LMFDB - Embedded newform 1050.2.u.b.899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(299,1050)]

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([3, 3, 5]))

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

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

chi := DirichletCharacter("1050.299");

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.u (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.899
Dual form			1050.2.u.b.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.19615 - 3.00000i) q^{11} +(0.866025 + 1.50000i) q^{12} +1.73205 q^{13} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{18} +(1.50000 - 0.866025i) q^{19} +(-4.50000 - 0.866025i) q^{21} +6.00000i q^{22} +(3.00000 + 5.19615i) q^{23} +(0.866025 - 1.50000i) q^{24} +(-0.866025 - 1.50000i) q^{26} -5.19615 q^{27} +(2.59808 + 0.500000i) q^{28} +6.00000i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-9.00000 + 5.19615i) q^{33} +3.00000 q^{36} +(6.06218 - 3.50000i) q^{37} +(-1.50000 - 0.866025i) q^{38} +(1.50000 - 2.59808i) q^{39} -10.3923 q^{41} +(1.50000 + 4.33013i) q^{42} -4.00000i q^{43} +(5.19615 - 3.00000i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-9.00000 + 5.19615i) q^{47} -1.73205 q^{48} +(-5.50000 + 4.33013i) q^{49} +(-0.866025 + 1.50000i) q^{52} +(2.59808 + 4.50000i) q^{54} +(-0.866025 - 2.50000i) q^{56} -3.00000i q^{57} +(5.19615 - 3.00000i) q^{58} +(5.19615 - 9.00000i) q^{59} +(-4.50000 + 2.59808i) q^{61} +3.46410i q^{62} +(-5.19615 + 6.00000i) q^{63} +1.00000 q^{64} +(9.00000 + 5.19615i) q^{66} +(-9.52628 - 5.50000i) q^{67} +10.3923 q^{69} -6.00000i q^{71} +(-1.50000 - 2.59808i) q^{72} +(-0.866025 + 1.50000i) q^{73} +(-6.06218 - 3.50000i) q^{74} +1.73205i q^{76} +(-3.00000 + 15.5885i) q^{77} -3.00000 q^{78} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(5.19615 + 9.00000i) q^{82} -10.3923i q^{83} +(3.00000 - 3.46410i) q^{84} +(-3.46410 + 2.00000i) q^{86} +(9.00000 + 5.19615i) q^{87} +(-5.19615 - 3.00000i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-1.50000 - 4.33013i) q^{91} -6.00000 q^{92} +(-5.19615 + 3.00000i) q^{93} +(9.00000 + 5.19615i) q^{94} +(0.866025 + 1.50000i) q^{96} +15.5885 q^{97} +(6.50000 + 2.59808i) q^{98} +18.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 6 q^{9} - 2 q^{16} - 6 q^{18} + 6 q^{19} - 18 q^{21} + 12 q^{23} - 12 q^{31} - 2 q^{32} - 36 q^{33} + 12 q^{36} - 6 q^{38} + 6 q^{39} + 6 q^{42} + 12 q^{46} - 36 q^{47} - 22 q^{49} - 18 q^{61} + 4 q^{64} + 36 q^{66} - 6 q^{72} - 12 q^{77} - 12 q^{78} - 2 q^{79} - 18 q^{81} + 12 q^{84} + 36 q^{87} - 6 q^{91} - 24 q^{92} + 36 q^{94} + 26 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 6 * q^9 - 2 * q^16 - 6 * q^18 + 6 * q^19 - 18 * q^21 + 12 * q^23 - 12 * q^31 - 2 * q^32 - 36 * q^33 + 12 * q^36 - 6 * q^38 + 6 * q^39 + 6 * q^42 + 12 * q^46 - 36 * q^47 - 22 * q^49 - 18 * q^61 + 4 * q^64 + 36 * q^66 - 6 * q^72 - 12 * q^77 - 12 * q^78 - 2 * q^79 - 18 * q^81 + 12 * q^84 + 36 * q^87 - 6 * q^91 - 24 * q^92 + 36 * q^94 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	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
$6$	−1.73205			−0.707107
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	1.00000			0.353553
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−5.19615	−	3.00000i	−1.56670	−	0.904534i	−0.996550	−	0.0829925i	$-0.973552\pi$
$11$	−5.19615	−	3.00000i	−1.56670	−	0.904534i	−0.570149	−	0.821541i	$-0.693114\pi$
$12$	0.866025	+	1.50000i	0.250000	+	0.433013i
$13$	1.73205			0.480384			0.240192	−	0.970725i	$-0.422790\pi$
$13$	1.73205			0.480384			0.240192	+	0.970725i	$0.422790\pi$
$14$	−1.73205	+	2.00000i	−0.462910	+	0.534522i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	−0.317970	−	0.948101i	$-0.603001\pi$
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	0.662094	+	0.749421i	$0.269668\pi$
$20$		0			0
$21$	−4.50000	−	0.866025i	−0.981981	−	0.188982i
$22$			6.00000i			1.27920i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	0.866025	−	1.50000i	0.176777	−	0.306186i
$25$		0			0
$26$	−0.866025	−	1.50000i	−0.169842	−	0.294174i
$27$	−5.19615			−1.00000
$28$	2.59808	+	0.500000i	0.490990	+	0.0944911i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		0			0
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−9.00000	+	5.19615i	−1.56670	+	0.904534i
$34$		0			0
$35$		0			0
$36$	3.00000			0.500000
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.0893706	−	0.995998i	$-0.471514\pi$
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.907245	+	0.420602i	$0.138181\pi$
$38$	−1.50000	−	0.866025i	−0.243332	−	0.140488i
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$		0			0
$41$	−10.3923			−1.62301			−0.811503	−	0.584349i	$-0.801350\pi$
$41$	−10.3923			−1.62301			−0.811503	+	0.584349i	$0.801350\pi$
$42$	1.50000	+	4.33013i	0.231455	+	0.668153i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	5.19615	−	3.00000i	0.783349	−	0.452267i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−9.00000	+	5.19615i	−1.31278	+	0.757937i	−0.982556	−	0.185964i	$-0.940459\pi$
$47$	−9.00000	+	5.19615i	−1.31278	+	0.757937i	−0.330228	+	0.943901i	$0.607126\pi$
$48$	−1.73205			−0.250000
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$	−0.866025	+	1.50000i	−0.120096	+	0.208013i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	2.59808	+	4.50000i	0.353553	+	0.612372i
$55$		0			0
$56$	−0.866025	−	2.50000i	−0.115728	−	0.334077i
$57$		−	3.00000i		−	0.397360i
$58$	5.19615	−	3.00000i	0.682288	−	0.393919i
$59$	5.19615	−	9.00000i	0.676481	−	1.17170i	−0.299552	−	0.954080i	$-0.596837\pi$
$59$	5.19615	−	9.00000i	0.676481	−	1.17170i	0.976034	−	0.217620i	$-0.0698294\pi$
$60$		0			0
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	−0.759608	−	0.650381i	$-0.774609\pi$
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	0.183442	+	0.983030i	$0.441276\pi$
$62$			3.46410i			0.439941i
$63$	−5.19615	+	6.00000i	−0.654654	+	0.755929i
$64$	1.00000			0.125000
$65$		0			0
$66$	9.00000	+	5.19615i	1.10782	+	0.639602i
$67$	−9.52628	−	5.50000i	−1.16382	−	0.671932i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$	−9.52628	−	5.50000i	−1.16382	−	0.671932i	−0.952217	+	0.305424i	$0.901202\pi$
$68$		0			0
$69$	10.3923			1.25109
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−0.866025	+	1.50000i	−0.101361	+	0.175562i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$	−0.866025	+	1.50000i	−0.101361	+	0.175562i	0.810885	+	0.585206i	$0.198986\pi$
$74$	−6.06218	−	3.50000i	−0.704714	−	0.406867i
$75$		0			0
$76$			1.73205i			0.198680i
$77$	−3.00000	+	15.5885i	−0.341882	+	1.77647i
$78$	−3.00000			−0.339683
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.19615	+	9.00000i	0.573819	+	0.993884i
$83$		−	10.3923i		−	1.14070i	−0.821401	−	0.570352i	$-0.806807\pi$
