LMFDB - Embedded newform 693.2.i.d.298.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, 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:	$5.53363286007$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	693.298
Dual form			693.2.i.d.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{4} +(2.00000 + 3.46410i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{4} +(2.00000 + 3.46410i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{11} +5.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{17} +(1.50000 + 2.59808i) q^{19} +8.00000 q^{20} +(4.00000 + 6.92820i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(-4.00000 + 3.46410i) q^{28} +4.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-2.00000 - 10.3923i) q^{35} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{41} +1.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-4.00000 - 6.92820i) q^{47} +(5.50000 + 4.33013i) q^{49} +(5.00000 - 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} +4.00000 q^{55} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{64} +(10.0000 + 17.3205i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(-4.00000 - 6.92820i) q^{68} +4.00000 q^{71} +(5.50000 - 9.52628i) q^{73} +6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(-7.50000 - 12.9904i) q^{79} +(8.00000 - 13.8564i) q^{80} -12.0000 q^{83} +16.0000 q^{85} +(6.00000 + 10.3923i) q^{89} +(-12.5000 - 4.33013i) q^{91} +16.0000 q^{92} +(-6.00000 + 10.3923i) q^{95} -2.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} + 4 q^{5} - 5 q^{7}+O(q^{10}) $ 2 * q + 2 * q^4 + 4 * q^5 - 5 * q^7	$ 2 q + 2 q^{4} + 4 q^{5} - 5 q^{7} + q^{11} + 10 q^{13} - 4 q^{16} + 4 q^{17} + 3 q^{19} + 16 q^{20} + 8 q^{23} - 11 q^{25} - 8 q^{28} + 8 q^{29} - q^{31} - 4 q^{35} - 7 q^{37} + 8 q^{41} + 2 q^{43} - 2 q^{44} - 8 q^{47} + 11 q^{49} + 10 q^{52} - 12 q^{53} + 8 q^{55} + 2 q^{61} - 16 q^{64} + 20 q^{65} - 3 q^{67} - 8 q^{68} + 8 q^{71} + 11 q^{73} + 12 q^{76} - 4 q^{77} - 15 q^{79} + 16 q^{80} - 24 q^{83} + 32 q^{85} + 12 q^{89} - 25 q^{91} + 32 q^{92} - 12 q^{95} - 4 q^{97}+O(q^{100}) $ 2 * q + 2 * q^4 + 4 * q^5 - 5 * q^7 + q^11 + 10 * q^13 - 4 * q^16 + 4 * q^17 + 3 * q^19 + 16 * q^20 + 8 * q^23 - 11 * q^25 - 8 * q^28 + 8 * q^29 - q^31 - 4 * q^35 - 7 * q^37 + 8 * q^41 + 2 * q^43 - 2 * q^44 - 8 * q^47 + 11 * q^49 + 10 * q^52 - 12 * q^53 + 8 * q^55 + 2 * q^61 - 16 * q^64 + 20 * q^65 - 3 * q^67 - 8 * q^68 + 8 * q^71 + 11 * q^73 + 12 * q^76 - 4 * q^77 - 15 * q^79 + 16 * q^80 - 24 * q^83 + 32 * q^85 + 12 * q^89 - 25 * q^91 + 32 * q^92 - 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$	8.00000			1.78885
$21$		0			0
$22$		0			0
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$		0			0
$27$		0			0
$28$	−4.00000	+	3.46410i	−0.755929	+	0.654654i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.00000	−	10.3923i	−0.338062	−	1.75662i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$		0			0
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$	5.00000	−	8.66025i	0.693375	−	1.20096i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	10.0000	+	17.3205i	1.24035	+	2.14834i
$66$		0			0
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	−4.00000	−	6.92820i	−0.485071	−	0.840168i
$69$		0			0
$70$		0			0
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$		0			0
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$		0			0
$75$		0			0
$76$	6.00000			0.688247
$77$	−2.00000	+	1.73205i	−0.227921	+	0.197386i
$78$		0			0
$79$	−7.50000	−	12.9904i	−0.843816	−	1.46153i	−0.886646	−	0.462450i	$-0.846971\pi$
$79$	−7.50000	−	12.9904i	−0.843816	−	1.46153i	0.0428296	−	0.999082i	$-0.486363\pi$
$80$	8.00000	−	13.8564i	0.894427	−	1.54919i
$81$		0			0
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	16.0000			1.73544
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	0.986303	+	0.164946i	$0.0527450\pi$
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	−0.350304	+	0.936636i	$0.613922\pi$
$90$		0			0
$91$	−12.5000	−	4.33013i	−1.31036	−	0.453921i
$92$	16.0000			1.66812
$93$		0			0
$94$		0			0
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$		0			0
$100$	11.0000	+	19.0526i	1.10000	+	1.90526i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−4.50000	−	7.79423i	−0.443398	−	0.767988i	0.554541	−	0.832156i	$-0.312894\pi$
$103$	−4.50000	−	7.79423i	−0.443398	−	0.767988i	−0.997939	+	0.0641683i	$0.979561\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$		0			0
