LMFDB - Embedded newform 567.2.s.d.458.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(26,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("567.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.s (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			458.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	567.458
Dual form			567.2.s.d.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +1.41421i q^{11} +(4.50000 + 2.59808i) q^{13} +(-3.67423 - 0.707107i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.44949 + 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +5.65685i q^{23} +1.00000 q^{25} +(-3.67423 - 6.36396i) q^{26} +(-2.44949 + 1.41421i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(6.00000 - 3.46410i) q^{34} +(6.12372 - 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} -2.44949 q^{38} +6.92820i q^{40} +(3.67423 - 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} +(6.12372 - 10.6066i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.22474 - 0.707107i) q^{50} +(2.44949 + 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 7.07107i) q^{56} +4.00000 q^{58} +(-2.44949 - 4.24264i) q^{59} +(3.00000 + 1.73205i) q^{61} +2.44949 q^{62} -8.00000 q^{64} +(11.0227 + 6.36396i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-9.00000 - 1.73205i) q^{70} -7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} -1.41421i q^{74} +(1.22474 + 3.53553i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(4.89898 - 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(-3.67423 - 6.36396i) q^{83} +(-6.00000 + 10.3923i) q^{85} -1.41421i q^{86} -4.00000 q^{88} +(2.44949 + 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} +(3.67423 - 2.12132i) q^{95} +(-9.00000 + 5.19615i) q^{97} +(-9.79796 + 1.41421i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{7}+O(q^{10}) $ 4 * q + 10 * q^7	$ 4 q + 10 q^{7} - 12 q^{10} + 18 q^{13} + 8 q^{16} + 6 q^{19} + 4 q^{22} + 4 q^{25} - 6 q^{31} + 24 q^{34} + 2 q^{37} + 2 q^{43} + 16 q^{46} + 22 q^{49} + 16 q^{58} + 12 q^{61} - 32 q^{64} - 22 q^{67} - 36 q^{70} + 6 q^{73} - 10 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} + 54 q^{91} - 60 q^{94} - 36 q^{97}+O(q^{100}) $ 4 * q + 10 * q^7 - 12 * q^10 + 18 * q^13 + 8 * q^16 + 6 * q^19 + 4 * q^22 + 4 * q^25 - 6 * q^31 + 24 * q^34 + 2 * q^37 + 2 * q^43 + 16 * q^46 + 22 * q^49 + 16 * q^58 + 12 * q^61 - 32 * q^64 - 22 * q^67 - 36 * q^70 + 6 * q^73 - 10 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 + 54 * q^91 - 60 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.44949			1.09545			0.547723	−	0.836660i	$-0.315495\pi$
$5$	2.44949			1.09545			0.547723	+	0.836660i	$0.315495\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$			2.82843i			1.00000i
$9$		0			0
$10$	−3.00000	−	1.73205i	−0.948683	−	0.547723i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$		0			0
$13$	4.50000	+	2.59808i	1.24808	+	0.720577i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	4.50000	+	2.59808i	1.24808	+	0.720577i	0.277350	+	0.960769i	$0.410544\pi$
$14$	−3.67423	−	0.707107i	−0.981981	−	0.188982i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−2.44949	+	4.24264i	−0.594089	+	1.02899i	0.399586	+	0.916696i	$0.369154\pi$
$17$	−2.44949	+	4.24264i	−0.594089	+	1.02899i	−0.993675	+	0.112296i	$0.964180\pi$
$18$		0			0
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	−0.317970	−	0.948101i	$-0.603001\pi$
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	0.662094	+	0.749421i	$0.269668\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$			5.65685i			1.17954i	0.807573	+	0.589768i	$0.200781\pi$
$23$			5.65685i			1.17954i	−0.807573	+	0.589768i	$0.799219\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−3.67423	−	6.36396i	−0.720577	−	1.24808i
$27$		0			0
$28$		0			0
$29$	−2.44949	+	1.41421i	−0.454859	+	0.262613i	−0.709880	−	0.704323i	$-0.751251\pi$
$29$	−2.44949	+	1.41421i	−0.454859	+	0.262613i	0.255021	+	0.966935i	$0.417918\pi$
$30$		0			0
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$		0			0
$34$	6.00000	−	3.46410i	1.02899	−	0.594089i
$35$	6.12372	−	2.12132i	1.03510	−	0.358569i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−2.44949			−0.397360
$39$		0			0
$40$			6.92820i			1.09545i
$41$	3.67423	−	6.36396i	0.573819	−	0.993884i	−0.422350	−	0.906433i	$-0.638795\pi$
$41$	3.67423	−	6.36396i	0.573819	−	0.993884i	0.996169	−	0.0874508i	$-0.0278721\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$		0			0
$45$		0			0
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	6.12372	−	10.6066i	0.893237	−	1.54713i	0.0572655	−	0.998359i	$-0.481762\pi$
$47$	6.12372	−	10.6066i	0.893237	−	1.54713i	0.835971	−	0.548773i	$-0.184905\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−1.22474	−	0.707107i	−0.173205	−	0.100000i
$51$		0			0
$52$		0			0
$53$	2.44949	+	1.41421i	0.336463	+	0.194257i	0.658707	−	0.752400i	$-0.271104\pi$
$53$	2.44949	+	1.41421i	0.336463	+	0.194257i	−0.322244	+	0.946657i	$0.604437\pi$
$54$		0			0
$55$			3.46410i			0.467099i
$56$	2.44949	+	7.07107i	0.327327	+	0.944911i
$57$		0			0
$58$	4.00000			0.525226
$59$	−2.44949	−	4.24264i	−0.318896	−	0.552345i	0.661362	−	0.750067i	$-0.269979\pi$
$59$	−2.44949	−	4.24264i	−0.318896	−	0.552345i	−0.980258	+	0.197722i	$0.936646\pi$
$60$		0			0
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$	2.44949			0.311086
$63$		0			0
$64$	−8.00000			−1.00000
$65$	11.0227	+	6.36396i	1.36720	+	0.789352i
$66$		0			0
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	0.305424	−	0.952217i	$-0.401202\pi$
$68$		0			0
$69$		0			0
$70$	−9.00000	−	1.73205i	−1.07571	−	0.207020i
$71$		−	7.07107i		−	0.839181i	−0.907713	−	0.419591i	$-0.862174\pi$
$71$		−	7.07107i		−	0.839181i	0.907713	−	0.419591i	$-0.137826\pi$
$72$		0			0
$73$	1.50000	+	0.866025i	0.175562	+	0.101361i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	1.50000	+	0.866025i	0.175562	+	0.101361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$		−	1.41421i		−	0.164399i
$75$		0			0
$76$		0			0
$77$	1.22474	+	3.53553i	0.139573	+	0.402911i
$78$		0			0
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	4.89898	−	8.48528i	0.547723	−	0.948683i
$81$		0			0
$82$	−9.00000	+	5.19615i	−0.993884	+	0.573819i
$83$	−3.67423	−	6.36396i	−0.403300	−	0.698535i	0.590822	−	0.806802i	$-0.298803\pi$
$83$	−3.67423	−	6.36396i	−0.403300	−	0.698535i	−0.994122	+	0.108266i	$0.965470\pi$
$84$		0			0
$85$	−6.00000	+	10.3923i	−0.650791	+	1.12720i
$86$		−	1.41421i		−	0.152499i
$87$		0			0
$88$	−4.00000			−0.426401
$89$	2.44949	+	4.24264i	0.259645	+	0.449719i	0.966147	−	0.257993i	$-0.0830610\pi$
$89$	2.44949	+	4.24264i	0.259645	+	0.449719i	−0.706502	+	0.707712i	$0.749728\pi$
