LMFDB - Embedded newform 99.2.e.b.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			34.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	99.34
Dual form			99.2.e.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{11} -3.46410i q^{12} +(-1.00000 - 1.73205i) q^{13} -5.19615i q^{15} +(-2.00000 + 3.46410i) q^{16} -6.00000 q^{17} +2.00000 q^{19} +(-3.00000 + 5.19615i) q^{20} +(-6.00000 + 3.46410i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.19615i q^{27} +8.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(1.50000 - 0.866025i) q^{33} +12.0000 q^{35} +(-3.00000 + 5.19615i) q^{36} +2.00000 q^{37} +3.46410i q^{39} +(-4.00000 + 6.92820i) q^{43} -2.00000 q^{44} +(-4.50000 + 7.79423i) q^{45} +(-1.50000 + 2.59808i) q^{47} +(6.00000 - 3.46410i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(9.00000 + 5.19615i) q^{51} +(2.00000 - 3.46410i) q^{52} +3.00000 q^{53} -3.00000 q^{55} +(-3.00000 - 1.73205i) q^{57} +(9.00000 - 5.19615i) q^{60} +(-4.00000 + 6.92820i) q^{61} +12.0000 q^{63} -8.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(6.50000 + 11.2583i) q^{67} +(-6.00000 - 10.3923i) q^{68} +5.19615i q^{69} +2.00000 q^{73} +(6.00000 - 3.46410i) q^{75} +(2.00000 + 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +(-1.00000 + 1.73205i) q^{79} -12.0000 q^{80} +(-4.50000 + 7.79423i) q^{81} +(9.00000 - 15.5885i) q^{83} +(-12.0000 - 6.92820i) q^{84} +(-9.00000 - 15.5885i) q^{85} +(-9.00000 + 5.19615i) q^{87} +3.00000 q^{89} -8.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +13.8564i q^{93} +(3.00000 + 5.19615i) q^{95} +(-1.00000 + 1.73205i) q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 2 q^{4} + 3 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 2 * q^4 + 3 * q^5 + 4 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} + 2 q^{4} + 3 q^{5} + 4 q^{7} + 3 q^{9} - q^{11} - 2 q^{13} - 4 q^{16} - 12 q^{17} + 4 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} - 4 q^{25} + 16 q^{28} + 6 q^{29} - 8 q^{31} + 3 q^{33} + 24 q^{35} - 6 q^{36} + 4 q^{37} - 8 q^{43} - 4 q^{44} - 9 q^{45} - 3 q^{47} + 12 q^{48} - 9 q^{49} + 18 q^{51} + 4 q^{52} + 6 q^{53} - 6 q^{55} - 6 q^{57} + 18 q^{60} - 8 q^{61} + 24 q^{63} - 16 q^{64} + 6 q^{65} + 13 q^{67} - 12 q^{68} + 4 q^{73} + 12 q^{75} + 4 q^{76} + 4 q^{77} - 2 q^{79} - 24 q^{80} - 9 q^{81} + 18 q^{83} - 24 q^{84} - 18 q^{85} - 18 q^{87} + 6 q^{89} - 16 q^{91} + 6 q^{92} + 6 q^{95} - 2 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 2 * q^4 + 3 * q^5 + 4 * q^7 + 3 * q^9 - q^11 - 2 * q^13 - 4 * q^16 - 12 * q^17 + 4 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 - 4 * q^25 + 16 * q^28 + 6 * q^29 - 8 * q^31 + 3 * q^33 + 24 * q^35 - 6 * q^36 + 4 * q^37 - 8 * q^43 - 4 * q^44 - 9 * q^45 - 3 * q^47 + 12 * q^48 - 9 * q^49 + 18 * q^51 + 4 * q^52 + 6 * q^53 - 6 * q^55 - 6 * q^57 + 18 * q^60 - 8 * q^61 + 24 * q^63 - 16 * q^64 + 6 * q^65 + 13 * q^67 - 12 * q^68 + 4 * q^73 + 12 * q^75 + 4 * q^76 + 4 * q^77 - 2 * q^79 - 24 * q^80 - 9 * q^81 + 18 * q^83 - 24 * q^84 - 18 * q^85 - 18 * q^87 + 6 * q^89 - 16 * q^91 + 6 * q^92 + 6 * q^95 - 2 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		−	3.46410i		−	1.00000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		−	5.19615i		−	1.34164i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−3.00000	+	5.19615i	−0.670820	+	1.16190i
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$		0			0
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$	8.00000			1.51186
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$		0			0
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$		0			0
$35$	12.0000			2.02837
$36$	−3.00000	+	5.19615i	−0.500000	+	0.866025i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$			3.46410i			0.554700i
$40$		0			0
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−2.00000			−0.301511
$45$	−4.50000	+	7.79423i	−0.670820	+	1.16190i
$46$		0			0
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	6.00000	−	3.46410i	0.866025	−	0.500000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$		0			0
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	−3.00000	−	1.73205i	−0.397360	−	0.229416i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	9.00000	−	5.19615i	1.16190	−	0.670820i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		0			0
$63$	12.0000			1.51186
$64$	−8.00000			−1.00000
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$		0			0
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$	−6.00000	−	10.3923i	−0.727607	−	1.26025i
$69$			5.19615i			0.625543i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	2.00000	+	3.46410i	0.227921	+	0.394771i
$78$		0			0
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	−12.0000			−1.34164
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	9.00000	−	15.5885i	0.987878	−	1.71106i	0.359506	−	0.933143i	$-0.382945\pi$
$83$	9.00000	−	15.5885i	0.987878	−	1.71106i	0.628372	−	0.777913i	$-0.283721\pi$
$84$	−12.0000	−	6.92820i	−1.30931	−	0.755929i
$85$	−9.00000	−	15.5885i	−0.976187	−	1.69081i
$86$		0			0
$87$	−9.00000	+	5.19615i	−0.964901	+	0.557086i
$88$		0			0
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$			13.8564i			1.43684i
