LMFDB - Embedded newform 1152.2.i.a.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, 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("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.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:	$9.19876631285$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			769.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1152.769
Dual form			1152.2.i.a.385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(2.00000 - 3.46410i) q^{13} -3.46410i q^{15} +1.00000 q^{17} -5.00000 q^{19} +(-3.00000 - 1.73205i) q^{21} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(-3.00000 - 5.19615i) q^{29} +(7.50000 + 4.33013i) q^{33} -4.00000 q^{35} +10.0000 q^{37} +6.92820i q^{39} +(1.50000 - 2.59808i) q^{41} +(4.50000 + 7.79423i) q^{43} +(3.00000 + 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-1.50000 + 0.866025i) q^{51} +12.0000 q^{53} +10.0000 q^{55} +(7.50000 - 4.33013i) q^{57} +(-3.50000 + 6.06218i) q^{59} +(2.00000 + 3.46410i) q^{61} +6.00000 q^{63} +(4.00000 + 6.92820i) q^{65} +(3.50000 - 6.06218i) q^{67} +6.92820i q^{69} +6.00000 q^{71} -13.0000 q^{73} +(-1.50000 - 0.866025i) q^{75} +(5.00000 - 8.66025i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{83} +(-1.00000 + 1.73205i) q^{85} +(9.00000 + 5.19615i) q^{87} +10.0000 q^{89} +8.00000 q^{91} +(5.00000 - 8.66025i) q^{95} +(-6.50000 - 11.2583i) q^{97} -15.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 2 q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 2 * q^5 + 2 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} - 2 q^{5} + 2 q^{7} + 3 q^{9} - 5 q^{11} + 4 q^{13} + 2 q^{17} - 10 q^{19} - 6 q^{21} + 4 q^{23} + q^{25} - 6 q^{29} + 15 q^{33} - 8 q^{35} + 20 q^{37} + 3 q^{41} + 9 q^{43} + 6 q^{45} - 8 q^{47} + 3 q^{49} - 3 q^{51} + 24 q^{53} + 20 q^{55} + 15 q^{57} - 7 q^{59} + 4 q^{61} + 12 q^{63} + 8 q^{65} + 7 q^{67} + 12 q^{71} - 26 q^{73} - 3 q^{75} + 10 q^{77} - 2 q^{79} - 9 q^{81} - 12 q^{83} - 2 q^{85} + 18 q^{87} + 20 q^{89} + 16 q^{91} + 10 q^{95} - 13 q^{97} - 30 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 2 * q^5 + 2 * q^7 + 3 * q^9 - 5 * q^11 + 4 * q^13 + 2 * q^17 - 10 * q^19 - 6 * q^21 + 4 * q^23 + q^25 - 6 * q^29 + 15 * q^33 - 8 * q^35 + 20 * q^37 + 3 * q^41 + 9 * q^43 + 6 * q^45 - 8 * q^47 + 3 * q^49 - 3 * q^51 + 24 * q^53 + 20 * q^55 + 15 * q^57 - 7 * q^59 + 4 * q^61 + 12 * q^63 + 8 * q^65 + 7 * q^67 + 12 * q^71 - 26 * q^73 - 3 * q^75 + 10 * q^77 - 2 * q^79 - 9 * q^81 - 12 * q^83 - 2 * q^85 + 18 * q^87 + 20 * q^89 + 16 * q^91 + 10 * q^95 - 13 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$		0			0
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		−	3.46410i		−	0.894427i
$16$		0			0
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$		0			0
$21$	−3.00000	−	1.73205i	−0.654654	−	0.377964i
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$		0			0
$33$	7.50000	+	4.33013i	1.30558	+	0.753778i
$34$		0			0
$35$	−4.00000			−0.676123
$36$		0			0
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$			6.92820i			1.10940i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	4.50000	+	7.79423i	0.686244	+	1.18861i	0.973044	+	0.230618i	$0.0740749\pi$
$43$	4.50000	+	7.79423i	0.686244	+	1.18861i	−0.286801	+	0.957990i	$0.592592\pi$
$44$		0			0
$45$	3.00000	+	5.19615i	0.447214	+	0.774597i
$46$		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
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	−1.50000	+	0.866025i	−0.210042	+	0.121268i
$52$		0			0
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$		0			0
$55$	10.0000			1.34840
$56$		0			0
$57$	7.50000	−	4.33013i	0.993399	−	0.573539i
$58$		0			0
$59$	−3.50000	+	6.06218i	−0.455661	+	0.789228i	−0.998726	−	0.0504625i	$-0.983930\pi$
$59$	−3.50000	+	6.06218i	−0.455661	+	0.789228i	0.543065	+	0.839691i	$0.317264\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$		0			0
$63$	6.00000			0.755929
$64$		0			0
$65$	4.00000	+	6.92820i	0.496139	+	0.859338i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$		0			0
$69$			6.92820i			0.834058i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−13.0000			−1.52153			−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000			−1.52153			−0.760767	+	0.649025i	$0.775177\pi$
$74$		0			0
$75$	−1.50000	−	0.866025i	−0.173205	−	0.100000i
$76$		0			0
$77$	5.00000	−	8.66025i	0.569803	−	0.986928i
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$	−1.00000	+	1.73205i	−0.108465	+	0.187867i
$86$		0			0
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$	8.00000			0.838628
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.00000	−	8.66025i	0.512989	−	0.888523i
$96$		0			0
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	−0.980622	−	0.195911i	$-0.937234\pi$
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	0.320647	−	0.947199i	$-0.396100\pi$
$98$		0			0
$99$	−15.0000			−1.50756
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$		0			0
$105$	6.00000	−	3.46410i	0.585540	−	0.338062i
$106$		0			0