$83$		−	10.3923i		−	1.14070i	0.821401	−	0.570352i	$-0.193193\pi$
$84$	3.00000	−	3.46410i	0.327327	−	0.377964i
$85$		0			0
$86$	−3.46410	+	2.00000i	−0.373544	+	0.215666i
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$	−5.19615	−	3.00000i	−0.553912	−	0.319801i
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		0			0
$91$	−1.50000	−	4.33013i	−0.157243	−	0.453921i
$92$	−6.00000			−0.625543
$93$	−5.19615	+	3.00000i	−0.538816	+	0.311086i
$94$	9.00000	+	5.19615i	0.928279	+	0.535942i
$95$		0			0
$96$	0.866025	+	1.50000i	0.0883883	+	0.153093i
$97$	15.5885			1.58277			0.791384	−	0.611319i	$-0.209361\pi$
$97$	15.5885			1.58277			0.791384	+	0.611319i	$0.209361\pi$
$98$	6.50000	+	2.59808i	0.656599	+	0.262445i
$99$			18.0000i			1.80907i
$100$		0			0
$101$	5.19615	−	9.00000i	0.517036	−	0.895533i	−0.482768	−	0.875748i	$-0.660368\pi$
$101$	5.19615	−	9.00000i	0.517036	−	0.895533i	0.999804	−	0.0197851i	$-0.00629819\pi$
$102$		0			0
$103$	7.79423	+	13.5000i	0.767988	+	1.33019i	0.938652	+	0.344865i	$0.112075\pi$
$103$	7.79423	+	13.5000i	0.767988	+	1.33019i	−0.170664	+	0.985329i	$0.554591\pi$
$104$	1.73205			0.169842
$105$		0			0
$106$		0			0
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		0			0
$111$		−	12.1244i		−	1.15079i
$112$	−1.73205	+	2.00000i	−0.163663	+	0.188982i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	−2.59808	+	1.50000i	−0.243332	+	0.140488i
$115$		0			0
$116$	−5.19615	−	3.00000i	−0.482451	−	0.278543i
$117$	−2.59808	−	4.50000i	−0.240192	−	0.416025i
$118$	−10.3923			−0.956689
$119$		0			0
$120$		0			0
$121$	12.5000	+	21.6506i	1.13636	+	1.96824i
$122$	4.50000	+	2.59808i	0.407411	+	0.235219i
$123$	−9.00000	+	15.5885i	−0.811503	+	1.40556i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$		0			0
$126$	7.79423	+	1.50000i	0.694365	+	0.133631i
$127$		−	19.0000i		−	1.68598i	−0.537931	−	0.842989i	$-0.680794\pi$
$127$		−	19.0000i		−	1.68598i	0.537931	−	0.842989i	$-0.319206\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.00000	−	3.46410i	−0.528271	−	0.304997i
$130$		0			0
$131$	5.19615	+	9.00000i	0.453990	+	0.786334i	0.998630	−	0.0523366i	$-0.0166669\pi$
$131$	5.19615	+	9.00000i	0.453990	+	0.786334i	−0.544640	+	0.838670i	$0.683334\pi$
$132$		−	10.3923i		−	0.904534i
$133$	−3.46410	−	3.00000i	−0.300376	−	0.260133i
$134$			11.0000i			0.950255i
$135$		0			0
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$	−5.19615	−	9.00000i	−0.442326	−	0.766131i
$139$			5.19615i			0.440732i	0.975417	+	0.220366i	$0.0707252\pi$
$139$			5.19615i			0.440732i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$			18.0000i			1.51587i
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$	−9.00000	−	5.19615i	−0.752618	−	0.434524i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$		0			0
$146$	1.73205			0.143346
$147$	1.73205	+	12.0000i	0.142857	+	0.989743i
$148$			7.00000i			0.575396i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$		0			0
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	−0.279554	−	0.960130i	$-0.590186\pi$
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	0.971274	−	0.237964i	$-0.0764802\pi$
$152$	1.50000	−	0.866025i	0.121666	−	0.0702439i
$153$		0			0
$154$	15.0000	−	5.19615i	1.20873	−	0.418718i
$155$		0			0
$156$	1.50000	+	2.59808i	0.120096	+	0.208013i
$157$	−0.866025	+	1.50000i	−0.0691164	+	0.119713i	−0.898513	−	0.438948i	$-0.855351\pi$
$157$	−0.866025	+	1.50000i	−0.0691164	+	0.119713i	0.829396	+	0.558661i	$0.188685\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$		0			0
$160$		0			0
$161$	10.3923	−	12.0000i	0.819028	−	0.945732i
$162$	9.00000			0.707107
$163$	0.866025	−	0.500000i	0.0678323	−	0.0391630i	−0.465700	−	0.884943i	$-0.654198\pi$
$163$	0.866025	−	0.500000i	0.0678323	−	0.0391630i	0.533533	+	0.845780i	$0.320864\pi$
$164$	5.19615	−	9.00000i	0.405751	−	0.702782i
$165$		0			0
$166$	−9.00000	+	5.19615i	−0.698535	+	0.403300i
$167$		−	20.7846i		−	1.60836i	−0.594385	−	0.804181i	$-0.702604\pi$
$167$		−	20.7846i		−	1.60836i	0.594385	−	0.804181i	$-0.297396\pi$
$168$	−4.50000	−	0.866025i	−0.347183	−	0.0668153i
$169$	−10.0000			−0.769231
$170$		0			0
$171$	−4.50000	−	2.59808i	−0.344124	−	0.198680i
$172$	3.46410	+	2.00000i	0.264135	+	0.152499i
$173$	18.0000	−	10.3923i	1.36851	−	0.790112i	0.377776	−	0.925897i	$-0.376689\pi$
$173$	18.0000	−	10.3923i	1.36851	−	0.790112i	0.990738	+	0.135785i	$0.0433555\pi$
$174$		−	10.3923i		−	0.787839i
$175$		0			0
$176$			6.00000i			0.452267i
$177$	−9.00000	−	15.5885i	−0.676481	−	1.17170i
$178$	−5.19615	+	9.00000i	−0.389468	+	0.674579i
$179$	−15.5885	−	9.00000i	−1.16514	−	0.672692i	−0.212607	−	0.977138i	$-0.568195\pi$
$179$	−15.5885	−	9.00000i	−1.16514	−	0.672692i	−0.952529	+	0.304446i	$0.901529\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−3.00000	+	3.46410i	−0.222375	+	0.256776i
$183$			9.00000i			0.665299i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$	5.19615	+	3.00000i	0.381000	+	0.219971i
$187$		0			0
$188$		−	10.3923i		−	0.757937i
$189$	4.50000	+	12.9904i	0.327327	+	0.944911i
$190$		0			0
$191$	−15.5885	+	9.00000i	−1.12794	+	0.651217i	−0.943416	−	0.331611i	$-0.892408\pi$
$191$	−15.5885	+	9.00000i	−1.12794	+	0.651217i	−0.184525	+	0.982828i	$0.559075\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	−0.561041	+	0.827788i	$0.689599\pi$
$194$	−7.79423	−	13.5000i	−0.559593	−	0.969244i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	15.5885	−	9.00000i	1.10782	−	0.639602i
$199$	−10.5000	−	6.06218i	−0.744325	−	0.429736i	0.0793146	−	0.996850i	$-0.474727\pi$
$199$	−10.5000	−	6.06218i	−0.744325	−	0.429736i	−0.823640	+	0.567113i	$0.808060\pi$
$200$		0			0
$201$	−16.5000	+	9.52628i	−1.16382	+	0.671932i
$202$	−10.3923			−0.731200
$203$	15.0000	−	5.19615i	1.05279	−	0.364698i
$204$		0			0
$205$		0			0
$206$	7.79423	−	13.5000i	0.543050	−	0.940590i
$207$	9.00000	−	15.5885i	0.625543	−	1.08347i
$208$	−0.866025	−	1.50000i	−0.0600481	−	0.104006i
$209$	−10.3923			−0.718851
$210$		0			0
$211$	−11.0000			−0.757271			−0.378636	−	0.925546i	$-0.623607\pi$
$211$	−11.0000			−0.757271			−0.378636	+	0.925546i	$0.623607\pi$
$212$		0			0
$213$	−9.00000	−	5.19615i	−0.616670	−	0.356034i
$214$		0			0
$215$		0			0
$216$	−5.19615			−0.353553
$217$	−1.73205	+	9.00000i	−0.117579	+	0.610960i
$218$	11.0000			0.745014
$219$	1.50000	+	2.59808i	0.101361	+	0.175562i
$220$		0			0
$221$		0			0
$222$	−10.5000	+	6.06218i	−0.704714	+	0.406867i
$223$	8.66025			0.579934			0.289967	−	0.957037i	$-0.406356\pi$
$223$	8.66025			0.579934			0.289967	+	0.957037i	$0.406356\pi$
$224$	2.59808	+	0.500000i	0.173591	+	0.0334077i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	0.767999	−	0.640451i	$-0.221253\pi$
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	−0.170648	+	0.985332i	$0.554586\pi$
$228$	2.59808	+	1.50000i	0.172062	+	0.0993399i
