LMFDB - Embedded newform 1764.2.i.c.1537.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(373,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1764.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.i (of order $3$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1764.1537
Dual form			1764.2.i.c.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(4.50000 - 2.59808i) q^{15} +(3.00000 - 5.19615i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} -5.00000 q^{31} -5.19615i q^{33} +(-1.00000 - 1.73205i) q^{37} -1.73205i q^{39} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +9.00000 q^{45} +9.00000 q^{47} +(9.00000 - 5.19615i) q^{51} +(3.00000 - 5.19615i) q^{53} -9.00000 q^{55} -6.92820i q^{57} +3.00000 q^{59} +13.0000 q^{61} -3.00000 q^{65} -7.00000 q^{67} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-5.00000 + 8.66025i) q^{73} -6.92820i q^{75} +11.0000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} +(-4.50000 + 2.59808i) q^{87} +(3.00000 + 5.19615i) q^{89} +(-7.50000 - 4.33013i) q^{93} -12.0000 q^{95} +(5.50000 - 9.52628i) q^{97} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 3 q^{5} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 3 * q^5 + 3 * q^9	$ 2 q + 3 q^{3} + 3 q^{5} + 3 q^{9} - 3 q^{11} - q^{13} + 9 q^{15} + 6 q^{17} - 4 q^{19} + 3 q^{23} - 4 q^{25} - 3 q^{29} - 10 q^{31} - 2 q^{37} + 3 q^{41} + q^{43} + 18 q^{45} + 18 q^{47} + 18 q^{51} + 6 q^{53} - 18 q^{55} + 6 q^{59} + 26 q^{61} - 6 q^{65} - 14 q^{67} + 9 q^{69} - 24 q^{71} - 10 q^{73} + 22 q^{79} - 9 q^{81} - 9 q^{83} - 18 q^{85} - 9 q^{87} + 6 q^{89} - 15 q^{93} - 24 q^{95} + 11 q^{97} + 9 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 3 * q^5 + 3 * q^9 - 3 * q^11 - q^13 + 9 * q^15 + 6 * q^17 - 4 * q^19 + 3 * q^23 - 4 * q^25 - 3 * q^29 - 10 * q^31 - 2 * q^37 + 3 * q^41 + q^43 + 18 * q^45 + 18 * q^47 + 18 * q^51 + 6 * q^53 - 18 * q^55 + 6 * q^59 + 26 * q^61 - 6 * q^65 - 14 * q^67 + 9 * q^69 - 24 * q^71 - 10 * q^73 + 22 * q^79 - 9 * q^81 - 9 * q^83 - 18 * q^85 - 9 * q^87 + 6 * q^89 - 15 * q^93 - 24 * q^95 + 11 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	4.50000	−	2.59808i	1.16190	−	0.670820i
$16$		0			0
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−5.00000			−0.898027			−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000			−0.898027			−0.449013	+	0.893525i	$0.648224\pi$
$32$		0			0
$33$		−	5.19615i		−	0.904534i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$		−	1.73205i		−	0.277350i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		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
$45$	9.00000			1.34164
$46$		0			0
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	9.00000	−	5.19615i	1.26025	−	0.727607i
$52$		0			0
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$		−	6.92820i		−	0.917663i
$58$		0			0
$59$	3.00000			0.390567			0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000			0.390567			0.195283	+	0.980747i	$0.437437\pi$
$60$		0			0
$61$	13.0000			1.66448			0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000			1.66448			0.832240	+	0.554416i	$0.187058\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.00000			−0.372104
$66$		0			0
$67$	−7.00000			−0.855186			−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000			−0.855186			−0.427593	+	0.903971i	$0.640638\pi$
$68$		0			0
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$		−	6.92820i		−	0.800000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	−9.00000	−	15.5885i	−0.976187	−	1.69081i
$86$		0			0
$87$	−4.50000	+	2.59808i	−0.482451	+	0.278543i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.50000	−	4.33013i	−0.777714	−	0.449013i
$94$		0			0
$95$	−12.0000			−1.23117
$96$		0			0
$97$	5.50000	−	9.52628i	0.558440	−	0.967247i	−0.439187	−	0.898396i	$-0.644733\pi$
$97$	5.50000	−	9.52628i	0.558440	−	0.967247i	0.997627	−	0.0688512i	$-0.0219334\pi$
$98$		0			0
$99$	4.50000	−	7.79423i	0.452267	−	0.783349i
$100$		0			0
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$		0			0
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$		−	3.46410i		−	0.328798i
$112$		0			0
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	0.996262	−	0.0863794i	$-0.0275297\pi$
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	−0.572938	+	0.819599i	$0.694196\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$		0			0
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$			5.19615i			0.468521i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$		0			0
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.114024	−	0.993478i	$-0.463626\pi$
$131$	10.5000	−	18.1865i	0.917389	−	1.58896i	0.803365	−	0.595487i	$-0.203041\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	13.5000	+	7.79423i	1.16190	+	0.670820i