$107$	11.0000			1.06341			0.531705	−	0.846930i	$-0.321551\pi$
$107$	11.0000			1.06341			0.531705	+	0.846930i	$0.321551\pi$
$108$		0			0
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	−15.0000	+	8.66025i	−1.42374	+	0.821995i
$112$		0			0
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	0.322498	+	0.946570i	$0.395477\pi$
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	−0.981003	+	0.193993i	$0.937856\pi$
$114$		0			0
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$		0			0
$117$	−6.00000	−	10.3923i	−0.554700	−	0.960769i
$118$		0			0
$119$	1.00000	+	1.73205i	0.0916698	+	0.158777i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$			5.19615i			0.468521i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$	−13.5000	−	7.79423i	−1.18861	−	0.686244i
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−5.00000	−	8.66025i	−0.433555	−	0.750939i
$134$		0			0
$135$	−9.00000	−	5.19615i	−0.774597	−	0.447214i
$136$		0			0
$137$	−0.500000	−	0.866025i	−0.0427179	−	0.0739895i	0.843876	−	0.536538i	$-0.180268\pi$
$137$	−0.500000	−	0.866025i	−0.0427179	−	0.0739895i	−0.886594	+	0.462549i	$0.846935\pi$
$138$		0			0
$139$	−0.500000	+	0.866025i	−0.0424094	+	0.0734553i	−0.886451	−	0.462822i	$-0.846837\pi$
$139$	−0.500000	+	0.866025i	−0.0424094	+	0.0734553i	0.844042	+	0.536278i	$0.180170\pi$
$140$		0			0
$141$	12.0000	+	6.92820i	1.01058	+	0.583460i
$142$		0			0
$143$	−20.0000			−1.67248
$144$		0			0
$145$	12.0000			0.996546
$146$		0			0
$147$			5.19615i			0.428571i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$	1.50000	−	2.59808i	0.121268	−	0.210042i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.0000	+	20.7846i	−0.957704	+	1.65879i	−0.229650	+	0.973273i	$0.573758\pi$
$157$	−12.0000	+	20.7846i	−0.957704	+	1.65879i	−0.728055	+	0.685519i	$0.759575\pi$
$158$		0			0
$159$	−18.0000	+	10.3923i	−1.42749	+	0.824163i
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	−15.0000	+	8.66025i	−1.16775	+	0.674200i
$166$		0			0
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	−0.902120	−	0.431486i	$-0.857990\pi$
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	0.824737	+	0.565516i	$0.191323\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$	−7.50000	+	12.9904i	−0.573539	+	0.993399i
$172$		0			0
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$		0			0
$177$		−	12.1244i		−	0.911322i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$	−6.00000	−	3.46410i	−0.443533	−	0.256074i
$184$		0			0
$185$	−10.0000	+	17.3205i	−0.735215	+	1.27343i
$186$		0			0
$187$	−2.50000	−	4.33013i	−0.182818	−	0.316650i
$188$		0			0
$189$	−9.00000	+	5.19615i	−0.654654	+	0.377964i
$190$		0			0
$191$	1.00000	+	1.73205i	0.0723575	+	0.125327i	0.899934	−	0.436026i	$-0.143614\pi$
$191$	1.00000	+	1.73205i	0.0723575	+	0.125327i	−0.827577	+	0.561353i	$0.810281\pi$
$192$		0			0
$193$	−0.500000	+	0.866025i	−0.0359908	+	0.0623379i	−0.883460	−	0.468507i	$-0.844792\pi$
$193$	−0.500000	+	0.866025i	−0.0359908	+	0.0623379i	0.847469	+	0.530845i	$0.178125\pi$
$194$		0			0
$195$	−12.0000	−	6.92820i	−0.859338	−	0.496139i
$196$		0			0
$197$	−20.0000			−1.42494			−0.712470	−	0.701702i	$-0.752424\pi$
$197$	−20.0000			−1.42494			−0.712470	+	0.701702i	$0.752424\pi$
$198$		0			0
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$		0			0
$201$			12.1244i			0.855186i
$202$		0			0
$203$	6.00000	−	10.3923i	0.421117	−	0.729397i
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$		0			0
$207$	−6.00000	−	10.3923i	−0.417029	−	0.722315i
$208$		0			0
$209$	12.5000	+	21.6506i	0.864643	+	1.49761i
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$		0			0
$213$	−9.00000	+	5.19615i	−0.616670	+	0.356034i
$214$		0			0
$215$	−18.0000			−1.22759
$216$		0			0
$217$		0			0
$218$		0			0
$219$	19.5000	−	11.2583i	1.31769	−	0.760767i
$220$		0			0
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$	−12.0000	−	20.7846i	−0.803579	−	1.39184i	−0.917246	−	0.398321i	$-0.869593\pi$
$223$	−12.0000	−	20.7846i	−0.803579	−	1.39184i	0.113666	−	0.993519i	$-0.463740\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$		0			0
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$			17.3205i			1.13961i
$232$		0			0
$233$	−9.00000			−0.589610			−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000			−0.589610			−0.294805	+	0.955557i	$0.595255\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$		0			0
$237$	3.00000	+	1.73205i	0.194871	+	0.112509i
$238$		0			0
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$		0			0
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	0.110963	−	0.993825i	$-0.464606\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		0			0
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	−10.0000	+	17.3205i	−0.636285	+	1.10208i
$248$		0			0
$249$	18.0000	+	10.3923i	1.14070	+	0.658586i
$250$		0			0
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$		0			0
$255$		−	3.46410i		−	0.216930i
$256$		0			0
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	10.0000	+	17.3205i	0.621370	+	1.07624i
