593080	+	1.02725i
$775$	2.00000			0.0718421
$776$	5.50000	−	9.52628i	0.197438	−	0.341974i
$777$	24.0000	−	13.8564i	0.860995	−	0.497096i
$778$	18.0000	+	31.1769i	0.645331	+	1.11775i
$779$	7.50000	+	12.9904i	0.268715	+	0.465429i
$780$	6.00000	+	3.46410i	0.214834	+	0.124035i
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	−18.0000			−0.643679
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	9.00000			0.321429
$785$	−4.00000	+	6.92820i	−0.142766	+	0.247278i
$786$	18.0000	+	10.3923i	0.642039	+	0.370681i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$		0			0
$789$	36.0000	−	20.7846i	1.28163	−	0.739952i
$790$	7.00000	−	12.1244i	0.249049	−	0.431365i
$791$	−72.0000			−2.56003
$792$	9.00000			0.319801
$793$	40.0000			1.42044
$794$	4.00000	−	6.92820i	0.141955	−	0.245873i
$795$			10.3923i			0.368577i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	24.0000	+	41.5692i	0.850124	+	1.47246i	0.881096	+	0.472937i	$0.156806\pi$
$797$	24.0000	+	41.5692i	0.850124	+	1.47246i	−0.0309726	+	0.999520i	$0.509860\pi$
$798$			34.6410i			1.22628i
$799$		0			0
$800$	−1.00000			−0.0353553
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	−33.0000			−1.16527
$803$	10.5000	−	18.1865i	0.370537	−	0.641789i
$804$	7.50000	−	4.33013i	0.264505	−	0.152712i
$805$	12.0000	+	20.7846i	0.422944	+	0.732561i
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	−9.00000	−	5.19615i	−0.316815	−	0.182913i
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	12.0000	−	20.7846i	0.421117	−	0.729397i
$813$	24.0000	+	13.8564i	0.841717	+	0.485965i
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$	4.50000	−	2.59808i	0.157532	−	0.0909509i
$817$	−27.5000	+	47.6314i	−0.962103	+	1.66641i
$818$	31.0000			1.08389
$819$	24.0000	+	41.5692i	0.838628	+	1.45255i
$820$	−3.00000			−0.104765
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	−0.0542853	−	0.998525i	$-0.517288\pi$
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	0.891891	−	0.452250i	$-0.149379\pi$
$822$			15.5885i			0.543710i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$			5.19615i			0.180907i
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	−18.0000			−0.625543
$829$	44.0000			1.52818			0.764092	−	0.645108i	$-0.223188\pi$
$829$	44.0000			1.52818			0.764092	+	0.645108i	$0.223188\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$	−33.0000	+	19.0526i	−1.14476	+	0.660926i
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$	−13.5000	−	23.3827i	−0.467747	−	0.810162i
$834$	−1.50000	−	0.866025i	−0.0519408	−	0.0299880i
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$	15.0000			0.518786
$837$	−9.00000	+	5.19615i	−0.311086	+	0.179605i
$838$		0			0
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$	−6.00000	−	3.46410i	−0.207020	−	0.119523i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	1.00000	+	1.73205i	0.0344623	+	0.0596904i
$843$	−9.00000	+	5.19615i	−0.309976	+	0.178965i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	3.00000			0.103203
$846$		0			0
$847$	8.00000			0.274883
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$			34.6410i			1.18888i
$850$	1.50000	+	2.59808i	0.0514496	+	0.0891133i
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$			10.3923i			0.356034i
$853$	−22.0000	+	38.1051i	−0.753266	+	1.30469i	0.192966	+	0.981205i	$0.438189\pi$
$853$	−22.0000	+	38.1051i	−0.753266	+	1.30469i	−0.946232	+	0.323489i	$0.895144\pi$
$854$	−40.0000			−1.36877
$855$	7.50000	−	12.9904i	0.256495	−	0.444262i
$856$	9.00000			0.307614
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$	18.0000	−	10.3923i	0.614510	−	0.354787i
$859$	9.50000	+	16.4545i	0.324136	+	0.561420i	0.981337	−	0.192295i	$-0.0615932\pi$
$859$	9.50000	+	16.4545i	0.324136	+	0.561420i	−0.657201	+	0.753715i	$0.728260\pi$
$860$	−5.50000	−	9.52628i	−0.187548	−	0.324843i
$861$	−18.0000	−	10.3923i	−0.613438	−	0.354169i
$862$	12.0000	−	20.7846i	0.408722	−	0.707927i