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$	13.5000	+	7.79423i	1.13691	+	0.656392i
$142$		0			0
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$		0			0
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$		0			0
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	0.999430	+	0.0337724i	$0.0107521\pi$
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	−0.470467	+	0.882418i	$0.655915\pi$
$152$		0			0
$153$	18.0000			1.45521
$154$		0			0
$155$	−7.50000	+	12.9904i	−0.602414	+	1.04341i
$156$		0			0
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$		0			0
$159$	9.00000	−	5.19615i	0.713746	−	0.412082i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$		0			0
$165$	−13.5000	−	7.79423i	−1.05097	−	0.606780i
$166$		0			0
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	0.985933	−	0.167139i	$-0.0534527\pi$
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	−0.637713	+	0.770274i	$0.720119\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$		0			0
$173$	9.00000			0.684257			0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000			0.684257			0.342129	+	0.939653i	$0.388852\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.50000	+	2.59808i	0.338241	+	0.195283i
$178$		0			0
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	19.5000	+	11.2583i	1.44148	+	0.832240i
$184$		0			0
$185$	−6.00000			−0.441129
$186$		0			0
$187$	−18.0000			−1.31629
$188$		0			0
$189$		0			0
$190$		0			0
$191$	15.0000			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$		0			0
$195$	−4.50000	−	2.59808i	−0.322252	−	0.186052i
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	−10.5000	−	6.06218i	−0.740613	−	0.427593i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	9.00000			0.628587
$206$		0			0
$207$	9.00000			0.625543
$208$		0			0
$209$	−6.00000	+	10.3923i	−0.415029	+	0.718851i
$210$		0			0
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	−0.994855	−	0.101310i	$-0.967697\pi$
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	0.409691	−	0.912224i	$-0.365637\pi$
$212$		0			0
$213$	−18.0000	−	10.3923i	−1.23334	−	0.712069i
$214$		0			0
$215$	−1.50000	−	2.59808i	−0.102299	−	0.177187i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−15.0000	+	8.66025i	−1.01361	+	0.585206i
$220$		0			0
$221$	−6.00000			−0.403604
$222$		0			0
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	−0.882281	−	0.470723i	$-0.843993\pi$
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	0.848799	+	0.528716i	$0.177326\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$		0			0
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.832529	+	0.553981i	$0.186892\pi$
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.0634974	+	0.997982i	$0.479775\pi$
$228$		0			0
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	13.5000	−	23.3827i	0.880643	−	1.52532i
$236$		0			0
$237$	16.5000	+	9.52628i	1.07179	+	0.618798i
$238$		0			0
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.858623	+	0.512607i	$0.171320\pi$
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.0146191	+	0.999893i	$0.495346\pi$
$240$		0			0
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$		0			0
$249$	−13.5000	+	7.79423i	−0.855528	+	0.493939i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$		0			0
$255$		−	31.1769i		−	1.95237i
$256$		0			0
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	−0.971558	−	0.236802i	$-0.923901\pi$
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	0.690856	+	0.722993i	$0.257234\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−9.00000			−0.557086
$262$		0			0
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$		0			0
$265$	−9.00000	−	15.5885i	−0.552866	−	0.957591i
$266$		0			0
$267$			10.3923i			0.635999i
$268$		0			0
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		0			0
$279$	−7.50000	−	12.9904i	−0.449013	−	0.777714i
$280$		0			0
$281$	−1.50000	+	2.59808i	−0.0894825	+	0.154988i	−0.907293	−	0.420500i	$-0.861855\pi$
$281$	−1.50000	+	2.59808i	−0.0894825	+	0.154988i	0.817810	+	0.575488i	$0.195188\pi$
$282$		0			0
$283$	−5.00000			−0.297219			−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000			−0.297219			−0.148610	+	0.988896i	$0.547480\pi$
$284$		0			0
$285$	−18.0000	−	10.3923i	−1.06623	−	0.615587i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	16.5000	−	9.52628i	0.967247	−	0.558440i
$292$		0			0
$293$	−10.5000	−	18.1865i	−0.613417	−	1.06247i	−0.990660	−	0.136355i	$-0.956461\pi$
$293$	−10.5000	−	18.1865i	−0.613417	−	1.06247i	0.377244	−	0.926114i	$-0.376872\pi$
$294$		0			0
$295$	4.50000	−	7.79423i	0.262000	−	0.453798i
$296$		0			0
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$		0			0
$299$	−3.00000			−0.173494
$300$		0			0
$301$		0			0
$302$		0			0
