LMFDB - Embedded newform 450.2.j.a.349.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(49,450)] 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("450.49"); 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([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$450 = 2 \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	450.j (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,0,-6,0,0,-6,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	450.349
Dual form			450.2.j.a.49.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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

)

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−3.46410	−	2.00000i	−1.30931	−	0.755929i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	−3.46410	−	2.00000i	−1.30931	−	0.755929i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−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	$0.316051\pi$
$12$	1.73205			0.500000
$13$	−3.46410	+	2.00000i	−0.960769	+	0.554700i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.46410	+	2.00000i	−0.960769	+	0.554700i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$			3.00000i			0.707107i
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$		0			0
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$	2.59808	−	1.50000i	0.553912	−	0.319801i
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$		0			0
$26$	4.00000			0.784465
$27$	−5.19615			−1.00000
$28$		−	4.00000i		−	0.755929i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	−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	$0.890815\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.59808	+	4.50000i	0.452267	+	0.783349i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	4.33013	+	2.50000i	0.702439	+	0.405554i
$39$			6.92820i			1.10940i
$40$		0			0
$41$	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	$0.758066\pi$
$42$	6.92820			1.06904
$43$	−9.52628	−	5.50000i	−1.45274	−	0.838742i	−0.454108	−	0.890947i	$-0.650042\pi$
$43$	−9.52628	−	5.50000i	−1.45274	−	0.838742i	−0.998636	+	0.0522047i	$0.983375\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.866025	+	1.50000i	0.125000	+	0.216506i
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$		0			0
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	−3.46410	−	2.00000i	−0.480384	−	0.277350i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		0			0
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$	−4.33013	+	7.50000i	−0.573539	+	0.993399i
$58$	−5.19615	+	3.00000i	−0.682288	+	0.393919i
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	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	$-0.0544754\pi$
$62$			2.00000i			0.254000i
$63$			12.0000i			1.51186i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	5.19615i		−	0.639602i
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	−0.740613	−	0.671932i	$-0.765465\pi$
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	0.211604	+	0.977356i	$0.432131\pi$
$68$	2.59808	−	1.50000i	0.315063	−	0.181902i
$69$		−	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	$0.384129\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$		−	7.00000i		−	0.819288i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$		−	7.00000i		−	0.819288i	0.912245	−	0.409644i	$-0.134347\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	10.3923	−	6.00000i	1.18431	−	0.683763i
$78$	3.46410	−	6.00000i	0.392232	−	0.679366i
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		−	3.00000i		−	0.331295i
$83$	−10.3923	−	6.00000i	−1.14070	−	0.658586i	−0.194099	−	0.980982i	$-0.562178\pi$
$83$	−10.3923	−	6.00000i	−1.14070	−	0.658586i	−0.946605	+	0.322396i	$0.895512\pi$
$84$	−6.00000	−	3.46410i	−0.654654	−	0.377964i
$85$		0			0
$86$	5.50000	+	9.52628i	0.593080	+	1.02725i
$87$	−5.19615	−	9.00000i	−0.557086	−	0.964901i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$	−3.46410			−0.359211
$94$		0			0
$95$		0			0
$96$		−	1.73205i		−	0.176777i
$97$	9.52628	+	5.50000i	0.967247	+	0.558440i	0.898396	−	0.439187i	$-0.144733\pi$
$97$	9.52628	+	5.50000i	0.967247	+	0.558440i	0.0688512	+	0.997627i	$0.478067\pi$
$98$		−	9.00000i		−	0.909137i
$99$	9.00000			0.904534
$100$		0			0
$101$	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	$-0.0369830\pi$
$102$	2.59808	+	4.50000i	0.257248	+	0.445566i
$103$	−3.46410	+	2.00000i	−0.341328	+	0.197066i	−0.660859	−	0.750510i	$-0.729808\pi$
$103$	−3.46410	+	2.00000i	−0.341328	+	0.197066i	0.319531	+	0.947576i	$0.396475\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$			9.00000i			0.870063i	0.900415	+	0.435031i	$0.143263\pi$
$107$			9.00000i			0.870063i	−0.900415	+	0.435031i	$0.856737\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$		0			0
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	3.46410	−	2.00000i	0.327327	−	0.188982i
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.467143	−	0.884182i	$-0.345283\pi$
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.999295	+	0.0375328i	$0.0119499\pi$
$114$	7.50000	−	4.33013i	0.702439	−	0.405554i
$115$		0			0
$116$	6.00000			0.557086
$117$	10.3923	+	6.00000i	0.960769	+	0.554700i
$118$			3.00000i			0.276172i
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−8.66025	+	5.00000i	−0.784063	+	0.452679i
$123$	5.19615			0.468521
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	6.00000	−	10.3923i	0.534522	−	0.925820i
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−16.5000	+	9.52628i	−1.45274	+	0.838742i
$130$		0			0
$131$	−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	$-0.342311\pi$
$132$	−2.59808	+	4.50000i	−0.226134	+	0.391675i
$133$	17.3205	+	10.0000i	1.50188	+	0.867110i
$134$	5.00000			0.431934
$135$		0			0
$136$	−3.00000			−0.257248
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$138$	−5.19615	+	9.00000i	−0.442326	+	0.766131i
