LMFDB - Embedded newform 2028.2.i.g.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2028,2,Mod(529,2028)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2028, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("2028.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2028 = 2^{2} \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2028.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:	$16.1936615299$
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 156)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2028.529
Dual form			2028.2.i.g.2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +4.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +4.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(2.00000 - 3.46410i) q^{15} +(-1.00000 - 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{19} -2.00000 q^{21} +11.0000 q^{25} -1.00000 q^{27} +(3.00000 - 5.19615i) q^{29} +10.0000 q^{31} +(2.00000 + 3.46410i) q^{33} +(-4.00000 - 6.92820i) q^{35} +(5.00000 - 8.66025i) q^{37} +(4.00000 - 6.92820i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-2.00000 - 3.46410i) q^{45} +4.00000 q^{47} +(1.50000 - 2.59808i) q^{49} -2.00000 q^{51} -10.0000 q^{53} +(-8.00000 + 13.8564i) q^{55} -2.00000 q^{57} +(-4.00000 - 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-1.00000 + 1.73205i) q^{63} +(1.00000 - 1.73205i) q^{67} +(8.00000 + 13.8564i) q^{71} +10.0000 q^{73} +(5.50000 - 9.52628i) q^{75} +8.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{85} +(-3.00000 - 5.19615i) q^{87} +(-2.00000 + 3.46410i) q^{89} +(5.00000 - 8.66025i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 8 q^{5} - 2 q^{7} - q^{9}+O(q^{10}) $ 2 * q + q^3 + 8 * q^5 - 2 * q^7 - q^9	$ 2 q + q^{3} + 8 q^{5} - 2 q^{7} - q^{9} - 4 q^{11} + 4 q^{15} - 2 q^{17} - 2 q^{19} - 4 q^{21} + 22 q^{25} - 2 q^{27} + 6 q^{29} + 20 q^{31} + 4 q^{33} - 8 q^{35} + 10 q^{37} + 8 q^{41} - 4 q^{43} - 4 q^{45} + 8 q^{47} + 3 q^{49} - 4 q^{51} - 20 q^{53} - 16 q^{55} - 4 q^{57} - 8 q^{59} + 14 q^{61} - 2 q^{63} + 2 q^{67} + 16 q^{71} + 20 q^{73} + 11 q^{75} + 16 q^{77} - 32 q^{79} - q^{81} - 8 q^{85} - 6 q^{87} - 4 q^{89} + 10 q^{93} - 8 q^{95} - 2 q^{97} + 8 q^{99}+O(q^{100}) $ 2 * q + q^3 + 8 * q^5 - 2 * q^7 - q^9 - 4 * q^11 + 4 * q^15 - 2 * q^17 - 2 * q^19 - 4 * q^21 + 22 * q^25 - 2 * q^27 + 6 * q^29 + 20 * q^31 + 4 * q^33 - 8 * q^35 + 10 * q^37 + 8 * q^41 - 4 * q^43 - 4 * q^45 + 8 * q^47 + 3 * q^49 - 4 * q^51 - 20 * q^53 - 16 * q^55 - 4 * q^57 - 8 * q^59 + 14 * q^61 - 2 * q^63 + 2 * q^67 + 16 * q^71 + 20 * q^73 + 11 * q^75 + 16 * q^77 - 32 * q^79 - q^81 - 8 * q^85 - 6 * q^87 - 4 * q^89 + 10 * q^93 - 8 * q^95 - 2 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1861$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	4.00000			1.78885			0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000			1.78885			0.894427	+	0.447214i	$0.147584\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	2.00000	−	3.46410i	0.516398	−	0.894427i
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	11.0000			2.20000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$		0			0
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$		0			0
$35$	−4.00000	−	6.92820i	−0.676123	−	1.17108i
$36$		0			0
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	−0.363905	−	0.931436i	$-0.618557\pi$
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	0.988600	−	0.150567i	$-0.0481100\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$		0			0
$45$	−2.00000	−	3.46410i	−0.298142	−	0.516398i
$46$		0			0
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$	−10.0000			−1.37361			−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000			−1.37361			−0.686803	+	0.726844i	$0.740986\pi$
$54$		0			0
$55$	−8.00000	+	13.8564i	−1.07872	+	1.86840i
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	−1.00000	+	1.73205i	−0.125988	+	0.218218i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.00000	+	13.8564i	0.949425	+	1.64445i	0.746639	+	0.665230i	$0.231667\pi$
$71$	8.00000	+	13.8564i	0.949425	+	1.64445i	0.202787	+	0.979223i	$0.435000\pi$
$72$		0			0
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$	5.50000	−	9.52628i	0.635085	−	1.10000i
$76$		0			0
$77$	8.00000			0.911685
$78$		0			0
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$		0			0
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	−0.952340	−	0.305038i	$-0.901331\pi$
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	0.740341	+	0.672232i	$0.234664\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$		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
