LMFDB - Embedded newform 567.2.i.d.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(215,567)]

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([5, 5]))

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

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

chi := DirichletCharacter("567.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.i (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	567.269
Dual form			567.2.i.d.215.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(1.22474 - 2.12132i) q^{5} +(-2.00000 - 1.73205i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q-1.41421i q^{2} +(1.22474 - 2.12132i) q^{5} +(-2.00000 - 1.73205i) q^{7} -2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +(-1.22474 + 0.707107i) q^{11} +(-4.50000 + 2.59808i) q^{13} +(-2.44949 + 2.82843i) q^{14} -4.00000 q^{16} +(2.44949 - 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 + 1.73205i) q^{22} +(4.89898 + 2.82843i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.67423 + 6.36396i) q^{26} +(-2.44949 - 1.41421i) q^{29} -1.73205i q^{31} +(-6.00000 - 3.46410i) q^{34} +(-6.12372 + 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.22474 - 2.12132i) q^{38} +(-6.00000 - 3.46410i) q^{40} +(-3.67423 - 6.36396i) q^{41} +(0.500000 - 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} +12.2474 q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.22474 + 0.707107i) q^{50} +(-2.44949 - 1.41421i) q^{53} +3.46410i q^{55} +(-4.89898 + 5.65685i) q^{56} +(-2.00000 + 3.46410i) q^{58} -4.89898 q^{59} -3.46410i q^{61} -2.44949 q^{62} -8.00000 q^{64} +12.7279i q^{65} +11.0000 q^{67} +(3.00000 + 8.66025i) q^{70} +7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} +(1.22474 - 0.707107i) q^{74} +(3.67423 + 0.707107i) q^{77} +5.00000 q^{79} +(-4.89898 + 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(3.67423 - 6.36396i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(-1.22474 - 0.707107i) q^{86} +(2.00000 + 3.46410i) q^{88} +(-2.44949 - 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} -17.3205i q^{94} -4.24264i q^{95} +(9.00000 + 5.19615i) q^{97} +(9.79796 - 1.41421i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{7}+O(q^{10}) $ 4 * q - 8 * q^7	$ 4 q - 8 q^{7} - 12 q^{10} - 18 q^{13} - 16 q^{16} + 6 q^{19} + 4 q^{22} - 2 q^{25} - 24 q^{34} + 2 q^{37} - 24 q^{40} + 2 q^{43} + 16 q^{46} + 4 q^{49} - 8 q^{58} - 32 q^{64} + 44 q^{67} + 12 q^{70} + 6 q^{73} + 20 q^{79} - 36 q^{82} - 24 q^{85} + 8 q^{88} + 54 q^{91} + 36 q^{97}+O(q^{100}) $ 4 * q - 8 * q^7 - 12 * q^10 - 18 * q^13 - 16 * q^16 + 6 * q^19 + 4 * q^22 - 2 * q^25 - 24 * q^34 + 2 * q^37 - 24 * q^40 + 2 * q^43 + 16 * q^46 + 4 * q^49 - 8 * q^58 - 32 * q^64 + 44 * q^67 + 12 * q^70 + 6 * q^73 + 20 * q^79 - 36 * q^82 - 24 * q^85 + 8 * q^88 + 54 * q^91 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.41421i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$		−	1.41421i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	−0.450708	−	0.892672i	$-0.648828\pi$
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	0.998430	−	0.0560116i	$-0.0178384\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	−3.00000	−	1.73205i	−0.948683	−	0.547723i
$11$	−1.22474	+	0.707107i	−0.369274	+	0.213201i	−0.673141	−	0.739514i	$-0.735055\pi$
$11$	−1.22474	+	0.707107i	−0.369274	+	0.213201i	0.303867	+	0.952714i	$0.401722\pi$
$12$		0			0
$13$	−4.50000	+	2.59808i	−1.24808	+	0.720577i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−4.50000	+	2.59808i	−1.24808	+	0.720577i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−2.44949	+	2.82843i	−0.654654	+	0.755929i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	2.44949	−	4.24264i	0.594089	−	1.02899i	−0.399586	−	0.916696i	$-0.630846\pi$
$17$	2.44949	−	4.24264i	0.594089	−	1.02899i	0.993675	−	0.112296i	$-0.0358205\pi$
$18$		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
$23$	4.89898	+	2.82843i	1.02151	+	0.589768i	0.914540	−	0.404495i	$-0.132553\pi$
$23$	4.89898	+	2.82843i	1.02151	+	0.589768i	0.106967	+	0.994263i	$0.465886\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.67423	+	6.36396i	0.720577	+	1.24808i
$27$		0			0
$28$		0			0
$29$	−2.44949	−	1.41421i	−0.454859	−	0.262613i	0.255021	−	0.966935i	$-0.417918\pi$
$29$	−2.44949	−	1.41421i	−0.454859	−	0.262613i	−0.709880	+	0.704323i	$0.751251\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		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	$0.807139\pi$
$38$	−1.22474	−	2.12132i	−0.198680	−	0.344124i
$39$		0			0
$40$	−6.00000	−	3.46410i	−0.948683	−	0.547723i
$41$	−3.67423	−	6.36396i	−0.573819	−	0.993884i	−0.996169	−	0.0874508i	$-0.972128\pi$
$41$	−3.67423	−	6.36396i	−0.573819	−	0.993884i	0.422350	−	0.906433i	$-0.361205\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$		0			0
$45$		0			0
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	12.2474			1.78647			0.893237	−	0.449586i	$-0.148429\pi$
$47$	12.2474			1.78647			0.893237	+	0.449586i	$0.148429\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−1.22474	+	0.707107i	−0.173205	+	0.100000i
$51$		0			0
$52$		0			0
$53$	−2.44949	−	1.41421i	−0.336463	−	0.194257i	0.322244	−	0.946657i	$-0.395563\pi$
$53$	−2.44949	−	1.41421i	−0.336463	−	0.194257i	−0.658707	+	0.752400i	$0.728896\pi$
$54$		0			0
$55$			3.46410i			0.467099i
$56$	−4.89898	+	5.65685i	−0.654654	+	0.755929i
$57$		0			0
$58$	−2.00000	+	3.46410i	−0.262613	+	0.454859i
$59$	−4.89898			−0.637793			−0.318896	−	0.947790i	$-0.603312\pi$
$59$	−4.89898			−0.637793			−0.318896	+	0.947790i	$0.603312\pi$
$60$		0			0
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$	−2.44949			−0.311086
$63$		0			0
$64$	−8.00000			−1.00000
$65$			12.7279i			1.57870i
$66$		0			0
$67$	11.0000			1.34386			0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000			1.34386			0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$	3.00000	+	8.66025i	0.358569	+	1.03510i
