LMFDB - Embedded newform 1050.2.o.i.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.38429221223$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.499
Dual form			1050.2.o.i.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.866025 + 0.500000i) q^{12} -1.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.866025 - 0.500000i) q^{18} +(-1.50000 + 2.59808i) q^{19} +(2.50000 + 0.866025i) q^{21} +1.00000i q^{22} +(6.06218 + 3.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{26} -1.00000i q^{27} +(-0.866025 + 2.50000i) q^{28} +8.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.866025 + 0.500000i) q^{33} +1.00000 q^{36} +(-9.52628 - 5.50000i) q^{37} +(-2.59808 + 1.50000i) q^{38} +(-0.500000 - 0.866025i) q^{39} -11.0000 q^{41} +(1.73205 + 2.00000i) q^{42} -8.00000i q^{43} +(-0.500000 + 0.866025i) q^{44} +(3.50000 + 6.06218i) q^{46} +(4.33013 + 2.50000i) q^{47} +1.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(0.866025 - 0.500000i) q^{52} +(9.52628 - 5.50000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} +3.00000i q^{57} +(6.92820 + 4.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +2.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +7.00000 q^{69} -6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(-5.50000 - 9.52628i) q^{74} -3.00000 q^{76} +(-0.866025 + 2.50000i) q^{77} -1.00000i q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-9.52628 - 5.50000i) q^{82} -8.00000i q^{83} +(0.500000 + 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +(6.92820 - 4.00000i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} +7.00000i q^{92} +(1.73205 + 1.00000i) q^{93} +(2.50000 + 4.33013i) q^{94} +(-0.500000 + 0.866025i) q^{96} -16.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 2 q^{16} - 6 q^{19} + 10 q^{21} + 2 q^{24} + 2 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{36} - 2 q^{39} - 44 q^{41} - 2 q^{44} + 14 q^{46} - 4 q^{49} + 2 q^{54} - 8 q^{56} + 8 q^{59} - 4 q^{64} + 2 q^{66} + 28 q^{69} - 24 q^{71} - 22 q^{74} - 12 q^{76} - 16 q^{79} - 2 q^{81} + 2 q^{84} + 16 q^{86} - 20 q^{89} + 8 q^{91} + 10 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 2 * q^16 - 6 * q^19 + 10 * q^21 + 2 * q^24 + 2 * q^26 + 32 * q^29 + 4 * q^31 + 4 * q^36 - 2 * q^39 - 44 * q^41 - 2 * q^44 + 14 * q^46 - 4 * q^49 + 2 * q^54 - 8 * q^56 + 8 * q^59 - 4 * q^64 + 2 * q^66 + 28 * q^69 - 24 * q^71 - 22 * q^74 - 12 * q^76 - 16 * q^79 - 2 * q^81 + 2 * q^84 + 16 * q^86 - 20 * q^89 + 8 * q^91 + 10 * q^94 - 2 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$			1.00000i			0.213201i
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.973856	−	0.227167i	$-0.0729463\pi$
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.290196	+	0.956967i	$0.406280\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$		−	1.00000i		−	0.192450i
$28$	−0.866025	+	2.50000i	−0.163663	+	0.472456i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.866025	+	0.500000i	0.150756	+	0.0870388i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	−9.52628	−	5.50000i	−1.56611	−	0.904194i	−0.996616	−	0.0821995i	$-0.973806\pi$
$37$	−9.52628	−	5.50000i	−1.56611	−	0.904194i	−0.569495	−	0.821995i	$-0.692861\pi$
$38$	−2.59808	+	1.50000i	−0.421464	+	0.243332i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−11.0000			−1.71791			−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000			−1.71791			−0.858956	+	0.512050i	$0.828886\pi$
$42$	1.73205	+	2.00000i	0.267261	+	0.308607i
$43$		−	8.00000i		−	1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$		−	8.00000i		−	1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	4.33013	+	2.50000i	0.631614	+	0.364662i	0.781377	−	0.624059i	$-0.214518\pi$
$47$	4.33013	+	2.50000i	0.631614	+	0.364662i	−0.149763	+	0.988722i	$0.547851\pi$
$48$			1.00000i			0.144338i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	9.52628	−	5.50000i	1.30854	−	0.755483i	0.326683	−	0.945134i	$-0.394069\pi$
$53$	9.52628	−	5.50000i	1.30854	−	0.755483i	0.981852	+	0.189651i	$0.0607356\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$			3.00000i			0.397360i
$58$	6.92820	+	4.00000i	0.909718	+	0.525226i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$			2.00000i			0.254000i
$63$	2.59808	−	0.500000i	0.327327	−	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.500000	+	0.866025i	0.0615457	+	0.106600i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	7.00000			0.842701
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	−0.164083	−	0.986447i	$-0.552466\pi$
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	0.772246	+	0.635323i	$0.219133\pi$
$74$	−5.50000	−	9.52628i	−0.639362	−	1.10741i
$75$		0			0
$76$	−3.00000			−0.344124
$77$	−0.866025	+	2.50000i	−0.0986928	+	0.284901i
$78$		−	1.00000i		−	0.113228i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−9.52628	−	5.50000i	−1.05200	−	0.607373i
$83$		−	8.00000i		−	0.878114i	−0.898459	−	0.439057i	$-0.855313\pi$
$83$		−	8.00000i		−	0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$	0.500000	+	2.59808i	0.0545545	+	0.283473i
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	6.92820	−	4.00000i	0.742781	−	0.428845i
$88$	−0.866025	+	0.500000i	−0.0923186	+	0.0533002i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$			7.00000i			0.729800i
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$	2.50000	+	4.33013i	0.257855	+	0.446619i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	16.0000i		−	1.62455i	−0.583272	−	0.812277i	$-0.698228\pi$
$97$		−	16.0000i		−	1.62455i	0.583272	−	0.812277i	$-0.301772\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$	1.00000			0.100504
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−13.8564	−	8.00000i	−1.36531	−	0.788263i	−0.374987	−	0.927030i	$-0.622353\pi$
$103$	−13.8564	−	8.00000i	−1.36531	−	0.788263i	−0.990325	+	0.138767i	$0.955686\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	11.0000			1.06841
$107$	8.66025	+	5.00000i	0.837218	+	0.483368i	0.856318	−	0.516449i	$-0.172747\pi$
$107$	8.66025	+	5.00000i	0.837218	+	0.483368i	−0.0190994	+	0.999818i	$0.506080\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	0.973176	−	0.230063i	$-0.0738931\pi$
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	−0.685828	+	0.727764i	$0.740560\pi$
$110$		0			0
$111$	−11.0000			−1.04407
$112$	−2.59808	+	0.500000i	−0.245495	+	0.0472456i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$		0			0
