LMFDB - Embedded newform 450.2.e.d.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(151,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$450 = 2 \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	450.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,3,-1,0,-3,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.59326809096$
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:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	450.301
Dual form			450.2.e.d.151.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$ .

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−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			0
$5$		0			0
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	−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	$-0.439481\pi$
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$			1.73205i			0.500000i
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	−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			0
$21$	−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	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$		0			0
$26$	4.00000			0.784465
$27$		−	5.19615i		−	1.00000i
$28$	4.00000			0.755929
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−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
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	−2.50000	−	4.33013i	−0.405554	−	0.702439i
$39$			6.92820i			1.10940i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$			6.92820i			1.06904i
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	0.890947	+	0.454108i	$0.150042\pi$
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	−0.0522047	+	0.998636i	$0.516625\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$		0			0
$51$	−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	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	−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	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	2.00000			0.254000
$63$	−12.0000			−1.51186
$64$	1.00000			0.125000
$65$		0			0
$66$			5.19615i			0.639602i
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		−	10.3923i		−	1.25109i
$70$		0			0
$71$	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	$-0.365653\pi$
$73$	7.00000			0.819288			0.409644	+	0.912245i	$0.365653\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−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	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−3.00000			−0.331295
$83$	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
$85$		0			0
$86$	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	$0.396989\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$			3.46410i			0.359211i
$94$		0			0
$95$		0			0
$96$			1.73205i			0.176777i
$97$	5.50000	+	9.52628i	0.558440	+	0.967247i	0.997627	+	0.0688512i	$0.0219334\pi$
$97$	5.50000	+	9.52628i	0.558440	+	0.967247i	−0.439187	+	0.898396i	$0.644733\pi$
$98$	9.00000			0.909137
$99$	−9.00000			−0.904534
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	9.00000			0.870063			0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000			0.870063			0.435031	+	0.900415i	$0.356737\pi$
$108$	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	$0.561356\pi$
$110$		0			0
$111$	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	−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	9.00000	−	15.5885i	0.846649	−	1.46644i	0.884182	−	0.467143i	$-0.154717\pi$
$114$	−7.50000	−	4.33013i	−0.702439	−	0.405554i
$115$		0			0
$116$	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
$120$		0			0
$121$	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
$125$		0			0
$126$	6.00000	+	10.3923i	0.534522	+	0.925820i
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	16.5000	+	9.52628i	1.45274	+	0.838742i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	4.50000	−	2.59808i	0.391675	−	0.226134i
$133$	−10.0000	−	17.3205i	−0.867110	−	1.50188i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	−3.00000			−0.257248
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$	−9.00000	+	5.19615i	−0.766131	+	0.442326i
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	−0.844042	−	0.536278i	$-0.819830\pi$
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	0.886451	+	0.462822i	$0.153163\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	12.0000			1.00349
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−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	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	5.00000			0.405554
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$	12.0000			0.966988
$155$		0			0
$156$	−6.00000	−	3.46410i	−0.480384	−	0.277350i
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	−0.661094	−	0.750303i	$-0.729907\pi$
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	0.980329	+	0.197372i	$0.0632408\pi$
$158$	−7.00000	+	12.1244i	−0.556890	+	0.964562i
$159$	−9.00000	+	5.19615i	−0.713746	+	0.412082i
