LMFDB - Embedded newform 126.2.g.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00611506547$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.2.g.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +(5.00000 - 8.66025i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-1.50000 + 2.59808i) q^{40} -4.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-6.00000 + 10.3923i) q^{47} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(1.50000 + 2.59808i) q^{59} +(2.00000 - 3.46410i) q^{61} -7.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(7.50000 - 2.59808i) q^{70} +(-1.00000 - 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(-1.50000 - 2.59808i) q^{80} +9.00000 q^{83} +18.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} -6.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} +(-3.00000 - 5.19615i) q^{95} -13.0000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} - 3 q^{10} + 3 q^{11} + 4 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 2 q^{19} + 6 q^{20} - 6 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 5 q^{28} + 18 q^{29} + 7 q^{31} - q^{32} + 12 q^{34} - 12 q^{35} + 10 q^{37} - 2 q^{38} - 3 q^{40} - 8 q^{43} + 3 q^{44} + 6 q^{46} - 12 q^{47} - 13 q^{49} + 8 q^{50} - 2 q^{52} + 3 q^{53} - 18 q^{55} - q^{56} - 9 q^{58} + 3 q^{59} + 4 q^{61} - 14 q^{62} + 2 q^{64} - 6 q^{65} - 2 q^{67} - 6 q^{68} + 15 q^{70} - 2 q^{73} + 10 q^{74} + 4 q^{76} - 15 q^{77} - 5 q^{79} - 3 q^{80} + 18 q^{83} + 36 q^{85} + 4 q^{86} + 3 q^{88} + 6 q^{89} - 2 q^{91} - 12 q^{92} - 12 q^{94} - 6 q^{95} - 26 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 - 3 * q^10 + 3 * q^11 + 4 * q^13 - 4 * q^14 - q^16 - 6 * q^17 - 2 * q^19 + 6 * q^20 - 6 * q^22 + 6 * q^23 - 4 * q^25 - 2 * q^26 + 5 * q^28 + 18 * q^29 + 7 * q^31 - q^32 + 12 * q^34 - 12 * q^35 + 10 * q^37 - 2 * q^38 - 3 * q^40 - 8 * q^43 + 3 * q^44 + 6 * q^46 - 12 * q^47 - 13 * q^49 + 8 * q^50 - 2 * q^52 + 3 * q^53 - 18 * q^55 - q^56 - 9 * q^58 + 3 * q^59 + 4 * q^61 - 14 * q^62 + 2 * q^64 - 6 * q^65 - 2 * q^67 - 6 * q^68 + 15 * q^70 - 2 * q^73 + 10 * q^74 + 4 * q^76 - 15 * q^77 - 5 * q^79 - 3 * q^80 + 18 * q^83 + 36 * q^85 + 4 * q^86 + 3 * q^88 + 6 * q^89 - 2 * q^91 - 12 * q^92 - 12 * q^94 - 6 * q^95 - 26 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	−3.00000			−0.639602
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	6.00000			1.02899
$35$	−6.00000	−	5.19615i	−1.01419	−	0.878310i
$36$		0			0
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	4.00000			0.565685
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$		0			0
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	−7.00000			−0.889001
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$	7.50000	−	2.59808i	0.896421	−	0.310530i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$		0			0
$76$	2.00000			0.229416
$77$	−7.50000	+	2.59808i	−0.854704	+	0.296078i
$78$		0			0
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$		0			0
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	18.0000			1.95237
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−1.00000	+	5.19615i	−0.104828	+	0.544705i
$92$	−6.00000			−0.625543
$93$		0			0
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$		0			0
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−3.00000			−0.291386
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$		0			0
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	15.0000	−	5.19615i	1.37505	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	2.00000	+	3.46410i	0.181071	+	0.313625i
$123$		0			0
$124$	3.50000	−	6.06218i	0.314309	−	0.544400i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$		0			0
$133$	−4.00000	−	3.46410i	−0.346844	−	0.300376i
$134$	2.00000			0.172774
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$	−1.50000	+	7.79423i	−0.126773	+	0.658733i
$141$		0			0
$142$		0			0
$143$	3.00000	+	5.19615i	0.250873	+	0.434524i
$144$		0			0
$145$	−13.5000	+	23.3827i	−1.12111	+	1.94183i
$146$	2.00000			0.165521
$147$		0			0
$148$	−10.0000			−0.821995
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$	−21.0000			−1.68676
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$		0			0
$160$	3.00000			0.237171
$161$	12.0000	+	10.3923i	0.945732	+	0.819028i
$162$		0			0
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$		0			0