$90$		0			0
$91$	13.5000	+	2.59808i	1.41518	+	0.272352i
$92$		0			0
$93$		0			0
$94$	−15.0000	+	8.66025i	−1.54713	+	0.893237i
$95$	3.67423	−	2.12132i	0.376969	−	0.217643i
$96$		0			0
$97$	−9.00000	+	5.19615i	−0.913812	+	0.527589i	−0.881656	−	0.471894i	$-0.843571\pi$
$97$	−9.00000	+	5.19615i	−0.913812	+	0.527589i	−0.0321560	+	0.999483i	$0.510237\pi$
$98$	−9.79796	+	1.41421i	−0.989743	+	0.142857i
$99$		0			0
$100$		0			0
$101$	−17.1464			−1.70613			−0.853067	−	0.521802i	$-0.825260\pi$
$101$	−17.1464			−1.70613			−0.853067	+	0.521802i	$0.825260\pi$
$102$		0			0
$103$		−	8.66025i		−	0.853320i	−0.904412	−	0.426660i	$-0.859690\pi$
$103$		−	8.66025i		−	0.853320i	0.904412	−	0.426660i	$-0.140310\pi$
$104$	−7.34847	+	12.7279i	−0.720577	+	1.24808i
$105$		0			0
$106$	−2.00000	−	3.46410i	−0.194257	−	0.336463i
$107$	−2.44949	+	1.41421i	−0.236801	+	0.136717i	−0.613706	−	0.789535i	$-0.710322\pi$
$107$	−2.44949	+	1.41421i	−0.236801	+	0.136717i	0.376905	+	0.926252i	$0.376988\pi$
$108$		0			0
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$	2.44949	−	4.24264i	0.233550	−	0.404520i
$111$		0			0
$112$	2.00000	−	10.3923i	0.188982	−	0.981981i
$113$	−1.22474	−	0.707107i	−0.115214	−	0.0665190i	0.441285	−	0.897367i	$-0.354523\pi$
$113$	−1.22474	−	0.707107i	−0.115214	−	0.0665190i	−0.556500	+	0.830848i	$0.687856\pi$
$114$		0			0
$115$			13.8564i			1.29212i
$116$		0			0
$117$		0			0
$118$			6.92820i			0.637793i
$119$	−2.44949	+	12.7279i	−0.224544	+	1.16677i
$120$		0			0
$121$	9.00000			0.818182
$122$	−2.44949	−	4.24264i	−0.221766	−	0.384111i
$123$		0			0
$124$		0			0
$125$	−9.79796			−0.876356
$126$		0			0
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	9.79796	+	5.65685i	0.866025	+	0.500000i
$129$		0			0
$130$	−9.00000	−	15.5885i	−0.789352	−	1.36720i
$131$	2.44949			0.214013			0.107006	−	0.994258i	$-0.465873\pi$
$131$	2.44949			0.214013			0.107006	+	0.994258i	$0.465873\pi$
$132$		0			0
$133$	3.00000	−	3.46410i	0.260133	−	0.300376i
$134$			15.5563i			1.34386i
$135$		0			0
$136$	−12.0000	−	6.92820i	−1.02899	−	0.594089i
$137$		−	11.3137i		−	0.966595i	−0.875456	−	0.483298i	$-0.839439\pi$
$137$		−	11.3137i		−	0.966595i	0.875456	−	0.483298i	$-0.160561\pi$
$138$		0			0
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	−0.296866	+	0.954919i	$0.595942\pi$
$140$		0			0
$141$		0			0
$142$	−5.00000	+	8.66025i	−0.419591	+	0.726752i
$143$	−3.67423	+	6.36396i	−0.307255	+	0.532181i
$144$		0			0
$145$	−6.00000	+	3.46410i	−0.498273	+	0.287678i
$146$	−1.22474	−	2.12132i	−0.101361	−	0.175562i
$147$		0			0
$148$		0			0
$149$			5.65685i			0.463428i	0.972784	+	0.231714i	$0.0744333\pi$
$149$			5.65685i			0.463428i	−0.972784	+	0.231714i	$0.925567\pi$
$150$		0			0
$151$	−22.0000			−1.79033			−0.895167	−	0.445730i	$-0.852944\pi$
$151$	−22.0000			−1.79033			−0.895167	+	0.445730i	$0.852944\pi$
$152$	2.44949	+	4.24264i	0.198680	+	0.344124i
$153$		0			0
$154$	1.00000	−	5.19615i	0.0805823	−	0.418718i
$155$	−3.67423	+	2.12132i	−0.295122	+	0.170389i
$156$		0			0
$157$	−15.0000	+	8.66025i	−1.19713	+	0.691164i	−0.959914	−	0.280293i	$-0.909568\pi$
$157$	−15.0000	+	8.66025i	−1.19713	+	0.691164i	−0.237216	+	0.971457i	$0.576235\pi$
$158$	6.12372	−	3.53553i	0.487177	−	0.281272i
$159$		0			0
$160$		0			0
$161$	4.89898	+	14.1421i	0.386094	+	1.11456i
$162$		0			0
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$		0			0
$165$		0			0
$166$			10.3923i			0.806599i
$167$	3.67423	−	6.36396i	0.284321	−	0.492458i	−0.688123	−	0.725594i	$-0.741565\pi$
$167$	3.67423	−	6.36396i	0.284321	−	0.492458i	0.972444	+	0.233136i	$0.0748986\pi$
$168$		0			0
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$	14.6969	−	8.48528i	1.12720	−	0.650791i
$171$		0			0
$172$		0			0
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	−0.989944	−	0.141462i	$-0.954820\pi$
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	0.617481	+	0.786586i	$0.288153\pi$
$174$		0			0
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$	4.89898	+	2.82843i	0.369274	+	0.213201i
$177$		0			0
$178$		−	6.92820i		−	0.519291i
$179$	−8.57321	−	4.94975i	−0.640792	−	0.369961i	0.144127	−	0.989559i	$-0.453962\pi$
$179$	−8.57321	−	4.94975i	−0.640792	−	0.369961i	−0.784920	+	0.619598i	$0.787296\pi$
$180$		0			0
$181$			15.5885i			1.15868i	0.815086	+	0.579340i	$0.196690\pi$
$181$			15.5885i			1.15868i	−0.815086	+	0.579340i	$0.803310\pi$
$182$	−14.6969	−	12.7279i	−1.08941	−	0.943456i
$183$		0			0
$184$	−16.0000			−1.17954
$185$	1.22474	+	2.12132i	0.0900450	+	0.155963i
$186$		0			0
$187$	−6.00000	−	3.46410i	−0.438763	−	0.253320i
$188$		0			0
$189$		0			0
$190$	−6.00000			−0.435286
$191$	−1.22474	−	0.707107i	−0.0886194	−	0.0511645i	0.455035	−	0.890473i	$-0.349627\pi$
$191$	−1.22474	−	0.707107i	−0.0886194	−	0.0511645i	−0.543655	+	0.839309i	$0.682960\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	14.6969			1.05518
$195$		0			0
$196$		0			0
$197$		−	19.7990i		−	1.41062i	−0.708899	−	0.705310i	$-0.750808\pi$
$197$		−	19.7990i		−	1.41062i	0.708899	−	0.705310i	$-0.249192\pi$
$198$		0			0
$199$	−12.0000	−	6.92820i	−0.850657	−	0.491127i	0.0102152	−	0.999948i	$-0.496748\pi$
$199$	−12.0000	−	6.92820i	−0.850657	−	0.491127i	−0.860873	+	0.508821i	$0.830082\pi$
$200$			2.82843i			0.200000i
$201$		0			0
$202$	21.0000	+	12.1244i	1.47755	+	0.853067i
$203$	−4.89898	+	5.65685i	−0.343841	+	0.397033i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$	−6.12372	+	10.6066i	−0.426660	+	0.738997i
$207$		0			0
$208$	18.0000	−	10.3923i	1.24808	−	0.720577i
$209$	1.22474	+	2.12132i	0.0847174	+	0.146735i
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$		0			0
$213$		0			0
$214$	4.00000			0.273434
$215$	1.22474	+	2.12132i	0.0835269	+	0.144673i
$216$		0			0
$217$	−3.00000	+	3.46410i	−0.203653	+	0.235159i
$218$	−1.22474	+	0.707107i	−0.0829502	+	0.0478913i
$219$		0			0
$220$		0			0
$221$	−22.0454	+	12.7279i	−1.48293	+	0.856173i
$222$		0			0
$223$	18.0000	−	10.3923i	1.20537	−	0.695920i	0.243625	−	0.969870i	$-0.421663\pi$
$223$	18.0000	−	10.3923i	1.20537	−	0.695920i	0.961744	+	0.273949i	$0.0883300\pi$
$224$		0			0
$225$		0			0
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$	26.9444			1.78836			0.894181	−	0.447706i	$-0.147759\pi$
$227$	26.9444			1.78836			0.894181	+	0.447706i	$0.147759\pi$
$228$		0			0
$229$			22.5167i			1.48794i	0.668211	+	0.743971i	$0.267060\pi$
$229$			22.5167i			1.48794i	−0.668211	+	0.743971i	$0.732940\pi$
$230$	9.79796	−	16.9706i	0.646058	−	1.11901i
$231$		0			0
$232$	−4.00000	−	6.92820i	−0.262613	−	0.454859i
$233$	8.57321	−	4.94975i	0.561650	−	0.324269i	−0.192158	−	0.981364i	$-0.561548\pi$
$233$	8.57321	−	4.94975i	0.561650	−	0.324269i	0.753807	+	0.657095i	$0.228215\pi$
