LMFDB - Embedded newform 1216.2.n.b.255.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(255,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1216.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			255.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1216.255
Dual form			1216.2.n.b.639.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} -3.46410i q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} -3.46410i q^{7} +(1.00000 + 1.73205i) q^{9} -3.46410i q^{11} +(4.50000 - 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-3.00000 - 1.73205i) q^{21} +(-4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +5.00000 q^{27} +(-7.50000 + 4.33013i) q^{29} +4.00000 q^{31} +(-3.00000 - 1.73205i) q^{33} +(-9.00000 - 5.19615i) q^{35} -5.19615i q^{39} +(7.50000 + 4.33013i) q^{41} +(-10.5000 - 6.06218i) q^{43} +6.00000 q^{45} +(1.50000 - 0.866025i) q^{47} -5.00000 q^{49} +(1.50000 + 2.59808i) q^{51} +(-1.50000 + 0.866025i) q^{53} +(-9.00000 - 5.19615i) q^{55} +(3.50000 - 2.59808i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(3.50000 + 6.06218i) q^{61} +(6.00000 - 3.46410i) q^{63} -15.5885i q^{65} +(-2.50000 - 4.33013i) q^{67} +5.19615i q^{69} +(-4.50000 + 7.79423i) q^{71} +(-3.50000 + 6.06218i) q^{73} -4.00000 q^{75} -12.0000 q^{77} +(3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.46410i q^{83} +(4.50000 + 7.79423i) q^{85} +8.66025i q^{87} +(7.50000 - 4.33013i) q^{89} +(-9.00000 - 15.5885i) q^{91} +(2.00000 - 3.46410i) q^{93} +(10.5000 - 7.79423i) q^{95} +(7.50000 + 4.33013i) q^{97} +(6.00000 - 3.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 3 q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + 3 * q^5 + 2 * q^9	$ 2 q + q^{3} + 3 q^{5} + 2 q^{9} + 9 q^{13} - 3 q^{15} - 3 q^{17} + 8 q^{19} - 6 q^{21} - 9 q^{23} - 4 q^{25} + 10 q^{27} - 15 q^{29} + 8 q^{31} - 6 q^{33} - 18 q^{35} + 15 q^{41} - 21 q^{43} + 12 q^{45} + 3 q^{47} - 10 q^{49} + 3 q^{51} - 3 q^{53} - 18 q^{55} + 7 q^{57} - 3 q^{59} + 7 q^{61} + 12 q^{63} - 5 q^{67} - 9 q^{71} - 7 q^{73} - 8 q^{75} - 24 q^{77} + 7 q^{79} - q^{81} + 9 q^{85} + 15 q^{89} - 18 q^{91} + 4 q^{93} + 21 q^{95} + 15 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + q^3 + 3 * q^5 + 2 * q^9 + 9 * q^13 - 3 * q^15 - 3 * q^17 + 8 * q^19 - 6 * q^21 - 9 * q^23 - 4 * q^25 + 10 * q^27 - 15 * q^29 + 8 * q^31 - 6 * q^33 - 18 * q^35 + 15 * q^41 - 21 * q^43 + 12 * q^45 + 3 * q^47 - 10 * q^49 + 3 * q^51 - 3 * q^53 - 18 * q^55 + 7 * q^57 - 3 * q^59 + 7 * q^61 + 12 * q^63 - 5 * q^67 - 9 * q^71 - 7 * q^73 - 8 * q^75 - 24 * q^77 + 7 * q^79 - q^81 + 9 * q^85 + 15 * q^89 - 18 * q^91 + 4 * q^93 + 21 * q^95 + 15 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$		−	3.46410i		−	1.30931i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$		−	3.46410i		−	1.30931i	0.755929	−	0.654654i	$-0.227186\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$		0			0
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$	−1.50000	−	2.59808i	−0.387298	−	0.670820i
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$		0			0
$21$	−3.00000	−	1.73205i	−0.654654	−	0.377964i
$22$		0			0
$23$	−4.50000	+	2.59808i	−0.938315	+	0.541736i	−0.889432	−	0.457068i	$-0.848900\pi$
$23$	−4.50000	+	2.59808i	−0.938315	+	0.541736i	−0.0488832	+	0.998805i	$0.515566\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−7.50000	+	4.33013i	−1.39272	+	0.804084i	−0.993615	−	0.112823i	$-0.964011\pi$
$29$	−7.50000	+	4.33013i	−1.39272	+	0.804084i	−0.399100	+	0.916907i	$0.630677\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−3.00000	−	1.73205i	−0.522233	−	0.301511i
$34$		0			0
$35$	−9.00000	−	5.19615i	−1.52128	−	0.878310i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		−	5.19615i		−	0.832050i
$40$		0			0
$41$	7.50000	+	4.33013i	1.17130	+	0.676252i	0.953987	−	0.299849i	$-0.0969363\pi$
$41$	7.50000	+	4.33013i	1.17130	+	0.676252i	0.217317	+	0.976101i	$0.430270\pi$
$42$		0			0
$43$	−10.5000	−	6.06218i	−1.60123	−	0.924473i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−10.5000	−	6.06218i	−1.60123	−	0.924473i	−0.609994	−	0.792406i	$-0.708828\pi$
$44$		0			0
$45$	6.00000			0.894427
$46$		0			0
$47$	1.50000	−	0.866025i	0.218797	−	0.126323i	−0.386596	−	0.922249i	$-0.626349\pi$
$47$	1.50000	−	0.866025i	0.218797	−	0.126323i	0.605393	+	0.795926i	$0.293016\pi$
$48$		0			0
$49$	−5.00000			−0.714286
$50$		0			0
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$		0			0
$53$	−1.50000	+	0.866025i	−0.206041	+	0.118958i	−0.599470	−	0.800397i	$-0.704622\pi$
$53$	−1.50000	+	0.866025i	−0.206041	+	0.118958i	0.393429	+	0.919355i	$0.371289\pi$
$54$		0			0
$55$	−9.00000	−	5.19615i	−1.21356	−	0.700649i
$56$		0			0
$57$	3.50000	−	2.59808i	0.463586	−	0.344124i
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$	6.00000	−	3.46410i	0.755929	−	0.436436i
$64$		0			0
$65$		−	15.5885i		−	1.93351i
$66$		0			0
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$			5.19615i			0.625543i
$70$		0			0
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	0.465157	+	0.885228i	$0.345998\pi$
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	−0.999209	+	0.0397765i	$0.987335\pi$
$72$		0			0
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$	−4.00000			−0.461880
$76$		0			0
$77$	−12.0000			−1.36753
$78$		0			0
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$		0			0
$87$			8.66025i			0.928477i
$88$		0			0
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	−0.0467209	−	0.998908i	$-0.514877\pi$
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	0.841719	+	0.539915i	$0.181544\pi$
$90$		0			0
$91$	−9.00000	−	15.5885i	−0.943456	−	1.63411i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$	10.5000	−	7.79423i	1.07728	−	0.799671i