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−18.0000			−1.39288			−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000			−1.39288			−0.696441	+	0.717614i	$0.745234\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−9.00000	+	15.5885i	−0.690268	+	1.19558i
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	10.0000	−	3.46410i	0.755929	−	0.261861i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−4.00000	−	3.46410i	−0.296500	−	0.256776i
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	15.0000	+	25.9808i	1.10282	+	1.91014i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$	12.0000			0.875190
$189$		0			0
$190$	6.00000			0.435286
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	6.50000	−	11.2583i	0.466673	−	0.808301i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−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
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		0			0
$202$	6.00000			0.422159
$203$	−4.50000	+	23.3827i	−0.315838	+	1.64114i
$204$		0			0
$205$		0			0
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$		0			0
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$		0			0
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$		0			0
$217$	−17.5000	+	6.06218i	−1.18798	+	0.411527i
$218$	−10.0000			−0.677285
$219$		0			0
$220$	4.50000	+	7.79423i	0.303390	+	0.525487i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	−1.00000			−0.0669650			−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000			−0.0669650			−0.0334825	+	0.999439i	$0.510660\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$		0			0
$226$		0			0
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	0.502204	−	0.864749i	$-0.332523\pi$
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	−0.999997	+	0.00254715i	$0.999189\pi$
$228$		0			0
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	−18.0000			−1.18688
$231$		0			0
$232$	9.00000			0.590879
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$	−18.0000	−	31.1769i	−1.17419	−	2.03376i
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$		0			0
$238$	−3.00000	+	15.5885i	−0.194461	+	1.01045i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	−4.00000			−0.256074
$245$	16.5000	−	12.9904i	1.05415	−	0.829925i
$246$		0			0
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	3.50000	+	6.06218i	0.222250	+	0.384949i
$249$		0			0
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	0.500000	−	0.866025i	0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	20.0000	+	17.3205i	1.24274	+	1.07624i
$260$	6.00000			0.372104
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$	5.00000	−	1.73205i	0.306570	−	0.106199i
$267$		0			0
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	9.50000	−	16.4545i	0.577084	−	0.999539i	−0.418728	−	0.908112i	$-0.637524\pi$
$271$	9.50000	−	16.4545i	0.577084	−	0.999539i	0.995812	−	0.0914269i	$-0.0291428\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	6.00000			0.362473
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	0.919834	−	0.392308i	$-0.128323\pi$
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	−0.799666	+	0.600446i	$0.794990\pi$
$278$	−1.00000	+	1.73205i	−0.0599760	+	0.103882i
$279$		0			0
$280$	−6.00000	−	5.19615i	−0.358569	−	0.310530i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$		0			0
$285$		0			0
$286$	−6.00000			−0.354787
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−13.5000	−	23.3827i	−0.792747	−	1.37308i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$	−9.00000			−0.524000
$296$	5.00000	−	8.66025i	0.290619	−	0.503367i
$297$		0			0
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$		0			0
$301$	2.00000	−	10.3923i	0.115278	−	0.599002i
$302$	5.00000			0.287718
$303$		0			0
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$	6.00000	+	5.19615i	0.341882	+	0.296078i
$309$		0			0
$310$	10.5000	−	18.1865i	0.596360	−	1.03293i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	−0.999748	−	0.0224310i	$-0.992859\pi$
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	0.519300	+	0.854592i	$0.326193\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	5.00000			0.281272
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	0.404528	+	0.914526i	$0.367436\pi$
$317$	−10.5000	+	18.1865i	−0.589739	+	1.02146i	−0.994266	+	0.106932i	$0.965897\pi$