$229$	13.5000	−	7.79423i	0.892105	−	0.515057i	0.0174746	−	0.999847i	$-0.494437\pi$
$229$	13.5000	−	7.79423i	0.892105	−	0.515057i	0.874630	+	0.484790i	$0.161104\pi$
$230$		0			0
$231$	20.7846	+	18.0000i	1.36753	+	1.18431i
$232$			6.00000i			0.393919i
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	−2.59808	+	4.50000i	−0.169842	+	0.294174i
$235$		0			0
$236$	5.19615	+	9.00000i	0.338241	+	0.585850i
$237$	−1.73205			−0.112509
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	7.50000	+	4.33013i	0.483117	+	0.278928i	0.721715	−	0.692191i	$-0.243354\pi$
$241$	7.50000	+	4.33013i	0.483117	+	0.278928i	−0.238597	+	0.971119i	$0.576688\pi$
$242$	12.5000	−	21.6506i	0.803530	−	1.39176i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		−	5.19615i		−	0.332650i
$245$		0			0
$246$	18.0000			1.14764
$247$	2.59808	−	1.50000i	0.165312	−	0.0954427i
$248$	−3.00000	−	1.73205i	−0.190500	−	0.109985i
$249$	−15.5885	−	9.00000i	−0.987878	−	0.570352i
$250$		0			0
$251$	20.7846			1.31191			0.655956	−	0.754799i	$-0.272265\pi$
$251$	20.7846			1.31191			0.655956	+	0.754799i	$0.272265\pi$
$252$	−2.59808	−	7.50000i	−0.163663	−	0.472456i
$253$		−	36.0000i		−	2.26330i
$254$	−16.4545	+	9.50000i	−1.03245	+	0.596083i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$			6.92820i			0.431331i
$259$	−14.0000	−	12.1244i	−0.869918	−	0.753371i
$260$		0			0
$261$	15.5885	−	9.00000i	0.964901	−	0.557086i
$262$	5.19615	−	9.00000i	0.321019	−	0.556022i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$	−9.00000	+	5.19615i	−0.553912	+	0.319801i
$265$		0			0
$266$	−0.866025	+	4.50000i	−0.0530994	+	0.275913i
$267$	−18.0000			−1.10158
$268$	9.52628	−	5.50000i	0.581910	−	0.335966i
$269$	10.3923	−	18.0000i	0.633630	−	1.09748i	−0.353174	−	0.935558i	$-0.614898\pi$
$269$	10.3923	−	18.0000i	0.633630	−	1.09748i	0.986804	−	0.161922i	$-0.0517692\pi$
$270$		0			0
$271$	15.0000	−	8.66025i	0.911185	−	0.526073i	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	15.0000	−	8.66025i	0.911185	−	0.526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$		0			0
$273$	−7.79423	−	1.50000i	−0.471728	−	0.0907841i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	−5.19615	+	9.00000i	−0.312772	+	0.541736i
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	0.525792	−	0.850613i	$-0.323769\pi$
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	−0.473757	+	0.880656i	$0.657103\pi$
$278$	4.50000	−	2.59808i	0.269892	−	0.155822i
$279$			10.3923i			0.622171i
$280$		0			0
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$	15.5885	−	9.00000i	0.928279	−	0.535942i
$283$	7.79423	−	13.5000i	0.463319	−	0.802492i	−0.535805	−	0.844342i	$-0.679992\pi$
$283$	7.79423	−	13.5000i	0.463319	−	0.802492i	0.999124	+	0.0418500i	$0.0133252\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$		0			0
$286$			10.3923i			0.614510i
$287$	9.00000	+	25.9808i	0.531253	+	1.53360i
$288$	3.00000			0.176777
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	13.5000	−	23.3827i	0.791384	−	1.37072i
$292$	−0.866025	−	1.50000i	−0.0506803	−	0.0877809i
$293$			10.3923i			0.607125i	0.952812	+	0.303562i	$0.0981761\pi$
$293$			10.3923i			0.607125i	−0.952812	+	0.303562i	$0.901824\pi$
$294$	9.52628	−	7.50000i	0.555584	−	0.437409i
$295$		0			0
$296$	6.06218	−	3.50000i	0.352357	−	0.203433i
$297$	27.0000	+	15.5885i	1.56670	+	0.904534i
$298$	5.19615	+	3.00000i	0.301005	+	0.173785i
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	−10.0000	+	3.46410i	−0.576390	+	0.199667i
$302$	−17.0000			−0.978240
$303$	−9.00000	−	15.5885i	−0.517036	−	0.895533i
$304$	−1.50000	−	0.866025i	−0.0860309	−	0.0496700i
$305$		0			0
$306$		0			0
$307$	−24.2487			−1.38395			−0.691974	−	0.721923i	$-0.743259\pi$
$307$	−24.2487			−1.38395			−0.691974	+	0.721923i	$0.743259\pi$
$308$	−12.0000	−	10.3923i	−0.683763	−	0.592157i
$309$	27.0000			1.53598
$310$		0			0
$311$	10.3923	−	18.0000i	0.589294	−	1.02069i	−0.405032	−	0.914303i	$-0.632739\pi$
$311$	10.3923	−	18.0000i	0.589294	−	1.02069i	0.994325	−	0.106384i	$-0.0339272\pi$
$312$	1.50000	−	2.59808i	0.0849208	−	0.147087i
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	1.73205			0.0977453
$315$		0			0
$316$	1.00000			0.0562544
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$		0			0
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$		0			0
$321$		0			0
$322$	−15.5885	−	3.00000i	−0.868711	−	0.167183i
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	−0.866025	−	0.500000i	−0.0479647	−	0.0276924i
$327$	9.52628	+	16.5000i	0.526804	+	0.912452i
$328$	−10.3923			−0.573819
$329$	20.7846	+	18.0000i	1.14589	+	0.992372i
$330$		0			0
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	0.926516	−	0.376254i	$-0.122788\pi$
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	−0.789104	+	0.614260i	$0.789455\pi$
$332$	9.00000	+	5.19615i	0.493939	+	0.285176i
$333$	−18.1865	−	10.5000i	−0.996616	−	0.575396i
$334$	−18.0000	+	10.3923i	−0.984916	+	0.568642i
$335$		0			0
$336$	1.50000	+	4.33013i	0.0818317	+	0.236228i
$337$			22.0000i			1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$			22.0000i			1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$	5.00000	+	8.66025i	0.271964	+	0.471056i
$339$	10.3923	−	18.0000i	0.564433	−	0.977626i
$340$		0			0
$341$	10.3923	+	18.0000i	0.562775	+	0.974755i
$342$			5.19615i			0.280976i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		−	4.00000i		−	0.215666i
$345$		0			0
$346$	−18.0000	−	10.3923i	−0.967686	−	0.558694i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	−9.00000	+	5.19615i	−0.482451	+	0.278543i
$349$			27.7128i			1.48343i	0.670714	+	0.741716i	$0.265988\pi$
$349$			27.7128i			1.48343i	−0.670714	+	0.741716i	$0.734012\pi$
$350$		0			0
$351$	−9.00000			−0.480384
$352$	5.19615	−	3.00000i	0.276956	−	0.159901i
$353$	−9.00000	−	5.19615i	−0.479022	−	0.276563i	0.240987	−	0.970528i	$-0.422529\pi$
$353$	−9.00000	−	5.19615i	−0.479022	−	0.276563i	−0.720009	+	0.693965i	$0.755862\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$		0			0
$356$	10.3923			0.550791
$357$		0			0
$358$			18.0000i			0.951330i
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	−0.356572	−	0.934268i	$-0.616054\pi$
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	0.630814	+	0.775934i	$0.282721\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$		0			0
$363$	43.3013			2.27273
$364$	4.50000	+	0.866025i	0.235864	+	0.0453921i
$365$		0			0
$366$	7.79423	−	4.50000i	0.407411	−	0.235219i
$367$	5.19615	−	9.00000i	0.271237	−	0.469796i	−0.697942	−	0.716154i	$-0.745901\pi$
$367$	5.19615	−	9.00000i	0.271237	−	0.469796i	0.969179	+	0.246358i	$0.0792340\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	15.5885	+	27.0000i	0.811503	+	1.40556i
$370$		0			0
$371$		0			0
$372$		−	6.00000i		−	0.311086i
$373$	−25.1147	+	14.5000i	−1.30039	+	0.750782i	−0.980471	−	0.196663i	$-0.936990\pi$
