LMFDB - Embedded newform 648.2.n.k.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(109,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("648.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			541.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	648.541
Dual form			648.2.n.k.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.73205 - 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.73205 - 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.00000 - 2.00000i) q^{10} +(-3.46410 + 2.00000i) q^{13} +(0.732051 - 2.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} -2.00000 q^{17} +4.00000i q^{19} +(2.00000 - 3.46410i) q^{20} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.00000 + 4.00000i) q^{26} -4.00000i q^{28} +(5.19615 + 3.00000i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(1.46410 - 5.46410i) q^{32} +(-2.73205 + 0.732051i) q^{34} -4.00000i q^{35} +8.00000i q^{37} +(1.46410 + 5.46410i) q^{38} +(1.46410 - 5.46410i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(3.46410 + 2.00000i) q^{43} +(-4.00000 - 4.00000i) q^{46} +(6.00000 - 10.3923i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-0.366025 + 1.36603i) q^{50} +(-4.00000 + 6.92820i) q^{52} +6.00000i q^{53} +(-1.46410 - 5.46410i) q^{56} +(8.19615 + 2.19615i) q^{58} +(3.46410 - 2.00000i) q^{59} +(-2.00000 - 2.00000i) q^{62} -8.00000i q^{64} +(-4.00000 + 6.92820i) q^{65} +(-10.3923 + 6.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(-1.46410 - 5.46410i) q^{70} +12.0000 q^{71} -6.00000 q^{73} +(2.92820 + 10.9282i) q^{74} +(4.00000 + 6.92820i) q^{76} +(-5.00000 + 8.66025i) q^{79} -8.00000i q^{80} +(-2.00000 - 2.00000i) q^{82} +(-13.8564 - 8.00000i) q^{83} +(-3.46410 + 2.00000i) q^{85} +(5.46410 + 1.46410i) q^{86} -10.0000 q^{89} +8.00000i q^{91} +(-6.92820 - 4.00000i) q^{92} +(4.39230 - 16.3923i) q^{94} +(4.00000 + 6.92820i) q^{95} +(1.00000 - 1.73205i) q^{97} +(3.00000 + 3.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^7 + 8 * q^8	$ 4 q + 2 q^{2} + 4 q^{7} + 8 q^{8} + 8 q^{10} - 4 q^{14} + 8 q^{16} - 8 q^{17} + 8 q^{20} - 8 q^{23} - 2 q^{25} - 16 q^{26} - 4 q^{31} - 8 q^{32} - 4 q^{34} - 8 q^{38} - 8 q^{40} - 4 q^{41} - 16 q^{46} + 24 q^{47} + 6 q^{49} + 2 q^{50} - 16 q^{52} + 8 q^{56} + 12 q^{58} - 8 q^{62} - 16 q^{65} + 8 q^{70} + 48 q^{71} - 24 q^{73} - 16 q^{74} + 16 q^{76} - 20 q^{79} - 8 q^{82} + 8 q^{86} - 40 q^{89} - 24 q^{94} + 16 q^{95} + 4 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^7 + 8 * q^8 + 8 * q^10 - 4 * q^14 + 8 * q^16 - 8 * q^17 + 8 * q^20 - 8 * q^23 - 2 * q^25 - 16 * q^26 - 4 * q^31 - 8 * q^32 - 4 * q^34 - 8 * q^38 - 8 * q^40 - 4 * q^41 - 16 * q^46 + 24 * q^47 + 6 * q^49 + 2 * q^50 - 16 * q^52 + 8 * q^56 + 12 * q^58 - 8 * q^62 - 16 * q^65 + 8 * q^70 + 48 * q^71 - 24 * q^73 - 16 * q^74 + 16 * q^76 - 20 * q^79 - 8 * q^82 + 8 * q^86 - 40 * q^89 - 24 * q^94 + 16 * q^95 + 4 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	1.73205	−	1.00000i	0.774597	−	0.447214i	−0.0599153	−	0.998203i	$-0.519083\pi$
$5$	1.73205	−	1.00000i	0.774597	−	0.447214i	0.834512	+	0.550990i	$0.185750\pi$
$6$		0			0
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−3.46410	+	2.00000i	−0.960769	+	0.554700i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.46410	+	2.00000i	−0.960769	+	0.554700i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	0.732051	−	2.73205i	0.195649	−	0.730171i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	2.00000	−	3.46410i	0.447214	−	0.774597i
$21$		0			0
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.00000	+	4.00000i	−0.784465	+	0.784465i
$27$		0			0
$28$		−	4.00000i		−	0.755929i
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.897678	−	0.440652i	$-0.145253\pi$
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.0672232	+	0.997738i	$0.478586\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$		0			0
$34$	−2.73205	+	0.732051i	−0.468543	+	0.125546i
$35$		−	4.00000i		−	0.676123i
$36$		0			0
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	1.46410	+	5.46410i	0.237509	+	0.886394i
$39$		0			0
$40$	1.46410	−	5.46410i	0.231495	−	0.863950i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	3.46410	+	2.00000i	0.528271	+	0.304997i	0.740312	−	0.672264i	$-0.234678\pi$
$43$	3.46410	+	2.00000i	0.528271	+	0.304997i	−0.212041	+	0.977261i	$0.568011\pi$
$44$		0			0
$45$		0			0
$46$	−4.00000	−	4.00000i	−0.589768	−	0.589768i
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.0186297	−	0.999826i	$-0.494070\pi$
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.856560	−	0.516047i	$-0.172597\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−0.366025	+	1.36603i	−0.0517638	+	0.193185i
$51$		0			0
$52$	−4.00000	+	6.92820i	−0.554700	+	0.960769i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$	−1.46410	−	5.46410i	−0.195649	−	0.730171i
$57$		0			0
$58$	8.19615	+	2.19615i	1.07621	+	0.288369i
$59$	3.46410	−	2.00000i	0.450988	−	0.260378i	−0.257260	−	0.966342i	$-0.582820\pi$
$59$	3.46410	−	2.00000i	0.450988	−	0.260378i	0.708247	+	0.705965i	$0.249486\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$	−2.00000	−	2.00000i	−0.254000	−	0.254000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−4.00000	+	6.92820i	−0.496139	+	0.859338i
$66$		0			0
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.974916	−	0.222571i	$-0.928555\pi$
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.294706	+	0.955588i	$0.595222\pi$
$68$	−3.46410	+	2.00000i	−0.420084	+	0.242536i
$69$		0			0
$70$	−1.46410	−	5.46410i	−0.174994	−	0.653085i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.92820	+	10.9282i	0.340397	+	1.27038i
$75$		0			0
$76$	4.00000	+	6.92820i	0.458831	+	0.794719i
$77$		0			0
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$		−	8.00000i		−	0.894427i
$81$		0			0
$82$	−2.00000	−	2.00000i	−0.220863	−	0.220863i
$83$	−13.8564	−	8.00000i	−1.52094	−	0.878114i	−0.999695	−	0.0247060i	$-0.992135\pi$
$83$	−13.8564	−	8.00000i	−1.52094	−	0.878114i	−0.521243	−	0.853408i	$-0.674532\pi$
$84$		0			0
$85$	−3.46410	+	2.00000i	−0.375735	+	0.216930i
$86$	5.46410	+	1.46410i	0.589209	+	0.157878i
$87$		0			0
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$			8.00000i			0.838628i
$92$	−6.92820	−	4.00000i	−0.722315	−	0.417029i
$93$		0			0
$94$	4.39230	−	16.3923i	0.453032	−	1.69074i
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		0			0