$96$		0			0
$97$	7.50000	+	4.33013i	0.761510	+	0.439658i	0.829837	−	0.558005i	$-0.188433\pi$
$97$	7.50000	+	4.33013i	0.761510	+	0.439658i	−0.0683279	+	0.997663i	$0.521766\pi$
$98$		0			0
$99$	6.00000	−	3.46410i	0.603023	−	0.348155i
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$	−9.00000	+	5.19615i	−0.878310	+	0.507093i
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−13.5000	−	7.79423i	−1.29307	−	0.746552i	−0.313869	−	0.949466i	$-0.601625\pi$
$109$	−13.5000	−	7.79423i	−1.29307	−	0.746552i	−0.979196	+	0.202915i	$0.934959\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	6.92820i		−	0.651751i	−0.945413	−	0.325875i	$-0.894341\pi$
$113$		−	6.92820i		−	0.651751i	0.945413	−	0.325875i	$-0.105659\pi$
$114$		0			0
$115$			15.5885i			1.45363i
$116$		0			0
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$		0			0
$119$	9.00000	+	5.19615i	0.825029	+	0.476331i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$		0			0
$123$	7.50000	−	4.33013i	0.676252	−	0.390434i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−3.50000	−	6.06218i	−0.310575	−	0.537931i	0.667912	−	0.744240i	$-0.267188\pi$
$127$	−3.50000	−	6.06218i	−0.310575	−	0.537931i	−0.978487	+	0.206309i	$0.933855\pi$
$128$		0			0
$129$	−10.5000	+	6.06218i	−0.924473	+	0.533745i
$130$		0			0
$131$	−4.50000	−	2.59808i	−0.393167	−	0.226995i	0.290365	−	0.956916i	$-0.406223\pi$
$131$	−4.50000	−	2.59808i	−0.393167	−	0.226995i	−0.683531	+	0.729921i	$0.739557\pi$
$132$		0			0
$133$	6.00000	−	13.8564i	0.520266	−	1.20150i
$134$		0			0
$135$	7.50000	−	12.9904i	0.645497	−	1.11803i
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	16.5000	−	9.52628i	1.39951	−	0.808008i	0.405170	−	0.914241i	$-0.367212\pi$
$139$	16.5000	−	9.52628i	1.39951	−	0.808008i	0.994341	+	0.106233i	$0.0338788\pi$
$140$		0			0
$141$		−	1.73205i		−	0.145865i
$142$		0			0
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$		0			0
$145$			25.9808i			2.15758i
$146$		0			0
$147$	−2.50000	+	4.33013i	−0.206197	+	0.357143i
$148$		0			0
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	6.00000	−	10.3923i	0.481932	−	0.834730i
$156$		0			0
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$		0			0
$159$			1.73205i			0.137361i
$160$		0			0
$161$	9.00000	+	15.5885i	0.709299	+	1.22854i
$162$		0			0
$163$			10.3923i			0.813988i	0.913431	+	0.406994i	$0.133423\pi$
$163$			10.3923i			0.813988i	−0.913431	+	0.406994i	$0.866577\pi$
$164$		0			0
$165$	−9.00000	+	5.19615i	−0.700649	+	0.404520i
$166$		0			0
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	0.911099	+	0.412188i	$0.135235\pi$
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	−0.0985846	+	0.995129i	$0.531432\pi$
$168$		0			0
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$		0			0
$171$	1.00000	+	8.66025i	0.0764719	+	0.662266i
$172$		0			0
$173$	−7.50000	−	4.33013i	−0.570214	−	0.329213i	0.187021	−	0.982356i	$-0.440117\pi$
$173$	−7.50000	−	4.33013i	−0.570214	−	0.329213i	−0.757235	+	0.653143i	$0.773450\pi$
$174$		0			0
$175$	−12.0000	+	6.92820i	−0.907115	+	0.523723i
$176$		0			0
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$		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
$181$	−1.50000	+	0.866025i	−0.111494	+	0.0643712i	−0.554710	−	0.832044i	$-0.687171\pi$
$181$	−1.50000	+	0.866025i	−0.111494	+	0.0643712i	0.443216	+	0.896415i	$0.353837\pi$
$182$		0			0
$183$	7.00000			0.517455
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.00000	+	5.19615i	0.658145	+	0.379980i
$188$		0			0
$189$		−	17.3205i		−	1.25988i
$190$		0			0
$191$			24.2487i			1.75458i	0.479965	+	0.877288i	$0.340649\pi$
$191$			24.2487i			1.75458i	−0.479965	+	0.877288i	$0.659351\pi$
$192$		0			0
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	−0.827788	+	0.561041i	$0.810401\pi$
$194$		0			0
$195$	−13.5000	−	7.79423i	−0.966755	−	0.558156i
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−10.5000	+	6.06218i	−0.744325	+	0.429736i	−0.823640	−	0.567113i	$-0.808060\pi$
$199$	−10.5000	+	6.06218i	−0.744325	+	0.429736i	0.0793146	+	0.996850i	$0.474727\pi$
$200$		0			0
$201$	−5.00000			−0.352673
$202$		0			0
$203$	15.0000	+	25.9808i	1.05279	+	1.82349i
$204$		0			0
$205$	22.5000	−	12.9904i	1.57147	−	0.907288i
$206$		0			0
$207$	−9.00000	−	5.19615i	−0.625543	−	0.361158i
$208$		0			0
$209$	6.00000	−	13.8564i	0.415029	−	0.958468i
$210$		0			0
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$		0			0
$213$	4.50000	+	7.79423i	0.308335	+	0.534052i
$214$		0			0
$215$	−31.5000	+	18.1865i	−2.14828	+	1.24031i
$216$		0			0
$217$		−	13.8564i		−	0.940634i
$218$		0			0
$219$	3.50000	+	6.06218i	0.236508	+	0.409644i
$220$		0			0
$221$			15.5885i			1.04859i
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$		0			0
$225$	4.00000	−	6.92820i	0.266667	−	0.461880i
$226$		0			0
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−6.00000	+	10.3923i	−0.394771	+	0.683763i
$232$		0			0
$233$	−13.5000	+	23.3827i	−0.884414	+	1.53185i	−0.0380310	+	0.999277i	$0.512109\pi$
$233$	−13.5000	+	23.3827i	−0.884414	+	1.53185i	−0.846383	+	0.532574i	$0.821225\pi$
$234$		0			0
$235$		−	5.19615i		−	0.338960i
$236$		0			0
$237$	−3.50000	−	6.06218i	−0.227349	−	0.393781i
$238$		0			0
$239$			17.3205i			1.12037i	0.828367	+	0.560185i	$0.189270\pi$
$239$			17.3205i			1.12037i	−0.828367	+	0.560185i	$0.810730\pi$
$240$		0			0
$241$	19.5000	−	11.2583i	1.25611	−	0.725213i	0.283790	−	0.958886i	$-0.408408\pi$
$241$	19.5000	−	11.2583i	1.25611	−	0.725213i	0.972315	+	0.233674i	$0.0750747\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$		0			0
$245$	−7.50000	+	12.9904i	−0.479157	+	0.829925i
$246$		0			0