$139$	−0.500000	−	0.866025i	−0.0424094	−	0.0734553i	0.844042	−	0.536278i	$-0.180170\pi$
$139$	−0.500000	−	0.866025i	−0.0424094	−	0.0734553i	−0.886451	+	0.462822i	$0.846837\pi$
$140$		0			0
$141$		0			0
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$		−	12.0000i		−	1.00349i
$144$	3.00000			0.250000
$145$		0			0
$146$	−3.50000	+	6.06218i	−0.289662	+	0.501709i
$147$	15.5885			1.28571
$148$	−3.46410	+	2.00000i	−0.284747	+	0.164399i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	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	$0.0332784\pi$
$152$			5.00000i			0.405554i
$153$	−7.79423	+	4.50000i	−0.630126	+	0.363803i
$154$	−12.0000			−0.966988
$155$		0			0
$156$	−6.00000	+	3.46410i	−0.480384	+	0.277350i
$157$	−6.92820	+	4.00000i	−0.552931	+	0.319235i	−0.750303	−	0.661094i	$-0.770093\pi$
$157$	−6.92820	+	4.00000i	−0.552931	+	0.319235i	0.197372	+	0.980329i	$0.436759\pi$
$158$	−12.1244	+	7.00000i	−0.964562	+	0.556890i
$159$	9.00000	+	5.19615i	0.713746	+	0.412082i
$160$		0			0
$161$	−24.0000			−1.89146
$162$	7.79423	−	4.50000i	0.612372	−	0.353553i
$163$		−	16.0000i		−	1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$		−	16.0000i		−	1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	15.5885	−	9.00000i	1.20627	−	0.696441i	0.244328	−	0.969693i	$-0.421432\pi$
$167$	15.5885	−	9.00000i	1.20627	−	0.696441i	0.961943	+	0.273252i	$0.0880992\pi$
$168$	3.46410	+	6.00000i	0.267261	+	0.462910i
$169$	1.50000	−	2.59808i	0.115385	−	0.199852i
$170$		0			0
$171$	7.50000	+	12.9904i	0.573539	+	0.993399i
$172$		−	11.0000i		−	0.838742i
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.957205	−	0.289412i	$-0.0934598\pi$
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.227964	+	0.973670i	$0.426793\pi$
$174$			10.3923i			0.787839i
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−5.19615			−0.390567
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$		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	$0.702704\pi$
$182$	−13.8564	−	8.00000i	−1.02711	−	0.592999i
$183$	−8.66025	−	15.0000i	−0.640184	−	1.10883i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	7.79423	+	4.50000i	0.569970	+	0.329073i
$188$		0			0
$189$	18.0000	+	10.3923i	1.30931	+	0.755929i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−0.866025	+	1.50000i	−0.0625000	+	0.108253i
$193$	−11.2583	+	6.50000i	−0.810392	+	0.467880i	−0.847092	−	0.531446i	$-0.821649\pi$
$193$	−11.2583	+	6.50000i	−0.810392	+	0.467880i	0.0366998	+	0.999326i	$0.488315\pi$
$194$	−5.50000	−	9.52628i	−0.394877	−	0.683947i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−7.79423	−	4.50000i	−0.553912	−	0.319801i
$199$	−20.0000			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$		0			0
$201$			8.66025i			0.610847i
$202$	−10.3923	+	6.00000i	−0.731200	+	0.422159i
$203$	−20.7846	+	12.0000i	−1.45879	+	0.842235i
$204$		−	5.19615i		−	0.363803i
$205$		0			0
$206$	4.00000			0.278693
$207$	−15.5885	−	9.00000i	−1.08347	−	0.625543i
$208$		−	4.00000i		−	0.277350i
$209$	7.50000	−	12.9904i	0.518786	−	0.898563i
$210$		0			0
$211$	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	$0.789367\pi$
$212$	−5.19615	+	3.00000i	−0.356873	+	0.206041i
$213$	5.19615	−	9.00000i	0.356034	−	0.616670i
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$		0			0
$216$			5.19615i			0.353553i
$217$			8.00000i			0.543075i
$218$	−3.46410	−	2.00000i	−0.234619	−	0.135457i
$219$	−10.5000	−	6.06218i	−0.709524	−	0.409644i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	−3.46410	−	6.00000i	−0.232495	−	0.402694i
$223$	19.0526	+	11.0000i	1.27585	+	0.736614i	0.976083	−	0.217397i	$-0.0697566\pi$
$223$	19.0526	+	11.0000i	1.27585	+	0.736614i	0.299770	+	0.954011i	$0.403090\pi$
$224$	−4.00000			−0.267261
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−2.59808	−	1.50000i	−0.172440	−	0.0995585i	0.411296	−	0.911502i	$-0.365076\pi$
$227$	−2.59808	−	1.50000i	−0.172440	−	0.0995585i	−0.583736	+	0.811943i	$0.698410\pi$
$228$	−8.66025			−0.573539
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$		0			0
$231$		−	20.7846i		−	1.36753i
$232$	−5.19615	−	3.00000i	−0.341144	−	0.196960i
$233$			21.0000i			1.37576i	0.725826	+	0.687878i	$0.241458\pi$
$233$			21.0000i			1.37576i	−0.725826	+	0.687878i	$0.758542\pi$
$234$	−6.00000	−	10.3923i	−0.392232	−	0.679366i
$235$		0			0
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$	−12.1244	−	21.0000i	−0.787562	−	1.36410i
$238$	10.3923	−	6.00000i	0.673633	−	0.388922i
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	0.946590	−	0.322440i	$-0.104503\pi$
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	−0.752536	+	0.658551i	$0.771170\pi$
$240$		0			0
$241$	−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	$0.982234\pi$
$242$		−	2.00000i		−	0.128565i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$	10.0000			0.640184
$245$		0			0
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	17.3205	−	10.0000i	1.10208	−	0.636285i
$248$	−1.73205	+	1.00000i	−0.109985	+	0.0635001i
$249$	−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	$0.730613\pi$
$252$	−10.3923	+	6.00000i	−0.654654	+	0.377964i
$253$			18.0000i			1.13165i
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.79423	+	4.50000i	−0.486191	+	0.280702i	−0.722993	−	0.690856i	$-0.757234\pi$
$257$	−7.79423	+	4.50000i	−0.486191	+	0.280702i	0.236802	+	0.971558i	$0.423901\pi$
$258$	19.0526			1.18616
$259$	8.00000	−	13.8564i	0.497096	−	0.860995i
$260$		0			0
$261$	−18.0000			−1.11417
$262$			12.0000i			0.741362i
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$	4.50000	−	2.59808i	0.276956	−	0.159901i
$265$		0			0
$266$	−10.0000	−	17.3205i	−0.613139	−	1.06199i
$267$	−5.19615	+	9.00000i	−0.317999	+	0.550791i
$268$	−4.33013	−	2.50000i	−0.264505	−	0.152712i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	2.59808	+	1.50000i	0.157532	+	0.0909509i