$234$		0			0
$235$	15.0000	−	25.9808i	0.978492	−	1.69480i
$236$		0			0
$237$		0			0
$238$	12.0000	−	13.8564i	0.777844	−	0.898177i
$239$	−23.2702	−	13.4350i	−1.50522	−	0.869040i	−0.999982	−	0.00606055i	$-0.998071\pi$
$239$	−23.2702	−	13.4350i	−1.50522	−	0.869040i	−0.505239	−	0.862979i	$-0.668596\pi$
$240$		0			0
$241$			13.8564i			0.892570i	0.894891	+	0.446285i	$0.147253\pi$
$241$			13.8564i			0.892570i	−0.894891	+	0.446285i	$0.852747\pi$
$242$	−11.0227	−	6.36396i	−0.708566	−	0.409091i
$243$		0			0
$244$		0			0
$245$	13.4722	−	10.6066i	0.860707	−	0.677631i
$246$		0			0
$247$	9.00000			0.572656
$248$	−2.44949	−	4.24264i	−0.155543	−	0.269408i
$249$		0			0
$250$	12.0000	+	6.92820i	0.758947	+	0.438178i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$	−13.4722	−	7.77817i	−0.845321	−	0.488046i
$255$		0			0
$256$		0			0
$257$	2.44949			0.152795			0.0763975	−	0.997077i	$-0.475658\pi$
$257$	2.44949			0.152795			0.0763975	+	0.997077i	$0.475658\pi$
$258$		0			0
$259$	2.00000	+	1.73205i	0.124274	+	0.107624i
$260$		0			0
$261$		0			0
$262$	−3.00000	−	1.73205i	−0.185341	−	0.107006i
$263$			14.1421i			0.872041i	0.899937	+	0.436021i	$0.143613\pi$
$263$			14.1421i			0.872041i	−0.899937	+	0.436021i	$0.856387\pi$
$264$		0			0
$265$	6.00000	+	3.46410i	0.368577	+	0.212798i
$266$	−6.12372	+	2.12132i	−0.375470	+	0.130066i
$267$		0			0
$268$		0			0
$269$	8.57321	−	14.8492i	0.522718	−	0.905374i	−0.476932	−	0.878940i	$-0.658251\pi$
$269$	8.57321	−	14.8492i	0.522718	−	0.905374i	0.999651	−	0.0264343i	$-0.00841529\pi$
$270$		0			0
$271$	−12.0000	+	6.92820i	−0.728948	+	0.420858i	−0.818037	−	0.575165i	$-0.804938\pi$
$271$	−12.0000	+	6.92820i	−0.728948	+	0.420858i	0.0890891	+	0.996024i	$0.471604\pi$
$272$	9.79796	+	16.9706i	0.594089	+	1.02899i
$273$		0			0
$274$	−8.00000	+	13.8564i	−0.483298	+	0.837096i
$275$			1.41421i			0.0852803i
$276$		0			0
$277$	23.0000			1.38194			0.690968	−	0.722885i	$-0.257185\pi$
$277$	23.0000			1.38194			0.690968	+	0.722885i	$0.257185\pi$
$278$	−3.67423	−	6.36396i	−0.220366	−	0.381685i
$279$		0			0
$280$	6.00000	+	17.3205i	0.358569	+	1.03510i
$281$	19.5959	−	11.3137i	1.16899	−	0.674919i	0.215551	−	0.976492i	$-0.430845\pi$
$281$	19.5959	−	11.3137i	1.16899	−	0.674919i	0.953443	+	0.301573i	$0.0975118\pi$
$282$		0			0
$283$	−1.50000	+	0.866025i	−0.0891657	+	0.0514799i	−0.543920	−	0.839137i	$-0.683060\pi$
$283$	−1.50000	+	0.866025i	−0.0891657	+	0.0514799i	0.454754	+	0.890617i	$0.349727\pi$
$284$		0			0
$285$		0			0
$286$	9.00000	−	5.19615i	0.532181	−	0.307255i
$287$	3.67423	−	19.0919i	0.216883	−	1.12696i
$288$		0			0
$289$	−3.50000	−	6.06218i	−0.205882	−	0.356599i
$290$	9.79796			0.575356
$291$		0			0
$292$		0			0
$293$	−7.34847	+	12.7279i	−0.429302	+	0.743573i	−0.996811	−	0.0797939i	$-0.974574\pi$
$293$	−7.34847	+	12.7279i	−0.429302	+	0.743573i	0.567509	+	0.823367i	$0.307907\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	−2.44949	+	1.41421i	−0.142374	+	0.0821995i
$297$		0			0
$298$	4.00000	−	6.92820i	0.231714	−	0.401340i
$299$	−14.6969	+	25.4558i	−0.849946	+	1.47215i
$300$		0			0
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	26.9444	+	15.5563i	1.55048	+	0.895167i
$303$		0			0
$304$		−	6.92820i		−	0.397360i
$305$	7.34847	+	4.24264i	0.420772	+	0.242933i
$306$		0			0
$307$		−	15.5885i		−	0.889680i	−0.895610	−	0.444840i	$-0.853260\pi$
$307$		−	15.5885i		−	0.889680i	0.895610	−	0.444840i	$-0.146740\pi$
$308$		0			0
$309$		0			0
$310$	6.00000			0.340777
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	0.999873	−	0.0159282i	$-0.00507031\pi$
$311$	8.57321	+	14.8492i	0.486142	+	0.842023i	−0.513731	+	0.857951i	$0.671737\pi$
$312$		0			0
$313$	−10.5000	−	6.06218i	−0.593495	−	0.342655i	0.172983	−	0.984925i	$-0.444659\pi$
$313$	−10.5000	−	6.06218i	−0.593495	−	0.342655i	−0.766478	+	0.642270i	$0.777993\pi$
$314$	24.4949			1.38233
$315$		0			0
$316$		0			0
$317$	−12.2474	−	7.07107i	−0.687885	−	0.397151i	0.114934	−	0.993373i	$-0.463334\pi$
$317$	−12.2474	−	7.07107i	−0.687885	−	0.397151i	−0.802819	+	0.596222i	$0.796668\pi$
$318$		0			0
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$	−19.5959			−1.09545
$321$		0			0
$322$	4.00000	−	20.7846i	0.222911	−	1.15828i
$323$			8.48528i			0.472134i
$324$		0			0
$325$	4.50000	+	2.59808i	0.249615	+	0.144115i
$326$		−	14.1421i		−	0.783260i
$327$		0			0
$328$	18.0000	+	10.3923i	0.993884	+	0.573819i
$329$	6.12372	−	31.8198i	0.337612	−	1.75428i
$330$		0			0
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	0.879440	−	0.476011i	$-0.157918\pi$
$332$		0			0
$333$		0			0
$334$	−9.00000	+	5.19615i	−0.492458	+	0.284321i
$335$	−13.4722	−	23.3345i	−0.736065	−	1.27490i
$336$		0			0
$337$	−11.5000	+	19.9186i	−0.626445	+	1.08503i	0.361815	+	0.932250i	$0.382157\pi$
$337$	−11.5000	+	19.9186i	−0.626445	+	1.08503i	−0.988260	+	0.152784i	$0.951176\pi$
$338$		−	19.7990i		−	1.07692i
$339$		0			0
$340$		0			0
$341$	−1.22474	−	2.12132i	−0.0663237	−	0.114876i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−2.44949	+	1.41421i	−0.132068	+	0.0762493i
$345$		0			0
$346$	12.0000	−	6.92820i	0.645124	−	0.372463i
$347$	26.9444	−	15.5563i	1.44645	−	0.835109i	0.448183	−	0.893942i	$-0.352071\pi$
$347$	26.9444	−	15.5563i	1.44645	−	0.835109i	0.998268	+	0.0588334i	$0.0187381\pi$
$348$		0			0
$349$	−9.00000	+	5.19615i	−0.481759	+	0.278144i	−0.721149	−	0.692780i	$-0.756386\pi$
$349$	−9.00000	+	5.19615i	−0.481759	+	0.278144i	0.239390	+	0.970923i	$0.423052\pi$
$350$	−3.67423	−	0.707107i	−0.196396	−	0.0377964i
$351$		0			0
$352$		0			0
$353$	−17.1464			−0.912612			−0.456306	−	0.889823i	$-0.650828\pi$
$353$	−17.1464			−0.912612			−0.456306	+	0.889823i	$0.650828\pi$
$354$		0			0
$355$		−	17.3205i		−	0.919277i
$356$		0			0
$357$		0			0
$358$	7.00000	+	12.1244i	0.369961	+	0.640792i
$359$	−24.4949	+	14.1421i	−1.29279	+	0.746393i	−0.979148	−	0.203148i	$-0.934883\pi$
$359$	−24.4949	+	14.1421i	−1.29279	+	0.746393i	−0.313643	+	0.949541i	$0.601550\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	11.0227	−	19.0919i	0.579340	−	1.00345i
$363$		0			0
$364$		0			0
$365$	3.67423	+	2.12132i	0.192318	+	0.111035i
$366$		0			0
$367$		−	1.73205i		−	0.0904123i	−0.998978	−	0.0452062i	$-0.985606\pi$
$367$		−	1.73205i		−	0.0904123i	0.998978	−	0.0452062i	$-0.0143945\pi$
$368$	19.5959	+	11.3137i	1.02151	+	0.589768i
$369$		0			0
$370$		−	3.46410i		−	0.180090i
$371$	7.34847	+	1.41421i	0.381514	+	0.0734223i
$372$		0			0
$373$	29.0000			1.50156			0.750782	−	0.660551i	$-0.229677\pi$
$373$	29.0000			1.50156			0.750782	+	0.660551i	$0.229677\pi$
$374$	4.89898	+	8.48528i	0.253320	+	0.438763i
$375$		0			0
$376$	30.0000	+	17.3205i	1.54713	+	0.893237i
$377$	−14.6969			−0.756931
$378$		0			0