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−5.00000	−	8.66025i	−0.474579	−	0.821995i
$112$		0			0
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$		0			0
$125$	24.0000			2.14663
$126$		0			0
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$		0			0
$129$	−4.00000			−0.352180
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$		0			0
$135$	−4.00000			−0.344265
$136$		0			0
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	0.984757	−	0.173939i	$-0.0556494\pi$
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	−0.643013	+	0.765855i	$0.722316\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$	2.00000	−	3.46410i	0.168430	−	0.291730i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	12.0000	−	20.7846i	0.996546	−	1.72607i
$146$		0			0
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$		0			0
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$		0			0
$153$	−1.00000	+	1.73205i	−0.0808452	+	0.140028i
$154$		0			0
$155$	40.0000			3.21288
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$		0			0
$165$	8.00000	+	13.8564i	0.622799	+	1.07872i
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	0.825505	−	0.564396i	$-0.190891\pi$
$173$	−1.00000	−	1.73205i	−0.0760286	−	0.131685i	−0.901533	+	0.432710i	$0.857557\pi$
$174$		0			0
$175$	−11.0000	−	19.0526i	−0.831522	−	1.44024i
$176$		0			0
$177$	−8.00000			−0.601317
$178$		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	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$	20.0000	−	34.6410i	1.47043	−	2.54686i
$186$		0			0
$187$	8.00000			0.585018
$188$		0			0
$189$	1.00000	+	1.73205i	0.0727393	+	0.125988i
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$		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
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$		0			0
$203$	−12.0000			−0.842235
$204$		0			0
$205$	16.0000	−	27.7128i	1.11749	−	1.93555i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.00000			0.553372
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$		0			0
$213$	16.0000			1.09630
$214$		0			0
$215$	−8.00000	−	13.8564i	−0.545595	−	0.944999i
$216$		0			0
$217$	−10.0000	−	17.3205i	−0.678844	−	1.17579i
$218$		0			0
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	−0.530607	−	0.847618i	$-0.678036\pi$
$223$	7.00000	−	12.1244i	0.468755	−	0.811907i	0.999362	+	0.0357107i	$0.0113695\pi$
$224$		0			0
$225$	−5.50000	−	9.52628i	−0.366667	−	0.635085i
$226$		0			0
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	0.791989	−	0.610535i	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$		0			0
$229$	2.00000			0.132164			0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000			0.132164			0.0660819	+	0.997814i	$0.478950\pi$
$230$		0			0
$231$	4.00000	−	6.92820i	0.263181	−	0.455842i
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$		0			0
$237$	−8.00000	+	13.8564i	−0.519656	+	0.900070i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	6.00000	−	10.3923i	0.383326	−	0.663940i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.0000	+	17.3205i	0.631194	+	1.09326i	0.987308	+	0.158818i	$0.0507683\pi$
$251$	10.0000	+	17.3205i	0.631194	+	1.09326i	−0.356113	+	0.934443i	$0.615898\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−8.00000			−0.500979
$256$		0			0
$257$	−15.0000	+	25.9808i	−0.935674	+	1.62064i	−0.162247	+	0.986750i	$0.551874\pi$
$257$	−15.0000	+	25.9808i	−0.935674	+	1.62064i	−0.773427	+	0.633885i	$0.781459\pi$
$258$		0			0
$259$	−20.0000			−1.24274
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	−40.0000			−2.45718
$266$		0			0
$267$	2.00000	+	3.46410i	0.122398	+	0.212000i
$268$		0			0
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	−5.00000	+	8.66025i	−0.303728	+	0.526073i	−0.976977	−	0.213343i	$-0.931565\pi$
$271$	−5.00000	+	8.66025i	−0.303728	+	0.526073i	0.673249	+	0.739416i	$0.264898\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−22.0000	+	38.1051i	−1.32665	+	2.29783i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$		0			0
$279$	−5.00000	−	8.66025i	−0.299342	−	0.518476i
$280$		0			0
$281$	8.00000			0.477240			0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000			0.477240			0.238620	+	0.971113i	$0.423305\pi$
$282$		0			0
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	−0.524057	−	0.851683i	$-0.675582\pi$
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	0.999608	+	0.0280052i	$0.00891551\pi$
$284$		0			0
$285$	−8.00000			−0.473879
$286$		0			0
