LMFDB - Embedded newform 342.2.h.c.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.c.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(-1.50000 + 0.866025i) q^{12} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-0.500000 + 4.33013i) q^{19} +(-6.00000 + 3.46410i) q^{21} +5.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(1.50000 + 0.866025i) q^{24} -5.00000 q^{25} +5.19615i q^{27} +(-2.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(-0.500000 + 0.866025i) q^{32} +(-7.50000 + 4.33013i) q^{33} -7.00000 q^{34} -3.00000 q^{36} +10.0000 q^{37} +(4.00000 - 1.73205i) q^{38} +2.00000 q^{41} +(6.00000 + 3.46410i) q^{42} +(-4.50000 - 7.79423i) q^{43} +(-2.50000 - 4.33013i) q^{44} -4.00000 q^{46} +8.00000 q^{47} -1.73205i q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.50000 + 4.33013i) q^{50} +(10.5000 - 6.06218i) q^{51} +(1.00000 + 1.73205i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-2.00000 + 3.46410i) q^{56} +(-4.50000 + 6.06218i) q^{57} +(-3.00000 - 5.19615i) q^{58} -4.00000 q^{59} +8.00000 q^{61} -12.0000 q^{63} +1.00000 q^{64} +(7.50000 + 4.33013i) q^{66} +(-6.00000 + 10.3923i) q^{67} +(3.50000 + 6.06218i) q^{68} +(6.00000 - 3.46410i) q^{69} +(4.00000 - 6.92820i) q^{71} +(1.50000 + 2.59808i) q^{72} +(-3.50000 + 6.06218i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-7.50000 - 4.33013i) q^{75} +(-3.50000 - 2.59808i) q^{76} +(-10.0000 - 17.3205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.00000 - 1.73205i) q^{82} +(2.50000 - 4.33013i) q^{83} -6.92820i q^{84} +(-4.50000 + 7.79423i) q^{86} +(9.00000 + 5.19615i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-7.00000 - 12.1244i) q^{89} +(2.00000 + 3.46410i) q^{92} +(-4.00000 - 6.92820i) q^{94} +(-1.50000 + 0.866025i) q^{96} +(3.50000 + 6.06218i) q^{97} +(-4.50000 + 7.79423i) q^{98} -15.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 5 q^{11} - 3 q^{12} + 8 q^{14} - q^{16} + 7 q^{17} + 3 q^{18} - q^{19} - 12 q^{21} + 10 q^{22} + 4 q^{23} + 3 q^{24} - 10 q^{25} - 4 q^{28} + 12 q^{29} - q^{32} - 15 q^{33} - 14 q^{34} - 6 q^{36} + 20 q^{37} + 8 q^{38} + 4 q^{41} + 12 q^{42} - 9 q^{43} - 5 q^{44} - 8 q^{46} + 16 q^{47} - 9 q^{49} + 5 q^{50} + 21 q^{51} + 2 q^{53} + 9 q^{54} - 4 q^{56} - 9 q^{57} - 6 q^{58} - 8 q^{59} + 16 q^{61} - 24 q^{63} + 2 q^{64} + 15 q^{66} - 12 q^{67} + 7 q^{68} + 12 q^{69} + 8 q^{71} + 3 q^{72} - 7 q^{73} - 10 q^{74} - 15 q^{75} - 7 q^{76} - 20 q^{77} - 10 q^{79} - 9 q^{81} - 2 q^{82} + 5 q^{83} - 9 q^{86} + 18 q^{87} - 5 q^{88} - 14 q^{89} + 4 q^{92} - 8 q^{94} - 3 q^{96} + 7 q^{97} - 9 q^{98} - 30 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 5 * q^11 - 3 * q^12 + 8 * q^14 - q^16 + 7 * q^17 + 3 * q^18 - q^19 - 12 * q^21 + 10 * q^22 + 4 * q^23 + 3 * q^24 - 10 * q^25 - 4 * q^28 + 12 * q^29 - q^32 - 15 * q^33 - 14 * q^34 - 6 * q^36 + 20 * q^37 + 8 * q^38 + 4 * q^41 + 12 * q^42 - 9 * q^43 - 5 * q^44 - 8 * q^46 + 16 * q^47 - 9 * q^49 + 5 * q^50 + 21 * q^51 + 2 * q^53 + 9 * q^54 - 4 * q^56 - 9 * q^57 - 6 * q^58 - 8 * q^59 + 16 * q^61 - 24 * q^63 + 2 * q^64 + 15 * q^66 - 12 * q^67 + 7 * q^68 + 12 * q^69 + 8 * q^71 + 3 * q^72 - 7 * q^73 - 10 * q^74 - 15 * q^75 - 7 * q^76 - 20 * q^77 - 10 * q^79 - 9 * q^81 - 2 * q^82 + 5 * q^83 - 9 * q^86 + 18 * q^87 - 5 * q^88 - 14 * q^89 + 4 * q^92 - 8 * q^94 - 3 * q^96 + 7 * q^97 - 9 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		−	1.73205i		−	0.707107i
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$	4.00000			1.06904
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	−0.0333386	−	0.999444i	$-0.510614\pi$
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	0.882213	−	0.470850i	$-0.156053\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$		0			0
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$	5.00000			1.06600
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−5.00000			−1.00000
$26$		0			0
$27$			5.19615i			1.00000i
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−7.50000	+	4.33013i	−1.30558	+	0.753778i
$34$	−7.00000			−1.20049
$35$		0			0
$36$	−3.00000			−0.500000
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$	4.00000	−	1.73205i	0.648886	−	0.280976i
$39$		0			0
$40$		0			0
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$	6.00000	+	3.46410i	0.925820	+	0.534522i
$43$	−4.50000	−	7.79423i	−0.686244	−	1.18861i	−0.973044	−	0.230618i	$-0.925925\pi$
$43$	−4.50000	−	7.79423i	−0.686244	−	1.18861i	0.286801	−	0.957990i	$-0.407408\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$		0			0
$46$	−4.00000			−0.589768
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		−	1.73205i		−	0.250000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	10.5000	−	6.06218i	1.47029	−	0.848875i
$52$		0			0
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$		0			0
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$	−4.50000	+	6.06218i	−0.596040	+	0.802955i
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$		0			0
$63$	−12.0000			−1.51186
$64$	1.00000			0.125000
$65$		0			0
$66$	7.50000	+	4.33013i	0.923186	+	0.533002i
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	3.50000	+	6.06218i	0.424437	+	0.735147i
$69$	6.00000	−	3.46410i	0.722315	−	0.417029i
$70$		0			0
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	−0.524868	−	0.851184i	$-0.675885\pi$
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	0.999581	+	0.0289572i	$0.00921865\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	0.585206	+	0.810885i	$0.301014\pi$
$74$	−5.00000	−	8.66025i	−0.581238	−	1.00673i
$75$	−7.50000	−	4.33013i	−0.866025	−	0.500000i
$76$	−3.50000	−	2.59808i	−0.401478	−	0.298020i
$77$	−10.0000	−	17.3205i	−1.13961	−	1.97386i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	2.50000	−	4.33013i	0.274411	−	0.475293i	−0.695576	−	0.718453i	$-0.744851\pi$
$83$	2.50000	−	4.33013i	0.274411	−	0.475293i	0.969986	+	0.243160i	$0.0781839\pi$
$84$		−	6.92820i		−	0.755929i
$85$		0			0
$86$	−4.50000	+	7.79423i	−0.485247	+	0.840473i
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$		0			0
$91$		0			0
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$		0			0