$260$		0			0
$261$	−18.0000			−1.11417
$262$		0			0
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$		0			0
$265$	−12.0000	+	20.7846i	−0.737154	+	1.27679i
$266$		0			0
$267$	−15.0000	+	8.66025i	−0.917985	+	0.529999i
$268$		0			0
$269$	4.00000			0.243884			0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000			0.243884			0.121942	+	0.992537i	$0.461088\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$	−12.0000	+	6.92820i	−0.726273	+	0.419314i
$274$		0			0
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−15.0000	−	25.9808i	−0.894825	−	1.54988i	−0.834021	−	0.551733i	$-0.813967\pi$
$281$	−15.0000	−	25.9808i	−0.894825	−	1.54988i	−0.0608039	−	0.998150i	$-0.519366\pi$
$282$		0			0
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	−0.250276	−	0.968175i	$-0.580521\pi$
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	0.963602	−	0.267342i	$-0.0861454\pi$
$284$		0			0
$285$			17.3205i			1.02598i
$286$		0			0
$287$	6.00000			0.354169
$288$		0			0
$289$	−16.0000			−0.941176
$290$		0			0
$291$	19.5000	+	11.2583i	1.14311	+	0.659975i
$292$		0			0
$293$	−5.00000	+	8.66025i	−0.292103	+	0.505937i	−0.974307	−	0.225225i	$-0.927688\pi$
$293$	−5.00000	+	8.66025i	−0.292103	+	0.505937i	0.682204	+	0.731162i	$0.261022\pi$
$294$		0			0
$295$	−7.00000	−	12.1244i	−0.407556	−	0.705907i
$296$		0			0
$297$	22.5000	−	12.9904i	1.30558	−	0.753778i
$298$		0			0
$299$	−8.00000	−	13.8564i	−0.462652	−	0.801337i
$300$		0			0
$301$	−9.00000	+	15.5885i	−0.518751	+	0.898504i
$302$		0			0
$303$	9.00000	+	5.19615i	0.517036	+	0.298511i
$304$		0			0
$305$	−8.00000			−0.458079
$306$		0			0
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$		0			0
$309$			13.8564i			0.788263i
$310$		0			0
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	−0.972250	−	0.233944i	$-0.924837\pi$
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	0.688726	+	0.725022i	$0.258170\pi$
$312$		0			0
$313$	−12.5000	−	21.6506i	−0.706542	−	1.22377i	−0.966132	−	0.258047i	$-0.916921\pi$
$313$	−12.5000	−	21.6506i	−0.706542	−	1.22377i	0.259590	−	0.965719i	$-0.416412\pi$
$314$		0			0
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$		0			0
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$		0			0
$319$	−15.0000	+	25.9808i	−0.839839	+	1.45464i
$320$		0			0
$321$	−16.5000	+	9.52628i	−0.920940	+	0.531705i
$322$		0			0
$323$	−5.00000			−0.278207
$324$		0			0
$325$	4.00000			0.221880
$326$		0			0
$327$	−18.0000	+	10.3923i	−0.995402	+	0.574696i
$328$		0			0
$329$	8.00000	−	13.8564i	0.441054	−	0.763928i
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	15.0000	−	25.9808i	0.821995	−	1.42374i
$334$		0			0
$335$	7.00000	+	12.1244i	0.382451	+	0.662424i
$336$		0			0
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$		0			0
$339$		−	24.2487i		−	1.31701i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$	−12.0000	−	6.92820i	−0.646058	−	0.373002i
$346$		0			0
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	−0.822951	−	0.568112i	$-0.807674\pi$
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	0.903475	+	0.428640i	$0.141007\pi$
$348$		0			0
$349$	−8.00000	−	13.8564i	−0.428230	−	0.741716i	0.568486	−	0.822693i	$-0.307529\pi$
$349$	−8.00000	−	13.8564i	−0.428230	−	0.741716i	−0.996716	+	0.0809766i	$0.974196\pi$
$350$		0			0
$351$	18.0000	+	10.3923i	0.960769	+	0.554700i
$352$		0			0
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$		0			0
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$		0			0
$357$	−3.00000	−	1.73205i	−0.158777	−	0.0916698i
$358$		0			0
$359$	34.0000			1.79445			0.897226	−	0.441572i	$-0.145579\pi$
$359$	34.0000			1.79445			0.897226	+	0.441572i	$0.145579\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$		0			0
$363$		−	24.2487i		−	1.27273i
$364$		0			0
$365$	13.0000	−	22.5167i	0.680451	−	1.17858i
$366$		0			0
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	0.996129	+	0.0879086i	$0.0280183\pi$
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	−0.421933	+	0.906627i	$0.638648\pi$
$368$		0			0
$369$	−4.50000	−	7.79423i	−0.234261	−	0.405751i
$370$		0			0
$371$	12.0000	+	20.7846i	0.623009	+	1.07908i
$372$		0			0
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	−0.0708063	−	0.997490i	$-0.522557\pi$
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	0.899255	−	0.437425i	$-0.144109\pi$
$374$		0			0
$375$	18.0000	−	10.3923i	0.929516	−	0.536656i
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	−25.0000			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$380$		0			0
$381$	−30.0000	+	17.3205i	−1.53695	+	0.887357i
$382$		0			0
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$		0			0
$385$	10.0000	+	17.3205i	0.509647	+	0.882735i
$386$		0			0
$387$	27.0000			1.37249
$388$		0			0
$389$	19.0000	+	32.9090i	0.963338	+	1.66855i	0.714015	+	0.700130i	$0.246875\pi$
$389$	19.0000	+	32.9090i	0.963338	+	1.66855i	0.249323	+	0.968420i	$0.419792\pi$
$390$		0			0
$391$	2.00000	−	3.46410i	0.101144	−	0.175187i
$392$		0			0
$393$			20.7846i			1.04844i
$394$		0			0