$71$			7.07107i			0.839181i	0.907713	+	0.419591i	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$		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	$0.634347\pi$
$74$	1.22474	−	0.707107i	0.142374	−	0.0821995i
$75$		0			0
$76$		0			0
$77$	3.67423	+	0.707107i	0.418718	+	0.0805823i
$78$		0			0
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$	−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	$-0.701197\pi$
$83$	3.67423	−	6.36396i	0.403300	−	0.698535i	0.994122	+	0.108266i	$0.0345299\pi$
$84$		0			0
$85$	−6.00000	−	10.3923i	−0.650791	−	1.12720i
$86$	−1.22474	−	0.707107i	−0.132068	−	0.0762493i
$87$		0			0
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−2.44949	−	4.24264i	−0.259645	−	0.449719i	0.706502	−	0.707712i	$-0.250272\pi$
$89$	−2.44949	−	4.24264i	−0.259645	−	0.449719i	−0.966147	+	0.257993i	$0.916939\pi$
$90$		0			0
$91$	13.5000	+	2.59808i	1.41518	+	0.272352i
$92$		0			0
$93$		0			0
$94$		−	17.3205i		−	1.78647i
$95$		−	4.24264i		−	0.435286i
$96$		0			0
$97$	9.00000	+	5.19615i	0.913812	+	0.527589i	0.881656	−	0.471894i	$-0.156429\pi$
$97$	9.00000	+	5.19615i	0.913812	+	0.527589i	0.0321560	+	0.999483i	$0.489763\pi$
$98$	9.79796	−	1.41421i	0.989743	−	0.142857i
$99$		0			0
$100$		0			0
$101$	−8.57321	−	14.8492i	−0.853067	−	1.47755i	−0.878427	−	0.477876i	$-0.841407\pi$
$101$	−8.57321	−	14.8492i	−0.853067	−	1.47755i	0.0253604	−	0.999678i	$-0.491927\pi$
$102$		0			0
$103$	7.50000	+	4.33013i	0.738997	+	0.426660i	0.821705	−	0.569914i	$-0.193023\pi$
$103$	7.50000	+	4.33013i	0.738997	+	0.426660i	−0.0827075	+	0.996574i	$0.526357\pi$
$104$	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	−0.376905	−	0.926252i	$-0.623012\pi$
$107$	2.44949	−	1.41421i	0.236801	−	0.136717i	0.613706	+	0.789535i	$0.289678\pi$
$108$		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	$0.151417\pi$
$110$	4.89898			0.467099
$111$		0			0
$112$	8.00000	+	6.92820i	0.755929	+	0.654654i
$113$	−1.22474	+	0.707107i	−0.115214	+	0.0665190i	−0.556500	−	0.830848i	$-0.687856\pi$
$113$	−1.22474	+	0.707107i	−0.115214	+	0.0665190i	0.441285	+	0.897367i	$0.354523\pi$
$114$		0			0
$115$	12.0000	−	6.92820i	1.11901	−	0.646058i
$116$		0			0
$117$		0			0
$118$			6.92820i			0.637793i
$119$	−12.2474	+	4.24264i	−1.12272	+	0.388922i
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$	−4.89898			−0.443533
$123$		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	$0.337710\pi$
$128$			11.3137i			1.00000i
$129$		0			0
$130$	18.0000			1.57870
$131$	1.22474	−	2.12132i	0.107006	−	0.185341i	−0.807550	−	0.589799i	$-0.799207\pi$
$131$	1.22474	−	2.12132i	0.107006	−	0.185341i	0.914556	+	0.404459i	$0.132540\pi$
$132$		0			0
$133$	−4.50000	−	0.866025i	−0.390199	−	0.0750939i
$134$		−	15.5563i		−	1.34386i
$135$		0			0
$136$	−12.0000	−	6.92820i	−1.02899	−	0.594089i
$137$	9.79796	−	5.65685i	0.837096	−	0.483298i	−0.0191800	−	0.999816i	$-0.506106\pi$
$137$	9.79796	−	5.65685i	0.837096	−	0.483298i	0.856276	+	0.516518i	$0.172772\pi$
$138$		0			0
$139$	−4.50000	+	2.59808i	−0.381685	+	0.220366i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−4.50000	+	2.59808i	−0.381685	+	0.220366i	0.296866	+	0.954919i	$0.404058\pi$
$140$		0			0
$141$		0			0
$142$	10.0000			0.839181
$143$	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
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	0.687062	−	0.726599i	$-0.258900\pi$
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	−0.285722	+	0.958313i	$0.592233\pi$
$150$		0			0
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.833597	+	0.552372i	$0.186277\pi$
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.0615699	+	0.998103i	$0.480389\pi$
$152$	−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
$157$		−	17.3205i		−	1.38233i	−0.722698	−	0.691164i	$-0.757098\pi$
$157$		−	17.3205i		−	1.38233i	0.722698	−	0.691164i	$-0.242902\pi$
$158$		−	7.07107i		−	0.562544i
$159$		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
$166$	−9.00000	−	5.19615i	−0.698535	−	0.403300i
$167$	−3.67423	−	6.36396i	−0.284321	−	0.492458i	0.688123	−	0.725594i	$-0.258435\pi$
$167$	−3.67423	−	6.36396i	−0.284321	−	0.492458i	−0.972444	+	0.233136i	$0.925101\pi$
$168$		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
$173$	−9.79796			−0.744925			−0.372463	−	0.928047i	$-0.621486\pi$
$173$	−9.79796			−0.744925			−0.372463	+	0.928047i	$0.621486\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$	4.89898	−	2.82843i	0.369274	−	0.213201i
$177$		0			0
$178$	−6.00000	+	3.46410i	−0.449719	+	0.259645i
$179$	8.57321	+	4.94975i	0.640792	+	0.369961i	0.784920	−	0.619598i	$-0.212704\pi$
$179$	8.57321	+	4.94975i	0.640792	+	0.369961i	−0.144127	+	0.989559i	$0.546038\pi$
$180$		0			0
$181$			15.5885i			1.15868i	0.815086	+	0.579340i	$0.196690\pi$
$181$			15.5885i			1.15868i	−0.815086	+	0.579340i	$0.803310\pi$
$182$	3.67423	−	19.0919i	0.272352	−	1.41518i
$183$		0			0
$184$	8.00000	−	13.8564i	0.589768	−	1.02151i
$185$	2.44949			0.180090
$186$		0			0
$187$			6.92820i			0.506640i
$188$		0			0
$189$		0			0
$190$	−6.00000			−0.435286
$191$		−	1.41421i		−	0.102329i	−0.998690	−	0.0511645i	$-0.983707\pi$
$191$		−	1.41421i		−	0.102329i	0.998690	−	0.0511645i	$-0.0162933\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	7.34847	−	12.7279i	0.527589	−	0.913812i
$195$		0			0
$196$		0			0
$197$			19.7990i			1.41062i	0.708899	+	0.705310i	$0.249192\pi$
$197$			19.7990i			1.41062i	−0.708899	+	0.705310i	$0.750808\pi$
$198$		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	$0.830082\pi$
$200$	−2.44949	+	1.41421i	−0.173205	+	0.100000i
$201$		0			0
$202$	−21.0000	+	12.1244i	−1.47755	+	0.853067i
$203$	2.44949	+	7.07107i	0.171920	+	0.496292i
$204$		0			0
$205$	−18.0000			−1.25717
$206$	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	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$		0			0