$379$	−7.00000			−0.359566			−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000			−0.359566			−0.179783	+	0.983706i	$0.557540\pi$
$380$		0			0
$381$		0			0
$382$	1.00000	+	1.73205i	0.0511645	+	0.0886194i
$383$	−19.5959			−1.00130			−0.500652	−	0.865648i	$-0.666906\pi$
$383$	−19.5959			−1.00130			−0.500652	+	0.865648i	$0.666906\pi$
$384$		0			0
$385$	3.00000	+	8.66025i	0.152894	+	0.441367i
$386$			15.5563i			0.791797i
$387$		0			0
$388$		0			0
$389$			26.8701i			1.36237i	0.732113	+	0.681183i	$0.238534\pi$
$389$			26.8701i			1.36237i	−0.732113	+	0.681183i	$0.761466\pi$
$390$		0			0
$391$	−24.0000	−	13.8564i	−1.21373	−	0.700749i
$392$	12.2474	+	15.5563i	0.618590	+	0.785714i
$393$		0			0
$394$	−14.0000	+	24.2487i	−0.705310	+	1.22163i
$395$	−6.12372	+	10.6066i	−0.308118	+	0.533676i
$396$		0			0
$397$	1.50000	−	0.866025i	0.0752828	−	0.0434646i	−0.461886	−	0.886939i	$-0.652827\pi$
$397$	1.50000	−	0.866025i	0.0752828	−	0.0434646i	0.537169	+	0.843475i	$0.319494\pi$
$398$	9.79796	+	16.9706i	0.491127	+	0.850657i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$		−	19.7990i		−	0.988714i	−0.869259	−	0.494357i	$-0.835403\pi$
$401$		−	19.7990i		−	0.988714i	0.869259	−	0.494357i	$-0.164597\pi$
$402$		0			0
$403$	−9.00000			−0.448322
$404$		0			0
$405$		0			0
$406$	10.0000	−	3.46410i	0.496292	−	0.171920i
$407$	−1.22474	+	0.707107i	−0.0607083	+	0.0350500i
$408$		0			0
$409$	−28.5000	+	16.4545i	−1.40923	+	0.813622i	−0.995314	−	0.0966915i	$-0.969174\pi$
$409$	−28.5000	+	16.4545i	−1.40923	+	0.813622i	−0.413920	+	0.910313i	$0.635841\pi$
$410$	−22.0454	+	12.7279i	−1.08875	+	0.628587i
$411$		0			0
$412$		0			0
$413$	−9.79796	−	8.48528i	−0.482126	−	0.417533i
$414$		0			0
$415$	−9.00000	−	15.5885i	−0.441793	−	0.765207i
$416$		0			0
$417$		0			0
$418$		−	3.46410i		−	0.169435i
$419$	−18.3712	+	31.8198i	−0.897491	+	1.55450i	−0.0667989	+	0.997766i	$0.521279\pi$
$419$	−18.3712	+	31.8198i	−0.897491	+	1.55450i	−0.830692	+	0.556733i	$0.812055\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$	−26.9444	+	15.5563i	−1.31163	+	0.757271i
$423$		0			0
$424$	−4.00000	+	6.92820i	−0.194257	+	0.336463i
$425$	−2.44949	+	4.24264i	−0.118818	+	0.205798i
$426$		0			0
$427$	9.00000	+	1.73205i	0.435541	+	0.0838198i
$428$		0			0
$429$		0			0
$430$		−	3.46410i		−	0.167054i
$431$	13.4722	+	7.77817i	0.648933	+	0.374661i	0.788047	−	0.615615i	$-0.211092\pi$
$431$	13.4722	+	7.77817i	0.648933	+	0.374661i	−0.139114	+	0.990276i	$0.544426\pi$
$432$		0			0
$433$			15.5885i			0.749133i	0.927200	+	0.374567i	$0.122209\pi$
$433$			15.5885i			0.749133i	−0.927200	+	0.374567i	$0.877791\pi$
$434$	6.12372	−	2.12132i	0.293948	−	0.101827i
$435$		0			0
$436$		0			0
$437$	4.89898	+	8.48528i	0.234350	+	0.405906i
$438$		0			0
$439$	−24.0000	−	13.8564i	−1.14546	−	0.661330i	−0.197681	−	0.980266i	$-0.563341\pi$
$439$	−24.0000	−	13.8564i	−1.14546	−	0.661330i	−0.947776	+	0.318936i	$0.896674\pi$
$440$	−9.79796			−0.467099
$441$		0			0
$442$	36.0000			1.71235
$443$	−34.2929	−	19.7990i	−1.62930	−	0.940678i	−0.984301	−	0.176497i	$-0.943523\pi$
$443$	−34.2929	−	19.7990i	−1.62930	−	0.940678i	−0.645002	−	0.764181i	$-0.723143\pi$
$444$		0			0
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−29.3939			−1.39184
$447$		0			0
$448$	−20.0000	+	6.92820i	−0.944911	+	0.327327i
$449$		−	7.07107i		−	0.333704i	−0.985982	−	0.166852i	$-0.946640\pi$
$449$		−	7.07107i		−	0.333704i	0.985982	−	0.166852i	$-0.0533603\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$		0			0
$453$		0			0
$454$	−33.0000	−	19.0526i	−1.54877	−	0.894181i
$455$	33.0681	+	6.36396i	1.55026	+	0.298347i
$456$		0			0
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	−0.918556	−	0.395292i	$-0.870643\pi$
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	0.801611	+	0.597847i	$0.203977\pi$
$458$	15.9217	−	27.5772i	0.743971	−	1.28860i
$459$		0			0
$460$		0			0
$461$	7.34847	+	12.7279i	0.342252	+	0.592798i	0.984851	−	0.173405i	$-0.0554769\pi$
$461$	7.34847	+	12.7279i	0.342252	+	0.592798i	−0.642598	+	0.766203i	$0.722144\pi$
$462$		0			0
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	−0.674526	−	0.738251i	$-0.735652\pi$
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	0.976607	+	0.215032i	$0.0689855\pi$
$464$			11.3137i			0.525226i
$465$		0			0
$466$	−14.0000			−0.648537
$467$	13.4722	+	23.3345i	0.623419	+	1.07979i	0.988844	+	0.148952i	$0.0475901\pi$
$467$	13.4722	+	23.3345i	0.623419	+	1.07979i	−0.365426	+	0.930841i	$0.619077\pi$
$468$		0			0
$469$	−22.0000	−	19.0526i	−1.01587	−	0.879765i
$470$	−36.7423	+	21.2132i	−1.69480	+	0.978492i
$471$		0			0
$472$	12.0000	−	6.92820i	0.552345	−	0.318896i
$473$	−1.22474	+	0.707107i	−0.0563138	+	0.0325128i
$474$		0			0
$475$	1.50000	−	0.866025i	0.0688247	−	0.0397360i
$476$		0			0
$477$		0			0
$478$	19.0000	+	32.9090i	0.869040	+	1.50522i
$479$	4.89898			0.223840			0.111920	−	0.993717i	$-0.464300\pi$
$479$	4.89898			0.223840			0.111920	+	0.993717i	$0.464300\pi$
$480$		0			0
$481$			5.19615i			0.236924i
$482$	9.79796	−	16.9706i	0.446285	−	0.772988i
$483$		0			0
$484$		0			0
$485$	−22.0454	+	12.7279i	−1.00103	+	0.577945i
$486$		0			0
$487$	−8.50000	+	14.7224i	−0.385172	+	0.667137i	−0.991793	−	0.127854i	$-0.959191\pi$
$487$	−8.50000	+	14.7224i	−0.385172	+	0.667137i	0.606621	+	0.794991i	$0.292524\pi$
$488$	−4.89898	+	8.48528i	−0.221766	+	0.384111i
$489$		0			0
$490$	−24.0000	+	3.46410i	−1.08421	+	0.156492i
$491$	9.79796	+	5.65685i	0.442176	+	0.255290i	0.704520	−	0.709684i	$-0.251162\pi$
$491$	9.79796	+	5.65685i	0.442176	+	0.255290i	−0.262344	+	0.964974i	$0.584496\pi$
$492$		0			0
$493$		−	13.8564i		−	0.624061i
$494$	−11.0227	−	6.36396i	−0.495935	−	0.286328i
$495$		0			0
$496$			6.92820i			0.311086i
$497$	−6.12372	−	17.6777i	−0.274687	−	0.792952i
$498$		0			0
$499$	−25.0000			−1.11915			−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000			−1.11915			−0.559577	+	0.828778i	$0.689036\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.0454			0.982956			0.491478	−	0.870890i	$-0.336457\pi$
$503$	22.0454			0.982956			0.491478	+	0.870890i	$0.336457\pi$
$504$		0			0
$505$	−42.0000			−1.86898
$506$	9.79796	+	5.65685i	0.435572	+	0.251478i
$507$		0			0
$508$		0			0
$509$	2.44949			0.108572			0.0542859	−	0.998525i	$-0.482712\pi$
$509$	2.44949			0.108572			0.0542859	+	0.998525i	$0.482712\pi$
$510$		0			0
$511$	4.50000	+	0.866025i	0.199068	+	0.0383107i
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$	−3.00000	−	1.73205i	−0.132324	−	0.0763975i
$515$		−	21.2132i		−	0.934765i
$516$		0			0
$517$	15.0000	+	8.66025i	0.659699	+	0.380878i
$518$	−1.22474	−	3.53553i	−0.0538122	−	0.155342i
$519$		0			0
$520$	−18.0000	+	31.1769i	−0.789352	+	1.36720i