$287$	−16.0000			−0.944450
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−2.00000			−0.117242
$292$		0			0
$293$	4.00000	+	6.92820i	0.233682	+	0.404750i	0.958889	−	0.283782i	$-0.0915890\pi$
$293$	4.00000	+	6.92820i	0.233682	+	0.404750i	−0.725206	+	0.688531i	$0.758256\pi$
$294$		0			0
$295$	−16.0000	−	27.7128i	−0.931556	−	1.61350i
$296$		0			0
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$		0			0
$303$	5.00000	+	8.66025i	0.287242	+	0.497519i
$304$		0			0
$305$	28.0000	+	48.4974i	1.60328	+	2.77695i
$306$		0			0
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$	−4.00000	+	6.92820i	−0.227552	+	0.394132i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$		0			0
$315$	−4.00000	+	6.92820i	−0.225374	+	0.390360i
$316$		0			0
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$		0			0
$319$	12.0000	+	20.7846i	0.671871	+	1.16371i
$320$		0			0
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$	−2.00000	+	3.46410i	−0.111283	+	0.192748i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$	−4.00000	−	6.92820i	−0.220527	−	0.381964i
$330$		0			0
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	0.892199	−	0.451643i	$-0.149162\pi$
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	−0.837234	+	0.546845i	$0.815829\pi$
$332$		0			0
$333$	−10.0000			−0.547997
$334$		0			0
$335$	4.00000	−	6.92820i	0.218543	−	0.378528i
$336$		0			0
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$		0			0
$341$	−20.0000	+	34.6410i	−1.08306	+	1.87592i
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	−0.518022	−	0.855367i	$-0.673331\pi$
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	0.999781	+	0.0209364i	$0.00666475\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.00000	+	13.8564i	−0.425797	+	0.737502i	−0.996495	−	0.0836583i	$-0.973340\pi$
$353$	−8.00000	+	13.8564i	−0.425797	+	0.737502i	0.570697	+	0.821160i	$0.306673\pi$
$354$		0			0
$355$	32.0000	+	55.4256i	1.69838	+	2.94169i
$356$		0			0
$357$	2.00000	+	3.46410i	0.105851	+	0.183340i
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	−5.00000			−0.262432
$364$		0			0
$365$	40.0000			2.09370
$366$		0			0
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$368$		0			0
$369$	−8.00000			−0.416463
$370$		0			0
$371$	10.0000	+	17.3205i	0.519174	+	0.899236i
$372$		0			0
$373$	9.00000	+	15.5885i	0.466002	+	0.807140i	0.999246	−	0.0388219i	$-0.0123605\pi$
$373$	9.00000	+	15.5885i	0.466002	+	0.807140i	−0.533244	+	0.845962i	$0.679027\pi$
$374$		0			0
$375$	12.0000	−	20.7846i	0.619677	−	1.07331i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	3.00000	−	5.19615i	0.154100	−	0.266908i	−0.778631	−	0.627482i	$-0.784086\pi$
$379$	3.00000	−	5.19615i	0.154100	−	0.266908i	0.932731	+	0.360573i	$0.117419\pi$
$380$		0			0
$381$	6.00000	+	10.3923i	0.307389	+	0.532414i
$382$		0			0
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$	32.0000			1.63087
$386$		0			0
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$		0			0
$389$	−26.0000			−1.31825			−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000			−1.31825			−0.659126	+	0.752032i	$0.729074\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	2.00000	−	3.46410i	0.100887	−	0.174741i
$394$		0			0
$395$	−64.0000			−3.22019
$396$		0			0
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$		0			0
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$		0			0
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	−0.976050	−	0.217545i	$-0.930195\pi$
$401$	−6.00000	+	10.3923i	−0.299626	+	0.518967i	0.676425	+	0.736512i	$0.263528\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−2.00000	+	3.46410i	−0.0993808	+	0.172133i
$406$		0			0
$407$	20.0000	+	34.6410i	0.991363	+	1.71709i
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$	8.00000			0.394611
$412$		0			0
$413$	−8.00000	+	13.8564i	−0.393654	+	0.681829i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.0000	−	17.3205i	0.488532	−	0.846162i	−0.511381	−	0.859354i	$-0.670866\pi$
$419$	10.0000	−	17.3205i	0.488532	−	0.846162i	0.999913	+	0.0131919i	$0.00419923\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$	−2.00000	−	3.46410i	−0.0972433	−	0.168430i
$424$		0			0
$425$	−11.0000	−	19.0526i	−0.533578	−	0.924185i
$426$		0			0
$427$	14.0000	−	24.2487i	0.677507	−	1.17348i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.0000	+	17.3205i	−0.481683	+	0.834300i	−0.999779	−	0.0210230i	$-0.993308\pi$
$431$	−10.0000	+	17.3205i	−0.481683	+	0.834300i	0.518096	+	0.855323i	$0.326641\pi$
$432$		0			0