$247$	22.5000	−	2.59808i	1.43164	−	0.165312i
$248$		0			0
$249$	3.00000	+	1.73205i	0.190117	+	0.109764i
$250$		0			0
$251$	4.50000	−	2.59808i	0.284037	−	0.163989i	−0.351212	−	0.936296i	$-0.614230\pi$
$251$	4.50000	−	2.59808i	0.284037	−	0.163989i	0.635250	+	0.772307i	$0.280897\pi$
$252$		0			0
$253$	9.00000	+	15.5885i	0.565825	+	0.980038i
$254$		0			0
$255$	9.00000			0.563602
$256$		0			0
$257$	13.5000	−	7.79423i	0.842107	−	0.486191i	−0.0158730	−	0.999874i	$-0.505053\pi$
$257$	13.5000	−	7.79423i	0.842107	−	0.486191i	0.857980	+	0.513683i	$0.171719\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−15.0000	−	8.66025i	−0.928477	−	0.536056i
$262$		0			0
$263$	10.5000	+	6.06218i	0.647458	+	0.373810i	0.787482	−	0.616338i	$-0.211385\pi$
$263$	10.5000	+	6.06218i	0.647458	+	0.373810i	−0.140024	+	0.990148i	$0.544718\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$		0			0
$267$		−	8.66025i		−	0.529999i
$268$		0			0
$269$	22.5000	+	12.9904i	1.37185	+	0.792038i	0.991161	−	0.132666i	$-0.0423537\pi$
$269$	22.5000	+	12.9904i	1.37185	+	0.792038i	0.380688	+	0.924703i	$0.375687\pi$
$270$		0			0
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	0.783778	−	0.621041i	$-0.213290\pi$
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	−0.145948	+	0.989292i	$0.546623\pi$
$272$		0			0
$273$	−18.0000			−1.08941
$274$		0			0
$275$	−12.0000	+	6.92820i	−0.723627	+	0.417786i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$		0			0
$281$	13.5000	−	7.79423i	0.805342	−	0.464965i	−0.0399934	−	0.999200i	$-0.512734\pi$
$281$	13.5000	−	7.79423i	0.805342	−	0.464965i	0.845336	+	0.534235i	$0.179400\pi$
$282$		0			0
$283$	−4.50000	−	2.59808i	−0.267497	−	0.154440i	0.360252	−	0.932855i	$-0.382691\pi$
$283$	−4.50000	−	2.59808i	−0.267497	−	0.154440i	−0.627750	+	0.778415i	$0.716024\pi$
$284$		0			0
$285$	−1.50000	−	12.9904i	−0.0888523	−	0.769484i
$286$		0			0
$287$	15.0000	−	25.9808i	0.885422	−	1.53360i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	7.50000	−	4.33013i	0.439658	−	0.253837i
$292$		0			0
$293$		−	13.8564i		−	0.809500i	−0.914427	−	0.404750i	$-0.867359\pi$
$293$		−	13.8564i		−	0.809500i	0.914427	−	0.404750i	$-0.132641\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$		0			0
$297$		−	17.3205i		−	1.00504i
$298$		0			0
$299$	−13.5000	+	23.3827i	−0.780725	+	1.35226i
$300$		0			0
$301$	−21.0000	+	36.3731i	−1.21042	+	2.09651i
$302$		0			0
$303$	3.00000			0.172345
$304$		0			0
$305$	21.0000			1.20246
$306$		0			0
$307$	2.50000	−	4.33013i	0.142683	−	0.247133i	−0.785823	−	0.618451i	$-0.787761\pi$
$307$	2.50000	−	4.33013i	0.142683	−	0.247133i	0.928506	+	0.371318i	$0.121094\pi$
$308$		0			0
$309$	−8.00000	+	13.8564i	−0.455104	+	0.788263i
$310$		0			0
$311$			3.46410i			0.196431i	0.995165	+	0.0982156i	$0.0313135\pi$
$311$			3.46410i			0.196431i	−0.995165	+	0.0982156i	$0.968687\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$		0			0
$315$		−	20.7846i		−	1.17108i
$316$		0			0
$317$	4.50000	−	2.59808i	0.252745	−	0.145922i	−0.368275	−	0.929717i	$-0.620052\pi$
$317$	4.50000	−	2.59808i	0.252745	−	0.145922i	0.621021	+	0.783794i	$0.286718\pi$
$318$		0			0
$319$	15.0000	+	25.9808i	0.839839	+	1.45464i
$320$		0			0
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	−10.5000	+	7.79423i	−0.584236	+	0.433682i
$324$		0			0
$325$	−18.0000	−	10.3923i	−0.998460	−	0.576461i
$326$		0			0
$327$	−13.5000	+	7.79423i	−0.746552	+	0.431022i
$328$		0			0
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−15.0000			−0.819538
$336$		0			0
$337$	−28.5000	−	16.4545i	−1.55249	−	0.896333i	−0.997938	−	0.0641864i	$-0.979555\pi$
$337$	−28.5000	−	16.4545i	−1.55249	−	0.896333i	−0.554556	−	0.832146i	$-0.687112\pi$
$338$		0			0
$339$	−6.00000	−	3.46410i	−0.325875	−	0.188144i
$340$		0			0
$341$		−	13.8564i		−	0.750366i
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$		0			0
$345$	13.5000	+	7.79423i	0.726816	+	0.419627i
$346$		0			0
$347$	13.5000	+	7.79423i	0.724718	+	0.418416i	0.816487	−	0.577364i	$-0.195919\pi$
$347$	13.5000	+	7.79423i	0.724718	+	0.418416i	−0.0917687	+	0.995780i	$0.529252\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	22.5000	−	12.9904i	1.20096	−	0.693375i
$352$		0			0
$353$	−18.0000			−0.958043			−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000			−0.958043			−0.479022	+	0.877803i	$0.659008\pi$
$354$		0			0
$355$	13.5000	+	23.3827i	0.716506	+	1.24102i
$356$		0			0
$357$	9.00000	−	5.19615i	0.476331	−	0.275010i
$358$		0			0
$359$	−13.5000	−	7.79423i	−0.712503	−	0.411364i	0.0994843	−	0.995039i	$-0.468281\pi$
$359$	−13.5000	−	7.79423i	−0.712503	−	0.411364i	−0.811987	+	0.583675i	$0.801614\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	−0.500000	+	0.866025i	−0.0262432	+	0.0454545i
$364$		0			0
$365$	10.5000	+	18.1865i	0.549595	+	0.951927i
$366$		0			0
$367$	13.5000	−	7.79423i	0.704694	−	0.406855i	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	13.5000	−	7.79423i	0.704694	−	0.406855i	0.809093	+	0.587680i	$0.199959\pi$
$368$		0			0
$369$			17.3205i			0.901670i
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$		0			0
$373$			6.92820i			0.358729i	0.983783	+	0.179364i	$0.0574041\pi$
$373$			6.92820i			0.358729i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$		0			0
$377$	−22.5000	+	38.9711i	−1.15881	+	2.00712i
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	−7.00000			−0.358621
$382$		0			0
$383$	−16.5000	+	28.5788i	−0.843111	+	1.46031i	0.0441413	+	0.999025i	$0.485945\pi$
$383$	−16.5000	+	28.5788i	−0.843111	+	1.46031i	−0.887252	+	0.461285i	$0.847389\pi$
$384$		0			0
$385$	−18.0000	+	31.1769i	−0.917365	+	1.58892i
$386$		0			0
$387$		−	24.2487i		−	1.23263i
$388$		0			0