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	−0.866025	−	0.500000i	−0.0800641	−	0.0462250i
$118$			4.00000i			0.368230i
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	−9.52628	+	5.50000i	−0.858956	+	0.495918i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$		−	17.0000i		−	1.50851i	−0.656584	−	0.754253i	$-0.727999\pi$
$127$		−	17.0000i		−	1.50851i	0.656584	−	0.754253i	$-0.272001\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	−0.735901	−	0.677089i	$-0.763241\pi$
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	0.954327	+	0.298764i	$0.0965744\pi$
$132$			1.00000i			0.0870388i
$133$	−7.79423	+	1.50000i	−0.675845	+	0.130066i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$	6.06218	+	3.50000i	0.516047	+	0.297940i
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$		0			0
$141$	5.00000			0.421076
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$	0.866025	−	0.500000i	0.0724207	−	0.0418121i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	6.00000			0.496564
$147$	2.59808	+	6.50000i	0.214286	+	0.536111i
$148$		−	11.0000i		−	0.904194i
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	0.717752	−	0.696299i	$-0.245171\pi$
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	−0.961888	+	0.273442i	$0.911838\pi$
$152$	−2.59808	−	1.50000i	−0.210732	−	0.121666i
$153$		0			0
$154$	−2.00000	+	1.73205i	−0.161165	+	0.139573i
$155$		0			0
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	−6.06218	+	3.50000i	−0.483814	+	0.279330i	−0.722005	−	0.691888i	$-0.756779\pi$
$157$	−6.06218	+	3.50000i	−0.483814	+	0.279330i	0.238190	+	0.971219i	$0.423446\pi$
$158$	−6.92820	+	4.00000i	−0.551178	+	0.318223i
$159$	5.50000	−	9.52628i	0.436178	−	0.755483i
$160$		0			0
$161$	3.50000	+	18.1865i	0.275839	+	1.43330i
$162$		−	1.00000i		−	0.0785674i
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.932326	−	0.361619i	$-0.117776\pi$
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.152992	+	0.988227i	$0.451109\pi$
$164$	−5.50000	−	9.52628i	−0.429478	−	0.743877i
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$		−	3.00000i		−	0.232147i	−0.993241	−	0.116073i	$-0.962969\pi$
$167$		−	3.00000i		−	0.232147i	0.993241	−	0.116073i	$-0.0370308\pi$
$168$	−0.866025	+	2.50000i	−0.0668153	+	0.192879i
$169$	12.0000			0.923077
$170$		0			0
$171$	1.50000	+	2.59808i	0.114708	+	0.198680i
$172$	6.92820	−	4.00000i	0.528271	−	0.304997i
$173$	−12.9904	−	7.50000i	−0.987640	−	0.570214i	−0.0830722	−	0.996544i	$-0.526473\pi$
$173$	−12.9904	−	7.50000i	−0.987640	−	0.570214i	−0.904568	+	0.426329i	$0.859807\pi$
$174$	8.00000			0.606478
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	3.46410	+	2.00000i	0.260378	+	0.150329i
$178$	−8.66025	+	5.00000i	−0.649113	+	0.374766i
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	−0.964833	−	0.262864i	$-0.915333\pi$
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	0.254770	−	0.967002i	$-0.418000\pi$
$180$		0			0
$181$	−24.0000			−1.78391			−0.891953	−	0.452128i	$-0.850665\pi$
$181$	−24.0000			−1.78391			−0.891953	+	0.452128i	$0.850665\pi$
$182$	2.59808	−	0.500000i	0.192582	−	0.0370625i
$183$		0			0
$184$	−3.50000	+	6.06218i	−0.258023	+	0.446910i
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$			5.00000i			0.364662i
$189$	2.00000	−	1.73205i	0.145479	−	0.125988i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−19.0526	+	11.0000i	−1.37143	+	0.791797i	−0.991109	−	0.133056i	$-0.957521\pi$
$193$	−19.0526	+	11.0000i	−1.37143	+	0.791797i	−0.380325	+	0.924853i	$0.624188\pi$
$194$	8.00000	−	13.8564i	0.574367	−	0.994832i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$		−	1.00000i		−	0.0712470i	−0.999365	−	0.0356235i	$-0.988658\pi$
$197$		−	1.00000i		−	0.0712470i	0.999365	−	0.0356235i	$-0.0113417\pi$
$198$	0.866025	+	0.500000i	0.0615457	+	0.0355335i
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	−0.880616	−	0.473831i	$-0.842871\pi$
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	0.0299585	−	0.999551i	$-0.490462\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	13.8564	+	16.0000i	0.972529	+	1.12298i
$204$		0			0
$205$		0			0
$206$	−8.00000	−	13.8564i	−0.557386	−	0.965422i
$207$	6.06218	−	3.50000i	0.421350	−	0.243267i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	9.52628	+	5.50000i	0.654268	+	0.377742i
$213$	−5.19615	+	3.00000i	−0.356034	+	0.205557i
$214$	5.00000	+	8.66025i	0.341793	+	0.592003i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−1.73205	+	5.00000i	−0.117579	+	0.339422i
$218$			6.00000i			0.406371i
$219$	3.00000	−	5.19615i	0.202721	−	0.351123i
$220$		0			0
$221$		0			0
$222$	−9.52628	−	5.50000i	−0.639362	−	0.369136i
$223$		−	12.0000i		−	0.803579i	−0.915732	−	0.401790i	$-0.868388\pi$
$223$		−	12.0000i		−	0.803579i	0.915732	−	0.401790i	$-0.131612\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	−0.252136	−	0.967692i	$-0.581133\pi$
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	0.711977	+	0.702202i	$0.247800\pi$
$228$	−2.59808	+	1.50000i	−0.172062	+	0.0993399i
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$	0.500000	+	2.59808i	0.0328976	+	0.170941i
$232$			8.00000i			0.525226i
$233$	15.5885	+	9.00000i	1.02123	+	0.589610i	0.914461	−	0.404674i	$-0.132615\pi$
$233$	15.5885	+	9.00000i	1.02123	+	0.589610i	0.106773	+	0.994283i	$0.465948\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$		0			0
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$			8.00000i			0.519656i
$238$		0			0
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	8.66025	−	5.00000i	0.556702	−	0.321412i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$	−11.0000			−0.701334
$247$	2.59808	+	1.50000i	0.165312	+	0.0954427i
$248$	−1.73205	+	1.00000i	−0.109985	+	0.0635001i
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$		0			0
$251$	13.0000			0.820553			0.410276	−	0.911961i	$-0.365432\pi$
$251$	13.0000			0.820553			0.410276	+	0.911961i	$0.365432\pi$
$252$	1.73205	+	2.00000i	0.109109	+	0.125988i
$253$			7.00000i			0.440086i
$254$	8.50000	−	14.7224i	0.533337	−	0.923768i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.3205	+	10.0000i	1.08042	+	0.623783i	0.931011	−	0.364992i	$-0.118928\pi$
$257$	17.3205	+	10.0000i	1.08042	+	0.623783i	0.149413	+	0.988775i	$0.452262\pi$
$258$		−	8.00000i		−	0.498058i
$259$	−5.50000	−	28.5788i	−0.341753	−	1.77580i
$260$		0			0