$94$		0			0
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$	−8.00000			−0.800000
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$		0			0
$105$	−18.0000	−	10.3923i	−1.75662	−	1.01419i
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	−3.00000	−	1.73205i	−0.284747	−	0.164399i
$112$	8.00000	+	13.8564i	0.755929	+	1.30931i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$	4.50000	−	7.79423i	0.419627	−	0.726816i
$116$	12.0000			1.11417
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$		0			0
$119$	−12.0000	+	20.7846i	−1.10004	+	1.90532i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$	8.00000	−	13.8564i	0.718421	−	1.24434i
$125$	3.00000			0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$		0			0
$129$	12.0000	−	6.92820i	1.05654	−	0.609994i
$130$		0			0
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	3.00000	+	1.73205i	0.261116	+	0.150756i
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$		0			0
$135$	13.5000	−	7.79423i	1.16190	−	0.670820i
$136$		0			0
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	5.00000	+	8.66025i	0.424094	+	0.734553i	0.996335	−	0.0855324i	$-0.0272591\pi$
$139$	5.00000	+	8.66025i	0.424094	+	0.734553i	−0.572241	+	0.820086i	$0.693926\pi$
$140$	12.0000	+	20.7846i	1.01419	+	1.75662i
$141$	4.50000	−	2.59808i	0.378968	−	0.218797i
$142$		0			0
$143$	2.00000			0.167248
$144$	−12.0000			−1.00000
$145$	18.0000			1.49482
$146$		0			0
$147$			15.5885i			1.28571i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$		0			0
$153$	−9.00000	−	15.5885i	−0.727607	−	1.26025i
$154$		0			0
$155$	12.0000	−	20.7846i	0.963863	−	1.66946i
$156$	−6.00000	+	3.46410i	−0.480384	+	0.277350i
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$		0			0
$159$	−4.50000	−	2.59808i	−0.356873	−	0.206041i
$160$		0			0
$161$	−12.0000			−0.945732
$162$		0			0
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$		0			0
$165$	4.50000	+	2.59808i	0.350325	+	0.202260i
$166$		0			0
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$	−16.0000			−1.21999
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$	8.00000	+	13.8564i	0.604743	+	1.04745i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$		0			0
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$	−18.0000			−1.34164
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$		0			0
$183$	12.0000	−	6.92820i	0.887066	−	0.512148i
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	−6.00000			−0.437595
$189$	−18.0000	−	10.3923i	−1.30931	−	0.755929i
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$	12.0000	+	6.92820i	0.866025	+	0.500000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$		0			0
$195$	−9.00000	+	5.19615i	−0.644503	+	0.372104i
$196$	9.00000	−	15.5885i	0.642857	−	1.11346i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	11.0000			0.779769			0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000			0.779769			0.389885	+	0.920864i	$0.372515\pi$
$200$		0			0
$201$		−	22.5167i		−	1.58820i
$202$		0			0
$203$	−12.0000	−	20.7846i	−0.842235	−	1.45879i
$204$			20.7846i			1.45521i
$205$		0			0
$206$		0			0
$207$	4.50000	−	7.79423i	0.312772	−	0.541736i
$208$	8.00000			0.554700
$209$	−1.00000	+	1.73205i	−0.0691714	+	0.119808i
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$		0			0
$215$	−24.0000			−1.63679
$216$		0			0
$217$	−32.0000			−2.17230
$218$		0			0
$219$	−3.00000	−	1.73205i	−0.202721	−	0.117041i
$220$	−3.00000	−	5.19615i	−0.202260	−	0.350325i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−5.50000	+	9.52628i	−0.368307	+	0.637927i	−0.989301	−	0.145889i	$-0.953396\pi$
$223$	−5.50000	+	9.52628i	−0.368307	+	0.637927i	0.620994	+	0.783815i	$0.286729\pi$
$224$		0			0
$225$	−12.0000			−0.800000
$226$		0			0
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$		−	6.92820i		−	0.458831i
$229$	−11.5000	−	19.9186i	−0.759941	−	1.31626i	−0.942880	−	0.333133i	$-0.891894\pi$
$229$	−11.5000	−	19.9186i	−0.759941	−	1.31626i	0.182939	−	0.983124i	$-0.441439\pi$
$230$		0			0
$231$		−	6.92820i		−	0.455842i
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$		0			0
$237$	3.00000	−	1.73205i	0.194871	−	0.112509i
$238$		0			0
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$	18.0000	+	10.3923i	1.16190	+	0.670820i
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−16.0000			−1.02430
$245$	13.5000	−	23.3827i	0.862483	−	1.49387i
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$		0			0
$249$	−27.0000	+	15.5885i	−1.71106	+	0.987878i
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	12.0000	+	20.7846i	0.755929	+	1.30931i
$253$	3.00000			0.188608
$254$		0			0
$255$			31.1769i			1.95237i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	4.00000	−	6.92820i	0.248548	−	0.430498i
$260$	12.0000			0.744208
$261$	18.0000			1.11417
$262$		0			0
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		0			0
$265$	4.50000	+	7.79423i	0.276433	+	0.478796i
$266$		0			0
$267$	−4.50000	−	2.59808i	−0.275396	−	0.159000i
$268$	−13.0000	+	22.5167i	−0.794101	+	1.37542i
$269$	27.0000			1.64622			0.823110	−	0.567883i	$-0.192237\pi$