$373$	−25.1147	+	14.5000i	−1.30039	+	0.750782i	−0.319921	+	0.947444i	$0.603656\pi$
$374$		0			0
$375$		0			0
$376$	−9.00000	+	5.19615i	−0.464140	+	0.267971i
$377$			10.3923i			0.535231i
$378$	9.00000	−	10.3923i	0.462910	−	0.534522i
$379$	35.0000			1.79783			0.898915	−	0.438124i	$-0.144357\pi$
$379$	35.0000			1.79783			0.898915	+	0.438124i	$0.144357\pi$
$380$		0			0
$381$	−28.5000	−	16.4545i	−1.46010	−	0.842989i
$382$	15.5885	+	9.00000i	0.797575	+	0.460480i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−1.73205			−0.0883883
$385$		0			0
$386$			2.00000i			0.101797i
$387$	−10.3923	+	6.00000i	−0.528271	+	0.304997i
$388$	−7.79423	+	13.5000i	−0.395692	+	0.685359i
$389$	−10.3923	−	6.00000i	−0.526911	−	0.304212i	0.212847	−	0.977086i	$-0.431726\pi$
$389$	−10.3923	−	6.00000i	−0.526911	−	0.304212i	−0.739758	+	0.672874i	$0.765060\pi$
$390$		0			0
$391$		0			0
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$	18.0000			0.907980
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	−15.5885	−	9.00000i	−0.783349	−	0.452267i
$397$	−6.92820	−	12.0000i	−0.347717	−	0.602263i	0.638127	−	0.769931i	$-0.279710\pi$
$397$	−6.92820	−	12.0000i	−0.347717	−	0.602263i	−0.985843	+	0.167668i	$0.946376\pi$
$398$			12.1244i			0.607739i
$399$	−7.50000	+	2.59808i	−0.375470	+	0.130066i
$400$		0			0
$401$	−20.7846	+	12.0000i	−1.03793	+	0.599251i	−0.919247	−	0.393680i	$-0.871202\pi$
$401$	−20.7846	+	12.0000i	−1.03793	+	0.599251i	−0.118686	+	0.992932i	$0.537868\pi$
$402$	16.5000	+	9.52628i	0.822945	+	0.475128i
$403$	−5.19615	−	3.00000i	−0.258839	−	0.149441i
$404$	5.19615	+	9.00000i	0.258518	+	0.447767i
$405$		0			0
$406$	−12.0000	−	10.3923i	−0.595550	−	0.515761i
$407$	−42.0000			−2.08186
$408$		0			0
$409$	−10.5000	−	6.06218i	−0.519192	−	0.299755i	0.217412	−	0.976080i	$-0.430238\pi$
$409$	−10.5000	−	6.06218i	−0.519192	−	0.299755i	−0.736604	+	0.676324i	$0.763572\pi$
$410$		0			0
$411$	−15.5885	−	27.0000i	−0.768922	−	1.33181i
$412$	−15.5885			−0.767988
$413$	−27.0000	−	5.19615i	−1.32858	−	0.255686i
$414$	−18.0000			−0.884652
$415$		0			0
$416$	−0.866025	+	1.50000i	−0.0424604	+	0.0735436i
$417$	7.79423	+	4.50000i	0.381685	+	0.220366i
$418$	5.19615	+	9.00000i	0.254152	+	0.440204i
$419$	−20.7846			−1.01539			−0.507697	−	0.861536i	$-0.669503\pi$
$419$	−20.7846			−1.01539			−0.507697	+	0.861536i	$0.669503\pi$
$420$		0			0
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$	5.50000	+	9.52628i	0.267736	+	0.463732i
$423$	27.0000	+	15.5885i	1.31278	+	0.757937i
$424$		0			0
$425$		0			0
$426$			10.3923i			0.503509i
$427$	10.3923	+	9.00000i	0.502919	+	0.435541i
$428$		0			0
$429$	−15.5885	+	9.00000i	−0.752618	+	0.434524i
$430$		0			0
$431$	−31.1769	−	18.0000i	−1.50174	−	0.867029i	−0.999998	−	0.00201168i	$-0.999360\pi$
$431$	−31.1769	−	18.0000i	−1.50174	−	0.867029i	−0.501741	−	0.865018i	$-0.667307\pi$
$432$	2.59808	+	4.50000i	0.125000	+	0.216506i
$433$	−34.6410			−1.66474			−0.832370	−	0.554220i	$-0.813017\pi$
$433$	−34.6410			−1.66474			−0.832370	+	0.554220i	$0.813017\pi$
$434$	8.66025	−	3.00000i	0.415705	−	0.144005i
$435$		0			0
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	9.00000	+	5.19615i	0.430528	+	0.248566i
$438$	1.50000	−	2.59808i	0.0716728	−	0.124141i
$439$	28.5000	−	16.4545i	1.36023	−	0.785330i	0.370576	−	0.928802i	$-0.379160\pi$
$439$	28.5000	−	16.4545i	1.36023	−	0.785330i	0.989654	+	0.143472i	$0.0458268\pi$
$440$		0			0
$441$	19.5000	+	7.79423i	0.928571	+	0.371154i
$442$		0			0
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$	10.5000	+	6.06218i	0.498308	+	0.287698i
$445$		0			0
$446$	−4.33013	−	7.50000i	−0.205037	−	0.355135i
$447$			10.3923i			0.491539i
$448$	−0.866025	−	2.50000i	−0.0409159	−	0.118114i
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$		0			0
$451$	54.0000	+	31.1769i	2.54276	+	1.46806i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	−14.7224	−	25.5000i	−0.691720	−	1.19809i
$454$		−	10.3923i		−	0.487735i
$455$		0			0
$456$		−	3.00000i		−	0.140488i
$457$	−4.33013	+	2.50000i	−0.202555	+	0.116945i	−0.597847	−	0.801611i	$-0.703977\pi$
$457$	−4.33013	+	2.50000i	−0.202555	+	0.116945i	0.395292	+	0.918556i	$0.370643\pi$
$458$	−13.5000	−	7.79423i	−0.630814	−	0.364200i
$459$		0			0
$460$		0			0
$461$	−10.3923			−0.484018			−0.242009	−	0.970274i	$-0.577806\pi$
$461$	−10.3923			−0.484018			−0.242009	+	0.970274i	$0.577806\pi$
$462$	5.19615	−	27.0000i	0.241747	−	1.25615i
$463$		−	11.0000i		−	0.511213i	−0.966781	−	0.255607i	$-0.917725\pi$
$463$		−	11.0000i		−	0.511213i	0.966781	−	0.255607i	$-0.0822752\pi$
$464$	5.19615	−	3.00000i	0.241225	−	0.139272i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	18.0000	−	10.3923i	0.832941	−	0.480899i	−0.0219178	−	0.999760i	$-0.506977\pi$
$467$	18.0000	−	10.3923i	0.832941	−	0.480899i	0.854858	+	0.518861i	$0.173644\pi$
$468$	5.19615			0.240192
$469$	−5.50000	+	28.5788i	−0.253966	+	1.31965i
$470$		0			0
$471$	1.50000	+	2.59808i	0.0691164	+	0.119713i
$472$	5.19615	−	9.00000i	0.239172	−	0.414259i
$473$	−12.0000	+	20.7846i	−0.551761	+	0.955677i
$474$	0.866025	+	1.50000i	0.0397779	+	0.0688973i
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.5885	+	27.0000i	−0.712255	+	1.23366i	0.251754	+	0.967791i	$0.418993\pi$
$479$	−15.5885	+	27.0000i	−0.712255	+	1.23366i	−0.964009	+	0.265870i	$0.914341\pi$
$480$		0			0
$481$	10.5000	−	6.06218i	0.478759	−	0.276412i
$482$		−	8.66025i		−	0.394464i
$483$	−9.00000	−	25.9808i	−0.409514	−	1.18217i
$484$	−25.0000			−1.13636
$485$		0			0
$486$	7.79423	−	13.5000i	0.353553	−	0.612372i
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	−4.50000	+	2.59808i	−0.203705	+	0.117609i
$489$		−	1.73205i		−	0.0783260i
$490$		0			0
$491$			12.0000i			0.541552i	0.962642	+	0.270776i	$0.0872803\pi$
$491$			12.0000i			0.541552i	−0.962642	+	0.270776i	$0.912720\pi$
$492$	−9.00000	−	15.5885i	−0.405751	−	0.702782i
$493$		0			0
$494$	−2.59808	−	1.50000i	−0.116893	−	0.0674882i
$495$		0			0
$496$			3.46410i			0.155543i
$497$	−15.0000	+	5.19615i	−0.672842	+	0.233079i
$498$			18.0000i			0.806599i
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$		0			0
$501$	−31.1769	−	18.0000i	−1.39288	−	0.804181i
$502$	−10.3923	−	18.0000i	−0.463831	−	0.803379i
$503$			31.1769i			1.39011i	0.718957	+	0.695055i	$0.244620\pi$
$503$			31.1769i			1.39011i	−0.718957	+	0.695055i	$0.755380\pi$
$504$	−5.19615	+	6.00000i	−0.231455	+	0.267261i
$505$		0			0
$506$	−31.1769	+	18.0000i	−1.38598	+	0.800198i
$507$	−8.66025	+	15.0000i	−0.384615	+	0.666173i
$508$	16.4545	+	9.50000i	0.730050	+	0.421494i
$509$	5.19615	+	9.00000i	0.230315	+	0.398918i	0.957901	−	0.287099i	$-0.0926909\pi$
$509$	5.19615	+	9.00000i	0.230315	+	0.398918i	−0.727586	+	0.686017i	$0.759358\pi$
$510$		0			0
$511$	4.50000	+	0.866025i	0.199068	+	0.0383107i