$395$	4.00000			0.201262
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		0			0
$399$	15.0000	+	8.66025i	0.750939	+	0.433555i
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	18.0000			0.894427
$406$		0			0
$407$	−25.0000	−	43.3013i	−1.23920	−	2.14636i
$408$		0			0
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$		0			0
$411$	1.50000	+	0.866025i	0.0739895	+	0.0427179i
$412$		0			0
$413$	−14.0000			−0.688895
$414$		0			0
$415$	24.0000			1.17811
$416$		0			0
$417$		−	1.73205i		−	0.0848189i
$418$		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
$421$	1.00000	+	1.73205i	0.0487370	+	0.0844150i	0.889365	−	0.457198i	$-0.151147\pi$
$421$	1.00000	+	1.73205i	0.0487370	+	0.0844150i	−0.840628	+	0.541613i	$0.817814\pi$
$422$		0			0
$423$	−24.0000			−1.16692
$424$		0			0
$425$	0.500000	+	0.866025i	0.0242536	+	0.0420084i
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$		0			0
$429$	30.0000	−	17.3205i	1.44841	−	0.836242i
$430$		0			0
$431$	−10.0000			−0.481683			−0.240842	−	0.970564i	$-0.577423\pi$
$431$	−10.0000			−0.481683			−0.240842	+	0.970564i	$0.577423\pi$
$432$		0			0
$433$	33.0000			1.58588			0.792939	−	0.609301i	$-0.208550\pi$
$433$	33.0000			1.58588			0.792939	+	0.609301i	$0.208550\pi$
$434$		0			0
$435$	−18.0000	+	10.3923i	−0.863034	+	0.498273i
$436$		0			0
$437$	−10.0000	+	17.3205i	−0.478365	+	0.828552i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	0.631010	−	0.775775i	$-0.282641\pi$
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	−0.987346	+	0.158583i	$0.949307\pi$
$444$		0			0
$445$	−10.0000	+	17.3205i	−0.474045	+	0.821071i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	17.0000			0.802280			0.401140	−	0.916017i	$-0.368614\pi$
$449$	17.0000			0.802280			0.401140	+	0.916017i	$0.368614\pi$
$450$		0			0
$451$	−15.0000			−0.706322
$452$		0			0
$453$	−24.0000	−	13.8564i	−1.12762	−	0.651031i
$454$		0			0
$455$	−8.00000	+	13.8564i	−0.375046	+	0.649598i
$456$		0			0
$457$	1.50000	+	2.59808i	0.0701670	+	0.121533i	0.898974	−	0.438001i	$-0.144313\pi$
$457$	1.50000	+	2.59808i	0.0701670	+	0.121533i	−0.828807	+	0.559534i	$0.810980\pi$
$458$		0			0
$459$			5.19615i			0.242536i
$460$		0			0
$461$	10.0000	+	17.3205i	0.465746	+	0.806696i	0.999235	−	0.0391109i	$-0.0124526\pi$
$461$	10.0000	+	17.3205i	0.465746	+	0.806696i	−0.533488	+	0.845807i	$0.679119\pi$
$462$		0			0
$463$	−1.00000	+	1.73205i	−0.0464739	+	0.0804952i	−0.888327	−	0.459212i	$-0.848132\pi$
$463$	−1.00000	+	1.73205i	−0.0464739	+	0.0804952i	0.841853	+	0.539707i	$0.181465\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.0000			1.34196			0.670980	−	0.741475i	$-0.265874\pi$
$467$	29.0000			1.34196			0.670980	+	0.741475i	$0.265874\pi$
$468$		0			0
$469$	14.0000			0.646460
$470$		0			0
$471$		−	41.5692i		−	1.91541i
$472$		0			0
$473$	22.5000	−	38.9711i	1.03455	−	1.79190i
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$		0			0
$477$	18.0000	−	31.1769i	0.824163	−	1.42749i
$478$		0			0
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	20.0000	−	34.6410i	0.911922	−	1.57949i
$482$		0			0
$483$	−12.0000	+	6.92820i	−0.546019	+	0.315244i
$484$		0			0
$485$	26.0000			1.18060
$486$		0			0
$487$	−10.0000			−0.453143			−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000			−0.453143			−0.226572	+	0.973995i	$0.572752\pi$
$488$		0			0
$489$	−6.00000	+	3.46410i	−0.271329	+	0.156652i
$490$		0			0
$491$	−12.5000	+	21.6506i	−0.564117	+	0.977079i	0.433014	+	0.901387i	$0.357450\pi$
$491$	−12.5000	+	21.6506i	−0.564117	+	0.977079i	−0.997131	+	0.0756923i	$0.975883\pi$
$492$		0			0
$493$	−3.00000	−	5.19615i	−0.135113	−	0.234023i
$494$		0			0
$495$	15.0000	−	25.9808i	0.674200	−	1.16775i
$496$		0			0
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$		0			0
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$		0			0
$501$		−	3.46410i		−	0.154765i
$502$		0			0
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$		0			0
$507$	4.50000	+	2.59808i	0.199852	+	0.115385i
$508$		0			0
$509$	−14.0000	+	24.2487i	−0.620539	+	1.07481i	0.368846	+	0.929490i	$0.379753\pi$
$509$	−14.0000	+	24.2487i	−0.620539	+	1.07481i	−0.989385	+	0.145315i	$0.953580\pi$
$510$		0			0
$511$	−13.0000	−	22.5167i	−0.575086	−	0.996078i
$512$		0			0
$513$		−	25.9808i		−	1.14708i
$514$		0			0
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	−20.0000	+	34.6410i	−0.879599	+	1.52351i
$518$		0			0
$519$	27.0000	+	15.5885i	1.18517	+	0.684257i
$520$		0			0
$521$	−7.00000			−0.306676			−0.153338	−	0.988174i	$-0.549002\pi$
$521$	−7.00000			−0.306676			−0.153338	+	0.988174i	$0.549002\pi$
$522$		0			0
$523$	−44.0000			−1.92399			−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000			−1.92399			−0.961993	+	0.273075i	$0.911959\pi$
$524$		0			0
$525$		−	3.46410i		−	0.151186i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	10.5000	+	18.1865i	0.455661	+	0.789228i
$532$		0			0
$533$	−6.00000	−	10.3923i	−0.259889	−	0.450141i
$534$		0			0
$535$	−11.0000	+	19.0526i	−0.475571	+	0.823714i
$536$		0			0