$273$	13.8564	−	24.0000i	0.838628	−	1.45255i
$274$	4.50000	+	7.79423i	0.271855	+	0.470867i
$275$		0			0
$276$	9.00000	−	5.19615i	0.541736	−	0.312772i
$277$	−19.0526	−	11.0000i	−1.14476	−	0.660926i	−0.197153	−	0.980373i	$-0.563170\pi$
$277$	−19.0526	−	11.0000i	−1.14476	−	0.660926i	−0.947604	+	0.319447i	$0.896503\pi$
$278$			1.00000i			0.0599760i
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$		0			0
$281$	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
$283$	17.3205	−	10.0000i	1.02960	−	0.594438i	0.112728	−	0.993626i	$-0.464041\pi$
$283$	17.3205	−	10.0000i	1.02960	−	0.594438i	0.916869	+	0.399188i	$0.130708\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		−	12.0000i		−	0.708338i
$288$	−2.59808	−	1.50000i	−0.153093	−	0.0883883i
$289$	8.00000			0.470588
$290$		0			0
$291$	16.5000	−	9.52628i	0.967247	−	0.558440i
$292$	6.06218	−	3.50000i	0.354762	−	0.204822i
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.880652	−	0.473763i	$-0.842895\pi$
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.0300351	+	0.999549i	$0.509562\pi$
$294$	−13.5000	−	7.79423i	−0.787336	−	0.454569i
$295$		0			0
$296$	4.00000			0.232495
$297$	7.79423	−	13.5000i	0.452267	−	0.783349i
$298$		0			0
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$		0			0
$301$	22.0000	+	38.1051i	1.26806	+	2.19634i
$302$	−8.66025	+	5.00000i	−0.498342	+	0.287718i
$303$	−10.3923	−	18.0000i	−0.597022	−	1.03407i
$304$	2.50000	−	4.33013i	0.143385	−	0.248350i
$305$		0			0
$306$	9.00000			0.514496
$307$			7.00000i			0.399511i	0.979846	+	0.199756i	$0.0640148\pi$
$307$			7.00000i			0.399511i	−0.979846	+	0.199756i	$0.935985\pi$
$308$	10.3923	+	6.00000i	0.592157	+	0.341882i
$309$			6.92820i			0.394132i
$310$		0			0
$311$	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	$0.778920\pi$
$312$	6.92820			0.392232
$313$	0.866025	+	0.500000i	0.0489506	+	0.0282617i	0.524276	−	0.851549i	$-0.324336\pi$
$313$	0.866025	+	0.500000i	0.0489506	+	0.0282617i	−0.475325	+	0.879810i	$0.657669\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	14.0000			0.787562
$317$	20.7846	+	12.0000i	1.16738	+	0.673987i	0.953062	−	0.302777i	$-0.0979136\pi$
$317$	20.7846	+	12.0000i	1.16738	+	0.673987i	0.214318	+	0.976764i	$0.431247\pi$
$318$	−5.19615	−	9.00000i	−0.291386	−	0.504695i
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	13.5000	+	7.79423i	0.753497	+	0.435031i
$322$	20.7846	+	12.0000i	1.15828	+	0.668734i
$323$			15.0000i			0.834622i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	3.46410	−	6.00000i	0.191565	−	0.331801i
$328$	2.59808	−	1.50000i	0.143455	−	0.0828236i
$329$		0			0
$330$		0			0
$331$	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	$0.131604\pi$
$332$		−	12.0000i		−	0.658586i
$333$	10.3923	−	6.00000i	0.569495	−	0.328798i
$334$	−18.0000			−0.984916
$335$		0			0
$336$		−	6.92820i		−	0.377964i
$337$	26.8468	−	15.5000i	1.46244	−	0.844339i	0.463314	−	0.886194i	$-0.346660\pi$
$337$	26.8468	−	15.5000i	1.46244	−	0.844339i	0.999124	+	0.0418554i	$0.0133269\pi$
$338$	−2.59808	+	1.50000i	−0.141317	+	0.0815892i
$339$		−	31.1769i		−	1.69330i
$340$		0			0
$341$	6.00000			0.324918
$342$		−	15.0000i		−	0.811107i
$343$		−	8.00000i		−	0.431959i
$344$	−5.50000	+	9.52628i	−0.296540	+	0.513623i
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.901152	−	0.433503i	$-0.857278\pi$
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.0751519	+	0.997172i	$0.523944\pi$
$348$	5.19615	−	9.00000i	0.278543	−	0.482451i
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	−0.996716	−	0.0809766i	$-0.974196\pi$
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	0.568486	+	0.822693i	$0.307529\pi$
$350$		0			0
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$			3.00000i			0.159901i
$353$	−7.79423	−	4.50000i	−0.414845	−	0.239511i	0.278024	−	0.960574i	$-0.410320\pi$
$353$	−7.79423	−	4.50000i	−0.414845	−	0.239511i	−0.692869	+	0.721063i	$0.743654\pi$
$354$	4.50000	+	2.59808i	0.239172	+	0.138086i
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	10.3923	+	18.0000i	0.550019	+	0.952661i
$358$		0			0
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	13.8564	+	8.00000i	0.728277	+	0.420471i
$363$	3.46410			0.181818
$364$	8.00000	+	13.8564i	0.419314	+	0.726273i
$365$		0			0
$366$			17.3205i			0.905357i
$367$	6.92820	+	4.00000i	0.361649	+	0.208798i	0.669804	−	0.742538i	$-0.266378\pi$
$367$	6.92820	+	4.00000i	0.361649	+	0.208798i	−0.308155	+	0.951336i	$0.599711\pi$
$368$			6.00000i			0.312772i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$	12.0000	−	20.7846i	0.623009	−	1.07908i
$372$	−1.73205	−	3.00000i	−0.0898027	−	0.155543i
$373$	−8.66025	+	5.00000i	−0.448411	+	0.258890i	−0.707159	−	0.707055i	$-0.750023\pi$
$373$	−8.66025	+	5.00000i	−0.448411	+	0.258890i	0.258748	+	0.965945i	$0.416690\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$		0			0
$376$		0			0
$377$			24.0000i			1.23606i
$378$	−10.3923	−	18.0000i	−0.534522	−	0.925820i
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$	−3.00000	−	1.73205i	−0.153695	−	0.0887357i
$382$		0			0
$383$	10.3923	−	6.00000i	0.531022	−	0.306586i	−0.210411	−	0.977613i	$-0.567480\pi$
$383$	10.3923	−	6.00000i	0.531022	−	0.306586i	0.741433	+	0.671027i	$0.234147\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$	13.0000			0.661683
$387$			33.0000i			1.67748i
$388$			11.0000i			0.558440i
$389$	18.0000	−	31.1769i	0.912636	−	1.58073i	0.102311	−	0.994753i	$-0.467376\pi$
$389$	18.0000	−	31.1769i	0.912636	−	1.58073i	0.810326	−	0.585980i	$-0.199290\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	7.79423	−	4.50000i	0.393668	−	0.227284i
$393$	−20.7846			−1.04844
$394$		0			0
$395$		0			0
$396$	4.50000	+	7.79423i	0.226134	+	0.391675i
$397$		−	8.00000i		−	0.401508i	−0.979642	−	0.200754i	$-0.935661\pi$