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$		0			0
$391$		−	15.5885i		−	0.788342i
$392$		0			0
$393$	−4.50000	+	2.59808i	−0.226995	+	0.131056i
$394$		0			0
$395$	−10.5000	−	18.1865i	−0.528312	−	0.915064i
$396$		0			0
$397$	5.50000	−	9.52628i	0.276037	−	0.478110i	−0.694359	−	0.719629i	$-0.744312\pi$
$397$	5.50000	−	9.52628i	0.276037	−	0.478110i	0.970396	+	0.241518i	$0.0776454\pi$
$398$		0			0
$399$	−9.00000	−	12.1244i	−0.450564	−	0.606977i
$400$		0			0
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	0.383414	−	0.923576i	$-0.374748\pi$
$401$	−4.50000	−	2.59808i	−0.224719	−	0.129742i	−0.608134	+	0.793835i	$0.708081\pi$
$402$		0			0
$403$	18.0000	−	10.3923i	0.896644	−	0.517678i
$404$		0			0
$405$	1.50000	+	2.59808i	0.0745356	+	0.129099i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.50000	−	0.866025i	0.0741702	−	0.0428222i	−0.462456	−	0.886642i	$-0.653032\pi$
$409$	1.50000	−	0.866025i	0.0741702	−	0.0428222i	0.536626	+	0.843820i	$0.319698\pi$
$410$		0			0
$411$	−3.00000			−0.147979
$412$		0			0
$413$	9.00000	+	5.19615i	0.442861	+	0.255686i
$414$		0			0
$415$	9.00000	+	5.19615i	0.441793	+	0.255069i
$416$		0			0
$417$		−	19.0526i		−	0.933008i
$418$		0			0
$419$			24.2487i			1.18463i	0.805708	+	0.592314i	$0.201785\pi$
$419$			24.2487i			1.18463i	−0.805708	+	0.592314i	$0.798215\pi$
$420$		0			0
$421$	−19.5000	−	11.2583i	−0.950372	−	0.548697i	−0.0571754	−	0.998364i	$-0.518209\pi$
$421$	−19.5000	−	11.2583i	−0.950372	−	0.548697i	−0.893196	+	0.449667i	$0.851543\pi$
$422$		0			0
$423$	3.00000	+	1.73205i	0.145865	+	0.0842152i
$424$		0			0
$425$	12.0000			0.582086
$426$		0			0
$427$	21.0000	−	12.1244i	1.01626	−	0.586739i
$428$		0			0
$429$	−18.0000			−0.869048
$430$		0			0
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	0.626907	−	0.779094i	$-0.284321\pi$
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	−0.988169	+	0.153370i	$0.950987\pi$
$432$		0			0
$433$	1.50000	−	0.866025i	0.0720854	−	0.0416185i	−0.463524	−	0.886084i	$-0.653415\pi$
$433$	1.50000	−	0.866025i	0.0720854	−	0.0416185i	0.535609	+	0.844466i	$0.320082\pi$
$434$		0			0
$435$	22.5000	+	12.9904i	1.07879	+	0.622841i
$436$		0			0
$437$	−22.5000	+	2.59808i	−1.07632	+	0.124283i
$438$		0			0
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	−0.994401	−	0.105675i	$-0.966300\pi$
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	0.588718	+	0.808339i	$0.299633\pi$
$440$		0			0
$441$	−5.00000	−	8.66025i	−0.238095	−	0.412393i
$442$		0			0
$443$	−19.5000	+	11.2583i	−0.926473	+	0.534899i	−0.885694	−	0.464269i	$-0.846317\pi$
$443$	−19.5000	+	11.2583i	−0.926473	+	0.534899i	−0.0407786	+	0.999168i	$0.512984\pi$
$444$		0			0
$445$		−	25.9808i		−	1.23161i
$446$		0			0
$447$	−7.50000	−	12.9904i	−0.354738	−	0.614424i
$448$		0			0
$449$			6.92820i			0.326962i	0.986546	+	0.163481i	$0.0522723\pi$
$449$			6.92820i			0.326962i	−0.986546	+	0.163481i	$0.947728\pi$
$450$		0			0
$451$	15.0000	−	25.9808i	0.706322	−	1.22339i
$452$		0			0
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$		0			0
$455$	−54.0000			−2.53156
$456$		0			0
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$		0			0
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		0			0
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	−0.636817	−	0.771015i	$-0.719749\pi$
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	0.986127	+	0.165992i	$0.0530827\pi$
$462$		0			0
$463$		−	10.3923i		−	0.482971i	−0.970404	−	0.241486i	$-0.922365\pi$
$463$		−	10.3923i		−	0.482971i	0.970404	−	0.241486i	$-0.0776347\pi$
$464$		0			0
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$		0			0
$467$		−	17.3205i		−	0.801498i	−0.916188	−	0.400749i	$-0.868750\pi$
$467$		−	17.3205i		−	0.801498i	0.916188	−	0.400749i	$-0.131250\pi$
$468$		0			0
$469$	−15.0000	+	8.66025i	−0.692636	+	0.399893i
$470$		0			0
$471$	2.50000	+	4.33013i	0.115194	+	0.199522i
$472$		0			0
$473$	−21.0000	+	36.3731i	−0.965581	+	1.67244i
$474$		0			0
$475$	−2.00000	−	17.3205i	−0.0917663	−	0.794719i
$476$		0			0
$477$	−3.00000	−	1.73205i	−0.137361	−	0.0793052i
$478$		0			0
$479$	13.5000	−	7.79423i	0.616831	−	0.356127i	−0.158803	−	0.987310i	$-0.550764\pi$
$479$	13.5000	−	7.79423i	0.616831	−	0.356127i	0.775634	+	0.631183i	$0.217430\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	18.0000			0.819028
$484$		0			0
$485$	22.5000	−	12.9904i	1.02167	−	0.589863i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$		0			0
$489$	9.00000	+	5.19615i	0.406994	+	0.234978i
$490$		0			0
$491$	−16.5000	−	9.52628i	−0.744635	−	0.429915i	0.0791174	−	0.996865i	$-0.474790\pi$
$491$	−16.5000	−	9.52628i	−0.744635	−	0.429915i	−0.823752	+	0.566950i	$0.808123\pi$
$492$		0			0
$493$		−	25.9808i		−	1.17011i
$494$		0			0
$495$		−	20.7846i		−	0.934199i
$496$		0			0
$497$	27.0000	+	15.5885i	1.21112	+	0.699238i
$498$		0			0
$499$	−10.5000	−	6.06218i	−0.470045	−	0.271380i	0.246214	−	0.969216i	$-0.420813\pi$
$499$	−10.5000	−	6.06218i	−0.470045	−	0.271380i	−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$	21.0000			0.938211
$502$		0			0
$503$	7.50000	−	4.33013i	0.334408	−	0.193071i	−0.323388	−	0.946266i	$-0.604822\pi$
$503$	7.50000	−	4.33013i	0.334408	−	0.193071i	0.657797	+	0.753196i	$0.271489\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$	−7.00000	−	12.1244i	−0.310881	−	0.538462i
$508$		0			0
$509$	16.5000	−	9.52628i	0.731350	−	0.422245i	−0.0875661	−	0.996159i	$-0.527909\pi$
$509$	16.5000	−	9.52628i	0.731350	−	0.422245i	0.818916	+	0.573914i	$0.194576\pi$
$510$		0			0
$511$	21.0000	+	12.1244i	0.928985	+	0.536350i
$512$		0			0
$513$	20.0000	+	8.66025i	0.883022	+	0.382360i
$514$		0			0
$515$	−24.0000	+	41.5692i	−1.05757	+	1.83176i