$537$	18.0000	−	10.3923i	0.776757	−	0.448461i
$538$		0			0
$539$	−15.0000			−0.646096
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$	−30.0000	+	17.3205i	−1.28742	+	0.743294i
$544$		0			0
$545$	−12.0000	+	20.7846i	−0.514024	+	0.890315i
$546$		0			0
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$	12.0000			0.512148
$550$		0			0
$551$	15.0000	+	25.9808i	0.639021	+	1.10682i
$552$		0			0
$553$	2.00000	−	3.46410i	0.0850487	−	0.147309i
$554$		0			0
$555$		−	34.6410i		−	1.47043i
$556$		0			0
$557$	26.0000			1.10166			0.550828	−	0.834619i	$-0.314312\pi$
$557$	26.0000			1.10166			0.550828	+	0.834619i	$0.314312\pi$
$558$		0			0
$559$	36.0000			1.52264
$560$		0			0
$561$	7.50000	+	4.33013i	0.316650	+	0.182818i
$562$		0			0
$563$	−16.5000	+	28.5788i	−0.695392	+	1.20445i	0.274656	+	0.961542i	$0.411436\pi$
$563$	−16.5000	+	28.5788i	−0.695392	+	1.20445i	−0.970048	+	0.242912i	$0.921897\pi$
$564$		0			0
$565$	−14.0000	−	24.2487i	−0.588984	−	1.02015i
$566$		0			0
$567$	9.00000	−	15.5885i	0.377964	−	0.654654i
$568$		0			0
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	0.993511	−	0.113732i	$-0.0362806\pi$
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	−0.595251	+	0.803540i	$0.702947\pi$
$570$		0			0
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	−0.993425	−	0.114488i	$-0.963477\pi$
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	0.595862	+	0.803087i	$0.296811\pi$
$572$		0			0
$573$	−3.00000	−	1.73205i	−0.125327	−	0.0723575i
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	23.0000			0.957503			0.478751	−	0.877951i	$-0.341090\pi$
$577$	23.0000			0.957503			0.478751	+	0.877951i	$0.341090\pi$
$578$		0			0
$579$		−	1.73205i		−	0.0719816i
$580$		0			0
$581$	12.0000	−	20.7846i	0.497844	−	0.862291i
$582$		0			0
$583$	−30.0000	−	51.9615i	−1.24247	−	2.15203i
$584$		0			0
$585$	24.0000			0.992278
$586$		0			0
$587$	2.50000	+	4.33013i	0.103186	+	0.178723i	0.912996	−	0.407969i	$-0.133763\pi$
$587$	2.50000	+	4.33013i	0.103186	+	0.178723i	−0.809810	+	0.586693i	$0.800430\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	30.0000	−	17.3205i	1.23404	−	0.712470i
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−4.00000			−0.163984
$596$		0			0
$597$	3.00000	−	1.73205i	0.122782	−	0.0708881i
$598$		0			0
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	0.0157622	+	0.999876i	$0.494983\pi$
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	−0.873799	+	0.486287i	$0.838351\pi$
$600$		0			0
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	0.943090	−	0.332538i	$-0.107905\pi$
$601$	4.50000	+	7.79423i	0.183559	+	0.317933i	−0.759531	+	0.650471i	$0.774572\pi$
$602$		0			0
$603$	−10.5000	−	18.1865i	−0.427593	−	0.740613i
$604$		0			0
$605$	−14.0000	−	24.2487i	−0.569181	−	0.985850i
$606$		0			0
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$		0			0
$609$			20.7846i			0.842235i
$610$		0			0
$611$	−32.0000			−1.29458
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$		0			0
$615$	−9.00000	−	5.19615i	−0.362915	−	0.209529i
$616$		0			0
$617$	8.50000	−	14.7224i	0.342197	−	0.592703i	−0.642643	−	0.766165i	$-0.722162\pi$
$617$	8.50000	−	14.7224i	0.342197	−	0.592703i	0.984840	+	0.173463i	$0.0554956\pi$
$618$		0			0
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$		0			0
$621$	18.0000	+	10.3923i	0.722315	+	0.417029i
$622$		0			0
$623$	10.0000	+	17.3205i	0.400642	+	0.693932i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$	−37.5000	−	21.6506i	−1.49761	−	0.864643i
$628$		0			0
$629$	10.0000			0.398726
$630$		0			0
$631$	−22.0000			−0.875806			−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000			−0.875806			−0.437903	+	0.899022i	$0.644279\pi$
$632$		0			0
$633$			34.6410i			1.37686i
$634$		0			0
$635$	−20.0000	+	34.6410i	−0.793676	+	1.37469i
$636$		0			0
$637$	−6.00000	−	10.3923i	−0.237729	−	0.411758i
$638$		0			0
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	10.5000	−	18.1865i	0.414080	−	0.717207i	−0.581252	−	0.813724i	$-0.697437\pi$
$643$	10.5000	−	18.1865i	0.414080	−	0.717207i	0.995331	+	0.0965169i	$0.0307702\pi$
$644$		0			0
$645$	27.0000	−	15.5885i	1.06312	−	0.613795i
$646$		0			0
$647$	42.0000			1.65119			0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000			1.65119			0.825595	+	0.564263i	$0.190840\pi$
$648$		0			0
$649$	35.0000			1.37387
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$		0			0
$655$	12.0000	+	20.7846i	0.468879	+	0.812122i
$656$		0			0
$657$	−19.5000	+	33.7750i	−0.760767	+	1.31769i
$658$		0			0
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	0.999309	−	0.0371821i	$-0.0118382\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$		0			0
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	−0.845922	−	0.533306i	$-0.820949\pi$
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	0.884818	+	0.465937i	$0.154283\pi$
$662$		0			0
$663$			6.92820i			0.269069i
$664$		0			0
$665$	20.0000			0.775567
$666$		0			0
$667$	−24.0000			−0.929284
$668$		0			0
$669$	36.0000	+	20.7846i	1.39184	+	0.803579i