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$		0			0
$111$		0			0
$112$	2.00000	+	10.3923i	0.188982	+	0.981981i
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	−16.0000	+	27.7128i	−1.49201	+	2.58423i
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$		0			0
$118$		0			0
$119$	−8.00000	+	6.92820i	−0.733359	+	0.635107i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$	−1.50000	−	7.79423i	−0.130066	−	0.675845i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−19.0000			−1.61156			−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000			−1.61156			−0.805779	+	0.592216i	$0.798253\pi$
$140$	−20.0000	−	6.92820i	−1.69031	−	0.585540i
$141$		0			0
$142$		0			0
$143$	2.50000	−	4.33013i	0.209061	−	0.362103i
$144$		0			0
$145$	8.00000	+	13.8564i	0.664364	+	1.15071i
$146$		0			0
$147$		0			0
$148$	−14.0000			−1.15079
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	0.936245	−	0.351348i	$-0.114277\pi$
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	−0.772399	+	0.635138i	$0.780943\pi$
$150$		0			0
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	−0.823359	−	0.567521i	$-0.807902\pi$
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	0.903167	+	0.429289i	$0.141236\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.00000	−	20.7846i	−0.315244	−	1.63806i
$162$		0			0
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	4.00000	−	6.92820i	0.312348	−	0.541002i
$165$		0			0
$166$		0			0
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$		0			0
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	10.0000	+	17.3205i	0.760286	+	1.31685i	0.942703	+	0.333633i	$0.108275\pi$
$173$	10.0000	+	17.3205i	0.760286	+	1.31685i	−0.182417	+	0.983221i	$0.558392\pi$
$174$		0			0
$175$	22.0000	−	19.0526i	1.66304	−	1.44024i
$176$	−4.00000			−0.301511
$177$		0			0
$178$		0			0
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.0000	−	24.2487i	1.02930	−	1.78280i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	−16.0000			−1.16692
$189$		0			0
$190$		0			0
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		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
$195$		0			0
$196$	13.0000	−	5.19615i	0.928571	−	0.371154i
$197$	−24.0000			−1.70993			−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000			−1.70993			−0.854965	+	0.518686i	$0.826421\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.0000	−	3.46410i	−0.701862	−	0.243132i
$204$		0			0
$205$	8.00000	+	13.8564i	0.558744	+	0.967773i
$206$		0			0
$207$		0			0
$208$	−10.0000	−	17.3205i	−0.693375	−	1.20096i
$209$	3.00000			0.207514
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	12.0000	+	20.7846i	0.824163	+	1.42749i
$213$		0			0
$214$		0			0
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$		0			0
$217$	2.00000	−	1.73205i	0.135769	−	0.117579i
$218$		0			0
$219$		0			0
$220$	4.00000	−	6.92820i	0.269680	−	0.467099i
$221$	10.0000	−	17.3205i	0.672673	−	1.16510i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	0.468368	+	0.883534i	$0.344842\pi$
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	−0.999346	+	0.0361484i	$0.988491\pi$
$228$		0			0
$229$	−8.50000	−	14.7224i	−0.561696	−	0.972886i	−0.997349	−	0.0727709i	$-0.976816\pi$
$229$	−8.50000	−	14.7224i	−0.561696	−	0.972886i	0.435653	−	0.900115i	$-0.356518\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	0.992853	−	0.119342i	$-0.0380786\pi$
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	−0.599780	+	0.800165i	$0.704745\pi$
$234$		0			0
$235$	16.0000	−	27.7128i	1.04372	−	1.80778i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	28.0000			1.81117			0.905585	−	0.424165i	$-0.139432\pi$
$239$	28.0000			1.81117			0.905585	+	0.424165i	$0.139432\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$		0			0
$243$		0			0
$244$	4.00000			0.256074
$245$	−4.00000	+	27.7128i	−0.255551	+	1.77051i
$246$		0			0
$247$	7.50000	+	12.9904i	0.477214	+	0.826558i
$248$		0			0
$249$		0			0
$250$		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
$253$	8.00000			0.502956
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$		0			0
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$	40.0000			2.48069
$261$		0			0
$262$		0			0
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		0			0
$265$	−48.0000			−2.94862
$266$		0			0
$267$		0			0