$160$		0			0
$161$	−24.0000			−1.89146
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$	−6.00000	−	3.46410i	−0.462910	−	0.267261i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$	7.50000	−	12.9904i	0.573539	−	0.993399i
$172$	−11.0000			−0.838742
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$			10.3923i			0.787839i
$175$		0			0
$176$	−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	$0.5\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$	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
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$	5.50000	−	9.52628i	0.394877	−	0.683947i
$195$		0			0
$196$	−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			0
$201$		−	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
$205$		0			0
$206$	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
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	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
$215$		0			0
$216$		−	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
$220$		0			0
$221$	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	−0.954011	−	0.299770i	$-0.903090\pi$
$223$	−11.0000	−	19.0526i	−0.736614	−	1.27585i	0.217397	−	0.976083i	$-0.430243\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$			8.66025i			0.573539i
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$		0			0
$231$			20.7846i			1.36753i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$	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	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$		0			0
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$	−2.00000			−0.128565
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	−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			0
$251$	−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
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	−0.690856	−	0.722993i	$-0.742766\pi$
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	0.971558	+	0.236802i	$0.0760993\pi$
$258$		−	19.0526i		−	1.18616i
$259$	−8.00000	−	13.8564i	−0.497096	−	0.860995i
$260$		0			0
$261$	−18.0000			−1.11417
$262$	12.0000			0.741362
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$	−4.50000	−	2.59808i	−0.276956	−	0.159901i
$265$		0			0
$266$	−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	$0.441447\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	9.00000	+	5.19615i	0.541736	+	0.312772i
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	−1.00000			−0.0599760
$279$	3.00000	+	5.19615i	0.179605	+	0.311086i
$280$		0			0
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$		0			0
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−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
$290$		0			0
$291$	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	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$	13.5000	−	7.79423i	0.787336	−	0.454569i
$295$		0			0
$296$	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
$300$		0			0
$301$	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
$305$		0			0
$306$	9.00000			0.514496
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$	−6.00000	−	10.3923i	−0.341882	−	0.592157i
$309$			6.92820i			0.394132i
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$			6.92820i			0.392232i
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$	−8.00000			−0.451466
$315$		0			0
$316$	14.0000			0.787562
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$	9.00000	+	5.19615i	0.504695	+	0.291386i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	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
$325$		0			0
$326$	−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
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−12.0000			−0.658586
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$	18.0000			0.984916
$335$		0			0
$336$			6.92820i			0.377964i
$337$	−15.5000	+	26.8468i	−0.844339	+	1.46244i	0.0418554	+	0.999124i	$0.486673\pi$
$337$	−15.5000	+	26.8468i	−0.844339	+	1.46244i	−0.886194	+	0.463314i	$0.846660\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$		−	31.1769i		−	1.69330i
$340$		0			0
$341$	6.00000			0.324918
$342$	−15.0000			−0.811107
$343$	8.00000			0.431959
$344$	5.50000	+	9.52628i	0.296540	+	0.513623i
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	10.5000	−	18.1865i	0.563670	−	0.976304i	−0.433503	−	0.901152i	$-0.642722\pi$
$347$	10.5000	−	18.1865i	0.563670	−	0.976304i	0.997172	−	0.0751519i	$-0.0239442\pi$
$348$	9.00000	−	5.19615i	0.482451	−	0.278543i
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$		0			0
$351$	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	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$	−4.50000	+	2.59808i	−0.239172	+	0.138086i
$355$		0			0
$356$	−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	$0.718315\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$		−	17.3205i		−	0.905357i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	−6.00000			−0.312772
