LMFDB - Embedded newform 720.2.by.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(49,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("720.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.by (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:	$5.74922894553$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	720.49
Dual form			720.2.by.a.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.50000i) q^{3} +(2.23205 + 0.133975i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(-5.19615 - 3.00000i) q^{13} +(2.13397 - 3.23205i) q^{15} -2.00000i q^{17} +6.00000 q^{19} -1.73205i q^{21} +(-0.866025 - 0.500000i) q^{23} +(4.96410 + 0.598076i) q^{25} -5.19615 q^{27} +(4.50000 + 7.79423i) q^{29} +(-1.00000 + 1.73205i) q^{31} -3.46410 q^{33} +(2.00000 - 1.00000i) q^{35} +2.00000i q^{37} +(-9.00000 + 5.19615i) q^{39} +(5.50000 - 9.52628i) q^{41} +(-3.46410 + 2.00000i) q^{43} +(-3.00000 - 6.00000i) q^{45} +(6.06218 - 3.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(-3.00000 - 1.73205i) q^{51} +(-2.00000 - 4.00000i) q^{55} +(5.19615 - 9.00000i) q^{57} +(2.00000 - 3.46410i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-2.59808 - 1.50000i) q^{63} +(-11.1962 - 7.39230i) q^{65} +(-9.52628 - 5.50000i) q^{67} +(-1.50000 + 0.866025i) q^{69} +6.00000 q^{71} +4.00000i q^{73} +(5.19615 - 6.92820i) q^{75} +(-1.73205 - 1.00000i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-9.52628 + 5.50000i) q^{83} +(0.267949 - 4.46410i) q^{85} +15.5885 q^{87} -1.00000 q^{89} -6.00000 q^{91} +(1.73205 + 3.00000i) q^{93} +(13.3923 + 0.803848i) q^{95} +(-6.92820 + 4.00000i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 6 q^{9} - 4 q^{11} + 12 q^{15} + 24 q^{19} + 6 q^{25} + 18 q^{29} - 4 q^{31} + 8 q^{35} - 36 q^{39} + 22 q^{41} - 12 q^{45} - 12 q^{49} - 12 q^{51} - 8 q^{55} + 8 q^{59} + 14 q^{61} - 24 q^{65}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^5 - 6 * q^9 - 4 * q^11 + 12 * q^15 + 24 * q^19 + 6 * q^25 + 18 * q^29 - 4 * q^31 + 8 * q^35 - 36 * q^39 + 22 * q^41 - 12 * q^45 - 12 * q^49 - 12 * q^51 - 8 * q^55 + 8 * q^59 + 14 * q^61 - 24 * q^65 - 6 * q^69 + 24 * q^71 + 24 * q^79 - 18 * q^81 + 8 * q^85 - 4 * q^89 - 24 * q^91 + 12 * q^95 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$		0			0
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$5$	2.23205	+	0.133975i	0.998203	+	0.0599153i
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i	0.654654	+	0.755929i	$0.272814\pi$
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−5.19615	−	3.00000i	−1.44115	−	0.832050i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	−5.19615	−	3.00000i	−1.44115	−	0.832050i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$		0			0
$15$	2.13397	−	3.23205i	0.550990	−	0.834512i
$16$		0			0
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		0			0
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$		0			0
$21$		−	1.73205i		−	0.377964i
$22$		0			0
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	0.406986	−	0.913434i	$-0.366580\pi$
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	−0.587565	+	0.809177i	$0.699913\pi$
$24$		0			0
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		0			0
$33$	−3.46410			−0.603023
$34$		0			0
$35$	2.00000	−	1.00000i	0.338062	−	0.169031i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$	−9.00000	+	5.19615i	−1.44115	+	0.832050i
$40$		0			0
$41$	5.50000	−	9.52628i	0.858956	−	1.48775i	−0.0139704	−	0.999902i	$-0.504447\pi$
$41$	5.50000	−	9.52628i	0.858956	−	1.48775i	0.872926	−	0.487852i	$-0.162220\pi$
$42$		0			0
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	−0.740312	−	0.672264i	$-0.765322\pi$
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	0.212041	+	0.977261i	$0.431989\pi$
$44$		0			0
$45$	−3.00000	−	6.00000i	−0.447214	−	0.894427i
$46$		0			0
$47$	6.06218	−	3.50000i	0.884260	−	0.510527i	0.0121990	−	0.999926i	$-0.496117\pi$
$47$	6.06218	−	3.50000i	0.884260	−	0.510527i	0.872060	+	0.489398i	$0.162783\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	−3.00000	−	1.73205i	−0.420084	−	0.242536i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$		0			0
$57$	5.19615	−	9.00000i	0.688247	−	1.19208i
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$	−2.59808	−	1.50000i	−0.327327	−	0.188982i
$64$		0			0
$65$	−11.1962	−	7.39230i	−1.38871	−	0.916903i
$66$		0			0
$67$	−9.52628	−	5.50000i	−1.16382	−	0.671932i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$	−9.52628	−	5.50000i	−1.16382	−	0.671932i	−0.952217	+	0.305424i	$0.901202\pi$
$68$		0			0
$69$	−1.50000	+	0.866025i	−0.180579	+	0.104257i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$		0			0
$75$	5.19615	−	6.92820i	0.600000	−	0.800000i
$76$		0			0
$77$	−1.73205	−	1.00000i	−0.197386	−	0.113961i
$78$		0			0
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−9.52628	+	5.50000i	−1.04565	+	0.603703i	−0.921427	−	0.388552i	$-0.872976\pi$
$83$	−9.52628	+	5.50000i	−1.04565	+	0.603703i	−0.124218	+	0.992255i	$0.539642\pi$
$84$		0			0
$85$	0.267949	−	4.46410i	0.0290632	−	0.484200i
$86$		0			0
$87$	15.5885			1.67126
$88$		0			0
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$		0			0
$93$	1.73205	+	3.00000i	0.179605	+	0.311086i
$94$		0			0
$95$	13.3923	+	0.803848i	1.37402	+	0.0824730i
$96$		0			0
$97$	−6.92820	+	4.00000i	−0.703452	+	0.406138i	−0.808632	−	0.588315i	$-0.799792\pi$
$97$	−6.92820	+	4.00000i	−0.703452	+	0.406138i	0.105180	+	0.994453i	$0.466458\pi$
