LMFDB - Embedded newform 1008.2.cz.b.367.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, 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:	$8.04892052375$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.367
Dual form			1008.2.cz.b.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q-1.73205i q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +(-4.50000 + 2.59808i) q^{11} +(4.50000 - 2.59808i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(1.50000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-3.00000 + 3.46410i) q^{21} +(1.50000 + 0.866025i) q^{23} +(-1.00000 - 1.73205i) q^{25} +5.19615i q^{27} +(-4.50000 + 7.79423i) q^{29} -8.00000 q^{31} +(4.50000 + 7.79423i) q^{33} +(1.50000 + 4.33013i) q^{35} +(5.50000 + 9.52628i) q^{37} +(-4.50000 - 7.79423i) q^{39} +(1.50000 - 0.866025i) q^{41} +(-7.50000 - 4.33013i) q^{43} +(4.50000 + 2.59808i) q^{45} +12.0000 q^{47} +(1.00000 + 6.92820i) q^{49} +(1.50000 - 2.59808i) q^{51} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(1.50000 - 0.866025i) q^{57} -12.0000 q^{59} +(6.00000 + 5.19615i) q^{63} -9.00000 q^{65} -3.46410i q^{67} +(1.50000 - 2.59808i) q^{69} +3.46410i q^{71} +(-10.5000 - 6.06218i) q^{73} +(-3.00000 + 1.73205i) q^{75} +(13.5000 + 2.59808i) q^{77} -10.3923i q^{79} +9.00000 q^{81} +(-4.50000 + 7.79423i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(13.5000 + 7.79423i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(-13.5000 - 2.59808i) q^{91} +13.8564i q^{93} -1.73205i q^{95} +(1.50000 + 0.866025i) q^{97} +(13.5000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 3 * q^5 - 4 * q^7 - 6 * q^9	$ 2 q - 3 q^{5} - 4 q^{7} - 6 q^{9} - 9 q^{11} + 9 q^{13} - 3 q^{15} + 3 q^{17} + q^{19} - 6 q^{21} + 3 q^{23} - 2 q^{25} - 9 q^{29} - 16 q^{31} + 9 q^{33} + 3 q^{35} + 11 q^{37} - 9 q^{39} + 3 q^{41} - 15 q^{43} + 9 q^{45} + 24 q^{47} + 2 q^{49} + 3 q^{51} + 3 q^{53} + 18 q^{55} + 3 q^{57} - 24 q^{59} + 12 q^{63} - 18 q^{65} + 3 q^{69} - 21 q^{73} - 6 q^{75} + 27 q^{77} + 18 q^{81} - 9 q^{83} - 3 q^{85} + 27 q^{87} - 9 q^{89} - 27 q^{91} + 3 q^{97} + 27 q^{99}+O(q^{100}) $ 2 * q - 3 * q^5 - 4 * q^7 - 6 * q^9 - 9 * q^11 + 9 * q^13 - 3 * q^15 + 3 * q^17 + q^19 - 6 * q^21 + 3 * q^23 - 2 * q^25 - 9 * q^29 - 16 * q^31 + 9 * q^33 + 3 * q^35 + 11 * q^37 - 9 * q^39 + 3 * q^41 - 15 * q^43 + 9 * q^45 + 24 * q^47 + 2 * q^49 + 3 * q^51 + 3 * q^53 + 18 * q^55 + 3 * q^57 - 24 * q^59 + 12 * q^63 - 18 * q^65 + 3 * q^69 - 21 * q^73 - 6 * q^75 + 27 * q^77 + 18 * q^81 - 9 * q^83 - 3 * q^85 + 27 * q^87 - 9 * q^89 - 27 * q^91 + 3 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$		0			0
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.367610	+	0.929980i	$0.619824\pi$
$12$		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	+	0.866025i	0.363803	+	0.210042i	0.670748	−	0.741685i	$-0.265973\pi$
$17$	1.50000	+	0.866025i	0.363803	+	0.210042i	−0.306944	+	0.951727i	$0.599307\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−3.00000	+	3.46410i	−0.654654	+	0.755929i
$22$		0			0
$23$	1.50000	+	0.866025i	0.312772	+	0.180579i	0.648166	−	0.761499i	$-0.275536\pi$
$23$	1.50000	+	0.866025i	0.312772	+	0.180579i	−0.335394	+	0.942078i	$0.608870\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$		0			0
$33$	4.50000	+	7.79423i	0.783349	+	1.35680i
$34$		0			0
$35$	1.50000	+	4.33013i	0.253546	+	0.731925i
$36$		0			0
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$		0			0
$39$	−4.50000	−	7.79423i	−0.720577	−	1.24808i
$40$		0			0
$41$	1.50000	−	0.866025i	0.234261	−	0.135250i	−0.378275	−	0.925693i	$-0.623483\pi$
$41$	1.50000	−	0.866025i	0.234261	−	0.135250i	0.612536	+	0.790443i	$0.290149\pi$
$42$		0			0
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.196385	−	0.980527i	$-0.562920\pi$
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.947354	+	0.320189i	$0.896254\pi$
$44$		0			0
$45$	4.50000	+	2.59808i	0.670820	+	0.387298i
$46$		0			0
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$		0			0
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$	1.50000	−	0.866025i	0.198680	−	0.114708i
$58$		0			0
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		0			0
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$		0			0
$65$	−9.00000			−1.11631
$66$		0			0
$67$		−	3.46410i		−	0.423207i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$		−	3.46410i		−	0.423207i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	−10.5000	−	6.06218i	−1.22893	−	0.709524i	−0.262126	−	0.965034i	$-0.584423\pi$
$73$	−10.5000	−	6.06218i	−1.22893	−	0.709524i	−0.966807	+	0.255510i	$0.917757\pi$
$74$		0			0
$75$	−3.00000	+	1.73205i	−0.346410	+	0.200000i
$76$		0			0
$77$	13.5000	+	2.59808i	1.53847	+	0.296078i
$78$		0			0
$79$		−	10.3923i		−	1.16923i	−0.811312	−	0.584613i	$-0.801246\pi$
$79$		−	10.3923i		−	1.16923i	0.811312	−	0.584613i	$-0.198754\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$		0			0
$87$	13.5000	+	7.79423i	1.44735	+	0.835629i
$88$		0			0
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	−0.719165	−	0.694839i	$-0.755475\pi$
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	0.242166	+	0.970235i	$0.422142\pi$
$90$		0			0
$91$	−13.5000	−	2.59808i	−1.41518	−	0.272352i
$92$		0			0
$93$			13.8564i			1.43684i
$94$		0			0
$95$		−	1.73205i		−	0.177705i
$96$		0			0
$97$	1.50000	+	0.866025i	0.152302	+	0.0879316i	0.574214	−	0.818705i	$-0.305308\pi$
$97$	1.50000	+	0.866025i	0.152302	+	0.0879316i	−0.421912	+	0.906637i	$0.638641\pi$
$98$		0			0
$99$	13.5000	−	7.79423i	1.35680	−	0.783349i
$100$		0			0