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	−16.0000			−0.970143
$273$		0			0
$274$		0			0
$275$	5.50000	+	9.52628i	0.331662	+	0.574456i
$276$		0			0
$277$	−10.5000	+	18.1865i	−0.630884	+	1.09272i	0.356488	+	0.934300i	$0.383974\pi$
$277$	−10.5000	+	18.1865i	−0.630884	+	1.09272i	−0.987371	+	0.158423i	$0.949359\pi$
$278$		0			0
$279$		0			0
$280$		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
$283$	−10.5000	+	18.1865i	−0.624160	+	1.08108i	0.364542	+	0.931187i	$0.381225\pi$
$283$	−10.5000	+	18.1865i	−0.624160	+	1.08108i	−0.988703	+	0.149890i	$0.952108\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$		0			0
$286$		0			0
$287$	−10.0000	−	3.46410i	−0.590281	−	0.204479i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$		0			0
$292$	−11.0000	−	19.0526i	−0.643726	−	1.11497i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	20.0000	+	34.6410i	1.15663	+	2.00334i
$300$		0			0
$301$	−2.50000	−	0.866025i	−0.144098	−	0.0499169i
$302$		0			0
$303$		0			0
$304$	6.00000	−	10.3923i	0.344124	−	0.596040i
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	23.0000			1.31268			0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000			1.31268			0.656340	+	0.754466i	$0.272104\pi$
$308$	1.00000	+	5.19615i	0.0569803	+	0.296078i
$309$		0			0
$310$		0			0
$311$	14.0000	−	24.2487i	0.793867	−	1.37502i	−0.129689	−	0.991555i	$-0.541398\pi$
$311$	14.0000	−	24.2487i	0.793867	−	1.37502i	0.923556	−	0.383464i	$-0.125269\pi$
$312$		0			0
$313$	2.50000	+	4.33013i	0.141308	+	0.244753i	0.927990	−	0.372606i	$-0.121536\pi$
$313$	2.50000	+	4.33013i	0.141308	+	0.244753i	−0.786681	+	0.617359i	$0.788202\pi$
$314$		0			0
$315$		0			0
$316$	−30.0000			−1.68763
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−16.0000	−	27.7128i	−0.894427	−	1.54919i
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	−27.5000	+	47.6314i	−1.52543	+	2.64211i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.00000	+	20.7846i	0.220527	+	1.14589i
$330$		0			0
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	0.999298	−	0.0374662i	$-0.0119287\pi$
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	−0.532096	+	0.846684i	$0.678595\pi$
$332$	−12.0000	+	20.7846i	−0.658586	+	1.14070i
$333$		0			0
$334$		0			0
$335$	−12.0000			−0.655630
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$		0			0
$339$		0			0
$340$	16.0000	−	27.7128i	0.867722	−	1.50294i
$341$	0.500000	+	0.866025i	0.0270765	+	0.0468979i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	0.462244	+	0.886753i	$0.347044\pi$
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	−0.999072	+	0.0430610i	$0.986289\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	24.0000			1.27200
$357$		0			0
$358$		0			0
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	−0.886100	−	0.463494i	$-0.846596\pi$
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	0.0416523	−	0.999132i	$-0.486738\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$		0			0
$363$		0			0
$364$	−20.0000	+	17.3205i	−1.04828	+	0.907841i
$365$	44.0000			2.30307
$366$		0			0
$367$	14.5000	−	25.1147i	0.756894	−	1.31098i	−0.187533	−	0.982258i	$-0.560049\pi$
$367$	14.5000	−	25.1147i	0.756894	−	1.31098i	0.944427	−	0.328720i	$-0.106617\pi$
$368$	16.0000	−	27.7128i	0.834058	−	1.44463i
$369$		0			0
$370$		0			0
$371$	24.0000	−	20.7846i	1.24602	−	1.07908i
$372$		0			0
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.0000			1.03005
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$	12.0000	+	20.7846i	0.615587	+	1.06623i
$381$		0			0
$382$		0			0
$383$	−10.0000	−	17.3205i	−0.510976	−	0.885037i	−0.999919	−	0.0127209i	$-0.995951\pi$
$383$	−10.0000	−	17.3205i	−0.510976	−	0.885037i	0.488943	−	0.872316i	$-0.337383\pi$
$384$		0			0
$385$	−10.0000	−	3.46410i	−0.509647	−	0.176547i
$386$		0			0
$387$		0			0
$388$	−2.00000	+	3.46410i	−0.101535	+	0.175863i
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$		0			0
$393$		0			0
$394$		0			0
$395$	30.0000	−	51.9615i	1.50946	−	2.61447i
$396$		0			0
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	0.825926	−	0.563778i	$-0.190653\pi$
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	−0.901209	+	0.433384i	$0.857319\pi$
$398$		0			0
$399$		0			0
$400$	44.0000			2.20000
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$	−2.50000	+	4.33013i	−0.124534	+	0.215699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.00000			−0.346977
$408$		0			0