$670$		0			0
$671$	10.0000	−	17.3205i	0.386046	−	0.668651i
$672$		0			0
$673$	−5.00000	−	8.66025i	−0.192736	−	0.333828i	0.753420	−	0.657539i	$-0.228403\pi$
$673$	−5.00000	−	8.66025i	−0.192736	−	0.333828i	−0.946156	+	0.323711i	$0.895069\pi$
$674$		0			0
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$		0			0
$677$	14.0000	+	24.2487i	0.538064	+	0.931954i	0.999008	+	0.0445248i	$0.0141774\pi$
$677$	14.0000	+	24.2487i	0.538064	+	0.931954i	−0.460945	+	0.887429i	$0.652489\pi$
$678$		0			0
$679$	13.0000	−	22.5167i	0.498894	−	0.864110i
$680$		0			0
$681$	−4.50000	−	2.59808i	−0.172440	−	0.0995585i
$682$		0			0
$683$	15.0000			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$		0			0
$687$			24.2487i			0.925146i
$688$		0			0
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	0.957290	−	0.289130i	$-0.0933661\pi$
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	−0.729039	+	0.684472i	$0.760033\pi$
$692$		0			0
$693$	−15.0000	−	25.9808i	−0.569803	−	0.986928i
$694$		0			0
$695$	−1.00000	−	1.73205i	−0.0379322	−	0.0657004i
$696$		0			0
$697$	1.50000	−	2.59808i	0.0568166	−	0.0984092i
$698$		0			0
$699$	13.5000	−	7.79423i	0.510617	−	0.294805i
$700$		0			0
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$		0			0
$703$	−50.0000			−1.88579
$704$		0			0
$705$	−24.0000	+	13.8564i	−0.903892	+	0.521862i
$706$		0			0
$707$	6.00000	−	10.3923i	0.225653	−	0.390843i
$708$		0			0
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	0.614852	−	0.788642i	$-0.289216\pi$
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	−0.990410	+	0.138157i	$0.955882\pi$
$710$		0			0
$711$	−6.00000			−0.225018
$712$		0			0
$713$		0			0
$714$		0			0
$715$	20.0000	−	34.6410i	0.747958	−	1.29550i
$716$		0			0
$717$			20.7846i			0.776215i
$718$		0			0
$719$	30.0000			1.11881			0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000			1.11881			0.559406	+	0.828894i	$0.311029\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$		0			0
$723$	37.5000	+	21.6506i	1.39464	+	0.805196i
$724$		0			0
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	24.0000	+	41.5692i	0.890111	+	1.54172i	0.839742	+	0.542986i	$0.182706\pi$
$727$	24.0000	+	41.5692i	0.890111	+	1.54172i	0.0503692	+	0.998731i	$0.483960\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	4.50000	+	7.79423i	0.166439	+	0.288280i
$732$		0			0
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	−0.982986	−	0.183679i	$-0.941199\pi$
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	0.650564	+	0.759452i	$0.274533\pi$
$734$		0			0
$735$	−9.00000	−	5.19615i	−0.331970	−	0.191663i
$736$		0			0
$737$	−35.0000			−1.28924
$738$		0			0
$739$	−21.0000			−0.772497			−0.386249	−	0.922395i	$-0.626229\pi$
$739$	−21.0000			−0.772497			−0.386249	+	0.922395i	$0.626229\pi$
$740$		0			0
$741$		−	34.6410i		−	1.27257i
$742$		0			0
$743$	19.0000	−	32.9090i	0.697042	−	1.20731i	−0.272445	−	0.962171i	$-0.587832\pi$
$743$	19.0000	−	32.9090i	0.697042	−	1.20731i	0.969487	−	0.245141i	$-0.0788344\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−36.0000			−1.31717
$748$		0			0
$749$	11.0000	+	19.0526i	0.401931	+	0.696165i
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$		0			0
$753$	4.50000	−	2.59808i	0.163989	−	0.0946792i
$754$		0			0
$755$	−32.0000			−1.16460
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$	30.0000	−	17.3205i	1.08893	−	0.628695i
$760$		0			0
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	−0.942306	−	0.334752i	$-0.891348\pi$
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	0.761057	+	0.648686i	$0.224681\pi$
$762$		0			0
$763$	12.0000	+	20.7846i	0.434429	+	0.752453i
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$		−	5.19615i		−	0.187135i
$772$		0			0
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−30.0000	−	17.3205i	−1.07624	−	0.621370i
$778$		0			0
$779$	−7.50000	+	12.9904i	−0.268715	+	0.465429i
$780$		0			0
$781$	−15.0000	−	25.9808i	−0.536742	−	0.929665i
$782$		0			0
$783$	27.0000	−	15.5885i	0.964901	−	0.557086i
$784$		0			0
$785$	−24.0000	−	41.5692i	−0.856597	−	1.48367i
$786$		0			0
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$		0			0
$789$	27.0000	+	15.5885i	0.961225	+	0.554964i
$790$		0			0
$791$	−28.0000			−0.995565
$792$		0			0
$793$	16.0000			0.568177
$794$		0			0
$795$		−	41.5692i		−	1.47431i
$796$		0			0
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$		0			0
$799$	−4.00000	−	6.92820i	−0.141510	−	0.245102i
$800$		0			0
$801$	15.0000	−	25.9808i	0.529999	−	0.917985i
$802$		0			0
$803$	32.5000	+	56.2917i	1.14690	+	1.98649i
$804$		0			0
$805$	−8.00000	+	13.8564i	−0.281963	+	0.488374i
$806$		0			0
$807$	−6.00000	+	3.46410i	−0.211210	+	0.121942i
$808$		0			0
$809$	−3.00000			−0.105474			−0.0527372	−	0.998608i	$-0.516795\pi$
$809$	−3.00000			−0.105474			−0.0527372	+	0.998608i	$0.516795\pi$
$810$		0			0
$811$	9.00000			0.316033			0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000			0.316033			0.158016	+	0.987436i	$0.449490\pi$
$812$		0			0
$813$	12.0000	−	6.92820i	0.420858	−	0.242983i