$101$	−7.50000	+	4.33013i	−0.746278	+	0.430864i	−0.824347	−	0.566084i	$-0.808458\pi$
$101$	−7.50000	+	4.33013i	−0.746278	+	0.430864i	0.0780696	+	0.996948i	$0.475124\pi$
$102$		0			0
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$	7.50000	−	2.59808i	0.731925	−	0.253546i
$106$		0			0
$107$	−10.5000	+	6.06218i	−1.01507	+	0.586053i	−0.912673	−	0.408690i	$-0.865986\pi$
$107$	−10.5000	+	6.06218i	−1.01507	+	0.586053i	−0.102400	+	0.994743i	$0.532652\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$	16.5000	−	9.52628i	1.56611	−	0.904194i
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$		0			0
$117$	−13.5000	+	7.79423i	−1.24808	+	0.720577i
$118$		0			0
$119$	−1.50000	−	4.33013i	−0.137505	−	0.396942i
$120$		0			0
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$		0			0
$123$	−1.50000	−	2.59808i	−0.135250	−	0.234261i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$		−	10.3923i		−	0.922168i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$		−	10.3923i		−	0.922168i	0.887357	−	0.461084i	$-0.152539\pi$
$128$		0			0
$129$	−7.50000	+	12.9904i	−0.660338	+	1.14374i
$130$		0			0
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$	0.500000	−	2.59808i	0.0433555	−	0.225282i
$134$		0			0
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$		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
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		−	20.7846i		−	1.75038i
$142$		0			0
$143$	−13.5000	+	23.3827i	−1.12893	+	1.95536i
$144$		0			0
$145$	13.5000	−	7.79423i	1.12111	−	0.647275i
$146$		0			0
$147$	12.0000	−	1.73205i	0.989743	−	0.142857i
$148$		0			0
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	4.50000	−	2.59808i	0.366205	−	0.211428i	−0.305594	−	0.952162i	$-0.598855\pi$
$151$	4.50000	−	2.59808i	0.366205	−	0.211428i	0.671799	+	0.740733i	$0.265522\pi$
$152$		0			0
$153$	−4.50000	−	2.59808i	−0.363803	−	0.210042i
$154$		0			0
$155$	12.0000	+	6.92820i	0.963863	+	0.556487i
$156$		0			0
$157$		−	6.92820i		−	0.552931i	−0.961024	−	0.276465i	$-0.910837\pi$
$157$		−	6.92820i		−	0.552931i	0.961024	−	0.276465i	$-0.0891631\pi$
$158$		0			0
$159$	−4.50000	−	2.59808i	−0.356873	−	0.206041i
$160$		0			0
$161$	−1.50000	−	4.33013i	−0.118217	−	0.341262i
$162$		0			0
$163$	7.50000	−	4.33013i	0.587445	−	0.339162i	−0.176641	−	0.984275i	$-0.556523\pi$
$163$	7.50000	−	4.33013i	0.587445	−	0.339162i	0.764087	+	0.645114i	$0.223190\pi$
$164$		0			0
$165$		−	15.5885i		−	1.21356i
$166$		0			0
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$		0			0
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$		0			0
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$		0			0
$173$		−	13.8564i		−	1.05348i	−0.850026	−	0.526742i	$-0.823414\pi$
$173$		−	13.8564i		−	1.05348i	0.850026	−	0.526742i	$-0.176586\pi$
$174$		0			0
$175$	−1.00000	+	5.19615i	−0.0755929	+	0.392792i
$176$		0			0
$177$			20.7846i			1.56227i
$178$		0			0
$179$	−19.5000	−	11.2583i	−1.45750	−	0.841487i	−0.458611	−	0.888637i	$-0.651653\pi$
$179$	−19.5000	−	11.2583i	−1.45750	−	0.841487i	−0.998888	+	0.0471502i	$0.984986\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	19.0526i		−	1.40077i
$186$		0			0
$187$	−9.00000			−0.658145
$188$		0			0
$189$	9.00000	−	10.3923i	0.654654	−	0.755929i
$190$		0			0
$191$		−	10.3923i		−	0.751961i	−0.926628	−	0.375980i	$-0.877306\pi$
$191$		−	10.3923i		−	0.751961i	0.926628	−	0.375980i	$-0.122694\pi$
$192$		0			0
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$		0			0
$195$			15.5885i			1.11631i
$196$		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
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	0.602549	+	0.798082i	$0.294152\pi$
$200$		0			0
$201$	−6.00000			−0.423207
$202$		0			0
$203$	22.5000	−	7.79423i	1.57919	−	0.547048i
$204$		0			0
$205$	−3.00000			−0.209529
$206$		0			0
$207$	−4.50000	−	2.59808i	−0.312772	−	0.180579i
$208$		0			0
$209$	−4.50000	−	2.59808i	−0.311272	−	0.179713i
$210$		0			0
$211$	−10.5000	+	6.06218i	−0.722850	+	0.417338i	−0.815801	−	0.578333i	$-0.803703\pi$
$211$	−10.5000	+	6.06218i	−0.722850	+	0.417338i	0.0929509	+	0.995671i	$0.470370\pi$
$212$		0			0
$213$	6.00000			0.411113
$214$		0			0
$215$	7.50000	+	12.9904i	0.511496	+	0.885937i
$216$		0			0
$217$	16.0000	+	13.8564i	1.08615	+	0.940634i
$218$		0			0
$219$	−10.5000	+	18.1865i	−0.709524	+	1.22893i
$220$		0			0
$221$	9.00000			0.605406
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$		0			0
$225$	3.00000	+	5.19615i	0.200000	+	0.346410i
$226$		0			0
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	−19.5000	−	11.2583i	−1.28860	−	0.743971i	−0.310192	−	0.950674i	$-0.600393\pi$
$229$	−19.5000	−	11.2583i	−1.28860	−	0.743971i	−0.978404	+	0.206702i	$0.933727\pi$
$230$		0			0
$231$	4.50000	−	23.3827i	0.296078	−	1.53847i
$232$		0			0
$233$	4.50000	+	7.79423i	0.294805	+	0.510617i	0.974939	−	0.222470i	$-0.0714120\pi$
$233$	4.50000	+	7.79423i	0.294805	+	0.510617i	−0.680135	+	0.733087i	$0.738079\pi$
$234$		0			0
$235$	−18.0000	−	10.3923i	−1.17419	−	0.677919i
$236$		0			0
$237$	−18.0000			−1.16923
$238$		0			0
$239$	−1.50000	+	0.866025i	−0.0970269	+	0.0560185i	−0.547728	−	0.836656i	$-0.684507\pi$
$239$	−1.50000	+	0.866025i	−0.0970269	+	0.0560185i	0.450701	+	0.892675i	$0.351174\pi$
$240$		0			0
$241$	25.5000	−	14.7224i	1.64260	−	0.948355i	0.662695	−	0.748890i	$-0.269413\pi$
$241$	25.5000	−	14.7224i	1.64260	−	0.948355i	0.979905	−	0.199465i	$-0.0639205\pi$
$242$		0			0
$243$		−	15.5885i		−	1.00000i
$244$		0			0
$245$	4.50000	−	11.2583i	0.287494	−	0.719268i
$246$		0			0
$247$	4.50000	+	2.59808i	0.286328	+	0.165312i
$248$		0			0