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	4.33013	−	2.50000i	0.267516	−	0.154451i
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$		0			0
$266$	−7.50000	−	2.59808i	−0.459855	−	0.159298i
$267$			10.0000i			0.611990i
$268$		0			0
$269$	10.0000	+	17.3205i	0.609711	+	1.05605i	0.991288	+	0.131713i	$0.0420477\pi$
$269$	10.0000	+	17.3205i	0.609711	+	1.05605i	−0.381577	+	0.924337i	$0.624619\pi$
$270$		0			0
$271$	−16.0000	+	27.7128i	−0.971931	+	1.68343i	−0.282218	+	0.959350i	$0.591070\pi$
$271$	−16.0000	+	27.7128i	−0.971931	+	1.68343i	−0.689713	+	0.724083i	$0.742263\pi$
$272$		0			0
$273$	0.866025	−	2.50000i	0.0524142	−	0.151307i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	3.50000	+	6.06218i	0.210675	+	0.364900i
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.947604	−	0.319447i	$-0.896503\pi$
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.197153	+	0.980373i	$0.563170\pi$
$278$	−17.3205	−	10.0000i	−1.03882	−	0.599760i
$279$	2.00000			0.119737
$280$		0			0
$281$	−1.00000			−0.0596550			−0.0298275	−	0.999555i	$-0.509496\pi$
$281$	−1.00000			−0.0596550			−0.0298275	+	0.999555i	$0.509496\pi$
$282$	4.33013	+	2.50000i	0.257855	+	0.148873i
$283$	12.1244	−	7.00000i	0.720718	−	0.416107i	−0.0942988	−	0.995544i	$-0.530061\pi$
$283$	12.1244	−	7.00000i	0.720718	−	0.416107i	0.815017	+	0.579437i	$0.196728\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	1.00000			0.0591312
$287$	−19.0526	−	22.0000i	−1.12464	−	1.29862i
$288$			1.00000i			0.0589256i
$289$	−8.50000	+	14.7224i	−0.500000	+	0.866025i
$290$		0			0
$291$	−8.00000	−	13.8564i	−0.468968	−	0.812277i
$292$	5.19615	+	3.00000i	0.304082	+	0.175562i
$293$		−	27.0000i		−	1.57736i	−0.614806	−	0.788678i	$-0.710766\pi$
$293$		−	27.0000i		−	1.57736i	0.614806	−	0.788678i	$-0.289234\pi$
$294$	−1.00000	+	6.92820i	−0.0583212	+	0.404061i
$295$		0			0
$296$	5.50000	−	9.52628i	0.319681	−	0.553704i
$297$	0.866025	−	0.500000i	0.0502519	−	0.0290129i
$298$		0			0
$299$	3.50000	−	6.06218i	0.202410	−	0.350585i
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$		−	6.00000i		−	0.345261i
$303$		0			0
$304$	−1.50000	−	2.59808i	−0.0860309	−	0.149010i
$305$		0			0
$306$		0			0
$307$			20.0000i			1.14146i	0.821138	+	0.570730i	$0.193340\pi$
$307$			20.0000i			1.14146i	−0.821138	+	0.570730i	$0.806660\pi$
$308$	−2.59808	+	0.500000i	−0.148039	+	0.0284901i
$309$	−16.0000			−0.910208
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	0.866025	−	0.500000i	0.0490290	−	0.0283069i
$313$	−10.3923	−	6.00000i	−0.587408	−	0.339140i	0.176664	−	0.984271i	$-0.443469\pi$
$313$	−10.3923	−	6.00000i	−0.587408	−	0.339140i	−0.764072	+	0.645131i	$0.776803\pi$
$314$	−7.00000			−0.395033
$315$		0			0
$316$	−8.00000			−0.450035
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	9.52628	−	5.50000i	0.534207	−	0.308425i
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$		0			0
$321$	10.0000			0.558146
$322$	−6.06218	+	17.5000i	−0.337832	+	0.975237i
$323$		0			0
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$	5.19615	+	3.00000i	0.287348	+	0.165900i
$328$		−	11.0000i		−	0.607373i
$329$	2.50000	+	12.9904i	0.137829	+	0.716183i
$330$		0			0
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	−0.630232	−	0.776407i	$-0.717040\pi$
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	0.987504	+	0.157593i	$0.0503735\pi$
$332$	6.92820	−	4.00000i	0.380235	−	0.219529i
$333$	−9.52628	+	5.50000i	−0.522037	+	0.301398i
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$		0			0
$336$	−2.00000	+	1.73205i	−0.109109	+	0.0944911i
$337$		−	12.0000i		−	0.653682i	−0.945079	−	0.326841i	$-0.894016\pi$
$337$		−	12.0000i		−	0.653682i	0.945079	−	0.326841i	$-0.105984\pi$
$338$	10.3923	+	6.00000i	0.565267	+	0.326357i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	−1.00000	+	1.73205i	−0.0541530	+	0.0937958i
$342$			3.00000i			0.162221i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	8.00000			0.431331
$345$		0			0
$346$	−7.50000	−	12.9904i	−0.403202	−	0.698367i
$347$	12.1244	−	7.00000i	0.650870	−	0.375780i	−0.137920	−	0.990443i	$-0.544042\pi$
$347$	12.1244	−	7.00000i	0.650870	−	0.375780i	0.788789	+	0.614664i	$0.210708\pi$
$348$	6.92820	+	4.00000i	0.371391	+	0.214423i
$349$	−12.0000			−0.642345			−0.321173	−	0.947021i	$-0.604077\pi$
$349$	−12.0000			−0.642345			−0.321173	+	0.947021i	$0.604077\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	−0.866025	−	0.500000i	−0.0461593	−	0.0266501i
$353$	−20.7846	+	12.0000i	−1.10625	+	0.638696i	−0.937856	−	0.347024i	$-0.887192\pi$
$353$	−20.7846	+	12.0000i	−1.10625	+	0.638696i	−0.168397	+	0.985719i	$0.553859\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$	−10.0000			−0.529999
$357$		0			0
$358$		−	19.0000i		−	1.00418i
$359$	2.00000	−	3.46410i	0.105556	−	0.182828i	−0.808409	−	0.588621i	$-0.799671\pi$
$359$	2.00000	−	3.46410i	0.105556	−	0.182828i	0.913965	+	0.405793i	$0.133004\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	−20.7846	−	12.0000i	−1.09241	−	0.630706i
$363$		−	10.0000i		−	0.524864i
$364$	2.50000	+	0.866025i	0.131036	+	0.0453921i
$365$		0			0
$366$		0			0
$367$	21.6506	−	12.5000i	1.13015	−	0.652495i	0.186180	−	0.982516i	$-0.440389\pi$
$367$	21.6506	−	12.5000i	1.13015	−	0.652495i	0.943974	+	0.330021i	$0.107056\pi$
$368$	−6.06218	+	3.50000i	−0.316013	+	0.182450i
$369$	−5.50000	+	9.52628i	−0.286319	+	0.495918i
$370$		0			0
$371$	27.5000	+	9.52628i	1.42773	+	0.494580i
$372$			2.00000i			0.103695i
$373$	5.19615	+	3.00000i	0.269047	+	0.155334i	0.628454	−	0.777847i	$-0.283688\pi$
$373$	5.19615	+	3.00000i	0.269047	+	0.155334i	−0.359408	+	0.933181i	$0.617021\pi$
$374$		0			0
$375$		0			0
$376$	−2.50000	+	4.33013i	−0.128928	+	0.223309i
$377$		−	8.00000i		−	0.412021i
$378$	2.59808	−	0.500000i	0.133631	−	0.0257172i
$379$	19.0000			0.975964			0.487982	−	0.872854i	$-0.337733\pi$
$379$	19.0000			0.975964			0.487982	+	0.872854i	$0.337733\pi$
$380$		0			0
$381$	−8.50000	−	14.7224i	−0.435468	−	0.754253i
$382$	5.19615	−	3.00000i	0.265858	−	0.153493i
$383$	30.3109	+	17.5000i	1.54881	+	0.894208i	0.998233	+	0.0594268i	$0.0189273\pi$
$383$	30.3109	+	17.5000i	1.54881	+	0.894208i	0.550581	+	0.834781i	$0.314406\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−22.0000			−1.11977
$387$	−6.92820	−	4.00000i	−0.352180	−	0.203331i
$388$	13.8564	−	8.00000i	0.703452	−	0.406138i
$389$	5.00000	+	8.66025i	0.253510	+	0.439092i	0.964490	−	0.264120i	$-0.0850816\pi$
