LMFDB - Embedded newform 1764.2.l.a.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

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, 4]))

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

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

chi := DirichletCharacter("1764.949");

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.l (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:	$1$
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			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1764.961
Dual form			1764.2.l.a.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(1.50000 - 2.59808i) q^{9} +3.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(4.50000 - 2.59808i) q^{15} +(3.00000 + 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} -3.00000 q^{23} +4.00000 q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(2.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-4.50000 + 7.79423i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(-9.00000 - 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} -9.00000 q^{55} -6.92820i q^{57} +(-1.50000 + 2.59808i) q^{59} +(-6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-6.00000 + 3.46410i) q^{75} +(-5.50000 - 9.52628i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} -5.19615i q^{87} +(3.00000 - 5.19615i) q^{89} +8.66025i q^{93} +(6.00000 - 10.3923i) q^{95} +(5.50000 - 9.52628i) q^{97} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 6 * q^5 + 3 * q^9	$ 2 q - 3 q^{3} - 6 q^{5} + 3 q^{9} + 6 q^{11} - q^{13} + 9 q^{15} + 6 q^{17} - 4 q^{19} - 6 q^{23} + 8 q^{25} - 3 q^{29} + 5 q^{31} - 9 q^{33} - 2 q^{37} + 3 q^{39} + 3 q^{41} + q^{43} - 9 q^{45} - 9 q^{47} - 18 q^{51} + 6 q^{53} - 18 q^{55} - 3 q^{59} - 13 q^{61} + 3 q^{65} + 7 q^{67} + 9 q^{69} - 24 q^{71} - 10 q^{73} - 12 q^{75} - 11 q^{79} - 9 q^{81} - 9 q^{83} - 18 q^{85} + 6 q^{89} + 12 q^{95} + 11 q^{97} + 9 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 6 * q^5 + 3 * q^9 + 6 * q^11 - q^13 + 9 * q^15 + 6 * q^17 - 4 * q^19 - 6 * q^23 + 8 * q^25 - 3 * q^29 + 5 * q^31 - 9 * q^33 - 2 * q^37 + 3 * q^39 + 3 * q^41 + q^43 - 9 * q^45 - 9 * q^47 - 18 * q^51 + 6 * q^53 - 18 * q^55 - 3 * q^59 - 13 * q^61 + 3 * q^65 + 7 * q^67 + 9 * q^69 - 24 * q^71 - 10 * q^73 - 12 * q^75 - 11 * q^79 - 9 * q^81 - 9 * q^83 - 18 * q^85 + 6 * q^89 + 12 * q^95 + 11 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$		0			0
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		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	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		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
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$		0			0
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$		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
$45$	−4.50000	+	7.79423i	−0.670820	+	1.16190i
$46$		0			0
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$		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	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$		−	6.92820i		−	0.917663i
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	−6.50000	−	11.2583i	−0.832240	−	1.44148i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−6.50000	−	11.2583i	−0.832240	−	1.44148i	0.0640184	−	0.997949i	$-0.479608\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$		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	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$		0			0
$75$	−6.00000	+	3.46410i	−0.692820	+	0.400000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		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
$87$		−	5.19615i		−	0.557086i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$			8.66025i			0.898027i
$94$		0			0
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$		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
$101$	−15.0000			−1.49256			−0.746278	−	0.665635i	$-0.768161\pi$
$101$	−15.0000			−1.49256			−0.746278	+	0.665635i	$0.768161\pi$
$102$		0			0
$103$	7.00000			0.689730			0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000			0.689730			0.344865	+	0.938652i	$0.387925\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		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
$115$	9.00000			0.839254
$116$		0			0
$117$	−3.00000			−0.277350
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$		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
