LMFDB - Embedded newform 216.3.j.a.125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(125,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.1
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99267 - 0.171037i) q^{2} +(3.94149 + 0.681643i) q^{4} +(-0.344546 + 0.596772i) q^{5} +(3.20652 + 5.55385i) q^{7} +(-7.73752 - 2.03243i) q^{8} +O(q^{10})$	\(q+(-1.99267 - 0.171037i) q^{2} +(3.94149 + 0.681643i) q^{4} +(-0.344546 + 0.596772i) q^{5} +(3.20652 + 5.55385i) q^{7} +(-7.73752 - 2.03243i) q^{8} +(0.788638 - 1.13024i) q^{10} +(2.32696 + 4.03041i) q^{11} +(-10.7333 - 6.19686i) q^{13} +(-5.43963 - 11.6154i) q^{14} +(15.0707 + 5.37338i) q^{16} +26.4461i q^{17} -11.2183i q^{19} +(-1.76481 + 2.11731i) q^{20} +(-3.94751 - 8.42928i) q^{22} +(1.52939 + 0.882996i) q^{23} +(12.2626 + 21.2394i) q^{25} +(20.3280 + 14.1841i) q^{26} +(8.85273 + 24.0762i) q^{28} +(11.0947 + 19.2167i) q^{29} +(-27.1504 + 47.0258i) q^{31} +(-29.1120 - 13.2850i) q^{32} +(4.52327 - 52.6985i) q^{34} -4.41918 q^{35} +57.9113i q^{37} +(-1.91875 + 22.3544i) q^{38} +(3.87883 - 3.91727i) q^{40} +(47.1063 + 27.1968i) q^{41} +(24.2869 - 14.0220i) q^{43} +(6.42438 + 17.4720i) q^{44} +(-2.89656 - 2.02111i) q^{46} +(20.3310 - 11.7381i) q^{47} +(3.93648 - 6.81818i) q^{49} +(-20.8026 - 44.4205i) q^{50} +(-38.0811 - 31.7412i) q^{52} -97.9804 q^{53} -3.20698 q^{55} +(-13.5227 - 49.4901i) q^{56} +(-18.8214 - 40.1901i) q^{58} +(38.4944 - 66.6742i) q^{59} +(-0.493096 + 0.284689i) q^{61} +(62.1450 - 89.0634i) q^{62} +(55.7384 + 31.4520i) q^{64} +(7.39622 - 4.27021i) q^{65} +(-58.9776 - 34.0507i) q^{67} +(-18.0268 + 104.237i) q^{68} +(8.80597 + 0.755844i) q^{70} -59.1054i q^{71} +19.6537 q^{73} +(9.90499 - 115.398i) q^{74} +(7.64687 - 44.2169i) q^{76} +(-14.9229 + 25.8471i) q^{77} +(-63.2440 - 109.542i) q^{79} +(-8.39924 + 7.14240i) q^{80} +(-89.2157 - 62.2513i) q^{82} +(40.9430 + 70.9154i) q^{83} +(-15.7823 - 9.11191i) q^{85} +(-50.7941 + 23.7874i) q^{86} +(-9.81334 - 35.9147i) q^{88} -46.6512i q^{89} -79.4814i q^{91} +(5.42621 + 4.52282i) q^{92} +(-42.5206 + 19.9128i) q^{94} +(6.69477 + 3.86522i) q^{95} +(32.6904 + 56.6215i) q^{97} +(-9.01028 + 12.9131i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.99267	−	0.171037i	−0.996337	−	0.0855186i
$2$	−1.99267	−	0.171037i	−0.996337	−	0.0855186i
$3$		0			0
$3$		0			0
$4$	3.94149	+	0.681643i	0.985373	+	0.170411i
$5$	−0.344546	+	0.596772i	−0.0689093	+	0.119354i	−0.898421	−	0.439134i	$-0.855285\pi$
$5$	−0.344546	+	0.596772i	−0.0689093	+	0.119354i	0.829512	+	0.558489i	$0.188619\pi$
$6$		0			0
$7$	3.20652	+	5.55385i	0.458074	+	0.793408i	0.998859	−	0.0477532i	$-0.0152061\pi$
$7$	3.20652	+	5.55385i	0.458074	+	0.793408i	−0.540785	+	0.841161i	$0.681873\pi$
$8$	−7.73752	−	2.03243i	−0.967190	−	0.254054i
$9$		0			0
$10$	0.788638	−	1.13024i	0.0788638	−	0.113024i
$11$	2.32696	+	4.03041i	0.211541	+	0.366400i	0.952197	−	0.305484i	$-0.0988183\pi$
$11$	2.32696	+	4.03041i	0.211541	+	0.366400i	−0.740656	+	0.671885i	$0.765485\pi$
$12$		0			0
$13$	−10.7333	−	6.19686i	−0.825637	−	0.476682i	0.0267194	−	0.999643i	$-0.491494\pi$
$13$	−10.7333	−	6.19686i	−0.825637	−	0.476682i	−0.852357	+	0.522961i	$0.824827\pi$
$14$	−5.43963	−	11.6154i	−0.388545	−	0.829675i
$15$		0			0
$16$	15.0707	+	5.37338i	0.941920	+	0.335836i
$17$			26.4461i			1.55565i	0.628479	+	0.777827i	$0.283678\pi$
$17$			26.4461i			1.55565i	−0.628479	+	0.777827i	$0.716322\pi$
$18$		0			0
$19$		−	11.2183i		−	0.590437i	−0.955430	−	0.295219i	$-0.904608\pi$
$19$		−	11.2183i		−	0.590437i	0.955430	−	0.295219i	$-0.0953925\pi$
$20$	−1.76481	+	2.11731i	−0.0882406	+	0.105866i
$21$		0			0
$22$	−3.94751	−	8.42928i	−0.179432	−	0.383149i
$23$	1.52939	+	0.882996i	0.0664954	+	0.0383911i	0.532879	−	0.846191i	$-0.321110\pi$
$23$	1.52939	+	0.882996i	0.0664954	+	0.0383911i	−0.466384	+	0.884583i	$0.654443\pi$
$24$		0			0
$25$	12.2626	+	21.2394i	0.490503	+	0.849576i
$26$	20.3280	+	14.1841i	0.781847	+	0.545543i
$27$		0			0
$28$	8.85273	+	24.0762i	0.316169	+	0.859863i
$29$	11.0947	+	19.2167i	0.382577	+	0.662643i	0.991430	−	0.130640i	$-0.0417032\pi$
$29$	11.0947	+	19.2167i	0.382577	+	0.662643i	−0.608853	+	0.793283i	$0.708370\pi$
$30$		0			0
$31$	−27.1504	+	47.0258i	−0.875819	+	1.51696i	−0.0199305	+	0.999801i	$0.506344\pi$
$31$	−27.1504	+	47.0258i	−0.875819	+	1.51696i	−0.855888	+	0.517161i	$0.826989\pi$
$32$	−29.1120	−	13.2850i	−0.909750	−	0.415158i
$33$		0			0
$34$	4.52327	−	52.6985i	0.133037	−	1.54995i
$35$	−4.41918			−0.126262
$36$		0			0
$37$			57.9113i			1.56517i	0.622543	+	0.782585i	$0.286099\pi$
$37$			57.9113i			1.56517i	−0.622543	+	0.782585i	$0.713901\pi$
$38$	−1.91875	+	22.3544i	−0.0504934	+	0.588274i
$39$		0			0
$40$	3.87883	−	3.91727i	0.0969708	−	0.0979316i
$41$	47.1063	+	27.1968i	1.14893	+	0.663337i	0.948627	−	0.316396i	$-0.102473\pi$
$41$	47.1063	+	27.1968i	1.14893	+	0.663337i	0.200306	+	0.979733i	$0.435806\pi$
$42$		0			0
$43$	24.2869	−	14.0220i	0.564811	−	0.326094i	−0.190263	−	0.981733i	$-0.560934\pi$
$43$	24.2869	−	14.0220i	0.564811	−	0.326094i	0.755074	+	0.655639i	$0.227601\pi$
$44$	6.42438	+	17.4720i	0.146009	+	0.397090i
$45$		0			0
$46$	−2.89656	−	2.02111i	−0.0629687	−	0.0439371i
$47$	20.3310	−	11.7381i	0.432574	−	0.249747i	−0.267869	−	0.963455i	$-0.586319\pi$
$47$	20.3310	−	11.7381i	0.432574	−	0.249747i	0.700442	+	0.713709i	$0.252986\pi$
$48$		0			0
$49$	3.93648	−	6.81818i	0.0803363	−	0.139147i
$50$	−20.8026	−	44.4205i	−0.416052	−	0.888411i
$51$		0			0
$52$	−38.0811	−	31.7412i	−0.732329	−	0.610407i
$53$	−97.9804			−1.84869			−0.924343	−	0.381563i	$-0.875386\pi$
$53$	−97.9804			−1.84869			−0.924343	+	0.381563i	$0.875386\pi$
$54$		0			0
$55$	−3.20698			−0.0583086
$56$	−13.5227	−	49.4901i	−0.241476	−	0.883751i
$57$		0			0
$58$	−18.8214	−	40.1901i	−0.324507	−	0.692933i
$59$	38.4944	−	66.6742i	0.652447	−	1.13007i	−0.330080	−	0.943953i	$-0.607076\pi$
$59$	38.4944	−	66.6742i	0.652447	−	1.13007i	0.982527	−	0.186119i	$-0.0595909\pi$
$60$		0			0
$61$	−0.493096	+	0.284689i	−0.00808354	+	0.00466703i	−0.504036	−	0.863682i	$-0.668152\pi$
$61$	−0.493096	+	0.284689i	−0.00808354	+	0.00466703i	0.495953	+	0.868349i	$0.334819\pi$
$62$	62.1450	−	89.0634i	1.00234	−	1.43651i
$63$		0			0
$64$	55.7384	+	31.4520i	0.870913	+	0.491437i
$65$	7.39622	−	4.27021i	0.113788	−	0.0656956i
$66$		0			0
$67$	−58.9776	−	34.0507i	−0.880263	−	0.508220i	−0.00951785	−	0.999955i	$-0.503030\pi$
$67$	−58.9776	−	34.0507i	−0.880263	−	0.508220i	−0.870745	+	0.491735i	$0.836363\pi$
$68$	−18.0268	+	104.237i	−0.265100	+	1.53290i
$69$		0			0
$70$	8.80597	+	0.755844i	0.125800	+	0.0107978i
$71$		−	59.1054i		−	0.832471i	−0.909257	−	0.416235i	$-0.863349\pi$
$71$		−	59.1054i		−	0.832471i	0.909257	−	0.416235i	$-0.136651\pi$
$72$		0			0
$73$	19.6537			0.269228			0.134614	−	0.990898i	$-0.457020\pi$
$73$	19.6537			0.269228			0.134614	+	0.990898i	$0.457020\pi$
$74$	9.90499	−	115.398i	0.133851	−	1.55944i
$75$		0			0
$76$	7.64687	−	44.2169i	0.100617	−	0.581801i
$77$	−14.9229	+	25.8471i	−0.193803	+	0.335677i
$78$		0			0
$79$	−63.2440	−	109.542i	−0.800556	−	1.38660i	−0.919250	−	0.393673i	$-0.871204\pi$
$79$	−63.2440	−	109.542i	−0.800556	−	1.38660i	0.118694	−	0.992931i	$-0.462129\pi$
$80$	−8.39924	+	7.14240i	−0.104991	+	0.0892801i
$81$		0			0
$82$	−89.2157	−	62.2513i	−1.08800	−	0.759162i
$83$	40.9430	+	70.9154i	0.493290	+	0.854403i	0.999970	−	0.00773131i	$-0.00246098\pi$
$83$	40.9430	+	70.9154i	0.493290	+	0.854403i	−0.506681	+	0.862134i	$0.669128\pi$