$269$	27.0000			1.64622			0.823110	+	0.567883i	$0.192237\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	12.0000	−	20.7846i	0.727607	−	1.26025i
$273$	12.0000	+	6.92820i	0.726273	+	0.419314i
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	−9.00000	+	5.19615i	−0.541736	+	0.312772i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$		0			0
$279$	12.0000	−	20.7846i	0.718421	−	1.24434i
$280$		0			0
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	−0.629685	−	0.776851i	$-0.716816\pi$
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	0.987615	+	0.156898i	$0.0501493\pi$
$282$		0			0
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	0.975499	−	0.220005i	$-0.0706075\pi$
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	−0.678280	+	0.734804i	$0.737274\pi$
$284$		0			0
$285$		−	10.3923i		−	0.615587i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$	3.00000	−	1.73205i	0.175863	−	0.101535i
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.50000	+	2.59808i	0.261116	+	0.150756i
$298$		0			0
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	12.0000	+	6.92820i	0.692820	+	0.400000i
$301$	16.0000	+	27.7128i	0.922225	+	1.59734i
$302$		0			0
$303$	9.00000	−	5.19615i	0.517036	−	0.298511i
$304$	−4.00000	+	6.92820i	−0.229416	+	0.397360i
$305$	−24.0000			−1.37424
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	−4.00000	+	6.92820i	−0.227921	+	0.394771i
$309$			8.66025i			0.492665i
$310$		0			0
$311$	1.50000	+	2.59808i	0.0850572	+	0.147323i	0.905416	−	0.424526i	$-0.139559\pi$
$311$	1.50000	+	2.59808i	0.0850572	+	0.147323i	−0.820358	+	0.571850i	$0.806226\pi$
$312$		0			0
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$		0			0
$315$	18.0000	+	31.1769i	1.01419	+	1.75662i
$316$	−4.00000			−0.225018
$317$	13.5000	−	23.3827i	0.758236	−	1.31330i	−0.185514	−	0.982642i	$-0.559395\pi$
$317$	13.5000	−	23.3827i	0.758236	−	1.31330i	0.943750	−	0.330661i	$-0.107272\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	−12.0000	−	20.7846i	−0.670820	−	1.16190i
$321$	18.0000	+	10.3923i	1.00466	+	0.580042i
$322$		0			0
$323$	−12.0000			−0.667698
$324$	−18.0000			−1.00000
$325$	8.00000			0.443760
$326$		0			0
$327$	−21.0000	−	12.1244i	−1.16130	−	0.670478i
$328$		0			0
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	−14.5000	+	25.1147i	−0.796992	+	1.38043i	0.124574	+	0.992210i	$0.460243\pi$
$331$	−14.5000	+	25.1147i	−0.796992	+	1.38043i	−0.921567	+	0.388221i	$0.873090\pi$
$332$	36.0000			1.97576
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$		0			0
$335$	−19.5000	+	33.7750i	−1.06540	+	1.84532i
$336$		−	27.7128i		−	1.51186i
$337$	−16.0000	−	27.7128i	−0.871576	−	1.50961i	−0.860366	−	0.509676i	$-0.829765\pi$
$337$	−16.0000	−	27.7128i	−0.871576	−	1.50961i	−0.0112091	−	0.999937i	$-0.503568\pi$
$338$		0			0
$339$		−	10.3923i		−	0.564433i
$340$	18.0000	−	31.1769i	0.976187	−	1.69081i
$341$	8.00000			0.433224
$342$		0			0
$343$	−8.00000			−0.431959
$344$		0			0
$345$	−13.5000	+	7.79423i	−0.726816	+	0.419627i
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	−18.0000	−	10.3923i	−0.964901	−	0.557086i
$349$	14.0000	−	24.2487i	0.749403	−	1.29800i	−0.198706	−	0.980059i	$-0.563674\pi$
$349$	14.0000	−	24.2487i	0.749403	−	1.29800i	0.948109	−	0.317945i	$-0.102993\pi$
$350$		0			0
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$		0			0
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$354$		0			0
$355$		0			0
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$	36.0000	−	20.7846i	1.90532	−	1.10004i
$358$		0			0
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$			1.73205i			0.0909091i
$364$	−8.00000	−	13.8564i	−0.419314	−	0.726273i
$365$	3.00000	+	5.19615i	0.157027	+	0.271979i
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$	12.0000			0.625543
$369$		0			0
$370$		0			0
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$	−24.0000	+	13.8564i	−1.24434	+	0.718421i
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$		0			0
$375$	−4.50000	−	2.59808i	−0.232379	−	0.134164i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−13.0000			−0.667765			−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000			−0.667765			−0.333883	+	0.942615i	$0.608359\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$	6.00000	+	3.46410i	0.307389	+	0.177471i
$382$		0			0
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	0.971897	+	0.235408i	$0.0756427\pi$
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	−0.282079	+	0.959391i	$0.591024\pi$
$384$		0			0
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$		0			0
$387$	−24.0000			−1.21999
$388$	−4.00000			−0.203069
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$		0			0
$393$			31.1769i			1.57267i
$394$		0			0
$395$	−6.00000			−0.301893
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	17.0000			0.853206			0.426603	−	0.904439i	$-0.359710\pi$
$397$	17.0000			0.853206			0.426603	+	0.904439i	$0.359710\pi$
$398$		0			0
$399$	−12.0000	+	6.92820i	−0.600751	+	0.346844i
$400$	−8.00000	−	13.8564i	−0.400000	−	0.692820i
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$		0			0
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$	−12.0000			−0.597022
$405$	−27.0000			−1.34164
$406$		0			0