$318$		0			0
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$	−15.0000	+	5.19615i	−0.835917	+	0.289570i
$323$	12.0000			0.667698
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	5.00000	+	8.66025i	0.276924	+	0.479647i
$327$		0			0
$328$		0			0
$329$	−24.0000	−	20.7846i	−1.32316	−	1.14589i
$330$		0			0
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$		0			0
$334$	9.00000	−	15.5885i	0.492458	−	0.852962i
$335$	6.00000			0.327815
$336$		0			0
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$	−10.5000	+	18.1865i	−0.568607	+	0.984856i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	−2.00000	+	10.3923i	−0.106904	+	0.555492i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−10.0000	+	17.3205i	−0.525588	+	0.910346i
$363$		0			0
$364$	5.00000	−	1.73205i	0.262071	−	0.0907841i
$365$	6.00000			0.314054
$366$		0			0
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.707744	+	0.706469i	$0.249713\pi$
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.257948	+	0.966159i	$0.416954\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	−30.0000			−1.55963
$371$	−7.50000	+	2.59808i	−0.389381	+	0.134885i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$	−6.00000	+	10.3923i	−0.309426	+	0.535942i
$377$	18.0000			0.927047
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−3.00000	+	5.19615i	−0.153897	+	0.266557i
$381$		0			0
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	−15.0000	+	25.9808i	−0.766464	+	1.32755i	0.173005	+	0.984921i	$0.444652\pi$
$383$	−15.0000	+	25.9808i	−0.766464	+	1.32755i	−0.939469	+	0.342634i	$0.888681\pi$
$384$		0			0
$385$	4.50000	−	23.3827i	0.229341	−	1.19169i
$386$	−7.00000			−0.356291
$387$		0			0
$388$	6.50000	+	11.2583i	0.329988	+	0.571555i
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−7.50000	−	12.9904i	−0.377366	−	0.653617i
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$	8.00000			0.401004
$399$		0			0
$400$	4.00000			0.200000
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$		0			0
$403$	7.00000	+	12.1244i	0.348695	+	0.603957i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$		0			0
$406$	−18.0000	−	15.5885i	−0.893325	−	0.773642i
$407$	30.0000			1.48704
$408$		0			0
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$		0			0
$411$		0			0
$412$	−16.0000			−0.788263
$413$	−7.50000	+	2.59808i	−0.369051	+	0.127843i
$414$		0			0
$415$	−13.5000	+	23.3827i	−0.662689	+	1.14781i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	8.00000	−	13.8564i	0.389434	−	0.674519i
$423$		0			0
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$		0			0
$427$	8.00000	+	6.92820i	0.387147	+	0.335279i
$428$	3.00000			0.145010
$429$		0			0
$430$	6.00000	+	10.3923i	0.289346	+	0.501161i
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	3.50000	−	18.1865i	0.168005	−	0.872982i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$		0			0
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	−0.545185	−	0.838316i	$-0.683541\pi$
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	0.998595	+	0.0529862i	$0.0168739\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	12.0000			0.570782
$443$	7.50000	−	12.9904i	0.356336	−	0.617192i	−0.631010	−	0.775775i	$-0.717359\pi$
$443$	7.50000	−	12.9904i	0.356336	−	0.617192i	0.987346	+	0.158583i	$0.0506926\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	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
$451$		0			0
$452$		0			0
$453$		0			0
$454$	15.0000			0.703985
$455$	−12.0000	−	10.3923i	−0.562569	−	0.487199i
$456$		0			0
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	−0.672994	−	0.739648i	$-0.734992\pi$
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	0.977051	+	0.213006i	$0.0683253\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$		0			0
$460$	9.00000	−	15.5885i	0.419627	−	0.726816i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$		0			0
$469$	5.00000	−	1.73205i	0.230879	−	0.0799787i
$470$	36.0000			1.66056
$471$		0			0
$472$	1.50000	+	2.59808i	0.0690431	+	0.119586i
$473$	−6.00000	−	10.3923i	−0.275880	−	0.477839i
$474$		0			0
$475$	8.00000			0.367065
$476$	−12.0000	−	10.3923i	−0.550019	−	0.476331i
$477$		0			0
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$	23.0000			1.04762
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	19.5000	−	33.7750i	0.885449	−	1.53364i