$84$		0			0
$85$	−15.7823	−	9.11191i	−0.185674	−	0.107199i
$86$	−50.7941	+	23.7874i	−0.590629	+	0.276597i
$87$		0			0
$88$	−9.81334	−	35.9147i	−0.111515	−	0.408122i
$89$		−	46.6512i		−	0.524171i	−0.965045	−	0.262085i	$-0.915590\pi$
$89$		−	46.6512i		−	0.524171i	0.965045	−	0.262085i	$-0.0844102\pi$
$90$		0			0
$91$		−	79.4814i		−	0.873422i
$92$	5.42621	+	4.52282i	0.0589805	+	0.0491611i
$93$		0			0
$94$	−42.5206	+	19.9128i	−0.452347	+	0.211839i
$95$	6.69477	+	3.86522i	0.0704712	+	0.0406866i
$96$		0			0
$97$	32.6904	+	56.6215i	0.337015	+	0.583727i	0.983870	−	0.178886i	$-0.0572494\pi$
$97$	32.6904	+	56.6215i	0.337015	+	0.583727i	−0.646855	+	0.762613i	$0.723916\pi$
$98$	−9.01028	+	12.9131i	−0.0919416	+	0.131767i
$99$		0			0
$100$	33.8552	+	92.0736i	0.338552	+	0.920736i
$101$	−0.0318630	−	0.0551884i	−0.000315475	−	0.000546419i	0.865868	−	0.500273i	$-0.166767\pi$
$101$	−0.0318630	−	0.0551884i	−0.000315475	−	0.000546419i	−0.866183	+	0.499727i	$0.833434\pi$
$102$		0			0
$103$	26.9988	−	46.7633i	0.262124	−	0.454013i	−0.704682	−	0.709523i	$-0.748910\pi$
$103$	26.9988	−	46.7633i	0.262124	−	0.454013i	0.966806	+	0.255511i	$0.0822436\pi$
$104$	70.4543	+	69.7630i	0.677445	+	0.670798i
$105$		0			0
$106$	195.243	+	16.7583i	1.84191	+	0.158097i
$107$	87.1896			0.814857			0.407428	−	0.913237i	$-0.366426\pi$
$107$	87.1896			0.814857			0.407428	+	0.913237i	$0.366426\pi$
$108$		0			0
$109$			128.464i			1.17856i	0.807927	+	0.589282i	$0.200589\pi$
$109$			128.464i			1.17856i	−0.807927	+	0.589282i	$0.799411\pi$
$110$	6.39045	+	0.548512i	0.0580950	+	0.00498647i
$111$		0			0
$112$	18.4816	+	100.930i	0.165014	+	0.901165i
$113$	−14.5659	−	8.40964i	−0.128902	−	0.0744216i	0.434162	−	0.900835i	$-0.357044\pi$
$113$	−14.5659	−	8.40964i	−0.128902	−	0.0744216i	−0.563064	+	0.826413i	$0.690378\pi$
$114$		0			0
$115$	−1.05389	+	0.608466i	−0.00916430	+	0.00529101i
$116$	30.6310	+	83.3050i	0.264060	+	0.718146i
$117$		0			0
$118$	−88.1105	+	126.276i	−0.746699	+	1.07014i
$119$	−146.878	+	84.7999i	−1.23427	+	0.712605i
$120$		0			0
$121$	49.6706	−	86.0319i	0.410500	−	0.711008i
$122$	1.03127	−	0.482955i	0.00845305	−	0.00395864i
$123$		0			0
$124$	−139.068	+	166.845i	−1.12151	+	1.34553i
$125$	−34.1274			−0.273019
$126$		0			0
$127$	−26.5353			−0.208939			−0.104470	−	0.994528i	$-0.533315\pi$
$127$	−26.5353			−0.208939			−0.104470	+	0.994528i	$0.533315\pi$
$128$	−105.689	−	72.2069i	−0.825695	−	0.564116i
$129$		0			0
$130$	−15.4686	+	7.24411i	−0.118989	+	0.0557239i
$131$	66.8072	−	115.713i	0.509979	−	0.883309i	−0.489955	−	0.871748i	$-0.662987\pi$
$131$	66.8072	−	115.713i	0.509979	−	0.883309i	0.999933	−	0.0115609i	$-0.00368004\pi$
$132$		0			0
$133$	62.3048	−	35.9717i	0.468457	−	0.270464i
$134$	111.699	+	77.9394i	0.833576	+	0.581637i
$135$		0			0
$136$	53.7499	−	204.627i	0.395220	−	1.50461i
$137$	−119.255	+	68.8518i	−0.870473	+	0.502568i	−0.867505	−	0.497428i	$-0.834278\pi$
$137$	−119.255	+	68.8518i	−0.870473	+	0.502568i	−0.00296748	+	0.999996i	$0.500945\pi$
$138$		0			0
$139$	113.971	+	65.8013i	0.819937	+	0.473391i	0.850395	−	0.526145i	$-0.176363\pi$
$139$	113.971	+	65.8013i	0.819937	+	0.473391i	−0.0304578	+	0.999536i	$0.509697\pi$
$140$	−17.4181	−	3.01230i	−0.124415	−	0.0215164i
$141$		0			0
$142$	−10.1092	+	117.778i	−0.0711917	+	0.829421i
$143$		−	57.6793i		−	0.403352i
$144$		0			0
$145$	−15.2906			−0.105452
$146$	−39.1633	−	3.36151i	−0.268242	−	0.0230240i
$147$		0			0
$148$	−39.4748	+	228.257i	−0.266722	+	1.54228i
$149$	37.1025	−	64.2633i	0.249010	−	0.431298i	−0.714242	−	0.699899i	$-0.753228\pi$
$149$	37.1025	−	64.2633i	0.249010	−	0.431298i	0.963251	+	0.268602i	$0.0865615\pi$
$150$		0			0
$151$	6.22351	+	10.7794i	0.0412153	+	0.0713870i	0.885897	−	0.463882i	$-0.153544\pi$
$151$	6.22351	+	10.7794i	0.0412153	+	0.0713870i	−0.844682	+	0.535269i	$0.820210\pi$
$152$	−22.8004	+	86.8019i	−0.150003	+	0.571065i
$153$		0			0
$154$	34.1572	−	48.9525i	0.221800	−	0.317874i
$155$	−18.7091	−	32.4051i	−0.120704	−	0.209065i
$156$		0			0
$157$	98.0287	+	56.5969i	0.624387	+	0.360490i	0.778575	−	0.627552i	$-0.215943\pi$
$157$	98.0287	+	56.5969i	0.624387	+	0.360490i	−0.154188	+	0.988041i	$0.549276\pi$
$158$	107.289	+	229.098i	0.679043	+	1.44999i
$159$		0			0
$160$	17.9586	−	12.7959i	0.112241	−	0.0799743i
$161$			11.3254i			0.0703440i
$162$		0			0
$163$		−	90.6053i		−	0.555861i	−0.960601	−	0.277930i	$-0.910352\pi$
$163$		−	90.6053i		−	0.555861i	0.960601	−	0.277930i	$-0.0896484\pi$
$164$	167.131	+	139.306i	1.01909	+	0.849425i
$165$		0			0
$166$	−69.4569	−	148.314i	−0.418415	−	0.893458i
$167$	−161.834	−	93.4346i	−0.969063	−	0.559489i	−0.0701127	−	0.997539i	$-0.522336\pi$
$167$	−161.834	−	93.4346i	−0.969063	−	0.559489i	−0.898951	+	0.438050i	$0.855669\pi$
$168$		0			0
$169$	−7.69776	−	13.3329i	−0.0455489	−	0.0788930i
$170$	29.8905	+	20.8564i	0.175826	+	0.122685i
$171$		0			0
$172$	105.285	−	38.7128i	0.612120	−	0.225074i
$173$	62.7132	+	108.622i	0.362504	+	0.627875i	0.988372	−	0.152053i	$-0.0485886\pi$
$173$	62.7132	+	108.622i	0.362504	+	0.627875i	−0.625868	+	0.779929i	$0.715255\pi$
$174$		0			0
$175$	−78.6404	+	136.209i	−0.449373	+	0.778338i
$176$	13.4120	+	73.2447i	0.0762047	+	0.416163i
$177$		0			0
$178$	−7.97909	+	92.9606i	−0.0448263	+	0.522250i
$179$	−231.928			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$179$	−231.928			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$180$		0			0
$181$		−	159.136i		−	0.879203i	−0.898193	−	0.439602i	$-0.855120\pi$
$181$		−	159.136i		−	0.879203i	0.898193	−	0.439602i	$-0.144880\pi$
$182$	−13.5943	+	158.381i	−0.0746939	+	0.870223i
$183$		0			0
$184$	−10.0391	−	9.94059i	−0.0545603	−	0.0540250i
$185$	−34.5598	−	19.9531i	−0.186810	−	0.107855i
$186$		0			0
$187$	−106.589	+	61.5389i	−0.569992	+	0.329085i
$188$	88.1355	−	32.4071i	0.468806	−	0.172378i
$189$		0			0
$190$	−12.6794	−	8.84718i	−0.0667336	−	0.0465641i
$191$	172.293	−	99.4735i	0.902058	−	0.520804i	0.0241909	−	0.999707i	$-0.492299\pi$
$191$	172.293	−	99.4735i	0.902058	−	0.520804i	0.877867	+	0.478904i	$0.158966\pi$
$192$		0			0
$193$	103.575	−	179.397i	0.536658	−	0.929520i	−0.462423	−	0.886660i	$-0.653020\pi$
$193$	103.575	−	179.397i	0.536658	−	0.929520i	0.999081	−	0.0428600i	$-0.0136469\pi$
$194$	−55.4570	−	118.419i	−0.285861	−	0.610409i
$195$		0			0
$196$	20.1632	−	24.1905i	0.102873	−	0.123421i
$197$	−37.2829			−0.189254			−0.0946268	−	0.995513i	$-0.530166\pi$
$197$	−37.2829			−0.189254			−0.0946268	+	0.995513i	$0.530166\pi$
$198$		0			0
$199$	349.988			1.75873			0.879366	−	0.476147i	$-0.157967\pi$
$199$	349.988			1.75873			0.879366	+	0.476147i	$0.157967\pi$
$200$	−51.7143	−	189.263i	−0.258571	−	0.946316i
$201$		0			0
$202$	0.0540533	+	0.115422i	0.000267591	+	0.000571397i
$203$	−71.1510	+	123.237i	−0.350498	+	0.607080i
$204$		0			0
$205$	−32.4606	+	18.7411i	−0.158344	+	0.0914201i
$206$	−61.7981	+	88.5662i	−0.299991	+	0.429933i
$207$		0			0
$208$	−128.460	−	151.065i	−0.617597	−	0.726275i
$209$	45.2143	−	26.1045i	0.216336	−	0.124902i
$210$		0			0
$211$	275.500	+	159.060i	1.30569	+	0.753840i	0.981374	−	0.192109i	$-0.0615326\pi$
$211$	275.500	+	159.060i	1.30569	+	0.753840i	0.324316	+	0.945949i	$0.394866\pi$
$212$	−386.189	−	66.7876i	−1.82165	−	0.315036i
$213$		0			0
$214$	−173.740	−	14.9127i	−0.811871	−	0.0696854i
$215$			19.3250i			0.0898836i
$216$		0			0
$217$	−348.233			−1.60476
$218$	21.9721	−	255.986i	0.100789	−	1.17425i
$219$		0			0