$249$	13.5000	+	7.79423i	0.855528	+	0.493939i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$		0			0
$255$	−4.50000	+	2.59808i	−0.281801	+	0.162698i
$256$		0			0
$257$	−16.5000	−	9.52628i	−1.02924	−	0.594233i	−0.112474	−	0.993655i	$-0.535878\pi$
$257$	−16.5000	−	9.52628i	−1.02924	−	0.594233i	−0.916767	+	0.399422i	$0.869211\pi$
$258$		0			0
$259$	5.50000	−	28.5788i	0.341753	−	1.77580i
$260$		0			0
$261$	13.5000	−	23.3827i	0.835629	−	1.44735i
$262$		0			0
$263$	10.5000	−	6.06218i	0.647458	−	0.373810i	−0.140024	−	0.990148i	$-0.544718\pi$
$263$	10.5000	−	6.06218i	0.647458	−	0.373810i	0.787482	+	0.616338i	$0.211385\pi$
$264$		0			0
$265$	−4.50000	+	2.59808i	−0.276433	+	0.159599i
$266$		0			0
$267$	4.50000	+	7.79423i	0.275396	+	0.476999i
$268$		0			0
$269$	−1.50000	−	0.866025i	−0.0914566	−	0.0528025i	0.453574	−	0.891219i	$-0.350149\pi$
$269$	−1.50000	−	0.866025i	−0.0914566	−	0.0528025i	−0.545031	+	0.838416i	$0.683482\pi$
$270$		0			0
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	0.983312	−	0.181928i	$-0.0582339\pi$
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	−0.649211	+	0.760609i	$0.724901\pi$
$272$		0			0
$273$	−4.50000	+	23.3827i	−0.272352	+	1.41518i
$274$		0			0
$275$	9.00000	+	5.19615i	0.542720	+	0.313340i
$276$		0			0
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$		0			0
$285$	−3.00000			−0.177705
$286$		0			0
$287$	−4.50000	−	0.866025i	−0.265627	−	0.0511199i
$288$		0			0
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$		0			0
$291$	1.50000	−	2.59808i	0.0879316	−	0.152302i
$292$		0			0
$293$	22.5000	−	12.9904i	1.31446	−	0.758906i	0.331632	−	0.943409i	$-0.392401\pi$
$293$	22.5000	−	12.9904i	1.31446	−	0.758906i	0.982832	+	0.184503i	$0.0590674\pi$
$294$		0			0
$295$	18.0000	+	10.3923i	1.04800	+	0.605063i
$296$		0			0
$297$	−13.5000	−	23.3827i	−0.783349	−	1.35680i
$298$		0			0
$299$	9.00000			0.520483
$300$		0			0
$301$	7.50000	+	21.6506i	0.432293	+	1.24792i
$302$		0			0
$303$	7.50000	+	12.9904i	0.430864	+	0.746278i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	10.5000	+	6.06218i	0.597324	+	0.344865i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$			20.7846i			1.17482i	0.809291	+	0.587408i	$0.199852\pi$
$313$			20.7846i			1.17482i	−0.809291	+	0.587408i	$0.800148\pi$
$314$		0			0
$315$	−4.50000	−	12.9904i	−0.253546	−	0.731925i
$316$		0			0
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$		0			0
$319$		−	46.7654i		−	2.61836i
$320$		0			0
$321$	10.5000	+	18.1865i	0.586053	+	1.01507i
$322$		0			0
$323$			1.73205i			0.0963739i
$324$		0			0
$325$	−9.00000	−	5.19615i	−0.499230	−	0.288231i
$326$		0			0
$327$	7.50000	+	4.33013i	0.414751	+	0.239457i
$328$		0			0
$329$	−24.0000	−	20.7846i	−1.32316	−	1.14589i
$330$		0			0
$331$			17.3205i			0.952021i	0.879440	+	0.476011i	$0.157918\pi$
$331$			17.3205i			0.952021i	−0.879440	+	0.476011i	$0.842082\pi$
$332$		0			0
$333$	−16.5000	−	28.5788i	−0.904194	−	1.56611i
$334$		0			0
$335$	−3.00000	+	5.19615i	−0.163908	+	0.283896i
$336$		0			0
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$		0			0
$339$	−22.5000	+	12.9904i	−1.22203	+	0.705541i
$340$		0			0
$341$	36.0000	−	20.7846i	1.94951	−	1.12555i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	−4.50000	+	2.59808i	−0.242272	+	0.139876i
$346$		0			0
$347$			10.3923i			0.557888i	0.960307	+	0.278944i	$0.0899844\pi$
$347$			10.3923i			0.557888i	−0.960307	+	0.278944i	$0.910016\pi$
$348$		0			0
$349$	16.5000	+	9.52628i	0.883225	+	0.509930i	0.871720	−	0.490004i	$-0.163005\pi$
$349$	16.5000	+	9.52628i	0.883225	+	0.509930i	0.0115044	+	0.999934i	$0.496338\pi$
$350$		0			0
$351$	13.5000	+	23.3827i	0.720577	+	1.24808i
$352$		0			0
$353$	−10.5000	+	6.06218i	−0.558859	+	0.322657i	−0.752687	−	0.658378i	$-0.771243\pi$
$353$	−10.5000	+	6.06218i	−0.558859	+	0.322657i	0.193829	+	0.981035i	$0.437909\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$		0			0
$357$	−7.50000	+	2.59808i	−0.396942	+	0.137505i
$358$		0			0
$359$	−7.50000	+	4.33013i	−0.395835	+	0.228535i	−0.684685	−	0.728839i	$-0.740060\pi$
$359$	−7.50000	+	4.33013i	−0.395835	+	0.228535i	0.288850	+	0.957374i	$0.406727\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−24.0000	−	13.8564i	−1.25967	−	0.727273i
$364$		0			0
$365$	10.5000	+	18.1865i	0.549595	+	0.951927i
$366$		0			0
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	0.793370	−	0.608740i	$-0.208325\pi$
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	−0.923869	+	0.382709i	$0.874991\pi$
$368$		0			0
$369$	−4.50000	+	2.59808i	−0.234261	+	0.135250i
$370$		0			0
$371$	−7.50000	+	2.59808i	−0.389381	+	0.134885i
$372$		0			0
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$		0			0
$375$	21.0000			1.08444
$376$		0			0
$377$			46.7654i			2.40854i
$378$		0			0
$379$			17.3205i			0.889695i	0.895606	+	0.444847i	$0.146742\pi$
$379$			17.3205i			0.889695i	−0.895606	+	0.444847i	$0.853258\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$		0			0
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	−0.727851	−	0.685736i	$-0.759481\pi$
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	0.957790	+	0.287469i	$0.0928139\pi$
$384$		0			0
$385$	−18.0000	−	15.5885i	−0.917365	−	0.794461i
$386$		0			0
$387$	22.5000	+	12.9904i	1.14374	+	0.660338i
$388$		0			0
$389$	19.5000	+	33.7750i	0.988689	+	1.71246i	0.624230	+	0.781241i	$0.285413\pi$
$389$	19.5000	+	33.7750i	0.988689	+	1.71246i	0.364459	+	0.931219i	$0.381254\pi$
$390$		0			0
$391$	1.50000	+	2.59808i	0.0758583	+	0.131390i
$392$		0			0
$393$	13.5000	+	7.79423i	0.680985	+	0.393167i
$394$		0			0
$395$	−9.00000	+	15.5885i	−0.452839	+	0.784340i