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	3.00000	+	3.00000i	0.303046	+	0.303046i
$99$		0			0
$100$			2.00000i			0.200000i
$101$	8.66025	+	5.00000i	0.861727	+	0.497519i	0.864590	−	0.502477i	$-0.167578\pi$
$101$	8.66025	+	5.00000i	0.861727	+	0.497519i	−0.00286291	+	0.999996i	$0.500911\pi$
$102$		0			0
$103$	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	$0.737814\pi$
$104$	−2.92820	+	10.9282i	−0.287134	+	1.07160i
$105$		0			0
$106$	2.19615	+	8.19615i	0.213309	+	0.796081i
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$		0			0
$111$		0			0
$112$	−4.00000	−	6.92820i	−0.377964	−	0.654654i
$113$	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
$115$	−6.92820	−	4.00000i	−0.646058	−	0.373002i
$116$	12.0000			1.11417
$117$		0			0
$118$	4.00000	−	4.00000i	0.368230	−	0.368230i
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$			12.0000i			1.07331i
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$		0			0
$130$	−2.92820	+	10.9282i	−0.256820	+	0.958467i
$131$	−17.3205	+	10.0000i	−1.51330	+	0.873704i	−0.513421	+	0.858137i	$0.671622\pi$
$131$	−17.3205	+	10.0000i	−1.51330	+	0.873704i	−0.999879	+	0.0155672i	$0.995045\pi$
$132$		0			0
$133$	6.92820	+	4.00000i	0.600751	+	0.346844i
$134$	−12.0000	+	12.0000i	−1.03664	+	1.03664i
$135$		0			0
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$	−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
$139$	3.46410	−	2.00000i	0.293821	−	0.169638i	−0.345843	−	0.938293i	$-0.612407\pi$
$139$	3.46410	−	2.00000i	0.293821	−	0.169638i	0.639664	+	0.768655i	$0.279074\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$		0			0
$142$	16.3923	−	4.39230i	1.37561	−	0.368594i
$143$		0			0
$144$		0			0
$145$	12.0000			0.996546
$146$	−8.19615	+	2.19615i	−0.678318	+	0.181755i
$147$		0			0
$148$	8.00000	+	13.8564i	0.657596	+	1.13899i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$		0			0
$151$	9.00000	−	15.5885i	0.732410	−	1.26857i	−0.223441	−	0.974717i	$-0.571729\pi$
$151$	9.00000	−	15.5885i	0.732410	−	1.26857i	0.955851	−	0.293853i	$-0.0949377\pi$
$152$	8.00000	+	8.00000i	0.648886	+	0.648886i
$153$		0			0
$154$		0			0
$155$	−3.46410	−	2.00000i	−0.278243	−	0.160644i
$156$		0			0
$157$	6.92820	−	4.00000i	0.552931	−	0.319235i	−0.197372	−	0.980329i	$-0.563241\pi$
$157$	6.92820	−	4.00000i	0.552931	−	0.319235i	0.750303	+	0.661094i	$0.229907\pi$
$158$	−3.66025	+	13.6603i	−0.291194	+	1.08675i
$159$		0			0
$160$	−2.92820	−	10.9282i	−0.231495	−	0.863950i
$161$	−8.00000			−0.630488
$162$		0			0
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−3.46410	−	2.00000i	−0.270501	−	0.156174i
$165$		0			0
$166$	−21.8564	−	5.85641i	−1.69639	−	0.454545i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$		0			0
$169$	1.50000	−	2.59808i	0.115385	−	0.199852i
$170$	−4.00000	+	4.00000i	−0.306786	+	0.306786i
$171$		0			0
$172$	8.00000			0.609994
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$		0			0
$175$	1.00000	+	1.73205i	0.0755929	+	0.130931i
$176$		0			0
$177$		0			0
$178$	−13.6603	+	3.66025i	−1.02388	+	0.274348i
$179$			4.00000i			0.298974i	0.988764	+	0.149487i	$0.0477622\pi$
$179$			4.00000i			0.298974i	−0.988764	+	0.149487i	$0.952238\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	2.92820	+	10.9282i	0.217053	+	0.810052i
$183$		0			0
$184$	−10.9282	−	2.92820i	−0.805638	−	0.215870i
$185$	8.00000	+	13.8564i	0.588172	+	1.01874i
$186$		0			0
$187$		0			0
$188$		−	24.0000i		−	1.75038i
$189$		0			0
$190$	8.00000	+	8.00000i	0.580381	+	0.580381i
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$		0			0
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	0.953564	−	0.301189i	$-0.0973836\pi$
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	−0.737620	+	0.675216i	$0.764050\pi$
$194$	0.732051	−	2.73205i	0.0525582	−	0.196150i
$195$		0			0
$196$	5.19615	+	3.00000i	0.371154	+	0.214286i
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	0.732051	+	2.73205i	0.0517638	+	0.193185i
$201$		0			0
$202$	13.6603	+	3.66025i	0.961132	+	0.257535i
$203$	10.3923	−	6.00000i	0.729397	−	0.421117i
$204$		0			0
$205$	−3.46410	−	2.00000i	−0.241943	−	0.139686i
$206$	6.00000	+	6.00000i	0.418040	+	0.418040i
$207$		0			0
$208$			16.0000i			1.10940i
$209$		0			0
$210$		0			0
$211$	17.3205	−	10.0000i	1.19239	−	0.688428i	0.233544	−	0.972346i	$-0.424968\pi$
$211$	17.3205	−	10.0000i	1.19239	−	0.688428i	0.958849	+	0.283918i	$0.0916343\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$	−4.39230	−	16.3923i	−0.300252	−	1.12055i
$215$	8.00000			0.545595
$216$		0			0
$217$	−4.00000			−0.271538
$218$	1.46410	+	5.46410i	0.0991615	+	0.370076i
$219$		0			0
$220$		0			0
$221$	6.92820	−	4.00000i	0.466041	−	0.269069i
$222$		0			0
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	−0.999362	−	0.0357107i	$-0.988630\pi$
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	0.530607	+	0.847618i	$0.321964\pi$
$224$	−8.00000	−	8.00000i	−0.534522	−	0.534522i
$225$		0			0
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$	−6.92820	−	4.00000i	−0.459841	−	0.265489i	0.252136	−	0.967692i	$-0.418867\pi$
$227$	−6.92820	−	4.00000i	−0.459841	−	0.265489i	−0.711977	+	0.702202i	$0.752200\pi$
$228$		0			0
$229$	3.46410	−	2.00000i	0.228914	−	0.132164i	−0.381157	−	0.924510i	$-0.624474\pi$
$229$	3.46410	−	2.00000i	0.228914	−	0.132164i	0.610071	+	0.792347i	$0.291141\pi$
$230$	−10.9282	−	2.92820i	−0.720584	−	0.193080i
$231$		0			0
$232$	16.3923	−	4.39230i	1.07621	−	0.288369i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$		0			0
$235$		−	24.0000i		−	1.56559i
$236$	4.00000	−	6.92820i	0.260378	−	0.450988i
$237$		0			0
$238$	−1.46410	+	5.46410i	−0.0949036	+	0.354185i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−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	$0.187185\pi$
$242$	−11.0000	−	11.0000i	−0.707107	−	0.707107i
$243$		0			0
$244$		0			0
$245$	5.19615	+	3.00000i	0.331970	+	0.191663i
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	−5.46410	−	1.46410i	−0.346971	−	0.0929705i
$249$		0			0
$250$	4.39230	+	16.3923i	0.277794	+	1.03674i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$	−2.73205	+	0.732051i	−0.171424	+	0.0459330i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	13.8564	+	8.00000i	0.860995	+	0.497096i
$260$			16.0000i			0.992278i
$261$		0			0
$262$	−20.0000	+	20.0000i	−1.23560	+	1.23560i
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	6.00000	+	10.3923i	0.368577	+	0.638394i