$220$	−12.6403	−	2.18601i	−0.0574558	−	0.00993641i
$221$	163.883	−	283.854i	0.741552	−	1.28441i
$222$		0			0
$223$	−78.2350	−	135.507i	−0.350829	−	0.607654i	0.635566	−	0.772047i	$-0.280767\pi$
$223$	−78.2350	−	135.507i	−0.350829	−	0.607654i	−0.986395	+	0.164393i	$0.947434\pi$
$224$	−19.5650	−	204.282i	−0.0873435	−	0.911975i
$225$		0			0
$226$	27.5867	+	19.2490i	0.122065	+	0.0851724i
$227$	54.4814	+	94.3646i	0.240006	+	0.415703i	0.960716	−	0.277534i	$-0.0895172\pi$
$227$	54.4814	+	94.3646i	0.240006	+	0.415703i	−0.720710	+	0.693237i	$0.756184\pi$
$228$		0			0
$229$	−375.558	−	216.829i	−1.63999	−	0.946851i	−0.980833	−	0.194848i	$-0.937579\pi$
$229$	−375.558	−	216.829i	−1.63999	−	0.946851i	−0.659160	−	0.752003i	$-0.729088\pi$
$230$	2.20414	−	1.03222i	0.00958321	−	0.00448791i
$231$		0			0
$232$	−46.7892	−	171.239i	−0.201678	−	0.738097i
$233$		−	50.2111i		−	0.215498i	−0.994178	−	0.107749i	$-0.965636\pi$
$233$		−	50.2111i		−	0.215498i	0.994178	−	0.107749i	$-0.0343643\pi$
$234$		0			0
$235$			16.1773i			0.0688394i
$236$	197.173	−	236.557i	0.835480	−	1.00236i
$237$		0			0
$238$	307.183	−	143.857i	1.29069	−	0.604441i
$239$	299.914	+	173.155i	1.25487	+	0.724500i	0.972073	−	0.234680i	$-0.0754043\pi$
$239$	299.914	+	173.155i	1.25487	+	0.724500i	0.282797	+	0.959180i	$0.408738\pi$
$240$		0			0
$241$	60.4009	+	104.617i	0.250626	+	0.434097i	0.963698	−	0.266993i	$-0.0860302\pi$
$241$	60.4009	+	104.617i	0.250626	+	0.434097i	−0.713072	+	0.701091i	$0.752697\pi$
$242$	−113.692	+	162.938i	−0.469801	+	0.673298i
$243$		0			0
$244$	−2.13759	+	0.785985i	−0.00876062	+	0.00322125i
$245$	2.71260	+	4.69836i	0.0110718	+	0.0191770i
$246$		0			0
$247$	−69.5183	+	120.409i	−0.281451	+	0.487487i
$248$	305.653	−	308.682i	1.23247	−	1.24469i
$249$		0			0
$250$	68.0048	+	5.83706i	0.272019	+	0.0233482i
$251$	−242.223			−0.965030			−0.482515	−	0.875888i	$-0.660277\pi$
$251$	−242.223			−0.965030			−0.482515	+	0.875888i	$0.660277\pi$
$252$		0			0
$253$			8.21877i			0.0324853i
$254$	52.8761	+	4.53852i	0.208174	+	0.0178682i
$255$		0			0
$256$	198.254	+	161.961i	0.774428	+	0.632662i
$257$	−54.7821	−	31.6285i	−0.213160	−	0.123068i	0.389619	−	0.920976i	$-0.372607\pi$
$257$	−54.7821	−	31.6285i	−0.213160	−	0.123068i	−0.602779	+	0.797908i	$0.705940\pi$
$258$		0			0
$259$	−321.631	+	185.694i	−1.24182	+	0.716964i
$260$	32.0629	−	11.7894i	0.123319	−	0.0453440i
$261$		0			0
$262$	−152.916	+	219.153i	−0.583650	+	0.836460i
$263$	−15.1868	+	8.76812i	−0.0577446	+	0.0333389i	−0.528594	−	0.848875i	$-0.677281\pi$
$263$	−15.1868	+	8.76812i	−0.0577446	+	0.0333389i	0.470850	+	0.882213i	$0.343947\pi$
$264$		0			0
$265$	33.7588	−	58.4719i	0.127392	−	0.220649i
$266$	−130.306	+	61.0234i	−0.489871	+	0.229411i
$267$		0			0
$268$	−209.249	−	174.412i	−0.780781	−	0.650793i
$269$	481.717			1.79077			0.895386	−	0.445292i	$-0.146900\pi$
$269$	481.717			1.79077			0.895386	+	0.445292i	$0.146900\pi$
$270$		0			0
$271$	16.5268			0.0609845			0.0304923	−	0.999535i	$-0.490293\pi$
$271$	16.5268			0.0609845			0.0304923	+	0.999535i	$0.490293\pi$
$272$	−142.105	+	398.562i	−0.522445	+	1.46530i
$273$		0			0
$274$	249.412	−	116.802i	0.910263	−	0.426285i
$275$	−57.0689	+	98.8463i	−0.207523	+	0.359441i
$276$		0			0
$277$	134.270	−	77.5206i	0.484728	−	0.279858i	−0.237657	−	0.971349i	$-0.576379\pi$
$277$	134.270	−	77.5206i	0.484728	−	0.279858i	0.722385	+	0.691491i	$0.243046\pi$
$278$	−215.853	−	150.614i	−0.776449	−	0.541776i
$279$		0			0
$280$	34.1935	+	8.98168i	0.122120	+	0.0320774i
$281$	218.046	−	125.889i	0.775963	−	0.448003i	−0.0590345	−	0.998256i	$-0.518802\pi$
$281$	218.046	−	125.889i	0.775963	−	0.448003i	0.834998	+	0.550253i	$0.185469\pi$
$282$		0			0
$283$	−64.8702	−	37.4528i	−0.229223	−	0.132342i	0.380990	−	0.924579i	$-0.375583\pi$
$283$	−64.8702	−	37.4528i	−0.229223	−	0.132342i	−0.610214	+	0.792237i	$0.708916\pi$
$284$	40.2888	−	232.964i	0.141862	−	0.820294i
$285$		0			0
$286$	−9.86531	+	114.936i	−0.0344941	+	0.401874i
$287$			348.828i			1.21543i
$288$		0			0
$289$	−410.397			−1.42006
$290$	30.4692	+	2.61526i	0.105066	+	0.00901815i
$291$		0			0
$292$	77.4648	+	13.3968i	0.265290	+	0.0458794i
$293$	−189.350	+	327.963i	−0.646245	+	1.11933i	0.337768	+	0.941229i	$0.390328\pi$
$293$	−189.350	+	327.963i	−0.646245	+	1.11933i	−0.984013	+	0.178099i	$0.943005\pi$
$294$		0			0
$295$	26.5262	+	45.9447i	0.0899193	+	0.155745i
$296$	117.701	−	448.090i	0.397638	−	1.51382i
$297$		0			0
$298$	−84.9245	+	121.710i	−0.284982	+	0.408423i
$299$	−10.9436	−	18.9549i	−0.0366007	−	0.0633943i
$300$		0			0
$301$	155.753	+	89.9239i	0.517451	+	0.298750i
$302$	−10.5577	−	22.5443i	−0.0349594	−	0.0746501i
$303$		0			0
$304$	60.2802	−	169.068i	0.198290	−	0.556145i
$305$		−	0.392354i		−	0.00128641i
$306$		0			0
$307$			58.4035i			0.190240i	0.995466	+	0.0951198i	$0.0303234\pi$
$307$			58.4035i			0.190240i	−0.995466	+	0.0951198i	$0.969677\pi$
$308$	−76.4368	+	91.7042i	−0.248171	+	0.297741i
$309$		0			0
$310$	31.7387	+	67.7728i	0.102383	+	0.218622i
$311$	156.919	+	90.5973i	0.504563	+	0.291309i	0.730596	−	0.682810i	$-0.239242\pi$
$311$	156.919	+	90.5973i	0.504563	+	0.291309i	−0.226033	+	0.974120i	$0.572576\pi$
$312$		0			0
$313$	191.603	+	331.866i	0.612151	+	1.06028i	0.990877	+	0.134767i	$0.0430288\pi$
$313$	191.603	+	331.866i	0.612151	+	1.06028i	−0.378727	+	0.925509i	$0.623638\pi$
$314$	−185.659	−	129.546i	−0.591271	−	0.412566i
$315$		0			0
$316$	−174.607	−	474.868i	−0.552555	−	1.50275i
$317$	−59.4476	−	102.966i	−0.187532	−	0.324815i	0.756895	−	0.653537i	$-0.226716\pi$
$317$	−59.4476	−	102.966i	−0.187532	−	0.324815i	−0.944427	+	0.328722i	$0.893382\pi$
$318$		0			0
$319$	−51.6339	+	89.4326i	−0.161862	+	0.280353i
$320$	−37.9741	+	22.4265i	−0.118669	+	0.0700827i
$321$		0			0
$322$	1.93706	−	22.5678i	0.00601572	−	0.0700863i
$323$	296.681			0.918516
$324$		0			0
$325$		−	303.958i		−	0.935256i
$326$	−15.4969	+	180.547i	−0.0475364	+	0.553824i
$327$		0			0
$328$	−309.210	−	306.176i	−0.942713	−	0.933464i
$329$	130.383	+	75.2768i	0.396302	+	0.228805i
$330$		0			0
$331$	−321.877	+	185.836i	−0.972438	+	0.561437i	−0.899979	−	0.435934i	$-0.856418\pi$
$331$	−321.877	+	185.836i	−0.972438	+	0.561437i	−0.0724591	+	0.997371i	$0.523085\pi$
$332$	113.038	+	307.421i	0.340475	+	0.925967i
$333$		0			0
$334$	306.501	+	213.864i	0.917666	+	0.640312i
$335$	40.6410	−	23.4641i	0.121317	−	0.0700421i
$336$		0			0
$337$	−170.817	+	295.864i	−0.506876	+	0.877934i	0.493093	+	0.869977i	$0.335866\pi$
$337$	−170.817	+	295.864i	−0.506876	+	0.877934i	−0.999968	+	0.00795767i	$0.997467\pi$
$338$	13.0587	+	27.8847i	0.0386352	+	0.0824993i
$339$		0			0
$340$	−55.9947	−	46.6724i	−0.164690	−	0.137272i
$341$	−252.711			−0.741088
$342$		0			0
$343$	364.728			1.06335
$344$	−216.419	+	59.1344i	−0.629125	+	0.171902i
$345$		0			0
$346$	−106.388	−	227.175i	−0.307481	−	0.656576i
$347$	−216.035	+	374.184i	−0.622579	+	1.07834i	0.366425	+	0.930448i	$0.380582\pi$
$347$	−216.035	+	374.184i	−0.622579	+	1.07834i	−0.989004	+	0.147891i	$0.952752\pi$
$348$		0			0
$349$	371.775	−	214.645i	1.06526	−	0.615027i	0.138377	−	0.990380i	$-0.455812\pi$
$349$	371.775	−	214.645i	1.06526	−	0.615027i	0.926882	+	0.375352i	$0.122478\pi$
$350$	180.001	−	257.970i	0.514290	−	0.737056i
$351$		0			0
$352$	−14.1982	−	148.247i	−0.0403358	−	0.421156i
$353$	111.294	−	64.2559i	0.315282	−	0.182028i	−0.334006	−	0.942571i	$-0.608401\pi$
$353$	111.294	−	64.2559i	0.315282	−	0.182028i	0.649287	+	0.760543i	$0.275067\pi$
