LMFDB - Embedded newform 1458.2.c.f.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1458,2,Mod(487,1458)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1458, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1458.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1458 = 2 \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1458.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.6421886147$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.4
Root			$0.500000 - 0.168222i$ of defining polynomial
Character	$\chi$	$=$	1458.487
Dual form			1458.2.c.f.973.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.370360 + 0.641483i) q^{5} +(-2.06641 + 3.57913i) q^{7} +1.00000 q^{8} -0.740720 q^{10} +(-2.27316 + 3.93723i) q^{11} +(-0.432575 - 0.749242i) q^{13} +(-2.06641 - 3.57913i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.35950 q^{17} +1.55593 q^{19} +(0.370360 - 0.641483i) q^{20} +(-2.27316 - 3.93723i) q^{22} +(1.75222 + 3.03493i) q^{23} +(2.22567 - 3.85497i) q^{25} +0.865150 q^{26} +4.13282 q^{28} +(1.63383 - 2.82988i) q^{29} +(-5.34926 - 9.26519i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.17975 - 3.77544i) q^{34} -3.06126 q^{35} -1.76168 q^{37} +(-0.777964 + 1.34747i) q^{38} +(0.370360 + 0.641483i) q^{40} +(1.28845 + 2.23165i) q^{41} +(1.37682 - 2.38471i) q^{43} +4.54632 q^{44} -3.50443 q^{46} +(-4.84824 + 8.39741i) q^{47} +(-5.04010 - 8.72971i) q^{49} +(2.22567 + 3.85497i) q^{50} +(-0.432575 + 0.749242i) q^{52} +4.00839 q^{53} -3.36756 q^{55} +(-2.06641 + 3.57913i) q^{56} +(1.63383 + 2.82988i) q^{58} +(-0.715749 - 1.23971i) q^{59} +(2.16447 - 3.74897i) q^{61} +10.6985 q^{62} +1.00000 q^{64} +(0.320417 - 0.554979i) q^{65} +(-6.55601 - 11.3553i) q^{67} +(2.17975 + 3.77544i) q^{68} +(1.53063 - 2.65113i) q^{70} -5.08426 q^{71} -0.573273 q^{73} +(0.880842 - 1.52566i) q^{74} +(-0.777964 - 1.34747i) q^{76} +(-9.39457 - 16.2719i) q^{77} +(-3.37983 + 5.85403i) q^{79} -0.740720 q^{80} -2.57689 q^{82} +(-4.61172 + 7.98773i) q^{83} +(-1.61459 - 2.79654i) q^{85} +(1.37682 + 2.38471i) q^{86} +(-2.27316 + 3.93723i) q^{88} -12.3989 q^{89} +3.57551 q^{91} +(1.75222 - 3.03493i) q^{92} +(-4.84824 - 8.39741i) q^{94} +(0.576254 + 0.998101i) q^{95} +(-2.87738 + 4.98377i) q^{97} +10.0802 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 12 q^{8} + 6 q^{10} - 3 q^{11} - 9 q^{13} - 6 q^{14} - 6 q^{16} + 12 q^{17} + 18 q^{19} - 3 q^{20} - 3 q^{22} + 3 q^{23} - 15 q^{25} + 18 q^{26} + 12 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 12 * q^8 + 6 * q^10 - 3 * q^11 - 9 * q^13 - 6 * q^14 - 6 * q^16 + 12 * q^17 + 18 * q^19 - 3 * q^20 - 3 * q^22 + 3 * q^23 - 15 * q^25 + 18 * q^26 + 12 * q^28 - 3 * q^29 - 12 * q^31 - 6 * q^32 - 6 * q^34 - 6 * q^35 + 30 * q^37 - 9 * q^38 - 3 * q^40 - 3 * q^41 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 9 * q^47 - 12 * q^49 - 15 * q^50 - 9 * q^52 - 12 * q^53 + 18 * q^55 - 6 * q^56 - 3 * q^58 + 3 * q^59 - 12 * q^61 + 24 * q^62 + 12 * q^64 + 3 * q^65 - 21 * q^67 - 6 * q^68 + 3 * q^70 - 24 * q^71 + 42 * q^73 - 15 * q^74 - 9 * q^76 + 3 * q^77 + 6 * q^80 + 6 * q^82 + 27 * q^83 - 12 * q^86 - 3 * q^88 - 24 * q^89 + 12 * q^91 + 3 * q^92 + 9 * q^94 + 30 * q^95 - 18 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times$.

$n$	$731$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	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
$5$	0.370360	+	0.641483i	0.165630	+	0.286880i	0.936879	−	0.349654i	$-0.113701\pi$
$5$	0.370360	+	0.641483i	0.165630	+	0.286880i	−0.771249	+	0.636534i	$0.780368\pi$
$6$		0			0
$7$	−2.06641	+	3.57913i	−0.781029	+	1.35278i	0.150313	+	0.988638i	$0.451972\pi$
$7$	−2.06641	+	3.57913i	−0.781029	+	1.35278i	−0.931343	+	0.364144i	$0.881361\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.740720			−0.234236
$11$	−2.27316	+	3.93723i	−0.685384	+	1.18712i	0.287932	+	0.957651i	$0.407032\pi$
$11$	−2.27316	+	3.93723i	−0.685384	+	1.18712i	−0.973316	+	0.229469i	$0.926301\pi$
$12$		0			0
$13$	−0.432575	−	0.749242i	−0.119975	−	0.207802i	0.799783	−	0.600290i	$-0.204948\pi$
$13$	−0.432575	−	0.749242i	−0.119975	−	0.207802i	−0.919757	+	0.392487i	$0.871615\pi$
$14$	−2.06641	−	3.57913i	−0.552271	−	0.956562i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.35950			−1.05733			−0.528667	−	0.848829i	$-0.677308\pi$
$17$	−4.35950			−1.05733			−0.528667	+	0.848829i	$0.677308\pi$
$18$		0			0
$19$	1.55593			0.356954			0.178477	−	0.983944i	$-0.442883\pi$
$19$	1.55593			0.356954			0.178477	+	0.983944i	$0.442883\pi$
$20$	0.370360	−	0.641483i	0.0828151	−	0.143440i
$21$		0			0
$22$	−2.27316	−	3.93723i	−0.484640	−	0.839421i
$23$	1.75222	+	3.03493i	0.365363	+	0.632827i	0.988834	−	0.149019i	$-0.0476117\pi$
$23$	1.75222	+	3.03493i	0.365363	+	0.632827i	−0.623472	+	0.781846i	$0.714278\pi$
$24$		0			0
$25$	2.22567	−	3.85497i	0.445133	−	0.770994i
$26$	0.865150			0.169670
$27$		0			0
$28$	4.13282			0.781029
$29$	1.63383	−	2.82988i	0.303395	−	0.525496i	−0.673507	−	0.739181i	$-0.735213\pi$
$29$	1.63383	−	2.82988i	0.303395	−	0.525496i	0.976903	+	0.213684i	$0.0685463\pi$
$30$		0			0
$31$	−5.34926	−	9.26519i	−0.960755	−	1.66408i	−0.720611	−	0.693340i	$-0.756138\pi$
$31$	−5.34926	−	9.26519i	−0.960755	−	1.66408i	−0.240145	−	0.970737i	$-0.577195\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.17975	−	3.77544i	0.373824	−	0.647482i
$35$	−3.06126			−0.517448
$36$		0			0
$37$	−1.76168			−0.289619			−0.144810	−	0.989460i	$-0.546257\pi$
$37$	−1.76168			−0.289619			−0.144810	+	0.989460i	$0.546257\pi$
$38$	−0.777964	+	1.34747i	−0.126202	+	0.218589i
$39$		0			0
$40$	0.370360	+	0.641483i	0.0585591	+	0.101427i
$41$	1.28845	+	2.23165i	0.201221	+	0.348526i	0.948922	−	0.315510i	$-0.102176\pi$
$41$	1.28845	+	2.23165i	0.201221	+	0.348526i	−0.747701	+	0.664036i	$0.768842\pi$
$42$		0			0
$43$	1.37682	−	2.38471i	0.209962	−	0.363665i	−0.741740	−	0.670687i	$-0.765999\pi$
$43$	1.37682	−	2.38471i	0.209962	−	0.363665i	0.951702	+	0.307022i	$0.0993325\pi$
$44$	4.54632			0.685384
$45$		0			0
$46$	−3.50443			−0.516701
$47$	−4.84824	+	8.39741i	−0.707189	+	1.22489i	0.258707	+	0.965956i	$0.416704\pi$
$47$	−4.84824	+	8.39741i	−0.707189	+	1.22489i	−0.965896	+	0.258931i	$0.916630\pi$
$48$		0			0
$49$	−5.04010	−	8.72971i	−0.720014	−	1.24710i
$50$	2.22567	+	3.85497i	0.314757	+	0.545175i
$51$		0			0
$52$	−0.432575	+	0.749242i	−0.0599874	+	0.103901i
$53$	4.00839			0.550595			0.275297	−	0.961359i	$-0.411224\pi$
$53$	4.00839			0.550595			0.275297	+	0.961359i	$0.411224\pi$
$54$		0			0
$55$	−3.36756			−0.454081
$56$	−2.06641	+	3.57913i	−0.276136	+	0.478281i
$57$		0			0
$58$	1.63383	+	2.82988i	0.214533	+	0.371582i
$59$	−0.715749	−	1.23971i	−0.0931826	−	0.161397i	0.815666	−	0.578523i	$-0.196371\pi$
$59$	−0.715749	−	1.23971i	−0.0931826	−	0.161397i	−0.908849	+	0.417126i	$0.863037\pi$
$60$		0			0
$61$	2.16447	−	3.74897i	0.277132	−	0.480006i	−0.693539	−	0.720419i	$-0.743950\pi$
$61$	2.16447	−	3.74897i	0.277132	−	0.480006i	0.970671	+	0.240413i	$0.0772829\pi$
$62$	10.6985			1.35871
$63$		0			0
$64$	1.00000			0.125000
$65$	0.320417	−	0.554979i	0.0397429	−	0.0688367i
$66$		0			0
$67$	−6.55601	−	11.3553i	−0.800944	−	1.38728i	−0.918995	−	0.394269i	$-0.870998\pi$
$67$	−6.55601	−	11.3553i	−0.800944	−	1.38728i	0.118051	−	0.993008i	$-0.462335\pi$