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	−18.0000			−0.612018
$866$	−6.50000	+	11.2583i	−0.220879	+	0.382574i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$	4.00000	+	6.92820i	0.135769	+	0.235159i
$869$	−21.0000	−	36.3731i	−0.712376	−	1.23387i
$870$	−9.00000	+	5.19615i	−0.305129	+	0.176166i
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$	4.00000			0.135457
$873$	−33.0000			−1.11688
$874$	−30.0000			−1.01477
$875$	2.00000	−	3.46410i	0.0676123	−	0.117108i
$876$		−	12.1244i		−	0.409644i
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$		−	31.1769i		−	1.05157i
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	−13.5000	−	23.3827i	−0.454569	−	0.787336i
$883$	41.0000			1.37976			0.689880	−	0.723924i	$-0.257663\pi$
$883$	41.0000			1.37976			0.689880	+	0.723924i	$0.257663\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$	−4.50000	+	2.59808i	−0.151266	+	0.0873334i
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	0.966651	+	0.256096i	$0.0824362\pi$
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	−0.261540	+	0.965193i	$0.584230\pi$
$888$	−6.00000	−	3.46410i	−0.201347	−	0.116248i
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$	−6.00000			−0.201120
$891$	−13.5000	−	23.3827i	−0.452267	−	0.783349i
$892$	−22.0000			−0.736614
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$	−36.0000	+	20.7846i	−1.20201	+	0.693978i
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	12.0000			0.400222
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$	18.0000			0.599667
$902$	−4.50000	+	7.79423i	−0.149834	+	0.259519i
$903$		−	76.2102i		−	2.53612i
$904$	9.00000	+	15.5885i	0.299336	+	0.518464i
$905$	8.00000	+	13.8564i	0.265929	+	0.460603i
$906$			17.3205i			0.575435i
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	−0.904542	−	0.426385i	$-0.859787\pi$
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	0.821531	+	0.570164i	$0.193120\pi$
$908$	−3.00000			−0.0995585
$909$	36.0000			1.19404
$910$	−16.0000			−0.530395
$911$	15.0000	−	25.9808i	0.496972	−	0.860781i	−0.503022	−	0.864274i	$-0.667778\pi$
$911$	15.0000	−	25.9808i	0.496972	−	0.860781i	0.999994	+	0.00349271i	$0.00111177\pi$
$912$	7.50000	−	4.33013i	0.248350	−	0.143385i
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$	−0.500000	−	0.866025i	−0.0165385	−	0.0286456i
$915$	15.0000	+	8.66025i	0.495885	+	0.286299i
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	−48.0000			−1.58510
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	−34.0000			−1.12156			−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000			−1.12156			−0.560778	+	0.827966i	$0.689498\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	10.5000	+	6.06218i	0.345987	+	0.199756i
$922$		0			0
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$	−18.0000	+	10.3923i	−0.592157	+	0.341882i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	−20.0000			−0.657241
$927$	−6.00000	+	10.3923i	−0.197066	+	0.341328i
$928$	−6.00000			−0.196960
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		−	3.46410i		−	0.113592i
$931$	−22.5000	−	38.9711i	−0.737408	−	1.27723i
$932$	−10.5000	−	18.1865i	−0.343939	−	0.595720i
$933$		−	10.3923i		−	0.340229i
$934$	10.5000	−	18.1865i	0.343570	−	0.595082i
$935$	9.00000			0.294331
$936$	6.00000	−	10.3923i	0.196116	−	0.339683i
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	−10.0000	+	17.3205i	−0.326512	+	0.565535i
$939$	−1.50000	+	0.866025i	−0.0489506	+	0.0282617i
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$	12.0000	+	6.92820i	0.390981	+	0.225733i
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$	−3.00000			−0.0976417
$945$			20.7846i			0.676123i
$946$	−33.0000			−1.07292
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	−0.997589	−	0.0694014i	$-0.977891\pi$
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	0.558898	+	0.829237i	$0.311224\pi$