$213$		0			0
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	−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
$221$			25.4558i			1.71235i
$222$		0			0
$223$	−18.0000	−	10.3923i	−1.20537	−	0.695920i	−0.243625	−	0.969870i	$-0.578337\pi$
$223$	−18.0000	−	10.3923i	−1.20537	−	0.695920i	−0.961744	+	0.273949i	$0.911670\pi$
$224$		0			0
$225$		0			0
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$	13.4722	+	23.3345i	0.894181	+	1.54877i	0.834815	+	0.550530i	$0.185575\pi$
$227$	13.4722	+	23.3345i	0.894181	+	1.54877i	0.0593658	+	0.998236i	$0.481092\pi$
$228$		0			0
$229$	−19.5000	−	11.2583i	−1.28860	−	0.743971i	−0.310192	−	0.950674i	$-0.600393\pi$
$229$	−19.5000	−	11.2583i	−1.28860	−	0.743971i	−0.978404	+	0.206702i	$0.933727\pi$
$230$	−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	−0.753807	−	0.657095i	$-0.771785\pi$
$233$	−8.57321	+	4.94975i	−0.561650	+	0.324269i	0.192158	+	0.981364i	$0.438452\pi$
$234$		0			0
$235$	15.0000	−	25.9808i	0.978492	−	1.69480i
$236$		0			0
$237$		0			0
$238$	6.00000	+	17.3205i	0.388922	+	1.12272i
$239$	−23.2702	+	13.4350i	−1.50522	+	0.869040i	−0.505239	+	0.862979i	$0.668596\pi$
$239$	−23.2702	+	13.4350i	−1.50522	+	0.869040i	−0.999982	+	0.00606055i	$0.998071\pi$
$240$		0			0
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	−0.0609515	−	0.998141i	$-0.519414\pi$
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	0.833939	+	0.551856i	$0.186080\pi$
$242$	11.0227	+	6.36396i	0.708566	+	0.409091i
$243$		0			0
$244$		0			0
$245$	15.9217	+	6.36396i	1.01720	+	0.406579i
$246$		0			0
$247$	−4.50000	+	7.79423i	−0.286328	+	0.495935i
$248$	−4.89898			−0.311086
$249$		0			0
$250$		−	13.8564i		−	0.876356i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$		−	15.5563i		−	0.976092i
$255$		0			0
$256$		0			0
$257$	1.22474	−	2.12132i	0.0763975	−	0.132324i	−0.825296	−	0.564701i	$-0.808992\pi$
$257$	1.22474	−	2.12132i	0.0763975	−	0.132324i	0.901693	+	0.432377i	$0.142325\pi$
$258$		0			0
$259$	0.500000	−	2.59808i	0.0310685	−	0.161437i
$260$		0			0
$261$		0			0
$262$	−3.00000	−	1.73205i	−0.185341	−	0.107006i
$263$	−12.2474	+	7.07107i	−0.755210	+	0.436021i	−0.827573	−	0.561358i	$-0.810279\pi$
$263$	−12.2474	+	7.07107i	−0.755210	+	0.436021i	0.0723633	+	0.997378i	$0.476946\pi$
$264$		0			0
$265$	−6.00000	+	3.46410i	−0.368577	+	0.212798i
$266$	−1.22474	+	6.36396i	−0.0750939	+	0.390199i
$267$		0			0
$268$		0			0
$269$	−8.57321	+	14.8492i	−0.522718	+	0.905374i	0.476932	+	0.878940i	$0.341749\pi$
$269$	−8.57321	+	14.8492i	−0.522718	+	0.905374i	−0.999651	+	0.0264343i	$0.991585\pi$
$270$		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
$275$	1.22474	+	0.707107i	0.0738549	+	0.0426401i
$276$		0			0
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	−0.971521	−	0.236953i	$-0.923851\pi$
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	0.280553	−	0.959839i	$-0.409482\pi$
$278$	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	0.953443	−	0.301573i	$-0.0975118\pi$
$281$	19.5959	+	11.3137i	1.16899	+	0.674919i	0.215551	+	0.976492i	$0.430845\pi$
$282$		0			0
$283$		−	1.73205i		−	0.102960i	−0.998674	−	0.0514799i	$-0.983606\pi$
$283$		−	1.73205i		−	0.102960i	0.998674	−	0.0514799i	$-0.0163938\pi$
$284$		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
$290$	4.89898	+	8.48528i	0.287678	+	0.498273i
$291$		0			0
$292$		0			0
$293$	7.34847	+	12.7279i	0.429302	+	0.743573i	0.996811	−	0.0797939i	$-0.0254262\pi$
$293$	7.34847	+	12.7279i	0.429302	+	0.743573i	−0.567509	+	0.823367i	$0.692093\pi$
$294$		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
$299$	−29.3939			−1.69989
$300$		0			0
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$	26.9444	−	15.5563i	1.55048	−	0.895167i
$303$		0			0
$304$	−6.00000	+	3.46410i	−0.344124	+	0.198680i
$305$	−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
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	17.1464			0.972285			0.486142	−	0.873880i	$-0.338404\pi$
$311$	17.1464			0.972285			0.486142	+	0.873880i	$0.338404\pi$
$312$		0			0
$313$			12.1244i			0.685309i	0.939461	+	0.342655i	$0.111326\pi$
$313$			12.1244i			0.685309i	−0.939461	+	0.342655i	$0.888674\pi$
$314$	−24.4949			−1.38233
$315$		0			0
$316$		0			0
$317$		−	14.1421i		−	0.794301i	−0.917753	−	0.397151i	$-0.869999\pi$
$317$		−	14.1421i		−	0.794301i	0.917753	−	0.397151i	$-0.130001\pi$
$318$		0			0
$319$	4.00000			0.223957
$320$	−9.79796	+	16.9706i	−0.547723	+	0.948683i
$321$		0			0
$322$	−20.0000	+	6.92820i	−1.11456	+	0.386094i
$323$		−	8.48528i		−	0.472134i
$324$		0			0
$325$	4.50000	+	2.59808i	0.249615	+	0.144115i
$326$	12.2474	−	7.07107i	0.678323	−	0.391630i
$327$		0			0
$328$	−18.0000	+	10.3923i	−0.993884	+	0.573819i
$329$	−24.4949	−	21.2132i	−1.35045	−	1.16952i
$330$		0			0
$331$	−31.0000			−1.70391			−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−31.0000			−1.70391			−0.851957	+	0.523612i	$0.824584\pi$
$332$		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	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$	−17.1464	−	9.89949i	−0.932643	−	0.538462i
$339$		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
$346$			13.8564i			0.744925i
$347$		−	31.1127i		−	1.67022i	−0.550085	−	0.835109i	$-0.685405\pi$
$347$		−	31.1127i		−	1.67022i	0.550085	−	0.835109i	$-0.314595\pi$
$348$		0			0
$349$	9.00000	+	5.19615i	0.481759	+	0.278144i	0.721149	−	0.692780i	$-0.243614\pi$
$349$	9.00000	+	5.19615i	0.481759	+	0.278144i	−0.239390	+	0.970923i	$0.576948\pi$
$350$	3.67423	+	0.707107i	0.196396	+	0.0377964i
$351$		0			0
$352$		0			0
$353$	−8.57321	−	14.8492i	−0.456306	−	0.790345i	0.542456	−	0.840084i	$-0.317494\pi$
$353$	−8.57321	−	14.8492i	−0.456306	−	0.790345i	−0.998762	+	0.0497387i	$0.984161\pi$
$354$		0			0
$355$	15.0000	+	8.66025i	0.796117	+	0.459639i
$356$		0			0
$357$		0			0