$266$	10.9282	+	2.92820i	0.670051	+	0.179540i
$267$		0			0
$268$	−12.0000	+	20.7846i	−0.733017	+	1.26962i
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$	−18.0000			−1.09342			−0.546711	−	0.837321i	$-0.684120\pi$
$271$	−18.0000			−1.09342			−0.546711	+	0.837321i	$0.684120\pi$
$272$	−4.00000	+	6.92820i	−0.242536	+	0.420084i
$273$		0			0
$274$	−6.58846	+	24.5885i	−0.398023	+	1.48544i
$275$		0			0
$276$		0			0
$277$	−24.2487	−	14.0000i	−1.45696	−	0.841178i	−0.458103	−	0.888899i	$-0.651471\pi$
$277$	−24.2487	−	14.0000i	−1.45696	−	0.841178i	−0.998861	+	0.0477206i	$0.984804\pi$
$278$	4.00000	−	4.00000i	0.239904	−	0.239904i
$279$		0			0
$280$	−8.00000	−	8.00000i	−0.478091	−	0.478091i
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$		0			0
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	−0.599414	−	0.800439i	$-0.704600\pi$
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	0.393494	+	0.919327i	$0.371266\pi$
$284$	20.7846	−	12.0000i	1.23334	−	0.712069i
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$		0			0
$289$	−13.0000			−0.764706
$290$	16.3923	−	4.39230i	0.962589	−	0.257925i
$291$		0			0
$292$	−10.3923	+	6.00000i	−0.608164	+	0.351123i
$293$	5.19615	−	3.00000i	0.303562	−	0.175262i	−0.340480	−	0.940252i	$-0.610589\pi$
$293$	5.19615	−	3.00000i	0.303562	−	0.175262i	0.644042	+	0.764990i	$0.277256\pi$
$294$		0			0
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$	16.0000	+	16.0000i	0.929981	+	0.929981i
$297$		0			0
$298$	−6.00000	+	6.00000i	−0.347571	+	0.347571i
$299$	13.8564	+	8.00000i	0.801337	+	0.462652i
$300$		0			0
$301$	6.92820	−	4.00000i	0.399335	−	0.230556i
$302$	6.58846	−	24.5885i	0.379123	−	1.41491i
$303$		0			0
$304$	13.8564	+	8.00000i	0.794719	+	0.458831i
$305$		0			0
$306$		0			0
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$		0			0
$310$	−5.46410	−	1.46410i	−0.310340	−	0.0831554i
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	0.956864	−	0.290537i	$-0.0938340\pi$
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	−0.730044	+	0.683400i	$0.760501\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	8.00000	−	8.00000i	0.451466	−	0.451466i
$315$		0			0
$316$			20.0000i			1.12509i
$317$	19.0526	+	11.0000i	1.07010	+	0.617822i	0.928208	−	0.372061i	$-0.121349\pi$
$317$	19.0526	+	11.0000i	1.07010	+	0.617822i	0.141890	+	0.989882i	$0.454682\pi$
$318$		0			0
$319$		0			0
$320$	−8.00000	−	13.8564i	−0.447214	−	0.774597i
$321$		0			0
$322$	−10.9282	+	2.92820i	−0.609005	+	0.163182i
$323$		−	8.00000i		−	0.445132i
$324$		0			0
$325$		−	4.00000i		−	0.221880i
$326$	−1.46410	−	5.46410i	−0.0810891	−	0.302629i
$327$		0			0
$328$	−5.46410	−	1.46410i	−0.301705	−	0.0808415i
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$		0			0
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.0583130	−	0.998298i	$-0.518572\pi$
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.893708	+	0.448649i	$0.851905\pi$
$332$	−32.0000			−1.75623
$333$		0			0
$334$	−8.00000	−	8.00000i	−0.437741	−	0.437741i
$335$	−12.0000	+	20.7846i	−0.655630	+	1.13558i
$336$		0			0
$337$	1.00000	+	1.73205i	0.0544735	+	0.0943508i	0.891976	−	0.452082i	$-0.149319\pi$
$337$	1.00000	+	1.73205i	0.0544735	+	0.0943508i	−0.837503	+	0.546433i	$0.815985\pi$
$338$	1.09808	−	4.09808i	0.0597275	−	0.222906i
$339$		0			0
$340$	−4.00000	+	6.92820i	−0.216930	+	0.375735i
$341$		0			0
$342$		0			0
$343$	20.0000			1.07990
$344$	10.9282	−	2.92820i	0.589209	−	0.157878i
$345$		0			0
$346$	−8.19615	−	2.19615i	−0.440628	−	0.118066i
$347$	6.92820	−	4.00000i	0.371925	−	0.214731i	−0.302374	−	0.953189i	$-0.597779\pi$
$347$	6.92820	−	4.00000i	0.371925	−	0.214731i	0.674299	+	0.738458i	$0.264446\pi$
$348$		0			0
$349$	13.8564	+	8.00000i	0.741716	+	0.428230i	0.822693	−	0.568486i	$-0.192471\pi$
$349$	13.8564	+	8.00000i	0.741716	+	0.428230i	−0.0809766	+	0.996716i	$0.525804\pi$
$350$	2.00000	+	2.00000i	0.106904	+	0.106904i
$351$		0			0
$352$		0			0
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	20.7846	−	12.0000i	1.10313	−	0.636894i
$356$	−17.3205	+	10.0000i	−0.917985	+	0.529999i
$357$		0			0
$358$	1.46410	+	5.46410i	0.0773802	+	0.288787i
$359$	−20.0000			−1.05556			−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000			−1.05556			−0.527780	+	0.849381i	$0.676975\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−7.32051	−	27.3205i	−0.384757	−	1.43593i
$363$		0			0
$364$	8.00000	+	13.8564i	0.419314	+	0.726273i
$365$	−10.3923	+	6.00000i	−0.543958	+	0.314054i
$366$		0			0
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	−0.999404	−	0.0345320i	$-0.989006\pi$
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$368$	−16.0000			−0.834058
$369$		0			0
$370$	16.0000	+	16.0000i	0.831800	+	0.831800i
$371$	10.3923	+	6.00000i	0.539542	+	0.311504i
$372$		0			0
$373$	13.8564	−	8.00000i	0.717458	−	0.414224i	−0.0963587	−	0.995347i	$-0.530720\pi$
$373$	13.8564	−	8.00000i	0.717458	−	0.414224i	0.813816	+	0.581122i	$0.197386\pi$
$374$		0			0
$375$		0			0
$376$	−8.78461	−	32.7846i	−0.453032	−	1.69074i
$377$	−24.0000			−1.23606
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$	13.8564	+	8.00000i	0.710819	+	0.410391i
$381$		0			0
$382$	2.92820	−	10.9282i	0.149820	−	0.559136i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		0			0
$385$		0			0
$386$	6.00000	+	6.00000i	0.305392	+	0.305392i
$387$		0			0
$388$		−	4.00000i		−	0.203069i
$389$	−29.4449	−	17.0000i	−1.49291	−	0.861934i	−0.492947	−	0.870059i	$-0.664080\pi$
$389$	−29.4449	−	17.0000i	−1.49291	−	0.861934i	−0.999967	+	0.00812520i	$0.997414\pi$
$390$		0			0
$391$	4.00000	+	6.92820i	0.202289	+	0.350374i
$392$	8.19615	+	2.19615i	0.413968	+	0.110922i
$393$		0			0
$394$	−0.732051	−	2.73205i	−0.0368802	−	0.137639i
$395$			20.0000i			1.00631i
$396$		0			0
$397$		−	32.0000i		−	1.60603i	−0.595956	−	0.803017i	$-0.703227\pi$
$397$		−	32.0000i		−	1.60603i	0.595956	−	0.803017i	$-0.296773\pi$
$398$	13.6603	−	3.66025i	0.684727	−	0.183472i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	6.92820	+	4.00000i	0.345118	+	0.199254i
$404$	20.0000			0.995037
$405$		0			0
$406$	12.0000	−	12.0000i	0.595550	−	0.595550i
$407$		0			0
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	−5.46410	−	1.46410i	−0.269853	−	0.0723068i
$411$		0			0
$412$	10.3923	+	6.00000i	0.511992	+	0.295599i
$413$		−	8.00000i		−	0.393654i
$414$		0			0
$415$	−32.0000			−1.57082