$512$	1.00000			0.0441942
$513$	−7.79423	+	4.50000i	−0.344124	+	0.198680i
$514$		0			0
$515$		0			0
$516$	6.00000	−	3.46410i	0.264135	−	0.152499i
$517$	62.3538			2.74232
$518$	−3.50000	+	18.1865i	−0.153781	+	0.799070i
$519$		−	36.0000i		−	1.58022i
$520$		0			0
$521$	15.5885	−	27.0000i	0.682943	−	1.18289i	−0.291136	−	0.956682i	$-0.594033\pi$
$521$	15.5885	−	27.0000i	0.682943	−	1.18289i	0.974079	−	0.226210i	$-0.0726335\pi$
$522$	−15.5885	−	9.00000i	−0.682288	−	0.393919i
$523$	−1.73205	−	3.00000i	−0.0757373	−	0.131181i	0.825669	−	0.564154i	$-0.190798\pi$
$523$	−1.73205	−	3.00000i	−0.0757373	−	0.131181i	−0.901407	+	0.432973i	$0.857464\pi$
$524$	−10.3923			−0.453990
$525$		0			0
$526$	−12.0000			−0.523225
$527$		0			0
$528$	9.00000	+	5.19615i	0.391675	+	0.226134i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−31.1769			−1.35296
$532$	4.33013	−	1.50000i	0.187735	−	0.0650332i
$533$	−18.0000			−0.779667
$534$	9.00000	+	15.5885i	0.389468	+	0.674579i
$535$		0			0
$536$	−9.52628	−	5.50000i	−0.411473	−	0.237564i
$537$	−27.0000	+	15.5885i	−1.16514	+	0.672692i
$538$	−20.7846			−0.896088
$539$	41.5692	−	6.00000i	1.79051	−	0.258438i
$540$		0			0
$541$	0.500000	+	0.866025i	0.0214967	+	0.0372333i	0.876574	−	0.481268i	$-0.159824\pi$
$541$	0.500000	+	0.866025i	0.0214967	+	0.0372333i	−0.855077	+	0.518501i	$0.826490\pi$
$542$	−15.0000	−	8.66025i	−0.644305	−	0.371990i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	2.59808	+	7.50000i	0.111187	+	0.320970i
$547$		−	4.00000i		−	0.171028i	−0.996337	−	0.0855138i	$-0.972747\pi$
$547$		−	4.00000i		−	0.171028i	0.996337	−	0.0855138i	$-0.0272532\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	13.5000	+	7.79423i	0.576166	+	0.332650i
$550$		0			0
$551$	5.19615	+	9.00000i	0.221364	+	0.383413i
$552$	10.3923			0.442326
$553$	−1.73205	+	2.00000i	−0.0736543	+	0.0850487i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	−4.50000	−	2.59808i	−0.190843	−	0.110183i
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$	9.00000	−	5.19615i	0.381000	−	0.219971i
$559$		−	6.92820i		−	0.293032i
$560$		0			0
$561$		0			0
$562$	10.3923	−	6.00000i	0.438373	−	0.253095i
$563$	−36.0000	−	20.7846i	−1.51722	−	0.875967i	−0.999795	−	0.0202376i	$-0.993558\pi$
$563$	−36.0000	−	20.7846i	−1.51722	−	0.875967i	−0.517424	−	0.855729i	$-0.673109\pi$
$564$	−15.5885	−	9.00000i	−0.656392	−	0.378968i
$565$		0			0
$566$	−15.5885			−0.655232
$567$	23.3827	+	4.50000i	0.981981	+	0.188982i
$568$		−	6.00000i		−	0.251754i
$569$	5.19615	−	3.00000i	0.217834	−	0.125767i	−0.387113	−	0.922032i	$-0.626528\pi$
$569$	5.19615	−	3.00000i	0.217834	−	0.125767i	0.604947	+	0.796266i	$0.293194\pi$
$570$		0			0
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	0.384957	+	0.922934i	$0.374216\pi$
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	−0.991763	+	0.128085i	$0.959117\pi$
$572$	9.00000	−	5.19615i	0.376309	−	0.217262i
$573$			31.1769i			1.30243i
$574$	18.0000	−	20.7846i	0.751305	−	0.867533i
$575$		0			0
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	−17.3205	+	30.0000i	−0.721062	+	1.24892i	0.239512	+	0.970893i	$0.423012\pi$
$577$	−17.3205	+	30.0000i	−0.721062	+	1.24892i	−0.960574	+	0.278023i	$0.910321\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$	−3.00000	+	1.73205i	−0.124676	+	0.0719816i
$580$		0			0
$581$	−25.9808	+	9.00000i	−1.07786	+	0.373383i
$582$	−27.0000			−1.11919
$583$		0			0
$584$	−0.866025	+	1.50000i	−0.0358364	+	0.0620704i
$585$		0			0
$586$	9.00000	−	5.19615i	0.371787	−	0.214651i
$587$			10.3923i			0.428936i	0.976731	+	0.214468i	$0.0688018\pi$
$587$			10.3923i			0.428936i	−0.976731	+	0.214468i	$0.931198\pi$
$588$	−11.2583	−	4.50000i	−0.464286	−	0.185577i
$589$	−6.00000			−0.247226
$590$		0			0
$591$	−5.19615	+	9.00000i	−0.213741	+	0.370211i
$592$	−6.06218	−	3.50000i	−0.249154	−	0.143849i
$593$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$593$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$594$		−	31.1769i		−	1.27920i
$595$		0			0
$596$		−	6.00000i		−	0.245770i
$597$	−18.1865	+	10.5000i	−0.744325	+	0.429736i
$598$	5.19615	−	9.00000i	0.212486	−	0.368037i
$599$	20.7846	+	12.0000i	0.849236	+	0.490307i	0.860393	−	0.509631i	$-0.170218\pi$
$599$	20.7846	+	12.0000i	0.849236	+	0.490307i	−0.0111569	+	0.999938i	$0.503551\pi$
$600$		0			0
$601$		−	36.3731i		−	1.48369i	−0.670572	−	0.741844i	$-0.733951\pi$
$601$		−	36.3731i		−	1.48369i	0.670572	−	0.741844i	$-0.266049\pi$
$602$	8.00000	+	6.92820i	0.326056	+	0.282372i
$603$			33.0000i			1.34386i
$604$	8.50000	+	14.7224i	0.345860	+	0.599047i
$605$		0			0
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	4.33013	+	7.50000i	0.175754	+	0.304416i	0.940422	−	0.340009i	$-0.110430\pi$
$607$	4.33013	+	7.50000i	0.175754	+	0.304416i	−0.764668	+	0.644425i	$0.777097\pi$
$608$			1.73205i			0.0702439i
$609$	5.19615	−	27.0000i	0.210559	−	1.09410i
$610$		0			0
$611$	−15.5885	+	9.00000i	−0.630641	+	0.364101i
$612$		0			0
$613$	22.5167	+	13.0000i	0.909439	+	0.525065i	0.880251	−	0.474509i	$-0.157374\pi$
$613$	22.5167	+	13.0000i	0.909439	+	0.525065i	0.0291886	+	0.999574i	$0.490708\pi$
$614$	12.1244	+	21.0000i	0.489299	+	0.847491i
$615$		0			0
$616$	−3.00000	+	15.5885i	−0.120873	+	0.628077i
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$	−13.5000	−	23.3827i	−0.543050	−	0.940590i
$619$	39.0000	+	22.5167i	1.56754	+	0.905021i	0.996455	+	0.0841320i	$0.0268117\pi$
$619$	39.0000	+	22.5167i	1.56754	+	0.905021i	0.571088	+	0.820889i	$0.306522\pi$
$620$		0			0
$621$	−15.5885	−	27.0000i	−0.625543	−	1.08347i
$622$	−20.7846			−0.833387
$623$	−18.0000	+	20.7846i	−0.721155	+	0.832718i
$624$	−3.00000			−0.120096
$625$		0			0
$626$		0			0
$627$	−9.00000	+	15.5885i	−0.359425	+	0.622543i
$628$	−0.866025	−	1.50000i	−0.0345582	−	0.0598565i
$629$		0			0
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$	−0.500000	−	0.866025i	−0.0198889	−	0.0344486i
$633$	−9.52628	+	16.5000i	−0.378636	+	0.655816i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$		0			0
$637$	−9.52628	+	7.50000i	−0.377445	+	0.297161i
$638$	−36.0000			−1.42525
$639$	−15.5885	+	9.00000i	−0.616670	+	0.356034i
$640$		0			0
$641$	10.3923	+	6.00000i	0.410471	+	0.236986i	0.690992	−	0.722862i	$-0.257174\pi$
$641$	10.3923	+	6.00000i	0.410471	+	0.236986i	−0.280521	+	0.959848i	$0.590507\pi$
$642$		0			0
$643$	19.0526			0.751360			0.375680	−	0.926750i	$-0.377409\pi$
$643$	19.0526			0.751360			0.375680	+	0.926750i	$0.377409\pi$
$644$	5.19615	+	15.0000i	0.204757	+	0.591083i
$645$		0			0
$646$		0			0
$647$	36.0000	+	20.7846i	1.41531	+	0.817127i	0.995882	−	0.0906629i	$-0.0288986\pi$
$647$	36.0000	+	20.7846i	1.41531	+	0.817127i	0.419424	+	0.907790i	$0.362232\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	−54.0000	+	31.1769i	−2.11969	+	1.22380i
$650$		0			0
$651$	12.0000	+	10.3923i	0.470317	+	0.407307i