$68$	2.17975	+	3.77544i	0.264334	+	0.457839i
$69$		0			0
$70$	1.53063	−	2.65113i	0.182946	−	0.316871i
$71$	−5.08426			−0.603390			−0.301695	−	0.953404i	$-0.597552\pi$
$71$	−5.08426			−0.603390			−0.301695	+	0.953404i	$0.597552\pi$
$72$		0			0
$73$	−0.573273			−0.0670965			−0.0335483	−	0.999437i	$-0.510681\pi$
$73$	−0.573273			−0.0670965			−0.0335483	+	0.999437i	$0.510681\pi$
$74$	0.880842	−	1.52566i	0.102396	−	0.177355i
$75$		0			0
$76$	−0.777964	−	1.34747i	−0.0892386	−	0.154566i
$77$	−9.39457	−	16.2719i	−1.07061	−	1.85435i
$78$		0			0
$79$	−3.37983	+	5.85403i	−0.380260	+	0.658630i	−0.991099	−	0.133125i	$-0.957499\pi$
$79$	−3.37983	+	5.85403i	−0.380260	+	0.658630i	0.610839	+	0.791755i	$0.290832\pi$
$80$	−0.740720			−0.0828151
$81$		0			0
$82$	−2.57689			−0.284570
$83$	−4.61172	+	7.98773i	−0.506202	+	0.876767i	0.493772	+	0.869591i	$0.335618\pi$
$83$	−4.61172	+	7.98773i	−0.506202	+	0.876767i	−0.999974	+	0.00717617i	$0.997716\pi$
$84$		0			0
$85$	−1.61459	−	2.79654i	−0.175126	−	0.303328i
$86$	1.37682	+	2.38471i	0.148466	+	0.257150i
$87$		0			0
$88$	−2.27316	+	3.93723i	−0.242320	+	0.419710i
$89$	−12.3989			−1.31428			−0.657142	−	0.753766i	$-0.728235\pi$
$89$	−12.3989			−1.31428			−0.657142	+	0.753766i	$0.728235\pi$
$90$		0			0
$91$	3.57551			0.374815
$92$	1.75222	−	3.03493i	0.182681	−	0.316413i
$93$		0			0
$94$	−4.84824	−	8.39741i	−0.500058	−	0.866126i
$95$	0.576254	+	0.998101i	0.0591224	+	0.102403i
$96$		0			0
$97$	−2.87738	+	4.98377i	−0.292154	+	0.506025i	−0.974319	−	0.225173i	$-0.927705\pi$
$97$	−2.87738	+	4.98377i	−0.292154	+	0.506025i	0.682165	+	0.731198i	$0.261039\pi$
$98$	10.0802			1.01825
$99$		0			0
$100$	−4.45133			−0.445133
$101$	5.51977	−	9.56053i	0.549238	−	0.951308i	−0.449089	−	0.893487i	$-0.648251\pi$
$101$	5.51977	−	9.56053i	0.549238	−	0.951308i	0.998327	−	0.0578210i	$-0.0184153\pi$
$102$		0			0
$103$	3.21073	+	5.56114i	0.316362	+	0.547956i	0.979726	−	0.200341i	$-0.0642052\pi$
$103$	3.21073	+	5.56114i	0.316362	+	0.547956i	−0.663364	+	0.748297i	$0.730872\pi$
$104$	−0.432575	−	0.749242i	−0.0424175	−	0.0734692i
$105$		0			0
$106$	−2.00419	+	3.47137i	−0.194665	+	0.337169i
$107$	−17.2923			−1.67171			−0.835854	−	0.548952i	$-0.815027\pi$
$107$	−17.2923			−1.67171			−0.835854	+	0.548952i	$0.815027\pi$
$108$		0			0
$109$	−9.94570			−0.952626			−0.476313	−	0.879276i	$-0.658027\pi$
$109$	−9.94570			−0.952626			−0.476313	+	0.879276i	$0.658027\pi$
$110$	1.68378	−	2.91639i	0.160542	−	0.278067i
$111$		0			0
$112$	−2.06641	−	3.57913i	−0.195257	−	0.338196i
$113$	−1.22567	−	2.12292i	−0.115301	−	0.199707i	0.802599	−	0.596519i	$-0.203450\pi$
$113$	−1.22567	−	2.12292i	−0.115301	−	0.199707i	−0.917900	+	0.396812i	$0.870117\pi$
$114$		0			0
$115$	−1.29790	+	2.24803i	−0.121030	+	0.209630i
$116$	−3.26767			−0.303395
$117$		0			0
$118$	1.43150			0.131780
$119$	9.00852	−	15.6032i	0.825809	−	1.43034i
$120$		0			0
$121$	−4.83453	−	8.37365i	−0.439503	−	0.761241i
$122$	2.16447	+	3.74897i	0.195962	+	0.339415i
$123$		0			0
$124$	−5.34926	+	9.26519i	−0.480378	+	0.832039i
$125$	7.00080			0.626170
$126$		0			0
$127$	8.10271			0.718999			0.359500	−	0.933145i	$-0.382947\pi$
$127$	8.10271			0.718999			0.359500	+	0.933145i	$0.382947\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	0.320417	+	0.554979i	0.0281025	+	0.0486749i
$131$	7.94732	+	13.7652i	0.694360	+	1.20267i	0.970396	+	0.241520i	$0.0776459\pi$
$131$	7.94732	+	13.7652i	0.694360	+	1.20267i	−0.276036	+	0.961147i	$0.589021\pi$
$132$		0			0
$133$	−3.21518	+	5.56886i	−0.278792	+	0.482882i
$134$	13.1120			1.13271
$135$		0			0
$136$	−4.35950			−0.373824
$137$	6.17817	−	10.7009i	0.527837	−	0.914240i	−0.471637	−	0.881793i	$-0.656337\pi$
$137$	6.17817	−	10.7009i	0.527837	−	0.914240i	0.999473	−	0.0324472i	$-0.0103301\pi$
$138$		0			0
$139$	2.19170	+	3.79613i	0.185897	+	0.321984i	0.943879	−	0.330293i	$-0.107147\pi$
$139$	2.19170	+	3.79613i	0.185897	+	0.321984i	−0.757981	+	0.652276i	$0.773814\pi$
$140$	1.53063	+	2.65113i	0.129362	+	0.224062i
$141$		0			0
$142$	2.54213	−	4.40310i	0.213331	−	0.369500i
$143$	3.93325			0.328915
$144$		0			0
$145$	2.42043			0.201006
$146$	0.286636	−	0.496469i	0.0237222	−	0.0410881i
$147$		0			0
$148$	0.880842	+	1.52566i	0.0724048	+	0.125409i
$149$	−3.41675	−	5.91798i	−0.279911	−	0.484820i	0.691452	−	0.722423i	$-0.256972\pi$
$149$	−3.41675	−	5.91798i	−0.279911	−	0.484820i	−0.971362	+	0.237603i	$0.923638\pi$
$150$		0			0
$151$	2.60327	−	4.50899i	0.211851	−	0.366936i	−0.740443	−	0.672119i	$-0.765384\pi$
$151$	2.60327	−	4.50899i	0.211851	−	0.366936i	0.952294	+	0.305183i	$0.0987176\pi$
$152$	1.55593			0.126202
$153$		0			0
$154$	18.7891			1.51407
$155$	3.96231	−	6.86291i	0.318260	−	0.551243i
$156$		0			0
$157$	−1.98607	−	3.43998i	−0.158506	−	0.274540i	0.775824	−	0.630949i	$-0.217334\pi$
$157$	−1.98607	−	3.43998i	−0.158506	−	0.274540i	−0.934330	+	0.356409i	$0.884001\pi$
$158$	−3.37983	−	5.85403i	−0.268885	−	0.465722i
$159$		0			0
$160$	0.370360	−	0.641483i	0.0292795	−	0.0507137i
$161$	−14.4832			−1.14144
$162$		0			0
$163$	2.34707			0.183837			0.0919184	−	0.995767i	$-0.470700\pi$
$163$	2.34707			0.183837			0.0919184	+	0.995767i	$0.470700\pi$
$164$	1.28845	−	2.23165i	0.100611	−	0.174263i
$165$		0			0
$166$	−4.61172	−	7.98773i	−0.357939	−	0.619968i
$167$	0.526311	+	0.911597i	0.0407272	+	0.0705415i	0.885670	−	0.464314i	$-0.153699\pi$
$167$	0.526311	+	0.911597i	0.0407272	+	0.0705415i	−0.844943	+	0.534856i	$0.820366\pi$
$168$		0			0
$169$	6.12576	−	10.6101i	0.471212	−	0.816163i
$170$	3.22917			0.247666
$171$		0			0
$172$	−2.75363			−0.209962
$173$	−3.41644	+	5.91745i	−0.259747	+	0.449896i	−0.966174	−	0.257890i	$-0.916973\pi$
$173$	−3.41644	+	5.91745i	−0.259747	+	0.449896i	0.706427	+	0.707786i	$0.250306\pi$
$174$		0			0
$175$	9.19828	+	15.9319i	0.695324	+	1.20434i
$176$	−2.27316	−	3.93723i	−0.171346	−	0.296780i
$177$		0			0
$178$	6.19947	−	10.7378i	0.464670	−	0.804832i
$179$	−2.19754			−0.164252			−0.0821258	−	0.996622i	$-0.526171\pi$
$179$	−2.19754			−0.164252			−0.0821258	+	0.996622i	$0.526171\pi$
$180$		0			0
$181$	−15.7400			−1.16994			−0.584971	−	0.811054i	$-0.698894\pi$
$181$	−15.7400			−1.16994			−0.584971	+	0.811054i	$0.698894\pi$
$182$	−1.78776	+	3.09648i	−0.132517	+	0.229527i
$183$		0			0
$184$	1.75222	+	3.03493i	0.129175	+	0.223738i
$185$	−0.652458	−	1.13009i	−0.0479696	−	0.0830859i
$186$		0			0
$187$	9.90985	−	17.1644i	0.724680	−	1.25518i
$188$	9.69649			0.707189
$189$		0			0
$190$	−1.15251			−0.0836117
$191$	−3.92070	+	6.79085i	−0.283692	+	0.491369i	−0.972291	−	0.233773i	$-0.924893\pi$
$191$	−3.92070	+	6.79085i	−0.283692	+	0.491369i	0.688599	+	0.725142i	$0.258226\pi$
$192$		0			0
$193$	8.27028	+	14.3246i	0.595308	+	1.03110i	0.993503	+	0.113803i	$0.0363033\pi$
$193$	8.27028	+	14.3246i	0.595308	+	1.03110i	−0.398195	+	0.917301i	$0.630363\pi$
$194$	−2.87738	−	4.98377i	−0.206584	−	0.357814i
$195$		0			0
$196$	−5.04010	+	8.72971i	−0.360007	+	0.623551i
$197$	−11.3762			−0.810520			−0.405260	−	0.914201i	$-0.632819\pi$
$197$	−11.3762			−0.810520			−0.405260	+	0.914201i	$0.632819\pi$
$198$		0			0
$199$	1.87252			0.132739			0.0663696	−	0.997795i	$-0.478858\pi$
$199$	1.87252			0.132739			0.0663696	+	0.997795i	$0.478858\pi$
$200$	2.22567	−	3.85497i	0.157378	−	0.272587i