$433$	9.00000	+	15.5885i	0.432512	+	0.749133i	0.997089	−	0.0762473i	$-0.0242938\pi$
$433$	9.00000	+	15.5885i	0.432512	+	0.749133i	−0.564577	+	0.825381i	$0.690961\pi$
$434$		0			0
$435$	−12.0000	−	20.7846i	−0.575356	−	0.996546i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$		0			0
$445$	−8.00000	+	13.8564i	−0.379236	+	0.656857i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$450$		0			0
$451$	16.0000	+	27.7128i	0.753411	+	1.30495i
$452$		0			0
$453$	−9.00000	+	15.5885i	−0.422857	+	0.732410i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$		0			0
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$		0			0
$465$	20.0000	−	34.6410i	0.927478	−	1.60644i
$466$		0			0
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$		0			0
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$		0			0
$473$	16.0000			0.735681
$474$		0			0
$475$	−11.0000	−	19.0526i	−0.504715	−	0.874191i
$476$		0			0
$477$	5.00000	+	8.66025i	0.228934	+	0.396526i
$478$		0			0
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	−0.994352	−	0.106129i	$-0.966154\pi$
$487$	−13.0000	−	22.5167i	−0.589086	−	1.02033i	0.405266	−	0.914199i	$-0.367179\pi$
$488$		0			0
$489$	2.00000			0.0904431
$490$		0			0
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$		0			0
$493$	−12.0000			−0.540453
$494$		0			0
$495$	16.0000			0.719147
$496$		0			0
$497$	16.0000	−	27.7128i	0.717698	−	1.24309i
$498$		0			0
$499$	6.00000			0.268597			0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000			0.268597			0.134298	+	0.990941i	$0.457122\pi$
$500$		0			0
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$		0			0
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	0.630705	−	0.776022i	$-0.282766\pi$
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	−0.987408	+	0.158196i	$0.949432\pi$
$504$		0			0
$505$	−20.0000	+	34.6410i	−0.889988	+	1.54150i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.00000	−	10.3923i	0.265945	−	0.460631i	−0.701866	−	0.712309i	$-0.747649\pi$
$509$	6.00000	−	10.3923i	0.265945	−	0.460631i	0.967811	+	0.251679i	$0.0809826\pi$
$510$		0			0
$511$	−10.0000	−	17.3205i	−0.442374	−	0.766214i
$512$		0			0
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$		0			0
$515$	−32.0000			−1.41009
$516$		0			0
$517$	−8.00000	+	13.8564i	−0.351840	+	0.609404i
$518$		0			0
$519$	−2.00000			−0.0877903
$520$		0			0
$521$	−2.00000			−0.0876216			−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000			−0.0876216			−0.0438108	+	0.999040i	$0.513950\pi$
$522$		0			0
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$		0			0
$525$	−22.0000			−0.960159
$526$		0			0
$527$	−10.0000	−	17.3205i	−0.435607	−	0.754493i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	−4.00000	+	6.92820i	−0.173585	+	0.300658i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−24.0000	+	41.5692i	−1.03761	+	1.79719i
$536$		0			0
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$		0			0
$539$	6.00000	+	10.3923i	0.258438	+	0.447628i
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$		0			0
$543$	1.00000	−	1.73205i	0.0429141	−	0.0743294i
$544$		0			0
$545$	8.00000			0.342682
$546$		0			0
$547$	32.0000			1.36822			0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000			1.36822			0.684111	+	0.729378i	$0.260191\pi$
$548$		0			0
$549$	7.00000	−	12.1244i	0.298753	−	0.517455i
$550$		0			0
$551$	−12.0000			−0.511217
$552$		0			0
$553$	16.0000	+	27.7128i	0.680389	+	1.17847i
$554$		0			0
$555$	−20.0000	−	34.6410i	−0.848953	−	1.47043i
$556$		0			0
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	−0.491496	−	0.870880i	$-0.663550\pi$
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	0.999952	−	0.00979220i	$-0.00311700\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	4.00000	−	6.92820i	0.168880	−	0.292509i
$562$		0			0
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	−0.994228	−	0.107290i	$-0.965783\pi$
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	0.404198	−	0.914671i	$-0.367551\pi$
$564$		0			0
$565$	−12.0000	−	20.7846i	−0.504844	−	0.874415i
$566$		0			0
$567$	2.00000			0.0839921
$568$		0			0
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$		0			0
$575$		0			0
$576$		0			0
$577$	30.0000			1.24892			0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000			1.24892			0.624458	+	0.781058i	$0.285320\pi$
$578$		0			0
$579$	7.00000	+	12.1244i	0.290910	+	0.503871i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	20.0000	−	34.6410i	0.828315	−	1.43468i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.00000	+	6.92820i	−0.165098	+	0.285958i	−0.936690	−	0.350160i	$-0.886127\pi$