$396$		0			0
$397$	−13.5000	+	7.79423i	−0.677546	+	0.391181i	−0.798930	−	0.601424i	$-0.794600\pi$
$397$	−13.5000	+	7.79423i	−0.677546	+	0.391181i	0.121384	+	0.992606i	$0.461267\pi$
$398$		0			0
$399$	−4.50000	−	0.866025i	−0.225282	−	0.0433555i
$400$		0			0
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$		0			0
$403$	−36.0000	+	20.7846i	−1.79329	+	1.03536i
$404$		0			0
$405$	−13.5000	−	7.79423i	−0.670820	−	0.387298i
$406$		0			0
$407$	−49.5000	−	28.5788i	−2.45362	−	1.41660i
$408$		0			0
$409$			6.92820i			0.342578i	0.985221	+	0.171289i	$0.0547931\pi$
$409$			6.92820i			0.342578i	−0.985221	+	0.171289i	$0.945207\pi$
$410$		0			0
$411$	−4.50000	+	2.59808i	−0.221969	+	0.128154i
$412$		0			0
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$		0			0
$415$	13.5000	−	7.79423i	0.662689	−	0.382604i
$416$		0			0
$417$	7.50000	−	4.33013i	0.367277	−	0.212047i
$418$		0			0
$419$	−1.50000	−	2.59808i	−0.0732798	−	0.126924i	0.827057	−	0.562118i	$-0.190013\pi$
$419$	−1.50000	−	2.59808i	−0.0732798	−	0.126924i	−0.900337	+	0.435194i	$0.856680\pi$
$420$		0			0
$421$	−12.5000	+	21.6506i	−0.609213	+	1.05519i	0.382158	+	0.924097i	$0.375181\pi$
$421$	−12.5000	+	21.6506i	−0.609213	+	1.05519i	−0.991370	+	0.131090i	$0.958152\pi$
$422$		0			0
$423$	−36.0000			−1.75038
$424$		0			0
$425$		−	3.46410i		−	0.168034i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	40.5000	+	23.3827i	1.95536	+	1.12893i
$430$		0			0
$431$	−10.5000	−	6.06218i	−0.505767	−	0.292005i	0.225325	−	0.974284i	$-0.427656\pi$
$431$	−10.5000	−	6.06218i	−0.505767	−	0.292005i	−0.731092	+	0.682279i	$0.760989\pi$
$432$		0			0
$433$			6.92820i			0.332948i	0.986046	+	0.166474i	$0.0532382\pi$
$433$			6.92820i			0.332948i	−0.986046	+	0.166474i	$0.946762\pi$
$434$		0			0
$435$	−13.5000	−	23.3827i	−0.647275	−	1.12111i
$436$		0			0
$437$			1.73205i			0.0828552i
$438$		0			0
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$		−	38.1051i		−	1.81043i	−0.424955	−	0.905214i	$-0.639710\pi$
$443$		−	38.1051i		−	1.81043i	0.424955	−	0.905214i	$-0.360290\pi$
$444$		0			0
$445$	9.00000			0.426641
$446$		0			0
$447$	−4.50000	−	2.59808i	−0.212843	−	0.122885i
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$		0			0
$453$	−4.50000	−	7.79423i	−0.211428	−	0.366205i
$454$		0			0
$455$	18.0000	+	15.5885i	0.843853	+	0.730798i
$456$		0			0
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$		0			0
$459$	−4.50000	+	7.79423i	−0.210042	+	0.363803i
$460$		0			0
$461$	−13.5000	−	7.79423i	−0.628758	−	0.363013i	0.151513	−	0.988455i	$-0.451585\pi$
$461$	−13.5000	−	7.79423i	−0.628758	−	0.363013i	−0.780271	+	0.625442i	$0.784919\pi$
$462$		0			0
$463$	−19.5000	+	11.2583i	−0.906242	+	0.523219i	−0.879220	−	0.476416i	$-0.841936\pi$
$463$	−19.5000	+	11.2583i	−0.906242	+	0.523219i	−0.0270218	+	0.999635i	$0.508602\pi$
$464$		0			0
$465$	12.0000	−	20.7846i	0.556487	−	0.963863i
$466$		0			0
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$		0			0
$469$	−6.00000	+	6.92820i	−0.277054	+	0.319915i
$470$		0			0
$471$	−12.0000			−0.552931
$472$		0			0
$473$	45.0000			2.06910
$474$		0			0
$475$	1.00000	−	1.73205i	0.0458831	−	0.0794719i
$476$		0			0
$477$	−4.50000	+	7.79423i	−0.206041	+	0.356873i
$478$		0			0
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	0.898257	−	0.439470i	$-0.144834\pi$
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	−0.829721	+	0.558179i	$0.811500\pi$
$480$		0			0
$481$	49.5000	+	28.5788i	2.25701	+	1.30308i
$482$		0			0
$483$	−7.50000	+	2.59808i	−0.341262	+	0.118217i
$484$		0			0
$485$	−1.50000	−	2.59808i	−0.0681115	−	0.117973i
$486$		0			0
$487$	7.50000	+	4.33013i	0.339857	+	0.196217i	0.660209	−	0.751082i	$-0.270468\pi$
$487$	7.50000	+	4.33013i	0.339857	+	0.196217i	−0.320352	+	0.947299i	$0.603801\pi$
$488$		0			0
$489$	−7.50000	−	12.9904i	−0.339162	−	0.587445i
$490$		0			0
$491$	−10.5000	+	6.06218i	−0.473858	+	0.273582i	−0.717853	−	0.696194i	$-0.754875\pi$
$491$	−10.5000	+	6.06218i	−0.473858	+	0.273582i	0.243995	+	0.969776i	$0.421542\pi$
$492$		0			0
$493$	−13.5000	+	7.79423i	−0.608009	+	0.351034i
$494$		0			0
$495$	−27.0000			−1.21356
$496$		0			0
$497$	6.00000	−	6.92820i	0.269137	−	0.310772i
$498$		0			0
$499$	34.5000	+	19.9186i	1.54443	+	0.891678i	0.998551	+	0.0538157i	$0.0171384\pi$
$499$	34.5000	+	19.9186i	1.54443	+	0.891678i	0.545881	+	0.837863i	$0.316195\pi$
$500$		0			0
$501$	4.50000	−	2.59808i	0.201045	−	0.116073i
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$		0			0
$507$	−21.0000	−	12.1244i	−0.932643	−	0.538462i
$508$		0			0
$509$	−7.50000	−	4.33013i	−0.332432	−	0.191930i	0.324489	−	0.945890i	$-0.394808\pi$
$509$	−7.50000	−	4.33013i	−0.332432	−	0.191930i	−0.656920	+	0.753960i	$0.728141\pi$
$510$		0			0
$511$	10.5000	+	30.3109i	0.464493	+	1.34087i
$512$		0			0
$513$	−4.50000	+	2.59808i	−0.198680	+	0.114708i
$514$		0			0
$515$	10.5000	−	6.06218i	0.462685	−	0.267131i
$516$		0			0
$517$	−54.0000	+	31.1769i	−2.37492	+	1.37116i
$518$		0			0
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−4.50000	−	2.59808i	−0.197149	−	0.113824i	0.398176	−	0.917309i	$-0.369643\pi$
$521$	−4.50000	−	2.59808i	−0.197149	−	0.113824i	−0.595325	+	0.803485i	$0.702977\pi$
$522$		0			0
$523$	14.5000	+	25.1147i	0.634041	+	1.09819i	0.986718	+	0.162446i	$0.0519382\pi$
$523$	14.5000	+	25.1147i	0.634041	+	1.09819i	−0.352677	+	0.935745i	$0.614728\pi$
$524$		0			0
$525$	9.00000	+	1.73205i	0.392792	+	0.0755929i
$526$		0			0
$527$	−12.0000	−	6.92820i	−0.522728	−	0.301797i
$528$		0			0
$529$	−10.0000	−	17.3205i	−0.434783	−	0.753066i
$530$		0			0