$129$			1.73205i			0.152499i
$130$		0			0
$131$	−21.0000			−1.83478			−0.917389	−	0.397991i	$-0.869707\pi$
$131$	−21.0000			−1.83478			−0.917389	+	0.397991i	$0.869707\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		−	15.5885i		−	1.34164i
$136$		0			0
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$		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
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$		0			0
$151$	−13.0000			−1.05792			−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000			−1.05792			−0.528962	+	0.848645i	$0.677419\pi$
$152$		0			0
$153$	18.0000			1.45521
$154$		0			0
$155$	−7.50000	+	12.9904i	−0.602414	+	1.04341i
$156$		0			0
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	0.481006	+	0.876717i	$0.340272\pi$
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	−0.999762	+	0.0217953i	$0.993062\pi$
$158$		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	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		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
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	5.19615i		−	0.390567i
$178$		0			0
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		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
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	−0.998749	−	0.0500060i	$-0.984076\pi$
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	0.456068	−	0.889945i	$-0.349257\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$		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	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$			12.1244i			0.855186i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$		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
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$		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
$227$	−27.0000			−1.79205			−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000			−1.79205			−0.896026	+	0.444001i	$0.853559\pi$
$228$		0			0
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		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
$241$	1.00000			0.0644157			0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000			0.0644157			0.0322078	+	0.999481i	$0.489746\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000			0.254514
$248$		0			0
$249$		−	15.5885i		−	0.987878i
$250$		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
$255$	27.0000	+	15.5885i	1.69081	+	0.976187i
$256$		0			0
$257$	9.00000			0.561405			0.280702	−	0.959795i	$-0.409433\pi$
$257$	9.00000			0.561405			0.280702	+	0.959795i	$0.409433\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$		0			0
$263$	−21.0000			−1.29492			−0.647458	−	0.762101i	$-0.724168\pi$
$263$	−21.0000			−1.29492			−0.647458	+	0.762101i	$0.724168\pi$
$264$		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	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.0000			0.723627
$276$		0			0
$277$	−1.00000			−0.0600842			−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000			−0.0600842			−0.0300421	+	0.999549i	$0.509564\pi$
$278$		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
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	−0.782104	−	0.623148i	$-0.785854\pi$
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	0.930714	+	0.365748i	$0.119187\pi$
$284$		0			0
$285$			20.7846i			1.23117i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$			19.0526i			1.11688i
$292$		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
$297$			15.5885i			0.904534i
$298$		0			0
$299$	1.50000	+	2.59808i	0.0867472	+	0.150251i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	22.5000	−	12.9904i	1.29259	−	0.746278i
$304$		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
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	−0.398090	−	0.917346i	$-0.630327\pi$
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	0.993490	−	0.113917i	$-0.0363399\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	0.994266	+	0.106932i	$0.0341026\pi$
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	−0.404528	+	0.914526i	$0.632564\pi$
$318$		0			0
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$		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
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$		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