$358$	7.00000	−	12.1244i	0.369961	−	0.640792i
$359$	24.4949	−	14.1421i	1.29279	−	0.746393i	0.313643	−	0.949541i	$-0.398450\pi$
$359$	24.4949	−	14.1421i	1.29279	−	0.746393i	0.979148	+	0.203148i	$0.0651171\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	22.0454			1.15868
$363$		0			0
$364$		0			0
$365$	3.67423	−	2.12132i	0.192318	−	0.111035i
$366$		0			0
$367$	−1.50000	+	0.866025i	−0.0782994	+	0.0452062i	−0.538639	−	0.842537i	$-0.681061\pi$
$367$	−1.50000	+	0.866025i	−0.0782994	+	0.0452062i	0.460339	+	0.887743i	$0.347728\pi$
$368$	−19.5959	−	11.3137i	−1.02151	−	0.589768i
$369$		0			0
$370$		−	3.46410i		−	0.180090i
$371$	2.44949	+	7.07107i	0.127171	+	0.367112i
$372$		0			0
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$	9.79796			0.506640
$375$		0			0
$376$		−	34.6410i		−	1.78647i
$377$	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
$382$	−2.00000			−0.102329
$383$	−9.79796	+	16.9706i	−0.500652	+	0.867155i	0.499347	+	0.866402i	$0.333573\pi$
$383$	−9.79796	+	16.9706i	−0.500652	+	0.867155i	−1.00000		0.000753393i	$0.999760\pi$
$384$		0			0
$385$	6.00000	−	6.92820i	0.305788	−	0.353094i
$386$		−	15.5563i		−	0.791797i
$387$		0			0
$388$		0			0
$389$	−23.2702	+	13.4350i	−1.17984	+	0.681183i	−0.955978	−	0.293437i	$-0.905201\pi$
$389$	−23.2702	+	13.4350i	−1.17984	+	0.681183i	−0.223865	+	0.974620i	$0.571868\pi$
$390$		0			0
$391$	24.0000	−	13.8564i	1.21373	−	0.700749i
$392$	19.5959	−	2.82843i	0.989743	−	0.142857i
$393$		0			0
$394$	28.0000			1.41062
$395$	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
$401$	−17.1464	−	9.89949i	−0.856252	−	0.494357i	0.00650355	−	0.999979i	$-0.497930\pi$
$401$	−17.1464	−	9.89949i	−0.856252	−	0.494357i	−0.862755	+	0.505622i	$0.831263\pi$
$402$		0			0
$403$	4.50000	+	7.79423i	0.224161	+	0.388258i
$404$		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
$409$		−	32.9090i		−	1.62724i	−0.581394	−	0.813622i	$-0.697493\pi$
$409$		−	32.9090i		−	1.62724i	0.581394	−	0.813622i	$-0.302507\pi$
$410$			25.4558i			1.25717i
$411$		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
$418$	3.00000	+	1.73205i	0.146735	+	0.0847174i
$419$	18.3712	+	31.8198i	0.897491	+	1.55450i	0.830692	+	0.556733i	$0.187945\pi$
$419$	18.3712	+	31.8198i	0.897491	+	1.55450i	0.0667989	+	0.997766i	$0.478721\pi$
$420$		0			0
$421$	0.500000	−	0.866025i	0.0243685	−	0.0422075i	−0.853584	−	0.520955i	$-0.825576\pi$
$421$	0.500000	−	0.866025i	0.0243685	−	0.0422075i	0.877952	+	0.478748i	$0.158909\pi$
$422$	26.9444	−	15.5563i	1.31163	−	0.757271i
$423$		0			0
$424$	−4.00000	+	6.92820i	−0.194257	+	0.336463i
$425$	−4.89898			−0.237635
$426$		0			0
$427$	−6.00000	+	6.92820i	−0.290360	+	0.335279i
$428$		0			0
$429$		0			0
$430$	−3.00000	+	1.73205i	−0.144673	+	0.0835269i
$431$	−13.4722	−	7.77817i	−0.648933	−	0.374661i	0.139114	−	0.990276i	$-0.455574\pi$
$431$	−13.4722	−	7.77817i	−0.648933	−	0.374661i	−0.788047	+	0.615615i	$0.788908\pi$
$432$		0			0
$433$			15.5885i			0.749133i	0.927200	+	0.374567i	$0.122209\pi$
$433$			15.5885i			0.749133i	−0.927200	+	0.374567i	$0.877791\pi$
$434$	4.89898	+	4.24264i	0.235159	+	0.203653i
$435$		0			0
$436$		0			0
$437$	9.79796			0.468700
$438$		0			0
$439$			27.7128i			1.32266i	0.750095	+	0.661330i	$0.230008\pi$
$439$			27.7128i			1.32266i	−0.750095	+	0.661330i	$0.769992\pi$
$440$	9.79796			0.467099
$441$		0			0
$442$	36.0000			1.71235
$443$		−	39.5980i		−	1.88136i	−0.339300	−	0.940678i	$-0.610190\pi$
$443$		−	39.5980i		−	1.88136i	0.339300	−	0.940678i	$-0.389810\pi$
$444$		0			0
$445$	−12.0000			−0.568855
$446$	−14.6969	+	25.4558i	−0.695920	+	1.20537i
$447$		0			0
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$			7.07107i			0.333704i	0.985982	+	0.166852i	$0.0533603\pi$
$449$			7.07107i			0.333704i	−0.985982	+	0.166852i	$0.946640\pi$
$450$		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
$455$	22.0454	−	25.4558i	1.03350	−	1.19339i
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	−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	$-0.944523\pi$
$461$	−7.34847	+	12.7279i	−0.342252	+	0.592798i	0.642598	+	0.766203i	$0.277856\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$	9.79796	+	5.65685i	0.454859	+	0.262613i
$465$		0			0
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−13.4722	−	23.3345i	−0.623419	−	1.07979i	−0.988844	−	0.148952i	$-0.952410\pi$
$467$	−13.4722	−	23.3345i	−0.623419	−	1.07979i	0.365426	−	0.930841i	$-0.380923\pi$
$468$		0			0
$469$	−22.0000	−	19.0526i	−1.01587	−	0.879765i
$470$	−36.7423	−	21.2132i	−1.69480	−	0.978492i
$471$		0			0
$472$			13.8564i			0.637793i
$473$			1.41421i			0.0650256i
$474$		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
$479$	2.44949	+	4.24264i	0.111920	+	0.193851i	0.916544	−	0.399933i	$-0.130967\pi$
$479$	2.44949	+	4.24264i	0.111920	+	0.193851i	−0.804624	+	0.593784i	$0.797633\pi$
$480$		0			0
$481$	−4.50000	−	2.59808i	−0.205182	−	0.118462i
$482$	−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	$0.292524\pi$
$488$	−9.79796			−0.443533
$489$		0			0
$490$	9.00000	−	22.5167i	0.406579	−	1.01720i
$491$	9.79796	−	5.65685i	0.442176	−	0.255290i	−0.262344	−	0.964974i	$-0.584496\pi$
$491$	9.79796	−	5.65685i	0.442176	−	0.255290i	0.704520	+	0.709684i	$0.251162\pi$
$492$		0			0
$493$	−12.0000	+	6.92820i	−0.540453	+	0.312031i
$494$	11.0227	+	6.36396i	0.495935	+	0.286328i
$495$		0			0
$496$			6.92820i			0.311086i
$497$	12.2474	−	14.1421i	0.549373	−	0.634361i
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.0454			−0.982956			−0.491478	−	0.870890i	$-0.663543\pi$
$503$	−22.0454			−0.982956			−0.491478	+	0.870890i	$0.663543\pi$
$504$		0			0
$505$	−42.0000			−1.86898
$506$			11.3137i			0.502956i
$507$		0			0
$508$		0			0
$509$	1.22474	−	2.12132i	0.0542859	−	0.0940259i	−0.837605	−	0.546276i	$-0.816045\pi$
$509$	1.22474	−	2.12132i	0.0542859	−	0.0940259i	0.891891	+	0.452250i	$0.149378\pi$