$416$	5.85641	+	21.8564i	0.287134	+	1.07160i
$417$		0			0
$418$		0			0
$419$	20.7846	−	12.0000i	1.01539	−	0.586238i	0.102628	−	0.994720i	$-0.467275\pi$
$419$	20.7846	−	12.0000i	1.01539	−	0.586238i	0.912767	+	0.408481i	$0.133942\pi$
$420$		0			0
$421$	17.3205	+	10.0000i	0.844150	+	0.487370i	0.858673	−	0.512524i	$-0.171290\pi$
$421$	17.3205	+	10.0000i	0.844150	+	0.487370i	−0.0145228	+	0.999895i	$0.504623\pi$
$422$	20.0000	−	20.0000i	0.973585	−	0.973585i
$423$		0			0
$424$	12.0000	+	12.0000i	0.582772	+	0.582772i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$	−12.0000	−	20.7846i	−0.580042	−	1.00466i
$429$		0			0
$430$	10.9282	−	2.92820i	0.527005	−	0.141210i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−5.46410	+	1.46410i	−0.262285	+	0.0702791i
$435$		0			0
$436$	4.00000	+	6.92820i	0.191565	+	0.331801i
$437$	13.8564	−	8.00000i	0.662842	−	0.382692i
$438$		0			0
$439$	15.0000	−	25.9808i	0.715911	−	1.23999i	−0.246696	−	0.969093i	$-0.579345\pi$
$439$	15.0000	−	25.9808i	0.715911	−	1.23999i	0.962607	−	0.270901i	$-0.0873217\pi$
$440$		0			0
$441$		0			0
$442$	8.00000	−	8.00000i	0.380521	−	0.380521i
$443$	20.7846	+	12.0000i	0.987507	+	0.570137i	0.904528	−	0.426414i	$-0.140223\pi$
$443$	20.7846	+	12.0000i	0.987507	+	0.570137i	0.0829786	+	0.996551i	$0.473557\pi$
$444$		0			0
$445$	−17.3205	+	10.0000i	−0.821071	+	0.474045i
$446$	−5.12436	+	19.1244i	−0.242645	+	0.905564i
$447$		0			0
$448$	−13.8564	−	8.00000i	−0.654654	−	0.377964i
$449$	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
$452$	10.3923	+	6.00000i	0.488813	+	0.282216i
$453$		0			0
$454$	−10.9282	−	2.92820i	−0.512886	−	0.137427i
$455$	8.00000	+	13.8564i	0.375046	+	0.649598i
$456$		0			0
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	−0.485299	−	0.874348i	$-0.661289\pi$
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	0.999857	−	0.0168929i	$-0.00537742\pi$
$458$	4.00000	−	4.00000i	0.186908	−	0.186908i
$459$		0			0
$460$	−16.0000			−0.746004
$461$	−25.9808	−	15.0000i	−1.21004	−	0.698620i	−0.247276	−	0.968945i	$-0.579535\pi$
$461$	−25.9808	−	15.0000i	−1.21004	−	0.698620i	−0.962769	+	0.270326i	$0.912869\pi$
$462$		0			0
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	0.992183	+	0.124788i	$0.0398251\pi$
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	−0.388022	+	0.921650i	$0.626842\pi$
$464$	20.7846	−	12.0000i	0.964901	−	0.557086i
$465$		0			0
$466$	19.1244	−	5.12436i	0.885919	−	0.237381i
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$		0			0
$469$			24.0000i			1.10822i
$470$	−8.78461	−	32.7846i	−0.405204	−	1.51224i
$471$		0			0
$472$	2.92820	−	10.9282i	0.134781	−	0.503011i
$473$		0			0
$474$		0			0
$475$	−3.46410	−	2.00000i	−0.158944	−	0.0917663i
$476$			8.00000i			0.366679i
$477$		0			0
$478$		0			0
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$		0			0
$481$	−16.0000	−	27.7128i	−0.729537	−	1.26360i
$482$	−0.732051	+	2.73205i	−0.0333440	+	0.124442i
$483$		0			0
$484$	−19.0526	−	11.0000i	−0.866025	−	0.500000i
$485$		−	4.00000i		−	0.181631i
$486$		0			0
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$		0			0
$489$		0			0
$490$	8.19615	+	2.19615i	0.370264	+	0.0992121i
$491$	−17.3205	+	10.0000i	−0.781664	+	0.451294i	−0.837020	−	0.547173i	$-0.815704\pi$
$491$	−17.3205	+	10.0000i	−0.781664	+	0.451294i	0.0553560	+	0.998467i	$0.482371\pi$
$492$		0			0
$493$	−10.3923	−	6.00000i	−0.468046	−	0.270226i
$494$	−16.0000	−	16.0000i	−0.719874	−	0.719874i
$495$		0			0
$496$	−8.00000			−0.359211
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$		0			0
$499$	−31.1769	+	18.0000i	−1.39567	+	0.805791i	−0.993935	−	0.109965i	$-0.964926\pi$
$499$	−31.1769	+	18.0000i	−1.39567	+	0.805791i	−0.401735	+	0.915756i	$0.631593\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$		0			0
$502$		0			0
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	20.0000			0.889988
$506$		0			0
$507$		0			0
$508$	−3.46410	+	2.00000i	−0.153695	+	0.0887357i
$509$	−5.19615	+	3.00000i	−0.230315	+	0.132973i	−0.610718	−	0.791849i	$-0.709119\pi$
$509$	−5.19615	+	3.00000i	−0.230315	+	0.132973i	0.380402	+	0.924821i	$0.375786\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−18.0000	−	18.0000i	−0.793946	−	0.793946i
$515$	10.3923	+	6.00000i	0.457940	+	0.264392i
$516$		0			0
$517$		0			0
$518$	21.8564	+	5.85641i	0.960315	+	0.257316i
$519$		0			0
$520$	5.85641	+	21.8564i	0.256820	+	0.958467i
$521$	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
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$	−20.0000	+	34.6410i	−0.873704	+	1.51330i
$525$		0			0
$526$	5.85641	−	21.8564i	0.255351	−	0.952985i
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	12.0000	+	12.0000i	0.521247	+	0.521247i
$531$		0			0
$532$	16.0000			0.693688
$533$	6.92820	+	4.00000i	0.300094	+	0.173259i
$534$		0			0
$535$	−12.0000	−	20.7846i	−0.518805	−	0.898597i
$536$	−8.78461	+	32.7846i	−0.379437	+	1.41608i
$537$		0			0
$538$	−2.19615	−	8.19615i	−0.0946829	−	0.353361i
$539$		0			0
$540$		0			0
$541$			20.0000i			0.859867i	0.902861	+	0.429934i	$0.141463\pi$
$541$			20.0000i			0.859867i	−0.902861	+	0.429934i	$0.858537\pi$
$542$	−24.5885	+	6.58846i	−1.05616	+	0.282998i
$543$		0			0
$544$	−2.92820	+	10.9282i	−0.125546	+	0.468543i
$545$	4.00000	+	6.92820i	0.171341	+	0.296772i
$546$		0			0
$547$	−24.2487	−	14.0000i	−1.03680	−	0.598597i	−0.117875	−	0.993028i	$-0.537608\pi$
$547$	−24.2487	−	14.0000i	−1.03680	−	0.598597i	−0.918925	+	0.394432i	$0.870941\pi$
$548$			36.0000i			1.53784i
$549$		0			0
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$		0			0
$553$	10.0000	+	17.3205i	0.425243	+	0.736543i
$554$	−38.2487	−	10.2487i	−1.62503	−	0.435426i
$555$		0			0
$556$	4.00000	−	6.92820i	0.169638	−	0.293821i
$557$		−	42.0000i		−	1.77960i	−0.456354	−	0.889799i	$-0.650845\pi$
$557$		−	42.0000i		−	1.77960i	0.456354	−	0.889799i	$-0.349155\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$	−13.8564	−	8.00000i	−0.585540	−	0.338062i
$561$		0			0
$562$	6.58846	−	24.5885i	0.277917	−	1.03720i
$563$	−20.7846	+	12.0000i	−0.875967	+	0.505740i	−0.869326	−	0.494238i	$-0.835447\pi$
$563$	−20.7846	+	12.0000i	−0.875967	+	0.505740i	−0.00664037	+	0.999978i	$0.502114\pi$
$564$		0			0
$565$	10.3923	+	6.00000i	0.437208	+	0.252422i
$566$	−4.00000	+	4.00000i	−0.168133	+	0.168133i
$567$		0			0
$568$	24.0000	−	24.0000i	1.00702	−	1.00702i