$201$		0			0
$202$	5.51977	+	9.56053i	0.388370	+	0.672676i
$203$	6.75234	+	11.6954i	0.473922	+	0.820856i
$204$		0			0
$205$	−0.954378	+	1.65303i	−0.0666567	+	0.115453i
$206$	−6.42145			−0.447404
$207$		0			0
$208$	0.865150			0.0599874
$209$	−3.53688	+	6.12605i	−0.244651	+	0.423748i
$210$		0			0
$211$	−2.73507	−	4.73728i	−0.188290	−	0.326128i	0.756390	−	0.654121i	$-0.226961\pi$
$211$	−2.73507	−	4.73728i	−0.188290	−	0.326128i	−0.944680	+	0.327993i	$0.893628\pi$
$212$	−2.00419	−	3.47137i	−0.137649	−	0.238414i
$213$		0			0
$214$	8.64614	−	14.9755i	0.591038	−	1.02371i
$215$	2.03967			0.139104
$216$		0			0
$217$	44.2150			3.00151
$218$	4.97285	−	8.61323i	0.336804	−	0.583362i
$219$		0			0
$220$	1.68378	+	2.91639i	0.113520	+	0.196623i
$221$	1.88581	+	3.26632i	0.126853	+	0.219717i
$222$		0			0
$223$	0.632422	−	1.09539i	0.0423501	−	0.0733525i	−0.844073	−	0.536228i	$-0.819849\pi$
$223$	0.632422	−	1.09539i	0.0423501	−	0.0733525i	0.886423	+	0.462875i	$0.153182\pi$
$224$	4.13282			0.276136
$225$		0			0
$226$	2.45133			0.163060
$227$	−4.97072	+	8.60954i	−0.329918	+	0.571435i	−0.982495	−	0.186287i	$-0.940354\pi$
$227$	−4.97072	+	8.60954i	−0.329918	+	0.571435i	0.652577	+	0.757722i	$0.273688\pi$
$228$		0			0
$229$	4.99117	+	8.64496i	0.329826	+	0.571275i	0.982477	−	0.186383i	$-0.0596766\pi$
$229$	4.99117	+	8.64496i	0.329826	+	0.571275i	−0.652651	+	0.757658i	$0.726343\pi$
$230$	−1.29790	−	2.24803i	−0.0855812	−	0.148231i
$231$		0			0
$232$	1.63383	−	2.82988i	0.107266	−	0.185791i
$233$	−27.1531			−1.77886			−0.889428	−	0.457076i	$-0.848897\pi$
$233$	−27.1531			−1.77886			−0.889428	+	0.457076i	$0.848897\pi$
$234$		0			0
$235$	−7.18239			−0.468527
$236$	−0.715749	+	1.23971i	−0.0465913	+	0.0806985i
$237$		0			0
$238$	9.00852	+	15.6032i	0.583935	+	1.01141i
$239$	9.76807	+	16.9188i	0.631844	+	1.09439i	0.987175	+	0.159645i	$0.0510349\pi$
$239$	9.76807	+	16.9188i	0.631844	+	1.09439i	−0.355331	+	0.934741i	$0.615632\pi$
$240$		0			0
$241$	−8.10761	+	14.0428i	−0.522257	+	0.904575i	0.477408	+	0.878682i	$0.341576\pi$
$241$	−8.10761	+	14.0428i	−0.522257	+	0.904575i	−0.999665	+	0.0258936i	$0.991757\pi$
$242$	9.66906			0.621551
$243$		0			0
$244$	−4.32893			−0.277132
$245$	3.73330	−	6.46627i	0.238512	−	0.413115i
$246$		0			0
$247$	−0.673056	−	1.16577i	−0.0428255	−	0.0741760i
$248$	−5.34926	−	9.26519i	−0.339678	−	0.588340i
$249$		0			0
$250$	−3.50040	+	6.06287i	−0.221385	+	0.383449i
$251$	23.4605			1.48082			0.740408	−	0.672158i	$-0.234632\pi$
$251$	23.4605			1.48082			0.740408	+	0.672158i	$0.234632\pi$
$252$		0			0
$253$	−15.9323			−1.00165
$254$	−4.05136	+	7.01715i	−0.254205	+	0.440295i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.9952	−	19.0443i	−0.685862	−	1.18795i	−0.973165	−	0.230109i	$-0.926092\pi$
$257$	−10.9952	−	19.0443i	−0.685862	−	1.18795i	0.287303	−	0.957840i	$-0.407241\pi$
$258$		0			0
$259$	3.64036	−	6.30529i	0.226201	−	0.391792i
$260$	−0.640835			−0.0397429
$261$		0			0
$262$	−15.8946			−0.981974
$263$	11.7414	−	20.3366i	0.724003	−	1.25401i	−0.235380	−	0.971903i	$-0.575633\pi$
$263$	11.7414	−	20.3366i	0.724003	−	1.25401i	0.959383	−	0.282107i	$-0.0910333\pi$
$264$		0			0
$265$	1.48455	+	2.57131i	0.0911951	+	0.157954i
$266$	−3.21518	−	5.56886i	−0.197136	−	0.341449i
$267$		0			0
$268$	−6.55601	+	11.3553i	−0.400472	+	0.693638i
$269$	18.3001			1.11578			0.557888	−	0.829916i	$-0.311612\pi$
$269$	18.3001			1.11578			0.557888	+	0.829916i	$0.311612\pi$
$270$		0			0
$271$	−16.4825			−1.00124			−0.500620	−	0.865667i	$-0.666895\pi$
$271$	−16.4825			−1.00124			−0.500620	+	0.865667i	$0.666895\pi$
$272$	2.17975	−	3.77544i	0.132167	−	0.228920i
$273$		0			0
$274$	6.17817	+	10.7009i	0.373237	+	0.646465i
$275$	10.1186	+	17.5259i	0.610175	+	1.05685i
$276$		0			0
$277$	−5.63600	+	9.76184i	−0.338634	+	0.586532i	−0.984176	−	0.177193i	$-0.943298\pi$
$277$	−5.63600	+	9.76184i	−0.338634	+	0.586532i	0.645542	+	0.763725i	$0.276632\pi$
$278$	−4.38340			−0.262899
$279$		0			0
$280$	−3.06126			−0.182946
$281$	0.362672	−	0.628167i	0.0216352	−	0.0374733i	−0.855005	−	0.518620i	$-0.826446\pi$
$281$	0.362672	−	0.628167i	0.0216352	−	0.0374733i	0.876640	+	0.481146i	$0.159779\pi$
$282$		0			0
$283$	11.0691	+	19.1723i	0.657991	+	1.13967i	0.981135	+	0.193324i	$0.0619268\pi$
$283$	11.0691	+	19.1723i	0.657991	+	1.13967i	−0.323144	+	0.946350i	$0.604740\pi$
$284$	2.54213	+	4.40310i	0.150848	+	0.261276i
$285$		0			0
$286$	−1.96663	+	3.40630i	−0.116289	+	0.201419i
$287$	−10.6498			−0.628639
$288$		0			0
$289$	2.00525			0.117956
$290$	−1.21021	+	2.09615i	−0.0710663	+	0.123090i
$291$		0			0
$292$	0.286636	+	0.496469i	0.0167741	+	0.0290536i
$293$	3.27929	+	5.67990i	0.191578	+	0.331823i	0.945773	−	0.324827i	$-0.105306\pi$
$293$	3.27929	+	5.67990i	0.191578	+	0.331823i	−0.754195	+	0.656650i	$0.771973\pi$
$294$		0			0
$295$	0.530170	−	0.918281i	0.0308677	−	0.0534644i
$296$	−1.76168			−0.102396
$297$		0			0
$298$	6.83349			0.395854
$299$	1.51593	−	2.62567i	0.0876686	−	0.151846i
$300$		0			0
$301$	5.69013	+	9.85559i	0.327974	+	0.568067i
$302$	2.60327	+	4.50899i	0.149801	+	0.259463i
$303$		0			0
$304$	−0.777964	+	1.34747i	−0.0446193	+	0.0772829i
$305$	3.20653			0.183605
$306$		0			0
$307$	7.97481			0.455146			0.227573	−	0.973761i	$-0.426921\pi$
$307$	7.97481			0.455146			0.227573	+	0.973761i	$0.426921\pi$
$308$	−9.39457	+	16.2719i	−0.535305	+	0.927176i
$309$		0			0
$310$	3.96231	+	6.86291i	0.225044	+	0.389787i
$311$	−7.07402	−	12.2526i	−0.401131	−	0.694779i	0.592732	−	0.805400i	$-0.298049\pi$
$311$	−7.07402	−	12.2526i	−0.401131	−	0.694779i	−0.993863	+	0.110621i	$0.964716\pi$
$312$		0			0
$313$	−12.0208	+	20.8206i	−0.679454	+	1.17685i	0.295691	+	0.955284i	$0.404450\pi$
$313$	−12.0208	+	20.8206i	−0.679454	+	1.17685i	−0.975145	+	0.221566i	$0.928883\pi$
$314$	3.97215			0.224161
$315$		0			0
$316$	6.75965			0.380260
$317$	−9.09636	+	15.7554i	−0.510903	+	0.884909i	0.489018	+	0.872274i	$0.337355\pi$
$317$	−9.09636	+	15.7554i	−0.510903	+	0.884909i	−0.999920	+	0.0126352i	$0.995978\pi$
$318$		0			0
$319$	7.42794	+	12.8656i	0.415885	+	0.720334i
$320$	0.370360	+	0.641483i	0.0207038	+	0.0358600i
$321$		0			0
$322$	7.24160	−	12.5428i	0.403558	−	0.698984i
$323$	−6.78307			−0.377420
$324$		0			0
$325$	−3.85107			−0.213619
$326$	−1.17354	+	2.03262i	−0.0649961	+	0.112577i
$327$		0			0
$328$	1.28845	+	2.23165i	0.0711425	+	0.123222i
$329$	−20.0369	−	34.7050i	−1.10467	−	1.91335i
$330$		0			0
$331$	−8.98035	+	15.5544i	−0.493605	+	0.854949i	−0.999973	−	0.00736884i	$-0.997654\pi$
$331$	−8.98035	+	15.5544i	−0.493605	+	0.854949i	0.506368	+	0.862317i	$0.330988\pi$
$332$	9.22344			0.506202
$333$		0			0
$334$	−1.05262			−0.0575969
$335$	4.85617	−	8.41114i	0.265321	−	0.459549i
$336$		0			0
$337$	11.7479	+	20.3480i	0.639951	+	1.10843i	0.985443	+	0.170006i	$0.0543787\pi$
$337$	11.7479	+	20.3480i	0.639951	+	1.10843i	−0.345492	+	0.938422i	$0.612288\pi$
$338$	6.12576	+	10.6101i	0.333197	+	0.577115i
$339$		0			0
$340$	−1.61459	+	2.79654i	−0.0875632	+	0.151664i
$341$	48.6389			2.63395
$342$		0			0
$343$	12.7299			0.687350
$344$	1.37682	−	2.38471i	0.0742329	−	0.128575i
$345$		0			0
$346$	−3.41644	−	5.91745i	−0.183669	−	0.318124i
$347$	−4.16620	−	7.21608i	−0.223654	−	0.387379i	0.732261	−	0.681024i	$-0.238465\pi$