$521$	−2.44949	+	4.24264i	−0.107314	+	0.185873i	−0.914681	−	0.404176i	$-0.867558\pi$
$521$	−2.44949	+	4.24264i	−0.107314	+	0.185873i	0.807367	+	0.590049i	$0.200892\pi$
$522$		0			0
$523$	1.50000	−	0.866025i	0.0655904	−	0.0378686i	−0.466846	−	0.884339i	$-0.654610\pi$
$523$	1.50000	−	0.866025i	0.0655904	−	0.0378686i	0.532437	+	0.846470i	$0.321276\pi$
$524$		0			0
$525$		0			0
$526$	10.0000	−	17.3205i	0.436021	−	0.755210i
$527$		−	8.48528i		−	0.369625i
$528$		0			0
$529$	−9.00000			−0.391304
$530$	−4.89898	−	8.48528i	−0.212798	−	0.368577i
$531$		0			0
$532$		0			0
$533$	33.0681	−	19.0919i	1.43234	−	0.826961i
$534$		0			0
$535$	−6.00000	+	3.46410i	−0.259403	+	0.149766i
$536$	26.9444	−	15.5563i	1.16382	−	0.671932i
$537$		0			0
$538$	−21.0000	+	12.1244i	−0.905374	+	0.522718i
$539$	6.12372	+	7.77817i	0.263767	+	0.335030i
$540$		0			0
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	19.5959			0.841717
$543$		0			0
$544$		0			0
$545$	1.22474	−	2.12132i	0.0524623	−	0.0908674i
$546$		0			0
$547$	5.00000	+	8.66025i	0.213785	+	0.370286i	0.952896	−	0.303298i	$-0.0980876\pi$
$547$	5.00000	+	8.66025i	0.213785	+	0.370286i	−0.739111	+	0.673583i	$0.764754\pi$
$548$		0			0
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−2.44949	+	4.24264i	−0.104352	+	0.180743i
$552$		0			0
$553$	−2.50000	+	12.9904i	−0.106311	+	0.552407i
$554$	−28.1691	−	16.2635i	−1.19679	−	0.690968i
$555$		0			0
$556$		0			0
$557$	13.4722	+	7.77817i	0.570835	+	0.329572i	0.757483	−	0.652855i	$-0.226429\pi$
$557$	13.4722	+	7.77817i	0.570835	+	0.329572i	−0.186648	+	0.982427i	$0.559762\pi$
$558$		0			0
$559$			5.19615i			0.219774i
$560$	4.89898	−	25.4558i	0.207020	−	1.07571i
$561$		0			0
$562$	−32.0000			−1.34984
$563$	−13.4722	−	23.3345i	−0.567785	−	0.983433i	−0.996785	−	0.0801281i	$-0.974467\pi$
$563$	−13.4722	−	23.3345i	−0.567785	−	0.983433i	0.428999	−	0.903305i	$-0.358866\pi$
$564$		0			0
$565$	−3.00000	−	1.73205i	−0.126211	−	0.0728679i
$566$	2.44949			0.102960
$567$		0			0
$568$	20.0000			0.839181
$569$	−1.22474	−	0.707107i	−0.0513440	−	0.0296435i	0.474108	−	0.880467i	$-0.342771\pi$
$569$	−1.22474	−	0.707107i	−0.0513440	−	0.0296435i	−0.525452	+	0.850823i	$0.676104\pi$
$570$		0			0
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	0.727690	−	0.685907i	$-0.240594\pi$
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	−0.957857	+	0.287244i	$0.907261\pi$
$572$		0			0
$573$		0			0
$574$	−18.0000	+	20.7846i	−0.751305	+	0.867533i
$575$			5.65685i			0.235907i
$576$		0			0
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	0.530898	−	0.847436i	$-0.321855\pi$
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	−0.468452	+	0.883489i	$0.655188\pi$
$578$			9.89949i			0.411765i
$579$		0			0
$580$		0			0
$581$	−14.6969	−	12.7279i	−0.609732	−	0.528043i
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−2.44949	+	4.24264i	−0.101361	+	0.175562i
$585$		0			0
$586$	18.0000	−	10.3923i	0.743573	−	0.429302i
$587$	7.34847	+	12.7279i	0.303304	+	0.525338i	0.976882	−	0.213778i	$-0.0685770\pi$
$587$	7.34847	+	12.7279i	0.303304	+	0.525338i	−0.673578	+	0.739116i	$0.735244\pi$
$588$		0			0
$589$	−1.50000	+	2.59808i	−0.0618064	+	0.107052i
$590$			16.9706i			0.698667i
$591$		0			0
$592$	4.00000			0.164399
$593$	−8.57321	−	14.8492i	−0.352060	−	0.609785i	0.634550	−	0.772881i	$-0.281185\pi$
$593$	−8.57321	−	14.8492i	−0.352060	−	0.609785i	−0.986610	+	0.163096i	$0.947852\pi$
$594$		0			0
$595$	−6.00000	+	31.1769i	−0.245976	+	1.27813i
$596$		0			0
$597$		0			0
$598$	36.0000	−	20.7846i	1.47215	−	0.849946i
$599$	4.89898	−	2.82843i	0.200167	−	0.115566i	−0.396566	−	0.918006i	$-0.629798\pi$
$599$	4.89898	−	2.82843i	0.200167	−	0.115566i	0.596733	+	0.802440i	$0.296465\pi$
$600$		0			0
$601$	−22.5000	+	12.9904i	−0.917794	+	0.529889i	−0.882931	−	0.469503i	$-0.844433\pi$
$601$	−22.5000	+	12.9904i	−0.917794	+	0.529889i	−0.0348635	+	0.999392i	$0.511100\pi$
$602$	−1.22474	−	3.53553i	−0.0499169	−	0.144098i
$603$		0			0
$604$		0			0
$605$	22.0454			0.896273
$606$		0			0
$607$		−	39.8372i		−	1.61694i	−0.588537	−	0.808470i	$-0.700296\pi$
$607$		−	39.8372i		−	1.61694i	0.588537	−	0.808470i	$-0.299704\pi$
$608$		0			0
$609$		0			0
$610$	−6.00000	−	10.3923i	−0.242933	−	0.420772i
$611$	55.1135	−	31.8198i	2.22965	−	1.28729i
$612$		0			0
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$	−11.0227	+	19.0919i	−0.444840	+	0.770486i
$615$		0			0
$616$	−10.0000	+	3.46410i	−0.402911	+	0.139573i
$617$	20.8207	+	12.0208i	0.838208	+	0.483940i	0.856655	−	0.515890i	$-0.172539\pi$
$617$	20.8207	+	12.0208i	0.838208	+	0.483940i	−0.0184465	+	0.999830i	$0.505872\pi$
$618$		0			0
$619$			29.4449i			1.18349i	0.806126	+	0.591744i	$0.201561\pi$
$619$			29.4449i			1.18349i	−0.806126	+	0.591744i	$0.798439\pi$
$620$		0			0
$621$		0			0
$622$		−	24.2487i		−	0.972285i
$623$	9.79796	+	8.48528i	0.392547	+	0.339956i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	8.57321	+	14.8492i	0.342655	+	0.593495i
$627$		0			0
$628$		0			0
$629$	−4.89898			−0.195335
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	−12.2474	−	7.07107i	−0.487177	−	0.281272i
$633$		0			0
$634$	10.0000	+	17.3205i	0.397151	+	0.687885i
$635$	26.9444			1.06926
$636$		0			0
$637$	36.0000	−	5.19615i	1.42637	−	0.205879i
$638$			5.65685i			0.223957i
$639$		0			0
$640$	24.0000	+	13.8564i	0.948683	+	0.547723i
$641$			14.1421i			0.558581i	0.960207	+	0.279290i	$0.0900992\pi$
$641$			14.1421i			0.558581i	−0.960207	+	0.279290i	$0.909901\pi$
$642$		0			0
$643$	−22.5000	−	12.9904i	−0.887313	−	0.512291i	−0.0142506	−	0.999898i	$-0.504536\pi$
$643$	−22.5000	−	12.9904i	−0.887313	−	0.512291i	−0.873063	+	0.487608i	$0.837870\pi$
$644$		0			0
$645$		0			0
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	8.57321	−	14.8492i	0.337048	−	0.583784i	−0.646828	−	0.762636i	$-0.723905\pi$
$647$	8.57321	−	14.8492i	0.337048	−	0.583784i	0.983876	+	0.178852i	$0.0572383\pi$
$648$		0			0
$649$	6.00000	−	3.46410i	0.235521	−	0.135978i
$650$	−3.67423	−	6.36396i	−0.144115	−	0.249615i
$651$		0			0
$652$		0			0
$653$		−	7.07107i		−	0.276712i	−0.990383	−	0.138356i	$-0.955818\pi$
$653$		−	7.07107i		−	0.276712i	0.990383	−	0.138356i	$-0.0441819\pi$
$654$		0			0
$655$	6.00000			0.234439
$656$	−14.6969	−	25.4558i	−0.573819	−	0.993884i
$657$		0			0
$658$	−30.0000	+	34.6410i	−1.16952	+	1.35045i
$659$	19.5959	−	11.3137i	0.763349	−	0.440720i	−0.0671481	−	0.997743i	$-0.521390\pi$
$659$	19.5959	−	11.3137i	0.763349	−	0.440720i	0.830497	+	0.557024i	$0.188057\pi$
$660$		0			0
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.0860127	−	0.996294i	$-0.472587\pi$
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.905822	+	0.423658i	$0.139254\pi$