$389$	5.00000	+	8.66025i	0.253510	+	0.439092i	−0.710980	+	0.703213i	$0.751748\pi$
$390$		0			0
$391$		0			0
$392$	−6.92820	−	1.00000i	−0.349927	−	0.0505076i
$393$		−	5.00000i		−	0.252217i
$394$	0.500000	−	0.866025i	0.0251896	−	0.0436297i
$395$		0			0
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	0.163876	−	0.986481i	$-0.447600\pi$
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	−0.772380	+	0.635161i	$0.780934\pi$
$398$		−	24.0000i		−	1.20301i
$399$	−6.00000	+	5.19615i	−0.300376	+	0.260133i
$400$		0			0
$401$	2.50000	−	4.33013i	0.124844	−	0.216236i	−0.796828	−	0.604206i	$-0.793490\pi$
$401$	2.50000	−	4.33013i	0.124844	−	0.216236i	0.921672	+	0.387970i	$0.126824\pi$
$402$		0			0
$403$	1.73205	−	1.00000i	0.0862796	−	0.0498135i
$404$		0			0
$405$		0			0
$406$	4.00000	+	20.7846i	0.198517	+	1.03152i
$407$		−	11.0000i		−	0.545250i
$408$		0			0
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	0.889689	−	0.456566i	$-0.150921\pi$
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	−0.840243	+	0.542211i	$0.817588\pi$
$410$		0			0
$411$	−9.00000	+	15.5885i	−0.443937	+	0.768922i
$412$		−	16.0000i		−	0.788263i
$413$	−3.46410	+	10.0000i	−0.170457	+	0.492068i
$414$	7.00000			0.344031
$415$		0			0
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−17.3205	+	10.0000i	−0.848189	+	0.489702i
$418$	−2.59808	−	1.50000i	−0.127076	−	0.0733674i
$419$	5.00000			0.244266			0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000			0.244266			0.122133	+	0.992514i	$0.461027\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	4.33013	+	2.50000i	0.210787	+	0.121698i
$423$	4.33013	−	2.50000i	0.210538	−	0.121554i
$424$	5.50000	+	9.52628i	0.267104	+	0.462637i
$425$		0			0
$426$	−6.00000			−0.290701
$427$		0			0
$428$			10.0000i			0.483368i
$429$	0.500000	−	0.866025i	0.0241402	−	0.0418121i
$430$		0			0
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			32.0000i			1.53782i	0.639356	+	0.768911i	$0.279201\pi$
$433$			32.0000i			1.53782i	−0.639356	+	0.768911i	$0.720799\pi$
$434$	−4.00000	+	3.46410i	−0.192006	+	0.166282i
$435$		0			0
$436$	−3.00000	+	5.19615i	−0.143674	+	0.248851i
$437$	−18.1865	+	10.5000i	−0.869980	+	0.502283i
$438$	5.19615	−	3.00000i	0.248282	−	0.143346i
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	13.8564	+	8.00000i	0.658338	+	0.380091i	0.791643	−	0.610984i	$-0.209226\pi$
$443$	13.8564	+	8.00000i	0.658338	+	0.380091i	−0.133306	+	0.991075i	$0.542559\pi$
$444$	−5.50000	−	9.52628i	−0.261018	−	0.452097i
$445$		0			0
$446$	6.00000	−	10.3923i	0.284108	−	0.492090i
$447$		0			0
$448$	−1.73205	−	2.00000i	−0.0818317	−	0.0944911i
$449$	−11.0000			−0.519122			−0.259561	−	0.965727i	$-0.583578\pi$
$449$	−11.0000			−0.519122			−0.259561	+	0.965727i	$0.583578\pi$
$450$		0			0
$451$	−5.50000	−	9.52628i	−0.258985	−	0.448575i
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	−5.19615	−	3.00000i	−0.244137	−	0.140952i
$454$	8.00000			0.375459
$455$		0			0
$456$	−3.00000			−0.140488
$457$	15.5885	+	9.00000i	0.729197	+	0.421002i	0.818128	−	0.575036i	$-0.195012\pi$
$457$	15.5885	+	9.00000i	0.729197	+	0.421002i	−0.0889312	+	0.996038i	$0.528345\pi$
$458$	12.1244	−	7.00000i	0.566534	−	0.327089i
$459$		0			0
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$	−0.866025	+	2.50000i	−0.0402911	+	0.116311i
$463$			13.0000i			0.604161i	0.953282	+	0.302081i	$0.0976812\pi$
$463$			13.0000i			0.604161i	−0.953282	+	0.302081i	$0.902319\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$		0			0
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$		−	1.00000i		−	0.0462250i
$469$		0			0
$470$		0			0
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$	−3.46410	+	2.00000i	−0.159448	+	0.0920575i
$473$	6.92820	−	4.00000i	0.318559	−	0.183920i
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$		0			0
$476$		0			0
$477$		−	11.0000i		−	0.503655i
$478$	15.5885	+	9.00000i	0.712999	+	0.411650i
$479$	11.0000	+	19.0526i	0.502603	+	0.870534i	0.999995	+	0.00300810i	$0.000957509\pi$
$479$	11.0000	+	19.0526i	0.502603	+	0.870534i	−0.497393	+	0.867526i	$0.665709\pi$
$480$		0			0
$481$	−5.50000	+	9.52628i	−0.250778	+	0.434361i
$482$		−	7.00000i		−	0.318841i
$483$	12.1244	+	14.0000i	0.551677	+	0.637022i
$484$	10.0000			0.454545
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−13.8564	+	8.00000i	−0.627894	+	0.362515i	−0.779936	−	0.625859i	$-0.784748\pi$
$487$	−13.8564	+	8.00000i	−0.627894	+	0.362515i	0.152042	+	0.988374i	$0.451415\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	−9.52628	−	5.50000i	−0.429478	−	0.247959i
$493$		0			0
$494$	1.50000	+	2.59808i	0.0674882	+	0.116893i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	−10.3923	−	12.0000i	−0.466159	−	0.538274i
$498$		−	8.00000i		−	0.358489i
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$		0			0
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$	11.2583	+	6.50000i	0.502484	+	0.290109i
$503$		−	36.0000i		−	1.60516i	−0.596544	−	0.802580i	$-0.703460\pi$
$503$		−	36.0000i		−	1.60516i	0.596544	−	0.802580i	$-0.296540\pi$
$504$	0.500000	+	2.59808i	0.0222718	+	0.115728i
$505$		0			0
$506$	−3.50000	+	6.06218i	−0.155594	+	0.269497i
$507$	10.3923	−	6.00000i	0.461538	−	0.266469i
$508$	14.7224	−	8.50000i	0.653202	−	0.377127i
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	0.192599	+	0.981278i	$0.438308\pi$
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$510$		0			0
$511$	15.0000	+	5.19615i	0.663561	+	0.229864i
$512$		−	1.00000i		−	0.0441942i
$513$	2.59808	+	1.50000i	0.114708	+	0.0662266i
$514$	10.0000	+	17.3205i	0.441081	+	0.763975i
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$			5.00000i			0.219900i
$518$	9.52628	−	27.5000i	0.418561	−	1.20828i
$519$	−15.0000			−0.658427
$520$		0			0
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	0.959841	+	0.280543i	$0.0905145\pi$
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	−0.236963	+	0.971519i	$0.576152\pi$
$522$	6.92820	−	4.00000i	0.303239	−	0.175075i
$523$	1.73205	+	1.00000i	0.0757373	+	0.0437269i	0.537390	−	0.843334i	$-0.319410\pi$
$523$	1.73205	+	1.00000i	0.0757373	+	0.0437269i	−0.461653	+	0.887061i	$0.652744\pi$
$524$	5.00000			0.218426
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$	−0.866025	+	0.500000i	−0.0376889	+	0.0217597i
$529$	13.0000	+	22.5167i	0.565217	+	0.978985i
$530$		0			0
$531$	4.00000			0.173585
$532$	−5.19615	−	6.00000i	−0.225282	−	0.260133i