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−17.3205	+	10.0000i	−0.724841	+	0.418487i	−0.816532	−	0.577301i	$-0.804106\pi$
$571$	−17.3205	+	10.0000i	−0.724841	+	0.418487i	0.0916910	+	0.995788i	$0.470773\pi$
$572$		0			0
$573$		0			0
$574$	−5.46410	+	1.46410i	−0.228067	+	0.0611104i
$575$	4.00000			0.166812
$576$		0			0
$577$	−42.0000			−1.74848			−0.874241	−	0.485491i	$-0.838641\pi$
$577$	−42.0000			−1.74848			−0.874241	+	0.485491i	$0.838641\pi$
$578$	−17.7583	+	4.75833i	−0.738649	+	0.197920i
$579$		0			0
$580$	20.7846	−	12.0000i	0.863034	−	0.498273i
$581$	−27.7128	+	16.0000i	−1.14972	+	0.663792i
$582$		0			0
$583$		0			0
$584$	−12.0000	+	12.0000i	−0.496564	+	0.496564i
$585$		0			0
$586$	6.00000	−	6.00000i	0.247858	−	0.247858i
$587$	−24.2487	−	14.0000i	−1.00085	−	0.577842i	−0.0923513	−	0.995726i	$-0.529438\pi$
$587$	−24.2487	−	14.0000i	−1.00085	−	0.577842i	−0.908500	+	0.417885i	$0.862772\pi$
$588$		0			0
$589$	6.92820	−	4.00000i	0.285472	−	0.164817i
$590$	2.92820	−	10.9282i	0.120552	−	0.449907i
$591$		0			0
$592$	27.7128	+	16.0000i	1.13899	+	0.657596i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$			8.00000i			0.327968i
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$		0			0
$598$	21.8564	+	5.85641i	0.893775	+	0.239486i
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	0.994732	−	0.102511i	$-0.0326876\pi$
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	−0.586143	+	0.810208i	$0.699354\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	−0.885700	−	0.464258i	$-0.846321\pi$
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	0.844909	+	0.534910i	$0.179654\pi$
$602$	8.00000	−	8.00000i	0.326056	−	0.326056i
$603$		0			0
$604$		−	36.0000i		−	1.46482i
$605$	−19.0526	−	11.0000i	−0.774597	−	0.447214i
$606$		0			0
$607$	1.00000	+	1.73205i	0.0405887	+	0.0703018i	0.885606	−	0.464437i	$-0.153743\pi$
$607$	1.00000	+	1.73205i	0.0405887	+	0.0703018i	−0.845017	+	0.534739i	$0.820410\pi$
$608$	21.8564	+	5.85641i	0.886394	+	0.237509i
$609$		0			0
$610$		0			0
$611$			48.0000i			1.94187i
$612$		0			0
$613$			16.0000i			0.646234i	0.946359	+	0.323117i	$0.104731\pi$
$613$			16.0000i			0.646234i	−0.946359	+	0.323117i	$0.895269\pi$
$614$	−4.39230	−	16.3923i	−0.177259	−	0.661540i
$615$		0			0
$616$		0			0
$617$	1.00000	+	1.73205i	0.0402585	+	0.0697297i	0.885453	−	0.464730i	$-0.153849\pi$
$617$	1.00000	+	1.73205i	0.0402585	+	0.0697297i	−0.845194	+	0.534460i	$0.820515\pi$
$618$		0			0
$619$	31.1769	+	18.0000i	1.25311	+	0.723481i	0.971725	−	0.236115i	$-0.0758742\pi$
$619$	31.1769	+	18.0000i	1.25311	+	0.723481i	0.281381	+	0.959596i	$0.409208\pi$
$620$	−8.00000			−0.321288
$621$		0			0
$622$	8.00000	+	8.00000i	0.320771	+	0.320771i
$623$	−10.0000	+	17.3205i	−0.400642	+	0.693932i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−5.12436	+	19.1244i	−0.204810	+	0.764363i
$627$		0			0
$628$	8.00000	−	13.8564i	0.319235	−	0.552931i
$629$		−	16.0000i		−	0.637962i
$630$		0			0
$631$	22.0000			0.875806			0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000			0.875806			0.437903	+	0.899022i	$0.355721\pi$
$632$	7.32051	+	27.3205i	0.291194	+	1.08675i
$633$		0			0
$634$	30.0526	+	8.05256i	1.19354	+	0.319808i
$635$	−3.46410	+	2.00000i	−0.137469	+	0.0793676i
$636$		0			0
$637$	−10.3923	−	6.00000i	−0.411758	−	0.237729i
$638$		0			0
$639$		0			0
$640$	−16.0000	−	16.0000i	−0.632456	−	0.632456i
$641$	−11.0000	+	19.0526i	−0.434474	+	0.752531i	−0.997253	−	0.0740768i	$-0.976399\pi$
$641$	−11.0000	+	19.0526i	−0.434474	+	0.752531i	0.562779	+	0.826608i	$0.309732\pi$
$642$		0			0
$643$	−3.46410	+	2.00000i	−0.136611	+	0.0788723i	−0.566748	−	0.823891i	$-0.691799\pi$
$643$	−3.46410	+	2.00000i	−0.136611	+	0.0788723i	0.430137	+	0.902764i	$0.358465\pi$
$644$	−13.8564	+	8.00000i	−0.546019	+	0.315244i
$645$		0			0
$646$	−2.92820	−	10.9282i	−0.115209	−	0.429964i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$		0			0
$649$		0			0
$650$	−1.46410	−	5.46410i	−0.0574268	−	0.214320i
$651$		0			0
$652$	−4.00000	−	6.92820i	−0.156652	−	0.271329i
$653$	5.19615	−	3.00000i	0.203341	−	0.117399i	−0.394872	−	0.918736i	$-0.629211\pi$
$653$	5.19615	−	3.00000i	0.203341	−	0.117399i	0.598213	+	0.801337i	$0.295878\pi$
$654$		0			0
$655$	−20.0000	+	34.6410i	−0.781465	+	1.35354i
$656$	−8.00000			−0.312348
$657$		0			0
$658$	−24.0000	−	24.0000i	−0.935617	−	0.935617i
$659$	31.1769	+	18.0000i	1.21448	+	0.701180i	0.963732	−	0.266872i	$-0.0859901\pi$
$659$	31.1769	+	18.0000i	1.21448	+	0.701180i	0.250748	+	0.968052i	$0.419323\pi$
$660$		0			0
$661$	−34.6410	+	20.0000i	−1.34738	+	0.777910i	−0.987878	−	0.155235i	$-0.950387\pi$
$661$	−34.6410	+	20.0000i	−1.34738	+	0.777910i	−0.359502	+	0.933144i	$0.617053\pi$
$662$	−27.3205	−	7.32051i	−1.06184	−	0.284520i
$663$		0			0
$664$	−43.7128	+	11.7128i	−1.69639	+	0.454545i
$665$	16.0000			0.620453
$666$		0			0
$667$		−	24.0000i		−	0.929284i
$668$	−13.8564	−	8.00000i	−0.536120	−	0.309529i
$669$		0			0
$670$	−8.78461	+	32.7846i	−0.339379	+	1.26658i
$671$		0			0
$672$		0			0
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	2.00000	+	2.00000i	0.0770371	+	0.0770371i
$675$		0			0
$676$		−	6.00000i		−	0.230769i
$677$	−15.5885	−	9.00000i	−0.599113	−	0.345898i	0.169580	−	0.985517i	$-0.445759\pi$
$677$	−15.5885	−	9.00000i	−0.599113	−	0.345898i	−0.768693	+	0.639618i	$0.779092\pi$
$678$		0			0
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	−2.92820	+	10.9282i	−0.112291	+	0.419077i
$681$		0			0
$682$		0			0
$683$			16.0000i			0.612223i	0.951996	+	0.306111i	$0.0990280\pi$
$683$			16.0000i			0.612223i	−0.951996	+	0.306111i	$0.900972\pi$
$684$		0			0
$685$			36.0000i			1.37549i
$686$	27.3205	−	7.32051i	1.04310	−	0.279498i
$687$		0			0
$688$	13.8564	−	8.00000i	0.528271	−	0.304997i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$		0			0
$691$	17.3205	+	10.0000i	0.658903	+	0.380418i	0.791859	−	0.610704i	$-0.209113\pi$
$691$	17.3205	+	10.0000i	0.658903	+	0.380418i	−0.132956	+	0.991122i	$0.542447\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	8.00000	−	8.00000i	0.303676	−	0.303676i
$695$	4.00000	−	6.92820i	0.151729	−	0.262802i
$696$		0			0
$697$	2.00000	+	3.46410i	0.0757554	+	0.131212i
$698$	21.8564	+	5.85641i	0.827277	+	0.221668i
$699$		0			0
$700$	3.46410	+	2.00000i	0.130931	+	0.0755929i
$701$			50.0000i			1.88847i	0.329267	+	0.944237i	$0.393198\pi$
$701$			50.0000i			1.88847i	−0.329267	+	0.944237i	$0.606802\pi$
$702$		0			0
$703$	−32.0000			−1.20690