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	−0.00141047	−	0.999999i	$-0.500449\pi$
$409$	17.5000	−	30.3109i	0.865319	−	1.49878i	0.866730	−	0.498778i	$-0.166218\pi$
$410$		0			0
$411$		0			0
$412$	−18.0000			−0.886796
$413$		0			0
$414$		0			0
$415$	−24.0000	−	41.5692i	−1.17811	−	2.04055i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	−11.0000			−0.536107			−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000			−0.536107			−0.268054	+	0.963404i	$0.586380\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	22.0000	+	38.1051i	1.06716	+	1.84837i
$426$		0			0
$427$	−1.00000	−	5.19615i	−0.0483934	−	0.251459i
$428$	−16.0000			−0.773389
$429$		0			0
$430$		0			0
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	−0.991817	−	0.127666i	$-0.959251\pi$
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	0.606471	+	0.795106i	$0.292585\pi$
$432$		0			0
$433$	35.0000			1.68199			0.840996	−	0.541041i	$-0.181970\pi$
$433$	35.0000			1.68199			0.840996	+	0.541041i	$0.181970\pi$
$434$		0			0
$435$		0			0
$436$	−11.0000	−	19.0526i	−0.526804	−	0.912452i
$437$	−12.0000	+	20.7846i	−0.574038	+	0.994263i
$438$		0			0
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$		0			0
$445$	−24.0000	+	41.5692i	−1.13771	+	1.97057i
$446$		0			0
$447$		0			0
$448$	20.0000	+	6.92820i	0.944911	+	0.327327i
$449$	−36.0000			−1.69895			−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000			−1.69895			−0.849473	+	0.527633i	$0.823080\pi$
$450$		0			0
$451$	2.00000	−	3.46410i	0.0941763	−	0.163118i
$452$	−16.0000	+	27.7128i	−0.752577	+	1.30350i
$453$		0			0
$454$		0			0
$455$	−10.0000	−	51.9615i	−0.468807	−	2.43599i
$456$		0			0
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	−0.975498	−	0.220008i	$-0.929392\pi$
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	0.297217	−	0.954810i	$-0.403942\pi$
$458$		0			0
$459$		0			0
$460$	32.0000	+	55.4256i	1.49201	+	2.58423i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	7.00000			0.325318			0.162659	−	0.986682i	$-0.447993\pi$
$463$	7.00000			0.325318			0.162659	+	0.986682i	$0.447993\pi$
$464$	−8.00000	−	13.8564i	−0.371391	−	0.643268i
$465$		0			0
$466$		0			0
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$		0			0
$469$	6.00000	−	5.19615i	0.277054	−	0.239936i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.500000	−	0.866025i	0.0229900	−	0.0398199i
$474$		0			0
$475$	−33.0000			−1.51414
$476$	4.00000	+	20.7846i	0.183340	+	0.952661i
$477$		0			0
$478$		0			0
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	−0.816711	−	0.577047i	$-0.804205\pi$
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	0.908093	+	0.418769i	$0.137538\pi$
$480$		0			0
$481$	−17.5000	−	30.3109i	−0.797931	−	1.38206i
$482$		0			0
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	−0.854475	−	0.519493i	$-0.826121\pi$
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	0.877132	+	0.480250i	$0.159454\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	8.00000	−	13.8564i	0.360302	−	0.624061i
$494$		0			0
$495$		0			0
$496$	4.00000			0.179605
$497$	−10.0000	−	3.46410i	−0.448561	−	0.155386i
$498$		0			0
$499$	9.50000	+	16.4545i	0.425278	+	0.736604i	0.996446	−	0.0842294i	$-0.0268429\pi$
$499$	9.50000	+	16.4545i	0.425278	+	0.736604i	−0.571168	+	0.820833i	$0.693510\pi$
$500$	−24.0000	+	41.5692i	−1.07331	+	1.85903i
$501$		0			0
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−7.00000	+	12.1244i	−0.310575	+	0.537931i
$509$	−4.00000	−	6.92820i	−0.177297	−	0.307087i	0.763657	−	0.645622i	$-0.223402\pi$
$509$	−4.00000	−	6.92820i	−0.177297	−	0.307087i	−0.940954	+	0.338535i	$0.890069\pi$
$510$		0			0
$511$	−22.0000	+	19.0526i	−0.973223	+	0.842836i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	18.0000	−	31.1769i	0.793175	−	1.37382i
$516$		0			0
$517$	−8.00000			−0.351840
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$	−24.0000			−1.04844
$525$		0			0
$526$		0			0
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$		0			0
$532$	−15.0000	−	5.19615i	−0.650332	−	0.225282i
$533$	20.0000			0.866296
$534$		0			0
$535$	16.0000	−	27.7128i	0.691740	−	1.19813i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.50000	−	2.59808i	0.279975	−	0.111907i
$540$		0			0
$541$	3.50000	+	6.06218i	0.150477	+	0.260633i	0.931403	−	0.363990i	$-0.118586\pi$
$541$	3.50000	+	6.06218i	0.150477	+	0.260633i	−0.780926	+	0.624623i	$0.785252\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	44.0000			1.88475