$98$		0			0
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$		0			0
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$		0			0
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	0.800855	−	0.598858i	$-0.204379\pi$
$103$	6.92820	+	4.00000i	0.682656	+	0.394132i	−0.118199	+	0.992990i	$0.537712\pi$
$104$		0			0
$105$	0.232051	−	3.86603i	0.0226458	−	0.377285i
$106$		0			0
$107$		−	3.00000i		−	0.290021i	−0.989430	−	0.145010i	$-0.953678\pi$
$107$		−	3.00000i		−	0.290021i	0.989430	−	0.145010i	$-0.0463216\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$		0			0
$111$	3.00000	+	1.73205i	0.284747	+	0.164399i
$112$		0			0
$113$	10.3923	+	6.00000i	0.977626	+	0.564433i	0.901553	−	0.432670i	$-0.142428\pi$
$113$	10.3923	+	6.00000i	0.977626	+	0.564433i	0.0760733	+	0.997102i	$0.475762\pi$
$114$		0			0
$115$	−1.86603	−	1.23205i	−0.174008	−	0.114889i
$116$		0			0
$117$			18.0000i			1.66410i
$118$		0			0
$119$	−1.00000	−	1.73205i	−0.0916698	−	0.158777i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−9.52628	−	16.5000i	−0.858956	−	1.48775i
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$			19.0000i			1.68598i	0.537931	+	0.842989i	$0.319206\pi$
$127$			19.0000i			1.68598i	−0.537931	+	0.842989i	$0.680794\pi$
$128$		0			0
$129$			6.92820i			0.609994i
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	5.19615	−	3.00000i	0.450564	−	0.260133i
$134$		0			0
$135$	−11.5981	−	0.696152i	−0.998203	−	0.0599153i
$136$		0			0
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		−	12.1244i		−	1.02105i
$142$		0			0
$143$			12.0000i			1.00349i
$144$		0			0
$145$	9.00000	+	18.0000i	0.747409	+	1.49482i
$146$		0			0
$147$	5.19615	+	9.00000i	0.428571	+	0.742307i
$148$		0			0
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$	−5.19615	+	3.00000i	−0.420084	+	0.242536i
$154$		0			0
$155$	−2.46410	+	3.73205i	−0.197921	+	0.299766i
$156$		0			0
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	0.355357	−	0.934731i	$-0.384359\pi$
$157$	−3.46410	−	2.00000i	−0.276465	−	0.159617i	−0.631822	+	0.775113i	$0.717693\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.00000			−0.0788110
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$		0			0
$165$	−7.73205	−	0.464102i	−0.601939	−	0.0361303i
$166$		0			0
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$		0			0
$169$	11.5000	+	19.9186i	0.884615	+	1.53220i
$170$		0			0
$171$	−9.00000	−	15.5885i	−0.688247	−	1.19208i
$172$		0			0
$173$	3.46410	−	2.00000i	0.263371	−	0.152057i	−0.362500	−	0.931984i	$-0.618077\pi$
$173$	3.46410	−	2.00000i	0.263371	−	0.152057i	0.625871	+	0.779926i	$0.284744\pi$
$174$		0			0
$175$	4.59808	−	1.96410i	0.347582	−	0.148472i
$176$		0			0
$177$	−3.46410	−	6.00000i	−0.260378	−	0.450988i
$178$		0			0
$179$	2.00000			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$180$		0			0
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$	12.1244			0.896258
$184$		0			0
$185$	−0.267949	+	4.46410i	−0.0197000	+	0.328207i
$186$		0			0
$187$	−3.46410	+	2.00000i	−0.253320	+	0.146254i
$188$		0			0
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	0.154805	−	0.987945i	$-0.450525\pi$
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	−0.778183	+	0.628037i	$0.783859\pi$
$194$		0			0
$195$	−20.7846	+	10.3923i	−1.48842	+	0.744208i
$196$		0			0
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$		0			0
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$		0			0
$201$	−16.5000	+	9.52628i	−1.16382	+	0.671932i
$202$		0			0
$203$	7.79423	+	4.50000i	0.547048	+	0.315838i
$204$		0			0
$205$	13.5526	−	20.5263i	0.946552	−	1.43362i
$206$		0			0
$207$			3.00000i			0.208514i
$208$		0			0
$209$	−6.00000	−	10.3923i	−0.415029	−	0.718851i
$210$		0			0
$211$	9.00000	−	15.5885i	0.619586	−	1.07315i	−0.369976	−	0.929041i	$-0.620634\pi$
$211$	9.00000	−	15.5885i	0.619586	−	1.07315i	0.989561	−	0.144112i	$-0.0460326\pi$
$212$		0			0
$213$	5.19615	−	9.00000i	0.356034	−	0.616670i
$214$		0			0
$215$	−8.00000	+	4.00000i	−0.545595	+	0.272798i
$216$		0			0
$217$			2.00000i			0.135769i
$218$		0			0
$219$	6.00000	+	3.46410i	0.405442	+	0.234082i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	19.9186	−	11.5000i	1.33385	−	0.770097i	0.347960	−	0.937509i	$-0.386874\pi$
$223$	19.9186	−	11.5000i	1.33385	−	0.770097i	0.985887	+	0.167412i	$0.0535411\pi$
$224$		0			0
$225$	−5.89230	−	13.7942i	−0.392820	−	0.919615i
$226$		0			0
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	−0.252136	−	0.967692i	$-0.581133\pi$
$227$	6.92820	−	4.00000i	0.459841	−	0.265489i	0.711977	+	0.702202i	$0.247800\pi$
$228$		0			0
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−3.00000	+	1.73205i	−0.197386	+	0.113961i
$232$		0			0
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$		0			0
$235$	14.0000	−	7.00000i	0.913259	−	0.456630i
$236$		0			0
$237$	20.7846			1.35011
$238$		0			0
$239$	−14.0000	+	24.2487i	−0.905585	+	1.56852i	−0.0854543	+	0.996342i	$0.527234\pi$
$239$	−14.0000	+	24.2487i	−0.905585	+	1.56852i	−0.820130	+	0.572177i	$0.806099\pi$
$240$		0			0
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		0			0
$245$	−7.39230	+	11.1962i	−0.472277	+	0.715296i
$246$		0			0
$247$	−31.1769	−	18.0000i	−1.98374	−	1.14531i
$248$		0			0
$249$			19.0526i			1.20741i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$			2.00000i			0.125739i
$254$		0			0
$255$	−6.46410	−	4.26795i	−0.404798	−	0.267269i
$256$		0			0
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$		0			0