$587$	−4.00000	+	6.92820i	−0.165098	+	0.285958i	0.771592	+	0.636117i	$0.219461\pi$
$588$		0			0
$589$	−10.0000	−	17.3205i	−0.412043	−	0.713679i
$590$		0			0
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$		0			0
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	−8.00000	+	13.8564i	−0.327968	+	0.568057i
$596$		0			0
$597$	−4.00000			−0.163709
$598$		0			0
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$		0			0
$603$	−2.00000			−0.0814463
$604$		0			0
$605$	−10.0000	−	17.3205i	−0.406558	−	0.704179i
$606$		0			0
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$		0			0
$609$	−6.00000	+	10.3923i	−0.243132	+	0.421117i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	−0.972056	−	0.234751i	$-0.924572\pi$
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	0.689328	+	0.724449i	$0.257906\pi$
$614$		0			0
$615$	−16.0000	−	27.7128i	−0.645182	−	1.11749i
$616$		0			0
$617$	−24.0000	−	41.5692i	−0.966204	−	1.67351i	−0.706346	−	0.707867i	$-0.749658\pi$
$617$	−24.0000	−	41.5692i	−0.966204	−	1.67351i	−0.259858	−	0.965647i	$-0.583676\pi$
$618$		0			0
$619$	−14.0000			−0.562708			−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000			−0.562708			−0.281354	+	0.959604i	$0.590783\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.00000			0.320513
$624$		0			0
$625$	41.0000			1.64000
$626$		0			0
$627$	4.00000	−	6.92820i	0.159745	−	0.276686i
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$	−15.0000	−	25.9808i	−0.597141	−	1.03428i	−0.993241	−	0.116071i	$-0.962970\pi$
$631$	−15.0000	−	25.9808i	−0.597141	−	1.03428i	0.396100	−	0.918207i	$-0.370363\pi$
$632$		0			0
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$		0			0
$635$	−24.0000	+	41.5692i	−0.952411	+	1.64962i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	8.00000	−	13.8564i	0.316475	−	0.548151i
$640$		0			0
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	−0.999878	−	0.0156233i	$-0.995027\pi$
$641$	−13.0000	−	22.5167i	−0.513469	−	0.889355i	0.486409	−	0.873731i	$-0.338307\pi$
$642$		0			0
$643$	13.0000	+	22.5167i	0.512670	+	0.887970i	0.999892	+	0.0146923i	$0.00467688\pi$
$643$	13.0000	+	22.5167i	0.512670	+	0.887970i	−0.487222	+	0.873278i	$0.661990\pi$
$644$		0			0
$645$	−16.0000			−0.629999
$646$		0			0
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$		0			0
$649$	32.0000			1.25611
$650$		0			0
$651$	−20.0000			−0.783862
$652$		0			0
$653$	23.0000	−	39.8372i	0.900060	−	1.55895i	0.0726446	−	0.997358i	$-0.476856\pi$
$653$	23.0000	−	39.8372i	0.900060	−	1.55895i	0.827415	−	0.561591i	$-0.189811\pi$
$654$		0			0
$655$	16.0000			0.625172
$656$		0			0
$657$	−5.00000	−	8.66025i	−0.195069	−	0.337869i
$658$		0			0
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.00000	+	13.8564i	−0.310227	+	0.537328i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−7.00000	−	12.1244i	−0.270636	−	0.468755i
$670$		0			0
$671$	−56.0000			−2.16186
$672$		0			0
$673$	−11.0000	+	19.0526i	−0.424019	+	0.734422i	−0.996328	−	0.0856156i	$-0.972714\pi$
$673$	−11.0000	+	19.0526i	−0.424019	+	0.734422i	0.572309	+	0.820038i	$0.306048\pi$
$674$		0			0
$675$	−11.0000			−0.423390
$676$		0			0
$677$	38.0000			1.46046			0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000			1.46046			0.730229	+	0.683202i	$0.239413\pi$
$678$		0			0
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$		0			0
$681$	−4.00000			−0.153280
$682$		0			0
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	0.991439	−	0.130573i	$-0.0416818\pi$
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	−0.608799	+	0.793324i	$0.708349\pi$
$684$		0			0
$685$	16.0000	+	27.7128i	0.611329	+	1.05885i
$686$		0			0
$687$	1.00000	−	1.73205i	0.0381524	−	0.0660819i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	−0.755110	−	0.655598i	$-0.772417\pi$
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	0.945319	+	0.326146i	$0.105750\pi$
$692$		0			0
$693$	−4.00000	−	6.92820i	−0.151947	−	0.263181i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−16.0000			−0.606043
$698$		0			0
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	−20.0000			−0.754314
$704$		0			0
$705$	8.00000	−	13.8564i	0.301297	−	0.521862i
$706$		0			0
$707$	20.0000			0.752177
$708$		0			0
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	0.916845	−	0.399244i	$-0.130727\pi$
$709$	3.00000	+	5.19615i	0.112667	+	0.195146i	−0.804178	+	0.594389i	$0.797394\pi$
$710$		0			0
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$		0			0