$369$	−4.50000	−	7.79423i	−0.234261	−	0.405751i
$370$		0			0
$371$	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	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$		0			0
$376$		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	$0.232538\pi$
$380$		0			0
$381$	−3.00000	+	1.73205i	−0.153695	+	0.0887357i
$382$		0			0
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$		0			0
$386$	13.0000			0.661683
$387$	33.0000			1.67748
$388$	−11.0000			−0.558440
$389$	−18.0000	−	31.1769i	−0.912636	−	1.58073i	−0.810326	−	0.585980i	$-0.800710\pi$
$389$	−18.0000	−	31.1769i	−0.912636	−	1.58073i	−0.102311	−	0.994753i	$-0.532624\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	4.50000	−	7.79423i	0.226134	−	0.391675i
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$	−10.0000	−	17.3205i	−0.501255	−	0.868199i
$399$	−30.0000	−	17.3205i	−1.50188	−	0.867110i
$400$		0			0
$401$	−16.5000	+	28.5788i	−0.823971	+	1.42716i	0.0787327	+	0.996896i	$0.474913\pi$
$401$	−16.5000	+	28.5788i	−0.823971	+	1.42716i	−0.902703	+	0.430263i	$0.858421\pi$
$402$	−7.50000	+	4.33013i	−0.374066	+	0.215967i
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$	−12.0000			−0.597022
$405$		0			0
$406$	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	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	−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	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$	−1.00000	−	1.73205i	−0.0487370	−	0.0844150i	0.840628	−	0.541613i	$-0.182186\pi$
$421$	−1.00000	−	1.73205i	−0.0487370	−	0.0844150i	−0.889365	+	0.457198i	$0.848853\pi$
$422$	−4.00000			−0.194717
$423$		0			0
$424$	−6.00000			−0.291386
$425$		0			0
$426$	−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
$430$		0			0
$431$	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	$-0.398877\pi$
$433$	13.0000			0.624740			0.312370	+	0.949960i	$0.398877\pi$
$434$	−4.00000	−	6.92820i	−0.192006	−	0.332564i
$435$		0			0
$436$	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	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$		0			0
$441$	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	$-0.143962\pi$
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	−0.828190	+	0.560448i	$0.810629\pi$
$444$			6.92820i			0.328798i
$445$		0			0
$446$	−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	$0.615161\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	7.50000	−	4.33013i	0.351220	−	0.202777i
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	0.854094	−	0.520119i	$-0.174112\pi$
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	−0.877483	+	0.479608i	$0.840779\pi$
$458$	20.0000			0.934539
$459$			15.5885i			0.727607i
$460$		0			0
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$	18.0000	−	10.3923i	0.837436	−	0.483494i
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	−0.534450	−	0.845200i	$-0.679481\pi$
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	0.999190	+	0.0402476i	$0.0128147\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	−21.0000			−0.971764			−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000			−0.971764			−0.485882	+	0.874024i	$0.661502\pi$
$468$	−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
$475$		0			0
$476$	−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	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$			15.5885i			0.707107i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	24.0000	−	13.8564i	1.08532	−	0.626608i
$490$		0			0
$491$	16.5000	−	28.5788i	0.744635	−	1.28974i	−0.205731	−	0.978609i	$-0.565957\pi$
$491$	16.5000	−	28.5788i	0.744635	−	1.28974i	0.950365	−	0.311136i	$-0.100710\pi$
$492$	4.50000	+	2.59808i	0.202876	+	0.117130i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	20.0000			0.899843
$495$		0			0
$496$	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	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$		0			0
$501$			31.1769i			1.39288i
$502$	10.5000	+	18.1865i	0.468638	+	0.811705i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	−12.0000			−0.534522
$505$		0			0
$506$	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	−0.701866	−	0.712309i	$-0.747649\pi$
$509$	6.00000	−	10.3923i	0.265945	−	0.460631i	0.967811	+	0.251679i	$0.0809826\pi$
$510$		0			0
$511$	−14.0000	−	24.2487i	−0.619324	−	1.07270i
$512$	1.00000			0.0441942
$513$		−	25.9808i		−	1.14708i
$514$	−9.00000			−0.396973
$515$		0			0
$516$	−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
$520$		0			0
$521$	−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	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		0			0
$541$	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
$545$		0			0
$546$	−24.0000	−	13.8564i	−1.02711	−	0.592999i
$547$	−0.500000	−	0.866025i	−0.0213785	−	0.0370286i	0.855138	−	0.518400i	$-0.173472\pi$
$547$	−0.500000	−	0.866025i	−0.0213785	−	0.0370286i	−0.876517	+	0.481371i	$0.840139\pi$
$548$	9.00000			0.384461