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	0.987181	−	0.159602i	$-0.0510211\pi$
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	−0.631810	+	0.775123i	$0.717688\pi$
$98$	−4.50000	+	7.79423i	−0.454569	+	0.787336i
$99$	−15.0000			−1.50756
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−14.0000			−1.39305			−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000			−1.39305			−0.696526	+	0.717532i	$0.745272\pi$
$102$	−10.5000	−	6.06218i	−1.03965	−	0.600245i
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	0.975124	−	0.221660i	$-0.0711475\pi$
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	−0.679525	+	0.733652i	$0.737814\pi$
$104$		0			0
$105$		0			0
$106$	1.00000	−	1.73205i	0.0971286	−	0.168232i
$107$	−11.0000			−1.06341			−0.531705	−	0.846930i	$-0.678449\pi$
$107$	−11.0000			−1.06341			−0.531705	+	0.846930i	$0.678449\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$		0			0
$111$	15.0000	+	8.66025i	1.42374	+	0.821995i
$112$	4.00000			0.377964
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$	7.50000	+	0.866025i	0.702439	+	0.0811107i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$		0			0
$118$	2.00000	+	3.46410i	0.184115	+	0.318896i
$119$	14.0000	+	24.2487i	1.28338	+	2.22288i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	3.00000	+	1.73205i	0.270501	+	0.156174i
$124$		0			0
$125$		0			0
$126$	6.00000	+	10.3923i	0.534522	+	0.925820i
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		−	15.5885i		−	1.37249i
$130$		0			0
$131$	21.0000			1.83478			0.917389	−	0.397991i	$-0.130293\pi$
$131$	21.0000			1.83478			0.917389	+	0.397991i	$0.130293\pi$
$132$		−	8.66025i		−	0.753778i
$133$	−14.0000	−	10.3923i	−1.21395	−	0.901127i
$134$	12.0000			1.03664
$135$		0			0
$136$	3.50000	−	6.06218i	0.300123	−	0.519827i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$	−6.00000	−	3.46410i	−0.510754	−	0.294884i
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$		0			0
$141$	12.0000	+	6.92820i	1.01058	+	0.583460i
$142$	−8.00000			−0.671345
$143$		0			0
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	7.00000			0.579324
$147$		−	15.5885i		−	1.28571i
$148$	−5.00000	+	8.66025i	−0.410997	+	0.711868i
$149$	−20.0000			−1.63846			−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000			−1.63846			−0.819232	+	0.573462i	$0.805600\pi$
$150$			8.66025i			0.707107i
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−0.500000	+	4.33013i	−0.0405554	+	0.351220i
$153$	21.0000			1.69775
$154$	−10.0000	+	17.3205i	−0.805823	+	1.39573i
$155$		0			0
$156$		0			0
$157$	24.0000			1.91541			0.957704	−	0.287754i	$-0.0929087\pi$
$157$	24.0000			1.91541			0.957704	+	0.287754i	$0.0929087\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$			3.46410i			0.274721i
$160$		0			0
$161$	8.00000	+	13.8564i	0.630488	+	1.09204i
$162$	9.00000			0.707107
$163$	17.0000			1.33154			0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000			1.33154			0.665771	+	0.746156i	$0.268103\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$		0			0
$166$	−5.00000			−0.388075
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	−6.00000	+	3.46410i	−0.462910	+	0.267261i
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$		0			0
$171$	−12.0000	+	5.19615i	−0.917663	+	0.397360i
$172$	9.00000			0.686244
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		−	10.3923i		−	0.787839i
$175$	10.0000	−	17.3205i	0.755929	−	1.30931i
$176$	5.00000			0.376889
$177$	−6.00000	−	3.46410i	−0.450988	−	0.260378i
$178$	−7.00000	+	12.1244i	−0.524672	+	0.908759i
$179$	5.00000			0.373718			0.186859	−	0.982387i	$-0.440169\pi$
$179$	5.00000			0.373718			0.186859	+	0.982387i	$0.440169\pi$
$180$		0			0
$181$	6.00000	+	10.3923i	0.445976	+	0.772454i	0.998120	−	0.0612954i	$-0.0195232\pi$
$181$	6.00000	+	10.3923i	0.445976	+	0.772454i	−0.552143	+	0.833749i	$0.686190\pi$
$182$		0			0
$183$	12.0000	+	6.92820i	0.887066	+	0.512148i
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$		0			0
$186$		0			0
$187$	17.5000	+	30.3109i	1.27973	+	2.21655i
$188$	−4.00000	+	6.92820i	−0.291730	+	0.505291i
$189$	−18.0000	−	10.3923i	−1.30931	−	0.755929i
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	9.00000			0.642857
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	7.50000	+	12.9904i	0.533002	+	0.923186i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	−5.00000			−0.353553
$201$	−18.0000	+	10.3923i	−1.26962	+	0.733017i
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	−12.0000	+	20.7846i	−0.842235	+	1.45879i
$204$			12.1244i			0.848875i
$205$		0			0
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	12.0000			0.834058
$208$		0			0
$209$	−17.5000	−	12.9904i	−1.21050	−	0.898563i
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−2.00000			−0.137361
$213$	12.0000	−	6.92820i	0.822226	−	0.474713i
$214$	5.50000	+	9.52628i	0.375972	+	0.651203i
$215$		0			0
$216$			5.19615i			0.353553i
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−10.5000	+	6.06218i	−0.709524	+	0.409644i
$220$		0			0
$221$		0			0
$222$		−	17.3205i		−	1.16248i
$223$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$223$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$	−7.50000	−	12.9904i	−0.500000	−	0.866025i
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	5.50000	−	9.52628i	0.365048	−	0.632281i	−0.623736	−	0.781635i	$-0.714386\pi$
$227$	5.50000	−	9.52628i	0.365048	−	0.632281i	0.988784	+	0.149354i	$0.0477193\pi$
$228$	−3.00000	−	6.92820i	−0.198680	−	0.458831i
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$		0			0
$231$		−	34.6410i		−	2.27921i
$232$	6.00000			0.393919
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$		0			0
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$		−	17.3205i		−	1.12509i
$238$	14.0000	−	24.2487i	0.907485	−	1.57181i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$		0			0
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$		0			0
$246$		−	3.46410i		−	0.220863i
$247$		0			0
$248$		0			0
$249$	7.50000	−	4.33013i	0.475293	−	0.274411i
$250$		0			0
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	6.00000	−	10.3923i	0.377964	−	0.654654i
$253$	10.0000	+	17.3205i	0.628695	+	1.08893i