$510$		0			0
$511$	−1.50000	−	4.33013i	−0.0663561	−	0.191554i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−3.00000	−	1.73205i	−0.132324	−	0.0763975i
$515$	18.3712	−	10.6066i	0.809531	−	0.467383i
$516$		0			0
$517$	−15.0000	+	8.66025i	−0.659699	+	0.380878i
$518$	−3.67423	−	0.707107i	−0.161437	−	0.0310685i
$519$		0			0
$520$	36.0000			1.57870
$521$	2.44949	−	4.24264i	0.107314	−	0.185873i	−0.807367	−	0.590049i	$-0.799108\pi$
$521$	2.44949	−	4.24264i	0.107314	−	0.185873i	0.914681	+	0.404176i	$0.132442\pi$
$522$		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
$527$	−7.34847	−	4.24264i	−0.320104	−	0.184812i
$528$		0			0
$529$	4.50000	+	7.79423i	0.195652	+	0.338880i
$530$	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
$535$		−	6.92820i		−	0.299532i
$536$		−	31.1127i		−	1.34386i
$537$		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	$0.952416\pi$
$542$	9.79796	+	16.9706i	0.420858	+	0.728948i
$543$		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	−0.739111	−	0.673583i	$-0.764754\pi$
$547$	5.00000	−	8.66025i	0.213785	−	0.370286i	0.952896	+	0.303298i	$0.0980876\pi$
$548$		0			0
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−4.89898			−0.208704
$552$		0			0
$553$	−10.0000	−	8.66025i	−0.425243	−	0.368271i
$554$	−28.1691	+	16.2635i	−1.19679	+	0.690968i
$555$		0			0
$556$		0			0
$557$	−13.4722	−	7.77817i	−0.570835	−	0.329572i	0.186648	−	0.982427i	$-0.440238\pi$
$557$	−13.4722	−	7.77817i	−0.570835	−	0.329572i	−0.757483	+	0.652855i	$0.773571\pi$
$558$		0			0
$559$			5.19615i			0.219774i
$560$	24.4949	−	8.48528i	1.03510	−	0.358569i
$561$		0			0
$562$	16.0000	−	27.7128i	0.674919	−	1.16899i
$563$	−26.9444			−1.13557			−0.567785	−	0.823177i	$-0.692200\pi$
$563$	−26.9444			−1.13557			−0.567785	+	0.823177i	$0.692200\pi$
$564$		0			0
$565$			3.46410i			0.145736i
$566$	−2.44949			−0.102960
$567$		0			0
$568$	20.0000			0.839181
$569$		−	1.41421i		−	0.0592869i	−0.999561	−	0.0296435i	$-0.990563\pi$
$569$		−	1.41421i		−	0.0592869i	0.999561	−	0.0296435i	$-0.00943719\pi$
$570$		0			0
$571$	11.0000			0.460336			0.230168	−	0.973151i	$-0.426072\pi$
$571$	11.0000			0.460336			0.230168	+	0.973151i	$0.426072\pi$
$572$		0			0
$573$		0			0
$574$	27.0000	+	5.19615i	1.12696	+	0.216883i
$575$		−	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	$0.655188\pi$
$578$	−8.57321	+	4.94975i	−0.356599	+	0.205882i
$579$		0			0
$580$		0			0
$581$	−18.3712	+	6.36396i	−0.762165	+	0.264022i
$582$		0			0
$583$	4.00000			0.165663
$584$	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	$-0.931423\pi$
$587$	−7.34847	+	12.7279i	−0.303304	+	0.525338i	0.673578	+	0.739116i	$0.264756\pi$
$588$		0			0
$589$	−1.50000	−	2.59808i	−0.0618064	−	0.107052i
$590$	14.6969	+	8.48528i	0.605063	+	0.349334i
$591$		0			0
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	8.57321	+	14.8492i	0.352060	+	0.609785i	0.986610	−	0.163096i	$-0.0521481\pi$
$593$	8.57321	+	14.8492i	0.352060	+	0.609785i	−0.634550	+	0.772881i	$0.718815\pi$
$594$		0			0
$595$	−6.00000	+	31.1769i	−0.245976	+	1.27813i
$596$		0			0
$597$		0			0
$598$			41.5692i			1.69989i
$599$		−	5.65685i		−	0.231133i	−0.993300	−	0.115566i	$-0.963132\pi$
$599$		−	5.65685i		−	0.231133i	0.993300	−	0.115566i	$-0.0368683\pi$
$600$		0			0
$601$	22.5000	+	12.9904i	0.917794	+	0.529889i	0.882931	−	0.469503i	$-0.155567\pi$
$601$	22.5000	+	12.9904i	0.917794	+	0.529889i	0.0348635	+	0.999392i	$0.488900\pi$
$602$	1.22474	+	3.53553i	0.0499169	+	0.144098i
$603$		0			0
$604$		0			0
$605$	11.0227	+	19.0919i	0.448137	+	0.776195i
$606$		0			0
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.994424	−	0.105453i	$-0.0336291\pi$
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.405887	+	0.913923i	$0.366962\pi$
$608$		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	$0.218319\pi$
$614$	−22.0454			−0.889680
$615$		0			0
$616$	2.00000	−	10.3923i	0.0805823	−	0.418718i
$617$	20.8207	−	12.0208i	0.838208	−	0.483940i	−0.0184465	−	0.999830i	$-0.505872\pi$
$617$	20.8207	−	12.0208i	0.838208	−	0.483940i	0.856655	+	0.515890i	$0.172539\pi$
$618$		0			0
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.109403	−	0.993997i	$-0.465106\pi$
$619$	25.5000	−	14.7224i	1.02493	−	0.591744i	0.915529	+	0.402253i	$0.131773\pi$
$620$		0			0
$621$		0			0
$622$		−	24.2487i		−	0.972285i
$623$	−2.44949	+	12.7279i	−0.0981367	+	0.509933i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	17.1464			0.685309
$627$		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	$0.226967\pi$
$632$		−	14.1421i		−	0.562544i
$633$		0			0
$634$	−20.0000			−0.794301
$635$	13.4722	−	23.3345i	0.534628	−	0.926002i
$636$		0			0
$637$	−22.5000	−	28.5788i	−0.891482	−	1.13233i
$638$		−	5.65685i		−	0.223957i
$639$		0			0
$640$	24.0000	+	13.8564i	0.948683	+	0.547723i
$641$	−12.2474	+	7.07107i	−0.483745	+	0.279290i	−0.721976	−	0.691918i	$-0.756766\pi$
$641$	−12.2474	+	7.07107i	−0.483745	+	0.279290i	0.238231	+	0.971209i	$0.423433\pi$
$642$		0			0
$643$	22.5000	−	12.9904i	0.887313	−	0.512291i	0.0142506	−	0.999898i	$-0.495464\pi$
$643$	22.5000	−	12.9904i	0.887313	−	0.512291i	0.873063	+	0.487608i	$0.162130\pi$
$644$		0			0
$645$		0			0
$646$	−12.0000			−0.472134
$647$	−8.57321	+	14.8492i	−0.337048	+	0.583784i	−0.983876	−	0.178852i	$-0.942762\pi$
$647$	−8.57321	+	14.8492i	−0.337048	+	0.583784i	0.646828	+	0.762636i	$0.276095\pi$
$648$		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
$653$	−6.12372	−	3.53553i	−0.239640	−	0.138356i	0.375371	−	0.926875i	$-0.377515\pi$
$653$	−6.12372	−	3.53553i	−0.239640	−	0.138356i	−0.615011	+	0.788518i	$0.710849\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$	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	0.830497	−	0.557024i	$-0.188057\pi$
$659$	19.5959	+	11.3137i	0.763349	+	0.440720i	−0.0671481	+	0.997743i	$0.521390\pi$
$660$		0			0