$397$		−	8.00000i		−	0.401508i	0.979642	−	0.200754i	$-0.0643393\pi$
$398$	17.3205	+	10.0000i	0.868199	+	0.501255i
$399$	30.0000	−	17.3205i	1.50188	−	0.867110i
$400$		0			0
$401$	−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	$-0.474913\pi$
$402$	4.33013	−	7.50000i	0.215967	−	0.374066i
$403$	6.92820	+	4.00000i	0.345118	+	0.199254i
$404$	12.0000			0.597022
$405$		0			0
$406$	24.0000			1.19110
$407$	−10.3923	−	6.00000i	−0.515127	−	0.297409i
$408$	−2.59808	+	4.50000i	−0.128624	+	0.222783i
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	0.173064	−	0.984911i	$-0.444633\pi$
$410$		0			0
$411$	−13.5000	+	7.79423i	−0.665906	+	0.384461i
$412$	−3.46410	−	2.00000i	−0.170664	−	0.0985329i
$413$			12.0000i			0.590481i
$414$	9.00000	+	15.5885i	0.442326	+	0.766131i
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	−1.73205			−0.0848189
$418$	−12.9904	+	7.50000i	−0.635380	+	0.366837i
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	−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	$0.182186\pi$
$422$		−	4.00000i		−	0.194717i
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$	−9.00000	+	5.19615i	−0.436051	+	0.251754i
$427$	−34.6410	+	20.0000i	−1.67640	+	0.967868i
$428$	−7.79423	+	4.50000i	−0.376748	+	0.217516i
$429$	−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	$0.303826\pi$
$432$	2.59808	−	4.50000i	0.125000	−	0.216506i
$433$		−	13.0000i		−	0.624740i	−0.949960	−	0.312370i	$-0.898877\pi$
$433$		−	13.0000i		−	0.624740i	0.949960	−	0.312370i	$-0.101123\pi$
$434$	4.00000	−	6.92820i	0.192006	−	0.332564i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−25.9808	+	15.0000i	−1.24283	+	0.717547i
$438$	6.06218	+	10.5000i	0.289662	+	0.501709i
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$		−	12.0000i		−	0.570782i
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	0.437009	−	0.899457i	$-0.356038\pi$
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	−0.560448	+	0.828190i	$0.689371\pi$
$444$			6.92820i			0.328798i
$445$		0			0
$446$	−11.0000	−	19.0526i	−0.520865	−	0.902165i
$447$		0			0
$448$	3.46410	+	2.00000i	0.163663	+	0.0944911i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	−9.00000			−0.423793
$452$	15.5885	+	9.00000i	0.733219	+	0.423324i
$453$	−8.66025	−	15.0000i	−0.406894	−	0.704761i
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$		0			0
$456$	7.50000	+	4.33013i	0.351220	+	0.202777i
$457$	−0.866025	−	0.500000i	−0.0405110	−	0.0233890i	0.479608	−	0.877483i	$-0.340779\pi$
$457$	−0.866025	−	0.500000i	−0.0405110	−	0.0233890i	−0.520119	+	0.854094i	$0.674112\pi$
$458$		−	20.0000i		−	0.934539i
$459$			15.5885i			0.727607i
$460$		0			0
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$	−10.3923	+	18.0000i	−0.483494	+	0.837436i
$463$	17.3205	−	10.0000i	0.804952	−	0.464739i	−0.0402476	−	0.999190i	$-0.512815\pi$
$463$	17.3205	−	10.0000i	0.804952	−	0.464739i	0.845200	+	0.534450i	$0.179481\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$		−	21.0000i		−	0.971764i	−0.874024	−	0.485882i	$-0.838498\pi$
$467$		−	21.0000i		−	0.971764i	0.874024	−	0.485882i	$-0.161502\pi$
$468$			12.0000i			0.554700i
$469$	20.0000			0.923514
$470$		0			0
$471$			13.8564i			0.638470i
$472$	−2.59808	+	1.50000i	−0.119586	+	0.0690431i
$473$	28.5788	−	16.5000i	1.31406	−	0.758671i
$474$			24.2487i			1.11378i
$475$		0			0
$476$	−12.0000			−0.550019
$477$	15.5885	−	9.00000i	0.713746	−	0.412082i
$478$		−	6.00000i		−	0.274434i
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	14.7224	−	8.50000i	0.670588	−	0.387164i
$483$	−20.7846	+	36.0000i	−0.945732	+	1.63806i
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$		−	15.5885i		−	0.707107i
$487$		−	2.00000i		−	0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$		−	2.00000i		−	0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$	−8.66025	−	5.00000i	−0.392031	−	0.226339i
$489$	−24.0000	−	13.8564i	−1.08532	−	0.626608i
$490$		0			0
$491$	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	$0.565957\pi$
$492$	2.59808	+	4.50000i	0.117130	+	0.202876i
$493$	−15.5885	−	9.00000i	−0.702069	−	0.405340i
$494$	−20.0000			−0.899843
$495$		0			0
$496$	2.00000			0.0898027
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$	20.7846			0.931381
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	−0.970558	−	0.240866i	$-0.922569\pi$
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	0.276683	−	0.960961i	$-0.410765\pi$
$500$		0			0
$501$		−	31.1769i		−	1.39288i
$502$	18.1865	+	10.5000i	0.811705	+	0.468638i
$503$			6.00000i			0.267527i	0.991013	+	0.133763i	$0.0427062\pi$
$503$			6.00000i			0.267527i	−0.991013	+	0.133763i	$0.957294\pi$
$504$	12.0000			0.534522
$505$		0			0
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$	−2.59808	−	4.50000i	−0.115385	−	0.199852i
$508$	1.73205	−	1.00000i	0.0768473	−	0.0443678i
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	0.701866	−	0.712309i	$-0.252351\pi$
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	−0.967811	+	0.251679i	$0.919017\pi$
$510$		0			0
$511$	−14.0000	+	24.2487i	−0.619324	+	1.07270i
$512$			1.00000i			0.0441942i
$513$	25.9808			1.14708
$514$	9.00000			0.396973
$515$		0			0
$516$	−16.5000	−	9.52628i	−0.726372	−	0.419371i
$517$		0			0
$518$	−13.8564	+	8.00000i	−0.608816	+	0.351500i
$519$	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	$0.520933\pi$
$522$	15.5885	+	9.00000i	0.682288	+	0.393919i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	−5.19615	+	3.00000i	−0.226348	+	0.130682i
$528$	−5.19615			−0.226134
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$			20.0000i			0.867110i
$533$	−10.3923	−	6.00000i	−0.450141	−	0.259889i
$534$	9.00000	−	5.19615i	0.389468	−	0.224860i
$535$		0			0
$536$	2.50000	+	4.33013i	0.107984	+	0.187033i
$537$		0			0
$538$	5.19615	+	3.00000i	0.224022	+	0.129339i