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	−13.5000	+	7.79423i	−0.840473	+	0.485247i
$259$	−20.0000	+	34.6410i	−1.24274	+	2.15249i
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	−10.5000	−	18.1865i	−0.648692	−	1.12357i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$	−7.50000	+	4.33013i	−0.461593	+	0.266501i
$265$		0			0
$266$	−2.00000	+	17.3205i	−0.122628	+	1.06199i
$267$		−	24.2487i		−	1.48400i
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	0.0243472	+	0.999704i	$0.492249\pi$
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	−0.877942	+	0.478766i	$0.841084\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$	−7.00000			−0.424437
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	12.5000	−	21.6506i	0.753778	−	1.30558i
$276$			6.92820i			0.417029i
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	−7.00000			−0.419832
$279$		0			0
$280$		0			0
$281$	−1.00000			−0.0596550			−0.0298275	−	0.999555i	$-0.509496\pi$
$281$	−1.00000			−0.0596550			−0.0298275	+	0.999555i	$0.509496\pi$
$282$		−	13.8564i		−	0.825137i
$283$	−11.0000			−0.653882			−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000			−0.653882			−0.326941	+	0.945045i	$0.606018\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$		0			0
$286$		0			0
$287$	−4.00000	+	6.92820i	−0.236113	+	0.408959i
$288$	−3.00000			−0.176777
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$			12.1244i			0.710742i
$292$	−3.50000	−	6.06218i	−0.204822	−	0.354762i
$293$	1.00000	+	1.73205i	0.0584206	+	0.101187i	0.893757	−	0.448552i	$-0.148060\pi$
$293$	1.00000	+	1.73205i	0.0584206	+	0.101187i	−0.835336	+	0.549740i	$0.814727\pi$
$294$	−13.5000	+	7.79423i	−0.787336	+	0.454569i
$295$		0			0
$296$	10.0000			0.581238
$297$	−22.5000	−	12.9904i	−1.30558	−	0.753778i
$298$	10.0000	+	17.3205i	0.579284	+	1.00335i
$299$		0			0
$300$	7.50000	−	4.33013i	0.433013	−	0.250000i
$301$	36.0000			2.07501
$302$	−2.00000			−0.115087
$303$	−21.0000	−	12.1244i	−1.20642	−	0.696526i
$304$	4.00000	−	1.73205i	0.229416	−	0.0993399i
$305$		0			0
$306$	−10.5000	−	18.1865i	−0.600245	−	1.03965i
$307$	−6.00000	+	10.3923i	−0.342438	+	0.593120i	−0.984885	−	0.173210i	$-0.944586\pi$
$307$	−6.00000	+	10.3923i	−0.342438	+	0.593120i	0.642447	+	0.766330i	$0.277919\pi$
$308$	20.0000			1.13961
$309$			10.3923i			0.591198i
$310$		0			0
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	0.596412	−	0.802678i	$-0.296592\pi$
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	−0.993346	+	0.115169i	$0.963259\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−12.0000	−	20.7846i	−0.677199	−	1.17294i
$315$		0			0
$316$	10.0000			0.562544
$317$	24.0000			1.34797			0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000			1.34797			0.673987	+	0.738743i	$0.264580\pi$
$318$	3.00000	−	1.73205i	0.168232	−	0.0971286i
$319$	−15.0000	+	25.9808i	−0.839839	+	1.45464i
$320$		0			0
$321$	−16.5000	−	9.52628i	−0.920940	−	0.531705i
$322$	8.00000	−	13.8564i	0.445823	−	0.772187i
$323$	24.5000	+	18.1865i	1.36322	+	1.01193i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	−8.50000	−	14.7224i	−0.470771	−	0.815400i
$327$	15.0000	−	8.66025i	0.829502	−	0.478913i
$328$	2.00000			0.110432
$329$	−16.0000	+	27.7128i	−0.882109	+	1.52786i
$330$		0			0
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	−0.209544	−	0.977799i	$-0.567198\pi$
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	0.951571	−	0.307429i	$-0.0994688\pi$
$332$	2.50000	+	4.33013i	0.137205	+	0.237647i
$333$	15.0000	+	25.9808i	0.821995	+	1.42374i
$334$		0			0
$335$		0			0
$336$	6.00000	+	3.46410i	0.327327	+	0.188982i
$337$	−1.00000			−0.0544735			−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000			−0.0544735			−0.0272367	+	0.999629i	$0.508671\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$			1.73205i			0.0940721i
$340$		0			0
$341$		0			0
$342$	10.5000	+	7.79423i	0.567775	+	0.421464i
$343$	8.00000			0.431959
$344$	−4.50000	−	7.79423i	−0.242624	−	0.420237i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	5.00000			0.268414			0.134207	−	0.990953i	$-0.457151\pi$
$347$	5.00000			0.268414			0.134207	+	0.990953i	$0.457151\pi$
$348$	−9.00000	+	5.19615i	−0.482451	+	0.278543i
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	−0.274011	−	0.961727i	$-0.588351\pi$
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$	−20.0000			−1.06904
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$			6.92820i			0.368230i
$355$		0			0
$356$	14.0000			0.741999
$357$			48.4974i			2.56676i
$358$	−2.50000	−	4.33013i	−0.132129	−	0.228854i
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	−0.524588	−	0.851356i	$-0.675781\pi$
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	0.999590	+	0.0286287i	$0.00911406\pi$
$360$		0			0
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	6.00000	−	10.3923i	0.315353	−	0.546207i
$363$		−	24.2487i		−	1.27273i
$364$		0			0
$365$		0			0
$366$		−	13.8564i		−	0.724286i
$367$	14.0000			0.730794			0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000			0.730794			0.365397	+	0.930852i	$0.380933\pi$
$368$	−4.00000			−0.208514
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$	−8.00000			−0.415339
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	17.5000	−	30.3109i	0.904903	−	1.56734i
$375$		0			0
$376$	8.00000			0.412568
$377$		0			0
$378$			20.7846i			1.06904i
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$		0			0
$381$			13.8564i			0.709885i
$382$	8.00000			0.409316
$383$	−14.0000			−0.715367			−0.357683	−	0.933843i	$-0.616433\pi$
$383$	−14.0000			−0.715367			−0.357683	+	0.933843i	$0.616433\pi$
$384$		−	1.73205i		−	0.0883883i
$385$		0			0
$386$	−2.50000	−	4.33013i	−0.127247	−	0.220398i
$387$	13.5000	−	23.3827i	0.686244	−	1.18861i
$388$	−7.00000			−0.355371
$389$	4.00000			0.202808			0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000			0.202808			0.101404	+	0.994845i	$0.467667\pi$
$390$		0			0
$391$	−14.0000	−	24.2487i	−0.708010	−	1.22631i
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$	31.5000	+	18.1865i	1.58896	+	0.917389i
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$		0			0
$396$	7.50000	−	12.9904i	0.376889	−	0.652791i