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$	12.0000	+	20.7846i	0.512615	+	0.887875i
$549$		0			0
$550$		0			0
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$		0			0
$553$	7.50000	+	38.9711i	0.318932	+	1.65722i
$554$		0			0
$555$		0			0
$556$	−19.0000	+	32.9090i	−0.805779	+	1.39565i
$557$	14.0000	−	24.2487i	0.593199	−	1.02745i	−0.400599	−	0.916253i	$-0.631198\pi$
$557$	14.0000	−	24.2487i	0.593199	−	1.02745i	0.993798	−	0.111198i	$-0.0354686\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$	−32.0000	+	27.7128i	−1.35225	+	1.17108i
$561$		0			0
$562$		0			0
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	−0.646737	−	0.762713i	$-0.723867\pi$
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	0.983897	+	0.178735i	$0.0572004\pi$
$564$		0			0
$565$	−32.0000	−	55.4256i	−1.34625	−	2.33177i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	−0.969378	−	0.245573i	$-0.921024\pi$
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	0.697362	+	0.716720i	$0.254357\pi$
$572$	−5.00000	−	8.66025i	−0.209061	−	0.362103i
$573$		0			0
$574$		0			0
$575$	−88.0000			−3.66985
$576$		0			0
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$		0			0
$579$		0			0
$580$	32.0000			1.32873
$581$	30.0000	+	10.3923i	1.24461	+	0.431145i
$582$		0			0
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	−3.00000			−0.123613
$590$		0			0
$591$		0			0
$592$	−14.0000	+	24.2487i	−0.575396	+	0.996616i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$	−40.0000	−	13.8564i	−1.63984	−	0.568057i
$596$	8.00000			0.327693
$597$		0			0
$598$		0			0
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$		0			0
$603$		0			0
$604$	−12.0000	−	20.7846i	−0.488273	−	0.845714i
$605$	2.00000	−	3.46410i	0.0813116	−	0.140836i
$606$		0			0
$607$	18.5000	+	32.0429i	0.750892	+	1.30058i	0.947391	+	0.320079i	$0.103709\pi$
$607$	18.5000	+	32.0429i	0.750892	+	1.30058i	−0.196499	+	0.980504i	$0.562957\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−20.0000	−	34.6410i	−0.809113	−	1.40143i
$612$		0			0
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	−0.474509	−	0.880251i	$-0.657374\pi$
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	0.999574	−	0.0291886i	$-0.00929235\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$		0			0
$619$	0.500000	−	0.866025i	0.0200967	−	0.0348085i	−0.855802	−	0.517303i	$-0.826936\pi$
$619$	0.500000	−	0.866025i	0.0200967	−	0.0348085i	0.875899	+	0.482495i	$0.160269\pi$
$620$	−4.00000	+	6.92820i	−0.160644	+	0.278243i
$621$		0			0
$622$		0			0
$623$	−6.00000	−	31.1769i	−0.240385	−	1.24908i
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$		0			0
$627$		0			0
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$	−28.0000			−1.11643
$630$		0			0
$631$	12.0000			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−14.0000	−	24.2487i	−0.555573	−	0.962281i
$636$		0			0
$637$	27.5000	+	21.6506i	1.08959	+	0.857829i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	24.0000	−	41.5692i	0.947943	−	1.64189i	0.198194	−	0.980163i	$-0.436492\pi$
$641$	24.0000	−	41.5692i	0.947943	−	1.64189i	0.749749	−	0.661723i	$-0.230174\pi$
$642$		0			0
$643$	25.0000			0.985904			0.492952	−	0.870057i	$-0.335918\pi$
$643$	25.0000			0.985904			0.492952	+	0.870057i	$0.335918\pi$
$644$	−40.0000	−	13.8564i	−1.57622	−	0.546019i
$645$		0			0
$646$		0			0
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	16.0000			0.626608
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	0.824236	−	0.566247i	$-0.191605\pi$
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	−0.902502	+	0.430686i	$0.858272\pi$
$654$		0			0
$655$	24.0000	−	41.5692i	0.937758	−	1.62424i
$656$	−8.00000	−	13.8564i	−0.312348	−	0.541002i
$657$		0			0
$658$		0			0
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	24.0000	−	20.7846i	0.930680	−	0.805993i
$666$		0			0
$667$	16.0000	+	27.7128i	0.619522	+	1.07304i
$668$	−8.00000	+	13.8564i	−0.309529	+	0.536120i
$669$		0			0
$670$		0			0
$671$	2.00000			0.0772091
$672$		0			0
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$		0			0
$675$		0			0
$676$	12.0000	−	20.7846i	0.461538	−	0.799408i
$677$	−16.0000	−	27.7128i	−0.614930	−	1.06509i	−0.990397	−	0.138254i	$-0.955851\pi$
$677$	−16.0000	−	27.7128i	−0.614930	−	1.06509i	0.375467	−	0.926836i	$-0.377482\pi$
$678$		0			0