$339$	−13.5000	−	7.79423i	−0.733219	−	0.423324i
$340$		0			0
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−13.5000	+	7.79423i	−0.726816	+	0.419627i
$346$		0			0
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	−0.961162	−	0.275983i	$-0.910997\pi$
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	0.719590	+	0.694399i	$0.244330\pi$
$348$		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
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	36.0000			1.91068
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		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
$367$	13.0000			0.678594			0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000			0.678594			0.339297	+	0.940679i	$0.389811\pi$
$368$		0			0
$369$	9.00000			0.468521
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.00000			−0.0517780			−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000			−0.0517780			−0.0258890	+	0.999665i	$0.508242\pi$
$374$		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
$383$	15.0000			0.766464			0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000			0.766464			0.383232	+	0.923652i	$0.374811\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$		0			0
$389$	15.0000			0.760530			0.380265	−	0.924878i	$-0.375833\pi$
$389$	15.0000			0.760530			0.380265	+	0.924878i	$0.375833\pi$
$390$		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	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$		0			0
$403$	−5.00000			−0.249068
$404$		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
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	−0.428063	−	0.903749i	$-0.640804\pi$
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	0.996701	−	0.0811615i	$-0.0258630\pi$
$410$		0			0
$411$	−4.50000	+	2.59808i	−0.221969	+	0.128154i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	13.5000	−	23.3827i	0.662689	−	1.14781i
$416$		0			0
$417$	−7.50000	−	4.33013i	−0.367277	−	0.212047i
$418$		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
$423$	−27.0000			−1.31278
$424$		0			0
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		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	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$		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
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$		0			0
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$		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
$453$	19.5000	−	11.2583i	0.916190	−	0.528962i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	0.866656	+	0.498906i	$0.166265\pi$
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	−0.00126243	+	0.999999i	$0.500402\pi$
$458$		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
$465$		−	25.9808i		−	1.20483i
$466$		0			0
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		−	22.5167i		−	1.03751i
$472$		0			0
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$		0			0
$475$	−8.00000	+	13.8564i	−0.367065	+	0.635776i
$476$		0			0
$477$	18.0000			0.824163
$478$		0			0
$479$	−27.0000			−1.23366			−0.616831	−	0.787096i	$-0.711584\pi$
$479$	−27.0000			−1.23366			−0.616831	+	0.787096i	$0.711584\pi$
$480$		0			0
$481$	2.00000			0.0911922
$482$		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	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$		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
$493$	−18.0000			−0.810679
$494$		0			0
$495$	−13.5000	+	23.3827i	−0.606780	+	1.05097i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	5.00000			0.223831			0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000			0.223831			0.111915	+	0.993718i	$0.464301\pi$
$500$		0			0
$501$	−13.5000	−	7.79423i	−0.603136	−	0.348220i
$502$		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
$507$			20.7846i			0.923077i
$508$		0			0
$509$	−39.0000			−1.72864			−0.864322	−	0.502938i	$-0.832252\pi$
$509$	−39.0000			−1.72864			−0.864322	+	0.502938i	$0.832252\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−18.0000	−	10.3923i	−0.794719	−	0.458831i
$514$		0			0
$515$	−21.0000			−0.925371
$516$		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	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$		0			0
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	0.940129	+	0.340818i	$0.110704\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	30.0000			1.30682
$528$		0			0
$529$	−14.0000			−0.608696