$533$			11.0000i			0.476463i
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$		0			0
$536$		0			0
$537$	−16.4545	−	9.50000i	−0.710063	−	0.409955i
$538$			20.0000i			0.862261i
$539$	−6.50000	+	2.59808i	−0.279975	+	0.111907i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−27.7128	+	16.0000i	−1.19037	+	0.687259i
$543$	−20.7846	+	12.0000i	−0.891953	+	0.514969i
$544$		0			0
$545$		0			0
$546$	2.00000	−	1.73205i	0.0855921	−	0.0741249i
$547$			16.0000i			0.684111i	0.939680	+	0.342055i	$0.111123\pi$
$547$			16.0000i			0.684111i	−0.939680	+	0.342055i	$0.888877\pi$
$548$	−15.5885	−	9.00000i	−0.665906	−	0.384461i
$549$		0			0
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$			7.00000i			0.297940i
$553$	−20.7846	+	4.00000i	−0.883852	+	0.170097i
$554$	−22.0000			−0.934690
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−28.5788	+	16.5000i	−1.21092	+	0.699127i	−0.962961	−	0.269642i	$-0.913095\pi$
$557$	−28.5788	+	16.5000i	−1.21092	+	0.699127i	−0.247964	+	0.968769i	$0.579761\pi$
$558$	1.73205	+	1.00000i	0.0733236	+	0.0423334i
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	−0.866025	−	0.500000i	−0.0365311	−	0.0210912i
$563$	32.9090	−	19.0000i	1.38695	−	0.800755i	0.393977	−	0.919120i	$-0.371099\pi$
$563$	32.9090	−	19.0000i	1.38695	−	0.800755i	0.992970	+	0.118366i	$0.0377655\pi$
$564$	2.50000	+	4.33013i	0.105269	+	0.182331i
$565$		0			0
$566$	14.0000			0.588464
$567$	0.866025	−	2.50000i	0.0363696	−	0.104990i
$568$		−	6.00000i		−	0.251754i
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$		0			0
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$	0.866025	+	0.500000i	0.0362103	+	0.0209061i
$573$		−	6.00000i		−	0.250654i
$574$	−5.50000	−	28.5788i	−0.229566	−	1.19286i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−12.1244	+	7.00000i	−0.504744	+	0.291414i	−0.730670	−	0.682730i	$-0.760792\pi$
$577$	−12.1244	+	7.00000i	−0.504744	+	0.291414i	0.225927	+	0.974144i	$0.427459\pi$
$578$	−14.7224	+	8.50000i	−0.612372	+	0.353553i
$579$	−11.0000	+	19.0526i	−0.457144	+	0.791797i
$580$		0			0
$581$	16.0000	−	13.8564i	0.663792	−	0.574861i
$582$		−	16.0000i		−	0.663221i
$583$	9.52628	+	5.50000i	0.394538	+	0.227787i
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$		0			0
$586$	13.5000	−	23.3827i	0.557680	−	0.965930i
$587$		−	18.0000i		−	0.742940i	−0.928445	−	0.371470i	$-0.878854\pi$
$587$		−	18.0000i		−	0.742940i	0.928445	−	0.371470i	$-0.121146\pi$
$588$	−4.33013	+	5.50000i	−0.178571	+	0.226816i
$589$	−6.00000			−0.247226
$590$		0			0
$591$	−0.500000	−	0.866025i	−0.0205673	−	0.0356235i
$592$	9.52628	−	5.50000i	0.391528	−	0.226049i
$593$	13.8564	+	8.00000i	0.569014	+	0.328521i	0.756756	−	0.653698i	$-0.226783\pi$
$593$	13.8564	+	8.00000i	0.569014	+	0.328521i	−0.187741	+	0.982219i	$0.560117\pi$
$594$	1.00000			0.0410305
$595$		0			0
$596$		0			0
$597$	−20.7846	−	12.0000i	−0.850657	−	0.491127i
$598$	6.06218	−	3.50000i	0.247901	−	0.143126i
$599$	1.00000	+	1.73205i	0.0408589	+	0.0707697i	0.885732	−	0.464198i	$-0.153657\pi$
$599$	1.00000	+	1.73205i	0.0408589	+	0.0707697i	−0.844873	+	0.534967i	$0.820324\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$	20.7846	−	4.00000i	0.847117	−	0.163028i
$603$		0			0
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$		0			0
$606$		0			0
$607$	32.0429	+	18.5000i	1.30058	+	0.750892i	0.980504	−	0.196499i	$-0.0629573\pi$
$607$	32.0429	+	18.5000i	1.30058	+	0.750892i	0.320079	+	0.947391i	$0.396291\pi$
$608$		−	3.00000i		−	0.121666i
$609$	20.0000	+	6.92820i	0.810441	+	0.280745i
$610$		0			0
$611$	2.50000	−	4.33013i	0.101139	−	0.175178i
$612$		0			0
$613$	35.5070	−	20.5000i	1.43412	−	0.827987i	0.436684	−	0.899615i	$-0.356153\pi$
$613$	35.5070	−	20.5000i	1.43412	−	0.827987i	0.997431	+	0.0716275i	$0.0228193\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$		0			0
$616$	−2.50000	−	0.866025i	−0.100728	−	0.0348932i
$617$			28.0000i			1.12724i	0.826035	+	0.563619i	$0.190591\pi$
$617$			28.0000i			1.12724i	−0.826035	+	0.563619i	$0.809409\pi$
$618$	−13.8564	−	8.00000i	−0.557386	−	0.321807i
$619$	14.5000	+	25.1147i	0.582804	+	1.00945i	0.995145	+	0.0984169i	$0.0313779\pi$
$619$	14.5000	+	25.1147i	0.582804	+	1.00945i	−0.412341	+	0.911030i	$0.635289\pi$
$620$		0			0
$621$	3.50000	−	6.06218i	0.140450	−	0.243267i
$622$		−	12.0000i		−	0.481156i
$623$	−25.9808	+	5.00000i	−1.04090	+	0.200321i
$624$	1.00000			0.0400320
$625$		0			0
$626$	−6.00000	−	10.3923i	−0.239808	−	0.415360i
$627$	−2.59808	+	1.50000i	−0.103757	+	0.0599042i
$628$	−6.06218	−	3.50000i	−0.241907	−	0.139665i
$629$		0			0
$630$		0			0
$631$	−26.0000			−1.03504			−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000			−1.03504			−0.517522	+	0.855670i	$0.673145\pi$
$632$	−6.92820	−	4.00000i	−0.275589	−	0.159111i
$633$	4.33013	−	2.50000i	0.172107	−	0.0993661i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$	11.0000			0.436178
$637$	6.92820	+	1.00000i	0.274505	+	0.0396214i
$638$			8.00000i			0.316723i
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$	8.66025	+	5.00000i	0.341793	+	0.197334i
$643$			10.0000i			0.394362i	0.980367	+	0.197181i	$0.0631786\pi$
$643$			10.0000i			0.394362i	−0.980367	+	0.197181i	$0.936821\pi$
$644$	−14.0000	+	12.1244i	−0.551677	+	0.477767i
$645$		0			0
$646$		0			0
$647$	−14.7224	+	8.50000i	−0.578799	+	0.334169i	−0.760656	−	0.649155i	$-0.775122\pi$
$647$	−14.7224	+	8.50000i	−0.578799	+	0.334169i	0.181857	+	0.983325i	$0.441789\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$		0			0
$651$	1.00000	+	5.19615i	0.0391931	+	0.203653i
$652$			16.0000i			0.626608i
$653$	6.06218	+	3.50000i	0.237231	+	0.136966i	0.613904	−	0.789381i	$-0.289598\pi$
$653$	6.06218	+	3.50000i	0.237231	+	0.136966i	−0.376672	+	0.926347i	$0.622932\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$		0			0
$656$	5.50000	−	9.52628i	0.214739	−	0.371939i
$657$		−	6.00000i		−	0.234082i
$658$	−4.33013	+	12.5000i	−0.168806	+	0.487301i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	12.0000	+	20.7846i	0.466746	+	0.808428i	0.999278	−	0.0379819i	$-0.0120929\pi$
$661$	12.0000	+	20.7846i	0.466746	+	0.808428i	−0.532533	+	0.846410i	$0.678760\pi$
$662$	11.2583	−	6.50000i	0.437567	−	0.252630i
$663$		0			0
$664$	8.00000			0.310460
$665$		0			0
$666$	−11.0000			−0.426241
$667$	48.4974	+	28.0000i	1.87783	+	1.08416i
$668$	2.59808	−	1.50000i	0.100523	−	0.0580367i
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$		0			0