$486$		0			0
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	0.714083	−	0.700061i	$-0.246844\pi$
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	−0.963312	+	0.268384i	$0.913510\pi$
$488$	2.00000	−	3.46410i	0.0905357	−	0.156813i
$489$		0			0
$490$	3.00000	+	20.7846i	0.135526	+	0.938953i
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	−27.0000	−	46.7654i	−1.21602	−	2.10621i
$494$	−2.00000	−	3.46410i	−0.0899843	−	0.155857i
$495$		0			0
$496$	−7.00000			−0.314309
$497$		0			0
$498$		0			0
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	0.0301498	+	0.999545i	$0.490402\pi$
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	−0.880707	+	0.473662i	$0.842932\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	−4.50000	+	7.79423i	−0.200845	+	0.347873i
$503$	18.0000			0.802580			0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$		0			0
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	5.00000	−	1.73205i	0.221187	−	0.0766214i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	24.0000	+	41.5692i	1.05757	+	1.83176i
$516$		0			0
$517$	−36.0000			−1.58328
$518$	−25.0000	+	8.66025i	−1.09844	+	0.380510i
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	−12.0000	−	20.7846i	−0.525730	−	0.910590i	−0.999551	−	0.0299693i	$-0.990459\pi$
$521$	−12.0000	−	20.7846i	−0.525730	−	0.910590i	0.473821	−	0.880621i	$-0.342874\pi$
$522$		0			0
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$	−15.0000			−0.655278
$525$		0			0
$526$	24.0000			1.04645
$527$	21.0000	−	36.3731i	0.914774	−	1.58444i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$		0			0
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$		0			0
$534$		0			0
$535$	−4.50000	−	7.79423i	−0.194552	−	0.336974i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	−3.00000			−0.129339
$539$	−3.00000	−	20.7846i	−0.129219	−	0.895257i
$540$		0			0
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$	9.50000	+	16.4545i	0.408060	+	0.706781i
$543$		0			0
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	−30.0000			−1.28506
$546$		0			0
$547$	14.0000			0.598597			0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000			0.598597			0.299298	+	0.954160i	$0.403247\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$		0			0
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	−9.00000	+	15.5885i	−0.383413	+	0.664091i
$552$		0			0
$553$	−10.0000	−	8.66025i	−0.425243	−	0.368271i
$554$	−4.00000			−0.169944
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−7.50000	−	12.9904i	−0.317785	−	0.550420i	0.662240	−	0.749291i	$-0.269606\pi$
$557$	−7.50000	−	12.9904i	−0.317785	−	0.550420i	−0.980026	+	0.198871i	$0.936272\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	7.50000	−	2.59808i	0.316933	−	0.109789i
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	0.895902	−	0.444252i	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$		0			0
$565$		0			0
$566$	20.0000			0.840663
$567$		0			0
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$		0			0
$574$		0			0
$575$	−24.0000			−1.00087
$576$		0			0
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	0.876245	−	0.481865i	$-0.160040\pi$
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	−0.855430	+	0.517918i	$0.826707\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$	27.0000			1.12111
$581$	−4.50000	+	23.3827i	−0.186691	+	0.970077i
$582$		0			0
$583$	−4.50000	+	7.79423i	−0.186371	+	0.322804i
$584$	−1.00000	−	1.73205i	−0.0413803	−	0.0716728i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$	27.0000			1.11441			0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000			1.11441			0.557205	+	0.830375i	$0.311874\pi$
$588$		0			0
$589$	−14.0000			−0.576860
$590$	4.50000	−	7.79423i	0.185262	−	0.320883i
$591$		0			0
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	0.374236	+	0.927333i	$0.377905\pi$
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	−0.990212	+	0.139569i	$0.955428\pi$
$594$		0			0
$595$	−9.00000	+	46.7654i	−0.368964	+	1.91719i
$596$	−6.00000			−0.245770
$597$		0			0
$598$	6.00000	+	10.3923i	0.245358	+	0.424973i
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	23.0000			0.938190			0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000			0.938190			0.469095	+	0.883148i	$0.344580\pi$
$602$	8.00000	+	6.92820i	0.326056	+	0.282372i
$603$		0			0