$530$		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
$535$	18.0000	−	31.1769i	0.778208	−	1.34790i
$536$		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	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$		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
$549$	−39.0000			−1.66448
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$			10.3923i			0.441129i
$556$		0			0
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$	−27.0000	−	15.5885i	−1.13994	−	0.658145i
$562$		0			0
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	−0.755482	−	0.655169i	$-0.772597\pi$
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	0.945134	+	0.326682i	$0.105931\pi$
$564$		0			0
$565$	−13.5000	−	23.3827i	−0.567949	−	0.983717i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	15.5000	−	26.8468i	0.648655	−	1.12350i	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	15.5000	−	26.8468i	0.648655	−	1.12350i	0.983444	−	0.181210i	$-0.0580014\pi$
$572$		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	0.742980	−	0.669314i	$-0.233412\pi$
$577$	−5.00000	−	8.66025i	−0.208153	−	0.360531i	−0.951133	+	0.308783i	$0.900078\pi$
$578$		0			0
$579$		−	19.0526i		−	0.791797i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$		0			0
$585$	9.00000			0.372104
$586$		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	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.00000	+	3.46410i	0.245564	+	0.141776i
$598$		0			0
$599$	19.5000	−	33.7750i	0.796748	−	1.38001i	−0.124975	−	0.992160i	$-0.539885\pi$
$599$	19.5000	−	33.7750i	0.796748	−	1.38001i	0.921723	−	0.387849i	$-0.126782\pi$
$600$		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
$605$	6.00000			0.243935
$606$		0			0
$607$	−41.0000			−1.66414			−0.832069	−	0.554672i	$-0.812844\pi$
$607$	−41.0000			−1.66414			−0.832069	+	0.554672i	$0.812844\pi$
$608$		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	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$		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
$619$	13.0000			0.522514			0.261257	−	0.965269i	$-0.415863\pi$
$619$	13.0000			0.522514			0.261257	+	0.965269i	$0.415863\pi$
$620$		0			0
$621$		−	15.5885i		−	0.625543i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		−	20.7846i		−	0.830057i
$628$		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
$633$	25.5000	+	14.7224i	1.01353	+	0.585164i
$634$		0			0
$635$	48.0000			1.90482
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$		0			0
$641$	−33.0000			−1.30342			−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000			−1.30342			−0.651711	+	0.758468i	$0.725948\pi$
$642$		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	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0000			−0.821794			−0.410897	−	0.911682i	$-0.634784\pi$
$653$	−21.0000			−0.821794			−0.410897	+	0.911682i	$0.634784\pi$
$654$		0			0
$655$	63.0000			2.46161
$656$		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
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	0.952940	+	0.303160i	$0.0980418\pi$
$662$		0			0
$663$			10.3923i			0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.50000	−	7.79423i	0.174241	−	0.301794i
$668$		0			0
$669$		−	1.73205i		−	0.0669650i
$670$		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
$675$			20.7846i			0.800000i
$676$		0			0
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	0.973392	−	0.229147i	$-0.0735938\pi$
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	−0.685143	+	0.728408i	$0.740260\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	40.5000	−	23.3827i	1.55196	−	0.896026i
$682$		0			0
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	0.972242	+	0.233977i	$0.0751739\pi$
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	−0.283491	+	0.958975i	$0.591493\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	−19.5000	+	11.2583i	−0.743971	+	0.429532i
$688$		0			0
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	0.856358	−	0.516382i	$-0.172722\pi$
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	−0.875379	+	0.483437i	$0.839388\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.50000	−	12.9904i	−0.284491	−	0.492753i
$696$		0			0
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$		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
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	0.999390	−	0.0349269i	$-0.0111198\pi$