$948$	−21.0000	−	12.1244i	−0.682048	−	0.393781i
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$	2.50000	+	4.33013i	0.0811107	+	0.140488i
$951$	36.0000	−	20.7846i	1.16738	−	0.673987i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	51.0000			1.65205			0.826026	−	0.563632i	$-0.190596\pi$
$953$	51.0000			1.65205			0.826026	+	0.563632i	$0.190596\pi$
$954$	18.0000			0.582772
$955$		0			0
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$			31.1769i			1.00781i
$958$	−3.00000	−	5.19615i	−0.0969256	−	0.167880i
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$			1.73205i			0.0559017i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−16.0000			−0.515861
$963$	−13.5000	−	23.3827i	−0.435031	−	0.753497i
$964$	17.0000			0.547533
$965$	6.50000	−	11.2583i	0.209242	−	0.362418i
$966$	36.0000	−	20.7846i	1.15828	−	0.668734i
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	−22.5000	−	12.9904i	−0.722804	−	0.417311i
$970$	5.50000	−	9.52628i	0.176594	−	0.305870i
$971$	60.0000			1.92549			0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000			1.92549			0.962746	+	0.270408i	$0.0871586\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	4.00000			0.128234
$974$	1.00000	−	1.73205i	0.0320421	−	0.0554985i
$975$	6.00000	+	3.46410i	0.192154	+	0.110940i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	4.50000	+	7.79423i	0.143968	+	0.249359i	0.928987	−	0.370111i	$-0.120681\pi$
$977$	4.50000	+	7.79423i	0.143968	+	0.249359i	−0.785020	+	0.619471i	$0.787347\pi$
$978$	24.0000	−	13.8564i	0.767435	−	0.443079i
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$	9.00000			0.287494
$981$	−6.00000	−	10.3923i	−0.191565	−	0.331801i
$982$	33.0000			1.05307
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$			5.19615i			0.165647i
$985$		0			0
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$		0			0
$988$	10.0000	−	17.3205i	0.318142	−	0.551039i
$989$	66.0000			2.09868
$990$	9.00000			0.286039
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	−6.00000	+	3.46410i	−0.190404	+	0.109930i
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$	−10.0000	−	17.3205i	−0.317021	−	0.549097i
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$	31.0000			0.981288
$999$			20.7846i			0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.e.b.61.1	yes	2
3.2	odd	2		270.2.e.a.181.1		2
4.3	odd	2		720.2.q.c.241.1		2
5.2	odd	4		450.2.j.a.349.2		4
5.3	odd	4		450.2.j.a.349.1		4
5.4	even	2		450.2.e.d.151.1		2
9.2	odd	6		810.2.a.e.1.1		1
9.4	even	3	inner	90.2.e.b.31.1	✓	2
9.5	odd	6		270.2.e.a.91.1		2
9.7	even	3		810.2.a.a.1.1		1
12.11	even	2		2160.2.q.d.721.1		2
15.2	even	4		1350.2.j.c.1099.1		4
15.8	even	4		1350.2.j.c.1099.2		4
15.14	odd	2		1350.2.e.g.451.1		2
36.7	odd	6		6480.2.a.z.1.1		1
36.11	even	6		6480.2.a.l.1.1		1
36.23	even	6		2160.2.q.d.1441.1		2
36.31	odd	6		720.2.q.c.481.1		2
45.2	even	12		4050.2.c.d.649.2		2
45.4	even	6		450.2.e.d.301.1		2
45.7	odd	12		4050.2.c.p.649.1		2
45.13	odd	12		450.2.j.a.49.2		4
45.14	odd	6		1350.2.e.g.901.1		2
45.22	odd	12		450.2.j.a.49.1		4
45.23	even	12		1350.2.j.c.199.1		4
45.29	odd	6		4050.2.a.q.1.1		1
45.32	even	12		1350.2.j.c.199.2		4
45.34	even	6		4050.2.a.bi.1.1		1
45.38	even	12		4050.2.c.d.649.1		2
45.43	odd	12		4050.2.c.p.649.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.b.31.1	✓	2	9.4	even	3	inner
90.2.e.b.61.1	yes	2	1.1	even	1	trivial
270.2.e.a.91.1		2	9.5	odd	6
270.2.e.a.181.1		2	3.2	odd	2
450.2.e.d.151.1		2	5.4	even	2
450.2.e.d.301.1		2	45.4	even	6
450.2.j.a.49.1		4	45.22	odd	12
450.2.j.a.49.2		4	45.13	odd	12
450.2.j.a.349.1		4	5.3	odd	4
450.2.j.a.349.2		4	5.2	odd	4
720.2.q.c.241.1		2	4.3	odd	2
720.2.q.c.481.1		2	36.31	odd	6
810.2.a.a.1.1		1	9.7	even	3
810.2.a.e.1.1		1	9.2	odd	6
1350.2.e.g.451.1		2	15.14	odd	2
1350.2.e.g.901.1		2	45.14	odd	6
1350.2.j.c.199.1		4	45.23	even	12
1350.2.j.c.199.2		4	45.32	even	12
1350.2.j.c.1099.1		4	15.2	even	4