$354$		0			0
$355$	35.2724	+	20.3646i	0.0993590	+	0.0573649i
$356$	31.7994	−	183.875i	0.0893243	−	0.516504i
$357$		0			0
$358$	462.156	+	39.6683i	1.29094	+	0.110805i
$359$			281.214i			0.783326i	0.920109	+	0.391663i	$0.128100\pi$
$359$			281.214i			0.783326i	−0.920109	+	0.391663i	$0.871900\pi$
$360$		0			0
$361$	235.150			0.651384
$362$	−27.2181	+	317.106i	−0.0751883	+	0.875982i
$363$		0			0
$364$	54.1779	−	313.275i	0.148840	−	0.860647i
$365$	−6.77160	+	11.7288i	−0.0185523	+	0.0321336i
$366$		0			0
$367$	76.3017	+	132.159i	0.207907	+	0.360105i	0.951055	−	0.309022i	$-0.100002\pi$
$367$	76.3017	+	132.159i	0.207907	+	0.360105i	−0.743148	+	0.669127i	$0.766668\pi$
$368$	18.3044	+	21.5254i	0.0497403	+	0.0584930i
$369$		0			0
$370$	65.4537	+	45.6711i	0.176902	+	0.123435i
$371$	−314.176	−	544.168i	−0.846835	−	1.46676i
$372$		0			0
$373$	−292.979	−	169.152i	−0.785467	−	0.453489i	0.0528976	−	0.998600i	$-0.483154\pi$
$373$	−292.979	−	169.152i	−0.785467	−	0.453489i	−0.838364	+	0.545111i	$0.816488\pi$
$374$	222.922	−	104.396i	0.596047	−	0.279135i
$375$		0			0
$376$	−181.168	+	49.5024i	−0.481830	+	0.131655i
$377$		−	275.010i		−	0.729471i
$378$		0			0
$379$			126.854i			0.334708i	0.985897	+	0.167354i	$0.0535222\pi$
$379$			126.854i			0.334708i	−0.985897	+	0.167354i	$0.946478\pi$
$380$	23.7527	+	19.7982i	0.0625070	+	0.0521005i
$381$		0			0
$382$	−360.338	+	168.750i	−0.943292	+	0.441753i
$383$	−81.3736	−	46.9810i	−0.212464	−	0.122666i	0.389992	−	0.920818i	$-0.372478\pi$
$383$	−81.3736	−	46.9810i	−0.212464	−	0.122666i	−0.602456	+	0.798152i	$0.705811\pi$
$384$		0			0
$385$	−10.2832	−	17.8111i	−0.0267097	−	0.0462625i
$386$	−237.075	+	339.765i	−0.614184	+	0.880220i
$387$		0			0
$388$	90.2535	+	245.456i	0.232612	+	0.632620i
$389$	−280.771	−	486.310i	−0.721776	−	1.25015i	−0.960287	−	0.279013i	$-0.909993\pi$
$389$	−280.771	−	486.310i	−0.721776	−	1.25015i	0.238511	−	0.971140i	$-0.423341\pi$
$390$		0			0
$391$	−23.3518	+	40.4465i	−0.0597233	+	0.103444i
$392$	−44.3161	+	44.7552i	−0.113051	+	0.114171i
$393$		0			0
$394$	74.2927	+	6.37677i	0.188560	+	0.0161847i
$395$	87.1619			0.220663
$396$		0			0
$397$			684.768i			1.72486i	0.506180	+	0.862428i	$0.331057\pi$
$397$			684.768i			1.72486i	−0.506180	+	0.862428i	$0.668943\pi$
$398$	−697.411	−	59.8609i	−1.75229	−	0.150404i
$399$		0			0
$400$	70.6786	+	385.985i	0.176696	+	0.964962i
$401$	−331.159	−	191.195i	−0.825833	−	0.476795i	0.0265909	−	0.999646i	$-0.491535\pi$
$401$	−331.159	−	191.195i	−0.825833	−	0.476795i	−0.852424	+	0.522852i	$0.824868\pi$
$402$		0			0
$403$	582.825	−	336.494i	1.44622	−	0.834974i
$404$	−0.0879691	−	0.239244i	−0.000217745	−	0.000592187i
$405$		0			0
$406$	162.859	−	233.402i	0.401130	−	0.574881i
$407$	−233.406	+	134.757i	−0.573479	+	0.331098i
$408$		0			0
$409$	−129.544	+	224.376i	−0.316733	+	0.548597i	−0.979804	−	0.199959i	$-0.935919\pi$
$409$	−129.544	+	224.376i	−0.316733	+	0.548597i	0.663072	+	0.748556i	$0.269252\pi$
$410$	67.8888	−	31.7930i	0.165582	−	0.0775438i
$411$		0			0
$412$	138.291	−	165.914i	0.335659	−	0.402703i
$413$	493.732			1.19548
$414$		0			0
$415$	−56.4271			−0.135969
$416$	230.142	+	322.995i	0.553225	+	0.776431i
$417$		0			0
$418$	−94.5622	+	44.2844i	−0.226225	+	0.105944i
$419$	−173.844	+	301.106i	−0.414902	+	0.718631i	−0.995418	−	0.0956178i	$-0.969517\pi$
$419$	−173.844	+	301.106i	−0.414902	+	0.718631i	0.580516	+	0.814248i	$0.302851\pi$
$420$		0			0
$421$	45.8476	−	26.4701i	0.108902	−	0.0628743i	−0.444560	−	0.895749i	$-0.646640\pi$
$421$	45.8476	−	26.4701i	0.108902	−	0.0628743i	0.553462	+	0.832875i	$0.313307\pi$
$422$	−521.777	−	364.076i	−1.23644	−	0.862739i
$423$		0			0
$424$	758.125	+	199.138i	1.78803	+	0.469666i
$425$	−561.700	+	324.297i	−1.32165	+	0.763053i
$426$		0			0
$427$	−3.16224	−	1.82572i	−0.00740572	−	0.00427570i
$428$	343.657	+	59.4322i	0.802938	+	0.138860i
$429$		0			0
$430$	3.30529	−	38.5083i	0.00768672	−	0.0895543i
$431$		−	133.087i		−	0.308788i	−0.988009	−	0.154394i	$-0.950658\pi$
$431$		−	133.087i		−	0.308788i	0.988009	−	0.154394i	$-0.0493424\pi$
$432$		0			0
$433$	223.870			0.517020			0.258510	−	0.966009i	$-0.416769\pi$
$433$	223.870			0.517020			0.258510	+	0.966009i	$0.416769\pi$
$434$	693.914	+	59.5608i	1.59888	+	0.137237i
$435$		0			0
$436$	−87.5662	+	506.338i	−0.200840	+	1.16133i
$437$	9.90572	−	17.1572i	0.0226676	−	0.0392614i
$438$		0			0
$439$	−187.035	−	323.955i	−0.426049	−	0.737938i	0.570469	−	0.821319i	$-0.306761\pi$
$439$	−187.035	−	323.955i	−0.426049	−	0.737938i	−0.996518	+	0.0833810i	$0.973428\pi$
$440$	24.8140	+	6.51796i	0.0563955	+	0.0148135i
$441$		0			0
$442$	−375.115	+	537.597i	−0.848676	+	1.21628i
$443$	124.344	+	215.369i	0.280685	+	0.486161i	0.971554	−	0.236819i	$-0.0761049\pi$
$443$	124.344	+	215.369i	0.280685	+	0.486161i	−0.690868	+	0.722981i	$0.742772\pi$
$444$		0			0
$445$	27.8401	+	16.0735i	0.0625620	+	0.0361202i
$446$	132.720	+	283.402i	0.297578	+	0.635431i
$447$		0			0
$448$	4.04666	+	410.414i	0.00903272	+	0.916104i
$449$			395.982i			0.881920i	0.897527	+	0.440960i	$0.145362\pi$
$449$			395.982i			0.881920i	−0.897527	+	0.440960i	$0.854638\pi$
$450$		0			0
$451$			253.143i			0.561293i
$452$	−51.6791	−	43.0753i	−0.114334	−	0.0952993i
$453$		0			0
$454$	−92.4238	−	197.356i	−0.203577	−	0.434705i
$455$	47.4323	+	27.3850i	0.104247	+	0.0601869i
$456$		0			0
$457$	−211.318	−	366.014i	−0.462404	−	0.800907i	0.536676	−	0.843788i	$-0.319680\pi$
$457$	−211.318	−	366.014i	−0.462404	−	0.800907i	−0.999080	+	0.0428814i	$0.986346\pi$
$458$	711.280	+	496.303i	1.55301	+	1.08363i
$459$		0			0
$460$	−4.56867	+	1.67989i	−0.00993190	+	0.00365193i
$461$	323.389	+	560.127i	0.701495	+	1.21503i	0.967941	+	0.251176i	$0.0808173\pi$
$461$	323.389	+	560.127i	0.701495	+	1.21503i	−0.266446	+	0.963850i	$0.585849\pi$
$462$		0			0
$463$	131.343	−	227.494i	0.283679	−	0.491347i	−0.688609	−	0.725133i	$-0.741778\pi$
$463$	131.343	−	227.494i	0.283679	−	0.491347i	0.972288	+	0.233786i	$0.0751116\pi$
$464$	63.9475	+	349.225i	0.137818	+	0.752641i
$465$		0			0
$466$	−8.58797	+	100.054i	−0.0184291	+	0.214709i
$467$	508.274			1.08838			0.544190	−	0.838962i	$-0.316837\pi$
$467$	508.274			1.08838			0.544190	+	0.838962i	$0.316837\pi$
$468$		0			0
$469$		−	436.737i		−	0.931210i
$470$	2.76691	−	32.2360i	0.00588705	−	0.0685872i
$471$		0			0
$472$	−433.362	+	437.656i	−0.918140	+	0.927237i
$473$	113.029	+	65.2573i	0.238962	+	0.137965i
$474$		0			0
$475$	238.270	−	137.565i	0.501621	−	0.289611i
$476$	−636.721	+	234.120i	−1.33765	+	0.491849i
$477$		0			0
$478$	−568.014	−	396.339i	−1.18831	−	0.829160i
$479$	159.669	−	92.1851i	0.333339	−	0.192453i	−0.323984	−	0.946063i	$-0.605022\pi$
$479$	159.669	−	92.1851i	0.333339	−	0.192453i	0.657322	+	0.753609i	$0.271689\pi$
$480$		0			0
$481$	358.868	−	621.578i	0.746088	−	1.29226i
$482$	−102.466	−	218.799i	−0.212585	−	0.453940i
$483$		0			0
$484$	254.419	−	305.237i	0.525659	−	0.630654i
$485$	−45.0535			−0.0928938
$486$		0			0
$487$	−334.169			−0.686178			−0.343089	−	0.939303i	$-0.611473\pi$
$487$	−334.169			−0.686178			−0.343089	+	0.939303i	$0.611473\pi$
$488$	4.39395	−	1.20060i	0.00900400	−	0.00246025i
$489$		0			0
$490$	−4.60173	−	9.82624i	−0.00939128	−	0.0200536i
$491$	381.116	−	660.113i	0.776205	−	1.34443i	−0.157910	−	0.987453i	$-0.550476\pi$
$491$	381.116	−	660.113i	0.776205	−	1.34443i	0.934115	−	0.356972i	$-0.116191\pi$
$492$		0			0
$493$	−508.206	+	293.413i	−1.03084	+	0.595158i