$397$	3.00000	−	5.19615i	0.150566	−	0.260787i	−0.780870	−	0.624694i	$-0.785224\pi$
$397$	3.00000	−	5.19615i	0.150566	−	0.260787i	0.931436	+	0.363906i	$0.118557\pi$
$398$	2.00000	−	3.46410i	0.100251	−	0.173640i
$399$	−12.0000	−	27.7128i	−0.600751	−	1.38738i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$	18.0000	+	10.3923i	0.897758	+	0.518321i
$403$		0			0
$404$	7.00000	−	12.1244i	0.348263	−	0.603209i
$405$		0			0
$406$	24.0000			1.19110
$407$	−25.0000	+	43.3013i	−1.23920	+	2.14636i
$408$	10.5000	−	6.06218i	0.519827	−	0.300123i
$409$	−9.00000	+	15.5885i	−0.445021	+	0.770800i	−0.998054	−	0.0623602i	$-0.980137\pi$
$409$	−9.00000	+	15.5885i	−0.445021	+	0.770800i	0.553032	+	0.833160i	$0.313471\pi$
$410$		0			0
$411$	−4.50000	−	2.59808i	−0.221969	−	0.128154i
$412$	−6.00000			−0.295599
$413$	8.00000	−	13.8564i	0.393654	−	0.681829i
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$		0			0
$416$		0			0
$417$	10.5000	−	6.06218i	0.514187	−	0.296866i
$418$	−2.50000	+	21.6506i	−0.122279	+	1.05897i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	13.0000	+	22.5167i	0.633581	+	1.09739i	0.986814	+	0.161859i	$0.0517491\pi$
$421$	13.0000	+	22.5167i	0.633581	+	1.09739i	−0.353233	+	0.935536i	$0.614918\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$	12.0000	+	20.7846i	0.583460	+	1.01058i
$424$	1.00000	+	1.73205i	0.0485643	+	0.0841158i
$425$	−17.5000	+	30.3109i	−0.848875	+	1.47029i
$426$	−12.0000	−	6.92820i	−0.581402	−	0.335673i
$427$	−16.0000	+	27.7128i	−0.774294	+	1.34112i
$428$	5.50000	−	9.52628i	0.265853	−	0.460470i
$429$		0			0
$430$		0			0
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	−4.50000	−	7.79423i	−0.216256	−	0.374567i	0.737404	−	0.675452i	$-0.236051\pi$
$433$	−4.50000	−	7.79423i	−0.216256	−	0.374567i	−0.953660	+	0.300885i	$0.902718\pi$
$434$		0			0
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	14.0000	+	10.3923i	0.669711	+	0.497131i
$438$	10.5000	+	6.06218i	0.501709	+	0.289662i
$439$	−17.0000	−	29.4449i	−0.811366	−	1.40533i	−0.911908	−	0.410394i	$-0.865391\pi$
$439$	−17.0000	−	29.4449i	−0.811366	−	1.40533i	0.100543	−	0.994933i	$-0.467942\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$		0			0
$443$	3.00000			0.142534			0.0712672	−	0.997457i	$-0.477296\pi$
$443$	3.00000			0.142534			0.0712672	+	0.997457i	$0.477296\pi$
$444$	−15.0000	+	8.66025i	−0.711868	+	0.410997i
$445$		0			0
$446$		0			0
$447$	−30.0000	−	17.3205i	−1.41895	−	0.819232i
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	−7.50000	+	12.9904i	−0.353553	+	0.612372i
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	−1.00000			−0.0470360
$453$	3.00000	−	1.73205i	0.140952	−	0.0813788i
$454$	−11.0000			−0.516256
$455$		0			0
$456$	−4.50000	+	6.06218i	−0.210732	+	0.283887i
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$	31.5000	+	18.1865i	1.47029	+	0.848875i
$460$		0			0
$461$	−21.0000	−	36.3731i	−0.978068	−	1.69406i	−0.669417	−	0.742887i	$-0.733456\pi$
$461$	−21.0000	−	36.3731i	−0.978068	−	1.69406i	−0.308651	−	0.951175i	$-0.599877\pi$
$462$	−30.0000	+	17.3205i	−1.39573	+	0.805823i
$463$	−3.00000	−	5.19615i	−0.139422	−	0.241486i	0.787856	−	0.615859i	$-0.211191\pi$
$463$	−3.00000	−	5.19615i	−0.139422	−	0.241486i	−0.927278	+	0.374374i	$0.877858\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	−18.0000			−0.833834
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	−24.0000	−	41.5692i	−1.10822	−	1.91949i
$470$		0			0
$471$	36.0000	+	20.7846i	1.65879	+	0.957704i
$472$	−4.00000			−0.184115
$473$	45.0000			2.06910
$474$	−15.0000	+	8.66025i	−0.688973	+	0.397779i
$475$	2.50000	−	21.6506i	0.114708	−	0.993399i
$476$	−28.0000			−1.28338
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$	7.00000	+	12.1244i	0.318841	+	0.552249i
$483$			27.7128i			1.26098i
$484$	14.0000			0.636364
$485$		0			0
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	8.00000			0.362143
$489$	25.5000	+	14.7224i	1.15315	+	0.665771i
$490$		0			0
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$	−3.00000	+	1.73205i	−0.135250	+	0.0780869i
$493$	21.0000	−	36.3731i	0.945792	−	1.63816i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.0000	+	27.7128i	0.717698	+	1.24309i
$498$	−7.50000	−	4.33013i	−0.336083	−	0.194038i
$499$	8.00000			0.358129			0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000			0.358129			0.179065	+	0.983837i	$0.442693\pi$
$500$		0			0
$501$		0			0
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	0.842870	−	0.538117i	$-0.180864\pi$
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	−0.887458	+	0.460889i	$0.847531\pi$
$504$	−12.0000			−0.534522
$505$		0			0
$506$	10.0000	−	17.3205i	0.444554	−	0.769991i
$507$			22.5167i			1.00000i
$508$	−8.00000			−0.354943
$509$	4.00000	−	6.92820i	0.177297	−	0.307087i	−0.763657	−	0.645622i	$-0.776598\pi$
$509$	4.00000	−	6.92820i	0.177297	−	0.307087i	0.940954	+	0.338535i	$0.109931\pi$
$510$		0			0
$511$	−14.0000	−	24.2487i	−0.619324	−	1.07270i
$512$	1.00000			0.0441942
$513$	−22.5000	−	2.59808i	−0.993399	−	0.114708i
$514$	6.00000			0.264649
$515$		0			0
$516$	13.5000	+	7.79423i	0.594304	+	0.343122i
$517$	−20.0000	+	34.6410i	−0.879599	+	1.52351i
$518$	40.0000			1.75750
$519$		−	10.3923i		−	0.456172i
$520$		0			0
$521$	−31.0000			−1.35813			−0.679067	−	0.734076i	$-0.737616\pi$
$521$	−31.0000			−1.35813			−0.679067	+	0.734076i	$0.737616\pi$
$522$	9.00000	−	15.5885i	0.393919	−	0.682288i
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	−0.990873	−	0.134801i	$-0.956961\pi$
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	0.378695	−	0.925521i	$-0.376373\pi$
$524$	−10.5000	+	18.1865i	−0.458695	+	0.794482i
$525$	30.0000	−	17.3205i	1.30931	−	0.755929i
$526$	−6.00000	+	10.3923i	−0.261612	+	0.453126i
$527$		0			0
$528$	7.50000	+	4.33013i	0.326396	+	0.188445i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	16.0000	−	6.92820i	0.693688	−	0.300376i
$533$		0			0
$534$	−21.0000	+	12.1244i	−0.908759	+	0.524672i
$535$		0			0
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$	7.50000	+	4.33013i	0.323649	+	0.186859i
$538$	28.0000			1.20717
$539$	45.0000			1.93829
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	8.00000			0.343629