$661$			29.4449i			1.14527i	0.819810	+	0.572636i	$0.194079\pi$
$661$			29.4449i			1.14527i	−0.819810	+	0.572636i	$0.805921\pi$
$662$			43.8406i			1.70391i
$663$		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
$670$	−33.0000	−	19.0526i	−1.27490	−	0.736065i
$671$	2.44949	+	4.24264i	0.0945615	+	0.163785i
$672$		0			0
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	0.302017	+	0.953302i	$0.402340\pi$
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	−0.976593	+	0.215096i	$0.930993\pi$
$674$	−28.1691	+	16.2635i	−1.08503	+	0.626445i
$675$		0			0
$676$		0			0
$677$	−9.79796			−0.376566			−0.188283	−	0.982115i	$-0.560292\pi$
$677$	−9.79796			−0.376566			−0.188283	+	0.982115i	$0.560292\pi$
$678$		0			0
$679$	−9.00000	−	25.9808i	−0.345388	−	0.997050i
$680$	−29.3939	+	16.9706i	−1.12720	+	0.650791i
$681$		0			0
$682$	3.00000	−	1.73205i	0.114876	−	0.0663237i
$683$	41.6413	+	24.0416i	1.59336	+	0.919927i	0.992725	+	0.120405i	$0.0384193\pi$
$683$	41.6413	+	24.0416i	1.59336	+	0.919927i	0.600636	+	0.799522i	$0.294914\pi$
$684$		0			0
$685$		−	27.7128i		−	1.05885i
$686$	−22.0454	−	14.1421i	−0.841698	−	0.539949i
$687$		0			0
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	14.6969			0.559909
$690$		0			0
$691$			43.3013i			1.64726i	0.567129	+	0.823629i	$0.308054\pi$
$691$			43.3013i			1.64726i	−0.567129	+	0.823629i	$0.691946\pi$
$692$		0			0
$693$		0			0
$694$	−44.0000			−1.67022
$695$			12.7279i			0.482798i
$696$		0			0
$697$	−36.0000			−1.36360
$698$	7.34847	−	12.7279i	0.278144	−	0.481759i
$699$		0			0
$700$		0			0
$701$		−	5.65685i		−	0.213656i	−0.994277	−	0.106828i	$-0.965931\pi$
$701$		−	5.65685i		−	0.213656i	0.994277	−	0.106828i	$-0.0340695\pi$
$702$		0			0
$703$	1.50000	+	0.866025i	0.0565736	+	0.0326628i
$704$	9.79796	−	5.65685i	0.369274	−	0.213201i
$705$		0			0
$706$	−21.0000	+	12.1244i	−0.790345	+	0.456306i
$707$	−8.57321	+	44.5477i	−0.322429	+	1.67539i
$708$		0			0
$709$	−40.0000			−1.50223			−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000			−1.50223			−0.751116	+	0.660171i	$0.770484\pi$
$710$	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
$718$	−20.0000	−	34.6410i	−0.746393	−	1.29279i
$719$	−13.4722	−	23.3345i	−0.502428	−	0.870231i	−0.999996	−	0.00280593i	$-0.999107\pi$
$719$	−13.4722	−	23.3345i	−0.502428	−	0.870231i	0.497568	−	0.867425i	$-0.334226\pi$
$720$		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
$725$			2.82843i			0.105045i
$726$		0			0
$727$	22.5000	+	12.9904i	0.834479	+	0.481787i	0.855384	−	0.517995i	$-0.173321\pi$
$727$	22.5000	+	12.9904i	0.834479	+	0.481787i	−0.0209049	+	0.999781i	$0.506655\pi$
$728$	7.34847	−	38.1838i	0.272352	−	1.41518i
$729$		0			0
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	−2.44949	−	4.24264i	−0.0905977	−	0.156920i
$732$		0			0
$733$	34.5000	+	19.9186i	1.27429	+	0.735710i	0.975792	−	0.218702i	$-0.0701821\pi$
$733$	34.5000	+	19.9186i	1.27429	+	0.735710i	0.298495	+	0.954411i	$0.403515\pi$
$734$	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
$742$	10.0000	−	3.46410i	0.367112	−	0.127171i
$743$	20.8207	−	12.0208i	0.763836	−	0.441001i	−0.0668353	−	0.997764i	$-0.521290\pi$
$743$	20.8207	−	12.0208i	0.763836	−	0.441001i	0.830671	+	0.556763i	$0.187957\pi$
$744$		0			0
$745$	12.0000	−	6.92820i	0.439646	−	0.253830i
$746$	35.5176	+	20.5061i	1.30039	+	0.750782i
$747$		0			0
$748$		0			0
$749$	−7.34847	−	1.41421i	−0.268507	−	0.0516742i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	−48.9898			−1.78647
$753$		0			0
$754$		−	20.7846i		−	0.756931i
$755$	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	$0.488428\pi$
$758$			9.89949i			0.359566i
$759$		0			0
$760$	−12.0000			−0.435286
$761$	12.2474	−	21.2132i	0.443970	−	0.768978i	−0.554010	−	0.832510i	$-0.686903\pi$
$761$	12.2474	−	21.2132i	0.443970	−	0.768978i	0.997980	+	0.0635319i	$0.0202365\pi$
$762$		0			0
$763$	−2.50000	+	0.866025i	−0.0905061	+	0.0313522i
$764$		0			0
$765$		0			0
$766$	24.0000	+	13.8564i	0.867155	+	0.500652i
$767$	22.0454	−	12.7279i	0.796014	−	0.459579i
$768$		0			0
$769$	22.5000	−	12.9904i	0.811371	−	0.468445i	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	22.5000	−	12.9904i	0.811371	−	0.468445i	0.847432	+	0.530904i	$0.178148\pi$
$770$	−9.79796	−	8.48528i	−0.353094	−	0.305788i
$771$		0			0
$772$		0			0
$773$	13.4722	−	23.3345i	0.484561	−	0.839284i	−0.515282	−	0.857021i	$-0.672313\pi$
$773$	13.4722	−	23.3345i	0.484561	−	0.839284i	0.999843	+	0.0177365i	$0.00564599\pi$
$774$		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
$779$	−11.0227	−	6.36396i	−0.394929	−	0.228013i
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	−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
$787$			45.0333i			1.60526i	0.596474	+	0.802632i	$0.296568\pi$
$787$			45.0333i			1.60526i	−0.596474	+	0.802632i	$0.703432\pi$
$788$		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
$794$	−1.22474	−	2.12132i	−0.0434646	−	0.0752828i
$795$		0			0
$796$		0			0
$797$	−14.6969	−	25.4558i	−0.520592	−	0.901692i	−0.999713	−	0.0239434i	$-0.992378\pi$
$797$	−14.6969	−	25.4558i	−0.520592	−	0.901692i	0.479121	−	0.877749i	$-0.340955\pi$
$798$		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
$803$	−2.44949			−0.0864406
$804$		0			0
$805$	−36.0000	−	6.92820i	−1.26883	−	0.244187i
$806$	11.0227	−	6.36396i	0.388258	−	0.224161i
$807$		0			0
$808$	−42.0000	+	24.2487i	−1.47755	+	0.853067i
$809$	−35.5176	−	20.5061i	−1.24873	−	0.720956i	−0.277876	−	0.960617i	$-0.589630\pi$
$809$	−35.5176	−	20.5061i	−1.24873	−	0.720956i	−0.970857	+	0.239661i	$0.922964\pi$
$810$		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
$814$	−1.00000	+	1.73205i	−0.0350500	+	0.0607083i
$815$	24.4949			0.858019
$816$		0			0
$817$		−	1.73205i		−	0.0605968i
$818$	−46.5403			−1.62724
$819$		0			0
$820$		0			0
$821$			24.0416i			0.839059i	0.907742	+	0.419529i	$0.137805\pi$