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	−0.529943	+	0.848034i	$0.677787\pi$
$710$		0			0
$711$	−33.0000			−1.23760
$712$		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
$717$	−40.5000	−	23.3827i	−1.51250	−	0.873242i
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.50000	+	0.866025i	−0.0557856	+	0.0322078i
$724$		0			0
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		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
$731$	6.00000			0.221918
$732$		0			0
$733$	−23.0000			−0.849524			−0.424762	−	0.905305i	$-0.639642\pi$
$733$	−23.0000			−0.849524			−0.424762	+	0.905305i	$0.639642\pi$
$734$		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	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		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
$745$	−45.0000			−1.64867
$746$		0			0
$747$	13.5000	+	23.3827i	0.493939	+	0.855528i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−31.0000			−1.13121			−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000			−1.13121			−0.565603	+	0.824678i	$0.691357\pi$
$752$		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
$761$	−27.0000			−0.978749			−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000			−0.978749			−0.489375	+	0.872074i	$0.662775\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−54.0000			−1.95237
$766$		0			0
$767$	3.00000			0.108324
$768$		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	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$		0			0
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000			−0.429945
$780$		0			0
$781$	−36.0000			−1.28818
$782$		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
$787$	−21.5000	+	37.2391i	−0.766392	+	1.32743i	0.173115	+	0.984902i	$0.444617\pi$
$787$	−21.5000	+	37.2391i	−0.766392	+	1.32743i	−0.939507	+	0.342529i	$0.888717\pi$
$788$		0			0
$789$	31.5000	−	18.1865i	1.12143	−	0.647458i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.50000	+	11.2583i	−0.230822	+	0.399795i
$794$		0			0
$795$	27.0000	+	15.5885i	0.957591	+	0.552866i
$796$		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
$803$	−15.0000	−	25.9808i	−0.529339	−	0.916841i
$804$		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	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$		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
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.839926	−	0.542702i	$-0.817401\pi$
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.0500305	−	0.998748i	$-0.515932\pi$
$822$		0			0
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	−0.651588	−	0.758573i	$-0.725897\pi$
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	0.982737	+	0.185006i	$0.0592303\pi$
$824$		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	0.863747	+	0.503926i	$0.168111\pi$
$829$	25.0000	+	43.3013i	0.868286	+	1.50392i	0.00453881	+	0.999990i	$0.498555\pi$
$830$		0			0
$831$	1.50000	−	0.866025i	0.0520344	−	0.0300421i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13.5000	−	23.3827i	−0.467187	−	0.809191i
$836$		0			0
$837$	22.5000	+	12.9904i	0.777714	+	0.449013i
$838$		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
$843$		−	5.19615i		−	0.178965i
$844$		0			0
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$		0			0
$848$		0			0
$849$			8.66025i			0.297219i
$850$		0			0
$851$	3.00000	−	5.19615i	0.102839	−	0.178122i
$852$		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
$857$	−27.0000			−0.922302			−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000			−0.922302			−0.461151	+	0.887322i	$0.652563\pi$
$858$		0			0
$859$	−41.0000			−1.39890			−0.699451	−	0.714681i	$-0.746572\pi$
$859$	−41.0000			−1.39890			−0.699451	+	0.714681i	$0.746572\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$		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
$871$	−7.00000			−0.237186
$872$		0			0
$873$	−16.5000	−	28.5788i	−0.558440	−	0.967247i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.0000			0.776655			0.388327	−	0.921521i	$-0.373053\pi$
$877$	23.0000			0.776655			0.388327	+	0.921521i	$0.373053\pi$
$878$		0			0
$879$	31.5000	+	18.1865i	1.06247	+	0.613417i
$880$		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
$885$			15.5885i			0.524000i
$886$		0			0
$887$	−21.0000			−0.705111			−0.352555	−	0.935791i	$-0.614687\pi$