1350.2.j.c.1099.2		4	15.8	even	4
2160.2.q.d.721.1		2	12.11	even	2
2160.2.q.d.1441.1		2	36.23	even	6
4050.2.a.q.1.1		1	45.29	odd	6
4050.2.a.bi.1.1		1	45.34	even	6
4050.2.c.d.649.1		2	45.38	even	12
4050.2.c.d.649.2		2	45.2	even	12
4050.2.c.p.649.1		2	45.7	odd	12
4050.2.c.p.649.2		2	45.43	odd	12
6480.2.a.l.1.1		1	36.11	even	6
6480.2.a.z.1.1		1	36.7	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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	90.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} +(-1.50000 + 0.866025i) q^{6} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.00000 - 3.46410i) q^{14} +1.73205i q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +3.00000 q^{18} +5.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-6.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{26} -5.19615i q^{27} -4.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(1.50000 + 0.866025i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.50000 - 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} -4.00000 q^{35} +(1.50000 - 2.59808i) q^{36} -4.00000 q^{37} +(2.50000 - 4.33013i) q^{38} -6.92820i q^{39} +(0.500000 + 0.866025i) q^{40} +(1.50000 + 2.59808i) q^{41} +6.92820i q^{42} +(-5.50000 + 9.52628i) q^{43} +3.00000 q^{44} +(1.50000 - 2.59808i) q^{45} -6.00000 q^{46} +(1.50000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +6.00000 q^{53} +(-4.50000 - 2.59808i) q^{54} +3.00000 q^{55} +(-2.00000 + 3.46410i) q^{56} +(-7.50000 - 4.33013i) q^{57} +(3.00000 + 5.19615i) q^{58} +(1.50000 + 2.59808i) q^{59} +(1.50000 - 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +12.0000 q^{63} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} -5.19615i q^{66} +(-2.50000 - 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +10.3923i q^{69} +(-2.00000 + 3.46410i) q^{70} +6.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} -7.00000 q^{73} +(-2.00000 + 3.46410i) q^{74} +(1.50000 - 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(6.00000 + 10.3923i) q^{77} +(-6.00000 - 3.46410i) q^{78} +(-7.00000 + 12.1244i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +3.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(6.00000 + 3.46410i) q^{84} +(-1.50000 - 2.59808i) q^{85} +(5.50000 + 9.52628i) q^{86} +(9.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +(-1.50000 - 2.59808i) q^{90} +16.0000 q^{91} +(-3.00000 + 5.19615i) q^{92} +3.46410i q^{93} +(-2.50000 - 4.33013i) q^{95} -1.73205i q^{96} +(-5.50000 + 9.52628i) q^{97} -9.00000 q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} - q^{5} - 3 q^{6} + 4 q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} - 3 q^{11} + 4 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 6 q^{18} + 10 q^{19} - q^{20} - 12 q^{21} + 3 q^{22}+ \cdots - 18 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 - q^5 - 3 * q^6 + 4 * q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 - 3 * q^11 + 4 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 6 * q^18 + 10 * q^19 - q^20 - 12 * q^21 + 3 * q^22 - 6 * q^23 + 3 * q^24 - q^25 + 8 * q^26 - 8 * q^28 - 6 * q^29 + 3 * q^30 - 2 * q^31 + q^32 + 9 * q^33 + 3 * q^34 - 8 * q^35 + 3 * q^36 - 8 * q^37 + 5 * q^38 + q^40 + 3 * q^41 - 11 * q^43 + 6 * q^44 + 3 * q^45 - 12 * q^46 + 3 * q^48 - 9 * q^49 + q^50 - 9 * q^51 + 4 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 - 4 * q^56 - 15 * q^57 + 6 * q^58 + 3 * q^59 + 3 * q^60 + 10 * q^61 - 4 * q^62 + 24 * q^63 + 2 * q^64 + 4 * q^65 - 5 * q^67 - 3 * q^68 - 4 * q^70 + 12 * q^71 - 3 * q^72 - 14 * q^73 - 4 * q^74 + 3 * q^75 - 5 * q^76 + 12 * q^77 - 12 * q^78 - 14 * q^79 + 2 * q^80 - 9 * q^81 + 6 * q^82 - 12 * q^83 + 12 * q^84 - 3 * q^85 + 11 * q^86 + 18 * q^87 + 3 * q^88 + 12 * q^89 - 3 * q^90 + 32 * q^91 - 6 * q^92 - 5 * q^95 - 11 * q^97 - 18 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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