$652$			1.00000i			0.0391630i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$	9.52628	−	16.5000i	0.372507	−	0.645201i
$655$		0			0
$656$	5.19615	+	9.00000i	0.202876	+	0.351391i
$657$	5.19615			0.202721
$658$	5.19615	−	27.0000i	0.202567	−	1.05257i
$659$			36.0000i			1.40236i	0.712984	+	0.701180i	$0.247343\pi$
$659$			36.0000i			1.40236i	−0.712984	+	0.701180i	$0.752657\pi$
$660$		0			0
$661$	−16.5000	−	9.52628i	−0.641776	−	0.370529i	0.143523	−	0.989647i	$-0.454157\pi$
$661$	−16.5000	−	9.52628i	−0.641776	−	0.370529i	−0.785298	+	0.619118i	$0.787490\pi$
$662$	2.50000	−	4.33013i	0.0971653	−	0.168295i
$663$		0			0
$664$		−	10.3923i		−	0.403300i
$665$		0			0
$666$			21.0000i			0.813733i
$667$	−31.1769	+	18.0000i	−1.20717	+	0.696963i
$668$	18.0000	+	10.3923i	0.696441	+	0.402090i
$669$	7.50000	−	12.9904i	0.289967	−	0.502237i
$670$		0			0
$671$	31.1769			1.20357
$672$	3.00000	−	3.46410i	0.115728	−	0.133631i
$673$		−	13.0000i		−	0.501113i	−0.968102	−	0.250557i	$-0.919386\pi$
$673$		−	13.0000i		−	0.501113i	0.968102	−	0.250557i	$-0.0806136\pi$
$674$	19.0526	−	11.0000i	0.733877	−	0.423704i
$675$		0			0
$676$	5.00000	−	8.66025i	0.192308	−	0.333087i
$677$	9.00000	−	5.19615i	0.345898	−	0.199704i	−0.316979	−	0.948433i	$-0.602668\pi$
$677$	9.00000	−	5.19615i	0.345898	−	0.199704i	0.662877	+	0.748728i	$0.269335\pi$
$678$	−20.7846			−0.798228
$679$	−13.5000	−	38.9711i	−0.518082	−	1.49558i
$680$		0			0
$681$	15.5885	−	9.00000i	0.597351	−	0.344881i
$682$	10.3923	−	18.0000i	0.397942	−	0.689256i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	4.50000	−	2.59808i	0.172062	−	0.0993399i
$685$		0			0
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$		−	27.0000i		−	1.03011i
$688$	−3.46410	+	2.00000i	−0.132068	+	0.0762493i
$689$		0			0
$690$		0			0
$691$	25.5000	−	14.7224i	0.970066	−	0.560068i	0.0708094	−	0.997490i	$-0.477442\pi$
$691$	25.5000	−	14.7224i	0.970066	−	0.560068i	0.899256	+	0.437422i	$0.144108\pi$
$692$			20.7846i			0.790112i
$693$	45.0000	−	15.5885i	1.70941	−	0.592157i
$694$	−12.0000			−0.455514
$695$		0			0
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$		0			0
$698$	24.0000	−	13.8564i	0.908413	−	0.524473i
$699$	−10.3923			−0.393073
$700$		0			0
$701$		−	18.0000i		−	0.679851i	−0.940452	−	0.339925i	$-0.889598\pi$
$701$		−	18.0000i		−	0.679851i	0.940452	−	0.339925i	$-0.110402\pi$
$702$	4.50000	+	7.79423i	0.169842	+	0.294174i
$703$	6.06218	−	10.5000i	0.228639	−	0.396015i
$704$	−5.19615	−	3.00000i	−0.195837	−	0.113067i
$705$		0			0
$706$			10.3923i			0.391120i
$707$	−27.0000	−	5.19615i	−1.01544	−	0.195421i
$708$	18.0000			0.676481
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$	−5.19615	−	9.00000i	−0.194734	−	0.337289i
$713$		−	20.7846i		−	0.778390i
$714$		0			0
$715$		0			0
$716$	15.5885	−	9.00000i	0.582568	−	0.336346i
$717$		0			0
$718$	−5.19615	−	3.00000i	−0.193919	−	0.111959i
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	0.752717	−	0.658344i	$-0.228743\pi$
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	−0.946501	+	0.322700i	$0.895409\pi$
$720$		0			0
$721$	27.0000	−	31.1769i	1.00553	−	1.16109i
$722$	16.0000			0.595458
$723$	12.9904	−	7.50000i	0.483117	−	0.278928i
$724$		0			0
$725$		0			0
$726$	−21.6506	−	37.5000i	−0.803530	−	1.39176i
$727$	36.3731			1.34900			0.674501	−	0.738274i	$-0.264359\pi$
$727$	36.3731			1.34900			0.674501	+	0.738274i	$0.264359\pi$
$728$	−1.50000	−	4.33013i	−0.0555937	−	0.160485i
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$	−7.79423	−	4.50000i	−0.288083	−	0.166325i
$733$	0.866025	+	1.50000i	0.0319874	+	0.0554038i	0.881576	−	0.472042i	$-0.156483\pi$
$733$	0.866025	+	1.50000i	0.0319874	+	0.0554038i	−0.849589	+	0.527446i	$0.823150\pi$
$734$	−10.3923			−0.383587
$735$		0			0
$736$	−6.00000			−0.221163
$737$	33.0000	+	57.1577i	1.21557	+	2.10543i
$738$	15.5885	−	27.0000i	0.573819	−	0.993884i
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	−0.875075	−	0.483987i	$-0.839188\pi$
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	0.856683	+	0.515844i	$0.172522\pi$
$740$		0			0
$741$		−	5.19615i		−	0.190885i
$742$		0			0
$743$	−18.0000			−0.660356			−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000			−0.660356			−0.330178	+	0.943919i	$0.607109\pi$
$744$	−5.19615	+	3.00000i	−0.190500	+	0.109985i
$745$		0			0
$746$	25.1147	+	14.5000i	0.919516	+	0.530883i
$747$	−27.0000	+	15.5885i	−0.987878	+	0.570352i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−21.5000	−	37.2391i	−0.784546	−	1.35887i	−0.929270	−	0.369402i	$-0.879563\pi$
$751$	−21.5000	−	37.2391i	−0.784546	−	1.35887i	0.144724	−	0.989472i	$-0.453771\pi$
$752$	9.00000	+	5.19615i	0.328196	+	0.189484i
$753$	18.0000	−	31.1769i	0.655956	−	1.13615i
$754$	9.00000	−	5.19615i	0.327761	−	0.189233i
$755$		0			0
$756$	−13.5000	−	2.59808i	−0.490990	−	0.0944911i
$757$		−	11.0000i		−	0.399802i	−0.979816	−	0.199901i	$-0.935938\pi$
$757$		−	11.0000i		−	0.399802i	0.979816	−	0.199901i	$-0.0640620\pi$
$758$	−17.5000	−	30.3109i	−0.635629	−	1.10094i
$759$	−54.0000	−	31.1769i	−1.96008	−	1.13165i
$760$		0			0
$761$	10.3923	+	18.0000i	0.376721	+	0.652499i	0.990583	−	0.136914i	$-0.0437183\pi$
$761$	10.3923	+	18.0000i	0.376721	+	0.652499i	−0.613862	+	0.789413i	$0.710385\pi$
$762$			32.9090i			1.19217i
$763$	28.5788	+	5.50000i	1.03462	+	0.199113i
$764$		−	18.0000i		−	0.651217i
$765$		0			0
$766$		0			0
$767$	9.00000	−	15.5885i	0.324971	−	0.562867i
$768$	0.866025	+	1.50000i	0.0312500	+	0.0541266i
$769$			20.7846i			0.749512i	0.927123	+	0.374756i	$0.122274\pi$
$769$			20.7846i			0.749512i	−0.927123	+	0.374756i	$0.877726\pi$
$770$		0			0
$771$		0			0
$772$	1.73205	−	1.00000i	0.0623379	−	0.0359908i
$773$	18.0000	+	10.3923i	0.647415	+	0.373785i	0.787465	−	0.616359i	$-0.211393\pi$
$773$	18.0000	+	10.3923i	0.647415	+	0.373785i	−0.140050	+	0.990144i	$0.544726\pi$
$774$	10.3923	+	6.00000i	0.373544	+	0.215666i
$775$		0			0
$776$	15.5885			0.559593
$777$	−30.3109	+	10.5000i	−1.08740	+	0.376685i
$778$			12.0000i			0.430221i
$779$	−15.5885	+	9.00000i	−0.558514	+	0.322458i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$		0			0
$783$		−	31.1769i		−	1.11417i
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$		0			0
$786$	−9.00000	−	15.5885i	−0.321019	−	0.556022i
$787$	−12.9904	+	22.5000i	−0.463057	+	0.802038i	−0.999112	−	0.0421450i	$-0.986581\pi$
$787$	−12.9904	+	22.5000i	−0.463057	+	0.802038i	0.536054	+	0.844183i	$0.319914\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$	−10.3923	−	18.0000i	−0.369976	−	0.640817i
$790$		0			0
$791$	−10.3923	−	30.0000i	−0.369508	−	1.06668i
$792$			18.0000i			0.639602i
$793$	−7.79423	+	4.50000i	−0.276781	+	0.159800i
$794$	−6.92820	+	12.0000i	−0.245873	+	0.425864i
$795$		0			0
$796$	10.5000	−	6.06218i	0.372163	−	0.214868i