$531$	36.0000			1.56227
$532$		0			0
$533$	4.50000	−	7.79423i	0.194917	−	0.337606i
$534$		0			0
$535$	21.0000			0.907909
$536$		0			0
$537$	−19.5000	+	33.7750i	−0.841487	+	1.45750i
$538$		0			0
$539$	−22.5000	−	28.5788i	−0.969144	−	1.23098i
$540$		0			0
$541$	−12.5000	−	21.6506i	−0.537417	−	0.930834i	−0.999042	−	0.0437584i	$-0.986067\pi$
$541$	−12.5000	−	21.6506i	−0.537417	−	0.930834i	0.461625	−	0.887075i	$-0.347267\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.50000	−	4.33013i	0.321265	−	0.185482i
$546$		0			0
$547$	22.5000	+	12.9904i	0.962031	+	0.555429i	0.896797	−	0.442441i	$-0.145888\pi$
$547$	22.5000	+	12.9904i	0.962031	+	0.555429i	0.0652331	+	0.997870i	$0.479221\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.00000			−0.383413
$552$		0			0
$553$	−18.0000	+	20.7846i	−0.765438	+	0.883852i
$554$		0			0
$555$	−33.0000			−1.40077
$556$		0			0
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$		0			0
$559$	−45.0000			−1.90330
$560$		0			0
$561$			15.5885i			0.658145i
$562$		0			0
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$		0			0
$565$			25.9808i			1.09302i
$566$		0			0
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$		0			0
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$		−	10.3923i		−	0.434904i	−0.976071	−	0.217452i	$-0.930225\pi$
$571$		−	10.3923i		−	0.434904i	0.976071	−	0.217452i	$-0.0697746\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$		−	3.46410i		−	0.144463i
$576$		0			0
$577$	−10.5000	−	6.06218i	−0.437121	−	0.252372i	0.265255	−	0.964178i	$-0.414544\pi$
$577$	−10.5000	−	6.06218i	−0.437121	−	0.252372i	−0.702376	+	0.711807i	$0.747877\pi$
$578$		0			0
$579$			24.2487i			1.00774i
$580$		0			0
$581$	22.5000	−	7.79423i	0.933457	−	0.323359i
$582$		0			0
$583$			15.5885i			0.645608i
$584$		0			0
$585$	27.0000			1.11631
$586$		0			0
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$		0			0
$589$	−4.00000	−	6.92820i	−0.164817	−	0.285472i
$590$		0			0
$591$			31.1769i			1.28245i
$592$		0			0
$593$	−4.50000	+	2.59808i	−0.184793	+	0.106690i	−0.589543	−	0.807737i	$-0.700692\pi$
$593$	−4.50000	+	2.59808i	−0.184793	+	0.106690i	0.404750	+	0.914428i	$0.367359\pi$
$594$		0			0
$595$	−1.50000	+	7.79423i	−0.0614940	+	0.319532i
$596$		0			0
$597$	16.5000	+	9.52628i	0.675300	+	0.389885i
$598$		0			0
$599$		−	3.46410i		−	0.141539i	−0.997493	−	0.0707697i	$-0.977454\pi$
$599$		−	3.46410i		−	0.141539i	0.997493	−	0.0707697i	$-0.0225455\pi$
$600$		0			0
$601$	−22.5000	−	12.9904i	−0.917794	−	0.529889i	−0.0348635	−	0.999392i	$-0.511100\pi$
$601$	−22.5000	−	12.9904i	−0.917794	−	0.529889i	−0.882931	+	0.469503i	$0.844433\pi$
$602$		0			0
$603$			10.3923i			0.423207i
$604$		0			0
$605$	−24.0000	+	13.8564i	−0.975739	+	0.563343i
$606$		0			0
$607$	−17.5000	+	30.3109i	−0.710303	+	1.23028i	0.254440	+	0.967088i	$0.418109\pi$
$607$	−17.5000	+	30.3109i	−0.710303	+	1.23028i	−0.964743	+	0.263193i	$0.915225\pi$
$608$		0			0
$609$	−13.5000	−	38.9711i	−0.547048	−	1.57919i
$610$		0			0
$611$	54.0000	−	31.1769i	2.18461	−	1.26128i
$612$		0			0
$613$	−20.5000	+	35.5070i	−0.827987	+	1.43412i	0.0716275	+	0.997431i	$0.477181\pi$
$613$	−20.5000	+	35.5070i	−0.827987	+	1.43412i	−0.899615	+	0.436684i	$0.856153\pi$
$614$		0			0
$615$			5.19615i			0.209529i
$616$		0			0
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$		0			0
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$	−4.50000	+	7.79423i	−0.180579	+	0.312772i
$622$		0			0
$623$	13.5000	+	2.59808i	0.540866	+	0.104090i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$		0			0
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$		0			0
$629$			19.0526i			0.759675i
$630$		0			0
$631$		−	24.2487i		−	0.965326i	−0.875806	−	0.482663i	$-0.839670\pi$
$631$		−	24.2487i		−	0.965326i	0.875806	−	0.482663i	$-0.160330\pi$
$632$		0			0
$633$	10.5000	+	18.1865i	0.417338	+	0.722850i
$634$		0			0
$635$	−9.00000	+	15.5885i	−0.357154	+	0.618609i
$636$		0			0
$637$	22.5000	+	28.5788i	0.891482	+	1.13233i
$638$		0			0
$639$		−	10.3923i		−	0.411113i
$640$		0			0
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$		0			0
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$		0			0
$645$	22.5000	−	12.9904i	0.885937	−	0.511496i
$646$		0			0
$647$	22.5000	−	38.9711i	0.884566	−	1.53211i	0.0383563	−	0.999264i	$-0.487788\pi$
$647$	22.5000	−	38.9711i	0.884566	−	1.53211i	0.846210	−	0.532850i	$-0.178879\pi$
$648$		0			0
$649$	54.0000	−	31.1769i	2.11969	−	1.22380i
$650$		0			0
$651$	24.0000	−	27.7128i	0.940634	−	1.08615i
$652$		0			0
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		0			0
$655$	13.5000	−	7.79423i	0.527489	−	0.304546i
$656$		0			0
$657$	31.5000	+	18.1865i	1.22893	+	0.709524i
$658$		0			0
$659$	−1.50000	−	0.866025i	−0.0584317	−	0.0337356i	0.470500	−	0.882400i	$-0.344074\pi$
$659$	−1.50000	−	0.866025i	−0.0584317	−	0.0337356i	−0.528931	+	0.848665i	$0.677407\pi$
$660$		0			0
$661$			27.7128i			1.07790i	0.842337	+	0.538952i	$0.181179\pi$
$661$			27.7128i			1.07790i	−0.842337	+	0.538952i	$0.818821\pi$
$662$		0			0
$663$		−	15.5885i		−	0.605406i
$664$		0			0
$665$	−3.00000	+	3.46410i	−0.116335	+	0.134332i
$666$		0			0
$667$	−13.5000	+	7.79423i	−0.522722	+	0.301794i
$668$		0			0
$669$	−1.50000	−	0.866025i	−0.0579934	−	0.0334825i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	−0.988968	−	0.148132i	$-0.952674\pi$
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	0.622770	+	0.782405i	$0.286007\pi$
$674$		0			0
$675$	9.00000	−	5.19615i	0.346410	−	0.200000i
$676$		0			0
$677$		−	20.7846i		−	0.798817i	−0.916773	−	0.399409i	$-0.869215\pi$