$539$	−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	$0.444986\pi$
$542$	13.8564	+	8.00000i	0.595184	+	0.343629i
$543$	−13.8564	+	24.0000i	−0.594635	+	1.02994i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	−24.0000	+	13.8564i	−1.02711	+	0.592999i
$547$	−0.866025	−	0.500000i	−0.0370286	−	0.0213785i	0.481371	−	0.876517i	$-0.340139\pi$
$547$	−0.866025	−	0.500000i	−0.0370286	−	0.0213785i	−0.518400	+	0.855138i	$0.673472\pi$
$548$		−	9.00000i		−	0.384461i
$549$	−30.0000			−1.28037
$550$		0			0
$551$	−15.0000	+	25.9808i	−0.639021	+	1.10682i
$552$	−10.3923			−0.442326
$553$	−48.4974	+	28.0000i	−2.06232	+	1.19068i
$554$	11.0000	+	19.0526i	0.467345	+	0.809466i
$555$		0			0
$556$	0.500000	−	0.866025i	0.0212047	−	0.0367277i
$557$			12.0000i			0.508456i	0.967144	+	0.254228i	$0.0818214\pi$
$557$			12.0000i			0.508456i	−0.967144	+	0.254228i	$0.918179\pi$
$558$	5.19615	−	3.00000i	0.219971	−	0.127000i
$559$	44.0000			1.86100
$560$		0			0
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	−5.19615	+	3.00000i	−0.219186	+	0.126547i
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	−0.553748	−	0.832684i	$-0.686803\pi$
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	0.444252	+	0.895902i	$0.353470\pi$
$564$		0			0
$565$		0			0
$566$	−20.0000			−0.840663
$567$	31.1769	−	18.0000i	1.30931	−	0.755929i
$568$		−	6.00000i		−	0.251754i
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	0.0900490	+	0.995937i	$0.471298\pi$
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	−0.907532	+	0.419984i	$0.862036\pi$
$570$		0			0
$571$	−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	$-0.374216\pi$
$572$	10.3923	−	6.00000i	0.434524	−	0.250873i
$573$		0			0
$574$	−6.00000	+	10.3923i	−0.250435	+	0.433766i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$			7.00000i			0.291414i	0.989328	+	0.145707i	$0.0465456\pi$
$577$			7.00000i			0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$			22.5167i			0.935760i
$580$		0			0
$581$	24.0000	+	41.5692i	0.995688	+	1.72458i
$582$	−19.0526			−0.789754
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$	−7.00000			−0.289662
$585$		0			0
$586$	18.0000			0.743573
$587$	33.7750	+	19.5000i	1.39404	+	0.804851i	0.993760	−	0.111540i	$-0.0355784\pi$
$587$	33.7750	+	19.5000i	1.39404	+	0.804851i	0.400283	+	0.916392i	$0.368912\pi$
$588$	7.79423	+	13.5000i	0.321429	+	0.556731i
$589$	5.00000	+	8.66025i	0.206021	+	0.356840i
$590$		0			0
$591$		0			0
$592$	−3.46410	−	2.00000i	−0.142374	−	0.0821995i
$593$		−	18.0000i		−	0.739171i	−0.929197	−	0.369586i	$-0.879500\pi$
$593$		−	18.0000i		−	0.739171i	0.929197	−	0.369586i	$-0.120500\pi$
$594$	−13.5000	+	7.79423i	−0.553912	+	0.319801i
$595$		0			0
$596$		0			0
$597$	−17.3205	+	30.0000i	−0.708881	+	1.22782i
$598$	20.7846	−	12.0000i	0.849946	−	0.490716i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	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	$-0.00364562\pi$
$602$		−	44.0000i		−	1.79331i
$603$	12.9904	+	7.50000i	0.529009	+	0.305424i
$604$	10.0000			0.406894
$605$		0			0
$606$			20.7846i			0.844317i
$607$	−6.92820	+	4.00000i	−0.281207	+	0.162355i	−0.633970	−	0.773358i	$-0.718576\pi$
$607$	−6.92820	+	4.00000i	−0.281207	+	0.162355i	0.352763	+	0.935713i	$0.385242\pi$
$608$	−4.33013	+	2.50000i	−0.175610	+	0.101388i
$609$			41.5692i			1.68447i
$610$		0			0
$611$		0			0
$612$	−7.79423	−	4.50000i	−0.315063	−	0.181902i
$613$			2.00000i			0.0807792i	0.999184	+	0.0403896i	$0.0128599\pi$
$613$			2.00000i			0.0807792i	−0.999184	+	0.0403896i	$0.987140\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$		0			0
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	33.7750	−	19.5000i	1.35973	−	0.785040i	0.370143	−	0.928975i	$-0.379309\pi$
$617$	33.7750	−	19.5000i	1.35973	−	0.785040i	0.989587	+	0.143934i	$0.0459755\pi$
$618$	3.46410	−	6.00000i	0.139347	−	0.241355i
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$		0			0
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$		−	6.00000i		−	0.240578i
$623$	20.7846	+	12.0000i	0.832718	+	0.480770i
$624$	−6.00000	−	3.46410i	−0.240192	−	0.138675i
$625$		0			0
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$	−12.9904	−	22.5000i	−0.518786	−	0.898563i
$628$	−6.92820	−	4.00000i	−0.276465	−	0.159617i
$629$	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	$0.736616\pi$
$632$	−12.1244	−	7.00000i	−0.482281	−	0.278445i
$633$	6.92820			0.275371
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$		0			0
$636$			10.3923i			0.412082i
$637$	−31.1769	−	18.0000i	−1.23527	−	0.713186i
$638$		−	18.0000i		−	0.712627i
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$		0			0
$641$	−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	$0.223545\pi$
$642$	−7.79423	−	13.5000i	−0.307614	−	0.532803i
$643$	19.9186	−	11.5000i	0.785512	−	0.453516i	−0.0528680	−	0.998602i	$-0.516836\pi$
$643$	19.9186	−	11.5000i	0.785512	−	0.453516i	0.838380	+	0.545086i	$0.183503\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$		0			0
$646$	7.50000	−	12.9904i	0.295084	−	0.511100i
$647$		−	6.00000i		−	0.235884i	−0.993020	−	0.117942i	$-0.962370\pi$
$647$		−	6.00000i		−	0.235884i	0.993020	−	0.117942i	$-0.0376297\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	9.00000			0.353281
$650$		0			0
$651$	12.0000	+	6.92820i	0.470317	+	0.271538i
$652$	13.8564	−	8.00000i	0.542659	−	0.313304i
$653$	36.3731	−	21.0000i	1.42339	−	0.821794i	0.426801	−	0.904345i	$-0.359640\pi$
$653$	36.3731	−	21.0000i	1.42339	−	0.821794i	0.996587	+	0.0825519i	$0.0263070\pi$
$654$	−6.00000	+	3.46410i	−0.234619	+	0.135457i
$655$		0			0
$656$	−3.00000			−0.117130
$657$	−18.1865	+	10.5000i	−0.709524	+	0.409644i
$658$		0			0
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	−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	$-0.380480\pi$