$347$	−4.16620	−	7.21608i	−0.223654	−	0.387379i	−0.955915	+	0.293645i	$0.905132\pi$
$348$		0			0
$349$	2.64749	−	4.58558i	0.141717	−	0.245461i	−0.786426	−	0.617684i	$-0.788071\pi$
$349$	2.64749	−	4.58558i	0.141717	−	0.245461i	0.928143	+	0.372223i	$0.121404\pi$
$350$	−18.3966			−0.983337
$351$		0			0
$352$	4.54632			0.242320
$353$	−17.2809	+	29.9314i	−0.919770	+	1.59309i	−0.120007	+	0.992773i	$0.538292\pi$
$353$	−17.2809	+	29.9314i	−0.919770	+	1.59309i	−0.799763	+	0.600316i	$0.795042\pi$
$354$		0			0
$355$	−1.88301	−	3.26146i	−0.0999396	−	0.173101i
$356$	6.19947	+	10.7378i	0.328571	+	0.569102i
$357$		0			0
$358$	1.09877	−	1.90312i	0.0580717	−	0.100583i
$359$	−25.6978			−1.35628			−0.678138	−	0.734935i	$-0.737213\pi$
$359$	−25.6978			−1.35628			−0.678138	+	0.734935i	$0.737213\pi$
$360$		0			0
$361$	−16.5791			−0.872584
$362$	7.86998	−	13.6312i	0.413637	−	0.716441i
$363$		0			0
$364$	−1.78776	−	3.09648i	−0.0937038	−	0.162300i
$365$	−0.212317	−	0.367745i	−0.0111132	−	0.0192486i
$366$		0			0
$367$	−5.67947	+	9.83713i	−0.296466	+	0.513494i	−0.975325	−	0.220775i	$-0.929141\pi$
$367$	−5.67947	+	9.83713i	−0.296466	+	0.513494i	0.678859	+	0.734269i	$0.262475\pi$
$368$	−3.50443			−0.182681
$369$		0			0
$370$	1.30492			0.0678393
$371$	−8.28298	+	14.3465i	−0.430031	+	0.744835i
$372$		0			0
$373$	14.3521	+	24.8585i	0.743122	+	1.28712i	0.951067	+	0.308984i	$0.0999889\pi$
$373$	14.3521	+	24.8585i	0.743122	+	1.28712i	−0.207946	+	0.978140i	$0.566678\pi$
$374$	9.90985	+	17.1644i	0.512426	+	0.887548i
$375$		0			0
$376$	−4.84824	+	8.39741i	−0.250029	+	0.433063i
$377$	−2.82703			−0.145599
$378$		0			0
$379$	−23.0493			−1.18396			−0.591981	−	0.805952i	$-0.701654\pi$
$379$	−23.0493			−1.18396			−0.591981	+	0.805952i	$0.701654\pi$
$380$	0.576254	−	0.998101i	0.0295612	−	0.0512015i
$381$		0			0
$382$	−3.92070	−	6.79085i	−0.200601	−	0.347450i
$383$	12.3025	+	21.3086i	0.628629	+	1.08882i	0.987827	+	0.155556i	$0.0497168\pi$
$383$	12.3025	+	21.3086i	0.628629	+	1.08882i	−0.359198	+	0.933261i	$0.616950\pi$
$384$		0			0
$385$	6.95875	−	12.0529i	0.354651	−	0.614273i
$386$	−16.5406			−0.841893
$387$		0			0
$388$	5.75476			0.292154
$389$	−18.5634	+	32.1528i	−0.941202	+	1.63021i	−0.178019	+	0.984027i	$0.556969\pi$
$389$	−18.5634	+	32.1528i	−0.941202	+	1.63021i	−0.763183	+	0.646183i	$0.776364\pi$
$390$		0			0
$391$	−7.63879	−	13.2308i	−0.386310	−	0.669109i
$392$	−5.04010	−	8.72971i	−0.254563	−	0.440917i
$393$		0			0
$394$	5.68810	−	9.85208i	0.286562	−	0.496340i
$395$	−5.00701			−0.251930
$396$		0			0
$397$	6.39258			0.320834			0.160417	−	0.987049i	$-0.448716\pi$
$397$	6.39258			0.320834			0.160417	+	0.987049i	$0.448716\pi$
$398$	−0.936258	+	1.62165i	−0.0469304	+	0.0812858i
$399$		0			0
$400$	2.22567	+	3.85497i	0.111283	+	0.192748i
$401$	−16.3433	−	28.3075i	−0.816148	−	1.41361i	−0.908501	−	0.417883i	$-0.862772\pi$
$401$	−16.3433	−	28.3075i	−0.816148	−	1.41361i	0.0923529	−	0.995726i	$-0.470561\pi$
$402$		0			0
$403$	−4.62791	+	8.01578i	−0.230533	+	0.399295i
$404$	−11.0395			−0.549238
$405$		0			0
$406$	−13.5047			−0.670226
$407$	4.00459	−	6.93616i	0.198500	−	0.343813i
$408$		0			0
$409$	10.9279	+	18.9277i	0.540350	+	0.935914i	0.998884	+	0.0472370i	$0.0150416\pi$
$409$	10.9279	+	18.9277i	0.540350	+	0.935914i	−0.458533	+	0.888677i	$0.651625\pi$
$410$	−0.954378	−	1.65303i	−0.0471334	−	0.0816374i
$411$		0			0
$412$	3.21073	−	5.56114i	0.158181	−	0.273978i
$413$	5.91612			0.291113
$414$		0			0
$415$	−6.83199			−0.335369
$416$	−0.432575	+	0.749242i	−0.0212087	+	0.0367346i
$417$		0			0
$418$	−3.53688	−	6.12605i	−0.172994	−	0.299635i
$419$	13.0555	+	22.6127i	0.637801	+	1.10470i	0.985914	+	0.167252i	$0.0534892\pi$
$419$	13.0555	+	22.6127i	0.637801	+	1.10470i	−0.348113	+	0.937453i	$0.613177\pi$
$420$		0			0
$421$	18.7488	−	32.4739i	0.913760	−	1.58268i	0.105054	−	0.994466i	$-0.466498\pi$
$421$	18.7488	−	32.4739i	0.913760	−	1.58268i	0.808706	−	0.588213i	$-0.200168\pi$
$422$	5.47014			0.266282
$423$		0			0
$424$	4.00839			0.194665
$425$	−9.70280	+	16.8057i	−0.470655	+	0.815198i
$426$		0			0
$427$	8.94535	+	15.4938i	0.432896	+	0.749798i
$428$	8.64614	+	14.9755i	0.417927	+	0.723871i
$429$		0			0
$430$	−1.01984	+	1.76641i	−0.0491808	+	0.0851837i
$431$	6.13162			0.295350			0.147675	−	0.989036i	$-0.452821\pi$
$431$	6.13162			0.295350			0.147675	+	0.989036i	$0.452821\pi$
$432$		0			0
$433$	−20.9401			−1.00632			−0.503158	−	0.864195i	$-0.667829\pi$
$433$	−20.9401			−1.00632			−0.503158	+	0.864195i	$0.667829\pi$
$434$	−22.1075	+	38.2914i	−1.06120	+	1.83804i
$435$		0			0
$436$	4.97285	+	8.61323i	0.238156	+	0.412499i
$437$	2.72632	+	4.72213i	0.130418	+	0.225890i
$438$		0			0
$439$	14.3574	−	24.8678i	0.685244	−	1.18688i	−0.288116	−	0.957595i	$-0.593029\pi$
$439$	14.3574	−	24.8678i	0.685244	−	1.18688i	0.973360	−	0.229282i	$-0.0736376\pi$
$440$	−3.36756			−0.160542
$441$		0			0
$442$	−3.77162			−0.179398
$443$	7.60262	−	13.1681i	0.361211	−	0.625636i	−0.626949	−	0.779060i	$-0.715697\pi$
$443$	7.60262	−	13.1681i	0.361211	−	0.625636i	0.988160	+	0.153424i	$0.0490300\pi$
$444$		0			0
$445$	−4.59207	−	7.95371i	−0.217685	−	0.377042i
$446$	0.632422	+	1.09539i	0.0299460	+	0.0518680i
$447$		0			0
$448$	−2.06641	+	3.57913i	−0.0976287	+	0.169098i
$449$	−12.4210			−0.586182			−0.293091	−	0.956085i	$-0.594684\pi$
$449$	−12.4210			−0.586182			−0.293091	+	0.956085i	$0.594684\pi$
$450$		0			0
$451$	−11.7154			−0.551656
$452$	−1.22567	+	2.12292i	−0.0576505	+	0.0998536i
$453$		0			0
$454$	−4.97072	−	8.60954i	−0.233287	−	0.404066i
$455$	1.32423	+	2.29363i	0.0620807	+	0.107527i
$456$		0			0
$457$	5.42219	−	9.39152i	0.253640	−	0.439317i	−0.710886	−	0.703308i	$-0.751706\pi$
$457$	5.42219	−	9.39152i	0.253640	−	0.439317i	0.964525	+	0.263991i	$0.0850390\pi$
$458$	−9.98234			−0.466444
$459$		0			0
$460$	2.59581			0.121030
$461$	4.10083	−	7.10284i	0.190995	−	0.330812i	−0.754586	−	0.656202i	$-0.772162\pi$
$461$	4.10083	−	7.10284i	0.190995	−	0.330812i	0.945580	+	0.325389i	$0.105495\pi$
$462$		0			0
$463$	16.8257	+	29.1429i	0.781956	+	1.35439i	0.930801	+	0.365527i	$0.119111\pi$
$463$	16.8257	+	29.1429i	0.781956	+	1.35439i	−0.148845	+	0.988861i	$0.547555\pi$
$464$	1.63383	+	2.82988i	0.0758489	+	0.131374i
$465$		0			0
$466$	13.5765	−	23.5152i	0.628920	−	1.08932i
$467$	10.8685			0.502935			0.251467	−	0.967866i	$-0.419087\pi$
$467$	10.8685			0.502935			0.251467	+	0.967866i	$0.419087\pi$
$468$		0			0
$469$	54.1896			2.50224
$470$	3.59119	−	6.22013i	0.165649	−	0.286913i
$471$		0			0
$472$	−0.715749	−	1.23971i	−0.0329450	−	0.0570624i
$473$	6.25945	+	10.8417i	0.287810	+	0.498501i
$474$		0			0
$475$	3.46298	−	5.99805i	0.158892	−	0.275209i
$476$	−18.0170			−0.825809
$477$		0			0
$478$	−19.5361			−0.893562
$479$	9.41394	−	16.3054i	0.430134	−	0.745014i	−0.566751	−	0.823889i	$-0.691800\pi$
$479$	9.41394	−	16.3054i	0.430134	−	0.745014i	0.996884	+	0.0788756i	$0.0251330\pi$
$480$		0			0
$481$	0.762061	+	1.31993i	0.0347470	+	0.0601835i
$482$	−8.10761	−	14.0428i	−0.369291	−	0.639631i
$483$		0			0
$484$	−4.83453	+	8.37365i	−0.219751	+	0.380621i
$485$	−4.26267			−0.193558
$486$		0			0
$487$	32.9521			1.49320			0.746601	−	0.665272i	$-0.231685\pi$
$487$	32.9521			1.49320			0.746601	+	0.665272i	$0.231685\pi$