$261$	13.5000	−	23.3827i	0.835629	−	1.44735i
$262$		0			0
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	−0.00771799	−	0.999970i	$-0.502457\pi$
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	0.862141	+	0.506669i	$0.169123\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.866025	+	1.50000i	−0.0529999	+	0.0917985i
$268$		0			0
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$		0			0
$271$	14.0000			0.850439			0.425220	−	0.905090i	$-0.360197\pi$
$271$	14.0000			0.850439			0.425220	+	0.905090i	$0.360197\pi$
$272$		0			0
$273$	−5.19615	+	9.00000i	−0.314485	+	0.544705i
$274$		0			0
$275$	−3.92820	−	9.19615i	−0.236880	−	0.554549i
$276$		0			0
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.947604	−	0.319447i	$-0.896503\pi$
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.197153	+	0.980373i	$0.563170\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$		0			0
$283$	−0.866025	−	0.500000i	−0.0514799	−	0.0297219i	0.474039	−	0.880504i	$-0.342796\pi$
$283$	−0.866025	−	0.500000i	−0.0514799	−	0.0297219i	−0.525519	+	0.850782i	$0.676129\pi$
$284$		0			0
$285$	12.8038	−	19.3923i	0.758434	−	1.14870i
$286$		0			0
$287$		−	11.0000i		−	0.649309i
$288$		0			0
$289$	13.0000			0.764706
$290$		0			0
$291$			13.8564i			0.812277i
$292$		0			0
$293$	−15.5885	−	9.00000i	−0.910687	−	0.525786i	−0.0300351	−	0.999549i	$-0.509562\pi$
$293$	−15.5885	−	9.00000i	−0.910687	−	0.525786i	−0.880652	+	0.473763i	$0.842895\pi$
$294$		0			0
$295$	4.92820	−	7.46410i	0.286931	−	0.434577i
$296$		0			0
$297$	5.19615	+	9.00000i	0.301511	+	0.522233i
$298$		0			0
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$		0			0
$303$	−3.46410			−0.199007
$304$		0			0
$305$	7.00000	+	14.0000i	0.400819	+	0.801638i
$306$		0			0
$307$			9.00000i			0.513657i	0.966457	+	0.256829i	$0.0826776\pi$
$307$			9.00000i			0.513657i	−0.966457	+	0.256829i	$0.917322\pi$
$308$		0			0
$309$	12.0000	−	6.92820i	0.682656	−	0.394132i
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	19.0526	−	11.0000i	1.07691	−	0.621757i	0.146852	−	0.989158i	$-0.453086\pi$
$313$	19.0526	−	11.0000i	1.07691	−	0.621757i	0.930062	+	0.367402i	$0.119753\pi$
$314$		0			0
$315$	−5.59808	−	3.69615i	−0.315416	−	0.208255i
$316$		0			0
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	−0.547852	−	0.836576i	$-0.684554\pi$
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	0.450570	+	0.892741i	$0.351221\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$		0			0
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$	−24.0000	−	18.0000i	−1.33128	−	0.998460i
$326$		0			0
$327$	−6.06218	+	10.5000i	−0.335239	+	0.580651i
$328$		0			0
$329$	3.50000	−	6.06218i	0.192961	−	0.334219i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$	5.19615	−	3.00000i	0.284747	−	0.164399i
$334$		0			0
$335$	−20.5263	−	13.5526i	−1.12147	−	0.740455i
$336$		0			0
$337$	−6.92820	−	4.00000i	−0.377403	−	0.217894i	0.299285	−	0.954164i	$-0.403252\pi$
$337$	−6.92820	−	4.00000i	−0.377403	−	0.217894i	−0.676688	+	0.736270i	$0.736585\pi$
$338$		0			0
$339$	18.0000	−	10.3923i	0.977626	−	0.564433i
$340$		0			0
$341$	4.00000			0.216612
$342$		0			0
$343$			13.0000i			0.701934i
$344$		0			0
$345$	−3.46410	+	1.73205i	−0.186501	+	0.0932505i
$346$		0			0
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$		0			0
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	0.680439	−	0.732805i	$-0.261789\pi$
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	−0.974847	+	0.222875i	$0.928456\pi$
$350$		0			0
$351$	27.0000	+	15.5885i	1.44115	+	0.832050i
$352$		0			0
$353$	13.8564	−	8.00000i	0.737502	−	0.425797i	−0.0836583	−	0.996495i	$-0.526660\pi$
$353$	13.8564	−	8.00000i	0.737502	−	0.425797i	0.821160	+	0.570697i	$0.193327\pi$
$354$		0			0
$355$	13.3923	+	0.803848i	0.710790	+	0.0426638i
$356$		0			0
$357$	−3.46410			−0.183340
$358$		0			0
$359$	30.0000			1.58334			0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000			1.58334			0.791670	+	0.610949i	$0.209212\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$		0			0
$363$	−6.06218	−	10.5000i	−0.318182	−	0.551107i
$364$		0			0
$365$	−0.535898	+	8.92820i	−0.0280502	+	0.467324i
$366$		0			0
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	−0.0926670	−	0.995697i	$-0.529539\pi$
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	0.815966	+	0.578101i	$0.196206\pi$
$368$		0			0
$369$	−33.0000			−1.71791
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.3923	+	6.00000i	0.538093	+	0.310668i	0.744306	−	0.667839i	$-0.232781\pi$
$373$	10.3923	+	6.00000i	0.538093	+	0.310668i	−0.206213	+	0.978507i	$0.566114\pi$
$374$		0			0
$375$	12.5263	−	14.7679i	0.646854	−	0.762614i
$376$		0			0
$377$		−	54.0000i		−	2.78114i
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	28.5000	+	16.4545i	1.46010	+	0.842989i
$382$		0			0
$383$	−27.7128	−	16.0000i	−1.41606	−	0.817562i	−0.420109	−	0.907474i	$-0.638008\pi$
$383$	−27.7128	−	16.0000i	−1.41606	−	0.817562i	−0.995950	+	0.0899119i	$0.971341\pi$
$384$		0			0
$385$	−3.73205	−	2.46410i	−0.190203	−	0.125582i
$386$		0			0
$387$	10.3923	+	6.00000i	0.528271	+	0.304997i
$388$		0			0
$389$	9.50000	+	16.4545i	0.481669	+	0.834275i	0.999779	−	0.0210389i	$-0.00669738\pi$
$389$	9.50000	+	16.4545i	0.481669	+	0.834275i	−0.518110	+	0.855314i	$0.673364\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$	−10.3923	−	18.0000i	−0.524222	−	0.907980i
$394$		0			0