$797$		−	10.3923i		−	0.368114i	−0.982916	−	0.184057i	$-0.941077\pi$
$797$		−	10.3923i		−	0.368114i	0.982916	−	0.184057i	$-0.0589232\pi$
$798$	6.00000	+	5.19615i	0.212398	+	0.183942i
$799$		0			0
$800$		0			0
$801$	−15.5885	+	27.0000i	−0.550791	+	0.953998i
$802$	20.7846	+	12.0000i	0.733930	+	0.423735i
$803$	9.00000	−	5.19615i	0.317603	−	0.183368i
$804$		−	19.0526i		−	0.671932i
$805$		0			0
$806$			6.00000i			0.211341i
$807$	−18.0000	−	31.1769i	−0.633630	−	1.09748i
$808$	5.19615	−	9.00000i	0.182800	−	0.316619i
$809$	25.9808	+	15.0000i	0.913435	+	0.527372i	0.881535	−	0.472119i	$-0.156511\pi$
$809$	25.9808	+	15.0000i	0.913435	+	0.527372i	0.0319002	+	0.999491i	$0.489844\pi$
$810$		0			0
$811$			29.4449i			1.03395i	0.856001	+	0.516975i	$0.172942\pi$
$811$			29.4449i			1.03395i	−0.856001	+	0.516975i	$0.827058\pi$
$812$	−3.00000	+	15.5885i	−0.105279	+	0.547048i
$813$		−	30.0000i		−	1.05215i
$814$	21.0000	+	36.3731i	0.736050	+	1.27488i
$815$		0			0
$816$		0			0
$817$	−3.46410	−	6.00000i	−0.121194	−	0.209913i
$818$			12.1244i			0.423918i
$819$	−9.00000	+	10.3923i	−0.314485	+	0.363137i
$820$		0			0
$821$	−15.5885	+	9.00000i	−0.544041	+	0.314102i	−0.746715	−	0.665144i	$-0.768370\pi$
$821$	−15.5885	+	9.00000i	−0.544041	+	0.314102i	0.202674	+	0.979246i	$0.435037\pi$
$822$	−15.5885	+	27.0000i	−0.543710	+	0.941733i
$823$	9.52628	+	5.50000i	0.332065	+	0.191718i	0.656758	−	0.754102i	$-0.271927\pi$
$823$	9.52628	+	5.50000i	0.332065	+	0.191718i	−0.324692	+	0.945820i	$0.605261\pi$
$824$	7.79423	+	13.5000i	0.271525	+	0.470295i
$825$		0			0
$826$	9.00000	+	25.9808i	0.313150	+	0.903986i
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$	9.00000	+	15.5885i	0.312772	+	0.541736i
$829$	7.50000	+	4.33013i	0.260486	+	0.150392i	0.624556	−	0.780980i	$-0.285280\pi$
$829$	7.50000	+	4.33013i	0.260486	+	0.150392i	−0.364070	+	0.931371i	$0.618613\pi$
$830$		0			0
$831$	1.50000	−	0.866025i	0.0520344	−	0.0300421i
$832$	1.73205			0.0600481
$833$		0			0
$834$		−	9.00000i		−	0.311645i
$835$		0			0
$836$	5.19615	−	9.00000i	0.179713	−	0.311272i
$837$	15.5885	+	9.00000i	0.538816	+	0.311086i
$838$	10.3923	+	18.0000i	0.358996	+	0.621800i
$839$	31.1769			1.07635			0.538173	−	0.842834i	$-0.319115\pi$
$839$	31.1769			1.07635			0.538173	+	0.842834i	$0.319115\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	−11.5000	−	19.9186i	−0.396316	−	0.686440i
$843$	18.0000	+	10.3923i	0.619953	+	0.357930i
$844$	5.50000	−	9.52628i	0.189318	−	0.327908i
$845$		0			0
$846$		−	31.1769i		−	1.07188i
$847$	43.3013	−	50.0000i	1.48785	−	1.71802i
$848$		0			0
$849$	−13.5000	−	23.3827i	−0.463319	−	0.802492i
$850$		0			0
$851$	36.3731	+	21.0000i	1.24685	+	0.719871i
$852$	9.00000	−	5.19615i	0.308335	−	0.178017i
$853$	41.5692			1.42330			0.711651	−	0.702533i	$-0.247948\pi$
$853$	41.5692			1.42330			0.711651	+	0.702533i	$0.247948\pi$
$854$	2.59808	−	13.5000i	0.0889043	−	0.461960i
$855$		0			0
$856$		0			0
$857$	−36.0000	−	20.7846i	−1.22974	−	0.709989i	−0.262762	−	0.964861i	$-0.584633\pi$
$857$	−36.0000	−	20.7846i	−1.22974	−	0.709989i	−0.966975	+	0.254872i	$0.917967\pi$
$858$	15.5885	+	9.00000i	0.532181	+	0.307255i
$859$	39.0000	−	22.5167i	1.33066	−	0.768259i	0.345262	−	0.938506i	$-0.387790\pi$
$859$	39.0000	−	22.5167i	1.33066	−	0.768259i	0.985401	+	0.170248i	$0.0544569\pi$
$860$		0			0
$861$	46.7654	+	9.00000i	1.59376	+	0.306719i
$862$			36.0000i			1.22616i
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	2.59808	−	4.50000i	0.0883883	−	0.153093i
$865$		0			0
$866$	17.3205	+	30.0000i	0.588575	+	1.01944i
$867$	−29.4449			−1.00000
$868$	−6.92820	−	6.00000i	−0.235159	−	0.203653i
$869$			6.00000i			0.203536i
$870$		0			0
$871$	−16.5000	−	9.52628i	−0.559081	−	0.322786i
$872$	−5.50000	+	9.52628i	−0.186254	+	0.322601i
$873$	−23.3827	−	40.5000i	−0.791384	−	1.37072i
$874$		−	10.3923i		−	0.351525i
$875$		0			0
$876$	−3.00000			−0.101361
$877$	4.33013	−	2.50000i	0.146218	−	0.0844190i	−0.425106	−	0.905143i	$-0.639763\pi$
$877$	4.33013	−	2.50000i	0.146218	−	0.0844190i	0.571324	+	0.820724i	$0.306430\pi$
$878$	−28.5000	−	16.4545i	−0.961828	−	0.555312i
$879$	15.5885	+	9.00000i	0.525786	+	0.303562i
$880$		0			0
$881$	31.1769			1.05038			0.525188	−	0.850986i	$-0.323995\pi$
$881$	31.1769			1.05038			0.525188	+	0.850986i	$0.323995\pi$
$882$	−3.00000	−	20.7846i	−0.101015	−	0.699854i
$883$		−	1.00000i		−	0.0336527i	−0.999858	−	0.0168263i	$-0.994644\pi$
$883$		−	1.00000i		−	0.0336527i	0.999858	−	0.0168263i	$-0.00535624\pi$
$884$		0			0
$885$		0			0
$886$	18.0000	−	31.1769i	0.604722	−	1.04741i
$887$	18.0000	−	10.3923i	0.604381	−	0.348939i	−0.166382	−	0.986061i	$-0.553209\pi$
$887$	18.0000	−	10.3923i	0.604381	−	0.348939i	0.770763	+	0.637122i	$0.219875\pi$
$888$		−	12.1244i		−	0.406867i
$889$	−47.5000	+	16.4545i	−1.59310	+	0.551866i
$890$		0			0
$891$	46.7654	−	27.0000i	1.56670	−	0.904534i
$892$	−4.33013	+	7.50000i	−0.144983	+	0.251119i
$893$	−9.00000	+	15.5885i	−0.301174	+	0.521648i
$894$	9.00000	−	5.19615i	0.301005	−	0.173785i
$895$		0			0
$896$	−1.73205	+	2.00000i	−0.0578638	+	0.0668153i
$897$	18.0000			0.601003
$898$	−5.19615	+	3.00000i	−0.173398	+	0.100111i
$899$	10.3923	−	18.0000i	0.346603	−	0.600334i
$900$		0			0
$901$		0			0
$902$		−	62.3538i		−	2.07616i
$903$	−3.46410	+	18.0000i	−0.115278	+	0.599002i
$904$	12.0000			0.399114
$905$		0			0
$906$	−14.7224	+	25.5000i	−0.489120	+	0.847181i
$907$	−16.4545	−	9.50000i	−0.546362	−	0.315442i	0.201291	−	0.979531i	$-0.435486\pi$
$907$	−16.4545	−	9.50000i	−0.546362	−	0.315442i	−0.747653	+	0.664089i	$0.768820\pi$
$908$	−9.00000	+	5.19615i	−0.298675	+	0.172440i
$909$	−31.1769			−1.03407
$910$		0			0
$911$			42.0000i			1.39152i	0.718273	+	0.695761i	$0.244933\pi$
$911$			42.0000i			1.39152i	−0.718273	+	0.695761i	$0.755067\pi$
$912$	−2.59808	+	1.50000i	−0.0860309	+	0.0496700i
$913$	−31.1769	+	54.0000i	−1.03181	+	1.78714i
$914$	4.33013	+	2.50000i	0.143228	+	0.0826927i
$915$		0			0
$916$			15.5885i			0.515057i
$917$	18.0000	−	20.7846i	0.594412	−	0.686368i
$918$		0			0
$919$	−22.0000	−	38.1051i	−0.725713	−	1.25697i	−0.958680	−	0.284487i	$-0.908177\pi$
$919$	−22.0000	−	38.1051i	−0.725713	−	1.25697i	0.232967	−	0.972485i	$-0.425157\pi$
$920$		0			0
$921$	−21.0000	+	36.3731i	−0.691974	+	1.19853i
$922$	5.19615	+	9.00000i	0.171126	+	0.296399i
$923$		−	10.3923i		−	0.342067i
$924$	−25.9808	+	9.00000i	−0.854704	+	0.296078i
$925$		0			0
$926$	−9.52628	+	5.50000i	−0.313053	+	0.180741i
$927$	23.3827	−	40.5000i	0.767988	−	1.33019i
$928$	−5.19615	−	3.00000i	−0.170572	−	0.0984798i
$929$	−10.3923	−	18.0000i	−0.340960	−	0.590561i	0.643651	−	0.765319i	$-0.277419\pi$
$929$	−10.3923	−	18.0000i	−0.340960	−	0.590561i	−0.984611	+	0.174758i	$0.944086\pi$
$930$		0			0
$931$	−4.50000	+	11.2583i	−0.147482	+	0.368977i
$932$	6.00000			0.196537
$933$	−18.0000	−	31.1769i	−0.589294	−	1.02069i