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$		0			0
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$		0			0
$411$	27.0000	−	15.5885i	1.33181	−	0.768922i
$412$	5.00000	−	8.66025i	0.246332	−	0.426660i
$413$		0			0
$414$		0			0
$415$	54.0000			2.65076
$416$		0			0
$417$		−	17.3205i		−	0.848189i
$418$		0			0
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	0.999887	+	0.0150285i	$0.00478389\pi$
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	−0.486928	+	0.873442i	$0.661883\pi$
$420$		−	41.5692i		−	2.02837i
$421$	3.50000	−	6.06218i	0.170580	−	0.295452i	−0.768043	−	0.640398i	$-0.778769\pi$
$421$	3.50000	−	6.06218i	0.170580	−	0.295452i	0.938623	+	0.344946i	$0.112103\pi$
$422$		0			0
$423$	−9.00000			−0.437595
$424$		0			0
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$		0			0
$427$	16.0000	+	27.7128i	0.774294	+	1.34112i
$428$	−12.0000	−	20.7846i	−0.580042	−	1.00466i
$429$	−3.00000	−	1.73205i	−0.144841	−	0.0836242i
$430$		0			0
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$	18.0000	+	10.3923i	0.866025	+	0.500000i
$433$	17.0000			0.816968			0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000			0.816968			0.408484	+	0.912766i	$0.366058\pi$
$434$		0			0
$435$	−27.0000	−	15.5885i	−1.29455	−	0.747409i
$436$	14.0000	+	24.2487i	0.670478	+	1.16130i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		0			0
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	0.368945	+	0.929451i	$0.379719\pi$
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	−0.989401	+	0.145210i	$0.953614\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$		0			0
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$		−	6.92820i		−	0.328798i
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$		0			0
$447$		−	20.7846i		−	0.983078i
$448$	−16.0000	+	27.7128i	−0.755929	+	1.30931i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$		0			0
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	12.0000	−	6.92820i	0.563809	−	0.325515i
$454$		0			0
$455$	−12.0000	−	20.7846i	−0.562569	−	0.974398i
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$		0			0
$459$			31.1769i			1.45521i
$460$	18.0000			0.839254
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	−14.5000	−	25.1147i	−0.673872	−	1.16718i	−0.976797	−	0.214166i	$-0.931297\pi$
$463$	−14.5000	−	25.1147i	−0.673872	−	1.16718i	0.302925	−	0.953014i	$-0.402037\pi$
$464$	12.0000	+	20.7846i	0.557086	+	0.964901i
$465$	−36.0000	+	20.7846i	−1.66946	+	0.963863i
$466$		0			0
$467$	15.0000			0.694117			0.347059	−	0.937843i	$-0.387180\pi$
$467$	15.0000			0.694117			0.347059	+	0.937843i	$0.387180\pi$
$468$	12.0000			0.554700
$469$	52.0000			2.40114
$470$		0			0
$471$		−	12.1244i		−	0.558661i
$472$		0			0
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$		0			0
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	−48.0000			−2.20008
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$		0			0
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$		0			0
$483$	18.0000	+	10.3923i	0.819028	+	0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−6.00000			−0.272446
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$		0			0
$489$	1.50000	+	0.866025i	0.0678323	+	0.0391630i
$490$		0			0
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	0.975898	+	0.218229i	$0.0700279\pi$
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	−0.298957	+	0.954267i	$0.596639\pi$
$492$		0			0
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$		0			0
$495$	−4.50000	−	7.79423i	−0.202260	−	0.350325i
$496$	32.0000			1.43684
$497$		0			0
$498$		0			0
$499$	−20.5000	−	35.5070i	−0.917706	−	1.58951i	−0.802890	−	0.596127i	$-0.796706\pi$
$499$	−20.5000	−	35.5070i	−0.917706	−	1.58951i	−0.114816	−	0.993387i	$-0.536628\pi$
$500$	3.00000	+	5.19615i	0.134164	+	0.232379i
$501$			31.1769i			1.39288i
$502$		0			0
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	0.948353	−	0.317217i	$-0.102748\pi$
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	−0.748894	+	0.662690i	$0.769415\pi$
$510$		0			0
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$		0			0
$513$		−	10.3923i		−	0.458831i
$514$		0			0
$515$	7.50000	−	12.9904i	0.330489	−	0.572425i
$516$	24.0000	+	13.8564i	1.05654	+	0.609994i
$517$	−1.50000	−	2.59808i	−0.0659699	−	0.114263i
$518$		0			0
$519$	27.0000	−	15.5885i	1.18517	−	0.684257i
$520$		0			0
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$	−34.0000			−1.48672			−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000			−1.48672			−0.743358	+	0.668894i	$0.766768\pi$
$524$	18.0000	−	31.1769i	0.786334	−	1.36197i
$525$		−	27.7128i		−	1.20949i
$526$		0			0
$527$	24.0000	+	41.5692i	1.04546	+	1.81078i
$528$			6.92820i			0.301511i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$		0			0
$532$	16.0000			0.693688
$533$		0			0
$534$		0			0
$535$	−18.0000	−	31.1769i	−0.778208	−	1.34790i
$536$		0			0
$537$	−22.5000	−	12.9904i	−0.970947	−	0.560576i
$538$		0			0
$539$	9.00000			0.387657
$540$	27.0000	+	15.5885i	1.16190	+	0.670820i
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$		0			0
$543$	1.50000	+	0.866025i	0.0643712	+	0.0371647i
$544$		0			0
$545$	21.0000	+	36.3731i	0.899541	+	1.55805i