$677$		−	20.7846i		−	0.798817i	0.916773	−	0.399409i	$-0.130785\pi$
$678$		0			0
$679$	−1.50000	−	4.33013i	−0.0575647	−	0.166175i
$680$		0			0
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$		0			0
$683$	−19.5000	−	11.2583i	−0.746147	−	0.430788i	0.0781532	−	0.996941i	$-0.475098\pi$
$683$	−19.5000	−	11.2583i	−0.746147	−	0.430788i	−0.824300	+	0.566153i	$0.808431\pi$
$684$		0			0
$685$			5.19615i			0.198535i
$686$		0			0
$687$	−19.5000	+	33.7750i	−0.743971	+	1.28860i
$688$		0			0
$689$		−	15.5885i		−	0.593873i
$690$		0			0
$691$	40.0000			1.52167			0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000			1.52167			0.760836	+	0.648944i	$0.224789\pi$
$692$		0			0
$693$	−40.5000	−	7.79423i	−1.53847	−	0.296078i
$694$		0			0
$695$		−	8.66025i		−	0.328502i
$696$		0			0
$697$	3.00000			0.113633
$698$		0			0
$699$	13.5000	−	7.79423i	0.510617	−	0.294805i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−5.50000	+	9.52628i	−0.207436	+	0.359290i
$704$		0			0
$705$	−18.0000	+	31.1769i	−0.677919	+	1.17419i
$706$		0			0
$707$	22.5000	+	4.33013i	0.846200	+	0.162851i
$708$		0			0
$709$	14.0000			0.525781			0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000			0.525781			0.262891	+	0.964826i	$0.415324\pi$
$710$		0			0
$711$			31.1769i			1.16923i
$712$		0			0
$713$	−12.0000	−	6.92820i	−0.449404	−	0.259463i
$714$		0			0
$715$	40.5000	−	23.3827i	1.51461	−	0.874463i
$716$		0			0
$717$	1.50000	+	2.59808i	0.0560185	+	0.0970269i
$718$		0			0
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	0.601075	−	0.799193i	$-0.294739\pi$
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	−0.992659	+	0.120950i	$0.961406\pi$
$720$		0			0
$721$	17.5000	−	6.06218i	0.651734	−	0.225767i
$722$		0			0
$723$	−25.5000	−	44.1673i	−0.948355	−	1.64260i
$724$		0			0
$725$	18.0000			0.668503
$726$		0			0
$727$	−9.50000	+	16.4545i	−0.352335	+	0.610263i	−0.986658	−	0.162805i	$-0.947946\pi$
$727$	−9.50000	+	16.4545i	−0.352335	+	0.610263i	0.634323	+	0.773068i	$0.281279\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−7.50000	−	12.9904i	−0.277398	−	0.480467i
$732$		0			0
$733$	22.5000	+	12.9904i	0.831056	+	0.479811i	0.854214	−	0.519921i	$-0.174039\pi$
$733$	22.5000	+	12.9904i	0.831056	+	0.479811i	−0.0231578	+	0.999732i	$0.507372\pi$
$734$		0			0
$735$	−19.5000	−	7.79423i	−0.719268	−	0.287494i
$736$		0			0
$737$	9.00000	+	15.5885i	0.331519	+	0.574208i
$738$		0			0
$739$	−13.5000	−	7.79423i	−0.496606	−	0.286715i	0.230705	−	0.973024i	$-0.425897\pi$
$739$	−13.5000	−	7.79423i	−0.496606	−	0.286715i	−0.727311	+	0.686308i	$0.759230\pi$
$740$		0			0
$741$	4.50000	−	7.79423i	0.165312	−	0.286328i
$742$		0			0
$743$	40.5000	−	23.3827i	1.48580	−	0.857828i	0.485932	−	0.873997i	$-0.338480\pi$
$743$	40.5000	−	23.3827i	1.48580	−	0.857828i	0.999869	+	0.0161693i	$0.00514707\pi$
$744$		0			0
$745$	−4.50000	+	2.59808i	−0.164867	+	0.0951861i
$746$		0			0
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$		0			0
$749$	31.5000	+	6.06218i	1.15098	+	0.221507i
$750$		0			0
$751$	13.5000	+	7.79423i	0.492622	+	0.284415i	0.725662	−	0.688052i	$-0.241534\pi$
$751$	13.5000	+	7.79423i	0.492622	+	0.284415i	−0.233040	+	0.972467i	$0.574867\pi$
$752$		0			0
$753$		−	20.7846i		−	0.757433i
$754$		0			0
$755$	−9.00000			−0.327544
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$			15.5885i			0.565825i
$760$		0			0
$761$	−28.5000	−	16.4545i	−1.03312	−	0.596475i	−0.115246	−	0.993337i	$-0.536766\pi$
$761$	−28.5000	−	16.4545i	−1.03312	−	0.596475i	−0.917878	+	0.396862i	$0.870099\pi$
$762$		0			0
$763$	12.5000	−	4.33013i	0.452530	−	0.156761i
$764$		0			0
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$		0			0
$767$	−54.0000	+	31.1769i	−1.94983	+	1.12573i
$768$		0			0
$769$	19.5000	−	11.2583i	0.703188	−	0.405986i	−0.105346	−	0.994436i	$-0.533595\pi$
$769$	19.5000	−	11.2583i	0.703188	−	0.405986i	0.808534	+	0.588450i	$0.200262\pi$
$770$		0			0
$771$	−16.5000	+	28.5788i	−0.594233	+	1.02924i
$772$		0			0
$773$	46.5000	+	26.8468i	1.67249	+	0.965612i	0.966238	+	0.257650i	$0.0829480\pi$
$773$	46.5000	+	26.8468i	1.67249	+	0.965612i	0.706250	+	0.707962i	$0.250385\pi$
$774$		0			0
$775$	8.00000	+	13.8564i	0.287368	+	0.497737i
$776$		0			0
$777$	−49.5000	−	9.52628i	−1.77580	−	0.341753i
$778$		0			0
$779$	1.50000	+	0.866025i	0.0537431	+	0.0310286i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$		0			0
$783$	−40.5000	−	23.3827i	−1.44735	−	0.835629i
$784$		0			0
$785$	−6.00000	+	10.3923i	−0.214149	+	0.370917i
$786$		0			0
$787$	28.0000			0.998092			0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000			0.998092			0.499046	+	0.866575i	$0.333684\pi$
$788$		0			0
$789$	−10.5000	−	18.1865i	−0.373810	−	0.647458i
$790$		0			0
$791$	−7.50000	+	38.9711i	−0.266669	+	1.38565i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	4.50000	+	7.79423i	0.159599	+	0.276433i
$796$		0			0
$797$	−19.5000	+	11.2583i	−0.690725	+	0.398791i	−0.803884	−	0.594786i	$-0.797237\pi$
$797$	−19.5000	+	11.2583i	−0.690725	+	0.398791i	0.113158	+	0.993577i	$0.463903\pi$
$798$		0			0
$799$	18.0000	+	10.3923i	0.636794	+	0.367653i
$800$		0			0
$801$	13.5000	−	7.79423i	0.476999	−	0.275396i
$802$		0			0
$803$	63.0000			2.22322
$804$		0			0
$805$	−1.50000	+	7.79423i	−0.0528681	+	0.274710i
$806$		0			0
$807$	−1.50000	+	2.59808i	−0.0528025	+	0.0914566i
$808$		0			0
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.0646355	+	0.997909i	$0.520588\pi$
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.831897	+	0.554930i	$0.812745\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	16.5000	−	9.52628i	0.578680	−	0.334101i