$887$	−21.0000			−0.705111			−0.352555	+	0.935791i	$0.614687\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−13.5000	−	23.3827i	−0.452267	−	0.783349i
$892$		0			0
$893$	36.0000			1.20469
$894$		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
$905$	6.00000			0.199447
$906$		0			0
$907$	47.0000			1.56061			0.780305	−	0.625400i	$-0.215064\pi$
$907$	47.0000			1.56061			0.780305	+	0.625400i	$0.215064\pi$
$908$		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
$913$	−13.5000	+	23.3827i	−0.446785	+	0.773854i
$914$		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	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		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
$927$	10.5000	−	18.1865i	0.344865	−	0.597324i
$928$		0			0
$929$	13.5000	+	23.3827i	0.442921	+	0.767161i	0.997905	−	0.0646999i	$-0.0206090\pi$
$929$	13.5000	+	23.3827i	0.442921	+	0.767161i	−0.554984	+	0.831861i	$0.687276\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$			36.3731i			1.19080i
$934$		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
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	−0.984858	−	0.173365i	$-0.944536\pi$
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	0.642567	+	0.766229i	$0.277869\pi$
$942$		0			0
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	0.558898	−	0.829237i	$-0.311224\pi$
$947$	−13.5000	−	23.3827i	−0.438691	−	0.759835i	−0.997589	+	0.0694014i	$0.977891\pi$
$948$		0			0
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$		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
$957$		−	15.5885i		−	0.503903i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		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	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.00000	+	3.46410i	0.192154	+	0.110940i
$976$		0			0
$977$	28.5000	−	49.3634i	0.911796	−	1.57928i	0.100270	−	0.994960i	$-0.468029\pi$
$977$	28.5000	−	49.3634i	0.911796	−	1.57928i	0.811526	−	0.584316i	$-0.198637\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	−6.00000			−0.191565
$982$		0			0
$983$	−51.0000			−1.62665			−0.813324	−	0.581811i	$-0.802344\pi$
$983$	−51.0000			−1.62665			−0.813324	+	0.581811i	$0.802344\pi$
$984$		0			0
$985$	−18.0000			−0.573528
$986$		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	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$		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
$997$	1.00000			0.0316703			0.0158352	−	0.999875i	$-0.494959\pi$
$997$	1.00000			0.0316703			0.0158352	+	0.999875i	$0.494959\pi$
$998$		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.l.a.961.1		2
3.2	odd	2		5292.2.l.c.3313.1		2
7.2	even	3		1764.2.j.b.1177.1		2
7.3	odd	6		1764.2.i.a.1537.1		2
7.4	even	3		1764.2.i.c.1537.1		2
7.5	odd	6		36.2.e.a.25.1	yes	2
7.6	odd	2		1764.2.l.c.961.1		2
9.4	even	3		1764.2.i.c.373.1		2
9.5	odd	6		5292.2.i.a.1549.1		2
21.2	odd	6		5292.2.j.a.3529.1		2
21.5	even	6		108.2.e.a.73.1		2
21.11	odd	6		5292.2.i.a.2125.1		2
21.17	even	6		5292.2.i.c.2125.1		2
21.20	even	2		5292.2.l.a.3313.1		2
28.19	even	6		144.2.i.a.97.1		2
35.12	even	12		900.2.s.b.349.2		4
35.19	odd	6		900.2.i.b.601.1		2
35.33	even	12		900.2.s.b.349.1		4
56.5	odd	6		576.2.i.f.385.1		2
56.19	even	6		576.2.i.e.385.1		2
63.4	even	3	inner	1764.2.l.a.949.1		2
63.5	even	6		108.2.e.a.37.1		2
63.13	odd	6		1764.2.i.a.373.1		2
63.23	odd	6		5292.2.j.a.1765.1		2
63.31	odd	6		1764.2.l.c.949.1		2
63.32	odd	6		5292.2.l.c.361.1		2
63.40	odd	6		36.2.e.a.13.1	✓	2
63.41	even	6		5292.2.i.c.1549.1		2
63.47	even	6		324.2.a.a.1.1		1
63.58	even	3		1764.2.j.b.589.1		2
63.59	even	6		5292.2.l.a.361.1		2
63.61	odd	6		324.2.a.c.1.1		1
84.47	odd	6		432.2.i.c.289.1		2
105.47	odd	12		2700.2.s.b.2449.2		4
105.68	odd	12		2700.2.s.b.2449.1		4
105.89	even	6		2700.2.i.b.1801.1		2
168.5	even	6		1728.2.i.d.1153.1		2
168.131	odd	6		1728.2.i.c.1153.1		2
252.47	odd	6		1296.2.a.b.1.1		1
252.103	even	6		144.2.i.a.49.1		2
252.131	odd	6		432.2.i.c.145.1		2
252.187	even	6		1296.2.a.k.1.1		1
315.47	odd	12		8100.2.d.c.649.1		2
315.68	odd	12		2700.2.s.b.1549.2		4
315.103	even	12		900.2.s.b.49.2		4
315.124	odd	6		8100.2.a.j.1.1		1
315.173	odd	12		8100.2.d.c.649.2		2
315.187	even	12		8100.2.d.h.649.1		2
315.194	even	6		2700.2.i.b.901.1		2
315.229	odd	6		900.2.i.b.301.1		2
315.257	odd	12		2700.2.s.b.1549.1		4
315.292	even	12		900.2.s.b.49.1		4
315.299	even	6		8100.2.a.g.1.1		1
315.313	even	12		8100.2.d.h.649.2		2
504.5	even	6		1728.2.i.d.577.1		2