$934$	−18.0000	−	10.3923i	−0.588978	−	0.340047i
$935$		0			0
$936$	−2.59808	−	4.50000i	−0.0849208	−	0.147087i
$937$	−6.92820			−0.226335			−0.113167	−	0.993576i	$-0.536100\pi$
$937$	−6.92820			−0.226335			−0.113167	+	0.993576i	$0.536100\pi$
$938$	27.5000	−	9.52628i	0.897907	−	0.311044i
$939$		0			0
$940$		0			0
$941$	10.3923	−	18.0000i	0.338779	−	0.586783i	−0.645424	−	0.763825i	$-0.723319\pi$
$941$	10.3923	−	18.0000i	0.338779	−	0.586783i	0.984203	+	0.177041i	$0.0566526\pi$
$942$	1.50000	−	2.59808i	0.0488726	−	0.0846499i
$943$	−31.1769	−	54.0000i	−1.01526	−	1.75848i
$944$	−10.3923			−0.338241
$945$		0			0
$946$	24.0000			0.780307
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	0.866025	−	1.50000i	0.0281272	−	0.0487177i
$949$	−1.50000	+	2.59808i	−0.0486921	+	0.0843371i
$950$		0			0
$951$	−20.7846			−0.673987
$952$		0			0
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−31.1769	−	54.0000i	−1.00781	−	1.74557i
$958$	31.1769			1.00728
$959$	−46.7654	−	9.00000i	−1.51013	−	0.290625i
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	−10.5000	−	6.06218i	−0.338534	−	0.195452i
$963$		0			0
$964$	−7.50000	+	4.33013i	−0.241559	+	0.139464i
$965$		0			0
$966$	−18.0000	+	20.7846i	−0.579141	+	0.668734i
$967$		−	13.0000i		−	0.418052i	−0.977910	−	0.209026i	$-0.932971\pi$
$967$		−	13.0000i		−	0.418052i	0.977910	−	0.209026i	$-0.0670293\pi$
$968$	12.5000	+	21.6506i	0.401765	+	0.695878i
$969$		0			0
$970$		0			0
$971$	20.7846	+	36.0000i	0.667010	+	1.15529i	0.978736	+	0.205123i	$0.0657595\pi$
$971$	20.7846	+	36.0000i	0.667010	+	1.15529i	−0.311726	+	0.950172i	$0.600907\pi$
$972$	−15.5885			−0.500000
$973$	12.9904	−	4.50000i	0.416452	−	0.144263i
$974$			16.0000i			0.512673i
$975$		0			0
$976$	4.50000	+	2.59808i	0.144041	+	0.0831624i
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$	−1.50000	+	0.866025i	−0.0479647	+	0.0276924i
$979$			62.3538i			1.99284i
$980$		0			0
$981$	33.0000			1.05361
$982$	10.3923	−	6.00000i	0.331632	−	0.191468i
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	−9.00000	+	15.5885i	−0.286910	+	0.496942i
$985$		0			0
$986$		0			0
$987$	45.0000	−	15.5885i	1.43237	−	0.496186i
$988$			3.00000i			0.0954427i
$989$	20.7846	−	12.0000i	0.660912	−	0.381578i
$990$		0			0
$991$	22.0000	−	38.1051i	0.698853	−	1.21045i	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	22.0000	−	38.1051i	0.698853	−	1.21045i	0.968864	−	0.247592i	$-0.0796392\pi$
$992$	3.00000	−	1.73205i	0.0952501	−	0.0549927i
$993$	8.66025			0.274825
$994$	12.0000	+	10.3923i	0.380617	+	0.329624i
$995$		0			0
$996$	15.5885	−	9.00000i	0.493939	−	0.285176i
$997$	4.33013	−	7.50000i	0.137136	−	0.237527i	−0.789275	−	0.614040i	$-0.789543\pi$
$997$	4.33013	−	7.50000i	0.137136	−	0.237527i	0.926412	+	0.376512i	$0.122877\pi$
$998$	−2.50000	+	4.33013i	−0.0791361	+	0.137068i
$999$	−31.5000	+	18.1865i	−0.996616	+	0.575396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.u.b.899.2		4
3.2	odd	2		1050.2.u.c.899.2		4
5.2	odd	4		1050.2.s.a.101.2	yes	4
5.3	odd	4		1050.2.s.c.101.1	yes	4
5.4	even	2		1050.2.u.c.899.1		4
7.5	odd	6	inner	1050.2.u.b.299.1		4
15.2	even	4		1050.2.s.a.101.1	✓	4
15.8	even	4		1050.2.s.c.101.2	yes	4
15.14	odd	2	inner	1050.2.u.b.899.1		4
21.5	even	6		1050.2.u.c.299.1		4
35.12	even	12		1050.2.s.a.551.1	yes	4
35.19	odd	6		1050.2.u.c.299.2		4
35.33	even	12		1050.2.s.c.551.2	yes	4
105.47	odd	12		1050.2.s.a.551.2	yes	4
105.68	odd	12		1050.2.s.c.551.1	yes	4
105.89	even	6	inner	1050.2.u.b.299.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.s.a.101.1	✓	4	15.2	even	4
1050.2.s.a.101.2	yes	4	5.2	odd	4
1050.2.s.a.551.1	yes	4	35.12	even	12
1050.2.s.a.551.2	yes	4	105.47	odd	12
1050.2.s.c.101.1	yes	4	5.3	odd	4
1050.2.s.c.101.2	yes	4	15.8	even	4
1050.2.s.c.551.1	yes	4	105.68	odd	12
1050.2.s.c.551.2	yes	4	35.33	even	12
1050.2.u.b.299.1		4	7.5	odd	6	inner
1050.2.u.b.299.2		4	105.89	even	6	inner
1050.2.u.b.899.1		4	15.14	odd	2	inner
1050.2.u.b.899.2		4	1.1	even	1	trivial
1050.2.u.c.299.1		4	21.5	even	6
1050.2.u.c.299.2		4	35.19	odd	6
1050.2.u.c.899.1		4	5.4	even	2
1050.2.u.c.899.2		4	3.2	odd	2

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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.19615 - 3.00000i) q^{11} +(0.866025 + 1.50000i) q^{12} +1.73205 q^{13} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{18} +(1.50000 - 0.866025i) q^{19} +(-4.50000 - 0.866025i) q^{21} +6.00000i q^{22} +(3.00000 + 5.19615i) q^{23} +(0.866025 - 1.50000i) q^{24} +(-0.866025 - 1.50000i) q^{26} -5.19615 q^{27} +(2.59808 + 0.500000i) q^{28} +6.00000i q^{29} +(-3.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-9.00000 + 5.19615i) q^{33} +3.00000 q^{36} +(6.06218 - 3.50000i) q^{37} +(-1.50000 - 0.866025i) q^{38} +(1.50000 - 2.59808i) q^{39} -10.3923 q^{41} +(1.50000 + 4.33013i) q^{42} -4.00000i q^{43} +(5.19615 - 3.00000i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-9.00000 + 5.19615i) q^{47} -1.73205 q^{48} +(-5.50000 + 4.33013i) q^{49} +(-0.866025 + 1.50000i) q^{52} +(2.59808 + 4.50000i) q^{54} +(-0.866025 - 2.50000i) q^{56} -3.00000i q^{57} +(5.19615 - 3.00000i) q^{58} +(5.19615 - 9.00000i) q^{59} +(-4.50000 + 2.59808i) q^{61} +3.46410i q^{62} +(-5.19615 + 6.00000i) q^{63} +1.00000 q^{64} +(9.00000 + 5.19615i) q^{66} +(-9.52628 - 5.50000i) q^{67} +10.3923 q^{69} -6.00000i q^{71} +(-1.50000 - 2.59808i) q^{72} +(-0.866025 + 1.50000i) q^{73} +(-6.06218 - 3.50000i) q^{74} +1.73205i q^{76} +(-3.00000 + 15.5885i) q^{77} -3.00000 q^{78} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(5.19615 + 9.00000i) q^{82} -10.3923i q^{83} +(3.00000 - 3.46410i) q^{84} +(-3.46410 + 2.00000i) q^{86} +(9.00000 + 5.19615i) q^{87} +(-5.19615 - 3.00000i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(-1.50000 - 4.33013i) q^{91} -6.00000 q^{92} +(-5.19615 + 3.00000i) q^{93} +(9.00000 + 5.19615i) q^{94} +(0.866025 + 1.50000i) q^{96} +15.5885 q^{97} +(6.50000 + 2.59808i) q^{98} +18.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 6 q^{9} - 2 q^{16} - 6 q^{18} + 6 q^{19} - 18 q^{21} + 12 q^{23} - 12 q^{31} - 2 q^{32} - 36 q^{33} + 12 q^{36} - 6 q^{38} + 6 q^{39} + 6 q^{42} + 12 q^{46} - 36 q^{47} - 22 q^{49} - 18 q^{61} + 4 q^{64} + 36 q^{66} - 6 q^{72} - 12 q^{77} - 12 q^{78} - 2 q^{79} - 18 q^{81} + 12 q^{84} + 36 q^{87} - 6 q^{91} - 24 q^{92} + 36 q^{94} + 26 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 6 * q^9 - 2 * q^16 - 6 * q^18 + 6 * q^19 - 18 * q^21 + 12 * q^23 - 12 * q^31 - 2 * q^32 - 36 * q^33 + 12 * q^36 - 6 * q^38 + 6 * q^39 + 6 * q^42 + 12 * q^46 - 36 * q^47 - 22 * q^49 - 18 * q^61 + 4 * q^64 + 36 * q^66 - 6 * q^72 - 12 * q^77 - 12 * q^78 - 2 * q^79 - 18 * q^81 + 12 * q^84 + 36 * q^87 - 6 * q^91 - 24 * q^92 + 36 * q^94 + 26 * q^98

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