$546$		0			0
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	−0.394432	−	0.918925i	$-0.629059\pi$
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	0.993028	−	0.117875i	$-0.0376081\pi$
$548$	−36.0000			−1.53784
$549$	−24.0000			−1.02430
$550$		0			0
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$		0			0
$555$		−	10.3923i		−	0.441129i
$556$	−10.0000	+	17.3205i	−0.424094	+	0.734553i
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$	−24.0000	+	41.5692i	−1.01419	+	1.75662i
$561$	−9.00000	+	5.19615i	−0.379980	+	0.219382i
$562$		0			0
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	9.00000	+	5.19615i	0.378968	+	0.218797i
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$		0			0
$567$	18.0000	+	31.1769i	0.755929	+	1.30931i
$568$		0			0
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$	4.50000	−	2.59808i	0.187990	−	0.108536i
$574$		0			0
$575$	12.0000			0.500435
$576$	−12.0000	−	20.7846i	−0.500000	−	0.866025i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$		0			0
$579$		−	6.92820i		−	0.287926i
$580$	18.0000	+	31.1769i	0.747409	+	1.29455i
$581$	−36.0000	−	62.3538i	−1.49353	−	2.58687i
$582$		0			0
$583$	−1.50000	+	2.59808i	−0.0621237	+	0.107601i
$584$		0			0
$585$	18.0000			0.744208
$586$		0			0
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$	−27.0000	+	15.5885i	−1.11346	+	0.642857i
$589$	−8.00000	−	13.8564i	−0.329634	−	0.570943i
$590$		0			0
$591$	−27.0000	−	15.5885i	−1.11063	−	0.641223i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$		0			0
$595$	−72.0000			−2.95171
$596$	−12.0000	+	20.7846i	−0.491539	+	0.851371i
$597$	−16.5000	−	9.52628i	−0.675300	−	0.389885i
$598$		0			0
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	−0.0929227	−	0.995673i	$-0.529621\pi$
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	0.908740	−	0.417363i	$-0.137046\pi$
$602$		0			0
$603$	−19.5000	+	33.7750i	−0.794101	+	1.37542i
$604$	−16.0000			−0.651031
$605$	1.50000	−	2.59808i	0.0609837	−	0.105627i
$606$		0			0
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	0.996740	+	0.0806818i	$0.0257098\pi$
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	−0.428497	+	0.903543i	$0.640957\pi$
$608$		0			0
$609$			41.5692i			1.68447i
$610$		0			0
$611$	6.00000			0.242734
$612$	18.0000	−	31.1769i	0.727607	−	1.26025i
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	0.761114	−	0.648618i	$-0.224653\pi$
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	−0.942277	+	0.334835i	$0.891320\pi$
$618$		0			0
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$	48.0000			1.92773
$621$	−13.5000	+	7.79423i	−0.541736	+	0.312772i
$622$		0			0
$623$	6.00000	−	10.3923i	0.240385	−	0.416359i
$624$	−12.0000	−	6.92820i	−0.480384	−	0.277350i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$	3.00000	−	1.73205i	0.119808	−	0.0691714i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$		0			0
$633$		−	6.92820i		−	0.275371i
$634$		0			0
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$		−	10.3923i		−	0.412082i
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		0			0
$643$	15.5000	+	26.8468i	0.611260	+	1.05873i	0.991028	+	0.133652i	$0.0426705\pi$
$643$	15.5000	+	26.8468i	0.611260	+	1.05873i	−0.379768	+	0.925082i	$0.623996\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$	36.0000	+	20.7846i	1.41750	+	0.818393i
$646$		0			0
$647$	21.0000			0.825595			0.412798	−	0.910823i	$-0.364552\pi$
$647$	21.0000			0.825595			0.412798	+	0.910823i	$0.364552\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	48.0000	+	27.7128i	1.88127	+	1.08615i
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	27.0000	−	46.7654i	1.05498	−	1.82727i
$656$		0			0
$657$	3.00000	+	5.19615i	0.117041	+	0.202721i
$658$		0			0
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	−0.531855	−	0.846836i	$-0.678505\pi$
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	0.999309	+	0.0371821i	$0.0118382\pi$
$660$			10.3923i			0.404520i
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$		0			0
$663$		−	20.7846i		−	0.807207i
$664$		0			0
$665$	24.0000			0.930680
$666$		0			0
$667$	−18.0000			−0.696963
$668$	18.0000	−	31.1769i	0.696441	−	1.20627i
$669$	16.5000	−	9.52628i	0.637927	−	0.368307i
$670$		0			0
$671$	−4.00000	−	6.92820i	−0.154418	−	0.267460i
$672$		0			0
$673$	17.0000	−	29.4449i	0.655302	−	1.13502i	−0.326516	−	0.945192i	$-0.605875\pi$
$673$	17.0000	−	29.4449i	0.655302	−	1.13502i	0.981818	−	0.189824i	$-0.0607919\pi$
$674$		0			0
$675$	18.0000	+	10.3923i	0.692820	+	0.400000i
$676$	18.0000			0.692308
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	0.279453	+	0.960159i	$0.409847\pi$
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	−0.971249	+	0.238067i	$0.923486\pi$
$678$		0			0
$679$	4.00000	+	6.92820i	0.153506	+	0.265880i
$680$		0			0
$681$	27.0000	−	15.5885i	1.03464	−	0.597351i
$682$		0			0
$683$	15.0000			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$684$	−6.00000	+	10.3923i	−0.229416	+	0.397360i
$685$	−54.0000			−2.06323
$686$		0			0
$687$			39.8372i			1.51988i
$688$	−16.0000	−	27.7128i	−0.609994	−	1.05654i
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$		0			0