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−22.5000	−	38.9711i	−0.787175	−	1.36343i
$818$		0			0
$819$	12.0000	−	20.7846i	0.419314	−	0.726273i
$820$		0			0
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$		0			0
$823$	−17.0000	+	29.4449i	−0.592583	+	1.02638i	0.401300	+	0.915947i	$0.368558\pi$
$823$	−17.0000	+	29.4449i	−0.592583	+	1.02638i	−0.993883	+	0.110437i	$0.964775\pi$
$824$		0			0
$825$			8.66025i			0.301511i
$826$		0			0
$827$	44.0000			1.53003			0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000			1.53003			0.765015	+	0.644013i	$0.222732\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.50000	−	2.59808i	0.0519719	−	0.0900180i
$834$		0			0
$835$	−2.00000	−	3.46410i	−0.0692129	−	0.119880i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	45.0000	+	25.9808i	1.54988	+	0.894825i
$844$		0			0
$845$	6.00000			0.206406
$846$		0			0
$847$	−28.0000			−0.962091
$848$		0			0
$849$			41.5692i			1.42665i
$850$		0			0
$851$	20.0000	−	34.6410i	0.685591	−	1.18748i
$852$		0			0
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$854$		0			0
$855$	−15.0000	−	25.9808i	−0.512989	−	0.888523i
$856$		0			0
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	−0.733571	−	0.679613i	$-0.762148\pi$
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	0.955348	+	0.295484i	$0.0954809\pi$
$860$		0			0
$861$	−9.00000	+	5.19615i	−0.306719	+	0.177084i
$862$		0			0
$863$	−22.0000			−0.748889			−0.374444	−	0.927249i	$-0.622167\pi$
$863$	−22.0000			−0.748889			−0.374444	+	0.927249i	$0.622167\pi$
$864$		0			0
$865$	36.0000			1.22404
$866$		0			0
$867$	24.0000	−	13.8564i	0.815083	−	0.470588i
$868$		0			0
$869$	−5.00000	+	8.66025i	−0.169613	+	0.293779i
$870$		0			0
$871$	−14.0000	−	24.2487i	−0.474372	−	0.821636i
$872$		0			0
$873$	−39.0000			−1.31995
$874$		0			0
$875$	−12.0000	−	20.7846i	−0.405674	−	0.702648i
$876$		0			0
$877$	8.00000	−	13.8564i	0.270141	−	0.467898i	−0.698757	−	0.715359i	$-0.746263\pi$
$877$	8.00000	−	13.8564i	0.270141	−	0.467898i	0.968898	+	0.247462i	$0.0795964\pi$
$878$		0			0
$879$		−	17.3205i		−	0.584206i
$880$		0			0
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$		0			0
$885$	21.0000	+	12.1244i	0.705907	+	0.407556i
$886$		0			0
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	0.496340	+	0.868128i	$0.334677\pi$
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	−0.999991	+	0.00422062i	$0.998657\pi$
$888$		0			0
$889$	20.0000	+	34.6410i	0.670778	+	1.16182i
$890$		0			0
$891$	−22.5000	+	38.9711i	−0.753778	+	1.30558i
$892$		0			0
$893$	20.0000	+	34.6410i	0.669274	+	1.15922i
$894$		0			0
$895$	12.0000	−	20.7846i	0.401116	−	0.694753i
$896$		0			0
$897$	24.0000	+	13.8564i	0.801337	+	0.462652i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$		−	31.1769i		−	1.03750i
$904$		0			0
$905$	−20.0000	+	34.6410i	−0.664822	+	1.15151i
$906$		0			0
$907$	5.50000	+	9.52628i	0.182625	+	0.316315i	0.942773	−	0.333434i	$-0.108207\pi$
$907$	5.50000	+	9.52628i	0.182625	+	0.316315i	−0.760149	+	0.649749i	$0.774874\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		0			0
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	0.948136	−	0.317865i	$-0.102966\pi$
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	−0.749347	+	0.662177i	$0.769633\pi$
$912$		0			0
$913$	−30.0000	+	51.9615i	−0.992855	+	1.71968i
$914$		0			0
$915$	12.0000	−	6.92820i	0.396708	−	0.229039i
$916$		0			0
$917$	24.0000			0.792550
$918$		0			0
$919$	36.0000			1.18753			0.593765	−	0.804638i	$-0.297641\pi$
$919$	36.0000			1.18753			0.593765	+	0.804638i	$0.297641\pi$
$920$		0			0
$921$	4.50000	−	2.59808i	0.148280	−	0.0856095i
$922$		0			0
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	5.00000	+	8.66025i	0.164399	+	0.284747i
$926$		0			0
$927$	−12.0000	−	20.7846i	−0.394132	−	0.682656i
$928$		0			0
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	−7.50000	+	12.9904i	−0.245803	+	0.425743i
$932$		0			0
$933$		−	17.3205i		−	0.567048i
$934$		0			0
$935$	10.0000			0.327035
$936$		0			0
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$		0			0
$939$	37.5000	+	21.6506i	1.22377	+	0.706542i
$940$		0			0
$941$	−14.0000	+	24.2487i	−0.456387	+	0.790485i	−0.998767	−	0.0496480i	$-0.984190\pi$
$941$	−14.0000	+	24.2487i	−0.456387	+	0.790485i	0.542380	+	0.840133i	$0.317523\pi$
$942$		0			0
$943$	−6.00000	−	10.3923i	−0.195387	−	0.338420i
$944$		0			0
$945$		−	20.7846i		−	0.676123i
$946$		0			0
$947$	−11.5000	−	19.9186i	−0.373700	−	0.647267i	0.616432	−	0.787408i	$-0.288578\pi$
$947$	−11.5000	−	19.9186i	−0.373700	−	0.647267i	−0.990132	+	0.140141i	$0.955244\pi$
$948$		0			0
$949$	−26.0000	+	45.0333i	−0.843996	+	1.46184i
$950$		0			0
$951$	18.0000	+	10.3923i	0.583690	+	0.336994i
$952$		0			0
$953$	1.00000			0.0323932			0.0161966	−	0.999869i	$-0.494844\pi$
$953$	1.00000			0.0323932			0.0161966	+	0.999869i	$0.494844\pi$
$954$		0			0
$955$	−4.00000			−0.129437
$956$		0			0
$957$		−	51.9615i		−	1.67968i
$958$		0			0
$959$	1.00000	−	1.73205i	0.0322917	−	0.0559308i