$704$		0			0
$705$		0			0
$706$	2.19615	−	8.19615i	0.0826533	−	0.308466i
$707$	17.3205	−	10.0000i	0.651405	−	0.376089i
$708$		0			0
$709$	−3.46410	−	2.00000i	−0.130097	−	0.0751116i	0.433539	−	0.901135i	$-0.357265\pi$
$709$	−3.46410	−	2.00000i	−0.130097	−	0.0751116i	−0.563636	+	0.826023i	$0.690598\pi$
$710$	24.0000	−	24.0000i	0.900704	−	0.900704i
$711$		0			0
$712$	−20.0000	+	20.0000i	−0.749532	+	0.749532i
$713$	−4.00000	+	6.92820i	−0.149801	+	0.259463i
$714$		0			0
$715$		0			0
$716$	4.00000	+	6.92820i	0.149487	+	0.258919i
$717$		0			0
$718$	−27.3205	+	7.32051i	−1.01959	+	0.273199i
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	4.09808	−	1.09808i	0.152515	−	0.0408662i
$723$		0			0
$724$	−20.0000	−	34.6410i	−0.743294	−	1.28742i
$725$	−5.19615	+	3.00000i	−0.192980	+	0.111417i
$726$		0			0
$727$	21.0000	−	36.3731i	0.778847	−	1.34900i	−0.153760	−	0.988108i	$-0.549138\pi$
$727$	21.0000	−	36.3731i	0.778847	−	1.34900i	0.932607	−	0.360894i	$-0.117528\pi$
$728$	16.0000	+	16.0000i	0.592999	+	0.592999i
$729$		0			0
$730$	−12.0000	+	12.0000i	−0.444140	+	0.444140i
$731$	−6.92820	−	4.00000i	−0.256249	−	0.147945i
$732$		0			0
$733$	−3.46410	+	2.00000i	−0.127950	+	0.0738717i	−0.562609	−	0.826723i	$-0.690202\pi$
$733$	−3.46410	+	2.00000i	−0.127950	+	0.0738717i	0.434659	+	0.900595i	$0.356869\pi$
$734$	−6.58846	+	24.5885i	−0.243184	+	0.907577i
$735$		0			0
$736$	−21.8564	+	5.85641i	−0.805638	+	0.215870i
$737$		0			0
$738$		0			0
$739$			44.0000i			1.61857i	0.587419	+	0.809283i	$0.300144\pi$
$739$			44.0000i			1.61857i	−0.587419	+	0.809283i	$0.699856\pi$
$740$	27.7128	+	16.0000i	1.01874	+	0.588172i
$741$		0			0
$742$	16.3923	+	4.39230i	0.601780	+	0.161247i
$743$	8.00000	+	13.8564i	0.293492	+	0.508342i	0.974633	−	0.223810i	$-0.0718494\pi$
$743$	8.00000	+	13.8564i	0.293492	+	0.508342i	−0.681141	+	0.732152i	$0.738516\pi$
$744$		0			0
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	16.0000	−	16.0000i	0.585802	−	0.585802i
$747$		0			0
$748$		0			0
$749$	−20.7846	−	12.0000i	−0.759453	−	0.438470i
$750$		0			0
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	0.847203	−	0.531269i	$-0.178285\pi$
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	−0.883694	+	0.468065i	$0.844951\pi$
$752$	−24.0000	−	41.5692i	−0.875190	−	1.51587i
$753$		0			0
$754$	−32.7846	+	8.78461i	−1.19395	+	0.319917i
$755$		−	36.0000i		−	1.31017i
$756$		0			0
$757$		−	12.0000i		−	0.436147i	−0.975932	−	0.218074i	$-0.930023\pi$
$757$		−	12.0000i		−	0.436147i	0.975932	−	0.218074i	$-0.0699773\pi$
$758$	1.46410	+	5.46410i	0.0531786	+	0.198465i
$759$		0			0
$760$	21.8564	+	5.85641i	0.792815	+	0.212434i
$761$	19.0000	+	32.9090i	0.688749	+	1.19295i	0.972243	+	0.233975i	$0.0751733\pi$
$761$	19.0000	+	32.9090i	0.688749	+	1.19295i	−0.283493	+	0.958974i	$0.591493\pi$
$762$		0			0
$763$	6.92820	+	4.00000i	0.250818	+	0.144810i
$764$		−	16.0000i		−	0.578860i
$765$		0			0
$766$	−24.0000	−	24.0000i	−0.867155	−	0.867155i
$767$	−8.00000	+	13.8564i	−0.288863	+	0.500326i
$768$		0			0
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$		0			0
$771$		0			0
$772$	10.3923	+	6.00000i	0.374027	+	0.215945i
$773$		−	34.0000i		−	1.22290i	−0.791285	−	0.611448i	$-0.790588\pi$
$773$		−	34.0000i		−	1.22290i	0.791285	−	0.611448i	$-0.209412\pi$
$774$		0			0
$775$	2.00000			0.0718421
$776$	−1.46410	−	5.46410i	−0.0525582	−	0.196150i
$777$		0			0
$778$	−46.4449	−	12.4449i	−1.66513	−	0.446170i
$779$	6.92820	−	4.00000i	0.248229	−	0.143315i
$780$		0			0
$781$		0			0
$782$	8.00000	+	8.00000i	0.286079	+	0.286079i
$783$		0			0
$784$	12.0000			0.428571
$785$	8.00000	−	13.8564i	0.285532	−	0.494556i
$786$		0			0
$787$	−10.3923	+	6.00000i	−0.370446	+	0.213877i	−0.673653	−	0.739048i	$-0.735276\pi$
$787$	−10.3923	+	6.00000i	−0.370446	+	0.213877i	0.303207	+	0.952925i	$0.401942\pi$
$788$	−2.00000	−	3.46410i	−0.0712470	−	0.123404i
$789$		0			0
$790$	7.32051	+	27.3205i	0.260452	+	0.972020i
$791$	12.0000			0.426671
$792$		0			0
$793$		0			0
$794$	−11.7128	−	43.7128i	−0.415672	−	1.55131i
$795$		0			0
$796$	17.3205	−	10.0000i	0.613909	−	0.354441i
$797$	−1.73205	+	1.00000i	−0.0613524	+	0.0354218i	−0.530362	−	0.847771i	$-0.677944\pi$
$797$	−1.73205	+	1.00000i	−0.0613524	+	0.0354218i	0.469010	+	0.883193i	$0.344611\pi$
$798$		0			0
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$		0			0
$802$	18.0000	+	18.0000i	0.635602	+	0.635602i
$803$		0			0
$804$		0			0
$805$	−13.8564	+	8.00000i	−0.488374	+	0.281963i
$806$	10.9282	+	2.92820i	0.384930	+	0.103142i
$807$		0			0
$808$	27.3205	−	7.32051i	0.961132	−	0.257535i
$809$	−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
$811$			20.0000i			0.702295i	0.936320	+	0.351147i	$0.114208\pi$
$811$			20.0000i			0.702295i	−0.936320	+	0.351147i	$0.885792\pi$
$812$	12.0000	−	20.7846i	0.421117	−	0.729397i
$813$		0			0
$814$		0			0
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	−10.0000	−	10.0000i	−0.349642	−	0.349642i
$819$		0			0
$820$	−8.00000			−0.279372
$821$	8.66025	+	5.00000i	0.302245	+	0.174501i	0.643451	−	0.765487i	$-0.277502\pi$
$821$	8.66025	+	5.00000i	0.302245	+	0.174501i	−0.341206	+	0.939989i	$0.610835\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	16.3923	+	4.39230i	0.571053	+	0.153013i
$825$		0			0
$826$	−2.92820	−	10.9282i	−0.101885	−	0.380241i
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$		0			0
$829$			4.00000i			0.138926i	0.997585	+	0.0694629i	$0.0221285\pi$
$829$			4.00000i			0.138926i	−0.997585	+	0.0694629i	$0.977871\pi$
$830$	−43.7128	+	11.7128i	−1.51729	+	0.406558i
$831$		0			0
$832$	16.0000	+	27.7128i	0.554700	+	0.960769i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	−13.8564	−	8.00000i	−0.479521	−	0.276851i
$836$		0			0
$837$		0			0
$838$	24.0000	−	24.0000i	0.829066	−	0.829066i
$839$	−10.0000	+	17.3205i	−0.345238	+	0.597970i	−0.985397	−	0.170272i	$-0.945535\pi$
$839$	−10.0000	+	17.3205i	−0.345238	+	0.597970i	0.640159	+	0.768243i	$0.278869\pi$
$840$		0			0
$841$	3.50000	+	6.06218i	0.120690	+	0.209041i
$842$	27.3205	+	7.32051i	0.941527	+	0.252281i
$843$		0			0
$844$	20.0000	−	34.6410i	0.688428	−	1.19239i
$845$		−	6.00000i		−	0.206406i
$846$		0			0
$847$	−22.0000			−0.755929
$848$	20.7846	+	12.0000i	0.713746	+	0.412082i
$849$		0			0
$850$	0.732051	−	2.73205i	0.0251091	−	0.0937086i
$851$	27.7128	−	16.0000i	0.949983	−	0.548473i
$852$		0			0
$853$	20.7846	+	12.0000i	0.711651	+	0.410872i	0.811672	−	0.584113i	$-0.198558\pi$