$543$			20.7846i			0.891953i
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$		0			0
$546$		0			0
$547$	−43.0000			−1.83855			−0.919274	−	0.393619i	$-0.871223\pi$
$547$	−43.0000			−1.83855			−0.919274	+	0.393619i	$0.871223\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	12.0000	+	20.7846i	0.512148	+	0.887066i
$550$	−25.0000			−1.06600
$551$	−3.00000	+	25.9808i	−0.127804	+	1.10682i
$552$	6.00000	−	3.46410i	0.255377	−	0.147442i
$553$	40.0000			1.70097
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	8.00000	+	13.8564i	0.338971	+	0.587115i	0.984239	−	0.176841i	$-0.0565879\pi$
$557$	8.00000	+	13.8564i	0.338971	+	0.587115i	−0.645269	+	0.763956i	$0.723255\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$			60.6218i			2.55945i
$562$	0.500000	+	0.866025i	0.0210912	+	0.0365311i
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	0.555354	−	0.831614i	$-0.312583\pi$
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	−0.997876	+	0.0651433i	$0.979250\pi$
$564$	−12.0000	+	6.92820i	−0.505291	+	0.291730i
$565$		0			0
$566$	5.50000	+	9.52628i	0.231182	+	0.400419i
$567$	−18.0000	−	31.1769i	−0.755929	−	1.30931i
$568$	4.00000	−	6.92820i	0.167836	−	0.290701i
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	−0.431011	−	0.902347i	$-0.641843\pi$
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	0.996961	−	0.0779066i	$-0.0248236\pi$
$570$		0			0
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	0.727690	−	0.685907i	$-0.240594\pi$
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	−0.957857	+	0.287244i	$0.907261\pi$
$572$		0			0
$573$	−12.0000	+	6.92820i	−0.501307	+	0.289430i
$574$	8.00000			0.333914
$575$	−10.0000	+	17.3205i	−0.417029	+	0.722315i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$	−16.0000	+	27.7128i	−0.665512	+	1.15270i
$579$	7.50000	+	4.33013i	0.311689	+	0.179954i
$580$		0			0
$581$	10.0000	+	17.3205i	0.414870	+	0.718576i
$582$	10.5000	−	6.06218i	0.435239	−	0.251285i
$583$	−10.0000			−0.414158
$584$	−3.50000	+	6.06218i	−0.144831	+	0.250855i
$585$		0			0
$586$	1.00000	−	1.73205i	0.0413096	−	0.0715504i
$587$	3.50000	+	6.06218i	0.144460	+	0.250213i	0.929172	−	0.369649i	$-0.120522\pi$
$587$	3.50000	+	6.06218i	0.144460	+	0.250213i	−0.784711	+	0.619862i	$0.787189\pi$
$588$	13.5000	+	7.79423i	0.556731	+	0.321429i
$589$		0			0
$590$		0			0
$591$	3.00000	+	1.73205i	0.123404	+	0.0712470i
$592$	−5.00000	−	8.66025i	−0.205499	−	0.355934i
$593$	−17.5000	−	30.3109i	−0.718639	−	1.24472i	−0.961539	−	0.274668i	$-0.911432\pi$
$593$	−17.5000	−	30.3109i	−0.718639	−	1.24472i	0.242900	−	0.970051i	$-0.421901\pi$
$594$			25.9808i			1.06600i
$595$		0			0
$596$	10.0000	−	17.3205i	0.409616	−	0.709476i
$597$			6.92820i			0.283552i
$598$		0			0
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.0699877	−	0.997548i	$-0.477704\pi$
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.828908	−	0.559385i	$-0.188963\pi$
$600$	−7.50000	−	4.33013i	−0.306186	−	0.176777i
$601$	−15.0000	+	25.9808i	−0.611863	+	1.05978i	0.379063	+	0.925371i	$0.376246\pi$
$601$	−15.0000	+	25.9808i	−0.611863	+	1.05978i	−0.990926	+	0.134407i	$0.957087\pi$
$602$	−18.0000	−	31.1769i	−0.733625	−	1.27068i
$603$	−36.0000			−1.46603
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$		0			0
$606$			24.2487i			0.985037i
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	−3.50000	−	2.59808i	−0.141944	−	0.105366i
$609$	−36.0000	+	20.7846i	−1.45879	+	0.842235i
$610$		0			0
$611$		0			0
$612$	−10.5000	+	18.1865i	−0.424437	+	0.735147i
$613$	−16.0000	+	27.7128i	−0.646234	+	1.11931i	0.337781	+	0.941225i	$0.390324\pi$
$613$	−16.0000	+	27.7128i	−0.646234	+	1.11931i	−0.984015	+	0.178085i	$0.943010\pi$
$614$	12.0000			0.484281
$615$		0			0
$616$	−10.0000	−	17.3205i	−0.402911	−	0.697863i
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$	9.00000	−	5.19615i	0.362033	−	0.209020i
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$		0			0
$621$	18.0000	+	10.3923i	0.722315	+	0.417029i
$622$	−7.00000	+	12.1244i	−0.280674	+	0.486142i
$623$	56.0000			2.24359
$624$		0			0
$625$	25.0000			1.00000
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	−15.0000	−	34.6410i	−0.599042	−	1.38343i
$628$	−12.0000	+	20.7846i	−0.478852	+	0.829396i
$629$	35.0000	−	60.6218i	1.39554	−	2.41715i
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	−12.0000	−	6.92820i	−0.476957	−	0.275371i
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$		0			0
$636$	−3.00000	−	1.73205i	−0.118958	−	0.0686803i
$637$		0			0
$638$	30.0000			1.18771
$639$	24.0000			0.949425
$640$		0			0
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	0.812421	−	0.583071i	$-0.198149\pi$
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	−0.911165	+	0.412042i	$0.864816\pi$
$642$			19.0526i			0.751945i
$643$	−5.00000			−0.197181			−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000			−0.197181			−0.0985904	+	0.995128i	$0.531433\pi$
$644$	−16.0000			−0.630488
$645$		0			0
$646$	3.50000	−	30.3109i	0.137706	−	1.19257i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$		0			0
$651$		0			0
$652$	−8.50000	+	14.7224i	−0.332886	+	0.576575i
$653$	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	$0.718768\pi$
$654$	−15.0000	−	8.66025i	−0.586546	−	0.338643i
$655$		0			0
$656$	−1.00000	−	1.73205i	−0.0390434	−	0.0676252i
$657$	−21.0000			−0.819288
$658$	32.0000			1.24749
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	−0.902297	−	0.431116i	$-0.858120\pi$
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	0.824506	+	0.565854i	$0.191453\pi$
$662$	−27.0000			−1.04938
$663$		0			0
$664$	2.50000	−	4.33013i	0.0970188	−	0.168042i
$665$		0			0
$666$	15.0000	−	25.9808i	0.581238	−	1.00673i
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−20.0000	+	34.6410i	−0.772091	+	1.33730i
$672$		−	6.92820i		−	0.267261i
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	−0.572309	−	0.820038i	$-0.693952\pi$
$673$	11.0000	−	19.0526i	0.424019	−	0.734422i	0.996328	+	0.0856156i	$0.0272857\pi$
$674$	0.500000	+	0.866025i	0.0192593	+	0.0333581i
$675$		−	25.9808i		−	1.00000i
$676$	−13.0000			−0.500000
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$	1.50000	−	0.866025i	0.0576072	−	0.0332595i