$395$	12.0000	+	24.0000i	0.603786	+	1.20757i
$396$		0			0
$397$		−	4.00000i		−	0.200754i	−0.994949	−	0.100377i	$-0.967995\pi$
$397$		−	4.00000i		−	0.200754i	0.994949	−	0.100377i	$-0.0320049\pi$
$398$		0			0
$399$		−	10.3923i		−	0.520266i
$400$		0			0
$401$	5.00000	−	8.66025i	0.249688	−	0.432472i	−0.713751	−	0.700399i	$-0.753005\pi$
$401$	5.00000	−	8.66025i	0.249688	−	0.432472i	0.963439	+	0.267927i	$0.0863386\pi$
$402$		0			0
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$		0			0
$405$	−11.0885	+	16.7942i	−0.550990	+	0.834512i
$406$		0			0
$407$	3.46410	−	2.00000i	0.171709	−	0.0991363i
$408$		0			0
$409$	19.0000	−	32.9090i	0.939490	−	1.62724i	0.173064	−	0.984911i	$-0.444633\pi$
$409$	19.0000	−	32.9090i	0.939490	−	1.62724i	0.766426	−	0.642333i	$-0.222033\pi$
$410$		0			0
$411$		−	20.7846i		−	1.02523i
$412$		0			0
$413$		−	4.00000i		−	0.196827i
$414$		0			0
$415$	−22.0000	+	11.0000i	−1.07994	+	0.539969i
$416$		0			0
$417$	13.8564	+	24.0000i	0.678551	+	1.17529i
$418$		0			0
$419$	−17.0000	+	29.4449i	−0.830504	+	1.43848i	0.0671345	+	0.997744i	$0.478614\pi$
$419$	−17.0000	+	29.4449i	−0.830504	+	1.43848i	−0.897639	+	0.440732i	$0.854719\pi$
$420$		0			0
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	0.463002	−	0.886357i	$-0.346772\pi$
$422$		0			0
$423$	−18.1865	−	10.5000i	−0.884260	−	0.510527i
$424$		0			0
$425$	1.19615	−	9.92820i	0.0580219	−	0.481589i
$426$		0			0
$427$	6.06218	+	3.50000i	0.293369	+	0.169377i
$428$		0			0
$429$	18.0000	+	10.3923i	0.869048	+	0.501745i
$430$		0			0
$431$	−16.0000			−0.770693			−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000			−0.770693			−0.385346	+	0.922772i	$0.625918\pi$
$432$		0			0
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$		0			0
$435$	34.7942	+	2.08846i	1.66826	+	0.100134i
$436$		0			0
$437$	−5.19615	−	3.00000i	−0.248566	−	0.143509i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$		0			0
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$		0			0
$445$	−2.23205	−	0.133975i	−0.105809	−	0.00635100i
$446$		0			0
$447$	0.866025	+	1.50000i	0.0409616	+	0.0709476i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−22.0000			−1.03594
$452$		0			0
$453$	17.3205			0.813788
$454$		0			0
$455$	−13.3923	−	0.803848i	−0.627841	−	0.0376850i
$456$		0			0
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	−0.688686	−	0.725059i	$-0.741812\pi$
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	0.283577	+	0.958950i	$0.408479\pi$
$458$		0			0
$459$			10.3923i			0.485071i
$460$		0			0
$461$	10.5000	+	18.1865i	0.489034	+	0.847031i	0.999920	−	0.0126168i	$-0.00401615\pi$
$461$	10.5000	+	18.1865i	0.489034	+	0.847031i	−0.510887	+	0.859648i	$0.670683\pi$
$462$		0			0
$463$	−31.1769	−	18.0000i	−1.44891	−	0.836531i	−0.450497	−	0.892778i	$-0.648753\pi$
$463$	−31.1769	−	18.0000i	−1.44891	−	0.836531i	−0.998417	+	0.0562469i	$0.982087\pi$
$464$		0			0
$465$	3.46410	+	6.92820i	0.160644	+	0.321288i
$466$		0			0
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$		0			0
$469$	−11.0000			−0.507933
$470$		0			0
$471$	−6.00000	+	3.46410i	−0.276465	+	0.159617i
$472$		0			0
$473$	6.92820	+	4.00000i	0.318559	+	0.183920i
$474$		0			0
$475$	29.7846	+	3.58846i	1.36661	+	0.164650i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$	−0.866025	+	1.50000i	−0.0394055	+	0.0682524i
$484$		0			0
$485$	−16.0000	+	8.00000i	−0.726523	+	0.363261i
$486$		0			0
$487$			12.0000i			0.543772i	0.962329	+	0.271886i	$0.0876473\pi$
$487$			12.0000i			0.543772i	−0.962329	+	0.271886i	$0.912353\pi$
$488$		0			0
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$	15.5885	−	9.00000i	0.702069	−	0.405340i
$494$		0			0
$495$	−7.39230	+	11.1962i	−0.332259	+	0.503230i
$496$		0			0
$497$	5.19615	−	3.00000i	0.233079	−	0.134568i
$498$		0			0
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	−0.461860	−	0.886953i	$-0.652818\pi$
$499$	12.0000	−	20.7846i	0.537194	−	0.930447i	0.999054	−	0.0434940i	$-0.0138489\pi$
$500$		0			0
$501$	−4.50000	+	2.59808i	−0.201045	+	0.116073i
$502$		0			0
$503$			27.0000i			1.20387i	0.798545	+	0.601935i	$0.205603\pi$
$503$			27.0000i			1.20387i	−0.798545	+	0.601935i	$0.794397\pi$
$504$		0			0
$505$	−2.00000	−	4.00000i	−0.0889988	−	0.177998i
$506$		0			0
$507$	39.8372			1.76923
$508$		0			0
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$		0			0
$513$	−31.1769			−1.37649
$514$		0			0
$515$	14.9282	+	9.85641i	0.657815	+	0.434325i
$516$		0			0
$517$	−12.1244	−	7.00000i	−0.533229	−	0.307860i
$518$		0			0
$519$		−	6.92820i		−	0.304114i
$520$		0			0
$521$	−37.0000			−1.62100			−0.810500	−	0.585739i	$-0.800804\pi$
$521$	−37.0000			−1.62100			−0.810500	+	0.585739i	$0.800804\pi$
$522$		0			0
$523$		−	29.0000i		−	1.26808i	−0.773300	−	0.634041i	$-0.781395\pi$
$523$		−	29.0000i		−	1.26808i	0.773300	−	0.634041i	$-0.218605\pi$
$524$		0			0
$525$	1.03590	−	8.59808i	0.0452103	−	0.375251i
$526$		0			0
$527$	3.46410	+	2.00000i	0.150899	+	0.0871214i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	−57.1577	+	33.0000i	−2.47577	+	1.42939i
$534$		0			0
$535$	0.401924	−	6.69615i	0.0173767	−	0.289500i
$536$		0			0
$537$	1.73205	−	3.00000i	0.0747435	−	0.129460i
$538$		0			0
$539$	12.0000			0.516877
$540$		0			0
$541$	−17.0000			−0.730887			−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000			−0.730887			−0.365444	+	0.930834i	$0.619083\pi$
$542$		0			0
$543$	−11.2583	+	19.5000i	−0.483141	+	0.836825i
$544$		0			0
$545$	−15.6244	−	0.937822i	−0.669274	−	0.0401719i