$604$	−2.50000	+	4.33013i	−0.101724	+	0.176190i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$	−12.0000			−0.485866
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$		0			0
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$	−13.0000	+	22.5167i	−0.524637	+	0.908698i
$615$		0			0
$616$	−7.50000	+	2.59808i	−0.302184	+	0.104679i
$617$	36.0000			1.44931			0.724653	−	0.689114i	$-0.242000\pi$
$617$	36.0000			1.44931			0.724653	+	0.689114i	$0.242000\pi$
$618$		0			0
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$	10.5000	+	18.1865i	0.421690	+	0.730389i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−8.50000	−	14.7224i	−0.339728	−	0.588427i
$627$		0			0
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	−60.0000			−2.39236
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$	−2.50000	+	4.33013i	−0.0994447	+	0.172243i
$633$		0			0
$634$	−10.5000	−	18.1865i	−0.417008	−	0.722280i
$635$	1.50000	−	2.59808i	0.0595257	−	0.103102i
$636$		0			0
$637$	−13.0000	−	5.19615i	−0.515079	−	0.205879i
$638$	−27.0000			−1.06894
$639$		0			0
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	0.959848	−	0.280521i	$-0.0905072\pi$
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	−0.722862	+	0.690992i	$0.757174\pi$
$642$		0			0
$643$	38.0000			1.49857			0.749287	−	0.662246i	$-0.230396\pi$
$643$	38.0000			1.49857			0.749287	+	0.662246i	$0.230396\pi$
$644$	3.00000	−	15.5885i	0.118217	−	0.614271i
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	8.00000			0.313786
$651$		0			0
$652$	−10.0000			−0.391630
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$		0			0
$655$	22.5000	+	38.9711i	0.879148	+	1.52273i
$656$		0			0
$657$		0			0
$658$	30.0000	−	10.3923i	1.16952	−	0.405134i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$	−4.00000	−	6.92820i	−0.155464	−	0.269272i
$663$		0			0
$664$	9.00000			0.349268
$665$	15.0000	−	5.19615i	0.581675	−	0.201498i
$666$		0			0
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	9.00000	+	15.5885i	0.348220	+	0.603136i
$669$		0			0
$670$	−3.00000	+	5.19615i	−0.115900	+	0.200745i
$671$	12.0000			0.463255
$672$		0			0
$673$	17.0000			0.655302			0.327651	−	0.944799i	$-0.393743\pi$
$673$	17.0000			0.655302			0.327651	+	0.944799i	$0.393743\pi$
$674$	−2.50000	+	4.33013i	−0.0962964	+	0.166790i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	16.5000	−	28.5788i	0.634147	−	1.09837i	−0.352549	−	0.935793i	$-0.614685\pi$
$677$	16.5000	−	28.5788i	0.634147	−	1.09837i	0.986695	−	0.162581i	$-0.0519817\pi$
$678$		0			0
$679$	6.50000	−	33.7750i	0.249447	−	1.29617i
$680$	18.0000			0.690268
$681$		0			0
$682$	−10.5000	−	18.1865i	−0.402066	−	0.696398i
$683$	−25.5000	−	44.1673i	−0.975730	−	1.69001i	−0.677503	−	0.735520i	$-0.736938\pi$
$683$	−25.5000	−	44.1673i	−0.975730	−	1.69001i	−0.298227	−	0.954495i	$-0.596395\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−3.00000	+	5.19615i	−0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$		0			0
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	10.0000	+	17.3205i	0.377157	+	0.653255i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	24.0000			0.903252
$707$	15.0000	−	5.19615i	0.564133	−	0.195421i
$708$		0			0
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	42.0000			1.57291
$714$		0			0
$715$	−18.0000			−0.673162
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	21.0000	−	36.3731i	0.783168	−	1.35649i	−0.146920	−	0.989148i	$-0.546936\pi$
$719$	21.0000	−	36.3731i	0.783168	−	1.35649i	0.930087	−	0.367338i	$-0.119731\pi$
$720$		0			0
$721$	32.0000	+	27.7128i	1.19174	+	1.03208i
$722$	−15.0000			−0.558242
$723$		0			0
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$	−18.0000	−	31.1769i	−0.668503	−	1.15788i
$726$		0			0
$727$	−31.0000			−1.14973			−0.574863	−	0.818250i	$-0.694945\pi$
$727$	−31.0000			−1.14973			−0.574863	+	0.818250i	$0.694945\pi$
$728$	−1.00000	+	5.19615i	−0.0370625	+	0.192582i
$729$		0			0
$730$	−3.00000	+	5.19615i	−0.111035	+	0.192318i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	−10.0000	+	17.3205i	−0.369358	+	0.639748i	−0.989465	−	0.144770i	$-0.953756\pi$
$733$	−10.0000	+	17.3205i	−0.369358	+	0.639748i	0.620107	+	0.784517i	$0.287089\pi$
$734$	−37.0000			−1.36569
$735$		0			0
$736$	−6.00000			−0.221163
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$		0			0