$679$	−28.0000			−1.07454
$680$		0			0
$681$	16.5000	−	9.52628i	0.632281	−	0.365048i
$682$		0			0
$683$	33.0000			1.26271			0.631355	−	0.775494i	$-0.282499\pi$
$683$	33.0000			1.26271			0.631355	+	0.775494i	$0.282499\pi$
$684$	1.50000	−	12.9904i	0.0573539	−	0.496700i
$685$		0			0
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		−	38.1051i		−	1.45380i
$688$	−4.50000	+	7.79423i	−0.171561	+	0.297152i
$689$		0			0
$690$		0			0
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	0.466691	+	0.884420i	$0.345446\pi$
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	−0.999276	+	0.0380440i	$0.987887\pi$
$692$	6.00000			0.228086
$693$	30.0000	−	51.9615i	1.13961	−	1.97386i
$694$	−2.50000	−	4.33013i	−0.0948987	−	0.164369i
$695$		0			0
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	7.00000	−	12.1244i	0.265144	−	0.459243i
$698$	−26.0000			−0.984115
$699$	27.0000	−	15.5885i	1.02123	−	0.589610i
$700$	10.0000	+	17.3205i	0.377964	+	0.654654i
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	−0.580013	−	0.814607i	$-0.696952\pi$
$701$	11.0000	−	19.0526i	0.415464	−	0.719605i	0.995477	+	0.0950021i	$0.0302858\pi$
$702$		0			0
$703$	−5.00000	+	43.3013i	−0.188579	+	1.63314i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$		0			0
$706$	3.00000			0.112906
$707$	28.0000	−	48.4974i	1.05305	−	1.82393i
$708$	6.00000	−	3.46410i	0.225494	−	0.130189i
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$		0			0
$711$	15.0000	−	25.9808i	0.562544	−	0.974355i
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$		0			0
$714$	42.0000	−	24.2487i	1.57181	−	0.907485i
$715$		0			0
$716$	−2.50000	+	4.33013i	−0.0934294	+	0.161824i
$717$		−	10.3923i		−	0.388108i
$718$	−18.0000			−0.671754
$719$	−25.0000	+	43.3013i	−0.932343	+	1.61486i	−0.153037	+	0.988220i	$0.548906\pi$
$719$	−25.0000	+	43.3013i	−0.932343	+	1.61486i	−0.779305	+	0.626644i	$0.784428\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	5.50000	+	18.1865i	0.204689	+	0.676833i
$723$	−21.0000	−	12.1244i	−0.780998	−	0.450910i
$724$	−12.0000			−0.445976
$725$	−30.0000			−1.11417
$726$	−21.0000	+	12.1244i	−0.779383	+	0.449977i
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	0.706523	−	0.707690i	$-0.250263\pi$
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	−0.966139	+	0.258022i	$0.916929\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−63.0000			−2.33014
$732$	−12.0000	+	6.92820i	−0.443533	+	0.256074i
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	−7.00000	−	12.1244i	−0.258375	−	0.447518i
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	−30.0000	−	51.9615i	−1.10506	−	1.91403i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	−0.900464	−	0.434930i	$-0.856773\pi$
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	0.826893	+	0.562360i	$0.190106\pi$
$740$		0			0
$741$		0			0
$742$	4.00000	+	6.92820i	0.146845	+	0.254342i
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$		0			0
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	15.0000			0.548821
$748$	−35.0000			−1.27973
$749$	22.0000	−	38.1051i	0.803863	−	1.39233i
$750$		0			0
$751$	−26.0000	+	45.0333i	−0.948753	+	1.64329i	−0.200698	+	0.979653i	$0.564321\pi$
$751$	−26.0000	+	45.0333i	−0.948753	+	1.64329i	−0.748056	+	0.663636i	$0.769012\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$			20.7846i			0.757433i
$754$		0			0
$755$		0			0
$756$	18.0000	−	10.3923i	0.654654	−	0.377964i
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	−0.593899	−	0.804539i	$-0.702412\pi$
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	0.993701	+	0.112062i	$0.0357456\pi$
$758$	9.50000	+	16.4545i	0.345056	+	0.597654i
$759$			34.6410i			1.25739i
$760$		0			0
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	0.856821	−	0.515615i	$-0.172436\pi$
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	−0.874946	+	0.484221i	$0.839103\pi$
$762$	12.0000	−	6.92820i	0.434714	−	0.250982i
$763$	20.0000	+	34.6410i	0.724049	+	1.25409i
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$		0			0
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	−21.0000	+	36.3731i	−0.757279	+	1.31165i	0.186954	+	0.982369i	$0.440139\pi$
$769$	−21.0000	+	36.3731i	−0.757279	+	1.31165i	−0.944233	+	0.329278i	$0.893195\pi$
$770$		0			0
$771$	−9.00000	+	5.19615i	−0.324127	+	0.187135i
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	−27.0000			−0.970495
$775$		0			0
$776$	3.50000	+	6.06218i	0.125643	+	0.217620i
$777$	−60.0000	+	34.6410i	−2.15249	+	1.24274i
$778$	−2.00000	−	3.46410i	−0.0717035	−	0.124194i
$779$	−1.00000	+	8.66025i	−0.0358287	+	0.310286i
$780$		0			0
$781$	20.0000	+	34.6410i	0.715656	+	1.23955i
$782$	−14.0000	+	24.2487i	−0.500639	+	0.867132i
$783$			31.1769i			1.11417i
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$		0			0
$786$		−	36.3731i		−	1.29738i
$787$	17.5000	+	30.3109i	0.623808	+	1.08047i	0.988770	+	0.149444i	$0.0477485\pi$
$787$	17.5000	+	30.3109i	0.623808	+	1.08047i	−0.364963	+	0.931022i	$0.618918\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$		−	20.7846i		−	0.739952i
$790$		0			0
$791$	−4.00000			−0.142224
$792$	−15.0000			−0.533002
$793$		0			0
$794$	−6.00000			−0.212932
$795$		0			0
$796$	−4.00000			−0.141776
$797$	22.0000	+	38.1051i	0.779280	+	1.34975i	0.932357	+	0.361538i	$0.117748\pi$
$797$	22.0000	+	38.1051i	0.779280	+	1.34975i	−0.153077	+	0.988214i	$0.548918\pi$
$798$	−18.0000	+	24.2487i	−0.637193	+	0.858395i
$799$	28.0000	−	48.4974i	0.990569	−	1.71572i
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	21.0000	−	36.3731i	0.741999	−	1.28518i
$802$	13.5000	+	23.3827i	0.476702	+	0.825671i
$803$	−17.5000	−	30.3109i	−0.617562	−	1.06965i
$804$		−	20.7846i		−	0.733017i
$805$		0			0
$806$		0			0
$807$	−42.0000	+	24.2487i	−1.47847	+	0.853595i
$808$	−14.0000			−0.492518
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$	2.50000	+	4.33013i	0.0877869	+	0.152051i	0.906575	−	0.422044i	$-0.138687\pi$
$811$	2.50000	+	4.33013i	0.0877869	+	0.152051i	−0.818788	+	0.574095i	$0.805354\pi$
$812$	−12.0000	−	20.7846i	−0.421117	−	0.729397i
$813$	−12.0000	+	6.92820i	−0.420858	+	0.242983i
$814$	50.0000			1.75250
$815$		0			0