$814$		0			0
$815$	−15.0000			−0.525427
$816$		0			0
$817$		−	8.66025i		−	0.302984i
$818$		0			0
$819$	40.5000	+	7.79423i	1.41518	+	0.272352i
$820$		0			0
$821$	−6.00000			−0.209401			−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000			−0.209401			−0.104701	+	0.994504i	$0.533388\pi$
$822$		0			0
$823$			3.46410i			0.120751i	0.998176	+	0.0603755i	$0.0192298\pi$
$823$			3.46410i			0.120751i	−0.998176	+	0.0603755i	$0.980770\pi$
$824$		0			0
$825$	9.00000	−	15.5885i	0.313340	−	0.542720i
$826$		0			0
$827$			31.1769i			1.08413i	0.840337	+	0.542064i	$0.182357\pi$
$827$			31.1769i			1.08413i	−0.840337	+	0.542064i	$0.817643\pi$
$828$		0			0
$829$	−19.5000	−	11.2583i	−0.677263	−	0.391018i	0.121560	−	0.992584i	$-0.461210\pi$
$829$	−19.5000	−	11.2583i	−0.677263	−	0.391018i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	−1.50000	+	0.866025i	−0.0520344	+	0.0300421i
$832$		0			0
$833$	−4.50000	+	11.2583i	−0.155916	+	0.390078i
$834$		0			0
$835$		−	5.19615i		−	0.179820i
$836$		0			0
$837$		−	41.5692i		−	1.43684i
$838$		0			0
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$	22.5000	+	12.9904i	0.774941	+	0.447412i
$844$		0			0
$845$	−21.0000	+	12.1244i	−0.722422	+	0.417091i
$846$		0			0
$847$	−40.0000	+	13.8564i	−1.37442	+	0.476112i
$848$		0			0
$849$			6.92820i			0.237775i
$850$		0			0
$851$			19.0526i			0.653113i
$852$		0			0
$853$	−19.5000	−	11.2583i	−0.667667	−	0.385478i	0.127525	−	0.991835i	$-0.459297\pi$
$853$	−19.5000	−	11.2583i	−0.667667	−	0.385478i	−0.795192	+	0.606357i	$0.792630\pi$
$854$		0			0
$855$			5.19615i			0.177705i
$856$		0			0
$857$	19.5000	−	11.2583i	0.666107	−	0.384577i	−0.128493	−	0.991710i	$-0.541014\pi$
$857$	19.5000	−	11.2583i	0.666107	−	0.384577i	0.794600	+	0.607133i	$0.207681\pi$
$858$		0			0
$859$	−20.5000	+	35.5070i	−0.699451	+	1.21148i	0.269206	+	0.963083i	$0.413239\pi$
$859$	−20.5000	+	35.5070i	−0.699451	+	1.21148i	−0.968657	+	0.248402i	$0.920095\pi$
$860$		0			0
$861$	−1.50000	+	7.79423i	−0.0511199	+	0.265627i
$862$		0			0
$863$	4.50000	−	2.59808i	0.153182	−	0.0884395i	−0.421450	−	0.906852i	$-0.638479\pi$
$863$	4.50000	−	2.59808i	0.153182	−	0.0884395i	0.574632	+	0.818412i	$0.305145\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$		0			0
$867$	−21.0000	+	12.1244i	−0.713197	+	0.411765i
$868$		0			0
$869$	27.0000	+	46.7654i	0.915912	+	1.58641i
$870$		0			0
$871$	−9.00000	−	15.5885i	−0.304953	−	0.528195i
$872$		0			0
$873$	−4.50000	−	2.59808i	−0.152302	−	0.0879316i
$874$		0			0
$875$	21.0000	−	24.2487i	0.709930	−	0.819756i
$876$		0			0
$877$	15.5000	−	26.8468i	0.523398	−	0.906552i	−0.476231	−	0.879320i	$-0.657998\pi$
$877$	15.5000	−	26.8468i	0.523398	−	0.906552i	0.999629	−	0.0272316i	$-0.00866915\pi$
$878$		0			0
$879$	−22.5000	−	38.9711i	−0.758906	−	1.31446i
$880$		0			0
$881$		−	48.4974i		−	1.63392i	−0.576695	−	0.816960i	$-0.695658\pi$
$881$		−	48.4974i		−	1.63392i	0.576695	−	0.816960i	$-0.304342\pi$
$882$		0			0
$883$		−	24.2487i		−	0.816034i	−0.912974	−	0.408017i	$-0.866220\pi$
$883$		−	24.2487i		−	0.816034i	0.912974	−	0.408017i	$-0.133780\pi$
$884$		0			0
$885$	18.0000	−	31.1769i	0.605063	−	1.04800i
$886$		0			0
$887$	22.5000	−	38.9711i	0.755476	−	1.30852i	−0.189661	−	0.981850i	$-0.560739\pi$
$887$	22.5000	−	38.9711i	0.755476	−	1.30852i	0.945137	−	0.326673i	$-0.105928\pi$
$888$		0			0
$889$	−18.0000	+	20.7846i	−0.603701	+	0.697093i
$890$		0			0
$891$	−40.5000	+	23.3827i	−1.35680	+	0.783349i
$892$		0			0
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$	19.5000	+	33.7750i	0.651813	+	1.12897i
$896$		0			0
$897$		−	15.5885i		−	0.520483i
$898$		0			0
$899$	36.0000	−	62.3538i	1.20067	−	2.07962i
$900$		0			0
$901$	4.50000	−	2.59808i	0.149917	−	0.0865545i
$902$		0			0
$903$	37.5000	−	12.9904i	1.24792	−	0.432293i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	31.5000	−	18.1865i	1.04594	−	0.603874i	0.124430	−	0.992228i	$-0.460290\pi$
$907$	31.5000	−	18.1865i	1.04594	−	0.603874i	0.921510	+	0.388354i	$0.126956\pi$
$908$		0			0
$909$	22.5000	−	12.9904i	0.746278	−	0.430864i
$910$		0			0
$911$	−40.5000	−	23.3827i	−1.34182	−	0.774703i	−0.354750	−	0.934961i	$-0.615434\pi$
$911$	−40.5000	−	23.3827i	−1.34182	−	0.774703i	−0.987075	+	0.160258i	$0.948767\pi$
$912$		0			0
$913$		−	46.7654i		−	1.54771i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	22.5000	−	7.79423i	0.743015	−	0.257388i
$918$		0			0
$919$	16.5000	−	9.52628i	0.544285	−	0.314243i	−0.202529	−	0.979276i	$-0.564916\pi$
$919$	16.5000	−	9.52628i	0.544285	−	0.314243i	0.746814	+	0.665033i	$0.231583\pi$
$920$		0			0
$921$		−	34.6410i		−	1.14146i
$922$		0			0
$923$	9.00000	+	15.5885i	0.296239	+	0.513100i
$924$		0			0
$925$	11.0000	−	19.0526i	0.361678	−	0.626444i
$926$		0			0
$927$	10.5000	−	18.1865i	0.344865	−	0.597324i
$928$		0			0
$929$		−	34.6410i		−	1.13653i	−0.822844	−	0.568267i	$-0.807614\pi$
$929$		−	34.6410i		−	1.13653i	0.822844	−	0.568267i	$-0.192386\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$		0			0
$933$		−	41.5692i		−	1.36092i
$934$		0			0
$935$	13.5000	+	7.79423i	0.441497	+	0.254899i
$936$		0			0
$937$			34.6410i			1.13167i	0.824518	+	0.565836i	$0.191447\pi$
$937$			34.6410i			1.13167i	−0.824518	+	0.565836i	$0.808553\pi$
$938$		0			0
$939$	36.0000			1.17482
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$	3.00000			0.0976934
$944$		0			0
$945$	−22.5000	+	7.79423i	−0.731925	+	0.253546i
$946$		0			0
$947$			17.3205i			0.562841i	0.959585	+	0.281420i	$0.0908056\pi$
$947$			17.3205i			0.562841i	−0.959585	+	0.281420i	$0.909194\pi$
$948$		0			0
$949$	−63.0000			−2.04507