$662$	−3.46410	+	2.00000i	−0.134636	+	0.0777322i
$663$	20.7846			0.807207
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$	−12.0000			−0.464991
$667$		−	36.0000i		−	1.39393i
$668$	15.5885	+	9.00000i	0.603136	+	0.348220i
$669$	33.0000	−	19.0526i	1.27585	−	0.736614i
$670$		0			0
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$	−3.46410	+	6.00000i	−0.133631	+	0.231455i
$673$	−12.1244	−	7.00000i	−0.467360	−	0.269830i	0.247774	−	0.968818i	$-0.420301\pi$
$673$	−12.1244	−	7.00000i	−0.467360	−	0.269830i	−0.715134	+	0.698988i	$0.753634\pi$
$674$	−31.0000			−1.19408
$675$		0			0
$676$	3.00000			0.115385
$677$	−31.1769	−	18.0000i	−1.19823	−	0.691796i	−0.238067	−	0.971249i	$-0.576514\pi$
$677$	−31.1769	−	18.0000i	−1.19823	−	0.691796i	−0.960159	+	0.279453i	$0.909847\pi$
$678$	−15.5885	+	27.0000i	−0.598671	+	1.03693i
$679$	−22.0000	−	38.1051i	−0.844283	−	1.46234i
$680$		0			0
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	−5.19615	−	3.00000i	−0.198971	−	0.114876i
$683$		−	21.0000i		−	0.803543i	−0.915740	−	0.401771i	$-0.868395\pi$
$683$		−	21.0000i		−	0.803543i	0.915740	−	0.401771i	$-0.131605\pi$
$684$	−7.50000	+	12.9904i	−0.286770	+	0.496700i
$685$		0			0
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$	34.6410			1.32164
$688$	9.52628	−	5.50000i	0.363186	−	0.209686i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$		0			0
$691$	−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	$0.215292\pi$
$692$			18.0000i			0.684257i
$693$	−31.1769	−	18.0000i	−1.18431	−	0.683763i
$694$	21.0000			0.797149
$695$		0			0
$696$	−9.00000	+	5.19615i	−0.341144	+	0.196960i
$697$	7.79423	−	4.50000i	0.295227	−	0.170450i
$698$	13.8564	−	8.00000i	0.524473	−	0.302804i
$699$	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	$0.208435\pi$
$702$	−20.7846			−0.784465
$703$		−	20.0000i		−	0.754314i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	−41.5692	+	24.0000i	−1.56337	+	0.902613i
$708$	−2.59808	−	4.50000i	−0.0976417	−	0.169120i
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	0.347325	+	0.937745i	$0.387090\pi$
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	−0.985773	+	0.168080i	$0.946243\pi$
$710$		0			0
$711$	−42.0000			−1.57512
$712$			6.00000i			0.224860i
$713$	−10.3923	−	6.00000i	−0.389195	−	0.224702i
$714$		−	20.7846i		−	0.777844i
$715$		0			0
$716$		0			0
$717$	10.3923			0.388108
$718$	−20.7846	−	12.0000i	−0.775675	−	0.447836i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	−5.19615	−	3.00000i	−0.193381	−	0.111648i
$723$	14.7224	+	25.5000i	0.547533	+	0.948355i
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$		0			0
$726$	−3.00000	−	1.73205i	−0.111340	−	0.0642824i
$727$	−24.2487	−	14.0000i	−0.899335	−	0.519231i	−0.0223506	−	0.999750i	$-0.507115\pi$
$727$	−24.2487	−	14.0000i	−0.899335	−	0.519231i	−0.876984	+	0.480519i	$0.840448\pi$
$728$		−	16.0000i		−	0.592999i
$729$	27.0000			1.00000
$730$		0			0
$731$	−16.5000	+	28.5788i	−0.610275	+	1.05703i
$732$	8.66025	−	15.0000i	0.320092	−	0.554416i
$733$	27.7128	−	16.0000i	1.02360	−	0.590973i	0.108453	−	0.994102i	$-0.465410\pi$
$733$	27.7128	−	16.0000i	1.02360	−	0.590973i	0.915144	+	0.403128i	$0.132077\pi$
$734$	−4.00000	−	6.92820i	−0.147643	−	0.255725i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$		−	15.0000i		−	0.552532i
$738$	−7.79423	+	4.50000i	−0.286910	+	0.165647i
$739$	−29.0000			−1.06678			−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000			−1.06678			−0.533391	+	0.845869i	$0.679083\pi$
$740$		0			0
$741$		−	34.6410i		−	1.27257i
$742$	−20.7846	+	12.0000i	−0.763027	+	0.440534i
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	−0.592277	−	0.805735i	$-0.701771\pi$
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	0.401648	+	0.915794i	$0.368437\pi$
$744$			3.46410i			0.127000i
$745$		0			0
$746$	10.0000			0.366126
$747$			36.0000i			1.31717i
$748$			9.00000i			0.329073i
$749$	18.0000	−	31.1769i	0.657706	−	1.13918i
$750$		0			0
$751$	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
$753$	−18.1865	+	31.5000i	−0.662754	+	1.14792i
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$		0			0
$756$			20.7846i			0.755929i
$757$		−	38.0000i		−	1.38113i	−0.723269	−	0.690567i	$-0.757361\pi$
$757$		−	38.0000i		−	1.38113i	0.723269	−	0.690567i	$-0.242639\pi$
$758$	25.1147	+	14.5000i	0.912208	+	0.526664i
$759$	27.0000	+	15.5885i	0.980038	+	0.565825i
$760$		0			0
$761$	−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	$0.939118\pi$
$762$	1.73205	+	3.00000i	0.0627456	+	0.108679i
$763$	−13.8564	−	8.00000i	−0.501636	−	0.289619i
$764$		0			0
$765$		0			0
$766$	−12.0000			−0.433578
$767$	10.3923	+	6.00000i	0.375244	+	0.216647i
$768$	−1.73205			−0.0625000
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$			15.5885i			0.561405i
$772$	−11.2583	−	6.50000i	−0.405196	−	0.233940i
$773$		−	30.0000i		−	1.07903i	−0.841978	−	0.539513i	$-0.818609\pi$
$773$		−	30.0000i		−	1.07903i	0.841978	−	0.539513i	$-0.181391\pi$
$774$	16.5000	−	28.5788i	0.593080	−	1.02725i
$775$		0			0
$776$	5.50000	−	9.52628i	0.197438	−	0.341974i
$777$	−13.8564	−	24.0000i	−0.497096	−	0.860995i
$778$	−31.1769	+	18.0000i	−1.11775	+	0.645331i
$779$	−7.50000	−	12.9904i	−0.268715	−	0.465429i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$			18.0000i			0.643679i
$783$	−15.5885	+	27.0000i	−0.557086	+	0.964901i
$784$	−9.00000			−0.321429
$785$		0			0
$786$	18.0000	+	10.3923i	0.642039	+	0.370681i
$787$	3.46410	−	2.00000i	0.123482	−	0.0712923i	−0.436987	−	0.899468i	$-0.643954\pi$
$787$	3.46410	−	2.00000i	0.123482	−	0.0712923i	0.560469	+	0.828176i	$0.310621\pi$
$788$		0			0
$789$	−36.0000	+	20.7846i	−1.28163	+	0.739952i
$790$		0			0
$791$	−72.0000			−2.56003
$792$		−	9.00000i		−	0.319801i
$793$			40.0000i			1.42044i