$816$	−10.5000	−	6.06218i	−0.367574	−	0.212219i
$817$	36.0000	−	15.5885i	1.25948	−	0.545371i
$818$	18.0000			0.629355
$819$		0			0
$820$		0			0
$821$	24.0000			0.837606			0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000			0.837606			0.418803	+	0.908077i	$0.362450\pi$
$822$			5.19615i			0.181237i
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	−0.172379	−	0.985031i	$-0.555146\pi$
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	0.939251	−	0.343230i	$-0.111521\pi$
$824$	3.00000	+	5.19615i	0.104510	+	0.181017i
$825$	37.5000	−	21.6506i	1.30558	−	0.753778i
$826$	−16.0000			−0.556711
$827$	7.50000	+	12.9904i	0.260801	+	0.451720i	0.966455	−	0.256836i	$-0.0826802\pi$
$827$	7.50000	+	12.9904i	0.260801	+	0.451720i	−0.705654	+	0.708556i	$0.749347\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−52.0000			−1.80603			−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000			−1.80603			−0.903017	+	0.429604i	$0.858653\pi$
$830$		0			0
$831$	3.00000	−	1.73205i	0.104069	−	0.0600842i
$832$		0			0
$833$	−63.0000			−2.18282
$834$	−10.5000	−	6.06218i	−0.363585	−	0.209916i
$835$		0			0
$836$	20.0000	−	8.66025i	0.691714	−	0.299521i
$837$		0			0
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	13.0000	−	22.5167i	0.448010	−	0.775975i
$843$	−1.50000	−	0.866025i	−0.0516627	−	0.0298275i
$844$	4.00000	−	6.92820i	0.137686	−	0.238479i
$845$		0			0
$846$	12.0000	−	20.7846i	0.412568	−	0.714590i
$847$	56.0000			1.92418
$848$	1.00000	−	1.73205i	0.0343401	−	0.0594789i
$849$	−16.5000	−	9.52628i	−0.566279	−	0.326941i
$850$	35.0000			1.20049
$851$	20.0000	−	34.6410i	0.685591	−	1.18748i
$852$			13.8564i			0.474713i
$853$	21.0000	+	36.3731i	0.719026	+	1.24539i	0.961386	+	0.275204i	$0.0887453\pi$
$853$	21.0000	+	36.3731i	0.719026	+	1.24539i	−0.242360	+	0.970186i	$0.577921\pi$
$854$	32.0000			1.09502
$855$		0			0
$856$	−11.0000			−0.375972
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	0.890507	−	0.454969i	$-0.150350\pi$
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	−0.839268	+	0.543718i	$0.817016\pi$
$858$		0			0
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	−0.505248	−	0.862974i	$-0.668599\pi$
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	0.999982	+	0.00607046i	$0.00193230\pi$
$860$		0			0
$861$	−12.0000	+	6.92820i	−0.408959	+	0.236113i
$862$	1.00000	−	1.73205i	0.0340601	−	0.0589939i
$863$	52.0000			1.77010			0.885050	−	0.465495i	$-0.154124\pi$
$863$	52.0000			1.77010			0.885050	+	0.465495i	$0.154124\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$		0			0
$866$	−4.50000	+	7.79423i	−0.152916	+	0.264859i
$867$		−	55.4256i		−	1.88235i
$868$		0			0
$869$	50.0000			1.69613
$870$		0			0
$871$		0			0
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$	−10.5000	+	18.1865i	−0.355371	+	0.615521i
$874$	2.00000	−	17.3205i	0.0676510	−	0.585875i
$875$		0			0
$876$		−	12.1244i		−	0.409644i
$877$	−34.0000			−1.14810			−0.574049	−	0.818821i	$-0.694628\pi$
$877$	−34.0000			−1.14810			−0.574049	+	0.818821i	$0.694628\pi$
$878$	−17.0000	+	29.4449i	−0.573722	+	0.993716i
$879$			3.46410i			0.116841i
$880$		0			0
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$	−27.0000			−0.909137
$883$	−24.0000	−	41.5692i	−0.807664	−	1.39892i	−0.914478	−	0.404637i	$-0.867398\pi$
$883$	−24.0000	−	41.5692i	−0.807664	−	1.39892i	0.106813	−	0.994279i	$-0.465935\pi$
$884$		0			0
$885$		0			0
$886$	−1.50000	−	2.59808i	−0.0503935	−	0.0872841i
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	−0.911986	−	0.410222i	$-0.865451\pi$
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	0.811256	+	0.584692i	$0.198785\pi$
$888$	15.0000	+	8.66025i	0.503367	+	0.290619i
$889$	−32.0000			−1.07325
$890$		0			0
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$		0			0
$893$	−4.00000	+	34.6410i	−0.133855	+	1.15922i
$894$			34.6410i			1.15857i
$895$		0			0
$896$	4.00000			0.133631
$897$		0			0
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$		0			0
$900$	15.0000			0.500000
$901$	14.0000			0.466408
$902$	10.0000			0.332964
$903$	54.0000	+	31.1769i	1.79701	+	1.03750i
$904$	0.500000	+	0.866025i	0.0166298	+	0.0288036i
$905$		0			0
$906$	−3.00000	−	1.73205i	−0.0996683	−	0.0575435i
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$	5.50000	+	9.52628i	0.182524	+	0.316141i
$909$	−21.0000	−	36.3731i	−0.696526	−	1.20642i
$910$		0			0
$911$	−3.00000	+	5.19615i	−0.0993944	+	0.172156i	−0.911434	−	0.411446i	$-0.865024\pi$
$911$	−3.00000	+	5.19615i	−0.0993944	+	0.172156i	0.812040	+	0.583602i	$0.198357\pi$
$912$	7.50000	+	0.866025i	0.248350	+	0.0286770i
$913$	12.5000	+	21.6506i	0.413690	+	0.716531i
$914$	29.0000			0.959235
$915$		0			0
$916$	22.0000			0.726900
$917$	−42.0000	+	72.7461i	−1.38696	+	2.40229i
$918$		−	36.3731i		−	1.20049i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$	−18.0000	+	10.3923i	−0.593120	+	0.342438i
$922$	−21.0000	+	36.3731i	−0.691598	+	1.19788i
$923$		0			0
$924$	30.0000	+	17.3205i	0.986928	+	0.569803i
$925$	−50.0000			−1.64399
$926$	−3.00000	+	5.19615i	−0.0985861	+	0.170756i
$927$	−9.00000	+	15.5885i	−0.295599	+	0.511992i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	0.962431	−	0.271526i	$-0.0875283\pi$
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	−0.716364	+	0.697727i	$0.754195\pi$
$930$		0			0
$931$	36.0000	−	15.5885i	1.17985	−	0.510891i
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$		−	24.2487i		−	0.793867i
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$		0			0
$936$		0			0
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$	−24.0000	+	41.5692i	−0.783628	+	1.35728i
$939$	−9.00000	−	5.19615i	−0.293704	−	0.169570i
$940$		0			0
$941$	−16.0000	+	27.7128i	−0.521585	+	0.903412i	0.478100	+	0.878306i	$0.341326\pi$
$941$	−16.0000	+	27.7128i	−0.521585	+	0.903412i	−0.999685	+	0.0251063i	$0.992008\pi$
$942$		−	41.5692i		−	1.35440i
$943$	4.00000	−	6.92820i	0.130258	−	0.225613i
$944$	2.00000	+	3.46410i	0.0650945	+	0.112747i
$945$		0			0
$946$	−22.5000	−	38.9711i	−0.731538	−	1.26706i
$947$	−8.50000	−	14.7224i	−0.276213	−	0.478415i	0.694228	−	0.719756i	$-0.255746\pi$
$947$	−8.50000	−	14.7224i	−0.276213	−	0.478415i	−0.970440	+	0.241341i	$0.922413\pi$