$691$	12.5000	−	21.6506i	0.475522	−	0.823629i	−0.524084	−	0.851666i	$-0.675592\pi$
$691$	12.5000	−	21.6506i	0.475522	−	0.823629i	0.999607	+	0.0280373i	$0.00892572\pi$
$692$	−36.0000			−1.36851
$693$	−6.00000	+	10.3923i	−0.227921	+	0.394771i
$694$		0			0
$695$	−15.0000	+	25.9808i	−0.568982	+	0.985506i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	9.00000	+	5.19615i	0.340411	+	0.196537i
$700$	−16.0000	+	27.7128i	−0.604743	+	1.04745i
$701$	36.0000			1.35970			0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000			1.35970			0.679851	+	0.733351i	$0.262045\pi$
$702$		0			0
$703$	4.00000			0.150863
$704$	4.00000	−	6.92820i	0.150756	−	0.261116i
$705$	13.5000	+	7.79423i	0.508439	+	0.293548i
$706$		0			0
$707$	12.0000	+	20.7846i	0.451306	+	0.781686i
$708$		0			0
$709$	−11.5000	+	19.9186i	−0.431892	+	0.748058i	−0.997036	−	0.0769337i	$-0.975487\pi$
$709$	−11.5000	+	19.9186i	−0.431892	+	0.748058i	0.565145	+	0.824992i	$0.308820\pi$
$710$		0			0
$711$	−6.00000			−0.225018
$712$		0			0
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$	3.00000	+	5.19615i	0.112194	+	0.194325i
$716$	15.0000	+	25.9808i	0.560576	+	0.970947i
$717$		−	20.7846i		−	0.776215i
$718$		0			0
$719$	−3.00000			−0.111881			−0.0559406	−	0.998434i	$-0.517816\pi$
$719$	−3.00000			−0.111881			−0.0559406	+	0.998434i	$0.517816\pi$
$720$	−18.0000	−	31.1769i	−0.670820	−	1.16190i
$721$	−20.0000			−0.744839
$722$		0			0
$723$	3.00000	−	1.73205i	0.111571	−	0.0644157i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$		0			0
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	24.0000	+	13.8564i	0.887066	+	0.512148i
$733$	20.0000	+	34.6410i	0.738717	+	1.27950i	0.953073	+	0.302740i	$0.0979013\pi$
$733$	20.0000	+	34.6410i	0.738717	+	1.27950i	−0.214356	+	0.976756i	$0.568765\pi$
$734$		0			0
$735$	−40.5000	+	23.3827i	−1.49387	+	0.862483i
$736$		0			0
$737$	−13.0000			−0.478861
$738$		0			0
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	−6.00000	+	10.3923i	−0.220564	+	0.382029i
$741$			6.92820i			0.254514i
$742$		0			0
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		0			0
$745$	−18.0000	+	31.1769i	−0.659469	+	1.14223i
$746$		0			0
$747$	54.0000			1.97576
$748$	12.0000			0.438763
$749$	−24.0000	+	41.5692i	−0.876941	+	1.51891i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$	22.5000	+	12.9904i	0.819946	+	0.473396i
$754$		0			0
$755$	−24.0000			−0.873449
$756$		−	41.5692i		−	1.51186i
$757$	29.0000			1.05402			0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000			1.05402			0.527011	+	0.849858i	$0.323312\pi$
$758$		0			0
$759$	−4.50000	−	2.59808i	−0.163340	−	0.0943042i
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		0			0
$763$	28.0000	−	48.4974i	1.01367	−	1.75572i
$764$	−6.00000			−0.217072
$765$	27.0000	−	46.7654i	0.976187	−	1.69081i
$766$		0			0
$767$		0			0
$768$			27.7128i			1.00000i
$769$	−4.00000	−	6.92820i	−0.144244	−	0.249837i	0.784847	−	0.619690i	$-0.212742\pi$
$769$	−4.00000	−	6.92820i	−0.144244	−	0.249837i	−0.929091	+	0.369852i	$0.879408\pi$
$770$		0			0
$771$			10.3923i			0.374270i
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$		0			0
$775$	32.0000			1.14947
$776$		0			0
$777$	−12.0000	+	6.92820i	−0.430498	+	0.248548i
$778$		0			0
$779$		0			0
$780$	−18.0000	−	10.3923i	−0.644503	−	0.372104i
$781$		0			0
$782$		0			0
$783$	−27.0000	−	15.5885i	−0.964901	−	0.557086i
$784$	36.0000			1.28571
$785$	−10.5000	+	18.1865i	−0.374761	+	0.649105i
$786$		0			0
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	18.0000	+	31.1769i	0.641223	+	1.11063i
$789$	−36.0000	+	20.7846i	−1.28163	+	0.739952i
$790$		0			0
$791$	24.0000			0.853342
$792$		0			0
$793$	16.0000			0.568177
$794$		0			0
$795$		−	15.5885i		−	0.552866i
$796$	11.0000	+	19.0526i	0.389885	+	0.675300i
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	−0.999331	−	0.0365596i	$-0.988360\pi$
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	0.468004	−	0.883726i	$-0.344973\pi$
$798$		0			0
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$		0			0
$801$	4.50000	+	7.79423i	0.159000	+	0.275396i
$802$		0			0
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$	39.0000	−	22.5167i	1.37542	−	0.794101i
$805$	−18.0000	−	31.1769i	−0.634417	−	1.09884i
$806$		0			0
$807$	−40.5000	−	23.3827i	−1.42567	−	0.823110i
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	24.0000	−	41.5692i	0.842235	−	1.45879i
$813$	−3.00000	−	1.73205i	−0.105215	−	0.0607457i
$814$		0			0
$815$	−1.50000	−	2.59808i	−0.0525427	−	0.0910066i
$816$	−36.0000	+	20.7846i	−1.26025	+	0.727607i
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$		0			0
$819$	−12.0000	−	20.7846i	−0.419314	−	0.726273i
$820$		0			0
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	−0.951526	−	0.307568i	$-0.900485\pi$
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	0.742125	+	0.670262i	$0.233818\pi$
$822$		0			0
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	0.877555	+	0.479477i	$0.159174\pi$
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	−0.0235383	+	0.999723i	$0.507493\pi$
$824$		0			0
$825$			6.92820i			0.241209i
$826$		0			0
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	18.0000			0.625543