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	0.521475	−	0.853266i	$-0.325382\pi$
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	−0.999688	+	0.0249776i	$0.992049\pi$
$740$	15.0000	−	25.9808i	0.551411	−	0.955072i
$741$		0			0
$742$	1.50000	−	7.79423i	0.0550667	−	0.286135i
$743$	−54.0000			−1.98107			−0.990534	−	0.137268i	$-0.956168\pi$
$743$	−54.0000			−1.98107			−0.990534	+	0.137268i	$0.956168\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$		0			0
$748$	−18.0000			−0.658145
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	−11.5000	+	19.9186i	−0.419641	+	0.726839i	−0.995903	−	0.0904254i	$-0.971177\pi$
$751$	−11.5000	+	19.9186i	−0.419641	+	0.726839i	0.576262	+	0.817265i	$0.304511\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$		0			0
$754$	−9.00000	+	15.5885i	−0.327761	+	0.567698i
$755$	15.0000			0.545906
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$		0			0
$760$	−3.00000	−	5.19615i	−0.108821	−	0.188484i
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$		0			0
$763$	−25.0000	+	8.66025i	−0.905061	+	0.313522i
$764$	12.0000			0.434145
$765$		0			0
$766$	−15.0000	−	25.9808i	−0.541972	−	0.938723i
$767$	3.00000	+	5.19615i	0.108324	+	0.187622i
$768$		0			0
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$	18.0000	+	15.5885i	0.648675	+	0.561769i
$771$		0			0
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$		0			0
$775$	14.0000	−	24.2487i	0.502895	−	0.871039i
$776$	−13.0000			−0.466673
$777$		0			0
$778$	−30.0000			−1.07555
$779$		0			0
$780$		0			0
$781$		0			0
$782$	18.0000	−	31.1769i	0.643679	−	1.11488i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−12.0000			−0.428298
$786$		0			0
$787$	8.00000	+	13.8564i	0.285169	+	0.493928i	0.972650	−	0.232275i	$-0.0746169\pi$
$787$	8.00000	+	13.8564i	0.285169	+	0.493928i	−0.687481	+	0.726202i	$0.741284\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$	15.0000			0.533676
$791$		0			0
$792$		0			0
$793$	4.00000	−	6.92820i	0.142044	−	0.246028i
$794$	−4.00000	−	6.92820i	−0.141955	−	0.245873i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	27.0000			0.956389			0.478195	−	0.878254i	$-0.341291\pi$
$797$	27.0000			0.956389			0.478195	+	0.878254i	$0.341291\pi$
$798$		0			0
$799$	72.0000			2.54718
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	12.0000	+	20.7846i	0.423735	+	0.733930i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$	−45.0000	+	15.5885i	−1.58604	+	0.549421i
$806$	−14.0000			−0.493129
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	22.5000	−	7.79423i	0.789595	−	0.273524i
$813$		0			0
$814$	−15.0000	+	25.9808i	−0.525750	+	0.910625i
$815$	15.0000	+	25.9808i	0.525427	+	0.910066i
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	11.0000			0.384606
$819$		0			0
$820$		0			0
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$	1.50000	−	7.79423i	0.0521917	−	0.271196i
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$		0			0
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$	−13.5000	−	23.3827i	−0.468592	−	0.811625i
$831$		0			0
$832$	2.00000			0.0693375
$833$	6.00000	+	41.5692i	0.207888	+	1.44029i
$834$		0			0
$835$	27.0000	−	46.7654i	0.934374	−	1.61838i
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		0			0
$838$	18.0000	−	31.1769i	0.621800	−	1.07699i
$839$	−54.0000			−1.86429			−0.932144	−	0.362089i	$-0.882064\pi$
$839$	−54.0000			−1.86429			−0.932144	+	0.362089i	$0.882064\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−4.00000	+	6.92820i	−0.137849	+	0.238762i
$843$		0			0
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	13.5000	−	23.3827i	0.464414	−	0.804389i
$846$		0			0
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	−3.00000			−0.103020
$849$		0			0
$850$	−12.0000	−	20.7846i	−0.411597	−	0.712906i
$851$	−30.0000	−	51.9615i	−1.02839	−	1.78122i
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$	−10.0000	+	3.46410i	−0.342193	+	0.118539i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$		0			0
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	−0.696661	−	0.717400i	$-0.745332\pi$
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	0.969618	+	0.244626i	$0.0786652\pi$
$860$	−12.0000			−0.409197
$861$		0			0
$862$	24.0000			0.817443
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	−13.0000	+	22.5167i	−0.441758	+	0.765147i
$867$		0			0