504.61	odd	6		5184.2.a.e.1.1		1
504.131	odd	6		1728.2.i.c.577.1		2
504.173	even	6		5184.2.a.ba.1.1		1
504.187	even	6		5184.2.a.f.1.1		1
504.229	odd	6		576.2.i.f.193.1		2
504.299	odd	6		5184.2.a.bb.1.1		1
504.355	even	6		576.2.i.e.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.e.a.13.1	✓	2	63.40	odd	6
36.2.e.a.25.1	yes	2	7.5	odd	6
108.2.e.a.37.1		2	63.5	even	6
108.2.e.a.73.1		2	21.5	even	6
144.2.i.a.49.1		2	252.103	even	6
144.2.i.a.97.1		2	28.19	even	6
324.2.a.a.1.1		1	63.47	even	6
324.2.a.c.1.1		1	63.61	odd	6
432.2.i.c.145.1		2	252.131	odd	6
432.2.i.c.289.1		2	84.47	odd	6
576.2.i.e.193.1		2	504.355	even	6
576.2.i.e.385.1		2	56.19	even	6
576.2.i.f.193.1		2	504.229	odd	6
576.2.i.f.385.1		2	56.5	odd	6
900.2.i.b.301.1		2	315.229	odd	6
900.2.i.b.601.1		2	35.19	odd	6
900.2.s.b.49.1		4	315.292	even	12
900.2.s.b.49.2		4	315.103	even	12
900.2.s.b.349.1		4	35.33	even	12
900.2.s.b.349.2		4	35.12	even	12
1296.2.a.b.1.1		1	252.47	odd	6
1296.2.a.k.1.1		1	252.187	even	6
1728.2.i.c.577.1		2	504.131	odd	6
1728.2.i.c.1153.1		2	168.131	odd	6
1728.2.i.d.577.1		2	504.5	even	6
1728.2.i.d.1153.1		2	168.5	even	6
1764.2.i.a.373.1		2	63.13	odd	6
1764.2.i.a.1537.1		2	7.3	odd	6
1764.2.i.c.373.1		2	9.4	even	3
1764.2.i.c.1537.1		2	7.4	even	3
1764.2.j.b.589.1		2	63.58	even	3
1764.2.j.b.1177.1		2	7.2	even	3
1764.2.l.a.949.1		2	63.4	even	3	inner
1764.2.l.a.961.1		2	1.1	even	1	trivial
1764.2.l.c.949.1		2	63.31	odd	6
1764.2.l.c.961.1		2	7.6	odd	2
2700.2.i.b.901.1		2	315.194	even	6
2700.2.i.b.1801.1		2	105.89	even	6
2700.2.s.b.1549.1		4	315.257	odd	12
2700.2.s.b.1549.2		4	315.68	odd	12
2700.2.s.b.2449.1		4	105.68	odd	12
2700.2.s.b.2449.2		4	105.47	odd	12
5184.2.a.e.1.1		1	504.61	odd	6
5184.2.a.f.1.1		1	504.187	even	6
5184.2.a.ba.1.1		1	504.173	even	6
5184.2.a.bb.1.1		1	504.299	odd	6
5292.2.i.a.1549.1		2	9.5	odd	6
5292.2.i.a.2125.1		2	21.11	odd	6
5292.2.i.c.1549.1		2	63.41	even	6
5292.2.i.c.2125.1		2	21.17	even	6
5292.2.j.a.1765.1		2	63.23	odd	6
5292.2.j.a.3529.1		2	21.2	odd	6
5292.2.l.a.361.1		2	63.59	even	6
5292.2.l.a.3313.1		2	21.20	even	2
5292.2.l.c.361.1		2	63.32	odd	6
5292.2.l.c.3313.1		2	3.2	odd	2
8100.2.a.g.1.1		1	315.299	even	6
8100.2.a.j.1.1		1	315.124	odd	6
8100.2.d.c.649.1		2	315.47	odd	12
8100.2.d.c.649.2		2	315.173	odd	12
8100.2.d.h.649.1		2	315.187	even	12
8100.2.d.h.649.2		2	315.313	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.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(1.50000 - 2.59808i) q^{9} +3.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(4.50000 - 2.59808i) q^{15} +(3.00000 + 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} -3.00000 q^{23} +4.00000 q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(2.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-4.50000 + 7.79423i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(-9.00000 - 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} -9.00000 q^{55} -6.92820i q^{57} +(-1.50000 + 2.59808i) q^{59} +(-6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{65} +(3.50000 - 6.06218i) q^{67} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-6.00000 + 3.46410i) q^{75} +(-5.50000 - 9.52628i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} -5.19615i q^{87} +(3.00000 - 5.19615i) q^{89} +8.66025i q^{93} +(6.00000 - 10.3923i) q^{95} +(5.50000 - 9.52628i) q^{97} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 6 * q^5 + 3 * q^9	\( 2 q - 3 q^{3} - 6 q^{5} + 3 q^{9} + 6 q^{11} - q^{13} + 9 q^{15} + 6 q^{17} - 4 q^{19} - 6 q^{23} + 8 q^{25} - 3 q^{29} + 5 q^{31} - 9 q^{33} - 2 q^{37} + 3 q^{39} + 3 q^{41} + q^{43} - 9 q^{45} - 9 q^{47} - 18 q^{51} + 6 q^{53} - 18 q^{55} - 3 q^{59} - 13 q^{61} + 3 q^{65} + 7 q^{67} + 9 q^{69} - 24 q^{71} - 10 q^{73} - 12 q^{75} - 11 q^{79} - 9 q^{81} - 9 q^{83} - 18 q^{85} + 6 q^{89} + 12 q^{95} + 11 q^{97} + 9 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 6 * q^5 + 3 * q^9 + 6 * q^11 - q^13 + 9 * q^15 + 6 * q^17 - 4 * q^19 - 6 * q^23 + 8 * q^25 - 3 * q^29 + 5 * q^31 - 9 * q^33 - 2 * q^37 + 3 * q^39 + 3 * q^41 + q^43 - 9 * q^45 - 9 * q^47 - 18 * q^51 + 6 * q^53 - 18 * q^55 - 3 * q^59 - 13 * q^61 + 3 * q^65 + 7 * q^67 + 9 * q^69 - 24 * q^71 - 10 * q^73 - 12 * q^75 - 11 * q^79 - 9 * q^81 - 9 * q^83 - 18 * q^85 + 6 * q^89 + 12 * q^95 + 11 * q^97 + 9 * q^99

Introduction

L-functions

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