$516$		0			0
$517$	−3.00000	−	5.19615i	−0.131940	−	0.228527i
$518$		0			0
$519$	−7.50000	+	4.33013i	−0.329213	+	0.190071i
$520$		0			0
$521$		−	41.5692i		−	1.82118i	−0.413310	−	0.910590i	$-0.635627\pi$
$521$		−	41.5692i		−	1.82118i	0.413310	−	0.910590i	$-0.364373\pi$
$522$		0			0
$523$	−2.50000	−	4.33013i	−0.109317	−	0.189343i	0.806177	−	0.591675i	$-0.201533\pi$
$523$	−2.50000	−	4.33013i	−0.109317	−	0.189343i	−0.915494	+	0.402332i	$0.868200\pi$
$524$		0			0
$525$			13.8564i			0.604743i
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	2.00000	−	3.46410i	0.0869565	−	0.150613i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	45.0000			1.94917
$534$		0			0
$535$	18.0000	−	31.1769i	0.778208	−	1.34790i
$536$		0			0
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$		0			0
$539$			17.3205i			0.746047i
$540$		0			0
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	0.807267	−	0.590187i	$-0.200946\pi$
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	−0.914750	+	0.404020i	$0.867613\pi$
$542$		0			0
$543$			1.73205i			0.0743294i
$544$		0			0
$545$	−40.5000	+	23.3827i	−1.73483	+	1.00160i
$546$		0			0
$547$	−0.500000	−	0.866025i	−0.0213785	−	0.0370286i	0.855138	−	0.518400i	$-0.173472\pi$
$547$	−0.500000	−	0.866025i	−0.0213785	−	0.0370286i	−0.876517	+	0.481371i	$0.840139\pi$
$548$		0			0
$549$	−7.00000	+	12.1244i	−0.298753	+	0.517455i
$550$		0			0
$551$	−37.5000	+	4.33013i	−1.59755	+	0.184470i
$552$		0			0
$553$	−21.0000	−	12.1244i	−0.893011	−	0.515580i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$		0			0
$559$	−63.0000			−2.66462
$560$		0			0
$561$	9.00000	−	5.19615i	0.379980	−	0.219382i
$562$		0			0
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−18.0000	−	10.3923i	−0.757266	−	0.437208i
$566$		0			0
$567$	3.00000	+	1.73205i	0.125988	+	0.0727393i
$568$		0			0
$569$		−	20.7846i		−	0.871336i	−0.900107	−	0.435668i	$-0.856512\pi$
$569$		−	20.7846i		−	0.871336i	0.900107	−	0.435668i	$-0.143488\pi$
$570$		0			0
$571$			10.3923i			0.434904i	0.976071	+	0.217452i	$0.0697746\pi$
$571$			10.3923i			0.434904i	−0.976071	+	0.217452i	$0.930225\pi$
$572$		0			0
$573$	21.0000	+	12.1244i	0.877288	+	0.506502i
$574$		0			0
$575$	18.0000	+	10.3923i	0.750652	+	0.433389i
$576$		0			0
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$		0			0
$579$	−10.5000	+	6.06218i	−0.436365	+	0.251936i
$580$		0			0
$581$	12.0000			0.497844
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$		0			0
$585$	27.0000	−	15.5885i	1.11631	−	0.644503i
$586$		0			0
$587$	−4.50000	−	2.59808i	−0.185735	−	0.107234i	0.404249	−	0.914649i	$-0.367533\pi$
$587$	−4.50000	−	2.59808i	−0.185735	−	0.107234i	−0.589984	+	0.807415i	$0.700866\pi$
$588$		0			0
$589$	16.0000	+	6.92820i	0.659269	+	0.285472i
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$		0			0
$593$	−1.50000	−	2.59808i	−0.0615976	−	0.106690i	0.833582	−	0.552396i	$-0.186286\pi$
$593$	−1.50000	−	2.59808i	−0.0615976	−	0.106690i	−0.895180	+	0.445705i	$0.852953\pi$
$594$		0			0
$595$	27.0000	−	15.5885i	1.10689	−	0.639064i
$596$		0			0
$597$			12.1244i			0.496217i
$598$		0			0
$599$	4.50000	+	7.79423i	0.183865	+	0.318464i	0.943193	−	0.332244i	$-0.107806\pi$
$599$	4.50000	+	7.79423i	0.183865	+	0.318464i	−0.759328	+	0.650708i	$0.774472\pi$
$600$		0			0
$601$			6.92820i			0.282607i	0.989966	+	0.141304i	$0.0451294\pi$
$601$			6.92820i			0.282607i	−0.989966	+	0.141304i	$0.954871\pi$
$602$		0			0
$603$	5.00000	−	8.66025i	0.203616	−	0.352673i
$604$		0			0
$605$	−1.50000	+	2.59808i	−0.0609837	+	0.105627i
$606$		0			0
$607$	40.0000			1.62355			0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000			1.62355			0.811775	+	0.583970i	$0.198502\pi$
$608$		0			0
$609$	30.0000			1.21566
$610$		0			0
$611$	4.50000	−	7.79423i	0.182051	−	0.315321i
$612$		0			0
$613$	−8.50000	+	14.7224i	−0.343312	+	0.594633i	−0.985046	−	0.172294i	$-0.944882\pi$
$613$	−8.50000	+	14.7224i	−0.343312	+	0.594633i	0.641734	+	0.766927i	$0.278215\pi$
$614$		0			0
$615$		−	25.9808i		−	1.04765i
$616$		0			0
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$		0			0
$619$		−	31.1769i		−	1.25311i	−0.779379	−	0.626553i	$-0.784465\pi$
$619$		−	31.1769i		−	1.25311i	0.779379	−	0.626553i	$-0.215535\pi$
$620$		0			0
$621$	−22.5000	+	12.9904i	−0.902894	+	0.521286i
$622$		0			0
$623$	−15.0000	−	25.9808i	−0.600962	−	1.04090i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	−9.00000	−	12.1244i	−0.359425	−	0.484200i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	13.5000	−	7.79423i	0.537427	−	0.310283i	−0.206609	−	0.978424i	$-0.566243\pi$
$631$	13.5000	−	7.79423i	0.537427	−	0.310283i	0.744035	+	0.668140i	$0.232909\pi$
$632$		0			0
$633$	11.5000	+	19.9186i	0.457084	+	0.791693i
$634$		0			0
$635$	−21.0000			−0.833360
$636$		0			0
$637$	−22.5000	+	12.9904i	−0.891482	+	0.514698i
$638$		0			0
$639$	−18.0000			−0.712069
$640$		0			0
$641$	−34.5000	−	19.9186i	−1.36267	−	0.786737i	−0.372690	−	0.927956i	$-0.621564\pi$
$641$	−34.5000	−	19.9186i	−1.36267	−	0.786737i	−0.989978	+	0.141219i	$0.954898\pi$
$642$		0			0
$643$	1.50000	+	0.866025i	0.0591542	+	0.0341527i	0.529285	−	0.848444i	$-0.322460\pi$
$643$	1.50000	+	0.866025i	0.0591542	+	0.0341527i	−0.470131	+	0.882597i	$0.655793\pi$
$644$		0			0
$645$			36.3731i			1.43219i
$646$		0			0
$647$		−	3.46410i		−	0.136188i	−0.997679	−	0.0680939i	$-0.978308\pi$
$647$		−	3.46410i		−	0.136188i	0.997679	−	0.0680939i	$-0.0216918\pi$
$648$		0			0
$649$	9.00000	+	5.19615i	0.353281	+	0.203967i
$650$		0			0
$651$	−12.0000	−	6.92820i	−0.470317	−	0.271538i
$652$		0			0
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$		0			0
$655$	−13.5000	+	7.79423i	−0.527489	+	0.304546i