$868$	14.0000	+	12.1244i	0.475191	+	0.411527i
$869$	−15.0000			−0.508840
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$		0			0
$874$	−12.0000			−0.405906
$875$	1.50000	−	7.79423i	0.0507093	−	0.263493i
$876$		0			0
$877$	−28.0000	+	48.4974i	−0.945493	+	1.63764i	−0.190731	+	0.981642i	$0.561086\pi$
$877$	−28.0000	+	48.4974i	−0.945493	+	1.63764i	−0.754761	+	0.655999i	$0.772247\pi$
$878$	9.50000	+	16.4545i	0.320609	+	0.555312i
$879$		0			0
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	−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
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	7.50000	+	12.9904i	0.251967	+	0.436420i
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$		0			0
$889$	0.500000	−	2.59808i	0.0167695	−	0.0871367i
$890$	−18.0000			−0.603361
$891$		0			0
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$	−12.0000	−	20.7846i	−0.401565	−	0.695530i
$894$		0			0
$895$	−36.0000			−1.20335
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$		0			0
$898$	−9.00000	+	15.5885i	−0.300334	+	0.520194i
$899$	31.5000	+	54.5596i	1.05058	+	1.81966i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.0000	+	51.9615i	−0.997234	+	1.72726i
$906$		0			0
$907$	−25.0000	−	43.3013i	−0.830111	−	1.43780i	−0.897949	−	0.440099i	$-0.854943\pi$
$907$	−25.0000	−	43.3013i	−0.830111	−	1.43780i	0.0678380	−	0.997696i	$-0.478390\pi$
$908$	−7.50000	+	12.9904i	−0.248896	+	0.431101i
$909$		0			0
$910$	15.0000	−	5.19615i	0.497245	−	0.172251i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$	6.50000	+	11.2583i	0.215001	+	0.372392i
$915$		0			0
$916$	20.0000			0.660819
$917$	30.0000	+	25.9808i	0.990687	+	0.857960i
$918$		0			0
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	−0.537234	−	0.843433i	$-0.680531\pi$
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	0.999052	+	0.0435419i	$0.0138642\pi$
$920$	9.00000	+	15.5885i	0.296721	+	0.513936i
$921$		0			0
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$		0			0
$924$		0			0
$925$	−40.0000			−1.31519
$926$	2.00000	−	3.46410i	0.0657241	−	0.113837i
$927$		0			0
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	12.0000	−	20.7846i	0.393707	−	0.681921i	−0.599228	−	0.800578i	$-0.704526\pi$
$929$	12.0000	−	20.7846i	0.393707	−	0.681921i	0.992935	+	0.118657i	$0.0378590\pi$
$930$		0			0
$931$	11.0000	−	8.66025i	0.360510	−	0.283828i
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	27.0000	+	46.7654i	0.882994	+	1.52939i
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−1.00000	+	5.19615i	−0.0326512	+	0.169660i
$939$		0			0
$940$	−18.0000	+	31.1769i	−0.587095	+	1.01688i
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	0.717496	−	0.696563i	$-0.245288\pi$
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	−0.961989	+	0.273088i	$0.911955\pi$
$942$		0			0
$943$		0			0
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	12.0000			0.390154
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	−4.00000	+	6.92820i	−0.129777	+	0.224781i
$951$		0			0
$952$	15.0000	−	5.19615i	0.486153	−	0.168408i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	−18.0000	−	31.1769i	−0.582466	−	1.00886i
$956$	−9.00000	−	15.5885i	−0.291081	−	0.504167i
$957$		0			0
$958$	24.0000			0.775405
$959$	15.0000	−	5.19615i	0.484375	−	0.167793i
$960$		0			0
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	10.0000	+	17.3205i	0.322413	+	0.558436i
$963$		0			0
$964$	−11.5000	+	19.9186i	−0.370390	+	0.641534i
$965$	−21.0000			−0.676014
$966$		0			0
$967$	29.0000			0.932577			0.466289	−	0.884633i	$-0.345591\pi$
$967$	29.0000			0.932577			0.466289	+	0.884633i	$0.345591\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	19.5000	+	33.7750i	0.626107	+	1.08445i
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	0.362604	+	0.931943i	$0.381888\pi$
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	−0.988389	+	0.151948i	$0.951445\pi$
$972$		0			0
$973$	−1.00000	+	5.19615i	−0.0320585	+	0.166581i
$974$	11.0000			0.352463
$975$		0			0
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$		0			0
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$	54.0000			1.71971
$987$		0			0
$988$	4.00000			0.127257
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	9.50000	+	16.4545i	0.301777	+	0.522694i	0.976539	−	0.215342i	$-0.0690867\pi$
$991$	9.50000	+	16.4545i	0.301777	+	0.522694i	−0.674761	+	0.738036i	$0.735753\pi$