$679$	5.00000	+	1.73205i	0.191882	+	0.0664700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	−0.998917	−	0.0465244i	$-0.985185\pi$
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	0.539750	+	0.841825i	$0.318519\pi$
$684$		0			0
$685$	−48.0000			−1.83399
$686$		0			0
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−30.0000	+	51.9615i	−1.14291	+	1.97958i
$690$		0			0
$691$	−7.50000	−	12.9904i	−0.285313	−	0.494177i	0.687372	−	0.726306i	$-0.258764\pi$
$691$	−7.50000	−	12.9904i	−0.285313	−	0.494177i	−0.972685	+	0.232128i	$0.925431\pi$
$692$	40.0000			1.52057
$693$		0			0
$694$		0			0
$695$	−38.0000	−	65.8179i	−1.44142	−	2.49662i
$696$		0			0
$697$	8.00000	−	13.8564i	0.303022	−	0.524849i
$698$		0			0
$699$		0			0
$700$	−11.0000	−	57.1577i	−0.415761	−	2.16036i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	10.5000	−	18.1865i	0.396015	−	0.685918i
$704$	−4.00000	+	6.92820i	−0.150756	+	0.261116i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		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
$711$		0			0
$712$		0			0
$713$	−8.00000			−0.299602
$714$		0			0
$715$	20.0000			0.747958
$716$	4.00000	+	6.92820i	0.149487	+	0.258919i
$717$		0			0
$718$		0			0
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$		0			0
$721$	4.50000	+	23.3827i	0.167589	+	0.870817i
$722$		0			0
$723$		0			0
$724$	−7.00000	+	12.1244i	−0.260153	+	0.450598i
$725$	−22.0000	+	38.1051i	−0.817059	+	1.41519i
$726$		0			0
$727$	23.0000			0.853023			0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000			0.853023			0.426511	+	0.904482i	$0.359742\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$		0			0
$733$	9.50000	+	16.4545i	0.350891	+	0.607760i	0.986406	−	0.164328i	$-0.0525456\pi$
$733$	9.50000	+	16.4545i	0.350891	+	0.607760i	−0.635515	+	0.772088i	$0.719212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.50000	+	2.59808i	0.0552532	+	0.0957014i
$738$		0			0
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	−28.0000	−	48.4974i	−1.02930	−	1.78280i
$741$		0			0
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$		0			0
$745$	−8.00000	+	13.8564i	−0.293097	+	0.507659i
$746$		0			0
$747$		0			0
$748$	−8.00000			−0.292509
$749$	4.00000	+	20.7846i	0.146157	+	0.759453i
$750$		0			0
$751$	23.5000	+	40.7032i	0.857527	+	1.48528i	0.874281	+	0.485421i	$0.161334\pi$
$751$	23.5000	+	40.7032i	0.857527	+	1.48528i	−0.0167534	+	0.999860i	$0.505333\pi$
$752$	−16.0000	+	27.7128i	−0.583460	+	1.01058i
$753$		0			0
$754$		0			0
$755$	48.0000			1.74690
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.0000	−	31.1769i	−0.652499	−	1.13016i	−0.982514	−	0.186187i	$-0.940387\pi$
$761$	−18.0000	−	31.1769i	−0.652499	−	1.13016i	0.330015	−	0.943976i	$-0.392946\pi$
$762$		0			0
$763$	−22.0000	+	19.0526i	−0.796453	+	0.689749i
$764$	−16.0000			−0.578860
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$		0			0
$771$		0			0
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	−0.00558380	−	0.999984i	$-0.501777\pi$
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	0.868804	−	0.495156i	$-0.164889\pi$
$774$		0			0
$775$	−5.50000	−	9.52628i	−0.197566	−	0.342194i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	+	10.3923i	0.214972	+	0.372343i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$		0			0
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	8.00000			0.285532
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	−24.0000	+	41.5692i	−0.854965	+	1.48084i
$789$		0			0
$790$		0			0
$791$	40.0000	+	13.8564i	1.42224	+	0.492677i
$792$		0			0
$793$	5.00000	+	8.66025i	0.177555	+	0.307535i
$794$		0			0
$795$		0			0
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.50000	−	9.52628i	−0.194091	−	0.336175i
$804$		0			0
$805$	64.0000	−	55.4256i	2.25570	−	1.95350i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	−16.0000	+	13.8564i	−0.561490	+	0.486265i
$813$		0			0
$814$		0			0
$815$	−16.0000	+	27.7128i	−0.560456	+	0.970737i
$816$		0			0
$817$	1.50000	+	2.59808i	0.0524784	+	0.0908952i
$818$		0			0
$819$		0			0
$820$	32.0000			1.11749
$821$	−6.00000	−	10.3923i	−0.209401	−	0.362694i	0.742125	−	0.670262i	$-0.233818\pi$
$821$	−6.00000	−	10.3923i	−0.209401	−	0.362694i	−0.951526	+	0.307568i	$0.900485\pi$
$822$		0			0
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.0000			−0.556375			−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000			−0.556375			−0.278187	+	0.960527i	$0.589734\pi$