$488$	2.16447	−	3.74897i	0.0979808	−	0.169708i
$489$		0			0
$490$	3.73330	+	6.46627i	0.168654	+	0.292116i
$491$	−17.3191	−	29.9975i	−0.781598	−	1.35377i	−0.931010	−	0.364993i	$-0.881072\pi$
$491$	−17.3191	−	29.9975i	−0.781598	−	1.35377i	0.149412	−	0.988775i	$-0.452262\pi$
$492$		0			0
$493$	−7.12270	+	12.3369i	−0.320790	+	0.555625i
$494$	1.34611			0.0605644
$495$		0			0
$496$	10.6985			0.480378
$497$	10.5062	−	18.1972i	0.471266	−	0.816256i
$498$		0			0
$499$	−11.8600	−	20.5422i	−0.530928	−	0.919593i	−0.999349	−	0.0360881i	$-0.988510\pi$
$499$	−11.8600	−	20.5422i	−0.530928	−	0.919593i	0.468421	−	0.883505i	$-0.344823\pi$
$500$	−3.50040	−	6.06287i	−0.156543	−	0.271140i
$501$		0			0
$502$	−11.7303	+	20.3174i	−0.523548	+	0.906811i
$503$	32.0133			1.42740			0.713701	−	0.700450i	$-0.247017\pi$
$503$	32.0133			1.42740			0.713701	+	0.700450i	$0.247017\pi$
$504$		0			0
$505$	8.17722			0.363881
$506$	7.96615	−	13.7978i	0.354138	−	0.613386i
$507$		0			0
$508$	−4.05136	−	7.01715i	−0.179750	−	0.311336i
$509$	−19.9106	−	34.4862i	−0.882522	−	1.52857i	−0.848528	−	0.529150i	$-0.822511\pi$
$509$	−19.9106	−	34.4862i	−0.882522	−	1.52857i	−0.0339933	−	0.999422i	$-0.510822\pi$
$510$		0			0
$511$	1.18462	−	2.05182i	0.0524044	−	0.0907670i
$512$	1.00000			0.0441942
$513$		0			0
$514$	21.9904			0.969956
$515$	−2.37825	+	4.11925i	−0.104798	+	0.181516i
$516$		0			0
$517$	−22.0417	−	38.1773i	−0.969392	−	1.67904i
$518$	3.64036	+	6.30529i	0.159948	+	0.277039i
$519$		0			0
$520$	0.320417	−	0.554979i	0.0140512	−	0.0243374i
$521$	3.63217			0.159128			0.0795642	−	0.996830i	$-0.474647\pi$
$521$	3.63217			0.159128			0.0795642	+	0.996830i	$0.474647\pi$
$522$		0			0
$523$	13.0021			0.568541			0.284270	−	0.958744i	$-0.408249\pi$
$523$	13.0021			0.568541			0.284270	+	0.958744i	$0.408249\pi$
$524$	7.94732	−	13.7652i	0.347180	−	0.601334i
$525$		0			0
$526$	11.7414	+	20.3366i	0.511948	+	0.886719i
$527$	23.3201	+	40.3916i	1.01584	+	1.75949i
$528$		0			0
$529$	5.35947	−	9.28287i	0.233020	−	0.403603i
$530$	−2.96910			−0.128969
$531$		0			0
$532$	6.43037			0.278792
$533$	1.11470	−	1.93072i	0.0482830	−	0.0836286i
$534$		0			0
$535$	−6.40437	−	11.0927i	−0.276885	−	0.479579i
$536$	−6.55601	−	11.3553i	−0.283177	−	0.490476i
$537$		0			0
$538$	−9.15004	+	15.8483i	−0.394486	+	0.683270i
$539$	45.8278			1.97394
$540$		0			0
$541$	−31.1320			−1.33847			−0.669235	−	0.743051i	$-0.733378\pi$
$541$	−31.1320			−1.33847			−0.669235	+	0.743051i	$0.733378\pi$
$542$	8.24124	−	14.2743i	0.353992	−	0.613132i
$543$		0			0
$544$	2.17975	+	3.77544i	0.0934560	+	0.161871i
$545$	−3.68349	−	6.38000i	−0.157784	−	0.273289i
$546$		0			0
$547$	−9.66819	+	16.7458i	−0.413382	+	0.715999i	−0.995257	−	0.0972795i	$-0.968986\pi$
$547$	−9.66819	+	16.7458i	−0.413382	+	0.715999i	0.581875	+	0.813278i	$0.302319\pi$
$548$	−12.3563			−0.527837
$549$		0			0
$550$	−20.2372			−0.862917
$551$	2.54213	−	4.40310i	0.108298	−	0.187578i
$552$		0			0
$553$	−13.9682	−	24.1937i	−0.593989	−	1.02882i
$554$	−5.63600	−	9.76184i	−0.239451	−	0.414741i
$555$		0			0
$556$	2.19170	−	3.79613i	0.0929487	−	0.160992i
$557$	−1.23702			−0.0524141			−0.0262070	−	0.999657i	$-0.508343\pi$
$557$	−1.23702			−0.0524141			−0.0262070	+	0.999657i	$0.508343\pi$
$558$		0			0
$559$	−2.38230			−0.100761
$560$	1.53063	−	2.65113i	0.0646810	−	0.112031i
$561$		0			0
$562$	0.362672	+	0.628167i	0.0152984	+	0.0264976i
$563$	10.4573	+	18.1126i	0.440724	+	0.763357i	0.997743	−	0.0671429i	$-0.0213883\pi$
$563$	10.4573	+	18.1126i	0.440724	+	0.763357i	−0.557019	+	0.830500i	$0.688055\pi$
$564$		0			0
$565$	0.907876	−	1.57249i	0.0381946	−	0.0661551i
$566$	−22.1382			−0.930539
$567$		0			0
$568$	−5.08426			−0.213331
$569$	3.06997	−	5.31734i	0.128700	−	0.222915i	−0.794473	−	0.607299i	$-0.792253\pi$
$569$	3.06997	−	5.31734i	0.128700	−	0.222915i	0.923173	+	0.384384i	$0.125586\pi$
$570$		0			0
$571$	−8.60102	−	14.8974i	−0.359941	−	0.623437i	0.628009	−	0.778206i	$-0.283870\pi$
$571$	−8.60102	−	14.8974i	−0.359941	−	0.623437i	−0.987951	+	0.154769i	$0.950537\pi$
$572$	−1.96663	−	3.40630i	−0.0822288	−	0.142424i
$573$		0			0
$574$	5.32491	−	9.22302i	0.222258	−	0.384961i
$575$	15.5994			0.650540
$576$		0			0
$577$	−14.1696			−0.589889			−0.294945	−	0.955514i	$-0.595301\pi$
$577$	−14.1696			−0.589889			−0.294945	+	0.955514i	$0.595301\pi$
$578$	−1.00263	+	1.73660i	−0.0417037	+	0.0722330i
$579$		0			0
$580$	−1.21021	−	2.09615i	−0.0502514	−	0.0870380i
$581$	−19.0594	−	33.0119i	−0.790717	−	1.36956i
$582$		0			0
$583$	−9.11172	+	15.7820i	−0.377369	+	0.653622i
$584$	−0.573273			−0.0237222
$585$		0			0
$586$	−6.55858			−0.270933
$587$	−16.8097	+	29.1153i	−0.693811	+	1.20172i	0.276769	+	0.960937i	$0.410736\pi$
$587$	−16.8097	+	29.1153i	−0.693811	+	1.20172i	−0.970580	+	0.240779i	$0.922597\pi$
$588$		0			0
$589$	−8.32306	−	14.4160i	−0.342946	−	0.594000i
$590$	0.530170	+	0.918281i	0.0218268	+	0.0378050i
$591$		0			0
$592$	0.880842	−	1.52566i	0.0362024	−	0.0627044i
$593$	6.82673			0.280340			0.140170	−	0.990127i	$-0.455235\pi$
$593$	6.82673			0.280340			0.140170	+	0.990127i	$0.455235\pi$
$594$		0			0
$595$	13.3456			0.547116
$596$	−3.41675	+	5.91798i	−0.139955	+	0.242410i
$597$		0			0
$598$	1.51593	+	2.62567i	0.0619910	+	0.107372i
$599$	14.6537	+	25.3809i	0.598733	+	1.03704i	0.993008	+	0.118043i	$0.0376622\pi$
$599$	14.6537	+	25.3809i	0.598733	+	1.03704i	−0.394276	+	0.918992i	$0.629005\pi$
$600$		0			0
$601$	2.31289	−	4.00604i	0.0943446	−	0.163410i	−0.814990	−	0.579475i	$-0.803258\pi$
$601$	2.31289	−	4.00604i	0.0943446	−	0.163410i	0.909335	+	0.416065i	$0.136591\pi$
$602$	−11.3803			−0.463825
$603$		0			0
$604$	−5.20653			−0.211851
$605$	3.58104	−	6.20253i	0.145590	−	0.252169i
$606$		0			0
$607$	6.77149	+	11.7286i	0.274846	+	0.476048i	0.970096	−	0.242720i	$-0.0780397\pi$
$607$	6.77149	+	11.7286i	0.274846	+	0.476048i	−0.695250	+	0.718768i	$0.744706\pi$
$608$	−0.777964	−	1.34747i	−0.0315506	−	0.0546473i
$609$		0			0
$610$	−1.60326	+	2.77694i	−0.0649143	+	0.112435i
$611$	8.38892			0.339379
$612$		0			0
$613$	29.8272			1.20471			0.602354	−	0.798229i	$-0.294230\pi$
$613$	29.8272			1.20471			0.602354	+	0.798229i	$0.294230\pi$
$614$	−3.98740	+	6.90639i	−0.160919	+	0.278719i
$615$		0			0
$616$	−9.39457	−	16.2719i	−0.378518	−	0.655612i
$617$	16.8401	+	29.1679i	0.677957	+	1.17426i	0.975595	+	0.219577i	$0.0704678\pi$
$617$	16.8401	+	29.1679i	0.677957	+	1.17426i	−0.297638	+	0.954679i	$0.596199\pi$
$618$		0			0
$619$	−17.8083	+	30.8448i	−0.715775	+	1.23976i	0.246885	+	0.969045i	$0.420593\pi$
$619$	−17.8083	+	30.8448i	−0.715775	+	1.23976i	−0.962660	+	0.270714i	$0.912740\pi$
$620$	−7.92461			−0.318260
$621$		0			0
$622$	14.1480			0.567285
$623$	25.6213	−	44.3774i	1.02650	−	1.77794i
$624$		0			0
$625$	−8.53552	−	14.7839i	−0.341421	−	0.591358i
$626$	−12.0208	−	20.8206i	−0.480447	−	0.832158i
$627$		0			0
$628$	−1.98607	+	3.43998i	−0.0792530	+	0.137270i
$629$	7.68006			0.306224
$630$		0			0
$631$	−39.3091			−1.56487			−0.782436	−	0.622731i	$-0.786023\pi$
$631$	−39.3091			−1.56487			−0.782436	+	0.622731i	$0.786023\pi$
$632$	−3.37983	+	5.85403i	−0.134442	+	0.232861i
$633$		0			0
$634$	−9.09636	−	15.7554i	−0.361263	−	0.625725i
$635$	3.00092	+	5.19775i	0.119088	+	0.206266i
$636$		0			0
$637$	−4.36044	+	7.55251i	−0.172767	+	0.299241i