$303$			25.9808i			1.49256i
$304$		0			0
$305$	19.5000	−	33.7750i	1.11657	−	1.93395i
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−10.5000	+	6.06218i	−0.597324	+	0.344865i
$310$		0			0
$311$	−21.0000			−1.19080			−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000			−1.19080			−0.595400	+	0.803429i	$0.703007\pi$
$312$		0			0
$313$	1.00000			0.0565233			0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000			0.0565233			0.0282617	+	0.999601i	$0.491003\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.0000			−1.17948			−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000			−1.17948			−0.589739	+	0.807594i	$0.700769\pi$
$318$		0			0
$319$	9.00000			0.503903
$320$		0			0
$321$		−	20.7846i		−	1.16008i
$322$		0			0
$323$	−24.0000			−1.33540
$324$		0			0
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$		0			0
$327$	−3.00000	+	1.73205i	−0.165900	+	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.0000			0.604615			0.302307	−	0.953211i	$-0.402243\pi$
$331$	11.0000			0.604615			0.302307	+	0.953211i	$0.402243\pi$
$332$		0			0
$333$	3.00000	−	5.19615i	0.164399	−	0.284747i
$334$		0			0
$335$	−10.5000	+	18.1865i	−0.573676	+	0.993636i
$336$		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	$-0.382157\pi$
$338$		0			0
$339$			15.5885i			0.846649i
$340$		0			0
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		−	15.5885i		−	0.839254i
$346$		0			0
$347$	9.00000			0.483145			0.241573	−	0.970383i	$-0.422337\pi$
$347$	9.00000			0.483145			0.241573	+	0.970383i	$0.422337\pi$
$348$		0			0
$349$	−0.500000	+	0.866025i	−0.0267644	+	0.0463573i	−0.879097	−	0.476642i	$-0.841854\pi$
$349$	−0.500000	+	0.866025i	−0.0267644	+	0.0463573i	0.852333	+	0.523000i	$0.175187\pi$
$350$		0			0
$351$	4.50000	−	2.59808i	0.240192	−	0.138675i
$352$		0			0
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$	3.00000	−	1.73205i	0.157459	−	0.0909091i
$364$		0			0
$365$	15.0000	+	25.9808i	0.785136	+	1.35990i
$366$		0			0
$367$	−6.50000	−	11.2583i	−0.339297	−	0.587680i	0.645003	−	0.764180i	$-0.276856\pi$
$367$	−6.50000	−	11.2583i	−0.339297	−	0.587680i	−0.984301	+	0.176500i	$0.943523\pi$
$368$		0			0
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$		0			0
$375$	4.50000	+	2.59808i	0.232379	+	0.134164i
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	−24.0000	−	13.8564i	−1.22956	−	0.709885i
$382$		0			0
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.00000			0.152499
$388$		0			0
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$		0			0
$393$	31.5000	−	18.1865i	1.58896	−	0.917389i
$394$		0			0
$395$	16.5000	−	28.5788i	0.830205	−	1.43796i
$396$		0			0
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	0.890028	−	0.455905i	$-0.150684\pi$
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	−0.839840	+	0.542834i	$0.817351\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	2.50000	+	4.33013i	0.124534	+	0.215699i
$404$		0			0
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$		0			0
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	−23.0000			−1.13728			−0.568638	−	0.822588i	$-0.692530\pi$
$409$	−23.0000			−1.13728			−0.568638	+	0.822588i	$0.692530\pi$
$410$		0			0
$411$		−	5.19615i		−	0.256307i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$		0			0
$417$			8.66025i			0.424094i
$418$		0			0
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$		0			0
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$		0			0
$423$	13.5000	+	23.3827i	0.656392	+	1.13691i
$424$		0			0
$425$	−24.0000			−1.16417
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.50000	+	2.59808i	−0.217262	+	0.125436i
$430$		0			0
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$			15.5885i			0.747409i
$436$		0			0
$437$	−12.0000			−0.574038
$438$		0			0
$439$	−35.0000			−1.67046			−0.835229	−	0.549902i	$-0.814665\pi$
$439$	−35.0000			−1.67046			−0.835229	+	0.549902i	$0.814665\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.00000			−0.427603			−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000			−0.427603			−0.213801	+	0.976877i	$0.568585\pi$
$444$		0			0
$445$	18.0000			0.853282
$446$		0			0
$447$	−22.5000	+	12.9904i	−1.06421	+	0.614424i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$		0			0
$453$			22.5167i			1.05792i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−37.0000			−1.73079			−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000			−1.73079			−0.865393	+	0.501093i	$0.832931\pi$
$458$		0			0
$459$	27.0000	+	15.5885i	1.26025	+	0.727607i
$460$		0			0
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	−0.828978	−	0.559281i	$-0.811077\pi$
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	0.898840	+	0.438276i	$0.144411\pi$
$462$		0			0