$821$			24.0416i			0.839059i	−0.907742	+	0.419529i	$0.862195\pi$
$822$		0			0
$823$	−34.0000			−1.18517			−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000			−1.18517			−0.592583	+	0.805510i	$0.701892\pi$
$824$	12.2474	−	21.2132i	0.426660	−	0.738997i
$825$		0			0
$826$	12.0000	−	13.8564i	0.417533	−	0.482126i
$827$			7.07107i			0.245885i	0.992414	+	0.122943i	$0.0392331\pi$
$827$			7.07107i			0.245885i	−0.992414	+	0.122943i	$0.960767\pi$
$828$		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	$0.657091\pi$
$830$	−22.0454	+	12.7279i	−0.765207	+	0.441793i
$831$		0			0
$832$	36.0000	−	20.7846i	1.24808	−	0.720577i
$833$	31.8434	+	12.7279i	1.10331	+	0.440996i
$834$		0			0
$835$	−18.0000			−0.622916
$836$		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	$-0.914980\pi$
$839$	−7.34847	+	12.7279i	−0.253697	+	0.439417i	0.710844	+	0.703350i	$0.248313\pi$
$840$		0			0
$841$	−10.5000	−	18.1865i	−0.362069	−	0.627122i
$842$	−1.22474	−	0.707107i	−0.0422075	−	0.0243685i
$843$		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
$850$			6.92820i			0.237635i
$851$			5.65685i			0.193914i
$852$		0			0
$853$	−31.5000	−	18.1865i	−1.07854	−	0.622695i	−0.148037	−	0.988982i	$-0.547296\pi$
$853$	−31.5000	−	18.1865i	−1.07854	−	0.622695i	−0.930502	+	0.366287i	$0.880629\pi$
$854$	9.79796	+	8.48528i	0.335279	+	0.290360i
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	−19.5959	−	33.9411i	−0.669384	−	1.15941i	−0.978077	−	0.208245i	$-0.933225\pi$
$857$	−19.5959	−	33.9411i	−0.669384	−	1.15941i	0.308693	−	0.951162i	$-0.400108\pi$
$858$		0			0
$859$	−33.0000	−	19.0526i	−1.12595	−	0.650065i	−0.183033	−	0.983107i	$-0.558592\pi$
$859$	−33.0000	−	19.0526i	−1.12595	−	0.650065i	−0.942912	+	0.333042i	$0.891925\pi$
$860$		0			0
$861$		0			0
$862$	−11.0000	+	19.0526i	−0.374661	+	0.648933i
$863$	35.5176	−	20.5061i	1.20903	−	0.698036i	0.246485	−	0.969147i	$-0.420724\pi$
$863$	35.5176	−	20.5061i	1.20903	−	0.698036i	0.962548	+	0.271111i	$0.0873910\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$	22.0454			0.749133
$867$		0			0
$868$		0			0
$869$	−6.12372	+	3.53553i	−0.207733	+	0.119935i
$870$		0			0
$871$	−49.5000	+	28.5788i	−1.67724	+	0.968357i
$872$	−2.44949	−	1.41421i	−0.0829502	−	0.0478913i
$873$		0			0
$874$		−	13.8564i		−	0.468700i
$875$	−19.5959	−	16.9706i	−0.662463	−	0.573710i
$876$		0			0
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	−0.983995	−	0.178195i	$-0.942974\pi$
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	0.646319	+	0.763067i	$0.276307\pi$
$878$	39.1918			1.32266
$879$		0			0
$880$		−	13.8564i		−	0.467099i
$881$		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
$886$	−56.0000			−1.88136
$887$	−20.8207	+	36.0624i	−0.699089	+	1.21086i	0.269693	+	0.962946i	$0.413078\pi$
$887$	−20.8207	+	36.0624i	−0.699089	+	1.21086i	−0.968783	+	0.247912i	$0.920256\pi$
$888$		0			0
$889$	−22.0000	−	19.0526i	−0.737856	−	0.639002i
$890$			16.9706i			0.568855i
$891$		0			0
$892$		0			0
$893$	18.3712	−	10.6066i	0.614768	−	0.354936i
$894$		0			0
$895$	21.0000	−	12.1244i	0.701953	−	0.405273i
$896$	19.5959	−	22.6274i	0.654654	−	0.755929i
$897$		0			0
$898$	10.0000			0.333704
$899$	−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
$905$	33.0681	+	19.0919i	1.09922	+	0.634636i
$906$		0			0
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$		0			0
$909$		0			0
$910$	−36.0000	−	31.1769i	−1.19339	−	1.03350i
$911$	−46.5403	−	26.8701i	−1.54195	−	0.890245i	−0.998716	−	0.0506629i	$-0.983867\pi$
$911$	−46.5403	−	26.8701i	−1.54195	−	0.890245i	−0.543233	−	0.839582i	$-0.682800\pi$
$912$		0			0
$913$			10.3923i			0.343935i
$914$		−	7.07107i		−	0.233890i
$915$		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	$0.923797\pi$
$920$	−19.5959	−	33.9411i	−0.646058	−	1.11901i
$921$		0			0
$922$	18.0000	+	10.3923i	0.592798	+	0.342252i
$923$	−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
$929$	56.3383			1.84840			0.924199	−	0.381911i	$-0.124734\pi$
$929$	56.3383			1.84840			0.924199	+	0.381911i	$0.124734\pi$
$930$		0			0
$931$	7.50000	+	9.52628i	0.245803	+	0.312211i
$932$		0			0
$933$		0			0
$934$	−33.0000	+	19.0526i	−1.07979	+	0.623419i
$935$	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	$0.723292\pi$
$938$	−26.9444	+	31.1127i	−0.879765	+	1.01587i
$939$		0			0
$940$		0			0
$941$	−48.9898			−1.59702			−0.798511	−	0.601980i	$-0.794379\pi$
$941$	−48.9898			−1.59702			−0.798511	+	0.601980i	$0.794379\pi$
$942$		0			0
$943$		−	41.5692i		−	1.35368i
$944$	19.5959			0.637793
$945$		0			0
$946$	2.00000			0.0650256
$947$			49.4975i			1.60845i	0.594324	+	0.804226i	$0.297420\pi$
$947$			49.4975i			1.60845i	−0.594324	+	0.804226i	$0.702580\pi$
$948$		0			0
$949$	−9.00000			−0.292152
$950$	−1.22474	+	2.12132i	−0.0397360	+	0.0688247i
$951$		0			0
$952$	12.0000	+	34.6410i	0.388922	+	1.12272i
$953$		−	5.65685i		−	0.183243i	−0.995794	−	0.0916217i	$-0.970795\pi$
$953$		−	5.65685i		−	0.183243i	0.995794	−	0.0916217i	$-0.0292051\pi$
$954$		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
$959$	−29.3939	−	5.65685i	−0.949178	−	0.182669i
$960$		0			0
$961$	28.0000			0.903226
$962$	−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	0.951408	−	0.307933i	$-0.0996374\pi$
$967$	6.50000	+	11.2583i	0.209026	+	0.362043i	−0.742382	+	0.669977i	$0.766304\pi$
$968$	22.0454	+	12.7279i	0.708566	+	0.409091i
$969$		0			0
$970$	−18.0000	−	31.1769i	−0.577945	−	1.00103i
$971$	19.5959	+	33.9411i	0.628863	+	1.08922i	0.987780	+	0.155853i	$0.0498127\pi$
$971$	19.5959	+	33.9411i	0.628863	+	1.08922i	−0.358917	+	0.933369i	$0.616854\pi$
$972$		0			0
$973$	13.5000	+	2.59808i	0.432790	+	0.0832905i
$974$	20.8207	+	12.0208i	0.667137	+	0.385172i
$975$		0			0
$976$			13.8564i			0.443533i
$977$			7.07107i			0.226224i	0.993582	+	0.113112i	$0.0360818\pi$
$977$			7.07107i			0.226224i	−0.993582	+	0.113112i	$0.963918\pi$