$549$	30.0000			1.28037
$550$		0			0
$551$	−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
$555$		0			0
$556$	0.500000	+	0.866025i	0.0212047	+	0.0367277i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$	3.00000	−	5.19615i	0.127000	−	0.219971i
$559$	−44.0000			−1.86100
$560$		0			0
$561$	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	$-0.853470\pi$
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	0.832684	+	0.553748i	$0.186803\pi$
$564$		0			0
$565$		0			0
$566$	−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	0.907532	+	0.419984i	$0.137964\pi$
$569$	19.5000	+	33.7750i	0.817483	+	1.41592i	−0.0900490	+	0.995937i	$0.528702\pi$
$570$		0			0
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	0.384957	+	0.922934i	$0.374216\pi$
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	−0.991763	+	0.128085i	$0.959117\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$		0			0
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	7.00000			0.291414			0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000			0.291414			0.145707	+	0.989328i	$0.453454\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$			22.5167i			0.935760i
$580$		0			0
$581$	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
$585$		0			0
$586$	18.0000			0.743573
$587$	19.5000	+	33.7750i	0.804851	+	1.39404i	0.916392	+	0.400283i	$0.131088\pi$
$587$	19.5000	+	33.7750i	0.804851	+	1.39404i	−0.111540	+	0.993760i	$0.535578\pi$
$588$	−13.5000	−	7.79423i	−0.556731	−	0.321429i
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$		0			0
$591$		0			0
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$	13.5000	+	7.79423i	0.553912	+	0.319801i
$595$		0			0
$596$		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	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	0.999934	+	0.0114528i	$0.00364562\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$	−44.0000			−1.79331
$603$	−7.50000	−	12.9904i	−0.305424	−	0.529009i
$604$	−10.0000			−0.406894
$605$		0			0
$606$		−	20.7846i		−	0.844317i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$			41.5692i			1.68447i
$610$		0			0
$611$		0			0
$612$	−4.50000	−	7.79423i	−0.181902	−	0.315063i
$613$	−2.00000			−0.0807792			−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000			−0.0807792			−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$	−6.00000	+	10.3923i	−0.241747	+	0.418718i
$617$	−19.5000	+	33.7750i	−0.785040	+	1.35973i	0.143934	+	0.989587i	$0.454025\pi$
$617$	−19.5000	+	33.7750i	−0.785040	+	1.35973i	−0.928975	+	0.370143i	$0.879309\pi$
$618$	6.00000	−	3.46410i	0.241355	−	0.139347i
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$		0			0
$621$	−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			0
$626$	−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
$630$		0			0
$631$	−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
$635$		0			0
$636$		−	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
$640$		0			0
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$	−13.5000	−	7.79423i	−0.532803	−	0.307614i
$643$	11.5000	−	19.9186i	0.453516	−	0.785512i	−0.545086	−	0.838380i	$-0.683503\pi$
$643$	11.5000	−	19.9186i	0.453516	−	0.785512i	0.998602	+	0.0528680i	$0.0168363\pi$
$644$	12.0000	−	20.7846i	0.472866	−	0.819028i
$645$		0			0
$646$	7.50000	+	12.9904i	0.295084	+	0.511100i
$647$	−6.00000			−0.235884			−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000			−0.235884			−0.117942	+	0.993020i	$0.537630\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−9.00000			−0.353281
$650$		0			0
$651$	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	−0.0825519	−	0.996587i	$-0.526307\pi$
$653$	21.0000	−	36.3731i	0.821794	−	1.42339i	0.904345	−	0.426801i	$-0.140360\pi$
$654$	6.00000	+	3.46410i	0.234619	+	0.135457i
$655$		0			0
$656$	−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	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		−	20.7846i		−	0.807207i
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$		0			0
$666$	−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
$670$		0			0
$671$	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	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$	31.0000			1.19408
$675$		0			0
$676$	3.00000			0.115385
$677$	−18.0000	−	31.1769i	−0.691796	−	1.19823i	−0.971249	−	0.238067i	$-0.923486\pi$
$677$	−18.0000	−	31.1769i	−0.691796	−	1.19823i	0.279453	−	0.960159i	$-0.409847\pi$
$678$	−27.0000	+	15.5885i	−1.03693	+	0.598671i
$679$	22.0000	−	38.1051i	0.844283	−	1.46234i
$680$		0			0
$681$	−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	$-0.368395\pi$
$683$	21.0000			0.803543			0.401771	+	0.915740i	$0.368395\pi$
$684$	7.50000	+	12.9904i	0.286770	+	0.496700i
$685$		0			0
$686$	−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
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	18.0000			0.684257
$693$	18.0000	+	31.1769i	0.683763	+	1.18431i
$694$	−21.0000			−0.797149
$695$		0			0