$463$	9.50000	+	16.4545i	0.441502	+	0.764705i	0.997801	−	0.0662777i	$-0.0211123\pi$
$463$	9.50000	+	16.4545i	0.441502	+	0.764705i	−0.556299	+	0.830982i	$0.687779\pi$
$464$		0			0
$465$	−22.5000	+	12.9904i	−1.04341	+	0.602414i
$466$		0			0
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	19.5000	+	11.2583i	0.898513	+	0.518756i
$472$		0			0
$473$	−3.00000			−0.137940
$474$		0			0
$475$	−8.00000	+	13.8564i	−0.367065	+	0.635776i
$476$		0			0
$477$	18.0000			0.824163
$478$		0			0
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	0.990060	+	0.140643i	$0.0449170\pi$
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	−0.373230	+	0.927739i	$0.621750\pi$
$480$		0			0
$481$	−1.00000	+	1.73205i	−0.0455961	+	0.0789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.5000	−	28.5788i	−0.749226	−	1.29770i
$486$		0			0
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	0.233933	+	0.972253i	$0.424840\pi$
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	−0.958962	+	0.283535i	$0.908493\pi$
$488$		0			0
$489$		−	34.6410i		−	1.56652i
$490$		0			0
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	0.897886	−	0.440228i	$-0.145102\pi$
$491$	1.50000	+	2.59808i	0.0676941	+	0.117250i	−0.830192	+	0.557478i	$0.811769\pi$
$492$		0			0
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$		0			0
$495$	−13.5000	−	23.3827i	−0.606780	−	1.05097i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$		0			0
$501$			15.5885i			0.696441i
$502$		0			0
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		0			0
$505$	45.0000			2.00247
$506$		0			0
$507$	18.0000	−	10.3923i	0.799408	−	0.461538i
$508$		0			0
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	−0.00339621	−	0.999994i	$-0.501081\pi$
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	0.867719	−	0.497056i	$-0.165586\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	18.0000	−	10.3923i	0.794719	−	0.458831i
$514$		0			0
$515$	10.5000	+	18.1865i	0.462685	+	0.801394i
$516$		0			0
$517$	−13.5000	−	23.3827i	−0.593729	−	1.02837i
$518$		0			0
$519$	13.5000	+	7.79423i	0.592584	+	0.342129i
$520$		0			0
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$		0			0
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	0.940129	−	0.340818i	$-0.110704\pi$
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	−0.765222	+	0.643767i	$0.777371\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	4.50000	+	7.79423i	0.195283	+	0.338241i
$532$		0			0
$533$	1.50000	−	2.59808i	0.0649722	−	0.112535i
$534$		0			0
$535$	−36.0000			−1.55642
$536$		0			0
$537$	−18.0000	+	10.3923i	−0.776757	+	0.448461i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	0.956504	+	0.291718i	$0.0942267\pi$
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	−0.225617	+	0.974216i	$0.572440\pi$
$542$		0			0
$543$	−3.00000	−	1.73205i	−0.128742	−	0.0743294i
$544$		0			0
$545$	3.00000	+	5.19615i	0.128506	+	0.222579i
$546$		0			0
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	−0.692948	−	0.720988i	$-0.743688\pi$
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	0.970868	+	0.239616i	$0.0770217\pi$
$548$		0			0
$549$	19.5000	+	33.7750i	0.832240	+	1.44148i
$550$		0			0
$551$	12.0000			0.511217
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−9.00000	−	5.19615i	−0.382029	−	0.220564i
$556$		0			0
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$	−27.0000	−	15.5885i	−1.13994	−	0.658145i
$562$		0			0
$563$	−9.00000			−0.379305			−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000			−0.379305			−0.189652	+	0.981851i	$0.560736\pi$
$564$		0			0
$565$	27.0000			1.13590
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$		0			0
$571$	−31.0000			−1.29731			−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−31.0000			−1.29731			−0.648655	+	0.761083i	$0.724668\pi$
$572$		0			0
$573$	22.5000	+	12.9904i	0.939951	+	0.542681i
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−5.00000	+	8.66025i	−0.208153	+	0.360531i	−0.951133	−	0.308783i	$-0.900078\pi$
$577$	−5.00000	+	8.66025i	−0.208153	+	0.360531i	0.742980	+	0.669314i	$0.233412\pi$
$578$		0			0
$579$	16.5000	+	9.52628i	0.685717	+	0.395899i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−18.0000			−0.745484
$584$		0			0
$585$	−4.50000	−	7.79423i	−0.186052	−	0.322252i
$586$		0			0
$587$	7.50000	−	12.9904i	0.309558	−	0.536170i	−0.668708	−	0.743525i	$-0.733152\pi$
$587$	7.50000	−	12.9904i	0.309558	−	0.536170i	0.978266	+	0.207355i	$0.0664855\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$	9.00000	+	5.19615i	0.370211	+	0.213741i
$592$		0			0
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.00000	+	3.46410i	−0.245564	+	0.141776i
$598$		0			0
$599$	−39.0000			−1.59350			−0.796748	−	0.604311i	$-0.793448\pi$