$546$		0			0
$547$	−30.3109	+	17.5000i	−1.29600	+	0.748246i	−0.979711	−	0.200417i	$-0.935770\pi$
$547$	−30.3109	+	17.5000i	−1.29600	+	0.748246i	−0.316289	+	0.948663i	$0.602437\pi$
$548$		0			0
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$		0			0
$551$	27.0000	+	46.7654i	1.15024	+	1.99227i
$552$		0			0
$553$	10.3923	+	6.00000i	0.441926	+	0.255146i
$554$		0			0
$555$	6.46410	+	4.26795i	0.274386	+	0.181164i
$556$		0			0
$557$		−	24.0000i		−	1.01691i	−0.861088	−	0.508456i	$-0.830216\pi$
$557$		−	24.0000i		−	1.01691i	0.861088	−	0.508456i	$-0.169784\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$		0			0
$561$			6.92820i			0.292509i
$562$		0			0
$563$	32.0429	+	18.5000i	1.35045	+	0.779682i	0.988312	−	0.152443i	$-0.0487140\pi$
$563$	32.0429	+	18.5000i	1.35045	+	0.779682i	0.362137	+	0.932125i	$0.382047\pi$
$564$		0			0
$565$	22.3923	+	14.7846i	0.942051	+	0.621993i
$566$		0			0
$567$			9.00000i			0.377964i
$568$		0			0
$569$	−1.00000	−	1.73205i	−0.0419222	−	0.0726113i	0.844303	−	0.535866i	$-0.180015\pi$
$569$	−1.00000	−	1.73205i	−0.0419222	−	0.0726113i	−0.886225	+	0.463255i	$0.846681\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$	10.3923			0.434145
$574$		0			0
$575$	−4.00000	−	3.00000i	−0.166812	−	0.125109i
$576$		0			0
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$		0			0
$579$	−15.0000	+	8.66025i	−0.623379	+	0.359908i
$580$		0			0
$581$	−5.50000	+	9.52628i	−0.228178	+	0.395217i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−2.41154	+	40.1769i	−0.0997050	+	1.66111i
$586$		0			0
$587$	−2.59808	+	1.50000i	−0.107234	+	0.0619116i	−0.552658	−	0.833408i	$-0.686386\pi$
$587$	−2.59808	+	1.50000i	−0.107234	+	0.0619116i	0.445424	+	0.895320i	$0.353053\pi$
$588$		0			0
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$		0			0
$591$	12.0000	+	6.92820i	0.493614	+	0.284988i
$592$		0			0
$593$			30.0000i			1.23195i	0.787765	+	0.615976i	$0.211238\pi$
$593$			30.0000i			1.23195i	−0.787765	+	0.615976i	$0.788762\pi$
$594$		0			0
$595$	−2.00000	−	4.00000i	−0.0819920	−	0.163984i
$596$		0			0
$597$	−15.5885	+	27.0000i	−0.637993	+	1.10504i
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$		0			0
$603$			33.0000i			1.34386i
$604$		0			0
$605$	8.62436	−	13.0622i	0.350630	−	0.531053i
$606$		0			0
$607$	0.866025	+	0.500000i	0.0351509	+	0.0202944i	0.517472	−	0.855700i	$-0.326873\pi$
$607$	0.866025	+	0.500000i	0.0351509	+	0.0202944i	−0.482322	+	0.875994i	$0.660206\pi$
$608$		0			0
$609$	13.5000	−	7.79423i	0.547048	−	0.315838i
$610$		0			0
$611$	−42.0000			−1.69914
$612$		0			0
$613$			34.0000i			1.37325i	0.727013	+	0.686624i	$0.240908\pi$
$613$			34.0000i			1.37325i	−0.727013	+	0.686624i	$0.759092\pi$
$614$		0			0
$615$	−19.0526	−	38.1051i	−0.768273	−	1.53655i
$616$		0			0
$617$	27.7128	+	16.0000i	1.11568	+	0.644136i	0.940294	−	0.340365i	$-0.110551\pi$
$617$	27.7128	+	16.0000i	1.11568	+	0.644136i	0.175382	+	0.984500i	$0.443884\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$	4.50000	+	2.59808i	0.180579	+	0.104257i
$622$		0			0
$623$	−0.866025	+	0.500000i	−0.0346966	+	0.0200321i
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$		0			0
$627$	−20.7846			−0.830057
$628$		0			0
$629$	4.00000			0.159490
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$	−15.5885	−	27.0000i	−0.619586	−	1.07315i
$634$		0			0
$635$	−2.54552	+	42.4090i	−0.101016	+	1.68295i
$636$		0			0
$637$	31.1769	−	18.0000i	1.23527	−	0.713186i
$638$		0			0
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$		0			0
$641$	−6.50000	−	11.2583i	−0.256735	−	0.444677i	0.708631	−	0.705580i	$-0.249313\pi$
$641$	−6.50000	−	11.2583i	−0.256735	−	0.444677i	−0.965365	+	0.260902i	$0.915980\pi$
$642$		0			0
$643$	28.5788	+	16.5000i	1.12704	+	0.650696i	0.943189	−	0.332258i	$-0.107810\pi$
$643$	28.5788	+	16.5000i	1.12704	+	0.650696i	0.183851	+	0.982954i	$0.441144\pi$
$644$		0			0
$645$	−0.928203	+	15.4641i	−0.0365480	+	0.608898i
$646$		0			0
$647$		−	33.0000i		−	1.29736i	−0.761060	−	0.648682i	$-0.775321\pi$
$647$		−	33.0000i		−	1.29736i	0.761060	−	0.648682i	$-0.224679\pi$
$648$		0			0
$649$	−8.00000			−0.314027
$650$		0			0
$651$	3.00000	+	1.73205i	0.117579	+	0.0678844i
$652$		0			0
$653$	−22.5167	−	13.0000i	−0.881145	−	0.508729i	−0.0101092	−	0.999949i	$-0.503218\pi$
$653$	−22.5167	−	13.0000i	−0.881145	−	0.508729i	−0.871036	+	0.491220i	$0.836551\pi$
$654$		0			0
$655$	14.7846	−	22.3923i	0.577683	−	0.874940i
$656$		0			0
$657$	10.3923	−	6.00000i	0.405442	−	0.234082i
$658$		0			0
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$		0			0
$663$	10.3923	+	18.0000i	0.403604	+	0.699062i
$664$		0			0
$665$	12.0000	−	6.00000i	0.465340	−	0.232670i
$666$		0			0
$667$		−	9.00000i		−	0.348481i
$668$		0			0
$669$		−	39.8372i		−	1.54019i
$670$		0			0
$671$	7.00000	−	12.1244i	0.270232	−	0.468056i
$672$		0			0
$673$	−5.19615	+	3.00000i	−0.200297	+	0.115642i	−0.596794	−	0.802395i	$-0.703559\pi$
$673$	−5.19615	+	3.00000i	−0.200297	+	0.115642i	0.396497	+	0.918036i	$0.370226\pi$
$674$		0			0
$675$	−25.7942	−	3.10770i	−0.992820	−	0.119615i
$676$		0			0
$677$	19.0526	−	11.0000i	0.732249	−	0.422764i	−0.0869952	−	0.996209i	$-0.527726\pi$
$677$	19.0526	−	11.0000i	0.732249	−	0.422764i	0.819244	+	0.573444i	$0.194393\pi$
$678$		0			0
$679$	−4.00000	+	6.92820i	−0.153506	+	0.265880i
$680$		0			0
$681$		−	13.8564i		−	0.530979i
$682$		0			0
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	24.0000	−	12.0000i	0.916993	−	0.458496i