$494$	159.122	−	228.046i	0.322109	−	0.461632i
$495$		0			0
$496$	−661.864	+	562.824i	−1.33440	+	1.13473i
$497$	328.263	−	189.523i	0.660489	−	0.381333i
$498$		0			0
$499$	−472.870	−	273.012i	−0.947635	−	0.547118i	−0.0552899	−	0.998470i	$-0.517608\pi$
$499$	−472.870	−	273.012i	−0.947635	−	0.547118i	−0.892346	+	0.451353i	$0.850942\pi$
$500$	−134.513	−	23.2627i	−0.269026	−	0.0465254i
$501$		0			0
$502$	482.671	+	41.4291i	0.961495	+	0.0825281i
$503$		−	928.831i		−	1.84658i	−0.384101	−	0.923291i	$-0.625489\pi$
$503$		−	928.831i		−	1.84658i	0.384101	−	0.923291i	$-0.374511\pi$
$504$		0			0
$505$	0.0439131			8.69567e−5
$506$	1.40572	−	16.3773i	0.00277810	−	0.0323663i
$507$		0			0
$508$	−104.589	−	18.0876i	−0.205883	−	0.0356055i
$509$	−160.826	+	278.559i	−0.315965	+	0.547268i	−0.979642	−	0.200751i	$-0.935662\pi$
$509$	−160.826	+	278.559i	−0.315965	+	0.547268i	0.663677	+	0.748019i	$0.268995\pi$
$510$		0			0
$511$	63.0199	+	109.154i	0.123327	+	0.213608i
$512$	−367.353	−	356.645i	−0.717487	−	0.696572i
$513$		0			0
$514$	103.753	+	72.3950i	0.201855	+	0.140846i
$515$	18.6047	+	32.2243i	0.0361256	+	0.0625714i
$516$		0			0
$517$	94.6185	+	54.6280i	0.183015	+	0.105663i
$518$	672.666	−	315.016i	1.29858	−	0.608139i
$519$		0			0
$520$	−65.9074	+	18.0085i	−0.126745	+	0.0346318i
$521$			313.785i			0.602274i	0.953581	+	0.301137i	$0.0973662\pi$
$521$			313.785i			0.602274i	−0.953581	+	0.301137i	$0.902634\pi$
$522$		0			0
$523$		−	509.974i		−	0.975094i	−0.873097	−	0.487547i	$-0.837892\pi$
$523$		−	509.974i		−	0.975094i	0.873097	−	0.487547i	$-0.162108\pi$
$524$	342.195	−	410.545i	0.653044	−	0.783483i
$525$		0			0
$526$	31.7621	−	14.8745i	0.0603842	−	0.0282785i
$527$	−1243.65	−	718.022i	−2.35987	−	1.36247i
$528$		0			0
$529$	−262.941	−	455.427i	−0.497052	−	0.860920i
$530$	−77.2711	+	110.741i	−0.145794	+	0.208946i
$531$		0			0
$532$	270.094	−	99.3126i	0.507695	−	0.186678i
$533$	−337.070	−	583.822i	−0.632401	−	1.09535i
$534$		0			0
$535$	−30.0409	+	52.0323i	−0.0561512	+	0.0972566i
$536$	387.135	+	383.336i	0.722266	+	0.715180i
$537$		0			0
$538$	−959.905	−	82.3916i	−1.78421	−	0.153144i
$539$	36.6400			0.0679778
$540$		0			0
$541$			718.403i			1.32792i	0.747769	+	0.663959i	$0.231125\pi$
$541$			718.403i			1.32792i	−0.747769	+	0.663959i	$0.768875\pi$
$542$	−32.9325	−	2.82670i	−0.0607611	−	0.00521531i
$543$		0			0
$544$	351.338	−	769.899i	0.645841	−	1.41526i
$545$	−76.6634	−	44.2616i	−0.140667	−	0.0812140i
$546$		0			0
$547$	37.4863	−	21.6427i	0.0685307	−	0.0395662i	−0.465343	−	0.885130i	$-0.654069\pi$
$547$	37.4863	−	21.6427i	0.0685307	−	0.0395662i	0.533874	+	0.845564i	$0.320736\pi$
$548$	−516.974	+	190.090i	−0.943383	+	0.346879i
$549$		0			0
$550$	130.626	−	187.207i	0.237502	−	0.340377i
$551$	215.578	−	124.464i	0.391249	−	0.225888i
$552$		0			0
$553$	405.586	−	702.495i	0.733428	−	1.27034i
$554$	−280.814	+	131.508i	−0.506885	+	0.237379i
$555$		0			0
$556$	404.364	+	337.043i	0.727273	+	0.606193i
$557$	97.1654			0.174444			0.0872221	−	0.996189i	$-0.472201\pi$
$557$	97.1654			0.174444			0.0872221	+	0.996189i	$0.472201\pi$
$558$		0			0
$559$	−347.571			−0.621772
$560$	−66.6002	−	23.7459i	−0.118929	−	0.0424034i
$561$		0			0
$562$	−456.025	+	213.561i	−0.811433	+	0.380002i
$563$	122.710	−	212.541i	0.217958	−	0.377514i	−0.736225	−	0.676736i	$-0.763394\pi$
$563$	122.710	−	212.541i	0.217958	−	0.377514i	0.954184	+	0.299222i	$0.0967271\pi$
$564$		0			0
$565$	10.0373	−	5.79502i	0.0177651	−	0.0102567i
$566$	122.859	+	85.7264i	0.217066	+	0.151460i
$567$		0			0
$568$	−120.128	+	457.329i	−0.211493	+	0.805157i
$569$	405.841	−	234.312i	0.713253	−	0.411797i	−0.0990115	−	0.995086i	$-0.531568\pi$
$569$	405.841	−	234.312i	0.713253	−	0.411797i	0.812264	+	0.583290i	$0.198235\pi$
$570$		0			0
$571$	110.563	+	63.8339i	0.193631	+	0.111793i	0.593681	−	0.804700i	$-0.297674\pi$
$571$	110.563	+	63.8339i	0.193631	+	0.111793i	−0.400050	+	0.916493i	$0.631007\pi$
$572$	39.3167	−	227.343i	0.0687354	−	0.397452i
$573$		0			0
$574$	59.6626	−	695.101i	0.103942	−	1.21098i
$575$			43.3112i			0.0753239i
$576$		0			0
$577$	419.138			0.726409			0.363204	−	0.931709i	$-0.381683\pi$
$577$	419.138			0.726409			0.363204	+	0.931709i	$0.381683\pi$
$578$	817.787	+	70.1931i	1.41486	+	0.121441i
$579$		0			0
$580$	−60.2678	−	10.4227i	−0.103910	−	0.0179702i
$581$	−262.569	+	454.783i	−0.451926	+	0.782759i
$582$		0			0
$583$	−227.996	−	394.901i	−0.391074	−	0.677359i
$584$	−152.071	−	39.9448i	−0.260395	−	0.0683986i
$585$		0			0
$586$	433.406	−	621.138i	0.739600	−	1.05996i
$587$	−282.420	−	489.166i	−0.481124	−	0.833332i	0.518641	−	0.854992i	$-0.326438\pi$
$587$	−282.420	−	489.166i	−0.481124	−	0.833332i	−0.999765	+	0.0216604i	$0.993105\pi$
$588$		0			0
$589$	527.550	+	304.581i	0.895671	+	0.517116i
$590$	−44.9998	−	96.0898i	−0.0762708	−	0.162864i
$591$		0			0
$592$	−311.179	+	872.766i	−0.525641	+	1.47427i
$593$		−	48.0528i		−	0.0810334i	−0.999179	−	0.0405167i	$-0.987100\pi$
$593$		−	48.0528i		−	0.0810334i	0.999179	−	0.0405167i	$-0.0129004\pi$
$594$		0			0
$595$		−	116.870i		−	0.196420i
$596$	190.044	−	228.003i	0.318865	−	0.382555i
$597$		0			0
$598$	18.5651	+	39.6427i	0.0310452	+	0.0662921i
$599$	242.288	+	139.885i	0.404488	+	0.233531i	0.688419	−	0.725314i	$-0.258305\pi$
$599$	242.288	+	139.885i	0.404488	+	0.233531i	−0.283931	+	0.958845i	$0.591639\pi$
$600$		0			0
$601$	23.2653	+	40.2967i	0.0387110	+	0.0670495i	0.884732	−	0.466100i	$-0.154341\pi$
$601$	23.2653	+	40.2967i	0.0387110	+	0.0670495i	−0.846021	+	0.533150i	$0.821008\pi$
$602$	−294.984	−	205.828i	−0.490006	−	0.341908i
$603$		0			0
$604$	17.1822	+	46.7293i	0.0284473	+	0.0773663i
$605$	34.2276	+	59.2840i	0.0565746	+	0.0979900i
$606$		0			0
$607$	226.123	−	391.657i	0.372526	−	0.645234i	−0.617428	−	0.786628i	$-0.711825\pi$
$607$	226.123	−	391.657i	0.372526	−	0.645234i	0.989953	+	0.141394i	$0.0451584\pi$
$608$	−149.036	+	326.587i	−0.245124	+	0.537150i
$609$		0			0
$610$	−0.0671072	+	0.781834i	−0.000110012	+	0.00128169i
$611$	−290.957			−0.476199
$612$		0			0
$613$			157.326i			0.256649i	0.991732	+	0.128324i	$0.0409599\pi$
$613$			157.326i			0.256649i	−0.991732	+	0.128324i	$0.959040\pi$
$614$	9.98918	−	116.379i	0.0162690	−	0.189543i
$615$		0			0
$616$	167.998	−	169.663i	0.272725	−	0.275427i
$617$	−211.270	−	121.977i	−0.342415	−	0.197693i	0.318924	−	0.947780i	$-0.396678\pi$
$617$	−211.270	−	121.977i	−0.342415	−	0.197693i	−0.661339	+	0.750087i	$0.730012\pi$
$618$		0			0
$619$	720.047	−	415.719i	1.16324	−	0.671598i	0.211164	−	0.977451i	$-0.432275\pi$
$619$	720.047	−	415.719i	1.16324	−	0.671598i	0.952079	+	0.305852i	$0.0989414\pi$
$620$	−51.6531	−	140.478i	−0.0833115	−	0.226577i
$621$		0			0
$622$	−297.193	−	207.370i	−0.477802	−	0.333392i
$623$	259.094	−	149.588i	0.415881	−	0.240109i
$624$		0			0
$625$	−294.806	+	510.619i	−0.471689	+	0.816990i
$626$	−325.041	−	694.073i	−0.519235	−	1.10874i
$627$		0			0
$628$	347.801	+	289.897i	0.553823	+	0.461619i
$629$	−1531.53			−2.43486
$630$		0			0
$631$	−618.395			−0.980024			−0.490012	−	0.871716i	$-0.663008\pi$
$631$	−618.395			−0.980024			−0.490012	+	0.871716i	$0.663008\pi$
$632$	266.715	+	976.121i	0.422018	+	1.54449i
$633$		0			0
$634$	100.849	+	215.346i	0.159067	+	0.339663i
$635$	9.14263	−	15.8355i	0.0143978	−	0.0249378i
$636$		0			0
$637$	−84.5026	+	48.7876i	−0.132657	+	0.0765897i
$638$	118.186	−	169.379i	0.185244	−	0.265484i
$639$		0			0
$640$	79.5058	−	38.1936i	0.124228	−	0.0596775i