$599$	−39.0000			−1.59350			−0.796748	+	0.604311i	$0.793448\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$		0			0
$603$	−10.5000	−	18.1865i	−0.427593	−	0.740613i
$604$		0			0
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	−0.0643251	−	0.997929i	$-0.520489\pi$
$607$	20.5000	−	35.5070i	0.832069	−	1.44119i	0.896394	−	0.443257i	$-0.146177\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.50000	−	7.79423i	−0.182051	−	0.315321i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$		0			0
$615$	13.5000	+	7.79423i	0.544373	+	0.314294i
$616$		0			0
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$		0			0
$619$	−6.50000	−	11.2583i	−0.261257	−	0.452510i	0.705319	−	0.708890i	$-0.250804\pi$
$619$	−6.50000	−	11.2583i	−0.261257	−	0.452510i	−0.966576	+	0.256379i	$0.917470\pi$
$620$		0			0
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	−18.0000	+	10.3923i	−0.718851	+	0.415029i
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$		−	29.4449i		−	1.17033i
$634$		0			0
$635$	−24.0000	+	41.5692i	−0.952411	+	1.64962i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−18.0000	−	31.1769i	−0.712069	−	1.23334i
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	20.5000	+	35.5070i	0.808441	+	1.40026i	0.913943	+	0.405842i	$0.133022\pi$
$643$	20.5000	+	35.5070i	0.808441	+	1.40026i	−0.105502	+	0.994419i	$0.533645\pi$
$644$		0			0
$645$		−	5.19615i		−	0.204598i
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$		0			0
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	−0.584091	−	0.811688i	$-0.698549\pi$
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	0.994988	+	0.0999939i	$0.0318823\pi$
$654$		0			0
$655$	−31.5000	−	54.5596i	−1.23081	−	2.13182i
$656$		0			0
$657$	−30.0000			−1.17041
$658$		0			0
$659$	10.5000	−	18.1865i	0.409022	−	0.708447i	−0.585758	−	0.810486i	$-0.699203\pi$
$659$	10.5000	−	18.1865i	0.409022	−	0.708447i	0.994780	+	0.102039i	$0.0325366\pi$
$660$		0			0
$661$	−11.0000			−0.427850			−0.213925	−	0.976850i	$-0.568625\pi$
$661$	−11.0000			−0.427850			−0.213925	+	0.976850i	$0.568625\pi$
$662$		0			0
$663$	−9.00000	−	5.19615i	−0.349531	−	0.201802i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.50000	+	7.79423i	0.174241	+	0.301794i
$668$		0			0
$669$	−1.50000	+	0.866025i	−0.0579934	+	0.0334825i
$670$		0			0
$671$	−19.5000	−	33.7750i	−0.752789	−	1.30387i
$672$		0			0
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$		0			0
$675$	18.0000	−	10.3923i	0.692820	−	0.400000i
$676$		0			0
$677$	−15.0000			−0.576497			−0.288248	−	0.957556i	$-0.593073\pi$
$677$	−15.0000			−0.576497			−0.288248	+	0.957556i	$0.593073\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			46.7654i			1.79205i
$682$		0			0
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	−0.283491	−	0.958975i	$-0.591493\pi$
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	0.972242	−	0.233977i	$-0.0751739\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	−19.5000	+	11.2583i	−0.743971	+	0.429532i
$688$		0			0
$689$	−6.00000			−0.228582
$690$		0			0
$691$	1.00000			0.0380418			0.0190209	−	0.999819i	$-0.493945\pi$
$691$	1.00000			0.0380418			0.0190209	+	0.999819i	$0.493945\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.0000			0.568982
$696$		0			0
$697$	18.0000			0.681799
$698$		0			0
$699$			10.3923i			0.393073i
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$		0			0
$705$	40.5000	−	23.3827i	1.52532	−	0.880643i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−25.0000			−0.938895			−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000			−0.938895			−0.469447	+	0.882960i	$0.655547\pi$
$710$		0			0
$711$	16.5000	+	28.5788i	0.618798	+	1.07179i
$712$		0			0
$713$	−7.50000	+	12.9904i	−0.280877	+	0.486494i
$714$		0			0
$715$	4.50000	+	7.79423i	0.168290	+	0.291488i
$716$		0			0
$717$			46.7654i			1.74648i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		−	1.73205i		−	0.0644157i
$724$		0			0
$725$	12.0000			0.445669
$726$		0			0
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	0.286954	+	0.957944i	$0.407357\pi$
$727$	−18.5000	+	32.0429i	−0.686127	+	1.18841i	−0.973081	+	0.230463i	$0.925976\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$		0			0
$733$	11.5000	−	19.9186i	0.424762	−	0.735710i	−0.571636	−	0.820507i	$-0.693691\pi$
$733$	11.5000	−	19.9186i	0.424762	−	0.735710i	0.996398	+	0.0847976i	$0.0270244\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.5000	+	18.1865i	0.386772	+	0.669910i
$738$		0			0
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	−6.00000	+	3.46410i	−0.220416	+	0.127257i
$742$		0			0
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	0.771598	−	0.636111i	$-0.219458\pi$
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	−0.936687	+	0.350168i	$0.886124\pi$
$744$		0			0
$745$	22.5000	+	38.9711i	0.824336	+	1.42779i