$794$	−4.00000	+	6.92820i	−0.141955	+	0.245873i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	41.5692	−	24.0000i	1.47246	−	0.850124i	0.472937	−	0.881096i	$-0.343194\pi$
$797$	41.5692	−	24.0000i	1.47246	−	0.850124i	0.999520	+	0.0309726i	$0.00986046\pi$
$798$	−34.6410			−1.22628
$799$		0			0
$800$		0			0
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$			33.0000i			1.16527i
$803$	18.1865	+	10.5000i	0.641789	+	0.370537i
$804$	−7.50000	+	4.33013i	−0.264505	+	0.152712i
$805$		0			0
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	−5.19615	+	9.00000i	−0.182913	+	0.316815i
$808$	−10.3923	−	6.00000i	−0.365600	−	0.211079i
$809$	39.0000			1.37117			0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000			1.37117			0.685583	+	0.727994i	$0.259547\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	−20.7846	−	12.0000i	−0.729397	−	0.421117i
$813$	−13.8564	+	24.0000i	−0.485965	+	0.841717i
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$		0			0
$816$	4.50000	−	2.59808i	0.157532	−	0.0909509i
$817$	47.6314	+	27.5000i	1.66641	+	0.962103i
$818$			31.0000i			1.08389i
$819$	−24.0000	−	41.5692i	−0.838628	−	1.45255i
$820$		0			0
$821$	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	$-0.149379\pi$
$822$	15.5885			0.543710
$823$	−3.46410	+	2.00000i	−0.120751	+	0.0697156i	−0.559159	−	0.829060i	$-0.688876\pi$
$823$	−3.46410	+	2.00000i	−0.120751	+	0.0697156i	0.438408	+	0.898776i	$0.355543\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		−	18.0000i		−	0.625543i
$829$	−44.0000			−1.52818			−0.764092	−	0.645108i	$-0.776812\pi$
$829$	−44.0000			−1.52818			−0.764092	+	0.645108i	$0.776812\pi$
$830$		0			0
$831$	−33.0000	+	19.0526i	−1.14476	+	0.660926i
$832$	3.46410	−	2.00000i	0.120096	−	0.0693375i
$833$	23.3827	−	13.5000i	0.810162	−	0.467747i
$834$	1.50000	+	0.866025i	0.0519408	+	0.0299880i
$835$		0			0
$836$	15.0000			0.518786
$837$	5.19615	+	9.00000i	0.179605	+	0.311086i
$838$		0			0
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	0.481927	+	0.876211i	$0.339937\pi$
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	−0.999785	+	0.0207443i	$0.993396\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	1.73205	−	1.00000i	0.0596904	−	0.0344623i
$843$	−5.19615	−	9.00000i	−0.178965	−	0.309976i
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$		0			0
$846$		0			0
$847$		−	8.00000i		−	0.274883i
$848$	−5.19615	−	3.00000i	−0.178437	−	0.103020i
$849$		−	34.6410i		−	1.18888i
$850$		0			0
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$	10.3923			0.356034
$853$	−38.1051	−	22.0000i	−1.30469	−	0.753266i	−0.323489	−	0.946232i	$-0.604856\pi$
$853$	−38.1051	−	22.0000i	−1.30469	−	0.753266i	−0.981205	+	0.192966i	$0.938189\pi$
$854$	40.0000			1.36877
$855$		0			0
$856$	9.00000			0.307614
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	0.209539	−	0.977800i	$-0.432804\pi$
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	−0.742030	+	0.670366i	$0.766137\pi$
$858$	10.3923	+	18.0000i	0.354787	+	0.614510i
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	0.657201	−	0.753715i	$-0.271740\pi$
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	−0.981337	+	0.192295i	$0.938407\pi$
$860$		0			0
$861$	−18.0000	−	10.3923i	−0.613438	−	0.354169i
$862$	−20.7846	−	12.0000i	−0.707927	−	0.408722i
$863$		−	6.00000i		−	0.204242i	−0.994772	−	0.102121i	$-0.967437\pi$
$863$		−	6.00000i		−	0.204242i	0.994772	−	0.102121i	$-0.0325630\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		0			0
$866$	−6.50000	+	11.2583i	−0.220879	+	0.382574i
$867$	6.92820	−	12.0000i	0.235294	−	0.407541i
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$	21.0000	+	36.3731i	0.712376	+	1.23387i
$870$		0			0
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$		−	4.00000i		−	0.135457i
$873$		−	33.0000i		−	1.11688i
$874$	30.0000			1.01477
$875$		0			0
$876$		−	12.1244i		−	0.409644i
$877$	−1.73205	+	1.00000i	−0.0584872	+	0.0337676i	−0.528958	−	0.848648i	$-0.677417\pi$
$877$	−1.73205	+	1.00000i	−0.0584872	+	0.0337676i	0.470471	+	0.882415i	$0.344084\pi$
$878$	8.66025	−	5.00000i	0.292269	−	0.168742i
$879$			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	$0.331359\pi$
$882$	−23.3827	+	13.5000i	−0.787336	+	0.454569i
$883$			41.0000i			1.37976i	0.723924	+	0.689880i	$0.242337\pi$
$883$			41.0000i			1.37976i	−0.723924	+	0.689880i	$0.757663\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	36.3731	−	21.0000i	1.22129	−	0.705111i	0.256096	−	0.966651i	$-0.417564\pi$
$887$	36.3731	−	21.0000i	1.22129	−	0.705111i	0.965193	+	0.261540i	$0.0842305\pi$
$888$	3.46410	−	6.00000i	0.116248	−	0.201347i
$889$	−4.00000	+	6.92820i	−0.134156	+	0.232364i
$890$		0			0
$891$	−13.5000	−	23.3827i	−0.452267	−	0.783349i
$892$			22.0000i			0.736614i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$	20.7846	+	36.0000i	0.693978	+	1.20201i
$898$	−12.9904	−	7.50000i	−0.433495	−	0.250278i
$899$	−12.0000			−0.400222
$900$		0			0
$901$	18.0000			0.599667
$902$	7.79423	+	4.50000i	0.259519	+	0.149834i
$903$	76.2102			2.53612
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$		0			0
$906$			17.3205i			0.575435i
$907$	4.33013	+	2.50000i	0.143780	+	0.0830111i	0.570164	−	0.821531i	$-0.306880\pi$
$907$	4.33013	+	2.50000i	0.143780	+	0.0830111i	−0.426385	+	0.904542i	$0.640213\pi$
$908$		−	3.00000i		−	0.0995585i
$909$	−36.0000			−1.19404
$910$		0			0
$911$	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	$0.00111177\pi$
$912$	−4.33013	−	7.50000i	−0.143385	−	0.248350i
$913$	31.1769	−	18.0000i	1.03181	−	0.595713i
$914$	0.500000	+	0.866025i	0.0165385	+	0.0286456i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$			48.0000i			1.58510i
$918$	7.79423	−	13.5000i	0.257248	−	0.445566i
$919$	34.0000			1.12156			0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000			1.12156			0.560778	+	0.827966i	$0.310502\pi$
$920$		0			0
$921$	10.5000	+	6.06218i	0.345987	+	0.199756i