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		0			0
$721$	8.00000	+	13.8564i	0.297936	+	0.516040i
$722$		0			0
$723$	−2.00000			−0.0743808
$724$		0			0
$725$	33.0000	−	57.1577i	1.22559	−	2.12278i
$726$		0			0
$727$	44.0000			1.63187			0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000			1.63187			0.815935	+	0.578144i	$0.196223\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$		0			0
$735$	−6.00000	−	10.3923i	−0.221313	−	0.383326i
$736$		0			0
$737$	4.00000	+	6.92820i	0.147342	+	0.255204i
$738$		0			0
$739$	11.0000	−	19.0526i	0.404642	−	0.700860i	−0.589638	−	0.807668i	$-0.700730\pi$
$739$	11.0000	−	19.0526i	0.404642	−	0.700860i	0.994280	+	0.106808i	$0.0340630\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$		0			0
$753$	20.0000			0.728841
$754$		0			0
$755$	−72.0000			−2.62035
$756$		0			0
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−9.00000	+	15.5885i	−0.327111	+	0.566572i	0.654827	+	0.755779i	$0.272742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20.0000	+	34.6410i	0.724999	+	1.25574i	0.958974	+	0.283493i	$0.0914933\pi$
$761$	20.0000	+	34.6410i	0.724999	+	1.25574i	−0.233975	+	0.972243i	$0.575173\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$		0			0
$765$	−4.00000	+	6.92820i	−0.144620	+	0.250490i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−11.0000	+	19.0526i	−0.396670	+	0.687053i	−0.993313	−	0.115454i	$-0.963168\pi$
$769$	−11.0000	+	19.0526i	−0.396670	+	0.687053i	0.596643	+	0.802507i	$0.296501\pi$
$770$		0			0
$771$	15.0000	+	25.9808i	0.540212	+	0.935674i
$772$		0			0
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	−0.868804	−	0.495156i	$-0.835111\pi$
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	0.00558380	−	0.999984i	$-0.498223\pi$
$774$		0			0
$775$	110.000			3.95132
$776$		0			0
$777$	−10.0000	+	17.3205i	−0.358748	+	0.621370i
$778$		0			0
$779$	−16.0000			−0.573259
$780$		0			0
$781$	−64.0000			−2.29010
$782$		0			0
$783$	−3.00000	+	5.19615i	−0.107211	+	0.185695i
$784$		0			0
$785$	8.00000			0.285532
$786$		0			0
$787$	−25.0000	−	43.3013i	−0.891154	−	1.54352i	−0.838494	−	0.544911i	$-0.816563\pi$
$787$	−25.0000	−	43.3013i	−0.891154	−	1.54352i	−0.0526599	−	0.998613i	$-0.516770\pi$
$788$		0			0
$789$	−8.00000	−	13.8564i	−0.284808	−	0.493301i
$790$		0			0
$791$	−6.00000	+	10.3923i	−0.213335	+	0.369508i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−20.0000	+	34.6410i	−0.709327	+	1.22859i
$796$		0			0
$797$	13.0000	+	22.5167i	0.460484	+	0.797581i	0.998985	−	0.0450436i	$-0.0143427\pi$
$797$	13.0000	+	22.5167i	0.460484	+	0.797581i	−0.538501	+	0.842625i	$0.681009\pi$
$798$		0			0
$799$	−4.00000	−	6.92820i	−0.141510	−	0.245102i
$800$		0			0
$801$	4.00000			0.141333
$802$		0			0
$803$	−20.0000	+	34.6410i	−0.705785	+	1.22245i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.0000			0.492823
$808$		0			0
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	0.310457	+	0.950587i	$0.399518\pi$
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	−0.978461	+	0.206430i	$0.933815\pi$
$810$		0			0
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$		0			0
$813$	5.00000	+	8.66025i	0.175358	+	0.303728i
$814$		0			0
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$	−4.00000	+	6.92820i	−0.139942	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$		0			0
$825$	22.0000	+	38.1051i	0.765942	+	1.32665i
$826$		0			0
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$		0			0
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$		0			0
$831$	−22.0000			−0.763172
$832$		0			0
$833$	−6.00000			−0.207888
$834$		0			0
$835$	−24.0000	+	41.5692i	−0.830554	+	1.43856i
$836$		0			0
$837$	−10.0000			−0.345651
$838$		0			0
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	0.694244	−	0.719740i	$-0.255739\pi$
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	−0.970435	+	0.241363i	$0.922405\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	4.00000	−	6.92820i	0.137767	−	0.238620i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.00000	+	8.66025i	−0.171802	+	0.297570i
$848$		0			0
$849$	−8.00000	−	13.8564i	−0.274559	−	0.475551i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	−4.00000	+	6.92820i	−0.136797	+	0.236940i
$856$		0			0
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	52.0000			1.77422			0.887109	−	0.461561i	$-0.152710\pi$
$859$	52.0000			1.77422			0.887109	+	0.461561i	$0.152710\pi$
$860$		0			0
$861$	−8.00000	+	13.8564i	−0.272639	+	0.472225i
$862$		0			0
$863$	−4.00000			−0.136162			−0.0680808	−	0.997680i	$-0.521688\pi$