$746$		0			0
$747$	−27.0000			−0.987878
$748$		0			0
$749$		0			0
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$	−18.0000	−	10.3923i	−0.655956	−	0.378717i
$754$		0			0
$755$	39.0000			1.41936
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$	−13.5000	−	7.79423i	−0.490019	−	0.282913i
$760$		0			0
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	−0.510551	−	0.859848i	$-0.670558\pi$
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	0.999925	+	0.0122260i	$0.00389175\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	27.0000	−	46.7654i	0.976187	−	1.69081i
$766$		0			0
$767$	−1.50000	−	2.59808i	−0.0541619	−	0.0938111i
$768$		0			0
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	0.856869	−	0.515534i	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$		0			0
$771$	−13.5000	+	7.79423i	−0.486191	+	0.280702i
$772$		0			0
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	10.0000	+	17.3205i	0.359211	+	0.622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$	−13.5000	−	7.79423i	−0.482451	−	0.278543i
$784$		0			0
$785$	19.5000	−	33.7750i	0.695985	−	1.20548i
$786$		0			0
$787$	43.0000			1.53278			0.766392	−	0.642373i	$-0.222050\pi$
$787$	43.0000			1.53278			0.766392	+	0.642373i	$0.222050\pi$
$788$		0			0
$789$			36.3731i			1.29492i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.50000	−	11.2583i	−0.230822	−	0.399795i
$794$		0			0
$795$		−	31.1769i		−	1.10573i
$796$		0			0
$797$	−4.50000	−	7.79423i	−0.159398	−	0.276086i	0.775254	−	0.631650i	$-0.217622\pi$
$797$	−4.50000	−	7.79423i	−0.159398	−	0.276086i	−0.934652	+	0.355564i	$0.884289\pi$
$798$		0			0
$799$	27.0000	−	46.7654i	0.955191	−	1.65444i
$800$		0			0
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$		0			0
$803$	30.0000			1.05868
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.00000	+	5.19615i	−0.316815	+	0.182913i
$808$		0			0
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$			13.8564i			0.485965i
$814$		0			0
$815$	−60.0000			−2.10171
$816$		0			0
$817$	−4.00000			−0.139942
$818$		0			0
$819$		0			0
$820$		0			0
$821$	51.0000			1.77991			0.889956	−	0.456046i	$-0.150735\pi$
$821$	51.0000			1.77991			0.889956	+	0.456046i	$0.150735\pi$
$822$		0			0
$823$	−19.0000			−0.662298			−0.331149	−	0.943578i	$-0.607436\pi$
$823$	−19.0000			−0.662298			−0.331149	+	0.943578i	$0.607436\pi$
$824$		0			0
$825$	−18.0000	+	10.3923i	−0.626680	+	0.361814i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.00453881	−	0.999990i	$-0.498555\pi$
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.863747	−	0.503926i	$-0.168111\pi$
$830$		0			0
$831$			1.73205i			0.0600842i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	27.0000			0.934374
$836$		0			0
$837$		−	25.9808i		−	0.898027i
$838$		0			0
$839$	−4.50000	+	7.79423i	−0.155357	+	0.269087i	−0.933189	−	0.359386i	$-0.882986\pi$
$839$	−4.50000	+	7.79423i	−0.155357	+	0.269087i	0.777832	+	0.628473i	$0.216320\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−4.50000	+	2.59808i	−0.154988	+	0.0894825i
$844$		0			0
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7.50000	−	4.33013i	−0.257399	−	0.148610i
$850$		0			0
$851$	−6.00000			−0.205677
$852$		0			0
$853$	−6.50000	+	11.2583i	−0.222556	+	0.385478i	−0.955583	−	0.294721i	$-0.904773\pi$
$853$	−6.50000	+	11.2583i	−0.222556	+	0.385478i	0.733028	+	0.680199i	$0.238107\pi$
$854$		0			0
$855$	−18.0000	−	31.1769i	−0.615587	−	1.06623i
$856$		0			0
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	0.999019	−	0.0442921i	$-0.0141032\pi$
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	−0.537867	+	0.843029i	$0.680770\pi$
$858$		0			0
$859$	20.5000	−	35.5070i	0.699451	−	1.21148i	−0.269206	−	0.963083i	$-0.586761\pi$
$859$	20.5000	−	35.5070i	0.699451	−	1.21148i	0.968657	−	0.248402i	$-0.0799054\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$		0			0
$865$	13.5000	−	23.3827i	0.459014	−	0.795035i
$866$		0			0
$867$		−	32.9090i		−	1.11765i
$868$		0			0
$869$	−16.5000	−	28.5788i	−0.559724	−	0.969471i
$870$		0			0
$871$	3.50000	+	6.06218i	0.118593	+	0.205409i
$872$		0			0
$873$	33.0000			1.11688
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$		0			0
$879$		−	36.3731i		−	1.22683i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$	13.5000	−	7.79423i	0.453798	−	0.262000i
$886$		0			0
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	−0.634141	−	0.773217i	$-0.718646\pi$
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	0.986696	+	0.162573i	$0.0519794\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	27.0000			0.904534
$892$		0			0
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$		0			0
$895$	18.0000	+	31.1769i	0.601674	+	1.04213i
$896$		0			0
$897$	−4.50000	−	2.59808i	−0.150251	−	0.0867472i