$922$		0			0
$923$	−20.7846	+	12.0000i	−0.684134	+	0.394985i
$924$	18.0000	−	10.3923i	0.592157	−	0.341882i
$925$		0			0
$926$	−20.0000			−0.657241
$927$	10.3923	+	6.00000i	0.341328	+	0.197066i
$928$		−	6.00000i		−	0.196960i
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$		0			0
$931$	−22.5000	−	38.9711i	−0.737408	−	1.27723i
$932$	−18.1865	+	10.5000i	−0.595720	+	0.343939i
$933$	10.3923			0.340229
$934$	−10.5000	+	18.1865i	−0.343570	+	0.595082i
$935$		0			0
$936$	6.00000	−	10.3923i	0.196116	−	0.339683i
$937$			10.0000i			0.326686i	0.986569	+	0.163343i	$0.0522277\pi$
$937$			10.0000i			0.326686i	−0.986569	+	0.163343i	$0.947772\pi$
$938$	−17.3205	−	10.0000i	−0.565535	−	0.326512i
$939$	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	$0.961269\pi$
$942$	6.92820	−	12.0000i	0.225733	−	0.390981i
$943$	15.5885	+	9.00000i	0.507630	+	0.293080i
$944$	3.00000			0.0976417
$945$		0			0
$946$	−33.0000			−1.07292
$947$	23.3827	+	13.5000i	0.759835	+	0.438691i	0.829237	−	0.558898i	$-0.188776\pi$
$947$	23.3827	+	13.5000i	0.759835	+	0.438691i	−0.0694014	+	0.997589i	$0.522109\pi$
$948$	12.1244	−	21.0000i	0.393781	−	0.682048i
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$	36.0000	−	20.7846i	1.16738	−	0.673987i
$952$	10.3923	+	6.00000i	0.336817	+	0.194461i
$953$			51.0000i			1.65205i	0.563632	+	0.826026i	$0.309404\pi$
$953$			51.0000i			1.65205i	−0.563632	+	0.826026i	$0.690596\pi$
$954$	−18.0000			−0.582772
$955$		0			0
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	31.1769			1.00781
$958$	5.19615	−	3.00000i	0.167880	−	0.0969256i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$			16.0000i			0.515861i
$963$	23.3827	−	13.5000i	0.753497	−	0.435031i
$964$	−17.0000			−0.547533
$965$		0			0
$966$	36.0000	−	20.7846i	1.15828	−	0.668734i
$967$	19.0526	−	11.0000i	0.612689	−	0.353736i	−0.161328	−	0.986901i	$-0.551578\pi$
$967$	19.0526	−	11.0000i	0.612689	−	0.353736i	0.774017	+	0.633165i	$0.218244\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	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	$0.0871586\pi$
$972$	−7.79423	+	13.5000i	−0.250000	+	0.433013i
$973$			4.00000i			0.128234i
$974$	−1.00000	+	1.73205i	−0.0320421	+	0.0554985i
$975$		0			0
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	7.79423	−	4.50000i	0.249359	−	0.143968i	−0.370111	−	0.928987i	$-0.620681\pi$
$977$	7.79423	−	4.50000i	0.249359	−	0.143968i	0.619471	+	0.785020i	$0.287347\pi$
$978$	13.8564	+	24.0000i	0.443079	+	0.767435i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	−6.00000	−	10.3923i	−0.191565	−	0.331801i
$982$		−	33.0000i		−	1.05307i
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.0878058	−	0.996138i	$-0.527985\pi$
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.906583	+	0.422027i	$0.861319\pi$
$984$		−	5.19615i		−	0.165647i
$985$		0			0
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$		0			0
$988$	17.3205	+	10.0000i	0.551039	+	0.318142i
$989$	−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	$0.397103\pi$
$992$	−1.73205	−	1.00000i	−0.0549927	−	0.0317500i
$993$	−3.46410	−	6.00000i	−0.109930	−	0.190404i
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$		0			0
$996$	−18.0000	−	10.3923i	−0.570352	−	0.329293i
$997$	22.5167	+	13.0000i	0.713110	+	0.411714i	0.812211	−	0.583363i	$-0.198264\pi$
$997$	22.5167	+	13.0000i	0.713110	+	0.411714i	−0.0991016	+	0.995077i	$0.531597\pi$
$998$			31.0000i			0.981288i
$999$		−	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.j.a.349.1		4
3.2	odd	2		1350.2.j.c.1099.2		4
5.2	odd	4		90.2.e.b.61.1	yes	2
5.3	odd	4		450.2.e.d.151.1		2
5.4	even	2	inner	450.2.j.a.349.2		4
9.2	odd	6		4050.2.c.d.649.1		2
9.4	even	3	inner	450.2.j.a.49.2		4
9.5	odd	6		1350.2.j.c.199.1		4
9.7	even	3		4050.2.c.p.649.2		2
15.2	even	4		270.2.e.a.181.1		2
15.8	even	4		1350.2.e.g.451.1		2
15.14	odd	2		1350.2.j.c.1099.1		4
20.7	even	4		720.2.q.c.241.1		2
45.2	even	12		810.2.a.e.1.1		1
45.4	even	6	inner	450.2.j.a.49.1		4
45.7	odd	12		810.2.a.a.1.1		1
45.13	odd	12		450.2.e.d.301.1		2
45.14	odd	6		1350.2.j.c.199.2		4
45.22	odd	12		90.2.e.b.31.1	✓	2
45.23	even	12		1350.2.e.g.901.1		2
45.29	odd	6		4050.2.c.d.649.2		2
45.32	even	12		270.2.e.a.91.1		2
45.34	even	6		4050.2.c.p.649.1		2
45.38	even	12		4050.2.a.q.1.1		1
45.43	odd	12		4050.2.a.bi.1.1		1
60.47	odd	4		2160.2.q.d.721.1		2
180.7	even	12		6480.2.a.z.1.1		1
180.47	odd	12		6480.2.a.l.1.1		1
180.67	even	12		720.2.q.c.481.1		2
180.167	odd	12		2160.2.q.d.1441.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.b.31.1	✓	2	45.22	odd	12
90.2.e.b.61.1	yes	2	5.2	odd	4
270.2.e.a.91.1		2	45.32	even	12
270.2.e.a.181.1		2	15.2	even	4
450.2.e.d.151.1		2	5.3	odd	4
450.2.e.d.301.1		2	45.13	odd	12
450.2.j.a.49.1		4	45.4	even	6	inner
450.2.j.a.49.2		4	9.4	even	3	inner
450.2.j.a.349.1		4	1.1	even	1	trivial
450.2.j.a.349.2		4	5.4	even	2	inner
720.2.q.c.241.1		2	20.7	even	4
720.2.q.c.481.1		2	180.67	even	12
810.2.a.a.1.1		1	45.7	odd	12
810.2.a.e.1.1		1	45.2	even	12
1350.2.e.g.451.1		2	15.8	even	4
1350.2.e.g.901.1		2	45.23	even	12
1350.2.j.c.199.1		4	9.5	odd	6
1350.2.j.c.199.2		4	45.14	odd	6
1350.2.j.c.1099.1		4	15.14	odd	2
1350.2.j.c.1099.2		4	3.2	odd	2
2160.2.q.d.721.1		2	60.47	odd	4
2160.2.q.d.1441.1		2	180.167	odd	12
4050.2.a.q.1.1		1	45.38	even	12
4050.2.a.bi.1.1		1	45.43	odd	12
4050.2.c.d.649.1		2	9.2	odd	6
4050.2.c.d.649.2		2	45.29	odd	6
4050.2.c.p.649.1		2	45.34	even	6
4050.2.c.p.649.2		2	9.7	even	3
6480.2.a.l.1.1		1	180.47	odd	12
6480.2.a.z.1.1		1	180.7	even	12

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

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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.j.a.349.1

Level	$450$
Weight	$2$
Character	450.349
Analytic conductor	$3.593$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$