$829$	−7.00000			−0.243120			−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000			−0.243120			−0.121560	+	0.992584i	$0.538790\pi$
$830$		0			0
$831$	3.00000	−	1.73205i	0.104069	−	0.0600842i
$832$	8.00000	+	13.8564i	0.277350	+	0.480384i
$833$	27.0000	+	46.7654i	0.935495	+	1.62032i
$834$		0			0
$835$	27.0000	−	46.7654i	0.934374	−	1.61838i
$836$	−4.00000			−0.138343
$837$	−36.0000	+	20.7846i	−1.24434	+	0.718421i
$838$		0			0
$839$	−7.50000	+	12.9904i	−0.258929	+	0.448478i	−0.965955	−	0.258709i	$-0.916703\pi$
$839$	−7.50000	+	12.9904i	−0.258929	+	0.448478i	0.707026	+	0.707187i	$0.250036\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	−18.0000	+	10.3923i	−0.619953	+	0.357930i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	27.0000			0.928828
$846$		0			0
$847$	−4.00000			−0.137442
$848$	−6.00000	+	10.3923i	−0.206041	+	0.356873i
$849$		−	17.3205i		−	0.594438i
$850$		0			0
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$		0			0
$853$	−22.0000	+	38.1051i	−0.753266	+	1.30469i	0.192966	+	0.981205i	$0.438189\pi$
$853$	−22.0000	+	38.1051i	−0.753266	+	1.30469i	−0.946232	+	0.323489i	$0.895144\pi$
$854$		0			0
$855$	−9.00000	+	15.5885i	−0.307794	+	0.533114i
$856$		0			0
$857$	6.00000	−	10.3923i	0.204956	−	0.354994i	−0.745163	−	0.666883i	$-0.767628\pi$
$857$	6.00000	−	10.3923i	0.204956	−	0.354994i	0.950119	+	0.311888i	$0.100962\pi$
$858$		0			0
$859$	6.50000	+	11.2583i	0.221777	+	0.384129i	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	6.50000	+	11.2583i	0.221777	+	0.384129i	−0.733571	+	0.679613i	$0.762148\pi$
$860$	−24.0000	−	41.5692i	−0.818393	−	1.41750i
$861$		0			0
$862$		0			0
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	−54.0000			−1.83606
$866$		0			0
$867$	−28.5000	−	16.4545i	−0.967911	−	0.558824i
$868$	−32.0000	−	55.4256i	−1.08615	−	1.88127i
$869$	−1.00000	−	1.73205i	−0.0339227	−	0.0587558i
$870$		0			0
$871$	13.0000	−	22.5167i	0.440488	−	0.762948i
$872$		0			0
$873$	−6.00000			−0.203069
$874$		0			0
$875$	6.00000	−	10.3923i	0.202837	−	0.351324i
$876$		−	6.92820i		−	0.234082i
$877$	20.0000	+	34.6410i	0.675352	+	1.16974i	0.976366	+	0.216124i	$0.0693416\pi$
$877$	20.0000	+	34.6410i	0.675352	+	1.16974i	−0.301014	+	0.953620i	$0.597325\pi$
$878$		0			0
$879$			10.3923i			0.350524i
$880$	6.00000	−	10.3923i	0.202260	−	0.350325i
$881$	−39.0000			−1.31394			−0.656972	−	0.753915i	$-0.728163\pi$
$881$	−39.0000			−1.31394			−0.656972	+	0.753915i	$0.728163\pi$
$882$		0			0
$883$	5.00000			0.168263			0.0841317	−	0.996455i	$-0.473188\pi$
$883$	5.00000			0.168263			0.0841317	+	0.996455i	$0.473188\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$		0			0
$887$	15.0000	+	25.9808i	0.503651	+	0.872349i	0.999991	+	0.00422062i	$0.00134347\pi$
$887$	15.0000	+	25.9808i	0.503651	+	0.872349i	−0.496340	+	0.868128i	$0.665323\pi$
$888$		0			0
$889$	−8.00000	+	13.8564i	−0.268311	+	0.464729i
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	−22.0000			−0.736614
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$		0			0
$895$	22.5000	+	38.9711i	0.752092	+	1.30266i
$896$		0			0
$897$	9.00000	−	5.19615i	0.300501	−	0.173494i
$898$		0			0
$899$	−48.0000			−1.60089
$900$	−12.0000	−	20.7846i	−0.400000	−	0.692820i
$901$	−18.0000			−0.599667
$902$		0			0
$903$		−	55.4256i		−	1.84445i
$904$		0			0
$905$	−1.50000	−	2.59808i	−0.0498617	−	0.0863630i
$906$		0			0
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	−36.0000			−1.19470
$909$	−18.0000			−0.597022
$910$		0			0
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$	12.0000	−	6.92820i	0.397360	−	0.229416i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$		0			0
$915$	36.0000	+	20.7846i	1.19012	+	0.687118i
$916$	23.0000	−	39.8372i	0.759941	−	1.31626i
$917$	−72.0000			−2.37765
$918$		0			0
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$		0			0
$921$	24.0000	+	13.8564i	0.790827	+	0.456584i
$922$		0			0
$923$		0			0
$924$	12.0000	−	6.92820i	0.394771	−	0.227921i
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$		0			0
$927$	7.50000	−	12.9904i	0.246332	−	0.426660i
$928$		0			0
$929$	−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
$931$	−9.00000	−	15.5885i	−0.294963	−	0.510891i
$932$	−6.00000	−	10.3923i	−0.196537	−	0.340411i
$933$		−	5.19615i		−	0.170114i
$934$		0			0
$935$	18.0000			0.588663
$936$		0			0
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$		0			0
$939$	16.5000	−	9.52628i	0.538457	−	0.310878i
$940$	−9.00000	−	15.5885i	−0.293548	−	0.508439i
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		−	62.3538i		−	2.02837i
$946$		0			0
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	−0.889368	−	0.457193i	$-0.848855\pi$
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	0.840624	+	0.541619i	$0.182188\pi$
$948$	6.00000	+	3.46410i	0.194871	+	0.112509i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	−40.5000	+	23.3827i	−1.31330	+	0.758236i
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	−9.00000			−0.291233
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		−	10.3923i		−	0.335936i
$958$		0			0
$959$	36.0000	+	62.3538i	1.16250	+	2.01351i