$638$	−14.8559			−0.588150
$639$		0			0
$640$	−0.740720			−0.0292795
$641$	13.7978	−	23.8986i	0.544982	−	0.943936i	−0.453626	−	0.891192i	$-0.649870\pi$
$641$	13.7978	−	23.8986i	0.544982	−	0.943936i	0.998608	−	0.0527443i	$-0.0167968\pi$
$642$		0			0
$643$	−16.2824	−	28.2020i	−0.642117	−	1.11218i	−0.984959	−	0.172786i	$-0.944723\pi$
$643$	−16.2824	−	28.2020i	−0.642117	−	1.11218i	0.342843	−	0.939393i	$-0.388610\pi$
$644$	7.24160	+	12.5428i	0.285359	+	0.494256i
$645$		0			0
$646$	3.39153	−	5.87431i	0.133438	−	0.231122i
$647$	−11.8337			−0.465232			−0.232616	−	0.972569i	$-0.574728\pi$
$647$	−11.8337			−0.465232			−0.232616	+	0.972569i	$0.574728\pi$
$648$		0			0
$649$	6.50805			0.255463
$650$	1.92554	−	3.33513i	0.0755257	−	0.130814i
$651$		0			0
$652$	−1.17354	−	2.03262i	−0.0459592	−	0.0796037i
$653$	1.01566	+	1.75917i	0.0397458	+	0.0688418i	0.885214	−	0.465184i	$-0.154012\pi$
$653$	1.01566	+	1.75917i	0.0397458	+	0.0688418i	−0.845468	+	0.534026i	$0.820679\pi$
$654$		0			0
$655$	−5.88674	+	10.1961i	−0.230014	+	0.398396i
$656$	−2.57689			−0.100611
$657$		0			0
$658$	40.0738			1.56224
$659$	−24.1787	+	41.8787i	−0.941867	+	1.63136i	−0.179961	+	0.983674i	$0.557597\pi$
$659$	−24.1787	+	41.8787i	−0.941867	+	1.63136i	−0.761906	+	0.647688i	$0.775736\pi$
$660$		0			0
$661$	8.53657	+	14.7858i	0.332034	+	0.575100i	0.982911	−	0.184084i	$-0.0589318\pi$
$661$	8.53657	+	14.7858i	0.332034	+	0.575100i	−0.650876	+	0.759184i	$0.725598\pi$
$662$	−8.98035	−	15.5544i	−0.349031	−	0.604540i
$663$		0			0
$664$	−4.61172	+	7.98773i	−0.178969	+	0.309984i
$665$	−4.76311			−0.184705
$666$		0			0
$667$	11.4513			0.443397
$668$	0.526311	−	0.911597i	0.0203636	−	0.0352708i
$669$		0			0
$670$	4.85617	+	8.41114i	0.187610	+	0.324951i
$671$	9.84037	+	17.0440i	0.379883	+	0.657977i
$672$		0			0
$673$	14.9049	−	25.8160i	0.574541	−	0.995134i	−0.421551	−	0.906805i	$-0.638514\pi$
$673$	14.9049	−	25.8160i	0.574541	−	0.995134i	0.996091	−	0.0883288i	$-0.0281526\pi$
$674$	−23.4959			−0.905027
$675$		0			0
$676$	−12.2515			−0.471212
$677$	−3.98367	+	6.89992i	−0.153105	+	0.265185i	−0.932367	−	0.361512i	$-0.882261\pi$
$677$	−3.98367	+	6.89992i	−0.153105	+	0.265185i	0.779262	+	0.626698i	$0.215594\pi$
$678$		0			0
$679$	−11.8917	−	20.5970i	−0.456361	−	0.790441i
$680$	−1.61459	−	2.79654i	−0.0619165	−	0.107243i
$681$		0			0
$682$	−24.3195	+	42.1225i	−0.931240	+	1.61296i
$683$	−30.3186			−1.16011			−0.580054	−	0.814578i	$-0.696968\pi$
$683$	−30.3186			−1.16011			−0.580054	+	0.814578i	$0.696968\pi$
$684$		0			0
$685$	9.15260			0.349703
$686$	−6.36495	+	11.0244i	−0.243015	+	0.420914i
$687$		0			0
$688$	1.37682	+	2.38471i	0.0524906	+	0.0909164i
$689$	−1.73393	−	3.00325i	−0.0660575	−	0.114415i
$690$		0			0
$691$	−13.2595	+	22.9662i	−0.504416	+	0.873674i	0.495571	+	0.868567i	$0.334959\pi$
$691$	−13.2595	+	22.9662i	−0.504416	+	0.873674i	−0.999987	+	0.00510653i	$0.998375\pi$
$692$	6.83289			0.259747
$693$		0			0
$694$	8.33241			0.316294
$695$	−1.62344	+	2.81187i	−0.0615804	+	0.106660i
$696$		0			0
$697$	−5.61698	−	9.72890i	−0.212758	−	0.368508i
$698$	2.64749	+	4.58558i	0.100209	+	0.173567i
$699$		0			0
$700$	9.19828	−	15.9319i	0.347662	−	0.602169i
$701$	46.2262			1.74594			0.872971	−	0.487773i	$-0.162191\pi$
$701$	46.2262			1.74594			0.872971	+	0.487773i	$0.162191\pi$
$702$		0			0
$703$	−2.74105			−0.103381
$704$	−2.27316	+	3.93723i	−0.0856730	+	0.148390i
$705$		0			0
$706$	−17.2809	−	29.9314i	−0.650376	−	1.12648i
$707$	22.8122	+	39.5119i	0.857942	+	1.48600i
$708$		0			0
$709$	−15.2702	+	26.4488i	−0.573484	+	0.993304i	0.422720	+	0.906260i	$0.361075\pi$
$709$	−15.2702	+	26.4488i	−0.573484	+	0.993304i	−0.996204	+	0.0870438i	$0.972258\pi$
$710$	3.76601			0.141336
$711$		0			0
$712$	−12.3989			−0.464670
$713$	18.7461	−	32.4692i	0.702048	−	1.21598i
$714$		0			0
$715$	1.45672	+	2.52311i	0.0544783	+	0.0943591i
$716$	1.09877	+	1.90312i	0.0410629	+	0.0711230i
$717$		0			0
$718$	12.8489	−	22.2549i	0.479516	−	0.830546i
$719$	6.92512			0.258263			0.129132	−	0.991627i	$-0.458781\pi$
$719$	6.92512			0.258263			0.129132	+	0.991627i	$0.458781\pi$
$720$		0			0
$721$	−26.5387			−0.988353
$722$	8.28954	−	14.3579i	0.308505	−	0.534346i
$723$		0			0
$724$	7.86998	+	13.6312i	0.292486	+	0.506600i
$725$	−7.27274	−	12.5968i	−0.270103	−	0.467832i
$726$		0			0
$727$	10.8500	−	18.7927i	0.402403	−	0.696983i	−0.591612	−	0.806223i	$-0.701508\pi$
$727$	10.8500	−	18.7927i	0.402403	−	0.696983i	0.994015	+	0.109240i	$0.0348417\pi$
$728$	3.57551			0.132517
$729$		0			0
$730$	0.424635			0.0157164
$731$	−6.00223	+	10.3962i	−0.222000	+	0.384516i
$732$		0			0
$733$	−19.6023	−	33.9522i	−0.724028	−	1.25405i	−0.959373	−	0.282142i	$-0.908955\pi$
$733$	−19.6023	−	33.9522i	−0.724028	−	1.25405i	0.235344	−	0.971912i	$-0.424378\pi$
$734$	−5.67947	−	9.83713i	−0.209633	−	0.363095i
$735$		0			0
$736$	1.75222	−	3.03493i	0.0645876	−	0.111869i
$737$	59.6115			2.19582
$738$		0			0
$739$	−30.8079			−1.13329			−0.566643	−	0.823964i	$-0.691758\pi$
$739$	−30.8079			−1.13329			−0.566643	+	0.823964i	$0.691758\pi$
$740$	−0.652458	+	1.13009i	−0.0239848	+	0.0415429i
$741$		0			0
$742$	−8.28298	−	14.3465i	−0.304078	−	0.526678i
$743$	−15.9652	−	27.6526i	−0.585708	−	1.01448i	−0.994787	−	0.101977i	$-0.967483\pi$
$743$	−15.9652	−	27.6526i	−0.585708	−	1.01448i	0.409079	−	0.912499i	$-0.365850\pi$
$744$		0			0
$745$	2.53085	−	4.38357i	0.0927233	−	0.160601i
$746$	−28.7041			−1.05093
$747$		0			0
$748$	−19.8197			−0.724680
$749$	35.7329	−	61.8912i	1.30565	−	2.26146i
$750$		0			0
$751$	−1.51747	−	2.62834i	−0.0553733	−	0.0959094i	0.837010	−	0.547188i	$-0.184302\pi$
$751$	−1.51747	−	2.62834i	−0.0553733	−	0.0959094i	−0.892383	+	0.451278i	$0.850968\pi$
$752$	−4.84824	−	8.39741i	−0.176797	−	0.306222i
$753$		0			0
$754$	1.41351	−	2.44828i	0.0514771	−	0.0891609i
$755$	3.85659			0.140356
$756$		0			0
$757$	10.7254			0.389823			0.194912	−	0.980821i	$-0.437558\pi$
$757$	10.7254			0.389823			0.194912	+	0.980821i	$0.437558\pi$
$758$	11.5246	−	19.9613i	0.418594	−	0.725026i
$759$		0			0
$760$	0.576254	+	0.998101i	0.0209029	+	0.0362049i
$761$	−13.5499	−	23.4692i	−0.491185	−	0.850757i	0.508763	−	0.860906i	$-0.330103\pi$
$761$	−13.5499	−	23.4692i	−0.491185	−	0.850757i	−0.999948	+	0.0101489i	$0.996769\pi$
$762$		0			0
$763$	20.5519	−	35.5969i	0.744029	−	1.28870i
$764$	7.84140			0.283692
$765$		0			0
$766$	−24.6050			−0.889015
$767$	−0.619231	+	1.07254i	−0.0223591	+	0.0387271i
$768$		0			0
$769$	−13.4648	−	23.3217i	−0.485553	−	0.841002i	0.514310	−	0.857605i	$-0.328048\pi$
$769$	−13.4648	−	23.3217i	−0.485553	−	0.841002i	−0.999862	+	0.0166029i	$0.994715\pi$
$770$	6.95875	+	12.0529i	0.250776	+	0.434357i
$771$		0			0
$772$	8.27028	−	14.3246i	0.297654	−	0.515552i
$773$	−14.3966			−0.517811			−0.258906	−	0.965903i	$-0.583362\pi$
$773$	−14.3966			−0.517811			−0.258906	+	0.965903i	$0.583362\pi$
$774$		0			0
$775$	−47.6227			−1.71066
$776$	−2.87738	+	4.98377i	−0.103292	+	0.178907i
$777$		0			0
$778$	−18.5634	−	32.1528i	−0.665530	−	1.15273i
$779$	2.00473	+	3.47229i	0.0718269	+	0.124408i
$780$		0			0
$781$	11.5573	−	20.0179i	0.413554	−	0.716297i
$782$	15.2776			0.546325
$783$		0			0
$784$	10.0802			0.360007
$785$	1.47113	−	2.54807i	0.0525067	−	0.0909443i
$786$		0			0