$853$	20.7846	+	12.0000i	0.711651	+	0.410872i	−0.100021	+	0.994985i	$0.531891\pi$
$854$		0			0
$855$		0			0
$856$	−24.0000	−	24.0000i	−0.820303	−	0.820303i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	38.1051	−	22.0000i	1.30013	−	0.750630i	0.319704	−	0.947518i	$-0.396417\pi$
$859$	38.1051	−	22.0000i	1.30013	−	0.750630i	0.980426	+	0.196887i	$0.0630833\pi$
$860$	13.8564	−	8.00000i	0.472500	−	0.272798i
$861$		0			0
$862$	16.3923	−	4.39230i	0.558324	−	0.149602i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$	19.1244	−	5.12436i	0.649872	−	0.174133i
$867$		0			0
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$		0			0
$870$		0			0
$871$	24.0000	−	41.5692i	0.813209	−	1.40852i
$872$	8.00000	+	8.00000i	0.270914	+	0.270914i
$873$		0			0
$874$	16.0000	−	16.0000i	0.541208	−	0.541208i
$875$	20.7846	+	12.0000i	0.702648	+	0.405674i
$876$		0			0
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.888640	−	0.458606i	$-0.848349\pi$
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.0471555	+	0.998888i	$0.515016\pi$
$878$	10.9808	−	40.9808i	0.370583	−	1.38303i
$879$		0			0
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$	8.00000	−	13.8564i	0.269069	−	0.466041i
$885$		0			0
$886$	32.7846	+	8.78461i	1.10142	+	0.295125i
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		0			0
$889$	−2.00000	+	3.46410i	−0.0670778	+	0.116182i
$890$	−20.0000	+	20.0000i	−0.670402	+	0.670402i
$891$		0			0
$892$			28.0000i			0.937509i
$893$	41.5692	+	24.0000i	1.39106	+	0.803129i
$894$		0			0
$895$	4.00000	+	6.92820i	0.133705	+	0.231584i
$896$	−21.8564	−	5.85641i	−0.730171	−	0.195649i
$897$		0			0
$898$	40.9808	−	10.9808i	1.36755	−	0.366433i
$899$		−	12.0000i		−	0.400222i
$900$		0			0
$901$		−	12.0000i		−	0.399778i
$902$		0			0
$903$		0			0
$904$	16.3923	+	4.39230i	0.545200	+	0.146086i
$905$	−20.0000	−	34.6410i	−0.664822	−	1.15151i
$906$		0			0
$907$	−24.2487	−	14.0000i	−0.805165	−	0.464862i	0.0401089	−	0.999195i	$-0.487230\pi$
$907$	−24.2487	−	14.0000i	−0.805165	−	0.464862i	−0.845274	+	0.534333i	$0.820563\pi$
$908$	−16.0000			−0.530979
$909$		0			0
$910$	16.0000	+	16.0000i	0.530395	+	0.530395i
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	−0.127585	−	0.991828i	$-0.540723\pi$
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	0.922740	−	0.385422i	$-0.125944\pi$
$912$		0			0
$913$		0			0
$914$	8.05256	−	30.0526i	0.266355	−	0.994050i
$915$		0			0
$916$	4.00000	−	6.92820i	0.132164	−	0.228914i
$917$			40.0000i			1.32092i
$918$		0			0
$919$	30.0000			0.989609			0.494804	−	0.869004i	$-0.335240\pi$
$919$	30.0000			0.989609			0.494804	+	0.869004i	$0.335240\pi$
$920$	−21.8564	+	5.85641i	−0.720584	+	0.193080i
$921$		0			0
$922$	−40.9808	−	10.9808i	−1.34963	−	0.361632i
$923$	−41.5692	+	24.0000i	−1.36827	+	0.789970i
$924$		0			0
$925$	−6.92820	−	4.00000i	−0.227798	−	0.131519i
$926$	26.0000	+	26.0000i	0.854413	+	0.854413i
$927$		0			0
$928$	24.0000	−	24.0000i	0.787839	−	0.787839i
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	−0.0852924	−	0.996356i	$-0.527182\pi$
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	0.905516	−	0.424313i	$-0.139484\pi$
$930$		0			0
$931$	−10.3923	+	6.00000i	−0.340594	+	0.196642i
$932$	24.2487	−	14.0000i	0.794293	−	0.458585i
$933$		0			0
$934$	2.92820	+	10.9282i	0.0958137	+	0.357582i
$935$		0			0
$936$		0			0
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	8.78461	+	32.7846i	0.286828	+	1.07046i
$939$		0			0
$940$	−24.0000	−	41.5692i	−0.782794	−	1.35584i
$941$	25.9808	−	15.0000i	0.846949	−	0.488986i	−0.0126715	−	0.999920i	$-0.504034\pi$
$941$	25.9808	−	15.0000i	0.846949	−	0.488986i	0.859620	+	0.510934i	$0.170700\pi$
$942$		0			0
$943$	−4.00000	+	6.92820i	−0.130258	+	0.225613i
$944$		−	16.0000i		−	0.520756i
$945$		0			0
$946$		0			0
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	0.659256	−	0.751918i	$-0.270871\pi$
$947$	10.3923	+	6.00000i	0.337705	+	0.194974i	−0.321552	+	0.946892i	$0.604204\pi$
$948$		0			0
$949$	20.7846	−	12.0000i	0.674697	−	0.389536i
$950$	−5.46410	−	1.46410i	−0.177279	−	0.0475017i
$951$		0			0
$952$	2.92820	+	10.9282i	0.0949036	+	0.354185i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		−	16.0000i		−	0.517748i
$956$		0			0
$957$		0			0
$958$	−7.32051	+	27.3205i	−0.236515	+	0.882686i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−32.0000	−	32.0000i	−1.03172	−	1.03172i
$963$		0			0
$964$			4.00000i			0.128831i
$965$	10.3923	+	6.00000i	0.334540	+	0.193147i
$966$		0			0
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	−30.0526	−	8.05256i	−0.965926	−	0.258819i
$969$		0			0
$970$	−1.46410	−	5.46410i	−0.0470095	−	0.175442i
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$		0			0
$973$		−	8.00000i		−	0.256468i
$974$	51.9090	−	13.9090i	1.66327	−	0.445672i
$975$		0			0
$976$		0			0
$977$	1.00000	+	1.73205i	0.0319928	+	0.0554132i	0.881579	−	0.472037i	$-0.156481\pi$
$977$	1.00000	+	1.73205i	0.0319928	+	0.0554132i	−0.849586	+	0.527451i	$0.823148\pi$
$978$		0			0
$979$		0			0
$980$	12.0000			0.383326
$981$		0			0
$982$	−20.0000	+	20.0000i	−0.638226	+	0.638226i
$983$	8.00000	−	13.8564i	0.255160	−	0.441951i	−0.709779	−	0.704425i	$-0.751205\pi$
$983$	8.00000	−	13.8564i	0.255160	−	0.441951i	0.964939	+	0.262474i	$0.0845384\pi$
$984$		0			0
$985$	−2.00000	−	3.46410i	−0.0637253	−	0.110375i
$986$	−16.3923	−	4.39230i	−0.522037	−	0.139879i
$987$		0			0
$988$	−27.7128	−	16.0000i	−0.881662	−	0.509028i
$989$		−	16.0000i		−	0.508770i
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	−10.9282	+	2.92820i	−0.346971	+	0.0929705i
$993$		0			0
$994$	8.78461	−	32.7846i	0.278631	−	1.03986i
$995$	17.3205	−	10.0000i	0.549097	−	0.317021i
$996$		0			0
$997$	−41.5692	−	24.0000i	−1.31651	−	0.760088i	−0.333345	−	0.942805i	$-0.608177\pi$
$997$	−41.5692	−	24.0000i	−1.31651	−	0.760088i	−0.983165	+	0.182717i	$0.941511\pi$
$998$	−36.0000	+	36.0000i	−1.13956	+	1.13956i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.n.k.541.2		4
3.2	odd	2		648.2.n.c.541.1		4
4.3	odd	2		2592.2.r.f.2161.2		4
8.3	odd	2		2592.2.r.f.2161.1		4
8.5	even	2	inner	648.2.n.k.541.1		4
9.2	odd	6		72.2.d.b.37.2		2
9.4	even	3	inner	648.2.n.k.109.1		4
9.5	odd	6		648.2.n.c.109.2		4
9.7	even	3		24.2.d.a.13.1	✓	2
12.11	even	2		2592.2.r.g.2161.1		4
24.5	odd	2		648.2.n.c.541.2		4
24.11	even	2		2592.2.r.g.2161.2		4
36.7	odd	6		96.2.d.a.49.2		2
36.11	even	6		288.2.d.b.145.1		2