$898$		0			0
$899$	7.50000	−	12.9904i	0.250139	−	0.433253i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$		0			0
$907$	−23.5000	−	40.7032i	−0.780305	−	1.35153i	−0.931764	−	0.363064i	$-0.881731\pi$
$907$	−23.5000	−	40.7032i	−0.780305	−	1.35153i	0.151460	−	0.988463i	$-0.451603\pi$
$908$		0			0
$909$	−22.5000	+	38.9711i	−0.746278	+	1.29259i
$910$		0			0
$911$	22.5000	−	38.9711i	0.745458	−	1.29117i	−0.204522	−	0.978862i	$-0.565564\pi$
$911$	22.5000	−	38.9711i	0.745458	−	1.29117i	0.949980	−	0.312310i	$-0.101103\pi$
$912$		0			0
$913$	27.0000			0.893570
$914$		0			0
$915$	58.5000	−	33.7750i	1.93395	−	1.11657i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	−30.0000	−	17.3205i	−0.988534	−	0.570730i
$922$		0			0
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$		0			0
$927$	−21.0000			−0.689730
$928$		0			0
$929$	−27.0000			−0.885841			−0.442921	−	0.896561i	$-0.646058\pi$
$929$	−27.0000			−0.885841			−0.442921	+	0.896561i	$0.646058\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−31.5000	−	18.1865i	−1.03126	−	0.595400i
$934$		0			0
$935$	−27.0000	+	46.7654i	−0.882994	+	1.52939i
$936$		0			0
$937$	34.0000			1.11073			0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000			1.11073			0.555366	+	0.831606i	$0.312578\pi$
$938$		0			0
$939$	1.50000	+	0.866025i	0.0489506	+	0.0282617i
$940$		0			0
$941$	21.0000			0.684580			0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000			0.684580			0.342290	+	0.939594i	$0.388797\pi$
$942$		0			0
$943$	9.00000			0.293080
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.0000			0.877382			0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000			0.877382			0.438691	+	0.898638i	$0.355442\pi$
$948$		0			0
$949$	10.0000			0.324614
$950$		0			0
$951$	−31.5000	−	18.1865i	−1.02146	−	0.589739i
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	22.5000	−	38.9711i	0.728083	−	1.26108i
$956$		0			0
$957$	13.5000	+	7.79423i	0.436393	+	0.251952i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.00000			−0.193548
$962$		0			0
$963$	18.0000	−	31.1769i	0.580042	−	1.00466i
$964$		0			0
$965$	16.5000	−	28.5788i	0.531154	−	0.919985i
$966$		0			0
$967$	21.5000	+	37.2391i	0.691393	+	1.19753i	0.971381	+	0.237525i	$0.0763362\pi$
$967$	21.5000	+	37.2391i	0.691393	+	1.19753i	−0.279988	+	0.960003i	$0.590331\pi$
$968$		0			0
$969$	−36.0000	−	20.7846i	−1.15649	−	0.667698i
$970$		0			0
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−6.00000	+	3.46410i	−0.192154	+	0.110940i
$976$		0			0
$977$	−57.0000			−1.82359			−0.911796	−	0.410644i	$-0.865304\pi$
$977$	−57.0000			−1.82359			−0.911796	+	0.410644i	$0.865304\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	−6.00000			−0.191565
$982$		0			0
$983$	25.5000	+	44.1673i	0.813324	+	1.40872i	0.910525	+	0.413453i	$0.135677\pi$
$983$	25.5000	+	44.1673i	0.813324	+	1.40872i	−0.0972017	+	0.995265i	$0.530989\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.50000	−	2.59808i	−0.0476972	−	0.0826140i
$990$		0			0
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$		0			0
$993$	16.5000	+	9.52628i	0.523612	+	0.302307i
$994$		0			0
$995$	6.00000	+	10.3923i	0.190213	+	0.329458i
$996$		0			0
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	0.857999	−	0.513651i	$-0.171707\pi$
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	−0.873834	+	0.486224i	$0.838374\pi$
$998$		0			0
$999$	9.00000	−	5.19615i	0.284747	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.c.1537.1		2
3.2	odd	2		5292.2.i.a.2125.1		2
7.2	even	3		1764.2.l.a.961.1		2
7.3	odd	6		36.2.e.a.25.1	yes	2
7.4	even	3		1764.2.j.b.1177.1		2
7.5	odd	6		1764.2.l.c.961.1		2
7.6	odd	2		1764.2.i.a.1537.1		2
9.4	even	3		1764.2.l.a.949.1		2
9.5	odd	6		5292.2.l.c.361.1		2
21.2	odd	6		5292.2.l.c.3313.1		2
21.5	even	6		5292.2.l.a.3313.1		2
21.11	odd	6		5292.2.j.a.3529.1		2
21.17	even	6		108.2.e.a.73.1		2
21.20	even	2		5292.2.i.c.2125.1		2
28.3	even	6		144.2.i.a.97.1		2
35.3	even	12		900.2.s.b.349.1		4
35.17	even	12		900.2.s.b.349.2		4
35.24	odd	6		900.2.i.b.601.1		2
56.3	even	6		576.2.i.e.385.1		2
56.45	odd	6		576.2.i.f.385.1		2
63.4	even	3		1764.2.j.b.589.1		2
63.5	even	6		5292.2.i.c.1549.1		2
63.13	odd	6		1764.2.l.c.949.1		2
63.23	odd	6		5292.2.i.a.1549.1		2
63.31	odd	6		36.2.e.a.13.1	✓	2
63.32	odd	6		5292.2.j.a.1765.1		2
63.38	even	6		324.2.a.a.1.1		1
63.40	odd	6		1764.2.i.a.373.1		2
63.41	even	6		5292.2.l.a.361.1		2
63.52	odd	6		324.2.a.c.1.1		1
63.58	even	3	inner	1764.2.i.c.373.1		2
63.59	even	6		108.2.e.a.37.1		2
84.59	odd	6		432.2.i.c.289.1		2
105.17	odd	12		2700.2.s.b.2449.2		4
105.38	odd	12		2700.2.s.b.2449.1		4
105.59	even	6		2700.2.i.b.1801.1		2
168.59	odd	6		1728.2.i.c.1153.1		2
168.101	even	6		1728.2.i.d.1153.1		2
252.31	even	6		144.2.i.a.49.1		2