$992$	3.50000	−	6.06218i	0.111125	−	0.192474i
$993$		0			0
$994$		0			0
$995$	24.0000			0.760851
$996$		0			0
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$	−19.0000	−	32.9090i	−0.601434	−	1.04172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.g.a.37.1	✓	2
3.2	odd	2		126.2.g.d.37.1	yes	2
4.3	odd	2		1008.2.s.b.289.1		2
7.2	even	3		882.2.a.j.1.1		1
7.3	odd	6		882.2.g.e.361.1		2
7.4	even	3	inner	126.2.g.a.109.1	yes	2
7.5	odd	6		882.2.a.h.1.1		1
7.6	odd	2		882.2.g.e.667.1		2
9.2	odd	6		1134.2.e.g.919.1		2
9.4	even	3		1134.2.h.f.541.1		2
9.5	odd	6		1134.2.h.j.541.1		2
9.7	even	3		1134.2.e.k.919.1		2
12.11	even	2		1008.2.s.o.289.1		2
21.2	odd	6		882.2.a.a.1.1		1
21.5	even	6		882.2.a.e.1.1		1
21.11	odd	6		126.2.g.d.109.1	yes	2
21.17	even	6		882.2.g.g.361.1		2
21.20	even	2		882.2.g.g.667.1		2
28.11	odd	6		1008.2.s.b.865.1		2
28.19	even	6		7056.2.a.h.1.1		1
28.23	odd	6		7056.2.a.by.1.1		1
63.4	even	3		1134.2.e.k.865.1		2
63.11	odd	6		1134.2.h.j.109.1		2
63.25	even	3		1134.2.h.f.109.1		2
63.32	odd	6		1134.2.e.g.865.1		2
84.11	even	6		1008.2.s.o.865.1		2
84.23	even	6		7056.2.a.e.1.1		1
84.47	odd	6		7056.2.a.bx.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.g.a.37.1	✓	2	1.1	even	1	trivial
126.2.g.a.109.1	yes	2	7.4	even	3	inner
126.2.g.d.37.1	yes	2	3.2	odd	2
126.2.g.d.109.1	yes	2	21.11	odd	6
882.2.a.a.1.1		1	21.2	odd	6
882.2.a.e.1.1		1	21.5	even	6
882.2.a.h.1.1		1	7.5	odd	6
882.2.a.j.1.1		1	7.2	even	3
882.2.g.e.361.1		2	7.3	odd	6
882.2.g.e.667.1		2	7.6	odd	2
882.2.g.g.361.1		2	21.17	even	6
882.2.g.g.667.1		2	21.20	even	2
1008.2.s.b.289.1		2	4.3	odd	2
1008.2.s.b.865.1		2	28.11	odd	6
1008.2.s.o.289.1		2	12.11	even	2
1008.2.s.o.865.1		2	84.11	even	6
1134.2.e.g.865.1		2	63.32	odd	6
1134.2.e.g.919.1		2	9.2	odd	6
1134.2.e.k.865.1		2	63.4	even	3
1134.2.e.k.919.1		2	9.7	even	3
1134.2.h.f.109.1		2	63.25	even	3
1134.2.h.f.541.1		2	9.4	even	3
1134.2.h.j.109.1		2	63.11	odd	6
1134.2.h.j.541.1		2	9.5	odd	6
7056.2.a.e.1.1		1	84.23	even	6
7056.2.a.h.1.1		1	28.19	even	6
7056.2.a.bx.1.1		1	84.47	odd	6
7056.2.a.by.1.1		1	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +3.00000 q^{20} -3.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +(5.00000 - 8.66025i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-1.50000 + 2.59808i) q^{40} -4.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-6.00000 + 10.3923i) q^{47} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(1.50000 + 2.59808i) q^{59} +(2.00000 - 3.46410i) q^{61} -7.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(7.50000 - 2.59808i) q^{70} +(-1.00000 - 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(-1.50000 - 2.59808i) q^{80} +9.00000 q^{83} +18.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} -6.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} +(-3.00000 - 5.19615i) q^{95} -13.0000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} - 3 q^{10} + 3 q^{11} + 4 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 2 q^{19} + 6 q^{20} - 6 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 5 q^{28} + 18 q^{29} + 7 q^{31} - q^{32} + 12 q^{34} - 12 q^{35} + 10 q^{37} - 2 q^{38} - 3 q^{40} - 8 q^{43} + 3 q^{44} + 6 q^{46} - 12 q^{47} - 13 q^{49} + 8 q^{50} - 2 q^{52} + 3 q^{53} - 18 q^{55} - q^{56} - 9 q^{58} + 3 q^{59} + 4 q^{61} - 14 q^{62} + 2 q^{64} - 6 q^{65} - 2 q^{67} - 6 q^{68} + 15 q^{70} - 2 q^{73} + 10 q^{74} + 4 q^{76} - 15 q^{77} - 5 q^{79} - 3 q^{80} + 18 q^{83} + 36 q^{85} + 4 q^{86} + 3 q^{88} + 6 q^{89} - 2 q^{91} - 12 q^{92} - 12 q^{94} - 6 q^{95} - 26 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 - 3 * q^10 + 3 * q^11 + 4 * q^13 - 4 * q^14 - q^16 - 6 * q^17 - 2 * q^19 + 6 * q^20 - 6 * q^22 + 6 * q^23 - 4 * q^25 - 2 * q^26 + 5 * q^28 + 18 * q^29 + 7 * q^31 - q^32 + 12 * q^34 - 12 * q^35 + 10 * q^37 - 2 * q^38 - 3 * q^40 - 8 * q^43 + 3 * q^44 + 6 * q^46 - 12 * q^47 - 13 * q^49 + 8 * q^50 - 2 * q^52 + 3 * q^53 - 18 * q^55 - q^56 - 9 * q^58 + 3 * q^59 + 4 * q^61 - 14 * q^62 + 2 * q^64 - 6 * q^65 - 2 * q^67 - 6 * q^68 + 15 * q^70 - 2 * q^73 + 10 * q^74 + 4 * q^76 - 15 * q^77 - 5 * q^79 - 3 * q^80 + 18 * q^83 + 36 * q^85 + 4 * q^86 + 3 * q^88 + 6 * q^89 - 2 * q^91 - 12 * q^92 - 12 * q^94 - 6 * q^95 - 26 * q^97 + 11 * q^98

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