$662$	−37.9671	+	21.9203i	−1.47563	+	0.851957i
$663$		0			0
$664$	18.0000	−	10.3923i	0.698535	−	0.403300i
$665$	7.34847	−	8.48528i	0.284961	−	0.329045i
$666$		0			0
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$		0			0
$669$		0			0
$670$			38.1051i			1.47213i
$671$	−2.44949	+	4.24264i	−0.0945615	+	0.163785i
$672$		0			0
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$	28.1691	−	16.2635i	1.08503	−	0.626445i
$675$		0			0
$676$		0			0
$677$	−4.89898	+	8.48528i	−0.188283	+	0.326116i	−0.944678	−	0.327999i	$-0.893626\pi$
$677$	−4.89898	+	8.48528i	−0.188283	+	0.326116i	0.756395	+	0.654115i	$0.226959\pi$
$678$		0			0
$679$	−18.0000	+	20.7846i	−0.690777	+	0.797640i
$680$	−29.3939	−	16.9706i	−1.12720	−	0.650791i
$681$		0			0
$682$			3.46410i			0.132647i
$683$	−41.6413	−	24.0416i	−1.59336	−	0.919927i	−0.992725	−	0.120405i	$-0.961581\pi$
$683$	−41.6413	−	24.0416i	−1.59336	−	0.919927i	−0.600636	−	0.799522i	$-0.705086\pi$
$684$		0			0
$685$		−	27.7128i		−	1.05885i
$686$	−23.2702	+	12.0208i	−0.888459	+	0.458957i
$687$		0			0
$688$	4.00000			0.152499
$689$	7.34847	+	12.7279i	0.279954	+	0.484895i
$690$		0			0
$691$	−37.5000	−	21.6506i	−1.42657	−	0.823629i	−0.429719	−	0.902963i	$-0.641387\pi$
$691$	−37.5000	−	21.6506i	−1.42657	−	0.823629i	−0.996848	+	0.0793336i	$0.974721\pi$
$692$		0			0
$693$		0			0
$694$	−44.0000			−1.67022
$695$	11.0227	+	6.36396i	0.418115	+	0.241399i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	14.6969			0.556287
$699$		0			0
$700$		0			0
$701$			5.65685i			0.213656i	0.994277	+	0.106828i	$0.0340695\pi$
$701$			5.65685i			0.213656i	−0.994277	+	0.106828i	$0.965931\pi$
$702$		0			0
$703$	1.50000	+	0.866025i	0.0565736	+	0.0326628i
$704$		−	11.3137i		−	0.426401i
$705$		0			0
$706$	21.0000	+	12.1244i	0.790345	+	0.456306i
$707$	−42.8661	+	14.8492i	−1.61214	+	0.558463i
$708$		0			0
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	−0.196167	−	0.980571i	$-0.562849\pi$
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	0.947282	−	0.320400i	$-0.103817\pi$
$710$	−12.2474	+	21.2132i	−0.459639	+	0.796117i
$711$		0			0
$712$	−12.0000	+	6.92820i	−0.449719	+	0.259645i
$713$	−4.89898	−	8.48528i	−0.183468	−	0.317776i
$714$		0			0
$715$	−9.00000	+	15.5885i	−0.336581	+	0.582975i
$716$		0			0
$717$		0			0
$718$	40.0000			1.49279
$719$	13.4722	+	23.3345i	0.502428	+	0.870231i	0.999996	+	0.00280593i	$0.000893157\pi$
$719$	13.4722	+	23.3345i	0.502428	+	0.870231i	−0.497568	+	0.867425i	$0.665774\pi$
$720$		0			0
$721$	−7.50000	−	21.6506i	−0.279315	−	0.806312i
$722$	19.5959	−	11.3137i	0.729285	−	0.421053i
$723$		0			0
$724$		0			0
$725$	−2.44949	+	1.41421i	−0.0909718	+	0.0525226i
$726$		0			0
$727$	−22.5000	+	12.9904i	−0.834479	+	0.481787i	−0.855384	−	0.517995i	$-0.826679\pi$
$727$	−22.5000	+	12.9904i	−0.834479	+	0.481787i	0.0209049	+	0.999781i	$0.493345\pi$
$728$	−7.34847	+	38.1838i	−0.272352	+	1.41518i
$729$		0			0
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	−4.89898			−0.181195
$732$		0			0
$733$		−	39.8372i		−	1.47142i	−0.677297	−	0.735710i	$-0.736849\pi$
$733$		−	39.8372i		−	1.47142i	0.677297	−	0.735710i	$-0.263151\pi$
$734$	−1.22474	+	2.12132i	−0.0452062	+	0.0782994i
$735$		0			0
$736$		0			0
$737$	13.4722	−	7.77817i	0.496255	−	0.286513i
$738$		0			0
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	−0.856683	−	0.515844i	$-0.827478\pi$
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	0.875075	+	0.483987i	$0.160812\pi$
$740$		0			0
$741$		0			0
$742$	−8.00000	−	6.92820i	−0.293689	−	0.254342i
$743$	20.8207	+	12.0208i	0.763836	+	0.441001i	0.830671	−	0.556763i	$-0.187957\pi$
$743$	20.8207	+	12.0208i	0.763836	+	0.441001i	−0.0668353	+	0.997764i	$0.521290\pi$
$744$		0			0
$745$			13.8564i			0.507659i
$746$	−35.5176	−	20.5061i	−1.30039	−	0.750782i
$747$		0			0
$748$		0			0
$749$	−4.89898	+	5.65685i	−0.179005	+	0.206697i
$750$		0			0
$751$	29.0000			1.05823			0.529113	−	0.848552i	$-0.322525\pi$
$751$	29.0000			1.05823			0.529113	+	0.848552i	$0.322525\pi$
$752$	−24.4949	−	42.4264i	−0.893237	−	1.54713i
$753$		0			0
$754$	18.0000	+	10.3923i	0.655521	+	0.378465i
$755$	−53.8888			−1.96121
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	8.57321	+	4.94975i	0.311393	+	0.179783i
$759$		0			0
$760$	6.00000	+	10.3923i	0.217643	+	0.376969i
$761$	24.4949			0.887939			0.443970	−	0.896042i	$-0.353570\pi$
$761$	24.4949			0.887939			0.443970	+	0.896042i	$0.353570\pi$
$762$		0			0
$763$	0.500000	−	2.59808i	0.0181012	−	0.0940567i
$764$		0			0
$765$		0			0
$766$	24.0000	+	13.8564i	0.867155	+	0.500652i
$767$		−	25.4558i		−	0.919157i
$768$		0			0
$769$	−22.5000	−	12.9904i	−0.811371	−	0.468445i	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	−22.5000	−	12.9904i	−0.811371	−	0.468445i	−0.847432	+	0.530904i	$0.821852\pi$
$770$	2.44949	−	12.7279i	0.0882735	−	0.458682i
$771$		0			0
$772$		0			0
$773$	−13.4722	+	23.3345i	−0.484561	+	0.839284i	−0.999843	−	0.0177365i	$-0.994354\pi$
$773$	−13.4722	+	23.3345i	−0.484561	+	0.839284i	0.515282	+	0.857021i	$0.327687\pi$
$774$		0			0
$775$	−1.50000	+	0.866025i	−0.0538816	+	0.0311086i
$776$	−14.6969	−	25.4558i	−0.527589	−	0.913812i
$777$		0			0
$778$	19.0000	−	32.9090i	0.681183	−	1.17984i
$779$		−	12.7279i		−	0.456025i
$780$		0			0
$781$	10.0000			0.357828
$782$	19.5959	+	33.9411i	0.700749	+	1.21373i
$783$		0			0
$784$	−4.00000	−	27.7128i	−0.142857	−	0.989743i
$785$	−36.7423	+	21.2132i	−1.31139	+	0.757132i
$786$		0			0
$787$	39.0000	−	22.5167i	1.39020	−	0.802632i	0.396863	−	0.917878i	$-0.370099\pi$
$787$	39.0000	−	22.5167i	1.39020	−	0.802632i	0.993337	+	0.115246i	$0.0367655\pi$
$788$		0			0
$789$		0			0
$790$	15.0000	−	8.66025i	0.533676	−	0.308118i
$791$	−3.67423	−	0.707107i	−0.130641	−	0.0251418i
$792$		0			0
$793$	9.00000	+	15.5885i	0.319599	+	0.553562i
$794$	−2.44949			−0.0869291
$795$		0			0
$796$		0			0
$797$	14.6969	−	25.4558i	0.520592	−	0.901692i	−0.479121	−	0.877749i	$-0.659045\pi$
$797$	14.6969	−	25.4558i	0.520592	−	0.901692i	0.999713	−	0.0239434i	$-0.00762216\pi$
$798$		0			0
$799$	30.0000	+	51.9615i	1.06132	+	1.83827i
$800$		0			0
$801$		0			0
$802$	−14.0000	+	24.2487i	−0.494357	+	0.856252i
$803$	−1.22474	+	2.12132i	−0.0432203	+	0.0748598i
$804$		0			0
$805$	12.0000	+	34.6410i	0.422944	+	1.22094i
$806$	11.0227	+	6.36396i	0.388258	+	0.224161i
$807$		0			0
$808$		−	48.4974i		−	1.70613i
$809$	35.5176	+	20.5061i	1.24873	+	0.720956i	0.970857	−	0.239661i	$-0.0770363\pi$
$809$	35.5176	+	20.5061i	1.24873	+	0.720956i	0.277876	+	0.960617i	$0.410370\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$		0			0
$813$		0			0
$814$	2.00000			0.0701000
$815$	12.2474	+	21.2132i	0.429009	+	0.743066i
$816$		0			0
$817$	1.50000	+	0.866025i	0.0524784	+	0.0302984i