$828$		0			0
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$		0			0
$831$		0			0
$832$	−40.0000			−1.38675
$833$	26.0000	−	10.3923i	0.900847	−	0.360072i
$834$		0			0
$835$	−16.0000	−	27.7128i	−0.553703	−	0.959041i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$		0			0
$838$		0			0
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$		0			0
$844$	−8.00000	+	13.8564i	−0.275371	+	0.476957i
$845$	24.0000	+	41.5692i	0.825625	+	1.43002i
$846$		0			0
$847$	0.500000	+	2.59808i	0.0171802	+	0.0892710i
$848$	48.0000			1.64833
$849$		0			0
$850$		0			0
$851$	28.0000	−	48.4974i	0.959828	−	1.66247i
$852$		0			0
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	0.451958	+	0.892039i	$0.350726\pi$
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	−0.998508	+	0.0546125i	$0.982608\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$		0			0
$863$	10.0000	+	17.3205i	0.340404	+	0.589597i	0.984508	−	0.175341i	$-0.0561028\pi$
$863$	10.0000	+	17.3205i	0.340404	+	0.589597i	−0.644104	+	0.764938i	$0.722770\pi$
$864$		0			0
$865$	−40.0000	+	69.2820i	−1.36004	+	2.35566i
$866$		0			0
$867$		0			0
$868$	−1.00000	−	5.19615i	−0.0339422	−	0.176369i
$869$	−15.0000			−0.508840
$870$		0			0
$871$	−7.50000	+	12.9904i	−0.254128	+	0.440162i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	60.0000	+	20.7846i	2.02837	+	0.702648i
$876$		0			0
$877$	25.0000	+	43.3013i	0.844190	+	1.46218i	0.886323	+	0.463068i	$0.153251\pi$
$877$	25.0000	+	43.3013i	0.844190	+	1.46218i	−0.0421327	+	0.999112i	$0.513415\pi$
$878$		0			0
$879$		0			0
$880$	−8.00000	−	13.8564i	−0.269680	−	0.467099i
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$	−41.0000			−1.37976			−0.689880	−	0.723924i	$-0.742337\pi$
$883$	−41.0000			−1.37976			−0.689880	+	0.723924i	$0.742337\pi$
$884$	−20.0000	−	34.6410i	−0.672673	−	1.16510i
$885$		0			0
$886$		0			0
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$		0			0
$889$	17.5000	+	6.06218i	0.586931	+	0.203319i
$890$		0			0
$891$		0			0
$892$	4.00000	−	6.92820i	0.133930	−	0.231973i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	−16.0000			−0.534821
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.00000	+	3.46410i	−0.0667037	+	0.115534i
$900$		0			0
$901$	24.0000	+	41.5692i	0.799556	+	1.38487i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.0000	−	24.2487i	−0.465376	−	0.806054i
$906$		0			0
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$	16.0000	+	27.7128i	0.530979	+	0.919682i
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$		0			0
$915$		0			0
$916$	−34.0000			−1.12339
$917$	6.00000	+	31.1769i	0.198137	+	1.02955i
$918$		0			0
$919$	22.5000	+	38.9711i	0.742207	+	1.28554i	0.951489	+	0.307684i	$0.0995540\pi$
$919$	22.5000	+	38.9711i	0.742207	+	1.28554i	−0.209282	+	0.977855i	$0.567113\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	20.0000			0.658308
$924$		0			0
$925$	77.0000			2.53174
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	0.994157	+	0.107944i	$0.0344268\pi$
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	−0.403596	+	0.914937i	$0.632240\pi$
$930$		0			0
$931$	−3.00000	+	20.7846i	−0.0983210	+	0.681188i
$932$	24.0000			0.786146
$933$		0			0
$934$		0			0
$935$	8.00000	−	13.8564i	0.261628	−	0.453153i
$936$		0			0
$937$	15.0000			0.490029			0.245014	−	0.969519i	$-0.421207\pi$
$937$	15.0000			0.490029			0.245014	+	0.969519i	$0.421207\pi$
$938$		0			0
$939$		0			0
$940$	−32.0000	−	55.4256i	−1.04372	−	1.80778i
$941$	4.00000	−	6.92820i	0.130396	−	0.225853i	−0.793433	−	0.608657i	$-0.791708\pi$
$941$	4.00000	−	6.92820i	0.130396	−	0.225853i	0.923829	+	0.382804i	$0.125042\pi$
$942$		0			0
$943$	16.0000	+	27.7128i	0.521032	+	0.902453i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.00000	−	6.92820i	−0.129983	−	0.225136i	0.793687	−	0.608326i	$-0.208159\pi$
$947$	−4.00000	−	6.92820i	−0.129983	−	0.225136i	−0.923670	+	0.383190i	$0.874825\pi$
$948$		0			0
$949$	27.5000	−	47.6314i	0.892688	−	1.54618i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$		0			0
$955$	16.0000	−	27.7128i	0.517748	−	0.896766i
$956$	28.0000	−	48.4974i	0.905585	−	1.56852i
$957$		0			0
$958$		0			0
$959$	24.0000	−	20.7846i	0.775000	−	0.671170i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$		0			0
$964$	−18.0000	−	31.1769i	−0.579741	−	1.00414i
$965$	−44.0000			−1.41641
$966$		0			0
$967$	−49.0000			−1.57573			−0.787867	−	0.615846i	$-0.788815\pi$