$671$		0			0
$672$	−2.59808	+	0.500000i	−0.100223	+	0.0192879i
$673$		−	28.0000i		−	1.07932i	−0.841883	−	0.539660i	$-0.818553\pi$
$673$		−	28.0000i		−	1.07932i	0.841883	−	0.539660i	$-0.181447\pi$
$674$	6.00000	−	10.3923i	0.231111	−	0.400297i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	11.2583	+	6.50000i	0.432693	+	0.249815i	0.700493	−	0.713659i	$-0.252963\pi$
$677$	11.2583	+	6.50000i	0.432693	+	0.249815i	−0.267800	+	0.963474i	$0.586297\pi$
$678$		−	6.00000i		−	0.230429i
$679$	32.0000	−	27.7128i	1.22805	−	1.06352i
$680$		0			0
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$	−1.73205	+	1.00000i	−0.0663237	+	0.0382920i
$683$	−3.46410	+	2.00000i	−0.132550	+	0.0765279i	−0.564809	−	0.825222i	$-0.691050\pi$
$683$	−3.46410	+	2.00000i	−0.132550	+	0.0765279i	0.432259	+	0.901750i	$0.357717\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$		−	14.0000i		−	0.534133i
$688$	6.92820	+	4.00000i	0.264135	+	0.152499i
$689$	−5.50000	−	9.52628i	−0.209533	−	0.362922i
$690$		0			0
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$		−	15.0000i		−	0.570214i
$693$	1.73205	+	2.00000i	0.0657952	+	0.0759737i
$694$	14.0000			0.531433
$695$		0			0
$696$	4.00000	+	6.92820i	0.151620	+	0.262613i
$697$		0			0
$698$	−10.3923	−	6.00000i	−0.393355	−	0.227103i
$699$	18.0000			0.680823
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−0.866025	−	0.500000i	−0.0326860	−	0.0188713i
$703$	28.5788	−	16.5000i	1.07787	−	0.622309i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$			4.00000i			0.150329i
$709$	22.0000	−	38.1051i	0.826227	−	1.43107i	−0.0747503	−	0.997202i	$-0.523816\pi$
$709$	22.0000	−	38.1051i	0.826227	−	1.43107i	0.900978	−	0.433865i	$-0.142851\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	−8.66025	−	5.00000i	−0.324557	−	0.187383i
$713$			14.0000i			0.524304i
$714$		0			0
$715$		0			0
$716$	9.50000	−	16.4545i	0.355032	−	0.614933i
$717$	15.5885	−	9.00000i	0.582162	−	0.336111i
$718$	3.46410	−	2.00000i	0.129279	−	0.0746393i
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	−0.846776	−	0.531949i	$-0.821460\pi$
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	0.884070	+	0.467355i	$0.154793\pi$
$720$		0			0
$721$	−8.00000	−	41.5692i	−0.297936	−	1.54812i
$722$			10.0000i			0.372161i
$723$	−6.06218	−	3.50000i	−0.225455	−	0.130166i
$724$	−12.0000	−	20.7846i	−0.445976	−	0.772454i
$725$		0			0
$726$	5.00000	−	8.66025i	0.185567	−	0.321412i
$727$			11.0000i			0.407967i	0.978974	+	0.203984i	$0.0653890\pi$
$727$			11.0000i			0.407967i	−0.978974	+	0.203984i	$0.934611\pi$
$728$	1.73205	+	2.00000i	0.0641941	+	0.0741249i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	9.52628	+	5.50000i	0.351861	+	0.203147i	0.665505	−	0.746394i	$-0.268216\pi$
$733$	9.52628	+	5.50000i	0.351861	+	0.203147i	−0.313644	+	0.949541i	$0.601550\pi$
$734$	25.0000			0.922767
$735$		0			0
$736$	−7.00000			−0.258023
$737$		0			0
$738$	−9.52628	+	5.50000i	−0.350667	+	0.202458i
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$		0			0
$741$	3.00000			0.110208
$742$	19.0526	+	22.0000i	0.699441	+	0.807645i
$743$		−	49.0000i		−	1.79764i	−0.438322	−	0.898818i	$-0.644427\pi$
$743$		−	49.0000i		−	1.79764i	0.438322	−	0.898818i	$-0.355573\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$		0			0
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$		0			0
$749$	5.00000	+	25.9808i	0.182696	+	0.949316i
$750$		0			0
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	−4.33013	+	2.50000i	−0.157903	+	0.0911656i
$753$	11.2583	−	6.50000i	0.410276	−	0.236873i
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$		0			0
$756$	2.50000	+	0.866025i	0.0909241	+	0.0314970i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	16.4545	+	9.50000i	0.597654	+	0.345056i
$759$	3.50000	+	6.06218i	0.127042	+	0.220043i
$760$		0			0
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		−	17.0000i		−	0.615845i
$763$	−5.19615	+	15.0000i	−0.188113	+	0.543036i
$764$	6.00000			0.217072
$765$		0			0
$766$	17.5000	+	30.3109i	0.632301	+	1.09518i
$767$	3.46410	−	2.00000i	0.125081	−	0.0722158i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$		0			0
$771$	20.0000			0.720282
$772$	−19.0526	−	11.0000i	−0.685717	−	0.395899i
$773$	−28.5788	+	16.5000i	−1.02791	+	0.593464i	−0.916385	−	0.400298i	$-0.868907\pi$
$773$	−28.5788	+	16.5000i	−1.02791	+	0.593464i	−0.111524	+	0.993762i	$0.535573\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$		0			0
$776$	16.0000			0.574367
$777$	−19.0526	−	22.0000i	−0.683507	−	0.789246i
$778$			10.0000i			0.358517i
$779$	16.5000	−	28.5788i	0.591174	−	1.02394i
$780$		0			0
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$		0			0
$783$		−	8.00000i		−	0.285897i
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		0			0
$786$	2.50000	−	4.33013i	0.0891720	−	0.154451i
$787$	19.0526	−	11.0000i	0.679150	−	0.392108i	−0.120384	−	0.992727i	$-0.538413\pi$
$787$	19.0526	−	11.0000i	0.679150	−	0.392108i	0.799535	+	0.600620i	$0.205079\pi$
$788$	0.866025	−	0.500000i	0.0308509	−	0.0178118i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$		0			0
$791$	12.0000	−	10.3923i	0.426671	−	0.369508i
$792$			1.00000i			0.0355335i
$793$		0			0
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$		0			0
$796$	12.0000	−	20.7846i	0.425329	−	0.736691i
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$	−7.79423	+	1.50000i	−0.275913	+	0.0530994i
$799$		0			0
$800$		0			0
$801$	5.00000	+	8.66025i	0.176666	+	0.305995i
$802$	4.33013	−	2.50000i	0.152902	−	0.0882781i
$803$	5.19615	+	3.00000i	0.183368	+	0.105868i
$804$		0			0
$805$		0			0
$806$	2.00000			0.0704470
$807$	17.3205	+	10.0000i	0.609711	+	0.352017i
$808$		0			0
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	−0.973253	−	0.229736i	$-0.926214\pi$
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	0.287670	−	0.957730i	$-0.407120\pi$
$810$		0			0
$811$	9.00000			0.316033			0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000			0.316033			0.158016	+	0.987436i	$0.449490\pi$
$812$	−6.92820	+	20.0000i	−0.243132	+	0.701862i
$813$			32.0000i			1.12229i
$814$	5.50000	−	9.52628i	0.192775	−	0.333896i
$815$		0			0
$816$		0			0
$817$	20.7846	+	12.0000i	0.727161	+	0.419827i
$818$			2.00000i			0.0699284i
$819$	−0.500000	−	2.59808i	−0.0174714	−	0.0907841i
$820$		0			0
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$	−15.5885	+	9.00000i	−0.543710	+	0.313911i