$818$	46.5403			1.62724
$819$		0			0
$820$		0			0
$821$	20.8207	+	12.0208i	0.726646	+	0.419529i	0.817194	−	0.576363i	$-0.195528\pi$
$821$	20.8207	+	12.0208i	0.726646	+	0.419529i	−0.0905478	+	0.995892i	$0.528862\pi$
$822$		0			0
$823$	17.0000	+	29.4449i	0.592583	+	1.02638i	0.993883	+	0.110437i	$0.0352250\pi$
$823$	17.0000	+	29.4449i	0.592583	+	1.02638i	−0.401300	+	0.915947i	$0.631442\pi$
$824$	24.4949			0.853320
$825$		0			0
$826$	6.00000	+	17.3205i	0.208767	+	0.602658i
$827$		−	7.07107i		−	0.245885i	−0.992414	−	0.122943i	$-0.960767\pi$
$827$		−	7.07107i		−	0.245885i	0.992414	−	0.122943i	$-0.0392331\pi$
$828$		0			0
$829$	1.50000	+	0.866025i	0.0520972	+	0.0300783i	0.525822	−	0.850594i	$-0.323758\pi$
$829$	1.50000	+	0.866025i	0.0520972	+	0.0300783i	−0.473725	+	0.880673i	$0.657091\pi$
$830$			25.4558i			0.883585i
$831$		0			0
$832$	−36.0000	−	20.7846i	−1.24808	−	0.720577i
$833$	4.89898	+	33.9411i	0.169740	+	1.17599i
$834$		0			0
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$		0			0
$837$		0			0
$838$	45.0000	−	25.9808i	1.55450	−	0.897491i
$839$	7.34847	+	12.7279i	0.253697	+	0.439417i	0.964541	−	0.263933i	$-0.0850199\pi$
$839$	7.34847	+	12.7279i	0.253697	+	0.439417i	−0.710844	+	0.703350i	$0.751687\pi$
$840$		0			0
$841$	−10.5000	+	18.1865i	−0.362069	+	0.627122i
$842$		−	1.41421i		−	0.0487370i
$843$		0			0
$844$		0			0
$845$	17.1464	+	29.6985i	0.589855	+	1.02166i
$846$		0			0
$847$	22.5000	−	7.79423i	0.773109	−	0.267813i
$848$	9.79796	−	5.65685i	0.336463	−	0.194257i
$849$		0			0
$850$	6.00000	−	3.46410i	0.205798	−	0.118818i
$851$	−4.89898	+	2.82843i	−0.167935	+	0.0969572i
$852$		0			0
$853$	31.5000	−	18.1865i	1.07854	−	0.622695i	0.148037	−	0.988982i	$-0.452704\pi$
$853$	31.5000	−	18.1865i	1.07854	−	0.622695i	0.930502	+	0.366287i	$0.119371\pi$
$854$	−9.79796	−	8.48528i	−0.335279	−	0.290360i
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	−39.1918			−1.33877			−0.669384	−	0.742917i	$-0.733442\pi$
$857$	−39.1918			−1.33877			−0.669384	+	0.742917i	$0.733442\pi$
$858$		0			0
$859$			38.1051i			1.30013i	0.759879	+	0.650065i	$0.225258\pi$
$859$			38.1051i			1.30013i	−0.759879	+	0.650065i	$0.774742\pi$
$860$		0			0
$861$		0			0
$862$	−11.0000	−	19.0526i	−0.374661	−	0.648933i
$863$	−35.5176	+	20.5061i	−1.20903	+	0.698036i	−0.962548	−	0.271111i	$-0.912609\pi$
$863$	−35.5176	+	20.5061i	−1.20903	+	0.698036i	−0.246485	+	0.969147i	$0.579276\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$	11.0227	−	19.0919i	0.374567	−	0.648769i
$867$		0			0
$868$		0			0
$869$	−6.12372	−	3.53553i	−0.207733	−	0.119935i
$870$		0			0
$871$		−	57.1577i		−	1.93671i
$872$	2.44949	+	1.41421i	0.0829502	+	0.0478913i
$873$		0			0
$874$		−	13.8564i		−	0.468700i
$875$	−24.4949	+	8.48528i	−0.828079	+	0.286855i
$876$		0			0
$877$	20.0000			0.675352			0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000			0.675352			0.337676	+	0.941262i	$0.390359\pi$
$878$	19.5959	+	33.9411i	0.661330	+	1.14546i
$879$		0			0
$880$	12.0000	+	6.92820i	0.404520	+	0.233550i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	11.0000			0.370179			0.185090	−	0.982722i	$-0.440742\pi$
$883$	11.0000			0.370179			0.185090	+	0.982722i	$0.440742\pi$
$884$		0			0
$885$		0			0
$886$	28.0000	+	48.4974i	0.940678	+	1.62930i
$887$	−41.6413			−1.39818			−0.699089	−	0.715034i	$-0.746411\pi$
$887$	−41.6413			−1.39818			−0.699089	+	0.715034i	$0.746411\pi$
$888$		0			0
$889$	27.5000	−	9.52628i	0.922320	−	0.319501i
$890$		−	16.9706i		−	0.568855i
$891$		0			0
$892$		0			0
$893$		−	21.2132i		−	0.709873i
$894$		0			0
$895$	−21.0000	−	12.1244i	−0.701953	−	0.405273i
$896$	29.3939	+	5.65685i	0.981981	+	0.188982i
$897$		0			0
$898$	−5.00000	+	8.66025i	−0.166852	+	0.288996i
$899$	2.44949	−	4.24264i	0.0816951	−	0.141500i
$900$		0			0
$901$	−12.0000	+	6.92820i	−0.399778	+	0.230812i
$902$	−7.34847	−	12.7279i	−0.244677	−	0.423793i
$903$		0			0
$904$	2.00000	−	3.46410i	0.0665190	−	0.115214i
$905$			38.1838i			1.26927i
$906$		0			0
$907$	5.00000			0.166022			0.0830111	−	0.996549i	$-0.473546\pi$
$907$	5.00000			0.166022			0.0830111	+	0.996549i	$0.473546\pi$
$908$		0			0
$909$		0			0
$910$	−36.0000	−	31.1769i	−1.19339	−	1.03350i
$911$	−46.5403	+	26.8701i	−1.54195	+	0.890245i	−0.543233	+	0.839582i	$0.682800\pi$
$911$	−46.5403	+	26.8701i	−1.54195	+	0.890245i	−0.998716	+	0.0506629i	$0.983867\pi$
$912$		0			0
$913$	9.00000	−	5.19615i	0.297857	−	0.171968i
$914$	6.12372	−	3.53553i	0.202555	−	0.116945i
$915$		0			0
$916$		0			0
$917$	6.12372	−	2.12132i	0.202223	−	0.0700522i
$918$		0			0
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	0.691091	−	0.722767i	$-0.257130\pi$
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	−0.971481	+	0.237119i	$0.923797\pi$
$920$	−39.1918			−1.29212
$921$		0			0
$922$		−	20.7846i		−	0.684505i
$923$	18.3712	−	31.8198i	0.604695	−	1.04736i
$924$		0			0
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	−15.9217	+	9.19239i	−0.523219	+	0.302081i
$927$		0			0
$928$		0			0
$929$	28.1691	−	48.7904i	0.924199	−	1.60076i	0.131355	−	0.991335i	$-0.458067\pi$
$929$	28.1691	−	48.7904i	0.924199	−	1.60076i	0.792844	−	0.609425i	$-0.208600\pi$
$930$		0			0
$931$	4.50000	−	11.2583i	0.147482	−	0.368977i
$932$		0			0
$933$		0			0
$934$		−	38.1051i		−	1.24684i
$935$	−14.6969	−	8.48528i	−0.480641	−	0.277498i
$936$		0			0
$937$			46.7654i			1.52776i	0.645359	+	0.763879i	$0.276708\pi$
$937$			46.7654i			1.52776i	−0.645359	+	0.763879i	$0.723292\pi$
$938$	13.4722	+	38.8909i	0.439883	+	1.26983i
$939$		0			0
$940$		0			0
$941$	−24.4949	−	42.4264i	−0.798511	−	1.38306i	−0.920586	−	0.390540i	$-0.872288\pi$
$941$	−24.4949	−	42.4264i	−0.798511	−	1.38306i	0.122075	−	0.992521i	$-0.461045\pi$
$942$		0			0
$943$	36.0000	+	20.7846i	1.17232	+	0.676840i
$944$	−19.5959			−0.637793
$945$		0			0
$946$	2.00000			0.0650256
$947$	42.8661	+	24.7487i	1.39296	+	0.804226i	0.993642	−	0.112586i	$-0.0359135\pi$
$947$	42.8661	+	24.7487i	1.39296	+	0.804226i	0.399318	+	0.916812i	$0.369247\pi$
$948$		0			0
$949$	4.50000	+	7.79423i	0.146076	+	0.253011i
$950$	−2.44949			−0.0794719
$951$		0			0
$952$	−36.0000	−	6.92820i	−1.16677	−	0.224544i
$953$			5.65685i			0.183243i	0.995794	+	0.0916217i	$0.0292051\pi$
$953$			5.65685i			0.183243i	−0.995794	+	0.0916217i	$0.970795\pi$
$954$		0			0
$955$	−3.00000	−	1.73205i	−0.0970777	−	0.0560478i
$956$		0			0
$957$		0			0
$958$	−6.00000	−	3.46410i	−0.193851	−	0.111920i
$959$	−9.79796	−	28.2843i	−0.316393	−	0.913347i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$	3.67423	−	6.36396i	0.118462	−	0.205182i
$963$		0			0
$964$		0			0
$965$	−13.4722	−	23.3345i	−0.433685	−	0.751165i
$966$		0			0