36.23	even	6		2592.2.r.g.433.2		4
36.31	odd	6		2592.2.r.f.433.1		4
45.2	even	12		1800.2.d.b.1549.2		2
45.7	odd	12		600.2.d.c.349.1		2
45.29	odd	6		1800.2.k.a.901.1		2
45.34	even	6		600.2.k.b.301.2		2
45.38	even	12		1800.2.d.i.1549.1		2
45.43	odd	12		600.2.d.b.349.2		2
63.34	odd	6		1176.2.c.a.589.1		2
72.5	odd	6		648.2.n.c.109.1		4
72.11	even	6		288.2.d.b.145.2		2
72.13	even	6	inner	648.2.n.k.109.2		4
72.29	odd	6		72.2.d.b.37.1		2
72.43	odd	6		96.2.d.a.49.1		2
72.59	even	6		2592.2.r.g.433.1		4
72.61	even	6		24.2.d.a.13.2	yes	2
72.67	odd	6		2592.2.r.f.433.2		4
144.11	even	12		2304.2.a.l.1.1		1
144.29	odd	12		2304.2.a.e.1.1		1
144.43	odd	12		768.2.a.e.1.1		1
144.61	even	12		768.2.a.h.1.1		1
144.83	even	12		2304.2.a.b.1.1		1
144.101	odd	12		2304.2.a.o.1.1		1
144.115	odd	12		768.2.a.d.1.1		1
144.133	even	12		768.2.a.a.1.1		1
180.7	even	12		2400.2.d.c.49.2		2
180.43	even	12		2400.2.d.b.49.1		2
180.47	odd	12		7200.2.d.d.2449.2		2
180.79	odd	6		2400.2.k.a.1201.1		2
180.83	odd	12		7200.2.d.g.2449.1		2
180.119	even	6		7200.2.k.d.3601.2		2
252.223	even	6		4704.2.c.a.2353.1		2
360.29	odd	6		1800.2.k.a.901.2		2
360.43	even	12		2400.2.d.c.49.1		2
360.83	odd	12		7200.2.d.d.2449.1		2
360.133	odd	12		600.2.d.c.349.2		2
360.173	even	12		1800.2.d.b.1549.1		2
360.187	even	12		2400.2.d.b.49.2		2
360.227	odd	12		7200.2.d.g.2449.2		2
360.259	odd	6		2400.2.k.a.1201.2		2
360.277	odd	12		600.2.d.b.349.1		2
360.299	even	6		7200.2.k.d.3601.1		2
360.317	even	12		1800.2.d.i.1549.2		2
360.349	even	6		600.2.k.b.301.1		2
504.349	odd	6		1176.2.c.a.589.2		2
504.475	even	6		4704.2.c.a.2353.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.2.d.a.13.1	✓	2	9.7	even	3
24.2.d.a.13.2	yes	2	72.61	even	6
72.2.d.b.37.1		2	72.29	odd	6
72.2.d.b.37.2		2	9.2	odd	6
96.2.d.a.49.1		2	72.43	odd	6
96.2.d.a.49.2		2	36.7	odd	6
288.2.d.b.145.1		2	36.11	even	6
288.2.d.b.145.2		2	72.11	even	6
600.2.d.b.349.1		2	360.277	odd	12
600.2.d.b.349.2		2	45.43	odd	12
600.2.d.c.349.1		2	45.7	odd	12
600.2.d.c.349.2		2	360.133	odd	12
600.2.k.b.301.1		2	360.349	even	6
600.2.k.b.301.2		2	45.34	even	6
648.2.n.c.109.1		4	72.5	odd	6
648.2.n.c.109.2		4	9.5	odd	6
648.2.n.c.541.1		4	3.2	odd	2
648.2.n.c.541.2		4	24.5	odd	2
648.2.n.k.109.1		4	9.4	even	3	inner
648.2.n.k.109.2		4	72.13	even	6	inner
648.2.n.k.541.1		4	8.5	even	2	inner
648.2.n.k.541.2		4	1.1	even	1	trivial
768.2.a.a.1.1		1	144.133	even	12
768.2.a.d.1.1		1	144.115	odd	12
768.2.a.e.1.1		1	144.43	odd	12
768.2.a.h.1.1		1	144.61	even	12
1176.2.c.a.589.1		2	63.34	odd	6
1176.2.c.a.589.2		2	504.349	odd	6
1800.2.d.b.1549.1		2	360.173	even	12
1800.2.d.b.1549.2		2	45.2	even	12
1800.2.d.i.1549.1		2	45.38	even	12
1800.2.d.i.1549.2		2	360.317	even	12
1800.2.k.a.901.1		2	45.29	odd	6
1800.2.k.a.901.2		2	360.29	odd	6
2304.2.a.b.1.1		1	144.83	even	12
2304.2.a.e.1.1		1	144.29	odd	12
2304.2.a.l.1.1		1	144.11	even	12
2304.2.a.o.1.1		1	144.101	odd	12
2400.2.d.b.49.1		2	180.43	even	12
2400.2.d.b.49.2		2	360.187	even	12
2400.2.d.c.49.1		2	360.43	even	12
2400.2.d.c.49.2		2	180.7	even	12
2400.2.k.a.1201.1		2	180.79	odd	6
2400.2.k.a.1201.2		2	360.259	odd	6
2592.2.r.f.433.1		4	36.31	odd	6
2592.2.r.f.433.2		4	72.67	odd	6
2592.2.r.f.2161.1		4	8.3	odd	2
2592.2.r.f.2161.2		4	4.3	odd	2
2592.2.r.g.433.1		4	72.59	even	6
2592.2.r.g.433.2		4	36.23	even	6
2592.2.r.g.2161.1		4	12.11	even	2
2592.2.r.g.2161.2		4	24.11	even	2
4704.2.c.a.2353.1		2	252.223	even	6
4704.2.c.a.2353.2		2	504.475	even	6
7200.2.d.d.2449.1		2	360.83	odd	12
7200.2.d.d.2449.2		2	180.47	odd	12
7200.2.d.g.2449.1		2	180.83	odd	12
7200.2.d.g.2449.2		2	360.227	odd	12
7200.2.k.d.3601.1		2	360.299	even	6
7200.2.k.d.3601.2		2	180.119	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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.73205 - 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.73205 - 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.00000 - 2.00000i) q^{10} +(-3.46410 + 2.00000i) q^{13} +(0.732051 - 2.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} -2.00000 q^{17} +4.00000i q^{19} +(2.00000 - 3.46410i) q^{20} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.00000 + 4.00000i) q^{26} -4.00000i q^{28} +(5.19615 + 3.00000i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(1.46410 - 5.46410i) q^{32} +(-2.73205 + 0.732051i) q^{34} -4.00000i q^{35} +8.00000i q^{37} +(1.46410 + 5.46410i) q^{38} +(1.46410 - 5.46410i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(3.46410 + 2.00000i) q^{43} +(-4.00000 - 4.00000i) q^{46} +(6.00000 - 10.3923i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-0.366025 + 1.36603i) q^{50} +(-4.00000 + 6.92820i) q^{52} +6.00000i q^{53} +(-1.46410 - 5.46410i) q^{56} +(8.19615 + 2.19615i) q^{58} +(3.46410 - 2.00000i) q^{59} +(-2.00000 - 2.00000i) q^{62} -8.00000i q^{64} +(-4.00000 + 6.92820i) q^{65} +(-10.3923 + 6.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(-1.46410 - 5.46410i) q^{70} +12.0000 q^{71} -6.00000 q^{73} +(2.92820 + 10.9282i) q^{74} +(4.00000 + 6.92820i) q^{76} +(-5.00000 + 8.66025i) q^{79} -8.00000i q^{80} +(-2.00000 - 2.00000i) q^{82} +(-13.8564 - 8.00000i) q^{83} +(-3.46410 + 2.00000i) q^{85} +(5.46410 + 1.46410i) q^{86} -10.0000 q^{89} +8.00000i q^{91} +(-6.92820 - 4.00000i) q^{92} +(4.39230 - 16.3923i) q^{94} +(4.00000 + 6.92820i) q^{95} +(1.00000 - 1.73205i) q^{97} +(3.00000 + 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^7 + 8 * q^8	\( 4 q + 2 q^{2} + 4 q^{7} + 8 q^{8} + 8 q^{10} - 4 q^{14} + 8 q^{16} - 8 q^{17} + 8 q^{20} - 8 q^{23} - 2 q^{25} - 16 q^{26} - 4 q^{31} - 8 q^{32} - 4 q^{34} - 8 q^{38} - 8 q^{40} - 4 q^{41} - 16 q^{46} + 24 q^{47} + 6 q^{49} + 2 q^{50} - 16 q^{52} + 8 q^{56} + 12 q^{58} - 8 q^{62} - 16 q^{65} + 8 q^{70} + 48 q^{71} - 24 q^{73} - 16 q^{74} + 16 q^{76} - 20 q^{79} - 8 q^{82} + 8 q^{86} - 40 q^{89} - 24 q^{94} + 16 q^{95} + 4 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^7 + 8 * q^8 + 8 * q^10 - 4 * q^14 + 8 * q^16 - 8 * q^17 + 8 * q^20 - 8 * q^23 - 2 * q^25 - 16 * q^26 - 4 * q^31 - 8 * q^32 - 4 * q^34 - 8 * q^38 - 8 * q^40 - 4 * q^41 - 16 * q^46 + 24 * q^47 + 6 * q^49 + 2 * q^50 - 16 * q^52 + 8 * q^56 + 12 * q^58 - 8 * q^62 - 16 * q^65 + 8 * q^70 + 48 * q^71 - 24 * q^73 - 16 * q^74 + 16 * q^76 - 20 * q^79 - 8 * q^82 + 8 * q^86 - 40 * q^89 - 24 * q^94 + 16 * q^95 + 4 * q^97 + 12 * q^98

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