$686$		0			0
$687$	6.06218	+	10.5000i	0.231287	+	0.400600i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$		0			0
$693$			6.00000i			0.227921i
$694$		0			0
$695$	−19.7128	+	29.8564i	−0.747750	+	1.13252i
$696$		0			0
$697$	−19.0526	−	11.0000i	−0.721667	−	0.416655i
$698$		0			0
$699$	15.0000	+	8.66025i	0.567352	+	0.327561i
$700$		0			0
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$		0			0
$703$			12.0000i			0.452589i
$704$		0			0
$705$	1.62436	−	27.0622i	0.0611768	−	1.01922i
$706$		0			0
$707$	−1.73205	−	1.00000i	−0.0651405	−	0.0376089i
$708$		0			0
$709$	−13.5000	−	23.3827i	−0.507003	−	0.878155i	−0.999967	−	0.00810550i	$-0.997420\pi$
$709$	−13.5000	−	23.3827i	−0.507003	−	0.878155i	0.492964	−	0.870050i	$-0.335913\pi$
$710$		0			0
$711$	18.0000	−	31.1769i	0.675053	−	1.16923i
$712$		0			0
$713$	1.73205	−	1.00000i	0.0648658	−	0.0374503i
$714$		0			0
$715$	−1.60770	+	26.7846i	−0.0601244	+	1.00169i
$716$		0			0
$717$	24.2487	+	42.0000i	0.905585	+	1.56852i
$718$		0			0
$719$	−44.0000			−1.64092			−0.820462	−	0.571702i	$-0.806283\pi$
$719$	−44.0000			−1.64092			−0.820462	+	0.571702i	$0.806283\pi$
$720$		0			0
$721$	8.00000			0.297936
$722$		0			0
$723$	−1.73205			−0.0644157
$724$		0			0
$725$	17.6769	+	41.3827i	0.656504	+	1.53691i
$726$		0			0
$727$	−18.1865	+	10.5000i	−0.674501	+	0.389423i	−0.797780	−	0.602949i	$-0.793992\pi$
$727$	−18.1865	+	10.5000i	−0.674501	+	0.389423i	0.123279	+	0.992372i	$0.460659\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	3.46410	+	2.00000i	0.127950	+	0.0738717i	0.562609	−	0.826723i	$-0.309798\pi$
$733$	3.46410	+	2.00000i	0.127950	+	0.0738717i	−0.434659	+	0.900595i	$0.643131\pi$
$734$		0			0
$735$	10.3923	+	20.7846i	0.383326	+	0.766652i
$736$		0			0
$737$			22.0000i			0.810380i
$738$		0			0
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$		0			0
$741$	−54.0000	+	31.1769i	−1.98374	+	1.14531i
$742$		0			0
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	0.718986	−	0.695024i	$-0.244606\pi$
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	−0.242415	+	0.970173i	$0.577940\pi$
$744$		0			0
$745$	−1.23205	+	1.86603i	−0.0451388	+	0.0683659i
$746$		0			0
$747$	28.5788	+	16.5000i	1.04565	+	0.603703i
$748$		0			0
$749$	−1.50000	−	2.59808i	−0.0548088	−	0.0949316i
$750$		0			0
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	−0.525193	−	0.850983i	$-0.676007\pi$
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	0.999570	+	0.0293387i	$0.00934013\pi$
$752$		0			0
$753$	−15.5885	+	27.0000i	−0.568075	+	0.983935i
$754$		0			0
$755$	10.0000	+	20.0000i	0.363937	+	0.727875i
$756$		0			0
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$		0			0
$759$	3.00000	+	1.73205i	0.108893	+	0.0628695i
$760$		0			0
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$		0			0
$763$	−6.06218	+	3.50000i	−0.219466	+	0.126709i
$764$		0			0
$765$	−12.0000	+	6.00000i	−0.433861	+	0.216930i
$766$		0			0
$767$	−20.7846	+	12.0000i	−0.750489	+	0.433295i
$768$		0			0
$769$	−7.50000	+	12.9904i	−0.270457	+	0.468445i	−0.968979	−	0.247143i	$-0.920508\pi$
$769$	−7.50000	+	12.9904i	−0.270457	+	0.468445i	0.698522	+	0.715589i	$0.253841\pi$
$770$		0			0
$771$	−18.0000	+	10.3923i	−0.648254	+	0.374270i
$772$		0			0
$773$		−	12.0000i		−	0.431610i	−0.976436	−	0.215805i	$-0.930762\pi$
$773$		−	12.0000i		−	0.431610i	0.976436	−	0.215805i	$-0.0692376\pi$
$774$		0			0
$775$	−6.00000	+	8.00000i	−0.215526	+	0.287368i
$776$		0			0
$777$	3.46410			0.124274
$778$		0			0
$779$	33.0000	−	57.1577i	1.18235	−	2.04789i
$780$		0			0
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$		0			0
$783$	−23.3827	−	40.5000i	−0.835629	−	1.44735i
$784$		0			0
$785$	−7.46410	−	4.92820i	−0.266405	−	0.175895i
$786$		0			0
$787$	38.1051	+	22.0000i	1.35830	+	0.784215i	0.989395	−	0.145251i	$-0.0463991\pi$
$787$	38.1051	+	22.0000i	1.35830	+	0.784215i	0.368906	+	0.929467i	$0.379732\pi$
$788$		0			0
$789$		−	27.7128i		−	0.986602i
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$		−	42.0000i		−	1.49146i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.73205	+	1.00000i	0.0613524	+	0.0354218i	0.530362	−	0.847771i	$-0.322056\pi$
$797$	1.73205	+	1.00000i	0.0613524	+	0.0354218i	−0.469010	+	0.883193i	$0.655389\pi$
$798$		0			0
$799$	−7.00000	−	12.1244i	−0.247642	−	0.428929i
$800$		0			0
$801$	1.50000	+	2.59808i	0.0529999	+	0.0917985i
$802$		0			0
$803$	6.92820	−	4.00000i	0.244491	−	0.141157i
$804$		0			0
$805$	−2.23205	−	0.133975i	−0.0786695	−	0.00472198i
$806$		0			0
$807$	−2.59808	+	4.50000i	−0.0914566	+	0.158408i
$808$		0			0
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		0			0
$813$	12.1244	−	21.0000i	0.425220	−	0.736502i
$814$		0			0
$815$	−0.535898	+	8.92820i	−0.0187717	+	0.312741i
$816$		0			0
$817$	−20.7846	+	12.0000i	−0.727161	+	0.419827i
$818$		0			0
$819$	9.00000	+	15.5885i	0.314485	+	0.544705i
$820$		0			0
$821$	15.5000	+	26.8468i	0.540954	+	0.936959i	0.998850	+	0.0479535i	$0.0152699\pi$
$821$	15.5000	+	26.8468i	0.540954	+	0.936959i	−0.457896	+	0.889006i	$0.651397\pi$
$822$		0			0
$823$	−12.9904	−	7.50000i	−0.452816	−	0.261434i	0.256203	−	0.966623i	$-0.417529\pi$
$823$	−12.9904	−	7.50000i	−0.452816	−	0.261434i	−0.709019	+	0.705190i	$0.750862\pi$
$824$		0			0
$825$	−17.1962	−	2.07180i	−0.598693	−	0.0721307i
$826$		0			0
$827$			35.0000i			1.21707i	0.793527	+	0.608535i	$0.208242\pi$
$827$			35.0000i			1.21707i	−0.793527	+	0.608535i	$0.791758\pi$
$828$		0			0