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	−0.0919029	−	0.995768i	$-0.529295\pi$
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	0.816409	+	0.577474i	$0.195962\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$	−8.00000	+	6.92820i	−0.278356	+	0.241063i
$827$		−	10.0000i		−	0.347734i	−0.984769	−	0.173867i	$-0.944374\pi$
$827$		−	10.0000i		−	0.347734i	0.984769	−	0.173867i	$-0.0556263\pi$
$828$	6.06218	+	3.50000i	0.210675	+	0.121633i
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	0.788165	−	0.615465i	$-0.211032\pi$
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	−0.927090	+	0.374838i	$0.877698\pi$
$830$		0			0
$831$	−11.0000	+	19.0526i	−0.381586	+	0.660926i
$832$			1.00000i			0.0346688i
$833$		0			0
$834$	−20.0000			−0.692543
$835$		0			0
$836$	−1.50000	−	2.59808i	−0.0518786	−	0.0898563i
$837$	1.73205	−	1.00000i	0.0598684	−	0.0345651i
$838$	4.33013	+	2.50000i	0.149582	+	0.0863611i
$839$	40.0000			1.38095			0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000			1.38095			0.690477	+	0.723355i	$0.257401\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	19.0526	+	11.0000i	0.656595	+	0.379085i
$843$	−0.866025	+	0.500000i	−0.0298275	+	0.0172209i
$844$	2.50000	+	4.33013i	0.0860535	+	0.149049i
$845$		0			0
$846$	5.00000			0.171904
$847$	25.9808	−	5.00000i	0.892710	−	0.171802i
$848$			11.0000i			0.377742i
$849$	7.00000	−	12.1244i	0.240239	−	0.416107i
$850$		0			0
$851$	−38.5000	−	66.6840i	−1.31976	−	2.28590i
$852$	−5.19615	−	3.00000i	−0.178017	−	0.102778i
$853$			41.0000i			1.40381i	0.712269	+	0.701907i	$0.247668\pi$
$853$			41.0000i			1.40381i	−0.712269	+	0.701907i	$0.752332\pi$
$854$		0			0
$855$		0			0
$856$	−5.00000	+	8.66025i	−0.170896	+	0.296001i
$857$	−12.1244	+	7.00000i	−0.414160	+	0.239115i	−0.692576	−	0.721345i	$-0.743524\pi$
$857$	−12.1244	+	7.00000i	−0.414160	+	0.239115i	0.278416	+	0.960461i	$0.410191\pi$
$858$	0.866025	−	0.500000i	0.0295656	−	0.0170697i
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	−0.745325	−	0.666701i	$-0.767706\pi$
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	0.950043	+	0.312120i	$0.101039\pi$
$860$		0			0
$861$	−27.5000	−	9.52628i	−0.937197	−	0.324655i
$862$		0			0
$863$	−45.8993	−	26.5000i	−1.56243	−	0.902070i	−0.997010	−	0.0772684i	$-0.975380\pi$
$863$	−45.8993	−	26.5000i	−1.56243	−	0.902070i	−0.565422	−	0.824802i	$-0.691287\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−16.0000	+	27.7128i	−0.543702	+	0.941720i
$867$			17.0000i			0.577350i
$868$	−5.19615	+	1.00000i	−0.176369	+	0.0339422i
$869$	−8.00000			−0.271381
$870$		0			0
$871$		0			0
$872$	−5.19615	+	3.00000i	−0.175964	+	0.101593i
$873$	−13.8564	−	8.00000i	−0.468968	−	0.270759i
$874$	−21.0000			−0.710336
$875$		0			0
$876$	6.00000			0.202721
$877$	−14.7224	−	8.50000i	−0.497141	−	0.287025i	0.230391	−	0.973098i	$-0.425999\pi$
$877$	−14.7224	−	8.50000i	−0.497141	−	0.287025i	−0.727532	+	0.686074i	$0.759333\pi$
$878$	27.7128	−	16.0000i	0.935262	−	0.539974i
$879$	−13.5000	−	23.3827i	−0.455344	−	0.788678i
$880$		0			0
$881$	−53.0000			−1.78562			−0.892808	−	0.450438i	$-0.851268\pi$
$881$	−53.0000			−1.78562			−0.892808	+	0.450438i	$0.851268\pi$
$882$	2.59808	+	6.50000i	0.0874818	+	0.218866i
$883$			42.0000i			1.41341i	0.707507	+	0.706706i	$0.249820\pi$
$883$			42.0000i			1.41341i	−0.707507	+	0.706706i	$0.750180\pi$
$884$		0			0
$885$		0			0
$886$	8.00000	+	13.8564i	0.268765	+	0.465515i
$887$	−38.1051	−	22.0000i	−1.27944	−	0.738688i	−0.302698	−	0.953086i	$-0.597887\pi$
$887$	−38.1051	−	22.0000i	−1.27944	−	0.738688i	−0.976746	+	0.214399i	$0.931221\pi$
$888$		−	11.0000i		−	0.369136i
$889$	34.0000	−	29.4449i	1.14032	−	0.987549i
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	10.3923	−	6.00000i	0.347960	−	0.200895i
$893$	−12.9904	+	7.50000i	−0.434707	+	0.250978i
$894$		0			0
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$		−	7.00000i		−	0.233723i
$898$	−9.52628	−	5.50000i	−0.317896	−	0.183537i
$899$	8.00000	+	13.8564i	0.266815	+	0.462137i
$900$		0			0
$901$		0			0
$902$		−	11.0000i		−	0.366260i
$903$	6.92820	−	20.0000i	0.230556	−	0.665558i
$904$	6.00000			0.199557
$905$		0			0
$906$	−3.00000	−	5.19615i	−0.0996683	−	0.172631i
$907$	−8.66025	+	5.00000i	−0.287559	+	0.166022i	−0.636841	−	0.770996i	$-0.719759\pi$
$907$	−8.66025	+	5.00000i	−0.287559	+	0.166022i	0.349281	+	0.937018i	$0.386426\pi$
$908$	6.92820	+	4.00000i	0.229920	+	0.132745i
$909$		0			0
$910$		0			0
$911$	−2.00000			−0.0662630			−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000			−0.0662630			−0.0331315	+	0.999451i	$0.510548\pi$
$912$	−2.59808	−	1.50000i	−0.0860309	−	0.0496700i
$913$	6.92820	−	4.00000i	0.229290	−	0.132381i
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$		0			0
$916$	14.0000			0.462573
$917$	12.9904	−	2.50000i	0.428980	−	0.0825573i
$918$		0			0
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	0.399955	+	0.916535i	$0.369026\pi$
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	−0.993720	+	0.111897i	$0.964307\pi$
$920$		0			0
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	−10.3923	−	6.00000i	−0.342252	−	0.197599i
$923$			6.00000i			0.197492i
$924$	−2.00000	+	1.73205i	−0.0657952	+	0.0569803i
$925$		0			0
$926$	−6.50000	+	11.2583i	−0.213603	+	0.369972i
$927$	−13.8564	+	8.00000i	−0.455104	+	0.262754i
$928$	−6.92820	+	4.00000i	−0.227429	+	0.131306i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	−16.5000	−	12.9904i	−0.540766	−	0.425743i
$932$			18.0000i			0.589610i
$933$	−10.3923	−	6.00000i	−0.340229	−	0.196431i
$934$		0			0
$935$		0			0
$936$	0.500000	−	0.866025i	0.0163430	−	0.0283069i
$937$			12.0000i			0.392023i	0.980602	+	0.196011i	$0.0627990\pi$
$937$			12.0000i			0.392023i	−0.980602	+	0.196011i	$0.937201\pi$
$938$		0			0
$939$	−12.0000			−0.391605
$940$		0			0
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.851146	−	0.524929i	$-0.824092\pi$
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.0290288	−	0.999579i	$-0.509241\pi$
$942$	−6.06218	+	3.50000i	−0.197516	+	0.114036i
$943$	−66.6840	−	38.5000i	−2.17153	−	1.25373i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	8.00000			0.260102
$947$	−19.0526	−	11.0000i	−0.619125	−	0.357452i	0.157403	−	0.987534i	$-0.449688\pi$
$947$	−19.0526	−	11.0000i	−0.619125	−	0.357452i	−0.776528	+	0.630082i	$0.783021\pi$
$948$	−6.92820	+	4.00000i	−0.225018	+	0.129914i