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	−0.742382	−	0.669977i	$-0.766304\pi$
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	0.951408	+	0.307933i	$0.0996374\pi$
$968$			25.4558i			0.818182i
$969$		0			0
$970$	36.0000			1.15589
$971$	−19.5959	−	33.9411i	−0.628863	−	1.08922i	−0.987780	−	0.155853i	$-0.950187\pi$
$971$	−19.5959	−	33.9411i	−0.628863	−	1.08922i	0.358917	−	0.933369i	$-0.383146\pi$
$972$		0			0
$973$	13.5000	+	2.59808i	0.432790	+	0.0832905i
$974$	20.8207	−	12.0208i	0.667137	−	0.385172i
$975$		0			0
$976$	12.0000	−	6.92820i	0.384111	−	0.221766i
$977$	−6.12372	+	3.53553i	−0.195915	+	0.113112i	−0.594749	−	0.803912i	$-0.702748\pi$
$977$	−6.12372	+	3.53553i	−0.195915	+	0.113112i	0.398833	+	0.917023i	$0.369415\pi$
$978$		0			0
$979$	−6.00000	+	3.46410i	−0.191761	+	0.110713i
$980$		0			0
$981$		0			0
$982$	−8.00000	−	13.8564i	−0.255290	−	0.442176i
$983$	4.89898			0.156253			0.0781266	−	0.996943i	$-0.475106\pi$
$983$	4.89898			0.156253			0.0781266	+	0.996943i	$0.475106\pi$
$984$		0			0
$985$		−	48.4974i		−	1.54526i
$986$	−9.79796	+	16.9706i	−0.312031	+	0.540453i
$987$		0			0
$988$		0			0
$989$	−4.89898	+	2.82843i	−0.155778	+	0.0899388i
$990$		0			0
$991$	−17.5000	+	30.3109i	−0.555906	+	0.962857i	0.441927	+	0.897051i	$0.354295\pi$
$991$	−17.5000	+	30.3109i	−0.555906	+	0.962857i	−0.997832	+	0.0658059i	$0.979038\pi$
$992$		0			0
$993$		0			0
$994$	−5.00000	+	25.9808i	−0.158590	+	0.824060i
$995$	−29.3939	−	16.9706i	−0.931849	−	0.538003i
$996$		0			0
$997$			29.4449i			0.932528i	0.884646	+	0.466264i	$0.154400\pi$
$997$			29.4449i			0.932528i	−0.884646	+	0.466264i	$0.845600\pi$
$998$	30.6186	+	17.6777i	0.969216	+	0.559577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.s.d.458.1		4
3.2	odd	2	inner	567.2.s.d.458.2		4
7.5	odd	6		567.2.i.d.215.2		4
9.2	odd	6		567.2.i.d.269.1		4
9.4	even	3		63.2.p.a.17.2	yes	4
9.5	odd	6		63.2.p.a.17.1	✓	4
9.7	even	3		567.2.i.d.269.2		4
21.5	even	6		567.2.i.d.215.1		4
36.23	even	6		1008.2.bt.b.17.2		4
36.31	odd	6		1008.2.bt.b.17.1		4
45.4	even	6		1575.2.bk.c.1151.1		4
45.13	odd	12		1575.2.bc.a.899.2		8
45.14	odd	6		1575.2.bk.c.1151.2		4
45.22	odd	12		1575.2.bc.a.899.3		8
45.23	even	12		1575.2.bc.a.899.4		8
45.32	even	12		1575.2.bc.a.899.1		8
63.4	even	3		441.2.c.a.440.4		4
63.5	even	6		63.2.p.a.26.2	yes	4
63.13	odd	6		441.2.p.a.80.2		4
63.23	odd	6		441.2.p.a.215.2		4
63.31	odd	6		441.2.c.a.440.3		4
63.32	odd	6		441.2.c.a.440.1		4
63.40	odd	6		63.2.p.a.26.1	yes	4
63.41	even	6		441.2.p.a.80.1		4
63.47	even	6	inner	567.2.s.d.26.1		4
63.58	even	3		441.2.p.a.215.1		4
63.59	even	6		441.2.c.a.440.2		4
63.61	odd	6	inner	567.2.s.d.26.2		4
252.31	even	6		7056.2.k.b.881.1		4
252.59	odd	6		7056.2.k.b.881.4		4
252.67	odd	6		7056.2.k.b.881.3		4
252.95	even	6		7056.2.k.b.881.2		4
252.103	even	6		1008.2.bt.b.593.2		4
252.131	odd	6		1008.2.bt.b.593.1		4
315.68	odd	12		1575.2.bc.a.1349.3		8
315.103	even	12		1575.2.bc.a.1349.1		8
315.194	even	6		1575.2.bk.c.26.1		4
315.229	odd	6		1575.2.bk.c.26.2		4
315.257	odd	12		1575.2.bc.a.1349.2		8
315.292	even	12		1575.2.bc.a.1349.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.p.a.17.1	✓	4	9.5	odd	6
63.2.p.a.17.2	yes	4	9.4	even	3
63.2.p.a.26.1	yes	4	63.40	odd	6
63.2.p.a.26.2	yes	4	63.5	even	6
441.2.c.a.440.1		4	63.32	odd	6
441.2.c.a.440.2		4	63.59	even	6
441.2.c.a.440.3		4	63.31	odd	6
441.2.c.a.440.4		4	63.4	even	3
441.2.p.a.80.1		4	63.41	even	6
441.2.p.a.80.2		4	63.13	odd	6
441.2.p.a.215.1		4	63.58	even	3
441.2.p.a.215.2		4	63.23	odd	6
567.2.i.d.215.1		4	21.5	even	6
567.2.i.d.215.2		4	7.5	odd	6
567.2.i.d.269.1		4	9.2	odd	6
567.2.i.d.269.2		4	9.7	even	3
567.2.s.d.26.1		4	63.47	even	6	inner
567.2.s.d.26.2		4	63.61	odd	6	inner
567.2.s.d.458.1		4	1.1	even	1	trivial
567.2.s.d.458.2		4	3.2	odd	2	inner
1008.2.bt.b.17.1		4	36.31	odd	6
1008.2.bt.b.17.2		4	36.23	even	6
1008.2.bt.b.593.1		4	252.131	odd	6
1008.2.bt.b.593.2		4	252.103	even	6
1575.2.bc.a.899.1		8	45.32	even	12
1575.2.bc.a.899.2		8	45.13	odd	12
1575.2.bc.a.899.3		8	45.22	odd	12
1575.2.bc.a.899.4		8	45.23	even	12
1575.2.bc.a.1349.1		8	315.103	even	12
1575.2.bc.a.1349.2		8	315.257	odd	12
1575.2.bc.a.1349.3		8	315.68	odd	12
1575.2.bc.a.1349.4		8	315.292	even	12
1575.2.bk.c.26.1		4	315.194	even	6
1575.2.bk.c.26.2		4	315.229	odd	6
1575.2.bk.c.1151.1		4	45.4	even	6
1575.2.bk.c.1151.2		4	45.14	odd	6
7056.2.k.b.881.1		4	252.31	even	6
7056.2.k.b.881.2		4	252.95	even	6
7056.2.k.b.881.3		4	252.67	odd	6
7056.2.k.b.881.4		4	252.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +1.41421i q^{11} +(4.50000 + 2.59808i) q^{13} +(-3.67423 - 0.707107i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.44949 + 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +5.65685i q^{23} +1.00000 q^{25} +(-3.67423 - 6.36396i) q^{26} +(-2.44949 + 1.41421i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(6.00000 - 3.46410i) q^{34} +(6.12372 - 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} -2.44949 q^{38} +6.92820i q^{40} +(3.67423 - 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} +(6.12372 - 10.6066i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.22474 - 0.707107i) q^{50} +(2.44949 + 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 7.07107i) q^{56} +4.00000 q^{58} +(-2.44949 - 4.24264i) q^{59} +(3.00000 + 1.73205i) q^{61} +2.44949 q^{62} -8.00000 q^{64} +(11.0227 + 6.36396i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-9.00000 - 1.73205i) q^{70} -7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} -1.41421i q^{74} +(1.22474 + 3.53553i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(4.89898 - 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(-3.67423 - 6.36396i) q^{83} +(-6.00000 + 10.3923i) q^{85} -1.41421i q^{86} -4.00000 q^{88} +(2.44949 + 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} +(3.67423 - 2.12132i) q^{95} +(-9.00000 + 5.19615i) q^{97} +(-9.79796 + 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{7}+O(q^{10}) \) 4 * q + 10 * q^7	\( 4 q + 10 q^{7} - 12 q^{10} + 18 q^{13} + 8 q^{16} + 6 q^{19} + 4 q^{22} + 4 q^{25} - 6 q^{31} + 24 q^{34} + 2 q^{37} + 2 q^{43} + 16 q^{46} + 22 q^{49} + 16 q^{58} + 12 q^{61} - 32 q^{64} - 22 q^{67} - 36 q^{70} + 6 q^{73} - 10 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} + 54 q^{91} - 60 q^{94} - 36 q^{97}+O(q^{100}) \) 4 * q + 10 * q^7 - 12 * q^10 + 18 * q^13 + 8 * q^16 + 6 * q^19 + 4 * q^22 + 4 * q^25 - 6 * q^31 + 24 * q^34 + 2 * q^37 + 2 * q^43 + 16 * q^46 + 22 * q^49 + 16 * q^58 + 12 * q^61 - 32 * q^64 - 22 * q^67 - 36 * q^70 + 6 * q^73 - 10 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 + 54 * q^91 - 60 * q^94 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more