$948$	15.0000	+	8.66025i	0.487177	+	0.281272i
$949$		0			0
$950$	−20.0000	+	8.66025i	−0.648886	+	0.280976i
$951$	36.0000	+	20.7846i	1.16738	+	0.673987i
$952$	14.0000	+	24.2487i	0.453743	+	0.785905i
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	−0.718604	−	0.695419i	$-0.755219\pi$
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	0.961553	+	0.274620i	$0.0885520\pi$
$954$	6.00000			0.194257
$955$		0			0
$956$	6.00000			0.194054
$957$	−45.0000	+	25.9808i	−1.45464	+	0.839839i
$958$		0			0
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$	−16.5000	−	28.5788i	−0.531705	−	0.920940i
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$		0			0
$966$	24.0000	−	13.8564i	0.772187	−	0.445823i
$967$	6.00000			0.192947			0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000			0.192947			0.0964735	+	0.995336i	$0.469244\pi$
$968$	−7.00000	−	12.1244i	−0.224989	−	0.389692i
$969$	21.0000	+	48.4974i	0.674617	+	1.55796i
$970$		0			0
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.107135	+	0.994244i	$0.534168\pi$
$971$	−28.5000	+	49.3634i	−0.914609	+	1.58415i	−0.807473	+	0.589904i	$0.799166\pi$
$972$		−	15.5885i		−	0.500000i
$973$	14.0000	+	24.2487i	0.448819	+	0.777378i
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		−	29.4449i		−	0.941543i
$979$	70.0000			2.23721
$980$		0			0
$981$	30.0000			0.957826
$982$	−13.5000	−	23.3827i	−0.430802	−	0.746171i
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$	3.00000	+	1.73205i	0.0956365	+	0.0552158i
$985$		0			0
$986$	−42.0000			−1.33755
$987$	−48.0000	+	27.7128i	−1.52786	+	0.882109i
$988$		0			0
$989$	−36.0000			−1.14473
$990$		0			0
$991$	−23.0000	+	39.8372i	−0.730619	+	1.26547i	0.226000	+	0.974127i	$0.427435\pi$
$991$	−23.0000	+	39.8372i	−0.730619	+	1.26547i	−0.956619	+	0.291342i	$0.905898\pi$
$992$		0			0
$993$	40.5000	−	23.3827i	1.28523	−	0.742027i
$994$	16.0000	−	27.7128i	0.507489	−	0.878997i
$995$		0			0
$996$			8.66025i			0.274411i
$997$	14.0000			0.443384			0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000			0.443384			0.221692	+	0.975117i	$0.428842\pi$
$998$	−4.00000	−	6.92820i	−0.126618	−	0.219308i
$999$			51.9615i			1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.c.277.1	yes	2
3.2	odd	2		1026.2.h.c.505.1		2
9.4	even	3		342.2.f.a.49.1	yes	2
9.5	odd	6		1026.2.f.b.847.1		2
19.7	even	3		342.2.f.a.7.1	✓	2
57.26	odd	6		1026.2.f.b.235.1		2
171.121	even	3	inner	342.2.h.c.121.1	yes	2
171.140	odd	6		1026.2.h.c.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.a.7.1	✓	2	19.7	even	3
342.2.f.a.49.1	yes	2	9.4	even	3
342.2.h.c.121.1	yes	2	171.121	even	3	inner
342.2.h.c.277.1	yes	2	1.1	even	1	trivial
1026.2.f.b.235.1		2	57.26	odd	6
1026.2.f.b.847.1		2	9.5	odd	6
1026.2.h.c.505.1		2	3.2	odd	2
1026.2.h.c.577.1		2	171.140	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205i q^{6} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(-1.50000 + 0.866025i) q^{12} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-0.500000 + 4.33013i) q^{19} +(-6.00000 + 3.46410i) q^{21} +5.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(1.50000 + 0.866025i) q^{24} -5.00000 q^{25} +5.19615i q^{27} +(-2.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(-0.500000 + 0.866025i) q^{32} +(-7.50000 + 4.33013i) q^{33} -7.00000 q^{34} -3.00000 q^{36} +10.0000 q^{37} +(4.00000 - 1.73205i) q^{38} +2.00000 q^{41} +(6.00000 + 3.46410i) q^{42} +(-4.50000 - 7.79423i) q^{43} +(-2.50000 - 4.33013i) q^{44} -4.00000 q^{46} +8.00000 q^{47} -1.73205i q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.50000 + 4.33013i) q^{50} +(10.5000 - 6.06218i) q^{51} +(1.00000 + 1.73205i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-2.00000 + 3.46410i) q^{56} +(-4.50000 + 6.06218i) q^{57} +(-3.00000 - 5.19615i) q^{58} -4.00000 q^{59} +8.00000 q^{61} -12.0000 q^{63} +1.00000 q^{64} +(7.50000 + 4.33013i) q^{66} +(-6.00000 + 10.3923i) q^{67} +(3.50000 + 6.06218i) q^{68} +(6.00000 - 3.46410i) q^{69} +(4.00000 - 6.92820i) q^{71} +(1.50000 + 2.59808i) q^{72} +(-3.50000 + 6.06218i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-7.50000 - 4.33013i) q^{75} +(-3.50000 - 2.59808i) q^{76} +(-10.0000 - 17.3205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.00000 - 1.73205i) q^{82} +(2.50000 - 4.33013i) q^{83} -6.92820i q^{84} +(-4.50000 + 7.79423i) q^{86} +(9.00000 + 5.19615i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-7.00000 - 12.1244i) q^{89} +(2.00000 + 3.46410i) q^{92} +(-4.00000 - 6.92820i) q^{94} +(-1.50000 + 0.866025i) q^{96} +(3.50000 + 6.06218i) q^{97} +(-4.50000 + 7.79423i) q^{98} -15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 5 q^{11} - 3 q^{12} + 8 q^{14} - q^{16} + 7 q^{17} + 3 q^{18} - q^{19} - 12 q^{21} + 10 q^{22} + 4 q^{23} + 3 q^{24} - 10 q^{25} - 4 q^{28} + 12 q^{29} - q^{32} - 15 q^{33} - 14 q^{34} - 6 q^{36} + 20 q^{37} + 8 q^{38} + 4 q^{41} + 12 q^{42} - 9 q^{43} - 5 q^{44} - 8 q^{46} + 16 q^{47} - 9 q^{49} + 5 q^{50} + 21 q^{51} + 2 q^{53} + 9 q^{54} - 4 q^{56} - 9 q^{57} - 6 q^{58} - 8 q^{59} + 16 q^{61} - 24 q^{63} + 2 q^{64} + 15 q^{66} - 12 q^{67} + 7 q^{68} + 12 q^{69} + 8 q^{71} + 3 q^{72} - 7 q^{73} - 10 q^{74} - 15 q^{75} - 7 q^{76} - 20 q^{77} - 10 q^{79} - 9 q^{81} - 2 q^{82} + 5 q^{83} - 9 q^{86} + 18 q^{87} - 5 q^{88} - 14 q^{89} + 4 q^{92} - 8 q^{94} - 3 q^{96} + 7 q^{97} - 9 q^{98} - 30 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 5 * q^11 - 3 * q^12 + 8 * q^14 - q^16 + 7 * q^17 + 3 * q^18 - q^19 - 12 * q^21 + 10 * q^22 + 4 * q^23 + 3 * q^24 - 10 * q^25 - 4 * q^28 + 12 * q^29 - q^32 - 15 * q^33 - 14 * q^34 - 6 * q^36 + 20 * q^37 + 8 * q^38 + 4 * q^41 + 12 * q^42 - 9 * q^43 - 5 * q^44 - 8 * q^46 + 16 * q^47 - 9 * q^49 + 5 * q^50 + 21 * q^51 + 2 * q^53 + 9 * q^54 - 4 * q^56 - 9 * q^57 - 6 * q^58 - 8 * q^59 + 16 * q^61 - 24 * q^63 + 2 * q^64 + 15 * q^66 - 12 * q^67 + 7 * q^68 + 12 * q^69 + 8 * q^71 + 3 * q^72 - 7 * q^73 - 10 * q^74 - 15 * q^75 - 7 * q^76 - 20 * q^77 - 10 * q^79 - 9 * q^81 - 2 * q^82 + 5 * q^83 - 9 * q^86 + 18 * q^87 - 5 * q^88 - 14 * q^89 + 4 * q^92 - 8 * q^94 - 3 * q^96 + 7 * q^97 - 9 * q^98 - 30 * q^99

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