$656$		0			0
$657$	−14.0000			−0.546192
$658$		0			0
$659$	−22.5000	−	38.9711i	−0.876476	−	1.51810i	−0.855183	−	0.518327i	$-0.826555\pi$
$659$	−22.5000	−	38.9711i	−0.876476	−	1.51810i	−0.0212930	−	0.999773i	$-0.506778\pi$
$660$		0			0
$661$	−19.5000	+	11.2583i	−0.758462	+	0.437898i	−0.828743	−	0.559629i	$-0.810944\pi$
$661$	−19.5000	+	11.2583i	−0.758462	+	0.437898i	0.0702812	+	0.997527i	$0.477610\pi$
$662$		0			0
$663$	13.5000	+	7.79423i	0.524297	+	0.302703i
$664$		0			0
$665$	−27.0000	−	36.3731i	−1.04702	−	1.41049i
$666$		0			0
$667$	22.5000	−	38.9711i	0.871203	−	1.50897i
$668$		0			0
$669$	−9.50000	−	16.4545i	−0.367291	−	0.636167i
$670$		0			0
$671$	21.0000	−	12.1244i	0.810696	−	0.468056i
$672$		0			0
$673$		−	48.4974i		−	1.86944i	−0.355387	−	0.934719i	$-0.615651\pi$
$673$		−	48.4974i		−	1.86944i	0.355387	−	0.934719i	$-0.384349\pi$
$674$		0			0
$675$	−10.0000	−	17.3205i	−0.384900	−	0.666667i
$676$		0			0
$677$		−	41.5692i		−	1.59763i	−0.601574	−	0.798817i	$-0.705459\pi$
$677$		−	41.5692i		−	1.59763i	0.601574	−	0.798817i	$-0.294541\pi$
$678$		0			0
$679$	15.0000	−	25.9808i	0.575647	−	0.997050i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	11.0000	−	19.0526i	0.419676	−	0.726900i
$688$		0			0
$689$	−4.50000	+	7.79423i	−0.171436	+	0.296936i
$690$		0			0
$691$			10.3923i			0.395342i	0.980268	+	0.197671i	$0.0633378\pi$
$691$			10.3923i			0.395342i	−0.980268	+	0.197671i	$0.936662\pi$
$692$		0			0
$693$	−12.0000	−	20.7846i	−0.455842	−	0.789542i
$694$		0			0
$695$		−	57.1577i		−	2.16811i
$696$		0			0
$697$	−22.5000	+	12.9904i	−0.852248	+	0.492046i
$698$		0			0
$699$	13.5000	+	23.3827i	0.510617	+	0.884414i
$700$		0			0
$701$	−16.5000	+	28.5788i	−0.623196	+	1.07941i	0.365690	+	0.930737i	$0.380833\pi$
$701$	−16.5000	+	28.5788i	−0.623196	+	1.07941i	−0.988887	+	0.148671i	$0.952500\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−4.50000	−	2.59808i	−0.169480	−	0.0978492i
$706$		0			0
$707$	9.00000	−	5.19615i	0.338480	−	0.195421i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	14.0000			0.525041
$712$		0			0
$713$	−18.0000	+	10.3923i	−0.674105	+	0.389195i
$714$		0			0
$715$	−54.0000			−2.01949
$716$		0			0
$717$	15.0000	+	8.66025i	0.560185	+	0.323423i
$718$		0			0
$719$	−1.50000	−	0.866025i	−0.0559406	−	0.0322973i	0.471769	−	0.881722i	$-0.343616\pi$
$719$	−1.50000	−	0.866025i	−0.0559406	−	0.0322973i	−0.527709	+	0.849425i	$0.676949\pi$
$720$		0			0
$721$			55.4256i			2.06416i
$722$		0			0
$723$		−	22.5167i		−	0.837404i
$724$		0			0
$725$	30.0000	+	17.3205i	1.11417	+	0.643268i
$726$		0			0
$727$	−1.50000	−	0.866025i	−0.0556319	−	0.0321191i	0.471926	−	0.881638i	$-0.343559\pi$
$727$	−1.50000	−	0.866025i	−0.0556319	−	0.0321191i	−0.527558	+	0.849519i	$0.676892\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	31.5000	−	18.1865i	1.16507	−	0.672653i
$732$		0			0
$733$	−10.0000			−0.369358			−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000			−0.369358			−0.184679	+	0.982799i	$0.559125\pi$
$734$		0			0
$735$	7.50000	+	12.9904i	0.276642	+	0.479157i
$736$		0			0
$737$	−15.0000	+	8.66025i	−0.552532	+	0.319005i
$738$		0			0
$739$	1.50000	+	0.866025i	0.0551784	+	0.0318573i	0.527335	−	0.849657i	$-0.323191\pi$
$739$	1.50000	+	0.866025i	0.0551784	+	0.0318573i	−0.472157	+	0.881514i	$0.656524\pi$
$740$		0			0
$741$	9.00000	−	20.7846i	0.330623	−	0.763542i
$742$		0			0
$743$	1.50000	−	2.59808i	0.0550297	−	0.0953142i	−0.837198	−	0.546899i	$-0.815808\pi$
$743$	1.50000	−	2.59808i	0.0550297	−	0.0953142i	0.892228	+	0.451585i	$0.149141\pi$
$744$		0			0
$745$	−22.5000	−	38.9711i	−0.824336	−	1.42779i
$746$		0			0
$747$	−6.00000	+	3.46410i	−0.219529	+	0.126745i
$748$		0			0
$749$		−	41.5692i		−	1.51891i
$750$		0			0
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	0.576262	−	0.817265i	$-0.304511\pi$
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	−0.995903	+	0.0904254i	$0.971177\pi$
$752$		0			0
$753$		−	5.19615i		−	0.189358i
$754$		0			0
$755$	12.0000	−	20.7846i	0.436725	−	0.756429i
$756$		0			0
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$		0			0
$759$	18.0000			0.653359
$760$		0			0
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		0			0
$763$	−27.0000	+	46.7654i	−0.977466	+	1.69302i
$764$		0			0
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$		0			0
$767$			15.5885i			0.562867i
$768$		0			0
$769$	20.5000	+	35.5070i	0.739249	+	1.28042i	0.952834	+	0.303492i	$0.0981526\pi$
$769$	20.5000	+	35.5070i	0.739249	+	1.28042i	−0.213585	+	0.976924i	$0.568514\pi$
$770$		0			0
$771$		−	15.5885i		−	0.561405i
$772$		0			0
$773$	−37.5000	+	21.6506i	−1.34878	+	0.778719i	−0.988077	−	0.153961i	$-0.950797\pi$
$773$	−37.5000	+	21.6506i	−1.34878	+	0.778719i	−0.360704	+	0.932680i	$0.617464\pi$
$774$		0			0
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	22.5000	+	30.3109i	0.806146	+	1.08600i
$780$		0			0
$781$	27.0000	+	15.5885i	0.966136	+	0.557799i
$782$		0			0
$783$	−37.5000	+	21.6506i	−1.34014	+	0.773731i
$784$		0			0
$785$	7.50000	+	12.9904i	0.267686	+	0.463647i
$786$		0			0
$787$	−28.0000			−0.998092			−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000			−0.998092			−0.499046	+	0.866575i	$0.666316\pi$
$788$		0			0
$789$	10.5000	−	6.06218i	0.373810	−	0.215819i
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	31.5000	+	18.1865i	1.11860	+	0.645823i
$794$		0			0
$795$	4.50000	+	2.59808i	0.159599	+	0.0921443i
$796$		0			0
$797$			13.8564i			0.490819i	0.969419	+	0.245410i	$0.0789224\pi$
$797$			13.8564i			0.490819i	−0.969419	+	0.245410i	$0.921078\pi$
$798$		0			0
$799$			5.19615i			0.183827i
$800$		0			0
$801$	15.0000	+	8.66025i	0.529999	+	0.305995i
$802$		0			0