$960$			41.5692i			1.34164i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$	−18.0000	−	31.1769i	−0.580042	−	1.00466i
$964$	−4.00000			−0.128831
$965$	−6.00000	+	10.3923i	−0.193147	+	0.334540i
$966$		0			0
$967$	20.0000	+	34.6410i	0.643157	+	1.11398i	0.984724	+	0.174123i	$0.0557089\pi$
$967$	20.0000	+	34.6410i	0.643157	+	1.11398i	−0.341567	+	0.939857i	$0.610958\pi$
$968$		0			0
$969$	18.0000	+	10.3923i	0.578243	+	0.333849i
$970$		0			0
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$	27.0000	+	15.5885i	0.866025	+	0.500000i
$973$	40.0000			1.28234
$974$		0			0
$975$	−12.0000	−	6.92820i	−0.384308	−	0.221880i
$976$	−16.0000	−	27.7128i	−0.512148	−	0.887066i
$977$	−22.5000	−	38.9711i	−0.719839	−	1.24680i	−0.961063	−	0.276328i	$-0.910882\pi$
$977$	−22.5000	−	38.9711i	−0.719839	−	1.24680i	0.241225	−	0.970469i	$-0.422451\pi$
$978$		0			0
$979$	−1.50000	+	2.59808i	−0.0479402	+	0.0830349i
$980$	54.0000			1.72497
$981$	21.0000	+	36.3731i	0.670478	+	1.16130i
$982$		0			0
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$		0			0
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$		0			0
$987$		−	20.7846i		−	0.661581i
$988$	4.00000	−	6.92820i	0.127257	−	0.220416i
$989$	24.0000			0.763156
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	43.5000	−	25.1147i	1.38043	−	0.796992i
$994$		0			0
$995$	16.5000	+	28.5788i	0.523085	+	0.906010i
$996$	−54.0000	−	31.1769i	−1.71106	−	0.987878i
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$		0			0
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.b.34.1	✓	2
3.2	odd	2		297.2.e.b.100.1		2
9.2	odd	6		891.2.a.e.1.1		1
9.4	even	3	inner	99.2.e.b.67.1	yes	2
9.5	odd	6		297.2.e.b.199.1		2
9.7	even	3		891.2.a.d.1.1		1
11.10	odd	2		1089.2.e.b.727.1		2
99.43	odd	6		9801.2.a.f.1.1		1
99.65	even	6		9801.2.a.g.1.1		1
99.76	odd	6		1089.2.e.b.364.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.b.34.1	✓	2	1.1	even	1	trivial
99.2.e.b.67.1	yes	2	9.4	even	3	inner
297.2.e.b.100.1		2	3.2	odd	2
297.2.e.b.199.1		2	9.5	odd	6
891.2.a.d.1.1		1	9.7	even	3
891.2.a.e.1.1		1	9.2	odd	6
1089.2.e.b.364.1		2	99.76	odd	6
1089.2.e.b.727.1		2	11.10	odd	2
9801.2.a.f.1.1		1	99.43	odd	6
9801.2.a.g.1.1		1	99.65	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{11} -3.46410i q^{12} +(-1.00000 - 1.73205i) q^{13} -5.19615i q^{15} +(-2.00000 + 3.46410i) q^{16} -6.00000 q^{17} +2.00000 q^{19} +(-3.00000 + 5.19615i) q^{20} +(-6.00000 + 3.46410i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.19615i q^{27} +8.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(1.50000 - 0.866025i) q^{33} +12.0000 q^{35} +(-3.00000 + 5.19615i) q^{36} +2.00000 q^{37} +3.46410i q^{39} +(-4.00000 + 6.92820i) q^{43} -2.00000 q^{44} +(-4.50000 + 7.79423i) q^{45} +(-1.50000 + 2.59808i) q^{47} +(6.00000 - 3.46410i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(9.00000 + 5.19615i) q^{51} +(2.00000 - 3.46410i) q^{52} +3.00000 q^{53} -3.00000 q^{55} +(-3.00000 - 1.73205i) q^{57} +(9.00000 - 5.19615i) q^{60} +(-4.00000 + 6.92820i) q^{61} +12.0000 q^{63} -8.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(6.50000 + 11.2583i) q^{67} +(-6.00000 - 10.3923i) q^{68} +5.19615i q^{69} +2.00000 q^{73} +(6.00000 - 3.46410i) q^{75} +(2.00000 + 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +(-1.00000 + 1.73205i) q^{79} -12.0000 q^{80} +(-4.50000 + 7.79423i) q^{81} +(9.00000 - 15.5885i) q^{83} +(-12.0000 - 6.92820i) q^{84} +(-9.00000 - 15.5885i) q^{85} +(-9.00000 + 5.19615i) q^{87} +3.00000 q^{89} -8.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +13.8564i q^{93} +(3.00000 + 5.19615i) q^{95} +(-1.00000 + 1.73205i) q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 2 q^{4} + 3 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 2 * q^4 + 3 * q^5 + 4 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} + 2 q^{4} + 3 q^{5} + 4 q^{7} + 3 q^{9} - q^{11} - 2 q^{13} - 4 q^{16} - 12 q^{17} + 4 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} - 4 q^{25} + 16 q^{28} + 6 q^{29} - 8 q^{31} + 3 q^{33} + 24 q^{35} - 6 q^{36} + 4 q^{37} - 8 q^{43} - 4 q^{44} - 9 q^{45} - 3 q^{47} + 12 q^{48} - 9 q^{49} + 18 q^{51} + 4 q^{52} + 6 q^{53} - 6 q^{55} - 6 q^{57} + 18 q^{60} - 8 q^{61} + 24 q^{63} - 16 q^{64} + 6 q^{65} + 13 q^{67} - 12 q^{68} + 4 q^{73} + 12 q^{75} + 4 q^{76} + 4 q^{77} - 2 q^{79} - 24 q^{80} - 9 q^{81} + 18 q^{83} - 24 q^{84} - 18 q^{85} - 18 q^{87} + 6 q^{89} - 16 q^{91} + 6 q^{92} + 6 q^{95} - 2 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 2 * q^4 + 3 * q^5 + 4 * q^7 + 3 * q^9 - q^11 - 2 * q^13 - 4 * q^16 - 12 * q^17 + 4 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 - 4 * q^25 + 16 * q^28 + 6 * q^29 - 8 * q^31 + 3 * q^33 + 24 * q^35 - 6 * q^36 + 4 * q^37 - 8 * q^43 - 4 * q^44 - 9 * q^45 - 3 * q^47 + 12 * q^48 - 9 * q^49 + 18 * q^51 + 4 * q^52 + 6 * q^53 - 6 * q^55 - 6 * q^57 + 18 * q^60 - 8 * q^61 + 24 * q^63 - 16 * q^64 + 6 * q^65 + 13 * q^67 - 12 * q^68 + 4 * q^73 + 12 * q^75 + 4 * q^76 + 4 * q^77 - 2 * q^79 - 24 * q^80 - 9 * q^81 + 18 * q^83 - 24 * q^84 - 18 * q^85 - 18 * q^87 + 6 * q^89 - 16 * q^91 + 6 * q^92 + 6 * q^95 - 2 * q^97 - 6 * q^99

Introduction

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