$863$	−4.00000			−0.136162			−0.0680808	+	0.997680i	$0.521688\pi$
$864$		0			0
$865$	−4.00000	−	6.92820i	−0.136004	−	0.235566i
$866$		0			0
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$		0			0
$869$	32.0000	−	55.4256i	1.08553	−	1.88019i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.00000	+	1.73205i	−0.0338449	+	0.0586210i
$874$		0			0
$875$	−24.0000	−	41.5692i	−0.811348	−	1.40530i
$876$		0			0
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$		0			0
$879$	8.00000			0.269833
$880$		0			0
$881$	−7.00000	+	12.1244i	−0.235836	+	0.408480i	−0.959515	−	0.281656i	$-0.909116\pi$
$881$	−7.00000	+	12.1244i	−0.235836	+	0.408480i	0.723679	+	0.690136i	$0.242449\pi$
$882$		0			0
$883$	−32.0000			−1.07689			−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000			−1.07689			−0.538443	+	0.842662i	$0.680987\pi$
$884$		0			0
$885$	−32.0000			−1.07567
$886$		0			0
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$		0			0
$889$	24.0000			0.804934
$890$		0			0
$891$	−2.00000	−	3.46410i	−0.0670025	−	0.116052i
$892$		0			0
$893$	−4.00000	−	6.92820i	−0.133855	−	0.231843i
$894$		0			0
$895$	−24.0000	+	41.5692i	−0.802232	+	1.38951i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	30.0000	−	51.9615i	1.00056	−	1.73301i
$900$		0			0
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$		0			0
$903$	4.00000	+	6.92820i	0.133112	+	0.230556i
$904$		0			0
$905$	8.00000			0.265929
$906$		0			0
$907$	28.0000	−	48.4974i	0.929725	−	1.61033i	0.145944	−	0.989293i	$-0.453378\pi$
$907$	28.0000	−	48.4974i	0.929725	−	1.61033i	0.783781	−	0.621038i	$-0.213289\pi$
$908$		0			0
$909$	10.0000			0.331679
$910$		0			0
$911$	−56.0000			−1.85536			−0.927681	−	0.373373i	$-0.878201\pi$
$911$	−56.0000			−1.85536			−0.927681	+	0.373373i	$0.878201\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	56.0000			1.85130
$916$		0			0
$917$	−4.00000	−	6.92820i	−0.132092	−	0.228789i
$918$		0			0
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.793742	−	0.608254i	$-0.791870\pi$
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.129893	−	0.991528i	$-0.541463\pi$
$920$		0			0
$921$	−11.0000	+	19.0526i	−0.362462	+	0.627803i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	55.0000	−	95.2628i	1.80839	−	3.13222i
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	8.00000	+	13.8564i	0.262471	+	0.454614i	0.966898	−	0.255163i	$-0.0821291\pi$
$929$	8.00000	+	13.8564i	0.262471	+	0.454614i	−0.704427	+	0.709777i	$0.748796\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$		0			0
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		0			0
$935$	32.0000			1.04651
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$		0			0
$941$	−8.00000			−0.260793			−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000			−0.260793			−0.130396	+	0.991462i	$0.541625\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	4.00000	+	6.92820i	0.130120	+	0.225374i
$946$		0			0
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	−0.793687	−	0.608326i	$-0.791841\pi$
$947$	4.00000	−	6.92820i	0.129983	−	0.225136i	0.923670	+	0.383190i	$0.125175\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	6.00000	−	10.3923i	0.194563	−	0.336994i
$952$		0			0
$953$	21.0000	+	36.3731i	0.680257	+	1.17824i	0.974902	+	0.222633i	$0.0714650\pi$
$953$	21.0000	+	36.3731i	0.680257	+	1.17824i	−0.294646	+	0.955607i	$0.595202\pi$
$954$		0			0
$955$	16.0000	+	27.7128i	0.517748	+	0.896766i
$956$		0			0
$957$	24.0000			0.775810
$958$		0			0
$959$	8.00000	−	13.8564i	0.258333	−	0.447447i
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	12.0000			0.386695
$964$		0			0
$965$	−28.0000	+	48.4974i	−0.901352	+	1.56119i
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$	2.00000	+	3.46410i	0.0642493	+	0.111283i
$970$		0			0
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	0.998339	−	0.0576061i	$-0.0183467\pi$
$971$	14.0000	+	24.2487i	0.449281	+	0.778178i	−0.549058	+	0.835784i	$0.685013\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$		0			0
$979$	−8.00000	−	13.8564i	−0.255681	−	0.442853i
$980$		0			0
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$		0			0
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	−24.0000	+	41.5692i	−0.764704	+	1.32451i
$986$		0			0
$987$	−8.00000			−0.254643
$988$		0			0
$989$		0			0
$990$		0			0
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	−0.424594	−	0.905384i	$-0.639583\pi$
$991$	18.0000	−	31.1769i	0.571789	−	0.990367i	0.996382	−	0.0849833i	$-0.0270837\pi$
$992$		0			0
$993$	2.00000			0.0634681
$994$		0			0