$978$		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
$983$	2.44949	+	4.24264i	0.0781266	+	0.135319i	0.902442	−	0.430812i	$-0.141773\pi$
$983$	2.44949	+	4.24264i	0.0781266	+	0.135319i	−0.824315	+	0.566131i	$0.808439\pi$
$984$		0			0
$985$	42.0000	+	24.2487i	1.33823	+	0.772628i
$986$	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
$994$	−20.0000	−	17.3205i	−0.634361	−	0.549373i
$995$	−29.3939	+	16.9706i	−0.931849	+	0.538003i
$996$		0			0
$997$	25.5000	−	14.7224i	0.807593	−	0.466264i	−0.0385262	−	0.999258i	$-0.512266\pi$
$997$	25.5000	−	14.7224i	0.807593	−	0.466264i	0.846119	+	0.532993i	$0.178933\pi$
$998$	−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.i.d.269.1		4
3.2	odd	2	inner	567.2.i.d.269.2		4
7.5	odd	6		567.2.s.d.26.1		4
9.2	odd	6		63.2.p.a.17.2	yes	4
9.4	even	3		567.2.s.d.458.2		4
9.5	odd	6		567.2.s.d.458.1		4
9.7	even	3		63.2.p.a.17.1	✓	4
21.5	even	6		567.2.s.d.26.2		4
36.7	odd	6		1008.2.bt.b.17.2		4
36.11	even	6		1008.2.bt.b.17.1		4
45.2	even	12		1575.2.bc.a.899.3		8
45.7	odd	12		1575.2.bc.a.899.1		8
45.29	odd	6		1575.2.bk.c.1151.1		4
45.34	even	6		1575.2.bk.c.1151.2		4
45.38	even	12		1575.2.bc.a.899.2		8
45.43	odd	12		1575.2.bc.a.899.4		8
63.2	odd	6		441.2.p.a.215.1		4
63.5	even	6	inner	567.2.i.d.215.2		4
63.11	odd	6		441.2.c.a.440.4		4
63.16	even	3		441.2.p.a.215.2		4
63.20	even	6		441.2.p.a.80.2		4
63.25	even	3		441.2.c.a.440.1		4
63.34	odd	6		441.2.p.a.80.1		4
63.38	even	6		441.2.c.a.440.3		4
63.40	odd	6	inner	567.2.i.d.215.1		4
63.47	even	6		63.2.p.a.26.1	yes	4
63.52	odd	6		441.2.c.a.440.2		4
63.61	odd	6		63.2.p.a.26.2	yes	4
252.11	even	6		7056.2.k.b.881.3		4
252.47	odd	6		1008.2.bt.b.593.2		4
252.115	even	6		7056.2.k.b.881.4		4
252.151	odd	6		7056.2.k.b.881.2		4
252.187	even	6		1008.2.bt.b.593.1		4
252.227	odd	6		7056.2.k.b.881.1		4
315.47	odd	12		1575.2.bc.a.1349.4		8
315.124	odd	6		1575.2.bk.c.26.1		4
315.173	odd	12		1575.2.bc.a.1349.1		8
315.187	even	12		1575.2.bc.a.1349.2		8
315.299	even	6		1575.2.bk.c.26.2		4
315.313	even	12		1575.2.bc.a.1349.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.p.a.17.1	✓	4	9.7	even	3
63.2.p.a.17.2	yes	4	9.2	odd	6
63.2.p.a.26.1	yes	4	63.47	even	6
63.2.p.a.26.2	yes	4	63.61	odd	6
441.2.c.a.440.1		4	63.25	even	3
441.2.c.a.440.2		4	63.52	odd	6
441.2.c.a.440.3		4	63.38	even	6
441.2.c.a.440.4		4	63.11	odd	6
441.2.p.a.80.1		4	63.34	odd	6
441.2.p.a.80.2		4	63.20	even	6
441.2.p.a.215.1		4	63.2	odd	6
441.2.p.a.215.2		4	63.16	even	3
567.2.i.d.215.1		4	63.40	odd	6	inner
567.2.i.d.215.2		4	63.5	even	6	inner
567.2.i.d.269.1		4	1.1	even	1	trivial
567.2.i.d.269.2		4	3.2	odd	2	inner
567.2.s.d.26.1		4	7.5	odd	6
567.2.s.d.26.2		4	21.5	even	6
567.2.s.d.458.1		4	9.5	odd	6
567.2.s.d.458.2		4	9.4	even	3
1008.2.bt.b.17.1		4	36.11	even	6
1008.2.bt.b.17.2		4	36.7	odd	6
1008.2.bt.b.593.1		4	252.187	even	6
1008.2.bt.b.593.2		4	252.47	odd	6
1575.2.bc.a.899.1		8	45.7	odd	12
1575.2.bc.a.899.2		8	45.38	even	12
1575.2.bc.a.899.3		8	45.2	even	12
1575.2.bc.a.899.4		8	45.43	odd	12
1575.2.bc.a.1349.1		8	315.173	odd	12
1575.2.bc.a.1349.2		8	315.187	even	12
1575.2.bc.a.1349.3		8	315.313	even	12
1575.2.bc.a.1349.4		8	315.47	odd	12
1575.2.bk.c.26.1		4	315.124	odd	6
1575.2.bk.c.26.2		4	315.299	even	6
1575.2.bk.c.1151.1		4	45.29	odd	6
1575.2.bk.c.1151.2		4	45.34	even	6
7056.2.k.b.881.1		4	252.227	odd	6
7056.2.k.b.881.2		4	252.151	odd	6
7056.2.k.b.881.3		4	252.11	even	6
7056.2.k.b.881.4		4	252.115	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(1.22474 - 2.12132i) q^{5} +(-2.00000 - 1.73205i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q-1.41421i q^{2} +(1.22474 - 2.12132i) q^{5} +(-2.00000 - 1.73205i) q^{7} -2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +(-1.22474 + 0.707107i) q^{11} +(-4.50000 + 2.59808i) q^{13} +(-2.44949 + 2.82843i) q^{14} -4.00000 q^{16} +(2.44949 - 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 + 1.73205i) q^{22} +(4.89898 + 2.82843i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.67423 + 6.36396i) q^{26} +(-2.44949 - 1.41421i) q^{29} -1.73205i q^{31} +(-6.00000 - 3.46410i) q^{34} +(-6.12372 + 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.22474 - 2.12132i) q^{38} +(-6.00000 - 3.46410i) q^{40} +(-3.67423 - 6.36396i) q^{41} +(0.500000 - 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} +12.2474 q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.22474 + 0.707107i) q^{50} +(-2.44949 - 1.41421i) q^{53} +3.46410i q^{55} +(-4.89898 + 5.65685i) q^{56} +(-2.00000 + 3.46410i) q^{58} -4.89898 q^{59} -3.46410i q^{61} -2.44949 q^{62} -8.00000 q^{64} +12.7279i q^{65} +11.0000 q^{67} +(3.00000 + 8.66025i) q^{70} +7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} +(1.22474 - 0.707107i) q^{74} +(3.67423 + 0.707107i) q^{77} +5.00000 q^{79} +(-4.89898 + 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(3.67423 - 6.36396i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(-1.22474 - 0.707107i) q^{86} +(2.00000 + 3.46410i) q^{88} +(-2.44949 - 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} -17.3205i q^{94} -4.24264i q^{95} +(9.00000 + 5.19615i) q^{97} +(9.79796 - 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{7}+O(q^{10}) \) 4 * q - 8 * q^7	\( 4 q - 8 q^{7} - 12 q^{10} - 18 q^{13} - 16 q^{16} + 6 q^{19} + 4 q^{22} - 2 q^{25} - 24 q^{34} + 2 q^{37} - 24 q^{40} + 2 q^{43} + 16 q^{46} + 4 q^{49} - 8 q^{58} - 32 q^{64} + 44 q^{67} + 12 q^{70} + 6 q^{73} + 20 q^{79} - 36 q^{82} - 24 q^{85} + 8 q^{88} + 54 q^{91} + 36 q^{97}+O(q^{100}) \) 4 * q - 8 * q^7 - 12 * q^10 - 18 * q^13 - 16 * q^16 + 6 * q^19 + 4 * q^22 - 2 * q^25 - 24 * q^34 + 2 * q^37 - 24 * q^40 + 2 * q^43 + 16 * q^46 + 4 * q^49 - 8 * q^58 - 32 * q^64 + 44 * q^67 + 12 * q^70 + 6 * q^73 + 20 * q^79 - 36 * q^82 - 24 * q^85 + 8 * q^88 + 54 * q^91 + 36 * q^97

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