$829$	−15.0000			−0.520972			−0.260486	−	0.965478i	$-0.583883\pi$
$829$	−15.0000			−0.520972			−0.260486	+	0.965478i	$0.583883\pi$
$830$		0			0
$831$			38.1051i			1.32185i
$832$		0			0
$833$	10.3923	+	6.00000i	0.360072	+	0.207888i
$834$		0			0
$835$	−5.59808	−	3.69615i	−0.193729	−	0.127911i
$836$		0			0
$837$	5.19615	−	9.00000i	0.179605	−	0.311086i
$838$		0			0
$839$	−19.0000	−	32.9090i	−0.655953	−	1.13614i	−0.981654	−	0.190671i	$-0.938934\pi$
$839$	−19.0000	−	32.9090i	−0.655953	−	1.13614i	0.325701	−	0.945473i	$-0.394400\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	5.19615			0.178965
$844$		0			0
$845$	23.0000	+	46.0000i	0.791224	+	1.58245i
$846$		0			0
$847$		−	7.00000i		−	0.240523i
$848$		0			0
$849$	−1.50000	+	0.866025i	−0.0514799	+	0.0297219i
$850$		0			0
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$		0			0
$853$	−39.8372	+	23.0000i	−1.36400	+	0.787505i	−0.990153	−	0.139986i	$-0.955294\pi$
$853$	−39.8372	+	23.0000i	−1.36400	+	0.787505i	−0.373845	+	0.927491i	$0.621961\pi$
$854$		0			0
$855$	−18.0000	−	36.0000i	−0.615587	−	1.23117i
$856$		0			0
$857$	−15.5885	+	9.00000i	−0.532492	+	0.307434i	−0.742030	−	0.670366i	$-0.766137\pi$
$857$	−15.5885	+	9.00000i	−0.532492	+	0.307434i	0.209539	+	0.977800i	$0.432804\pi$
$858$		0			0
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	−0.960381	−	0.278691i	$-0.910099\pi$
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	0.721544	+	0.692369i	$0.243433\pi$
$860$		0			0
$861$	−16.5000	−	9.52628i	−0.562318	−	0.324655i
$862$		0			0
$863$		−	45.0000i		−	1.53182i	−0.642949	−	0.765909i	$-0.722289\pi$
$863$		−	45.0000i		−	1.53182i	0.642949	−	0.765909i	$-0.277711\pi$
$864$		0			0
$865$	8.00000	−	4.00000i	0.272008	−	0.136004i
$866$		0			0
$867$	11.2583	−	19.5000i	0.382353	−	0.662255i
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	33.0000	+	57.1577i	1.11816	+	1.93671i
$872$		0			0
$873$	20.7846	+	12.0000i	0.703452	+	0.406138i
$874$		0			0
$875$	10.5263	−	3.76795i	0.355853	−	0.127380i
$876$		0			0
$877$	−39.8372	−	23.0000i	−1.34521	−	0.776655i	−0.357640	−	0.933860i	$-0.616418\pi$
$877$	−39.8372	−	23.0000i	−1.34521	−	0.776655i	−0.987566	+	0.157205i	$0.949752\pi$
$878$		0			0
$879$	−27.0000	+	15.5885i	−0.910687	+	0.525786i
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$		0			0
$883$			3.00000i			0.100958i	0.998725	+	0.0504790i	$0.0160748\pi$
$883$			3.00000i			0.100958i	−0.998725	+	0.0504790i	$0.983925\pi$
$884$		0			0
$885$	−6.92820	−	13.8564i	−0.232889	−	0.465778i
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	9.50000	+	16.4545i	0.318620	+	0.551866i
$890$		0			0
$891$	18.0000			0.603023
$892$		0			0
$893$	36.3731	−	21.0000i	1.21718	−	0.702738i
$894$		0			0
$895$	4.46410	+	0.267949i	0.149218	+	0.00895655i
$896$		0			0
$897$	10.3923			0.346989
$898$		0			0
$899$	−18.0000			−0.600334
$900$		0			0
$901$		0			0
$902$		0			0
$903$	3.46410	+	6.00000i	0.115278	+	0.199667i
$904$		0			0
$905$	−29.0167	−	1.74167i	−0.964546	−	0.0578951i
$906$		0			0
$907$	−28.5788	+	16.5000i	−0.948945	+	0.547874i	−0.892753	−	0.450546i	$-0.851229\pi$
$907$	−28.5788	+	16.5000i	−0.948945	+	0.547874i	−0.0561918	+	0.998420i	$0.517896\pi$
$908$		0			0
$909$	−3.00000	+	5.19615i	−0.0995037	+	0.172345i
$910$		0			0
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	0.948136	−	0.317865i	$-0.102966\pi$
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	−0.749347	+	0.662177i	$0.769633\pi$
$912$		0			0
$913$	19.0526	+	11.0000i	0.630548	+	0.364047i
$914$		0			0
$915$	27.0622	+	1.62436i	0.894648	+	0.0536995i
$916$		0			0
$917$		−	12.0000i		−	0.396275i
$918$		0			0
$919$	−36.0000			−1.18753			−0.593765	−	0.804638i	$-0.702359\pi$
$919$	−36.0000			−1.18753			−0.593765	+	0.804638i	$0.702359\pi$
$920$		0			0
$921$	13.5000	+	7.79423i	0.444840	+	0.256829i
$922$		0			0
$923$	−31.1769	−	18.0000i	−1.02620	−	0.592477i
$924$		0			0
$925$	−1.19615	+	9.92820i	−0.0393292	+	0.326437i
$926$		0			0
$927$		−	24.0000i		−	0.788263i
$928$		0			0
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	−18.0000	+	31.1769i	−0.589926	+	1.02178i
$932$		0			0
$933$	−5.19615	−	9.00000i	−0.170114	−	0.294647i
$934$		0			0
$935$	−8.00000	+	4.00000i	−0.261628	+	0.130814i
$936$		0			0
$937$			52.0000i			1.69877i	0.527777	+	0.849383i	$0.323026\pi$
$937$			52.0000i			1.69877i	−0.527777	+	0.849383i	$0.676974\pi$
$938$		0			0
$939$		−	38.1051i		−	1.24351i
$940$		0			0
$941$	20.5000	−	35.5070i	0.668281	−	1.15750i	−0.310104	−	0.950703i	$-0.600364\pi$
$941$	20.5000	−	35.5070i	0.668281	−	1.15750i	0.978385	−	0.206794i	$-0.0663029\pi$
$942$		0			0
$943$	−9.52628	+	5.50000i	−0.310218	+	0.179105i
$944$		0			0
$945$	−10.3923	+	5.19615i	−0.338062	+	0.169031i
$946$		0			0
$947$	44.1673	−	25.5000i	1.43524	−	0.828639i	0.437730	−	0.899106i	$-0.355783\pi$
$947$	44.1673	−	25.5000i	1.43524	−	0.828639i	0.997514	+	0.0704677i	$0.0224492\pi$
$948$		0			0
$949$	12.0000	−	20.7846i	0.389536	−	0.674697i
$950$		0			0
$951$			3.46410i			0.112331i
$952$		0			0
$953$		−	2.00000i		−	0.0647864i	−0.999475	−	0.0323932i	$-0.989687\pi$
$953$		−	2.00000i		−	0.0647864i	0.999475	−	0.0323932i	$-0.0103129\pi$
$954$		0			0
$955$	6.00000	+	12.0000i	0.194155	+	0.388311i
$956$		0			0
$957$	−15.5885	−	27.0000i	−0.503903	−	0.872786i
$958$		0			0
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−7.79423	+	4.50000i	−0.251166	+	0.145010i
$964$		0			0
$965$	−18.6603	−	12.3205i	−0.600695	−	0.396611i
$966$		0			0