$995$	−8.00000	−	13.8564i	−0.253617	−	0.439278i
$996$		0			0
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$		0			0
$999$	−5.00000	+	8.66025i	−0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2028.2.i.g.529.1		2
13.2	odd	12		2028.2.q.h.361.1		4
13.3	even	3	inner	2028.2.i.g.2005.1		2
13.4	even	6		156.2.a.a.1.1	✓	1
13.5	odd	4		2028.2.q.h.1837.1		4
13.6	odd	12		2028.2.b.a.337.1		2
13.7	odd	12		2028.2.b.a.337.2		2
13.8	odd	4		2028.2.q.h.1837.2		4
13.9	even	3		2028.2.a.c.1.1		1
13.10	even	6		2028.2.i.e.2005.1		2
13.11	odd	12		2028.2.q.h.361.2		4
13.12	even	2		2028.2.i.e.529.1		2
39.17	odd	6		468.2.a.d.1.1		1
39.20	even	12		6084.2.b.j.4393.1		2
39.32	even	12		6084.2.b.j.4393.2		2
39.35	odd	6		6084.2.a.b.1.1		1
52.35	odd	6		8112.2.a.bi.1.1		1
52.43	odd	6		624.2.a.e.1.1		1
65.4	even	6		3900.2.a.m.1.1		1
65.17	odd	12		3900.2.h.b.1249.2		2
65.43	odd	12		3900.2.h.b.1249.1		2
91.69	odd	6		7644.2.a.k.1.1		1
104.43	odd	6		2496.2.a.o.1.1		1
104.69	even	6		2496.2.a.bc.1.1		1
117.4	even	6		4212.2.i.l.2809.1		2
117.43	even	6		4212.2.i.l.1405.1		2
117.56	odd	6		4212.2.i.b.1405.1		2
117.95	odd	6		4212.2.i.b.2809.1		2
156.95	even	6		1872.2.a.s.1.1		1
312.173	odd	6		7488.2.a.c.1.1		1
312.251	even	6		7488.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.a.a.1.1	✓	1	13.4	even	6
468.2.a.d.1.1		1	39.17	odd	6
624.2.a.e.1.1		1	52.43	odd	6
1872.2.a.s.1.1		1	156.95	even	6
2028.2.a.c.1.1		1	13.9	even	3
2028.2.b.a.337.1		2	13.6	odd	12
2028.2.b.a.337.2		2	13.7	odd	12
2028.2.i.e.529.1		2	13.12	even	2
2028.2.i.e.2005.1		2	13.10	even	6
2028.2.i.g.529.1		2	1.1	even	1	trivial
2028.2.i.g.2005.1		2	13.3	even	3	inner
2028.2.q.h.361.1		4	13.2	odd	12
2028.2.q.h.361.2		4	13.11	odd	12
2028.2.q.h.1837.1		4	13.5	odd	4
2028.2.q.h.1837.2		4	13.8	odd	4
2496.2.a.o.1.1		1	104.43	odd	6
2496.2.a.bc.1.1		1	104.69	even	6
3900.2.a.m.1.1		1	65.4	even	6
3900.2.h.b.1249.1		2	65.43	odd	12
3900.2.h.b.1249.2		2	65.17	odd	12
4212.2.i.b.1405.1		2	117.56	odd	6
4212.2.i.b.2809.1		2	117.95	odd	6
4212.2.i.l.1405.1		2	117.43	even	6
4212.2.i.l.2809.1		2	117.4	even	6
6084.2.a.b.1.1		1	39.35	odd	6
6084.2.b.j.4393.1		2	39.20	even	12
6084.2.b.j.4393.2		2	39.32	even	12
7488.2.a.c.1.1		1	312.173	odd	6
7488.2.a.d.1.1		1	312.251	even	6
7644.2.a.k.1.1		1	91.69	odd	6
8112.2.a.bi.1.1		1	52.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2028.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +4.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +4.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(2.00000 - 3.46410i) q^{15} +(-1.00000 - 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{19} -2.00000 q^{21} +11.0000 q^{25} -1.00000 q^{27} +(3.00000 - 5.19615i) q^{29} +10.0000 q^{31} +(2.00000 + 3.46410i) q^{33} +(-4.00000 - 6.92820i) q^{35} +(5.00000 - 8.66025i) q^{37} +(4.00000 - 6.92820i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-2.00000 - 3.46410i) q^{45} +4.00000 q^{47} +(1.50000 - 2.59808i) q^{49} -2.00000 q^{51} -10.0000 q^{53} +(-8.00000 + 13.8564i) q^{55} -2.00000 q^{57} +(-4.00000 - 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-1.00000 + 1.73205i) q^{63} +(1.00000 - 1.73205i) q^{67} +(8.00000 + 13.8564i) q^{71} +10.0000 q^{73} +(5.50000 - 9.52628i) q^{75} +8.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{85} +(-3.00000 - 5.19615i) q^{87} +(-2.00000 + 3.46410i) q^{89} +(5.00000 - 8.66025i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 8 q^{5} - 2 q^{7} - q^{9}+O(q^{10}) \) 2 * q + q^3 + 8 * q^5 - 2 * q^7 - q^9	\( 2 q + q^{3} + 8 q^{5} - 2 q^{7} - q^{9} - 4 q^{11} + 4 q^{15} - 2 q^{17} - 2 q^{19} - 4 q^{21} + 22 q^{25} - 2 q^{27} + 6 q^{29} + 20 q^{31} + 4 q^{33} - 8 q^{35} + 10 q^{37} + 8 q^{41} - 4 q^{43} - 4 q^{45} + 8 q^{47} + 3 q^{49} - 4 q^{51} - 20 q^{53} - 16 q^{55} - 4 q^{57} - 8 q^{59} + 14 q^{61} - 2 q^{63} + 2 q^{67} + 16 q^{71} + 20 q^{73} + 11 q^{75} + 16 q^{77} - 32 q^{79} - q^{81} - 8 q^{85} - 6 q^{87} - 4 q^{89} + 10 q^{93} - 8 q^{95} - 2 q^{97} + 8 q^{99}+O(q^{100}) \) 2 * q + q^3 + 8 * q^5 - 2 * q^7 - q^9 - 4 * q^11 + 4 * q^15 - 2 * q^17 - 2 * q^19 - 4 * q^21 + 22 * q^25 - 2 * q^27 + 6 * q^29 + 20 * q^31 + 4 * q^33 - 8 * q^35 + 10 * q^37 + 8 * q^41 - 4 * q^43 - 4 * q^45 + 8 * q^47 + 3 * q^49 - 4 * q^51 - 20 * q^53 - 16 * q^55 - 4 * q^57 - 8 * q^59 + 14 * q^61 - 2 * q^63 + 2 * q^67 + 16 * q^71 + 20 * q^73 + 11 * q^75 + 16 * q^77 - 32 * q^79 - q^81 - 8 * q^85 - 6 * q^87 - 4 * q^89 + 10 * q^93 - 8 * q^95 - 2 * q^97 + 8 * q^99

Introduction

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