$949$	−3.00000	−	5.19615i	−0.0973841	−	0.168674i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$			20.0000i			0.647864i	0.946080	+	0.323932i	$0.105005\pi$
$953$			20.0000i			0.647864i	−0.946080	+	0.323932i	$0.894995\pi$
$954$	5.50000	−	9.52628i	0.178069	−	0.308425i
$955$		0			0
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$	6.92820	+	4.00000i	0.223957	+	0.129302i
$958$			22.0000i			0.710788i
$959$	−45.0000	−	15.5885i	−1.45313	−	0.503378i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−9.52628	+	5.50000i	−0.307140	+	0.177327i
$963$	8.66025	−	5.00000i	0.279073	−	0.161123i
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$		0			0
$966$	3.50000	+	18.1865i	0.112611	+	0.585142i
$967$		−	20.0000i		−	0.643157i	−0.946883	−	0.321578i	$-0.895787\pi$
$967$		−	20.0000i		−	0.643157i	0.946883	−	0.321578i	$-0.104213\pi$
$968$	8.66025	+	5.00000i	0.278351	+	0.160706i
$969$		0			0
$970$		0			0
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	−0.238114	−	0.971237i	$-0.576529\pi$
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	0.960173	−	0.279406i	$-0.0901376\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−34.6410	−	40.0000i	−1.11054	−	1.28234i
$974$	−16.0000			−0.512673
$975$		0			0
$976$		0			0
$977$	46.7654	−	27.0000i	1.49616	−	0.863807i	0.496167	−	0.868227i	$-0.334741\pi$
$977$	46.7654	−	27.0000i	1.49616	−	0.863807i	0.999990	+	0.00442082i	$0.00140720\pi$
$978$	13.8564	+	8.00000i	0.443079	+	0.255812i
$979$	−10.0000			−0.319601
$980$		0			0
$981$	6.00000			0.191565
$982$	17.3205	+	10.0000i	0.552720	+	0.319113i
$983$	−42.4352	+	24.5000i	−1.35347	+	0.781429i	−0.988734	−	0.149681i	$-0.952175\pi$
$983$	−42.4352	+	24.5000i	−1.35347	+	0.781429i	−0.364740	+	0.931110i	$0.618842\pi$
$984$	−5.50000	−	9.52628i	−0.175334	−	0.303687i
$985$		0			0
$986$		0			0
$987$	8.66025	+	10.0000i	0.275659	+	0.318304i
$988$			3.00000i			0.0954427i
$989$	28.0000	−	48.4974i	0.890348	−	1.54213i
$990$		0			0
$991$	−11.0000	−	19.0526i	−0.349427	−	0.605224i	0.636721	−	0.771094i	$-0.280290\pi$
$991$	−11.0000	−	19.0526i	−0.349427	−	0.605224i	−0.986148	+	0.165870i	$0.946957\pi$
$992$	−1.73205	−	1.00000i	−0.0549927	−	0.0317500i
$993$		−	13.0000i		−	0.412543i
$994$	−3.00000	−	15.5885i	−0.0951542	−	0.494436i
$995$		0			0
$996$	4.00000	−	6.92820i	0.126745	−	0.219529i
$997$	12.1244	−	7.00000i	0.383982	−	0.221692i	−0.295567	−	0.955322i	$-0.595509\pi$
$997$	12.1244	−	7.00000i	0.383982	−	0.221692i	0.679549	+	0.733630i	$0.262175\pi$
$998$	−27.7128	+	16.0000i	−0.877234	+	0.506471i
$999$	−5.50000	+	9.52628i	−0.174012	+	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.i.499.2		4
5.2	odd	4		1050.2.i.b.751.1		2
5.3	odd	4		210.2.i.d.121.1	✓	2
5.4	even	2	inner	1050.2.o.i.499.1		4
7.4	even	3	inner	1050.2.o.i.949.1		4
15.8	even	4		630.2.k.c.541.1		2
20.3	even	4		1680.2.bg.g.961.1		2
35.2	odd	12		7350.2.a.cp.1.1		1
35.3	even	12		1470.2.i.m.361.1		2
35.4	even	6	inner	1050.2.o.i.949.2		4
35.12	even	12		7350.2.a.bu.1.1		1
35.13	even	4		1470.2.i.m.961.1		2
35.18	odd	12		210.2.i.d.151.1	yes	2
35.23	odd	12		1470.2.a.a.1.1		1
35.32	odd	12		1050.2.i.b.151.1		2
35.33	even	12		1470.2.a.h.1.1		1
105.23	even	12		4410.2.a.bj.1.1		1
105.53	even	12		630.2.k.c.361.1		2
105.68	odd	12		4410.2.a.ba.1.1		1
140.123	even	12		1680.2.bg.g.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.d.121.1	✓	2	5.3	odd	4
210.2.i.d.151.1	yes	2	35.18	odd	12
630.2.k.c.361.1		2	105.53	even	12
630.2.k.c.541.1		2	15.8	even	4
1050.2.i.b.151.1		2	35.32	odd	12
1050.2.i.b.751.1		2	5.2	odd	4
1050.2.o.i.499.1		4	5.4	even	2	inner
1050.2.o.i.499.2		4	1.1	even	1	trivial
1050.2.o.i.949.1		4	7.4	even	3	inner
1050.2.o.i.949.2		4	35.4	even	6	inner
1470.2.a.a.1.1		1	35.23	odd	12
1470.2.a.h.1.1		1	35.33	even	12
1470.2.i.m.361.1		2	35.3	even	12
1470.2.i.m.961.1		2	35.13	even	4
1680.2.bg.g.961.1		2	20.3	even	4
1680.2.bg.g.1201.1		2	140.123	even	12
4410.2.a.ba.1.1		1	105.68	odd	12
4410.2.a.bj.1.1		1	105.23	even	12
7350.2.a.bu.1.1		1	35.12	even	12
7350.2.a.cp.1.1		1	35.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.866025 + 0.500000i) q^{12} -1.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.866025 - 0.500000i) q^{18} +(-1.50000 + 2.59808i) q^{19} +(2.50000 + 0.866025i) q^{21} +1.00000i q^{22} +(6.06218 + 3.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{26} -1.00000i q^{27} +(-0.866025 + 2.50000i) q^{28} +8.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.866025 + 0.500000i) q^{33} +1.00000 q^{36} +(-9.52628 - 5.50000i) q^{37} +(-2.59808 + 1.50000i) q^{38} +(-0.500000 - 0.866025i) q^{39} -11.0000 q^{41} +(1.73205 + 2.00000i) q^{42} -8.00000i q^{43} +(-0.500000 + 0.866025i) q^{44} +(3.50000 + 6.06218i) q^{46} +(4.33013 + 2.50000i) q^{47} +1.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(0.866025 - 0.500000i) q^{52} +(9.52628 - 5.50000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} +3.00000i q^{57} +(6.92820 + 4.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +2.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +7.00000 q^{69} -6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(-5.50000 - 9.52628i) q^{74} -3.00000 q^{76} +(-0.866025 + 2.50000i) q^{77} -1.00000i q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-9.52628 - 5.50000i) q^{82} -8.00000i q^{83} +(0.500000 + 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +(6.92820 - 4.00000i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} +7.00000i q^{92} +(1.73205 + 1.00000i) q^{93} +(2.50000 + 4.33013i) q^{94} +(-0.500000 + 0.866025i) q^{96} -16.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 2 q^{16} - 6 q^{19} + 10 q^{21} + 2 q^{24} + 2 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{36} - 2 q^{39} - 44 q^{41} - 2 q^{44} + 14 q^{46} - 4 q^{49} + 2 q^{54} - 8 q^{56} + 8 q^{59} - 4 q^{64} + 2 q^{66} + 28 q^{69} - 24 q^{71} - 22 q^{74} - 12 q^{76} - 16 q^{79} - 2 q^{81} + 2 q^{84} + 16 q^{86} - 20 q^{89} + 8 q^{91} + 10 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 2 * q^16 - 6 * q^19 + 10 * q^21 + 2 * q^24 + 2 * q^26 + 32 * q^29 + 4 * q^31 + 4 * q^36 - 2 * q^39 - 44 * q^41 - 2 * q^44 + 14 * q^46 - 4 * q^49 + 2 * q^54 - 8 * q^56 + 8 * q^59 - 4 * q^64 + 2 * q^66 + 28 * q^69 - 24 * q^71 - 22 * q^74 - 12 * q^76 - 16 * q^79 - 2 * q^81 + 2 * q^84 + 16 * q^86 - 20 * q^89 + 8 * q^91 + 10 * q^94 - 2 * q^96 + 4 * q^99

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