$967$	−49.0000			−1.57573			−0.787867	+	0.615846i	$0.788815\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	0.985024	+	0.172418i	$0.0551581\pi$
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	−0.343193	+	0.939265i	$0.611509\pi$
$972$		0			0
$973$	47.5000	+	16.4545i	1.52278	+	0.527506i
$974$		0			0
$975$		0			0
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	−10.0000	+	17.3205i	−0.319928	+	0.554132i	−0.980473	−	0.196655i	$-0.936992\pi$
$977$	−10.0000	+	17.3205i	−0.319928	+	0.554132i	0.660544	+	0.750787i	$0.270326\pi$
$978$		0			0
$979$	12.0000			0.383522
$980$	44.0000	+	34.6410i	1.40553	+	1.10657i
$981$		0			0
$982$		0			0
$983$	6.00000	−	10.3923i	0.191370	−	0.331463i	−0.754334	−	0.656490i	$-0.772040\pi$
$983$	6.00000	−	10.3923i	0.191370	−	0.331463i	0.945705	+	0.325027i	$0.105374\pi$
$984$		0			0
$985$	−48.0000	−	83.1384i	−1.52941	−	2.64901i
$986$		0			0
$987$		0			0
$988$	30.0000			0.954427
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$		0			0
$991$	11.5000	−	19.9186i	0.365310	−	0.632735i	−0.623516	−	0.781810i	$-0.714296\pi$
$991$	11.5000	−	19.9186i	0.365310	−	0.632735i	0.988826	+	0.149076i	$0.0476298\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.0000			−0.507234
$996$		0			0
$997$	10.5000	−	18.1865i	0.332538	−	0.575973i	−0.650471	−	0.759532i	$-0.725428\pi$
$997$	10.5000	−	18.1865i	0.332538	−	0.575973i	0.983009	+	0.183558i	$0.0587616\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.d.298.1	yes	2
3.2	odd	2		693.2.i.c.298.1	yes	2
7.2	even	3	inner	693.2.i.d.100.1	yes	2
7.3	odd	6		4851.2.a.l.1.1		1
7.4	even	3		4851.2.a.h.1.1		1
21.2	odd	6		693.2.i.c.100.1	✓	2
21.11	odd	6		4851.2.a.m.1.1		1
21.17	even	6		4851.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.i.c.100.1	✓	2	21.2	odd	6
693.2.i.c.298.1	yes	2	3.2	odd	2
693.2.i.d.100.1	yes	2	7.2	even	3	inner
693.2.i.d.298.1	yes	2	1.1	even	1	trivial
4851.2.a.h.1.1		1	7.4	even	3
4851.2.a.i.1.1		1	21.17	even	6
4851.2.a.l.1.1		1	7.3	odd	6
4851.2.a.m.1.1		1	21.11	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{4} +(2.00000 + 3.46410i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{4} +(2.00000 + 3.46410i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{11} +5.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{17} +(1.50000 + 2.59808i) q^{19} +8.00000 q^{20} +(4.00000 + 6.92820i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(-4.00000 + 3.46410i) q^{28} +4.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-2.00000 - 10.3923i) q^{35} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{41} +1.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-4.00000 - 6.92820i) q^{47} +(5.50000 + 4.33013i) q^{49} +(5.00000 - 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} +4.00000 q^{55} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{64} +(10.0000 + 17.3205i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(-4.00000 - 6.92820i) q^{68} +4.00000 q^{71} +(5.50000 - 9.52628i) q^{73} +6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(-7.50000 - 12.9904i) q^{79} +(8.00000 - 13.8564i) q^{80} -12.0000 q^{83} +16.0000 q^{85} +(6.00000 + 10.3923i) q^{89} +(-12.5000 - 4.33013i) q^{91} +16.0000 q^{92} +(-6.00000 + 10.3923i) q^{95} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} + 4 q^{5} - 5 q^{7}+O(q^{10}) \) 2 * q + 2 * q^4 + 4 * q^5 - 5 * q^7	\( 2 q + 2 q^{4} + 4 q^{5} - 5 q^{7} + q^{11} + 10 q^{13} - 4 q^{16} + 4 q^{17} + 3 q^{19} + 16 q^{20} + 8 q^{23} - 11 q^{25} - 8 q^{28} + 8 q^{29} - q^{31} - 4 q^{35} - 7 q^{37} + 8 q^{41} + 2 q^{43} - 2 q^{44} - 8 q^{47} + 11 q^{49} + 10 q^{52} - 12 q^{53} + 8 q^{55} + 2 q^{61} - 16 q^{64} + 20 q^{65} - 3 q^{67} - 8 q^{68} + 8 q^{71} + 11 q^{73} + 12 q^{76} - 4 q^{77} - 15 q^{79} + 16 q^{80} - 24 q^{83} + 32 q^{85} + 12 q^{89} - 25 q^{91} + 32 q^{92} - 12 q^{95} - 4 q^{97}+O(q^{100}) \) 2 * q + 2 * q^4 + 4 * q^5 - 5 * q^7 + q^11 + 10 * q^13 - 4 * q^16 + 4 * q^17 + 3 * q^19 + 16 * q^20 + 8 * q^23 - 11 * q^25 - 8 * q^28 + 8 * q^29 - q^31 - 4 * q^35 - 7 * q^37 + 8 * q^41 + 2 * q^43 - 2 * q^44 - 8 * q^47 + 11 * q^49 + 10 * q^52 - 12 * q^53 + 8 * q^55 + 2 * q^61 - 16 * q^64 + 20 * q^65 - 3 * q^67 - 8 * q^68 + 8 * q^71 + 11 * q^73 + 12 * q^76 - 4 * q^77 - 15 * q^79 + 16 * q^80 - 24 * q^83 + 32 * q^85 + 12 * q^89 - 25 * q^91 + 32 * q^92 - 12 * q^95 - 4 * q^97

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