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$		0			0
$963$	16.5000	−	28.5788i	0.531705	−	0.920940i
$964$		0			0
$965$	−1.00000	−	1.73205i	−0.0321911	−	0.0557567i
$966$		0			0
$967$	−7.00000	+	12.1244i	−0.225105	+	0.389893i	−0.956351	−	0.292221i	$-0.905606\pi$
$967$	−7.00000	+	12.1244i	−0.225105	+	0.389893i	0.731246	+	0.682114i	$0.238939\pi$
$968$		0			0
$969$	7.50000	−	4.33013i	0.240935	−	0.139104i
$970$		0			0
$971$	28.0000			0.898563			0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000			0.898563			0.449281	+	0.893390i	$0.351680\pi$
$972$		0			0
$973$	−2.00000			−0.0641171
$974$		0			0
$975$	−6.00000	+	3.46410i	−0.192154	+	0.110940i
$976$		0			0
$977$	−28.5000	+	49.3634i	−0.911796	+	1.57928i	−0.100270	+	0.994960i	$0.531971\pi$
$977$	−28.5000	+	49.3634i	−0.911796	+	1.57928i	−0.811526	+	0.584316i	$0.801363\pi$
$978$		0			0
$979$	−25.0000	−	43.3013i	−0.799003	−	1.38391i
$980$		0			0
$981$	18.0000	−	31.1769i	0.574696	−	0.995402i
$982$		0			0
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	−0.955341	−	0.295506i	$-0.904512\pi$
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	0.221755	−	0.975102i	$-0.428822\pi$
$984$		0			0
$985$	20.0000	−	34.6410i	0.637253	−	1.10375i
$986$		0			0
$987$			27.7128i			0.882109i
$988$		0			0
$989$	36.0000			1.14473
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$		0			0
$993$	−30.0000	−	17.3205i	−0.952021	−	0.549650i
$994$		0			0
$995$	2.00000	−	3.46410i	0.0634043	−	0.109819i
$996$		0			0
$997$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$997$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$998$		0			0
$999$			51.9615i			1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.a.769.1	yes	2
3.2	odd	2		3456.2.i.d.2305.1		2
4.3	odd	2		1152.2.i.c.769.1	yes	2
8.3	odd	2		1152.2.i.b.769.1	yes	2
8.5	even	2		1152.2.i.d.769.1	yes	2
9.2	odd	6		3456.2.i.d.1153.1		2
9.7	even	3	inner	1152.2.i.a.385.1	✓	2
12.11	even	2		3456.2.i.c.2305.1		2
24.5	odd	2		3456.2.i.b.2305.1		2
24.11	even	2		3456.2.i.a.2305.1		2
36.7	odd	6		1152.2.i.c.385.1	yes	2
36.11	even	6		3456.2.i.c.1153.1		2
72.11	even	6		3456.2.i.a.1153.1		2
72.29	odd	6		3456.2.i.b.1153.1		2
72.43	odd	6		1152.2.i.b.385.1	yes	2
72.61	even	6		1152.2.i.d.385.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.a.385.1	✓	2	9.7	even	3	inner
1152.2.i.a.769.1	yes	2	1.1	even	1	trivial
1152.2.i.b.385.1	yes	2	72.43	odd	6
1152.2.i.b.769.1	yes	2	8.3	odd	2
1152.2.i.c.385.1	yes	2	36.7	odd	6
1152.2.i.c.769.1	yes	2	4.3	odd	2
1152.2.i.d.385.1	yes	2	72.61	even	6
1152.2.i.d.769.1	yes	2	8.5	even	2
3456.2.i.a.1153.1		2	72.11	even	6
3456.2.i.a.2305.1		2	24.11	even	2
3456.2.i.b.1153.1		2	72.29	odd	6
3456.2.i.b.2305.1		2	24.5	odd	2
3456.2.i.c.1153.1		2	36.11	even	6
3456.2.i.c.2305.1		2	12.11	even	2
3456.2.i.d.1153.1		2	9.2	odd	6
3456.2.i.d.2305.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(2.00000 - 3.46410i) q^{13} -3.46410i q^{15} +1.00000 q^{17} -5.00000 q^{19} +(-3.00000 - 1.73205i) q^{21} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(-3.00000 - 5.19615i) q^{29} +(7.50000 + 4.33013i) q^{33} -4.00000 q^{35} +10.0000 q^{37} +6.92820i q^{39} +(1.50000 - 2.59808i) q^{41} +(4.50000 + 7.79423i) q^{43} +(3.00000 + 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-1.50000 + 0.866025i) q^{51} +12.0000 q^{53} +10.0000 q^{55} +(7.50000 - 4.33013i) q^{57} +(-3.50000 + 6.06218i) q^{59} +(2.00000 + 3.46410i) q^{61} +6.00000 q^{63} +(4.00000 + 6.92820i) q^{65} +(3.50000 - 6.06218i) q^{67} +6.92820i q^{69} +6.00000 q^{71} -13.0000 q^{73} +(-1.50000 - 0.866025i) q^{75} +(5.00000 - 8.66025i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{83} +(-1.00000 + 1.73205i) q^{85} +(9.00000 + 5.19615i) q^{87} +10.0000 q^{89} +8.00000 q^{91} +(5.00000 - 8.66025i) q^{95} +(-6.50000 - 11.2583i) q^{97} -15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 2 q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 2 * q^5 + 2 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} - 2 q^{5} + 2 q^{7} + 3 q^{9} - 5 q^{11} + 4 q^{13} + 2 q^{17} - 10 q^{19} - 6 q^{21} + 4 q^{23} + q^{25} - 6 q^{29} + 15 q^{33} - 8 q^{35} + 20 q^{37} + 3 q^{41} + 9 q^{43} + 6 q^{45} - 8 q^{47} + 3 q^{49} - 3 q^{51} + 24 q^{53} + 20 q^{55} + 15 q^{57} - 7 q^{59} + 4 q^{61} + 12 q^{63} + 8 q^{65} + 7 q^{67} + 12 q^{71} - 26 q^{73} - 3 q^{75} + 10 q^{77} - 2 q^{79} - 9 q^{81} - 12 q^{83} - 2 q^{85} + 18 q^{87} + 20 q^{89} + 16 q^{91} + 10 q^{95} - 13 q^{97} - 30 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 2 * q^5 + 2 * q^7 + 3 * q^9 - 5 * q^11 + 4 * q^13 + 2 * q^17 - 10 * q^19 - 6 * q^21 + 4 * q^23 + q^25 - 6 * q^29 + 15 * q^33 - 8 * q^35 + 20 * q^37 + 3 * q^41 + 9 * q^43 + 6 * q^45 - 8 * q^47 + 3 * q^49 - 3 * q^51 + 24 * q^53 + 20 * q^55 + 15 * q^57 - 7 * q^59 + 4 * q^61 + 12 * q^63 + 8 * q^65 + 7 * q^67 + 12 * q^71 - 26 * q^73 - 3 * q^75 + 10 * q^77 - 2 * q^79 - 9 * q^81 - 12 * q^83 - 2 * q^85 + 18 * q^87 + 20 * q^89 + 16 * q^91 + 10 * q^95 - 13 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more