$787$	4.44864	+	7.70528i	0.158577	+	0.274663i	0.934356	−	0.356342i	$-0.115976\pi$
$787$	4.44864	+	7.70528i	0.158577	+	0.274663i	−0.775779	+	0.631005i	$0.782643\pi$
$788$	5.68810	+	9.85208i	0.202630	+	0.350966i
$789$		0			0
$790$	2.50351	−	4.33620i	0.0890708	−	0.154275i
$791$	10.1309			0.360214
$792$		0			0
$793$	−3.74518			−0.132995
$794$	−3.19629	+	5.53614i	−0.113432	+	0.196470i
$795$		0			0
$796$	−0.936258	−	1.62165i	−0.0331848	−	0.0574777i
$797$	−15.0286	−	26.0303i	−0.532340	−	0.922039i	−0.999287	−	0.0377541i	$-0.987980\pi$
$797$	−15.0286	−	26.0303i	−0.532340	−	0.922039i	0.466948	−	0.884285i	$-0.345354\pi$
$798$		0			0
$799$	21.1359	−	36.6085i	0.747735	−	1.29512i
$800$	−4.45133			−0.157378
$801$		0			0
$802$	32.6867			1.15421
$803$	1.30314	−	2.25711i	0.0459869	−	0.0796516i
$804$		0			0
$805$	−5.36400	−	9.29072i	−0.189056	−	0.327455i
$806$	−4.62791	−	8.01578i	−0.163011	−	0.282344i
$807$		0			0
$808$	5.51977	−	9.56053i	0.194185	−	0.336338i
$809$	−22.4607			−0.789676			−0.394838	−	0.918751i	$-0.629199\pi$
$809$	−22.4607			−0.789676			−0.394838	+	0.918751i	$0.629199\pi$
$810$		0			0
$811$	21.1008			0.740949			0.370474	−	0.928843i	$-0.379195\pi$
$811$	21.1008			0.740949			0.370474	+	0.928843i	$0.379195\pi$
$812$	6.75234	−	11.6954i	0.236961	−	0.410428i
$813$		0			0
$814$	4.00459	+	6.93616i	0.140361	+	0.243112i
$815$	0.869262	+	1.50561i	0.0304489	+	0.0527391i
$816$		0			0
$817$	2.14223	−	3.71044i	0.0749470	−	0.129812i
$818$	−21.8558			−0.764171
$819$		0			0
$820$	1.90876			0.0666567
$821$	3.36708	−	5.83195i	0.117512	−	0.203536i	−0.801269	−	0.598304i	$-0.795842\pi$
$821$	3.36708	−	5.83195i	0.117512	−	0.203536i	0.918781	+	0.394768i	$0.129175\pi$
$822$		0			0
$823$	−15.1302	−	26.2062i	−0.527404	−	0.913490i	−0.999490	−	0.0319378i	$-0.989832\pi$
$823$	−15.1302	−	26.2062i	−0.527404	−	0.913490i	0.472086	−	0.881553i	$-0.343501\pi$
$824$	3.21073	+	5.56114i	0.111851	+	0.193732i
$825$		0			0
$826$	−2.95806	+	5.12351i	−0.102924	+	0.178270i
$827$	5.64740			0.196379			0.0981897	−	0.995168i	$-0.468695\pi$
$827$	5.64740			0.196379			0.0981897	+	0.995168i	$0.468695\pi$
$828$		0			0
$829$	22.6214			0.785674			0.392837	−	0.919608i	$-0.371494\pi$
$829$	22.6214			0.785674			0.392837	+	0.919608i	$0.371494\pi$
$830$	3.41599	−	5.91668i	0.118571	−	0.205371i
$831$		0			0
$832$	−0.432575	−	0.749242i	−0.0149968	−	0.0259753i
$833$	21.9723	+	38.0572i	0.761296	+	1.31860i
$834$		0			0
$835$	−0.389849	+	0.675239i	−0.0134913	+	0.0233676i
$836$	7.07375			0.244651
$837$		0			0
$838$	−26.1109			−0.901987
$839$	5.30940	−	9.19615i	0.183301	−	0.317486i	−0.759702	−	0.650272i	$-0.774655\pi$
$839$	5.30940	−	9.19615i	0.183301	−	0.317486i	0.943003	+	0.332785i	$0.107988\pi$
$840$		0			0
$841$	9.16117	+	15.8676i	0.315902	+	0.547159i
$842$	18.7488	+	32.4739i	0.646126	+	1.11912i
$843$		0			0
$844$	−2.73507	+	4.73728i	−0.0941450	+	0.163064i
$845$	9.07495			0.312188
$846$		0			0
$847$	39.9605			1.37306
$848$	−2.00419	+	3.47137i	−0.0688243	+	0.119207i
$849$		0			0
$850$	−9.70280	−	16.8057i	−0.332803	−	0.576432i
$851$	−3.08685	−	5.34659i	−0.105816	−	0.183279i
$852$		0			0
$853$	8.55572	−	14.8189i	0.292942	−	0.507391i	−0.681562	−	0.731760i	$-0.738699\pi$
$853$	8.55572	−	14.8189i	0.292942	−	0.507391i	0.974504	+	0.224370i	$0.0720323\pi$
$854$	−17.8907			−0.612207
$855$		0			0
$856$	−17.2923			−0.591038
$857$	−16.6385	+	28.8187i	−0.568359	+	0.984427i	0.428370	+	0.903604i	$0.359088\pi$
$857$	−16.6385	+	28.8187i	−0.568359	+	0.984427i	−0.996728	+	0.0808229i	$0.974245\pi$
$858$		0			0
$859$	0.371521	+	0.643493i	0.0126761	+	0.0219557i	0.872294	−	0.488982i	$-0.162632\pi$
$859$	0.371521	+	0.643493i	0.0126761	+	0.0219557i	−0.859618	+	0.510938i	$0.829298\pi$
$860$	−1.01984	−	1.76641i	−0.0347761	−	0.0602340i
$861$		0			0
$862$	−3.06581	+	5.31014i	−0.104422	+	0.180864i
$863$	14.4375			0.491457			0.245728	−	0.969339i	$-0.420973\pi$
$863$	14.4375			0.491457			0.245728	+	0.969339i	$0.420973\pi$
$864$		0			0
$865$	−5.06126			−0.172088
$866$	10.4700	−	18.1346i	0.355786	−	0.616240i
$867$		0			0
$868$	−22.1075	−	38.2914i	−0.750378	−	1.29969i
$869$	−15.3658	−	26.6143i	−0.521249	−	0.902829i
$870$		0			0
$871$	−5.67194	+	9.82408i	−0.192186	+	0.332876i
$872$	−9.94570			−0.336804
$873$		0			0
$874$	−5.45265			−0.184439
$875$	−14.4665	+	25.0567i	−0.489057	+	0.847072i
$876$		0			0
$877$	14.6156	+	25.3150i	0.493535	+	0.854827i	0.999972	−	0.00744930i	$-0.00237121\pi$
$877$	14.6156	+	25.3150i	0.493535	+	0.854827i	−0.506437	+	0.862277i	$0.669038\pi$
$878$	14.3574	+	24.8678i	0.484540	+	0.839249i
$879$		0			0
$880$	1.68378	−	2.91639i	0.0567601	−	0.0983114i
$881$	−6.05530			−0.204008			−0.102004	−	0.994784i	$-0.532525\pi$
$881$	−6.05530			−0.204008			−0.102004	+	0.994784i	$0.532525\pi$
$882$		0			0
$883$	6.13268			0.206381			0.103190	−	0.994662i	$-0.467095\pi$
$883$	6.13268			0.206381			0.103190	+	0.994662i	$0.467095\pi$
$884$	1.88581	−	3.26632i	0.0634267	−	0.109858i
$885$		0			0
$886$	7.60262	+	13.1681i	0.255415	+	0.442392i
$887$	−27.2638	−	47.2224i	−0.915430	−	1.58557i	−0.806270	−	0.591548i	$-0.798517\pi$
$887$	−27.2638	−	47.2224i	−0.915430	−	1.58557i	−0.109161	−	0.994024i	$-0.534816\pi$
$888$		0			0
$889$	−16.7435	+	29.0006i	−0.561560	+	0.972650i
$890$	9.18415			0.307853
$891$		0			0
$892$	−1.26484			−0.0423501
$893$	−7.54352	+	13.0658i	−0.252434	+	0.437229i
$894$		0			0
$895$	−0.813880	−	1.40968i	−0.0272050	−	0.0471204i
$896$	−2.06641	−	3.57913i	−0.0690339	−	0.119570i
$897$		0			0
$898$	6.21048	−	10.7569i	0.207247	−	0.358962i
$899$	−34.9592			−1.16596
$900$		0			0
$901$	−17.4746			−0.582163
$902$	5.85769	−	10.1458i	0.195040	−	0.337819i
$903$		0			0
$904$	−1.22567	−	2.12292i	−0.0407651	−	0.0706072i
$905$	−5.82946	−	10.0969i	−0.193778	−	0.335633i
$906$		0			0
$907$	1.93610	−	3.35343i	0.0642872	−	0.111349i	−0.832090	−	0.554640i	$-0.812856\pi$
$907$	1.93610	−	3.35343i	0.0642872	−	0.111349i	0.896378	+	0.443291i	$0.146189\pi$
$908$	9.94144			0.329918
$909$		0			0
$910$	−2.64845			−0.0877954
$911$	2.17667	−	3.77010i	0.0721162	−	0.124909i	−0.827712	−	0.561153i	$-0.810358\pi$
$911$	2.17667	−	3.77010i	0.0721162	−	0.124909i	0.899829	+	0.436244i	$0.143691\pi$
$912$		0			0
$913$	−20.9664	−	36.3148i	−0.693885	−	1.20184i
$914$	5.42219	+	9.39152i	0.179350	+	0.310644i
$915$		0			0
$916$	4.99117	−	8.64496i	0.164913	−	0.285638i
$917$	−65.6896			−2.16926
$918$		0			0
$919$	23.4247			0.772710			0.386355	−	0.922350i	$-0.373734\pi$
$919$	23.4247			0.772710			0.386355	+	0.922350i	$0.373734\pi$
$920$	−1.29790	+	2.24803i	−0.0427906	+	0.0741155i
$921$		0			0
$922$	4.10083	+	7.10284i	0.135054	+	0.233920i
$923$	2.19932	+	3.80934i	0.0723916	+	0.125386i
$924$		0			0
$925$	−3.92092	+	6.79124i	−0.128919	+	0.223294i
$926$	−33.6514			−1.10585
$927$		0			0
$928$	−3.26767			−0.107266
$929$	20.3943	−	35.3239i	0.669114	−	1.15894i	−0.309039	−	0.951049i	$-0.600007\pi$
$929$	20.3943	−	35.3239i	0.669114	−	1.15894i	0.978152	−	0.207889i	$-0.0666594\pi$
$930$		0			0
$931$	−7.84203	−	13.5828i	−0.257012	−	0.445158i
$932$	13.5765	+	23.5152i	0.444714	+	0.770267i
$933$		0			0
$934$	−5.43426	+	9.41241i	−0.177814	+	0.307983i
$935$	14.6809			0.480115
$936$		0			0
$937$	−20.4961			−0.669577			−0.334789	−	0.942293i	$-0.608665\pi$
$937$	−20.4961			−0.669577			−0.334789	+	0.942293i	$0.608665\pi$