$950$		0			0
$951$			51.9615i			1.68497i
$952$		0			0
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$		0			0
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$		0			0
$957$	−81.0000			−2.61836
$958$		0			0
$959$	−1.50000	+	7.79423i	−0.0484375	+	0.251689i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	31.5000	−	18.1865i	1.01507	−	0.586053i
$964$		0			0
$965$	21.0000	+	12.1244i	0.676014	+	0.390297i
$966$		0			0
$967$	28.5000	−	16.4545i	0.916498	−	0.529140i	0.0339820	−	0.999422i	$-0.489181\pi$
$967$	28.5000	−	16.4545i	0.916498	−	0.529140i	0.882516	+	0.470282i	$0.155848\pi$
$968$		0			0
$969$	3.00000			0.0963739
$970$		0			0
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	0.563914	−	0.825833i	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$		0			0
$973$	2.50000	−	12.9904i	0.0801463	−	0.416452i
$974$		0			0
$975$	−9.00000	+	15.5885i	−0.288231	+	0.499230i
$976$		0			0
$977$	−42.0000			−1.34370			−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000			−1.34370			−0.671850	+	0.740688i	$0.734500\pi$
$978$		0			0
$979$	13.5000	−	23.3827i	0.431462	−	0.747314i
$980$		0			0
$981$	7.50000	−	12.9904i	0.239457	−	0.414751i
$982$		0			0
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$		0			0
$985$	27.0000	+	15.5885i	0.860292	+	0.496690i
$986$		0			0
$987$	−36.0000	+	41.5692i	−1.14589	+	1.32316i
$988$		0			0
$989$	−7.50000	−	12.9904i	−0.238486	−	0.413070i
$990$		0			0
$991$	7.50000	+	4.33013i	0.238245	+	0.137551i	0.614370	−	0.789018i	$-0.289410\pi$
$991$	7.50000	+	4.33013i	0.238245	+	0.137551i	−0.376125	+	0.926569i	$0.622744\pi$
$992$		0			0
$993$	30.0000			0.952021
$994$		0			0
$995$	16.5000	−	9.52628i	0.523085	−	0.302003i
$996$		0			0
$997$	−19.5000	+	11.2583i	−0.617571	+	0.356555i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−19.5000	+	11.2583i	−0.617571	+	0.356555i	0.158352	+	0.987383i	$0.449382\pi$
$998$		0			0
$999$	−49.5000	+	28.5788i	−1.56611	+	0.904194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.b.367.1	yes	2
3.2	odd	2		3024.2.cz.c.2719.1		2
4.3	odd	2		1008.2.cz.c.367.1	yes	2
7.5	odd	6		1008.2.bf.a.943.1	yes	2
9.4	even	3		1008.2.bf.d.31.1	yes	2
9.5	odd	6		3024.2.bf.d.1711.1		2
12.11	even	2		3024.2.cz.d.2719.1		2
21.5	even	6		3024.2.bf.a.2287.1		2
28.19	even	6		1008.2.bf.d.943.1	yes	2
36.23	even	6		3024.2.bf.a.1711.1		2
36.31	odd	6		1008.2.bf.a.31.1	✓	2
63.5	even	6		3024.2.cz.d.1279.1		2
63.40	odd	6		1008.2.cz.c.607.1	yes	2
84.47	odd	6		3024.2.bf.d.2287.1		2
252.103	even	6	inner	1008.2.cz.b.607.1	yes	2
252.131	odd	6		3024.2.cz.c.1279.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.a.31.1	✓	2	36.31	odd	6
1008.2.bf.a.943.1	yes	2	7.5	odd	6
1008.2.bf.d.31.1	yes	2	9.4	even	3
1008.2.bf.d.943.1	yes	2	28.19	even	6
1008.2.cz.b.367.1	yes	2	1.1	even	1	trivial
1008.2.cz.b.607.1	yes	2	252.103	even	6	inner
1008.2.cz.c.367.1	yes	2	4.3	odd	2
1008.2.cz.c.607.1	yes	2	63.40	odd	6
3024.2.bf.a.1711.1		2	36.23	even	6
3024.2.bf.a.2287.1		2	21.5	even	6
3024.2.bf.d.1711.1		2	9.5	odd	6
3024.2.bf.d.2287.1		2	84.47	odd	6
3024.2.cz.c.1279.1		2	252.131	odd	6
3024.2.cz.c.2719.1		2	3.2	odd	2
3024.2.cz.d.1279.1		2	63.5	even	6
3024.2.cz.d.2719.1		2	12.11	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q-1.73205i q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +(-4.50000 + 2.59808i) q^{11} +(4.50000 - 2.59808i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(1.50000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-3.00000 + 3.46410i) q^{21} +(1.50000 + 0.866025i) q^{23} +(-1.00000 - 1.73205i) q^{25} +5.19615i q^{27} +(-4.50000 + 7.79423i) q^{29} -8.00000 q^{31} +(4.50000 + 7.79423i) q^{33} +(1.50000 + 4.33013i) q^{35} +(5.50000 + 9.52628i) q^{37} +(-4.50000 - 7.79423i) q^{39} +(1.50000 - 0.866025i) q^{41} +(-7.50000 - 4.33013i) q^{43} +(4.50000 + 2.59808i) q^{45} +12.0000 q^{47} +(1.00000 + 6.92820i) q^{49} +(1.50000 - 2.59808i) q^{51} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(1.50000 - 0.866025i) q^{57} -12.0000 q^{59} +(6.00000 + 5.19615i) q^{63} -9.00000 q^{65} -3.46410i q^{67} +(1.50000 - 2.59808i) q^{69} +3.46410i q^{71} +(-10.5000 - 6.06218i) q^{73} +(-3.00000 + 1.73205i) q^{75} +(13.5000 + 2.59808i) q^{77} -10.3923i q^{79} +9.00000 q^{81} +(-4.50000 + 7.79423i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(13.5000 + 7.79423i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(-13.5000 - 2.59808i) q^{91} +13.8564i q^{93} -1.73205i q^{95} +(1.50000 + 0.866025i) q^{97} +(13.5000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 3 * q^5 - 4 * q^7 - 6 * q^9	\( 2 q - 3 q^{5} - 4 q^{7} - 6 q^{9} - 9 q^{11} + 9 q^{13} - 3 q^{15} + 3 q^{17} + q^{19} - 6 q^{21} + 3 q^{23} - 2 q^{25} - 9 q^{29} - 16 q^{31} + 9 q^{33} + 3 q^{35} + 11 q^{37} - 9 q^{39} + 3 q^{41} - 15 q^{43} + 9 q^{45} + 24 q^{47} + 2 q^{49} + 3 q^{51} + 3 q^{53} + 18 q^{55} + 3 q^{57} - 24 q^{59} + 12 q^{63} - 18 q^{65} + 3 q^{69} - 21 q^{73} - 6 q^{75} + 27 q^{77} + 18 q^{81} - 9 q^{83} - 3 q^{85} + 27 q^{87} - 9 q^{89} - 27 q^{91} + 3 q^{97} + 27 q^{99}+O(q^{100}) \) 2 * q - 3 * q^5 - 4 * q^7 - 6 * q^9 - 9 * q^11 + 9 * q^13 - 3 * q^15 + 3 * q^17 + q^19 - 6 * q^21 + 3 * q^23 - 2 * q^25 - 9 * q^29 - 16 * q^31 + 9 * q^33 + 3 * q^35 + 11 * q^37 - 9 * q^39 + 3 * q^41 - 15 * q^43 + 9 * q^45 + 24 * q^47 + 2 * q^49 + 3 * q^51 + 3 * q^53 + 18 * q^55 + 3 * q^57 - 24 * q^59 + 12 * q^63 - 18 * q^65 + 3 * q^69 - 21 * q^73 - 6 * q^75 + 27 * q^77 + 18 * q^81 - 9 * q^83 - 3 * q^85 + 27 * q^87 - 9 * q^89 - 27 * q^91 + 3 * q^97 + 27 * q^99

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