$696$	−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
$700$		0			0
$701$	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	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$		0			0
$711$	−42.0000			−1.57512
$712$	6.00000			0.224860
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		−	20.7846i		−	0.777844i
$715$		0			0
$716$		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	$0.5\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−3.00000	+	1.73205i	−0.111340	+	0.0642824i
$727$	−14.0000	−	24.2487i	−0.519231	−	0.899335i	−0.999750	−	0.0223506i	$-0.992885\pi$
$727$	−14.0000	−	24.2487i	−0.519231	−	0.899335i	0.480519	−	0.876984i	$-0.340448\pi$
$728$	16.0000			0.592999
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−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	−0.403128	−	0.915144i	$-0.632077\pi$
$733$	16.0000	−	27.7128i	0.590973	−	1.02360i	0.994102	−	0.108453i	$-0.0345896\pi$
$734$	4.00000	−	6.92820i	0.147643	−	0.255725i
$735$		0			0
$736$	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	$0.320917\pi$
$740$		0			0
$741$			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	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$			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
$750$		0			0
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	−0.489053	−	0.872254i	$-0.662658\pi$
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	0.999921	−	0.0125942i	$-0.00400897\pi$
$752$		0			0
$753$	−31.5000	+	18.1865i	−1.14792	+	0.662754i
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$		0			0
$756$		−	20.7846i		−	0.755929i
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	−14.5000	−	25.1147i	−0.526664	−	0.912208i
$759$	−27.0000	+	15.5885i	−0.980038	+	0.565825i
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	3.00000	+	1.73205i	0.108679	+	0.0627456i
$763$	8.00000	+	13.8564i	0.289619	+	0.501636i
$764$		0			0
$765$		0			0
$766$	−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	−0.0760054	+	0.997107i	$0.524217\pi$
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.825518	+	0.564376i	$0.809117\pi$
$770$		0			0
$771$		−	15.5885i		−	0.561405i
$772$	−6.50000	−	11.2583i	−0.233940	−	0.405196i
$773$	30.0000			1.07903			0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000			1.07903			0.539513	+	0.841978i	$0.318609\pi$
$774$	−16.5000	−	28.5788i	−0.593080	−	1.02725i
$775$		0			0
$776$	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
$780$		0			0
$781$	−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
$785$		0			0
$786$	18.0000	−	10.3923i	0.642039	−	0.370681i
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$		0			0
$789$	36.0000	+	20.7846i	1.28163	+	0.739952i
$790$		0			0
$791$	−72.0000			−2.56003
$792$	−9.00000			−0.319801
$793$	−40.0000			−1.42044
$794$	4.00000	+	6.92820i	0.141955	+	0.245873i
$795$		0			0
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	−24.0000	+	41.5692i	−0.850124	+	1.47246i	0.0309726	+	0.999520i	$0.490140\pi$
$797$	−24.0000	+	41.5692i	−0.850124	+	1.47246i	−0.881096	+	0.472937i	$0.843194\pi$
$798$			34.6410i			1.22628i
$799$		0			0
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	$0.740453\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	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
$820$		0			0
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	0.891891	+	0.452250i	$0.149379\pi$
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	−0.0542853	+	0.998525i	$0.517288\pi$
$822$			15.5885i			0.543710i
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	−0.898776	−	0.438408i	$-0.855543\pi$
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	0.829060	+	0.559159i	$0.188876\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	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	$0.223188\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	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	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$		0			0
$847$	−8.00000			−0.274883
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$		−	34.6410i		−	1.18888i
$850$		0			0
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$			10.3923i			0.356034i
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	0.946232	+	0.323489i	$0.104856\pi$
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	−0.192966	+	0.981205i	$0.561811\pi$
$854$	−40.0000			−1.36877
$855$		0			0
$856$	9.00000			0.307614
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$	−18.0000	−	10.3923i	−0.614510	−	0.354787i
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	−0.657201	−	0.753715i	$-0.728260\pi$
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	0.981337	+	0.192295i	$0.0615932\pi$
$860$		0			0
$861$	−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	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		0			0
$866$	−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
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	−4.00000			−0.135457