$938$	−27.0948	+	46.9296i	−0.884677	+	1.53231i
$939$		0			0
$940$	3.59119	+	6.22013i	0.117132	+	0.202878i
$941$	−4.30508	−	7.45662i	−0.140342	−	0.243079i	0.787284	−	0.616591i	$-0.211487\pi$
$941$	−4.30508	−	7.45662i	−0.140342	−	0.243079i	−0.927625	+	0.373512i	$0.878153\pi$
$942$		0			0
$943$	−4.51527	+	7.82068i	−0.147038	+	0.254677i
$944$	1.43150			0.0465913
$945$		0			0
$946$	−12.5189			−0.407024
$947$	−20.5561	+	35.6041i	−0.667982	+	1.15698i	0.310485	+	0.950578i	$0.399508\pi$
$947$	−20.5561	+	35.6041i	−0.667982	+	1.15698i	−0.978467	+	0.206401i	$0.933825\pi$
$948$		0			0
$949$	0.247984	+	0.429520i	0.00804989	+	0.0139428i
$950$	3.46298	+	5.99805i	0.112354	+	0.194602i
$951$		0			0
$952$	9.00852	−	15.6032i	0.291968	−	0.505703i
$953$	27.6750			0.896480			0.448240	−	0.893913i	$-0.352051\pi$
$953$	27.6750			0.896480			0.448240	+	0.893913i	$0.352051\pi$
$954$		0			0
$955$	−5.80829			−0.187952
$956$	9.76807	−	16.9188i	0.315922	−	0.547193i
$957$		0			0
$958$	9.41394	+	16.3054i	0.304151	+	0.526804i
$959$	25.5333	+	44.2249i	0.824512	+	1.42810i
$960$		0			0
$961$	−41.7291	+	72.2770i	−1.34610	+	2.33152i
$962$	−1.52412			−0.0491397
$963$		0			0
$964$	16.2152			0.522257
$965$	−6.12597	+	10.6105i	−0.197202	+	0.341564i
$966$		0			0
$967$	−29.8889	−	51.7691i	−0.961162	−	1.66478i	−0.719591	−	0.694399i	$-0.755671\pi$
$967$	−29.8889	−	51.7691i	−0.961162	−	1.66478i	−0.241571	−	0.970383i	$-0.577663\pi$
$968$	−4.83453	−	8.37365i	−0.155388	−	0.269139i
$969$		0			0
$970$	2.13133	−	3.69158i	0.0684330	−	0.118529i
$971$	−3.80514			−0.122113			−0.0610564	−	0.998134i	$-0.519447\pi$
$971$	−3.80514			−0.122113			−0.0610564	+	0.998134i	$0.519447\pi$
$972$		0			0
$973$	−18.1158			−0.580765
$974$	−16.4760	+	28.5373i	−0.527926	+	0.914396i
$975$		0			0
$976$	2.16447	+	3.74897i	0.0692829	+	0.120001i
$977$	−14.1900	−	24.5778i	−0.453979	−	0.786314i	0.544650	−	0.838663i	$-0.316662\pi$
$977$	−14.1900	−	24.5778i	−0.453979	−	0.786314i	−0.998629	+	0.0523491i	$0.983329\pi$
$978$		0			0
$979$	28.1848	−	48.8175i	0.900790	−	1.56021i
$980$	−7.46661			−0.238512
$981$		0			0
$982$	34.6381			1.10535
$983$	−8.86886	+	15.3613i	−0.282873	+	0.489950i	−0.972091	−	0.234604i	$-0.924621\pi$
$983$	−8.86886	+	15.3613i	−0.282873	+	0.489950i	0.689218	+	0.724554i	$0.257954\pi$
$984$		0			0
$985$	−4.21329	−	7.29763i	−0.134247	−	0.232522i
$986$	−7.12270	−	12.3369i	−0.226833	−	0.392886i
$987$		0			0
$988$	−0.673056	+	1.16577i	−0.0214128	+	0.0370880i
$989$	9.64992			0.306850
$990$		0			0
$991$	−13.1921			−0.419059			−0.209530	−	0.977802i	$-0.567193\pi$
$991$	−13.1921			−0.419059			−0.209530	+	0.977802i	$0.567193\pi$
$992$	−5.34926	+	9.26519i	−0.169839	+	0.294170i
$993$		0			0
$994$	10.5062	+	18.1972i	0.333235	+	0.577180i
$995$	0.693505	+	1.20119i	0.0219856	+	0.0380802i
$996$		0			0
$997$	−29.4911	+	51.0801i	−0.933992	+	1.61772i	−0.157571	+	0.987508i	$0.550366\pi$
$997$	−29.4911	+	51.0801i	−0.933992	+	1.61772i	−0.776421	+	0.630214i	$0.782967\pi$
$998$	23.7200			0.750845
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1458.2.c.f.487.4		12
3.2	odd	2		1458.2.c.g.487.3		12
9.2	odd	6		1458.2.a.f.1.4		6
9.4	even	3	inner	1458.2.c.f.973.4		12
9.5	odd	6		1458.2.c.g.973.3		12
9.7	even	3		1458.2.a.g.1.3		6
27.2	odd	18		162.2.e.b.37.1		12
27.4	even	9		486.2.e.h.55.1		12
27.5	odd	18		162.2.e.b.127.1		12
27.7	even	9		486.2.e.f.271.1		12
27.11	odd	18		486.2.e.e.433.2		12
27.13	even	9		486.2.e.f.217.1		12
27.14	odd	18		486.2.e.g.217.2		12
27.16	even	9		486.2.e.h.433.1		12
27.20	odd	18		486.2.e.g.271.2		12
27.22	even	9		54.2.e.b.43.1	✓	12
27.23	odd	18		486.2.e.e.55.2		12
27.25	even	9		54.2.e.b.49.1	yes	12
108.79	odd	18		432.2.u.b.49.2		12
108.103	odd	18		432.2.u.b.97.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.1	✓	12	27.22	even	9
54.2.e.b.49.1	yes	12	27.25	even	9
162.2.e.b.37.1		12	27.2	odd	18
162.2.e.b.127.1		12	27.5	odd	18
432.2.u.b.49.2		12	108.79	odd	18
432.2.u.b.97.2		12	108.103	odd	18
486.2.e.e.55.2		12	27.23	odd	18
486.2.e.e.433.2		12	27.11	odd	18
486.2.e.f.217.1		12	27.13	even	9
486.2.e.f.271.1		12	27.7	even	9
486.2.e.g.217.2		12	27.14	odd	18
486.2.e.g.271.2		12	27.20	odd	18
486.2.e.h.55.1		12	27.4	even	9
486.2.e.h.433.1		12	27.16	even	9
1458.2.a.f.1.4		6	9.2	odd	6
1458.2.a.g.1.3		6	9.7	even	3
1458.2.c.f.487.4		12	1.1	even	1	trivial
1458.2.c.f.973.4		12	9.4	even	3	inner
1458.2.c.g.487.3		12	3.2	odd	2
1458.2.c.g.973.3		12	9.5	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:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1458.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.370360 + 0.641483i) q^{5} +(-2.06641 + 3.57913i) q^{7} +1.00000 q^{8} -0.740720 q^{10} +(-2.27316 + 3.93723i) q^{11} +(-0.432575 - 0.749242i) q^{13} +(-2.06641 - 3.57913i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.35950 q^{17} +1.55593 q^{19} +(0.370360 - 0.641483i) q^{20} +(-2.27316 - 3.93723i) q^{22} +(1.75222 + 3.03493i) q^{23} +(2.22567 - 3.85497i) q^{25} +0.865150 q^{26} +4.13282 q^{28} +(1.63383 - 2.82988i) q^{29} +(-5.34926 - 9.26519i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.17975 - 3.77544i) q^{34} -3.06126 q^{35} -1.76168 q^{37} +(-0.777964 + 1.34747i) q^{38} +(0.370360 + 0.641483i) q^{40} +(1.28845 + 2.23165i) q^{41} +(1.37682 - 2.38471i) q^{43} +4.54632 q^{44} -3.50443 q^{46} +(-4.84824 + 8.39741i) q^{47} +(-5.04010 - 8.72971i) q^{49} +(2.22567 + 3.85497i) q^{50} +(-0.432575 + 0.749242i) q^{52} +4.00839 q^{53} -3.36756 q^{55} +(-2.06641 + 3.57913i) q^{56} +(1.63383 + 2.82988i) q^{58} +(-0.715749 - 1.23971i) q^{59} +(2.16447 - 3.74897i) q^{61} +10.6985 q^{62} +1.00000 q^{64} +(0.320417 - 0.554979i) q^{65} +(-6.55601 - 11.3553i) q^{67} +(2.17975 + 3.77544i) q^{68} +(1.53063 - 2.65113i) q^{70} -5.08426 q^{71} -0.573273 q^{73} +(0.880842 - 1.52566i) q^{74} +(-0.777964 - 1.34747i) q^{76} +(-9.39457 - 16.2719i) q^{77} +(-3.37983 + 5.85403i) q^{79} -0.740720 q^{80} -2.57689 q^{82} +(-4.61172 + 7.98773i) q^{83} +(-1.61459 - 2.79654i) q^{85} +(1.37682 + 2.38471i) q^{86} +(-2.27316 + 3.93723i) q^{88} -12.3989 q^{89} +3.57551 q^{91} +(1.75222 - 3.03493i) q^{92} +(-4.84824 - 8.39741i) q^{94} +(0.576254 + 0.998101i) q^{95} +(-2.87738 + 4.98377i) q^{97} +10.0802 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 12 q^{8} + 6 q^{10} - 3 q^{11} - 9 q^{13} - 6 q^{14} - 6 q^{16} + 12 q^{17} + 18 q^{19} - 3 q^{20} - 3 q^{22} + 3 q^{23} - 15 q^{25} + 18 q^{26} + 12 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 12 * q^8 + 6 * q^10 - 3 * q^11 - 9 * q^13 - 6 * q^14 - 6 * q^16 + 12 * q^17 + 18 * q^19 - 3 * q^20 - 3 * q^22 + 3 * q^23 - 15 * q^25 + 18 * q^26 + 12 * q^28 - 3 * q^29 - 12 * q^31 - 6 * q^32 - 6 * q^34 - 6 * q^35 + 30 * q^37 - 9 * q^38 - 3 * q^40 - 3 * q^41 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 9 * q^47 - 12 * q^49 - 15 * q^50 - 9 * q^52 - 12 * q^53 + 18 * q^55 - 6 * q^56 - 3 * q^58 + 3 * q^59 - 12 * q^61 + 24 * q^62 + 12 * q^64 + 3 * q^65 - 21 * q^67 - 6 * q^68 + 3 * q^70 - 24 * q^71 + 42 * q^73 - 15 * q^74 - 9 * q^76 + 3 * q^77 + 6 * q^80 + 6 * q^82 + 27 * q^83 - 12 * q^86 - 3 * q^88 - 24 * q^89 + 12 * q^91 + 3 * q^92 + 9 * q^94 + 30 * q^95 - 18 * q^97 + 24 * q^98

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