$803$	21.0000	+	12.1244i	0.741074	+	0.427859i
$804$		0			0
$805$	54.0000			1.90325
$806$		0			0
$807$	22.5000	−	12.9904i	0.792038	−	0.457283i
$808$		0			0
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$		0			0
$811$	−6.50000	−	11.2583i	−0.228246	−	0.395333i	0.729042	−	0.684468i	$-0.239966\pi$
$811$	−6.50000	−	11.2583i	−0.228246	−	0.395333i	−0.957288	+	0.289135i	$0.906632\pi$
$812$		0			0
$813$	10.5000	−	6.06218i	0.368251	−	0.212610i
$814$		0			0
$815$	27.0000	+	15.5885i	0.945769	+	0.546040i
$816$		0			0
$817$	−31.5000	−	42.4352i	−1.10205	−	1.48462i
$818$		0			0
$819$	18.0000	−	31.1769i	0.628971	−	1.08941i
$820$		0			0
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	−0.928846	−	0.370465i	$-0.879198\pi$
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	0.143591	−	0.989637i	$-0.454135\pi$
$822$		0			0
$823$	1.50000	−	0.866025i	0.0522867	−	0.0301877i	−0.473629	−	0.880725i	$-0.657056\pi$
$823$	1.50000	−	0.866025i	0.0522867	−	0.0301877i	0.525915	+	0.850537i	$0.323723\pi$
$824$		0			0
$825$			13.8564i			0.482418i
$826$		0			0
$827$	19.5000	+	33.7750i	0.678081	+	1.17447i	0.975558	+	0.219742i	$0.0705217\pi$
$827$	19.5000	+	33.7750i	0.678081	+	1.17447i	−0.297477	+	0.954729i	$0.596145\pi$
$828$		0			0
$829$			6.92820i			0.240626i	0.992736	+	0.120313i	$0.0383899\pi$
$829$			6.92820i			0.240626i	−0.992736	+	0.120313i	$0.961610\pi$
$830$		0			0
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$		0			0
$833$	7.50000	−	12.9904i	0.259860	−	0.450090i
$834$		0			0
$835$	63.0000			2.18020
$836$		0			0
$837$	20.0000			0.691301
$838$		0			0
$839$	−10.5000	+	18.1865i	−0.362500	+	0.627869i	−0.988372	−	0.152057i	$-0.951410\pi$
$839$	−10.5000	+	18.1865i	−0.362500	+	0.627869i	0.625871	+	0.779926i	$0.284743\pi$
$840$		0			0
$841$	23.0000	−	39.8372i	0.793103	−	1.37370i
$842$		0			0
$843$		−	15.5885i		−	0.536895i
$844$		0			0
$845$	−21.0000	−	36.3731i	−0.722422	−	1.25127i
$846$		0			0
$847$			3.46410i			0.119028i
$848$		0			0
$849$	−4.50000	+	2.59808i	−0.154440	+	0.0891657i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	17.5000	−	30.3109i	0.599189	−	1.03783i	−0.393753	−	0.919216i	$-0.628823\pi$
$853$	17.5000	−	30.3109i	0.599189	−	1.03783i	0.992941	−	0.118609i	$-0.0378434\pi$
$854$		0			0
$855$	24.0000	+	10.3923i	0.820783	+	0.355409i
$856$		0			0
$857$	37.5000	+	21.6506i	1.28098	+	0.739572i	0.977027	−	0.213117i	$-0.0683615\pi$
$857$	37.5000	+	21.6506i	1.28098	+	0.739572i	0.303949	+	0.952688i	$0.401695\pi$
$858$		0			0
$859$	−49.5000	+	28.5788i	−1.68892	+	0.975097i	−0.733571	+	0.679613i	$0.762148\pi$
$859$	−49.5000	+	28.5788i	−1.68892	+	0.975097i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$	−15.0000	−	25.9808i	−0.511199	−	0.885422i
$862$		0			0
$863$	12.0000			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$864$		0			0
$865$	−22.5000	+	12.9904i	−0.765023	+	0.441686i
$866$		0			0
$867$	8.00000			0.271694
$868$		0			0
$869$	−21.0000	−	12.1244i	−0.712376	−	0.411291i
$870$		0			0
$871$	−22.5000	−	12.9904i	−0.762383	−	0.440162i
$872$		0			0
$873$			17.3205i			0.586210i
$874$		0			0
$875$		−	10.3923i		−	0.351324i
$876$		0			0
$877$	22.5000	+	12.9904i	0.759771	+	0.438654i	0.829214	−	0.558932i	$-0.188789\pi$
$877$	22.5000	+	12.9904i	0.759771	+	0.438654i	−0.0694425	+	0.997586i	$0.522122\pi$
$878$		0			0
$879$	−12.0000	−	6.92820i	−0.404750	−	0.233682i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	4.50000	−	2.59808i	0.151437	−	0.0874322i	−0.422367	−	0.906425i	$-0.638801\pi$
$883$	4.50000	−	2.59808i	0.151437	−	0.0874322i	0.573804	+	0.818993i	$0.305467\pi$
$884$		0			0
$885$	9.00000			0.302532
$886$		0			0
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	0.839744	−	0.542983i	$-0.182705\pi$
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	−0.890109	+	0.455748i	$0.849372\pi$
$888$		0			0
$889$	−21.0000	+	12.1244i	−0.704317	+	0.406638i
$890$		0			0
$891$	3.00000	+	1.73205i	0.100504	+	0.0580259i
$892$		0			0
$893$	7.50000	−	0.866025i	0.250978	−	0.0289804i
$894$		0			0
$895$	−18.0000	+	31.1769i	−0.601674	+	1.04213i
$896$		0			0
$897$	13.5000	+	23.3827i	0.450752	+	0.780725i
$898$		0			0
$899$	−30.0000	+	17.3205i	−1.00056	+	0.577671i
$900$		0			0
$901$		−	5.19615i		−	0.173109i
$902$		0			0
$903$	21.0000	+	36.3731i	0.698836	+	1.21042i
$904$		0			0
$905$			5.19615i			0.172726i
$906$		0			0
$907$	6.50000	−	11.2583i	0.215829	−	0.373827i	−0.737700	−	0.675129i	$-0.764088\pi$
$907$	6.50000	−	11.2583i	0.215829	−	0.373827i	0.953529	+	0.301302i	$0.0974213\pi$
$908$		0			0
$909$	−3.00000	+	5.19615i	−0.0995037	+	0.172345i
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	12.0000			0.397142
$914$		0			0
$915$	10.5000	−	18.1865i	0.347119	−	0.601228i
$916$		0			0
$917$	−9.00000	+	15.5885i	−0.297206	+	0.514776i
$918$		0			0
$919$			38.1051i			1.25697i	0.777821	+	0.628486i	$0.216325\pi$
$919$			38.1051i			1.25697i	−0.777821	+	0.628486i	$0.783675\pi$
$920$		0			0
$921$	−2.50000	−	4.33013i	−0.0823778	−	0.142683i
$922$		0			0
$923$			46.7654i			1.53930i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−16.0000	−	27.7128i	−0.525509	−	0.910208i
$928$		0			0
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$930$		0			0
$931$	−20.0000	−	8.66025i	−0.655474	−	0.283828i
$932$		0			0
$933$	3.00000	+	1.73205i	0.0982156	+	0.0567048i
$934$		0			0
$935$	27.0000	−	15.5885i	0.882994	−	0.509797i
$936$		0			0
$937$	24.5000	+	42.4352i	0.800380	+	1.38630i	0.919366	+	0.393403i	$0.128702\pi$
$937$	24.5000	+	42.4352i	0.800380	+	1.38630i	−0.118986	+	0.992896i	$0.537964\pi$
$938$		0			0
$939$	−19.0000			−0.620042
$940$		0			0
$941$	−13.5000	+	7.79423i	−0.440087	+	0.254085i	−0.703635	−	0.710562i	$-0.748441\pi$