$641$	−487.272	+	281.327i	−0.760175	+	0.438887i	−0.829358	−	0.558717i	$-0.811294\pi$
$641$	−487.272	+	281.327i	−0.760175	+	0.438887i	0.0691838	+	0.997604i	$0.477960\pi$
$642$		0			0
$643$	−39.3143	−	22.6981i	−0.0611421	−	0.0353004i	0.469117	−	0.883136i	$-0.344572\pi$
$643$	−39.3143	−	22.6981i	−0.0611421	−	0.0353004i	−0.530259	+	0.847835i	$0.677905\pi$
$644$	−7.71986	+	44.6389i	−0.0119874	+	0.0693151i
$645$		0			0
$646$	−591.187	−	50.7434i	−0.915151	−	0.0785502i
$647$		−	177.072i		−	0.273682i	−0.990593	−	0.136841i	$-0.956305\pi$
$647$		−	177.072i		−	0.273682i	0.990593	−	0.136841i	$-0.0436949\pi$
$648$		0			0
$649$	358.299			0.552078
$650$	−51.9881	+	605.689i	−0.0799818	+	0.931829i
$651$		0			0
$652$	61.7604	−	357.120i	0.0947246	−	0.547730i
$653$	234.606	−	406.350i	0.359275	−	0.622282i	−0.628565	−	0.777757i	$-0.716357\pi$
$653$	234.606	−	406.350i	0.359275	−	0.622282i	0.987840	+	0.155475i	$0.0496907\pi$
$654$		0			0
$655$	46.0363	+	79.7373i	0.0702845	+	0.121736i
$656$	563.787	+	662.996i	0.859431	+	1.01066i
$657$		0			0
$658$	−246.936	−	172.302i	−0.375283	−	0.261858i
$659$	260.099	+	450.505i	0.394688	+	0.683619i	0.993061	−	0.117598i	$-0.0375194\pi$
$659$	260.099	+	450.505i	0.394688	+	0.683619i	−0.598373	+	0.801217i	$0.704186\pi$
$660$		0			0
$661$	−316.162	−	182.536i	−0.478309	−	0.276152i	0.241403	−	0.970425i	$-0.422393\pi$
$661$	−316.162	−	182.536i	−0.478309	−	0.276152i	−0.719711	+	0.694273i	$0.755726\pi$
$662$	673.180	−	315.257i	1.01689	−	0.476219i
$663$		0			0
$664$	−172.667	−	631.923i	−0.260040	−	0.951692i
$665$			49.5757i			0.0745499i
$666$		0			0
$667$			39.1865i			0.0587503i
$668$	−574.177	−	478.585i	−0.859546	−	0.716444i
$669$		0			0
$670$	−84.9975	+	39.8052i	−0.126862	+	0.0594107i
$671$	−2.29482	−	1.32492i	−0.00342001	−	0.00197454i
$672$		0			0
$673$	460.689	+	797.937i	0.684531	+	1.18564i	0.973584	+	0.228329i	$0.0733263\pi$
$673$	460.689	+	797.937i	0.684531	+	1.18564i	−0.289053	+	0.957313i	$0.593340\pi$
$674$	390.986	−	560.344i	0.580099	−	0.831371i
$675$		0			0
$676$	−21.2524	−	57.7987i	−0.0314384	−	0.0855011i
$677$	−49.7464	−	86.1634i	−0.0734807	−	0.127272i	0.826944	−	0.562284i	$-0.190077\pi$
$677$	−49.7464	−	86.1634i	−0.0734807	−	0.127272i	−0.900425	+	0.435012i	$0.856744\pi$
$678$		0			0
$679$	−209.645	+	363.116i	−0.308756	+	0.534780i
$680$	103.596	+	102.580i	0.152348	+	0.150853i
$681$		0			0
$682$	503.570	+	43.2230i	0.738373	+	0.0633768i
$683$	852.186			1.24771			0.623855	−	0.781540i	$-0.285566\pi$
$683$	852.186			1.24771			0.623855	+	0.781540i	$0.285566\pi$
$684$		0			0
$685$		−	94.8905i		−	0.138526i
$686$	−726.784	−	62.3821i	−1.05945	−	0.0909360i
$687$		0			0
$688$	441.367	−	80.8197i	0.641521	−	0.117471i
$689$	1051.65	+	607.171i	1.52634	+	0.881235i
$690$		0			0
$691$	−541.246	+	312.489i	−0.783279	+	0.452227i	−0.837591	−	0.546297i	$-0.816037\pi$
$691$	−541.246	+	312.489i	−0.783279	+	0.452227i	0.0543119	+	0.998524i	$0.482703\pi$
$692$	173.142	+	470.883i	0.250205	+	0.680466i
$693$		0			0
$694$	494.486	−	708.675i	0.712516	−	1.02115i
$695$	−78.5367	+	45.3432i	−0.113002	+	0.0652420i
$696$		0			0
$697$	−719.250	+	1245.78i	−1.03192	+	1.78734i
$698$	−777.539	+	364.129i	−1.11395	+	0.521675i
$699$		0			0
$700$	−402.806	+	483.262i	−0.575438	+	0.690375i
$701$	989.905			1.41213			0.706067	−	0.708145i	$-0.250468\pi$
$701$	989.905			1.41213			0.706067	+	0.708145i	$0.250468\pi$
$702$		0			0
$703$	649.667			0.924135
$704$	2.93664	+	297.836i	0.00417137	+	0.423062i
$705$		0			0
$706$	−232.764	+	109.005i	−0.329693	+	0.154399i
$707$	0.204339	−	0.353925i	0.000289022	−	0.000500601i
$708$		0			0
$709$	−701.850	+	405.213i	−0.989916	+	0.571528i	−0.905249	−	0.424881i	$-0.860316\pi$
$709$	−701.850	+	405.213i	−0.989916	+	0.571528i	−0.0846666	+	0.996409i	$0.526983\pi$
$710$	−66.8033	−	46.6128i	−0.0940892	−	0.0656518i
$711$		0			0
$712$	−94.8154	+	360.965i	−0.133168	+	0.506973i
$713$	−83.0473	+	47.9474i	−0.116476	+	0.0672474i
$714$		0			0
$715$	34.4214	+	19.8732i	0.0481418	+	0.0277947i
$716$	−914.142	−	158.092i	−1.27673	−	0.220799i
$717$		0			0
$718$	48.0981	−	560.368i	0.0669890	−	0.780456i
$719$			1390.54i			1.93400i	0.254783	+	0.966998i	$0.417996\pi$
$719$			1390.54i			1.93400i	−0.254783	+	0.966998i	$0.582004\pi$
$720$		0			0
$721$	346.289			0.480290
$722$	−468.576	−	40.2193i	−0.648998	−	0.0557055i
$723$		0			0
$724$	108.474	−	627.233i	0.149826	−	0.866343i
$725$	−272.100	+	471.291i	−0.375311	+	0.650057i
$726$		0			0
$727$	437.599	+	757.944i	0.601925	+	1.04256i	0.992529	+	0.122006i	$0.0389327\pi$
$727$	437.599	+	757.944i	0.601925	+	1.04256i	−0.390604	+	0.920559i	$0.627734\pi$
$728$	−161.541	+	614.989i	−0.221897	+	0.844765i
$729$		0			0
$730$	15.4996	−	22.2134i	0.0212324	−	0.0304293i
$731$	370.828	+	642.294i	0.507289	+	0.878651i
$732$		0			0
$733$	935.962	+	540.378i	1.27689	+	0.737214i	0.976276	−	0.216531i	$-0.0694743\pi$
$733$	935.962	+	540.378i	1.27689	+	0.737214i	0.300616	+	0.953745i	$0.402808\pi$
$734$	−129.440	−	276.399i	−0.176349	−	0.376566i
$735$		0			0
$736$	−32.7931	−	46.0239i	−0.0445558	−	0.0625324i
$737$		−	316.938i		−	0.430038i
$738$		0			0
$739$		−	1112.59i		−	1.50553i	−0.658290	−	0.752764i	$-0.728720\pi$
$739$		−	1112.59i		−	1.50553i	0.658290	−	0.752764i	$-0.271280\pi$
$740$	−122.616	−	102.203i	−0.165698	−	0.138112i
$741$		0			0
$742$	532.977	+	1138.09i	0.718297	+	1.53381i
$743$	925.632	+	534.414i	1.24580	+	0.719265i	0.970270	−	0.242026i	$-0.0778120\pi$
$743$	925.632	+	534.414i	1.24580	+	0.719265i	0.275534	+	0.961291i	$0.411145\pi$
$744$		0			0
$745$	25.5670	+	44.2834i	0.0343182	+	0.0594408i
$746$	554.880	+	387.174i	0.743807	+	0.519000i
$747$		0			0
$748$	−462.065	+	169.900i	−0.617735	+	0.227139i
$749$	279.575	+	484.238i	0.373265	+	0.646513i
$750$		0			0
$751$	−78.8412	+	136.557i	−0.104982	+	0.181833i	−0.913731	−	0.406320i	$-0.866812\pi$
$751$	−78.8412	+	136.557i	−0.104982	+	0.181833i	0.808749	+	0.588154i	$0.200145\pi$
$752$	369.476	−	67.6556i	0.491324	−	0.0899675i
$753$		0			0
$754$	−47.0370	+	548.006i	−0.0623833	+	0.726798i
$755$	−8.57715			−0.0113605
$756$		0			0
$757$		−	789.328i		−	1.04270i	−0.853341	−	0.521352i	$-0.825428\pi$
$757$		−	789.328i		−	1.04270i	0.853341	−	0.521352i	$-0.174572\pi$
$758$	21.6968	−	252.779i	0.0286237	−	0.333482i
$759$		0			0
$760$	−43.9451	−	43.5139i	−0.0578225	−	0.0572552i
$761$	−136.946	−	79.0658i	−0.179955	−	0.103897i	0.407316	−	0.913287i	$-0.366465\pi$
$761$	−136.946	−	79.0658i	−0.179955	−	0.103897i	−0.587272	+	0.809390i	$0.699798\pi$
$762$		0			0
$763$	−713.468	+	411.921i	−0.935082	+	0.539870i
$764$	746.898	−	274.632i	0.977615	−	0.359466i
$765$		0			0
$766$	154.115	+	107.536i	0.201195	+	0.140386i
$767$	−826.342	+	477.089i	−1.07737	+	0.622019i
$768$		0			0
$769$	−236.175	+	409.067i	−0.307119	+	0.531946i	−0.977731	−	0.209862i	$-0.932698\pi$
$769$	−236.175	+	409.067i	−0.307119	+	0.531946i	0.670612	+	0.741809i	$0.266032\pi$
$770$	17.4448	+	37.2505i	0.0226555	+	0.0483772i
$771$		0			0
$772$	530.525	−	636.492i	0.687209	−	0.824471i
$773$	−1160.01			−1.50066			−0.750329	−	0.661065i	$-0.770105\pi$
$773$	−1160.01			−1.50066			−0.750329	+	0.661065i	$0.770105\pi$
$774$		0			0
$775$	−1331.73			−1.71837
$776$	−137.864	−	504.551i	−0.177659	−	0.650195i
$777$		0			0
$778$	476.308	+	1017.08i	0.612221	+	1.30730i
$779$	305.102	−	528.452i	0.391659	−	0.678373i
$780$		0			0
$781$	238.219	−	137.536i	0.305018	−	0.176102i
$782$	53.4504	−	76.6027i	0.0683509	−	0.0979574i
$783$		0			0
$784$	95.9622	−	81.6027i	0.122401	−	0.104085i