$967$	−14.7224	−	8.50000i	−0.473441	−	0.273342i	0.244238	−	0.969715i	$-0.421462\pi$
$967$	−14.7224	−	8.50000i	−0.473441	−	0.273342i	−0.717679	+	0.696374i	$0.754796\pi$
$968$		0			0
$969$	−18.0000	−	10.3923i	−0.578243	−	0.333849i
$970$		0			0
$971$	42.0000			1.34784			0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000			1.34784			0.673922	+	0.738802i	$0.264608\pi$
$972$		0			0
$973$			16.0000i			0.512936i
$974$		0			0
$975$	−47.7846	+	20.4115i	−1.53033	+	0.653693i
$976$		0			0
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.496167	−	0.868227i	$-0.665259\pi$
$977$	−46.7654	−	27.0000i	−1.49616	−	0.863807i	−0.999990	+	0.00442082i	$0.998593\pi$
$978$		0			0
$979$	1.00000	+	1.73205i	0.0319601	+	0.0553566i
$980$		0			0
$981$	10.5000	+	18.1865i	0.335239	+	0.580651i
$982$		0			0
$983$	−16.4545	+	9.50000i	−0.524816	+	0.303003i	−0.738903	−	0.673812i	$-0.764656\pi$
$983$	−16.4545	+	9.50000i	−0.524816	+	0.303003i	0.214087	+	0.976815i	$0.431323\pi$
$984$		0			0
$985$	−1.07180	+	17.8564i	−0.0341503	+	0.568952i
$986$		0			0
$987$	−6.06218	−	10.5000i	−0.192961	−	0.334219i
$988$		0			0
$989$	4.00000			0.127193
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$	−13.8564			−0.439720
$994$		0			0
$995$	−40.1769	−	2.41154i	−1.27369	−	0.0764510i
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.by.a.49.2		4
3.2	odd	2		2160.2.by.b.1009.1		4
4.3	odd	2		90.2.i.a.49.2	yes	4
5.4	even	2	inner	720.2.by.a.49.1		4
9.2	odd	6		2160.2.by.b.289.2		4
9.7	even	3	inner	720.2.by.a.529.1		4
12.11	even	2		270.2.i.a.199.1		4
15.14	odd	2		2160.2.by.b.1009.2		4
20.3	even	4		450.2.e.b.301.1		2
20.7	even	4		450.2.e.g.301.1		2
20.19	odd	2		90.2.i.a.49.1	✓	4
36.7	odd	6		90.2.i.a.79.1	yes	4
36.11	even	6		270.2.i.a.19.2		4
36.23	even	6		810.2.c.c.649.1		2
36.31	odd	6		810.2.c.b.649.2		2
45.29	odd	6		2160.2.by.b.289.1		4
45.34	even	6	inner	720.2.by.a.529.2		4
60.23	odd	4		1350.2.e.i.901.1		2
60.47	odd	4		1350.2.e.a.901.1		2
60.59	even	2		270.2.i.a.199.2		4
180.7	even	12		450.2.e.g.151.1		2
180.23	odd	12		4050.2.a.g.1.1		1
180.43	even	12		450.2.e.b.151.1		2
180.47	odd	12		1350.2.e.a.451.1		2
180.59	even	6		810.2.c.c.649.2		2
180.67	even	12		4050.2.a.j.1.1		1
180.79	odd	6		90.2.i.a.79.2	yes	4
180.83	odd	12		1350.2.e.i.451.1		2
180.103	even	12		4050.2.a.x.1.1		1
180.119	even	6		270.2.i.a.19.1		4
180.139	odd	6		810.2.c.b.649.1		2
180.167	odd	12		4050.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.a.49.1	✓	4	20.19	odd	2
90.2.i.a.49.2	yes	4	4.3	odd	2
90.2.i.a.79.1	yes	4	36.7	odd	6
90.2.i.a.79.2	yes	4	180.79	odd	6
270.2.i.a.19.1		4	180.119	even	6
270.2.i.a.19.2		4	36.11	even	6
270.2.i.a.199.1		4	12.11	even	2
270.2.i.a.199.2		4	60.59	even	2
450.2.e.b.151.1		2	180.43	even	12
450.2.e.b.301.1		2	20.3	even	4
450.2.e.g.151.1		2	180.7	even	12
450.2.e.g.301.1		2	20.7	even	4
720.2.by.a.49.1		4	5.4	even	2	inner
720.2.by.a.49.2		4	1.1	even	1	trivial
720.2.by.a.529.1		4	9.7	even	3	inner
720.2.by.a.529.2		4	45.34	even	6	inner
810.2.c.b.649.1		2	180.139	odd	6
810.2.c.b.649.2		2	36.31	odd	6
810.2.c.c.649.1		2	36.23	even	6
810.2.c.c.649.2		2	180.59	even	6
1350.2.e.a.451.1		2	180.47	odd	12
1350.2.e.a.901.1		2	60.47	odd	4
1350.2.e.i.451.1		2	180.83	odd	12
1350.2.e.i.901.1		2	60.23	odd	4
2160.2.by.b.289.1		4	45.29	odd	6
2160.2.by.b.289.2		4	9.2	odd	6
2160.2.by.b.1009.1		4	3.2	odd	2
2160.2.by.b.1009.2		4	15.14	odd	2
4050.2.a.g.1.1		1	180.23	odd	12
4050.2.a.j.1.1		1	180.67	even	12
4050.2.a.x.1.1		1	180.103	even	12
4050.2.a.be.1.1		1	180.167	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(2.23205 + 0.133975i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(-5.19615 - 3.00000i) q^{13} +(2.13397 - 3.23205i) q^{15} -2.00000i q^{17} +6.00000 q^{19} -1.73205i q^{21} +(-0.866025 - 0.500000i) q^{23} +(4.96410 + 0.598076i) q^{25} -5.19615 q^{27} +(4.50000 + 7.79423i) q^{29} +(-1.00000 + 1.73205i) q^{31} -3.46410 q^{33} +(2.00000 - 1.00000i) q^{35} +2.00000i q^{37} +(-9.00000 + 5.19615i) q^{39} +(5.50000 - 9.52628i) q^{41} +(-3.46410 + 2.00000i) q^{43} +(-3.00000 - 6.00000i) q^{45} +(6.06218 - 3.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(-3.00000 - 1.73205i) q^{51} +(-2.00000 - 4.00000i) q^{55} +(5.19615 - 9.00000i) q^{57} +(2.00000 - 3.46410i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-2.59808 - 1.50000i) q^{63} +(-11.1962 - 7.39230i) q^{65} +(-9.52628 - 5.50000i) q^{67} +(-1.50000 + 0.866025i) q^{69} +6.00000 q^{71} +4.00000i q^{73} +(5.19615 - 6.92820i) q^{75} +(-1.73205 - 1.00000i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-9.52628 + 5.50000i) q^{83} +(0.267949 - 4.46410i) q^{85} +15.5885 q^{87} -1.00000 q^{89} -6.00000 q^{91} +(1.73205 + 3.00000i) q^{93} +(13.3923 + 0.803848i) q^{95} +(-6.92820 + 4.00000i) q^{97} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 6 q^{9} - 4 q^{11} + 12 q^{15} + 24 q^{19} + 6 q^{25} + 18 q^{29} - 4 q^{31} + 8 q^{35} - 36 q^{39} + 22 q^{41} - 12 q^{45} - 12 q^{49} - 12 q^{51} - 8 q^{55} + 8 q^{59} + 14 q^{61} - 24 q^{65}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^5 - 6 * q^9 - 4 * q^11 + 12 * q^15 + 24 * q^19 + 6 * q^25 + 18 * q^29 - 4 * q^31 + 8 * q^35 - 36 * q^39 + 22 * q^41 - 12 * q^45 - 12 * q^49 - 12 * q^51 - 8 * q^55 + 8 * q^59 + 14 * q^61 - 24 * q^65 - 6 * q^69 + 24 * q^71 + 24 * q^79 - 18 * q^81 + 8 * q^85 - 4 * q^89 - 24 * q^91 + 12 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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