$873$	33.0000			1.11688
$874$	−30.0000			−1.01477
$875$		0			0
$876$			12.1244i			0.409644i
$877$	1.00000	−	1.73205i	0.0337676	−	0.0584872i	−0.848648	−	0.528958i	$-0.822583\pi$
$877$	1.00000	−	1.73205i	0.0337676	−	0.0584872i	0.882415	+	0.470471i	$0.155916\pi$
$878$	5.00000	−	8.66025i	0.168742	−	0.292269i
$879$			31.1769i			1.05157i
$880$		0			0
$881$	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	$-0.742337\pi$
$883$	−41.0000			−1.37976			−0.689880	+	0.723924i	$0.742337\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	1.50000	−	2.59808i	0.0503935	−	0.0872841i
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	0.261540	+	0.965193i	$0.415770\pi$
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	−0.966651	+	0.256096i	$0.917564\pi$
$888$	6.00000	−	3.46410i	0.201347	−	0.116248i
$889$	4.00000	+	6.92820i	0.134156	+	0.232364i
$890$		0			0
$891$	−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
$900$		0			0
$901$	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
$905$		0			0
$906$		−	17.3205i		−	0.575435i
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	0.904542	−	0.426385i	$-0.140213\pi$
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	−0.821531	+	0.570164i	$0.806880\pi$
$908$	3.00000			0.0995585
$909$	36.0000			1.19404
$910$		0			0
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	0.999994	−	0.00349271i	$-0.00111177\pi$
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$912$	−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
$915$		0			0
$916$	−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	$0.689498\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	−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	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	6.00000	+	10.3923i	0.196116	+	0.339683i
$937$	10.0000			0.326686			0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000			0.326686			0.163343	+	0.986569i	$0.447772\pi$
$938$	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	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$	−12.0000	+	6.92820i	−0.390981	+	0.225733i
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	−33.0000			−1.07292
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$	21.0000	−	12.1244i	0.682048	−	0.393781i
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$		0			0
$951$	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	$-0.809404\pi$
$953$	−51.0000			−1.65205			−0.826026	+	0.563632i	$0.809404\pi$
$954$	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
$960$		0			0
$961$	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
$965$		0			0
$966$	36.0000	+	20.7846i	1.15828	+	0.668734i
$967$	−11.0000	+	19.0526i	−0.353736	+	0.612689i	−0.986901	−	0.161328i	$-0.948422\pi$
$967$	−11.0000	+	19.0526i	−0.353736	+	0.612689i	0.633165	+	0.774017i	$0.281756\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	−22.5000	+	12.9904i	−0.722804	+	0.417311i
$970$		0			0
$971$	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
$975$		0			0
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	−4.50000	+	7.79423i	−0.143968	+	0.249359i	−0.928987	−	0.370111i	$-0.879319\pi$
$977$	−4.50000	+	7.79423i	−0.143968	+	0.249359i	0.785020	+	0.619471i	$0.212653\pi$
$978$	−24.0000	−	13.8564i	−0.767435	−	0.443079i
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$		0			0
$981$	−6.00000	+	10.3923i	−0.191565	+	0.331801i
$982$	−33.0000			−1.05307
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		−	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
$990$		0			0
$991$	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
$995$		0			0
$996$	−18.0000	+	10.3923i	−0.570352	+	0.329293i
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$	−31.0000			−0.981288
$999$		−	20.7846i		−	0.657596i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.b.31.1	✓	2	5.4	even	2
90.2.e.b.61.1	yes	2	45.34	even	6
270.2.e.a.91.1		2	15.14	odd	2
270.2.e.a.181.1		2	45.29	odd	6
450.2.e.d.151.1		2	9.7	even	3	inner
450.2.e.d.301.1		2	1.1	even	1	trivial
450.2.j.a.49.1		4	5.3	odd	4
450.2.j.a.49.2		4	5.2	odd	4
450.2.j.a.349.1		4	45.7	odd	12
450.2.j.a.349.2		4	45.43	odd	12
720.2.q.c.241.1		2	180.79	odd	6
720.2.q.c.481.1		2	20.19	odd	2
810.2.a.a.1.1		1	45.4	even	6
810.2.a.e.1.1		1	45.14	odd	6
1350.2.e.g.451.1		2	9.2	odd	6
1350.2.e.g.901.1		2	3.2	odd	2
1350.2.j.c.199.1		4	15.2	even	4
1350.2.j.c.199.2		4	15.8	even	4
1350.2.j.c.1099.1		4	45.38	even	12
1350.2.j.c.1099.2		4	45.2	even	12
2160.2.q.d.721.1		2	180.119	even	6
2160.2.q.d.1441.1		2	60.59	even	2
4050.2.a.q.1.1		1	9.5	odd	6
4050.2.a.bi.1.1		1	9.4	even	3
4050.2.c.d.649.1		2	45.32	even	12
4050.2.c.d.649.2		2	45.23	even	12
4050.2.c.p.649.1		2	45.13	odd	12
4050.2.c.p.649.2		2	45.22	odd	12
6480.2.a.l.1.1		1	180.59	even	6
6480.2.a.z.1.1		1	180.139	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	450.2.e.d.301.1

Level	$450$
Weight	$2$
Character	450.301
Analytic conductor	$3.593$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$