$941$	−13.5000	+	7.79423i	−0.440087	+	0.254085i	0.263547	+	0.964646i	$0.415107\pi$
$942$		0			0
$943$	−45.0000			−1.46540
$944$		0			0
$945$	−45.0000	−	25.9808i	−1.46385	−	0.845154i
$946$		0			0
$947$	25.5000	+	14.7224i	0.828639	+	0.478415i	0.853386	−	0.521279i	$-0.174545\pi$
$947$	25.5000	+	14.7224i	0.828639	+	0.478415i	−0.0247477	+	0.999694i	$0.507878\pi$
$948$		0			0
$949$			36.3731i			1.18072i
$950$		0			0
$951$		−	5.19615i		−	0.168497i
$952$		0			0
$953$	−10.5000	−	6.06218i	−0.340128	−	0.196373i	0.320200	−	0.947350i	$-0.396250\pi$
$953$	−10.5000	−	6.06218i	−0.340128	−	0.196373i	−0.660329	+	0.750977i	$0.729583\pi$
$954$		0			0
$955$	63.0000	+	36.3731i	2.03863	+	1.17700i
$956$		0			0
$957$	30.0000			0.969762
$958$		0			0
$959$	−9.00000	+	5.19615i	−0.290625	+	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	12.0000	+	20.7846i	0.386695	+	0.669775i
$964$		0			0
$965$	−31.5000	+	18.1865i	−1.01402	+	0.585445i
$966$		0			0
$967$	−43.5000	−	25.1147i	−1.39887	−	0.807635i	−0.404592	−	0.914497i	$-0.632586\pi$
$967$	−43.5000	−	25.1147i	−1.39887	−	0.807635i	−0.994274	+	0.106862i	$0.965920\pi$
$968$		0			0
$969$	1.50000	+	12.9904i	0.0481869	+	0.417311i
$970$		0			0
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$		0			0
$973$	−33.0000	−	57.1577i	−1.05793	−	1.83239i
$974$		0			0
$975$	−18.0000	+	10.3923i	−0.576461	+	0.332820i
$976$		0			0
$977$			6.92820i			0.221653i	0.993840	+	0.110826i	$0.0353498\pi$
$977$			6.92820i			0.221653i	−0.993840	+	0.110826i	$0.964650\pi$
$978$		0			0
$979$	−15.0000	−	25.9808i	−0.479402	−	0.830349i
$980$		0			0
$981$		−	31.1769i		−	0.995402i
$982$		0			0
$983$	−4.50000	+	7.79423i	−0.143528	+	0.248597i	−0.928823	−	0.370525i	$-0.879178\pi$
$983$	−4.50000	+	7.79423i	−0.143528	+	0.248597i	0.785295	+	0.619122i	$0.212511\pi$
$984$		0			0
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$		0			0
$987$	−6.00000			−0.190982
$988$		0			0
$989$	63.0000			2.00328
$990$		0			0
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	−0.993364	−	0.115015i	$-0.963308\pi$
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	0.596288	+	0.802771i	$0.296642\pi$
$992$		0			0
$993$	14.0000	−	24.2487i	0.444277	−	0.769510i
$994$		0			0
$995$			36.3731i			1.15310i
$996$		0			0
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.n.b.255.1		2
4.3	odd	2		1216.2.n.a.255.1		2
8.3	odd	2		304.2.n.b.255.1	yes	2
8.5	even	2		304.2.n.a.255.1	yes	2
19.12	odd	6		1216.2.n.a.639.1		2
24.5	odd	2		2736.2.bm.g.559.1		2
24.11	even	2		2736.2.bm.h.559.1		2
76.31	even	6	inner	1216.2.n.b.639.1		2
152.69	odd	6		304.2.n.b.31.1	yes	2
152.107	even	6		304.2.n.a.31.1	✓	2
456.107	odd	6		2736.2.bm.g.1855.1		2
456.221	even	6		2736.2.bm.h.1855.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.n.a.31.1	✓	2	152.107	even	6
304.2.n.a.255.1	yes	2	8.5	even	2
304.2.n.b.31.1	yes	2	152.69	odd	6
304.2.n.b.255.1	yes	2	8.3	odd	2
1216.2.n.a.255.1		2	4.3	odd	2
1216.2.n.a.639.1		2	19.12	odd	6
1216.2.n.b.255.1		2	1.1	even	1	trivial
1216.2.n.b.639.1		2	76.31	even	6	inner
2736.2.bm.g.559.1		2	24.5	odd	2
2736.2.bm.g.1855.1		2	456.107	odd	6
2736.2.bm.h.559.1		2	24.11	even	2
2736.2.bm.h.1855.1		2	456.221	even	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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} -3.46410i q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} -3.46410i q^{7} +(1.00000 + 1.73205i) q^{9} -3.46410i q^{11} +(4.50000 - 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-3.00000 - 1.73205i) q^{21} +(-4.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +5.00000 q^{27} +(-7.50000 + 4.33013i) q^{29} +4.00000 q^{31} +(-3.00000 - 1.73205i) q^{33} +(-9.00000 - 5.19615i) q^{35} -5.19615i q^{39} +(7.50000 + 4.33013i) q^{41} +(-10.5000 - 6.06218i) q^{43} +6.00000 q^{45} +(1.50000 - 0.866025i) q^{47} -5.00000 q^{49} +(1.50000 + 2.59808i) q^{51} +(-1.50000 + 0.866025i) q^{53} +(-9.00000 - 5.19615i) q^{55} +(3.50000 - 2.59808i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(3.50000 + 6.06218i) q^{61} +(6.00000 - 3.46410i) q^{63} -15.5885i q^{65} +(-2.50000 - 4.33013i) q^{67} +5.19615i q^{69} +(-4.50000 + 7.79423i) q^{71} +(-3.50000 + 6.06218i) q^{73} -4.00000 q^{75} -12.0000 q^{77} +(3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.46410i q^{83} +(4.50000 + 7.79423i) q^{85} +8.66025i q^{87} +(7.50000 - 4.33013i) q^{89} +(-9.00000 - 15.5885i) q^{91} +(2.00000 - 3.46410i) q^{93} +(10.5000 - 7.79423i) q^{95} +(7.50000 + 4.33013i) q^{97} +(6.00000 - 3.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 3 q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + 3 * q^5 + 2 * q^9	\( 2 q + q^{3} + 3 q^{5} + 2 q^{9} + 9 q^{13} - 3 q^{15} - 3 q^{17} + 8 q^{19} - 6 q^{21} - 9 q^{23} - 4 q^{25} + 10 q^{27} - 15 q^{29} + 8 q^{31} - 6 q^{33} - 18 q^{35} + 15 q^{41} - 21 q^{43} + 12 q^{45} + 3 q^{47} - 10 q^{49} + 3 q^{51} - 3 q^{53} - 18 q^{55} + 7 q^{57} - 3 q^{59} + 7 q^{61} + 12 q^{63} - 5 q^{67} - 9 q^{71} - 7 q^{73} - 8 q^{75} - 24 q^{77} + 7 q^{79} - q^{81} + 9 q^{85} + 15 q^{89} - 18 q^{91} + 4 q^{93} + 21 q^{95} + 15 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + q^3 + 3 * q^5 + 2 * q^9 + 9 * q^13 - 3 * q^15 - 3 * q^17 + 8 * q^19 - 6 * q^21 - 9 * q^23 - 4 * q^25 + 10 * q^27 - 15 * q^29 + 8 * q^31 - 6 * q^33 - 18 * q^35 + 15 * q^41 - 21 * q^43 + 12 * q^45 + 3 * q^47 - 10 * q^49 + 3 * q^51 - 3 * q^53 - 18 * q^55 + 7 * q^57 - 3 * q^59 + 7 * q^61 + 12 * q^63 - 5 * q^67 - 9 * q^71 - 7 * q^73 - 8 * q^75 - 24 * q^77 + 7 * q^79 - q^81 + 9 * q^85 + 15 * q^89 - 18 * q^91 + 4 * q^93 + 21 * q^95 + 15 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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