$785$	−67.5508	+	39.0005i	−0.0860520	+	0.0496822i
$786$		0			0
$787$	−147.079	−	84.9160i	−0.186885	−	0.107898i	0.403638	−	0.914919i	$-0.367745\pi$
$787$	−147.079	−	84.9160i	−0.186885	−	0.107898i	−0.590524	+	0.807020i	$0.701079\pi$
$788$	−146.950	−	25.4136i	−0.186485	−	0.0322508i
$789$		0			0
$790$	−173.685	−	14.9079i	−0.219855	−	0.0188708i
$791$		−	107.863i		−	0.136362i
$792$		0			0
$793$	7.05672			0.00889876
$794$	117.121	−	1364.52i	0.147507	−	1.71854i
$795$		0			0
$796$	1379.47	+	238.566i	1.73301	+	0.299707i
$797$	115.199	−	199.531i	0.144541	−	0.250353i	−0.784661	−	0.619926i	$-0.787163\pi$
$797$	115.199	−	199.531i	0.144541	−	0.250353i	0.929202	+	0.369573i	$0.120496\pi$
$798$		0			0
$799$	310.427	+	537.675i	0.388519	+	0.672935i
$800$	−74.8216	−	781.230i	−0.0935269	−	0.976538i
$801$		0			0
$802$	627.190	+	437.629i	0.782033	+	0.545672i
$803$	45.7332	+	79.2123i	0.0569530	+	0.0986454i
$804$		0			0
$805$	−6.75866	−	3.90212i	−0.00839586	−	0.00484735i
$806$	−1218.93	+	570.838i	−1.51232	+	0.708236i
$807$		0			0
$808$	0.134374	+	0.491781i	0.000166305	+	0.000608639i
$809$			1300.79i			1.60790i	0.594700	+	0.803948i	$0.297271\pi$
$809$			1300.79i			1.60790i	−0.594700	+	0.803948i	$0.702729\pi$
$810$		0			0
$811$			785.643i			0.968734i	0.874865	+	0.484367i	$0.160950\pi$
$811$			785.643i			0.968734i	−0.874865	+	0.484367i	$0.839050\pi$
$812$	−364.445	+	437.239i	−0.448824	+	0.538471i
$813$		0			0
$814$	488.150	−	228.606i	0.599693	−	0.280842i
$815$	54.0707	+	31.2177i	0.0663444	+	0.0383039i
$816$		0			0
$817$	−157.304	−	272.458i	−0.192538	−	0.333486i
$818$	296.515	−	424.951i	0.362487	−	0.519501i
$819$		0			0
$820$	−140.718	+	51.7415i	−0.171607	+	0.0630994i
$821$	397.579	+	688.627i	0.484262	+	0.838766i	0.999837	−	0.0180787i	$-0.00575494\pi$
$821$	397.579	+	688.627i	0.484262	+	0.838766i	−0.515575	+	0.856845i	$0.672422\pi$
$822$		0			0
$823$	493.143	−	854.149i	0.599202	−	1.03785i	−0.393737	−	0.919223i	$-0.628818\pi$
$823$	493.143	−	854.149i	0.599202	−	1.03785i	0.992939	−	0.118625i	$-0.0378488\pi$
$824$	−303.947	+	306.959i	−0.368868	+	0.372523i
$825$		0			0
$826$	−983.846	−	84.4465i	−1.19110	−	0.102236i
$827$	−741.870			−0.897061			−0.448531	−	0.893767i	$-0.648052\pi$
$827$	−741.870			−0.897061			−0.448531	+	0.893767i	$0.648052\pi$
$828$		0			0
$829$			114.643i			0.138291i	0.997607	+	0.0691453i	$0.0220272\pi$
$829$			114.643i			0.138291i	−0.997607	+	0.0691453i	$0.977973\pi$
$830$	112.441	+	9.65113i	0.135471	+	0.0116279i
$831$		0			0
$832$	−403.353	−	682.986i	−0.484799	−	0.820897i
$833$	180.314	+	104.105i	0.216464	+	0.124975i
$834$		0			0
$835$	111.518	−	64.3851i	0.133555	−	0.0771079i
$836$	196.006	−	72.0707i	0.234457	−	0.0862089i
$837$		0			0
$838$	397.914	−	570.273i	0.474838	−	0.680516i
$839$	−422.474	+	243.916i	−0.503545	+	0.290722i	−0.730176	−	0.683259i	$-0.760562\pi$
$839$	−422.474	+	243.916i	−0.503545	+	0.290722i	0.226631	+	0.973981i	$0.427229\pi$
$840$		0			0
$841$	174.313	−	301.920i	0.207269	−	0.359001i
$842$	−95.8866	+	44.9046i	−0.113880	+	0.0533309i
$843$		0			0
$844$	977.461	+	814.728i	1.15813	+	0.965317i
$845$	10.6089			0.0125550
$846$		0			0
$847$	637.078			0.752159
$848$	−1476.64	−	526.485i	−1.74132	−	0.620856i
$849$		0			0
$850$	1174.75	−	550.147i	1.38206	−	0.647232i
$851$	−51.1355	+	88.5692i	−0.0600887	+	0.104077i
$852$		0			0
$853$	−396.719	+	229.046i	−0.465086	+	0.268518i	−0.714181	−	0.699962i	$-0.753200\pi$
$853$	−396.719	+	229.046i	−0.465086	+	0.268518i	0.249094	+	0.968479i	$0.419867\pi$
$854$	5.98905	+	4.17893i	0.00701294	+	0.00489336i
$855$		0			0
$856$	−674.632	−	177.207i	−0.788121	−	0.207018i
$857$	576.627	−	332.916i	0.672844	−	0.388467i	−0.124309	−	0.992244i	$-0.539671\pi$
$857$	576.627	−	332.916i	0.672844	−	0.388467i	0.797153	+	0.603777i	$0.206338\pi$
$858$		0			0
$859$	−920.895	−	531.679i	−1.07205	−	0.618951i	−0.143313	−	0.989677i	$-0.545775\pi$
$859$	−920.895	−	531.679i	−1.07205	−	0.618951i	−0.928742	+	0.370726i	$0.879109\pi$
$860$	−13.1727	+	76.1692i	−0.0153171	+	0.0885688i
$861$		0			0
$862$	−22.7629	+	265.200i	−0.0264071	+	0.307656i
$863$		−	1381.64i		−	1.60097i	−0.599353	−	0.800485i	$-0.704575\pi$
$863$		−	1381.64i		−	1.60097i	0.599353	−	0.800485i	$-0.295425\pi$
$864$		0			0
$865$	−86.4304			−0.0999195
$866$	−446.099	−	38.2900i	−0.515126	−	0.0442148i
$867$		0			0
$868$	−1372.56	−	237.370i	−1.58129	−	0.273468i
$869$	294.332	−	509.798i	0.338702	−	0.586648i
$870$		0			0
$871$	422.016	+	730.953i	0.484519	+	0.839211i
$872$	261.094	−	993.989i	0.299419	−	1.13990i
$873$		0			0
$874$	−22.6734	+	32.4945i	−0.0259421	+	0.0371790i
$875$	−109.430	−	189.539i	−0.125063	−	0.216616i
$876$		0			0
$877$	104.099	+	60.1015i	0.118699	+	0.0685308i	0.558174	−	0.829724i	$-0.311502\pi$
$877$	104.099	+	60.1015i	0.118699	+	0.0685308i	−0.439475	+	0.898255i	$0.644836\pi$
$878$	317.292	+	677.526i	0.361381	+	0.771670i
$879$		0			0
$880$	−48.3314	−	17.2323i	−0.0549221	−	0.0195821i
$881$		−	1404.21i		−	1.59388i	−0.604060	−	0.796939i	$-0.706451\pi$
$881$		−	1404.21i		−	1.59388i	0.604060	−	0.796939i	$-0.293549\pi$
$882$		0			0
$883$			1355.32i			1.53491i	0.641104	+	0.767454i	$0.278477\pi$
$883$			1355.32i			1.53491i	−0.641104	+	0.767454i	$0.721523\pi$
$884$	839.430	−	1007.10i	0.949581	−	1.13925i
$885$		0			0
$886$	−210.940	−	450.428i	−0.238081	−	0.508384i
$887$	1281.30	+	739.757i	1.44453	+	0.833998i	0.998147	−	0.0608448i	$-0.0193795\pi$
$887$	1281.30	+	739.757i	1.44453	+	0.833998i	0.446380	+	0.894843i	$0.352713\pi$
$888$		0			0
$889$	−85.0859	−	147.373i	−0.0957097	−	0.165774i
$890$	−52.7271	−	36.7909i	−0.0592439	−	0.0413381i
$891$		0			0
$892$	−215.995	−	587.428i	−0.242147	−	0.658551i
$893$	−131.681	−	228.079i	−0.147460	−	0.255408i
$894$		0			0
$895$	79.9099	−	138.408i	0.0892848	−	0.154646i
$896$	62.1325	−	818.514i	0.0693443	−	0.913520i
$897$		0			0
$898$	67.7276	−	789.062i	0.0754205	−	0.878689i
$899$	−1204.91			−1.34027
$900$		0			0
$901$		−	2591.20i		−	2.87591i
$902$	43.2969	−	504.432i	0.0480010	−	0.559237i
$903$		0			0
$904$	95.6120	+	94.6740i	0.105766	+	0.104728i
$905$	94.9677	+	54.8296i	0.104937	+	0.0605852i
$906$		0			0
$907$	1094.22	−	631.747i	1.20641	−	0.696524i	0.244440	−	0.969664i	$-0.421396\pi$
$907$	1094.22	−	631.747i	1.20641	−	0.696524i	0.961974	+	0.273141i	$0.0880625\pi$
$908$	150.415	+	409.074i	0.165655	+	0.450522i
$909$		0			0
$910$	−89.8331	−	62.6821i	−0.0987177	−	0.0688814i
$911$	1027.04	−	592.963i	1.12738	−	0.650893i	0.184105	−	0.982907i	$-0.441061\pi$
$911$	1027.04	−	592.963i	1.12738	−	0.650893i	0.943275	+	0.332014i	$0.107728\pi$
$912$		0			0
$913$	−190.545	+	330.034i	−0.208702	+	0.361483i
$914$	358.487	+	765.490i	0.392217	+	0.837517i
$915$		0			0
$916$	−1332.46	−	1110.63i	−1.45465	−	1.21247i
$917$	856.874			0.934432
$918$		0			0
$919$	−1008.44			−1.09733			−0.548664	−	0.836043i	$-0.684863\pi$
$919$	−1008.44			−1.09733			−0.548664	+	0.836043i	$0.684863\pi$
$920$	9.39120	−	2.56605i	0.0102078	−	0.00278918i
$921$		0			0
$922$	−548.607	−	1171.46i	−0.595018	−	1.27057i
$923$	−366.268	+	634.395i	−0.396824	+	0.687319i
$924$		0			0
$925$	−1230.00	+	710.142i	−1.32973	+	0.767721i
$926$	−300.634	+	430.856i	−0.324659	+	0.465287i
$927$		0			0
$928$	−67.6959	−	706.829i	−0.0729482	−	0.761669i
$929$	−545.890	+	315.170i	−0.587610	+	0.339257i	−0.764152	−	0.645036i	$-0.776842\pi$
$929$	−545.890	+	315.170i	−0.587610	+	0.339257i	0.176542	+	0.984293i	$0.443509\pi$
$930$		0			0
$931$	−76.4884	−	44.1606i	−0.0821573	−	0.0474335i