252.59	odd	6		432.2.i.c.145.1		2
252.115	even	6		1296.2.a.k.1.1		1
252.227	odd	6		1296.2.a.b.1.1		1
315.38	odd	12		8100.2.d.c.649.2		2
315.52	even	12		8100.2.d.h.649.1		2
315.59	even	6		2700.2.i.b.901.1		2
315.94	odd	6		900.2.i.b.301.1		2
315.122	odd	12		2700.2.s.b.1549.1		4
315.157	even	12		900.2.s.b.49.1		4
315.164	even	6		8100.2.a.g.1.1		1
315.178	even	12		8100.2.d.h.649.2		2
315.227	odd	12		8100.2.d.c.649.1		2
315.248	odd	12		2700.2.s.b.1549.2		4
315.283	even	12		900.2.s.b.49.2		4
315.304	odd	6		8100.2.a.j.1.1		1
504.59	odd	6		1728.2.i.c.577.1		2
504.101	even	6		5184.2.a.ba.1.1		1
504.115	even	6		5184.2.a.f.1.1		1
504.157	odd	6		576.2.i.f.193.1		2
504.227	odd	6		5184.2.a.bb.1.1		1
504.283	even	6		576.2.i.e.193.1		2
504.437	even	6		1728.2.i.d.577.1		2
504.493	odd	6		5184.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.e.a.13.1	✓	2	63.31	odd	6
36.2.e.a.25.1	yes	2	7.3	odd	6
108.2.e.a.37.1		2	63.59	even	6
108.2.e.a.73.1		2	21.17	even	6
144.2.i.a.49.1		2	252.31	even	6
144.2.i.a.97.1		2	28.3	even	6
324.2.a.a.1.1		1	63.38	even	6
324.2.a.c.1.1		1	63.52	odd	6
432.2.i.c.145.1		2	252.59	odd	6
432.2.i.c.289.1		2	84.59	odd	6
576.2.i.e.193.1		2	504.283	even	6
576.2.i.e.385.1		2	56.3	even	6
576.2.i.f.193.1		2	504.157	odd	6
576.2.i.f.385.1		2	56.45	odd	6
900.2.i.b.301.1		2	315.94	odd	6
900.2.i.b.601.1		2	35.24	odd	6
900.2.s.b.49.1		4	315.157	even	12
900.2.s.b.49.2		4	315.283	even	12
900.2.s.b.349.1		4	35.3	even	12
900.2.s.b.349.2		4	35.17	even	12
1296.2.a.b.1.1		1	252.227	odd	6
1296.2.a.k.1.1		1	252.115	even	6
1728.2.i.c.577.1		2	504.59	odd	6
1728.2.i.c.1153.1		2	168.59	odd	6
1728.2.i.d.577.1		2	504.437	even	6
1728.2.i.d.1153.1		2	168.101	even	6
1764.2.i.a.373.1		2	63.40	odd	6
1764.2.i.a.1537.1		2	7.6	odd	2
1764.2.i.c.373.1		2	63.58	even	3	inner
1764.2.i.c.1537.1		2	1.1	even	1	trivial
1764.2.j.b.589.1		2	63.4	even	3
1764.2.j.b.1177.1		2	7.4	even	3
1764.2.l.a.949.1		2	9.4	even	3
1764.2.l.a.961.1		2	7.2	even	3
1764.2.l.c.949.1		2	63.13	odd	6
1764.2.l.c.961.1		2	7.5	odd	6
2700.2.i.b.901.1		2	315.59	even	6
2700.2.i.b.1801.1		2	105.59	even	6
2700.2.s.b.1549.1		4	315.122	odd	12
2700.2.s.b.1549.2		4	315.248	odd	12
2700.2.s.b.2449.1		4	105.38	odd	12
2700.2.s.b.2449.2		4	105.17	odd	12
5184.2.a.e.1.1		1	504.493	odd	6
5184.2.a.f.1.1		1	504.115	even	6
5184.2.a.ba.1.1		1	504.101	even	6
5184.2.a.bb.1.1		1	504.227	odd	6
5292.2.i.a.1549.1		2	63.23	odd	6
5292.2.i.a.2125.1		2	3.2	odd	2
5292.2.i.c.1549.1		2	63.5	even	6
5292.2.i.c.2125.1		2	21.20	even	2
5292.2.j.a.1765.1		2	63.32	odd	6
5292.2.j.a.3529.1		2	21.11	odd	6
5292.2.l.a.361.1		2	63.41	even	6
5292.2.l.a.3313.1		2	21.5	even	6
5292.2.l.c.361.1		2	9.5	odd	6
5292.2.l.c.3313.1		2	21.2	odd	6
8100.2.a.g.1.1		1	315.164	even	6
8100.2.a.j.1.1		1	315.304	odd	6
8100.2.d.c.649.1		2	315.227	odd	12
8100.2.d.c.649.2		2	315.38	odd	12
8100.2.d.h.649.1		2	315.52	even	12
8100.2.d.h.649.2		2	315.178	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(4.50000 - 2.59808i) q^{15} +(3.00000 - 5.19615i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} -5.00000 q^{31} -5.19615i q^{33} +(-1.00000 - 1.73205i) q^{37} -1.73205i q^{39} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +9.00000 q^{45} +9.00000 q^{47} +(9.00000 - 5.19615i) q^{51} +(3.00000 - 5.19615i) q^{53} -9.00000 q^{55} -6.92820i q^{57} +3.00000 q^{59} +13.0000 q^{61} -3.00000 q^{65} -7.00000 q^{67} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-5.00000 + 8.66025i) q^{73} -6.92820i q^{75} +11.0000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} +(-4.50000 + 2.59808i) q^{87} +(3.00000 + 5.19615i) q^{89} +(-7.50000 - 4.33013i) q^{93} -12.0000 q^{95} +(5.50000 - 9.52628i) q^{97} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 3 q^{5} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 3 * q^5 + 3 * q^9	\( 2 q + 3 q^{3} + 3 q^{5} + 3 q^{9} - 3 q^{11} - q^{13} + 9 q^{15} + 6 q^{17} - 4 q^{19} + 3 q^{23} - 4 q^{25} - 3 q^{29} - 10 q^{31} - 2 q^{37} + 3 q^{41} + q^{43} + 18 q^{45} + 18 q^{47} + 18 q^{51} + 6 q^{53} - 18 q^{55} + 6 q^{59} + 26 q^{61} - 6 q^{65} - 14 q^{67} + 9 q^{69} - 24 q^{71} - 10 q^{73} + 22 q^{79} - 9 q^{81} - 9 q^{83} - 18 q^{85} - 9 q^{87} + 6 q^{89} - 15 q^{93} - 24 q^{95} + 11 q^{97} + 9 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 3 * q^5 + 3 * q^9 - 3 * q^11 - q^13 + 9 * q^15 + 6 * q^17 - 4 * q^19 + 3 * q^23 - 4 * q^25 - 3 * q^29 - 10 * q^31 - 2 * q^37 + 3 * q^41 + q^43 + 18 * q^45 + 18 * q^47 + 18 * q^51 + 6 * q^53 - 18 * q^55 + 6 * q^59 + 26 * q^61 - 6 * q^65 - 14 * q^67 + 9 * q^69 - 24 * q^71 - 10 * q^73 + 22 * q^79 - 9 * q^81 - 9 * q^83 - 18 * q^85 - 9 * q^87 + 6 * q^89 - 15 * q^93 - 24 * q^95 + 11 * q^97 + 9 * q^99

Introduction

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