$932$	34.2260	−	197.907i	0.0367232	−	0.212346i
$933$		0			0
$934$	−1012.82	−	86.9337i	−1.08439	−	0.0930768i
$935$		−	84.8120i		−	0.0907080i
$936$		0			0
$937$	326.890			0.348869			0.174434	−	0.984669i	$-0.444190\pi$
$937$	326.890			0.348869			0.174434	+	0.984669i	$0.444190\pi$
$938$	−74.6983	+	870.275i	−0.0796358	+	0.927798i
$939$		0			0
$940$	−11.0271	+	63.7625i	−0.0117310	+	0.0678325i
$941$	466.688	−	808.328i	0.495949	−	0.859009i	−0.504040	−	0.863680i	$-0.668154\pi$
$941$	466.688	−	808.328i	0.495949	−	0.859009i	0.999989	+	0.00467102i	$0.00148684\pi$
$942$		0			0
$943$	48.0294	+	83.1893i	0.0509325	+	0.0882177i
$944$	938.404	−	797.984i	0.994072	−	0.845322i
$945$		0			0
$946$	−214.068	−	149.369i	−0.226288	−	0.157895i
$947$	109.434	+	189.545i	0.115558	+	0.200153i	0.918003	−	0.396574i	$-0.129801\pi$
$947$	109.434	+	189.545i	0.115558	+	0.200153i	−0.802444	+	0.596727i	$0.796468\pi$
$948$		0			0
$949$	−210.948	−	121.791i	−0.222285	−	0.128336i
$950$	−498.323	+	233.370i	−0.524551	+	0.245652i
$951$		0			0
$952$	1308.82	−	357.622i	1.37481	−	0.375653i
$953$		−	1682.78i		−	1.76577i	−0.469589	−	0.882885i	$-0.655598\pi$
$953$		−	1682.78i		−	1.76577i	0.469589	−	0.882885i	$-0.344402\pi$
$954$		0			0
$955$			137.093i			0.143553i
$956$	1064.08	+	886.925i	1.11305	+	0.927746i
$957$		0			0
$958$	−333.936	+	156.385i	−0.348576	+	0.163242i
$959$	−764.785	−	441.549i	−0.797482	−	0.460426i
$960$		0			0
$961$	−993.786	−	1721.29i	−1.03412	−	1.79114i
$962$	−821.421	+	1177.22i	−0.853868	+	1.22372i
$963$		0			0
$964$	166.758	+	453.520i	0.172985	+	0.470457i
$965$	71.3728	+	123.621i	0.0739615	+	0.128105i
$966$		0			0
$967$	315.848	−	547.065i	0.326627	−	0.565734i	−0.655214	−	0.755444i	$-0.727421\pi$
$967$	315.848	−	547.065i	0.326627	−	0.565734i	0.981840	+	0.189710i	$0.0607547\pi$
$968$	−559.181	+	564.722i	−0.577666	+	0.583390i
$969$		0			0
$970$	89.7768	+	7.70582i	0.0925535	+	0.00794415i
$971$	−1335.07			−1.37495			−0.687473	−	0.726210i	$-0.741280\pi$
$971$	−1335.07			−1.37495			−0.687473	+	0.726210i	$0.741280\pi$
$972$		0			0
$973$			843.973i			0.867392i
$974$	665.889	+	57.1553i	0.683664	+	0.0586810i
$975$		0			0
$976$	−8.96106	+	1.64088i	−0.00918141	+	0.00168123i
$977$	−344.080	−	198.655i	−0.352180	−	0.203331i	0.313465	−	0.949600i	$-0.398510\pi$
$977$	−344.080	−	198.655i	−0.352180	−	0.203331i	−0.665645	+	0.746268i	$0.731844\pi$
$978$		0			0
$979$	188.023	−	108.555i	0.192056	−	0.110884i
$980$	7.48908	+	20.3676i	0.00764192	+	0.0207832i
$981$		0			0
$982$	−872.344	+	1250.20i	−0.888334	+	1.27312i
$983$	101.390	−	58.5375i	0.103143	−	0.0595499i	−0.447541	−	0.894263i	$-0.647700\pi$
$983$	101.390	−	58.5375i	0.103143	−	0.0595499i	0.550684	+	0.834714i	$0.314367\pi$
$984$		0			0
$985$	12.8457	−	22.2494i	0.0130413	−	0.0225882i
$986$	1062.87	−	497.754i	1.07796	−	0.504821i
$987$		0			0
$988$	−356.082	+	427.205i	−0.360407	+	0.432394i
$989$	49.5256			0.0500765
$990$		0			0
$991$	250.248			0.252520			0.126260	−	0.991997i	$-0.459703\pi$
$991$	250.248			0.252520			0.126260	+	0.991997i	$0.459703\pi$
$992$	1415.14	−	1008.32i	1.42655	−	1.01645i
$993$		0			0
$994$	−686.536	+	321.511i	−0.690680	+	0.323452i
$995$	−120.587	+	208.863i	−0.121193	+	0.209912i
$996$		0			0
$997$	1029.57	−	594.423i	1.03267	−	0.596211i	0.114920	−	0.993375i	$-0.463339\pi$
$997$	1029.57	−	594.423i	1.03267	−	0.596211i	0.917748	+	0.397164i	$0.130005\pi$
$998$	895.580	+	624.901i	0.897375	+	0.626154i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.j.a.125.1		44
3.2	odd	2		72.3.j.a.5.22	yes	44
4.3	odd	2		864.3.n.a.17.11		44
8.3	odd	2		864.3.n.a.17.12		44
8.5	even	2	inner	216.3.j.a.125.8		44
9.2	odd	6	inner	216.3.j.a.197.8		44
9.4	even	3		648.3.h.a.485.29		44
9.5	odd	6		648.3.h.a.485.16		44
9.7	even	3		72.3.j.a.29.15	yes	44
12.11	even	2		288.3.n.a.113.15		44
24.5	odd	2		72.3.j.a.5.15	✓	44
24.11	even	2		288.3.n.a.113.8		44
36.7	odd	6		288.3.n.a.209.8		44
36.11	even	6		864.3.n.a.305.12		44
36.23	even	6		2592.3.h.a.1457.22		44
36.31	odd	6		2592.3.h.a.1457.24		44
72.5	odd	6		648.3.h.a.485.30		44
72.11	even	6		864.3.n.a.305.11		44
72.13	even	6		648.3.h.a.485.15		44
72.29	odd	6	inner	216.3.j.a.197.1		44
72.43	odd	6		288.3.n.a.209.15		44
72.59	even	6		2592.3.h.a.1457.23		44
72.61	even	6		72.3.j.a.29.22	yes	44
72.67	odd	6		2592.3.h.a.1457.21		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.15	✓	44	24.5	odd	2
72.3.j.a.5.22	yes	44	3.2	odd	2
72.3.j.a.29.15	yes	44	9.7	even	3
72.3.j.a.29.22	yes	44	72.61	even	6
216.3.j.a.125.1		44	1.1	even	1	trivial
216.3.j.a.125.8		44	8.5	even	2	inner
216.3.j.a.197.1		44	72.29	odd	6	inner
216.3.j.a.197.8		44	9.2	odd	6	inner
288.3.n.a.113.8		44	24.11	even	2
288.3.n.a.113.15		44	12.11	even	2
288.3.n.a.209.8		44	36.7	odd	6
288.3.n.a.209.15		44	72.43	odd	6
648.3.h.a.485.15		44	72.13	even	6
648.3.h.a.485.16		44	9.5	odd	6
648.3.h.a.485.29		44	9.4	even	3
648.3.h.a.485.30		44	72.5	odd	6
864.3.n.a.17.11		44	4.3	odd	2
864.3.n.a.17.12		44	8.3	odd	2
864.3.n.a.305.11		44	72.11	even	6
864.3.n.a.305.12		44	36.11	even	6
2592.3.h.a.1457.21		44	72.67	odd	6
2592.3.h.a.1457.22		44	36.23	even	6
2592.3.h.a.1457.23		44	72.59	even	6
2592.3.h.a.1457.24		44	36.31	odd	6

Overview	Random
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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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99267 - 0.171037i) q^{2} +(3.94149 + 0.681643i) q^{4} +(-0.344546 + 0.596772i) q^{5} +(3.20652 + 5.55385i) q^{7} +(-7.73752 - 2.03243i) q^{8} +O(q^{10})\)	\(q+(-1.99267 - 0.171037i) q^{2} +(3.94149 + 0.681643i) q^{4} +(-0.344546 + 0.596772i) q^{5} +(3.20652 + 5.55385i) q^{7} +(-7.73752 - 2.03243i) q^{8} +(0.788638 - 1.13024i) q^{10} +(2.32696 + 4.03041i) q^{11} +(-10.7333 - 6.19686i) q^{13} +(-5.43963 - 11.6154i) q^{14} +(15.0707 + 5.37338i) q^{16} +26.4461i q^{17} -11.2183i q^{19} +(-1.76481 + 2.11731i) q^{20} +(-3.94751 - 8.42928i) q^{22} +(1.52939 + 0.882996i) q^{23} +(12.2626 + 21.2394i) q^{25} +(20.3280 + 14.1841i) q^{26} +(8.85273 + 24.0762i) q^{28} +(11.0947 + 19.2167i) q^{29} +(-27.1504 + 47.0258i) q^{31} +(-29.1120 - 13.2850i) q^{32} +(4.52327 - 52.6985i) q^{34} -4.41918 q^{35} +57.9113i q^{37} +(-1.91875 + 22.3544i) q^{38} +(3.87883 - 3.91727i) q^{40} +(47.1063 + 27.1968i) q^{41} +(24.2869 - 14.0220i) q^{43} +(6.42438 + 17.4720i) q^{44} +(-2.89656 - 2.02111i) q^{46} +(20.3310 - 11.7381i) q^{47} +(3.93648 - 6.81818i) q^{49} +(-20.8026 - 44.4205i) q^{50} +(-38.0811 - 31.7412i) q^{52} -97.9804 q^{53} -3.20698 q^{55} +(-13.5227 - 49.4901i) q^{56} +(-18.8214 - 40.1901i) q^{58} +(38.4944 - 66.6742i) q^{59} +(-0.493096 + 0.284689i) q^{61} +(62.1450 - 89.0634i) q^{62} +(55.7384 + 31.4520i) q^{64} +(7.39622 - 4.27021i) q^{65} +(-58.9776 - 34.0507i) q^{67} +(-18.0268 + 104.237i) q^{68} +(8.80597 + 0.755844i) q^{70} -59.1054i q^{71} +19.6537 q^{73} +(9.90499 - 115.398i) q^{74} +(7.64687 - 44.2169i) q^{76} +(-14.9229 + 25.8471i) q^{77} +(-63.2440 - 109.542i) q^{79} +(-8.39924 + 7.14240i) q^{80} +(-89.2157 - 62.2513i) q^{82} +(40.9430 + 70.9154i) q^{83} +(-15.7823 - 9.11191i) q^{85} +(-50.7941 + 23.7874i) q^{86} +(-9.81334 - 35.9147i) q^{88} -46.6512i q^{89} -79.4814i q^{91} +(5.42621 + 4.52282i) q^{92} +(-42.5206 + 19.9128i) q^{94} +(6.69477 + 3.86522i) q^{95} +(32.6904 + 56.6215i) q^{97} +(-9.01028 + 12.9131i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

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